id	sid	tid	token	lemma	pos
ejpam-6596	1	1	european	european	PROPN
ejpam-6596	1	2	journal	journal	PROPN
ejpam-6596	1	3	of	of	ADP
ejpam-6596	1	4	pure	pure	ADJ
ejpam-6596	1	5	and	and	CCONJ
ejpam-6596	1	6	applied	applied	ADJ
ejpam-6596	1	7	mathematics	mathematic	NOUN
ejpam-6596	1	8	2025	2025	NUM
ejpam-6596	1	9	,	,	PUNCT
ejpam-6596	1	10	vol	vol	NOUN
ejpam-6596	1	11	.	.	PROPN
ejpam-6596	1	12	18	18	NUM
ejpam-6596	1	13	,	,	PUNCT
ejpam-6596	1	14	issue	issue	NOUN
ejpam-6596	1	15	4	4	NUM
ejpam-6596	1	16	,	,	PUNCT
ejpam-6596	1	17	article	article	NOUN
ejpam-6596	1	18	number	number	NOUN
ejpam-6596	1	19	6596	6596	NUM
ejpam-6596	1	20	issn	issn	PROPN
ejpam-6596	1	21	1307	1307	NUM
ejpam-6596	1	22	-	-	SYM
ejpam-6596	1	23	5543	5543	NUM
ejpam-6596	1	24	–	–	PUNCT
ejpam-6596	1	25	ejpam.com	ejpam.com	X
ejpam-6596	1	26	published	publish	VERB
ejpam-6596	1	27	by	by	ADP
ejpam-6596	1	28	new	new	PROPN
ejpam-6596	1	29	york	york	PROPN
ejpam-6596	1	30	business	business	PROPN
ejpam-6596	1	31	global	global	ADJ
ejpam-6596	1	32	stability	stability	NOUN
ejpam-6596	1	33	and	and	CCONJ
ejpam-6596	1	34	optimal	optimal	ADJ
ejpam-6596	1	35	control	control	NOUN
ejpam-6596	1	36	analysis	analysis	NOUN
ejpam-6596	1	37	of	of	ADP
ejpam-6596	1	38	an	an	DET
ejpam-6596	1	39	seiqr	seiqr	ADJ
ejpam-6596	1	40	epidemic	epidemic	NOUN
ejpam-6596	1	41	model	model	NOUN
ejpam-6596	1	42	with	with	ADP
ejpam-6596	1	43	saturated	saturate	VERB
ejpam-6596	1	44	incidence	incidence	NOUN
ejpam-6596	1	45	rate	rate	NOUN
ejpam-6596	1	46	noshi	noshi	NOUN
ejpam-6596	1	47	gul1	gul1	PROPN
ejpam-6596	1	48	,	,	PUNCT
ejpam-6596	1	49	ismail	ismail	PROPN
ejpam-6596	1	50	shah2	shah2	PROPN
ejpam-6596	1	51	,	,	PUNCT
ejpam-6596	1	52	saeed	saeed	PROPN
ejpam-6596	1	53	ahmad1,∗	ahmad1,∗	PROPN
ejpam-6596	1	54	,	,	PUNCT
ejpam-6596	1	55	ihsan	ihsan	PROPN
ejpam-6596	1	56	ullah1	ullah1	PROPN
ejpam-6596	1	57	,	,	PUNCT
ejpam-6596	1	58	manuel	manuel	PROPN
ejpam-6596	1	59	de	de	X
ejpam-6596	1	60	la	la	X
ejpam-6596	1	61	sen3	sen3	PROPN
ejpam-6596	1	62	1	1	NUM
ejpam-6596	1	63	department	department	NOUN
ejpam-6596	1	64	of	of	ADP
ejpam-6596	1	65	mathematics	mathematic	NOUN
ejpam-6596	1	66	,	,	PUNCT
ejpam-6596	1	67	university	university	NOUN
ejpam-6596	1	68	of	of	ADP
ejpam-6596	1	69	malakand	malakand	PROPN
ejpam-6596	1	70	,	,	PUNCT
ejpam-6596	1	71	chakdara	chakdara	PROPN
ejpam-6596	1	72	,	,	PUNCT
ejpam-6596	1	73	dir(l	dir(l	PROPN
ejpam-6596	1	74	)	)	PUNCT
ejpam-6596	1	75	,	,	PUNCT
ejpam-6596	1	76	18800	18800	NUM
ejpam-6596	1	77	,	,	PUNCT
ejpam-6596	1	78	pakistan	pakistan	PROPN
ejpam-6596	1	79	2	2	NUM
ejpam-6596	1	80	department	department	NOUN
ejpam-6596	1	81	of	of	ADP
ejpam-6596	1	82	mathematics	mathematic	NOUN
ejpam-6596	1	83	,	,	PUNCT
ejpam-6596	1	84	university	university	PROPN
ejpam-6596	1	85	of	of	ADP
ejpam-6596	1	86	nottingham	nottingham	PROPN
ejpam-6596	1	87	ningbo	ningbo	PROPN
ejpam-6596	1	88	china	china	PROPN
ejpam-6596	1	89	,	,	PUNCT
ejpam-6596	1	90	199	199	NUM
ejpam-6596	1	91	taikang	taikang	PROPN
ejpam-6596	1	92	east	east	PROPN
ejpam-6596	1	93	road	road	PROPN
ejpam-6596	1	94	,	,	PUNCT
ejpam-6596	1	95	ningbo	ningbo	PROPN
ejpam-6596	1	96	315100	315100	NUM
ejpam-6596	1	97	,	,	PUNCT
ejpam-6596	1	98	china	china	PROPN
ejpam-6596	1	99	3	3	NUM
ejpam-6596	1	100	department	department	NOUN
ejpam-6596	1	101	of	of	ADP
ejpam-6596	1	102	electricity	electricity	NOUN
ejpam-6596	1	103	and	and	CCONJ
ejpam-6596	1	104	electronics	electronic	NOUN
ejpam-6596	1	105	,	,	PUNCT
ejpam-6596	1	106	institute	institute	NOUN
ejpam-6596	1	107	of	of	ADP
ejpam-6596	1	108	research	research	NOUN
ejpam-6596	1	109	and	and	CCONJ
ejpam-6596	1	110	development	development	NOUN
ejpam-6596	1	111	of	of	ADP
ejpam-6596	1	112	process	process	NOUN
ejpam-6596	1	113	,	,	PUNCT
ejpam-6596	1	114	university	university	NOUN
ejpam-6596	1	115	of	of	ADP
ejpam-6596	1	116	the	the	DET
ejpam-6596	1	117	basque	basque	ADJ
ejpam-6596	1	118	country	country	NOUN
ejpam-6596	1	119	,	,	PUNCT
ejpam-6596	1	120	campus	campus	NOUN
ejpam-6596	1	121	of	of	ADP
ejpam-6596	1	122	leioa	leioa	PROPN
ejpam-6596	1	123	(	(	PUNCT
ejpam-6596	1	124	bizkaia	bizkaia	PROPN
ejpam-6596	1	125	)	)	PUNCT
ejpam-6596	1	126	,	,	PUNCT
ejpam-6596	1	127	leioa	leioa	PROPN
ejpam-6596	1	128	48940	48940	NUM
ejpam-6596	1	129	,	,	PUNCT
ejpam-6596	1	130	spain	spain	PROPN
ejpam-6596	1	131	abstract	abstract	NOUN
ejpam-6596	1	132	.	.	PUNCT
ejpam-6596	2	1	in	in	ADP
ejpam-6596	2	2	this	this	DET
ejpam-6596	2	3	article	article	NOUN
ejpam-6596	2	4	,	,	PUNCT
ejpam-6596	2	5	we	we	PRON
ejpam-6596	2	6	proposed	propose	VERB
ejpam-6596	2	7	a	a	DET
ejpam-6596	2	8	new	new	ADJ
ejpam-6596	2	9	mathematical	mathematical	ADJ
ejpam-6596	2	10	model	model	NOUN
ejpam-6596	2	11	to	to	PART
ejpam-6596	2	12	investigate	investigate	VERB
ejpam-6596	2	13	the	the	DET
ejpam-6596	2	14	dynamics	dynamic	NOUN
ejpam-6596	2	15	of	of	ADP
ejpam-6596	2	16	the	the	DET
ejpam-6596	2	17	infectious	infectious	ADJ
ejpam-6596	2	18	disease	disease	NOUN
ejpam-6596	2	19	,	,	PUNCT
ejpam-6596	2	20	control	control	NOUN
ejpam-6596	2	21	,	,	PUNCT
ejpam-6596	2	22	and	and	CCONJ
ejpam-6596	2	23	general	general	ADJ
ejpam-6596	2	24	disease	disease	NOUN
ejpam-6596	2	25	transmission	transmission	NOUN
ejpam-6596	2	26	.	.	PUNCT
ejpam-6596	3	1	the	the	DET
ejpam-6596	3	2	model	model	NOUN
ejpam-6596	3	3	exhibits	exhibit	VERB
ejpam-6596	3	4	two	two	NUM
ejpam-6596	3	5	distinct	distinct	ADJ
ejpam-6596	3	6	non	non	ADJ
ejpam-6596	3	7	-	-	ADJ
ejpam-6596	3	8	trivial	trivial	ADJ
ejpam-6596	3	9	equilibrium	equilibrium	NOUN
ejpam-6596	3	10	states	state	NOUN
ejpam-6596	3	11	.	.	PUNCT
ejpam-6596	4	1	as	as	ADP
ejpam-6596	4	2	a	a	DET
ejpam-6596	4	3	fundamental	fundamental	ADJ
ejpam-6596	4	4	prerequisite	prerequisite	NOUN
ejpam-6596	4	5	for	for	ADP
ejpam-6596	4	6	stability	stability	NOUN
ejpam-6596	4	7	analysis	analysis	NOUN
ejpam-6596	4	8	,	,	PUNCT
ejpam-6596	4	9	we	we	PRON
ejpam-6596	4	10	first	first	ADV
ejpam-6596	4	11	derive	derive	VERB
ejpam-6596	4	12	the	the	DET
ejpam-6596	4	13	epidemiological	epidemiological	ADJ
ejpam-6596	4	14	threshold	threshold	NOUN
ejpam-6596	4	15	parameter	parameter	NOUN
ejpam-6596	4	16	r0	r0	NOUN
ejpam-6596	4	17	through	through	ADP
ejpam-6596	4	18	next	next	ADJ
ejpam-6596	4	19	-	-	PUNCT
ejpam-6596	4	20	generation	generation	NOUN
ejpam-6596	4	21	matrix	matrix	NOUN
ejpam-6596	4	22	methodology	methodology	NOUN
ejpam-6596	4	23	.	.	PUNCT
ejpam-6596	5	1	according	accord	VERB
ejpam-6596	5	2	to	to	ADP
ejpam-6596	5	3	our	our	PRON
ejpam-6596	5	4	investigation	investigation	NOUN
ejpam-6596	5	5	,	,	PUNCT
ejpam-6596	5	6	r0	r0	NOUN
ejpam-6596	5	7	plays	play	VERB
ejpam-6596	5	8	an	an	DET
ejpam-6596	5	9	essential	essential	ADJ
ejpam-6596	5	10	role	role	NOUN
ejpam-6596	5	11	in	in	ADP
ejpam-6596	5	12	describing	describe	VERB
ejpam-6596	5	13	the	the	DET
ejpam-6596	5	14	model	model	NOUN
ejpam-6596	5	15	’s	’s	PART
ejpam-6596	5	16	dynamics	dynamic	NOUN
ejpam-6596	5	17	.	.	PUNCT
ejpam-6596	6	1	we	we	PRON
ejpam-6596	6	2	demonstrate	demonstrate	VERB
ejpam-6596	6	3	that	that	SCONJ
ejpam-6596	6	4	in	in	ADP
ejpam-6596	6	5	the	the	DET
ejpam-6596	6	6	case	case	NOUN
ejpam-6596	6	7	when	when	SCONJ
ejpam-6596	6	8	r0	r0	NOUN
ejpam-6596	6	9	takes	take	VERB
ejpam-6596	6	10	values	value	NOUN
ejpam-6596	6	11	less	less	ADJ
ejpam-6596	6	12	or	or	CCONJ
ejpam-6596	6	13	greater	great	ADJ
ejpam-6596	6	14	than	than	ADP
ejpam-6596	6	15	unity	unity	NOUN
ejpam-6596	6	16	,	,	PUNCT
ejpam-6596	6	17	the	the	DET
ejpam-6596	6	18	endemic	endemic	ADJ
ejpam-6596	6	19	(	(	PUNCT
ejpam-6596	6	20	disease	disease	NOUN
ejpam-6596	6	21	-	-	PUNCT
ejpam-6596	6	22	free	free	ADJ
ejpam-6596	6	23	)	)	PUNCT
ejpam-6596	6	24	condition	condition	NOUN
ejpam-6596	6	25	is	be	AUX
ejpam-6596	6	26	asymptotically	asymptotically	ADV
ejpam-6596	6	27	stable	stable	ADJ
ejpam-6596	6	28	both	both	CCONJ
ejpam-6596	6	29	locally	locally	ADV
ejpam-6596	6	30	and	and	CCONJ
ejpam-6596	6	31	globally	globally	ADV
ejpam-6596	6	32	.	.	PUNCT
ejpam-6596	7	1	to	to	PART
ejpam-6596	7	2	try	try	VERB
ejpam-6596	7	3	to	to	PART
ejpam-6596	7	4	stop	stop	VERB
ejpam-6596	7	5	the	the	DET
ejpam-6596	7	6	general	general	ADJ
ejpam-6596	7	7	disease	disease	NOUN
ejpam-6596	7	8	from	from	ADP
ejpam-6596	7	9	spreading	spread	VERB
ejpam-6596	7	10	throughout	throughout	ADP
ejpam-6596	7	11	a	a	DET
ejpam-6596	7	12	community	community	NOUN
ejpam-6596	7	13	,	,	PUNCT
ejpam-6596	7	14	we	we	PRON
ejpam-6596	7	15	add	add	VERB
ejpam-6596	7	16	control	control	NOUN
ejpam-6596	7	17	parameters	parameter	NOUN
ejpam-6596	7	18	,	,	PUNCT
ejpam-6596	7	19	create	create	VERB
ejpam-6596	7	20	a	a	DET
ejpam-6596	7	21	control	control	NOUN
ejpam-6596	7	22	model	model	NOUN
ejpam-6596	7	23	,	,	PUNCT
ejpam-6596	7	24	and	and	CCONJ
ejpam-6596	7	25	suggest	suggest	VERB
ejpam-6596	7	26	control	control	NOUN
ejpam-6596	7	27	techniques	technique	NOUN
ejpam-6596	7	28	.	.	PUNCT
ejpam-6596	8	1	the	the	DET
ejpam-6596	8	2	maximum	maximum	ADJ
ejpam-6596	8	3	principle	principle	NOUN
ejpam-6596	8	4	of	of	ADP
ejpam-6596	8	5	pontryagin	pontryagin	NOUN
ejpam-6596	8	6	is	be	AUX
ejpam-6596	8	7	used	use	VERB
ejpam-6596	8	8	to	to	PART
ejpam-6596	8	9	derive	derive	VERB
ejpam-6596	8	10	the	the	DET
ejpam-6596	8	11	optimality	optimality	NOUN
ejpam-6596	8	12	system	system	NOUN
ejpam-6596	8	13	.	.	PUNCT
ejpam-6596	9	1	finally	finally	ADV
ejpam-6596	9	2	,	,	PUNCT
ejpam-6596	9	3	the	the	DET
ejpam-6596	9	4	numerical	numerical	ADJ
ejpam-6596	9	5	simulations	simulation	NOUN
ejpam-6596	9	6	are	be	AUX
ejpam-6596	9	7	performed	perform	VERB
ejpam-6596	9	8	using	use	VERB
ejpam-6596	9	9	the	the	DET
ejpam-6596	9	10	fourth	fourth	ADJ
ejpam-6596	9	11	-	-	PUNCT
ejpam-6596	9	12	order	order	NOUN
ejpam-6596	9	13	runge	runge	NOUN
ejpam-6596	9	14	-	-	PUNCT
ejpam-6596	9	15	kutta	kutta	NOUN
ejpam-6596	9	16	technique	technique	NOUN
ejpam-6596	9	17	to	to	PART
ejpam-6596	9	18	validate	validate	VERB
ejpam-6596	9	19	and	and	CCONJ
ejpam-6596	9	20	confirm	confirm	VERB
ejpam-6596	9	21	our	our	PRON
ejpam-6596	9	22	analytical	analytical	ADJ
ejpam-6596	9	23	conclusions	conclusion	NOUN
ejpam-6596	9	24	.	.	PUNCT
ejpam-6596	10	1	phase	phase	NOUN
ejpam-6596	10	2	portrait	portrait	NOUN
ejpam-6596	10	3	analysis	analysis	NOUN
ejpam-6596	10	4	further	far	ADV
ejpam-6596	10	5	illustrates	illustrate	VERB
ejpam-6596	10	6	the	the	DET
ejpam-6596	10	7	convergence	convergence	NOUN
ejpam-6596	10	8	of	of	ADP
ejpam-6596	10	9	system	system	NOUN
ejpam-6596	10	10	trajectories	trajectory	NOUN
ejpam-6596	10	11	toward	toward	ADP
ejpam-6596	10	12	disease	disease	NOUN
ejpam-6596	10	13	-	-	PUNCT
ejpam-6596	10	14	free	free	ADJ
ejpam-6596	10	15	or	or	CCONJ
ejpam-6596	10	16	endemic	endemic	ADJ
ejpam-6596	10	17	equilibria	equilibrium	NOUN
ejpam-6596	10	18	under	under	ADP
ejpam-6596	10	19	different	different	ADJ
ejpam-6596	10	20	control	control	NOUN
ejpam-6596	10	21	scenarios	scenario	NOUN
ejpam-6596	10	22	,	,	PUNCT
ejpam-6596	10	23	reinforcing	reinforce	VERB
ejpam-6596	10	24	the	the	DET
ejpam-6596	10	25	stability	stability	NOUN
ejpam-6596	10	26	criteria	criterion	NOUN
ejpam-6596	10	27	derived	derive	VERB
ejpam-6596	10	28	for	for	ADP
ejpam-6596	10	29	r0	r0	NOUN
ejpam-6596	10	30	.	.	PUNCT
ejpam-6596	11	1	2020	2020	NUM
ejpam-6596	11	2	mathematics	mathematic	NOUN
ejpam-6596	11	3	subject	subject	NOUN
ejpam-6596	11	4	classifications	classification	NOUN
ejpam-6596	11	5	:	:	PUNCT
ejpam-6596	11	6	92d30	92d30	NUM
ejpam-6596	11	7	,	,	PUNCT
ejpam-6596	11	8	93c15	93c15	NUM
ejpam-6596	11	9	,	,	PUNCT
ejpam-6596	11	10	93d20	93d20	NUM
ejpam-6596	11	11	,	,	PUNCT
ejpam-6596	11	12	34d23	34d23	NUM
ejpam-6596	11	13	key	key	ADJ
ejpam-6596	11	14	words	word	NOUN
ejpam-6596	11	15	and	and	CCONJ
ejpam-6596	11	16	phrases	phrase	NOUN
ejpam-6596	11	17	:	:	PUNCT
ejpam-6596	11	18	mathematical	mathematical	ADJ
ejpam-6596	11	19	model	model	NOUN
ejpam-6596	11	20	,	,	PUNCT
ejpam-6596	11	21	epidemic	epidemic	NOUN
ejpam-6596	11	22	disease	disease	NOUN
ejpam-6596	11	23	,	,	PUNCT
ejpam-6596	11	24	asymptotical	asymptotical	ADJ
ejpam-6596	11	25	stability	stability	NOUN
ejpam-6596	11	26	,	,	PUNCT
ejpam-6596	11	27	optimal	optimal	ADJ
ejpam-6596	11	28	control	control	NOUN
ejpam-6596	11	29	theory	theory	NOUN
ejpam-6596	11	30	,	,	PUNCT
ejpam-6596	11	31	phase	phase	NOUN
ejpam-6596	11	32	portrait	portrait	NOUN
ejpam-6596	11	33	,	,	PUNCT
ejpam-6596	11	34	numerical	numerical	PROPN
ejpam-6596	11	35	simulation	simulation	PROPN
ejpam-6596	11	36	1	1	NUM
ejpam-6596	11	37	.	.	PUNCT
ejpam-6596	12	1	introduction	introduction	NOUN
ejpam-6596	12	2	infectious	infectious	ADJ
ejpam-6596	12	3	diseases	disease	NOUN
ejpam-6596	12	4	are	be	AUX
ejpam-6596	12	5	one	one	NUM
ejpam-6596	12	6	of	of	ADP
ejpam-6596	12	7	the	the	DET
ejpam-6596	12	8	main	main	ADJ
ejpam-6596	12	9	causes	cause	NOUN
ejpam-6596	12	10	of	of	ADP
ejpam-6596	12	11	mortality	mortality	NOUN
ejpam-6596	12	12	around	around	ADP
ejpam-6596	12	13	the	the	DET
ejpam-6596	12	14	globe	globe	NOUN
ejpam-6596	12	15	.	.	PUNCT
ejpam-6596	13	1	infectious	infectious	ADJ
ejpam-6596	13	2	diseases	disease	NOUN
ejpam-6596	13	3	have	have	AUX
ejpam-6596	13	4	existed	exist	VERB
ejpam-6596	13	5	for	for	ADP
ejpam-6596	13	6	as	as	ADV
ejpam-6596	13	7	long	long	ADV
ejpam-6596	13	8	as	as	SCONJ
ejpam-6596	13	9	humans	human	NOUN
ejpam-6596	13	10	have	have	AUX
ejpam-6596	13	11	been	be	AUX
ejpam-6596	13	12	on	on	ADP
ejpam-6596	13	13	earth	earth	NOUN
ejpam-6596	13	14	.	.	PUNCT
ejpam-6596	14	1	due	due	ADP
ejpam-6596	14	2	to	to	ADP
ejpam-6596	14	3	the	the	DET
ejpam-6596	14	4	emergence	emergence	NOUN
ejpam-6596	14	5	and	and	CCONJ
ejpam-6596	14	6	reemergence	reemergence	NOUN
ejpam-6596	14	7	of	of	ADP
ejpam-6596	14	8	some	some	DET
ejpam-6596	14	9	catastrophic	catastrophic	ADJ
ejpam-6596	14	10	diseases	disease	NOUN
ejpam-6596	14	11	in	in	ADP
ejpam-6596	14	12	recent	recent	ADJ
ejpam-6596	14	13	decades	decade	NOUN
ejpam-6596	14	14	,	,	PUNCT
ejpam-6596	14	15	infectious	infectious	ADJ
ejpam-6596	14	16	diseases	disease	NOUN
ejpam-6596	14	17	have	have	AUX
ejpam-6596	14	18	attracted	attract	VERB
ejpam-6596	14	19	the	the	DET
ejpam-6596	14	20	attention	attention	NOUN
ejpam-6596	14	21	of	of	ADP
ejpam-6596	14	22	many	many	ADJ
ejpam-6596	14	23	researchers	researcher	NOUN
ejpam-6596	14	24	[	[	X
ejpam-6596	14	25	1–5	1–5	X
ejpam-6596	14	26	]	]	X
ejpam-6596	14	27	the	the	DET
ejpam-6596	14	28	main	main	ADJ
ejpam-6596	14	29	challenges	challenge	NOUN
ejpam-6596	14	30	regarding	regard	VERB
ejpam-6596	14	31	infectious	infectious	ADJ
ejpam-6596	14	32	∗corresponding	∗corresponding	NOUN
ejpam-6596	14	33	author	author	NOUN
ejpam-6596	14	34	.	.	PUNCT
ejpam-6596	15	1	doi	doi	NOUN
ejpam-6596	15	2	:	:	PUNCT
ejpam-6596	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6596	https://doi.org/10.29020/nybg.ejpam.v18i4.6596	ADJ
ejpam-6596	15	4	email	email	NOUN
ejpam-6596	15	5	addresses	address	VERB
ejpam-6596	15	6	:	:	PUNCT
ejpam-6596	15	7	noshiguluom@gmail.com	noshiguluom@gmail.com	X
ejpam-6596	15	8	(	(	PUNCT
ejpam-6596	15	9	n.	n.	PROPN
ejpam-6596	15	10	gul	gul	PROPN
ejpam-6596	15	11	)	)	PUNCT
ejpam-6596	15	12	,	,	PUNCT
ejpam-6596	15	13	ismail8leu@gmail.com	ismail8leu@gmail.com	PROPN
ejpam-6596	15	14	(	(	PUNCT
ejpam-6596	15	15	i.	i.	PROPN
ejpam-6596	15	16	shah	shah	PROPN
ejpam-6596	15	17	)	)	PUNCT
ejpam-6596	15	18	,	,	PUNCT
ejpam-6596	15	19	saeedahmad@uom.edu.pk	saeedahmad@uom.edu.pk	NOUN
ejpam-6596	15	20	(	(	PUNCT
ejpam-6596	15	21	s.	s.	PROPN
ejpam-6596	15	22	ahmad	ahmad	PROPN
ejpam-6596	15	23	)	)	PUNCT
ejpam-6596	15	24	,	,	PUNCT
ejpam-6596	15	25	ihsansf3@gmail.com	ihsansf3@gmail.com	X
ejpam-6596	15	26	(	(	PUNCT
ejpam-6596	15	27	i.	i.	PROPN
ejpam-6596	15	28	ullah	ullah	PROPN
ejpam-6596	15	29	)	)	PUNCT
ejpam-6596	15	30	,	,	PUNCT
ejpam-6596	15	31	manuel.delasen@ehu.eus	manuel.delasen@ehu.eus	PROPN
ejpam-6596	15	32	(	(	PUNCT
ejpam-6596	15	33	m.	m.	NOUN
ejpam-6596	15	34	de	de	X
ejpam-6596	15	35	la	la	X
ejpam-6596	15	36	sen	sen	PROPN
ejpam-6596	15	37	)	)	PUNCT
ejpam-6596	15	38	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6596	15	39	1	1	NUM
ejpam-6596	15	40	copyright	copyright	NOUN
ejpam-6596	15	41	:	:	PUNCT
ejpam-6596	16	1	©	©	PROPN
ejpam-6596	16	2	2025	2025	NUM
ejpam-6596	16	3	the	the	DET
ejpam-6596	16	4	author(s	author(s	NOUN
ejpam-6596	16	5	)	)	PUNCT
ejpam-6596	16	6	.	.	PUNCT
ejpam-6596	17	1	(	(	PUNCT
ejpam-6596	17	2	cc	cc	NOUN
ejpam-6596	17	3	by	by	ADP
ejpam-6596	17	4	-	-	PUNCT
ejpam-6596	17	5	nc	nc	PROPN
ejpam-6596	17	6	4.0	4.0	NUM
ejpam-6596	17	7	)	)	PUNCT
ejpam-6596	17	8	n.	n.	NOUN
ejpam-6596	17	9	gul	gul	PROPN
ejpam-6596	17	10	et	et	PROPN
ejpam-6596	17	11	al	al	PROPN
ejpam-6596	17	12	.	.	PUNCT
ejpam-6596	17	13	/	/	SYM
ejpam-6596	17	14	eur	eur	PROPN
ejpam-6596	17	15	.	.	PUNCT
ejpam-6596	18	1	j.	j.	PROPN
ejpam-6596	18	2	pure	pure	PROPN
ejpam-6596	18	3	appl	appl	PROPN
ejpam-6596	18	4	.	.	PROPN
ejpam-6596	18	5	math	math	PROPN
ejpam-6596	18	6	,	,	PUNCT
ejpam-6596	18	7	18	18	NUM
ejpam-6596	18	8	(	(	PUNCT
ejpam-6596	18	9	4	4	NUM
ejpam-6596	18	10	)	)	PUNCT
ejpam-6596	18	11	(	(	PUNCT
ejpam-6596	18	12	2025	2025	NUM
ejpam-6596	18	13	)	)	PUNCT
ejpam-6596	18	14	,	,	PUNCT
ejpam-6596	18	15	6596	6596	NUM
ejpam-6596	18	16	2	2	NUM
ejpam-6596	18	17	of	of	ADP
ejpam-6596	18	18	23	23	NUM
ejpam-6596	18	19	diseases	disease	NOUN
ejpam-6596	18	20	include	include	VERB
ejpam-6596	18	21	studying	study	VERB
ejpam-6596	18	22	the	the	DET
ejpam-6596	18	23	nature	nature	NOUN
ejpam-6596	18	24	of	of	ADP
ejpam-6596	18	25	their	their	PRON
ejpam-6596	18	26	spread	spread	NOUN
ejpam-6596	18	27	by	by	ADP
ejpam-6596	18	28	considering	consider	VERB
ejpam-6596	18	29	possible	possible	ADJ
ejpam-6596	18	30	factors	factor	NOUN
ejpam-6596	18	31	causing	cause	VERB
ejpam-6596	18	32	the	the	DET
ejpam-6596	18	33	diseases	disease	NOUN
ejpam-6596	18	34	and	and	CCONJ
ejpam-6596	18	35	predicting	predict	VERB
ejpam-6596	18	36	their	their	PRON
ejpam-6596	18	37	future	future	ADJ
ejpam-6596	18	38	states	state	NOUN
ejpam-6596	18	39	.	.	PUNCT
ejpam-6596	19	1	one	one	NUM
ejpam-6596	19	2	way	way	NOUN
ejpam-6596	19	3	is	be	AUX
ejpam-6596	19	4	to	to	PART
ejpam-6596	19	5	express	express	VERB
ejpam-6596	19	6	these	these	DET
ejpam-6596	19	7	relations	relation	NOUN
ejpam-6596	19	8	in	in	ADP
ejpam-6596	19	9	mathematical	mathematical	ADJ
ejpam-6596	19	10	language	language	NOUN
ejpam-6596	19	11	.	.	PUNCT
ejpam-6596	20	1	to	to	PART
ejpam-6596	20	2	look	look	VERB
ejpam-6596	20	3	into	into	ADP
ejpam-6596	20	4	it	it	PRON
ejpam-6596	20	5	the	the	DET
ejpam-6596	20	6	mechanisms	mechanism	NOUN
ejpam-6596	20	7	of	of	ADP
ejpam-6596	20	8	infectious	infectious	ADJ
ejpam-6596	20	9	disease	disease	NOUN
ejpam-6596	20	10	transfer	transfer	NOUN
ejpam-6596	20	11	and	and	CCONJ
ejpam-6596	20	12	forecast	forecast	VERB
ejpam-6596	20	13	its	its	PRON
ejpam-6596	20	14	future	future	ADJ
ejpam-6596	20	15	spread	spread	NOUN
ejpam-6596	20	16	,	,	PUNCT
ejpam-6596	20	17	mathematical	mathematical	ADJ
ejpam-6596	20	18	models	model	NOUN
ejpam-6596	20	19	are	be	AUX
ejpam-6596	20	20	crucial	crucial	ADJ
ejpam-6596	20	21	[	[	X
ejpam-6596	20	22	6	6	NUM
ejpam-6596	20	23	]	]	PUNCT
ejpam-6596	20	24	.	.	PUNCT
ejpam-6596	21	1	the	the	DET
ejpam-6596	21	2	estimation	estimation	NOUN
ejpam-6596	21	3	of	of	ADP
ejpam-6596	21	4	parameters	parameter	NOUN
ejpam-6596	21	5	,	,	PUNCT
ejpam-6596	21	6	the	the	DET
ejpam-6596	21	7	development	development	NOUN
ejpam-6596	21	8	and	and	CCONJ
ejpam-6596	21	9	testing	testing	NOUN
ejpam-6596	21	10	of	of	ADP
ejpam-6596	21	11	hypotheses	hypothesis	NOUN
ejpam-6596	21	12	that	that	PRON
ejpam-6596	21	13	aid	aid	NOUN
ejpam-6596	21	14	in	in	ADP
ejpam-6596	21	15	disease	disease	NOUN
ejpam-6596	21	16	prediction	prediction	NOUN
ejpam-6596	21	17	and	and	CCONJ
ejpam-6596	21	18	disease	disease	NOUN
ejpam-6596	21	19	control	control	NOUN
ejpam-6596	21	20	are	be	AUX
ejpam-6596	21	21	some	some	PRON
ejpam-6596	21	22	of	of	ADP
ejpam-6596	21	23	the	the	DET
ejpam-6596	21	24	fundamental	fundamental	ADJ
ejpam-6596	21	25	characteristics	characteristic	NOUN
ejpam-6596	21	26	of	of	ADP
ejpam-6596	21	27	mathematical	mathematical	ADJ
ejpam-6596	21	28	models	model	NOUN
ejpam-6596	21	29	.	.	PUNCT
ejpam-6596	22	1	the	the	DET
ejpam-6596	22	2	health	health	PROPN
ejpam-6596	22	3	department	department	PROPN
ejpam-6596	22	4	can	can	AUX
ejpam-6596	22	5	use	use	VERB
ejpam-6596	22	6	the	the	DET
ejpam-6596	22	7	mathematical	mathematical	ADJ
ejpam-6596	22	8	model	model	NOUN
ejpam-6596	22	9	’s	’s	PART
ejpam-6596	22	10	valuable	valuable	ADJ
ejpam-6596	22	11	guidelines	guideline	NOUN
ejpam-6596	22	12	to	to	PART
ejpam-6596	22	13	take	take	VERB
ejpam-6596	22	14	action	action	NOUN
ejpam-6596	22	15	towards	towards	ADP
ejpam-6596	22	16	the	the	DET
ejpam-6596	22	17	control	control	NOUN
ejpam-6596	22	18	and	and	CCONJ
ejpam-6596	22	19	eradication	eradication	NOUN
ejpam-6596	22	20	of	of	ADP
ejpam-6596	22	21	diseases	disease	NOUN
ejpam-6596	22	22	,	,	PUNCT
ejpam-6596	22	23	which	which	PRON
ejpam-6596	22	24	is	be	AUX
ejpam-6596	22	25	one	one	NUM
ejpam-6596	22	26	of	of	ADP
ejpam-6596	22	27	its	its	PRON
ejpam-6596	22	28	most	most	ADV
ejpam-6596	22	29	significant	significant	ADJ
ejpam-6596	22	30	features	feature	NOUN
ejpam-6596	22	31	.	.	PUNCT
ejpam-6596	23	1	such	such	ADJ
ejpam-6596	23	2	models	model	NOUN
ejpam-6596	23	3	are	be	AUX
ejpam-6596	23	4	helpful	helpful	ADJ
ejpam-6596	23	5	for	for	ADP
ejpam-6596	23	6	identifying	identify	VERB
ejpam-6596	23	7	how	how	SCONJ
ejpam-6596	23	8	people	people	NOUN
ejpam-6596	23	9	are	be	AUX
ejpam-6596	23	10	simultaneously	simultaneously	ADV
ejpam-6596	23	11	infected	infect	VERB
ejpam-6596	23	12	with	with	ADP
ejpam-6596	23	13	a	a	DET
ejpam-6596	23	14	disease	disease	NOUN
ejpam-6596	23	15	and	and	CCONJ
ejpam-6596	23	16	what	what	DET
ejpam-6596	23	17	strategy	strategy	NOUN
ejpam-6596	23	18	should	should	AUX
ejpam-6596	23	19	be	be	AUX
ejpam-6596	23	20	used	use	VERB
ejpam-6596	23	21	to	to	PART
ejpam-6596	23	22	treat	treat	VERB
ejpam-6596	23	23	the	the	DET
ejpam-6596	23	24	condition	condition	NOUN
ejpam-6596	23	25	brilliantly	brilliantly	ADV
ejpam-6596	23	26	.	.	PUNCT
ejpam-6596	24	1	mathematical	mathematical	ADJ
ejpam-6596	24	2	modelling	modelling	NOUN
ejpam-6596	24	3	is	be	AUX
ejpam-6596	24	4	one	one	NUM
ejpam-6596	24	5	of	of	ADP
ejpam-6596	24	6	the	the	DET
ejpam-6596	24	7	effective	effective	ADJ
ejpam-6596	24	8	methods	method	NOUN
ejpam-6596	24	9	for	for	ADP
ejpam-6596	24	10	predicting	predict	VERB
ejpam-6596	24	11	the	the	DET
ejpam-6596	24	12	dynamics	dynamic	NOUN
ejpam-6596	24	13	of	of	ADP
ejpam-6596	24	14	infectious	infectious	ADJ
ejpam-6596	24	15	diseases	disease	NOUN
ejpam-6596	24	16	in	in	ADP
ejpam-6596	24	17	the	the	DET
ejpam-6596	24	18	realm	realm	NOUN
ejpam-6596	24	19	of	of	ADP
ejpam-6596	24	20	applied	apply	VERB
ejpam-6596	24	21	sciences	science	NOUN
ejpam-6596	24	22	.	.	PUNCT
ejpam-6596	25	1	numerous	numerous	ADJ
ejpam-6596	25	2	publications	publication	NOUN
ejpam-6596	25	3	have	have	AUX
ejpam-6596	25	4	been	be	AUX
ejpam-6596	25	5	read	read	VERB
ejpam-6596	25	6	to	to	PART
ejpam-6596	25	7	research	research	VERB
ejpam-6596	25	8	the	the	DET
ejpam-6596	25	9	dynamics	dynamic	NOUN
ejpam-6596	25	10	and	and	CCONJ
ejpam-6596	25	11	control	control	NOUN
ejpam-6596	25	12	of	of	ADP
ejpam-6596	25	13	numerous	numerous	ADJ
ejpam-6596	25	14	infectious	infectious	ADJ
ejpam-6596	25	15	diseases	disease	NOUN
ejpam-6596	25	16	[	[	X
ejpam-6596	25	17	7–9	7–9	X
ejpam-6596	25	18	]	]	X
ejpam-6596	25	19	using	use	VERB
ejpam-6596	25	20	mathematical	mathematical	ADJ
ejpam-6596	25	21	modelling	modelling	NOUN
ejpam-6596	25	22	of	of	ADP
ejpam-6596	25	23	infectious	infectious	ADJ
ejpam-6596	25	24	diseases	disease	NOUN
ejpam-6596	25	25	,	,	PUNCT
ejpam-6596	25	26	which	which	PRON
ejpam-6596	25	27	has	have	VERB
ejpam-6596	25	28	a	a	DET
ejpam-6596	25	29	rich	rich	ADJ
ejpam-6596	25	30	literature	literature	NOUN
ejpam-6596	25	31	[	[	X
ejpam-6596	25	32	10–15	10–15	NUM
ejpam-6596	25	33	]	]	PUNCT
ejpam-6596	25	34	.	.	PUNCT
ejpam-6596	26	1	in	in	ADP
ejpam-6596	26	2	order	order	NOUN
ejpam-6596	26	3	to	to	PART
ejpam-6596	26	4	research	research	VERB
ejpam-6596	26	5	how	how	SCONJ
ejpam-6596	26	6	to	to	PART
ejpam-6596	26	7	control	control	VERB
ejpam-6596	26	8	the	the	DET
ejpam-6596	26	9	transmission	transmission	NOUN
ejpam-6596	26	10	of	of	ADP
ejpam-6596	26	11	viruses	virus	NOUN
ejpam-6596	26	12	,	,	PUNCT
ejpam-6596	26	13	some	some	DET
ejpam-6596	26	14	modified	modify	VERB
ejpam-6596	26	15	epidemic	epidemic	NOUN
ejpam-6596	26	16	models	model	NOUN
ejpam-6596	26	17	are	be	AUX
ejpam-6596	26	18	developed	develop	VERB
ejpam-6596	26	19	due	due	ADP
ejpam-6596	26	20	to	to	ADP
ejpam-6596	26	21	the	the	DET
ejpam-6596	26	22	strong	strong	ADJ
ejpam-6596	26	23	resemblance	resemblance	NOUN
ejpam-6596	26	24	between	between	ADP
ejpam-6596	26	25	software	software	NOUN
ejpam-6596	26	26	viruses	virus	NOUN
ejpam-6596	26	27	and	and	CCONJ
ejpam-6596	26	28	viruses	virus	NOUN
ejpam-6596	26	29	that	that	PRON
ejpam-6596	26	30	are	be	AUX
ejpam-6596	26	31	living	live	VERB
ejpam-6596	26	32	.	.	PUNCT
ejpam-6596	27	1	the	the	DET
ejpam-6596	27	2	results	result	NOUN
ejpam-6596	27	3	of	of	ADP
ejpam-6596	27	4	the	the	DET
ejpam-6596	27	5	investigation	investigation	NOUN
ejpam-6596	27	6	have	have	AUX
ejpam-6596	27	7	shown	show	VERB
ejpam-6596	27	8	how	how	SCONJ
ejpam-6596	27	9	crucial	crucial	ADJ
ejpam-6596	27	10	the	the	DET
ejpam-6596	27	11	incidence	incidence	NOUN
ejpam-6596	27	12	rate	rate	NOUN
ejpam-6596	27	13	is	be	AUX
ejpam-6596	27	14	to	to	ADP
ejpam-6596	27	15	understanding	understand	VERB
ejpam-6596	27	16	the	the	DET
ejpam-6596	27	17	nature	nature	NOUN
ejpam-6596	27	18	of	of	ADP
ejpam-6596	27	19	epidemic	epidemic	NOUN
ejpam-6596	27	20	models	model	NOUN
ejpam-6596	27	21	[	[	X
ejpam-6596	27	22	16	16	NUM
ejpam-6596	27	23	]	]	PUNCT
ejpam-6596	27	24	.	.	PUNCT
ejpam-6596	28	1	mathematical	mathematical	ADJ
ejpam-6596	28	2	modeling	modeling	NOUN
ejpam-6596	28	3	uses	use	VERB
ejpam-6596	28	4	various	various	ADJ
ejpam-6596	28	5	incident	incident	NOUN
ejpam-6596	28	6	rates	rate	NOUN
ejpam-6596	28	7	to	to	PART
ejpam-6596	28	8	study	study	VERB
ejpam-6596	28	9	the	the	DET
ejpam-6596	28	10	transmission	transmission	NOUN
ejpam-6596	28	11	dynamics	dynamic	NOUN
ejpam-6596	28	12	of	of	ADP
ejpam-6596	28	13	infectious	infectious	ADJ
ejpam-6596	28	14	disease	disease	NOUN
ejpam-6596	28	15	[	[	X
ejpam-6596	28	16	17	17	NUM
ejpam-6596	28	17	]	]	PUNCT
ejpam-6596	28	18	.	.	PUNCT
ejpam-6596	29	1	let	let	VERB
ejpam-6596	29	2	h	h	NOUN
ejpam-6596	29	3	denote	denote	VERB
ejpam-6596	29	4	the	the	DET
ejpam-6596	29	5	disease	disease	NOUN
ejpam-6596	29	6	transmission	transmission	NOUN
ejpam-6596	29	7	rate	rate	NOUN
ejpam-6596	29	8	,	,	PUNCT
ejpam-6596	29	9	s	s	PART
ejpam-6596	29	10	and	and	CCONJ
ejpam-6596	29	11	i	i	PRON
ejpam-6596	29	12	are	be	AUX
ejpam-6596	29	13	respectively	respectively	ADV
ejpam-6596	29	14	used	use	VERB
ejpam-6596	29	15	for	for	ADP
ejpam-6596	29	16	susceptible	susceptible	ADJ
ejpam-6596	29	17	and	and	CCONJ
ejpam-6596	29	18	infected	infected	ADJ
ejpam-6596	29	19	individuals	individual	NOUN
ejpam-6596	29	20	.	.	PUNCT
ejpam-6596	30	1	the	the	DET
ejpam-6596	30	2	ratio	ratio	NOUN
ejpam-6596	30	3	hsi	hsi	PROPN
ejpam-6596	30	4	denotes	denote	VERB
ejpam-6596	30	5	an	an	DET
ejpam-6596	30	6	incidence	incidence	NOUN
ejpam-6596	30	7	rate	rate	NOUN
ejpam-6596	30	8	,	,	PUNCT
ejpam-6596	30	9	known	know	VERB
ejpam-6596	30	10	as	as	ADP
ejpam-6596	30	11	the	the	DET
ejpam-6596	30	12	bilinear	bilinear	ADJ
ejpam-6596	30	13	incidence	incidence	NOUN
ejpam-6596	30	14	rate	rate	NOUN
ejpam-6596	30	15	.	.	PUNCT
ejpam-6596	31	1	this	this	DET
ejpam-6596	31	2	type	type	NOUN
ejpam-6596	31	3	of	of	ADP
ejpam-6596	31	4	incidence	incidence	NOUN
ejpam-6596	31	5	rate	rate	NOUN
ejpam-6596	31	6	is	be	AUX
ejpam-6596	31	7	used	use	VERB
ejpam-6596	31	8	in	in	ADP
ejpam-6596	31	9	various	various	ADJ
ejpam-6596	31	10	epidemic	epidemic	NOUN
ejpam-6596	31	11	models	model	NOUN
ejpam-6596	31	12	[	[	X
ejpam-6596	31	13	18–21	18–21	NUM
ejpam-6596	31	14	]	]	PUNCT
ejpam-6596	31	15	.	.	PUNCT
ejpam-6596	32	1	the	the	DET
ejpam-6596	32	2	saturated	saturate	VERB
ejpam-6596	32	3	incidence	incidence	NOUN
ejpam-6596	32	4	rate	rate	NOUN
ejpam-6596	32	5	hsi	hsi	PROPN
ejpam-6596	32	6	1+αi	1+αi	NUM
ejpam-6596	32	7	was	be	AUX
ejpam-6596	32	8	first	first	ADV
ejpam-6596	32	9	proposed	propose	VERB
ejpam-6596	32	10	by	by	ADP
ejpam-6596	32	11	capasso	capasso	PROPN
ejpam-6596	32	12	and	and	CCONJ
ejpam-6596	32	13	serlo	serlo	PROPN
ejpam-6596	33	1	[	[	X
ejpam-6596	33	2	22	22	NUM
ejpam-6596	33	3	]	]	PUNCT
ejpam-6596	33	4	.	.	PUNCT
ejpam-6596	34	1	whereas	whereas	SCONJ
ejpam-6596	34	2	hi	hi	INTJ
ejpam-6596	34	3	1+αi	1+αi	NUM
ejpam-6596	34	4	tends	tend	VERB
ejpam-6596	34	5	to	to	ADP
ejpam-6596	34	6	a	a	DET
ejpam-6596	34	7	saturation	saturation	NOUN
ejpam-6596	34	8	level	level	NOUN
ejpam-6596	34	9	when	when	SCONJ
ejpam-6596	34	10	i	i	PRON
ejpam-6596	34	11	is	be	AUX
ejpam-6596	34	12	big	big	ADJ
ejpam-6596	34	13	hi	hi	ADJ
ejpam-6596	34	14	measures	measure	NOUN
ejpam-6596	34	15	the	the	DET
ejpam-6596	34	16	force	force	NOUN
ejpam-6596	34	17	of	of	ADP
ejpam-6596	34	18	infection	infection	NOUN
ejpam-6596	34	19	when	when	SCONJ
ejpam-6596	34	20	the	the	DET
ejpam-6596	34	21	disease	disease	NOUN
ejpam-6596	34	22	is	be	AUX
ejpam-6596	34	23	entering	enter	VERB
ejpam-6596	34	24	a	a	DET
ejpam-6596	34	25	fully	fully	ADV
ejpam-6596	34	26	susceptible	susceptible	ADJ
ejpam-6596	34	27	population	population	NOUN
ejpam-6596	34	28	,	,	PUNCT
ejpam-6596	34	29	and	and	CCONJ
ejpam-6596	34	30	1	1	NUM
ejpam-6596	34	31	1+αi	1+αi	NUM
ejpam-6596	34	32	measures	measure	VERB
ejpam-6596	34	33	the	the	DET
ejpam-6596	34	34	inhibition	inhibition	NOUN
ejpam-6596	34	35	effect	effect	NOUN
ejpam-6596	34	36	from	from	ADP
ejpam-6596	34	37	behavioural	behavioural	ADJ
ejpam-6596	34	38	changes	change	NOUN
ejpam-6596	34	39	in	in	ADP
ejpam-6596	34	40	susceptible	susceptible	ADJ
ejpam-6596	34	41	individuals	individual	NOUN
ejpam-6596	34	42	as	as	SCONJ
ejpam-6596	34	43	their	their	PRON
ejpam-6596	34	44	numbers	number	NOUN
ejpam-6596	34	45	rise	rise	VERB
ejpam-6596	34	46	or	or	CCONJ
ejpam-6596	34	47	from	from	ADP
ejpam-6596	34	48	the	the	DET
ejpam-6596	34	49	overpopulation	overpopulation	NOUN
ejpam-6596	34	50	effect	effect	NOUN
ejpam-6596	34	51	of	of	ADP
ejpam-6596	34	52	the	the	DET
ejpam-6596	34	53	infected	infected	ADJ
ejpam-6596	34	54	people	people	NOUN
ejpam-6596	34	55	.	.	PUNCT
ejpam-6596	35	1	due	due	ADP
ejpam-6596	35	2	to	to	ADP
ejpam-6596	35	3	the	the	DET
ejpam-6596	35	4	inclusion	inclusion	NOUN
ejpam-6596	35	5	of	of	ADP
ejpam-6596	35	6	the	the	DET
ejpam-6596	35	7	behavioral	behavioral	ADJ
ejpam-6596	35	8	changes	change	NOUN
ejpam-6596	35	9	and	and	CCONJ
ejpam-6596	35	10	crowding	crowd	VERB
ejpam-6596	35	11	effects	effect	NOUN
ejpam-6596	35	12	of	of	ADP
ejpam-6596	35	13	the	the	DET
ejpam-6596	35	14	infected	infected	ADJ
ejpam-6596	35	15	peoples	people	NOUN
ejpam-6596	35	16	and	and	CCONJ
ejpam-6596	35	17	the	the	DET
ejpam-6596	35	18	prevention	prevention	NOUN
ejpam-6596	35	19	of	of	ADP
ejpam-6596	35	20	the	the	DET
ejpam-6596	35	21	contact	contact	NOUN
ejpam-6596	35	22	rate	rate	NOUN
ejpam-6596	35	23	’s	’s	PART
ejpam-6596	35	24	unboundedness	unboundedness	NOUN
ejpam-6596	35	25	by	by	ADP
ejpam-6596	35	26	the	the	DET
ejpam-6596	35	27	selection	selection	NOUN
ejpam-6596	35	28	of	of	ADP
ejpam-6596	35	29	acceptable	acceptable	ADJ
ejpam-6596	35	30	parameters	parameter	NOUN
ejpam-6596	35	31	,	,	PUNCT
ejpam-6596	35	32	this	this	DET
ejpam-6596	35	33	incidence	incidence	NOUN
ejpam-6596	35	34	rate	rate	NOUN
ejpam-6596	35	35	is	be	AUX
ejpam-6596	35	36	more	more	ADV
ejpam-6596	35	37	rational	rational	ADJ
ejpam-6596	35	38	than	than	ADP
ejpam-6596	35	39	the	the	DET
ejpam-6596	35	40	bilinear	bilinear	ADJ
ejpam-6596	35	41	incidence	incidence	NOUN
ejpam-6596	35	42	rate	rate	NOUN
ejpam-6596	35	43	and	and	CCONJ
ejpam-6596	35	44	has	have	AUX
ejpam-6596	35	45	been	be	AUX
ejpam-6596	35	46	utilized	utilize	VERB
ejpam-6596	35	47	in	in	ADP
ejpam-6596	35	48	numerous	numerous	ADJ
ejpam-6596	35	49	pandemic	pandemic	ADJ
ejpam-6596	35	50	simulations	simulation	NOUN
ejpam-6596	35	51	.	.	PUNCT
ejpam-6596	36	1	2	2	X
ejpam-6596	36	2	.	.	X
ejpam-6596	36	3	model	model	NOUN
ejpam-6596	36	4	formulation	formulation	NOUN
ejpam-6596	36	5	in	in	ADP
ejpam-6596	36	6	this	this	DET
ejpam-6596	36	7	section	section	NOUN
ejpam-6596	36	8	,	,	PUNCT
ejpam-6596	36	9	we	we	PRON
ejpam-6596	36	10	construct	construct	VERB
ejpam-6596	36	11	a	a	DET
ejpam-6596	36	12	general	general	ADJ
ejpam-6596	36	13	disease	disease	NOUN
ejpam-6596	36	14	model	model	NOUN
ejpam-6596	36	15	and	and	CCONJ
ejpam-6596	36	16	partition	partition	VERB
ejpam-6596	36	17	the	the	DET
ejpam-6596	36	18	total	total	ADJ
ejpam-6596	36	19	population	population	NOUN
ejpam-6596	36	20	n(t	n(t	PROPN
ejpam-6596	36	21	)	)	PUNCT
ejpam-6596	36	22	into	into	ADP
ejpam-6596	36	23	five	five	NUM
ejpam-6596	36	24	parts	part	NOUN
ejpam-6596	36	25	:	:	PUNCT
ejpam-6596	36	26	s	s	VERB
ejpam-6596	36	27	specially	specially	ADV
ejpam-6596	36	28	the	the	DET
ejpam-6596	36	29	susceptible	susceptible	ADJ
ejpam-6596	36	30	individuals	individual	NOUN
ejpam-6596	36	31	,	,	PUNCT
ejpam-6596	36	32	e	e	X
ejpam-6596	36	33	the	the	DET
ejpam-6596	36	34	exposed	expose	VERB
ejpam-6596	36	35	people	people	NOUN
ejpam-6596	36	36	,	,	PUNCT
ejpam-6596	36	37	i	i	PRON
ejpam-6596	36	38	the	the	DET
ejpam-6596	36	39	infectious	infectious	ADJ
ejpam-6596	36	40	density	density	NOUN
ejpam-6596	36	41	,	,	PUNCT
ejpam-6596	36	42	q	q	NOUN
ejpam-6596	36	43	the	the	DET
ejpam-6596	36	44	quarantine	quarantine	NOUN
ejpam-6596	36	45	density	density	NOUN
ejpam-6596	36	46	,	,	PUNCT
ejpam-6596	36	47	and	and	CCONJ
ejpam-6596	36	48	r	r	X
ejpam-6596	36	49	the	the	DET
ejpam-6596	36	50	people	people	NOUN
ejpam-6596	36	51	which	which	PRON
ejpam-6596	36	52	recovered	recover	VERB
ejpam-6596	36	53	from	from	ADP
ejpam-6596	36	54	disease	disease	NOUN
ejpam-6596	36	55	.	.	PUNCT
ejpam-6596	37	1	the	the	DET
ejpam-6596	37	2	saturated	saturate	VERB
ejpam-6596	37	3	incidence	incidence	NOUN
ejpam-6596	37	4	rate	rate	NOUN
ejpam-6596	37	5	hsi	hsi	PROPN
ejpam-6596	37	6	1+αi	1+αi	NUM
ejpam-6596	37	7	is	be	AUX
ejpam-6596	37	8	adopted	adopt	VERB
ejpam-6596	37	9	to	to	PART
ejpam-6596	37	10	enhance	enhance	VERB
ejpam-6596	37	11	biological	biological	ADJ
ejpam-6596	37	12	realism	realism	NOUN
ejpam-6596	37	13	.	.	PUNCT
ejpam-6596	38	1	unlike	unlike	ADP
ejpam-6596	38	2	the	the	DET
ejpam-6596	38	3	bilinear	bilinear	NOUN
ejpam-6596	38	4	form	form	NOUN
ejpam-6596	38	5	hsi	hsi	PROPN
ejpam-6596	38	6	,	,	PUNCT
ejpam-6596	38	7	it	it	PRON
ejpam-6596	38	8	incorporates	incorporate	VERB
ejpam-6596	38	9	saturation	saturation	NOUN
ejpam-6596	38	10	effects	effect	NOUN
ejpam-6596	38	11	:	:	PUNCT
ejpam-6596	38	12	as	as	ADP
ejpam-6596	38	13	the	the	DET
ejpam-6596	38	14	infected	infected	ADJ
ejpam-6596	38	15	population	population	NOUN
ejpam-6596	38	16	i	i	PRON
ejpam-6596	38	17	grows	grow	VERB
ejpam-6596	38	18	,	,	PUNCT
ejpam-6596	38	19	the	the	DET
ejpam-6596	38	20	term	term	NOUN
ejpam-6596	38	21	1	1	NUM
ejpam-6596	38	22	1+αi	1+αi	NUM
ejpam-6596	38	23	models	model	NOUN
ejpam-6596	38	24	reduced	reduce	VERB
ejpam-6596	38	25	transmission	transmission	NOUN
ejpam-6596	38	26	due	due	ADP
ejpam-6596	38	27	to	to	ADP
ejpam-6596	38	28	behavioral	behavioral	ADJ
ejpam-6596	38	29	changes	change	NOUN
ejpam-6596	38	30	or	or	CCONJ
ejpam-6596	38	31	limited	limited	ADJ
ejpam-6596	38	32	contact	contact	NOUN
ejpam-6596	38	33	capacity	capacity	NOUN
ejpam-6596	38	34	.	.	PUNCT
ejpam-6596	39	1	this	this	PRON
ejpam-6596	39	2	prevents	prevent	VERB
ejpam-6596	39	3	unrealistic	unrealistic	ADJ
ejpam-6596	39	4	unbounded	unbounded	ADJ
ejpam-6596	39	5	growth	growth	NOUN
ejpam-6596	39	6	in	in	ADP
ejpam-6596	39	7	infection	infection	NOUN
ejpam-6596	39	8	force	force	NOUN
ejpam-6596	39	9	,	,	PUNCT
ejpam-6596	39	10	offering	offer	VERB
ejpam-6596	39	11	a	a	DET
ejpam-6596	39	12	more	more	ADV
ejpam-6596	39	13	accurate	accurate	ADJ
ejpam-6596	39	14	representation	representation	NOUN
ejpam-6596	39	15	of	of	ADP
ejpam-6596	39	16	real	real	ADJ
ejpam-6596	39	17	-	-	PUNCT
ejpam-6596	39	18	world	world	NOUN
ejpam-6596	39	19	epidemic	epidemic	NOUN
ejpam-6596	39	20	dynamics	dynamic	NOUN
ejpam-6596	39	21	.	.	PUNCT
ejpam-6596	40	1	the	the	DET
ejpam-6596	40	2	suggested	suggest	VERB
ejpam-6596	40	3	general	general	ADJ
ejpam-6596	40	4	disease	disease	PROPN
ejpam-6596	40	5	n.	n.	PROPN
ejpam-6596	40	6	gul	gul	PROPN
ejpam-6596	40	7	et	et	PROPN
ejpam-6596	40	8	al	al	PROPN
ejpam-6596	40	9	.	.	PUNCT
ejpam-6596	40	10	/	/	SYM
ejpam-6596	40	11	eur	eur	PROPN
ejpam-6596	40	12	.	.	PUNCT
ejpam-6596	41	1	j.	j.	PROPN
ejpam-6596	41	2	pure	pure	PROPN
ejpam-6596	41	3	appl	appl	PROPN
ejpam-6596	41	4	.	.	PROPN
ejpam-6596	41	5	math	math	PROPN
ejpam-6596	41	6	,	,	PUNCT
ejpam-6596	41	7	18	18	NUM
ejpam-6596	41	8	(	(	PUNCT
ejpam-6596	41	9	4	4	NUM
ejpam-6596	41	10	)	)	PUNCT
ejpam-6596	41	11	(	(	PUNCT
ejpam-6596	41	12	2025	2025	NUM
ejpam-6596	41	13	)	)	PUNCT
ejpam-6596	41	14	,	,	PUNCT
ejpam-6596	41	15	6596	6596	NUM
ejpam-6596	41	16	3	3	NUM
ejpam-6596	41	17	of	of	ADP
ejpam-6596	41	18	23	23	NUM
ejpam-6596	41	19	model	model	NOUN
ejpam-6596	41	20	is	be	AUX
ejpam-6596	41	21	represented	represent	VERB
ejpam-6596	41	22	by	by	ADP
ejpam-6596	41	23	the	the	DET
ejpam-6596	41	24	set	set	NOUN
ejpam-6596	41	25	of	of	ADP
ejpam-6596	41	26	autonomous	autonomous	ADJ
ejpam-6596	41	27	differential	differential	ADJ
ejpam-6596	41	28	equations	equation	NOUN
ejpam-6596	41	29	below:	below:	NOUN
ejpam-6596	41	30	ds	ds	NOUN
ejpam-6596	41	31	dt	dt	NOUN
ejpam-6596	41	32	=	=	SYM
ejpam-6596	41	33	g	g	PROPN
ejpam-6596	41	34	−	−	PROPN
ejpam-6596	41	35	hsi	hsi	PROPN
ejpam-6596	41	36	1	1	NUM
ejpam-6596	41	37	+	+	CCONJ
ejpam-6596	41	38	αi	αi	VERB
ejpam-6596	41	39	−	−	X
ejpam-6596	42	1	(	(	PUNCT
ejpam-6596	42	2	m+	m+	NUM
ejpam-6596	42	3	b1)s	b1)s	PROPN
ejpam-6596	42	4	,	,	PUNCT
ejpam-6596	42	5	de	de	X
ejpam-6596	42	6	dt	dt	NOUN
ejpam-6596	42	7	=	=	SYM
ejpam-6596	42	8	hsi	hsi	PROPN
ejpam-6596	42	9	1	1	NUM
ejpam-6596	43	1	+	+	CCONJ
ejpam-6596	43	2	αi	αi	VERB
ejpam-6596	43	3	−	−	PROPN
ejpam-6596	44	1	(	(	PUNCT
ejpam-6596	44	2	m+	m+	NUM
ejpam-6596	44	3	c+	c+	NOUN
ejpam-6596	44	4	b2)e	b2)e	PROPN
ejpam-6596	44	5	,	,	PUNCT
ejpam-6596	44	6	di	di	NOUN
ejpam-6596	44	7	dt	dt	NOUN
ejpam-6596	44	8	=	=	SYM
ejpam-6596	44	9	ce	ce	PROPN
ejpam-6596	44	10	−	−	PROPN
ejpam-6596	45	1	(	(	PUNCT
ejpam-6596	45	2	m+	m+	NUM
ejpam-6596	45	3	b3	b3	PROPN
ejpam-6596	45	4	+	+	CCONJ
ejpam-6596	45	5	q	q	PROPN
ejpam-6596	45	6	+	+	NUM
ejpam-6596	45	7	µ	µ	X
ejpam-6596	45	8	)	)	PUNCT
ejpam-6596	45	9	i	i	NOUN
ejpam-6596	45	10	,	,	PUNCT
ejpam-6596	45	11	dq	dq	NOUN
ejpam-6596	45	12	dt	dt	NOUN
ejpam-6596	45	13	=	=	PUNCT
ejpam-6596	45	14	b1s	b1s	PROPN
ejpam-6596	45	15	+	+	CCONJ
ejpam-6596	45	16	b2e	b2e	X
ejpam-6596	45	17	+	+	CCONJ
ejpam-6596	45	18	b3i	b3i	NOUN
ejpam-6596	45	19	−	−	PROPN
ejpam-6596	45	20	(	(	PUNCT
ejpam-6596	45	21	m+	m+	NUM
ejpam-6596	45	22	p)q	p)q	NOUN
ejpam-6596	45	23	,	,	PUNCT
ejpam-6596	45	24	dr	dr	PROPN
ejpam-6596	45	25	dt	dt	PROPN
ejpam-6596	45	26	=	=	PUNCT
ejpam-6596	45	27	qi	qi	PROPN
ejpam-6596	45	28	+	+	NOUN
ejpam-6596	45	29	pq−mr	pq−mr	PROPN
ejpam-6596	45	30	.	.	PUNCT
ejpam-6596	46	1	(	(	PUNCT
ejpam-6596	46	2	1	1	X
ejpam-6596	46	3	)	)	PUNCT
ejpam-6596	46	4	the	the	DET
ejpam-6596	46	5	system	system	NOUN
ejpam-6596	46	6	indicated	indicate	VERB
ejpam-6596	46	7	above	above	ADV
ejpam-6596	46	8	is	be	AUX
ejpam-6596	46	9	subject	subject	ADJ
ejpam-6596	46	10	to	to	ADP
ejpam-6596	46	11	the	the	DET
ejpam-6596	46	12	following	follow	VERB
ejpam-6596	46	13	preconditions	precondition	NOUN
ejpam-6596	46	14	.	.	PUNCT
ejpam-6596	47	1	s(0	s(0	PROPN
ejpam-6596	47	2	)	)	PUNCT
ejpam-6596	47	3	>	>	X
ejpam-6596	47	4	0	0	NUM
ejpam-6596	47	5	,	,	PUNCT
ejpam-6596	47	6	e(0	e(0	NOUN
ejpam-6596	47	7	)	)	PUNCT
ejpam-6596	47	8	≥	≥	NOUN
ejpam-6596	47	9	0	0	NUM
ejpam-6596	47	10	,	,	PUNCT
ejpam-6596	47	11	i(0	i(0	PROPN
ejpam-6596	47	12	)	)	PUNCT
ejpam-6596	47	13	≥	≥	NOUN
ejpam-6596	47	14	0	0	NUM
ejpam-6596	47	15	,	,	PUNCT
ejpam-6596	47	16	q(0	q(0	PROPN
ejpam-6596	47	17	)	)	PUNCT
ejpam-6596	47	18	≥	≥	NOUN
ejpam-6596	47	19	0	0	NUM
ejpam-6596	47	20	,	,	PUNCT
ejpam-6596	47	21	r(0	r(0	PROPN
ejpam-6596	47	22	)	)	PUNCT
ejpam-6596	47	23	≥	≥	NOUN
ejpam-6596	47	24	0	0	NUM
ejpam-6596	47	25	.	.	PUNCT
ejpam-6596	48	1	n(t	n(t	PROPN
ejpam-6596	48	2	)	)	PUNCT
ejpam-6596	49	1	=	=	SYM
ejpam-6596	49	2	s	s	PART
ejpam-6596	50	1	+	+	NUM
ejpam-6596	50	2	e	e	NOUN
ejpam-6596	50	3	+	+	CCONJ
ejpam-6596	50	4	i	i	PRON
ejpam-6596	50	5	+	+	VERB
ejpam-6596	50	6	q+r	q+r	VERB
ejpam-6596	50	7	displays	display	VERB
ejpam-6596	50	8	the	the	DET
ejpam-6596	50	9	total	total	ADJ
ejpam-6596	50	10	size	size	NOUN
ejpam-6596	50	11	of	of	ADP
ejpam-6596	50	12	the	the	DET
ejpam-6596	50	13	community	community	NOUN
ejpam-6596	50	14	.	.	PUNCT
ejpam-6596	51	1	with	with	ADP
ejpam-6596	51	2	the	the	DET
ejpam-6596	51	3	use	use	NOUN
ejpam-6596	51	4	of	of	ADP
ejpam-6596	51	5	the	the	DET
ejpam-6596	51	6	derivative	derivative	NOUN
ejpam-6596	51	7	and	and	CCONJ
ejpam-6596	51	8	model	model	NOUN
ejpam-6596	51	9	(	(	PUNCT
ejpam-6596	51	10	3.0.1	3.0.1	NUM
ejpam-6596	51	11	)	)	PUNCT
ejpam-6596	51	12	,	,	PUNCT
ejpam-6596	51	13	we	we	PRON
ejpam-6596	51	14	can	can	AUX
ejpam-6596	51	15	dn	dn	VERB
ejpam-6596	51	16	dt	dt	PUNCT
ejpam-6596	52	1	=	=	PUNCT
ejpam-6596	52	2	g	g	PROPN
ejpam-6596	52	3	−ms	−ms	NOUN
ejpam-6596	52	4	−me	−me	NOUN
ejpam-6596	53	1	−mi	−mi	PROPN
ejpam-6596	53	2	−mq−mr−	−mq−mr−	X
ejpam-6596	53	3	µi	µi	ADV
ejpam-6596	53	4	=	=	PUNCT
ejpam-6596	53	5	g	g	NOUN
ejpam-6596	53	6	−m(s	−m(s	NOUN
ejpam-6596	54	1	+	+	CCONJ
ejpam-6596	54	2	e	e	X
ejpam-6596	54	3	+	+	CCONJ
ejpam-6596	54	4	i	i	PRON
ejpam-6596	54	5	+	+	PROPN
ejpam-6596	54	6	q+r)−	q+r)−	NOUN
ejpam-6596	54	7	µi	µi	INTJ
ejpam-6596	54	8	.	.	PUNCT
ejpam-6596	55	1	however	however	ADV
ejpam-6596	55	2	,	,	PUNCT
ejpam-6596	55	3	s	s	PART
ejpam-6596	56	1	+	+	NUM
ejpam-6596	56	2	e	e	NOUN
ejpam-6596	56	3	+	+	CCONJ
ejpam-6596	56	4	i	i	PRON
ejpam-6596	56	5	+	+	VERB
ejpam-6596	56	6	q+r	q+r	NUM
ejpam-6596	56	7	=	=	SYM
ejpam-6596	56	8	n	n	CCONJ
ejpam-6596	56	9	,	,	PUNCT
ejpam-6596	56	10	the	the	DET
ejpam-6596	56	11	final	final	ADJ
ejpam-6596	56	12	equation	equation	NOUN
ejpam-6596	56	13	has	have	VERB
ejpam-6596	56	14	the	the	DET
ejpam-6596	56	15	following	follow	VERB
ejpam-6596	56	16	form	form	NOUN
ejpam-6596	56	17	:	:	PUNCT
ejpam-6596	56	18	dn	dn	NOUN
ejpam-6596	56	19	dt	dt	NOUN
ejpam-6596	57	1	=	=	PUNCT
ejpam-6596	57	2	g	g	PROPN
ejpam-6596	57	3	−mn	−mn	NUM
ejpam-6596	57	4	−	−	PROPN
ejpam-6596	58	1	µi	µi	PROPN
ejpam-6596	58	2	.	.	PUNCT
ejpam-6596	59	1	this	this	PRON
ejpam-6596	59	2	may	may	AUX
ejpam-6596	59	3	be	be	AUX
ejpam-6596	59	4	stated	state	VERB
ejpam-6596	59	5	even	even	ADV
ejpam-6596	59	6	more	more	ADV
ejpam-6596	59	7	simply	simply	ADV
ejpam-6596	59	8	as	as	SCONJ
ejpam-6596	59	9	:	:	PUNCT
ejpam-6596	59	10	dn	dn	NOUN
ejpam-6596	59	11	dt	dt	NOUN
ejpam-6596	59	12	≤	≤	PROPN
ejpam-6596	59	13	g	g	ADP
ejpam-6596	59	14	−mn	−mn	PROPN
ejpam-6596	59	15	.	.	PUNCT
ejpam-6596	60	1	(	(	PUNCT
ejpam-6596	60	2	2	2	X
ejpam-6596	60	3	)	)	PUNCT
ejpam-6596	60	4	the	the	DET
ejpam-6596	60	5	final	final	ADJ
ejpam-6596	60	6	inequality	inequality	NOUN
ejpam-6596	60	7	can	can	AUX
ejpam-6596	60	8	be	be	AUX
ejpam-6596	60	9	solved	solve	VERB
ejpam-6596	60	10	as	as	SCONJ
ejpam-6596	60	11	follows	follow	VERB
ejpam-6596	60	12	by	by	ADP
ejpam-6596	60	13	integrating	integrate	VERB
ejpam-6596	60	14	with	with	ADP
ejpam-6596	60	15	respect	respect	NOUN
ejpam-6596	60	16	to	to	ADP
ejpam-6596	60	17	t	t	NOUN
ejpam-6596	60	18	and	and	CCONJ
ejpam-6596	60	19	using	use	VERB
ejpam-6596	60	20	the	the	DET
ejpam-6596	60	21	provided	provide	VERB
ejpam-6596	60	22	initial	initial	ADJ
ejpam-6596	60	23	 	 	SPACE
ejpam-6596	60	24	conditions	condition	NOUN
ejpam-6596	60	25	:	:	PUNCT
ejpam-6596	60	26	n(t	n(t	X
ejpam-6596	60	27	)	)	PUNCT
ejpam-6596	61	1	=	=	PUNCT
ejpam-6596	61	2	g	g	PROPN
ejpam-6596	61	3	m	m	PROPN
ejpam-6596	61	4	+	+	CCONJ
ejpam-6596	61	5	ce−mt	ce−mt	ADJ
ejpam-6596	61	6	.	.	PUNCT
ejpam-6596	62	1	simplifying	simplify	VERB
ejpam-6596	62	2	further	far	ADV
ejpam-6596	62	3	and	and	CCONJ
ejpam-6596	62	4	using	use	VERB
ejpam-6596	62	5	the	the	DET
ejpam-6596	62	6	initial	initial	ADJ
ejpam-6596	62	7	conditions	condition	NOUN
ejpam-6596	62	8	 	 	SPACE
ejpam-6596	62	9	n(0	n(0	PROPN
ejpam-6596	62	10	)	)	PUNCT
ejpam-6596	62	11	=	=	SYM
ejpam-6596	62	12	n0	n0	PROPN
ejpam-6596	62	13	,	,	PUNCT
ejpam-6596	62	14	we	we	PRON
ejpam-6596	62	15	obtain	obtain	VERB
ejpam-6596	62	16	n(t	n(t	NOUN
ejpam-6596	62	17	)	)	PUNCT
ejpam-6596	62	18	≤	≤	NOUN
ejpam-6596	63	1	g	g	ADP
ejpam-6596	63	2	m	m	PROPN
ejpam-6596	63	3	+	+	CCONJ
ejpam-6596	63	4	[	[	PUNCT
ejpam-6596	63	5	n(0)−	n(0)−	NUM
ejpam-6596	63	6	g	g	NOUN
ejpam-6596	63	7	m	m	PROPN
ejpam-6596	63	8	]	]	PUNCT
ejpam-6596	63	9	e−mt	e−mt	PROPN
ejpam-6596	63	10	.	.	PUNCT
ejpam-6596	64	1	on	on	ADP
ejpam-6596	64	2	re	re	VERB
ejpam-6596	64	3	-	-	VERB
ejpam-6596	64	4	arranging	arrange	VERB
ejpam-6596	64	5	we	we	PRON
ejpam-6596	64	6	have	have	VERB
ejpam-6596	64	7	,	,	PUNCT
ejpam-6596	64	8	n(t	n(t	PROPN
ejpam-6596	64	9	)	)	PUNCT
ejpam-6596	64	10	≤	≤	NOUN
ejpam-6596	64	11	g	g	ADP
ejpam-6596	64	12	m	m	PROPN
ejpam-6596	64	13	(	(	PUNCT
ejpam-6596	64	14	1−	1−	NUM
ejpam-6596	64	15	e−mt	e−mt	PROPN
ejpam-6596	64	16	)	)	PUNCT
ejpam-6596	65	1	+	+	NOUN
ejpam-6596	65	2	n(0)e−mt	n(0)e−mt	NOUN
ejpam-6596	65	3	it	it	PRON
ejpam-6596	65	4	is	be	AUX
ejpam-6596	65	5	confirmed	confirm	VERB
ejpam-6596	65	6	by	by	ADP
ejpam-6596	65	7	initial	initial	ADJ
ejpam-6596	65	8	conditions	condition	NOUN
ejpam-6596	65	9	that	that	SCONJ
ejpam-6596	65	10	n(0	n(0	PROPN
ejpam-6596	65	11	)	)	PUNCT
ejpam-6596	65	12	≥	≥	NOUN
ejpam-6596	65	13	0	0	NUM
ejpam-6596	65	14	.	.	PUNCT
ejpam-6596	66	1	it	it	PRON
ejpam-6596	66	2	may	may	AUX
ejpam-6596	66	3	also	also	ADV
ejpam-6596	66	4	be	be	AUX
ejpam-6596	66	5	noted	note	VERB
ejpam-6596	66	6	from	from	ADP
ejpam-6596	66	7	the	the	DET
ejpam-6596	66	8	last	last	ADJ
ejpam-6596	66	9	inequality	inequality	NOUN
ejpam-6596	66	10	that	that	SCONJ
ejpam-6596	66	11	the	the	DET
ejpam-6596	66	12	feasible	feasible	ADJ
ejpam-6596	66	13	area	area	NOUN
ejpam-6596	66	14	of	of	ADP
ejpam-6596	66	15	the	the	DET
ejpam-6596	66	16	system	system	NOUN
ejpam-6596	66	17	is	be	AUX
ejpam-6596	66	18	reached	reach	VERB
ejpam-6596	66	19	when	when	SCONJ
ejpam-6596	66	20	the	the	DET
ejpam-6596	66	21	total	total	ADJ
ejpam-6596	66	22	population	population	NOUN
ejpam-6596	66	23	n(t	n(t	NOUN
ejpam-6596	66	24	)	)	PUNCT
ejpam-6596	66	25	remains	remain	VERB
ejpam-6596	66	26	positive	positive	ADJ
ejpam-6596	66	27	and	and	CCONJ
ejpam-6596	66	28	bounded	bound	VERB
ejpam-6596	66	29	.	.	PUNCT
ejpam-6596	67	1	n.	n.	PROPN
ejpam-6596	67	2	gul	gul	PROPN
ejpam-6596	67	3	et	et	PROPN
ejpam-6596	67	4	al	al	PROPN
ejpam-6596	67	5	.	.	PUNCT
ejpam-6596	67	6	/	/	SYM
ejpam-6596	67	7	eur	eur	PROPN
ejpam-6596	67	8	.	.	PUNCT
ejpam-6596	68	1	j.	j.	PROPN
ejpam-6596	68	2	pure	pure	PROPN
ejpam-6596	68	3	appl	appl	PROPN
ejpam-6596	68	4	.	.	PROPN
ejpam-6596	68	5	math	math	PROPN
ejpam-6596	68	6	,	,	PUNCT
ejpam-6596	68	7	18	18	NUM
ejpam-6596	68	8	(	(	PUNCT
ejpam-6596	68	9	4	4	NUM
ejpam-6596	68	10	)	)	PUNCT
ejpam-6596	68	11	(	(	PUNCT
ejpam-6596	68	12	2025	2025	NUM
ejpam-6596	68	13	)	)	PUNCT
ejpam-6596	68	14	,	,	PUNCT
ejpam-6596	68	15	6596	6596	NUM
ejpam-6596	68	16	4	4	NUM
ejpam-6596	68	17	of	of	ADP
ejpam-6596	68	18	23	23	NUM
ejpam-6596	68	19	3	3	NUM
ejpam-6596	68	20	.	.	PUNCT
ejpam-6596	69	1	positivity	positivity	NOUN
ejpam-6596	69	2	of	of	ADP
ejpam-6596	69	3	solution	solution	NOUN
ejpam-6596	69	4	this	this	PRON
ejpam-6596	69	5	proves	prove	VERB
ejpam-6596	69	6	that	that	SCONJ
ejpam-6596	69	7	every	every	DET
ejpam-6596	69	8	phase	phase	NOUN
ejpam-6596	69	9	pathway	pathway	NOUN
ejpam-6596	69	10	that	that	PRON
ejpam-6596	69	11	begins	begin	VERB
ejpam-6596	69	12	in	in	ADP
ejpam-6596	69	13	the	the	DET
ejpam-6596	69	14	positive	positive	ADJ
ejpam-6596	69	15	area	area	NOUN
ejpam-6596	69	16	r5	r5	PROPN
ejpam-6596	69	17	ultimately	ultimately	ADV
ejpam-6596	69	18	occurs	occur	VERB
ejpam-6596	69	19	in	in	ADP
ejpam-6596	69	20	the	the	DET
ejpam-6596	69	21	phase	phase	NOUN
ejpam-6596	69	22	space	space	NOUN
ejpam-6596	69	23	reaches	reach	VERB
ejpam-6596	69	24	and	and	CCONJ
ejpam-6596	69	25	remains	remain	VERB
ejpam-6596	69	26	in	in	ADP
ejpam-6596	69	27	the	the	DET
ejpam-6596	69	28	possibility	possibility	NOUN
ejpam-6596	69	29	area	area	NOUN
ejpam-6596	69	30	triangle	triangle	NOUN
ejpam-6596	69	31	(	(	PUNCT
ejpam-6596	69	32	the	the	DET
ejpam-6596	69	33	model	model	NOUN
ejpam-6596	69	34	falls	fall	VERB
ejpam-6596	69	35	into	into	ADP
ejpam-6596	69	36	the	the	DET
ejpam-6596	69	37	biologically	biologically	ADV
ejpam-6596	69	38	possible	possible	ADJ
ejpam-6596	69	39	area	area	NOUN
ejpam-6596	69	40	)	)	PUNCT
ejpam-6596	69	41	.	.	PUNCT
ejpam-6596	70	1	this	this	PRON
ejpam-6596	70	2	can	can	AUX
ejpam-6596	70	3	be	be	AUX
ejpam-6596	70	4	accomplished	accomplish	VERB
ejpam-6596	70	5	by	by	ADP
ejpam-6596	70	6	demonstrating	demonstrate	VERB
ejpam-6596	70	7	that	that	SCONJ
ejpam-6596	70	8	the	the	DET
ejpam-6596	70	9	triangle	triangle	NOUN
ejpam-6596	70	10	is	be	AUX
ejpam-6596	70	11	a	a	DET
ejpam-6596	70	12	positively	positively	ADV
ejpam-6596	70	13	invariant	invariant	ADJ
ejpam-6596	70	14	set	set	NOUN
ejpam-6596	70	15	and	and	CCONJ
ejpam-6596	70	16	the	the	DET
ejpam-6596	70	17	systems	system	NOUN
ejpam-6596	70	18	global	global	ADJ
ejpam-6596	70	19	attractor	attractor	NOUN
ejpam-6596	70	20	.	.	PUNCT
ejpam-6596	71	1	the	the	DET
ejpam-6596	71	2	positivity	positivity	NOUN
ejpam-6596	71	3	of	of	ADP
ejpam-6596	71	4	the	the	DET
ejpam-6596	71	5	proof	proof	NOUN
ejpam-6596	71	6	is	be	AUX
ejpam-6596	71	7	determined	determine	VERB
ejpam-6596	71	8	by	by	ADP
ejpam-6596	71	9	the	the	DET
ejpam-6596	71	10	following	follow	VERB
ejpam-6596	71	11	theorem	theorem	PROPN
ejpam-6596	71	12	.	.	PUNCT
ejpam-6596	71	13	theorem	theorem	NOUN
ejpam-6596	71	14	1	1	NUM
ejpam-6596	71	15	.	.	PUNCT
ejpam-6596	72	1	the	the	DET
ejpam-6596	72	2	system	system	NOUN
ejpam-6596	72	3	(	(	PUNCT
ejpam-6596	72	4	1	1	X
ejpam-6596	72	5	)	)	PUNCT
ejpam-6596	72	6	novel	novel	ADJ
ejpam-6596	72	7	general	general	ADJ
ejpam-6596	72	8	disease	disease	NOUN
ejpam-6596	72	9	 	 	SPACE
ejpam-6596	72	10	model	model	NOUN
ejpam-6596	72	11	has	have	VERB
ejpam-6596	72	12	a	a	DET
ejpam-6596	72	13	positive	positive	ADJ
ejpam-6596	72	14	solution	solution	NOUN
ejpam-6596	72	15	for	for	ADP
ejpam-6596	72	16	all	all	DET
ejpam-6596	72	17	beginning	begin	VERB
ejpam-6596	72	18	values	value	NOUN
ejpam-6596	72	19	that	that	PRON
ejpam-6596	72	20	are	be	AUX
ejpam-6596	72	21	supplied	supply	VERB
ejpam-6596	72	22	.	.	PUNCT
ejpam-6596	73	1	proof	proof	NOUN
ejpam-6596	73	2	.	.	PUNCT
ejpam-6596	74	1	the	the	DET
ejpam-6596	74	2	first	first	ADJ
ejpam-6596	74	3	equation	equation	NOUN
ejpam-6596	74	4	in	in	ADP
ejpam-6596	74	5	the	the	DET
ejpam-6596	74	6	model	model	NOUN
ejpam-6596	74	7	,	,	PUNCT
ejpam-6596	74	8	may	may	AUX
ejpam-6596	74	9	be	be	AUX
ejpam-6596	74	10	extracted	extract	VERB
ejpam-6596	74	11	as	as	SCONJ
ejpam-6596	74	12	follows	follow	VERB
ejpam-6596	74	13	.	.	PUNCT
ejpam-6596	75	1	ds	ds	ADJ
ejpam-6596	75	2	dt	dt	NOUN
ejpam-6596	75	3	=	=	PUNCT
ejpam-6596	75	4	g	g	PROPN
ejpam-6596	75	5	−	−	PROPN
ejpam-6596	75	6	hsi	hsi	PROPN
ejpam-6596	75	7	1	1	NUM
ejpam-6596	75	8	+	+	CCONJ
ejpam-6596	75	9	αi	αi	VERB
ejpam-6596	75	10	−	−	X
ejpam-6596	75	11	(	(	PUNCT
ejpam-6596	75	12	m+	m+	NUM
ejpam-6596	75	13	b1)s	b1)s	NOUN
ejpam-6596	75	14	.	.	PUNCT
ejpam-6596	76	1	this	this	PRON
ejpam-6596	76	2	can	can	AUX
ejpam-6596	76	3	be	be	AUX
ejpam-6596	76	4	written	write	VERB
ejpam-6596	76	5	as	as	ADP
ejpam-6596	76	6	:	:	PUNCT
ejpam-6596	76	7	ds	ds	INTJ
ejpam-6596	76	8	dt	dt	X
ejpam-6596	76	9	≥	≥	X
ejpam-6596	76	10	(	(	PUNCT
ejpam-6596	76	11	λ(t	λ(t	PROPN
ejpam-6596	76	12	)	)	PUNCT
ejpam-6596	76	13	+	+	CCONJ
ejpam-6596	76	14	(	(	PUNCT
ejpam-6596	76	15	m+	m+	NUM
ejpam-6596	76	16	b1))s	b1))s	PUNCT
ejpam-6596	76	17	≥	≥	NOUN
ejpam-6596	76	18	g	g	NOUN
ejpam-6596	76	19	,	,	PUNCT
ejpam-6596	76	20	by	by	ADP
ejpam-6596	76	21	using	use	VERB
ejpam-6596	76	22	the	the	DET
ejpam-6596	76	23	given	give	VERB
ejpam-6596	76	24	initial	initial	ADJ
ejpam-6596	76	25	conditions	condition	NOUN
ejpam-6596	76	26	,	,	PUNCT
ejpam-6596	76	27	this	this	DET
ejpam-6596	76	28	first	first	ADJ
ejpam-6596	76	29	order	order	NOUN
ejpam-6596	76	30	differential	differential	ADJ
ejpam-6596	76	31	equation	equation	NOUN
ejpam-6596	76	32	’s	’s	PART
ejpam-6596	76	33	solution	solution	NOUN
ejpam-6596	76	34	is	be	AUX
ejpam-6596	76	35	provided	provide	VERB
ejpam-6596	76	36	as	as	ADP
ejpam-6596	76	37	:	:	PUNCT
ejpam-6596	76	38	s(t	s(t	PROPN
ejpam-6596	76	39	)	)	PUNCT
ejpam-6596	76	40	≥	≥	NOUN
ejpam-6596	76	41	e−(m+b1)t−	e−(m+b1)t−	PRON
ejpam-6596	76	42	∫	∫	PROPN
ejpam-6596	76	43	t	t	PROPN
ejpam-6596	76	44	0	0	NUM
ejpam-6596	77	1	λ(t)dt	λ(t)dt	PRON
ejpam-6596	77	2	(	(	PUNCT
ejpam-6596	77	3	s(0	s(0	PROPN
ejpam-6596	77	4	)	)	PUNCT
ejpam-6596	77	5	+	+	CCONJ
ejpam-6596	77	6	g	g	PROPN
ejpam-6596	77	7	∫	∫	PROPN
ejpam-6596	77	8	t	t	PROPN
ejpam-6596	77	9	0	0	NUM
ejpam-6596	78	1	[	[	X
ejpam-6596	78	2	e(m+b1)t1	e(m+b1)t1	PRON
ejpam-6596	78	3	+	+	CCONJ
ejpam-6596	78	4	∫	∫	PROPN
ejpam-6596	78	5	t	t	PROPN
ejpam-6596	78	6	0	0	NUM
ejpam-6596	78	7	λ(t)dt	λ(t)dt	NOUN
ejpam-6596	78	8	]	]	X
ejpam-6596	78	9	)	)	PUNCT
ejpam-6596	78	10	.	.	PUNCT
ejpam-6596	79	1	due	due	ADP
ejpam-6596	79	2	to	to	ADP
ejpam-6596	79	3	the	the	DET
ejpam-6596	79	4	fact	fact	NOUN
ejpam-6596	79	5	that	that	SCONJ
ejpam-6596	79	6	under	under	ADP
ejpam-6596	79	7	integration	integration	NOUN
ejpam-6596	79	8	all	all	DET
ejpam-6596	79	9	the	the	DET
ejpam-6596	79	10	constants	constant	NOUN
ejpam-6596	79	11	in	in	ADP
ejpam-6596	79	12	the	the	DET
ejpam-6596	79	13	suggested	suggest	VERB
ejpam-6596	79	14	model	model	NOUN
ejpam-6596	79	15	are	be	AUX
ejpam-6596	79	16	positive	positive	ADJ
ejpam-6596	79	17	which	which	PRON
ejpam-6596	79	18	possesses	possess	VERB
ejpam-6596	79	19	the	the	DET
ejpam-6596	79	20	nonnegativity	nonnegativity	NOUN
ejpam-6596	79	21	in	in	ADP
ejpam-6596	79	22	both	both	CCONJ
ejpam-6596	79	23	the	the	DET
ejpam-6596	79	24	invariant	invariant	ADJ
ejpam-6596	79	25	and	and	CCONJ
ejpam-6596	79	26	results	result	NOUN
ejpam-6596	79	27	:	:	PUNCT
ejpam-6596	79	28	△	△	X
ejpam-6596	79	29	=	=	SYM
ejpam-6596	79	30	{	{	PUNCT
ejpam-6596	79	31	s(t	s(t	PROPN
ejpam-6596	79	32	)	)	PUNCT
ejpam-6596	79	33	,	,	PUNCT
ejpam-6596	79	34	e(t	e(t	NOUN
ejpam-6596	79	35	)	)	PUNCT
ejpam-6596	79	36	,	,	PUNCT
ejpam-6596	79	37	i(t	i(t	PROPN
ejpam-6596	79	38	)	)	PUNCT
ejpam-6596	79	39	,	,	PUNCT
ejpam-6596	79	40	q(t	q(t	PROPN
ejpam-6596	79	41	)	)	PUNCT
ejpam-6596	79	42	,	,	PUNCT
ejpam-6596	79	43	r(t	r(t	NOUN
ejpam-6596	79	44	)	)	PUNCT
ejpam-6596	79	45	∈	∈	PROPN
ejpam-6596	79	46	r5	r5	PROPN
ejpam-6596	79	47	:	:	PUNCT
ejpam-6596	79	48	s	s	X
ejpam-6596	79	49	>	>	X
ejpam-6596	79	50	‘	'	PUNCT
ejpam-6596	79	51	0(e	0(e	NUM
ejpam-6596	79	52	,	,	PUNCT
ejpam-6596	79	53	i	i	PRON
ejpam-6596	79	54	,	,	PUNCT
ejpam-6596	79	55	q	q	NOUN
ejpam-6596	79	56	,	,	PUNCT
ejpam-6596	79	57	r	r	NOUN
ejpam-6596	79	58	≥	≥	NOUN
ejpam-6596	79	59	0	0	NUM
ejpam-6596	79	60	)	)	PUNCT
ejpam-6596	79	61	,	,	PUNCT
ejpam-6596	79	62	n(t	n(t	PROPN
ejpam-6596	79	63	)	)	PUNCT
ejpam-6596	79	64	≤	≤	NOUN
ejpam-6596	79	65	g	g	NOUN
ejpam-6596	79	66	m	m	NOUN
ejpam-6596	79	67	}	}	PUNCT
ejpam-6596	79	68	.	.	PUNCT
ejpam-6596	80	1	4	4	X
ejpam-6596	80	2	.	.	X
ejpam-6596	80	3	steady	steady	ADJ
ejpam-6596	80	4	states	state	NOUN
ejpam-6596	80	5	to	to	PART
ejpam-6596	80	6	determine	determine	VERB
ejpam-6596	80	7	how	how	SCONJ
ejpam-6596	80	8	the	the	DET
ejpam-6596	80	9	suggested	suggested	ADJ
ejpam-6596	80	10	model	model	NOUN
ejpam-6596	80	11	behaves	behave	VERB
ejpam-6596	80	12	qualitatively	qualitatively	ADV
ejpam-6596	80	13	,	,	PUNCT
ejpam-6596	80	14	there	there	PRON
ejpam-6596	80	15	are	be	VERB
ejpam-6596	80	16	two	two	NUM
ejpam-6596	80	17	different	different	ADJ
ejpam-6596	80	18	kinds	kind	NOUN
ejpam-6596	80	19	of	of	ADP
ejpam-6596	80	20	stable	stable	ADJ
ejpam-6596	80	21	states	state	NOUN
ejpam-6596	80	22	:	:	PUNCT
ejpam-6596	80	23	endemic	endemic	ADJ
ejpam-6596	80	24	equilibriums	equilibrium	NOUN
ejpam-6596	80	25	and	and	CCONJ
ejpam-6596	80	26	equilibriums	equilibrium	NOUN
ejpam-6596	80	27	absence	absence	NOUN
ejpam-6596	80	28	of	of	ADP
ejpam-6596	80	29	illness	illness	NOUN
ejpam-6596	80	30	.	.	PUNCT
ejpam-6596	81	1	the	the	DET
ejpam-6596	81	2	endemic	endemic	ADJ
ejpam-6596	81	3	equilibrium	equilibrium	NOUN
ejpam-6596	81	4	point	point	NOUN
ejpam-6596	81	5	is	be	AUX
ejpam-6596	81	6	represented	represent	VERB
ejpam-6596	81	7	by	by	ADP
ejpam-6596	81	8	e1	e1	NOUN
ejpam-6596	81	9	,	,	PUNCT
ejpam-6596	81	10	while	while	SCONJ
ejpam-6596	81	11	the	the	DET
ejpam-6596	81	12	equilibrium	equilibrium	NOUN
ejpam-6596	81	13	point	point	NOUN
ejpam-6596	81	14	devoid	devoid	ADJ
ejpam-6596	81	15	of	of	ADP
ejpam-6596	81	16	illness	illness	NOUN
ejpam-6596	81	17	is	be	AUX
ejpam-6596	81	18	represented	represent	VERB
ejpam-6596	81	19	by	by	ADP
ejpam-6596	81	20	e0	e0	PROPN
ejpam-6596	81	21	.	.	PUNCT
ejpam-6596	82	1	4.1	4.1	NUM
ejpam-6596	82	2	.	.	PUNCT
ejpam-6596	82	3	disease	disease	NOUN
ejpam-6596	82	4	free	free	ADJ
ejpam-6596	82	5	equilibrium	equilibrium	NOUN
ejpam-6596	82	6	point	point	NOUN
ejpam-6596	82	7	,	,	PUNCT
ejpam-6596	82	8	e0	e0	PROPN
ejpam-6596	82	9	the	the	DET
ejpam-6596	82	10	disease	disease	NOUN
ejpam-6596	82	11	-	-	PUNCT
ejpam-6596	82	12	free	free	ADJ
ejpam-6596	82	13	stationary	stationary	ADJ
ejpam-6596	82	14	point	point	NOUN
ejpam-6596	82	15	designates	designate	VERB
ejpam-6596	82	16	the	the	DET
ejpam-6596	82	17	location	location	NOUN
ejpam-6596	82	18	at	at	ADP
ejpam-6596	82	19	which	which	PRON
ejpam-6596	82	20	the	the	DET
ejpam-6596	82	21	illness	illness	NOUN
ejpam-6596	82	22	has	have	AUX
ejpam-6596	82	23	been	be	AUX
ejpam-6596	82	24	totally	totally	ADV
ejpam-6596	82	25	eradicated	eradicate	VERB
ejpam-6596	82	26	from	from	ADP
ejpam-6596	82	27	the	the	DET
ejpam-6596	82	28	local	local	ADJ
ejpam-6596	82	29	population	population	NOUN
ejpam-6596	82	30	.	.	PUNCT
ejpam-6596	83	1	for	for	SCONJ
ejpam-6596	83	2	the	the	DET
ejpam-6596	83	3	suggested	suggest	VERB
ejpam-6596	83	4	model	model	PROPN
ejpam-6596	83	5	’s	’s	PART
ejpam-6596	83	6	no	no	DET
ejpam-6596	83	7	-	-	PUNCT
ejpam-6596	83	8	disease	disease	NOUN
ejpam-6596	83	9	equilibrium	equilibrium	NOUN
ejpam-6596	83	10	to	to	PART
ejpam-6596	83	11	be	be	AUX
ejpam-6596	83	12	found	find	VERB
ejpam-6596	83	13	,	,	PUNCT
ejpam-6596	83	14	given	give	VERB
ejpam-6596	83	15	that	that	SCONJ
ejpam-6596	83	16	the	the	DET
ejpam-6596	83	17	illness	illness	NOUN
ejpam-6596	83	18	is	be	AUX
ejpam-6596	83	19	not	not	PART
ejpam-6596	83	20	found	find	VERB
ejpam-6596	83	21	in	in	ADP
ejpam-6596	83	22	the	the	DET
ejpam-6596	83	23	population	population	NOUN
ejpam-6596	83	24	,	,	PUNCT
ejpam-6596	83	25	every	every	DET
ejpam-6596	83	26	equation	equation	NOUN
ejpam-6596	83	27	has	have	VERB
ejpam-6596	83	28	a	a	DET
ejpam-6596	83	29	zero	zero	NUM
ejpam-6596	83	30	on	on	ADP
ejpam-6596	83	31	its	its	PRON
ejpam-6596	83	32	right	right	ADJ
ejpam-6596	83	33	hand	hand	NOUN
ejpam-6596	83	34	,	,	PUNCT
ejpam-6596	83	35	resulting	result	VERB
ejpam-6596	83	36	in	in	ADP
ejpam-6596	83	37	e	e	X
ejpam-6596	83	38	=	=	NOUN
ejpam-6596	83	39	i	i	PROPN
ejpam-6596	83	40	=	=	NOUN
ejpam-6596	83	41	0	0	X
ejpam-6596	83	42	.	.	PUNCT
ejpam-6596	84	1	the	the	DET
ejpam-6596	84	2	no	no	DET
ejpam-6596	84	3	-	-	PUNCT
ejpam-6596	84	4	sickness	sickness	NOUN
ejpam-6596	84	5	stationary	stationary	ADJ
ejpam-6596	84	6	point	point	NOUN
ejpam-6596	84	7	is	be	AUX
ejpam-6596	84	8	achieved	achieve	VERB
ejpam-6596	84	9	by	by	ADP
ejpam-6596	84	10	computation	computation	NOUN
ejpam-6596	84	11	and	and	CCONJ
ejpam-6596	84	12	is	be	AUX
ejpam-6596	84	13	denoted	denote	VERB
ejpam-6596	84	14	by	by	ADP
ejpam-6596	84	15	e0	e0	PROPN
ejpam-6596	84	16	,	,	PUNCT
ejpam-6596	84	17	as	as	SCONJ
ejpam-6596	84	18	seen	see	VERB
ejpam-6596	84	19	below	below	ADV
ejpam-6596	84	20	:	:	PUNCT
ejpam-6596	84	21	e0	e0	PROPN
ejpam-6596	84	22	=	=	SYM
ejpam-6596	84	23	(	(	PUNCT
ejpam-6596	84	24	s0	s0	PROPN
ejpam-6596	84	25	,	,	PUNCT
ejpam-6596	84	26	e0	e0	PROPN
ejpam-6596	84	27	,	,	PUNCT
ejpam-6596	84	28	i0	i0	PROPN
ejpam-6596	84	29	,	,	PUNCT
ejpam-6596	84	30	q0	q0	PROPN
ejpam-6596	84	31	,	,	PUNCT
ejpam-6596	84	32	r0	r0	NOUN
ejpam-6596	84	33	)	)	PUNCT
ejpam-6596	84	34	=	=	PUNCT
ejpam-6596	85	1	(	(	PUNCT
ejpam-6596	85	2	g	g	PROPN
ejpam-6596	85	3	m+	m+	NUM
ejpam-6596	85	4	b1	b1	NOUN
ejpam-6596	85	5	,	,	PUNCT
ejpam-6596	85	6	0	0	NUM
ejpam-6596	85	7	,	,	PUNCT
ejpam-6596	85	8	0	0	NUM
ejpam-6596	85	9	,	,	PUNCT
ejpam-6596	85	10	b1	b1	NOUN
ejpam-6596	85	11	g	g	PROPN
ejpam-6596	85	12	(	(	PUNCT
ejpam-6596	85	13	m+	m+	NOUN
ejpam-6596	85	14	p)(m+	p)(m+	NOUN
ejpam-6596	85	15	b1	b1	NOUN
ejpam-6596	85	16	)	)	PUNCT
ejpam-6596	85	17	,	,	PUNCT
ejpam-6596	85	18	b1gp	b1gp	PUNCT
ejpam-6596	85	19	m(m+	m(m+	X
ejpam-6596	85	20	p	p	X
ejpam-6596	85	21	)	)	PUNCT
ejpam-6596	85	22	)	)	PUNCT
ejpam-6596	85	23	.	.	PUNCT
ejpam-6596	86	1	n.	n.	PROPN
ejpam-6596	86	2	gul	gul	PROPN
ejpam-6596	86	3	et	et	PROPN
ejpam-6596	86	4	al	al	PROPN
ejpam-6596	86	5	.	.	PUNCT
ejpam-6596	86	6	/	/	SYM
ejpam-6596	86	7	eur	eur	PROPN
ejpam-6596	86	8	.	.	PUNCT
ejpam-6596	87	1	j.	j.	PROPN
ejpam-6596	87	2	pure	pure	PROPN
ejpam-6596	87	3	appl	appl	PROPN
ejpam-6596	87	4	.	.	PROPN
ejpam-6596	87	5	math	math	PROPN
ejpam-6596	87	6	,	,	PUNCT
ejpam-6596	87	7	18	18	NUM
ejpam-6596	87	8	(	(	PUNCT
ejpam-6596	87	9	4	4	NUM
ejpam-6596	87	10	)	)	PUNCT
ejpam-6596	87	11	(	(	PUNCT
ejpam-6596	87	12	2025	2025	NUM
ejpam-6596	87	13	)	)	PUNCT
ejpam-6596	87	14	,	,	PUNCT
ejpam-6596	87	15	6596	6596	NUM
ejpam-6596	87	16	5	5	NUM
ejpam-6596	87	17	of	of	ADP
ejpam-6596	87	18	23	23	NUM
ejpam-6596	87	19	4.2	4.2	NUM
ejpam-6596	87	20	.	.	PUNCT
ejpam-6596	88	1	endemic	endemic	ADJ
ejpam-6596	88	2	equilibria	equilibrium	NOUN
ejpam-6596	88	3	according	accord	VERB
ejpam-6596	88	4	to	to	ADP
ejpam-6596	88	5	the	the	DET
ejpam-6596	88	6	endemic	endemic	ADJ
ejpam-6596	88	7	equilibrium	equilibrium	NOUN
ejpam-6596	88	8	,	,	PUNCT
ejpam-6596	88	9	this	this	PRON
ejpam-6596	88	10	occurs	occur	VERB
ejpam-6596	88	11	when	when	SCONJ
ejpam-6596	88	12	the	the	DET
ejpam-6596	88	13	illness	illness	NOUN
ejpam-6596	88	14	affects	affect	VERB
ejpam-6596	88	15	a	a	DET
ejpam-6596	88	16	community	community	NOUN
ejpam-6596	88	17	for	for	ADP
ejpam-6596	88	18	a	a	DET
ejpam-6596	88	19	lengthy	lengthy	ADJ
ejpam-6596	88	20	period	period	NOUN
ejpam-6596	88	21	of	of	ADP
ejpam-6596	88	22	time	time	NOUN
ejpam-6596	88	23	.	.	PUNCT
ejpam-6596	89	1	we	we	PRON
ejpam-6596	89	2	shall	shall	AUX
ejpam-6596	89	3	put	put	VERB
ejpam-6596	89	4	the	the	DET
ejpam-6596	89	5	right	right	ADJ
ejpam-6596	89	6	side	side	NOUN
ejpam-6596	89	7	of	of	ADP
ejpam-6596	89	8	the	the	DET
ejpam-6596	89	9	proposed	propose	VERB
ejpam-6596	89	10	model	model	NOUN
ejpam-6596	89	11	equal	equal	ADJ
ejpam-6596	89	12	to	to	ADP
ejpam-6596	89	13	zero	zero	NUM
ejpam-6596	89	14	in	in	ADP
ejpam-6596	89	15	order	order	NOUN
ejpam-6596	89	16	to	to	PART
ejpam-6596	89	17	locate	locate	VERB
ejpam-6596	89	18	the	the	DET
ejpam-6596	89	19	endemic	endemic	ADJ
ejpam-6596	89	20	equilibria	equilibrium	NOUN
ejpam-6596	89	21	.	.	PUNCT
ejpam-6596	90	1	the	the	DET
ejpam-6596	90	2	endemic	endemic	ADJ
ejpam-6596	90	3	equilibria	equilibrium	NOUN
ejpam-6596	90	4	for	for	ADP
ejpam-6596	90	5	the	the	DET
ejpam-6596	90	6	system	system	NOUN
ejpam-6596	90	7	(	(	PUNCT
ejpam-6596	90	8	3.0.1	3.0.1	NUM
ejpam-6596	90	9	)	)	PUNCT
ejpam-6596	90	10	at	at	ADP
ejpam-6596	90	11	e1	e1	NOUN
ejpam-6596	90	12	=	=	SYM
ejpam-6596	90	13	(	(	PUNCT
ejpam-6596	90	14	s∗	s∗	PROPN
ejpam-6596	90	15	,	,	PUNCT
ejpam-6596	90	16	e∗	e∗	NOUN
ejpam-6596	90	17	,	,	PUNCT
ejpam-6596	90	18	i∗	i∗	NOUN
ejpam-6596	90	19	,	,	PUNCT
ejpam-6596	90	20	q∗	q∗	NOUN
ejpam-6596	90	21	,	,	PUNCT
ejpam-6596	90	22	r∗	r∗	PROPN
ejpam-6596	90	23	)	)	PUNCT
ejpam-6596	90	24	are	are	NOUN
ejpam-6596	90	25	s∗	s∗	PROPN
ejpam-6596	90	26	=	=	SYM
ejpam-6596	90	27	(	(	PUNCT
ejpam-6596	90	28	m+	m+	NOUN
ejpam-6596	90	29	c+	c+	X
ejpam-6596	90	30	b2)(m+	b2)(m+	ADP
ejpam-6596	90	31	b3	b3	PROPN
ejpam-6596	90	32	+	+	CCONJ
ejpam-6596	90	33	q	q	X
ejpam-6596	90	34	+	+	NUM
ejpam-6596	90	35	µ)(1	µ)(1	X
ejpam-6596	90	36	+	+	CCONJ
ejpam-6596	90	37	αi∗	αi∗	NOUN
ejpam-6596	90	38	)	)	PUNCT
ejpam-6596	90	39	hc	hc	PROPN
ejpam-6596	90	40	,	,	PUNCT
ejpam-6596	90	41	e∗	e∗	PROPN
ejpam-6596	90	42	=	=	SYM
ejpam-6596	90	43	(	(	PUNCT
ejpam-6596	90	44	m+	m+	NUM
ejpam-6596	90	45	b3	b3	PROPN
ejpam-6596	90	46	+	+	CCONJ
ejpam-6596	90	47	q	q	PROPN
ejpam-6596	91	1	+	+	NUM
ejpam-6596	91	2	µ)i∗	µ)i∗	DET
ejpam-6596	91	3	c	c	NOUN
ejpam-6596	91	4	,	,	PUNCT
ejpam-6596	91	5	i∗	i∗	NOUN
ejpam-6596	91	6	=	=	SYM
ejpam-6596	91	7	hgc−	hgc−	PROPN
ejpam-6596	91	8	(	(	PUNCT
ejpam-6596	91	9	m+	m+	NOUN
ejpam-6596	91	10	b1)(m+	b1)(m+	NOUN
ejpam-6596	91	11	b2	b2	NOUN
ejpam-6596	91	12	+	+	CCONJ
ejpam-6596	91	13	c)(m+	c)(m+	NOUN
ejpam-6596	91	14	b3	b3	NOUN
ejpam-6596	91	15	+	+	CCONJ
ejpam-6596	91	16	q	q	PROPN
ejpam-6596	91	17	+	+	NUM
ejpam-6596	91	18	µ	µ	X
ejpam-6596	91	19	)	)	PUNCT
ejpam-6596	91	20	(	(	PUNCT
ejpam-6596	91	21	m+	m+	NUM
ejpam-6596	91	22	b2	b2	NOUN
ejpam-6596	91	23	+	+	CCONJ
ejpam-6596	91	24	c)(m+	c)(m+	NOUN
ejpam-6596	91	25	b3	b3	NOUN
ejpam-6596	91	26	+	+	CCONJ
ejpam-6596	91	27	q	q	PROPN
ejpam-6596	92	1	+	+	NUM
ejpam-6596	92	2	µ)(h+	µ)(h+	PROPN
ejpam-6596	92	3	α(m+	α(m+	ADJ
ejpam-6596	92	4	b1	b1	NOUN
ejpam-6596	92	5	)	)	PUNCT
ejpam-6596	92	6	)	)	PUNCT
ejpam-6596	92	7	,	,	PUNCT
ejpam-6596	92	8	q∗	q∗	NOUN
ejpam-6596	92	9	=	=	SYM
ejpam-6596	92	10	b1s	b1	NOUN
ejpam-6596	92	11	∗	∗	NOUN
ejpam-6596	92	12	+	+	NUM
ejpam-6596	92	13	b2e	b2e	X
ejpam-6596	92	14	∗	∗	NOUN
ejpam-6596	92	15	+	+	NUM
ejpam-6596	93	1	b3i	b3i	NUM
ejpam-6596	93	2	∗	∗	NOUN
ejpam-6596	93	3	m+	m+	NUM
ejpam-6596	93	4	p	p	NOUN
ejpam-6596	93	5	,	,	PUNCT
ejpam-6596	93	6	r∗	r∗	PROPN
ejpam-6596	93	7	=	=	PUNCT
ejpam-6596	93	8	qi∗	qi∗	NOUN
ejpam-6596	93	9	+	+	NUM
ejpam-6596	93	10	pq∗	pq∗	NOUN
ejpam-6596	93	11	m	m	NOUN
ejpam-6596	93	12	.	.	PUNCT
ejpam-6596	94	1	4.3	4.3	NUM
ejpam-6596	94	2	.	.	PUNCT
ejpam-6596	94	3	basic	basic	ADJ
ejpam-6596	94	4	threshold	threshold	NOUN
ejpam-6596	94	5	number	number	NOUN
ejpam-6596	94	6	the	the	DET
ejpam-6596	94	7	basic	basic	ADJ
ejpam-6596	94	8	reproduction	reproduction	NOUN
ejpam-6596	94	9	number	number	NOUN
ejpam-6596	94	10	r0	r0	NOUN
ejpam-6596	94	11	is	be	AUX
ejpam-6596	94	12	defined	define	VERB
ejpam-6596	94	13	as	as	ADP
ejpam-6596	94	14	the	the	DET
ejpam-6596	94	15	average	average	ADJ
ejpam-6596	94	16	number	number	NOUN
ejpam-6596	94	17	of	of	ADP
ejpam-6596	94	18	secondary	secondary	ADJ
ejpam-6596	94	19	infections	infection	NOUN
ejpam-6596	94	20	produced	produce	VERB
ejpam-6596	94	21	by	by	ADP
ejpam-6596	94	22	one	one	NUM
ejpam-6596	94	23	infected	infect	VERB
ejpam-6596	94	24	individual	individual	NOUN
ejpam-6596	94	25	in	in	ADP
ejpam-6596	94	26	a	a	DET
ejpam-6596	94	27	completely	completely	ADV
ejpam-6596	94	28	susceptible	susceptible	ADJ
ejpam-6596	94	29	population	population	NOUN
ejpam-6596	94	30	.	.	PUNCT
ejpam-6596	95	1	this	this	DET
ejpam-6596	95	2	time	time	NOUN
ejpam-6596	95	3	,	,	PUNCT
ejpam-6596	95	4	r0	r0	NOUN
ejpam-6596	95	5	is	be	AUX
ejpam-6596	95	6	calculated	calculate	VERB
ejpam-6596	95	7	as	as	SCONJ
ejpam-6596	95	8	typically	typically	ADV
ejpam-6596	95	9	there	there	PRON
ejpam-6596	95	10	are	be	VERB
ejpam-6596	95	11	how	how	SCONJ
ejpam-6596	95	12	many	many	ADJ
ejpam-6596	95	13	secondary	secondary	ADJ
ejpam-6596	95	14	cases	case	NOUN
ejpam-6596	95	15	of	of	ADP
ejpam-6596	95	16	general	general	ADJ
ejpam-6596	95	17	illness	illness	NOUN
ejpam-6596	95	18	peeople	peeople	NOUN
ejpam-6596	95	19	that	that	PRON
ejpam-6596	95	20	an	an	DET
ejpam-6596	95	21	individual	individual	NOUN
ejpam-6596	95	22	with	with	ADP
ejpam-6596	95	23	a	a	DET
ejpam-6596	95	24	general	general	ADJ
ejpam-6596	95	25	disease	disease	NOUN
ejpam-6596	95	26	who	who	PRON
ejpam-6596	95	27	was	be	AUX
ejpam-6596	95	28	not	not	PART
ejpam-6596	95	29	receiving	receive	VERB
ejpam-6596	95	30	treatment	treatment	NOUN
ejpam-6596	95	31	throughout	throughout	ADP
ejpam-6596	95	32	his	his	PRON
ejpam-6596	95	33	or	or	CCONJ
ejpam-6596	95	34	her	her	PRON
ejpam-6596	95	35	general	general	ADJ
ejpam-6596	95	36	disease	disease	NOUN
ejpam-6596	95	37	caused	cause	VERB
ejpam-6596	95	38	in	in	ADP
ejpam-6596	95	39	a	a	DET
ejpam-6596	95	40	population	population	NOUN
ejpam-6596	95	41	of	of	ADP
ejpam-6596	95	42	potential	potential	ADJ
ejpam-6596	95	43	general	general	ADJ
ejpam-6596	95	44	disease	disease	NOUN
ejpam-6596	95	45	patients	patient	NOUN
ejpam-6596	95	46	.	.	PUNCT
ejpam-6596	96	1	the	the	DET
ejpam-6596	96	2	well	well	ADV
ejpam-6596	96	3	-	-	PUNCT
ejpam-6596	96	4	known	know	VERB
ejpam-6596	96	5	next	next	ADJ
ejpam-6596	96	6	generation	generation	NOUN
ejpam-6596	96	7	matrix	matrix	NOUN
ejpam-6596	96	8	may	may	AUX
ejpam-6596	96	9	be	be	AUX
ejpam-6596	96	10	used	use	VERB
ejpam-6596	96	11	to	to	PART
ejpam-6596	96	12	establish	establish	VERB
ejpam-6596	96	13	the	the	DET
ejpam-6596	96	14	fundamental	fundamental	ADJ
ejpam-6596	96	15	reproduction	reproduction	NOUN
ejpam-6596	96	16	number	number	NOUN
ejpam-6596	96	17	.	.	PUNCT
ejpam-6596	97	1	for	for	ADP
ejpam-6596	97	2	this	this	PRON
ejpam-6596	97	3	,	,	PUNCT
ejpam-6596	97	4	we	we	PRON
ejpam-6596	97	5	separate	separate	VERB
ejpam-6596	97	6	patients	patient	NOUN
ejpam-6596	97	7	who	who	PRON
ejpam-6596	97	8	are	be	AUX
ejpam-6596	97	9	infected	infect	VERB
ejpam-6596	97	10	and	and	CCONJ
ejpam-6596	97	11	those	those	PRON
ejpam-6596	97	12	who	who	PRON
ejpam-6596	97	13	are	be	AUX
ejpam-6596	97	14	not	not	PART
ejpam-6596	97	15	.	.	PUNCT
ejpam-6596	98	1	according	accord	VERB
ejpam-6596	98	2	to	to	ADP
ejpam-6596	98	3	model	model	NOUN
ejpam-6596	98	4	,	,	PUNCT
ejpam-6596	98	5	the	the	DET
ejpam-6596	98	6	infected	infect	VERB
ejpam-6596	98	7	classes	class	NOUN
ejpam-6596	98	8	are	be	AUX
ejpam-6596	98	9	e	e	NOUN
ejpam-6596	98	10	and	and	CCONJ
ejpam-6596	98	11	i.	i.	NOUN
ejpam-6596	98	12	consider	consider	VERB
ejpam-6596	98	13	only	only	ADV
ejpam-6596	98	14	those	those	DET
ejpam-6596	98	15	classes	class	NOUN
ejpam-6596	98	16	which	which	DET
ejpam-6596	98	17	infection	infection	NOUN
ejpam-6596	98	18	of	of	ADP
ejpam-6596	98	19	the	the	DET
ejpam-6596	98	20	disease	disease	NOUN
ejpam-6596	98	21	posses	posse	NOUN
ejpam-6596	98	22	,	,	PUNCT
ejpam-6596	98	23	the	the	DET
ejpam-6596	98	24	model	model	NOUN
ejpam-6596	98	25	becomes	become	VERB
ejpam-6596	98	26	j1	j1	NOUN
ejpam-6596	98	27	=	=	PUNCT
ejpam-6596	98	28	(	(	PUNCT
ejpam-6596	98	29	e	e	NOUN
ejpam-6596	98	30	,	,	PUNCT
ejpam-6596	98	31	i	i	PROPN
ejpam-6596	98	32	)	)	PUNCT
ejpam-6596	98	33	,	,	PUNCT
ejpam-6596	98	34	dj1	dj1	NOUN
ejpam-6596	98	35	dt	dt	X
ejpam-6596	99	1	=	=	PUNCT
ejpam-6596	99	2	d	d	X
ejpam-6596	99	3	dt	dt	X
ejpam-6596	99	4	(	(	PUNCT
ejpam-6596	99	5	e	e	NOUN
ejpam-6596	99	6	,	,	PUNCT
ejpam-6596	99	7	i	i	NOUN
ejpam-6596	99	8	)	)	PUNCT
ejpam-6596	99	9	.	.	PUNCT
ejpam-6596	100	1	de	de	PROPN
ejpam-6596	100	2	dt	dt	PROPN
ejpam-6596	101	1	=	=	SYM
ejpam-6596	101	2	hsi	hsi	PROPN
ejpam-6596	101	3	1	1	NUM
ejpam-6596	102	1	+	+	CCONJ
ejpam-6596	102	2	αi	αi	VERB
ejpam-6596	102	3	−	−	PROPN
ejpam-6596	103	1	(	(	PUNCT
ejpam-6596	103	2	m+	m+	NUM
ejpam-6596	103	3	c+	c+	NOUN
ejpam-6596	103	4	b2)e	b2)e	PROPN
ejpam-6596	103	5	,	,	PUNCT
ejpam-6596	103	6	di	di	NOUN
ejpam-6596	103	7	dt	dt	NOUN
ejpam-6596	103	8	=	=	SYM
ejpam-6596	103	9	ce	ce	PROPN
ejpam-6596	103	10	−	−	PROPN
ejpam-6596	104	1	(	(	PUNCT
ejpam-6596	104	2	m+	m+	NUM
ejpam-6596	104	3	b3	b3	PROPN
ejpam-6596	104	4	+	+	CCONJ
ejpam-6596	104	5	q	q	X
ejpam-6596	104	6	+	+	X
ejpam-6596	104	7	µ)i	µ)i	ADJ
ejpam-6596	104	8	.	.	PUNCT
ejpam-6596	105	1	(	(	PUNCT
ejpam-6596	105	2	3	3	X
ejpam-6596	105	3	)	)	PUNCT
ejpam-6596	105	4	using	use	VERB
ejpam-6596	105	5	the	the	DET
ejpam-6596	105	6	system	system	NOUN
ejpam-6596	105	7	’s	’	VERB
ejpam-6596	105	8	making	make	VERB
ejpam-6596	105	9	the	the	DET
ejpam-6596	105	10	matrices	matrix	NOUN
ejpam-6596	105	11	f	f	PROPN
ejpam-6596	105	12	and	and	CCONJ
ejpam-6596	105	13	v	v	ADP
ejpam-6596	105	14	which	which	PRON
ejpam-6596	105	15	show	show	VERB
ejpam-6596	105	16	the	the	DET
ejpam-6596	105	17	susceptible	susceptible	ADJ
ejpam-6596	105	18	people	people	NOUN
ejpam-6596	105	19	and	and	CCONJ
ejpam-6596	105	20	infected	infected	ADJ
ejpam-6596	105	21	people	people	NOUN
ejpam-6596	105	22	.	.	PUNCT
ejpam-6596	106	1	dx	dx	PROPN
ejpam-6596	106	2	dt	dt	PROPN
ejpam-6596	107	1	=	=	PUNCT
ejpam-6596	107	2	f	f	PROPN
ejpam-6596	107	3	−	−	PROPN
ejpam-6596	107	4	v	v	NOUN
ejpam-6596	107	5	,	,	PUNCT
ejpam-6596	107	6	n.	n.	PROPN
ejpam-6596	107	7	gul	gul	PROPN
ejpam-6596	107	8	et	et	PROPN
ejpam-6596	107	9	al	al	PROPN
ejpam-6596	107	10	.	.	PUNCT
ejpam-6596	107	11	/	/	SYM
ejpam-6596	107	12	eur	eur	PROPN
ejpam-6596	107	13	.	.	PUNCT
ejpam-6596	108	1	j.	j.	PROPN
ejpam-6596	108	2	pure	pure	PROPN
ejpam-6596	108	3	appl	appl	PROPN
ejpam-6596	108	4	.	.	PROPN
ejpam-6596	108	5	math	math	PROPN
ejpam-6596	108	6	,	,	PUNCT
ejpam-6596	108	7	18	18	NUM
ejpam-6596	108	8	(	(	PUNCT
ejpam-6596	108	9	4	4	NUM
ejpam-6596	108	10	)	)	PUNCT
ejpam-6596	108	11	(	(	PUNCT
ejpam-6596	108	12	2025	2025	NUM
ejpam-6596	108	13	)	)	PUNCT
ejpam-6596	108	14	,	,	PUNCT
ejpam-6596	108	15	6596	6596	NUM
ejpam-6596	108	16	6	6	NUM
ejpam-6596	108	17	of	of	ADP
ejpam-6596	108	18	23	23	NUM
ejpam-6596	108	19	where	where	SCONJ
ejpam-6596	108	20	,	,	PUNCT
ejpam-6596	108	21	f	f	PROPN
ejpam-6596	108	22	=	=	X
ejpam-6596	108	23	[	[	PUNCT
ejpam-6596	108	24	hsi	hsi	PROPN
ejpam-6596	108	25	1+αi	1+αi	NUM
ejpam-6596	108	26	0	0	NUM
ejpam-6596	108	27	]	]	PUNCT
ejpam-6596	108	28	,	,	PUNCT
ejpam-6596	108	29	v	v	X
ejpam-6596	108	30	=	=	PUNCT
ejpam-6596	108	31	[	[	PUNCT
ejpam-6596	108	32	(	(	PUNCT
ejpam-6596	108	33	m+	m+	NOUN
ejpam-6596	108	34	c+	c+	VERB
ejpam-6596	108	35	b2)e	b2)e	ADJ
ejpam-6596	108	36	−ce	−ce	PROPN
ejpam-6596	109	1	+	+	CCONJ
ejpam-6596	109	2	(	(	PUNCT
ejpam-6596	109	3	m+	m+	NUM
ejpam-6596	109	4	b3	b3	PROPN
ejpam-6596	109	5	+	+	CCONJ
ejpam-6596	109	6	q	q	X
ejpam-6596	109	7	+	+	X
ejpam-6596	109	8	µ)i	µ)i	X
ejpam-6596	109	9	]	]	PUNCT
ejpam-6596	109	10	,	,	PUNCT
ejpam-6596	109	11	then	then	ADV
ejpam-6596	109	12	by	by	ADP
ejpam-6596	109	13	finding	find	VERB
ejpam-6596	109	14	the	the	DET
ejpam-6596	109	15	maximum	maximum	ADJ
ejpam-6596	109	16	spectram	spectram	NOUN
ejpam-6596	109	17	of	of	ADP
ejpam-6596	109	18	the	the	DET
ejpam-6596	109	19	system	system	NOUN
ejpam-6596	109	20	f	f	NOUN
ejpam-6596	109	21	∗v	∗v	ADJ
ejpam-6596	109	22	−1∗	−1∗	ADJ
ejpam-6596	109	23	r0	r0	NOUN
ejpam-6596	109	24	=	=	SYM
ejpam-6596	109	25	hcg	hcg	PROPN
ejpam-6596	109	26	(	(	PUNCT
ejpam-6596	109	27	m+	m+	NOUN
ejpam-6596	109	28	b1)(m+	b1)(m+	NOUN
ejpam-6596	109	29	c+	c+	X
ejpam-6596	109	30	b2)(m+	b2)(m+	ADP
ejpam-6596	109	31	b3	b3	PROPN
ejpam-6596	109	32	+	+	CCONJ
ejpam-6596	109	33	q	q	PROPN
ejpam-6596	109	34	+	+	NUM
ejpam-6596	109	35	µ	µ	NOUN
ejpam-6596	109	36	)	)	PUNCT
ejpam-6596	109	37	.	.	PUNCT
ejpam-6596	110	1	which	which	PRON
ejpam-6596	110	2	is	be	AUX
ejpam-6596	110	3	the	the	DET
ejpam-6596	110	4	basic	basic	ADJ
ejpam-6596	110	5	reproductive	reproductive	ADJ
ejpam-6596	110	6	value	value	NOUN
ejpam-6596	110	7	r0	r0	NOUN
ejpam-6596	110	8	.	.	PUNCT
ejpam-6596	111	1	the	the	DET
ejpam-6596	111	2	basic	basic	ADJ
ejpam-6596	111	3	reproduction	reproduction	NOUN
ejpam-6596	111	4	number	number	NOUN
ejpam-6596	111	5	r0	r0	NOUN
ejpam-6596	111	6	acts	act	VERB
ejpam-6596	111	7	as	as	ADP
ejpam-6596	111	8	a	a	DET
ejpam-6596	111	9	key	key	ADJ
ejpam-6596	111	10	epidemiological	epidemiological	ADJ
ejpam-6596	111	11	threshold	threshold	NOUN
ejpam-6596	111	12	governing	govern	VERB
ejpam-6596	111	13	system	system	NOUN
ejpam-6596	111	14	dynamics	dynamic	NOUN
ejpam-6596	111	15	.	.	PUNCT
ejpam-6596	112	1	if	if	SCONJ
ejpam-6596	112	2	r0	r0	NOUN
ejpam-6596	112	3	<	<	X
ejpam-6596	112	4	1	1	NUM
ejpam-6596	112	5	,	,	PUNCT
ejpam-6596	112	6	the	the	DET
ejpam-6596	112	7	disease	disease	NOUN
ejpam-6596	112	8	-	-	PUNCT
ejpam-6596	112	9	free	free	ADJ
ejpam-6596	112	10	equilibrium	equilibrium	NOUN
ejpam-6596	112	11	is	be	AUX
ejpam-6596	112	12	both	both	PRON
ejpam-6596	112	13	locally	locally	ADV
ejpam-6596	112	14	and	and	CCONJ
ejpam-6596	112	15	globally	globally	ADV
ejpam-6596	112	16	asymptotically	asymptotically	ADV
ejpam-6596	112	17	stable	stable	ADJ
ejpam-6596	112	18	,	,	PUNCT
ejpam-6596	112	19	leading	lead	VERB
ejpam-6596	112	20	to	to	ADP
ejpam-6596	112	21	disease	disease	NOUN
ejpam-6596	112	22	eradication	eradication	NOUN
ejpam-6596	112	23	.	.	PUNCT
ejpam-6596	113	1	if	if	SCONJ
ejpam-6596	113	2	r0	r0	NOUN
ejpam-6596	113	3	>	>	X
ejpam-6596	113	4	1	1	NUM
ejpam-6596	113	5	,	,	PUNCT
ejpam-6596	113	6	the	the	DET
ejpam-6596	113	7	disease	disease	NOUN
ejpam-6596	113	8	-	-	PUNCT
ejpam-6596	113	9	free	free	ADJ
ejpam-6596	113	10	equilibrium	equilibrium	NOUN
ejpam-6596	113	11	becomes	become	VERB
ejpam-6596	113	12	unstable	unstable	ADJ
ejpam-6596	113	13	,	,	PUNCT
ejpam-6596	113	14	and	and	CCONJ
ejpam-6596	113	15	the	the	DET
ejpam-6596	113	16	endemic	endemic	ADJ
ejpam-6596	113	17	equilibrium	equilibrium	NOUN
ejpam-6596	113	18	is	be	AUX
ejpam-6596	113	19	asymptotically	asymptotically	ADV
ejpam-6596	113	20	stable	stable	ADJ
ejpam-6596	113	21	,	,	PUNCT
ejpam-6596	113	22	reflecting	reflect	VERB
ejpam-6596	113	23	disease	disease	NOUN
ejpam-6596	113	24	persistence	persistence	NOUN
ejpam-6596	113	25	.	.	PUNCT
ejpam-6596	114	1	thus	thus	ADV
ejpam-6596	114	2	,	,	PUNCT
ejpam-6596	114	3	r0	r0	NOUN
ejpam-6596	114	4	directly	directly	ADV
ejpam-6596	114	5	determines	determine	VERB
ejpam-6596	114	6	the	the	DET
ejpam-6596	114	7	long	long	ADJ
ejpam-6596	114	8	-	-	PUNCT
ejpam-6596	114	9	term	term	NOUN
ejpam-6596	114	10	behavior	behavior	NOUN
ejpam-6596	114	11	of	of	ADP
ejpam-6596	114	12	the	the	DET
ejpam-6596	114	13	infection	infection	NOUN
ejpam-6596	114	14	within	within	ADP
ejpam-6596	114	15	the	the	DET
ejpam-6596	114	16	population	population	NOUN
ejpam-6596	114	17	.	.	PUNCT
ejpam-6596	115	1	n.	n.	PROPN
ejpam-6596	115	2	gul	gul	PROPN
ejpam-6596	115	3	et	et	PROPN
ejpam-6596	115	4	al	al	PROPN
ejpam-6596	115	5	.	.	PUNCT
ejpam-6596	115	6	/	/	SYM
ejpam-6596	115	7	eur	eur	PROPN
ejpam-6596	115	8	.	.	PUNCT
ejpam-6596	116	1	j.	j.	PROPN
ejpam-6596	116	2	pure	pure	PROPN
ejpam-6596	116	3	appl	appl	PROPN
ejpam-6596	116	4	.	.	PROPN
ejpam-6596	116	5	math	math	PROPN
ejpam-6596	116	6	,	,	PUNCT
ejpam-6596	116	7	18	18	NUM
ejpam-6596	116	8	(	(	PUNCT
ejpam-6596	116	9	4	4	NUM
ejpam-6596	116	10	)	)	PUNCT
ejpam-6596	116	11	(	(	PUNCT
ejpam-6596	116	12	2025	2025	NUM
ejpam-6596	116	13	)	)	PUNCT
ejpam-6596	116	14	,	,	PUNCT
ejpam-6596	116	15	6596	6596	NUM
ejpam-6596	116	16	7	7	NUM
ejpam-6596	116	17	of	of	ADP
ejpam-6596	116	18	23	23	NUM
ejpam-6596	116	19	0	0	NUM
ejpam-6596	116	20	1	1	NUM
ejpam-6596	116	21	0.2	0.2	NUM
ejpam-6596	116	22	0.4	0.4	NUM
ejpam-6596	116	23	1	1	NUM
ejpam-6596	116	24	r	r	NOUN
ejpam-6596	116	25	0	0	NUM
ejpam-6596	116	26	0.6	0.6	NUM
ejpam-6596	116	27	0.8	0.8	NUM
ejpam-6596	116	28	b	b	SYM
ejpam-6596	116	29	2	2	NUM
ejpam-6596	116	30	0.8	0.8	NUM
ejpam-6596	116	31	0.5	0.5	NUM
ejpam-6596	116	32	0.6	0.6	NUM
ejpam-6596	116	33	b	b	SYM
ejpam-6596	116	34	1	1	NUM
ejpam-6596	116	35	1	1	NUM
ejpam-6596	116	36	0.4	0.4	NUM
ejpam-6596	116	37	0.2	0.2	NUM
ejpam-6596	116	38	0	0	NUM
ejpam-6596	116	39	0	0	NUM
ejpam-6596	116	40	0	0	NUM
ejpam-6596	116	41	1	1	NUM
ejpam-6596	116	42	2	2	NUM
ejpam-6596	116	43	1	1	NUM
ejpam-6596	116	44	r	r	NOUN
ejpam-6596	116	45	0	0	NUM
ejpam-6596	116	46	4	4	NUM
ejpam-6596	116	47	0.8	0.8	NUM
ejpam-6596	116	48	µ	µ	NUM
ejpam-6596	116	49	0.5	0.5	NUM
ejpam-6596	116	50	0.6	0.6	NUM
ejpam-6596	116	51	b	b	SYM
ejpam-6596	116	52	2	2	NUM
ejpam-6596	116	53	6	6	NUM
ejpam-6596	116	54	0.4	0.4	NUM
ejpam-6596	116	55	0.2	0.2	NUM
ejpam-6596	116	56	0	0	NUM
ejpam-6596	116	57	0	0	NUM
ejpam-6596	116	58	1	1	NUM
ejpam-6596	116	59	1	1	NUM
ejpam-6596	116	60	2	2	NUM
ejpam-6596	116	61	1	1	NUM
ejpam-6596	116	62	r	r	NOUN
ejpam-6596	116	63	0	0	NUM
ejpam-6596	116	64	0.8	0.8	NUM
ejpam-6596	116	65	3	3	NUM
ejpam-6596	116	66	µ	µ	DET
ejpam-6596	116	67	0.5	0.5	NUM
ejpam-6596	116	68	0.6	0.6	NUM
ejpam-6596	116	69	b	b	NOUN
ejpam-6596	116	70	3	3	NUM
ejpam-6596	116	71	0.4	0.4	NUM
ejpam-6596	116	72	0.2	0.2	NUM
ejpam-6596	116	73	0	0	NUM
ejpam-6596	116	74	0	0	NUM
ejpam-6596	116	75	0	0	NUM
ejpam-6596	116	76	1	1	NUM
ejpam-6596	116	77	2	2	NUM
ejpam-6596	116	78	1	1	NUM
ejpam-6596	116	79	r	r	NOUN
ejpam-6596	116	80	0	0	NUM
ejpam-6596	116	81	4	4	NUM
ejpam-6596	116	82	0.8	0.8	NUM
ejpam-6596	116	83	µ	µ	NUM
ejpam-6596	116	84	0.5	0.5	NUM
ejpam-6596	116	85	6	6	NUM
ejpam-6596	116	86	0.6	0.6	NUM
ejpam-6596	116	87	c	c	NOUN
ejpam-6596	116	88	0.4	0.4	NUM
ejpam-6596	117	1	0.2	0.2	NUM
ejpam-6596	117	2	0	0	NUM
ejpam-6596	117	3	0	0	NUM
ejpam-6596	117	4	0	0	NUM
ejpam-6596	117	5	1	1	NUM
ejpam-6596	117	6	20	20	NUM
ejpam-6596	117	7	1	1	NUM
ejpam-6596	117	8	r	r	NOUN
ejpam-6596	117	9	0	0	NUM
ejpam-6596	117	10	40	40	NUM
ejpam-6596	117	11	0.8	0.8	NUM
ejpam-6596	117	12	m	m	NUM
ejpam-6596	117	13	0.5	0.5	NUM
ejpam-6596	117	14	0.6	0.6	NUM
ejpam-6596	117	15	h	h	NOUN
ejpam-6596	117	16	60	60	NUM
ejpam-6596	117	17	0.4	0.4	NUM
ejpam-6596	117	18	0.2	0.2	NUM
ejpam-6596	117	19	0	0	NUM
ejpam-6596	117	20	0	0	NUM
ejpam-6596	117	21	0	0	NUM
ejpam-6596	117	22	1	1	NUM
ejpam-6596	117	23	1	1	NUM
ejpam-6596	117	24	1	1	NUM
ejpam-6596	117	25	r	r	NOUN
ejpam-6596	117	26	0	0	NUM
ejpam-6596	117	27	2	2	NUM
ejpam-6596	117	28	0.8	0.8	NUM
ejpam-6596	117	29	µ	µ	NUM
ejpam-6596	117	30	0.5	0.5	NUM
ejpam-6596	117	31	0.6	0.6	NUM
ejpam-6596	117	32	b	b	SYM
ejpam-6596	117	33	1	1	NUM
ejpam-6596	117	34	3	3	NUM
ejpam-6596	117	35	0.4	0.4	NUM
ejpam-6596	117	36	0.2	0.2	NUM
ejpam-6596	117	37	0	0	NUM
ejpam-6596	117	38	0	0	NUM
ejpam-6596	117	39	figure	figure	NOUN
ejpam-6596	117	40	1	1	NUM
ejpam-6596	117	41	:	:	PUNCT
ejpam-6596	117	42	behaviour	behaviour	NOUN
ejpam-6596	117	43	of	of	ADP
ejpam-6596	117	44	the	the	DET
ejpam-6596	117	45	basic	basic	ADJ
ejpam-6596	117	46	reproduction	reproduction	NOUN
ejpam-6596	117	47	number	number	NOUN
ejpam-6596	117	48	in	in	ADP
ejpam-6596	117	49	three	three	NUM
ejpam-6596	117	50	dimensions	dimension	NOUN
ejpam-6596	117	51	in	in	ADP
ejpam-6596	117	52	relation	relation	NOUN
ejpam-6596	117	53	to	to	ADP
ejpam-6596	117	54	different	different	ADJ
ejpam-6596	117	55	model	model	NOUN
ejpam-6596	117	56	parameters	parameter	NOUN
ejpam-6596	117	57	.	.	PUNCT
ejpam-6596	118	1	n.	n.	PROPN
ejpam-6596	118	2	gul	gul	PROPN
ejpam-6596	118	3	et	et	PROPN
ejpam-6596	118	4	al	al	PROPN
ejpam-6596	118	5	.	.	PUNCT
ejpam-6596	118	6	/	/	SYM
ejpam-6596	118	7	eur	eur	PROPN
ejpam-6596	118	8	.	.	PUNCT
ejpam-6596	119	1	j.	j.	PROPN
ejpam-6596	119	2	pure	pure	PROPN
ejpam-6596	119	3	appl	appl	PROPN
ejpam-6596	119	4	.	.	PROPN
ejpam-6596	119	5	math	math	PROPN
ejpam-6596	119	6	,	,	PUNCT
ejpam-6596	119	7	18	18	NUM
ejpam-6596	119	8	(	(	PUNCT
ejpam-6596	119	9	4	4	NUM
ejpam-6596	119	10	)	)	PUNCT
ejpam-6596	119	11	(	(	PUNCT
ejpam-6596	119	12	2025	2025	NUM
ejpam-6596	119	13	)	)	PUNCT
ejpam-6596	119	14	,	,	PUNCT
ejpam-6596	119	15	6596	6596	NUM
ejpam-6596	119	16	8	8	NUM
ejpam-6596	119	17	of	of	ADP
ejpam-6596	119	18	23	23	NUM
ejpam-6596	119	19	5	5	NUM
ejpam-6596	119	20	.	.	PUNCT
ejpam-6596	120	1	local	local	ADJ
ejpam-6596	120	2	stability	stability	NOUN
ejpam-6596	120	3	analysis	analysis	NOUN
ejpam-6596	120	4	in	in	ADP
ejpam-6596	120	5	this	this	DET
ejpam-6596	120	6	section	section	NOUN
ejpam-6596	120	7	,	,	PUNCT
ejpam-6596	120	8	we	we	PRON
ejpam-6596	120	9	examine	examine	VERB
ejpam-6596	120	10	the	the	DET
ejpam-6596	120	11	model	model	NOUN
ejpam-6596	120	12	’s	’s	PART
ejpam-6596	120	13	(	(	PUNCT
ejpam-6596	120	14	1	1	NUM
ejpam-6596	120	15	)	)	PUNCT
ejpam-6596	120	16	endemic	endemic	ADJ
ejpam-6596	120	17	equilibrium	equilibrium	NOUN
ejpam-6596	120	18	point	point	NOUN
ejpam-6596	120	19	(	(	PUNCT
ejpam-6596	120	20	e∗	e∗	PROPN
ejpam-6596	120	21	)	)	PUNCT
ejpam-6596	120	22	and	and	CCONJ
ejpam-6596	120	23	without	without	ADP
ejpam-6596	120	24	illness	illness	NOUN
ejpam-6596	120	25	equilibrium	equilibrium	NOUN
ejpam-6596	120	26	point	point	NOUN
ejpam-6596	120	27	’s	’s	PART
ejpam-6596	120	28	(	(	PUNCT
ejpam-6596	120	29	e0	e0	PROPN
ejpam-6596	120	30	)	)	PUNCT
ejpam-6596	120	31	local	local	ADJ
ejpam-6596	120	32	and	and	CCONJ
ejpam-6596	120	33	global	global	ADJ
ejpam-6596	120	34	stability	stability	NOUN
ejpam-6596	120	35	analyses	analysis	NOUN
ejpam-6596	120	36	.	.	PUNCT
ejpam-6596	121	1	5.1	5.1	NUM
ejpam-6596	121	2	.	.	PUNCT
ejpam-6596	122	1	local	local	ADJ
ejpam-6596	122	2	stability	stability	NOUN
ejpam-6596	122	3	analysis	analysis	NOUN
ejpam-6596	122	4	of	of	ADP
ejpam-6596	122	5	general	general	ADJ
ejpam-6596	122	6	disease	disease	NOUN
ejpam-6596	122	7	model	model	NOUN
ejpam-6596	122	8	theorem	theorem	VERB
ejpam-6596	122	9	2	2	NUM
ejpam-6596	122	10	.	.	PUNCT
ejpam-6596	123	1	if	if	SCONJ
ejpam-6596	123	2	r0	r0	NOUN
ejpam-6596	123	3	<	<	X
ejpam-6596	123	4	1	1	NUM
ejpam-6596	123	5	,	,	PUNCT
ejpam-6596	123	6	then	then	ADV
ejpam-6596	123	7	the	the	DET
ejpam-6596	123	8	system	system	NOUN
ejpam-6596	123	9	’s	’s	PART
ejpam-6596	123	10	disease	disease	NOUN
ejpam-6596	123	11	-	-	PUNCT
ejpam-6596	123	12	free	free	ADJ
ejpam-6596	123	13	equilibrium	equilibrium	NOUN
ejpam-6596	123	14	point	point	NOUN
ejpam-6596	123	15	e0	e0	PROPN
ejpam-6596	123	16	is	be	AUX
ejpam-6596	123	17	locally	locally	ADV
ejpam-6596	123	18	asymptotically	asymptotically	ADV
ejpam-6596	123	19	stable	stable	ADJ
ejpam-6596	123	20	.	.	PUNCT
ejpam-6596	124	1	proof	proof	NOUN
ejpam-6596	124	2	.	.	PUNCT
ejpam-6596	125	1	the	the	DET
ejpam-6596	125	2	jacobin	jacobin	PROPN
ejpam-6596	125	3	matrix	matrix	NOUN
ejpam-6596	125	4	at	at	ADP
ejpam-6596	125	5	disease	disease	NOUN
ejpam-6596	125	6	free	free	ADJ
ejpam-6596	125	7	equilibrium	equilibrium	NOUN
ejpam-6596	125	8	is	be	AUX
ejpam-6596	125	9	;	;	PUNCT
ejpam-6596	125	10	j(e0	j(e0	ADJ
ejpam-6596	125	11	)	)	PUNCT
ejpam-6596	125	12	=	=	SYM
ejpam-6596	125	13			NOUN
ejpam-6596	125	14	−(m+	−(m+	NUM
ejpam-6596	125	15	b1	b1	NOUN
ejpam-6596	125	16	)	)	PUNCT
ejpam-6596	125	17	0	0	NUM
ejpam-6596	126	1	−	−	PROPN
ejpam-6596	126	2	hg	hg	NOUN
ejpam-6596	126	3	m+b1	m+b1	VERB
ejpam-6596	126	4	0	0	NUM
ejpam-6596	126	5	0	0	NUM
ejpam-6596	126	6	0	0	NUM
ejpam-6596	126	7	−(m+	−(m+	NOUN
ejpam-6596	126	8	c+	c+	NOUN
ejpam-6596	126	9	b2	b2	NOUN
ejpam-6596	126	10	)	)	PUNCT
ejpam-6596	126	11	hg	hg	NOUN
ejpam-6596	126	12	m+b1	m+b1	VERB
ejpam-6596	126	13	0	0	NUM
ejpam-6596	126	14	0	0	NUM
ejpam-6596	126	15	0	0	NUM
ejpam-6596	126	16	c	c	NOUN
ejpam-6596	126	17	−(m+	−(m+	X
ejpam-6596	126	18	b3	b3	PROPN
ejpam-6596	126	19	+	+	CCONJ
ejpam-6596	126	20	q	q	PROPN
ejpam-6596	126	21	+	+	NUM
ejpam-6596	126	22	µ	µ	X
ejpam-6596	126	23	)	)	PUNCT
ejpam-6596	126	24	0	0	NUM
ejpam-6596	126	25	0	0	NUM
ejpam-6596	126	26	b1	b1	NOUN
ejpam-6596	126	27	b2	b2	NOUN
ejpam-6596	126	28	b3	b3	PROPN
ejpam-6596	126	29	−(m+	−(m+	X
ejpam-6596	126	30	p	p	NOUN
ejpam-6596	126	31	)	)	PUNCT
ejpam-6596	126	32	0	0	NUM
ejpam-6596	126	33	0	0	NUM
ejpam-6596	126	34	0	0	NUM
ejpam-6596	127	1	q	q	NOUN
ejpam-6596	127	2	p	p	X
ejpam-6596	127	3	−m	−m	NOUN
ejpam-6596	127	4			NOUN
ejpam-6596	127	5	.	.	PUNCT
ejpam-6596	128	1	the	the	DET
ejpam-6596	128	2	three	three	NUM
ejpam-6596	128	3	eigenvalues	eigenvalue	NOUN
ejpam-6596	128	4	are	be	AUX
ejpam-6596	128	5	λ1	λ1	ADJ
ejpam-6596	128	6	=	=	SYM
ejpam-6596	128	7	−m	−m	NOUN
ejpam-6596	128	8	,	,	PUNCT
ejpam-6596	128	9	λ2	λ2	NOUN
ejpam-6596	128	10	=	=	SYM
ejpam-6596	128	11	−(m+	−(m+	NUM
ejpam-6596	128	12	p	p	NOUN
ejpam-6596	128	13	)	)	PUNCT
ejpam-6596	128	14	and	and	CCONJ
ejpam-6596	128	15	λ3	λ3	PROPN
ejpam-6596	128	16	=	=	SYM
ejpam-6596	128	17	−(m+	−(m+	NUM
ejpam-6596	128	18	b1	b1	NOUN
ejpam-6596	128	19	)	)	PUNCT
ejpam-6596	128	20	.	.	PUNCT
ejpam-6596	129	1	to	to	PART
ejpam-6596	129	2	find	find	VERB
ejpam-6596	129	3	the	the	DET
ejpam-6596	129	4	next	next	ADJ
ejpam-6596	129	5	eigenvalues	eigenvalue	NOUN
ejpam-6596	129	6	,	,	PUNCT
ejpam-6596	129	7	we	we	PRON
ejpam-6596	129	8	use	use	VERB
ejpam-6596	129	9	the	the	DET
ejpam-6596	129	10	2×	2×	NUM
ejpam-6596	129	11	2	2	NUM
ejpam-6596	129	12	matrix	matrix	NOUN
ejpam-6596	129	13	and	and	CCONJ
ejpam-6596	129	14	after	after	ADP
ejpam-6596	129	15	algebraic	algebraic	ADJ
ejpam-6596	129	16	manipulation	manipulation	NOUN
ejpam-6596	129	17	we	we	PRON
ejpam-6596	129	18	reached	reach	VERB
ejpam-6596	129	19	to	to	ADP
ejpam-6596	129	20	λ2	λ2	PROPN
ejpam-6596	129	21	+	+	CCONJ
ejpam-6596	129	22	λ(2m+	λ(2m+	NOUN
ejpam-6596	129	23	c+	c+	PROPN
ejpam-6596	129	24	b2	b2	NOUN
ejpam-6596	129	25	+	+	CCONJ
ejpam-6596	129	26	b3	b3	PROPN
ejpam-6596	129	27	+	+	CCONJ
ejpam-6596	129	28	q	q	PROPN
ejpam-6596	129	29	+	+	NUM
ejpam-6596	129	30	µ	µ	X
ejpam-6596	129	31	)	)	PUNCT
ejpam-6596	129	32	+	+	CCONJ
ejpam-6596	129	33	(	(	PUNCT
ejpam-6596	129	34	m+	m+	NOUN
ejpam-6596	129	35	c+	c+	X
ejpam-6596	129	36	b2)(m+	b2)(m+	ADP
ejpam-6596	129	37	b3	b3	PROPN
ejpam-6596	129	38	+	+	CCONJ
ejpam-6596	129	39	q	q	PROPN
ejpam-6596	129	40	+	+	PUNCT
ejpam-6596	129	41	µ)−	µ)−	PROPN
ejpam-6596	129	42	hgc	hgc	NOUN
ejpam-6596	129	43	m+	m+	NUM
ejpam-6596	129	44	b1	b1	NOUN
ejpam-6596	129	45	=	=	SYM
ejpam-6596	129	46	0	0	PROPN
ejpam-6596	129	47	.	.	PUNCT
ejpam-6596	130	1	(	(	PUNCT
ejpam-6596	130	2	4	4	X
ejpam-6596	130	3	)	)	PUNCT
ejpam-6596	130	4	when	when	SCONJ
ejpam-6596	130	5	r0	r0	NOUN
ejpam-6596	130	6	>	>	X
ejpam-6596	130	7	1	1	NUM
ejpam-6596	130	8	,	,	PUNCT
ejpam-6596	130	9	then	then	ADV
ejpam-6596	130	10	the	the	DET
ejpam-6596	130	11	above	above	ADJ
ejpam-6596	130	12	equation	equation	NOUN
ejpam-6596	130	13	(	(	PUNCT
ejpam-6596	130	14	m+c+b2)(m+b3+q+µ)−	m+c+b2)(m+b3+q+µ)−	NOUN
ejpam-6596	130	15	hgc	hgc	NOUN
ejpam-6596	130	16	m+b1	m+b1	NOUN
ejpam-6596	130	17	<	<	X
ejpam-6596	130	18	0	0	NUM
ejpam-6596	130	19	,	,	PUNCT
ejpam-6596	130	20	this	this	PRON
ejpam-6596	130	21	implies	imply	VERB
ejpam-6596	130	22	that	that	SCONJ
ejpam-6596	130	23	eq	eq	ADP
ejpam-6596	130	24	.	.	PUNCT
ejpam-6596	131	1	(	(	PUNCT
ejpam-6596	131	2	4	4	X
ejpam-6596	131	3	)	)	PUNCT
ejpam-6596	131	4	has	have	VERB
ejpam-6596	131	5	a	a	DET
ejpam-6596	131	6	positive	positive	ADJ
ejpam-6596	131	7	and	and	CCONJ
ejpam-6596	131	8	negative	negative	ADJ
ejpam-6596	131	9	root	root	NOUN
ejpam-6596	131	10	.	.	PUNCT
ejpam-6596	132	1	therefore	therefore	ADV
ejpam-6596	132	2	,	,	PUNCT
ejpam-6596	132	3	the	the	DET
ejpam-6596	132	4	disease	disease	NOUN
ejpam-6596	132	5	-	-	PUNCT
ejpam-6596	132	6	free	free	ADJ
ejpam-6596	132	7	equilibrium	equilibrium	NOUN
ejpam-6596	132	8	e0	e0	PROPN
ejpam-6596	132	9	is	be	AUX
ejpam-6596	132	10	unstable	unstable	ADJ
ejpam-6596	132	11	.	.	PUNCT
ejpam-6596	133	1	5.2	5.2	NUM
ejpam-6596	133	2	.	.	PUNCT
ejpam-6596	134	1	global	global	ADJ
ejpam-6596	134	2	asymptotic	asymptotic	ADJ
ejpam-6596	134	3	stability	stability	NOUN
ejpam-6596	134	4	of	of	ADP
ejpam-6596	134	5	the	the	DET
ejpam-6596	134	6	disease	disease	NOUN
ejpam-6596	134	7	free	free	ADJ
ejpam-6596	134	8	equilibrium	equilibrium	NOUN
ejpam-6596	134	9	in	in	ADP
ejpam-6596	134	10	order	order	NOUN
ejpam-6596	134	11	to	to	PART
ejpam-6596	134	12	demonstrate	demonstrate	VERB
ejpam-6596	134	13	the	the	DET
ejpam-6596	134	14	globally	globally	ADV
ejpam-6596	134	15	asymptotically	asymptotically	ADV
ejpam-6596	134	16	stable	stable	ADJ
ejpam-6596	134	17	nature	nature	NOUN
ejpam-6596	134	18	of	of	ADP
ejpam-6596	134	19	the	the	DET
ejpam-6596	134	20	disease	disease	NOUN
ejpam-6596	134	21	-	-	PUNCT
ejpam-6596	134	22	free	free	ADJ
ejpam-6596	134	23	equilibrium	equilibrium	NOUN
ejpam-6596	134	24	e0	e0	PROPN
ejpam-6596	134	25	,	,	PUNCT
ejpam-6596	134	26	we	we	PRON
ejpam-6596	134	27	examine	examine	VERB
ejpam-6596	134	28	the	the	DET
ejpam-6596	134	29	lyapunov	lyapunov	ADJ
ejpam-6596	134	30	function	function	NOUN
ejpam-6596	134	31	for	for	ADP
ejpam-6596	134	32	r0	r0	NOUN
ejpam-6596	134	33	≤	≤	NOUN
ejpam-6596	134	34	1	1	NUM
ejpam-6596	134	35	,	,	PUNCT
ejpam-6596	134	36	.	.	PUNCT
ejpam-6596	135	1	h(e	h(e	PROPN
ejpam-6596	135	2	,	,	PUNCT
ejpam-6596	135	3	i	i	NOUN
ejpam-6596	135	4	)	)	PUNCT
ejpam-6596	135	5	=	=	PUNCT
ejpam-6596	135	6	b1e	b1e	X
ejpam-6596	135	7	+	+	ADJ
ejpam-6596	135	8	b2i	b2i	PUNCT
ejpam-6596	135	9	the	the	DET
ejpam-6596	135	10	derivation	derivation	NOUN
ejpam-6596	135	11	of	of	ADP
ejpam-6596	135	12	h(e	h(e	PROPN
ejpam-6596	135	13	,	,	PUNCT
ejpam-6596	135	14	i	i	NOUN
ejpam-6596	135	15	)	)	PUNCT
ejpam-6596	135	16	with	with	ADP
ejpam-6596	135	17	regrd	regrd	NOUN
ejpam-6596	135	18	to	to	ADP
ejpam-6596	135	19	t	t	PROPN
ejpam-6596	135	20	gives	give	VERB
ejpam-6596	135	21	,	,	PUNCT
ejpam-6596	135	22	dh	dh	NOUN
ejpam-6596	135	23	dt	dt	NOUN
ejpam-6596	135	24	=	=	PUNCT
ejpam-6596	135	25	b1	b1	PROPN
ejpam-6596	135	26	de	de	ADP
ejpam-6596	135	27	dt	dt	X
ejpam-6596	135	28	+	+	PROPN
ejpam-6596	135	29	b2	b2	NOUN
ejpam-6596	135	30	di	di	NOUN
ejpam-6596	135	31	dt	dt	NOUN
ejpam-6596	135	32	,	,	PUNCT
ejpam-6596	135	33	di	di	INTJ
ejpam-6596	135	34	dt	dt	NOUN
ejpam-6596	135	35	=	=	SYM
ejpam-6596	135	36	b1	b1	PROPN
ejpam-6596	135	37	(	(	PUNCT
ejpam-6596	135	38	hsi	hsi	PROPN
ejpam-6596	135	39	1	1	NUM
ejpam-6596	136	1	+	+	CCONJ
ejpam-6596	136	2	αi	αi	VERB
ejpam-6596	136	3	−	−	X
ejpam-6596	137	1	(	(	PUNCT
ejpam-6596	137	2	m+	m+	NUM
ejpam-6596	137	3	c+	c+	NOUN
ejpam-6596	137	4	b2)e	b2)e	ADJ
ejpam-6596	137	5	)	)	PUNCT
ejpam-6596	138	1	+	+	NUM
ejpam-6596	138	2	b2	b2	NOUN
ejpam-6596	138	3	(	(	PUNCT
ejpam-6596	138	4	ce	ce	PROPN
ejpam-6596	138	5	−	−	PROPN
ejpam-6596	138	6	(	(	PUNCT
ejpam-6596	138	7	m+	m+	NUM
ejpam-6596	138	8	b3	b3	PROPN
ejpam-6596	138	9	+	+	CCONJ
ejpam-6596	138	10	q	q	X
ejpam-6596	138	11	+	+	X
ejpam-6596	138	12	µ)i	µ)i	X
ejpam-6596	138	13	)	)	PUNCT
ejpam-6596	138	14	,	,	PUNCT
ejpam-6596	139	1	=	=	SYM
ejpam-6596	139	2	b1	b1	PROPN
ejpam-6596	139	3	hsi	hsi	PROPN
ejpam-6596	139	4	1	1	NUM
ejpam-6596	139	5	+	+	CCONJ
ejpam-6596	139	6	αi	αi	PRON
ejpam-6596	139	7	−b1(m+	−b1(m+	VERB
ejpam-6596	139	8	c+	c+	NOUN
ejpam-6596	139	9	b2)e	b2)e	VERB
ejpam-6596	139	10	+	+	PROPN
ejpam-6596	139	11	b2ce	b2ce	X
ejpam-6596	139	12	−b2(m+	−b2(m+	PUNCT
ejpam-6596	139	13	b3	b3	NOUN
ejpam-6596	139	14	+	+	CCONJ
ejpam-6596	139	15	q	q	X
ejpam-6596	139	16	+	+	X
ejpam-6596	139	17	µ)i	µ)i	ADJ
ejpam-6596	139	18	,	,	PUNCT
ejpam-6596	139	19	(	(	PUNCT
ejpam-6596	139	20	5	5	X
ejpam-6596	139	21	)	)	PUNCT
ejpam-6596	139	22	n.	n.	NOUN
ejpam-6596	139	23	gul	gul	PROPN
ejpam-6596	139	24	et	et	PROPN
ejpam-6596	139	25	al	al	PROPN
ejpam-6596	139	26	.	.	PUNCT
ejpam-6596	139	27	/	/	SYM
ejpam-6596	139	28	eur	eur	PROPN
ejpam-6596	139	29	.	.	PUNCT
ejpam-6596	140	1	j.	j.	PROPN
ejpam-6596	140	2	pure	pure	PROPN
ejpam-6596	140	3	appl	appl	PROPN
ejpam-6596	140	4	.	.	PROPN
ejpam-6596	140	5	math	math	PROPN
ejpam-6596	140	6	,	,	PUNCT
ejpam-6596	140	7	18	18	NUM
ejpam-6596	140	8	(	(	PUNCT
ejpam-6596	140	9	4	4	NUM
ejpam-6596	140	10	)	)	PUNCT
ejpam-6596	140	11	(	(	PUNCT
ejpam-6596	140	12	2025	2025	NUM
ejpam-6596	140	13	)	)	PUNCT
ejpam-6596	140	14	,	,	PUNCT
ejpam-6596	140	15	6596	6596	NUM
ejpam-6596	140	16	9	9	NUM
ejpam-6596	140	17	of	of	ADP
ejpam-6596	140	18	23	23	NUM
ejpam-6596	140	19	calculating	calculate	VERB
ejpam-6596	140	20	the	the	DET
ejpam-6596	140	21	above	above	ADJ
ejpam-6596	140	22	equation	equation	NOUN
ejpam-6596	140	23	which	which	PRON
ejpam-6596	140	24	gives	give	VERB
ejpam-6596	140	25	b1	b1	NOUN
ejpam-6596	140	26	=	=	SYM
ejpam-6596	140	27	c	c	NOUN
ejpam-6596	140	28	,	,	PUNCT
ejpam-6596	140	29	and	and	CCONJ
ejpam-6596	140	30	b2	b2	NOUN
ejpam-6596	140	31	=	=	SYM
ejpam-6596	140	32	(	(	PUNCT
ejpam-6596	140	33	m+	m+	NOUN
ejpam-6596	140	34	c+	c+	NOUN
ejpam-6596	140	35	b2	b2	NOUN
ejpam-6596	140	36	)	)	PUNCT
ejpam-6596	140	37	.	.	PUNCT
ejpam-6596	141	1	so	so	ADV
ejpam-6596	141	2	,	,	PUNCT
ejpam-6596	141	3	dh	dh	NOUN
ejpam-6596	141	4	dt	dt	NOUN
ejpam-6596	142	1	=	=	PUNCT
ejpam-6596	142	2	[	[	PUNCT
ejpam-6596	142	3	chs	chs	X
ejpam-6596	142	4	1	1	NUM
ejpam-6596	142	5	+	+	CCONJ
ejpam-6596	142	6	αi	αi	VERB
ejpam-6596	142	7	−	−	X
ejpam-6596	142	8	(	(	PUNCT
ejpam-6596	142	9	m+	m+	NOUN
ejpam-6596	142	10	c+	c+	X
ejpam-6596	142	11	b2)(m+	b2)(m+	ADP
ejpam-6596	142	12	b3	b3	PROPN
ejpam-6596	142	13	+	+	CCONJ
ejpam-6596	142	14	q	q	PROPN
ejpam-6596	142	15	+	+	NUM
ejpam-6596	142	16	µ	µ	X
ejpam-6596	142	17	)	)	PUNCT
ejpam-6596	142	18	]	]	PUNCT
ejpam-6596	142	19	≤	≤	NOUN
ejpam-6596	142	20	[	[	PUNCT
ejpam-6596	142	21	chs	chs	X
ejpam-6596	142	22	1	1	NUM
ejpam-6596	143	1	+	+	CCONJ
ejpam-6596	143	2	αi	αi	VERB
ejpam-6596	143	3	−	−	X
ejpam-6596	144	1	(	(	PUNCT
ejpam-6596	144	2	m+	m+	NOUN
ejpam-6596	144	3	c+	c+	X
ejpam-6596	144	4	b2)(m+	b2)(m+	ADP
ejpam-6596	144	5	b3	b3	PROPN
ejpam-6596	144	6	+	+	CCONJ
ejpam-6596	144	7	q	q	PROPN
ejpam-6596	144	8	+	+	NUM
ejpam-6596	144	9	µ	µ	X
ejpam-6596	144	10	)	)	PUNCT
ejpam-6596	144	11	]	]	PUNCT
ejpam-6596	144	12	≤	≤	NUM
ejpam-6596	144	13	chs0	chs0	PROPN
ejpam-6596	144	14	r0	r0	NOUN
ejpam-6596	144	15	[	[	PUNCT
ejpam-6596	144	16	r0s	r0	NOUN
ejpam-6596	144	17	s0	s0	NOUN
ejpam-6596	144	18	−	−	PROPN
ejpam-6596	144	19	1	1	NUM
ejpam-6596	144	20	]	]	PUNCT
ejpam-6596	144	21	i	i	PRON
ejpam-6596	144	22	≤	≤	ADV
ejpam-6596	144	23	0	0	NUM
ejpam-6596	144	24	.	.	PUNCT
ejpam-6596	145	1	(	(	PUNCT
ejpam-6596	145	2	6	6	NUM
ejpam-6596	145	3	)	)	PUNCT
ejpam-6596	145	4	furthermore	furthermore	ADV
ejpam-6596	145	5	dh(e	dh(e	VERB
ejpam-6596	145	6	,	,	PUNCT
ejpam-6596	145	7	i	i	NOUN
ejpam-6596	145	8	)	)	PUNCT
ejpam-6596	145	9	dt	dt	PROPN
ejpam-6596	146	1	=	=	PUNCT
ejpam-6596	146	2	0	0	PUNCT
ejpam-6596	147	1	if	if	SCONJ
ejpam-6596	147	2	and	and	CCONJ
ejpam-6596	147	3	only	only	ADV
ejpam-6596	147	4	if	if	SCONJ
ejpam-6596	147	5	i	i	PRON
ejpam-6596	147	6	=	=	NOUN
ejpam-6596	147	7	0	0	X
ejpam-6596	147	8	.	.	PUNCT
ejpam-6596	148	1	in	in	ADP
ejpam-6596	148	2	light	light	NOUN
ejpam-6596	148	3	of	of	ADP
ejpam-6596	148	4	this	this	PRON
ejpam-6596	148	5	,	,	PUNCT
ejpam-6596	148	6	the	the	DET
ejpam-6596	148	7	greatest	great	ADJ
ejpam-6596	148	8	compact	compact	ADJ
ejpam-6596	148	9	invariant	invariant	ADJ
ejpam-6596	148	10	set	set	VERB
ejpam-6596	148	11	in	in	ADP
ejpam-6596	148	12	{	{	PUNCT
ejpam-6596	148	13	(	(	PUNCT
ejpam-6596	148	14	s	s	X
ejpam-6596	148	15	,	,	PUNCT
ejpam-6596	148	16	e	e	NOUN
ejpam-6596	148	17	,	,	PUNCT
ejpam-6596	148	18	i	i	PRON
ejpam-6596	148	19	,	,	PUNCT
ejpam-6596	148	20	q	q	X
ejpam-6596	148	21	,	,	PUNCT
ejpam-6596	148	22	r)|h(e	r)|h(e	PROPN
ejpam-6596	148	23	,	,	PUNCT
ejpam-6596	148	24	i	i	NOUN
ejpam-6596	148	25	)	)	PUNCT
ejpam-6596	149	1	=	=	PUNCT
ejpam-6596	149	2	0	0	NUM
ejpam-6596	149	3	}	}	PUNCT
ejpam-6596	149	4	.	.	PUNCT
ejpam-6596	150	1	when	when	SCONJ
ejpam-6596	150	2	r0	r0	NOUN
ejpam-6596	150	3	≤	≤	NOUN
ejpam-6596	150	4	1	1	NUM
ejpam-6596	150	5	,	,	PUNCT
ejpam-6596	150	6	is	be	AUX
ejpam-6596	150	7	the	the	DET
ejpam-6596	150	8	singleton	singleton	PROPN
ejpam-6596	150	9	e0	e0	PROPN
ejpam-6596	150	10	.	.	PUNCT
ejpam-6596	151	1	lasalle	lasalle	PROPN
ejpam-6596	151	2	’s	’s	PART
ejpam-6596	151	3	invariance	invariance	NOUN
ejpam-6596	151	4	principle	principle	NOUN
ejpam-6596	151	5	implies	imply	VERB
ejpam-6596	151	6	that	that	SCONJ
ejpam-6596	151	7	e0	e0	PROPN
ejpam-6596	151	8	is	be	AUX
ejpam-6596	151	9	locally	locally	ADV
ejpam-6596	151	10	asymptotically	asymptotically	ADV
ejpam-6596	151	11	stable	stable	ADJ
ejpam-6596	151	12	.	.	PUNCT
ejpam-6596	152	1	5.3	5.3	NUM
ejpam-6596	152	2	.	.	PUNCT
ejpam-6596	153	1	local	local	ADJ
ejpam-6596	153	2	asymptotic	asymptotic	ADJ
ejpam-6596	153	3	stability	stability	NOUN
ejpam-6596	153	4	of	of	ADP
ejpam-6596	153	5	endemic	endemic	ADJ
ejpam-6596	153	6	equilibrium	equilibrium	NOUN
ejpam-6596	153	7	theorem	theorem	NOUN
ejpam-6596	153	8	3	3	X
ejpam-6596	153	9	.	.	PUNCT
ejpam-6596	154	1	if	if	SCONJ
ejpam-6596	154	2	1	1	NUM
ejpam-6596	154	3	<	<	X
ejpam-6596	154	4	r0	r0	NOUN
ejpam-6596	154	5	then	then	ADV
ejpam-6596	154	6	(	(	PUNCT
ejpam-6596	154	7	1	1	X
ejpam-6596	154	8	)	)	PUNCT
ejpam-6596	154	9	at	at	ADP
ejpam-6596	154	10	endemic	endemic	ADJ
ejpam-6596	154	11	equilibrium	equilibrium	NOUN
ejpam-6596	154	12	,	,	PUNCT
ejpam-6596	154	13	is	be	AUX
ejpam-6596	154	14	locally	locally	ADV
ejpam-6596	154	15	asymptotically	asymptotically	ADV
ejpam-6596	154	16	stable	stable	ADJ
ejpam-6596	154	17	.	.	PUNCT
ejpam-6596	155	1	the	the	DET
ejpam-6596	155	2	situation	situation	NOUN
ejpam-6596	155	3	of	of	ADP
ejpam-6596	155	4	endemicity	endemicity	NOUN
ejpam-6596	155	5	state	state	NOUN
ejpam-6596	155	6	is	be	AUX
ejpam-6596	155	7	unstable	unstable	ADJ
ejpam-6596	155	8	whenever	whenever	SCONJ
ejpam-6596	155	9	1	1	NUM
ejpam-6596	155	10	>	>	X
ejpam-6596	155	11	r0	r0	NOUN
ejpam-6596	155	12	.	.	PUNCT
ejpam-6596	156	1	proof	proof	NOUN
ejpam-6596	156	2	.	.	PUNCT
ejpam-6596	157	1	jacobian	jacobian	ADJ
ejpam-6596	157	2	matrix	matrix	NOUN
ejpam-6596	157	3	j	j	PROPN
ejpam-6596	157	4	at	at	ADP
ejpam-6596	157	5	e∗	e∗	PROPN
ejpam-6596	157	6	shows	show	VERB
ejpam-6596	157	7	that	that	SCONJ
ejpam-6596	157	8	j	j	PROPN
ejpam-6596	157	9	(	(	PUNCT
ejpam-6596	157	10	e∗	e∗	PROPN
ejpam-6596	157	11	)	)	PUNCT
ejpam-6596	157	12	=	=	PRON
ejpam-6596	157	13			VERB
ejpam-6596	157	14	−	−	PROPN
ejpam-6596	157	15	hi∗	hi∗	NOUN
ejpam-6596	157	16	1+αi∗	1+αi∗	NUM
ejpam-6596	157	17	−	−	PROPN
ejpam-6596	157	18	(	(	PUNCT
ejpam-6596	157	19	m+	m+	NUM
ejpam-6596	157	20	b1	b1	NOUN
ejpam-6596	157	21	)	)	PUNCT
ejpam-6596	157	22	0	0	NUM
ejpam-6596	157	23	hs∗	hs∗	PROPN
ejpam-6596	157	24	(	(	PUNCT
ejpam-6596	157	25	1+αi∗)2	1+αi∗)2	NUM
ejpam-6596	157	26	0	0	NUM
ejpam-6596	157	27	0	0	NUM
ejpam-6596	157	28	hi∗	hi∗	NOUN
ejpam-6596	157	29	1+αi∗	1+αi∗	NUM
ejpam-6596	157	30	−(m+	−(m+	NOUN
ejpam-6596	157	31	c+	c+	NOUN
ejpam-6596	157	32	b2	b2	NOUN
ejpam-6596	157	33	)	)	PUNCT
ejpam-6596	157	34	hs∗	hs∗	NOUN
ejpam-6596	157	35	(	(	PUNCT
ejpam-6596	157	36	1+αi∗)2	1+αi∗)2	NUM
ejpam-6596	157	37	0	0	NUM
ejpam-6596	157	38	0	0	NUM
ejpam-6596	157	39	0	0	NUM
ejpam-6596	157	40	c	c	NOUN
ejpam-6596	157	41	−(m+	−(m+	X
ejpam-6596	157	42	b3	b3	PROPN
ejpam-6596	157	43	+	+	CCONJ
ejpam-6596	157	44	q	q	PROPN
ejpam-6596	157	45	+	+	NUM
ejpam-6596	157	46	µ	µ	X
ejpam-6596	157	47	)	)	PUNCT
ejpam-6596	157	48	0	0	NUM
ejpam-6596	157	49	0	0	NUM
ejpam-6596	157	50	b1	b1	NOUN
ejpam-6596	157	51	b2	b2	NOUN
ejpam-6596	157	52	b3	b3	PROPN
ejpam-6596	157	53	−(m+	−(m+	X
ejpam-6596	157	54	p	p	NOUN
ejpam-6596	157	55	)	)	PUNCT
ejpam-6596	157	56	0	0	NUM
ejpam-6596	157	57	0	0	NUM
ejpam-6596	157	58	0	0	NUM
ejpam-6596	158	1	q	q	NOUN
ejpam-6596	158	2	p	p	X
ejpam-6596	158	3	−m	−m	NOUN
ejpam-6596	158	4			NOUN
ejpam-6596	158	5	.	.	PUNCT
ejpam-6596	159	1	eigenvalues	eigenvalue	NOUN
ejpam-6596	159	2	of	of	ADP
ejpam-6596	159	3	j(e∗	j(e∗	NOUN
ejpam-6596	159	4	)	)	PUNCT
ejpam-6596	159	5	are	be	AUX
ejpam-6596	159	6	negative	negative	ADJ
ejpam-6596	159	7	numbers	number	NOUN
ejpam-6596	159	8	that	that	PRON
ejpam-6596	159	9	are	be	AUX
ejpam-6596	159	10	λ1	λ1	ADJ
ejpam-6596	159	11	=	=	SYM
ejpam-6596	159	12	−m	−m	NOUN
ejpam-6596	159	13	,	,	PUNCT
ejpam-6596	160	1	λ2	λ2	NOUN
ejpam-6596	160	2	=	=	SYM
ejpam-6596	160	3	−(m	−(m	PROPN
ejpam-6596	161	1	+	+	CCONJ
ejpam-6596	161	2	p	p	X
ejpam-6596	161	3	)	)	PUNCT
ejpam-6596	161	4	then	then	ADV
ejpam-6596	161	5	we	we	PRON
ejpam-6596	161	6	only	only	ADV
ejpam-6596	161	7	need	need	VERB
ejpam-6596	161	8	to	to	PART
ejpam-6596	161	9	consider	consider	VERB
ejpam-6596	161	10	the	the	DET
ejpam-6596	161	11	roots	root	NOUN
ejpam-6596	161	12	of	of	ADP
ejpam-6596	161	13	λ3	λ3	PROPN
ejpam-6596	161	14	+	+	PROPN
ejpam-6596	161	15	b1λ	b1λ	PROPN
ejpam-6596	161	16	2	2	NUM
ejpam-6596	161	17	+	+	NOUN
ejpam-6596	161	18	b2λ+b3	b2λ+b3	ADJ
ejpam-6596	161	19	=	=	ADJ
ejpam-6596	161	20	0	0	NUM
ejpam-6596	161	21	,	,	PUNCT
ejpam-6596	161	22	where	where	SCONJ
ejpam-6596	161	23	b1	b1	NOUN
ejpam-6596	161	24	=	=	SYM
ejpam-6596	161	25	hi∗	hi∗	NOUN
ejpam-6596	161	26	1	1	NUM
ejpam-6596	161	27	+	+	NUM
ejpam-6596	161	28	αi∗	αi∗	NOUN
ejpam-6596	161	29	+	+	CCONJ
ejpam-6596	161	30	3m+	3m+	NUM
ejpam-6596	161	31	2b1	2b1	NUM
ejpam-6596	161	32	+	+	NUM
ejpam-6596	161	33	b3	b3	PROPN
ejpam-6596	161	34	+	+	CCONJ
ejpam-6596	161	35	c+	c+	X
ejpam-6596	161	36	q	q	X
ejpam-6596	161	37	>	>	X
ejpam-6596	161	38	0	0	NUM
ejpam-6596	161	39	,	,	PUNCT
ejpam-6596	161	40	b2	b2	NOUN
ejpam-6596	161	41	=	=	SYM
ejpam-6596	161	42	(	(	PUNCT
ejpam-6596	161	43	hi∗	hi∗	NOUN
ejpam-6596	161	44	1	1	NUM
ejpam-6596	161	45	+	+	NUM
ejpam-6596	161	46	αi∗	αi∗	NOUN
ejpam-6596	162	1	+	+	ADJ
ejpam-6596	162	2	m+	m+	NOUN
ejpam-6596	162	3	b1	b1	NOUN
ejpam-6596	162	4	)	)	PUNCT
ejpam-6596	162	5	(	(	PUNCT
ejpam-6596	162	6	2m+	2m+	NUM
ejpam-6596	162	7	b2	b2	NOUN
ejpam-6596	162	8	+	+	CCONJ
ejpam-6596	162	9	b3	b3	PROPN
ejpam-6596	162	10	+	+	CCONJ
ejpam-6596	162	11	c+	c+	X
ejpam-6596	162	12	q	q	X
ejpam-6596	162	13	+	+	NUM
ejpam-6596	162	14	µ	µ	X
ejpam-6596	162	15	)	)	PUNCT
ejpam-6596	162	16	+	+	CCONJ
ejpam-6596	162	17	(	(	PUNCT
ejpam-6596	162	18	m+	m+	NUM
ejpam-6596	162	19	c+	c+	NOUN
ejpam-6596	162	20	b1	b1	NOUN
ejpam-6596	162	21	)	)	PUNCT
ejpam-6596	162	22	(	(	PUNCT
ejpam-6596	162	23	m+	m+	NUM
ejpam-6596	162	24	b3	b3	PROPN
ejpam-6596	162	25	+	+	CCONJ
ejpam-6596	162	26	q	q	PROPN
ejpam-6596	162	27	+	+	PUNCT
ejpam-6596	162	28	µ)−	µ)−	NOUN
ejpam-6596	162	29	chs∗	chs∗	NOUN
ejpam-6596	162	30	(	(	PUNCT
ejpam-6596	162	31	1	1	NUM
ejpam-6596	162	32	+	+	NUM
ejpam-6596	162	33	αi∗)2	αi∗)2	NUM
ejpam-6596	162	34	>	>	PUNCT
ejpam-6596	162	35	(	(	PUNCT
ejpam-6596	162	36	hi∗	hi∗	NOUN
ejpam-6596	162	37	1	1	NUM
ejpam-6596	162	38	+	+	NUM
ejpam-6596	162	39	αi∗	αi∗	NOUN
ejpam-6596	163	1	+	+	ADJ
ejpam-6596	163	2	m+	m+	NOUN
ejpam-6596	163	3	b1	b1	NOUN
ejpam-6596	163	4	)	)	PUNCT
ejpam-6596	163	5	(	(	PUNCT
ejpam-6596	163	6	2m+	2m+	NUM
ejpam-6596	163	7	b2	b2	NOUN
ejpam-6596	163	8	+	+	CCONJ
ejpam-6596	163	9	b3	b3	PROPN
ejpam-6596	163	10	+	+	CCONJ
ejpam-6596	163	11	c+	c+	X
ejpam-6596	163	12	q	q	X
ejpam-6596	163	13	+	+	NUM
ejpam-6596	163	14	µ	µ	X
ejpam-6596	163	15	)	)	PUNCT
ejpam-6596	163	16	>	>	X
ejpam-6596	163	17	0	0	NUM
ejpam-6596	163	18	,	,	PUNCT
ejpam-6596	163	19	b3	b3	NOUN
ejpam-6596	163	20	=	=	SYM
ejpam-6596	163	21	(	(	PUNCT
ejpam-6596	163	22	hi∗	hi∗	NOUN
ejpam-6596	163	23	1	1	NUM
ejpam-6596	163	24	+	+	NUM
ejpam-6596	163	25	αi∗	αi∗	NOUN
ejpam-6596	164	1	+	+	PROPN
ejpam-6596	164	2	m+	m+	NOUN
ejpam-6596	164	3	b1	b1	NOUN
ejpam-6596	164	4	)	)	PUNCT
ejpam-6596	164	5	(	(	PUNCT
ejpam-6596	164	6	(	(	PUNCT
ejpam-6596	164	7	m+	m+	NUM
ejpam-6596	164	8	c+	c+	NOUN
ejpam-6596	164	9	b1	b1	NOUN
ejpam-6596	164	10	)	)	PUNCT
ejpam-6596	164	11	(	(	PUNCT
ejpam-6596	164	12	m+	m+	NUM
ejpam-6596	164	13	b3	b3	PROPN
ejpam-6596	164	14	+	+	CCONJ
ejpam-6596	164	15	q	q	PROPN
ejpam-6596	165	1	+	+	PUNCT
ejpam-6596	166	1	µ)−	µ)−	NOUN
ejpam-6596	166	2	chs∗	chs∗	NOUN
ejpam-6596	166	3	(	(	PUNCT
ejpam-6596	166	4	1	1	NUM
ejpam-6596	166	5	+	+	NUM
ejpam-6596	166	6	αi∗)2	αi∗)2	NUM
ejpam-6596	166	7	)	)	PUNCT
ejpam-6596	167	1	+	+	CCONJ
ejpam-6596	167	2	ch2s∗i∗	ch2s∗i∗	PROPN
ejpam-6596	167	3	(	(	PUNCT
ejpam-6596	167	4	1	1	NUM
ejpam-6596	167	5	+	+	CCONJ
ejpam-6596	167	6	αi∗)3	αi∗)3	ADV
ejpam-6596	167	7	>	>	X
ejpam-6596	167	8	0	0	X
ejpam-6596	167	9	.	.	PUNCT
ejpam-6596	167	10	based	base	VERB
ejpam-6596	167	11	on	on	ADP
ejpam-6596	167	12	the	the	DET
ejpam-6596	167	13	following	follow	VERB
ejpam-6596	167	14	relation	relation	NOUN
ejpam-6596	167	15	chs∗	chs∗	NOUN
ejpam-6596	167	16	1+αi∗	1+αi∗	NUM
ejpam-6596	167	17	=	=	SYM
ejpam-6596	167	18	(	(	PUNCT
ejpam-6596	167	19	m+	m+	NOUN
ejpam-6596	167	20	c+	c+	NOUN
ejpam-6596	167	21	b1	b1	PROPN
ejpam-6596	167	22	)	)	PUNCT
ejpam-6596	167	23	(	(	PUNCT
ejpam-6596	167	24	m+	m+	NUM
ejpam-6596	167	25	b3	b3	PROPN
ejpam-6596	167	26	+	+	CCONJ
ejpam-6596	167	27	q	q	PROPN
ejpam-6596	167	28	+	+	NUM
ejpam-6596	167	29	µ	µ	NOUN
ejpam-6596	167	30	)	)	PUNCT
ejpam-6596	167	31	.	.	PUNCT
ejpam-6596	168	1	by	by	ADP
ejpam-6596	168	2	a	a	DET
ejpam-6596	168	3	direct	direct	ADJ
ejpam-6596	168	4	calculation	calculation	NOUN
ejpam-6596	168	5	,	,	PUNCT
ejpam-6596	168	6	we	we	PRON
ejpam-6596	168	7	have	have	VERB
ejpam-6596	168	8	that	that	PRON
ejpam-6596	168	9	b1b2−b3	b1b2−b3	VERB
ejpam-6596	168	10	>	>	X
ejpam-6596	168	11	0	0	X
ejpam-6596	168	12	.	.	PUNCT
ejpam-6596	169	1	following	follow	VERB
ejpam-6596	169	2	routh	routh	PROPN
ejpam-6596	169	3	-	-	PUNCT
ejpam-6596	169	4	harwitz	harwitz	PROPN
ejpam-6596	169	5	criteria	criterion	NOUN
ejpam-6596	169	6	one	one	PRON
ejpam-6596	169	7	can	can	AUX
ejpam-6596	169	8	easily	easily	ADV
ejpam-6596	169	9	confirm	confirm	VERB
ejpam-6596	169	10	endemic	endemic	ADJ
ejpam-6596	169	11	equilibrium	equilibrium	NOUN
ejpam-6596	169	12	e∗	e∗	NOUN
ejpam-6596	169	13	is	be	AUX
ejpam-6596	169	14	locally	locally	ADV
ejpam-6596	169	15	asymptotically	asymptotically	ADV
ejpam-6596	169	16	stable	stable	ADJ
ejpam-6596	169	17	.	.	PUNCT
ejpam-6596	170	1	this	this	PRON
ejpam-6596	170	2	completes	complete	VERB
ejpam-6596	170	3	the	the	DET
ejpam-6596	170	4	proof	proof	NOUN
ejpam-6596	170	5	.	.	PUNCT
ejpam-6596	171	1	n.	n.	PROPN
ejpam-6596	171	2	gul	gul	PROPN
ejpam-6596	171	3	et	et	PROPN
ejpam-6596	171	4	al	al	PROPN
ejpam-6596	171	5	.	.	PUNCT
ejpam-6596	171	6	/	/	SYM
ejpam-6596	171	7	eur	eur	PROPN
ejpam-6596	171	8	.	.	PUNCT
ejpam-6596	172	1	j.	j.	PROPN
ejpam-6596	172	2	pure	pure	PROPN
ejpam-6596	172	3	appl	appl	PROPN
ejpam-6596	172	4	.	.	PROPN
ejpam-6596	172	5	math	math	PROPN
ejpam-6596	172	6	,	,	PUNCT
ejpam-6596	172	7	18	18	NUM
ejpam-6596	172	8	(	(	PUNCT
ejpam-6596	172	9	4	4	NUM
ejpam-6596	172	10	)	)	PUNCT
ejpam-6596	172	11	(	(	PUNCT
ejpam-6596	172	12	2025	2025	NUM
ejpam-6596	172	13	)	)	PUNCT
ejpam-6596	172	14	,	,	PUNCT
ejpam-6596	172	15	6596	6596	NUM
ejpam-6596	172	16	10	10	NUM
ejpam-6596	172	17	of	of	ADP
ejpam-6596	172	18	23	23	NUM
ejpam-6596	172	19	6	6	NUM
ejpam-6596	172	20	.	.	PUNCT
ejpam-6596	173	1	global	global	ADJ
ejpam-6596	173	2	stability	stability	NOUN
ejpam-6596	173	3	analysis	analysis	NOUN
ejpam-6596	173	4	theorem	theorem	VERB
ejpam-6596	173	5	4	4	NUM
ejpam-6596	173	6	.	.	PUNCT
ejpam-6596	174	1	if	if	SCONJ
ejpam-6596	174	2	r0	r0	NOUN
ejpam-6596	174	3	>	>	X
ejpam-6596	174	4	1	1	NUM
ejpam-6596	174	5	,	,	PUNCT
ejpam-6596	174	6	the	the	DET
ejpam-6596	174	7	endemic	endemic	ADJ
ejpam-6596	174	8	equilibrium	equilibrium	NOUN
ejpam-6596	174	9	e∗	e∗	NOUN
ejpam-6596	174	10	is	be	AUX
ejpam-6596	174	11	globally	globally	ADV
ejpam-6596	174	12	asymptotically	asymptotically	ADV
ejpam-6596	174	13	stable	stable	ADJ
ejpam-6596	174	14	.	.	PUNCT
ejpam-6596	175	1	proof	proof	NOUN
ejpam-6596	175	2	.	.	PUNCT
ejpam-6596	176	1	taking	take	VERB
ejpam-6596	176	2	the	the	DET
ejpam-6596	176	3	subsystems	subsystem	NOUN
ejpam-6596	176	4	in	in	ADP
ejpam-6596	176	5	this	this	DET
ejpam-6596	176	6	case	case	NOUN
ejpam-6596	176	7	,	,	PUNCT
ejpam-6596	176	8	ds	ds	ADJ
ejpam-6596	176	9	dt	dt	NOUN
ejpam-6596	176	10	=	=	SYM
ejpam-6596	176	11	g	g	PROPN
ejpam-6596	176	12	−	−	PROPN
ejpam-6596	176	13	hsi	hsi	PROPN
ejpam-6596	176	14	1	1	NUM
ejpam-6596	177	1	+	+	CCONJ
ejpam-6596	177	2	αi	αi	VERB
ejpam-6596	177	3	−	−	X
ejpam-6596	178	1	(	(	PUNCT
ejpam-6596	178	2	m+	m+	NUM
ejpam-6596	178	3	b1)s	b1)s	PROPN
ejpam-6596	178	4	,	,	PUNCT
ejpam-6596	178	5	de	de	X
ejpam-6596	178	6	dt	dt	NOUN
ejpam-6596	178	7	=	=	SYM
ejpam-6596	178	8	hsi	hsi	PROPN
ejpam-6596	178	9	1	1	NUM
ejpam-6596	179	1	+	+	CCONJ
ejpam-6596	179	2	αi	αi	VERB
ejpam-6596	179	3	−	−	PROPN
ejpam-6596	180	1	(	(	PUNCT
ejpam-6596	180	2	m+	m+	NUM
ejpam-6596	180	3	c+	c+	NOUN
ejpam-6596	180	4	b2)e	b2)e	PROPN
ejpam-6596	180	5	,	,	PUNCT
ejpam-6596	180	6	di	di	NOUN
ejpam-6596	180	7	dt	dt	NOUN
ejpam-6596	180	8	=	=	SYM
ejpam-6596	180	9	ce	ce	PROPN
ejpam-6596	180	10	−	−	PROPN
ejpam-6596	181	1	(	(	PUNCT
ejpam-6596	181	2	m+	m+	NUM
ejpam-6596	181	3	b3	b3	PROPN
ejpam-6596	181	4	+	+	CCONJ
ejpam-6596	181	5	q	q	PROPN
ejpam-6596	181	6	+	+	NUM
ejpam-6596	181	7	µ	µ	X
ejpam-6596	181	8	)	)	PUNCT
ejpam-6596	181	9	i.	i.	NOUN
ejpam-6596	181	10	(	(	PUNCT
ejpam-6596	181	11	7	7	NUM
ejpam-6596	181	12	)	)	PUNCT
ejpam-6596	181	13	the	the	DET
ejpam-6596	181	14	jacobian	jacobian	ADJ
ejpam-6596	181	15	matrix	matrix	NOUN
ejpam-6596	181	16	of	of	ADP
ejpam-6596	181	17	the	the	DET
ejpam-6596	181	18	system	system	NOUN
ejpam-6596	181	19	is	be	AUX
ejpam-6596	181	20	given	give	VERB
ejpam-6596	181	21	as	as	ADP
ejpam-6596	181	22	j.	j.	PROPN
ejpam-6596	181	23	j	j	PROPN
ejpam-6596	181	24	=	=	PUNCT
ejpam-6596	181	25			NOUN
ejpam-6596	182	1	−	−	PROPN
ejpam-6596	182	2	hi	hi	INTJ
ejpam-6596	182	3	1+αi	1+αi	NUM
ejpam-6596	182	4	−	−	PROPN
ejpam-6596	183	1	(	(	PUNCT
ejpam-6596	183	2	m+	m+	NUM
ejpam-6596	183	3	b1	b1	NOUN
ejpam-6596	183	4	)	)	PUNCT
ejpam-6596	183	5	0	0	NUM
ejpam-6596	184	1	−	−	PROPN
ejpam-6596	184	2	hs	hs	INTJ
ejpam-6596	184	3	(	(	PUNCT
ejpam-6596	184	4	1+α)2	1+α)2	NUM
ejpam-6596	184	5	hi	hi	INTJ
ejpam-6596	184	6	1+αi	1+αi	NUM
ejpam-6596	184	7	−	−	PROPN
ejpam-6596	184	8	(	(	PUNCT
ejpam-6596	184	9	m+	m+	NUM
ejpam-6596	184	10	c+	c+	NOUN
ejpam-6596	184	11	b2	b2	NOUN
ejpam-6596	184	12	)	)	PUNCT
ejpam-6596	184	13	hs	hs	PROPN
ejpam-6596	184	14	(	(	PUNCT
ejpam-6596	184	15	1+α)2	1+α)2	NUM
ejpam-6596	184	16	0	0	NUM
ejpam-6596	184	17	c	c	NOUN
ejpam-6596	184	18	−(m+	−(m+	X
ejpam-6596	184	19	b3	b3	PROPN
ejpam-6596	184	20	+	+	CCONJ
ejpam-6596	184	21	q	q	PROPN
ejpam-6596	184	22	+	+	NUM
ejpam-6596	184	23	µ	µ	X
ejpam-6596	184	24	)	)	PUNCT
ejpam-6596	184	25			NUM
ejpam-6596	184	26	,	,	PUNCT
ejpam-6596	184	27	where	where	SCONJ
ejpam-6596	184	28	j	j	PROPN
ejpam-6596	184	29	|2|	|2|	PROPN
ejpam-6596	184	30	stands	stand	VERB
ejpam-6596	184	31	for	for	ADP
ejpam-6596	184	32	the	the	DET
ejpam-6596	184	33	second	second	ADJ
ejpam-6596	184	34	additive	additive	ADJ
ejpam-6596	184	35	matrix	matrix	NOUN
ejpam-6596	184	36	of	of	ADP
ejpam-6596	184	37	j.	j.	PROPN
ejpam-6596	184	38	this	this	DET
ejpam-6596	184	39	matrix	matrix	NOUN
ejpam-6596	184	40	form	form	NOUN
ejpam-6596	184	41	exists	exist	VERB
ejpam-6596	184	42	in	in	ADP
ejpam-6596	184	43	j	j	PROPN
ejpam-6596	184	44	|2|	|2|	PROPN
ejpam-6596	184	45	=	=	SYM
ejpam-6596	184	46			X
ejpam-6596	185	1	−	−	NOUN
ejpam-6596	185	2	hi	hi	INTJ
ejpam-6596	186	1	1+αi	1+αi	NUM
ejpam-6596	186	2	−	−	PROPN
ejpam-6596	186	3	k	k	PROPN
ejpam-6596	186	4	hs	hs	PROPN
ejpam-6596	186	5	(	(	PUNCT
ejpam-6596	186	6	1+αi)2	1+αi)2	PROPN
ejpam-6596	186	7	hs	hs	INTJ
ejpam-6596	186	8	(	(	PUNCT
ejpam-6596	186	9	1+α)2	1+α)2	NUM
ejpam-6596	186	10	c	c	NOUN
ejpam-6596	186	11	−	−	NOUN
ejpam-6596	186	12	hi	hi	INTJ
ejpam-6596	186	13	1+αi	1+αi	NUM
ejpam-6596	186	14	−	−	PROPN
ejpam-6596	186	15	l	l	NOUN
ejpam-6596	186	16	0	0	NUM
ejpam-6596	186	17	0	0	NUM
ejpam-6596	187	1	hi	hi	INTJ
ejpam-6596	187	2	1+αi	1+αi	NUM
ejpam-6596	187	3	−m	−m	NOUN
ejpam-6596	187	4			NUM
ejpam-6596	187	5	.	.	PUNCT
ejpam-6596	188	1	entries	entry	NOUN
ejpam-6596	188	2	of	of	ADP
ejpam-6596	188	3	the	the	DET
ejpam-6596	188	4	last	last	ADJ
ejpam-6596	188	5	matrix	matrix	NOUN
ejpam-6596	188	6	are	be	AUX
ejpam-6596	188	7	defined	define	VERB
ejpam-6596	188	8	in	in	ADP
ejpam-6596	188	9	the	the	DET
ejpam-6596	188	10	following	following	ADJ
ejpam-6596	188	11	way	way	NOUN
ejpam-6596	188	12	,	,	PUNCT
ejpam-6596	188	13	k	k	NOUN
ejpam-6596	188	14	=	=	SYM
ejpam-6596	188	15	2m+	2m+	NUM
ejpam-6596	188	16	c+	c+	NOUN
ejpam-6596	188	17	b1	b1	NOUN
ejpam-6596	188	18	+	+	CCONJ
ejpam-6596	188	19	b2	b2	NOUN
ejpam-6596	188	20	,	,	PUNCT
ejpam-6596	188	21	l	l	NOUN
ejpam-6596	188	22	=	=	SYM
ejpam-6596	188	23	2m+	2m+	NUM
ejpam-6596	188	24	b1	b1	NOUN
ejpam-6596	188	25	+	+	CCONJ
ejpam-6596	188	26	b3	b3	PROPN
ejpam-6596	188	27	+	+	CCONJ
ejpam-6596	188	28	q	q	PROPN
ejpam-6596	188	29	+	+	NUM
ejpam-6596	188	30	µ	µ	NUM
ejpam-6596	188	31	,	,	PUNCT
ejpam-6596	188	32	m	m	NOUN
ejpam-6596	188	33	=	=	NOUN
ejpam-6596	188	34	2m+	2m+	NUM
ejpam-6596	188	35	c+	c+	NOUN
ejpam-6596	188	36	b2	b2	NOUN
ejpam-6596	188	37	+	+	CCONJ
ejpam-6596	188	38	b3	b3	PROPN
ejpam-6596	188	39	+	+	CCONJ
ejpam-6596	188	40	q	q	PROPN
ejpam-6596	188	41	+	+	X
ejpam-6596	188	42	µ	µ	NUM
ejpam-6596	188	43	,	,	PUNCT
ejpam-6596	188	44	let	let	VERB
ejpam-6596	188	45	us	we	PRON
ejpam-6596	188	46	consider	consider	VERB
ejpam-6596	188	47	the	the	DET
ejpam-6596	188	48	function	function	NOUN
ejpam-6596	188	49	x(x	x(x	PROPN
ejpam-6596	188	50	)	)	PUNCT
ejpam-6596	189	1	=	=	SYM
ejpam-6596	189	2	x	x	X
ejpam-6596	189	3	(	(	PUNCT
ejpam-6596	189	4	s	s	X
ejpam-6596	189	5	,	,	PUNCT
ejpam-6596	189	6	e	e	NOUN
ejpam-6596	189	7	,	,	PUNCT
ejpam-6596	189	8	i	i	NOUN
ejpam-6596	189	9	)	)	PUNCT
ejpam-6596	190	1	=	=	PUNCT
ejpam-6596	190	2	diag	diag	NOUN
ejpam-6596	190	3	{	{	PUNCT
ejpam-6596	190	4	1	1	NUM
ejpam-6596	190	5	,	,	PUNCT
ejpam-6596	190	6	e	e	X
ejpam-6596	190	7	i	i	PRON
ejpam-6596	190	8	,	,	PUNCT
ejpam-6596	190	9	e	e	VERB
ejpam-6596	190	10	i	i	PROPN
ejpam-6596	190	11	}	}	PUNCT
ejpam-6596	190	12	then	then	ADV
ejpam-6596	190	13	,	,	PUNCT
ejpam-6596	190	14	x−1	x−1	PROPN
ejpam-6596	190	15	=	=	PROPN
ejpam-6596	190	16	diag	diag	PROPN
ejpam-6596	190	17	{	{	PUNCT
ejpam-6596	190	18	1	1	NUM
ejpam-6596	190	19	,	,	PUNCT
ejpam-6596	190	20	i	i	PRON
ejpam-6596	190	21	e	e	NOUN
ejpam-6596	190	22	,	,	PUNCT
ejpam-6596	190	23	i	i	PRON
ejpam-6596	190	24	e	e	VERB
ejpam-6596	190	25	}	}	PUNCT
ejpam-6596	190	26	,	,	PUNCT
ejpam-6596	190	27	xf	xf	PROPN
ejpam-6596	190	28	=	=	PROPN
ejpam-6596	190	29	diag	diag	PROPN
ejpam-6596	190	30	{	{	PUNCT
ejpam-6596	190	31	0	0	NUM
ejpam-6596	190	32	,	,	PUNCT
ejpam-6596	190	33	ė	ė	ADJ
ejpam-6596	191	1	i	i	PRON
ejpam-6596	191	2	−	−	NOUN
ejpam-6596	191	3	ei̇	ei̇	PROPN
ejpam-6596	191	4	i2	i2	PROPN
ejpam-6596	191	5	,	,	PUNCT
ejpam-6596	191	6	ė	ė	ADJ
ejpam-6596	192	1	i	i	PRON
ejpam-6596	192	2	−	−	NOUN
ejpam-6596	192	3	ei̇	ei̇	PROPN
ejpam-6596	192	4	i2	i2	PROPN
ejpam-6596	192	5	}	}	PUNCT
ejpam-6596	192	6	.	.	PUNCT
ejpam-6596	193	1	direct	direct	ADJ
ejpam-6596	193	2	calculation	calculation	NOUN
ejpam-6596	193	3	demonstrates	demonstrate	VERB
ejpam-6596	193	4	that	that	SCONJ
ejpam-6596	193	5	which	which	PRON
ejpam-6596	193	6	can	can	AUX
ejpam-6596	193	7	be	be	AUX
ejpam-6596	193	8	seen	see	VERB
ejpam-6596	193	9	further	far	ADV
ejpam-6596	193	10	as	as	ADP
ejpam-6596	193	11	xfx	xfx	PROPN
ejpam-6596	193	12	−1	−1	NOUN
ejpam-6596	193	13	=	=	PUNCT
ejpam-6596	193	14	diag	diag	NOUN
ejpam-6596	193	15	{	{	PUNCT
ejpam-6596	193	16	0	0	NUM
ejpam-6596	193	17	,	,	PUNCT
ejpam-6596	193	18	ė	ė	ADJ
ejpam-6596	193	19	e	e	NOUN
ejpam-6596	194	1	−	−	PROPN
ejpam-6596	194	2	i̇	i̇	PROPN
ejpam-6596	195	1	i	i	INTJ
ejpam-6596	195	2	,	,	PUNCT
ejpam-6596	195	3	ė	ė	PROPN
ejpam-6596	195	4	e	e	NOUN
ejpam-6596	195	5	−	−	PROPN
ejpam-6596	195	6	i̇	i̇	PROPN
ejpam-6596	196	1	i	i	NOUN
ejpam-6596	196	2	}	}	PUNCT
ejpam-6596	196	3	.	.	PUNCT
ejpam-6596	197	1	xj	xj	PROPN
ejpam-6596	197	2	|2|x−1	|2|x−1	PROPN
ejpam-6596	197	3	=	=	SYM
ejpam-6596	197	4			NUM
ejpam-6596	197	5	x11	x11	PROPN
ejpam-6596	197	6	hsi	hsi	PROPN
ejpam-6596	197	7	e(1+αi)2	e(1+αi)2	PROPN
ejpam-6596	197	8	hsi	hsi	PROPN
ejpam-6596	198	1	e(1+αi)2	e(1+αi)2	PROPN
ejpam-6596	198	2	ec	ec	PROPN
ejpam-6596	199	1	i	i	PRON
ejpam-6596	199	2	x22	x22	PROPN
ejpam-6596	199	3	0	0	NUM
ejpam-6596	199	4	0	0	NUM
ejpam-6596	200	1	hi	hi	INTJ
ejpam-6596	200	2	1+αi	1+αi	NUM
ejpam-6596	200	3	x33	x33	PROPN
ejpam-6596	200	4			PROPN
ejpam-6596	200	5	n.	n.	PROPN
ejpam-6596	200	6	gul	gul	PROPN
ejpam-6596	200	7	et	et	PROPN
ejpam-6596	200	8	al	al	PROPN
ejpam-6596	200	9	.	.	PUNCT
ejpam-6596	200	10	/	/	SYM
ejpam-6596	200	11	eur	eur	PROPN
ejpam-6596	200	12	.	.	PUNCT
ejpam-6596	201	1	j.	j.	PROPN
ejpam-6596	201	2	pure	pure	PROPN
ejpam-6596	201	3	appl	appl	PROPN
ejpam-6596	201	4	.	.	PROPN
ejpam-6596	201	5	math	math	PROPN
ejpam-6596	201	6	,	,	PUNCT
ejpam-6596	201	7	18	18	NUM
ejpam-6596	201	8	(	(	PUNCT
ejpam-6596	201	9	4	4	NUM
ejpam-6596	201	10	)	)	PUNCT
ejpam-6596	201	11	(	(	PUNCT
ejpam-6596	201	12	2025	2025	NUM
ejpam-6596	201	13	)	)	PUNCT
ejpam-6596	201	14	,	,	PUNCT
ejpam-6596	201	15	6596	6596	NUM
ejpam-6596	201	16	11	11	NUM
ejpam-6596	201	17	of	of	ADP
ejpam-6596	201	18	23	23	NUM
ejpam-6596	202	1	where	where	SCONJ
ejpam-6596	202	2	x11	x11	NOUN
ejpam-6596	202	3	=	=	SYM
ejpam-6596	203	1	−hi	−hi	PROPN
ejpam-6596	204	1	1+αi	1+αi	NUM
ejpam-6596	205	1	−	−	PROPN
ejpam-6596	206	1	(	(	PUNCT
ejpam-6596	206	2	2m+	2m+	NUM
ejpam-6596	206	3	c+	c+	NOUN
ejpam-6596	206	4	b1	b1	NOUN
ejpam-6596	206	5	+	+	CCONJ
ejpam-6596	206	6	b2	b2	NOUN
ejpam-6596	206	7	)	)	PUNCT
ejpam-6596	206	8	,	,	PUNCT
ejpam-6596	206	9	x22	x22	NOUN
ejpam-6596	206	10	=	=	SYM
ejpam-6596	206	11	−hi	−hi	PROPN
ejpam-6596	206	12	1+αi	1+αi	NUM
ejpam-6596	206	13	−	−	PROPN
ejpam-6596	206	14	(	(	PUNCT
ejpam-6596	206	15	2m+	2m+	NUM
ejpam-6596	206	16	b1	b1	NOUN
ejpam-6596	206	17	+	+	CCONJ
ejpam-6596	206	18	b3	b3	PROPN
ejpam-6596	206	19	+	+	CCONJ
ejpam-6596	206	20	q	q	PROPN
ejpam-6596	206	21	+	+	NUM
ejpam-6596	206	22	µ	µ	NOUN
ejpam-6596	206	23	)	)	PUNCT
ejpam-6596	206	24	,	,	PUNCT
ejpam-6596	206	25	x33	x33	NOUN
ejpam-6596	206	26	=	=	SYM
ejpam-6596	207	1	−(2m+	−(2m+	VERB
ejpam-6596	207	2	c+	c+	NOUN
ejpam-6596	207	3	b2	b2	NOUN
ejpam-6596	207	4	+	+	CCONJ
ejpam-6596	207	5	b3	b3	PROPN
ejpam-6596	207	6	+	+	CCONJ
ejpam-6596	207	7	q	q	PROPN
ejpam-6596	207	8	+	+	NUM
ejpam-6596	207	9	µ	µ	NOUN
ejpam-6596	207	10	)	)	PUNCT
ejpam-6596	207	11	.	.	PUNCT
ejpam-6596	208	1	thus	thus	ADV
ejpam-6596	208	2	,	,	PUNCT
ejpam-6596	208	3	we	we	PRON
ejpam-6596	208	4	are	be	AUX
ejpam-6596	208	5	able	able	ADJ
ejpam-6596	208	6	to	to	PART
ejpam-6596	208	7	write	write	VERB
ejpam-6596	208	8	q	q	PROPN
ejpam-6596	208	9	=	=	PUNCT
ejpam-6596	208	10	xfx	xfx	PROPN
ejpam-6596	208	11	−1	−1	NOUN
ejpam-6596	208	12	+	+	NOUN
ejpam-6596	208	13	xj	xj	NOUN
ejpam-6596	208	14	|2|x−1	|2|x−1	NOUN
ejpam-6596	208	15	.	.	PUNCT
ejpam-6596	209	1	it	it	PRON
ejpam-6596	209	2	is	be	AUX
ejpam-6596	209	3	simple	simple	ADJ
ejpam-6596	209	4	to	to	PART
ejpam-6596	209	5	check	check	VERB
ejpam-6596	209	6	if	if	SCONJ
ejpam-6596	209	7	the	the	DET
ejpam-6596	209	8	matrix	matrix	NOUN
ejpam-6596	209	9	b	b	NOUN
ejpam-6596	209	10	has	have	VERB
ejpam-6596	209	11	the	the	DET
ejpam-6596	209	12	specified	specified	ADJ
ejpam-6596	209	13	form	form	NOUN
ejpam-6596	209	14	after	after	SCONJ
ejpam-6596	209	15	values	value	NOUN
ejpam-6596	209	16	have	have	AUX
ejpam-6596	209	17	been	be	AUX
ejpam-6596	209	18	inserted	insert	VERB
ejpam-6596	209	19	.	.	PUNCT
ejpam-6596	209	20	q	q	PUNCT
ejpam-6596	210	1	=	=	PUNCT
ejpam-6596	210	2	[	[	PUNCT
ejpam-6596	210	3	q11	q11	NOUN
ejpam-6596	210	4	q12	q12	NOUN
ejpam-6596	210	5	q21	q21	PROPN
ejpam-6596	210	6	q22	q22	NOUN
ejpam-6596	210	7	]	]	PUNCT
ejpam-6596	210	8	.	.	PUNCT
ejpam-6596	211	1	take	take	VERB
ejpam-6596	211	2	note	note	VERB
ejpam-6596	211	3	that	that	SCONJ
ejpam-6596	211	4	the	the	DET
ejpam-6596	211	5	entries	entry	NOUN
ejpam-6596	211	6	in	in	ADP
ejpam-6596	211	7	matrix	matrix	NOUN
ejpam-6596	211	8	q	q	NOUN
ejpam-6596	211	9	are	be	AUX
ejpam-6596	211	10	computed	compute	VERB
ejpam-6596	211	11	as	as	ADP
ejpam-6596	211	12	q11	q11	NOUN
ejpam-6596	211	13	=	=	SYM
ejpam-6596	211	14	x11	x11	NOUN
ejpam-6596	211	15	,	,	PUNCT
ejpam-6596	211	16	q12	q12	NOUN
ejpam-6596	211	17	=	=	PROPN
ejpam-6596	211	18	hsi	hsi	PROPN
ejpam-6596	211	19	e(1	e(1	PROPN
ejpam-6596	212	1	+	+	CCONJ
ejpam-6596	212	2	αi)2	αi)2	PROPN
ejpam-6596	212	3	,	,	PUNCT
ejpam-6596	212	4	hsi	hsi	PROPN
ejpam-6596	212	5	e(1	e(1	PROPN
ejpam-6596	212	6	+	+	CCONJ
ejpam-6596	212	7	αi)2	αi)2	ADJ
ejpam-6596	212	8	,	,	PUNCT
ejpam-6596	212	9	q21	q21	NOUN
ejpam-6596	212	10	=	=	SYM
ejpam-6596	212	11	[	[	PUNCT
ejpam-6596	212	12	ce	ce	X
ejpam-6596	212	13	i	i	NOUN
ejpam-6596	212	14	0	0	NUM
ejpam-6596	212	15	]	]	PUNCT
ejpam-6596	212	16	,	,	PUNCT
ejpam-6596	212	17	q22	q22	NOUN
ejpam-6596	212	18	=	=	PUNCT
ejpam-6596	212	19	[	[	PUNCT
ejpam-6596	212	20	x22	x22	NOUN
ejpam-6596	212	21	+	+	CCONJ
ejpam-6596	212	22	iė−ei̇	iė−ei̇	NOUN
ejpam-6596	212	23	ie	ie	X
ejpam-6596	212	24	0	0	NUM
ejpam-6596	212	25	hi	hi	INTJ
ejpam-6596	212	26	1+αi	1+αi	NUM
ejpam-6596	212	27	x33	x33	NOUN
ejpam-6596	212	28	+	+	X
ejpam-6596	212	29	iė−ei̇	iė−ei̇	NOUN
ejpam-6596	212	30	ie	ie	ADV
ejpam-6596	212	31	]	]	PUNCT
ejpam-6596	212	32	.	.	PUNCT
ejpam-6596	213	1	let	let	VERB
ejpam-6596	213	2	(	(	PUNCT
ejpam-6596	213	3	u	u	NOUN
ejpam-6596	213	4	,	,	PUNCT
ejpam-6596	213	5	v	v	NOUN
ejpam-6596	213	6	,	,	PUNCT
ejpam-6596	213	7	w	w	NOUN
ejpam-6596	213	8	)	)	PUNCT
ejpam-6596	213	9	be	be	VERB
ejpam-6596	213	10	a	a	DET
ejpam-6596	213	11	vector	vector	NOUN
ejpam-6596	213	12	in	in	ADP
ejpam-6596	213	13	r3	r3	PROPN
ejpam-6596	213	14	.	.	PUNCT
ejpam-6596	214	1	its	its	PRON
ejpam-6596	214	2	norm	norm	NOUN
ejpam-6596	214	3	∥·∥	∥·∥	PROPN
ejpam-6596	214	4	is	be	AUX
ejpam-6596	214	5	defined	define	VERB
ejpam-6596	214	6	as	as	ADP
ejpam-6596	214	7	∥(u	∥(u	ADJ
ejpam-6596	214	8	,	,	PUNCT
ejpam-6596	214	9	v	v	NOUN
ejpam-6596	214	10	,	,	PUNCT
ejpam-6596	214	11	w)∥	w)∥	X
ejpam-6596	214	12	=	=	SYM
ejpam-6596	214	13	max{|u|	max{|u|	X
ejpam-6596	214	14	,	,	PUNCT
ejpam-6596	214	15	|v|+	|v|+	PROPN
ejpam-6596	214	16	|w|	|w|	PROPN
ejpam-6596	214	17	}	}	PUNCT
ejpam-6596	214	18	.	.	PUNCT
ejpam-6596	215	1	let	let	AUX
ejpam-6596	215	2	µ(q	µ(q	PROPN
ejpam-6596	215	3	)	)	PUNCT
ejpam-6596	215	4	be	be	AUX
ejpam-6596	215	5	the	the	DET
ejpam-6596	215	6	lozinskiĭ	lozinskiĭ	ADJ
ejpam-6596	215	7	measure	measure	NOUN
ejpam-6596	215	8	with	with	ADP
ejpam-6596	215	9	respect	respect	NOUN
ejpam-6596	215	10	to	to	ADP
ejpam-6596	215	11	this	this	DET
ejpam-6596	215	12	norm	norm	NOUN
ejpam-6596	215	13	.	.	PUNCT
ejpam-6596	216	1	then	then	ADV
ejpam-6596	216	2	µ(q	µ(q	PROPN
ejpam-6596	216	3	)	)	PUNCT
ejpam-6596	216	4	≤	≤	NOUN
ejpam-6596	216	5	sup{g1	sup{g1	NOUN
ejpam-6596	216	6	,	,	PUNCT
ejpam-6596	216	7	g2	g2	PROPN
ejpam-6596	216	8	}	}	PUNCT
ejpam-6596	216	9	,	,	PUNCT
ejpam-6596	216	10	where	where	SCONJ
ejpam-6596	216	11	g1	g1	PROPN
ejpam-6596	216	12	=	=	SYM
ejpam-6596	216	13	µ1(q11	µ1(q11	NOUN
ejpam-6596	216	14	)	)	PUNCT
ejpam-6596	216	15	+	+	CCONJ
ejpam-6596	216	16	∥q12∥	∥q12∥	PROPN
ejpam-6596	216	17	,	,	PUNCT
ejpam-6596	216	18	g2	g2	PROPN
ejpam-6596	216	19	=	=	PUNCT
ejpam-6596	216	20	∥q21∥+	∥q21∥+	PROPN
ejpam-6596	216	21	µ1(q22	µ1(q22	NOUN
ejpam-6596	216	22	)	)	PUNCT
ejpam-6596	216	23	.	.	PUNCT
ejpam-6596	217	1	here	here	ADV
ejpam-6596	217	2	∥q12∥	∥q12∥	PROPN
ejpam-6596	217	3	and	and	CCONJ
ejpam-6596	217	4	∥q21∥	∥q21∥	PROPN
ejpam-6596	217	5	are	be	AUX
ejpam-6596	217	6	matrix	matrix	NOUN
ejpam-6596	217	7	norms	norm	NOUN
ejpam-6596	217	8	with	with	ADP
ejpam-6596	217	9	respect	respect	NOUN
ejpam-6596	217	10	to	to	ADP
ejpam-6596	217	11	the	the	DET
ejpam-6596	217	12	ℓ1	ℓ1	ADJ
ejpam-6596	217	13	vector	vector	NOUN
ejpam-6596	217	14	norm	norm	NOUN
ejpam-6596	217	15	,	,	PUNCT
ejpam-6596	217	16	and	and	CCONJ
ejpam-6596	217	17	µ1	µ1	NOUN
ejpam-6596	217	18	denotes	denote	VERB
ejpam-6596	217	19	the	the	DET
ejpam-6596	217	20	lozinskiĭ	lozinskiĭ	ADJ
ejpam-6596	217	21	measure	measure	NOUN
ejpam-6596	217	22	with	with	ADP
ejpam-6596	217	23	respect	respect	NOUN
ejpam-6596	217	24	to	to	ADP
ejpam-6596	217	25	this	this	DET
ejpam-6596	217	26	ℓ1	ℓ1	ADJ
ejpam-6596	217	27	norm	norm	NOUN
ejpam-6596	217	28	.	.	PUNCT
ejpam-6596	218	1	then	then	ADV
ejpam-6596	218	2	µ1(q11	µ1(q11	ADV
ejpam-6596	218	3	)	)	PUNCT
ejpam-6596	218	4	=	=	PUNCT
ejpam-6596	219	1	−	−	PROPN
ejpam-6596	220	1	hi	hi	INTJ
ejpam-6596	220	2	1	1	NUM
ejpam-6596	220	3	+	+	CCONJ
ejpam-6596	220	4	αi	αi	PRON
ejpam-6596	220	5	−	−	X
ejpam-6596	221	1	(	(	PUNCT
ejpam-6596	221	2	2m+	2m+	NUM
ejpam-6596	221	3	c+	c+	NOUN
ejpam-6596	221	4	b1	b1	NOUN
ejpam-6596	221	5	+	+	CCONJ
ejpam-6596	221	6	b2	b2	NOUN
ejpam-6596	221	7	)	)	PUNCT
ejpam-6596	221	8	,	,	PUNCT
ejpam-6596	221	9	∥q21∥	∥q21∥	PROPN
ejpam-6596	221	10	=	=	SYM
ejpam-6596	221	11	ce	ce	PROPN
ejpam-6596	221	12	i	i	PRON
ejpam-6596	221	13	,	,	PUNCT
ejpam-6596	221	14	∥q12∥	∥q12∥	PROPN
ejpam-6596	221	15	=	=	SYM
ejpam-6596	221	16	max	max	X
ejpam-6596	221	17	{	{	PUNCT
ejpam-6596	221	18	hsi	hsi	PROPN
ejpam-6596	221	19	e(1	e(1	PROPN
ejpam-6596	222	1	+	+	CCONJ
ejpam-6596	222	2	αi)2	αi)2	PROPN
ejpam-6596	222	3	,	,	PUNCT
ejpam-6596	222	4	hsi	hsi	PROPN
ejpam-6596	222	5	e(1	e(1	PROPN
ejpam-6596	222	6	+	+	CCONJ
ejpam-6596	222	7	αi)2	αi)2	ADJ
ejpam-6596	222	8	}	}	PUNCT
ejpam-6596	222	9	=	=	PUNCT
ejpam-6596	223	1	hsi	hsi	PROPN
ejpam-6596	223	2	e(1	e(1	PROPN
ejpam-6596	223	3	+	+	CCONJ
ejpam-6596	223	4	αi)2	αi)2	PROPN
ejpam-6596	223	5	,	,	PUNCT
ejpam-6596	223	6	n.	n.	PROPN
ejpam-6596	223	7	gul	gul	PROPN
ejpam-6596	223	8	et	et	PROPN
ejpam-6596	223	9	al	al	PROPN
ejpam-6596	223	10	.	.	PUNCT
ejpam-6596	223	11	/	/	SYM
ejpam-6596	223	12	eur	eur	PROPN
ejpam-6596	223	13	.	.	PUNCT
ejpam-6596	224	1	j.	j.	PROPN
ejpam-6596	224	2	pure	pure	PROPN
ejpam-6596	224	3	appl	appl	PROPN
ejpam-6596	224	4	.	.	PROPN
ejpam-6596	224	5	math	math	PROPN
ejpam-6596	224	6	,	,	PUNCT
ejpam-6596	224	7	18	18	NUM
ejpam-6596	224	8	(	(	PUNCT
ejpam-6596	224	9	4	4	NUM
ejpam-6596	224	10	)	)	PUNCT
ejpam-6596	224	11	(	(	PUNCT
ejpam-6596	224	12	2025	2025	NUM
ejpam-6596	224	13	)	)	PUNCT
ejpam-6596	224	14	,	,	PUNCT
ejpam-6596	224	15	6596	6596	NUM
ejpam-6596	224	16	12	12	NUM
ejpam-6596	224	17	of	of	ADP
ejpam-6596	224	18	23	23	NUM
ejpam-6596	224	19	and	and	CCONJ
ejpam-6596	224	20	µ1(q22	µ1(q22	VERB
ejpam-6596	224	21	)	)	PUNCT
ejpam-6596	224	22	=	=	SYM
ejpam-6596	224	23	max	max	PROPN
ejpam-6596	224	24	{	{	PUNCT
ejpam-6596	224	25	ė	ė	PROPN
ejpam-6596	224	26	e	e	PROPN
ejpam-6596	224	27	−	−	PROPN
ejpam-6596	225	1	i̇	i̇	PROPN
ejpam-6596	226	1	i	i	PRON
ejpam-6596	226	2	−	−	VERB
ejpam-6596	227	1	hi	hi	INTJ
ejpam-6596	227	2	1	1	NUM
ejpam-6596	227	3	+	+	CCONJ
ejpam-6596	227	4	αi	αi	NOUN
ejpam-6596	227	5	−n	−n	NOUN
ejpam-6596	227	6	,	,	PUNCT
ejpam-6596	227	7	hi	hi	INTJ
ejpam-6596	227	8	1	1	NUM
ejpam-6596	228	1	+	+	CCONJ
ejpam-6596	228	2	αi	αi	NOUN
ejpam-6596	228	3	,	,	PUNCT
ejpam-6596	229	1	ė	ė	PROPN
ejpam-6596	229	2	e	e	X
ejpam-6596	229	3	−	−	PROPN
ejpam-6596	229	4	i̇	i̇	PROPN
ejpam-6596	230	1	i	i	PRON
ejpam-6596	230	2	−k	−k	VERB
ejpam-6596	230	3	}	}	PUNCT
ejpam-6596	230	4	=	=	PUNCT
ejpam-6596	231	1	ė	ė	ADJ
ejpam-6596	231	2	e	e	X
ejpam-6596	231	3	−	−	PROPN
ejpam-6596	231	4	i̇	i̇	PROPN
ejpam-6596	232	1	i	i	NOUN
ejpam-6596	232	2	−min(n	−min(n	NOUN
ejpam-6596	232	3	,	,	PUNCT
ejpam-6596	232	4	k	k	NOUN
ejpam-6596	232	5	)	)	PUNCT
ejpam-6596	232	6	.	.	PUNCT
ejpam-6596	233	1	therefore	therefore	ADV
ejpam-6596	233	2	,	,	PUNCT
ejpam-6596	233	3	we	we	PRON
ejpam-6596	233	4	have	have	VERB
ejpam-6596	233	5	g1	g1	NOUN
ejpam-6596	233	6	=	=	PUNCT
ejpam-6596	233	7	−	−	PROPN
ejpam-6596	234	1	hi	hi	INTJ
ejpam-6596	234	2	1	1	NUM
ejpam-6596	234	3	+	+	CCONJ
ejpam-6596	234	4	αi	αi	VERB
ejpam-6596	234	5	−m	−m	NOUN
ejpam-6596	234	6	+	+	CCONJ
ejpam-6596	234	7	hsi	hsi	PROPN
ejpam-6596	234	8	e(1	e(1	PROPN
ejpam-6596	235	1	+	+	CCONJ
ejpam-6596	235	2	αi)2	αi)2	PROPN
ejpam-6596	235	3	,	,	PUNCT
ejpam-6596	235	4	g2	g2	PROPN
ejpam-6596	235	5	=	=	SYM
ejpam-6596	235	6	ce	ce	PROPN
ejpam-6596	236	1	i	i	PROPN
ejpam-6596	236	2	+	+	CCONJ
ejpam-6596	236	3	ė	ė	ADJ
ejpam-6596	236	4	e	e	NOUN
ejpam-6596	236	5	−	−	PROPN
ejpam-6596	236	6	i̇	i̇	PROPN
ejpam-6596	237	1	i	i	NOUN
ejpam-6596	237	2	−min(n	−min(n	NOUN
ejpam-6596	237	3	,	,	PUNCT
ejpam-6596	237	4	k	k	NOUN
ejpam-6596	237	5	)	)	PUNCT
ejpam-6596	237	6	.	.	PUNCT
ejpam-6596	238	1	from	from	ADP
ejpam-6596	238	2	the	the	DET
ejpam-6596	238	3	proposed	propose	VERB
ejpam-6596	238	4	model	model	NOUN
ejpam-6596	238	5	(	(	PUNCT
ejpam-6596	238	6	1.1	1.1	NUM
ejpam-6596	238	7	)	)	PUNCT
ejpam-6596	238	8	,	,	PUNCT
ejpam-6596	238	9	we	we	PRON
ejpam-6596	238	10	get	get	VERB
ejpam-6596	238	11	ė	ė	ADJ
ejpam-6596	238	12	e	e	NOUN
ejpam-6596	238	13	=	=	PROPN
ejpam-6596	238	14	hsi	hsi	PROPN
ejpam-6596	238	15	e(1	e(1	PROPN
ejpam-6596	238	16	+	+	CCONJ
ejpam-6596	238	17	αi	αi	NOUN
ejpam-6596	238	18	)	)	PUNCT
ejpam-6596	238	19	−	−	PROPN
ejpam-6596	239	1	(	(	PUNCT
ejpam-6596	239	2	m+	m+	NUM
ejpam-6596	239	3	c+	c+	NOUN
ejpam-6596	239	4	b2	b2	NOUN
ejpam-6596	239	5	)	)	PUNCT
ejpam-6596	239	6	,	,	PUNCT
ejpam-6596	239	7	i̇	i̇	PROPN
ejpam-6596	240	1	i	i	NOUN
ejpam-6596	240	2	=	=	PUNCT
ejpam-6596	240	3	ce	ce	PROPN
ejpam-6596	241	1	i	i	PRON
ejpam-6596	241	2	−	−	PROPN
ejpam-6596	241	3	(	(	PUNCT
ejpam-6596	241	4	m+	m+	NUM
ejpam-6596	241	5	b3	b3	PROPN
ejpam-6596	241	6	+	+	CCONJ
ejpam-6596	241	7	q	q	PROPN
ejpam-6596	241	8	+	+	NUM
ejpam-6596	241	9	µ	µ	NOUN
ejpam-6596	241	10	)	)	PUNCT
ejpam-6596	241	11	.	.	PUNCT
ejpam-6596	242	1	then	then	ADV
ejpam-6596	242	2	we	we	PRON
ejpam-6596	242	3	have	have	VERB
ejpam-6596	242	4	g1	g1	NOUN
ejpam-6596	242	5	=	=	PUNCT
ejpam-6596	242	6	−	−	PROPN
ejpam-6596	243	1	hi	hi	INTJ
ejpam-6596	243	2	1	1	NUM
ejpam-6596	243	3	+	+	CCONJ
ejpam-6596	243	4	αi	αi	PRON
ejpam-6596	243	5	−	−	X
ejpam-6596	244	1	(	(	PUNCT
ejpam-6596	244	2	2m+	2m+	NUM
ejpam-6596	244	3	c+	c+	NOUN
ejpam-6596	244	4	b1	b1	NOUN
ejpam-6596	244	5	+	+	CCONJ
ejpam-6596	244	6	b2	b2	NOUN
ejpam-6596	244	7	)	)	PUNCT
ejpam-6596	244	8	+	+	CCONJ
ejpam-6596	244	9	hsi	hsi	PROPN
ejpam-6596	244	10	e(1	e(1	PROPN
ejpam-6596	245	1	+	+	CCONJ
ejpam-6596	245	2	αi)2	αi)2	PROPN
ejpam-6596	245	3	+	+	PUNCT
ejpam-6596	245	4	[	[	PUNCT
ejpam-6596	245	5	hsi	hsi	PROPN
ejpam-6596	245	6	e(1	e(1	PROPN
ejpam-6596	245	7	+	+	CCONJ
ejpam-6596	245	8	αi)2	αi)2	PROPN
ejpam-6596	245	9	−	−	PROPN
ejpam-6596	245	10	hsi	hsi	PROPN
ejpam-6596	245	11	e(1	e(1	PROPN
ejpam-6596	245	12	+	+	CCONJ
ejpam-6596	245	13	αi	αi	NOUN
ejpam-6596	245	14	)	)	PUNCT
ejpam-6596	245	15	]	]	PUNCT
ejpam-6596	246	1	≤	≤	ADV
ejpam-6596	246	2	−	−	NOUN
ejpam-6596	247	1	hi	hi	INTJ
ejpam-6596	247	2	1	1	NUM
ejpam-6596	248	1	+	+	CCONJ
ejpam-6596	248	2	αi	αi	VERB
ejpam-6596	248	3	−	−	X
ejpam-6596	249	1	(	(	PUNCT
ejpam-6596	249	2	m+	m+	NUM
ejpam-6596	249	3	b1	b1	NOUN
ejpam-6596	249	4	)	)	PUNCT
ejpam-6596	250	1	+	+	CCONJ
ejpam-6596	251	1	ė	ė	ADJ
ejpam-6596	251	2	e	e	NOUN
ejpam-6596	251	3	,	,	PUNCT
ejpam-6596	251	4	g2	g2	PROPN
ejpam-6596	251	5	=	=	PUNCT
ejpam-6596	251	6	ce	ce	PROPN
ejpam-6596	252	1	i	i	PROPN
ejpam-6596	252	2	+	+	CCONJ
ejpam-6596	252	3	ė	ė	ADJ
ejpam-6596	252	4	e	e	NOUN
ejpam-6596	252	5	−	−	PROPN
ejpam-6596	252	6	i̇	i̇	PROPN
ejpam-6596	253	1	i	i	NOUN
ejpam-6596	253	2	−min(n	−min(n	NOUN
ejpam-6596	253	3	,	,	PUNCT
ejpam-6596	253	4	k	k	NOUN
ejpam-6596	253	5	)	)	PUNCT
ejpam-6596	253	6	≤	≤	NOUN
ejpam-6596	254	1	ė	ė	ADJ
ejpam-6596	254	2	e	e	NOUN
ejpam-6596	254	3	−m	−m	NOUN
ejpam-6596	254	4	.	.	PUNCT
ejpam-6596	255	1	since	since	SCONJ
ejpam-6596	255	2	ce	ce	PROPN
ejpam-6596	255	3	i	i	PRON
ejpam-6596	255	4	=	=	PUNCT
ejpam-6596	255	5	i̇	i̇	PROPN
ejpam-6596	256	1	i	i	PRON
ejpam-6596	256	2	−	−	PROPN
ejpam-6596	257	1	(	(	PUNCT
ejpam-6596	257	2	m+	m+	NUM
ejpam-6596	257	3	b3	b3	PROPN
ejpam-6596	257	4	+	+	CCONJ
ejpam-6596	257	5	q	q	NOUN
ejpam-6596	257	6	)	)	PUNCT
ejpam-6596	257	7	.	.	PUNCT
ejpam-6596	258	1	furthermore	furthermore	ADV
ejpam-6596	258	2	,	,	PUNCT
ejpam-6596	258	3	we	we	PRON
ejpam-6596	258	4	obtain	obtain	VERB
ejpam-6596	258	5	:	:	PUNCT
ejpam-6596	258	6	µ(q	µ(q	PROPN
ejpam-6596	258	7	)	)	PUNCT
ejpam-6596	258	8	≤	≤	NOUN
ejpam-6596	258	9	sup{g1	sup{g1	NOUN
ejpam-6596	258	10	,	,	PUNCT
ejpam-6596	258	11	g2	g2	PROPN
ejpam-6596	258	12	}	}	PUNCT
ejpam-6596	258	13	≤	≤	NUM
ejpam-6596	258	14	sup	sup	NOUN
ejpam-6596	258	15	{	{	PUNCT
ejpam-6596	258	16	−	−	PUNCT
ejpam-6596	259	1	hi	hi	INTJ
ejpam-6596	259	2	1	1	NUM
ejpam-6596	259	3	+	+	CCONJ
ejpam-6596	259	4	αi	αi	VERB
ejpam-6596	259	5	−	−	X
ejpam-6596	260	1	(	(	PUNCT
ejpam-6596	260	2	m+	m+	NUM
ejpam-6596	260	3	b1	b1	NOUN
ejpam-6596	260	4	)	)	PUNCT
ejpam-6596	261	1	+	+	CCONJ
ejpam-6596	262	1	ė	ė	ADJ
ejpam-6596	262	2	e	e	NOUN
ejpam-6596	262	3	,	,	PUNCT
ejpam-6596	262	4	ė	ė	ADJ
ejpam-6596	262	5	e	e	X
ejpam-6596	262	6	−m	−m	ADJ
ejpam-6596	262	7	}	}	PUNCT
ejpam-6596	262	8	≤	≤	NUM
ejpam-6596	262	9	ė	ė	ADJ
ejpam-6596	262	10	e	e	NOUN
ejpam-6596	262	11	−m	−m	NOUN
ejpam-6596	262	12	,	,	PUNCT
ejpam-6596	262	13	then	then	ADV
ejpam-6596	262	14	1	1	NUM
ejpam-6596	262	15	t	t	NOUN
ejpam-6596	262	16	∫	∫	PROPN
ejpam-6596	262	17	t	t	NOUN
ejpam-6596	262	18	0	0	PUNCT
ejpam-6596	262	19	µ(q	µ(q	ADJ
ejpam-6596	262	20	)	)	PUNCT
ejpam-6596	262	21	ds	ds	ADJ
ejpam-6596	262	22	≤	≤	NUM
ejpam-6596	262	23	1	1	NUM
ejpam-6596	262	24	t	t	NOUN
ejpam-6596	262	25	∫	∫	PROPN
ejpam-6596	262	26	t	t	PROPN
ejpam-6596	262	27	0	0	NUM
ejpam-6596	262	28	(	(	PUNCT
ejpam-6596	262	29	ė	ė	ADJ
ejpam-6596	262	30	e	e	X
ejpam-6596	262	31	−m	−m	NOUN
ejpam-6596	262	32	)	)	PUNCT
ejpam-6596	262	33	ds	ds	NOUN
ejpam-6596	262	34	=	=	SYM
ejpam-6596	262	35	1	1	NUM
ejpam-6596	262	36	t	t	NOUN
ejpam-6596	262	37	ln	ln	ADJ
ejpam-6596	262	38	e(t	e(t	NOUN
ejpam-6596	262	39	)	)	PUNCT
ejpam-6596	262	40	e(0	e(0	NOUN
ejpam-6596	262	41	)	)	PUNCT
ejpam-6596	262	42	−m	−m	NOUN
ejpam-6596	262	43	,	,	PUNCT
ejpam-6596	262	44	which	which	PRON
ejpam-6596	262	45	implies	imply	VERB
ejpam-6596	262	46	q	q	PROPN
ejpam-6596	262	47	≤	≤	NUM
ejpam-6596	262	48	m	m	VERB
ejpam-6596	262	49	2	2	NUM
ejpam-6596	262	50	<	<	X
ejpam-6596	262	51	0	0	NUM
ejpam-6596	262	52	.	.	PUNCT
ejpam-6596	263	1	we	we	PRON
ejpam-6596	263	2	know	know	VERB
ejpam-6596	263	3	that	that	SCONJ
ejpam-6596	263	4	positive	positive	ADJ
ejpam-6596	263	5	equilibrium	equilibrium	NOUN
ejpam-6596	263	6	(	(	PUNCT
ejpam-6596	263	7	s∗	s∗	PROPN
ejpam-6596	263	8	,	,	PUNCT
ejpam-6596	263	9	e∗	e∗	NOUN
ejpam-6596	263	10	,	,	PUNCT
ejpam-6596	263	11	i∗	i∗	NOUN
ejpam-6596	263	12	)	)	PUNCT
ejpam-6596	263	13	is	be	AUX
ejpam-6596	263	14	globally	globally	ADV
ejpam-6596	263	15	asymptotically	asymptotically	ADV
ejpam-6596	263	16	stable	stable	ADJ
ejpam-6596	263	17	.	.	PUNCT
ejpam-6596	264	1	in	in	ADP
ejpam-6596	264	2	this	this	DET
ejpam-6596	264	3	section	section	NOUN
ejpam-6596	264	4	,	,	PUNCT
ejpam-6596	264	5	it	it	PRON
ejpam-6596	264	6	is	be	AUX
ejpam-6596	264	7	described	describe	VERB
ejpam-6596	264	8	how	how	SCONJ
ejpam-6596	264	9	the	the	DET
ejpam-6596	264	10	general	general	ADJ
ejpam-6596	264	11	disease	disease	NOUN
ejpam-6596	264	12	model	model	NOUN
ejpam-6596	264	13	may	may	AUX
ejpam-6596	264	14	be	be	AUX
ejpam-6596	264	15	used	use	VERB
ejpam-6596	264	16	to	to	PART
ejpam-6596	264	17	optimise	optimise	VERB
ejpam-6596	264	18	control	control	NOUN
ejpam-6596	264	19	concepts	concept	NOUN
ejpam-6596	264	20	.	.	PUNCT
ejpam-6596	265	1	n.	n.	PROPN
ejpam-6596	265	2	gul	gul	PROPN
ejpam-6596	265	3	et	et	PROPN
ejpam-6596	265	4	al	al	PROPN
ejpam-6596	265	5	.	.	PUNCT
ejpam-6596	265	6	/	/	SYM
ejpam-6596	265	7	eur	eur	PROPN
ejpam-6596	265	8	.	.	PUNCT
ejpam-6596	266	1	j.	j.	PROPN
ejpam-6596	266	2	pure	pure	PROPN
ejpam-6596	266	3	appl	appl	PROPN
ejpam-6596	266	4	.	.	PROPN
ejpam-6596	266	5	math	math	PROPN
ejpam-6596	266	6	,	,	PUNCT
ejpam-6596	266	7	18	18	NUM
ejpam-6596	266	8	(	(	PUNCT
ejpam-6596	266	9	4	4	NUM
ejpam-6596	266	10	)	)	PUNCT
ejpam-6596	266	11	(	(	PUNCT
ejpam-6596	266	12	2025	2025	NUM
ejpam-6596	266	13	)	)	PUNCT
ejpam-6596	266	14	,	,	PUNCT
ejpam-6596	266	15	6596	6596	NUM
ejpam-6596	266	16	13	13	NUM
ejpam-6596	266	17	of	of	ADP
ejpam-6596	266	18	23	23	NUM
ejpam-6596	266	19	7	7	NUM
ejpam-6596	266	20	.	.	PUNCT
ejpam-6596	267	1	formulation	formulation	NOUN
ejpam-6596	267	2	of	of	ADP
ejpam-6596	267	3	optimal	optimal	ADJ
ejpam-6596	267	4	control	control	NOUN
ejpam-6596	267	5	problem	problem	NOUN
ejpam-6596	267	6	in	in	ADP
ejpam-6596	267	7	order	order	NOUN
ejpam-6596	267	8	to	to	PART
ejpam-6596	267	9	design	design	VERB
ejpam-6596	267	10	our	our	PRON
ejpam-6596	267	11	control	control	NOUN
ejpam-6596	267	12	approach	approach	NOUN
ejpam-6596	267	13	in	in	ADP
ejpam-6596	267	14	this	this	DET
ejpam-6596	267	15	part	part	NOUN
ejpam-6596	267	16	,	,	PUNCT
ejpam-6596	267	17	we	we	PRON
ejpam-6596	267	18	take	take	VERB
ejpam-6596	267	19	into	into	ADP
ejpam-6596	267	20	consideration	consideration	NOUN
ejpam-6596	267	21	the	the	DET
ejpam-6596	267	22	general	general	ADJ
ejpam-6596	267	23	illness	illness	NOUN
ejpam-6596	267	24	pandemic	pandemic	ADJ
ejpam-6596	267	25	model	model	NOUN
ejpam-6596	267	26	.	.	PUNCT
ejpam-6596	268	1	through	through	ADP
ejpam-6596	268	2	the	the	DET
ejpam-6596	268	3	use	use	NOUN
ejpam-6596	268	4	of	of	ADP
ejpam-6596	268	5	the	the	DET
ejpam-6596	268	6	three	three	NUM
ejpam-6596	268	7	control	control	NOUN
ejpam-6596	268	8	variables	variable	NOUN
ejpam-6596	268	9	u1(t	u1(t	ADP
ejpam-6596	268	10	)	)	PUNCT
ejpam-6596	268	11	,	,	PUNCT
ejpam-6596	268	12	which	which	PRON
ejpam-6596	268	13	denote	denote	VERB
ejpam-6596	268	14	the	the	DET
ejpam-6596	268	15	effort	effort	NOUN
ejpam-6596	268	16	that	that	PRON
ejpam-6596	268	17	reduces	reduce	VERB
ejpam-6596	268	18	the	the	DET
ejpam-6596	268	19	contact	contact	NOUN
ejpam-6596	268	20	between	between	ADP
ejpam-6596	268	21	the	the	DET
ejpam-6596	268	22	susceptibles	susceptible	NOUN
ejpam-6596	268	23	and	and	CCONJ
ejpam-6596	268	24	infectious	infectious	ADJ
ejpam-6596	268	25	individuals	individual	NOUN
ejpam-6596	268	26	;	;	PUNCT
ejpam-6596	268	27	u2(t	u2(t	NOUN
ejpam-6596	268	28	)	)	PUNCT
ejpam-6596	268	29	,	,	PUNCT
ejpam-6596	268	30	denote	denote	VERB
ejpam-6596	268	31	the	the	DET
ejpam-6596	268	32	rate	rate	NOUN
ejpam-6596	268	33	at	at	ADP
ejpam-6596	268	34	which	which	PRON
ejpam-6596	268	35	infectious	infectious	ADJ
ejpam-6596	268	36	individuals	individual	NOUN
ejpam-6596	268	37	are	be	AUX
ejpam-6596	268	38	treated	treat	VERB
ejpam-6596	268	39	and	and	CCONJ
ejpam-6596	268	40	u3(t	u3(t	NUM
ejpam-6596	268	41	)	)	PUNCT
ejpam-6596	268	42	,	,	PUNCT
ejpam-6596	268	43	shows	show	VERB
ejpam-6596	268	44	the	the	DET
ejpam-6596	268	45	vaccination	vaccination	NOUN
ejpam-6596	268	46	coverage	coverage	NOUN
ejpam-6596	268	47	.	.	PUNCT
ejpam-6596	269	1	thus	thus	ADV
ejpam-6596	269	2	,	,	PUNCT
ejpam-6596	269	3	by	by	ADP
ejpam-6596	269	4	including	include	VERB
ejpam-6596	269	5	the	the	DET
ejpam-6596	269	6	above	above	ADV
ejpam-6596	269	7	-	-	PUNCT
ejpam-6596	269	8	mentioned	mention	VERB
ejpam-6596	269	9	control	control	NOUN
ejpam-6596	269	10	variables	variable	NOUN
ejpam-6596	269	11	,	,	PUNCT
ejpam-6596	269	12	the	the	DET
ejpam-6596	269	13	general	general	ADJ
ejpam-6596	269	14	disease	disease	NOUN
ejpam-6596	269	15	control	control	NOUN
ejpam-6596	269	16	model	model	NOUN
ejpam-6596	269	17	is	be	AUX
ejpam-6596	269	18	created	create	VERB
ejpam-6596	269	19	,	,	PUNCT
ejpam-6596	269	20	and	and	CCONJ
ejpam-6596	269	21	it	it	PRON
ejpam-6596	269	22	looks	look	VERB
ejpam-6596	269	23	like	like	ADP
ejpam-6596	269	24	this:	this:	PRON
ejpam-6596	269	25	ds	ds	ADJ
ejpam-6596	269	26	dt	dt	NOUN
ejpam-6596	269	27	=	=	PUNCT
ejpam-6596	269	28	g	g	PROPN
ejpam-6596	269	29	−	−	PROPN
ejpam-6596	270	1	(	(	PUNCT
ejpam-6596	270	2	1−	1−	NUM
ejpam-6596	270	3	u1	u1	NOUN
ejpam-6596	270	4	)	)	PUNCT
ejpam-6596	270	5	hsi	hsi	PROPN
ejpam-6596	270	6	1	1	NUM
ejpam-6596	271	1	+	+	CCONJ
ejpam-6596	271	2	αi	αi	VERB
ejpam-6596	271	3	−	−	PROPN
ejpam-6596	272	1	(	(	PUNCT
ejpam-6596	272	2	m+	m+	NUM
ejpam-6596	272	3	b1)s	b1)s	PROPN
ejpam-6596	272	4	−	−	PROPN
ejpam-6596	272	5	u3s	u3s	PROPN
ejpam-6596	272	6	,	,	PUNCT
ejpam-6596	272	7	de	de	X
ejpam-6596	272	8	dt	dt	X
ejpam-6596	272	9	=	=	SYM
ejpam-6596	272	10	(	(	PUNCT
ejpam-6596	272	11	1−	1−	NUM
ejpam-6596	272	12	u1	u1	NOUN
ejpam-6596	272	13	)	)	PUNCT
ejpam-6596	272	14	hsi	hsi	PROPN
ejpam-6596	272	15	1	1	NUM
ejpam-6596	273	1	+	+	CCONJ
ejpam-6596	273	2	αi	αi	VERB
ejpam-6596	273	3	−	−	PROPN
ejpam-6596	274	1	(	(	PUNCT
ejpam-6596	274	2	m+	m+	NUM
ejpam-6596	274	3	c+	c+	NOUN
ejpam-6596	274	4	b2)e	b2)e	PROPN
ejpam-6596	274	5	,	,	PUNCT
ejpam-6596	274	6	di	di	NOUN
ejpam-6596	274	7	dt	dt	NOUN
ejpam-6596	274	8	=	=	SYM
ejpam-6596	274	9	ce	ce	PROPN
ejpam-6596	274	10	−	−	PROPN
ejpam-6596	275	1	(	(	PUNCT
ejpam-6596	275	2	m+	m+	NUM
ejpam-6596	275	3	b3	b3	PROPN
ejpam-6596	275	4	+	+	CCONJ
ejpam-6596	275	5	µ	µ	X
ejpam-6596	275	6	)	)	PUNCT
ejpam-6596	275	7	i	i	PRON
ejpam-6596	275	8	−	−	PROPN
ejpam-6596	275	9	(	(	PUNCT
ejpam-6596	275	10	1	1	NUM
ejpam-6596	275	11	+	+	CCONJ
ejpam-6596	275	12	u2	u2	NOUN
ejpam-6596	275	13	)	)	PUNCT
ejpam-6596	275	14	qi	qi	PROPN
ejpam-6596	275	15	,	,	PUNCT
ejpam-6596	275	16	dq	dq	NOUN
ejpam-6596	275	17	dt	dt	NOUN
ejpam-6596	275	18	=	=	PUNCT
ejpam-6596	275	19	b1s	b1s	PROPN
ejpam-6596	275	20	+	+	CCONJ
ejpam-6596	275	21	b2e	b2e	X
ejpam-6596	275	22	+	+	CCONJ
ejpam-6596	275	23	b3i	b3i	NOUN
ejpam-6596	275	24	−	−	PROPN
ejpam-6596	275	25	(	(	PUNCT
ejpam-6596	275	26	m+	m+	NUM
ejpam-6596	275	27	p)q	p)q	NOUN
ejpam-6596	275	28	,	,	PUNCT
ejpam-6596	275	29	dr	dr	PROPN
ejpam-6596	275	30	dt	dt	PROPN
ejpam-6596	275	31	=	=	PUNCT
ejpam-6596	275	32	(	(	PUNCT
ejpam-6596	275	33	1	1	NUM
ejpam-6596	275	34	+	+	CCONJ
ejpam-6596	275	35	u2)qi	u2)qi	PROPN
ejpam-6596	275	36	+	+	CCONJ
ejpam-6596	275	37	pq−mr+	pq−mr+	PROPN
ejpam-6596	275	38	u3s	u3s	PROPN
ejpam-6596	275	39	.	.	PUNCT
ejpam-6596	276	1	(	(	PUNCT
ejpam-6596	276	2	8)	8)	NUM
ejpam-6596	276	3	the	the	DET
ejpam-6596	276	4	system	system	NOUN
ejpam-6596	276	5	(	(	PUNCT
ejpam-6596	276	6	8)	8)	NUM
ejpam-6596	276	7	is	be	AUX
ejpam-6596	276	8	subject	subject	ADJ
ejpam-6596	276	9	to	to	ADP
ejpam-6596	276	10	the	the	DET
ejpam-6596	276	11	nonnegative	nonnegative	ADJ
ejpam-6596	276	12	initial	initial	ADJ
ejpam-6596	276	13	conditions	condition	NOUN
ejpam-6596	276	14	[	[	X
ejpam-6596	276	15	23	23	NUM
ejpam-6596	276	16	,	,	PUNCT
ejpam-6596	276	17	24	24	NUM
ejpam-6596	276	18	]	]	PUNCT
ejpam-6596	276	19	s(0	s(0	PROPN
ejpam-6596	276	20	)	)	PUNCT
ejpam-6596	276	21	>	>	X
ejpam-6596	276	22	0	0	NUM
ejpam-6596	276	23	,	,	PUNCT
ejpam-6596	276	24	e	e	X
ejpam-6596	276	25	≥	≥	NOUN
ejpam-6596	276	26	0	0	NUM
ejpam-6596	276	27	,	,	PUNCT
ejpam-6596	276	28	i	i	PRON
ejpam-6596	276	29	≥	≥	VERB
ejpam-6596	276	30	0	0	NUM
ejpam-6596	276	31	,	,	PUNCT
ejpam-6596	276	32	q	q	X
ejpam-6596	276	33	≥	≥	NOUN
ejpam-6596	276	34	0	0	NUM
ejpam-6596	276	35	and	and	CCONJ
ejpam-6596	276	36	r(0	r(0	PROPN
ejpam-6596	276	37	)	)	PUNCT
ejpam-6596	276	38	≥	≥	NOUN
ejpam-6596	276	39	0	0	NUM
ejpam-6596	276	40	.	.	PUNCT
ejpam-6596	277	1	we	we	PRON
ejpam-6596	277	2	define	define	VERB
ejpam-6596	277	3	the	the	DET
ejpam-6596	277	4	goal	goal	NOUN
ejpam-6596	277	5	functional	functional	ADJ
ejpam-6596	277	6	function	function	NOUN
ejpam-6596	277	7	,	,	PUNCT
ejpam-6596	277	8	which	which	PRON
ejpam-6596	277	9	aims	aim	VERB
ejpam-6596	277	10	to	to	PART
ejpam-6596	277	11	decrease	decrease	VERB
ejpam-6596	277	12	the	the	DET
ejpam-6596	277	13	spread	spread	NOUN
ejpam-6596	277	14	of	of	ADP
ejpam-6596	277	15	the	the	DET
ejpam-6596	277	16	general	general	ADJ
ejpam-6596	277	17	disease	disease	NOUN
ejpam-6596	277	18	infection	infection	NOUN
ejpam-6596	277	19	,	,	PUNCT
ejpam-6596	277	20	can	can	AUX
ejpam-6596	277	21	be	be	AUX
ejpam-6596	277	22	described	describe	VERB
ejpam-6596	277	23	as	as	ADP
ejpam-6596	277	24	;	;	PUNCT
ejpam-6596	277	25	j(u1(t	j(u1(t	PROPN
ejpam-6596	277	26	)	)	PUNCT
ejpam-6596	277	27	,	,	PUNCT
ejpam-6596	277	28	u2(t	u2(t	PROPN
ejpam-6596	277	29	)	)	PUNCT
ejpam-6596	277	30	,	,	PUNCT
ejpam-6596	277	31	u3(t	u3(t	PROPN
ejpam-6596	277	32	)	)	PUNCT
ejpam-6596	277	33	)	)	PUNCT
ejpam-6596	278	1	=	=	SYM
ejpam-6596	278	2	∫	∫	PROPN
ejpam-6596	279	1	tf	tf	INTJ
ejpam-6596	279	2	0	0	PUNCT
ejpam-6596	280	1	a1e	a1e	ADP
ejpam-6596	280	2	+	+	ADJ
ejpam-6596	280	3	a2i	a2i	NOUN
ejpam-6596	280	4	−a3r+	−a3r+	NOUN
ejpam-6596	280	5	1	1	NUM
ejpam-6596	280	6	2	2	NUM
ejpam-6596	280	7	[	[	PUNCT
ejpam-6596	280	8	a4u	a4u	NOUN
ejpam-6596	280	9	2	2	NUM
ejpam-6596	280	10	1(t	1(t	NUM
ejpam-6596	280	11	)	)	PUNCT
ejpam-6596	281	1	+	+	X
ejpam-6596	281	2	a5u	a5u	X
ejpam-6596	281	3	2	2	NUM
ejpam-6596	281	4	2(t	2(t	NUM
ejpam-6596	281	5	)	)	PUNCT
ejpam-6596	282	1	+	+	X
ejpam-6596	282	2	a6u	a6u	PROPN
ejpam-6596	282	3	2	2	NUM
ejpam-6596	282	4	3(t	3(t	NUM
ejpam-6596	282	5	)	)	PUNCT
ejpam-6596	282	6	]	]	PUNCT
ejpam-6596	282	7	.(9	.(9	X
ejpam-6596	282	8	)	)	PUNCT
ejpam-6596	282	9	the	the	DET
ejpam-6596	282	10	values	value	NOUN
ejpam-6596	282	11	a1	a1	NOUN
ejpam-6596	282	12	,	,	PUNCT
ejpam-6596	282	13	a2	a2	PROPN
ejpam-6596	282	14	and	and	CCONJ
ejpam-6596	282	15	a3	a3	NOUN
ejpam-6596	282	16	are	be	AUX
ejpam-6596	282	17	weight	weight	NOUN
ejpam-6596	282	18	constants	constant	NOUN
ejpam-6596	282	19	.	.	PUNCT
ejpam-6596	283	1	the	the	DET
ejpam-6596	283	2	objective	objective	ADJ
ejpam-6596	283	3	functional	functional	NOUN
ejpam-6596	283	4	serves	serve	VERB
ejpam-6596	283	5	the	the	DET
ejpam-6596	283	6	purpose	purpose	NOUN
ejpam-6596	283	7	of	of	ADP
ejpam-6596	283	8	minimising	minimise	VERB
ejpam-6596	283	9	the	the	DET
ejpam-6596	283	10	number	number	NOUN
ejpam-6596	283	11	of	of	ADP
ejpam-6596	283	12	affected	affected	ADJ
ejpam-6596	283	13	individuals	individual	NOUN
ejpam-6596	283	14	.	.	PUNCT
ejpam-6596	284	1	in	in	ADP
ejpam-6596	284	2	this	this	DET
ejpam-6596	284	3	way	way	NOUN
ejpam-6596	284	4	,	,	PUNCT
ejpam-6596	284	5	we	we	PRON
ejpam-6596	284	6	determine	determine	VERB
ejpam-6596	284	7	an	an	DET
ejpam-6596	284	8	optimal	optimal	ADJ
ejpam-6596	284	9	 	 	SPACE
ejpam-6596	284	10	control	control	NOUN
ejpam-6596	284	11	triplet	triplet	NOUN
ejpam-6596	284	12	:	:	PUNCT
ejpam-6596	284	13	j(u∗1(t	j(u∗1(t	NOUN
ejpam-6596	284	14	)	)	PUNCT
ejpam-6596	284	15	,	,	PUNCT
ejpam-6596	284	16	u	u	NOUN
ejpam-6596	284	17	∗	∗	NOUN
ejpam-6596	284	18	2(t	2(t	NUM
ejpam-6596	284	19	)	)	PUNCT
ejpam-6596	284	20	,	,	PUNCT
ejpam-6596	284	21	u	u	NOUN
ejpam-6596	284	22	∗	∗	NOUN
ejpam-6596	284	23	3(t	3(t	NUM
ejpam-6596	284	24	)	)	PUNCT
ejpam-6596	284	25	)	)	PUNCT
ejpam-6596	285	1	=	=	PUNCT
ejpam-6596	285	2	min{j(u1(t	min{j(u1(t	ADJ
ejpam-6596	285	3	)	)	PUNCT
ejpam-6596	285	4	,	,	PUNCT
ejpam-6596	285	5	u2(t	u2(t	NOUN
ejpam-6596	285	6	)	)	PUNCT
ejpam-6596	285	7	,	,	PUNCT
ejpam-6596	285	8	u3(t	u3(t	PROPN
ejpam-6596	285	9	)	)	PUNCT
ejpam-6596	285	10	)	)	PUNCT
ejpam-6596	286	1	∈	∈	PROPN
ejpam-6596	286	2	u	u	NOUN
ejpam-6596	286	3	}	}	PUNCT
ejpam-6596	286	4	.	.	PUNCT
ejpam-6596	287	1	(	(	PUNCT
ejpam-6596	287	2	10	10	NUM
ejpam-6596	287	3	)	)	PUNCT
ejpam-6596	287	4	according	accord	VERB
ejpam-6596	287	5	to	to	ADP
ejpam-6596	287	6	the	the	DET
ejpam-6596	287	7	problem	problem	NOUN
ejpam-6596	287	8	being	be	AUX
ejpam-6596	287	9	considered	consider	VERB
ejpam-6596	287	10	,	,	PUNCT
ejpam-6596	287	11	the	the	DET
ejpam-6596	287	12	control	control	NOUN
ejpam-6596	287	13	set	set	NOUN
ejpam-6596	287	14	is	be	AUX
ejpam-6596	287	15	provided	provide	VERB
ejpam-6596	287	16	by	by	ADP
ejpam-6596	287	17	u	u	NOUN
ejpam-6596	287	18	=	=	NOUN
ejpam-6596	287	19	{	{	PUNCT
ejpam-6596	287	20	u1	u1	NOUN
ejpam-6596	287	21	,	,	PUNCT
ejpam-6596	287	22	u2	u2	NOUN
ejpam-6596	287	23	,	,	PUNCT
ejpam-6596	287	24	u3	u3	NOUN
ejpam-6596	287	25	)	)	PUNCT
ejpam-6596	287	26	:	:	PUNCT
ejpam-6596	288	1	[	[	X
ejpam-6596	288	2	0	0	NUM
ejpam-6596	288	3	,	,	PUNCT
ejpam-6596	288	4	tf	tf	X
ejpam-6596	288	5	]	]	PUNCT
ejpam-6596	288	6	→	→	PUNCT
ejpam-6596	288	7	[	[	X
ejpam-6596	288	8	0	0	NUM
ejpam-6596	288	9	,	,	PUNCT
ejpam-6596	288	10	1	1	NUM
ejpam-6596	288	11	]	]	PUNCT
ejpam-6596	288	12	,	,	PUNCT
ejpam-6596	288	13	(	(	PUNCT
ejpam-6596	288	14	u1	u1	NOUN
ejpam-6596	288	15	,	,	PUNCT
ejpam-6596	288	16	u2	u2	NOUN
ejpam-6596	288	17	,	,	PUNCT
ejpam-6596	288	18	u3)is	u3)is	VERB
ejpam-6596	288	19	a	a	DET
ejpam-6596	288	20	labesgue	labesgue	NOUN
ejpam-6596	288	21	measurable	measurable	NOUN
ejpam-6596	288	22	}	}	PUNCT
ejpam-6596	288	23	.	.	PUNCT
ejpam-6596	289	1	next	next	ADV
ejpam-6596	289	2	,	,	PUNCT
ejpam-6596	289	3	we	we	PRON
ejpam-6596	289	4	demonstrate	demonstrate	VERB
ejpam-6596	289	5	that	that	SCONJ
ejpam-6596	289	6	the	the	DET
ejpam-6596	289	7	optimum	optimum	ADJ
ejpam-6596	289	8	control	control	NOUN
ejpam-6596	289	9	problem	problem	NOUN
ejpam-6596	289	10	exists	exist	VERB
ejpam-6596	289	11	.	.	PUNCT
ejpam-6596	290	1	7.1	7.1	NUM
ejpam-6596	290	2	.	.	PUNCT
ejpam-6596	291	1	existence	existence	NOUN
ejpam-6596	291	2	of	of	ADP
ejpam-6596	291	3	the	the	DET
ejpam-6596	291	4	optimal	optimal	ADJ
ejpam-6596	291	5	control	control	NOUN
ejpam-6596	291	6	problem	problem	NOUN
ejpam-6596	291	7	here	here	ADV
ejpam-6596	291	8	,	,	PUNCT
ejpam-6596	291	9	we	we	PRON
ejpam-6596	291	10	provide	provide	VERB
ejpam-6596	291	11	proof	proof	NOUN
ejpam-6596	291	12	that	that	PRON
ejpam-6596	291	13	shows	show	VERB
ejpam-6596	291	14	the	the	DET
ejpam-6596	291	15	control	control	NOUN
ejpam-6596	291	16	problem	problem	NOUN
ejpam-6596	291	17	exists	exist	VERB
ejpam-6596	291	18	.	.	PUNCT
ejpam-6596	292	1	for	for	ADP
ejpam-6596	292	2	the	the	DET
ejpam-6596	292	3	optimum	optimum	ADJ
ejpam-6596	292	4	control	control	NOUN
ejpam-6596	292	5	issue	issue	NOUN
ejpam-6596	292	6	,	,	PUNCT
ejpam-6596	292	7	we	we	PRON
ejpam-6596	292	8	provide	provide	VERB
ejpam-6596	292	9	the	the	DET
ejpam-6596	292	10	following	follow	VERB
ejpam-6596	292	11	definition	definition	NOUN
ejpam-6596	292	12	of	of	ADP
ejpam-6596	292	13	hamiltonian	hamiltonian	ADJ
ejpam-6596	292	14	h	h	NOUN
ejpam-6596	292	15	:	:	PUNCT
ejpam-6596	292	16	h	h	PROPN
ejpam-6596	292	17	=	=	SYM
ejpam-6596	292	18	l(e(t	l(e(t	ADJ
ejpam-6596	292	19	)	)	PUNCT
ejpam-6596	292	20	,	,	PUNCT
ejpam-6596	292	21	i(t	i(t	PROPN
ejpam-6596	292	22	)	)	PUNCT
ejpam-6596	292	23	,	,	PUNCT
ejpam-6596	292	24	r(t	r(t	NOUN
ejpam-6596	292	25	)	)	PUNCT
ejpam-6596	292	26	,	,	PUNCT
ejpam-6596	292	27	u1(t	u1(t	PROPN
ejpam-6596	292	28	)	)	PUNCT
ejpam-6596	292	29	,	,	PUNCT
ejpam-6596	292	30	u2(t	u2(t	PROPN
ejpam-6596	292	31	)	)	PUNCT
ejpam-6596	292	32	,	,	PUNCT
ejpam-6596	292	33	u3(t	u3(t	PROPN
ejpam-6596	292	34	)	)	PUNCT
ejpam-6596	292	35	)	)	PUNCT
ejpam-6596	293	1	+	+	CCONJ
ejpam-6596	293	2	λ1	λ1	ADJ
ejpam-6596	293	3	ds	ds	ADJ
ejpam-6596	293	4	dt	dt	NOUN
ejpam-6596	293	5	+	+	CCONJ
ejpam-6596	293	6	λ2	λ2	X
ejpam-6596	293	7	de	de	X
ejpam-6596	293	8	dt	dt	PROPN
ejpam-6596	293	9	+	+	CCONJ
ejpam-6596	293	10	λ3	λ3	PROPN
ejpam-6596	293	11	di	di	NOUN
ejpam-6596	293	12	dt	dt	NOUN
ejpam-6596	294	1	+	+	CCONJ
ejpam-6596	294	2	λ4	λ4	VERB
ejpam-6596	294	3	dq	dq	ADP
ejpam-6596	294	4	dt	dt	PROPN
ejpam-6596	295	1	+	+	CCONJ
ejpam-6596	295	2	λ5	λ5	PROPN
ejpam-6596	296	1	dr	dr	PROPN
ejpam-6596	296	2	dt	dt	PROPN
ejpam-6596	296	3	.(11	.(11	PROPN
ejpam-6596	296	4	)	)	PUNCT
ejpam-6596	296	5	n.	n.	PROPN
ejpam-6596	296	6	gul	gul	PROPN
ejpam-6596	296	7	et	et	PROPN
ejpam-6596	296	8	al	al	PROPN
ejpam-6596	296	9	.	.	PUNCT
ejpam-6596	296	10	/	/	SYM
ejpam-6596	296	11	eur	eur	PROPN
ejpam-6596	296	12	.	.	PUNCT
ejpam-6596	297	1	j.	j.	PROPN
ejpam-6596	297	2	pure	pure	PROPN
ejpam-6596	297	3	appl	appl	PROPN
ejpam-6596	297	4	.	.	PROPN
ejpam-6596	297	5	math	math	PROPN
ejpam-6596	297	6	,	,	PUNCT
ejpam-6596	297	7	18	18	NUM
ejpam-6596	297	8	(	(	PUNCT
ejpam-6596	297	9	4	4	NUM
ejpam-6596	297	10	)	)	PUNCT
ejpam-6596	297	11	(	(	PUNCT
ejpam-6596	297	12	2025	2025	NUM
ejpam-6596	297	13	)	)	PUNCT
ejpam-6596	297	14	,	,	PUNCT
ejpam-6596	297	15	6596	6596	NUM
ejpam-6596	297	16	14	14	NUM
ejpam-6596	297	17	of	of	ADP
ejpam-6596	297	18	23	23	NUM
ejpam-6596	297	19	theorem	theorem	NOUN
ejpam-6596	297	20	5	5	NUM
ejpam-6596	297	21	.	.	X
ejpam-6596	298	1	for	for	ADP
ejpam-6596	298	2	control	control	NOUN
ejpam-6596	298	3	issue	issue	NOUN
ejpam-6596	298	4	(	(	PUNCT
ejpam-6596	298	5	4.1	4.1	NUM
ejpam-6596	298	6	)	)	PUNCT
ejpam-6596	298	7	,	,	PUNCT
ejpam-6596	298	8	there	there	PRON
ejpam-6596	298	9	is	be	VERB
ejpam-6596	298	10	u∗(t	u∗(t	NOUN
ejpam-6596	298	11	)	)	PUNCT
ejpam-6596	298	12	=	=	SYM
ejpam-6596	298	13	(	(	PUNCT
ejpam-6596	298	14	u∗1(t	u∗1(t	PROPN
ejpam-6596	298	15	)	)	PUNCT
ejpam-6596	298	16	,	,	PUNCT
ejpam-6596	299	1	u	u	NOUN
ejpam-6596	299	2	∗	∗	NOUN
ejpam-6596	299	3	2(t	2(t	NUM
ejpam-6596	299	4	)	)	PUNCT
ejpam-6596	299	5	,	,	PUNCT
ejpam-6596	299	6	u	u	NOUN
ejpam-6596	299	7	∗	∗	NOUN
ejpam-6596	299	8	3(t	3(t	NUM
ejpam-6596	299	9	)	)	PUNCT
ejpam-6596	299	10	)	)	PUNCT
ejpam-6596	300	1	∈	∈	PROPN
ejpam-6596	300	2	u	u	NOUN
ejpam-6596	300	3	,	,	PUNCT
ejpam-6596	300	4	in	in	ADP
ejpam-6596	300	5	such	such	ADJ
ejpam-6596	300	6	away	away	ADV
ejpam-6596	300	7	that	that	SCONJ
ejpam-6596	300	8	min(u1(t),u2(t),u3(t)∈u)j(u1(t	min(u1(t),u2(t),u3(t)∈u)j(u1(t	VERB
ejpam-6596	300	9	)	)	PUNCT
ejpam-6596	300	10	,	,	PUNCT
ejpam-6596	300	11	u2(t	u2(t	NOUN
ejpam-6596	300	12	)	)	PUNCT
ejpam-6596	300	13	,	,	PUNCT
ejpam-6596	300	14	u3(t	u3(t	PROPN
ejpam-6596	300	15	)	)	PUNCT
ejpam-6596	300	16	)	)	PUNCT
ejpam-6596	301	1	=	=	SYM
ejpam-6596	301	2	j(u∗1	j(u∗1	PROPN
ejpam-6596	301	3	,	,	PUNCT
ejpam-6596	301	4	u	u	NOUN
ejpam-6596	301	5	∗	∗	NOUN
ejpam-6596	301	6	2	2	NUM
ejpam-6596	301	7	,	,	PUNCT
ejpam-6596	301	8	u	u	NOUN
ejpam-6596	301	9	∗	∗	NOUN
ejpam-6596	301	10	3(t	3(t	NUM
ejpam-6596	301	11	)	)	PUNCT
ejpam-6596	301	12	)	)	PUNCT
ejpam-6596	301	13	.	.	PUNCT
ejpam-6596	302	1	proof	proof	NOUN
ejpam-6596	302	2	.	.	PUNCT
ejpam-6596	303	1	for	for	ADP
ejpam-6596	303	2	the	the	DET
ejpam-6596	303	3	purpose	purpose	NOUN
ejpam-6596	303	4	of	of	ADP
ejpam-6596	303	5	validating	validate	VERB
ejpam-6596	303	6	the	the	DET
ejpam-6596	303	7	optimal	optimal	ADJ
ejpam-6596	303	8	control	control	NOUN
ejpam-6596	303	9	rate	rate	NOUN
ejpam-6596	303	10	,	,	PUNCT
ejpam-6596	303	11	we	we	PRON
ejpam-6596	303	12	used	use	VERB
ejpam-6596	303	13	a	a	DET
ejpam-6596	303	14	variety	variety	NOUN
ejpam-6596	303	15	of	of	ADP
ejpam-6596	303	16	methodologies	methodology	NOUN
ejpam-6596	303	17	.	.	PUNCT
ejpam-6596	304	1	thus	thus	ADV
ejpam-6596	304	2	,	,	PUNCT
ejpam-6596	304	3	each	each	PRON
ejpam-6596	304	4	and	and	CCONJ
ejpam-6596	304	5	every	every	DET
ejpam-6596	304	6	control	control	NOUN
ejpam-6596	304	7	and	and	CCONJ
ejpam-6596	304	8	state	state	NOUN
ejpam-6596	304	9	variable	variable	NOUN
ejpam-6596	304	10	has	have	VERB
ejpam-6596	304	11	a	a	DET
ejpam-6596	304	12	positive	positive	ADJ
ejpam-6596	304	13	value	value	NOUN
ejpam-6596	304	14	.	.	PUNCT
ejpam-6596	305	1	due	due	ADP
ejpam-6596	305	2	to	to	ADP
ejpam-6596	305	3	this	this	PRON
ejpam-6596	305	4	,	,	PUNCT
ejpam-6596	305	5	the	the	DET
ejpam-6596	305	6	issue	issue	NOUN
ejpam-6596	305	7	is	be	AUX
ejpam-6596	305	8	being	be	AUX
ejpam-6596	305	9	reduced	reduce	VERB
ejpam-6596	305	10	,	,	PUNCT
ejpam-6596	305	11	so	so	ADV
ejpam-6596	305	12	,	,	PUNCT
ejpam-6596	305	13	u1(t	u1(t	PROPN
ejpam-6596	305	14	)	)	PUNCT
ejpam-6596	305	15	,	,	PUNCT
ejpam-6596	305	16	u2(t	u2(t	PROPN
ejpam-6596	305	17	)	)	PUNCT
ejpam-6596	305	18	and	and	CCONJ
ejpam-6596	305	19	u3(t	u3(t	NUM
ejpam-6596	305	20	)	)	PUNCT
ejpam-6596	305	21	elaborates	elaborate	VERB
ejpam-6596	305	22	the	the	DET
ejpam-6596	305	23	required	require	VERB
ejpam-6596	305	24	convexity	convexity	NOUN
ejpam-6596	305	25	of	of	ADP
ejpam-6596	305	26	the	the	DET
ejpam-6596	305	27	goal	goal	NOUN
ejpam-6596	305	28	functional	functional	ADJ
ejpam-6596	305	29	and	and	CCONJ
ejpam-6596	305	30	is	be	AUX
ejpam-6596	305	31	satisfied	satisfied	ADJ
ejpam-6596	305	32	.	.	PUNCT
ejpam-6596	306	1	the	the	DET
ejpam-6596	306	2	collection	collection	NOUN
ejpam-6596	306	3	of	of	ADP
ejpam-6596	306	4	control	control	PROPN
ejpam-6596	306	5	variables	variable	NOUN
ejpam-6596	306	6	u1	u1	NOUN
ejpam-6596	306	7	,	,	PUNCT
ejpam-6596	306	8	u2	u2	NOUN
ejpam-6596	306	9	,	,	PUNCT
ejpam-6596	306	10	u3	u3	NOUN
ejpam-6596	306	11	∈	∈	PROPN
ejpam-6596	306	12	u	u	NOUN
ejpam-6596	306	13	is	be	AUX
ejpam-6596	306	14	by	by	ADP
ejpam-6596	306	15	definition	definition	NOUN
ejpam-6596	306	16	convex	convex	NOUN
ejpam-6596	306	17	and	and	CCONJ
ejpam-6596	306	18	closed	close	VERB
ejpam-6596	306	19	.	.	PUNCT
ejpam-6596	307	1	there	there	PRON
ejpam-6596	307	2	is	be	VERB
ejpam-6596	307	3	a	a	DET
ejpam-6596	307	4	defined	define	VERB
ejpam-6596	307	5	optimum	optimum	ADJ
ejpam-6596	307	6	system	system	NOUN
ejpam-6596	307	7	,	,	PUNCT
ejpam-6596	307	8	furthermore	furthermore	ADV
ejpam-6596	307	9	,	,	PUNCT
ejpam-6596	307	10	it	it	PRON
ejpam-6596	307	11	supplies	supply	VERB
ejpam-6596	307	12	the	the	DET
ejpam-6596	307	13	confidence	confidence	NOUN
ejpam-6596	307	14	regarding	regard	VERB
ejpam-6596	307	15	the	the	DET
ejpam-6596	307	16	solidity	solidity	NOUN
ejpam-6596	307	17	required	require	VERB
ejpam-6596	307	18	for	for	ADP
ejpam-6596	307	19	the	the	DET
ejpam-6596	307	20	verification	verification	NOUN
ejpam-6596	307	21	of	of	ADP
ejpam-6596	307	22	the	the	DET
ejpam-6596	307	23	optimal	optimal	ADJ
ejpam-6596	307	24	control	control	NOUN
ejpam-6596	307	25	system	system	NOUN
ejpam-6596	307	26	.	.	PUNCT
ejpam-6596	308	1	moreover	moreover	ADV
ejpam-6596	308	2	,	,	PUNCT
ejpam-6596	308	3	an	an	DET
ejpam-6596	308	4	integral	integral	ADJ
ejpam-6596	308	5	in	in	ADP
ejpam-6596	308	6	the	the	DET
ejpam-6596	308	7	practical	practical	ADJ
ejpam-6596	308	8	purpose	purpose	NOUN
ejpam-6596	308	9	a1e+a2i−a3r+	a1e+a2i−a3r+	NUM
ejpam-6596	308	10	1	1	NUM
ejpam-6596	308	11	2(a4u	2(a4u	NUM
ejpam-6596	308	12	2	2	NUM
ejpam-6596	308	13	1	1	NUM
ejpam-6596	308	14	+	+	NUM
ejpam-6596	308	15	a5u	a5u	NOUN
ejpam-6596	308	16	2	2	NUM
ejpam-6596	308	17	2	2	NUM
ejpam-6596	308	18	+	+	ADJ
ejpam-6596	308	19	a6u	a6u	PROPN
ejpam-6596	308	20	2	2	NUM
ejpam-6596	308	21	3	3	NUM
ejpam-6596	308	22	)	)	PUNCT
ejpam-6596	308	23	which	which	PRON
ejpam-6596	308	24	confirms	confirm	VERB
ejpam-6596	308	25	the	the	DET
ejpam-6596	308	26	evidence	evidence	NOUN
ejpam-6596	308	27	,	,	PUNCT
ejpam-6596	308	28	is	be	AUX
ejpam-6596	308	29	convex	convex	ADJ
ejpam-6596	308	30	on	on	ADP
ejpam-6596	308	31	the	the	DET
ejpam-6596	308	32	control	control	NOUN
ejpam-6596	308	33	set	set	VERB
ejpam-6596	308	34	u.	u.	PROPN
ejpam-6596	308	35	8	8	NUM
ejpam-6596	308	36	.	.	PUNCT
ejpam-6596	308	37	optimality	optimality	NOUN
ejpam-6596	308	38	system	system	NOUN
ejpam-6596	308	39	theorem	theorem	VERB
ejpam-6596	308	40	6	6	NUM
ejpam-6596	308	41	.	.	PUNCT
ejpam-6596	309	1	given	give	VERB
ejpam-6596	309	2	optimal	optimal	ADJ
ejpam-6596	309	3	controls	control	NOUN
ejpam-6596	309	4	u∗1(t	u∗1(t	PROPN
ejpam-6596	309	5	)	)	PUNCT
ejpam-6596	309	6	,	,	PUNCT
ejpam-6596	309	7	u	u	NOUN
ejpam-6596	309	8	∗	∗	NOUN
ejpam-6596	309	9	2(t	2(t	NUM
ejpam-6596	309	10	)	)	PUNCT
ejpam-6596	309	11	,	,	PUNCT
ejpam-6596	309	12	u	u	NOUN
ejpam-6596	309	13	∗	∗	NOUN
ejpam-6596	309	14	3(t	3(t	NUM
ejpam-6596	309	15	)	)	PUNCT
ejpam-6596	309	16	and	and	CCONJ
ejpam-6596	309	17	solutions	solution	NOUN
ejpam-6596	309	18	s∗	s∗	PROPN
ejpam-6596	309	19	,	,	PUNCT
ejpam-6596	309	20	e∗	e∗	NOUN
ejpam-6596	309	21	,	,	PUNCT
ejpam-6596	309	22	i∗	i∗	NOUN
ejpam-6596	309	23	,	,	PUNCT
ejpam-6596	309	24	q∗	q∗	NOUN
ejpam-6596	309	25	,	,	PUNCT
ejpam-6596	309	26	r∗	r∗	NOUN
ejpam-6596	309	27	of	of	ADP
ejpam-6596	309	28	the	the	DET
ejpam-6596	309	29	corresponding	correspond	VERB
ejpam-6596	309	30	state	state	NOUN
ejpam-6596	309	31	system	system	NOUN
ejpam-6596	309	32	(	(	PUNCT
ejpam-6596	309	33	8)	8)	NUM
ejpam-6596	309	34	there	there	PRON
ejpam-6596	309	35	is	be	VERB
ejpam-6596	309	36	adjoint	adjoint	NOUN
ejpam-6596	309	37	variables	variable	NOUN
ejpam-6596	309	38	λn(t	λn(t	PRON
ejpam-6596	309	39	)	)	PUNCT
ejpam-6596	309	40	,	,	PUNCT
ejpam-6596	309	41	n	n	NOUN
ejpam-6596	309	42	=	=	SYM
ejpam-6596	309	43	1	1	NUM
ejpam-6596	309	44	,	,	PUNCT
ejpam-6596	309	45	...	...	PUNCT
ejpam-6596	309	46	,	,	PUNCT
ejpam-6596	309	47	5,	5,	NUM
ejpam-6596	309	48	dλ1	dλ1	NOUN
ejpam-6596	309	49	dt	dt	NOUN
ejpam-6596	309	50	=	=	SYM
ejpam-6596	309	51	(	(	PUNCT
ejpam-6596	309	52	λ1	λ1	INTJ
ejpam-6596	309	53	−	−	NOUN
ejpam-6596	309	54	λ2)(1−	λ2)(1−	PROPN
ejpam-6596	309	55	u1	u1	NOUN
ejpam-6596	309	56	)	)	PUNCT
ejpam-6596	309	57	hi	hi	NOUN
ejpam-6596	309	58	1	1	NUM
ejpam-6596	309	59	+	+	CCONJ
ejpam-6596	309	60	αi	αi	X
ejpam-6596	310	1	+	+	CCONJ
ejpam-6596	310	2	(	(	PUNCT
ejpam-6596	310	3	λ1	λ1	ADJ
ejpam-6596	310	4	−	−	PROPN
ejpam-6596	310	5	λ4)b1	λ4)b1	X
ejpam-6596	310	6	+	+	CCONJ
ejpam-6596	310	7	(	(	PUNCT
ejpam-6596	310	8	λ1	λ1	ADJ
ejpam-6596	310	9	−	−	PROPN
ejpam-6596	310	10	λ5)u3	λ5)u3	PROPN
ejpam-6596	310	11	+	+	PROPN
ejpam-6596	310	12	mλ1	mλ1	NOUN
ejpam-6596	310	13	,	,	PUNCT
ejpam-6596	310	14	dλ2	dλ2	NOUN
ejpam-6596	310	15	dt	dt	NOUN
ejpam-6596	310	16	=	=	PUNCT
ejpam-6596	310	17	−a1	−a1	PROPN
ejpam-6596	310	18	+	+	CCONJ
ejpam-6596	310	19	(	(	PUNCT
ejpam-6596	310	20	λ2	λ2	NOUN
ejpam-6596	310	21	−	−	PROPN
ejpam-6596	310	22	λ3)c+	λ3)c+	PROPN
ejpam-6596	310	23	(	(	PUNCT
ejpam-6596	310	24	λ2	λ2	PROPN
ejpam-6596	310	25	−	−	PROPN
ejpam-6596	310	26	λ4)b2	λ4)b2	PROPN
ejpam-6596	311	1	+	+	PROPN
ejpam-6596	311	2	mλ2	mλ2	PROPN
ejpam-6596	311	3	,	,	PUNCT
ejpam-6596	311	4	dλ3	dλ3	NOUN
ejpam-6596	311	5	dt	dt	NOUN
ejpam-6596	311	6	=	=	PUNCT
ejpam-6596	311	7	−a2	−a2	PROPN
ejpam-6596	311	8	+	+	CCONJ
ejpam-6596	311	9	(	(	PUNCT
ejpam-6596	311	10	λ1	λ1	ADJ
ejpam-6596	311	11	−	−	NOUN
ejpam-6596	311	12	λ2)(1−	λ2)(1−	PROPN
ejpam-6596	311	13	u1	u1	PROPN
ejpam-6596	311	14	)	)	PUNCT
ejpam-6596	311	15	hs	hs	PROPN
ejpam-6596	311	16	(	(	PUNCT
ejpam-6596	311	17	1	1	NUM
ejpam-6596	311	18	+	+	CCONJ
ejpam-6596	311	19	αi)2	αi)2	PROPN
ejpam-6596	311	20	+	+	CCONJ
ejpam-6596	311	21	(	(	PUNCT
ejpam-6596	311	22	λ3	λ3	PROPN
ejpam-6596	311	23	−	−	PROPN
ejpam-6596	311	24	λ4)b3	λ4)b3	PROPN
ejpam-6596	311	25	+	+	CCONJ
ejpam-6596	311	26	(	(	PUNCT
ejpam-6596	311	27	λ3	λ3	PROPN
ejpam-6596	311	28	−	−	PROPN
ejpam-6596	311	29	λ5)(1	λ5)(1	PRON
ejpam-6596	312	1	+	+	NUM
ejpam-6596	312	2	u2)q	u2)q	NOUN
ejpam-6596	312	3	+	+	CCONJ
ejpam-6596	312	4	(	(	PUNCT
ejpam-6596	312	5	m+	m+	NOUN
ejpam-6596	312	6	µ)λ3	µ)λ3	NOUN
ejpam-6596	312	7	dλ4	dλ4	VERB
ejpam-6596	312	8	dt	dt	NOUN
ejpam-6596	313	1	=	=	PUNCT
ejpam-6596	314	1	(	(	PUNCT
ejpam-6596	314	2	λ4	λ4	ADJ
ejpam-6596	314	3	−	−	NOUN
ejpam-6596	314	4	λ5)p+mλ4	λ5)p+mλ4	AUX
ejpam-6596	314	5	dλ5	dλ5	VERB
ejpam-6596	314	6	dt	dt	NOUN
ejpam-6596	314	7	=	=	SYM
ejpam-6596	314	8	−a3	−a3	PROPN
ejpam-6596	315	1	+	+	SYM
ejpam-6596	315	2	mλ5	mλ5	X
ejpam-6596	315	3	,	,	PUNCT
ejpam-6596	315	4	with	with	ADP
ejpam-6596	315	5	transversality	transversality	NOUN
ejpam-6596	315	6	conditions	condition	NOUN
ejpam-6596	315	7	λn(tf	λn(tf	X
ejpam-6596	315	8	)	)	PUNCT
ejpam-6596	316	1	=	=	SYM
ejpam-6596	316	2	0	0	NUM
ejpam-6596	316	3	,	,	PUNCT
ejpam-6596	316	4	n	n	NOUN
ejpam-6596	316	5	=	=	SYM
ejpam-6596	316	6	1	1	NUM
ejpam-6596	316	7	,	,	PUNCT
ejpam-6596	316	8	...	...	PUNCT
ejpam-6596	316	9	,	,	PUNCT
ejpam-6596	316	10	5	5	X
ejpam-6596	316	11	.	.	PUNCT
ejpam-6596	317	1	proof	proof	NOUN
ejpam-6596	317	2	.	.	PUNCT
ejpam-6596	318	1	when	when	SCONJ
ejpam-6596	318	2	we	we	PRON
ejpam-6596	318	3	consider	consider	VERB
ejpam-6596	318	4	the	the	DET
ejpam-6596	318	5	values	value	NOUN
ejpam-6596	318	6	as	as	ADP
ejpam-6596	318	7	s(t	s(t	PROPN
ejpam-6596	318	8	)	)	PUNCT
ejpam-6596	318	9	=	=	PUNCT
ejpam-6596	318	10	s∗	s∗	PROPN
ejpam-6596	318	11	,	,	PUNCT
ejpam-6596	318	12	e(t	e(t	NOUN
ejpam-6596	318	13	)	)	PUNCT
ejpam-6596	318	14	=	=	SYM
ejpam-6596	318	15	e∗	e∗	NOUN
ejpam-6596	318	16	,	,	PUNCT
ejpam-6596	318	17	i(t	i(t	PROPN
ejpam-6596	318	18	)	)	PUNCT
ejpam-6596	318	19	=	=	SYM
ejpam-6596	318	20	i∗	i∗	NOUN
ejpam-6596	318	21	,	,	PUNCT
ejpam-6596	318	22	q(t	q(t	ADJ
ejpam-6596	318	23	)	)	PUNCT
ejpam-6596	318	24	=	=	SYM
ejpam-6596	318	25	q∗	q∗	NOUN
ejpam-6596	318	26	,	,	PUNCT
ejpam-6596	318	27	and	and	CCONJ
ejpam-6596	318	28	r(t	r(t	NOUN
ejpam-6596	318	29	)	)	PUNCT
ejpam-6596	318	30	=	=	SYM
ejpam-6596	318	31	r∗	r∗	VERB
ejpam-6596	318	32	and	and	CCONJ
ejpam-6596	318	33	differentiate	differentiate	VERB
ejpam-6596	318	34	the	the	DET
ejpam-6596	318	35	hamiltonian	hamiltonian	NOUN
ejpam-6596	318	36	with	with	ADP
ejpam-6596	318	37	respect	respect	NOUN
ejpam-6596	318	38	to	to	ADP
ejpam-6596	318	39	state	state	NOUN
ejpam-6596	318	40	variables	variable	NOUN
ejpam-6596	318	41	s(t	s(t	PROPN
ejpam-6596	318	42	)	)	PUNCT
ejpam-6596	318	43	,	,	PUNCT
ejpam-6596	318	44	e(t	e(t	NOUN
ejpam-6596	318	45	)	)	PUNCT
ejpam-6596	318	46	,	,	PUNCT
ejpam-6596	318	47	i(t	i(t	PROPN
ejpam-6596	318	48	)	)	PUNCT
ejpam-6596	318	49	,	,	PUNCT
ejpam-6596	318	50	q(t	q(t	PROPN
ejpam-6596	318	51	)	)	PUNCT
ejpam-6596	318	52	and	and	CCONJ
ejpam-6596	318	53	r(t	r(t	NOUN
ejpam-6596	318	54	)	)	PUNCT
ejpam-6596	318	55	,	,	PUNCT
ejpam-6596	318	56	respectively	respectively	ADV
ejpam-6596	318	57	,	,	PUNCT
ejpam-6596	318	58	we	we	PRON
ejpam-6596	318	59	get	get	VERB
ejpam-6596	318	60	the	the	DET
ejpam-6596	318	61	adjoint	adjoint	NOUN
ejpam-6596	318	62	system	system	NOUN
ejpam-6596	318	63	(	(	PUNCT
ejpam-6596	318	64	12	12	NUM
ejpam-6596	318	65	)	)	PUNCT
ejpam-6596	318	66	with	with	ADP
ejpam-6596	318	67	transversality	transversality	NOUN
ejpam-6596	318	68	conditions	condition	NOUN
ejpam-6596	318	69	λn(t	λn(t	PRON
ejpam-6596	318	70	)	)	PUNCT
ejpam-6596	318	71	=	=	SYM
ejpam-6596	319	1	0	0	NUM
ejpam-6596	319	2	,	,	PUNCT
ejpam-6596	319	3	n	n	NOUN
ejpam-6596	319	4	=	=	SYM
ejpam-6596	319	5	1	1	NUM
ejpam-6596	319	6	,	,	PUNCT
ejpam-6596	319	7	2	2	NUM
ejpam-6596	319	8	,	,	PUNCT
ejpam-6596	319	9	...	...	PUNCT
ejpam-6596	319	10	,	,	PUNCT
ejpam-6596	319	11	5	5	X
ejpam-6596	319	12	.	.	PUNCT
ejpam-6596	320	1	in	in	ADP
ejpam-6596	320	2	coming	come	VERB
ejpam-6596	320	3	part	part	NOUN
ejpam-6596	320	4	,	,	PUNCT
ejpam-6596	320	5	we	we	PRON
ejpam-6596	320	6	develop	develop	VERB
ejpam-6596	320	7	the	the	DET
ejpam-6596	320	8	principles	principle	NOUN
ejpam-6596	320	9	of	of	ADP
ejpam-6596	320	10	optimal	optimal	ADJ
ejpam-6596	320	11	control	control	NOUN
ejpam-6596	320	12	variables	variable	NOUN
ejpam-6596	320	13	as	as	SCONJ
ejpam-6596	320	14	follows	follow	VERB
ejpam-6596	320	15	:	:	PUNCT
ejpam-6596	320	16	while	while	SCONJ
ejpam-6596	320	17	using	use	VERB
ejpam-6596	320	18	optimal	optimal	ADJ
ejpam-6596	320	19	conditions	condition	NOUN
ejpam-6596	320	20	for	for	ADP
ejpam-6596	320	21	solution	solution	NOUN
ejpam-6596	320	22	∂h	∂h	PROPN
ejpam-6596	320	23	∂u1	∂u1	PROPN
ejpam-6596	320	24	=	=	SYM
ejpam-6596	320	25	0	0	NUM
ejpam-6596	320	26	,	,	PUNCT
ejpam-6596	320	27	∂h	∂h	PROPN
ejpam-6596	320	28	∂u2	∂u2	NOUN
ejpam-6596	320	29	=	=	SYM
ejpam-6596	320	30	0	0	PUNCT
ejpam-6596	320	31	and	and	CCONJ
ejpam-6596	320	32	∂h	∂h	PROPN
ejpam-6596	320	33	∂u3	∂u3	NOUN
ejpam-6596	320	34	=	=	NOUN
ejpam-6596	320	35	0	0	NUM
ejpam-6596	320	36	on	on	ADP
ejpam-6596	320	37	the	the	DET
ejpam-6596	320	38	inside	inside	NOUN
ejpam-6596	320	39	of	of	ADP
ejpam-6596	320	40	the	the	DET
ejpam-6596	320	41	control	control	NOUN
ejpam-6596	320	42	setup	setup	NOUN
ejpam-6596	320	43	.	.	PUNCT
ejpam-6596	321	1	lastly	lastly	ADV
ejpam-6596	321	2	,	,	PUNCT
ejpam-6596	321	3	 	 	SPACE
ejpam-6596	321	4	we	we	PRON
ejpam-6596	321	5	employ	employ	VERB
ejpam-6596	321	6	the	the	DET
ejpam-6596	321	7	control	control	NOUN
ejpam-6596	321	8	area	area	NOUN
ejpam-6596	321	9	characteristic	characteristic	ADJ
ejpam-6596	321	10	while	while	SCONJ
ejpam-6596	321	11	writing	write	VERB
ejpam-6596	321	12	.	.	PUNCT
ejpam-6596	322	1	u1(t	u1(t	X
ejpam-6596	322	2	)	)	PUNCT
ejpam-6596	322	3	=	=	SYM
ejpam-6596	322	4	(	(	PUNCT
ejpam-6596	322	5	λ2	λ2	NOUN
ejpam-6596	322	6	−	−	PROPN
ejpam-6596	322	7	λ1	λ1	PROPN
ejpam-6596	322	8	)	)	PUNCT
ejpam-6596	322	9	a4	a4	NOUN
ejpam-6596	322	10	hsi	hsi	NOUN
ejpam-6596	322	11	1	1	NUM
ejpam-6596	323	1	+	+	CCONJ
ejpam-6596	323	2	αi	αi	NOUN
ejpam-6596	323	3	,	,	PUNCT
ejpam-6596	323	4	n.	n.	PROPN
ejpam-6596	323	5	gul	gul	PROPN
ejpam-6596	323	6	et	et	PROPN
ejpam-6596	323	7	al	al	PROPN
ejpam-6596	323	8	.	.	PUNCT
ejpam-6596	323	9	/	/	SYM
ejpam-6596	323	10	eur	eur	PROPN
ejpam-6596	323	11	.	.	PUNCT
ejpam-6596	324	1	j.	j.	PROPN
ejpam-6596	324	2	pure	pure	PROPN
ejpam-6596	324	3	appl	appl	PROPN
ejpam-6596	324	4	.	.	PROPN
ejpam-6596	324	5	math	math	PROPN
ejpam-6596	324	6	,	,	PUNCT
ejpam-6596	324	7	18	18	NUM
ejpam-6596	324	8	(	(	PUNCT
ejpam-6596	324	9	4	4	NUM
ejpam-6596	324	10	)	)	PUNCT
ejpam-6596	324	11	(	(	PUNCT
ejpam-6596	324	12	2025	2025	NUM
ejpam-6596	324	13	)	)	PUNCT
ejpam-6596	324	14	,	,	PUNCT
ejpam-6596	324	15	6596	6596	NUM
ejpam-6596	324	16	15	15	NUM
ejpam-6596	324	17	of	of	ADP
ejpam-6596	324	18	23	23	NUM
ejpam-6596	324	19	u2(t	u2(t	NOUN
ejpam-6596	324	20	)	)	PUNCT
ejpam-6596	324	21	=	=	SYM
ejpam-6596	325	1	(	(	PUNCT
ejpam-6596	325	2	λ3	λ3	PROPN
ejpam-6596	325	3	−	−	PROPN
ejpam-6596	325	4	λ5)qi	λ5)qi	PROPN
ejpam-6596	325	5	a5	a5	PROPN
ejpam-6596	325	6	,	,	PUNCT
ejpam-6596	325	7	u3(t	u3(t	PROPN
ejpam-6596	325	8	)	)	PUNCT
ejpam-6596	325	9	=	=	SYM
ejpam-6596	325	10	(	(	PUNCT
ejpam-6596	325	11	λ1	λ1	PROPN
ejpam-6596	325	12	−	−	PROPN
ejpam-6596	325	13	λ5)s	λ5)s	PROPN
ejpam-6596	325	14	a6	a6	NOUN
ejpam-6596	325	15	.	.	PUNCT
ejpam-6596	326	1	(	(	PUNCT
ejpam-6596	326	2	12	12	NUM
ejpam-6596	326	3	)	)	PUNCT
ejpam-6596	326	4	as	as	SCONJ
ejpam-6596	326	5	one	one	PRON
ejpam-6596	326	6	can	can	AUX
ejpam-6596	326	7	see	see	VERB
ejpam-6596	326	8	,	,	PUNCT
ejpam-6596	326	9	the	the	DET
ejpam-6596	326	10	equation	equation	NOUN
ejpam-6596	326	11	(	(	PUNCT
ejpam-6596	326	12	12	12	NUM
ejpam-6596	326	13	)	)	PUNCT
ejpam-6596	326	14	for	for	ADP
ejpam-6596	326	15	u∗	u∗	ADJ
ejpam-6596	326	16	=	=	SYM
ejpam-6596	326	17	(	(	PUNCT
ejpam-6596	326	18	u∗1	u∗1	PROPN
ejpam-6596	326	19	,	,	PUNCT
ejpam-6596	326	20	u	u	NOUN
ejpam-6596	326	21	∗	∗	NOUN
ejpam-6596	326	22	2	2	NUM
ejpam-6596	326	23	,	,	PUNCT
ejpam-6596	326	24	u	u	NOUN
ejpam-6596	326	25	∗	∗	NOUN
ejpam-6596	326	26	3	3	NUM
ejpam-6596	326	27	)	)	PUNCT
ejpam-6596	326	28	is	be	AUX
ejpam-6596	326	29	made	make	VERB
ejpam-6596	326	30	reference	reference	NOUN
ejpam-6596	326	31	to	to	ADP
ejpam-6596	326	32	as	as	ADP
ejpam-6596	326	33	a	a	DET
ejpam-6596	326	34	representation	representation	NOUN
ejpam-6596	326	35	of	of	ADP
ejpam-6596	326	36	optimal	optimal	ADJ
ejpam-6596	326	37	controls	control	NOUN
ejpam-6596	326	38	.	.	PUNCT
ejpam-6596	327	1	state	state	NOUN
ejpam-6596	327	2	variables	variable	NOUN
ejpam-6596	327	3	and	and	CCONJ
ejpam-6596	327	4	optimum	optimum	ADJ
ejpam-6596	327	5	control	control	NOUN
ejpam-6596	327	6	are	be	AUX
ejpam-6596	327	7	obtained	obtain	VERB
ejpam-6596	327	8	by	by	ADP
ejpam-6596	327	9	solving	solve	VERB
ejpam-6596	327	10	the	the	DET
ejpam-6596	327	11	optimality	optimality	NOUN
ejpam-6596	327	12	system	system	NOUN
ejpam-6596	327	13	.	.	PUNCT
ejpam-6596	328	1	when	when	SCONJ
ejpam-6596	328	2	values	value	NOUN
ejpam-6596	328	3	are	be	AUX
ejpam-6596	328	4	entered	enter	VERB
ejpam-6596	328	5	for	for	ADP
ejpam-6596	328	6	u1	u1	NOUN
ejpam-6596	328	7	,	,	PUNCT
ejpam-6596	328	8	u2	u2	NOUN
ejpam-6596	328	9	and	and	CCONJ
ejpam-6596	328	10	u3	u3	NOUN
ejpam-6596	328	11	in	in	ADP
ejpam-6596	328	12	the	the	DET
ejpam-6596	328	13	system	system	NOUN
ejpam-6596	328	14	,	,	PUNCT
ejpam-6596	328	15	we	we	PRON
ejpam-6596	328	16	obtain	obtain	VERB
ejpam-6596	328	17	the	the	DET
ejpam-6596	328	18	underlying	underlie	VERB
ejpam-6596	328	19	syste,:	syste,:	NOUN
ejpam-6596	328	20	ds∗	ds∗	NOUN
ejpam-6596	328	21	dt	dt	NOUN
ejpam-6596	329	1	=	=	PUNCT
ejpam-6596	329	2	g	g	PROPN
ejpam-6596	329	3	−	−	PROPN
ejpam-6596	329	4	hs∗i∗	hs∗i∗	PROPN
ejpam-6596	329	5	1	1	NUM
ejpam-6596	329	6	+	+	NUM
ejpam-6596	329	7	αi∗	αi∗	NOUN
ejpam-6596	329	8	−	−	NOUN
ejpam-6596	329	9	(	(	PUNCT
ejpam-6596	329	10	m+	m+	NUM
ejpam-6596	329	11	b1)s	b1)s	NOUN
ejpam-6596	329	12	∗	∗	NOUN
ejpam-6596	329	13	−	−	PROPN
ejpam-6596	330	1	(	(	PUNCT
ejpam-6596	330	2	(	(	PUNCT
ejpam-6596	330	3	λ1	λ1	PROPN
ejpam-6596	330	4	−	−	PROPN
ejpam-6596	330	5	λ5)s	λ5)s	PROPN
ejpam-6596	330	6	a6	a6	NOUN
ejpam-6596	330	7	)	)	PUNCT
ejpam-6596	330	8	s∗	s∗	PROPN
ejpam-6596	330	9	,	,	PUNCT
ejpam-6596	330	10	de∗	de∗	VERB
ejpam-6596	330	11	dt	dt	PUNCT
ejpam-6596	331	1	=	=	PUNCT
ejpam-6596	332	1	(	(	PUNCT
ejpam-6596	332	2	1−	1−	NUM
ejpam-6596	332	3	(	(	PUNCT
ejpam-6596	332	4	(	(	PUNCT
ejpam-6596	332	5	λ2	λ2	NOUN
ejpam-6596	332	6	−	−	PROPN
ejpam-6596	332	7	λ1	λ1	PROPN
ejpam-6596	332	8	)	)	PUNCT
ejpam-6596	332	9	a4	a4	NOUN
ejpam-6596	332	10	hsi	hsi	NOUN
ejpam-6596	332	11	1	1	NUM
ejpam-6596	333	1	+	+	CCONJ
ejpam-6596	333	2	αi	αi	NOUN
ejpam-6596	333	3	)	)	PUNCT
ejpam-6596	333	4	)	)	PUNCT
ejpam-6596	334	1	hs∗i∗	hs∗i∗	PROPN
ejpam-6596	334	2	1	1	NUM
ejpam-6596	334	3	+	+	NUM
ejpam-6596	334	4	αi∗	αi∗	NOUN
ejpam-6596	334	5	−	−	NOUN
ejpam-6596	334	6	(	(	PUNCT
ejpam-6596	334	7	m+	m+	NUM
ejpam-6596	334	8	c+	c+	VERB
ejpam-6596	334	9	b2)e	b2)e	ADJ
ejpam-6596	334	10	∗	∗	NOUN
ejpam-6596	334	11	,	,	PUNCT
ejpam-6596	334	12	di∗	di∗	NOUN
ejpam-6596	334	13	dt	dt	NOUN
ejpam-6596	334	14	=	=	PUNCT
ejpam-6596	334	15	ce∗	ce∗	NOUN
ejpam-6596	334	16	−	−	PROPN
ejpam-6596	335	1	(	(	PUNCT
ejpam-6596	335	2	m+	m+	NUM
ejpam-6596	335	3	b3	b3	NOUN
ejpam-6596	335	4	+	+	CCONJ
ejpam-6596	335	5	(	(	PUNCT
ejpam-6596	335	6	1	1	NUM
ejpam-6596	335	7	+	+	CCONJ
ejpam-6596	335	8	(	(	PUNCT
ejpam-6596	335	9	(	(	PUNCT
ejpam-6596	335	10	λ3	λ3	PROPN
ejpam-6596	335	11	−	−	PROPN
ejpam-6596	335	12	λ5)qi	λ5)qi	PROPN
ejpam-6596	335	13	a5	a5	PROPN
ejpam-6596	335	14	)	)	PUNCT
ejpam-6596	335	15	)	)	PUNCT
ejpam-6596	335	16	q	q	PROPN
ejpam-6596	336	1	+	+	NUM
ejpam-6596	336	2	µ	µ	X
ejpam-6596	336	3	)	)	PUNCT
ejpam-6596	336	4	i∗	i∗	NOUN
ejpam-6596	336	5	,	,	PUNCT
ejpam-6596	336	6	dq∗	dq∗	NOUN
ejpam-6596	336	7	dt	dt	NOUN
ejpam-6596	336	8	=	=	SYM
ejpam-6596	336	9	b1s	b1s	PROPN
ejpam-6596	336	10	∗	∗	NOUN
ejpam-6596	336	11	+	+	NUM
ejpam-6596	336	12	b2e	b2e	X
ejpam-6596	336	13	∗	∗	NOUN
ejpam-6596	336	14	+	+	NUM
ejpam-6596	336	15	b3i	b3i	NUM
ejpam-6596	336	16	∗	∗	NOUN
ejpam-6596	336	17	−	−	PROPN
ejpam-6596	336	18	(	(	PUNCT
ejpam-6596	336	19	m+	m+	NUM
ejpam-6596	336	20	p)q∗	p)q∗	NOUN
ejpam-6596	336	21	,	,	PUNCT
ejpam-6596	336	22	dr∗	dr∗	ADJ
ejpam-6596	336	23	dt	dt	NOUN
ejpam-6596	336	24	=	=	PUNCT
ejpam-6596	336	25	(	(	PUNCT
ejpam-6596	336	26	1	1	NUM
ejpam-6596	336	27	+	+	CCONJ
ejpam-6596	336	28	(	(	PUNCT
ejpam-6596	336	29	(	(	PUNCT
ejpam-6596	336	30	λ3	λ3	PROPN
ejpam-6596	336	31	−	−	PROPN
ejpam-6596	336	32	λ5)qi	λ5)qi	PROPN
ejpam-6596	336	33	a5	a5	PROPN
ejpam-6596	336	34	)	)	PUNCT
ejpam-6596	336	35	)	)	PUNCT
ejpam-6596	336	36	qi∗	qi∗	PROPN
ejpam-6596	337	1	+	+	NUM
ejpam-6596	337	2	pq∗	pq∗	NOUN
ejpam-6596	338	1	−mr∗	−mr∗	NOUN
ejpam-6596	338	2	+	+	CCONJ
ejpam-6596	338	3	(	(	PUNCT
ejpam-6596	338	4	(	(	PUNCT
ejpam-6596	338	5	λ1	λ1	ADJ
ejpam-6596	338	6	−	−	PROPN
ejpam-6596	338	7	λ5)s	λ5)s	PROPN
ejpam-6596	338	8	a6	a6	NOUN
ejpam-6596	338	9	)	)	PUNCT
ejpam-6596	338	10	s∗.	s∗.	ADJ
ejpam-6596	338	11	(	(	PUNCT
ejpam-6596	338	12	13	13	NUM
ejpam-6596	338	13	)	)	PUNCT
ejpam-6596	338	14	the	the	DET
ejpam-6596	338	15	next	next	ADJ
ejpam-6596	338	16	section	section	NOUN
ejpam-6596	338	17	includes	include	VERB
ejpam-6596	338	18	several	several	ADJ
ejpam-6596	338	19	numerical	numerical	ADJ
ejpam-6596	338	20	simulations	simulation	NOUN
ejpam-6596	338	21	.	.	PUNCT
ejpam-6596	339	1	to	to	PART
ejpam-6596	339	2	verify	verify	VERB
ejpam-6596	339	3	the	the	DET
ejpam-6596	339	4	analytical	analytical	ADJ
ejpam-6596	339	5	findings	finding	NOUN
ejpam-6596	339	6	from	from	ADP
ejpam-6596	339	7	the	the	DET
ejpam-6596	339	8	previous	previous	ADJ
ejpam-6596	339	9	section	section	NOUN
ejpam-6596	339	10	.	.	PUNCT
ejpam-6596	340	1	the	the	DET
ejpam-6596	340	2	numerical	numerical	ADJ
ejpam-6596	340	3	simulations	simulation	NOUN
ejpam-6596	340	4	are	be	AUX
ejpam-6596	340	5	also	also	ADV
ejpam-6596	340	6	briefly	briefly	ADV
ejpam-6596	340	7	discussed	discuss	VERB
ejpam-6596	340	8	.	.	PUNCT
ejpam-6596	341	1	9	9	X
ejpam-6596	341	2	.	.	X
ejpam-6596	341	3	numerical	numerical	ADJ
ejpam-6596	341	4	results	result	NOUN
ejpam-6596	341	5	9.1	9.1	NUM
ejpam-6596	341	6	.	.	PUNCT
ejpam-6596	342	1	numerical	numerical	ADJ
ejpam-6596	342	2	simulations	simulation	NOUN
ejpam-6596	342	3	for	for	ADP
ejpam-6596	342	4	the	the	DET
ejpam-6596	342	5	problem	problem	NOUN
ejpam-6596	342	6	(	(	PUNCT
ejpam-6596	342	7	without	without	ADP
ejpam-6596	342	8	control	control	NOUN
ejpam-6596	342	9	variables	variable	NOUN
ejpam-6596	342	10	)	)	PUNCT
ejpam-6596	342	11	the	the	DET
ejpam-6596	342	12	numerical	numerical	ADJ
ejpam-6596	342	13	simulations	simulation	NOUN
ejpam-6596	342	14	used	use	VERB
ejpam-6596	342	15	to	to	PART
ejpam-6596	342	16	validate	validate	VERB
ejpam-6596	342	17	the	the	DET
ejpam-6596	342	18	results	result	NOUN
ejpam-6596	342	19	of	of	ADP
ejpam-6596	342	20	analysis	analysis	NOUN
ejpam-6596	342	21	examined	examine	VERB
ejpam-6596	342	22	in	in	ADP
ejpam-6596	342	23	the	the	DET
ejpam-6596	342	24	earlier	early	ADJ
ejpam-6596	342	25	chapters	chapter	NOUN
ejpam-6596	342	26	are	be	AUX
ejpam-6596	342	27	the	the	DET
ejpam-6596	342	28	focus	focus	NOUN
ejpam-6596	342	29	of	of	ADP
ejpam-6596	342	30	this	this	DET
ejpam-6596	342	31	portion	portion	NOUN
ejpam-6596	342	32	of	of	ADP
ejpam-6596	342	33	the	the	DET
ejpam-6596	342	34	thesis	thesis	NOUN
ejpam-6596	342	35	.	.	PUNCT
ejpam-6596	343	1	we	we	PRON
ejpam-6596	343	2	employ	employ	VERB
ejpam-6596	343	3	the	the	DET
ejpam-6596	343	4	widely	widely	ADV
ejpam-6596	343	5	established	establish	VERB
ejpam-6596	343	6	runge	runge	NOUN
ejpam-6596	343	7	-	-	PUNCT
ejpam-6596	343	8	kutta	kutta	NOUN
ejpam-6596	343	9	method	method	NOUN
ejpam-6596	343	10	of	of	ADP
ejpam-6596	343	11	fourth	fourth	ADJ
ejpam-6596	343	12	order	order	NOUN
ejpam-6596	343	13	(	(	PUNCT
ejpam-6596	343	14	rk4	rk4	NOUN
ejpam-6596	343	15	)	)	PUNCT
ejpam-6596	343	16	.	.	PUNCT
ejpam-6596	344	1	in	in	ADP
ejpam-6596	344	2	the	the	DET
ejpam-6596	344	3	beginning	beginning	NOUN
ejpam-6596	344	4	,	,	PUNCT
ejpam-6596	344	5	we	we	PRON
ejpam-6596	344	6	run	run	VERB
ejpam-6596	344	7	numerical	numerical	ADJ
ejpam-6596	344	8	simulations	simulation	NOUN
ejpam-6596	344	9	for	for	ADP
ejpam-6596	344	10	a	a	DET
ejpam-6596	344	11	case	case	NOUN
ejpam-6596	344	12	in	in	ADP
ejpam-6596	344	13	which	which	PRON
ejpam-6596	344	14	an	an	DET
ejpam-6596	344	15	area	area	NOUN
ejpam-6596	344	16	is	be	AUX
ejpam-6596	344	17	free	free	ADJ
ejpam-6596	344	18	of	of	ADP
ejpam-6596	344	19	disease	disease	NOUN
ejpam-6596	344	20	,	,	PUNCT
ejpam-6596	344	21	i.e	i.e	CCONJ
ejpam-6596	344	22	the	the	DET
ejpam-6596	344	23	so	so	ADV
ejpam-6596	344	24	-	-	PUNCT
ejpam-6596	344	25	called	call	VERB
ejpam-6596	344	26	condition	condition	NOUN
ejpam-6596	344	27	devoid	devoid	ADJ
ejpam-6596	344	28	of	of	ADP
ejpam-6596	344	29	infections	infection	NOUN
ejpam-6596	344	30	.	.	PUNCT
ejpam-6596	345	1	the	the	DET
ejpam-6596	345	2	threshold	threshold	NOUN
ejpam-6596	345	3	quantity	quantity	NOUN
ejpam-6596	345	4	’s	’s	PART
ejpam-6596	345	5	value	value	NOUN
ejpam-6596	345	6	is	be	AUX
ejpam-6596	345	7	assumed	assume	VERB
ejpam-6596	345	8	to	to	PART
ejpam-6596	345	9	be	be	AUX
ejpam-6596	345	10	smaller	small	ADJ
ejpam-6596	345	11	than	than	ADP
ejpam-6596	345	12	unity	unity	NOUN
ejpam-6596	345	13	by	by	ADP
ejpam-6596	345	14	selecting	select	VERB
ejpam-6596	345	15	parameter	parameter	NOUN
ejpam-6596	345	16	values	value	NOUN
ejpam-6596	345	17	in	in	ADP
ejpam-6596	345	18	the	the	DET
ejpam-6596	345	19	model	model	NOUN
ejpam-6596	345	20	under	under	ADP
ejpam-6596	345	21	consideration	consideration	NOUN
ejpam-6596	345	22	.	.	PUNCT
ejpam-6596	346	1	n.	n.	PROPN
ejpam-6596	346	2	gul	gul	PROPN
ejpam-6596	346	3	et	et	PROPN
ejpam-6596	346	4	al	al	PROPN
ejpam-6596	346	5	.	.	PUNCT
ejpam-6596	346	6	/	/	SYM
ejpam-6596	346	7	eur	eur	PROPN
ejpam-6596	346	8	.	.	PUNCT
ejpam-6596	347	1	j.	j.	PROPN
ejpam-6596	347	2	pure	pure	PROPN
ejpam-6596	347	3	appl	appl	PROPN
ejpam-6596	347	4	.	.	PROPN
ejpam-6596	347	5	math	math	PROPN
ejpam-6596	347	6	,	,	PUNCT
ejpam-6596	347	7	18	18	NUM
ejpam-6596	347	8	(	(	PUNCT
ejpam-6596	347	9	4	4	NUM
ejpam-6596	347	10	)	)	PUNCT
ejpam-6596	347	11	(	(	PUNCT
ejpam-6596	347	12	2025	2025	NUM
ejpam-6596	347	13	)	)	PUNCT
ejpam-6596	347	14	,	,	PUNCT
ejpam-6596	347	15	6596	6596	NUM
ejpam-6596	347	16	16	16	NUM
ejpam-6596	347	17	of	of	ADP
ejpam-6596	347	18	23	23	NUM
ejpam-6596	347	19	0	0	NUM
ejpam-6596	347	20	20	20	NUM
ejpam-6596	347	21	40	40	NUM
ejpam-6596	347	22	60	60	NUM
ejpam-6596	347	23	80	80	NUM
ejpam-6596	347	24	100	100	NUM
ejpam-6596	347	25	time	time	NOUN
ejpam-6596	347	26	20	20	NUM
ejpam-6596	347	27	40	40	NUM
ejpam-6596	347	28	60	60	NUM
ejpam-6596	347	29	80	80	NUM
ejpam-6596	347	30	100	100	NUM
ejpam-6596	347	31	120	120	NUM
ejpam-6596	347	32	140	140	NUM
ejpam-6596	347	33	160	160	NUM
ejpam-6596	347	34	180	180	NUM
ejpam-6596	347	35	s	s	NOUN
ejpam-6596	347	36	u	u	X
ejpam-6596	347	37	sc	sc	PROPN
ejpam-6596	347	38	ep	ep	PROPN
ejpam-6596	347	39	ti	ti	PROPN
ejpam-6596	347	40	b	b	X
ejpam-6596	347	41	le	le	X
ejpam-6596	347	42	c	c	X
ejpam-6596	347	43	la	la	INTJ
ejpam-6596	347	44	ss	ss	PROPN
ejpam-6596	347	45	s(0)=180	s(0)=180	X
ejpam-6596	347	46	s(0)=160	s(0)=160	X
ejpam-6596	347	47	s(0)=140	s(0)=140	X
ejpam-6596	347	48	s(0)=120	s(0)=120	ADV
ejpam-6596	347	49	0	0	NUM
ejpam-6596	347	50	20	20	NUM
ejpam-6596	347	51	40	40	NUM
ejpam-6596	347	52	60	60	NUM
ejpam-6596	347	53	80	80	NUM
ejpam-6596	347	54	100	100	NUM
ejpam-6596	347	55	time	time	NOUN
ejpam-6596	347	56	0	0	NUM
ejpam-6596	347	57	20	20	NUM
ejpam-6596	347	58	40	40	NUM
ejpam-6596	347	59	60	60	NUM
ejpam-6596	347	60	80	80	NUM
ejpam-6596	347	61	100	100	NUM
ejpam-6596	347	62	120	120	NUM
ejpam-6596	347	63	140	140	NUM
ejpam-6596	347	64	160	160	NUM
ejpam-6596	347	65	180	180	NUM
ejpam-6596	347	66	e	e	NOUN
ejpam-6596	347	67	xp	xp	NOUN
ejpam-6596	347	68	o	o	PROPN
ejpam-6596	347	69	se	se	PROPN
ejpam-6596	348	1	d	d	X
ejpam-6596	348	2	c	c	VERB
ejpam-6596	348	3	la	la	INTJ
ejpam-6596	348	4	ss	ss	ADP
ejpam-6596	348	5	e(0)=180	e(0)=180	PROPN
ejpam-6596	348	6	e(0)=160	e(0)=160	X
ejpam-6596	348	7	e(0)=140	e(0)=140	X
ejpam-6596	348	8	e(0)=120	e(0)=120	X
ejpam-6596	348	9	0	0	NUM
ejpam-6596	348	10	50	50	NUM
ejpam-6596	348	11	100	100	NUM
ejpam-6596	348	12	150	150	NUM
ejpam-6596	348	13	time	time	NOUN
ejpam-6596	348	14	0	0	NUM
ejpam-6596	348	15	50	50	NUM
ejpam-6596	348	16	100	100	NUM
ejpam-6596	348	17	150	150	NUM
ejpam-6596	348	18	200	200	NUM
ejpam-6596	348	19	250	250	NUM
ejpam-6596	348	20	300	300	NUM
ejpam-6596	348	21	in	in	ADP
ejpam-6596	348	22	fe	fe	X
ejpam-6596	348	23	ct	ct	NUM
ejpam-6596	348	24	ed	ed	PROPN
ejpam-6596	348	25	c	c	PROPN
ejpam-6596	348	26	la	la	PRON
ejpam-6596	348	27	ss	ss	X
ejpam-6596	348	28	i(0)=180	i(0)=180	X
ejpam-6596	348	29	i(0)=160	i(0)=160	X
ejpam-6596	348	30	i(0)=140	i(0)=140	X
ejpam-6596	348	31	i(0)=120	i(0)=120	PROPN
ejpam-6596	348	32	0	0	NUM
ejpam-6596	348	33	50	50	NUM
ejpam-6596	348	34	100	100	NUM
ejpam-6596	348	35	150	150	NUM
ejpam-6596	348	36	time	time	NOUN
ejpam-6596	348	37	0	0	NUM
ejpam-6596	348	38	50	50	NUM
ejpam-6596	348	39	100	100	NUM
ejpam-6596	348	40	150	150	NUM
ejpam-6596	348	41	200	200	NUM
ejpam-6596	348	42	250	250	NUM
ejpam-6596	348	43	300	300	NUM
ejpam-6596	348	44	q	q	NOUN
ejpam-6596	348	45	u	u	PROPN
ejpam-6596	348	46	a	a	DET
ejpam-6596	348	47	ra	ra	NOUN
ejpam-6596	348	48	n	n	CCONJ
ejpam-6596	348	49	ti	ti	NOUN
ejpam-6596	348	50	n	n	NOUN
ejpam-6596	348	51	e	e	NOUN
ejpam-6596	348	52	c	c	X
ejpam-6596	348	53	la	la	PROPN
ejpam-6596	348	54	ss	ss	PROPN
ejpam-6596	348	55	q(0)=180	q(0)=180	X
ejpam-6596	348	56	q(0)=160	q(0)=160	CCONJ
ejpam-6596	348	57	q(0)=140	q(0)=140	X
ejpam-6596	348	58	q(0)=120	q(0)=120	X
ejpam-6596	348	59	0	0	NUM
ejpam-6596	348	60	20	20	NUM
ejpam-6596	348	61	40	40	NUM
ejpam-6596	348	62	60	60	NUM
ejpam-6596	348	63	80	80	NUM
ejpam-6596	348	64	100	100	NUM
ejpam-6596	348	65	time	time	NOUN
ejpam-6596	348	66	100	100	NUM
ejpam-6596	348	67	150	150	NUM
ejpam-6596	348	68	200	200	NUM
ejpam-6596	348	69	250	250	NUM
ejpam-6596	348	70	300	300	NUM
ejpam-6596	348	71	350	350	NUM
ejpam-6596	348	72	400	400	NUM
ejpam-6596	348	73	450	450	NUM
ejpam-6596	348	74	500	500	NUM
ejpam-6596	348	75	r	r	NOUN
ejpam-6596	348	76	e	e	NOUN
ejpam-6596	348	77	c	c	NOUN
ejpam-6596	348	78	o	o	X
ejpam-6596	348	79	v	v	NOUN
ejpam-6596	348	80	e	e	NOUN
ejpam-6596	348	81	r	r	NOUN
ejpam-6596	348	82	e	e	NOUN
ejpam-6596	348	83	d	d	X
ejpam-6596	348	84	c	c	X
ejpam-6596	348	85	la	la	PROPN
ejpam-6596	348	86	s	s	PROPN
ejpam-6596	348	87	s	s	PART
ejpam-6596	348	88	r(0)=180	r(0)=180	NOUN
ejpam-6596	348	89	r(0)=160	r(0)=160	X
ejpam-6596	348	90	r(0)=140	r(0)=140	ADJ
ejpam-6596	348	91	r(0)=120	r(0)=120	NOUN
ejpam-6596	348	92	figure	figure	NOUN
ejpam-6596	348	93	2	2	NUM
ejpam-6596	348	94	:	:	PUNCT
ejpam-6596	348	95	dynamical	dynamical	ADJ
ejpam-6596	348	96	behaviour	behaviour	NOUN
ejpam-6596	348	97	of	of	ADP
ejpam-6596	348	98	the	the	DET
ejpam-6596	348	99	trajectories	trajectory	NOUN
ejpam-6596	348	100	of	of	ADP
ejpam-6596	348	101	the	the	DET
ejpam-6596	348	102	total	total	ADJ
ejpam-6596	348	103	classes	class	NOUN
ejpam-6596	348	104	of	of	ADP
ejpam-6596	348	105	the	the	DET
ejpam-6596	348	106	model	model	NOUN
ejpam-6596	348	107	for	for	ADP
ejpam-6596	348	108	the	the	DET
ejpam-6596	348	109	no	no	DET
ejpam-6596	348	110	-	-	PUNCT
ejpam-6596	348	111	infection	infection	NOUN
ejpam-6596	348	112	state	state	NOUN
ejpam-6596	348	113	.	.	PUNCT
ejpam-6596	349	1	in	in	ADP
ejpam-6596	349	2	fig	fig	NOUN
ejpam-6596	349	3	.	.	PUNCT
ejpam-6596	350	1	(	(	PUNCT
ejpam-6596	350	2	2	2	X
ejpam-6596	350	3	)	)	PUNCT
ejpam-6596	350	4	(	(	PUNCT
ejpam-6596	350	5	susceptible	susceptible	ADJ
ejpam-6596	350	6	population	population	NOUN
ejpam-6596	350	7	graph	graph	NOUN
ejpam-6596	350	8	)	)	PUNCT
ejpam-6596	350	9	we	we	PRON
ejpam-6596	350	10	plot	plot	VERB
ejpam-6596	350	11	the	the	DET
ejpam-6596	350	12	trajectories	trajectory	NOUN
ejpam-6596	350	13	of	of	ADP
ejpam-6596	350	14	the	the	DET
ejpam-6596	350	15	susceptible	susceptible	ADJ
ejpam-6596	350	16	compartment	compartment	NOUN
ejpam-6596	350	17	of	of	ADP
ejpam-6596	350	18	the	the	DET
ejpam-6596	350	19	model	model	NOUN
ejpam-6596	350	20	under	under	ADP
ejpam-6596	350	21	consideration	consideration	NOUN
ejpam-6596	350	22	for	for	ADP
ejpam-6596	350	23	the	the	DET
ejpam-6596	350	24	infection	infection	NOUN
ejpam-6596	350	25	-	-	PUNCT
ejpam-6596	350	26	free	free	ADJ
ejpam-6596	350	27	condition	condition	NOUN
ejpam-6596	350	28	versus	versus	ADP
ejpam-6596	350	29	time	time	NOUN
ejpam-6596	350	30	t	t	PROPN
ejpam-6596	350	31	,	,	PUNCT
ejpam-6596	350	32	for	for	ADP
ejpam-6596	350	33	varied	varied	ADJ
ejpam-6596	350	34	initial	initial	ADJ
ejpam-6596	350	35	sizes	size	NOUN
ejpam-6596	350	36	of	of	ADP
ejpam-6596	350	37	the	the	DET
ejpam-6596	350	38	compartment	compartment	NOUN
ejpam-6596	350	39	.	.	PUNCT
ejpam-6596	351	1	from	from	ADP
ejpam-6596	351	2	this	this	DET
ejpam-6596	351	3	figure	figure	NOUN
ejpam-6596	351	4	,	,	PUNCT
ejpam-6596	351	5	we	we	PRON
ejpam-6596	351	6	observe	observe	VERB
ejpam-6596	351	7	that	that	SCONJ
ejpam-6596	351	8	the	the	DET
ejpam-6596	351	9	susceptible	susceptible	ADJ
ejpam-6596	351	10	population	population	NOUN
ejpam-6596	351	11	decreases	decrease	VERB
ejpam-6596	351	12	and	and	CCONJ
ejpam-6596	351	13	gradually	gradually	ADV
ejpam-6596	351	14	tend	tend	VERB
ejpam-6596	351	15	to	to	ADP
ejpam-6596	351	16	the	the	DET
ejpam-6596	351	17	no	no	DET
ejpam-6596	351	18	-	-	PUNCT
ejpam-6596	351	19	disease	disease	NOUN
ejpam-6596	351	20	state	state	NOUN
ejpam-6596	351	21	s0	s0	PROPN
ejpam-6596	351	22	.	.	PUNCT
ejpam-6596	352	1	we	we	PRON
ejpam-6596	352	2	also	also	ADV
ejpam-6596	352	3	observe	observe	VERB
ejpam-6596	352	4	that	that	SCONJ
ejpam-6596	352	5	this	this	DET
ejpam-6596	352	6	equilibrium	equilibrium	NOUN
ejpam-6596	352	7	is	be	AUX
ejpam-6596	352	8	nonzero	nonzero	NOUN
ejpam-6596	352	9	.	.	PUNCT
ejpam-6596	353	1	it	it	PRON
ejpam-6596	353	2	means	mean	VERB
ejpam-6596	353	3	that	that	SCONJ
ejpam-6596	353	4	there	there	PRON
ejpam-6596	353	5	will	will	AUX
ejpam-6596	353	6	always	always	ADV
ejpam-6596	353	7	be	be	AUX
ejpam-6596	353	8	chance	chance	NOUN
ejpam-6596	353	9	to	to	ADP
ejpam-6596	353	10	people	people	NOUN
ejpam-6596	353	11	to	to	PART
ejpam-6596	353	12	catch	catch	VERB
ejpam-6596	353	13	the	the	DET
ejpam-6596	353	14	disease	disease	NOUN
ejpam-6596	353	15	,	,	PUNCT
ejpam-6596	353	16	which	which	PRON
ejpam-6596	353	17	is	be	AUX
ejpam-6596	353	18	biologically	biologically	ADV
ejpam-6596	353	19	relevant	relevant	ADJ
ejpam-6596	353	20	.	.	PUNCT
ejpam-6596	354	1	(	(	PUNCT
ejpam-6596	354	2	exposed	expose	VERB
ejpam-6596	354	3	population	population	NOUN
ejpam-6596	354	4	graph	graph	NOUN
ejpam-6596	354	5	)	)	PUNCT
ejpam-6596	354	6	demonstrates	demonstrate	VERB
ejpam-6596	354	7	how	how	SCONJ
ejpam-6596	354	8	the	the	DET
ejpam-6596	354	9	exposed	exposed	ADJ
ejpam-6596	354	10	class	class	NOUN
ejpam-6596	354	11	of	of	ADP
ejpam-6596	354	12	infection	infection	NOUN
ejpam-6596	354	13	behave	behave	VERB
ejpam-6596	354	14	dynamically	dynamically	ADV
ejpam-6596	354	15	.	.	PUNCT
ejpam-6596	355	1	the	the	DET
ejpam-6596	355	2	class	class	NOUN
ejpam-6596	355	3	is	be	AUX
ejpam-6596	355	4	rapidly	rapidly	ADV
ejpam-6596	355	5	decreasing	decrease	VERB
ejpam-6596	355	6	at	at	ADP
ejpam-6596	355	7	the	the	DET
ejpam-6596	355	8	no	no	DET
ejpam-6596	355	9	illness	illness	NOUN
ejpam-6596	355	10	state	state	NOUN
ejpam-6596	355	11	.	.	PUNCT
ejpam-6596	356	1	as	as	ADP
ejpam-6596	356	2	time	time	NOUN
ejpam-6596	356	3	increases	increase	NOUN
ejpam-6596	356	4	,	,	PUNCT
ejpam-6596	356	5	the	the	DET
ejpam-6596	356	6	class	class	NOUN
ejpam-6596	356	7	becomes	become	VERB
ejpam-6596	356	8	closer	close	ADJ
ejpam-6596	356	9	to	to	ADP
ejpam-6596	356	10	the	the	DET
ejpam-6596	356	11	zero	zero	NUM
ejpam-6596	356	12	state	state	NOUN
ejpam-6596	356	13	,	,	PUNCT
ejpam-6596	356	14	or	or	CCONJ
ejpam-6596	356	15	the	the	DET
ejpam-6596	356	16	equilibrium	equilibrium	NOUN
ejpam-6596	356	17	free	free	ADJ
ejpam-6596	356	18	of	of	ADP
ejpam-6596	356	19	sickness	sickness	NOUN
ejpam-6596	356	20	.	.	PUNCT
ejpam-6596	357	1	in	in	ADP
ejpam-6596	357	2	fig	fig	NOUN
ejpam-6596	357	3	.	.	PUNCT
ejpam-6596	358	1	(	(	PUNCT
ejpam-6596	358	2	infected	infect	VERB
ejpam-6596	358	3	population	population	NOUN
ejpam-6596	358	4	graph	graph	NOUN
ejpam-6596	358	5	)	)	PUNCT
ejpam-6596	358	6	we	we	PRON
ejpam-6596	358	7	depict	depict	VERB
ejpam-6596	358	8	the	the	DET
ejpam-6596	358	9	infected	infected	ADJ
ejpam-6596	358	10	class	class	NOUN
ejpam-6596	358	11	.	.	PUNCT
ejpam-6596	359	1	at	at	ADP
ejpam-6596	359	2	the	the	DET
ejpam-6596	359	3	disease	disease	NOUN
ejpam-6596	359	4	-	-	PUNCT
ejpam-6596	359	5	free	free	ADJ
ejpam-6596	359	6	condition	condition	NOUN
ejpam-6596	359	7	,	,	PUNCT
ejpam-6596	359	8	there	there	PRON
ejpam-6596	359	9	is	be	VERB
ejpam-6596	359	10	a	a	DET
ejpam-6596	359	11	quickly	quickly	ADV
ejpam-6596	359	12	increase	increase	NOUN
ejpam-6596	359	13	for	for	ADP
ejpam-6596	359	14	first	first	ADJ
ejpam-6596	359	15	few	few	ADJ
ejpam-6596	359	16	weeks	week	NOUN
ejpam-6596	359	17	in	in	ADP
ejpam-6596	359	18	the	the	DET
ejpam-6596	359	19	class	class	NOUN
ejpam-6596	359	20	.	.	PUNCT
ejpam-6596	360	1	as	as	ADP
ejpam-6596	360	2	time	time	NOUN
ejpam-6596	360	3	increases	increase	NOUN
ejpam-6596	360	4	,	,	PUNCT
ejpam-6596	360	5	the	the	DET
ejpam-6596	360	6	class	class	NOUN
ejpam-6596	360	7	becomes	become	VERB
ejpam-6596	360	8	closer	close	ADJ
ejpam-6596	360	9	to	to	ADP
ejpam-6596	360	10	the	the	DET
ejpam-6596	360	11	zero	zero	NUM
ejpam-6596	360	12	condition	condition	NOUN
ejpam-6596	360	13	,	,	PUNCT
ejpam-6596	360	14	n.	n.	PROPN
ejpam-6596	360	15	gul	gul	PROPN
ejpam-6596	360	16	et	et	PROPN
ejpam-6596	360	17	al	al	PROPN
ejpam-6596	360	18	.	.	PUNCT
ejpam-6596	360	19	/	/	SYM
ejpam-6596	360	20	eur	eur	PROPN
ejpam-6596	360	21	.	.	PUNCT
ejpam-6596	361	1	j.	j.	PROPN
ejpam-6596	361	2	pure	pure	PROPN
ejpam-6596	361	3	appl	appl	PROPN
ejpam-6596	361	4	.	.	PROPN
ejpam-6596	361	5	math	math	PROPN
ejpam-6596	361	6	,	,	PUNCT
ejpam-6596	361	7	18	18	NUM
ejpam-6596	361	8	(	(	PUNCT
ejpam-6596	361	9	4	4	NUM
ejpam-6596	361	10	)	)	PUNCT
ejpam-6596	361	11	(	(	PUNCT
ejpam-6596	361	12	2025	2025	NUM
ejpam-6596	361	13	)	)	PUNCT
ejpam-6596	361	14	,	,	PUNCT
ejpam-6596	361	15	6596	6596	NUM
ejpam-6596	361	16	17	17	NUM
ejpam-6596	361	17	of	of	ADP
ejpam-6596	361	18	23	23	NUM
ejpam-6596	361	19	or	or	CCONJ
ejpam-6596	361	20	the	the	DET
ejpam-6596	361	21	equilibrium	equilibrium	NOUN
ejpam-6596	361	22	free	free	ADJ
ejpam-6596	361	23	from	from	ADP
ejpam-6596	361	24	sickness	sickness	NOUN
ejpam-6596	361	25	.	.	PUNCT
ejpam-6596	362	1	in	in	ADP
ejpam-6596	362	2	other	other	ADJ
ejpam-6596	362	3	words	word	NOUN
ejpam-6596	362	4	,	,	PUNCT
ejpam-6596	362	5	the	the	DET
ejpam-6596	362	6	infection	infection	NOUN
ejpam-6596	362	7	population	population	NOUN
ejpam-6596	362	8	reaches	reach	VERB
ejpam-6596	362	9	its	its	PRON
ejpam-6596	362	10	convergence	convergence	NOUN
ejpam-6596	362	11	at	at	ADP
ejpam-6596	362	12	the	the	DET
ejpam-6596	362	13	zero	zero	NUM
ejpam-6596	362	14	condition	condition	NOUN
ejpam-6596	362	15	as	as	SCONJ
ejpam-6596	362	16	time	time	NOUN
ejpam-6596	362	17	goes	go	VERB
ejpam-6596	362	18	on	on	ADP
ejpam-6596	362	19	.	.	PUNCT
ejpam-6596	363	1	this	this	PRON
ejpam-6596	363	2	agrees	agree	VERB
ejpam-6596	363	3	with	with	ADP
ejpam-6596	363	4	the	the	DET
ejpam-6596	363	5	value	value	NOUN
ejpam-6596	363	6	of	of	ADP
ejpam-6596	363	7	i0	i0	PROPN
ejpam-6596	363	8	already	already	ADV
ejpam-6596	363	9	determined	determine	VERB
ejpam-6596	363	10	for	for	ADP
ejpam-6596	363	11	the	the	DET
ejpam-6596	363	12	no	no	DET
ejpam-6596	363	13	-	-	PUNCT
ejpam-6596	363	14	infection	infection	NOUN
ejpam-6596	363	15	state	state	NOUN
ejpam-6596	363	16	.	.	PUNCT
ejpam-6596	364	1	in	in	ADP
ejpam-6596	364	2	fig	fig	NOUN
ejpam-6596	364	3	.	.	PUNCT
ejpam-6596	365	1	(	(	PUNCT
ejpam-6596	365	2	quarantine	quarantine	NOUN
ejpam-6596	365	3	population	population	NOUN
ejpam-6596	365	4	graph	graph	NOUN
ejpam-6596	365	5	)	)	PUNCT
ejpam-6596	365	6	the	the	DET
ejpam-6596	365	7	quarantine	quarantine	NOUN
ejpam-6596	365	8	class	class	NOUN
ejpam-6596	365	9	’s	’s	PART
ejpam-6596	365	10	solution	solution	NOUN
ejpam-6596	365	11	curve	curve	NOUN
ejpam-6596	365	12	is	be	AUX
ejpam-6596	365	13	displayed	display	VERB
ejpam-6596	365	14	.	.	PUNCT
ejpam-6596	366	1	the	the	DET
ejpam-6596	366	2	class	class	NOUN
ejpam-6596	366	3	is	be	AUX
ejpam-6596	366	4	growing	grow	VERB
ejpam-6596	366	5	over	over	ADP
ejpam-6596	366	6	time	time	NOUN
ejpam-6596	366	7	and	and	CCONJ
ejpam-6596	366	8	eventually	eventually	ADV
ejpam-6596	366	9	converges	converge	VERB
ejpam-6596	366	10	to	to	ADP
ejpam-6596	366	11	an	an	DET
ejpam-6596	366	12	infection	infection	NOUN
ejpam-6596	366	13	-	-	PUNCT
ejpam-6596	366	14	free	free	ADJ
ejpam-6596	366	15	state	state	NOUN
ejpam-6596	366	16	,	,	PUNCT
ejpam-6596	366	17	demonstrating	demonstrate	VERB
ejpam-6596	366	18	that	that	SCONJ
ejpam-6596	366	19	this	this	DET
ejpam-6596	366	20	class	class	NOUN
ejpam-6596	366	21	’s	’s	PART
ejpam-6596	366	22	equilibrium	equilibrium	NOUN
ejpam-6596	366	23	is	be	AUX
ejpam-6596	366	24	non	non	ADJ
ejpam-6596	366	25	-	-	ADJ
ejpam-6596	366	26	zero	zero	NUM
ejpam-6596	366	27	.	.	PUNCT
ejpam-6596	367	1	in	in	ADP
ejpam-6596	367	2	fig	fig	NOUN
ejpam-6596	367	3	.	.	PUNCT
ejpam-6596	368	1	(	(	PUNCT
ejpam-6596	368	2	recovered	recover	VERB
ejpam-6596	368	3	population	population	NOUN
ejpam-6596	368	4	graph	graph	NOUN
ejpam-6596	368	5	)	)	PUNCT
ejpam-6596	368	6	different	different	ADJ
ejpam-6596	368	7	beginning	beginning	NOUN
ejpam-6596	368	8	conditions	condition	NOUN
ejpam-6596	368	9	are	be	AUX
ejpam-6596	368	10	used	use	VERB
ejpam-6596	368	11	to	to	PART
ejpam-6596	368	12	run	run	VERB
ejpam-6596	368	13	the	the	DET
ejpam-6596	368	14	simulations	simulation	NOUN
ejpam-6596	368	15	.	.	PUNCT
ejpam-6596	369	1	as	as	SCONJ
ejpam-6596	369	2	time	time	NOUN
ejpam-6596	369	3	goes	go	VERB
ejpam-6596	369	4	on	on	ADP
ejpam-6596	369	5	,	,	PUNCT
ejpam-6596	369	6	we	we	PRON
ejpam-6596	369	7	see	see	VERB
ejpam-6596	369	8	a	a	DET
ejpam-6596	369	9	sharp	sharp	ADJ
ejpam-6596	369	10	rise	rise	NOUN
ejpam-6596	369	11	in	in	ADP
ejpam-6596	369	12	the	the	DET
ejpam-6596	369	13	recovered	recovered	ADJ
ejpam-6596	369	14	population	population	NOUN
ejpam-6596	369	15	and	and	CCONJ
ejpam-6596	369	16	a	a	DET
ejpam-6596	369	17	tendency	tendency	NOUN
ejpam-6596	369	18	of	of	ADP
ejpam-6596	369	19	the	the	DET
ejpam-6596	369	20	class	class	NOUN
ejpam-6596	369	21	towards	towards	ADP
ejpam-6596	369	22	zero	zero	NUM
ejpam-6596	369	23	,	,	PUNCT
ejpam-6596	369	24	the	the	DET
ejpam-6596	369	25	no	no	DET
ejpam-6596	369	26	-	-	PUNCT
ejpam-6596	369	27	infection	infection	NOUN
ejpam-6596	369	28	equilibrium	equilibrium	NOUN
ejpam-6596	369	29	condition	condition	NOUN
ejpam-6596	369	30	.	.	PUNCT
ejpam-6596	370	1	now	now	ADV
ejpam-6596	370	2	,	,	PUNCT
ejpam-6596	370	3	we	we	PRON
ejpam-6596	370	4	consider	consider	VERB
ejpam-6596	370	5	the	the	DET
ejpam-6596	370	6	case	case	NOUN
ejpam-6596	370	7	of	of	ADP
ejpam-6596	370	8	persistence	persistence	NOUN
ejpam-6596	370	9	of	of	ADP
ejpam-6596	370	10	the	the	DET
ejpam-6596	370	11	disease	disease	NOUN
ejpam-6596	370	12	in	in	ADP
ejpam-6596	370	13	a	a	DET
ejpam-6596	370	14	community	community	NOUN
ejpam-6596	370	15	.	.	PUNCT
ejpam-6596	371	1	for	for	ADP
ejpam-6596	371	2	this	this	PRON
ejpam-6596	371	3	we	we	PRON
ejpam-6596	371	4	take	take	VERB
ejpam-6596	371	5	the	the	DET
ejpam-6596	371	6	values	value	NOUN
ejpam-6596	371	7	:	:	PUNCT
ejpam-6596	371	8	g	g	NOUN
ejpam-6596	371	9	=	=	SYM
ejpam-6596	371	10	10	10	NUM
ejpam-6596	371	11	,	,	PUNCT
ejpam-6596	371	12	h	h	NOUN
ejpam-6596	372	1	=	=	NOUN
ejpam-6596	372	2	0.01	0.01	NUM
ejpam-6596	372	3	,	,	PUNCT
ejpam-6596	372	4	m	m	VERB
ejpam-6596	372	5	=	=	NOUN
ejpam-6596	372	6	0.0124	0.0124	NUM
ejpam-6596	372	7	,	,	PUNCT
ejpam-6596	372	8	b1	b1	NOUN
ejpam-6596	372	9	=	=	SYM
ejpam-6596	372	10	0.05	0.05	NUM
ejpam-6596	372	11	,	,	PUNCT
ejpam-6596	372	12	c	c	NOUN
ejpam-6596	372	13	=	=	SYM
ejpam-6596	372	14	0.04	0.04	NUM
ejpam-6596	372	15	,	,	PUNCT
ejpam-6596	372	16	b2	b2	NOUN
ejpam-6596	372	17	=	=	SYM
ejpam-6596	372	18	0.0246	0.0246	NUM
ejpam-6596	372	19	,	,	PUNCT
ejpam-6596	372	20	b3	b3	PROPN
ejpam-6596	372	21	=	=	SYM
ejpam-6596	372	22	0.015	0.015	NUM
ejpam-6596	372	23	,	,	PUNCT
ejpam-6596	372	24	q	q	NOUN
ejpam-6596	372	25	=	=	NUM
ejpam-6596	372	26	0.2	0.2	NUM
ejpam-6596	372	27	,	,	PUNCT
ejpam-6596	372	28	µ	µ	X
ejpam-6596	372	29	=	=	SYM
ejpam-6596	372	30	0.2	0.2	NUM
ejpam-6596	372	31	,	,	PUNCT
ejpam-6596	372	32	p	p	X
ejpam-6596	372	33	=	=	PROPN
ejpam-6596	372	34	0.4	0.4	NUM
ejpam-6596	372	35	,	,	PUNCT
ejpam-6596	372	36	α	α	NOUN
ejpam-6596	372	37	=	=	NOUN
ejpam-6596	372	38	0.2	0.2	NUM
ejpam-6596	372	39	and	and	CCONJ
ejpam-6596	372	40	perform	perform	VERB
ejpam-6596	372	41	numerical	numerical	ADJ
ejpam-6596	372	42	simulations	simulation	NOUN
ejpam-6596	372	43	.	.	PUNCT
ejpam-6596	373	1	0	0	NUM
ejpam-6596	374	1	20	20	NUM
ejpam-6596	374	2	40	40	NUM
ejpam-6596	374	3	60	60	NUM
ejpam-6596	374	4	80	80	NUM
ejpam-6596	374	5	100	100	NUM
ejpam-6596	374	6	time	time	NOUN
ejpam-6596	374	7	90	90	NUM
ejpam-6596	374	8	100	100	NUM
ejpam-6596	374	9	110	110	NUM
ejpam-6596	374	10	120	120	NUM
ejpam-6596	374	11	130	130	NUM
ejpam-6596	374	12	140	140	NUM
ejpam-6596	374	13	150	150	NUM
ejpam-6596	374	14	160	160	NUM
ejpam-6596	374	15	170	170	NUM
ejpam-6596	374	16	180	180	NUM
ejpam-6596	374	17	s	s	NOUN
ejpam-6596	374	18	u	u	X
ejpam-6596	374	19	sc	sc	PROPN
ejpam-6596	374	20	ep	ep	PROPN
ejpam-6596	374	21	ti	ti	PROPN
ejpam-6596	374	22	b	b	X
ejpam-6596	374	23	le	le	X
ejpam-6596	374	24	c	c	X
ejpam-6596	374	25	la	la	INTJ
ejpam-6596	374	26	ss	ss	PROPN
ejpam-6596	374	27	s(0)=180	s(0)=180	X
ejpam-6596	374	28	s(0)=160	s(0)=160	X
ejpam-6596	374	29	s(0)=140	s(0)=140	X
ejpam-6596	374	30	s(0)=120	s(0)=120	ADV
ejpam-6596	374	31	0	0	NUM
ejpam-6596	374	32	10	10	NUM
ejpam-6596	374	33	20	20	NUM
ejpam-6596	374	34	30	30	NUM
ejpam-6596	374	35	40	40	NUM
ejpam-6596	374	36	50	50	NUM
ejpam-6596	374	37	time	time	NOUN
ejpam-6596	374	38	0	0	NUM
ejpam-6596	374	39	20	20	NUM
ejpam-6596	374	40	40	40	NUM
ejpam-6596	374	41	60	60	NUM
ejpam-6596	374	42	80	80	NUM
ejpam-6596	374	43	100	100	NUM
ejpam-6596	374	44	120	120	NUM
ejpam-6596	374	45	140	140	NUM
ejpam-6596	374	46	160	160	NUM
ejpam-6596	374	47	180	180	NUM
ejpam-6596	374	48	e	e	NOUN
ejpam-6596	374	49	xp	xp	NOUN
ejpam-6596	374	50	o	o	PROPN
ejpam-6596	374	51	se	se	PROPN
ejpam-6596	375	1	d	d	X
ejpam-6596	375	2	c	c	VERB
ejpam-6596	375	3	la	la	INTJ
ejpam-6596	375	4	ss	ss	ADP
ejpam-6596	375	5	e(0)=180	e(0)=180	PROPN
ejpam-6596	375	6	e(0)=160	e(0)=160	X
ejpam-6596	375	7	e(0)=140	e(0)=140	X
ejpam-6596	375	8	e(0)=120	e(0)=120	X
ejpam-6596	375	9	0	0	NUM
ejpam-6596	375	10	10	10	NUM
ejpam-6596	375	11	20	20	NUM
ejpam-6596	375	12	30	30	NUM
ejpam-6596	375	13	40	40	NUM
ejpam-6596	375	14	50	50	NUM
ejpam-6596	375	15	time	time	NOUN
ejpam-6596	375	16	0	0	NUM
ejpam-6596	375	17	50	50	NUM
ejpam-6596	375	18	100	100	NUM
ejpam-6596	375	19	150	150	NUM
ejpam-6596	375	20	200	200	NUM
ejpam-6596	375	21	250	250	NUM
ejpam-6596	375	22	300	300	NUM
ejpam-6596	375	23	in	in	ADP
ejpam-6596	375	24	fe	fe	X
ejpam-6596	375	25	ct	ct	NUM
ejpam-6596	375	26	ed	ed	PROPN
ejpam-6596	375	27	c	c	PROPN
ejpam-6596	375	28	la	la	PRON
ejpam-6596	375	29	ss	ss	X
ejpam-6596	375	30	i(0)=180	i(0)=180	X
ejpam-6596	375	31	i(0)=160	i(0)=160	X
ejpam-6596	375	32	i(0)=140	i(0)=140	X
ejpam-6596	375	33	i(0)=120	i(0)=120	PROPN
ejpam-6596	375	34	0	0	NUM
ejpam-6596	375	35	10	10	NUM
ejpam-6596	375	36	20	20	NUM
ejpam-6596	375	37	30	30	NUM
ejpam-6596	375	38	40	40	NUM
ejpam-6596	375	39	50	50	NUM
ejpam-6596	375	40	time	time	NOUN
ejpam-6596	375	41	0	0	NUM
ejpam-6596	375	42	20	20	NUM
ejpam-6596	375	43	40	40	NUM
ejpam-6596	375	44	60	60	NUM
ejpam-6596	375	45	80	80	NUM
ejpam-6596	375	46	100	100	NUM
ejpam-6596	375	47	120	120	NUM
ejpam-6596	375	48	140	140	NUM
ejpam-6596	375	49	160	160	NUM
ejpam-6596	375	50	180	180	NUM
ejpam-6596	375	51	q	q	NOUN
ejpam-6596	375	52	u	u	PROPN
ejpam-6596	375	53	a	a	DET
ejpam-6596	375	54	ra	ra	NOUN
ejpam-6596	375	55	n	n	CCONJ
ejpam-6596	375	56	ti	ti	NOUN
ejpam-6596	375	57	n	n	NOUN
ejpam-6596	375	58	e	e	NOUN
ejpam-6596	375	59	c	c	X
ejpam-6596	375	60	la	la	PROPN
ejpam-6596	375	61	ss	ss	PROPN
ejpam-6596	375	62	q(0)=180	q(0)=180	X
ejpam-6596	375	63	q(0)=160	q(0)=160	CCONJ
ejpam-6596	375	64	q(0)=140	q(0)=140	X
ejpam-6596	375	65	q(0)=120	q(0)=120	X
ejpam-6596	375	66	0	0	NUM
ejpam-6596	375	67	100	100	NUM
ejpam-6596	375	68	200	200	NUM
ejpam-6596	375	69	300	300	NUM
ejpam-6596	375	70	400	400	NUM
ejpam-6596	375	71	500	500	NUM
ejpam-6596	375	72	time	time	NOUN
ejpam-6596	375	73	0	0	NUM
ejpam-6596	375	74	500	500	NUM
ejpam-6596	375	75	1000	1000	NUM
ejpam-6596	375	76	1500	1500	NUM
ejpam-6596	375	77	2000	2000	NUM
ejpam-6596	375	78	2500	2500	NUM
ejpam-6596	375	79	3000	3000	NUM
ejpam-6596	375	80	r	r	NOUN
ejpam-6596	375	81	e	e	NOUN
ejpam-6596	375	82	c	c	NOUN
ejpam-6596	375	83	o	o	X
ejpam-6596	375	84	v	v	NOUN
ejpam-6596	375	85	e	e	NOUN
ejpam-6596	375	86	r	r	NOUN
ejpam-6596	375	87	e	e	NOUN
ejpam-6596	375	88	d	d	X
ejpam-6596	375	89	c	c	X
ejpam-6596	375	90	la	la	PROPN
ejpam-6596	375	91	s	s	PROPN
ejpam-6596	375	92	s	s	PART
ejpam-6596	375	93	r(0)=180	r(0)=180	NOUN
ejpam-6596	375	94	r(0)=160	r(0)=160	X
ejpam-6596	375	95	r(0)=140	r(0)=140	ADJ
ejpam-6596	375	96	r(0)=120	r(0)=120	NOUN
ejpam-6596	375	97	figure	figure	NOUN
ejpam-6596	375	98	3	3	NUM
ejpam-6596	375	99	:	:	PUNCT
ejpam-6596	375	100	dynamical	dynamical	ADJ
ejpam-6596	375	101	behaviour	behaviour	NOUN
ejpam-6596	375	102	of	of	ADP
ejpam-6596	375	103	the	the	DET
ejpam-6596	375	104	trajectories	trajectory	NOUN
ejpam-6596	375	105	of	of	ADP
ejpam-6596	375	106	the	the	DET
ejpam-6596	375	107	total	total	ADJ
ejpam-6596	375	108	classes	class	NOUN
ejpam-6596	375	109	of	of	ADP
ejpam-6596	375	110	the	the	DET
ejpam-6596	375	111	model	model	NOUN
ejpam-6596	375	112	for	for	ADP
ejpam-6596	375	113	the	the	DET
ejpam-6596	375	114	infection	infection	NOUN
ejpam-6596	375	115	state	state	NOUN
ejpam-6596	375	116	.	.	PUNCT
ejpam-6596	376	1	n.	n.	PROPN
ejpam-6596	376	2	gul	gul	PROPN
ejpam-6596	376	3	et	et	PROPN
ejpam-6596	376	4	al	al	PROPN
ejpam-6596	376	5	.	.	PUNCT
ejpam-6596	376	6	/	/	SYM
ejpam-6596	376	7	eur	eur	PROPN
ejpam-6596	376	8	.	.	PUNCT
ejpam-6596	377	1	j.	j.	PROPN
ejpam-6596	377	2	pure	pure	PROPN
ejpam-6596	377	3	appl	appl	PROPN
ejpam-6596	377	4	.	.	PROPN
ejpam-6596	377	5	math	math	PROPN
ejpam-6596	377	6	,	,	PUNCT
ejpam-6596	377	7	18	18	NUM
ejpam-6596	377	8	(	(	PUNCT
ejpam-6596	377	9	4	4	NUM
ejpam-6596	377	10	)	)	PUNCT
ejpam-6596	377	11	(	(	PUNCT
ejpam-6596	377	12	2025	2025	NUM
ejpam-6596	377	13	)	)	PUNCT
ejpam-6596	377	14	,	,	PUNCT
ejpam-6596	377	15	6596	6596	NUM
ejpam-6596	377	16	18	18	NUM
ejpam-6596	377	17	of	of	ADP
ejpam-6596	377	18	23	23	NUM
ejpam-6596	377	19	fig	fig	NOUN
ejpam-6596	377	20	.	.	PUNCT
ejpam-6596	378	1	(	(	PUNCT
ejpam-6596	378	2	3	3	X
ejpam-6596	378	3	)	)	PUNCT
ejpam-6596	378	4	displays	display	VERB
ejpam-6596	378	5	the	the	DET
ejpam-6596	378	6	infected	infected	ADJ
ejpam-6596	378	7	compartment	compartment	NOUN
ejpam-6596	378	8	in	in	ADP
ejpam-6596	378	9	the	the	DET
ejpam-6596	378	10	event	event	NOUN
ejpam-6596	378	11	that	that	SCONJ
ejpam-6596	378	12	the	the	DET
ejpam-6596	378	13	disease	disease	NOUN
ejpam-6596	378	14	continues	continue	VERB
ejpam-6596	378	15	to	to	PART
ejpam-6596	378	16	spread	spread	VERB
ejpam-6596	378	17	throughout	throughout	ADP
ejpam-6596	378	18	a	a	DET
ejpam-6596	378	19	community	community	NOUN
ejpam-6596	378	20	for	for	ADP
ejpam-6596	378	21	different	different	ADJ
ejpam-6596	378	22	beginning	begin	VERB
ejpam-6596	378	23	compartment	compartment	NOUN
ejpam-6596	378	24	sizes	size	NOUN
ejpam-6596	378	25	.	.	PUNCT
ejpam-6596	379	1	the	the	DET
ejpam-6596	379	2	compartment	compartment	NOUN
ejpam-6596	379	3	is	be	AUX
ejpam-6596	379	4	initially	initially	ADV
ejpam-6596	379	5	shown	show	VERB
ejpam-6596	379	6	to	to	PART
ejpam-6596	379	7	be	be	AUX
ejpam-6596	379	8	rising	rise	VERB
ejpam-6596	379	9	;	;	PUNCT
ejpam-6596	379	10	as	as	SCONJ
ejpam-6596	379	11	time	time	NOUN
ejpam-6596	379	12	goes	go	VERB
ejpam-6596	379	13	on	on	ADP
ejpam-6596	379	14	,	,	PUNCT
ejpam-6596	379	15	the	the	DET
ejpam-6596	379	16	compartment	compartment	NOUN
ejpam-6596	379	17	falls	fall	VERB
ejpam-6596	379	18	and	and	CCONJ
ejpam-6596	379	19	converges	converge	VERB
ejpam-6596	379	20	to	to	ADP
ejpam-6596	379	21	the	the	DET
ejpam-6596	379	22	illness	illness	NOUN
ejpam-6596	379	23	endamic	endamic	ADJ
ejpam-6596	379	24	state	state	NOUN
ejpam-6596	379	25	.	.	PUNCT
ejpam-6596	380	1	this	this	PRON
ejpam-6596	380	2	validates	validate	VERB
ejpam-6596	380	3	our	our	PRON
ejpam-6596	380	4	analytical	analytical	ADJ
ejpam-6596	380	5	findings	finding	NOUN
ejpam-6596	380	6	.	.	PUNCT
ejpam-6596	381	1	while	while	SCONJ
ejpam-6596	381	2	in	in	ADP
ejpam-6596	381	3	the	the	DET
ejpam-6596	381	4	last	last	ADJ
ejpam-6596	381	5	figure	figure	NOUN
ejpam-6596	381	6	(	(	PUNCT
ejpam-6596	381	7	recovered	recover	VERB
ejpam-6596	381	8	population	population	NOUN
ejpam-6596	381	9	graph	graph	NOUN
ejpam-6596	381	10	)	)	PUNCT
ejpam-6596	381	11	show	show	VERB
ejpam-6596	381	12	the	the	DET
ejpam-6596	381	13	picture	picture	NOUN
ejpam-6596	381	14	of	of	ADP
ejpam-6596	381	15	the	the	DET
ejpam-6596	381	16	recovered	recovered	ADJ
ejpam-6596	381	17	population	population	NOUN
ejpam-6596	381	18	versus	versus	ADP
ejpam-6596	381	19	time	time	NOUN
ejpam-6596	381	20	for	for	ADP
ejpam-6596	381	21	various	various	ADJ
ejpam-6596	381	22	initial	initial	ADJ
ejpam-6596	381	23	conditions	condition	NOUN
ejpam-6596	381	24	.	.	PUNCT
ejpam-6596	382	1	we	we	PRON
ejpam-6596	382	2	see	see	VERB
ejpam-6596	382	3	that	that	SCONJ
ejpam-6596	382	4	throughout	throughout	ADP
ejpam-6596	382	5	the	the	DET
ejpam-6596	382	6	first	first	ADJ
ejpam-6596	382	7	several	several	ADJ
ejpam-6596	382	8	weeks	week	NOUN
ejpam-6596	382	9	,	,	PUNCT
ejpam-6596	382	10	this	this	DET
ejpam-6596	382	11	class	class	NOUN
ejpam-6596	382	12	grows	grow	VERB
ejpam-6596	382	13	and	and	CCONJ
ejpam-6596	382	14	then	then	ADV
ejpam-6596	382	15	progressively	progressively	ADV
ejpam-6596	382	16	approaches	approach	VERB
ejpam-6596	382	17	the	the	DET
ejpam-6596	382	18	endemic	endemic	ADJ
ejpam-6596	382	19	stability	stability	NOUN
ejpam-6596	382	20	threshold	threshold	NOUN
ejpam-6596	382	21	.	.	PUNCT
ejpam-6596	383	1	9.2	9.2	NUM
ejpam-6596	383	2	.	.	PUNCT
ejpam-6596	384	1	numerical	numerical	ADJ
ejpam-6596	384	2	simulations	simulation	NOUN
ejpam-6596	384	3	for	for	ADP
ejpam-6596	384	4	the	the	DET
ejpam-6596	384	5	optimal	optimal	ADJ
ejpam-6596	384	6	control	control	NOUN
ejpam-6596	384	7	problem	problem	NOUN
ejpam-6596	384	8	we	we	PRON
ejpam-6596	384	9	numerically	numerically	ADV
ejpam-6596	384	10	solve	solve	VERB
ejpam-6596	384	11	the	the	DET
ejpam-6596	384	12	optimal	optimal	ADJ
ejpam-6596	384	13	control	control	NOUN
ejpam-6596	384	14	model	model	NOUN
ejpam-6596	384	15	(	(	PUNCT
ejpam-6596	384	16	8)	8)	NUM
ejpam-6596	384	17	using	use	VERB
ejpam-6596	384	18	the	the	DET
ejpam-6596	384	19	runge	runge	NOUN
ejpam-6596	384	20	-	-	PUNCT
ejpam-6596	384	21	kutta	kutta	NOUN
ejpam-6596	384	22	method	method	NOUN
ejpam-6596	384	23	of	of	ADP
ejpam-6596	384	24	order	order	NOUN
ejpam-6596	384	25	4	4	NUM
ejpam-6596	384	26	.	.	PUNCT
ejpam-6596	385	1	the	the	DET
ejpam-6596	385	2	parametric	parametric	ADJ
ejpam-6596	385	3	values	value	NOUN
ejpam-6596	385	4	are	be	AUX
ejpam-6596	385	5	taken	take	VERB
ejpam-6596	385	6	as	as	ADP
ejpam-6596	385	7	:	:	PUNCT
ejpam-6596	385	8	a1	a1	NOUN
ejpam-6596	385	9	=	=	SYM
ejpam-6596	385	10	2	2	NUM
ejpam-6596	385	11	,	,	PUNCT
ejpam-6596	385	12	,	,	PUNCT
ejpam-6596	385	13	a2	a2	PROPN
ejpam-6596	385	14	=	=	SYM
ejpam-6596	385	15	3	3	NUM
ejpam-6596	385	16	,	,	PUNCT
ejpam-6596	385	17	a3	a3	NOUN
ejpam-6596	385	18	=	=	SYM
ejpam-6596	385	19	4	4	NUM
ejpam-6596	385	20	,	,	PUNCT
ejpam-6596	385	21	a4	a4	NOUN
ejpam-6596	385	22	=	=	SYM
ejpam-6596	385	23	5	5	NUM
ejpam-6596	385	24	,	,	PUNCT
ejpam-6596	385	25	a5	a5	NOUN
ejpam-6596	385	26	=	=	SYM
ejpam-6596	385	27	a6	a6	NOUN
ejpam-6596	385	28	=	=	SYM
ejpam-6596	385	29	1	1	NUM
ejpam-6596	385	30	,	,	PUNCT
ejpam-6596	385	31	g	g	NOUN
ejpam-6596	385	32	=	=	SYM
ejpam-6596	385	33	10	10	NUM
ejpam-6596	385	34	,	,	PUNCT
ejpam-6596	385	35	h	h	NOUN
ejpam-6596	385	36	=	=	SYM
ejpam-6596	385	37	0.00245	0.00245	NUM
ejpam-6596	385	38	,	,	PUNCT
ejpam-6596	385	39	m	m	PROPN
ejpam-6596	385	40	=	=	NOUN
ejpam-6596	385	41	0.0124	0.0124	NUM
ejpam-6596	385	42	,	,	PUNCT
ejpam-6596	385	43	b1	b1	NOUN
ejpam-6596	385	44	=	=	NUM
ejpam-6596	385	45	0.4	0.4	NUM
ejpam-6596	385	46	,	,	PUNCT
ejpam-6596	385	47	c	c	NOUN
ejpam-6596	385	48	=	=	SYM
ejpam-6596	385	49	0.4	0.4	NUM
ejpam-6596	385	50	,	,	PUNCT
ejpam-6596	385	51	b2	b2	NOUN
ejpam-6596	385	52	=	=	SYM
ejpam-6596	385	53	0.5	0.5	NUM
ejpam-6596	385	54	,	,	PUNCT
ejpam-6596	385	55	b3	b3	NOUN
ejpam-6596	385	56	=	=	SYM
ejpam-6596	385	57	0.45	0.45	NUM
ejpam-6596	385	58	,	,	PUNCT
ejpam-6596	385	59	q	q	NOUN
ejpam-6596	385	60	=	=	SYM
ejpam-6596	385	61	0.5	0.5	NUM
ejpam-6596	385	62	,	,	PUNCT
ejpam-6596	385	63	µ	µ	X
ejpam-6596	385	64	=	=	SYM
ejpam-6596	385	65	0.023	0.023	NUM
ejpam-6596	385	66	,	,	PUNCT
ejpam-6596	385	67	p	p	NOUN
ejpam-6596	385	68	=	=	PROPN
ejpam-6596	385	69	0.4	0.4	NUM
ejpam-6596	385	70	,	,	PUNCT
ejpam-6596	385	71	α	α	NOUN
ejpam-6596	385	72	=	=	NOUN
ejpam-6596	385	73	0.2	0.2	NUM
ejpam-6596	385	74	,	,	PUNCT
ejpam-6596	385	75	the	the	DET
ejpam-6596	385	76	fig	fig	NOUN
ejpam-6596	385	77	.	.	PUNCT
ejpam-6596	386	1	(	(	PUNCT
ejpam-6596	386	2	4	4	X
ejpam-6596	386	3	)	)	PUNCT
ejpam-6596	386	4	are	be	AUX
ejpam-6596	386	5	the	the	DET
ejpam-6596	386	6	solution	solution	NOUN
ejpam-6596	386	7	curves	curve	NOUN
ejpam-6596	386	8	of	of	ADP
ejpam-6596	386	9	the	the	DET
ejpam-6596	386	10	susceptible	susceptible	ADJ
ejpam-6596	386	11	class	class	NOUN
ejpam-6596	386	12	both	both	CCONJ
ejpam-6596	386	13	in	in	ADP
ejpam-6596	386	14	the	the	DET
ejpam-6596	386	15	absence	absence	NOUN
ejpam-6596	386	16	and	and	CCONJ
ejpam-6596	386	17	presence	presence	NOUN
ejpam-6596	386	18	of	of	ADP
ejpam-6596	386	19	the	the	DET
ejpam-6596	386	20	optimal	optimal	ADJ
ejpam-6596	386	21	control	control	NOUN
ejpam-6596	386	22	parameters	parameter	NOUN
ejpam-6596	386	23	.	.	PUNCT
ejpam-6596	387	1	we	we	PRON
ejpam-6596	387	2	observe	observe	VERB
ejpam-6596	387	3	from	from	ADP
ejpam-6596	387	4	the	the	DET
ejpam-6596	387	5	figure	figure	NOUN
ejpam-6596	387	6	,	,	PUNCT
ejpam-6596	387	7	that	that	SCONJ
ejpam-6596	387	8	the	the	DET
ejpam-6596	387	9	susceptible	susceptible	ADJ
ejpam-6596	387	10	population	population	NOUN
ejpam-6596	387	11	can	can	AUX
ejpam-6596	387	12	be	be	AUX
ejpam-6596	387	13	increased	increase	VERB
ejpam-6596	387	14	once	once	SCONJ
ejpam-6596	387	15	one	one	NOUN
ejpam-6596	387	16	applies	apply	VERB
ejpam-6596	387	17	the	the	DET
ejpam-6596	387	18	control	control	NOUN
ejpam-6596	387	19	stratifies	stratify	VERB
ejpam-6596	387	20	.	.	PUNCT
ejpam-6596	388	1	in	in	ADP
ejpam-6596	388	2	other	other	ADJ
ejpam-6596	388	3	words	word	NOUN
ejpam-6596	388	4	,	,	PUNCT
ejpam-6596	388	5	the	the	DET
ejpam-6596	388	6	number	number	NOUN
ejpam-6596	388	7	of	of	ADP
ejpam-6596	388	8	susceptible	susceptible	ADJ
ejpam-6596	388	9	individuals	individual	NOUN
ejpam-6596	388	10	increase	increase	VERB
ejpam-6596	388	11	when	when	SCONJ
ejpam-6596	388	12	the	the	DET
ejpam-6596	388	13	control	control	NOUN
ejpam-6596	388	14	measures	measure	NOUN
ejpam-6596	388	15	are	be	AUX
ejpam-6596	388	16	adopted	adopt	VERB
ejpam-6596	388	17	.	.	PUNCT
ejpam-6596	389	1	the	the	DET
ejpam-6596	389	2	figure	figure	NOUN
ejpam-6596	389	3	also	also	ADV
ejpam-6596	389	4	show	show	VERB
ejpam-6596	389	5	that	that	SCONJ
ejpam-6596	389	6	the	the	DET
ejpam-6596	389	7	class	class	NOUN
ejpam-6596	389	8	s(t	s(t	PROPN
ejpam-6596	389	9	)	)	PUNCT
ejpam-6596	389	10	decreases	decrease	VERB
ejpam-6596	389	11	whenever	whenever	SCONJ
ejpam-6596	389	12	these	these	DET
ejpam-6596	389	13	measures	measure	NOUN
ejpam-6596	389	14	are	be	AUX
ejpam-6596	389	15	avoided	avoid	VERB
ejpam-6596	389	16	.	.	PUNCT
ejpam-6596	389	17	0	0	NUM
ejpam-6596	389	18	10	10	NUM
ejpam-6596	389	19	20	20	NUM
ejpam-6596	389	20	30	30	NUM
ejpam-6596	389	21	40	40	NUM
ejpam-6596	389	22	50	50	NUM
ejpam-6596	389	23	time	time	NOUN
ejpam-6596	389	24	0	0	NUM
ejpam-6596	390	1	200	200	NUM
ejpam-6596	390	2	400	400	NUM
ejpam-6596	390	3	600	600	NUM
ejpam-6596	390	4	800	800	NUM
ejpam-6596	390	5	1000	1000	NUM
ejpam-6596	390	6	s	s	PART
ejpam-6596	390	7	u	u	NOUN
ejpam-6596	390	8	sc	sc	PROPN
ejpam-6596	390	9	e	e	PROPN
ejpam-6596	390	10	p	p	PROPN
ejpam-6596	390	11	ib	ib	X
ejpam-6596	390	12	le	le	X
ejpam-6596	390	13	c	c	PROPN
ejpam-6596	390	14	la	la	INTJ
ejpam-6596	390	15	ss	ss	PROPN
ejpam-6596	390	16	with	with	ADP
ejpam-6596	390	17	control	control	NOUN
ejpam-6596	390	18	without	without	ADP
ejpam-6596	390	19	control	control	NOUN
ejpam-6596	390	20	figure	figure	NOUN
ejpam-6596	390	21	4	4	NUM
ejpam-6596	390	22	:	:	PUNCT
ejpam-6596	390	23	solution	solution	NOUN
ejpam-6596	390	24	curves	curve	NOUN
ejpam-6596	390	25	of	of	ADP
ejpam-6596	390	26	the	the	DET
ejpam-6596	390	27	trajectories	trajectory	NOUN
ejpam-6596	390	28	of	of	ADP
ejpam-6596	390	29	susceptible	susceptible	ADJ
ejpam-6596	390	30	class	class	NOUN
ejpam-6596	390	31	of	of	ADP
ejpam-6596	390	32	the	the	DET
ejpam-6596	390	33	model	model	NOUN
ejpam-6596	390	34	under	under	ADP
ejpam-6596	390	35	consideration	consideration	NOUN
ejpam-6596	390	36	with	with	ADP
ejpam-6596	390	37	and	and	CCONJ
ejpam-6596	390	38	without	without	ADP
ejpam-6596	390	39	control	control	NOUN
ejpam-6596	390	40	parameters	parameter	NOUN
ejpam-6596	390	41	.	.	PUNCT
ejpam-6596	391	1	plotted	plot	VERB
ejpam-6596	391	2	in	in	ADP
ejpam-6596	391	3	the	the	DET
ejpam-6596	391	4	second	second	ADJ
ejpam-6596	391	5	panel	panel	NOUN
ejpam-6596	391	6	of	of	ADP
ejpam-6596	391	7	fig	fig	NOUN
ejpam-6596	391	8	.	.	PUNCT
ejpam-6596	392	1	(	(	PUNCT
ejpam-6596	392	2	5	5	X
ejpam-6596	392	3	)	)	PUNCT
ejpam-6596	392	4	are	be	AUX
ejpam-6596	392	5	the	the	DET
ejpam-6596	392	6	trajectories	trajectory	NOUN
ejpam-6596	392	7	of	of	ADP
ejpam-6596	392	8	the	the	DET
ejpam-6596	392	9	exposed	expose	VERB
ejpam-6596	392	10	and	and	CCONJ
ejpam-6596	392	11	quarantine	quarantine	NOUN
ejpam-6596	392	12	classes	class	NOUN
ejpam-6596	392	13	both	both	CCONJ
ejpam-6596	392	14	in	in	ADP
ejpam-6596	392	15	the	the	DET
ejpam-6596	392	16	absence	absence	NOUN
ejpam-6596	392	17	and	and	CCONJ
ejpam-6596	392	18	presence	presence	NOUN
ejpam-6596	392	19	of	of	ADP
ejpam-6596	392	20	the	the	DET
ejpam-6596	392	21	control	control	NOUN
ejpam-6596	392	22	measures	measure	NOUN
ejpam-6596	392	23	.	.	PUNCT
ejpam-6596	393	1	it	it	PRON
ejpam-6596	393	2	is	be	AUX
ejpam-6596	393	3	observed	observe	VERB
ejpam-6596	393	4	from	from	ADP
ejpam-6596	393	5	both	both	DET
ejpam-6596	393	6	figures	figure	NOUN
ejpam-6596	393	7	that	that	SCONJ
ejpam-6596	393	8	the	the	DET
ejpam-6596	393	9	population	population	NOUN
ejpam-6596	393	10	can	can	AUX
ejpam-6596	393	11	be	be	AUX
ejpam-6596	393	12	decreased	decrease	VERB
ejpam-6596	393	13	with	with	ADP
ejpam-6596	393	14	the	the	DET
ejpam-6596	393	15	application	application	NOUN
ejpam-6596	393	16	of	of	ADP
ejpam-6596	393	17	the	the	DET
ejpam-6596	393	18	control	control	NOUN
ejpam-6596	393	19	measures	measure	NOUN
ejpam-6596	393	20	,	,	PUNCT
ejpam-6596	393	21	which	which	PRON
ejpam-6596	393	22	is	be	AUX
ejpam-6596	393	23	the	the	DET
ejpam-6596	393	24	aim	aim	NOUN
ejpam-6596	393	25	of	of	ADP
ejpam-6596	393	26	the	the	DET
ejpam-6596	393	27	optimal	optimal	ADJ
ejpam-6596	393	28	control	control	NOUN
ejpam-6596	393	29	problem	problem	NOUN
ejpam-6596	393	30	.	.	PUNCT
ejpam-6596	394	1	n.	n.	PROPN
ejpam-6596	394	2	gul	gul	PROPN
ejpam-6596	394	3	et	et	PROPN
ejpam-6596	394	4	al	al	PROPN
ejpam-6596	394	5	.	.	PUNCT
ejpam-6596	394	6	/	/	SYM
ejpam-6596	394	7	eur	eur	PROPN
ejpam-6596	394	8	.	.	PUNCT
ejpam-6596	395	1	j.	j.	PROPN
ejpam-6596	395	2	pure	pure	PROPN
ejpam-6596	395	3	appl	appl	PROPN
ejpam-6596	395	4	.	.	PROPN
ejpam-6596	395	5	math	math	PROPN
ejpam-6596	395	6	,	,	PUNCT
ejpam-6596	395	7	18	18	NUM
ejpam-6596	395	8	(	(	PUNCT
ejpam-6596	395	9	4	4	NUM
ejpam-6596	395	10	)	)	PUNCT
ejpam-6596	395	11	(	(	PUNCT
ejpam-6596	395	12	2025	2025	NUM
ejpam-6596	395	13	)	)	PUNCT
ejpam-6596	395	14	,	,	PUNCT
ejpam-6596	395	15	6596	6596	NUM
ejpam-6596	395	16	19	19	NUM
ejpam-6596	395	17	of	of	ADP
ejpam-6596	395	18	23	23	NUM
ejpam-6596	395	19	0	0	NUM
ejpam-6596	395	20	50	50	NUM
ejpam-6596	395	21	100	100	NUM
ejpam-6596	395	22	150	150	NUM
ejpam-6596	395	23	200	200	NUM
ejpam-6596	395	24	250	250	NUM
ejpam-6596	395	25	300	300	NUM
ejpam-6596	395	26	time	time	NOUN
ejpam-6596	395	27	0	0	NUM
ejpam-6596	395	28	100	100	NUM
ejpam-6596	395	29	200	200	NUM
ejpam-6596	395	30	300	300	NUM
ejpam-6596	395	31	400	400	NUM
ejpam-6596	395	32	500	500	NUM
ejpam-6596	395	33	600	600	NUM
ejpam-6596	395	34	700	700	NUM
ejpam-6596	395	35	e	e	NOUN
ejpam-6596	395	36	x	x	X
ejpam-6596	395	37	p	p	X
ejpam-6596	395	38	o	o	X
ejpam-6596	395	39	se	se	PROPN
ejpam-6596	395	40	d	d	X
ejpam-6596	395	41	c	c	VERB
ejpam-6596	395	42	la	la	PRON
ejpam-6596	395	43	ss	ss	PROPN
ejpam-6596	395	44	control	control	NOUN
ejpam-6596	395	45	in	in	ADP
ejpam-6596	395	46	the	the	DET
ejpam-6596	395	47	exposed	expose	VERB
ejpam-6596	395	48	class	class	NOUN
ejpam-6596	395	49	without	without	ADP
ejpam-6596	395	50	control	control	NOUN
ejpam-6596	395	51	with	with	ADP
ejpam-6596	395	52	control	control	NOUN
ejpam-6596	395	53	0	0	NUM
ejpam-6596	395	54	10	10	NUM
ejpam-6596	395	55	20	20	NUM
ejpam-6596	395	56	30	30	NUM
ejpam-6596	395	57	40	40	NUM
ejpam-6596	395	58	50	50	NUM
ejpam-6596	395	59	time	time	NOUN
ejpam-6596	395	60	0	0	NUM
ejpam-6596	395	61	500	500	NUM
ejpam-6596	395	62	1000	1000	NUM
ejpam-6596	395	63	1500	1500	NUM
ejpam-6596	395	64	c	c	NOUN
ejpam-6596	395	65	o	o	NOUN
ejpam-6596	395	66	n	n	PRON
ejpam-6596	395	67	tr	tr	NOUN
ejpam-6596	395	68	o	o	PROPN
ejpam-6596	395	69	l	l	NOUN
ejpam-6596	396	1	o	o	NOUN
ejpam-6596	396	2	n	n	ADP
ejpam-6596	396	3	t	t	NOUN
ejpam-6596	396	4	h	h	NOUN
ejpam-6596	396	5	e	e	X
ejpam-6596	396	6	c	c	X
ejpam-6596	396	7	la	la	INTJ
ejpam-6596	396	8	ss	ss	NOUN
ejpam-6596	396	9	q	q	X
ejpam-6596	396	10	(	(	PUNCT
ejpam-6596	396	11	t	t	NOUN
ejpam-6596	396	12	)	)	PUNCT
ejpam-6596	396	13	control	control	NOUN
ejpam-6596	396	14	in	in	ADP
ejpam-6596	396	15	the	the	DET
ejpam-6596	396	16	infectious	infectious	ADJ
ejpam-6596	396	17	class	class	NOUN
ejpam-6596	396	18	without	without	ADP
ejpam-6596	396	19	control	control	NOUN
ejpam-6596	396	20	with	with	ADP
ejpam-6596	396	21	control	control	NOUN
ejpam-6596	396	22	figure	figure	NOUN
ejpam-6596	396	23	5	5	NUM
ejpam-6596	396	24	:	:	PUNCT
ejpam-6596	396	25	solution	solution	NOUN
ejpam-6596	396	26	curves	curve	NOUN
ejpam-6596	396	27	of	of	ADP
ejpam-6596	396	28	the	the	DET
ejpam-6596	396	29	trajectories	trajectory	NOUN
ejpam-6596	396	30	of	of	ADP
ejpam-6596	396	31	various	various	ADJ
ejpam-6596	396	32	classes	class	NOUN
ejpam-6596	396	33	of	of	ADP
ejpam-6596	396	34	the	the	DET
ejpam-6596	396	35	model	model	NOUN
ejpam-6596	396	36	under	under	ADP
ejpam-6596	396	37	consideration	consideration	NOUN
ejpam-6596	396	38	with	with	ADP
ejpam-6596	396	39	and	and	CCONJ
ejpam-6596	396	40	without	without	ADP
ejpam-6596	396	41	control	control	NOUN
ejpam-6596	396	42	parameters	parameter	NOUN
ejpam-6596	396	43	.	.	PUNCT
ejpam-6596	397	1	in	in	ADP
ejpam-6596	397	2	the	the	DET
ejpam-6596	397	3	same	same	ADJ
ejpam-6596	397	4	way	way	NOUN
ejpam-6596	397	5	,	,	PUNCT
ejpam-6596	397	6	other	other	ADJ
ejpam-6596	397	7	panels	panel	NOUN
ejpam-6596	397	8	of	of	ADP
ejpam-6596	397	9	the	the	DET
ejpam-6596	397	10	figure	figure	NOUN
ejpam-6596	397	11	fig	fig	NOUN
ejpam-6596	397	12	.	.	PUNCT
ejpam-6596	398	1	(	(	PUNCT
ejpam-6596	398	2	6	6	X
ejpam-6596	398	3	)	)	PUNCT
ejpam-6596	398	4	shows	show	VERB
ejpam-6596	398	5	that	that	SCONJ
ejpam-6596	398	6	the	the	DET
ejpam-6596	398	7	infected	infected	ADJ
ejpam-6596	398	8	population	population	NOUN
ejpam-6596	398	9	can	can	AUX
ejpam-6596	398	10	be	be	AUX
ejpam-6596	398	11	decreased	decrease	VERB
ejpam-6596	398	12	once	once	SCONJ
ejpam-6596	398	13	the	the	DET
ejpam-6596	398	14	control	control	NOUN
ejpam-6596	398	15	measures	measure	NOUN
ejpam-6596	398	16	are	be	AUX
ejpam-6596	398	17	adopted	adopt	VERB
ejpam-6596	398	18	.	.	PUNCT
ejpam-6596	399	1	similarly	similarly	ADV
ejpam-6596	399	2	the	the	DET
ejpam-6596	399	3	recovered	recovered	ADJ
ejpam-6596	399	4	populations	population	NOUN
ejpam-6596	399	5	are	be	AUX
ejpam-6596	399	6	enhanced	enhance	VERB
ejpam-6596	399	7	with	with	ADP
ejpam-6596	399	8	the	the	DET
ejpam-6596	399	9	control	control	NOUN
ejpam-6596	399	10	measures	measure	NOUN
ejpam-6596	399	11	suggested	suggest	VERB
ejpam-6596	399	12	in	in	ADP
ejpam-6596	399	13	our	our	PRON
ejpam-6596	399	14	control	control	NOUN
ejpam-6596	399	15	problem	problem	NOUN
ejpam-6596	399	16	.	.	PUNCT
ejpam-6596	400	1	0	0	NUM
ejpam-6596	400	2	10	10	NUM
ejpam-6596	400	3	20	20	NUM
ejpam-6596	400	4	30	30	NUM
ejpam-6596	400	5	40	40	NUM
ejpam-6596	400	6	50	50	NUM
ejpam-6596	400	7	time	time	NOUN
ejpam-6596	400	8	0	0	NUM
ejpam-6596	400	9	100	100	NUM
ejpam-6596	400	10	200	200	NUM
ejpam-6596	400	11	300	300	NUM
ejpam-6596	400	12	400	400	NUM
ejpam-6596	400	13	500	500	NUM
ejpam-6596	400	14	in	in	ADP
ejpam-6596	400	15	fe	fe	X
ejpam-6596	400	16	ct	ct	PROPN
ejpam-6596	400	17	ed	ed	PROPN
ejpam-6596	401	1	c	c	PROPN
ejpam-6596	401	2	la	la	INTJ
ejpam-6596	401	3	ss	ss	INTJ
ejpam-6596	402	1	i	i	PRON
ejpam-6596	402	2	(	(	PUNCT
ejpam-6596	402	3	t	t	PROPN
ejpam-6596	402	4	)	)	PUNCT
ejpam-6596	402	5	without	without	ADP
ejpam-6596	402	6	control	control	NOUN
ejpam-6596	402	7	with	with	ADP
ejpam-6596	402	8	control	control	NOUN
ejpam-6596	402	9	0	0	NUM
ejpam-6596	402	10	50	50	NUM
ejpam-6596	402	11	100	100	NUM
ejpam-6596	402	12	150	150	NUM
ejpam-6596	402	13	200	200	NUM
ejpam-6596	402	14	250	250	NUM
ejpam-6596	402	15	300	300	NUM
ejpam-6596	402	16	time	time	NOUN
ejpam-6596	402	17	0	0	NUM
ejpam-6596	402	18	500	500	NUM
ejpam-6596	402	19	1000	1000	NUM
ejpam-6596	402	20	1500	1500	NUM
ejpam-6596	402	21	2000	2000	NUM
ejpam-6596	402	22	r	r	NOUN
ejpam-6596	402	23	e	e	NOUN
ejpam-6596	402	24	c	c	NOUN
ejpam-6596	402	25	o	o	X
ejpam-6596	402	26	v	v	X
ejpam-6596	402	27	e	e	X
ejpam-6596	402	28	re	re	NOUN
ejpam-6596	402	29	d	d	PROPN
ejpam-6596	402	30	c	c	X
ejpam-6596	402	31	la	la	PRON
ejpam-6596	402	32	ss	ss	NOUN
ejpam-6596	402	33	r	r	NOUN
ejpam-6596	402	34	(	(	PUNCT
ejpam-6596	402	35	t	t	PROPN
ejpam-6596	402	36	)	)	PUNCT
ejpam-6596	402	37	without	without	ADP
ejpam-6596	402	38	control	control	NOUN
ejpam-6596	402	39	with	with	ADP
ejpam-6596	402	40	control	control	NOUN
ejpam-6596	402	41	figure	figure	NOUN
ejpam-6596	402	42	6	6	NUM
ejpam-6596	402	43	:	:	PUNCT
ejpam-6596	402	44	solution	solution	NOUN
ejpam-6596	402	45	curves	curve	NOUN
ejpam-6596	402	46	of	of	ADP
ejpam-6596	402	47	the	the	DET
ejpam-6596	402	48	trajectories	trajectory	NOUN
ejpam-6596	402	49	of	of	ADP
ejpam-6596	402	50	various	various	ADJ
ejpam-6596	402	51	classes	class	NOUN
ejpam-6596	402	52	of	of	ADP
ejpam-6596	402	53	the	the	DET
ejpam-6596	402	54	model	model	NOUN
ejpam-6596	402	55	under	under	ADP
ejpam-6596	402	56	consideration	consideration	NOUN
ejpam-6596	402	57	with	with	ADP
ejpam-6596	402	58	and	and	CCONJ
ejpam-6596	402	59	without	without	ADP
ejpam-6596	402	60	control	control	NOUN
ejpam-6596	402	61	parameters	parameter	NOUN
ejpam-6596	402	62	.	.	PUNCT
ejpam-6596	403	1	10	10	NUM
ejpam-6596	403	2	.	.	X
ejpam-6596	403	3	phase	phase	NOUN
ejpam-6596	403	4	portrait	portrait	NOUN
ejpam-6596	403	5	study	study	NOUN
ejpam-6596	403	6	for	for	ADP
ejpam-6596	403	7	proposed	propose	VERB
ejpam-6596	403	8	model	model	NOUN
ejpam-6596	403	9	the	the	DET
ejpam-6596	403	10	phase	phase	NOUN
ejpam-6596	403	11	portrait	portrait	NOUN
ejpam-6596	403	12	analysis	analysis	NOUN
ejpam-6596	403	13	provides	provide	VERB
ejpam-6596	403	14	a	a	DET
ejpam-6596	403	15	comprehensive	comprehensive	ADJ
ejpam-6596	403	16	visualization	visualization	NOUN
ejpam-6596	403	17	of	of	ADP
ejpam-6596	403	18	the	the	DET
ejpam-6596	403	19	system	system	NOUN
ejpam-6596	403	20	’s	’s	PART
ejpam-6596	403	21	trajectories	trajectory	NOUN
ejpam-6596	403	22	under	under	ADP
ejpam-6596	403	23	both	both	DET
ejpam-6596	403	24	controlled	control	VERB
ejpam-6596	403	25	and	and	CCONJ
ejpam-6596	403	26	uncontrolled	uncontrolled	ADJ
ejpam-6596	403	27	scenarios	scenario	NOUN
ejpam-6596	403	28	,	,	PUNCT
ejpam-6596	403	29	highlighting	highlight	VERB
ejpam-6596	403	30	the	the	DET
ejpam-6596	403	31	impact	impact	NOUN
ejpam-6596	403	32	of	of	ADP
ejpam-6596	403	33	intervention	intervention	NOUN
ejpam-6596	403	34	strategies	strategy	NOUN
ejpam-6596	403	35	on	on	ADP
ejpam-6596	403	36	disease	disease	NOUN
ejpam-6596	403	37	dynamics	dynamic	NOUN
ejpam-6596	403	38	.	.	PUNCT
ejpam-6596	404	1	system	system	NOUN
ejpam-6596	404	2	of	of	ADP
ejpam-6596	404	3	figure	figure	NOUN
ejpam-6596	404	4	(	(	PUNCT
ejpam-6596	404	5	7	7	NUM
ejpam-6596	404	6	)	)	PUNCT
ejpam-6596	404	7	illustrates	illustrate	VERB
ejpam-6596	404	8	the	the	DET
ejpam-6596	404	9	interplay	interplay	NOUN
ejpam-6596	404	10	between	between	ADP
ejpam-6596	404	11	different	different	ADJ
ejpam-6596	404	12	populations	population	NOUN
ejpam-6596	404	13	,	,	PUNCT
ejpam-6596	404	14	demonstrating	demonstrate	VERB
ejpam-6596	404	15	distinct	distinct	ADJ
ejpam-6596	404	16	behavioral	behavioral	ADJ
ejpam-6596	404	17	patterns	pattern	NOUN
ejpam-6596	404	18	.	.	PUNCT
ejpam-6596	405	1	in	in	ADP
ejpam-6596	405	2	the	the	DET
ejpam-6596	405	3	absence	absence	NOUN
ejpam-6596	405	4	of	of	ADP
ejpam-6596	405	5	control	control	NOUN
ejpam-6596	405	6	measures	measure	NOUN
ejpam-6596	405	7	,	,	PUNCT
ejpam-6596	405	8	trajectories	trajectory	NOUN
ejpam-6596	405	9	diverge	diverge	VERB
ejpam-6596	405	10	toward	toward	ADP
ejpam-6596	405	11	higher	high	ADJ
ejpam-6596	405	12	infection	infection	NOUN
ejpam-6596	405	13	levels	level	NOUN
ejpam-6596	405	14	,	,	PUNCT
ejpam-6596	405	15	aligning	align	VERB
ejpam-6596	405	16	with	with	ADP
ejpam-6596	405	17	the	the	DET
ejpam-6596	405	18	endemic	endemic	ADJ
ejpam-6596	405	19	equilibrium	equilibrium	NOUN
ejpam-6596	405	20	.	.	PUNCT
ejpam-6596	406	1	conversely	conversely	ADV
ejpam-6596	406	2	,	,	PUNCT
ejpam-6596	406	3	with	with	ADP
ejpam-6596	406	4	optimal	optimal	ADJ
ejpam-6596	406	5	controls	control	NOUN
ejpam-6596	406	6	u1	u1	NOUN
ejpam-6596	406	7	,	,	PUNCT
ejpam-6596	406	8	u2	u2	NOUN
ejpam-6596	406	9	,	,	PUNCT
ejpam-6596	406	10	and	and	CCONJ
ejpam-6596	406	11	u3	u3	NOUN
ejpam-6596	406	12	applied	apply	VERB
ejpam-6596	406	13	,	,	PUNCT
ejpam-6596	406	14	trajectories	trajectorie	VERB
ejpam-6596	406	15	n.	n.	PROPN
ejpam-6596	406	16	gul	gul	PROPN
ejpam-6596	406	17	et	et	PROPN
ejpam-6596	406	18	al	al	PROPN
ejpam-6596	406	19	.	.	PUNCT
ejpam-6596	406	20	/	/	SYM
ejpam-6596	406	21	eur	eur	PROPN
ejpam-6596	406	22	.	.	PUNCT
ejpam-6596	407	1	j.	j.	PROPN
ejpam-6596	407	2	pure	pure	PROPN
ejpam-6596	407	3	appl	appl	PROPN
ejpam-6596	407	4	.	.	PROPN
ejpam-6596	407	5	math	math	PROPN
ejpam-6596	407	6	,	,	PUNCT
ejpam-6596	407	7	18	18	NUM
ejpam-6596	407	8	(	(	PUNCT
ejpam-6596	407	9	4	4	NUM
ejpam-6596	407	10	)	)	PUNCT
ejpam-6596	407	11	(	(	PUNCT
ejpam-6596	407	12	2025	2025	NUM
ejpam-6596	407	13	)	)	PUNCT
ejpam-6596	407	14	,	,	PUNCT
ejpam-6596	407	15	6596	6596	NUM
ejpam-6596	407	16	20	20	NUM
ejpam-6596	407	17	of	of	ADP
ejpam-6596	407	18	23	23	NUM
ejpam-6596	407	19	converge	converge	NOUN
ejpam-6596	407	20	toward	toward	ADP
ejpam-6596	407	21	regions	region	NOUN
ejpam-6596	407	22	of	of	ADP
ejpam-6596	407	23	reduced	reduce	VERB
ejpam-6596	407	24	infection	infection	NOUN
ejpam-6596	407	25	density	density	NOUN
ejpam-6596	407	26	,	,	PUNCT
ejpam-6596	407	27	reflecting	reflect	VERB
ejpam-6596	407	28	the	the	DET
ejpam-6596	407	29	efficacy	efficacy	NOUN
ejpam-6596	407	30	of	of	ADP
ejpam-6596	407	31	interventions	intervention	NOUN
ejpam-6596	407	32	in	in	ADP
ejpam-6596	407	33	steering	steer	VERB
ejpam-6596	407	34	the	the	DET
ejpam-6596	407	35	system	system	NOUN
ejpam-6596	407	36	closer	close	ADV
ejpam-6596	407	37	to	to	ADP
ejpam-6596	407	38	the	the	DET
ejpam-6596	407	39	disease	disease	NOUN
ejpam-6596	407	40	-	-	PUNCT
ejpam-6596	407	41	free	free	ADJ
ejpam-6596	407	42	equilibrium	equilibrium	NOUN
ejpam-6596	407	43	.	.	PUNCT
ejpam-6596	408	1	similarly	similarly	ADV
ejpam-6596	408	2	,	,	PUNCT
ejpam-6596	408	3	system	system	NOUN
ejpam-6596	408	4	of	of	ADP
ejpam-6596	408	5	(	(	PUNCT
ejpam-6596	408	6	8)	8)	NUM
ejpam-6596	408	7	also	also	ADV
ejpam-6596	408	8	compares	compare	VERB
ejpam-6596	408	9	the	the	DET
ejpam-6596	408	10	temporal	temporal	ADJ
ejpam-6596	408	11	evolution	evolution	NOUN
ejpam-6596	408	12	of	of	ADP
ejpam-6596	408	13	different	different	ADJ
ejpam-6596	408	14	compartments	compartment	NOUN
ejpam-6596	408	15	,	,	PUNCT
ejpam-6596	408	16	revealing	reveal	VERB
ejpam-6596	408	17	that	that	SCONJ
ejpam-6596	408	18	control	control	NOUN
ejpam-6596	408	19	implementation	implementation	NOUN
ejpam-6596	408	20	suppresses	suppress	VERB
ejpam-6596	408	21	e	e	NOUN
ejpam-6596	408	22	while	while	SCONJ
ejpam-6596	408	23	elevating	elevate	VERB
ejpam-6596	408	24	q	q	ADJ
ejpam-6596	408	25	,	,	PUNCT
ejpam-6596	408	26	consistent	consistent	ADJ
ejpam-6596	408	27	with	with	ADP
ejpam-6596	408	28	enhanced	enhanced	ADJ
ejpam-6596	408	29	quarantine	quarantine	NOUN
ejpam-6596	408	30	efforts	effort	NOUN
ejpam-6596	408	31	.	.	PUNCT
ejpam-6596	409	1	the	the	DET
ejpam-6596	409	2	shrinking	shrinking	NOUN
ejpam-6596	409	3	of	of	ADP
ejpam-6596	409	4	phase	phase	NOUN
ejpam-6596	409	5	space	space	NOUN
ejpam-6596	409	6	near	near	ADP
ejpam-6596	409	7	endemic	endemic	ADJ
ejpam-6596	409	8	states	state	NOUN
ejpam-6596	409	9	under	under	ADP
ejpam-6596	409	10	control	control	NOUN
ejpam-6596	409	11	shows	show	VERB
ejpam-6596	409	12	stable	stable	ADJ
ejpam-6596	409	13	dynamics	dynamic	NOUN
ejpam-6596	409	14	,	,	PUNCT
ejpam-6596	409	15	conforming	conform	VERB
ejpam-6596	409	16	the	the	DET
ejpam-6596	409	17	global	global	ADJ
ejpam-6596	409	18	stability	stability	NOUN
ejpam-6596	409	19	that	that	PRON
ejpam-6596	409	20	has	have	AUX
ejpam-6596	409	21	been	be	AUX
ejpam-6596	409	22	mathematically	mathematically	ADV
ejpam-6596	409	23	proven	prove	VERB
ejpam-6596	409	24	.	.	PUNCT
ejpam-6596	410	1	the	the	DET
ejpam-6596	410	2	visualizations	visualization	NOUN
ejpam-6596	410	3	above	above	ADV
ejpam-6596	410	4	show	show	VERB
ejpam-6596	410	5	how	how	SCONJ
ejpam-6596	410	6	control	control	NOUN
ejpam-6596	410	7	parameters	parameter	NOUN
ejpam-6596	410	8	influence	influence	VERB
ejpam-6596	410	9	the	the	DET
ejpam-6596	410	10	attractors	attractor	NOUN
ejpam-6596	410	11	of	of	ADP
ejpam-6596	410	12	the	the	DET
ejpam-6596	410	13	system	system	NOUN
ejpam-6596	410	14	,	,	PUNCT
ejpam-6596	410	15	proving	prove	VERB
ejpam-6596	410	16	their	their	PRON
ejpam-6596	410	17	role	role	NOUN
ejpam-6596	410	18	in	in	ADP
ejpam-6596	410	19	reducing	reduce	VERB
ejpam-6596	410	20	the	the	DET
ejpam-6596	410	21	severity	severity	NOUN
ejpam-6596	410	22	of	of	ADP
ejpam-6596	410	23	outbreaks	outbreak	NOUN
ejpam-6596	410	24	.	.	PUNCT
ejpam-6596	411	1	the	the	DET
ejpam-6596	411	2	convergence	convergence	NOUN
ejpam-6596	411	3	patterns	pattern	NOUN
ejpam-6596	411	4	we	we	PRON
ejpam-6596	411	5	witness	witness	VERB
ejpam-6596	411	6	confirm	confirm	VERB
ejpam-6596	411	7	the	the	DET
ejpam-6596	411	8	theoretical	theoretical	ADJ
ejpam-6596	411	9	stability	stability	NOUN
ejpam-6596	411	10	criteria	criterion	NOUN
ejpam-6596	411	11	of	of	ADP
ejpam-6596	411	12	r0	r0	NOUN
ejpam-6596	411	13	,	,	PUNCT
ejpam-6596	411	14	showing	show	VERB
ejpam-6596	411	15	that	that	SCONJ
ejpam-6596	411	16	efficient	efficient	ADJ
ejpam-6596	411	17	strategies	strategy	NOUN
ejpam-6596	411	18	can	can	AUX
ejpam-6596	411	19	readily	readily	ADV
ejpam-6596	411	20	break	break	VERB
ejpam-6596	411	21	transmission	transmission	NOUN
ejpam-6596	411	22	networks	network	NOUN
ejpam-6596	411	23	,	,	PUNCT
ejpam-6596	411	24	as	as	SCONJ
ejpam-6596	411	25	testified	testify	VERB
ejpam-6596	411	26	by	by	ADP
ejpam-6596	411	27	fewer	few	ADJ
ejpam-6596	411	28	cycles	cycle	NOUN
ejpam-6596	411	29	and	and	CCONJ
ejpam-6596	411	30	faster	fast	ADJ
ejpam-6596	411	31	stabilization	stabilization	NOUN
ejpam-6596	411	32	.	.	PUNCT
ejpam-6596	412	1	this	this	DET
ejpam-6596	412	2	geometric	geometric	ADJ
ejpam-6596	412	3	analysis	analysis	NOUN
ejpam-6596	412	4	is	be	AUX
ejpam-6596	412	5	corroborated	corroborate	VERB
ejpam-6596	412	6	by	by	ADP
ejpam-6596	412	7	numerical	numerical	ADJ
ejpam-6596	412	8	results	result	NOUN
ejpam-6596	412	9	,	,	PUNCT
ejpam-6596	412	10	providing	provide	VERB
ejpam-6596	412	11	easy	easy	ADJ
ejpam-6596	412	12	-	-	PUNCT
ejpam-6596	412	13	to	to	AUX
ejpam-6596	412	14	-	-	PUNCT
ejpam-6596	412	15	interpret	interpret	VERB
ejpam-6596	412	16	evidence	evidence	NOUN
ejpam-6596	412	17	of	of	ADP
ejpam-6596	412	18	the	the	DET
ejpam-6596	412	19	model	model	NOUN
ejpam-6596	412	20	’s	’s	PART
ejpam-6596	412	21	ability	ability	NOUN
ejpam-6596	412	22	to	to	PART
ejpam-6596	412	23	make	make	VERB
ejpam-6596	412	24	predictions	prediction	NOUN
ejpam-6596	412	25	under	under	ADP
ejpam-6596	412	26	intervention	intervention	NOUN
ejpam-6596	412	27	.	.	PUNCT
ejpam-6596	413	1	0	0	NUM
ejpam-6596	414	1	50	50	NUM
ejpam-6596	414	2	100	100	NUM
ejpam-6596	414	3	150	150	NUM
ejpam-6596	414	4	s	s	NOUN
ejpam-6596	414	5	0	0	NUM
ejpam-6596	414	6	1	1	NUM
ejpam-6596	414	7	2	2	NUM
ejpam-6596	414	8	3	3	NUM
ejpam-6596	414	9	4	4	NUM
ejpam-6596	414	10	5	5	NUM
ejpam-6596	414	11	6	6	NUM
ejpam-6596	414	12	7	7	NUM
ejpam-6596	414	13	e	e	NOUN
ejpam-6596	414	14	s	s	X
ejpam-6596	414	15	vs	vs	ADP
ejpam-6596	414	16	e	e	NOUN
ejpam-6596	414	17	(	(	PUNCT
ejpam-6596	414	18	with	with	ADP
ejpam-6596	414	19	/	/	SYM
ejpam-6596	414	20	without	without	ADP
ejpam-6596	414	21	control	control	NOUN
ejpam-6596	414	22	)	)	PUNCT
ejpam-6596	414	23	without	without	ADP
ejpam-6596	414	24	controlled	control	VERB
ejpam-6596	414	25	with	with	ADP
ejpam-6596	414	26	controlled	control	VERB
ejpam-6596	414	27	equilibrium	equilibrium	NOUN
ejpam-6596	414	28	0	0	NUM
ejpam-6596	414	29	50	50	NUM
ejpam-6596	414	30	100	100	NUM
ejpam-6596	414	31	150	150	NUM
ejpam-6596	414	32	s	s	NOUN
ejpam-6596	414	33	0	0	NUM
ejpam-6596	414	34	0.1	0.1	NUM
ejpam-6596	414	35	0.2	0.2	NUM
ejpam-6596	414	36	0.3	0.3	NUM
ejpam-6596	414	37	0.4	0.4	NUM
ejpam-6596	414	38	0.5	0.5	NUM
ejpam-6596	414	39	0.6	0.6	NUM
ejpam-6596	414	40	0.7	0.7	NUM
ejpam-6596	414	41	0.8	0.8	NUM
ejpam-6596	414	42	0.9	0.9	NUM
ejpam-6596	414	43	1	1	NUM
ejpam-6596	415	1	i	i	PRON
ejpam-6596	415	2	s	s	VERB
ejpam-6596	415	3	vs	vs	ADP
ejpam-6596	415	4	i	i	PRON
ejpam-6596	415	5	(	(	PUNCT
ejpam-6596	415	6	with	with	ADP
ejpam-6596	415	7	/	/	SYM
ejpam-6596	415	8	without	without	ADP
ejpam-6596	415	9	control	control	NOUN
ejpam-6596	415	10	)	)	PUNCT
ejpam-6596	415	11	without	without	ADP
ejpam-6596	415	12	controlled	control	VERB
ejpam-6596	415	13	with	with	ADP
ejpam-6596	415	14	controlled	control	VERB
ejpam-6596	415	15	equilibrium	equilibrium	NOUN
ejpam-6596	415	16	0	0	NUM
ejpam-6596	416	1	50	50	NUM
ejpam-6596	416	2	100	100	NUM
ejpam-6596	416	3	150	150	NUM
ejpam-6596	416	4	s	s	NOUN
ejpam-6596	416	5	0	0	NUM
ejpam-6596	416	6	2	2	NUM
ejpam-6596	416	7	4	4	NUM
ejpam-6596	416	8	6	6	NUM
ejpam-6596	416	9	8	8	NUM
ejpam-6596	416	10	10	10	NUM
ejpam-6596	416	11	12	12	NUM
ejpam-6596	416	12	14	14	NUM
ejpam-6596	416	13	q	q	NOUN
ejpam-6596	416	14	s	s	PROPN
ejpam-6596	416	15	vs	vs	ADP
ejpam-6596	416	16	q	q	X
ejpam-6596	416	17	(	(	PUNCT
ejpam-6596	416	18	with	with	ADP
ejpam-6596	416	19	/	/	SYM
ejpam-6596	416	20	without	without	ADP
ejpam-6596	416	21	control	control	NOUN
ejpam-6596	416	22	)	)	PUNCT
ejpam-6596	416	23	without	without	ADP
ejpam-6596	416	24	controlled	control	VERB
ejpam-6596	416	25	with	with	ADP
ejpam-6596	416	26	controlled	control	VERB
ejpam-6596	416	27	equilibrium	equilibrium	NOUN
ejpam-6596	416	28	0	0	NUM
ejpam-6596	416	29	50	50	NUM
ejpam-6596	416	30	100	100	NUM
ejpam-6596	416	31	150	150	NUM
ejpam-6596	416	32	s	s	NOUN
ejpam-6596	416	33	0	0	NUM
ejpam-6596	416	34	20	20	NUM
ejpam-6596	416	35	40	40	NUM
ejpam-6596	416	36	60	60	NUM
ejpam-6596	416	37	80	80	NUM
ejpam-6596	416	38	100	100	NUM
ejpam-6596	416	39	120	120	NUM
ejpam-6596	416	40	140	140	NUM
ejpam-6596	416	41	r	r	NOUN
ejpam-6596	416	42	s	s	NOUN
ejpam-6596	416	43	vs	vs	ADP
ejpam-6596	416	44	r	r	NOUN
ejpam-6596	416	45	(	(	PUNCT
ejpam-6596	416	46	with	with	ADP
ejpam-6596	416	47	/	/	SYM
ejpam-6596	416	48	without	without	ADP
ejpam-6596	416	49	control	control	NOUN
ejpam-6596	416	50	)	)	PUNCT
ejpam-6596	416	51	without	without	ADP
ejpam-6596	416	52	controlled	control	VERB
ejpam-6596	416	53	with	with	ADP
ejpam-6596	416	54	controlled	control	VERB
ejpam-6596	416	55	equilibrium	equilibrium	NOUN
ejpam-6596	416	56	0	0	NUM
ejpam-6596	417	1	1	1	NUM
ejpam-6596	417	2	2	2	NUM
ejpam-6596	417	3	3	3	NUM
ejpam-6596	417	4	4	4	NUM
ejpam-6596	417	5	5	5	NUM
ejpam-6596	417	6	6	6	NUM
ejpam-6596	417	7	7	7	NUM
ejpam-6596	417	8	e	e	NOUN
ejpam-6596	417	9	0	0	NUM
ejpam-6596	417	10	0.1	0.1	NUM
ejpam-6596	417	11	0.2	0.2	NUM
ejpam-6596	417	12	0.3	0.3	NUM
ejpam-6596	417	13	0.4	0.4	NUM
ejpam-6596	417	14	0.5	0.5	NUM
ejpam-6596	417	15	0.6	0.6	NUM
ejpam-6596	417	16	0.7	0.7	NUM
ejpam-6596	417	17	0.8	0.8	NUM
ejpam-6596	417	18	0.9	0.9	NUM
ejpam-6596	417	19	1	1	NUM
ejpam-6596	417	20	i	i	NOUN
ejpam-6596	417	21	e	e	PROPN
ejpam-6596	417	22	vs	vs	ADP
ejpam-6596	417	23	i	i	PRON
ejpam-6596	417	24	(	(	PUNCT
ejpam-6596	417	25	with	with	ADP
ejpam-6596	417	26	/	/	SYM
ejpam-6596	417	27	without	without	ADP
ejpam-6596	417	28	control	control	NOUN
ejpam-6596	417	29	)	)	PUNCT
ejpam-6596	417	30	without	without	ADP
ejpam-6596	417	31	controlled	control	VERB
ejpam-6596	417	32	with	with	ADP
ejpam-6596	417	33	controlled	control	VERB
ejpam-6596	417	34	equilibrium	equilibrium	NOUN
ejpam-6596	417	35	0	0	NUM
ejpam-6596	417	36	1	1	NUM
ejpam-6596	417	37	2	2	NUM
ejpam-6596	417	38	3	3	NUM
ejpam-6596	417	39	4	4	NUM
ejpam-6596	417	40	5	5	NUM
ejpam-6596	417	41	6	6	NUM
ejpam-6596	417	42	7	7	NUM
ejpam-6596	417	43	e	e	NOUN
ejpam-6596	417	44	0	0	NUM
ejpam-6596	417	45	2	2	NUM
ejpam-6596	417	46	4	4	NUM
ejpam-6596	417	47	6	6	NUM
ejpam-6596	417	48	8	8	NUM
ejpam-6596	417	49	10	10	NUM
ejpam-6596	417	50	12	12	NUM
ejpam-6596	417	51	14	14	NUM
ejpam-6596	417	52	q	q	NOUN
ejpam-6596	417	53	e	e	NOUN
ejpam-6596	417	54	vs	vs	ADP
ejpam-6596	417	55	q	q	X
ejpam-6596	417	56	(	(	PUNCT
ejpam-6596	417	57	with	with	ADP
ejpam-6596	417	58	/	/	SYM
ejpam-6596	417	59	without	without	ADP
ejpam-6596	417	60	control	control	NOUN
ejpam-6596	417	61	)	)	PUNCT
ejpam-6596	417	62	without	without	ADP
ejpam-6596	417	63	controlled	control	VERB
ejpam-6596	417	64	with	with	ADP
ejpam-6596	417	65	controlled	control	VERB
ejpam-6596	417	66	equilibrium	equilibrium	NOUN
ejpam-6596	417	67	0	0	NUM
ejpam-6596	418	1	1	1	NUM
ejpam-6596	418	2	2	2	NUM
ejpam-6596	418	3	3	3	NUM
ejpam-6596	418	4	4	4	NUM
ejpam-6596	418	5	5	5	NUM
ejpam-6596	418	6	6	6	NUM
ejpam-6596	418	7	7	7	NUM
ejpam-6596	418	8	e	e	NOUN
ejpam-6596	418	9	0	0	NUM
ejpam-6596	418	10	20	20	NUM
ejpam-6596	418	11	40	40	NUM
ejpam-6596	418	12	60	60	NUM
ejpam-6596	418	13	80	80	NUM
ejpam-6596	418	14	100	100	NUM
ejpam-6596	418	15	120	120	NUM
ejpam-6596	418	16	140	140	NUM
ejpam-6596	418	17	r	r	NOUN
ejpam-6596	418	18	e	e	NOUN
ejpam-6596	418	19	vs	vs	ADP
ejpam-6596	418	20	r	r	NOUN
ejpam-6596	418	21	(	(	PUNCT
ejpam-6596	418	22	with	with	ADP
ejpam-6596	418	23	/	/	SYM
ejpam-6596	418	24	without	without	ADP
ejpam-6596	418	25	control	control	NOUN
ejpam-6596	418	26	)	)	PUNCT
ejpam-6596	418	27	without	without	ADP
ejpam-6596	418	28	controlled	control	VERB
ejpam-6596	418	29	with	with	ADP
ejpam-6596	418	30	controlled	control	VERB
ejpam-6596	418	31	equilibrium	equilibrium	NOUN
ejpam-6596	418	32	0	0	NUM
ejpam-6596	418	33	0.2	0.2	NUM
ejpam-6596	418	34	0.4	0.4	NUM
ejpam-6596	418	35	0.6	0.6	NUM
ejpam-6596	418	36	0.8	0.8	NUM
ejpam-6596	418	37	1	1	NUM
ejpam-6596	418	38	i	i	NOUN
ejpam-6596	418	39	0	0	NUM
ejpam-6596	418	40	2	2	NUM
ejpam-6596	418	41	4	4	NUM
ejpam-6596	418	42	6	6	NUM
ejpam-6596	418	43	8	8	NUM
ejpam-6596	418	44	10	10	NUM
ejpam-6596	418	45	12	12	NUM
ejpam-6596	418	46	14	14	NUM
ejpam-6596	418	47	q	q	NOUN
ejpam-6596	418	48	i	i	PRON
ejpam-6596	418	49	vs	vs	ADP
ejpam-6596	418	50	q	q	X
ejpam-6596	418	51	(	(	PUNCT
ejpam-6596	418	52	with	with	ADP
ejpam-6596	418	53	/	/	SYM
ejpam-6596	418	54	without	without	ADP
ejpam-6596	418	55	control	control	NOUN
ejpam-6596	418	56	)	)	PUNCT
ejpam-6596	418	57	without	without	ADP
ejpam-6596	418	58	controlled	control	VERB
ejpam-6596	418	59	with	with	ADP
ejpam-6596	418	60	controlled	control	VERB
ejpam-6596	418	61	equilibrium	equilibrium	NOUN
ejpam-6596	418	62	0	0	NUM
ejpam-6596	418	63	0.2	0.2	NUM
ejpam-6596	418	64	0.4	0.4	NUM
ejpam-6596	418	65	0.6	0.6	NUM
ejpam-6596	418	66	0.8	0.8	NUM
ejpam-6596	418	67	1	1	NUM
ejpam-6596	419	1	i	i	NOUN
ejpam-6596	419	2	0	0	NUM
ejpam-6596	419	3	20	20	NUM
ejpam-6596	419	4	40	40	NUM
ejpam-6596	419	5	60	60	NUM
ejpam-6596	419	6	80	80	NUM
ejpam-6596	419	7	100	100	NUM
ejpam-6596	419	8	120	120	NUM
ejpam-6596	419	9	140	140	NUM
ejpam-6596	419	10	r	r	NOUN
ejpam-6596	419	11	i	i	PRON
ejpam-6596	419	12	vs	vs	ADP
ejpam-6596	419	13	r	r	NOUN
ejpam-6596	419	14	(	(	PUNCT
ejpam-6596	419	15	with	with	ADP
ejpam-6596	419	16	/	/	SYM
ejpam-6596	419	17	without	without	ADP
ejpam-6596	419	18	control	control	NOUN
ejpam-6596	419	19	)	)	PUNCT
ejpam-6596	419	20	without	without	ADP
ejpam-6596	419	21	controlled	control	VERB
ejpam-6596	419	22	with	with	ADP
ejpam-6596	419	23	controlled	control	VERB
ejpam-6596	419	24	equilibrium	equilibrium	NOUN
ejpam-6596	419	25	figure	figure	NOUN
ejpam-6596	419	26	7	7	NUM
ejpam-6596	419	27	:	:	PUNCT
ejpam-6596	419	28	phase	phase	NOUN
ejpam-6596	419	29	photrate	photrate	ADJ
ejpam-6596	419	30	system	system	NOUN
ejpam-6596	419	31	n.	n.	PROPN
ejpam-6596	419	32	gul	gul	PROPN
ejpam-6596	419	33	et	et	PROPN
ejpam-6596	419	34	al	al	PROPN
ejpam-6596	419	35	.	.	PUNCT
ejpam-6596	419	36	/	/	SYM
ejpam-6596	419	37	eur	eur	PROPN
ejpam-6596	419	38	.	.	PUNCT
ejpam-6596	420	1	j.	j.	PROPN
ejpam-6596	420	2	pure	pure	PROPN
ejpam-6596	420	3	appl	appl	PROPN
ejpam-6596	420	4	.	.	PROPN
ejpam-6596	420	5	math	math	PROPN
ejpam-6596	420	6	,	,	PUNCT
ejpam-6596	420	7	18	18	NUM
ejpam-6596	420	8	(	(	PUNCT
ejpam-6596	420	9	4	4	NUM
ejpam-6596	420	10	)	)	PUNCT
ejpam-6596	420	11	(	(	PUNCT
ejpam-6596	420	12	2025	2025	NUM
ejpam-6596	420	13	)	)	PUNCT
ejpam-6596	420	14	,	,	PUNCT
ejpam-6596	420	15	6596	6596	NUM
ejpam-6596	420	16	21	21	NUM
ejpam-6596	420	17	of	of	ADP
ejpam-6596	420	18	23	23	NUM
ejpam-6596	420	19	0	0	NUM
ejpam-6596	420	20	2	2	NUM
ejpam-6596	420	21	4	4	NUM
ejpam-6596	420	22	6	6	NUM
ejpam-6596	420	23	8	8	NUM
ejpam-6596	420	24	10	10	NUM
ejpam-6596	420	25	12	12	NUM
ejpam-6596	420	26	14	14	NUM
ejpam-6596	420	27	q	q	NOUN
ejpam-6596	420	28	0	0	NUM
ejpam-6596	420	29	20	20	NUM
ejpam-6596	420	30	40	40	NUM
ejpam-6596	420	31	60	60	NUM
ejpam-6596	420	32	80	80	NUM
ejpam-6596	420	33	100	100	NUM
ejpam-6596	420	34	120	120	NUM
ejpam-6596	420	35	140	140	NUM
ejpam-6596	420	36	r	r	NOUN
ejpam-6596	420	37	q	q	NOUN
ejpam-6596	420	38	vs	vs	ADP
ejpam-6596	420	39	r	r	NOUN
ejpam-6596	420	40	(	(	PUNCT
ejpam-6596	420	41	with	with	ADP
ejpam-6596	420	42	/	/	SYM
ejpam-6596	420	43	without	without	ADP
ejpam-6596	420	44	control	control	NOUN
ejpam-6596	420	45	)	)	PUNCT
ejpam-6596	420	46	without	without	ADP
ejpam-6596	420	47	controlled	control	VERB
ejpam-6596	420	48	with	with	ADP
ejpam-6596	420	49	controlled	control	VERB
ejpam-6596	420	50	equilibrium	equilibrium	NOUN
ejpam-6596	420	51	0	0	NUM
ejpam-6596	420	52	1	1	NUM
ejpam-6596	420	53	2	2	NUM
ejpam-6596	420	54	3	3	NUM
ejpam-6596	420	55	4	4	NUM
ejpam-6596	420	56	5	5	NUM
ejpam-6596	420	57	6	6	NUM
ejpam-6596	420	58	7	7	NUM
ejpam-6596	420	59	e	e	NOUN
ejpam-6596	420	60	0	0	NUM
ejpam-6596	420	61	50	50	NUM
ejpam-6596	420	62	100	100	NUM
ejpam-6596	420	63	150	150	NUM
ejpam-6596	420	64	s	s	NOUN
ejpam-6596	420	65	e	e	NOUN
ejpam-6596	420	66	vs	vs	ADP
ejpam-6596	420	67	s	s	X
ejpam-6596	420	68	(	(	PUNCT
ejpam-6596	420	69	with	with	ADP
ejpam-6596	420	70	/	/	SYM
ejpam-6596	420	71	without	without	ADP
ejpam-6596	420	72	control	control	NOUN
ejpam-6596	420	73	)	)	PUNCT
ejpam-6596	420	74	without	without	ADP
ejpam-6596	420	75	controlled	control	VERB
ejpam-6596	420	76	with	with	ADP
ejpam-6596	420	77	controlled	control	VERB
ejpam-6596	420	78	equilibrium	equilibrium	NOUN
ejpam-6596	420	79	0	0	NUM
ejpam-6596	420	80	0.2	0.2	NUM
ejpam-6596	420	81	0.4	0.4	NUM
ejpam-6596	420	82	0.6	0.6	NUM
ejpam-6596	420	83	0.8	0.8	NUM
ejpam-6596	420	84	1	1	NUM
ejpam-6596	421	1	i	i	NOUN
ejpam-6596	421	2	0	0	NUM
ejpam-6596	421	3	50	50	NUM
ejpam-6596	421	4	100	100	NUM
ejpam-6596	421	5	150	150	NUM
ejpam-6596	421	6	s	s	VERB
ejpam-6596	421	7	i	i	PRON
ejpam-6596	421	8	vs	vs	ADP
ejpam-6596	421	9	s	s	X
ejpam-6596	421	10	(	(	PUNCT
ejpam-6596	421	11	with	with	ADP
ejpam-6596	421	12	/	/	SYM
ejpam-6596	421	13	without	without	ADP
ejpam-6596	421	14	control	control	NOUN
ejpam-6596	421	15	)	)	PUNCT
ejpam-6596	421	16	without	without	ADP
ejpam-6596	421	17	controlled	control	VERB
ejpam-6596	421	18	with	with	ADP
ejpam-6596	421	19	controlled	control	VERB
ejpam-6596	421	20	equilibrium	equilibrium	NOUN
ejpam-6596	421	21	0	0	NUM
ejpam-6596	421	22	2	2	NUM
ejpam-6596	421	23	4	4	NUM
ejpam-6596	421	24	6	6	NUM
ejpam-6596	421	25	8	8	NUM
ejpam-6596	421	26	10	10	NUM
ejpam-6596	421	27	12	12	NUM
ejpam-6596	421	28	14	14	NUM
ejpam-6596	421	29	q	q	NOUN
ejpam-6596	421	30	0	0	NUM
ejpam-6596	421	31	50	50	NUM
ejpam-6596	421	32	100	100	NUM
ejpam-6596	421	33	150	150	NUM
ejpam-6596	421	34	s	s	NOUN
ejpam-6596	421	35	q	q	NOUN
ejpam-6596	421	36	vs	vs	ADP
ejpam-6596	421	37	s	s	X
ejpam-6596	421	38	(	(	PUNCT
ejpam-6596	421	39	with	with	ADP
ejpam-6596	421	40	/	/	SYM
ejpam-6596	421	41	without	without	ADP
ejpam-6596	421	42	control	control	NOUN
ejpam-6596	421	43	)	)	PUNCT
ejpam-6596	421	44	without	without	ADP
ejpam-6596	421	45	controlled	control	VERB
ejpam-6596	421	46	with	with	ADP
ejpam-6596	421	47	controlled	control	VERB
ejpam-6596	421	48	equilibrium	equilibrium	NOUN
ejpam-6596	421	49	0	0	NUM
ejpam-6596	421	50	20	20	NUM
ejpam-6596	421	51	40	40	NUM
ejpam-6596	421	52	60	60	NUM
ejpam-6596	421	53	80	80	NUM
ejpam-6596	421	54	100	100	NUM
ejpam-6596	421	55	120	120	NUM
ejpam-6596	421	56	140	140	NUM
ejpam-6596	421	57	r	r	NOUN
ejpam-6596	421	58	0	0	NUM
ejpam-6596	421	59	50	50	NUM
ejpam-6596	421	60	100	100	NUM
ejpam-6596	421	61	150	150	NUM
ejpam-6596	421	62	s	s	NOUN
ejpam-6596	421	63	r	r	NOUN
ejpam-6596	421	64	vs	vs	ADP
ejpam-6596	421	65	s	s	X
ejpam-6596	421	66	(	(	PUNCT
ejpam-6596	421	67	with	with	ADP
ejpam-6596	421	68	/	/	SYM
ejpam-6596	421	69	without	without	ADP
ejpam-6596	421	70	control	control	NOUN
ejpam-6596	421	71	)	)	PUNCT
ejpam-6596	421	72	without	without	ADP
ejpam-6596	421	73	controlled	control	VERB
ejpam-6596	421	74	with	with	ADP
ejpam-6596	421	75	controlled	control	VERB
ejpam-6596	421	76	equilibrium	equilibrium	NOUN
ejpam-6596	421	77	0	0	NUM
ejpam-6596	421	78	20	20	NUM
ejpam-6596	421	79	40	40	NUM
ejpam-6596	421	80	60	60	NUM
ejpam-6596	421	81	80	80	NUM
ejpam-6596	421	82	100	100	NUM
ejpam-6596	421	83	120	120	NUM
ejpam-6596	421	84	140	140	NUM
ejpam-6596	421	85	r	r	NOUN
ejpam-6596	421	86	0	0	NUM
ejpam-6596	421	87	1	1	NUM
ejpam-6596	421	88	2	2	NUM
ejpam-6596	421	89	3	3	NUM
ejpam-6596	421	90	4	4	NUM
ejpam-6596	421	91	5	5	NUM
ejpam-6596	421	92	6	6	NUM
ejpam-6596	421	93	7	7	NUM
ejpam-6596	421	94	e	e	NOUN
ejpam-6596	421	95	r	r	NOUN
ejpam-6596	421	96	vs	vs	ADP
ejpam-6596	421	97	e	e	NOUN
ejpam-6596	421	98	(	(	PUNCT
ejpam-6596	421	99	with	with	ADP
ejpam-6596	421	100	/	/	SYM
ejpam-6596	421	101	without	without	ADP
ejpam-6596	421	102	control	control	NOUN
ejpam-6596	421	103	)	)	PUNCT
ejpam-6596	421	104	without	without	ADP
ejpam-6596	421	105	controlled	control	VERB
ejpam-6596	421	106	with	with	ADP
ejpam-6596	421	107	controlled	control	VERB
ejpam-6596	421	108	equilibrium	equilibrium	NOUN
ejpam-6596	421	109	0	0	NUM
ejpam-6596	421	110	2	2	NUM
ejpam-6596	421	111	4	4	NUM
ejpam-6596	421	112	6	6	NUM
ejpam-6596	421	113	8	8	NUM
ejpam-6596	421	114	10	10	NUM
ejpam-6596	421	115	12	12	NUM
ejpam-6596	421	116	14	14	NUM
ejpam-6596	421	117	q	q	NOUN
ejpam-6596	421	118	0	0	NUM
ejpam-6596	421	119	0.1	0.1	NUM
ejpam-6596	421	120	0.2	0.2	NUM
ejpam-6596	421	121	0.3	0.3	NUM
ejpam-6596	421	122	0.4	0.4	NUM
ejpam-6596	421	123	0.5	0.5	NUM
ejpam-6596	421	124	0.6	0.6	NUM
ejpam-6596	421	125	0.7	0.7	NUM
ejpam-6596	421	126	0.8	0.8	NUM
ejpam-6596	421	127	0.9	0.9	NUM
ejpam-6596	421	128	1	1	NUM
ejpam-6596	422	1	i	i	PRON
ejpam-6596	423	1	q	q	NOUN
ejpam-6596	424	1	vs	vs	ADP
ejpam-6596	424	2	i	i	PRON
ejpam-6596	424	3	(	(	PUNCT
ejpam-6596	424	4	with	with	ADP
ejpam-6596	424	5	/	/	SYM
ejpam-6596	424	6	without	without	ADP
ejpam-6596	424	7	control	control	NOUN
ejpam-6596	424	8	)	)	PUNCT
ejpam-6596	424	9	without	without	ADP
ejpam-6596	424	10	controlled	control	VERB
ejpam-6596	424	11	with	with	ADP
ejpam-6596	424	12	controlled	control	VERB
ejpam-6596	424	13	equilibrium	equilibrium	NOUN
ejpam-6596	424	14	0	0	NUM
ejpam-6596	424	15	20	20	NUM
ejpam-6596	424	16	40	40	NUM
ejpam-6596	424	17	60	60	NUM
ejpam-6596	424	18	80	80	NUM
ejpam-6596	424	19	100	100	NUM
ejpam-6596	424	20	120	120	NUM
ejpam-6596	424	21	140	140	NUM
ejpam-6596	424	22	r	r	NOUN
ejpam-6596	424	23	0	0	NUM
ejpam-6596	424	24	0.1	0.1	NUM
ejpam-6596	424	25	0.2	0.2	NUM
ejpam-6596	424	26	0.3	0.3	NUM
ejpam-6596	424	27	0.4	0.4	NUM
ejpam-6596	424	28	0.5	0.5	NUM
ejpam-6596	424	29	0.6	0.6	NUM
ejpam-6596	424	30	0.7	0.7	NUM
ejpam-6596	424	31	0.8	0.8	NUM
ejpam-6596	424	32	0.9	0.9	NUM
ejpam-6596	424	33	1	1	NUM
ejpam-6596	425	1	i	i	NOUN
ejpam-6596	425	2	r	r	VERB
ejpam-6596	425	3	vs	vs	ADP
ejpam-6596	425	4	i	i	PRON
ejpam-6596	425	5	(	(	PUNCT
ejpam-6596	425	6	with	with	ADP
ejpam-6596	425	7	/	/	SYM
ejpam-6596	425	8	without	without	ADP
ejpam-6596	425	9	control	control	NOUN
ejpam-6596	425	10	)	)	PUNCT
ejpam-6596	425	11	without	without	ADP
ejpam-6596	425	12	controlled	control	VERB
ejpam-6596	425	13	with	with	ADP
ejpam-6596	425	14	controlled	control	VERB
ejpam-6596	425	15	equilibrium	equilibrium	NOUN
ejpam-6596	425	16	0	0	NUM
ejpam-6596	425	17	20	20	NUM
ejpam-6596	425	18	40	40	NUM
ejpam-6596	425	19	60	60	NUM
ejpam-6596	425	20	80	80	NUM
ejpam-6596	425	21	100	100	NUM
ejpam-6596	425	22	120	120	NUM
ejpam-6596	425	23	140	140	NUM
ejpam-6596	425	24	r	r	NOUN
ejpam-6596	425	25	0	0	NUM
ejpam-6596	425	26	2	2	NUM
ejpam-6596	425	27	4	4	NUM
ejpam-6596	425	28	6	6	NUM
ejpam-6596	425	29	8	8	NUM
ejpam-6596	425	30	10	10	NUM
ejpam-6596	425	31	12	12	NUM
ejpam-6596	425	32	14	14	NUM
ejpam-6596	425	33	q	q	NOUN
ejpam-6596	425	34	r	r	NOUN
ejpam-6596	425	35	vs	vs	ADP
ejpam-6596	425	36	q	q	X
ejpam-6596	425	37	(	(	PUNCT
ejpam-6596	425	38	with	with	ADP
ejpam-6596	425	39	/	/	SYM
ejpam-6596	425	40	without	without	ADP
ejpam-6596	425	41	control	control	NOUN
ejpam-6596	425	42	)	)	PUNCT
ejpam-6596	425	43	without	without	ADP
ejpam-6596	425	44	controlled	control	VERB
ejpam-6596	425	45	with	with	ADP
ejpam-6596	425	46	controlled	control	VERB
ejpam-6596	425	47	equilibrium	equilibrium	NOUN
ejpam-6596	425	48	figure	figure	NOUN
ejpam-6596	425	49	8	8	NUM
ejpam-6596	425	50	:	:	PUNCT
ejpam-6596	425	51	phase	phase	NOUN
ejpam-6596	425	52	photrate	photrate	ADJ
ejpam-6596	425	53	system	system	NOUN
ejpam-6596	425	54	11	11	NUM
ejpam-6596	425	55	.	.	PUNCT
ejpam-6596	426	1	conclusions	conclusion	NOUN
ejpam-6596	426	2	we	we	PRON
ejpam-6596	426	3	examined	examine	VERB
ejpam-6596	426	4	the	the	DET
ejpam-6596	426	5	mathematical	mathematical	ADJ
ejpam-6596	426	6	model	model	NOUN
ejpam-6596	426	7	of	of	ADP
ejpam-6596	426	8	epidemics	epidemic	NOUN
ejpam-6596	426	9	in	in	ADP
ejpam-6596	426	10	this	this	DET
ejpam-6596	426	11	manuscript	manuscript	NOUN
ejpam-6596	426	12	.	.	PUNCT
ejpam-6596	427	1	we	we	PRON
ejpam-6596	427	2	talked	talk	VERB
ejpam-6596	427	3	about	about	ADP
ejpam-6596	427	4	a	a	DET
ejpam-6596	427	5	few	few	ADJ
ejpam-6596	427	6	key	key	ADJ
ejpam-6596	427	7	characteristics	characteristic	NOUN
ejpam-6596	427	8	,	,	PUNCT
ejpam-6596	427	9	such	such	ADJ
ejpam-6596	427	10	as	as	ADP
ejpam-6596	427	11	the	the	DET
ejpam-6596	427	12	investigated	investigated	ADJ
ejpam-6596	427	13	model	model	NOUN
ejpam-6596	427	14	’s	’s	PART
ejpam-6596	427	15	solutions	solution	NOUN
ejpam-6596	427	16	’	'	PUNCT
ejpam-6596	427	17	positivity	positivity	NOUN
ejpam-6596	427	18	and	and	CCONJ
ejpam-6596	427	19	boundedness	boundedness	NOUN
ejpam-6596	427	20	within	within	ADP
ejpam-6596	427	21	a	a	DET
ejpam-6596	427	22	biologically	biologically	ADV
ejpam-6596	427	23	acceptable	acceptable	ADJ
ejpam-6596	427	24	range	range	NOUN
ejpam-6596	427	25	.	.	PUNCT
ejpam-6596	428	1	we	we	PRON
ejpam-6596	428	2	calculated	calculate	VERB
ejpam-6596	428	3	the	the	DET
ejpam-6596	428	4	fundamental	fundamental	ADJ
ejpam-6596	428	5	threshold	threshold	NOUN
ejpam-6596	428	6	number	number	NOUN
ejpam-6596	428	7	r0	r0	NOUN
ejpam-6596	428	8	in	in	ADP
ejpam-6596	428	9	order	order	NOUN
ejpam-6596	428	10	to	to	PART
ejpam-6596	428	11	talk	talk	VERB
ejpam-6596	428	12	about	about	ADP
ejpam-6596	428	13	the	the	DET
ejpam-6596	428	14	stability	stability	NOUN
ejpam-6596	428	15	analysis	analysis	NOUN
ejpam-6596	428	16	of	of	ADP
ejpam-6596	428	17	the	the	DET
ejpam-6596	428	18	potential	potential	ADJ
ejpam-6596	428	19	nontrivial	nontrivial	ADJ
ejpam-6596	428	20	equilibria	equilibrium	NOUN
ejpam-6596	428	21	of	of	ADP
ejpam-6596	428	22	the	the	DET
ejpam-6596	428	23	suggested	suggest	VERB
ejpam-6596	428	24	model	model	NOUN
ejpam-6596	428	25	.	.	PUNCT
ejpam-6596	429	1	this	this	PRON
ejpam-6596	429	2	was	be	AUX
ejpam-6596	429	3	accomplished	accomplish	VERB
ejpam-6596	429	4	by	by	ADP
ejpam-6596	429	5	utilising	utilise	VERB
ejpam-6596	429	6	a	a	DET
ejpam-6596	429	7	well	well	ADV
ejpam-6596	429	8	-	-	PUNCT
ejpam-6596	429	9	known	know	VERB
ejpam-6596	429	10	the	the	DET
ejpam-6596	429	11	next	next	ADJ
ejpam-6596	429	12	-	-	PUNCT
ejpam-6596	429	13	generation	generation	NOUN
ejpam-6596	429	14	techniques	technique	NOUN
ejpam-6596	429	15	for	for	ADP
ejpam-6596	429	16	technology	technology	NOUN
ejpam-6596	429	17	.	.	PUNCT
ejpam-6596	430	1	we	we	PRON
ejpam-6596	430	2	’ve	’ve	AUX
ejpam-6596	430	3	set	set	VERB
ejpam-6596	430	4	criteria	criterion	NOUN
ejpam-6596	430	5	for	for	ADP
ejpam-6596	430	6	both	both	CCONJ
ejpam-6596	430	7	the	the	DET
ejpam-6596	430	8	local	local	ADJ
ejpam-6596	430	9	and	and	CCONJ
ejpam-6596	430	10	global	global	ADJ
ejpam-6596	430	11	stability	stability	NOUN
ejpam-6596	430	12	of	of	ADP
ejpam-6596	430	13	the	the	DET
ejpam-6596	430	14	simulation	simulation	NOUN
ejpam-6596	430	15	under	under	ADP
ejpam-6596	430	16	consideration	consideration	NOUN
ejpam-6596	430	17	’s	’s	PART
ejpam-6596	430	18	no	no	DET
ejpam-6596	430	19	-	-	PUNCT
ejpam-6596	430	20	infection	infection	NOUN
ejpam-6596	430	21	and	and	CCONJ
ejpam-6596	430	22	disease	disease	NOUN
ejpam-6596	430	23	-	-	PUNCT
ejpam-6596	430	24	endemic	endemic	ADJ
ejpam-6596	430	25	states	state	NOUN
ejpam-6596	430	26	.	.	PUNCT
ejpam-6596	431	1	using	use	VERB
ejpam-6596	431	2	the	the	DET
ejpam-6596	431	3	linearization	linearization	NOUN
ejpam-6596	431	4	technique	technique	NOUN
ejpam-6596	431	5	,	,	PUNCT
ejpam-6596	431	6	we	we	PRON
ejpam-6596	431	7	conducted	conduct	VERB
ejpam-6596	431	8	the	the	DET
ejpam-6596	431	9	studies	study	NOUN
ejpam-6596	431	10	of	of	ADP
ejpam-6596	431	11	local	local	ADJ
ejpam-6596	431	12	stability	stability	NOUN
ejpam-6596	431	13	.	.	PUNCT
ejpam-6596	432	1	the	the	DET
ejpam-6596	432	2	castillo	castillo	PROPN
ejpam-6596	432	3	-	-	PUNCT
ejpam-6596	432	4	chavez	chavez	PROPN
ejpam-6596	432	5	approach	approach	NOUN
ejpam-6596	432	6	and	and	CCONJ
ejpam-6596	432	7	geometric	geometric	ADJ
ejpam-6596	432	8	method	method	NOUN
ejpam-6596	432	9	are	be	AUX
ejpam-6596	432	10	used	use	VERB
ejpam-6596	432	11	accordingly	accordingly	ADV
ejpam-6596	432	12	to	to	PART
ejpam-6596	432	13	explore	explore	VERB
ejpam-6596	432	14	the	the	DET
ejpam-6596	432	15	global	global	ADJ
ejpam-6596	432	16	stability	stability	NOUN
ejpam-6596	432	17	assessments	assessment	NOUN
ejpam-6596	432	18	of	of	ADP
ejpam-6596	432	19	a	a	DET
ejpam-6596	432	20	disease	disease	NOUN
ejpam-6596	432	21	-	-	PUNCT
ejpam-6596	432	22	endemic	endemic	ADJ
ejpam-6596	432	23	condition	condition	NOUN
ejpam-6596	432	24	and	and	CCONJ
ejpam-6596	432	25	the	the	DET
ejpam-6596	432	26	no	no	DET
ejpam-6596	432	27	-	-	PUNCT
ejpam-6596	432	28	infection	infection	NOUN
ejpam-6596	432	29	state	state	NOUN
ejpam-6596	432	30	.	.	PUNCT
ejpam-6596	433	1	research	research	NOUN
ejpam-6596	433	2	has	have	AUX
ejpam-6596	433	3	shown	show	VERB
ejpam-6596	433	4	that	that	SCONJ
ejpam-6596	433	5	when	when	SCONJ
ejpam-6596	433	6	the	the	DET
ejpam-6596	433	7	fundamental	fundamental	ADJ
ejpam-6596	433	8	threshold	threshold	NOUN
ejpam-6596	433	9	number	number	NOUN
ejpam-6596	433	10	r0	r0	NOUN
ejpam-6596	433	11	takes	take	VERB
ejpam-6596	433	12	values	value	NOUN
ejpam-6596	433	13	smaller	small	ADJ
ejpam-6596	433	14	or	or	CCONJ
ejpam-6596	433	15	larger	large	ADJ
ejpam-6596	433	16	than	than	ADP
ejpam-6596	433	17	unity	unity	NOUN
ejpam-6596	433	18	,	,	PUNCT
ejpam-6596	433	19	the	the	DET
ejpam-6596	433	20	no	no	DET
ejpam-6596	433	21	-	-	PUNCT
ejpam-6596	433	22	infection	infection	NOUN
ejpam-6596	433	23	(	(	PUNCT
ejpam-6596	433	24	endemic	endemic	ADJ
ejpam-6596	433	25	)	)	PUNCT
ejpam-6596	433	26	condition	condition	NOUN
ejpam-6596	433	27	is	be	AUX
ejpam-6596	433	28	maintained	maintain	VERB
ejpam-6596	433	29	on	on	ADP
ejpam-6596	433	30	a	a	DET
ejpam-6596	433	31	global	global	ADJ
ejpam-6596	433	32	and	and	CCONJ
ejpam-6596	433	33	local	local	ADJ
ejpam-6596	433	34	scale	scale	NOUN
ejpam-6596	433	35	.	.	PUNCT
ejpam-6596	434	1	in	in	ADP
ejpam-6596	434	2	order	order	NOUN
ejpam-6596	434	3	to	to	PART
ejpam-6596	434	4	stop	stop	VERB
ejpam-6596	434	5	a	a	DET
ejpam-6596	434	6	general	general	ADJ
ejpam-6596	434	7	illness	illness	NOUN
ejpam-6596	434	8	infection	infection	NOUN
ejpam-6596	434	9	from	from	ADP
ejpam-6596	434	10	spreading	spread	VERB
ejpam-6596	434	11	,	,	PUNCT
ejpam-6596	434	12	we	we	PRON
ejpam-6596	434	13	include	include	VERB
ejpam-6596	434	14	three	three	NUM
ejpam-6596	434	15	control	control	NOUN
ejpam-6596	434	16	variables	variable	NOUN
ejpam-6596	434	17	:	:	PUNCT
ejpam-6596	434	18	u1(t	u1(t	X
ejpam-6596	434	19	)	)	PUNCT
ejpam-6596	434	20	,	,	PUNCT
ejpam-6596	434	21	which	which	PRON
ejpam-6596	434	22	denote	denote	VERB
ejpam-6596	434	23	the	the	DET
ejpam-6596	434	24	effort	effort	NOUN
ejpam-6596	434	25	that	that	PRON
ejpam-6596	434	26	reduces	reduce	VERB
ejpam-6596	434	27	the	the	DET
ejpam-6596	434	28	contact	contact	NOUN
ejpam-6596	434	29	between	between	ADP
ejpam-6596	434	30	the	the	DET
ejpam-6596	434	31	susceptible	susceptible	ADJ
ejpam-6596	434	32	and	and	CCONJ
ejpam-6596	434	33	infectious	infectious	ADJ
ejpam-6596	434	34	individuals	individual	NOUN
ejpam-6596	434	35	;	;	PUNCT
ejpam-6596	434	36	u2(t	u2(t	NOUN
ejpam-6596	434	37	)	)	PUNCT
ejpam-6596	434	38	,	,	PUNCT
ejpam-6596	434	39	denote	denote	VERB
ejpam-6596	434	40	the	the	DET
ejpam-6596	434	41	rate	rate	NOUN
ejpam-6596	434	42	at	at	ADP
ejpam-6596	434	43	which	which	PRON
ejpam-6596	434	44	infectious	infectious	ADJ
ejpam-6596	434	45	individuals	individual	NOUN
ejpam-6596	434	46	are	be	AUX
ejpam-6596	434	47	treated	treat	VERB
ejpam-6596	434	48	n.	n.	PROPN
ejpam-6596	434	49	gul	gul	PROPN
ejpam-6596	434	50	et	et	PROPN
ejpam-6596	434	51	al	al	PROPN
ejpam-6596	434	52	.	.	PUNCT
ejpam-6596	434	53	/	/	SYM
ejpam-6596	434	54	eur	eur	PROPN
ejpam-6596	434	55	.	.	PUNCT
ejpam-6596	435	1	j.	j.	PROPN
ejpam-6596	435	2	pure	pure	PROPN
ejpam-6596	435	3	appl	appl	PROPN
ejpam-6596	435	4	.	.	PROPN
ejpam-6596	435	5	math	math	PROPN
ejpam-6596	435	6	,	,	PUNCT
ejpam-6596	435	7	18	18	NUM
ejpam-6596	435	8	(	(	PUNCT
ejpam-6596	435	9	4	4	NUM
ejpam-6596	435	10	)	)	PUNCT
ejpam-6596	435	11	(	(	PUNCT
ejpam-6596	435	12	2025	2025	NUM
ejpam-6596	435	13	)	)	PUNCT
ejpam-6596	435	14	,	,	PUNCT
ejpam-6596	435	15	6596	6596	NUM
ejpam-6596	435	16	22	22	NUM
ejpam-6596	435	17	of	of	ADP
ejpam-6596	435	18	23	23	NUM
ejpam-6596	435	19	and	and	CCONJ
ejpam-6596	435	20	u3(t	u3(t	NUM
ejpam-6596	435	21	)	)	PUNCT
ejpam-6596	435	22	,	,	PUNCT
ejpam-6596	435	23	shows	show	VERB
ejpam-6596	435	24	the	the	DET
ejpam-6596	435	25	vaccination	vaccination	NOUN
ejpam-6596	435	26	coverage	coverage	NOUN
ejpam-6596	435	27	.	.	PUNCT
ejpam-6596	436	1	we	we	PRON
ejpam-6596	436	2	numerically	numerically	ADV
ejpam-6596	436	3	solve	solve	VERB
ejpam-6596	436	4	the	the	DET
ejpam-6596	436	5	proposed	propose	VERB
ejpam-6596	436	6	model	model	NOUN
ejpam-6596	436	7	using	use	VERB
ejpam-6596	436	8	the	the	DET
ejpam-6596	436	9	widely	widely	ADV
ejpam-6596	436	10	recognised	recognise	VERB
ejpam-6596	436	11	fourth	fourth	ADJ
ejpam-6596	436	12	order	order	NOUN
ejpam-6596	436	13	runge	runge	NOUN
ejpam-6596	436	14	-	-	PUNCT
ejpam-6596	436	15	kutta	kutta	NOUN
ejpam-6596	436	16	(	(	PUNCT
ejpam-6596	436	17	rk-4	rk-4	NOUN
ejpam-6596	436	18	)	)	PUNCT
ejpam-6596	436	19	approach	approach	NOUN
ejpam-6596	436	20	.	.	PUNCT
ejpam-6596	437	1	our	our	PRON
ejpam-6596	437	2	numerically	numerically	ADV
ejpam-6596	437	3	obtained	obtain	VERB
ejpam-6596	437	4	results	result	NOUN
ejpam-6596	437	5	well	well	ADV
ejpam-6596	437	6	support	support	VERB
ejpam-6596	437	7	the	the	DET
ejpam-6596	437	8	analytical	analytical	ADJ
ejpam-6596	437	9	findings	finding	NOUN
ejpam-6596	437	10	.	.	PUNCT
ejpam-6596	438	1	the	the	DET
ejpam-6596	438	2	phase	phase	NOUN
ejpam-6596	438	3	portrait	portrait	NOUN
ejpam-6596	438	4	analysis	analysis	NOUN
ejpam-6596	438	5	further	far	ADV
ejpam-6596	438	6	demonstrates	demonstrate	VERB
ejpam-6596	438	7	how	how	SCONJ
ejpam-6596	438	8	system	system	NOUN
ejpam-6596	438	9	trajectories	trajectory	NOUN
ejpam-6596	438	10	evolve	evolve	VERB
ejpam-6596	438	11	under	under	ADP
ejpam-6596	438	12	different	different	ADJ
ejpam-6596	438	13	control	control	NOUN
ejpam-6596	438	14	strategies	strategy	NOUN
ejpam-6596	438	15	,	,	PUNCT
ejpam-6596	438	16	visually	visually	ADV
ejpam-6596	438	17	confirming	confirm	VERB
ejpam-6596	438	18	the	the	DET
ejpam-6596	438	19	stabilization	stabilization	NOUN
ejpam-6596	438	20	toward	toward	ADP
ejpam-6596	438	21	disease	disease	NOUN
ejpam-6596	438	22	-	-	PUNCT
ejpam-6596	438	23	free	free	ADJ
ejpam-6596	438	24	equilibrium	equilibrium	NOUN
ejpam-6596	438	25	when	when	SCONJ
ejpam-6596	438	26	interventions	intervention	NOUN
ejpam-6596	438	27	are	be	AUX
ejpam-6596	438	28	applied	apply	VERB
ejpam-6596	438	29	.	.	PUNCT
ejpam-6596	439	1	the	the	DET
ejpam-6596	439	2	current	current	ADJ
ejpam-6596	439	3	work	work	NOUN
ejpam-6596	439	4	may	may	AUX
ejpam-6596	439	5	be	be	AUX
ejpam-6596	439	6	extended	extend	VERB
ejpam-6596	439	7	to	to	ADP
ejpam-6596	439	8	fractional	fractional	ADJ
ejpam-6596	439	9	order	order	NOUN
ejpam-6596	439	10	differential	differential	ADJ
ejpam-6596	439	11	equations	equation	NOUN
ejpam-6596	439	12	and	and	CCONJ
ejpam-6596	439	13	various	various	ADJ
ejpam-6596	439	14	approaches	approach	NOUN
ejpam-6596	439	15	can	can	AUX
ejpam-6596	439	16	be	be	AUX
ejpam-6596	439	17	used	use	VERB
ejpam-6596	439	18	to	to	PART
ejpam-6596	439	19	study	study	VERB
ejpam-6596	439	20	the	the	DET
ejpam-6596	439	21	transmission	transmission	NOUN
ejpam-6596	439	22	dynamics	dynamic	NOUN
ejpam-6596	439	23	of	of	ADP
ejpam-6596	439	24	a	a	DET
ejpam-6596	439	25	general	general	ADJ
ejpam-6596	439	26	infection	infection	NOUN
ejpam-6596	439	27	.	.	PUNCT
ejpam-6596	440	1	work	work	NOUN
ejpam-6596	440	2	on	on	ADP
ejpam-6596	440	3	such	such	ADJ
ejpam-6596	440	4	problems	problem	NOUN
ejpam-6596	440	5	is	be	AUX
ejpam-6596	440	6	under	under	ADP
ejpam-6596	440	7	investigation	investigation	NOUN
ejpam-6596	440	8	and	and	CCONJ
ejpam-6596	440	9	will	will	AUX
ejpam-6596	440	10	be	be	AUX
ejpam-6596	440	11	reported	report	VERB
ejpam-6596	440	12	in	in	ADP
ejpam-6596	440	13	a	a	DET
ejpam-6596	440	14	near	near	ADJ
ejpam-6596	440	15	publication	publication	NOUN
ejpam-6596	440	16	.	.	PUNCT
ejpam-6596	441	1	acknowledgements	acknowledgement	NOUN
ejpam-6596	441	2	manuel	manuel	PROPN
ejpam-6596	441	3	de	de	X
ejpam-6596	441	4	la	la	PROPN
ejpam-6596	441	5	sen	sen	PROPN
ejpam-6596	441	6	is	be	AUX
ejpam-6596	441	7	thankful	thankful	ADJ
ejpam-6596	441	8	to	to	ADP
ejpam-6596	441	9	the	the	DET
ejpam-6596	441	10	basque	basque	ADJ
ejpam-6596	441	11	government	government	NOUN
ejpam-6596	441	12	,	,	PUNCT
ejpam-6596	441	13	grants	grant	VERB
ejpam-6596	441	14	it1555	it1555	NOUN
ejpam-6596	441	15	-	-	PUNCT
ejpam-6596	441	16	22	22	NUM
ejpam-6596	441	17	,	,	PUNCT
ejpam-6596	441	18	for	for	ADP
ejpam-6596	441	19	the	the	DET
ejpam-6596	441	20	financial	financial	ADJ
ejpam-6596	441	21	support	support	NOUN
ejpam-6596	441	22	.	.	PUNCT
ejpam-6596	442	1	references	reference	NOUN
ejpam-6596	442	2	[	[	X
ejpam-6596	442	3	1	1	NUM
ejpam-6596	442	4	]	]	PUNCT
ejpam-6596	442	5	a.	a.	NOUN
ejpam-6596	442	6	omame	omame	NOUN
ejpam-6596	442	7	,	,	PUNCT
ejpam-6596	442	8	h.	h.	PROPN
ejpam-6596	442	9	rwezaura	rwezaura	PROPN
ejpam-6596	442	10	,	,	PUNCT
ejpam-6596	442	11	m.	m.	PROPN
ejpam-6596	442	12	l.	l.	PROPN
ejpam-6596	442	13	diagne	diagne	PROPN
ejpam-6596	442	14	,	,	PUNCT
ejpam-6596	442	15	s.	s.	PROPN
ejpam-6596	442	16	c.	c.	PROPN
ejpam-6596	442	17	inyama	inyama	PROPN
ejpam-6596	442	18	,	,	PUNCT
ejpam-6596	442	19	and	and	CCONJ
ejpam-6596	442	20	j.	j.	PROPN
ejpam-6596	442	21	m.	m.	PROPN
ejpam-6596	442	22	tchuenche	tchuenche	PROPN
ejpam-6596	442	23	.	.	PUNCT
ejpam-6596	443	1	covid19	covid19	NOUN
ejpam-6596	443	2	and	and	CCONJ
ejpam-6596	443	3	dengue	dengue	NOUN
ejpam-6596	443	4	co	co	NOUN
ejpam-6596	443	5	-	-	NOUN
ejpam-6596	443	6	infection	infection	NOUN
ejpam-6596	443	7	in	in	ADP
ejpam-6596	443	8	brazil	brazil	PROPN
ejpam-6596	443	9	:	:	PUNCT
ejpam-6596	443	10	optimal	optimal	ADJ
ejpam-6596	443	11	control	control	NOUN
ejpam-6596	443	12	and	and	CCONJ
ejpam-6596	443	13	cost	cost	NOUN
ejpam-6596	443	14	-	-	PUNCT
ejpam-6596	443	15	effectiveness	effectiveness	NOUN
ejpam-6596	443	16	analysis	analysis	NOUN
ejpam-6596	443	17	.	.	PUNCT
ejpam-6596	444	1	european	european	PROPN
ejpam-6596	444	2	physical	physical	PROPN
ejpam-6596	444	3	journal	journal	PROPN
ejpam-6596	444	4	plus	plus	CCONJ
ejpam-6596	444	5	,	,	PUNCT
ejpam-6596	444	6	136(10):1090	136(10):1090	PROPN
ejpam-6596	444	7	,	,	PUNCT
ejpam-6596	444	8	2021	2021	NUM
ejpam-6596	444	9	.	.	PUNCT
ejpam-6596	445	1	[	[	X
ejpam-6596	445	2	2	2	NUM
ejpam-6596	445	3	]	]	PUNCT
ejpam-6596	445	4	a.	a.	NOUN
ejpam-6596	445	5	abidemi	abidemi	PROPN
ejpam-6596	445	6	,	,	PUNCT
ejpam-6596	445	7	z.	z.	PROPN
ejpam-6596	445	8	m.	m.	PROPN
ejpam-6596	445	9	zainuddin	zainuddin	PROPN
ejpam-6596	445	10	,	,	PUNCT
ejpam-6596	445	11	and	and	CCONJ
ejpam-6596	445	12	n.	n.	PROPN
ejpam-6596	445	13	a.	a.	PROPN
ejpam-6596	445	14	b.	b.	PROPN
ejpam-6596	445	15	aziz	aziz	PROPN
ejpam-6596	445	16	.	.	PUNCT
ejpam-6596	445	17	impact	impact	NOUN
ejpam-6596	445	18	of	of	ADP
ejpam-6596	445	19	control	control	NOUN
ejpam-6596	445	20	interventions	intervention	NOUN
ejpam-6596	445	21	on	on	ADP
ejpam-6596	445	22	covid-19	covid-19	PROPN
ejpam-6596	445	23	population	population	NOUN
ejpam-6596	445	24	dynamics	dynamic	NOUN
ejpam-6596	445	25	in	in	ADP
ejpam-6596	445	26	malaysia	malaysia	PROPN
ejpam-6596	445	27	:	:	PUNCT
ejpam-6596	445	28	a	a	DET
ejpam-6596	445	29	mathematical	mathematical	ADJ
ejpam-6596	445	30	study	study	NOUN
ejpam-6596	445	31	.	.	PUNCT
ejpam-6596	446	1	european	european	PROPN
ejpam-6596	446	2	physical	physical	PROPN
ejpam-6596	446	3	journal	journal	PROPN
ejpam-6596	446	4	plus	plus	CCONJ
ejpam-6596	446	5	,	,	PUNCT
ejpam-6596	446	6	136:1–35	136:1–35	NUM
ejpam-6596	446	7	,	,	PUNCT
ejpam-6596	446	8	2021	2021	NUM
ejpam-6596	446	9	.	.	PUNCT
ejpam-6596	447	1	[	[	X
ejpam-6596	447	2	3	3	X
ejpam-6596	447	3	]	]	PUNCT
ejpam-6596	447	4	k.	k.	PROPN
ejpam-6596	447	5	wang	wang	PROPN
ejpam-6596	447	6	,	,	PUNCT
ejpam-6596	447	7	a.	a.	NOUN
ejpam-6596	447	8	fan	fan	PROPN
ejpam-6596	447	9	,	,	PUNCT
ejpam-6596	447	10	and	and	CCONJ
ejpam-6596	447	11	a.	a.	NOUN
ejpam-6596	447	12	torres	torre	NOUN
ejpam-6596	447	13	.	.	PUNCT
ejpam-6596	448	1	global	global	ADJ
ejpam-6596	448	2	properties	property	NOUN
ejpam-6596	448	3	of	of	ADP
ejpam-6596	448	4	an	an	DET
ejpam-6596	448	5	improved	improved	ADJ
ejpam-6596	448	6	hepatitis	hepatitis	PROPN
ejpam-6596	448	7	b	b	PROPN
ejpam-6596	448	8	virus	virus	NOUN
ejpam-6596	448	9	model	model	NOUN
ejpam-6596	448	10	.	.	PUNCT
ejpam-6596	449	1	nonlinear	nonlinear	ADJ
ejpam-6596	449	2	analysis	analysis	NOUN
ejpam-6596	449	3	:	:	PUNCT
ejpam-6596	449	4	real	real	ADJ
ejpam-6596	449	5	world	world	NOUN
ejpam-6596	449	6	applications	application	NOUN
ejpam-6596	449	7	,	,	PUNCT
ejpam-6596	449	8	11(4):3131–3138	11(4):3131–3138	NUM
ejpam-6596	449	9	,	,	PUNCT
ejpam-6596	449	10	2010	2010	NUM
ejpam-6596	449	11	.	.	PUNCT
ejpam-6596	450	1	[	[	X
ejpam-6596	450	2	4	4	X
ejpam-6596	450	3	]	]	PUNCT
ejpam-6596	450	4	x.	x.	NOUN
ejpam-6596	450	5	liu	liu	PROPN
ejpam-6596	450	6	,	,	PUNCT
ejpam-6596	450	7	m.	m.	PROPN
ejpam-6596	450	8	u.	u.	PROPN
ejpam-6596	450	9	rahman	rahman	PROPN
ejpam-6596	450	10	,	,	PUNCT
ejpam-6596	450	11	s.	s.	PROPN
ejpam-6596	450	12	ahmad	ahmad	PROPN
ejpam-6596	450	13	,	,	PUNCT
ejpam-6596	450	14	d.	d.	PROPN
ejpam-6596	450	15	baleanu	baleanu	PROPN
ejpam-6596	450	16	,	,	PUNCT
ejpam-6596	450	17	and	and	CCONJ
ejpam-6596	450	18	y.	y.	PROPN
ejpam-6596	450	19	n.	n.	PROPN
ejpam-6596	450	20	anjum	anjum	PROPN
ejpam-6596	450	21	.	.	PUNCT
ejpam-6596	451	1	a	a	DET
ejpam-6596	451	2	new	new	ADJ
ejpam-6596	451	3	fractional	fractional	ADJ
ejpam-6596	451	4	infectious	infectious	ADJ
ejpam-6596	451	5	disease	disease	NOUN
ejpam-6596	451	6	model	model	NOUN
ejpam-6596	451	7	under	under	ADP
ejpam-6596	451	8	the	the	DET
ejpam-6596	451	9	non	non	ADJ
ejpam-6596	451	10	-	-	ADJ
ejpam-6596	451	11	singular	singular	ADJ
ejpam-6596	451	12	mittag	mittag	ADJ
ejpam-6596	451	13	–	–	PUNCT
ejpam-6596	451	14	leffler	leffler	NOUN
ejpam-6596	451	15	derivative	derivative	NOUN
ejpam-6596	451	16	.	.	PUNCT
ejpam-6596	452	1	waves	wave	NOUN
ejpam-6596	452	2	in	in	ADP
ejpam-6596	452	3	random	random	ADJ
ejpam-6596	452	4	and	and	CCONJ
ejpam-6596	452	5	complex	complex	ADJ
ejpam-6596	452	6	media	medium	NOUN
ejpam-6596	452	7	,	,	PUNCT
ejpam-6596	452	8	pages	page	NOUN
ejpam-6596	452	9	1–27	1–27	PROPN
ejpam-6596	452	10	,	,	PUNCT
ejpam-6596	452	11	2022	2022	NUM
ejpam-6596	452	12	.	.	PUNCT
ejpam-6596	453	1	[	[	X
ejpam-6596	453	2	5	5	NUM
ejpam-6596	453	3	]	]	PUNCT
ejpam-6596	453	4	m.	m.	NOUN
ejpam-6596	453	5	g.	g.	PROPN
ejpam-6596	453	6	m.	m.	PROPN
ejpam-6596	453	7	gomes	gomes	PROPN
ejpam-6596	453	8	,	,	PUNCT
ejpam-6596	453	9	a.	a.	PROPN
ejpam-6596	453	10	margheri	margheri	PROPN
ejpam-6596	453	11	,	,	PUNCT
ejpam-6596	453	12	g.	g.	PROPN
ejpam-6596	453	13	f.	f.	PROPN
ejpam-6596	453	14	medley	medley	PROPN
ejpam-6596	453	15	,	,	PUNCT
ejpam-6596	453	16	and	and	CCONJ
ejpam-6596	453	17	c.	c.	NOUN
ejpam-6596	453	18	rebelo	rebelo	NOUN
ejpam-6596	453	19	.	.	PUNCT
ejpam-6596	454	1	dynamical	dynamical	ADJ
ejpam-6596	454	2	behaviour	behaviour	NOUN
ejpam-6596	454	3	of	of	ADP
ejpam-6596	454	4	epidemiological	epidemiological	ADJ
ejpam-6596	454	5	models	model	NOUN
ejpam-6596	454	6	with	with	ADP
ejpam-6596	454	7	sub	sub	ADJ
ejpam-6596	454	8	-	-	ADJ
ejpam-6596	454	9	optimal	optimal	ADJ
ejpam-6596	454	10	immunity	immunity	NOUN
ejpam-6596	454	11	and	and	CCONJ
ejpam-6596	454	12	nonlinear	nonlinear	ADJ
ejpam-6596	454	13	incidence	incidence	NOUN
ejpam-6596	454	14	.	.	PUNCT
ejpam-6596	455	1	journal	journal	NOUN
ejpam-6596	455	2	of	of	ADP
ejpam-6596	455	3	mathematical	mathematical	ADJ
ejpam-6596	455	4	biology	biology	NOUN
ejpam-6596	455	5	,	,	PUNCT
ejpam-6596	455	6	51:414–430	51:414–430	PROPN
ejpam-6596	455	7	,	,	PUNCT
ejpam-6596	455	8	2005	2005	NUM
ejpam-6596	455	9	.	.	PUNCT
ejpam-6596	456	1	[	[	X
ejpam-6596	456	2	6	6	NUM
ejpam-6596	456	3	]	]	PUNCT
ejpam-6596	456	4	o.	o.	PROPN
ejpam-6596	456	5	zakary	zakary	PROPN
ejpam-6596	456	6	,	,	PUNCT
ejpam-6596	456	7	m.	m.	NOUN
ejpam-6596	456	8	rachik	rachik	NOUN
ejpam-6596	456	9	,	,	PUNCT
ejpam-6596	456	10	and	and	CCONJ
ejpam-6596	456	11	i.	i.	PROPN
ejpam-6596	456	12	elmouki	elmouki	PROPN
ejpam-6596	456	13	.	.	PUNCT
ejpam-6596	457	1	on	on	ADP
ejpam-6596	457	2	the	the	DET
ejpam-6596	457	3	analysis	analysis	NOUN
ejpam-6596	457	4	of	of	ADP
ejpam-6596	457	5	a	a	DET
ejpam-6596	457	6	multiregions	multiregion	NOUN
ejpam-6596	457	7	discrete	discrete	ADJ
ejpam-6596	457	8	sir	sir	NOUN
ejpam-6596	457	9	epidemic	epidemic	NOUN
ejpam-6596	457	10	model	model	NOUN
ejpam-6596	457	11	:	:	PUNCT
ejpam-6596	457	12	an	an	DET
ejpam-6596	457	13	optimal	optimal	ADJ
ejpam-6596	457	14	control	control	NOUN
ejpam-6596	457	15	approach	approach	NOUN
ejpam-6596	457	16	.	.	PUNCT
ejpam-6596	458	1	international	international	ADJ
ejpam-6596	458	2	journal	journal	PROPN
ejpam-6596	458	3	of	of	ADP
ejpam-6596	458	4	dynamics	dynamic	NOUN
ejpam-6596	458	5	and	and	CCONJ
ejpam-6596	458	6	control	control	NOUN
ejpam-6596	458	7	,	,	PUNCT
ejpam-6596	458	8	5:917–930	5:917–930	NUM
ejpam-6596	458	9	,	,	PUNCT
ejpam-6596	458	10	2017	2017	NUM
ejpam-6596	458	11	.	.	PUNCT
ejpam-6596	459	1	[	[	X
ejpam-6596	459	2	7	7	X
ejpam-6596	459	3	]	]	X
ejpam-6596	459	4	s.	s.	PROPN
ejpam-6596	459	5	ullah	ullah	PROPN
ejpam-6596	459	6	,	,	PUNCT
ejpam-6596	459	7	m.	m.	PROPN
ejpam-6596	459	8	f.	f.	PROPN
ejpam-6596	459	9	khan	khan	PROPN
ejpam-6596	459	10	,	,	PUNCT
ejpam-6596	459	11	s.	s.	PROPN
ejpam-6596	459	12	a.	a.	PROPN
ejpam-6596	459	13	a.	a.	PROPN
ejpam-6596	459	14	shah	shah	PROPN
ejpam-6596	459	15	,	,	PUNCT
ejpam-6596	459	16	m.	m.	NOUN
ejpam-6596	459	17	farooq	farooq	PROPN
ejpam-6596	459	18	,	,	PUNCT
ejpam-6596	459	19	m.	m.	NOUN
ejpam-6596	459	20	a.	a.	PROPN
ejpam-6596	459	21	khan	khan	PROPN
ejpam-6596	459	22	,	,	PUNCT
ejpam-6596	459	23	and	and	CCONJ
ejpam-6596	459	24	m.	m.	PROPN
ejpam-6596	459	25	b.	b.	PROPN
ejpam-6596	459	26	mamat	mamat	PROPN
ejpam-6596	459	27	.	.	PUNCT
ejpam-6596	460	1	optimal	optimal	ADJ
ejpam-6596	460	2	control	control	NOUN
ejpam-6596	460	3	analysis	analysis	NOUN
ejpam-6596	460	4	of	of	ADP
ejpam-6596	460	5	vector	vector	NOUN
ejpam-6596	460	6	-	-	PUNCT
ejpam-6596	460	7	host	host	NOUN
ejpam-6596	460	8	model	model	NOUN
ejpam-6596	460	9	with	with	ADP
ejpam-6596	460	10	saturated	saturate	VERB
ejpam-6596	460	11	treatment	treatment	NOUN
ejpam-6596	460	12	.	.	PUNCT
ejpam-6596	461	1	european	european	PROPN
ejpam-6596	461	2	physical	physical	PROPN
ejpam-6596	461	3	journal	journal	PROPN
ejpam-6596	461	4	plus	plus	CCONJ
ejpam-6596	461	5	,	,	PUNCT
ejpam-6596	461	6	135(10):1–25	135(10):1–25	NUM
ejpam-6596	461	7	,	,	PUNCT
ejpam-6596	461	8	2020	2020	NUM
ejpam-6596	461	9	.	.	PUNCT
ejpam-6596	462	1	[	[	X
ejpam-6596	462	2	8	8	NUM
ejpam-6596	462	3	]	]	X
ejpam-6596	462	4	g.	g.	PROPN
ejpam-6596	462	5	zaman	zaman	PROPN
ejpam-6596	462	6	,	,	PUNCT
ejpam-6596	462	7	y.	y.	PROPN
ejpam-6596	462	8	h.	h.	PROPN
ejpam-6596	462	9	kang	kang	PROPN
ejpam-6596	462	10	,	,	PUNCT
ejpam-6596	462	11	and	and	CCONJ
ejpam-6596	462	12	i.	i.	PROPN
ejpam-6596	462	13	h.	h.	PROPN
ejpam-6596	462	14	jung	jung	PROPN
ejpam-6596	462	15	.	.	PUNCT
ejpam-6596	463	1	stability	stability	NOUN
ejpam-6596	463	2	and	and	CCONJ
ejpam-6596	463	3	optimal	optimal	ADJ
ejpam-6596	463	4	vaccination	vaccination	NOUN
ejpam-6596	463	5	of	of	ADP
ejpam-6596	463	6	an	an	DET
ejpam-6596	463	7	sir	sir	NOUN
ejpam-6596	463	8	epidemic	epidemic	NOUN
ejpam-6596	463	9	model	model	NOUN
ejpam-6596	463	10	.	.	PUNCT
ejpam-6596	464	1	biosystems	biosystems	PROPN
ejpam-6596	464	2	,	,	PUNCT
ejpam-6596	464	3	93:240–249	93:240–249	PROPN
ejpam-6596	464	4	,	,	PUNCT
ejpam-6596	464	5	2008	2008	NUM
ejpam-6596	464	6	.	.	PUNCT
ejpam-6596	465	1	[	[	X
ejpam-6596	465	2	9	9	NUM
ejpam-6596	465	3	]	]	PUNCT
ejpam-6596	465	4	a.	a.	NOUN
ejpam-6596	465	5	v.	v.	PROPN
ejpam-6596	465	6	kamyad	kamyad	PROPN
ejpam-6596	465	7	,	,	PUNCT
ejpam-6596	465	8	r.	r.	PROPN
ejpam-6596	465	9	akbari	akbari	PROPN
ejpam-6596	465	10	,	,	PUNCT
ejpam-6596	465	11	and	and	CCONJ
ejpam-6596	465	12	a.	a.	NOUN
ejpam-6596	465	13	heydari	heydari	NOUN
ejpam-6596	465	14	.	.	PUNCT
ejpam-6596	466	1	mathematical	mathematical	ADJ
ejpam-6596	466	2	modeling	modeling	NOUN
ejpam-6596	466	3	of	of	ADP
ejpam-6596	466	4	transmission	transmission	NOUN
ejpam-6596	466	5	dynamics	dynamic	NOUN
ejpam-6596	466	6	and	and	CCONJ
ejpam-6596	466	7	optimal	optimal	ADJ
ejpam-6596	466	8	control	control	NOUN
ejpam-6596	466	9	of	of	ADP
ejpam-6596	466	10	vaccination	vaccination	NOUN
ejpam-6596	466	11	and	and	CCONJ
ejpam-6596	466	12	treatment	treatment	NOUN
ejpam-6596	466	13	for	for	ADP
ejpam-6596	466	14	hepatitis	hepatitis	PROPN
ejpam-6596	466	15	b	b	PROPN
ejpam-6596	466	16	virus	virus	NOUN
ejpam-6596	466	17	.	.	PUNCT
ejpam-6596	467	1	computational	computational	ADJ
ejpam-6596	467	2	and	and	CCONJ
ejpam-6596	467	3	mathematical	mathematical	ADJ
ejpam-6596	467	4	methods	method	NOUN
ejpam-6596	467	5	in	in	ADP
ejpam-6596	467	6	medicine	medicine	NOUN
ejpam-6596	467	7	,	,	PUNCT
ejpam-6596	467	8	pages	page	NOUN
ejpam-6596	467	9	1–15	1–15	PROPN
ejpam-6596	467	10	,	,	PUNCT
ejpam-6596	467	11	2004	2004	NUM
ejpam-6596	467	12	.	.	PUNCT
ejpam-6596	468	1	[	[	X
ejpam-6596	468	2	10	10	NUM
ejpam-6596	468	3	]	]	X
ejpam-6596	468	4	g.	g.	PROPN
ejpam-6596	468	5	zaman	zaman	PROPN
ejpam-6596	468	6	,	,	PUNCT
ejpam-6596	468	7	y.	y.	PROPN
ejpam-6596	468	8	h.	h.	PROPN
ejpam-6596	468	9	kang	kang	PROPN
ejpam-6596	468	10	,	,	PUNCT
ejpam-6596	468	11	and	and	CCONJ
ejpam-6596	468	12	i.	i.	PROPN
ejpam-6596	468	13	h.	h.	PROPN
ejpam-6596	468	14	jung	jung	PROPN
ejpam-6596	468	15	.	.	PUNCT
ejpam-6596	469	1	optimal	optimal	ADJ
ejpam-6596	469	2	treatment	treatment	NOUN
ejpam-6596	469	3	of	of	ADP
ejpam-6596	469	4	an	an	DET
ejpam-6596	469	5	sir	sir	NOUN
ejpam-6596	469	6	epidemic	epidemic	NOUN
ejpam-6596	469	7	model	model	NOUN
ejpam-6596	469	8	with	with	ADP
ejpam-6596	469	9	time	time	NOUN
ejpam-6596	469	10	delay	delay	NOUN
ejpam-6596	469	11	.	.	PUNCT
ejpam-6596	470	1	biosystems	biosystem	NOUN
ejpam-6596	470	2	,	,	PUNCT
ejpam-6596	470	3	98:43–50	98:43–50	NOUN
ejpam-6596	470	4	,	,	PUNCT
ejpam-6596	470	5	2009	2009	NUM
ejpam-6596	470	6	.	.	PUNCT
ejpam-6596	471	1	n.	n.	PROPN
ejpam-6596	471	2	gul	gul	PROPN
ejpam-6596	471	3	et	et	PROPN
ejpam-6596	471	4	al	al	PROPN
ejpam-6596	471	5	.	.	PUNCT
ejpam-6596	471	6	/	/	SYM
ejpam-6596	471	7	eur	eur	PROPN
ejpam-6596	471	8	.	.	PUNCT
ejpam-6596	472	1	j.	j.	PROPN
ejpam-6596	472	2	pure	pure	PROPN
ejpam-6596	472	3	appl	appl	PROPN
ejpam-6596	472	4	.	.	PROPN
ejpam-6596	472	5	math	math	PROPN
ejpam-6596	472	6	,	,	PUNCT
ejpam-6596	472	7	18	18	NUM
ejpam-6596	472	8	(	(	PUNCT
ejpam-6596	472	9	4	4	NUM
ejpam-6596	472	10	)	)	PUNCT
ejpam-6596	472	11	(	(	PUNCT
ejpam-6596	472	12	2025	2025	NUM
ejpam-6596	472	13	)	)	PUNCT
ejpam-6596	472	14	,	,	PUNCT
ejpam-6596	472	15	6596	6596	NUM
ejpam-6596	472	16	23	23	NUM
ejpam-6596	472	17	of	of	ADP
ejpam-6596	472	18	23	23	NUM
ejpam-6596	473	1	[	[	SYM
ejpam-6596	473	2	11	11	NUM
ejpam-6596	473	3	]	]	PUNCT
ejpam-6596	473	4	i.	i.	NOUN
ejpam-6596	473	5	shah	shah	PROPN
ejpam-6596	473	6	,	,	PUNCT
ejpam-6596	473	7	h.	h.	PROPN
ejpam-6596	473	8	alrabaiah	alrabaiah	PROPN
ejpam-6596	473	9	,	,	PUNCT
ejpam-6596	473	10	and	and	CCONJ
ejpam-6596	473	11	b.	b.	PROPN
ejpam-6596	473	12	ozdemir	ozdemir	PROPN
ejpam-6596	473	13	.	.	PUNCT
ejpam-6596	474	1	using	use	VERB
ejpam-6596	474	2	advanced	advanced	ADJ
ejpam-6596	474	3	analysis	analysis	NOUN
ejpam-6596	474	4	together	together	ADV
ejpam-6596	474	5	with	with	ADP
ejpam-6596	474	6	fractional	fractional	ADJ
ejpam-6596	474	7	order	order	NOUN
ejpam-6596	474	8	derivative	derivative	NOUN
ejpam-6596	474	9	to	to	PART
ejpam-6596	474	10	investigate	investigate	VERB
ejpam-6596	474	11	a	a	DET
ejpam-6596	474	12	smoking	smoking	NOUN
ejpam-6596	474	13	tobacco	tobacco	NOUN
ejpam-6596	474	14	cancer	cancer	NOUN
ejpam-6596	474	15	model	model	NOUN
ejpam-6596	474	16	.	.	PUNCT
ejpam-6596	475	1	results	result	NOUN
ejpam-6596	475	2	in	in	ADP
ejpam-6596	475	3	physics	physics	NOUN
ejpam-6596	475	4	,	,	PUNCT
ejpam-6596	475	5	51:106700	51:106700	NUM
ejpam-6596	475	6	,	,	PUNCT
ejpam-6596	475	7	2023	2023	NUM
ejpam-6596	475	8	.	.	PUNCT
ejpam-6596	476	1	[	[	X
ejpam-6596	476	2	12	12	NUM
ejpam-6596	476	3	]	]	PUNCT
ejpam-6596	476	4	s.	s.	PROPN
ejpam-6596	476	5	ahmad	ahmad	PROPN
ejpam-6596	476	6	,	,	PUNCT
ejpam-6596	476	7	n.	n.	PROPN
ejpam-6596	476	8	ahmad	ahmad	PROPN
ejpam-6596	476	9	,	,	PUNCT
ejpam-6596	476	10	and	and	CCONJ
ejpam-6596	476	11	i.	i.	PROPN
ejpam-6596	476	12	shah	shah	PROPN
ejpam-6596	476	13	.	.	PUNCT
ejpam-6596	477	1	stability	stability	NOUN
ejpam-6596	477	2	and	and	CCONJ
ejpam-6596	477	3	sensitivity	sensitivity	NOUN
ejpam-6596	477	4	analysis	analysis	NOUN
ejpam-6596	477	5	of	of	ADP
ejpam-6596	477	6	cyberattack	cyberattack	NOUN
ejpam-6596	477	7	propagation	propagation	NOUN
ejpam-6596	477	8	models	model	NOUN
ejpam-6596	477	9	in	in	ADP
ejpam-6596	477	10	computer	computer	NOUN
ejpam-6596	477	11	networks	network	NOUN
ejpam-6596	477	12	.	.	PUNCT
ejpam-6596	478	1	european	european	ADJ
ejpam-6596	478	2	journal	journal	PROPN
ejpam-6596	478	3	of	of	ADP
ejpam-6596	478	4	pure	pure	ADJ
ejpam-6596	478	5	and	and	CCONJ
ejpam-6596	478	6	applied	applied	ADJ
ejpam-6596	478	7	mathematics	mathematic	NOUN
ejpam-6596	478	8	,	,	PUNCT
ejpam-6596	478	9	18(3):6336	18(3):6336	NUM
ejpam-6596	478	10	,	,	PUNCT
ejpam-6596	478	11	2025	2025	NUM
ejpam-6596	478	12	.	.	PUNCT
ejpam-6596	479	1	[	[	X
ejpam-6596	479	2	13	13	NUM
ejpam-6596	479	3	]	]	SYM
ejpam-6596	479	4	i.	i.	NOUN
ejpam-6596	479	5	shah	shah	PROPN
ejpam-6596	479	6	,	,	PUNCT
ejpam-6596	479	7	i.	i.	PROPN
ejpam-6596	479	8	ali	ali	PROPN
ejpam-6596	479	9	,	,	PUNCT
ejpam-6596	479	10	a.	a.	PROPN
ejpam-6596	479	11	ali	ali	PROPN
ejpam-6596	479	12	,	,	PUNCT
ejpam-6596	479	13	i.	i.	PROPN
ejpam-6596	479	14	ahmad	ahmad	PROPN
ejpam-6596	479	15	,	,	PUNCT
ejpam-6596	479	16	s.	s.	PROPN
ejpam-6596	479	17	islam	islam	PROPN
ejpam-6596	479	18	,	,	PUNCT
ejpam-6596	479	19	g.	g.	PROPN
ejpam-6596	479	20	rasool	rasool	PROPN
ejpam-6596	479	21	,	,	PUNCT
ejpam-6596	479	22	s.	s.	PROPN
ejpam-6596	479	23	formanova	formanova	PROPN
ejpam-6596	479	24	,	,	PUNCT
ejpam-6596	479	25	and	and	CCONJ
ejpam-6596	479	26	m.	m.	NOUN
ejpam-6596	479	27	kallel	kallel	NOUN
ejpam-6596	479	28	.	.	PUNCT
ejpam-6596	480	1	optimal	optimal	ADJ
ejpam-6596	480	2	control	control	NOUN
ejpam-6596	480	3	and	and	CCONJ
ejpam-6596	480	4	sensitivity	sensitivity	NOUN
ejpam-6596	480	5	analysis	analysis	NOUN
ejpam-6596	480	6	of	of	ADP
ejpam-6596	480	7	a	a	DET
ejpam-6596	480	8	mathematical	mathematical	ADJ
ejpam-6596	480	9	model	model	NOUN
ejpam-6596	480	10	for	for	ADP
ejpam-6596	480	11	mdr	mdr	PROPN
ejpam-6596	480	12	-	-	PROPN
ejpam-6596	480	13	tb	tb	ADP
ejpam-6596	480	14	transmission	transmission	NOUN
ejpam-6596	480	15	with	with	ADP
ejpam-6596	480	16	advanced	advanced	ADJ
ejpam-6596	480	17	treatment	treatment	NOUN
ejpam-6596	480	18	strategies	strategy	NOUN
ejpam-6596	480	19	.	.	PUNCT
ejpam-6596	481	1	european	european	PROPN
ejpam-6596	481	2	physical	physical	PROPN
ejpam-6596	481	3	journal	journal	PROPN
ejpam-6596	481	4	plus	plus	CCONJ
ejpam-6596	481	5	,	,	PUNCT
ejpam-6596	481	6	140(6):1	140(6):1	X
ejpam-6596	481	7	–	–	PUNCT
ejpam-6596	481	8	15	15	NUM
ejpam-6596	481	9	,	,	PUNCT
ejpam-6596	481	10	2025	2025	NUM
ejpam-6596	481	11	.	.	PUNCT
ejpam-6596	482	1	[	[	X
ejpam-6596	482	2	14	14	NUM
ejpam-6596	482	3	]	]	X
ejpam-6596	482	4	i.	i.	PROPN
ejpam-6596	482	5	ullah	ullah	PROPN
ejpam-6596	482	6	,	,	PUNCT
ejpam-6596	482	7	s.	s.	PROPN
ejpam-6596	482	8	ahmad	ahmad	PROPN
ejpam-6596	482	9	,	,	PUNCT
ejpam-6596	482	10	m.	m.	NOUN
ejpam-6596	482	11	arfan	arfan	NOUN
ejpam-6596	482	12	,	,	PUNCT
ejpam-6596	482	13	and	and	CCONJ
ejpam-6596	482	14	m.	m.	PROPN
ejpam-6596	482	15	de	de	PROPN
ejpam-6596	482	16	la	la	PROPN
ejpam-6596	482	17	sen	sen	PROPN
ejpam-6596	482	18	.	.	PROPN
ejpam-6596	482	19	investigation	investigation	NOUN
ejpam-6596	482	20	of	of	ADP
ejpam-6596	482	21	fractional	fractional	ADJ
ejpam-6596	482	22	order	order	NOUN
ejpam-6596	482	23	dynamics	dynamic	NOUN
ejpam-6596	482	24	of	of	ADP
ejpam-6596	482	25	tuberculosis	tuberculosis	NOUN
ejpam-6596	482	26	under	under	ADP
ejpam-6596	482	27	caputo	caputo	PROPN
ejpam-6596	482	28	operator	operator	NOUN
ejpam-6596	482	29	.	.	PUNCT
ejpam-6596	483	1	fractal	fractal	PROPN
ejpam-6596	483	2	and	and	CCONJ
ejpam-6596	483	3	fractional	fractional	ADJ
ejpam-6596	483	4	,	,	PUNCT
ejpam-6596	483	5	7(4):300	7(4):300	NUM
ejpam-6596	483	6	,	,	PUNCT
ejpam-6596	483	7	2023	2023	NUM
ejpam-6596	483	8	.	.	PUNCT
ejpam-6596	484	1	[	[	X
ejpam-6596	484	2	15	15	NUM
ejpam-6596	484	3	]	]	X
ejpam-6596	484	4	h.	h.	PROPN
ejpam-6596	484	5	inaba	inaba	PROPN
ejpam-6596	484	6	.	.	PUNCT
ejpam-6596	485	1	mathematical	mathematical	ADJ
ejpam-6596	485	2	analysis	analysis	NOUN
ejpam-6596	485	3	of	of	ADP
ejpam-6596	485	4	an	an	DET
ejpam-6596	485	5	age	age	NOUN
ejpam-6596	485	6	-	-	PUNCT
ejpam-6596	485	7	structured	structure	VERB
ejpam-6596	485	8	sir	sir	NOUN
ejpam-6596	485	9	epidemic	epidemic	NOUN
ejpam-6596	485	10	model	model	NOUN
ejpam-6596	485	11	with	with	ADP
ejpam-6596	485	12	vertical	vertical	ADJ
ejpam-6596	485	13	transmission	transmission	NOUN
ejpam-6596	485	14	.	.	PUNCT
ejpam-6596	486	1	discrete	discrete	ADJ
ejpam-6596	486	2	and	and	CCONJ
ejpam-6596	486	3	continuous	continuous	ADJ
ejpam-6596	486	4	dynamical	dynamical	ADJ
ejpam-6596	486	5	systems	system	NOUN
ejpam-6596	486	6	series	series	PROPN
ejpam-6596	486	7	b	b	PROPN
ejpam-6596	486	8	,	,	PUNCT
ejpam-6596	486	9	6:69	6:69	NUM
ejpam-6596	486	10	,	,	PUNCT
ejpam-6596	486	11	2006	2006	NUM
ejpam-6596	486	12	.	.	PUNCT
ejpam-6596	487	1	[	[	X
ejpam-6596	487	2	16	16	NUM
ejpam-6596	487	3	]	]	PUNCT
ejpam-6596	487	4	x.	x.	NOUN
ejpam-6596	487	5	liu	liu	PROPN
ejpam-6596	487	6	and	and	CCONJ
ejpam-6596	487	7	l.	l.	PROPN
ejpam-6596	487	8	yang	yang	PROPN
ejpam-6596	487	9	.	.	PUNCT
ejpam-6596	488	1	stability	stability	NOUN
ejpam-6596	488	2	analysis	analysis	NOUN
ejpam-6596	488	3	of	of	ADP
ejpam-6596	488	4	an	an	DET
ejpam-6596	488	5	seiqv	seiqv	ADJ
ejpam-6596	488	6	epidemic	epidemic	NOUN
ejpam-6596	488	7	model	model	NOUN
ejpam-6596	488	8	with	with	ADP
ejpam-6596	488	9	saturated	saturate	VERB
ejpam-6596	488	10	incidence	incidence	NOUN
ejpam-6596	488	11	rate	rate	NOUN
ejpam-6596	488	12	.	.	PUNCT
ejpam-6596	489	1	nonlinear	nonlinear	ADJ
ejpam-6596	489	2	analysis	analysis	NOUN
ejpam-6596	489	3	:	:	PUNCT
ejpam-6596	489	4	real	real	ADJ
ejpam-6596	489	5	world	world	NOUN
ejpam-6596	489	6	applications	application	NOUN
ejpam-6596	489	7	,	,	PUNCT
ejpam-6596	489	8	13(6):2671–2679	13(6):2671–2679	NUM
ejpam-6596	489	9	,	,	PUNCT
ejpam-6596	489	10	2012	2012	NUM
ejpam-6596	489	11	.	.	PUNCT
ejpam-6596	490	1	[	[	X
ejpam-6596	490	2	17	17	NUM
ejpam-6596	490	3	]	]	X
ejpam-6596	490	4	l.	l.	PROPN
ejpam-6596	490	5	esteva	esteva	PROPN
ejpam-6596	490	6	and	and	CCONJ
ejpam-6596	490	7	m.	m.	PROPN
ejpam-6596	490	8	matias	matias	PROPN
ejpam-6596	490	9	.	.	PUNCT
ejpam-6596	491	1	a	a	DET
ejpam-6596	491	2	model	model	NOUN
ejpam-6596	491	3	for	for	ADP
ejpam-6596	491	4	vector	vector	NOUN
ejpam-6596	491	5	transmitted	transmit	VERB
ejpam-6596	491	6	diseases	disease	NOUN
ejpam-6596	491	7	with	with	ADP
ejpam-6596	491	8	saturation	saturation	NOUN
ejpam-6596	491	9	incidence	incidence	NOUN
ejpam-6596	491	10	.	.	PUNCT
ejpam-6596	492	1	journal	journal	NOUN
ejpam-6596	492	2	of	of	ADP
ejpam-6596	492	3	biological	biological	ADJ
ejpam-6596	492	4	systems	system	NOUN
ejpam-6596	492	5	,	,	PUNCT
ejpam-6596	492	6	9(4):235–245	9(4):235–245	NUM
ejpam-6596	492	7	,	,	PUNCT
ejpam-6596	492	8	2001	2001	NUM
ejpam-6596	492	9	.	.	PUNCT
ejpam-6596	493	1	[	[	X
ejpam-6596	493	2	18	18	NUM
ejpam-6596	493	3	]	]	X
ejpam-6596	493	4	s.	s.	PROPN
ejpam-6596	493	5	r.	r.	PROPN
ejpam-6596	493	6	chawla	chawla	PROPN
ejpam-6596	493	7	,	,	PUNCT
ejpam-6596	493	8	s.	s.	PROPN
ejpam-6596	493	9	ahmad	ahmad	PROPN
ejpam-6596	493	10	,	,	PUNCT
ejpam-6596	493	11	and	and	CCONJ
ejpam-6596	493	12	a.	a.	PROPN
ejpam-6596	493	13	khan	khan	PROPN
ejpam-6596	493	14	.	.	PUNCT
ejpam-6596	494	1	sensitivity	sensitivity	NOUN
ejpam-6596	494	2	and	and	CCONJ
ejpam-6596	494	3	bifurcation	bifurcation	NOUN
ejpam-6596	494	4	analysis	analysis	NOUN
ejpam-6596	494	5	of	of	ADP
ejpam-6596	494	6	pine	pine	ADJ
ejpam-6596	494	7	wilt	wilt	ADJ
ejpam-6596	494	8	disease	disease	NOUN
ejpam-6596	494	9	with	with	ADP
ejpam-6596	494	10	harmonic	harmonic	ADJ
ejpam-6596	494	11	mean	mean	NOUN
ejpam-6596	494	12	type	type	NOUN
ejpam-6596	494	13	incidence	incidence	NOUN
ejpam-6596	494	14	rate	rate	NOUN
ejpam-6596	494	15	.	.	PUNCT
ejpam-6596	495	1	physica	physica	PROPN
ejpam-6596	495	2	scripta	scripta	PROPN
ejpam-6596	495	3	,	,	PUNCT
ejpam-6596	495	4	97(5):055006	97(5):055006	NUM
ejpam-6596	495	5	,	,	PUNCT
ejpam-6596	495	6	2022	2022	NUM
ejpam-6596	495	7	.	.	PUNCT
ejpam-6596	496	1	[	[	X
ejpam-6596	496	2	19	19	NUM
ejpam-6596	496	3	]	]	PUNCT
ejpam-6596	496	4	a.	a.	NOUN
ejpam-6596	496	5	korobeinikov	korobeinikov	NOUN
ejpam-6596	496	6	and	and	CCONJ
ejpam-6596	496	7	p.	p.	PROPN
ejpam-6596	496	8	k.	k.	PROPN
ejpam-6596	497	1	maini	maini	PROPN
ejpam-6596	497	2	.	.	PUNCT
ejpam-6596	498	1	non	non	ADJ
ejpam-6596	498	2	-	-	ADJ
ejpam-6596	498	3	linear	linear	ADJ
ejpam-6596	498	4	incidence	incidence	NOUN
ejpam-6596	498	5	and	and	CCONJ
ejpam-6596	498	6	stability	stability	NOUN
ejpam-6596	498	7	of	of	ADP
ejpam-6596	498	8	infectious	infectious	ADJ
ejpam-6596	498	9	disease	disease	NOUN
ejpam-6596	498	10	models	model	NOUN
ejpam-6596	498	11	.	.	PUNCT
ejpam-6596	499	1	mathematical	mathematical	ADJ
ejpam-6596	499	2	medicine	medicine	NOUN
ejpam-6596	499	3	and	and	CCONJ
ejpam-6596	499	4	biology	biology	NOUN
ejpam-6596	499	5	,	,	PUNCT
ejpam-6596	499	6	22(2):113–128	22(2):113–128	NOUN
ejpam-6596	499	7	,	,	PUNCT
ejpam-6596	499	8	2005	2005	NUM
ejpam-6596	499	9	.	.	PUNCT
ejpam-6596	500	1	[	[	X
ejpam-6596	500	2	20	20	NUM
ejpam-6596	500	3	]	]	PUNCT
ejpam-6596	500	4	m.	m.	PROPN
ejpam-6596	500	5	d.	d.	PROPN
ejpam-6596	500	6	samsuzzoha	samsuzzoha	PROPN
ejpam-6596	500	7	,	,	PUNCT
ejpam-6596	500	8	m.	m.	NOUN
ejpam-6596	500	9	singh	singh	PROPN
ejpam-6596	500	10	,	,	PUNCT
ejpam-6596	500	11	and	and	CCONJ
ejpam-6596	500	12	d.	d.	PROPN
ejpam-6596	500	13	lucy	lucy	PROPN
ejpam-6596	500	14	.	.	PUNCT
ejpam-6596	501	1	uncertainty	uncertainty	NOUN
ejpam-6596	501	2	and	and	CCONJ
ejpam-6596	501	3	sensitivity	sensitivity	NOUN
ejpam-6596	501	4	analysis	analysis	NOUN
ejpam-6596	501	5	of	of	ADP
ejpam-6596	501	6	the	the	DET
ejpam-6596	501	7	basic	basic	ADJ
ejpam-6596	501	8	reproduction	reproduction	NOUN
ejpam-6596	501	9	number	number	NOUN
ejpam-6596	501	10	of	of	ADP
ejpam-6596	501	11	a	a	DET
ejpam-6596	501	12	vaccinated	vaccinated	ADJ
ejpam-6596	501	13	epidemic	epidemic	NOUN
ejpam-6596	501	14	model	model	NOUN
ejpam-6596	501	15	of	of	ADP
ejpam-6596	501	16	influenza	influenza	NOUN
ejpam-6596	501	17	.	.	PUNCT
ejpam-6596	502	1	applied	apply	VERB
ejpam-6596	502	2	mathematical	mathematical	ADJ
ejpam-6596	502	3	modelling	modelling	NOUN
ejpam-6596	502	4	,	,	PUNCT
ejpam-6596	502	5	37(3):903–915	37(3):903–915	PROPN
ejpam-6596	502	6	,	,	PUNCT
ejpam-6596	502	7	2013	2013	NUM
ejpam-6596	502	8	.	.	PUNCT
ejpam-6596	503	1	[	[	X
ejpam-6596	503	2	21	21	NUM
ejpam-6596	503	3	]	]	X
ejpam-6596	503	4	h.	h.	PROPN
ejpam-6596	503	5	s.	s.	PROPN
ejpam-6596	503	6	rodrigues	rodrigues	PROPN
ejpam-6596	503	7	,	,	PUNCT
ejpam-6596	503	8	m.	m.	NOUN
ejpam-6596	503	9	t.	t.	PROPN
ejpam-6596	503	10	t.	t.	PROPN
ejpam-6596	503	11	monteiro	monteiro	PROPN
ejpam-6596	503	12	,	,	PUNCT
ejpam-6596	503	13	and	and	CCONJ
ejpam-6596	503	14	d.	d.	PROPN
ejpam-6596	503	15	f.	f.	PROPN
ejpam-6596	503	16	m.	m.	PROPN
ejpam-6596	503	17	torres	torres	PROPN
ejpam-6596	503	18	.	.	PUNCT
ejpam-6596	504	1	seasonality	seasonality	NOUN
ejpam-6596	504	2	effects	effect	NOUN
ejpam-6596	504	3	on	on	ADP
ejpam-6596	504	4	dengue	dengue	NOUN
ejpam-6596	504	5	:	:	PUNCT
ejpam-6596	504	6	basic	basic	ADJ
ejpam-6596	504	7	reproduction	reproduction	NOUN
ejpam-6596	504	8	number	number	NOUN
ejpam-6596	504	9	,	,	PUNCT
ejpam-6596	504	10	sensitivity	sensitivity	NOUN
ejpam-6596	504	11	analysis	analysis	NOUN
ejpam-6596	504	12	and	and	CCONJ
ejpam-6596	504	13	optimal	optimal	ADJ
ejpam-6596	504	14	control	control	NOUN
ejpam-6596	504	15	.	.	PUNCT
ejpam-6596	505	1	mathematical	mathematical	ADJ
ejpam-6596	505	2	methods	method	NOUN
ejpam-6596	505	3	in	in	ADP
ejpam-6596	505	4	the	the	DET
ejpam-6596	505	5	applied	apply	VERB
ejpam-6596	505	6	sciences	science	NOUN
ejpam-6596	505	7	,	,	PUNCT
ejpam-6596	505	8	39(16):4671–4679	39(16):4671–4679	NUM
ejpam-6596	505	9	,	,	PUNCT
ejpam-6596	505	10	2016	2016	NUM
ejpam-6596	505	11	.	.	PUNCT
ejpam-6596	506	1	[	[	X
ejpam-6596	506	2	22	22	NUM
ejpam-6596	506	3	]	]	PUNCT
ejpam-6596	506	4	v.	v.	CCONJ
ejpam-6596	506	5	capasso	capasso	PROPN
ejpam-6596	506	6	and	and	CCONJ
ejpam-6596	506	7	g.	g.	PROPN
ejpam-6596	506	8	serio	serio	PROPN
ejpam-6596	506	9	.	.	PUNCT
ejpam-6596	507	1	a	a	DET
ejpam-6596	507	2	generalization	generalization	NOUN
ejpam-6596	507	3	of	of	ADP
ejpam-6596	507	4	the	the	DET
ejpam-6596	507	5	kermack	kermack	NOUN
ejpam-6596	507	6	-	-	PUNCT
ejpam-6596	507	7	mckendrick	mckendrick	NOUN
ejpam-6596	507	8	deterministic	deterministic	ADJ
ejpam-6596	507	9	epidemic	epidemic	NOUN
ejpam-6596	507	10	model	model	NOUN
ejpam-6596	507	11	.	.	PUNCT
ejpam-6596	508	1	mathematical	mathematical	ADJ
ejpam-6596	508	2	biosciences	bioscience	NOUN
ejpam-6596	508	3	,	,	PUNCT
ejpam-6596	508	4	42(1	42(1	NOUN
ejpam-6596	508	5	-	-	PUNCT
ejpam-6596	508	6	2):43–61	2):43–61	NUM
ejpam-6596	508	7	,	,	PUNCT
ejpam-6596	508	8	1978	1978	NUM
ejpam-6596	508	9	.	.	PUNCT
ejpam-6596	509	1	[	[	X
ejpam-6596	509	2	23	23	NUM
ejpam-6596	509	3	]	]	X
ejpam-6596	509	4	s.	s.	PROPN
ejpam-6596	509	5	r.	r.	PROPN
ejpam-6596	509	6	chawla	chawla	PROPN
ejpam-6596	509	7	,	,	PUNCT
ejpam-6596	509	8	s.	s.	PROPN
ejpam-6596	509	9	ahmad	ahmad	PROPN
ejpam-6596	509	10	,	,	PUNCT
ejpam-6596	509	11	w.	w.	PROPN
ejpam-6596	509	12	albalawi	albalawi	PROPN
ejpam-6596	509	13	,	,	PUNCT
ejpam-6596	509	14	a.	a.	PROPN
ejpam-6596	509	15	khan	khan	PROPN
ejpam-6596	509	16	,	,	PUNCT
ejpam-6596	509	17	i.	i.	NOUN
ejpam-6596	509	18	shah	shah	PROPN
ejpam-6596	509	19	,	,	PUNCT
ejpam-6596	509	20	and	and	CCONJ
ejpam-6596	509	21	m.	m.	PROPN
ejpam-6596	509	22	r.	r.	PROPN
ejpam-6596	509	23	eid	eid	PROPN
ejpam-6596	509	24	.	.	PUNCT
ejpam-6596	510	1	stability	stability	NOUN
ejpam-6596	510	2	analysis	analysis	NOUN
ejpam-6596	510	3	of	of	ADP
ejpam-6596	510	4	a	a	DET
ejpam-6596	510	5	modified	modify	VERB
ejpam-6596	510	6	general	general	ADJ
ejpam-6596	510	7	seir	seir	NOUN
ejpam-6596	510	8	model	model	NOUN
ejpam-6596	510	9	with	with	ADP
ejpam-6596	510	10	harmonic	harmonic	ADJ
ejpam-6596	510	11	mean	mean	NOUN
ejpam-6596	510	12	type	type	NOUN
ejpam-6596	510	13	of	of	ADP
ejpam-6596	510	14	incidence	incidence	NOUN
ejpam-6596	510	15	rate	rate	NOUN
ejpam-6596	510	16	.	.	PUNCT
ejpam-6596	511	1	alexandria	alexandria	PROPN
ejpam-6596	511	2	engineering	engineering	PROPN
ejpam-6596	511	3	journal	journal	PROPN
ejpam-6596	511	4	,	,	PUNCT
ejpam-6596	511	5	127:1183–1192	127:1183–1192	NUM
ejpam-6596	511	6	,	,	PUNCT
ejpam-6596	511	7	2025	2025	NUM
ejpam-6596	511	8	.	.	PUNCT
ejpam-6596	512	1	[	[	X
ejpam-6596	512	2	24	24	NUM
ejpam-6596	512	3	]	]	PUNCT
ejpam-6596	512	4	a.	a.	NOUN
ejpam-6596	512	5	korobeinikov	korobeinikov	NOUN
ejpam-6596	512	6	and	and	CCONJ
ejpam-6596	512	7	p.	p.	PROPN
ejpam-6596	512	8	k.	k.	PROPN
ejpam-6596	513	1	maini	maini	PROPN
ejpam-6596	513	2	.	.	PUNCT
ejpam-6596	514	1	non	non	ADJ
ejpam-6596	514	2	-	-	ADJ
ejpam-6596	514	3	linear	linear	ADJ
ejpam-6596	514	4	incidence	incidence	NOUN
ejpam-6596	514	5	and	and	CCONJ
ejpam-6596	514	6	stability	stability	NOUN
ejpam-6596	514	7	of	of	ADP
ejpam-6596	514	8	infectious	infectious	ADJ
ejpam-6596	514	9	disease	disease	NOUN
ejpam-6596	514	10	models	model	NOUN
ejpam-6596	514	11	.	.	PUNCT
ejpam-6596	515	1	mathematical	mathematical	ADJ
ejpam-6596	515	2	medicine	medicine	NOUN
ejpam-6596	515	3	and	and	CCONJ
ejpam-6596	515	4	biology	biology	NOUN
ejpam-6596	515	5	,	,	PUNCT
ejpam-6596	515	6	22(2):113–128	22(2):113–128	NOUN
ejpam-6596	515	7	,	,	PUNCT
ejpam-6596	515	8	2005	2005	NUM
ejpam-6596	515	9	.	.	PUNCT