id	sid	tid	token	lemma	pos
ejpam-6254	1	1	european	european	PROPN
ejpam-6254	1	2	journal	journal	PROPN
ejpam-6254	1	3	of	of	ADP
ejpam-6254	1	4	pure	pure	ADJ
ejpam-6254	1	5	and	and	CCONJ
ejpam-6254	1	6	applied	applied	ADJ
ejpam-6254	1	7	mathematics	mathematic	NOUN
ejpam-6254	1	8	2025	2025	NUM
ejpam-6254	1	9	,	,	PUNCT
ejpam-6254	1	10	vol	vol	NOUN
ejpam-6254	1	11	.	.	PROPN
ejpam-6254	1	12	18	18	NUM
ejpam-6254	1	13	,	,	PUNCT
ejpam-6254	1	14	issue	issue	NOUN
ejpam-6254	1	15	4	4	NUM
ejpam-6254	1	16	,	,	PUNCT
ejpam-6254	1	17	article	article	NOUN
ejpam-6254	1	18	number	number	NOUN
ejpam-6254	1	19	6254	6254	NUM
ejpam-6254	1	20	issn	issn	PROPN
ejpam-6254	1	21	1307	1307	NUM
ejpam-6254	1	22	-	-	SYM
ejpam-6254	1	23	5543	5543	NUM
ejpam-6254	1	24	–	–	PUNCT
ejpam-6254	1	25	ejpam.com	ejpam.com	X
ejpam-6254	1	26	published	publish	VERB
ejpam-6254	1	27	by	by	ADP
ejpam-6254	1	28	new	new	PROPN
ejpam-6254	1	29	york	york	PROPN
ejpam-6254	1	30	business	business	PROPN
ejpam-6254	1	31	global	global	PROPN
ejpam-6254	1	32	mathematical	mathematical	ADJ
ejpam-6254	1	33	modeling	modeling	NOUN
ejpam-6254	1	34	of	of	ADP
ejpam-6254	1	35	seirv	seirv	ADJ
ejpam-6254	1	36	epidemic	epidemic	NOUN
ejpam-6254	1	37	model	model	NOUN
ejpam-6254	1	38	with	with	ADP
ejpam-6254	1	39	delay	delay	NOUN
ejpam-6254	1	40	and	and	CCONJ
ejpam-6254	1	41	optimal	optimal	ADJ
ejpam-6254	1	42	control	control	NOUN
ejpam-6254	1	43	of	of	ADP
ejpam-6254	1	44	holling	holle	VERB
ejpam-6254	1	45	type	type	NOUN
ejpam-6254	1	46	ii	ii	PROPN
ejpam-6254	1	47	shumaila	shumaila	PROPN
ejpam-6254	1	48	irum1	irum1	PROPN
ejpam-6254	1	49	,	,	PUNCT
ejpam-6254	1	50	anwar	anwar	PROPN
ejpam-6254	1	51	zeb1,∗	zeb1,∗	PROPN
ejpam-6254	1	52	,	,	PUNCT
ejpam-6254	1	53	ahmed	ahmed	PROPN
ejpam-6254	1	54	a.	a.	PROPN
ejpam-6254	1	55	mohsen2,3	mohsen2,3	PROPN
ejpam-6254	1	56	,	,	PUNCT
ejpam-6254	1	57	thoraya	thoraya	NOUN
ejpam-6254	1	58	n.	n.	PROPN
ejpam-6254	1	59	alharthi4	alharthi4	PROPN
ejpam-6254	1	60	,	,	PUNCT
ejpam-6254	1	61	ilyas	ilyas	PROPN
ejpam-6254	1	62	khan5,6,7	khan5,6,7	PROPN
ejpam-6254	1	63	,	,	PUNCT
ejpam-6254	1	64	osama	osama	PROPN
ejpam-6254	1	65	oqilat8	oqilat8	PROPN
ejpam-6254	1	66	,	,	PUNCT
ejpam-6254	1	67	wei	wei	PROPN
ejpam-6254	1	68	sin	sin	PROPN
ejpam-6254	1	69	koh9	koh9	PROPN
ejpam-6254	1	70	1	1	NUM
ejpam-6254	1	71	department	department	NOUN
ejpam-6254	1	72	of	of	ADP
ejpam-6254	1	73	mathematics	mathematic	NOUN
ejpam-6254	1	74	,	,	PUNCT
ejpam-6254	1	75	comsats	comsats	PROPN
ejpam-6254	1	76	university	university	PROPN
ejpam-6254	1	77	islamabad	islamabad	PROPN
ejpam-6254	1	78	,	,	PUNCT
ejpam-6254	1	79	abbottabad	abbottabad	PROPN
ejpam-6254	1	80	campus	campus	PROPN
ejpam-6254	1	81	,	,	PUNCT
ejpam-6254	1	82	pakistan	pakistan	PROPN
ejpam-6254	1	83	2	2	NUM
ejpam-6254	1	84	department	department	NOUN
ejpam-6254	1	85	of	of	ADP
ejpam-6254	1	86	mathematics	mathematic	NOUN
ejpam-6254	1	87	,	,	PUNCT
ejpam-6254	1	88	open	open	ADJ
ejpam-6254	1	89	education	education	NOUN
ejpam-6254	1	90	college	college	NOUN
ejpam-6254	1	91	,	,	PUNCT
ejpam-6254	1	92	iraq	iraq	PROPN
ejpam-6254	1	93	3	3	NUM
ejpam-6254	1	94	department	department	NOUN
ejpam-6254	1	95	of	of	ADP
ejpam-6254	1	96	mathematics	mathematics	PROPN
ejpam-6254	1	97	,	,	PUNCT
ejpam-6254	1	98	college	college	NOUN
ejpam-6254	1	99	of	of	ADP
ejpam-6254	1	100	education	education	NOUN
ejpam-6254	1	101	for	for	ADP
ejpam-6254	1	102	pure	pure	ADJ
ejpam-6254	1	103	science	science	NOUN
ejpam-6254	1	104	(	(	PUNCT
ejpam-6254	1	105	ibn	ibn	PROPN
ejpam-6254	1	106	al	al	PROPN
ejpam-6254	1	107	-	-	PUNCT
ejpam-6254	1	108	haitham	haitham	PROPN
ejpam-6254	1	109	)	)	PUNCT
ejpam-6254	1	110	,	,	PUNCT
ejpam-6254	1	111	university	university	NOUN
ejpam-6254	1	112	of	of	ADP
ejpam-6254	1	113	baghdad	baghdad	PROPN
ejpam-6254	1	114	,	,	PUNCT
ejpam-6254	1	115	baghdad	baghdad	PROPN
ejpam-6254	1	116	,	,	PUNCT
ejpam-6254	1	117	iraq	iraq	PROPN
ejpam-6254	1	118	4	4	NUM
ejpam-6254	1	119	department	department	NOUN
ejpam-6254	1	120	of	of	ADP
ejpam-6254	1	121	mathematics	mathematic	NOUN
ejpam-6254	1	122	,	,	PUNCT
ejpam-6254	1	123	college	college	NOUN
ejpam-6254	1	124	of	of	ADP
ejpam-6254	1	125	science	science	NOUN
ejpam-6254	1	126	,	,	PUNCT
ejpam-6254	1	127	university	university	NOUN
ejpam-6254	1	128	of	of	ADP
ejpam-6254	1	129	bisha	bisha	PROPN
ejpam-6254	1	130	,	,	PUNCT
ejpam-6254	1	131	p.o	p.o	PROPN
ejpam-6254	1	132	.	.	PROPN
ejpam-6254	1	133	box	box	PROPN
ejpam-6254	1	134	551	551	NUM
ejpam-6254	1	135	,	,	PUNCT
ejpam-6254	1	136	bisha	bisha	PROPN
ejpam-6254	1	137	61922	61922	NUM
ejpam-6254	1	138	,	,	PUNCT
ejpam-6254	1	139	saudi	saudi	PROPN
ejpam-6254	1	140	arabia	arabia	PROPN
ejpam-6254	1	141	5	5	NUM
ejpam-6254	1	142	department	department	NOUN
ejpam-6254	1	143	of	of	ADP
ejpam-6254	1	144	mathematical	mathematical	ADJ
ejpam-6254	1	145	sciences	sciences	PROPN
ejpam-6254	1	146	,	,	PUNCT
ejpam-6254	1	147	saveetha	saveetha	PROPN
ejpam-6254	1	148	school	school	NOUN
ejpam-6254	1	149	of	of	ADP
ejpam-6254	1	150	engineering	engineering	NOUN
ejpam-6254	1	151	,	,	PUNCT
ejpam-6254	1	152	simats	simat	NOUN
ejpam-6254	1	153	,	,	PUNCT
ejpam-6254	1	154	chennai	chennai	PROPN
ejpam-6254	1	155	,	,	PUNCT
ejpam-6254	1	156	tamil	tamil	PROPN
ejpam-6254	1	157	nadu	nadu	PROPN
ejpam-6254	1	158	,	,	PUNCT
ejpam-6254	1	159	india	india	PROPN
ejpam-6254	1	160	6	6	NUM
ejpam-6254	1	161	hourani	hourani	PROPN
ejpam-6254	1	162	center	center	NOUN
ejpam-6254	1	163	for	for	ADP
ejpam-6254	1	164	applied	apply	VERB
ejpam-6254	1	165	scientific	scientific	ADJ
ejpam-6254	1	166	research	research	NOUN
ejpam-6254	1	167	,	,	PUNCT
ejpam-6254	1	168	al	al	PROPN
ejpam-6254	1	169	-	-	PUNCT
ejpam-6254	1	170	ahliyya	ahliyya	PROPN
ejpam-6254	1	171	amman	amman	PROPN
ejpam-6254	1	172	university	university	PROPN
ejpam-6254	1	173	,	,	PUNCT
ejpam-6254	1	174	amman	amman	PROPN
ejpam-6254	1	175	,	,	PUNCT
ejpam-6254	1	176	jordan	jordan	PROPN
ejpam-6254	1	177	7	7	NUM
ejpam-6254	1	178	department	department	PROPN
ejpam-6254	1	179	of	of	ADP
ejpam-6254	1	180	mathematics	mathematic	NOUN
ejpam-6254	1	181	,	,	PUNCT
ejpam-6254	1	182	college	college	NOUN
ejpam-6254	1	183	of	of	ADP
ejpam-6254	1	184	science	science	PROPN
ejpam-6254	1	185	al	al	PROPN
ejpam-6254	1	186	-	-	PUNCT
ejpam-6254	1	187	zulfi	zulfi	PROPN
ejpam-6254	1	188	,	,	PUNCT
ejpam-6254	1	189	majmaah	majmaah	PROPN
ejpam-6254	1	190	university	university	PROPN
ejpam-6254	1	191	,	,	PUNCT
ejpam-6254	1	192	al	al	PROPN
ejpam-6254	1	193	-	-	PUNCT
ejpam-6254	1	194	majmaah	majmaah	PROPN
ejpam-6254	1	195	11952	11952	NUM
ejpam-6254	1	196	,	,	PUNCT
ejpam-6254	1	197	saudi	saudi	PROPN
ejpam-6254	1	198	arabia	arabia	PROPN
ejpam-6254	1	199	8	8	NUM
ejpam-6254	1	200	hourani	hourani	PROPN
ejpam-6254	1	201	center	center	NOUN
ejpam-6254	1	202	for	for	ADP
ejpam-6254	1	203	applied	apply	VERB
ejpam-6254	1	204	scientific	scientific	ADJ
ejpam-6254	1	205	research	research	NOUN
ejpam-6254	1	206	,	,	PUNCT
ejpam-6254	1	207	department	department	NOUN
ejpam-6254	1	208	of	of	ADP
ejpam-6254	1	209	basic	basic	ADJ
ejpam-6254	1	210	sciences	science	NOUN
ejpam-6254	1	211	,	,	PUNCT
ejpam-6254	1	212	faculty	faculty	NOUN
ejpam-6254	1	213	of	of	ADP
ejpam-6254	1	214	arts	art	NOUN
ejpam-6254	1	215	and	and	CCONJ
ejpam-6254	1	216	science	science	NOUN
ejpam-6254	1	217	,	,	PUNCT
ejpam-6254	1	218	al	al	PROPN
ejpam-6254	1	219	-	-	PUNCT
ejpam-6254	1	220	ahliyya	ahliyya	PROPN
ejpam-6254	1	221	amman	amman	PROPN
ejpam-6254	1	222	university	university	PROPN
ejpam-6254	1	223	,	,	PUNCT
ejpam-6254	1	224	amman	amman	PROPN
ejpam-6254	1	225	,	,	PUNCT
ejpam-6254	1	226	jordan	jordan	PROPN
ejpam-6254	1	227	9	9	NUM
ejpam-6254	1	228	inti	inti	PROPN
ejpam-6254	1	229	international	international	PROPN
ejpam-6254	1	230	university	university	PROPN
ejpam-6254	1	231	,	,	PUNCT
ejpam-6254	1	232	persiaran	persiaran	VERB
ejpam-6254	1	233	perdana	perdana	PROPN
ejpam-6254	1	234	bbn	bbn	PROPN
ejpam-6254	1	235	putra	putra	PROPN
ejpam-6254	1	236	nilai	nilai	PROPN
ejpam-6254	1	237	,	,	PUNCT
ejpam-6254	1	238	71800	71800	PROPN
ejpam-6254	1	239	nilai	nilai	PROPN
ejpam-6254	1	240	,	,	PUNCT
ejpam-6254	1	241	negeri	negeri	PROPN
ejpam-6254	1	242	sembilan	sembilan	PROPN
ejpam-6254	1	243	,	,	PUNCT
ejpam-6254	1	244	malaysia	malaysia	PROPN
ejpam-6254	1	245	abstract	abstract	NOUN
ejpam-6254	1	246	.	.	PUNCT
ejpam-6254	2	1	this	this	DET
ejpam-6254	2	2	work	work	NOUN
ejpam-6254	2	3	proposes	propose	VERB
ejpam-6254	2	4	a	a	DET
ejpam-6254	2	5	mathematical	mathematical	ADJ
ejpam-6254	2	6	model	model	NOUN
ejpam-6254	2	7	of	of	ADP
ejpam-6254	2	8	the	the	DET
ejpam-6254	2	9	seirv	seirv	NOUN
ejpam-6254	2	10	epidemic	epidemic	NOUN
ejpam-6254	2	11	framework	framework	NOUN
ejpam-6254	2	12	incorporating	incorporate	VERB
ejpam-6254	2	13	time	time	NOUN
ejpam-6254	2	14	delays	delay	NOUN
ejpam-6254	2	15	and	and	CCONJ
ejpam-6254	2	16	optimal	optimal	ADJ
ejpam-6254	2	17	control	control	NOUN
ejpam-6254	2	18	strategies	strategy	NOUN
ejpam-6254	2	19	based	base	VERB
ejpam-6254	2	20	on	on	ADP
ejpam-6254	2	21	holling	holle	VERB
ejpam-6254	2	22	type	type	NOUN
ejpam-6254	2	23	ii	ii	NOUN
ejpam-6254	2	24	functional	functional	ADJ
ejpam-6254	2	25	responses	response	NOUN
ejpam-6254	2	26	.	.	PUNCT
ejpam-6254	3	1	the	the	DET
ejpam-6254	3	2	seirv	seirv	NOUN
ejpam-6254	3	3	model	model	NOUN
ejpam-6254	3	4	,	,	PUNCT
ejpam-6254	3	5	which	which	PRON
ejpam-6254	3	6	includes	include	VERB
ejpam-6254	3	7	compartments	compartment	NOUN
ejpam-6254	3	8	for	for	ADP
ejpam-6254	3	9	susceptible	susceptible	ADJ
ejpam-6254	3	10	,	,	PUNCT
ejpam-6254	3	11	exposed	expose	VERB
ejpam-6254	3	12	,	,	PUNCT
ejpam-6254	3	13	infectious	infectious	ADJ
ejpam-6254	3	14	,	,	PUNCT
ejpam-6254	3	15	recovered	recover	VERB
ejpam-6254	3	16	,	,	PUNCT
ejpam-6254	3	17	and	and	CCONJ
ejpam-6254	3	18	vaccinated	vaccinated	ADJ
ejpam-6254	3	19	individuals	individual	NOUN
ejpam-6254	3	20	,	,	PUNCT
ejpam-6254	3	21	is	be	AUX
ejpam-6254	3	22	extended	extend	VERB
ejpam-6254	3	23	to	to	PART
ejpam-6254	3	24	account	account	VERB
ejpam-6254	3	25	for	for	ADP
ejpam-6254	3	26	delays	delay	NOUN
ejpam-6254	3	27	in	in	ADP
ejpam-6254	3	28	the	the	DET
ejpam-6254	3	29	transmission	transmission	NOUN
ejpam-6254	3	30	and	and	CCONJ
ejpam-6254	3	31	vaccination	vaccination	NOUN
ejpam-6254	3	32	processes	process	NOUN
ejpam-6254	3	33	.	.	PUNCT
ejpam-6254	4	1	the	the	DET
ejpam-6254	4	2	stability	stability	NOUN
ejpam-6254	4	3	and	and	CCONJ
ejpam-6254	4	4	behavior	behavior	NOUN
ejpam-6254	4	5	of	of	ADP
ejpam-6254	4	6	the	the	DET
ejpam-6254	4	7	model	model	NOUN
ejpam-6254	4	8	are	be	AUX
ejpam-6254	4	9	analyzed	analyze	VERB
ejpam-6254	4	10	using	use	VERB
ejpam-6254	4	11	differential	differential	ADJ
ejpam-6254	4	12	equations	equation	NOUN
ejpam-6254	4	13	and	and	CCONJ
ejpam-6254	4	14	delay	delay	VERB
ejpam-6254	4	15	differential	differential	ADJ
ejpam-6254	4	16	equations	equation	NOUN
ejpam-6254	4	17	.	.	PUNCT
ejpam-6254	5	1	optimal	optimal	ADJ
ejpam-6254	5	2	control	control	NOUN
ejpam-6254	5	3	technique	technique	NOUN
ejpam-6254	5	4	is	be	AUX
ejpam-6254	5	5	applied	apply	VERB
ejpam-6254	5	6	to	to	PART
ejpam-6254	5	7	minimize	minimize	VERB
ejpam-6254	5	8	the	the	DET
ejpam-6254	5	9	spread	spread	NOUN
ejpam-6254	5	10	of	of	ADP
ejpam-6254	5	11	infection	infection	NOUN
ejpam-6254	5	12	and	and	CCONJ
ejpam-6254	5	13	optimize	optimize	VERB
ejpam-6254	5	14	vaccination	vaccination	NOUN
ejpam-6254	5	15	strategies	strategy	NOUN
ejpam-6254	5	16	,	,	PUNCT
ejpam-6254	5	17	considering	consider	VERB
ejpam-6254	5	18	resource	resource	NOUN
ejpam-6254	5	19	limitations	limitation	NOUN
ejpam-6254	5	20	and	and	CCONJ
ejpam-6254	5	21	practical	practical	ADJ
ejpam-6254	5	22	constraints	constraint	NOUN
ejpam-6254	5	23	.	.	PUNCT
ejpam-6254	6	1	numerical	numerical	ADJ
ejpam-6254	6	2	simulations	simulation	NOUN
ejpam-6254	6	3	demonstrate	demonstrate	VERB
ejpam-6254	6	4	the	the	DET
ejpam-6254	6	5	effectiveness	effectiveness	NOUN
ejpam-6254	6	6	of	of	ADP
ejpam-6254	6	7	the	the	DET
ejpam-6254	6	8	proposed	propose	VERB
ejpam-6254	6	9	control	control	NOUN
ejpam-6254	6	10	strategies	strategy	NOUN
ejpam-6254	6	11	in	in	ADP
ejpam-6254	6	12	reducing	reduce	VERB
ejpam-6254	6	13	infection	infection	NOUN
ejpam-6254	6	14	rates	rate	NOUN
ejpam-6254	6	15	and	and	CCONJ
ejpam-6254	6	16	achieving	achieve	VERB
ejpam-6254	6	17	disease	disease	NOUN
ejpam-6254	6	18	eradication	eradication	NOUN
ejpam-6254	6	19	.	.	PUNCT
ejpam-6254	7	1	the	the	DET
ejpam-6254	7	2	findings	finding	NOUN
ejpam-6254	7	3	contribute	contribute	VERB
ejpam-6254	7	4	to	to	ADP
ejpam-6254	7	5	the	the	DET
ejpam-6254	7	6	understanding	understanding	NOUN
ejpam-6254	7	7	of	of	ADP
ejpam-6254	7	8	epidemic	epidemic	NOUN
ejpam-6254	7	9	dynamics	dynamic	NOUN
ejpam-6254	7	10	and	and	CCONJ
ejpam-6254	7	11	provide	provide	VERB
ejpam-6254	7	12	valuable	valuable	ADJ
ejpam-6254	7	13	information	information	NOUN
ejpam-6254	7	14	for	for	ADP
ejpam-6254	7	15	public	public	ADJ
ejpam-6254	7	16	health	health	NOUN
ejpam-6254	7	17	policy	policy	NOUN
ejpam-6254	7	18	and	and	CCONJ
ejpam-6254	7	19	intervention	intervention	NOUN
ejpam-6254	7	20	planning	planning	NOUN
ejpam-6254	7	21	.	.	PUNCT
ejpam-6254	8	1	2020	2020	NUM
ejpam-6254	8	2	mathematics	mathematic	NOUN
ejpam-6254	8	3	subject	subject	NOUN
ejpam-6254	8	4	classifications	classification	NOUN
ejpam-6254	8	5	:	:	PUNCT
ejpam-6254	8	6	92d30	92d30	NUM
ejpam-6254	8	7	,	,	PUNCT
ejpam-6254	8	8	49n90	49n90	NUM
ejpam-6254	8	9	,	,	PUNCT
ejpam-6254	8	10	34k20	34k20	NUM
ejpam-6254	8	11	key	key	ADJ
ejpam-6254	8	12	words	word	NOUN
ejpam-6254	8	13	and	and	CCONJ
ejpam-6254	8	14	phrases	phrase	NOUN
ejpam-6254	8	15	:	:	PUNCT
ejpam-6254	8	16	diseases	disease	NOUN
ejpam-6254	8	17	,	,	PUNCT
ejpam-6254	8	18	seirv	seirv	ADJ
ejpam-6254	8	19	epidemic	epidemic	NOUN
ejpam-6254	8	20	model	model	NOUN
ejpam-6254	8	21	,	,	PUNCT
ejpam-6254	8	22	time	time	NOUN
ejpam-6254	8	23	delay	delay	NOUN
ejpam-6254	8	24	,	,	PUNCT
ejpam-6254	8	25	optimal	optimal	ADJ
ejpam-6254	8	26	control	control	NOUN
ejpam-6254	8	27	∗corresponding	∗corresponde	VERB
ejpam-6254	8	28	author	author	NOUN
ejpam-6254	8	29	.	.	PUNCT
ejpam-6254	9	1	doi	doi	NOUN
ejpam-6254	9	2	:	:	PUNCT
ejpam-6254	9	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6254	https://doi.org/10.29020/nybg.ejpam.v18i4.6254	NOUN
ejpam-6254	9	4	email	email	NOUN
ejpam-6254	9	5	addresses	address	NOUN
ejpam-6254	9	6	:	:	PUNCT
ejpam-6254	9	7	shumaila@cuiatd.edu.pk	shumaila@cuiatd.edu.pk	PROPN
ejpam-6254	9	8	(	(	PUNCT
ejpam-6254	9	9	s.	s.	PROPN
ejpam-6254	9	10	irum	irum	PROPN
ejpam-6254	9	11	)	)	PUNCT
ejpam-6254	9	12	,	,	PUNCT
ejpam-6254	9	13	anwar@cuiatd.edu.pk	anwar@cuiatd.edu.pk	NOUN
ejpam-6254	9	14	(	(	PUNCT
ejpam-6254	9	15	a.	a.	NOUN
ejpam-6254	9	16	zeb	zeb	PROPN
ejpam-6254	9	17	)	)	PUNCT
ejpam-6254	9	18	,	,	PUNCT
ejpam-6254	9	19	aamuhseen@gmail.com	aamuhseen@gmail.com	X
ejpam-6254	9	20	(	(	PUNCT
ejpam-6254	9	21	a.	a.	PROPN
ejpam-6254	9	22	a.	a.	PROPN
ejpam-6254	9	23	mohsen	mohsen	PROPN
ejpam-6254	9	24	)	)	PUNCT
ejpam-6254	9	25	,	,	PUNCT
ejpam-6254	9	26	talhrthe@ub.edu.sa	talhrthe@ub.edu.sa	PROPN
ejpam-6254	9	27	(	(	PUNCT
ejpam-6254	9	28	t.	t.	PROPN
ejpam-6254	9	29	n.	n.	PROPN
ejpam-6254	9	30	alharthi	alharthi	PROPN
ejpam-6254	9	31	)	)	PUNCT
ejpam-6254	9	32	,	,	PUNCT
ejpam-6254	9	33	i.said@mu.edu.sa	i.said@mu.edu.sa	PROPN
ejpam-6254	9	34	(	(	PUNCT
ejpam-6254	9	35	i.	i.	PROPN
ejpam-6254	9	36	khan	khan	PROPN
ejpam-6254	9	37	)	)	PUNCT
ejpam-6254	9	38	,	,	PUNCT
ejpam-6254	9	39	weisin.koh@newinti.edu.my	weisin.koh@newinti.edu.my	NOUN
ejpam-6254	9	40	(	(	PUNCT
ejpam-6254	9	41	w.	w.	PROPN
ejpam-6254	9	42	s.	s.	PROPN
ejpam-6254	9	43	koh	koh	PROPN
ejpam-6254	9	44	)	)	PUNCT
ejpam-6254	9	45	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6254	10	1	1	1	NUM
ejpam-6254	10	2	copyright	copyright	NOUN
ejpam-6254	10	3	:	:	PUNCT
ejpam-6254	10	4	©	©	PROPN
ejpam-6254	10	5	2025	2025	NUM
ejpam-6254	10	6	the	the	DET
ejpam-6254	10	7	author(s	author(s	NOUN
ejpam-6254	10	8	)	)	PUNCT
ejpam-6254	10	9	.	.	PUNCT
ejpam-6254	11	1	(	(	PUNCT
ejpam-6254	11	2	cc	cc	NOUN
ejpam-6254	11	3	by	by	ADP
ejpam-6254	11	4	-	-	PUNCT
ejpam-6254	11	5	nc	nc	PROPN
ejpam-6254	11	6	4.0	4.0	NUM
ejpam-6254	11	7	)	)	PUNCT
ejpam-6254	11	8	s.	s.	PROPN
ejpam-6254	11	9	irum	irum	PROPN
ejpam-6254	11	10	et	et	PROPN
ejpam-6254	11	11	al	al	PROPN
ejpam-6254	11	12	.	.	PUNCT
ejpam-6254	11	13	/	/	SYM
ejpam-6254	11	14	eur	eur	PROPN
ejpam-6254	11	15	.	.	PUNCT
ejpam-6254	12	1	j.	j.	PROPN
ejpam-6254	12	2	pure	pure	PROPN
ejpam-6254	12	3	appl	appl	PROPN
ejpam-6254	12	4	.	.	PROPN
ejpam-6254	12	5	math	math	PROPN
ejpam-6254	12	6	,	,	PUNCT
ejpam-6254	12	7	18	18	NUM
ejpam-6254	12	8	(	(	PUNCT
ejpam-6254	12	9	4	4	NUM
ejpam-6254	12	10	)	)	PUNCT
ejpam-6254	12	11	(	(	PUNCT
ejpam-6254	12	12	2025	2025	NUM
ejpam-6254	12	13	)	)	PUNCT
ejpam-6254	12	14	,	,	PUNCT
ejpam-6254	12	15	6254	6254	NUM
ejpam-6254	12	16	2	2	NUM
ejpam-6254	12	17	of	of	ADP
ejpam-6254	12	18	23	23	NUM
ejpam-6254	12	19	1	1	NUM
ejpam-6254	12	20	.	.	PUNCT
ejpam-6254	12	21	introduction	introduction	NOUN
ejpam-6254	12	22	throughout	throughout	ADP
ejpam-6254	12	23	the	the	DET
ejpam-6254	12	24	last	last	ADJ
ejpam-6254	12	25	several	several	ADJ
ejpam-6254	12	26	decades	decade	NOUN
ejpam-6254	12	27	,	,	PUNCT
ejpam-6254	12	28	infectious	infectious	ADJ
ejpam-6254	12	29	diseases	disease	NOUN
ejpam-6254	12	30	have	have	AUX
ejpam-6254	12	31	posed	pose	VERB
ejpam-6254	12	32	significant	significant	ADJ
ejpam-6254	12	33	challenges	challenge	NOUN
ejpam-6254	12	34	to	to	ADP
ejpam-6254	12	35	public	public	ADJ
ejpam-6254	12	36	health	health	NOUN
ejpam-6254	12	37	worldwide	worldwide	ADV
ejpam-6254	12	38	.	.	PUNCT
ejpam-6254	13	1	despite	despite	SCONJ
ejpam-6254	13	2	advances	advance	NOUN
ejpam-6254	13	3	in	in	ADP
ejpam-6254	13	4	medical	medical	ADJ
ejpam-6254	13	5	science	science	NOUN
ejpam-6254	13	6	,	,	PUNCT
ejpam-6254	13	7	diseases	disease	NOUN
ejpam-6254	13	8	such	such	ADJ
ejpam-6254	13	9	as	as	ADP
ejpam-6254	13	10	malaria	malaria	NOUN
ejpam-6254	13	11	and	and	CCONJ
ejpam-6254	13	12	tuberculosis	tuberculosis	NOUN
ejpam-6254	13	13	continue	continue	VERB
ejpam-6254	13	14	to	to	PART
ejpam-6254	13	15	affect	affect	VERB
ejpam-6254	13	16	millions	million	NOUN
ejpam-6254	13	17	.	.	PUNCT
ejpam-6254	14	1	although	although	SCONJ
ejpam-6254	14	2	numerous	numerous	ADJ
ejpam-6254	14	3	studies	study	NOUN
ejpam-6254	14	4	have	have	AUX
ejpam-6254	14	5	been	be	AUX
ejpam-6254	14	6	conducted	conduct	VERB
ejpam-6254	14	7	on	on	ADP
ejpam-6254	14	8	prevention	prevention	NOUN
ejpam-6254	14	9	and	and	CCONJ
ejpam-6254	14	10	treatment	treatment	NOUN
ejpam-6254	14	11	,	,	PUNCT
ejpam-6254	14	12	a	a	DET
ejpam-6254	14	13	significant	significant	ADJ
ejpam-6254	14	14	knowledge	knowledge	NOUN
ejpam-6254	14	15	gap	gap	NOUN
ejpam-6254	14	16	persists	persist	VERB
ejpam-6254	14	17	on	on	ADP
ejpam-6254	14	18	the	the	DET
ejpam-6254	14	19	mechanisms	mechanism	NOUN
ejpam-6254	14	20	of	of	ADP
ejpam-6254	14	21	disease	disease	NOUN
ejpam-6254	14	22	spread	spread	VERB
ejpam-6254	14	23	under	under	ADP
ejpam-6254	14	24	varying	vary	VERB
ejpam-6254	14	25	environmental	environmental	ADJ
ejpam-6254	14	26	conditions	condition	NOUN
ejpam-6254	14	27	.	.	PUNCT
ejpam-6254	15	1	this	this	DET
ejpam-6254	15	2	research	research	NOUN
ejpam-6254	15	3	aims	aim	VERB
ejpam-6254	15	4	to	to	PART
ejpam-6254	15	5	develop	develop	VERB
ejpam-6254	15	6	a	a	DET
ejpam-6254	15	7	comprehensive	comprehensive	ADJ
ejpam-6254	15	8	model	model	NOUN
ejpam-6254	15	9	for	for	ADP
ejpam-6254	15	10	predicting	predict	VERB
ejpam-6254	15	11	infectious	infectious	ADJ
ejpam-6254	15	12	disease	disease	NOUN
ejpam-6254	15	13	outbreaks	outbreak	NOUN
ejpam-6254	15	14	.	.	PUNCT
ejpam-6254	16	1	the	the	DET
ejpam-6254	16	2	study	study	NOUN
ejpam-6254	16	3	tells	tell	VERB
ejpam-6254	16	4	us	we	PRON
ejpam-6254	16	5	about	about	ADP
ejpam-6254	16	6	the	the	DET
ejpam-6254	16	7	influence	influence	NOUN
ejpam-6254	16	8	of	of	ADP
ejpam-6254	16	9	climate	climate	NOUN
ejpam-6254	16	10	variations	variation	NOUN
ejpam-6254	16	11	on	on	ADP
ejpam-6254	16	12	disease	disease	NOUN
ejpam-6254	16	13	transmission	transmission	NOUN
ejpam-6254	16	14	.	.	PUNCT
ejpam-6254	17	1	and	and	CCONJ
ejpam-6254	17	2	also	also	ADV
ejpam-6254	17	3	tells	tell	VERB
ejpam-6254	17	4	the	the	DET
ejpam-6254	17	5	role	role	NOUN
ejpam-6254	17	6	of	of	ADP
ejpam-6254	17	7	human	human	ADJ
ejpam-6254	17	8	behaviors	behavior	NOUN
ejpam-6254	17	9	in	in	ADP
ejpam-6254	17	10	spreading	spread	VERB
ejpam-6254	17	11	infections	infection	NOUN
ejpam-6254	17	12	.	.	PUNCT
ejpam-6254	18	1	this	this	DET
ejpam-6254	18	2	research	research	NOUN
ejpam-6254	18	3	aims	aim	VERB
ejpam-6254	18	4	to	to	PART
ejpam-6254	18	5	contribute	contribute	VERB
ejpam-6254	18	6	to	to	ADP
ejpam-6254	18	7	the	the	DET
ejpam-6254	18	8	development	development	NOUN
ejpam-6254	18	9	of	of	ADP
ejpam-6254	18	10	more	more	ADV
ejpam-6254	18	11	effective	effective	ADJ
ejpam-6254	18	12	disease	disease	NOUN
ejpam-6254	18	13	control	control	NOUN
ejpam-6254	18	14	strategies	strategy	NOUN
ejpam-6254	18	15	.	.	PUNCT
ejpam-6254	19	1	however	however	ADV
ejpam-6254	19	2	,	,	PUNCT
ejpam-6254	19	3	this	this	DET
ejpam-6254	19	4	study	study	NOUN
ejpam-6254	19	5	is	be	AUX
ejpam-6254	19	6	limited	limit	VERB
ejpam-6254	19	7	to	to	ADP
ejpam-6254	19	8	data	datum	NOUN
ejpam-6254	19	9	from	from	ADP
ejpam-6254	19	10	specific	specific	ADJ
ejpam-6254	19	11	regions	region	NOUN
ejpam-6254	19	12	and	and	CCONJ
ejpam-6254	19	13	may	may	AUX
ejpam-6254	19	14	not	not	PART
ejpam-6254	19	15	be	be	AUX
ejpam-6254	19	16	universally	universally	ADV
ejpam-6254	19	17	applicable	applicable	ADJ
ejpam-6254	19	18	.	.	PUNCT
ejpam-6254	20	1	this	this	DET
ejpam-6254	20	2	paper	paper	NOUN
ejpam-6254	20	3	argues	argue	VERB
ejpam-6254	20	4	that	that	SCONJ
ejpam-6254	20	5	incorporating	incorporate	VERB
ejpam-6254	20	6	environmental	environmental	ADJ
ejpam-6254	20	7	factors	factor	NOUN
ejpam-6254	20	8	into	into	ADP
ejpam-6254	20	9	disease	disease	NOUN
ejpam-6254	20	10	prediction	prediction	NOUN
ejpam-6254	20	11	models	model	NOUN
ejpam-6254	20	12	significantly	significantly	ADV
ejpam-6254	20	13	improves	improve	VERB
ejpam-6254	20	14	their	their	PRON
ejpam-6254	20	15	accuracy	accuracy	NOUN
ejpam-6254	20	16	.	.	PUNCT
ejpam-6254	21	1	mathematical	mathematical	ADJ
ejpam-6254	21	2	modeling	modeling	NOUN
ejpam-6254	21	3	has	have	AUX
ejpam-6254	21	4	proven	prove	VERB
ejpam-6254	21	5	indispensable	indispensable	ADJ
ejpam-6254	21	6	in	in	ADP
ejpam-6254	21	7	understanding	understanding	NOUN
ejpam-6254	21	8	and	and	CCONJ
ejpam-6254	21	9	containing	contain	VERB
ejpam-6254	21	10	infectious	infectious	ADJ
ejpam-6254	21	11	diseases	disease	NOUN
ejpam-6254	21	12	.	.	PUNCT
ejpam-6254	22	1	the	the	DET
ejpam-6254	22	2	seirv	seirv	NOUN
ejpam-6254	22	3	model	model	NOUN
ejpam-6254	22	4	,	,	PUNCT
ejpam-6254	22	5	which	which	PRON
ejpam-6254	22	6	includes	include	VERB
ejpam-6254	22	7	compartments	compartment	NOUN
ejpam-6254	22	8	for	for	ADP
ejpam-6254	22	9	susceptible	susceptible	ADJ
ejpam-6254	22	10	,	,	PUNCT
ejpam-6254	22	11	exposed	expose	VERB
ejpam-6254	22	12	,	,	PUNCT
ejpam-6254	22	13	infectious	infectious	ADJ
ejpam-6254	22	14	,	,	PUNCT
ejpam-6254	22	15	recovered	recover	VERB
ejpam-6254	22	16	,	,	PUNCT
ejpam-6254	22	17	and	and	CCONJ
ejpam-6254	22	18	vaccinated	vaccinated	ADJ
ejpam-6254	22	19	individuals	individual	NOUN
ejpam-6254	22	20	,	,	PUNCT
ejpam-6254	22	21	provides	provide	VERB
ejpam-6254	22	22	a	a	DET
ejpam-6254	22	23	comprehensive	comprehensive	ADJ
ejpam-6254	22	24	framework	framework	NOUN
ejpam-6254	22	25	for	for	ADP
ejpam-6254	22	26	studying	study	VERB
ejpam-6254	22	27	disease	disease	NOUN
ejpam-6254	22	28	dynamics	dynamic	NOUN
ejpam-6254	22	29	.	.	PUNCT
ejpam-6254	23	1	these	these	DET
ejpam-6254	23	2	models	model	NOUN
ejpam-6254	23	3	were	be	AUX
ejpam-6254	23	4	also	also	ADV
ejpam-6254	23	5	used	use	VERB
ejpam-6254	23	6	during	during	ADP
ejpam-6254	23	7	the	the	DET
ejpam-6254	23	8	covid-19	covid-19	PROPN
ejpam-6254	23	9	pandemic	pandemic	NOUN
ejpam-6254	24	1	[	[	X
ejpam-6254	24	2	1–6	1–6	NUM
ejpam-6254	24	3	]	]	X
ejpam-6254	24	4	.	.	PUNCT
ejpam-6254	25	1	the	the	DET
ejpam-6254	25	2	classical	classical	ADJ
ejpam-6254	25	3	seir	seir	NOUN
ejpam-6254	25	4	(	(	PUNCT
ejpam-6254	25	5	susceptible	susceptible	ADJ
ejpam-6254	25	6	–	–	PUNCT
ejpam-6254	25	7	exposed	exposed	ADJ
ejpam-6254	25	8	–	–	PUNCT
ejpam-6254	25	9	infectious	infectious	ADJ
ejpam-6254	25	10	–	–	PUNCT
ejpam-6254	25	11	recovered	recovered	ADJ
ejpam-6254	25	12	)	)	PUNCT
ejpam-6254	25	13	model	model	NOUN
ejpam-6254	25	14	has	have	AUX
ejpam-6254	25	15	been	be	AUX
ejpam-6254	25	16	widely	widely	ADV
ejpam-6254	25	17	used	use	VERB
ejpam-6254	25	18	to	to	PART
ejpam-6254	25	19	study	study	VERB
ejpam-6254	25	20	the	the	DET
ejpam-6254	25	21	dynamics	dynamic	NOUN
ejpam-6254	25	22	of	of	ADP
ejpam-6254	25	23	infectious	infectious	ADJ
ejpam-6254	25	24	diseases	disease	NOUN
ejpam-6254	25	25	.	.	PUNCT
ejpam-6254	26	1	however	however	ADV
ejpam-6254	26	2	,	,	PUNCT
ejpam-6254	26	3	the	the	DET
ejpam-6254	26	4	emergence	emergence	NOUN
ejpam-6254	26	5	of	of	ADP
ejpam-6254	26	6	vaccination	vaccination	NOUN
ejpam-6254	26	7	as	as	ADP
ejpam-6254	26	8	a	a	DET
ejpam-6254	26	9	pivotal	pivotal	ADJ
ejpam-6254	26	10	public	public	ADJ
ejpam-6254	26	11	health	health	NOUN
ejpam-6254	26	12	strategy	strategy	NOUN
ejpam-6254	26	13	necessitates	necessitate	VERB
ejpam-6254	26	14	the	the	DET
ejpam-6254	26	15	inclusion	inclusion	NOUN
ejpam-6254	26	16	of	of	ADP
ejpam-6254	26	17	a	a	DET
ejpam-6254	26	18	vaccinated	vaccinate	VERB
ejpam-6254	26	19	(	(	PUNCT
ejpam-6254	26	20	v	v	NOUN
ejpam-6254	26	21	)	)	PUNCT
ejpam-6254	26	22	compartment	compartment	NOUN
ejpam-6254	26	23	,	,	PUNCT
ejpam-6254	26	24	resulting	result	VERB
ejpam-6254	26	25	in	in	ADP
ejpam-6254	26	26	the	the	DET
ejpam-6254	26	27	extended	extended	ADJ
ejpam-6254	26	28	seirv	seirv	NOUN
ejpam-6254	26	29	framework	framework	NOUN
ejpam-6254	26	30	.	.	PUNCT
ejpam-6254	27	1	the	the	DET
ejpam-6254	27	2	motivation	motivation	NOUN
ejpam-6254	27	3	for	for	ADP
ejpam-6254	27	4	this	this	DET
ejpam-6254	27	5	work	work	NOUN
ejpam-6254	27	6	stems	stem	VERB
ejpam-6254	27	7	from	from	ADP
ejpam-6254	27	8	the	the	DET
ejpam-6254	27	9	need	need	NOUN
ejpam-6254	27	10	to	to	PART
ejpam-6254	27	11	understand	understand	VERB
ejpam-6254	27	12	how	how	SCONJ
ejpam-6254	27	13	vaccination	vaccination	NOUN
ejpam-6254	27	14	policies	policy	NOUN
ejpam-6254	27	15	influence	influence	NOUN
ejpam-6254	27	16	disease	disease	NOUN
ejpam-6254	27	17	spread	spread	VERB
ejpam-6254	27	18	,	,	PUNCT
ejpam-6254	27	19	especially	especially	ADV
ejpam-6254	27	20	in	in	ADP
ejpam-6254	27	21	realistic	realistic	ADJ
ejpam-6254	27	22	settings	setting	NOUN
ejpam-6254	27	23	that	that	PRON
ejpam-6254	27	24	involve	involve	VERB
ejpam-6254	27	25	time	time	NOUN
ejpam-6254	27	26	delays	delay	NOUN
ejpam-6254	27	27	,	,	PUNCT
ejpam-6254	27	28	control	control	NOUN
ejpam-6254	27	29	strategies	strategy	NOUN
ejpam-6254	27	30	,	,	PUNCT
ejpam-6254	27	31	and	and	CCONJ
ejpam-6254	27	32	nonlinear	nonlinear	ADJ
ejpam-6254	27	33	incidence	incidence	NOUN
ejpam-6254	27	34	rates	rate	NOUN
ejpam-6254	27	35	.	.	PUNCT
ejpam-6254	28	1	the	the	DET
ejpam-6254	28	2	novelty	novelty	NOUN
ejpam-6254	28	3	of	of	ADP
ejpam-6254	28	4	this	this	DET
ejpam-6254	28	5	study	study	NOUN
ejpam-6254	28	6	lies	lie	VERB
ejpam-6254	28	7	in	in	ADP
ejpam-6254	28	8	incorporating	incorporate	VERB
ejpam-6254	28	9	a	a	DET
ejpam-6254	28	10	time	time	NOUN
ejpam-6254	28	11	-	-	PUNCT
ejpam-6254	28	12	delayed	delay	VERB
ejpam-6254	28	13	transmission	transmission	NOUN
ejpam-6254	28	14	dynamic	dynamic	ADJ
ejpam-6254	28	15	and	and	CCONJ
ejpam-6254	28	16	an	an	DET
ejpam-6254	28	17	optimal	optimal	ADJ
ejpam-6254	28	18	control	control	NOUN
ejpam-6254	28	19	approach	approach	NOUN
ejpam-6254	28	20	in	in	ADP
ejpam-6254	28	21	the	the	DET
ejpam-6254	28	22	seirv	seirv	NOUN
ejpam-6254	28	23	model	model	NOUN
ejpam-6254	28	24	,	,	PUNCT
ejpam-6254	28	25	enabling	enable	VERB
ejpam-6254	28	26	the	the	DET
ejpam-6254	28	27	analysis	analysis	NOUN
ejpam-6254	28	28	of	of	ADP
ejpam-6254	28	29	how	how	SCONJ
ejpam-6254	28	30	delays	delay	NOUN
ejpam-6254	28	31	in	in	ADP
ejpam-6254	28	32	exposure	exposure	NOUN
ejpam-6254	28	33	or	or	CCONJ
ejpam-6254	28	34	treatment	treatment	NOUN
ejpam-6254	28	35	impact	impact	NOUN
ejpam-6254	28	36	epidemic	epidemic	NOUN
ejpam-6254	28	37	control	control	NOUN
ejpam-6254	28	38	.	.	PUNCT
ejpam-6254	29	1	furthermore	furthermore	ADV
ejpam-6254	29	2	,	,	PUNCT
ejpam-6254	29	3	the	the	DET
ejpam-6254	29	4	model	model	NOUN
ejpam-6254	29	5	accommodates	accommodate	VERB
ejpam-6254	29	6	a	a	DET
ejpam-6254	29	7	holling	holle	VERB
ejpam-6254	29	8	type	type	NOUN
ejpam-6254	29	9	ii	ii	NOUN
ejpam-6254	29	10	incidence	incidence	NOUN
ejpam-6254	29	11	function	function	NOUN
ejpam-6254	29	12	,	,	PUNCT
ejpam-6254	29	13	which	which	PRON
ejpam-6254	29	14	better	well	ADV
ejpam-6254	29	15	captures	capture	VERB
ejpam-6254	29	16	the	the	DET
ejpam-6254	29	17	saturation	saturation	NOUN
ejpam-6254	29	18	effects	effect	NOUN
ejpam-6254	29	19	in	in	ADP
ejpam-6254	29	20	disease	disease	NOUN
ejpam-6254	29	21	transmission	transmission	NOUN
ejpam-6254	29	22	,	,	PUNCT
ejpam-6254	29	23	reflecting	reflect	VERB
ejpam-6254	29	24	the	the	DET
ejpam-6254	29	25	limitations	limitation	NOUN
ejpam-6254	29	26	of	of	ADP
ejpam-6254	29	27	the	the	DET
ejpam-6254	29	28	behavioral	behavioral	ADJ
ejpam-6254	29	29	and	and	CCONJ
ejpam-6254	29	30	medical	medical	ADJ
ejpam-6254	29	31	response	response	NOUN
ejpam-6254	29	32	.	.	PUNCT
ejpam-6254	30	1	this	this	DET
ejpam-6254	30	2	extended	extend	VERB
ejpam-6254	30	3	seirv	seirv	NOUN
ejpam-6254	30	4	model	model	NOUN
ejpam-6254	30	5	is	be	AUX
ejpam-6254	30	6	applicable	applicable	ADJ
ejpam-6254	30	7	to	to	ADP
ejpam-6254	30	8	the	the	DET
ejpam-6254	30	9	evaluation	evaluation	NOUN
ejpam-6254	30	10	and	and	CCONJ
ejpam-6254	30	11	design	design	NOUN
ejpam-6254	30	12	of	of	ADP
ejpam-6254	30	13	effective	effective	ADJ
ejpam-6254	30	14	vaccination	vaccination	NOUN
ejpam-6254	30	15	campaigns	campaign	NOUN
ejpam-6254	30	16	and	and	CCONJ
ejpam-6254	30	17	public	public	ADJ
ejpam-6254	30	18	health	health	NOUN
ejpam-6254	30	19	interventions	intervention	NOUN
ejpam-6254	30	20	during	during	ADP
ejpam-6254	30	21	outbreaks	outbreak	NOUN
ejpam-6254	30	22	such	such	ADJ
ejpam-6254	30	23	as	as	ADP
ejpam-6254	30	24	covid-19	covid-19	PROPN
ejpam-6254	30	25	,	,	PUNCT
ejpam-6254	30	26	measles	measle	NOUN
ejpam-6254	30	27	,	,	PUNCT
ejpam-6254	30	28	or	or	CCONJ
ejpam-6254	30	29	influenza	influenza	NOUN
ejpam-6254	30	30	.	.	PUNCT
ejpam-6254	31	1	it	it	PRON
ejpam-6254	31	2	can	can	AUX
ejpam-6254	31	3	assist	assist	VERB
ejpam-6254	31	4	policymakers	policymaker	NOUN
ejpam-6254	31	5	in	in	ADP
ejpam-6254	31	6	determining	determine	VERB
ejpam-6254	31	7	optimal	optimal	ADJ
ejpam-6254	31	8	resource	resource	NOUN
ejpam-6254	31	9	allocation	allocation	NOUN
ejpam-6254	31	10	for	for	ADP
ejpam-6254	31	11	vaccination	vaccination	NOUN
ejpam-6254	31	12	and	and	CCONJ
ejpam-6254	31	13	treatment	treatment	NOUN
ejpam-6254	31	14	,	,	PUNCT
ejpam-6254	31	15	timing	timing	NOUN
ejpam-6254	31	16	of	of	ADP
ejpam-6254	31	17	intervention	intervention	NOUN
ejpam-6254	31	18	strategies	strategy	NOUN
ejpam-6254	31	19	,	,	PUNCT
ejpam-6254	31	20	and	and	CCONJ
ejpam-6254	31	21	understanding	understand	VERB
ejpam-6254	31	22	the	the	DET
ejpam-6254	31	23	long	long	ADJ
ejpam-6254	31	24	-	-	PUNCT
ejpam-6254	31	25	term	term	NOUN
ejpam-6254	31	26	impact	impact	NOUN
ejpam-6254	31	27	of	of	ADP
ejpam-6254	31	28	delayed	delay	VERB
ejpam-6254	31	29	responses	response	NOUN
ejpam-6254	31	30	.	.	PUNCT
ejpam-6254	32	1	the	the	DET
ejpam-6254	32	2	model	model	NOUN
ejpam-6254	32	3	is	be	AUX
ejpam-6254	32	4	particularly	particularly	ADV
ejpam-6254	32	5	relevant	relevant	ADJ
ejpam-6254	32	6	for	for	ADP
ejpam-6254	32	7	guiding	guide	VERB
ejpam-6254	32	8	decision	decision	NOUN
ejpam-6254	32	9	making	making	NOUN
ejpam-6254	32	10	in	in	ADP
ejpam-6254	32	11	regions	region	NOUN
ejpam-6254	32	12	with	with	ADP
ejpam-6254	32	13	constrained	constrain	VERB
ejpam-6254	32	14	healthcare	healthcare	NOUN
ejpam-6254	32	15	infrastructure	infrastructure	NOUN
ejpam-6254	32	16	and	and	CCONJ
ejpam-6254	32	17	variable	variable	ADJ
ejpam-6254	32	18	public	public	ADJ
ejpam-6254	32	19	response	response	NOUN
ejpam-6254	32	20	[	[	X
ejpam-6254	32	21	7	7	NUM
ejpam-6254	32	22	,	,	PUNCT
ejpam-6254	32	23	8	8	NUM
ejpam-6254	32	24	]	]	PUNCT
ejpam-6254	32	25	.	.	PUNCT
ejpam-6254	33	1	however	however	ADV
ejpam-6254	33	2	,	,	PUNCT
ejpam-6254	33	3	existing	exist	VERB
ejpam-6254	33	4	models	model	NOUN
ejpam-6254	33	5	often	often	ADV
ejpam-6254	33	6	overlook	overlook	VERB
ejpam-6254	33	7	the	the	DET
ejpam-6254	33	8	impact	impact	NOUN
ejpam-6254	33	9	of	of	ADP
ejpam-6254	33	10	delays	delay	NOUN
ejpam-6254	33	11	and	and	CCONJ
ejpam-6254	33	12	optimal	optimal	ADJ
ejpam-6254	33	13	control	control	NOUN
ejpam-6254	33	14	mechanisms	mechanism	NOUN
ejpam-6254	33	15	.	.	PUNCT
ejpam-6254	34	1	this	this	DET
ejpam-6254	34	2	study	study	NOUN
ejpam-6254	34	3	aims	aim	VERB
ejpam-6254	34	4	to	to	PART
ejpam-6254	34	5	develop	develop	VERB
ejpam-6254	34	6	and	and	CCONJ
ejpam-6254	34	7	analyze	analyze	VERB
ejpam-6254	34	8	a	a	DET
ejpam-6254	34	9	delayed	delay	VERB
ejpam-6254	34	10	seirv	seirv	NOUN
ejpam-6254	34	11	epidemic	epidemic	NOUN
ejpam-6254	34	12	model	model	NOUN
ejpam-6254	34	13	incorporating	incorporate	VERB
ejpam-6254	34	14	optimal	optimal	ADJ
ejpam-6254	34	15	control	control	NOUN
ejpam-6254	34	16	with	with	ADP
ejpam-6254	34	17	a	a	DET
ejpam-6254	34	18	holling	holle	VERB
ejpam-6254	34	19	-	-	PUNCT
ejpam-6254	34	20	type	type	NOUN
ejpam-6254	34	21	ii	ii	NOUN
ejpam-6254	34	22	functional	functional	ADJ
ejpam-6254	34	23	response	response	NOUN
ejpam-6254	34	24	.	.	PUNCT
ejpam-6254	35	1	by	by	ADP
ejpam-6254	35	2	incorporating	incorporate	VERB
ejpam-6254	35	3	delays	delay	NOUN
ejpam-6254	35	4	,	,	PUNCT
ejpam-6254	35	5	we	we	PRON
ejpam-6254	35	6	seek	seek	VERB
ejpam-6254	35	7	to	to	PART
ejpam-6254	35	8	understand	understand	VERB
ejpam-6254	35	9	their	their	PRON
ejpam-6254	35	10	effect	effect	NOUN
ejpam-6254	35	11	on	on	ADP
ejpam-6254	35	12	disease	disease	NOUN
ejpam-6254	35	13	spread	spread	VERB
ejpam-6254	35	14	and	and	CCONJ
ejpam-6254	35	15	identify	identify	VERB
ejpam-6254	35	16	optimal	optimal	ADJ
ejpam-6254	35	17	control	control	NOUN
ejpam-6254	35	18	strategies	strategy	NOUN
ejpam-6254	35	19	to	to	PART
ejpam-6254	35	20	mitigate	mitigate	VERB
ejpam-6254	35	21	outbreaks	outbreak	NOUN
ejpam-6254	35	22	.	.	PUNCT
ejpam-6254	36	1	this	this	DET
ejpam-6254	36	2	study	study	NOUN
ejpam-6254	36	3	addressed	address	VERB
ejpam-6254	36	4	how	how	SCONJ
ejpam-6254	36	5	do	do	AUX
ejpam-6254	36	6	delays	delay	NOUN
ejpam-6254	36	7	influence	influence	VERB
ejpam-6254	36	8	the	the	DET
ejpam-6254	36	9	transmission	transmission	NOUN
ejpam-6254	36	10	dynamics	dynamic	NOUN
ejpam-6254	36	11	of	of	ADP
ejpam-6254	36	12	the	the	DET
ejpam-6254	36	13	disease	disease	NOUN
ejpam-6254	36	14	and	and	CCONJ
ejpam-6254	36	15	what	what	PRON
ejpam-6254	36	16	are	be	AUX
ejpam-6254	36	17	the	the	DET
ejpam-6254	36	18	most	most	ADV
ejpam-6254	36	19	effective	effective	ADJ
ejpam-6254	36	20	control	control	NOUN
ejpam-6254	36	21	strategies	strategy	NOUN
ejpam-6254	36	22	under	under	ADP
ejpam-6254	36	23	different	different	ADJ
ejpam-6254	36	24	scenarios	scenario	NOUN
ejpam-6254	36	25	.	.	PUNCT
ejpam-6254	37	1	the	the	DET
ejpam-6254	37	2	scope	scope	NOUN
ejpam-6254	37	3	of	of	ADP
ejpam-6254	37	4	this	this	DET
ejpam-6254	37	5	research	research	NOUN
ejpam-6254	37	6	is	be	AUX
ejpam-6254	37	7	restricted	restrict	VERB
ejpam-6254	37	8	to	to	ADP
ejpam-6254	37	9	theoretical	theoretical	ADJ
ejpam-6254	37	10	analysis	analysis	NOUN
ejpam-6254	37	11	and	and	CCONJ
ejpam-6254	37	12	simulations	simulation	NOUN
ejpam-6254	37	13	based	base	VERB
ejpam-6254	37	14	on	on	ADP
ejpam-6254	37	15	specific	specific	ADJ
ejpam-6254	37	16	parameter	parameter	NOUN
ejpam-6254	37	17	values	value	NOUN
ejpam-6254	37	18	.	.	PUNCT
ejpam-6254	38	1	this	this	DET
ejpam-6254	38	2	paper	paper	NOUN
ejpam-6254	38	3	s.	s.	PROPN
ejpam-6254	38	4	irum	irum	PROPN
ejpam-6254	38	5	et	et	PROPN
ejpam-6254	38	6	al	al	PROPN
ejpam-6254	38	7	.	.	PUNCT
ejpam-6254	38	8	/	/	SYM
ejpam-6254	38	9	eur	eur	PROPN
ejpam-6254	38	10	.	.	PUNCT
ejpam-6254	39	1	j.	j.	PROPN
ejpam-6254	39	2	pure	pure	PROPN
ejpam-6254	39	3	appl	appl	PROPN
ejpam-6254	39	4	.	.	PROPN
ejpam-6254	39	5	math	math	PROPN
ejpam-6254	39	6	,	,	PUNCT
ejpam-6254	39	7	18	18	NUM
ejpam-6254	39	8	(	(	PUNCT
ejpam-6254	39	9	4	4	NUM
ejpam-6254	39	10	)	)	PUNCT
ejpam-6254	39	11	(	(	PUNCT
ejpam-6254	39	12	2025	2025	NUM
ejpam-6254	39	13	)	)	PUNCT
ejpam-6254	39	14	,	,	PUNCT
ejpam-6254	39	15	6254	6254	NUM
ejpam-6254	39	16	3	3	NUM
ejpam-6254	39	17	of	of	ADP
ejpam-6254	39	18	23	23	NUM
ejpam-6254	39	19	argues	argue	VERB
ejpam-6254	39	20	that	that	SCONJ
ejpam-6254	39	21	incorporating	incorporate	VERB
ejpam-6254	39	22	delays	delay	NOUN
ejpam-6254	39	23	and	and	CCONJ
ejpam-6254	39	24	optimal	optimal	ADJ
ejpam-6254	39	25	control	control	NOUN
ejpam-6254	39	26	into	into	ADP
ejpam-6254	39	27	the	the	DET
ejpam-6254	39	28	seirv	seirv	NOUN
ejpam-6254	39	29	model	model	NOUN
ejpam-6254	39	30	significantly	significantly	ADV
ejpam-6254	39	31	enhances	enhance	VERB
ejpam-6254	39	32	its	its	PRON
ejpam-6254	39	33	predictive	predictive	ADJ
ejpam-6254	39	34	accuracy	accuracy	NOUN
ejpam-6254	39	35	and	and	CCONJ
ejpam-6254	39	36	effectiveness	effectiveness	NOUN
ejpam-6254	39	37	in	in	ADP
ejpam-6254	39	38	disease	disease	NOUN
ejpam-6254	39	39	management	management	NOUN
ejpam-6254	39	40	.	.	PUNCT
ejpam-6254	40	1	mathematical	mathematical	ADJ
ejpam-6254	40	2	modeling	modeling	NOUN
ejpam-6254	40	3	using	use	VERB
ejpam-6254	40	4	the	the	DET
ejpam-6254	40	5	seirv	seirv	ADJ
ejpam-6254	40	6	epidemic	epidemic	NOUN
ejpam-6254	40	7	framework	framework	NOUN
ejpam-6254	40	8	(	(	PUNCT
ejpam-6254	40	9	especially	especially	ADV
ejpam-6254	40	10	with	with	ADP
ejpam-6254	40	11	its	its	PRON
ejpam-6254	40	12	complexities	complexity	NOUN
ejpam-6254	40	13	like	like	ADP
ejpam-6254	40	14	delays	delay	NOUN
ejpam-6254	40	15	and	and	CCONJ
ejpam-6254	40	16	the	the	DET
ejpam-6254	40	17	quest	quest	NOUN
ejpam-6254	40	18	for	for	ADP
ejpam-6254	40	19	optimal	optimal	ADJ
ejpam-6254	40	20	control	control	NOUN
ejpam-6254	40	21	)	)	PUNCT
ejpam-6254	40	22	is	be	AUX
ejpam-6254	40	23	far	far	ADV
ejpam-6254	40	24	more	more	ADJ
ejpam-6254	40	25	than	than	ADP
ejpam-6254	40	26	an	an	DET
ejpam-6254	40	27	academic	academic	ADJ
ejpam-6254	40	28	exercise	exercise	NOUN
ejpam-6254	40	29	.	.	PUNCT
ejpam-6254	41	1	it	it	PRON
ejpam-6254	41	2	stands	stand	VERB
ejpam-6254	41	3	as	as	ADP
ejpam-6254	41	4	a	a	DET
ejpam-6254	41	5	guiding	guide	VERB
ejpam-6254	41	6	light	light	NOUN
ejpam-6254	41	7	in	in	ADP
ejpam-6254	41	8	the	the	DET
ejpam-6254	41	9	global	global	ADJ
ejpam-6254	41	10	fight	fight	NOUN
ejpam-6254	41	11	against	against	ADP
ejpam-6254	41	12	infectious	infectious	ADJ
ejpam-6254	41	13	diseases	disease	NOUN
ejpam-6254	41	14	.	.	PUNCT
ejpam-6254	42	1	in	in	ADP
ejpam-6254	42	2	exploring	explore	VERB
ejpam-6254	42	3	this	this	DET
ejpam-6254	42	4	model	model	NOUN
ejpam-6254	42	5	’s	’s	PART
ejpam-6254	42	6	depth	depth	NOUN
ejpam-6254	42	7	,	,	PUNCT
ejpam-6254	42	8	we	we	PRON
ejpam-6254	42	9	are	be	AUX
ejpam-6254	42	10	not	not	PART
ejpam-6254	42	11	merely	merely	ADV
ejpam-6254	42	12	working	work	VERB
ejpam-6254	42	13	with	with	ADP
ejpam-6254	42	14	equations	equation	NOUN
ejpam-6254	42	15	or	or	CCONJ
ejpam-6254	42	16	computations	computation	NOUN
ejpam-6254	42	17	but	but	CCONJ
ejpam-6254	42	18	we	we	PRON
ejpam-6254	42	19	are	be	AUX
ejpam-6254	42	20	developing	develop	VERB
ejpam-6254	42	21	powerful	powerful	ADJ
ejpam-6254	42	22	tools	tool	NOUN
ejpam-6254	42	23	to	to	PART
ejpam-6254	42	24	forecast	forecast	VERB
ejpam-6254	42	25	,	,	PUNCT
ejpam-6254	42	26	manage	manage	VERB
ejpam-6254	42	27	,	,	PUNCT
ejpam-6254	42	28	and	and	CCONJ
ejpam-6254	42	29	ultimately	ultimately	ADV
ejpam-6254	42	30	overcome	overcome	VERB
ejpam-6254	42	31	epidemics	epidemic	NOUN
ejpam-6254	42	32	.	.	PUNCT
ejpam-6254	43	1	diving	dive	VERB
ejpam-6254	43	2	into	into	ADP
ejpam-6254	43	3	the	the	DET
ejpam-6254	43	4	seirv	seirv	NOUN
ejpam-6254	43	5	epidemic	epidemic	NOUN
ejpam-6254	43	6	model	model	NOUN
ejpam-6254	43	7	with	with	ADP
ejpam-6254	43	8	delay	delay	NOUN
ejpam-6254	43	9	and	and	CCONJ
ejpam-6254	43	10	holling	holle	VERB
ejpam-6254	43	11	type	type	NOUN
ejpam-6254	43	12	delay	delay	NOUN
ejpam-6254	43	13	optimal	optimal	ADJ
ejpam-6254	43	14	control	control	NOUN
ejpam-6254	43	15	,	,	PUNCT
ejpam-6254	43	16	we	we	PRON
ejpam-6254	43	17	are	be	AUX
ejpam-6254	43	18	not	not	PART
ejpam-6254	43	19	just	just	ADV
ejpam-6254	43	20	working	work	VERB
ejpam-6254	43	21	with	with	ADP
ejpam-6254	43	22	numbers	number	NOUN
ejpam-6254	43	23	and	and	CCONJ
ejpam-6254	43	24	equations	equation	NOUN
ejpam-6254	43	25	we	we	PRON
ejpam-6254	43	26	are	be	AUX
ejpam-6254	43	27	forging	forge	VERB
ejpam-6254	43	28	advanced	advanced	ADJ
ejpam-6254	43	29	tools	tool	NOUN
ejpam-6254	43	30	for	for	ADP
ejpam-6254	43	31	public	public	ADJ
ejpam-6254	43	32	health	health	NOUN
ejpam-6254	43	33	.	.	PUNCT
ejpam-6254	44	1	this	this	DET
ejpam-6254	44	2	model	model	NOUN
ejpam-6254	44	3	is	be	AUX
ejpam-6254	44	4	not	not	PART
ejpam-6254	44	5	merely	merely	ADV
ejpam-6254	44	6	theoretical	theoretical	ADJ
ejpam-6254	44	7	it	it	PRON
ejpam-6254	44	8	is	be	AUX
ejpam-6254	44	9	a	a	DET
ejpam-6254	44	10	blueprint	blueprint	NOUN
ejpam-6254	44	11	for	for	ADP
ejpam-6254	44	12	predicting	predict	VERB
ejpam-6254	44	13	and	and	CCONJ
ejpam-6254	44	14	controlling	control	VERB
ejpam-6254	44	15	outbreaks	outbreak	NOUN
ejpam-6254	44	16	,	,	PUNCT
ejpam-6254	44	17	potentially	potentially	ADV
ejpam-6254	44	18	saving	save	VERB
ejpam-6254	44	19	countless	countless	ADJ
ejpam-6254	44	20	lives	life	NOUN
ejpam-6254	44	21	.	.	PUNCT
ejpam-6254	45	1	stay	stay	VERB
ejpam-6254	45	2	motivated	motivated	ADJ
ejpam-6254	45	3	,	,	PUNCT
ejpam-6254	45	4	as	as	SCONJ
ejpam-6254	45	5	our	our	PRON
ejpam-6254	45	6	contributions	contribution	NOUN
ejpam-6254	45	7	could	could	AUX
ejpam-6254	45	8	well	well	ADV
ejpam-6254	45	9	be	be	AUX
ejpam-6254	45	10	the	the	DET
ejpam-6254	45	11	key	key	NOUN
ejpam-6254	45	12	to	to	ADP
ejpam-6254	45	13	unlocking	unlock	VERB
ejpam-6254	45	14	the	the	DET
ejpam-6254	45	15	mysteries	mystery	NOUN
ejpam-6254	45	16	of	of	ADP
ejpam-6254	45	17	infectious	infectious	ADJ
ejpam-6254	45	18	disease	disease	NOUN
ejpam-6254	45	19	dynamics	dynamic	NOUN
ejpam-6254	45	20	.	.	PUNCT
ejpam-6254	46	1	this	this	DET
ejpam-6254	46	2	model	model	NOUN
ejpam-6254	46	3	helps	help	VERB
ejpam-6254	46	4	in	in	ADP
ejpam-6254	46	5	understanding	understand	VERB
ejpam-6254	46	6	the	the	DET
ejpam-6254	46	7	spread	spread	NOUN
ejpam-6254	46	8	and	and	CCONJ
ejpam-6254	46	9	control	control	NOUN
ejpam-6254	46	10	of	of	ADP
ejpam-6254	46	11	infectious	infectious	ADJ
ejpam-6254	46	12	diseases	disease	NOUN
ejpam-6254	46	13	through	through	ADP
ejpam-6254	46	14	the	the	DET
ejpam-6254	46	15	incorporation	incorporation	NOUN
ejpam-6254	46	16	of	of	ADP
ejpam-6254	46	17	various	various	ADJ
ejpam-6254	46	18	factors	factor	NOUN
ejpam-6254	46	19	such	such	ADJ
ejpam-6254	46	20	as	as	ADP
ejpam-6254	46	21	susceptible	susceptible	ADJ
ejpam-6254	46	22	,	,	PUNCT
ejpam-6254	46	23	exposed	expose	VERB
ejpam-6254	46	24	,	,	PUNCT
ejpam-6254	46	25	infected	infect	VERB
ejpam-6254	46	26	,	,	PUNCT
ejpam-6254	46	27	recovered	recover	VERB
ejpam-6254	46	28	,	,	PUNCT
ejpam-6254	46	29	and	and	CCONJ
ejpam-6254	46	30	vaccinated	vaccinated	ADJ
ejpam-6254	46	31	individuals	individual	NOUN
ejpam-6254	46	32	.	.	PUNCT
ejpam-6254	47	1	the	the	DET
ejpam-6254	47	2	delay	delay	NOUN
ejpam-6254	47	3	aspect	aspect	NOUN
ejpam-6254	47	4	accounts	account	VERB
ejpam-6254	47	5	for	for	ADP
ejpam-6254	47	6	the	the	DET
ejpam-6254	47	7	incubation	incubation	NOUN
ejpam-6254	47	8	period	period	NOUN
ejpam-6254	47	9	of	of	ADP
ejpam-6254	47	10	the	the	DET
ejpam-6254	47	11	disease	disease	NOUN
ejpam-6254	47	12	,	,	PUNCT
ejpam-6254	47	13	making	make	VERB
ejpam-6254	47	14	the	the	DET
ejpam-6254	47	15	model	model	NOUN
ejpam-6254	47	16	more	more	ADV
ejpam-6254	47	17	realistic	realistic	ADJ
ejpam-6254	47	18	[	[	X
ejpam-6254	47	19	9	9	NUM
ejpam-6254	47	20	,	,	PUNCT
ejpam-6254	47	21	10	10	NUM
ejpam-6254	47	22	]	]	PUNCT
ejpam-6254	47	23	.	.	PUNCT
ejpam-6254	48	1	after	after	ADP
ejpam-6254	48	2	reading	read	VERB
ejpam-6254	48	3	the	the	DET
ejpam-6254	48	4	paper	paper	NOUN
ejpam-6254	48	5	[	[	X
ejpam-6254	48	6	11	11	NUM
ejpam-6254	48	7	]	]	PUNCT
ejpam-6254	48	8	,	,	PUNCT
ejpam-6254	48	9	we	we	PRON
ejpam-6254	48	10	were	be	AUX
ejpam-6254	48	11	inspired	inspire	VERB
ejpam-6254	48	12	to	to	PART
ejpam-6254	48	13	extend	extend	VERB
ejpam-6254	48	14	the	the	DET
ejpam-6254	48	15	research	research	NOUN
ejpam-6254	48	16	.	.	PUNCT
ejpam-6254	49	1	we	we	PRON
ejpam-6254	49	2	observed	observe	VERB
ejpam-6254	49	3	that	that	SCONJ
ejpam-6254	49	4	incorporating	incorporate	VERB
ejpam-6254	49	5	time	time	NOUN
ejpam-6254	49	6	delay	delay	NOUN
ejpam-6254	49	7	and	and	CCONJ
ejpam-6254	49	8	optimal	optimal	ADJ
ejpam-6254	49	9	control	control	NOUN
ejpam-6254	49	10	had	have	AUX
ejpam-6254	49	11	not	not	PART
ejpam-6254	49	12	yet	yet	ADV
ejpam-6254	49	13	been	be	AUX
ejpam-6254	49	14	explored	explore	VERB
ejpam-6254	49	15	in	in	ADP
ejpam-6254	49	16	this	this	DET
ejpam-6254	49	17	context	context	NOUN
ejpam-6254	49	18	,	,	PUNCT
ejpam-6254	49	19	so	so	ADV
ejpam-6254	49	20	we	we	PRON
ejpam-6254	49	21	introduced	introduce	VERB
ejpam-6254	49	22	these	these	DET
ejpam-6254	49	23	elements	element	NOUN
ejpam-6254	49	24	as	as	ADP
ejpam-6254	49	25	novel	novel	ADJ
ejpam-6254	49	26	contributions	contribution	NOUN
ejpam-6254	49	27	.	.	PUNCT
ejpam-6254	50	1	by	by	ADP
ejpam-6254	50	2	applying	apply	VERB
ejpam-6254	50	3	optimal	optimal	ADJ
ejpam-6254	50	4	control	control	NOUN
ejpam-6254	50	5	theory	theory	NOUN
ejpam-6254	50	6	,	,	PUNCT
ejpam-6254	50	7	the	the	DET
ejpam-6254	50	8	model	model	NOUN
ejpam-6254	50	9	identifies	identify	VERB
ejpam-6254	50	10	the	the	DET
ejpam-6254	50	11	most	most	ADV
ejpam-6254	50	12	effective	effective	ADJ
ejpam-6254	50	13	strategies	strategy	NOUN
ejpam-6254	50	14	to	to	PART
ejpam-6254	50	15	curb	curb	VERB
ejpam-6254	50	16	the	the	DET
ejpam-6254	50	17	spread	spread	NOUN
ejpam-6254	50	18	of	of	ADP
ejpam-6254	50	19	infectious	infectious	ADJ
ejpam-6254	50	20	diseases	disease	NOUN
ejpam-6254	50	21	while	while	SCONJ
ejpam-6254	50	22	accounting	account	VERB
ejpam-6254	50	23	for	for	ADP
ejpam-6254	50	24	resource	resource	NOUN
ejpam-6254	50	25	limitations	limitation	NOUN
ejpam-6254	50	26	.	.	PUNCT
ejpam-6254	51	1	this	this	DET
ejpam-6254	51	2	approach	approach	NOUN
ejpam-6254	51	3	is	be	AUX
ejpam-6254	51	4	essential	essential	ADJ
ejpam-6254	51	5	for	for	ADP
ejpam-6254	51	6	effective	effective	ADJ
ejpam-6254	51	7	public	public	ADJ
ejpam-6254	51	8	health	health	NOUN
ejpam-6254	51	9	planning	planning	NOUN
ejpam-6254	51	10	and	and	CCONJ
ejpam-6254	51	11	intervention	intervention	NOUN
ejpam-6254	51	12	[	[	X
ejpam-6254	51	13	12	12	NUM
ejpam-6254	51	14	]	]	PUNCT
ejpam-6254	51	15	.	.	PUNCT
ejpam-6254	52	1	to	to	PART
ejpam-6254	52	2	better	well	ADV
ejpam-6254	52	3	capture	capture	VERB
ejpam-6254	52	4	the	the	DET
ejpam-6254	52	5	dynamics	dynamic	NOUN
ejpam-6254	52	6	between	between	ADP
ejpam-6254	52	7	the	the	DET
ejpam-6254	52	8	disease	disease	NOUN
ejpam-6254	52	9	and	and	CCONJ
ejpam-6254	52	10	the	the	DET
ejpam-6254	52	11	population	population	NOUN
ejpam-6254	52	12	,	,	PUNCT
ejpam-6254	52	13	the	the	DET
ejpam-6254	52	14	model	model	NOUN
ejpam-6254	52	15	utilizes	utilize	VERB
ejpam-6254	52	16	the	the	DET
ejpam-6254	52	17	holling	holle	VERB
ejpam-6254	52	18	type	type	NOUN
ejpam-6254	52	19	ii	ii	PROPN
ejpam-6254	52	20	functional	functional	ADJ
ejpam-6254	52	21	response	response	NOUN
ejpam-6254	52	22	,	,	PUNCT
ejpam-6254	52	23	which	which	PRON
ejpam-6254	52	24	offers	offer	VERB
ejpam-6254	52	25	a	a	DET
ejpam-6254	52	26	more	more	ADV
ejpam-6254	52	27	realistic	realistic	ADJ
ejpam-6254	52	28	depiction	depiction	NOUN
ejpam-6254	52	29	of	of	ADP
ejpam-6254	52	30	how	how	SCONJ
ejpam-6254	52	31	infections	infection	NOUN
ejpam-6254	52	32	progress	progress	VERB
ejpam-6254	52	33	and	and	CCONJ
ejpam-6254	52	34	impact	impact	VERB
ejpam-6254	52	35	the	the	DET
ejpam-6254	52	36	population	population	NOUN
ejpam-6254	53	1	[	[	X
ejpam-6254	53	2	13	13	NUM
ejpam-6254	53	3	]	]	PUNCT
ejpam-6254	53	4	.	.	PUNCT
ejpam-6254	54	1	the	the	DET
ejpam-6254	54	2	insights	insight	NOUN
ejpam-6254	54	3	gained	gain	VERB
ejpam-6254	54	4	from	from	ADP
ejpam-6254	54	5	this	this	DET
ejpam-6254	54	6	model	model	NOUN
ejpam-6254	54	7	can	can	AUX
ejpam-6254	54	8	aid	aid	VERB
ejpam-6254	54	9	policymakers	policymaker	NOUN
ejpam-6254	54	10	in	in	ADP
ejpam-6254	54	11	determining	determine	VERB
ejpam-6254	54	12	optimal	optimal	ADJ
ejpam-6254	54	13	strategies	strategy	NOUN
ejpam-6254	54	14	for	for	ADP
ejpam-6254	54	15	controlling	control	VERB
ejpam-6254	54	16	epidemics	epidemic	NOUN
ejpam-6254	54	17	,	,	PUNCT
ejpam-6254	54	18	such	such	ADJ
ejpam-6254	54	19	as	as	ADP
ejpam-6254	54	20	vaccination	vaccination	NOUN
ejpam-6254	54	21	,	,	PUNCT
ejpam-6254	54	22	quarantine	quarantine	NOUN
ejpam-6254	54	23	,	,	PUNCT
ejpam-6254	54	24	and	and	CCONJ
ejpam-6254	54	25	other	other	ADJ
ejpam-6254	54	26	public	public	ADJ
ejpam-6254	54	27	health	health	NOUN
ejpam-6254	54	28	measures	measure	NOUN
ejpam-6254	54	29	[	[	X
ejpam-6254	54	30	12	12	NUM
ejpam-6254	54	31	,	,	PUNCT
ejpam-6254	54	32	14	14	NUM
ejpam-6254	54	33	]	]	PUNCT
ejpam-6254	54	34	.	.	PUNCT
ejpam-6254	55	1	this	this	DET
ejpam-6254	55	2	framework	framework	NOUN
ejpam-6254	55	3	also	also	ADV
ejpam-6254	55	4	lays	lay	VERB
ejpam-6254	55	5	the	the	DET
ejpam-6254	55	6	groundwork	groundwork	NOUN
ejpam-6254	55	7	for	for	ADP
ejpam-6254	55	8	future	future	ADJ
ejpam-6254	55	9	epidemiological	epidemiological	ADJ
ejpam-6254	55	10	research	research	NOUN
ejpam-6254	55	11	,	,	PUNCT
ejpam-6254	55	12	enabling	enable	VERB
ejpam-6254	55	13	scientists	scientist	NOUN
ejpam-6254	55	14	to	to	PART
ejpam-6254	55	15	develop	develop	VERB
ejpam-6254	55	16	innovative	innovative	ADJ
ejpam-6254	55	17	approaches	approach	NOUN
ejpam-6254	55	18	for	for	ADP
ejpam-6254	55	19	disease	disease	NOUN
ejpam-6254	55	20	prevention	prevention	NOUN
ejpam-6254	55	21	and	and	CCONJ
ejpam-6254	55	22	health	health	NOUN
ejpam-6254	55	23	improvement	improvement	NOUN
ejpam-6254	55	24	[	[	X
ejpam-6254	55	25	9	9	NUM
ejpam-6254	55	26	]	]	PUNCT
ejpam-6254	55	27	.	.	PUNCT
ejpam-6254	56	1	ultimately	ultimately	ADV
ejpam-6254	56	2	,	,	PUNCT
ejpam-6254	56	3	studying	study	VERB
ejpam-6254	56	4	this	this	DET
ejpam-6254	56	5	model	model	NOUN
ejpam-6254	56	6	empowers	empower	VERB
ejpam-6254	56	7	researchers	researcher	NOUN
ejpam-6254	56	8	to	to	PART
ejpam-6254	56	9	contribute	contribute	VERB
ejpam-6254	56	10	significantly	significantly	ADV
ejpam-6254	56	11	to	to	ADP
ejpam-6254	56	12	efforts	effort	NOUN
ejpam-6254	56	13	aimed	aim	VERB
ejpam-6254	56	14	at	at	ADP
ejpam-6254	56	15	controlling	control	VERB
ejpam-6254	56	16	and	and	CCONJ
ejpam-6254	56	17	preventing	prevent	VERB
ejpam-6254	56	18	the	the	DET
ejpam-6254	56	19	spread	spread	NOUN
ejpam-6254	56	20	of	of	ADP
ejpam-6254	56	21	infectious	infectious	ADJ
ejpam-6254	56	22	diseases	disease	NOUN
ejpam-6254	56	23	,	,	PUNCT
ejpam-6254	56	24	thereby	thereby	ADV
ejpam-6254	56	25	saving	save	VERB
ejpam-6254	56	26	lives	life	NOUN
ejpam-6254	56	27	and	and	CCONJ
ejpam-6254	56	28	enhancing	enhance	VERB
ejpam-6254	56	29	public	public	ADJ
ejpam-6254	56	30	health	health	NOUN
ejpam-6254	56	31	outcomes	outcome	NOUN
ejpam-6254	56	32	[	[	X
ejpam-6254	56	33	12	12	NUM
ejpam-6254	56	34	]	]	PUNCT
ejpam-6254	56	35	.	.	PUNCT
ejpam-6254	57	1	this	this	DET
ejpam-6254	57	2	paper	paper	NOUN
ejpam-6254	57	3	is	be	AUX
ejpam-6254	57	4	structured	structure	VERB
ejpam-6254	57	5	as	as	SCONJ
ejpam-6254	57	6	follows	follow	VERB
ejpam-6254	57	7	:	:	PUNCT
ejpam-6254	57	8	in	in	ADP
ejpam-6254	57	9	section	section	NOUN
ejpam-6254	57	10	2	2	NUM
ejpam-6254	57	11	,	,	PUNCT
ejpam-6254	57	12	we	we	PRON
ejpam-6254	57	13	introduce	introduce	VERB
ejpam-6254	57	14	the	the	DET
ejpam-6254	57	15	mathematical	mathematical	ADJ
ejpam-6254	57	16	model	model	NOUN
ejpam-6254	57	17	with	with	ADP
ejpam-6254	57	18	time	time	NOUN
ejpam-6254	57	19	delay	delay	NOUN
ejpam-6254	57	20	and	and	CCONJ
ejpam-6254	57	21	its	its	PRON
ejpam-6254	57	22	solution	solution	NOUN
ejpam-6254	57	23	.	.	PUNCT
ejpam-6254	58	1	in	in	ADP
ejpam-6254	58	2	section	section	NOUN
ejpam-6254	58	3	3	3	NUM
ejpam-6254	58	4	,	,	PUNCT
ejpam-6254	58	5	we	we	PRON
ejpam-6254	58	6	formulate	formulate	VERB
ejpam-6254	58	7	the	the	DET
ejpam-6254	58	8	mathematical	mathematical	ADJ
ejpam-6254	58	9	epidemic	epidemic	NOUN
ejpam-6254	58	10	model	model	NOUN
ejpam-6254	58	11	seirv	seirv	NOUN
ejpam-6254	58	12	with	with	ADP
ejpam-6254	58	13	optimal	optimal	ADJ
ejpam-6254	58	14	control	control	NOUN
ejpam-6254	58	15	and	and	CCONJ
ejpam-6254	58	16	its	its	PRON
ejpam-6254	58	17	solution	solution	NOUN
ejpam-6254	58	18	are	be	AUX
ejpam-6254	58	19	find	find	ADJ
ejpam-6254	58	20	.	.	PUNCT
ejpam-6254	59	1	in	in	ADP
ejpam-6254	59	2	section	section	NOUN
ejpam-6254	59	3	4	4	NUM
ejpam-6254	59	4	,	,	PUNCT
ejpam-6254	59	5	we	we	PRON
ejpam-6254	59	6	provide	provide	VERB
ejpam-6254	59	7	a	a	DET
ejpam-6254	59	8	numerical	numerical	ADJ
ejpam-6254	59	9	method	method	NOUN
ejpam-6254	59	10	alongside	alongside	ADP
ejpam-6254	59	11	the	the	DET
ejpam-6254	59	12	relevant	relevant	ADJ
ejpam-6254	59	13	simulation	simulation	NOUN
ejpam-6254	59	14	results	result	VERB
ejpam-6254	59	15	.	.	PUNCT
ejpam-6254	60	1	in	in	ADP
ejpam-6254	60	2	summery	summery	ADJ
ejpam-6254	60	3	,	,	PUNCT
ejpam-6254	60	4	section	section	NOUN
ejpam-6254	60	5	5	5	NUM
ejpam-6254	60	6	compiles	compile	VERB
ejpam-6254	60	7	the	the	DET
ejpam-6254	60	8	final	final	ADJ
ejpam-6254	60	9	conclusion	conclusion	NOUN
ejpam-6254	60	10	and	and	CCONJ
ejpam-6254	60	11	discussion	discussion	NOUN
ejpam-6254	60	12	.	.	PUNCT
ejpam-6254	61	1	2	2	X
ejpam-6254	61	2	.	.	X
ejpam-6254	61	3	formulation	formulation	NOUN
ejpam-6254	61	4	of	of	ADP
ejpam-6254	61	5	seirv	seirv	NOUN
ejpam-6254	61	6	model	model	NOUN
ejpam-6254	61	7	with	with	ADP
ejpam-6254	61	8	time	time	NOUN
ejpam-6254	61	9	delay	delay	NOUN
ejpam-6254	61	10	in	in	ADP
ejpam-6254	61	11	this	this	DET
ejpam-6254	61	12	paper	paper	NOUN
ejpam-6254	61	13	,	,	PUNCT
ejpam-6254	61	14	we	we	PRON
ejpam-6254	61	15	consider	consider	VERB
ejpam-6254	61	16	the	the	DET
ejpam-6254	61	17	model	model	NOUN
ejpam-6254	61	18	presented	present	VERB
ejpam-6254	61	19	in	in	ADP
ejpam-6254	61	20	[	[	X
ejpam-6254	61	21	11	11	NUM
ejpam-6254	61	22	]	]	PUNCT
ejpam-6254	61	23	,	,	PUNCT
ejpam-6254	61	24	which	which	PRON
ejpam-6254	61	25	was	be	AUX
ejpam-6254	61	26	discussed	discuss	VERB
ejpam-6254	61	27	without	without	ADP
ejpam-6254	61	28	delay	delay	NOUN
ejpam-6254	61	29	and	and	CCONJ
ejpam-6254	61	30	optimal	optimal	ADJ
ejpam-6254	61	31	control	control	NOUN
ejpam-6254	61	32	.	.	PUNCT
ejpam-6254	62	1	in	in	ADP
ejpam-6254	62	2	their	their	PRON
ejpam-6254	62	3	model	model	NOUN
ejpam-6254	62	4	,	,	PUNCT
ejpam-6254	62	5	they	they	PRON
ejpam-6254	62	6	have	have	AUX
ejpam-6254	62	7	divided	divide	VERB
ejpam-6254	62	8	the	the	DET
ejpam-6254	62	9	total	total	ADJ
ejpam-6254	62	10	population	population	NOUN
ejpam-6254	62	11	n(t	n(t	PROPN
ejpam-6254	62	12	)	)	PUNCT
ejpam-6254	62	13	at	at	ADP
ejpam-6254	62	14	time	time	NOUN
ejpam-6254	62	15	t	t	X
ejpam-6254	62	16	>	>	X
ejpam-6254	62	17	0	0	PUNCT
ejpam-6254	62	18	into	into	ADP
ejpam-6254	62	19	five	five	NUM
ejpam-6254	62	20	compartments	compartment	NOUN
ejpam-6254	62	21	.	.	PUNCT
ejpam-6254	63	1	these	these	PRON
ejpam-6254	63	2	are	be	AUX
ejpam-6254	63	3	s(t	s(t	ADJ
ejpam-6254	63	4	)	)	PUNCT
ejpam-6254	63	5	susceptible	susceptible	ADJ
ejpam-6254	63	6	populations	population	NOUN
ejpam-6254	63	7	that	that	PRON
ejpam-6254	63	8	are	be	AUX
ejpam-6254	63	9	at	at	ADP
ejpam-6254	63	10	risk	risk	NOUN
ejpam-6254	63	11	of	of	ADP
ejpam-6254	63	12	infection	infection	NOUN
ejpam-6254	63	13	but	but	CCONJ
ejpam-6254	63	14	have	have	AUX
ejpam-6254	63	15	not	not	PART
ejpam-6254	63	16	been	be	AUX
ejpam-6254	63	17	exposed	expose	VERB
ejpam-6254	63	18	to	to	ADP
ejpam-6254	63	19	the	the	DET
ejpam-6254	63	20	infected	infect	VERB
ejpam-6254	63	21	yet	yet	ADV
ejpam-6254	63	22	,	,	PUNCT
ejpam-6254	63	23	exposed	expose	VERB
ejpam-6254	63	24	e(t	e(t	NOUN
ejpam-6254	63	25	)	)	PUNCT
ejpam-6254	63	26	des	des	PROPN
ejpam-6254	63	27	.	.	PROPN
ejpam-6254	63	28	irum	irum	PROPN
ejpam-6254	63	29	et	et	PROPN
ejpam-6254	63	30	al	al	PROPN
ejpam-6254	63	31	.	.	PUNCT
ejpam-6254	63	32	/	/	SYM
ejpam-6254	63	33	eur	eur	PROPN
ejpam-6254	63	34	.	.	PUNCT
ejpam-6254	64	1	j.	j.	PROPN
ejpam-6254	64	2	pure	pure	PROPN
ejpam-6254	64	3	appl	appl	PROPN
ejpam-6254	64	4	.	.	PROPN
ejpam-6254	64	5	math	math	PROPN
ejpam-6254	64	6	,	,	PUNCT
ejpam-6254	64	7	18	18	NUM
ejpam-6254	64	8	(	(	PUNCT
ejpam-6254	64	9	4	4	NUM
ejpam-6254	64	10	)	)	PUNCT
ejpam-6254	64	11	(	(	PUNCT
ejpam-6254	64	12	2025	2025	NUM
ejpam-6254	64	13	)	)	PUNCT
ejpam-6254	64	14	,	,	PUNCT
ejpam-6254	64	15	6254	6254	NUM
ejpam-6254	64	16	4	4	NUM
ejpam-6254	64	17	of	of	ADP
ejpam-6254	64	18	23	23	NUM
ejpam-6254	64	19	notes	note	NOUN
ejpam-6254	64	20	the	the	DET
ejpam-6254	64	21	exposed	expose	VERB
ejpam-6254	64	22	population	population	NOUN
ejpam-6254	64	23	that	that	PRON
ejpam-6254	64	24	has	have	AUX
ejpam-6254	64	25	come	come	VERB
ejpam-6254	64	26	into	into	ADP
ejpam-6254	64	27	contact	contact	NOUN
ejpam-6254	64	28	with	with	ADP
ejpam-6254	64	29	the	the	DET
ejpam-6254	64	30	infected	infected	ADJ
ejpam-6254	64	31	people	people	NOUN
ejpam-6254	64	32	but	but	CCONJ
ejpam-6254	64	33	is	be	AUX
ejpam-6254	64	34	not	not	PART
ejpam-6254	64	35	infectious	infectious	ADJ
ejpam-6254	64	36	.	.	PUNCT
ejpam-6254	65	1	these	these	DET
ejpam-6254	65	2	people	people	NOUN
ejpam-6254	65	3	are	be	AUX
ejpam-6254	65	4	in	in	ADP
ejpam-6254	65	5	a	a	DET
ejpam-6254	65	6	latent	latent	NOUN
ejpam-6254	65	7	state	state	NOUN
ejpam-6254	65	8	,	,	PUNCT
ejpam-6254	65	9	i(t	i(t	PROPN
ejpam-6254	65	10	)	)	PUNCT
ejpam-6254	65	11	refers	refer	VERB
ejpam-6254	65	12	to	to	ADP
ejpam-6254	65	13	infectious	infectious	ADJ
ejpam-6254	65	14	people	people	NOUN
ejpam-6254	65	15	that	that	PRON
ejpam-6254	65	16	spread	spread	VERB
ejpam-6254	65	17	the	the	DET
ejpam-6254	65	18	infection	infection	NOUN
ejpam-6254	65	19	to	to	ADP
ejpam-6254	65	20	other	other	ADJ
ejpam-6254	65	21	people	people	NOUN
ejpam-6254	65	22	,	,	PUNCT
ejpam-6254	65	23	r(t	r(t	NOUN
ejpam-6254	65	24	)	)	PUNCT
ejpam-6254	65	25	indicates	indicate	VERB
ejpam-6254	65	26	recovered	recover	VERB
ejpam-6254	65	27	people	people	NOUN
ejpam-6254	65	28	who	who	PRON
ejpam-6254	65	29	are	be	AUX
ejpam-6254	65	30	no	no	ADV
ejpam-6254	65	31	longer	long	ADV
ejpam-6254	65	32	infected	infect	VERB
ejpam-6254	65	33	by	by	ADP
ejpam-6254	65	34	the	the	DET
ejpam-6254	65	35	infection	infection	NOUN
ejpam-6254	65	36	.	.	PUNCT
ejpam-6254	66	1	,	,	PUNCT
ejpam-6254	66	2	and	and	CCONJ
ejpam-6254	66	3	v	v	NOUN
ejpam-6254	66	4	(	(	PUNCT
ejpam-6254	66	5	t	t	PROPN
ejpam-6254	66	6	)	)	PUNCT
ejpam-6254	66	7	stands	stand	VERB
ejpam-6254	66	8	for	for	ADP
ejpam-6254	66	9	the	the	DET
ejpam-6254	66	10	vaccinated	vaccinated	ADJ
ejpam-6254	66	11	population	population	NOUN
ejpam-6254	66	12	.	.	PUNCT
ejpam-6254	67	1	therefore	therefore	ADV
ejpam-6254	67	2	n(t)=s(t)+e(t)+i(t)+r(t)+v	n(t)=s(t)+e(t)+i(t)+r(t)+v	ADV
ejpam-6254	67	3	(	(	PUNCT
ejpam-6254	67	4	t	t	PROPN
ejpam-6254	67	5	)	)	PUNCT
ejpam-6254	67	6	.	.	PUNCT
ejpam-6254	68	1	each	each	DET
ejpam-6254	68	2	compartment	compartment	NOUN
ejpam-6254	68	3	presents	present	VERB
ejpam-6254	68	4	a	a	DET
ejpam-6254	68	5	unique	unique	ADJ
ejpam-6254	68	6	scenarios.for	scenarios.for	PUNCT
ejpam-6254	68	7	example	example	NOUN
ejpam-6254	68	8	the	the	DET
ejpam-6254	68	9	population	population	NOUN
ejpam-6254	68	10	of	of	ADP
ejpam-6254	68	11	s(t	s(t	PROPN
ejpam-6254	68	12	)	)	PUNCT
ejpam-6254	68	13	compartment	compartment	NOUN
ejpam-6254	68	14	increased	increase	VERB
ejpam-6254	68	15	by	by	ADP
ejpam-6254	68	16	recruitment	recruitment	NOUN
ejpam-6254	68	17	rate	rate	NOUN
ejpam-6254	68	18	∆	∆	PROPN
ejpam-6254	68	19	and	and	CCONJ
ejpam-6254	68	20	passed	pass	VERB
ejpam-6254	68	21	away	away	ADP
ejpam-6254	68	22	naturally	naturally	ADV
ejpam-6254	68	23	at	at	ADP
ejpam-6254	68	24	a	a	DET
ejpam-6254	68	25	rate	rate	NOUN
ejpam-6254	68	26	of	of	ADP
ejpam-6254	68	27	µ	µ	NUM
ejpam-6254	68	28	,	,	PUNCT
ejpam-6254	68	29	vaccination	vaccination	NOUN
ejpam-6254	68	30	at	at	ADP
ejpam-6254	68	31	a	a	DET
ejpam-6254	68	32	rate	rate	NOUN
ejpam-6254	68	33	of	of	ADP
ejpam-6254	68	34	γ2	γ2	NOUN
ejpam-6254	68	35	and	and	CCONJ
ejpam-6254	68	36	transmission	transmission	NOUN
ejpam-6254	68	37	at	at	ADP
ejpam-6254	68	38	a	a	DET
ejpam-6254	68	39	rate	rate	NOUN
ejpam-6254	68	40	of	of	ADP
ejpam-6254	68	41	β	β	NOUN
ejpam-6254	68	42	with	with	ADP
ejpam-6254	68	43	term	term	NOUN
ejpam-6254	68	44	βsi	βsi	NOUN
ejpam-6254	68	45	1+αi	1+αi	NUM
ejpam-6254	68	46	,	,	PUNCT
ejpam-6254	68	47	where	where	SCONJ
ejpam-6254	68	48	α	α	PRON
ejpam-6254	68	49	being	be	AUX
ejpam-6254	68	50	the	the	DET
ejpam-6254	68	51	saturated	saturate	VERB
ejpam-6254	68	52	rate.the	rate.the	ADJ
ejpam-6254	68	53	population	population	NOUN
ejpam-6254	68	54	of	of	ADP
ejpam-6254	68	55	e(t	e(t	PROPN
ejpam-6254	68	56	)	)	PUNCT
ejpam-6254	68	57	compartment	compartment	NOUN
ejpam-6254	68	58	passed	pass	VERB
ejpam-6254	68	59	away	away	ADP
ejpam-6254	68	60	naturally	naturally	ADV
ejpam-6254	68	61	at	at	ADP
ejpam-6254	68	62	a	a	DET
ejpam-6254	68	63	rate	rate	NOUN
ejpam-6254	68	64	of	of	ADP
ejpam-6254	68	65	µ	µ	NOUN
ejpam-6254	68	66	,	,	PUNCT
ejpam-6254	68	67	with	with	ADP
ejpam-6254	68	68	latency	latency	NOUN
ejpam-6254	68	69	period	period	NOUN
ejpam-6254	68	70	σ	σ	PROPN
ejpam-6254	68	71	.	.	PUNCT
ejpam-6254	69	1	the	the	DET
ejpam-6254	69	2	population	population	NOUN
ejpam-6254	69	3	of	of	ADP
ejpam-6254	69	4	i(t	i(t	PROPN
ejpam-6254	69	5	)	)	PUNCT
ejpam-6254	69	6	compartment	compartment	NOUN
ejpam-6254	69	7	decreased	decrease	VERB
ejpam-6254	69	8	by	by	ADP
ejpam-6254	69	9	natural	natural	ADJ
ejpam-6254	69	10	death	death	NOUN
ejpam-6254	69	11	at	at	ADP
ejpam-6254	69	12	a	a	DET
ejpam-6254	69	13	rate	rate	NOUN
ejpam-6254	69	14	of	of	ADP
ejpam-6254	69	15	µ	µ	NOUN
ejpam-6254	69	16	,	,	PUNCT
ejpam-6254	69	17	with	with	ADP
ejpam-6254	69	18	speed	speed	NOUN
ejpam-6254	69	19	of	of	ADP
ejpam-6254	69	20	recovery	recovery	NOUN
ejpam-6254	69	21	rate	rate	NOUN
ejpam-6254	69	22	γ1	γ1	PROPN
ejpam-6254	69	23	.	.	PUNCT
ejpam-6254	70	1	the	the	DET
ejpam-6254	70	2	population	population	NOUN
ejpam-6254	70	3	of	of	ADP
ejpam-6254	70	4	the	the	DET
ejpam-6254	70	5	r(t	r(t	NOUN
ejpam-6254	70	6	)	)	PUNCT
ejpam-6254	70	7	compartment	compartment	NOUN
ejpam-6254	70	8	decreased	decrease	VERB
ejpam-6254	70	9	of	of	ADP
ejpam-6254	70	10	natural	natural	ADJ
ejpam-6254	70	11	causes	cause	NOUN
ejpam-6254	70	12	at	at	ADP
ejpam-6254	70	13	a	a	DET
ejpam-6254	70	14	rate	rate	NOUN
ejpam-6254	70	15	of	of	ADP
ejpam-6254	70	16	µ	µ	NOUN
ejpam-6254	70	17	,	,	PUNCT
ejpam-6254	70	18	and	and	CCONJ
ejpam-6254	70	19	vaccinated	vaccinate	VERB
ejpam-6254	70	20	at	at	ADP
ejpam-6254	70	21	a	a	DET
ejpam-6254	70	22	rate	rate	NOUN
ejpam-6254	70	23	of	of	ADP
ejpam-6254	70	24	γ3	γ3	NOUN
ejpam-6254	70	25	.	.	PUNCT
ejpam-6254	71	1	similarly	similarly	ADV
ejpam-6254	71	2	,	,	PUNCT
ejpam-6254	71	3	the	the	DET
ejpam-6254	71	4	population	population	NOUN
ejpam-6254	71	5	of	of	ADP
ejpam-6254	71	6	the	the	DET
ejpam-6254	71	7	v	v	NOUN
ejpam-6254	71	8	(	(	PUNCT
ejpam-6254	71	9	t	t	NOUN
ejpam-6254	71	10	)	)	PUNCT
ejpam-6254	71	11	compartment	compartment	NOUN
ejpam-6254	71	12	passed	pass	VERB
ejpam-6254	71	13	away	away	ADP
ejpam-6254	71	14	naturally	naturally	ADV
ejpam-6254	71	15	at	at	ADP
ejpam-6254	71	16	a	a	DET
ejpam-6254	71	17	rate	rate	NOUN
ejpam-6254	71	18	of	of	ADP
ejpam-6254	71	19	µ.	µ.	NOUN
ejpam-6254	71	20	however	however	ADV
ejpam-6254	71	21	,	,	PUNCT
ejpam-6254	71	22	delay	delay	NOUN
ejpam-6254	71	23	and	and	CCONJ
ejpam-6254	71	24	optimal	optimal	ADJ
ejpam-6254	71	25	control	control	NOUN
ejpam-6254	71	26	play	play	VERB
ejpam-6254	71	27	a	a	DET
ejpam-6254	71	28	crucial	crucial	ADJ
ejpam-6254	71	29	role	role	NOUN
ejpam-6254	71	30	in	in	ADP
ejpam-6254	71	31	the	the	DET
ejpam-6254	71	32	dynamics	dynamic	NOUN
ejpam-6254	71	33	of	of	ADP
ejpam-6254	71	34	epidemic	epidemic	NOUN
ejpam-6254	71	35	models	model	NOUN
ejpam-6254	71	36	.	.	PUNCT
ejpam-6254	72	1	therefore	therefore	ADV
ejpam-6254	72	2	,	,	PUNCT
ejpam-6254	72	3	in	in	ADP
ejpam-6254	72	4	this	this	DET
ejpam-6254	72	5	study	study	NOUN
ejpam-6254	72	6	,	,	PUNCT
ejpam-6254	72	7	we	we	PRON
ejpam-6254	72	8	investigate	investigate	VERB
ejpam-6254	72	9	a	a	DET
ejpam-6254	72	10	system	system	NOUN
ejpam-6254	72	11	of	of	ADP
ejpam-6254	72	12	differential	differential	ADJ
ejpam-6254	72	13	equations	equation	NOUN
ejpam-6254	72	14	incorporating	incorporate	VERB
ejpam-6254	72	15	time	time	NOUN
ejpam-6254	72	16	delays	delay	NOUN
ejpam-6254	72	17	to	to	PART
ejpam-6254	72	18	capture	capture	VERB
ejpam-6254	72	19	these	these	DET
ejpam-6254	72	20	essential	essential	ADJ
ejpam-6254	72	21	effects	effect	NOUN
ejpam-6254	72	22	more	more	ADV
ejpam-6254	72	23	accurately	accurately	ADV
ejpam-6254	72	24	.	.	PUNCT
ejpam-6254	73	1	here	here	ADV
ejpam-6254	73	2	τ	τ	X
ejpam-6254	73	3	>	>	X
ejpam-6254	73	4	0	0	NUM
ejpam-6254	73	5	represents	represent	VERB
ejpam-6254	73	6	the	the	DET
ejpam-6254	73	7	response	response	NOUN
ejpam-6254	73	8	time	time	NOUN
ejpam-6254	73	9	of	of	ADP
ejpam-6254	73	10	disease	disease	NOUN
ejpam-6254	73	11	,	,	PUNCT
ejpam-6254	73	12	which	which	PRON
ejpam-6254	73	13	follows	follow	VERB
ejpam-6254	73	14	a	a	DET
ejpam-6254	73	15	similar	similar	ADJ
ejpam-6254	73	16	argument	argument	NOUN
ejpam-6254	73	17	in	in	ADP
ejpam-6254	73	18	[	[	X
ejpam-6254	73	19	15	15	NUM
ejpam-6254	73	20	,	,	PUNCT
ejpam-6254	73	21	16	16	NUM
ejpam-6254	73	22	]	]	PUNCT
ejpam-6254	73	23	in	in	ADP
ejpam-6254	73	24	the	the	DET
ejpam-6254	73	25	model	model	NOUN
ejpam-6254	73	26	presented	present	VERB
ejpam-6254	73	27	in	in	ADP
ejpam-6254	73	28	[	[	X
ejpam-6254	73	29	11	11	NUM
ejpam-6254	73	30	]	]	PUNCT
ejpam-6254	73	31	.	.	PUNCT
ejpam-6254	74	1	the	the	DET
ejpam-6254	74	2	model	model	NOUN
ejpam-6254	74	3	is	be	AUX
ejpam-6254	74	4	as	as	SCONJ
ejpam-6254	74	5	follows	follow	VERB
ejpam-6254	74	6	for	for	ADP
ejpam-6254	74	7	the	the	DET
ejpam-6254	74	8	seirv	seirv	NOUN
ejpam-6254	74	9	framework	framework	NOUN
ejpam-6254	74	10	.	.	PUNCT
ejpam-6254	75	1	ds(t	ds(t	NOUN
ejpam-6254	75	2	)	)	PUNCT
ejpam-6254	75	3	dt	dt	NOUN
ejpam-6254	76	1	=	=	PUNCT
ejpam-6254	76	2	∆−	∆−	NOUN
ejpam-6254	76	3	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	76	4	)	)	PUNCT
ejpam-6254	76	5	1	1	NUM
ejpam-6254	76	6	+	+	NUM
ejpam-6254	76	7	αi(t	αi(t	NOUN
ejpam-6254	76	8	)	)	PUNCT
ejpam-6254	76	9	−	−	PROPN
ejpam-6254	76	10	µs(t)−	µs(t)−	PROPN
ejpam-6254	76	11	γ2s(t	γ2s(t	PROPN
ejpam-6254	76	12	)	)	PUNCT
ejpam-6254	76	13	,	,	PUNCT
ejpam-6254	76	14	de(t	de(t	X
ejpam-6254	76	15	)	)	PUNCT
ejpam-6254	76	16	dt	dt	NOUN
ejpam-6254	77	1	=	=	SYM
ejpam-6254	77	2	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	77	3	)	)	PUNCT
ejpam-6254	77	4	1	1	NUM
ejpam-6254	77	5	+	+	NUM
ejpam-6254	77	6	αi(t	αi(t	NOUN
ejpam-6254	77	7	)	)	PUNCT
ejpam-6254	77	8	−	−	PROPN
ejpam-6254	77	9	σe(t−	σe(t−	PROPN
ejpam-6254	77	10	τ)−	τ)−	PROPN
ejpam-6254	77	11	µe(t	µe(t	PRON
ejpam-6254	77	12	)	)	PUNCT
ejpam-6254	77	13	,	,	PUNCT
ejpam-6254	77	14	di(t	di(t	NOUN
ejpam-6254	77	15	)	)	PUNCT
ejpam-6254	77	16	dt	dt	NOUN
ejpam-6254	78	1	=	=	SYM
ejpam-6254	78	2	σe(t−	σe(t−	PROPN
ejpam-6254	78	3	τ)−	τ)−	PROPN
ejpam-6254	78	4	γ1i(t)−	γ1i(t)−	PROPN
ejpam-6254	78	5	µi(t	µi(t	ADP
ejpam-6254	78	6	)	)	PUNCT
ejpam-6254	78	7	,	,	PUNCT
ejpam-6254	78	8	dr(t	dr(t	NUM
ejpam-6254	78	9	)	)	PUNCT
ejpam-6254	78	10	dt	dt	X
ejpam-6254	79	1	=	=	SYM
ejpam-6254	79	2	γ1i(t)−	γ1i(t)−	PROPN
ejpam-6254	79	3	γ3r(t)−	γ3r(t)−	PROPN
ejpam-6254	79	4	µr(t	µr(t	NUM
ejpam-6254	79	5	)	)	PUNCT
ejpam-6254	79	6	,	,	PUNCT
ejpam-6254	79	7	dv	dv	PROPN
ejpam-6254	79	8	(	(	PUNCT
ejpam-6254	79	9	t	t	PROPN
ejpam-6254	79	10	)	)	PUNCT
ejpam-6254	79	11	dt	dt	NOUN
ejpam-6254	79	12	=	=	SYM
ejpam-6254	79	13	γ2s(t	γ2s(t	PROPN
ejpam-6254	79	14	)	)	PUNCT
ejpam-6254	79	15	+	+	CCONJ
ejpam-6254	79	16	γ3r(t)−	γ3r(t)−	PROPN
ejpam-6254	79	17	µv	µv	PROPN
ejpam-6254	79	18	(	(	PUNCT
ejpam-6254	79	19	t	t	PROPN
ejpam-6254	79	20	)	)	PUNCT
ejpam-6254	79	21	.	.	PUNCT
ejpam-6254	80	1	(	(	PUNCT
ejpam-6254	80	2	1	1	X
ejpam-6254	80	3	)	)	PUNCT
ejpam-6254	80	4	the	the	DET
ejpam-6254	80	5	initial	initial	ADJ
ejpam-6254	80	6	conditions	condition	NOUN
ejpam-6254	80	7	of	of	ADP
ejpam-6254	80	8	the	the	DET
ejpam-6254	80	9	above	above	ADJ
ejpam-6254	80	10	system	system	NOUN
ejpam-6254	80	11	as	as	SCONJ
ejpam-6254	80	12	follows	follow	VERB
ejpam-6254	80	13	:	:	PUNCT
ejpam-6254	80	14	{	{	PUNCT
ejpam-6254	80	15	s(0	s(0	PROPN
ejpam-6254	80	16	)	)	PUNCT
ejpam-6254	80	17	=	=	PUNCT
ejpam-6254	81	1	s(θ	s(θ	PROPN
ejpam-6254	81	2	)	)	PUNCT
ejpam-6254	81	3	>	>	X
ejpam-6254	81	4	0	0	NUM
ejpam-6254	81	5	,	,	PUNCT
ejpam-6254	81	6	e(0	e(0	NOUN
ejpam-6254	81	7	)	)	PUNCT
ejpam-6254	81	8	=	=	SYM
ejpam-6254	81	9	e(θ	e(θ	ADJ
ejpam-6254	81	10	)	)	PUNCT
ejpam-6254	81	11	≥	≥	NOUN
ejpam-6254	81	12	0	0	NUM
ejpam-6254	81	13	,	,	PUNCT
ejpam-6254	81	14	i(0	i(0	PROPN
ejpam-6254	81	15	)	)	PUNCT
ejpam-6254	81	16	=	=	SYM
ejpam-6254	81	17	i(θ	i(θ	PROPN
ejpam-6254	81	18	)	)	PUNCT
ejpam-6254	81	19	≥	≥	NOUN
ejpam-6254	81	20	0	0	NUM
ejpam-6254	81	21	,	,	PUNCT
ejpam-6254	81	22	r(0	r(0	PROPN
ejpam-6254	81	23	)	)	PUNCT
ejpam-6254	81	24	=	=	SYM
ejpam-6254	81	25	r(θ	r(θ	NOUN
ejpam-6254	81	26	)	)	PUNCT
ejpam-6254	81	27	≥	≥	NOUN
ejpam-6254	81	28	0	0	NUM
ejpam-6254	81	29	,	,	PUNCT
ejpam-6254	81	30	v	v	NOUN
ejpam-6254	81	31	(	(	PUNCT
ejpam-6254	81	32	0	0	NUM
ejpam-6254	81	33	)	)	PUNCT
ejpam-6254	81	34	=	=	NOUN
ejpam-6254	81	35	v	v	X
ejpam-6254	81	36	(	(	PUNCT
ejpam-6254	81	37	θ	θ	NOUN
ejpam-6254	81	38	)	)	PUNCT
ejpam-6254	81	39	≥	≥	NOUN
ejpam-6254	81	40	0	0	NUM
ejpam-6254	81	41	,	,	PUNCT
ejpam-6254	81	42	(	(	PUNCT
ejpam-6254	81	43	2	2	NUM
ejpam-6254	81	44	)	)	PUNCT
ejpam-6254	81	45	where	where	SCONJ
ejpam-6254	81	46	,	,	PUNCT
ejpam-6254	81	47	θ	θ	PROPN
ejpam-6254	81	48	∈	∈	PROPN
ejpam-6254	82	1	[	[	X
ejpam-6254	82	2	−τ	−τ	NOUN
ejpam-6254	82	3	,	,	PUNCT
ejpam-6254	82	4	0	0	NUM
ejpam-6254	82	5	]	]	PUNCT
ejpam-6254	82	6	is	be	AUX
ejpam-6254	82	7	assumed	assume	VERB
ejpam-6254	82	8	.	.	PUNCT
ejpam-6254	83	1	the	the	DET
ejpam-6254	83	2	proposed	propose	VERB
ejpam-6254	83	3	model	model	NOUN
ejpam-6254	83	4	has	have	VERB
ejpam-6254	83	5	two	two	NUM
ejpam-6254	83	6	equilibrium	equilibrium	NOUN
ejpam-6254	83	7	points	point	NOUN
ejpam-6254	83	8	that	that	PRON
ejpam-6254	83	9	are	be	AUX
ejpam-6254	83	10	disease	disease	NOUN
ejpam-6254	83	11	-	-	PUNCT
ejpam-6254	83	12	free	free	ADJ
ejpam-6254	83	13	equilibrium	equilibrium	NOUN
ejpam-6254	83	14	point	point	NOUN
ejpam-6254	83	15	:	:	PUNCT
ejpam-6254	83	16	e0(s0.e0	e0(s0.e0	NOUN
ejpam-6254	83	17	,	,	PUNCT
ejpam-6254	83	18	i0	i0	PROPN
ejpam-6254	83	19	,	,	PUNCT
ejpam-6254	83	20	r0	r0	NOUN
ejpam-6254	83	21	,	,	PUNCT
ejpam-6254	83	22	v0	v0	NOUN
ejpam-6254	83	23	)	)	PUNCT
ejpam-6254	84	1	=	=	SYM
ejpam-6254	84	2	e0	e0	PROPN
ejpam-6254	84	3	(	(	PUNCT
ejpam-6254	84	4	λ	λ	X
ejpam-6254	84	5	µ+γ2	µ+γ2	PROPN
ejpam-6254	84	6	,	,	PUNCT
ejpam-6254	84	7	0	0	NUM
ejpam-6254	84	8	,	,	PUNCT
ejpam-6254	84	9	0	0	NUM
ejpam-6254	84	10	,	,	PUNCT
ejpam-6254	84	11	0	0	NUM
ejpam-6254	84	12	,	,	PUNCT
ejpam-6254	84	13	γ2λ	γ2λ	PROPN
ejpam-6254	84	14	µ(µ+γ2	µ(µ+γ2	PROPN
ejpam-6254	84	15	)	)	PUNCT
ejpam-6254	84	16	)	)	PUNCT
ejpam-6254	84	17	,	,	PUNCT
ejpam-6254	84	18	and	and	CCONJ
ejpam-6254	84	19	endemic	endemic	ADJ
ejpam-6254	84	20	equilibrium	equilibrium	NOUN
ejpam-6254	84	21	point	point	NOUN
ejpam-6254	84	22	:	:	PUNCT
ejpam-6254	84	23	e∗(s∗.e∗	e∗(s∗.e∗	NOUN
ejpam-6254	84	24	,	,	PUNCT
ejpam-6254	84	25	i∗	i∗	NOUN
ejpam-6254	84	26	,	,	PUNCT
ejpam-6254	84	27	r∗	r∗	PROPN
ejpam-6254	84	28	,	,	PUNCT
ejpam-6254	84	29	v∗	v∗	ADJ
ejpam-6254	84	30	)	)	PUNCT
ejpam-6254	84	31	=	=	SYM
ejpam-6254	84	32	e∗	e∗	NOUN
ejpam-6254	84	33	(	(	PUNCT
ejpam-6254	84	34	(	(	PUNCT
ejpam-6254	84	35	σ+µ)(γ1+µ)(1+αi∗	σ+µ)(γ1+µ)(1+αi∗	NOUN
ejpam-6254	84	36	)	)	PUNCT
ejpam-6254	84	37	βσ	βσ	X
ejpam-6254	84	38	,	,	PUNCT
ejpam-6254	84	39	(	(	PUNCT
ejpam-6254	84	40	γ1+µ)(γ2+µ)(r0−1	γ1+µ)(γ2+µ)(r0−1	ADJ
ejpam-6254	84	41	)	)	PUNCT
ejpam-6254	84	42	σ(β+α(µ+γ2	σ(β+α(µ+γ2	NOUN
ejpam-6254	84	43	)	)	PUNCT
ejpam-6254	84	44	)	)	PUNCT
ejpam-6254	84	45	,	,	PUNCT
ejpam-6254	84	46	(	(	PUNCT
ejpam-6254	84	47	µ+γ2)(r0−1	µ+γ2)(r0−1	NOUN
ejpam-6254	84	48	)	)	PUNCT
ejpam-6254	84	49	β+α(µ+γ2	β+α(µ+γ2	NOUN
ejpam-6254	84	50	)	)	PUNCT
ejpam-6254	84	51	,	,	PUNCT
ejpam-6254	84	52	γ1(r0−1	γ1(r0−1	NOUN
ejpam-6254	84	53	)	)	PUNCT
ejpam-6254	84	54	β+α(µ+γ2	β+α(µ+γ2	NOUN
ejpam-6254	84	55	)	)	PUNCT
ejpam-6254	84	56	,	,	PUNCT
ejpam-6254	84	57	γ2(s∗+r∗	γ2(s∗+r∗	PROPN
ejpam-6254	84	58	)	)	PUNCT
ejpam-6254	84	59	µ	µ	PROPN
ejpam-6254	84	60	)	)	PUNCT
ejpam-6254	84	61	.	.	PUNCT
ejpam-6254	85	1	reproductive	reproductive	ADJ
ejpam-6254	85	2	number	number	NOUN
ejpam-6254	85	3	is	be	AUX
ejpam-6254	85	4	give	give	VERB
ejpam-6254	85	5	as	as	ADP
ejpam-6254	85	6	:	:	PUNCT
ejpam-6254	85	7	r0	r0	NOUN
ejpam-6254	85	8	=	=	SYM
ejpam-6254	85	9	βλσ	βλσ	PROPN
ejpam-6254	85	10	(	(	PUNCT
ejpam-6254	85	11	σ+µ)(γ1+µ)(γ2+µ	σ+µ)(γ1+µ)(γ2+µ	NOUN
ejpam-6254	85	12	)	)	PUNCT
ejpam-6254	85	13	.	.	PUNCT
ejpam-6254	86	1	on	on	ADP
ejpam-6254	86	2	the	the	DET
ejpam-6254	86	3	same	same	ADJ
ejpam-6254	86	4	way	way	NOUN
ejpam-6254	86	5	,	,	PUNCT
ejpam-6254	86	6	the	the	DET
ejpam-6254	86	7	first	first	ADJ
ejpam-6254	86	8	three	three	NUM
ejpam-6254	86	9	equations	equation	NOUN
ejpam-6254	86	10	of	of	ADP
ejpam-6254	86	11	system	system	NOUN
ejpam-6254	86	12	(	(	PUNCT
ejpam-6254	86	13	1	1	X
ejpam-6254	86	14	)	)	PUNCT
ejpam-6254	86	15	are	be	AUX
ejpam-6254	86	16	independent	independent	ADJ
ejpam-6254	86	17	of	of	ADP
ejpam-6254	86	18	fourth	fourth	ADJ
ejpam-6254	86	19	and	and	CCONJ
ejpam-6254	86	20	fifth	fifth	ADJ
ejpam-6254	86	21	variables	variable	NOUN
ejpam-6254	86	22	r	r	NOUN
ejpam-6254	86	23	and	and	CCONJ
ejpam-6254	86	24	v	v	NOUN
ejpam-6254	86	25	,	,	PUNCT
ejpam-6254	86	26	enabling	enable	VERB
ejpam-6254	86	27	us	we	PRON
ejpam-6254	86	28	to	to	PART
ejpam-6254	86	29	analyze	analyze	VERB
ejpam-6254	86	30	the	the	DET
ejpam-6254	86	31	system	system	NOUN
ejpam-6254	86	32	by	by	ADP
ejpam-6254	86	33	examining	examine	VERB
ejpam-6254	86	34	the	the	DET
ejpam-6254	86	35	subsystem	subsystem	NOUN
ejpam-6254	86	36	,	,	PUNCT
ejpam-6254	86	37	s.	s.	PROPN
ejpam-6254	86	38	irum	irum	PROPN
ejpam-6254	86	39	et	et	PROPN
ejpam-6254	86	40	al	al	PROPN
ejpam-6254	86	41	.	.	PUNCT
ejpam-6254	86	42	/	/	SYM
ejpam-6254	86	43	eur	eur	PROPN
ejpam-6254	86	44	.	.	PUNCT
ejpam-6254	87	1	j.	j.	PROPN
ejpam-6254	87	2	pure	pure	PROPN
ejpam-6254	87	3	appl	appl	PROPN
ejpam-6254	87	4	.	.	PROPN
ejpam-6254	87	5	math	math	PROPN
ejpam-6254	87	6	,	,	PUNCT
ejpam-6254	87	7	18	18	NUM
ejpam-6254	87	8	(	(	PUNCT
ejpam-6254	87	9	4	4	NUM
ejpam-6254	87	10	)	)	PUNCT
ejpam-6254	87	11	(	(	PUNCT
ejpam-6254	87	12	2025	2025	NUM
ejpam-6254	87	13	)	)	PUNCT
ejpam-6254	87	14	,	,	PUNCT
ejpam-6254	87	15	6254	6254	NUM
ejpam-6254	87	16	5	5	NUM
ejpam-6254	87	17	of	of	ADP
ejpam-6254	87	18	23	23	NUM
ejpam-6254	87	19	as	as	ADP
ejpam-6254	87	20	ds(t	ds(t	NOUN
ejpam-6254	87	21	)	)	PUNCT
ejpam-6254	87	22	dt	dt	NOUN
ejpam-6254	88	1	=	=	PUNCT
ejpam-6254	88	2	∆−	∆−	NOUN
ejpam-6254	88	3	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	88	4	)	)	PUNCT
ejpam-6254	88	5	1	1	NUM
ejpam-6254	88	6	+	+	NUM
ejpam-6254	88	7	αi(t	αi(t	NOUN
ejpam-6254	88	8	)	)	PUNCT
ejpam-6254	88	9	−	−	PROPN
ejpam-6254	88	10	µs(t)−	µs(t)−	PROPN
ejpam-6254	88	11	γ2s(t	γ2s(t	PROPN
ejpam-6254	88	12	)	)	PUNCT
ejpam-6254	88	13	,	,	PUNCT
ejpam-6254	88	14	de(t	de(t	X
ejpam-6254	88	15	)	)	PUNCT
ejpam-6254	88	16	dt	dt	NOUN
ejpam-6254	89	1	=	=	SYM
ejpam-6254	89	2	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	89	3	)	)	PUNCT
ejpam-6254	89	4	1	1	NUM
ejpam-6254	89	5	+	+	NUM
ejpam-6254	89	6	αi(t	αi(t	NOUN
ejpam-6254	89	7	)	)	PUNCT
ejpam-6254	89	8	−	−	PROPN
ejpam-6254	89	9	σe(t−	σe(t−	PROPN
ejpam-6254	89	10	τ)−	τ)−	PROPN
ejpam-6254	89	11	µe(t	µe(t	PRON
ejpam-6254	89	12	)	)	PUNCT
ejpam-6254	89	13	,	,	PUNCT
ejpam-6254	89	14	di(t	di(t	NOUN
ejpam-6254	89	15	)	)	PUNCT
ejpam-6254	89	16	dt	dt	NOUN
ejpam-6254	90	1	=	=	SYM
ejpam-6254	90	2	σe(t−	σe(t−	PROPN
ejpam-6254	90	3	τ)−	τ)−	PROPN
ejpam-6254	90	4	γ1i(t)−	γ1i(t)−	PROPN
ejpam-6254	90	5	µi(t	µi(t	ADP
ejpam-6254	90	6	)	)	PUNCT
ejpam-6254	90	7	.	.	PUNCT
ejpam-6254	91	1	(	(	PUNCT
ejpam-6254	91	2	3	3	X
ejpam-6254	91	3	)	)	PUNCT
ejpam-6254	91	4	theorem	theorem	NOUN
ejpam-6254	91	5	1	1	NUM
ejpam-6254	91	6	.	.	PUNCT
ejpam-6254	92	1	the	the	DET
ejpam-6254	92	2	solutions	solution	NOUN
ejpam-6254	92	3	of	of	ADP
ejpam-6254	92	4	system	system	NOUN
ejpam-6254	92	5	(	(	PUNCT
ejpam-6254	92	6	3	3	X
ejpam-6254	92	7	)	)	PUNCT
ejpam-6254	92	8	remain	remain	VERB
ejpam-6254	92	9	bounded	bounded	ADJ
ejpam-6254	92	10	and	and	CCONJ
ejpam-6254	92	11	non	non	ADJ
ejpam-6254	92	12	-	-	ADJ
ejpam-6254	92	13	negative	negative	ADJ
ejpam-6254	92	14	for	for	ADP
ejpam-6254	92	15	all	all	DET
ejpam-6254	92	16	time	time	NOUN
ejpam-6254	92	17	t	t	PROPN
ejpam-6254	92	18	≥	≥	NOUN
ejpam-6254	92	19	0	0	NUM
ejpam-6254	92	20	,	,	PUNCT
ejpam-6254	92	21	provided	provide	VERB
ejpam-6254	92	22	that	that	SCONJ
ejpam-6254	92	23	the	the	DET
ejpam-6254	92	24	initial	initial	ADJ
ejpam-6254	92	25	conditions	condition	NOUN
ejpam-6254	92	26	are	be	AUX
ejpam-6254	92	27	non	non	ADJ
ejpam-6254	92	28	-	-	ADJ
ejpam-6254	92	29	negative	negative	ADJ
ejpam-6254	92	30	.	.	PUNCT
ejpam-6254	93	1	that	that	PRON
ejpam-6254	93	2	is	is	ADV
ejpam-6254	93	3	,	,	PUNCT
ejpam-6254	93	4	every	every	DET
ejpam-6254	93	5	solution	solution	NOUN
ejpam-6254	93	6	remains	remain	VERB
ejpam-6254	93	7	in	in	ADP
ejpam-6254	93	8	a	a	DET
ejpam-6254	93	9	positively	positively	ADV
ejpam-6254	93	10	invariant	invariant	ADJ
ejpam-6254	93	11	set	set	NOUN
ejpam-6254	93	12	ω	ω	PROPN
ejpam-6254	93	13	⊂	⊂	PROPN
ejpam-6254	93	14	r3	r3	PROPN
ejpam-6254	93	15	+	+	ADV
ejpam-6254	93	16	,	,	PUNCT
ejpam-6254	93	17	and	and	CCONJ
ejpam-6254	93	18	(	(	PUNCT
ejpam-6254	93	19	s(t	s(t	PROPN
ejpam-6254	93	20	)	)	PUNCT
ejpam-6254	93	21	,	,	PUNCT
ejpam-6254	93	22	e(t	e(t	NOUN
ejpam-6254	93	23	)	)	PUNCT
ejpam-6254	93	24	,	,	PUNCT
ejpam-6254	93	25	i(t	i(t	PROPN
ejpam-6254	93	26	)	)	PUNCT
ejpam-6254	93	27	)	)	PUNCT
ejpam-6254	94	1	∈	∈	PROPN
ejpam-6254	94	2	r3	r3	PROPN
ejpam-6254	94	3	+	+	CCONJ
ejpam-6254	94	4	for	for	ADP
ejpam-6254	94	5	all	all	DET
ejpam-6254	94	6	t	t	PROPN
ejpam-6254	94	7	≥	≥	NOUN
ejpam-6254	94	8	0	0	NUM
ejpam-6254	94	9	.	.	PUNCT
ejpam-6254	95	1	proof	proof	NOUN
ejpam-6254	95	2	.	.	PUNCT
ejpam-6254	96	1	suppose	suppose	VERB
ejpam-6254	96	2	n(t)=s(t)+e(t)+i(t	n(t)=s(t)+e(t)+i(t	PROPN
ejpam-6254	96	3	)	)	PUNCT
ejpam-6254	96	4	,	,	PUNCT
ejpam-6254	96	5	then	then	ADV
ejpam-6254	96	6	dn	dn	PROPN
ejpam-6254	96	7	dt	dt	NOUN
ejpam-6254	97	1	=	=	PUNCT
ejpam-6254	97	2	d	d	X
ejpam-6254	97	3	dt	dt	X
ejpam-6254	97	4	(	(	PUNCT
ejpam-6254	97	5	s(t	s(t	PROPN
ejpam-6254	97	6	)	)	PUNCT
ejpam-6254	97	7	)	)	PUNCT
ejpam-6254	98	1	+	+	CCONJ
ejpam-6254	98	2	d	d	X
ejpam-6254	98	3	dt	dt	X
ejpam-6254	98	4	(	(	PUNCT
ejpam-6254	98	5	e(t	e(t	NOUN
ejpam-6254	98	6	)	)	PUNCT
ejpam-6254	98	7	)	)	PUNCT
ejpam-6254	99	1	+	+	CCONJ
ejpam-6254	99	2	d	d	X
ejpam-6254	99	3	dt	dt	X
ejpam-6254	99	4	(	(	PUNCT
ejpam-6254	99	5	i(t	i(t	PROPN
ejpam-6254	99	6	)	)	PUNCT
ejpam-6254	99	7	)	)	PUNCT
ejpam-6254	99	8	,	,	PUNCT
ejpam-6254	99	9	dn	dn	ADP
ejpam-6254	99	10	dt	dt	NOUN
ejpam-6254	99	11	=	=	SYM
ejpam-6254	99	12	∆−	∆−	PROPN
ejpam-6254	99	13	µ	µ	X
ejpam-6254	99	14	(	(	PUNCT
ejpam-6254	99	15	s(t	s(t	PROPN
ejpam-6254	99	16	)	)	PUNCT
ejpam-6254	99	17	+	+	SYM
ejpam-6254	99	18	e(t	e(t	NOUN
ejpam-6254	99	19	)	)	PUNCT
ejpam-6254	100	1	+	+	CCONJ
ejpam-6254	100	2	i(t))−	i(t))−	NOUN
ejpam-6254	100	3	γ2s(t)−	γ2s(t)−	PROPN
ejpam-6254	100	4	γ1i(t	γ1i(t	PROPN
ejpam-6254	100	5	)	)	PUNCT
ejpam-6254	100	6	,	,	PUNCT
ejpam-6254	100	7	dn(t	dn(t	NUM
ejpam-6254	100	8	)	)	PUNCT
ejpam-6254	100	9	dt	dt	NOUN
ejpam-6254	100	10	=	=	SYM
ejpam-6254	100	11	∆−	∆−	PROPN
ejpam-6254	100	12	µn(t)−	µn(t)−	PROPN
ejpam-6254	100	13	γ2s(t)−	γ2s(t)−	PROPN
ejpam-6254	100	14	γ1i(t	γ1i(t	PROPN
ejpam-6254	100	15	)	)	PUNCT
ejpam-6254	100	16	≤	≤	NOUN
ejpam-6254	100	17	∆−	∆−	NOUN
ejpam-6254	100	18	µn(t	µn(t	NUM
ejpam-6254	100	19	)	)	PUNCT
ejpam-6254	100	20	,	,	PUNCT
ejpam-6254	100	21	d	d	X
ejpam-6254	100	22	dt	dt	X
ejpam-6254	100	23	(	(	PUNCT
ejpam-6254	100	24	neµt	neµt	PROPN
ejpam-6254	100	25	)	)	PUNCT
ejpam-6254	100	26	≤	≤	NOUN
ejpam-6254	100	27	∆eµt	∆eµt	NOUN
ejpam-6254	100	28	,	,	PUNCT
ejpam-6254	100	29	implies	imply	VERB
ejpam-6254	100	30	that	that	SCONJ
ejpam-6254	100	31	n(t	n(t	NOUN
ejpam-6254	100	32	)	)	PUNCT
ejpam-6254	100	33	≤	≤	NOUN
ejpam-6254	100	34	∆	∆	X
ejpam-6254	100	35	µ	µ	X
ejpam-6254	100	36	+	+	X
ejpam-6254	100	37	be−µ(t	be−µ(t	NOUN
ejpam-6254	100	38	)	)	PUNCT
ejpam-6254	100	39	.	.	PUNCT
ejpam-6254	101	1	thus	thus	ADV
ejpam-6254	101	2	,	,	PUNCT
ejpam-6254	101	3	0	0	NUM
ejpam-6254	101	4	≤	≤	NUM
ejpam-6254	101	5	n(t	n(t	PROPN
ejpam-6254	101	6	)	)	PUNCT
ejpam-6254	101	7	≤	≤	NOUN
ejpam-6254	101	8	∆	∆	X
ejpam-6254	101	9	µ	µ	X
ejpam-6254	101	10	as	as	ADP
ejpam-6254	101	11	t→	t→	DET
ejpam-6254	101	12	∞.	∞.	PROPN
ejpam-6254	101	13	consequently	consequently	ADV
ejpam-6254	101	14	,	,	PUNCT
ejpam-6254	101	15	the	the	DET
ejpam-6254	101	16	dynamic	dynamic	NOUN
ejpam-6254	101	17	of	of	ADP
ejpam-6254	101	18	the	the	DET
ejpam-6254	101	19	model	model	NOUN
ejpam-6254	101	20	can	can	AUX
ejpam-6254	101	21	be	be	AUX
ejpam-6254	101	22	analyzed	analyze	VERB
ejpam-6254	101	23	within	within	ADP
ejpam-6254	101	24	the	the	DET
ejpam-6254	101	25	region	region	NOUN
ejpam-6254	101	26	:	:	PUNCT
ejpam-6254	101	27	ω	ω	X
ejpam-6254	101	28	=	=	SYM
ejpam-6254	101	29	{	{	PUNCT
ejpam-6254	101	30	(	(	PUNCT
ejpam-6254	101	31	s(t	s(t	PROPN
ejpam-6254	101	32	)	)	PUNCT
ejpam-6254	101	33	,	,	PUNCT
ejpam-6254	101	34	e(t	e(t	NOUN
ejpam-6254	101	35	)	)	PUNCT
ejpam-6254	101	36	,	,	PUNCT
ejpam-6254	101	37	i(t	i(t	PROPN
ejpam-6254	101	38	)	)	PUNCT
ejpam-6254	101	39	)	)	PUNCT
ejpam-6254	102	1	∈	∈	PROPN
ejpam-6254	102	2	r3	r3	PROPN
ejpam-6254	102	3	+	+	CCONJ
ejpam-6254	102	4	:	:	PUNCT
ejpam-6254	102	5	n	n	PRON
ejpam-6254	102	6	≤	≤	NUM
ejpam-6254	102	7	∆	∆	X
ejpam-6254	102	8	µ	µ	X
ejpam-6254	102	9	}	}	PUNCT
ejpam-6254	102	10	,	,	PUNCT
ejpam-6254	102	11	then	then	ADV
ejpam-6254	102	12	the	the	DET
ejpam-6254	102	13	set	set	NOUN
ejpam-6254	102	14	ω	ω	PROPN
ejpam-6254	102	15	is	be	AUX
ejpam-6254	102	16	positive	positive	ADJ
ejpam-6254	102	17	invariant	invariant	NOUN
ejpam-6254	102	18	with	with	ADP
ejpam-6254	102	19	respect	respect	NOUN
ejpam-6254	102	20	system	system	NOUN
ejpam-6254	102	21	(	(	PUNCT
ejpam-6254	102	22	3	3	NUM
ejpam-6254	102	23	)	)	PUNCT
ejpam-6254	102	24	and	and	CCONJ
ejpam-6254	102	25	hence	hence	ADV
ejpam-6254	102	26	it	it	PRON
ejpam-6254	102	27	is	be	AUX
ejpam-6254	102	28	closed	closed	ADJ
ejpam-6254	102	29	.	.	PUNCT
ejpam-6254	103	1	2.1	2.1	NUM
ejpam-6254	103	2	.	.	PUNCT
ejpam-6254	103	3	linearization	linearization	NOUN
ejpam-6254	103	4	to	to	ADP
ejpam-6254	103	5	linearized	linearize	VERB
ejpam-6254	103	6	the	the	DET
ejpam-6254	103	7	system	system	NOUN
ejpam-6254	103	8	(	(	PUNCT
ejpam-6254	103	9	3	3	NUM
ejpam-6254	103	10	)	)	PUNCT
ejpam-6254	103	11	,	,	PUNCT
ejpam-6254	103	12	we	we	PRON
ejpam-6254	103	13	apply	apply	VERB
ejpam-6254	103	14	taylor	taylor	PROPN
ejpam-6254	103	15	series	series	PROPN
ejpam-6254	103	16	.	.	PUNCT
ejpam-6254	104	1	for	for	ADP
ejpam-6254	104	2	simplicity	simplicity	NOUN
ejpam-6254	104	3	,	,	PUNCT
ejpam-6254	104	4	we	we	PRON
ejpam-6254	104	5	represent	represent	VERB
ejpam-6254	104	6	this	this	DET
ejpam-6254	104	7	process	process	NOUN
ejpam-6254	104	8	as	as	SCONJ
ejpam-6254	104	9	follows	follow	VERB
ejpam-6254	104	10	:	:	PUNCT
ejpam-6254	104	11	ds	ds	ADJ
ejpam-6254	104	12	dt	dt	NOUN
ejpam-6254	104	13	=	=	SYM
ejpam-6254	104	14	f(s(t	f(s(t	PROPN
ejpam-6254	104	15	)	)	PUNCT
ejpam-6254	104	16	,	,	PUNCT
ejpam-6254	104	17	e(t	e(t	NOUN
ejpam-6254	104	18	)	)	PUNCT
ejpam-6254	104	19	,	,	PUNCT
ejpam-6254	104	20	i(t	i(t	PROPN
ejpam-6254	104	21	)	)	PUNCT
ejpam-6254	104	22	)	)	PUNCT
ejpam-6254	104	23	,	,	PUNCT
ejpam-6254	104	24	where	where	SCONJ
ejpam-6254	104	25	f(s(t	f(s(t	PROPN
ejpam-6254	104	26	)	)	PUNCT
ejpam-6254	104	27	,	,	PUNCT
ejpam-6254	104	28	e(t	e(t	NOUN
ejpam-6254	104	29	)	)	PUNCT
ejpam-6254	104	30	,	,	PUNCT
ejpam-6254	104	31	i(t	i(t	PROPN
ejpam-6254	104	32	)	)	PUNCT
ejpam-6254	104	33	)	)	PUNCT
ejpam-6254	105	1	=	=	PUNCT
ejpam-6254	105	2	∆−	∆−	NOUN
ejpam-6254	105	3	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	105	4	)	)	PUNCT
ejpam-6254	105	5	1	1	NUM
ejpam-6254	105	6	+	+	NUM
ejpam-6254	105	7	αi(t	αi(t	NOUN
ejpam-6254	105	8	)	)	PUNCT
ejpam-6254	105	9	−	−	PROPN
ejpam-6254	105	10	µs(t)−	µs(t)−	PROPN
ejpam-6254	105	11	γ2s(t	γ2s(t	PROPN
ejpam-6254	105	12	)	)	PUNCT
ejpam-6254	105	13	de	de	X
ejpam-6254	105	14	dt	dt	X
ejpam-6254	105	15	=	=	SYM
ejpam-6254	105	16	g(s(t	g(s(t	PROPN
ejpam-6254	105	17	)	)	PUNCT
ejpam-6254	105	18	,	,	PUNCT
ejpam-6254	105	19	e(t	e(t	NOUN
ejpam-6254	105	20	)	)	PUNCT
ejpam-6254	105	21	,	,	PUNCT
ejpam-6254	105	22	i(t	i(t	PROPN
ejpam-6254	105	23	)	)	PUNCT
ejpam-6254	105	24	)	)	PUNCT
ejpam-6254	105	25	,	,	PUNCT
ejpam-6254	105	26	s.	s.	PROPN
ejpam-6254	105	27	irum	irum	PROPN
ejpam-6254	105	28	et	et	PROPN
ejpam-6254	105	29	al	al	PROPN
ejpam-6254	105	30	.	.	PUNCT
ejpam-6254	105	31	/	/	SYM
ejpam-6254	105	32	eur	eur	PROPN
ejpam-6254	105	33	.	.	PUNCT
ejpam-6254	106	1	j.	j.	PROPN
ejpam-6254	106	2	pure	pure	PROPN
ejpam-6254	106	3	appl	appl	PROPN
ejpam-6254	106	4	.	.	PROPN
ejpam-6254	106	5	math	math	PROPN
ejpam-6254	106	6	,	,	PUNCT
ejpam-6254	106	7	18	18	NUM
ejpam-6254	106	8	(	(	PUNCT
ejpam-6254	106	9	4	4	NUM
ejpam-6254	106	10	)	)	PUNCT
ejpam-6254	106	11	(	(	PUNCT
ejpam-6254	106	12	2025	2025	NUM
ejpam-6254	106	13	)	)	PUNCT
ejpam-6254	106	14	,	,	PUNCT
ejpam-6254	106	15	6254	6254	NUM
ejpam-6254	106	16	6	6	NUM
ejpam-6254	106	17	of	of	ADP
ejpam-6254	106	18	23	23	NUM
ejpam-6254	106	19	where	where	SCONJ
ejpam-6254	106	20	g(s(t	g(s(t	NOUN
ejpam-6254	106	21	)	)	PUNCT
ejpam-6254	106	22	,	,	PUNCT
ejpam-6254	106	23	e(t	e(t	NOUN
ejpam-6254	106	24	)	)	PUNCT
ejpam-6254	106	25	,	,	PUNCT
ejpam-6254	106	26	i(t	i(t	PROPN
ejpam-6254	106	27	)	)	PUNCT
ejpam-6254	106	28	)	)	PUNCT
ejpam-6254	107	1	=	=	PUNCT
ejpam-6254	108	1	βs(t)i(t	βs(t)i(t	ADJ
ejpam-6254	108	2	)	)	PUNCT
ejpam-6254	108	3	1	1	NUM
ejpam-6254	108	4	+	+	NUM
ejpam-6254	108	5	αi(t	αi(t	NOUN
ejpam-6254	108	6	)	)	PUNCT
ejpam-6254	109	1	−	−	PROPN
ejpam-6254	110	1	σe(t−	σe(t−	PROPN
ejpam-6254	110	2	τ)−	τ)−	PROPN
ejpam-6254	110	3	µe(t	µe(t	PUNCT
ejpam-6254	110	4	)	)	PUNCT
ejpam-6254	110	5	di	di	NOUN
ejpam-6254	110	6	dt	dt	NOUN
ejpam-6254	110	7	=	=	SYM
ejpam-6254	110	8	h(s(t	h(s(t	PROPN
ejpam-6254	110	9	)	)	PUNCT
ejpam-6254	110	10	,	,	PUNCT
ejpam-6254	110	11	e(t	e(t	NOUN
ejpam-6254	110	12	)	)	PUNCT
ejpam-6254	110	13	,	,	PUNCT
ejpam-6254	110	14	i(t	i(t	PROPN
ejpam-6254	110	15	)	)	PUNCT
ejpam-6254	110	16	)	)	PUNCT
ejpam-6254	110	17	where	where	SCONJ
ejpam-6254	110	18	h(s(t	h(s(t	PROPN
ejpam-6254	110	19	)	)	PUNCT
ejpam-6254	110	20	,	,	PUNCT
ejpam-6254	110	21	e(t	e(t	NOUN
ejpam-6254	110	22	)	)	PUNCT
ejpam-6254	110	23	,	,	PUNCT
ejpam-6254	110	24	i(t	i(t	PROPN
ejpam-6254	110	25	)	)	PUNCT
ejpam-6254	110	26	)	)	PUNCT
ejpam-6254	111	1	=	=	SYM
ejpam-6254	111	2	σe(t−	σe(t−	PROPN
ejpam-6254	111	3	τ)−	τ)−	PROPN
ejpam-6254	111	4	γ1i(t)−	γ1i(t)−	PROPN
ejpam-6254	111	5	µi(t	µi(t	ADP
ejpam-6254	111	6	)	)	PUNCT
ejpam-6254	111	7	.	.	PUNCT
ejpam-6254	112	1	we	we	PRON
ejpam-6254	112	2	define	define	VERB
ejpam-6254	112	3	s	s	PRON
ejpam-6254	112	4	−	−	PROPN
ejpam-6254	112	5	s∗	s∗	PROPN
ejpam-6254	112	6	=	=	SYM
ejpam-6254	112	7	u	u	PROPN
ejpam-6254	112	8	,	,	PUNCT
ejpam-6254	112	9	e	e	NOUN
ejpam-6254	112	10	−	−	PROPN
ejpam-6254	112	11	e∗	e∗	PROPN
ejpam-6254	112	12	=	=	SYM
ejpam-6254	112	13	v	v	PROPN
ejpam-6254	112	14	,	,	PUNCT
ejpam-6254	112	15	i	i	PRON
ejpam-6254	112	16	−	−	VERB
ejpam-6254	112	17	i∗	i∗	NOUN
ejpam-6254	112	18	=	=	PUNCT
ejpam-6254	112	19	w.	w.	NOUN
ejpam-6254	112	20	now	now	ADV
ejpam-6254	112	21	expansion	expansion	NOUN
ejpam-6254	112	22	of	of	ADP
ejpam-6254	112	23	model	model	NOUN
ejpam-6254	112	24	(	(	PUNCT
ejpam-6254	112	25	3	3	NUM
ejpam-6254	112	26	)	)	PUNCT
ejpam-6254	112	27	around	around	ADP
ejpam-6254	112	28	the	the	DET
ejpam-6254	112	29	point	point	NOUN
ejpam-6254	112	30	(	(	PUNCT
ejpam-6254	112	31	s∗	s∗	PROPN
ejpam-6254	112	32	,	,	PUNCT
ejpam-6254	112	33	e∗	e∗	NOUN
ejpam-6254	112	34	,	,	PUNCT
ejpam-6254	112	35	i∗	i∗	NOUN
ejpam-6254	112	36	)	)	PUNCT
ejpam-6254	112	37	is	be	AUX
ejpam-6254	112	38	given	give	VERB
ejpam-6254	112	39	by	by	ADP
ejpam-6254	112	40	:	:	PUNCT
ejpam-6254	112	41	u̇	u̇	PROPN
ejpam-6254	112	42	=	=	SYM
ejpam-6254	112	43	u	u	PROPN
ejpam-6254	112	44	(	(	PUNCT
ejpam-6254	112	45	−	−	PROPN
ejpam-6254	112	46	βi∗	βi∗	NOUN
ejpam-6254	112	47	1	1	NUM
ejpam-6254	112	48	+	+	NUM
ejpam-6254	112	49	αi∗	αi∗	NOUN
ejpam-6254	112	50	−	−	NOUN
ejpam-6254	112	51	µ−	µ−	PROPN
ejpam-6254	112	52	γ2	γ2	NOUN
ejpam-6254	112	53	)	)	PUNCT
ejpam-6254	112	54	+	+	PUNCT
ejpam-6254	112	55	v(0	v(0	NOUN
ejpam-6254	112	56	)	)	PUNCT
ejpam-6254	113	1	+	+	CCONJ
ejpam-6254	113	2	w	w	X
ejpam-6254	113	3	(	(	PUNCT
ejpam-6254	113	4	−	−	PROPN
ejpam-6254	113	5	βs∗	βs∗	X
ejpam-6254	113	6	(	(	PUNCT
ejpam-6254	113	7	1	1	NUM
ejpam-6254	113	8	+	+	NUM
ejpam-6254	113	9	αi∗)2	αi∗)2	NUM
ejpam-6254	113	10	)	)	PUNCT
ejpam-6254	113	11	,	,	PUNCT
ejpam-6254	113	12	similarly	similarly	ADV
ejpam-6254	113	13	v̇	v̇	NOUN
ejpam-6254	113	14	=	=	SYM
ejpam-6254	113	15	u	u	NOUN
ejpam-6254	113	16	(	(	PUNCT
ejpam-6254	113	17	βi∗	βi∗	NOUN
ejpam-6254	113	18	1	1	NUM
ejpam-6254	113	19	+	+	NUM
ejpam-6254	113	20	αi∗	αi∗	NOUN
ejpam-6254	113	21	−	−	NOUN
ejpam-6254	113	22	)	)	PUNCT
ejpam-6254	114	1	+	+	CCONJ
ejpam-6254	114	2	v(−µ−	v(−µ−	NOUN
ejpam-6254	114	3	σe−λτ	σe−λτ	NOUN
ejpam-6254	114	4	)	)	PUNCT
ejpam-6254	115	1	+	+	CCONJ
ejpam-6254	115	2	w	w	X
ejpam-6254	115	3	(	(	PUNCT
ejpam-6254	115	4	βs∗	βs∗	X
ejpam-6254	115	5	(	(	PUNCT
ejpam-6254	115	6	1	1	NUM
ejpam-6254	115	7	+	+	NUM
ejpam-6254	115	8	αi∗)2	αi∗)2	NUM
ejpam-6254	115	9	)	)	PUNCT
ejpam-6254	115	10	,	,	PUNCT
ejpam-6254	115	11	ẇ	ẇ	PROPN
ejpam-6254	115	12	=	=	SYM
ejpam-6254	115	13	u(0	u(0	PROPN
ejpam-6254	115	14	)	)	PUNCT
ejpam-6254	116	1	+	+	NUM
ejpam-6254	116	2	v(−σ)e−λτ	v(−σ)e−λτ	NOUN
ejpam-6254	116	3	+	+	CCONJ
ejpam-6254	116	4	w(−µ−	w(−µ−	ADJ
ejpam-6254	116	5	γ1	γ1	NOUN
ejpam-6254	116	6	)	)	PUNCT
ejpam-6254	116	7	.	.	PUNCT
ejpam-6254	117	1	2.2	2.2	NUM
ejpam-6254	117	2	.	.	PUNCT
ejpam-6254	117	3	matrix	matrix	NOUN
ejpam-6254	117	4	representation	representation	NOUN
ejpam-6254	117	5	of	of	ADP
ejpam-6254	117	6	the	the	DET
ejpam-6254	117	7	linearized	linearize	VERB
ejpam-6254	117	8	system	system	NOUN
ejpam-6254	117	9	the	the	DET
ejpam-6254	117	10	linearized	linearize	VERB
ejpam-6254	117	11	system	system	NOUN
ejpam-6254	117	12	for	for	ADP
ejpam-6254	117	13	(	(	PUNCT
ejpam-6254	117	14	3	3	NUM
ejpam-6254	117	15	)	)	PUNCT
ejpam-6254	117	16	is	be	AUX
ejpam-6254	117	17	expressed	express	VERB
ejpam-6254	117	18	in	in	ADP
ejpam-6254	117	19	matrix	matrix	NOUN
ejpam-6254	117	20	form	form	NOUN
ejpam-6254	117	21	as	as	SCONJ
ejpam-6254	117	22	follows	follow	VERB
ejpam-6254	117	23	:	:	PUNCT
ejpam-6254	118	1	u̇	u̇	PROPN
ejpam-6254	118	2	v̇	v̇	NOUN
ejpam-6254	118	3	ẇ	ẇ	ADP
ejpam-6254	118	4			NOUN
ejpam-6254	118	5	=	=	PRON
ejpam-6254	118	6			NUM
ejpam-6254	118	7	∂f	∂f	PROPN
ejpam-6254	118	8	∂s	∂s	PROPN
ejpam-6254	118	9	∂f	∂f	PROPN
ejpam-6254	118	10	∂e	∂e	PROPN
ejpam-6254	118	11	∂f	∂f	PROPN
ejpam-6254	118	12	∂i	∂i	PROPN
ejpam-6254	118	13	∂g	∂g	PROPN
ejpam-6254	118	14	∂s	∂s	PROPN
ejpam-6254	118	15	∂g	∂g	PROPN
ejpam-6254	119	1	∂e	∂e	PROPN
ejpam-6254	120	1	∂g	∂g	PROPN
ejpam-6254	120	2	∂i	∂i	PROPN
ejpam-6254	121	1	∂h	∂h	PROPN
ejpam-6254	121	2	∂s	∂s	PROPN
ejpam-6254	122	1	∂h	∂h	PROPN
ejpam-6254	122	2	∂e	∂e	NOUN
ejpam-6254	122	3	∂g	∂g	PROPN
ejpam-6254	122	4	∂i	∂i	PROPN
ejpam-6254	122	5			PROPN
ejpam-6254	122	6	u	u	PUNCT
ejpam-6254	122	7	v	v	NOUN
ejpam-6254	122	8	w	w	NOUN
ejpam-6254	122	9			PROPN
ejpam-6254	122	10	.	.	PUNCT
ejpam-6254	123	1	alternatively	alternatively	ADV
ejpam-6254	123	2	,	,	PUNCT
ejpam-6254	123	3	in	in	ADP
ejpam-6254	123	4	simplified	simplified	ADJ
ejpam-6254	123	5	notation	notation	NOUN
ejpam-6254	123	6	:	:	PUNCT
ejpam-6254	123	7	ẋ	ẋ	PROPN
ejpam-6254	123	8	=	=	SYM
ejpam-6254	123	9	jx	jx	PROPN
ejpam-6254	123	10	,	,	PUNCT
ejpam-6254	123	11	where	where	SCONJ
ejpam-6254	123	12	j	j	PROPN
ejpam-6254	123	13	represents	represent	VERB
ejpam-6254	123	14	the	the	DET
ejpam-6254	123	15	jacobian	jacobian	ADJ
ejpam-6254	123	16	matrix	matrix	NOUN
ejpam-6254	123	17	,	,	PUNCT
ejpam-6254	123	18	composed	compose	VERB
ejpam-6254	123	19	of	of	ADP
ejpam-6254	123	20	the	the	DET
ejpam-6254	123	21	derivatives	derivative	NOUN
ejpam-6254	123	22	of	of	ADP
ejpam-6254	123	23	each	each	DET
ejpam-6254	123	24	term	term	NOUN
ejpam-6254	123	25	on	on	ADP
ejpam-6254	123	26	the	the	DET
ejpam-6254	123	27	righthand	righthand	NOUN
ejpam-6254	123	28	side	side	NOUN
ejpam-6254	123	29	of	of	ADP
ejpam-6254	123	30	the	the	DET
ejpam-6254	123	31	model	model	NOUN
ejpam-6254	123	32	’s	’s	PART
ejpam-6254	123	33	equations	equation	NOUN
ejpam-6254	123	34	,	,	PUNCT
ejpam-6254	123	35	namely	namely	ADV
ejpam-6254	123	36	(	(	PUNCT
ejpam-6254	123	37	s	s	X
ejpam-6254	123	38	,	,	PUNCT
ejpam-6254	123	39	e	e	NOUN
ejpam-6254	123	40	,	,	PUNCT
ejpam-6254	123	41	i	i	NOUN
ejpam-6254	123	42	)	)	PUNCT
ejpam-6254	123	43	.	.	PUNCT
ejpam-6254	124	1	so	so	ADV
ejpam-6254	124	2	,	,	PUNCT
ejpam-6254	124	3	with	with	ADP
ejpam-6254	124	4	linearization	linearization	NOUN
ejpam-6254	124	5	the	the	DET
ejpam-6254	124	6	system	system	NOUN
ejpam-6254	124	7	obtains	obtain	VERB
ejpam-6254	124	8	the	the	DET
ejpam-6254	124	9	following	follow	VERB
ejpam-6254	124	10	form	form	NOUN
ejpam-6254	124	11	:	:	PUNCT
ejpam-6254	124	12			PUNCT
ejpam-6254	124	13	du	du	NOUN
ejpam-6254	124	14	dt	dt	NOUN
ejpam-6254	124	15	=	=	SYM
ejpam-6254	124	16	a11u+	a11u+	PROPN
ejpam-6254	124	17	a13w	a13w	PROPN
ejpam-6254	124	18	,	,	PUNCT
ejpam-6254	124	19	dv	dv	PROPN
ejpam-6254	124	20	dt	dt	X
ejpam-6254	124	21	=	=	SYM
ejpam-6254	124	22	a21u+	a21u+	PROPN
ejpam-6254	124	23	ua22v	ua22v	NOUN
ejpam-6254	124	24	+	+	X
ejpam-6254	124	25	b22u	b22u	PROPN
ejpam-6254	124	26	(	(	PUNCT
ejpam-6254	124	27	t−	t−	PROPN
ejpam-6254	124	28	τ	τ	PROPN
ejpam-6254	124	29	)	)	PUNCT
ejpam-6254	125	1	+	+	CCONJ
ejpam-6254	125	2	a23w	a23w	PROPN
ejpam-6254	125	3	,	,	PUNCT
ejpam-6254	125	4	dw	dw	NOUN
ejpam-6254	125	5	dt	dt	NOUN
ejpam-6254	125	6	=	=	SYM
ejpam-6254	125	7	b32v	b32v	PROPN
ejpam-6254	125	8	(	(	PUNCT
ejpam-6254	125	9	t−	t−	PROPN
ejpam-6254	125	10	τ	τ	PROPN
ejpam-6254	125	11	)	)	PUNCT
ejpam-6254	126	1	+	+	CCONJ
ejpam-6254	127	1	a33w	a33w	PROPN
ejpam-6254	127	2	,	,	PUNCT
ejpam-6254	127	3	(	(	PUNCT
ejpam-6254	127	4	4	4	X
ejpam-6254	127	5	)	)	PUNCT
ejpam-6254	127	6	where	where	SCONJ
ejpam-6254	127	7	a11	a11	PROPN
ejpam-6254	127	8	=	=	SYM
ejpam-6254	127	9	−	−	PROPN
ejpam-6254	127	10	βi∗	βi∗	NOUN
ejpam-6254	127	11	1	1	NUM
ejpam-6254	127	12	+	+	NUM
ejpam-6254	127	13	αi∗	αi∗	NOUN
ejpam-6254	127	14	−	−	NOUN
ejpam-6254	127	15	µ−	µ−	PROPN
ejpam-6254	127	16	γ2	γ2	NOUN
ejpam-6254	127	17	,	,	PUNCT
ejpam-6254	127	18	a13	a13	NOUN
ejpam-6254	127	19	=	=	SYM
ejpam-6254	127	20	−	−	PROPN
ejpam-6254	127	21	βs∗	βs∗	NOUN
ejpam-6254	127	22	(	(	PUNCT
ejpam-6254	127	23	1	1	NUM
ejpam-6254	127	24	+	+	NUM
ejpam-6254	127	25	αi∗)2	αi∗)2	NUM
ejpam-6254	127	26	,	,	PUNCT
ejpam-6254	127	27	a21	a21	NOUN
ejpam-6254	127	28	=	=	NOUN
ejpam-6254	127	29	βi∗	βi∗	NOUN
ejpam-6254	127	30	1	1	NUM
ejpam-6254	127	31	+	+	NUM
ejpam-6254	127	32	αi∗	αi∗	NOUN
ejpam-6254	127	33	−	−	NOUN
ejpam-6254	127	34	µ−	µ−	PROPN
ejpam-6254	127	35	γ2	γ2	NOUN
ejpam-6254	127	36	,	,	PUNCT
ejpam-6254	127	37	s.	s.	PROPN
ejpam-6254	127	38	irum	irum	PROPN
ejpam-6254	127	39	et	et	PROPN
ejpam-6254	127	40	al	al	PROPN
ejpam-6254	127	41	.	.	PUNCT
ejpam-6254	127	42	/	/	SYM
ejpam-6254	127	43	eur	eur	PROPN
ejpam-6254	127	44	.	.	PUNCT
ejpam-6254	128	1	j.	j.	PROPN
ejpam-6254	128	2	pure	pure	PROPN
ejpam-6254	128	3	appl	appl	PROPN
ejpam-6254	128	4	.	.	PROPN
ejpam-6254	128	5	math	math	PROPN
ejpam-6254	128	6	,	,	PUNCT
ejpam-6254	128	7	18	18	NUM
ejpam-6254	128	8	(	(	PUNCT
ejpam-6254	128	9	4	4	NUM
ejpam-6254	128	10	)	)	PUNCT
ejpam-6254	128	11	(	(	PUNCT
ejpam-6254	128	12	2025	2025	NUM
ejpam-6254	128	13	)	)	PUNCT
ejpam-6254	128	14	,	,	PUNCT
ejpam-6254	128	15	6254	6254	NUM
ejpam-6254	128	16	7	7	NUM
ejpam-6254	128	17	of	of	ADP
ejpam-6254	128	18	23	23	NUM
ejpam-6254	128	19	a22	a22	NOUN
ejpam-6254	128	20	=	=	SYM
ejpam-6254	128	21	−µ	−µ	PROPN
ejpam-6254	128	22	,	,	PUNCT
ejpam-6254	128	23	a23	a23	PROPN
ejpam-6254	128	24	=	=	PRON
ejpam-6254	128	25	βs∗	βs∗	X
ejpam-6254	128	26	(	(	PUNCT
ejpam-6254	128	27	1	1	NUM
ejpam-6254	128	28	+	+	NUM
ejpam-6254	128	29	αi∗)2	αi∗)2	NUM
ejpam-6254	128	30	,	,	PUNCT
ejpam-6254	128	31	a33	a33	NOUN
ejpam-6254	128	32	=	=	SYM
ejpam-6254	128	33	−γ1	−γ1	PROPN
ejpam-6254	128	34	−	−	PROPN
ejpam-6254	128	35	µ	µ	PROPN
ejpam-6254	128	36	,	,	PUNCT
ejpam-6254	128	37	b22	b22	PROPN
ejpam-6254	128	38	=	=	SYM
ejpam-6254	128	39	−σ	−σ	NOUN
ejpam-6254	128	40	b32	b32	PROPN
ejpam-6254	128	41	=	=	PROPN
ejpam-6254	128	42	σ	σ	PROPN
ejpam-6254	128	43	.	.	PUNCT
ejpam-6254	129	1	thus	thus	ADV
ejpam-6254	129	2	,	,	PUNCT
ejpam-6254	129	3	the	the	DET
ejpam-6254	129	4	jacobian	jacobian	NOUN
ejpam-6254	129	5	of	of	ADP
ejpam-6254	129	6	system	system	NOUN
ejpam-6254	129	7	(	(	PUNCT
ejpam-6254	129	8	4	4	NUM
ejpam-6254	129	9	)	)	PUNCT
ejpam-6254	129	10	is	be	AUX
ejpam-6254	129	11	j	j	PROPN
ejpam-6254	129	12	=	=	SYM
ejpam-6254	129	13	a11	a11	PROPN
ejpam-6254	129	14	0	0	NUM
ejpam-6254	129	15	a13	a13	PROPN
ejpam-6254	129	16	a21	a21	PROPN
ejpam-6254	129	17	a22	a22	PROPN
ejpam-6254	129	18	+	+	CCONJ
ejpam-6254	129	19	b22e	b22e	NOUN
ejpam-6254	129	20	−λτ	−λτ	PROPN
ejpam-6254	129	21	a23	a23	PROPN
ejpam-6254	129	22	0	0	PROPN
ejpam-6254	130	1	b32e	b32e	PROPN
ejpam-6254	130	2	−λτ	−λτ	PROPN
ejpam-6254	130	3	a33	a33	VERB
ejpam-6254	130	4			PRON
ejpam-6254	130	5	.	.	PUNCT
ejpam-6254	131	1	for	for	ADP
ejpam-6254	131	2	eigen	eigen	PROPN
ejpam-6254	131	3	values	value	NOUN
ejpam-6254	131	4	,	,	PUNCT
ejpam-6254	131	5	solve	solve	VERB
ejpam-6254	131	6	|λi	|λi	PROPN
ejpam-6254	131	7	−	−	NOUN
ejpam-6254	131	8	j	j	NOUN
ejpam-6254	132	1	|	|	ADV
ejpam-6254	132	2	=	=	SYM
ejpam-6254	132	3	0,∣∣∣∣∣∣	0,∣∣∣∣∣∣	NUM
ejpam-6254	133	1	λ−	λ−	PROPN
ejpam-6254	133	2	a11	a11	PROPN
ejpam-6254	133	3	0	0	NUM
ejpam-6254	133	4	−a13	−a13	X
ejpam-6254	133	5	−a21	−a21	X
ejpam-6254	133	6	λ−	λ−	PROPN
ejpam-6254	133	7	(	(	PUNCT
ejpam-6254	133	8	a22	a22	PROPN
ejpam-6254	133	9	+	+	CCONJ
ejpam-6254	133	10	b22e	b22e	NOUN
ejpam-6254	133	11	−λτ	−λτ	X
ejpam-6254	133	12	)	)	PUNCT
ejpam-6254	133	13	−a23	−a23	SYM
ejpam-6254	133	14	0	0	NUM
ejpam-6254	133	15	−b32e−λτ	−b32e−λτ	PROPN
ejpam-6254	133	16	λ−	λ−	PROPN
ejpam-6254	133	17	a33	a33	NOUN
ejpam-6254	133	18	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6254	133	19	=	=	SYM
ejpam-6254	133	20	0	0	X
ejpam-6254	133	21	.	.	PUNCT
ejpam-6254	134	1	after	after	ADP
ejpam-6254	134	2	solving	solve	VERB
ejpam-6254	134	3	the	the	DET
ejpam-6254	134	4	determinant	determinant	ADJ
ejpam-6254	134	5	we	we	PRON
ejpam-6254	134	6	acquire	acquire	VERB
ejpam-6254	134	7	the	the	DET
ejpam-6254	134	8	characteristic	characteristic	ADJ
ejpam-6254	134	9	equation	equation	NOUN
ejpam-6254	134	10	:	:	PUNCT
ejpam-6254	135	1	λ3	λ3	PROPN
ejpam-6254	135	2	+	+	NUM
ejpam-6254	135	3	p1λ	p1λ	PROPN
ejpam-6254	135	4	2	2	NUM
ejpam-6254	135	5	+	+	CCONJ
ejpam-6254	135	6	p2λ+	p2λ+	PROPN
ejpam-6254	135	7	p3	p3	PROPN
ejpam-6254	135	8	+	+	CCONJ
ejpam-6254	135	9	(	(	PUNCT
ejpam-6254	135	10	q1λ	q1λ	PROPN
ejpam-6254	135	11	2	2	NUM
ejpam-6254	135	12	+	+	CCONJ
ejpam-6254	135	13	q2λ+	q2λ+	CCONJ
ejpam-6254	135	14	q3	q3	PROPN
ejpam-6254	135	15	)	)	PUNCT
ejpam-6254	135	16	e−λτ	e−λτ	PROPN
ejpam-6254	136	1	=	=	PUNCT
ejpam-6254	136	2	0	0	X
ejpam-6254	136	3	.	.	PUNCT
ejpam-6254	137	1	(	(	PUNCT
ejpam-6254	137	2	5	5	X
ejpam-6254	137	3	)	)	PUNCT
ejpam-6254	137	4	here	here	ADV
ejpam-6254	137	5	p1	p1	PROPN
ejpam-6254	137	6	=	=	PUNCT
ejpam-6254	137	7	−a11	−a11	PROPN
ejpam-6254	137	8	+	+	NUM
ejpam-6254	137	9	a22	a22	PROPN
ejpam-6254	137	10	+	+	NUM
ejpam-6254	137	11	a33	a33	NOUN
ejpam-6254	137	12	,	,	PUNCT
ejpam-6254	137	13	p2	p2	PROPN
ejpam-6254	137	14	=	=	PUNCT
ejpam-6254	137	15	a11a22	a11a22	PROPN
ejpam-6254	137	16	+	+	CCONJ
ejpam-6254	137	17	a11a33	a11a33	ADJ
ejpam-6254	137	18	+	+	CCONJ
ejpam-6254	137	19	a22a33	a22a33	ADJ
ejpam-6254	137	20	,	,	PUNCT
ejpam-6254	137	21	p3	p3	PROPN
ejpam-6254	137	22	=	=	SYM
ejpam-6254	137	23	−a11a22a33	−a11a22a33	PROPN
ejpam-6254	137	24	,	,	PUNCT
ejpam-6254	137	25	q1	q1	NOUN
ejpam-6254	137	26	=	=	SYM
ejpam-6254	137	27	−b22	−b22	PROPN
ejpam-6254	137	28	,	,	PUNCT
ejpam-6254	137	29	q2	q2	NOUN
ejpam-6254	137	30	=	=	SYM
ejpam-6254	137	31	a33b22	a33b22	PROPN
ejpam-6254	137	32	−	−	PROPN
ejpam-6254	137	33	a23b32	a23b32	PROPN
ejpam-6254	137	34	+	+	CCONJ
ejpam-6254	137	35	a11b22	a11b22	VERB
ejpam-6254	137	36	,	,	PUNCT
ejpam-6254	137	37	q3	q3	NOUN
ejpam-6254	137	38	=	=	SYM
ejpam-6254	137	39	a13a23b32	a13a23b32	PROPN
ejpam-6254	137	40	+	+	CCONJ
ejpam-6254	137	41	a13a22b32d6	a13a22b32d6	PROPN
ejpam-6254	137	42	−	−	PROPN
ejpam-6254	137	43	a11b22a33	a11b22a33	NOUN
ejpam-6254	138	1	when	when	SCONJ
ejpam-6254	138	2	τ	τ	X
ejpam-6254	138	3	=	=	SYM
ejpam-6254	138	4	0	0	PROPN
ejpam-6254	138	5	,	,	PUNCT
ejpam-6254	138	6	then	then	ADV
ejpam-6254	138	7	λ3	λ3	PROPN
ejpam-6254	138	8	+	+	PROPN
ejpam-6254	138	9	(	(	PUNCT
ejpam-6254	138	10	p1	p1	NOUN
ejpam-6254	138	11	+	+	CCONJ
ejpam-6254	138	12	q1)λ	q1)λ	NOUN
ejpam-6254	138	13	2	2	NUM
ejpam-6254	138	14	+	+	CCONJ
ejpam-6254	138	15	(	(	PUNCT
ejpam-6254	138	16	p2	p2	X
ejpam-6254	138	17	+	+	CCONJ
ejpam-6254	138	18	q2)λ+	q2)λ+	NOUN
ejpam-6254	138	19	(	(	PUNCT
ejpam-6254	138	20	p3	p3	NOUN
ejpam-6254	138	21	+	+	CCONJ
ejpam-6254	138	22	q3	q3	PROPN
ejpam-6254	138	23	)	)	PUNCT
ejpam-6254	138	24	=	=	SYM
ejpam-6254	139	1	0	0	X
ejpam-6254	139	2	.	.	PUNCT
ejpam-6254	140	1	(	(	PUNCT
ejpam-6254	140	2	6	6	X
ejpam-6254	140	3	)	)	PUNCT
ejpam-6254	140	4	let	let	AUX
ejpam-6254	140	5	suppose	suppose	VERB
ejpam-6254	140	6	:	:	PUNCT
ejpam-6254	140	7	d2	d2	PROPN
ejpam-6254	140	8	=	=	SYM
ejpam-6254	140	9	p1	p1	PROPN
ejpam-6254	140	10	+	+	CCONJ
ejpam-6254	140	11	q1	q1	PROPN
ejpam-6254	140	12	,	,	PUNCT
ejpam-6254	140	13	d1	d1	PROPN
ejpam-6254	140	14	=	=	SYM
ejpam-6254	140	15	p2	p2	PROPN
ejpam-6254	140	16	+	+	CCONJ
ejpam-6254	140	17	q2	q2	NOUN
ejpam-6254	140	18	,	,	PUNCT
ejpam-6254	140	19	d0	d0	NOUN
ejpam-6254	140	20	=	=	SYM
ejpam-6254	140	21	p3	p3	PROPN
ejpam-6254	140	22	+	+	CCONJ
ejpam-6254	140	23	q3	q3	PROPN
ejpam-6254	140	24	.	.	PUNCT
ejpam-6254	141	1	equation	equation	NOUN
ejpam-6254	141	2	(	(	PUNCT
ejpam-6254	141	3	6	6	NUM
ejpam-6254	141	4	)	)	PUNCT
ejpam-6254	141	5	become	become	VERB
ejpam-6254	141	6	:	:	PUNCT
ejpam-6254	142	1	λ3	λ3	PROPN
ejpam-6254	142	2	+	+	PROPN
ejpam-6254	142	3	d2λ	d2λ	PROPN
ejpam-6254	142	4	2	2	NUM
ejpam-6254	142	5	+	+	NOUN
ejpam-6254	142	6	d1λ+d0	d1λ+d0	ADJ
ejpam-6254	142	7	=	=	SYM
ejpam-6254	142	8	0	0	PROPN
ejpam-6254	142	9	.	.	PUNCT
ejpam-6254	143	1	(	(	PUNCT
ejpam-6254	143	2	7	7	NUM
ejpam-6254	143	3	)	)	PUNCT
ejpam-6254	143	4	by	by	ADP
ejpam-6254	143	5	using	use	VERB
ejpam-6254	143	6	the	the	DET
ejpam-6254	143	7	hurwitz	hurwitz	PROPN
ejpam-6254	143	8	criteria	criterion	NOUN
ejpam-6254	143	9	,	,	PUNCT
ejpam-6254	143	10	e∗	e∗	NOUN
ejpam-6254	143	11	exhibits	exhibit	VERB
ejpam-6254	143	12	local	local	ADJ
ejpam-6254	143	13	asymptotic	asymptotic	ADJ
ejpam-6254	143	14	stability	stability	NOUN
ejpam-6254	143	15	at	at	ADP
ejpam-6254	143	16	τ	τ	PROPN
ejpam-6254	143	17	=	=	SYM
ejpam-6254	143	18	0	0	PROPN
ejpam-6254	143	19	,	,	PUNCT
ejpam-6254	143	20	under	under	ADP
ejpam-6254	143	21	the	the	DET
ejpam-6254	143	22	following	following	ADJ
ejpam-6254	143	23	conditions	condition	NOUN
ejpam-6254	143	24	:	:	PUNCT
ejpam-6254	143	25	s.	s.	PROPN
ejpam-6254	143	26	irum	irum	PROPN
ejpam-6254	143	27	et	et	PROPN
ejpam-6254	143	28	al	al	PROPN
ejpam-6254	143	29	.	.	PUNCT
ejpam-6254	143	30	/	/	SYM
ejpam-6254	143	31	eur	eur	PROPN
ejpam-6254	143	32	.	.	PUNCT
ejpam-6254	144	1	j.	j.	PROPN
ejpam-6254	144	2	pure	pure	PROPN
ejpam-6254	144	3	appl	appl	PROPN
ejpam-6254	144	4	.	.	PROPN
ejpam-6254	144	5	math	math	PROPN
ejpam-6254	144	6	,	,	PUNCT
ejpam-6254	144	7	18	18	NUM
ejpam-6254	144	8	(	(	PUNCT
ejpam-6254	144	9	4	4	NUM
ejpam-6254	144	10	)	)	PUNCT
ejpam-6254	144	11	(	(	PUNCT
ejpam-6254	144	12	2025	2025	NUM
ejpam-6254	144	13	)	)	PUNCT
ejpam-6254	144	14	,	,	PUNCT
ejpam-6254	144	15	6254	6254	NUM
ejpam-6254	144	16	8	8	NUM
ejpam-6254	144	17	of	of	ADP
ejpam-6254	144	18	23	23	NUM
ejpam-6254	144	19	det1	det1	NOUN
ejpam-6254	144	20	=	=	SYM
ejpam-6254	144	21	d2	d2	PROPN
ejpam-6254	144	22	>	>	X
ejpam-6254	144	23	0	0	PROPN
ejpam-6254	144	24	,	,	PUNCT
ejpam-6254	144	25	(	(	PUNCT
ejpam-6254	144	26	8)	8)	NUM
ejpam-6254	144	27	det2	det2	NOUN
ejpam-6254	144	28	=	=	SYM
ejpam-6254	144	29	(	(	PUNCT
ejpam-6254	144	30	d2	d2	PROPN
ejpam-6254	144	31	1	1	NUM
ejpam-6254	144	32	d0	d0	NOUN
ejpam-6254	144	33	d1	d1	PROPN
ejpam-6254	144	34	)	)	PUNCT
ejpam-6254	144	35	>	>	X
ejpam-6254	144	36	0	0	NUM
ejpam-6254	144	37	,	,	PUNCT
ejpam-6254	144	38	(	(	PUNCT
ejpam-6254	144	39	9	9	X
ejpam-6254	144	40	)	)	PUNCT
ejpam-6254	144	41	det3	det3	ADJ
ejpam-6254	144	42	=	=	PUNCT
ejpam-6254	144	43	d2	d2	ADP
ejpam-6254	144	44	1	1	NUM
ejpam-6254	144	45	0	0	NUM
ejpam-6254	144	46	d0	d0	NOUN
ejpam-6254	144	47	d1	d1	PROPN
ejpam-6254	144	48	d2	d2	PROPN
ejpam-6254	144	49	0	0	NOUN
ejpam-6254	144	50	0	0	NUM
ejpam-6254	144	51	d0	d0	NOUN
ejpam-6254	144	52			PROPN
ejpam-6254	144	53	>	>	X
ejpam-6254	144	54	0	0	NUM
ejpam-6254	144	55	.	.	PUNCT
ejpam-6254	145	1	(	(	PUNCT
ejpam-6254	145	2	10	10	NUM
ejpam-6254	145	3	)	)	PUNCT
ejpam-6254	145	4	since	since	SCONJ
ejpam-6254	145	5	the	the	DET
ejpam-6254	145	6	model	model	NOUN
ejpam-6254	145	7	parameters	parameter	NOUN
ejpam-6254	145	8	are	be	AUX
ejpam-6254	145	9	all	all	ADV
ejpam-6254	145	10	positive	positive	ADJ
ejpam-6254	145	11	,	,	PUNCT
ejpam-6254	145	12	then	then	ADV
ejpam-6254	145	13	it	it	PRON
ejpam-6254	145	14	is	be	AUX
ejpam-6254	145	15	always	always	ADV
ejpam-6254	145	16	asymptotically	asymptotically	ADV
ejpam-6254	145	17	stable	stable	ADJ
ejpam-6254	145	18	,	,	PUNCT
ejpam-6254	145	19	which	which	PRON
ejpam-6254	145	20	shows	show	VERB
ejpam-6254	145	21	all	all	DET
ejpam-6254	145	22	roots	root	NOUN
ejpam-6254	145	23	lie	lie	VERB
ejpam-6254	145	24	on	on	ADP
ejpam-6254	145	25	the	the	DET
ejpam-6254	145	26	left	left	ADJ
ejpam-6254	145	27	half	half	ADJ
ejpam-6254	145	28	plane	plane	NOUN
ejpam-6254	145	29	.	.	PUNCT
ejpam-6254	146	1	in	in	ADP
ejpam-6254	146	2	the	the	DET
ejpam-6254	146	3	same	same	ADJ
ejpam-6254	146	4	way	way	NOUN
ejpam-6254	146	5	,	,	PUNCT
ejpam-6254	146	6	when	when	SCONJ
ejpam-6254	146	7	τ	τ	X
ejpam-6254	146	8	>	>	X
ejpam-6254	146	9	0	0	PROPN
ejpam-6254	146	10	,	,	PUNCT
ejpam-6254	146	11	we	we	PRON
ejpam-6254	146	12	consider	consider	VERB
ejpam-6254	146	13	the	the	DET
ejpam-6254	146	14	characteristics	characteristic	NOUN
ejpam-6254	146	15	equation	equation	NOUN
ejpam-6254	146	16	provided	provide	VERB
ejpam-6254	146	17	in	in	ADP
ejpam-6254	146	18	eq	eq	NOUN
ejpam-6254	146	19	(	(	PUNCT
ejpam-6254	146	20	5	5	NUM
ejpam-6254	146	21	)	)	PUNCT
ejpam-6254	146	22	and	and	CCONJ
ejpam-6254	146	23	,	,	PUNCT
ejpam-6254	146	24	setting	set	VERB
ejpam-6254	146	25	λ	λ	PROPN
ejpam-6254	146	26	=	=	SYM
ejpam-6254	146	27	ιω	ιω	NOUN
ejpam-6254	146	28	,	,	PUNCT
ejpam-6254	146	29	we	we	PRON
ejpam-6254	146	30	have	have	VERB
ejpam-6254	146	31	λ3	λ3	PROPN
ejpam-6254	146	32	+	+	ADJ
ejpam-6254	146	33	p1λ	p1λ	PROPN
ejpam-6254	146	34	2	2	NUM
ejpam-6254	146	35	+	+	CCONJ
ejpam-6254	146	36	p2λ+	p2λ+	PROPN
ejpam-6254	146	37	p3	p3	PROPN
ejpam-6254	147	1	+	+	CCONJ
ejpam-6254	148	1	(	(	PUNCT
ejpam-6254	148	2	q1λ	q1λ	PROPN
ejpam-6254	148	3	2	2	NUM
ejpam-6254	148	4	+	+	CCONJ
ejpam-6254	148	5	q2λ+	q2λ+	CCONJ
ejpam-6254	148	6	q3	q3	NOUN
ejpam-6254	148	7	)	)	PUNCT
ejpam-6254	148	8	e−ιωτ	e−ιωτ	VERB
ejpam-6254	148	9	=	=	NOUN
ejpam-6254	148	10	0	0	X
ejpam-6254	148	11	.	.	PUNCT
ejpam-6254	149	1	(	(	PUNCT
ejpam-6254	149	2	11	11	NUM
ejpam-6254	149	3	)	)	PUNCT
ejpam-6254	149	4	by	by	ADP
ejpam-6254	149	5	separated	separate	VERB
ejpam-6254	149	6	the	the	DET
ejpam-6254	149	7	real	real	ADJ
ejpam-6254	149	8	and	and	CCONJ
ejpam-6254	149	9	imaginary	imaginary	ADJ
ejpam-6254	149	10	parts	part	NOUN
ejpam-6254	149	11	of	of	ADP
ejpam-6254	149	12	above	above	ADJ
ejpam-6254	149	13	equation	equation	NOUN
ejpam-6254	149	14	we	we	PRON
ejpam-6254	149	15	have	have	VERB
ejpam-6254	149	16	(	(	PUNCT
ejpam-6254	149	17	q3	q3	NOUN
ejpam-6254	149	18	−	−	PROPN
ejpam-6254	149	19	q1ω	q1ω	NOUN
ejpam-6254	149	20	2	2	NUM
ejpam-6254	149	21	)	)	PUNCT
ejpam-6254	149	22	cos(ωτ	cos(ωτ	NOUN
ejpam-6254	149	23	)	)	PUNCT
ejpam-6254	150	1	+	+	CCONJ
ejpam-6254	150	2	q2ω	q2ω	PROPN
ejpam-6254	150	3	sin(ωτ	sin(ωτ	NOUN
ejpam-6254	150	4	)	)	PUNCT
ejpam-6254	150	5	=	=	SYM
ejpam-6254	150	6	p1ω	p1ω	NOUN
ejpam-6254	150	7	2	2	NUM
ejpam-6254	150	8	−	−	PROPN
ejpam-6254	150	9	p3	p3	PROPN
ejpam-6254	150	10	,	,	PUNCT
ejpam-6254	150	11	(	(	PUNCT
ejpam-6254	150	12	12	12	NUM
ejpam-6254	150	13	)	)	PUNCT
ejpam-6254	150	14	q2ω	q2ω	PROPN
ejpam-6254	150	15	cos(ωτ)−	cos(ωτ)−	PROPN
ejpam-6254	150	16	(	(	PUNCT
ejpam-6254	150	17	q3	q3	PROPN
ejpam-6254	150	18	−	−	PROPN
ejpam-6254	150	19	q1ω	q1ω	NOUN
ejpam-6254	150	20	2	2	NUM
ejpam-6254	150	21	)	)	PUNCT
ejpam-6254	150	22	sin(ωτ	sin(ωτ	NOUN
ejpam-6254	150	23	)	)	PUNCT
ejpam-6254	150	24	=	=	SYM
ejpam-6254	150	25	ω3	ω3	NOUN
ejpam-6254	150	26	−	−	PROPN
ejpam-6254	150	27	p2ω	p2ω	NOUN
ejpam-6254	150	28	(	(	PUNCT
ejpam-6254	150	29	13	13	NUM
ejpam-6254	150	30	)	)	PUNCT
ejpam-6254	150	31	which	which	PRON
ejpam-6254	150	32	leads	lead	VERB
ejpam-6254	150	33	to	to	ADP
ejpam-6254	150	34	ω6	ω6	PROPN
ejpam-6254	150	35	+	+	CCONJ
ejpam-6254	150	36	(	(	PUNCT
ejpam-6254	150	37	p21	p21	NOUN
ejpam-6254	150	38	+	+	CCONJ
ejpam-6254	150	39	2p2	2p2	NUM
ejpam-6254	150	40	−	−	NOUN
ejpam-6254	150	41	q21	q21	NOUN
ejpam-6254	150	42	)	)	PUNCT
ejpam-6254	150	43	ω4	ω4	NOUN
ejpam-6254	151	1	+	+	CCONJ
ejpam-6254	151	2	(	(	PUNCT
ejpam-6254	151	3	p22	p22	NOUN
ejpam-6254	151	4	−	−	PROPN
ejpam-6254	151	5	2p1p3	2p1p3	NOUN
ejpam-6254	151	6	−	−	NOUN
ejpam-6254	151	7	q22	q22	NOUN
ejpam-6254	152	1	+	+	CCONJ
ejpam-6254	152	2	2q1q3)ω	2q1q3)ω	NOUN
ejpam-6254	152	3	2	2	NUM
ejpam-6254	153	1	+	+	CCONJ
ejpam-6254	153	2	(	(	PUNCT
ejpam-6254	153	3	p23	p23	NOUN
ejpam-6254	153	4	+	+	CCONJ
ejpam-6254	153	5	q23	q23	VERB
ejpam-6254	153	6	)	)	PUNCT
ejpam-6254	153	7	=	=	SYM
ejpam-6254	153	8	0	0	X
ejpam-6254	153	9	.	.	PUNCT
ejpam-6254	154	1	(	(	PUNCT
ejpam-6254	154	2	14	14	NUM
ejpam-6254	154	3	)	)	PUNCT
ejpam-6254	154	4	if	if	SCONJ
ejpam-6254	154	5	t	t	NOUN
ejpam-6254	154	6	=	=	SYM
ejpam-6254	154	7	ω2	ω2	PROPN
ejpam-6254	154	8	,	,	PUNCT
ejpam-6254	154	9	then	then	ADV
ejpam-6254	154	10	above	above	ADP
ejpam-6254	154	11	equation	equation	NOUN
ejpam-6254	154	12	becomes	become	VERB
ejpam-6254	154	13	t3	t3	PROPN
ejpam-6254	154	14	+	+	CCONJ
ejpam-6254	154	15	s1	s1	PROPN
ejpam-6254	154	16	t	t	NOUN
ejpam-6254	154	17	2	2	NUM
ejpam-6254	154	18	+	+	CCONJ
ejpam-6254	154	19	s2t+	s2t+	NOUN
ejpam-6254	154	20	s3	s3	NOUN
ejpam-6254	154	21	=	=	SYM
ejpam-6254	154	22	0	0	PROPN
ejpam-6254	154	23	.	.	PUNCT
ejpam-6254	155	1	(	(	PUNCT
ejpam-6254	155	2	15	15	NUM
ejpam-6254	155	3	)	)	PUNCT
ejpam-6254	155	4	where	where	SCONJ
ejpam-6254	155	5			PROPN
ejpam-6254	155	6	s1	s1	NOUN
ejpam-6254	155	7	=	=	PUNCT
ejpam-6254	155	8	(	(	PUNCT
ejpam-6254	155	9	p21	p21	NOUN
ejpam-6254	155	10	+	+	CCONJ
ejpam-6254	155	11	2p2	2p2	NUM
ejpam-6254	155	12	−	−	NOUN
ejpam-6254	155	13	q21	q21	NOUN
ejpam-6254	155	14	)	)	PUNCT
ejpam-6254	155	15	,	,	PUNCT
ejpam-6254	155	16	s2	s2	NOUN
ejpam-6254	155	17	=	=	SYM
ejpam-6254	155	18	(	(	PUNCT
ejpam-6254	155	19	p22	p22	X
ejpam-6254	155	20	−	−	PROPN
ejpam-6254	155	21	2p1p3	2p1p3	NOUN
ejpam-6254	155	22	−	−	NOUN
ejpam-6254	155	23	q22	q22	NOUN
ejpam-6254	155	24	+	+	CCONJ
ejpam-6254	155	25	2q1q3	2q1q3	NUM
ejpam-6254	155	26	)	)	PUNCT
ejpam-6254	155	27	,	,	PUNCT
ejpam-6254	155	28	s3	s3	PROPN
ejpam-6254	155	29	=	=	SYM
ejpam-6254	155	30	(	(	PUNCT
ejpam-6254	155	31	p23	p23	NOUN
ejpam-6254	155	32	+	+	CCONJ
ejpam-6254	155	33	q23	q23	NOUN
ejpam-6254	155	34	)	)	PUNCT
ejpam-6254	155	35	,	,	PUNCT
ejpam-6254	155	36	thus	thus	ADV
ejpam-6254	155	37	by	by	ADP
ejpam-6254	155	38	substituting	substitute	VERB
ejpam-6254	155	39	s1	s1	NOUN
ejpam-6254	155	40	,	,	PUNCT
ejpam-6254	155	41	s2	s2	PROPN
ejpam-6254	155	42	,	,	PUNCT
ejpam-6254	155	43	s3	s3	PROPN
ejpam-6254	155	44	in	in	ADP
ejpam-6254	155	45	above	above	ADP
ejpam-6254	155	46	equation	equation	NOUN
ejpam-6254	155	47	,	,	PUNCT
ejpam-6254	155	48	we	we	PRON
ejpam-6254	155	49	have	have	VERB
ejpam-6254	155	50	negative	negative	ADJ
ejpam-6254	155	51	roots	root	NOUN
ejpam-6254	155	52	which	which	PRON
ejpam-6254	155	53	implies	imply	VERB
ejpam-6254	155	54	that	that	SCONJ
ejpam-6254	155	55	it	it	PRON
ejpam-6254	155	56	is	be	AUX
ejpam-6254	155	57	asymptotically	asymptotically	ADV
ejpam-6254	155	58	stable	stable	ADJ
ejpam-6254	155	59	.	.	PUNCT
ejpam-6254	156	1	3	3	X
ejpam-6254	156	2	.	.	X
ejpam-6254	156	3	epidemic	epidemic	NOUN
ejpam-6254	156	4	model	model	NOUN
ejpam-6254	156	5	seirv	seirv	NOUN
ejpam-6254	156	6	-	-	PUNCT
ejpam-6254	156	7	formulation	formulation	NOUN
ejpam-6254	156	8	with	with	ADP
ejpam-6254	156	9	optimal	optimal	ADJ
ejpam-6254	156	10	control	control	NOUN
ejpam-6254	156	11	in	in	ADP
ejpam-6254	156	12	this	this	DET
ejpam-6254	156	13	section	section	NOUN
ejpam-6254	156	14	,	,	PUNCT
ejpam-6254	156	15	we	we	PRON
ejpam-6254	156	16	examine	examine	VERB
ejpam-6254	156	17	control	control	NOUN
ejpam-6254	156	18	strategy	strategy	NOUN
ejpam-6254	156	19	of	of	ADP
ejpam-6254	156	20	model	model	NOUN
ejpam-6254	156	21	model	model	NOUN
ejpam-6254	156	22	presented	present	VERB
ejpam-6254	156	23	in	in	ADP
ejpam-6254	156	24	[	[	X
ejpam-6254	156	25	11	11	NUM
ejpam-6254	156	26	]	]	PUNCT
ejpam-6254	156	27	.	.	PUNCT
ejpam-6254	157	1	the	the	DET
ejpam-6254	157	2	population	population	NOUN
ejpam-6254	157	3	of	of	ADP
ejpam-6254	157	4	e(t	e(t	PROPN
ejpam-6254	157	5	)	)	PUNCT
ejpam-6254	157	6	reduced	reduce	VERB
ejpam-6254	157	7	with	with	ADP
ejpam-6254	157	8	control	control	NOUN
ejpam-6254	157	9	u1	u1	NOUN
ejpam-6254	157	10	as	as	ADP
ejpam-6254	157	11	quarantine	quarantine	NOUN
ejpam-6254	157	12	.	.	PUNCT
ejpam-6254	158	1	the	the	DET
ejpam-6254	158	2	population	population	NOUN
ejpam-6254	158	3	of	of	ADP
ejpam-6254	158	4	i(t	i(t	PROPN
ejpam-6254	158	5	)	)	PUNCT
ejpam-6254	158	6	compartment	compartment	NOUN
ejpam-6254	158	7	decreased	decrease	VERB
ejpam-6254	158	8	with	with	ADP
ejpam-6254	158	9	control	control	NOUN
ejpam-6254	158	10	u2	u2	NOUN
ejpam-6254	158	11	as	as	ADP
ejpam-6254	158	12	treatment	treatment	NOUN
ejpam-6254	158	13	.	.	PUNCT
ejpam-6254	159	1	the	the	DET
ejpam-6254	159	2	population	population	NOUN
ejpam-6254	159	3	of	of	ADP
ejpam-6254	159	4	the	the	DET
ejpam-6254	159	5	r(t	r(t	NOUN
ejpam-6254	159	6	)	)	PUNCT
ejpam-6254	159	7	compartment	compartment	NOUN
ejpam-6254	159	8	is	be	AUX
ejpam-6254	159	9	increased	increase	VERB
ejpam-6254	159	10	by	by	ADP
ejpam-6254	159	11	control	control	NOUN
ejpam-6254	159	12	u1	u1	PROPN
ejpam-6254	159	13	of	of	ADP
ejpam-6254	159	14	the	the	DET
ejpam-6254	159	15	exposed	expose	VERB
ejpam-6254	159	16	class	class	NOUN
ejpam-6254	159	17	and	and	CCONJ
ejpam-6254	159	18	cotrol	cotrol	NOUN
ejpam-6254	159	19	u2	u2	NOUN
ejpam-6254	159	20	of	of	ADP
ejpam-6254	159	21	infected	infected	ADJ
ejpam-6254	159	22	class	class	NOUN
ejpam-6254	159	23	.	.	PUNCT
ejpam-6254	160	1	thus	thus	ADV
ejpam-6254	160	2	the	the	DET
ejpam-6254	160	3	optimal	optimal	ADJ
ejpam-6254	160	4	control	control	NOUN
ejpam-6254	160	5	model	model	NOUN
ejpam-6254	160	6	can	can	AUX
ejpam-6254	160	7	be	be	AUX
ejpam-6254	160	8	expressed	express	VERB
ejpam-6254	160	9	as	as	ADP
ejpam-6254	160	10	:	:	PUNCT
ejpam-6254	160	11	s.	s.	PROPN
ejpam-6254	160	12	irum	irum	PROPN
ejpam-6254	160	13	et	et	PROPN
ejpam-6254	160	14	al	al	PROPN
ejpam-6254	160	15	.	.	PUNCT
ejpam-6254	160	16	/	/	SYM
ejpam-6254	160	17	eur	eur	PROPN
ejpam-6254	160	18	.	.	PUNCT
ejpam-6254	161	1	j.	j.	PROPN
ejpam-6254	161	2	pure	pure	PROPN
ejpam-6254	161	3	appl	appl	PROPN
ejpam-6254	161	4	.	.	PROPN
ejpam-6254	161	5	math	math	PROPN
ejpam-6254	161	6	,	,	PUNCT
ejpam-6254	161	7	18	18	NUM
ejpam-6254	161	8	(	(	PUNCT
ejpam-6254	161	9	4	4	NUM
ejpam-6254	161	10	)	)	PUNCT
ejpam-6254	161	11	(	(	PUNCT
ejpam-6254	161	12	2025	2025	NUM
ejpam-6254	161	13	)	)	PUNCT
ejpam-6254	161	14	,	,	PUNCT
ejpam-6254	161	15	6254	6254	NUM
ejpam-6254	161	16	9	9	NUM
ejpam-6254	161	17	of	of	ADP
ejpam-6254	161	18	23	23	NUM
ejpam-6254	161	19	ds(t	ds(t	NOUN
ejpam-6254	161	20	)	)	PUNCT
ejpam-6254	161	21	dt	dt	NOUN
ejpam-6254	162	1	=	=	PUNCT
ejpam-6254	162	2	∆−	∆−	NOUN
ejpam-6254	162	3	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	162	4	)	)	PUNCT
ejpam-6254	162	5	1	1	NUM
ejpam-6254	162	6	+	+	NUM
ejpam-6254	162	7	αi(t	αi(t	NOUN
ejpam-6254	162	8	)	)	PUNCT
ejpam-6254	162	9	−	−	PROPN
ejpam-6254	162	10	µs(t)−	µs(t)−	PROPN
ejpam-6254	162	11	γ2s(t	γ2s(t	PROPN
ejpam-6254	162	12	)	)	PUNCT
ejpam-6254	162	13	,	,	PUNCT
ejpam-6254	162	14	de(t	de(t	X
ejpam-6254	162	15	)	)	PUNCT
ejpam-6254	162	16	dt	dt	NOUN
ejpam-6254	163	1	=	=	SYM
ejpam-6254	163	2	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	163	3	)	)	PUNCT
ejpam-6254	163	4	1	1	NUM
ejpam-6254	163	5	+	+	NUM
ejpam-6254	163	6	αi(t	αi(t	NOUN
ejpam-6254	163	7	)	)	PUNCT
ejpam-6254	164	1	−	−	PROPN
ejpam-6254	164	2	σe(t)−	σe(t)−	PROPN
ejpam-6254	164	3	µe(t)−	µe(t)−	PROPN
ejpam-6254	164	4	u1e(t	u1e(t	PROPN
ejpam-6254	164	5	)	)	PUNCT
ejpam-6254	164	6	,	,	PUNCT
ejpam-6254	164	7	di(t	di(t	NOUN
ejpam-6254	164	8	)	)	PUNCT
ejpam-6254	164	9	dt	dt	X
ejpam-6254	165	1	=	=	PROPN
ejpam-6254	165	2	σe(t)−	σe(t)−	PROPN
ejpam-6254	165	3	γ1i(t)−	γ1i(t)−	PROPN
ejpam-6254	165	4	µi(t)−	µi(t)−	PROPN
ejpam-6254	165	5	u2i(t	u2i(t	PROPN
ejpam-6254	165	6	)	)	PUNCT
ejpam-6254	165	7	,	,	PUNCT
ejpam-6254	165	8	dr(t	dr(t	NUM
ejpam-6254	165	9	)	)	PUNCT
ejpam-6254	165	10	dt	dt	X
ejpam-6254	166	1	=	=	SYM
ejpam-6254	166	2	γ1i(t)−	γ1i(t)−	PROPN
ejpam-6254	166	3	γ3r(t)−	γ3r(t)−	PROPN
ejpam-6254	166	4	µr(t	µr(t	NUM
ejpam-6254	166	5	)	)	PUNCT
ejpam-6254	167	1	+	+	CCONJ
ejpam-6254	167	2	u1e(t	u1e(t	PROPN
ejpam-6254	167	3	)	)	PUNCT
ejpam-6254	168	1	+	+	CCONJ
ejpam-6254	168	2	u2i(t	u2i(t	PROPN
ejpam-6254	168	3	)	)	PUNCT
ejpam-6254	168	4	,	,	PUNCT
ejpam-6254	168	5	dv	dv	PROPN
ejpam-6254	168	6	(	(	PUNCT
ejpam-6254	168	7	t	t	PROPN
ejpam-6254	168	8	)	)	PUNCT
ejpam-6254	168	9	dt	dt	NOUN
ejpam-6254	168	10	=	=	SYM
ejpam-6254	168	11	γ2s(t	γ2s(t	PROPN
ejpam-6254	168	12	)	)	PUNCT
ejpam-6254	168	13	+	+	CCONJ
ejpam-6254	168	14	γ3r(t)−	γ3r(t)−	PROPN
ejpam-6254	168	15	µv	µv	PROPN
ejpam-6254	168	16	(	(	PUNCT
ejpam-6254	168	17	t	t	PROPN
ejpam-6254	168	18	)	)	PUNCT
ejpam-6254	168	19	.	.	PUNCT
ejpam-6254	169	1	(	(	PUNCT
ejpam-6254	169	2	16	16	NUM
ejpam-6254	169	3	)	)	PUNCT
ejpam-6254	169	4	our	our	PRON
ejpam-6254	169	5	aim	aim	NOUN
ejpam-6254	169	6	to	to	PART
ejpam-6254	169	7	decrease	decrease	VERB
ejpam-6254	169	8	the	the	DET
ejpam-6254	169	9	number	number	NOUN
ejpam-6254	169	10	of	of	ADP
ejpam-6254	169	11	exposed	expose	VERB
ejpam-6254	169	12	and	and	CCONJ
ejpam-6254	169	13	infected	infect	VERB
ejpam-6254	169	14	individuals	individual	NOUN
ejpam-6254	169	15	while	while	SCONJ
ejpam-6254	169	16	increase	increase	VERB
ejpam-6254	169	17	the	the	DET
ejpam-6254	169	18	count	count	NOUN
ejpam-6254	169	19	of	of	ADP
ejpam-6254	169	20	recovering	recover	VERB
ejpam-6254	169	21	throughout	throughout	ADP
ejpam-6254	169	22	the	the	DET
ejpam-6254	169	23	epidemic	epidemic	NOUN
ejpam-6254	169	24	.	.	PUNCT
ejpam-6254	170	1	mathematically	mathematically	ADV
ejpam-6254	170	2	,	,	PUNCT
ejpam-6254	170	3	for	for	ADP
ejpam-6254	170	4	a	a	DET
ejpam-6254	170	5	fixed	fix	VERB
ejpam-6254	170	6	terminal	terminal	ADJ
ejpam-6254	170	7	time	time	NOUN
ejpam-6254	170	8	ti	ti	NOUN
ejpam-6254	170	9	,	,	PUNCT
ejpam-6254	170	10	the	the	DET
ejpam-6254	170	11	problem	problem	NOUN
ejpam-6254	170	12	is	be	AUX
ejpam-6254	170	13	to	to	PART
ejpam-6254	170	14	minimize	minimize	VERB
ejpam-6254	170	15	the	the	DET
ejpam-6254	170	16	objective	objective	ADJ
ejpam-6254	170	17	function	function	NOUN
ejpam-6254	170	18	,	,	PUNCT
ejpam-6254	170	19	which	which	PRON
ejpam-6254	170	20	is	be	AUX
ejpam-6254	170	21	given	give	VERB
ejpam-6254	170	22	as	as	ADP
ejpam-6254	170	23	:	:	PUNCT
ejpam-6254	170	24	j(u1	j(u1	NOUN
ejpam-6254	170	25	,	,	PUNCT
ejpam-6254	170	26	u2	u2	PROPN
ejpam-6254	170	27	)	)	PUNCT
ejpam-6254	170	28	=	=	SYM
ejpam-6254	171	1	∫	∫	PROPN
ejpam-6254	171	2	t	t	NOUN
ejpam-6254	171	3	0	0	NUM
ejpam-6254	171	4	[	[	PUNCT
ejpam-6254	171	5	a1s(t	a1s(t	PROPN
ejpam-6254	171	6	)	)	PUNCT
ejpam-6254	171	7	+	+	NOUN
ejpam-6254	171	8	a2e(t	a2e(t	PROPN
ejpam-6254	171	9	)	)	PUNCT
ejpam-6254	172	1	+	+	SYM
ejpam-6254	172	2	a3i(t)−a4r(t	a3i(t)−a4r(t	NOUN
ejpam-6254	172	3	)	)	PUNCT
ejpam-6254	172	4	+	+	PROPN
ejpam-6254	172	5	a5v	a5v	PROPN
ejpam-6254	172	6	(	(	PUNCT
ejpam-6254	172	7	t	t	PROPN
ejpam-6254	172	8	)	)	PUNCT
ejpam-6254	172	9	+	+	CCONJ
ejpam-6254	172	10	a6	a6	X
ejpam-6254	172	11	2	2	NUM
ejpam-6254	172	12	u21(t	u21(t	ADJ
ejpam-6254	172	13	)	)	PUNCT
ejpam-6254	173	1	+	+	CCONJ
ejpam-6254	173	2	a7	a7	PROPN
ejpam-6254	173	3	2	2	NUM
ejpam-6254	173	4	u22	u22	PROPN
ejpam-6254	173	5	]	]	PUNCT
ejpam-6254	173	6	dt	dt	X
ejpam-6254	173	7	.	.	PUNCT
ejpam-6254	174	1	(	(	PUNCT
ejpam-6254	174	2	17	17	NUM
ejpam-6254	174	3	)	)	PUNCT
ejpam-6254	174	4	in	in	ADP
ejpam-6254	174	5	the	the	DET
ejpam-6254	174	6	above	above	ADJ
ejpam-6254	174	7	expression	expression	NOUN
ejpam-6254	174	8	,	,	PUNCT
ejpam-6254	174	9	ai	ai	VERB
ejpam-6254	174	10	≥	≥	NOUN
ejpam-6254	174	11	0	0	NUM
ejpam-6254	174	12	(	(	PUNCT
ejpam-6254	174	13	for	for	ADP
ejpam-6254	174	14	i	i	PRON
ejpam-6254	174	15	=	=	SYM
ejpam-6254	174	16	1	1	NUM
ejpam-6254	174	17	..	..	SYM
ejpam-6254	174	18	7	7	NUM
ejpam-6254	174	19	)	)	PUNCT
ejpam-6254	174	20	represents	represent	VERB
ejpam-6254	174	21	the	the	DET
ejpam-6254	174	22	scaling	scale	VERB
ejpam-6254	174	23	factors	factor	NOUN
ejpam-6254	174	24	that	that	PRON
ejpam-6254	174	25	adjust	adjust	VERB
ejpam-6254	174	26	the	the	DET
ejpam-6254	174	27	contribution	contribution	NOUN
ejpam-6254	174	28	of	of	ADP
ejpam-6254	174	29	each	each	DET
ejpam-6254	174	30	term	term	NOUN
ejpam-6254	174	31	in	in	ADP
ejpam-6254	174	32	the	the	DET
ejpam-6254	174	33	functional	functional	NOUN
ejpam-6254	174	34	.	.	PUNCT
ejpam-6254	175	1	the	the	DET
ejpam-6254	175	2	objective	objective	NOUN
ejpam-6254	175	3	is	be	AUX
ejpam-6254	175	4	to	to	PART
ejpam-6254	175	5	find	find	VERB
ejpam-6254	175	6	the	the	DET
ejpam-6254	175	7	optimal	optimal	ADJ
ejpam-6254	175	8	control	control	NOUN
ejpam-6254	175	9	pairs	pair	NOUN
ejpam-6254	175	10	u∗1,u	u∗1,u	PROPN
ejpam-6254	175	11	∗	∗	NOUN
ejpam-6254	175	12	2	2	NUM
ejpam-6254	175	13	such	such	ADJ
ejpam-6254	175	14	that	that	PRON
ejpam-6254	175	15	:	:	PUNCT
ejpam-6254	175	16	j(u∗1	j(u∗1	PROPN
ejpam-6254	175	17	,	,	PUNCT
ejpam-6254	175	18	u∗2	u∗2	NOUN
ejpam-6254	175	19	)	)	PUNCT
ejpam-6254	175	20	=	=	SYM
ejpam-6254	175	21	min{j(u1	min{j(u1	NOUN
ejpam-6254	175	22	,	,	PUNCT
ejpam-6254	175	23	u2	u2	NOUN
ejpam-6254	175	24	)	)	PUNCT
ejpam-6254	175	25	:	:	PUNCT
ejpam-6254	175	26	u1	u1	NOUN
ejpam-6254	175	27	,	,	PUNCT
ejpam-6254	175	28	u2	u2	PROPN
ejpam-6254	175	29	∈	∈	PROPN
ejpam-6254	175	30	u	u	NOUN
ejpam-6254	175	31	}	}	PUNCT
ejpam-6254	175	32	.	.	PUNCT
ejpam-6254	176	1	(	(	PUNCT
ejpam-6254	176	2	18	18	NUM
ejpam-6254	176	3	)	)	PUNCT
ejpam-6254	176	4	in	in	ADP
ejpam-6254	176	5	this	this	DET
ejpam-6254	176	6	setting	setting	NOUN
ejpam-6254	176	7	,	,	PUNCT
ejpam-6254	176	8	u	u	PRON
ejpam-6254	176	9	denotes	denote	VERB
ejpam-6254	176	10	the	the	DET
ejpam-6254	176	11	pair	pair	NOUN
ejpam-6254	176	12	of	of	ADP
ejpam-6254	176	13	feasible	feasible	ADJ
ejpam-6254	176	14	controls	control	NOUN
ejpam-6254	176	15	,	,	PUNCT
ejpam-6254	176	16	given	give	VERB
ejpam-6254	176	17	by	by	ADP
ejpam-6254	176	18	:	:	PUNCT
ejpam-6254	176	19	u	u	NOUN
ejpam-6254	176	20	=	=	PUNCT
ejpam-6254	176	21	{	{	PUNCT
ejpam-6254	176	22	u	u	NOUN
ejpam-6254	176	23	=	=	NOUN
ejpam-6254	176	24	ui(t	ui(t	NOUN
ejpam-6254	176	25	)	)	PUNCT
ejpam-6254	176	26	:	:	PUNCT
ejpam-6254	176	27	0	0	NUM
ejpam-6254	176	28	≤	≤	NUM
ejpam-6254	176	29	ui(t	ui(t	NOUN
ejpam-6254	176	30	)	)	PUNCT
ejpam-6254	176	31	≤	≤	NUM
ejpam-6254	176	32	umax	umax	VERB
ejpam-6254	176	33	i	i	NOUN
ejpam-6254	176	34	≤	≤	ADJ
ejpam-6254	176	35	1	1	NUM
ejpam-6254	176	36	,	,	PUNCT
ejpam-6254	176	37	t	t	PROPN
ejpam-6254	176	38	∈	∈	PROPN
ejpam-6254	177	1	[	[	X
ejpam-6254	177	2	0	0	NUM
ejpam-6254	177	3	,	,	PUNCT
ejpam-6254	177	4	t	t	X
ejpam-6254	177	5	]	]	PUNCT
ejpam-6254	177	6	,	,	PUNCT
ejpam-6254	177	7	i	i	PRON
ejpam-6254	177	8	=	=	NOUN
ejpam-6254	177	9	1	1	NUM
ejpam-6254	177	10	,	,	PUNCT
ejpam-6254	177	11	2	2	NUM
ejpam-6254	177	12	}	}	PUNCT
ejpam-6254	177	13	.	.	PUNCT
ejpam-6254	178	1	(	(	PUNCT
ejpam-6254	178	2	19	19	NUM
ejpam-6254	178	3	)	)	PUNCT
ejpam-6254	178	4	here	here	ADV
ejpam-6254	178	5	u	u	NOUN
ejpam-6254	178	6	is	be	AUX
ejpam-6254	178	7	lebesgue	lebesgue	NOUN
ejpam-6254	178	8	measurable	measurable	ADJ
ejpam-6254	178	9	.	.	PUNCT
ejpam-6254	179	1	the	the	DET
ejpam-6254	179	2	flow	flow	NOUN
ejpam-6254	179	3	chart	chart	NOUN
ejpam-6254	179	4	of	of	ADP
ejpam-6254	179	5	the	the	DET
ejpam-6254	179	6	model	model	NOUN
ejpam-6254	179	7	(	(	PUNCT
ejpam-6254	179	8	16	16	NUM
ejpam-6254	179	9	)	)	PUNCT
ejpam-6254	179	10	is	be	AUX
ejpam-6254	179	11	presented	present	VERB
ejpam-6254	179	12	in	in	ADP
ejpam-6254	179	13	fig	fig	NOUN
ejpam-6254	179	14	.	.	PUNCT
ejpam-6254	180	1	(	(	PUNCT
ejpam-6254	180	2	1	1	NUM
ejpam-6254	180	3	)	)	PUNCT
ejpam-6254	180	4	.	.	PUNCT
ejpam-6254	181	1	s.	s.	PROPN
ejpam-6254	181	2	irum	irum	PROPN
ejpam-6254	181	3	et	et	PROPN
ejpam-6254	181	4	al	al	PROPN
ejpam-6254	181	5	.	.	PUNCT
ejpam-6254	181	6	/	/	SYM
ejpam-6254	181	7	eur	eur	PROPN
ejpam-6254	181	8	.	.	PUNCT
ejpam-6254	182	1	j.	j.	PROPN
ejpam-6254	182	2	pure	pure	PROPN
ejpam-6254	182	3	appl	appl	PROPN
ejpam-6254	182	4	.	.	PROPN
ejpam-6254	182	5	math	math	PROPN
ejpam-6254	182	6	,	,	PUNCT
ejpam-6254	182	7	18	18	NUM
ejpam-6254	182	8	(	(	PUNCT
ejpam-6254	182	9	4	4	NUM
ejpam-6254	182	10	)	)	PUNCT
ejpam-6254	182	11	(	(	PUNCT
ejpam-6254	182	12	2025	2025	NUM
ejpam-6254	182	13	)	)	PUNCT
ejpam-6254	182	14	,	,	PUNCT
ejpam-6254	182	15	6254	6254	NUM
ejpam-6254	182	16	10	10	NUM
ejpam-6254	182	17	of	of	ADP
ejpam-6254	182	18	23	23	NUM
ejpam-6254	182	19	figure	figure	NOUN
ejpam-6254	182	20	1	1	NUM
ejpam-6254	182	21	:	:	PUNCT
ejpam-6254	182	22	flow	flow	VERB
ejpam-6254	182	23	chart	chart	NOUN
ejpam-6254	182	24	of	of	ADP
ejpam-6254	182	25	model	model	NOUN
ejpam-6254	182	26	(	(	PUNCT
ejpam-6254	182	27	16	16	NUM
ejpam-6254	182	28	)	)	PUNCT
ejpam-6254	182	29	now	now	ADV
ejpam-6254	182	30	,	,	PUNCT
ejpam-6254	182	31	we	we	PRON
ejpam-6254	182	32	first	first	ADV
ejpam-6254	182	33	find	find	VERB
ejpam-6254	182	34	the	the	DET
ejpam-6254	182	35	kernels	kernel	NOUN
ejpam-6254	182	36	of	of	ADP
ejpam-6254	182	37	control	control	PROPN
ejpam-6254	182	38	model	model	PROPN
ejpam-6254	182	39	.	.	PUNCT
ejpam-6254	183	1	for	for	ADP
ejpam-6254	183	2	this	this	DET
ejpam-6254	183	3	purpose	purpose	NOUN
ejpam-6254	183	4	,	,	PUNCT
ejpam-6254	183	5	we	we	PRON
ejpam-6254	183	6	introduce	introduce	VERB
ejpam-6254	183	7	the	the	DET
ejpam-6254	183	8	functions	function	NOUN
ejpam-6254	183	9	ki	ki	PROPN
ejpam-6254	183	10	where	where	SCONJ
ejpam-6254	183	11	i	i	PRON
ejpam-6254	183	12	∈	∈	PROPN
ejpam-6254	183	13	{	{	PUNCT
ejpam-6254	183	14	1	1	NUM
ejpam-6254	183	15	,	,	PUNCT
ejpam-6254	183	16	.	.	PUNCT
ejpam-6254	183	17	.	.	PUNCT
ejpam-6254	184	1	.	.	PUNCT
ejpam-6254	185	1	,	,	PUNCT
ejpam-6254	185	2	5	5	NUM
ejpam-6254	185	3	}	}	PUNCT
ejpam-6254	185	4	,	,	PUNCT
ejpam-6254	185	5	while	while	SCONJ
ejpam-6254	185	6	assuming	assume	VERB
ejpam-6254	185	7	l[0	l[0	NOUN
ejpam-6254	185	8	,	,	PUNCT
ejpam-6254	185	9	1	1	NUM
ejpam-6254	185	10	]	]	PUNCT
ejpam-6254	185	11	.	.	PUNCT
ejpam-6254	186	1	we	we	PRON
ejpam-6254	186	2	describe	describe	VERB
ejpam-6254	186	3	these	these	DET
ejpam-6254	186	4	functions	function	NOUN
ejpam-6254	186	5	in	in	ADP
ejpam-6254	186	6	the	the	DET
ejpam-6254	186	7	following	following	ADJ
ejpam-6254	186	8	manner	manner	NOUN
ejpam-6254	186	9	:	:	PUNCT
ejpam-6254	186	10	k1(t	k1(t	PROPN
ejpam-6254	186	11	,	,	PUNCT
ejpam-6254	186	12	s	s	X
ejpam-6254	186	13	)	)	PUNCT
ejpam-6254	186	14	=	=	PUNCT
ejpam-6254	186	15	∆−	∆−	NOUN
ejpam-6254	186	16	βs(t)i(t	βs(t)i(t	ADV
ejpam-6254	186	17	)	)	PUNCT
ejpam-6254	186	18	1	1	NUM
ejpam-6254	186	19	+	+	NUM
ejpam-6254	186	20	αi(t	αi(t	NOUN
ejpam-6254	186	21	)	)	PUNCT
ejpam-6254	186	22	−	−	PROPN
ejpam-6254	187	1	(	(	PUNCT
ejpam-6254	187	2	γ2	γ2	PROPN
ejpam-6254	187	3	+	+	CCONJ
ejpam-6254	187	4	µ)s(t	µ)s(t	PROPN
ejpam-6254	187	5	)	)	PUNCT
ejpam-6254	187	6	,	,	PUNCT
ejpam-6254	187	7	k2(t	k2(t	PROPN
ejpam-6254	187	8	,	,	PUNCT
ejpam-6254	187	9	e	e	NOUN
ejpam-6254	187	10	)	)	PUNCT
ejpam-6254	187	11	=	=	SYM
ejpam-6254	187	12	βs(t)i(t	βs(t)i(t	ADJ
ejpam-6254	187	13	)	)	PUNCT
ejpam-6254	187	14	1	1	NUM
ejpam-6254	187	15	+	+	NUM
ejpam-6254	187	16	αi(t	αi(t	NOUN
ejpam-6254	187	17	)	)	PUNCT
ejpam-6254	187	18	−	−	PROPN
ejpam-6254	188	1	(	(	PUNCT
ejpam-6254	188	2	σ	σ	PROPN
ejpam-6254	188	3	+	+	PROPN
ejpam-6254	188	4	µ)e(t)−	µ)e(t)−	PROPN
ejpam-6254	188	5	u1e(t	u1e(t	PROPN
ejpam-6254	188	6	)	)	PUNCT
ejpam-6254	188	7	,	,	PUNCT
ejpam-6254	189	1	k3(t	k3(t	PROPN
ejpam-6254	189	2	,	,	PUNCT
ejpam-6254	189	3	i	i	NOUN
ejpam-6254	189	4	)	)	PUNCT
ejpam-6254	189	5	=	=	SYM
ejpam-6254	189	6	σe(t)−	σe(t)−	PROPN
ejpam-6254	189	7	(	(	PUNCT
ejpam-6254	189	8	γ1	γ1	PROPN
ejpam-6254	189	9	+	+	CCONJ
ejpam-6254	189	10	µ)i(t)−	µ)i(t)−	PROPN
ejpam-6254	189	11	u2i(t	u2i(t	PROPN
ejpam-6254	189	12	)	)	PUNCT
ejpam-6254	189	13	k4(t	k4(t	PROPN
ejpam-6254	189	14	,	,	PUNCT
ejpam-6254	189	15	r	r	NOUN
ejpam-6254	189	16	)	)	PUNCT
ejpam-6254	189	17	=	=	SYM
ejpam-6254	190	1	γ1i(t)−	γ1i(t)−	PROPN
ejpam-6254	190	2	γ3r(t)−	γ3r(t)−	PROPN
ejpam-6254	190	3	µr(t	µr(t	NUM
ejpam-6254	190	4	)	)	PUNCT
ejpam-6254	190	5	+	+	CCONJ
ejpam-6254	190	6	u1e(t	u1e(t	PROPN
ejpam-6254	190	7	)	)	PUNCT
ejpam-6254	190	8	+	+	CCONJ
ejpam-6254	190	9	u2i(t	u2i(t	PROPN
ejpam-6254	190	10	)	)	PUNCT
ejpam-6254	190	11	,	,	PUNCT
ejpam-6254	190	12	k5(t	k5(t	INTJ
ejpam-6254	190	13	,	,	PUNCT
ejpam-6254	190	14	v	v	NOUN
ejpam-6254	190	15	)	)	PUNCT
ejpam-6254	190	16	=	=	SYM
ejpam-6254	190	17	γ2s(t	γ2s(t	PROPN
ejpam-6254	190	18	)	)	PUNCT
ejpam-6254	190	19	+	+	CCONJ
ejpam-6254	190	20	γ3r(t)−	γ3r(t)−	AUX
ejpam-6254	190	21	µv	µv	PROPN
ejpam-6254	190	22	(	(	PUNCT
ejpam-6254	190	23	t	t	NOUN
ejpam-6254	190	24	)	)	PUNCT
ejpam-6254	190	25	theorem	theorem	NOUN
ejpam-6254	190	26	2	2	NUM
ejpam-6254	190	27	.	.	PUNCT
ejpam-6254	190	28	given	give	VERB
ejpam-6254	190	29	the	the	DET
ejpam-6254	190	30	assumptions	assumption	NOUN
ejpam-6254	190	31	stated	state	VERB
ejpam-6254	190	32	above	above	ADV
ejpam-6254	190	33	,	,	PUNCT
ejpam-6254	190	34	the	the	DET
ejpam-6254	190	35	kernels	kernel	NOUN
ejpam-6254	190	36	ki	ki	PROPN
ejpam-6254	190	37	satisfy	satisfy	VERB
ejpam-6254	190	38	the	the	DET
ejpam-6254	190	39	lipschitz	lipschitz	NOUN
ejpam-6254	190	40	condition	condition	NOUN
ejpam-6254	190	41	and	and	CCONJ
ejpam-6254	190	42	are	be	AUX
ejpam-6254	190	43	contractions	contraction	NOUN
ejpam-6254	190	44	if	if	SCONJ
ejpam-6254	190	45	and	and	CCONJ
ejpam-6254	190	46	only	only	ADV
ejpam-6254	190	47	if	if	SCONJ
ejpam-6254	190	48	the	the	DET
ejpam-6254	190	49	lipschitz	lipschitz	NOUN
ejpam-6254	190	50	constants	constant	VERB
ejpam-6254	190	51	ψj	ψj	ADV
ejpam-6254	190	52	<	<	X
ejpam-6254	190	53	1	1	NUM
ejpam-6254	190	54	where	where	SCONJ
ejpam-6254	190	55	j	j	PROPN
ejpam-6254	190	56	∈	∈	PROPN
ejpam-6254	190	57	{	{	PUNCT
ejpam-6254	190	58	1	1	NUM
ejpam-6254	190	59	,	,	PUNCT
ejpam-6254	190	60	.	.	PUNCT
ejpam-6254	190	61	.	.	PUNCT
ejpam-6254	190	62	.	.	PUNCT
ejpam-6254	191	1	,	,	PUNCT
ejpam-6254	191	2	5	5	NUM
ejpam-6254	191	3	}	}	PUNCT
ejpam-6254	191	4	,	,	PUNCT
ejpam-6254	191	5	for	for	ADP
ejpam-6254	191	6	each	each	DET
ejpam-6254	191	7	i	i	PRON
ejpam-6254	191	8	∈	∈	PROPN
ejpam-6254	191	9	{	{	PUNCT
ejpam-6254	191	10	1	1	NUM
ejpam-6254	191	11	,	,	PUNCT
ejpam-6254	191	12	.	.	PUNCT
ejpam-6254	191	13	.	.	PUNCT
ejpam-6254	191	14	.	.	PUNCT
ejpam-6254	192	1	,	,	PUNCT
ejpam-6254	192	2	5	5	NUM
ejpam-6254	192	3	}	}	PUNCT
ejpam-6254	192	4	.	.	PUNCT
ejpam-6254	193	1	proof	proof	NOUN
ejpam-6254	193	2	.	.	PUNCT
ejpam-6254	194	1	for	for	ADP
ejpam-6254	194	2	proof	proof	NOUN
ejpam-6254	194	3	of	of	ADP
ejpam-6254	194	4	this	this	DET
ejpam-6254	194	5	theorem	theorem	NOUN
ejpam-6254	194	6	we	we	PRON
ejpam-6254	194	7	are	be	AUX
ejpam-6254	194	8	employing	employ	VERB
ejpam-6254	194	9	certain	certain	ADJ
ejpam-6254	194	10	conditions	condition	NOUN
ejpam-6254	194	11	on	on	ADP
ejpam-6254	194	12	the	the	DET
ejpam-6254	194	13	kernels	kernel	NOUN
ejpam-6254	194	14	:	:	PUNCT
ejpam-6254	194	15	lipschitz	lipschitz	NOUN
ejpam-6254	194	16	condition	condition	NOUN
ejpam-6254	194	17	for	for	ADP
ejpam-6254	194	18	k1(s	k1(s	PROPN
ejpam-6254	194	19	):	):	PUNCT
ejpam-6254	194	20	∥k1(s)−k1(s	∥k1(s)−k1(	NOUN
ejpam-6254	194	21	∗)∥	∗)∥	NOUN
ejpam-6254	194	22	=	=	SYM
ejpam-6254	194	23	∥∥∥∥∆−	∥∥∥∥∆−	NUM
ejpam-6254	194	24	βsi	βsi	NOUN
ejpam-6254	194	25	1	1	NUM
ejpam-6254	194	26	+	+	CCONJ
ejpam-6254	194	27	αi	αi	PRON
ejpam-6254	194	28	−	−	PROPN
ejpam-6254	195	1	(	(	PUNCT
ejpam-6254	195	2	γ2	γ2	NOUN
ejpam-6254	195	3	+	+	CCONJ
ejpam-6254	195	4	µ)s	µ)s	NOUN
ejpam-6254	195	5	−	−	NOUN
ejpam-6254	195	6	(	(	PUNCT
ejpam-6254	195	7	∆−	∆−	NOUN
ejpam-6254	195	8	βs∗i	βs∗i	VERB
ejpam-6254	195	9	1	1	NUM
ejpam-6254	195	10	+	+	CCONJ
ejpam-6254	195	11	αi	αi	VERB
ejpam-6254	195	12	−	−	PROPN
ejpam-6254	196	1	(	(	PUNCT
ejpam-6254	196	2	γ2	γ2	PROPN
ejpam-6254	196	3	+	+	CCONJ
ejpam-6254	196	4	µ)s∗	µ)s∗	ADJ
ejpam-6254	196	5	)	)	PUNCT
ejpam-6254	196	6	∥	∥	PROPN
ejpam-6254	196	7	,	,	PUNCT
ejpam-6254	196	8	≤	≤	NOUN
ejpam-6254	196	9	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	196	10	βi	βi	SYM
ejpam-6254	196	11	1	1	NUM
ejpam-6254	196	12	+	+	CCONJ
ejpam-6254	196	13	αi	αi	X
ejpam-6254	197	1	+	+	CCONJ
ejpam-6254	197	2	(	(	PUNCT
ejpam-6254	197	3	γ2	γ2	PROPN
ejpam-6254	197	4	+	+	CCONJ
ejpam-6254	197	5	µ	µ	NOUN
ejpam-6254	197	6	)	)	PUNCT
ejpam-6254	197	7	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	198	1	∥s	∥s	NOUN
ejpam-6254	198	2	−	−	PROPN
ejpam-6254	198	3	s∗∥	s∗∥	PROPN
ejpam-6254	198	4	,	,	PUNCT
ejpam-6254	198	5	=	=	SYM
ejpam-6254	198	6	ψ1∥s	ψ1∥s	NOUN
ejpam-6254	198	7	−	−	PROPN
ejpam-6254	198	8	s∗∥	s∗∥	PROPN
ejpam-6254	198	9	,	,	PUNCT
ejpam-6254	198	10	s.	s.	PROPN
ejpam-6254	198	11	irum	irum	PROPN
ejpam-6254	198	12	et	et	PROPN
ejpam-6254	198	13	al	al	PROPN
ejpam-6254	198	14	.	.	PUNCT
ejpam-6254	198	15	/	/	SYM
ejpam-6254	198	16	eur	eur	PROPN
ejpam-6254	198	17	.	.	PUNCT
ejpam-6254	199	1	j.	j.	PROPN
ejpam-6254	199	2	pure	pure	PROPN
ejpam-6254	199	3	appl	appl	PROPN
ejpam-6254	199	4	.	.	PROPN
ejpam-6254	199	5	math	math	PROPN
ejpam-6254	199	6	,	,	PUNCT
ejpam-6254	199	7	18	18	NUM
ejpam-6254	199	8	(	(	PUNCT
ejpam-6254	199	9	4	4	NUM
ejpam-6254	199	10	)	)	PUNCT
ejpam-6254	199	11	(	(	PUNCT
ejpam-6254	199	12	2025	2025	NUM
ejpam-6254	199	13	)	)	PUNCT
ejpam-6254	199	14	,	,	PUNCT
ejpam-6254	199	15	6254	6254	NUM
ejpam-6254	199	16	11	11	NUM
ejpam-6254	199	17	of	of	ADP
ejpam-6254	199	18	23	23	NUM
ejpam-6254	199	19	where	where	SCONJ
ejpam-6254	199	20	ψ1	ψ1	NOUN
ejpam-6254	199	21	=	=	SYM
ejpam-6254	199	22	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	199	23	βi	βi	NUM
ejpam-6254	199	24	1	1	NUM
ejpam-6254	199	25	+	+	CCONJ
ejpam-6254	199	26	αi	αi	X
ejpam-6254	200	1	+	+	CCONJ
ejpam-6254	201	1	(	(	PUNCT
ejpam-6254	201	2	γ2	γ2	PROPN
ejpam-6254	201	3	+	+	CCONJ
ejpam-6254	201	4	µ	µ	NUM
ejpam-6254	201	5	)	)	PUNCT
ejpam-6254	201	6	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	201	7	.	.	PUNCT
ejpam-6254	202	1	lipschitz	lipschitz	NOUN
ejpam-6254	202	2	condition	condition	NOUN
ejpam-6254	202	3	for	for	ADP
ejpam-6254	202	4	k2(e	k2(e	PROPN
ejpam-6254	202	5	):	):	PUNCT
ejpam-6254	202	6	∥k2(e)−k2(e	∥k2(e)−k2(e	NOUN
ejpam-6254	202	7	∗)∥	∗)∥	PROPN
ejpam-6254	202	8	=	=	SYM
ejpam-6254	202	9	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	202	10	βsi	βsi	NOUN
ejpam-6254	202	11	1	1	NUM
ejpam-6254	202	12	+	+	CCONJ
ejpam-6254	202	13	αi	αi	PRON
ejpam-6254	202	14	−	−	PROPN
ejpam-6254	203	1	(	(	PUNCT
ejpam-6254	203	2	σ	σ	NOUN
ejpam-6254	203	3	+	+	CCONJ
ejpam-6254	203	4	µ)e	µ)e	NOUN
ejpam-6254	203	5	−	−	NOUN
ejpam-6254	203	6	u1e	u1e	NOUN
ejpam-6254	203	7	−	−	NOUN
ejpam-6254	204	1	[	[	PUNCT
ejpam-6254	204	2	βsi	βsi	NOUN
ejpam-6254	204	3	1	1	NUM
ejpam-6254	204	4	+	+	NUM
ejpam-6254	204	5	αi	αi	VERB
ejpam-6254	204	6	−	−	PROPN
ejpam-6254	204	7	(	(	PUNCT
ejpam-6254	204	8	σ	σ	PROPN
ejpam-6254	204	9	+	+	NOUN
ejpam-6254	204	10	µ)e∗	µ)e∗	ADJ
ejpam-6254	204	11	−	−	PROPN
ejpam-6254	204	12	u1e	u1e	NOUN
ejpam-6254	204	13	∗	∗	NOUN
ejpam-6254	204	14	]	]	PUNCT
ejpam-6254	204	15	∥	∥	NUM
ejpam-6254	204	16	,	,	PUNCT
ejpam-6254	204	17	≤	≤	ADJ
ejpam-6254	204	18	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	204	19	βsi	βsi	NOUN
ejpam-6254	204	20	1	1	NUM
ejpam-6254	204	21	+	+	NUM
ejpam-6254	204	22	αi	αi	X
ejpam-6254	205	1	+	+	CCONJ
ejpam-6254	205	2	(	(	PUNCT
ejpam-6254	205	3	σ	σ	PROPN
ejpam-6254	205	4	+	+	X
ejpam-6254	205	5	µ	µ	X
ejpam-6254	205	6	)	)	PUNCT
ejpam-6254	205	7	+	+	CCONJ
ejpam-6254	205	8	u1	u1	PROPN
ejpam-6254	205	9	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6254	206	1	∥e	∥e	PROPN
ejpam-6254	206	2	−	−	PROPN
ejpam-6254	206	3	e∗∥	e∗∥	PROPN
ejpam-6254	206	4	,	,	PUNCT
ejpam-6254	206	5	=	=	SYM
ejpam-6254	206	6	ψ2∥e	ψ2∥e	NOUN
ejpam-6254	206	7	−	−	PROPN
ejpam-6254	206	8	e∗∥	e∗∥	PROPN
ejpam-6254	206	9	,	,	PUNCT
ejpam-6254	206	10	where	where	SCONJ
ejpam-6254	206	11	ψ2	ψ2	NOUN
ejpam-6254	206	12	=	=	SYM
ejpam-6254	206	13	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	206	14	βsi	βsi	NOUN
ejpam-6254	206	15	1	1	NUM
ejpam-6254	206	16	+	+	NUM
ejpam-6254	206	17	αi	αi	X
ejpam-6254	206	18	+	+	CCONJ
ejpam-6254	206	19	(	(	PUNCT
ejpam-6254	206	20	σ	σ	PROPN
ejpam-6254	206	21	+	+	X
ejpam-6254	206	22	µ	µ	X
ejpam-6254	206	23	)	)	PUNCT
ejpam-6254	206	24	+	+	CCONJ
ejpam-6254	206	25	u1	u1	PROPN
ejpam-6254	206	26	∥∥∥∥	∥∥∥∥	NUM
ejpam-6254	206	27	.	.	PUNCT
ejpam-6254	207	1	lipschitz	lipschitz	NOUN
ejpam-6254	207	2	condition	condition	NOUN
ejpam-6254	207	3	for	for	ADP
ejpam-6254	207	4	k3(i	k3(i	PROPN
ejpam-6254	207	5	):	):	PUNCT
ejpam-6254	207	6	∥k3(i)−k3(i	∥k3(i)−k3(i	PROPN
ejpam-6254	207	7	∗)∥	∗)∥	NUM
ejpam-6254	207	8	=	=	SYM
ejpam-6254	207	9	∥σe	∥σe	X
ejpam-6254	207	10	−	−	PROPN
ejpam-6254	207	11	(	(	PUNCT
ejpam-6254	207	12	γ1	γ1	PROPN
ejpam-6254	207	13	+	+	CCONJ
ejpam-6254	207	14	µ)i	µ)i	X
ejpam-6254	207	15	−	−	PROPN
ejpam-6254	208	1	u2i	u2i	NUM
ejpam-6254	208	2	−	−	PROPN
ejpam-6254	209	1	[	[	X
ejpam-6254	209	2	σe	σe	INTJ
ejpam-6254	209	3	−	−	PROPN
ejpam-6254	209	4	(	(	PUNCT
ejpam-6254	209	5	γ1	γ1	NOUN
ejpam-6254	209	6	+	+	CCONJ
ejpam-6254	209	7	µ)i∗	µ)i∗	PRON
ejpam-6254	209	8	−	−	NUM
ejpam-6254	209	9	u2i	u2i	NUM
ejpam-6254	209	10	∗]∥	∗]∥	NOUN
ejpam-6254	209	11	,	,	PUNCT
ejpam-6254	209	12	≤	≤	NUM
ejpam-6254	209	13	∥(γ1	∥(γ1	NOUN
ejpam-6254	209	14	+	+	X
ejpam-6254	209	15	µ	µ	X
ejpam-6254	209	16	)	)	PUNCT
ejpam-6254	209	17	+	+	CCONJ
ejpam-6254	209	18	u2∥	u2∥	NOUN
ejpam-6254	209	19	∥i	∥i	NOUN
ejpam-6254	209	20	−	−	NOUN
ejpam-6254	209	21	i∗∥	i∗∥	NOUN
ejpam-6254	209	22	,	,	PUNCT
ejpam-6254	209	23	=	=	SYM
ejpam-6254	209	24	ψ3∥i	ψ3∥i	ADJ
ejpam-6254	209	25	−	−	NUM
ejpam-6254	209	26	i∗∥	i∗∥	NOUN
ejpam-6254	209	27	,	,	PUNCT
ejpam-6254	209	28	where	where	SCONJ
ejpam-6254	209	29	ψ3	ψ3	NOUN
ejpam-6254	209	30	=	=	NOUN
ejpam-6254	209	31	∥(γ1	∥(γ1	NOUN
ejpam-6254	209	32	+	+	X
ejpam-6254	209	33	µ	µ	X
ejpam-6254	209	34	)	)	PUNCT
ejpam-6254	209	35	+	+	CCONJ
ejpam-6254	209	36	u2∥	u2∥	NOUN
ejpam-6254	209	37	.	.	PUNCT
ejpam-6254	210	1	lipschitz	lipschitz	PROPN
ejpam-6254	210	2	condition	condition	NOUN
ejpam-6254	210	3	for	for	ADP
ejpam-6254	210	4	k4(r	k4(r	PROPN
ejpam-6254	210	5	):	):	PUNCT
ejpam-6254	210	6	∥k4(r)−k4(r	∥k4(r)−k4(r	PROPN
ejpam-6254	210	7	∗)∥	∗)∥	NUM
ejpam-6254	210	8	=	=	SYM
ejpam-6254	210	9	∥γ1i	∥γ1i	PROPN
ejpam-6254	210	10	−	−	PROPN
ejpam-6254	210	11	µr+	µr+	NOUN
ejpam-6254	210	12	u1e	u1e	PROPN
ejpam-6254	210	13	+	+	CCONJ
ejpam-6254	210	14	u2i	u2i	NUM
ejpam-6254	210	15	−	−	PROPN
ejpam-6254	211	1	[	[	X
ejpam-6254	211	2	γ1i	γ1i	X
ejpam-6254	211	3	−	−	PROPN
ejpam-6254	211	4	µr∗	µr∗	NOUN
ejpam-6254	211	5	+	+	CCONJ
ejpam-6254	211	6	u1e	u1e	NOUN
ejpam-6254	211	7	+	+	CCONJ
ejpam-6254	211	8	u2i]∥	u2i]∥	NOUN
ejpam-6254	211	9	,	,	PUNCT
ejpam-6254	211	10	≤	≤	NUM
ejpam-6254	211	11	∥µ∥	∥µ∥	NUM
ejpam-6254	211	12	∥r−r∗∥	∥r−r∗∥	NOUN
ejpam-6254	211	13	,	,	PUNCT
ejpam-6254	211	14	=	=	SYM
ejpam-6254	211	15	ψ3∥r−r∗∥	ψ3∥r−r∗∥	NOUN
ejpam-6254	211	16	,	,	PUNCT
ejpam-6254	211	17	where	where	SCONJ
ejpam-6254	211	18	ψ4	ψ4	NOUN
ejpam-6254	211	19	=	=	SYM
ejpam-6254	211	20	∥µ∥	∥µ∥	PROPN
ejpam-6254	211	21	.	.	PUNCT
ejpam-6254	212	1	lipschitz	lipschitz	NOUN
ejpam-6254	212	2	condition	condition	NOUN
ejpam-6254	212	3	for	for	ADP
ejpam-6254	212	4	k5(v	k5(v	PROPN
ejpam-6254	212	5	):	):	PUNCT
ejpam-6254	212	6	∥k5(v	∥k5(v	PROPN
ejpam-6254	212	7	)	)	PUNCT
ejpam-6254	212	8	−k5(v	−k5(v	NOUN
ejpam-6254	212	9	∗)∥	∗)∥	NUM
ejpam-6254	212	10	=	=	SYM
ejpam-6254	212	11	∥γ2s	∥γ2s	PROPN
ejpam-6254	212	12	−	−	PROPN
ejpam-6254	212	13	γ3r−	γ3r−	PROPN
ejpam-6254	212	14	µv	µv	VERB
ejpam-6254	212	15	−	−	PROPN
ejpam-6254	213	1	[	[	X
ejpam-6254	213	2	γ2s	γ2s	NUM
ejpam-6254	213	3	−	−	PROPN
ejpam-6254	213	4	γ3r−	γ3r−	PROPN
ejpam-6254	213	5	µv	µv	PROPN
ejpam-6254	213	6	∗]∥	∗]∥	ADJ
ejpam-6254	213	7	,	,	PUNCT
ejpam-6254	213	8	≤	≤	NUM
ejpam-6254	213	9	∥µ∥	∥µ∥	VERB
ejpam-6254	213	10	∥v	∥v	PROPN
ejpam-6254	213	11	−	−	PROPN
ejpam-6254	213	12	v	v	NOUN
ejpam-6254	213	13	∗∥	∗∥	NUM
ejpam-6254	213	14	,	,	PUNCT
ejpam-6254	213	15	=	=	PUNCT
ejpam-6254	213	16	ψ5∥v	ψ5∥v	NOUN
ejpam-6254	213	17	−	−	PROPN
ejpam-6254	213	18	v	v	NOUN
ejpam-6254	213	19	∗∥	∗∥	NOUN
ejpam-6254	213	20	,	,	PUNCT
ejpam-6254	213	21	where	where	SCONJ
ejpam-6254	213	22	ψ5	ψ5	PROPN
ejpam-6254	213	23	=	=	SYM
ejpam-6254	213	24	∥µ∥	∥µ∥	PROPN
ejpam-6254	213	25	.	.	PUNCT
ejpam-6254	214	1	therefore	therefore	ADV
ejpam-6254	214	2	,	,	PUNCT
ejpam-6254	214	3	the	the	DET
ejpam-6254	214	4	analysis	analysis	NOUN
ejpam-6254	214	5	of	of	ADP
ejpam-6254	214	6	the	the	DET
ejpam-6254	214	7	lipschitz	lipschitz	NOUN
ejpam-6254	214	8	conditions	condition	NOUN
ejpam-6254	214	9	demonstrates	demonstrate	VERB
ejpam-6254	214	10	that	that	SCONJ
ejpam-6254	214	11	the	the	DET
ejpam-6254	214	12	kernels	kernel	NOUN
ejpam-6254	214	13	satisfy	satisfy	VERB
ejpam-6254	214	14	the	the	DET
ejpam-6254	214	15	criteria	criterion	NOUN
ejpam-6254	214	16	for	for	ADP
ejpam-6254	214	17	being	be	AUX
ejpam-6254	214	18	contractions	contraction	NOUN
ejpam-6254	214	19	.	.	PUNCT
ejpam-6254	215	1	s.	s.	PROPN
ejpam-6254	215	2	irum	irum	PROPN
ejpam-6254	215	3	et	et	PROPN
ejpam-6254	215	4	al	al	PROPN
ejpam-6254	215	5	.	.	PUNCT
ejpam-6254	215	6	/	/	SYM
ejpam-6254	215	7	eur	eur	PROPN
ejpam-6254	215	8	.	.	PUNCT
ejpam-6254	216	1	j.	j.	PROPN
ejpam-6254	216	2	pure	pure	PROPN
ejpam-6254	216	3	appl	appl	PROPN
ejpam-6254	216	4	.	.	PROPN
ejpam-6254	216	5	math	math	PROPN
ejpam-6254	216	6	,	,	PUNCT
ejpam-6254	216	7	18	18	NUM
ejpam-6254	216	8	(	(	PUNCT
ejpam-6254	216	9	4	4	NUM
ejpam-6254	216	10	)	)	PUNCT
ejpam-6254	216	11	(	(	PUNCT
ejpam-6254	216	12	2025	2025	NUM
ejpam-6254	216	13	)	)	PUNCT
ejpam-6254	216	14	,	,	PUNCT
ejpam-6254	216	15	6254	6254	NUM
ejpam-6254	216	16	12	12	NUM
ejpam-6254	216	17	of	of	ADP
ejpam-6254	216	18	23	23	NUM
ejpam-6254	216	19	3.1	3.1	NUM
ejpam-6254	216	20	.	.	PUNCT
ejpam-6254	217	1	existence	existence	NOUN
ejpam-6254	217	2	of	of	ADP
ejpam-6254	217	3	an	an	DET
ejpam-6254	217	4	optimal	optimal	ADJ
ejpam-6254	217	5	control	control	NOUN
ejpam-6254	217	6	pair	pair	NOUN
ejpam-6254	217	7	this	this	DET
ejpam-6254	217	8	section	section	NOUN
ejpam-6254	217	9	presents	present	VERB
ejpam-6254	217	10	a	a	DET
ejpam-6254	217	11	finding	finding	NOUN
ejpam-6254	217	12	on	on	ADP
ejpam-6254	217	13	whether	whether	SCONJ
ejpam-6254	217	14	an	an	DET
ejpam-6254	217	15	optimal	optimal	ADJ
ejpam-6254	217	16	control	control	NOUN
ejpam-6254	217	17	exists	exist	VERB
ejpam-6254	217	18	within	within	ADP
ejpam-6254	217	19	the	the	DET
ejpam-6254	217	20	model	model	NOUN
ejpam-6254	217	21	we	we	PRON
ejpam-6254	217	22	proposed	propose	VERB
ejpam-6254	217	23	.	.	PUNCT
ejpam-6254	218	1	theorem	theorem	NOUN
ejpam-6254	218	2	3	3	X
ejpam-6254	218	3	.	.	PUNCT
ejpam-6254	218	4	consider	consider	VERB
ejpam-6254	218	5	the	the	DET
ejpam-6254	218	6	control	control	NOUN
ejpam-6254	218	7	problem	problem	NOUN
ejpam-6254	218	8	with	with	ADP
ejpam-6254	218	9	the	the	DET
ejpam-6254	218	10	system	system	NOUN
ejpam-6254	218	11	(	(	PUNCT
ejpam-6254	218	12	16	16	NUM
ejpam-6254	218	13	)	)	PUNCT
ejpam-6254	218	14	.	.	PUNCT
ejpam-6254	219	1	there	there	PRON
ejpam-6254	219	2	exists	exist	VERB
ejpam-6254	219	3	an	an	DET
ejpam-6254	219	4	optimal	optimal	ADJ
ejpam-6254	219	5	control	control	NOUN
ejpam-6254	219	6	pair	pair	NOUN
ejpam-6254	219	7	u∗i	u∗i	PUNCT
ejpam-6254	219	8	∈	∈	NOUN
ejpam-6254	219	9	u	u	NOUN
ejpam-6254	219	10	such	such	ADJ
ejpam-6254	219	11	that	that	SCONJ
ejpam-6254	219	12	:	:	PUNCT
ejpam-6254	219	13	j(u∗i	j(u∗i	PROPN
ejpam-6254	219	14	)	)	PUNCT
ejpam-6254	219	15	=	=	SYM
ejpam-6254	219	16	min{j(ui	min{j(ui	NOUN
ejpam-6254	219	17	)	)	PUNCT
ejpam-6254	219	18	:	:	PUNCT
ejpam-6254	219	19	ui	ui	PROPN
ejpam-6254	219	20	∈	∈	PROPN
ejpam-6254	219	21	u	u	PROPN
ejpam-6254	219	22	,	,	PUNCT
ejpam-6254	219	23	i	i	PRON
ejpam-6254	219	24	=	=	NOUN
ejpam-6254	219	25	1	1	NUM
ejpam-6254	219	26	,	,	PUNCT
ejpam-6254	219	27	2	2	NUM
ejpam-6254	219	28	}	}	PUNCT
ejpam-6254	219	29	.	.	PUNCT
ejpam-6254	220	1	(	(	PUNCT
ejpam-6254	220	2	20	20	X
ejpam-6254	220	3	)	)	PUNCT
ejpam-6254	220	4	proof	proof	NOUN
ejpam-6254	220	5	.	.	PUNCT
ejpam-6254	221	1	to	to	PART
ejpam-6254	221	2	establish	establish	VERB
ejpam-6254	221	3	the	the	DET
ejpam-6254	221	4	existence	existence	NOUN
ejpam-6254	221	5	of	of	ADP
ejpam-6254	221	6	an	an	DET
ejpam-6254	221	7	optimal	optimal	ADJ
ejpam-6254	221	8	control	control	NOUN
ejpam-6254	221	9	,	,	PUNCT
ejpam-6254	221	10	we	we	PRON
ejpam-6254	221	11	utilize	utilize	VERB
ejpam-6254	221	12	a	a	DET
ejpam-6254	221	13	result	result	NOUN
ejpam-6254	221	14	by	by	ADP
ejpam-6254	221	15	fleming	fleming	NOUN
ejpam-6254	221	16	and	and	CCONJ
ejpam-6254	221	17	rishel	rishel	PROPN
ejpam-6254	222	1	[	[	X
ejpam-6254	222	2	17	17	NUM
ejpam-6254	222	3	]	]	PUNCT
ejpam-6254	222	4	.	.	PUNCT
ejpam-6254	223	1	the	the	DET
ejpam-6254	223	2	following	follow	VERB
ejpam-6254	223	3	conditions	condition	NOUN
ejpam-6254	223	4	are	be	AUX
ejpam-6254	223	5	be	be	AUX
ejpam-6254	223	6	checked	check	VERB
ejpam-6254	223	7	:	:	PUNCT
ejpam-6254	223	8	(	(	PUNCT
ejpam-6254	223	9	i	i	NOUN
ejpam-6254	223	10	)	)	PUNCT
ejpam-6254	223	11	the	the	DET
ejpam-6254	223	12	set	set	NOUN
ejpam-6254	223	13	of	of	ADP
ejpam-6254	223	14	controls	control	NOUN
ejpam-6254	223	15	and	and	CCONJ
ejpam-6254	223	16	the	the	DET
ejpam-6254	223	17	corresponding	correspond	VERB
ejpam-6254	223	18	state	state	NOUN
ejpam-6254	223	19	variables	variable	NOUN
ejpam-6254	223	20	must	must	AUX
ejpam-6254	223	21	be	be	AUX
ejpam-6254	223	22	nonempty	nonempty	ADJ
ejpam-6254	223	23	.	.	PUNCT
ejpam-6254	224	1	the	the	DET
ejpam-6254	224	2	existence	existence	NOUN
ejpam-6254	224	3	of	of	ADP
ejpam-6254	224	4	solution	solution	NOUN
ejpam-6254	224	5	for	for	ADP
ejpam-6254	224	6	system	system	NOUN
ejpam-6254	224	7	(	(	PUNCT
ejpam-6254	224	8	16	16	NUM
ejpam-6254	224	9	)	)	PUNCT
ejpam-6254	224	10	is	be	AUX
ejpam-6254	224	11	proved	prove	VERB
ejpam-6254	224	12	using	use	VERB
ejpam-6254	224	13	result	result	NOUN
ejpam-6254	224	14	by	by	ADP
ejpam-6254	224	15	lukes	luke	NOUN
ejpam-6254	224	16	[	[	X
ejpam-6254	224	17	18	18	NUM
ejpam-6254	224	18	]	]	PUNCT
ejpam-6254	224	19	.	.	PUNCT
ejpam-6254	225	1	(	(	PUNCT
ejpam-6254	225	2	ii	ii	NOUN
ejpam-6254	225	3	)	)	PUNCT
ejpam-6254	225	4	the	the	DET
ejpam-6254	225	5	set	set	ADJ
ejpam-6254	225	6	u	u	NOUN
ejpam-6254	225	7	of	of	ADP
ejpam-6254	225	8	control	control	NOUN
ejpam-6254	225	9	is	be	AUX
ejpam-6254	225	10	convex	convex	ADJ
ejpam-6254	225	11	and	and	CCONJ
ejpam-6254	225	12	closed	closed	ADJ
ejpam-6254	225	13	.	.	PUNCT
ejpam-6254	226	1	(	(	PUNCT
ejpam-6254	226	2	iii	iii	X
ejpam-6254	226	3	)	)	PUNCT
ejpam-6254	226	4	the	the	DET
ejpam-6254	226	5	right	right	ADJ
ejpam-6254	226	6	-	-	PUNCT
ejpam-6254	226	7	hand	hand	NOUN
ejpam-6254	226	8	side	side	NOUN
ejpam-6254	226	9	of	of	ADP
ejpam-6254	226	10	the	the	DET
ejpam-6254	226	11	system	system	NOUN
ejpam-6254	226	12	(	(	PUNCT
ejpam-6254	226	13	16	16	NUM
ejpam-6254	226	14	)	)	PUNCT
ejpam-6254	226	15	is	be	AUX
ejpam-6254	226	16	bounded	bound	VERB
ejpam-6254	226	17	by	by	ADP
ejpam-6254	226	18	a	a	DET
ejpam-6254	226	19	linear	linear	ADJ
ejpam-6254	226	20	function	function	NOUN
ejpam-6254	226	21	of	of	ADP
ejpam-6254	226	22	the	the	DET
ejpam-6254	226	23	state	state	NOUN
ejpam-6254	226	24	and	and	CCONJ
ejpam-6254	226	25	control	control	NOUN
ejpam-6254	226	26	variables	variable	NOUN
ejpam-6254	226	27	.	.	PUNCT
ejpam-6254	227	1	(	(	PUNCT
ejpam-6254	227	2	iv	iv	X
ejpam-6254	227	3	)	)	PUNCT
ejpam-6254	227	4	the	the	DET
ejpam-6254	227	5	integrand	integrand	NOUN
ejpam-6254	227	6	of	of	ADP
ejpam-6254	227	7	the	the	DET
ejpam-6254	227	8	objective	objective	ADJ
ejpam-6254	227	9	functional	functional	NOUN
ejpam-6254	227	10	is	be	AUX
ejpam-6254	227	11	convex	convex	ADJ
ejpam-6254	227	12	with	with	ADP
ejpam-6254	227	13	respect	respect	NOUN
ejpam-6254	227	14	to	to	ADP
ejpam-6254	227	15	u.	u.	PROPN
ejpam-6254	227	16	(	(	PUNCT
ejpam-6254	227	17	v	v	NOUN
ejpam-6254	227	18	)	)	PUNCT
ejpam-6254	227	19	there	there	PRON
ejpam-6254	227	20	exist	exist	VERB
ejpam-6254	227	21	constants	constant	NOUN
ejpam-6254	227	22	m1,m2	m1,m2	PROPN
ejpam-6254	227	23	>	>	PUNCT
ejpam-6254	227	24	0	0	PROPN
ejpam-6254	227	25	and	and	CCONJ
ejpam-6254	227	26	ρ	ρ	NOUN
ejpam-6254	227	27	>	>	X
ejpam-6254	227	28	1	1	NUM
ejpam-6254	227	29	such	such	ADJ
ejpam-6254	227	30	that	that	SCONJ
ejpam-6254	227	31	the	the	DET
ejpam-6254	227	32	integrand	integrand	PROPN
ejpam-6254	227	33	l(s	l(s	PROPN
ejpam-6254	227	34	,	,	PUNCT
ejpam-6254	227	35	e	e	PROPN
ejpam-6254	227	36	,	,	PUNCT
ejpam-6254	227	37	i	i	PRON
ejpam-6254	227	38	,	,	PUNCT
ejpam-6254	227	39	u1	u1	NOUN
ejpam-6254	227	40	,	,	PUNCT
ejpam-6254	227	41	u2	u2	PROPN
ejpam-6254	227	42	)	)	PUNCT
ejpam-6254	227	43	of	of	ADP
ejpam-6254	227	44	the	the	DET
ejpam-6254	227	45	objective	objective	ADJ
ejpam-6254	227	46	functional	functional	ADJ
ejpam-6254	227	47	satisfies	satisfie	NOUN
ejpam-6254	227	48	:	:	PUNCT
ejpam-6254	227	49	l(s	l(s	PROPN
ejpam-6254	227	50	,	,	PUNCT
ejpam-6254	227	51	e	e	NOUN
ejpam-6254	227	52	,	,	PUNCT
ejpam-6254	227	53	i	i	PRON
ejpam-6254	227	54	,	,	PUNCT
ejpam-6254	227	55	u1	u1	NOUN
ejpam-6254	227	56	,	,	PUNCT
ejpam-6254	227	57	u2	u2	PROPN
ejpam-6254	227	58	)	)	PUNCT
ejpam-6254	227	59	≥	≥	NOUN
ejpam-6254	227	60	m2	m2	PROPN
ejpam-6254	227	61	+	+	PROPN
ejpam-6254	227	62	m1(|u|2)ρ/2	m1(|u|2)ρ/2	PROPN
ejpam-6254	227	63	.	.	PUNCT
ejpam-6254	227	64	therefore	therefore	ADV
ejpam-6254	227	65	,	,	PUNCT
ejpam-6254	227	66	using	use	VERB
ejpam-6254	227	67	these	these	DET
ejpam-6254	227	68	conditions	condition	NOUN
ejpam-6254	227	69	,	,	PUNCT
ejpam-6254	227	70	we	we	PRON
ejpam-6254	227	71	confirm	confirm	VERB
ejpam-6254	227	72	that	that	SCONJ
ejpam-6254	227	73	an	an	DET
ejpam-6254	227	74	optimal	optimal	ADJ
ejpam-6254	227	75	control	control	NOUN
ejpam-6254	227	76	exists	exist	VERB
ejpam-6254	227	77	.	.	PUNCT
ejpam-6254	228	1	3.2	3.2	NUM
ejpam-6254	228	2	.	.	PUNCT
ejpam-6254	228	3	characterization	characterization	NOUN
ejpam-6254	228	4	of	of	ADP
ejpam-6254	228	5	the	the	DET
ejpam-6254	228	6	optimal	optimal	ADJ
ejpam-6254	228	7	control	control	NOUN
ejpam-6254	228	8	for	for	ADP
ejpam-6254	228	9	deriving	derive	VERB
ejpam-6254	228	10	the	the	DET
ejpam-6254	228	11	necessary	necessary	ADJ
ejpam-6254	228	12	conditions	condition	NOUN
ejpam-6254	228	13	for	for	SCONJ
ejpam-6254	228	14	a	a	DET
ejpam-6254	228	15	control	control	NOUN
ejpam-6254	228	16	to	to	PART
ejpam-6254	228	17	be	be	AUX
ejpam-6254	228	18	optimal	optimal	ADJ
ejpam-6254	228	19	,	,	PUNCT
ejpam-6254	228	20	pontryagin	pontryagin	NOUN
ejpam-6254	228	21	’s	’s	PART
ejpam-6254	228	22	maximum	maximum	ADJ
ejpam-6254	228	23	principle	principle	NOUN
ejpam-6254	228	24	is	be	AUX
ejpam-6254	228	25	applied	apply	VERB
ejpam-6254	228	26	.	.	PUNCT
ejpam-6254	229	1	based	base	VERB
ejpam-6254	229	2	on	on	ADP
ejpam-6254	229	3	this	this	DET
ejpam-6254	229	4	principle	principle	NOUN
ejpam-6254	229	5	we	we	PRON
ejpam-6254	229	6	transform	transform	VERB
ejpam-6254	229	7	our	our	PRON
ejpam-6254	229	8	system	system	NOUN
ejpam-6254	229	9	into	into	ADP
ejpam-6254	229	10	a	a	DET
ejpam-6254	229	11	minimization	minimization	NOUN
ejpam-6254	229	12	problem	problem	NOUN
ejpam-6254	229	13	for	for	ADP
ejpam-6254	229	14	the	the	DET
ejpam-6254	229	15	hamiltonian	hamiltonian	ADJ
ejpam-6254	229	16	h	h	NOUN
ejpam-6254	229	17	,	,	PUNCT
ejpam-6254	229	18	which	which	PRON
ejpam-6254	229	19	is	be	AUX
ejpam-6254	229	20	given	give	VERB
ejpam-6254	229	21	by	by	ADP
ejpam-6254	229	22	:	:	PUNCT
ejpam-6254	229	23	h	h	PROPN
ejpam-6254	229	24	=	=	SYM
ejpam-6254	229	25	a1s(t	a1s(t	PROPN
ejpam-6254	229	26	)	)	PUNCT
ejpam-6254	230	1	+	+	NOUN
ejpam-6254	230	2	a2e(t	a2e(t	PROPN
ejpam-6254	230	3	)	)	PUNCT
ejpam-6254	231	1	+	+	SYM
ejpam-6254	231	2	a3i(t)−a4r(t	a3i(t)−a4r(t	NOUN
ejpam-6254	231	3	)	)	PUNCT
ejpam-6254	231	4	+	+	PROPN
ejpam-6254	231	5	a5v	a5v	PROPN
ejpam-6254	231	6	(	(	PUNCT
ejpam-6254	231	7	t	t	PROPN
ejpam-6254	231	8	)	)	PUNCT
ejpam-6254	231	9	+	+	CCONJ
ejpam-6254	231	10	a6	a6	X
ejpam-6254	231	11	2	2	NUM
ejpam-6254	231	12	u21(t	u21(t	ADJ
ejpam-6254	231	13	)	)	PUNCT
ejpam-6254	232	1	+	+	CCONJ
ejpam-6254	232	2	a7	a7	PROPN
ejpam-6254	232	3	2	2	NUM
ejpam-6254	232	4	u22	u22	NOUN
ejpam-6254	232	5	+	+	CCONJ
ejpam-6254	232	6	5∑	5∑	PROPN
ejpam-6254	232	7	i=1	i=1	PROPN
ejpam-6254	232	8	λiki	λiki	PROPN
ejpam-6254	232	9	.	.	PUNCT
ejpam-6254	233	1	the	the	DET
ejpam-6254	233	2	right	right	ADJ
ejpam-6254	233	3	-	-	PUNCT
ejpam-6254	233	4	hand	hand	NOUN
ejpam-6254	233	5	terms	term	NOUN
ejpam-6254	233	6	of	of	ADP
ejpam-6254	233	7	differential	differential	ADJ
ejpam-6254	233	8	equations	equation	NOUN
ejpam-6254	233	9	are	be	AUX
ejpam-6254	233	10	represented	represent	VERB
ejpam-6254	233	11	by	by	ADP
ejpam-6254	233	12	ki	ki	PROPN
ejpam-6254	233	13	corresponding	correspond	VERB
ejpam-6254	233	14	to	to	ADP
ejpam-6254	233	15	the	the	DET
ejpam-6254	233	16	i	i	PROPN
ejpam-6254	233	17	-	-	PUNCT
ejpam-6254	233	18	th	th	X
ejpam-6254	233	19	state	state	NOUN
ejpam-6254	233	20	variable	variable	NOUN
ejpam-6254	233	21	.	.	PUNCT
ejpam-6254	234	1	theorem	theorem	ADJ
ejpam-6254	234	2	4	4	NUM
ejpam-6254	234	3	.	.	PUNCT
ejpam-6254	234	4	given	give	VERB
ejpam-6254	234	5	an	an	DET
ejpam-6254	234	6	optimal	optimal	ADJ
ejpam-6254	234	7	control	control	NOUN
ejpam-6254	234	8	u∗	u∗	NOUN
ejpam-6254	235	1	=	=	PUNCT
ejpam-6254	235	2	(	(	PUNCT
ejpam-6254	235	3	u∗1	u∗1	PROPN
ejpam-6254	235	4	,	,	PUNCT
ejpam-6254	235	5	u	u	NOUN
ejpam-6254	235	6	∗	∗	NOUN
ejpam-6254	235	7	2	2	NUM
ejpam-6254	235	8	)	)	PUNCT
ejpam-6254	235	9	∈	∈	PROPN
ejpam-6254	235	10	u	u	NOUN
ejpam-6254	235	11	and	and	CCONJ
ejpam-6254	235	12	corresponding	corresponding	ADJ
ejpam-6254	235	13	variables	variable	NOUN
ejpam-6254	235	14	s	s	PROPN
ejpam-6254	235	15	,	,	PUNCT
ejpam-6254	235	16	e	e	NOUN
ejpam-6254	235	17	,	,	PUNCT
ejpam-6254	235	18	i	i	PRON
ejpam-6254	235	19	,	,	PUNCT
ejpam-6254	235	20	r	r	NOUN
ejpam-6254	235	21	,	,	PUNCT
ejpam-6254	235	22	and	and	CCONJ
ejpam-6254	235	23	v	v	NOUN
ejpam-6254	235	24	,	,	PUNCT
ejpam-6254	235	25	there	there	PRON
ejpam-6254	235	26	exist	exist	VERB
ejpam-6254	235	27	adjoint	adjoint	NOUN
ejpam-6254	235	28	variables	variable	NOUN
ejpam-6254	235	29	λ1	λ1	PROPN
ejpam-6254	235	30	,	,	PUNCT
ejpam-6254	235	31	...	...	PUNCT
ejpam-6254	235	32	,	,	PUNCT
ejpam-6254	235	33	λ4	λ4	PROPN
ejpam-6254	235	34	,	,	PUNCT
ejpam-6254	235	35	and	and	CCONJ
ejpam-6254	235	36	λ5	λ5	NOUN
ejpam-6254	235	37	that	that	PRON
ejpam-6254	235	38	must	must	AUX
ejpam-6254	235	39	fulfill	fulfill	VERB
ejpam-6254	235	40	the	the	DET
ejpam-6254	235	41	following	follow	VERB
ejpam-6254	235	42	adjoint	adjoint	NOUN
ejpam-6254	235	43	equations	equation	NOUN
ejpam-6254	235	44	:	:	PUNCT
ejpam-6254	236	1	λ̇1	λ̇1	SYM
ejpam-6254	236	2	=	=	SYM
ejpam-6254	236	3	−a1	−a1	PROPN
ejpam-6254	236	4	+	+	X
ejpam-6254	236	5	λ1	λ1	PROPN
ejpam-6254	236	6	(	(	PUNCT
ejpam-6254	236	7	βi	βi	NOUN
ejpam-6254	236	8	1	1	NUM
ejpam-6254	236	9	+	+	CCONJ
ejpam-6254	236	10	αi	αi	VERB
ejpam-6254	236	11	+	+	CCONJ
ejpam-6254	236	12	(	(	PUNCT
ejpam-6254	236	13	γ2	γ2	PROPN
ejpam-6254	236	14	+	+	CCONJ
ejpam-6254	236	15	µ	µ	NUM
ejpam-6254	236	16	)	)	PUNCT
ejpam-6254	236	17	)	)	PUNCT
ejpam-6254	236	18	−	−	PROPN
ejpam-6254	237	1	λ2	λ2	NOUN
ejpam-6254	237	2	(	(	PUNCT
ejpam-6254	237	3	βi	βi	NOUN
ejpam-6254	237	4	1	1	NUM
ejpam-6254	237	5	+	+	CCONJ
ejpam-6254	237	6	αi	αi	VERB
ejpam-6254	237	7	)	)	PUNCT
ejpam-6254	238	1	−	−	PUNCT
ejpam-6254	239	1	λ5γ2	λ5γ2	NOUN
ejpam-6254	239	2	,	,	PUNCT
ejpam-6254	239	3	λ̇2	λ̇2	PROPN
ejpam-6254	239	4	=	=	PROPN
ejpam-6254	239	5	−a2	−a2	PROPN
ejpam-6254	240	1	+	+	CCONJ
ejpam-6254	240	2	λ2	λ2	PROPN
ejpam-6254	240	3	(	(	PUNCT
ejpam-6254	240	4	σ	σ	X
ejpam-6254	240	5	+	+	NUM
ejpam-6254	240	6	µ+	µ+	PROPN
ejpam-6254	240	7	u1	u1	NOUN
ejpam-6254	240	8	)	)	PUNCT
ejpam-6254	241	1	+	+	CCONJ
ejpam-6254	242	1	σλ3	σλ3	NOUN
ejpam-6254	242	2	−	−	NOUN
ejpam-6254	242	3	u1λ4	u1λ4	PROPN
ejpam-6254	242	4	,	,	PUNCT
ejpam-6254	242	5	λ̇3	λ̇3	PROPN
ejpam-6254	242	6	=	=	PUNCT
ejpam-6254	242	7	−a3	−a3	PROPN
ejpam-6254	242	8	+	+	CCONJ
ejpam-6254	242	9	λ1	λ1	PROPN
ejpam-6254	242	10	(	(	PUNCT
ejpam-6254	242	11	βs	βs	X
ejpam-6254	242	12	(	(	PUNCT
ejpam-6254	242	13	1	1	NUM
ejpam-6254	242	14	+	+	CCONJ
ejpam-6254	242	15	αi)2	αi)2	ADJ
ejpam-6254	242	16	)	)	PUNCT
ejpam-6254	243	1	−	−	PROPN
ejpam-6254	243	2	λ2	λ2	NOUN
ejpam-6254	243	3	(	(	PUNCT
ejpam-6254	243	4	βs	βs	X
ejpam-6254	243	5	(	(	PUNCT
ejpam-6254	243	6	1	1	NUM
ejpam-6254	243	7	+	+	CCONJ
ejpam-6254	243	8	αi)2	αi)2	ADJ
ejpam-6254	243	9	)	)	PUNCT
ejpam-6254	244	1	+	+	CCONJ
ejpam-6254	244	2	λ3(γ1	λ3(γ1	NOUN
ejpam-6254	244	3	+	+	CCONJ
ejpam-6254	244	4	µ+	µ+	PUNCT
ejpam-6254	244	5	u2)−	u2)−	ADJ
ejpam-6254	244	6	λ4(γ1	λ4(γ1	X
ejpam-6254	244	7	+	+	CCONJ
ejpam-6254	244	8	u2	u2	NOUN
ejpam-6254	244	9	)	)	PUNCT
ejpam-6254	244	10	s.	s.	PROPN
ejpam-6254	244	11	irum	irum	PROPN
ejpam-6254	244	12	et	et	PROPN
ejpam-6254	244	13	al	al	PROPN
ejpam-6254	244	14	.	.	PUNCT
ejpam-6254	244	15	/	/	SYM
ejpam-6254	244	16	eur	eur	PROPN
ejpam-6254	244	17	.	.	PUNCT
ejpam-6254	245	1	j.	j.	PROPN
ejpam-6254	245	2	pure	pure	PROPN
ejpam-6254	245	3	appl	appl	PROPN
ejpam-6254	245	4	.	.	PROPN
ejpam-6254	245	5	math	math	PROPN
ejpam-6254	245	6	,	,	PUNCT
ejpam-6254	245	7	18	18	NUM
ejpam-6254	245	8	(	(	PUNCT
ejpam-6254	245	9	4	4	NUM
ejpam-6254	245	10	)	)	PUNCT
ejpam-6254	245	11	(	(	PUNCT
ejpam-6254	245	12	2025	2025	NUM
ejpam-6254	245	13	)	)	PUNCT
ejpam-6254	245	14	,	,	PUNCT
ejpam-6254	245	15	6254	6254	NUM
ejpam-6254	245	16	13	13	NUM
ejpam-6254	245	17	of	of	ADP
ejpam-6254	245	18	23	23	NUM
ejpam-6254	245	19	λ̇4	λ̇4	PROPN
ejpam-6254	245	20	=	=	SYM
ejpam-6254	245	21	a4	a4	PROPN
ejpam-6254	245	22	+	+	CCONJ
ejpam-6254	245	23	µλ4	µλ4	NOUN
ejpam-6254	245	24	+	+	CCONJ
ejpam-6254	245	25	γ2λ5	γ2λ5	ADJ
ejpam-6254	245	26	,	,	PUNCT
ejpam-6254	245	27	λ̇5	λ̇5	PROPN
ejpam-6254	245	28	=	=	SYM
ejpam-6254	245	29	a5	a5	PROPN
ejpam-6254	246	1	+	+	CCONJ
ejpam-6254	246	2	µλ5	µλ5	PROPN
ejpam-6254	246	3	,	,	PUNCT
ejpam-6254	246	4	following	follow	VERB
ejpam-6254	246	5	the	the	DET
ejpam-6254	246	6	transversality	transversality	NOUN
ejpam-6254	246	7	conditions	condition	NOUN
ejpam-6254	246	8	:	:	PUNCT
ejpam-6254	246	9	λ1(t	λ1(t	PUNCT
ejpam-6254	246	10	)	)	PUNCT
ejpam-6254	247	1	=	=	SYM
ejpam-6254	247	2	λ2(t	λ2(t	X
ejpam-6254	247	3	)	)	PUNCT
ejpam-6254	247	4	=	=	PUNCT
ejpam-6254	247	5	λ3(t	λ3(t	PUNCT
ejpam-6254	247	6	)	)	PUNCT
ejpam-6254	247	7	=	=	SYM
ejpam-6254	247	8	λ4(t	λ4(t	PROPN
ejpam-6254	247	9	)	)	PUNCT
ejpam-6254	247	10	=	=	SYM
ejpam-6254	248	1	λ5(t	λ5(t	PROPN
ejpam-6254	248	2	)	)	PUNCT
ejpam-6254	249	1	=	=	PUNCT
ejpam-6254	249	2	0	0	X
ejpam-6254	249	3	.	.	PUNCT
ejpam-6254	250	1	additionally	additionally	ADV
ejpam-6254	250	2	,	,	PUNCT
ejpam-6254	250	3	the	the	DET
ejpam-6254	250	4	optimal	optimal	ADJ
ejpam-6254	250	5	control	control	NOUN
ejpam-6254	250	6	u∗1(t	u∗1(t	PROPN
ejpam-6254	250	7	)	)	PUNCT
ejpam-6254	250	8	and	and	CCONJ
ejpam-6254	250	9	u	u	NOUN
ejpam-6254	250	10	∗	∗	NOUN
ejpam-6254	250	11	2(t	2(t	NUM
ejpam-6254	250	12	)	)	PUNCT
ejpam-6254	250	13	is	be	AUX
ejpam-6254	250	14	characterized	characterize	VERB
ejpam-6254	250	15	by	by	ADP
ejpam-6254	250	16	:	:	PUNCT
ejpam-6254	250	17	u∗1(t	u∗1(t	PROPN
ejpam-6254	250	18	)	)	PUNCT
ejpam-6254	250	19	=	=	SYM
ejpam-6254	250	20	min	min	PROPN
ejpam-6254	250	21	(	(	PUNCT
ejpam-6254	250	22	1,max	1,max	NUM
ejpam-6254	250	23	(	(	PUNCT
ejpam-6254	250	24	0	0	NUM
ejpam-6254	250	25	,	,	PUNCT
ejpam-6254	250	26	(	(	PUNCT
ejpam-6254	250	27	λ4	λ4	VERB
ejpam-6254	250	28	−	−	PROPN
ejpam-6254	250	29	λ2	λ2	NOUN
ejpam-6254	250	30	)	)	PUNCT
ejpam-6254	250	31	a1	a1	NOUN
ejpam-6254	250	32	e	e	NOUN
ejpam-6254	250	33	)	)	PUNCT
ejpam-6254	250	34	)	)	PUNCT
ejpam-6254	250	35	,	,	PUNCT
ejpam-6254	250	36	u∗2(t	u∗2(t	PROPN
ejpam-6254	250	37	)	)	PUNCT
ejpam-6254	250	38	=	=	SYM
ejpam-6254	250	39	min	min	PROPN
ejpam-6254	250	40	(	(	PUNCT
ejpam-6254	250	41	1,max	1,max	NUM
ejpam-6254	250	42	(	(	PUNCT
ejpam-6254	250	43	0	0	NUM
ejpam-6254	250	44	,	,	PUNCT
ejpam-6254	250	45	(	(	PUNCT
ejpam-6254	250	46	λ4	λ4	PROPN
ejpam-6254	250	47	−	−	PROPN
ejpam-6254	250	48	λ3	λ3	PROPN
ejpam-6254	250	49	)	)	PUNCT
ejpam-6254	250	50	a2	a2	PROPN
ejpam-6254	250	51	i	i	PROPN
ejpam-6254	250	52	)	)	PUNCT
ejpam-6254	250	53	)	)	PUNCT
ejpam-6254	250	54	.	.	PUNCT
ejpam-6254	251	1	using	use	VERB
ejpam-6254	251	2	pontryagin	pontryagin	NOUN
ejpam-6254	251	3	’s	’s	PART
ejpam-6254	251	4	maximum	maximum	ADJ
ejpam-6254	251	5	principle	principle	ADJ
ejpam-6254	251	6	adjoint	adjoint	NOUN
ejpam-6254	251	7	equations	equation	NOUN
ejpam-6254	251	8	and	and	CCONJ
ejpam-6254	251	9	transversality	transversality	NOUN
ejpam-6254	251	10	conditions	condition	NOUN
ejpam-6254	251	11	are	be	AUX
ejpam-6254	251	12	derived	derive	VERB
ejpam-6254	251	13	.	.	PUNCT
ejpam-6254	252	1	specifically	specifically	ADV
ejpam-6254	252	2	:	:	PUNCT
ejpam-6254	252	3	(	(	PUNCT
ejpam-6254	252	4	i	i	NOUN
ejpam-6254	252	5	)	)	PUNCT
ejpam-6254	252	6	adjoint	adjoint	PROPN
ejpam-6254	252	7	equations	equation	NOUN
ejpam-6254	252	8	:	:	PUNCT
ejpam-6254	252	9	the	the	DET
ejpam-6254	252	10	adjoint	adjoint	PROPN
ejpam-6254	252	11	equations	equation	NOUN
ejpam-6254	252	12	take	take	VERB
ejpam-6254	252	13	the	the	DET
ejpam-6254	252	14	following	follow	VERB
ejpam-6254	252	15	form	form	NOUN
ejpam-6254	252	16	:	:	PUNCT
ejpam-6254	252	17	λ̇1	λ̇1	X
ejpam-6254	252	18	=	=	PUNCT
ejpam-6254	252	19	−∂h	−∂h	SYM
ejpam-6254	252	20	∂s	∂s	PROPN
ejpam-6254	252	21	,	,	PUNCT
ejpam-6254	252	22	λ̇2	λ̇2	PROPN
ejpam-6254	252	23	=	=	PROPN
ejpam-6254	252	24	−∂h	−∂h	PROPN
ejpam-6254	252	25	∂e	∂e	PROPN
ejpam-6254	252	26	,	,	PUNCT
ejpam-6254	252	27	λ̇3	λ̇3	PROPN
ejpam-6254	252	28	=	=	PUNCT
ejpam-6254	252	29	−∂h	−∂h	PROPN
ejpam-6254	252	30	∂i	∂i	PROPN
ejpam-6254	252	31	,	,	PUNCT
ejpam-6254	252	32	λ̇4	λ̇4	PROPN
ejpam-6254	252	33	=	=	PUNCT
ejpam-6254	252	34	−∂h	−∂h	PROPN
ejpam-6254	252	35	∂r	∂r	ADJ
ejpam-6254	252	36	,	,	PUNCT
ejpam-6254	252	37	λ̇5	λ̇5	PROPN
ejpam-6254	252	38	=	=	PUNCT
ejpam-6254	252	39	−∂h	−∂h	PROPN
ejpam-6254	252	40	∂v	∂v	PROPN
ejpam-6254	252	41	.	.	PUNCT
ejpam-6254	253	1	(	(	PUNCT
ejpam-6254	253	2	ii	ii	NOUN
ejpam-6254	253	3	)	)	PUNCT
ejpam-6254	253	4	optimal	optimal	ADJ
ejpam-6254	253	5	control	control	NOUN
ejpam-6254	253	6	:	:	PUNCT
ejpam-6254	253	7	the	the	DET
ejpam-6254	253	8	optimal	optimal	ADJ
ejpam-6254	253	9	control	control	NOUN
ejpam-6254	253	10	u∗1	u∗1	NOUN
ejpam-6254	253	11	and	and	CCONJ
ejpam-6254	253	12	u∗2	u∗2	NOUN
ejpam-6254	253	13	can	can	AUX
ejpam-6254	253	14	be	be	AUX
ejpam-6254	253	15	determined	determine	VERB
ejpam-6254	253	16	from	from	ADP
ejpam-6254	253	17	the	the	DET
ejpam-6254	253	18	optimality	optimality	NOUN
ejpam-6254	253	19	condition	condition	NOUN
ejpam-6254	253	20	,	,	PUNCT
ejpam-6254	253	21	which	which	PRON
ejpam-6254	253	22	involves	involves	AUX
ejpam-6254	253	23	partially	partially	ADV
ejpam-6254	253	24	differentiating	differentiate	VERB
ejpam-6254	253	25	the	the	DET
ejpam-6254	253	26	hamiltonian	hamiltonian	NOUN
ejpam-6254	253	27	in	in	ADP
ejpam-6254	253	28	terms	term	NOUN
ejpam-6254	253	29	of	of	ADP
ejpam-6254	253	30	ui	ui	NOUN
ejpam-6254	253	31	to	to	ADP
ejpam-6254	253	32	zero	zero	NUM
ejpam-6254	253	33	:	:	PUNCT
ejpam-6254	254	1	∂h	∂h	PROPN
ejpam-6254	254	2	∂u1	∂u1	PROPN
ejpam-6254	254	3	=	=	SYM
ejpam-6254	254	4	0	0	X
ejpam-6254	254	5	.	.	PUNCT
ejpam-6254	255	1	∂h	∂h	VERB
ejpam-6254	255	2	∂u2	∂u2	NOUN
ejpam-6254	255	3	=	=	PUNCT
ejpam-6254	255	4	0	0	X
ejpam-6254	255	5	.	.	PUNCT
ejpam-6254	256	1	this	this	DET
ejpam-6254	256	2	yields	yield	VERB
ejpam-6254	256	3	:	:	PUNCT
ejpam-6254	256	4	−a1u	−a1u	X
ejpam-6254	256	5	∗	∗	NOUN
ejpam-6254	256	6	1	1	NUM
ejpam-6254	256	7	+	+	CCONJ
ejpam-6254	256	8	(	(	PUNCT
ejpam-6254	256	9	λ4	λ4	PROPN
ejpam-6254	256	10	−	−	PROPN
ejpam-6254	256	11	λ2)(e	λ2)(e	PROPN
ejpam-6254	256	12	)	)	PUNCT
ejpam-6254	256	13	=	=	SYM
ejpam-6254	257	1	0	0	X
ejpam-6254	257	2	.	.	PUNCT
ejpam-6254	257	3	−a2u	−a2u	NUM
ejpam-6254	257	4	∗	∗	NOUN
ejpam-6254	257	5	2	2	NUM
ejpam-6254	257	6	+	+	CCONJ
ejpam-6254	257	7	(	(	PUNCT
ejpam-6254	257	8	λ4	λ4	ADJ
ejpam-6254	257	9	−	−	PROPN
ejpam-6254	257	10	λ3)(i	λ3)(i	PROPN
ejpam-6254	257	11	)	)	PUNCT
ejpam-6254	257	12	=	=	SYM
ejpam-6254	258	1	0	0	X
ejpam-6254	258	2	.	.	PUNCT
ejpam-6254	259	1	s.	s.	PROPN
ejpam-6254	259	2	irum	irum	PROPN
ejpam-6254	259	3	et	et	PROPN
ejpam-6254	259	4	al	al	PROPN
ejpam-6254	259	5	.	.	PUNCT
ejpam-6254	259	6	/	/	SYM
ejpam-6254	259	7	eur	eur	PROPN
ejpam-6254	259	8	.	.	PUNCT
ejpam-6254	260	1	j.	j.	PROPN
ejpam-6254	260	2	pure	pure	PROPN
ejpam-6254	260	3	appl	appl	PROPN
ejpam-6254	260	4	.	.	PROPN
ejpam-6254	260	5	math	math	PROPN
ejpam-6254	260	6	,	,	PUNCT
ejpam-6254	260	7	18	18	NUM
ejpam-6254	260	8	(	(	PUNCT
ejpam-6254	260	9	4	4	NUM
ejpam-6254	260	10	)	)	PUNCT
ejpam-6254	260	11	(	(	PUNCT
ejpam-6254	260	12	2025	2025	NUM
ejpam-6254	260	13	)	)	PUNCT
ejpam-6254	260	14	,	,	PUNCT
ejpam-6254	260	15	6254	6254	NUM
ejpam-6254	260	16	14	14	NUM
ejpam-6254	260	17	of	of	ADP
ejpam-6254	260	18	23	23	NUM
ejpam-6254	260	19	given	give	VERB
ejpam-6254	260	20	the	the	DET
ejpam-6254	260	21	bounds	bound	NOUN
ejpam-6254	260	22	on	on	ADP
ejpam-6254	260	23	the	the	DET
ejpam-6254	260	24	control	control	NOUN
ejpam-6254	260	25	ui	ui	PROPN
ejpam-6254	260	26	specified	specify	VERB
ejpam-6254	260	27	by	by	ADP
ejpam-6254	260	28	the	the	DET
ejpam-6254	260	29	set	set	ADJ
ejpam-6254	260	30	u	u	NOUN
ejpam-6254	260	31	,	,	PUNCT
ejpam-6254	260	32	we	we	PRON
ejpam-6254	260	33	express	express	VERB
ejpam-6254	260	34	the	the	DET
ejpam-6254	260	35	optimal	optimal	ADJ
ejpam-6254	260	36	control	control	NOUN
ejpam-6254	260	37	u∗1	u∗1	NOUN
ejpam-6254	260	38	and	and	CCONJ
ejpam-6254	260	39	u∗2	u∗2	NOUN
ejpam-6254	260	40	in	in	ADP
ejpam-6254	260	41	the	the	DET
ejpam-6254	260	42	following	follow	VERB
ejpam-6254	260	43	form	form	NOUN
ejpam-6254	260	44	:	:	PUNCT
ejpam-6254	260	45	u∗1(t	u∗1(t	PROPN
ejpam-6254	260	46	)	)	PUNCT
ejpam-6254	260	47	=	=	SYM
ejpam-6254	260	48	min	min	PROPN
ejpam-6254	260	49	(	(	PUNCT
ejpam-6254	260	50	1,max	1,max	NUM
ejpam-6254	260	51	(	(	PUNCT
ejpam-6254	260	52	0	0	NUM
ejpam-6254	260	53	,	,	PUNCT
ejpam-6254	260	54	(	(	PUNCT
ejpam-6254	260	55	λ4	λ4	VERB
ejpam-6254	260	56	−	−	PROPN
ejpam-6254	260	57	λ2	λ2	NOUN
ejpam-6254	260	58	)	)	PUNCT
ejpam-6254	260	59	a1	a1	NOUN
ejpam-6254	260	60	e	e	NOUN
ejpam-6254	260	61	)	)	PUNCT
ejpam-6254	260	62	)	)	PUNCT
ejpam-6254	260	63	,	,	PUNCT
ejpam-6254	260	64	u∗2(t	u∗2(t	PROPN
ejpam-6254	260	65	)	)	PUNCT
ejpam-6254	260	66	=	=	SYM
ejpam-6254	260	67	min	min	PROPN
ejpam-6254	260	68	(	(	PUNCT
ejpam-6254	260	69	1,max	1,max	NUM
ejpam-6254	260	70	(	(	PUNCT
ejpam-6254	260	71	0	0	NUM
ejpam-6254	260	72	,	,	PUNCT
ejpam-6254	260	73	(	(	PUNCT
ejpam-6254	260	74	λ4	λ4	PROPN
ejpam-6254	260	75	−	−	PROPN
ejpam-6254	260	76	λ3	λ3	PROPN
ejpam-6254	260	77	)	)	PUNCT
ejpam-6254	260	78	a2	a2	PROPN
ejpam-6254	260	79	i	i	PROPN
ejpam-6254	260	80	)	)	PUNCT
ejpam-6254	260	81	)	)	PUNCT
ejpam-6254	260	82	.	.	PUNCT
ejpam-6254	261	1	4	4	X
ejpam-6254	261	2	.	.	X
ejpam-6254	261	3	numerical	numerical	PROPN
ejpam-6254	261	4	simulation	simulation	PROPN
ejpam-6254	261	5	to	to	PART
ejpam-6254	261	6	discuss	discuss	VERB
ejpam-6254	261	7	the	the	DET
ejpam-6254	261	8	dynamics	dynamic	NOUN
ejpam-6254	261	9	of	of	ADP
ejpam-6254	261	10	disease	disease	NOUN
ejpam-6254	261	11	spread	spread	VERB
ejpam-6254	261	12	and	and	CCONJ
ejpam-6254	261	13	study	study	VERB
ejpam-6254	261	14	the	the	DET
ejpam-6254	261	15	impact	impact	NOUN
ejpam-6254	261	16	of	of	ADP
ejpam-6254	261	17	both	both	DET
ejpam-6254	261	18	time	time	NOUN
ejpam-6254	261	19	delay	delay	NOUN
ejpam-6254	261	20	and	and	CCONJ
ejpam-6254	261	21	control	control	NOUN
ejpam-6254	261	22	strategies	strategy	NOUN
ejpam-6254	261	23	,	,	PUNCT
ejpam-6254	261	24	we	we	PRON
ejpam-6254	261	25	performed	perform	VERB
ejpam-6254	261	26	a	a	DET
ejpam-6254	261	27	numerical	numerical	ADJ
ejpam-6254	261	28	simulation	simulation	NOUN
ejpam-6254	261	29	of	of	ADP
ejpam-6254	261	30	the	the	DET
ejpam-6254	261	31	solution	solution	NOUN
ejpam-6254	261	32	trajectories	trajectory	NOUN
ejpam-6254	261	33	of	of	ADP
ejpam-6254	261	34	the	the	DET
ejpam-6254	261	35	model	model	NOUN
ejpam-6254	261	36	described	describe	VERB
ejpam-6254	261	37	in	in	ADP
ejpam-6254	261	38	model	model	NOUN
ejpam-6254	261	39	(	(	PUNCT
ejpam-6254	261	40	3	3	NUM
ejpam-6254	261	41	)	)	PUNCT
ejpam-6254	261	42	,	,	PUNCT
ejpam-6254	261	43	where	where	SCONJ
ejpam-6254	261	44	classes	class	NOUN
ejpam-6254	261	45	(	(	PUNCT
ejpam-6254	261	46	s	s	X
ejpam-6254	261	47	,	,	PUNCT
ejpam-6254	261	48	i	i	PRON
ejpam-6254	261	49	,	,	PUNCT
ejpam-6254	261	50	e	e	NOUN
ejpam-6254	261	51	)	)	PUNCT
ejpam-6254	261	52	are	be	AUX
ejpam-6254	261	53	independent	independent	ADJ
ejpam-6254	261	54	of	of	ADP
ejpam-6254	261	55	(	(	PUNCT
ejpam-6254	261	56	r	r	NOUN
ejpam-6254	261	57	,	,	PUNCT
ejpam-6254	261	58	v	v	NOUN
ejpam-6254	261	59	)	)	PUNCT
ejpam-6254	261	60	and	and	CCONJ
ejpam-6254	261	61	the	the	DET
ejpam-6254	261	62	adjoint	adjoint	PROPN
ejpam-6254	261	63	model	model	NOUN
ejpam-6254	261	64	in	in	ADP
ejpam-6254	261	65	theorem	theorem	PROPN
ejpam-6254	261	66	(	(	PUNCT
ejpam-6254	261	67	4.2	4.2	NUM
ejpam-6254	261	68	)	)	PUNCT
ejpam-6254	261	69	.	.	PUNCT
ejpam-6254	262	1	the	the	DET
ejpam-6254	262	2	parameter	parameter	NOUN
ejpam-6254	262	3	values	value	NOUN
ejpam-6254	262	4	model	model	NOUN
ejpam-6254	262	5	simulations	simulation	NOUN
ejpam-6254	262	6	are	be	AUX
ejpam-6254	262	7	shown	show	VERB
ejpam-6254	262	8	in	in	ADP
ejpam-6254	262	9	table	table	NOUN
ejpam-6254	262	10	1	1	NUM
ejpam-6254	262	11	.	.	PUNCT
ejpam-6254	262	12	table	table	NOUN
ejpam-6254	262	13	1	1	NUM
ejpam-6254	262	14	.	.	PUNCT
ejpam-6254	263	1	parameter	parameter	NOUN
ejpam-6254	263	2	values	value	NOUN
ejpam-6254	263	3	of	of	ADP
ejpam-6254	263	4	model	model	NOUN
ejpam-6254	263	5	(	(	PUNCT
ejpam-6254	263	6	3	3	NUM
ejpam-6254	263	7	)	)	PUNCT
ejpam-6254	263	8	.	.	PUNCT
ejpam-6254	264	1	parameters	parameter	NOUN
ejpam-6254	264	2	value	value	NOUN
ejpam-6254	264	3	∆	∆	PROPN
ejpam-6254	264	4	0.87	0.87	NUM
ejpam-6254	264	5	β	β	NOUN
ejpam-6254	264	6	0.01	0.01	NUM
ejpam-6254	264	7	α	α	NUM
ejpam-6254	264	8	0.1	0.1	NUM
ejpam-6254	264	9	µ	µ	NOUN
ejpam-6254	264	10	0.1	0.1	NUM
ejpam-6254	264	11	γ2	γ2	NOUN
ejpam-6254	264	12	=	=	SYM
ejpam-6254	264	13	γ3	γ3	NOUN
ejpam-6254	264	14	0.1	0.1	NUM
ejpam-6254	264	15	γ1	γ1	NOUN
ejpam-6254	264	16	0.01	0.01	NUM
ejpam-6254	264	17	σ	σ	PROPN
ejpam-6254	264	18	0.2	0.2	NUM
ejpam-6254	264	19	the	the	DET
ejpam-6254	264	20	simulation	simulation	NOUN
ejpam-6254	264	21	of	of	ADP
ejpam-6254	264	22	the	the	DET
ejpam-6254	264	23	model	model	NOUN
ejpam-6254	264	24	(	(	PUNCT
ejpam-6254	264	25	3	3	X
ejpam-6254	264	26	)	)	PUNCT
ejpam-6254	264	27	illustrated	illustrate	VERB
ejpam-6254	264	28	in	in	ADP
ejpam-6254	264	29	figure	figure	NOUN
ejpam-6254	264	30	1	1	NUM
ejpam-6254	264	31	,	,	PUNCT
ejpam-6254	264	32	shows	show	VERB
ejpam-6254	264	33	the	the	DET
ejpam-6254	264	34	dynamic	dynamic	ADJ
ejpam-6254	264	35	behavior	behavior	NOUN
ejpam-6254	264	36	of	of	ADP
ejpam-6254	264	37	the	the	DET
ejpam-6254	264	38	model	model	NOUN
ejpam-6254	264	39	(	(	PUNCT
ejpam-6254	264	40	3	3	NUM
ejpam-6254	264	41	)	)	PUNCT
ejpam-6254	264	42	that	that	PRON
ejpam-6254	264	43	approaches	approach	VERB
ejpam-6254	264	44	the	the	DET
ejpam-6254	264	45	extinction	extinction	NOUN
ejpam-6254	264	46	of	of	ADP
ejpam-6254	264	47	the	the	DET
ejpam-6254	264	48	disease	disease	NOUN
ejpam-6254	264	49	.	.	PUNCT
ejpam-6254	265	1	s.	s.	PROPN
ejpam-6254	265	2	irum	irum	PROPN
ejpam-6254	265	3	et	et	PROPN
ejpam-6254	265	4	al	al	PROPN
ejpam-6254	265	5	.	.	PUNCT
ejpam-6254	265	6	/	/	SYM
ejpam-6254	265	7	eur	eur	PROPN
ejpam-6254	265	8	.	.	PUNCT
ejpam-6254	266	1	j.	j.	PROPN
ejpam-6254	266	2	pure	pure	PROPN
ejpam-6254	266	3	appl	appl	PROPN
ejpam-6254	266	4	.	.	PROPN
ejpam-6254	266	5	math	math	PROPN
ejpam-6254	266	6	,	,	PUNCT
ejpam-6254	266	7	18	18	NUM
ejpam-6254	266	8	(	(	PUNCT
ejpam-6254	266	9	4	4	NUM
ejpam-6254	266	10	)	)	PUNCT
ejpam-6254	266	11	(	(	PUNCT
ejpam-6254	266	12	2025	2025	NUM
ejpam-6254	266	13	)	)	PUNCT
ejpam-6254	266	14	,	,	PUNCT
ejpam-6254	266	15	6254	6254	NUM
ejpam-6254	266	16	15	15	NUM
ejpam-6254	266	17	of	of	ADP
ejpam-6254	266	18	23	23	NUM
ejpam-6254	266	19	0	0	NUM
ejpam-6254	266	20	0.2	0.2	NUM
ejpam-6254	266	21	0.2	0.2	NUM
ejpam-6254	266	22	5	5	NUM
ejpam-6254	267	1	i	i	PROPN
ejpam-6254	267	2	(	(	PUNCT
ejpam-6254	267	3	t	t	PROPN
ejpam-6254	267	4	)	)	PUNCT
ejpam-6254	267	5	e(t	e(t	NOUN
ejpam-6254	267	6	)	)	PUNCT
ejpam-6254	267	7	0	0	NUM
ejpam-6254	267	8	s(t	s(t	PROPN
ejpam-6254	267	9	)	)	PUNCT
ejpam-6254	267	10	0.4	0.4	NUM
ejpam-6254	267	11	-0.2	-0.2	NOUN
ejpam-6254	267	12	0	0	NUM
ejpam-6254	267	13	0	0	NUM
ejpam-6254	267	14	500	500	NUM
ejpam-6254	267	15	1000	1000	NUM
ejpam-6254	267	16	1500	1500	NUM
ejpam-6254	267	17	2000	2000	NUM
ejpam-6254	267	18	t	t	NOUN
ejpam-6254	267	19	0	0	NUM
ejpam-6254	267	20	2	2	NUM
ejpam-6254	267	21	4	4	NUM
ejpam-6254	267	22	6	6	NUM
ejpam-6254	267	23	s	s	NOUN
ejpam-6254	267	24	(	(	PUNCT
ejpam-6254	267	25	t	t	PROPN
ejpam-6254	267	26	)	)	PUNCT
ejpam-6254	267	27	0	0	NUM
ejpam-6254	268	1	500	500	NUM
ejpam-6254	268	2	1000	1000	NUM
ejpam-6254	268	3	1500	1500	NUM
ejpam-6254	268	4	2000	2000	NUM
ejpam-6254	268	5	t	t	NOUN
ejpam-6254	268	6	0	0	NUM
ejpam-6254	268	7	0.05	0.05	NUM
ejpam-6254	268	8	0.1	0.1	NUM
ejpam-6254	268	9	0.15	0.15	NUM
ejpam-6254	268	10	0.2	0.2	NUM
ejpam-6254	268	11	e	e	NOUN
ejpam-6254	268	12	(	(	PUNCT
ejpam-6254	268	13	t	t	PROPN
ejpam-6254	268	14	)	)	PUNCT
ejpam-6254	268	15	0	0	NUM
ejpam-6254	268	16	500	500	NUM
ejpam-6254	268	17	1000	1000	NUM
ejpam-6254	268	18	1500	1500	NUM
ejpam-6254	268	19	2000	2000	NUM
ejpam-6254	268	20	t	t	NOUN
ejpam-6254	268	21	0	0	NUM
ejpam-6254	268	22	0.1	0.1	NUM
ejpam-6254	268	23	0.2	0.2	NUM
ejpam-6254	268	24	0.3	0.3	NUM
ejpam-6254	268	25	0.4	0.4	NUM
ejpam-6254	269	1	i	i	PROPN
ejpam-6254	269	2	(	(	PUNCT
ejpam-6254	269	3	t	t	PROPN
ejpam-6254	269	4	)	)	PUNCT
ejpam-6254	269	5	stable	stable	ADJ
ejpam-6254	269	6	point	point	NOUN
ejpam-6254	269	7	figure	figure	NOUN
ejpam-6254	269	8	2	2	NUM
ejpam-6254	269	9	:	:	PUNCT
ejpam-6254	269	10	the	the	DET
ejpam-6254	269	11	trajectory	trajectory	NOUN
ejpam-6254	269	12	of	of	ADP
ejpam-6254	269	13	the	the	DET
ejpam-6254	269	14	system	system	NOUN
ejpam-6254	269	15	(	(	PUNCT
ejpam-6254	269	16	3	3	X
ejpam-6254	269	17	)	)	PUNCT
ejpam-6254	269	18	using	use	VERB
ejpam-6254	269	19	the	the	DET
ejpam-6254	269	20	parameters	parameter	NOUN
ejpam-6254	269	21	set	set	VERB
ejpam-6254	269	22	in	in	ADP
ejpam-6254	269	23	table	table	NOUN
ejpam-6254	269	24	1	1	NUM
ejpam-6254	269	25	.	.	PUNCT
ejpam-6254	270	1	now	now	ADV
ejpam-6254	270	2	,	,	PUNCT
ejpam-6254	270	3	we	we	PRON
ejpam-6254	270	4	show	show	VERB
ejpam-6254	270	5	the	the	DET
ejpam-6254	270	6	effect	effect	NOUN
ejpam-6254	270	7	of	of	ADP
ejpam-6254	270	8	increasing	increase	VERB
ejpam-6254	270	9	the	the	DET
ejpam-6254	270	10	infection	infection	NOUN
ejpam-6254	270	11	rate	rate	NOUN
ejpam-6254	270	12	on	on	ADP
ejpam-6254	270	13	the	the	DET
ejpam-6254	270	14	dynamics	dynamic	NOUN
ejpam-6254	270	15	of	of	ADP
ejpam-6254	270	16	the	the	DET
ejpam-6254	270	17	model	model	NOUN
ejpam-6254	270	18	(	(	PUNCT
ejpam-6254	270	19	3	3	NUM
ejpam-6254	270	20	)	)	PUNCT
ejpam-6254	270	21	,	,	PUNCT
ejpam-6254	270	22	by	by	ADP
ejpam-6254	270	23	keeping	keep	VERB
ejpam-6254	270	24	the	the	DET
ejpam-6254	270	25	values	value	NOUN
ejpam-6254	270	26	of	of	ADP
ejpam-6254	270	27	all	all	DET
ejpam-6254	270	28	parameters	parameter	NOUN
ejpam-6254	270	29	in	in	ADP
ejpam-6254	270	30	table	table	NOUN
ejpam-6254	270	31	1	1	NUM
ejpam-6254	270	32	except	except	SCONJ
ejpam-6254	270	33	the	the	DET
ejpam-6254	270	34	value	value	NOUN
ejpam-6254	270	35	of	of	ADP
ejpam-6254	270	36	β	β	NOUN
ejpam-6254	270	37	we	we	PRON
ejpam-6254	270	38	change	change	VERB
ejpam-6254	270	39	it	it	PRON
ejpam-6254	270	40	from	from	ADP
ejpam-6254	270	41	0.01	0.01	NUM
ejpam-6254	270	42	to	to	ADP
ejpam-6254	270	43	0.1	0.1	NUM
ejpam-6254	270	44	and	and	CCONJ
ejpam-6254	270	45	τ	τ	X
ejpam-6254	270	46	<	<	X
ejpam-6254	270	47	18.5	18.5	NUM
ejpam-6254	270	48	,	,	PUNCT
ejpam-6254	270	49	we	we	PRON
ejpam-6254	270	50	get	get	VERB
ejpam-6254	270	51	the	the	DET
ejpam-6254	270	52	solution	solution	NOUN
ejpam-6254	270	53	of	of	ADP
ejpam-6254	270	54	model	model	NOUN
ejpam-6254	270	55	1	1	NUM
ejpam-6254	270	56	,	,	PUNCT
ejpam-6254	270	57	which	which	PRON
ejpam-6254	270	58	tends	tend	VERB
ejpam-6254	270	59	to	to	ADP
ejpam-6254	270	60	the	the	DET
ejpam-6254	270	61	endemic	endemic	ADJ
ejpam-6254	270	62	point	point	NOUN
ejpam-6254	270	63	;	;	PUNCT
ejpam-6254	270	64	see	see	VERB
ejpam-6254	270	65	figure	figure	NOUN
ejpam-6254	270	66	2	2	NUM
ejpam-6254	270	67	.	.	NOUN
ejpam-6254	270	68	0	0	NUM
ejpam-6254	270	69	2	2	NUM
ejpam-6254	270	70	2	2	NUM
ejpam-6254	270	71	4	4	NUM
ejpam-6254	270	72	i	i	PROPN
ejpam-6254	270	73	(	(	PUNCT
ejpam-6254	270	74	t	t	PROPN
ejpam-6254	270	75	)	)	PUNCT
ejpam-6254	270	76	e(t	e(t	NOUN
ejpam-6254	270	77	)	)	PUNCT
ejpam-6254	270	78	1	1	NUM
ejpam-6254	270	79	s(t	s(t	PROPN
ejpam-6254	270	80	)	)	PUNCT
ejpam-6254	270	81	4	4	NUM
ejpam-6254	270	82	2	2	NUM
ejpam-6254	270	83	0	0	NUM
ejpam-6254	270	84	0	0	NUM
ejpam-6254	270	85	0	0	NUM
ejpam-6254	270	86	500	500	NUM
ejpam-6254	270	87	1000	1000	NUM
ejpam-6254	270	88	1500	1500	NUM
ejpam-6254	270	89	2000	2000	NUM
ejpam-6254	270	90	t	t	NOUN
ejpam-6254	270	91	0	0	NUM
ejpam-6254	270	92	1	1	NUM
ejpam-6254	270	93	2	2	NUM
ejpam-6254	270	94	3	3	NUM
ejpam-6254	270	95	4	4	NUM
ejpam-6254	270	96	s	s	PART
ejpam-6254	270	97	(	(	PUNCT
ejpam-6254	270	98	t	t	PROPN
ejpam-6254	270	99	)	)	PUNCT
ejpam-6254	270	100	0	0	NUM
ejpam-6254	270	101	500	500	NUM
ejpam-6254	270	102	1000	1000	NUM
ejpam-6254	270	103	1500	1500	NUM
ejpam-6254	270	104	2000	2000	NUM
ejpam-6254	270	105	t	t	NOUN
ejpam-6254	270	106	0	0	NUM
ejpam-6254	270	107	0.5	0.5	NUM
ejpam-6254	270	108	1	1	NUM
ejpam-6254	270	109	1.5	1.5	NUM
ejpam-6254	270	110	2	2	NUM
ejpam-6254	270	111	e	e	NOUN
ejpam-6254	270	112	(	(	PUNCT
ejpam-6254	270	113	t	t	PROPN
ejpam-6254	270	114	)	)	PUNCT
ejpam-6254	270	115	0	0	NUM
ejpam-6254	270	116	500	500	NUM
ejpam-6254	270	117	1000	1000	NUM
ejpam-6254	270	118	1500	1500	NUM
ejpam-6254	270	119	2000	2000	NUM
ejpam-6254	270	120	t	t	NOUN
ejpam-6254	270	121	0	0	NUM
ejpam-6254	270	122	1	1	NUM
ejpam-6254	270	123	2	2	NUM
ejpam-6254	270	124	3	3	NUM
ejpam-6254	270	125	i	i	PROPN
ejpam-6254	270	126	(	(	PUNCT
ejpam-6254	270	127	t	t	NOUN
ejpam-6254	270	128	)	)	PUNCT
ejpam-6254	270	129	stable	stable	ADJ
ejpam-6254	270	130	point	point	NOUN
ejpam-6254	270	131	figure	figure	NOUN
ejpam-6254	270	132	3	3	NUM
ejpam-6254	270	133	:	:	PUNCT
ejpam-6254	270	134	the	the	DET
ejpam-6254	270	135	trajectory	trajectory	NOUN
ejpam-6254	270	136	of	of	ADP
ejpam-6254	270	137	the	the	DET
ejpam-6254	270	138	system	system	NOUN
ejpam-6254	270	139	(	(	PUNCT
ejpam-6254	270	140	3	3	X
ejpam-6254	270	141	)	)	PUNCT
ejpam-6254	270	142	using	use	VERB
ejpam-6254	270	143	the	the	DET
ejpam-6254	270	144	parameters	parameter	NOUN
ejpam-6254	270	145	set	set	VERB
ejpam-6254	270	146	in	in	ADP
ejpam-6254	270	147	table	table	NOUN
ejpam-6254	270	148	1	1	NUM
ejpam-6254	270	149	with	with	ADP
ejpam-6254	270	150	β	β	X
ejpam-6254	270	151	=	=	SYM
ejpam-6254	270	152	0.1	0.1	NUM
ejpam-6254	270	153	.	.	PUNCT
ejpam-6254	271	1	s.	s.	PROPN
ejpam-6254	271	2	irum	irum	PROPN
ejpam-6254	271	3	et	et	PROPN
ejpam-6254	271	4	al	al	PROPN
ejpam-6254	271	5	.	.	PUNCT
ejpam-6254	271	6	/	/	SYM
ejpam-6254	271	7	eur	eur	PROPN
ejpam-6254	271	8	.	.	PUNCT
ejpam-6254	272	1	j.	j.	PROPN
ejpam-6254	272	2	pure	pure	PROPN
ejpam-6254	272	3	appl	appl	PROPN
ejpam-6254	272	4	.	.	PROPN
ejpam-6254	272	5	math	math	PROPN
ejpam-6254	272	6	,	,	PUNCT
ejpam-6254	272	7	18	18	NUM
ejpam-6254	272	8	(	(	PUNCT
ejpam-6254	272	9	4	4	NUM
ejpam-6254	272	10	)	)	PUNCT
ejpam-6254	272	11	(	(	PUNCT
ejpam-6254	272	12	2025	2025	NUM
ejpam-6254	272	13	)	)	PUNCT
ejpam-6254	272	14	,	,	PUNCT
ejpam-6254	272	15	6254	6254	NUM
ejpam-6254	272	16	16	16	NUM
ejpam-6254	272	17	of	of	ADP
ejpam-6254	272	18	23	23	NUM
ejpam-6254	272	19	in	in	ADP
ejpam-6254	272	20	addition	addition	NOUN
ejpam-6254	272	21	,	,	PUNCT
ejpam-6254	272	22	we	we	PRON
ejpam-6254	272	23	also	also	ADV
ejpam-6254	272	24	need	need	VERB
ejpam-6254	272	25	to	to	PART
ejpam-6254	272	26	know	know	VERB
ejpam-6254	272	27	the	the	DET
ejpam-6254	272	28	impact	impact	NOUN
ejpam-6254	272	29	of	of	ADP
ejpam-6254	272	30	time	time	NOUN
ejpam-6254	272	31	delay	delay	NOUN
ejpam-6254	272	32	on	on	ADP
ejpam-6254	272	33	the	the	DET
ejpam-6254	272	34	solution	solution	NOUN
ejpam-6254	272	35	of	of	ADP
ejpam-6254	272	36	the	the	DET
ejpam-6254	272	37	model	model	NOUN
ejpam-6254	272	38	(	(	PUNCT
ejpam-6254	272	39	3	3	NUM
ejpam-6254	272	40	)	)	PUNCT
ejpam-6254	272	41	.	.	PUNCT
ejpam-6254	273	1	in	in	ADP
ejpam-6254	273	2	figure	figure	NOUN
ejpam-6254	273	3	3	3	NUM
ejpam-6254	273	4	,	,	PUNCT
ejpam-6254	273	5	if	if	SCONJ
ejpam-6254	273	6	we	we	PRON
ejpam-6254	273	7	choose	choose	VERB
ejpam-6254	273	8	the	the	DET
ejpam-6254	273	9	value	value	NOUN
ejpam-6254	273	10	of	of	ADP
ejpam-6254	273	11	the	the	DET
ejpam-6254	273	12	parameter	parameter	NOUN
ejpam-6254	273	13	τ	τ	PROPN
ejpam-6254	273	14	=	=	SYM
ejpam-6254	273	15	τ0	τ0	NOUN
ejpam-6254	273	16	=	=	PUNCT
ejpam-6254	274	1	18.5	18.5	NUM
ejpam-6254	274	2	.	.	PUNCT
ejpam-6254	275	1	the	the	DET
ejpam-6254	275	2	figure	figure	NOUN
ejpam-6254	275	3	tells	tell	VERB
ejpam-6254	275	4	us	we	PRON
ejpam-6254	275	5	loss	loss	NOUN
ejpam-6254	275	6	of	of	ADP
ejpam-6254	275	7	stability	stability	NOUN
ejpam-6254	275	8	of	of	ADP
ejpam-6254	275	9	the	the	DET
ejpam-6254	275	10	endemic	endemic	ADJ
ejpam-6254	275	11	point	point	NOUN
ejpam-6254	275	12	and	and	CCONJ
ejpam-6254	275	13	change	change	NOUN
ejpam-6254	275	14	of	of	ADP
ejpam-6254	275	15	the	the	DET
ejpam-6254	275	16	system	system	NOUN
ejpam-6254	275	17	’s	’s	PART
ejpam-6254	275	18	behavior	behavior	NOUN
ejpam-6254	275	19	to	to	ADP
ejpam-6254	275	20	the	the	DET
ejpam-6254	275	21	periodic	periodic	ADJ
ejpam-6254	275	22	state	state	NOUN
ejpam-6254	275	23	(	(	PUNCT
ejpam-6254	275	24	occurring	occur	VERB
ejpam-6254	275	25	hopf	hopf	ADJ
ejpam-6254	275	26	bifurcation	bifurcation	NOUN
ejpam-6254	275	27	)	)	PUNCT
ejpam-6254	275	28	.	.	PUNCT
ejpam-6254	276	1	however	however	ADV
ejpam-6254	276	2	,	,	PUNCT
ejpam-6254	276	3	both	both	DET
ejpam-6254	276	4	figures	figure	NOUN
ejpam-6254	276	5	(	(	PUNCT
ejpam-6254	276	6	4	4	NUM
ejpam-6254	276	7	)	)	PUNCT
ejpam-6254	276	8	and	and	CCONJ
ejpam-6254	276	9	(	(	PUNCT
ejpam-6254	276	10	5	5	X
ejpam-6254	276	11	)	)	PUNCT
ejpam-6254	276	12	tell	tell	VERB
ejpam-6254	276	13	us	we	PRON
ejpam-6254	276	14	the	the	DET
ejpam-6254	276	15	high	high	ADJ
ejpam-6254	276	16	periodic	periodic	ADJ
ejpam-6254	276	17	state	state	NOUN
ejpam-6254	276	18	when	when	SCONJ
ejpam-6254	276	19	we	we	PRON
ejpam-6254	276	20	increase	increase	VERB
ejpam-6254	276	21	the	the	DET
ejpam-6254	276	22	time	time	NOUN
ejpam-6254	276	23	delay	delay	NOUN
ejpam-6254	276	24	such	such	ADJ
ejpam-6254	276	25	as	as	ADP
ejpam-6254	276	26	τ	τ	PROPN
ejpam-6254	276	27	=	=	SYM
ejpam-6254	276	28	20	20	NUM
ejpam-6254	276	29	,	,	PUNCT
ejpam-6254	276	30	25	25	NUM
ejpam-6254	276	31	,	,	PUNCT
ejpam-6254	276	32	respectively	respectively	ADV
ejpam-6254	276	33	.	.	PUNCT
ejpam-6254	277	1	0	0	NUM
ejpam-6254	278	1	4	4	NUM
ejpam-6254	278	2	4	4	NUM
ejpam-6254	278	3	i	i	PROPN
ejpam-6254	278	4	(	(	PUNCT
ejpam-6254	278	5	t	t	PROPN
ejpam-6254	278	6	)	)	PUNCT
ejpam-6254	278	7	e(t	e(t	NOUN
ejpam-6254	278	8	)	)	PUNCT
ejpam-6254	278	9	2	2	NUM
ejpam-6254	278	10	s(t	s(t	PROPN
ejpam-6254	278	11	)	)	PUNCT
ejpam-6254	278	12	5	5	NUM
ejpam-6254	278	13	2	2	NUM
ejpam-6254	278	14	0	0	NUM
ejpam-6254	278	15	0	0	NUM
ejpam-6254	278	16	0	0	NUM
ejpam-6254	278	17	500	500	NUM
ejpam-6254	278	18	1000	1000	NUM
ejpam-6254	278	19	1500	1500	NUM
ejpam-6254	278	20	2000	2000	NUM
ejpam-6254	278	21	t	t	NOUN
ejpam-6254	278	22	0	0	NUM
ejpam-6254	278	23	1	1	NUM
ejpam-6254	278	24	2	2	NUM
ejpam-6254	278	25	3	3	NUM
ejpam-6254	278	26	4	4	NUM
ejpam-6254	278	27	s	s	PART
ejpam-6254	278	28	(	(	PUNCT
ejpam-6254	278	29	t	t	PROPN
ejpam-6254	278	30	)	)	PUNCT
ejpam-6254	278	31	0	0	NUM
ejpam-6254	278	32	500	500	NUM
ejpam-6254	278	33	1000	1000	NUM
ejpam-6254	278	34	1500	1500	NUM
ejpam-6254	278	35	2000	2000	NUM
ejpam-6254	278	36	t	t	NOUN
ejpam-6254	278	37	0	0	NUM
ejpam-6254	278	38	1	1	NUM
ejpam-6254	278	39	2	2	NUM
ejpam-6254	278	40	3	3	NUM
ejpam-6254	278	41	e	e	X
ejpam-6254	278	42	(	(	PUNCT
ejpam-6254	278	43	t	t	PROPN
ejpam-6254	278	44	)	)	PUNCT
ejpam-6254	278	45	0	0	NUM
ejpam-6254	278	46	500	500	NUM
ejpam-6254	278	47	1000	1000	NUM
ejpam-6254	278	48	1500	1500	NUM
ejpam-6254	278	49	2000	2000	NUM
ejpam-6254	278	50	t	t	NOUN
ejpam-6254	278	51	0	0	NUM
ejpam-6254	278	52	2	2	NUM
ejpam-6254	278	53	4	4	NUM
ejpam-6254	278	54	6	6	NUM
ejpam-6254	278	55	i	i	PROPN
ejpam-6254	278	56	(	(	PUNCT
ejpam-6254	278	57	t	t	PROPN
ejpam-6254	278	58	)	)	PUNCT
ejpam-6254	278	59	figure	figure	NOUN
ejpam-6254	278	60	4	4	NUM
ejpam-6254	278	61	:	:	PUNCT
ejpam-6254	278	62	the	the	DET
ejpam-6254	278	63	trajectory	trajectory	NOUN
ejpam-6254	278	64	of	of	ADP
ejpam-6254	278	65	the	the	DET
ejpam-6254	278	66	model	model	NOUN
ejpam-6254	278	67	(	(	PUNCT
ejpam-6254	278	68	3	3	X
ejpam-6254	278	69	)	)	PUNCT
ejpam-6254	278	70	using	use	VERB
ejpam-6254	278	71	the	the	DET
ejpam-6254	278	72	parameters	parameter	NOUN
ejpam-6254	278	73	set	set	VERB
ejpam-6254	278	74	in	in	ADP
ejpam-6254	278	75	table	table	NOUN
ejpam-6254	278	76	1	1	NUM
ejpam-6254	278	77	with	with	ADP
ejpam-6254	278	78	τ	τ	PROPN
ejpam-6254	278	79	=	=	SYM
ejpam-6254	278	80	18.5	18.5	NUM
ejpam-6254	278	81	.	.	PUNCT
ejpam-6254	279	1	s.	s.	PROPN
ejpam-6254	279	2	irum	irum	PROPN
ejpam-6254	279	3	et	et	PROPN
ejpam-6254	279	4	al	al	PROPN
ejpam-6254	279	5	.	.	PUNCT
ejpam-6254	279	6	/	/	SYM
ejpam-6254	279	7	eur	eur	PROPN
ejpam-6254	279	8	.	.	PUNCT
ejpam-6254	280	1	j.	j.	PROPN
ejpam-6254	280	2	pure	pure	PROPN
ejpam-6254	280	3	appl	appl	PROPN
ejpam-6254	280	4	.	.	PROPN
ejpam-6254	280	5	math	math	PROPN
ejpam-6254	280	6	,	,	PUNCT
ejpam-6254	280	7	18	18	NUM
ejpam-6254	280	8	(	(	PUNCT
ejpam-6254	280	9	4	4	NUM
ejpam-6254	280	10	)	)	PUNCT
ejpam-6254	280	11	(	(	PUNCT
ejpam-6254	280	12	2025	2025	NUM
ejpam-6254	280	13	)	)	PUNCT
ejpam-6254	280	14	,	,	PUNCT
ejpam-6254	280	15	6254	6254	NUM
ejpam-6254	280	16	17	17	NUM
ejpam-6254	280	17	of	of	ADP
ejpam-6254	280	18	23	23	NUM
ejpam-6254	280	19	0	0	NUM
ejpam-6254	280	20	4	4	NUM
ejpam-6254	280	21	5	5	NUM
ejpam-6254	280	22	4	4	NUM
ejpam-6254	280	23	i	i	PROPN
ejpam-6254	280	24	(	(	PUNCT
ejpam-6254	280	25	t	t	PROPN
ejpam-6254	280	26	)	)	PUNCT
ejpam-6254	280	27	e(t	e(t	NOUN
ejpam-6254	280	28	)	)	PUNCT
ejpam-6254	280	29	2	2	NUM
ejpam-6254	280	30	s(t	s(t	PROPN
ejpam-6254	280	31	)	)	PUNCT
ejpam-6254	280	32	10	10	NUM
ejpam-6254	280	33	2	2	NUM
ejpam-6254	280	34	0	0	NUM
ejpam-6254	280	35	0	0	NUM
ejpam-6254	280	36	0	0	NUM
ejpam-6254	280	37	500	500	NUM
ejpam-6254	280	38	1000	1000	NUM
ejpam-6254	280	39	1500	1500	NUM
ejpam-6254	280	40	2000	2000	NUM
ejpam-6254	280	41	t	t	NOUN
ejpam-6254	280	42	0	0	NUM
ejpam-6254	280	43	1	1	NUM
ejpam-6254	280	44	2	2	NUM
ejpam-6254	280	45	3	3	NUM
ejpam-6254	280	46	4	4	NUM
ejpam-6254	280	47	s	s	PART
ejpam-6254	280	48	(	(	PUNCT
ejpam-6254	280	49	t	t	PROPN
ejpam-6254	280	50	)	)	PUNCT
ejpam-6254	280	51	0	0	NUM
ejpam-6254	281	1	500	500	NUM
ejpam-6254	281	2	1000	1000	NUM
ejpam-6254	281	3	1500	1500	NUM
ejpam-6254	281	4	2000	2000	NUM
ejpam-6254	281	5	t	t	NOUN
ejpam-6254	281	6	0	0	NUM
ejpam-6254	281	7	1	1	NUM
ejpam-6254	281	8	2	2	NUM
ejpam-6254	281	9	3	3	NUM
ejpam-6254	281	10	4	4	NUM
ejpam-6254	281	11	e	e	NOUN
ejpam-6254	281	12	(	(	PUNCT
ejpam-6254	281	13	t	t	PROPN
ejpam-6254	281	14	)	)	PUNCT
ejpam-6254	281	15	0	0	NUM
ejpam-6254	281	16	500	500	NUM
ejpam-6254	281	17	1000	1000	NUM
ejpam-6254	281	18	1500	1500	NUM
ejpam-6254	281	19	2000	2000	NUM
ejpam-6254	281	20	t	t	NOUN
ejpam-6254	281	21	0	0	NUM
ejpam-6254	281	22	2	2	NUM
ejpam-6254	281	23	4	4	NUM
ejpam-6254	281	24	6	6	NUM
ejpam-6254	281	25	i	i	PROPN
ejpam-6254	281	26	(	(	PUNCT
ejpam-6254	281	27	t	t	PROPN
ejpam-6254	281	28	)	)	PUNCT
ejpam-6254	281	29	figure	figure	NOUN
ejpam-6254	281	30	5	5	NUM
ejpam-6254	281	31	:	:	PUNCT
ejpam-6254	281	32	the	the	DET
ejpam-6254	281	33	trajectory	trajectory	NOUN
ejpam-6254	281	34	of	of	ADP
ejpam-6254	281	35	the	the	DET
ejpam-6254	281	36	model	model	NOUN
ejpam-6254	281	37	(	(	PUNCT
ejpam-6254	281	38	3	3	X
ejpam-6254	281	39	)	)	PUNCT
ejpam-6254	281	40	using	use	VERB
ejpam-6254	281	41	the	the	DET
ejpam-6254	281	42	parameters	parameter	NOUN
ejpam-6254	281	43	set	set	VERB
ejpam-6254	281	44	in	in	ADP
ejpam-6254	281	45	table	table	NOUN
ejpam-6254	281	46	1	1	NUM
ejpam-6254	281	47	with	with	ADP
ejpam-6254	281	48	τ	τ	PROPN
ejpam-6254	281	49	=	=	SYM
ejpam-6254	281	50	20	20	NUM
ejpam-6254	281	51	.	.	NOUN
ejpam-6254	281	52	0	0	NUM
ejpam-6254	281	53	4	4	NUM
ejpam-6254	281	54	5	5	NUM
ejpam-6254	281	55	4	4	NUM
ejpam-6254	281	56	i	i	PROPN
ejpam-6254	281	57	(	(	PUNCT
ejpam-6254	281	58	t	t	PROPN
ejpam-6254	281	59	)	)	PUNCT
ejpam-6254	281	60	e(t	e(t	NOUN
ejpam-6254	281	61	)	)	PUNCT
ejpam-6254	281	62	2	2	NUM
ejpam-6254	281	63	s(t	s(t	PROPN
ejpam-6254	281	64	)	)	PUNCT
ejpam-6254	281	65	10	10	NUM
ejpam-6254	281	66	2	2	NUM
ejpam-6254	281	67	0	0	NUM
ejpam-6254	281	68	0	0	NUM
ejpam-6254	281	69	0	0	NUM
ejpam-6254	281	70	500	500	NUM
ejpam-6254	281	71	1000	1000	NUM
ejpam-6254	281	72	1500	1500	NUM
ejpam-6254	281	73	2000	2000	NUM
ejpam-6254	281	74	t	t	NOUN
ejpam-6254	281	75	0	0	NUM
ejpam-6254	281	76	1	1	NUM
ejpam-6254	281	77	2	2	NUM
ejpam-6254	281	78	3	3	NUM
ejpam-6254	281	79	4	4	NUM
ejpam-6254	281	80	s	s	PART
ejpam-6254	281	81	(	(	PUNCT
ejpam-6254	281	82	t	t	PROPN
ejpam-6254	281	83	)	)	PUNCT
ejpam-6254	281	84	0	0	NUM
ejpam-6254	281	85	500	500	NUM
ejpam-6254	281	86	1000	1000	NUM
ejpam-6254	281	87	1500	1500	NUM
ejpam-6254	281	88	2000	2000	NUM
ejpam-6254	281	89	t	t	NOUN
ejpam-6254	281	90	0	0	NUM
ejpam-6254	281	91	1	1	NUM
ejpam-6254	281	92	2	2	NUM
ejpam-6254	281	93	3	3	NUM
ejpam-6254	281	94	4	4	NUM
ejpam-6254	281	95	e	e	NOUN
ejpam-6254	281	96	(	(	PUNCT
ejpam-6254	281	97	t	t	PROPN
ejpam-6254	281	98	)	)	PUNCT
ejpam-6254	281	99	0	0	NUM
ejpam-6254	282	1	500	500	NUM
ejpam-6254	282	2	1000	1000	NUM
ejpam-6254	282	3	1500	1500	NUM
ejpam-6254	282	4	2000	2000	NUM
ejpam-6254	282	5	t	t	NOUN
ejpam-6254	282	6	0	0	NUM
ejpam-6254	282	7	2	2	NUM
ejpam-6254	282	8	4	4	NUM
ejpam-6254	282	9	6	6	NUM
ejpam-6254	282	10	8	8	NUM
ejpam-6254	282	11	i	i	PROPN
ejpam-6254	282	12	(	(	PUNCT
ejpam-6254	282	13	t	t	PROPN
ejpam-6254	282	14	)	)	PUNCT
ejpam-6254	282	15	figure	figure	NOUN
ejpam-6254	282	16	6	6	NUM
ejpam-6254	282	17	:	:	PUNCT
ejpam-6254	282	18	the	the	DET
ejpam-6254	282	19	trajectory	trajectory	NOUN
ejpam-6254	282	20	of	of	ADP
ejpam-6254	282	21	the	the	DET
ejpam-6254	282	22	system	system	NOUN
ejpam-6254	282	23	(	(	PUNCT
ejpam-6254	282	24	3	3	X
ejpam-6254	282	25	)	)	PUNCT
ejpam-6254	282	26	using	use	VERB
ejpam-6254	282	27	the	the	DET
ejpam-6254	282	28	parameters	parameter	NOUN
ejpam-6254	282	29	set	set	VERB
ejpam-6254	282	30	in	in	ADP
ejpam-6254	282	31	table	table	NOUN
ejpam-6254	282	32	1	1	NUM
ejpam-6254	282	33	with	with	ADP
ejpam-6254	282	34	τ	τ	PROPN
ejpam-6254	282	35	=	=	SYM
ejpam-6254	282	36	25	25	NUM
ejpam-6254	282	37	.	.	PUNCT
ejpam-6254	283	1	for	for	ADP
ejpam-6254	283	2	the	the	DET
ejpam-6254	283	3	simulation	simulation	NOUN
ejpam-6254	283	4	analysis	analysis	NOUN
ejpam-6254	283	5	to	to	ADP
ejpam-6254	283	6	the	the	DET
ejpam-6254	283	7	each	each	DET
ejpam-6254	283	8	control	control	NOUN
ejpam-6254	283	9	strategies	strategy	NOUN
ejpam-6254	283	10	are	be	AUX
ejpam-6254	283	11	quarantine	quarantine	NOUN
ejpam-6254	283	12	and	and	CCONJ
ejpam-6254	283	13	treatment	treatment	NOUN
ejpam-6254	283	14	and	and	CCONJ
ejpam-6254	283	15	represented	represent	VERB
ejpam-6254	283	16	by	by	ADP
ejpam-6254	283	17	the	the	DET
ejpam-6254	283	18	parameters	parameter	NOUN
ejpam-6254	283	19	u1	u1	VERB
ejpam-6254	283	20	and	and	CCONJ
ejpam-6254	283	21	u2	u2	NOUN
ejpam-6254	283	22	respectively	respectively	ADV
ejpam-6254	283	23	.	.	PUNCT
ejpam-6254	284	1	the	the	DET
ejpam-6254	284	2	four	four	NUM
ejpam-6254	284	3	scenarios	scenario	NOUN
ejpam-6254	284	4	for	for	ADP
ejpam-6254	284	5	numerical	numerical	ADJ
ejpam-6254	284	6	simulation	simulation	NOUN
ejpam-6254	284	7	of	of	ADP
ejpam-6254	284	8	the	the	DET
ejpam-6254	284	9	adjoint	adjoint	PROPN
ejpam-6254	284	10	model	model	NOUN
ejpam-6254	284	11	are	be	AUX
ejpam-6254	284	12	given	give	VERB
ejpam-6254	284	13	below	below	ADV
ejpam-6254	284	14	:	:	PUNCT
ejpam-6254	284	15	(	(	PUNCT
ejpam-6254	284	16	i	i	NOUN
ejpam-6254	284	17	)	)	PUNCT
ejpam-6254	284	18	scenario	scenario	NOUN
ejpam-6254	284	19	a	a	NOUN
ejpam-6254	284	20	:	:	PUNCT
ejpam-6254	284	21	there	there	PRON
ejpam-6254	284	22	is	be	VERB
ejpam-6254	284	23	no	no	DET
ejpam-6254	284	24	quarantine	quarantine	NOUN
ejpam-6254	284	25	and	and	CCONJ
ejpam-6254	284	26	no	no	DET
ejpam-6254	284	27	treatment	treatment	NOUN
ejpam-6254	284	28	available	available	ADJ
ejpam-6254	284	29	for	for	ADP
ejpam-6254	284	30	the	the	DET
ejpam-6254	284	31	infected	infect	VERB
ejpam-6254	284	32	(	(	PUNCT
ejpam-6254	284	33	u1	u1	NOUN
ejpam-6254	284	34	=	=	SYM
ejpam-6254	284	35	u2	u2	PROPN
ejpam-6254	284	36	=	=	NOUN
ejpam-6254	284	37	0	0	NUM
ejpam-6254	284	38	)	)	PUNCT
ejpam-6254	284	39	.	.	PUNCT
ejpam-6254	285	1	s.	s.	PROPN
ejpam-6254	285	2	irum	irum	PROPN
ejpam-6254	285	3	et	et	PROPN
ejpam-6254	285	4	al	al	PROPN
ejpam-6254	285	5	.	.	PUNCT
ejpam-6254	285	6	/	/	SYM
ejpam-6254	285	7	eur	eur	PROPN
ejpam-6254	285	8	.	.	PUNCT
ejpam-6254	286	1	j.	j.	PROPN
ejpam-6254	286	2	pure	pure	PROPN
ejpam-6254	286	3	appl	appl	PROPN
ejpam-6254	286	4	.	.	PROPN
ejpam-6254	286	5	math	math	PROPN
ejpam-6254	286	6	,	,	PUNCT
ejpam-6254	286	7	18	18	NUM
ejpam-6254	286	8	(	(	PUNCT
ejpam-6254	286	9	4	4	NUM
ejpam-6254	286	10	)	)	PUNCT
ejpam-6254	286	11	(	(	PUNCT
ejpam-6254	286	12	2025	2025	NUM
ejpam-6254	286	13	)	)	PUNCT
ejpam-6254	286	14	,	,	PUNCT
ejpam-6254	286	15	6254	6254	NUM
ejpam-6254	286	16	18	18	NUM
ejpam-6254	286	17	of	of	ADP
ejpam-6254	286	18	23	23	NUM
ejpam-6254	286	19	(	(	PUNCT
ejpam-6254	286	20	ii	ii	NOUN
ejpam-6254	286	21	)	)	PUNCT
ejpam-6254	286	22	scenario	scenario	NOUN
ejpam-6254	286	23	b	b	NOUN
ejpam-6254	286	24	:	:	PUNCT
ejpam-6254	286	25	only	only	ADJ
ejpam-6254	286	26	quarantine	quarantine	NOUN
ejpam-6254	286	27	is	be	AUX
ejpam-6254	286	28	implemented	implement	VERB
ejpam-6254	286	29	(	(	PUNCT
ejpam-6254	286	30	u1	u1	NOUN
ejpam-6254	286	31	̸=	̸=	PROPN
ejpam-6254	286	32	0	0	NUM
ejpam-6254	286	33	,	,	PUNCT
ejpam-6254	286	34	u2	u2	NOUN
ejpam-6254	286	35	=	=	NOUN
ejpam-6254	286	36	0	0	NUM
ejpam-6254	286	37	)	)	PUNCT
ejpam-6254	286	38	.	.	PUNCT
ejpam-6254	287	1	(	(	PUNCT
ejpam-6254	287	2	iii	iii	X
ejpam-6254	287	3	)	)	PUNCT
ejpam-6254	287	4	scenario	scenario	NOUN
ejpam-6254	287	5	c	c	NOUN
ejpam-6254	287	6	:	:	PUNCT
ejpam-6254	287	7	only	only	ADV
ejpam-6254	287	8	treatment	treatment	NOUN
ejpam-6254	287	9	for	for	ADP
ejpam-6254	287	10	the	the	DET
ejpam-6254	287	11	infected	infected	NOUN
ejpam-6254	287	12	is	be	AUX
ejpam-6254	287	13	provided	provide	VERB
ejpam-6254	287	14	(	(	PUNCT
ejpam-6254	287	15	u1	u1	NOUN
ejpam-6254	287	16	=	=	SYM
ejpam-6254	287	17	0	0	NUM
ejpam-6254	287	18	,	,	PUNCT
ejpam-6254	287	19	u2	u2	PROPN
ejpam-6254	287	20	̸=	̸=	PROPN
ejpam-6254	287	21	0	0	NUM
ejpam-6254	287	22	)	)	PUNCT
ejpam-6254	287	23	.	.	PUNCT
ejpam-6254	288	1	(	(	PUNCT
ejpam-6254	288	2	iv	iv	X
ejpam-6254	288	3	)	)	PUNCT
ejpam-6254	288	4	scenario	scenario	NOUN
ejpam-6254	288	5	d	d	NOUN
ejpam-6254	288	6	:	:	PUNCT
ejpam-6254	288	7	a	a	DET
ejpam-6254	288	8	combination	combination	NOUN
ejpam-6254	288	9	of	of	ADP
ejpam-6254	288	10	both	both	CCONJ
ejpam-6254	288	11	quarantine	quarantine	NOUN
ejpam-6254	288	12	and	and	CCONJ
ejpam-6254	288	13	treatment	treatment	NOUN
ejpam-6254	288	14	is	be	AUX
ejpam-6254	288	15	implemented	implement	VERB
ejpam-6254	288	16	(	(	PUNCT
ejpam-6254	288	17	u1	u1	NOUN
ejpam-6254	288	18	̸=	̸=	PROPN
ejpam-6254	288	19	0	0	NUM
ejpam-6254	288	20	,	,	PUNCT
ejpam-6254	288	21	u2	u2	PROPN
ejpam-6254	288	22	̸=	̸=	PROPN
ejpam-6254	288	23	0	0	NUM
ejpam-6254	288	24	)	)	PUNCT
ejpam-6254	288	25	.	.	PUNCT
ejpam-6254	289	1	it	it	PRON
ejpam-6254	289	2	is	be	AUX
ejpam-6254	289	3	clear	clear	ADJ
ejpam-6254	289	4	that	that	SCONJ
ejpam-6254	289	5	,	,	PUNCT
ejpam-6254	289	6	figure	figure	NOUN
ejpam-6254	289	7	6	6	NUM
ejpam-6254	289	8	,	,	PUNCT
ejpam-6254	289	9	shows	show	VERB
ejpam-6254	289	10	that	that	SCONJ
ejpam-6254	289	11	the	the	DET
ejpam-6254	289	12	impact	impact	NOUN
ejpam-6254	289	13	of	of	ADP
ejpam-6254	289	14	both	both	DET
ejpam-6254	289	15	scenarios	scenario	NOUN
ejpam-6254	289	16	(	(	PUNCT
ejpam-6254	289	17	a	a	X
ejpam-6254	289	18	)	)	PUNCT
ejpam-6254	289	19	and	and	CCONJ
ejpam-6254	289	20	(	(	PUNCT
ejpam-6254	289	21	b	b	NOUN
ejpam-6254	289	22	)	)	PUNCT
ejpam-6254	289	23	and	and	CCONJ
ejpam-6254	289	24	this	this	DET
ejpam-6254	289	25	figure	figure	NOUN
ejpam-6254	289	26	tell	tell	VERB
ejpam-6254	289	27	us	we	PRON
ejpam-6254	289	28	when	when	SCONJ
ejpam-6254	289	29	we	we	PRON
ejpam-6254	289	30	increasing	increase	VERB
ejpam-6254	289	31	the	the	DET
ejpam-6254	289	32	quarantine	quarantine	NOUN
ejpam-6254	289	33	rate	rate	NOUN
ejpam-6254	289	34	(	(	PUNCT
ejpam-6254	289	35	i.e.	i.e.	X
ejpam-6254	289	36	u1	u1	PROPN
ejpam-6254	289	37	≥	≥	NOUN
ejpam-6254	289	38	0.5	0.5	NUM
ejpam-6254	289	39	)	)	PUNCT
ejpam-6254	289	40	with	with	ADP
ejpam-6254	289	41	keeping	keep	VERB
ejpam-6254	289	42	the	the	DET
ejpam-6254	289	43	other	other	ADJ
ejpam-6254	289	44	parameters	parameter	NOUN
ejpam-6254	289	45	in	in	ADP
ejpam-6254	289	46	table	table	NOUN
ejpam-6254	289	47	1	1	NUM
ejpam-6254	289	48	with	with	ADP
ejpam-6254	289	49	β	β	X
ejpam-6254	289	50	=	=	SYM
ejpam-6254	289	51	0.1	0.1	NUM
ejpam-6254	289	52	and	and	CCONJ
ejpam-6254	289	53	τ	τ	X
ejpam-6254	289	54	<	<	X
ejpam-6254	289	55	18.5	18.5	NUM
ejpam-6254	289	56	,	,	PUNCT
ejpam-6254	289	57	we	we	PRON
ejpam-6254	289	58	get	get	VERB
ejpam-6254	289	59	the	the	DET
ejpam-6254	289	60	dynamical	dynamical	ADJ
ejpam-6254	289	61	behavior	behavior	NOUN
ejpam-6254	289	62	of	of	ADP
ejpam-6254	289	63	system	system	NOUN
ejpam-6254	289	64	(	(	PUNCT
ejpam-6254	289	65	3	3	X
ejpam-6254	289	66	)	)	PUNCT
ejpam-6254	289	67	tend	tend	VERB
ejpam-6254	289	68	towards	towards	ADP
ejpam-6254	289	69	disease	disease	NOUN
ejpam-6254	289	70	extinction	extinction	NOUN
ejpam-6254	289	71	point	point	NOUN
ejpam-6254	289	72	.	.	PUNCT
ejpam-6254	290	1	0	0	NUM
ejpam-6254	291	1	100	100	NUM
ejpam-6254	291	2	200	200	NUM
ejpam-6254	291	3	300	300	NUM
ejpam-6254	291	4	400	400	NUM
ejpam-6254	291	5	days	day	NOUN
ejpam-6254	291	6	0	0	NUM
ejpam-6254	291	7	2	2	NUM
ejpam-6254	291	8	4	4	NUM
ejpam-6254	291	9	6	6	NUM
ejpam-6254	291	10	s	s	NOUN
ejpam-6254	291	11	µ	µ	PRON
ejpam-6254	291	12	1	1	NUM
ejpam-6254	291	13	=	=	SYM
ejpam-6254	291	14	µ	µ	PRON
ejpam-6254	291	15	2	2	NUM
ejpam-6254	291	16	=	=	SYM
ejpam-6254	291	17	0	0	NUM
ejpam-6254	291	18	µ	µ	NUM
ejpam-6254	291	19	1	1	NUM
ejpam-6254	291	20	=	=	NOUN
ejpam-6254	291	21	0.1,µ	0.1,µ	NOUN
ejpam-6254	291	22	2	2	NUM
ejpam-6254	291	23	=	=	SYM
ejpam-6254	291	24	0	0	NUM
ejpam-6254	291	25	µ	µ	NUM
ejpam-6254	291	26	1	1	NUM
ejpam-6254	291	27	=	=	NOUN
ejpam-6254	291	28	0.2,µ	0.2,µ	NOUN
ejpam-6254	291	29	2	2	NUM
ejpam-6254	292	1	=	=	SYM
ejpam-6254	292	2	0	0	NUM
ejpam-6254	292	3	µ	µ	NUM
ejpam-6254	292	4	1	1	NUM
ejpam-6254	292	5	=	=	NOUN
ejpam-6254	292	6	0.5,µ	0.5,µ	NOUN
ejpam-6254	292	7	2	2	NUM
ejpam-6254	292	8	=	=	SYM
ejpam-6254	292	9	0	0	NUM
ejpam-6254	292	10	0	0	NUM
ejpam-6254	292	11	100	100	NUM
ejpam-6254	292	12	200	200	NUM
ejpam-6254	292	13	300	300	NUM
ejpam-6254	292	14	400	400	NUM
ejpam-6254	292	15	days	day	NOUN
ejpam-6254	292	16	0	0	NUM
ejpam-6254	292	17	0.5	0.5	NUM
ejpam-6254	292	18	1	1	NUM
ejpam-6254	292	19	e	e	NOUN
ejpam-6254	292	20	0	0	NUM
ejpam-6254	292	21	100	100	NUM
ejpam-6254	292	22	200	200	NUM
ejpam-6254	292	23	300	300	NUM
ejpam-6254	292	24	400	400	NUM
ejpam-6254	292	25	days	day	NOUN
ejpam-6254	292	26	0	0	NUM
ejpam-6254	292	27	0.5	0.5	NUM
ejpam-6254	292	28	1	1	NUM
ejpam-6254	292	29	1.5	1.5	NUM
ejpam-6254	292	30	2	2	NUM
ejpam-6254	292	31	i	i	NOUN
ejpam-6254	292	32	0	0	NUM
ejpam-6254	292	33	1	1	NUM
ejpam-6254	292	34	1	1	NUM
ejpam-6254	292	35	5	5	NUM
ejpam-6254	292	36	i	i	NOUN
ejpam-6254	292	37	e	e	VERB
ejpam-6254	292	38	0.5	0.5	NUM
ejpam-6254	292	39	s	s	NOUN
ejpam-6254	292	40	2	2	NUM
ejpam-6254	292	41	0	0	NUM
ejpam-6254	292	42	0	0	NUM
ejpam-6254	292	43	figure	figure	NOUN
ejpam-6254	292	44	7	7	NUM
ejpam-6254	292	45	:	:	PUNCT
ejpam-6254	292	46	the	the	DET
ejpam-6254	292	47	trajectory	trajectory	NOUN
ejpam-6254	292	48	of	of	ADP
ejpam-6254	292	49	the	the	DET
ejpam-6254	292	50	model	model	NOUN
ejpam-6254	292	51	(	(	PUNCT
ejpam-6254	292	52	3	3	NUM
ejpam-6254	292	53	)	)	PUNCT
ejpam-6254	292	54	with	with	ADP
ejpam-6254	292	55	µ2	µ2	PROPN
ejpam-6254	292	56	=	=	PROPN
ejpam-6254	292	57	0	0	NUM
ejpam-6254	292	58	and	and	CCONJ
ejpam-6254	292	59	different	different	ADJ
ejpam-6254	292	60	values	value	NOUN
ejpam-6254	292	61	of	of	ADP
ejpam-6254	292	62	µ1	µ1	PROPN
ejpam-6254	292	63	.	.	PUNCT
ejpam-6254	293	1	thus	thus	ADV
ejpam-6254	293	2	,	,	PUNCT
ejpam-6254	293	3	figure	figure	VERB
ejpam-6254	293	4	7	7	NUM
ejpam-6254	293	5	,	,	PUNCT
ejpam-6254	293	6	presents	present	VERB
ejpam-6254	293	7	that	that	SCONJ
ejpam-6254	293	8	the	the	DET
ejpam-6254	293	9	impact	impact	NOUN
ejpam-6254	293	10	of	of	ADP
ejpam-6254	293	11	both	both	DET
ejpam-6254	293	12	scenarios	scenario	NOUN
ejpam-6254	293	13	(	(	PUNCT
ejpam-6254	293	14	a	a	X
ejpam-6254	293	15	)	)	PUNCT
ejpam-6254	293	16	and	and	CCONJ
ejpam-6254	293	17	(	(	PUNCT
ejpam-6254	293	18	c	c	NOUN
ejpam-6254	293	19	)	)	PUNCT
ejpam-6254	293	20	and	and	CCONJ
ejpam-6254	293	21	this	this	DET
ejpam-6254	293	22	figure	figure	NOUN
ejpam-6254	293	23	tell	tell	VERB
ejpam-6254	293	24	us	we	PRON
ejpam-6254	293	25	when	when	SCONJ
ejpam-6254	293	26	we	we	PRON
ejpam-6254	293	27	increasing	increase	VERB
ejpam-6254	293	28	the	the	DET
ejpam-6254	293	29	treatment	treatment	NOUN
ejpam-6254	293	30	rate	rate	NOUN
ejpam-6254	293	31	(	(	PUNCT
ejpam-6254	293	32	i.e.	i.e.	X
ejpam-6254	293	33	u2	u2	PROPN
ejpam-6254	293	34	≥	≥	NOUN
ejpam-6254	293	35	0.2	0.2	NUM
ejpam-6254	293	36	)	)	PUNCT
ejpam-6254	293	37	with	with	ADP
ejpam-6254	293	38	keeping	keep	VERB
ejpam-6254	293	39	the	the	DET
ejpam-6254	293	40	other	other	ADJ
ejpam-6254	293	41	parameters	parameter	NOUN
ejpam-6254	293	42	in	in	ADP
ejpam-6254	293	43	table	table	NOUN
ejpam-6254	293	44	1	1	NUM
ejpam-6254	293	45	with	with	ADP
ejpam-6254	293	46	β	β	X
ejpam-6254	293	47	=	=	SYM
ejpam-6254	293	48	0.1	0.1	NUM
ejpam-6254	293	49	and	and	CCONJ
ejpam-6254	293	50	τ	τ	X
ejpam-6254	293	51	<	<	X
ejpam-6254	293	52	18.5	18.5	NUM
ejpam-6254	293	53	,	,	PUNCT
ejpam-6254	293	54	we	we	PRON
ejpam-6254	293	55	get	get	VERB
ejpam-6254	293	56	the	the	DET
ejpam-6254	293	57	dynamical	dynamical	ADJ
ejpam-6254	293	58	behavior	behavior	NOUN
ejpam-6254	293	59	of	of	ADP
ejpam-6254	293	60	model	model	NOUN
ejpam-6254	293	61	(	(	PUNCT
ejpam-6254	293	62	3	3	X
ejpam-6254	293	63	)	)	PUNCT
ejpam-6254	293	64	tend	tend	VERB
ejpam-6254	293	65	towards	towards	ADP
ejpam-6254	293	66	disease	disease	NOUN
ejpam-6254	293	67	extinction	extinction	NOUN
ejpam-6254	293	68	point	point	NOUN
ejpam-6254	293	69	.	.	PUNCT
ejpam-6254	294	1	s.	s.	PROPN
ejpam-6254	294	2	irum	irum	PROPN
ejpam-6254	294	3	et	et	PROPN
ejpam-6254	294	4	al	al	PROPN
ejpam-6254	294	5	.	.	PUNCT
ejpam-6254	294	6	/	/	SYM
ejpam-6254	294	7	eur	eur	PROPN
ejpam-6254	294	8	.	.	PUNCT
ejpam-6254	295	1	j.	j.	PROPN
ejpam-6254	295	2	pure	pure	PROPN
ejpam-6254	295	3	appl	appl	PROPN
ejpam-6254	295	4	.	.	PROPN
ejpam-6254	295	5	math	math	PROPN
ejpam-6254	295	6	,	,	PUNCT
ejpam-6254	295	7	18	18	NUM
ejpam-6254	295	8	(	(	PUNCT
ejpam-6254	295	9	4	4	NUM
ejpam-6254	295	10	)	)	PUNCT
ejpam-6254	295	11	(	(	PUNCT
ejpam-6254	295	12	2025	2025	NUM
ejpam-6254	295	13	)	)	PUNCT
ejpam-6254	295	14	,	,	PUNCT
ejpam-6254	295	15	6254	6254	NUM
ejpam-6254	295	16	19	19	NUM
ejpam-6254	295	17	of	of	ADP
ejpam-6254	295	18	23	23	NUM
ejpam-6254	295	19	0	0	NUM
ejpam-6254	295	20	100	100	NUM
ejpam-6254	295	21	200	200	NUM
ejpam-6254	295	22	300	300	NUM
ejpam-6254	295	23	400	400	NUM
ejpam-6254	295	24	days	day	NOUN
ejpam-6254	295	25	0	0	NUM
ejpam-6254	295	26	2	2	NUM
ejpam-6254	295	27	4	4	NUM
ejpam-6254	295	28	6	6	NUM
ejpam-6254	295	29	s	s	NOUN
ejpam-6254	295	30	µ	µ	DET
ejpam-6254	295	31	1	1	NUM
ejpam-6254	295	32	=	=	SYM
ejpam-6254	295	33	0,µ	0,µ	NOUN
ejpam-6254	295	34	2	2	NUM
ejpam-6254	295	35	=	=	SYM
ejpam-6254	295	36	0	0	NUM
ejpam-6254	295	37	µ	µ	NUM
ejpam-6254	295	38	1	1	NUM
ejpam-6254	295	39	=	=	SYM
ejpam-6254	295	40	0,µ	0,µ	NOUN
ejpam-6254	295	41	2	2	NUM
ejpam-6254	295	42	=	=	SYM
ejpam-6254	295	43	0.1	0.1	NUM
ejpam-6254	295	44	µ	µ	DET
ejpam-6254	295	45	1	1	NUM
ejpam-6254	295	46	=	=	SYM
ejpam-6254	295	47	0,µ	0,µ	NOUN
ejpam-6254	295	48	2	2	NUM
ejpam-6254	295	49	=	=	SYM
ejpam-6254	295	50	0.2	0.2	NUM
ejpam-6254	295	51	µ	µ	NUM
ejpam-6254	295	52	1	1	NUM
ejpam-6254	295	53	=	=	SYM
ejpam-6254	295	54	0,µ	0,µ	NOUN
ejpam-6254	295	55	2	2	NUM
ejpam-6254	295	56	=	=	SYM
ejpam-6254	295	57	0.5	0.5	NUM
ejpam-6254	295	58	0	0	NUM
ejpam-6254	295	59	100	100	NUM
ejpam-6254	295	60	200	200	NUM
ejpam-6254	295	61	300	300	NUM
ejpam-6254	295	62	400	400	NUM
ejpam-6254	295	63	days	day	NOUN
ejpam-6254	295	64	0	0	NUM
ejpam-6254	295	65	0.5	0.5	NUM
ejpam-6254	295	66	1	1	NUM
ejpam-6254	295	67	e	e	NOUN
ejpam-6254	295	68	0	0	NUM
ejpam-6254	295	69	100	100	NUM
ejpam-6254	295	70	200	200	NUM
ejpam-6254	295	71	300	300	NUM
ejpam-6254	295	72	400	400	NUM
ejpam-6254	295	73	days	day	NOUN
ejpam-6254	295	74	0	0	NUM
ejpam-6254	295	75	0.5	0.5	NUM
ejpam-6254	295	76	1	1	NUM
ejpam-6254	295	77	1.5	1.5	NUM
ejpam-6254	295	78	2	2	NUM
ejpam-6254	295	79	i	i	NOUN
ejpam-6254	295	80	0	0	NUM
ejpam-6254	295	81	1	1	NUM
ejpam-6254	295	82	1	1	NUM
ejpam-6254	295	83	5	5	NUM
ejpam-6254	295	84	i	i	NOUN
ejpam-6254	295	85	e	e	VERB
ejpam-6254	295	86	0.5	0.5	NUM
ejpam-6254	295	87	s	s	NOUN
ejpam-6254	295	88	2	2	NUM
ejpam-6254	295	89	0	0	NUM
ejpam-6254	295	90	0	0	NUM
ejpam-6254	295	91	figure	figure	NOUN
ejpam-6254	295	92	8	8	NUM
ejpam-6254	295	93	:	:	PUNCT
ejpam-6254	295	94	the	the	DET
ejpam-6254	295	95	trajectory	trajectory	NOUN
ejpam-6254	295	96	of	of	ADP
ejpam-6254	295	97	the	the	DET
ejpam-6254	295	98	system	system	NOUN
ejpam-6254	295	99	(	(	PUNCT
ejpam-6254	295	100	3	3	NUM
ejpam-6254	295	101	)	)	PUNCT
ejpam-6254	295	102	with	with	ADP
ejpam-6254	295	103	µ1	µ1	PROPN
ejpam-6254	295	104	=	=	SYM
ejpam-6254	295	105	0	0	NUM
ejpam-6254	295	106	and	and	CCONJ
ejpam-6254	295	107	different	different	ADJ
ejpam-6254	295	108	values	value	NOUN
ejpam-6254	295	109	of	of	ADP
ejpam-6254	295	110	µ2	µ2	PROPN
ejpam-6254	295	111	.	.	PUNCT
ejpam-6254	296	1	finally	finally	ADV
ejpam-6254	296	2	,	,	PUNCT
ejpam-6254	296	3	as	as	SCONJ
ejpam-6254	296	4	depicted	depict	VERB
ejpam-6254	296	5	in	in	ADP
ejpam-6254	296	6	figure	figure	NOUN
ejpam-6254	296	7	7	7	NUM
ejpam-6254	296	8	,	,	PUNCT
ejpam-6254	296	9	scenario	scenario	NOUN
ejpam-6254	296	10	(	(	PUNCT
ejpam-6254	296	11	d	d	NOUN
ejpam-6254	296	12	)	)	PUNCT
ejpam-6254	296	13	leads	lead	VERB
ejpam-6254	296	14	to	to	ADP
ejpam-6254	296	15	a	a	DET
ejpam-6254	296	16	more	more	ADV
ejpam-6254	296	17	rapid	rapid	ADJ
ejpam-6254	296	18	progression	progression	NOUN
ejpam-6254	296	19	toward	toward	ADP
ejpam-6254	296	20	disease	disease	NOUN
ejpam-6254	296	21	extinction	extinction	NOUN
ejpam-6254	296	22	compared	compare	VERB
ejpam-6254	296	23	to	to	ADP
ejpam-6254	296	24	scenarios	scenario	NOUN
ejpam-6254	296	25	(	(	PUNCT
ejpam-6254	296	26	b	b	NOUN
ejpam-6254	296	27	)	)	PUNCT
ejpam-6254	296	28	and	and	CCONJ
ejpam-6254	296	29	(	(	PUNCT
ejpam-6254	296	30	c	c	NOUN
ejpam-6254	296	31	)	)	PUNCT
ejpam-6254	296	32	,	,	PUNCT
ejpam-6254	296	33	highlighting	highlight	VERB
ejpam-6254	296	34	the	the	DET
ejpam-6254	296	35	enhanced	enhanced	ADJ
ejpam-6254	296	36	effectiveness	effectiveness	NOUN
ejpam-6254	296	37	of	of	ADP
ejpam-6254	296	38	the	the	DET
ejpam-6254	296	39	interventions	intervention	NOUN
ejpam-6254	296	40	assumed	assume	VERB
ejpam-6254	296	41	in	in	ADP
ejpam-6254	296	42	this	this	DET
ejpam-6254	296	43	scenario	scenario	NOUN
ejpam-6254	296	44	.	.	PUNCT
ejpam-6254	297	1	0	0	NUM
ejpam-6254	298	1	100	100	NUM
ejpam-6254	298	2	200	200	NUM
ejpam-6254	298	3	300	300	NUM
ejpam-6254	298	4	400	400	NUM
ejpam-6254	298	5	days	day	NOUN
ejpam-6254	298	6	0	0	NUM
ejpam-6254	298	7	2	2	NUM
ejpam-6254	298	8	4	4	NUM
ejpam-6254	298	9	6	6	NUM
ejpam-6254	298	10	s	s	NOUN
ejpam-6254	298	11	µ	µ	PRON
ejpam-6254	298	12	1	1	NUM
ejpam-6254	298	13	=	=	SYM
ejpam-6254	298	14	0,µ	0,µ	NOUN
ejpam-6254	298	15	2	2	NUM
ejpam-6254	298	16	=	=	SYM
ejpam-6254	298	17	0	0	NUM
ejpam-6254	298	18	µ	µ	NUM
ejpam-6254	298	19	1	1	NUM
ejpam-6254	298	20	=	=	NOUN
ejpam-6254	298	21	0.1,µ	0.1,µ	NOUN
ejpam-6254	298	22	2	2	NUM
ejpam-6254	298	23	=	=	SYM
ejpam-6254	298	24	0.1	0.1	NUM
ejpam-6254	298	25	µ	µ	PRON
ejpam-6254	298	26	1	1	NUM
ejpam-6254	298	27	=	=	NOUN
ejpam-6254	298	28	0.2,µ	0.2,µ	NOUN
ejpam-6254	298	29	2	2	NUM
ejpam-6254	299	1	=	=	SYM
ejpam-6254	299	2	0.2	0.2	NUM
ejpam-6254	299	3	0	0	NUM
ejpam-6254	299	4	100	100	NUM
ejpam-6254	299	5	200	200	NUM
ejpam-6254	299	6	300	300	NUM
ejpam-6254	299	7	400	400	NUM
ejpam-6254	299	8	days	day	NOUN
ejpam-6254	299	9	0	0	NUM
ejpam-6254	299	10	0.5	0.5	NUM
ejpam-6254	299	11	1	1	NUM
ejpam-6254	299	12	e	e	NOUN
ejpam-6254	299	13	0	0	NUM
ejpam-6254	299	14	100	100	NUM
ejpam-6254	299	15	200	200	NUM
ejpam-6254	299	16	300	300	NUM
ejpam-6254	299	17	400	400	NUM
ejpam-6254	299	18	days	day	NOUN
ejpam-6254	299	19	0	0	NUM
ejpam-6254	299	20	0.5	0.5	NUM
ejpam-6254	299	21	1	1	NUM
ejpam-6254	299	22	1.5	1.5	NUM
ejpam-6254	299	23	2	2	NUM
ejpam-6254	299	24	i	i	NOUN
ejpam-6254	299	25	0	0	NUM
ejpam-6254	299	26	1	1	NUM
ejpam-6254	299	27	1	1	NUM
ejpam-6254	299	28	6	6	NUM
ejpam-6254	299	29	i	i	NOUN
ejpam-6254	299	30	e	e	NOUN
ejpam-6254	299	31	0.5	0.5	NUM
ejpam-6254	299	32	4	4	NUM
ejpam-6254	299	33	s	s	NOUN
ejpam-6254	299	34	2	2	NUM
ejpam-6254	299	35	2	2	NUM
ejpam-6254	299	36	0	0	NUM
ejpam-6254	299	37	0	0	NUM
ejpam-6254	299	38	figure	figure	NOUN
ejpam-6254	299	39	9	9	NUM
ejpam-6254	299	40	:	:	PUNCT
ejpam-6254	299	41	the	the	DET
ejpam-6254	299	42	trajectory	trajectory	NOUN
ejpam-6254	299	43	of	of	ADP
ejpam-6254	299	44	the	the	DET
ejpam-6254	299	45	system	system	NOUN
ejpam-6254	299	46	(	(	PUNCT
ejpam-6254	299	47	3	3	NUM
ejpam-6254	299	48	)	)	PUNCT
ejpam-6254	299	49	with	with	ADP
ejpam-6254	299	50	µ1	µ1	PROPN
ejpam-6254	299	51	=	=	SYM
ejpam-6254	299	52	0.2	0.2	NUM
ejpam-6254	299	53	and	and	CCONJ
ejpam-6254	299	54	µ2	µ2	PROPN
ejpam-6254	299	55	=	=	PROPN
ejpam-6254	299	56	0.2	0.2	NUM
ejpam-6254	299	57	.	.	PUNCT
ejpam-6254	300	1	s.	s.	PROPN
ejpam-6254	300	2	irum	irum	PROPN
ejpam-6254	300	3	et	et	PROPN
ejpam-6254	300	4	al	al	PROPN
ejpam-6254	300	5	.	.	PUNCT
ejpam-6254	300	6	/	/	SYM
ejpam-6254	300	7	eur	eur	PROPN
ejpam-6254	300	8	.	.	PUNCT
ejpam-6254	301	1	j.	j.	PROPN
ejpam-6254	301	2	pure	pure	PROPN
ejpam-6254	301	3	appl	appl	PROPN
ejpam-6254	301	4	.	.	PROPN
ejpam-6254	301	5	math	math	PROPN
ejpam-6254	301	6	,	,	PUNCT
ejpam-6254	301	7	18	18	NUM
ejpam-6254	301	8	(	(	PUNCT
ejpam-6254	301	9	4	4	NUM
ejpam-6254	301	10	)	)	PUNCT
ejpam-6254	301	11	(	(	PUNCT
ejpam-6254	301	12	2025	2025	NUM
ejpam-6254	301	13	)	)	PUNCT
ejpam-6254	301	14	,	,	PUNCT
ejpam-6254	301	15	6254	6254	NUM
ejpam-6254	301	16	20	20	NUM
ejpam-6254	301	17	of	of	ADP
ejpam-6254	301	18	23	23	NUM
ejpam-6254	301	19	0	0	NUM
ejpam-6254	301	20	5	5	NUM
ejpam-6254	301	21	10	10	NUM
ejpam-6254	301	22	15	15	NUM
ejpam-6254	301	23	20	20	NUM
ejpam-6254	301	24	25	25	NUM
ejpam-6254	301	25	30	30	NUM
ejpam-6254	301	26	0	0	NUM
ejpam-6254	301	27	100	100	NUM
ejpam-6254	301	28	200	200	NUM
ejpam-6254	301	29	300	300	NUM
ejpam-6254	301	30	400	400	NUM
ejpam-6254	301	31	500	500	NUM
ejpam-6254	301	32	600	600	NUM
ejpam-6254	301	33	700	700	NUM
ejpam-6254	301	34	800	800	NUM
ejpam-6254	301	35	900	900	NUM
ejpam-6254	301	36	time	time	NOUN
ejpam-6254	301	37	(	(	PUNCT
ejpam-6254	301	38	days	day	NOUN
ejpam-6254	301	39	)	)	PUNCT
ejpam-6254	302	1	p	p	X
ejpam-6254	302	2	o	o	X
ejpam-6254	302	3	p	p	X
ejpam-6254	302	4	u	u	X
ejpam-6254	302	5	la	la	X
ejpam-6254	302	6	tio	tio	NOUN
ejpam-6254	302	7	n	n	CCONJ
ejpam-6254	302	8	seirv	seirv	NOUN
ejpam-6254	302	9	model	model	NOUN
ejpam-6254	302	10	with	with	ADP
ejpam-6254	302	11	control	control	NOUN
ejpam-6254	302	12	susceptible	susceptible	ADJ
ejpam-6254	302	13	exposed	expose	VERB
ejpam-6254	302	14	infected	infected	ADJ
ejpam-6254	302	15	recovered	recover	VERB
ejpam-6254	302	16	vaccinated	vaccinated	ADJ
ejpam-6254	302	17	figure	figure	NOUN
ejpam-6254	302	18	10	10	NUM
ejpam-6254	302	19	:	:	PUNCT
ejpam-6254	302	20	control	control	NOUN
ejpam-6254	302	21	model	model	NOUN
ejpam-6254	302	22	(	(	PUNCT
ejpam-6254	302	23	16	16	NUM
ejpam-6254	302	24	)	)	PUNCT
ejpam-6254	302	25	.	.	PUNCT
ejpam-6254	303	1	the	the	DET
ejpam-6254	303	2	figure	figure	NOUN
ejpam-6254	303	3	10	10	NUM
ejpam-6254	303	4	,	,	PUNCT
ejpam-6254	303	5	demonstrates	demonstrate	VERB
ejpam-6254	303	6	the	the	DET
ejpam-6254	303	7	impact	impact	NOUN
ejpam-6254	303	8	of	of	ADP
ejpam-6254	303	9	optimal	optimal	ADJ
ejpam-6254	303	10	control	control	NOUN
ejpam-6254	303	11	strategies	strategy	NOUN
ejpam-6254	303	12	on	on	ADP
ejpam-6254	303	13	disease	disease	NOUN
ejpam-6254	303	14	progression	progression	NOUN
ejpam-6254	303	15	.	.	PUNCT
ejpam-6254	304	1	the	the	DET
ejpam-6254	304	2	interventions	intervention	NOUN
ejpam-6254	304	3	reduce	reduce	VERB
ejpam-6254	304	4	the	the	DET
ejpam-6254	304	5	infection	infection	NOUN
ejpam-6254	304	6	peak	peak	NOUN
ejpam-6254	304	7	and	and	CCONJ
ejpam-6254	304	8	overall	overall	ADJ
ejpam-6254	304	9	number	number	NOUN
ejpam-6254	304	10	of	of	ADP
ejpam-6254	304	11	cases	case	NOUN
ejpam-6254	304	12	,	,	PUNCT
ejpam-6254	304	13	showcasing	showcase	VERB
ejpam-6254	304	14	the	the	DET
ejpam-6254	304	15	effectiveness	effectiveness	NOUN
ejpam-6254	304	16	of	of	ADP
ejpam-6254	304	17	control	control	NOUN
ejpam-6254	304	18	measures	measure	NOUN
ejpam-6254	304	19	like	like	ADP
ejpam-6254	304	20	vaccination	vaccination	NOUN
ejpam-6254	304	21	,	,	PUNCT
ejpam-6254	304	22	treatment	treatment	NOUN
ejpam-6254	304	23	,	,	PUNCT
ejpam-6254	304	24	or	or	CCONJ
ejpam-6254	304	25	public	public	ADJ
ejpam-6254	304	26	awareness	awareness	NOUN
ejpam-6254	304	27	.	.	PUNCT
ejpam-6254	305	1	0	0	NUM
ejpam-6254	306	1	5	5	NUM
ejpam-6254	306	2	10	10	NUM
ejpam-6254	306	3	15	15	NUM
ejpam-6254	306	4	20	20	NUM
ejpam-6254	306	5	25	25	NUM
ejpam-6254	306	6	30	30	NUM
ejpam-6254	306	7	0	0	NUM
ejpam-6254	306	8	100	100	NUM
ejpam-6254	306	9	200	200	NUM
ejpam-6254	306	10	300	300	NUM
ejpam-6254	306	11	400	400	NUM
ejpam-6254	306	12	500	500	NUM
ejpam-6254	306	13	600	600	NUM
ejpam-6254	306	14	700	700	NUM
ejpam-6254	306	15	800	800	NUM
ejpam-6254	306	16	time	time	NOUN
ejpam-6254	306	17	(	(	PUNCT
ejpam-6254	306	18	days	day	NOUN
ejpam-6254	306	19	)	)	PUNCT
ejpam-6254	307	1	p	p	X
ejpam-6254	307	2	o	o	X
ejpam-6254	307	3	p	p	X
ejpam-6254	307	4	u	u	X
ejpam-6254	307	5	la	la	X
ejpam-6254	307	6	tio	tio	NOUN
ejpam-6254	307	7	n	n	DET
ejpam-6254	307	8	simple	simple	ADJ
ejpam-6254	307	9	seirv	seirv	NOUN
ejpam-6254	307	10	model	model	NOUN
ejpam-6254	307	11	susceptible	susceptible	ADJ
ejpam-6254	307	12	exposed	expose	VERB
ejpam-6254	307	13	infected	infected	ADJ
ejpam-6254	307	14	recovered	recover	VERB
ejpam-6254	307	15	vaccinated	vaccinated	ADJ
ejpam-6254	307	16	figure	figure	NOUN
ejpam-6254	307	17	11	11	NUM
ejpam-6254	307	18	:	:	PUNCT
ejpam-6254	307	19	without	without	ADP
ejpam-6254	307	20	delay	delay	NOUN
ejpam-6254	307	21	and	and	CCONJ
ejpam-6254	307	22	control	control	NOUN
ejpam-6254	307	23	for	for	ADP
ejpam-6254	307	24	model	model	NOUN
ejpam-6254	307	25	(	(	PUNCT
ejpam-6254	307	26	16	16	NUM
ejpam-6254	307	27	)	)	PUNCT
ejpam-6254	307	28	.	.	PUNCT
ejpam-6254	308	1	s.	s.	PROPN
ejpam-6254	308	2	irum	irum	PROPN
ejpam-6254	308	3	et	et	PROPN
ejpam-6254	308	4	al	al	PROPN
ejpam-6254	308	5	.	.	PUNCT
ejpam-6254	308	6	/	/	SYM
ejpam-6254	308	7	eur	eur	PROPN
ejpam-6254	308	8	.	.	PUNCT
ejpam-6254	309	1	j.	j.	PROPN
ejpam-6254	309	2	pure	pure	PROPN
ejpam-6254	309	3	appl	appl	PROPN
ejpam-6254	309	4	.	.	PROPN
ejpam-6254	309	5	math	math	PROPN
ejpam-6254	309	6	,	,	PUNCT
ejpam-6254	309	7	18	18	NUM
ejpam-6254	309	8	(	(	PUNCT
ejpam-6254	309	9	4	4	NUM
ejpam-6254	309	10	)	)	PUNCT
ejpam-6254	309	11	(	(	PUNCT
ejpam-6254	309	12	2025	2025	NUM
ejpam-6254	309	13	)	)	PUNCT
ejpam-6254	309	14	,	,	PUNCT
ejpam-6254	309	15	6254	6254	NUM
ejpam-6254	309	16	21	21	NUM
ejpam-6254	309	17	of	of	ADP
ejpam-6254	309	18	23	23	NUM
ejpam-6254	309	19	the	the	DET
ejpam-6254	309	20	figure	figure	NOUN
ejpam-6254	309	21	11	11	NUM
ejpam-6254	309	22	,	,	PUNCT
ejpam-6254	309	23	illustrates	illustrate	VERB
ejpam-6254	309	24	the	the	DET
ejpam-6254	309	25	baseline	baseline	ADJ
ejpam-6254	309	26	epidemic	epidemic	NOUN
ejpam-6254	309	27	dynamics	dynamic	NOUN
ejpam-6254	309	28	without	without	ADP
ejpam-6254	309	29	any	any	DET
ejpam-6254	309	30	delay	delay	NOUN
ejpam-6254	309	31	or	or	CCONJ
ejpam-6254	309	32	control	control	NOUN
ejpam-6254	309	33	interventions	intervention	NOUN
ejpam-6254	309	34	.	.	PUNCT
ejpam-6254	310	1	the	the	DET
ejpam-6254	310	2	disease	disease	NOUN
ejpam-6254	310	3	spreads	spread	VERB
ejpam-6254	310	4	naturally	naturally	ADV
ejpam-6254	310	5	according	accord	VERB
ejpam-6254	310	6	to	to	ADP
ejpam-6254	310	7	the	the	DET
ejpam-6254	310	8	model	model	NOUN
ejpam-6254	310	9	’s	’s	PART
ejpam-6254	310	10	parameters	parameter	NOUN
ejpam-6254	310	11	,	,	PUNCT
ejpam-6254	310	12	showing	show	VERB
ejpam-6254	310	13	typical	typical	ADJ
ejpam-6254	310	14	infection	infection	NOUN
ejpam-6254	310	15	peaks	peak	NOUN
ejpam-6254	310	16	and	and	CCONJ
ejpam-6254	310	17	declines	decline	NOUN
ejpam-6254	310	18	.	.	PUNCT
ejpam-6254	311	1	0	0	NUM
ejpam-6254	312	1	5	5	NUM
ejpam-6254	312	2	10	10	NUM
ejpam-6254	312	3	15	15	NUM
ejpam-6254	312	4	20	20	NUM
ejpam-6254	312	5	25	25	NUM
ejpam-6254	312	6	30	30	NUM
ejpam-6254	312	7	0	0	NUM
ejpam-6254	312	8	100	100	NUM
ejpam-6254	312	9	200	200	NUM
ejpam-6254	312	10	300	300	NUM
ejpam-6254	312	11	400	400	NUM
ejpam-6254	312	12	500	500	NUM
ejpam-6254	312	13	600	600	NUM
ejpam-6254	312	14	700	700	NUM
ejpam-6254	312	15	800	800	NUM
ejpam-6254	312	16	time	time	NOUN
ejpam-6254	312	17	(	(	PUNCT
ejpam-6254	312	18	days	day	NOUN
ejpam-6254	312	19	)	)	PUNCT
ejpam-6254	313	1	p	p	X
ejpam-6254	313	2	o	o	X
ejpam-6254	313	3	p	p	X
ejpam-6254	313	4	u	u	X
ejpam-6254	313	5	la	la	X
ejpam-6254	313	6	tio	tio	NOUN
ejpam-6254	313	7	n	n	CCONJ
ejpam-6254	313	8	seirv	seirv	NOUN
ejpam-6254	313	9	model	model	NOUN
ejpam-6254	313	10	with	with	ADP
ejpam-6254	313	11	delay	delay	PROPN
ejpam-6254	313	12	susceptible	susceptible	ADJ
ejpam-6254	313	13	exposed	expose	VERB
ejpam-6254	313	14	infected	infected	ADJ
ejpam-6254	313	15	recovered	recover	VERB
ejpam-6254	313	16	veccinated	veccinate	VERB
ejpam-6254	313	17	figure	figure	NOUN
ejpam-6254	313	18	12	12	NUM
ejpam-6254	313	19	:	:	PUNCT
ejpam-6254	313	20	without	without	ADP
ejpam-6254	313	21	delay	delay	NOUN
ejpam-6254	313	22	for	for	ADP
ejpam-6254	313	23	model	model	NOUN
ejpam-6254	313	24	(	(	PUNCT
ejpam-6254	313	25	16	16	NUM
ejpam-6254	313	26	)	)	PUNCT
ejpam-6254	313	27	.	.	PUNCT
ejpam-6254	314	1	the	the	DET
ejpam-6254	314	2	figure	figure	NOUN
ejpam-6254	314	3	12	12	NUM
ejpam-6254	314	4	,	,	PUNCT
ejpam-6254	314	5	reflects	reflect	VERB
ejpam-6254	314	6	the	the	DET
ejpam-6254	314	7	influence	influence	NOUN
ejpam-6254	314	8	of	of	ADP
ejpam-6254	314	9	time	time	NOUN
ejpam-6254	314	10	delays	delay	NOUN
ejpam-6254	314	11	in	in	ADP
ejpam-6254	314	12	the	the	DET
ejpam-6254	314	13	epidemic	epidemic	NOUN
ejpam-6254	314	14	model	model	NOUN
ejpam-6254	314	15	,	,	PUNCT
ejpam-6254	314	16	such	such	ADJ
ejpam-6254	314	17	as	as	ADP
ejpam-6254	314	18	delayed	delay	VERB
ejpam-6254	314	19	response	response	NOUN
ejpam-6254	314	20	to	to	ADP
ejpam-6254	314	21	infection	infection	NOUN
ejpam-6254	314	22	or	or	CCONJ
ejpam-6254	314	23	incubation	incubation	NOUN
ejpam-6254	314	24	periods	period	NOUN
ejpam-6254	314	25	.	.	PUNCT
ejpam-6254	315	1	the	the	DET
ejpam-6254	315	2	delay	delay	NOUN
ejpam-6254	315	3	affects	affect	VERB
ejpam-6254	315	4	the	the	DET
ejpam-6254	315	5	timing	timing	NOUN
ejpam-6254	315	6	and	and	CCONJ
ejpam-6254	315	7	height	height	NOUN
ejpam-6254	315	8	of	of	ADP
ejpam-6254	315	9	the	the	DET
ejpam-6254	315	10	epidemic	epidemic	NOUN
ejpam-6254	315	11	peak	peak	NOUN
ejpam-6254	315	12	,	,	PUNCT
ejpam-6254	315	13	potentially	potentially	ADV
ejpam-6254	315	14	causing	cause	VERB
ejpam-6254	315	15	oscillatory	oscillatory	ADJ
ejpam-6254	315	16	or	or	CCONJ
ejpam-6254	315	17	more	more	ADJ
ejpam-6254	315	18	prolonged	prolonged	ADJ
ejpam-6254	315	19	outbreaks	outbreak	NOUN
ejpam-6254	315	20	.	.	PUNCT
ejpam-6254	316	1	s.	s.	PROPN
ejpam-6254	316	2	irum	irum	PROPN
ejpam-6254	316	3	et	et	PROPN
ejpam-6254	316	4	al	al	PROPN
ejpam-6254	316	5	.	.	PUNCT
ejpam-6254	316	6	/	/	SYM
ejpam-6254	316	7	eur	eur	PROPN
ejpam-6254	316	8	.	.	PUNCT
ejpam-6254	317	1	j.	j.	PROPN
ejpam-6254	317	2	pure	pure	PROPN
ejpam-6254	317	3	appl	appl	PROPN
ejpam-6254	317	4	.	.	PROPN
ejpam-6254	317	5	math	math	PROPN
ejpam-6254	317	6	,	,	PUNCT
ejpam-6254	317	7	18	18	NUM
ejpam-6254	317	8	(	(	PUNCT
ejpam-6254	317	9	4	4	NUM
ejpam-6254	317	10	)	)	PUNCT
ejpam-6254	317	11	(	(	PUNCT
ejpam-6254	317	12	2025	2025	NUM
ejpam-6254	317	13	)	)	PUNCT
ejpam-6254	317	14	,	,	PUNCT
ejpam-6254	317	15	6254	6254	NUM
ejpam-6254	317	16	22	22	NUM
ejpam-6254	317	17	of	of	ADP
ejpam-6254	317	18	23	23	NUM
ejpam-6254	317	19	5	5	NUM
ejpam-6254	317	20	.	.	PUNCT
ejpam-6254	317	21	conclusion	conclusion	NOUN
ejpam-6254	317	22	and	and	CCONJ
ejpam-6254	317	23	discussion	discussion	NOUN
ejpam-6254	317	24	in	in	ADP
ejpam-6254	317	25	recent	recent	ADJ
ejpam-6254	317	26	paper	paper	NOUN
ejpam-6254	318	1	,	,	PUNCT
ejpam-6254	318	2	we	we	PRON
ejpam-6254	318	3	formulate	formulate	VERB
ejpam-6254	318	4	an	an	DET
ejpam-6254	318	5	epidemic	epidemic	NOUN
ejpam-6254	318	6	model	model	NOUN
ejpam-6254	318	7	with	with	ADP
ejpam-6254	318	8	time	time	NOUN
ejpam-6254	318	9	delay	delay	NOUN
ejpam-6254	318	10	,	,	PUNCT
ejpam-6254	318	11	consisting	consist	VERB
ejpam-6254	318	12	of	of	ADP
ejpam-6254	318	13	five	five	NUM
ejpam-6254	318	14	state	state	NOUN
ejpam-6254	318	15	variables	variable	NOUN
ejpam-6254	318	16	and	and	CCONJ
ejpam-6254	318	17	nine	nine	NUM
ejpam-6254	318	18	parameters	parameter	NOUN
ejpam-6254	318	19	.	.	PUNCT
ejpam-6254	319	1	based	base	VERB
ejpam-6254	319	2	on	on	ADP
ejpam-6254	319	3	the	the	DET
ejpam-6254	319	4	analytical	analytical	ADJ
ejpam-6254	319	5	results	result	NOUN
ejpam-6254	319	6	,	,	PUNCT
ejpam-6254	319	7	two	two	NUM
ejpam-6254	319	8	equilibrium	equilibrium	NOUN
ejpam-6254	319	9	points	point	NOUN
ejpam-6254	319	10	are	be	AUX
ejpam-6254	319	11	identified	identify	VERB
ejpam-6254	319	12	:	:	PUNCT
ejpam-6254	319	13	disease	disease	NOUN
ejpam-6254	319	14	-	-	PUNCT
ejpam-6254	319	15	free	free	ADJ
ejpam-6254	319	16	equilibrium	equilibrium	NOUN
ejpam-6254	319	17	and	and	CCONJ
ejpam-6254	319	18	endemic	endemic	ADJ
ejpam-6254	319	19	equilibrium	equilibrium	NOUN
ejpam-6254	319	20	.	.	PUNCT
ejpam-6254	320	1	the	the	DET
ejpam-6254	320	2	results	result	NOUN
ejpam-6254	320	3	show	show	VERB
ejpam-6254	320	4	that	that	SCONJ
ejpam-6254	320	5	the	the	DET
ejpam-6254	320	6	system	system	NOUN
ejpam-6254	320	7	exhibits	exhibit	VERB
ejpam-6254	320	8	stable	stable	ADJ
ejpam-6254	320	9	behavior	behavior	NOUN
ejpam-6254	320	10	in	in	ADP
ejpam-6254	320	11	disease	disease	NOUN
ejpam-6254	320	12	-	-	PUNCT
ejpam-6254	320	13	free	free	ADJ
ejpam-6254	320	14	equilibrium	equilibrium	NOUN
ejpam-6254	320	15	for	for	ADP
ejpam-6254	320	16	all	all	DET
ejpam-6254	320	17	time	time	NOUN
ejpam-6254	320	18	delay	delay	NOUN
ejpam-6254	320	19	values	value	NOUN
ejpam-6254	320	20	,	,	PUNCT
ejpam-6254	320	21	given	give	VERB
ejpam-6254	320	22	the	the	DET
ejpam-6254	320	23	parameter	parameter	NOUN
ejpam-6254	320	24	values	value	NOUN
ejpam-6254	320	25	presented	present	VERB
ejpam-6254	320	26	in	in	ADP
ejpam-6254	320	27	table	table	NOUN
ejpam-6254	320	28	1	1	NUM
ejpam-6254	320	29	(	(	PUNCT
ejpam-6254	320	30	see	see	VERB
ejpam-6254	320	31	figure	figure	NOUN
ejpam-6254	320	32	2	2	NUM
ejpam-6254	320	33	)	)	PUNCT
ejpam-6254	320	34	.	.	PUNCT
ejpam-6254	321	1	however	however	ADV
ejpam-6254	321	2	,	,	PUNCT
ejpam-6254	321	3	when	when	SCONJ
ejpam-6254	321	4	the	the	DET
ejpam-6254	321	5	infection	infection	NOUN
ejpam-6254	321	6	rate	rate	NOUN
ejpam-6254	321	7	increases	increase	NOUN
ejpam-6254	321	8	,	,	PUNCT
ejpam-6254	321	9	the	the	DET
ejpam-6254	321	10	system	system	NOUN
ejpam-6254	321	11	transitions	transition	NOUN
ejpam-6254	321	12	to	to	ADP
ejpam-6254	321	13	a	a	DET
ejpam-6254	321	14	stable	stable	ADJ
ejpam-6254	321	15	endemic	endemic	ADJ
ejpam-6254	321	16	equilibrium	equilibrium	NOUN
ejpam-6254	321	17	,	,	PUNCT
ejpam-6254	321	18	provided	provide	VERB
ejpam-6254	321	19	that	that	SCONJ
ejpam-6254	321	20	the	the	DET
ejpam-6254	321	21	time	time	NOUN
ejpam-6254	321	22	delay	delay	NOUN
ejpam-6254	321	23	is	be	AUX
ejpam-6254	321	24	below	below	ADP
ejpam-6254	321	25	18.5	18.5	NUM
ejpam-6254	321	26	(	(	PUNCT
ejpam-6254	321	27	see	see	VERB
ejpam-6254	321	28	figure	figure	NOUN
ejpam-6254	321	29	3	3	NUM
ejpam-6254	321	30	)	)	PUNCT
ejpam-6254	321	31	.	.	PUNCT
ejpam-6254	322	1	this	this	DET
ejpam-6254	322	2	stability	stability	NOUN
ejpam-6254	322	3	is	be	AUX
ejpam-6254	322	4	lost	lose	VERB
ejpam-6254	322	5	when	when	SCONJ
ejpam-6254	322	6	the	the	DET
ejpam-6254	322	7	time	time	NOUN
ejpam-6254	322	8	delay	delay	NOUN
ejpam-6254	322	9	exceeds	exceed	VERB
ejpam-6254	322	10	this	this	DET
ejpam-6254	322	11	threshold	threshold	NOUN
ejpam-6254	322	12	(	(	PUNCT
ejpam-6254	322	13	see	see	VERB
ejpam-6254	322	14	figures	figure	NOUN
ejpam-6254	322	15	4	4	NUM
ejpam-6254	322	16	-	-	SYM
ejpam-6254	322	17	6	6	NUM
ejpam-6254	322	18	)	)	PUNCT
ejpam-6254	322	19	.	.	PUNCT
ejpam-6254	323	1	furthermore	furthermore	ADV
ejpam-6254	323	2	,	,	PUNCT
ejpam-6254	323	3	control	control	NOUN
ejpam-6254	323	4	variables	variable	NOUN
ejpam-6254	323	5	are	be	AUX
ejpam-6254	323	6	incorporated	incorporate	VERB
ejpam-6254	323	7	into	into	ADP
ejpam-6254	323	8	the	the	DET
ejpam-6254	323	9	model	model	NOUN
ejpam-6254	323	10	,	,	PUNCT
ejpam-6254	323	11	namely	namely	ADV
ejpam-6254	323	12	quarantine	quarantine	NOUN
ejpam-6254	323	13	and	and	CCONJ
ejpam-6254	323	14	treatment	treatment	NOUN
ejpam-6254	323	15	.	.	PUNCT
ejpam-6254	324	1	pontryagin	pontryagin	NOUN
ejpam-6254	324	2	’s	’s	PART
ejpam-6254	324	3	maximum	maximum	ADJ
ejpam-6254	324	4	principle	principle	NOUN
ejpam-6254	324	5	is	be	AUX
ejpam-6254	324	6	applied	apply	VERB
ejpam-6254	324	7	to	to	PART
ejpam-6254	324	8	solve	solve	VERB
ejpam-6254	324	9	the	the	DET
ejpam-6254	324	10	optimal	optimal	ADJ
ejpam-6254	324	11	control	control	NOUN
ejpam-6254	324	12	problem	problem	NOUN
ejpam-6254	324	13	.	.	PUNCT
ejpam-6254	325	1	numerical	numerical	ADJ
ejpam-6254	325	2	simulations	simulation	NOUN
ejpam-6254	325	3	with	with	ADP
ejpam-6254	325	4	specified	specified	ADJ
ejpam-6254	325	5	weights	weight	NOUN
ejpam-6254	325	6	indicate	indicate	VERB
ejpam-6254	325	7	that	that	SCONJ
ejpam-6254	325	8	the	the	DET
ejpam-6254	325	9	optimal	optimal	ADJ
ejpam-6254	325	10	strategy	strategy	NOUN
ejpam-6254	325	11	to	to	PART
ejpam-6254	325	12	control	control	VERB
ejpam-6254	325	13	the	the	DET
ejpam-6254	325	14	disease	disease	NOUN
ejpam-6254	325	15	spread	spread	VERB
ejpam-6254	325	16	is	be	AUX
ejpam-6254	325	17	the	the	DET
ejpam-6254	325	18	combination	combination	NOUN
ejpam-6254	325	19	of	of	ADP
ejpam-6254	325	20	both	both	DET
ejpam-6254	325	21	control	control	NOUN
ejpam-6254	325	22	measures	measure	NOUN
ejpam-6254	325	23	(	(	PUNCT
ejpam-6254	325	24	see	see	VERB
ejpam-6254	325	25	figure	figure	NOUN
ejpam-6254	325	26	7	7	NUM
ejpam-6254	325	27	-	-	SYM
ejpam-6254	325	28	9	9	NUM
ejpam-6254	325	29	)	)	PUNCT
ejpam-6254	325	30	.	.	PUNCT
ejpam-6254	326	1	further	further	ADJ
ejpam-6254	326	2	direction	direction	NOUN
ejpam-6254	326	3	is	be	AUX
ejpam-6254	326	4	to	to	PART
ejpam-6254	326	5	apply	apply	VERB
ejpam-6254	326	6	the	the	DET
ejpam-6254	326	7	optimal	optimal	ADJ
ejpam-6254	326	8	control	control	NOUN
ejpam-6254	326	9	over	over	ADP
ejpam-6254	326	10	a	a	DET
ejpam-6254	326	11	delayed	delay	VERB
ejpam-6254	326	12	system	system	NOUN
ejpam-6254	326	13	.	.	PUNCT
ejpam-6254	327	1	references	reference	NOUN
ejpam-6254	327	2	[	[	X
ejpam-6254	327	3	1	1	X
ejpam-6254	327	4	]	]	PUNCT
ejpam-6254	327	5	elham	elham	PROPN
ejpam-6254	327	6	taghizadeh	taghizadeh	PROPN
ejpam-6254	327	7	and	and	CCONJ
ejpam-6254	327	8	ali	ali	PROPN
ejpam-6254	327	9	mohammad	mohammad	PROPN
ejpam-6254	327	10	-	-	PUNCT
ejpam-6254	327	11	djafari	djafari	PROPN
ejpam-6254	327	12	.	.	PUNCT
ejpam-6254	328	1	seir	seir	PROPN
ejpam-6254	328	2	modeling	modeling	PROPN
ejpam-6254	328	3	,	,	PUNCT
ejpam-6254	328	4	simulation	simulation	NOUN
ejpam-6254	328	5	,	,	PUNCT
ejpam-6254	328	6	parameter	parameter	NOUN
ejpam-6254	328	7	estimation	estimation	NOUN
ejpam-6254	328	8	,	,	PUNCT
ejpam-6254	328	9	and	and	CCONJ
ejpam-6254	328	10	their	their	PRON
ejpam-6254	328	11	application	application	NOUN
ejpam-6254	328	12	for	for	ADP
ejpam-6254	328	13	covid-19	covid-19	PROPN
ejpam-6254	328	14	epidemic	epidemic	NOUN
ejpam-6254	328	15	prediction	prediction	NOUN
ejpam-6254	328	16	.	.	PUNCT
ejpam-6254	329	1	phys	phy	NOUN
ejpam-6254	329	2	.	.	PUNCT
ejpam-6254	330	1	sci	sci	PROPN
ejpam-6254	330	2	.	.	PROPN
ejpam-6254	330	3	forum	forum	PROPN
ejpam-6254	330	4	,	,	PUNCT
ejpam-6254	330	5	5(1):18	5(1):18	NUM
ejpam-6254	330	6	,	,	PUNCT
ejpam-6254	330	7	2022	2022	NUM
ejpam-6254	330	8	.	.	PUNCT
ejpam-6254	331	1	[	[	X
ejpam-6254	331	2	2	2	NUM
ejpam-6254	331	3	]	]	X
ejpam-6254	331	4	r.	r.	PROPN
ejpam-6254	331	5	paulo	paulo	PROPN
ejpam-6254	331	6	and	and	CCONJ
ejpam-6254	331	7	j.p.z	j.p.z	NOUN
ejpam-6254	331	8	.	.	PUNCT
ejpam-6254	332	1	zingano	zingano	PROPN
ejpam-6254	332	2	.	.	PUNCT
ejpam-6254	333	1	a	a	DET
ejpam-6254	333	2	matlab	matlab	PROPN
ejpam-6254	333	3	code	code	NOUN
ejpam-6254	333	4	to	to	PART
ejpam-6254	333	5	compute	compute	VERB
ejpam-6254	333	6	reproduction	reproduction	NOUN
ejpam-6254	333	7	numbers	number	NOUN
ejpam-6254	333	8	with	with	ADP
ejpam-6254	333	9	applications	application	NOUN
ejpam-6254	333	10	to	to	ADP
ejpam-6254	333	11	the	the	DET
ejpam-6254	333	12	covid-19	covid-19	PROPN
ejpam-6254	333	13	outbreak	outbreak	NOUN
ejpam-6254	333	14	,	,	PUNCT
ejpam-6254	333	15	2020	2020	NUM
ejpam-6254	333	16	.	.	PUNCT
ejpam-6254	334	1	arxiv:2006.13752	arxiv:2006.13752	PROPN
ejpam-6254	334	2	.	.	PUNCT
ejpam-6254	335	1	[	[	X
ejpam-6254	335	2	3	3	X
ejpam-6254	335	3	]	]	PUNCT
ejpam-6254	335	4	s.	s.	PROPN
ejpam-6254	335	5	he	he	PRON
ejpam-6254	335	6	,	,	PUNCT
ejpam-6254	335	7	y.	y.	PROPN
ejpam-6254	335	8	peng	peng	PROPN
ejpam-6254	335	9	,	,	PUNCT
ejpam-6254	335	10	and	and	CCONJ
ejpam-6254	335	11	k.	k.	PROPN
ejpam-6254	335	12	sun	sun	PROPN
ejpam-6254	335	13	.	.	PUNCT
ejpam-6254	335	14	seir	seir	NOUN
ejpam-6254	335	15	modeling	modeling	NOUN
ejpam-6254	335	16	of	of	ADP
ejpam-6254	335	17	the	the	DET
ejpam-6254	335	18	covid-19	covid-19	PROPN
ejpam-6254	335	19	.	.	PUNCT
ejpam-6254	336	1	nonlinear	nonlinear	PROPN
ejpam-6254	336	2	dyn	dyn	PROPN
ejpam-6254	336	3	,	,	PUNCT
ejpam-6254	336	4	101:1667–1680	101:1667–1680	NUM
ejpam-6254	336	5	,	,	PUNCT
ejpam-6254	336	6	2020	2020	NUM
ejpam-6254	336	7	.	.	PUNCT
ejpam-6254	337	1	[	[	X
ejpam-6254	337	2	4	4	NUM
ejpam-6254	337	3	]	]	X
ejpam-6254	337	4	j.p	j.p	PROPN
ejpam-6254	337	5	.	.	PROPN
ejpam-6254	337	6	gleeson	gleeson	PROPN
ejpam-6254	337	7	,	,	PUNCT
ejpam-6254	337	8	t.b	t.b	PROPN
ejpam-6254	337	9	.	.	PROPN
ejpam-6254	337	10	murphy	murphy	PROPN
ejpam-6254	337	11	,	,	PUNCT
ejpam-6254	337	12	j.d	j.d	PROPN
ejpam-6254	337	13	.	.	PROPN
ejpam-6254	337	14	brien	brien	PROPN
ejpam-6254	337	15	,	,	PUNCT
ejpam-6254	337	16	and	and	CCONJ
ejpam-6254	337	17	d.j	d.j	PROPN
ejpam-6254	337	18	.	.	PROPN
ejpam-6254	337	19	sullivan	sullivan	PROPN
ejpam-6254	337	20	.	.	PUNCT
ejpam-6254	338	1	a	a	DET
ejpam-6254	338	2	population	population	NOUN
ejpam-6254	338	3	-	-	PUNCT
ejpam-6254	338	4	level	level	NOUN
ejpam-6254	338	5	seir	seir	NOUN
ejpam-6254	338	6	model	model	NOUN
ejpam-6254	338	7	for	for	ADP
ejpam-6254	338	8	covid-19	covid-19	PROPN
ejpam-6254	338	9	scenarios	scenario	NOUN
ejpam-6254	338	10	,	,	PUNCT
ejpam-6254	338	11	2020	2020	NUM
ejpam-6254	338	12	.	.	PUNCT
ejpam-6254	339	1	technical	technical	ADJ
ejpam-6254	339	2	note	note	NOUN
ejpam-6254	339	3	of	of	ADP
ejpam-6254	339	4	the	the	DET
ejpam-6254	339	5	irish	irish	ADJ
ejpam-6254	339	6	epidemiological	epidemiological	ADJ
ejpam-6254	339	7	modelling	model	VERB
ejpam-6254	339	8	advisory	advisory	ADJ
ejpam-6254	339	9	group	group	NOUN
ejpam-6254	339	10	to	to	PART
ejpam-6254	339	11	nphet	nphet	VERB
ejpam-6254	339	12	,	,	PUNCT
ejpam-6254	339	13	department	department	NOUN
ejpam-6254	339	14	of	of	ADP
ejpam-6254	339	15	health	health	NOUN
ejpam-6254	339	16	,	,	PUNCT
ejpam-6254	339	17	government	government	NOUN
ejpam-6254	339	18	of	of	ADP
ejpam-6254	339	19	ireland	ireland	PROPN
ejpam-6254	339	20	.	.	PUNCT
ejpam-6254	340	1	[	[	X
ejpam-6254	340	2	5	5	X
ejpam-6254	340	3	]	]	X
ejpam-6254	340	4	ahmed	ahmed	PROPN
ejpam-6254	340	5	a.	a.	PROPN
ejpam-6254	340	6	mohsen	mohsen	PROPN
ejpam-6254	340	7	,	,	PUNCT
ejpam-6254	340	8	hassan	hassan	PROPN
ejpam-6254	340	9	f.	f.	PROPN
ejpam-6254	340	10	al	al	PROPN
ejpam-6254	340	11	-	-	PUNCT
ejpam-6254	340	12	husseiny	husseiny	PROPN
ejpam-6254	340	13	,	,	PUNCT
ejpam-6254	340	14	and	and	CCONJ
ejpam-6254	340	15	raid	raid	NOUN
ejpam-6254	340	16	kamel	kamel	PROPN
ejpam-6254	340	17	naji	naji	PROPN
ejpam-6254	340	18	.	.	PUNCT
ejpam-6254	341	1	the	the	DET
ejpam-6254	341	2	dynamics	dynamic	NOUN
ejpam-6254	341	3	of	of	ADP
ejpam-6254	341	4	corona	corona	PROPN
ejpam-6254	341	5	virus	virus	NOUN
ejpam-6254	341	6	pandemic	pandemic	ADJ
ejpam-6254	341	7	disease	disease	NOUN
ejpam-6254	341	8	model	model	NOUN
ejpam-6254	341	9	in	in	ADP
ejpam-6254	341	10	the	the	DET
ejpam-6254	341	11	existence	existence	NOUN
ejpam-6254	341	12	of	of	ADP
ejpam-6254	341	13	a	a	DET
ejpam-6254	341	14	curfew	curfew	NOUN
ejpam-6254	341	15	strategy	strategy	NOUN
ejpam-6254	341	16	.	.	PUNCT
ejpam-6254	342	1	journal	journal	NOUN
ejpam-6254	342	2	of	of	ADP
ejpam-6254	342	3	interdisciplinary	interdisciplinary	ADJ
ejpam-6254	342	4	mathematics	mathematic	NOUN
ejpam-6254	342	5	,	,	PUNCT
ejpam-6254	342	6	2022	2022	NUM
ejpam-6254	342	7	.	.	PUNCT
ejpam-6254	343	1	[	[	X
ejpam-6254	343	2	6	6	NUM
ejpam-6254	343	3	]	]	X
ejpam-6254	343	4	hassan	hassan	PROPN
ejpam-6254	343	5	f.	f.	PROPN
ejpam-6254	343	6	al	al	PROPN
ejpam-6254	343	7	-	-	PUNCT
ejpam-6254	343	8	husseiny	husseiny	PROPN
ejpam-6254	343	9	,	,	PUNCT
ejpam-6254	343	10	nidhal	nidhal	PROPN
ejpam-6254	343	11	f.	f.	PROPN
ejpam-6254	343	12	ali	ali	PROPN
ejpam-6254	343	13	,	,	PUNCT
ejpam-6254	343	14	and	and	CCONJ
ejpam-6254	343	15	ahmed	ahmed	PROPN
ejpam-6254	343	16	a.	a.	PROPN
ejpam-6254	343	17	mohsen	mohsen	PROPN
ejpam-6254	343	18	.	.	PUNCT
ejpam-6254	344	1	the	the	DET
ejpam-6254	344	2	effect	effect	NOUN
ejpam-6254	344	3	of	of	ADP
ejpam-6254	344	4	epidemic	epidemic	NOUN
ejpam-6254	344	5	disease	disease	NOUN
ejpam-6254	344	6	outbreaks	outbreak	NOUN
ejpam-6254	344	7	on	on	ADP
ejpam-6254	344	8	the	the	DET
ejpam-6254	344	9	dynamic	dynamic	ADJ
ejpam-6254	344	10	behavior	behavior	NOUN
ejpam-6254	344	11	of	of	ADP
ejpam-6254	344	12	a	a	DET
ejpam-6254	344	13	prey	prey	NOUN
ejpam-6254	344	14	-	-	PUNCT
ejpam-6254	344	15	predator	predator	NOUN
ejpam-6254	344	16	model	model	NOUN
ejpam-6254	344	17	with	with	ADP
ejpam-6254	344	18	holling	holle	VERB
ejpam-6254	344	19	type	type	NOUN
ejpam-6254	344	20	ii	ii	NOUN
ejpam-6254	344	21	functional	functional	ADJ
ejpam-6254	344	22	response	response	NOUN
ejpam-6254	344	23	.	.	PUNCT
ejpam-6254	345	1	commun	commun	PROPN
ejpam-6254	345	2	.	.	PUNCT
ejpam-6254	346	1	math	math	NOUN
ejpam-6254	346	2	.	.	PUNCT
ejpam-6254	347	1	biol	biol	PROPN
ejpam-6254	347	2	.	.	PUNCT
ejpam-6254	348	1	neurosci	neurosci	PROPN
ejpam-6254	348	2	.	.	PUNCT
ejpam-6254	348	3	,	,	PUNCT
ejpam-6254	348	4	2021	2021	NUM
ejpam-6254	348	5	.	.	PUNCT
ejpam-6254	349	1	article	article	NOUN
ejpam-6254	349	2	i	i	PROPN
ejpam-6254	349	3	d	d	PROPN
ejpam-6254	349	4	72	72	NUM
ejpam-6254	349	5	.	.	PUNCT
ejpam-6254	350	1	[	[	X
ejpam-6254	350	2	7	7	NUM
ejpam-6254	350	3	]	]	PUNCT
ejpam-6254	350	4	a.	a.	NOUN
ejpam-6254	350	5	acharya	acharya	PROPN
ejpam-6254	350	6	,	,	PUNCT
ejpam-6254	350	7	s.	s.	PROPN
ejpam-6254	350	8	paul	paul	PROPN
ejpam-6254	350	9	,	,	PUNCT
ejpam-6254	350	10	m.a	m.a	PROPN
ejpam-6254	350	11	.	.	PROPN
ejpam-6254	350	12	biswas	biswas	PROPN
ejpam-6254	350	13	,	,	PUNCT
ejpam-6254	350	14	a.	a.	NOUN
ejpam-6254	350	15	mahata	mahata	PROPN
ejpam-6254	350	16	,	,	PUNCT
ejpam-6254	350	17	s.	s.	PROPN
ejpam-6254	350	18	mukherjee	mukherjee	PROPN
ejpam-6254	350	19	,	,	PUNCT
ejpam-6254	350	20	and	and	CCONJ
ejpam-6254	350	21	b.	b.	PROPN
ejpam-6254	350	22	roy	roy	PROPN
ejpam-6254	350	23	.	.	PROPN
ejpam-6254	350	24	study	study	PROPN
ejpam-6254	350	25	of	of	ADP
ejpam-6254	350	26	seirv	seirv	NOUN
ejpam-6254	350	27	epidemic	epidemic	NOUN
ejpam-6254	350	28	model	model	NOUN
ejpam-6254	350	29	in	in	ADP
ejpam-6254	350	30	imprecise	imprecise	ADJ
ejpam-6254	350	31	environment	environment	NOUN
ejpam-6254	350	32	.	.	PUNCT
ejpam-6254	351	1	in	in	ADP
ejpam-6254	351	2	advances	advance	NOUN
ejpam-6254	351	3	in	in	ADP
ejpam-6254	351	4	intelligent	intelligent	ADJ
ejpam-6254	351	5	system	system	NOUN
ejpam-6254	351	6	and	and	CCONJ
ejpam-6254	351	7	computing	computing	NOUN
ejpam-6254	351	8	,	,	PUNCT
ejpam-6254	351	9	icmmcs	icmmcs	ADJ
ejpam-6254	351	10	,	,	PUNCT
ejpam-6254	351	11	pages	page	NOUN
ejpam-6254	351	12	371–380	371–380	NUM
ejpam-6254	351	13	.	.	PUNCT
ejpam-6254	351	14	2023	2023	NUM
ejpam-6254	351	15	.	.	PUNCT
ejpam-6254	352	1	[	[	X
ejpam-6254	352	2	8	8	NUM
ejpam-6254	352	3	]	]	PUNCT
ejpam-6254	352	4	s.	s.	PROPN
ejpam-6254	352	5	paul	paul	PROPN
ejpam-6254	352	6	,	,	PUNCT
ejpam-6254	352	7	a.	a.	PROPN
ejpam-6254	352	8	acharya	acharya	PROPN
ejpam-6254	352	9	,	,	PUNCT
ejpam-6254	352	10	m.a	m.a	PROPN
ejpam-6254	352	11	.	.	PROPN
ejpam-6254	352	12	biswas	biswas	PROPN
ejpam-6254	352	13	,	,	PUNCT
ejpam-6254	352	14	a.	a.	NOUN
ejpam-6254	352	15	mahata	mahata	PROPN
ejpam-6254	352	16	,	,	PUNCT
ejpam-6254	352	17	s.	s.	PROPN
ejpam-6254	352	18	mukherjee	mukherjee	PROPN
ejpam-6254	352	19	,	,	PUNCT
ejpam-6254	352	20	p.c	p.c	PROPN
ejpam-6254	352	21	.	.	PROPN
ejpam-6254	352	22	mali	mali	PROPN
ejpam-6254	352	23	,	,	PUNCT
ejpam-6254	352	24	and	and	CCONJ
ejpam-6254	352	25	b.	b.	PROPN
ejpam-6254	352	26	roy	roy	PROPN
ejpam-6254	352	27	.	.	PUNCT
ejpam-6254	353	1	the	the	DET
ejpam-6254	353	2	scenario	scenario	NOUN
ejpam-6254	353	3	of	of	ADP
ejpam-6254	353	4	covid	covid	PROPN
ejpam-6254	353	5	19	19	NUM
ejpam-6254	353	6	pandemic	pandemic	ADJ
ejpam-6254	353	7	in	in	ADP
ejpam-6254	353	8	brazil	brazil	PROPN
ejpam-6254	353	9	using	use	VERB
ejpam-6254	353	10	seir	seir	ADJ
ejpam-6254	353	11	epidemic	epidemic	NOUN
ejpam-6254	353	12	model	model	NOUN
ejpam-6254	353	13	.	.	PUNCT
ejpam-6254	354	1	in	in	ADP
ejpam-6254	354	2	advances	advance	NOUN
ejpam-6254	354	3	in	in	ADP
ejpam-6254	354	4	intelligent	intelligent	ADJ
ejpam-6254	354	5	system	system	NOUN
ejpam-6254	354	6	and	and	CCONJ
ejpam-6254	354	7	computing	computing	NOUN
ejpam-6254	354	8	,	,	PUNCT
ejpam-6254	354	9	icmmcs	icmmcs	ADJ
ejpam-6254	354	10	,	,	PUNCT
ejpam-6254	354	11	pages	page	NOUN
ejpam-6254	354	12	419–426	419–426	NUM
ejpam-6254	354	13	.	.	PUNCT
ejpam-6254	354	14	2023	2023	NUM
ejpam-6254	354	15	.	.	PUNCT
ejpam-6254	355	1	[	[	X
ejpam-6254	355	2	9	9	NUM
ejpam-6254	355	3	]	]	X
ejpam-6254	355	4	ping	ping	PROPN
ejpam-6254	355	5	yan	yan	PROPN
ejpam-6254	355	6	and	and	CCONJ
ejpam-6254	355	7	shengqiang	shengqiang	PROPN
ejpam-6254	355	8	li	li	PROPN
ejpam-6254	355	9	.	.	PROPN
ejpam-6254	355	10	seir	seir	PROPN
ejpam-6254	355	11	epidimic	epidimic	ADJ
ejpam-6254	355	12	model	model	NOUN
ejpam-6254	355	13	with	with	ADP
ejpam-6254	355	14	delay	delay	NOUN
ejpam-6254	355	15	.	.	PUNCT
ejpam-6254	356	1	anziam	anziam	PROPN
ejpam-6254	356	2	j	j	PROPN
ejpam-6254	356	3	,	,	PUNCT
ejpam-6254	356	4	48:119–134	48:119–134	PROPN
ejpam-6254	356	5	,	,	PUNCT
ejpam-6254	356	6	2006	2006	NUM
ejpam-6254	356	7	.	.	PUNCT
ejpam-6254	357	1	[	[	X
ejpam-6254	357	2	10	10	NUM
ejpam-6254	357	3	]	]	X
ejpam-6254	357	4	ahmed	ahmed	PROPN
ejpam-6254	357	5	a.	a.	PROPN
ejpam-6254	357	6	mohsen	mohsen	PROPN
ejpam-6254	357	7	and	and	CCONJ
ejpam-6254	357	8	raid	raid	PROPN
ejpam-6254	357	9	kamel	kamel	PROPN
ejpam-6254	357	10	naji	naji	PROPN
ejpam-6254	357	11	.	.	PUNCT
ejpam-6254	358	1	stability	stability	NOUN
ejpam-6254	358	2	and	and	CCONJ
ejpam-6254	358	3	bifurcation	bifurcation	NOUN
ejpam-6254	358	4	of	of	ADP
ejpam-6254	358	5	a	a	DET
ejpam-6254	358	6	delay	delay	NOUN
ejpam-6254	358	7	cancer	cancer	NOUN
ejpam-6254	358	8	model	model	NOUN
ejpam-6254	358	9	in	in	ADP
ejpam-6254	358	10	the	the	DET
ejpam-6254	358	11	polluted	polluted	ADJ
ejpam-6254	358	12	environment	environment	NOUN
ejpam-6254	358	13	.	.	PUNCT
ejpam-6254	359	1	advances	advance	NOUN
ejpam-6254	359	2	in	in	ADP
ejpam-6254	359	3	systems	system	NOUN
ejpam-6254	359	4	science	science	NOUN
ejpam-6254	359	5	and	and	CCONJ
ejpam-6254	359	6	applications	application	NOUN
ejpam-6254	359	7	,	,	PUNCT
ejpam-6254	359	8	22(3):1–17	22(3):1–17	NUM
ejpam-6254	359	9	,	,	PUNCT
ejpam-6254	359	10	2022	2022	NUM
ejpam-6254	359	11	.	.	PUNCT
ejpam-6254	360	1	[	[	X
ejpam-6254	360	2	11	11	NUM
ejpam-6254	360	3	]	]	X
ejpam-6254	360	4	sajal	sajal	ADJ
ejpam-6254	360	5	and	and	CCONJ
ejpam-6254	360	6	fahad	fahad	PROPN
ejpam-6254	360	7	mostafa	mostafa	PROPN
ejpam-6254	360	8	.	.	PUNCT
ejpam-6254	360	9	seirv	seirv	NOUN
ejpam-6254	360	10	-	-	PUNCT
ejpam-6254	360	11	holling	holle	VERB
ejpam-6254	360	12	type	type	NOUN
ejpam-6254	360	13	-	-	PUNCT
ejpam-6254	360	14	ii	ii	NOUN
ejpam-6254	360	15	:	:	PUNCT
ejpam-6254	360	16	implementing	implement	VERB
ejpam-6254	360	17	holling	holle	VERB
ejpam-6254	360	18	type	type	NOUN
ejpam-6254	360	19	functional	functional	ADJ
ejpam-6254	360	20	response	response	NOUN
ejpam-6254	360	21	in	in	ADP
ejpam-6254	360	22	covid-19	covid-19	PROPN
ejpam-6254	360	23	disease	disease	NOUN
ejpam-6254	360	24	modeling	modeling	NOUN
ejpam-6254	360	25	.	.	PUNCT
ejpam-6254	361	1	ssrn	ssrn	PROPN
ejpam-6254	361	2	.	.	PUNCT
ejpam-6254	362	1	https://ssrn.com/abstract=4953603	https://ssrn.com/abstract=4953603	PROPN
ejpam-6254	362	2	.	.	PUNCT
ejpam-6254	363	1	[	[	X
ejpam-6254	363	2	12	12	NUM
ejpam-6254	363	3	]	]	X
ejpam-6254	363	4	animesh	animesh	NOUN
ejpam-6254	363	5	,	,	PUNCT
ejpam-6254	363	6	subrata	subrata	PROPN
ejpam-6254	363	7	paul	paul	PROPN
ejpam-6254	363	8	,	,	PUNCT
ejpam-6254	363	9	supriya	supriya	PROPN
ejpam-6254	363	10	mukherjee	mukherjee	PROPN
ejpam-6254	363	11	,	,	PUNCT
ejpam-6254	363	12	meghadri	meghadri	PROPN
ejpam-6254	363	13	das	das	PROPN
ejpam-6254	363	14	,	,	PUNCT
ejpam-6254	363	15	and	and	CCONJ
ejpam-6254	363	16	banamali	banamali	PROPN
ejpam-6254	363	17	roy	roy	PROPN
ejpam-6254	363	18	.	.	PROPN
ejpam-6254	363	19	dynamics	dynamic	NOUN
ejpam-6254	363	20	of	of	ADP
ejpam-6254	363	21	caputo	caputo	PROPN
ejpam-6254	363	22	fractional	fractional	PROPN
ejpam-6254	363	23	order	order	NOUN
ejpam-6254	363	24	seirv	seirv	NOUN
ejpam-6254	363	25	epidimic	epidimic	ADJ
ejpam-6254	363	26	model	model	NOUN
ejpam-6254	363	27	with	with	ADP
ejpam-6254	363	28	optimal	optimal	ADJ
ejpam-6254	363	29	control	control	NOUN
ejpam-6254	363	30	and	and	CCONJ
ejpam-6254	363	31	stability	stability	NOUN
ejpam-6254	363	32	analysis	analysis	NOUN
ejpam-6254	363	33	.	.	PUNCT
ejpam-6254	364	1	international	international	ADJ
ejpam-6254	364	2	journal	journal	NOUN
ejpam-6254	364	3	of	of	ADP
ejpam-6254	364	4	applied	applied	ADJ
ejpam-6254	364	5	and	and	CCONJ
ejpam-6254	364	6	computational	computational	ADJ
ejpam-6254	364	7	mathematics	mathematic	NOUN
ejpam-6254	364	8	,	,	PUNCT
ejpam-6254	364	9	8:28	8:28	NUM
ejpam-6254	364	10	,	,	PUNCT
ejpam-6254	364	11	2022	2022	NUM
ejpam-6254	364	12	.	.	PUNCT
ejpam-6254	365	1	[	[	X
ejpam-6254	365	2	13	13	NUM
ejpam-6254	365	3	]	]	X
ejpam-6254	365	4	sarah	sarah	PROPN
ejpam-6254	365	5	a.	a.	PROPN
ejpam-6254	365	6	al	al	PROPN
ejpam-6254	365	7	-	-	PUNCT
ejpam-6254	365	8	sheikh	sheikh	NOUN
ejpam-6254	365	9	.	.	PUNCT
ejpam-6254	366	1	modeling	modeling	NOUN
ejpam-6254	366	2	and	and	CCONJ
ejpam-6254	366	3	analysis	analysis	NOUN
ejpam-6254	366	4	of	of	ADP
ejpam-6254	366	5	seir	seir	PRON
ejpam-6254	366	6	epidimic	epidimic	ADJ
ejpam-6254	366	7	model	model	NOUN
ejpam-6254	366	8	with	with	ADP
ejpam-6254	366	9	limited	limited	ADJ
ejpam-6254	366	10	resource	resource	NOUN
ejpam-6254	366	11	of	of	ADP
ejpam-6254	366	12	s.	s.	PROPN
ejpam-6254	366	13	irum	irum	PROPN
ejpam-6254	366	14	et	et	PROPN
ejpam-6254	366	15	al	al	PROPN
ejpam-6254	366	16	.	.	PUNCT
ejpam-6254	366	17	/	/	SYM
ejpam-6254	366	18	eur	eur	PROPN
ejpam-6254	366	19	.	.	PUNCT
ejpam-6254	367	1	j.	j.	PROPN
ejpam-6254	367	2	pure	pure	PROPN
ejpam-6254	367	3	appl	appl	PROPN
ejpam-6254	367	4	.	.	PROPN
ejpam-6254	367	5	math	math	PROPN
ejpam-6254	367	6	,	,	PUNCT
ejpam-6254	367	7	18	18	NUM
ejpam-6254	367	8	(	(	PUNCT
ejpam-6254	367	9	4	4	NUM
ejpam-6254	367	10	)	)	PUNCT
ejpam-6254	367	11	(	(	PUNCT
ejpam-6254	367	12	2025	2025	NUM
ejpam-6254	367	13	)	)	PUNCT
ejpam-6254	367	14	,	,	PUNCT
ejpam-6254	367	15	6254	6254	NUM
ejpam-6254	367	16	23	23	NUM
ejpam-6254	367	17	of	of	ADP
ejpam-6254	367	18	23	23	NUM
ejpam-6254	367	19	treatment	treatment	NOUN
ejpam-6254	367	20	.	.	PUNCT
ejpam-6254	368	1	global	global	ADJ
ejpam-6254	368	2	journal	journal	PROPN
ejpam-6254	368	3	of	of	ADP
ejpam-6254	368	4	science	science	PROPN
ejpam-6254	368	5	frontier	frontier	NOUN
ejpam-6254	368	6	research	research	NOUN
ejpam-6254	368	7	mathematics	mathematic	NOUN
ejpam-6254	368	8	and	and	CCONJ
ejpam-6254	368	9	decision	decision	NOUN
ejpam-6254	368	10	sciences	science	NOUN
ejpam-6254	368	11	.	.	PUNCT
ejpam-6254	369	1	print	print	PROPN
ejpam-6254	369	2	issn	issn	PROPN
ejpam-6254	369	3	:	:	PUNCT
ejpam-6254	369	4	0975	0975	NUM
ejpam-6254	369	5	-	-	SYM
ejpam-6254	369	6	5896	5896	NUM
ejpam-6254	369	7	.	.	PUNCT
ejpam-6254	370	1	[	[	X
ejpam-6254	370	2	14	14	NUM
ejpam-6254	370	3	]	]	X
ejpam-6254	370	4	ahmed	ahmed	PROPN
ejpam-6254	370	5	a.	a.	PROPN
ejpam-6254	370	6	mohsen	mohsen	PROPN
ejpam-6254	370	7	and	and	CCONJ
ejpam-6254	370	8	raid	raid	PROPN
ejpam-6254	370	9	kamel	kamel	PROPN
ejpam-6254	370	10	naji	naji	PROPN
ejpam-6254	370	11	.	.	PUNCT
ejpam-6254	371	1	dynamical	dynamical	ADJ
ejpam-6254	371	2	analysis	analysis	NOUN
ejpam-6254	371	3	within	within	ADP
ejpam-6254	371	4	-	-	PUNCT
ejpam-6254	371	5	host	host	NOUN
ejpam-6254	371	6	and	and	CCONJ
ejpam-6254	371	7	betweenhost	betweenhost	NOUN
ejpam-6254	371	8	for	for	ADP
ejpam-6254	371	9	hiv	hiv	PROPN
ejpam-6254	371	10	/	/	SYM
ejpam-6254	371	11	aids	aids	PROPN
ejpam-6254	371	12	with	with	ADP
ejpam-6254	371	13	the	the	DET
ejpam-6254	371	14	application	application	NOUN
ejpam-6254	371	15	of	of	ADP
ejpam-6254	371	16	optimal	optimal	ADJ
ejpam-6254	371	17	control	control	NOUN
ejpam-6254	371	18	strategy	strategy	NOUN
ejpam-6254	371	19	.	.	PUNCT
ejpam-6254	372	1	iraqi	iraqi	ADJ
ejpam-6254	372	2	journal	journal	PROPN
ejpam-6254	372	3	of	of	ADP
ejpam-6254	372	4	science	science	NOUN
ejpam-6254	372	5	,	,	PUNCT
ejpam-6254	372	6	61(5):1173–1189	61(5):1173–1189	NUM
ejpam-6254	372	7	,	,	PUNCT
ejpam-6254	372	8	2020	2020	NUM
ejpam-6254	372	9	.	.	PUNCT
ejpam-6254	373	1	[	[	X
ejpam-6254	373	2	15	15	NUM
ejpam-6254	373	3	]	]	X
ejpam-6254	373	4	oluwatosin	oluwatosin	PROPN
ejpam-6254	373	5	babasola	babasola	NOUN
ejpam-6254	373	6	,	,	PUNCT
ejpam-6254	373	7	oshinubi	oshinubi	ADJ
ejpam-6254	373	8	kayode	kayode	PROPN
ejpam-6254	373	9	,	,	PUNCT
ejpam-6254	373	10	olumuyiwa	olumuyiwa	PROPN
ejpam-6254	373	11	james	james	PROPN
ejpam-6254	373	12	peter	peter	PROPN
ejpam-6254	373	13	,	,	PUNCT
ejpam-6254	373	14	faithful	faithful	ADJ
ejpam-6254	373	15	chiagoziem	chiagoziem	ADJ
ejpam-6254	373	16	onwuegbuche	onwuegbuche	NOUN
ejpam-6254	373	17	,	,	PUNCT
ejpam-6254	373	18	and	and	CCONJ
ejpam-6254	373	19	festus	festus	PROPN
ejpam-6254	373	20	abiodun	abiodun	PROPN
ejpam-6254	373	21	oguntolu	oguntolu	PROPN
ejpam-6254	373	22	.	.	PUNCT
ejpam-6254	374	1	time	time	NOUN
ejpam-6254	374	2	-	-	PUNCT
ejpam-6254	374	3	delayed	delay	VERB
ejpam-6254	374	4	modelling	modelling	NOUN
ejpam-6254	374	5	of	of	ADP
ejpam-6254	374	6	the	the	DET
ejpam-6254	374	7	covid-19	covid-19	PROPN
ejpam-6254	374	8	dynamics	dynamic	NOUN
ejpam-6254	374	9	with	with	ADP
ejpam-6254	374	10	a	a	DET
ejpam-6254	374	11	convex	convex	ADJ
ejpam-6254	374	12	incidence	incidence	NOUN
ejpam-6254	374	13	rate	rate	NOUN
ejpam-6254	374	14	.	.	PUNCT
ejpam-6254	375	1	informatics	informatic	NOUN
ejpam-6254	375	2	in	in	ADP
ejpam-6254	375	3	medicine	medicine	NOUN
ejpam-6254	375	4	unlocked	unlock	VERB
ejpam-6254	375	5	,	,	PUNCT
ejpam-6254	375	6	35:101124	35:101124	NUM
ejpam-6254	375	7	,	,	PUNCT
ejpam-6254	375	8	2022	2022	NUM
ejpam-6254	375	9	.	.	PUNCT
ejpam-6254	376	1	[	[	X
ejpam-6254	376	2	16	16	NUM
ejpam-6254	376	3	]	]	X
ejpam-6254	376	4	s.	s.	PROPN
ejpam-6254	376	5	tipsri	tipsri	PROPN
ejpam-6254	376	6	and	and	CCONJ
ejpam-6254	376	7	w.	w.	PROPN
ejpam-6254	376	8	chinviriyasit	chinviriyasit	PROPN
ejpam-6254	376	9	.	.	PUNCT
ejpam-6254	377	1	the	the	DET
ejpam-6254	377	2	effect	effect	NOUN
ejpam-6254	377	3	of	of	ADP
ejpam-6254	377	4	time	time	NOUN
ejpam-6254	377	5	delay	delay	NOUN
ejpam-6254	377	6	on	on	ADP
ejpam-6254	377	7	the	the	DET
ejpam-6254	377	8	dynamics	dynamic	NOUN
ejpam-6254	377	9	of	of	ADP
ejpam-6254	377	10	an	an	DET
ejpam-6254	377	11	seir	seir	ADJ
ejpam-6254	377	12	model	model	NOUN
ejpam-6254	377	13	with	with	ADP
ejpam-6254	377	14	nonlinear	nonlinear	ADJ
ejpam-6254	377	15	incidence	incidence	NOUN
ejpam-6254	377	16	.	.	PUNCT
ejpam-6254	378	1	chaos	chaos	NOUN
ejpam-6254	378	2	solitons	soliton	NOUN
ejpam-6254	378	3	fractals	fractal	NOUN
ejpam-6254	378	4	,	,	PUNCT
ejpam-6254	378	5	75:153–172	75:153–172	NUM
ejpam-6254	378	6	,	,	PUNCT
ejpam-6254	378	7	2015	2015	NUM
ejpam-6254	378	8	.	.	PUNCT
ejpam-6254	379	1	[	[	X
ejpam-6254	379	2	17	17	NUM
ejpam-6254	379	3	]	]	X
ejpam-6254	379	4	w.h	w.h	PROPN
ejpam-6254	379	5	.	.	PROPN
ejpam-6254	379	6	fleming	fleming	PROPN
ejpam-6254	379	7	and	and	CCONJ
ejpam-6254	379	8	r.w	r.w	PROPN
ejpam-6254	379	9	.	.	PROPN
ejpam-6254	379	10	rishel	rishel	PROPN
ejpam-6254	379	11	.	.	PUNCT
ejpam-6254	380	1	deterministic	deterministic	ADJ
ejpam-6254	380	2	and	and	CCONJ
ejpam-6254	380	3	stochastic	stochastic	ADJ
ejpam-6254	380	4	optimal	optimal	ADJ
ejpam-6254	380	5	control	control	NOUN
ejpam-6254	380	6	.	.	PUNCT
ejpam-6254	381	1	springer	springer	NOUN
ejpam-6254	381	2	,	,	PUNCT
ejpam-6254	381	3	new	new	PROPN
ejpam-6254	381	4	york	york	PROPN
ejpam-6254	381	5	,	,	PUNCT
ejpam-6254	381	6	ny	ny	PROPN
ejpam-6254	381	7	,	,	PUNCT
ejpam-6254	381	8	usa	usa	PROPN
ejpam-6254	381	9	,	,	PUNCT
ejpam-6254	381	10	1975	1975	NUM
ejpam-6254	381	11	.	.	PUNCT
ejpam-6254	382	1	[	[	X
ejpam-6254	382	2	18	18	NUM
ejpam-6254	382	3	]	]	X
ejpam-6254	382	4	d.l	d.l	PROPN
ejpam-6254	382	5	.	.	PROPN
ejpam-6254	382	6	lukes	lukes	PROPN
ejpam-6254	382	7	.	.	PUNCT
ejpam-6254	383	1	differential	differential	ADJ
ejpam-6254	383	2	equations	equation	NOUN
ejpam-6254	383	3	:	:	PUNCT
ejpam-6254	383	4	classical	classical	ADJ
ejpam-6254	383	5	to	to	ADP
ejpam-6254	383	6	controlled	control	VERB
ejpam-6254	383	7	.	.	PUNCT
ejpam-6254	384	1	academic	academic	ADJ
ejpam-6254	384	2	press	press	NOUN
ejpam-6254	384	3	,	,	PUNCT
ejpam-6254	384	4	new	new	PROPN
ejpam-6254	384	5	york	york	PROPN
ejpam-6254	384	6	,	,	PUNCT
ejpam-6254	384	7	1982	1982	NUM
ejpam-6254	384	8	.	.	PUNCT