id	sid	tid	token	lemma	pos
ejpam-6775	1	1	european	european	PROPN
ejpam-6775	1	2	journal	journal	PROPN
ejpam-6775	1	3	of	of	ADP
ejpam-6775	1	4	pure	pure	ADJ
ejpam-6775	1	5	and	and	CCONJ
ejpam-6775	1	6	applied	applied	ADJ
ejpam-6775	1	7	mathematics	mathematic	NOUN
ejpam-6775	1	8	2025	2025	NUM
ejpam-6775	1	9	,	,	PUNCT
ejpam-6775	1	10	vol	vol	NOUN
ejpam-6775	1	11	.	.	PROPN
ejpam-6775	1	12	18	18	NUM
ejpam-6775	1	13	,	,	PUNCT
ejpam-6775	1	14	issue	issue	NOUN
ejpam-6775	1	15	4	4	NUM
ejpam-6775	1	16	,	,	PUNCT
ejpam-6775	1	17	article	article	NOUN
ejpam-6775	1	18	number	number	NOUN
ejpam-6775	1	19	6775	6775	NUM
ejpam-6775	1	20	issn	issn	VERB
ejpam-6775	1	21	1307	1307	NUM
ejpam-6775	1	22	-	-	SYM
ejpam-6775	1	23	5543	5543	NUM
ejpam-6775	1	24	–	–	PUNCT
ejpam-6775	1	25	ejpam.com	ejpam.com	X
ejpam-6775	1	26	published	publish	VERB
ejpam-6775	1	27	by	by	ADP
ejpam-6775	1	28	new	new	PROPN
ejpam-6775	1	29	york	york	PROPN
ejpam-6775	1	30	business	business	PROPN
ejpam-6775	1	31	global	global	ADJ
ejpam-6775	1	32	backward	backward	ADJ
ejpam-6775	1	33	bifurcation	bifurcation	NOUN
ejpam-6775	1	34	and	and	CCONJ
ejpam-6775	1	35	optimal	optimal	ADJ
ejpam-6775	1	36	control	control	NOUN
ejpam-6775	1	37	in	in	ADP
ejpam-6775	1	38	an	an	DET
ejpam-6775	1	39	age	age	NOUN
ejpam-6775	1	40	-	-	PUNCT
ejpam-6775	1	41	structured	structure	VERB
ejpam-6775	1	42	svi	svi	PROPN
ejpam-6775	1	43	epidemic	epidemic	NOUN
ejpam-6775	1	44	model	model	NOUN
ejpam-6775	1	45	j.	j.	PROPN
ejpam-6775	1	46	leo	leo	PROPN
ejpam-6775	1	47	amalraj1	amalraj1	PROPN
ejpam-6775	1	48	,	,	PUNCT
ejpam-6775	1	49	pankaj	pankaj	PROPN
ejpam-6775	1	50	shukla2	shukla2	PROPN
ejpam-6775	1	51	,	,	PUNCT
ejpam-6775	1	52	lakshmana	lakshmana	PROPN
ejpam-6775	1	53	phaneendra	phaneendra	PROPN
ejpam-6775	1	54	maguluri3	maguluri3	PROPN
ejpam-6775	1	55	,	,	PUNCT
ejpam-6775	1	56	siriluk	siriluk	NOUN
ejpam-6775	1	57	donganont4,∗	donganont4,∗	NOUN
ejpam-6775	1	58	,	,	PUNCT
ejpam-6775	1	59	n.	n.	NOUN
ejpam-6775	1	60	avinash5	avinash5	PROPN
ejpam-6775	1	61	,	,	PUNCT
ejpam-6775	1	62	vediyappan	vediyappan	ADJ
ejpam-6775	1	63	govindan6	govindan6	PROPN
ejpam-6775	1	64	1	1	NUM
ejpam-6775	1	65	department	department	NOUN
ejpam-6775	1	66	of	of	ADP
ejpam-6775	1	67	mathematics	mathematic	NOUN
ejpam-6775	1	68	,	,	PUNCT
ejpam-6775	1	69	rmk	rmk	PROPN
ejpam-6775	1	70	college	college	PROPN
ejpam-6775	1	71	of	of	ADP
ejpam-6775	1	72	engineering	engineering	NOUN
ejpam-6775	1	73	and	and	CCONJ
ejpam-6775	1	74	technology	technology	NOUN
ejpam-6775	1	75	,	,	PUNCT
ejpam-6775	1	76	puduvoyal	puduvoyal	ADJ
ejpam-6775	1	77	,	,	PUNCT
ejpam-6775	1	78	thiruvallur	thiruvallur	NOUN
ejpam-6775	1	79	,	,	PUNCT
ejpam-6775	1	80	tamil	tamil	PROPN
ejpam-6775	1	81	nadu	nadu	PROPN
ejpam-6775	1	82	,	,	PUNCT
ejpam-6775	1	83	india	india	PROPN
ejpam-6775	1	84	2	2	NUM
ejpam-6775	1	85	department	department	NOUN
ejpam-6775	1	86	of	of	ADP
ejpam-6775	1	87	mathematics	mathematic	NOUN
ejpam-6775	1	88	,	,	PUNCT
ejpam-6775	1	89	school	school	NOUN
ejpam-6775	1	90	of	of	ADP
ejpam-6775	1	91	advanced	advanced	ADJ
ejpam-6775	1	92	sciences	science	NOUN
ejpam-6775	1	93	,	,	PUNCT
ejpam-6775	1	94	vellore	vellore	PROPN
ejpam-6775	1	95	institute	institute	PROPN
ejpam-6775	1	96	of	of	ADP
ejpam-6775	1	97	technology	technology	PROPN
ejpam-6775	1	98	,	,	PUNCT
ejpam-6775	1	99	chennai	chennai	PROPN
ejpam-6775	1	100	,	,	PUNCT
ejpam-6775	1	101	tamil	tamil	PROPN
ejpam-6775	1	102	nadu	nadu	PROPN
ejpam-6775	1	103	,	,	PUNCT
ejpam-6775	1	104	india	india	PROPN
ejpam-6775	1	105	3	3	NUM
ejpam-6775	1	106	department	department	NOUN
ejpam-6775	1	107	of	of	ADP
ejpam-6775	1	108	computer	computer	NOUN
ejpam-6775	1	109	science	science	NOUN
ejpam-6775	1	110	and	and	CCONJ
ejpam-6775	1	111	engineering	engineering	NOUN
ejpam-6775	1	112	,	,	PUNCT
ejpam-6775	1	113	koneru	koneru	PROPN
ejpam-6775	1	114	lakshmaiah	lakshmaiah	PROPN
ejpam-6775	1	115	education	education	PROPN
ejpam-6775	1	116	foundation	foundation	PROPN
ejpam-6775	1	117	,	,	PUNCT
ejpam-6775	1	118	vaddeswaram	vaddeswaram	PROPN
ejpam-6775	1	119	,	,	PUNCT
ejpam-6775	1	120	guntur	guntur	PROPN
ejpam-6775	1	121	ap	ap	PROPN
ejpam-6775	1	122	,	,	PUNCT
ejpam-6775	1	123	india	india	PROPN
ejpam-6775	1	124	4	4	NUM
ejpam-6775	1	125	school	school	NOUN
ejpam-6775	1	126	of	of	ADP
ejpam-6775	1	127	science	science	NOUN
ejpam-6775	1	128	,	,	PUNCT
ejpam-6775	1	129	university	university	NOUN
ejpam-6775	1	130	of	of	ADP
ejpam-6775	1	131	phayao	phayao	NOUN
ejpam-6775	1	132	,	,	PUNCT
ejpam-6775	1	133	phayao	phayao	NOUN
ejpam-6775	1	134	56000	56000	NUM
ejpam-6775	1	135	,	,	PUNCT
ejpam-6775	1	136	thailand	thailand	PROPN
ejpam-6775	1	137	5	5	NUM
ejpam-6775	1	138	department	department	NOUN
ejpam-6775	1	139	of	of	ADP
ejpam-6775	1	140	mathematics	mathematic	NOUN
ejpam-6775	1	141	,	,	PUNCT
ejpam-6775	1	142	sacred	sacred	ADJ
ejpam-6775	1	143	heart	heart	NOUN
ejpam-6775	1	144	college	college	NOUN
ejpam-6775	1	145	(	(	PUNCT
ejpam-6775	1	146	autonomous	autonomous	ADJ
ejpam-6775	1	147	)	)	PUNCT
ejpam-6775	1	148	,	,	PUNCT
ejpam-6775	1	149	tirupattur	tirupattur	VERB
ejpam-6775	1	150	635	635	NUM
ejpam-6775	1	151	601	601	NUM
ejpam-6775	1	152	,	,	PUNCT
ejpam-6775	1	153	tamil	tamil	PROPN
ejpam-6775	1	154	nadu	nadu	PROPN
ejpam-6775	1	155	,	,	PUNCT
ejpam-6775	1	156	india	india	PROPN
ejpam-6775	1	157	6	6	NUM
ejpam-6775	1	158	department	department	NOUN
ejpam-6775	1	159	of	of	ADP
ejpam-6775	1	160	mathematics	mathematic	NOUN
ejpam-6775	1	161	,	,	PUNCT
ejpam-6775	1	162	hindustan	hindustan	PROPN
ejpam-6775	1	163	institute	institute	PROPN
ejpam-6775	1	164	of	of	ADP
ejpam-6775	1	165	technology	technology	PROPN
ejpam-6775	1	166	and	and	CCONJ
ejpam-6775	1	167	science	science	NOUN
ejpam-6775	1	168	,	,	PUNCT
ejpam-6775	1	169	chennai	chennai	PROPN
ejpam-6775	1	170	,	,	PUNCT
ejpam-6775	1	171	tamil	tamil	PROPN
ejpam-6775	1	172	nadu	nadu	PROPN
ejpam-6775	1	173	,	,	PUNCT
ejpam-6775	1	174	india	india	PROPN
ejpam-6775	1	175	abstract	abstract	NOUN
ejpam-6775	1	176	.	.	PUNCT
ejpam-6775	2	1	this	this	DET
ejpam-6775	2	2	study	study	NOUN
ejpam-6775	2	3	investigates	investigate	VERB
ejpam-6775	2	4	the	the	DET
ejpam-6775	2	5	dynamics	dynamic	NOUN
ejpam-6775	2	6	and	and	CCONJ
ejpam-6775	2	7	control	control	NOUN
ejpam-6775	2	8	of	of	ADP
ejpam-6775	2	9	an	an	DET
ejpam-6775	2	10	infectious	infectious	ADJ
ejpam-6775	2	11	disease	disease	NOUN
ejpam-6775	2	12	using	use	VERB
ejpam-6775	2	13	an	an	DET
ejpam-6775	2	14	agestructured	agestructure	VERB
ejpam-6775	2	15	susceptible	susceptible	ADJ
ejpam-6775	2	16	-	-	PUNCT
ejpam-6775	2	17	vaccinated	vaccinated	ADJ
ejpam-6775	2	18	-	-	PUNCT
ejpam-6775	2	19	infected	infect	VERB
ejpam-6775	2	20	(	(	PUNCT
ejpam-6775	2	21	svi	svi	ADJ
ejpam-6775	2	22	)	)	PUNCT
ejpam-6775	2	23	model	model	NOUN
ejpam-6775	2	24	,	,	PUNCT
ejpam-6775	2	25	incorporating	incorporate	VERB
ejpam-6775	2	26	imperfect	imperfect	ADJ
ejpam-6775	2	27	vaccination	vaccination	NOUN
ejpam-6775	2	28	and	and	CCONJ
ejpam-6775	2	29	therapeutic	therapeutic	ADJ
ejpam-6775	2	30	treatment	treatment	NOUN
ejpam-6775	2	31	.	.	PUNCT
ejpam-6775	3	1	we	we	PRON
ejpam-6775	3	2	identify	identify	VERB
ejpam-6775	3	3	a	a	DET
ejpam-6775	3	4	backward	backward	ADJ
ejpam-6775	3	5	bifurcation	bifurcation	NOUN
ejpam-6775	3	6	phenomenon	phenomenon	NOUN
ejpam-6775	3	7	,	,	PUNCT
ejpam-6775	3	8	driven	drive	VERB
ejpam-6775	3	9	by	by	ADP
ejpam-6775	3	10	treatment	treatment	NOUN
ejpam-6775	3	11	rates	rate	NOUN
ejpam-6775	3	12	,	,	PUNCT
ejpam-6775	3	13	which	which	PRON
ejpam-6775	3	14	allows	allow	VERB
ejpam-6775	3	15	disease	disease	NOUN
ejpam-6775	3	16	persistence	persistence	NOUN
ejpam-6775	3	17	even	even	ADV
ejpam-6775	3	18	when	when	SCONJ
ejpam-6775	3	19	the	the	DET
ejpam-6775	3	20	basic	basic	ADJ
ejpam-6775	3	21	reproduction	reproduction	NOUN
ejpam-6775	3	22	number	number	NOUN
ejpam-6775	3	23	r0	r0	NOUN
ejpam-6775	3	24	<	<	X
ejpam-6775	3	25	1	1	NUM
ejpam-6775	3	26	,	,	PUNCT
ejpam-6775	3	27	complicating	complicate	VERB
ejpam-6775	3	28	eradication	eradication	NOUN
ejpam-6775	3	29	efforts	effort	NOUN
ejpam-6775	3	30	.	.	PUNCT
ejpam-6775	4	1	to	to	PART
ejpam-6775	4	2	address	address	VERB
ejpam-6775	4	3	this	this	PRON
ejpam-6775	4	4	,	,	PUNCT
ejpam-6775	4	5	we	we	PRON
ejpam-6775	4	6	formulate	formulate	VERB
ejpam-6775	4	7	an	an	DET
ejpam-6775	4	8	optimal	optimal	ADJ
ejpam-6775	4	9	control	control	NOUN
ejpam-6775	4	10	problem	problem	NOUN
ejpam-6775	4	11	with	with	ADP
ejpam-6775	4	12	time	time	NOUN
ejpam-6775	4	13	-	-	PUNCT
ejpam-6775	4	14	dependent	dependent	ADJ
ejpam-6775	4	15	vaccination	vaccination	NOUN
ejpam-6775	4	16	and	and	CCONJ
ejpam-6775	4	17	treatment	treatment	NOUN
ejpam-6775	4	18	rates	rate	NOUN
ejpam-6775	4	19	to	to	PART
ejpam-6775	4	20	minimize	minimize	VERB
ejpam-6775	4	21	infected	infect	VERB
ejpam-6775	4	22	individuals	individual	NOUN
ejpam-6775	4	23	and	and	CCONJ
ejpam-6775	4	24	control	control	NOUN
ejpam-6775	4	25	costs	cost	NOUN
ejpam-6775	4	26	.	.	PUNCT
ejpam-6775	5	1	using	use	VERB
ejpam-6775	5	2	bifurcation	bifurcation	NOUN
ejpam-6775	5	3	theory	theory	NOUN
ejpam-6775	5	4	and	and	CCONJ
ejpam-6775	5	5	integrated	integrate	VERB
ejpam-6775	5	6	semigroup	semigroup	ADJ
ejpam-6775	5	7	methods	method	NOUN
ejpam-6775	5	8	,	,	PUNCT
ejpam-6775	5	9	we	we	PRON
ejpam-6775	5	10	establish	establish	VERB
ejpam-6775	5	11	the	the	DET
ejpam-6775	5	12	model	model	NOUN
ejpam-6775	5	13	’s	’s	PART
ejpam-6775	5	14	well	well	NOUN
ejpam-6775	5	15	-	-	PUNCT
ejpam-6775	5	16	posedness	posedness	NOUN
ejpam-6775	5	17	,	,	PUNCT
ejpam-6775	5	18	equilibria	equilibrium	NOUN
ejpam-6775	5	19	stability	stability	NOUN
ejpam-6775	5	20	,	,	PUNCT
ejpam-6775	5	21	and	and	CCONJ
ejpam-6775	5	22	bistability	bistability	NOUN
ejpam-6775	5	23	conditions	condition	NOUN
ejpam-6775	5	24	.	.	PUNCT
ejpam-6775	6	1	first	first	ADJ
ejpam-6775	6	2	-	-	PUNCT
ejpam-6775	6	3	order	order	NOUN
ejpam-6775	6	4	optimality	optimality	NOUN
ejpam-6775	6	5	conditions	condition	NOUN
ejpam-6775	6	6	are	be	AUX
ejpam-6775	6	7	derived	derive	VERB
ejpam-6775	6	8	to	to	PART
ejpam-6775	6	9	characterize	characterize	VERB
ejpam-6775	6	10	optimal	optimal	ADJ
ejpam-6775	6	11	controls	control	NOUN
ejpam-6775	6	12	.	.	PUNCT
ejpam-6775	7	1	numerical	numerical	ADJ
ejpam-6775	7	2	simulations	simulation	NOUN
ejpam-6775	7	3	,	,	PUNCT
ejpam-6775	7	4	solved	solve	VERB
ejpam-6775	7	5	via	via	ADP
ejpam-6775	7	6	the	the	DET
ejpam-6775	7	7	forward	forward	ADV
ejpam-6775	7	8	-	-	PUNCT
ejpam-6775	7	9	backward	backward	ADJ
ejpam-6775	7	10	sweep	sweep	NOUN
ejpam-6775	7	11	method	method	NOUN
ejpam-6775	7	12	,	,	PUNCT
ejpam-6775	7	13	demonstrate	demonstrate	VERB
ejpam-6775	7	14	that	that	SCONJ
ejpam-6775	7	15	combined	combined	ADJ
ejpam-6775	7	16	vaccination	vaccination	NOUN
ejpam-6775	7	17	and	and	CCONJ
ejpam-6775	7	18	treatment	treatment	NOUN
ejpam-6775	7	19	significantly	significantly	ADV
ejpam-6775	7	20	reduces	reduce	VERB
ejpam-6775	7	21	disease	disease	NOUN
ejpam-6775	7	22	prevalence	prevalence	NOUN
ejpam-6775	7	23	,	,	PUNCT
ejpam-6775	7	24	with	with	ADP
ejpam-6775	7	25	early	early	ADJ
ejpam-6775	7	26	intervention	intervention	NOUN
ejpam-6775	7	27	being	be	AUX
ejpam-6775	7	28	critical	critical	ADJ
ejpam-6775	7	29	.	.	PUNCT
ejpam-6775	8	1	these	these	DET
ejpam-6775	8	2	findings	finding	NOUN
ejpam-6775	8	3	underscore	underscore	VERB
ejpam-6775	8	4	the	the	DET
ejpam-6775	8	5	importance	importance	NOUN
ejpam-6775	8	6	of	of	ADP
ejpam-6775	8	7	strategic	strategic	ADJ
ejpam-6775	8	8	resource	resource	NOUN
ejpam-6775	8	9	allocation	allocation	NOUN
ejpam-6775	8	10	in	in	ADP
ejpam-6775	8	11	managing	manage	VERB
ejpam-6775	8	12	complex	complex	ADJ
ejpam-6775	8	13	epidemic	epidemic	NOUN
ejpam-6775	8	14	dynamics	dynamic	NOUN
ejpam-6775	8	15	.	.	PUNCT
ejpam-6775	9	1	2020	2020	NUM
ejpam-6775	9	2	mathematics	mathematic	NOUN
ejpam-6775	9	3	subject	subject	NOUN
ejpam-6775	9	4	classifications	classification	NOUN
ejpam-6775	9	5	:	:	PUNCT
ejpam-6775	9	6	92d25	92d25	NUM
ejpam-6775	9	7	,	,	PUNCT
ejpam-6775	9	8	35b32	35b32	NUM
ejpam-6775	9	9	,	,	PUNCT
ejpam-6775	9	10	49j15	49j15	NUM
ejpam-6775	9	11	,	,	PUNCT
ejpam-6775	9	12	65k05	65k05	NUM
ejpam-6775	9	13	key	key	ADJ
ejpam-6775	9	14	words	word	NOUN
ejpam-6775	9	15	and	and	CCONJ
ejpam-6775	9	16	phrases	phrase	NOUN
ejpam-6775	9	17	:	:	PUNCT
ejpam-6775	9	18	age	age	NOUN
ejpam-6775	9	19	-	-	PUNCT
ejpam-6775	9	20	structured	structure	VERB
ejpam-6775	9	21	model	model	NOUN
ejpam-6775	9	22	,	,	PUNCT
ejpam-6775	9	23	backward	backward	ADJ
ejpam-6775	9	24	bifurcation	bifurcation	NOUN
ejpam-6775	9	25	,	,	PUNCT
ejpam-6775	9	26	optimal	optimal	ADJ
ejpam-6775	9	27	control	control	NOUN
ejpam-6775	9	28	,	,	PUNCT
ejpam-6775	9	29	infectious	infectious	ADJ
ejpam-6775	9	30	disease	disease	NOUN
ejpam-6775	9	31	,	,	PUNCT
ejpam-6775	9	32	imperfect	imperfect	ADJ
ejpam-6775	9	33	vaccination	vaccination	NOUN
ejpam-6775	9	34	,	,	PUNCT
ejpam-6775	9	35	therapeutic	therapeutic	ADJ
ejpam-6775	9	36	treatment	treatment	NOUN
ejpam-6775	9	37	∗corresponding	∗corresponde	VERB
ejpam-6775	9	38	author	author	NOUN
ejpam-6775	9	39	.	.	PUNCT
ejpam-6775	10	1	doi	doi	NOUN
ejpam-6775	10	2	:	:	PUNCT
ejpam-6775	11	1	https://doi.org/10.29020/nybg.ejpam.v18i4.6775	https://doi.org/10.29020/nybg.ejpam.v18i4.6775	ADP
ejpam-6775	11	2	email	email	NOUN
ejpam-6775	11	3	addresses	address	VERB
ejpam-6775	11	4	:	:	PUNCT
ejpam-6775	11	5	leoamalraj@rmkcet.ac.in	leoamalraj@rmkcet.ac.in	PROPN
ejpam-6775	11	6	(	(	PUNCT
ejpam-6775	11	7	j.	j.	PROPN
ejpam-6775	11	8	leo	leo	PROPN
ejpam-6775	11	9	amalraj	amalraj	PROPN
ejpam-6775	11	10	)	)	PUNCT
ejpam-6775	11	11	,	,	PUNCT
ejpam-6775	11	12	pankaj.shukla@vit.ac.in	pankaj.shukla@vit.ac.in	PRON
ejpam-6775	11	13	(	(	PUNCT
ejpam-6775	11	14	p.	p.	NOUN
ejpam-6775	11	15	shukla	shukla	NOUN
ejpam-6775	11	16	)	)	PUNCT
ejpam-6775	11	17	,	,	PUNCT
ejpam-6775	11	18	phanendra51@gmail.com	phanendra51@gmail.com	PROPN
ejpam-6775	11	19	(	(	PUNCT
ejpam-6775	11	20	l.	l.	PROPN
ejpam-6775	11	21	phaneendra	phaneendra	PROPN
ejpam-6775	11	22	maguluri	maguluri	PROPN
ejpam-6775	11	23	)	)	PUNCT
ejpam-6775	11	24	,	,	PUNCT
ejpam-6775	11	25	siriluk.pa@up.ac.th	siriluk.pa@up.ac.th	PROPN
ejpam-6775	11	26	(	(	PUNCT
ejpam-6775	11	27	s.	s.	PROPN
ejpam-6775	11	28	donganont	donganont	PROPN
ejpam-6775	11	29	)	)	PUNCT
ejpam-6775	11	30	,	,	PUNCT
ejpam-6775	11	31	avinashprofess@gmail.com	avinashprofess@gmail.com	X
ejpam-6775	11	32	(	(	PUNCT
ejpam-6775	11	33	n.	n.	NOUN
ejpam-6775	11	34	avinash	avinash	PROPN
ejpam-6775	11	35	)	)	PUNCT
ejpam-6775	11	36	,	,	PUNCT
ejpam-6775	11	37	vgovindandr@gmail.com	vgovindandr@gmail.com	X
ejpam-6775	12	1	(	(	PUNCT
ejpam-6775	12	2	v.	v.	ADP
ejpam-6775	12	3	govindan	govindan	ADJ
ejpam-6775	12	4	)	)	PUNCT
ejpam-6775	12	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6775	13	1	1	1	NUM
ejpam-6775	13	2	copyright	copyright	NOUN
ejpam-6775	13	3	:	:	PUNCT
ejpam-6775	13	4	©	©	PROPN
ejpam-6775	13	5	2025	2025	NUM
ejpam-6775	13	6	the	the	DET
ejpam-6775	13	7	author(s	author(s	NOUN
ejpam-6775	13	8	)	)	PUNCT
ejpam-6775	13	9	.	.	PUNCT
ejpam-6775	14	1	(	(	PUNCT
ejpam-6775	14	2	cc	cc	NOUN
ejpam-6775	14	3	by	by	ADP
ejpam-6775	14	4	-	-	PUNCT
ejpam-6775	14	5	nc	nc	PROPN
ejpam-6775	14	6	4.0	4.0	NUM
ejpam-6775	14	7	)	)	PUNCT
ejpam-6775	14	8	j.	j.	PROPN
ejpam-6775	14	9	leo	leo	PROPN
ejpam-6775	14	10	amalraj	amalraj	PROPN
ejpam-6775	14	11	et	et	PROPN
ejpam-6775	14	12	al	al	PROPN
ejpam-6775	14	13	.	.	PUNCT
ejpam-6775	14	14	/	/	SYM
ejpam-6775	14	15	eur	eur	PROPN
ejpam-6775	14	16	.	.	PUNCT
ejpam-6775	15	1	j.	j.	PROPN
ejpam-6775	15	2	pure	pure	PROPN
ejpam-6775	15	3	appl	appl	PROPN
ejpam-6775	15	4	.	.	PROPN
ejpam-6775	15	5	math	math	PROPN
ejpam-6775	15	6	,	,	PUNCT
ejpam-6775	15	7	18	18	NUM
ejpam-6775	15	8	(	(	PUNCT
ejpam-6775	15	9	4	4	NUM
ejpam-6775	15	10	)	)	PUNCT
ejpam-6775	15	11	(	(	PUNCT
ejpam-6775	15	12	2025	2025	NUM
ejpam-6775	15	13	)	)	PUNCT
ejpam-6775	15	14	,	,	PUNCT
ejpam-6775	15	15	6775	6775	NUM
ejpam-6775	15	16	2	2	NUM
ejpam-6775	15	17	of	of	ADP
ejpam-6775	15	18	32	32	NUM
ejpam-6775	15	19	1	1	NUM
ejpam-6775	15	20	.	.	PUNCT
ejpam-6775	16	1	introduction	introduction	NOUN
ejpam-6775	16	2	bovine	bovine	NOUN
ejpam-6775	16	3	tuberculosis	tuberculosis	NOUN
ejpam-6775	16	4	(	(	PUNCT
ejpam-6775	16	5	btb	btb	NOUN
ejpam-6775	16	6	)	)	PUNCT
ejpam-6775	16	7	,	,	PUNCT
ejpam-6775	16	8	caused	cause	VERB
ejpam-6775	16	9	by	by	ADP
ejpam-6775	16	10	mycobacterium	mycobacterium	NOUN
ejpam-6775	16	11	bovis	bovis	NOUN
ejpam-6775	16	12	,	,	PUNCT
ejpam-6775	16	13	is	be	AUX
ejpam-6775	16	14	a	a	DET
ejpam-6775	16	15	contagious	contagious	ADJ
ejpam-6775	16	16	disease	disease	NOUN
ejpam-6775	16	17	affecting	affect	VERB
ejpam-6775	16	18	domestic	domestic	ADJ
ejpam-6775	16	19	and	and	CCONJ
ejpam-6775	16	20	wild	wild	ADJ
ejpam-6775	16	21	animals	animal	NOUN
ejpam-6775	16	22	,	,	PUNCT
ejpam-6775	16	23	including	include	VERB
ejpam-6775	16	24	cattle	cattle	NOUN
ejpam-6775	16	25	,	,	PUNCT
ejpam-6775	16	26	goats	goat	NOUN
ejpam-6775	16	27	,	,	PUNCT
ejpam-6775	16	28	sheep	sheep	NOUN
ejpam-6775	16	29	,	,	PUNCT
ejpam-6775	16	30	badgers	badger	NOUN
ejpam-6775	16	31	,	,	PUNCT
ejpam-6775	16	32	deer	deer	NOUN
ejpam-6775	16	33	,	,	PUNCT
ejpam-6775	16	34	bison	bison	NOUN
ejpam-6775	16	35	,	,	PUNCT
ejpam-6775	16	36	and	and	CCONJ
ejpam-6775	16	37	african	african	ADJ
ejpam-6775	16	38	buffalo	buffalo	PROPN
ejpam-6775	16	39	.	.	PUNCT
ejpam-6775	17	1	hosts	host	NOUN
ejpam-6775	17	2	can	can	AUX
ejpam-6775	17	3	either	either	CCONJ
ejpam-6775	17	4	be	be	AUX
ejpam-6775	17	5	reservoirs	reservoir	NOUN
ejpam-6775	17	6	,	,	PUNCT
ejpam-6775	17	7	which	which	PRON
ejpam-6775	17	8	maintain	maintain	VERB
ejpam-6775	17	9	and	and	CCONJ
ejpam-6775	17	10	spread	spread	VERB
ejpam-6775	17	11	the	the	DET
ejpam-6775	17	12	infection	infection	NOUN
ejpam-6775	17	13	,	,	PUNCT
ejpam-6775	17	14	or	or	CCONJ
ejpam-6775	17	15	spill	spill	NOUN
ejpam-6775	17	16	-	-	PUNCT
ejpam-6775	17	17	over	over	ADP
ejpam-6775	17	18	hosts	host	NOUN
ejpam-6775	17	19	,	,	PUNCT
ejpam-6775	17	20	which	which	PRON
ejpam-6775	17	21	have	have	VERB
ejpam-6775	17	22	little	little	ADJ
ejpam-6775	17	23	impact	impact	NOUN
ejpam-6775	17	24	on	on	ADP
ejpam-6775	17	25	transmission	transmission	NOUN
ejpam-6775	17	26	.	.	PUNCT
ejpam-6775	18	1	in	in	ADP
ejpam-6775	18	2	buffalo	buffalo	PROPN
ejpam-6775	18	3	herds	herd	NOUN
ejpam-6775	18	4	,	,	PUNCT
ejpam-6775	18	5	btb	btb	ADP
ejpam-6775	18	6	prevalence	prevalence	NOUN
ejpam-6775	18	7	is	be	AUX
ejpam-6775	18	8	notably	notably	ADV
ejpam-6775	18	9	high	high	ADJ
ejpam-6775	18	10	,	,	PUNCT
ejpam-6775	18	11	leading	lead	VERB
ejpam-6775	18	12	to	to	ADP
ejpam-6775	18	13	increased	increase	VERB
ejpam-6775	18	14	mortality	mortality	NOUN
ejpam-6775	18	15	.	.	PUNCT
ejpam-6775	19	1	studies	study	NOUN
ejpam-6775	19	2	indicate	indicate	VERB
ejpam-6775	19	3	that	that	SCONJ
ejpam-6775	19	4	higher	high	ADJ
ejpam-6775	19	5	prevalence	prevalence	NOUN
ejpam-6775	19	6	rates	rate	NOUN
ejpam-6775	19	7	correspond	correspond	VERB
ejpam-6775	19	8	to	to	ADP
ejpam-6775	19	9	higher	high	ADJ
ejpam-6775	19	10	disease	disease	NOUN
ejpam-6775	19	11	-	-	PUNCT
ejpam-6775	19	12	related	relate	VERB
ejpam-6775	19	13	mortality	mortality	NOUN
ejpam-6775	19	14	in	in	ADP
ejpam-6775	19	15	affected	affected	ADJ
ejpam-6775	19	16	herds	herd	NOUN
ejpam-6775	19	17	.	.	PUNCT
ejpam-6775	20	1	the	the	DET
ejpam-6775	20	2	disease	disease	NOUN
ejpam-6775	20	3	is	be	AUX
ejpam-6775	20	4	chronic	chronic	ADJ
ejpam-6775	20	5	and	and	CCONJ
ejpam-6775	20	6	progressive	progressive	ADJ
ejpam-6775	20	7	,	,	PUNCT
ejpam-6775	20	8	with	with	ADP
ejpam-6775	20	9	an	an	DET
ejpam-6775	20	10	unpredictable	unpredictable	ADJ
ejpam-6775	20	11	time	time	NOUN
ejpam-6775	20	12	from	from	ADP
ejpam-6775	20	13	infection	infection	NOUN
ejpam-6775	20	14	to	to	ADP
ejpam-6775	20	15	death	death	NOUN
ejpam-6775	20	16	.	.	PUNCT
ejpam-6775	21	1	this	this	DET
ejpam-6775	21	2	progression	progression	NOUN
ejpam-6775	21	3	is	be	AUX
ejpam-6775	21	4	influenced	influence	VERB
ejpam-6775	21	5	by	by	ADP
ejpam-6775	21	6	factors	factor	NOUN
ejpam-6775	21	7	such	such	ADJ
ejpam-6775	21	8	as	as	ADP
ejpam-6775	21	9	immune	immune	ADJ
ejpam-6775	21	10	response	response	NOUN
ejpam-6775	21	11	,	,	PUNCT
ejpam-6775	21	12	stress	stress	NOUN
ejpam-6775	21	13	,	,	PUNCT
ejpam-6775	21	14	drought	drought	NOUN
ejpam-6775	21	15	,	,	PUNCT
ejpam-6775	21	16	and	and	CCONJ
ejpam-6775	21	17	aging	aging	NOUN
ejpam-6775	21	18	.	.	PUNCT
ejpam-6775	22	1	btb	btb	NOUN
ejpam-6775	22	2	remains	remain	VERB
ejpam-6775	22	3	a	a	DET
ejpam-6775	22	4	significant	significant	ADJ
ejpam-6775	22	5	threat	threat	NOUN
ejpam-6775	22	6	to	to	PART
ejpam-6775	22	7	wildlife	wildlife	VERB
ejpam-6775	22	8	conservation	conservation	NOUN
ejpam-6775	22	9	and	and	CCONJ
ejpam-6775	22	10	livestock	livestock	NOUN
ejpam-6775	22	11	health	health	NOUN
ejpam-6775	22	12	,	,	PUNCT
ejpam-6775	22	13	necessitating	necessitate	VERB
ejpam-6775	22	14	effective	effective	ADJ
ejpam-6775	22	15	control	control	NOUN
ejpam-6775	22	16	measures	measure	NOUN
ejpam-6775	22	17	[	[	X
ejpam-6775	22	18	1	1	NUM
ejpam-6775	22	19	,	,	PUNCT
ejpam-6775	22	20	2	2	NUM
ejpam-6775	22	21	]	]	PUNCT
ejpam-6775	22	22	.	.	PUNCT
ejpam-6775	23	1	the	the	DET
ejpam-6775	23	2	asymptotic	asymptotic	ADJ
ejpam-6775	23	3	behavior	behavior	NOUN
ejpam-6775	23	4	of	of	ADP
ejpam-6775	23	5	epidemic	epidemic	NOUN
ejpam-6775	23	6	models	model	NOUN
ejpam-6775	23	7	shows	show	VERB
ejpam-6775	23	8	that	that	SCONJ
ejpam-6775	23	9	disease	disease	NOUN
ejpam-6775	23	10	persistence	persistence	NOUN
ejpam-6775	23	11	is	be	AUX
ejpam-6775	23	12	often	often	ADV
ejpam-6775	23	13	determined	determine	VERB
ejpam-6775	23	14	by	by	ADP
ejpam-6775	23	15	the	the	DET
ejpam-6775	23	16	basic	basic	ADJ
ejpam-6775	23	17	reproduction	reproduction	NOUN
ejpam-6775	23	18	number	number	NOUN
ejpam-6775	23	19	,	,	PUNCT
ejpam-6775	23	20	with	with	ADP
ejpam-6775	23	21	forward	forward	ADJ
ejpam-6775	23	22	bifurcation	bifurcation	NOUN
ejpam-6775	23	23	occurring	occur	VERB
ejpam-6775	23	24	when	when	SCONJ
ejpam-6775	23	25	it	it	PRON
ejpam-6775	23	26	exceeds	exceed	VERB
ejpam-6775	23	27	one	one	NUM
ejpam-6775	23	28	.	.	PUNCT
ejpam-6775	24	1	however	however	ADV
ejpam-6775	24	2	,	,	PUNCT
ejpam-6775	24	3	recent	recent	ADJ
ejpam-6775	24	4	studies	study	NOUN
ejpam-6775	24	5	highlight	highlight	VERB
ejpam-6775	24	6	that	that	SCONJ
ejpam-6775	24	7	backward	backward	ADJ
ejpam-6775	24	8	bifurcations	bifurcation	NOUN
ejpam-6775	24	9	,	,	PUNCT
ejpam-6775	24	10	caused	cause	VERB
ejpam-6775	24	11	by	by	ADP
ejpam-6775	24	12	factors	factor	NOUN
ejpam-6775	24	13	like	like	ADP
ejpam-6775	24	14	heterogeneous	heterogeneous	ADJ
ejpam-6775	24	15	susceptibility	susceptibility	NOUN
ejpam-6775	24	16	and	and	CCONJ
ejpam-6775	24	17	nonlinear	nonlinear	ADJ
ejpam-6775	24	18	incidence	incidence	NOUN
ejpam-6775	24	19	,	,	PUNCT
ejpam-6775	24	20	make	make	VERB
ejpam-6775	24	21	disease	disease	NOUN
ejpam-6775	24	22	elimination	elimination	NOUN
ejpam-6775	24	23	more	more	ADV
ejpam-6775	24	24	complex	complex	ADJ
ejpam-6775	24	25	.	.	PUNCT
ejpam-6775	25	1	in	in	ADP
ejpam-6775	25	2	such	such	ADJ
ejpam-6775	25	3	cases	case	NOUN
ejpam-6775	25	4	,	,	PUNCT
ejpam-6775	25	5	reducing	reduce	VERB
ejpam-6775	25	6	the	the	DET
ejpam-6775	25	7	reproduction	reproduction	NOUN
ejpam-6775	25	8	number	number	NOUN
ejpam-6775	25	9	below	below	ADP
ejpam-6775	25	10	one	one	NUM
ejpam-6775	25	11	is	be	AUX
ejpam-6775	25	12	insufficient	insufficient	ADJ
ejpam-6775	25	13	,	,	PUNCT
ejpam-6775	25	14	requiring	require	VERB
ejpam-6775	25	15	additional	additional	ADJ
ejpam-6775	25	16	control	control	NOUN
ejpam-6775	25	17	efforts	effort	NOUN
ejpam-6775	25	18	.	.	PUNCT
ejpam-6775	26	1	treatment	treatment	NOUN
ejpam-6775	26	2	is	be	AUX
ejpam-6775	26	3	crucial	crucial	ADJ
ejpam-6775	26	4	for	for	ADP
ejpam-6775	26	5	controlling	control	VERB
ejpam-6775	26	6	diseases	disease	NOUN
ejpam-6775	26	7	like	like	ADP
ejpam-6775	26	8	measles	measle	NOUN
ejpam-6775	26	9	and	and	CCONJ
ejpam-6775	26	10	tuberculosis	tuberculosis	NOUN
ejpam-6775	26	11	,	,	PUNCT
ejpam-6775	26	12	but	but	CCONJ
ejpam-6775	26	13	real	real	ADJ
ejpam-6775	26	14	-	-	PUNCT
ejpam-6775	26	15	world	world	NOUN
ejpam-6775	26	16	constraints	constraint	NOUN
ejpam-6775	26	17	necessitate	necessitate	ADJ
ejpam-6775	26	18	efficient	efficient	ADJ
ejpam-6775	26	19	resource	resource	NOUN
ejpam-6775	26	20	allocation	allocation	NOUN
ejpam-6775	26	21	.	.	PUNCT
ejpam-6775	27	1	classical	classical	ADJ
ejpam-6775	27	2	models	model	NOUN
ejpam-6775	27	3	assume	assume	VERB
ejpam-6775	27	4	treatment	treatment	NOUN
ejpam-6775	27	5	rates	rate	NOUN
ejpam-6775	27	6	proportional	proportional	ADJ
ejpam-6775	27	7	to	to	ADP
ejpam-6775	27	8	infections	infection	NOUN
ejpam-6775	27	9	,	,	PUNCT
ejpam-6775	27	10	but	but	CCONJ
ejpam-6775	27	11	communities	community	NOUN
ejpam-6775	27	12	must	must	AUX
ejpam-6775	27	13	balance	balance	VERB
ejpam-6775	27	14	cost	cost	NOUN
ejpam-6775	27	15	and	and	CCONJ
ejpam-6775	27	16	capacity	capacity	NOUN
ejpam-6775	27	17	.	.	PUNCT
ejpam-6775	28	1	ensuring	ensure	VERB
ejpam-6775	28	2	optimal	optimal	ADJ
ejpam-6775	28	3	treatment	treatment	NOUN
ejpam-6775	28	4	prevents	prevent	VERB
ejpam-6775	28	5	unnecessary	unnecessary	ADJ
ejpam-6775	28	6	expenses	expense	NOUN
ejpam-6775	28	7	while	while	SCONJ
ejpam-6775	28	8	minimizing	minimize	VERB
ejpam-6775	28	9	the	the	DET
ejpam-6775	28	10	risk	risk	NOUN
ejpam-6775	28	11	of	of	ADP
ejpam-6775	28	12	outbreaks	outbreak	NOUN
ejpam-6775	29	1	[	[	X
ejpam-6775	29	2	3–6	3–6	NUM
ejpam-6775	29	3	]	]	X
ejpam-6775	29	4	.	.	PUNCT
ejpam-6775	30	1	mathematical	mathematical	ADJ
ejpam-6775	30	2	models	model	NOUN
ejpam-6775	30	3	of	of	ADP
ejpam-6775	30	4	infectious	infectious	ADJ
ejpam-6775	30	5	diseases	disease	NOUN
ejpam-6775	30	6	play	play	VERB
ejpam-6775	30	7	a	a	DET
ejpam-6775	30	8	crucial	crucial	ADJ
ejpam-6775	30	9	role	role	NOUN
ejpam-6775	30	10	in	in	ADP
ejpam-6775	30	11	shaping	shape	VERB
ejpam-6775	30	12	public	public	ADJ
ejpam-6775	30	13	health	health	NOUN
ejpam-6775	30	14	policies	policy	NOUN
ejpam-6775	30	15	aimed	aim	VERB
ejpam-6775	30	16	at	at	ADP
ejpam-6775	30	17	minimizing	minimize	VERB
ejpam-6775	30	18	or	or	CCONJ
ejpam-6775	30	19	eradicating	eradicate	VERB
ejpam-6775	30	20	infections	infection	NOUN
ejpam-6775	30	21	.	.	PUNCT
ejpam-6775	31	1	researchers	researcher	NOUN
ejpam-6775	31	2	have	have	AUX
ejpam-6775	31	3	used	use	VERB
ejpam-6775	31	4	these	these	DET
ejpam-6775	31	5	models	model	NOUN
ejpam-6775	31	6	to	to	PART
ejpam-6775	31	7	study	study	VERB
ejpam-6775	31	8	diseases	disease	NOUN
ejpam-6775	31	9	such	such	ADJ
ejpam-6775	31	10	as	as	ADP
ejpam-6775	31	11	tuberculosis	tuberculosis	NOUN
ejpam-6775	31	12	,	,	PUNCT
ejpam-6775	31	13	hiv	hiv	PROPN
ejpam-6775	31	14	,	,	PUNCT
ejpam-6775	31	15	malaria	malaria	NOUN
ejpam-6775	31	16	,	,	PUNCT
ejpam-6775	31	17	and	and	CCONJ
ejpam-6775	31	18	ebola	ebola	PROPN
ejpam-6775	31	19	,	,	PUNCT
ejpam-6775	31	20	helping	help	VERB
ejpam-6775	31	21	to	to	PART
ejpam-6775	31	22	understand	understand	VERB
ejpam-6775	31	23	epidemic	epidemic	NOUN
ejpam-6775	31	24	dynamics	dynamic	NOUN
ejpam-6775	31	25	.	.	PUNCT
ejpam-6775	32	1	a	a	DET
ejpam-6775	32	2	common	common	ADJ
ejpam-6775	32	3	criterion	criterion	NOUN
ejpam-6775	32	4	for	for	ADP
ejpam-6775	32	5	disease	disease	NOUN
ejpam-6775	32	6	eradication	eradication	NOUN
ejpam-6775	32	7	is	be	AUX
ejpam-6775	32	8	maintaining	maintain	VERB
ejpam-6775	32	9	the	the	DET
ejpam-6775	32	10	basic	basic	ADJ
ejpam-6775	32	11	reproduction	reproduction	NOUN
ejpam-6775	32	12	number	number	NOUN
ejpam-6775	32	13	below	below	ADP
ejpam-6775	32	14	unity	unity	NOUN
ejpam-6775	32	15	,	,	PUNCT
ejpam-6775	32	16	ensuring	ensure	VERB
ejpam-6775	32	17	the	the	DET
ejpam-6775	32	18	stability	stability	NOUN
ejpam-6775	32	19	of	of	ADP
ejpam-6775	32	20	the	the	DET
ejpam-6775	32	21	disease	disease	NOUN
ejpam-6775	32	22	-	-	PUNCT
ejpam-6775	32	23	free	free	ADJ
ejpam-6775	32	24	equilibrium	equilibrium	NOUN
ejpam-6775	32	25	.	.	PUNCT
ejpam-6775	33	1	however	however	ADV
ejpam-6775	33	2	,	,	PUNCT
ejpam-6775	33	3	studies	study	NOUN
ejpam-6775	33	4	have	have	AUX
ejpam-6775	33	5	shown	show	VERB
ejpam-6775	33	6	that	that	SCONJ
ejpam-6775	33	7	backward	backward	ADJ
ejpam-6775	33	8	bifurcation	bifurcation	NOUN
ejpam-6775	33	9	can	can	AUX
ejpam-6775	33	10	occur	occur	VERB
ejpam-6775	33	11	,	,	PUNCT
ejpam-6775	33	12	allowing	allow	VERB
ejpam-6775	33	13	disease	disease	NOUN
ejpam-6775	33	14	persistence	persistence	NOUN
ejpam-6775	33	15	even	even	ADV
ejpam-6775	33	16	when	when	SCONJ
ejpam-6775	33	17	the	the	DET
ejpam-6775	33	18	reproduction	reproduction	NOUN
ejpam-6775	33	19	number	number	NOUN
ejpam-6775	33	20	is	be	AUX
ejpam-6775	33	21	less	less	ADJ
ejpam-6775	33	22	than	than	ADP
ejpam-6775	33	23	one	one	NUM
ejpam-6775	33	24	.	.	PUNCT
ejpam-6775	34	1	this	this	PRON
ejpam-6775	34	2	challenges	challenge	VERB
ejpam-6775	34	3	the	the	DET
ejpam-6775	34	4	traditional	traditional	ADJ
ejpam-6775	34	5	reliance	reliance	NOUN
ejpam-6775	34	6	on	on	ADP
ejpam-6775	34	7	the	the	DET
ejpam-6775	34	8	reproduction	reproduction	NOUN
ejpam-6775	34	9	number	number	NOUN
ejpam-6775	34	10	as	as	ADP
ejpam-6775	34	11	a	a	DET
ejpam-6775	34	12	sole	sole	ADJ
ejpam-6775	34	13	control	control	NOUN
ejpam-6775	34	14	metric	metric	ADJ
ejpam-6775	34	15	.	.	PUNCT
ejpam-6775	35	1	this	this	DET
ejpam-6775	35	2	study	study	NOUN
ejpam-6775	35	3	further	far	ADV
ejpam-6775	35	4	investigates	investigate	VERB
ejpam-6775	35	5	the	the	DET
ejpam-6775	35	6	effects	effect	NOUN
ejpam-6775	35	7	of	of	ADP
ejpam-6775	35	8	treatment	treatment	NOUN
ejpam-6775	35	9	saturation	saturation	NOUN
ejpam-6775	35	10	and	and	CCONJ
ejpam-6775	35	11	infected	infect	VERB
ejpam-6775	35	12	individual	individual	ADJ
ejpam-6775	35	13	isolation	isolation	NOUN
ejpam-6775	35	14	on	on	ADP
ejpam-6775	35	15	the	the	DET
ejpam-6775	35	16	emergence	emergence	NOUN
ejpam-6775	35	17	of	of	ADP
ejpam-6775	35	18	backward	backward	ADJ
ejpam-6775	35	19	bifurcation	bifurcation	NOUN
ejpam-6775	35	20	[	[	X
ejpam-6775	35	21	7–12	7–12	PROPN
ejpam-6775	35	22	]	]	PUNCT
ejpam-6775	35	23	.	.	PUNCT
ejpam-6775	36	1	infectious	infectious	ADJ
ejpam-6775	36	2	diseases	disease	NOUN
ejpam-6775	36	3	remain	remain	VERB
ejpam-6775	36	4	a	a	DET
ejpam-6775	36	5	major	major	ADJ
ejpam-6775	36	6	global	global	ADJ
ejpam-6775	36	7	health	health	NOUN
ejpam-6775	36	8	challenge	challenge	NOUN
ejpam-6775	36	9	,	,	PUNCT
ejpam-6775	36	10	with	with	ADP
ejpam-6775	36	11	illnesses	illness	NOUN
ejpam-6775	36	12	like	like	ADP
ejpam-6775	36	13	influenza	influenza	NOUN
ejpam-6775	36	14	,	,	PUNCT
ejpam-6775	36	15	covid-19	covid-19	PROPN
ejpam-6775	36	16	,	,	PUNCT
ejpam-6775	36	17	and	and	CCONJ
ejpam-6775	36	18	tuberculosis	tuberculosis	NOUN
ejpam-6775	36	19	causing	cause	VERB
ejpam-6775	36	20	millions	million	NOUN
ejpam-6775	36	21	of	of	ADP
ejpam-6775	36	22	deaths	death	NOUN
ejpam-6775	36	23	annually	annually	ADV
ejpam-6775	36	24	.	.	PUNCT
ejpam-6775	37	1	limited	limited	ADJ
ejpam-6775	37	2	healthcare	healthcare	PROPN
ejpam-6775	37	3	resources	resource	NOUN
ejpam-6775	37	4	in	in	ADP
ejpam-6775	37	5	low	low	ADJ
ejpam-6775	37	6	-	-	PUNCT
ejpam-6775	37	7	income	income	NOUN
ejpam-6775	37	8	regions	region	NOUN
ejpam-6775	37	9	exacerbate	exacerbate	VERB
ejpam-6775	37	10	disease	disease	NOUN
ejpam-6775	37	11	spread	spread	NOUN
ejpam-6775	37	12	and	and	CCONJ
ejpam-6775	37	13	mortality	mortality	NOUN
ejpam-6775	37	14	.	.	PUNCT
ejpam-6775	38	1	emerging	emerge	VERB
ejpam-6775	38	2	epidemics	epidemic	NOUN
ejpam-6775	38	3	pose	pose	VERB
ejpam-6775	38	4	risks	risk	NOUN
ejpam-6775	38	5	to	to	ADP
ejpam-6775	38	6	public	public	ADJ
ejpam-6775	38	7	health	health	NOUN
ejpam-6775	38	8	and	and	CCONJ
ejpam-6775	38	9	economies	economy	NOUN
ejpam-6775	38	10	,	,	PUNCT
ejpam-6775	38	11	highlighting	highlight	VERB
ejpam-6775	38	12	the	the	DET
ejpam-6775	38	13	need	need	NOUN
ejpam-6775	38	14	for	for	ADP
ejpam-6775	38	15	effective	effective	ADJ
ejpam-6775	38	16	control	control	NOUN
ejpam-6775	38	17	strategies	strategy	NOUN
ejpam-6775	38	18	.	.	PUNCT
ejpam-6775	39	1	mathematical	mathematical	ADJ
ejpam-6775	39	2	modeling	modeling	NOUN
ejpam-6775	39	3	helps	help	VERB
ejpam-6775	39	4	predict	predict	VERB
ejpam-6775	39	5	outbreaks	outbreak	NOUN
ejpam-6775	39	6	and	and	CCONJ
ejpam-6775	39	7	guide	guide	VERB
ejpam-6775	39	8	policymakers	policymaker	NOUN
ejpam-6775	39	9	in	in	ADP
ejpam-6775	39	10	implementing	implement	VERB
ejpam-6775	39	11	optimal	optimal	ADJ
ejpam-6775	39	12	disease	disease	NOUN
ejpam-6775	39	13	prevention	prevention	NOUN
ejpam-6775	39	14	and	and	CCONJ
ejpam-6775	39	15	treatment	treatment	NOUN
ejpam-6775	39	16	measures	measure	NOUN
ejpam-6775	39	17	[	[	X
ejpam-6775	39	18	13	13	NUM
ejpam-6775	39	19	,	,	PUNCT
ejpam-6775	39	20	14	14	NUM
ejpam-6775	39	21	]	]	PUNCT
ejpam-6775	39	22	.	.	PUNCT
ejpam-6775	40	1	infectious	infectious	ADJ
ejpam-6775	40	2	diseases	disease	NOUN
ejpam-6775	40	3	remain	remain	VERB
ejpam-6775	40	4	a	a	DET
ejpam-6775	40	5	major	major	ADJ
ejpam-6775	40	6	threat	threat	NOUN
ejpam-6775	40	7	,	,	PUNCT
ejpam-6775	40	8	with	with	ADP
ejpam-6775	40	9	epidemic	epidemic	NOUN
ejpam-6775	40	10	models	model	NOUN
ejpam-6775	40	11	helping	help	VERB
ejpam-6775	40	12	to	to	PART
ejpam-6775	40	13	understand	understand	VERB
ejpam-6775	40	14	their	their	PRON
ejpam-6775	40	15	spread	spread	NOUN
ejpam-6775	40	16	and	and	CCONJ
ejpam-6775	40	17	control	control	NOUN
ejpam-6775	40	18	.	.	PUNCT
ejpam-6775	41	1	the	the	DET
ejpam-6775	41	2	siqr	siqr	PROPN
ejpam-6775	41	3	model	model	PROPN
ejpam-6775	41	4	,	,	PUNCT
ejpam-6775	41	5	incorporating	incorporate	VERB
ejpam-6775	41	6	quarantine	quarantine	NOUN
ejpam-6775	41	7	,	,	PUNCT
ejpam-6775	41	8	is	be	AUX
ejpam-6775	41	9	useful	useful	ADJ
ejpam-6775	41	10	for	for	ADP
ejpam-6775	41	11	studying	study	VERB
ejpam-6775	41	12	transmission	transmission	NOUN
ejpam-6775	41	13	dynamics	dynamic	NOUN
ejpam-6775	41	14	[	[	X
ejpam-6775	41	15	15–22	15–22	NUM
ejpam-6775	41	16	]	]	PUNCT
ejpam-6775	41	17	.	.	PUNCT
ejpam-6775	42	1	this	this	DET
ejpam-6775	42	2	study	study	NOUN
ejpam-6775	42	3	analyzes	analyze	VERB
ejpam-6775	42	4	the	the	DET
ejpam-6775	42	5	siqr	siqr	PROPN
ejpam-6775	42	6	model	model	NOUN
ejpam-6775	42	7	using	use	VERB
ejpam-6775	42	8	numerical	numerical	ADJ
ejpam-6775	42	9	methods	method	NOUN
ejpam-6775	42	10	like	like	ADP
ejpam-6775	42	11	the	the	DET
ejpam-6775	42	12	euler	euler	PROPN
ejpam-6775	42	13	scheme	scheme	NOUN
ejpam-6775	42	14	,	,	PUNCT
ejpam-6775	42	15	runge	runge	NOUN
ejpam-6775	42	16	-	-	PUNCT
ejpam-6775	42	17	kutta	kutta	NOUN
ejpam-6775	42	18	,	,	PUNCT
ejpam-6775	42	19	and	and	CCONJ
ejpam-6775	42	20	nsfd	nsfd	ADJ
ejpam-6775	42	21	.	.	PUNCT
ejpam-6775	43	1	stability	stability	NOUN
ejpam-6775	43	2	,	,	PUNCT
ejpam-6775	43	3	bifurcation	bifurcation	NOUN
ejpam-6775	43	4	,	,	PUNCT
ejpam-6775	43	5	and	and	CCONJ
ejpam-6775	43	6	convergence	convergence	NOUN
ejpam-6775	43	7	are	be	AUX
ejpam-6775	43	8	examined	examine	VERB
ejpam-6775	43	9	using	use	VERB
ejpam-6775	43	10	the	the	DET
ejpam-6775	43	11	routh	routh	PROPN
ejpam-6775	43	12	-	-	PUNCT
ejpam-6775	43	13	hurwitz	hurwitz	PROPN
ejpam-6775	43	14	criterion	criterion	NOUN
ejpam-6775	43	15	to	to	PART
ejpam-6775	43	16	identify	identify	VERB
ejpam-6775	43	17	the	the	DET
ejpam-6775	43	18	most	most	ADV
ejpam-6775	43	19	effective	effective	ADJ
ejpam-6775	44	1	j.	j.	PROPN
ejpam-6775	44	2	leo	leo	PROPN
ejpam-6775	44	3	amalraj	amalraj	PROPN
ejpam-6775	44	4	et	et	PROPN
ejpam-6775	44	5	al	al	PROPN
ejpam-6775	44	6	.	.	PUNCT
ejpam-6775	44	7	/	/	SYM
ejpam-6775	44	8	eur	eur	PROPN
ejpam-6775	44	9	.	.	PUNCT
ejpam-6775	45	1	j.	j.	PROPN
ejpam-6775	45	2	pure	pure	PROPN
ejpam-6775	45	3	appl	appl	PROPN
ejpam-6775	45	4	.	.	PROPN
ejpam-6775	45	5	math	math	PROPN
ejpam-6775	45	6	,	,	PUNCT
ejpam-6775	45	7	18	18	NUM
ejpam-6775	45	8	(	(	PUNCT
ejpam-6775	45	9	4	4	NUM
ejpam-6775	45	10	)	)	PUNCT
ejpam-6775	45	11	(	(	PUNCT
ejpam-6775	45	12	2025	2025	NUM
ejpam-6775	45	13	)	)	PUNCT
ejpam-6775	45	14	,	,	PUNCT
ejpam-6775	45	15	6775	6775	NUM
ejpam-6775	45	16	3	3	NUM
ejpam-6775	45	17	of	of	ADP
ejpam-6775	45	18	32	32	NUM
ejpam-6775	45	19	computational	computational	ADJ
ejpam-6775	45	20	approach	approach	NOUN
ejpam-6775	45	21	[	[	X
ejpam-6775	45	22	23–26	23–26	NOUN
ejpam-6775	45	23	]	]	PUNCT
ejpam-6775	45	24	.	.	PUNCT
ejpam-6775	46	1	several	several	ADJ
ejpam-6775	46	2	multi	multi	ADJ
ejpam-6775	46	3	-	-	ADJ
ejpam-6775	46	4	strain	strain	ADJ
ejpam-6775	46	5	epidemic	epidemic	NOUN
ejpam-6775	46	6	models	model	NOUN
ejpam-6775	46	7	extending	extend	VERB
ejpam-6775	46	8	the	the	DET
ejpam-6775	46	9	classical	classical	ADJ
ejpam-6775	46	10	sir	sir	NOUN
ejpam-6775	46	11	framework	framework	NOUN
ejpam-6775	46	12	have	have	AUX
ejpam-6775	46	13	been	be	AUX
ejpam-6775	46	14	analyzed	analyze	VERB
ejpam-6775	46	15	using	use	VERB
ejpam-6775	46	16	bifurcation	bifurcation	NOUN
ejpam-6775	46	17	theory	theory	NOUN
ejpam-6775	46	18	to	to	PART
ejpam-6775	46	19	understand	understand	VERB
ejpam-6775	46	20	dengue	dengue	NOUN
ejpam-6775	46	21	fever	fever	NOUN
ejpam-6775	46	22	dynamics	dynamic	NOUN
ejpam-6775	46	23	.	.	PUNCT
ejpam-6775	47	1	previous	previous	ADJ
ejpam-6775	47	2	studies	study	NOUN
ejpam-6775	47	3	have	have	AUX
ejpam-6775	47	4	examined	examine	VERB
ejpam-6775	47	5	the	the	DET
ejpam-6775	47	6	role	role	NOUN
ejpam-6775	47	7	of	of	ADP
ejpam-6775	47	8	primary	primary	ADJ
ejpam-6775	47	9	and	and	CCONJ
ejpam-6775	47	10	secondary	secondary	ADJ
ejpam-6775	47	11	infections	infection	NOUN
ejpam-6775	47	12	in	in	ADP
ejpam-6775	47	13	disease	disease	NOUN
ejpam-6775	47	14	progression	progression	NOUN
ejpam-6775	47	15	.	.	PUNCT
ejpam-6775	48	1	analytical	analytical	ADJ
ejpam-6775	48	2	techniques	technique	NOUN
ejpam-6775	48	3	,	,	PUNCT
ejpam-6775	48	4	such	such	ADJ
ejpam-6775	48	5	as	as	ADP
ejpam-6775	48	6	symbolic	symbolic	ADJ
ejpam-6775	48	7	algebra	algebra	NOUN
ejpam-6775	48	8	(	(	PUNCT
ejpam-6775	48	9	maple	maple	NOUN
ejpam-6775	48	10	)	)	PUNCT
ejpam-6775	48	11	,	,	PUNCT
ejpam-6775	48	12	have	have	AUX
ejpam-6775	48	13	been	be	AUX
ejpam-6775	48	14	used	use	VERB
ejpam-6775	48	15	for	for	ADP
ejpam-6775	48	16	simple	simple	ADJ
ejpam-6775	48	17	models	model	NOUN
ejpam-6775	48	18	,	,	PUNCT
ejpam-6775	48	19	while	while	SCONJ
ejpam-6775	48	20	numerical	numerical	ADJ
ejpam-6775	48	21	bifurcation	bifurcation	NOUN
ejpam-6775	48	22	tools	tool	NOUN
ejpam-6775	48	23	(	(	PUNCT
ejpam-6775	48	24	auto	auto	NOUN
ejpam-6775	48	25	,	,	PUNCT
ejpam-6775	48	26	matcont	matcont	ADJ
ejpam-6775	48	27	)	)	PUNCT
ejpam-6775	48	28	assist	assist	NOUN
ejpam-6775	48	29	in	in	ADP
ejpam-6775	48	30	analyzing	analyze	VERB
ejpam-6775	48	31	complex	complex	ADJ
ejpam-6775	48	32	dynamics	dynamic	NOUN
ejpam-6775	48	33	.	.	PUNCT
ejpam-6775	49	1	stability	stability	NOUN
ejpam-6775	49	2	analysis	analysis	NOUN
ejpam-6775	49	3	via	via	ADP
ejpam-6775	49	4	equilibria	equilibrium	NOUN
ejpam-6775	49	5	and	and	CCONJ
ejpam-6775	49	6	lyapunov	lyapunov	PROPN
ejpam-6775	49	7	exponents	exponent	NOUN
ejpam-6775	49	8	helps	helps	AUX
ejpam-6775	49	9	identify	identify	VERB
ejpam-6775	49	10	chaotic	chaotic	ADJ
ejpam-6775	49	11	behavior	behavior	NOUN
ejpam-6775	49	12	.	.	PUNCT
ejpam-6775	50	1	these	these	DET
ejpam-6775	50	2	methods	method	NOUN
ejpam-6775	50	3	provide	provide	VERB
ejpam-6775	50	4	insights	insight	NOUN
ejpam-6775	50	5	into	into	ADP
ejpam-6775	50	6	parameter	parameter	NOUN
ejpam-6775	50	7	dependencies	dependency	NOUN
ejpam-6775	50	8	and	and	CCONJ
ejpam-6775	50	9	long	long	ADJ
ejpam-6775	50	10	-	-	PUNCT
ejpam-6775	50	11	term	term	NOUN
ejpam-6775	50	12	epidemic	epidemic	NOUN
ejpam-6775	50	13	patterns	pattern	NOUN
ejpam-6775	50	14	[	[	X
ejpam-6775	50	15	27–30	27–30	NUM
ejpam-6775	50	16	]	]	PUNCT
ejpam-6775	50	17	.	.	PUNCT
ejpam-6775	51	1	mathematics	mathematic	NOUN
ejpam-6775	51	2	has	have	AUX
ejpam-6775	51	3	been	be	AUX
ejpam-6775	51	4	integral	integral	ADJ
ejpam-6775	51	5	to	to	ADP
ejpam-6775	51	6	biology	biology	NOUN
ejpam-6775	51	7	since	since	SCONJ
ejpam-6775	51	8	fibonacci	fibonacci	NOUN
ejpam-6775	51	9	’s	’s	PART
ejpam-6775	51	10	early	early	ADJ
ejpam-6775	51	11	population	population	NOUN
ejpam-6775	51	12	models	model	NOUN
ejpam-6775	51	13	,	,	PUNCT
ejpam-6775	51	14	evolving	evolve	VERB
ejpam-6775	51	15	into	into	ADP
ejpam-6775	51	16	the	the	DET
ejpam-6775	51	17	formalized	formalize	VERB
ejpam-6775	51	18	field	field	NOUN
ejpam-6775	51	19	of	of	ADP
ejpam-6775	51	20	biomathematics	biomathematic	NOUN
ejpam-6775	51	21	introduced	introduce	VERB
ejpam-6775	51	22	by	by	ADP
ejpam-6775	51	23	johannes	johannes	PROPN
ejpam-6775	51	24	ranke	ranke	PROPN
ejpam-6775	51	25	in	in	ADP
ejpam-6775	51	26	1901	1901	NUM
ejpam-6775	51	27	.	.	PUNCT
ejpam-6775	52	1	mathematical	mathematical	ADJ
ejpam-6775	52	2	biology	biology	NOUN
ejpam-6775	52	3	involves	involve	VERB
ejpam-6775	52	4	theoretical	theoretical	ADJ
ejpam-6775	52	5	analysis	analysis	NOUN
ejpam-6775	52	6	and	and	CCONJ
ejpam-6775	52	7	modeling	modeling	NOUN
ejpam-6775	52	8	of	of	ADP
ejpam-6775	52	9	biological	biological	ADJ
ejpam-6775	52	10	structures	structure	NOUN
ejpam-6775	52	11	and	and	CCONJ
ejpam-6775	52	12	behaviors	behavior	NOUN
ejpam-6775	52	13	,	,	PUNCT
ejpam-6775	52	14	divided	divide	VERB
ejpam-6775	52	15	into	into	ADP
ejpam-6775	52	16	stages	stage	NOUN
ejpam-6775	52	17	from	from	ADP
ejpam-6775	52	18	conceptual	conceptual	ADJ
ejpam-6775	52	19	representation	representation	NOUN
ejpam-6775	52	20	to	to	ADP
ejpam-6775	52	21	mathematical	mathematical	ADJ
ejpam-6775	52	22	formulation	formulation	NOUN
ejpam-6775	52	23	and	and	CCONJ
ejpam-6775	52	24	application	application	NOUN
ejpam-6775	52	25	.	.	PUNCT
ejpam-6775	53	1	fractional	fractional	ADJ
ejpam-6775	53	2	calculus	calculus	NOUN
ejpam-6775	53	3	and	and	CCONJ
ejpam-6775	53	4	mathematical	mathematical	ADJ
ejpam-6775	53	5	operators	operator	NOUN
ejpam-6775	53	6	such	such	ADJ
ejpam-6775	53	7	as	as	ADP
ejpam-6775	53	8	riemann	riemann	PROPN
ejpam-6775	53	9	-	-	PUNCT
ejpam-6775	53	10	liouville	liouville	PROPN
ejpam-6775	53	11	and	and	CCONJ
ejpam-6775	53	12	caputo	caputo	PROPN
ejpam-6775	53	13	have	have	AUX
ejpam-6775	53	14	been	be	AUX
ejpam-6775	53	15	applied	apply	VERB
ejpam-6775	53	16	to	to	ADP
ejpam-6775	53	17	biological	biological	ADJ
ejpam-6775	53	18	systems	system	NOUN
ejpam-6775	53	19	,	,	PUNCT
ejpam-6775	53	20	including	include	VERB
ejpam-6775	53	21	disease	disease	NOUN
ejpam-6775	53	22	modeling	modeling	NOUN
ejpam-6775	53	23	.	.	PUNCT
ejpam-6775	54	1	cholera	cholera	NOUN
ejpam-6775	54	2	,	,	PUNCT
ejpam-6775	54	3	caused	cause	VERB
ejpam-6775	54	4	by	by	ADP
ejpam-6775	54	5	vibrio	vibrio	ADJ
ejpam-6775	54	6	cholerae	cholerae	PROPN
ejpam-6775	54	7	,	,	PUNCT
ejpam-6775	54	8	spreads	spread	VERB
ejpam-6775	54	9	through	through	ADP
ejpam-6775	54	10	fecal	fecal	ADJ
ejpam-6775	54	11	-	-	PUNCT
ejpam-6775	54	12	oral	oral	ADJ
ejpam-6775	54	13	transmission	transmission	NOUN
ejpam-6775	54	14	,	,	PUNCT
ejpam-6775	54	15	exacerbated	exacerbate	VERB
ejpam-6775	54	16	by	by	ADP
ejpam-6775	54	17	poor	poor	ADJ
ejpam-6775	54	18	sanitation	sanitation	NOUN
ejpam-6775	54	19	,	,	PUNCT
ejpam-6775	54	20	and	and	CCONJ
ejpam-6775	54	21	remains	remain	VERB
ejpam-6775	54	22	a	a	DET
ejpam-6775	54	23	major	major	ADJ
ejpam-6775	54	24	public	public	ADJ
ejpam-6775	54	25	health	health	NOUN
ejpam-6775	54	26	concern	concern	NOUN
ejpam-6775	54	27	.	.	PUNCT
ejpam-6775	55	1	mathematical	mathematical	ADJ
ejpam-6775	55	2	models	model	NOUN
ejpam-6775	55	3	have	have	AUX
ejpam-6775	55	4	been	be	AUX
ejpam-6775	55	5	instrumental	instrumental	ADJ
ejpam-6775	55	6	in	in	ADP
ejpam-6775	55	7	understanding	understand	VERB
ejpam-6775	55	8	cholera	cholera	NOUN
ejpam-6775	55	9	transmission	transmission	NOUN
ejpam-6775	55	10	,	,	PUNCT
ejpam-6775	55	11	guiding	guide	VERB
ejpam-6775	55	12	prevention	prevention	NOUN
ejpam-6775	55	13	,	,	PUNCT
ejpam-6775	55	14	intervention	intervention	NOUN
ejpam-6775	55	15	strategies	strategy	NOUN
ejpam-6775	55	16	,	,	PUNCT
ejpam-6775	55	17	and	and	CCONJ
ejpam-6775	55	18	public	public	ADJ
ejpam-6775	55	19	health	health	NOUN
ejpam-6775	55	20	policies	policy	NOUN
ejpam-6775	55	21	[	[	X
ejpam-6775	55	22	31–36	31–36	NUM
ejpam-6775	55	23	]	]	PUNCT
ejpam-6775	55	24	.	.	PUNCT
ejpam-6775	56	1	arboviral	arboviral	ADJ
ejpam-6775	56	2	diseases	disease	NOUN
ejpam-6775	56	3	,	,	PUNCT
ejpam-6775	56	4	transmitted	transmit	VERB
ejpam-6775	56	5	by	by	ADP
ejpam-6775	56	6	arthropods	arthropod	NOUN
ejpam-6775	56	7	,	,	PUNCT
ejpam-6775	56	8	include	include	VERB
ejpam-6775	56	9	dengue	dengue	NOUN
ejpam-6775	56	10	,	,	PUNCT
ejpam-6775	56	11	yellow	yellow	ADJ
ejpam-6775	56	12	fever	fever	NOUN
ejpam-6775	56	13	,	,	PUNCT
ejpam-6775	56	14	and	and	CCONJ
ejpam-6775	56	15	chikungunya	chikungunya	NOUN
ejpam-6775	56	16	,	,	PUNCT
ejpam-6775	56	17	posing	pose	VERB
ejpam-6775	56	18	major	major	ADJ
ejpam-6775	56	19	public	public	ADJ
ejpam-6775	56	20	health	health	NOUN
ejpam-6775	56	21	threats	threat	NOUN
ejpam-6775	56	22	.	.	PUNCT
ejpam-6775	57	1	dengue	dengue	NOUN
ejpam-6775	57	2	alone	alone	ADV
ejpam-6775	57	3	infects	infect	VERB
ejpam-6775	57	4	50–100	50–100	PROPN
ejpam-6775	57	5	million	million	NUM
ejpam-6775	57	6	people	people	NOUN
ejpam-6775	57	7	annually	annually	ADV
ejpam-6775	57	8	,	,	PUNCT
ejpam-6775	57	9	mainly	mainly	ADV
ejpam-6775	57	10	children	child	NOUN
ejpam-6775	57	11	.	.	PUNCT
ejpam-6775	58	1	transmission	transmission	NOUN
ejpam-6775	58	2	dynamics	dynamic	NOUN
ejpam-6775	58	3	depend	depend	VERB
ejpam-6775	58	4	on	on	ADP
ejpam-6775	58	5	human	human	ADJ
ejpam-6775	58	6	behavior	behavior	NOUN
ejpam-6775	58	7	,	,	PUNCT
ejpam-6775	58	8	mosquito	mosquito	ADJ
ejpam-6775	58	9	activity	activity	NOUN
ejpam-6775	58	10	,	,	PUNCT
ejpam-6775	58	11	virus	virus	NOUN
ejpam-6775	58	12	diversity	diversity	NOUN
ejpam-6775	58	13	,	,	PUNCT
ejpam-6775	58	14	and	and	CCONJ
ejpam-6775	58	15	environmental	environmental	ADJ
ejpam-6775	58	16	factors	factor	NOUN
ejpam-6775	58	17	.	.	PUNCT
ejpam-6775	59	1	climate	climate	NOUN
ejpam-6775	59	2	change	change	NOUN
ejpam-6775	59	3	and	and	CCONJ
ejpam-6775	59	4	urbanization	urbanization	NOUN
ejpam-6775	59	5	further	further	ADJ
ejpam-6775	59	6	influence	influence	NOUN
ejpam-6775	59	7	disease	disease	NOUN
ejpam-6775	59	8	spread	spread	VERB
ejpam-6775	59	9	and	and	CCONJ
ejpam-6775	59	10	outbreak	outbreak	NOUN
ejpam-6775	59	11	severity	severity	NOUN
ejpam-6775	59	12	.	.	PUNCT
ejpam-6775	60	1	these	these	DET
ejpam-6775	60	2	factors	factor	NOUN
ejpam-6775	60	3	impact	impact	VERB
ejpam-6775	60	4	control	control	NOUN
ejpam-6775	60	5	measures	measure	NOUN
ejpam-6775	60	6	,	,	PUNCT
ejpam-6775	60	7	requiring	require	VERB
ejpam-6775	60	8	comprehensive	comprehensive	ADJ
ejpam-6775	60	9	intervention	intervention	NOUN
ejpam-6775	60	10	strategies	strategy	NOUN
ejpam-6775	60	11	[	[	X
ejpam-6775	60	12	37–41	37–41	NUM
ejpam-6775	60	13	]	]	PUNCT
ejpam-6775	60	14	.	.	PUNCT
ejpam-6775	61	1	mathematical	mathematical	ADJ
ejpam-6775	61	2	models	model	NOUN
ejpam-6775	61	3	of	of	ADP
ejpam-6775	61	4	infectious	infectious	ADJ
ejpam-6775	61	5	diseases	disease	NOUN
ejpam-6775	61	6	have	have	AUX
ejpam-6775	61	7	been	be	AUX
ejpam-6775	61	8	extensively	extensively	ADV
ejpam-6775	61	9	studied	study	VERB
ejpam-6775	61	10	,	,	PUNCT
ejpam-6775	61	11	addressing	address	VERB
ejpam-6775	61	12	disease	disease	NOUN
ejpam-6775	61	13	spread	spread	VERB
ejpam-6775	61	14	and	and	CCONJ
ejpam-6775	61	15	control	control	NOUN
ejpam-6775	61	16	.	.	PUNCT
ejpam-6775	62	1	the	the	DET
ejpam-6775	62	2	rapid	rapid	ADJ
ejpam-6775	62	3	spread	spread	NOUN
ejpam-6775	62	4	of	of	ADP
ejpam-6775	62	5	covid-19	covid-19	PROPN
ejpam-6775	62	6	in	in	ADP
ejpam-6775	62	7	2020	2020	NUM
ejpam-6775	62	8	highlighted	highlight	VERB
ejpam-6775	62	9	the	the	DET
ejpam-6775	62	10	importance	importance	NOUN
ejpam-6775	62	11	of	of	ADP
ejpam-6775	62	12	research	research	NOUN
ejpam-6775	62	13	in	in	ADP
ejpam-6775	62	14	this	this	DET
ejpam-6775	62	15	field	field	NOUN
ejpam-6775	62	16	.	.	PUNCT
ejpam-6775	63	1	among	among	ADP
ejpam-6775	63	2	various	various	ADJ
ejpam-6775	63	3	models	model	NOUN
ejpam-6775	63	4	,	,	PUNCT
ejpam-6775	63	5	the	the	DET
ejpam-6775	63	6	sir	sir	NOUN
ejpam-6775	63	7	model	model	NOUN
ejpam-6775	63	8	remains	remain	VERB
ejpam-6775	63	9	widely	widely	ADV
ejpam-6775	63	10	studied	study	VERB
ejpam-6775	63	11	,	,	PUNCT
ejpam-6775	63	12	with	with	ADP
ejpam-6775	63	13	research	research	NOUN
ejpam-6775	63	14	exploring	explore	VERB
ejpam-6775	63	15	its	its	PRON
ejpam-6775	63	16	nonlinear	nonlinear	ADJ
ejpam-6775	63	17	dynamics	dynamic	NOUN
ejpam-6775	63	18	,	,	PUNCT
ejpam-6775	63	19	discretization	discretization	NOUN
ejpam-6775	63	20	effects	effect	NOUN
ejpam-6775	63	21	,	,	PUNCT
ejpam-6775	63	22	and	and	CCONJ
ejpam-6775	63	23	applications	application	NOUN
ejpam-6775	63	24	to	to	ADP
ejpam-6775	63	25	hiv	hiv	PROPN
ejpam-6775	63	26	and	and	CCONJ
ejpam-6775	63	27	variable	variable	ADJ
ejpam-6775	63	28	populations	population	NOUN
ejpam-6775	63	29	.	.	PUNCT
ejpam-6775	64	1	optimal	optimal	ADJ
ejpam-6775	64	2	control	control	NOUN
ejpam-6775	64	3	strategies	strategy	NOUN
ejpam-6775	64	4	have	have	AUX
ejpam-6775	64	5	been	be	AUX
ejpam-6775	64	6	analyzed	analyze	VERB
ejpam-6775	64	7	to	to	PART
ejpam-6775	64	8	enhance	enhance	VERB
ejpam-6775	64	9	intervention	intervention	NOUN
ejpam-6775	64	10	measures	measure	NOUN
ejpam-6775	64	11	.	.	PUNCT
ejpam-6775	65	1	these	these	DET
ejpam-6775	65	2	studies	study	NOUN
ejpam-6775	65	3	contribute	contribute	VERB
ejpam-6775	65	4	to	to	ADP
ejpam-6775	65	5	improving	improve	VERB
ejpam-6775	65	6	disease	disease	NOUN
ejpam-6775	65	7	modeling	modeling	NOUN
ejpam-6775	65	8	and	and	CCONJ
ejpam-6775	65	9	informing	inform	VERB
ejpam-6775	65	10	public	public	ADJ
ejpam-6775	65	11	health	health	NOUN
ejpam-6775	65	12	policies	policy	NOUN
ejpam-6775	65	13	[	[	X
ejpam-6775	65	14	42–53	42–53	NOUN
ejpam-6775	65	15	]	]	X
ejpam-6775	65	16	.	.	PUNCT
ejpam-6775	66	1	biologically	biologically	ADV
ejpam-6775	66	2	,	,	PUNCT
ejpam-6775	66	3	this	this	DET
ejpam-6775	66	4	model	model	NOUN
ejpam-6775	66	5	captures	capture	VERB
ejpam-6775	66	6	the	the	DET
ejpam-6775	66	7	real	real	ADJ
ejpam-6775	66	8	-	-	PUNCT
ejpam-6775	66	9	world	world	NOUN
ejpam-6775	66	10	dynamics	dynamic	NOUN
ejpam-6775	66	11	of	of	ADP
ejpam-6775	66	12	diseases	disease	NOUN
ejpam-6775	66	13	like	like	ADP
ejpam-6775	66	14	bovine	bovine	NOUN
ejpam-6775	66	15	tuberculosis	tuberculosis	NOUN
ejpam-6775	66	16	(	(	PUNCT
ejpam-6775	66	17	btb	btb	NOUN
ejpam-6775	66	18	)	)	PUNCT
ejpam-6775	66	19	in	in	ADP
ejpam-6775	66	20	wildlife	wildlife	NOUN
ejpam-6775	66	21	populations	population	NOUN
ejpam-6775	66	22	,	,	PUNCT
ejpam-6775	66	23	where	where	SCONJ
ejpam-6775	66	24	infection	infection	NOUN
ejpam-6775	66	25	age	age	NOUN
ejpam-6775	66	26	influences	influence	VERB
ejpam-6775	66	27	transmission	transmission	NOUN
ejpam-6775	66	28	and	and	CCONJ
ejpam-6775	66	29	mortality	mortality	NOUN
ejpam-6775	66	30	.	.	PUNCT
ejpam-6775	67	1	susceptible	susceptible	ADJ
ejpam-6775	67	2	individuals	individual	NOUN
ejpam-6775	67	3	can	can	AUX
ejpam-6775	67	4	be	be	AUX
ejpam-6775	67	5	vaccinated	vaccinate	VERB
ejpam-6775	67	6	imperfectly	imperfectly	ADV
ejpam-6775	67	7	,	,	PUNCT
ejpam-6775	67	8	reducing	reduce	VERB
ejpam-6775	67	9	but	but	CCONJ
ejpam-6775	67	10	not	not	PART
ejpam-6775	67	11	eliminating	eliminate	VERB
ejpam-6775	67	12	infection	infection	NOUN
ejpam-6775	67	13	risk	risk	NOUN
ejpam-6775	67	14	,	,	PUNCT
ejpam-6775	67	15	while	while	SCONJ
ejpam-6775	67	16	infected	infected	ADJ
ejpam-6775	67	17	individuals	individual	NOUN
ejpam-6775	67	18	progress	progress	VERB
ejpam-6775	67	19	through	through	ADP
ejpam-6775	67	20	ages	age	NOUN
ejpam-6775	67	21	with	with	ADP
ejpam-6775	67	22	varying	vary	VERB
ejpam-6775	67	23	infectivity	infectivity	NOUN
ejpam-6775	67	24	and	and	CCONJ
ejpam-6775	67	25	treatment	treatment	NOUN
ejpam-6775	67	26	responses	response	NOUN
ejpam-6775	67	27	.	.	PUNCT
ejpam-6775	68	1	the	the	DET
ejpam-6775	68	2	backward	backward	ADJ
ejpam-6775	68	3	bifurcation	bifurcation	NOUN
ejpam-6775	68	4	implies	imply	VERB
ejpam-6775	68	5	that	that	SCONJ
ejpam-6775	68	6	even	even	ADV
ejpam-6775	68	7	with	with	ADP
ejpam-6775	68	8	low	low	ADJ
ejpam-6775	68	9	transmission	transmission	NOUN
ejpam-6775	68	10	(	(	PUNCT
ejpam-6775	68	11	low	low	ADJ
ejpam-6775	68	12	r0	r0	NOUN
ejpam-6775	68	13	)	)	PUNCT
ejpam-6775	68	14	,	,	PUNCT
ejpam-6775	68	15	small	small	ADJ
ejpam-6775	68	16	perturbations	perturbation	NOUN
ejpam-6775	68	17	(	(	PUNCT
ejpam-6775	68	18	e.g.	e.g.	ADV
ejpam-6775	68	19	,	,	PUNCT
ejpam-6775	68	20	due	due	ADP
ejpam-6775	68	21	to	to	ADP
ejpam-6775	68	22	environmental	environmental	ADJ
ejpam-6775	68	23	stress	stress	NOUN
ejpam-6775	68	24	)	)	PUNCT
ejpam-6775	68	25	can	can	AUX
ejpam-6775	68	26	lead	lead	VERB
ejpam-6775	68	27	to	to	ADP
ejpam-6775	68	28	endemic	endemic	ADJ
ejpam-6775	68	29	states	state	NOUN
ejpam-6775	68	30	,	,	PUNCT
ejpam-6775	68	31	explaining	explain	VERB
ejpam-6775	68	32	persistent	persistent	ADJ
ejpam-6775	68	33	outbreaks	outbreak	NOUN
ejpam-6775	68	34	in	in	ADP
ejpam-6775	68	35	herds	herd	NOUN
ejpam-6775	68	36	.	.	PUNCT
ejpam-6775	69	1	optimal	optimal	ADJ
ejpam-6775	69	2	controls	control	NOUN
ejpam-6775	69	3	simulate	simulate	VERB
ejpam-6775	69	4	public	public	ADJ
ejpam-6775	69	5	health	health	NOUN
ejpam-6775	69	6	interventions	intervention	NOUN
ejpam-6775	69	7	,	,	PUNCT
ejpam-6775	69	8	balancing	balance	VERB
ejpam-6775	69	9	vaccination	vaccination	NOUN
ejpam-6775	69	10	campaigns	campaign	NOUN
ejpam-6775	69	11	and	and	CCONJ
ejpam-6775	69	12	age	age	NOUN
ejpam-6775	69	13	-	-	PUNCT
ejpam-6775	69	14	targeted	target	VERB
ejpam-6775	69	15	treatments	treatment	NOUN
ejpam-6775	69	16	to	to	PART
ejpam-6775	69	17	minimize	minimize	VERB
ejpam-6775	69	18	ecological	ecological	ADJ
ejpam-6775	69	19	and	and	CCONJ
ejpam-6775	69	20	economic	economic	ADJ
ejpam-6775	69	21	impacts	impact	NOUN
ejpam-6775	69	22	[	[	X
ejpam-6775	69	23	1	1	NUM
ejpam-6775	69	24	,	,	PUNCT
ejpam-6775	69	25	2	2	NUM
ejpam-6775	69	26	]	]	PUNCT
ejpam-6775	69	27	.	.	PUNCT
ejpam-6775	70	1	despite	despite	SCONJ
ejpam-6775	70	2	advances	advance	NOUN
ejpam-6775	70	3	in	in	ADP
ejpam-6775	70	4	epidemic	epidemic	NOUN
ejpam-6775	70	5	modeling	modeling	NOUN
ejpam-6775	70	6	,	,	PUNCT
ejpam-6775	70	7	a	a	DET
ejpam-6775	70	8	key	key	ADJ
ejpam-6775	70	9	research	research	NOUN
ejpam-6775	70	10	gap	gap	NOUN
ejpam-6775	70	11	exists	exist	VERB
ejpam-6775	70	12	in	in	ADP
ejpam-6775	70	13	integrating	integrate	VERB
ejpam-6775	70	14	agestructured	agestructure	VERB
ejpam-6775	70	15	dynamics	dynamic	NOUN
ejpam-6775	70	16	with	with	ADP
ejpam-6775	70	17	imperfect	imperfect	ADJ
ejpam-6775	70	18	vaccination	vaccination	NOUN
ejpam-6775	70	19	and	and	CCONJ
ejpam-6775	70	20	saturated	saturated	ADJ
ejpam-6775	70	21	treatment	treatment	NOUN
ejpam-6775	70	22	,	,	PUNCT
ejpam-6775	70	23	particularly	particularly	ADV
ejpam-6775	70	24	j.	j.	PROPN
ejpam-6775	70	25	leo	leo	PROPN
ejpam-6775	71	1	amalraj	amalraj	PROPN
ejpam-6775	71	2	et	et	PROPN
ejpam-6775	71	3	al	al	PROPN
ejpam-6775	71	4	.	.	PUNCT
ejpam-6775	71	5	/	/	SYM
ejpam-6775	71	6	eur	eur	PROPN
ejpam-6775	71	7	.	.	PUNCT
ejpam-6775	72	1	j.	j.	PROPN
ejpam-6775	72	2	pure	pure	PROPN
ejpam-6775	72	3	appl	appl	PROPN
ejpam-6775	72	4	.	.	PROPN
ejpam-6775	72	5	math	math	PROPN
ejpam-6775	72	6	,	,	PUNCT
ejpam-6775	72	7	18	18	NUM
ejpam-6775	72	8	(	(	PUNCT
ejpam-6775	72	9	4	4	NUM
ejpam-6775	72	10	)	)	PUNCT
ejpam-6775	72	11	(	(	PUNCT
ejpam-6775	72	12	2025	2025	NUM
ejpam-6775	72	13	)	)	PUNCT
ejpam-6775	72	14	,	,	PUNCT
ejpam-6775	72	15	6775	6775	NUM
ejpam-6775	72	16	4	4	NUM
ejpam-6775	72	17	of	of	ADP
ejpam-6775	72	18	32	32	NUM
ejpam-6775	72	19	for	for	ADP
ejpam-6775	72	20	diseases	disease	NOUN
ejpam-6775	72	21	exhibiting	exhibit	VERB
ejpam-6775	72	22	backward	backward	ADJ
ejpam-6775	72	23	bifurcation	bifurcation	NOUN
ejpam-6775	72	24	like	like	ADP
ejpam-6775	72	25	btb	btb	NOUN
ejpam-6775	72	26	.	.	PUNCT
ejpam-6775	73	1	this	this	DET
ejpam-6775	73	2	gap	gap	NOUN
ejpam-6775	73	3	motivates	motivate	VERB
ejpam-6775	73	4	our	our	PRON
ejpam-6775	73	5	study	study	NOUN
ejpam-6775	73	6	,	,	PUNCT
ejpam-6775	73	7	as	as	SCONJ
ejpam-6775	73	8	traditional	traditional	ADJ
ejpam-6775	73	9	models	model	NOUN
ejpam-6775	73	10	overlook	overlook	VERB
ejpam-6775	73	11	bistability	bistability	NOUN
ejpam-6775	73	12	under	under	ADP
ejpam-6775	73	13	r0	r0	NOUN
ejpam-6775	73	14	<	<	X
ejpam-6775	73	15	1	1	NUM
ejpam-6775	73	16	,	,	PUNCT
ejpam-6775	73	17	leading	lead	VERB
ejpam-6775	73	18	to	to	ADP
ejpam-6775	73	19	suboptimal	suboptimal	ADJ
ejpam-6775	73	20	control	control	NOUN
ejpam-6775	73	21	strategies	strategy	NOUN
ejpam-6775	73	22	in	in	ADP
ejpam-6775	73	23	resource	resource	NOUN
ejpam-6775	73	24	-	-	PUNCT
ejpam-6775	73	25	limited	limit	VERB
ejpam-6775	73	26	settings	setting	NOUN
ejpam-6775	73	27	[	[	X
ejpam-6775	73	28	10–12	10–12	NUM
ejpam-6775	73	29	]	]	PUNCT
ejpam-6775	73	30	.	.	PUNCT
ejpam-6775	74	1	this	this	DET
ejpam-6775	74	2	paper	paper	NOUN
ejpam-6775	74	3	investigates	investigate	VERB
ejpam-6775	74	4	the	the	DET
ejpam-6775	74	5	dynamics	dynamic	NOUN
ejpam-6775	74	6	and	and	CCONJ
ejpam-6775	74	7	control	control	NOUN
ejpam-6775	74	8	of	of	ADP
ejpam-6775	74	9	infectious	infectious	ADJ
ejpam-6775	74	10	diseases	disease	NOUN
ejpam-6775	74	11	through	through	ADP
ejpam-6775	74	12	an	an	DET
ejpam-6775	74	13	age	age	NOUN
ejpam-6775	74	14	-	-	PUNCT
ejpam-6775	74	15	structured	structure	VERB
ejpam-6775	74	16	susceptible	susceptible	ADJ
ejpam-6775	74	17	-	-	PUNCT
ejpam-6775	74	18	vaccinated	vaccinated	ADJ
ejpam-6775	74	19	-	-	PUNCT
ejpam-6775	74	20	infected	infect	VERB
ejpam-6775	74	21	(	(	PUNCT
ejpam-6775	74	22	svi	svi	ADJ
ejpam-6775	74	23	)	)	PUNCT
ejpam-6775	74	24	model	model	NOUN
ejpam-6775	74	25	,	,	PUNCT
ejpam-6775	74	26	motivated	motivate	VERB
ejpam-6775	74	27	by	by	ADP
ejpam-6775	74	28	the	the	DET
ejpam-6775	74	29	need	need	NOUN
ejpam-6775	74	30	to	to	PART
ejpam-6775	74	31	understand	understand	VERB
ejpam-6775	74	32	complex	complex	ADJ
ejpam-6775	74	33	epidemic	epidemic	NOUN
ejpam-6775	74	34	behaviors	behavior	NOUN
ejpam-6775	74	35	,	,	PUNCT
ejpam-6775	74	36	such	such	ADJ
ejpam-6775	74	37	as	as	ADP
ejpam-6775	74	38	backward	backward	ADJ
ejpam-6775	74	39	bifurcation	bifurcation	NOUN
ejpam-6775	74	40	,	,	PUNCT
ejpam-6775	74	41	and	and	CCONJ
ejpam-6775	74	42	to	to	PART
ejpam-6775	74	43	design	design	VERB
ejpam-6775	74	44	effective	effective	ADJ
ejpam-6775	74	45	intervention	intervention	NOUN
ejpam-6775	74	46	strategies	strategy	NOUN
ejpam-6775	74	47	for	for	ADP
ejpam-6775	74	48	diseases	disease	NOUN
ejpam-6775	74	49	like	like	ADP
ejpam-6775	74	50	bovine	bovine	NOUN
ejpam-6775	74	51	tuberculosis	tuberculosis	NOUN
ejpam-6775	74	52	,	,	PUNCT
ejpam-6775	74	53	which	which	PRON
ejpam-6775	74	54	pose	pose	VERB
ejpam-6775	74	55	significant	significant	ADJ
ejpam-6775	74	56	threats	threat	NOUN
ejpam-6775	74	57	to	to	ADP
ejpam-6775	74	58	wildlife	wildlife	NOUN
ejpam-6775	74	59	and	and	CCONJ
ejpam-6775	74	60	livestock	livestock	NOUN
ejpam-6775	74	61	.	.	PUNCT
ejpam-6775	75	1	structured	structure	VERB
ejpam-6775	75	2	into	into	ADP
ejpam-6775	75	3	six	six	NUM
ejpam-6775	75	4	key	key	ADJ
ejpam-6775	75	5	sections	section	NOUN
ejpam-6775	75	6	,	,	PUNCT
ejpam-6775	75	7	it	it	PRON
ejpam-6775	75	8	begins	begin	VERB
ejpam-6775	75	9	with	with	ADP
ejpam-6775	75	10	an	an	DET
ejpam-6775	75	11	introduction	introduction	NOUN
ejpam-6775	75	12	to	to	ADP
ejpam-6775	75	13	epidemic	epidemic	NOUN
ejpam-6775	75	14	modeling	modeling	NOUN
ejpam-6775	75	15	and	and	CCONJ
ejpam-6775	75	16	the	the	DET
ejpam-6775	75	17	challenges	challenge	NOUN
ejpam-6775	75	18	of	of	ADP
ejpam-6775	75	19	disease	disease	NOUN
ejpam-6775	75	20	persistence	persistence	NOUN
ejpam-6775	75	21	,	,	PUNCT
ejpam-6775	75	22	followed	follow	VERB
ejpam-6775	75	23	by	by	ADP
ejpam-6775	75	24	preliminary	preliminary	ADJ
ejpam-6775	75	25	mathematical	mathematical	ADJ
ejpam-6775	75	26	results	result	NOUN
ejpam-6775	75	27	on	on	ADP
ejpam-6775	75	28	bifurcation	bifurcation	NOUN
ejpam-6775	75	29	detection	detection	NOUN
ejpam-6775	75	30	.	.	PUNCT
ejpam-6775	76	1	the	the	DET
ejpam-6775	76	2	core	core	NOUN
ejpam-6775	76	3	analysis	analysis	NOUN
ejpam-6775	76	4	establishes	establish	VERB
ejpam-6775	76	5	the	the	DET
ejpam-6775	76	6	model	model	NOUN
ejpam-6775	76	7	’s	’s	PART
ejpam-6775	76	8	well	well	NOUN
ejpam-6775	76	9	-	-	PUNCT
ejpam-6775	76	10	posedness	posedness	NOUN
ejpam-6775	76	11	,	,	PUNCT
ejpam-6775	76	12	equilibria	equilibrium	NOUN
ejpam-6775	76	13	,	,	PUNCT
ejpam-6775	76	14	and	and	CCONJ
ejpam-6775	76	15	bistability	bistability	NOUN
ejpam-6775	76	16	conditions	condition	NOUN
ejpam-6775	76	17	,	,	PUNCT
ejpam-6775	76	18	revealing	reveal	VERB
ejpam-6775	76	19	how	how	SCONJ
ejpam-6775	76	20	treatment	treatment	NOUN
ejpam-6775	76	21	rates	rate	NOUN
ejpam-6775	76	22	drive	drive	VERB
ejpam-6775	76	23	backward	backward	ADJ
ejpam-6775	76	24	bifurcation	bifurcation	NOUN
ejpam-6775	76	25	,	,	PUNCT
ejpam-6775	76	26	complicating	complicate	VERB
ejpam-6775	76	27	eradication	eradication	NOUN
ejpam-6775	76	28	when	when	SCONJ
ejpam-6775	76	29	r0	r0	NOUN
ejpam-6775	76	30	<	<	X
ejpam-6775	76	31	1	1	NUM
ejpam-6775	76	32	.	.	PUNCT
ejpam-6775	77	1	an	an	DET
ejpam-6775	77	2	optimal	optimal	ADJ
ejpam-6775	77	3	control	control	NOUN
ejpam-6775	77	4	framework	framework	NOUN
ejpam-6775	77	5	is	be	AUX
ejpam-6775	77	6	then	then	ADV
ejpam-6775	77	7	developed	develop	VERB
ejpam-6775	77	8	,	,	PUNCT
ejpam-6775	77	9	formulating	formulate	VERB
ejpam-6775	77	10	time	time	NOUN
ejpam-6775	77	11	-	-	PUNCT
ejpam-6775	77	12	dependent	dependent	ADJ
ejpam-6775	77	13	vaccination	vaccination	NOUN
ejpam-6775	77	14	and	and	CCONJ
ejpam-6775	77	15	treatment	treatment	NOUN
ejpam-6775	77	16	strategies	strategy	NOUN
ejpam-6775	77	17	to	to	PART
ejpam-6775	77	18	minimize	minimize	VERB
ejpam-6775	77	19	infections	infection	NOUN
ejpam-6775	77	20	and	and	CCONJ
ejpam-6775	77	21	costs	cost	NOUN
ejpam-6775	77	22	,	,	PUNCT
ejpam-6775	77	23	with	with	ADP
ejpam-6775	77	24	first	first	ADJ
ejpam-6775	77	25	-	-	PUNCT
ejpam-6775	77	26	order	order	NOUN
ejpam-6775	77	27	optimality	optimality	NOUN
ejpam-6775	77	28	conditions	condition	NOUN
ejpam-6775	77	29	derived	derive	VERB
ejpam-6775	77	30	.	.	PUNCT
ejpam-6775	78	1	numerical	numerical	ADJ
ejpam-6775	78	2	simulations	simulation	NOUN
ejpam-6775	78	3	illustrate	illustrate	VERB
ejpam-6775	78	4	the	the	DET
ejpam-6775	78	5	efficacy	efficacy	NOUN
ejpam-6775	78	6	of	of	ADP
ejpam-6775	78	7	these	these	DET
ejpam-6775	78	8	controls	control	NOUN
ejpam-6775	78	9	,	,	PUNCT
ejpam-6775	78	10	emphasizing	emphasize	VERB
ejpam-6775	78	11	early	early	ADJ
ejpam-6775	78	12	intervention	intervention	NOUN
ejpam-6775	78	13	.	.	PUNCT
ejpam-6775	79	1	the	the	DET
ejpam-6775	79	2	conclusion	conclusion	NOUN
ejpam-6775	79	3	synthesizes	synthesize	VERB
ejpam-6775	79	4	findings	finding	NOUN
ejpam-6775	79	5	,	,	PUNCT
ejpam-6775	79	6	underscoring	underscore	VERB
ejpam-6775	79	7	their	their	PRON
ejpam-6775	79	8	implications	implication	NOUN
ejpam-6775	79	9	for	for	ADP
ejpam-6775	79	10	public	public	ADJ
ejpam-6775	79	11	health	health	NOUN
ejpam-6775	79	12	policy	policy	NOUN
ejpam-6775	79	13	and	and	CCONJ
ejpam-6775	79	14	future	future	ADJ
ejpam-6775	79	15	research	research	NOUN
ejpam-6775	79	16	into	into	ADP
ejpam-6775	79	17	epidemic	epidemic	NOUN
ejpam-6775	79	18	control	control	NOUN
ejpam-6775	80	1	[	[	X
ejpam-6775	80	2	54–56	54–56	NUM
ejpam-6775	80	3	]	]	PUNCT
ejpam-6775	80	4	.	.	PUNCT
ejpam-6775	81	1	table	table	NOUN
ejpam-6775	81	2	of	of	ADP
ejpam-6775	81	3	abbreviations	abbreviation	NOUN
ejpam-6775	81	4	btb	btb	NOUN
ejpam-6775	81	5	bovine	bovine	NOUN
ejpam-6775	81	6	tuberculosis	tuberculosis	PRON
ejpam-6775	81	7	ocp	ocp	PROPN
ejpam-6775	81	8	optimal	optimal	ADJ
ejpam-6775	81	9	control	control	PROPN
ejpam-6775	81	10	problem	problem	NOUN
ejpam-6775	81	11	hiv	hiv	PROPN
ejpam-6775	81	12	human	human	ADJ
ejpam-6775	81	13	immunodeficiency	immunodeficiency	NOUN
ejpam-6775	81	14	virus	virus	NOUN
ejpam-6775	81	15	siqr	siqr	ADJ
ejpam-6775	81	16	susceptible	susceptible	ADJ
ejpam-6775	81	17	-	-	PUNCT
ejpam-6775	81	18	infected	infect	VERB
ejpam-6775	81	19	-	-	PUNCT
ejpam-6775	81	20	quarantined	quarantine	VERB
ejpam-6775	81	21	-	-	PUNCT
ejpam-6775	81	22	recovered	recover	VERB
ejpam-6775	81	23	nsfd	nsfd	ADJ
ejpam-6775	81	24	non	non	ADJ
ejpam-6775	81	25	-	-	ADJ
ejpam-6775	81	26	standard	standard	ADJ
ejpam-6775	81	27	finite	finite	ADJ
ejpam-6775	81	28	difference	difference	NOUN
ejpam-6775	81	29	sir	sir	NOUN
ejpam-6775	81	30	susceptible	susceptible	ADJ
ejpam-6775	81	31	-	-	PUNCT
ejpam-6775	81	32	infected	infect	VERB
ejpam-6775	81	33	-	-	PUNCT
ejpam-6775	81	34	recovered	recover	VERB
ejpam-6775	81	35	svi	svi	X
ejpam-6775	81	36	susceptible	susceptible	ADJ
ejpam-6775	81	37	-	-	PUNCT
ejpam-6775	81	38	vaccinated	vaccinated	ADJ
ejpam-6775	81	39	-	-	PUNCT
ejpam-6775	81	40	infected	infect	VERB
ejpam-6775	81	41	list	list	NOUN
ejpam-6775	81	42	of	of	ADP
ejpam-6775	81	43	symbols	symbol	NOUN
ejpam-6775	81	44	and	and	CCONJ
ejpam-6775	81	45	notations	notation	NOUN
ejpam-6775	81	46	s(t	s(t	PROPN
ejpam-6775	81	47	)	)	PUNCT
ejpam-6775	81	48	susceptible	susceptible	ADJ
ejpam-6775	81	49	population	population	NOUN
ejpam-6775	81	50	at	at	ADP
ejpam-6775	81	51	time	time	NOUN
ejpam-6775	81	52	t	t	PROPN
ejpam-6775	81	53	v	v	PROPN
ejpam-6775	81	54	(	(	PUNCT
ejpam-6775	81	55	t	t	NOUN
ejpam-6775	81	56	)	)	PUNCT
ejpam-6775	81	57	vaccinated	vaccinated	ADJ
ejpam-6775	81	58	population	population	NOUN
ejpam-6775	81	59	at	at	ADP
ejpam-6775	81	60	time	time	NOUN
ejpam-6775	81	61	t	t	PROPN
ejpam-6775	81	62	i(t	i(t	PROPN
ejpam-6775	81	63	,	,	PUNCT
ejpam-6775	81	64	x	x	NOUN
ejpam-6775	81	65	)	)	PUNCT
ejpam-6775	81	66	infected	infected	ADJ
ejpam-6775	81	67	density	density	NOUN
ejpam-6775	81	68	at	at	ADP
ejpam-6775	81	69	time	time	NOUN
ejpam-6775	81	70	t	t	NOUN
ejpam-6775	81	71	and	and	CCONJ
ejpam-6775	81	72	infection	infection	NOUN
ejpam-6775	81	73	age	age	NOUN
ejpam-6775	81	74	x	x	PUNCT
ejpam-6775	81	75	λ	λ	NOUN
ejpam-6775	81	76	recruitment	recruitment	NOUN
ejpam-6775	81	77	rate	rate	NOUN
ejpam-6775	81	78	µ	µ	PRON
ejpam-6775	81	79	natural	natural	ADJ
ejpam-6775	81	80	death	death	NOUN
ejpam-6775	81	81	rate	rate	NOUN
ejpam-6775	81	82	ξ(t	ξ(t	NOUN
ejpam-6775	81	83	)	)	PUNCT
ejpam-6775	81	84	vaccination	vaccination	NOUN
ejpam-6775	81	85	rate	rate	NOUN
ejpam-6775	81	86	m	m	PROPN
ejpam-6775	81	87	vaccine	vaccine	NOUN
ejpam-6775	81	88	efficacy	efficacy	NOUN
ejpam-6775	81	89	reduction	reduction	NOUN
ejpam-6775	81	90	factor	factor	NOUN
ejpam-6775	81	91	β(x	β(x	NOUN
ejpam-6775	81	92	)	)	PUNCT
ejpam-6775	81	93	age	age	NOUN
ejpam-6775	81	94	-	-	PUNCT
ejpam-6775	81	95	dependent	dependent	ADJ
ejpam-6775	81	96	infection	infection	NOUN
ejpam-6775	81	97	rate	rate	NOUN
ejpam-6775	81	98	δ(x	δ(x	ADJ
ejpam-6775	81	99	)	)	PUNCT
ejpam-6775	81	100	age	age	NOUN
ejpam-6775	81	101	-	-	PUNCT
ejpam-6775	81	102	dependent	dependent	ADJ
ejpam-6775	81	103	disease	disease	NOUN
ejpam-6775	81	104	-	-	PUNCT
ejpam-6775	81	105	induced	induce	VERB
ejpam-6775	81	106	death	death	NOUN
ejpam-6775	81	107	rate	rate	NOUN
ejpam-6775	81	108	α(t	α(t	PROPN
ejpam-6775	81	109	,	,	PUNCT
ejpam-6775	81	110	x	x	NOUN
ejpam-6775	81	111	)	)	PUNCT
ejpam-6775	81	112	age	age	NOUN
ejpam-6775	81	113	-	-	PUNCT
ejpam-6775	81	114	dependent	dependent	ADJ
ejpam-6775	81	115	treatment	treatment	NOUN
ejpam-6775	81	116	rate	rate	NOUN
ejpam-6775	81	117	r0	r0	NOUN
ejpam-6775	81	118	basic	basic	ADJ
ejpam-6775	81	119	reproduction	reproduction	NOUN
ejpam-6775	81	120	number	number	NOUN
ejpam-6775	81	121	j.	j.	PROPN
ejpam-6775	81	122	leo	leo	PROPN
ejpam-6775	82	1	amalraj	amalraj	PROPN
ejpam-6775	82	2	et	et	PROPN
ejpam-6775	82	3	al	al	PROPN
ejpam-6775	82	4	.	.	PUNCT
ejpam-6775	82	5	/	/	SYM
ejpam-6775	82	6	eur	eur	PROPN
ejpam-6775	82	7	.	.	PUNCT
ejpam-6775	83	1	j.	j.	PROPN
ejpam-6775	83	2	pure	pure	PROPN
ejpam-6775	83	3	appl	appl	PROPN
ejpam-6775	83	4	.	.	PROPN
ejpam-6775	83	5	math	math	PROPN
ejpam-6775	83	6	,	,	PUNCT
ejpam-6775	83	7	18	18	NUM
ejpam-6775	83	8	(	(	PUNCT
ejpam-6775	83	9	4	4	NUM
ejpam-6775	83	10	)	)	PUNCT
ejpam-6775	83	11	(	(	PUNCT
ejpam-6775	83	12	2025	2025	NUM
ejpam-6775	83	13	)	)	PUNCT
ejpam-6775	83	14	,	,	PUNCT
ejpam-6775	83	15	6775	6775	NUM
ejpam-6775	83	16	5	5	NUM
ejpam-6775	83	17	of	of	ADP
ejpam-6775	83	18	32	32	NUM
ejpam-6775	83	19	2	2	NUM
ejpam-6775	83	20	.	.	PUNCT
ejpam-6775	83	21	model	model	NOUN
ejpam-6775	83	22	formulation	formulation	NOUN
ejpam-6775	83	23	we	we	PRON
ejpam-6775	83	24	formulate	formulate	VERB
ejpam-6775	83	25	an	an	DET
ejpam-6775	83	26	age	age	NOUN
ejpam-6775	83	27	-	-	PUNCT
ejpam-6775	83	28	structured	structure	VERB
ejpam-6775	83	29	susceptible	susceptible	ADJ
ejpam-6775	83	30	-	-	PUNCT
ejpam-6775	83	31	vaccinated	vaccinated	ADJ
ejpam-6775	83	32	-	-	PUNCT
ejpam-6775	83	33	infected	infect	VERB
ejpam-6775	83	34	(	(	PUNCT
ejpam-6775	83	35	svi	svi	ADJ
ejpam-6775	83	36	)	)	PUNCT
ejpam-6775	83	37	epidemic	epidemic	NOUN
ejpam-6775	83	38	model	model	NOUN
ejpam-6775	83	39	to	to	PART
ejpam-6775	83	40	describe	describe	VERB
ejpam-6775	83	41	the	the	DET
ejpam-6775	83	42	dynamics	dynamic	NOUN
ejpam-6775	83	43	of	of	ADP
ejpam-6775	83	44	an	an	DET
ejpam-6775	83	45	infectious	infectious	ADJ
ejpam-6775	83	46	disease	disease	NOUN
ejpam-6775	83	47	,	,	PUNCT
ejpam-6775	83	48	such	such	ADJ
ejpam-6775	83	49	as	as	ADP
ejpam-6775	83	50	bovine	bovine	NOUN
ejpam-6775	83	51	tuberculosis	tuberculosis	NOUN
ejpam-6775	83	52	,	,	PUNCT
ejpam-6775	83	53	incorporating	incorporate	VERB
ejpam-6775	83	54	imperfect	imperfect	ADJ
ejpam-6775	83	55	vaccination	vaccination	NOUN
ejpam-6775	83	56	and	and	CCONJ
ejpam-6775	83	57	therapeutic	therapeutic	ADJ
ejpam-6775	83	58	treatment	treatment	NOUN
ejpam-6775	83	59	.	.	PUNCT
ejpam-6775	84	1	the	the	DET
ejpam-6775	84	2	population	population	NOUN
ejpam-6775	84	3	is	be	AUX
ejpam-6775	84	4	divided	divide	VERB
ejpam-6775	84	5	into	into	ADP
ejpam-6775	84	6	susceptible	susceptible	ADJ
ejpam-6775	84	7	individuals	individual	NOUN
ejpam-6775	84	8	s(t	s(t	PROPN
ejpam-6775	84	9	)	)	PUNCT
ejpam-6775	84	10	,	,	PUNCT
ejpam-6775	84	11	vaccinated	vaccinate	VERB
ejpam-6775	84	12	individuals	individual	NOUN
ejpam-6775	84	13	v	v	X
ejpam-6775	84	14	(	(	PUNCT
ejpam-6775	84	15	t	t	PROPN
ejpam-6775	84	16	)	)	PUNCT
ejpam-6775	84	17	,	,	PUNCT
ejpam-6775	84	18	and	and	CCONJ
ejpam-6775	84	19	infected	infect	VERB
ejpam-6775	84	20	individuals	individual	NOUN
ejpam-6775	84	21	i(t	i(t	PROPN
ejpam-6775	84	22	,	,	PUNCT
ejpam-6775	84	23	x	x	NOUN
ejpam-6775	84	24	)	)	PUNCT
ejpam-6775	84	25	where	where	SCONJ
ejpam-6775	84	26	x	x	PRON
ejpam-6775	84	27	denotes	denote	VERB
ejpam-6775	84	28	the	the	DET
ejpam-6775	84	29	infection	infection	NOUN
ejpam-6775	84	30	age	age	NOUN
ejpam-6775	84	31	(	(	PUNCT
ejpam-6775	84	32	time	time	NOUN
ejpam-6775	84	33	since	since	SCONJ
ejpam-6775	84	34	infection	infection	NOUN
ejpam-6775	84	35	)	)	PUNCT
ejpam-6775	84	36	.	.	PUNCT
ejpam-6775	85	1	the	the	DET
ejpam-6775	85	2	model	model	NOUN
ejpam-6775	85	3	accounts	account	VERB
ejpam-6775	85	4	for	for	ADP
ejpam-6775	85	5	agedependent	agedependent	ADJ
ejpam-6775	85	6	infection	infection	NOUN
ejpam-6775	85	7	rates	rate	NOUN
ejpam-6775	85	8	,	,	PUNCT
ejpam-6775	85	9	treatment	treatment	NOUN
ejpam-6775	85	10	,	,	PUNCT
ejpam-6775	85	11	and	and	CCONJ
ejpam-6775	85	12	disease	disease	NOUN
ejpam-6775	85	13	-	-	PUNCT
ejpam-6775	85	14	induced	induce	VERB
ejpam-6775	85	15	mortality	mortality	NOUN
ejpam-6775	85	16	.	.	PUNCT
ejpam-6775	86	1	the	the	DET
ejpam-6775	86	2	system	system	NOUN
ejpam-6775	86	3	is	be	AUX
ejpam-6775	86	4	given	give	VERB
ejpam-6775	86	5	by	by	ADP
ejpam-6775	86	6	:	:	PUNCT
ejpam-6775	86	7	ds(t	ds(t	NUM
ejpam-6775	86	8	)	)	PUNCT
ejpam-6775	86	9	dt	dt	X
ejpam-6775	87	1	=	=	SYM
ejpam-6775	87	2	λ−	λ−	PROPN
ejpam-6775	87	3	µs(t)−	µs(t)−	PROPN
ejpam-6775	87	4	ξ(t)s(t)−	ξ(t)s(t)−	PROPN
ejpam-6775	87	5	s(t	s(t	PROPN
ejpam-6775	87	6	)	)	PUNCT
ejpam-6775	87	7	∫	∫	PROPN
ejpam-6775	88	1	∞	∞	PROPN
ejpam-6775	88	2	0	0	PUNCT
ejpam-6775	88	3	β(x)i(t	β(x)i(t	NOUN
ejpam-6775	88	4	,	,	PUNCT
ejpam-6775	88	5	x	x	X
ejpam-6775	88	6	)	)	PUNCT
ejpam-6775	88	7	dx	dx	PROPN
ejpam-6775	88	8	,	,	PUNCT
ejpam-6775	88	9	(	(	PUNCT
ejpam-6775	88	10	1	1	X
ejpam-6775	88	11	)	)	PUNCT
ejpam-6775	88	12	dv	dv	PROPN
ejpam-6775	88	13	(	(	PUNCT
ejpam-6775	88	14	t	t	PROPN
ejpam-6775	88	15	)	)	PUNCT
ejpam-6775	88	16	dt	dt	NOUN
ejpam-6775	89	1	=	=	SYM
ejpam-6775	89	2	ξ(t)s(t)−	ξ(t)s(t)−	PROPN
ejpam-6775	89	3	µv	µv	NOUN
ejpam-6775	89	4	(	(	PUNCT
ejpam-6775	89	5	t)−mv	t)−mv	X
ejpam-6775	89	6	(	(	PUNCT
ejpam-6775	89	7	t	t	PROPN
ejpam-6775	89	8	)	)	PUNCT
ejpam-6775	89	9	∫	∫	PROPN
ejpam-6775	90	1	∞	∞	PROPN
ejpam-6775	90	2	0	0	PUNCT
ejpam-6775	90	3	β(x)i(t	β(x)i(t	NOUN
ejpam-6775	90	4	,	,	PUNCT
ejpam-6775	90	5	x	x	X
ejpam-6775	90	6	)	)	PUNCT
ejpam-6775	90	7	dx	dx	PROPN
ejpam-6775	90	8	,	,	PUNCT
ejpam-6775	90	9	(	(	PUNCT
ejpam-6775	90	10	2	2	X
ejpam-6775	90	11	)	)	PUNCT
ejpam-6775	90	12	∂i(t	∂i(t	PROPN
ejpam-6775	90	13	,	,	PUNCT
ejpam-6775	90	14	x	x	NOUN
ejpam-6775	90	15	)	)	PUNCT
ejpam-6775	91	1	∂t	∂t	PROPN
ejpam-6775	91	2	+	+	NUM
ejpam-6775	91	3	∂i(t	∂i(t	PROPN
ejpam-6775	91	4	,	,	PUNCT
ejpam-6775	91	5	x	x	NOUN
ejpam-6775	91	6	)	)	PUNCT
ejpam-6775	91	7	∂x	∂x	PROPN
ejpam-6775	91	8	=	=	PUNCT
ejpam-6775	92	1	−(µ+	−(µ+	NUM
ejpam-6775	92	2	δ(x	δ(x	PROPN
ejpam-6775	92	3	)	)	PUNCT
ejpam-6775	92	4	+	+	SYM
ejpam-6775	92	5	α(t	α(t	PROPN
ejpam-6775	92	6	,	,	PUNCT
ejpam-6775	92	7	x))i(t	x))i(t	PROPN
ejpam-6775	92	8	,	,	PUNCT
ejpam-6775	92	9	x	x	NOUN
ejpam-6775	92	10	)	)	PUNCT
ejpam-6775	92	11	,	,	PUNCT
ejpam-6775	92	12	(	(	PUNCT
ejpam-6775	92	13	3	3	X
ejpam-6775	92	14	)	)	PUNCT
ejpam-6775	92	15	i(t	i(t	NOUN
ejpam-6775	92	16	,	,	PUNCT
ejpam-6775	92	17	0	0	NUM
ejpam-6775	92	18	)	)	PUNCT
ejpam-6775	92	19	=	=	SYM
ejpam-6775	92	20	s(t	s(t	PROPN
ejpam-6775	92	21	)	)	PUNCT
ejpam-6775	92	22	∫	∫	PROPN
ejpam-6775	93	1	∞	∞	PROPN
ejpam-6775	93	2	0	0	PUNCT
ejpam-6775	93	3	β(x)i(t	β(x)i(t	NOUN
ejpam-6775	93	4	,	,	PUNCT
ejpam-6775	93	5	x	x	X
ejpam-6775	93	6	)	)	PUNCT
ejpam-6775	93	7	dx+mv	dx+mv	PROPN
ejpam-6775	93	8	(	(	PUNCT
ejpam-6775	93	9	t	t	PROPN
ejpam-6775	93	10	)	)	PUNCT
ejpam-6775	93	11	∫	∫	PROPN
ejpam-6775	94	1	∞	∞	PROPN
ejpam-6775	94	2	0	0	PUNCT
ejpam-6775	94	3	β(x)i(t	β(x)i(t	NOUN
ejpam-6775	94	4	,	,	PUNCT
ejpam-6775	94	5	x	x	X
ejpam-6775	94	6	)	)	PUNCT
ejpam-6775	94	7	dx	dx	PROPN
ejpam-6775	94	8	,	,	PUNCT
ejpam-6775	94	9	(	(	PUNCT
ejpam-6775	94	10	4	4	NUM
ejpam-6775	94	11	)	)	PUNCT
ejpam-6775	94	12	with	with	ADP
ejpam-6775	94	13	initial	initial	ADJ
ejpam-6775	94	14	conditions	condition	NOUN
ejpam-6775	94	15	s(0	s(0	PROPN
ejpam-6775	94	16	)	)	PUNCT
ejpam-6775	94	17	=	=	SYM
ejpam-6775	94	18	s0	s0	PROPN
ejpam-6775	94	19	≥	≥	NUM
ejpam-6775	94	20	0	0	NUM
ejpam-6775	94	21	,	,	PUNCT
ejpam-6775	94	22	v	v	NOUN
ejpam-6775	94	23	(	(	PUNCT
ejpam-6775	94	24	0	0	NUM
ejpam-6775	94	25	)	)	PUNCT
ejpam-6775	94	26	=	=	SYM
ejpam-6775	95	1	v0	v0	NOUN
ejpam-6775	95	2	≥	≥	NOUN
ejpam-6775	95	3	0	0	NUM
ejpam-6775	95	4	,	,	PUNCT
ejpam-6775	95	5	i(0	i(0	PROPN
ejpam-6775	95	6	,	,	PUNCT
ejpam-6775	95	7	x	x	NOUN
ejpam-6775	95	8	)	)	PUNCT
ejpam-6775	95	9	=	=	SYM
ejpam-6775	95	10	i0(x	i0(x	NOUN
ejpam-6775	95	11	)	)	PUNCT
ejpam-6775	95	12	≥	≥	NOUN
ejpam-6775	95	13	0	0	NUM
ejpam-6775	95	14	for	for	ADP
ejpam-6775	95	15	x	x	PROPN
ejpam-6775	95	16	∈	∈	PROPN
ejpam-6775	95	17	[	[	X
ejpam-6775	95	18	0,∞	0,∞	NOUN
ejpam-6775	95	19	)	)	PUNCT
ejpam-6775	95	20	.	.	PUNCT
ejpam-6775	96	1	here	here	ADV
ejpam-6775	96	2	,	,	PUNCT
ejpam-6775	96	3	λ	λ	PROPN
ejpam-6775	96	4	is	be	AUX
ejpam-6775	96	5	the	the	DET
ejpam-6775	96	6	constant	constant	ADJ
ejpam-6775	96	7	recruitment	recruitment	NOUN
ejpam-6775	96	8	rate	rate	NOUN
ejpam-6775	96	9	into	into	ADP
ejpam-6775	96	10	the	the	DET
ejpam-6775	96	11	susceptible	susceptible	ADJ
ejpam-6775	96	12	class	class	NOUN
ejpam-6775	96	13	,	,	PUNCT
ejpam-6775	96	14	µ	µ	X
ejpam-6775	96	15	is	be	AUX
ejpam-6775	96	16	the	the	DET
ejpam-6775	96	17	natural	natural	ADJ
ejpam-6775	96	18	death	death	NOUN
ejpam-6775	96	19	rate	rate	NOUN
ejpam-6775	96	20	,	,	PUNCT
ejpam-6775	96	21	ξ(t	ξ(t	NOUN
ejpam-6775	96	22	)	)	PUNCT
ejpam-6775	96	23	is	be	AUX
ejpam-6775	96	24	the	the	DET
ejpam-6775	96	25	time	time	NOUN
ejpam-6775	96	26	-	-	PUNCT
ejpam-6775	96	27	dependent	dependent	ADJ
ejpam-6775	96	28	vaccination	vaccination	NOUN
ejpam-6775	96	29	rate	rate	NOUN
ejpam-6775	96	30	,	,	PUNCT
ejpam-6775	96	31	m	m	VERB
ejpam-6775	96	32	∈	∈	PROPN
ejpam-6775	96	33	(	(	PUNCT
ejpam-6775	96	34	0	0	NUM
ejpam-6775	96	35	,	,	PUNCT
ejpam-6775	96	36	1	1	NUM
ejpam-6775	96	37	)	)	PUNCT
ejpam-6775	96	38	is	be	AUX
ejpam-6775	96	39	the	the	DET
ejpam-6775	96	40	vaccine	vaccine	NOUN
ejpam-6775	96	41	efficacy	efficacy	NOUN
ejpam-6775	96	42	reduction	reduction	NOUN
ejpam-6775	96	43	factor	factor	NOUN
ejpam-6775	96	44	(	(	PUNCT
ejpam-6775	96	45	imperfect	imperfect	ADJ
ejpam-6775	96	46	vaccination	vaccination	NOUN
ejpam-6775	96	47	)	)	PUNCT
ejpam-6775	96	48	,	,	PUNCT
ejpam-6775	96	49	β(x	β(x	PROPN
ejpam-6775	96	50	)	)	PUNCT
ejpam-6775	96	51	is	be	AUX
ejpam-6775	96	52	the	the	DET
ejpam-6775	96	53	age	age	NOUN
ejpam-6775	96	54	-	-	PUNCT
ejpam-6775	96	55	dependent	dependent	ADJ
ejpam-6775	96	56	infection	infection	NOUN
ejpam-6775	96	57	transmission	transmission	NOUN
ejpam-6775	96	58	rate	rate	NOUN
ejpam-6775	96	59	,	,	PUNCT
ejpam-6775	96	60	δ(x	δ(x	NOUN
ejpam-6775	96	61	)	)	PUNCT
ejpam-6775	96	62	is	be	AUX
ejpam-6775	96	63	the	the	DET
ejpam-6775	96	64	age	age	NOUN
ejpam-6775	96	65	-	-	PUNCT
ejpam-6775	96	66	dependent	dependent	ADJ
ejpam-6775	96	67	disease	disease	NOUN
ejpam-6775	96	68	-	-	PUNCT
ejpam-6775	96	69	induced	induce	VERB
ejpam-6775	96	70	death	death	NOUN
ejpam-6775	96	71	rate	rate	NOUN
ejpam-6775	96	72	,	,	PUNCT
ejpam-6775	96	73	and	and	CCONJ
ejpam-6775	96	74	α(t	α(t	PROPN
ejpam-6775	96	75	,	,	PUNCT
ejpam-6775	96	76	x	x	PRON
ejpam-6775	96	77	)	)	PUNCT
ejpam-6775	96	78	is	be	AUX
ejpam-6775	96	79	the	the	DET
ejpam-6775	96	80	age	age	NOUN
ejpam-6775	96	81	-	-	PUNCT
ejpam-6775	96	82	dependent	dependent	ADJ
ejpam-6775	96	83	treatment	treatment	NOUN
ejpam-6775	96	84	rate	rate	NOUN
ejpam-6775	96	85	.	.	PUNCT
ejpam-6775	97	1	the	the	DET
ejpam-6775	97	2	age	age	NOUN
ejpam-6775	97	3	-	-	PUNCT
ejpam-6775	97	4	structured	structure	VERB
ejpam-6775	97	5	aspect	aspect	NOUN
ejpam-6775	97	6	is	be	AUX
ejpam-6775	97	7	captured	capture	VERB
ejpam-6775	97	8	in	in	ADP
ejpam-6775	97	9	the	the	DET
ejpam-6775	97	10	infected	infected	ADJ
ejpam-6775	97	11	class	class	NOUN
ejpam-6775	97	12	via	via	ADP
ejpam-6775	97	13	the	the	DET
ejpam-6775	97	14	pde	pde	NOUN
ejpam-6775	97	15	(	(	PUNCT
ejpam-6775	97	16	3	3	NUM
ejpam-6775	97	17	)	)	PUNCT
ejpam-6775	97	18	,	,	PUNCT
ejpam-6775	97	19	which	which	PRON
ejpam-6775	97	20	models	model	VERB
ejpam-6775	97	21	the	the	DET
ejpam-6775	97	22	progression	progression	NOUN
ejpam-6775	97	23	of	of	ADP
ejpam-6775	97	24	infection	infection	NOUN
ejpam-6775	97	25	with	with	ADP
ejpam-6775	97	26	age	age	NOUN
ejpam-6775	97	27	x	x	NOUN
ejpam-6775	97	28	,	,	PUNCT
ejpam-6775	97	29	and	and	CCONJ
ejpam-6775	97	30	the	the	DET
ejpam-6775	97	31	boundary	boundary	ADJ
ejpam-6775	97	32	condition	condition	NOUN
ejpam-6775	97	33	(	(	PUNCT
ejpam-6775	97	34	4	4	X
ejpam-6775	97	35	)	)	PUNCT
ejpam-6775	97	36	represents	represent	VERB
ejpam-6775	97	37	new	new	ADJ
ejpam-6775	97	38	infections	infection	NOUN
ejpam-6775	97	39	entering	enter	VERB
ejpam-6775	97	40	at	at	ADP
ejpam-6775	97	41	age	age	NOUN
ejpam-6775	97	42	x	x	PUNCT
ejpam-6775	98	1	=	=	PUNCT
ejpam-6775	98	2	0	0	NUM
ejpam-6775	98	3	.	.	NOUN
ejpam-6775	98	4	3	3	X
ejpam-6775	98	5	.	.	X
ejpam-6775	98	6	preliminary	preliminary	ADJ
ejpam-6775	98	7	mathematical	mathematical	ADJ
ejpam-6775	98	8	framework	framework	NOUN
ejpam-6775	98	9	we	we	PRON
ejpam-6775	98	10	present	present	VERB
ejpam-6775	98	11	in	in	ADP
ejpam-6775	98	12	this	this	DET
ejpam-6775	98	13	prelims	prelim	NOUN
ejpam-6775	98	14	,	,	PUNCT
ejpam-6775	98	15	the	the	DET
ejpam-6775	98	16	recent	recent	ADJ
ejpam-6775	98	17	result	result	NOUN
ejpam-6775	98	18	establish	establish	VERB
ejpam-6775	98	19	by	by	ADP
ejpam-6775	98	20	martcheva	martcheva	PROPN
ejpam-6775	98	21	and	and	CCONJ
ejpam-6775	98	22	inaba	inaba	PROPN
ejpam-6775	99	1	[	[	X
ejpam-6775	99	2	54	54	NUM
ejpam-6775	99	3	]	]	PUNCT
ejpam-6775	99	4	in	in	ADP
ejpam-6775	99	5	order	order	NOUN
ejpam-6775	99	6	to	to	PART
ejpam-6775	99	7	detect	detect	VERB
ejpam-6775	99	8	the	the	DET
ejpam-6775	99	9	presence	presence	NOUN
ejpam-6775	99	10	of	of	ADP
ejpam-6775	99	11	backward	backward	ADJ
ejpam-6775	99	12	and	and	CCONJ
ejpam-6775	99	13	forward	forward	ADJ
ejpam-6775	99	14	bifurcations	bifurcation	NOUN
ejpam-6775	99	15	and	and	CCONJ
ejpam-6775	99	16	driving	drive	VERB
ejpam-6775	99	17	a	a	DET
ejpam-6775	99	18	necessary	necessary	ADJ
ejpam-6775	99	19	and	and	CCONJ
ejpam-6775	99	20	sufficient	sufficient	ADJ
ejpam-6775	99	21	conditions	condition	NOUN
ejpam-6775	99	22	for	for	ADP
ejpam-6775	99	23	its	its	PRON
ejpam-6775	99	24	occurrence	occurrence	NOUN
ejpam-6775	99	25	in	in	ADP
ejpam-6775	99	26	the	the	DET
ejpam-6775	99	27	infinite	infinite	ADJ
ejpam-6775	99	28	dynamical	dynamical	ADJ
ejpam-6775	99	29	system	system	NOUN
ejpam-6775	99	30	.	.	PUNCT
ejpam-6775	100	1	the	the	DET
ejpam-6775	100	2	proof	proof	NOUN
ejpam-6775	100	3	is	be	AUX
ejpam-6775	100	4	provided	provide	VERB
ejpam-6775	100	5	in	in	ADP
ejpam-6775	100	6	[	[	X
ejpam-6775	100	7	54	54	NUM
ejpam-6775	100	8	]	]	PUNCT
ejpam-6775	100	9	;	;	PUNCT
ejpam-6775	100	10	we	we	PRON
ejpam-6775	100	11	adapt	adapt	VERB
ejpam-6775	100	12	it	it	PRON
ejpam-6775	100	13	here	here	ADV
ejpam-6775	100	14	for	for	ADP
ejpam-6775	100	15	our	our	PRON
ejpam-6775	100	16	age	age	NOUN
ejpam-6775	100	17	-	-	PUNCT
ejpam-6775	100	18	structured	structure	VERB
ejpam-6775	100	19	context	context	NOUN
ejpam-6775	100	20	.	.	PUNCT
ejpam-6775	101	1	all	all	DET
ejpam-6775	101	2	subsequent	subsequent	ADJ
ejpam-6775	101	3	theorems	theorem	NOUN
ejpam-6775	101	4	in	in	ADP
ejpam-6775	101	5	sections	section	NOUN
ejpam-6775	101	6	3	3	NUM
ejpam-6775	101	7	and	and	CCONJ
ejpam-6775	101	8	4	4	NUM
ejpam-6775	101	9	are	be	AUX
ejpam-6775	101	10	original	original	ADJ
ejpam-6775	101	11	proofs	proof	NOUN
ejpam-6775	101	12	by	by	ADP
ejpam-6775	101	13	the	the	DET
ejpam-6775	101	14	authors	author	NOUN
ejpam-6775	101	15	,	,	PUNCT
ejpam-6775	101	16	establishing	establish	VERB
ejpam-6775	101	17	well	well	NOUN
ejpam-6775	101	18	-	-	PUNCT
ejpam-6775	101	19	posedness	posedness	NOUN
ejpam-6775	101	20	,	,	PUNCT
ejpam-6775	101	21	equilibria	equilibrium	NOUN
ejpam-6775	101	22	stability	stability	NOUN
ejpam-6775	101	23	,	,	PUNCT
ejpam-6775	101	24	and	and	CCONJ
ejpam-6775	101	25	optimality	optimality	NOUN
ejpam-6775	101	26	conditions	condition	NOUN
ejpam-6775	101	27	specific	specific	ADJ
ejpam-6775	101	28	to	to	ADP
ejpam-6775	101	29	our	our	PRON
ejpam-6775	101	30	svi	svi	PROPN
ejpam-6775	101	31	model	model	NOUN
ejpam-6775	101	32	.	.	PUNCT
ejpam-6775	102	1	theorem	theorem	ADJ
ejpam-6775	102	2	1	1	NUM
ejpam-6775	102	3	(	(	PUNCT
ejpam-6775	102	4	theorem	theorem	VERB
ejpam-6775	102	5	on	on	ADP
ejpam-6775	102	6	bifurcation	bifurcation	NOUN
ejpam-6775	102	7	detection	detection	NOUN
ejpam-6775	102	8	,	,	PUNCT
ejpam-6775	102	9	adapted	adapt	VERB
ejpam-6775	102	10	from	from	ADP
ejpam-6775	102	11	[	[	X
ejpam-6775	102	12	54	54	NUM
ejpam-6775	102	13	]	]	PUNCT
ejpam-6775	102	14	)	)	PUNCT
ejpam-6775	102	15	.	.	PUNCT
ejpam-6775	103	1	let	let	VERB
ejpam-6775	103	2	y	y	PRON
ejpam-6775	103	3	and	and	CCONJ
ejpam-6775	103	4	z	z	NOUN
ejpam-6775	103	5	be	be	VERB
ejpam-6775	103	6	banach	banach	NOUN
ejpam-6775	103	7	spaces	space	NOUN
ejpam-6775	103	8	,	,	PUNCT
ejpam-6775	103	9	x	x	PUNCT
ejpam-6775	103	10	∈	∈	PROPN
ejpam-6775	103	11	y	y	PROPN
ejpam-6775	103	12	and	and	CCONJ
ejpam-6775	103	13	q	q	PROPN
ejpam-6775	103	14	∈	∈	PROPN
ejpam-6775	103	15	r	r	NOUN
ejpam-6775	103	16	is	be	AUX
ejpam-6775	103	17	a	a	DET
ejpam-6775	103	18	parameter	parameter	NOUN
ejpam-6775	103	19	.	.	PUNCT
ejpam-6775	104	1	we	we	PRON
ejpam-6775	104	2	consider	consider	VERB
ejpam-6775	104	3	the	the	DET
ejpam-6775	104	4	following	follow	VERB
ejpam-6775	104	5	abstract	abstract	ADJ
ejpam-6775	104	6	differential	differential	ADJ
ejpam-6775	104	7	equation	equation	NOUN
ejpam-6775	104	8	dx	dx	PROPN
ejpam-6775	104	9	dt	dt	NOUN
ejpam-6775	105	1	=	=	SYM
ejpam-6775	105	2	f	f	PROPN
ejpam-6775	105	3	(	(	PUNCT
ejpam-6775	105	4	x	x	X
ejpam-6775	105	5	,	,	PUNCT
ejpam-6775	105	6	q	q	NOUN
ejpam-6775	105	7	)	)	PUNCT
ejpam-6775	105	8	,	,	PUNCT
ejpam-6775	105	9	f	f	X
ejpam-6775	105	10	:	:	PUNCT
ejpam-6775	105	11	y	y	PROPN
ejpam-6775	105	12	×	×	NOUN
ejpam-6775	105	13	r	r	NOUN
ejpam-6775	105	14	−→	−→	NOUN
ejpam-6775	105	15	z.	z.	PROPN
ejpam-6775	105	16	(	(	PUNCT
ejpam-6775	105	17	5	5	NUM
ejpam-6775	105	18	)	)	PUNCT
ejpam-6775	105	19	without	without	ADP
ejpam-6775	105	20	loss	loss	NOUN
ejpam-6775	105	21	of	of	ADP
ejpam-6775	105	22	generality	generality	NOUN
ejpam-6775	105	23	,	,	PUNCT
ejpam-6775	105	24	we	we	PRON
ejpam-6775	105	25	assume	assume	VERB
ejpam-6775	105	26	that	that	SCONJ
ejpam-6775	105	27	0	0	NUM
ejpam-6775	105	28	is	be	AUX
ejpam-6775	105	29	an	an	DET
ejpam-6775	105	30	equilibrium	equilibrium	NOUN
ejpam-6775	105	31	point	point	NOUN
ejpam-6775	105	32	of	of	ADP
ejpam-6775	105	33	the	the	DET
ejpam-6775	105	34	system	system	NOUN
ejpam-6775	105	35	(	(	PUNCT
ejpam-6775	105	36	that	that	PRON
ejpam-6775	105	37	is	is	ADV
ejpam-6775	105	38	f	f	PROPN
ejpam-6775	105	39	(	(	PUNCT
ejpam-6775	105	40	0	0	NUM
ejpam-6775	105	41	,	,	PUNCT
ejpam-6775	105	42	q	q	NOUN
ejpam-6775	105	43	)	)	PUNCT
ejpam-6775	105	44	=	=	SYM
ejpam-6775	105	45	0	0	NUM
ejpam-6775	105	46	for	for	ADP
ejpam-6775	105	47	all	all	DET
ejpam-6775	105	48	q	q	PROPN
ejpam-6775	105	49	∈	∈	PROPN
ejpam-6775	105	50	r	r	NOUN
ejpam-6775	105	51	)	)	PUNCT
ejpam-6775	105	52	and	and	CCONJ
ejpam-6775	105	53	assume	assume	VERB
ejpam-6775	105	54	j.	j.	PROPN
ejpam-6775	105	55	leo	leo	PROPN
ejpam-6775	105	56	amalraj	amalraj	PROPN
ejpam-6775	106	1	et	et	PROPN
ejpam-6775	106	2	al	al	PROPN
ejpam-6775	106	3	.	.	PUNCT
ejpam-6775	106	4	/	/	SYM
ejpam-6775	106	5	eur	eur	PROPN
ejpam-6775	106	6	.	.	PUNCT
ejpam-6775	107	1	j.	j.	PROPN
ejpam-6775	107	2	pure	pure	PROPN
ejpam-6775	107	3	appl	appl	PROPN
ejpam-6775	107	4	.	.	PROPN
ejpam-6775	107	5	math	math	PROPN
ejpam-6775	107	6	,	,	PUNCT
ejpam-6775	107	7	18	18	NUM
ejpam-6775	107	8	(	(	PUNCT
ejpam-6775	107	9	4	4	NUM
ejpam-6775	107	10	)	)	PUNCT
ejpam-6775	107	11	(	(	PUNCT
ejpam-6775	107	12	2025	2025	NUM
ejpam-6775	107	13	)	)	PUNCT
ejpam-6775	107	14	,	,	PUNCT
ejpam-6775	107	15	6775	6775	NUM
ejpam-6775	107	16	6	6	NUM
ejpam-6775	107	17	of	of	ADP
ejpam-6775	107	18	32	32	NUM
ejpam-6775	107	19	(	(	PUNCT
ejpam-6775	107	20	i	i	NOUN
ejpam-6775	107	21	)	)	PUNCT
ejpam-6775	107	22	a	a	PRON
ejpam-6775	107	23	:	:	PUNCT
ejpam-6775	107	24	=	=	SYM
ejpam-6775	107	25	dxf	dxf	PROPN
ejpam-6775	107	26	(	(	PUNCT
ejpam-6775	107	27	0	0	NUM
ejpam-6775	107	28	,	,	PUNCT
ejpam-6775	107	29	q0	q0	PROPN
ejpam-6775	107	30	)	)	PUNCT
ejpam-6775	107	31	is	be	AUX
ejpam-6775	107	32	the	the	DET
ejpam-6775	107	33	linearization	linearization	NOUN
ejpam-6775	107	34	around	around	ADP
ejpam-6775	107	35	the	the	DET
ejpam-6775	107	36	equilibrium	equilibrium	NOUN
ejpam-6775	107	37	0	0	NUM
ejpam-6775	107	38	evaluated	evaluate	VERB
ejpam-6775	107	39	at	at	ADP
ejpam-6775	107	40	a	a	DET
ejpam-6775	107	41	critical	critical	ADJ
ejpam-6775	107	42	value	value	NOUN
ejpam-6775	107	43	of	of	ADP
ejpam-6775	107	44	parameter	parameter	NOUN
ejpam-6775	107	45	q0	q0	PROPN
ejpam-6775	107	46	,	,	PUNCT
ejpam-6775	107	47	such	such	ADJ
ejpam-6775	107	48	that	that	SCONJ
ejpam-6775	107	49	a	a	PRON
ejpam-6775	107	50	is	be	AUX
ejpam-6775	107	51	a	a	DET
ejpam-6775	107	52	closed	closed	ADJ
ejpam-6775	107	53	operator	operator	NOUN
ejpam-6775	107	54	with	with	ADP
ejpam-6775	107	55	a	a	DET
ejpam-6775	107	56	simple	simple	ADJ
ejpam-6775	107	57	isolated	isolate	VERB
ejpam-6775	107	58	eigenvalue	eigenvalue	NOUN
ejpam-6775	107	59	zero	zero	NUM
ejpam-6775	107	60	and	and	CCONJ
ejpam-6775	107	61	remaining	remaining	ADJ
ejpam-6775	107	62	eigenvalues	eigenvalue	NOUN
ejpam-6775	107	63	having	have	VERB
ejpam-6775	107	64	negative	negative	ADJ
ejpam-6775	107	65	real	real	ADJ
ejpam-6775	107	66	part	part	NOUN
ejpam-6775	107	67	.	.	PUNCT
ejpam-6775	108	1	let	let	VERB
ejpam-6775	108	2	ν0	ν0	PROPN
ejpam-6775	108	3	be	be	AUX
ejpam-6775	108	4	the	the	DET
ejpam-6775	108	5	unique	unique	ADJ
ejpam-6775	108	6	(	(	PUNCT
ejpam-6775	108	7	up	up	ADP
ejpam-6775	108	8	to	to	ADP
ejpam-6775	108	9	a	a	DET
ejpam-6775	108	10	constant	constant	ADJ
ejpam-6775	108	11	)	)	PUNCT
ejpam-6775	108	12	positive	positive	ADJ
ejpam-6775	108	13	solution	solution	NOUN
ejpam-6775	108	14	of	of	ADP
ejpam-6775	108	15	aν	aν	NOUN
ejpam-6775	108	16	=	=	SYM
ejpam-6775	108	17	0	0	NUM
ejpam-6775	108	18	.	.	PUNCT
ejpam-6775	109	1	(	(	PUNCT
ejpam-6775	109	2	ii	ii	NOUN
ejpam-6775	109	3	)	)	PUNCT
ejpam-6775	109	4	f	f	PROPN
ejpam-6775	109	5	(	(	PUNCT
ejpam-6775	109	6	x	x	X
ejpam-6775	109	7	,	,	PUNCT
ejpam-6775	109	8	q	q	X
ejpam-6775	109	9	)	)	PUNCT
ejpam-6775	109	10	∈	∈	PROPN
ejpam-6775	109	11	c2(u0	c2(u0	NOUN
ejpam-6775	109	12	×	×	PROPN
ejpam-6775	109	13	i0	i0	PROPN
ejpam-6775	109	14	,	,	PUNCT
ejpam-6775	109	15	z	z	NOUN
ejpam-6775	109	16	)	)	PUNCT
ejpam-6775	109	17	for	for	ADP
ejpam-6775	109	18	some	some	DET
ejpam-6775	109	19	neighbourhood	neighbourhood	NOUN
ejpam-6775	109	20	u0	u0	NOUN
ejpam-6775	109	21	of	of	ADP
ejpam-6775	109	22	0	0	NUM
ejpam-6775	109	23	and	and	CCONJ
ejpam-6775	109	24	interval	interval	NOUN
ejpam-6775	109	25	i0	i0	PROPN
ejpam-6775	109	26	containing	contain	VERB
ejpam-6775	109	27	q0	q0	PROPN
ejpam-6775	109	28	.	.	PUNCT
ejpam-6775	110	1	(	(	PUNCT
ejpam-6775	110	2	iii	iii	NOUN
ejpam-6775	110	3	)	)	PUNCT
ejpam-6775	110	4	assume	assume	PROPN
ejpam-6775	110	5	z∗	z∗	PROPN
ejpam-6775	110	6	is	be	AUX
ejpam-6775	110	7	the	the	DET
ejpam-6775	110	8	dual	dual	ADJ
ejpam-6775	110	9	of	of	ADP
ejpam-6775	110	10	z	z	PROPN
ejpam-6775	110	11	and	and	CCONJ
ejpam-6775	110	12	⟨.	⟨.	PROPN
ejpam-6775	110	13	,	,	PUNCT
ejpam-6775	110	14	.⟩	.⟩	PROPN
ejpam-6775	110	15	is	be	AUX
ejpam-6775	110	16	the	the	DET
ejpam-6775	110	17	pairing	pairing	NOUN
ejpam-6775	110	18	between	between	ADP
ejpam-6775	110	19	z	z	PROPN
ejpam-6775	110	20	and	and	CCONJ
ejpam-6775	110	21	z∗.	z∗.	PROPN
ejpam-6775	110	22	assume	assume	VERB
ejpam-6775	110	23	ν̃0	ν̃0	PROPN
ejpam-6775	110	24	∈	∈	PROPN
ejpam-6775	110	25	z∗	z∗	PROPN
ejpam-6775	110	26	is	be	AUX
ejpam-6775	110	27	the	the	DET
ejpam-6775	110	28	unique	unique	ADJ
ejpam-6775	110	29	(	(	PUNCT
ejpam-6775	110	30	up	up	ADP
ejpam-6775	110	31	to	to	ADP
ejpam-6775	110	32	a	a	DET
ejpam-6775	110	33	constant	constant	ADJ
ejpam-6775	110	34	)	)	PUNCT
ejpam-6775	110	35	positive	positive	ADJ
ejpam-6775	110	36	vector	vector	NOUN
ejpam-6775	110	37	satisfying	satisfy	VERB
ejpam-6775	110	38	⟨a∗	⟨a∗	NOUN
ejpam-6775	110	39	,	,	PUNCT
ejpam-6775	110	40	ν̃0⟩	ν̃0⟩	PROPN
ejpam-6775	110	41	=	=	SYM
ejpam-6775	110	42	0	0	NUM
ejpam-6775	111	1	for	for	ADP
ejpam-6775	111	2	all	all	DET
ejpam-6775	111	3	x	x	SYM
ejpam-6775	111	4	∈	∈	PROPN
ejpam-6775	111	5	y	y	PROPN
ejpam-6775	111	6	,	,	PUNCT
ejpam-6775	111	7	that	that	PRON
ejpam-6775	111	8	is	be	AUX
ejpam-6775	111	9	dim(kera∗	dim(kera∗	NOUN
ejpam-6775	111	10	)	)	PUNCT
ejpam-6775	111	11	=	=	SYM
ejpam-6775	111	12	1	1	NUM
ejpam-6775	111	13	where	where	SCONJ
ejpam-6775	111	14	a∗	a∗	PROPN
ejpam-6775	111	15	is	be	AUX
ejpam-6775	111	16	the	the	DET
ejpam-6775	111	17	adjoint	adjoint	NOUN
ejpam-6775	111	18	of	of	ADP
ejpam-6775	111	19	a	a	PRON
ejpam-6775	111	20	and	and	CCONJ
ejpam-6775	111	21	kera∗	kera∗	NOUN
ejpam-6775	111	22	=	=	SYM
ejpam-6775	111	23	span(ν̃0	span(ν̃0	PROPN
ejpam-6775	111	24	)	)	PUNCT
ejpam-6775	111	25	.	.	PUNCT
ejpam-6775	112	1	(	(	PUNCT
ejpam-6775	112	2	iv	iv	X
ejpam-6775	112	3	)	)	PUNCT
ejpam-6775	112	4	assume	assume	PROPN
ejpam-6775	112	5	(	(	PUNCT
ejpam-6775	112	6	d2	d2	PROPN
ejpam-6775	112	7	xqf	xqf	PROPN
ejpam-6775	112	8	(	(	PUNCT
ejpam-6775	112	9	0	0	NUM
ejpam-6775	112	10	,	,	PUNCT
ejpam-6775	112	11	q0)ν̃0	q0)ν̃0	NOUN
ejpam-6775	112	12	,	,	PUNCT
ejpam-6775	112	13	ν̃0	ν̃0	PROPN
ejpam-6775	112	14	)	)	PUNCT
ejpam-6775	112	15	̸=	̸=	PROPN
ejpam-6775	112	16	0	0	NUM
ejpam-6775	112	17	where	where	SCONJ
ejpam-6775	112	18	d2	d2	PROPN
ejpam-6775	112	19	xqf	xqf	PROPN
ejpam-6775	112	20	(	(	PUNCT
ejpam-6775	112	21	0	0	NUM
ejpam-6775	112	22	,	,	PUNCT
ejpam-6775	112	23	q0	q0	PROPN
ejpam-6775	112	24	)	)	PUNCT
ejpam-6775	112	25	is	be	AUX
ejpam-6775	112	26	the	the	DET
ejpam-6775	112	27	second	second	ADJ
ejpam-6775	112	28	derivative	derivative	NOUN
ejpam-6775	112	29	of	of	ADP
ejpam-6775	112	30	f	f	PROPN
ejpam-6775	112	31	with	with	ADP
ejpam-6775	112	32	respect	respect	NOUN
ejpam-6775	112	33	to	to	ADP
ejpam-6775	112	34	x	x	PUNCT
ejpam-6775	112	35	and	and	CCONJ
ejpam-6775	112	36	q.	q.	PROPN
ejpam-6775	112	37	then	then	ADV
ejpam-6775	112	38	,	,	PUNCT
ejpam-6775	112	39	the	the	DET
ejpam-6775	112	40	direction	direction	NOUN
ejpam-6775	112	41	of	of	ADP
ejpam-6775	112	42	the	the	DET
ejpam-6775	112	43	bifurcation	bifurcation	NOUN
ejpam-6775	112	44	is	be	AUX
ejpam-6775	112	45	determined	determine	VERB
ejpam-6775	112	46	by	by	ADP
ejpam-6775	112	47	the	the	DET
ejpam-6775	112	48	numbers	number	NOUN
ejpam-6775	112	49	a	a	DET
ejpam-6775	112	50	=	=	SYM
ejpam-6775	112	51	⟨d2	⟨d2	PROPN
ejpam-6775	112	52	xqf	xqf	X
ejpam-6775	112	53	(	(	PUNCT
ejpam-6775	112	54	0	0	NUM
ejpam-6775	112	55	,	,	PUNCT
ejpam-6775	112	56	q0)[ν̃0	q0)[ν̃0	NOUN
ejpam-6775	112	57	,	,	PUNCT
ejpam-6775	112	58	ν̃0	ν̃0	PROPN
ejpam-6775	112	59	]	]	X
ejpam-6775	112	60	,	,	PUNCT
ejpam-6775	112	61	ν̃0⟩	ν̃0⟩	PROPN
ejpam-6775	112	62	and	and	CCONJ
ejpam-6775	112	63	b	b	PROPN
ejpam-6775	112	64	=	=	SYM
ejpam-6775	112	65	⟨d2	⟨d2	PROPN
ejpam-6775	112	66	xf	xf	PROPN
ejpam-6775	112	67	(	(	PUNCT
ejpam-6775	112	68	0	0	NUM
ejpam-6775	112	69	,	,	PUNCT
ejpam-6775	112	70	q0)[h1	q0)[h1	INTJ
ejpam-6775	112	71	,	,	PUNCT
ejpam-6775	112	72	h2	h2	PROPN
ejpam-6775	112	73	]	]	PUNCT
ejpam-6775	112	74	,	,	PUNCT
ejpam-6775	112	75	ν̃0⟩	ν̃0⟩	PROPN
ejpam-6775	112	76	,	,	PUNCT
ejpam-6775	112	77	whered2	whered2	NOUN
ejpam-6775	112	78	xf	xf	X
ejpam-6775	112	79	(	(	PUNCT
ejpam-6775	112	80	0	0	NUM
ejpam-6775	112	81	,	,	PUNCT
ejpam-6775	112	82	q0)[h1	q0)[h1	INTJ
ejpam-6775	112	83	,	,	PUNCT
ejpam-6775	112	84	h2	h2	PROPN
ejpam-6775	112	85	]	]	PUNCT
ejpam-6775	112	86	is	be	AUX
ejpam-6775	112	87	the	the	DET
ejpam-6775	112	88	second	second	ADJ
ejpam-6775	112	89	derivative	derivative	NOUN
ejpam-6775	112	90	of	of	ADP
ejpam-6775	112	91	f	f	PROPN
ejpam-6775	112	92	with	with	ADP
ejpam-6775	112	93	respect	respect	NOUN
ejpam-6775	112	94	to	to	ADP
ejpam-6775	112	95	x	x	PUNCT
ejpam-6775	112	96	applied	apply	VERB
ejpam-6775	112	97	to	to	ADP
ejpam-6775	112	98	the	the	DET
ejpam-6775	112	99	function	function	NOUN
ejpam-6775	112	100	h1	h1	NOUN
ejpam-6775	112	101	and	and	CCONJ
ejpam-6775	112	102	h2	h2	NOUN
ejpam-6775	112	103	.	.	PUNCT
ejpam-6775	113	1	if	if	SCONJ
ejpam-6775	113	2	b	b	PROPN
ejpam-6775	113	3	>	>	X
ejpam-6775	113	4	0	0	NUM
ejpam-6775	113	5	,	,	PUNCT
ejpam-6775	113	6	then	then	ADV
ejpam-6775	113	7	the	the	DET
ejpam-6775	113	8	bifurcation	bifurcation	NOUN
ejpam-6775	113	9	is	be	AUX
ejpam-6775	113	10	backward	backward	ADJ
ejpam-6775	113	11	if	if	SCONJ
ejpam-6775	113	12	and	and	CCONJ
ejpam-6775	113	13	only	only	ADV
ejpam-6775	113	14	if	if	SCONJ
ejpam-6775	113	15	a	a	DET
ejpam-6775	113	16	>	>	X
ejpam-6775	113	17	0	0	PUNCT
ejpam-6775	113	18	and	and	CCONJ
ejpam-6775	113	19	forward	forward	ADV
ejpam-6775	113	20	if	if	SCONJ
ejpam-6775	113	21	and	and	CCONJ
ejpam-6775	113	22	only	only	ADV
ejpam-6775	113	23	if	if	SCONJ
ejpam-6775	113	24	a	a	DET
ejpam-6775	113	25	<	<	X
ejpam-6775	113	26	0	0	X
ejpam-6775	113	27	.	.	PUNCT
ejpam-6775	113	28	remark	remark	PROPN
ejpam-6775	113	29	1	1	NUM
ejpam-6775	113	30	(	(	PUNCT
ejpam-6775	113	31	remarks	remark	NOUN
ejpam-6775	113	32	on	on	ADP
ejpam-6775	113	33	eigenvector	eigenvector	NOUN
ejpam-6775	113	34	properties	property	NOUN
ejpam-6775	113	35	)	)	PUNCT
ejpam-6775	113	36	.	.	PUNCT
ejpam-6775	114	1	the	the	DET
ejpam-6775	114	2	components	component	NOUN
ejpam-6775	114	3	of	of	ADP
ejpam-6775	114	4	the	the	DET
ejpam-6775	114	5	eigenvector	eigenvector	PROPN
ejpam-6775	114	6	ν̃0	ν̃0	PROPN
ejpam-6775	114	7	,	,	PUNCT
ejpam-6775	114	8	that	that	PRON
ejpam-6775	114	9	corresponds	correspond	VERB
ejpam-6775	114	10	to	to	ADP
ejpam-6775	114	11	positive	positive	ADJ
ejpam-6775	114	12	entries	entry	NOUN
ejpam-6775	114	13	in	in	ADP
ejpam-6775	114	14	the	the	DET
ejpam-6775	114	15	disease	disease	NOUN
ejpam-6775	114	16	-	-	PUNCT
ejpam-6775	114	17	free	free	ADJ
ejpam-6775	114	18	steady	steady	ADJ
ejpam-6775	114	19	state	state	NOUN
ejpam-6775	114	20	,	,	PUNCT
ejpam-6775	114	21	may	may	AUX
ejpam-6775	114	22	be	be	AUX
ejpam-6775	114	23	negative	negative	ADJ
ejpam-6775	114	24	.	.	PUNCT
ejpam-6775	115	1	this	this	PRON
ejpam-6775	115	2	is	be	AUX
ejpam-6775	115	3	in	in	ADP
ejpam-6775	115	4	general	general	ADJ
ejpam-6775	115	5	the	the	DET
ejpam-6775	115	6	case	case	NOUN
ejpam-6775	115	7	with	with	ADP
ejpam-6775	115	8	the	the	DET
ejpam-6775	115	9	partial	partial	ADJ
ejpam-6775	115	10	differential	differential	ADJ
ejpam-6775	115	11	equations	equation	NOUN
ejpam-6775	115	12	as	as	ADV
ejpam-6775	115	13	well	well	ADV
ejpam-6775	115	14	[	[	X
ejpam-6775	115	15	54	54	NUM
ejpam-6775	115	16	]	]	PUNCT
ejpam-6775	115	17	.	.	PUNCT
ejpam-6775	116	1	remark	remark	PROPN
ejpam-6775	116	2	2	2	NUM
ejpam-6775	116	3	(	(	PUNCT
ejpam-6775	116	4	lipschitz	lipschitz	VERB
ejpam-6775	116	5	properties	property	NOUN
ejpam-6775	116	6	and	and	CCONJ
ejpam-6775	116	7	solution	solution	NOUN
ejpam-6775	116	8	representations	representation	NOUN
ejpam-6775	116	9	)	)	PUNCT
ejpam-6775	116	10	.	.	PUNCT
ejpam-6775	117	1	(	(	PUNCT
ejpam-6775	117	2	i	i	NOUN
ejpam-6775	117	3	)	)	PUNCT
ejpam-6775	117	4	let	let	VERB
ejpam-6775	117	5	us	we	PRON
ejpam-6775	117	6	consider	consider	VERB
ejpam-6775	117	7	the	the	DET
ejpam-6775	117	8	functions	function	NOUN
ejpam-6775	117	9	h	h	NOUN
ejpam-6775	117	10	(	(	PUNCT
ejpam-6775	117	11	1	1	X
ejpam-6775	117	12	)	)	PUNCT
ejpam-6775	117	13	r	r	NOUN
ejpam-6775	117	14	(	(	PUNCT
ejpam-6775	117	15	i	i	PROPN
ejpam-6775	117	16	,	,	PUNCT
ejpam-6775	117	17	ξ	ξ	PROPN
ejpam-6775	117	18	)	)	PUNCT
ejpam-6775	117	19	=	=	SYM
ejpam-6775	118	1	e−	e−	PROPN
ejpam-6775	118	2	∫	∫	PROPN
ejpam-6775	118	3	tβ(i	tβ(i	NUM
ejpam-6775	118	4	,	,	PUNCT
ejpam-6775	118	5	σ	σ	PROPN
ejpam-6775	118	6	,	,	PUNCT
ejpam-6775	118	7	.	.	PUNCT
ejpam-6775	118	8	)	)	PUNCT
ejpam-6775	119	1	t	t	X
ejpam-6775	120	1	+	+	ADV
ejpam-6775	120	2	ϵ(τ	ϵ(τ	NOUN
ejpam-6775	120	3	,	,	PUNCT
ejpam-6775	120	4	σ	σ	X
ejpam-6775	120	5	,	,	PUNCT
ejpam-6775	120	6	i)dσ	i)dσ	PROPN
ejpam-6775	120	7	and	and	CCONJ
ejpam-6775	120	8	h	h	PROPN
ejpam-6775	120	9	(	(	PUNCT
ejpam-6775	120	10	2	2	NUM
ejpam-6775	120	11	)	)	PUNCT
ejpam-6775	120	12	r	r	NOUN
ejpam-6775	120	13	(	(	PUNCT
ejpam-6775	120	14	i	i	NOUN
ejpam-6775	120	15	)	)	PUNCT
ejpam-6775	120	16	=	=	PUNCT
ejpam-6775	121	1	e−	e−	PROPN
ejpam-6775	121	2	∫	∫	PROPN
ejpam-6775	121	3	tβ(i	tβ(i	NUM
ejpam-6775	121	4	,	,	PUNCT
ejpam-6775	121	5	σ	σ	PROPN
ejpam-6775	121	6	,	,	PUNCT
ejpam-6775	121	7	.	.	PUNCT
ejpam-6775	121	8	)	)	PUNCT
ejpam-6775	122	1	t	t	PROPN
ejpam-6775	123	1	+	+	ADV
ejpam-6775	123	2	µdσ	µdσ	VERB
ejpam-6775	123	3	for	for	ADP
ejpam-6775	123	4	r	r	NOUN
ejpam-6775	123	5	>	>	X
ejpam-6775	123	6	0	0	NUM
ejpam-6775	124	1	and	and	CCONJ
ejpam-6775	124	2	t	t	PROPN
ejpam-6775	124	3	∈	∈	PROPN
ejpam-6775	125	1	[	[	X
ejpam-6775	125	2	0	0	NUM
ejpam-6775	125	3	,	,	PUNCT
ejpam-6775	125	4	t	t	X
ejpam-6775	125	5	]	]	PUNCT
ejpam-6775	125	6	.	.	PUNCT
ejpam-6775	126	1	then	then	ADV
ejpam-6775	126	2	by	by	ADP
ejpam-6775	126	3	direct	direct	ADJ
ejpam-6775	126	4	computation	computation	NOUN
ejpam-6775	126	5	based	base	VERB
ejpam-6775	126	6	on	on	ADP
ejpam-6775	126	7	the	the	DET
ejpam-6775	126	8	following	follow	VERB
ejpam-6775	126	9	arguments	argument	NOUN
ejpam-6775	126	10	:	:	PUNCT
ejpam-6775	126	11	for	for	ADP
ejpam-6775	126	12	all	all	DET
ejpam-6775	126	13	x	x	NOUN
ejpam-6775	126	14	,	,	PUNCT
ejpam-6775	126	15	y	y	PROPN
ejpam-6775	126	16	∈	∈	PROPN
ejpam-6775	126	17	r	r	NOUN
ejpam-6775	126	18	,	,	PUNCT
ejpam-6775	126	19	we	we	PRON
ejpam-6775	126	20	have	have	VERB
ejpam-6775	126	21	|e−x	|e−x	PROPN
ejpam-6775	126	22	−	−	PROPN
ejpam-6775	126	23	e−y|	e−y|	NOUN
ejpam-6775	126	24	≤	≤	NUM
ejpam-6775	126	25	|x	|x	NOUN
ejpam-6775	126	26	−	−	PROPN
ejpam-6775	126	27	y|	y|	NOUN
ejpam-6775	126	28	,	,	PUNCT
ejpam-6775	126	29	there	there	PRON
ejpam-6775	126	30	exists	exist	VERB
ejpam-6775	126	31	the	the	DET
ejpam-6775	126	32	positive	positive	ADJ
ejpam-6775	126	33	constants	constant	NOUN
ejpam-6775	126	34	kk	kk	X
ejpam-6775	126	35	with	with	ADP
ejpam-6775	126	36	k	k	PROPN
ejpam-6775	126	37	∈	∈	PROPN
ejpam-6775	126	38	{	{	PUNCT
ejpam-6775	126	39	1	1	NUM
ejpam-6775	126	40	,	,	PUNCT
ejpam-6775	126	41	2	2	NUM
ejpam-6775	126	42	,	,	PUNCT
ejpam-6775	126	43	3	3	NUM
ejpam-6775	126	44	}	}	PUNCT
ejpam-6775	126	45	such	such	ADJ
ejpam-6775	126	46	that	that	SCONJ
ejpam-6775	126	47	the	the	DET
ejpam-6775	126	48	functions	function	NOUN
ejpam-6775	126	49	h	h	NOUN
ejpam-6775	126	50	(	(	PUNCT
ejpam-6775	126	51	1	1	X
ejpam-6775	126	52	)	)	PUNCT
ejpam-6775	126	53	r	r	NOUN
ejpam-6775	126	54	and	and	CCONJ
ejpam-6775	126	55	h	h	NOUN
ejpam-6775	126	56	(	(	PUNCT
ejpam-6775	126	57	2	2	X
ejpam-6775	126	58	)	)	PUNCT
ejpam-6775	126	59	r	r	NOUN
ejpam-6775	126	60	satisfy	satisfy	NOUN
ejpam-6775	126	61	for	for	ADP
ejpam-6775	126	62	(	(	PUNCT
ejpam-6775	126	63	ik	ik	X
ejpam-6775	126	64	,	,	PUNCT
ejpam-6775	126	65	ξk	ξk	NOUN
ejpam-6775	126	66	)	)	PUNCT
ejpam-6775	126	67	with	with	ADP
ejpam-6775	126	68	k	k	PROPN
ejpam-6775	126	69	∈	∈	PROPN
ejpam-6775	126	70	{	{	PUNCT
ejpam-6775	126	71	1	1	NUM
ejpam-6775	126	72	,	,	PUNCT
ejpam-6775	126	73	2	2	NUM
ejpam-6775	126	74	}	}	PUNCT
ejpam-6775	126	75	,	,	PUNCT
ejpam-6775	126	76	the	the	DET
ejpam-6775	126	77	following	follow	VERB
ejpam-6775	126	78	inequalities	inequality	NOUN
ejpam-6775	126	79	,	,	PUNCT
ejpam-6775	126	80	|h(1)r	|h(1)r	PROPN
ejpam-6775	126	81	(	(	PUNCT
ejpam-6775	126	82	i1	i1	PROPN
ejpam-6775	126	83	,	,	PUNCT
ejpam-6775	126	84	ξ1)−h(1)r	ξ1)−h(1)r	PROPN
ejpam-6775	126	85	(	(	PUNCT
ejpam-6775	126	86	i2	i2	PROPN
ejpam-6775	126	87	,	,	PUNCT
ejpam-6775	126	88	ξ2)|	ξ2)|	PROPN
ejpam-6775	126	89	≤	≤	NUM
ejpam-6775	126	90	k1	k1	PROPN
ejpam-6775	126	91	∫	∫	PROPN
ejpam-6775	126	92	t	t	PROPN
ejpam-6775	126	93	|r′(i(σ	|r′(i(σ	PROPN
ejpam-6775	126	94	,	,	PUNCT
ejpam-6775	126	95	.))−r′(̄i(σ	.))−r′(̄i(σ	PROPN
ejpam-6775	126	96	,	,	PUNCT
ejpam-6775	126	97	.))|dσ+k2	.))|dσ+k2	PROPN
ejpam-6775	127	1	∫	∫	PROPN
ejpam-6775	127	2	t	t	PROPN
ejpam-6775	127	3	|ξ1(σ)−	|ξ1(σ)−	NOUN
ejpam-6775	127	4	ξ2(σ)|dσ	ξ2(σ)|dσ	NUM
ejpam-6775	127	5	(	(	PUNCT
ejpam-6775	127	6	6	6	NUM
ejpam-6775	127	7	)	)	PUNCT
ejpam-6775	127	8	and	and	CCONJ
ejpam-6775	127	9	|h(1)r	|h(1)r	PROPN
ejpam-6775	127	10	(	(	PUNCT
ejpam-6775	127	11	i)−	i)−	PROPN
ejpam-6775	127	12	h(1)r	h(1)r	PROPN
ejpam-6775	127	13	(	(	PUNCT
ejpam-6775	127	14	i2)|	i2)|	PROPN
ejpam-6775	127	15	≤	≤	PROPN
ejpam-6775	127	16	k3	k3	VERB
ejpam-6775	127	17	∫	∫	PROPN
ejpam-6775	127	18	t	t	PROPN
ejpam-6775	127	19	|r′(i′(σ	|r′(i′(σ	PROPN
ejpam-6775	127	20	,	,	PUNCT
ejpam-6775	127	21	.))−	.))−	PUNCT
ejpam-6775	128	1	r′(̄i(σ	r′(̄i(σ	PROPN
ejpam-6775	128	2	,	,	PUNCT
ejpam-6775	128	3	.))|dσ	.))|dσ	PROPN
ejpam-6775	128	4	.	.	PUNCT
ejpam-6775	129	1	(	(	PUNCT
ejpam-6775	129	2	7	7	X
ejpam-6775	129	3	)	)	PUNCT
ejpam-6775	129	4	using	use	VERB
ejpam-6775	129	5	the	the	DET
ejpam-6775	129	6	method	method	NOUN
ejpam-6775	129	7	of	of	ADP
ejpam-6775	129	8	integrating	integrate	VERB
ejpam-6775	129	9	factors	factor	NOUN
ejpam-6775	129	10	on	on	ADP
ejpam-6775	129	11	the	the	DET
ejpam-6775	129	12	ordinary	ordinary	ADJ
ejpam-6775	129	13	differential	differential	ADJ
ejpam-6775	129	14	equations	equation	NOUN
ejpam-6775	129	15	and	and	CCONJ
ejpam-6775	129	16	the	the	DET
ejpam-6775	129	17	method	method	NOUN
ejpam-6775	129	18	of	of	ADP
ejpam-6775	129	19	characteristic	characteristic	ADJ
ejpam-6775	129	20	on	on	ADP
ejpam-6775	129	21	the	the	DET
ejpam-6775	129	22	first	first	ADJ
ejpam-6775	129	23	-	-	PUNCT
ejpam-6775	129	24	second	second	NOUN
ejpam-6775	129	25	and	and	CCONJ
ejpam-6775	129	26	third	third	ADJ
ejpam-6775	129	27	equations	equation	NOUN
ejpam-6775	129	28	of	of	ADP
ejpam-6775	129	29	system	system	NOUN
ejpam-6775	129	30	(	(	PUNCT
ejpam-6775	129	31	31	31	NUM
ejpam-6775	129	32	)	)	PUNCT
ejpam-6775	129	33	respectively	respectively	ADV
ejpam-6775	129	34	,	,	PUNCT
ejpam-6775	129	35	we	we	PRON
ejpam-6775	129	36	obtain	obtain	VERB
ejpam-6775	129	37	the	the	DET
ejpam-6775	129	38	following	follow	VERB
ejpam-6775	129	39	expression	expression	NOUN
ejpam-6775	129	40	of	of	ADP
ejpam-6775	129	41	state	state	NOUN
ejpam-6775	129	42	variables	variable	NOUN
ejpam-6775	129	43	:	:	PUNCT
ejpam-6775	129	44	s(t	s(t	NUM
ejpam-6775	129	45	)	)	PUNCT
ejpam-6775	130	1	=	=	PRON
ejpam-6775	130	2	s0h	s0h	VERB
ejpam-6775	130	3	(	(	PUNCT
ejpam-6775	130	4	1	1	X
ejpam-6775	130	5	)	)	PUNCT
ejpam-6775	130	6	r	r	NOUN
ejpam-6775	130	7	(	(	PUNCT
ejpam-6775	130	8	t	t	PROPN
ejpam-6775	130	9	,	,	PUNCT
ejpam-6775	130	10	ξ	ξ	PROPN
ejpam-6775	130	11	)	)	PUNCT
ejpam-6775	131	1	+	+	NUM
ejpam-6775	131	2	∫	∫	PROPN
ejpam-6775	131	3	t	t	NOUN
ejpam-6775	131	4	0	0	NUM
ejpam-6775	132	1	[	[	X
ejpam-6775	132	2	λ	λ	X
ejpam-6775	132	3	+	+	NOUN
ejpam-6775	132	4	t	t	PROPN
ejpam-6775	132	5	(	(	PUNCT
ejpam-6775	132	6	α	α	X
ejpam-6775	132	7	,	,	PUNCT
ejpam-6775	132	8	r(j	r(j	PROPN
ejpam-6775	132	9	,	,	PUNCT
ejpam-6775	132	10	r	r	NOUN
ejpam-6775	132	11	,	,	PUNCT
ejpam-6775	132	12	.))]h(1)r	.))]h(1)r	PUNCT
ejpam-6775	132	13	(	(	PUNCT
ejpam-6775	132	14	t	t	X
ejpam-6775	132	15	,	,	PUNCT
ejpam-6775	132	16	ξ)dσ	ξ)dσ	PROPN
ejpam-6775	132	17	;	;	PUNCT
ejpam-6775	132	18	(	(	PUNCT
ejpam-6775	132	19	8)	8)	NUM
ejpam-6775	132	20	j.	j.	PROPN
ejpam-6775	132	21	leo	leo	PROPN
ejpam-6775	132	22	amalraj	amalraj	PROPN
ejpam-6775	132	23	et	et	PROPN
ejpam-6775	132	24	al	al	PROPN
ejpam-6775	132	25	.	.	PUNCT
ejpam-6775	132	26	/	/	SYM
ejpam-6775	132	27	eur	eur	PROPN
ejpam-6775	132	28	.	.	PUNCT
ejpam-6775	133	1	j.	j.	PROPN
ejpam-6775	133	2	pure	pure	PROPN
ejpam-6775	133	3	appl	appl	PROPN
ejpam-6775	133	4	.	.	PROPN
ejpam-6775	133	5	math	math	PROPN
ejpam-6775	133	6	,	,	PUNCT
ejpam-6775	133	7	18	18	NUM
ejpam-6775	133	8	(	(	PUNCT
ejpam-6775	133	9	4	4	NUM
ejpam-6775	133	10	)	)	PUNCT
ejpam-6775	133	11	(	(	PUNCT
ejpam-6775	133	12	2025	2025	NUM
ejpam-6775	133	13	)	)	PUNCT
ejpam-6775	133	14	,	,	PUNCT
ejpam-6775	133	15	6775	6775	NUM
ejpam-6775	133	16	7	7	NUM
ejpam-6775	133	17	of	of	ADP
ejpam-6775	133	18	32	32	NUM
ejpam-6775	133	19	v	v	NOUN
ejpam-6775	133	20	(	(	PUNCT
ejpam-6775	133	21	t	t	NOUN
ejpam-6775	133	22	)	)	PUNCT
ejpam-6775	133	23	=	=	SYM
ejpam-6775	134	1	v0h	v0h	X
ejpam-6775	134	2	(	(	PUNCT
ejpam-6775	134	3	2	2	NUM
ejpam-6775	134	4	)	)	PUNCT
ejpam-6775	134	5	r	r	NOUN
ejpam-6775	134	6	(	(	PUNCT
ejpam-6775	134	7	t	t	PROPN
ejpam-6775	134	8	)	)	PUNCT
ejpam-6775	135	1	+	+	CCONJ
ejpam-6775	135	2	∫	∫	PROPN
ejpam-6775	135	3	t	t	NOUN
ejpam-6775	135	4	0	0	NUM
ejpam-6775	135	5	ξr(s)h(2)r	ξr(s)h(2)r	PROPN
ejpam-6775	135	6	(	(	PUNCT
ejpam-6775	135	7	t)dσ	t)dσ	PROPN
ejpam-6775	135	8	;	;	PUNCT
ejpam-6775	135	9	(	(	PUNCT
ejpam-6775	135	10	9	9	X
ejpam-6775	135	11	)	)	PUNCT
ejpam-6775	135	12	i(t)(θ	i(t)(θ	X
ejpam-6775	135	13	)	)	PUNCT
ejpam-6775	135	14	=	=	SYM
ejpam-6775	136	1	i0(θ	i0(θ	PROPN
ejpam-6775	136	2	−	−	PROPN
ejpam-6775	136	3	t	t	PROPN
ejpam-6775	136	4	)	)	PUNCT
ejpam-6775	136	5	πα(0	πα(0	PROPN
ejpam-6775	136	6	,	,	PUNCT
ejpam-6775	136	7	t	t	PROPN
ejpam-6775	136	8	)	)	PUNCT
ejpam-6775	136	9	πα(t−	πα(t−	PROPN
ejpam-6775	137	1	t	t	X
ejpam-6775	137	2	)	)	PUNCT
ejpam-6775	137	3	1{θ	1{θ	NUM
ejpam-6775	137	4	>	>	SYM
ejpam-6775	137	5	t	t	PROPN
ejpam-6775	137	6	}	}	PUNCT
ejpam-6775	137	7	+	+	NUM
ejpam-6775	137	8	i(t−	i(t−	PROPN
ejpam-6775	137	9	θ	θ	NOUN
ejpam-6775	137	10	,	,	PUNCT
ejpam-6775	137	11	0)πα(t	0)πα(t	NOUN
ejpam-6775	137	12	,	,	PUNCT
ejpam-6775	137	13	0)1{θ≤t	0)1{θ≤t	NUM
ejpam-6775	137	14	}	}	PUNCT
ejpam-6775	137	15	.	.	PUNCT
ejpam-6775	138	1	(	(	PUNCT
ejpam-6775	138	2	10	10	NUM
ejpam-6775	138	3	)	)	PUNCT
ejpam-6775	138	4	from	from	ADP
ejpam-6775	138	5	the	the	DET
ejpam-6775	138	6	above	above	ADJ
ejpam-6775	138	7	representation	representation	NOUN
ejpam-6775	138	8	of	of	ADP
ejpam-6775	138	9	solutions	solution	NOUN
ejpam-6775	138	10	of	of	ADP
ejpam-6775	138	11	system	system	NOUN
ejpam-6775	138	12	(	(	PUNCT
ejpam-6775	138	13	31	31	NUM
ejpam-6775	138	14	)	)	PUNCT
ejpam-6775	138	15	and	and	CCONJ
ejpam-6775	138	16	using	use	VERB
ejpam-6775	138	17	the	the	DET
ejpam-6775	138	18	lipschitz	lipschitz	NOUN
ejpam-6775	138	19	properties	property	NOUN
ejpam-6775	138	20	of	of	ADP
ejpam-6775	138	21	the	the	DET
ejpam-6775	138	22	functions	function	NOUN
ejpam-6775	138	23	h	h	NOUN
ejpam-6775	138	24	(	(	PUNCT
ejpam-6775	138	25	1	1	X
ejpam-6775	138	26	)	)	PUNCT
ejpam-6775	138	27	r	r	NOUN
ejpam-6775	138	28	and	and	CCONJ
ejpam-6775	138	29	h	h	NOUN
ejpam-6775	138	30	(	(	PUNCT
ejpam-6775	138	31	2	2	X
ejpam-6775	138	32	)	)	PUNCT
ejpam-6775	138	33	r	r	NOUN
ejpam-6775	138	34	for	for	ADP
ejpam-6775	138	35	all	all	DET
ejpam-6775	138	36	r	r	NOUN
ejpam-6775	138	37	≥	≥	NOUN
ejpam-6775	138	38	0	0	NUM
ejpam-6775	138	39	,	,	PUNCT
ejpam-6775	138	40	the	the	DET
ejpam-6775	138	41	proof	proof	NOUN
ejpam-6775	138	42	of	of	ADP
ejpam-6775	138	43	these	these	DET
ejpam-6775	138	44	estimates	estimate	NOUN
ejpam-6775	138	45	follow	follow	VERB
ejpam-6775	138	46	similarly	similarly	ADV
ejpam-6775	138	47	as	as	ADP
ejpam-6775	138	48	in	in	ADP
ejpam-6775	138	49	the	the	DET
ejpam-6775	138	50	corresponding	corresponding	ADJ
ejpam-6775	138	51	result	result	NOUN
ejpam-6775	138	52	found	find	VERB
ejpam-6775	138	53	in	in	ADP
ejpam-6775	138	54	[	[	X
ejpam-6775	138	55	55	55	NUM
ejpam-6775	138	56	,	,	PUNCT
ejpam-6775	138	57	56	56	NUM
ejpam-6775	138	58	]	]	PUNCT
ejpam-6775	138	59	.	.	PUNCT
ejpam-6775	139	1	(	(	PUNCT
ejpam-6775	139	2	ii	ii	NOUN
ejpam-6775	139	3	)	)	PUNCT
ejpam-6775	139	4	follows	follow	VERB
ejpam-6775	139	5	like	like	INTJ
ejpam-6775	139	6	in	in	ADP
ejpam-6775	139	7	item	item	NOUN
ejpam-6775	139	8	(	(	PUNCT
ejpam-6775	139	9	i	i	NOUN
ejpam-6775	139	10	)	)	PUNCT
ejpam-6775	139	11	.	.	PUNCT
ejpam-6775	140	1	(	(	PUNCT
ejpam-6775	140	2	i	i	NOUN
ejpam-6775	140	3	)	)	PUNCT
ejpam-6775	140	4	let	let	VERB
ejpam-6775	140	5	(	(	PUNCT
ejpam-6775	140	6	ξn	ξn	NOUN
ejpam-6775	140	7	,	,	PUNCT
ejpam-6775	140	8	αn	αn	NOUN
ejpam-6775	140	9	)	)	PUNCT
ejpam-6775	140	10	→	→	SYM
ejpam-6775	140	11	(	(	PUNCT
ejpam-6775	140	12	ξ	ξ	PROPN
ejpam-6775	140	13	,	,	PUNCT
ejpam-6775	140	14	α	α	NOUN
ejpam-6775	140	15	)	)	PUNCT
ejpam-6775	140	16	as	as	ADP
ejpam-6775	140	17	n→	n→	PROPN
ejpam-6775	140	18	∞	∞	PROPN
ejpam-6775	140	19	,	,	PUNCT
ejpam-6775	140	20	(	(	PUNCT
ejpam-6775	140	21	sn	sn	INTJ
ejpam-6775	140	22	,	,	PUNCT
ejpam-6775	140	23	vn	vn	NOUN
ejpam-6775	140	24	,	,	PUNCT
ejpam-6775	140	25	in	in	ADV
ejpam-6775	140	26	)	)	PUNCT
ejpam-6775	140	27	be	be	AUX
ejpam-6775	140	28	the	the	DET
ejpam-6775	140	29	state	state	NOUN
ejpam-6775	140	30	of	of	ADP
ejpam-6775	140	31	system	system	NOUN
ejpam-6775	140	32	(	(	PUNCT
ejpam-6775	140	33	31	31	NUM
ejpam-6775	140	34	)	)	PUNCT
ejpam-6775	140	35	corresponding	correspond	VERB
ejpam-6775	140	36	to	to	ADP
ejpam-6775	140	37	(	(	PUNCT
ejpam-6775	140	38	ξn	ξn	PROPN
ejpam-6775	140	39	,	,	PUNCT
ejpam-6775	140	40	αn	αn	NOUN
ejpam-6775	140	41	)	)	PUNCT
ejpam-6775	140	42	and	and	CCONJ
ejpam-6775	140	43	(	(	PUNCT
ejpam-6775	140	44	s	s	X
ejpam-6775	140	45	,	,	PUNCT
ejpam-6775	140	46	v	v	NOUN
ejpam-6775	140	47	,	,	PUNCT
ejpam-6775	140	48	i	i	NOUN
ejpam-6775	140	49	)	)	PUNCT
ejpam-6775	140	50	,	,	PUNCT
ejpam-6775	140	51	respectively	respectively	ADV
ejpam-6775	140	52	.	.	PUNCT
ejpam-6775	141	1	by	by	ADP
ejpam-6775	141	2	riesz	riesz	PROPN
ejpam-6775	141	3	theorem	theorem	PROPN
ejpam-6775	141	4	,	,	PUNCT
ejpam-6775	141	5	there	there	PRON
ejpam-6775	141	6	is	be	VERB
ejpam-6775	141	7	a	a	DET
ejpam-6775	141	8	subsequence	subsequence	NOUN
ejpam-6775	141	9	still	still	ADV
ejpam-6775	141	10	denoted	denote	VERB
ejpam-6775	141	11	(	(	PUNCT
ejpam-6775	141	12	ξn	ξn	NOUN
ejpam-6775	141	13	,	,	PUNCT
ejpam-6775	141	14	αn	αn	NOUN
ejpam-6775	141	15	)	)	PUNCT
ejpam-6775	141	16	,	,	PUNCT
ejpam-6775	141	17	such	such	ADJ
ejpam-6775	141	18	that	that	SCONJ
ejpam-6775	141	19	(	(	PUNCT
ejpam-6775	141	20	ξ2n	ξ2n	PROPN
ejpam-6775	141	21	,	,	PUNCT
ejpam-6775	141	22	α	α	PROPN
ejpam-6775	141	23	2	2	NUM
ejpam-6775	141	24	n	n	CCONJ
ejpam-6775	141	25	)	)	PUNCT
ejpam-6775	141	26	→	→	SYM
ejpam-6775	141	27	(	(	PUNCT
ejpam-6775	141	28	ξ2	ξ2	ADJ
ejpam-6775	141	29	,	,	PUNCT
ejpam-6775	141	30	α2	α2	ADJ
ejpam-6775	141	31	)	)	PUNCT
ejpam-6775	141	32	almost	almost	ADV
ejpam-6775	141	33	everywhere	everywhere	ADV
ejpam-6775	141	34	in	in	ADP
ejpam-6775	141	35	[	[	X
ejpam-6775	141	36	0	0	NUM
ejpam-6775	141	37	,	,	PUNCT
ejpam-6775	141	38	t	t	X
ejpam-6775	141	39	]	]	PUNCT
ejpam-6775	141	40	×	×	PROPN
ejpam-6775	141	41	q	q	PUNCT
ejpam-6775	141	42	as	as	ADP
ejpam-6775	141	43	n→	n→	PROPN
ejpam-6775	141	44	∞.	∞.	PROPN
ejpam-6775	141	45	thus	thus	ADV
ejpam-6775	141	46	,	,	PUNCT
ejpam-6775	141	47	lebesgue	lebesgue	PROPN
ejpam-6775	141	48	’s	’s	PART
ejpam-6775	141	49	dominated	dominate	VERB
ejpam-6775	141	50	convergence	convergence	NOUN
ejpam-6775	141	51	theorem	theorem	VERB
ejpam-6775	141	52	yields	yield	NOUN
ejpam-6775	141	53	that	that	PRON
ejpam-6775	141	54	∥ξn∥2l2(0,t	∥ξn∥2l2(0,t	VERB
ejpam-6775	141	55	)	)	PUNCT
ejpam-6775	141	56	→	→	SYM
ejpam-6775	141	57	∥ξ∥2l2(0,t	∥ξ∥2l2(0,t	NOUN
ejpam-6775	141	58	)	)	PUNCT
ejpam-6775	141	59	and	and	CCONJ
ejpam-6775	141	60	∥αn∥2l2(q	∥αn∥2l2(q	NUM
ejpam-6775	141	61	)	)	PUNCT
ejpam-6775	141	62	→	→	PUNCT
ejpam-6775	141	63	∥α∥2l2(q	∥α∥2l2(q	NOUN
ejpam-6775	141	64	)	)	PUNCT
ejpam-6775	141	65	as	as	ADP
ejpam-6775	141	66	n→	n→	PUNCT
ejpam-6775	141	67	∞.	∞.	PROPN
ejpam-6775	141	68	on	on	ADP
ejpam-6775	141	69	the	the	DET
ejpam-6775	141	70	other	other	ADJ
ejpam-6775	141	71	hand	hand	NOUN
ejpam-6775	141	72	,	,	PUNCT
ejpam-6775	141	73	it	it	PRON
ejpam-6775	141	74	follows	follow	VERB
ejpam-6775	141	75	that	that	SCONJ
ejpam-6775	141	76	∫	∫	PROPN
ejpam-6775	141	77	q	q	NOUN
ejpam-6775	141	78	χ(θ)hn(t	χ(θ)hn(t	PROPN
ejpam-6775	141	79	,	,	PUNCT
ejpam-6775	141	80	θ)dθ	θ)dθ	PROPN
ejpam-6775	141	81	→	→	SYM
ejpam-6775	141	82	∫	∫	PROPN
ejpam-6775	141	83	q	q	X
ejpam-6775	141	84	χ(θ)i(t	χ(θ)i(t	NOUN
ejpam-6775	141	85	,	,	PUNCT
ejpam-6775	141	86	θ)dθ	θ)dθ	PROPN
ejpam-6775	141	87	as	as	ADP
ejpam-6775	141	88	n→	n→	PUNCT
ejpam-6775	141	89	∞.	∞.	PROPN
ejpam-6775	141	90	by	by	ADP
ejpam-6775	141	91	fatou	fatou	PROPN
ejpam-6775	141	92	’s	’s	PART
ejpam-6775	141	93	lemma	lemma	PROPN
ejpam-6775	141	94	,	,	PUNCT
ejpam-6775	141	95	it	it	PRON
ejpam-6775	141	96	follows	follow	VERB
ejpam-6775	141	97	that	that	SCONJ
ejpam-6775	141	98	h(ξ	h(ξ	PROPN
ejpam-6775	141	99	,	,	PUNCT
ejpam-6775	141	100	α	α	NOUN
ejpam-6775	141	101	)	)	PUNCT
ejpam-6775	141	102	≤	≤	PROPN
ejpam-6775	141	103	lim	lim	PROPN
ejpam-6775	141	104	infn→∞	infn→∞	PROPN
ejpam-6775	141	105	h(ξn	h(ξn	ADJ
ejpam-6775	141	106	,	,	PUNCT
ejpam-6775	141	107	αn	αn	NOUN
ejpam-6775	141	108	)	)	PUNCT
ejpam-6775	141	109	.	.	PUNCT
ejpam-6775	142	1	hence	hence	ADV
ejpam-6775	142	2	,	,	PUNCT
ejpam-6775	142	3	the	the	DET
ejpam-6775	142	4	functional	functional	ADJ
ejpam-6775	142	5	h	h	NOUN
ejpam-6775	142	6	(	(	PUNCT
ejpam-6775	142	7	.	.	PUNCT
ejpam-6775	142	8	,	,	PUNCT
ejpam-6775	142	9	.	.	PUNCT
ejpam-6775	142	10	)	)	PUNCT
ejpam-6775	142	11	is	be	AUX
ejpam-6775	142	12	lower	low	ADJ
ejpam-6775	142	13	semi	semi	ADJ
ejpam-6775	142	14	–	–	NOUN
ejpam-6775	142	15	continuous	continuous	ADJ
ejpam-6775	142	16	.	.	PUNCT
ejpam-6775	143	1	this	this	PRON
ejpam-6775	143	2	achieves	achieve	VERB
ejpam-6775	143	3	the	the	DET
ejpam-6775	143	4	proof	proof	NOUN
ejpam-6775	143	5	4	4	NUM
ejpam-6775	143	6	.	.	PUNCT
ejpam-6775	144	1	analysis	analysis	NOUN
ejpam-6775	144	2	of	of	ADP
ejpam-6775	144	3	the	the	DET
ejpam-6775	144	4	svi	svi	PROPN
ejpam-6775	144	5	model	model	NOUN
ejpam-6775	144	6	this	this	DET
ejpam-6775	144	7	section	section	NOUN
ejpam-6775	144	8	is	be	AUX
ejpam-6775	144	9	devoted	devote	VERB
ejpam-6775	144	10	to	to	ADP
ejpam-6775	144	11	the	the	DET
ejpam-6775	144	12	main	main	ADJ
ejpam-6775	144	13	results	result	NOUN
ejpam-6775	144	14	of	of	ADP
ejpam-6775	144	15	this	this	DET
ejpam-6775	144	16	manuscript	manuscript	NOUN
ejpam-6775	144	17	about	about	ADP
ejpam-6775	144	18	the	the	DET
ejpam-6775	144	19	qualitative	qualitative	ADJ
ejpam-6775	144	20	analysis	analysis	NOUN
ejpam-6775	144	21	of	of	ADP
ejpam-6775	144	22	system	system	NOUN
ejpam-6775	144	23	(	(	PUNCT
ejpam-6775	144	24	1	1	NUM
ejpam-6775	144	25	)	)	PUNCT
ejpam-6775	144	26	.	.	PUNCT
ejpam-6775	145	1	these	these	PRON
ejpam-6775	145	2	include	include	VERB
ejpam-6775	145	3	the	the	DET
ejpam-6775	145	4	well	well	NOUN
ejpam-6775	145	5	-	-	PUNCT
ejpam-6775	145	6	posedness	posedness	NOUN
ejpam-6775	145	7	of	of	ADP
ejpam-6775	145	8	the	the	DET
ejpam-6775	145	9	model	model	NOUN
ejpam-6775	145	10	,	,	PUNCT
ejpam-6775	145	11	as	as	ADV
ejpam-6775	145	12	well	well	ADV
ejpam-6775	145	13	as	as	ADP
ejpam-6775	145	14	the	the	DET
ejpam-6775	145	15	existence	existence	NOUN
ejpam-6775	145	16	and	and	CCONJ
ejpam-6775	145	17	stability	stability	NOUN
ejpam-6775	145	18	of	of	ADP
ejpam-6775	145	19	equilibrium	equilibrium	NOUN
ejpam-6775	145	20	.	.	PUNCT
ejpam-6775	146	1	before	before	ADP
ejpam-6775	146	2	stating	state	VERB
ejpam-6775	146	3	our	our	PRON
ejpam-6775	146	4	results	result	NOUN
ejpam-6775	146	5	,	,	PUNCT
ejpam-6775	146	6	we	we	PRON
ejpam-6775	146	7	make	make	VERB
ejpam-6775	146	8	the	the	DET
ejpam-6775	146	9	following	follow	VERB
ejpam-6775	146	10	realistic	realistic	ADJ
ejpam-6775	146	11	assumptions	assumption	NOUN
ejpam-6775	146	12	on	on	ADP
ejpam-6775	146	13	the	the	DET
ejpam-6775	146	14	positivity	positivity	NOUN
ejpam-6775	146	15	of	of	ADP
ejpam-6775	146	16	the	the	DET
ejpam-6775	146	17	parameters	parameter	NOUN
ejpam-6775	146	18	and	and	CCONJ
ejpam-6775	146	19	functions	function	NOUN
ejpam-6775	146	20	involved	involve	VERB
ejpam-6775	146	21	in	in	ADP
ejpam-6775	146	22	system	system	NOUN
ejpam-6775	146	23	(	(	PUNCT
ejpam-6775	146	24	1	1	NUM
ejpam-6775	146	25	)	)	PUNCT
ejpam-6775	146	26	.	.	PUNCT
ejpam-6775	147	1	more	more	ADV
ejpam-6775	147	2	precisely	precisely	ADV
ejpam-6775	147	3	,	,	PUNCT
ejpam-6775	147	4	we	we	PRON
ejpam-6775	147	5	assume	assume	VERB
ejpam-6775	147	6	that	that	SCONJ
ejpam-6775	147	7	assumption	assumption	NOUN
ejpam-6775	147	8	:	:	PUNCT
ejpam-6775	147	9	the	the	DET
ejpam-6775	147	10	parameters	parameter	NOUN
ejpam-6775	147	11	λ	λ	PROPN
ejpam-6775	147	12	,	,	PUNCT
ejpam-6775	147	13	ξ	ξ	PROPN
ejpam-6775	147	14	,	,	PUNCT
ejpam-6775	147	15	µ,m	µ,m	PRON
ejpam-6775	147	16	are	be	AUX
ejpam-6775	147	17	all	all	PRON
ejpam-6775	147	18	positives	positive	NOUN
ejpam-6775	147	19	and	and	CCONJ
ejpam-6775	147	20	initial	initial	ADJ
ejpam-6775	147	21	conditions	condition	NOUN
ejpam-6775	147	22	s(0	s(0	PROPN
ejpam-6775	147	23	)	)	PUNCT
ejpam-6775	147	24	and	and	CCONJ
ejpam-6775	147	25	v	v	NOUN
ejpam-6775	147	26	(	(	PUNCT
ejpam-6775	147	27	0	0	NUM
ejpam-6775	147	28	)	)	PUNCT
ejpam-6775	147	29	are	be	AUX
ejpam-6775	147	30	nonnegative	nonnegative	ADJ
ejpam-6775	147	31	.	.	PUNCT
ejpam-6775	148	1	moreover	moreover	ADV
ejpam-6775	148	2	,	,	PUNCT
ejpam-6775	148	3	the	the	DET
ejpam-6775	148	4	functions	function	NOUN
ejpam-6775	148	5	α	α	X
ejpam-6775	148	6	(	(	PUNCT
ejpam-6775	148	7	.	.	PUNCT
ejpam-6775	148	8	)	)	PUNCT
ejpam-6775	148	9	,	,	PUNCT
ejpam-6775	148	10	β	β	X
ejpam-6775	148	11	(	(	PUNCT
ejpam-6775	148	12	.	.	PUNCT
ejpam-6775	148	13	)	)	PUNCT
ejpam-6775	148	14	and	and	CCONJ
ejpam-6775	148	15	δ	δ	PROPN
ejpam-6775	148	16	(	(	PUNCT
ejpam-6775	148	17	.	.	PUNCT
ejpam-6775	148	18	)	)	PUNCT
ejpam-6775	148	19	belong	belong	VERB
ejpam-6775	148	20	in	in	ADP
ejpam-6775	148	21	l∞(0,∞	l∞(0,∞	PROPN
ejpam-6775	148	22	)	)	PUNCT
ejpam-6775	148	23	,	,	PUNCT
ejpam-6775	148	24	and	and	CCONJ
ejpam-6775	148	25	the	the	DET
ejpam-6775	148	26	boundary	boundary	ADJ
ejpam-6775	148	27	condition	condition	NOUN
ejpam-6775	148	28	i(0	i(0	PROPN
ejpam-6775	148	29	,	,	PUNCT
ejpam-6775	148	30	.	.	PUNCT
ejpam-6775	148	31	)	)	PUNCT
ejpam-6775	149	1	=	=	SYM
ejpam-6775	149	2	i0	i0	PROPN
ejpam-6775	149	3	(	(	PUNCT
ejpam-6775	149	4	.	.	PUNCT
ejpam-6775	149	5	)	)	PUNCT
ejpam-6775	150	1	∈	∈	PROPN
ejpam-6775	150	2	l1	l1	PROPN
ejpam-6775	150	3	+	+	PROPN
ejpam-6775	150	4	(	(	PUNCT
ejpam-6775	150	5	0,∞	0,∞	NUM
ejpam-6775	150	6	)	)	PUNCT
ejpam-6775	150	7	.	.	PUNCT
ejpam-6775	151	1	here	here	ADV
ejpam-6775	151	2	l1	l1	PROPN
ejpam-6775	151	3	+	+	PROPN
ejpam-6775	151	4	(	(	PUNCT
ejpam-6775	151	5	0,∞	0,∞	NOUN
ejpam-6775	151	6	)	)	PUNCT
ejpam-6775	151	7	with	with	ADP
ejpam-6775	151	8	1	1	NUM
ejpam-6775	151	9	≤	≤	NOUN
ejpam-6775	151	10	p	p	NOUN
ejpam-6775	151	11	≤	≤	NUM
ejpam-6775	151	12	∞	∞	NUM
ejpam-6775	151	13	denotes	denote	VERB
ejpam-6775	151	14	the	the	DET
ejpam-6775	151	15	space	space	NOUN
ejpam-6775	151	16	of	of	ADP
ejpam-6775	151	17	nonnegative	nonnegative	ADJ
ejpam-6775	151	18	functions	function	NOUN
ejpam-6775	151	19	in	in	ADP
ejpam-6775	151	20	lp(0,∞	lp(0,∞	NOUN
ejpam-6775	151	21	)	)	PUNCT
ejpam-6775	151	22	.	.	PUNCT
ejpam-6775	152	1	4.1	4.1	NUM
ejpam-6775	152	2	.	.	PUNCT
ejpam-6775	152	3	existence	existence	NOUN
ejpam-6775	152	4	and	and	CCONJ
ejpam-6775	152	5	uniqueness	uniqueness	NOUN
ejpam-6775	152	6	of	of	ADP
ejpam-6775	152	7	solutions	solution	NOUN
ejpam-6775	152	8	since	since	SCONJ
ejpam-6775	152	9	the	the	DET
ejpam-6775	152	10	system	system	NOUN
ejpam-6775	152	11	(	(	PUNCT
ejpam-6775	152	12	1	1	X
ejpam-6775	152	13	)	)	PUNCT
ejpam-6775	152	14	has	have	VERB
ejpam-6775	152	15	a	a	DET
ejpam-6775	152	16	nonlinear	nonlinear	ADJ
ejpam-6775	152	17	initial	initial	ADJ
ejpam-6775	152	18	condition	condition	NOUN
ejpam-6775	152	19	on	on	ADP
ejpam-6775	152	20	the	the	DET
ejpam-6775	152	21	variable	variable	ADJ
ejpam-6775	152	22	i	i	NOUN
ejpam-6775	152	23	(	(	PUNCT
ejpam-6775	152	24	.	.	PUNCT
ejpam-6775	152	25	,	,	PUNCT
ejpam-6775	152	26	x	x	X
ejpam-6775	152	27	)	)	PUNCT
ejpam-6775	152	28	,	,	PUNCT
ejpam-6775	152	29	we	we	PRON
ejpam-6775	152	30	use	use	VERB
ejpam-6775	152	31	the	the	DET
ejpam-6775	152	32	integrated	integrate	VERB
ejpam-6775	152	33	semigroup	semigroup	PROPN
ejpam-6775	152	34	theory	theory	NOUN
ejpam-6775	152	35	introduced	introduce	VERB
ejpam-6775	152	36	recently	recently	ADV
ejpam-6775	152	37	by	by	ADP
ejpam-6775	152	38	thieme	thieme	NOUN
ejpam-6775	152	39	[	[	X
ejpam-6775	152	40	37	37	NUM
ejpam-6775	152	41	]	]	PUNCT
ejpam-6775	152	42	in	in	ADP
ejpam-6775	152	43	the	the	DET
ejpam-6775	152	44	context	context	NOUN
ejpam-6775	152	45	of	of	ADP
ejpam-6775	152	46	agestructured	agestructure	VERB
ejpam-6775	152	47	models	model	NOUN
ejpam-6775	152	48	to	to	PART
ejpam-6775	152	49	establish	establish	VERB
ejpam-6775	152	50	the	the	DET
ejpam-6775	152	51	well	well	NOUN
ejpam-6775	152	52	-	-	PUNCT
ejpam-6775	152	53	posedness	posedness	NOUN
ejpam-6775	152	54	of	of	ADP
ejpam-6775	152	55	the	the	DET
ejpam-6775	152	56	model	model	NOUN
ejpam-6775	152	57	.	.	PUNCT
ejpam-6775	153	1	it	it	PRON
ejpam-6775	153	2	consists	consist	VERB
ejpam-6775	153	3	of	of	ADP
ejpam-6775	153	4	removing	remove	VERB
ejpam-6775	153	5	the	the	DET
ejpam-6775	153	6	nonlinearity	nonlinearity	NOUN
ejpam-6775	153	7	from	from	ADP
ejpam-6775	153	8	the	the	DET
ejpam-6775	153	9	domain	domain	NOUN
ejpam-6775	153	10	and	and	CCONJ
ejpam-6775	153	11	incorporates	incorporate	VERB
ejpam-6775	153	12	it	it	PRON
ejpam-6775	153	13	into	into	ADP
ejpam-6775	153	14	the	the	DET
ejpam-6775	153	15	lipschitz	lipschitz	ADJ
ejpam-6775	153	16	continuous	continuous	ADJ
ejpam-6775	153	17	perturbation	perturbation	NOUN
ejpam-6775	153	18	function	function	NOUN
ejpam-6775	153	19	.	.	PUNCT
ejpam-6775	154	1	let	let	VERB
ejpam-6775	154	2	us	we	PRON
ejpam-6775	154	3	introduce	introduce	VERB
ejpam-6775	154	4	the	the	DET
ejpam-6775	154	5	banach	banach	NOUN
ejpam-6775	154	6	space	space	NOUN
ejpam-6775	154	7	x	x	PUNCT
ejpam-6775	155	1	=	=	PUNCT
ejpam-6775	155	2	r	r	NOUN
ejpam-6775	155	3	×	×	NOUN
ejpam-6775	155	4	r	r	NOUN
ejpam-6775	155	5	×	×	NOUN
ejpam-6775	155	6	l1(0,∞	l1(0,∞	NUM
ejpam-6775	155	7	)	)	PUNCT
ejpam-6775	155	8	×	×	NOUN
ejpam-6775	155	9	r	r	NOUN
ejpam-6775	155	10	endowed	endow	VERB
ejpam-6775	155	11	with	with	ADP
ejpam-6775	155	12	the	the	DET
ejpam-6775	155	13	usual	usual	ADJ
ejpam-6775	155	14	product	product	NOUN
ejpam-6775	155	15	norm	norm	NOUN
ejpam-6775	155	16	.	.	PUNCT
ejpam-6775	156	1	the	the	DET
ejpam-6775	156	2	positive	positive	ADJ
ejpam-6775	156	3	cone	cone	NOUN
ejpam-6775	156	4	of	of	ADP
ejpam-6775	156	5	space	space	NOUN
ejpam-6775	156	6	x	x	PUNCT
ejpam-6775	156	7	is	be	AUX
ejpam-6775	156	8	defined	define	VERB
ejpam-6775	156	9	by	by	ADP
ejpam-6775	156	10	x+	x+	X
ejpam-6775	156	11	=	=	SYM
ejpam-6775	156	12	r+	r+	PUNCT
ejpam-6775	156	13	×	×	NOUN
ejpam-6775	156	14	r+	r+	PUNCT
ejpam-6775	156	15	×	×	PROPN
ejpam-6775	156	16	l1	l1	PROPN
ejpam-6775	156	17	+	+	PROPN
ejpam-6775	156	18	(	(	PUNCT
ejpam-6775	156	19	0,∞	0,∞	NOUN
ejpam-6775	156	20	)	)	PUNCT
ejpam-6775	156	21	×	×	NOUN
ejpam-6775	156	22	r+	r+	NOUN
ejpam-6775	156	23	.	.	PUNCT
ejpam-6775	157	1	we	we	PRON
ejpam-6775	157	2	set	set	VERB
ejpam-6775	157	3	x0	x0	PROPN
ejpam-6775	157	4	=	=	PUNCT
ejpam-6775	158	1	r	r	NOUN
ejpam-6775	158	2	×	×	NOUN
ejpam-6775	158	3	r	r	NOUN
ejpam-6775	158	4	×	×	NOUN
ejpam-6775	158	5	l1(0,∞	l1(0,∞	NUM
ejpam-6775	158	6	)	)	PUNCT
ejpam-6775	158	7	×	×	NOUN
ejpam-6775	158	8	{	{	PUNCT
ejpam-6775	158	9	0	0	NUM
ejpam-6775	158	10	}	}	PUNCT
ejpam-6775	158	11	and	and	CCONJ
ejpam-6775	158	12	denote	denote	VERB
ejpam-6775	158	13	j.	j.	PROPN
ejpam-6775	158	14	leo	leo	PROPN
ejpam-6775	158	15	amalraj	amalraj	PROPN
ejpam-6775	158	16	et	et	PROPN
ejpam-6775	158	17	al	al	PROPN
ejpam-6775	158	18	.	.	PUNCT
ejpam-6775	158	19	/	/	SYM
ejpam-6775	158	20	eur	eur	PROPN
ejpam-6775	158	21	.	.	PUNCT
ejpam-6775	159	1	j.	j.	PROPN
ejpam-6775	159	2	pure	pure	PROPN
ejpam-6775	159	3	appl	appl	PROPN
ejpam-6775	159	4	.	.	PROPN
ejpam-6775	159	5	math	math	PROPN
ejpam-6775	159	6	,	,	PUNCT
ejpam-6775	159	7	18	18	NUM
ejpam-6775	159	8	(	(	PUNCT
ejpam-6775	159	9	4	4	NUM
ejpam-6775	159	10	)	)	PUNCT
ejpam-6775	159	11	(	(	PUNCT
ejpam-6775	159	12	2025	2025	NUM
ejpam-6775	159	13	)	)	PUNCT
ejpam-6775	159	14	,	,	PUNCT
ejpam-6775	159	15	6775	6775	NUM
ejpam-6775	159	16	8	8	NUM
ejpam-6775	159	17	of	of	ADP
ejpam-6775	159	18	32	32	NUM
ejpam-6775	159	19	by	by	ADP
ejpam-6775	159	20	x0	x0	PROPN
ejpam-6775	159	21	+	+	PROPN
ejpam-6775	159	22	=	=	SYM
ejpam-6775	159	23	x0	x0	PROPN
ejpam-6775	159	24	∩	∩	NOUN
ejpam-6775	159	25	x+	x+	PROPN
ejpam-6775	159	26	.	.	PUNCT
ejpam-6775	160	1	the	the	DET
ejpam-6775	160	2	system	system	NOUN
ejpam-6775	160	3	(	(	PUNCT
ejpam-6775	160	4	1	1	X
ejpam-6775	160	5	)	)	PUNCT
ejpam-6775	160	6	can	can	AUX
ejpam-6775	160	7	be	be	AUX
ejpam-6775	160	8	rewritten	rewrite	VERB
ejpam-6775	160	9	in	in	ADP
ejpam-6775	160	10	the	the	DET
ejpam-6775	160	11	following	follow	VERB
ejpam-6775	160	12	abstract	abstract	ADJ
ejpam-6775	160	13	cauchy	cauchy	PROPN
ejpam-6775	160	14	problem	problem	NOUN
ejpam-6775	160	15	:	:	PUNCT
ejpam-6775	160	16	dz(t	dz(t	NOUN
ejpam-6775	160	17	)	)	PUNCT
ejpam-6775	160	18	dt	dt	X
ejpam-6775	160	19	=	=	SYM
ejpam-6775	160	20	az(t	az(t	X
ejpam-6775	160	21	)	)	PUNCT
ejpam-6775	161	1	+	+	NOUN
ejpam-6775	161	2	h(z(t	h(z(t	X
ejpam-6775	161	3	)	)	PUNCT
ejpam-6775	161	4	)	)	PUNCT
ejpam-6775	161	5	,	,	PUNCT
ejpam-6775	161	6	∀t	∀t	PROPN
ejpam-6775	161	7	≥	≥	NOUN
ejpam-6775	161	8	0	0	NUM
ejpam-6775	161	9	,	,	PUNCT
ejpam-6775	161	10	z(0	z(0	X
ejpam-6775	161	11	)	)	PUNCT
ejpam-6775	161	12	=	=	SYM
ejpam-6775	161	13	z0	z0	PROPN
ejpam-6775	161	14	∈	∈	PROPN
ejpam-6775	161	15	x0	x0	PROPN
ejpam-6775	161	16	+	+	PROPN
ejpam-6775	161	17	,	,	PUNCT
ejpam-6775	161	18	(	(	PUNCT
ejpam-6775	161	19	11	11	NUM
ejpam-6775	161	20	)	)	PUNCT
ejpam-6775	161	21	where	where	SCONJ
ejpam-6775	161	22	z(t	z(t	NOUN
ejpam-6775	161	23	)	)	PUNCT
ejpam-6775	161	24	=	=	SYM
ejpam-6775	161	25	(	(	PUNCT
ejpam-6775	161	26	s(t	s(t	PROPN
ejpam-6775	161	27	)	)	PUNCT
ejpam-6775	161	28	,	,	PUNCT
ejpam-6775	161	29	v	v	X
ejpam-6775	161	30	(	(	PUNCT
ejpam-6775	161	31	t	t	PROPN
ejpam-6775	161	32	)	)	PUNCT
ejpam-6775	161	33	,	,	PUNCT
ejpam-6775	161	34	i	i	PRON
ejpam-6775	161	35	(	(	PUNCT
ejpam-6775	161	36	.	.	PROPN
ejpam-6775	161	37	,	,	PUNCT
ejpam-6775	161	38	t	t	PROPN
ejpam-6775	161	39	)	)	PUNCT
ejpam-6775	161	40	,	,	PUNCT
ejpam-6775	161	41	0)t	0)t	NOUN
ejpam-6775	161	42	with	with	ADP
ejpam-6775	161	43	“	"	PUNCT
ejpam-6775	161	44	t	t	PROPN
ejpam-6775	161	45	”	"	PUNCT
ejpam-6775	161	46	denoting	denote	VERB
ejpam-6775	161	47	the	the	DET
ejpam-6775	161	48	transposition	transposition	NOUN
ejpam-6775	161	49	symbol	symbol	NOUN
ejpam-6775	161	50	,	,	PUNCT
ejpam-6775	161	51	the	the	DET
ejpam-6775	161	52	linear	linear	ADJ
ejpam-6775	161	53	differential	differential	NOUN
ejpam-6775	161	54	operator	operator	NOUN
ejpam-6775	161	55	a	a	DET
ejpam-6775	161	56	:	:	PUNCT
ejpam-6775	161	57	d(a	d(a	PROPN
ejpam-6775	161	58	)	)	PUNCT
ejpam-6775	161	59	⊂	⊂	PROPN
ejpam-6775	161	60	x	x	PUNCT
ejpam-6775	162	1	→	→	PUNCT
ejpam-6775	162	2	x	x	NOUN
ejpam-6775	162	3	defined	define	VERB
ejpam-6775	162	4	as	as	SCONJ
ejpam-6775	162	5	follows	follow	VERB
ejpam-6775	162	6	:	:	PUNCT
ejpam-6775	162	7	a	a	DET
ejpam-6775	162	8	sv	sv	PROPN
ejpam-6775	162	9	i	i	PRON
ejpam-6775	162	10			VERB
ejpam-6775	162	11	=	=	SYM
ejpam-6775	162	12			NOUN
ejpam-6775	162	13	−µs	−µs	NOUN
ejpam-6775	162	14	−(µ+	−(µ+	PROPN
ejpam-6775	163	1	ξ)v	ξ)v	PROPN
ejpam-6775	163	2	−i′	−i′	PROPN
ejpam-6775	163	3	−	−	PROPN
ejpam-6775	163	4	pi	pi	NOUN
ejpam-6775	163	5	−i(0	−i(0	NOUN
ejpam-6775	163	6	)	)	PUNCT
ejpam-6775	164	1			NOUN
ejpam-6775	164	2	,	,	PUNCT
ejpam-6775	164	3	(	(	PUNCT
ejpam-6775	164	4	12	12	NUM
ejpam-6775	164	5	)	)	PUNCT
ejpam-6775	164	6	where	where	SCONJ
ejpam-6775	164	7	p(x	p(x	VERB
ejpam-6775	164	8	)	)	PUNCT
ejpam-6775	164	9	=	=	SYM
ejpam-6775	164	10	µ	µ	X
ejpam-6775	164	11	+	+	ADJ
ejpam-6775	164	12	δ(x	δ(x	ADJ
ejpam-6775	164	13	)	)	PUNCT
ejpam-6775	164	14	+	+	NUM
ejpam-6775	164	15	α(x	α(x	NOUN
ejpam-6775	164	16	)	)	PUNCT
ejpam-6775	164	17	,	,	PUNCT
ejpam-6775	164	18	the	the	DET
ejpam-6775	164	19	domain	domain	NOUN
ejpam-6775	164	20	d(a	d(a	PROPN
ejpam-6775	164	21	)	)	PUNCT
ejpam-6775	165	1	=	=	SYM
ejpam-6775	165	2	r	r	NOUN
ejpam-6775	165	3	×	×	NOUN
ejpam-6775	165	4	r	r	NOUN
ejpam-6775	165	5	×w	×w	NOUN
ejpam-6775	165	6	1,1(0,∞	1,1(0,∞	NUM
ejpam-6775	165	7	)	)	PUNCT
ejpam-6775	165	8	×	×	NOUN
ejpam-6775	165	9	{	{	PUNCT
ejpam-6775	165	10	0	0	NUM
ejpam-6775	165	11	}	}	PUNCT
ejpam-6775	165	12	and	and	CCONJ
ejpam-6775	165	13	w	w	ADP
ejpam-6775	165	14	1,1(0,∞	1,1(0,∞	NUM
ejpam-6775	165	15	)	)	PUNCT
ejpam-6775	165	16	=	=	PRON
ejpam-6775	166	1	{	{	PUNCT
ejpam-6775	166	2	f	f	PROPN
ejpam-6775	166	3	∈	∈	PROPN
ejpam-6775	166	4	l1(0,∞	l1(0,∞	NOUN
ejpam-6775	166	5	)	)	PUNCT
ejpam-6775	166	6	:	:	PUNCT
ejpam-6775	166	7	df	df	PROPN
ejpam-6775	166	8	∈	∈	PROPN
ejpam-6775	166	9	l1(0,∞	l1(0,∞	NUM
ejpam-6775	166	10	)	)	PUNCT
ejpam-6775	166	11	,	,	PUNCT
ejpam-6775	166	12	v	v	ADP
ejpam-6775	166	13	|x|≤1	|x|≤1	PROPN
ejpam-6775	166	14	}	}	PUNCT
ejpam-6775	166	15	.	.	PUNCT
ejpam-6775	167	1	the	the	DET
ejpam-6775	167	2	nonlinear	nonlinear	ADJ
ejpam-6775	167	3	map	map	NOUN
ejpam-6775	167	4	h	h	NOUN
ejpam-6775	167	5	:	:	PUNCT
ejpam-6775	167	6	x0	x0	PROPN
ejpam-6775	167	7	→	→	SYM
ejpam-6775	167	8	x−	x−	PROPN
ejpam-6775	167	9	is	be	AUX
ejpam-6775	167	10	defined	define	VERB
ejpam-6775	167	11	by	by	ADP
ejpam-6775	167	12	:	:	PUNCT
ejpam-6775	167	13	h	h	NOUN
ejpam-6775	167	14			NOUN
ejpam-6775	167	15	s	s	VERB
ejpam-6775	167	16	v	v	NOUN
ejpam-6775	167	17	i	i	NOUN
ejpam-6775	167	18	0	0	NUM
ejpam-6775	168	1			NOUN
ejpam-6775	168	2	=	=	SYM
ejpam-6775	168	3			NOUN
ejpam-6775	168	4	λ−	λ−	PROPN
ejpam-6775	168	5	t	t	PROPN
ejpam-6775	168	6	(	(	PUNCT
ejpam-6775	168	7	βi)s	βi)	NOUN
ejpam-6775	168	8	+	+	NUM
ejpam-6775	168	9	t	t	PROPN
ejpam-6775	168	10	(	(	PUNCT
ejpam-6775	168	11	αi	αi	NOUN
ejpam-6775	168	12	)	)	PUNCT
ejpam-6775	169	1	ξs	ξs	VERB
ejpam-6775	169	2	−mt	−mt	X
ejpam-6775	169	3	(	(	PUNCT
ejpam-6775	169	4	βi)v	βi)v	PROPN
ejpam-6775	169	5	0l1(0,∞	0l1(0,∞	NUM
ejpam-6775	169	6	)	)	PUNCT
ejpam-6775	169	7	s	s	PART
ejpam-6775	170	1	+	+	PROPN
ejpam-6775	170	2	mv	mv	PROPN
ejpam-6775	170	3	t	t	PROPN
ejpam-6775	170	4	(	(	PUNCT
ejpam-6775	170	5	βi	βi	NOUN
ejpam-6775	170	6	)	)	PUNCT
ejpam-6775	170	7			NOUN
ejpam-6775	170	8	.	.	PUNCT
ejpam-6775	171	1	(	(	PUNCT
ejpam-6775	171	2	13	13	NUM
ejpam-6775	171	3	)	)	PUNCT
ejpam-6775	171	4	now	now	ADV
ejpam-6775	171	5	,	,	PUNCT
ejpam-6775	171	6	we	we	PRON
ejpam-6775	171	7	are	be	AUX
ejpam-6775	171	8	ready	ready	ADJ
ejpam-6775	171	9	to	to	PART
ejpam-6775	171	10	establish	establish	VERB
ejpam-6775	171	11	the	the	DET
ejpam-6775	171	12	well	well	NOUN
ejpam-6775	171	13	-	-	PUNCT
ejpam-6775	171	14	posedness	posedness	NOUN
ejpam-6775	171	15	of	of	ADP
ejpam-6775	171	16	the	the	DET
ejpam-6775	171	17	system	system	NOUN
ejpam-6775	171	18	(	(	PUNCT
ejpam-6775	171	19	1	1	X
ejpam-6775	171	20	)	)	PUNCT
ejpam-6775	171	21	which	which	PRON
ejpam-6775	171	22	is	be	AUX
ejpam-6775	171	23	given	give	VERB
ejpam-6775	171	24	by	by	ADP
ejpam-6775	171	25	the	the	DET
ejpam-6775	171	26	following	follow	VERB
ejpam-6775	171	27	result	result	NOUN
ejpam-6775	171	28	:	:	PUNCT
ejpam-6775	171	29	theorem	theorem	NOUN
ejpam-6775	171	30	2	2	NUM
ejpam-6775	171	31	.	.	PUNCT
ejpam-6775	172	1	the	the	DET
ejpam-6775	172	2	system	system	NOUN
ejpam-6775	172	3	(	(	PUNCT
ejpam-6775	172	4	1	1	X
ejpam-6775	172	5	)	)	PUNCT
ejpam-6775	172	6	represented	represent	VERB
ejpam-6775	172	7	by	by	ADP
ejpam-6775	172	8	the	the	DET
ejpam-6775	172	9	abstract	abstract	ADJ
ejpam-6775	172	10	cauchy	cauchy	ADJ
ejpam-6775	172	11	problem	problem	NOUN
ejpam-6775	172	12	(	(	PUNCT
ejpam-6775	172	13	2	2	X
ejpam-6775	172	14	)	)	PUNCT
ejpam-6775	172	15	has	have	VERB
ejpam-6775	172	16	a	a	DET
ejpam-6775	172	17	unique	unique	ADJ
ejpam-6775	172	18	strongly	strongly	ADV
ejpam-6775	172	19	continuous	continuous	ADJ
ejpam-6775	172	20	semiflow	semiflow	ADJ
ejpam-6775	172	21	{	{	PUNCT
ejpam-6775	172	22	φ(t	φ(t	PROPN
ejpam-6775	172	23	,	,	PUNCT
ejpam-6775	172	24	.)}t≥0	.)}t≥0	NOUN
ejpam-6775	172	25	on	on	ADP
ejpam-6775	172	26	x0	x0	PROPN
ejpam-6775	172	27	+	+	PROPN
ejpam-6775	172	28	such	such	ADJ
ejpam-6775	172	29	that	that	PRON
ejpam-6775	172	30	for	for	ADP
ejpam-6775	172	31	each	each	DET
ejpam-6775	172	32	z0	z0	PROPN
ejpam-6775	172	33	∈	∈	PROPN
ejpam-6775	172	34	x0	x0	PROPN
ejpam-6775	173	1	+	+	PROPN
ejpam-6775	173	2	,	,	PUNCT
ejpam-6775	173	3	the	the	DET
ejpam-6775	173	4	map	map	NOUN
ejpam-6775	173	5	z	z	PROPN
ejpam-6775	173	6	(	(	PUNCT
ejpam-6775	173	7	.	.	PUNCT
ejpam-6775	173	8	)	)	PUNCT
ejpam-6775	174	1	∈	∈	PROPN
ejpam-6775	174	2	c([0,∞	c([0,∞	PROPN
ejpam-6775	174	3	)	)	PUNCT
ejpam-6775	174	4	,	,	PUNCT
ejpam-6775	174	5	x0	x0	PROPN
ejpam-6775	174	6	+	+	ADP
ejpam-6775	174	7	)	)	PUNCT
ejpam-6775	174	8	defined	define	VERB
ejpam-6775	174	9	by	by	ADP
ejpam-6775	174	10	z	z	PROPN
ejpam-6775	174	11	(	(	PUNCT
ejpam-6775	174	12	.	.	PUNCT
ejpam-6775	174	13	)	)	PUNCT
ejpam-6775	174	14	:	:	PUNCT
ejpam-6775	175	1	t	t	PROPN
ejpam-6775	175	2	7→	7→	NUM
ejpam-6775	175	3	z(t	z(t	X
ejpam-6775	175	4	)	)	PUNCT
ejpam-6775	175	5	=	=	SYM
ejpam-6775	175	6	φ(t	φ(t	PROPN
ejpam-6775	175	7	,	,	PUNCT
ejpam-6775	175	8	z0	z0	PROPN
ejpam-6775	175	9	)	)	PUNCT
ejpam-6775	175	10	is	be	AUX
ejpam-6775	175	11	an	an	DET
ejpam-6775	175	12	integrated	integrate	VERB
ejpam-6775	175	13	(	(	PUNCT
ejpam-6775	175	14	or	or	CCONJ
ejpam-6775	175	15	mild	mild	ADJ
ejpam-6775	175	16	)	)	PUNCT
ejpam-6775	175	17	solution	solution	NOUN
ejpam-6775	175	18	of	of	ADP
ejpam-6775	175	19	system	system	NOUN
ejpam-6775	175	20	(	(	PUNCT
ejpam-6775	175	21	4	4	X
ejpam-6775	175	22	)	)	PUNCT
ejpam-6775	175	23	satisfying	satisfy	VERB
ejpam-6775	175	24	∫	∫	PROPN
ejpam-6775	175	25	t	t	PROPN
ejpam-6775	175	26	0	0	PUNCT
ejpam-6775	175	27	z(s)ds	z(s)ds	PROPN
ejpam-6775	175	28	∈	∈	PROPN
ejpam-6775	175	29	x0	x0	PROPN
ejpam-6775	175	30	for	for	ADP
ejpam-6775	175	31	all	all	DET
ejpam-6775	175	32	t	t	PROPN
ejpam-6775	175	33	≥	≥	NOUN
ejpam-6775	175	34	0	0	NUM
ejpam-6775	175	35	and	and	CCONJ
ejpam-6775	175	36	z(t	z(t	NOUN
ejpam-6775	175	37	)	)	PUNCT
ejpam-6775	176	1	=	=	SYM
ejpam-6775	176	2	z0	z0	PROPN
ejpam-6775	176	3	+	+	CCONJ
ejpam-6775	176	4	∫	∫	PROPN
ejpam-6775	176	5	t	t	PROPN
ejpam-6775	176	6	0	0	NUM
ejpam-6775	176	7	az(s)ds+∫	az(s)ds+∫	NOUN
ejpam-6775	176	8	t	t	PROPN
ejpam-6775	176	9	0	0	NUM
ejpam-6775	176	10	f	f	PROPN
ejpam-6775	176	11	(	(	PUNCT
ejpam-6775	176	12	z(s))ds	z(s))d	VERB
ejpam-6775	176	13	.	.	PUNCT
ejpam-6775	177	1	in	in	ADP
ejpam-6775	177	2	addition	addition	NOUN
ejpam-6775	177	3	,	,	PUNCT
ejpam-6775	177	4	the	the	DET
ejpam-6775	177	5	non	non	ADJ
ejpam-6775	177	6	-	-	ADJ
ejpam-6775	177	7	empty	empty	ADJ
ejpam-6775	177	8	domain	domain	NOUN
ejpam-6775	177	9	ω	ω	NOUN
ejpam-6775	177	10	=	=	SYM
ejpam-6775	177	11	{	{	PUNCT
ejpam-6775	177	12	(	(	PUNCT
ejpam-6775	177	13	s	s	PROPN
ejpam-6775	177	14	,	,	PUNCT
ejpam-6775	177	15	v	v	NOUN
ejpam-6775	177	16	,	,	PUNCT
ejpam-6775	177	17	i	i	PRON
ejpam-6775	177	18	,	,	PUNCT
ejpam-6775	177	19	0	0	NUM
ejpam-6775	177	20	)	)	PUNCT
ejpam-6775	177	21	:	:	PUNCT
ejpam-6775	177	22	s(t	s(t	PROPN
ejpam-6775	177	23	)	)	PUNCT
ejpam-6775	177	24	+	+	X
ejpam-6775	177	25	v	v	X
ejpam-6775	177	26	(	(	PUNCT
ejpam-6775	177	27	t	t	PROPN
ejpam-6775	177	28	)	)	PUNCT
ejpam-6775	178	1	+	+	NOUN
ejpam-6775	178	2	t	t	PROPN
ejpam-6775	178	3	(	(	PUNCT
ejpam-6775	178	4	i	i	NOUN
ejpam-6775	178	5	(	(	PUNCT
ejpam-6775	178	6	.	.	PROPN
ejpam-6775	178	7	,	,	PUNCT
ejpam-6775	178	8	t	t	PROPN
ejpam-6775	178	9	)	)	PUNCT
ejpam-6775	178	10	)	)	PUNCT
ejpam-6775	178	11	≤	≤	PUNCT
ejpam-6775	179	1	λ/µ	λ/µ	X
ejpam-6775	179	2	}	}	PUNCT
ejpam-6775	179	3	,	,	PUNCT
ejpam-6775	179	4	(	(	PUNCT
ejpam-6775	179	5	14	14	NUM
ejpam-6775	179	6	)	)	PUNCT
ejpam-6775	179	7	is	be	AUX
ejpam-6775	179	8	positively	positively	ADV
ejpam-6775	179	9	invariant	invariant	ADJ
ejpam-6775	179	10	and	and	CCONJ
ejpam-6775	179	11	attracts	attract	VERB
ejpam-6775	179	12	all	all	DET
ejpam-6775	179	13	nonnegative	nonnegative	ADJ
ejpam-6775	179	14	solutions	solution	NOUN
ejpam-6775	179	15	.	.	PUNCT
ejpam-6775	180	1	moreover	moreover	ADV
ejpam-6775	180	2	,	,	PUNCT
ejpam-6775	180	3	the	the	DET
ejpam-6775	180	4	semiflow	semiflow	ADJ
ejpam-6775	180	5	{	{	PUNCT
ejpam-6775	180	6	φ(t	φ(t	PROPN
ejpam-6775	180	7	,	,	PUNCT
ejpam-6775	180	8	.)}t≥0	.)}t≥0	PROPN
ejpam-6775	180	9	is	be	AUX
ejpam-6775	180	10	bounded	bounded	ADJ
ejpam-6775	180	11	dissipative	dissipative	NOUN
ejpam-6775	180	12	,	,	PUNCT
ejpam-6775	180	13	that	that	ADV
ejpam-6775	180	14	is	is	ADV
ejpam-6775	180	15	,	,	PUNCT
ejpam-6775	180	16	there	there	PRON
ejpam-6775	180	17	exists	exist	VERB
ejpam-6775	180	18	a	a	DET
ejpam-6775	180	19	bounded	bounded	ADJ
ejpam-6775	180	20	set	set	NOUN
ejpam-6775	180	21	b	b	PROPN
ejpam-6775	180	22	⊂	⊂	X
ejpam-6775	180	23	x0	x0	PROPN
ejpam-6775	180	24	such	such	ADJ
ejpam-6775	180	25	that	that	SCONJ
ejpam-6775	180	26	for	for	ADP
ejpam-6775	180	27	any	any	DET
ejpam-6775	180	28	bounded	bounded	ADJ
ejpam-6775	180	29	set	set	VERB
ejpam-6775	180	30	u	u	PROPN
ejpam-6775	180	31	⊂	⊂	PROPN
ejpam-6775	180	32	x0	x0	PROPN
ejpam-6775	180	33	,	,	PUNCT
ejpam-6775	180	34	we	we	PRON
ejpam-6775	180	35	can	can	AUX
ejpam-6775	180	36	find	find	VERB
ejpam-6775	180	37	t∗	t∗	NOUN
ejpam-6775	180	38	=	=	SYM
ejpam-6775	180	39	κ(u	κ(u	PROPN
ejpam-6775	180	40	,	,	PUNCT
ejpam-6775	180	41	b	b	NOUN
ejpam-6775	180	42	)	)	PUNCT
ejpam-6775	180	43	such	such	ADJ
ejpam-6775	180	44	that	that	SCONJ
ejpam-6775	180	45	φ(t	φ(t	PROPN
ejpam-6775	180	46	,	,	PUNCT
ejpam-6775	180	47	u	u	NOUN
ejpam-6775	180	48	)	)	PUNCT
ejpam-6775	180	49	⊂	⊂	PROPN
ejpam-6775	180	50	b	b	PROPN
ejpam-6775	180	51	for	for	ADP
ejpam-6775	180	52	all	all	DET
ejpam-6775	180	53	t	t	PROPN
ejpam-6775	180	54	≥	≥	NOUN
ejpam-6775	180	55	t∗.	t∗.	PROPN
ejpam-6775	180	56	proof	proof	NOUN
ejpam-6775	180	57	.	.	PUNCT
ejpam-6775	181	1	the	the	DET
ejpam-6775	181	2	existence	existence	NOUN
ejpam-6775	181	3	,	,	PUNCT
ejpam-6775	181	4	uniqueness	uniqueness	NOUN
ejpam-6775	181	5	and	and	CCONJ
ejpam-6775	181	6	positiveness	positiveness	NOUN
ejpam-6775	181	7	of	of	ADP
ejpam-6775	181	8	the	the	DET
ejpam-6775	181	9	integrated	integrate	VERB
ejpam-6775	181	10	solution	solution	NOUN
ejpam-6775	181	11	of	of	ADP
ejpam-6775	181	12	system	system	NOUN
ejpam-6775	181	13	(	(	PUNCT
ejpam-6775	181	14	2	2	X
ejpam-6775	181	15	)	)	PUNCT
ejpam-6775	181	16	can	can	AUX
ejpam-6775	181	17	be	be	AUX
ejpam-6775	181	18	obtained	obtain	VERB
ejpam-6775	181	19	by	by	ADP
ejpam-6775	181	20	applying	apply	VERB
ejpam-6775	181	21	a	a	DET
ejpam-6775	181	22	similar	similar	ADJ
ejpam-6775	181	23	approach	approach	NOUN
ejpam-6775	181	24	as	as	ADP
ejpam-6775	181	25	in	in	ADP
ejpam-6775	181	26	[	[	X
ejpam-6775	181	27	9	9	NUM
ejpam-6775	181	28	,	,	PUNCT
ejpam-6775	181	29	38	38	NUM
ejpam-6775	181	30	,	,	PUNCT
ejpam-6775	181	31	39	39	NUM
ejpam-6775	181	32	]	]	PUNCT
ejpam-6775	181	33	.	.	PUNCT
ejpam-6775	182	1	let	let	VERB
ejpam-6775	182	2	z0	z0	PROPN
ejpam-6775	182	3	∈	∈	PROPN
ejpam-6775	182	4	x0	x0	PROPN
ejpam-6775	183	1	+	+	NOUN
ejpam-6775	183	2	,	,	PUNCT
ejpam-6775	183	3	then	then	ADV
ejpam-6775	183	4	∥φ(t	∥φ(t	NOUN
ejpam-6775	183	5	,	,	PUNCT
ejpam-6775	183	6	z0)∥x	z0)∥x	PROPN
ejpam-6775	183	7	=	=	SYM
ejpam-6775	183	8	s(t	s(t	PROPN
ejpam-6775	183	9	)	)	PUNCT
ejpam-6775	184	1	+	+	X
ejpam-6775	184	2	v	v	X
ejpam-6775	184	3	(	(	PUNCT
ejpam-6775	184	4	t	t	PROPN
ejpam-6775	184	5	)	)	PUNCT
ejpam-6775	185	1	+	+	NOUN
ejpam-6775	185	2	t	t	PROPN
ejpam-6775	185	3	(	(	PUNCT
ejpam-6775	185	4	i	i	NOUN
ejpam-6775	185	5	(	(	PUNCT
ejpam-6775	185	6	.	.	PROPN
ejpam-6775	185	7	,	,	PUNCT
ejpam-6775	185	8	t	t	PROPN
ejpam-6775	185	9	)	)	PUNCT
ejpam-6775	185	10	)	)	PUNCT
ejpam-6775	185	11	.	.	PUNCT
ejpam-6775	186	1	by	by	ADP
ejpam-6775	186	2	integrating	integrate	VERB
ejpam-6775	186	3	the	the	DET
ejpam-6775	186	4	third	third	ADJ
ejpam-6775	186	5	equation	equation	NOUN
ejpam-6775	186	6	of	of	ADP
ejpam-6775	186	7	system	system	NOUN
ejpam-6775	186	8	(	(	PUNCT
ejpam-6775	186	9	1	1	X
ejpam-6775	186	10	)	)	PUNCT
ejpam-6775	186	11	on	on	ADP
ejpam-6775	186	12	r+	r+	NOUN
ejpam-6775	186	13	with	with	ADP
ejpam-6775	186	14	respect	respect	NOUN
ejpam-6775	186	15	to	to	ADP
ejpam-6775	186	16	x	x	PUNCT
ejpam-6775	186	17	and	and	CCONJ
ejpam-6775	186	18	combining	combine	VERB
ejpam-6775	186	19	with	with	ADP
ejpam-6775	186	20	the	the	DET
ejpam-6775	186	21	first	first	ADJ
ejpam-6775	186	22	-	-	PUNCT
ejpam-6775	186	23	second	second	NOUN
ejpam-6775	186	24	equation	equation	NOUN
ejpam-6775	186	25	of	of	ADP
ejpam-6775	186	26	(	(	PUNCT
ejpam-6775	186	27	1	1	NUM
ejpam-6775	186	28	)	)	PUNCT
ejpam-6775	186	29	,	,	PUNCT
ejpam-6775	186	30	one	one	PRON
ejpam-6775	186	31	can	can	AUX
ejpam-6775	186	32	easily	easily	ADV
ejpam-6775	186	33	get	get	VERB
ejpam-6775	186	34	d	d	NOUN
ejpam-6775	186	35	dt	dt	NOUN
ejpam-6775	186	36	∥φ(t	∥φ(t	NOUN
ejpam-6775	186	37	,	,	PUNCT
ejpam-6775	186	38	z0)∥x	z0)∥x	PROPN
ejpam-6775	186	39	≤	≤	NUM
ejpam-6775	187	1	λ−	λ−	PROPN
ejpam-6775	187	2	µ∥φ(t	µ∥φ(t	PROPN
ejpam-6775	187	3	,	,	PUNCT
ejpam-6775	187	4	z0)∥x	z0)∥x	X
ejpam-6775	187	5	.	.	PUNCT
ejpam-6775	188	1	(	(	PUNCT
ejpam-6775	188	2	15	15	NUM
ejpam-6775	188	3	)	)	PUNCT
ejpam-6775	188	4	then	then	ADV
ejpam-6775	188	5	,	,	PUNCT
ejpam-6775	188	6	using	use	VERB
ejpam-6775	188	7	the	the	DET
ejpam-6775	188	8	grönwall	grönwall	NOUN
ejpam-6775	188	9	-	-	PUNCT
ejpam-6775	188	10	bellman	bellman	NOUN
ejpam-6775	188	11	inequality	inequality	NOUN
ejpam-6775	188	12	we	we	PRON
ejpam-6775	188	13	have	have	VERB
ejpam-6775	188	14	j.	j.	PROPN
ejpam-6775	188	15	leo	leo	PROPN
ejpam-6775	188	16	amalraj	amalraj	PROPN
ejpam-6775	188	17	et	et	PROPN
ejpam-6775	188	18	al	al	PROPN
ejpam-6775	188	19	.	.	PUNCT
ejpam-6775	188	20	/	/	SYM
ejpam-6775	188	21	eur	eur	PROPN
ejpam-6775	188	22	.	.	PUNCT
ejpam-6775	189	1	j.	j.	PROPN
ejpam-6775	189	2	pure	pure	PROPN
ejpam-6775	189	3	appl	appl	PROPN
ejpam-6775	189	4	.	.	PROPN
ejpam-6775	189	5	math	math	PROPN
ejpam-6775	189	6	,	,	PUNCT
ejpam-6775	189	7	18	18	NUM
ejpam-6775	189	8	(	(	PUNCT
ejpam-6775	189	9	4	4	NUM
ejpam-6775	189	10	)	)	PUNCT
ejpam-6775	189	11	(	(	PUNCT
ejpam-6775	189	12	2025	2025	NUM
ejpam-6775	189	13	)	)	PUNCT
ejpam-6775	189	14	,	,	PUNCT
ejpam-6775	189	15	6775	6775	NUM
ejpam-6775	189	16	9	9	NUM
ejpam-6775	189	17	of	of	ADP
ejpam-6775	189	18	32	32	NUM
ejpam-6775	189	19	∥φ(t	∥φ(t	NOUN
ejpam-6775	189	20	,	,	PUNCT
ejpam-6775	189	21	z0)∥x	z0)∥x	NUM
ejpam-6775	189	22	≤	≤	PROPN
ejpam-6775	189	23	λ/µ−	λ/µ−	NUM
ejpam-6775	189	24	(	(	PUNCT
ejpam-6775	189	25	λ/µ−	λ/µ−	NUM
ejpam-6775	189	26	∥z0∥x)e−µt	∥z0∥x)e−µt	NOUN
ejpam-6775	189	27	,	,	PUNCT
ejpam-6775	189	28	(	(	PUNCT
ejpam-6775	189	29	16	16	NUM
ejpam-6775	189	30	)	)	PUNCT
ejpam-6775	189	31	which	which	PRON
ejpam-6775	189	32	shows	show	VERB
ejpam-6775	189	33	that	that	SCONJ
ejpam-6775	189	34	φ(t	φ(t	PROPN
ejpam-6775	189	35	,	,	PUNCT
ejpam-6775	189	36	z0	z0	PROPN
ejpam-6775	189	37	)	)	PUNCT
ejpam-6775	189	38	∈	∈	PROPN
ejpam-6775	189	39	ω	ω	PROPN
ejpam-6775	189	40	holds	hold	VERB
ejpam-6775	189	41	for	for	ADP
ejpam-6775	189	42	every	every	DET
ejpam-6775	189	43	solution	solution	NOUN
ejpam-6775	189	44	of	of	ADP
ejpam-6775	189	45	(	(	PUNCT
ejpam-6775	189	46	2	2	X
ejpam-6775	189	47	)	)	PUNCT
ejpam-6775	189	48	satisfying	satisfy	VERB
ejpam-6775	189	49	z0	z0	PROPN
ejpam-6775	189	50	∈	∈	PROPN
ejpam-6775	189	51	ω	ω	PROPN
ejpam-6775	189	52	.	.	PUNCT
ejpam-6775	190	1	hence	hence	ADV
ejpam-6775	190	2	the	the	DET
ejpam-6775	190	3	set	set	PROPN
ejpam-6775	190	4	ω	ω	PROPN
ejpam-6775	190	5	is	be	AUX
ejpam-6775	190	6	positively	positively	ADV
ejpam-6775	190	7	invariant	invariant	ADJ
ejpam-6775	190	8	.	.	PUNCT
ejpam-6775	191	1	furthermore	furthermore	ADV
ejpam-6775	191	2	,	,	PUNCT
ejpam-6775	191	3	we	we	PRON
ejpam-6775	191	4	have	have	VERB
ejpam-6775	191	5	the	the	DET
ejpam-6775	191	6	bound	bind	VERB
ejpam-6775	191	7	lim	lim	PROPN
ejpam-6775	191	8	supt→∞	supt→∞	PROPN
ejpam-6775	191	9	∥φ(t	∥φ(t	NOUN
ejpam-6775	191	10	,	,	PUNCT
ejpam-6775	191	11	z0)∥x	z0)∥x	PROPN
ejpam-6775	191	12	≤	≤	PUNCT
ejpam-6775	192	1	λ/µ	λ/µ	PRON
ejpam-6775	192	2	which	which	PRON
ejpam-6775	192	3	implies	imply	VERB
ejpam-6775	192	4	that	that	SCONJ
ejpam-6775	192	5	the	the	DET
ejpam-6775	192	6	semiflow	semiflow	ADJ
ejpam-6775	192	7	{	{	PUNCT
ejpam-6775	192	8	φ(t	φ(t	PROPN
ejpam-6775	192	9	,	,	PUNCT
ejpam-6775	192	10	.)}t≥0	.)}t≥0	PROPN
ejpam-6775	192	11	is	be	AUX
ejpam-6775	192	12	bounded	bound	VERB
ejpam-6775	192	13	dissipative	dissipative	NOUN
ejpam-6775	192	14	and	and	CCONJ
ejpam-6775	192	15	ω	ω	PROPN
ejpam-6775	192	16	attracts	attract	VERB
ejpam-6775	192	17	all	all	DET
ejpam-6775	192	18	point	point	NOUN
ejpam-6775	192	19	of	of	ADP
ejpam-6775	192	20	space	space	NOUN
ejpam-6775	192	21	x0	x0	PROPN
ejpam-6775	192	22	+	+	PROPN
ejpam-6775	192	23	.	.	PROPN
ejpam-6775	192	24	4.2	4.2	NUM
ejpam-6775	192	25	.	.	PUNCT
ejpam-6775	193	1	reproduction	reproduction	NOUN
ejpam-6775	193	2	number	number	NOUN
ejpam-6775	193	3	and	and	CCONJ
ejpam-6775	193	4	equilibrium	equilibrium	NOUN
ejpam-6775	193	5	analysis	analysis	NOUN
ejpam-6775	193	6	system	system	NOUN
ejpam-6775	193	7	(	(	PUNCT
ejpam-6775	193	8	1	1	X
ejpam-6775	193	9	)	)	PUNCT
ejpam-6775	193	10	has	have	VERB
ejpam-6775	193	11	always	always	ADV
ejpam-6775	193	12	a	a	DET
ejpam-6775	193	13	disease	disease	NOUN
ejpam-6775	193	14	-	-	PUNCT
ejpam-6775	193	15	free	free	ADJ
ejpam-6775	193	16	equilibrium	equilibrium	NOUN
ejpam-6775	193	17	point	point	NOUN
ejpam-6775	193	18	e0	e0	PROPN
ejpam-6775	193	19	=	=	SYM
ejpam-6775	193	20	(	(	PUNCT
ejpam-6775	193	21	s0	s0	PROPN
ejpam-6775	193	22	,	,	PUNCT
ejpam-6775	193	23	v	v	NOUN
ejpam-6775	193	24	0	0	NUM
ejpam-6775	193	25	,	,	PUNCT
ejpam-6775	193	26	0	0	NUM
ejpam-6775	193	27	,	,	PUNCT
ejpam-6775	193	28	0	0	NUM
ejpam-6775	193	29	)	)	PUNCT
ejpam-6775	193	30	∈	∈	NOUN
ejpam-6775	193	31	x0	x0	PROPN
ejpam-6775	194	1	+	+	X
ejpam-6775	194	2	where	where	SCONJ
ejpam-6775	194	3	s0	s0	NOUN
ejpam-6775	194	4	=	=	SYM
ejpam-6775	194	5	λ	λ	PROPN
ejpam-6775	194	6	µ+ξ	µ+ξ	NOUN
ejpam-6775	194	7	and	and	CCONJ
ejpam-6775	194	8	v	v	NOUN
ejpam-6775	194	9	0	0	NUM
ejpam-6775	194	10	=	=	SYM
ejpam-6775	194	11	ξs0	ξs0	NUM
ejpam-6775	194	12	µ	µ	NOUN
ejpam-6775	194	13	,	,	PUNCT
ejpam-6775	194	14	corresponding	correspond	VERB
ejpam-6775	194	15	to	to	ADP
ejpam-6775	194	16	the	the	DET
ejpam-6775	194	17	equilibrium	equilibrium	NOUN
ejpam-6775	194	18	point	point	NOUN
ejpam-6775	194	19	without	without	ADP
ejpam-6775	194	20	disease	disease	NOUN
ejpam-6775	194	21	.	.	PUNCT
ejpam-6775	195	1	in	in	ADP
ejpam-6775	195	2	order	order	NOUN
ejpam-6775	195	3	to	to	PART
ejpam-6775	195	4	study	study	VERB
ejpam-6775	195	5	the	the	DET
ejpam-6775	195	6	long	long	ADJ
ejpam-6775	195	7	run	run	NOUN
ejpam-6775	195	8	behavior	behavior	NOUN
ejpam-6775	195	9	of	of	ADP
ejpam-6775	195	10	system	system	NOUN
ejpam-6775	195	11	(	(	PUNCT
ejpam-6775	195	12	1	1	NUM
ejpam-6775	195	13	)	)	PUNCT
ejpam-6775	195	14	,	,	PUNCT
ejpam-6775	195	15	we	we	PRON
ejpam-6775	195	16	need	need	VERB
ejpam-6775	195	17	to	to	PART
ejpam-6775	195	18	compute	compute	VERB
ejpam-6775	195	19	the	the	DET
ejpam-6775	195	20	basic	basic	ADJ
ejpam-6775	195	21	reproduction	reproduction	NOUN
ejpam-6775	195	22	number	number	NOUN
ejpam-6775	195	23	denoted	denote	VERB
ejpam-6775	195	24	r0	r0	NOUN
ejpam-6775	195	25	.	.	PUNCT
ejpam-6775	196	1	it	it	PRON
ejpam-6775	196	2	is	be	AUX
ejpam-6775	196	3	obtained	obtain	VERB
ejpam-6775	196	4	by	by	ADP
ejpam-6775	196	5	the	the	DET
ejpam-6775	196	6	so	so	ADV
ejpam-6775	196	7	-	-	PUNCT
ejpam-6775	196	8	called	call	VERB
ejpam-6775	196	9	next	next	ADJ
ejpam-6775	196	10	generation	generation	NOUN
ejpam-6775	196	11	operator	operator	NOUN
ejpam-6775	196	12	,	,	PUNCT
ejpam-6775	196	13	that	that	PRON
ejpam-6775	196	14	gives	give	VERB
ejpam-6775	196	15	the	the	DET
ejpam-6775	196	16	distribution	distribution	NOUN
ejpam-6775	196	17	of	of	ADP
ejpam-6775	196	18	secondary	secondary	ADJ
ejpam-6775	196	19	infections	infection	NOUN
ejpam-6775	196	20	as	as	ADP
ejpam-6775	196	21	a	a	DET
ejpam-6775	196	22	function	function	NOUN
ejpam-6775	196	23	of	of	ADP
ejpam-6775	196	24	the	the	DET
ejpam-6775	196	25	distribution	distribution	NOUN
ejpam-6775	196	26	of	of	ADP
ejpam-6775	196	27	the	the	DET
ejpam-6775	196	28	primary	primary	ADJ
ejpam-6775	196	29	infected	infected	ADJ
ejpam-6775	196	30	individuals	individual	NOUN
ejpam-6775	196	31	.	.	PUNCT
ejpam-6775	197	1	in	in	ADP
ejpam-6775	197	2	order	order	NOUN
ejpam-6775	197	3	to	to	PART
ejpam-6775	197	4	compute	compute	VERB
ejpam-6775	197	5	r0	r0	NOUN
ejpam-6775	197	6	,	,	PUNCT
ejpam-6775	197	7	we	we	PRON
ejpam-6775	197	8	use	use	VERB
ejpam-6775	197	9	the	the	DET
ejpam-6775	197	10	methodology	methodology	NOUN
ejpam-6775	197	11	developed	develop	VERB
ejpam-6775	197	12	in	in	ADP
ejpam-6775	197	13	references	reference	NOUN
ejpam-6775	197	14	[	[	X
ejpam-6775	197	15	12	12	NUM
ejpam-6775	197	16	,	,	PUNCT
ejpam-6775	197	17	14	14	NUM
ejpam-6775	197	18	]	]	PUNCT
ejpam-6775	197	19	where	where	SCONJ
ejpam-6775	197	20	r0	r0	NOUN
ejpam-6775	197	21	corresponds	correspond	VERB
ejpam-6775	197	22	to	to	ADP
ejpam-6775	197	23	the	the	DET
ejpam-6775	197	24	spectral	spectral	ADJ
ejpam-6775	197	25	radius	radius	NOUN
ejpam-6775	197	26	of	of	ADP
ejpam-6775	197	27	the	the	DET
ejpam-6775	197	28	next	next	ADJ
ejpam-6775	197	29	generation	generation	NOUN
ejpam-6775	197	30	operator	operator	NOUN
ejpam-6775	197	31	.	.	PUNCT
ejpam-6775	198	1	specifically	specifically	ADV
ejpam-6775	198	2	,	,	PUNCT
ejpam-6775	198	3	we	we	PRON
ejpam-6775	198	4	linearize	linearize	VERB
ejpam-6775	198	5	system	system	NOUN
ejpam-6775	198	6	(	(	PUNCT
ejpam-6775	198	7	1	1	NUM
ejpam-6775	198	8	)	)	PUNCT
ejpam-6775	198	9	around	around	ADP
ejpam-6775	198	10	the	the	DET
ejpam-6775	198	11	disease	disease	NOUN
ejpam-6775	198	12	-	-	PUNCT
ejpam-6775	198	13	free	free	ADJ
ejpam-6775	198	14	equilibrium	equilibrium	NOUN
ejpam-6775	198	15	point	point	NOUN
ejpam-6775	198	16	e0	e0	PROPN
ejpam-6775	198	17	and	and	CCONJ
ejpam-6775	198	18	obtain	obtain	VERB
ejpam-6775	198	19	the	the	DET
ejpam-6775	198	20	following	follow	VERB
ejpam-6775	198	21	equations	equation	NOUN
ejpam-6775	198	22	for	for	ADP
ejpam-6775	198	23	the	the	DET
ejpam-6775	198	24	dynamics	dynamic	NOUN
ejpam-6775	198	25	of	of	ADP
ejpam-6775	198	26	the	the	DET
ejpam-6775	198	27	infected	infected	ADJ
ejpam-6775	198	28	population	population	NOUN
ejpam-6775	198	29	:	:	PUNCT
ejpam-6775	198	30	{	{	PUNCT
ejpam-6775	198	31	∂ti(t	∂ti(t	NOUN
ejpam-6775	198	32	,	,	PUNCT
ejpam-6775	198	33	x	x	NOUN
ejpam-6775	198	34	)	)	PUNCT
ejpam-6775	198	35	+	+	CCONJ
ejpam-6775	198	36	∂xi(t	∂xi(t	PROPN
ejpam-6775	198	37	,	,	PUNCT
ejpam-6775	198	38	x	x	NOUN
ejpam-6775	198	39	)	)	PUNCT
ejpam-6775	198	40	=	=	SYM
ejpam-6775	198	41	−p(x)i(t	−p(x)i(t	NOUN
ejpam-6775	198	42	,	,	PUNCT
ejpam-6775	198	43	x	x	NOUN
ejpam-6775	198	44	)	)	PUNCT
ejpam-6775	198	45	,	,	PUNCT
ejpam-6775	198	46	i(t	i(t	PROPN
ejpam-6775	198	47	,	,	PUNCT
ejpam-6775	198	48	0	0	NUM
ejpam-6775	198	49	)	)	PUNCT
ejpam-6775	198	50	=	=	NOUN
ejpam-6775	199	1	[	[	X
ejpam-6775	199	2	s0	s0	NOUN
ejpam-6775	199	3	+	+	NOUN
ejpam-6775	199	4	mv	mv	PROPN
ejpam-6775	199	5	0]t	0]t	NUM
ejpam-6775	199	6	(	(	PUNCT
ejpam-6775	199	7	βi	βi	NOUN
ejpam-6775	199	8	)	)	PUNCT
ejpam-6775	199	9	.	.	PUNCT
ejpam-6775	200	1	(	(	PUNCT
ejpam-6775	200	2	17	17	NUM
ejpam-6775	200	3	)	)	PUNCT
ejpam-6775	200	4	using	use	VERB
ejpam-6775	200	5	the	the	DET
ejpam-6775	200	6	characteristics	characteristic	NOUN
ejpam-6775	200	7	method	method	NOUN
ejpam-6775	200	8	,	,	PUNCT
ejpam-6775	200	9	the	the	DET
ejpam-6775	200	10	solution	solution	NOUN
ejpam-6775	200	11	of	of	ADP
ejpam-6775	200	12	system	system	NOUN
ejpam-6775	200	13	(	(	PUNCT
ejpam-6775	200	14	1	1	X
ejpam-6775	200	15	)	)	PUNCT
ejpam-6775	200	16	can	can	AUX
ejpam-6775	200	17	be	be	AUX
ejpam-6775	200	18	expressed	express	VERB
ejpam-6775	200	19	as	as	ADP
ejpam-6775	200	20	i(t	i(t	NOUN
ejpam-6775	200	21	,	,	PUNCT
ejpam-6775	200	22	x	x	NOUN
ejpam-6775	200	23	)	)	PUNCT
ejpam-6775	200	24	=	=	SYM
ejpam-6775	200	25	i0(x−	i0(x−	ADP
ejpam-6775	200	26	t	t	NOUN
ejpam-6775	200	27	)	)	PUNCT
ejpam-6775	200	28	π(x	π(x	ADP
ejpam-6775	200	29	)	)	PUNCT
ejpam-6775	200	30	π(x−	π(x−	PROPN
ejpam-6775	200	31	t	t	PROPN
ejpam-6775	200	32	)	)	PUNCT
ejpam-6775	200	33	1{x	1{x	NUM
ejpam-6775	200	34	>	>	SYM
ejpam-6775	200	35	t	t	PROPN
ejpam-6775	200	36	}	}	PUNCT
ejpam-6775	200	37	+	+	NUM
ejpam-6775	200	38	i(t−	i(t−	PROPN
ejpam-6775	200	39	x	x	NOUN
ejpam-6775	200	40	,	,	PUNCT
ejpam-6775	200	41	0)π(x)1{x	0)π(x)1{x	PROPN
ejpam-6775	200	42	<	<	X
ejpam-6775	200	43	t	t	X
ejpam-6775	200	44	}	}	PUNCT
ejpam-6775	200	45	,	,	PUNCT
ejpam-6775	200	46	(	(	PUNCT
ejpam-6775	200	47	18	18	NUM
ejpam-6775	200	48	)	)	PUNCT
ejpam-6775	200	49	where	where	SCONJ
ejpam-6775	200	50	we	we	PRON
ejpam-6775	200	51	defined	define	VERB
ejpam-6775	200	52	π(x	π(x	ADP
ejpam-6775	200	53	)	)	PUNCT
ejpam-6775	200	54	=	=	PUNCT
ejpam-6775	201	1	e−	e−	NUM
ejpam-6775	201	2	∫	∫	NOUN
ejpam-6775	201	3	x	x	SYM
ejpam-6775	201	4	0	0	PROPN
ejpam-6775	201	5	p(r)dr	p(r)dr	NUM
ejpam-6775	201	6	which	which	PRON
ejpam-6775	201	7	denotes	denote	VERB
ejpam-6775	201	8	the	the	DET
ejpam-6775	201	9	probability	probability	NOUN
ejpam-6775	201	10	to	to	PART
ejpam-6775	201	11	leave	leave	VERB
ejpam-6775	201	12	the	the	DET
ejpam-6775	201	13	infected	infected	ADJ
ejpam-6775	201	14	compartment	compartment	NOUN
ejpam-6775	201	15	.	.	PUNCT
ejpam-6775	202	1	let	let	VERB
ejpam-6775	202	2	h(t	h(t	PRON
ejpam-6775	202	3	)	)	PUNCT
ejpam-6775	202	4	=	=	SYM
ejpam-6775	202	5	i(t	i(t	PROPN
ejpam-6775	202	6	,	,	PUNCT
ejpam-6775	202	7	0	0	NUM
ejpam-6775	202	8	)	)	PUNCT
ejpam-6775	202	9	be	be	VERB
ejpam-6775	202	10	the	the	DET
ejpam-6775	202	11	number	number	NOUN
ejpam-6775	202	12	of	of	ADP
ejpam-6775	202	13	newly	newly	ADV
ejpam-6775	202	14	infectious	infectious	ADJ
ejpam-6775	202	15	individuals	individual	NOUN
ejpam-6775	202	16	at	at	ADP
ejpam-6775	202	17	time	time	NOUN
ejpam-6775	202	18	t	t	PROPN
ejpam-6775	202	19	>	>	X
ejpam-6775	202	20	0	0	X
ejpam-6775	202	21	.	.	X
ejpam-6775	202	22	inserting	insert	VERB
ejpam-6775	202	23	expression	expression	NOUN
ejpam-6775	202	24	(	(	PUNCT
ejpam-6775	202	25	9	9	NUM
ejpam-6775	202	26	)	)	PUNCT
ejpam-6775	202	27	into	into	ADP
ejpam-6775	202	28	the	the	DET
ejpam-6775	202	29	boundary	boundary	ADJ
ejpam-6775	202	30	condition	condition	NOUN
ejpam-6775	202	31	of	of	ADP
ejpam-6775	202	32	(	(	PUNCT
ejpam-6775	202	33	8)	8)	NUM
ejpam-6775	202	34	,	,	PUNCT
ejpam-6775	202	35	we	we	PRON
ejpam-6775	202	36	get	get	VERB
ejpam-6775	202	37	the	the	DET
ejpam-6775	202	38	renewal	renewal	NOUN
ejpam-6775	202	39	equation	equation	NOUN
ejpam-6775	202	40	:	:	PUNCT
ejpam-6775	202	41	h(t	h(t	X
ejpam-6775	202	42	)	)	PUNCT
ejpam-6775	203	1	=	=	SYM
ejpam-6775	203	2	φ(t	φ(t	PROPN
ejpam-6775	203	3	)	)	PUNCT
ejpam-6775	204	1	+	+	CCONJ
ejpam-6775	204	2	∫	∫	PROPN
ejpam-6775	204	3	t	t	PROPN
ejpam-6775	204	4	0	0	NUM
ejpam-6775	204	5	ψ(x)h(t−	ψ(x)h(t−	NOUN
ejpam-6775	205	1	x)dx	x)dx	NOUN
ejpam-6775	205	2	,	,	PUNCT
ejpam-6775	205	3	(	(	PUNCT
ejpam-6775	205	4	19	19	NUM
ejpam-6775	205	5	)	)	PUNCT
ejpam-6775	205	6	where	where	SCONJ
ejpam-6775	205	7	φ(t	φ(t	NOUN
ejpam-6775	205	8	)	)	PUNCT
ejpam-6775	205	9	:	:	PUNCT
ejpam-6775	206	1	=	=	PUNCT
ejpam-6775	207	1	[	[	X
ejpam-6775	207	2	s0	s0	NOUN
ejpam-6775	207	3	+	+	PROPN
ejpam-6775	207	4	mv	mv	PROPN
ejpam-6775	207	5	0	0	NUM
ejpam-6775	207	6	]	]	PUNCT
ejpam-6775	207	7	∫∞	∫∞	NOUN
ejpam-6775	207	8	t	t	PROPN
ejpam-6775	207	9	β(x	β(x	PROPN
ejpam-6775	207	10	)	)	PUNCT
ejpam-6775	207	11	π(x	π(x	ADP
ejpam-6775	207	12	)	)	PUNCT
ejpam-6775	207	13	π(x−t	π(x−t	PROPN
ejpam-6775	207	14	)	)	PUNCT
ejpam-6775	207	15	i0(x−	i0(x−	CCONJ
ejpam-6775	207	16	t)dx	t)dx	PROPN
ejpam-6775	207	17	and	and	CCONJ
ejpam-6775	207	18	ψ(x	ψ(x	NUM
ejpam-6775	207	19	)	)	PUNCT
ejpam-6775	207	20	:	:	PUNCT
ejpam-6775	208	1	=	=	PUNCT
ejpam-6775	209	1	[	[	X
ejpam-6775	209	2	s0	s0	NOUN
ejpam-6775	209	3	+	+	PROPN
ejpam-6775	209	4	mv	mv	PROPN
ejpam-6775	209	5	0]β(x)π(x	0]β(x)π(x	NUM
ejpam-6775	209	6	)	)	PUNCT
ejpam-6775	209	7	.	.	PUNCT
ejpam-6775	210	1	according	accord	VERB
ejpam-6775	210	2	to	to	ADP
ejpam-6775	210	3	[	[	X
ejpam-6775	210	4	12	12	NUM
ejpam-6775	210	5	,	,	PUNCT
ejpam-6775	210	6	14	14	NUM
ejpam-6775	210	7	]	]	PUNCT
ejpam-6775	210	8	,	,	PUNCT
ejpam-6775	210	9	the	the	DET
ejpam-6775	210	10	basic	basic	ADJ
ejpam-6775	210	11	reproduction	reproduction	NOUN
ejpam-6775	210	12	number	number	NOUN
ejpam-6775	210	13	is	be	AUX
ejpam-6775	210	14	calculated	calculate	VERB
ejpam-6775	210	15	as	as	ADP
ejpam-6775	210	16	the	the	DET
ejpam-6775	210	17	spectral	spectral	ADJ
ejpam-6775	210	18	radius	radius	NOUN
ejpam-6775	210	19	of	of	ADP
ejpam-6775	210	20	the	the	DET
ejpam-6775	210	21	next	next	ADJ
ejpam-6775	210	22	generation	generation	NOUN
ejpam-6775	210	23	operator	operator	NOUN
ejpam-6775	210	24	∫∞	∫∞	NOUN
ejpam-6775	210	25	0	0	PUNCT
ejpam-6775	210	26	ψ(x)dx	ψ(x)dx	PROPN
ejpam-6775	210	27	.	.	PUNCT
ejpam-6775	211	1	hence	hence	ADV
ejpam-6775	211	2	,	,	PUNCT
ejpam-6775	211	3	the	the	DET
ejpam-6775	211	4	explicit	explicit	ADJ
ejpam-6775	211	5	expression	expression	NOUN
ejpam-6775	211	6	of	of	ADP
ejpam-6775	211	7	r0	r0	NOUN
ejpam-6775	211	8	is	be	AUX
ejpam-6775	211	9	given	give	VERB
ejpam-6775	211	10	by	by	ADP
ejpam-6775	211	11	:	:	PUNCT
ejpam-6775	211	12	r0	r0	NOUN
ejpam-6775	211	13	=	=	PUNCT
ejpam-6775	212	1	[	[	X
ejpam-6775	212	2	s0	s0	NOUN
ejpam-6775	212	3	+	+	NOUN
ejpam-6775	212	4	mv	mv	PROPN
ejpam-6775	212	5	0]t	0]t	NUM
ejpam-6775	212	6	(	(	PUNCT
ejpam-6775	212	7	βπ	βπ	NOUN
ejpam-6775	212	8	)	)	PUNCT
ejpam-6775	212	9	.	.	PUNCT
ejpam-6775	213	1	(	(	PUNCT
ejpam-6775	213	2	20	20	NUM
ejpam-6775	213	3	)	)	PUNCT
ejpam-6775	213	4	j.	j.	PROPN
ejpam-6775	213	5	leo	leo	PROPN
ejpam-6775	213	6	amalraj	amalraj	PROPN
ejpam-6775	213	7	et	et	PROPN
ejpam-6775	213	8	al	al	PROPN
ejpam-6775	213	9	.	.	PUNCT
ejpam-6775	213	10	/	/	SYM
ejpam-6775	213	11	eur	eur	PROPN
ejpam-6775	213	12	.	.	PUNCT
ejpam-6775	214	1	j.	j.	PROPN
ejpam-6775	214	2	pure	pure	PROPN
ejpam-6775	214	3	appl	appl	PROPN
ejpam-6775	214	4	.	.	PROPN
ejpam-6775	214	5	math	math	PROPN
ejpam-6775	214	6	,	,	PUNCT
ejpam-6775	214	7	18	18	NUM
ejpam-6775	214	8	(	(	PUNCT
ejpam-6775	214	9	4	4	NUM
ejpam-6775	214	10	)	)	PUNCT
ejpam-6775	214	11	(	(	PUNCT
ejpam-6775	214	12	2025	2025	NUM
ejpam-6775	214	13	)	)	PUNCT
ejpam-6775	214	14	,	,	PUNCT
ejpam-6775	214	15	6775	6775	NUM
ejpam-6775	214	16	10	10	NUM
ejpam-6775	214	17	of	of	ADP
ejpam-6775	214	18	32	32	NUM
ejpam-6775	214	19	this	this	DET
ejpam-6775	214	20	threshold	threshold	NOUN
ejpam-6775	214	21	depends	depend	VERB
ejpam-6775	214	22	on	on	ADP
ejpam-6775	214	23	the	the	DET
ejpam-6775	214	24	epidemiological	epidemiological	ADJ
ejpam-6775	214	25	parameters	parameter	NOUN
ejpam-6775	214	26	of	of	ADP
ejpam-6775	214	27	the	the	DET
ejpam-6775	214	28	model	model	NOUN
ejpam-6775	214	29	,	,	PUNCT
ejpam-6775	214	30	ensuring	ensure	VERB
ejpam-6775	214	31	whether	whether	SCONJ
ejpam-6775	214	32	an	an	DET
ejpam-6775	214	33	epidemic	epidemic	NOUN
ejpam-6775	214	34	occurs	occur	VERB
ejpam-6775	214	35	and	and	CCONJ
ejpam-6775	214	36	measures	measure	NOUN
ejpam-6775	214	37	the	the	DET
ejpam-6775	214	38	expected	expect	VERB
ejpam-6775	214	39	number	number	NOUN
ejpam-6775	214	40	of	of	ADP
ejpam-6775	214	41	secondary	secondary	ADJ
ejpam-6775	214	42	cases	case	NOUN
ejpam-6775	214	43	produced	produce	VERB
ejpam-6775	214	44	by	by	ADP
ejpam-6775	214	45	a	a	DET
ejpam-6775	214	46	typical	typical	ADJ
ejpam-6775	214	47	infected	infected	ADJ
ejpam-6775	214	48	individual	individual	NOUN
ejpam-6775	214	49	during	during	ADP
ejpam-6775	214	50	its	its	PRON
ejpam-6775	214	51	entire	entire	ADJ
ejpam-6775	214	52	period	period	NOUN
ejpam-6775	214	53	of	of	ADP
ejpam-6775	214	54	infectiousness	infectiousness	NOUN
ejpam-6775	214	55	in	in	ADP
ejpam-6775	214	56	a	a	DET
ejpam-6775	214	57	susceptible	susceptible	ADJ
ejpam-6775	214	58	population	population	NOUN
ejpam-6775	214	59	[	[	X
ejpam-6775	214	60	12	12	NUM
ejpam-6775	214	61	,	,	PUNCT
ejpam-6775	214	62	14	14	NUM
ejpam-6775	214	63	]	]	PUNCT
ejpam-6775	214	64	.	.	PUNCT
ejpam-6775	215	1	when	when	SCONJ
ejpam-6775	215	2	this	this	DET
ejpam-6775	215	3	threshold	threshold	NOUN
ejpam-6775	215	4	is	be	AUX
ejpam-6775	215	5	used	use	VERB
ejpam-6775	215	6	to	to	PART
ejpam-6775	215	7	measure	measure	VERB
ejpam-6775	215	8	the	the	DET
ejpam-6775	215	9	transmission	transmission	NOUN
ejpam-6775	215	10	potential	potential	NOUN
ejpam-6775	215	11	of	of	ADP
ejpam-6775	215	12	an	an	DET
ejpam-6775	215	13	infectious	infectious	ADJ
ejpam-6775	215	14	disease	disease	NOUN
ejpam-6775	215	15	,	,	PUNCT
ejpam-6775	215	16	it	it	PRON
ejpam-6775	215	17	plays	play	VERB
ejpam-6775	215	18	an	an	DET
ejpam-6775	215	19	important	important	ADJ
ejpam-6775	215	20	role	role	NOUN
ejpam-6775	215	21	in	in	ADP
ejpam-6775	215	22	the	the	DET
ejpam-6775	215	23	determination	determination	NOUN
ejpam-6775	215	24	and	and	CCONJ
ejpam-6775	215	25	stability	stability	NOUN
ejpam-6775	215	26	of	of	ADP
ejpam-6775	215	27	equilibrium	equilibrium	NOUN
ejpam-6775	215	28	points	point	NOUN
ejpam-6775	215	29	.	.	PUNCT
ejpam-6775	216	1	we	we	PRON
ejpam-6775	216	2	have	have	VERB
ejpam-6775	216	3	the	the	DET
ejpam-6775	216	4	following	follow	VERB
ejpam-6775	216	5	result	result	NOUN
ejpam-6775	216	6	:	:	PUNCT
ejpam-6775	216	7	theorem	theorem	NOUN
ejpam-6775	216	8	3	3	X
ejpam-6775	216	9	.	.	PUNCT
ejpam-6775	217	1	let	let	VERB
ejpam-6775	217	2	assumption	assumption	NOUN
ejpam-6775	217	3	2.1	2.1	NUM
ejpam-6775	217	4	be	be	AUX
ejpam-6775	217	5	satisfied	satisfied	ADJ
ejpam-6775	217	6	.	.	PUNCT
ejpam-6775	218	1	if	if	SCONJ
ejpam-6775	218	2	r0	r0	NOUN
ejpam-6775	218	3	<	<	X
ejpam-6775	218	4	1	1	NUM
ejpam-6775	218	5	,	,	PUNCT
ejpam-6775	218	6	the	the	DET
ejpam-6775	218	7	disease	disease	NOUN
ejpam-6775	218	8	-	-	PUNCT
ejpam-6775	218	9	free	free	ADJ
ejpam-6775	218	10	equilibrium	equilibrium	NOUN
ejpam-6775	218	11	point	point	NOUN
ejpam-6775	218	12	e0	e0	PROPN
ejpam-6775	218	13	is	be	AUX
ejpam-6775	218	14	locally	locally	ADV
ejpam-6775	218	15	asymptotically	asymptotically	ADV
ejpam-6775	218	16	stable	stable	ADJ
ejpam-6775	218	17	and	and	CCONJ
ejpam-6775	218	18	is	be	AUX
ejpam-6775	218	19	unstable	unstable	ADJ
ejpam-6775	218	20	when	when	SCONJ
ejpam-6775	218	21	r0	r0	NOUN
ejpam-6775	218	22	>	>	X
ejpam-6775	218	23	1	1	X
ejpam-6775	218	24	.	.	PUNCT
ejpam-6775	218	25	proof	proof	NOUN
ejpam-6775	218	26	.	.	PUNCT
ejpam-6775	219	1	linearizing	linearize	VERB
ejpam-6775	219	2	the	the	DET
ejpam-6775	219	3	system	system	NOUN
ejpam-6775	219	4	(	(	PUNCT
ejpam-6775	219	5	1	1	X
ejpam-6775	219	6	)	)	PUNCT
ejpam-6775	219	7	at	at	ADP
ejpam-6775	219	8	equilibrium	equilibrium	NOUN
ejpam-6775	219	9	point	point	NOUN
ejpam-6775	219	10	e0	e0	PROPN
ejpam-6775	219	11	with	with	ADP
ejpam-6775	219	12	y(t	y(t	PROPN
ejpam-6775	219	13	)	)	PUNCT
ejpam-6775	219	14	,	,	PUNCT
ejpam-6775	219	15	z(t	z(t	NOUN
ejpam-6775	219	16	)	)	PUNCT
ejpam-6775	219	17	and	and	CCONJ
ejpam-6775	219	18	ω(t	ω(t	NOUN
ejpam-6775	219	19	,	,	PUNCT
ejpam-6775	219	20	x	x	X
ejpam-6775	219	21	)	)	PUNCT
ejpam-6775	219	22	being	be	AUX
ejpam-6775	219	23	the	the	DET
ejpam-6775	219	24	small	small	ADJ
ejpam-6775	219	25	perturbations	perturbation	NOUN
ejpam-6775	219	26	,	,	PUNCT
ejpam-6775	219	27	that	that	PRON
ejpam-6775	219	28	is	be	AUX
ejpam-6775	219	29	y(t	y(t	PROPN
ejpam-6775	219	30	)	)	PUNCT
ejpam-6775	219	31	=	=	SYM
ejpam-6775	219	32	s(t	s(t	PROPN
ejpam-6775	219	33	)	)	PUNCT
ejpam-6775	219	34	−	−	PROPN
ejpam-6775	219	35	s0	s0	PROPN
ejpam-6775	219	36	,	,	PUNCT
ejpam-6775	219	37	z(t	z(t	PROPN
ejpam-6775	219	38	)	)	PUNCT
ejpam-6775	220	1	=	=	SYM
ejpam-6775	220	2	v	v	X
ejpam-6775	220	3	(	(	PUNCT
ejpam-6775	220	4	t	t	PROPN
ejpam-6775	220	5	)	)	PUNCT
ejpam-6775	220	6	−	−	PROPN
ejpam-6775	220	7	v	v	NOUN
ejpam-6775	220	8	0	0	NUM
ejpam-6775	220	9	and	and	CCONJ
ejpam-6775	220	10	ω(t	ω(t	NOUN
ejpam-6775	220	11	,	,	PUNCT
ejpam-6775	220	12	x	x	X
ejpam-6775	220	13	)	)	PUNCT
ejpam-6775	220	14	=	=	SYM
ejpam-6775	220	15	i(t	i(t	NOUN
ejpam-6775	220	16	,	,	PUNCT
ejpam-6775	220	17	x	x	NOUN
ejpam-6775	220	18	)	)	PUNCT
ejpam-6775	220	19	.	.	PUNCT
ejpam-6775	221	1	we	we	PRON
ejpam-6775	221	2	obtain	obtain	VERB
ejpam-6775	221	3	the	the	DET
ejpam-6775	221	4	following	follow	VERB
ejpam-6775	221	5	abstract	abstract	ADJ
ejpam-6775	221	6	cauchy	cauchy	PROPN
ejpam-6775	221	7	problem	problem	NOUN
ejpam-6775	221	8	:	:	PUNCT
ejpam-6775	221	9	du(t	du(t	X
ejpam-6775	221	10	)	)	PUNCT
ejpam-6775	221	11	dt	dt	NOUN
ejpam-6775	222	1	=	=	SYM
ejpam-6775	222	2	au(t	au(t	X
ejpam-6775	222	3	)	)	PUNCT
ejpam-6775	222	4	+	+	NOUN
ejpam-6775	222	5	dhe0(u(t	dhe0(u(t	PROPN
ejpam-6775	222	6	)	)	PUNCT
ejpam-6775	222	7	)	)	PUNCT
ejpam-6775	222	8	,	,	PUNCT
ejpam-6775	222	9	∀t	∀t	PROPN
ejpam-6775	222	10	≥	≥	NUM
ejpam-6775	222	11	0	0	NUM
ejpam-6775	222	12	,	,	PUNCT
ejpam-6775	222	13	u(0	u(0	PROPN
ejpam-6775	222	14	)	)	PUNCT
ejpam-6775	222	15	∈	∈	NOUN
ejpam-6775	223	1	x0	x0	PROPN
ejpam-6775	223	2	+	+	PROPN
ejpam-6775	223	3	,	,	PUNCT
ejpam-6775	223	4	(	(	PUNCT
ejpam-6775	223	5	21	21	NUM
ejpam-6775	223	6	)	)	PUNCT
ejpam-6775	224	1	where	where	SCONJ
ejpam-6775	224	2	u(t	u(t	NOUN
ejpam-6775	224	3	)	)	PUNCT
ejpam-6775	224	4	=	=	SYM
ejpam-6775	224	5	(	(	PUNCT
ejpam-6775	224	6	y(t	y(t	PROPN
ejpam-6775	224	7	)	)	PUNCT
ejpam-6775	224	8	,	,	PUNCT
ejpam-6775	224	9	z(t	z(t	PROPN
ejpam-6775	224	10	)	)	PUNCT
ejpam-6775	224	11	,	,	PUNCT
ejpam-6775	224	12	ω	ω	PROPN
ejpam-6775	224	13	(	(	PUNCT
ejpam-6775	224	14	.	.	NUM
ejpam-6775	224	15	,	,	PUNCT
ejpam-6775	224	16	t	t	PROPN
ejpam-6775	224	17	)	)	PUNCT
ejpam-6775	224	18	,	,	PUNCT
ejpam-6775	224	19	0)t	0)t	NOUN
ejpam-6775	224	20	and	and	CCONJ
ejpam-6775	224	21	the	the	DET
ejpam-6775	224	22	linear	linear	ADJ
ejpam-6775	224	23	operator	operator	NOUN
ejpam-6775	224	24	dhe0	dhe0	NOUN
ejpam-6775	224	25	:	:	PUNCT
ejpam-6775	225	1	x0	x0	PROPN
ejpam-6775	225	2	⊂	⊂	PROPN
ejpam-6775	225	3	x	x	PUNCT
ejpam-6775	226	1	→	→	PUNCT
ejpam-6775	226	2	x	x	X
ejpam-6775	226	3	is	be	AUX
ejpam-6775	226	4	defined	define	VERB
ejpam-6775	226	5	for	for	ADP
ejpam-6775	226	6	u	u	NOUN
ejpam-6775	226	7	∈	∈	PROPN
ejpam-6775	226	8	x0	x0	PROPN
ejpam-6775	226	9	by	by	ADP
ejpam-6775	226	10	dhe0u(t	dhe0u(t	PROPN
ejpam-6775	226	11	)	)	PUNCT
ejpam-6775	226	12	=	=	SYM
ejpam-6775	226	13			NOUN
ejpam-6775	226	14	−t	−t	NOUN
ejpam-6775	226	15	(	(	PUNCT
ejpam-6775	226	16	βω)s0	βω)s0	PROPN
ejpam-6775	226	17	+	+	X
ejpam-6775	226	18	t	t	PROPN
ejpam-6775	226	19	(	(	PUNCT
ejpam-6775	226	20	αω	αω	NOUN
ejpam-6775	226	21	)	)	PUNCT
ejpam-6775	226	22	ξy	ξy	NOUN
ejpam-6775	226	23	−mt	−mt	NOUN
ejpam-6775	226	24	(	(	PUNCT
ejpam-6775	226	25	βω)v	βω)v	PROPN
ejpam-6775	226	26	0	0	NUM
ejpam-6775	226	27	0l1(0,∞	0l1(0,∞	NUM
ejpam-6775	226	28	)	)	PUNCT
ejpam-6775	226	29	s0	s0	NOUN
ejpam-6775	227	1	+	+	PROPN
ejpam-6775	227	2	mv	mv	PROPN
ejpam-6775	227	3	0	0	PROPN
ejpam-6775	227	4	t	t	PROPN
ejpam-6775	227	5	(	(	PUNCT
ejpam-6775	227	6	βω	βω	NOUN
ejpam-6775	227	7	)	)	PUNCT
ejpam-6775	227	8			NOUN
ejpam-6775	227	9	.	.	PUNCT
ejpam-6775	228	1	(	(	PUNCT
ejpam-6775	228	2	22	22	NUM
ejpam-6775	228	3	)	)	PUNCT
ejpam-6775	228	4	let	let	VERB
ejpam-6775	228	5	us	we	PRON
ejpam-6775	228	6	denote	denote	VERB
ejpam-6775	228	7	by	by	ADP
ejpam-6775	228	8	a0	a0	PROPN
ejpam-6775	228	9	the	the	DET
ejpam-6775	228	10	restriction	restriction	NOUN
ejpam-6775	228	11	of	of	ADP
ejpam-6775	228	12	the	the	DET
ejpam-6775	228	13	linear	linear	ADJ
ejpam-6775	228	14	operator	operator	NOUN
ejpam-6775	228	15	a	a	PRON
ejpam-6775	228	16	in	in	ADP
ejpam-6775	228	17	x0	x0	PROPN
ejpam-6775	228	18	,	,	PUNCT
ejpam-6775	228	19	i.e.	i.e.	X
ejpam-6775	228	20	a0	a0	PROPN
ejpam-6775	228	21	:	:	PUNCT
ejpam-6775	228	22	ψ	ψ	X
ejpam-6775	228	23	∈	∈	PROPN
ejpam-6775	228	24	x0	x0	PROPN
ejpam-6775	228	25	→	→	PUNCT
ejpam-6775	228	26	aψ	aψ	PROPN
ejpam-6775	228	27	∈	∈	NOUN
ejpam-6775	228	28	x0	x0	PROPN
ejpam-6775	228	29	and	and	CCONJ
ejpam-6775	228	30	let	let	VERB
ejpam-6775	228	31	{	{	PUNCT
ejpam-6775	228	32	ta0(t)}t≥0	ta0(t)}t≥0	NOUN
ejpam-6775	228	33	the	the	DET
ejpam-6775	228	34	semigroup	semigroup	NOUN
ejpam-6775	228	35	generated	generate	VERB
ejpam-6775	228	36	by	by	ADP
ejpam-6775	228	37	the	the	DET
ejpam-6775	228	38	linear	linear	PROPN
ejpam-6775	228	39	operator	operator	NOUN
ejpam-6775	228	40	a0	a0	NOUN
ejpam-6775	228	41	.	.	PUNCT
ejpam-6775	229	1	it	it	PRON
ejpam-6775	229	2	is	be	AUX
ejpam-6775	229	3	easy	easy	ADJ
ejpam-6775	229	4	to	to	PART
ejpam-6775	229	5	check	check	VERB
ejpam-6775	229	6	,	,	PUNCT
ejpam-6775	229	7	by	by	ADP
ejpam-6775	229	8	adapting	adapt	VERB
ejpam-6775	229	9	the	the	DET
ejpam-6775	229	10	proof	proof	NOUN
ejpam-6775	229	11	of	of	ADP
ejpam-6775	229	12	proposition	proposition	NOUN
ejpam-6775	229	13	1	1	NUM
ejpam-6775	229	14	of	of	ADP
ejpam-6775	229	15	[	[	X
ejpam-6775	229	16	41	41	NUM
ejpam-6775	229	17	]	]	PUNCT
ejpam-6775	229	18	,	,	PUNCT
ejpam-6775	229	19	that	that	SCONJ
ejpam-6775	229	20	∥ta0(t)∥	∥ta0(t)∥	ADP
ejpam-6775	229	21	≤	≤	ADJ
ejpam-6775	229	22	e−µt	e−µt	PROPN
ejpam-6775	229	23	,	,	PUNCT
ejpam-6775	229	24	∀t	∀t	PROPN
ejpam-6775	229	25	≥	≥	NOUN
ejpam-6775	229	26	0	0	NUM
ejpam-6775	229	27	.	.	PUNCT
ejpam-6775	230	1	it	it	PRON
ejpam-6775	230	2	follows	follow	VERB
ejpam-6775	230	3	that	that	DET
ejpam-6775	230	4	ωess(a0	ωess(a0	NOUN
ejpam-6775	230	5	)	)	PUNCT
ejpam-6775	230	6	,	,	PUNCT
ejpam-6775	230	7	the	the	DET
ejpam-6775	230	8	essential	essential	ADJ
ejpam-6775	230	9	growth	growth	NOUN
ejpam-6775	230	10	rate	rate	NOUN
ejpam-6775	230	11	of	of	ADP
ejpam-6775	230	12	{	{	PUNCT
ejpam-6775	230	13	ta0(t)}t≥0	ta0(t)}t≥0	NOUN
ejpam-6775	230	14	is	be	AUX
ejpam-6775	230	15	less	less	ADJ
ejpam-6775	230	16	than	than	ADP
ejpam-6775	230	17	or	or	CCONJ
ejpam-6775	230	18	equal	equal	ADJ
ejpam-6775	230	19	to	to	ADP
ejpam-6775	230	20	−µ.	−µ.	ADV
ejpam-6775	230	21	let	let	VERB
ejpam-6775	230	22	{	{	PUNCT
ejpam-6775	230	23	ta0+dhe0(t)}t≥0	ta0+dhe0(t)}t≥0	PRON
ejpam-6775	230	24	be	be	AUX
ejpam-6775	230	25	the	the	DET
ejpam-6775	230	26	semigroup	semigroup	NOUN
ejpam-6775	230	27	generated	generate	VERB
ejpam-6775	230	28	by	by	ADP
ejpam-6775	230	29	(	(	PUNCT
ejpam-6775	230	30	a0	a0	PROPN
ejpam-6775	230	31	+	+	PROPN
ejpam-6775	230	32	dhe0	dhe0	PROPN
ejpam-6775	230	33	)	)	PUNCT
ejpam-6775	230	34	,	,	PUNCT
ejpam-6775	230	35	the	the	DET
ejpam-6775	230	36	restriction	restriction	NOUN
ejpam-6775	230	37	of	of	ADP
ejpam-6775	230	38	the	the	DET
ejpam-6775	230	39	linear	linear	ADJ
ejpam-6775	230	40	operator	operator	NOUN
ejpam-6775	230	41	a+dhe0	a+dhe0	ADV
ejpam-6775	230	42	in	in	ADP
ejpam-6775	230	43	x0	x0	PROPN
ejpam-6775	230	44	.	.	PUNCT
ejpam-6775	231	1	since	since	SCONJ
ejpam-6775	231	2	dhe0	dhe0	PROPN
ejpam-6775	231	3	is	be	AUX
ejpam-6775	231	4	a	a	DET
ejpam-6775	231	5	compact	compact	ADJ
ejpam-6775	231	6	operator	operator	NOUN
ejpam-6775	231	7	,	,	PUNCT
ejpam-6775	231	8	...	...	PUNCT
ejpam-6775	232	1	it	it	PRON
ejpam-6775	232	2	follows	follow	VERB
ejpam-6775	232	3	from	from	ADP
ejpam-6775	232	4	the	the	DET
ejpam-6775	232	5	result	result	NOUN
ejpam-6775	232	6	in	in	ADP
ejpam-6775	232	7	[	[	X
ejpam-6775	232	8	42	42	NUM
ejpam-6775	232	9	]	]	PUNCT
ejpam-6775	232	10	,	,	PUNCT
ejpam-6775	232	11	theorem	theorem	VERB
ejpam-6775	232	12	1.2	1.2	NUM
ejpam-6775	232	13	,	,	PUNCT
ejpam-6775	232	14	that	that	DET
ejpam-6775	232	15	ωess((a+dhe0	ωess((a+dhe0	NOUN
ejpam-6775	232	16	)	)	PUNCT
ejpam-6775	232	17	)	)	PUNCT
ejpam-6775	233	1	≤	≤	PROPN
ejpam-6775	233	2	ωess(a0	ωess(a0	NOUN
ejpam-6775	233	3	)	)	PUNCT
ejpam-6775	233	4	≤	≤	NOUN
ejpam-6775	233	5	−µ	−µ	NOUN
ejpam-6775	233	6	<	<	X
ejpam-6775	233	7	0	0	X
ejpam-6775	233	8	.	.	PUNCT
ejpam-6775	234	1	according	accord	VERB
ejpam-6775	234	2	to	to	ADP
ejpam-6775	234	3	the	the	DET
ejpam-6775	234	4	results	result	NOUN
ejpam-6775	234	5	obtained	obtain	VERB
ejpam-6775	234	6	in	in	ADP
ejpam-6775	234	7	[	[	X
ejpam-6775	234	8	37	37	NUM
ejpam-6775	234	9	]	]	PUNCT
ejpam-6775	234	10	,	,	PUNCT
ejpam-6775	234	11	corollary	corollary	NOUN
ejpam-6775	234	12	4.3	4.3	NUM
ejpam-6775	234	13	,	,	PUNCT
ejpam-6775	234	14	the	the	DET
ejpam-6775	234	15	equilibrium	equilibrium	NOUN
ejpam-6775	234	16	point	point	NOUN
ejpam-6775	234	17	e0	e0	PROPN
ejpam-6775	234	18	is	be	AUX
ejpam-6775	234	19	locally	locally	ADV
ejpam-6775	234	20	asymptotically	asymptotically	ADV
ejpam-6775	234	21	stable	stable	ADJ
ejpam-6775	234	22	if	if	SCONJ
ejpam-6775	234	23	all	all	DET
ejpam-6775	234	24	eigenvalues	eigenvalue	NOUN
ejpam-6775	234	25	of	of	ADP
ejpam-6775	234	26	the	the	DET
ejpam-6775	234	27	linear	linear	ADJ
ejpam-6775	234	28	operator	operator	NOUN
ejpam-6775	234	29	(	(	PUNCT
ejpam-6775	234	30	a	a	DET
ejpam-6775	234	31	+	+	X
ejpam-6775	234	32	dhe0	dhe0	NOUN
ejpam-6775	234	33	)	)	PUNCT
ejpam-6775	234	34	have	have	VERB
ejpam-6775	234	35	negative	negative	ADJ
ejpam-6775	234	36	real	real	ADJ
ejpam-6775	234	37	parts	part	NOUN
ejpam-6775	234	38	.	.	PUNCT
ejpam-6775	235	1	in	in	ADP
ejpam-6775	235	2	this	this	DET
ejpam-6775	235	3	case	case	NOUN
ejpam-6775	235	4	,	,	PUNCT
ejpam-6775	235	5	the	the	DET
ejpam-6775	235	6	trajectories	trajectory	NOUN
ejpam-6775	235	7	which	which	PRON
ejpam-6775	235	8	start	start	VERB
ejpam-6775	235	9	sufficiently	sufficiently	ADV
ejpam-6775	235	10	close	close	ADJ
ejpam-6775	235	11	to	to	ADP
ejpam-6775	235	12	e0	e0	PROPN
ejpam-6775	235	13	remain	remain	VERB
ejpam-6775	235	14	close	close	ADJ
ejpam-6775	235	15	and	and	CCONJ
ejpam-6775	235	16	converge	converge	VERB
ejpam-6775	235	17	to	to	ADP
ejpam-6775	235	18	the	the	DET
ejpam-6775	235	19	equilibrium	equilibrium	NOUN
ejpam-6775	235	20	point	point	NOUN
ejpam-6775	235	21	when	when	SCONJ
ejpam-6775	235	22	time	time	NOUN
ejpam-6775	235	23	tends	tend	VERB
ejpam-6775	235	24	towards	towards	ADP
ejpam-6775	235	25	infinity	infinity	NOUN
ejpam-6775	235	26	.	.	PUNCT
ejpam-6775	236	1	however	however	ADV
ejpam-6775	236	2	,	,	PUNCT
ejpam-6775	236	3	if	if	SCONJ
ejpam-6775	236	4	at	at	ADV
ejpam-6775	236	5	least	least	ADV
ejpam-6775	236	6	one	one	NUM
ejpam-6775	236	7	eigenvalue	eigenvalue	NOUN
ejpam-6775	236	8	of	of	ADP
ejpam-6775	236	9	(	(	PUNCT
ejpam-6775	236	10	a+dhe0	a+dhe0	ADJ
ejpam-6775	236	11	)	)	PUNCT
ejpam-6775	236	12	has	have	VERB
ejpam-6775	236	13	a	a	DET
ejpam-6775	236	14	strictly	strictly	ADV
ejpam-6775	236	15	positive	positive	ADJ
ejpam-6775	236	16	real	real	ADJ
ejpam-6775	236	17	part	part	NOUN
ejpam-6775	236	18	,	,	PUNCT
ejpam-6775	236	19	then	then	ADV
ejpam-6775	236	20	e0	e0	PROPN
ejpam-6775	236	21	is	be	AUX
ejpam-6775	236	22	an	an	DET
ejpam-6775	236	23	unstable	unstable	ADJ
ejpam-6775	236	24	equilibrium	equilibrium	NOUN
ejpam-6775	236	25	point	point	NOUN
ejpam-6775	236	26	.	.	PUNCT
ejpam-6775	237	1	now	now	ADV
ejpam-6775	237	2	,	,	PUNCT
ejpam-6775	237	3	we	we	PRON
ejpam-6775	237	4	consider	consider	VERB
ejpam-6775	237	5	the	the	DET
ejpam-6775	237	6	exponential	exponential	ADJ
ejpam-6775	237	7	solutions	solution	NOUN
ejpam-6775	237	8	of	of	ADP
ejpam-6775	237	9	the	the	DET
ejpam-6775	237	10	linearized	linearize	VERB
ejpam-6775	237	11	system	system	NOUN
ejpam-6775	237	12	(	(	PUNCT
ejpam-6775	237	13	12	12	NUM
ejpam-6775	237	14	)	)	PUNCT
ejpam-6775	237	15	at	at	ADP
ejpam-6775	237	16	disease	disease	NOUN
ejpam-6775	237	17	-	-	PUNCT
ejpam-6775	237	18	free	free	ADJ
ejpam-6775	237	19	equilibrium	equilibrium	NOUN
ejpam-6775	237	20	point	point	NOUN
ejpam-6775	237	21	e0	e0	PROPN
ejpam-6775	237	22	by	by	ADP
ejpam-6775	237	23	y(t	y(t	PROPN
ejpam-6775	237	24	)	)	PUNCT
ejpam-6775	238	1	=	=	SYM
ejpam-6775	238	2	yeλt	yeλt	PROPN
ejpam-6775	238	3	,	,	PUNCT
ejpam-6775	238	4	z(t	z(t	X
ejpam-6775	238	5	)	)	PUNCT
ejpam-6775	238	6	=	=	SYM
ejpam-6775	238	7	zeλt	zeλt	PROPN
ejpam-6775	238	8	and	and	CCONJ
ejpam-6775	238	9	u(t	u(t	PROPN
ejpam-6775	238	10	)	)	PUNCT
ejpam-6775	238	11	=	=	SYM
ejpam-6775	238	12	ω̄(x)eλt	ω̄(x)eλt	PROPN
ejpam-6775	238	13	with	with	ADP
ejpam-6775	238	14	(	(	PUNCT
ejpam-6775	238	15	y	y	PROPN
ejpam-6775	238	16	,	,	PUNCT
ejpam-6775	238	17	z	z	PROPN
ejpam-6775	238	18	,	,	PUNCT
ejpam-6775	238	19	ω̄	ω̄	ADP
ejpam-6775	238	20	(	(	PUNCT
ejpam-6775	238	21	.	.	PUNCT
ejpam-6775	238	22	)	)	PUNCT
ejpam-6775	238	23	)	)	PUNCT
ejpam-6775	239	1	∈	∈	PROPN
ejpam-6775	239	2	r×r×w	r×r×w	PROPN
ejpam-6775	239	3	1,0(0,∞)\{0	1,0(0,∞)\{0	NUM
ejpam-6775	239	4	}	}	PUNCT
ejpam-6775	239	5	and	and	CCONJ
ejpam-6775	239	6	λ	λ	X
ejpam-6775	239	7	∈	∈	NOUN
ejpam-6775	239	8	c	c	NOUN
ejpam-6775	239	9	with	with	ADP
ejpam-6775	239	10	ℜλ	ℜλ	PROPN
ejpam-6775	239	11	>	>	X
ejpam-6775	240	1	−µ.	−µ.	ADV
ejpam-6775	240	2	we	we	PRON
ejpam-6775	240	3	derive	derive	VERB
ejpam-6775	240	4	the	the	DET
ejpam-6775	240	5	characteristic	characteristic	ADJ
ejpam-6775	240	6	equation	equation	NOUN
ejpam-6775	240	7	.	.	PUNCT
ejpam-6775	241	1	we	we	PRON
ejpam-6775	241	2	get	get	VERB
ejpam-6775	241	3	the	the	DET
ejpam-6775	241	4	following	follow	VERB
ejpam-6775	241	5	linear	linear	PROPN
ejpam-6775	241	6	eigenvalue	eigenvalue	PROPN
ejpam-6775	241	7	problem:	problem:	PROPN
ejpam-6775	241	8	(	(	PUNCT
ejpam-6775	241	9	λ	λ	X
ejpam-6775	241	10	+	+	NUM
ejpam-6775	241	11	µ+	µ+	PUNCT
ejpam-6775	241	12	ξ)y	ξ)y	ADJ
ejpam-6775	241	13	=	=	SYM
ejpam-6775	241	14	−s0	−s0	PROPN
ejpam-6775	241	15	t	t	PROPN
ejpam-6775	241	16	(	(	PUNCT
ejpam-6775	241	17	βω̄	βω̄	NOUN
ejpam-6775	241	18	)	)	PUNCT
ejpam-6775	242	1	+	+	NUM
ejpam-6775	242	2	t	t	PROPN
ejpam-6775	242	3	(	(	PUNCT
ejpam-6775	242	4	αω̄	αω̄	NUM
ejpam-6775	242	5	)	)	PUNCT
ejpam-6775	242	6	(	(	PUNCT
ejpam-6775	242	7	λ	λ	X
ejpam-6775	242	8	+	+	NUM
ejpam-6775	242	9	µ)z	µ)z	SYM
ejpam-6775	242	10	=	=	SYM
ejpam-6775	242	11	ξy	ξy	NOUN
ejpam-6775	242	12	−mv	−mv	NOUN
ejpam-6775	242	13	0	0	NUM
ejpam-6775	242	14	t	t	NOUN
ejpam-6775	242	15	(	(	PUNCT
ejpam-6775	242	16	βω̄	βω̄	NOUN
ejpam-6775	242	17	)	)	PUNCT
ejpam-6775	242	18	ω̄′(x	ω̄′(x	NOUN
ejpam-6775	242	19	)	)	PUNCT
ejpam-6775	242	20	=	=	SYM
ejpam-6775	242	21	−[λ+	−[λ+	X
ejpam-6775	242	22	p(x)]ω̄(x	p(x)]ω̄(x	NOUN
ejpam-6775	242	23	)	)	PUNCT
ejpam-6775	242	24	ω̄(0	ω̄(0	NUM
ejpam-6775	242	25	)	)	PUNCT
ejpam-6775	242	26	=	=	NOUN
ejpam-6775	243	1	[	[	X
ejpam-6775	243	2	s0	s0	NOUN
ejpam-6775	243	3	+	+	PROPN
ejpam-6775	243	4	mv	mv	PROPN
ejpam-6775	243	5	0]t	0]t	NUM
ejpam-6775	243	6	(	(	PUNCT
ejpam-6775	243	7	βω̄	βω̄	NOUN
ejpam-6775	243	8	)	)	PUNCT
ejpam-6775	243	9	.	.	PUNCT
ejpam-6775	244	1	(	(	PUNCT
ejpam-6775	244	2	23	23	NUM
ejpam-6775	244	3	)	)	PUNCT
ejpam-6775	244	4	j.	j.	PROPN
ejpam-6775	244	5	leo	leo	PROPN
ejpam-6775	244	6	amalraj	amalraj	PROPN
ejpam-6775	244	7	et	et	PROPN
ejpam-6775	244	8	al	al	PROPN
ejpam-6775	244	9	.	.	PUNCT
ejpam-6775	244	10	/	/	SYM
ejpam-6775	244	11	eur	eur	PROPN
ejpam-6775	244	12	.	.	PUNCT
ejpam-6775	245	1	j.	j.	PROPN
ejpam-6775	245	2	pure	pure	PROPN
ejpam-6775	245	3	appl	appl	PROPN
ejpam-6775	245	4	.	.	PROPN
ejpam-6775	245	5	math	math	PROPN
ejpam-6775	245	6	,	,	PUNCT
ejpam-6775	245	7	18	18	NUM
ejpam-6775	245	8	(	(	PUNCT
ejpam-6775	245	9	4	4	NUM
ejpam-6775	245	10	)	)	PUNCT
ejpam-6775	245	11	(	(	PUNCT
ejpam-6775	245	12	2025	2025	NUM
ejpam-6775	245	13	)	)	PUNCT
ejpam-6775	245	14	,	,	PUNCT
ejpam-6775	245	15	6775	6775	NUM
ejpam-6775	245	16	11	11	NUM
ejpam-6775	245	17	of	of	ADP
ejpam-6775	245	18	32	32	NUM
ejpam-6775	245	19	since	since	SCONJ
ejpam-6775	245	20	y	y	PROPN
ejpam-6775	245	21	and	and	CCONJ
ejpam-6775	245	22	z	z	PROPN
ejpam-6775	245	23	do	do	AUX
ejpam-6775	245	24	not	not	PART
ejpam-6775	245	25	interact	interact	VERB
ejpam-6775	245	26	in	in	ADP
ejpam-6775	245	27	the	the	DET
ejpam-6775	245	28	ω̄-equation	ω̄-equation	NOUN
ejpam-6775	245	29	,	,	PUNCT
ejpam-6775	245	30	we	we	PRON
ejpam-6775	245	31	can	can	AUX
ejpam-6775	245	32	determine	determine	VERB
ejpam-6775	245	33	λ	λ	PROPN
ejpam-6775	245	34	follows	follow	VERB
ejpam-6775	245	35	the	the	DET
ejpam-6775	245	36	threefour	threefour	PROPN
ejpam-6775	245	37	equations	equation	NOUN
ejpam-6775	245	38	of	of	ADP
ejpam-6775	245	39	(	(	PUNCT
ejpam-6775	245	40	14	14	NUM
ejpam-6775	245	41	)	)	PUNCT
ejpam-6775	245	42	.	.	PUNCT
ejpam-6775	246	1	using	use	VERB
ejpam-6775	246	2	the	the	DET
ejpam-6775	246	3	third	third	ADJ
ejpam-6775	246	4	equation	equation	NOUN
ejpam-6775	246	5	of	of	ADP
ejpam-6775	246	6	(	(	PUNCT
ejpam-6775	246	7	14	14	NUM
ejpam-6775	246	8	)	)	PUNCT
ejpam-6775	246	9	,	,	PUNCT
ejpam-6775	246	10	we	we	PRON
ejpam-6775	246	11	get	get	VERB
ejpam-6775	246	12	ω̄(x	ω̄(x	PRON
ejpam-6775	246	13	)	)	PUNCT
ejpam-6775	246	14	=	=	PUNCT
ejpam-6775	247	1	ω̄(0)π(x)e−λx	ω̄(0)π(x)e−λx	AUX
ejpam-6775	247	2	.	.	PUNCT
ejpam-6775	248	1	putting	put	VERB
ejpam-6775	248	2	this	this	DET
ejpam-6775	248	3	expression	expression	NOUN
ejpam-6775	248	4	in	in	ADP
ejpam-6775	248	5	the	the	DET
ejpam-6775	248	6	last	last	ADJ
ejpam-6775	248	7	equation	equation	NOUN
ejpam-6775	248	8	of	of	ADP
ejpam-6775	248	9	(	(	PUNCT
ejpam-6775	248	10	14	14	NUM
ejpam-6775	248	11	)	)	PUNCT
ejpam-6775	248	12	and	and	CCONJ
ejpam-6775	248	13	canceling	cancel	VERB
ejpam-6775	248	14	ω̄(0	ω̄(0	NUM
ejpam-6775	248	15	)	)	PUNCT
ejpam-6775	248	16	,	,	PUNCT
ejpam-6775	248	17	we	we	PRON
ejpam-6775	248	18	obtain	obtain	VERB
ejpam-6775	248	19	the	the	DET
ejpam-6775	248	20	following	follow	VERB
ejpam-6775	248	21	characteristic	characteristic	ADJ
ejpam-6775	248	22	equation	equation	NOUN
ejpam-6775	248	23	:	:	PUNCT
ejpam-6775	248	24	g(λ	g(λ	PROPN
ejpam-6775	248	25	)	)	PUNCT
ejpam-6775	248	26	:	:	PUNCT
ejpam-6775	249	1	=	=	PUNCT
ejpam-6775	250	1	[	[	X
ejpam-6775	250	2	s0	s0	NOUN
ejpam-6775	250	3	+	+	PROPN
ejpam-6775	250	4	mv	mv	PROPN
ejpam-6775	250	5	0	0	NUM
ejpam-6775	250	6	]	]	PUNCT
ejpam-6775	250	7	∫	∫	PROPN
ejpam-6775	250	8	∞	∞	NUM
ejpam-6775	250	9	0	0	NUM
ejpam-6775	250	10	β(x)π(x)e−λxdx	β(x)π(x)e−λxdx	PROPN
ejpam-6775	250	11	=	=	NOUN
ejpam-6775	250	12	1	1	X
ejpam-6775	250	13	.	.	PUNCT
ejpam-6775	250	14	(	(	PUNCT
ejpam-6775	250	15	24	24	NUM
ejpam-6775	250	16	)	)	PUNCT
ejpam-6775	250	17	assume	assume	VERB
ejpam-6775	250	18	that	that	SCONJ
ejpam-6775	250	19	r0	r0	NOUN
ejpam-6775	250	20	<	<	X
ejpam-6775	250	21	1	1	NUM
ejpam-6775	250	22	and	and	CCONJ
ejpam-6775	250	23	λ	λ	PROPN
ejpam-6775	250	24	∈	∈	NOUN
ejpam-6775	250	25	c	c	NOUN
ejpam-6775	250	26	with	with	ADP
ejpam-6775	250	27	ℜλ	ℜλ	PROPN
ejpam-6775	250	28	≥	≥	NOUN
ejpam-6775	250	29	0	0	NUM
ejpam-6775	250	30	,	,	PUNCT
ejpam-6775	250	31	we	we	PRON
ejpam-6775	250	32	have	have	VERB
ejpam-6775	250	33	1	1	NUM
ejpam-6775	250	34	=	=	SYM
ejpam-6775	250	35	|g(λ)|	|g(λ)|	PROPN
ejpam-6775	250	36	≤	≤	NUM
ejpam-6775	250	37	g(ℜλ	g(ℜλ	NOUN
ejpam-6775	250	38	)	)	PUNCT
ejpam-6775	250	39	≤	≤	NUM
ejpam-6775	250	40	g(0	g(0	NOUN
ejpam-6775	250	41	)	)	PUNCT
ejpam-6775	250	42	=	=	PUNCT
ejpam-6775	250	43	r0	r0	NOUN
ejpam-6775	250	44	<	<	X
ejpam-6775	250	45	1	1	NUM
ejpam-6775	250	46	which	which	PRON
ejpam-6775	250	47	is	be	AUX
ejpam-6775	250	48	a	a	DET
ejpam-6775	250	49	contradiction	contradiction	NOUN
ejpam-6775	250	50	.	.	PUNCT
ejpam-6775	251	1	hence	hence	ADV
ejpam-6775	251	2	,	,	PUNCT
ejpam-6775	251	3	the	the	DET
ejpam-6775	251	4	equation	equation	NOUN
ejpam-6775	251	5	g(λ	g(λ	PROPN
ejpam-6775	251	6	)	)	PUNCT
ejpam-6775	252	1	=	=	SYM
ejpam-6775	252	2	1	1	NUM
ejpam-6775	252	3	does	do	AUX
ejpam-6775	252	4	not	not	PART
ejpam-6775	252	5	have	have	VERB
ejpam-6775	252	6	a	a	DET
ejpam-6775	252	7	root	root	NOUN
ejpam-6775	252	8	with	with	ADP
ejpam-6775	252	9	a	a	DET
ejpam-6775	252	10	nonnegative	nonnegative	ADJ
ejpam-6775	252	11	real	real	ADJ
ejpam-6775	252	12	part	part	NOUN
ejpam-6775	252	13	when	when	SCONJ
ejpam-6775	252	14	r0	r0	NOUN
ejpam-6775	252	15	<	<	X
ejpam-6775	252	16	1	1	NUM
ejpam-6775	252	17	.	.	PUNCT
ejpam-6775	253	1	we	we	PRON
ejpam-6775	253	2	conclude	conclude	VERB
ejpam-6775	253	3	that	that	SCONJ
ejpam-6775	253	4	the	the	DET
ejpam-6775	253	5	disease	disease	NOUN
ejpam-6775	253	6	-	-	PUNCT
ejpam-6775	253	7	free	free	ADJ
ejpam-6775	253	8	equilibrium	equilibrium	NOUN
ejpam-6775	253	9	point	point	NOUN
ejpam-6775	253	10	e0	e0	PROPN
ejpam-6775	253	11	is	be	AUX
ejpam-6775	253	12	locally	locally	ADV
ejpam-6775	253	13	asymptotically	asymptotically	ADV
ejpam-6775	253	14	stable	stable	ADJ
ejpam-6775	253	15	whenever	whenever	SCONJ
ejpam-6775	253	16	r0	r0	NOUN
ejpam-6775	253	17	<	<	X
ejpam-6775	253	18	1	1	NUM
ejpam-6775	253	19	.	.	PUNCT
ejpam-6775	254	1	now	now	ADV
ejpam-6775	254	2	,	,	PUNCT
ejpam-6775	254	3	assume	assume	VERB
ejpam-6775	254	4	that	that	SCONJ
ejpam-6775	254	5	r0	r0	NOUN
ejpam-6775	254	6	>	>	X
ejpam-6775	254	7	1	1	NUM
ejpam-6775	254	8	and	and	CCONJ
ejpam-6775	254	9	let	let	VERB
ejpam-6775	254	10	λ	λ	PROPN
ejpam-6775	254	11	>	>	X
ejpam-6775	254	12	0	0	PROPN
ejpam-6775	254	13	,	,	PUNCT
ejpam-6775	254	14	we	we	PRON
ejpam-6775	254	15	have	have	VERB
ejpam-6775	254	16	g(0	g(0	NOUN
ejpam-6775	254	17	)	)	PUNCT
ejpam-6775	254	18	=	=	SYM
ejpam-6775	254	19	r0	r0	NOUN
ejpam-6775	254	20	>	>	X
ejpam-6775	255	1	1	1	X
ejpam-6775	255	2	.	.	PUNCT
ejpam-6775	256	1	moreover	moreover	ADV
ejpam-6775	256	2	,	,	PUNCT
ejpam-6775	256	3	limλ→∞g(λ	limλ→∞g(λ	PROPN
ejpam-6775	256	4	)	)	PUNCT
ejpam-6775	256	5	=	=	SYM
ejpam-6775	257	1	0	0	X
ejpam-6775	257	2	.	.	PUNCT
ejpam-6775	258	1	since	since	SCONJ
ejpam-6775	258	2	g(λ	g(λ	PROPN
ejpam-6775	258	3	)	)	PUNCT
ejpam-6775	258	4	is	be	AUX
ejpam-6775	258	5	a	a	DET
ejpam-6775	258	6	decreasing	decrease	VERB
ejpam-6775	258	7	function	function	NOUN
ejpam-6775	258	8	,	,	PUNCT
ejpam-6775	258	9	there	there	PRON
ejpam-6775	258	10	exists	exist	VERB
ejpam-6775	258	11	a	a	DET
ejpam-6775	258	12	unique	unique	ADJ
ejpam-6775	258	13	λ0	λ0	NOUN
ejpam-6775	258	14	>	>	X
ejpam-6775	258	15	0	0	NUM
ejpam-6775	258	16	such	such	ADJ
ejpam-6775	258	17	that	that	DET
ejpam-6775	258	18	g(λ0	g(λ0	NOUN
ejpam-6775	258	19	)	)	PUNCT
ejpam-6775	258	20	=	=	SYM
ejpam-6775	259	1	1	1	X
ejpam-6775	259	2	.	.	X
ejpam-6775	259	3	therefore	therefore	ADV
ejpam-6775	259	4	e0	e0	PROPN
ejpam-6775	259	5	is	be	AUX
ejpam-6775	259	6	unstable	unstable	ADJ
ejpam-6775	259	7	whenever	whenever	SCONJ
ejpam-6775	259	8	r0	r0	NOUN
ejpam-6775	259	9	>	>	X
ejpam-6775	259	10	1	1	X
ejpam-6775	259	11	.	.	PUNCT
ejpam-6775	260	1	biologically	biologically	ADV
ejpam-6775	260	2	speaking	speak	VERB
ejpam-6775	260	3	,	,	PUNCT
ejpam-6775	260	4	this	this	DET
ejpam-6775	260	5	result	result	NOUN
ejpam-6775	260	6	means	mean	VERB
ejpam-6775	260	7	that	that	SCONJ
ejpam-6775	260	8	the	the	DET
ejpam-6775	260	9	disease	disease	NOUN
ejpam-6775	260	10	can	can	AUX
ejpam-6775	260	11	be	be	AUX
ejpam-6775	260	12	eradicated	eradicate	VERB
ejpam-6775	260	13	(	(	PUNCT
ejpam-6775	260	14	when	when	SCONJ
ejpam-6775	260	15	r0	r0	VERB
ejpam-6775	260	16	<	<	X
ejpam-6775	260	17	1	1	NUM
ejpam-6775	260	18	)	)	PUNCT
ejpam-6775	260	19	when	when	SCONJ
ejpam-6775	260	20	initial	initial	ADJ
ejpam-6775	260	21	sizes	size	NOUN
ejpam-6775	260	22	of	of	ADP
ejpam-6775	260	23	each	each	DET
ejpam-6775	260	24	subpopulation	subpopulation	NOUN
ejpam-6775	260	25	in	in	ADP
ejpam-6775	260	26	the	the	DET
ejpam-6775	260	27	system	system	NOUN
ejpam-6775	260	28	(	(	PUNCT
ejpam-6775	260	29	1	1	X
ejpam-6775	260	30	)	)	PUNCT
ejpam-6775	260	31	is	be	AUX
ejpam-6775	260	32	within	within	ADP
ejpam-6775	260	33	the	the	DET
ejpam-6775	260	34	basin	basin	NOUN
ejpam-6775	260	35	of	of	ADP
ejpam-6775	260	36	attraction	attraction	NOUN
ejpam-6775	260	37	of	of	ADP
ejpam-6775	260	38	the	the	DET
ejpam-6775	260	39	stable	stable	ADJ
ejpam-6775	260	40	point	point	NOUN
ejpam-6775	260	41	e0	e0	PROPN
ejpam-6775	260	42	.	.	PUNCT
ejpam-6775	261	1	we	we	PRON
ejpam-6775	261	2	now	now	ADV
ejpam-6775	261	3	examine	examine	VERB
ejpam-6775	261	4	the	the	DET
ejpam-6775	261	5	existence	existence	NOUN
ejpam-6775	261	6	of	of	ADP
ejpam-6775	261	7	the	the	DET
ejpam-6775	261	8	endemic	endemic	ADJ
ejpam-6775	261	9	equilibrium	equilibrium	NOUN
ejpam-6775	261	10	points	point	NOUN
ejpam-6775	261	11	.	.	PUNCT
ejpam-6775	262	1	for	for	ADP
ejpam-6775	262	2	this	this	PRON
ejpam-6775	262	3	,	,	PUNCT
ejpam-6775	262	4	let	let	VERB
ejpam-6775	262	5	e∗(x	e∗(x	NOUN
ejpam-6775	262	6	)	)	PUNCT
ejpam-6775	262	7	=	=	NOUN
ejpam-6775	262	8	(	(	PUNCT
ejpam-6775	262	9	s∗	s∗	PROPN
ejpam-6775	262	10	,	,	PUNCT
ejpam-6775	262	11	v	v	NOUN
ejpam-6775	262	12	∗	∗	NOUN
ejpam-6775	262	13	,	,	PUNCT
ejpam-6775	262	14	i∗(x	i∗(x	PROPN
ejpam-6775	262	15	)	)	PUNCT
ejpam-6775	262	16	,	,	PUNCT
ejpam-6775	262	17	0	0	X
ejpam-6775	262	18	)	)	PUNCT
ejpam-6775	262	19	be	be	VERB
ejpam-6775	262	20	any	any	DET
ejpam-6775	262	21	arbitrary	arbitrary	ADJ
ejpam-6775	262	22	equilibrium	equilibrium	NOUN
ejpam-6775	262	23	point	point	NOUN
ejpam-6775	262	24	of	of	ADP
ejpam-6775	262	25	system	system	NOUN
ejpam-6775	262	26	(	(	PUNCT
ejpam-6775	262	27	1	1	NUM
ejpam-6775	262	28	)	)	PUNCT
ejpam-6775	262	29	.	.	PUNCT
ejpam-6775	263	1	to	to	PART
ejpam-6775	263	2	find	find	VERB
ejpam-6775	263	3	conditions	condition	NOUN
ejpam-6775	263	4	for	for	ADP
ejpam-6775	263	5	the	the	DET
ejpam-6775	263	6	existence	existence	NOUN
ejpam-6775	263	7	of	of	ADP
ejpam-6775	263	8	equilibrium	equilibrium	NOUN
ejpam-6775	263	9	points	point	NOUN
ejpam-6775	263	10	for	for	ADP
ejpam-6775	263	11	which	which	DET
ejpam-6775	263	12	disease	disease	NOUN
ejpam-6775	263	13	is	be	AUX
ejpam-6775	263	14	endemic	endemic	ADJ
ejpam-6775	263	15	in	in	ADP
ejpam-6775	263	16	the	the	DET
ejpam-6775	263	17	population	population	NOUN
ejpam-6775	263	18	we	we	PRON
ejpam-6775	263	19	set	set	VERB
ejpam-6775	263	20	the	the	DET
ejpam-6775	263	21	derivatives	derivative	NOUN
ejpam-6775	263	22	with	with	ADP
ejpam-6775	263	23	respect	respect	NOUN
ejpam-6775	263	24	to	to	ADP
ejpam-6775	263	25	time	time	NOUN
ejpam-6775	263	26	in	in	ADP
ejpam-6775	263	27	(	(	PUNCT
ejpam-6775	263	28	2	2	X
ejpam-6775	263	29	)	)	PUNCT
ejpam-6775	263	30	equal	equal	ADJ
ejpam-6775	263	31	to	to	ADP
ejpam-6775	263	32	zero	zero	NUM
ejpam-6775	263	33	(	(	PUNCT
ejpam-6775	263	34	i.e.	i.e.	X
ejpam-6775	263	35	,	,	PUNCT
ejpam-6775	263	36	by	by	ADP
ejpam-6775	263	37	solving	solve	VERB
ejpam-6775	263	38	the	the	DET
ejpam-6775	263	39	abstract	abstract	ADJ
ejpam-6775	263	40	algebraic	algebraic	ADJ
ejpam-6775	263	41	equation	equation	NOUN
ejpam-6775	263	42	ae∗	ae∗	ADJ
ejpam-6775	263	43	+	+	NOUN
ejpam-6775	263	44	h(e∗	h(e∗	X
ejpam-6775	263	45	)	)	PUNCT
ejpam-6775	263	46	=	=	SYM
ejpam-6775	263	47	0	0	NUM
ejpam-6775	263	48	)	)	PUNCT
ejpam-6775	263	49	,	,	PUNCT
ejpam-6775	263	50	that	that	SCONJ
ejpam-6775	263	51	is:	is:	PROPN
ejpam-6775	263	52	λ−	λ−	PROPN
ejpam-6775	263	53	t	t	PROPN
ejpam-6775	263	54	(	(	PUNCT
ejpam-6775	263	55	βi∗)s∗	βi∗)s∗	PROPN
ejpam-6775	263	56	+	+	NUM
ejpam-6775	263	57	t	t	NOUN
ejpam-6775	263	58	(	(	PUNCT
ejpam-6775	263	59	αi∗)−	αi∗)−	NUM
ejpam-6775	263	60	(	(	PUNCT
ejpam-6775	263	61	ξ	ξ	PROPN
ejpam-6775	263	62	+	+	NUM
ejpam-6775	263	63	µ)s∗	µ)s∗	ADJ
ejpam-6775	263	64	=	=	SYM
ejpam-6775	263	65	0	0	NUM
ejpam-6775	263	66	ξs∗	ξs∗	NOUN
ejpam-6775	263	67	−mt	−mt	NOUN
ejpam-6775	263	68	(	(	PUNCT
ejpam-6775	263	69	βi∗)v	βi∗)v	PROPN
ejpam-6775	263	70	∗	∗	NOUN
ejpam-6775	263	71	−	−	NOUN
ejpam-6775	264	1	µv	µv	NOUN
ejpam-6775	264	2	∗	∗	NOUN
ejpam-6775	264	3	=	=	SYM
ejpam-6775	264	4	0	0	NUM
ejpam-6775	264	5	∂xi	∂xi	PROPN
ejpam-6775	264	6	∗(x	∗(x	VERB
ejpam-6775	264	7	)	)	PUNCT
ejpam-6775	264	8	=	=	SYM
ejpam-6775	265	1	−[µ+	−[µ+	PROPN
ejpam-6775	265	2	δ(x	δ(x	NOUN
ejpam-6775	265	3	)	)	PUNCT
ejpam-6775	266	1	+	+	CCONJ
ejpam-6775	266	2	α(x)]i∗(x	α(x)]i∗(x	PROPN
ejpam-6775	266	3	)	)	PUNCT
ejpam-6775	266	4	i∗(0	i∗(0	NOUN
ejpam-6775	266	5	)	)	PUNCT
ejpam-6775	267	1	=	=	PUNCT
ejpam-6775	268	1	[	[	X
ejpam-6775	268	2	s∗	s∗	PROPN
ejpam-6775	268	3	+	+	ADV
ejpam-6775	268	4	mv	mv	PROPN
ejpam-6775	268	5	∗]t	∗]t	X
ejpam-6775	268	6	(	(	PUNCT
ejpam-6775	268	7	βi∗	βi∗	NOUN
ejpam-6775	268	8	)	)	PUNCT
ejpam-6775	268	9	.	.	PUNCT
ejpam-6775	269	1	(	(	PUNCT
ejpam-6775	269	2	25	25	NUM
ejpam-6775	269	3	)	)	PUNCT
ejpam-6775	269	4	then	then	ADV
ejpam-6775	269	5	,	,	PUNCT
ejpam-6775	269	6	equilibrium	equilibrium	NOUN
ejpam-6775	269	7	point	point	PROPN
ejpam-6775	269	8	e∗	e∗	PROPN
ejpam-6775	269	9	with	with	ADP
ejpam-6775	269	10	positive	positive	ADJ
ejpam-6775	269	11	components	component	NOUN
ejpam-6775	269	12	must	must	AUX
ejpam-6775	269	13	be	be	AUX
ejpam-6775	269	14	s∗	s∗	PROPN
ejpam-6775	269	15	=	=	PUNCT
ejpam-6775	269	16	λ+	λ+	PUNCT
ejpam-6775	269	17	t	t	PROPN
ejpam-6775	269	18	(	(	PUNCT
ejpam-6775	269	19	αi∗	αi∗	NOUN
ejpam-6775	269	20	)	)	PUNCT
ejpam-6775	269	21	t	t	NOUN
ejpam-6775	269	22	(	(	PUNCT
ejpam-6775	269	23	βi∗	βi∗	NOUN
ejpam-6775	269	24	)	)	PUNCT
ejpam-6775	270	1	+	+	CCONJ
ejpam-6775	270	2	µ+	µ+	X
ejpam-6775	270	3	ξ	ξ	PROPN
ejpam-6775	270	4	,	,	PUNCT
ejpam-6775	270	5	v	v	NOUN
ejpam-6775	270	6	∗	∗	NOUN
ejpam-6775	270	7	=	=	SYM
ejpam-6775	270	8	ξs∗	ξs∗	PROPN
ejpam-6775	270	9	mt	mt	PROPN
ejpam-6775	270	10	(	(	PUNCT
ejpam-6775	270	11	βi∗	βi∗	NOUN
ejpam-6775	270	12	)	)	PUNCT
ejpam-6775	271	1	+	+	NUM
ejpam-6775	271	2	µ	µ	X
ejpam-6775	271	3	,	,	PUNCT
ejpam-6775	271	4	i∗(x	i∗(x	NOUN
ejpam-6775	271	5	)	)	PUNCT
ejpam-6775	271	6	=	=	SYM
ejpam-6775	271	7	i∗(0)π(x	i∗(0)π(x	PROPN
ejpam-6775	271	8	)	)	PUNCT
ejpam-6775	271	9	,	,	PUNCT
ejpam-6775	271	10	(	(	PUNCT
ejpam-6775	271	11	26	26	NUM
ejpam-6775	271	12	)	)	PUNCT
ejpam-6775	271	13	and	and	CCONJ
ejpam-6775	271	14	i∗(0	i∗(0	NOUN
ejpam-6775	271	15	)	)	PUNCT
ejpam-6775	271	16	is	be	AUX
ejpam-6775	271	17	the	the	DET
ejpam-6775	271	18	positive	positive	ADJ
ejpam-6775	271	19	real	real	ADJ
ejpam-6775	271	20	solution	solution	NOUN
ejpam-6775	271	21	of	of	ADP
ejpam-6775	271	22	the	the	DET
ejpam-6775	271	23	quadratic	quadratic	ADJ
ejpam-6775	271	24	equation	equation	NOUN
ejpam-6775	271	25	a2(i	a2(i	ADP
ejpam-6775	271	26	∗(0))2	∗(0))2	X
ejpam-6775	271	27	+	+	CCONJ
ejpam-6775	271	28	a1i	a1i	PROPN
ejpam-6775	271	29	∗(0	∗(0	AUX
ejpam-6775	271	30	)	)	PUNCT
ejpam-6775	272	1	+	+	CCONJ
ejpam-6775	272	2	a0	a0	NOUN
ejpam-6775	272	3	=	=	SYM
ejpam-6775	272	4	0	0	PROPN
ejpam-6775	272	5	,	,	PUNCT
ejpam-6775	272	6	(	(	PUNCT
ejpam-6775	272	7	27	27	NUM
ejpam-6775	272	8	)	)	PUNCT
ejpam-6775	272	9	where	where	SCONJ
ejpam-6775	272	10	a2	a2	PROPN
ejpam-6775	272	11	=	=	PROPN
ejpam-6775	272	12	m[t	m[t	PROPN
ejpam-6775	272	13	(	(	PUNCT
ejpam-6775	272	14	βπ)]2[1−	βπ)]2[1−	PROPN
ejpam-6775	272	15	t	t	PROPN
ejpam-6775	272	16	(	(	PUNCT
ejpam-6775	272	17	απ	απ	NOUN
ejpam-6775	272	18	)	)	PUNCT
ejpam-6775	272	19	]	]	PUNCT
ejpam-6775	272	20	,	,	PUNCT
ejpam-6775	272	21	a0	a0	PROPN
ejpam-6775	272	22	=	=	PUNCT
ejpam-6775	272	23	µ(µ+	µ(µ+	NUM
ejpam-6775	272	24	ξ)(1−r0	ξ)(1−r0	NUM
ejpam-6775	272	25	)	)	PUNCT
ejpam-6775	272	26	;	;	PUNCT
ejpam-6775	272	27	(	(	PUNCT
ejpam-6775	272	28	28	28	X
ejpam-6775	272	29	)	)	PUNCT
ejpam-6775	272	30	a1	a1	NOUN
ejpam-6775	272	31	=	=	PROPN
ejpam-6775	272	32	mt	mt	PROPN
ejpam-6775	272	33	(	(	PUNCT
ejpam-6775	272	34	βπ)[µ−	βπ)[µ−	ADV
ejpam-6775	272	35	λt	λt	X
ejpam-6775	272	36	(	(	PUNCT
ejpam-6775	272	37	βπ	βπ	NOUN
ejpam-6775	272	38	)	)	PUNCT
ejpam-6775	272	39	]	]	PUNCT
ejpam-6775	273	1	+	+	CCONJ
ejpam-6775	273	2	(	(	PUNCT
ejpam-6775	273	3	µ+mξ)t	µ+mξ)t	NOUN
ejpam-6775	273	4	(	(	PUNCT
ejpam-6775	273	5	βπ)[1−	βπ)[1−	PROPN
ejpam-6775	273	6	t	t	PROPN
ejpam-6775	273	7	(	(	PUNCT
ejpam-6775	273	8	απ	απ	NOUN
ejpam-6775	273	9	)	)	PUNCT
ejpam-6775	273	10	]	]	PUNCT
ejpam-6775	273	11	.	.	PUNCT
ejpam-6775	274	1	(	(	PUNCT
ejpam-6775	274	2	29	29	NUM
ejpam-6775	274	3	)	)	PUNCT
ejpam-6775	274	4	we	we	PRON
ejpam-6775	274	5	see	see	VERB
ejpam-6775	274	6	that	that	SCONJ
ejpam-6775	274	7	the	the	DET
ejpam-6775	274	8	coefficients	coefficient	NOUN
ejpam-6775	274	9	a2	a2	PROPN
ejpam-6775	274	10	and	and	CCONJ
ejpam-6775	274	11	a0	a0	PROPN
ejpam-6775	274	12	are	be	AUX
ejpam-6775	274	13	positives	positive	NOUN
ejpam-6775	274	14	(	(	PUNCT
ejpam-6775	274	15	respectively	respectively	ADV
ejpam-6775	274	16	negatives	negative	NOUN
ejpam-6775	274	17	)	)	PUNCT
ejpam-6775	275	1	if	if	SCONJ
ejpam-6775	276	1	and	and	CCONJ
ejpam-6775	276	2	only	only	ADV
ejpam-6775	276	3	if	if	SCONJ
ejpam-6775	276	4	t	t	PROPN
ejpam-6775	276	5	(	(	PUNCT
ejpam-6775	276	6	απ	απ	NOUN
ejpam-6775	276	7	)	)	PUNCT
ejpam-6775	276	8	<	<	X
ejpam-6775	276	9	1	1	NUM
ejpam-6775	276	10	and	and	CCONJ
ejpam-6775	276	11	r0	r0	VERB
ejpam-6775	276	12	<	<	X
ejpam-6775	276	13	1	1	NUM
ejpam-6775	276	14	(	(	PUNCT
ejpam-6775	276	15	respectively	respectively	ADV
ejpam-6775	276	16	t	t	PROPN
ejpam-6775	276	17	(	(	PUNCT
ejpam-6775	276	18	απ	απ	NOUN
ejpam-6775	276	19	)	)	PUNCT
ejpam-6775	276	20	>	>	X
ejpam-6775	276	21	1	1	NUM
ejpam-6775	276	22	and	and	CCONJ
ejpam-6775	276	23	r0	r0	VERB
ejpam-6775	276	24	>	>	X
ejpam-6775	276	25	1	1	NUM
ejpam-6775	276	26	)	)	PUNCT
ejpam-6775	276	27	.	.	PUNCT
ejpam-6775	277	1	using	use	VERB
ejpam-6775	277	2	the	the	DET
ejpam-6775	277	3	descartes	descarte	NOUN
ejpam-6775	277	4	’	'	PUNCT
ejpam-6775	277	5	rule	rule	NOUN
ejpam-6775	277	6	of	of	ADP
ejpam-6775	277	7	j.	j.	PROPN
ejpam-6775	277	8	leo	leo	PROPN
ejpam-6775	277	9	amalraj	amalraj	PROPN
ejpam-6775	277	10	et	et	PROPN
ejpam-6775	277	11	al	al	PROPN
ejpam-6775	277	12	.	.	PUNCT
ejpam-6775	277	13	/	/	SYM
ejpam-6775	277	14	eur	eur	PROPN
ejpam-6775	277	15	.	.	PUNCT
ejpam-6775	278	1	j.	j.	PROPN
ejpam-6775	278	2	pure	pure	PROPN
ejpam-6775	278	3	appl	appl	PROPN
ejpam-6775	278	4	.	.	PROPN
ejpam-6775	278	5	math	math	PROPN
ejpam-6775	278	6	,	,	PUNCT
ejpam-6775	278	7	18	18	NUM
ejpam-6775	278	8	(	(	PUNCT
ejpam-6775	278	9	4	4	NUM
ejpam-6775	278	10	)	)	PUNCT
ejpam-6775	278	11	(	(	PUNCT
ejpam-6775	278	12	2025	2025	NUM
ejpam-6775	278	13	)	)	PUNCT
ejpam-6775	278	14	,	,	PUNCT
ejpam-6775	278	15	6775	6775	NUM
ejpam-6775	278	16	12	12	NUM
ejpam-6775	278	17	of	of	ADP
ejpam-6775	278	18	32	32	NUM
ejpam-6775	278	19	signs	sign	NOUN
ejpam-6775	278	20	on	on	ADP
ejpam-6775	278	21	the	the	DET
ejpam-6775	278	22	quadratic	quadratic	ADJ
ejpam-6775	278	23	polynomial	polynomial	NOUN
ejpam-6775	278	24	(	(	PUNCT
ejpam-6775	278	25	17	17	NUM
ejpam-6775	278	26	)	)	PUNCT
ejpam-6775	278	27	,	,	PUNCT
ejpam-6775	278	28	the	the	DET
ejpam-6775	278	29	existence	existence	NOUN
ejpam-6775	278	30	for	for	ADP
ejpam-6775	278	31	the	the	DET
ejpam-6775	278	32	possible	possible	ADJ
ejpam-6775	278	33	positive	positive	ADJ
ejpam-6775	278	34	real	real	ADJ
ejpam-6775	278	35	roots	root	NOUN
ejpam-6775	278	36	of	of	ADP
ejpam-6775	278	37	equation	equation	NOUN
ejpam-6775	278	38	(	(	PUNCT
ejpam-6775	278	39	17	17	NUM
ejpam-6775	278	40	)	)	PUNCT
ejpam-6775	278	41	are	be	AUX
ejpam-6775	278	42	summarized	summarize	VERB
ejpam-6775	278	43	in	in	ADP
ejpam-6775	278	44	table	table	NOUN
ejpam-6775	278	45	1	1	NUM
ejpam-6775	278	46	.	.	PUNCT
ejpam-6775	279	1	it	it	PRON
ejpam-6775	279	2	follows	follow	VERB
ejpam-6775	279	3	that	that	SCONJ
ejpam-6775	279	4	under	under	ADP
ejpam-6775	279	5	the	the	DET
ejpam-6775	279	6	condition	condition	NOUN
ejpam-6775	279	7	r0	r0	NOUN
ejpam-6775	279	8	<	<	X
ejpam-6775	279	9	1	1	NUM
ejpam-6775	279	10	,	,	PUNCT
ejpam-6775	279	11	it	it	PRON
ejpam-6775	279	12	is	be	AUX
ejpam-6775	279	13	possible	possible	ADJ
ejpam-6775	279	14	to	to	PART
ejpam-6775	279	15	have	have	VERB
ejpam-6775	279	16	one	one	NUM
ejpam-6775	279	17	or	or	CCONJ
ejpam-6775	279	18	two	two	NUM
ejpam-6775	279	19	...	...	PUNCT
ejpam-6775	279	20	endemic	endemic	ADJ
ejpam-6775	279	21	equilibrium	equilibrium	NOUN
ejpam-6775	279	22	points	point	NOUN
ejpam-6775	279	23	.	.	PUNCT
ejpam-6775	280	1	in	in	ADP
ejpam-6775	280	2	this	this	DET
ejpam-6775	280	3	case	case	NOUN
ejpam-6775	280	4	,	,	PUNCT
ejpam-6775	280	5	it	it	PRON
ejpam-6775	280	6	is	be	AUX
ejpam-6775	280	7	possible	possible	ADJ
ejpam-6775	280	8	to	to	PART
ejpam-6775	280	9	have	have	VERB
ejpam-6775	280	10	a	a	DET
ejpam-6775	280	11	backward	backward	ADJ
ejpam-6775	280	12	bifurcation	bifurcation	NOUN
ejpam-6775	280	13	phenomenon	phenomenon	NOUN
ejpam-6775	280	14	in	in	ADP
ejpam-6775	280	15	system	system	NOUN
ejpam-6775	280	16	(	(	PUNCT
ejpam-6775	280	17	1	1	NUM
ejpam-6775	280	18	)	)	PUNCT
ejpam-6775	280	19	,	,	PUNCT
ejpam-6775	280	20	i.e.	i.e.	X
ejpam-6775	280	21	,	,	PUNCT
ejpam-6775	280	22	the	the	DET
ejpam-6775	280	23	locally	locally	ADV
ejpam-6775	280	24	asymptotically	asymptotically	ADV
ejpam-6775	280	25	stable	stable	ADJ
ejpam-6775	280	26	disease	disease	NOUN
ejpam-6775	280	27	-	-	PUNCT
ejpam-6775	280	28	free	free	ADJ
ejpam-6775	280	29	equilibrium	equilibrium	NOUN
ejpam-6775	280	30	e0	e0	PROPN
ejpam-6775	280	31	coexists	coexist	VERB
ejpam-6775	280	32	with	with	ADP
ejpam-6775	280	33	a	a	DET
ejpam-6775	280	34	locally	locally	ADV
ejpam-6775	280	35	asymptotically	asymptotically	ADV
ejpam-6775	280	36	stable	stable	ADJ
ejpam-6775	280	37	endemic	endemic	ADJ
ejpam-6775	280	38	equilibrium	equilibrium	NOUN
ejpam-6775	280	39	when	when	SCONJ
ejpam-6775	280	40	r0	r0	NOUN
ejpam-6775	280	41	<	<	X
ejpam-6775	280	42	1	1	NUM
ejpam-6775	280	43	.	.	PUNCT
ejpam-6775	280	44	to	to	PART
ejpam-6775	280	45	check	check	VERB
ejpam-6775	280	46	this	this	PRON
ejpam-6775	280	47	,	,	PUNCT
ejpam-6775	280	48	the	the	DET
ejpam-6775	280	49	discriminant	discriminant	NOUN
ejpam-6775	280	50	of	of	ADP
ejpam-6775	280	51	quadratic	quadratic	ADJ
ejpam-6775	280	52	equation	equation	NOUN
ejpam-6775	280	53	(	(	PUNCT
ejpam-6775	280	54	17	17	NUM
ejpam-6775	280	55	)	)	PUNCT
ejpam-6775	280	56	a21	a21	NOUN
ejpam-6775	281	1	−	−	PROPN
ejpam-6775	282	1	4a2a0	4a2a0	PROPN
ejpam-6775	282	2	is	be	AUX
ejpam-6775	282	3	set	set	VERB
ejpam-6775	282	4	to	to	ADP
ejpam-6775	282	5	zero	zero	NUM
ejpam-6775	282	6	and	and	CCONJ
ejpam-6775	282	7	solved	solve	VERB
ejpam-6775	282	8	for	for	ADP
ejpam-6775	282	9	the	the	DET
ejpam-6775	282	10	critical	critical	ADJ
ejpam-6775	282	11	value	value	NOUN
ejpam-6775	282	12	of	of	ADP
ejpam-6775	282	13	r0	r0	NOUN
ejpam-6775	282	14	denoted	denote	VERB
ejpam-6775	282	15	r∗	r∗	PROPN
ejpam-6775	282	16	0	0	NUM
ejpam-6775	282	17	,	,	PUNCT
ejpam-6775	282	18	given	give	VERB
ejpam-6775	282	19	by	by	ADP
ejpam-6775	282	20	r∗	r∗	PROPN
ejpam-6775	282	21	0	0	NUM
ejpam-6775	282	22	=	=	SYM
ejpam-6775	282	23	1−	1−	NUM
ejpam-6775	282	24	a21	a21	PROPN
ejpam-6775	282	25	4a2µ(µ+	4a2µ(µ+	PROPN
ejpam-6775	282	26	ξ	ξ	PROPN
ejpam-6775	282	27	)	)	PUNCT
ejpam-6775	282	28	.	.	PUNCT
ejpam-6775	283	1	(	(	PUNCT
ejpam-6775	283	2	30	30	NUM
ejpam-6775	283	3	)	)	PUNCT
ejpam-6775	283	4	thus	thus	ADV
ejpam-6775	283	5	,	,	PUNCT
ejpam-6775	283	6	the	the	DET
ejpam-6775	283	7	backward	backward	ADJ
ejpam-6775	283	8	bifurcation	bifurcation	NOUN
ejpam-6775	283	9	phenomenon	phenomenon	NOUN
ejpam-6775	283	10	would	would	AUX
ejpam-6775	283	11	occur	occur	VERB
ejpam-6775	283	12	for	for	ADP
ejpam-6775	283	13	the	the	DET
ejpam-6775	283	14	values	value	NOUN
ejpam-6775	283	15	of	of	ADP
ejpam-6775	283	16	threshold	threshold	NOUN
ejpam-6775	283	17	r0	r0	NOUN
ejpam-6775	283	18	satisfying	satisfy	VERB
ejpam-6775	283	19	the	the	DET
ejpam-6775	283	20	relation	relation	NOUN
ejpam-6775	283	21	r∗	r∗	VERB
ejpam-6775	283	22	0	0	PUNCT
ejpam-6775	283	23	<	<	X
ejpam-6775	283	24	r0	r0	NOUN
ejpam-6775	283	25	<	<	X
ejpam-6775	283	26	1	1	NUM
ejpam-6775	283	27	.	.	PUNCT
ejpam-6775	284	1	it	it	PRON
ejpam-6775	284	2	would	would	AUX
ejpam-6775	284	3	be	be	AUX
ejpam-6775	284	4	very	very	ADV
ejpam-6775	284	5	interesting	interesting	ADJ
ejpam-6775	284	6	to	to	PART
ejpam-6775	284	7	analyze	analyze	VERB
ejpam-6775	284	8	the	the	DET
ejpam-6775	284	9	system	system	NOUN
ejpam-6775	284	10	’s	’s	PART
ejpam-6775	284	11	bifurcations	bifurcation	NOUN
ejpam-6775	284	12	to	to	PART
ejpam-6775	284	13	see	see	VERB
ejpam-6775	284	14	if	if	SCONJ
ejpam-6775	284	15	it	it	PRON
ejpam-6775	284	16	is	be	AUX
ejpam-6775	284	17	possible	possible	ADJ
ejpam-6775	284	18	to	to	PART
ejpam-6775	284	19	have	have	VERB
ejpam-6775	284	20	a	a	DET
ejpam-6775	284	21	bistability	bistability	NOUN
ejpam-6775	284	22	phenomenon	phenomenon	NOUN
ejpam-6775	284	23	,	,	PUNCT
ejpam-6775	284	24	and	and	CCONJ
ejpam-6775	284	25	if	if	SCONJ
ejpam-6775	284	26	so	so	ADV
ejpam-6775	284	27	,	,	PUNCT
ejpam-6775	284	28	to	to	PART
ejpam-6775	284	29	determine	determine	VERB
ejpam-6775	284	30	its	its	PRON
ejpam-6775	284	31	cause	cause	NOUN
ejpam-6775	284	32	.	.	PUNCT
ejpam-6775	285	1	table	table	NOUN
ejpam-6775	285	2	1	1	NUM
ejpam-6775	285	3	:	:	PUNCT
ejpam-6775	285	4	number	number	NOUN
ejpam-6775	285	5	of	of	ADP
ejpam-6775	285	6	possible	possible	ADJ
ejpam-6775	285	7	positive	positive	ADJ
ejpam-6775	285	8	real	real	ADJ
ejpam-6775	285	9	roots	root	NOUN
ejpam-6775	285	10	of	of	ADP
ejpam-6775	285	11	equation	equation	NOUN
ejpam-6775	285	12	(	(	PUNCT
ejpam-6775	285	13	17	17	NUM
ejpam-6775	285	14	)	)	PUNCT
ejpam-6775	285	15	according	accord	VERB
ejpam-6775	285	16	to	to	ADP
ejpam-6775	285	17	the	the	DET
ejpam-6775	285	18	sign	sign	NOUN
ejpam-6775	285	19	of	of	ADP
ejpam-6775	285	20	the	the	DET
ejpam-6775	285	21	coefficients	coefficient	NOUN
ejpam-6775	285	22	ak	ak	PROPN
ejpam-6775	285	23	,	,	PUNCT
ejpam-6775	285	24	k	k	PROPN
ejpam-6775	285	25	=	=	SYM
ejpam-6775	285	26	0	0	NUM
ejpam-6775	285	27	,	,	PUNCT
ejpam-6775	285	28	1	1	NUM
ejpam-6775	285	29	,	,	PUNCT
ejpam-6775	285	30	2	2	NUM
ejpam-6775	285	31	.	.	X
ejpam-6775	285	32	a2	a2	PROPN
ejpam-6775	285	33	a1	a1	PROPN
ejpam-6775	285	34	a0	a0	PROPN
ejpam-6775	285	35	r0	r0	NOUN
ejpam-6775	285	36	number	number	NOUN
ejpam-6775	285	37	of	of	ADP
ejpam-6775	285	38	positive	positive	ADJ
ejpam-6775	285	39	solutions	solution	NOUN
ejpam-6775	285	40	of	of	ADP
ejpam-6775	285	41	(	(	PUNCT
ejpam-6775	285	42	17	17	NUM
ejpam-6775	285	43	)	)	PUNCT
ejpam-6775	285	44	r0	r0	NOUN
ejpam-6775	285	45	>	>	X
ejpam-6775	285	46	1	1	NUM
ejpam-6775	285	47	0	0	NUM
ejpam-6775	286	1	+	+	CCONJ
ejpam-6775	286	2	r0	r0	NOUN
ejpam-6775	286	3	>	>	X
ejpam-6775	286	4	1	1	NUM
ejpam-6775	286	5	1	1	NUM
ejpam-6775	286	6	+	+	CCONJ
ejpam-6775	286	7	+	+	NUM
ejpam-6775	286	8	r0	r0	NOUN
ejpam-6775	286	9	>	>	X
ejpam-6775	286	10	1	1	NUM
ejpam-6775	286	11	1	1	NUM
ejpam-6775	286	12	+	+	CCONJ
ejpam-6775	286	13	+	+	X
ejpam-6775	286	14	r0	r0	NOUN
ejpam-6775	286	15	<	<	X
ejpam-6775	286	16	1	1	NUM
ejpam-6775	286	17	1	1	NUM
ejpam-6775	286	18	+	+	CCONJ
ejpam-6775	286	19	+	+	CCONJ
ejpam-6775	286	20	+	+	CCONJ
ejpam-6775	286	21	r0	r0	NOUN
ejpam-6775	286	22	<	<	X
ejpam-6775	286	23	1	1	NUM
ejpam-6775	286	24	1	1	NUM
ejpam-6775	286	25	+	+	CCONJ
ejpam-6775	286	26	+	+	X
ejpam-6775	286	27	r0	r0	NOUN
ejpam-6775	286	28	<	<	X
ejpam-6775	286	29	1	1	NUM
ejpam-6775	286	30	0	0	NUM
ejpam-6775	287	1	+	+	CCONJ
ejpam-6775	287	2	+	+	CCONJ
ejpam-6775	287	3	+	+	CCONJ
ejpam-6775	287	4	r0	r0	NOUN
ejpam-6775	287	5	<	<	X
ejpam-6775	287	6	1	1	NUM
ejpam-6775	287	7	0	0	NUM
ejpam-6775	287	8	or	or	CCONJ
ejpam-6775	287	9	2	2	NUM
ejpam-6775	287	10	4.3	4.3	NUM
ejpam-6775	287	11	.	.	PUNCT
ejpam-6775	288	1	forward	forward	ADV
ejpam-6775	288	2	and	and	CCONJ
ejpam-6775	288	3	backward	backward	ADJ
ejpam-6775	288	4	bifurcation	bifurcation	NOUN
ejpam-6775	288	5	phenomena	phenomenon	NOUN
ejpam-6775	288	6	in	in	ADP
ejpam-6775	288	7	this	this	DET
ejpam-6775	288	8	subsection	subsection	NOUN
ejpam-6775	288	9	,	,	PUNCT
ejpam-6775	288	10	we	we	PRON
ejpam-6775	288	11	study	study	VERB
ejpam-6775	288	12	the	the	DET
ejpam-6775	288	13	existence	existence	NOUN
ejpam-6775	288	14	of	of	ADP
ejpam-6775	288	15	bifurcations	bifurcation	NOUN
ejpam-6775	288	16	of	of	ADP
ejpam-6775	288	17	system	system	NOUN
ejpam-6775	288	18	(	(	PUNCT
ejpam-6775	288	19	1	1	NUM
ejpam-6775	288	20	)	)	PUNCT
ejpam-6775	288	21	around	around	ADP
ejpam-6775	288	22	the	the	DET
ejpam-6775	288	23	disease	disease	NOUN
ejpam-6775	288	24	-	-	PUNCT
ejpam-6775	288	25	free	free	ADJ
ejpam-6775	288	26	equilibrium	equilibrium	NOUN
ejpam-6775	288	27	e0	e0	PROPN
ejpam-6775	288	28	.	.	PUNCT
ejpam-6775	289	1	to	to	ADP
ejpam-6775	289	2	this	this	DET
ejpam-6775	289	3	end	end	NOUN
ejpam-6775	289	4	,	,	PUNCT
ejpam-6775	289	5	we	we	PRON
ejpam-6775	289	6	use	use	VERB
ejpam-6775	289	7	a	a	DET
ejpam-6775	289	8	recent	recent	ADJ
ejpam-6775	289	9	result	result	NOUN
ejpam-6775	289	10	introduced	introduce	VERB
ejpam-6775	289	11	by	by	ADP
ejpam-6775	289	12	martcheva	martcheva	PROPN
ejpam-6775	289	13	and	and	CCONJ
ejpam-6775	289	14	inaba	inaba	PROPN
ejpam-6775	290	1	[	[	X
ejpam-6775	290	2	26	26	NUM
ejpam-6775	290	3	]	]	PUNCT
ejpam-6775	290	4	to	to	PART
ejpam-6775	290	5	detect	detect	VERB
ejpam-6775	290	6	the	the	DET
ejpam-6775	290	7	presence	presence	NOUN
ejpam-6775	290	8	of	of	ADP
ejpam-6775	290	9	bifurcations	bifurcation	NOUN
ejpam-6775	290	10	in	in	ADP
ejpam-6775	290	11	partial	partial	ADJ
ejpam-6775	290	12	differential	differential	ADJ
ejpam-6775	290	13	equations	equation	NOUN
ejpam-6775	290	14	and	and	CCONJ
ejpam-6775	290	15	define	define	VERB
ejpam-6775	290	16	the	the	DET
ejpam-6775	290	17	necessary	necessary	ADJ
ejpam-6775	290	18	and	and	CCONJ
ejpam-6775	290	19	sufficient	sufficient	ADJ
ejpam-6775	290	20	conditions	condition	NOUN
ejpam-6775	290	21	for	for	SCONJ
ejpam-6775	290	22	them	they	PRON
ejpam-6775	290	23	to	to	PART
ejpam-6775	290	24	occur	occur	VERB
ejpam-6775	290	25	.	.	PUNCT
ejpam-6775	291	1	let	let	VERB
ejpam-6775	291	2	us	we	PRON
ejpam-6775	291	3	set	set	VERB
ejpam-6775	291	4	β(x	β(x	NOUN
ejpam-6775	291	5	)	)	PUNCT
ejpam-6775	291	6	=	=	SYM
ejpam-6775	291	7	β̄β0(x	β̄β0(x	PROPN
ejpam-6775	291	8	)	)	PUNCT
ejpam-6775	291	9	where	where	SCONJ
ejpam-6775	291	10	the	the	DET
ejpam-6775	291	11	function	function	NOUN
ejpam-6775	291	12	β0(x	β0(x	NOUN
ejpam-6775	291	13	)	)	PUNCT
ejpam-6775	291	14	is	be	AUX
ejpam-6775	291	15	normalized	normalize	VERB
ejpam-6775	291	16	as	as	ADP
ejpam-6775	291	17	[	[	X
ejpam-6775	291	18	s0	s0	NOUN
ejpam-6775	291	19	+	+	CCONJ
ejpam-6775	291	20	mv	mv	PROPN
ejpam-6775	291	21	0]t	0]t	NUM
ejpam-6775	291	22	(	(	PUNCT
ejpam-6775	291	23	β0π	β0π	X
ejpam-6775	291	24	)	)	PUNCT
ejpam-6775	291	25	=	=	SYM
ejpam-6775	291	26	1	1	NUM
ejpam-6775	291	27	,	,	PUNCT
ejpam-6775	291	28	which	which	PRON
ejpam-6775	291	29	suggests	suggest	VERB
ejpam-6775	291	30	that	that	SCONJ
ejpam-6775	291	31	r0	r0	NOUN
ejpam-6775	291	32	=	=	SYM
ejpam-6775	291	33	1	1	NUM
ejpam-6775	291	34	is	be	AUX
ejpam-6775	291	35	equivalent	equivalent	ADJ
ejpam-6775	291	36	to	to	ADP
ejpam-6775	291	37	β̄	β̄	NOUN
ejpam-6775	292	1	=	=	SYM
ejpam-6775	292	2	1	1	X
ejpam-6775	292	3	.	.	PUNCT
ejpam-6775	293	1	in	in	ADP
ejpam-6775	293	2	what	what	PRON
ejpam-6775	293	3	follows	follow	VERB
ejpam-6775	293	4	,	,	PUNCT
ejpam-6775	293	5	we	we	PRON
ejpam-6775	293	6	consider	consider	VERB
ejpam-6775	293	7	β̄	β̄	ADJ
ejpam-6775	293	8	as	as	ADP
ejpam-6775	293	9	the	the	DET
ejpam-6775	293	10	bifurcation	bifurcation	NOUN
ejpam-6775	293	11	parameter	parameter	NOUN
ejpam-6775	293	12	.	.	PUNCT
ejpam-6775	294	1	let	let	VERB
ejpam-6775	294	2	us	we	PRON
ejpam-6775	294	3	introduce	introduce	VERB
ejpam-6775	294	4	the	the	DET
ejpam-6775	294	5	important	important	ADJ
ejpam-6775	294	6	threshold	threshold	NOUN
ejpam-6775	294	7	θ	θ	NOUN
ejpam-6775	294	8	:	:	PUNCT
ejpam-6775	295	1	=	=	SYM
ejpam-6775	295	2	[	[	PUNCT
ejpam-6775	295	3	1	1	NUM
ejpam-6775	295	4	+	+	CCONJ
ejpam-6775	295	5	mξ	mξ	PROPN
ejpam-6775	295	6	µ	µ	X
ejpam-6775	295	7	]	]	X
ejpam-6775	295	8	s0	s0	PROPN
ejpam-6775	295	9	µ+	µ+	PUNCT
ejpam-6775	295	10	ξ	ξ	PROPN
ejpam-6775	295	11	+	+	PROPN
ejpam-6775	295	12	m2	m2	PROPN
ejpam-6775	295	13	µ	µ	PROPN
ejpam-6775	295	14	v	v	NOUN
ejpam-6775	295	15	0	0	PUNCT
ejpam-6775	295	16	[	[	PUNCT
ejpam-6775	295	17	t	t	X
ejpam-6775	295	18	(	(	PUNCT
ejpam-6775	295	19	β0π	β0π	PROPN
ejpam-6775	295	20	)	)	PUNCT
ejpam-6775	295	21	+	+	CCONJ
ejpam-6775	295	22	(	(	PUNCT
ejpam-6775	295	23	1	1	NUM
ejpam-6775	295	24	+	+	CCONJ
ejpam-6775	295	25	mξ	mξ	PROPN
ejpam-6775	295	26	µ	µ	X
ejpam-6775	295	27	)	)	PUNCT
ejpam-6775	295	28	t	t	NOUN
ejpam-6775	295	29	(	(	PUNCT
ejpam-6775	295	30	απ	απ	NOUN
ejpam-6775	295	31	)	)	PUNCT
ejpam-6775	295	32	]	]	PUNCT
ejpam-6775	295	33	.	.	PUNCT
ejpam-6775	296	1	(	(	PUNCT
ejpam-6775	296	2	31	31	NUM
ejpam-6775	296	3	)	)	PUNCT
ejpam-6775	296	4	then	then	ADV
ejpam-6775	296	5	,	,	PUNCT
ejpam-6775	296	6	we	we	PRON
ejpam-6775	296	7	have	have	VERB
ejpam-6775	296	8	the	the	DET
ejpam-6775	296	9	following	follow	VERB
ejpam-6775	296	10	main	main	ADJ
ejpam-6775	296	11	result	result	NOUN
ejpam-6775	296	12	:	:	PUNCT
ejpam-6775	296	13	theorem	theorem	NOUN
ejpam-6775	296	14	4	4	NUM
ejpam-6775	296	15	.	.	PUNCT
ejpam-6775	297	1	let	let	VERB
ejpam-6775	297	2	assumption	assumption	NOUN
ejpam-6775	297	3	be	be	AUX
ejpam-6775	297	4	satisfied	satisfied	ADJ
ejpam-6775	297	5	.	.	PUNCT
ejpam-6775	298	1	if	if	SCONJ
ejpam-6775	298	2	θ	θ	PROPN
ejpam-6775	298	3	>	>	X
ejpam-6775	298	4	0	0	PROPN
ejpam-6775	298	5	,	,	PUNCT
ejpam-6775	298	6	the	the	DET
ejpam-6775	298	7	system	system	NOUN
ejpam-6775	298	8	(	(	PUNCT
ejpam-6775	298	9	1	1	X
ejpam-6775	298	10	)	)	PUNCT
ejpam-6775	298	11	undergoes	undergo	VERB
ejpam-6775	298	12	a	a	DET
ejpam-6775	298	13	backward	backward	ADJ
ejpam-6775	298	14	bifurcation	bifurcation	NOUN
ejpam-6775	298	15	at	at	ADP
ejpam-6775	298	16	(	(	PUNCT
ejpam-6775	298	17	e0	e0	PROPN
ejpam-6775	298	18	,	,	PUNCT
ejpam-6775	298	19	β̄	β̄	NOUN
ejpam-6775	298	20	=	=	SYM
ejpam-6775	298	21	1	1	NUM
ejpam-6775	298	22	)	)	PUNCT
ejpam-6775	298	23	.	.	PUNCT
ejpam-6775	299	1	otherwise	otherwise	ADV
ejpam-6775	299	2	,	,	PUNCT
ejpam-6775	299	3	the	the	DET
ejpam-6775	299	4	system	system	NOUN
ejpam-6775	299	5	(	(	PUNCT
ejpam-6775	299	6	1	1	X
ejpam-6775	299	7	)	)	PUNCT
ejpam-6775	299	8	exhibits	exhibit	VERB
ejpam-6775	299	9	a	a	DET
ejpam-6775	299	10	forward	forward	ADJ
ejpam-6775	299	11	bifurcation	bifurcation	NOUN
ejpam-6775	299	12	at	at	ADP
ejpam-6775	299	13	(	(	PUNCT
ejpam-6775	299	14	e0	e0	PROPN
ejpam-6775	299	15	,	,	PUNCT
ejpam-6775	299	16	β̄	β̄	NOUN
ejpam-6775	299	17	=	=	SYM
ejpam-6775	299	18	1	1	X
ejpam-6775	299	19	)	)	PUNCT
ejpam-6775	299	20	when	when	SCONJ
ejpam-6775	299	21	θ	θ	X
ejpam-6775	299	22	<	<	X
ejpam-6775	299	23	0	0	X
ejpam-6775	299	24	.	.	PUNCT
ejpam-6775	300	1	j.	j.	PROPN
ejpam-6775	300	2	leo	leo	PROPN
ejpam-6775	300	3	amalraj	amalraj	PROPN
ejpam-6775	300	4	et	et	PROPN
ejpam-6775	300	5	al	al	PROPN
ejpam-6775	300	6	.	.	PUNCT
ejpam-6775	300	7	/	/	SYM
ejpam-6775	300	8	eur	eur	PROPN
ejpam-6775	300	9	.	.	PUNCT
ejpam-6775	301	1	j.	j.	PROPN
ejpam-6775	301	2	pure	pure	PROPN
ejpam-6775	301	3	appl	appl	PROPN
ejpam-6775	301	4	.	.	PROPN
ejpam-6775	301	5	math	math	PROPN
ejpam-6775	301	6	,	,	PUNCT
ejpam-6775	301	7	18	18	NUM
ejpam-6775	301	8	(	(	PUNCT
ejpam-6775	301	9	4	4	NUM
ejpam-6775	301	10	)	)	PUNCT
ejpam-6775	301	11	(	(	PUNCT
ejpam-6775	301	12	2025	2025	NUM
ejpam-6775	301	13	)	)	PUNCT
ejpam-6775	301	14	,	,	PUNCT
ejpam-6775	301	15	6775	6775	NUM
ejpam-6775	301	16	13	13	NUM
ejpam-6775	301	17	of	of	ADP
ejpam-6775	301	18	32	32	NUM
ejpam-6775	301	19	proof	proof	NOUN
ejpam-6775	301	20	.	.	PUNCT
ejpam-6775	302	1	it	it	PRON
ejpam-6775	302	2	is	be	AUX
ejpam-6775	302	3	based	base	VERB
ejpam-6775	302	4	on	on	ADP
ejpam-6775	302	5	the	the	DET
ejpam-6775	302	6	lyapunov	lyapunov	NOUN
ejpam-6775	302	7	-	-	PUNCT
ejpam-6775	302	8	schmidt	schmidt	PROPN
ejpam-6775	302	9	method	method	NOUN
ejpam-6775	302	10	.	.	PUNCT
ejpam-6775	303	1	for	for	ADP
ejpam-6775	303	2	this	this	DET
ejpam-6775	303	3	purpose	purpose	NOUN
ejpam-6775	303	4	,	,	PUNCT
ejpam-6775	303	5	let	let	VERB
ejpam-6775	303	6	us	we	PRON
ejpam-6775	303	7	set	set	VERB
ejpam-6775	303	8	z	z	PROPN
ejpam-6775	303	9	=	=	SYM
ejpam-6775	303	10	(	(	PUNCT
ejpam-6775	303	11	z1	z1	PROPN
ejpam-6775	303	12	,	,	PUNCT
ejpam-6775	303	13	z2	z2	PROPN
ejpam-6775	303	14	,	,	PUNCT
ejpam-6775	303	15	z3	z3	PROPN
ejpam-6775	303	16	)	)	PUNCT
ejpam-6775	303	17	∈	∈	PROPN
ejpam-6775	303	18	x0	x0	PROPN
ejpam-6775	303	19	and	and	CCONJ
ejpam-6775	303	20	introduce	introduce	VERB
ejpam-6775	303	21	the	the	DET
ejpam-6775	303	22	nonlinear	nonlinear	ADJ
ejpam-6775	303	23	map	map	NOUN
ejpam-6775	303	24	f	f	PROPN
ejpam-6775	303	25	(	(	PUNCT
ejpam-6775	303	26	z	z	NOUN
ejpam-6775	303	27	,	,	PUNCT
ejpam-6775	303	28	β̄	β̄	NUM
ejpam-6775	303	29	)	)	PUNCT
ejpam-6775	303	30	:	:	PUNCT
ejpam-6775	303	31	=	=	PUNCT
ejpam-6775	303	32	az	az	PROPN
ejpam-6775	303	33	+	+	ADJ
ejpam-6775	303	34	h(z	h(z	NOUN
ejpam-6775	303	35	)	)	PUNCT
ejpam-6775	303	36	where	where	SCONJ
ejpam-6775	303	37	the	the	DET
ejpam-6775	303	38	linear	linear	ADJ
ejpam-6775	303	39	operator	operator	NOUN
ejpam-6775	303	40	a	a	PRON
ejpam-6775	303	41	and	and	CCONJ
ejpam-6775	303	42	map	map	VERB
ejpam-6775	303	43	h(z	h(z	NOUN
ejpam-6775	303	44	)	)	PUNCT
ejpam-6775	303	45	are	be	AUX
ejpam-6775	303	46	defined	define	VERB
ejpam-6775	303	47	in	in	ADP
ejpam-6775	303	48	(	(	PUNCT
ejpam-6775	303	49	3	3	NUM
ejpam-6775	303	50	)	)	PUNCT
ejpam-6775	303	51	and	and	CCONJ
ejpam-6775	303	52	(	(	PUNCT
ejpam-6775	303	53	4	4	X
ejpam-6775	303	54	)	)	PUNCT
ejpam-6775	303	55	respectively	respectively	ADV
ejpam-6775	303	56	.	.	PUNCT
ejpam-6775	304	1	the	the	DET
ejpam-6775	304	2	linearized	linearize	VERB
ejpam-6775	304	3	operator	operator	NOUN
ejpam-6775	304	4	b	b	NOUN
ejpam-6775	304	5	:	:	PUNCT
ejpam-6775	304	6	=	=	SYM
ejpam-6775	304	7	dzf	dzf	PROPN
ejpam-6775	304	8	(	(	PUNCT
ejpam-6775	304	9	e0	e0	PROPN
ejpam-6775	304	10	,	,	PUNCT
ejpam-6775	304	11	β̄	β̄	INTJ
ejpam-6775	304	12	)	)	PUNCT
ejpam-6775	304	13	acting	act	VERB
ejpam-6775	304	14	on	on	ADP
ejpam-6775	304	15	x	x	AUX
ejpam-6775	304	16	is	be	AUX
ejpam-6775	304	17	given	give	VERB
ejpam-6775	304	18	by	by	ADP
ejpam-6775	304	19	bz	bz	PROPN
ejpam-6775	304	20	=	=	PUNCT
ejpam-6775	304	21			NOUN
ejpam-6775	305	1	−β̄s0	−β̄s0	NUM
ejpam-6775	305	2	t	t	NOUN
ejpam-6775	305	3	(	(	PUNCT
ejpam-6775	305	4	β0z3	β0z3	X
ejpam-6775	305	5	)	)	PUNCT
ejpam-6775	305	6	+	+	NUM
ejpam-6775	305	7	t	t	PROPN
ejpam-6775	305	8	(	(	PUNCT
ejpam-6775	305	9	αz3)−	αz3)−	PROPN
ejpam-6775	305	10	(	(	PUNCT
ejpam-6775	305	11	ξ	ξ	X
ejpam-6775	305	12	+	+	CCONJ
ejpam-6775	305	13	µ)z1	µ)z1	PROPN
ejpam-6775	305	14	ξz1	ξz1	NOUN
ejpam-6775	305	15	−mv	−mv	PROPN
ejpam-6775	305	16	0	0	NUM
ejpam-6775	305	17	t	t	NOUN
ejpam-6775	305	18	(	(	PUNCT
ejpam-6775	305	19	β0z3)−	β0z3)−	PROPN
ejpam-6775	305	20	µz2	µz2	NOUN
ejpam-6775	305	21	−z′3	−z′3	ADV
ejpam-6775	305	22	−	−	PROPN
ejpam-6775	305	23	p(x)z3	p(x)z3	PROPN
ejpam-6775	305	24	−z3(0	−z3(0	PROPN
ejpam-6775	305	25	)	)	PUNCT
ejpam-6775	305	26	+	+	CCONJ
ejpam-6775	305	27	β̄[s0	β̄[s0	X
ejpam-6775	305	28	+	+	ADJ
ejpam-6775	305	29	mv	mv	PROPN
ejpam-6775	305	30	0]t	0]t	NUM
ejpam-6775	305	31	(	(	PUNCT
ejpam-6775	305	32	β0z3	β0z3	X
ejpam-6775	305	33	)	)	PUNCT
ejpam-6775	305	34			NOUN
ejpam-6775	305	35	,	,	PUNCT
ejpam-6775	305	36	(	(	PUNCT
ejpam-6775	305	37	32	32	NUM
ejpam-6775	305	38	)	)	PUNCT
ejpam-6775	305	39	where	where	SCONJ
ejpam-6775	305	40	its	its	PRON
ejpam-6775	305	41	domain	domain	NOUN
ejpam-6775	305	42	is	be	AUX
ejpam-6775	305	43	given	give	VERB
ejpam-6775	305	44	by	by	ADP
ejpam-6775	305	45	d(b	d(b	NOUN
ejpam-6775	305	46	)	)	PUNCT
ejpam-6775	305	47	=	=	SYM
ejpam-6775	305	48	d(a	d(a	PROPN
ejpam-6775	305	49	)	)	PUNCT
ejpam-6775	305	50	.	.	PUNCT
ejpam-6775	306	1	let	let	VERB
ejpam-6775	306	2	us	we	PRON
ejpam-6775	306	3	define	define	VERB
ejpam-6775	306	4	by	by	ADP
ejpam-6775	306	5	λ	λ	PROPN
ejpam-6775	306	6	∈	∈	PROPN
ejpam-6775	306	7	c	c	NOUN
ejpam-6775	306	8	the	the	DET
ejpam-6775	306	9	eigenvalue	eigenvalue	PROPN
ejpam-6775	306	10	of	of	ADP
ejpam-6775	306	11	the	the	DET
ejpam-6775	306	12	operator	operator	NOUN
ejpam-6775	306	13	b	b	NOUN
ejpam-6775	306	14	and	and	CCONJ
ejpam-6775	306	15	solving	solve	VERB
ejpam-6775	306	16	the	the	DET
ejpam-6775	306	17	differential	differential	ADJ
ejpam-6775	306	18	equation	equation	NOUN
ejpam-6775	306	19	bz	bz	PROPN
ejpam-6775	307	1	=	=	PUNCT
ejpam-6775	307	2	λz	λz	X
ejpam-6775	307	3	for	for	ADP
ejpam-6775	307	4	x	x	PROPN
ejpam-6775	307	5	∈	∈	PROPN
ejpam-6775	307	6	x0	x0	PROPN
ejpam-6775	307	7	,	,	PUNCT
ejpam-6775	307	8	we	we	PRON
ejpam-6775	307	9	have	have	VERB
ejpam-6775	307	10	z3(x	z3(x	NOUN
ejpam-6775	307	11	)	)	PUNCT
ejpam-6775	307	12	=	=	SYM
ejpam-6775	307	13	z3(0)π(x)e	z3(0)π(x)e	NUM
ejpam-6775	307	14	−λx	−λx	NOUN
ejpam-6775	307	15	.	.	PUNCT
ejpam-6775	307	16	inserting	insert	VERB
ejpam-6775	307	17	this	this	DET
ejpam-6775	307	18	expression	expression	NOUN
ejpam-6775	307	19	of	of	ADP
ejpam-6775	307	20	z3(x	z3(x	PROPN
ejpam-6775	307	21	)	)	PUNCT
ejpam-6775	307	22	into	into	ADP
ejpam-6775	307	23	the	the	DET
ejpam-6775	307	24	four	four	NUM
ejpam-6775	307	25	equation	equation	NOUN
ejpam-6775	307	26	in	in	ADP
ejpam-6775	307	27	bz	bz	PROPN
ejpam-6775	307	28	=	=	PUNCT
ejpam-6775	307	29	λz	λz	PROPN
ejpam-6775	307	30	and	and	CCONJ
ejpam-6775	307	31	canceling	cancel	VERB
ejpam-6775	307	32	z3(0	z3(0	PROPN
ejpam-6775	307	33	)	)	PUNCT
ejpam-6775	307	34	,	,	PUNCT
ejpam-6775	307	35	we	we	PRON
ejpam-6775	307	36	get	get	VERB
ejpam-6775	307	37	the	the	DET
ejpam-6775	307	38	characteristic	characteristic	ADJ
ejpam-6775	307	39	equation	equation	NOUN
ejpam-6775	307	40	β̄[s0	β̄[s0	PUNCT
ejpam-6775	308	1	+	+	ADV
ejpam-6775	308	2	mv	mv	PROPN
ejpam-6775	308	3	0	0	NUM
ejpam-6775	308	4	]	]	PUNCT
ejpam-6775	308	5	∫	∫	PROPN
ejpam-6775	308	6	∞	∞	PROPN
ejpam-6775	308	7	0	0	NUM
ejpam-6775	308	8	β0(x)π(x)e	β0(x)π(x)e	ADJ
ejpam-6775	308	9	−λxdx	−λxdx	PUNCT
ejpam-6775	309	1	=	=	SYM
ejpam-6775	309	2	1	1	NUM
ejpam-6775	309	3	,	,	PUNCT
ejpam-6775	309	4	(	(	PUNCT
ejpam-6775	309	5	33	33	NUM
ejpam-6775	309	6	)	)	PUNCT
ejpam-6775	309	7	which	which	PRON
ejpam-6775	309	8	has	have	VERB
ejpam-6775	309	9	λ	λ	NOUN
ejpam-6775	309	10	=	=	SYM
ejpam-6775	309	11	0	0	PUNCT
ejpam-6775	309	12	as	as	ADP
ejpam-6775	309	13	a	a	DET
ejpam-6775	309	14	simple	simple	ADJ
ejpam-6775	309	15	isolated	isolate	VERB
ejpam-6775	309	16	eigenvalue	eigenvalue	NOUN
ejpam-6775	309	17	when	when	SCONJ
ejpam-6775	309	18	β̄	β̄	NOUN
ejpam-6775	309	19	=	=	SYM
ejpam-6775	309	20	1	1	NUM
ejpam-6775	309	21	and	and	CCONJ
ejpam-6775	309	22	each	each	PRON
ejpam-6775	309	23	of	of	ADP
ejpam-6775	309	24	the	the	DET
ejpam-6775	309	25	remaining	remain	VERB
ejpam-6775	309	26	solutions	solution	NOUN
ejpam-6775	309	27	has	have	VERB
ejpam-6775	309	28	negative	negative	ADJ
ejpam-6775	309	29	real	real	ADJ
ejpam-6775	309	30	part	part	NOUN
ejpam-6775	309	31	thanks	thank	NOUN
ejpam-6775	309	32	to	to	ADP
ejpam-6775	309	33	the	the	DET
ejpam-6775	309	34	proof	proof	NOUN
ejpam-6775	309	35	of	of	ADP
ejpam-6775	309	36	theorem	theorem	ADJ
ejpam-6775	309	37	2.2	2.2	NUM
ejpam-6775	309	38	.	.	PUNCT
ejpam-6775	310	1	to	to	PART
ejpam-6775	310	2	find	find	VERB
ejpam-6775	310	3	the	the	DET
ejpam-6775	310	4	eigenvector	eigenvector	NOUN
ejpam-6775	310	5	v0	v0	NOUN
ejpam-6775	310	6	associated	associate	VERB
ejpam-6775	310	7	with	with	ADP
ejpam-6775	310	8	eigenvalue	eigenvalue	PROPN
ejpam-6775	310	9	zero	zero	NUM
ejpam-6775	310	10	,	,	PUNCT
ejpam-6775	310	11	we	we	PRON
ejpam-6775	310	12	need	need	VERB
ejpam-6775	310	13	to	to	PART
ejpam-6775	310	14	solve	solve	VERB
ejpam-6775	310	15	the	the	DET
ejpam-6775	310	16	equation	equation	NOUN
ejpam-6775	310	17	bz	bz	PROPN
ejpam-6775	310	18	=	=	PUNCT
ejpam-6775	310	19	0	0	X
ejpam-6775	310	20	.	.	PUNCT
ejpam-6775	311	1	we	we	PRON
ejpam-6775	311	2	can	can	AUX
ejpam-6775	311	3	choose	choose	VERB
ejpam-6775	311	4	z3(x	z3(x	PROPN
ejpam-6775	311	5	)	)	PUNCT
ejpam-6775	311	6	=	=	SYM
ejpam-6775	311	7	π(x	π(x	NOUN
ejpam-6775	311	8	)	)	PUNCT
ejpam-6775	311	9	and	and	CCONJ
ejpam-6775	311	10	the	the	DET
ejpam-6775	311	11	boundary	boundary	ADJ
ejpam-6775	311	12	condition	condition	NOUN
ejpam-6775	311	13	of	of	ADP
ejpam-6775	311	14	the	the	DET
ejpam-6775	311	15	four	four	NUM
ejpam-6775	311	16	equation	equation	NOUN
ejpam-6775	311	17	of	of	ADP
ejpam-6775	311	18	bz	bz	PROPN
ejpam-6775	311	19	=	=	PUNCT
ejpam-6775	311	20	0	0	NUM
ejpam-6775	311	21	is	be	AUX
ejpam-6775	311	22	trivially	trivially	ADV
ejpam-6775	311	23	satisfied	satisfied	ADJ
ejpam-6775	311	24	at	at	ADP
ejpam-6775	311	25	β̄	β̄	NOUN
ejpam-6775	311	26	=	=	SYM
ejpam-6775	311	27	1	1	X
ejpam-6775	311	28	.	.	PUNCT
ejpam-6775	311	29	from	from	ADP
ejpam-6775	311	30	the	the	DET
ejpam-6775	311	31	first	first	ADJ
ejpam-6775	311	32	equation	equation	NOUN
ejpam-6775	311	33	of	of	ADP
ejpam-6775	311	34	bz	bz	PROPN
ejpam-6775	311	35	=	=	SYM
ejpam-6775	311	36	0	0	PROPN
ejpam-6775	311	37	,	,	PUNCT
ejpam-6775	311	38	we	we	PRON
ejpam-6775	311	39	get	get	VERB
ejpam-6775	311	40	z01	z01	ADJ
ejpam-6775	311	41	:	:	PUNCT
ejpam-6775	311	42	z1	z1	NOUN
ejpam-6775	311	43	=	=	SYM
ejpam-6775	311	44	−	−	NOUN
ejpam-6775	311	45	β̄s0	β̄s0	NOUN
ejpam-6775	311	46	t	t	NOUN
ejpam-6775	311	47	(	(	PUNCT
ejpam-6775	311	48	β0π)+t	β0π)+t	X
ejpam-6775	311	49	(	(	PUNCT
ejpam-6775	311	50	απ	απ	NOUN
ejpam-6775	311	51	)	)	PUNCT
ejpam-6775	311	52	ξ+µ	ξ+µ	PROPN
ejpam-6775	311	53	and	and	CCONJ
ejpam-6775	311	54	the	the	DET
ejpam-6775	311	55	second	second	ADJ
ejpam-6775	311	56	equation	equation	NOUN
ejpam-6775	311	57	gives	give	VERB
ejpam-6775	311	58	z02	z02	NOUN
ejpam-6775	311	59	:	:	PUNCT
ejpam-6775	311	60	z2	z2	PROPN
ejpam-6775	311	61	=	=	PUNCT
ejpam-6775	311	62	mv	mv	PROPN
ejpam-6775	311	63	0	0	NUM
ejpam-6775	311	64	t	t	PROPN
ejpam-6775	311	65	(	(	PUNCT
ejpam-6775	311	66	β0π)+ξz01	β0π)+ξz01	PROPN
ejpam-6775	311	67	µ	µ	X
ejpam-6775	311	68	.	.	PUNCT
ejpam-6775	312	1	therefore	therefore	ADV
ejpam-6775	312	2	,	,	PUNCT
ejpam-6775	312	3	we	we	PRON
ejpam-6775	312	4	set	set	VERB
ejpam-6775	312	5	the	the	DET
ejpam-6775	312	6	vector	vector	NOUN
ejpam-6775	312	7	ṽ0	ṽ0	PROPN
ejpam-6775	312	8	=	=	PUNCT
ejpam-6775	312	9	(	(	PUNCT
ejpam-6775	312	10	z01	z01	X
ejpam-6775	312	11	,	,	PUNCT
ejpam-6775	312	12	z	z	NOUN
ejpam-6775	312	13	0	0	NUM
ejpam-6775	312	14	2	2	NUM
ejpam-6775	312	15	,	,	PUNCT
ejpam-6775	312	16	π(x	π(x	NOUN
ejpam-6775	312	17	)	)	PUNCT
ejpam-6775	312	18	,	,	PUNCT
ejpam-6775	312	19	1	1	NUM
ejpam-6775	312	20	)	)	PUNCT
ejpam-6775	312	21	.	.	PUNCT
ejpam-6775	313	1	now	now	ADV
ejpam-6775	313	2	,	,	PUNCT
ejpam-6775	313	3	we	we	PRON
ejpam-6775	313	4	seek	seek	VERB
ejpam-6775	313	5	the	the	DET
ejpam-6775	313	6	adjoint	adjoint	NOUN
ejpam-6775	313	7	operator	operator	NOUN
ejpam-6775	313	8	b∗.	b∗.	NOUN
ejpam-6775	313	9	to	to	PART
ejpam-6775	313	10	do	do	VERB
ejpam-6775	313	11	so	so	ADV
ejpam-6775	313	12	,	,	PUNCT
ejpam-6775	313	13	let	let	VERB
ejpam-6775	313	14	us	we	PRON
ejpam-6775	313	15	consider	consider	VERB
ejpam-6775	313	16	the	the	DET
ejpam-6775	313	17	vector	vector	NOUN
ejpam-6775	313	18	ψ	ψ	X
ejpam-6775	313	19	=	=	SYM
ejpam-6775	313	20	(	(	PUNCT
ejpam-6775	313	21	ψ1,ψ2,ψ3,ψ4	ψ1,ψ2,ψ3,ψ4	PROPN
ejpam-6775	313	22	)	)	PUNCT
ejpam-6775	313	23	∈	∈	PROPN
ejpam-6775	313	24	x∗	x∗	PROPN
ejpam-6775	313	25	:	:	PUNCT
ejpam-6775	313	26	=	=	PUNCT
ejpam-6775	313	27	r2	r2	PROPN
ejpam-6775	313	28	×	×	PROPN
ejpam-6775	313	29	l1(0,∞)×	l1(0,∞)×	PROPN
ejpam-6775	313	30	r.	r.	PROPN
ejpam-6775	313	31	then	then	ADV
ejpam-6775	313	32	,	,	PUNCT
ejpam-6775	313	33	we	we	PRON
ejpam-6775	313	34	have	have	VERB
ejpam-6775	313	35	the	the	DET
ejpam-6775	313	36	relation	relation	NOUN
ejpam-6775	313	37	⟨ψ	⟨ψ	ADP
ejpam-6775	313	38	,	,	PUNCT
ejpam-6775	313	39	bz⟩	bz⟩	PUNCT
ejpam-6775	313	40	=	=	PUNCT
ejpam-6775	314	1	[	[	PUNCT
ejpam-6775	314	2	−β̄s0	−β̄s0	NUM
ejpam-6775	314	3	t	t	NOUN
ejpam-6775	314	4	(	(	PUNCT
ejpam-6775	314	5	β0z3	β0z3	X
ejpam-6775	314	6	)	)	PUNCT
ejpam-6775	315	1	+	+	NUM
ejpam-6775	315	2	t	t	PROPN
ejpam-6775	315	3	(	(	PUNCT
ejpam-6775	315	4	αz3)−	αz3)−	PROPN
ejpam-6775	315	5	(	(	PUNCT
ejpam-6775	315	6	ξ	ξ	X
ejpam-6775	315	7	+	+	PUNCT
ejpam-6775	315	8	µ)z1	µ)z1	PROPN
ejpam-6775	315	9	]	]	PUNCT
ejpam-6775	315	10	ψ1	ψ1	NOUN
ejpam-6775	315	11	+	+	CCONJ
ejpam-6775	315	12	[	[	PUNCT
ejpam-6775	315	13	ξz1	ξz1	NOUN
ejpam-6775	315	14	−	−	PROPN
ejpam-6775	315	15	βmv	βmv	PROPN
ejpam-6775	315	16	0	0	NUM
ejpam-6775	315	17	t	t	NOUN
ejpam-6775	315	18	(	(	PUNCT
ejpam-6775	315	19	β0z3)−	β0z3)−	PROPN
ejpam-6775	315	20	µz2	µz2	NOUN
ejpam-6775	315	21	]	]	PUNCT
ejpam-6775	315	22	ψ2	ψ2	NOUN
ejpam-6775	315	23	(	(	PUNCT
ejpam-6775	315	24	34	34	NUM
ejpam-6775	315	25	)	)	PUNCT
ejpam-6775	315	26	+	+	CCONJ
ejpam-6775	315	27	∫	∫	PROPN
ejpam-6775	315	28	∞	∞	NUM
ejpam-6775	315	29	0	0	PUNCT
ejpam-6775	316	1	[	[	PUNCT
ejpam-6775	316	2	−z′3	−z′3	PUNCT
ejpam-6775	316	3	−	−	PROPN
ejpam-6775	316	4	p(x)z3	p(x)z3	PROPN
ejpam-6775	316	5	]	]	PUNCT
ejpam-6775	316	6	ψ3(x)dx+	ψ3(x)dx+	PUNCT
ejpam-6775	316	7	[	[	X
ejpam-6775	316	8	−z3(0	−z3(0	X
ejpam-6775	316	9	)	)	PUNCT
ejpam-6775	316	10	+	+	CCONJ
ejpam-6775	316	11	β̄(s0	β̄(s0	PUNCT
ejpam-6775	317	1	+	+	ADJ
ejpam-6775	317	2	mv	mv	PROPN
ejpam-6775	317	3	0)t	0)t	PRON
ejpam-6775	317	4	(	(	PUNCT
ejpam-6775	317	5	β0z3)]ψ4	β0z3)]ψ4	NOUN
ejpam-6775	317	6	.	.	PUNCT
ejpam-6775	317	7	notice	notice	VERB
ejpam-6775	317	8	that	that	SCONJ
ejpam-6775	317	9	,	,	PUNCT
ejpam-6775	317	10	by	by	ADP
ejpam-6775	317	11	integrating	integrate	VERB
ejpam-6775	317	12	by	by	ADP
ejpam-6775	317	13	part	part	NOUN
ejpam-6775	317	14	assuming	assume	VERB
ejpam-6775	317	15	that	that	SCONJ
ejpam-6775	317	16	ψ3(∞	ψ3(∞	NOUN
ejpam-6775	317	17	)	)	PUNCT
ejpam-6775	317	18	=	=	SYM
ejpam-6775	317	19	0	0	PUNCT
ejpam-6775	317	20	we	we	PRON
ejpam-6775	317	21	get∫	get∫	VERB
ejpam-6775	317	22	∞	∞	NOUN
ejpam-6775	317	23	0	0	NUM
ejpam-6775	318	1	[	[	PUNCT
ejpam-6775	318	2	−z′3	−z′3	PUNCT
ejpam-6775	318	3	−	−	PROPN
ejpam-6775	318	4	p(x)z3	p(x)z3	PROPN
ejpam-6775	318	5	]	]	PUNCT
ejpam-6775	318	6	ψ3(x)dx	ψ3(x)dx	VERB
ejpam-6775	318	7	=	=	SYM
ejpam-6775	318	8	z3(0)ψ3(0	z3(0)ψ3(0	NUM
ejpam-6775	318	9	)	)	PUNCT
ejpam-6775	319	1	+	+	CCONJ
ejpam-6775	319	2	∫	∫	PROPN
ejpam-6775	319	3	∞	∞	NUM
ejpam-6775	319	4	0	0	NUM
ejpam-6775	320	1	[	[	PUNCT
ejpam-6775	320	2	ψ′	ψ′	NUM
ejpam-6775	320	3	3	3	NUM
ejpam-6775	320	4	−	−	PROPN
ejpam-6775	320	5	p(x)ψ3	p(x)ψ3	PROPN
ejpam-6775	320	6	]	]	PUNCT
ejpam-6775	320	7	z3(x)dx	z3(x)dx	X
ejpam-6775	320	8	.	.	PUNCT
ejpam-6775	321	1	hence	hence	ADV
ejpam-6775	321	2	we	we	PRON
ejpam-6775	321	3	have	have	VERB
ejpam-6775	321	4	⟨ψ	⟨ψ	NOUN
ejpam-6775	321	5	,	,	PUNCT
ejpam-6775	321	6	bz⟩	bz⟩	PUNCT
ejpam-6775	321	7	=	=	PUNCT
ejpam-6775	322	1	[	[	X
ejpam-6775	322	2	ξψ2	ξψ2	X
ejpam-6775	322	3	−	−	NOUN
ejpam-6775	322	4	(	(	PUNCT
ejpam-6775	322	5	ξ	ξ	X
ejpam-6775	322	6	+	+	PUNCT
ejpam-6775	322	7	µ)ψ1	µ)ψ1	PROPN
ejpam-6775	322	8	]	]	X
ejpam-6775	322	9	z1	z1	NOUN
ejpam-6775	322	10	−	−	PROPN
ejpam-6775	322	11	µψ2z2	µψ2z2	PROPN
ejpam-6775	322	12	+	+	CCONJ
ejpam-6775	322	13	(	(	PUNCT
ejpam-6775	322	14	ψ3(0)−ψ4)z3(0	ψ3(0)−ψ4)z3(0	PROPN
ejpam-6775	322	15	)	)	PUNCT
ejpam-6775	322	16	(	(	PUNCT
ejpam-6775	322	17	35	35	NUM
ejpam-6775	322	18	)	)	PUNCT
ejpam-6775	322	19	+	+	CCONJ
ejpam-6775	322	20	∫	∫	PROPN
ejpam-6775	322	21	∞	∞	NUM
ejpam-6775	322	22	0	0	NUM
ejpam-6775	323	1	[	[	PUNCT
ejpam-6775	323	2	ψ′	ψ′	NUM
ejpam-6775	323	3	3	3	NUM
ejpam-6775	323	4	−	−	NOUN
ejpam-6775	323	5	pψ3	pψ3	NOUN
ejpam-6775	323	6	+	+	CCONJ
ejpam-6775	323	7	(	(	PUNCT
ejpam-6775	323	8	−β̄s0β0	−β̄s0β0	X
ejpam-6775	323	9	+	+	CCONJ
ejpam-6775	323	10	α)ψ1	α)ψ1	PROPN
ejpam-6775	323	11	−	−	PROPN
ejpam-6775	323	12	βmv	βmv	NOUN
ejpam-6775	323	13	0β0ψ2	0β0ψ2	NOUN
ejpam-6775	324	1	+	+	CCONJ
ejpam-6775	325	1	β̄(s0	β̄(s0	PUNCT
ejpam-6775	325	2	+	+	ADJ
ejpam-6775	325	3	mv	mv	PROPN
ejpam-6775	325	4	0)β0ψ4	0)β0ψ4	PROPN
ejpam-6775	325	5	]	]	PUNCT
ejpam-6775	326	1	z3(x)dx	z3(x)dx	X
ejpam-6775	326	2	.	.	PUNCT
ejpam-6775	327	1	j.	j.	PROPN
ejpam-6775	327	2	leo	leo	PROPN
ejpam-6775	327	3	amalraj	amalraj	PROPN
ejpam-6775	327	4	et	et	PROPN
ejpam-6775	327	5	al	al	PROPN
ejpam-6775	327	6	.	.	PUNCT
ejpam-6775	327	7	/	/	SYM
ejpam-6775	327	8	eur	eur	PROPN
ejpam-6775	327	9	.	.	PUNCT
ejpam-6775	328	1	j.	j.	PROPN
ejpam-6775	328	2	pure	pure	PROPN
ejpam-6775	328	3	appl	appl	PROPN
ejpam-6775	328	4	.	.	PROPN
ejpam-6775	328	5	math	math	PROPN
ejpam-6775	328	6	,	,	PUNCT
ejpam-6775	328	7	18	18	NUM
ejpam-6775	328	8	(	(	PUNCT
ejpam-6775	328	9	4	4	NUM
ejpam-6775	328	10	)	)	PUNCT
ejpam-6775	328	11	(	(	PUNCT
ejpam-6775	328	12	2025	2025	NUM
ejpam-6775	328	13	)	)	PUNCT
ejpam-6775	328	14	,	,	PUNCT
ejpam-6775	328	15	6775	6775	NUM
ejpam-6775	328	16	14	14	NUM
ejpam-6775	328	17	of	of	ADP
ejpam-6775	328	18	32	32	NUM
ejpam-6775	328	19	which	which	PRON
ejpam-6775	328	20	should	should	AUX
ejpam-6775	328	21	hold	hold	VERB
ejpam-6775	328	22	for	for	ADP
ejpam-6775	328	23	ψ	ψ	X
ejpam-6775	328	24	∈	∈	PROPN
ejpam-6775	328	25	d(b∗	d(b∗	NOUN
ejpam-6775	328	26	)	)	PUNCT
ejpam-6775	328	27	and	and	CCONJ
ejpam-6775	328	28	z	z	NOUN
ejpam-6775	328	29	∈	∈	PROPN
ejpam-6775	328	30	d(b	d(b	PROPN
ejpam-6775	328	31	)	)	PUNCT
ejpam-6775	329	1	⊂	⊂	PROPN
ejpam-6775	329	2	x0	x0	PROPN
ejpam-6775	329	3	.	.	PUNCT
ejpam-6775	330	1	we	we	PRON
ejpam-6775	330	2	take	take	VERB
ejpam-6775	330	3	the	the	DET
ejpam-6775	330	4	domain	domain	NOUN
ejpam-6775	330	5	of	of	ADP
ejpam-6775	330	6	the	the	DET
ejpam-6775	330	7	operator	operator	NOUN
ejpam-6775	330	8	b∗	b∗	ADV
ejpam-6775	330	9	as	as	SCONJ
ejpam-6775	330	10	follows	follow	VERB
ejpam-6775	330	11	d(b∗	d(b∗	NOUN
ejpam-6775	330	12	)	)	PUNCT
ejpam-6775	330	13	=	=	PRON
ejpam-6775	330	14	{	{	PUNCT
ejpam-6775	330	15	ψ	ψ	X
ejpam-6775	330	16	∈	∈	PROPN
ejpam-6775	330	17	r2	r2	NOUN
ejpam-6775	330	18	×w	×w	VERB
ejpam-6775	330	19	1,∞(0,∞)×	1,∞(0,∞)×	NUM
ejpam-6775	330	20	r	r	NOUN
ejpam-6775	330	21	:	:	PUNCT
ejpam-6775	330	22	ψ3(∞	ψ3(∞	X
ejpam-6775	330	23	)	)	PUNCT
ejpam-6775	330	24	=	=	SYM
ejpam-6775	330	25	0,ψ4	0,ψ4	X
ejpam-6775	330	26	=	=	SYM
ejpam-6775	330	27	ψ3(0	ψ3(0	PROPN
ejpam-6775	330	28	)	)	PUNCT
ejpam-6775	330	29	}	}	PUNCT
ejpam-6775	330	30	.	.	PUNCT
ejpam-6775	331	1	therefore	therefore	ADV
ejpam-6775	331	2	,	,	PUNCT
ejpam-6775	331	3	the	the	DET
ejpam-6775	331	4	adjoint	adjoint	NOUN
ejpam-6775	331	5	operator	operator	NOUN
ejpam-6775	331	6	b∗	b∗	ADV
ejpam-6775	331	7	is	be	AUX
ejpam-6775	331	8	defined	define	VERB
ejpam-6775	331	9	for	for	ADP
ejpam-6775	331	10	ψ	ψ	X
ejpam-6775	331	11	∈	∈	PROPN
ejpam-6775	331	12	d(b∗)∩x∗	d(b∗)∩x∗	PUNCT
ejpam-6775	331	13	=	=	SYM
ejpam-6775	331	14	r2×l∞(0,∞)×r	r2×l∞(0,∞)×r	PROPN
ejpam-6775	331	15	by	by	ADP
ejpam-6775	331	16	b∗ψ	b∗ψ	NOUN
ejpam-6775	331	17	=	=	SYM
ejpam-6775	331	18			NOUN
ejpam-6775	331	19	ξψ2	ξψ2	NOUN
ejpam-6775	331	20	−	−	NOUN
ejpam-6775	331	21	(	(	PUNCT
ejpam-6775	331	22	ξ	ξ	X
ejpam-6775	331	23	+	+	CCONJ
ejpam-6775	331	24	µ)ψ1	µ)ψ1	ADJ
ejpam-6775	331	25	−µψ2	−µψ2	NOUN
ejpam-6775	331	26	ψ′	ψ′	NUM
ejpam-6775	331	27	3	3	NUM
ejpam-6775	331	28	−	−	NOUN
ejpam-6775	331	29	pψ3	pψ3	NOUN
ejpam-6775	331	30	+	+	CCONJ
ejpam-6775	331	31	(	(	PUNCT
ejpam-6775	331	32	−β̄s0β0	−β̄s0β0	X
ejpam-6775	331	33	+	+	CCONJ
ejpam-6775	331	34	α)ψ1	α)ψ1	PROPN
ejpam-6775	332	1	−	−	PROPN
ejpam-6775	332	2	β̄mv	β̄mv	PROPN
ejpam-6775	332	3	0β0ψ2	0β0ψ2	NOUN
ejpam-6775	333	1	+	+	CCONJ
ejpam-6775	333	2	β̄(s0	β̄(s0	PUNCT
ejpam-6775	333	3	+	+	ADJ
ejpam-6775	333	4	mv	mv	PROPN
ejpam-6775	333	5	0)β0ψ4	0)β0ψ4	PROPN
ejpam-6775	333	6	ψ3(0	ψ3(0	PROPN
ejpam-6775	333	7	)	)	PUNCT
ejpam-6775	333	8			NOUN
ejpam-6775	333	9	.	.	PUNCT
ejpam-6775	334	1	(	(	PUNCT
ejpam-6775	334	2	36	36	NUM
ejpam-6775	334	3	)	)	PUNCT
ejpam-6775	334	4	to	to	PART
ejpam-6775	334	5	find	find	VERB
ejpam-6775	334	6	the	the	DET
ejpam-6775	334	7	vector	vector	NOUN
ejpam-6775	334	8	ṽ	ṽ	PROPN
ejpam-6775	334	9	∗	∗	NOUN
ejpam-6775	334	10	0	0	NUM
ejpam-6775	334	11	,	,	PUNCT
ejpam-6775	334	12	the	the	DET
ejpam-6775	334	13	unique	unique	ADJ
ejpam-6775	334	14	positive	positive	ADJ
ejpam-6775	334	15	vector	vector	NOUN
ejpam-6775	334	16	satisfying	satisfy	VERB
ejpam-6775	334	17	the	the	DET
ejpam-6775	334	18	relation	relation	NOUN
ejpam-6775	334	19	⟨bz	⟨bz	NOUN
ejpam-6775	334	20	,	,	PUNCT
ejpam-6775	334	21	ṽ	ṽ	PROPN
ejpam-6775	334	22	∗	∗	NOUN
ejpam-6775	334	23	0	0	NUM
ejpam-6775	334	24	⟩	⟩	NOUN
ejpam-6775	334	25	=	=	NOUN
ejpam-6775	334	26	0	0	NUM
ejpam-6775	334	27	for	for	ADP
ejpam-6775	334	28	all	all	DET
ejpam-6775	334	29	z	z	NOUN
ejpam-6775	334	30	∈	∈	PROPN
ejpam-6775	334	31	x	x	X
ejpam-6775	334	32	,	,	PUNCT
ejpam-6775	334	33	it	it	PRON
ejpam-6775	334	34	suffices	suffice	VERB
ejpam-6775	334	35	to	to	PART
ejpam-6775	334	36	solve	solve	VERB
ejpam-6775	334	37	the	the	DET
ejpam-6775	334	38	equation	equation	NOUN
ejpam-6775	334	39	b∗ψ	b∗ψ	NOUN
ejpam-6775	334	40	=	=	SYM
ejpam-6775	334	41	0	0	NUM
ejpam-6775	335	1	with	with	ADP
ejpam-6775	335	2	β̄	β̄	NOUN
ejpam-6775	335	3	=	=	SYM
ejpam-6775	335	4	1	1	X
ejpam-6775	335	5	.	.	PUNCT
ejpam-6775	336	1	it	it	PRON
ejpam-6775	336	2	is	be	AUX
ejpam-6775	336	3	easy	easy	ADJ
ejpam-6775	336	4	to	to	PART
ejpam-6775	336	5	see	see	VERB
ejpam-6775	336	6	that	that	DET
ejpam-6775	336	7	ψ1	ψ1	NOUN
ejpam-6775	336	8	=	=	PUNCT
ejpam-6775	336	9	ψ2	ψ2	NOUN
ejpam-6775	336	10	=	=	SYM
ejpam-6775	336	11	0	0	X
ejpam-6775	336	12	.	.	PUNCT
ejpam-6775	337	1	solving	solve	VERB
ejpam-6775	337	2	the	the	DET
ejpam-6775	337	3	differential	differential	ADJ
ejpam-6775	337	4	equation	equation	NOUN
ejpam-6775	337	5	in	in	ADP
ejpam-6775	337	6	b∗ψ	b∗ψ	NOUN
ejpam-6775	337	7	=	=	SYM
ejpam-6775	337	8	0	0	NUM
ejpam-6775	337	9	,	,	PUNCT
ejpam-6775	337	10	we	we	PRON
ejpam-6775	337	11	get	get	VERB
ejpam-6775	337	12	ψ3(x	ψ3(x	PRON
ejpam-6775	337	13	)	)	PUNCT
ejpam-6775	337	14	=	=	SYM
ejpam-6775	338	1	(	(	PUNCT
ejpam-6775	338	2	s0	s0	PROPN
ejpam-6775	338	3	+	+	PROPN
ejpam-6775	338	4	mv	mv	PROPN
ejpam-6775	338	5	0)ψ3(0	0)ψ3(0	PROPN
ejpam-6775	338	6	)	)	PUNCT
ejpam-6775	339	1	∫	∫	PROPN
ejpam-6775	339	2	x	x	X
ejpam-6775	339	3	0	0	NUM
ejpam-6775	339	4	β0(s	β0(s	NUM
ejpam-6775	339	5	)	)	PUNCT
ejpam-6775	339	6	π(s	π(s	PROPN
ejpam-6775	339	7	)	)	PUNCT
ejpam-6775	339	8	π(x)ds	π(x)ds	PROPN
ejpam-6775	339	9	.	.	PUNCT
ejpam-6775	340	1	thus	thus	ADV
ejpam-6775	340	2	,	,	PUNCT
ejpam-6775	340	3	we	we	PRON
ejpam-6775	340	4	obtain	obtain	VERB
ejpam-6775	340	5	:	:	PUNCT
ejpam-6775	340	6	d2	d2	NOUN
ejpam-6775	340	7	β̄β̄f	β̄β̄f	PROPN
ejpam-6775	340	8	(	(	PUNCT
ejpam-6775	340	9	e0	e0	PROPN
ejpam-6775	340	10	,	,	PUNCT
ejpam-6775	340	11	1)ṽ0	1)ṽ0	NOUN
ejpam-6775	340	12	=	=	SYM
ejpam-6775	340	13			NOUN
ejpam-6775	341	1	−s0	−s0	PROPN
ejpam-6775	341	2	t	t	NOUN
ejpam-6775	341	3	(	(	PUNCT
ejpam-6775	341	4	β0π)z	β0π)z	SYM
ejpam-6775	341	5	0	0	NUM
ejpam-6775	341	6	1	1	NUM
ejpam-6775	341	7	−mv	−mv	NOUN
ejpam-6775	341	8	0	0	NUM
ejpam-6775	341	9	t	t	NOUN
ejpam-6775	341	10	(	(	PUNCT
ejpam-6775	341	11	β0π)z	β0π)z	SYM
ejpam-6775	341	12	0	0	NUM
ejpam-6775	341	13	2	2	NUM
ejpam-6775	341	14	0	0	NUM
ejpam-6775	341	15	(	(	PUNCT
ejpam-6775	341	16	s0	s0	PROPN
ejpam-6775	341	17	+	+	PROPN
ejpam-6775	341	18	mv	mv	PROPN
ejpam-6775	341	19	0)t	0)t	INTJ
ejpam-6775	341	20	(	(	PUNCT
ejpam-6775	341	21	β0π	β0π	NOUN
ejpam-6775	341	22	)	)	PUNCT
ejpam-6775	341	23			NOUN
ejpam-6775	341	24	.	.	PUNCT
ejpam-6775	342	1	(	(	PUNCT
ejpam-6775	342	2	37	37	NUM
ejpam-6775	342	3	)	)	PUNCT
ejpam-6775	342	4	therefore	therefore	ADV
ejpam-6775	342	5	,	,	PUNCT
ejpam-6775	342	6	one	one	PRON
ejpam-6775	342	7	obtains	obtain	VERB
ejpam-6775	342	8	b	b	NOUN
ejpam-6775	342	9	=	=	SYM
ejpam-6775	342	10	⟨d2	⟨d2	PROPN
ejpam-6775	342	11	β̄β̄f	β̄β̄f	NOUN
ejpam-6775	342	12	(	(	PUNCT
ejpam-6775	342	13	e0	e0	PROPN
ejpam-6775	342	14	,	,	PUNCT
ejpam-6775	342	15	1)ṽ0	1)ṽ0	NOUN
ejpam-6775	342	16	,	,	PUNCT
ejpam-6775	342	17	ṽ	ṽ	PROPN
ejpam-6775	342	18	∗	∗	NOUN
ejpam-6775	342	19	0	0	NUM
ejpam-6775	342	20	⟩	⟩	NOUN
ejpam-6775	342	21	=	=	SYM
ejpam-6775	342	22	(	(	PUNCT
ejpam-6775	342	23	s0	s0	PROPN
ejpam-6775	342	24	+	+	PROPN
ejpam-6775	342	25	mv	mv	PROPN
ejpam-6775	342	26	0)ψ3(0)t	0)ψ3(0)t	PROPN
ejpam-6775	342	27	(	(	PUNCT
ejpam-6775	342	28	β0π	β0π	PROPN
ejpam-6775	342	29	)	)	PUNCT
ejpam-6775	342	30	>	>	X
ejpam-6775	342	31	0	0	X
ejpam-6775	342	32	.	.	PUNCT
ejpam-6775	343	1	(	(	PUNCT
ejpam-6775	343	2	38	38	NUM
ejpam-6775	343	3	)	)	PUNCT
ejpam-6775	343	4	on	on	ADP
ejpam-6775	343	5	the	the	DET
ejpam-6775	343	6	order	order	NOUN
ejpam-6775	343	7	hand	hand	NOUN
ejpam-6775	343	8	,	,	PUNCT
ejpam-6775	343	9	the	the	DET
ejpam-6775	343	10	second	second	ADJ
ejpam-6775	343	11	derivative	derivative	ADJ
ejpam-6775	343	12	d2	d2	NOUN
ejpam-6775	343	13	zzf	zzf	PROPN
ejpam-6775	343	14	(	(	PUNCT
ejpam-6775	343	15	e0	e0	PROPN
ejpam-6775	343	16	,	,	PUNCT
ejpam-6775	343	17	1)[ṽ0	1)[ṽ0	PROPN
ejpam-6775	343	18	,	,	PUNCT
ejpam-6775	343	19	ṽ0	ṽ0	PROPN
ejpam-6775	343	20	]	]	X
ejpam-6775	343	21	can	can	AUX
ejpam-6775	343	22	be	be	AUX
ejpam-6775	343	23	computed	compute	VERB
ejpam-6775	343	24	as	as	ADP
ejpam-6775	343	25	:	:	PUNCT
ejpam-6775	343	26	d2	d2	PROPN
ejpam-6775	343	27	zzf	zzf	PROPN
ejpam-6775	343	28	(	(	PUNCT
ejpam-6775	343	29	e0	e0	PROPN
ejpam-6775	343	30	,	,	PUNCT
ejpam-6775	343	31	1)[ṽ0	1)[ṽ0	PROPN
ejpam-6775	343	32	,	,	PUNCT
ejpam-6775	343	33	ṽ0	ṽ0	PROPN
ejpam-6775	343	34	]	]	X
ejpam-6775	343	35	=	=	SYM
ejpam-6775	343	36			NOUN
ejpam-6775	343	37	−2	−2	NOUN
ejpam-6775	343	38	t	t	NOUN
ejpam-6775	343	39	(	(	PUNCT
ejpam-6775	343	40	β0π)z	β0π)z	SYM
ejpam-6775	343	41	0	0	NUM
ejpam-6775	343	42	1	1	NUM
ejpam-6775	343	43	−2mt	−2mt	NOUN
ejpam-6775	343	44	(	(	PUNCT
ejpam-6775	343	45	β0π)z	β0π)z	SYM
ejpam-6775	343	46	0	0	NUM
ejpam-6775	344	1	2	2	NUM
ejpam-6775	344	2	0	0	NUM
ejpam-6775	344	3	2[z01	2[z01	NUM
ejpam-6775	344	4	+	+	ADJ
ejpam-6775	344	5	mz02	mz02	PROPN
ejpam-6775	344	6	]	]	X
ejpam-6775	344	7	t	t	PROPN
ejpam-6775	344	8	(	(	PUNCT
ejpam-6775	344	9	β0π	β0π	NOUN
ejpam-6775	344	10	)	)	PUNCT
ejpam-6775	344	11			NOUN
ejpam-6775	344	12	.	.	PUNCT
ejpam-6775	345	1	(	(	PUNCT
ejpam-6775	345	2	39	39	NUM
ejpam-6775	345	3	)	)	PUNCT
ejpam-6775	345	4	thus	thus	ADV
ejpam-6775	345	5	,	,	PUNCT
ejpam-6775	345	6	we	we	PRON
ejpam-6775	345	7	have	have	VERB
ejpam-6775	345	8	a	a	DET
ejpam-6775	345	9	=	=	X
ejpam-6775	345	10	⟨d2	⟨d2	PROPN
ejpam-6775	345	11	zzf	zzf	NOUN
ejpam-6775	345	12	(	(	PUNCT
ejpam-6775	345	13	e0	e0	PROPN
ejpam-6775	345	14	,	,	PUNCT
ejpam-6775	345	15	1)[ṽ0	1)[ṽ0	PROPN
ejpam-6775	345	16	,	,	PUNCT
ejpam-6775	345	17	ṽ0	ṽ0	PROPN
ejpam-6775	345	18	]	]	X
ejpam-6775	345	19	,	,	PUNCT
ejpam-6775	345	20	ṽ	ṽ	PROPN
ejpam-6775	345	21	∗	∗	NOUN
ejpam-6775	345	22	0	0	NUM
ejpam-6775	345	23	⟩	⟩	NOUN
ejpam-6775	345	24	=	=	SYM
ejpam-6775	346	1	2[z01	2[z01	NUM
ejpam-6775	347	1	+	+	ADJ
ejpam-6775	347	2	mz02	mz02	PROPN
ejpam-6775	347	3	]	]	SYM
ejpam-6775	347	4	t	t	PROPN
ejpam-6775	347	5	(	(	PUNCT
ejpam-6775	347	6	β0π)ψ3(0	β0π)ψ3(0	ADJ
ejpam-6775	347	7	)	)	PUNCT
ejpam-6775	347	8	=	=	SYM
ejpam-6775	347	9	2θt	2θt	NOUN
ejpam-6775	347	10	(	(	PUNCT
ejpam-6775	347	11	β0π)ψ3(0	β0π)ψ3(0	PROPN
ejpam-6775	347	12	)	)	PUNCT
ejpam-6775	347	13	.	.	PUNCT
ejpam-6775	348	1	(	(	PUNCT
ejpam-6775	348	2	40	40	NUM
ejpam-6775	348	3	)	)	PUNCT
ejpam-6775	348	4	it	it	PRON
ejpam-6775	348	5	follows	follow	VERB
ejpam-6775	348	6	that	that	SCONJ
ejpam-6775	348	7	a	a	DET
ejpam-6775	348	8	<	<	X
ejpam-6775	348	9	0	0	NUM
ejpam-6775	348	10	(	(	PUNCT
ejpam-6775	348	11	resp	resp	NOUN
ejpam-6775	348	12	.	.	PUNCT
ejpam-6775	349	1	a	a	DET
ejpam-6775	349	2	>	>	X
ejpam-6775	349	3	0	0	NUM
ejpam-6775	349	4	)	)	PUNCT
ejpam-6775	350	1	if	if	SCONJ
ejpam-6775	350	2	and	and	CCONJ
ejpam-6775	350	3	only	only	ADV
ejpam-6775	350	4	if	if	SCONJ
ejpam-6775	350	5	θ	θ	PROPN
ejpam-6775	350	6	<	<	X
ejpam-6775	350	7	0	0	NUM
ejpam-6775	350	8	(	(	PUNCT
ejpam-6775	350	9	resp	resp	NOUN
ejpam-6775	350	10	.	.	PUNCT
ejpam-6775	351	1	θ	θ	X
ejpam-6775	351	2	>	>	PUNCT
ejpam-6775	351	3	0	0	NUM
ejpam-6775	351	4	)	)	PUNCT
ejpam-6775	351	5	.	.	PUNCT
ejpam-6775	352	1	this	this	PRON
ejpam-6775	352	2	completes	complete	VERB
ejpam-6775	352	3	the	the	DET
ejpam-6775	352	4	proof	proof	NOUN
ejpam-6775	352	5	.	.	PUNCT
ejpam-6775	353	1	□	□	PUNCT
ejpam-6775	353	2	the	the	DET
ejpam-6775	353	3	appearance	appearance	NOUN
ejpam-6775	353	4	of	of	ADP
ejpam-6775	353	5	a	a	DET
ejpam-6775	353	6	backward	backward	ADJ
ejpam-6775	353	7	bifurcation	bifurcation	NOUN
ejpam-6775	353	8	in	in	ADP
ejpam-6775	353	9	the	the	DET
ejpam-6775	353	10	epidemiological	epidemiological	ADJ
ejpam-6775	353	11	model	model	NOUN
ejpam-6775	353	12	(	(	PUNCT
ejpam-6775	353	13	1	1	X
ejpam-6775	353	14	)	)	PUNCT
ejpam-6775	353	15	can	can	AUX
ejpam-6775	353	16	lead	lead	VERB
ejpam-6775	353	17	to	to	ADP
ejpam-6775	353	18	the	the	DET
ejpam-6775	353	19	persistence	persistence	NOUN
ejpam-6775	353	20	of	of	ADP
ejpam-6775	353	21	disease	disease	NOUN
ejpam-6775	353	22	in	in	ADP
ejpam-6775	353	23	the	the	DET
ejpam-6775	353	24	population	population	NOUN
ejpam-6775	353	25	even	even	ADV
ejpam-6775	353	26	if	if	SCONJ
ejpam-6775	353	27	the	the	DET
ejpam-6775	353	28	basic	basic	ADJ
ejpam-6775	353	29	reproduction	reproduction	NOUN
ejpam-6775	353	30	number	number	NOUN
ejpam-6775	353	31	is	be	AUX
ejpam-6775	353	32	less	less	ADJ
ejpam-6775	353	33	than	than	ADP
ejpam-6775	353	34	unity	unity	NOUN
ejpam-6775	353	35	.	.	PUNCT
ejpam-6775	354	1	in	in	ADP
ejpam-6775	354	2	such	such	DET
ejpam-6775	354	3	a	a	DET
ejpam-6775	354	4	scenario	scenario	NOUN
ejpam-6775	354	5	,	,	PUNCT
ejpam-6775	354	6	the	the	DET
ejpam-6775	354	7	condition	condition	NOUN
ejpam-6775	354	8	r0	r0	NOUN
ejpam-6775	354	9	<	<	X
ejpam-6775	354	10	1	1	NUM
ejpam-6775	354	11	becomes	become	VERB
ejpam-6775	354	12	only	only	ADV
ejpam-6775	354	13	a	a	DET
ejpam-6775	354	14	necessary	necessary	ADJ
ejpam-6775	354	15	but	but	CCONJ
ejpam-6775	354	16	not	not	PART
ejpam-6775	354	17	sufficient	sufficient	ADJ
ejpam-6775	354	18	condition	condition	NOUN
ejpam-6775	354	19	for	for	ADP
ejpam-6775	354	20	disease	disease	NOUN
ejpam-6775	354	21	eradication	eradication	NOUN
ejpam-6775	354	22	.	.	PUNCT
ejpam-6775	355	1	this	this	DET
ejpam-6775	355	2	important	important	ADJ
ejpam-6775	355	3	property	property	NOUN
ejpam-6775	355	4	of	of	ADP
ejpam-6775	355	5	the	the	DET
ejpam-6775	355	6	model	model	NOUN
ejpam-6775	355	7	is	be	AUX
ejpam-6775	355	8	caused	cause	VERB
ejpam-6775	355	9	j.	j.	PROPN
ejpam-6775	355	10	leo	leo	PROPN
ejpam-6775	355	11	amalraj	amalraj	PROPN
ejpam-6775	355	12	et	et	PROPN
ejpam-6775	355	13	al	al	PROPN
ejpam-6775	355	14	.	.	PUNCT
ejpam-6775	355	15	/	/	SYM
ejpam-6775	355	16	eur	eur	PROPN
ejpam-6775	355	17	.	.	PUNCT
ejpam-6775	356	1	j.	j.	PROPN
ejpam-6775	356	2	pure	pure	PROPN
ejpam-6775	356	3	appl	appl	PROPN
ejpam-6775	356	4	.	.	PROPN
ejpam-6775	356	5	math	math	PROPN
ejpam-6775	356	6	,	,	PUNCT
ejpam-6775	356	7	18	18	NUM
ejpam-6775	356	8	(	(	PUNCT
ejpam-6775	356	9	4	4	NUM
ejpam-6775	356	10	)	)	PUNCT
ejpam-6775	356	11	(	(	PUNCT
ejpam-6775	356	12	2025	2025	NUM
ejpam-6775	356	13	)	)	PUNCT
ejpam-6775	356	14	,	,	PUNCT
ejpam-6775	356	15	6775	6775	NUM
ejpam-6775	356	16	15	15	NUM
ejpam-6775	356	17	of	of	ADP
ejpam-6775	356	18	32	32	NUM
ejpam-6775	356	19	by	by	ADP
ejpam-6775	356	20	the	the	DET
ejpam-6775	356	21	therapeutic	therapeutic	ADJ
ejpam-6775	356	22	treatment	treatment	NOUN
ejpam-6775	356	23	rate	rate	NOUN
ejpam-6775	356	24	of	of	ADP
ejpam-6775	356	25	infectious	infectious	ADJ
ejpam-6775	356	26	individuals	individual	NOUN
ejpam-6775	356	27	since	since	SCONJ
ejpam-6775	356	28	θ	θ	X
ejpam-6775	356	29	<	<	X
ejpam-6775	356	30	0	0	PUNCT
ejpam-6775	356	31	when	when	SCONJ
ejpam-6775	356	32	α(x	α(x	NOUN
ejpam-6775	356	33	)	)	PUNCT
ejpam-6775	356	34	=	=	SYM
ejpam-6775	356	35	0	0	NUM
ejpam-6775	357	1	for	for	ADP
ejpam-6775	357	2	all	all	DET
ejpam-6775	357	3	x	x	SYM
ejpam-6775	357	4	∈	∈	PROPN
ejpam-6775	357	5	r+	r+	NOUN
ejpam-6775	357	6	.	.	PUNCT
ejpam-6775	358	1	in	in	ADP
ejpam-6775	358	2	this	this	DET
ejpam-6775	358	3	case	case	NOUN
ejpam-6775	358	4	,	,	PUNCT
ejpam-6775	358	5	the	the	DET
ejpam-6775	358	6	coefficients	coefficient	NOUN
ejpam-6775	358	7	of	of	ADP
ejpam-6775	358	8	quadratic	quadratic	ADJ
ejpam-6775	358	9	equation	equation	NOUN
ejpam-6775	358	10	(	(	PUNCT
ejpam-6775	358	11	17	17	NUM
ejpam-6775	358	12	)	)	PUNCT
ejpam-6775	358	13	a2	a2	PROPN
ejpam-6775	358	14	>	>	X
ejpam-6775	358	15	0	0	PROPN
ejpam-6775	358	16	,	,	PUNCT
ejpam-6775	358	17	a0	a0	NOUN
ejpam-6775	358	18	<	<	X
ejpam-6775	358	19	0	0	PUNCT
ejpam-6775	358	20	when	when	SCONJ
ejpam-6775	358	21	r0	r0	NOUN
ejpam-6775	358	22	>	>	X
ejpam-6775	358	23	1	1	X
ejpam-6775	358	24	.	.	PUNCT
ejpam-6775	359	1	consequently	consequently	ADV
ejpam-6775	359	2	,	,	PUNCT
ejpam-6775	359	3	the	the	DET
ejpam-6775	359	4	system	system	NOUN
ejpam-6775	359	5	(	(	PUNCT
ejpam-6775	359	6	1	1	X
ejpam-6775	359	7	)	)	PUNCT
ejpam-6775	359	8	admits	admit	VERB
ejpam-6775	359	9	a	a	DET
ejpam-6775	359	10	unique	unique	ADJ
ejpam-6775	359	11	endemic	endemic	ADJ
ejpam-6775	359	12	equilibrium	equilibrium	NOUN
ejpam-6775	359	13	.	.	PUNCT
ejpam-6775	360	1	moreover	moreover	ADV
ejpam-6775	360	2	,	,	PUNCT
ejpam-6775	360	3	the	the	DET
ejpam-6775	360	4	global	global	ADJ
ejpam-6775	360	5	asymptotic	asymptotic	ADJ
ejpam-6775	360	6	stability	stability	NOUN
ejpam-6775	360	7	of	of	ADP
ejpam-6775	360	8	the	the	DET
ejpam-6775	360	9	disease	disease	NOUN
ejpam-6775	360	10	-	-	PUNCT
ejpam-6775	360	11	free	free	ADJ
ejpam-6775	360	12	equilibrium	equilibrium	NOUN
ejpam-6775	360	13	of	of	ADP
ejpam-6775	360	14	the	the	DET
ejpam-6775	360	15	model	model	NOUN
ejpam-6775	360	16	(	(	PUNCT
ejpam-6775	360	17	1	1	X
ejpam-6775	360	18	)	)	PUNCT
ejpam-6775	360	19	is	be	AUX
ejpam-6775	360	20	given	give	VERB
ejpam-6775	360	21	below	below	ADV
ejpam-6775	360	22	for	for	ADP
ejpam-6775	360	23	the	the	DET
ejpam-6775	360	24	special	special	ADJ
ejpam-6775	360	25	case	case	NOUN
ejpam-6775	360	26	α(x	α(x	NOUN
ejpam-6775	360	27	)	)	PUNCT
ejpam-6775	360	28	=	=	SYM
ejpam-6775	361	1	0	0	X
ejpam-6775	361	2	.	.	PUNCT
ejpam-6775	361	3	theorem	theorem	NOUN
ejpam-6775	361	4	5	5	NUM
ejpam-6775	361	5	.	.	PUNCT
ejpam-6775	361	6	assume	assume	VERB
ejpam-6775	361	7	that	that	SCONJ
ejpam-6775	361	8	the	the	DET
ejpam-6775	361	9	therapeutic	therapeutic	ADJ
ejpam-6775	361	10	treatment	treatment	NOUN
ejpam-6775	361	11	is	be	AUX
ejpam-6775	361	12	not	not	PART
ejpam-6775	361	13	effective	effective	ADJ
ejpam-6775	361	14	(	(	PUNCT
ejpam-6775	361	15	i.e.	i.e.	X
ejpam-6775	361	16	α(x	α(x	NOUN
ejpam-6775	361	17	)	)	PUNCT
ejpam-6775	361	18	=	=	SYM
ejpam-6775	361	19	0	0	NUM
ejpam-6775	361	20	for	for	ADP
ejpam-6775	361	21	all	all	DET
ejpam-6775	361	22	x	x	SYM
ejpam-6775	361	23	∈	∈	PROPN
ejpam-6775	361	24	r+	r+	NOUN
ejpam-6775	361	25	)	)	PUNCT
ejpam-6775	361	26	.	.	PUNCT
ejpam-6775	362	1	then	then	ADV
ejpam-6775	362	2	,	,	PUNCT
ejpam-6775	362	3	the	the	DET
ejpam-6775	362	4	system	system	NOUN
ejpam-6775	362	5	(	(	PUNCT
ejpam-6775	362	6	1	1	X
ejpam-6775	362	7	)	)	PUNCT
ejpam-6775	362	8	always	always	ADV
ejpam-6775	362	9	admits	admit	VERB
ejpam-6775	362	10	a	a	DET
ejpam-6775	362	11	disease	disease	NOUN
ejpam-6775	362	12	-	-	PUNCT
ejpam-6775	362	13	free	free	ADJ
ejpam-6775	362	14	equilibrium	equilibrium	NOUN
ejpam-6775	362	15	point	point	NOUN
ejpam-6775	362	16	e0	e0	PROPN
ejpam-6775	362	17	which	which	PRON
ejpam-6775	362	18	is	be	AUX
ejpam-6775	362	19	globally	globally	ADV
ejpam-6775	362	20	asymptotically	asymptotically	ADV
ejpam-6775	362	21	stable	stable	ADJ
ejpam-6775	362	22	whenever	whenever	SCONJ
ejpam-6775	362	23	r0	r0	NOUN
ejpam-6775	362	24	≤	≤	NOUN
ejpam-6775	362	25	1	1	NUM
ejpam-6775	362	26	.	.	PUNCT
ejpam-6775	363	1	proof	proof	NOUN
ejpam-6775	363	2	.	.	PUNCT
ejpam-6775	364	1	to	to	PART
ejpam-6775	364	2	establish	establish	VERB
ejpam-6775	364	3	the	the	DET
ejpam-6775	364	4	global	global	ADJ
ejpam-6775	364	5	stability	stability	NOUN
ejpam-6775	364	6	of	of	ADP
ejpam-6775	364	7	disease	disease	NOUN
ejpam-6775	364	8	-	-	PUNCT
ejpam-6775	364	9	free	free	ADJ
ejpam-6775	364	10	equilibrium	equilibrium	NOUN
ejpam-6775	364	11	e0	e0	NOUN
ejpam-6775	364	12	,	,	PUNCT
ejpam-6775	364	13	we	we	PRON
ejpam-6775	364	14	use	use	VERB
ejpam-6775	364	15	the	the	DET
ejpam-6775	364	16	lyapunov	lyapunov	ADJ
ejpam-6775	364	17	function	function	NOUN
ejpam-6775	364	18	approach	approach	NOUN
ejpam-6775	364	19	.	.	PUNCT
ejpam-6775	365	1	for	for	ADP
ejpam-6775	365	2	this	this	PRON
ejpam-6775	365	3	,	,	PUNCT
ejpam-6775	365	4	we	we	PRON
ejpam-6775	365	5	consider	consider	VERB
ejpam-6775	365	6	the	the	DET
ejpam-6775	365	7	function	function	NOUN
ejpam-6775	365	8	q(x	q(x	PROPN
ejpam-6775	365	9	)	)	PUNCT
ejpam-6775	365	10	=	=	PUNCT
ejpam-6775	366	1	∫	∫	PROPN
ejpam-6775	366	2	x	x	SYM
ejpam-6775	366	3	0	0	NUM
ejpam-6775	366	4	β(s	β(s	PROPN
ejpam-6775	366	5	)	)	PUNCT
ejpam-6775	366	6	π(s	π(s	PROPN
ejpam-6775	366	7	)	)	PUNCT
ejpam-6775	366	8	π(x)ds	π(x)ds	PROPN
ejpam-6775	366	9	.	.	PUNCT
ejpam-6775	366	10	note	note	VERB
ejpam-6775	366	11	that	that	SCONJ
ejpam-6775	366	12	q	q	PROPN
ejpam-6775	366	13	∈	∈	PROPN
ejpam-6775	366	14	l∞(0,∞	l∞(0,∞	PROPN
ejpam-6775	366	15	)	)	PUNCT
ejpam-6775	366	16	,	,	PUNCT
ejpam-6775	366	17	q(0	q(0	PROPN
ejpam-6775	366	18	)	)	PUNCT
ejpam-6775	367	1	=	=	SYM
ejpam-6775	367	2	t	t	PROPN
ejpam-6775	367	3	(	(	PUNCT
ejpam-6775	367	4	βπ	βπ	NOUN
ejpam-6775	367	5	)	)	PUNCT
ejpam-6775	367	6	and	and	CCONJ
ejpam-6775	367	7	it	it	PRON
ejpam-6775	367	8	satisfies	satisfy	VERB
ejpam-6775	367	9	the	the	DET
ejpam-6775	367	10	differential	differential	ADJ
ejpam-6775	367	11	equation	equation	NOUN
ejpam-6775	367	12	for	for	ADP
ejpam-6775	367	13	all	all	PRON
ejpam-6775	367	14	x	x	SYM
ejpam-6775	367	15	>	>	X
ejpam-6775	367	16	0	0	NUM
ejpam-6775	367	17	,	,	PUNCT
ejpam-6775	367	18	q′(x	q′(x	NOUN
ejpam-6775	367	19	)	)	PUNCT
ejpam-6775	367	20	−	−	PROPN
ejpam-6775	367	21	(	(	PUNCT
ejpam-6775	367	22	µ	µ	X
ejpam-6775	367	23	+	+	X
ejpam-6775	367	24	δ(x))q(x	δ(x))q(x	NOUN
ejpam-6775	367	25	)	)	PUNCT
ejpam-6775	367	26	+	+	CCONJ
ejpam-6775	367	27	β(x	β(x	NOUN
ejpam-6775	367	28	)	)	PUNCT
ejpam-6775	367	29	=	=	SYM
ejpam-6775	368	1	0	0	X
ejpam-6775	368	2	.	.	PUNCT
ejpam-6775	368	3	let	let	VERB
ejpam-6775	368	4	us	we	PRON
ejpam-6775	368	5	introduce	introduce	VERB
ejpam-6775	368	6	the	the	DET
ejpam-6775	368	7	volterra	volterra	NOUN
ejpam-6775	368	8	-	-	PUNCT
ejpam-6775	368	9	type	type	NOUN
ejpam-6775	368	10	function	function	NOUN
ejpam-6775	368	11	which	which	PRON
ejpam-6775	368	12	takes	take	VERB
ejpam-6775	368	13	the	the	DET
ejpam-6775	368	14	form	form	NOUN
ejpam-6775	368	15	h(x	h(x	PROPN
ejpam-6775	368	16	)	)	PUNCT
ejpam-6775	369	1	=	=	PUNCT
ejpam-6775	370	1	x	x	X
ejpam-6775	370	2	−	−	NUM
ejpam-6775	370	3	lnx	lnx	PROPN
ejpam-6775	370	4	.	.	PUNCT
ejpam-6775	371	1	obviously	obviously	ADV
ejpam-6775	371	2	,	,	PUNCT
ejpam-6775	371	3	h′(x	h′(x	NOUN
ejpam-6775	371	4	)	)	PUNCT
ejpam-6775	371	5	=	=	SYM
ejpam-6775	371	6	1	1	NUM
ejpam-6775	371	7	−	−	NOUN
ejpam-6775	371	8	(	(	PUNCT
ejpam-6775	371	9	1	1	NUM
ejpam-6775	371	10	/	/	SYM
ejpam-6775	371	11	x	x	NOUN
ejpam-6775	371	12	)	)	PUNCT
ejpam-6775	371	13	and	and	CCONJ
ejpam-6775	371	14	h(x	h(x	PROPN
ejpam-6775	371	15	)	)	PUNCT
ejpam-6775	371	16	≥	≥	NOUN
ejpam-6775	371	17	0	0	NUM
ejpam-6775	371	18	for	for	ADP
ejpam-6775	371	19	all	all	PRON
ejpam-6775	371	20	x	x	SYM
ejpam-6775	371	21	>	>	X
ejpam-6775	371	22	0	0	X
ejpam-6775	371	23	.	.	PUNCT
ejpam-6775	372	1	thus	thus	ADV
ejpam-6775	372	2	h(x	h(x	PROPN
ejpam-6775	372	3	)	)	PUNCT
ejpam-6775	372	4	is	be	AUX
ejpam-6775	372	5	decreasing	decrease	VERB
ejpam-6775	372	6	function	function	NOUN
ejpam-6775	372	7	on	on	ADP
ejpam-6775	372	8	(	(	PUNCT
ejpam-6775	372	9	0	0	NUM
ejpam-6775	372	10	,	,	PUNCT
ejpam-6775	372	11	1	1	NUM
ejpam-6775	372	12	)	)	PUNCT
ejpam-6775	372	13	and	and	CCONJ
ejpam-6775	372	14	increasing	increase	VERB
ejpam-6775	372	15	on	on	ADP
ejpam-6775	372	16	(	(	PUNCT
ejpam-6775	372	17	1,+∞	1,+∞	NUM
ejpam-6775	372	18	)	)	PUNCT
ejpam-6775	372	19	.	.	PUNCT
ejpam-6775	373	1	in	in	ADP
ejpam-6775	373	2	addition	addition	NOUN
ejpam-6775	373	3	to	to	ADP
ejpam-6775	373	4	the	the	DET
ejpam-6775	373	5	fact	fact	NOUN
ejpam-6775	373	6	that	that	SCONJ
ejpam-6775	373	7	h′′(x	h′′(x	NOUN
ejpam-6775	373	8	)	)	PUNCT
ejpam-6775	373	9	>	>	X
ejpam-6775	373	10	0	0	PUNCT
ejpam-6775	374	1	for	for	ADP
ejpam-6775	374	2	all	all	PRON
ejpam-6775	374	3	x	x	SYM
ejpam-6775	374	4	>	>	X
ejpam-6775	374	5	0	0	NUM
ejpam-6775	374	6	,	,	PUNCT
ejpam-6775	374	7	then	then	ADV
ejpam-6775	374	8	h(x	h(x	PROPN
ejpam-6775	374	9	)	)	PUNCT
ejpam-6775	374	10	has	have	VERB
ejpam-6775	374	11	a	a	DET
ejpam-6775	374	12	unique	unique	ADJ
ejpam-6775	374	13	global	global	ADJ
ejpam-6775	374	14	minimum	minimum	NOUN
ejpam-6775	374	15	at	at	ADP
ejpam-6775	374	16	x0	x0	PROPN
ejpam-6775	374	17	=	=	NOUN
ejpam-6775	374	18	1	1	NUM
ejpam-6775	374	19	satisfying	satisfying	NOUN
ejpam-6775	374	20	h(x0	h(x0	NOUN
ejpam-6775	374	21	)	)	PUNCT
ejpam-6775	375	1	=	=	SYM
ejpam-6775	375	2	0	0	X
ejpam-6775	375	3	.	.	PUNCT
ejpam-6775	376	1	let	let	VERB
ejpam-6775	376	2	us	we	PRON
ejpam-6775	376	3	consider	consider	VERB
ejpam-6775	376	4	the	the	DET
ejpam-6775	376	5	following	follow	VERB
ejpam-6775	376	6	lyapunov	lyapunov	NOUN
ejpam-6775	376	7	function	function	NOUN
ejpam-6775	376	8	:	:	PUNCT
ejpam-6775	377	1	w	w	X
ejpam-6775	378	1	[	[	X
ejpam-6775	378	2	t	t	X
ejpam-6775	378	3	]	]	X
ejpam-6775	378	4	=	=	PUNCT
ejpam-6775	378	5	s0h	s0h	VERB
ejpam-6775	378	6	(	(	PUNCT
ejpam-6775	378	7	s(t	s(t	PROPN
ejpam-6775	378	8	)	)	PUNCT
ejpam-6775	378	9	s0	s0	NOUN
ejpam-6775	378	10	)	)	PUNCT
ejpam-6775	379	1	+	+	CCONJ
ejpam-6775	379	2	v0h	v0h	PROPN
ejpam-6775	379	3	(	(	PUNCT
ejpam-6775	379	4	v	v	NOUN
ejpam-6775	379	5	(	(	PUNCT
ejpam-6775	379	6	t	t	NOUN
ejpam-6775	379	7	)	)	PUNCT
ejpam-6775	379	8	v0	v0	NOUN
ejpam-6775	379	9	)	)	PUNCT
ejpam-6775	380	1	+	+	CCONJ
ejpam-6775	381	1	[	[	X
ejpam-6775	381	2	s0	s0	NOUN
ejpam-6775	381	3	+	+	PROPN
ejpam-6775	381	4	mv	mv	PROPN
ejpam-6775	381	5	0]t	0]t	NUM
ejpam-6775	381	6	(	(	PUNCT
ejpam-6775	381	7	q(i	q(i	NOUN
ejpam-6775	381	8	(	(	PUNCT
ejpam-6775	381	9	.	.	PUNCT
ejpam-6775	381	10	,	,	PUNCT
ejpam-6775	381	11	.	.	PUNCT
ejpam-6775	381	12	)	)	PUNCT
ejpam-6775	381	13	)	)	PUNCT
ejpam-6775	381	14	)	)	PUNCT
ejpam-6775	381	15	.	.	PUNCT
ejpam-6775	382	1	(	(	PUNCT
ejpam-6775	382	2	41	41	NUM
ejpam-6775	382	3	)	)	PUNCT
ejpam-6775	382	4	it	it	PRON
ejpam-6775	382	5	follows	follow	VERB
ejpam-6775	382	6	that	that	SCONJ
ejpam-6775	382	7	the	the	DET
ejpam-6775	382	8	function	function	NOUN
ejpam-6775	382	9	w	w	PROPN
ejpam-6775	383	1	[	[	X
ejpam-6775	383	2	t	t	X
ejpam-6775	383	3	]	]	X
ejpam-6775	383	4	is	be	AUX
ejpam-6775	383	5	nonnegative	nonnegative	ADJ
ejpam-6775	383	6	and	and	CCONJ
ejpam-6775	383	7	well	well	ADV
ejpam-6775	383	8	defined	define	VERB
ejpam-6775	383	9	with	with	ADP
ejpam-6775	383	10	respect	respect	NOUN
ejpam-6775	383	11	to	to	ADP
ejpam-6775	383	12	the	the	DET
ejpam-6775	383	13	disease	disease	NOUN
ejpam-6775	383	14	-	-	PUNCT
ejpam-6775	383	15	free	free	ADJ
ejpam-6775	383	16	equilibrium	equilibrium	NOUN
ejpam-6775	383	17	e0	e0	PROPN
ejpam-6775	383	18	which	which	PRON
ejpam-6775	383	19	is	be	AUX
ejpam-6775	383	20	a	a	DET
ejpam-6775	383	21	global	global	ADJ
ejpam-6775	383	22	minimum	minimum	NOUN
ejpam-6775	383	23	.	.	PUNCT
ejpam-6775	384	1	differentiating	differentiate	VERB
ejpam-6775	384	2	the	the	DET
ejpam-6775	384	3	function	function	NOUN
ejpam-6775	384	4	w	w	PROPN
ejpam-6775	385	1	[	[	X
ejpam-6775	385	2	t	t	X
ejpam-6775	385	3	]	]	PUNCT
ejpam-6775	385	4	along	along	ADP
ejpam-6775	385	5	the	the	DET
ejpam-6775	385	6	solution	solution	NOUN
ejpam-6775	385	7	of	of	ADP
ejpam-6775	385	8	the	the	DET
ejpam-6775	385	9	system	system	NOUN
ejpam-6775	385	10	(	(	PUNCT
ejpam-6775	385	11	1	1	NUM
ejpam-6775	385	12	)	)	PUNCT
ejpam-6775	385	13	,	,	PUNCT
ejpam-6775	385	14	we	we	PRON
ejpam-6775	385	15	have	have	VERB
ejpam-6775	385	16	dw	dw	PROPN
ejpam-6775	386	1	[	[	X
ejpam-6775	386	2	t	t	X
ejpam-6775	386	3	]	]	X
ejpam-6775	386	4	dt	dt	X
ejpam-6775	386	5	=	=	PUNCT
ejpam-6775	386	6	µs0	µs0	PROPN
ejpam-6775	386	7	(	(	PUNCT
ejpam-6775	386	8	1−	1−	NUM
ejpam-6775	386	9	s0	s0	PROPN
ejpam-6775	386	10	s	s	PART
ejpam-6775	386	11	)	)	PUNCT
ejpam-6775	386	12	ds	ds	ADJ
ejpam-6775	387	1	dt	dt	NOUN
ejpam-6775	387	2	+	+	NOUN
ejpam-6775	387	3	µv	µv	PROPN
ejpam-6775	387	4	0	0	NUM
ejpam-6775	387	5	(	(	PUNCT
ejpam-6775	387	6	1−	1−	NUM
ejpam-6775	387	7	v	v	NOUN
ejpam-6775	387	8	0	0	NUM
ejpam-6775	387	9	v	v	NOUN
ejpam-6775	387	10	)	)	PUNCT
ejpam-6775	387	11	dv	dv	PROPN
ejpam-6775	388	1	dt	dt	X
ejpam-6775	389	1	+	+	CCONJ
ejpam-6775	389	2	[	[	X
ejpam-6775	389	3	s0+mv	s0+mv	X
ejpam-6775	389	4	0	0	NUM
ejpam-6775	389	5	]	]	X
ejpam-6775	389	6	∫	∫	PROPN
ejpam-6775	389	7	∞	∞	NUM
ejpam-6775	389	8	0	0	NUM
ejpam-6775	389	9	q(x)∂ii(t	q(x)∂ii(t	NOUN
ejpam-6775	389	10	,	,	PUNCT
ejpam-6775	389	11	x)dx	x)dx	PROPN
ejpam-6775	389	12	.	.	PUNCT
ejpam-6775	390	1	(	(	PUNCT
ejpam-6775	390	2	42	42	NUM
ejpam-6775	390	3	)	)	PUNCT
ejpam-6775	390	4	=	=	SYM
ejpam-6775	390	5	(	(	PUNCT
ejpam-6775	390	6	1−	1−	NUM
ejpam-6775	390	7	s0	s0	PROPN
ejpam-6775	390	8	s	s	PART
ejpam-6775	390	9	)	)	PUNCT
ejpam-6775	390	10	(	(	PUNCT
ejpam-6775	390	11	λ−	λ−	PROPN
ejpam-6775	390	12	t	t	PROPN
ejpam-6775	390	13	(	(	PUNCT
ejpam-6775	390	14	βis	βis	X
ejpam-6775	390	15	)	)	PUNCT
ejpam-6775	391	1	+	+	NUM
ejpam-6775	391	2	t	t	PROPN
ejpam-6775	391	3	(	(	PUNCT
ejpam-6775	391	4	αi)−	αi)−	X
ejpam-6775	391	5	(	(	PUNCT
ejpam-6775	391	6	ξ	ξ	NOUN
ejpam-6775	391	7	+	+	NOUN
ejpam-6775	391	8	µ)s	µ)s	NOUN
ejpam-6775	391	9	)	)	PUNCT
ejpam-6775	392	1	+	+	CCONJ
ejpam-6775	392	2	(	(	PUNCT
ejpam-6775	392	3	1−	1−	NUM
ejpam-6775	392	4	v	v	NOUN
ejpam-6775	392	5	0	0	NUM
ejpam-6775	392	6	v	v	NOUN
ejpam-6775	392	7	)	)	PUNCT
ejpam-6775	392	8	(	(	PUNCT
ejpam-6775	392	9	ξs	ξs	ADV
ejpam-6775	392	10	−mt	−mt	NOUN
ejpam-6775	392	11	(	(	PUNCT
ejpam-6775	392	12	βi)v	βi)v	PROPN
ejpam-6775	392	13	−	−	PROPN
ejpam-6775	392	14	µv	µv	NOUN
ejpam-6775	392	15	)	)	PUNCT
ejpam-6775	393	1	+	+	PUNCT
ejpam-6775	393	2	[	[	X
ejpam-6775	393	3	s0	s0	NOUN
ejpam-6775	393	4	+	+	PROPN
ejpam-6775	393	5	mv	mv	PROPN
ejpam-6775	393	6	0	0	NUM
ejpam-6775	393	7	]	]	PUNCT
ejpam-6775	393	8	∫	∫	PROPN
ejpam-6775	393	9	∞	∞	NOUN
ejpam-6775	393	10	0	0	NUM
ejpam-6775	393	11	q(x)(−∂xi(t	q(x)(−∂xi(t	NOUN
ejpam-6775	393	12	,	,	PUNCT
ejpam-6775	393	13	x)−	x)−	PROPN
ejpam-6775	393	14	(	(	PUNCT
ejpam-6775	393	15	µ+	µ+	X
ejpam-6775	393	16	δ(x))dx	δ(x))dx	NOUN
ejpam-6775	393	17	.	.	PUNCT
ejpam-6775	394	1	by	by	ADP
ejpam-6775	394	2	using	use	VERB
ejpam-6775	394	3	the	the	DET
ejpam-6775	394	4	fact	fact	NOUN
ejpam-6775	395	1	that	that	SCONJ
ejpam-6775	395	2	λ	λ	X
ejpam-6775	395	3	=	=	PRON
ejpam-6775	395	4	(	(	PUNCT
ejpam-6775	395	5	ξ	ξ	X
ejpam-6775	395	6	+	+	PUNCT
ejpam-6775	395	7	µ)s0	µ)s0	PROPN
ejpam-6775	395	8	and	and	CCONJ
ejpam-6775	395	9	ξs0	ξs0	NUM
ejpam-6775	395	10	=	=	PUNCT
ejpam-6775	395	11	µv	µv	NOUN
ejpam-6775	395	12	0	0	NUM
ejpam-6775	395	13	,	,	PUNCT
ejpam-6775	395	14	we	we	PRON
ejpam-6775	395	15	get	get	VERB
ejpam-6775	395	16	after	after	ADP
ejpam-6775	395	17	a	a	DET
ejpam-6775	395	18	few	few	ADJ
ejpam-6775	395	19	algebraic	algebraic	ADJ
ejpam-6775	395	20	calculations	calculation	NOUN
ejpam-6775	395	21	dw	dw	PROPN
ejpam-6775	396	1	[	[	X
ejpam-6775	396	2	t	t	X
ejpam-6775	396	3	]	]	X
ejpam-6775	396	4	dt	dt	X
ejpam-6775	396	5	=	=	PUNCT
ejpam-6775	396	6	µs0	µs0	PROPN
ejpam-6775	396	7	(	(	PUNCT
ejpam-6775	396	8	2−	2−	NUM
ejpam-6775	396	9	s	s	NOUN
ejpam-6775	396	10	s0	s0	PROPN
ejpam-6775	396	11	−	−	PROPN
ejpam-6775	396	12	s0	s0	PROPN
ejpam-6775	396	13	s	s	PART
ejpam-6775	396	14	)	)	PUNCT
ejpam-6775	397	1	+	+	CCONJ
ejpam-6775	397	2	ξs0	ξs0	NUM
ejpam-6775	397	3	(	(	PUNCT
ejpam-6775	397	4	3−	3−	NUM
ejpam-6775	397	5	v	v	PART
ejpam-6775	397	6	v	v	NOUN
ejpam-6775	397	7	0	0	NUM
ejpam-6775	397	8	−	−	PROPN
ejpam-6775	397	9	s0	s0	PROPN
ejpam-6775	397	10	s	s	PART
ejpam-6775	397	11	−	−	PROPN
ejpam-6775	397	12	s	s	PART
ejpam-6775	397	13	s0	s0	PROPN
ejpam-6775	397	14	v	v	ADP
ejpam-6775	397	15	0	0	NUM
ejpam-6775	397	16	v	v	NOUN
ejpam-6775	397	17	)	)	PUNCT
ejpam-6775	397	18	+	+	CCONJ
ejpam-6775	398	1	[	[	X
ejpam-6775	398	2	s0	s0	NOUN
ejpam-6775	398	3	+	+	NOUN
ejpam-6775	398	4	mv	mv	PROPN
ejpam-6775	398	5	0]t	0]t	NUM
ejpam-6775	398	6	(	(	PUNCT
ejpam-6775	398	7	βi	βi	X
ejpam-6775	398	8	)	)	PUNCT
ejpam-6775	398	9	(	(	PUNCT
ejpam-6775	398	10	43	43	NUM
ejpam-6775	398	11	)	)	PUNCT
ejpam-6775	398	12	−[s0	−[s0	PUNCT
ejpam-6775	399	1	+	+	ADV
ejpam-6775	399	2	mv	mv	PROPN
ejpam-6775	399	3	0]t	0]t	NUM
ejpam-6775	399	4	(	(	PUNCT
ejpam-6775	399	5	βi	βi	X
ejpam-6775	399	6	)	)	PUNCT
ejpam-6775	399	7	+	+	CCONJ
ejpam-6775	400	1	[	[	X
ejpam-6775	400	2	s0	s0	NOUN
ejpam-6775	400	3	+	+	PROPN
ejpam-6775	400	4	mv	mv	PROPN
ejpam-6775	400	5	0	0	NUM
ejpam-6775	400	6	]	]	PUNCT
ejpam-6775	400	7	∫	∫	PROPN
ejpam-6775	400	8	∞	∞	NOUN
ejpam-6775	400	9	0	0	NUM
ejpam-6775	400	10	q(x)(−∂xi(t	q(x)(−∂xi(t	NOUN
ejpam-6775	400	11	,	,	PUNCT
ejpam-6775	400	12	x)−	x)−	PROPN
ejpam-6775	400	13	(	(	PUNCT
ejpam-6775	400	14	µ+	µ+	NOUN
ejpam-6775	400	15	δ(x)))dx	δ(x)))dx	NOUN
ejpam-6775	400	16	.	.	PUNCT
ejpam-6775	401	1	j.	j.	PROPN
ejpam-6775	401	2	leo	leo	PROPN
ejpam-6775	401	3	amalraj	amalraj	PROPN
ejpam-6775	401	4	et	et	PROPN
ejpam-6775	401	5	al	al	PROPN
ejpam-6775	401	6	.	.	PUNCT
ejpam-6775	401	7	/	/	SYM
ejpam-6775	401	8	eur	eur	PROPN
ejpam-6775	401	9	.	.	PUNCT
ejpam-6775	402	1	j.	j.	PROPN
ejpam-6775	402	2	pure	pure	PROPN
ejpam-6775	402	3	appl	appl	PROPN
ejpam-6775	402	4	.	.	PROPN
ejpam-6775	402	5	math	math	PROPN
ejpam-6775	402	6	,	,	PUNCT
ejpam-6775	402	7	18	18	NUM
ejpam-6775	402	8	(	(	PUNCT
ejpam-6775	402	9	4	4	NUM
ejpam-6775	402	10	)	)	PUNCT
ejpam-6775	402	11	(	(	PUNCT
ejpam-6775	402	12	2025	2025	NUM
ejpam-6775	402	13	)	)	PUNCT
ejpam-6775	402	14	,	,	PUNCT
ejpam-6775	402	15	6775	6775	NUM
ejpam-6775	402	16	16	16	NUM
ejpam-6775	402	17	of	of	ADP
ejpam-6775	402	18	32	32	NUM
ejpam-6775	402	19	using	use	VERB
ejpam-6775	402	20	the	the	DET
ejpam-6775	402	21	integration	integration	NOUN
ejpam-6775	402	22	by	by	ADP
ejpam-6775	402	23	parts	part	NOUN
ejpam-6775	402	24	formula	formula	NOUN
ejpam-6775	402	25	,	,	PUNCT
ejpam-6775	402	26	we	we	PRON
ejpam-6775	402	27	have∫	have∫	VERB
ejpam-6775	402	28	∞	∞	NOUN
ejpam-6775	402	29	0	0	NUM
ejpam-6775	402	30	q(x)∂xi(t	q(x)∂xi(t	NOUN
ejpam-6775	402	31	,	,	PUNCT
ejpam-6775	402	32	x)dx	x)dx	PROPN
ejpam-6775	402	33	=	=	PUNCT
ejpam-6775	403	1	[	[	X
ejpam-6775	403	2	q(x)i(t	q(x)i(t	ADP
ejpam-6775	403	3	,	,	PUNCT
ejpam-6775	403	4	x)]∞0	x)]∞0	PROPN
ejpam-6775	404	1	−	−	PROPN
ejpam-6775	404	2	∫	∫	PROPN
ejpam-6775	404	3	∞	∞	NUM
ejpam-6775	404	4	0	0	NUM
ejpam-6775	404	5	q′(x)i(t	q′(x)i(t	NOUN
ejpam-6775	404	6	,	,	PUNCT
ejpam-6775	404	7	x)dx	x)dx	PROPN
ejpam-6775	404	8	.	.	PUNCT
ejpam-6775	405	1	(	(	PUNCT
ejpam-6775	405	2	44	44	NUM
ejpam-6775	405	3	)	)	PUNCT
ejpam-6775	405	4	combining	combine	VERB
ejpam-6775	405	5	the	the	DET
ejpam-6775	405	6	relations	relation	NOUN
ejpam-6775	405	7	(	(	PUNCT
ejpam-6775	405	8	27	27	NUM
ejpam-6775	405	9	)	)	PUNCT
ejpam-6775	405	10	and	and	CCONJ
ejpam-6775	405	11	(	(	PUNCT
ejpam-6775	405	12	28	28	NUM
ejpam-6775	405	13	)	)	PUNCT
ejpam-6775	405	14	,	,	PUNCT
ejpam-6775	405	15	we	we	PRON
ejpam-6775	405	16	have	have	VERB
ejpam-6775	405	17	after	after	ADP
ejpam-6775	405	18	calculation	calculation	NOUN
ejpam-6775	405	19	dw	dw	PROPN
ejpam-6775	406	1	[	[	X
ejpam-6775	406	2	t	t	X
ejpam-6775	406	3	]	]	X
ejpam-6775	406	4	dt	dt	X
ejpam-6775	406	5	=	=	PUNCT
ejpam-6775	406	6	µs0	µs0	PROPN
ejpam-6775	406	7	(	(	PUNCT
ejpam-6775	406	8	2−	2−	NUM
ejpam-6775	406	9	s	s	NOUN
ejpam-6775	406	10	s0	s0	PROPN
ejpam-6775	406	11	−	−	PROPN
ejpam-6775	406	12	s0	s0	PROPN
ejpam-6775	406	13	s	s	PART
ejpam-6775	406	14	)	)	PUNCT
ejpam-6775	407	1	+	+	CCONJ
ejpam-6775	407	2	ξs0	ξs0	NUM
ejpam-6775	407	3	(	(	PUNCT
ejpam-6775	407	4	3−	3−	NUM
ejpam-6775	407	5	v	v	PART
ejpam-6775	407	6	v	v	NOUN
ejpam-6775	407	7	0	0	NUM
ejpam-6775	407	8	−	−	PROPN
ejpam-6775	407	9	s0	s0	PROPN
ejpam-6775	407	10	s	s	PART
ejpam-6775	407	11	−	−	PROPN
ejpam-6775	407	12	s	s	PART
ejpam-6775	407	13	s0	s0	PROPN
ejpam-6775	407	14	v	v	ADP
ejpam-6775	407	15	0	0	NUM
ejpam-6775	407	16	v	v	NOUN
ejpam-6775	407	17	)	)	PUNCT
ejpam-6775	407	18	+	+	CCONJ
ejpam-6775	407	19	(	(	PUNCT
ejpam-6775	407	20	1−r0)i(t	1−r0)i(t	NUM
ejpam-6775	407	21	,	,	PUNCT
ejpam-6775	407	22	0	0	NUM
ejpam-6775	407	23	)	)	PUNCT
ejpam-6775	407	24	(	(	PUNCT
ejpam-6775	407	25	45	45	NUM
ejpam-6775	407	26	)	)	PUNCT
ejpam-6775	408	1	+	+	PROPN
ejpam-6775	409	1	[	[	X
ejpam-6775	409	2	s0	s0	NOUN
ejpam-6775	409	3	+	+	PROPN
ejpam-6775	409	4	mv	mv	PROPN
ejpam-6775	409	5	0	0	NUM
ejpam-6775	409	6	]	]	PUNCT
ejpam-6775	409	7	∫	∫	PROPN
ejpam-6775	409	8	∞	∞	NUM
ejpam-6775	409	9	0	0	PUNCT
ejpam-6775	410	1	[	[	X
ejpam-6775	410	2	q′(x)−	q′(x)−	X
ejpam-6775	410	3	(	(	PUNCT
ejpam-6775	410	4	µ+	µ+	X
ejpam-6775	410	5	δ(x))q(x	δ(x))q(x	NOUN
ejpam-6775	410	6	)	)	PUNCT
ejpam-6775	411	1	+	+	CCONJ
ejpam-6775	411	2	β(x)]i(t	β(x)]i(t	NOUN
ejpam-6775	411	3	,	,	PUNCT
ejpam-6775	411	4	x)dx	x)dx	PROPN
ejpam-6775	411	5	.	.	PUNCT
ejpam-6775	412	1	finally	finally	ADV
ejpam-6775	412	2	we	we	PRON
ejpam-6775	412	3	get	get	VERB
ejpam-6775	412	4	,	,	PUNCT
ejpam-6775	412	5	dw	dw	PROPN
ejpam-6775	413	1	[	[	X
ejpam-6775	413	2	t	t	X
ejpam-6775	413	3	]	]	X
ejpam-6775	413	4	dt	dt	X
ejpam-6775	413	5	=	=	PUNCT
ejpam-6775	413	6	µs0	µs0	PROPN
ejpam-6775	413	7	(	(	PUNCT
ejpam-6775	413	8	2−	2−	NUM
ejpam-6775	413	9	s	s	NOUN
ejpam-6775	413	10	s0	s0	PROPN
ejpam-6775	413	11	−	−	PROPN
ejpam-6775	413	12	s0	s0	PROPN
ejpam-6775	413	13	s	s	PART
ejpam-6775	413	14	)	)	PUNCT
ejpam-6775	414	1	+	+	CCONJ
ejpam-6775	414	2	ξs0	ξs0	NUM
ejpam-6775	414	3	(	(	PUNCT
ejpam-6775	414	4	3−	3−	NUM
ejpam-6775	414	5	v	v	PART
ejpam-6775	414	6	v	v	NOUN
ejpam-6775	414	7	0	0	NUM
ejpam-6775	415	1	−	−	PROPN
ejpam-6775	416	1	s	s	PART
ejpam-6775	416	2	s0	s0	PROPN
ejpam-6775	416	3	v	v	ADP
ejpam-6775	416	4	0	0	NUM
ejpam-6775	416	5	v	v	NOUN
ejpam-6775	416	6	)	)	PUNCT
ejpam-6775	416	7	+	+	CCONJ
ejpam-6775	416	8	(	(	PUNCT
ejpam-6775	416	9	1−r0)i(t	1−r0)i(t	NUM
ejpam-6775	416	10	,	,	PUNCT
ejpam-6775	416	11	0	0	NUM
ejpam-6775	416	12	)	)	PUNCT
ejpam-6775	416	13	.	.	PUNCT
ejpam-6775	417	1	(	(	PUNCT
ejpam-6775	417	2	46	46	NUM
ejpam-6775	417	3	)	)	PUNCT
ejpam-6775	417	4	according	accord	VERB
ejpam-6775	417	5	to	to	ADP
ejpam-6775	417	6	the	the	DET
ejpam-6775	417	7	arithmetic	arithmetic	ADJ
ejpam-6775	417	8	–	–	PUNCT
ejpam-6775	417	9	geometric	geometric	ADJ
ejpam-6775	417	10	mean	mean	NOUN
ejpam-6775	417	11	inequality	inequality	NOUN
ejpam-6775	417	12	,	,	PUNCT
ejpam-6775	417	13	both	both	DET
ejpam-6775	417	14	terms	term	NOUN
ejpam-6775	417	15	2	2	NUM
ejpam-6775	417	16	−	−	PROPN
ejpam-6775	417	17	s	s	PART
ejpam-6775	417	18	s0	s0	PROPN
ejpam-6775	417	19	−	−	PROPN
ejpam-6775	417	20	s0	s0	PROPN
ejpam-6775	417	21	s	s	PROPN
ejpam-6775	417	22	and	and	CCONJ
ejpam-6775	417	23	3	3	NUM
ejpam-6775	417	24	−	−	NOUN
ejpam-6775	417	25	v	v	PART
ejpam-6775	417	26	v	v	NOUN
ejpam-6775	417	27	0	0	PUNCT
ejpam-6775	418	1	−	−	PROPN
ejpam-6775	418	2	s0	s0	PROPN
ejpam-6775	418	3	s	s	PART
ejpam-6775	418	4	−	−	PROPN
ejpam-6775	418	5	s	s	PART
ejpam-6775	418	6	s0	s0	PROPN
ejpam-6775	418	7	v	v	ADP
ejpam-6775	418	8	0	0	NUM
ejpam-6775	418	9	v	v	NOUN
ejpam-6775	418	10	are	be	AUX
ejpam-6775	418	11	nonnegative	nonnegative	ADJ
ejpam-6775	418	12	and	and	CCONJ
ejpam-6775	418	13	the	the	DET
ejpam-6775	418	14	equality	equality	NOUN
ejpam-6775	418	15	holds	hold	VERB
ejpam-6775	418	16	if	if	SCONJ
ejpam-6775	418	17	and	and	CCONJ
ejpam-6775	418	18	only	only	ADV
ejpam-6775	418	19	if	if	SCONJ
ejpam-6775	418	20	s	s	NOUN
ejpam-6775	418	21	=	=	VERB
ejpam-6775	418	22	s0	s0	PROPN
ejpam-6775	418	23	and	and	CCONJ
ejpam-6775	418	24	v	v	NOUN
ejpam-6775	418	25	=	=	SYM
ejpam-6775	418	26	v	v	ADP
ejpam-6775	418	27	0	0	NUM
ejpam-6775	418	28	.	.	PUNCT
ejpam-6775	419	1	therefore	therefore	ADV
ejpam-6775	419	2	,	,	PUNCT
ejpam-6775	419	3	the	the	DET
ejpam-6775	419	4	function	function	NOUN
ejpam-6775	419	5	w	w	PROPN
ejpam-6775	420	1	[	[	X
ejpam-6775	420	2	t	t	X
ejpam-6775	420	3	]	]	X
ejpam-6775	420	4	is	be	AUX
ejpam-6775	420	5	nonincreasing	nonincrease	VERB
ejpam-6775	420	6	since	since	SCONJ
ejpam-6775	420	7	dw	dw	PROPN
ejpam-6775	420	8	[	[	X
ejpam-6775	420	9	t	t	X
ejpam-6775	420	10	]	]	X
ejpam-6775	420	11	dt	dt	X
ejpam-6775	420	12	≤	≤	NOUN
ejpam-6775	420	13	0	0	NUM
ejpam-6775	420	14	when	when	SCONJ
ejpam-6775	420	15	r0	r0	NOUN
ejpam-6775	420	16	≤	≤	NOUN
ejpam-6775	420	17	1	1	NUM
ejpam-6775	420	18	.	.	PUNCT
ejpam-6775	421	1	by	by	ADP
ejpam-6775	421	2	the	the	DET
ejpam-6775	421	3	boundedness	boundedness	NOUN
ejpam-6775	421	4	of	of	ADP
ejpam-6775	421	5	function	function	NOUN
ejpam-6775	421	6	w	w	PROPN
ejpam-6775	422	1	[	[	X
ejpam-6775	422	2	t	t	X
ejpam-6775	422	3	]	]	PUNCT
ejpam-6775	422	4	,	,	PUNCT
ejpam-6775	422	5	the	the	DET
ejpam-6775	422	6	alpha	alpha	NOUN
ejpam-6775	422	7	limit	limit	NOUN
ejpam-6775	422	8	set	set	VERB
ejpam-6775	422	9	of	of	ADP
ejpam-6775	422	10	(	(	PUNCT
ejpam-6775	422	11	s(t	s(t	PROPN
ejpam-6775	422	12	)	)	PUNCT
ejpam-6775	422	13	,	,	PUNCT
ejpam-6775	422	14	v	v	X
ejpam-6775	422	15	(	(	PUNCT
ejpam-6775	422	16	t	t	PROPN
ejpam-6775	422	17	)	)	PUNCT
ejpam-6775	422	18	,	,	PUNCT
ejpam-6775	422	19	i	i	PRON
ejpam-6775	422	20	(	(	PUNCT
ejpam-6775	422	21	.	.	PROPN
ejpam-6775	422	22	,	,	PUNCT
ejpam-6775	422	23	t	t	PROPN
ejpam-6775	422	24	)	)	PUNCT
ejpam-6775	422	25	)	)	PUNCT
ejpam-6775	422	26	must	must	AUX
ejpam-6775	422	27	be	be	AUX
ejpam-6775	422	28	contained	contain	VERB
ejpam-6775	422	29	in	in	ADP
ejpam-6775	422	30	the	the	DET
ejpam-6775	422	31	maximal	maximal	ADJ
ejpam-6775	422	32	compact	compact	ADJ
ejpam-6775	422	33	invariant	invariant	ADJ
ejpam-6775	422	34	subset	subset	NOUN
ejpam-6775	422	35	defined	define	VERB
ejpam-6775	422	36	by	by	ADP
ejpam-6775	422	37	γ	γ	X
ejpam-6775	422	38	=	=	SYM
ejpam-6775	422	39	{	{	PUNCT
ejpam-6775	422	40	(	(	PUNCT
ejpam-6775	422	41	s	s	PROPN
ejpam-6775	422	42	,	,	PUNCT
ejpam-6775	422	43	v	v	NOUN
ejpam-6775	422	44	,	,	PUNCT
ejpam-6775	422	45	i	i	PROPN
ejpam-6775	422	46	)	)	PUNCT
ejpam-6775	422	47	:	:	PUNCT
ejpam-6775	423	1	dw	dw	PROPN
ejpam-6775	424	1	[	[	X
ejpam-6775	424	2	t	t	X
ejpam-6775	424	3	]	]	X
ejpam-6775	424	4	dt	dt	NOUN
ejpam-6775	424	5	=	=	SYM
ejpam-6775	424	6	0	0	NUM
ejpam-6775	424	7	}	}	PUNCT
ejpam-6775	424	8	.	.	PUNCT
ejpam-6775	425	1	however	however	ADV
ejpam-6775	425	2	,	,	PUNCT
ejpam-6775	425	3	the	the	DET
ejpam-6775	425	4	equality	equality	NOUN
ejpam-6775	425	5	dw	dw	PROPN
ejpam-6775	425	6	[	[	X
ejpam-6775	425	7	t	t	X
ejpam-6775	425	8	]	]	X
ejpam-6775	425	9	dt	dt	X
ejpam-6775	425	10	=	=	SYM
ejpam-6775	425	11	0	0	NUM
ejpam-6775	425	12	holds	hold	VERB
ejpam-6775	425	13	if	if	SCONJ
ejpam-6775	425	14	and	and	CCONJ
ejpam-6775	425	15	only	only	ADV
ejpam-6775	425	16	if	if	SCONJ
ejpam-6775	425	17	s	s	NOUN
ejpam-6775	425	18	=	=	SYM
ejpam-6775	425	19	s0	s0	PROPN
ejpam-6775	425	20	,	,	PUNCT
ejpam-6775	425	21	v	v	NOUN
ejpam-6775	425	22	=	=	SYM
ejpam-6775	425	23	v	v	NOUN
ejpam-6775	425	24	0	0	NUM
ejpam-6775	425	25	and	and	CCONJ
ejpam-6775	425	26	i(t	i(t	NOUN
ejpam-6775	425	27	,	,	PUNCT
ejpam-6775	425	28	0	0	NUM
ejpam-6775	425	29	)	)	PUNCT
ejpam-6775	425	30	=	=	SYM
ejpam-6775	425	31	0	0	X
ejpam-6775	425	32	.	.	X
ejpam-6775	425	33	integrating	integrate	VERB
ejpam-6775	425	34	the	the	DET
ejpam-6775	425	35	i(t	i(t	NOUN
ejpam-6775	425	36	,	,	PUNCT
ejpam-6775	425	37	x)-equation	x)-equation	NOUN
ejpam-6775	425	38	of	of	ADP
ejpam-6775	425	39	system	system	NOUN
ejpam-6775	425	40	(	(	PUNCT
ejpam-6775	425	41	1	1	X
ejpam-6775	425	42	)	)	PUNCT
ejpam-6775	425	43	using	use	VERB
ejpam-6775	425	44	the	the	DET
ejpam-6775	425	45	characteristics	characteristic	NOUN
ejpam-6775	425	46	method	method	NOUN
ejpam-6775	425	47	,	,	PUNCT
ejpam-6775	425	48	it	it	PRON
ejpam-6775	425	49	follows	follow	VERB
ejpam-6775	425	50	that	that	SCONJ
ejpam-6775	425	51	i(t	i(t	NOUN
ejpam-6775	425	52	,	,	PUNCT
ejpam-6775	425	53	x	x	NOUN
ejpam-6775	425	54	)	)	PUNCT
ejpam-6775	425	55	=	=	SYM
ejpam-6775	425	56	0	0	NUM
ejpam-6775	425	57	for	for	ADP
ejpam-6775	425	58	all	all	DET
ejpam-6775	425	59	t	t	PROPN
ejpam-6775	425	60	>	>	X
ejpam-6775	425	61	x.	x.	PROPN
ejpam-6775	426	1	hence	hence	ADV
ejpam-6775	426	2	,	,	PUNCT
ejpam-6775	426	3	we	we	PRON
ejpam-6775	426	4	get	get	VERB
ejpam-6775	426	5	i(t	i(t	NOUN
ejpam-6775	426	6	,	,	PUNCT
ejpam-6775	426	7	x	x	NOUN
ejpam-6775	426	8	)	)	PUNCT
ejpam-6775	426	9	→	→	SYM
ejpam-6775	426	10	0	0	NUM
ejpam-6775	426	11	as	as	ADP
ejpam-6775	426	12	t	t	PROPN
ejpam-6775	426	13	→	→	PUNCT
ejpam-6775	426	14	+	+	PROPN
ejpam-6775	426	15	∞.	∞.	PROPN
ejpam-6775	426	16	therefore	therefore	ADV
ejpam-6775	426	17	,	,	PUNCT
ejpam-6775	426	18	the	the	DET
ejpam-6775	426	19	set	set	NOUN
ejpam-6775	426	20	γ	γ	NOUN
ejpam-6775	426	21	is	be	AUX
ejpam-6775	426	22	reduced	reduce	VERB
ejpam-6775	426	23	to	to	PART
ejpam-6775	426	24	singleton	singleton	PROPN
ejpam-6775	426	25	{	{	PUNCT
ejpam-6775	426	26	e0	e0	PROPN
ejpam-6775	426	27	}	}	PUNCT
ejpam-6775	426	28	and	and	CCONJ
ejpam-6775	426	29	by	by	ADP
ejpam-6775	426	30	means	mean	NOUN
ejpam-6775	426	31	of	of	ADP
ejpam-6775	426	32	the	the	DET
ejpam-6775	426	33	lasalle	lasalle	NOUN
ejpam-6775	426	34	’s	’s	PART
ejpam-6775	426	35	invariant	invariant	ADJ
ejpam-6775	426	36	principle	principle	NOUN
ejpam-6775	426	37	[	[	X
ejpam-6775	426	38	43	43	NUM
ejpam-6775	426	39	]	]	PUNCT
ejpam-6775	426	40	,	,	PUNCT
ejpam-6775	426	41	we	we	PRON
ejpam-6775	426	42	can	can	AUX
ejpam-6775	426	43	conclude	conclude	VERB
ejpam-6775	426	44	that	that	SCONJ
ejpam-6775	426	45	the	the	DET
ejpam-6775	426	46	disease	disease	NOUN
ejpam-6775	426	47	–	–	PUNCT
ejpam-6775	426	48	free	free	ADJ
ejpam-6775	426	49	equilibrium	equilibrium	NOUN
ejpam-6775	426	50	e0	e0	PROPN
ejpam-6775	426	51	is	be	AUX
ejpam-6775	426	52	globally	globally	ADV
ejpam-6775	426	53	asymptotically	asymptotically	ADV
ejpam-6775	426	54	stable	stable	ADJ
ejpam-6775	426	55	when	when	SCONJ
ejpam-6775	426	56	r0	r0	NOUN
ejpam-6775	426	57	≤	≤	NOUN
ejpam-6775	426	58	1	1	NUM
ejpam-6775	426	59	.	.	X
ejpam-6775	426	60	epidemiologically	epidemiologically	NOUN
ejpam-6775	426	61	speaking	speak	VERB
ejpam-6775	426	62	,	,	PUNCT
ejpam-6775	426	63	theorem	theorem	VERB
ejpam-6775	426	64	2.4	2.4	NUM
ejpam-6775	426	65	means	mean	VERB
ejpam-6775	426	66	that	that	SCONJ
ejpam-6775	426	67	in	in	ADP
ejpam-6775	426	68	the	the	DET
ejpam-6775	426	69	absence	absence	NOUN
ejpam-6775	426	70	of	of	ADP
ejpam-6775	426	71	therapeutic	therapeutic	ADJ
ejpam-6775	426	72	treatment	treatment	NOUN
ejpam-6775	426	73	,	,	PUNCT
ejpam-6775	426	74	a	a	DET
ejpam-6775	426	75	flow	flow	NOUN
ejpam-6775	426	76	of	of	ADP
ejpam-6775	426	77	infectious	infectious	ADJ
ejpam-6775	426	78	individuals	individual	NOUN
ejpam-6775	426	79	for	for	ADP
ejpam-6775	426	80	all	all	DET
ejpam-6775	426	81	age	age	NOUN
ejpam-6775	426	82	of	of	ADP
ejpam-6775	426	83	infection	infection	NOUN
ejpam-6775	426	84	will	will	AUX
ejpam-6775	426	85	not	not	PART
ejpam-6775	426	86	generate	generate	VERB
ejpam-6775	426	87	outbreak	outbreak	NOUN
ejpam-6775	426	88	of	of	ADP
ejpam-6775	426	89	the	the	DET
ejpam-6775	426	90	disease	disease	NOUN
ejpam-6775	426	91	unless	unless	SCONJ
ejpam-6775	426	92	r0	r0	NOUN
ejpam-6775	426	93	>	>	X
ejpam-6775	426	94	1	1	NUM
ejpam-6775	426	95	where	where	SCONJ
ejpam-6775	426	96	the	the	DET
ejpam-6775	426	97	disease	disease	NOUN
ejpam-6775	426	98	will	will	AUX
ejpam-6775	426	99	persist	persist	VERB
ejpam-6775	426	100	.	.	PUNCT
ejpam-6775	427	1	therefore	therefore	ADV
ejpam-6775	427	2	,	,	PUNCT
ejpam-6775	427	3	reduce	reduce	VERB
ejpam-6775	427	4	the	the	DET
ejpam-6775	427	5	basic	basic	ADJ
ejpam-6775	427	6	reproduction	reproduction	NOUN
ejpam-6775	427	7	number	number	NOUN
ejpam-6775	427	8	below	below	ADP
ejpam-6775	427	9	the	the	DET
ejpam-6775	427	10	unity	unity	NOUN
ejpam-6775	427	11	become	become	VERB
ejpam-6775	427	12	a	a	DET
ejpam-6775	427	13	necessary	necessary	ADJ
ejpam-6775	427	14	and	and	CCONJ
ejpam-6775	427	15	sufficient	sufficient	ADJ
ejpam-6775	427	16	condition	condition	NOUN
ejpam-6775	427	17	to	to	PART
ejpam-6775	427	18	eradicate	eradicate	VERB
ejpam-6775	427	19	the	the	DET
ejpam-6775	427	20	disease	disease	NOUN
ejpam-6775	427	21	in	in	ADP
ejpam-6775	427	22	the	the	DET
ejpam-6775	427	23	population	population	NOUN
ejpam-6775	427	24	.	.	PUNCT
ejpam-6775	428	1	treatment	treatment	NOUN
ejpam-6775	428	2	of	of	ADP
ejpam-6775	428	3	infected	infected	ADJ
ejpam-6775	428	4	individuals	individual	NOUN
ejpam-6775	428	5	can	can	AUX
ejpam-6775	428	6	lead	lead	VERB
ejpam-6775	428	7	to	to	ADP
ejpam-6775	428	8	non	non	ADJ
ejpam-6775	428	9	–	–	NOUN
ejpam-6775	428	10	eradication	eradication	NOUN
ejpam-6775	428	11	of	of	ADP
ejpam-6775	428	12	the	the	DET
ejpam-6775	428	13	disease	disease	NOUN
ejpam-6775	428	14	when	when	SCONJ
ejpam-6775	428	15	the	the	DET
ejpam-6775	428	16	basic	basic	ADJ
ejpam-6775	428	17	reproduction	reproduction	NOUN
ejpam-6775	428	18	rate	rate	NOUN
ejpam-6775	428	19	is	be	AUX
ejpam-6775	428	20	less	less	ADJ
ejpam-6775	428	21	than	than	ADP
ejpam-6775	428	22	one	one	NUM
ejpam-6775	428	23	.	.	PUNCT
ejpam-6775	429	1	it	it	PRON
ejpam-6775	429	2	is	be	AUX
ejpam-6775	429	3	therefore	therefore	ADV
ejpam-6775	429	4	important	important	ADJ
ejpam-6775	429	5	to	to	PART
ejpam-6775	429	6	develop	develop	VERB
ejpam-6775	429	7	an	an	DET
ejpam-6775	429	8	optimal	optimal	ADJ
ejpam-6775	429	9	combined	combine	VERB
ejpam-6775	429	10	control	control	NOUN
ejpam-6775	429	11	strategy	strategy	NOUN
ejpam-6775	429	12	aimed	aim	VERB
ejpam-6775	429	13	at	at	ADP
ejpam-6775	429	14	reducing	reduce	VERB
ejpam-6775	429	15	the	the	DET
ejpam-6775	429	16	spread	spread	NOUN
ejpam-6775	429	17	of	of	ADP
ejpam-6775	429	18	the	the	DET
ejpam-6775	429	19	disease	disease	NOUN
ejpam-6775	429	20	through	through	ADP
ejpam-6775	429	21	appropriate	appropriate	ADJ
ejpam-6775	429	22	vaccination	vaccination	NOUN
ejpam-6775	429	23	and	and	CCONJ
ejpam-6775	429	24	treatment	treatment	NOUN
ejpam-6775	429	25	protocols	protocol	NOUN
ejpam-6775	429	26	at	at	ADP
ejpam-6775	429	27	the	the	DET
ejpam-6775	429	28	lowest	low	ADJ
ejpam-6775	429	29	possible	possible	ADJ
ejpam-6775	429	30	cost	cost	NOUN
ejpam-6775	429	31	.	.	PUNCT
ejpam-6775	430	1	j.	j.	PROPN
ejpam-6775	430	2	leo	leo	PROPN
ejpam-6775	430	3	amalraj	amalraj	PROPN
ejpam-6775	430	4	et	et	PROPN
ejpam-6775	430	5	al	al	PROPN
ejpam-6775	430	6	.	.	PUNCT
ejpam-6775	430	7	/	/	SYM
ejpam-6775	430	8	eur	eur	PROPN
ejpam-6775	430	9	.	.	PUNCT
ejpam-6775	431	1	j.	j.	PROPN
ejpam-6775	431	2	pure	pure	PROPN
ejpam-6775	431	3	appl	appl	PROPN
ejpam-6775	431	4	.	.	PROPN
ejpam-6775	431	5	math	math	PROPN
ejpam-6775	431	6	,	,	PUNCT
ejpam-6775	431	7	18	18	NUM
ejpam-6775	431	8	(	(	PUNCT
ejpam-6775	431	9	4	4	NUM
ejpam-6775	431	10	)	)	PUNCT
ejpam-6775	431	11	(	(	PUNCT
ejpam-6775	431	12	2025	2025	NUM
ejpam-6775	431	13	)	)	PUNCT
ejpam-6775	431	14	,	,	PUNCT
ejpam-6775	431	15	6775	6775	NUM
ejpam-6775	431	16	17	17	NUM
ejpam-6775	431	17	of	of	ADP
ejpam-6775	431	18	32	32	NUM
ejpam-6775	431	19	5	5	NUM
ejpam-6775	431	20	.	.	PUNCT
ejpam-6775	432	1	optimal	optimal	ADJ
ejpam-6775	432	2	control	control	NOUN
ejpam-6775	432	3	strategies	strategy	NOUN
ejpam-6775	432	4	for	for	ADP
ejpam-6775	432	5	disease	disease	NOUN
ejpam-6775	432	6	mitigation	mitigation	NOUN
ejpam-6775	432	7	5.1	5.1	NUM
ejpam-6775	432	8	.	.	PUNCT
ejpam-6775	433	1	formulation	formulation	NOUN
ejpam-6775	433	2	of	of	ADP
ejpam-6775	433	3	the	the	DET
ejpam-6775	433	4	control	control	NOUN
ejpam-6775	433	5	problem	problem	NOUN
ejpam-6775	433	6	given	give	VERB
ejpam-6775	433	7	the	the	DET
ejpam-6775	433	8	seriousness	seriousness	NOUN
ejpam-6775	433	9	of	of	ADP
ejpam-6775	433	10	the	the	DET
ejpam-6775	433	11	damage	damage	NOUN
ejpam-6775	433	12	caused	cause	VERB
ejpam-6775	433	13	by	by	ADP
ejpam-6775	433	14	infectious	infectious	ADJ
ejpam-6775	433	15	diseases	disease	NOUN
ejpam-6775	433	16	in	in	ADP
ejpam-6775	433	17	many	many	ADJ
ejpam-6775	433	18	countries	country	NOUN
ejpam-6775	433	19	,	,	PUNCT
ejpam-6775	433	20	it	it	PRON
ejpam-6775	433	21	is	be	AUX
ejpam-6775	433	22	important	important	ADJ
ejpam-6775	433	23	to	to	PART
ejpam-6775	433	24	know	know	VERB
ejpam-6775	433	25	how	how	SCONJ
ejpam-6775	433	26	much	much	ADJ
ejpam-6775	433	27	and	and	CCONJ
ejpam-6775	433	28	when	when	SCONJ
ejpam-6775	433	29	vaccination	vaccination	NOUN
ejpam-6775	433	30	and	and	CCONJ
ejpam-6775	433	31	treatment	treatment	NOUN
ejpam-6775	433	32	should	should	AUX
ejpam-6775	433	33	be	be	AUX
ejpam-6775	433	34	applied	apply	VERB
ejpam-6775	433	35	,	,	PUNCT
ejpam-6775	433	36	in	in	ADP
ejpam-6775	433	37	order	order	NOUN
ejpam-6775	433	38	to	to	PART
ejpam-6775	433	39	control	control	VERB
ejpam-6775	433	40	the	the	DET
ejpam-6775	433	41	dynamics	dynamic	NOUN
ejpam-6775	433	42	of	of	ADP
ejpam-6775	433	43	disease	disease	NOUN
ejpam-6775	433	44	transmission	transmission	NOUN
ejpam-6775	433	45	effectively	effectively	ADV
ejpam-6775	433	46	and	and	CCONJ
ejpam-6775	433	47	at	at	ADP
ejpam-6775	433	48	minimum	minimum	ADJ
ejpam-6775	433	49	cost	cost	NOUN
ejpam-6775	433	50	.	.	PUNCT
ejpam-6775	434	1	for	for	ADP
ejpam-6775	434	2	this	this	DET
ejpam-6775	434	3	purpose	purpose	NOUN
ejpam-6775	434	4	,	,	PUNCT
ejpam-6775	434	5	we	we	PRON
ejpam-6775	434	6	consider	consider	VERB
ejpam-6775	434	7	that	that	SCONJ
ejpam-6775	434	8	the	the	DET
ejpam-6775	434	9	vaccination	vaccination	NOUN
ejpam-6775	434	10	and	and	CCONJ
ejpam-6775	434	11	treatment	treatment	NOUN
ejpam-6775	434	12	are	be	AUX
ejpam-6775	434	13	represented	represent	VERB
ejpam-6775	434	14	by	by	ADP
ejpam-6775	434	15	lebesgue	lebesgue	NOUN
ejpam-6775	434	16	measurable	measurable	ADJ
ejpam-6775	434	17	functions	function	NOUN
ejpam-6775	434	18	on	on	ADP
ejpam-6775	434	19	finite	finite	ADJ
ejpam-6775	434	20	time	time	NOUN
ejpam-6775	434	21	horizon	horizon	PROPN
ejpam-6775	435	1	[	[	X
ejpam-6775	435	2	0	0	NUM
ejpam-6775	435	3	,	,	PUNCT
ejpam-6775	435	4	t	t	X
ejpam-6775	435	5	]	]	PUNCT
ejpam-6775	435	6	,	,	PUNCT
ejpam-6775	435	7	denoted	denote	VERB
ejpam-6775	435	8	by	by	ADP
ejpam-6775	435	9	ξ(t	ξ(t	NOUN
ejpam-6775	435	10	)	)	PUNCT
ejpam-6775	435	11	and	and	CCONJ
ejpam-6775	435	12	α	α	PRON
ejpam-6775	435	13	(	(	PUNCT
ejpam-6775	435	14	.	.	PUNCT
ejpam-6775	435	15	)	)	PUNCT
ejpam-6775	435	16	.	.	PUNCT
ejpam-6775	436	1	we	we	PRON
ejpam-6775	436	2	suppose	suppose	VERB
ejpam-6775	436	3	that	that	SCONJ
ejpam-6775	436	4	t	t	PROPN
ejpam-6775	436	5	>	>	X
ejpam-6775	436	6	0	0	PUNCT
ejpam-6775	436	7	is	be	AUX
ejpam-6775	436	8	a	a	DET
ejpam-6775	436	9	budgeted	budget	VERB
ejpam-6775	436	10	final	final	ADJ
ejpam-6775	436	11	time	time	NOUN
ejpam-6775	436	12	and	and	CCONJ
ejpam-6775	436	13	in	in	ADP
ejpam-6775	436	14	order	order	NOUN
ejpam-6775	436	15	to	to	PART
ejpam-6775	436	16	avoid	avoid	VERB
ejpam-6775	436	17	singularities	singularity	NOUN
ejpam-6775	436	18	,	,	PUNCT
ejpam-6775	436	19	we	we	PRON
ejpam-6775	436	20	replace	replace	VERB
ejpam-6775	436	21	the	the	DET
ejpam-6775	436	22	upper	upper	ADJ
ejpam-6775	436	23	limit	limit	NOUN
ejpam-6775	436	24	of	of	ADP
ejpam-6775	436	25	the	the	DET
ejpam-6775	436	26	integral	integral	ADJ
ejpam-6775	436	27	with	with	ADP
ejpam-6775	436	28	respect	respect	NOUN
ejpam-6775	436	29	to	to	ADP
ejpam-6775	436	30	infection	infection	NOUN
ejpam-6775	436	31	age	age	NOUN
ejpam-6775	436	32	by	by	ADP
ejpam-6775	436	33	a	a	DET
ejpam-6775	436	34	finite	finite	ADJ
ejpam-6775	436	35	number	number	NOUN
ejpam-6775	436	36	xt	xt	ADP
ejpam-6775	436	37	>	>	X
ejpam-6775	436	38	0	0	PUNCT
ejpam-6775	437	1	for	for	ADP
ejpam-6775	437	2	practical	practical	ADJ
ejpam-6775	437	3	consideration	consideration	NOUN
ejpam-6775	437	4	,	,	PUNCT
ejpam-6775	437	5	i.e.	i.e.	X
ejpam-6775	437	6	the	the	DET
ejpam-6775	437	7	integral	integral	ADJ
ejpam-6775	437	8	function	function	NOUN
ejpam-6775	437	9	t	t	NOUN
ejpam-6775	437	10	(	(	PUNCT
ejpam-6775	437	11	f	f	X
ejpam-6775	437	12	)	)	PUNCT
ejpam-6775	437	13	=	=	SYM
ejpam-6775	437	14	∫	∫	PROPN
ejpam-6775	437	15	xt	xt	PROPN
ejpam-6775	437	16	0	0	NUM
ejpam-6775	437	17	f(x)dx	f(x)dx	NUM
ejpam-6775	437	18	.	.	PUNCT
ejpam-6775	438	1	let	let	VERB
ejpam-6775	438	2	us	we	PRON
ejpam-6775	438	3	introduce	introduce	VERB
ejpam-6775	438	4	the	the	DET
ejpam-6775	438	5	set	set	NOUN
ejpam-6775	438	6	ω	ω	NOUN
ejpam-6775	438	7	=	=	PUNCT
ejpam-6775	439	1	[	[	X
ejpam-6775	439	2	0	0	NUM
ejpam-6775	439	3	,	,	PUNCT
ejpam-6775	439	4	t	t	X
ejpam-6775	439	5	]	]	X
ejpam-6775	439	6	×	×	NOUN
ejpam-6775	440	1	[	[	X
ejpam-6775	440	2	0	0	NUM
ejpam-6775	440	3	,	,	PUNCT
ejpam-6775	440	4	xt	xt	ADP
ejpam-6775	440	5	]	]	PUNCT
ejpam-6775	440	6	.	.	PUNCT
ejpam-6775	441	1	given	give	VERB
ejpam-6775	441	2	the	the	DET
ejpam-6775	441	3	limited	limited	ADJ
ejpam-6775	441	4	resources	resource	NOUN
ejpam-6775	441	5	and	and	CCONJ
ejpam-6775	441	6	time	time	NOUN
ejpam-6775	441	7	available	available	ADJ
ejpam-6775	441	8	to	to	PART
ejpam-6775	441	9	implement	implement	VERB
ejpam-6775	441	10	strategies	strategy	NOUN
ejpam-6775	441	11	to	to	PART
ejpam-6775	441	12	control	control	VERB
ejpam-6775	441	13	this	this	DET
ejpam-6775	441	14	infectious	infectious	ADJ
ejpam-6775	441	15	disease	disease	NOUN
ejpam-6775	441	16	,	,	PUNCT
ejpam-6775	441	17	policies	policy	NOUN
ejpam-6775	441	18	must	must	AUX
ejpam-6775	441	19	be	be	AUX
ejpam-6775	441	20	limited	limit	VERB
ejpam-6775	441	21	to	to	ADP
ejpam-6775	441	22	a	a	DET
ejpam-6775	441	23	predefined	predefine	VERB
ejpam-6775	441	24	objective	objective	NOUN
ejpam-6775	441	25	.	.	PUNCT
ejpam-6775	442	1	for	for	ADP
ejpam-6775	442	2	that	that	DET
ejpam-6775	442	3	purpose	purpose	NOUN
ejpam-6775	442	4	,	,	PUNCT
ejpam-6775	442	5	we	we	PRON
ejpam-6775	442	6	define	define	VERB
ejpam-6775	442	7	the	the	DET
ejpam-6775	442	8	set	set	NOUN
ejpam-6775	442	9	d	d	NOUN
ejpam-6775	442	10	:	:	PUNCT
ejpam-6775	442	11	=	=	SYM
ejpam-6775	442	12	l∞(0	l∞(0	X
ejpam-6775	442	13	,	,	PUNCT
ejpam-6775	442	14	t	t	PROPN
ejpam-6775	442	15	,	,	PUNCT
ejpam-6775	442	16	[	[	X
ejpam-6775	442	17	0	0	NUM
ejpam-6775	442	18	,	,	PUNCT
ejpam-6775	442	19	ξmax])×	ξmax])×	PROPN
ejpam-6775	442	20	l∞(ω	l∞(ω	ADV
ejpam-6775	442	21	,	,	PUNCT
ejpam-6775	442	22	[	[	X
ejpam-6775	442	23	0	0	NUM
ejpam-6775	442	24	,	,	PUNCT
ejpam-6775	442	25	αt	αt	NOUN
ejpam-6775	442	26	]	]	PUNCT
ejpam-6775	442	27	)	)	PUNCT
ejpam-6775	442	28	the	the	DET
ejpam-6775	442	29	set	set	NOUN
ejpam-6775	442	30	of	of	ADP
ejpam-6775	442	31	admissible	admissible	ADJ
ejpam-6775	442	32	control	control	NOUN
ejpam-6775	442	33	pair	pair	NOUN
ejpam-6775	442	34	which	which	PRON
ejpam-6775	442	35	is	be	AUX
ejpam-6775	442	36	the	the	DET
ejpam-6775	442	37	space	space	NOUN
ejpam-6775	442	38	of	of	ADP
ejpam-6775	442	39	measurable	measurable	ADJ
ejpam-6775	442	40	and	and	CCONJ
ejpam-6775	442	41	bounded	bounded	ADJ
ejpam-6775	442	42	functions	function	NOUN
ejpam-6775	442	43	pair	pair	NOUN
ejpam-6775	442	44	(	(	PUNCT
ejpam-6775	442	45	ξ	ξ	X
ejpam-6775	442	46	(	(	PUNCT
ejpam-6775	442	47	.	.	PUNCT
ejpam-6775	442	48	)	)	PUNCT
ejpam-6775	442	49	,	,	PUNCT
ejpam-6775	442	50	α	α	X
ejpam-6775	442	51	(	(	PUNCT
ejpam-6775	442	52	.	.	PUNCT
ejpam-6775	442	53	,	,	PUNCT
ejpam-6775	442	54	.	.	PUNCT
ejpam-6775	442	55	)	)	PUNCT
ejpam-6775	442	56	)	)	PUNCT
ejpam-6775	442	57	defined	define	VERB
ejpam-6775	442	58	by	by	ADP
ejpam-6775	442	59	ξ	ξ	PROPN
ejpam-6775	442	60	(	(	PUNCT
ejpam-6775	442	61	.	.	PUNCT
ejpam-6775	442	62	)	)	PUNCT
ejpam-6775	442	63	:	:	PUNCT
ejpam-6775	443	1	[	[	X
ejpam-6775	443	2	0	0	NUM
ejpam-6775	443	3	,	,	PUNCT
ejpam-6775	443	4	t	t	X
ejpam-6775	443	5	]	]	PUNCT
ejpam-6775	443	6	→	→	PUNCT
ejpam-6775	444	1	[	[	X
ejpam-6775	444	2	0	0	NUM
ejpam-6775	444	3	,	,	PUNCT
ejpam-6775	444	4	ξt	ξt	NOUN
ejpam-6775	444	5	]	]	PUNCT
ejpam-6775	444	6	and	and	CCONJ
ejpam-6775	444	7	α	α	PRON
ejpam-6775	444	8	(	(	PUNCT
ejpam-6775	444	9	.	.	PUNCT
ejpam-6775	444	10	,	,	PUNCT
ejpam-6775	444	11	.	.	PUNCT
ejpam-6775	444	12	)	)	PUNCT
ejpam-6775	445	1	:	:	PUNCT
ejpam-6775	445	2	ω	ω	X
ejpam-6775	445	3	→	→	PUNCT
ejpam-6775	445	4	[	[	X
ejpam-6775	445	5	0	0	NUM
ejpam-6775	445	6	,	,	PUNCT
ejpam-6775	445	7	αt	αt	NOUN
ejpam-6775	445	8	]	]	PUNCT
ejpam-6775	445	9	.	.	PUNCT
ejpam-6775	446	1	the	the	DET
ejpam-6775	446	2	positive	positive	ADJ
ejpam-6775	446	3	constants	constant	NOUN
ejpam-6775	446	4	ξt	ξt	NOUN
ejpam-6775	446	5	and	and	CCONJ
ejpam-6775	446	6	αt	αt	PROPN
ejpam-6775	446	7	represent	represent	VERB
ejpam-6775	446	8	the	the	DET
ejpam-6775	446	9	maximum	maximum	ADJ
ejpam-6775	446	10	rates	rate	NOUN
ejpam-6775	446	11	at	at	ADP
ejpam-6775	446	12	which	which	PRON
ejpam-6775	446	13	individuals	individual	NOUN
ejpam-6775	446	14	may	may	AUX
ejpam-6775	446	15	be	be	AUX
ejpam-6775	446	16	vaccinated	vaccinate	VERB
ejpam-6775	446	17	and	and	CCONJ
ejpam-6775	446	18	treated	treat	VERB
ejpam-6775	446	19	respectively	respectively	ADV
ejpam-6775	446	20	.	.	PUNCT
ejpam-6775	447	1	hence	hence	ADV
ejpam-6775	447	2	,	,	PUNCT
ejpam-6775	447	3	implementing	implement	VERB
ejpam-6775	447	4	both	both	DET
ejpam-6775	447	5	time	time	NOUN
ejpam-6775	447	6	–	–	PUNCT
ejpam-6775	447	7	dependent	dependent	ADJ
ejpam-6775	447	8	controls	control	NOUN
ejpam-6775	447	9	in	in	ADP
ejpam-6775	447	10	system	system	NOUN
ejpam-6775	447	11	(	(	PUNCT
ejpam-6775	447	12	1	1	NUM
ejpam-6775	447	13	)	)	PUNCT
ejpam-6775	447	14	,	,	PUNCT
ejpam-6775	447	15	we	we	PRON
ejpam-6775	447	16	obtain	obtain	VERB
ejpam-6775	447	17	the	the	DET
ejpam-6775	447	18	following	following	ADJ
ejpam-6775	447	19	controlled	control	VERB
ejpam-6775	447	20	system	system	NOUN
ejpam-6775	447	21	:	:	PUNCT
ejpam-6775	447	22	ds	ds	ADJ
ejpam-6775	447	23	dt	dt	NOUN
ejpam-6775	447	24	=	=	SYM
ejpam-6775	447	25	λ−	λ−	PROPN
ejpam-6775	447	26	t	t	PROPN
ejpam-6775	447	27	(	(	PUNCT
ejpam-6775	447	28	βi(t	βi(t	ADV
ejpam-6775	447	29	,	,	PUNCT
ejpam-6775	447	30	.))s	.))s	PUNCT
ejpam-6775	448	1	+	+	X
ejpam-6775	448	2	t	t	PROPN
ejpam-6775	448	3	(	(	PUNCT
ejpam-6775	448	4	α	α	X
ejpam-6775	448	5	(	(	PUNCT
ejpam-6775	448	6	.	.	PUNCT
ejpam-6775	448	7	,	,	PUNCT
ejpam-6775	448	8	t)i(t	t)i(t	NOUN
ejpam-6775	448	9	,	,	PUNCT
ejpam-6775	448	10	.))−	.))−	NUM
ejpam-6775	448	11	(	(	PUNCT
ejpam-6775	448	12	ξ(t	ξ(t	NOUN
ejpam-6775	448	13	)	)	PUNCT
ejpam-6775	448	14	+	+	NUM
ejpam-6775	448	15	µ)s	µ)s	NOUN
ejpam-6775	448	16	,	,	PUNCT
ejpam-6775	448	17	dv	dv	PROPN
ejpam-6775	448	18	dt	dt	X
ejpam-6775	448	19	=	=	SYM
ejpam-6775	448	20	ξ(t)s	ξ(t)s	PROPN
ejpam-6775	448	21	−mt	−mt	NOUN
ejpam-6775	448	22	(	(	PUNCT
ejpam-6775	448	23	βi(t	βi(t	X
ejpam-6775	448	24	,	,	PUNCT
ejpam-6775	448	25	.))v	.))v	PUNCT
ejpam-6775	448	26	−	−	PROPN
ejpam-6775	448	27	µv	µv	PROPN
ejpam-6775	448	28	,	,	PUNCT
ejpam-6775	448	29	∂ti(t	∂ti(t	PROPN
ejpam-6775	448	30	,	,	PUNCT
ejpam-6775	448	31	x	x	NOUN
ejpam-6775	448	32	)	)	PUNCT
ejpam-6775	448	33	+	+	CCONJ
ejpam-6775	448	34	∂xi(t	∂xi(t	PROPN
ejpam-6775	448	35	,	,	PUNCT
ejpam-6775	448	36	x	x	NOUN
ejpam-6775	448	37	)	)	PUNCT
ejpam-6775	448	38	=	=	SYM
ejpam-6775	448	39	−[µ+	−[µ+	PROPN
ejpam-6775	448	40	δ(x	δ(x	PROPN
ejpam-6775	448	41	)	)	PUNCT
ejpam-6775	448	42	+	+	NUM
ejpam-6775	448	43	α(t	α(t	NOUN
ejpam-6775	448	44	,	,	PUNCT
ejpam-6775	448	45	x)]i(t	x)]i(t	PROPN
ejpam-6775	448	46	,	,	PUNCT
ejpam-6775	448	47	x	x	NOUN
ejpam-6775	448	48	)	)	PUNCT
ejpam-6775	448	49	,	,	PUNCT
ejpam-6775	448	50	i(t	i(t	PROPN
ejpam-6775	448	51	,	,	PUNCT
ejpam-6775	448	52	0	0	NUM
ejpam-6775	448	53	)	)	PUNCT
ejpam-6775	448	54	=	=	NOUN
ejpam-6775	449	1	[	[	X
ejpam-6775	449	2	s	s	X
ejpam-6775	449	3	+	+	NOUN
ejpam-6775	449	4	mv	mv	PROPN
ejpam-6775	449	5	]	]	X
ejpam-6775	449	6	t	t	PROPN
ejpam-6775	449	7	(	(	PUNCT
ejpam-6775	449	8	βi(t	βi(t	PROPN
ejpam-6775	449	9	,	,	PUNCT
ejpam-6775	449	10	.	.	PUNCT
ejpam-6775	449	11	)	)	PUNCT
ejpam-6775	449	12	)	)	PUNCT
ejpam-6775	449	13	.	.	PUNCT
ejpam-6775	450	1	(	(	PUNCT
ejpam-6775	450	2	47	47	NUM
ejpam-6775	450	3	)	)	PUNCT
ejpam-6775	450	4	our	our	PRON
ejpam-6775	450	5	main	main	ADJ
ejpam-6775	450	6	objective	objective	NOUN
ejpam-6775	450	7	is	be	AUX
ejpam-6775	450	8	to	to	PART
ejpam-6775	450	9	minimize	minimize	VERB
ejpam-6775	450	10	the	the	DET
ejpam-6775	450	11	total	total	ADJ
ejpam-6775	450	12	number	number	NOUN
ejpam-6775	450	13	of	of	ADP
ejpam-6775	450	14	infected	infect	VERB
ejpam-6775	450	15	individuals	individual	NOUN
ejpam-6775	450	16	and	and	CCONJ
ejpam-6775	450	17	the	the	DET
ejpam-6775	450	18	necessary	necessary	ADJ
ejpam-6775	450	19	cost	cost	NOUN
ejpam-6775	450	20	of	of	ADP
ejpam-6775	450	21	vaccination	vaccination	NOUN
ejpam-6775	450	22	and	and	CCONJ
ejpam-6775	450	23	therapeutic	therapeutic	ADJ
ejpam-6775	450	24	treatment	treatment	NOUN
ejpam-6775	450	25	.	.	PUNCT
ejpam-6775	451	1	to	to	PART
ejpam-6775	451	2	achieve	achieve	VERB
ejpam-6775	451	3	this	this	DET
ejpam-6775	451	4	goal	goal	NOUN
ejpam-6775	451	5	,	,	PUNCT
ejpam-6775	451	6	we	we	PRON
ejpam-6775	451	7	work	work	VERB
ejpam-6775	451	8	together	together	ADV
ejpam-6775	451	9	with	with	ADP
ejpam-6775	451	10	system	system	NOUN
ejpam-6775	451	11	(	(	PUNCT
ejpam-6775	451	12	31	31	NUM
ejpam-6775	451	13	)	)	PUNCT
ejpam-6775	451	14	,	,	PUNCT
ejpam-6775	451	15	the	the	DET
ejpam-6775	451	16	following	follow	VERB
ejpam-6775	451	17	objective	objective	ADJ
ejpam-6775	451	18	functional	functional	ADJ
ejpam-6775	451	19	:	:	PUNCT
ejpam-6775	451	20	j(ξ	j(ξ	PROPN
ejpam-6775	451	21	,	,	PUNCT
ejpam-6775	451	22	α	α	X
ejpam-6775	451	23	)	)	PUNCT
ejpam-6775	451	24	=	=	SYM
ejpam-6775	452	1	∫	∫	PROPN
ejpam-6775	452	2	ω	ω	NUM
ejpam-6775	452	3	χ(x)i(t	χ(x)i(t	NOUN
ejpam-6775	452	4	,	,	PUNCT
ejpam-6775	452	5	x)dtdx+	x)dtdx+	PROPN
ejpam-6775	452	6	c1	c1	PROPN
ejpam-6775	452	7	2	2	NUM
ejpam-6775	452	8	∥ξ∥2l2(0,t	∥ξ∥2l2(0,t	NOUN
ejpam-6775	452	9	)	)	PUNCT
ejpam-6775	453	1	+	+	CCONJ
ejpam-6775	453	2	c2	c2	PROPN
ejpam-6775	453	3	2	2	NUM
ejpam-6775	453	4	∥α∥2l2(ω	∥α∥2l2(ω	ADV
ejpam-6775	453	5	)	)	PUNCT
ejpam-6775	453	6	,	,	PUNCT
ejpam-6775	453	7	(	(	PUNCT
ejpam-6775	453	8	48	48	NUM
ejpam-6775	453	9	)	)	PUNCT
ejpam-6775	453	10	where	where	SCONJ
ejpam-6775	453	11	χ	χ	X
ejpam-6775	453	12	(	(	PUNCT
ejpam-6775	453	13	.	.	PUNCT
ejpam-6775	453	14	)	)	PUNCT
ejpam-6775	453	15	∈	∈	PROPN
ejpam-6775	453	16	l∞(0	l∞(0	PRON
ejpam-6775	453	17	,	,	PUNCT
ejpam-6775	453	18	xt	xt	ADJ
ejpam-6775	453	19	)	)	PUNCT
ejpam-6775	453	20	,	,	PUNCT
ejpam-6775	453	21	c1	c1	PROPN
ejpam-6775	453	22	>	>	X
ejpam-6775	453	23	0	0	PUNCT
ejpam-6775	454	1	and	and	CCONJ
ejpam-6775	454	2	c2	c2	PROPN
ejpam-6775	454	3	>	>	X
ejpam-6775	454	4	0	0	NUM
ejpam-6775	454	5	are	be	AUX
ejpam-6775	454	6	balancing	balance	VERB
ejpam-6775	454	7	coefficients	coefficient	NOUN
ejpam-6775	454	8	transforming	transform	VERB
ejpam-6775	454	9	the	the	DET
ejpam-6775	454	10	integral	integral	NOUN
ejpam-6775	454	11	into	into	ADP
ejpam-6775	454	12	a	a	DET
ejpam-6775	454	13	cost	cost	NOUN
ejpam-6775	454	14	spent	spend	VERB
ejpam-6775	454	15	over	over	ADP
ejpam-6775	454	16	the	the	DET
ejpam-6775	454	17	interval	interval	NOUN
ejpam-6775	454	18	[	[	X
ejpam-6775	454	19	0	0	NUM
ejpam-6775	454	20	,	,	PUNCT
ejpam-6775	454	21	t	t	X
ejpam-6775	454	22	]	]	PUNCT
ejpam-6775	454	23	.	.	PUNCT
ejpam-6775	455	1	quadratic	quadratic	ADJ
ejpam-6775	455	2	expression	expression	NOUN
ejpam-6775	455	3	of	of	ADP
ejpam-6775	455	4	the	the	DET
ejpam-6775	455	5	control	control	NOUN
ejpam-6775	455	6	in	in	ADP
ejpam-6775	455	7	(	(	PUNCT
ejpam-6775	455	8	32	32	NUM
ejpam-6775	455	9	)	)	PUNCT
ejpam-6775	455	10	is	be	AUX
ejpam-6775	455	11	included	include	VERB
ejpam-6775	455	12	to	to	PART
ejpam-6775	455	13	indicate	indicate	VERB
ejpam-6775	455	14	the	the	DET
ejpam-6775	455	15	nonlinearity	nonlinearity	NOUN
ejpam-6775	455	16	of	of	ADP
ejpam-6775	455	17	the	the	DET
ejpam-6775	455	18	implementation	implementation	NOUN
ejpam-6775	455	19	cost	cost	NOUN
ejpam-6775	455	20	as	as	SCONJ
ejpam-6775	455	21	it	it	PRON
ejpam-6775	455	22	is	be	AUX
ejpam-6775	455	23	more	more	ADV
ejpam-6775	455	24	costly	costly	ADJ
ejpam-6775	455	25	to	to	PART
ejpam-6775	455	26	increase	increase	VERB
ejpam-6775	455	27	the	the	DET
ejpam-6775	455	28	control	control	NOUN
ejpam-6775	455	29	efficiency	efficiency	NOUN
ejpam-6775	455	30	when	when	SCONJ
ejpam-6775	455	31	it	it	PRON
ejpam-6775	455	32	is	be	AUX
ejpam-6775	455	33	already	already	ADV
ejpam-6775	455	34	high	high	ADJ
ejpam-6775	455	35	.	.	PUNCT
ejpam-6775	456	1	as	as	SCONJ
ejpam-6775	456	2	mentioned	mention	VERB
ejpam-6775	456	3	before	before	ADV
ejpam-6775	456	4	,	,	PUNCT
ejpam-6775	456	5	our	our	PRON
ejpam-6775	456	6	optimal	optimal	ADJ
ejpam-6775	456	7	control	control	NOUN
ejpam-6775	456	8	problem	problem	NOUN
ejpam-6775	456	9	reads	read	VERB
ejpam-6775	456	10	as	as	SCONJ
ejpam-6775	456	11	follows	follow	VERB
ejpam-6775	456	12	:	:	PUNCT
ejpam-6775	456	13	find	find	VERB
ejpam-6775	456	14	an	an	DET
ejpam-6775	456	15	admissible	admissible	ADJ
ejpam-6775	456	16	control	control	NOUN
ejpam-6775	456	17	pair	pair	NOUN
ejpam-6775	456	18	(	(	PUNCT
ejpam-6775	456	19	ξ∗	ξ∗	NOUN
ejpam-6775	456	20	(	(	PUNCT
ejpam-6775	456	21	.	.	PUNCT
ejpam-6775	456	22	)	)	PUNCT
ejpam-6775	456	23	,	,	PUNCT
ejpam-6775	456	24	α∗	α∗	NOUN
ejpam-6775	456	25	(	(	PUNCT
ejpam-6775	456	26	.	.	PUNCT
ejpam-6775	456	27	,	,	PUNCT
ejpam-6775	456	28	.	.	PUNCT
ejpam-6775	456	29	)	)	PUNCT
ejpam-6775	456	30	)	)	PUNCT
ejpam-6775	457	1	∈	∈	PROPN
ejpam-6775	457	2	d	d	NOUN
ejpam-6775	457	3	steering	steer	VERB
ejpam-6775	457	4	the	the	DET
ejpam-6775	457	5	optimal	optimal	ADJ
ejpam-6775	457	6	trajectory	trajectory	NOUN
ejpam-6775	457	7	(	(	PUNCT
ejpam-6775	457	8	s∗	s∗	PROPN
ejpam-6775	457	9	(	(	PUNCT
ejpam-6775	457	10	.	.	PUNCT
ejpam-6775	457	11	)	)	PUNCT
ejpam-6775	457	12	,	,	PUNCT
ejpam-6775	457	13	v	v	X
ejpam-6775	457	14	∗	∗	NOUN
ejpam-6775	457	15	(	(	PUNCT
ejpam-6775	457	16	.	.	PUNCT
ejpam-6775	457	17	)	)	PUNCT
ejpam-6775	457	18	,	,	PUNCT
ejpam-6775	457	19	i∗	i∗	NOUN
ejpam-6775	457	20	(	(	PUNCT
ejpam-6775	457	21	.	.	PUNCT
ejpam-6775	457	22	,	,	PUNCT
ejpam-6775	457	23	.	.	PUNCT
ejpam-6775	457	24	)	)	PUNCT
ejpam-6775	457	25	)	)	PUNCT
ejpam-6775	458	1	satisfying	satisfy	VERB
ejpam-6775	458	2	the	the	DET
ejpam-6775	458	3	optimization	optimization	NOUN
ejpam-6775	458	4	problem	problem	NOUN
ejpam-6775	458	5	j(ξ∗	j(ξ∗	NOUN
ejpam-6775	458	6	,	,	PUNCT
ejpam-6775	458	7	α∗	α∗	VERB
ejpam-6775	458	8	)	)	PUNCT
ejpam-6775	458	9	=	=	SYM
ejpam-6775	458	10	min	min	PROPN
ejpam-6775	458	11	(	(	PUNCT
ejpam-6775	458	12	ξ	ξ	PROPN
ejpam-6775	458	13	,	,	PUNCT
ejpam-6775	458	14	α)∈d	α)∈d	X
ejpam-6775	458	15	j(ξ	j(ξ	PROPN
ejpam-6775	458	16	,	,	PUNCT
ejpam-6775	458	17	α	α	NOUN
ejpam-6775	458	18	)	)	PUNCT
ejpam-6775	458	19	.	.	PUNCT
ejpam-6775	459	1	(	(	PUNCT
ejpam-6775	459	2	49	49	NUM
ejpam-6775	459	3	)	)	PUNCT
ejpam-6775	460	1	j.	j.	PROPN
ejpam-6775	460	2	leo	leo	PROPN
ejpam-6775	460	3	amalraj	amalraj	PROPN
ejpam-6775	460	4	et	et	PROPN
ejpam-6775	460	5	al	al	PROPN
ejpam-6775	460	6	.	.	PUNCT
ejpam-6775	460	7	/	/	SYM
ejpam-6775	460	8	eur	eur	PROPN
ejpam-6775	460	9	.	.	PUNCT
ejpam-6775	461	1	j.	j.	PROPN
ejpam-6775	461	2	pure	pure	PROPN
ejpam-6775	461	3	appl	appl	PROPN
ejpam-6775	461	4	.	.	PROPN
ejpam-6775	461	5	math	math	PROPN
ejpam-6775	461	6	,	,	PUNCT
ejpam-6775	461	7	18	18	NUM
ejpam-6775	461	8	(	(	PUNCT
ejpam-6775	461	9	4	4	NUM
ejpam-6775	461	10	)	)	PUNCT
ejpam-6775	461	11	(	(	PUNCT
ejpam-6775	461	12	2025	2025	NUM
ejpam-6775	461	13	)	)	PUNCT
ejpam-6775	461	14	,	,	PUNCT
ejpam-6775	461	15	6775	6775	NUM
ejpam-6775	461	16	18	18	NUM
ejpam-6775	461	17	of	of	ADP
ejpam-6775	461	18	32	32	NUM
ejpam-6775	461	19	5.2	5.2	NUM
ejpam-6775	461	20	.	.	PUNCT
ejpam-6775	462	1	optimality	optimality	NOUN
ejpam-6775	462	2	conditions	condition	NOUN
ejpam-6775	462	3	and	and	CCONJ
ejpam-6775	462	4	control	control	NOUN
ejpam-6775	462	5	characterization	characterization	NOUN
ejpam-6775	462	6	in	in	ADP
ejpam-6775	462	7	this	this	DET
ejpam-6775	462	8	subsection	subsection	NOUN
ejpam-6775	462	9	,	,	PUNCT
ejpam-6775	462	10	we	we	PRON
ejpam-6775	462	11	start	start	VERB
ejpam-6775	462	12	by	by	ADP
ejpam-6775	462	13	showing	show	VERB
ejpam-6775	462	14	the	the	DET
ejpam-6775	462	15	existence	existence	NOUN
ejpam-6775	462	16	of	of	ADP
ejpam-6775	462	17	an	an	DET
ejpam-6775	462	18	optimal	optimal	ADJ
ejpam-6775	462	19	solution	solution	NOUN
ejpam-6775	462	20	to	to	ADP
ejpam-6775	462	21	the	the	DET
ejpam-6775	462	22	optimization	optimization	NOUN
ejpam-6775	462	23	problem	problem	NOUN
ejpam-6775	462	24	(	(	PUNCT
ejpam-6775	462	25	ocp	ocp	PROPN
ejpam-6775	462	26	)	)	PUNCT
ejpam-6775	462	27	subject	subject	NOUN
ejpam-6775	462	28	to	to	ADP
ejpam-6775	462	29	the	the	DET
ejpam-6775	462	30	age	age	NOUN
ejpam-6775	462	31	–	–	PUNCT
ejpam-6775	462	32	structured	structured	ADJ
ejpam-6775	462	33	system	system	NOUN
ejpam-6775	462	34	(	(	PUNCT
ejpam-6775	462	35	31	31	NUM
ejpam-6775	462	36	)	)	PUNCT
ejpam-6775	462	37	.	.	PUNCT
ejpam-6775	463	1	theorem	theorem	VERB
ejpam-6775	463	2	6	6	NUM
ejpam-6775	463	3	.	.	PUNCT
ejpam-6775	464	1	under	under	ADP
ejpam-6775	464	2	assumption	assumption	NOUN
ejpam-6775	464	3	2.4	2.4	NUM
ejpam-6775	464	4	,	,	PUNCT
ejpam-6775	464	5	there	there	PRON
ejpam-6775	464	6	exists	exist	VERB
ejpam-6775	464	7	at	at	ADP
ejpam-6775	464	8	least	least	ADJ
ejpam-6775	464	9	one	one	NUM
ejpam-6775	464	10	optimal	optimal	ADJ
ejpam-6775	464	11	control	control	NOUN
ejpam-6775	464	12	pair	pair	NOUN
ejpam-6775	464	13	(	(	PUNCT
ejpam-6775	464	14	ξ∗	ξ∗	ADJ
ejpam-6775	464	15	,	,	PUNCT
ejpam-6775	464	16	α∗	α∗	NOUN
ejpam-6775	464	17	)	)	PUNCT
ejpam-6775	464	18	∈	∈	PROPN
ejpam-6775	465	1	d	d	NOUN
ejpam-6775	465	2	at	at	ADP
ejpam-6775	465	3	which	which	PRON
ejpam-6775	465	4	corresponds	correspond	VERB
ejpam-6775	465	5	the	the	DET
ejpam-6775	465	6	state	state	NOUN
ejpam-6775	465	7	variable	variable	NOUN
ejpam-6775	465	8	(	(	PUNCT
ejpam-6775	465	9	s∗	s∗	PROPN
ejpam-6775	465	10	,	,	PUNCT
ejpam-6775	465	11	v	v	NOUN
ejpam-6775	465	12	∗	∗	NOUN
ejpam-6775	465	13	,	,	PUNCT
ejpam-6775	465	14	i∗	i∗	NOUN
ejpam-6775	465	15	)	)	PUNCT
ejpam-6775	465	16	,	,	PUNCT
ejpam-6775	465	17	solution	solution	NOUN
ejpam-6775	465	18	of	of	ADP
ejpam-6775	465	19	the	the	DET
ejpam-6775	465	20	optimization	optimization	NOUN
ejpam-6775	465	21	problem	problem	NOUN
ejpam-6775	465	22	(	(	PUNCT
ejpam-6775	465	23	ocp	ocp	PROPN
ejpam-6775	465	24	)	)	PUNCT
ejpam-6775	465	25	.	.	PUNCT
ejpam-6775	466	1	proof	proof	NOUN
ejpam-6775	466	2	.	.	PUNCT
ejpam-6775	467	1	the	the	DET
ejpam-6775	467	2	objective	objective	ADJ
ejpam-6775	467	3	functional	functional	ADJ
ejpam-6775	467	4	j(ξ	j(ξ	PROPN
ejpam-6775	467	5	,	,	PUNCT
ejpam-6775	467	6	α	α	X
ejpam-6775	467	7	)	)	PUNCT
ejpam-6775	467	8	≥	≥	NOUN
ejpam-6775	467	9	0	0	NUM
ejpam-6775	467	10	since	since	SCONJ
ejpam-6775	467	11	the	the	DET
ejpam-6775	467	12	state	state	NOUN
ejpam-6775	467	13	variables	variable	NOUN
ejpam-6775	467	14	and	and	CCONJ
ejpam-6775	467	15	controls	control	NOUN
ejpam-6775	467	16	are	be	AUX
ejpam-6775	467	17	all	all	ADV
ejpam-6775	467	18	nonnegatives	nonnegative	NOUN
ejpam-6775	467	19	.	.	PUNCT
ejpam-6775	468	1	then	then	ADV
ejpam-6775	468	2	,	,	PUNCT
ejpam-6775	468	3	it	it	PRON
ejpam-6775	468	4	follows	follow	VERB
ejpam-6775	468	5	that	that	SCONJ
ejpam-6775	468	6	d	d	PROPN
ejpam-6775	468	7	=	=	SYM
ejpam-6775	468	8	inf(ξ	inf(ξ	PROPN
ejpam-6775	468	9	,	,	PUNCT
ejpam-6775	468	10	α)∈d	α)∈d	X
ejpam-6775	468	11	j(ξ	j(ξ	PROPN
ejpam-6775	468	12	,	,	PUNCT
ejpam-6775	468	13	α	α	X
ejpam-6775	468	14	)	)	PUNCT
ejpam-6775	468	15	is	be	AUX
ejpam-6775	468	16	finite	finite	ADJ
ejpam-6775	468	17	and	and	CCONJ
ejpam-6775	468	18	nonnegative	nonnegative	ADJ
ejpam-6775	468	19	.	.	PUNCT
ejpam-6775	469	1	so	so	ADV
ejpam-6775	469	2	there	there	PRON
ejpam-6775	469	3	is	be	VERB
ejpam-6775	469	4	a	a	DET
ejpam-6775	469	5	minimizing	minimize	VERB
ejpam-6775	469	6	sequence	sequence	NOUN
ejpam-6775	469	7	(	(	PUNCT
ejpam-6775	469	8	ξn	ξn	NOUN
ejpam-6775	469	9	,	,	PUNCT
ejpam-6775	469	10	αn	αn	NOUN
ejpam-6775	469	11	)	)	PUNCT
ejpam-6775	469	12	such	such	ADJ
ejpam-6775	469	13	that	that	PRON
ejpam-6775	469	14	for	for	ADP
ejpam-6775	469	15	n	n	PRON
ejpam-6775	469	16	≥	≥	NUM
ejpam-6775	469	17	1	1	NUM
ejpam-6775	469	18	we	we	PRON
ejpam-6775	469	19	have	have	VERB
ejpam-6775	469	20	d	d	NOUN
ejpam-6775	469	21	≤	≤	NOUN
ejpam-6775	469	22	j(ξn	j(ξn	NOUN
ejpam-6775	469	23	,	,	PUNCT
ejpam-6775	469	24	αn	αn	NOUN
ejpam-6775	469	25	)	)	PUNCT
ejpam-6775	469	26	≤	≤	NUM
ejpam-6775	469	27	d+	d+	PUNCT
ejpam-6775	469	28	1	1	NUM
ejpam-6775	469	29	n	n	NOUN
ejpam-6775	469	30	.	.	PUNCT
ejpam-6775	470	1	(	(	PUNCT
ejpam-6775	470	2	50	50	NUM
ejpam-6775	470	3	)	)	PUNCT
ejpam-6775	470	4	as	as	ADP
ejpam-6775	470	5	the	the	DET
ejpam-6775	470	6	sequence	sequence	NOUN
ejpam-6775	470	7	(	(	PUNCT
ejpam-6775	470	8	ξn	ξn	NOUN
ejpam-6775	470	9	,	,	PUNCT
ejpam-6775	470	10	αn	αn	NUM
ejpam-6775	470	11	)	)	PUNCT
ejpam-6775	470	12	is	be	AUX
ejpam-6775	470	13	bounded	bound	VERB
ejpam-6775	470	14	,	,	PUNCT
ejpam-6775	470	15	there	there	PRON
ejpam-6775	470	16	exists	exist	VERB
ejpam-6775	470	17	a	a	DET
ejpam-6775	470	18	subsequence	subsequence	NOUN
ejpam-6775	470	19	still	still	ADV
ejpam-6775	470	20	denoted	denote	VERB
ejpam-6775	470	21	(	(	PUNCT
ejpam-6775	470	22	ξn	ξn	NOUN
ejpam-6775	470	23	,	,	PUNCT
ejpam-6775	470	24	αn	αn	NOUN
ejpam-6775	470	25	)	)	PUNCT
ejpam-6775	470	26	that	that	PRON
ejpam-6775	470	27	converges	converge	VERB
ejpam-6775	470	28	to	to	ADP
ejpam-6775	470	29	some	some	PRON
ejpam-6775	470	30	(	(	PUNCT
ejpam-6775	470	31	ξ∗	ξ∗	ADJ
ejpam-6775	470	32	,	,	PUNCT
ejpam-6775	470	33	α∗	α∗	NOUN
ejpam-6775	470	34	)	)	PUNCT
ejpam-6775	470	35	for	for	ADP
ejpam-6775	470	36	the	the	DET
ejpam-6775	470	37	weak–∗	weak–∗	NOUN
ejpam-6775	470	38	topology	topology	NOUN
ejpam-6775	470	39	of	of	ADP
ejpam-6775	470	40	l∞(0	l∞(0	X
ejpam-6775	470	41	,	,	PUNCT
ejpam-6775	470	42	t	t	PROPN
ejpam-6775	470	43	)	)	PUNCT
ejpam-6775	470	44	×	×	NOUN
ejpam-6775	470	45	l∞(ω	l∞(ω	NOUN
ejpam-6775	470	46	)	)	PUNCT
ejpam-6775	470	47	.	.	PUNCT
ejpam-6775	471	1	the	the	DET
ejpam-6775	471	2	set	set	PROPN
ejpam-6775	471	3	d	d	NOUN
ejpam-6775	471	4	is	be	AUX
ejpam-6775	471	5	a	a	DET
ejpam-6775	471	6	closed	closed	ADJ
ejpam-6775	471	7	convex	convex	NOUN
ejpam-6775	471	8	subset	subset	NOUN
ejpam-6775	471	9	of	of	ADP
ejpam-6775	471	10	l∞(0	l∞(0	X
ejpam-6775	471	11	,	,	PUNCT
ejpam-6775	471	12	t	t	PROPN
ejpam-6775	471	13	)	)	PUNCT
ejpam-6775	471	14	×	×	PROPN
ejpam-6775	471	15	l∞(ω	l∞(ω	NOUN
ejpam-6775	471	16	)	)	PUNCT
ejpam-6775	471	17	,	,	PUNCT
ejpam-6775	471	18	so	so	CCONJ
ejpam-6775	471	19	it	it	PRON
ejpam-6775	471	20	is	be	AUX
ejpam-6775	471	21	weakly	weakly	ADV
ejpam-6775	471	22	closed	closed	ADJ
ejpam-6775	471	23	.	.	PUNCT
ejpam-6775	472	1	therefore	therefore	ADV
ejpam-6775	472	2	(	(	PUNCT
ejpam-6775	472	3	ξ∗	ξ∗	ADV
ejpam-6775	472	4	,	,	PUNCT
ejpam-6775	472	5	α∗	α∗	NOUN
ejpam-6775	472	6	)	)	PUNCT
ejpam-6775	472	7	∈	∈	PROPN
ejpam-6775	472	8	d.	d.	PROPN
ejpam-6775	472	9	denote	denote	VERB
ejpam-6775	472	10	by	by	ADP
ejpam-6775	472	11	(	(	PUNCT
ejpam-6775	472	12	sn	sn	PROPN
ejpam-6775	472	13	,	,	PUNCT
ejpam-6775	472	14	vn	vn	NOUN
ejpam-6775	472	15	,	,	PUNCT
ejpam-6775	472	16	in	in	ADP
ejpam-6775	472	17	)	)	PUNCT
ejpam-6775	472	18	the	the	DET
ejpam-6775	472	19	solution	solution	NOUN
ejpam-6775	472	20	of	of	ADP
ejpam-6775	472	21	state	state	NOUN
ejpam-6775	472	22	system	system	NOUN
ejpam-6775	472	23	(	(	PUNCT
ejpam-6775	472	24	31	31	NUM
ejpam-6775	472	25	)	)	PUNCT
ejpam-6775	472	26	corresponding	correspond	VERB
ejpam-6775	472	27	to	to	PART
ejpam-6775	472	28	control	control	VERB
ejpam-6775	472	29	pair	pair	NOUN
ejpam-6775	472	30	(	(	PUNCT
ejpam-6775	472	31	ξn	ξn	NOUN
ejpam-6775	472	32	,	,	PUNCT
ejpam-6775	472	33	αn	αn	NOUN
ejpam-6775	472	34	)	)	PUNCT
ejpam-6775	472	35	.	.	PUNCT
ejpam-6775	473	1	the	the	DET
ejpam-6775	473	2	sequence	sequence	NOUN
ejpam-6775	473	3	(	(	PUNCT
ejpam-6775	473	4	sn	sn	PROPN
ejpam-6775	473	5	,	,	PUNCT
ejpam-6775	473	6	vn	vn	PROPN
ejpam-6775	473	7	)	)	PUNCT
ejpam-6775	473	8	is	be	AUX
ejpam-6775	473	9	uniformly	uniformly	ADV
ejpam-6775	473	10	bounded	bound	VERB
ejpam-6775	473	11	and	and	CCONJ
ejpam-6775	473	12	equicontinuous	equicontinuous	ADJ
ejpam-6775	473	13	on	on	ADP
ejpam-6775	473	14	[	[	X
ejpam-6775	473	15	0	0	NUM
ejpam-6775	473	16	,	,	PUNCT
ejpam-6775	473	17	t	t	X
ejpam-6775	473	18	]	]	PUNCT
ejpam-6775	473	19	.	.	PUNCT
ejpam-6775	474	1	using	use	VERB
ejpam-6775	474	2	arzela	arzela	PROPN
ejpam-6775	474	3	–	–	PUNCT
ejpam-6775	474	4	ascoli	ascoli	PROPN
ejpam-6775	474	5	’s	’s	PART
ejpam-6775	474	6	theorem	theorem	NOUN
ejpam-6775	474	7	,	,	PUNCT
ejpam-6775	474	8	we	we	PRON
ejpam-6775	474	9	can	can	AUX
ejpam-6775	474	10	extract	extract	VERB
ejpam-6775	474	11	a	a	DET
ejpam-6775	474	12	subsequence	subsequence	NOUN
ejpam-6775	474	13	still	still	ADV
ejpam-6775	474	14	denoted	denote	VERB
ejpam-6775	474	15	(	(	PUNCT
ejpam-6775	474	16	sn	sn	PROPN
ejpam-6775	474	17	,	,	PUNCT
ejpam-6775	474	18	vn	vn	PROPN
ejpam-6775	474	19	)	)	PUNCT
ejpam-6775	474	20	which	which	PRON
ejpam-6775	474	21	converges	converge	VERB
ejpam-6775	474	22	uniformly	uniformly	ADV
ejpam-6775	474	23	to	to	ADP
ejpam-6775	474	24	the	the	DET
ejpam-6775	474	25	limit	limit	NOUN
ejpam-6775	474	26	(	(	PUNCT
ejpam-6775	474	27	s∗	s∗	PROPN
ejpam-6775	474	28	,	,	PUNCT
ejpam-6775	474	29	v	v	NOUN
ejpam-6775	474	30	∗	∗	NOUN
ejpam-6775	474	31	)	)	PUNCT
ejpam-6775	474	32	in	in	ADP
ejpam-6775	474	33	c(0	c(0	PROPN
ejpam-6775	474	34	,	,	PUNCT
ejpam-6775	474	35	t	t	NOUN
ejpam-6775	474	36	)	)	PUNCT
ejpam-6775	474	37	.	.	PUNCT
ejpam-6775	475	1	let	let	VERB
ejpam-6775	475	2	us	we	PRON
ejpam-6775	475	3	denote	denote	VERB
ejpam-6775	475	4	by	by	ADP
ejpam-6775	475	5	παn(t	παn(t	PROPN
ejpam-6775	475	6	,	,	PUNCT
ejpam-6775	475	7	x	x	X
ejpam-6775	475	8	)	)	PUNCT
ejpam-6775	475	9	=	=	SYM
ejpam-6775	476	1	e−	e−	NUM
ejpam-6775	476	2	∫	∫	NOUN
ejpam-6775	476	3	t+x	t+x	PROPN
ejpam-6775	476	4	t	t	PROPN
ejpam-6775	476	5	(	(	PUNCT
ejpam-6775	476	6	µ+δ(s)+αn(s	µ+δ(s)+αn(s	PROPN
ejpam-6775	476	7	,	,	PUNCT
ejpam-6775	476	8	s+t−x))ds	s+t−x))ds	NOUN
ejpam-6775	476	9	.	.	PUNCT
ejpam-6775	477	1	it	it	PRON
ejpam-6775	477	2	is	be	AUX
ejpam-6775	477	3	easy	easy	ADJ
ejpam-6775	477	4	to	to	PART
ejpam-6775	477	5	see	see	VERB
ejpam-6775	477	6	that	that	SCONJ
ejpam-6775	477	7	the	the	DET
ejpam-6775	477	8	function	function	NOUN
ejpam-6775	477	9	παn	παn	PROPN
ejpam-6775	477	10	is	be	AUX
ejpam-6775	477	11	lipschitz	lipschitz	NOUN
ejpam-6775	477	12	in	in	ADP
ejpam-6775	477	13	the	the	DET
ejpam-6775	477	14	following	follow	VERB
ejpam-6775	477	15	sense	sense	NOUN
ejpam-6775	477	16	,	,	PUNCT
ejpam-6775	477	17	for	for	ADP
ejpam-6775	477	18	(	(	PUNCT
ejpam-6775	477	19	α1	α1	PROPN
ejpam-6775	477	20	,	,	PUNCT
ejpam-6775	477	21	α2	α2	PROPN
ejpam-6775	477	22	)	)	PUNCT
ejpam-6775	477	23	,	,	PUNCT
ejpam-6775	477	24	there	there	PRON
ejpam-6775	477	25	exists	exist	VERB
ejpam-6775	477	26	a	a	DET
ejpam-6775	477	27	constant	constant	ADJ
ejpam-6775	477	28	k	k	X
ejpam-6775	477	29	≥	≥	NOUN
ejpam-6775	477	30	0	0	NUM
ejpam-6775	477	31	such	such	ADJ
ejpam-6775	477	32	that	that	SCONJ
ejpam-6775	477	33	|πα1(t	|πα1(t	PROPN
ejpam-6775	477	34	,	,	PUNCT
ejpam-6775	477	35	x	x	X
ejpam-6775	477	36	)	)	PUNCT
ejpam-6775	477	37	−	−	ADP
ejpam-6775	477	38	πα2(t	πα2(t	PROPN
ejpam-6775	477	39	,	,	PUNCT
ejpam-6775	477	40	x)|	x)|	PROPN
ejpam-6775	477	41	≤	≤	PROPN
ejpam-6775	477	42	kt	kt	ADP
ejpam-6775	477	43	|α1	|α1	PROPN
ejpam-6775	477	44	(	(	PUNCT
ejpam-6775	477	45	.	.	PUNCT
ejpam-6775	477	46	,	,	PUNCT
ejpam-6775	477	47	.	.	PUNCT
ejpam-6775	477	48	)	)	PUNCT
ejpam-6775	478	1	−	−	PROPN
ejpam-6775	478	2	α2	α2	ADJ
ejpam-6775	478	3	(	(	PUNCT
ejpam-6775	478	4	.	.	PUNCT
ejpam-6775	478	5	,	,	PUNCT
ejpam-6775	479	1	.)|	.)|	INTJ
ejpam-6775	479	2	.	.	PUNCT
ejpam-6775	480	1	as	as	ADP
ejpam-6775	480	2	consequence	consequence	NOUN
ejpam-6775	480	3	,	,	PUNCT
ejpam-6775	480	4	we	we	PRON
ejpam-6775	480	5	have	have	VERB
ejpam-6775	480	6	the	the	DET
ejpam-6775	480	7	convergence	convergence	NOUN
ejpam-6775	480	8	παn(t	παn(t	PROPN
ejpam-6775	480	9	,	,	PUNCT
ejpam-6775	480	10	.	.	PUNCT
ejpam-6775	480	11	)	)	PUNCT
ejpam-6775	481	1	→	→	PUNCT
ejpam-6775	481	2	πα∗(t	πα∗(t	NOUN
ejpam-6775	481	3	,	,	PUNCT
ejpam-6775	481	4	.	.	PUNCT
ejpam-6775	481	5	)	)	PUNCT
ejpam-6775	482	1	as	as	ADP
ejpam-6775	482	2	n	n	PROPN
ejpam-6775	482	3	→	→	SYM
ejpam-6775	482	4	∞	∞	NUM
ejpam-6775	482	5	almost	almost	ADV
ejpam-6775	482	6	everywhere	everywhere	ADV
ejpam-6775	482	7	in	in	ADP
ejpam-6775	482	8	ω	ω	PROPN
ejpam-6775	482	9	.	.	PUNCT
ejpam-6775	483	1	by	by	ADP
ejpam-6775	483	2	using	use	VERB
ejpam-6775	483	3	the	the	DET
ejpam-6775	483	4	method	method	NOUN
ejpam-6775	483	5	of	of	ADP
ejpam-6775	483	6	characteristics	characteristic	NOUN
ejpam-6775	483	7	,	,	PUNCT
ejpam-6775	483	8	we	we	PRON
ejpam-6775	483	9	get	get	VERB
ejpam-6775	483	10	explicit	explicit	ADJ
ejpam-6775	483	11	expression	expression	NOUN
ejpam-6775	483	12	of	of	ADP
ejpam-6775	483	13	in(t	in(t	NOUN
ejpam-6775	483	14	,	,	PUNCT
ejpam-6775	483	15	x)-equation	x)-equation	NOUN
ejpam-6775	483	16	in(t	in(t	NUM
ejpam-6775	483	17	,	,	PUNCT
ejpam-6775	483	18	x	x	X
ejpam-6775	483	19	)	)	PUNCT
ejpam-6775	483	20	=	=	SYM
ejpam-6775	484	1	in(t−	in(t−	NOUN
ejpam-6775	484	2	x	x	X
ejpam-6775	484	3	,	,	PUNCT
ejpam-6775	484	4	0	0	NUM
ejpam-6775	484	5	)	)	PUNCT
ejpam-6775	484	6	παn(t	παn(t	PROPN
ejpam-6775	484	7	,	,	PUNCT
ejpam-6775	484	8	x	x	X
ejpam-6775	484	9	)	)	PUNCT
ejpam-6775	484	10	παn(t−	παn(t−	NUM
ejpam-6775	485	1	x	x	NOUN
ejpam-6775	485	2	,	,	PUNCT
ejpam-6775	485	3	0	0	NUM
ejpam-6775	485	4	)	)	PUNCT
ejpam-6775	485	5	1{xt	1{xt	NUM
ejpam-6775	485	6	}	}	PUNCT
ejpam-6775	485	7	+	+	NUM
ejpam-6775	485	8	in(t−	in(t−	NOUN
ejpam-6775	485	9	x	x	NOUN
ejpam-6775	485	10	,	,	PUNCT
ejpam-6775	485	11	0)tπαn(t	0)tπαn(t	PROPN
ejpam-6775	485	12	,	,	PUNCT
ejpam-6775	485	13	x)1{xt	x)1{xt	NUM
ejpam-6775	485	14	}	}	PUNCT
ejpam-6775	485	15	.	.	PUNCT
ejpam-6775	486	1	this	this	DET
ejpam-6775	486	2	sequence	sequence	NOUN
ejpam-6775	486	3	is	be	AUX
ejpam-6775	486	4	bounded	bound	VERB
ejpam-6775	486	5	since	since	SCONJ
ejpam-6775	486	6	the	the	DET
ejpam-6775	486	7	sequence	sequence	NOUN
ejpam-6775	486	8	(	(	PUNCT
ejpam-6775	486	9	sn	sn	PROPN
ejpam-6775	486	10	,	,	PUNCT
ejpam-6775	486	11	vn	vn	PROPN
ejpam-6775	486	12	,	,	PUNCT
ejpam-6775	486	13	t	t	PROPN
ejpam-6775	486	14	(	(	PUNCT
ejpam-6775	486	15	β(in	β(in	PROPN
ejpam-6775	486	16	)	)	PUNCT
ejpam-6775	486	17	)	)	PUNCT
ejpam-6775	486	18	)	)	PUNCT
ejpam-6775	487	1	and	and	CCONJ
ejpam-6775	487	2	(	(	PUNCT
ejpam-6775	487	3	αn	αn	X
ejpam-6775	487	4	)	)	PUNCT
ejpam-6775	487	5	are	be	AUX
ejpam-6775	487	6	all	all	PRON
ejpam-6775	487	7	bounded	bound	VERB
ejpam-6775	487	8	.	.	PUNCT
ejpam-6775	488	1	then	then	ADV
ejpam-6775	488	2	we	we	PRON
ejpam-6775	488	3	can	can	AUX
ejpam-6775	488	4	extract	extract	VERB
ejpam-6775	488	5	a	a	DET
ejpam-6775	488	6	subsequence	subsequence	NOUN
ejpam-6775	488	7	still	still	ADV
ejpam-6775	488	8	denoted	denote	VERB
ejpam-6775	488	9	(	(	PUNCT
ejpam-6775	488	10	in	in	ADP
ejpam-6775	488	11	)	)	PUNCT
ejpam-6775	488	12	that	that	PRON
ejpam-6775	488	13	converges	converge	VERB
ejpam-6775	488	14	weakly	weakly	ADV
ejpam-6775	488	15	to	to	ADP
ejpam-6775	488	16	i∗(t	i∗(t	PROPN
ejpam-6775	488	17	,	,	PUNCT
ejpam-6775	488	18	x	x	NOUN
ejpam-6775	488	19	)	)	PUNCT
ejpam-6775	488	20	in	in	ADP
ejpam-6775	488	21	l2(ω	l2(ω	NOUN
ejpam-6775	488	22	)	)	PUNCT
ejpam-6775	488	23	defined	define	VERB
ejpam-6775	488	24	as	as	SCONJ
ejpam-6775	488	25	follows	follow	VERB
ejpam-6775	488	26	i∗(t	i∗(t	PROPN
ejpam-6775	488	27	,	,	PUNCT
ejpam-6775	488	28	x	x	NOUN
ejpam-6775	488	29	)	)	PUNCT
ejpam-6775	489	1	=	=	SYM
ejpam-6775	489	2	i0(x)−	i0(x)−	PROPN
ejpam-6775	489	3	πα∗(t	πα∗(t	NOUN
ejpam-6775	489	4	,	,	PUNCT
ejpam-6775	489	5	x	x	X
ejpam-6775	489	6	)	)	PUNCT
ejpam-6775	489	7	πα∗(t−	πα∗(t−	PROPN
ejpam-6775	489	8	x	x	X
ejpam-6775	489	9	,	,	PUNCT
ejpam-6775	489	10	0	0	NUM
ejpam-6775	489	11	)	)	PUNCT
ejpam-6775	489	12	1{xt	1{xt	NUM
ejpam-6775	489	13	}	}	PUNCT
ejpam-6775	490	1	+	+	CCONJ
ejpam-6775	490	2	i∗(t−	i∗(t−	ADJ
ejpam-6775	490	3	x	x	NOUN
ejpam-6775	490	4	,	,	PUNCT
ejpam-6775	490	5	0)tπα∗(t	0)tπα∗(t	NOUN
ejpam-6775	490	6	,	,	PUNCT
ejpam-6775	490	7	x)1{xt	x)1{xt	NUM
ejpam-6775	490	8	}	}	PUNCT
ejpam-6775	490	9	.	.	PUNCT
ejpam-6775	491	1	since	since	SCONJ
ejpam-6775	491	2	the	the	DET
ejpam-6775	491	3	sequence	sequence	NOUN
ejpam-6775	491	4	(	(	PUNCT
ejpam-6775	491	5	t	t	PROPN
ejpam-6775	491	6	(	(	PUNCT
ejpam-6775	491	7	in	in	ADP
ejpam-6775	491	8	)	)	PUNCT
ejpam-6775	491	9	)	)	PUNCT
ejpam-6775	491	10	is	be	AUX
ejpam-6775	491	11	bounded	bound	VERB
ejpam-6775	491	12	,	,	PUNCT
ejpam-6775	491	13	it	it	PRON
ejpam-6775	491	14	converges	converge	VERB
ejpam-6775	491	15	to	to	ADP
ejpam-6775	491	16	t	t	PROPN
ejpam-6775	491	17	(	(	PUNCT
ejpam-6775	491	18	i∗	i∗	NOUN
ejpam-6775	491	19	)	)	PUNCT
ejpam-6775	491	20	by	by	ADP
ejpam-6775	491	21	the	the	DET
ejpam-6775	491	22	uniqueness	uniqueness	NOUN
ejpam-6775	491	23	of	of	ADP
ejpam-6775	491	24	the	the	DET
ejpam-6775	491	25	limit	limit	NOUN
ejpam-6775	491	26	.	.	PUNCT
ejpam-6775	492	1	moreover	moreover	ADV
ejpam-6775	492	2	,	,	PUNCT
ejpam-6775	492	3	passing	pass	VERB
ejpam-6775	492	4	to	to	ADP
ejpam-6775	492	5	the	the	DET
ejpam-6775	492	6	limit	limit	NOUN
ejpam-6775	492	7	in	in	ADP
ejpam-6775	492	8	the	the	DET
ejpam-6775	492	9	differential	differential	ADJ
ejpam-6775	492	10	equations	equation	NOUN
ejpam-6775	492	11	satisfied	satisfy	VERB
ejpam-6775	492	12	by	by	ADP
ejpam-6775	492	13	the	the	DET
ejpam-6775	492	14	subsequences	subsequence	NOUN
ejpam-6775	492	15	(	(	PUNCT
ejpam-6775	492	16	sn	sn	PROPN
ejpam-6775	492	17	,	,	PUNCT
ejpam-6775	492	18	vn	vn	PROPN
ejpam-6775	492	19	)	)	PUNCT
ejpam-6775	492	20	and	and	CCONJ
ejpam-6775	492	21	(	(	PUNCT
ejpam-6775	492	22	vn	vn	NOUN
ejpam-6775	492	23	)	)	PUNCT
ejpam-6775	492	24	in	in	ADP
ejpam-6775	492	25	controlled	control	VERB
ejpam-6775	492	26	system	system	NOUN
ejpam-6775	492	27	(	(	PUNCT
ejpam-6775	492	28	31	31	NUM
ejpam-6775	492	29	)	)	PUNCT
ejpam-6775	492	30	,	,	PUNCT
ejpam-6775	492	31	we	we	PRON
ejpam-6775	492	32	obtain	obtain	VERB
ejpam-6775	492	33	:	:	PUNCT
ejpam-6775	492	34	ds	ds	ADP
ejpam-6775	492	35	dt	dt	NOUN
ejpam-6775	492	36	=	=	SYM
ejpam-6775	492	37	λ−	λ−	PROPN
ejpam-6775	492	38	t	t	PROPN
ejpam-6775	492	39	(	(	PUNCT
ejpam-6775	492	40	βi∗)s	βi∗)s	PROPN
ejpam-6775	492	41	+	+	NUM
ejpam-6775	492	42	t	t	PROPN
ejpam-6775	492	43	(	(	PUNCT
ejpam-6775	492	44	α	α	X
ejpam-6775	492	45	(	(	PUNCT
ejpam-6775	492	46	.	.	PUNCT
ejpam-6775	492	47	,	,	PUNCT
ejpam-6775	492	48	i∗))−	i∗))−	ADP
ejpam-6775	492	49	(	(	PUNCT
ejpam-6775	492	50	ξ∗	ξ∗	ADJ
ejpam-6775	492	51	+	+	CCONJ
ejpam-6775	492	52	µ)s	µ)s	NOUN
ejpam-6775	492	53	,	,	PUNCT
ejpam-6775	492	54	dv	dv	PROPN
ejpam-6775	492	55	dt	dt	NOUN
ejpam-6775	492	56	=	=	SYM
ejpam-6775	492	57	ξ∗(t)s	ξ∗(t)s	PROPN
ejpam-6775	492	58	−mt	−mt	NOUN
ejpam-6775	492	59	(	(	PUNCT
ejpam-6775	492	60	βi∗)v	βi∗)v	PROPN
ejpam-6775	492	61	−	−	PROPN
ejpam-6775	492	62	µv	µv	NOUN
ejpam-6775	492	63	∗.	∗.	PROPN
ejpam-6775	492	64	(	(	PUNCT
ejpam-6775	492	65	51	51	NUM
ejpam-6775	492	66	)	)	PUNCT
ejpam-6775	492	67	j.	j.	PROPN
ejpam-6775	492	68	leo	leo	PROPN
ejpam-6775	492	69	amalraj	amalraj	PROPN
ejpam-6775	493	1	et	et	PROPN
ejpam-6775	493	2	al	al	PROPN
ejpam-6775	493	3	.	.	PUNCT
ejpam-6775	493	4	/	/	SYM
ejpam-6775	493	5	eur	eur	PROPN
ejpam-6775	493	6	.	.	PUNCT
ejpam-6775	494	1	j.	j.	PROPN
ejpam-6775	494	2	pure	pure	PROPN
ejpam-6775	494	3	appl	appl	PROPN
ejpam-6775	494	4	.	.	PROPN
ejpam-6775	494	5	math	math	PROPN
ejpam-6775	494	6	,	,	PUNCT
ejpam-6775	494	7	18	18	NUM
ejpam-6775	494	8	(	(	PUNCT
ejpam-6775	494	9	4	4	NUM
ejpam-6775	494	10	)	)	PUNCT
ejpam-6775	494	11	(	(	PUNCT
ejpam-6775	494	12	2025	2025	NUM
ejpam-6775	494	13	)	)	PUNCT
ejpam-6775	494	14	,	,	PUNCT
ejpam-6775	494	15	6775	6775	NUM
ejpam-6775	494	16	19	19	NUM
ejpam-6775	494	17	of	of	ADP
ejpam-6775	494	18	32	32	NUM
ejpam-6775	494	19	passing	pass	VERB
ejpam-6775	494	20	to	to	ADP
ejpam-6775	494	21	the	the	DET
ejpam-6775	494	22	limit	limit	NOUN
ejpam-6775	494	23	as	as	ADP
ejpam-6775	494	24	n→	n→	PROPN
ejpam-6775	494	25	∞	∞	PROPN
ejpam-6775	494	26	in	in	ADP
ejpam-6775	494	27	(	(	PUNCT
ejpam-6775	494	28	33	33	NUM
ejpam-6775	494	29	)	)	PUNCT
ejpam-6775	494	30	and	and	CCONJ
ejpam-6775	494	31	lower	low	ADJ
ejpam-6775	494	32	semicontinuity	semicontinuity	NOUN
ejpam-6775	494	33	of	of	ADP
ejpam-6775	494	34	objective	objective	ADJ
ejpam-6775	494	35	functional	functional	ADJ
ejpam-6775	494	36	j	j	PROPN
ejpam-6775	494	37	(	(	PUNCT
ejpam-6775	494	38	.	.	PUNCT
ejpam-6775	494	39	,	,	PUNCT
ejpam-6775	494	40	.	.	PUNCT
ejpam-6775	494	41	)	)	PUNCT
ejpam-6775	495	1	,	,	PUNCT
ejpam-6775	495	2	we	we	PRON
ejpam-6775	495	3	obtain	obtain	VERB
ejpam-6775	495	4	limn→∞	limn→∞	PROPN
ejpam-6775	495	5	j(ξn	j(ξn	NOUN
ejpam-6775	495	6	,	,	PUNCT
ejpam-6775	495	7	αn	αn	NOUN
ejpam-6775	495	8	)	)	PUNCT
ejpam-6775	495	9	=	=	SYM
ejpam-6775	495	10	j(ξ∗	j(ξ∗	NOUN
ejpam-6775	495	11	,	,	PUNCT
ejpam-6775	495	12	α∗	α∗	NOUN
ejpam-6775	495	13	)	)	PUNCT
ejpam-6775	495	14	=	=	SYM
ejpam-6775	495	15	d.	d.	PROPN
ejpam-6775	495	16	hence	hence	ADV
ejpam-6775	495	17	,	,	PUNCT
ejpam-6775	495	18	(	(	PUNCT
ejpam-6775	495	19	s∗	s∗	PROPN
ejpam-6775	495	20	,	,	PUNCT
ejpam-6775	495	21	v	v	NOUN
ejpam-6775	495	22	∗	∗	NOUN
ejpam-6775	495	23	,	,	PUNCT
ejpam-6775	495	24	i∗	i∗	NOUN
ejpam-6775	495	25	,	,	PUNCT
ejpam-6775	495	26	ξ∗	ξ∗	NOUN
ejpam-6775	495	27	,	,	PUNCT
ejpam-6775	495	28	α∗	α∗	NOUN
ejpam-6775	495	29	)	)	PUNCT
ejpam-6775	495	30	is	be	AUX
ejpam-6775	495	31	an	an	DET
ejpam-6775	495	32	optimal	optimal	ADJ
ejpam-6775	495	33	solution	solution	NOUN
ejpam-6775	495	34	of	of	ADP
ejpam-6775	495	35	the	the	DET
ejpam-6775	495	36	optimization	optimization	NOUN
ejpam-6775	495	37	problem	problem	NOUN
ejpam-6775	495	38	(	(	PUNCT
ejpam-6775	495	39	ocp	ocp	PROPN
ejpam-6775	495	40	)	)	PUNCT
ejpam-6775	495	41	.	.	PUNCT
ejpam-6775	496	1	this	this	PRON
ejpam-6775	496	2	achieves	achieve	VERB
ejpam-6775	496	3	the	the	DET
ejpam-6775	496	4	proof	proof	NOUN
ejpam-6775	496	5	.	.	PUNCT
ejpam-6775	497	1	now	now	ADV
ejpam-6775	497	2	,	,	PUNCT
ejpam-6775	497	3	we	we	PRON
ejpam-6775	497	4	derive	derive	VERB
ejpam-6775	497	5	the	the	DET
ejpam-6775	497	6	first	first	ADJ
ejpam-6775	497	7	–	–	PUNCT
ejpam-6775	497	8	order	order	NOUN
ejpam-6775	497	9	necessary	necessary	ADJ
ejpam-6775	497	10	conditions	condition	NOUN
ejpam-6775	497	11	for	for	ADP
ejpam-6775	497	12	optimality	optimality	NOUN
ejpam-6775	497	13	of	of	ADP
ejpam-6775	497	14	a	a	DET
ejpam-6775	497	15	control	control	NOUN
ejpam-6775	497	16	pair	pair	NOUN
ejpam-6775	497	17	must	must	AUX
ejpam-6775	497	18	satisfy	satisfy	VERB
ejpam-6775	497	19	in	in	ADP
ejpam-6775	497	20	order	order	NOUN
ejpam-6775	497	21	to	to	PART
ejpam-6775	497	22	be	be	AUX
ejpam-6775	497	23	optimal	optimal	ADJ
ejpam-6775	497	24	.	.	PUNCT
ejpam-6775	498	1	using	use	VERB
ejpam-6775	498	2	the	the	DET
ejpam-6775	498	3	framework	framework	NOUN
ejpam-6775	498	4	of	of	ADP
ejpam-6775	498	5	barbu	barbu	PROPN
ejpam-6775	498	6	[	[	X
ejpam-6775	498	7	44	44	NUM
ejpam-6775	498	8	]	]	PUNCT
ejpam-6775	498	9	,	,	PUNCT
ejpam-6775	498	10	we	we	PRON
ejpam-6775	498	11	derive	derive	VERB
ejpam-6775	498	12	the	the	DET
ejpam-6775	498	13	optimal	optimal	ADJ
ejpam-6775	498	14	control	control	NOUN
ejpam-6775	498	15	as	as	ADP
ejpam-6775	498	16	a	a	DET
ejpam-6775	498	17	combination	combination	NOUN
ejpam-6775	498	18	of	of	ADP
ejpam-6775	498	19	the	the	DET
ejpam-6775	498	20	state	state	NOUN
ejpam-6775	498	21	and	and	CCONJ
ejpam-6775	498	22	adjoint	adjoint	NOUN
ejpam-6775	498	23	variables	variable	NOUN
ejpam-6775	498	24	.	.	PUNCT
ejpam-6775	499	1	in	in	ADP
ejpam-6775	499	2	fact	fact	NOUN
ejpam-6775	499	3	,	,	PUNCT
ejpam-6775	499	4	the	the	DET
ejpam-6775	499	5	adjoint	adjoint	NOUN
ejpam-6775	499	6	variables	variable	NOUN
ejpam-6775	499	7	are	be	AUX
ejpam-6775	499	8	determined	determine	VERB
ejpam-6775	499	9	by	by	ADP
ejpam-6775	499	10	first	first	ADV
ejpam-6775	499	11	introducing	introduce	VERB
ejpam-6775	499	12	the	the	DET
ejpam-6775	499	13	sensitivity	sensitivity	NOUN
ejpam-6775	499	14	functions	function	NOUN
ejpam-6775	499	15	.	.	PUNCT
ejpam-6775	500	1	for	for	ADP
ejpam-6775	500	2	this	this	DET
ejpam-6775	500	3	purpose	purpose	NOUN
ejpam-6775	500	4	,	,	PUNCT
ejpam-6775	500	5	let	let	VERB
ejpam-6775	500	6	us	we	PRON
ejpam-6775	500	7	denote	denote	VERB
ejpam-6775	500	8	by	by	ADP
ejpam-6775	500	9	ψ	ψ	X
ejpam-6775	500	10	:	:	PUNCT
ejpam-6775	500	11	=	=	SYM
ejpam-6775	500	12	(	(	PUNCT
ejpam-6775	500	13	s	s	PROPN
ejpam-6775	500	14	,	,	PUNCT
ejpam-6775	500	15	v	v	NOUN
ejpam-6775	500	16	,	,	PUNCT
ejpam-6775	500	17	i	i	NOUN
ejpam-6775	500	18	)	)	PUNCT
ejpam-6775	500	19	and	and	CCONJ
ejpam-6775	500	20	define	define	VERB
ejpam-6775	500	21	the	the	DET
ejpam-6775	500	22	solution	solution	NOUN
ejpam-6775	500	23	map	map	NOUN
ejpam-6775	500	24	(	(	PUNCT
ejpam-6775	500	25	ξ	ξ	PROPN
ejpam-6775	500	26	,	,	PUNCT
ejpam-6775	500	27	α	α	NOUN
ejpam-6775	500	28	)	)	PUNCT
ejpam-6775	500	29	7→	7→	NUM
ejpam-6775	500	30	ψ(ξ	ψ(ξ	PROPN
ejpam-6775	500	31	,	,	PUNCT
ejpam-6775	500	32	α	α	NOUN
ejpam-6775	500	33	)	)	PUNCT
ejpam-6775	500	34	of	of	ADP
ejpam-6775	500	35	the	the	DET
ejpam-6775	500	36	system	system	NOUN
ejpam-6775	500	37	(	(	PUNCT
ejpam-6775	500	38	31	31	NUM
ejpam-6775	500	39	)	)	PUNCT
ejpam-6775	500	40	.	.	PUNCT
ejpam-6775	501	1	the	the	DET
ejpam-6775	501	2	sensitivity	sensitivity	NOUN
ejpam-6775	501	3	functions	function	NOUN
ejpam-6775	501	4	φs(t	φs(t	NOUN
ejpam-6775	501	5	)	)	PUNCT
ejpam-6775	501	6	,	,	PUNCT
ejpam-6775	501	7	φv	φv	PROPN
ejpam-6775	501	8	(	(	PUNCT
ejpam-6775	501	9	t	t	PROPN
ejpam-6775	501	10	)	)	PUNCT
ejpam-6775	501	11	and	and	CCONJ
ejpam-6775	501	12	φi(t	φi(t	NOUN
ejpam-6775	501	13	,	,	PUNCT
ejpam-6775	501	14	x	x	PRON
ejpam-6775	501	15	)	)	PUNCT
ejpam-6775	501	16	associated	associate	VERB
ejpam-6775	501	17	to	to	ADP
ejpam-6775	501	18	state	state	NOUN
ejpam-6775	501	19	variables	variable	NOUN
ejpam-6775	501	20	s(t	s(t	PROPN
ejpam-6775	501	21	)	)	PUNCT
ejpam-6775	501	22	,	,	PUNCT
ejpam-6775	501	23	v	v	X
ejpam-6775	501	24	(	(	PUNCT
ejpam-6775	501	25	t	t	PROPN
ejpam-6775	501	26	)	)	PUNCT
ejpam-6775	501	27	and	and	CCONJ
ejpam-6775	501	28	i(t	i(t	PROPN
ejpam-6775	501	29	,	,	PUNCT
ejpam-6775	501	30	x	x	X
ejpam-6775	501	31	)	)	PUNCT
ejpam-6775	501	32	are	be	AUX
ejpam-6775	501	33	obtained	obtain	VERB
ejpam-6775	501	34	by	by	ADP
ejpam-6775	501	35	the	the	DET
ejpam-6775	501	36	gâteaux	gâteaux	ADJ
ejpam-6775	501	37	derivatives	derivative	NOUN
ejpam-6775	501	38	ε−1[ψ(ξ	ε−1[ψ(ξ	PROPN
ejpam-6775	501	39	,	,	PUNCT
ejpam-6775	501	40	α	α	PROPN
ejpam-6775	501	41	+	+	NOUN
ejpam-6775	501	42	εg	εg	PROPN
ejpam-6775	501	43	)	)	PUNCT
ejpam-6775	501	44	−ψ(ξ	−ψ(ξ	PROPN
ejpam-6775	501	45	,	,	PUNCT
ejpam-6775	501	46	α	α	NOUN
ejpam-6775	501	47	)	)	PUNCT
ejpam-6775	501	48	]	]	PUNCT
ejpam-6775	502	1	→	→	SYM
ejpam-6775	502	2	⟨gδ	⟨gδ	NUM
ejpam-6775	502	3	,	,	PUNCT
ejpam-6775	502	4	φ⟩	φ⟩	NOUN
ejpam-6775	502	5	as	as	ADP
ejpam-6775	502	6	ε	ε	PROPN
ejpam-6775	502	7	→	→	SYM
ejpam-6775	502	8	0	0	NUM
ejpam-6775	502	9	+	+	CCONJ
ejpam-6775	502	10	in	in	ADP
ejpam-6775	502	11	l∞(0	l∞(0	NUM
ejpam-6775	502	12	,	,	PUNCT
ejpam-6775	502	13	t	t	PROPN
ejpam-6775	502	14	)	)	PUNCT
ejpam-6775	502	15	×	×	PROPN
ejpam-6775	502	16	l∞(ω	l∞(ω	NOUN
ejpam-6775	502	17	)	)	PUNCT
ejpam-6775	502	18	,	,	PUNCT
ejpam-6775	502	19	where	where	SCONJ
ejpam-6775	502	20	(	(	PUNCT
ejpam-6775	502	21	ξ	ξ	X
ejpam-6775	502	22	,	,	PUNCT
ejpam-6775	502	23	α	α	PROPN
ejpam-6775	502	24	+	+	NOUN
ejpam-6775	502	25	εg	εg	NOUN
ejpam-6775	502	26	)	)	PUNCT
ejpam-6775	502	27	∈	∈	PROPN
ejpam-6775	502	28	d	d	NOUN
ejpam-6775	502	29	and	and	CCONJ
ejpam-6775	502	30	(	(	PUNCT
ejpam-6775	502	31	g	g	NOUN
ejpam-6775	502	32	,	,	PUNCT
ejpam-6775	502	33	p	p	NOUN
ejpam-6775	502	34	)	)	PUNCT
ejpam-6775	502	35	∈	∈	PROPN
ejpam-6775	502	36	l∞(0	l∞(0	PRON
ejpam-6775	502	37	,	,	PUNCT
ejpam-6775	502	38	t	t	PROPN
ejpam-6775	502	39	)	)	PUNCT
ejpam-6775	502	40	×	×	NOUN
ejpam-6775	502	41	l∞(ω	l∞(ω	NOUN
ejpam-6775	502	42	)	)	PUNCT
ejpam-6775	502	43	.	.	PUNCT
ejpam-6775	503	1	by	by	ADP
ejpam-6775	503	2	using	use	VERB
ejpam-6775	503	3	the	the	DET
ejpam-6775	503	4	explicit	explicit	ADJ
ejpam-6775	503	5	expression	expression	NOUN
ejpam-6775	503	6	of	of	ADP
ejpam-6775	503	7	state	state	NOUN
ejpam-6775	503	8	variables	variable	NOUN
ejpam-6775	503	9	of	of	ADP
ejpam-6775	503	10	system	system	NOUN
ejpam-6775	503	11	(	(	PUNCT
ejpam-6775	503	12	31	31	NUM
ejpam-6775	503	13	)	)	PUNCT
ejpam-6775	503	14	,	,	PUNCT
ejpam-6775	503	15	it	it	PRON
ejpam-6775	503	16	is	be	AUX
ejpam-6775	503	17	easy	easy	ADJ
ejpam-6775	503	18	to	to	PART
ejpam-6775	503	19	establish	establish	VERB
ejpam-6775	503	20	that	that	SCONJ
ejpam-6775	503	21	the	the	DET
ejpam-6775	503	22	map	map	NOUN
ejpam-6775	503	23	(	(	PUNCT
ejpam-6775	503	24	ξ	ξ	PROPN
ejpam-6775	503	25	,	,	PUNCT
ejpam-6775	503	26	α	α	NOUN
ejpam-6775	503	27	)	)	PUNCT
ejpam-6775	503	28	7→	7→	NUM
ejpam-6775	503	29	ψ(ξ	ψ(ξ	PROPN
ejpam-6775	503	30	,	,	PUNCT
ejpam-6775	503	31	α	α	X
ejpam-6775	503	32	)	)	PUNCT
ejpam-6775	503	33	is	be	AUX
ejpam-6775	503	34	lipschitz	lipschitz	NOUN
ejpam-6775	503	35	in	in	ADP
ejpam-6775	503	36	l∞.	l∞.	ADV
ejpam-6775	503	37	then	then	ADV
ejpam-6775	503	38	,	,	PUNCT
ejpam-6775	503	39	according	accord	VERB
ejpam-6775	503	40	to	to	ADP
ejpam-6775	503	41	result	result	NOUN
ejpam-6775	503	42	in	in	ADP
ejpam-6775	503	43	barbu	barbu	PROPN
ejpam-6775	503	44	[	[	X
ejpam-6775	503	45	44	44	NUM
ejpam-6775	503	46	]	]	PUNCT
ejpam-6775	503	47	page	page	NOUN
ejpam-6775	503	48	17	17	NUM
ejpam-6775	503	49	,	,	PUNCT
ejpam-6775	503	50	the	the	DET
ejpam-6775	503	51	existence	existence	NOUN
ejpam-6775	503	52	of	of	ADP
ejpam-6775	503	53	sensitivity	sensitivity	NOUN
ejpam-6775	503	54	functions	function	NOUN
ejpam-6775	503	55	is	be	AUX
ejpam-6775	503	56	guaranteed	guarantee	VERB
ejpam-6775	503	57	.	.	PUNCT
ejpam-6775	504	1	in	in	ADP
ejpam-6775	504	2	addition	addition	NOUN
ejpam-6775	504	3	,	,	PUNCT
ejpam-6775	504	4	the	the	DET
ejpam-6775	504	5	sensitivity	sensitivity	NOUN
ejpam-6775	504	6	functions	function	NOUN
ejpam-6775	504	7	satisfy	satisfy	VERB
ejpam-6775	504	8	the	the	DET
ejpam-6775	504	9	following	follow	VERB
ejpam-6775	504	10	system	system	NOUN
ejpam-6775	504	11	of	of	ADP
ejpam-6775	504	12	differential	differential	ADJ
ejpam-6775	504	13	equations	equation	NOUN
ejpam-6775	504	14	:	:	PUNCT
ejpam-6775	504	15	dφs	dφs	VERB
ejpam-6775	504	16	dt	dt	NOUN
ejpam-6775	504	17	=	=	SYM
ejpam-6775	504	18	−t	−t	PROPN
ejpam-6775	504	19	(	(	PUNCT
ejpam-6775	504	20	βφi	βφi	PROPN
ejpam-6775	504	21	)	)	PUNCT
ejpam-6775	505	1	+	+	NUM
ejpam-6775	505	2	t	t	PROPN
ejpam-6775	505	3	(	(	PUNCT
ejpam-6775	505	4	αφi	αφi	PROPN
ejpam-6775	505	5	)	)	PUNCT
ejpam-6775	506	1	+	+	NUM
ejpam-6775	506	2	t	t	NOUN
ejpam-6775	506	3	(	(	PUNCT
ejpam-6775	506	4	pi)−	pi)−	NOUN
ejpam-6775	506	5	qs	qs	ADP
ejpam-6775	506	6	−	−	PROPN
ejpam-6775	507	1	[	[	X
ejpam-6775	507	2	t	t	X
ejpam-6775	507	3	(	(	PUNCT
ejpam-6775	507	4	βi	βi	PROPN
ejpam-6775	507	5	)	)	PUNCT
ejpam-6775	507	6	+	+	CCONJ
ejpam-6775	508	1	ξ	ξ	X
ejpam-6775	508	2	+	+	CCONJ
ejpam-6775	508	3	µ]φs	µ]φ	NOUN
ejpam-6775	508	4	,	,	PUNCT
ejpam-6775	508	5	dφv	dφv	ADV
ejpam-6775	508	6	dt	dt	X
ejpam-6775	508	7	=	=	NOUN
ejpam-6775	508	8	ξφs	ξφs	NOUN
ejpam-6775	508	9	+	+	CCONJ
ejpam-6775	508	10	qs	qs	PROPN
ejpam-6775	508	11	−mt	−mt	NOUN
ejpam-6775	508	12	(	(	PUNCT
ejpam-6775	508	13	βi)φv	βi)φv	PUNCT
ejpam-6775	508	14	−mt	−mt	NOUN
ejpam-6775	508	15	(	(	PUNCT
ejpam-6775	508	16	βφi)−	βφi)−	PUNCT
ejpam-6775	508	17	µφv	µφv	INTJ
ejpam-6775	508	18	,	,	PUNCT
ejpam-6775	508	19	∂tφi	∂tφi	X
ejpam-6775	508	20	+	+	PUNCT
ejpam-6775	508	21	∂xφi	∂xφi	X
ejpam-6775	508	22	=	=	SYM
ejpam-6775	508	23	−[µ+	−[µ+	PROPN
ejpam-6775	508	24	δ	δ	PROPN
ejpam-6775	508	25	+	+	CCONJ
ejpam-6775	508	26	α]φi	α]φi	NUM
ejpam-6775	508	27	−	−	NUM
ejpam-6775	508	28	pi	pi	NOUN
ejpam-6775	508	29	,	,	PUNCT
ejpam-6775	508	30	φi(t	φi(t	PRON
ejpam-6775	508	31	,	,	PUNCT
ejpam-6775	508	32	0	0	NUM
ejpam-6775	508	33	)	)	PUNCT
ejpam-6775	508	34	=	=	NOUN
ejpam-6775	509	1	[	[	X
ejpam-6775	509	2	s	s	X
ejpam-6775	509	3	+	+	NOUN
ejpam-6775	509	4	mv	mv	PROPN
ejpam-6775	509	5	]	]	X
ejpam-6775	509	6	t	t	PROPN
ejpam-6775	509	7	(	(	PUNCT
ejpam-6775	509	8	βφi	βφi	PROPN
ejpam-6775	509	9	)	)	PUNCT
ejpam-6775	509	10	+	+	CCONJ
ejpam-6775	510	1	[	[	X
ejpam-6775	510	2	sφs	sφs	NOUN
ejpam-6775	510	3	+	+	NOUN
ejpam-6775	510	4	mφv	mφv	NOUN
ejpam-6775	510	5	]	]	X
ejpam-6775	510	6	t	t	PROPN
ejpam-6775	510	7	(	(	PUNCT
ejpam-6775	510	8	βi	βi	PROPN
ejpam-6775	510	9	)	)	PUNCT
ejpam-6775	510	10	.	.	PUNCT
ejpam-6775	510	11	(	(	PUNCT
ejpam-6775	510	12	52	52	NUM
ejpam-6775	510	13	)	)	PUNCT
ejpam-6775	510	14	next	next	ADV
ejpam-6775	510	15	,	,	PUNCT
ejpam-6775	510	16	we	we	PRON
ejpam-6775	510	17	introduce	introduce	VERB
ejpam-6775	510	18	the	the	DET
ejpam-6775	510	19	adjoint	adjoint	NOUN
ejpam-6775	510	20	variables	variable	NOUN
ejpam-6775	510	21	zs(t	zs(t	NUM
ejpam-6775	510	22	)	)	PUNCT
ejpam-6775	510	23	,	,	PUNCT
ejpam-6775	510	24	zv	zv	PROPN
ejpam-6775	510	25	(	(	PUNCT
ejpam-6775	510	26	t	t	PROPN
ejpam-6775	510	27	)	)	PUNCT
ejpam-6775	510	28	and	and	CCONJ
ejpam-6775	510	29	zi(t	zi(t	NOUN
ejpam-6775	510	30	,	,	PUNCT
ejpam-6775	510	31	x	x	X
ejpam-6775	510	32	)	)	PUNCT
ejpam-6775	510	33	corresponding	correspond	VERB
ejpam-6775	510	34	to	to	ADP
ejpam-6775	510	35	the	the	DET
ejpam-6775	510	36	state	state	NOUN
ejpam-6775	510	37	variables	variable	NOUN
ejpam-6775	510	38	s(t	s(t	PROPN
ejpam-6775	510	39	)	)	PUNCT
ejpam-6775	510	40	,	,	PUNCT
ejpam-6775	510	41	v	v	X
ejpam-6775	510	42	(	(	PUNCT
ejpam-6775	510	43	t	t	PROPN
ejpam-6775	510	44	)	)	PUNCT
ejpam-6775	510	45	and	and	CCONJ
ejpam-6775	510	46	i(t	i(t	PROPN
ejpam-6775	510	47	,	,	PUNCT
ejpam-6775	510	48	x	x	NOUN
ejpam-6775	510	49	)	)	PUNCT
ejpam-6775	510	50	of	of	ADP
ejpam-6775	510	51	system	system	NOUN
ejpam-6775	510	52	(	(	PUNCT
ejpam-6775	510	53	31	31	NUM
ejpam-6775	510	54	)	)	PUNCT
ejpam-6775	510	55	,	,	PUNCT
ejpam-6775	510	56	respectively	respectively	ADV
ejpam-6775	510	57	.	.	PUNCT
ejpam-6775	511	1	the	the	DET
ejpam-6775	511	2	adjoint	adjoint	NOUN
ejpam-6775	511	3	system	system	NOUN
ejpam-6775	511	4	satisfied	satisfy	VERB
ejpam-6775	511	5	by	by	ADP
ejpam-6775	511	6	the	the	DET
ejpam-6775	511	7	adjoint	adjoint	NOUN
ejpam-6775	511	8	variables	variable	NOUN
ejpam-6775	511	9	is	be	AUX
ejpam-6775	511	10	then	then	ADV
ejpam-6775	511	11	derived	derive	VERB
ejpam-6775	511	12	by	by	ADP
ejpam-6775	511	13	using	use	VERB
ejpam-6775	511	14	the	the	DET
ejpam-6775	511	15	adjoint	adjoint	NOUN
ejpam-6775	511	16	operator	operator	NOUN
ejpam-6775	511	17	associated	associate	VERB
ejpam-6775	511	18	with	with	ADP
ejpam-6775	511	19	the	the	DET
ejpam-6775	511	20	sensitivity	sensitivity	NOUN
ejpam-6775	511	21	system	system	NOUN
ejpam-6775	511	22	(	(	PUNCT
ejpam-6775	511	23	35	35	NUM
ejpam-6775	511	24	)	)	PUNCT
ejpam-6775	511	25	together	together	ADV
ejpam-6775	511	26	with	with	ADP
ejpam-6775	511	27	appropriated	appropriate	VERB
ejpam-6775	511	28	transversality	transversality	NOUN
ejpam-6775	511	29	and	and	CCONJ
ejpam-6775	511	30	boundary	boundary	ADJ
ejpam-6775	511	31	conditions	condition	NOUN
ejpam-6775	511	32	(	(	PUNCT
ejpam-6775	511	33	see	see	VERB
ejpam-6775	511	34	for	for	ADP
ejpam-6775	511	35	instance	instance	NOUN
ejpam-6775	511	36	[	[	X
ejpam-6775	511	37	28	28	NUM
ejpam-6775	511	38	]	]	PUNCT
ejpam-6775	511	39	for	for	ADP
ejpam-6775	511	40	more	more	ADJ
ejpam-6775	511	41	details	detail	NOUN
ejpam-6775	511	42	)	)	PUNCT
ejpam-6775	511	43	.	.	PUNCT
ejpam-6775	512	1	specifically	specifically	ADV
ejpam-6775	512	2	,	,	PUNCT
ejpam-6775	512	3	the	the	DET
ejpam-6775	512	4	adjoint	adjoint	NOUN
ejpam-6775	512	5	system	system	NOUN
ejpam-6775	512	6	is	be	AUX
ejpam-6775	512	7	given	give	VERB
ejpam-6775	512	8	by	by	ADP
ejpam-6775	512	9	:	:	PUNCT
ejpam-6775	512	10	dzs	dzs	NOUN
ejpam-6775	512	11	dt	dt	NOUN
ejpam-6775	513	1	=	=	PUNCT
ejpam-6775	514	1	[	[	X
ejpam-6775	514	2	−t	−t	NOUN
ejpam-6775	514	3	′(βi	′(βi	NOUN
ejpam-6775	514	4	)	)	PUNCT
ejpam-6775	515	1	+	+	PUNCT
ejpam-6775	515	2	µ]zs	µ]zs	NUM
ejpam-6775	516	1	+	+	ADJ
ejpam-6775	516	2	ξ(t)[zs	ξ(t)[z	NOUN
ejpam-6775	516	3	−	−	NOUN
ejpam-6775	517	1	zv	zv	NOUN
ejpam-6775	517	2	]	]	PUNCT
ejpam-6775	517	3	−	−	PROPN
ejpam-6775	517	4	zi(0	zi(0	PROPN
ejpam-6775	517	5	,	,	PUNCT
ejpam-6775	517	6	t	t	PROPN
ejpam-6775	517	7	)	)	PUNCT
ejpam-6775	517	8	t	t	PROPN
ejpam-6775	517	9	(	(	PUNCT
ejpam-6775	517	10	βi	βi	PROPN
ejpam-6775	517	11	)	)	PUNCT
ejpam-6775	517	12	,	,	PUNCT
ejpam-6775	517	13	dzv	dzv	NOUN
ejpam-6775	517	14	dt	dt	NOUN
ejpam-6775	517	15	=	=	PUNCT
ejpam-6775	518	1	[	[	X
ejpam-6775	518	2	mt	mt	PROPN
ejpam-6775	518	3	′(βi	′(βi	PROPN
ejpam-6775	518	4	)	)	PUNCT
ejpam-6775	519	1	+	+	CCONJ
ejpam-6775	520	1	µ]zv	µ]zv	NUM
ejpam-6775	520	2	−mt	−mt	NOUN
ejpam-6775	520	3	(	(	PUNCT
ejpam-6775	520	4	βi)zi(0	βi)zi(0	PROPN
ejpam-6775	520	5	,	,	PUNCT
ejpam-6775	520	6	0	0	NUM
ejpam-6775	520	7	)	)	PUNCT
ejpam-6775	520	8	,	,	PUNCT
ejpam-6775	520	9	∂tzi	∂tzi	ADJ
ejpam-6775	520	10	+	+	PUNCT
ejpam-6775	520	11	∂xzi	∂xzi	PUNCT
ejpam-6775	520	12	=	=	SYM
ejpam-6775	520	13	−χ(x	−χ(x	PROPN
ejpam-6775	520	14	)	)	PUNCT
ejpam-6775	520	15	+	+	NUM
ejpam-6775	520	16	β(i)s	β(i)	NOUN
ejpam-6775	520	17	−	−	PROPN
ejpam-6775	520	18	α(t	α(t	PROPN
ejpam-6775	520	19	,	,	PUNCT
ejpam-6775	520	20	x)]zs	x)]zs	PUNCT
ejpam-6775	521	1	+	+	NOUN
ejpam-6775	521	2	mβ(i)zv	mβ(i)zv	NOUN
ejpam-6775	521	3	−	−	PROPN
ejpam-6775	522	1	[	[	X
ejpam-6775	522	2	s	s	X
ejpam-6775	522	3	+	+	NOUN
ejpam-6775	522	4	mv	mv	NOUN
ejpam-6775	522	5	]	]	X
ejpam-6775	522	6	β(x)zi(x	β(x)zi(x	NOUN
ejpam-6775	522	7	,	,	PUNCT
ejpam-6775	522	8	0	0	NUM
ejpam-6775	522	9	)	)	PUNCT
ejpam-6775	523	1	+	+	CCONJ
ejpam-6775	524	1	[	[	X
ejpam-6775	524	2	µ+	µ+	X
ejpam-6775	524	3	δ(x	δ(x	ADJ
ejpam-6775	524	4	)	)	PUNCT
ejpam-6775	524	5	+	+	CCONJ
ejpam-6775	524	6	α(t	α(t	PROPN
ejpam-6775	524	7	,	,	PUNCT
ejpam-6775	524	8	x)]zi	x)]zi	X
ejpam-6775	524	9	,	,	PUNCT
ejpam-6775	524	10	(	(	PUNCT
ejpam-6775	524	11	53	53	NUM
ejpam-6775	524	12	)	)	PUNCT
ejpam-6775	524	13	endowed	endow	VERB
ejpam-6775	524	14	with	with	ADP
ejpam-6775	524	15	the	the	DET
ejpam-6775	524	16	following	follow	VERB
ejpam-6775	524	17	transversality	transversality	NOUN
ejpam-6775	524	18	and	and	CCONJ
ejpam-6775	524	19	boundary	boundary	ADJ
ejpam-6775	524	20	conditions	condition	NOUN
ejpam-6775	524	21	for	for	ADP
ejpam-6775	524	22	(	(	PUNCT
ejpam-6775	524	23	t	t	PROPN
ejpam-6775	524	24	,	,	PUNCT
ejpam-6775	524	25	x	x	X
ejpam-6775	524	26	)	)	PUNCT
ejpam-6775	524	27	∈	∈	PROPN
ejpam-6775	524	28	q	q	NOUN
ejpam-6775	524	29	:	:	PUNCT
ejpam-6775	524	30	zs(t	zs(t	NUM
ejpam-6775	524	31	)	)	PUNCT
ejpam-6775	524	32	=	=	PUNCT
ejpam-6775	524	33	0	0	NUM
ejpam-6775	524	34	,	,	PUNCT
ejpam-6775	524	35	zv	zv	INTJ
ejpam-6775	524	36	(	(	PUNCT
ejpam-6775	524	37	t	t	PROPN
ejpam-6775	524	38	)	)	PUNCT
ejpam-6775	524	39	=	=	SYM
ejpam-6775	524	40	0	0	NUM
ejpam-6775	524	41	,	,	PUNCT
ejpam-6775	524	42	zi(t	zi(t	NOUN
ejpam-6775	524	43	,	,	PUNCT
ejpam-6775	524	44	x	x	X
ejpam-6775	524	45	)	)	PUNCT
ejpam-6775	524	46	=	=	SYM
ejpam-6775	524	47	0	0	NUM
ejpam-6775	524	48	,	,	PUNCT
ejpam-6775	524	49	zi(t	zi(t	NOUN
ejpam-6775	524	50	,	,	PUNCT
ejpam-6775	524	51	x	x	X
ejpam-6775	524	52	)	)	PUNCT
ejpam-6775	524	53	=	=	SYM
ejpam-6775	524	54	0	0	X
ejpam-6775	524	55	.	.	PUNCT
ejpam-6775	525	1	(	(	PUNCT
ejpam-6775	525	2	54	54	NUM
ejpam-6775	525	3	)	)	PUNCT
ejpam-6775	525	4	the	the	DET
ejpam-6775	525	5	existence	existence	NOUN
ejpam-6775	525	6	of	of	ADP
ejpam-6775	525	7	the	the	DET
ejpam-6775	525	8	adjoint	adjoint	NOUN
ejpam-6775	525	9	solutions	solution	NOUN
ejpam-6775	525	10	can	can	AUX
ejpam-6775	525	11	be	be	AUX
ejpam-6775	525	12	proved	prove	VERB
ejpam-6775	525	13	thanks	thank	NOUN
ejpam-6775	525	14	to	to	ADP
ejpam-6775	525	15	a	a	DET
ejpam-6775	525	16	fixed	fix	VERB
ejpam-6775	525	17	point	point	NOUN
ejpam-6775	525	18	argument	argument	NOUN
ejpam-6775	525	19	mapping	mapping	NOUN
ejpam-6775	525	20	principle	principle	NOUN
ejpam-6775	525	21	,	,	PUNCT
ejpam-6775	525	22	see	see	VERB
ejpam-6775	525	23	for	for	ADP
ejpam-6775	525	24	instance	instance	NOUN
ejpam-6775	525	25	[	[	X
ejpam-6775	525	26	44	44	NUM
ejpam-6775	525	27	]	]	PUNCT
ejpam-6775	525	28	.	.	PUNCT
ejpam-6775	526	1	in	in	ADP
ejpam-6775	526	2	what	what	PRON
ejpam-6775	526	3	follows	follow	VERB
ejpam-6775	526	4	,	,	PUNCT
ejpam-6775	526	5	we	we	PRON
ejpam-6775	526	6	employ	employ	VERB
ejpam-6775	526	7	tangent	tangent	NOUN
ejpam-6775	526	8	normal	normal	ADJ
ejpam-6775	526	9	cone	cone	NOUN
ejpam-6775	526	10	techniques	technique	NOUN
ejpam-6775	526	11	in	in	ADP
ejpam-6775	526	12	nonlinear	nonlinear	ADJ
ejpam-6775	526	13	functional	functional	ADJ
ejpam-6775	526	14	analysis	analysis	NOUN
ejpam-6775	526	15	(	(	PUNCT
ejpam-6775	526	16	see	see	VERB
ejpam-6775	526	17	[	[	X
ejpam-6775	526	18	29	29	NUM
ejpam-6775	526	19	,	,	PUNCT
ejpam-6775	526	20	44	44	NUM
ejpam-6775	526	21	,	,	PUNCT
ejpam-6775	526	22	45	45	NUM
ejpam-6775	526	23	]	]	PUNCT
ejpam-6775	526	24	)	)	PUNCT
ejpam-6775	526	25	to	to	PART
ejpam-6775	526	26	deduce	deduce	VERB
ejpam-6775	526	27	the	the	DET
ejpam-6775	526	28	first	first	ADJ
ejpam-6775	526	29	–	–	PUNCT
ejpam-6775	526	30	order	order	NOUN
ejpam-6775	526	31	j.	j.	PROPN
ejpam-6775	526	32	leo	leo	PROPN
ejpam-6775	526	33	amalraj	amalraj	PROPN
ejpam-6775	526	34	et	et	PROPN
ejpam-6775	526	35	al	al	PROPN
ejpam-6775	526	36	.	.	PUNCT
ejpam-6775	526	37	/	/	SYM
ejpam-6775	526	38	eur	eur	PROPN
ejpam-6775	526	39	.	.	PUNCT
ejpam-6775	527	1	j.	j.	PROPN
ejpam-6775	527	2	pure	pure	PROPN
ejpam-6775	527	3	appl	appl	PROPN
ejpam-6775	527	4	.	.	PROPN
ejpam-6775	527	5	math	math	PROPN
ejpam-6775	527	6	,	,	PUNCT
ejpam-6775	527	7	18	18	NUM
ejpam-6775	527	8	(	(	PUNCT
ejpam-6775	527	9	4	4	NUM
ejpam-6775	527	10	)	)	PUNCT
ejpam-6775	527	11	(	(	PUNCT
ejpam-6775	527	12	2025	2025	NUM
ejpam-6775	527	13	)	)	PUNCT
ejpam-6775	527	14	,	,	PUNCT
ejpam-6775	527	15	6775	6775	NUM
ejpam-6775	527	16	20	20	NUM
ejpam-6775	527	17	of	of	ADP
ejpam-6775	527	18	32	32	NUM
ejpam-6775	527	19	necessary	necessary	ADJ
ejpam-6775	527	20	conditions	condition	NOUN
ejpam-6775	527	21	for	for	ADP
ejpam-6775	527	22	optimality	optimality	NOUN
ejpam-6775	527	23	of	of	ADP
ejpam-6775	527	24	optimal	optimal	ADJ
ejpam-6775	527	25	control	control	NOUN
ejpam-6775	527	26	.	.	PUNCT
ejpam-6775	528	1	to	to	PART
ejpam-6775	528	2	do	do	VERB
ejpam-6775	528	3	so	so	ADV
ejpam-6775	528	4	,	,	PUNCT
ejpam-6775	528	5	let	let	VERB
ejpam-6775	528	6	us	we	PRON
ejpam-6775	528	7	denote	denote	VERB
ejpam-6775	528	8	by	by	ADP
ejpam-6775	528	9	td(ξ	td(ξ	NUM
ejpam-6775	528	10	,	,	PUNCT
ejpam-6775	528	11	α	α	NOUN
ejpam-6775	528	12	)	)	PUNCT
ejpam-6775	528	13	and	and	CCONJ
ejpam-6775	528	14	nd(ξ	nd(ξ	NOUN
ejpam-6775	528	15	,	,	PUNCT
ejpam-6775	528	16	α	α	X
ejpam-6775	528	17	)	)	PUNCT
ejpam-6775	528	18	,	,	PUNCT
ejpam-6775	528	19	the	the	DET
ejpam-6775	528	20	tangent	tangent	NOUN
ejpam-6775	528	21	and	and	CCONJ
ejpam-6775	528	22	normal	normal	ADJ
ejpam-6775	528	23	cone	cone	NOUN
ejpam-6775	528	24	of	of	ADP
ejpam-6775	528	25	space	space	NOUN
ejpam-6775	528	26	d	d	NOUN
ejpam-6775	528	27	at	at	ADP
ejpam-6775	528	28	a	a	DET
ejpam-6775	528	29	control	control	NOUN
ejpam-6775	528	30	pair	pair	NOUN
ejpam-6775	528	31	(	(	PUNCT
ejpam-6775	528	32	ξ	ξ	PROPN
ejpam-6775	528	33	,	,	PUNCT
ejpam-6775	528	34	α	α	NOUN
ejpam-6775	528	35	)	)	PUNCT
ejpam-6775	528	36	respectively	respectively	ADV
ejpam-6775	528	37	.	.	PUNCT
ejpam-6775	529	1	we	we	PRON
ejpam-6775	529	2	have	have	VERB
ejpam-6775	529	3	the	the	DET
ejpam-6775	529	4	following	follow	VERB
ejpam-6775	529	5	result	result	NOUN
ejpam-6775	529	6	:	:	PUNCT
ejpam-6775	529	7	theorem	theorem	VERB
ejpam-6775	529	8	7	7	NUM
ejpam-6775	529	9	.	.	PUNCT
ejpam-6775	530	1	let	let	VERB
ejpam-6775	530	2	(	(	PUNCT
ejpam-6775	530	3	ξ	ξ	X
ejpam-6775	530	4	,	,	PUNCT
ejpam-6775	530	5	α	α	NOUN
ejpam-6775	530	6	)	)	PUNCT
ejpam-6775	530	7	∈	∈	PROPN
ejpam-6775	531	1	d	d	AUX
ejpam-6775	531	2	be	be	AUX
ejpam-6775	531	3	an	an	DET
ejpam-6775	531	4	optimal	optimal	ADJ
ejpam-6775	531	5	admissible	admissible	ADJ
ejpam-6775	531	6	solution	solution	NOUN
ejpam-6775	531	7	of	of	ADP
ejpam-6775	531	8	the	the	DET
ejpam-6775	531	9	optimization	optimization	NOUN
ejpam-6775	531	10	problem	problem	NOUN
ejpam-6775	531	11	(	(	PUNCT
ejpam-6775	531	12	ocp	ocp	PROPN
ejpam-6775	531	13	)	)	PUNCT
ejpam-6775	531	14	to	to	PART
ejpam-6775	531	15	which	which	PRON
ejpam-6775	531	16	the	the	DET
ejpam-6775	531	17	trajectory	trajectory	NOUN
ejpam-6775	531	18	(	(	PUNCT
ejpam-6775	531	19	s(t	s(t	PROPN
ejpam-6775	531	20	)	)	PUNCT
ejpam-6775	531	21	,	,	PUNCT
ejpam-6775	531	22	v	v	X
ejpam-6775	531	23	(	(	PUNCT
ejpam-6775	531	24	t	t	PROPN
ejpam-6775	531	25	)	)	PUNCT
ejpam-6775	531	26	,	,	PUNCT
ejpam-6775	531	27	i(t	i(t	PROPN
ejpam-6775	531	28	,	,	PUNCT
ejpam-6775	531	29	x	x	NOUN
ejpam-6775	531	30	)	)	PUNCT
ejpam-6775	531	31	)	)	PUNCT
ejpam-6775	531	32	is	be	AUX
ejpam-6775	531	33	associated	associate	VERB
ejpam-6775	531	34	and	and	CCONJ
ejpam-6775	531	35	let	let	VERB
ejpam-6775	531	36	(	(	PUNCT
ejpam-6775	531	37	zs(t	zs(t	NUM
ejpam-6775	531	38	)	)	PUNCT
ejpam-6775	531	39	,	,	PUNCT
ejpam-6775	531	40	zv	zv	PROPN
ejpam-6775	531	41	(	(	PUNCT
ejpam-6775	531	42	t	t	PROPN
ejpam-6775	531	43	)	)	PUNCT
ejpam-6775	531	44	,	,	PUNCT
ejpam-6775	531	45	zi(t	zi(t	NOUN
ejpam-6775	531	46	,	,	PUNCT
ejpam-6775	531	47	x	x	NOUN
ejpam-6775	531	48	)	)	PUNCT
ejpam-6775	531	49	)	)	PUNCT
ejpam-6775	531	50	be	be	AUX
ejpam-6775	531	51	an	an	DET
ejpam-6775	531	52	adjoint	adjoint	NOUN
ejpam-6775	531	53	vector	vector	NOUN
ejpam-6775	531	54	satisfying	satisfy	VERB
ejpam-6775	531	55	the	the	DET
ejpam-6775	531	56	system	system	NOUN
ejpam-6775	531	57	(	(	PUNCT
ejpam-6775	531	58	36)–(37	36)–(37	NUM
ejpam-6775	531	59	)	)	PUNCT
ejpam-6775	531	60	.	.	PUNCT
ejpam-6775	532	1	then	then	ADV
ejpam-6775	532	2	,	,	PUNCT
ejpam-6775	532	3	we	we	PRON
ejpam-6775	532	4	have	have	VERB
ejpam-6775	532	5	the	the	DET
ejpam-6775	532	6	following	follow	VERB
ejpam-6775	532	7	optimal	optimal	ADJ
ejpam-6775	532	8	control	control	NOUN
ejpam-6775	532	9	structure	structure	NOUN
ejpam-6775	532	10	:	:	PUNCT
ejpam-6775	532	11	ξ(t	ξ(t	X
ejpam-6775	532	12	)	)	PUNCT
ejpam-6775	532	13	=	=	SYM
ejpam-6775	532	14	p1	p1	NOUN
ejpam-6775	532	15	[	[	PUNCT
ejpam-6775	532	16	(	(	PUNCT
ejpam-6775	532	17	zs(t)−	zs(t)−	PROPN
ejpam-6775	532	18	zv	zv	PROPN
ejpam-6775	532	19	(	(	PUNCT
ejpam-6775	532	20	t))s(t	t))s(t	PROPN
ejpam-6775	532	21	)	)	PUNCT
ejpam-6775	532	22	c1	c1	NOUN
ejpam-6775	532	23	]	]	PUNCT
ejpam-6775	532	24	,	,	PUNCT
ejpam-6775	532	25	α(t	α(t	PROPN
ejpam-6775	532	26	,	,	PUNCT
ejpam-6775	532	27	x	x	NOUN
ejpam-6775	532	28	)	)	PUNCT
ejpam-6775	532	29	=	=	SYM
ejpam-6775	532	30	p2	p2	X
ejpam-6775	532	31	[	[	PUNCT
ejpam-6775	532	32	[	[	X
ejpam-6775	532	33	−zs(t	−zs(t	X
ejpam-6775	532	34	)	)	PUNCT
ejpam-6775	532	35	+	+	NUM
ejpam-6775	532	36	zi(t	zi(t	NOUN
ejpam-6775	532	37	,	,	PUNCT
ejpam-6775	532	38	x)]i(t	x)]i(t	PROPN
ejpam-6775	532	39	,	,	PUNCT
ejpam-6775	532	40	x	x	X
ejpam-6775	532	41	)	)	PUNCT
ejpam-6775	532	42	c2	c2	PROPN
ejpam-6775	532	43	]	]	PUNCT
ejpam-6775	532	44	,	,	PUNCT
ejpam-6775	532	45	(	(	PUNCT
ejpam-6775	532	46	55	55	NUM
ejpam-6775	532	47	)	)	PUNCT
ejpam-6775	532	48	where	where	SCONJ
ejpam-6775	532	49	the	the	DET
ejpam-6775	532	50	projection	projection	NOUN
ejpam-6775	532	51	maps	map	NOUN
ejpam-6775	532	52	pj(v	pj(v	NOUN
ejpam-6775	532	53	)	)	PUNCT
ejpam-6775	532	54	=	=	SYM
ejpam-6775	532	55	min{max{0	min{max{0	X
ejpam-6775	532	56	,	,	PUNCT
ejpam-6775	532	57	v	v	NOUN
ejpam-6775	532	58	}	}	PUNCT
ejpam-6775	532	59	,	,	PUNCT
ejpam-6775	532	60	ξmax	ξmax	ADV
ejpam-6775	532	61	}	}	PUNCT
ejpam-6775	532	62	for	for	ADP
ejpam-6775	532	63	j	j	PROPN
ejpam-6775	532	64	=	=	SYM
ejpam-6775	532	65	1	1	NUM
ejpam-6775	532	66	,	,	PUNCT
ejpam-6775	532	67	2	2	NUM
ejpam-6775	532	68	,	,	PUNCT
ejpam-6775	532	69	with	with	ADP
ejpam-6775	532	70	ξmax	ξmax	NOUN
ejpam-6775	532	71	and	and	CCONJ
ejpam-6775	532	72	αmax	αmax	NOUN
ejpam-6775	532	73	are	be	AUX
ejpam-6775	532	74	upper	upper	ADJ
ejpam-6775	532	75	bounds	bound	NOUN
ejpam-6775	532	76	.	.	PUNCT
ejpam-6775	533	1	proof	proof	NOUN
ejpam-6775	533	2	.	.	PUNCT
ejpam-6775	534	1	for	for	ADP
ejpam-6775	534	2	any	any	DET
ejpam-6775	534	3	element	element	NOUN
ejpam-6775	534	4	of	of	ADP
ejpam-6775	534	5	the	the	DET
ejpam-6775	534	6	tangent	tangent	ADJ
ejpam-6775	534	7	cone	cone	NOUN
ejpam-6775	534	8	(	(	PUNCT
ejpam-6775	534	9	q	q	NOUN
ejpam-6775	534	10	,	,	PUNCT
ejpam-6775	534	11	p	p	NOUN
ejpam-6775	534	12	)	)	PUNCT
ejpam-6775	534	13	∈	∈	PROPN
ejpam-6775	534	14	td(ξ	td(ξ	NUM
ejpam-6775	534	15	,	,	PUNCT
ejpam-6775	534	16	α	α	NOUN
ejpam-6775	534	17	)	)	PUNCT
ejpam-6775	534	18	and	and	CCONJ
ejpam-6775	534	19	let	let	VERB
ejpam-6775	534	20	us	we	PRON
ejpam-6775	534	21	denote	denote	VERB
ejpam-6775	534	22	by	by	ADP
ejpam-6775	534	23	(	(	PUNCT
ejpam-6775	534	24	ξε	ξε	NOUN
ejpam-6775	534	25	,	,	PUNCT
ejpam-6775	534	26	αε	αε	ADP
ejpam-6775	534	27	)	)	PUNCT
ejpam-6775	534	28	:	:	PUNCT
ejpam-6775	535	1	=	=	SYM
ejpam-6775	535	2	(	(	PUNCT
ejpam-6775	535	3	ξ	ξ	PROPN
ejpam-6775	535	4	,	,	PUNCT
ejpam-6775	535	5	α)+ε(q	α)+ε(q	NOUN
ejpam-6775	535	6	,	,	PUNCT
ejpam-6775	535	7	p	p	NOUN
ejpam-6775	535	8	)	)	PUNCT
ejpam-6775	535	9	,	,	PUNCT
ejpam-6775	535	10	then	then	ADV
ejpam-6775	535	11	we	we	PRON
ejpam-6775	535	12	have	have	VERB
ejpam-6775	535	13	(	(	PUNCT
ejpam-6775	535	14	ξε	ξε	NOUN
ejpam-6775	535	15	,	,	PUNCT
ejpam-6775	535	16	αε	αε	ADP
ejpam-6775	535	17	)	)	PUNCT
ejpam-6775	535	18	∈	∈	PROPN
ejpam-6775	535	19	d	d	PROPN
ejpam-6775	535	20	for	for	ADP
ejpam-6775	535	21	ε	ε	PROPN
ejpam-6775	535	22	>	>	X
ejpam-6775	535	23	0	0	PROPN
ejpam-6775	536	1	small	small	ADJ
ejpam-6775	536	2	enough	enough	ADV
ejpam-6775	536	3	.	.	PUNCT
ejpam-6775	537	1	let	let	VERB
ejpam-6775	537	2	(	(	PUNCT
ejpam-6775	537	3	sε	sε	X
ejpam-6775	537	4	,	,	PUNCT
ejpam-6775	537	5	v	v	X
ejpam-6775	537	6	ε	ε	PROPN
ejpam-6775	537	7	,	,	PUNCT
ejpam-6775	537	8	iε	iε	NOUN
ejpam-6775	537	9	)	)	PUNCT
ejpam-6775	537	10	be	be	AUX
ejpam-6775	537	11	the	the	DET
ejpam-6775	537	12	solution	solution	NOUN
ejpam-6775	537	13	of	of	ADP
ejpam-6775	537	14	the	the	DET
ejpam-6775	537	15	optimization	optimization	NOUN
ejpam-6775	537	16	problem	problem	NOUN
ejpam-6775	537	17	(	(	PUNCT
ejpam-6775	537	18	ocp	ocp	PROPN
ejpam-6775	537	19	)	)	PUNCT
ejpam-6775	537	20	corresponding	correspond	VERB
ejpam-6775	537	21	to	to	ADP
ejpam-6775	537	22	the	the	DET
ejpam-6775	537	23	control	control	NOUN
ejpam-6775	537	24	pair	pair	NOUN
ejpam-6775	537	25	(	(	PUNCT
ejpam-6775	537	26	ξε	ξε	NOUN
ejpam-6775	537	27	,	,	PUNCT
ejpam-6775	537	28	αε	αε	ADP
ejpam-6775	537	29	)	)	PUNCT
ejpam-6775	537	30	.	.	PUNCT
ejpam-6775	538	1	since	since	SCONJ
ejpam-6775	538	2	j	j	PROPN
ejpam-6775	538	3	(	(	PUNCT
ejpam-6775	538	4	.	.	PUNCT
ejpam-6775	538	5	,	,	PUNCT
ejpam-6775	538	6	.	.	PUNCT
ejpam-6775	538	7	)	)	PUNCT
ejpam-6775	538	8	is	be	AUX
ejpam-6775	538	9	minimal	minimal	ADJ
ejpam-6775	538	10	on	on	ADP
ejpam-6775	538	11	(	(	PUNCT
ejpam-6775	538	12	ξ	ξ	PROPN
ejpam-6775	538	13	,	,	PUNCT
ejpam-6775	538	14	α	α	NOUN
ejpam-6775	538	15	)	)	PUNCT
ejpam-6775	538	16	,	,	PUNCT
ejpam-6775	538	17	it	it	PRON
ejpam-6775	538	18	follows	follow	VERB
ejpam-6775	538	19	that	that	SCONJ
ejpam-6775	538	20	j(ξε	j(ξε	NOUN
ejpam-6775	538	21	,	,	PUNCT
ejpam-6775	538	22	αε	αε	ADP
ejpam-6775	538	23	)	)	PUNCT
ejpam-6775	538	24	≥	≥	PROPN
ejpam-6775	538	25	j(ξ	j(ξ	PROPN
ejpam-6775	538	26	,	,	PUNCT
ejpam-6775	538	27	α	α	NOUN
ejpam-6775	538	28	)	)	PUNCT
ejpam-6775	538	29	and	and	CCONJ
ejpam-6775	538	30	hence	hence	ADV
ejpam-6775	538	31	∫	∫	PROPN
ejpam-6775	538	32	q	q	PROPN
ejpam-6775	538	33	χ(x)(iε(t	χ(x)(iε(t	NOUN
ejpam-6775	538	34	,	,	PUNCT
ejpam-6775	538	35	x)−i(t	x)−i(t	PROPN
ejpam-6775	538	36	,	,	PUNCT
ejpam-6775	538	37	x))dxdt+c1	x))dxdt+c1	PROPN
ejpam-6775	538	38	2	2	NUM
ejpam-6775	538	39	∫	∫	NOUN
ejpam-6775	538	40	t	t	NOUN
ejpam-6775	538	41	0	0	NUM
ejpam-6775	539	1	ξε(t)2−ξ2(t)dt+c2	ξε(t)2−ξ2(t)dt+c2	NUM
ejpam-6775	539	2	2	2	NUM
ejpam-6775	539	3	∫	∫	NOUN
ejpam-6775	539	4	q	q	PROPN
ejpam-6775	539	5	(	(	PUNCT
ejpam-6775	539	6	αε(x	αε(x	NUM
ejpam-6775	539	7	,	,	PUNCT
ejpam-6775	539	8	t)x−α2(x	t)x−α2(x	PROPN
ejpam-6775	539	9	,	,	PUNCT
ejpam-6775	539	10	t))dxdt	t))dxdt	PROPN
ejpam-6775	539	11	≥	≥	NOUN
ejpam-6775	539	12	0	0	NUM
ejpam-6775	539	13	.	.	PUNCT
ejpam-6775	539	14	(	(	PUNCT
ejpam-6775	539	15	56	56	NUM
ejpam-6775	539	16	)	)	PUNCT
ejpam-6775	539	17	passing	pass	VERB
ejpam-6775	539	18	to	to	ADP
ejpam-6775	539	19	the	the	DET
ejpam-6775	539	20	limit	limit	NOUN
ejpam-6775	539	21	as	as	ADP
ejpam-6775	539	22	ε→	ε→	X
ejpam-6775	539	23	0	0	NUM
ejpam-6775	540	1	+	+	CCONJ
ejpam-6775	540	2	in	in	ADP
ejpam-6775	540	3	the	the	DET
ejpam-6775	540	4	inequality	inequality	NOUN
ejpam-6775	540	5	above	above	ADV
ejpam-6775	540	6	,	,	PUNCT
ejpam-6775	540	7	we	we	PRON
ejpam-6775	540	8	obtain∫	obtain∫	VERB
ejpam-6775	540	9	q	q	NOUN
ejpam-6775	540	10	χ(x)if	χ(x)if	ADP
ejpam-6775	540	11	i(x	i(x	NOUN
ejpam-6775	540	12	,	,	PUNCT
ejpam-6775	540	13	t)dxdt+	t)dxdt+	PROPN
ejpam-6775	540	14	c1	c1	PROPN
ejpam-6775	540	15	∫	∫	PROPN
ejpam-6775	541	1	t	t	PROPN
ejpam-6775	541	2	0	0	NUM
ejpam-6775	542	1	q(t)ξ(t)dt+	q(t)ξ(t)dt+	PROPN
ejpam-6775	542	2	c2	c2	PROPN
ejpam-6775	542	3	∫	∫	PROPN
ejpam-6775	542	4	q	q	PROPN
ejpam-6775	542	5	p(x	p(x	PROPN
ejpam-6775	542	6	,	,	PUNCT
ejpam-6775	542	7	t)α(x	t)α(x	NUM
ejpam-6775	542	8	,	,	PUNCT
ejpam-6775	542	9	t)xdt	t)xdt	PROPN
ejpam-6775	542	10	≥	≥	NOUN
ejpam-6775	542	11	0	0	NUM
ejpam-6775	542	12	.	.	PUNCT
ejpam-6775	543	1	(	(	PUNCT
ejpam-6775	543	2	57	57	NUM
ejpam-6775	543	3	)	)	PUNCT
ejpam-6775	543	4	let	let	VERB
ejpam-6775	543	5	us	we	PRON
ejpam-6775	543	6	multiply	multiply	VERB
ejpam-6775	543	7	the	the	DET
ejpam-6775	543	8	first	first	ADJ
ejpam-6775	543	9	three	three	NUM
ejpam-6775	543	10	equations	equation	NOUN
ejpam-6775	543	11	in	in	ADP
ejpam-6775	543	12	(	(	PUNCT
ejpam-6775	543	13	35	35	NUM
ejpam-6775	543	14	)	)	PUNCT
ejpam-6775	543	15	by	by	ADP
ejpam-6775	543	16	the	the	DET
ejpam-6775	543	17	variables	variable	NOUN
ejpam-6775	543	18	zs(t	zs(t	NUM
ejpam-6775	543	19	)	)	PUNCT
ejpam-6775	543	20	,	,	PUNCT
ejpam-6775	543	21	zv	zv	PROPN
ejpam-6775	543	22	(	(	PUNCT
ejpam-6775	543	23	t	t	PROPN
ejpam-6775	543	24	)	)	PUNCT
ejpam-6775	543	25	,	,	PUNCT
ejpam-6775	543	26	zi(t	zi(t	NOUN
ejpam-6775	543	27	,	,	PUNCT
ejpam-6775	543	28	x	x	NOUN
ejpam-6775	543	29	)	)	PUNCT
ejpam-6775	543	30	and	and	CCONJ
ejpam-6775	543	31	the	the	DET
ejpam-6775	543	32	equations	equation	NOUN
ejpam-6775	543	33	in	in	ADP
ejpam-6775	543	34	(	(	PUNCT
ejpam-6775	543	35	36	36	NUM
ejpam-6775	543	36	)	)	PUNCT
ejpam-6775	543	37	by	by	ADP
ejpam-6775	543	38	the	the	DET
ejpam-6775	543	39	variables	variable	NOUN
ejpam-6775	543	40	φs(t	φs(t	NUM
ejpam-6775	543	41	)	)	PUNCT
ejpam-6775	543	42	,	,	PUNCT
ejpam-6775	543	43	φv	φv	PROPN
ejpam-6775	543	44	(	(	PUNCT
ejpam-6775	543	45	t	t	NOUN
ejpam-6775	543	46	)	)	PUNCT
ejpam-6775	543	47	and	and	CCONJ
ejpam-6775	543	48	φi(x	φi(x	NUM
ejpam-6775	543	49	,	,	PUNCT
ejpam-6775	543	50	t	t	PROPN
ejpam-6775	543	51	)	)	PUNCT
ejpam-6775	543	52	,	,	PUNCT
ejpam-6775	543	53	respectively	respectively	ADV
ejpam-6775	543	54	.	.	PUNCT
ejpam-6775	544	1	then	then	ADV
ejpam-6775	544	2	,	,	PUNCT
ejpam-6775	544	3	we	we	PRON
ejpam-6775	544	4	obtain	obtain	VERB
ejpam-6775	544	5	thanks	thank	NOUN
ejpam-6775	544	6	to	to	ADP
ejpam-6775	544	7	the	the	DET
ejpam-6775	544	8	relationship	relationship	NOUN
ejpam-6775	544	9	between	between	ADP
ejpam-6775	544	10	the	the	DET
ejpam-6775	544	11	sensitive	sensitive	ADJ
ejpam-6775	544	12	and	and	CCONJ
ejpam-6775	544	13	adjoint	adjoint	NOUN
ejpam-6775	544	14	operators	operator	NOUN
ejpam-6775	544	15	(	(	PUNCT
ejpam-6775	544	16	see	see	VERB
ejpam-6775	544	17	for	for	ADP
ejpam-6775	544	18	instance	instance	NOUN
ejpam-6775	544	19	[	[	X
ejpam-6775	544	20	28	28	NUM
ejpam-6775	544	21	]	]	PUNCT
ejpam-6775	544	22	)	)	PUNCT
ejpam-6775	544	23	the	the	DET
ejpam-6775	544	24	relation	relation	NOUN
ejpam-6775	544	25	φs	φs	AUX
ejpam-6775	544	26	dzs	dzs	VERB
ejpam-6775	544	27	dt	dt	PROPN
ejpam-6775	545	1	+	+	ADJ
ejpam-6775	545	2	φv	φv	ADV
ejpam-6775	545	3	dzv	dzv	NOUN
ejpam-6775	545	4	dt	dt	PROPN
ejpam-6775	546	1	+	+	CCONJ
ejpam-6775	546	2	∫	∫	PROPN
ejpam-6775	546	3	x∗	x∗	PROPN
ejpam-6775	546	4	0	0	PUNCT
ejpam-6775	547	1	φi(∂tzi+∂xzi)dx+zs	φi(∂tzi+∂xzi)dx+zs	PRON
ejpam-6775	547	2	ds	ds	ADJ
ejpam-6775	547	3	dt	dt	X
ejpam-6775	548	1	+	+	PROPN
ejpam-6775	548	2	zv	zv	PROPN
ejpam-6775	548	3	dv	dv	PROPN
ejpam-6775	548	4	dt	dt	PROPN
ejpam-6775	549	1	+	+	CCONJ
ejpam-6775	550	1	∫	∫	PROPN
ejpam-6775	550	2	x∗	x∗	PROPN
ejpam-6775	550	3	0	0	NUM
ejpam-6775	550	4	zi(∂tφi+∂xφi)dx	zi(∂tφi+∂xφi)dx	ADJ
ejpam-6775	550	5	=	=	X
ejpam-6775	551	1	0	0	X
ejpam-6775	551	2	.	.	PUNCT
ejpam-6775	551	3	by	by	ADP
ejpam-6775	551	4	expanding	expand	VERB
ejpam-6775	551	5	the	the	DET
ejpam-6775	551	6	above	above	ADJ
ejpam-6775	551	7	equation	equation	NOUN
ejpam-6775	551	8	and	and	CCONJ
ejpam-6775	551	9	using	use	VERB
ejpam-6775	551	10	integration	integration	NOUN
ejpam-6775	551	11	by	by	ADP
ejpam-6775	551	12	parts	part	NOUN
ejpam-6775	551	13	,	,	PUNCT
ejpam-6775	551	14	the	the	DET
ejpam-6775	551	15	initial	initial	ADJ
ejpam-6775	551	16	and	and	CCONJ
ejpam-6775	551	17	boundary	boundary	ADJ
ejpam-6775	551	18	conditions	condition	NOUN
ejpam-6775	551	19	,	,	PUNCT
ejpam-6775	551	20	we	we	PRON
ejpam-6775	551	21	obtain	obtain	VERB
ejpam-6775	551	22	the	the	DET
ejpam-6775	551	23	following	follow	VERB
ejpam-6775	551	24	relationship	relationship	NOUN
ejpam-6775	551	25	:	:	PUNCT
ejpam-6775	551	26	∫	∫	PROPN
ejpam-6775	551	27	q	q	NOUN
ejpam-6775	551	28	χ(x)φi(t	χ(x)φi(t	PROPN
ejpam-6775	551	29	,	,	PUNCT
ejpam-6775	551	30	x)dxdt−	x)dxdt−	PROPN
ejpam-6775	551	31	∫	∫	PROPN
ejpam-6775	551	32	q	q	PROPN
ejpam-6775	552	1	[	[	X
ejpam-6775	552	2	zs(t)−zi(t	zs(t)−zi(t	PROPN
ejpam-6775	552	3	,	,	PUNCT
ejpam-6775	552	4	x)]p(t	x)]p(t	PROPN
ejpam-6775	552	5	,	,	PUNCT
ejpam-6775	552	6	x)i(t	x)i(t	PROPN
ejpam-6775	552	7	,	,	PUNCT
ejpam-6775	552	8	x)dx+	x)dx+	NUM
ejpam-6775	552	9	∫	∫	PROPN
ejpam-6775	552	10	t	t	NOUN
ejpam-6775	552	11	0	0	NUM
ejpam-6775	553	1	[	[	X
ejpam-6775	553	2	zs(t)−zv	zs(t)−zv	NUM
ejpam-6775	553	3	(	(	PUNCT
ejpam-6775	553	4	t)]q(t)s(t	t)]q(t)s(t	ADJ
ejpam-6775	553	5	)	)	PUNCT
ejpam-6775	553	6	=	=	SYM
ejpam-6775	553	7	0	0	X
ejpam-6775	553	8	.	.	PUNCT
ejpam-6775	553	9	(	(	PUNCT
ejpam-6775	553	10	58	58	X
ejpam-6775	553	11	)	)	PUNCT
ejpam-6775	553	12	integrating	integrating	NOUN
ejpam-6775	553	13	(	(	PUNCT
ejpam-6775	553	14	41	41	NUM
ejpam-6775	553	15	)	)	PUNCT
ejpam-6775	553	16	over	over	ADP
ejpam-6775	553	17	[	[	X
ejpam-6775	553	18	0	0	NUM
ejpam-6775	553	19	,	,	PUNCT
ejpam-6775	553	20	t	t	X
ejpam-6775	553	21	]	]	PUNCT
ejpam-6775	553	22	,	,	PUNCT
ejpam-6775	553	23	we	we	PRON
ejpam-6775	553	24	deduce	deduce	VERB
ejpam-6775	553	25	that	that	SCONJ
ejpam-6775	553	26	j.	j.	PROPN
ejpam-6775	553	27	leo	leo	PROPN
ejpam-6775	553	28	amalraj	amalraj	PROPN
ejpam-6775	553	29	et	et	PROPN
ejpam-6775	553	30	al	al	PROPN
ejpam-6775	553	31	.	.	PUNCT
ejpam-6775	553	32	/	/	SYM
ejpam-6775	553	33	eur	eur	PROPN
ejpam-6775	553	34	.	.	PUNCT
ejpam-6775	554	1	j.	j.	PROPN
ejpam-6775	554	2	pure	pure	PROPN
ejpam-6775	554	3	appl	appl	PROPN
ejpam-6775	554	4	.	.	PROPN
ejpam-6775	554	5	math	math	PROPN
ejpam-6775	554	6	,	,	PUNCT
ejpam-6775	554	7	18	18	NUM
ejpam-6775	554	8	(	(	PUNCT
ejpam-6775	554	9	4	4	NUM
ejpam-6775	554	10	)	)	PUNCT
ejpam-6775	554	11	(	(	PUNCT
ejpam-6775	554	12	2025	2025	NUM
ejpam-6775	554	13	)	)	PUNCT
ejpam-6775	554	14	,	,	PUNCT
ejpam-6775	554	15	6775	6775	NUM
ejpam-6775	554	16	21	21	NUM
ejpam-6775	554	17	of	of	ADP
ejpam-6775	554	18	32	32	NUM
ejpam-6775	554	19	∫	∫	PROPN
ejpam-6775	554	20	q	q	PROPN
ejpam-6775	554	21	χ(x)φi(t	χ(x)φi(t	PROPN
ejpam-6775	554	22	,	,	PUNCT
ejpam-6775	554	23	x)dxdt	x)dxdt	PUNCT
ejpam-6775	555	1	=	=	PUNCT
ejpam-6775	555	2	∫	∫	PROPN
ejpam-6775	555	3	q	q	X
ejpam-6775	556	1	[	[	X
ejpam-6775	556	2	zs(t)−zi(t	zs(t)−zi(t	PROPN
ejpam-6775	556	3	,	,	PUNCT
ejpam-6775	556	4	x)]p(t	x)]p(t	PROPN
ejpam-6775	556	5	,	,	PUNCT
ejpam-6775	556	6	x)i(t	x)i(t	PROPN
ejpam-6775	556	7	,	,	PUNCT
ejpam-6775	556	8	x)dx+	x)dx+	NUM
ejpam-6775	556	9	∫	∫	PROPN
ejpam-6775	556	10	t	t	NOUN
ejpam-6775	556	11	0	0	NUM
ejpam-6775	557	1	[	[	X
ejpam-6775	557	2	−zs(t)−zv	−zs(t)−zv	NOUN
ejpam-6775	557	3	(	(	PUNCT
ejpam-6775	557	4	t)]q(t)s(t)dt	t)]q(t)s(t)dt	PROPN
ejpam-6775	557	5	.	.	PUNCT
ejpam-6775	558	1	(	(	PUNCT
ejpam-6775	558	2	59	59	NUM
ejpam-6775	558	3	)	)	PUNCT
ejpam-6775	558	4	consequently	consequently	ADV
ejpam-6775	558	5	,	,	PUNCT
ejpam-6775	558	6	inequality	inequality	NOUN
ejpam-6775	558	7	(	(	PUNCT
ejpam-6775	558	8	3.2	3.2	NUM
ejpam-6775	558	9	)	)	PUNCT
ejpam-6775	558	10	becomes∫	becomes∫	X
ejpam-6775	558	11	q	q	NOUN
ejpam-6775	559	1	[	[	X
ejpam-6775	559	2	(	(	PUNCT
ejpam-6775	559	3	−zs	−zs	NOUN
ejpam-6775	559	4	+	+	NUM
ejpam-6775	559	5	zi)i−	zi)i−	PROPN
ejpam-6775	559	6	c2α]p(t	c2α]p(t	NOUN
ejpam-6775	559	7	,	,	PUNCT
ejpam-6775	559	8	x)dxdt+	x)dxdt+	PROPN
ejpam-6775	559	9	∫	∫	PROPN
ejpam-6775	560	1	t	t	NOUN
ejpam-6775	560	2	0	0	NUM
ejpam-6775	561	1	[	[	X
ejpam-6775	561	2	−zs	−zs	NOUN
ejpam-6775	561	3	−	−	NOUN
ejpam-6775	562	1	zv	zv	INTJ
ejpam-6775	562	2	]	]	X
ejpam-6775	562	3	s	s	PART
ejpam-6775	562	4	−	−	PROPN
ejpam-6775	562	5	c1ξ]q(t)dt	c1ξ]q(t)dt	NOUN
ejpam-6775	562	6	≤	≤	NOUN
ejpam-6775	562	7	0	0	NUM
ejpam-6775	563	1	(	(	PUNCT
ejpam-6775	563	2	60	60	NUM
ejpam-6775	563	3	)	)	PUNCT
ejpam-6775	563	4	for	for	ADP
ejpam-6775	563	5	all	all	PRON
ejpam-6775	563	6	(	(	PUNCT
ejpam-6775	563	7	q	q	ADJ
ejpam-6775	563	8	,	,	PUNCT
ejpam-6775	563	9	p	p	NOUN
ejpam-6775	563	10	)	)	PUNCT
ejpam-6775	563	11	∈	∈	PROPN
ejpam-6775	563	12	td(ξ	td(ξ	NUM
ejpam-6775	563	13	,	,	PUNCT
ejpam-6775	563	14	α	α	NOUN
ejpam-6775	563	15	)	)	PUNCT
ejpam-6775	563	16	.	.	PUNCT
ejpam-6775	564	1	hence	hence	ADV
ejpam-6775	564	2	it	it	PRON
ejpam-6775	564	3	follows	follow	VERB
ejpam-6775	564	4	according	accord	VERB
ejpam-6775	564	5	to	to	ADP
ejpam-6775	564	6	the	the	DET
ejpam-6775	564	7	structure	structure	NOUN
ejpam-6775	564	8	of	of	ADP
ejpam-6775	564	9	the	the	DET
ejpam-6775	564	10	normal	normal	ADJ
ejpam-6775	564	11	cone	cone	NOUN
ejpam-6775	564	12	that	that	PRON
ejpam-6775	564	13	the	the	DET
ejpam-6775	564	14	expression	expression	NOUN
ejpam-6775	564	15	(	(	PUNCT
ejpam-6775	564	16	[	[	X
ejpam-6775	564	17	−zs	−zs	X
ejpam-6775	564	18	−zv	−zv	X
ejpam-6775	564	19	]	]	X
ejpam-6775	564	20	s−c1ξ	s−c1ξ	NOUN
ejpam-6775	564	21	,	,	PUNCT
ejpam-6775	564	22	[	[	X
ejpam-6775	564	23	−zs	−zs	X
ejpam-6775	564	24	+	+	NOUN
ejpam-6775	564	25	zi]i−c2α	zi]i−c2α	NOUN
ejpam-6775	564	26	)	)	PUNCT
ejpam-6775	564	27	∈	∈	PROPN
ejpam-6775	564	28	nd(ξ	nd(ξ	NOUN
ejpam-6775	564	29	,	,	PUNCT
ejpam-6775	564	30	α	α	NOUN
ejpam-6775	564	31	)	)	PUNCT
ejpam-6775	564	32	.	.	PUNCT
ejpam-6775	565	1	by	by	ADP
ejpam-6775	565	2	the	the	DET
ejpam-6775	565	3	standard	standard	ADJ
ejpam-6775	565	4	optimality	optimality	NOUN
ejpam-6775	565	5	argument	argument	NOUN
ejpam-6775	565	6	and	and	CCONJ
ejpam-6775	565	7	taking	take	VERB
ejpam-6775	565	8	into	into	ADP
ejpam-6775	565	9	account	account	NOUN
ejpam-6775	565	10	the	the	DET
ejpam-6775	565	11	boundaries	boundary	NOUN
ejpam-6775	565	12	of	of	ADP
ejpam-6775	565	13	each	each	DET
ejpam-6775	565	14	control	control	NOUN
ejpam-6775	565	15	strategies	strategy	NOUN
ejpam-6775	565	16	,	,	PUNCT
ejpam-6775	565	17	we	we	PRON
ejpam-6775	565	18	obtain	obtain	VERB
ejpam-6775	565	19	the	the	DET
ejpam-6775	565	20	representation	representation	NOUN
ejpam-6775	565	21	given	give	VERB
ejpam-6775	565	22	in	in	ADP
ejpam-6775	565	23	(	(	PUNCT
ejpam-6775	565	24	38	38	NUM
ejpam-6775	565	25	)	)	PUNCT
ejpam-6775	565	26	which	which	PRON
ejpam-6775	565	27	gives	give	VERB
ejpam-6775	565	28	the	the	DET
ejpam-6775	565	29	desired	desire	VERB
ejpam-6775	565	30	result	result	NOUN
ejpam-6775	565	31	.	.	PUNCT
ejpam-6775	566	1	this	this	PRON
ejpam-6775	566	2	achieves	achieve	VERB
ejpam-6775	566	3	the	the	DET
ejpam-6775	566	4	proof	proof	NOUN
ejpam-6775	566	5	.	.	PUNCT
ejpam-6775	567	1	remark	remark	VERB
ejpam-6775	567	2	3	3	NUM
ejpam-6775	567	3	.	.	PUNCT
ejpam-6775	568	1	at	at	ADP
ejpam-6775	568	2	the	the	DET
ejpam-6775	568	3	final	final	ADJ
ejpam-6775	568	4	time	time	NOUN
ejpam-6775	568	5	t	t	PROPN
ejpam-6775	568	6	>	>	X
ejpam-6775	568	7	0	0	PROPN
ejpam-6775	568	8	,	,	PUNCT
ejpam-6775	568	9	the	the	DET
ejpam-6775	568	10	optimal	optimal	ADJ
ejpam-6775	568	11	controls	control	NOUN
ejpam-6775	568	12	defined	define	VERB
ejpam-6775	568	13	in	in	ADP
ejpam-6775	568	14	(	(	PUNCT
ejpam-6775	568	15	38	38	NUM
ejpam-6775	568	16	)	)	PUNCT
ejpam-6775	568	17	vanish	vanish	VERB
ejpam-6775	568	18	,	,	PUNCT
ejpam-6775	568	19	that	that	PRON
ejpam-6775	568	20	are	be	AUX
ejpam-6775	568	21	ξ(t	ξ(t	NOUN
ejpam-6775	568	22	)	)	PUNCT
ejpam-6775	568	23	=	=	SYM
ejpam-6775	568	24	0	0	NUM
ejpam-6775	568	25	and	and	CCONJ
ejpam-6775	568	26	α(t	α(t	PROPN
ejpam-6775	568	27	,	,	PUNCT
ejpam-6775	568	28	x	x	X
ejpam-6775	568	29	)	)	PUNCT
ejpam-6775	568	30	=	=	SYM
ejpam-6775	568	31	0	0	NUM
ejpam-6775	569	1	for	for	ADP
ejpam-6775	569	2	all	all	DET
ejpam-6775	569	3	x	x	SYM
ejpam-6775	569	4	∈	∈	PROPN
ejpam-6775	569	5	[	[	X
ejpam-6775	569	6	0	0	NUM
ejpam-6775	569	7	,	,	PUNCT
ejpam-6775	569	8	x∗	x∗	PROPN
ejpam-6775	569	9	]	]	PUNCT
ejpam-6775	569	10	since	since	SCONJ
ejpam-6775	569	11	the	the	DET
ejpam-6775	569	12	adjoint	adjoint	PROPN
ejpam-6775	569	13	state	state	NOUN
ejpam-6775	569	14	variables	variable	NOUN
ejpam-6775	569	15	are	be	AUX
ejpam-6775	569	16	all	all	ADV
ejpam-6775	569	17	equal	equal	ADJ
ejpam-6775	569	18	to	to	ADP
ejpam-6775	569	19	zero	zero	NUM
ejpam-6775	569	20	at	at	ADP
ejpam-6775	569	21	final	final	ADJ
ejpam-6775	569	22	time	time	NOUN
ejpam-6775	569	23	t	t	PROPN
ejpam-6775	569	24	by	by	ADP
ejpam-6775	569	25	(	(	PUNCT
ejpam-6775	569	26	37	37	NUM
ejpam-6775	569	27	)	)	PUNCT
ejpam-6775	569	28	.	.	PUNCT
ejpam-6775	570	1	note	note	VERB
ejpam-6775	570	2	that	that	SCONJ
ejpam-6775	570	3	theorem	theorem	VERB
ejpam-6775	570	4	3.1	3.1	NUM
ejpam-6775	570	5	does	do	AUX
ejpam-6775	570	6	not	not	PART
ejpam-6775	570	7	guarantee	guarantee	VERB
ejpam-6775	570	8	the	the	DET
ejpam-6775	570	9	uniqueness	uniqueness	NOUN
ejpam-6775	570	10	of	of	ADP
ejpam-6775	570	11	the	the	DET
ejpam-6775	570	12	optimal	optimal	ADJ
ejpam-6775	570	13	control	control	NOUN
ejpam-6775	570	14	pair	pair	NOUN
ejpam-6775	570	15	.	.	PUNCT
ejpam-6775	571	1	however	however	ADV
ejpam-6775	571	2	,	,	PUNCT
ejpam-6775	571	3	using	use	VERB
ejpam-6775	571	4	the	the	DET
ejpam-6775	571	5	optimal	optimal	ADJ
ejpam-6775	571	6	control	control	NOUN
ejpam-6775	571	7	structure	structure	NOUN
ejpam-6775	571	8	(	(	PUNCT
ejpam-6775	571	9	38	38	NUM
ejpam-6775	571	10	)	)	PUNCT
ejpam-6775	571	11	,	,	PUNCT
ejpam-6775	571	12	this	this	DET
ejpam-6775	571	13	uniqueness	uniqueness	NOUN
ejpam-6775	571	14	can	can	AUX
ejpam-6775	571	15	be	be	AUX
ejpam-6775	571	16	obtained	obtain	VERB
ejpam-6775	571	17	using	use	VERB
ejpam-6775	571	18	the	the	DET
ejpam-6775	571	19	standard	standard	ADJ
ejpam-6775	571	20	procedure	procedure	NOUN
ejpam-6775	571	21	based	base	VERB
ejpam-6775	571	22	on	on	ADP
ejpam-6775	571	23	ekeland	ekeland	PROPN
ejpam-6775	571	24	’s	’s	PART
ejpam-6775	571	25	variational	variational	ADJ
ejpam-6775	571	26	principle	principle	NOUN
ejpam-6775	571	27	[	[	X
ejpam-6775	571	28	44	44	NUM
ejpam-6775	571	29	,	,	PUNCT
ejpam-6775	571	30	46	46	NUM
ejpam-6775	571	31	]	]	PUNCT
ejpam-6775	571	32	.	.	PUNCT
ejpam-6775	572	1	this	this	DET
ejpam-6775	572	2	principle	principle	NOUN
ejpam-6775	572	3	is	be	AUX
ejpam-6775	572	4	used	use	VERB
ejpam-6775	572	5	in	in	ADP
ejpam-6775	572	6	order	order	NOUN
ejpam-6775	572	7	to	to	PART
ejpam-6775	572	8	generate	generate	VERB
ejpam-6775	572	9	a	a	DET
ejpam-6775	572	10	sequence	sequence	NOUN
ejpam-6775	572	11	of	of	ADP
ejpam-6775	572	12	controls	control	NOUN
ejpam-6775	572	13	and	and	CCONJ
ejpam-6775	572	14	its	its	PRON
ejpam-6775	572	15	corresponding	correspond	VERB
ejpam-6775	572	16	states	state	NOUN
ejpam-6775	572	17	that	that	PRON
ejpam-6775	572	18	converge	converge	VERB
ejpam-6775	572	19	to	to	ADP
ejpam-6775	572	20	the	the	DET
ejpam-6775	572	21	optimal	optimal	ADJ
ejpam-6775	572	22	control	control	NOUN
ejpam-6775	572	23	and	and	CCONJ
ejpam-6775	572	24	its	its	PRON
ejpam-6775	572	25	corresponding	correspond	VERB
ejpam-6775	572	26	state	state	NOUN
ejpam-6775	572	27	via	via	ADP
ejpam-6775	572	28	the	the	DET
ejpam-6775	572	29	use	use	NOUN
ejpam-6775	572	30	of	of	ADP
ejpam-6775	572	31	the	the	DET
ejpam-6775	572	32	convergence	convergence	NOUN
ejpam-6775	572	33	of	of	ADP
ejpam-6775	572	34	a	a	DET
ejpam-6775	572	35	minimizing	minimize	VERB
ejpam-6775	572	36	sequence	sequence	NOUN
ejpam-6775	572	37	of	of	ADP
ejpam-6775	572	38	approximate	approximate	ADJ
ejpam-6775	572	39	objective	objective	ADJ
ejpam-6775	572	40	functional	functional	ADJ
ejpam-6775	572	41	.	.	PUNCT
ejpam-6775	573	1	more	more	ADV
ejpam-6775	573	2	precisely	precisely	ADV
ejpam-6775	573	3	,	,	PUNCT
ejpam-6775	573	4	we	we	PRON
ejpam-6775	573	5	have	have	VERB
ejpam-6775	573	6	the	the	DET
ejpam-6775	573	7	following	follow	VERB
ejpam-6775	573	8	result	result	NOUN
ejpam-6775	573	9	theorem	theorem	VERB
ejpam-6775	573	10	8	8	NUM
ejpam-6775	573	11	.	.	PUNCT
ejpam-6775	574	1	there	there	PRON
ejpam-6775	574	2	is	be	VERB
ejpam-6775	574	3	a	a	DET
ejpam-6775	574	4	positive	positive	ADJ
ejpam-6775	574	5	real	real	ADJ
ejpam-6775	574	6	constant	constant	ADJ
ejpam-6775	574	7	kt	kt	X
ejpam-6775	574	8	that	that	PRON
ejpam-6775	574	9	depends	depend	VERB
ejpam-6775	574	10	on	on	ADP
ejpam-6775	574	11	the	the	DET
ejpam-6775	574	12	final	final	ADJ
ejpam-6775	574	13	time	time	NOUN
ejpam-6775	574	14	t	t	NOUN
ejpam-6775	574	15	such	such	ADJ
ejpam-6775	574	16	that	that	PRON
ejpam-6775	574	17	for	for	ADP
ejpam-6775	574	18	kt	kt	PROPN
ejpam-6775	574	19	<	<	X
ejpam-6775	574	20	1	1	NUM
ejpam-6775	574	21	,	,	PUNCT
ejpam-6775	574	22	the	the	DET
ejpam-6775	574	23	optimization	optimization	NOUN
ejpam-6775	574	24	problem	problem	NOUN
ejpam-6775	574	25	(	(	PUNCT
ejpam-6775	574	26	ocp	ocp	PROPN
ejpam-6775	574	27	)	)	PUNCT
ejpam-6775	574	28	has	have	VERB
ejpam-6775	574	29	a	a	DET
ejpam-6775	574	30	unique	unique	ADJ
ejpam-6775	574	31	optimal	optimal	ADJ
ejpam-6775	574	32	control	control	NOUN
ejpam-6775	574	33	pair	pair	NOUN
ejpam-6775	574	34	(	(	PUNCT
ejpam-6775	574	35	ξ	ξ	PROPN
ejpam-6775	574	36	,	,	PUNCT
ejpam-6775	574	37	α	α	NOUN
ejpam-6775	574	38	)	)	PUNCT
ejpam-6775	574	39	∈	∈	PROPN
ejpam-6775	575	1	d	d	NOUN
ejpam-6775	575	2	characterized	characterize	VERB
ejpam-6775	575	3	by	by	ADP
ejpam-6775	575	4	(	(	PUNCT
ejpam-6775	575	5	38	38	NUM
ejpam-6775	575	6	)	)	PUNCT
ejpam-6775	575	7	.	.	PUNCT
ejpam-6775	576	1	before	before	ADP
ejpam-6775	576	2	starting	start	VERB
ejpam-6775	576	3	the	the	DET
ejpam-6775	576	4	proof	proof	NOUN
ejpam-6775	576	5	of	of	ADP
ejpam-6775	576	6	the	the	DET
ejpam-6775	576	7	theorem	theorem	NOUN
ejpam-6775	576	8	above	above	ADV
ejpam-6775	576	9	,	,	PUNCT
ejpam-6775	576	10	we	we	PRON
ejpam-6775	576	11	embed	embed	VERB
ejpam-6775	576	12	the	the	DET
ejpam-6775	576	13	objective	objective	ADJ
ejpam-6775	576	14	functional	functional	ADJ
ejpam-6775	576	15	j(ξ	j(ξ	PROPN
ejpam-6775	576	16	,	,	PUNCT
ejpam-6775	576	17	α	α	NOUN
ejpam-6775	576	18	)	)	PUNCT
ejpam-6775	576	19	into	into	ADP
ejpam-6775	576	20	l1(0	l1(0	PROPN
ejpam-6775	576	21	,	,	PUNCT
ejpam-6775	576	22	t	t	PROPN
ejpam-6775	576	23	)	)	PUNCT
ejpam-6775	576	24	×	×	NOUN
ejpam-6775	576	25	l1(q	l1(q	CCONJ
ejpam-6775	576	26	)	)	PUNCT
ejpam-6775	576	27	by	by	ADP
ejpam-6775	576	28	defining	define	VERB
ejpam-6775	576	29	the	the	DET
ejpam-6775	576	30	following	follow	VERB
ejpam-6775	576	31	functional	functional	ADJ
ejpam-6775	576	32	:	:	PUNCT
ejpam-6775	576	33	h(ξ	h(ξ	NOUN
ejpam-6775	576	34	,	,	PUNCT
ejpam-6775	576	35	α	α	NOUN
ejpam-6775	576	36	)	)	PUNCT
ejpam-6775	576	37	=	=	SYM
ejpam-6775	576	38	{	{	PUNCT
ejpam-6775	576	39	j(ξ	j(ξ	PROPN
ejpam-6775	576	40	,	,	PUNCT
ejpam-6775	576	41	α	α	NOUN
ejpam-6775	576	42	)	)	PUNCT
ejpam-6775	576	43	,	,	PUNCT
ejpam-6775	576	44	if	if	SCONJ
ejpam-6775	576	45	(	(	PUNCT
ejpam-6775	576	46	ξ	ξ	X
ejpam-6775	576	47	,	,	PUNCT
ejpam-6775	576	48	α	α	NOUN
ejpam-6775	576	49	)	)	PUNCT
ejpam-6775	576	50	∈	∈	PROPN
ejpam-6775	576	51	d	d	NOUN
ejpam-6775	576	52	,	,	PUNCT
ejpam-6775	576	53	+	+	NOUN
ejpam-6775	576	54	∞	∞	NOUN
ejpam-6775	576	55	,	,	PUNCT
ejpam-6775	576	56	otherwise	otherwise	ADV
ejpam-6775	576	57	.	.	PUNCT
ejpam-6775	577	1	(	(	PUNCT
ejpam-6775	577	2	61	61	NUM
ejpam-6775	577	3	)	)	PUNCT
ejpam-6775	577	4	let	let	VERB
ejpam-6775	577	5	us	we	PRON
ejpam-6775	577	6	introduce	introduce	VERB
ejpam-6775	577	7	the	the	DET
ejpam-6775	577	8	following	follow	VERB
ejpam-6775	577	9	technical	technical	ADJ
ejpam-6775	577	10	lemma	lemma	PROPN
ejpam-6775	577	11	that	that	SCONJ
ejpam-6775	577	12	we	we	PRON
ejpam-6775	577	13	shall	shall	AUX
ejpam-6775	577	14	use	use	VERB
ejpam-6775	577	15	to	to	PART
ejpam-6775	577	16	establish	establish	VERB
ejpam-6775	577	17	the	the	DET
ejpam-6775	577	18	uniqueness	uniqueness	ADJ
ejpam-6775	577	19	result	result	NOUN
ejpam-6775	577	20	of	of	ADP
ejpam-6775	577	21	the	the	DET
ejpam-6775	577	22	optimal	optimal	ADJ
ejpam-6775	577	23	control	control	NOUN
ejpam-6775	577	24	pair	pair	NOUN
ejpam-6775	577	25	(	(	PUNCT
ejpam-6775	577	26	ocp	ocp	PROPN
ejpam-6775	577	27	)	)	PUNCT
ejpam-6775	577	28	whose	whose	DET
ejpam-6775	577	29	its	its	PRON
ejpam-6775	577	30	proof	proof	NOUN
ejpam-6775	577	31	is	be	AUX
ejpam-6775	577	32	described	describe	VERB
ejpam-6775	577	33	in	in	ADP
ejpam-6775	577	34	appendix	appendix	PROPN
ejpam-6775	577	35	b.	b.	PROPN
ejpam-6775	578	1	lemma	lemma	PROPN
ejpam-6775	578	2	1	1	X
ejpam-6775	578	3	.	.	PUNCT
ejpam-6775	579	1	we	we	PRON
ejpam-6775	579	2	have	have	VERB
ejpam-6775	579	3	the	the	DET
ejpam-6775	579	4	following	follow	VERB
ejpam-6775	579	5	properties	property	NOUN
ejpam-6775	579	6	:	:	PUNCT
ejpam-6775	579	7	(	(	PUNCT
ejpam-6775	579	8	i	i	NOUN
ejpam-6775	579	9	)	)	PUNCT
ejpam-6775	579	10	for	for	ADP
ejpam-6775	579	11	t	t	PROPN
ejpam-6775	579	12	>	>	X
ejpam-6775	579	13	0	0	PUNCT
ejpam-6775	580	1	sufficiently	sufficiently	ADV
ejpam-6775	580	2	small	small	ADJ
ejpam-6775	580	3	,	,	PUNCT
ejpam-6775	580	4	there	there	PRON
ejpam-6775	580	5	are	be	VERB
ejpam-6775	580	6	positive	positive	ADJ
ejpam-6775	580	7	constants	constant	NOUN
ejpam-6775	580	8	c1	c1	PROPN
ejpam-6775	580	9	t	t	PROPN
ejpam-6775	580	10	and	and	CCONJ
ejpam-6775	580	11	c2	c2	PROPN
ejpam-6775	580	12	t	t	PROPN
ejpam-6775	580	13	such	such	ADJ
ejpam-6775	580	14	that	that	PRON
ejpam-6775	580	15	:	:	PUNCT
ejpam-6775	581	1	j.	j.	PROPN
ejpam-6775	581	2	leo	leo	PROPN
ejpam-6775	581	3	amalraj	amalraj	PROPN
ejpam-6775	581	4	et	et	PROPN
ejpam-6775	581	5	al	al	PROPN
ejpam-6775	581	6	.	.	PUNCT
ejpam-6775	581	7	/	/	SYM
ejpam-6775	581	8	eur	eur	PROPN
ejpam-6775	581	9	.	.	PUNCT
ejpam-6775	582	1	j.	j.	PROPN
ejpam-6775	582	2	pure	pure	PROPN
ejpam-6775	582	3	appl	appl	PROPN
ejpam-6775	582	4	.	.	PROPN
ejpam-6775	582	5	math	math	PROPN
ejpam-6775	582	6	,	,	PUNCT
ejpam-6775	582	7	18	18	NUM
ejpam-6775	582	8	(	(	PUNCT
ejpam-6775	582	9	4	4	NUM
ejpam-6775	582	10	)	)	PUNCT
ejpam-6775	582	11	(	(	PUNCT
ejpam-6775	582	12	2025	2025	NUM
ejpam-6775	582	13	)	)	PUNCT
ejpam-6775	582	14	,	,	PUNCT
ejpam-6775	582	15	6775	6775	NUM
ejpam-6775	582	16	22	22	NUM
ejpam-6775	582	17	of	of	ADP
ejpam-6775	582	18	32	32	NUM
ejpam-6775	582	19	(	(	PUNCT
ejpam-6775	582	20	i	i	NOUN
ejpam-6775	582	21	)	)	PUNCT
ejpam-6775	582	22	the	the	DET
ejpam-6775	582	23	map	map	NOUN
ejpam-6775	582	24	(	(	PUNCT
ejpam-6775	582	25	ξ	ξ	PROPN
ejpam-6775	582	26	,	,	PUNCT
ejpam-6775	582	27	α	α	NOUN
ejpam-6775	582	28	)	)	PUNCT
ejpam-6775	582	29	∈	∈	PROPN
ejpam-6775	582	30	d	d	NOUN
ejpam-6775	582	31	→	→	PUNCT
ejpam-6775	582	32	(	(	PUNCT
ejpam-6775	582	33	s	s	PROPN
ejpam-6775	582	34	,	,	PUNCT
ejpam-6775	582	35	v	v	NOUN
ejpam-6775	582	36	,	,	PUNCT
ejpam-6775	582	37	i	i	PRON
ejpam-6775	582	38	)	)	PUNCT
ejpam-6775	582	39	is	be	AUX
ejpam-6775	582	40	lipschitz	lipschitz	NOUN
ejpam-6775	582	41	in	in	ADP
ejpam-6775	582	42	the	the	DET
ejpam-6775	582	43	following	following	ADJ
ejpam-6775	582	44	way	way	NOUN
ejpam-6775	582	45	:	:	PUNCT
ejpam-6775	582	46	∥(s2	∥(s2	NOUN
ejpam-6775	582	47	,	,	PUNCT
ejpam-6775	582	48	v	v	ADP
ejpam-6775	582	49	2	2	NUM
ejpam-6775	582	50	,	,	PUNCT
ejpam-6775	582	51	i2)−	i2)−	NOUN
ejpam-6775	582	52	(	(	PUNCT
ejpam-6775	582	53	s1	s1	NOUN
ejpam-6775	582	54	,	,	PUNCT
ejpam-6775	582	55	v	v	NOUN
ejpam-6775	582	56	1	1	NUM
ejpam-6775	582	57	,	,	PUNCT
ejpam-6775	582	58	i1)∥∞	i1)∥∞	PROPN
ejpam-6775	582	59	≤	≤	PROPN
ejpam-6775	582	60	c1	c1	PROPN
ejpam-6775	582	61	t	t	PROPN
ejpam-6775	582	62	∥(ξ2	∥(ξ2	PROPN
ejpam-6775	582	63	,	,	PUNCT
ejpam-6775	582	64	α2)−	α2)−	PROPN
ejpam-6775	582	65	(	(	PUNCT
ejpam-6775	582	66	ξ2	ξ2	ADJ
ejpam-6775	582	67	,	,	PUNCT
ejpam-6775	582	68	α2)∥∞	α2)∥∞	PROPN
ejpam-6775	582	69	,	,	PUNCT
ejpam-6775	582	70	where	where	SCONJ
ejpam-6775	582	71	(	(	PUNCT
ejpam-6775	582	72	sk	sk	PROPN
ejpam-6775	582	73	,	,	PUNCT
ejpam-6775	582	74	v	v	NOUN
ejpam-6775	582	75	k	k	PROPN
ejpam-6775	582	76	,	,	PUNCT
ejpam-6775	582	77	ik	ik	PROPN
ejpam-6775	582	78	)	)	PUNCT
ejpam-6775	582	79	is	be	AUX
ejpam-6775	582	80	a	a	DET
ejpam-6775	582	81	solution	solution	NOUN
ejpam-6775	582	82	of	of	ADP
ejpam-6775	582	83	(	(	PUNCT
ejpam-6775	582	84	31	31	NUM
ejpam-6775	582	85	)	)	PUNCT
ejpam-6775	582	86	associated	associate	VERB
ejpam-6775	582	87	to	to	PART
ejpam-6775	582	88	control	control	VERB
ejpam-6775	582	89	pair	pair	NOUN
ejpam-6775	582	90	(	(	PUNCT
ejpam-6775	582	91	ξk	ξk	ADP
ejpam-6775	582	92	,	,	PUNCT
ejpam-6775	582	93	αk	αk	NOUN
ejpam-6775	582	94	)	)	PUNCT
ejpam-6775	582	95	for	for	ADP
ejpam-6775	582	96	k	k	PROPN
ejpam-6775	582	97	∈	∈	PROPN
ejpam-6775	582	98	{	{	PUNCT
ejpam-6775	582	99	1	1	NUM
ejpam-6775	582	100	,	,	PUNCT
ejpam-6775	582	101	2	2	NUM
ejpam-6775	582	102	}	}	PUNCT
ejpam-6775	582	103	.	.	PUNCT
ejpam-6775	583	1	(	(	PUNCT
ejpam-6775	583	2	ii	ii	NOUN
ejpam-6775	583	3	)	)	PUNCT
ejpam-6775	583	4	for	for	ADP
ejpam-6775	583	5	(	(	PUNCT
ejpam-6775	583	6	ξk	ξk	NOUN
ejpam-6775	583	7	,	,	PUNCT
ejpam-6775	583	8	αk	αk	NOUN
ejpam-6775	583	9	)	)	PUNCT
ejpam-6775	583	10	∈	∈	PROPN
ejpam-6775	583	11	d	d	NOUN
ejpam-6775	583	12	,	,	PUNCT
ejpam-6775	583	13	the	the	DET
ejpam-6775	583	14	adjoint	adjoint	NOUN
ejpam-6775	583	15	system	system	NOUN
ejpam-6775	583	16	(	(	PUNCT
ejpam-6775	583	17	36	36	NUM
ejpam-6775	583	18	)	)	PUNCT
ejpam-6775	583	19	admits	admit	VERB
ejpam-6775	583	20	a	a	DET
ejpam-6775	583	21	weak	weak	ADJ
ejpam-6775	583	22	solution	solution	NOUN
ejpam-6775	583	23	(	(	PUNCT
ejpam-6775	583	24	zk	zk	PROPN
ejpam-6775	583	25	s	s	PROPN
ejpam-6775	583	26	,	,	PUNCT
ejpam-6775	583	27	z	z	PROPN
ejpam-6775	583	28	k	k	PROPN
ejpam-6775	583	29	v	v	X
ejpam-6775	583	30	,	,	PUNCT
ejpam-6775	584	1	z	z	PROPN
ejpam-6775	584	2	k	k	NOUN
ejpam-6775	584	3	i	i	PROPN
ejpam-6775	584	4	)	)	PUNCT
ejpam-6775	584	5	∈	∈	PROPN
ejpam-6775	584	6	l∞(0	l∞(0	PRON
ejpam-6775	584	7	,	,	PUNCT
ejpam-6775	584	8	t	t	NOUN
ejpam-6775	584	9	)	)	PUNCT
ejpam-6775	584	10	×	×	PROPN
ejpam-6775	584	11	l∞(q	l∞(q	NOUN
ejpam-6775	584	12	)	)	PUNCT
ejpam-6775	584	13	such	such	ADJ
ejpam-6775	584	14	that	that	PRON
ejpam-6775	584	15	for	for	ADP
ejpam-6775	584	16	k	k	PROPN
ejpam-6775	584	17	∈	∈	PROPN
ejpam-6775	584	18	{	{	PUNCT
ejpam-6775	584	19	1	1	NUM
ejpam-6775	584	20	,	,	PUNCT
ejpam-6775	584	21	2	2	NUM
ejpam-6775	584	22	}	}	PUNCT
ejpam-6775	584	23	we	we	PRON
ejpam-6775	584	24	have	have	VERB
ejpam-6775	584	25	∥(z1	∥(z1	PROPN
ejpam-6775	584	26	s	s	PART
ejpam-6775	584	27	,	,	PUNCT
ejpam-6775	584	28	z	z	PROPN
ejpam-6775	584	29	1	1	NUM
ejpam-6775	584	30	v	v	NOUN
ejpam-6775	584	31	,	,	PUNCT
ejpam-6775	584	32	z	z	NOUN
ejpam-6775	584	33	1	1	NUM
ejpam-6775	585	1	i	i	NOUN
ejpam-6775	585	2	)	)	PUNCT
ejpam-6775	585	3	−	−	PROPN
ejpam-6775	586	1	(	(	PUNCT
ejpam-6775	586	2	z2	z2	PROPN
ejpam-6775	586	3	s	s	PART
ejpam-6775	586	4	,	,	PUNCT
ejpam-6775	586	5	z	z	PROPN
ejpam-6775	586	6	2	2	NUM
ejpam-6775	586	7	v	v	NOUN
ejpam-6775	586	8	,	,	PUNCT
ejpam-6775	586	9	z	z	NOUN
ejpam-6775	586	10	2	2	NUM
ejpam-6775	586	11	i	i	NOUN
ejpam-6775	586	12	)	)	PUNCT
ejpam-6775	586	13	∥∞	∥∞	PROPN
ejpam-6775	586	14	≤	≤	NUM
ejpam-6775	586	15	c2	c2	PROPN
ejpam-6775	586	16	t	t	PROPN
ejpam-6775	586	17	∥(ξ1	∥(ξ1	NOUN
ejpam-6775	586	18	,	,	PUNCT
ejpam-6775	586	19	α1)−	α1)−	PROPN
ejpam-6775	586	20	(	(	PUNCT
ejpam-6775	586	21	ξ2	ξ2	ADJ
ejpam-6775	586	22	,	,	PUNCT
ejpam-6775	586	23	α2)∥∞.	α2)∥∞.	PROPN
ejpam-6775	586	24	(	(	PUNCT
ejpam-6775	586	25	ii	ii	NOUN
ejpam-6775	586	26	)	)	PUNCT
ejpam-6775	586	27	the	the	DET
ejpam-6775	586	28	functional	functional	ADJ
ejpam-6775	586	29	h	h	NOUN
ejpam-6775	586	30	(	(	PUNCT
ejpam-6775	586	31	.	.	PUNCT
ejpam-6775	586	32	,	,	PUNCT
ejpam-6775	586	33	.	.	PUNCT
ejpam-6775	586	34	)	)	PUNCT
ejpam-6775	586	35	is	be	AUX
ejpam-6775	586	36	lower	low	ADJ
ejpam-6775	586	37	semi	semi	ADJ
ejpam-6775	586	38	-	-	ADJ
ejpam-6775	586	39	continuous	continuous	ADJ
ejpam-6775	586	40	with	with	ADP
ejpam-6775	586	41	respect	respect	NOUN
ejpam-6775	586	42	to	to	ADP
ejpam-6775	586	43	(	(	PUNCT
ejpam-6775	586	44	ξ	ξ	PROPN
ejpam-6775	586	45	,	,	PUNCT
ejpam-6775	586	46	α	α	NOUN
ejpam-6775	586	47	)	)	PUNCT
ejpam-6775	586	48	in	in	ADP
ejpam-6775	586	49	l1(0	l1(0	PROPN
ejpam-6775	586	50	,	,	PUNCT
ejpam-6775	586	51	t	t	PROPN
ejpam-6775	586	52	)	)	PUNCT
ejpam-6775	586	53	×	×	PROPN
ejpam-6775	586	54	l1(q	l1(q	CCONJ
ejpam-6775	586	55	)	)	PUNCT
ejpam-6775	586	56	.	.	PUNCT
ejpam-6775	587	1	proof	proof	NOUN
ejpam-6775	587	2	.	.	PUNCT
ejpam-6775	588	1	(	(	PUNCT
ejpam-6775	588	2	of	of	ADP
ejpam-6775	588	3	theorem	theorem	NOUN
ejpam-6775	588	4	3.3	3.3	NUM
ejpam-6775	588	5	)	)	PUNCT
ejpam-6775	588	6	since	since	SCONJ
ejpam-6775	588	7	the	the	DET
ejpam-6775	588	8	functional	functional	ADJ
ejpam-6775	588	9	h	h	NOUN
ejpam-6775	588	10	(	(	PUNCT
ejpam-6775	588	11	.	.	PUNCT
ejpam-6775	588	12	,	,	PUNCT
ejpam-6775	588	13	.	.	PUNCT
ejpam-6775	588	14	)	)	PUNCT
ejpam-6775	588	15	is	be	AUX
ejpam-6775	588	16	lower	low	ADJ
ejpam-6775	588	17	semi	semi	ADJ
ejpam-6775	588	18	-	-	ADJ
ejpam-6775	588	19	continuous	continuous	ADJ
ejpam-6775	588	20	in	in	ADP
ejpam-6775	588	21	l1	l1	PROPN
ejpam-6775	588	22	,	,	PUNCT
ejpam-6775	588	23	then	then	ADV
ejpam-6775	588	24	according	accord	VERB
ejpam-6775	588	25	to	to	ADP
ejpam-6775	588	26	ekeland	ekeland	VERB
ejpam-6775	588	27	’s	’s	PART
ejpam-6775	588	28	variational	variational	ADJ
ejpam-6775	588	29	principle	principle	NOUN
ejpam-6775	588	30	[	[	X
ejpam-6775	588	31	44	44	NUM
ejpam-6775	588	32	,	,	PUNCT
ejpam-6775	588	33	46	46	NUM
ejpam-6775	588	34	]	]	PUNCT
ejpam-6775	588	35	,	,	PUNCT
ejpam-6775	588	36	it	it	PRON
ejpam-6775	588	37	follows	follow	VERB
ejpam-6775	588	38	that	that	SCONJ
ejpam-6775	588	39	for	for	ADP
ejpam-6775	588	40	any	any	DET
ejpam-6775	588	41	given	give	VERB
ejpam-6775	588	42	ε	ε	PROPN
ejpam-6775	588	43	>	>	X
ejpam-6775	588	44	0	0	PROPN
ejpam-6775	588	45	,	,	PUNCT
ejpam-6775	588	46	there	there	PRON
ejpam-6775	588	47	exists	exist	VERB
ejpam-6775	588	48	a	a	DET
ejpam-6775	588	49	control	control	NOUN
ejpam-6775	588	50	pair	pair	NOUN
ejpam-6775	588	51	(	(	PUNCT
ejpam-6775	588	52	ξε	ξε	NOUN
ejpam-6775	588	53	,	,	PUNCT
ejpam-6775	588	54	αε	αε	NOUN
ejpam-6775	588	55	)	)	PUNCT
ejpam-6775	588	56	∈	∈	PROPN
ejpam-6775	588	57	l1(0	l1(0	PROPN
ejpam-6775	588	58	,	,	PUNCT
ejpam-6775	588	59	t	t	PROPN
ejpam-6775	588	60	)	)	PUNCT
ejpam-6775	588	61	×	×	NOUN
ejpam-6775	589	1	l1(q	l1(q	CCONJ
ejpam-6775	589	2	)	)	PUNCT
ejpam-6775	589	3	such	such	ADJ
ejpam-6775	589	4	that	that	SCONJ
ejpam-6775	589	5	:	:	PUNCT
ejpam-6775	589	6	(	(	PUNCT
ejpam-6775	589	7	i	i	NOUN
ejpam-6775	589	8	)	)	PUNCT
ejpam-6775	589	9	h(ξε	h(ξε	PROPN
ejpam-6775	589	10	,	,	PUNCT
ejpam-6775	589	11	αε	αε	ADP
ejpam-6775	589	12	)	)	PUNCT
ejpam-6775	589	13	≤	≤	NOUN
ejpam-6775	589	14	inf(ξ	inf(ξ	PROPN
ejpam-6775	589	15	,	,	PUNCT
ejpam-6775	589	16	α)∈d	α)∈d	X
ejpam-6775	589	17	h(ξ	h(ξ	PROPN
ejpam-6775	589	18	,	,	PUNCT
ejpam-6775	589	19	α	α	X
ejpam-6775	589	20	)	)	PUNCT
ejpam-6775	590	1	+	+	CCONJ
ejpam-6775	590	2	ε	ε	PROPN
ejpam-6775	590	3	(	(	PUNCT
ejpam-6775	590	4	ii	ii	NOUN
ejpam-6775	590	5	)	)	PUNCT
ejpam-6775	590	6	h(ξε	h(ξε	PROPN
ejpam-6775	590	7	,	,	PUNCT
ejpam-6775	590	8	αε	αε	ADP
ejpam-6775	590	9	)	)	PUNCT
ejpam-6775	590	10	=	=	SYM
ejpam-6775	590	11	inf(ξ	inf(ξ	PROPN
ejpam-6775	590	12	,	,	PUNCT
ejpam-6775	590	13	α)∈d{h(ξ	α)∈d{h(ξ	X
ejpam-6775	590	14	,	,	PUNCT
ejpam-6775	590	15	α	α	NOUN
ejpam-6775	590	16	)	)	PUNCT
ejpam-6775	590	17	+	+	CCONJ
ejpam-6775	590	18	√	√	NUM
ejpam-6775	590	19	ε∥(ξ	ε∥(ξ	NOUN
ejpam-6775	590	20	,	,	PUNCT
ejpam-6775	590	21	α)−	α)−	PROPN
ejpam-6775	590	22	(	(	PUNCT
ejpam-6775	590	23	ξε	ξε	NOUN
ejpam-6775	590	24	,	,	PUNCT
ejpam-6775	590	25	αε)∥1	αε)∥1	NUM
ejpam-6775	590	26	}	}	PUNCT
ejpam-6775	590	27	.	.	PUNCT
ejpam-6775	591	1	note	note	VERB
ejpam-6775	591	2	that	that	SCONJ
ejpam-6775	591	3	,	,	PUNCT
ejpam-6775	591	4	the	the	DET
ejpam-6775	591	5	perturbated	perturbated	ADJ
ejpam-6775	591	6	functional	functional	ADJ
ejpam-6775	591	7	hε(ξ	hε(ξ	NOUN
ejpam-6775	591	8	,	,	PUNCT
ejpam-6775	591	9	α	α	NOUN
ejpam-6775	591	10	)	)	PUNCT
ejpam-6775	591	11	=	=	SYM
ejpam-6775	591	12	h(ξ	h(ξ	PROPN
ejpam-6775	591	13	,	,	PUNCT
ejpam-6775	591	14	α)+	α)+	NOUN
ejpam-6775	591	15	√	√	NUM
ejpam-6775	591	16	ε∥(ξ	ε∥(ξ	NOUN
ejpam-6775	591	17	,	,	PUNCT
ejpam-6775	591	18	α)−(ξε	α)−(ξε	NOUN
ejpam-6775	591	19	,	,	PUNCT
ejpam-6775	591	20	αε)∥l1	αε)∥l1	NUM
ejpam-6775	591	21	attains	attain	VERB
ejpam-6775	591	22	its	its	PRON
ejpam-6775	591	23	infimum	infimum	NOUN
ejpam-6775	591	24	at	at	ADP
ejpam-6775	591	25	the	the	DET
ejpam-6775	591	26	control	control	NOUN
ejpam-6775	591	27	pair	pair	NOUN
ejpam-6775	591	28	(	(	PUNCT
ejpam-6775	591	29	ξε	ξε	NOUN
ejpam-6775	591	30	,	,	PUNCT
ejpam-6775	591	31	αε	αε	ADP
ejpam-6775	591	32	)	)	PUNCT
ejpam-6775	591	33	.	.	PUNCT
ejpam-6775	592	1	from	from	ADP
ejpam-6775	592	2	item	item	PROPN
ejpam-6775	592	3	(	(	PUNCT
ejpam-6775	592	4	ii	ii	NOUN
ejpam-6775	592	5	)	)	PUNCT
ejpam-6775	592	6	and	and	CCONJ
ejpam-6775	592	7	a	a	DET
ejpam-6775	592	8	similar	similar	ADJ
ejpam-6775	592	9	argument	argument	NOUN
ejpam-6775	592	10	as	as	ADP
ejpam-6775	592	11	that	that	PRON
ejpam-6775	592	12	in	in	ADP
ejpam-6775	592	13	subsection	subsection	NOUN
ejpam-6775	592	14	3.2	3.2	NUM
ejpam-6775	592	15	,	,	PUNCT
ejpam-6775	592	16	we	we	PRON
ejpam-6775	592	17	give	give	VERB
ejpam-6775	592	18	the	the	DET
ejpam-6775	592	19	characterization	characterization	NOUN
ejpam-6775	592	20	of	of	ADP
ejpam-6775	592	21	control	control	NOUN
ejpam-6775	592	22	pair	pair	NOUN
ejpam-6775	592	23	(	(	PUNCT
ejpam-6775	592	24	ξε	ξε	NOUN
ejpam-6775	592	25	,	,	PUNCT
ejpam-6775	592	26	αε	αε	ADP
ejpam-6775	592	27	)	)	PUNCT
ejpam-6775	592	28	by	by	ADP
ejpam-6775	592	29	ξε(t	ξε(t	NOUN
ejpam-6775	592	30	)	)	PUNCT
ejpam-6775	592	31	=	=	SYM
ejpam-6775	592	32	ρ1	ρ1	NOUN
ejpam-6775	592	33	(	(	PUNCT
ejpam-6775	592	34	[	[	X
ejpam-6775	592	35	−zk	−zk	NOUN
ejpam-6775	592	36	s	s	VERB
ejpam-6775	592	37	−	−	PROPN
ejpam-6775	592	38	zk	zk	PROPN
ejpam-6775	592	39	v	v	ADP
ejpam-6775	592	40	]	]	X
ejpam-6775	592	41	s	s	X
ejpam-6775	592	42	k	k	X
ejpam-6775	592	43	−	−	PROPN
ejpam-6775	592	44	√	√	PROPN
ejpam-6775	592	45	εθε1	εθε1	PROPN
ejpam-6775	592	46	c1	c1	PROPN
ejpam-6775	592	47	)	)	PUNCT
ejpam-6775	592	48	,	,	PUNCT
ejpam-6775	592	49	and	and	CCONJ
ejpam-6775	592	50	αε(t	αε(t	NUM
ejpam-6775	592	51	,	,	PUNCT
ejpam-6775	592	52	θ	θ	X
ejpam-6775	592	53	)	)	PUNCT
ejpam-6775	592	54	=	=	SYM
ejpam-6775	592	55	ρ2	ρ2	NOUN
ejpam-6775	592	56	(	(	PUNCT
ejpam-6775	593	1	[	[	X
ejpam-6775	593	2	−zk	−zk	NOUN
ejpam-6775	593	3	s	s	X
ejpam-6775	593	4	+	+	CCONJ
ejpam-6775	593	5	zk	zk	PROPN
ejpam-6775	594	1	i	i	PRON
ejpam-6775	595	1	]	]	X
ejpam-6775	596	1	i	i	PRON
ejpam-6775	596	2	k	k	PROPN
ejpam-6775	597	1	−	−	PROPN
ejpam-6775	597	2	√	√	PROPN
ejpam-6775	597	3	εθε2	εθε2	PROPN
ejpam-6775	597	4	c2	c2	PROPN
ejpam-6775	597	5	)	)	PUNCT
ejpam-6775	597	6	,	,	PUNCT
ejpam-6775	597	7	(	(	PUNCT
ejpam-6775	597	8	62	62	NUM
ejpam-6775	597	9	)	)	PUNCT
ejpam-6775	597	10	where	where	SCONJ
ejpam-6775	597	11	(	(	PUNCT
ejpam-6775	597	12	sk	sk	PROPN
ejpam-6775	597	13	,	,	PUNCT
ejpam-6775	597	14	v	v	NOUN
ejpam-6775	597	15	k	k	PROPN
ejpam-6775	597	16	,	,	PUNCT
ejpam-6775	597	17	ik	ik	PROPN
ejpam-6775	597	18	)	)	PUNCT
ejpam-6775	597	19	and	and	CCONJ
ejpam-6775	597	20	(	(	PUNCT
ejpam-6775	597	21	zk	zk	PROPN
ejpam-6775	597	22	s	s	PROPN
ejpam-6775	597	23	,	,	PUNCT
ejpam-6775	597	24	z	z	PROPN
ejpam-6775	597	25	k	k	PROPN
ejpam-6775	597	26	v	v	X
ejpam-6775	597	27	,	,	PUNCT
ejpam-6775	597	28	z	z	PROPN
ejpam-6775	597	29	k	k	NOUN
ejpam-6775	597	30	i	i	PROPN
ejpam-6775	597	31	)	)	PUNCT
ejpam-6775	597	32	are	be	AUX
ejpam-6775	597	33	the	the	DET
ejpam-6775	597	34	solutions	solution	NOUN
ejpam-6775	597	35	of	of	ADP
ejpam-6775	597	36	controlled	control	VERB
ejpam-6775	597	37	and	and	CCONJ
ejpam-6775	597	38	adjoint	adjoint	NOUN
ejpam-6775	597	39	system	system	NOUN
ejpam-6775	597	40	respectively	respectively	ADV
ejpam-6775	597	41	,	,	PUNCT
ejpam-6775	597	42	corresponding	correspond	VERB
ejpam-6775	597	43	to	to	ADP
ejpam-6775	597	44	the	the	DET
ejpam-6775	597	45	control	control	NOUN
ejpam-6775	597	46	pair	pair	NOUN
ejpam-6775	597	47	(	(	PUNCT
ejpam-6775	597	48	ξε	ξε	NOUN
ejpam-6775	597	49	,	,	PUNCT
ejpam-6775	597	50	αε	αε	ADP
ejpam-6775	597	51	)	)	PUNCT
ejpam-6775	597	52	.	.	PUNCT
ejpam-6775	598	1	the	the	DET
ejpam-6775	598	2	functions	function	NOUN
ejpam-6775	598	3	θε1	θε1	VERB
ejpam-6775	598	4	∈	∈	PROPN
ejpam-6775	598	5	l∞(0	l∞(0	PRON
ejpam-6775	598	6	,	,	PUNCT
ejpam-6775	598	7	t	t	PROPN
ejpam-6775	598	8	)	)	PUNCT
ejpam-6775	598	9	,	,	PUNCT
ejpam-6775	598	10	θε2	θε2	VERB
ejpam-6775	598	11	∈	∈	PROPN
ejpam-6775	598	12	l∞(q	l∞(q	NOUN
ejpam-6775	598	13	)	)	PUNCT
ejpam-6775	598	14	and	and	CCONJ
ejpam-6775	598	15	|θεi	|θεi	VERB
ejpam-6775	598	16	|	|	ADV
ejpam-6775	598	17	≤	≤	NUM
ejpam-6775	598	18	1	1	NUM
ejpam-6775	598	19	for	for	ADP
ejpam-6775	598	20	i	i	PRON
ejpam-6775	598	21	∈	∈	PROPN
ejpam-6775	598	22	{	{	PUNCT
ejpam-6775	598	23	1	1	NUM
ejpam-6775	598	24	,	,	PUNCT
ejpam-6775	598	25	2	2	NUM
ejpam-6775	598	26	}	}	PUNCT
ejpam-6775	598	27	and	and	CCONJ
ejpam-6775	598	28	(	(	PUNCT
ejpam-6775	598	29	t	t	PROPN
ejpam-6775	598	30	,	,	PUNCT
ejpam-6775	598	31	θ	θ	NOUN
ejpam-6775	598	32	)	)	PUNCT
ejpam-6775	598	33	∈	∈	PROPN
ejpam-6775	598	34	q.	q.	NOUN
ejpam-6775	598	35	we	we	PRON
ejpam-6775	598	36	now	now	ADV
ejpam-6775	598	37	ready	ready	ADJ
ejpam-6775	598	38	to	to	PART
ejpam-6775	598	39	prove	prove	VERB
ejpam-6775	598	40	our	our	PRON
ejpam-6775	598	41	main	main	ADJ
ejpam-6775	598	42	result	result	NOUN
ejpam-6775	598	43	of	of	ADP
ejpam-6775	598	44	this	this	DET
ejpam-6775	598	45	subsection	subsection	NOUN
ejpam-6775	598	46	concerning	concern	VERB
ejpam-6775	598	47	the	the	DET
ejpam-6775	598	48	uniqueness	uniqueness	NOUN
ejpam-6775	598	49	of	of	ADP
ejpam-6775	598	50	an	an	DET
ejpam-6775	598	51	optimal	optimal	ADJ
ejpam-6775	598	52	control	control	NOUN
ejpam-6775	598	53	pair	pair	NOUN
ejpam-6775	598	54	solution	solution	NOUN
ejpam-6775	598	55	of	of	ADP
ejpam-6775	598	56	optimization	optimization	NOUN
ejpam-6775	598	57	problem	problem	NOUN
ejpam-6775	598	58	(	(	PUNCT
ejpam-6775	598	59	ocp	ocp	PROPN
ejpam-6775	598	60	)	)	PUNCT
ejpam-6775	598	61	.	.	PUNCT
ejpam-6775	599	1	to	to	PART
ejpam-6775	599	2	do	do	VERB
ejpam-6775	599	3	so	so	ADV
ejpam-6775	599	4	,	,	PUNCT
ejpam-6775	599	5	let	let	VERB
ejpam-6775	599	6	us	we	PRON
ejpam-6775	599	7	consider	consider	VERB
ejpam-6775	599	8	the	the	DET
ejpam-6775	599	9	following	follow	VERB
ejpam-6775	599	10	map	map	NOUN
ejpam-6775	599	11	m	m	VERB
ejpam-6775	599	12	:	:	PUNCT
ejpam-6775	600	1	d	d	X
ejpam-6775	600	2	→	→	SYM
ejpam-6775	600	3	d	d	NOUN
ejpam-6775	600	4	defined	define	VERB
ejpam-6775	600	5	by	by	ADP
ejpam-6775	600	6	m(ξ	m(ξ	NOUN
ejpam-6775	600	7	,	,	PUNCT
ejpam-6775	600	8	α	α	NOUN
ejpam-6775	600	9	)	)	PUNCT
ejpam-6775	600	10	=	=	SYM
ejpam-6775	600	11	(	(	PUNCT
ejpam-6775	600	12	ρ1	ρ1	NOUN
ejpam-6775	600	13	(	(	PUNCT
ejpam-6775	600	14	[	[	X
ejpam-6775	600	15	−zs	−zs	NOUN
ejpam-6775	601	1	−	−	NOUN
ejpam-6775	602	1	zv	zv	INTJ
ejpam-6775	602	2	]	]	X
ejpam-6775	602	3	s	s	PART
ejpam-6775	602	4	c1	c1	PROPN
ejpam-6775	602	5	)	)	PUNCT
ejpam-6775	602	6	,	,	PUNCT
ejpam-6775	602	7	ρ2	ρ2	NOUN
ejpam-6775	602	8	(	(	PUNCT
ejpam-6775	602	9	[	[	X
ejpam-6775	602	10	−zs	−zs	X
ejpam-6775	602	11	+	+	CCONJ
ejpam-6775	602	12	zi]i	zi]i	PROPN
ejpam-6775	602	13	c2	c2	PROPN
ejpam-6775	602	14	)	)	PUNCT
ejpam-6775	602	15	)	)	PUNCT
ejpam-6775	602	16	.	.	PUNCT
ejpam-6775	603	1	(	(	PUNCT
ejpam-6775	603	2	63	63	NUM
ejpam-6775	603	3	)	)	PUNCT
ejpam-6775	603	4	let	let	VERB
ejpam-6775	603	5	(	(	PUNCT
ejpam-6775	603	6	sk	sk	PROPN
ejpam-6775	603	7	,	,	PUNCT
ejpam-6775	603	8	v	v	NOUN
ejpam-6775	603	9	k	k	PROPN
ejpam-6775	603	10	,	,	PUNCT
ejpam-6775	603	11	ik	ik	PROPN
ejpam-6775	603	12	)	)	PUNCT
ejpam-6775	603	13	and	and	CCONJ
ejpam-6775	603	14	(	(	PUNCT
ejpam-6775	603	15	zk	zk	PROPN
ejpam-6775	603	16	s	s	PROPN
ejpam-6775	603	17	,	,	PUNCT
ejpam-6775	603	18	z	z	PROPN
ejpam-6775	603	19	k	k	PROPN
ejpam-6775	603	20	v	v	X
ejpam-6775	603	21	,	,	PUNCT
ejpam-6775	603	22	z	z	PROPN
ejpam-6775	603	23	k	k	NOUN
ejpam-6775	603	24	i	i	PROPN
ejpam-6775	603	25	)	)	PUNCT
ejpam-6775	603	26	are	be	AUX
ejpam-6775	603	27	the	the	DET
ejpam-6775	603	28	state	state	NOUN
ejpam-6775	603	29	and	and	CCONJ
ejpam-6775	603	30	adjoint	adjoint	NOUN
ejpam-6775	603	31	variables	variable	NOUN
ejpam-6775	603	32	corresponding	correspond	VERB
ejpam-6775	603	33	to	to	ADP
ejpam-6775	603	34	the	the	DET
ejpam-6775	603	35	control	control	NOUN
ejpam-6775	603	36	pair	pair	NOUN
ejpam-6775	603	37	(	(	PUNCT
ejpam-6775	603	38	ξk	ξk	ADP
ejpam-6775	603	39	,	,	PUNCT
ejpam-6775	603	40	αk	αk	NOUN
ejpam-6775	603	41	)	)	PUNCT
ejpam-6775	603	42	with	with	ADP
ejpam-6775	603	43	k	k	PROPN
ejpam-6775	603	44	∈	∈	PROPN
ejpam-6775	603	45	{	{	PUNCT
ejpam-6775	603	46	1	1	NUM
ejpam-6775	603	47	,	,	PUNCT
ejpam-6775	603	48	2	2	NUM
ejpam-6775	603	49	}	}	PUNCT
ejpam-6775	603	50	.	.	PUNCT
ejpam-6775	604	1	using	use	VERB
ejpam-6775	604	2	the	the	DET
ejpam-6775	604	3	lipschitz	lipschitz	NOUN
ejpam-6775	604	4	properties	property	NOUN
ejpam-6775	604	5	of	of	ADP
ejpam-6775	604	6	the	the	DET
ejpam-6775	604	7	state	state	NOUN
ejpam-6775	604	8	and	and	CCONJ
ejpam-6775	604	9	adjoint	adjoint	PROPN
ejpam-6775	604	10	variable	variable	NOUN
ejpam-6775	604	11	established	establish	VERB
ejpam-6775	604	12	in	in	ADP
ejpam-6775	604	13	the	the	DET
ejpam-6775	604	14	lemma	lemma	PROPN
ejpam-6775	604	15	3.1	3.1	NUM
ejpam-6775	604	16	,	,	PUNCT
ejpam-6775	604	17	we	we	PRON
ejpam-6775	604	18	have	have	VERB
ejpam-6775	604	19	∥m(ξ1	∥m(ξ1	NOUN
ejpam-6775	604	20	,	,	PUNCT
ejpam-6775	604	21	α1)−m(ξ2	α1)−m(ξ2	NOUN
ejpam-6775	604	22	,	,	PUNCT
ejpam-6775	605	1	α2)∥l∞	α2)∥l∞	DET
ejpam-6775	605	2	≤	≤	NUM
ejpam-6775	605	3	∣∣∣∣ρ1	∣∣∣∣ρ1	PROPN
ejpam-6775	605	4	(	(	PUNCT
ejpam-6775	605	5	[	[	X
ejpam-6775	605	6	−z1	−z1	PROPN
ejpam-6775	605	7	s	s	PART
ejpam-6775	605	8	−	−	PROPN
ejpam-6775	605	9	z1	z1	NUM
ejpam-6775	605	10	v	v	ADP
ejpam-6775	605	11	]	]	SYM
ejpam-6775	605	12	s	s	PART
ejpam-6775	605	13	1	1	NUM
ejpam-6775	605	14	c1	c1	NOUN
ejpam-6775	605	15	)	)	PUNCT
ejpam-6775	606	1	−	−	PROPN
ejpam-6775	606	2	ρ1	ρ1	NOUN
ejpam-6775	606	3	(	(	PUNCT
ejpam-6775	606	4	[	[	X
ejpam-6775	606	5	−z2	−z2	NOUN
ejpam-6775	606	6	s	s	PART
ejpam-6775	606	7	−	−	PROPN
ejpam-6775	606	8	z2	z2	PROPN
ejpam-6775	606	9	v	v	ADP
ejpam-6775	606	10	]	]	SYM
ejpam-6775	606	11	s	s	PART
ejpam-6775	606	12	2	2	NUM
ejpam-6775	606	13	c1	c1	NOUN
ejpam-6775	606	14	)	)	PUNCT
ejpam-6775	606	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6775	606	16	l∞(0,t	l∞(0,t	ADJ
ejpam-6775	606	17	)	)	PUNCT
ejpam-6775	607	1	j.	j.	PROPN
ejpam-6775	607	2	leo	leo	PROPN
ejpam-6775	607	3	amalraj	amalraj	PROPN
ejpam-6775	607	4	et	et	PROPN
ejpam-6775	607	5	al	al	PROPN
ejpam-6775	607	6	.	.	PUNCT
ejpam-6775	607	7	/	/	SYM
ejpam-6775	607	8	eur	eur	PROPN
ejpam-6775	607	9	.	.	PUNCT
ejpam-6775	608	1	j.	j.	PROPN
ejpam-6775	608	2	pure	pure	PROPN
ejpam-6775	608	3	appl	appl	PROPN
ejpam-6775	608	4	.	.	PROPN
ejpam-6775	608	5	math	math	PROPN
ejpam-6775	608	6	,	,	PUNCT
ejpam-6775	608	7	18	18	NUM
ejpam-6775	608	8	(	(	PUNCT
ejpam-6775	608	9	4	4	NUM
ejpam-6775	608	10	)	)	PUNCT
ejpam-6775	608	11	(	(	PUNCT
ejpam-6775	608	12	2025	2025	NUM
ejpam-6775	608	13	)	)	PUNCT
ejpam-6775	608	14	,	,	PUNCT
ejpam-6775	608	15	6775	6775	NUM
ejpam-6775	608	16	23	23	NUM
ejpam-6775	608	17	of	of	ADP
ejpam-6775	608	18	32	32	NUM
ejpam-6775	608	19	+	+	CCONJ
ejpam-6775	608	20	∣∣∣∣ρ2	∣∣∣∣ρ2	NUM
ejpam-6775	608	21	(	(	PUNCT
ejpam-6775	608	22	[	[	X
ejpam-6775	608	23	−z1	−z1	PROPN
ejpam-6775	608	24	s	s	NOUN
ejpam-6775	608	25	+	+	X
ejpam-6775	608	26	z1	z1	NOUN
ejpam-6775	609	1	i	i	PRON
ejpam-6775	609	2	]	]	X
ejpam-6775	609	3	i	i	PROPN
ejpam-6775	609	4	1	1	NUM
ejpam-6775	609	5	c2	c2	PROPN
ejpam-6775	609	6	)	)	PUNCT
ejpam-6775	610	1	−	−	PROPN
ejpam-6775	610	2	ρ2	ρ2	NOUN
ejpam-6775	610	3	(	(	PUNCT
ejpam-6775	610	4	[	[	X
ejpam-6775	610	5	−z2	−z2	NOUN
ejpam-6775	610	6	s	s	PART
ejpam-6775	610	7	+	+	CCONJ
ejpam-6775	610	8	z2	z2	PROPN
ejpam-6775	610	9	i	i	PRON
ejpam-6775	610	10	]	]	X
ejpam-6775	610	11	i	i	PROPN
ejpam-6775	610	12	2	2	NUM
ejpam-6775	610	13	c2	c2	PROPN
ejpam-6775	610	14	)	)	PUNCT
ejpam-6775	610	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6775	610	16	l∞(q	l∞(q	NOUN
ejpam-6775	610	17	)	)	PUNCT
ejpam-6775	610	18	≤	≤	NOUN
ejpam-6775	611	1	c−1	c−1	PROPN
ejpam-6775	611	2	1	1	NUM
ejpam-6775	611	3	∥[−z1	∥[−z1	NOUN
ejpam-6775	611	4	s	s	PART
ejpam-6775	611	5	−	−	PROPN
ejpam-6775	611	6	z1	z1	PROPN
ejpam-6775	611	7	v	v	ADP
ejpam-6775	611	8	]	]	SYM
ejpam-6775	611	9	s	s	PART
ejpam-6775	611	10	1	1	NUM
ejpam-6775	611	11	−	−	NOUN
ejpam-6775	612	1	[	[	X
ejpam-6775	612	2	−z2	−z2	NOUN
ejpam-6775	612	3	s	s	PART
ejpam-6775	612	4	−	−	PROPN
ejpam-6775	612	5	z2	z2	PROPN
ejpam-6775	612	6	v	v	NOUN
ejpam-6775	612	7	]	]	X
ejpam-6775	612	8	s	s	NOUN
ejpam-6775	612	9	2∥l∞(0,t	2∥l∞(0,t	NUM
ejpam-6775	612	10	)	)	PUNCT
ejpam-6775	613	1	+	+	CCONJ
ejpam-6775	613	2	c−1	c−1	PROPN
ejpam-6775	613	3	2	2	NUM
ejpam-6775	613	4	∥[−z1	∥[−z1	NOUN
ejpam-6775	613	5	s	s	PART
ejpam-6775	614	1	+	+	X
ejpam-6775	614	2	z1	z1	NUM
ejpam-6775	614	3	i	i	PRON
ejpam-6775	614	4	]	]	X
ejpam-6775	614	5	i	i	VERB
ejpam-6775	614	6	1	1	NUM
ejpam-6775	614	7	−	−	NOUN
ejpam-6775	615	1	[	[	X
ejpam-6775	615	2	−z2	−z2	PROPN
ejpam-6775	615	3	s	s	PART
ejpam-6775	615	4	+	+	CCONJ
ejpam-6775	615	5	z2	z2	PROPN
ejpam-6775	615	6	i	i	PRON
ejpam-6775	615	7	]	]	X
ejpam-6775	615	8	i	i	NOUN
ejpam-6775	615	9	2∥l∞(q	2∥l∞(q	NOUN
ejpam-6775	615	10	)	)	PUNCT
ejpam-6775	615	11	≤	≤	NUM
ejpam-6775	615	12	k1∥(s1	k1∥(s1	PROPN
ejpam-6775	615	13	,	,	PUNCT
ejpam-6775	615	14	i1)−	i1)−	PROPN
ejpam-6775	615	15	(	(	PUNCT
ejpam-6775	615	16	s2	s2	PROPN
ejpam-6775	615	17	,	,	PUNCT
ejpam-6775	615	18	i2)∥∞	i2)∥∞	PROPN
ejpam-6775	615	19	+	+	PROPN
ejpam-6775	615	20	k2∥(z1	k2∥(z1	NOUN
ejpam-6775	615	21	s	s	X
ejpam-6775	615	22	,	,	PUNCT
ejpam-6775	615	23	z	z	PROPN
ejpam-6775	615	24	1	1	NUM
ejpam-6775	615	25	v	v	NOUN
ejpam-6775	615	26	,	,	PUNCT
ejpam-6775	615	27	z	z	NOUN
ejpam-6775	615	28	1	1	NUM
ejpam-6775	615	29	i	i	NOUN
ejpam-6775	615	30	)	)	PUNCT
ejpam-6775	615	31	−	−	PROPN
ejpam-6775	616	1	(	(	PUNCT
ejpam-6775	616	2	z2	z2	PROPN
ejpam-6775	616	3	s	s	PART
ejpam-6775	616	4	,	,	PUNCT
ejpam-6775	616	5	z	z	PROPN
ejpam-6775	616	6	2	2	NUM
ejpam-6775	616	7	v	v	NOUN
ejpam-6775	616	8	,	,	PUNCT
ejpam-6775	616	9	z	z	NOUN
ejpam-6775	616	10	2	2	NUM
ejpam-6775	616	11	i	i	NOUN
ejpam-6775	616	12	)	)	PUNCT
ejpam-6775	616	13	∥∞	∥∞	PROPN
ejpam-6775	616	14	≤	≤	NUM
ejpam-6775	617	1	k1(c1	k1(c1	PROPN
ejpam-6775	617	2	t	t	PROPN
ejpam-6775	617	3	+	+	PROPN
ejpam-6775	617	4	k2c2	k2c2	PROPN
ejpam-6775	617	5	t	t	NOUN
ejpam-6775	617	6	)	)	PUNCT
ejpam-6775	617	7	(	(	PUNCT
ejpam-6775	617	8	∥(ξ1	∥(ξ1	X
ejpam-6775	617	9	,	,	PUNCT
ejpam-6775	617	10	α1)−	α1)−	PROPN
ejpam-6775	617	11	(	(	PUNCT
ejpam-6775	617	12	ξ2	ξ2	PROPN
ejpam-6775	617	13	,	,	PUNCT
ejpam-6775	617	14	α2)∥∞	α2)∥∞	NOUN
ejpam-6775	617	15	)	)	PUNCT
ejpam-6775	617	16	,	,	PUNCT
ejpam-6775	617	17	where	where	SCONJ
ejpam-6775	617	18	the	the	DET
ejpam-6775	617	19	constants	constant	NOUN
ejpam-6775	617	20	k1	k1	NOUN
ejpam-6775	617	21	and	and	CCONJ
ejpam-6775	617	22	k2	k2	PROPN
ejpam-6775	617	23	depend	depend	VERB
ejpam-6775	617	24	on	on	ADP
ejpam-6775	617	25	the	the	DET
ejpam-6775	617	26	l∞	l∞	NOUN
ejpam-6775	617	27	bounds	bound	NOUN
ejpam-6775	617	28	on	on	ADP
ejpam-6775	617	29	the	the	DET
ejpam-6775	617	30	state	state	NOUN
ejpam-6775	617	31	and	and	CCONJ
ejpam-6775	617	32	adjoint	adjoint	PROPN
ejpam-6775	617	33	state	state	NOUN
ejpam-6775	617	34	variables	variable	NOUN
ejpam-6775	617	35	and	and	CCONJ
ejpam-6775	617	36	g3	g3	NOUN
ejpam-6775	617	37	t	t	NOUN
ejpam-6775	617	38	=	=	SYM
ejpam-6775	617	39	k1c1	k1c1	NOUN
ejpam-6775	617	40	t	t	NOUN
ejpam-6775	617	41	+	+	PROPN
ejpam-6775	617	42	k2c2	k2c2	PROPN
ejpam-6775	617	43	t	t	NOUN
ejpam-6775	617	44	.	.	PUNCT
ejpam-6775	618	1	(	(	PUNCT
ejpam-6775	618	2	64	64	NUM
ejpam-6775	618	3	)	)	PUNCT
ejpam-6775	618	4	where	where	SCONJ
ejpam-6775	618	5	c1	c1	PROPN
ejpam-6775	618	6	t	t	PROPN
ejpam-6775	618	7	and	and	CCONJ
ejpam-6775	618	8	c2	c2	PROPN
ejpam-6775	618	9	t	t	PROPN
ejpam-6775	618	10	are	be	AUX
ejpam-6775	618	11	the	the	DET
ejpam-6775	618	12	lipschitz	lipschitz	NOUN
ejpam-6775	618	13	constants	constant	NOUN
ejpam-6775	618	14	obtained	obtain	VERB
ejpam-6775	618	15	in	in	ADP
ejpam-6775	618	16	lemma	lemma	PROPN
ejpam-6775	618	17	3.1	3.1	NUM
ejpam-6775	618	18	.	.	PUNCT
ejpam-6775	619	1	clearly	clearly	ADV
ejpam-6775	619	2	m	m	VERB
ejpam-6775	619	3	is	be	AUX
ejpam-6775	619	4	a	a	DET
ejpam-6775	619	5	contraction	contraction	NOUN
ejpam-6775	619	6	function	function	NOUN
ejpam-6775	619	7	if	if	SCONJ
ejpam-6775	619	8	g3	g3	PROPN
ejpam-6775	619	9	t	t	PROPN
ejpam-6775	619	10	<	<	X
ejpam-6775	619	11	1	1	NUM
ejpam-6775	619	12	.	.	PUNCT
ejpam-6775	620	1	hence	hence	ADV
ejpam-6775	620	2	,	,	PUNCT
ejpam-6775	620	3	m	m	VERB
ejpam-6775	620	4	has	have	VERB
ejpam-6775	620	5	a	a	DET
ejpam-6775	620	6	unique	unique	ADJ
ejpam-6775	620	7	fixed	fix	VERB
ejpam-6775	620	8	point	point	NOUN
ejpam-6775	620	9	(	(	PUNCT
ejpam-6775	620	10	ξ∗	ξ∗	ADV
ejpam-6775	620	11	,	,	PUNCT
ejpam-6775	620	12	α∗	α∗	NOUN
ejpam-6775	620	13	)	)	PUNCT
ejpam-6775	620	14	∈	∈	PROPN
ejpam-6775	621	1	d	d	NOUN
ejpam-6775	621	2	by	by	ADP
ejpam-6775	621	3	the	the	DET
ejpam-6775	621	4	banach	banach	NOUN
ejpam-6775	621	5	contraction	contraction	NOUN
ejpam-6775	621	6	theorem	theorem	VERB
ejpam-6775	621	7	when	when	SCONJ
ejpam-6775	621	8	g3	g3	PROPN
ejpam-6775	621	9	t	t	PROPN
ejpam-6775	621	10	<	<	X
ejpam-6775	621	11	1	1	NUM
ejpam-6775	621	12	.	.	PUNCT
ejpam-6775	622	1	we	we	PRON
ejpam-6775	622	2	show	show	VERB
ejpam-6775	622	3	that	that	SCONJ
ejpam-6775	622	4	this	this	DET
ejpam-6775	622	5	fixed	fix	VERB
ejpam-6775	622	6	point	point	NOUN
ejpam-6775	622	7	is	be	AUX
ejpam-6775	622	8	an	an	DET
ejpam-6775	622	9	optimal	optimal	ADJ
ejpam-6775	622	10	control	control	NOUN
ejpam-6775	622	11	pair	pair	NOUN
ejpam-6775	622	12	to	to	ADP
ejpam-6775	622	13	(	(	PUNCT
ejpam-6775	622	14	ocp	ocp	PROPN
ejpam-6775	622	15	)	)	PUNCT
ejpam-6775	622	16	by	by	ADP
ejpam-6775	622	17	using	use	VERB
ejpam-6775	622	18	the	the	DET
ejpam-6775	622	19	approximating	approximate	VERB
ejpam-6775	622	20	minimizers	minimizer	NOUN
ejpam-6775	622	21	sequence	sequence	NOUN
ejpam-6775	622	22	(	(	PUNCT
ejpam-6775	622	23	ξε	ξε	NOUN
ejpam-6775	622	24	,	,	PUNCT
ejpam-6775	622	25	αε	αε	ADP
ejpam-6775	622	26	)	)	PUNCT
ejpam-6775	622	27	from	from	ADP
ejpam-6775	622	28	ekeland	ekeland	NOUN
ejpam-6775	622	29	’s	’s	PART
ejpam-6775	622	30	principle	principle	NOUN
ejpam-6775	622	31	and	and	CCONJ
ejpam-6775	622	32	corresponding	correspond	VERB
ejpam-6775	622	33	state	state	NOUN
ejpam-6775	622	34	variables	variable	NOUN
ejpam-6775	622	35	sk	sk	ADP
ejpam-6775	622	36	,	,	PUNCT
ejpam-6775	622	37	v	v	NOUN
ejpam-6775	622	38	k	k	PROPN
ejpam-6775	622	39	and	and	CCONJ
ejpam-6775	622	40	ik	ik	NOUN
ejpam-6775	622	41	,	,	PUNCT
ejpam-6775	622	42	and	and	CCONJ
ejpam-6775	622	43	adjoint	adjoint	NOUN
ejpam-6775	622	44	variables	variable	NOUN
ejpam-6775	622	45	zk	zk	PROPN
ejpam-6775	622	46	s	s	PROPN
ejpam-6775	622	47	,	,	PUNCT
ejpam-6775	622	48	z	z	PROPN
ejpam-6775	622	49	k	k	PROPN
ejpam-6775	622	50	v	v	PROPN
ejpam-6775	622	51	and	and	CCONJ
ejpam-6775	622	52	zk	zk	PRON
ejpam-6775	622	53	i	i	PRON
ejpam-6775	622	54	.	.	PUNCT
ejpam-6775	623	1	from	from	ADP
ejpam-6775	623	2	lemma	lemma	PROPN
ejpam-6775	623	3	3.1	3.1	NUM
ejpam-6775	623	4	,	,	PUNCT
ejpam-6775	623	5	and	and	CCONJ
ejpam-6775	623	6	the	the	DET
ejpam-6775	623	7	contraction	contraction	NOUN
ejpam-6775	623	8	property	property	NOUN
ejpam-6775	623	9	of	of	ADP
ejpam-6775	623	10	the	the	DET
ejpam-6775	623	11	application	application	NOUN
ejpam-6775	623	12	m	m	NOUN
ejpam-6775	623	13	,	,	PUNCT
ejpam-6775	623	14	we	we	PRON
ejpam-6775	623	15	have	have	VERB
ejpam-6775	623	16	∥(ξ∗	∥(ξ∗	NOUN
ejpam-6775	623	17	,	,	PUNCT
ejpam-6775	623	18	α∗)−	α∗)−	NOUN
ejpam-6775	623	19	(	(	PUNCT
ejpam-6775	623	20	ξε	ξε	NOUN
ejpam-6775	623	21	,	,	PUNCT
ejpam-6775	623	22	αε)∥l∞	αε)∥l∞	ADV
ejpam-6775	623	23	≤	≤	NUM
ejpam-6775	623	24	∣∣∣∣m(ξ∗	∣∣∣∣m(ξ∗	NOUN
ejpam-6775	623	25	,	,	PUNCT
ejpam-6775	623	26	α∗)−	α∗)−	NOUN
ejpam-6775	623	27	ρ1	ρ1	NOUN
ejpam-6775	623	28	(	(	PUNCT
ejpam-6775	623	29	[	[	X
ejpam-6775	623	30	−z∗	−z∗	X
ejpam-6775	623	31	s	s	PART
ejpam-6775	623	32	−	−	PROPN
ejpam-6775	623	33	z∗	z∗	NOUN
ejpam-6775	623	34	v	v	NOUN
ejpam-6775	623	35	]	]	SYM
ejpam-6775	623	36	s	s	NOUN
ejpam-6775	623	37	∗	∗	NOUN
ejpam-6775	623	38	−	−	PROPN
ejpam-6775	623	39	√	√	PROPN
ejpam-6775	623	40	εθε1	εθε1	PROPN
ejpam-6775	623	41	c1	c1	PROPN
ejpam-6775	623	42	)	)	PUNCT
ejpam-6775	623	43	,	,	PUNCT
ejpam-6775	623	44	ρ2	ρ2	NOUN
ejpam-6775	623	45	(	(	PUNCT
ejpam-6775	623	46	[	[	X
ejpam-6775	623	47	−z∗	−z∗	NOUN
ejpam-6775	623	48	s	s	PART
ejpam-6775	623	49	+	+	X
ejpam-6775	623	50	z∗	z∗	ADJ
ejpam-6775	623	51	i	i	PRON
ejpam-6775	623	52	]	]	X
ejpam-6775	623	53	i	i	PRON
ejpam-6775	623	54	∗	∗	VERB
ejpam-6775	623	55	−	−	PROPN
ejpam-6775	623	56	√	√	PROPN
ejpam-6775	623	57	εθε2	εθε2	PROPN
ejpam-6775	623	58	c2	c2	PROPN
ejpam-6775	623	59	)	)	PUNCT
ejpam-6775	623	60	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6775	623	61	l∞	l∞	NOUN
ejpam-6775	623	62	≤	≤	NUM
ejpam-6775	623	63	g3	g3	PROPN
ejpam-6775	623	64	t	t	PROPN
ejpam-6775	623	65	∥(ξ∗	∥(ξ∗	NOUN
ejpam-6775	623	66	,	,	PUNCT
ejpam-6775	623	67	α∗)−	α∗)−	NOUN
ejpam-6775	623	68	(	(	PUNCT
ejpam-6775	623	69	ξε	ξε	NOUN
ejpam-6775	623	70	,	,	PUNCT
ejpam-6775	623	71	αε)∥l∞	αε)∥l∞	ADV
ejpam-6775	623	72	+	+	CCONJ
ejpam-6775	623	73	√	√	NUM
ejpam-6775	623	74	ε(c−1	ε(c−1	X
ejpam-6775	623	75	1	1	NUM
ejpam-6775	623	76	+	+	CCONJ
ejpam-6775	623	77	c−1	c−1	PROPN
ejpam-6775	623	78	2	2	NUM
ejpam-6775	623	79	)	)	PUNCT
ejpam-6775	623	80	.	.	PUNCT
ejpam-6775	624	1	then	then	ADV
ejpam-6775	624	2	for	for	ADP
ejpam-6775	624	3	g3	g3	PROPN
ejpam-6775	624	4	t	t	PROPN
ejpam-6775	624	5	<	<	X
ejpam-6775	624	6	1	1	NUM
ejpam-6775	624	7	,	,	PUNCT
ejpam-6775	624	8	we	we	PRON
ejpam-6775	624	9	obtain	obtain	VERB
ejpam-6775	624	10	∥(ξ∗	∥(ξ∗	NOUN
ejpam-6775	624	11	,	,	PUNCT
ejpam-6775	624	12	α∗)−	α∗)−	NOUN
ejpam-6775	624	13	(	(	PUNCT
ejpam-6775	624	14	ξε	ξε	NOUN
ejpam-6775	624	15	,	,	PUNCT
ejpam-6775	624	16	αε)∥l∞	αε)∥l∞	ADV
ejpam-6775	624	17	≤	≤	NUM
ejpam-6775	624	18	√	√	NUM
ejpam-6775	624	19	ε(c−1	ε(c−1	PROPN
ejpam-6775	624	20	1	1	NUM
ejpam-6775	624	21	+	+	CCONJ
ejpam-6775	624	22	c−1	c−1	PROPN
ejpam-6775	624	23	2	2	NUM
ejpam-6775	624	24	)	)	PUNCT
ejpam-6775	624	25	1−	1−	NUM
ejpam-6775	624	26	g3	g3	PROPN
ejpam-6775	624	27	t	t	PROPN
ejpam-6775	624	28	.	.	PUNCT
ejpam-6775	625	1	(	(	PUNCT
ejpam-6775	625	2	65	65	NUM
ejpam-6775	625	3	)	)	PUNCT
ejpam-6775	625	4	which	which	PRON
ejpam-6775	625	5	gives	give	VERB
ejpam-6775	625	6	passing	pass	VERB
ejpam-6775	625	7	to	to	ADP
ejpam-6775	625	8	the	the	DET
ejpam-6775	625	9	limit	limit	NOUN
ejpam-6775	625	10	as	as	ADP
ejpam-6775	625	11	ε	ε	PROPN
ejpam-6775	625	12	→	→	SYM
ejpam-6775	625	13	0	0	NUM
ejpam-6775	625	14	the	the	DET
ejpam-6775	625	15	convergence	convergence	NOUN
ejpam-6775	625	16	(	(	PUNCT
ejpam-6775	625	17	ξε	ξε	NOUN
ejpam-6775	625	18	,	,	PUNCT
ejpam-6775	625	19	αε	αε	ADP
ejpam-6775	625	20	)	)	PUNCT
ejpam-6775	625	21	−→	−→	NOUN
ejpam-6775	625	22	(	(	PUNCT
ejpam-6775	625	23	ξ∗	ξ∗	ADJ
ejpam-6775	625	24	,	,	PUNCT
ejpam-6775	625	25	α∗	α∗	NOUN
ejpam-6775	625	26	)	)	PUNCT
ejpam-6775	625	27	.	.	PUNCT
ejpam-6775	626	1	since	since	SCONJ
ejpam-6775	626	2	h	h	NOUN
ejpam-6775	626	3	is	be	AUX
ejpam-6775	626	4	lower	low	ADJ
ejpam-6775	626	5	semi	semi	ADJ
ejpam-6775	626	6	-	-	ADJ
ejpam-6775	626	7	continuous	continuous	ADJ
ejpam-6775	626	8	and	and	CCONJ
ejpam-6775	626	9	using	use	VERB
ejpam-6775	626	10	property	property	NOUN
ejpam-6775	626	11	(	(	PUNCT
ejpam-6775	626	12	i	i	NOUN
ejpam-6775	626	13	)	)	PUNCT
ejpam-6775	626	14	of	of	ADP
ejpam-6775	626	15	ekeland	ekeland	PROPN
ejpam-6775	626	16	’s	’s	PART
ejpam-6775	626	17	principle	principle	NOUN
ejpam-6775	626	18	,	,	PUNCT
ejpam-6775	626	19	the	the	DET
ejpam-6775	626	20	inequality	inequality	NOUN
ejpam-6775	626	21	h(ξε	h(ξε	PROPN
ejpam-6775	626	22	,	,	PUNCT
ejpam-6775	626	23	αε	αε	ADP
ejpam-6775	626	24	)	)	PUNCT
ejpam-6775	626	25	≤	≤	NOUN
ejpam-6775	626	26	inf(ξ	inf(ξ	PROPN
ejpam-6775	626	27	,	,	PUNCT
ejpam-6775	626	28	α)∈d	α)∈d	X
ejpam-6775	626	29	h(ξ	h(ξ	PROPN
ejpam-6775	626	30	,	,	PUNCT
ejpam-6775	626	31	α	α	X
ejpam-6775	626	32	)	)	PUNCT
ejpam-6775	626	33	+	+	CCONJ
ejpam-6775	626	34	ε	ε	PROPN
ejpam-6775	626	35	implies	imply	VERB
ejpam-6775	626	36	(	(	PUNCT
ejpam-6775	626	37	as	as	ADP
ejpam-6775	626	38	ε	ε	PROPN
ejpam-6775	626	39	→	→	SYM
ejpam-6775	626	40	0	0	NUM
ejpam-6775	626	41	)	)	PUNCT
ejpam-6775	626	42	that	that	DET
ejpam-6775	626	43	h(ξ∗	h(ξ∗	NOUN
ejpam-6775	626	44	,	,	PUNCT
ejpam-6775	626	45	α∗	α∗	NOUN
ejpam-6775	626	46	)	)	PUNCT
ejpam-6775	626	47	≤	≤	NOUN
ejpam-6775	626	48	inf(ξ	inf(ξ	PROPN
ejpam-6775	626	49	,	,	PUNCT
ejpam-6775	626	50	α)∈d	α)∈d	X
ejpam-6775	626	51	h(ξ	h(ξ	PROPN
ejpam-6775	626	52	,	,	PUNCT
ejpam-6775	626	53	α	α	NOUN
ejpam-6775	626	54	)	)	PUNCT
ejpam-6775	626	55	.	.	PUNCT
ejpam-6775	627	1	therefore	therefore	ADV
ejpam-6775	627	2	,	,	PUNCT
ejpam-6775	627	3	we	we	PRON
ejpam-6775	627	4	have	have	VERB
ejpam-6775	627	5	h(ξ∗	h(ξ∗	NOUN
ejpam-6775	627	6	,	,	PUNCT
ejpam-6775	627	7	α∗	α∗	NOUN
ejpam-6775	627	8	)	)	PUNCT
ejpam-6775	627	9	=	=	SYM
ejpam-6775	627	10	inf(ξ	inf(ξ	PROPN
ejpam-6775	627	11	,	,	PUNCT
ejpam-6775	627	12	α)∈d	α)∈d	X
ejpam-6775	627	13	h(ξ	h(ξ	PROPN
ejpam-6775	627	14	,	,	PUNCT
ejpam-6775	627	15	α	α	NOUN
ejpam-6775	627	16	)	)	PUNCT
ejpam-6775	627	17	.	.	PUNCT
ejpam-6775	628	1	hence	hence	ADV
ejpam-6775	628	2	,	,	PUNCT
ejpam-6775	628	3	it	it	PRON
ejpam-6775	628	4	suffices	suffice	VERB
ejpam-6775	628	5	to	to	PART
ejpam-6775	628	6	take	take	VERB
ejpam-6775	628	7	kt	kt	PROPN
ejpam-6775	628	8	=	=	SYM
ejpam-6775	628	9	g3	g3	PROPN
ejpam-6775	628	10	t	t	PROPN
ejpam-6775	628	11	and	and	CCONJ
ejpam-6775	628	12	we	we	PRON
ejpam-6775	628	13	obtain	obtain	VERB
ejpam-6775	628	14	the	the	DET
ejpam-6775	628	15	indicated	indicate	VERB
ejpam-6775	628	16	result	result	NOUN
ejpam-6775	628	17	.	.	PUNCT
ejpam-6775	629	1	□	□	PUNCT
ejpam-6775	629	2	6	6	NUM
ejpam-6775	629	3	.	.	PUNCT
ejpam-6775	629	4	numerical	numerical	ADJ
ejpam-6775	629	5	results	result	NOUN
ejpam-6775	629	6	and	and	CCONJ
ejpam-6775	629	7	control	control	NOUN
ejpam-6775	629	8	impact	impact	NOUN
ejpam-6775	629	9	in	in	ADP
ejpam-6775	629	10	this	this	DET
ejpam-6775	629	11	section	section	NOUN
ejpam-6775	629	12	,	,	PUNCT
ejpam-6775	629	13	we	we	PRON
ejpam-6775	629	14	present	present	VERB
ejpam-6775	629	15	numerical	numerical	ADJ
ejpam-6775	629	16	simulations	simulation	NOUN
ejpam-6775	629	17	to	to	PART
ejpam-6775	629	18	illustrate	illustrate	VERB
ejpam-6775	629	19	the	the	DET
ejpam-6775	629	20	impact	impact	NOUN
ejpam-6775	629	21	of	of	ADP
ejpam-6775	629	22	optimal	optimal	ADJ
ejpam-6775	629	23	control	control	NOUN
ejpam-6775	629	24	strategies	strategy	NOUN
ejpam-6775	629	25	on	on	ADP
ejpam-6775	629	26	the	the	DET
ejpam-6775	629	27	transmission	transmission	NOUN
ejpam-6775	629	28	dynamics	dynamic	NOUN
ejpam-6775	629	29	of	of	ADP
ejpam-6775	629	30	the	the	DET
ejpam-6775	629	31	age	age	NOUN
ejpam-6775	629	32	-	-	PUNCT
ejpam-6775	629	33	structured	structure	VERB
ejpam-6775	629	34	svi	svi	ADJ
ejpam-6775	629	35	epidemic	epidemic	NOUN
ejpam-6775	629	36	model	model	NOUN
ejpam-6775	629	37	.	.	PUNCT
ejpam-6775	630	1	due	due	ADP
ejpam-6775	630	2	to	to	ADP
ejpam-6775	630	3	the	the	DET
ejpam-6775	630	4	complexity	complexity	NOUN
ejpam-6775	630	5	of	of	ADP
ejpam-6775	630	6	solving	solve	VERB
ejpam-6775	630	7	optimal	optimal	ADJ
ejpam-6775	630	8	control	control	NOUN
ejpam-6775	630	9	problems	problem	NOUN
ejpam-6775	630	10	analytically	analytically	ADV
ejpam-6775	630	11	,	,	PUNCT
ejpam-6775	630	12	we	we	PRON
ejpam-6775	630	13	employ	employ	VERB
ejpam-6775	630	14	a	a	DET
ejpam-6775	630	15	numerical	numerical	ADJ
ejpam-6775	630	16	approach	approach	NOUN
ejpam-6775	630	17	to	to	PART
ejpam-6775	630	18	approximate	approximate	VERB
ejpam-6775	630	19	the	the	DET
ejpam-6775	630	20	solutions	solution	NOUN
ejpam-6775	630	21	.	.	PUNCT
ejpam-6775	631	1	specifically	specifically	ADV
ejpam-6775	631	2	,	,	PUNCT
ejpam-6775	631	3	we	we	PRON
ejpam-6775	631	4	utilize	utilize	VERB
ejpam-6775	631	5	the	the	DET
ejpam-6775	631	6	forwardbackward	forwardbackward	ADJ
ejpam-6775	631	7	sweep	sweep	NOUN
ejpam-6775	631	8	method	method	NOUN
ejpam-6775	632	1	[	[	X
ejpam-6775	632	2	55	55	NUM
ejpam-6775	632	3	]	]	PUNCT
ejpam-6775	632	4	to	to	PART
ejpam-6775	632	5	solve	solve	VERB
ejpam-6775	632	6	the	the	DET
ejpam-6775	632	7	optimal	optimal	ADJ
ejpam-6775	632	8	control	control	NOUN
ejpam-6775	632	9	problem	problem	NOUN
ejpam-6775	632	10	(	(	PUNCT
ejpam-6775	632	11	ocp	ocp	PROPN
ejpam-6775	632	12	)	)	PUNCT
ejpam-6775	632	13	numerically	numerically	ADV
ejpam-6775	632	14	.	.	PUNCT
ejpam-6775	633	1	j.	j.	PROPN
ejpam-6775	633	2	leo	leo	PROPN
ejpam-6775	633	3	amalraj	amalraj	PROPN
ejpam-6775	633	4	et	et	PROPN
ejpam-6775	633	5	al	al	PROPN
ejpam-6775	633	6	.	.	PUNCT
ejpam-6775	633	7	/	/	SYM
ejpam-6775	633	8	eur	eur	PROPN
ejpam-6775	633	9	.	.	PUNCT
ejpam-6775	634	1	j.	j.	PROPN
ejpam-6775	634	2	pure	pure	PROPN
ejpam-6775	634	3	appl	appl	PROPN
ejpam-6775	634	4	.	.	PROPN
ejpam-6775	634	5	math	math	PROPN
ejpam-6775	634	6	,	,	PUNCT
ejpam-6775	634	7	18	18	NUM
ejpam-6775	634	8	(	(	PUNCT
ejpam-6775	634	9	4	4	NUM
ejpam-6775	634	10	)	)	PUNCT
ejpam-6775	634	11	(	(	PUNCT
ejpam-6775	634	12	2025	2025	NUM
ejpam-6775	634	13	)	)	PUNCT
ejpam-6775	634	14	,	,	PUNCT
ejpam-6775	634	15	6775	6775	NUM
ejpam-6775	634	16	24	24	NUM
ejpam-6775	634	17	of	of	ADP
ejpam-6775	634	18	32	32	NUM
ejpam-6775	634	19	the	the	DET
ejpam-6775	634	20	parameter	parameter	NOUN
ejpam-6775	634	21	values	value	NOUN
ejpam-6775	634	22	for	for	ADP
ejpam-6775	634	23	the	the	DET
ejpam-6775	634	24	simulations	simulation	NOUN
ejpam-6775	634	25	are	be	AUX
ejpam-6775	634	26	chosen	choose	VERB
ejpam-6775	634	27	based	base	VERB
ejpam-6775	634	28	on	on	ADP
ejpam-6775	634	29	realistic	realistic	ADJ
ejpam-6775	634	30	epidemiological	epidemiological	ADJ
ejpam-6775	634	31	data	datum	NOUN
ejpam-6775	634	32	from	from	ADP
ejpam-6775	634	33	studies	study	NOUN
ejpam-6775	634	34	on	on	ADP
ejpam-6775	634	35	bovine	bovine	ADJ
ejpam-6775	634	36	tuberculosis	tuberculosis	NOUN
ejpam-6775	634	37	and	and	CCONJ
ejpam-6775	634	38	similar	similar	ADJ
ejpam-6775	634	39	infectious	infectious	ADJ
ejpam-6775	634	40	diseases	disease	NOUN
ejpam-6775	634	41	[	[	X
ejpam-6775	634	42	1	1	NUM
ejpam-6775	634	43	,	,	PUNCT
ejpam-6775	634	44	2	2	NUM
ejpam-6775	634	45	]	]	PUNCT
ejpam-6775	634	46	.	.	PUNCT
ejpam-6775	635	1	for	for	ADP
ejpam-6775	635	2	instance	instance	NOUN
ejpam-6775	635	3	,	,	PUNCT
ejpam-6775	635	4	the	the	DET
ejpam-6775	635	5	recruitment	recruitment	NOUN
ejpam-6775	635	6	rate	rate	NOUN
ejpam-6775	635	7	λ	λ	NOUN
ejpam-6775	635	8	=	=	NOUN
ejpam-6775	635	9	700	700	NUM
ejpam-6775	635	10	is	be	AUX
ejpam-6775	635	11	calibrated	calibrate	VERB
ejpam-6775	635	12	to	to	PART
ejpam-6775	635	13	represent	represent	VERB
ejpam-6775	635	14	annual	annual	ADJ
ejpam-6775	635	15	population	population	NOUN
ejpam-6775	635	16	influx	influx	VERB
ejpam-6775	635	17	in	in	ADP
ejpam-6775	635	18	wildlife	wildlife	NOUN
ejpam-6775	635	19	herds	herd	NOUN
ejpam-6775	635	20	,	,	PUNCT
ejpam-6775	635	21	while	while	SCONJ
ejpam-6775	635	22	µ	µ	X
ejpam-6775	635	23	=	=	SYM
ejpam-6775	635	24	0.04	0.04	NUM
ejpam-6775	635	25	corresponds	correspond	NOUN
ejpam-6775	635	26	to	to	ADP
ejpam-6775	635	27	a	a	DET
ejpam-6775	635	28	natural	natural	ADJ
ejpam-6775	635	29	lifespan	lifespan	NOUN
ejpam-6775	635	30	of	of	ADP
ejpam-6775	635	31	approximately	approximately	ADV
ejpam-6775	635	32	25	25	NUM
ejpam-6775	635	33	years	year	NOUN
ejpam-6775	635	34	.	.	PUNCT
ejpam-6775	636	1	the	the	DET
ejpam-6775	636	2	infection	infection	NOUN
ejpam-6775	636	3	rate	rate	NOUN
ejpam-6775	636	4	β(x	β(x	NOUN
ejpam-6775	636	5	)	)	PUNCT
ejpam-6775	636	6	=	=	SYM
ejpam-6775	636	7	0.00005	0.00005	NUM
ejpam-6775	636	8	(	(	PUNCT
ejpam-6775	636	9	1	1	NUM
ejpam-6775	636	10	+	+	CCONJ
ejpam-6775	636	11	x	x	SYM
ejpam-6775	636	12	1	1	NUM
ejpam-6775	636	13	+	+	NOUN
ejpam-6775	636	14	5x	5x	NOUN
ejpam-6775	636	15	)	)	PUNCT
ejpam-6775	636	16	is	be	AUX
ejpam-6775	636	17	age	age	NOUN
ejpam-6775	636	18	-	-	PUNCT
ejpam-6775	636	19	dependent	dependent	ADJ
ejpam-6775	636	20	to	to	PART
ejpam-6775	636	21	reflect	reflect	VERB
ejpam-6775	636	22	increasing	increase	VERB
ejpam-6775	636	23	infectivity	infectivity	NOUN
ejpam-6775	636	24	with	with	ADP
ejpam-6775	636	25	infection	infection	NOUN
ejpam-6775	636	26	duration	duration	NOUN
ejpam-6775	636	27	,	,	PUNCT
ejpam-6775	636	28	derived	derive	VERB
ejpam-6775	636	29	from	from	ADP
ejpam-6775	636	30	empirical	empirical	ADJ
ejpam-6775	636	31	observations	observation	NOUN
ejpam-6775	636	32	.	.	PUNCT
ejpam-6775	637	1	these	these	DET
ejpam-6775	637	2	values	value	NOUN
ejpam-6775	637	3	ensure	ensure	VERB
ejpam-6775	637	4	the	the	DET
ejpam-6775	637	5	basic	basic	ADJ
ejpam-6775	637	6	reproduction	reproduction	NOUN
ejpam-6775	637	7	number	number	NOUN
ejpam-6775	637	8	r0	r0	NOUN
ejpam-6775	637	9	is	be	AUX
ejpam-6775	637	10	around	around	ADP
ejpam-6775	637	11	1.2	1.2	NUM
ejpam-6775	637	12	for	for	ADP
ejpam-6775	637	13	baseline	baseline	ADJ
ejpam-6775	637	14	scenarios	scenario	NOUN
ejpam-6775	637	15	,	,	PUNCT
ejpam-6775	637	16	allowing	allow	VERB
ejpam-6775	637	17	exploration	exploration	NOUN
ejpam-6775	637	18	of	of	ADP
ejpam-6775	637	19	backward	backward	ADJ
ejpam-6775	637	20	bifurcation	bifurcation	NOUN
ejpam-6775	637	21	.	.	PUNCT
ejpam-6775	638	1	sensitivity	sensitivity	NOUN
ejpam-6775	638	2	analysis	analysis	NOUN
ejpam-6775	638	3	(	(	PUNCT
ejpam-6775	638	4	not	not	PART
ejpam-6775	638	5	shown	show	VERB
ejpam-6775	638	6	)	)	PUNCT
ejpam-6775	638	7	confirms	confirm	VERB
ejpam-6775	638	8	that	that	SCONJ
ejpam-6775	638	9	variations	variation	NOUN
ejpam-6775	638	10	within	within	ADP
ejpam-6775	638	11	10	10	NUM
ejpam-6775	638	12	%	%	NOUN
ejpam-6775	638	13	do	do	AUX
ejpam-6775	638	14	not	not	PART
ejpam-6775	638	15	alter	alter	VERB
ejpam-6775	638	16	qualitative	qualitative	ADJ
ejpam-6775	638	17	behaviors	behavior	NOUN
ejpam-6775	638	18	.	.	PUNCT
ejpam-6775	639	1	the	the	DET
ejpam-6775	639	2	chosen	choose	VERB
ejpam-6775	639	3	numerical	numerical	ADJ
ejpam-6775	639	4	values	value	NOUN
ejpam-6775	639	5	are	be	AUX
ejpam-6775	639	6	selected	select	VERB
ejpam-6775	639	7	to	to	PART
ejpam-6775	639	8	illustrate	illustrate	VERB
ejpam-6775	639	9	the	the	DET
ejpam-6775	639	10	model	model	NOUN
ejpam-6775	639	11	’s	’s	PART
ejpam-6775	639	12	behavior	behavior	NOUN
ejpam-6775	639	13	near	near	ADP
ejpam-6775	639	14	the	the	DET
ejpam-6775	639	15	bifurcation	bifurcation	NOUN
ejpam-6775	639	16	point	point	NOUN
ejpam-6775	639	17	,	,	PUNCT
ejpam-6775	639	18	where	where	SCONJ
ejpam-6775	639	19	r0	r0	NOUN
ejpam-6775	639	20	≈	≈	PROPN
ejpam-6775	639	21	1	1	NUM
ejpam-6775	639	22	.	.	PUNCT
ejpam-6775	640	1	while	while	SCONJ
ejpam-6775	640	2	arbitrary	arbitrary	ADJ
ejpam-6775	640	3	choices	choice	NOUN
ejpam-6775	640	4	could	could	AUX
ejpam-6775	640	5	theoretically	theoretically	ADV
ejpam-6775	640	6	shift	shift	VERB
ejpam-6775	640	7	stability	stability	NOUN
ejpam-6775	640	8	thresholds	threshold	NOUN
ejpam-6775	640	9	,	,	PUNCT
ejpam-6775	640	10	we	we	PRON
ejpam-6775	640	11	performed	perform	VERB
ejpam-6775	640	12	sensitivity	sensitivity	NOUN
ejpam-6775	640	13	analyses	analysis	NOUN
ejpam-6775	640	14	(	(	PUNCT
ejpam-6775	640	15	varying	vary	VERB
ejpam-6775	640	16	parameters	parameter	NOUN
ejpam-6775	640	17	by	by	ADP
ejpam-6775	640	18	±20	±20	PROPN
ejpam-6775	640	19	%	%	NOUN
ejpam-6775	640	20	)	)	PUNCT
ejpam-6775	640	21	to	to	PART
ejpam-6775	640	22	confirm	confirm	VERB
ejpam-6775	640	23	that	that	SCONJ
ejpam-6775	640	24	the	the	DET
ejpam-6775	640	25	backward	backward	ADJ
ejpam-6775	640	26	bifurcation	bifurcation	NOUN
ejpam-6775	640	27	and	and	CCONJ
ejpam-6775	640	28	control	control	NOUN
ejpam-6775	640	29	efficacy	efficacy	NOUN
ejpam-6775	640	30	persist	persist	VERB
ejpam-6775	640	31	qualitatively	qualitatively	ADV
ejpam-6775	640	32	.	.	PUNCT
ejpam-6775	641	1	for	for	ADP
ejpam-6775	641	2	example	example	NOUN
ejpam-6775	641	3	,	,	PUNCT
ejpam-6775	641	4	increasing	increase	VERB
ejpam-6775	641	5	β(x	β(x	NOUN
ejpam-6775	641	6	)	)	PUNCT
ejpam-6775	641	7	by	by	ADP
ejpam-6775	641	8	10	10	NUM
ejpam-6775	641	9	%	%	NOUN
ejpam-6775	641	10	raises	raise	VERB
ejpam-6775	641	11	r0	r0	NOUN
ejpam-6775	641	12	but	but	CCONJ
ejpam-6775	641	13	does	do	AUX
ejpam-6775	641	14	not	not	PART
ejpam-6775	641	15	eliminate	eliminate	VERB
ejpam-6775	641	16	bistability	bistability	NOUN
ejpam-6775	641	17	,	,	PUNCT
ejpam-6775	641	18	ensuring	ensure	VERB
ejpam-6775	641	19	robustness	robustness	NOUN
ejpam-6775	641	20	.	.	PUNCT
ejpam-6775	642	1	the	the	DET
ejpam-6775	642	2	simulations	simulation	NOUN
ejpam-6775	642	3	are	be	AUX
ejpam-6775	642	4	conducted	conduct	VERB
ejpam-6775	642	5	over	over	ADP
ejpam-6775	642	6	a	a	DET
ejpam-6775	642	7	control	control	NOUN
ejpam-6775	642	8	period	period	NOUN
ejpam-6775	642	9	of	of	ADP
ejpam-6775	642	10	t	t	NOUN
ejpam-6775	642	11	=	=	SYM
ejpam-6775	642	12	50	50	NUM
ejpam-6775	642	13	time	time	NOUN
ejpam-6775	642	14	units	unit	NOUN
ejpam-6775	642	15	,	,	PUNCT
ejpam-6775	642	16	with	with	ADP
ejpam-6775	642	17	a	a	DET
ejpam-6775	642	18	maximum	maximum	ADJ
ejpam-6775	642	19	infection	infection	NOUN
ejpam-6775	642	20	age	age	NOUN
ejpam-6775	642	21	of	of	ADP
ejpam-6775	642	22	xmax	xmax	PROPN
ejpam-6775	642	23	=	=	SYM
ejpam-6775	642	24	30	30	NUM
ejpam-6775	642	25	.	.	PUNCT
ejpam-6775	643	1	the	the	DET
ejpam-6775	643	2	baseline	baseline	ADJ
ejpam-6775	643	3	parameters	parameter	NOUN
ejpam-6775	643	4	are	be	AUX
ejpam-6775	643	5	chosen	choose	VERB
ejpam-6775	643	6	as	as	SCONJ
ejpam-6775	643	7	follows	follow	VERB
ejpam-6775	643	8	:	:	PUNCT
ejpam-6775	643	9	recruitment	recruitment	NOUN
ejpam-6775	643	10	rate	rate	NOUN
ejpam-6775	643	11	λ	λ	NOUN
ejpam-6775	643	12	=	=	NOUN
ejpam-6775	643	13	700	700	NUM
ejpam-6775	643	14	,	,	PUNCT
ejpam-6775	643	15	natural	natural	ADJ
ejpam-6775	643	16	death	death	NOUN
ejpam-6775	643	17	rate	rate	NOUN
ejpam-6775	643	18	µ	µ	X
ejpam-6775	643	19	=	=	SYM
ejpam-6775	643	20	0.04	0.04	NUM
ejpam-6775	643	21	,	,	PUNCT
ejpam-6775	643	22	vaccine	vaccine	NOUN
ejpam-6775	643	23	efficacy	efficacy	NOUN
ejpam-6775	643	24	reduction	reduction	NOUN
ejpam-6775	643	25	factor	factor	NOUN
ejpam-6775	643	26	m	m	NOUN
ejpam-6775	643	27	=	=	NOUN
ejpam-6775	643	28	0.25	0.25	NUM
ejpam-6775	643	29	,	,	PUNCT
ejpam-6775	643	30	and	and	CCONJ
ejpam-6775	643	31	constant	constant	ADJ
ejpam-6775	643	32	disease	disease	NOUN
ejpam-6775	643	33	-	-	PUNCT
ejpam-6775	643	34	induced	induce	VERB
ejpam-6775	643	35	death	death	NOUN
ejpam-6775	643	36	rate	rate	NOUN
ejpam-6775	643	37	δ(x	δ(x	PROPN
ejpam-6775	643	38	)	)	PUNCT
ejpam-6775	644	1	=	=	SYM
ejpam-6775	644	2	δ	δ	X
ejpam-6775	644	3	=	=	NOUN
ejpam-6775	644	4	0.05	0.05	NUM
ejpam-6775	644	5	.	.	PUNCT
ejpam-6775	645	1	the	the	DET
ejpam-6775	645	2	age	age	NOUN
ejpam-6775	645	3	-	-	PUNCT
ejpam-6775	645	4	dependent	dependent	ADJ
ejpam-6775	645	5	infection	infection	NOUN
ejpam-6775	645	6	rate	rate	NOUN
ejpam-6775	645	7	is	be	AUX
ejpam-6775	645	8	defined	define	VERB
ejpam-6775	645	9	as	as	ADP
ejpam-6775	645	10	β(x	β(x	NOUN
ejpam-6775	645	11	)	)	PUNCT
ejpam-6775	645	12	=	=	SYM
ejpam-6775	646	1	0.00005	0.00005	NUM
ejpam-6775	646	2	(	(	PUNCT
ejpam-6775	646	3	1	1	NUM
ejpam-6775	646	4	+	+	CCONJ
ejpam-6775	646	5	x	x	SYM
ejpam-6775	646	6	1	1	NUM
ejpam-6775	646	7	+	+	NOUN
ejpam-6775	646	8	5x	5x	NUM
ejpam-6775	646	9	)	)	PUNCT
ejpam-6775	646	10	.	.	PUNCT
ejpam-6775	647	1	initial	initial	ADJ
ejpam-6775	647	2	conditions	condition	NOUN
ejpam-6775	647	3	are	be	AUX
ejpam-6775	647	4	set	set	VERB
ejpam-6775	647	5	as	as	ADP
ejpam-6775	647	6	s(0	s(0	PROPN
ejpam-6775	647	7	)	)	PUNCT
ejpam-6775	647	8	=	=	SYM
ejpam-6775	647	9	104	104	NUM
ejpam-6775	647	10	,	,	PUNCT
ejpam-6775	647	11	v	v	NOUN
ejpam-6775	647	12	(	(	PUNCT
ejpam-6775	647	13	0	0	NUM
ejpam-6775	647	14	)	)	PUNCT
ejpam-6775	647	15	=	=	SYM
ejpam-6775	647	16	0	0	NUM
ejpam-6775	647	17	,	,	PUNCT
ejpam-6775	647	18	and	and	CCONJ
ejpam-6775	647	19	the	the	DET
ejpam-6775	647	20	initial	initial	ADJ
ejpam-6775	647	21	infected	infected	ADJ
ejpam-6775	647	22	distribution	distribution	NOUN
ejpam-6775	647	23	is	be	AUX
ejpam-6775	647	24	i0(x	i0(x	NOUN
ejpam-6775	647	25	)	)	PUNCT
ejpam-6775	647	26	=	=	SYM
ejpam-6775	647	27	100e−0.1(x−15)2	100e−0.1(x−15)2	NUM
ejpam-6775	647	28	,	,	PUNCT
ejpam-6775	647	29	ensuring	ensure	VERB
ejpam-6775	647	30	a	a	DET
ejpam-6775	647	31	significant	significant	ADJ
ejpam-6775	647	32	infected	infected	ADJ
ejpam-6775	647	33	population	population	NOUN
ejpam-6775	647	34	within	within	ADP
ejpam-6775	647	35	the	the	DET
ejpam-6775	647	36	domain	domain	NOUN
ejpam-6775	647	37	x	x	X
ejpam-6775	647	38	∈	∈	PROPN
ejpam-6775	648	1	[	[	X
ejpam-6775	648	2	0	0	NUM
ejpam-6775	648	3	,	,	PUNCT
ejpam-6775	648	4	30	30	NUM
ejpam-6775	648	5	]	]	PUNCT
ejpam-6775	648	6	.	.	PUNCT
ejpam-6775	649	1	the	the	DET
ejpam-6775	649	2	total	total	ADJ
ejpam-6775	649	3	number	number	NOUN
ejpam-6775	649	4	of	of	ADP
ejpam-6775	649	5	infected	infected	ADJ
ejpam-6775	649	6	individuals	individual	NOUN
ejpam-6775	649	7	is	be	AUX
ejpam-6775	649	8	computed	compute	VERB
ejpam-6775	649	9	as	as	ADP
ejpam-6775	649	10	i(t	i(t	NOUN
ejpam-6775	649	11	)	)	PUNCT
ejpam-6775	650	1	=	=	SYM
ejpam-6775	650	2	∫	∫	PROPN
ejpam-6775	650	3	xmax	xmax	PROPN
ejpam-6775	650	4	0	0	NUM
ejpam-6775	651	1	i(t	i(t	PROPN
ejpam-6775	651	2	,	,	PUNCT
ejpam-6775	651	3	x	x	X
ejpam-6775	651	4	)	)	PUNCT
ejpam-6775	651	5	dx	dx	PROPN
ejpam-6775	651	6	.	.	PUNCT
ejpam-6775	652	1	control	control	PROPN
ejpam-6775	652	2	bounds	bound	NOUN
ejpam-6775	652	3	are	be	AUX
ejpam-6775	652	4	set	set	VERB
ejpam-6775	652	5	as	as	ADP
ejpam-6775	652	6	ξ(t	ξ(t	NOUN
ejpam-6775	652	7	)	)	PUNCT
ejpam-6775	652	8	∈	∈	PROPN
ejpam-6775	653	1	[	[	X
ejpam-6775	653	2	0	0	NUM
ejpam-6775	653	3	,	,	PUNCT
ejpam-6775	653	4	0.2	0.2	NUM
ejpam-6775	653	5	]	]	PUNCT
ejpam-6775	653	6	for	for	ADP
ejpam-6775	653	7	vaccination	vaccination	NOUN
ejpam-6775	653	8	and	and	CCONJ
ejpam-6775	653	9	α(t	α(t	PROPN
ejpam-6775	653	10	,	,	PUNCT
ejpam-6775	653	11	x	x	X
ejpam-6775	653	12	)	)	PUNCT
ejpam-6775	653	13	∈	∈	PROPN
ejpam-6775	654	1	[	[	X
ejpam-6775	654	2	0	0	NUM
ejpam-6775	654	3	,	,	PUNCT
ejpam-6775	654	4	0.5	0.5	NUM
ejpam-6775	654	5	]	]	PUNCT
ejpam-6775	654	6	for	for	ADP
ejpam-6775	654	7	treatment	treatment	NOUN
ejpam-6775	654	8	.	.	PUNCT
ejpam-6775	655	1	we	we	PRON
ejpam-6775	655	2	explore	explore	VERB
ejpam-6775	655	3	two	two	NUM
ejpam-6775	655	4	scenarios	scenario	NOUN
ejpam-6775	655	5	by	by	ADP
ejpam-6775	655	6	varying	vary	VERB
ejpam-6775	655	7	the	the	DET
ejpam-6775	655	8	weight	weight	NOUN
ejpam-6775	655	9	factors	factor	NOUN
ejpam-6775	655	10	c1	c1	PROPN
ejpam-6775	655	11	and	and	CCONJ
ejpam-6775	655	12	c2	c2	PROPN
ejpam-6775	655	13	in	in	ADP
ejpam-6775	655	14	the	the	DET
ejpam-6775	655	15	objective	objective	ADJ
ejpam-6775	655	16	functional	functional	NOUN
ejpam-6775	655	17	,	,	PUNCT
ejpam-6775	655	18	which	which	PRON
ejpam-6775	655	19	balance	balance	VERB
ejpam-6775	655	20	the	the	DET
ejpam-6775	655	21	cost	cost	NOUN
ejpam-6775	655	22	of	of	ADP
ejpam-6775	655	23	vaccination	vaccination	NOUN
ejpam-6775	655	24	and	and	CCONJ
ejpam-6775	655	25	treatment	treatment	NOUN
ejpam-6775	655	26	,	,	PUNCT
ejpam-6775	655	27	respectively	respectively	ADV
ejpam-6775	655	28	:	:	PUNCT
ejpam-6775	655	29	•	•	NUM
ejpam-6775	655	30	scenario	scenario	NOUN
ejpam-6775	655	31	1	1	NUM
ejpam-6775	655	32	(	(	PUNCT
ejpam-6775	655	33	equal	equal	ADJ
ejpam-6775	655	34	costs	cost	NOUN
ejpam-6775	655	35	):	):	PUNCT
ejpam-6775	655	36	c1	c1	PROPN
ejpam-6775	655	37	=	=	PROPN
ejpam-6775	655	38	c2	c2	PROPN
ejpam-6775	655	39	=	=	SYM
ejpam-6775	655	40	1000	1000	NUM
ejpam-6775	655	41	,	,	PUNCT
ejpam-6775	655	42	representing	represent	VERB
ejpam-6775	655	43	equal	equal	ADJ
ejpam-6775	655	44	weighting	weighting	NOUN
ejpam-6775	655	45	of	of	ADP
ejpam-6775	655	46	vaccination	vaccination	NOUN
ejpam-6775	655	47	and	and	CCONJ
ejpam-6775	655	48	treatment	treatment	NOUN
ejpam-6775	655	49	costs	cost	NOUN
ejpam-6775	655	50	.	.	PUNCT
ejpam-6775	656	1	•	•	NUM
ejpam-6775	656	2	scenario	scenario	NOUN
ejpam-6775	656	3	2	2	NUM
ejpam-6775	656	4	(	(	PUNCT
ejpam-6775	656	5	higher	high	ADJ
ejpam-6775	656	6	treatment	treatment	NOUN
ejpam-6775	656	7	cost	cost	NOUN
ejpam-6775	656	8	):	):	PUNCT
ejpam-6775	656	9	c1	c1	NOUN
ejpam-6775	656	10	=	=	PUNCT
ejpam-6775	656	11	1000	1000	NUM
ejpam-6775	656	12	,	,	PUNCT
ejpam-6775	656	13	c2	c2	PROPN
ejpam-6775	656	14	=	=	SYM
ejpam-6775	656	15	5000	5000	NUM
ejpam-6775	656	16	,	,	PUNCT
ejpam-6775	656	17	emphasizing	emphasize	VERB
ejpam-6775	656	18	reduced	reduce	VERB
ejpam-6775	656	19	treatment	treatment	NOUN
ejpam-6775	656	20	effort	effort	NOUN
ejpam-6775	656	21	due	due	ADP
ejpam-6775	656	22	to	to	ADP
ejpam-6775	656	23	higher	high	ADJ
ejpam-6775	656	24	costs	cost	NOUN
ejpam-6775	656	25	.	.	PUNCT
ejpam-6775	657	1	figure	figure	VERB
ejpam-6775	657	2	5	5	NUM
ejpam-6775	657	3	highlights	highlight	NOUN
ejpam-6775	657	4	the	the	DET
ejpam-6775	657	5	age	age	NOUN
ejpam-6775	657	6	-	-	PUNCT
ejpam-6775	657	7	dependent	dependent	ADJ
ejpam-6775	657	8	nature	nature	NOUN
ejpam-6775	657	9	of	of	ADP
ejpam-6775	657	10	the	the	DET
ejpam-6775	657	11	optimal	optimal	ADJ
ejpam-6775	657	12	treatment	treatment	NOUN
ejpam-6775	657	13	control	control	NOUN
ejpam-6775	657	14	α(t	α(t	PROPN
ejpam-6775	657	15	,	,	PUNCT
ejpam-6775	657	16	x	x	NOUN
ejpam-6775	657	17	)	)	PUNCT
ejpam-6775	657	18	.	.	PUNCT
ejpam-6775	658	1	treatment	treatment	NOUN
ejpam-6775	658	2	is	be	AUX
ejpam-6775	658	3	more	more	ADV
ejpam-6775	658	4	intensive	intensive	ADJ
ejpam-6775	658	5	for	for	ADP
ejpam-6775	658	6	individuals	individual	NOUN
ejpam-6775	658	7	with	with	ADP
ejpam-6775	658	8	shorter	short	ADJ
ejpam-6775	658	9	infection	infection	NOUN
ejpam-6775	658	10	ages	age	NOUN
ejpam-6775	658	11	(	(	PUNCT
ejpam-6775	658	12	e.g.	e.g.	ADV
ejpam-6775	658	13	,	,	PUNCT
ejpam-6775	658	14	x	x	SYM
ejpam-6775	658	15	=	=	SYM
ejpam-6775	658	16	0	0	NUM
ejpam-6775	658	17	)	)	PUNCT
ejpam-6775	658	18	,	,	PUNCT
ejpam-6775	658	19	decreasing	decrease	VERB
ejpam-6775	658	20	as	as	ADP
ejpam-6775	658	21	the	the	DET
ejpam-6775	658	22	infection	infection	NOUN
ejpam-6775	658	23	age	age	NOUN
ejpam-6775	658	24	increases	increase	NOUN
ejpam-6775	658	25	(	(	PUNCT
ejpam-6775	658	26	e.g.	e.g.	ADV
ejpam-6775	658	27	,	,	PUNCT
ejpam-6775	658	28	x	x	SYM
ejpam-6775	658	29	=	=	SYM
ejpam-6775	658	30	20	20	NUM
ejpam-6775	658	31	)	)	PUNCT
ejpam-6775	658	32	.	.	PUNCT
ejpam-6775	659	1	in	in	ADP
ejpam-6775	659	2	scenario	scenario	NOUN
ejpam-6775	659	3	2	2	NUM
ejpam-6775	659	4	,	,	PUNCT
ejpam-6775	659	5	the	the	DET
ejpam-6775	659	6	higher	high	ADJ
ejpam-6775	659	7	treatment	treatment	NOUN
ejpam-6775	659	8	cost	cost	NOUN
ejpam-6775	659	9	leads	lead	VERB
ejpam-6775	659	10	to	to	ADP
ejpam-6775	659	11	reduced	reduce	VERB
ejpam-6775	659	12	treatment	treatment	NOUN
ejpam-6775	659	13	efforts	effort	NOUN
ejpam-6775	659	14	across	across	ADP
ejpam-6775	659	15	all	all	DET
ejpam-6775	659	16	ages	age	NOUN
ejpam-6775	659	17	,	,	PUNCT
ejpam-6775	659	18	as	as	SCONJ
ejpam-6775	659	19	evidenced	evidence	VERB
ejpam-6775	659	20	by	by	ADP
ejpam-6775	659	21	the	the	DET
ejpam-6775	659	22	lower	low	ADJ
ejpam-6775	659	23	values	value	NOUN
ejpam-6775	659	24	of	of	ADP
ejpam-6775	659	25	α(t	α(t	PROPN
ejpam-6775	659	26	,	,	PUNCT
ejpam-6775	659	27	x	x	PRON
ejpam-6775	659	28	)	)	PUNCT
ejpam-6775	659	29	compared	compare	VERB
ejpam-6775	659	30	to	to	ADP
ejpam-6775	659	31	scenario	scenario	NOUN
ejpam-6775	659	32	1	1	NUM
ejpam-6775	659	33	.	.	PUNCT
ejpam-6775	660	1	this	this	PRON
ejpam-6775	660	2	suggests	suggest	VERB
ejpam-6775	660	3	that	that	SCONJ
ejpam-6775	660	4	early	early	ADJ
ejpam-6775	660	5	treatment	treatment	NOUN
ejpam-6775	660	6	is	be	AUX
ejpam-6775	660	7	critical	critical	ADJ
ejpam-6775	660	8	for	for	ADP
ejpam-6775	660	9	effective	effective	ADJ
ejpam-6775	660	10	disease	disease	NOUN
ejpam-6775	660	11	control	control	NOUN
ejpam-6775	660	12	,	,	PUNCT
ejpam-6775	660	13	particularly	particularly	ADV
ejpam-6775	660	14	when	when	SCONJ
ejpam-6775	660	15	resources	resource	NOUN
ejpam-6775	660	16	are	be	AUX
ejpam-6775	660	17	constrained	constrain	VERB
ejpam-6775	660	18	.	.	PUNCT
ejpam-6775	661	1	a	a	DET
ejpam-6775	661	2	third	third	ADJ
ejpam-6775	661	3	scenario	scenario	NOUN
ejpam-6775	661	4	with	with	ADP
ejpam-6775	661	5	higher	high	ADJ
ejpam-6775	661	6	vaccination	vaccination	NOUN
ejpam-6775	661	7	cost	cost	NOUN
ejpam-6775	661	8	(	(	PUNCT
ejpam-6775	661	9	e.g.	e.g.	ADV
ejpam-6775	661	10	,	,	PUNCT
ejpam-6775	661	11	c1	c1	PROPN
ejpam-6775	661	12	=	=	PUNCT
ejpam-6775	661	13	5000	5000	NUM
ejpam-6775	661	14	,	,	PUNCT
ejpam-6775	661	15	c2	c2	PROPN
ejpam-6775	661	16	=	=	SYM
ejpam-6775	661	17	1000	1000	NUM
ejpam-6775	661	18	)	)	PUNCT
ejpam-6775	661	19	was	be	AUX
ejpam-6775	661	20	considered	consider	VERB
ejpam-6775	661	21	but	but	CCONJ
ejpam-6775	661	22	not	not	PART
ejpam-6775	661	23	presented	present	VERB
ejpam-6775	661	24	,	,	PUNCT
ejpam-6775	661	25	as	as	SCONJ
ejpam-6775	661	26	it	it	PRON
ejpam-6775	661	27	mirrors	mirror	VERB
ejpam-6775	661	28	scenario	scenario	NOUN
ejpam-6775	661	29	2	2	NUM
ejpam-6775	661	30	by	by	ADP
ejpam-6775	661	31	shifting	shift	VERB
ejpam-6775	661	32	emphasis	emphasis	NOUN
ejpam-6775	661	33	to	to	ADP
ejpam-6775	661	34	treatment	treatment	NOUN
ejpam-6775	661	35	,	,	PUNCT
ejpam-6775	661	36	yielding	yield	VERB
ejpam-6775	661	37	similar	similar	ADJ
ejpam-6775	661	38	qualitative	qualitative	ADJ
ejpam-6775	661	39	reductions	reduction	NOUN
ejpam-6775	661	40	in	in	ADP
ejpam-6775	661	41	infections	infection	NOUN
ejpam-6775	661	42	(	(	PUNCT
ejpam-6775	661	43	about	about	ADV
ejpam-6775	661	44	40	40	NUM
ejpam-6775	661	45	%	%	NOUN
ejpam-6775	661	46	lower	low	ADJ
ejpam-6775	661	47	prevalence	prevalence	NOUN
ejpam-6775	661	48	)	)	PUNCT
ejpam-6775	661	49	but	but	CCONJ
ejpam-6775	661	50	with	with	ADP
ejpam-6775	661	51	increased	increase	VERB
ejpam-6775	661	52	total	total	ADJ
ejpam-6775	661	53	costs	cost	NOUN
ejpam-6775	661	54	due	due	ADJ
ejpam-6775	661	55	to	to	ADP
ejpam-6775	661	56	vaccination	vaccination	NOUN
ejpam-6775	661	57	constraints	constraint	NOUN
ejpam-6775	661	58	.	.	PUNCT
ejpam-6775	662	1	this	this	DET
ejpam-6775	662	2	symmetry	symmetry	NOUN
ejpam-6775	662	3	supports	support	VERB
ejpam-6775	662	4	our	our	PRON
ejpam-6775	662	5	focus	focus	NOUN
ejpam-6775	662	6	on	on	ADP
ejpam-6775	662	7	balanced	balanced	ADJ
ejpam-6775	662	8	and	and	CCONJ
ejpam-6775	662	9	treatment	treatment	NOUN
ejpam-6775	662	10	-	-	PUNCT
ejpam-6775	662	11	heavy	heavy	ADJ
ejpam-6775	662	12	cases	case	NOUN
ejpam-6775	662	13	.	.	PUNCT
ejpam-6775	663	1	j.	j.	PROPN
ejpam-6775	663	2	leo	leo	PROPN
ejpam-6775	663	3	amalraj	amalraj	PROPN
ejpam-6775	663	4	et	et	PROPN
ejpam-6775	663	5	al	al	PROPN
ejpam-6775	663	6	.	.	PUNCT
ejpam-6775	663	7	/	/	SYM
ejpam-6775	663	8	eur	eur	PROPN
ejpam-6775	663	9	.	.	PUNCT
ejpam-6775	664	1	j.	j.	PROPN
ejpam-6775	664	2	pure	pure	PROPN
ejpam-6775	664	3	appl	appl	PROPN
ejpam-6775	664	4	.	.	PROPN
ejpam-6775	664	5	math	math	PROPN
ejpam-6775	664	6	,	,	PUNCT
ejpam-6775	664	7	18	18	NUM
ejpam-6775	664	8	(	(	PUNCT
ejpam-6775	664	9	4	4	NUM
ejpam-6775	664	10	)	)	PUNCT
ejpam-6775	664	11	(	(	PUNCT
ejpam-6775	664	12	2025	2025	NUM
ejpam-6775	664	13	)	)	PUNCT
ejpam-6775	664	14	,	,	PUNCT
ejpam-6775	664	15	6775	6775	NUM
ejpam-6775	664	16	25	25	NUM
ejpam-6775	664	17	of	of	ADP
ejpam-6775	664	18	32	32	NUM
ejpam-6775	664	19	figure	figure	NOUN
ejpam-6775	664	20	1	1	NUM
ejpam-6775	664	21	:	:	PUNCT
ejpam-6775	664	22	susceptible	susceptible	ADJ
ejpam-6775	664	23	population	population	NOUN
ejpam-6775	664	24	s(t	s(t	PROPN
ejpam-6775	664	25	)	)	PUNCT
ejpam-6775	664	26	of	of	ADP
ejpam-6775	664	27	the	the	DET
ejpam-6775	664	28	age	age	NOUN
ejpam-6775	664	29	-	-	PUNCT
ejpam-6775	664	30	structured	structure	VERB
ejpam-6775	664	31	svi	svi	PROPN
ejpam-6775	664	32	model	model	NOUN
ejpam-6775	664	33	(	(	PUNCT
ejpam-6775	664	34	system	system	NOUN
ejpam-6775	664	35	(	(	PUNCT
ejpam-6775	664	36	1	1	NUM
ejpam-6775	664	37	)	)	PUNCT
ejpam-6775	664	38	)	)	PUNCT
ejpam-6775	664	39	under	under	ADP
ejpam-6775	664	40	scenario	scenario	NOUN
ejpam-6775	664	41	2	2	NUM
ejpam-6775	664	42	with	with	ADP
ejpam-6775	664	43	higher	high	ADJ
ejpam-6775	664	44	treatment	treatment	NOUN
ejpam-6775	664	45	cost	cost	NOUN
ejpam-6775	664	46	(	(	PUNCT
ejpam-6775	664	47	c1	c1	NOUN
ejpam-6775	664	48	=	=	SYM
ejpam-6775	664	49	1000	1000	NUM
ejpam-6775	664	50	,	,	PUNCT
ejpam-6775	664	51	c2	c2	PROPN
ejpam-6775	664	52	=	=	SYM
ejpam-6775	664	53	5000	5000	NUM
ejpam-6775	664	54	)	)	PUNCT
ejpam-6775	664	55	.	.	PUNCT
ejpam-6775	665	1	figure	figure	NOUN
ejpam-6775	665	2	2	2	NUM
ejpam-6775	665	3	:	:	PUNCT
ejpam-6775	665	4	vaccinated	vaccinate	VERB
ejpam-6775	665	5	population	population	NOUN
ejpam-6775	665	6	v	v	ADP
ejpam-6775	665	7	(	(	PUNCT
ejpam-6775	665	8	t	t	PROPN
ejpam-6775	665	9	)	)	PUNCT
ejpam-6775	665	10	of	of	ADP
ejpam-6775	665	11	the	the	DET
ejpam-6775	665	12	age	age	NOUN
ejpam-6775	665	13	-	-	PUNCT
ejpam-6775	665	14	structured	structure	VERB
ejpam-6775	665	15	svi	svi	PROPN
ejpam-6775	665	16	model	model	NOUN
ejpam-6775	665	17	(	(	PUNCT
ejpam-6775	665	18	system	system	NOUN
ejpam-6775	665	19	(	(	PUNCT
ejpam-6775	665	20	1	1	NUM
ejpam-6775	665	21	)	)	PUNCT
ejpam-6775	665	22	)	)	PUNCT
ejpam-6775	665	23	under	under	ADP
ejpam-6775	665	24	scenario	scenario	NOUN
ejpam-6775	665	25	2	2	NUM
ejpam-6775	665	26	with	with	ADP
ejpam-6775	665	27	higher	high	ADJ
ejpam-6775	665	28	treatment	treatment	NOUN
ejpam-6775	665	29	cost	cost	NOUN
ejpam-6775	665	30	(	(	PUNCT
ejpam-6775	665	31	c1	c1	NOUN
ejpam-6775	665	32	=	=	SYM
ejpam-6775	665	33	1000	1000	NUM
ejpam-6775	665	34	,	,	PUNCT
ejpam-6775	665	35	c2	c2	PROPN
ejpam-6775	665	36	=	=	SYM
ejpam-6775	665	37	5000	5000	NUM
ejpam-6775	665	38	)	)	PUNCT
ejpam-6775	665	39	.	.	PUNCT
ejpam-6775	666	1	additional	additional	ADJ
ejpam-6775	666	2	example	example	NOUN
ejpam-6775	666	3	:	:	PUNCT
ejpam-6775	666	4	low	low	ADJ
ejpam-6775	666	5	resource	resource	NOUN
ejpam-6775	666	6	scenario	scenario	NOUN
ejpam-6775	666	7	.	.	PUNCT
ejpam-6775	667	1	with	with	ADP
ejpam-6775	667	2	λ	λ	PROPN
ejpam-6775	667	3	=	=	SYM
ejpam-6775	667	4	500	500	NUM
ejpam-6775	667	5	(	(	PUNCT
ejpam-6775	667	6	reduced	reduce	VERB
ejpam-6775	667	7	recruitment	recruitment	NOUN
ejpam-6775	667	8	,	,	PUNCT
ejpam-6775	667	9	simulating	simulate	VERB
ejpam-6775	667	10	drought	drought	NOUN
ejpam-6775	667	11	-	-	PUNCT
ejpam-6775	667	12	affected	affect	VERB
ejpam-6775	667	13	herds	herd	NOUN
ejpam-6775	667	14	)	)	PUNCT
ejpam-6775	667	15	and	and	CCONJ
ejpam-6775	667	16	c1	c1	PROPN
ejpam-6775	667	17	=	=	PROPN
ejpam-6775	667	18	c2	c2	PROPN
ejpam-6775	667	19	=	=	SYM
ejpam-6775	667	20	2000	2000	NUM
ejpam-6775	667	21	,	,	PUNCT
ejpam-6775	667	22	optimal	optimal	ADJ
ejpam-6775	667	23	controls	control	NOUN
ejpam-6775	667	24	reduce	reduce	VERB
ejpam-6775	667	25	i(t	i(t	NOUN
ejpam-6775	667	26	)	)	PUNCT
ejpam-6775	667	27	by	by	ADP
ejpam-6775	667	28	65	65	NUM
ejpam-6775	667	29	%	%	NOUN
ejpam-6775	667	30	over	over	ADP
ejpam-6775	667	31	50	50	NUM
ejpam-6775	667	32	units	unit	NOUN
ejpam-6775	667	33	,	,	PUNCT
ejpam-6775	667	34	applied	apply	VERB
ejpam-6775	667	35	to	to	PART
ejpam-6775	667	36	btb	btb	VERB
ejpam-6775	667	37	in	in	ADP
ejpam-6775	667	38	african	african	ADJ
ejpam-6775	667	39	buffalo	buffalo	NOUN
ejpam-6775	667	40	populations	population	NOUN
ejpam-6775	667	41	where	where	SCONJ
ejpam-6775	667	42	early	early	ADJ
ejpam-6775	667	43	vaccination	vaccination	NOUN
ejpam-6775	667	44	prevents	prevent	VERB
ejpam-6775	667	45	spill	spill	NOUN
ejpam-6775	667	46	-	-	PUNCT
ejpam-6775	667	47	over	over	NOUN
ejpam-6775	667	48	to	to	ADP
ejpam-6775	667	49	livestock	livestock	NOUN
ejpam-6775	667	50	.	.	PUNCT
ejpam-6775	668	1	additional	additional	ADJ
ejpam-6775	668	2	example	example	NOUN
ejpam-6775	668	3	:	:	PUNCT
ejpam-6775	668	4	high	high	ADJ
ejpam-6775	668	5	transmission	transmission	NOUN
ejpam-6775	668	6	scenario	scenario	NOUN
ejpam-6775	668	7	.	.	PUNCT
ejpam-6775	669	1	increasing	increase	VERB
ejpam-6775	669	2	β(x	β(x	NOUN
ejpam-6775	669	3	)	)	PUNCT
ejpam-6775	669	4	by	by	ADP
ejpam-6775	669	5	50	50	NUM
ejpam-6775	669	6	%	%	NOUN
ejpam-6775	669	7	(	(	PUNCT
ejpam-6775	669	8	r0	r0	NOUN
ejpam-6775	669	9	≈	≈	PROPN
ejpam-6775	669	10	1.8	1.8	NUM
ejpam-6775	669	11	)	)	PUNCT
ejpam-6775	669	12	,	,	PUNCT
ejpam-6775	669	13	controls	control	NOUN
ejpam-6775	669	14	still	still	ADV
ejpam-6775	669	15	achieve	achieve	VERB
ejpam-6775	669	16	50	50	NUM
ejpam-6775	669	17	%	%	NOUN
ejpam-6775	669	18	infection	infection	NOUN
ejpam-6775	669	19	reduction	reduction	NOUN
ejpam-6775	669	20	,	,	PUNCT
ejpam-6775	669	21	demonstrating	demonstrate	VERB
ejpam-6775	669	22	applicability	applicability	NOUN
ejpam-6775	669	23	to	to	ADP
ejpam-6775	669	24	urbanized	urbanized	ADJ
ejpam-6775	669	25	outbreaks	outbreak	NOUN
ejpam-6775	669	26	like	like	ADP
ejpam-6775	669	27	tuberculosis	tuberculosis	NOUN
ejpam-6775	669	28	in	in	ADP
ejpam-6775	669	29	dense	dense	ADJ
ejpam-6775	669	30	herds	herd	NOUN
ejpam-6775	669	31	.	.	PUNCT
ejpam-6775	670	1	additional	additional	ADJ
ejpam-6775	670	2	numerical	numerical	ADJ
ejpam-6775	670	3	properties	property	NOUN
ejpam-6775	670	4	include	include	VERB
ejpam-6775	670	5	convergence	convergence	NOUN
ejpam-6775	670	6	of	of	ADP
ejpam-6775	670	7	the	the	DET
ejpam-6775	670	8	forward	forward	ADV
ejpam-6775	670	9	-	-	PUNCT
ejpam-6775	670	10	backward	backward	ADJ
ejpam-6775	670	11	sweep	sweep	NOUN
ejpam-6775	670	12	method	method	NOUN
ejpam-6775	670	13	within	within	ADP
ejpam-6775	670	14	20	20	NUM
ejpam-6775	670	15	iterations	iteration	NOUN
ejpam-6775	670	16	(	(	PUNCT
ejpam-6775	670	17	error	error	NOUN
ejpam-6775	670	18	¡	¡	PROPN
ejpam-6775	670	19	10−4	10−4	NUM
ejpam-6775	670	20	)	)	PUNCT
ejpam-6775	670	21	.	.	PUNCT
ejpam-6775	671	1	sensitivity	sensitivity	NOUN
ejpam-6775	671	2	to	to	PART
ejpam-6775	671	3	r0	r0	VERB
ejpam-6775	671	4	:	:	PUNCT
ejpam-6775	671	5	for	for	ADP
ejpam-6775	671	6	r0	r0	NOUN
ejpam-6775	671	7	=	=	NOUN
ejpam-6775	671	8	0.9	0.9	NUM
ejpam-6775	671	9	,	,	PUNCT
ejpam-6775	671	10	no	no	DET
ejpam-6775	671	11	controls	control	NOUN
ejpam-6775	671	12	lead	lead	VERB
ejpam-6775	671	13	to	to	ADP
ejpam-6775	671	14	bistable	bistable	ADJ
ejpam-6775	671	15	persistence	persistence	NOUN
ejpam-6775	671	16	,	,	PUNCT
ejpam-6775	671	17	but	but	CCONJ
ejpam-6775	671	18	optimal	optimal	ADJ
ejpam-6775	671	19	controls	control	NOUN
ejpam-6775	671	20	stabilize	stabilize	VERB
ejpam-6775	671	21	to	to	ADP
ejpam-6775	671	22	disease	disease	NOUN
ejpam-6775	671	23	-	-	PUNCT
ejpam-6775	671	24	free	free	ADJ
ejpam-6775	671	25	in	in	ADP
ejpam-6775	671	26	30	30	NUM
ejpam-6775	671	27	units	unit	NOUN
ejpam-6775	671	28	.	.	PUNCT
ejpam-6775	672	1	overall	overall	ADV
ejpam-6775	672	2	,	,	PUNCT
ejpam-6775	672	3	the	the	DET
ejpam-6775	672	4	simulations	simulation	NOUN
ejpam-6775	672	5	confirm	confirm	VERB
ejpam-6775	672	6	that	that	SCONJ
ejpam-6775	672	7	optimal	optimal	ADJ
ejpam-6775	672	8	control	control	NOUN
ejpam-6775	672	9	strategies	strategy	NOUN
ejpam-6775	672	10	can	can	AUX
ejpam-6775	672	11	significantly	significantly	ADV
ejpam-6775	672	12	mitigate	mitigate	VERB
ejpam-6775	672	13	disease	disease	NOUN
ejpam-6775	672	14	spread	spread	VERB
ejpam-6775	672	15	.	.	PUNCT
ejpam-6775	673	1	however	however	ADV
ejpam-6775	673	2	,	,	PUNCT
ejpam-6775	673	3	the	the	DET
ejpam-6775	673	4	balance	balance	NOUN
ejpam-6775	673	5	between	between	ADP
ejpam-6775	673	6	vaccination	vaccination	NOUN
ejpam-6775	673	7	and	and	CCONJ
ejpam-6775	673	8	treatment	treatment	NOUN
ejpam-6775	673	9	depends	depend	VERB
ejpam-6775	673	10	heavily	heavily	ADV
ejpam-6775	673	11	on	on	ADP
ejpam-6775	673	12	their	their	PRON
ejpam-6775	673	13	relative	relative	ADJ
ejpam-6775	673	14	costs	cost	NOUN
ejpam-6775	673	15	,	,	PUNCT
ejpam-6775	673	16	with	with	ADP
ejpam-6775	673	17	higher	high	ADJ
ejpam-6775	673	18	treatment	treatment	NOUN
ejpam-6775	673	19	costs	cost	NOUN
ejpam-6775	673	20	shifting	shift	VERB
ejpam-6775	673	21	efforts	effort	NOUN
ejpam-6775	673	22	toward	toward	ADP
ejpam-6775	673	23	vaccination	vaccination	NOUN
ejpam-6775	673	24	.	.	PUNCT
ejpam-6775	674	1	these	these	DET
ejpam-6775	674	2	findings	finding	NOUN
ejpam-6775	674	3	underscore	underscore	VERB
ejpam-6775	674	4	the	the	DET
ejpam-6775	674	5	importance	importance	NOUN
ejpam-6775	674	6	of	of	ADP
ejpam-6775	674	7	early	early	ADJ
ejpam-6775	674	8	intervention	intervention	NOUN
ejpam-6775	674	9	and	and	CCONJ
ejpam-6775	674	10	resource	resource	NOUN
ejpam-6775	674	11	allocation	allocation	NOUN
ejpam-6775	674	12	in	in	ADP
ejpam-6775	674	13	managing	manage	VERB
ejpam-6775	674	14	infectious	infectious	ADJ
ejpam-6775	674	15	diseases	disease	NOUN
ejpam-6775	674	16	effectively	effectively	ADV
ejpam-6775	674	17	.	.	PUNCT
ejpam-6775	675	1	j.	j.	PROPN
ejpam-6775	675	2	leo	leo	PROPN
ejpam-6775	675	3	amalraj	amalraj	PROPN
ejpam-6775	675	4	et	et	PROPN
ejpam-6775	675	5	al	al	PROPN
ejpam-6775	675	6	.	.	PUNCT
ejpam-6775	675	7	/	/	SYM
ejpam-6775	675	8	eur	eur	PROPN
ejpam-6775	675	9	.	.	PUNCT
ejpam-6775	676	1	j.	j.	PROPN
ejpam-6775	676	2	pure	pure	PROPN
ejpam-6775	676	3	appl	appl	PROPN
ejpam-6775	676	4	.	.	PROPN
ejpam-6775	676	5	math	math	PROPN
ejpam-6775	676	6	,	,	PUNCT
ejpam-6775	676	7	18	18	NUM
ejpam-6775	676	8	(	(	PUNCT
ejpam-6775	676	9	4	4	NUM
ejpam-6775	676	10	)	)	PUNCT
ejpam-6775	676	11	(	(	PUNCT
ejpam-6775	676	12	2025	2025	NUM
ejpam-6775	676	13	)	)	PUNCT
ejpam-6775	676	14	,	,	PUNCT
ejpam-6775	676	15	6775	6775	NUM
ejpam-6775	676	16	26	26	NUM
ejpam-6775	676	17	of	of	ADP
ejpam-6775	676	18	32	32	NUM
ejpam-6775	676	19	figure	figure	NOUN
ejpam-6775	676	20	3	3	NUM
ejpam-6775	676	21	:	:	PUNCT
ejpam-6775	676	22	total	total	ADJ
ejpam-6775	676	23	infected	infect	VERB
ejpam-6775	676	24	population	population	NOUN
ejpam-6775	676	25	i(t	i(t	PROPN
ejpam-6775	676	26	)	)	PUNCT
ejpam-6775	676	27	of	of	ADP
ejpam-6775	676	28	the	the	DET
ejpam-6775	676	29	age	age	NOUN
ejpam-6775	676	30	-	-	PUNCT
ejpam-6775	676	31	structured	structure	VERB
ejpam-6775	676	32	svi	svi	PROPN
ejpam-6775	676	33	model	model	NOUN
ejpam-6775	676	34	(	(	PUNCT
ejpam-6775	676	35	system	system	NOUN
ejpam-6775	676	36	(	(	PUNCT
ejpam-6775	676	37	1	1	NUM
ejpam-6775	676	38	)	)	PUNCT
ejpam-6775	676	39	)	)	PUNCT
ejpam-6775	676	40	under	under	ADP
ejpam-6775	676	41	scenario	scenario	NOUN
ejpam-6775	676	42	2	2	NUM
ejpam-6775	676	43	with	with	ADP
ejpam-6775	676	44	higher	high	ADJ
ejpam-6775	676	45	treatment	treatment	NOUN
ejpam-6775	676	46	cost	cost	NOUN
ejpam-6775	676	47	(	(	PUNCT
ejpam-6775	676	48	c1	c1	NOUN
ejpam-6775	676	49	=	=	SYM
ejpam-6775	676	50	1000	1000	NUM
ejpam-6775	676	51	,	,	PUNCT
ejpam-6775	676	52	c2	c2	PROPN
ejpam-6775	676	53	=	=	SYM
ejpam-6775	676	54	5000	5000	NUM
ejpam-6775	676	55	)	)	PUNCT
ejpam-6775	676	56	.	.	PUNCT
ejpam-6775	677	1	figure	figure	VERB
ejpam-6775	677	2	4	4	NUM
ejpam-6775	677	3	:	:	PUNCT
ejpam-6775	677	4	optimal	optimal	ADJ
ejpam-6775	677	5	vaccination	vaccination	NOUN
ejpam-6775	677	6	control	control	NOUN
ejpam-6775	677	7	ξ(t	ξ(t	NOUN
ejpam-6775	677	8	)	)	PUNCT
ejpam-6775	677	9	of	of	ADP
ejpam-6775	677	10	the	the	DET
ejpam-6775	677	11	age	age	NOUN
ejpam-6775	677	12	-	-	PUNCT
ejpam-6775	677	13	structured	structure	VERB
ejpam-6775	677	14	svi	svi	PROPN
ejpam-6775	677	15	model	model	NOUN
ejpam-6775	677	16	(	(	PUNCT
ejpam-6775	677	17	system	system	NOUN
ejpam-6775	677	18	(	(	PUNCT
ejpam-6775	677	19	1	1	NUM
ejpam-6775	677	20	)	)	PUNCT
ejpam-6775	677	21	)	)	PUNCT
ejpam-6775	677	22	under	under	ADP
ejpam-6775	677	23	scenario	scenario	NOUN
ejpam-6775	677	24	2	2	NUM
ejpam-6775	677	25	with	with	ADP
ejpam-6775	677	26	higher	high	ADJ
ejpam-6775	677	27	treatment	treatment	NOUN
ejpam-6775	677	28	cost	cost	NOUN
ejpam-6775	677	29	(	(	PUNCT
ejpam-6775	677	30	c1	c1	NOUN
ejpam-6775	677	31	=	=	SYM
ejpam-6775	677	32	1000	1000	NUM
ejpam-6775	677	33	,	,	PUNCT
ejpam-6775	677	34	c2	c2	PROPN
ejpam-6775	677	35	=	=	SYM
ejpam-6775	677	36	5000	5000	NUM
ejpam-6775	677	37	)	)	PUNCT
ejpam-6775	677	38	.	.	PUNCT
ejpam-6775	678	1	j.	j.	PROPN
ejpam-6775	678	2	leo	leo	PROPN
ejpam-6775	678	3	amalraj	amalraj	PROPN
ejpam-6775	678	4	et	et	PROPN
ejpam-6775	678	5	al	al	PROPN
ejpam-6775	678	6	.	.	PUNCT
ejpam-6775	678	7	/	/	SYM
ejpam-6775	678	8	eur	eur	PROPN
ejpam-6775	678	9	.	.	PUNCT
ejpam-6775	679	1	j.	j.	PROPN
ejpam-6775	679	2	pure	pure	PROPN
ejpam-6775	679	3	appl	appl	PROPN
ejpam-6775	679	4	.	.	PROPN
ejpam-6775	679	5	math	math	PROPN
ejpam-6775	679	6	,	,	PUNCT
ejpam-6775	679	7	18	18	NUM
ejpam-6775	679	8	(	(	PUNCT
ejpam-6775	679	9	4	4	NUM
ejpam-6775	679	10	)	)	PUNCT
ejpam-6775	679	11	(	(	PUNCT
ejpam-6775	679	12	2025	2025	NUM
ejpam-6775	679	13	)	)	PUNCT
ejpam-6775	679	14	,	,	PUNCT
ejpam-6775	679	15	6775	6775	NUM
ejpam-6775	679	16	27	27	NUM
ejpam-6775	679	17	of	of	ADP
ejpam-6775	679	18	32	32	NUM
ejpam-6775	679	19	figure	figure	NOUN
ejpam-6775	679	20	5	5	NUM
ejpam-6775	679	21	:	:	PUNCT
ejpam-6775	679	22	optimal	optimal	ADJ
ejpam-6775	679	23	treatment	treatment	NOUN
ejpam-6775	679	24	control	control	NOUN
ejpam-6775	679	25	α(t	α(t	PROPN
ejpam-6775	679	26	,	,	PUNCT
ejpam-6775	679	27	x	x	PRON
ejpam-6775	679	28	)	)	PUNCT
ejpam-6775	679	29	at	at	ADP
ejpam-6775	679	30	infection	infection	NOUN
ejpam-6775	679	31	ages	age	NOUN
ejpam-6775	679	32	x	x	PUNCT
ejpam-6775	679	33	=	=	SYM
ejpam-6775	679	34	0	0	NUM
ejpam-6775	679	35	,	,	PUNCT
ejpam-6775	679	36	10	10	NUM
ejpam-6775	679	37	,	,	PUNCT
ejpam-6775	679	38	20	20	NUM
ejpam-6775	679	39	for	for	ADP
ejpam-6775	679	40	the	the	DET
ejpam-6775	679	41	age	age	NOUN
ejpam-6775	679	42	-	-	PUNCT
ejpam-6775	679	43	structured	structure	VERB
ejpam-6775	679	44	svi	svi	PROPN
ejpam-6775	679	45	model	model	NOUN
ejpam-6775	679	46	(	(	PUNCT
ejpam-6775	679	47	system	system	NOUN
ejpam-6775	679	48	(	(	PUNCT
ejpam-6775	679	49	1	1	NUM
ejpam-6775	679	50	)	)	PUNCT
ejpam-6775	679	51	)	)	PUNCT
ejpam-6775	679	52	,	,	PUNCT
ejpam-6775	679	53	comparing	compare	VERB
ejpam-6775	679	54	scenario	scenario	NOUN
ejpam-6775	679	55	1	1	NUM
ejpam-6775	679	56	(	(	PUNCT
ejpam-6775	679	57	equal	equal	ADJ
ejpam-6775	679	58	costs	cost	NOUN
ejpam-6775	679	59	,	,	PUNCT
ejpam-6775	679	60	solid	solid	ADJ
ejpam-6775	679	61	lines	line	NOUN
ejpam-6775	679	62	)	)	PUNCT
ejpam-6775	679	63	and	and	CCONJ
ejpam-6775	679	64	scenario	scenario	NOUN
ejpam-6775	679	65	2	2	NUM
ejpam-6775	679	66	(	(	PUNCT
ejpam-6775	679	67	higher	high	ADJ
ejpam-6775	679	68	treatment	treatment	NOUN
ejpam-6775	679	69	cost	cost	NOUN
ejpam-6775	679	70	,	,	PUNCT
ejpam-6775	679	71	dashed	dash	VERB
ejpam-6775	679	72	lines	line	NOUN
ejpam-6775	679	73	)	)	PUNCT
ejpam-6775	679	74	.	.	PUNCT
ejpam-6775	680	1	figure	figure	VERB
ejpam-6775	680	2	6	6	NUM
ejpam-6775	680	3	:	:	PUNCT
ejpam-6775	680	4	sensitivity	sensitivity	NOUN
ejpam-6775	680	5	of	of	ADP
ejpam-6775	680	6	i(t	i(t	NOUN
ejpam-6775	680	7	)	)	PUNCT
ejpam-6775	680	8	to	to	PART
ejpam-6775	680	9	r0	r0	VERB
ejpam-6775	680	10	variations	variation	NOUN
ejpam-6775	680	11	under	under	ADP
ejpam-6775	680	12	optimal	optimal	ADJ
ejpam-6775	680	13	control	control	NOUN
ejpam-6775	680	14	.	.	PUNCT
ejpam-6775	681	1	j.	j.	PROPN
ejpam-6775	681	2	leo	leo	PROPN
ejpam-6775	681	3	amalraj	amalraj	PROPN
ejpam-6775	681	4	et	et	PROPN
ejpam-6775	681	5	al	al	PROPN
ejpam-6775	681	6	.	.	PUNCT
ejpam-6775	681	7	/	/	SYM
ejpam-6775	681	8	eur	eur	PROPN
ejpam-6775	681	9	.	.	PUNCT
ejpam-6775	682	1	j.	j.	PROPN
ejpam-6775	682	2	pure	pure	PROPN
ejpam-6775	682	3	appl	appl	PROPN
ejpam-6775	682	4	.	.	PROPN
ejpam-6775	682	5	math	math	PROPN
ejpam-6775	682	6	,	,	PUNCT
ejpam-6775	682	7	18	18	NUM
ejpam-6775	682	8	(	(	PUNCT
ejpam-6775	682	9	4	4	NUM
ejpam-6775	682	10	)	)	PUNCT
ejpam-6775	682	11	(	(	PUNCT
ejpam-6775	682	12	2025	2025	NUM
ejpam-6775	682	13	)	)	PUNCT
ejpam-6775	682	14	,	,	PUNCT
ejpam-6775	682	15	6775	6775	NUM
ejpam-6775	682	16	28	28	NUM
ejpam-6775	682	17	of	of	ADP
ejpam-6775	682	18	32	32	NUM
ejpam-6775	682	19	7	7	NUM
ejpam-6775	682	20	.	.	PUNCT
ejpam-6775	682	21	findings	finding	NOUN
ejpam-6775	682	22	and	and	CCONJ
ejpam-6775	682	23	implications	implication	NOUN
ejpam-6775	682	24	in	in	ADP
ejpam-6775	682	25	this	this	DET
ejpam-6775	682	26	work	work	NOUN
ejpam-6775	682	27	,	,	PUNCT
ejpam-6775	682	28	we	we	PRON
ejpam-6775	682	29	analyzed	analyze	VERB
ejpam-6775	682	30	an	an	DET
ejpam-6775	682	31	age	age	NOUN
ejpam-6775	682	32	-	-	PUNCT
ejpam-6775	682	33	structured	structure	VERB
ejpam-6775	682	34	susceptible	susceptible	ADJ
ejpam-6775	682	35	-	-	PUNCT
ejpam-6775	682	36	vaccinated	vaccinated	ADJ
ejpam-6775	682	37	-	-	PUNCT
ejpam-6775	682	38	infected	infect	VERB
ejpam-6775	682	39	(	(	PUNCT
ejpam-6775	682	40	svi	svi	ADJ
ejpam-6775	682	41	)	)	PUNCT
ejpam-6775	682	42	model	model	NOUN
ejpam-6775	682	43	to	to	PART
ejpam-6775	682	44	study	study	VERB
ejpam-6775	682	45	the	the	DET
ejpam-6775	682	46	transmission	transmission	NOUN
ejpam-6775	682	47	dynamics	dynamic	NOUN
ejpam-6775	682	48	of	of	ADP
ejpam-6775	682	49	an	an	DET
ejpam-6775	682	50	infectious	infectious	ADJ
ejpam-6775	682	51	disease	disease	NOUN
ejpam-6775	682	52	,	,	PUNCT
ejpam-6775	682	53	incorporating	incorporate	VERB
ejpam-6775	682	54	imperfect	imperfect	ADJ
ejpam-6775	682	55	vaccination	vaccination	NOUN
ejpam-6775	682	56	and	and	CCONJ
ejpam-6775	682	57	therapeutic	therapeutic	ADJ
ejpam-6775	682	58	treatment	treatment	NOUN
ejpam-6775	682	59	.	.	PUNCT
ejpam-6775	683	1	our	our	PRON
ejpam-6775	683	2	analysis	analysis	NOUN
ejpam-6775	683	3	revealed	reveal	VERB
ejpam-6775	683	4	a	a	DET
ejpam-6775	683	5	backward	backward	ADJ
ejpam-6775	683	6	bifurcation	bifurcation	NOUN
ejpam-6775	683	7	phenomenon	phenomenon	NOUN
ejpam-6775	683	8	,	,	PUNCT
ejpam-6775	683	9	driven	drive	VERB
ejpam-6775	683	10	by	by	ADP
ejpam-6775	683	11	the	the	DET
ejpam-6775	683	12	therapeutic	therapeutic	ADJ
ejpam-6775	683	13	treatment	treatment	NOUN
ejpam-6775	683	14	rate	rate	NOUN
ejpam-6775	683	15	,	,	PUNCT
ejpam-6775	683	16	which	which	PRON
ejpam-6775	683	17	permits	permit	VERB
ejpam-6775	683	18	the	the	DET
ejpam-6775	683	19	coexistence	coexistence	NOUN
ejpam-6775	683	20	of	of	ADP
ejpam-6775	683	21	stable	stable	ADJ
ejpam-6775	683	22	disease	disease	NOUN
ejpam-6775	683	23	-	-	PUNCT
ejpam-6775	683	24	free	free	ADJ
ejpam-6775	683	25	and	and	CCONJ
ejpam-6775	683	26	endemic	endemic	ADJ
ejpam-6775	683	27	equilibria	equilibrium	NOUN
ejpam-6775	683	28	when	when	SCONJ
ejpam-6775	683	29	r0	r0	VERB
ejpam-6775	683	30	<	<	X
ejpam-6775	683	31	1	1	NUM
ejpam-6775	683	32	.	.	PUNCT
ejpam-6775	684	1	this	this	DET
ejpam-6775	684	2	bistability	bistability	NOUN
ejpam-6775	684	3	implies	imply	VERB
ejpam-6775	684	4	that	that	SCONJ
ejpam-6775	684	5	reducing	reduce	VERB
ejpam-6775	684	6	r0	r0	NOUN
ejpam-6775	684	7	below	below	ADP
ejpam-6775	684	8	unity	unity	NOUN
ejpam-6775	684	9	is	be	AUX
ejpam-6775	684	10	necessary	necessary	ADJ
ejpam-6775	684	11	but	but	CCONJ
ejpam-6775	684	12	insufficient	insufficient	ADJ
ejpam-6775	684	13	for	for	ADP
ejpam-6775	684	14	disease	disease	NOUN
ejpam-6775	684	15	eradication	eradication	NOUN
ejpam-6775	684	16	,	,	PUNCT
ejpam-6775	684	17	highlighting	highlight	VERB
ejpam-6775	684	18	the	the	DET
ejpam-6775	684	19	complexity	complexity	NOUN
ejpam-6775	684	20	of	of	ADP
ejpam-6775	684	21	controlling	control	VERB
ejpam-6775	684	22	such	such	ADJ
ejpam-6775	684	23	epidemics	epidemic	NOUN
ejpam-6775	684	24	.	.	PUNCT
ejpam-6775	685	1	by	by	ADP
ejpam-6775	685	2	formulating	formulate	VERB
ejpam-6775	685	3	an	an	DET
ejpam-6775	685	4	optimal	optimal	ADJ
ejpam-6775	685	5	control	control	NOUN
ejpam-6775	685	6	problem	problem	NOUN
ejpam-6775	685	7	with	with	ADP
ejpam-6775	685	8	time	time	NOUN
ejpam-6775	685	9	-	-	PUNCT
ejpam-6775	685	10	dependent	dependent	ADJ
ejpam-6775	685	11	vaccination	vaccination	NOUN
ejpam-6775	685	12	and	and	CCONJ
ejpam-6775	685	13	treatment	treatment	NOUN
ejpam-6775	685	14	rates	rate	NOUN
ejpam-6775	685	15	,	,	PUNCT
ejpam-6775	685	16	we	we	PRON
ejpam-6775	685	17	demonstrated	demonstrate	VERB
ejpam-6775	685	18	that	that	SCONJ
ejpam-6775	685	19	strategic	strategic	ADJ
ejpam-6775	685	20	interventions	intervention	NOUN
ejpam-6775	685	21	can	can	AUX
ejpam-6775	685	22	significantly	significantly	ADV
ejpam-6775	685	23	mitigate	mitigate	VERB
ejpam-6775	685	24	disease	disease	NOUN
ejpam-6775	685	25	spread	spread	VERB
ejpam-6775	685	26	while	while	SCONJ
ejpam-6775	685	27	minimizing	minimize	VERB
ejpam-6775	685	28	costs	cost	NOUN
ejpam-6775	685	29	.	.	PUNCT
ejpam-6775	686	1	numerical	numerical	ADJ
ejpam-6775	686	2	simulations	simulation	NOUN
ejpam-6775	686	3	confirmed	confirm	VERB
ejpam-6775	686	4	that	that	SCONJ
ejpam-6775	686	5	early	early	ADJ
ejpam-6775	686	6	and	and	CCONJ
ejpam-6775	686	7	age	age	NOUN
ejpam-6775	686	8	-	-	PUNCT
ejpam-6775	686	9	targeted	target	VERB
ejpam-6775	686	10	controls	control	NOUN
ejpam-6775	686	11	are	be	AUX
ejpam-6775	686	12	critical	critical	ADJ
ejpam-6775	686	13	for	for	ADP
ejpam-6775	686	14	reducing	reduce	VERB
ejpam-6775	686	15	prevalence	prevalence	NOUN
ejpam-6775	686	16	.	.	PUNCT
ejpam-6775	687	1	these	these	DET
ejpam-6775	687	2	results	result	NOUN
ejpam-6775	687	3	provide	provide	VERB
ejpam-6775	687	4	valuable	valuable	ADJ
ejpam-6775	687	5	insights	insight	NOUN
ejpam-6775	687	6	for	for	ADP
ejpam-6775	687	7	public	public	ADJ
ejpam-6775	687	8	health	health	NOUN
ejpam-6775	687	9	policymakers	policymaker	NOUN
ejpam-6775	687	10	in	in	ADP
ejpam-6775	687	11	designing	design	VERB
ejpam-6775	687	12	effective	effective	ADJ
ejpam-6775	687	13	intervention	intervention	NOUN
ejpam-6775	687	14	strategies	strategy	NOUN
ejpam-6775	687	15	.	.	PUNCT
ejpam-6775	688	1	future	future	ADJ
ejpam-6775	688	2	research	research	NOUN
ejpam-6775	688	3	could	could	AUX
ejpam-6775	688	4	explore	explore	VERB
ejpam-6775	688	5	multi	multi	ADJ
ejpam-6775	688	6	-	-	ADJ
ejpam-6775	688	7	strain	strain	ADJ
ejpam-6775	688	8	dynamics	dynamic	NOUN
ejpam-6775	688	9	or	or	CCONJ
ejpam-6775	688	10	stochastic	stochastic	ADJ
ejpam-6775	688	11	effects	effect	NOUN
ejpam-6775	688	12	to	to	PART
ejpam-6775	688	13	further	far	ADV
ejpam-6775	688	14	enhance	enhance	VERB
ejpam-6775	688	15	epidemic	epidemic	NOUN
ejpam-6775	688	16	control	control	NOUN
ejpam-6775	688	17	frameworks	framework	NOUN
ejpam-6775	688	18	.	.	PUNCT
ejpam-6775	689	1	key	key	ADJ
ejpam-6775	689	2	findings	finding	NOUN
ejpam-6775	689	3	include	include	VERB
ejpam-6775	689	4	backward	backward	ADJ
ejpam-6775	689	5	bifurcation	bifurcation	NOUN
ejpam-6775	689	6	driven	drive	VERB
ejpam-6775	689	7	by	by	ADP
ejpam-6775	689	8	treatment	treatment	NOUN
ejpam-6775	689	9	,	,	PUNCT
ejpam-6775	689	10	with	with	ADP
ejpam-6775	689	11	practical	practical	ADJ
ejpam-6775	689	12	implications	implication	NOUN
ejpam-6775	689	13	for	for	ADP
ejpam-6775	689	14	btb	btb	NOUN
ejpam-6775	689	15	control	control	NOUN
ejpam-6775	689	16	:	:	PUNCT
ejpam-6775	689	17	allocate	allocate	VERB
ejpam-6775	689	18	resources	resource	NOUN
ejpam-6775	689	19	to	to	ADP
ejpam-6775	689	20	early	early	ADJ
ejpam-6775	689	21	-	-	PUNCT
ejpam-6775	689	22	age	age	NOUN
ejpam-6775	689	23	treatment	treatment	NOUN
ejpam-6775	689	24	in	in	ADP
ejpam-6775	689	25	wildlife	wildlife	NOUN
ejpam-6775	689	26	reserves	reserve	NOUN
ejpam-6775	689	27	to	to	PART
ejpam-6775	689	28	prevent	prevent	VERB
ejpam-6775	689	29	economic	economic	ADJ
ejpam-6775	689	30	losses	loss	NOUN
ejpam-6775	689	31	in	in	ADP
ejpam-6775	689	32	livestock	livestock	NOUN
ejpam-6775	689	33	farming	farming	NOUN
ejpam-6775	689	34	.	.	PUNCT
ejpam-6775	690	1	8	8	X
ejpam-6775	690	2	.	.	X
ejpam-6775	690	3	conclusion	conclusion	NOUN
ejpam-6775	690	4	this	this	DET
ejpam-6775	690	5	study	study	NOUN
ejpam-6775	690	6	concludes	conclude	VERB
ejpam-6775	690	7	that	that	SCONJ
ejpam-6775	690	8	age	age	NOUN
ejpam-6775	690	9	-	-	PUNCT
ejpam-6775	690	10	structured	structure	VERB
ejpam-6775	690	11	svi	svi	NOUN
ejpam-6775	690	12	models	model	NOUN
ejpam-6775	690	13	with	with	ADP
ejpam-6775	690	14	optimal	optimal	ADJ
ejpam-6775	690	15	controls	control	NOUN
ejpam-6775	690	16	effectively	effectively	ADV
ejpam-6775	690	17	manage	manage	VERB
ejpam-6775	690	18	backward	backward	ADJ
ejpam-6775	690	19	bifurcation	bifurcation	NOUN
ejpam-6775	690	20	in	in	ADP
ejpam-6775	690	21	epidemics	epidemic	NOUN
ejpam-6775	690	22	,	,	PUNCT
ejpam-6775	690	23	finalizing	finalize	VERB
ejpam-6775	690	24	that	that	PRON
ejpam-6775	690	25	combined	combine	VERB
ejpam-6775	690	26	vaccination	vaccination	NOUN
ejpam-6775	690	27	and	and	CCONJ
ejpam-6775	690	28	treatment	treatment	NOUN
ejpam-6775	690	29	minimize	minimize	NOUN
ejpam-6775	690	30	infections	infection	NOUN
ejpam-6775	690	31	while	while	SCONJ
ejpam-6775	690	32	informing	inform	VERB
ejpam-6775	690	33	policy	policy	NOUN
ejpam-6775	690	34	for	for	ADP
ejpam-6775	690	35	diseases	disease	NOUN
ejpam-6775	690	36	like	like	ADP
ejpam-6775	690	37	btb	btb	NOUN
ejpam-6775	690	38	.	.	PUNCT
ejpam-6775	691	1	limitations	limitation	NOUN
ejpam-6775	691	2	include	include	VERB
ejpam-6775	691	3	assumptions	assumption	NOUN
ejpam-6775	691	4	of	of	ADP
ejpam-6775	691	5	constant	constant	ADJ
ejpam-6775	691	6	recruitment	recruitment	NOUN
ejpam-6775	691	7	and	and	CCONJ
ejpam-6775	691	8	no	no	DET
ejpam-6775	691	9	spatial	spatial	ADJ
ejpam-6775	691	10	dynamics	dynamic	NOUN
ejpam-6775	691	11	.	.	PUNCT
ejpam-6775	692	1	future	future	ADJ
ejpam-6775	692	2	work	work	NOUN
ejpam-6775	692	3	could	could	AUX
ejpam-6775	692	4	incorporate	incorporate	VERB
ejpam-6775	692	5	stochastic	stochastic	ADJ
ejpam-6775	692	6	effects	effect	NOUN
ejpam-6775	692	7	or	or	CCONJ
ejpam-6775	692	8	multi	multi	ADJ
ejpam-6775	692	9	-	-	ADJ
ejpam-6775	692	10	strain	strain	ADJ
ejpam-6775	692	11	interactions	interaction	NOUN
ejpam-6775	692	12	to	to	PART
ejpam-6775	692	13	enhance	enhance	VERB
ejpam-6775	692	14	realism	realism	NOUN
ejpam-6775	692	15	.	.	PUNCT
ejpam-6775	693	1	author	author	NOUN
ejpam-6775	693	2	contributions	contribution	NOUN
ejpam-6775	693	3	:	:	PUNCT
ejpam-6775	693	4	the	the	DET
ejpam-6775	693	5	authors	author	NOUN
ejpam-6775	693	6	equally	equally	ADV
ejpam-6775	693	7	conceived	conceive	VERB
ejpam-6775	693	8	of	of	ADP
ejpam-6775	693	9	the	the	DET
ejpam-6775	693	10	study	study	NOUN
ejpam-6775	693	11	,	,	PUNCT
ejpam-6775	693	12	participated	participate	VERB
ejpam-6775	693	13	in	in	ADP
ejpam-6775	693	14	its	its	PRON
ejpam-6775	693	15	design	design	NOUN
ejpam-6775	693	16	and	and	CCONJ
ejpam-6775	693	17	coordination	coordination	NOUN
ejpam-6775	693	18	,	,	PUNCT
ejpam-6775	693	19	drafted	draft	VERB
ejpam-6775	693	20	the	the	DET
ejpam-6775	693	21	manuscript	manuscript	NOUN
ejpam-6775	693	22	,	,	PUNCT
ejpam-6775	693	23	participated	participate	VERB
ejpam-6775	693	24	in	in	ADP
ejpam-6775	693	25	the	the	DET
ejpam-6775	693	26	sequence	sequence	NOUN
ejpam-6775	693	27	alignment	alignment	NOUN
ejpam-6775	693	28	,	,	PUNCT
ejpam-6775	693	29	and	and	CCONJ
ejpam-6775	693	30	read	read	VERB
ejpam-6775	693	31	and	and	CCONJ
ejpam-6775	693	32	approved	approve	VERB
ejpam-6775	693	33	the	the	DET
ejpam-6775	693	34	final	final	ADJ
ejpam-6775	693	35	manuscript	manuscript	NOUN
ejpam-6775	693	36	.	.	PUNCT
ejpam-6775	694	1	conflicts	conflict	NOUN
ejpam-6775	694	2	of	of	ADP
ejpam-6775	694	3	interest	interest	NOUN
ejpam-6775	694	4	:	:	PUNCT
ejpam-6775	694	5	the	the	DET
ejpam-6775	694	6	authors	author	NOUN
ejpam-6775	694	7	declare	declare	VERB
ejpam-6775	694	8	that	that	SCONJ
ejpam-6775	694	9	they	they	PRON
ejpam-6775	694	10	have	have	VERB
ejpam-6775	694	11	no	no	DET
ejpam-6775	694	12	competing	compete	VERB
ejpam-6775	694	13	interests	interest	NOUN
ejpam-6775	694	14	.	.	PUNCT
ejpam-6775	695	1	funding	funding	NOUN
ejpam-6775	695	2	:	:	PUNCT
ejpam-6775	695	3	this	this	DET
ejpam-6775	695	4	research	research	NOUN
ejpam-6775	695	5	was	be	AUX
ejpam-6775	695	6	supported	support	VERB
ejpam-6775	695	7	by	by	ADP
ejpam-6775	695	8	university	university	NOUN
ejpam-6775	695	9	of	of	ADP
ejpam-6775	695	10	phayao	phayao	NOUN
ejpam-6775	695	11	and	and	CCONJ
ejpam-6775	695	12	thailand	thailand	PROPN
ejpam-6775	695	13	science	science	PROPN
ejpam-6775	695	14	research	research	PROPN
ejpam-6775	695	15	and	and	CCONJ
ejpam-6775	695	16	innovation	innovation	NOUN
ejpam-6775	695	17	fund	fund	NOUN
ejpam-6775	695	18	(	(	PUNCT
ejpam-6775	695	19	fundamental	fundamental	ADJ
ejpam-6775	695	20	fund	fund	NOUN
ejpam-6775	695	21	2026	2026	NUM
ejpam-6775	695	22	,	,	PUNCT
ejpam-6775	695	23	grant	grant	VERB
ejpam-6775	695	24	no	no	NOUN
ejpam-6775	695	25	.	.	PUNCT
ejpam-6775	695	26	xxxx/2568	xxxx/2568	PROPN
ejpam-6775	695	27	)	)	PUNCT
ejpam-6775	695	28	.	.	PUNCT
ejpam-6775	696	1	references	reference	NOUN
ejpam-6775	696	2	[	[	X
ejpam-6775	696	3	1	1	NUM
ejpam-6775	696	4	]	]	X
ejpam-6775	696	5	g.w	g.w	PROPN
ejpam-6775	696	6	.	.	PROPN
ejpam-6775	696	7	de	de	X
ejpam-6775	696	8	lisle	lisle	PROPN
ejpam-6775	696	9	,	,	PUNCT
ejpam-6775	696	10	c.g	c.g	PROPN
ejpam-6775	696	11	.	.	PROPN
ejpam-6775	696	12	mackintosh	mackintosh	PROPN
ejpam-6775	696	13	,	,	PUNCT
ejpam-6775	696	14	and	and	CCONJ
ejpam-6775	696	15	r.g	r.g	PROPN
ejpam-6775	696	16	.	.	PROPN
ejpam-6775	696	17	bengis	bengis	PROPN
ejpam-6775	696	18	.	.	PUNCT
ejpam-6775	697	1	mycobacterium	mycobacterium	NOUN
ejpam-6775	697	2	bovis	bovi	VERB
ejpam-6775	697	3	in	in	ADP
ejpam-6775	697	4	free	free	ADJ
ejpam-6775	697	5	-	-	PUNCT
ejpam-6775	697	6	living	live	VERB
ejpam-6775	697	7	and	and	CCONJ
ejpam-6775	697	8	captive	captive	ADJ
ejpam-6775	697	9	wildlife	wildlife	NOUN
ejpam-6775	697	10	,	,	PUNCT
ejpam-6775	697	11	including	include	VERB
ejpam-6775	697	12	farmed	farm	VERB
ejpam-6775	697	13	deer	deer	NOUN
ejpam-6775	697	14	.	.	PUNCT
ejpam-6775	698	1	revue	revue	PROPN
ejpam-6775	698	2	scientifique	scientifique	PROPN
ejpam-6775	698	3	et	et	NOUN
ejpam-6775	698	4	technique	technique	NOUN
ejpam-6775	698	5	-	-	PUNCT
ejpam-6775	698	6	office	office	NOUN
ejpam-6775	698	7	international	international	ADJ
ejpam-6775	698	8	des	des	PROPN
ejpam-6775	698	9	epizooties	epizootie	NOUN
ejpam-6775	698	10	,	,	PUNCT
ejpam-6775	698	11	20(1):86–111	20(1):86–111	NUM
ejpam-6775	698	12	,	,	PUNCT
ejpam-6775	698	13	2001	2001	NUM
ejpam-6775	698	14	.	.	PUNCT
ejpam-6775	699	1	[	[	X
ejpam-6775	699	2	2	2	NUM
ejpam-6775	699	3	]	]	X
ejpam-6775	699	4	p.c	p.c	PROPN
ejpam-6775	699	5	.	.	PROPN
ejpam-6775	699	6	cross	cross	PROPN
ejpam-6775	699	7	and	and	CCONJ
ejpam-6775	699	8	w.m	w.m	PROPN
ejpam-6775	699	9	.	.	PROPN
ejpam-6775	699	10	getz	getz	PROPN
ejpam-6775	699	11	.	.	PUNCT
ejpam-6775	700	1	assessing	assess	VERB
ejpam-6775	700	2	vaccination	vaccination	NOUN
ejpam-6775	700	3	as	as	ADP
ejpam-6775	700	4	a	a	DET
ejpam-6775	700	5	control	control	NOUN
ejpam-6775	700	6	strategy	strategy	NOUN
ejpam-6775	700	7	in	in	ADP
ejpam-6775	700	8	an	an	DET
ejpam-6775	700	9	ongoing	ongoing	ADJ
ejpam-6775	700	10	epidemic	epidemic	NOUN
ejpam-6775	700	11	:	:	PUNCT
ejpam-6775	700	12	bovine	bovine	ADJ
ejpam-6775	700	13	tuberculosis	tuberculosis	NOUN
ejpam-6775	700	14	in	in	ADP
ejpam-6775	700	15	african	african	PROPN
ejpam-6775	700	16	buffalo	buffalo	PROPN
ejpam-6775	700	17	.	.	PUNCT
ejpam-6775	701	1	ecological	ecological	ADJ
ejpam-6775	701	2	modelling	modelling	NOUN
ejpam-6775	701	3	,	,	PUNCT
ejpam-6775	701	4	196(3	196(3	NUM
ejpam-6775	701	5	-	-	SYM
ejpam-6775	701	6	4):494	4):494	NUM
ejpam-6775	701	7	–	–	PUNCT
ejpam-6775	701	8	504	504	NUM
ejpam-6775	701	9	,	,	PUNCT
ejpam-6775	701	10	2006	2006	NUM
ejpam-6775	701	11	.	.	PUNCT
ejpam-6775	702	1	j.	j.	PROPN
ejpam-6775	702	2	leo	leo	PROPN
ejpam-6775	702	3	amalraj	amalraj	PROPN
ejpam-6775	702	4	et	et	PROPN
ejpam-6775	702	5	al	al	PROPN
ejpam-6775	702	6	.	.	PUNCT
ejpam-6775	702	7	/	/	SYM
ejpam-6775	702	8	eur	eur	PROPN
ejpam-6775	702	9	.	.	PUNCT
ejpam-6775	703	1	j.	j.	PROPN
ejpam-6775	703	2	pure	pure	PROPN
ejpam-6775	703	3	appl	appl	PROPN
ejpam-6775	703	4	.	.	PROPN
ejpam-6775	703	5	math	math	PROPN
ejpam-6775	703	6	,	,	PUNCT
ejpam-6775	703	7	18	18	NUM
ejpam-6775	703	8	(	(	PUNCT
ejpam-6775	703	9	4	4	NUM
ejpam-6775	703	10	)	)	PUNCT
ejpam-6775	703	11	(	(	PUNCT
ejpam-6775	703	12	2025	2025	NUM
ejpam-6775	703	13	)	)	PUNCT
ejpam-6775	703	14	,	,	PUNCT
ejpam-6775	703	15	6775	6775	NUM
ejpam-6775	703	16	29	29	NUM
ejpam-6775	703	17	of	of	ADP
ejpam-6775	703	18	32	32	NUM
ejpam-6775	703	19	[	[	SYM
ejpam-6775	703	20	3	3	NUM
ejpam-6775	703	21	]	]	X
ejpam-6775	703	22	k.p	k.p	PROPN
ejpam-6775	703	23	.	.	PROPN
ejpam-6775	703	24	hadeler	hadeler	NOUN
ejpam-6775	703	25	and	and	CCONJ
ejpam-6775	703	26	p.	p.	PROPN
ejpam-6775	703	27	van	van	PROPN
ejpam-6775	703	28	den	den	PROPN
ejpam-6775	703	29	driessche	driessche	PROPN
ejpam-6775	703	30	.	.	PUNCT
ejpam-6775	704	1	backward	backward	ADJ
ejpam-6775	704	2	bifurcation	bifurcation	NOUN
ejpam-6775	704	3	in	in	ADP
ejpam-6775	704	4	epidemic	epidemic	NOUN
ejpam-6775	704	5	control	control	NOUN
ejpam-6775	704	6	.	.	PUNCT
ejpam-6775	705	1	mathematical	mathematical	ADJ
ejpam-6775	705	2	biosciences	bioscience	NOUN
ejpam-6775	705	3	,	,	PUNCT
ejpam-6775	705	4	146(1):15–35	146(1):15–35	NUM
ejpam-6775	705	5	,	,	PUNCT
ejpam-6775	705	6	1997	1997	NUM
ejpam-6775	705	7	.	.	PUNCT
ejpam-6775	706	1	[	[	X
ejpam-6775	706	2	4	4	X
ejpam-6775	706	3	]	]	PUNCT
ejpam-6775	706	4	h.	h.	PROPN
ejpam-6775	706	5	inaba	inaba	PROPN
ejpam-6775	706	6	et	et	PROPN
ejpam-6775	706	7	al	al	PROPN
ejpam-6775	706	8	.	.	PUNCT
ejpam-6775	707	1	a	a	DET
ejpam-6775	707	2	mathematical	mathematical	ADJ
ejpam-6775	707	3	model	model	NOUN
ejpam-6775	707	4	for	for	ADP
ejpam-6775	707	5	chagas	chagas	NOUN
ejpam-6775	707	6	disease	disease	NOUN
ejpam-6775	707	7	with	with	ADP
ejpam-6775	707	8	infection	infection	NOUN
ejpam-6775	707	9	-	-	PUNCT
ejpam-6775	707	10	age	age	NOUN
ejpam-6775	707	11	-	-	PUNCT
ejpam-6775	707	12	dependent	dependent	ADJ
ejpam-6775	707	13	infectivity	infectivity	NOUN
ejpam-6775	707	14	.	.	PUNCT
ejpam-6775	708	1	mathematical	mathematical	ADJ
ejpam-6775	708	2	biosciences	bioscience	NOUN
ejpam-6775	708	3	,	,	PUNCT
ejpam-6775	708	4	2004	2004	NUM
ejpam-6775	708	5	.	.	PUNCT
ejpam-6775	709	1	[	[	X
ejpam-6775	709	2	5	5	X
ejpam-6775	709	3	]	]	PUNCT
ejpam-6775	709	4	s.	s.	PROPN
ejpam-6775	709	5	ruan	ruan	PROPN
ejpam-6775	709	6	and	and	CCONJ
ejpam-6775	709	7	w.	w.	PROPN
ejpam-6775	709	8	wang	wang	PROPN
ejpam-6775	709	9	.	.	PUNCT
ejpam-6775	710	1	dynamical	dynamical	ADJ
ejpam-6775	710	2	behavior	behavior	NOUN
ejpam-6775	710	3	of	of	ADP
ejpam-6775	710	4	an	an	DET
ejpam-6775	710	5	epidemic	epidemic	NOUN
ejpam-6775	710	6	model	model	NOUN
ejpam-6775	710	7	with	with	ADP
ejpam-6775	710	8	a	a	DET
ejpam-6775	710	9	nonlinear	nonlinear	ADJ
ejpam-6775	710	10	incidence	incidence	NOUN
ejpam-6775	710	11	rate	rate	NOUN
ejpam-6775	710	12	.	.	PUNCT
ejpam-6775	711	1	journal	journal	PROPN
ejpam-6775	711	2	of	of	ADP
ejpam-6775	711	3	differential	differential	ADJ
ejpam-6775	711	4	equations	equation	NOUN
ejpam-6775	711	5	,	,	PUNCT
ejpam-6775	711	6	188(1):135–163	188(1):135–163	NUM
ejpam-6775	711	7	,	,	PUNCT
ejpam-6775	711	8	2003	2003	NUM
ejpam-6775	711	9	.	.	PUNCT
ejpam-6775	712	1	[	[	X
ejpam-6775	712	2	6	6	NUM
ejpam-6775	712	3	]	]	PUNCT
ejpam-6775	712	4	w.	w.	PROPN
ejpam-6775	712	5	wang	wang	PROPN
ejpam-6775	712	6	and	and	CCONJ
ejpam-6775	712	7	s.	s.	PROPN
ejpam-6775	712	8	ruan	ruan	PROPN
ejpam-6775	712	9	.	.	PUNCT
ejpam-6775	713	1	bifurcations	bifurcation	NOUN
ejpam-6775	713	2	in	in	ADP
ejpam-6775	713	3	an	an	DET
ejpam-6775	713	4	epidemic	epidemic	NOUN
ejpam-6775	713	5	model	model	NOUN
ejpam-6775	713	6	with	with	ADP
ejpam-6775	713	7	constant	constant	ADJ
ejpam-6775	713	8	removal	removal	NOUN
ejpam-6775	713	9	rate	rate	NOUN
ejpam-6775	713	10	of	of	ADP
ejpam-6775	713	11	the	the	DET
ejpam-6775	713	12	infectives	infective	NOUN
ejpam-6775	713	13	.	.	PUNCT
ejpam-6775	714	1	journal	journal	PROPN
ejpam-6775	714	2	of	of	ADP
ejpam-6775	714	3	mathematical	mathematical	ADJ
ejpam-6775	714	4	analysis	analysis	NOUN
ejpam-6775	714	5	and	and	CCONJ
ejpam-6775	714	6	applications	application	NOUN
ejpam-6775	714	7	,	,	PUNCT
ejpam-6775	714	8	291(2):775–793	291(2):775–793	NUM
ejpam-6775	714	9	,	,	PUNCT
ejpam-6775	714	10	2004	2004	NUM
ejpam-6775	714	11	.	.	PUNCT
ejpam-6775	715	1	[	[	X
ejpam-6775	715	2	7	7	X
ejpam-6775	715	3	]	]	X
ejpam-6775	715	4	h.w	h.w	PROPN
ejpam-6775	715	5	.	.	PROPN
ejpam-6775	715	6	hethcote	hethcote	PROPN
ejpam-6775	715	7	.	.	PUNCT
ejpam-6775	716	1	the	the	DET
ejpam-6775	716	2	mathematics	mathematic	NOUN
ejpam-6775	716	3	of	of	ADP
ejpam-6775	716	4	infectious	infectious	ADJ
ejpam-6775	716	5	diseases	disease	NOUN
ejpam-6775	716	6	.	.	PUNCT
ejpam-6775	717	1	siam	siam	PROPN
ejpam-6775	717	2	review	review	PROPN
ejpam-6775	717	3	,	,	PUNCT
ejpam-6775	717	4	42(4):599–653	42(4):599–653	PROPN
ejpam-6775	717	5	,	,	PUNCT
ejpam-6775	717	6	2000	2000	NUM
ejpam-6775	717	7	.	.	PUNCT
ejpam-6775	718	1	[	[	X
ejpam-6775	718	2	8	8	NUM
ejpam-6775	718	3	]	]	X
ejpam-6775	718	4	d.	d.	PROPN
ejpam-6775	718	5	okuonghae	okuonghae	PROPN
ejpam-6775	718	6	and	and	CCONJ
ejpam-6775	718	7	v.u	v.u	PROPN
ejpam-6775	718	8	.	.	PROPN
ejpam-6775	718	9	aihie	aihie	PROPN
ejpam-6775	718	10	.	.	PUNCT
ejpam-6775	719	1	optimal	optimal	ADJ
ejpam-6775	719	2	control	control	NOUN
ejpam-6775	719	3	measures	measure	NOUN
ejpam-6775	719	4	for	for	ADP
ejpam-6775	719	5	tuberculosis	tuberculosis	NOUN
ejpam-6775	719	6	mathematical	mathematical	ADJ
ejpam-6775	719	7	models	model	NOUN
ejpam-6775	719	8	including	include	VERB
ejpam-6775	719	9	immigration	immigration	NOUN
ejpam-6775	719	10	and	and	CCONJ
ejpam-6775	719	11	isolation	isolation	NOUN
ejpam-6775	719	12	of	of	ADP
ejpam-6775	719	13	infective	infective	ADJ
ejpam-6775	719	14	.	.	PUNCT
ejpam-6775	720	1	journal	journal	PROPN
ejpam-6775	720	2	of	of	ADP
ejpam-6775	720	3	biological	biological	ADJ
ejpam-6775	720	4	systems	system	NOUN
ejpam-6775	720	5	,	,	PUNCT
ejpam-6775	720	6	18(01):17–54	18(01):17–54	NUM
ejpam-6775	720	7	,	,	PUNCT
ejpam-6775	720	8	2010	2010	NUM
ejpam-6775	720	9	.	.	PUNCT
ejpam-6775	721	1	[	[	X
ejpam-6775	721	2	9	9	NUM
ejpam-6775	721	3	]	]	X
ejpam-6775	721	4	d.	d.	PROPN
ejpam-6775	721	5	okuonghae	okuonghae	PROPN
ejpam-6775	721	6	and	and	CCONJ
ejpam-6775	721	7	s.e	s.e	PROPN
ejpam-6775	721	8	.	.	PROPN
ejpam-6775	721	9	omosigho	omosigho	PROPN
ejpam-6775	721	10	.	.	PUNCT
ejpam-6775	722	1	analysis	analysis	NOUN
ejpam-6775	722	2	of	of	ADP
ejpam-6775	722	3	a	a	DET
ejpam-6775	722	4	mathematical	mathematical	ADJ
ejpam-6775	722	5	model	model	NOUN
ejpam-6775	722	6	for	for	ADP
ejpam-6775	722	7	tuberculosis	tuberculosis	NOUN
ejpam-6775	722	8	:	:	PUNCT
ejpam-6775	722	9	what	what	PRON
ejpam-6775	722	10	could	could	AUX
ejpam-6775	722	11	be	be	AUX
ejpam-6775	722	12	done	do	VERB
ejpam-6775	722	13	to	to	PART
ejpam-6775	722	14	increase	increase	VERB
ejpam-6775	722	15	case	case	NOUN
ejpam-6775	722	16	detection	detection	NOUN
ejpam-6775	722	17	.	.	PUNCT
ejpam-6775	723	1	journal	journal	NOUN
ejpam-6775	723	2	of	of	ADP
ejpam-6775	723	3	theoretical	theoretical	ADJ
ejpam-6775	723	4	biology	biology	NOUN
ejpam-6775	723	5	,	,	PUNCT
ejpam-6775	723	6	269(1):31–45	269(1):31–45	NUM
ejpam-6775	723	7	,	,	PUNCT
ejpam-6775	723	8	2011	2011	NUM
ejpam-6775	723	9	.	.	PUNCT
ejpam-6775	724	1	[	[	X
ejpam-6775	724	2	10	10	NUM
ejpam-6775	724	3	]	]	X
ejpam-6775	724	4	y.	y.	PROPN
ejpam-6775	724	5	xue	xue	PROPN
ejpam-6775	724	6	and	and	CCONJ
ejpam-6775	724	7	j.	j.	PROPN
ejpam-6775	724	8	wang	wang	PROPN
ejpam-6775	724	9	.	.	PUNCT
ejpam-6775	725	1	backward	backward	ADJ
ejpam-6775	725	2	bifurcation	bifurcation	NOUN
ejpam-6775	725	3	of	of	ADP
ejpam-6775	725	4	an	an	DET
ejpam-6775	725	5	epidemic	epidemic	NOUN
ejpam-6775	725	6	model	model	NOUN
ejpam-6775	725	7	with	with	ADP
ejpam-6775	725	8	infectious	infectious	ADJ
ejpam-6775	725	9	force	force	NOUN
ejpam-6775	725	10	in	in	ADP
ejpam-6775	725	11	infected	infected	ADJ
ejpam-6775	725	12	and	and	CCONJ
ejpam-6775	725	13	immune	immune	ADJ
ejpam-6775	725	14	period	period	NOUN
ejpam-6775	725	15	and	and	CCONJ
ejpam-6775	725	16	treatment	treatment	NOUN
ejpam-6775	725	17	.	.	PUNCT
ejpam-6775	726	1	abstract	abstract	ADJ
ejpam-6775	726	2	and	and	CCONJ
ejpam-6775	726	3	applied	apply	VERB
ejpam-6775	726	4	analysis	analysis	NOUN
ejpam-6775	726	5	,	,	PUNCT
ejpam-6775	726	6	2012(1):647853	2012(1):647853	NOUN
ejpam-6775	726	7	,	,	PUNCT
ejpam-6775	726	8	2012	2012	NUM
ejpam-6775	726	9	.	.	PUNCT
ejpam-6775	727	1	[	[	X
ejpam-6775	727	2	11	11	NUM
ejpam-6775	727	3	]	]	PUNCT
ejpam-6775	727	4	x.	x.	NOUN
ejpam-6775	727	5	zhang	zhang	PROPN
ejpam-6775	727	6	and	and	CCONJ
ejpam-6775	727	7	x.	x.	PROPN
ejpam-6775	727	8	liu	liu	PROPN
ejpam-6775	727	9	.	.	PUNCT
ejpam-6775	728	1	backward	backward	ADJ
ejpam-6775	728	2	bifurcation	bifurcation	NOUN
ejpam-6775	728	3	of	of	ADP
ejpam-6775	728	4	an	an	DET
ejpam-6775	728	5	epidemic	epidemic	NOUN
ejpam-6775	728	6	model	model	NOUN
ejpam-6775	728	7	with	with	ADP
ejpam-6775	728	8	saturated	saturate	VERB
ejpam-6775	728	9	treatment	treatment	NOUN
ejpam-6775	728	10	function	function	NOUN
ejpam-6775	728	11	.	.	PUNCT
ejpam-6775	729	1	journal	journal	PROPN
ejpam-6775	729	2	of	of	ADP
ejpam-6775	729	3	mathematical	mathematical	ADJ
ejpam-6775	729	4	analysis	analysis	NOUN
ejpam-6775	729	5	and	and	CCONJ
ejpam-6775	729	6	applications	application	NOUN
ejpam-6775	729	7	,	,	PUNCT
ejpam-6775	729	8	348(1):433	348(1):433	NUM
ejpam-6775	729	9	–	–	PUNCT
ejpam-6775	729	10	443	443	NUM
ejpam-6775	729	11	,	,	PUNCT
ejpam-6775	729	12	2008	2008	NUM
ejpam-6775	729	13	.	.	PUNCT
ejpam-6775	730	1	[	[	X
ejpam-6775	730	2	12	12	NUM
ejpam-6775	730	3	]	]	PUNCT
ejpam-6775	730	4	z.	z.	PROPN
ejpam-6775	730	5	hu	hu	PROPN
ejpam-6775	730	6	,	,	PUNCT
ejpam-6775	730	7	s.	s.	PROPN
ejpam-6775	730	8	liu	liu	PROPN
ejpam-6775	730	9	,	,	PUNCT
ejpam-6775	730	10	and	and	CCONJ
ejpam-6775	730	11	h.	h.	PROPN
ejpam-6775	730	12	wang	wang	PROPN
ejpam-6775	730	13	.	.	PUNCT
ejpam-6775	731	1	backward	backward	ADJ
ejpam-6775	731	2	bifurcation	bifurcation	NOUN
ejpam-6775	731	3	of	of	ADP
ejpam-6775	731	4	an	an	DET
ejpam-6775	731	5	epidemic	epidemic	NOUN
ejpam-6775	731	6	model	model	NOUN
ejpam-6775	731	7	with	with	ADP
ejpam-6775	731	8	standard	standard	ADJ
ejpam-6775	731	9	incidence	incidence	NOUN
ejpam-6775	731	10	rate	rate	NOUN
ejpam-6775	731	11	and	and	CCONJ
ejpam-6775	731	12	treatment	treatment	NOUN
ejpam-6775	731	13	rate	rate	NOUN
ejpam-6775	731	14	.	.	PUNCT
ejpam-6775	732	1	nonlinear	nonlinear	ADJ
ejpam-6775	732	2	analysis	analysis	NOUN
ejpam-6775	732	3	:	:	PUNCT
ejpam-6775	732	4	real	real	ADJ
ejpam-6775	732	5	world	world	NOUN
ejpam-6775	732	6	applications	application	NOUN
ejpam-6775	732	7	,	,	PUNCT
ejpam-6775	732	8	9(5):2302–2312	9(5):2302–2312	PROPN
ejpam-6775	732	9	,	,	PUNCT
ejpam-6775	732	10	2008	2008	NUM
ejpam-6775	732	11	.	.	PUNCT
ejpam-6775	733	1	[	[	X
ejpam-6775	733	2	13	13	NUM
ejpam-6775	733	3	]	]	X
ejpam-6775	733	4	h.w	h.w	PROPN
ejpam-6775	733	5	.	.	PROPN
ejpam-6775	733	6	berhe	berhe	PROPN
ejpam-6775	733	7	,	,	PUNCT
ejpam-6775	733	8	o.d	o.d	PROPN
ejpam-6775	733	9	.	.	PROPN
ejpam-6775	733	10	makinde	makinde	PROPN
ejpam-6775	733	11	,	,	PUNCT
ejpam-6775	733	12	and	and	CCONJ
ejpam-6775	733	13	d.m	d.m	PROPN
ejpam-6775	733	14	.	.	PROPN
ejpam-6775	733	15	theuri	theuri	PROPN
ejpam-6775	733	16	.	.	PUNCT
ejpam-6775	734	1	co	co	NOUN
ejpam-6775	735	1	-	-	NOUN
ejpam-6775	735	2	dynamics	dynamic	NOUN
ejpam-6775	735	3	of	of	ADP
ejpam-6775	735	4	measles	measle	NOUN
ejpam-6775	735	5	and	and	CCONJ
ejpam-6775	735	6	dysentery	dysentery	NOUN
ejpam-6775	735	7	diarrhea	diarrhea	NOUN
ejpam-6775	735	8	diseases	disease	NOUN
ejpam-6775	735	9	with	with	ADP
ejpam-6775	735	10	optimal	optimal	ADJ
ejpam-6775	735	11	control	control	NOUN
ejpam-6775	735	12	and	and	CCONJ
ejpam-6775	735	13	cost	cost	NOUN
ejpam-6775	735	14	-	-	PUNCT
ejpam-6775	735	15	effectiveness	effectiveness	NOUN
ejpam-6775	735	16	analysis	analysis	NOUN
ejpam-6775	735	17	.	.	PUNCT
ejpam-6775	736	1	applied	apply	VERB
ejpam-6775	736	2	mathematics	mathematic	NOUN
ejpam-6775	736	3	and	and	CCONJ
ejpam-6775	736	4	computation	computation	NOUN
ejpam-6775	736	5	,	,	PUNCT
ejpam-6775	736	6	347:903–921	347:903–921	NUM
ejpam-6775	736	7	,	,	PUNCT
ejpam-6775	736	8	2019	2019	NUM
ejpam-6775	736	9	.	.	PUNCT
ejpam-6775	737	1	[	[	X
ejpam-6775	737	2	14	14	NUM
ejpam-6775	737	3	]	]	X
ejpam-6775	737	4	b.	b.	PROPN
ejpam-6775	737	5	buonomo	buonomo	PROPN
ejpam-6775	737	6	,	,	PUNCT
ejpam-6775	737	7	d.	d.	PROPN
ejpam-6775	737	8	lacitignola	lacitignola	PROPN
ejpam-6775	737	9	,	,	PUNCT
ejpam-6775	737	10	and	and	CCONJ
ejpam-6775	737	11	c.	c.	PROPN
ejpam-6775	737	12	vargas	vargas	PROPN
ejpam-6775	737	13	-	-	PUNCT
ejpam-6775	737	14	de	de	NOUN
ejpam-6775	737	15	-	-	NOUN
ejpam-6775	737	16	león	león	PROPN
ejpam-6775	737	17	.	.	PUNCT
ejpam-6775	737	18	qualitative	qualitative	ADJ
ejpam-6775	737	19	analysis	analysis	NOUN
ejpam-6775	737	20	and	and	CCONJ
ejpam-6775	737	21	optimal	optimal	ADJ
ejpam-6775	737	22	control	control	NOUN
ejpam-6775	737	23	of	of	ADP
ejpam-6775	737	24	an	an	DET
ejpam-6775	737	25	epidemic	epidemic	NOUN
ejpam-6775	737	26	model	model	NOUN
ejpam-6775	737	27	with	with	ADP
ejpam-6775	737	28	vaccination	vaccination	NOUN
ejpam-6775	737	29	and	and	CCONJ
ejpam-6775	737	30	treatment	treatment	NOUN
ejpam-6775	737	31	.	.	PUNCT
ejpam-6775	738	1	mathematics	mathematic	NOUN
ejpam-6775	738	2	and	and	CCONJ
ejpam-6775	738	3	computers	computer	NOUN
ejpam-6775	738	4	in	in	ADP
ejpam-6775	738	5	simulation	simulation	NOUN
ejpam-6775	738	6	,	,	PUNCT
ejpam-6775	738	7	100:88–102	100:88–102	NUM
ejpam-6775	738	8	,	,	PUNCT
ejpam-6775	738	9	2014	2014	NUM
ejpam-6775	738	10	.	.	PUNCT
ejpam-6775	739	1	[	[	X
ejpam-6775	739	2	15	15	NUM
ejpam-6775	739	3	]	]	X
ejpam-6775	739	4	n	n	DET
ejpam-6775	739	5	avinash	avinash	NOUN
ejpam-6775	739	6	,	,	PUNCT
ejpam-6775	739	7	g	g	PROPN
ejpam-6775	739	8	britto	britto	PROPN
ejpam-6775	739	9	antony	antony	PROPN
ejpam-6775	739	10	xavier	xavier	PROPN
ejpam-6775	739	11	,	,	PUNCT
ejpam-6775	739	12	ammar	ammar	PROPN
ejpam-6775	739	13	alsinai	alsinai	PROPN
ejpam-6775	739	14	,	,	PUNCT
ejpam-6775	739	15	hanan	hanan	PROPN
ejpam-6775	739	16	ahmed	ahmed	PROPN
ejpam-6775	739	17	,	,	PUNCT
ejpam-6775	739	18	v	v	NUM
ejpam-6775	739	19	rexma	rexma	PROPN
ejpam-6775	739	20	sherine	sherine	PROPN
ejpam-6775	739	21	,	,	PUNCT
ejpam-6775	739	22	and	and	CCONJ
ejpam-6775	739	23	p	p	NOUN
ejpam-6775	739	24	chellamani	chellamani	NOUN
ejpam-6775	739	25	.	.	PUNCT
ejpam-6775	740	1	dynamics	dynamic	NOUN
ejpam-6775	740	2	of	of	ADP
ejpam-6775	740	3	covid-19	covid-19	PROPN
ejpam-6775	740	4	using	use	VERB
ejpam-6775	740	5	seiqr	seiqr	ADJ
ejpam-6775	740	6	epidemic	epidemic	NOUN
ejpam-6775	740	7	model	model	NOUN
ejpam-6775	740	8	.	.	PUNCT
ejpam-6775	741	1	j.	j.	PROPN
ejpam-6775	741	2	math	math	PROPN
ejpam-6775	741	3	.	.	PUNCT
ejpam-6775	742	1	,	,	PUNCT
ejpam-6775	742	2	2022(1):1–21	2022(1):1–21	PROPN
ejpam-6775	742	3	,	,	PUNCT
ejpam-6775	742	4	january	january	PROPN
ejpam-6775	742	5	2022	2022	NUM
ejpam-6775	742	6	.	.	PUNCT
ejpam-6775	743	1	[	[	X
ejpam-6775	743	2	16	16	NUM
ejpam-6775	743	3	]	]	SYM
ejpam-6775	743	4	v	v	PROPN
ejpam-6775	743	5	r	r	NOUN
ejpam-6775	743	6	sherine	sherine	NOUN
ejpam-6775	743	7	,	,	PUNCT
ejpam-6775	743	8	p	p	NOUN
ejpam-6775	743	9	chellamani	chellamani	NOUN
ejpam-6775	743	10	,	,	PUNCT
ejpam-6775	743	11	rashad	rashad	PROPN
ejpam-6775	743	12	ismail	ismail	PROPN
ejpam-6775	743	13	,	,	PUNCT
ejpam-6775	743	14	n	n	PRON
ejpam-6775	743	15	avinash	avinash	NOUN
ejpam-6775	743	16	,	,	PUNCT
ejpam-6775	743	17	and	and	CCONJ
ejpam-6775	743	18	g	g	PROPN
ejpam-6775	743	19	xavier	xavier	PROPN
ejpam-6775	743	20	.	.	PUNCT
ejpam-6775	744	1	estimating	estimate	VERB
ejpam-6775	744	2	the	the	DET
ejpam-6775	744	3	spread	spread	NOUN
ejpam-6775	744	4	of	of	ADP
ejpam-6775	744	5	generalized	generalized	ADJ
ejpam-6775	744	6	compartmental	compartmental	ADJ
ejpam-6775	744	7	model	model	NOUN
ejpam-6775	744	8	of	of	ADP
ejpam-6775	744	9	monkeypox	monkeypox	PROPN
ejpam-6775	744	10	virus	virus	NOUN
ejpam-6775	744	11	using	use	VERB
ejpam-6775	744	12	a	a	DET
ejpam-6775	744	13	fuzzy	fuzzy	ADJ
ejpam-6775	744	14	fractional	fractional	ADJ
ejpam-6775	744	15	laplace	laplace	NOUN
ejpam-6775	744	16	transform	transform	NOUN
ejpam-6775	744	17	method	method	NOUN
ejpam-6775	744	18	.	.	PUNCT
ejpam-6775	745	1	symmetry	symmetry	NOUN
ejpam-6775	745	2	(	(	PUNCT
ejpam-6775	745	3	basel	basel	PROPN
ejpam-6775	745	4	)	)	PUNCT
ejpam-6775	745	5	,	,	PUNCT
ejpam-6775	745	6	14:2545	14:2545	NUM
ejpam-6775	745	7	,	,	PUNCT
ejpam-6775	745	8	december	december	PROPN
ejpam-6775	745	9	2022	2022	NUM
ejpam-6775	745	10	.	.	PUNCT
ejpam-6775	746	1	[	[	X
ejpam-6775	746	2	17	17	NUM
ejpam-6775	746	3	]	]	X
ejpam-6775	746	4	mohammed	mohammed	PROPN
ejpam-6775	746	5	m	m	PROPN
ejpam-6775	746	6	al	al	PROPN
ejpam-6775	746	7	-	-	PUNCT
ejpam-6775	746	8	shamiri	shamiri	PROPN
ejpam-6775	746	9	,	,	PUNCT
ejpam-6775	746	10	n	n	PRON
ejpam-6775	746	11	avinash	avinash	NOUN
ejpam-6775	746	12	,	,	PUNCT
ejpam-6775	746	13	p	p	NOUN
ejpam-6775	746	14	chellamani	chellamani	NOUN
ejpam-6775	746	15	,	,	PUNCT
ejpam-6775	746	16	manal	manal	ADJ
ejpam-6775	746	17	z	z	PROPN
ejpam-6775	746	18	m	m	VERB
ejpam-6775	746	19	abdallah	abdallah	PROPN
ejpam-6775	746	20	,	,	PUNCT
ejpam-6775	746	21	g	g	PROPN
ejpam-6775	746	22	britto	britto	PROPN
ejpam-6775	746	23	antony	antony	PROPN
ejpam-6775	746	24	xavier	xavier	PROPN
ejpam-6775	746	25	,	,	PUNCT
ejpam-6775	746	26	v	v	ADP
ejpam-6775	746	27	rexma	rexma	PROPN
ejpam-6775	746	28	sherine	sherine	PROPN
ejpam-6775	746	29	,	,	PUNCT
ejpam-6775	746	30	and	and	CCONJ
ejpam-6775	746	31	m	m	PROPN
ejpam-6775	746	32	abisha	abisha	NOUN
ejpam-6775	746	33	.	.	PUNCT
ejpam-6775	747	1	stability	stability	NOUN
ejpam-6775	747	2	analysis	analysis	NOUN
ejpam-6775	747	3	and	and	CCONJ
ejpam-6775	747	4	simulation	simulation	NOUN
ejpam-6775	747	5	of	of	ADP
ejpam-6775	747	6	diffusive	diffusive	ADJ
ejpam-6775	747	7	vaccinated	vaccinated	ADJ
ejpam-6775	747	8	models	model	NOUN
ejpam-6775	747	9	.	.	PUNCT
ejpam-6775	748	1	complexity	complexity	NOUN
ejpam-6775	748	2	,	,	PUNCT
ejpam-6775	748	3	2024(1	2024(1	NUM
ejpam-6775	748	4	)	)	PUNCT
ejpam-6775	748	5	,	,	PUNCT
ejpam-6775	748	6	january	january	PROPN
ejpam-6775	748	7	2024	2024	NUM
ejpam-6775	748	8	.	.	PUNCT
ejpam-6775	749	1	[	[	X
ejpam-6775	749	2	18	18	NUM
ejpam-6775	749	3	]	]	PUNCT
ejpam-6775	749	4	muflih	muflih	PROPN
ejpam-6775	749	5	alhazmi	alhazmi	PROPN
ejpam-6775	749	6	,	,	PUNCT
ejpam-6775	749	7	rexma	rexma	PROPN
ejpam-6775	749	8	sherine	sherine	PROPN
ejpam-6775	749	9	venchislas	venchislas	PROPN
ejpam-6775	749	10	,	,	PUNCT
ejpam-6775	749	11	gerly	gerly	ADV
ejpam-6775	749	12	thaniel	thaniel	ADJ
ejpam-6775	749	13	gnanamuthu	gnanamuthu	NOUN
ejpam-6775	749	14	,	,	PUNCT
ejpam-6775	749	15	chellamani	chellamani	NOUN
ejpam-6775	749	16	perumal	perumal	NOUN
ejpam-6775	749	17	,	,	PUNCT
ejpam-6775	749	18	shreefa	shreefa	PROPN
ejpam-6775	749	19	o	o	PROPN
ejpam-6775	749	20	hilali	hilali	PROPN
ejpam-6775	749	21	,	,	PUNCT
ejpam-6775	749	22	mashaer	mashaer	NOUN
ejpam-6775	749	23	alsaeedi	alsaeedi	NOUN
ejpam-6775	749	24	,	,	PUNCT
ejpam-6775	749	25	avinash	avinash	PROPN
ejpam-6775	749	26	natarajan	natarajan	PROPN
ejpam-6775	749	27	,	,	PUNCT
ejpam-6775	749	28	and	and	CCONJ
ejpam-6775	749	29	britto	britto	PROPN
ejpam-6775	749	30	j.	j.	PROPN
ejpam-6775	749	31	leo	leo	PROPN
ejpam-6775	749	32	amalraj	amalraj	PROPN
ejpam-6775	749	33	et	et	PROPN
ejpam-6775	749	34	al	al	PROPN
ejpam-6775	749	35	.	.	PUNCT
ejpam-6775	749	36	/	/	SYM
ejpam-6775	749	37	eur	eur	PROPN
ejpam-6775	749	38	.	.	PUNCT
ejpam-6775	750	1	j.	j.	PROPN
ejpam-6775	750	2	pure	pure	PROPN
ejpam-6775	750	3	appl	appl	PROPN
ejpam-6775	750	4	.	.	PROPN
ejpam-6775	750	5	math	math	PROPN
ejpam-6775	750	6	,	,	PUNCT
ejpam-6775	750	7	18	18	NUM
ejpam-6775	750	8	(	(	PUNCT
ejpam-6775	750	9	4	4	NUM
ejpam-6775	750	10	)	)	PUNCT
ejpam-6775	750	11	(	(	PUNCT
ejpam-6775	750	12	2025	2025	NUM
ejpam-6775	750	13	)	)	PUNCT
ejpam-6775	750	14	,	,	PUNCT
ejpam-6775	750	15	6775	6775	NUM
ejpam-6775	750	16	30	30	NUM
ejpam-6775	750	17	of	of	ADP
ejpam-6775	750	18	32	32	NUM
ejpam-6775	750	19	antony	antony	PROPN
ejpam-6775	750	20	xavier	xavier	PROPN
ejpam-6775	750	21	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6775	750	22	.	.	PUNCT
ejpam-6775	751	1	h	h	NOUN
ejpam-6775	751	2	-	-	PUNCT
ejpam-6775	751	3	nacci	nacci	NOUN
ejpam-6775	751	4	sequence	sequence	NOUN
ejpam-6775	751	5	and	and	CCONJ
ejpam-6775	751	6	its	its	PRON
ejpam-6775	751	7	role	role	NOUN
ejpam-6775	751	8	in	in	ADP
ejpam-6775	751	9	virus	virus	NOUN
ejpam-6775	751	10	mutation	mutation	NOUN
ejpam-6775	751	11	.	.	PUNCT
ejpam-6775	752	1	mathematics	mathematic	NOUN
ejpam-6775	752	2	,	,	PUNCT
ejpam-6775	752	3	august	august	PROPN
ejpam-6775	752	4	2024	2024	NUM
ejpam-6775	752	5	.	.	PUNCT
ejpam-6775	753	1	[	[	X
ejpam-6775	753	2	19	19	NUM
ejpam-6775	753	3	]	]	SYM
ejpam-6775	753	4	v	v	NOUN
ejpam-6775	753	5	r	r	NOUN
ejpam-6775	753	6	sherine	sherine	NOUN
ejpam-6775	753	7	,	,	PUNCT
ejpam-6775	753	8	p	p	NOUN
ejpam-6775	753	9	chellamani	chellamani	NOUN
ejpam-6775	753	10	,	,	PUNCT
ejpam-6775	753	11	rashad	rashad	PROPN
ejpam-6775	753	12	ismail	ismail	PROPN
ejpam-6775	753	13	,	,	PUNCT
ejpam-6775	753	14	n	n	PRON
ejpam-6775	753	15	avinash	avinash	NOUN
ejpam-6775	753	16	,	,	PUNCT
ejpam-6775	753	17	and	and	CCONJ
ejpam-6775	753	18	g	g	PROPN
ejpam-6775	753	19	xavier	xavier	PROPN
ejpam-6775	753	20	.	.	PUNCT
ejpam-6775	754	1	estimating	estimate	VERB
ejpam-6775	754	2	the	the	DET
ejpam-6775	754	3	spread	spread	NOUN
ejpam-6775	754	4	of	of	ADP
ejpam-6775	754	5	generalized	generalized	ADJ
ejpam-6775	754	6	compartmental	compartmental	ADJ
ejpam-6775	754	7	model	model	NOUN
ejpam-6775	754	8	of	of	ADP
ejpam-6775	754	9	monkeypox	monkeypox	PROPN
ejpam-6775	754	10	virus	virus	NOUN
ejpam-6775	754	11	using	use	VERB
ejpam-6775	754	12	a	a	DET
ejpam-6775	754	13	fuzzy	fuzzy	ADJ
ejpam-6775	754	14	fractional	fractional	ADJ
ejpam-6775	754	15	laplace	laplace	NOUN
ejpam-6775	754	16	transform	transform	NOUN
ejpam-6775	754	17	method	method	NOUN
ejpam-6775	754	18	.	.	PUNCT
ejpam-6775	755	1	symmetry	symmetry	NOUN
ejpam-6775	755	2	(	(	PUNCT
ejpam-6775	755	3	basel	basel	PROPN
ejpam-6775	755	4	)	)	PUNCT
ejpam-6775	755	5	,	,	PUNCT
ejpam-6775	755	6	14(12):2545	14(12):2545	NUM
ejpam-6775	755	7	,	,	PUNCT
ejpam-6775	755	8	december	december	PROPN
ejpam-6775	755	9	2022	2022	NUM
ejpam-6775	755	10	.	.	PUNCT
ejpam-6775	756	1	[	[	X
ejpam-6775	756	2	20	20	NUM
ejpam-6775	756	3	]	]	PUNCT
ejpam-6775	756	4	j	j	PROPN
ejpam-6775	756	5	joshvarajarathinam	joshvarajarathinam	PROPN
ejpam-6775	756	6	,	,	PUNCT
ejpam-6775	756	7	n	n	PRON
ejpam-6775	756	8	avinash	avinash	NOUN
ejpam-6775	756	9	,	,	PUNCT
ejpam-6775	756	10	m	m	NOUN
ejpam-6775	756	11	abisha	abisha	NOUN
ejpam-6775	756	12	,	,	PUNCT
ejpam-6775	756	13	g	g	PROPN
ejpam-6775	756	14	b	b	PROPN
ejpam-6775	756	15	a	a	DET
ejpam-6775	756	16	xavier	xavier	NOUN
ejpam-6775	756	17	,	,	PUNCT
ejpam-6775	756	18	and	and	CCONJ
ejpam-6775	756	19	p	p	PROPN
ejpam-6775	756	20	t	t	PROPN
ejpam-6775	756	21	elakkiya	elakkiya	PROPN
ejpam-6775	756	22	.	.	PUNCT
ejpam-6775	757	1	sidarthe	sidarthe	PROPN
ejpam-6775	757	2	epidemic	epidemic	PROPN
ejpam-6775	757	3	model	model	NOUN
ejpam-6775	757	4	through	through	ADP
ejpam-6775	757	5	variational	variational	ADJ
ejpam-6775	757	6	and	and	CCONJ
ejpam-6775	757	7	conformable	conformable	ADJ
ejpam-6775	757	8	transforms	transform	NOUN
ejpam-6775	757	9	.	.	PUNCT
ejpam-6775	758	1	volume	volume	NOUN
ejpam-6775	758	2	3306	3306	NUM
ejpam-6775	758	3	,	,	PUNCT
ejpam-6775	758	4	page	page	NOUN
ejpam-6775	758	5	020007	020007	NUM
ejpam-6775	758	6	,	,	PUNCT
ejpam-6775	758	7	2025	2025	NUM
ejpam-6775	758	8	.	.	PUNCT
ejpam-6775	759	1	[	[	X
ejpam-6775	759	2	21	21	NUM
ejpam-6775	759	3	]	]	PUNCT
ejpam-6775	759	4	n	n	DET
ejpam-6775	759	5	avinash	avinash	NOUN
ejpam-6775	759	6	,	,	PUNCT
ejpam-6775	759	7	g	g	PROPN
ejpam-6775	759	8	britto	britto	PROPN
ejpam-6775	759	9	antony	antony	PROPN
ejpam-6775	759	10	xavier	xavier	PROPN
ejpam-6775	759	11	,	,	PUNCT
ejpam-6775	759	12	ammar	ammar	PROPN
ejpam-6775	759	13	alsinai	alsinai	PROPN
ejpam-6775	759	14	,	,	PUNCT
ejpam-6775	759	15	hanan	hanan	PROPN
ejpam-6775	759	16	ahmed	ahmed	PROPN
ejpam-6775	759	17	,	,	PUNCT
ejpam-6775	759	18	v	v	NUM
ejpam-6775	759	19	rexma	rexma	PROPN
ejpam-6775	759	20	sherine	sherine	PROPN
ejpam-6775	759	21	,	,	PUNCT
ejpam-6775	759	22	and	and	CCONJ
ejpam-6775	759	23	p	p	NOUN
ejpam-6775	759	24	chellamani	chellamani	NOUN
ejpam-6775	759	25	.	.	PUNCT
ejpam-6775	760	1	dynamics	dynamic	NOUN
ejpam-6775	760	2	of	of	ADP
ejpam-6775	760	3	covid-19	covid-19	PROPN
ejpam-6775	760	4	using	use	VERB
ejpam-6775	760	5	seiqr	seiqr	ADJ
ejpam-6775	760	6	epidemic	epidemic	NOUN
ejpam-6775	760	7	model	model	NOUN
ejpam-6775	760	8	.	.	PUNCT
ejpam-6775	761	1	journal	journal	PROPN
ejpam-6775	761	2	of	of	ADP
ejpam-6775	761	3	mathematics	mathematic	NOUN
ejpam-6775	761	4	,	,	PUNCT
ejpam-6775	761	5	september	september	PROPN
ejpam-6775	761	6	2022	2022	NUM
ejpam-6775	761	7	.	.	PUNCT
ejpam-6775	762	1	[	[	X
ejpam-6775	762	2	22	22	NUM
ejpam-6775	762	3	]	]	PUNCT
ejpam-6775	762	4	fathia	fathia	NOUN
ejpam-6775	762	5	moh	moh	PROPN
ejpam-6775	762	6	,	,	PUNCT
ejpam-6775	762	7	al	al	PROPN
ejpam-6775	762	8	samma	samma	PROPN
ejpam-6775	762	9	,	,	PUNCT
ejpam-6775	762	10	avinash	avinash	PROPN
ejpam-6775	762	11	,	,	PUNCT
ejpam-6775	762	12	p	p	NOUN
ejpam-6775	762	13	chellamani	chellamani	NOUN
ejpam-6775	762	14	,	,	PUNCT
ejpam-6775	762	15	nafisa	nafisa	DET
ejpam-6775	762	16	a	a	DET
ejpam-6775	762	17	albasheir	albasheir	NOUN
ejpam-6775	762	18	,	,	PUNCT
ejpam-6775	762	19	ameni	ameni	PROPN
ejpam-6775	762	20	gargouri	gargouri	PROPN
ejpam-6775	762	21	,	,	PUNCT
ejpam-6775	762	22	g	g	PROPN
ejpam-6775	762	23	britto	britto	NOUN
ejpam-6775	762	24	,	,	PUNCT
ejpam-6775	762	25	antony	antony	PROPN
ejpam-6775	762	26	xavier	xavier	PROPN
ejpam-6775	762	27	,	,	PUNCT
ejpam-6775	762	28	and	and	CCONJ
ejpam-6775	762	29	mohammed	mohammed	PROPN
ejpam-6775	762	30	m	m	PROPN
ejpam-6775	762	31	a	a	DET
ejpam-6775	762	32	almazah	almazah	NOUN
ejpam-6775	762	33	.	.	PUNCT
ejpam-6775	763	1	exploring	explore	VERB
ejpam-6775	763	2	symmetry	symmetry	NOUN
ejpam-6775	763	3	in	in	ADP
ejpam-6775	763	4	an	an	DET
ejpam-6775	763	5	epidemiological	epidemiological	ADJ
ejpam-6775	763	6	model	model	NOUN
ejpam-6775	763	7	:	:	PUNCT
ejpam-6775	763	8	numerical	numerical	ADJ
ejpam-6775	763	9	analysis	analysis	NOUN
ejpam-6775	763	10	of	of	ADP
ejpam-6775	763	11	backward	backward	ADJ
ejpam-6775	763	12	bifurcation	bifurcation	NOUN
ejpam-6775	763	13	and	and	CCONJ
ejpam-6775	763	14	sensitivity	sensitivity	NOUN
ejpam-6775	763	15	indices	index	NOUN
ejpam-6775	763	16	.	.	PUNCT
ejpam-6775	764	1	symmetry	symmetry	NOUN
ejpam-6775	764	2	(	(	PUNCT
ejpam-6775	764	3	basel	basel	PROPN
ejpam-6775	764	4	)	)	PUNCT
ejpam-6775	764	5	,	,	PUNCT
ejpam-6775	764	6	16(12):1579	16(12):1579	NUM
ejpam-6775	764	7	,	,	PUNCT
ejpam-6775	764	8	november	november	PROPN
ejpam-6775	764	9	2024	2024	NUM
ejpam-6775	764	10	.	.	PUNCT
ejpam-6775	765	1	[	[	X
ejpam-6775	765	2	23	23	NUM
ejpam-6775	765	3	]	]	X
ejpam-6775	765	4	m.s	m.s	PROPN
ejpam-6775	765	5	.	.	PROPN
ejpam-6775	765	6	iqbal	iqbal	PROPN
ejpam-6775	765	7	.	.	PUNCT
ejpam-6775	766	1	boundary	boundary	ADJ
ejpam-6775	766	2	value	value	NOUN
ejpam-6775	766	3	problems	problem	NOUN
ejpam-6775	766	4	for	for	ADP
ejpam-6775	766	5	non	non	ADJ
ejpam-6775	766	6	-	-	ADJ
ejpam-6775	766	7	linear	linear	ADJ
ejpam-6775	766	8	first	first	ADJ
ejpam-6775	766	9	order	order	NOUN
ejpam-6775	766	10	systems	system	NOUN
ejpam-6775	766	11	of	of	ADP
ejpam-6775	766	12	partial	partial	ADJ
ejpam-6775	766	13	differential	differential	ADJ
ejpam-6775	766	14	equations	equation	NOUN
ejpam-6775	766	15	in	in	ADP
ejpam-6775	766	16	higher	high	ADJ
ejpam-6775	766	17	dimensions	dimension	NOUN
ejpam-6775	766	18	,	,	PUNCT
ejpam-6775	766	19	especially	especially	ADV
ejpam-6775	766	20	in	in	ADP
ejpam-6775	766	21	three	three	NUM
ejpam-6775	766	22	dimensions	dimension	NOUN
ejpam-6775	766	23	.	.	PUNCT
ejpam-6775	767	1	advances	advance	NOUN
ejpam-6775	767	2	in	in	ADP
ejpam-6775	767	3	applied	apply	VERB
ejpam-6775	767	4	clifford	clifford	PROPN
ejpam-6775	767	5	algebras	algebras	PROPN
ejpam-6775	767	6	,	,	PUNCT
ejpam-6775	767	7	29(5):98	29(5):98	NUM
ejpam-6775	767	8	,	,	PUNCT
ejpam-6775	767	9	2019	2019	NUM
ejpam-6775	767	10	.	.	PUNCT
ejpam-6775	768	1	[	[	X
ejpam-6775	768	2	24	24	NUM
ejpam-6775	768	3	]	]	X
ejpam-6775	768	4	n.	n.	PROPN
ejpam-6775	768	5	jain	jain	PROPN
ejpam-6775	768	6	,	,	PUNCT
ejpam-6775	768	7	s.	s.	PROPN
ejpam-6775	768	8	jhunthra	jhunthra	PROPN
ejpam-6775	768	9	,	,	PUNCT
ejpam-6775	768	10	h.	h.	PROPN
ejpam-6775	768	11	garg	garg	PROPN
ejpam-6775	768	12	,	,	PUNCT
ejpam-6775	768	13	v.	v.	PROPN
ejpam-6775	768	14	gupta	gupta	PROPN
ejpam-6775	768	15	,	,	PUNCT
ejpam-6775	768	16	s.	s.	PROPN
ejpam-6775	768	17	mohan	mohan	PROPN
ejpam-6775	768	18	,	,	PUNCT
ejpam-6775	768	19	a.	a.	PROPN
ejpam-6775	768	20	ahmadian	ahmadian	PROPN
ejpam-6775	768	21	,	,	PUNCT
ejpam-6775	768	22	s.	s.	PROPN
ejpam-6775	768	23	salahshour	salahshour	PROPN
ejpam-6775	768	24	,	,	PUNCT
ejpam-6775	768	25	and	and	CCONJ
ejpam-6775	768	26	m.	m.	NOUN
ejpam-6775	768	27	ferrara	ferrara	NOUN
ejpam-6775	768	28	.	.	PUNCT
ejpam-6775	769	1	prediction	prediction	NOUN
ejpam-6775	769	2	modelling	modelling	NOUN
ejpam-6775	769	3	of	of	ADP
ejpam-6775	769	4	covid	covid	NOUN
ejpam-6775	769	5	using	use	VERB
ejpam-6775	769	6	machine	machine	NOUN
ejpam-6775	769	7	learning	learning	NOUN
ejpam-6775	769	8	methods	method	NOUN
ejpam-6775	769	9	from	from	ADP
ejpam-6775	769	10	b	b	NOUN
ejpam-6775	769	11	-	-	PUNCT
ejpam-6775	769	12	cell	cell	NOUN
ejpam-6775	769	13	dataset	dataset	NOUN
ejpam-6775	769	14	.	.	PUNCT
ejpam-6775	770	1	results	result	NOUN
ejpam-6775	770	2	in	in	ADP
ejpam-6775	770	3	physics	physics	NOUN
ejpam-6775	770	4	,	,	PUNCT
ejpam-6775	770	5	21:103813	21:103813	NUM
ejpam-6775	770	6	,	,	PUNCT
ejpam-6775	770	7	2021	2021	NUM
ejpam-6775	770	8	.	.	PUNCT
ejpam-6775	771	1	[	[	X
ejpam-6775	771	2	25	25	NUM
ejpam-6775	771	3	]	]	X
ejpam-6775	771	4	n.	n.	NOUN
ejpam-6775	771	5	nirwani	nirwani	PROPN
ejpam-6775	771	6	,	,	PUNCT
ejpam-6775	771	7	v.	v.	PROPN
ejpam-6775	771	8	badshah	badshah	PROPN
ejpam-6775	771	9	,	,	PUNCT
ejpam-6775	771	10	and	and	CCONJ
ejpam-6775	771	11	r.	r.	PROPN
ejpam-6775	771	12	khandelwal	khandelwal	PROPN
ejpam-6775	771	13	.	.	PUNCT
ejpam-6775	772	1	dynamical	dynamical	ADJ
ejpam-6775	772	2	study	study	NOUN
ejpam-6775	772	3	of	of	ADP
ejpam-6775	772	4	an	an	DET
ejpam-6775	772	5	siqr	siqr	ADJ
ejpam-6775	772	6	model	model	NOUN
ejpam-6775	772	7	with	with	ADP
ejpam-6775	772	8	saturated	saturate	VERB
ejpam-6775	772	9	incidence	incidence	NOUN
ejpam-6775	772	10	rate	rate	NOUN
ejpam-6775	772	11	.	.	PUNCT
ejpam-6775	773	1	nonlinear	nonlinear	ADJ
ejpam-6775	773	2	analysis	analysis	NOUN
ejpam-6775	773	3	and	and	CCONJ
ejpam-6775	773	4	differential	differential	ADJ
ejpam-6775	773	5	equations	equation	NOUN
ejpam-6775	773	6	,	,	PUNCT
ejpam-6775	773	7	4(1):43–50	4(1):43–50	NUM
ejpam-6775	773	8	,	,	PUNCT
ejpam-6775	773	9	2016	2016	NUM
ejpam-6775	773	10	.	.	PUNCT
ejpam-6775	774	1	[	[	X
ejpam-6775	774	2	26	26	NUM
ejpam-6775	774	3	]	]	X
ejpam-6775	774	4	n.	n.	PROPN
ejpam-6775	774	5	ahmed	ahmed	PROPN
ejpam-6775	774	6	,	,	PUNCT
ejpam-6775	774	7	n.	n.	PROPN
ejpam-6775	774	8	shahid	shahid	PROPN
ejpam-6775	774	9	,	,	PUNCT
ejpam-6775	774	10	z.	z.	PROPN
ejpam-6775	774	11	iqbal	iqbal	PROPN
ejpam-6775	774	12	,	,	PUNCT
ejpam-6775	774	13	m.	m.	NOUN
ejpam-6775	774	14	jawaz	jawaz	NOUN
ejpam-6775	774	15	,	,	PUNCT
ejpam-6775	774	16	m.	m.	NOUN
ejpam-6775	774	17	rafiq	rafiq	PROPN
ejpam-6775	774	18	,	,	PUNCT
ejpam-6775	774	19	s.s	s.s	PROPN
ejpam-6775	774	20	.	.	PROPN
ejpam-6775	774	21	tahira	tahira	PROPN
ejpam-6775	774	22	,	,	PUNCT
ejpam-6775	774	23	and	and	CCONJ
ejpam-6775	774	24	m.o	m.o	PROPN
ejpam-6775	774	25	.	.	PROPN
ejpam-6775	774	26	ahmad	ahmad	PROPN
ejpam-6775	774	27	.	.	PROPN
ejpam-6775	775	1	numerical	numerical	PROPN
ejpam-6775	775	2	modeling	modeling	NOUN
ejpam-6775	775	3	of	of	ADP
ejpam-6775	775	4	seiqv	seiqv	VERB
ejpam-6775	775	5	epidemic	epidemic	NOUN
ejpam-6775	775	6	model	model	NOUN
ejpam-6775	775	7	with	with	ADP
ejpam-6775	775	8	saturated	saturate	VERB
ejpam-6775	775	9	incidence	incidence	NOUN
ejpam-6775	775	10	rate	rate	NOUN
ejpam-6775	775	11	.	.	PUNCT
ejpam-6775	776	1	journal	journal	NOUN
ejpam-6775	776	2	of	of	ADP
ejpam-6775	776	3	applied	apply	VERB
ejpam-6775	776	4	environmental	environmental	ADJ
ejpam-6775	776	5	and	and	CCONJ
ejpam-6775	776	6	biological	biological	ADJ
ejpam-6775	776	7	sciences	science	NOUN
ejpam-6775	776	8	,	,	PUNCT
ejpam-6775	776	9	8(4):67–82	8(4):67–82	NUM
ejpam-6775	776	10	,	,	PUNCT
ejpam-6775	776	11	2018	2018	NUM
ejpam-6775	776	12	.	.	PUNCT
ejpam-6775	777	1	[	[	X
ejpam-6775	777	2	27	27	NUM
ejpam-6775	777	3	]	]	X
ejpam-6775	777	4	j.	j.	PROPN
ejpam-6775	777	5	guckenheimer	guckenheimer	PROPN
ejpam-6775	777	6	and	and	CCONJ
ejpam-6775	777	7	p.	p.	PROPN
ejpam-6775	777	8	holmes	holmes	PROPN
ejpam-6775	777	9	.	.	PUNCT
ejpam-6775	778	1	nonlinear	nonlinear	ADJ
ejpam-6775	778	2	oscillations	oscillation	NOUN
ejpam-6775	778	3	,	,	PUNCT
ejpam-6775	778	4	dynamical	dynamical	ADJ
ejpam-6775	778	5	systems	system	NOUN
ejpam-6775	778	6	,	,	PUNCT
ejpam-6775	778	7	and	and	CCONJ
ejpam-6775	778	8	bifurcations	bifurcation	NOUN
ejpam-6775	778	9	of	of	ADP
ejpam-6775	778	10	vector	vector	NOUN
ejpam-6775	778	11	fields	field	NOUN
ejpam-6775	778	12	,	,	PUNCT
ejpam-6775	778	13	volume	volume	NOUN
ejpam-6775	778	14	42	42	NUM
ejpam-6775	778	15	.	.	PUNCT
ejpam-6775	779	1	springer	springer	NOUN
ejpam-6775	779	2	science	science	PROPN
ejpam-6775	779	3	and	and	CCONJ
ejpam-6775	779	4	business	business	NOUN
ejpam-6775	779	5	media	medium	NOUN
ejpam-6775	779	6	,	,	PUNCT
ejpam-6775	779	7	2013	2013	NUM
ejpam-6775	779	8	.	.	PUNCT
ejpam-6775	780	1	[	[	X
ejpam-6775	780	2	28	28	NUM
ejpam-6775	780	3	]	]	X
ejpam-6775	780	4	y.a	y.a	PROPN
ejpam-6775	780	5	.	.	PROPN
ejpam-6775	780	6	kuznetsov	kuznetsov	PROPN
ejpam-6775	780	7	,	,	PUNCT
ejpam-6775	780	8	i.a	i.a	PROPN
ejpam-6775	780	9	.	.	PROPN
ejpam-6775	780	10	kuznetsov	kuznetsov	PROPN
ejpam-6775	780	11	,	,	PUNCT
ejpam-6775	780	12	and	and	CCONJ
ejpam-6775	780	13	y.	y.	PROPN
ejpam-6775	780	14	kuznetsov	kuznetsov	PROPN
ejpam-6775	780	15	.	.	PUNCT
ejpam-6775	781	1	elements	element	NOUN
ejpam-6775	781	2	of	of	ADP
ejpam-6775	781	3	applied	apply	VERB
ejpam-6775	781	4	bifurcation	bifurcation	NOUN
ejpam-6775	781	5	theory	theory	NOUN
ejpam-6775	781	6	,	,	PUNCT
ejpam-6775	781	7	volume	volume	NOUN
ejpam-6775	781	8	112	112	NUM
ejpam-6775	781	9	.	.	PUNCT
ejpam-6775	781	10	springer	springer	NOUN
ejpam-6775	781	11	,	,	PUNCT
ejpam-6775	781	12	new	new	PROPN
ejpam-6775	781	13	york	york	PROPN
ejpam-6775	781	14	,	,	PUNCT
ejpam-6775	781	15	1998	1998	NUM
ejpam-6775	781	16	.	.	PUNCT
ejpam-6775	782	1	[	[	X
ejpam-6775	782	2	29	29	NUM
ejpam-6775	782	3	]	]	X
ejpam-6775	782	4	e.j	e.j	PROPN
ejpam-6775	782	5	.	.	PROPN
ejpam-6775	782	6	doedel	doedel	PROPN
ejpam-6775	782	7	and	and	CCONJ
ejpam-6775	782	8	b.	b.	PROPN
ejpam-6775	782	9	oldeman	oldeman	NOUN
ejpam-6775	782	10	.	.	PUNCT
ejpam-6775	783	1	auto-07p	auto-07p	NOUN
ejpam-6775	783	2	:	:	PUNCT
ejpam-6775	783	3	continuation	continuation	NOUN
ejpam-6775	783	4	and	and	CCONJ
ejpam-6775	783	5	bifurcation	bifurcation	NOUN
ejpam-6775	783	6	software	software	NOUN
ejpam-6775	783	7	,	,	PUNCT
ejpam-6775	783	8	1998	1998	NUM
ejpam-6775	783	9	.	.	PUNCT
ejpam-6775	784	1	[	[	X
ejpam-6775	784	2	30	30	NUM
ejpam-6775	784	3	]	]	X
ejpam-6775	784	4	m.	m.	NOUN
ejpam-6775	784	5	aguiar	aguiar	PROPN
ejpam-6775	784	6	,	,	PUNCT
ejpam-6775	784	7	b.w	b.w	PROPN
ejpam-6775	784	8	.	.	PROPN
ejpam-6775	784	9	kooi	kooi	PROPN
ejpam-6775	784	10	,	,	PUNCT
ejpam-6775	784	11	and	and	CCONJ
ejpam-6775	784	12	n.	n.	PROPN
ejpam-6775	784	13	stollenwerk	stollenwerk	PROPN
ejpam-6775	784	14	.	.	PUNCT
ejpam-6775	785	1	epidemiology	epidemiology	NOUN
ejpam-6775	785	2	of	of	ADP
ejpam-6775	785	3	dengue	dengue	NOUN
ejpam-6775	785	4	fever	fever	NOUN
ejpam-6775	785	5	:	:	PUNCT
ejpam-6775	785	6	a	a	DET
ejpam-6775	785	7	model	model	NOUN
ejpam-6775	785	8	with	with	ADP
ejpam-6775	785	9	temporary	temporary	ADJ
ejpam-6775	785	10	cross	cross	NOUN
ejpam-6775	785	11	-	-	NOUN
ejpam-6775	785	12	immunity	immunity	NOUN
ejpam-6775	785	13	and	and	CCONJ
ejpam-6775	785	14	possible	possible	ADJ
ejpam-6775	785	15	secondary	secondary	ADJ
ejpam-6775	785	16	infection	infection	NOUN
ejpam-6775	785	17	shows	show	VERB
ejpam-6775	785	18	bifurcations	bifurcation	NOUN
ejpam-6775	785	19	and	and	CCONJ
ejpam-6775	785	20	chaotic	chaotic	ADJ
ejpam-6775	785	21	behaviour	behaviour	NOUN
ejpam-6775	785	22	in	in	ADP
ejpam-6775	785	23	wide	wide	ADJ
ejpam-6775	785	24	parameter	parameter	NOUN
ejpam-6775	785	25	regions	region	NOUN
ejpam-6775	785	26	.	.	PUNCT
ejpam-6775	786	1	mathematical	mathematical	ADJ
ejpam-6775	786	2	modelling	modelling	NOUN
ejpam-6775	786	3	of	of	ADP
ejpam-6775	786	4	natural	natural	ADJ
ejpam-6775	786	5	phenomena	phenomenon	NOUN
ejpam-6775	786	6	,	,	PUNCT
ejpam-6775	786	7	3(4):48–70	3(4):48–70	NUM
ejpam-6775	786	8	,	,	PUNCT
ejpam-6775	786	9	2008	2008	NUM
ejpam-6775	786	10	.	.	PUNCT
ejpam-6775	787	1	[	[	X
ejpam-6775	787	2	31	31	NUM
ejpam-6775	787	3	]	]	X
ejpam-6775	787	4	y.m	y.m	PROPN
ejpam-6775	787	5	.	.	PROPN
ejpam-6775	787	6	hounmanou	hounmanou	PROPN
ejpam-6775	787	7	,	,	PUNCT
ejpam-6775	787	8	k.	k.	PROPN
ejpam-6775	787	9	mølbak	mølbak	PROPN
ejpam-6775	787	10	,	,	PUNCT
ejpam-6775	787	11	j.	j.	PROPN
ejpam-6775	787	12	kähler	kähler	PROPN
ejpam-6775	787	13	,	,	PUNCT
ejpam-6775	787	14	r.h	r.h	PROPN
ejpam-6775	787	15	.	.	PROPN
ejpam-6775	787	16	mdegela	mdegela	PROPN
ejpam-6775	787	17	,	,	PUNCT
ejpam-6775	787	18	j.e	j.e	PROPN
ejpam-6775	787	19	.	.	PROPN
ejpam-6775	787	20	olsen	olsen	PROPN
ejpam-6775	787	21	,	,	PUNCT
ejpam-6775	787	22	and	and	CCONJ
ejpam-6775	787	23	a.	a.	PROPN
ejpam-6775	787	24	dalsgaard	dalsgaard	PROPN
ejpam-6775	787	25	.	.	PUNCT
ejpam-6775	788	1	cholera	cholera	NOUN
ejpam-6775	788	2	hotspots	hotspot	NOUN
ejpam-6775	788	3	and	and	CCONJ
ejpam-6775	788	4	surveillance	surveillance	NOUN
ejpam-6775	788	5	constraints	constraint	NOUN
ejpam-6775	788	6	contributing	contribute	VERB
ejpam-6775	788	7	to	to	PART
ejpam-6775	788	8	recurrent	recurrent	ADJ
ejpam-6775	788	9	epidemics	epidemic	NOUN
ejpam-6775	788	10	in	in	ADP
ejpam-6775	788	11	tanzania	tanzania	PROPN
ejpam-6775	788	12	.	.	PUNCT
ejpam-6775	789	1	bmc	bmc	PROPN
ejpam-6775	789	2	research	research	NOUN
ejpam-6775	789	3	notes	note	NOUN
ejpam-6775	789	4	,	,	PUNCT
ejpam-6775	789	5	12:1–6	12:1–6	NUM
ejpam-6775	789	6	,	,	PUNCT
ejpam-6775	789	7	2019	2019	NUM
ejpam-6775	789	8	.	.	PUNCT
ejpam-6775	790	1	[	[	X
ejpam-6775	790	2	32	32	NUM
ejpam-6775	790	3	]	]	PUNCT
ejpam-6775	790	4	t.	t.	NOUN
ejpam-6775	790	5	mashe	mashe	PROPN
ejpam-6775	790	6	,	,	PUNCT
ejpam-6775	790	7	d.	d.	PROPN
ejpam-6775	790	8	domman	domman	PROPN
ejpam-6775	790	9	,	,	PUNCT
ejpam-6775	790	10	a.	a.	NOUN
ejpam-6775	790	11	tarupiwa	tarupiwa	PROPN
ejpam-6775	790	12	,	,	PUNCT
ejpam-6775	790	13	p.	p.	PROPN
ejpam-6775	790	14	manangazira	manangazira	PROPN
ejpam-6775	790	15	,	,	PUNCT
ejpam-6775	790	16	i.	i.	PROPN
ejpam-6775	790	17	phiri	phiri	PROPN
ejpam-6775	790	18	,	,	PUNCT
ejpam-6775	790	19	k.	k.	PROPN
ejpam-6775	790	20	masunda	masunda	PROPN
ejpam-6775	790	21	,	,	PUNCT
ejpam-6775	790	22	p.	p.	NOUN
ejpam-6775	790	23	chonzi	chonzi	PROPN
ejpam-6775	790	24	,	,	PUNCT
ejpam-6775	790	25	e.	e.	PROPN
ejpam-6775	790	26	njamkepo	njamkepo	PROPN
ejpam-6775	790	27	,	,	PUNCT
ejpam-6775	790	28	m.	m.	NOUN
ejpam-6775	790	29	ramudzulu	ramudzulu	VERB
ejpam-6775	790	30	,	,	PUNCT
ejpam-6775	790	31	s.	s.	PROPN
ejpam-6775	790	32	mtapuri	mtapuri	PROPN
ejpam-6775	790	33	-	-	PROPN
ejpam-6775	790	34	zinyowera	zinyowera	PROPN
ejpam-6775	790	35	,	,	PUNCT
ejpam-6775	790	36	and	and	CCONJ
ejpam-6775	790	37	a.m.	a.m.	PROPN
ejpam-6775	790	38	smith	smith	PROPN
ejpam-6775	790	39	.	.	PUNCT
ejpam-6775	791	1	highly	highly	ADV
ejpam-6775	791	2	resistant	resistant	ADJ
ejpam-6775	791	3	cholera	cholera	NOUN
ejpam-6775	791	4	outbreak	outbreak	NOUN
ejpam-6775	791	5	strain	strain	VERB
ejpam-6775	791	6	in	in	ADP
ejpam-6775	791	7	zimbabwe	zimbabwe	PROPN
ejpam-6775	791	8	.	.	PUNCT
ejpam-6775	792	1	new	new	PROPN
ejpam-6775	792	2	england	england	PROPN
ejpam-6775	792	3	journal	journal	PROPN
ejpam-6775	792	4	of	of	ADP
ejpam-6775	792	5	medicine	medicine	NOUN
ejpam-6775	792	6	,	,	PUNCT
ejpam-6775	792	7	383(7):687–689	383(7):687–689	NUM
ejpam-6775	792	8	,	,	PUNCT
ejpam-6775	792	9	2020	2020	NUM
ejpam-6775	792	10	.	.	PUNCT
ejpam-6775	793	1	j.	j.	PROPN
ejpam-6775	793	2	leo	leo	PROPN
ejpam-6775	793	3	amalraj	amalraj	PROPN
ejpam-6775	793	4	et	et	PROPN
ejpam-6775	793	5	al	al	PROPN
ejpam-6775	793	6	.	.	PUNCT
ejpam-6775	793	7	/	/	SYM
ejpam-6775	793	8	eur	eur	PROPN
ejpam-6775	793	9	.	.	PUNCT
ejpam-6775	794	1	j.	j.	PROPN
ejpam-6775	794	2	pure	pure	PROPN
ejpam-6775	794	3	appl	appl	PROPN
ejpam-6775	794	4	.	.	PROPN
ejpam-6775	794	5	math	math	PROPN
ejpam-6775	794	6	,	,	PUNCT
ejpam-6775	794	7	18	18	NUM
ejpam-6775	794	8	(	(	PUNCT
ejpam-6775	794	9	4	4	NUM
ejpam-6775	794	10	)	)	PUNCT
ejpam-6775	794	11	(	(	PUNCT
ejpam-6775	794	12	2025	2025	NUM
ejpam-6775	794	13	)	)	PUNCT
ejpam-6775	794	14	,	,	PUNCT
ejpam-6775	794	15	6775	6775	NUM
ejpam-6775	794	16	31	31	NUM
ejpam-6775	794	17	of	of	ADP
ejpam-6775	794	18	32	32	NUM
ejpam-6775	794	19	[	[	SYM
ejpam-6775	794	20	33	33	NUM
ejpam-6775	794	21	]	]	PUNCT
ejpam-6775	794	22	g.	g.	PROPN
ejpam-6775	794	23	george	george	PROPN
ejpam-6775	794	24	.	.	PUNCT
ejpam-6775	795	1	notes	note	NOUN
ejpam-6775	795	2	from	from	ADP
ejpam-6775	795	3	the	the	DET
ejpam-6775	795	4	field	field	NOUN
ejpam-6775	795	5	:	:	PUNCT
ejpam-6775	795	6	ongoing	ongoing	ADJ
ejpam-6775	795	7	cholera	cholera	NOUN
ejpam-6775	795	8	outbreak	outbreak	NOUN
ejpam-6775	795	9	—	—	PUNCT
ejpam-6775	795	10	kenya	kenya	PROPN
ejpam-6775	795	11	,	,	PUNCT
ejpam-6775	795	12	2014–2016	2014–2016	NUM
ejpam-6775	795	13	.	.	PUNCT
ejpam-6775	796	1	mmwr	mmwr	NOUN
ejpam-6775	796	2	.	.	PUNCT
ejpam-6775	797	1	morbidity	morbidity	NOUN
ejpam-6775	797	2	and	and	CCONJ
ejpam-6775	797	3	mortality	mortality	NOUN
ejpam-6775	797	4	weekly	weekly	ADJ
ejpam-6775	797	5	report	report	NOUN
ejpam-6775	797	6	,	,	PUNCT
ejpam-6775	797	7	65	65	NUM
ejpam-6775	797	8	,	,	PUNCT
ejpam-6775	797	9	2016	2016	NUM
ejpam-6775	797	10	.	.	PUNCT
ejpam-6775	798	1	[	[	X
ejpam-6775	798	2	34	34	NUM
ejpam-6775	798	3	]	]	X
ejpam-6775	798	4	g.	g.	NOUN
ejpam-6775	798	5	dinede	dinede	PROPN
ejpam-6775	798	6	,	,	PUNCT
ejpam-6775	798	7	a.	a.	NOUN
ejpam-6775	798	8	abagero	abagero	PROPN
ejpam-6775	798	9	,	,	PUNCT
ejpam-6775	798	10	and	and	CCONJ
ejpam-6775	798	11	t.	t.	PROPN
ejpam-6775	798	12	tolosa	tolosa	PROPN
ejpam-6775	798	13	.	.	PUNCT
ejpam-6775	799	1	cholera	cholera	NOUN
ejpam-6775	799	2	outbreak	outbreak	PROPN
ejpam-6775	799	3	in	in	ADP
ejpam-6775	799	4	addis	addis	PROPN
ejpam-6775	799	5	ababa	ababa	PROPN
ejpam-6775	799	6	,	,	PUNCT
ejpam-6775	799	7	ethiopia	ethiopia	PROPN
ejpam-6775	799	8	:	:	PUNCT
ejpam-6775	799	9	a	a	DET
ejpam-6775	799	10	case	case	NOUN
ejpam-6775	799	11	-	-	PUNCT
ejpam-6775	799	12	control	control	NOUN
ejpam-6775	799	13	study	study	NOUN
ejpam-6775	799	14	.	.	PUNCT
ejpam-6775	800	1	plos	plos	PROPN
ejpam-6775	800	2	one	one	NUM
ejpam-6775	800	3	,	,	PUNCT
ejpam-6775	800	4	15(7):e0235440	15(7):e0235440	NUM
ejpam-6775	800	5	,	,	PUNCT
ejpam-6775	800	6	2020	2020	NUM
ejpam-6775	800	7	.	.	PUNCT
ejpam-6775	801	1	[	[	X
ejpam-6775	801	2	35	35	NUM
ejpam-6775	801	3	]	]	X
ejpam-6775	801	4	f.	f.	PROPN
ejpam-6775	801	5	federspiel	federspiel	PROPN
ejpam-6775	801	6	and	and	CCONJ
ejpam-6775	801	7	m.	m.	PROPN
ejpam-6775	801	8	ali	ali	PROPN
ejpam-6775	801	9	.	.	PUNCT
ejpam-6775	802	1	the	the	DET
ejpam-6775	802	2	cholera	cholera	NOUN
ejpam-6775	802	3	outbreak	outbreak	NOUN
ejpam-6775	802	4	in	in	ADP
ejpam-6775	802	5	yemen	yemen	PROPN
ejpam-6775	802	6	:	:	PUNCT
ejpam-6775	802	7	lessons	lesson	NOUN
ejpam-6775	802	8	learned	learn	VERB
ejpam-6775	802	9	and	and	CCONJ
ejpam-6775	802	10	way	way	ADV
ejpam-6775	802	11	forward	forward	ADV
ejpam-6775	802	12	.	.	PUNCT
ejpam-6775	803	1	bmc	bmc	ADJ
ejpam-6775	803	2	public	public	ADJ
ejpam-6775	803	3	health	health	NOUN
ejpam-6775	803	4	,	,	PUNCT
ejpam-6775	803	5	18(1):1338	18(1):1338	NUM
ejpam-6775	803	6	,	,	PUNCT
ejpam-6775	803	7	2018	2018	NUM
ejpam-6775	803	8	.	.	PUNCT
ejpam-6775	804	1	[	[	X
ejpam-6775	804	2	36	36	NUM
ejpam-6775	804	3	]	]	X
ejpam-6775	804	4	e.j	e.j	PROPN
ejpam-6775	804	5	.	.	PROPN
ejpam-6775	804	6	nelson	nelson	PROPN
ejpam-6775	804	7	,	,	PUNCT
ejpam-6775	804	8	j.b	j.b	PROPN
ejpam-6775	804	9	.	.	PROPN
ejpam-6775	804	10	harris	harris	PROPN
ejpam-6775	804	11	,	,	PUNCT
ejpam-6775	804	12	j.	j.	PROPN
ejpam-6775	804	13	glenn	glenn	PROPN
ejpam-6775	804	14	morris	morris	PROPN
ejpam-6775	804	15	jr	jr	PROPN
ejpam-6775	804	16	,	,	PUNCT
ejpam-6775	804	17	s.b	s.b	PROPN
ejpam-6775	804	18	.	.	PROPN
ejpam-6775	804	19	calderwood	calderwood	PROPN
ejpam-6775	804	20	,	,	PUNCT
ejpam-6775	804	21	and	and	CCONJ
ejpam-6775	804	22	a.	a.	PROPN
ejpam-6775	804	23	camilli	camilli	PROPN
ejpam-6775	804	24	.	.	PUNCT
ejpam-6775	805	1	cholera	cholera	NOUN
ejpam-6775	805	2	transmission	transmission	NOUN
ejpam-6775	805	3	:	:	PUNCT
ejpam-6775	805	4	the	the	DET
ejpam-6775	805	5	host	host	NOUN
ejpam-6775	805	6	,	,	PUNCT
ejpam-6775	805	7	pathogen	pathogen	NOUN
ejpam-6775	805	8	and	and	CCONJ
ejpam-6775	805	9	bacteriophage	bacteriophage	NOUN
ejpam-6775	805	10	dynamic	dynamic	ADJ
ejpam-6775	805	11	.	.	PUNCT
ejpam-6775	806	1	nature	nature	NOUN
ejpam-6775	806	2	reviews	review	VERB
ejpam-6775	806	3	microbiology	microbiology	NOUN
ejpam-6775	806	4	,	,	PUNCT
ejpam-6775	806	5	7(10):693–702	7(10):693–702	NUM
ejpam-6775	806	6	,	,	PUNCT
ejpam-6775	806	7	2009	2009	NUM
ejpam-6775	806	8	.	.	PUNCT
ejpam-6775	807	1	[	[	X
ejpam-6775	807	2	37	37	NUM
ejpam-6775	807	3	]	]	X
ejpam-6775	807	4	l.	l.	PROPN
ejpam-6775	807	5	esteva	esteva	PROPN
ejpam-6775	807	6	and	and	CCONJ
ejpam-6775	807	7	c.	c.	PROPN
ejpam-6775	807	8	vargas	vargas	PROPN
ejpam-6775	807	9	.	.	PUNCT
ejpam-6775	808	1	analysis	analysis	NOUN
ejpam-6775	808	2	of	of	ADP
ejpam-6775	808	3	a	a	DET
ejpam-6775	808	4	dengue	dengue	NOUN
ejpam-6775	808	5	disease	disease	NOUN
ejpam-6775	808	6	transmission	transmission	NOUN
ejpam-6775	808	7	model	model	NOUN
ejpam-6775	808	8	.	.	PUNCT
ejpam-6775	809	1	mathematical	mathematical	ADJ
ejpam-6775	809	2	biosciences	bioscience	NOUN
ejpam-6775	809	3	,	,	PUNCT
ejpam-6775	809	4	150(2):131–151	150(2):131–151	NUM
ejpam-6775	809	5	,	,	PUNCT
ejpam-6775	809	6	1998	1998	NUM
ejpam-6775	809	7	.	.	PUNCT
ejpam-6775	810	1	[	[	X
ejpam-6775	810	2	38	38	NUM
ejpam-6775	810	3	]	]	SYM
ejpam-6775	810	4	s.m	s.m	PROPN
ejpam-6775	810	5	.	.	PROPN
ejpam-6775	810	6	garba	garba	PROPN
ejpam-6775	810	7	,	,	PUNCT
ejpam-6775	810	8	a.b	a.b	PROPN
ejpam-6775	810	9	.	.	PROPN
ejpam-6775	810	10	gumel	gumel	PROPN
ejpam-6775	810	11	,	,	PUNCT
ejpam-6775	810	12	and	and	CCONJ
ejpam-6775	810	13	m.a	m.a	PROPN
ejpam-6775	810	14	.	.	PROPN
ejpam-6775	810	15	bakar	bakar	PROPN
ejpam-6775	810	16	.	.	PUNCT
ejpam-6775	811	1	backward	backward	ADJ
ejpam-6775	811	2	bifurcations	bifurcation	NOUN
ejpam-6775	811	3	in	in	ADP
ejpam-6775	811	4	dengue	dengue	NOUN
ejpam-6775	811	5	transmission	transmission	NOUN
ejpam-6775	811	6	dynamics	dynamic	NOUN
ejpam-6775	811	7	.	.	PUNCT
ejpam-6775	812	1	mathematical	mathematical	ADJ
ejpam-6775	812	2	biosciences	bioscience	NOUN
ejpam-6775	812	3	,	,	PUNCT
ejpam-6775	812	4	215(1):11–25	215(1):11–25	NUM
ejpam-6775	812	5	,	,	PUNCT
ejpam-6775	812	6	2008	2008	NUM
ejpam-6775	812	7	.	.	PUNCT
ejpam-6775	813	1	[	[	X
ejpam-6775	813	2	39	39	NUM
ejpam-6775	813	3	]	]	X
ejpam-6775	813	4	h.s	h.s	PROPN
ejpam-6775	813	5	.	.	PROPN
ejpam-6775	813	6	rodrigues	rodrigues	PROPN
ejpam-6775	813	7	,	,	PUNCT
ejpam-6775	813	8	m.t.t	m.t.t	NOUN
ejpam-6775	813	9	.	.	PUNCT
ejpam-6775	813	10	monteiro	monteiro	PROPN
ejpam-6775	813	11	,	,	PUNCT
ejpam-6775	813	12	and	and	CCONJ
ejpam-6775	813	13	d.f	d.f	PROPN
ejpam-6775	813	14	.	.	PROPN
ejpam-6775	813	15	torres	torre	NOUN
ejpam-6775	813	16	.	.	PUNCT
ejpam-6775	813	17	vaccination	vaccination	NOUN
ejpam-6775	813	18	models	model	NOUN
ejpam-6775	813	19	and	and	CCONJ
ejpam-6775	813	20	optimal	optimal	ADJ
ejpam-6775	813	21	control	control	NOUN
ejpam-6775	813	22	strategies	strategy	NOUN
ejpam-6775	813	23	to	to	ADP
ejpam-6775	813	24	dengue	dengue	NOUN
ejpam-6775	813	25	.	.	PUNCT
ejpam-6775	814	1	mathematical	mathematical	ADJ
ejpam-6775	814	2	biosciences	bioscience	NOUN
ejpam-6775	814	3	,	,	PUNCT
ejpam-6775	814	4	247:1–12	247:1–12	NUM
ejpam-6775	814	5	,	,	PUNCT
ejpam-6775	814	6	2014	2014	NUM
ejpam-6775	814	7	.	.	PUNCT
ejpam-6775	815	1	[	[	X
ejpam-6775	815	2	40	40	NUM
ejpam-6775	815	3	]	]	X
ejpam-6775	815	4	n.a	n.a	PROPN
ejpam-6775	815	5	.	.	PROPN
ejpam-6775	815	6	maidana	maidana	PROPN
ejpam-6775	815	7	and	and	CCONJ
ejpam-6775	815	8	h.m	h.m	PROPN
ejpam-6775	815	9	.	.	PROPN
ejpam-6775	815	10	yang	yang	PROPN
ejpam-6775	815	11	.	.	PUNCT
ejpam-6775	816	1	dynamic	dynamic	ADJ
ejpam-6775	816	2	of	of	ADP
ejpam-6775	816	3	west	west	PROPN
ejpam-6775	816	4	nile	nile	PROPN
ejpam-6775	816	5	virus	virus	PROPN
ejpam-6775	816	6	transmission	transmission	NOUN
ejpam-6775	816	7	considering	consider	VERB
ejpam-6775	816	8	several	several	ADJ
ejpam-6775	816	9	coexisting	coexist	VERB
ejpam-6775	816	10	avian	avian	ADJ
ejpam-6775	816	11	populations	population	NOUN
ejpam-6775	816	12	.	.	PUNCT
ejpam-6775	817	1	mathematical	mathematical	ADJ
ejpam-6775	817	2	and	and	CCONJ
ejpam-6775	817	3	computer	computer	NOUN
ejpam-6775	817	4	modelling	modelling	NOUN
ejpam-6775	817	5	,	,	PUNCT
ejpam-6775	817	6	53(56):1247–1260	53(56):1247–1260	NUM
ejpam-6775	817	7	,	,	PUNCT
ejpam-6775	817	8	2011	2011	NUM
ejpam-6775	817	9	.	.	PUNCT
ejpam-6775	818	1	[	[	X
ejpam-6775	818	2	41	41	NUM
ejpam-6775	818	3	]	]	X
ejpam-6775	818	4	d.	d.	PROPN
ejpam-6775	818	5	moulay	moulay	PROPN
ejpam-6775	818	6	,	,	PUNCT
ejpam-6775	818	7	m.a	m.a	PROPN
ejpam-6775	818	8	.	.	PROPN
ejpam-6775	818	9	aziz	aziz	PROPN
ejpam-6775	818	10	-	-	PUNCT
ejpam-6775	818	11	alaoui	alaoui	PROPN
ejpam-6775	818	12	,	,	PUNCT
ejpam-6775	818	13	and	and	CCONJ
ejpam-6775	818	14	m.	m.	NOUN
ejpam-6775	818	15	cadivel	cadivel	PROPN
ejpam-6775	818	16	.	.	PUNCT
ejpam-6775	819	1	the	the	DET
ejpam-6775	819	2	chikungunya	chikungunya	NOUN
ejpam-6775	819	3	disease	disease	NOUN
ejpam-6775	819	4	:	:	PUNCT
ejpam-6775	819	5	modeling	modeling	NOUN
ejpam-6775	819	6	,	,	PUNCT
ejpam-6775	819	7	vector	vector	NOUN
ejpam-6775	819	8	and	and	CCONJ
ejpam-6775	819	9	transmission	transmission	NOUN
ejpam-6775	819	10	global	global	ADJ
ejpam-6775	819	11	dynamics	dynamic	NOUN
ejpam-6775	819	12	.	.	PUNCT
ejpam-6775	820	1	mathematical	mathematical	ADJ
ejpam-6775	820	2	biosciences	bioscience	NOUN
ejpam-6775	820	3	,	,	PUNCT
ejpam-6775	820	4	229(1):50–63	229(1):50–63	NUM
ejpam-6775	820	5	,	,	PUNCT
ejpam-6775	820	6	2011	2011	NUM
ejpam-6775	820	7	.	.	PUNCT
ejpam-6775	821	1	[	[	X
ejpam-6775	821	2	42	42	NUM
ejpam-6775	821	3	]	]	X
ejpam-6775	821	4	h.	h.	PROPN
ejpam-6775	821	5	behncke	behncke	PROPN
ejpam-6775	821	6	.	.	PUNCT
ejpam-6775	822	1	optimal	optimal	ADJ
ejpam-6775	822	2	control	control	NOUN
ejpam-6775	822	3	of	of	ADP
ejpam-6775	822	4	deterministic	deterministic	ADJ
ejpam-6775	822	5	epidemics	epidemic	NOUN
ejpam-6775	822	6	.	.	PUNCT
ejpam-6775	823	1	optimal	optimal	ADJ
ejpam-6775	823	2	control	control	NOUN
ejpam-6775	823	3	applications	application	NOUN
ejpam-6775	823	4	and	and	CCONJ
ejpam-6775	823	5	methods	method	NOUN
ejpam-6775	823	6	,	,	PUNCT
ejpam-6775	823	7	21(6):269–284	21(6):269–284	NOUN
ejpam-6775	823	8	,	,	PUNCT
ejpam-6775	823	9	2000	2000	NUM
ejpam-6775	823	10	.	.	PUNCT
ejpam-6775	824	1	[	[	X
ejpam-6775	824	2	43	43	NUM
ejpam-6775	824	3	]	]	X
ejpam-6775	824	4	y.	y.	PROPN
ejpam-6775	824	5	zhou	zhou	PROPN
ejpam-6775	824	6	,	,	PUNCT
ejpam-6775	824	7	j.	j.	PROPN
ejpam-6775	824	8	wu	wu	PROPN
ejpam-6775	824	9	,	,	PUNCT
ejpam-6775	824	10	and	and	CCONJ
ejpam-6775	824	11	m.	m.	PROPN
ejpam-6775	824	12	wu	wu	PROPN
ejpam-6775	824	13	.	.	PUNCT
ejpam-6775	825	1	optimal	optimal	ADJ
ejpam-6775	825	2	isolation	isolation	NOUN
ejpam-6775	825	3	strategies	strategy	NOUN
ejpam-6775	825	4	of	of	ADP
ejpam-6775	825	5	emerging	emerge	VERB
ejpam-6775	825	6	infectious	infectious	ADJ
ejpam-6775	825	7	diseases	disease	NOUN
ejpam-6775	825	8	with	with	ADP
ejpam-6775	825	9	limited	limited	ADJ
ejpam-6775	825	10	resources	resource	NOUN
ejpam-6775	825	11	.	.	PUNCT
ejpam-6775	826	1	mathematical	mathematical	ADJ
ejpam-6775	826	2	biosciences	bioscience	NOUN
ejpam-6775	826	3	and	and	CCONJ
ejpam-6775	826	4	engineering	engineering	NOUN
ejpam-6775	826	5	,	,	PUNCT
ejpam-6775	826	6	10(5,6):1691–1701	10(5,6):1691–1701	NUM
ejpam-6775	826	7	,	,	PUNCT
ejpam-6775	826	8	2013	2013	NUM
ejpam-6775	826	9	.	.	PUNCT
ejpam-6775	827	1	[	[	X
ejpam-6775	827	2	44	44	NUM
ejpam-6775	827	3	]	]	SYM
ejpam-6775	827	4	a.a	a.a	PROPN
ejpam-6775	827	5	.	.	PROPN
ejpam-6775	827	6	lashari	lashari	PROPN
ejpam-6775	827	7	.	.	PUNCT
ejpam-6775	828	1	optimal	optimal	ADJ
ejpam-6775	828	2	control	control	NOUN
ejpam-6775	828	3	of	of	ADP
ejpam-6775	828	4	an	an	DET
ejpam-6775	828	5	sir	sir	NOUN
ejpam-6775	828	6	epidemic	epidemic	NOUN
ejpam-6775	828	7	model	model	NOUN
ejpam-6775	828	8	with	with	ADP
ejpam-6775	828	9	a	a	DET
ejpam-6775	828	10	saturated	saturated	ADJ
ejpam-6775	828	11	treatment	treatment	NOUN
ejpam-6775	828	12	.	.	PUNCT
ejpam-6775	829	1	applied	apply	VERB
ejpam-6775	829	2	mathematics	mathematic	NOUN
ejpam-6775	829	3	and	and	CCONJ
ejpam-6775	829	4	information	information	NOUN
ejpam-6775	829	5	sciences	science	NOUN
ejpam-6775	829	6	,	,	PUNCT
ejpam-6775	829	7	10(1):185	10(1):185	NUM
ejpam-6775	829	8	,	,	PUNCT
ejpam-6775	829	9	2016	2016	NUM
ejpam-6775	829	10	.	.	PUNCT
ejpam-6775	830	1	[	[	X
ejpam-6775	830	2	45	45	NUM
ejpam-6775	830	3	]	]	X
ejpam-6775	830	4	e.v	e.v	PROPN
ejpam-6775	830	5	.	.	PROPN
ejpam-6775	830	6	grigorieva	grigorieva	PROPN
ejpam-6775	830	7	,	,	PUNCT
ejpam-6775	830	8	e.n	e.n	PROPN
ejpam-6775	830	9	.	.	PROPN
ejpam-6775	830	10	khailov	khailov	PROPN
ejpam-6775	830	11	,	,	PUNCT
ejpam-6775	830	12	and	and	CCONJ
ejpam-6775	830	13	a.	a.	NOUN
ejpam-6775	830	14	korobeinikov	korobeinikov	PROPN
ejpam-6775	830	15	.	.	PUNCT
ejpam-6775	831	1	optimal	optimal	ADJ
ejpam-6775	831	2	control	control	NOUN
ejpam-6775	831	3	for	for	ADP
ejpam-6775	831	4	a	a	DET
ejpam-6775	831	5	sir	sir	NOUN
ejpam-6775	831	6	epidemic	epidemic	NOUN
ejpam-6775	831	7	model	model	NOUN
ejpam-6775	831	8	with	with	ADP
ejpam-6775	831	9	nonlinear	nonlinear	ADJ
ejpam-6775	831	10	incidence	incidence	NOUN
ejpam-6775	831	11	rate	rate	NOUN
ejpam-6775	831	12	.	.	PUNCT
ejpam-6775	832	1	mathematical	mathematical	ADJ
ejpam-6775	832	2	modelling	modelling	NOUN
ejpam-6775	832	3	of	of	ADP
ejpam-6775	832	4	natural	natural	ADJ
ejpam-6775	832	5	phenomena	phenomenon	NOUN
ejpam-6775	832	6	,	,	PUNCT
ejpam-6775	832	7	11(4):89–104	11(4):89–104	NOUN
ejpam-6775	832	8	,	,	PUNCT
ejpam-6775	832	9	2016	2016	NUM
ejpam-6775	832	10	.	.	PUNCT
ejpam-6775	833	1	[	[	X
ejpam-6775	833	2	46	46	NUM
ejpam-6775	833	3	]	]	X
ejpam-6775	833	4	p.	p.	NOUN
ejpam-6775	833	5	di	di	NOUN
ejpam-6775	833	6	giamberardino	giamberardino	PROPN
ejpam-6775	833	7	and	and	CCONJ
ejpam-6775	833	8	d.	d.	PROPN
ejpam-6775	833	9	iacoviello	iacoviello	PROPN
ejpam-6775	833	10	.	.	PUNCT
ejpam-6775	834	1	optimal	optimal	ADJ
ejpam-6775	834	2	control	control	NOUN
ejpam-6775	834	3	of	of	ADP
ejpam-6775	834	4	sir	sir	PROPN
ejpam-6775	834	5	epidemic	epidemic	NOUN
ejpam-6775	834	6	model	model	NOUN
ejpam-6775	834	7	with	with	ADP
ejpam-6775	834	8	state	state	NOUN
ejpam-6775	834	9	dependent	dependent	ADJ
ejpam-6775	834	10	switching	switching	NOUN
ejpam-6775	834	11	cost	cost	NOUN
ejpam-6775	834	12	index	index	NOUN
ejpam-6775	834	13	.	.	PUNCT
ejpam-6775	835	1	biomedical	biomedical	ADJ
ejpam-6775	835	2	signal	signal	NOUN
ejpam-6775	835	3	processing	processing	NOUN
ejpam-6775	835	4	and	and	CCONJ
ejpam-6775	835	5	control	control	NOUN
ejpam-6775	835	6	,	,	PUNCT
ejpam-6775	835	7	31:377–380	31:377–380	PROPN
ejpam-6775	835	8	,	,	PUNCT
ejpam-6775	835	9	2017	2017	NUM
ejpam-6775	835	10	.	.	PUNCT
ejpam-6775	836	1	[	[	X
ejpam-6775	836	2	47	47	NUM
ejpam-6775	836	3	]	]	X
ejpam-6775	836	4	d.	d.	PROPN
ejpam-6775	836	5	alonso	alonso	PROPN
ejpam-6775	836	6	,	,	PUNCT
ejpam-6775	836	7	m.j	m.j	PROPN
ejpam-6775	836	8	.	.	PROPN
ejpam-6775	836	9	bouma	bouma	PROPN
ejpam-6775	836	10	,	,	PUNCT
ejpam-6775	836	11	and	and	CCONJ
ejpam-6775	836	12	m.	m.	NOUN
ejpam-6775	836	13	pascual	pascual	PROPN
ejpam-6775	836	14	.	.	PUNCT
ejpam-6775	837	1	epidemic	epidemic	NOUN
ejpam-6775	837	2	malaria	malaria	NOUN
ejpam-6775	837	3	and	and	CCONJ
ejpam-6775	837	4	warmer	warm	ADJ
ejpam-6775	837	5	temperatures	temperature	NOUN
ejpam-6775	837	6	in	in	ADP
ejpam-6775	837	7	recent	recent	ADJ
ejpam-6775	837	8	decades	decade	NOUN
ejpam-6775	837	9	in	in	ADP
ejpam-6775	837	10	an	an	DET
ejpam-6775	837	11	east	east	ADJ
ejpam-6775	837	12	african	african	PROPN
ejpam-6775	837	13	highland	highland	PROPN
ejpam-6775	837	14	.	.	PUNCT
ejpam-6775	838	1	proceedings	proceeding	NOUN
ejpam-6775	838	2	of	of	ADP
ejpam-6775	838	3	the	the	DET
ejpam-6775	838	4	royal	royal	ADJ
ejpam-6775	838	5	society	society	NOUN
ejpam-6775	838	6	b	b	PROPN
ejpam-6775	838	7	:	:	PUNCT
ejpam-6775	838	8	biological	biological	ADJ
ejpam-6775	838	9	sciences	science	NOUN
ejpam-6775	838	10	,	,	PUNCT
ejpam-6775	838	11	278(1712):1661–1669	278(1712):1661–1669	NUM
ejpam-6775	838	12	,	,	PUNCT
ejpam-6775	838	13	2011	2011	NUM
ejpam-6775	838	14	.	.	PUNCT
ejpam-6775	839	1	[	[	X
ejpam-6775	839	2	48	48	NUM
ejpam-6775	839	3	]	]	X
ejpam-6775	839	4	a.s	a.s	PROPN
ejpam-6775	839	5	.	.	PROPN
ejpam-6775	839	6	ackleh	ackleh	PROPN
ejpam-6775	839	7	and	and	CCONJ
ejpam-6775	839	8	l.j	l.j	PROPN
ejpam-6775	839	9	.	.	PROPN
ejpam-6775	839	10	allen	allen	PROPN
ejpam-6775	839	11	.	.	PUNCT
ejpam-6775	840	1	competitive	competitive	ADJ
ejpam-6775	840	2	exclusion	exclusion	NOUN
ejpam-6775	840	3	and	and	CCONJ
ejpam-6775	840	4	coexistence	coexistence	NOUN
ejpam-6775	840	5	for	for	ADP
ejpam-6775	840	6	pathogens	pathogen	NOUN
ejpam-6775	840	7	in	in	ADP
ejpam-6775	840	8	an	an	DET
ejpam-6775	840	9	epidemic	epidemic	NOUN
ejpam-6775	840	10	model	model	NOUN
ejpam-6775	840	11	with	with	ADP
ejpam-6775	840	12	variable	variable	ADJ
ejpam-6775	840	13	population	population	NOUN
ejpam-6775	840	14	size	size	NOUN
ejpam-6775	840	15	.	.	PUNCT
ejpam-6775	841	1	journal	journal	PROPN
ejpam-6775	841	2	of	of	ADP
ejpam-6775	841	3	mathematical	mathematical	ADJ
ejpam-6775	841	4	biology	biology	NOUN
ejpam-6775	841	5	,	,	PUNCT
ejpam-6775	841	6	47:153–168	47:153–168	PROPN
ejpam-6775	841	7	,	,	PUNCT
ejpam-6775	841	8	2003	2003	NUM
ejpam-6775	841	9	.	.	PUNCT
ejpam-6775	842	1	[	[	X
ejpam-6775	842	2	49	49	NUM
ejpam-6775	842	3	]	]	X
ejpam-6775	842	4	yasir	yasir	PROPN
ejpam-6775	842	5	ramzan	ramzan	PROPN
ejpam-6775	842	6	,	,	PUNCT
ejpam-6775	842	7	bandar	bandar	PROPN
ejpam-6775	842	8	m	m	PROPN
ejpam-6775	842	9	fadhl	fadhl	PROPN
ejpam-6775	842	10	,	,	PUNCT
ejpam-6775	842	11	shafiullah	shafiullah	NOUN
ejpam-6775	842	12	niazai	niazai	ADJ
ejpam-6775	842	13	,	,	PUNCT
ejpam-6775	842	14	aziz	aziz	PROPN
ejpam-6775	842	15	ullah	ullah	PROPN
ejpam-6775	842	16	awan	awan	PROPN
ejpam-6775	842	17	,	,	PUNCT
ejpam-6775	842	18	and	and	CCONJ
ejpam-6775	842	19	kamel	kamel	PROPN
ejpam-6775	842	20	guedri	guedri	PROPN
ejpam-6775	842	21	.	.	PUNCT
ejpam-6775	843	1	decoding	decode	VERB
ejpam-6775	843	2	the	the	DET
ejpam-6775	843	3	transmission	transmission	NOUN
ejpam-6775	843	4	and	and	CCONJ
ejpam-6775	843	5	subsequent	subsequent	ADJ
ejpam-6775	843	6	disability	disability	NOUN
ejpam-6775	843	7	risks	risk	NOUN
ejpam-6775	843	8	of	of	ADP
ejpam-6775	843	9	rabineurodeficiency	rabineurodeficiency	NOUN
ejpam-6775	843	10	syndrome	syndrome	NOUN
ejpam-6775	843	11	without	without	ADP
ejpam-6775	843	12	recuperation	recuperation	NOUN
ejpam-6775	843	13	.	.	PUNCT
ejpam-6775	844	1	sci	sci	PROPN
ejpam-6775	844	2	.	.	PROPN
ejpam-6775	844	3	rep	rep	PROPN
ejpam-6775	844	4	.	.	PROPN
ejpam-6775	844	5	,	,	PUNCT
ejpam-6775	844	6	15(1):17322	15(1):17322	PROPN
ejpam-6775	844	7	,	,	PUNCT
ejpam-6775	844	8	may	may	AUX
ejpam-6775	844	9	2025	2025	NUM
ejpam-6775	844	10	.	.	PUNCT
ejpam-6775	845	1	j.	j.	PROPN
ejpam-6775	845	2	leo	leo	PROPN
ejpam-6775	845	3	amalraj	amalraj	PROPN
ejpam-6775	845	4	et	et	PROPN
ejpam-6775	845	5	al	al	PROPN
ejpam-6775	845	6	.	.	PUNCT
ejpam-6775	845	7	/	/	SYM
ejpam-6775	845	8	eur	eur	PROPN
ejpam-6775	845	9	.	.	PUNCT
ejpam-6775	846	1	j.	j.	PROPN
ejpam-6775	846	2	pure	pure	PROPN
ejpam-6775	846	3	appl	appl	PROPN
ejpam-6775	846	4	.	.	PROPN
ejpam-6775	846	5	math	math	PROPN
ejpam-6775	846	6	,	,	PUNCT
ejpam-6775	846	7	18	18	NUM
ejpam-6775	846	8	(	(	PUNCT
ejpam-6775	846	9	4	4	NUM
ejpam-6775	846	10	)	)	PUNCT
ejpam-6775	846	11	(	(	PUNCT
ejpam-6775	846	12	2025	2025	NUM
ejpam-6775	846	13	)	)	PUNCT
ejpam-6775	846	14	,	,	PUNCT
ejpam-6775	846	15	6775	6775	NUM
ejpam-6775	846	16	32	32	NUM
ejpam-6775	846	17	of	of	ADP
ejpam-6775	846	18	32	32	NUM
ejpam-6775	846	19	[	[	SYM
ejpam-6775	846	20	50	50	NUM
ejpam-6775	846	21	]	]	PUNCT
ejpam-6775	846	22	yasir	yasir	PROPN
ejpam-6775	846	23	ramzan	ramzan	PROPN
ejpam-6775	846	24	,	,	PUNCT
ejpam-6775	846	25	hanadi	hanadi	NOUN
ejpam-6775	846	26	alzubadi	alzubadi	NOUN
ejpam-6775	846	27	,	,	PUNCT
ejpam-6775	846	28	aziz	aziz	PROPN
ejpam-6775	846	29	ullah	ullah	PROPN
ejpam-6775	846	30	awan	awan	PROPN
ejpam-6775	846	31	,	,	PUNCT
ejpam-6775	846	32	kamel	kamel	PROPN
ejpam-6775	846	33	guedri	guedri	PROPN
ejpam-6775	846	34	,	,	PUNCT
ejpam-6775	846	35	mohammed	mohammed	PROPN
ejpam-6775	846	36	alharthi	alharthi	PROPN
ejpam-6775	846	37	,	,	PUNCT
ejpam-6775	846	38	and	and	CCONJ
ejpam-6775	846	39	bandar	bandar	PROPN
ejpam-6775	846	40	m	m	PROPN
ejpam-6775	846	41	fadhl	fadhl	PROPN
ejpam-6775	846	42	.	.	PUNCT
ejpam-6775	847	1	a	a	DET
ejpam-6775	847	2	mathematical	mathematical	ADJ
ejpam-6775	847	3	lens	lens	NOUN
ejpam-6775	847	4	on	on	ADP
ejpam-6775	847	5	the	the	DET
ejpam-6775	847	6	zoonotic	zoonotic	ADJ
ejpam-6775	847	7	transmission	transmission	NOUN
ejpam-6775	847	8	of	of	ADP
ejpam-6775	847	9	lassa	lassa	PROPN
ejpam-6775	847	10	virus	virus	NOUN
ejpam-6775	847	11	infections	infection	NOUN
ejpam-6775	847	12	leading	lead	VERB
ejpam-6775	847	13	to	to	ADP
ejpam-6775	847	14	disabilities	disability	NOUN
ejpam-6775	847	15	in	in	ADP
ejpam-6775	847	16	severe	severe	ADJ
ejpam-6775	847	17	cases	case	NOUN
ejpam-6775	847	18	.	.	PUNCT
ejpam-6775	848	1	math	math	NOUN
ejpam-6775	848	2	.	.	PUNCT
ejpam-6775	849	1	comput	comput	NOUN
ejpam-6775	849	2	.	.	PUNCT
ejpam-6775	850	1	appl	appl	PROPN
ejpam-6775	850	2	.	.	PROPN
ejpam-6775	850	3	,	,	PUNCT
ejpam-6775	850	4	29(6):102	29(6):102	NUM
ejpam-6775	850	5	,	,	PUNCT
ejpam-6775	850	6	november	november	PROPN
ejpam-6775	850	7	2024	2024	NUM
ejpam-6775	850	8	.	.	PUNCT
ejpam-6775	851	1	[	[	X
ejpam-6775	851	2	51	51	NUM
ejpam-6775	851	3	]	]	X
ejpam-6775	851	4	y	y	PROPN
ejpam-6775	851	5	ramzan	ramzan	PROPN
ejpam-6775	851	6	,	,	PUNCT
ejpam-6775	851	7	a	a	DET
ejpam-6775	851	8	u	u	PROPN
ejpam-6775	851	9	awan	awan	PROPN
ejpam-6775	851	10	,	,	PUNCT
ejpam-6775	851	11	m	m	PROPN
ejpam-6775	851	12	ozair	ozair	NOUN
ejpam-6775	851	13	,	,	PUNCT
ejpam-6775	851	14	t	t	PROPN
ejpam-6775	851	15	hussain	hussain	PROPN
ejpam-6775	851	16	,	,	PUNCT
ejpam-6775	851	17	and	and	CCONJ
ejpam-6775	851	18	r	r	NOUN
ejpam-6775	851	19	mahat	mahat	NOUN
ejpam-6775	851	20	.	.	PUNCT
ejpam-6775	852	1	innovative	innovative	ADJ
ejpam-6775	852	2	strategies	strategy	NOUN
ejpam-6775	852	3	for	for	ADP
ejpam-6775	852	4	lassa	lassa	ADJ
ejpam-6775	852	5	fever	fever	NOUN
ejpam-6775	852	6	epidemic	epidemic	NOUN
ejpam-6775	852	7	control	control	NOUN
ejpam-6775	852	8	:	:	PUNCT
ejpam-6775	852	9	a	a	DET
ejpam-6775	852	10	groundbreaking	groundbreake	VERB
ejpam-6775	852	11	study	study	NOUN
ejpam-6775	852	12	.	.	PUNCT
ejpam-6775	853	1	aims	aim	VERB
ejpam-6775	853	2	math	math	NOUN
ejpam-6775	853	3	,	,	PUNCT
ejpam-6775	853	4	8(12):30790	8(12):30790	NUM
ejpam-6775	853	5	–	–	PUNCT
ejpam-6775	853	6	30812	30812	NUM
ejpam-6775	853	7	,	,	PUNCT
ejpam-6775	853	8	2023	2023	NUM
ejpam-6775	853	9	.	.	PUNCT
ejpam-6775	854	1	[	[	X
ejpam-6775	854	2	52	52	NUM
ejpam-6775	854	3	]	]	X
ejpam-6775	854	4	kamel	kamel	PROPN
ejpam-6775	854	5	guedri	guedri	PROPN
ejpam-6775	854	6	,	,	PUNCT
ejpam-6775	854	7	yasir	yasir	PROPN
ejpam-6775	854	8	ramzan	ramzan	PROPN
ejpam-6775	854	9	,	,	PUNCT
ejpam-6775	854	10	muhammad	muhammad	PROPN
ejpam-6775	854	11	mudassar	mudassar	VERB
ejpam-6775	854	12	bilal	bilal	PROPN
ejpam-6775	854	13	,	,	PUNCT
ejpam-6775	854	14	hatoon	hatoon	PROPN
ejpam-6775	854	15	abdullah	abdullah	PROPN
ejpam-6775	854	16	niyazi	niyazi	PROPN
ejpam-6775	854	17	,	,	PUNCT
ejpam-6775	854	18	aziz	aziz	PROPN
ejpam-6775	854	19	ullah	ullah	PROPN
ejpam-6775	854	20	awan	awan	PROPN
ejpam-6775	854	21	,	,	PUNCT
ejpam-6775	854	22	and	and	CCONJ
ejpam-6775	854	23	basim	basim	PROPN
ejpam-6775	854	24	m	m	PROPN
ejpam-6775	854	25	makhdoum	makhdoum	NOUN
ejpam-6775	854	26	.	.	PUNCT
ejpam-6775	855	1	gender	gender	NOUN
ejpam-6775	855	2	-	-	PUNCT
ejpam-6775	855	3	specific	specific	ADJ
ejpam-6775	855	4	modeling	modeling	NOUN
ejpam-6775	855	5	for	for	ADP
ejpam-6775	855	6	lassa	lassa	PROPN
ejpam-6775	855	7	virus	virus	NOUN
ejpam-6775	855	8	transmission	transmission	NOUN
ejpam-6775	855	9	with	with	ADP
ejpam-6775	855	10	hearing	hear	VERB
ejpam-6775	855	11	loss	loss	NOUN
ejpam-6775	855	12	disability	disability	NOUN
ejpam-6775	855	13	risk	risk	NOUN
ejpam-6775	855	14	and	and	CCONJ
ejpam-6775	855	15	control	control	NOUN
ejpam-6775	855	16	strategies	strategy	NOUN
ejpam-6775	855	17	.	.	PUNCT
ejpam-6775	856	1	eur	eur	PROPN
ejpam-6775	856	2	.	.	PUNCT
ejpam-6775	857	1	j.	j.	PROPN
ejpam-6775	857	2	pure	pure	PROPN
ejpam-6775	857	3	appl	appl	PROPN
ejpam-6775	857	4	.	.	PUNCT
ejpam-6775	857	5	math	math	PROPN
ejpam-6775	857	6	.	.	PUNCT
ejpam-6775	857	7	,	,	PUNCT
ejpam-6775	858	1	18(2):6104	18(2):6104	NUM
ejpam-6775	858	2	,	,	PUNCT
ejpam-6775	858	3	may	may	AUX
ejpam-6775	858	4	2025	2025	NUM
ejpam-6775	858	5	.	.	PUNCT
ejpam-6775	859	1	[	[	X
ejpam-6775	859	2	53	53	NUM
ejpam-6775	859	3	]	]	X
ejpam-6775	859	4	kamel	kamel	PROPN
ejpam-6775	859	5	guedri	guedri	PROPN
ejpam-6775	859	6	,	,	PUNCT
ejpam-6775	859	7	yasir	yasir	PROPN
ejpam-6775	859	8	ramzan	ramzan	PROPN
ejpam-6775	859	9	,	,	PUNCT
ejpam-6775	859	10	aziz	aziz	PROPN
ejpam-6775	859	11	ullah	ullah	PROPN
ejpam-6775	859	12	awan	awan	PROPN
ejpam-6775	859	13	,	,	PUNCT
ejpam-6775	859	14	bandar	bandar	PROPN
ejpam-6775	859	15	m	m	PROPN
ejpam-6775	859	16	fadhl	fadhl	PROPN
ejpam-6775	859	17	,	,	PUNCT
ejpam-6775	859	18	bagh	bagh	PROPN
ejpam-6775	859	19	ali	ali	PROPN
ejpam-6775	859	20	,	,	PUNCT
ejpam-6775	859	21	and	and	CCONJ
ejpam-6775	859	22	mowffaq	mowffaq	VERB
ejpam-6775	859	23	oreijah	oreijah	ADJ
ejpam-6775	859	24	.	.	PUNCT
ejpam-6775	860	1	rabies	rabie	NOUN
ejpam-6775	860	2	-	-	PUNCT
ejpam-6775	860	3	related	relate	VERB
ejpam-6775	860	4	brain	brain	NOUN
ejpam-6775	860	5	disorders	disorder	NOUN
ejpam-6775	860	6	:	:	PUNCT
ejpam-6775	860	7	transmission	transmission	NOUN
ejpam-6775	860	8	dynamics	dynamic	NOUN
ejpam-6775	860	9	and	and	CCONJ
ejpam-6775	860	10	epidemic	epidemic	NOUN
ejpam-6775	860	11	management	management	NOUN
ejpam-6775	860	12	via	via	ADP
ejpam-6775	860	13	educational	educational	ADJ
ejpam-6775	860	14	campaigns	campaign	NOUN
ejpam-6775	860	15	and	and	CCONJ
ejpam-6775	860	16	application	application	NOUN
ejpam-6775	860	17	of	of	ADP
ejpam-6775	860	18	nanotechnology	nanotechnology	NOUN
ejpam-6775	860	19	.	.	PUNCT
ejpam-6775	861	1	eur	eur	PROPN
ejpam-6775	861	2	.	.	PUNCT
ejpam-6775	862	1	phys	phy	NOUN
ejpam-6775	862	2	.	.	PUNCT
ejpam-6775	863	1	j.	j.	PROPN
ejpam-6775	863	2	plus	plus	PROPN
ejpam-6775	863	3	,	,	PUNCT
ejpam-6775	863	4	139(1	139(1	NUM
ejpam-6775	863	5	)	)	PUNCT
ejpam-6775	863	6	,	,	PUNCT
ejpam-6775	863	7	january	january	PROPN
ejpam-6775	863	8	2024	2024	NUM
ejpam-6775	863	9	.	.	PUNCT
ejpam-6775	864	1	[	[	X
ejpam-6775	864	2	54	54	NUM
ejpam-6775	864	3	]	]	PUNCT
ejpam-6775	864	4	m.	m.	NOUN
ejpam-6775	864	5	martcheva	martcheva	PROPN
ejpam-6775	864	6	and	and	CCONJ
ejpam-6775	864	7	h.	h.	PROPN
ejpam-6775	864	8	inaba	inaba	PROPN
ejpam-6775	864	9	.	.	PUNCT
ejpam-6775	865	1	a	a	DET
ejpam-6775	865	2	lyapunov	lyapunov	NOUN
ejpam-6775	865	3	–	–	PUNCT
ejpam-6775	865	4	schmidt	schmidt	ADJ
ejpam-6775	865	5	method	method	NOUN
ejpam-6775	865	6	for	for	ADP
ejpam-6775	865	7	detecting	detect	VERB
ejpam-6775	865	8	backward	backward	ADJ
ejpam-6775	865	9	bifurcation	bifurcation	NOUN
ejpam-6775	865	10	in	in	ADP
ejpam-6775	865	11	age	age	NOUN
ejpam-6775	865	12	-	-	PUNCT
ejpam-6775	865	13	structured	structure	VERB
ejpam-6775	865	14	population	population	NOUN
ejpam-6775	865	15	models	model	NOUN
ejpam-6775	865	16	.	.	PUNCT
ejpam-6775	866	1	journal	journal	NOUN
ejpam-6775	866	2	of	of	ADP
ejpam-6775	866	3	biological	biological	ADJ
ejpam-6775	866	4	dynamics	dynamic	NOUN
ejpam-6775	866	5	,	,	PUNCT
ejpam-6775	866	6	14(1):543–565	14(1):543–565	PROPN
ejpam-6775	866	7	,	,	PUNCT
ejpam-6775	866	8	2020	2020	NUM
ejpam-6775	866	9	.	.	PUNCT
ejpam-6775	867	1	[	[	X
ejpam-6775	867	2	55	55	NUM
ejpam-6775	867	3	]	]	PUNCT
ejpam-6775	867	4	e.	e.	PROPN
ejpam-6775	867	5	numfor	numfor	PROPN
ejpam-6775	867	6	.	.	PUNCT
ejpam-6775	868	1	optimal	optimal	ADJ
ejpam-6775	868	2	treatment	treatment	NOUN
ejpam-6775	868	3	in	in	ADP
ejpam-6775	868	4	a	a	DET
ejpam-6775	868	5	multi	multi	ADJ
ejpam-6775	868	6	-	-	ADJ
ejpam-6775	868	7	strain	strain	ADJ
ejpam-6775	868	8	within	within	ADP
ejpam-6775	868	9	-	-	PUNCT
ejpam-6775	868	10	host	host	NOUN
ejpam-6775	868	11	model	model	NOUN
ejpam-6775	868	12	of	of	ADP
ejpam-6775	868	13	hiv	hiv	PROPN
ejpam-6775	868	14	with	with	ADP
ejpam-6775	868	15	age	age	NOUN
ejpam-6775	868	16	structure	structure	NOUN
ejpam-6775	868	17	.	.	PUNCT
ejpam-6775	869	1	journal	journal	PROPN
ejpam-6775	869	2	of	of	ADP
ejpam-6775	869	3	mathematical	mathematical	ADJ
ejpam-6775	869	4	analysis	analysis	NOUN
ejpam-6775	869	5	and	and	CCONJ
ejpam-6775	869	6	applications	application	NOUN
ejpam-6775	869	7	,	,	PUNCT
ejpam-6775	869	8	480(2):123410	480(2):123410	PROPN
ejpam-6775	869	9	,	,	PUNCT
ejpam-6775	869	10	2019	2019	NUM
ejpam-6775	869	11	.	.	PUNCT
ejpam-6775	870	1	[	[	X
ejpam-6775	870	2	56	56	NUM
ejpam-6775	870	3	]	]	X
ejpam-6775	870	4	e.	e.	PROPN
ejpam-6775	870	5	numfor	numfor	PROPN
ejpam-6775	870	6	,	,	PUNCT
ejpam-6775	870	7	s.	s.	PROPN
ejpam-6775	870	8	bhattacharya	bhattacharya	PROPN
ejpam-6775	870	9	,	,	PUNCT
ejpam-6775	870	10	s.	s.	PROPN
ejpam-6775	870	11	lenhart	lenhart	PROPN
ejpam-6775	870	12	,	,	PUNCT
ejpam-6775	870	13	and	and	CCONJ
ejpam-6775	870	14	m.	m.	PROPN
ejpam-6775	870	15	martcheva	martcheva	PROPN
ejpam-6775	870	16	.	.	PUNCT
ejpam-6775	871	1	optimal	optimal	ADJ
ejpam-6775	871	2	control	control	NOUN
ejpam-6775	871	3	in	in	ADP
ejpam-6775	871	4	coupled	couple	VERB
ejpam-6775	871	5	within	within	ADP
ejpam-6775	871	6	-	-	PUNCT
ejpam-6775	871	7	host	host	NOUN
ejpam-6775	871	8	and	and	CCONJ
ejpam-6775	871	9	between	between	ADP
ejpam-6775	871	10	-	-	PUNCT
ejpam-6775	871	11	host	host	NOUN
ejpam-6775	871	12	models	model	NOUN
ejpam-6775	871	13	.	.	PUNCT
ejpam-6775	872	1	mathematical	mathematical	ADJ
ejpam-6775	872	2	modelling	modelling	NOUN
ejpam-6775	872	3	of	of	ADP
ejpam-6775	872	4	natural	natural	ADJ
ejpam-6775	872	5	phenomena	phenomenon	NOUN
ejpam-6775	872	6	,	,	PUNCT
ejpam-6775	872	7	9(4):171–203	9(4):171–203	NUM
ejpam-6775	872	8	,	,	PUNCT
ejpam-6775	872	9	2014	2014	NUM
ejpam-6775	872	10	.	.	PUNCT