id	sid	tid	token	lemma	pos
ejpam-6447	1	1	european	european	PROPN
ejpam-6447	1	2	journal	journal	PROPN
ejpam-6447	1	3	of	of	ADP
ejpam-6447	1	4	pure	pure	ADJ
ejpam-6447	1	5	and	and	CCONJ
ejpam-6447	1	6	applied	applied	ADJ
ejpam-6447	1	7	mathematics	mathematic	NOUN
ejpam-6447	1	8	2025	2025	NUM
ejpam-6447	1	9	,	,	PUNCT
ejpam-6447	1	10	vol	vol	NOUN
ejpam-6447	1	11	.	.	PROPN
ejpam-6447	1	12	18	18	NUM
ejpam-6447	1	13	,	,	PUNCT
ejpam-6447	1	14	issue	issue	NOUN
ejpam-6447	1	15	3	3	NUM
ejpam-6447	1	16	,	,	PUNCT
ejpam-6447	1	17	article	article	NOUN
ejpam-6447	1	18	number	number	NOUN
ejpam-6447	1	19	6447	6447	NUM
ejpam-6447	1	20	issn	issn	VERB
ejpam-6447	1	21	1307	1307	NUM
ejpam-6447	1	22	-	-	SYM
ejpam-6447	1	23	5543	5543	NUM
ejpam-6447	1	24	–	–	PUNCT
ejpam-6447	1	25	ejpam.com	ejpam.com	X
ejpam-6447	1	26	published	publish	VERB
ejpam-6447	1	27	by	by	ADP
ejpam-6447	1	28	new	new	PROPN
ejpam-6447	1	29	york	york	PROPN
ejpam-6447	1	30	business	business	PROPN
ejpam-6447	1	31	global	global	ADJ
ejpam-6447	1	32	analysis	analysis	NOUN
ejpam-6447	1	33	of	of	ADP
ejpam-6447	1	34	a	a	DET
ejpam-6447	1	35	smoking	smoking	NOUN
ejpam-6447	1	36	dynamics	dynamic	NOUN
ejpam-6447	1	37	model	model	NOUN
ejpam-6447	1	38	with	with	ADP
ejpam-6447	1	39	age	age	NOUN
ejpam-6447	1	40	-	-	PUNCT
ejpam-6447	1	41	dependent	dependent	ADJ
ejpam-6447	1	42	incidence	incidence	NOUN
ejpam-6447	1	43	function	function	NOUN
ejpam-6447	1	44	samia	samia	PROPN
ejpam-6447	1	45	bushnaq1	bushnaq1	PROPN
ejpam-6447	1	46	,	,	PUNCT
ejpam-6447	1	47	sameera	sameera	PROPN
ejpam-6447	1	48	bano2	bano2	PROPN
ejpam-6447	1	49	,	,	PUNCT
ejpam-6447	1	50	anwar	anwar	PROPN
ejpam-6447	1	51	zeb2,∗	zeb2,∗	PROPN
ejpam-6447	1	52	1	1	NUM
ejpam-6447	1	53	department	department	NOUN
ejpam-6447	1	54	of	of	ADP
ejpam-6447	1	55	basic	basic	ADJ
ejpam-6447	1	56	sciences	science	NOUN
ejpam-6447	1	57	,	,	PUNCT
ejpam-6447	1	58	princess	princess	NOUN
ejpam-6447	1	59	sumaya	sumaya	PROPN
ejpam-6447	1	60	university	university	PROPN
ejpam-6447	1	61	for	for	ADP
ejpam-6447	1	62	technology	technology	NOUN
ejpam-6447	1	63	,	,	PUNCT
ejpam-6447	1	64	amman	amman	PROPN
ejpam-6447	1	65	11941	11941	NUM
ejpam-6447	1	66	,	,	PUNCT
ejpam-6447	1	67	jordan	jordan	PROPN
ejpam-6447	1	68	2	2	NUM
ejpam-6447	1	69	department	department	NOUN
ejpam-6447	1	70	of	of	ADP
ejpam-6447	1	71	mathematics	mathematics	PROPN
ejpam-6447	1	72	comsats	comsats	PROPN
ejpam-6447	1	73	university	university	PROPN
ejpam-6447	1	74	islamabad	islamabad	PROPN
ejpam-6447	1	75	,	,	PUNCT
ejpam-6447	1	76	abbottabad	abbottabad	PROPN
ejpam-6447	1	77	campus	campus	PROPN
ejpam-6447	1	78	,	,	PUNCT
ejpam-6447	1	79	kpk	kpk	PROPN
ejpam-6447	1	80	,	,	PUNCT
ejpam-6447	1	81	pakistan	pakistan	PROPN
ejpam-6447	1	82	abstract	abstract	NOUN
ejpam-6447	1	83	.	.	PUNCT
ejpam-6447	2	1	smoking	smoking	NOUN
ejpam-6447	2	2	remains	remain	VERB
ejpam-6447	2	3	a	a	DET
ejpam-6447	2	4	major	major	ADJ
ejpam-6447	2	5	public	public	ADJ
ejpam-6447	2	6	health	health	NOUN
ejpam-6447	2	7	concern	concern	NOUN
ejpam-6447	2	8	,	,	PUNCT
ejpam-6447	2	9	influenced	influence	VERB
ejpam-6447	2	10	significantly	significantly	ADV
ejpam-6447	2	11	by	by	ADP
ejpam-6447	2	12	age	age	NOUN
ejpam-6447	2	13	structure	structure	NOUN
ejpam-6447	2	14	and	and	CCONJ
ejpam-6447	2	15	household	household	NOUN
ejpam-6447	2	16	environments	environment	NOUN
ejpam-6447	2	17	.	.	PUNCT
ejpam-6447	3	1	in	in	ADP
ejpam-6447	3	2	this	this	DET
ejpam-6447	3	3	study	study	NOUN
ejpam-6447	3	4	,	,	PUNCT
ejpam-6447	3	5	we	we	PRON
ejpam-6447	3	6	develop	develop	VERB
ejpam-6447	3	7	and	and	CCONJ
ejpam-6447	3	8	analyze	analyze	VERB
ejpam-6447	3	9	an	an	DET
ejpam-6447	3	10	age	age	NOUN
ejpam-6447	3	11	-	-	PUNCT
ejpam-6447	3	12	structured	structure	VERB
ejpam-6447	3	13	mathematical	mathematical	ADJ
ejpam-6447	3	14	model	model	NOUN
ejpam-6447	3	15	that	that	PRON
ejpam-6447	3	16	incorporates	incorporate	VERB
ejpam-6447	3	17	age	age	NOUN
ejpam-6447	3	18	-	-	PUNCT
ejpam-6447	3	19	dependent	dependent	ADJ
ejpam-6447	3	20	incidence	incidence	NOUN
ejpam-6447	3	21	and	and	CCONJ
ejpam-6447	3	22	household	household	NOUN
ejpam-6447	3	23	effects	effect	NOUN
ejpam-6447	3	24	to	to	PART
ejpam-6447	3	25	better	well	ADV
ejpam-6447	3	26	understand	understand	VERB
ejpam-6447	3	27	smoking	smoking	NOUN
ejpam-6447	3	28	dynamics	dynamic	NOUN
ejpam-6447	3	29	.	.	PUNCT
ejpam-6447	4	1	we	we	PRON
ejpam-6447	4	2	establish	establish	VERB
ejpam-6447	4	3	the	the	DET
ejpam-6447	4	4	model	model	NOUN
ejpam-6447	4	5	’s	’s	PART
ejpam-6447	4	6	well	well	ADV
ejpam-6447	4	7	-	-	PUNCT
ejpam-6447	4	8	posedness	posedness	NOUN
ejpam-6447	4	9	by	by	ADP
ejpam-6447	4	10	proving	prove	VERB
ejpam-6447	4	11	the	the	DET
ejpam-6447	4	12	existence	existence	NOUN
ejpam-6447	4	13	and	and	CCONJ
ejpam-6447	4	14	uniqueness	uniqueness	NOUN
ejpam-6447	4	15	of	of	ADP
ejpam-6447	4	16	solutions	solution	NOUN
ejpam-6447	4	17	.	.	PUNCT
ejpam-6447	5	1	the	the	DET
ejpam-6447	5	2	global	global	ADJ
ejpam-6447	5	3	stability	stability	NOUN
ejpam-6447	5	4	of	of	ADP
ejpam-6447	5	5	both	both	DET
ejpam-6447	5	6	smoking	smoking	NOUN
ejpam-6447	5	7	-	-	PUNCT
ejpam-6447	5	8	free	free	ADJ
ejpam-6447	5	9	and	and	CCONJ
ejpam-6447	5	10	endemic	endemic	ADJ
ejpam-6447	5	11	equilibria	equilibrium	NOUN
ejpam-6447	5	12	is	be	AUX
ejpam-6447	5	13	analyzed	analyze	VERB
ejpam-6447	5	14	using	use	VERB
ejpam-6447	5	15	a	a	DET
ejpam-6447	5	16	suitably	suitably	ADV
ejpam-6447	5	17	constructed	construct	VERB
ejpam-6447	5	18	lyapunov	lyapunov	ADJ
ejpam-6447	5	19	function	function	NOUN
ejpam-6447	5	20	.	.	PUNCT
ejpam-6447	6	1	for	for	ADP
ejpam-6447	6	2	numerical	numerical	ADJ
ejpam-6447	6	3	simulations	simulation	NOUN
ejpam-6447	6	4	,	,	PUNCT
ejpam-6447	6	5	we	we	PRON
ejpam-6447	6	6	apply	apply	VERB
ejpam-6447	6	7	the	the	DET
ejpam-6447	6	8	nonstandard	nonstandard	ADJ
ejpam-6447	6	9	finite	finite	ADJ
ejpam-6447	6	10	difference	difference	NOUN
ejpam-6447	6	11	(	(	PUNCT
ejpam-6447	6	12	nsfd	nsfd	ADJ
ejpam-6447	6	13	)	)	PUNCT
ejpam-6447	6	14	method	method	NOUN
ejpam-6447	6	15	and	and	CCONJ
ejpam-6447	6	16	compare	compare	VERB
ejpam-6447	6	17	the	the	DET
ejpam-6447	6	18	results	result	NOUN
ejpam-6447	6	19	with	with	ADP
ejpam-6447	6	20	those	those	PRON
ejpam-6447	6	21	obtained	obtain	VERB
ejpam-6447	6	22	via	via	ADP
ejpam-6447	6	23	the	the	DET
ejpam-6447	6	24	classical	classical	ADJ
ejpam-6447	6	25	fourth	fourth	ADJ
ejpam-6447	6	26	-	-	PUNCT
ejpam-6447	6	27	order	order	NOUN
ejpam-6447	6	28	runge	runge	NOUN
ejpam-6447	6	29	–	–	PUNCT
ejpam-6447	6	30	kutta	kutta	NOUN
ejpam-6447	6	31	(	(	PUNCT
ejpam-6447	6	32	rk4	rk4	NOUN
ejpam-6447	6	33	)	)	PUNCT
ejpam-6447	6	34	scheme	scheme	NOUN
ejpam-6447	6	35	.	.	PUNCT
ejpam-6447	7	1	the	the	DET
ejpam-6447	7	2	findings	finding	NOUN
ejpam-6447	7	3	underscore	underscore	VERB
ejpam-6447	7	4	the	the	DET
ejpam-6447	7	5	importance	importance	NOUN
ejpam-6447	7	6	of	of	ADP
ejpam-6447	7	7	age	age	NOUN
ejpam-6447	7	8	-	-	PUNCT
ejpam-6447	7	9	specific	specific	ADJ
ejpam-6447	7	10	interventions	intervention	NOUN
ejpam-6447	7	11	and	and	CCONJ
ejpam-6447	7	12	offer	offer	VERB
ejpam-6447	7	13	a	a	DET
ejpam-6447	7	14	framework	framework	NOUN
ejpam-6447	7	15	for	for	ADP
ejpam-6447	7	16	future	future	ADJ
ejpam-6447	7	17	studies	study	NOUN
ejpam-6447	7	18	incorporating	incorporate	VERB
ejpam-6447	7	19	relapse	relapse	NOUN
ejpam-6447	7	20	,	,	PUNCT
ejpam-6447	7	21	control	control	NOUN
ejpam-6447	7	22	strategies	strategy	NOUN
ejpam-6447	7	23	,	,	PUNCT
ejpam-6447	7	24	or	or	CCONJ
ejpam-6447	7	25	stochastic	stochastic	ADJ
ejpam-6447	7	26	effects	effect	NOUN
ejpam-6447	7	27	.	.	PUNCT
ejpam-6447	8	1	2020	2020	NUM
ejpam-6447	8	2	mathematics	mathematic	NOUN
ejpam-6447	8	3	subject	subject	NOUN
ejpam-6447	8	4	classifications	classification	NOUN
ejpam-6447	8	5	:	:	PUNCT
ejpam-6447	8	6	92d30	92d30	NUM
ejpam-6447	8	7	,	,	PUNCT
ejpam-6447	8	8	34d20	34d20	NUM
ejpam-6447	8	9	,	,	PUNCT
ejpam-6447	8	10	65l12	65l12	NUM
ejpam-6447	8	11	,	,	PUNCT
ejpam-6447	8	12	37n25	37n25	NUM
ejpam-6447	8	13	key	key	ADJ
ejpam-6447	8	14	words	word	NOUN
ejpam-6447	8	15	and	and	CCONJ
ejpam-6447	8	16	phrases	phrase	NOUN
ejpam-6447	8	17	:	:	PUNCT
ejpam-6447	8	18	age	age	NOUN
ejpam-6447	8	19	-	-	PUNCT
ejpam-6447	8	20	structured	structure	VERB
ejpam-6447	8	21	smoking	smoking	NOUN
ejpam-6447	8	22	model	model	NOUN
ejpam-6447	8	23	,	,	PUNCT
ejpam-6447	8	24	equilibria	equilibrium	NOUN
ejpam-6447	8	25	,	,	PUNCT
ejpam-6447	8	26	stability	stability	NOUN
ejpam-6447	8	27	analysis	analysis	NOUN
ejpam-6447	8	28	,	,	PUNCT
ejpam-6447	8	29	lyapunov	lyapunov	NOUN
ejpam-6447	8	30	function	function	NOUN
ejpam-6447	8	31	,	,	PUNCT
ejpam-6447	8	32	non	non	ADJ
ejpam-6447	8	33	-	-	ADJ
ejpam-6447	8	34	standard	standard	ADJ
ejpam-6447	8	35	finite	finite	ADJ
ejpam-6447	8	36	difference	difference	NOUN
ejpam-6447	8	37	technique	technique	NOUN
ejpam-6447	8	38	1	1	NUM
ejpam-6447	8	39	.	.	PUNCT
ejpam-6447	9	1	introduction	introduction	NOUN
ejpam-6447	9	2	mathematical	mathematical	ADJ
ejpam-6447	9	3	modeling	modeling	NOUN
ejpam-6447	9	4	has	have	AUX
ejpam-6447	9	5	become	become	VERB
ejpam-6447	9	6	an	an	DET
ejpam-6447	9	7	indispensable	indispensable	ADJ
ejpam-6447	9	8	tool	tool	NOUN
ejpam-6447	9	9	in	in	ADP
ejpam-6447	9	10	modern	modern	ADJ
ejpam-6447	9	11	epidemiology	epidemiology	NOUN
ejpam-6447	9	12	and	and	CCONJ
ejpam-6447	9	13	public	public	ADJ
ejpam-6447	9	14	health	health	NOUN
ejpam-6447	9	15	research	research	NOUN
ejpam-6447	9	16	.	.	PUNCT
ejpam-6447	10	1	these	these	DET
ejpam-6447	10	2	models	model	NOUN
ejpam-6447	10	3	have	have	AUX
ejpam-6447	10	4	been	be	AUX
ejpam-6447	10	5	extensively	extensively	ADV
ejpam-6447	10	6	employed	employ	VERB
ejpam-6447	10	7	to	to	PART
ejpam-6447	10	8	study	study	VERB
ejpam-6447	10	9	a	a	DET
ejpam-6447	10	10	wide	wide	ADJ
ejpam-6447	10	11	range	range	NOUN
ejpam-6447	10	12	of	of	ADP
ejpam-6447	10	13	diseases	disease	NOUN
ejpam-6447	10	14	,	,	PUNCT
ejpam-6447	10	15	including	include	VERB
ejpam-6447	10	16	infectious	infectious	ADJ
ejpam-6447	10	17	diseases	disease	NOUN
ejpam-6447	10	18	such	such	ADJ
ejpam-6447	10	19	as	as	ADP
ejpam-6447	10	20	influenza	influenza	NOUN
ejpam-6447	10	21	,	,	PUNCT
ejpam-6447	10	22	covid-19	covid-19	PROPN
ejpam-6447	10	23	,	,	PUNCT
ejpam-6447	10	24	hiv	hiv	PROPN
ejpam-6447	10	25	/	/	SYM
ejpam-6447	10	26	aids	aids	PROPN
ejpam-6447	10	27	,	,	PUNCT
ejpam-6447	10	28	and	and	CCONJ
ejpam-6447	10	29	tuberculosis	tuberculosis	NOUN
ejpam-6447	10	30	,	,	PUNCT
ejpam-6447	10	31	as	as	ADV
ejpam-6447	10	32	well	well	ADV
ejpam-6447	10	33	as	as	ADP
ejpam-6447	10	34	non	non	ADJ
ejpam-6447	10	35	-	-	ADJ
ejpam-6447	10	36	communicable	communicable	ADJ
ejpam-6447	10	37	diseases	disease	NOUN
ejpam-6447	10	38	like	like	ADP
ejpam-6447	10	39	cancer	cancer	NOUN
ejpam-6447	10	40	,	,	PUNCT
ejpam-6447	10	41	diabetes	diabetes	NOUN
ejpam-6447	10	42	,	,	PUNCT
ejpam-6447	10	43	and	and	CCONJ
ejpam-6447	10	44	cardiovascular	cardiovascular	ADJ
ejpam-6447	10	45	conditions	condition	NOUN
ejpam-6447	10	46	[	[	X
ejpam-6447	10	47	1–4	1–4	NOUN
ejpam-6447	10	48	]	]	X
ejpam-6447	10	49	.	.	PUNCT
ejpam-6447	11	1	by	by	ADP
ejpam-6447	11	2	incorporating	incorporate	VERB
ejpam-6447	11	3	biological	biological	ADJ
ejpam-6447	11	4	,	,	PUNCT
ejpam-6447	11	5	environmental	environmental	ADJ
ejpam-6447	11	6	,	,	PUNCT
ejpam-6447	11	7	social	social	ADJ
ejpam-6447	11	8	,	,	PUNCT
ejpam-6447	11	9	and	and	CCONJ
ejpam-6447	11	10	behavioral	behavioral	ADJ
ejpam-6447	11	11	variables	variable	NOUN
ejpam-6447	11	12	,	,	PUNCT
ejpam-6447	11	13	mathematical	mathematical	ADJ
ejpam-6447	11	14	models	model	NOUN
ejpam-6447	11	15	help	help	VERB
ejpam-6447	11	16	predict	predict	VERB
ejpam-6447	11	17	disease	disease	NOUN
ejpam-6447	11	18	dynamics	dynamic	NOUN
ejpam-6447	11	19	,	,	PUNCT
ejpam-6447	11	20	assess	assess	VERB
ejpam-6447	11	21	the	the	DET
ejpam-6447	11	22	impact	impact	NOUN
ejpam-6447	11	23	of	of	ADP
ejpam-6447	11	24	interventions	intervention	NOUN
ejpam-6447	11	25	,	,	PUNCT
ejpam-6447	11	26	and	and	CCONJ
ejpam-6447	11	27	formulate	formulate	VERB
ejpam-6447	11	28	effective	effective	ADJ
ejpam-6447	11	29	public	public	ADJ
ejpam-6447	11	30	health	health	NOUN
ejpam-6447	11	31	policies	policy	NOUN
ejpam-6447	11	32	[	[	X
ejpam-6447	11	33	5–7	5–7	X
ejpam-6447	11	34	]	]	PUNCT
ejpam-6447	11	35	.	.	PUNCT
ejpam-6447	12	1	for	for	ADP
ejpam-6447	12	2	instance	instance	NOUN
ejpam-6447	12	3	,	,	PUNCT
ejpam-6447	12	4	compartmental	compartmental	ADJ
ejpam-6447	12	5	models	model	NOUN
ejpam-6447	12	6	such	such	ADJ
ejpam-6447	12	7	as	as	ADP
ejpam-6447	12	8	sir	sir	NOUN
ejpam-6447	12	9	and	and	CCONJ
ejpam-6447	12	10	seir	seir	ADJ
ejpam-6447	12	11	frameworks	framework	NOUN
ejpam-6447	12	12	have	have	AUX
ejpam-6447	12	13	been	be	AUX
ejpam-6447	12	14	used	use	VERB
ejpam-6447	12	15	to	to	PART
ejpam-6447	12	16	analyze	analyze	VERB
ejpam-6447	12	17	the	the	DET
ejpam-6447	12	18	spread	spread	NOUN
ejpam-6447	12	19	of	of	ADP
ejpam-6447	12	20	infectious	infectious	ADJ
ejpam-6447	12	21	agents	agent	NOUN
ejpam-6447	12	22	,	,	PUNCT
ejpam-6447	12	23	while	while	SCONJ
ejpam-6447	12	24	more	more	ADJ
ejpam-6447	12	25	complex	complex	ADJ
ejpam-6447	12	26	models	model	NOUN
ejpam-6447	12	27	with	with	ADP
ejpam-6447	12	28	delays	delay	NOUN
ejpam-6447	12	29	,	,	PUNCT
ejpam-6447	12	30	spatial	spatial	ADJ
ejpam-6447	12	31	heterogeneity	heterogeneity	NOUN
ejpam-6447	12	32	,	,	PUNCT
ejpam-6447	12	33	and	and	CCONJ
ejpam-6447	12	34	control	control	NOUN
ejpam-6447	12	35	strategies	strategy	NOUN
ejpam-6447	12	36	have	have	AUX
ejpam-6447	12	37	been	be	AUX
ejpam-6447	12	38	applied	apply	VERB
ejpam-6447	12	39	to	to	ADP
ejpam-6447	12	40	cancer	cancer	NOUN
ejpam-6447	12	41	progression	progression	NOUN
ejpam-6447	12	42	,	,	PUNCT
ejpam-6447	12	43	substance	substance	NOUN
ejpam-6447	12	44	abuse	abuse	NOUN
ejpam-6447	12	45	,	,	PUNCT
ejpam-6447	12	46	and	and	CCONJ
ejpam-6447	12	47	mental	mental	ADJ
ejpam-6447	12	48	health	health	NOUN
ejpam-6447	12	49	disorders	disorder	NOUN
ejpam-6447	12	50	[	[	X
ejpam-6447	12	51	8	8	NUM
ejpam-6447	12	52	,	,	PUNCT
ejpam-6447	12	53	9	9	NUM
ejpam-6447	12	54	]	]	PUNCT
ejpam-6447	12	55	.	.	PUNCT
ejpam-6447	13	1	in	in	ADP
ejpam-6447	13	2	recent	recent	ADJ
ejpam-6447	13	3	years	year	NOUN
ejpam-6447	13	4	,	,	PUNCT
ejpam-6447	13	5	the	the	DET
ejpam-6447	13	6	scope	scope	NOUN
ejpam-6447	13	7	of	of	ADP
ejpam-6447	13	8	mathematical	mathematical	ADJ
ejpam-6447	13	9	modeling	modeling	NOUN
ejpam-6447	13	10	has	have	AUX
ejpam-6447	13	11	expanded	expand	VERB
ejpam-6447	13	12	to	to	ADP
ejpam-6447	13	13	behavioral	behavioral	ADJ
ejpam-6447	13	14	health	health	NOUN
ejpam-6447	13	15	problems	problem	NOUN
ejpam-6447	13	16	,	,	PUNCT
ejpam-6447	13	17	including	include	VERB
ejpam-6447	13	18	tobacco	tobacco	NOUN
ejpam-6447	13	19	use	use	NOUN
ejpam-6447	13	20	and	and	CCONJ
ejpam-6447	13	21	smoking	smoking	NOUN
ejpam-6447	13	22	.	.	PUNCT
ejpam-6447	14	1	smoking	smoking	NOUN
ejpam-6447	14	2	remains	remain	VERB
ejpam-6447	14	3	a	a	DET
ejpam-6447	14	4	persistent	persistent	ADJ
ejpam-6447	14	5	global	global	ADJ
ejpam-6447	14	6	health	health	NOUN
ejpam-6447	14	7	challenge	challenge	NOUN
ejpam-6447	14	8	,	,	PUNCT
ejpam-6447	14	9	contributing	contribute	VERB
ejpam-6447	14	10	significantly	significantly	ADV
ejpam-6447	14	11	to	to	ADP
ejpam-6447	14	12	mortality	mortality	NOUN
ejpam-6447	14	13	and	and	CCONJ
ejpam-6447	14	14	morbidity	morbidity	NOUN
ejpam-6447	14	15	rates	rate	NOUN
ejpam-6447	14	16	across	across	ADP
ejpam-6447	14	17	both	both	CCONJ
ejpam-6447	14	18	developed	developed	ADJ
ejpam-6447	14	19	and	and	CCONJ
ejpam-6447	14	20	developing	develop	VERB
ejpam-6447	14	21	nations	nation	NOUN
ejpam-6447	14	22	.	.	PUNCT
ejpam-6447	15	1	it	it	PRON
ejpam-6447	15	2	is	be	AUX
ejpam-6447	15	3	directly	directly	ADV
ejpam-6447	15	4	linked	link	VERB
ejpam-6447	15	5	to	to	ADP
ejpam-6447	15	6	multiple	multiple	ADJ
ejpam-6447	15	7	life	life	NOUN
ejpam-6447	15	8	-	-	PUNCT
ejpam-6447	15	9	threatening	threaten	VERB
ejpam-6447	15	10	conditions	condition	NOUN
ejpam-6447	15	11	,	,	PUNCT
ejpam-6447	15	12	including	include	VERB
ejpam-6447	15	13	respiratory	respiratory	ADJ
ejpam-6447	15	14	diseases	disease	NOUN
ejpam-6447	15	15	,	,	PUNCT
ejpam-6447	15	16	stroke	stroke	NOUN
ejpam-6447	15	17	,	,	PUNCT
ejpam-6447	15	18	cardiovascular	cardiovascular	ADJ
ejpam-6447	15	19	complications	complication	NOUN
ejpam-6447	15	20	,	,	PUNCT
ejpam-6447	15	21	and	and	CCONJ
ejpam-6447	15	22	various	various	ADJ
ejpam-6447	15	23	forms	form	NOUN
ejpam-6447	15	24	of	of	ADP
ejpam-6447	15	25	cancer	cancer	NOUN
ejpam-6447	15	26	.	.	PUNCT
ejpam-6447	16	1	statistically	statistically	ADV
ejpam-6447	16	2	,	,	PUNCT
ejpam-6447	16	3	a	a	DET
ejpam-6447	16	4	substantial	substantial	ADJ
ejpam-6447	16	5	proportion	proportion	NOUN
ejpam-6447	16	6	of	of	ADP
ejpam-6447	16	7	the	the	DET
ejpam-6447	16	8	adult	adult	NOUN
ejpam-6447	16	9	american	american	ADJ
ejpam-6447	16	10	population	population	NOUN
ejpam-6447	16	11	engages	engage	VERB
ejpam-6447	16	12	in	in	ADP
ejpam-6447	16	13	smoking	smoking	NOUN
ejpam-6447	16	14	,	,	PUNCT
ejpam-6447	16	15	with	with	ADP
ejpam-6447	16	16	prevalence	prevalence	NOUN
ejpam-6447	16	17	exceeding	exceed	VERB
ejpam-6447	16	18	that	that	PRON
ejpam-6447	16	19	of	of	ADP
ejpam-6447	16	20	the	the	DET
ejpam-6447	16	21	adult	adult	NOUN
ejpam-6447	16	22	female	female	ADJ
ejpam-6447	16	23	population	population	NOUN
ejpam-6447	17	1	[	[	X
ejpam-6447	17	2	10–12	10–12	NUM
ejpam-6447	17	3	]	]	PUNCT
ejpam-6447	17	4	.	.	PUNCT
ejpam-6447	18	1	epidemiological	epidemiological	ADJ
ejpam-6447	18	2	studies	study	NOUN
ejpam-6447	18	3	reveal	reveal	VERB
ejpam-6447	18	4	that	that	SCONJ
ejpam-6447	18	5	∗corresponding	∗corresponde	VERB
ejpam-6447	18	6	author	author	NOUN
ejpam-6447	18	7	.	.	PUNCT
ejpam-6447	19	1	doi	doi	NOUN
ejpam-6447	19	2	:	:	PUNCT
ejpam-6447	19	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6447	https://doi.org/10.29020/nybg.ejpam.v18i3.6447	PRON
ejpam-6447	19	4	email	email	NOUN
ejpam-6447	19	5	addresses	address	VERB
ejpam-6447	19	6	:	:	PUNCT
ejpam-6447	20	1	s.bushnaq@psut.edu.jo	s.bushnaq@psut.edu.jo	PROPN
ejpam-6447	20	2	(	(	PUNCT
ejpam-6447	20	3	s.	s.	PROPN
ejpam-6447	20	4	bushnaq	bushnaq	PROPN
ejpam-6447	20	5	)	)	PUNCT
ejpam-6447	20	6	,	,	PUNCT
ejpam-6447	20	7	sameera@cuiatd.edu.pk	sameera@cuiatd.edu.pk	NOUN
ejpam-6447	20	8	(	(	PUNCT
ejpam-6447	20	9	s.	s.	PROPN
ejpam-6447	20	10	bano	bano	PROPN
ejpam-6447	20	11	)	)	PUNCT
ejpam-6447	20	12	,	,	PUNCT
ejpam-6447	20	13	anwar@cuiatd.edu.pk	anwar@cuiatd.edu.pk	NOUN
ejpam-6447	20	14	(	(	PUNCT
ejpam-6447	20	15	a.	a.	NOUN
ejpam-6447	20	16	zeb	zeb	PROPN
ejpam-6447	20	17	)	)	PUNCT
ejpam-6447	20	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6447	20	19	1	1	NUM
ejpam-6447	20	20	copyright	copyright	NOUN
ejpam-6447	20	21	:	:	PUNCT
ejpam-6447	20	22	©	©	PROPN
ejpam-6447	20	23	2025	2025	NUM
ejpam-6447	20	24	the	the	DET
ejpam-6447	20	25	author(s	author(s	NOUN
ejpam-6447	20	26	)	)	PUNCT
ejpam-6447	20	27	.	.	PUNCT
ejpam-6447	21	1	(	(	PUNCT
ejpam-6447	21	2	cc	cc	NOUN
ejpam-6447	21	3	by	by	ADP
ejpam-6447	21	4	-	-	PUNCT
ejpam-6447	21	5	nc	nc	PROPN
ejpam-6447	21	6	4.0	4.0	NUM
ejpam-6447	21	7	)	)	PUNCT
ejpam-6447	21	8	s.	s.	PROPN
ejpam-6447	21	9	bushnaq	bushnaq	PROPN
ejpam-6447	21	10	,	,	PUNCT
ejpam-6447	21	11	s.	s.	PROPN
ejpam-6447	21	12	bano	bano	PROPN
ejpam-6447	21	13	,	,	PUNCT
ejpam-6447	21	14	a.	a.	PROPN
ejpam-6447	21	15	zeb	zeb	PROPN
ejpam-6447	21	16	/	/	SYM
ejpam-6447	21	17	eur	eur	PROPN
ejpam-6447	21	18	.	.	PUNCT
ejpam-6447	22	1	j.	j.	PROPN
ejpam-6447	22	2	pure	pure	PROPN
ejpam-6447	22	3	appl	appl	PROPN
ejpam-6447	22	4	.	.	PROPN
ejpam-6447	22	5	math	math	PROPN
ejpam-6447	22	6	,	,	PUNCT
ejpam-6447	22	7	18	18	NUM
ejpam-6447	22	8	(	(	PUNCT
ejpam-6447	22	9	3	3	NUM
ejpam-6447	22	10	)	)	PUNCT
ejpam-6447	22	11	(	(	PUNCT
ejpam-6447	22	12	2025	2025	NUM
ejpam-6447	22	13	)	)	PUNCT
ejpam-6447	22	14	,	,	PUNCT
ejpam-6447	22	15	6447	6447	NUM
ejpam-6447	22	16	2	2	NUM
ejpam-6447	22	17	of	of	ADP
ejpam-6447	22	18	12	12	NUM
ejpam-6447	22	19	smokers	smoker	NOUN
ejpam-6447	22	20	face	face	VERB
ejpam-6447	22	21	a	a	DET
ejpam-6447	22	22	fourteen	fourteen	NUM
ejpam-6447	22	23	-	-	ADJ
ejpam-6447	22	24	fold	fold	ADJ
ejpam-6447	22	25	increase	increase	NOUN
ejpam-6447	22	26	in	in	ADP
ejpam-6447	22	27	the	the	DET
ejpam-6447	22	28	mortality	mortality	NOUN
ejpam-6447	22	29	risk	risk	NOUN
ejpam-6447	22	30	from	from	ADP
ejpam-6447	22	31	cancers	cancer	NOUN
ejpam-6447	22	32	of	of	ADP
ejpam-6447	22	33	the	the	DET
ejpam-6447	22	34	respiratory	respiratory	ADJ
ejpam-6447	22	35	and	and	CCONJ
ejpam-6447	22	36	oral	oral	ADJ
ejpam-6447	22	37	systems	system	NOUN
ejpam-6447	22	38	compared	compare	VERB
ejpam-6447	22	39	to	to	ADP
ejpam-6447	22	40	nonsmokers	nonsmoker	NOUN
ejpam-6447	22	41	[	[	X
ejpam-6447	22	42	13–15	13–15	NUM
ejpam-6447	22	43	]	]	PUNCT
ejpam-6447	22	44	.	.	PUNCT
ejpam-6447	23	1	while	while	SCONJ
ejpam-6447	23	2	healthcare	healthcare	PROPN
ejpam-6447	23	3	professionals	professional	NOUN
ejpam-6447	23	4	and	and	CCONJ
ejpam-6447	23	5	pharmaceutical	pharmaceutical	NOUN
ejpam-6447	23	6	researchers	researcher	NOUN
ejpam-6447	23	7	are	be	AUX
ejpam-6447	23	8	actively	actively	ADV
ejpam-6447	23	9	striving	strive	VERB
ejpam-6447	23	10	to	to	AUX
ejpam-6447	23	11	combat	combat	NOUN
ejpam-6447	23	12	smoking	smoke	VERB
ejpam-6447	23	13	through	through	ADP
ejpam-6447	23	14	cessation	cessation	NOUN
ejpam-6447	23	15	programs	program	NOUN
ejpam-6447	23	16	and	and	CCONJ
ejpam-6447	23	17	drug	drug	NOUN
ejpam-6447	23	18	therapies	therapy	NOUN
ejpam-6447	23	19	,	,	PUNCT
ejpam-6447	23	20	mathematicians	mathematician	NOUN
ejpam-6447	23	21	also	also	ADV
ejpam-6447	23	22	play	play	VERB
ejpam-6447	23	23	a	a	DET
ejpam-6447	23	24	crucial	crucial	ADJ
ejpam-6447	23	25	role	role	NOUN
ejpam-6447	23	26	by	by	ADP
ejpam-6447	23	27	developing	develop	VERB
ejpam-6447	23	28	analytical	analytical	ADJ
ejpam-6447	23	29	models	model	NOUN
ejpam-6447	23	30	that	that	PRON
ejpam-6447	23	31	improve	improve	VERB
ejpam-6447	23	32	understanding	understanding	NOUN
ejpam-6447	23	33	of	of	ADP
ejpam-6447	23	34	smoking	smoking	NOUN
ejpam-6447	23	35	behaviors	behavior	NOUN
ejpam-6447	23	36	and	and	CCONJ
ejpam-6447	23	37	support	support	VERB
ejpam-6447	23	38	evidence	evidence	NOUN
ejpam-6447	23	39	-	-	PUNCT
ejpam-6447	23	40	based	base	VERB
ejpam-6447	23	41	medical	medical	ADJ
ejpam-6447	23	42	interventions	intervention	NOUN
ejpam-6447	23	43	.	.	PUNCT
ejpam-6447	24	1	these	these	DET
ejpam-6447	24	2	models	model	NOUN
ejpam-6447	24	3	help	help	VERB
ejpam-6447	24	4	analyze	analyze	VERB
ejpam-6447	24	5	smoking	smoking	NOUN
ejpam-6447	24	6	initiation	initiation	NOUN
ejpam-6447	24	7	,	,	PUNCT
ejpam-6447	24	8	continuation	continuation	NOUN
ejpam-6447	24	9	,	,	PUNCT
ejpam-6447	24	10	cessation	cessation	NOUN
ejpam-6447	24	11	,	,	PUNCT
ejpam-6447	24	12	and	and	CCONJ
ejpam-6447	24	13	relapse	relapse	VERB
ejpam-6447	24	14	by	by	ADP
ejpam-6447	24	15	integrating	integrate	VERB
ejpam-6447	24	16	behavioral	behavioral	ADJ
ejpam-6447	24	17	,	,	PUNCT
ejpam-6447	24	18	psychological	psychological	ADJ
ejpam-6447	24	19	,	,	PUNCT
ejpam-6447	24	20	and	and	CCONJ
ejpam-6447	24	21	social	social	ADJ
ejpam-6447	24	22	components	component	NOUN
ejpam-6447	24	23	into	into	ADP
ejpam-6447	24	24	the	the	DET
ejpam-6447	24	25	mathematical	mathematical	ADJ
ejpam-6447	24	26	framework	framework	NOUN
ejpam-6447	24	27	[	[	X
ejpam-6447	24	28	16–20	16–20	NUM
ejpam-6447	24	29	]	]	X
ejpam-6447	24	30	.	.	PUNCT
ejpam-6447	25	1	traditionally	traditionally	ADV
ejpam-6447	25	2	,	,	PUNCT
ejpam-6447	25	3	smoking	smoking	NOUN
ejpam-6447	25	4	behavior	behavior	NOUN
ejpam-6447	25	5	has	have	AUX
ejpam-6447	25	6	been	be	AUX
ejpam-6447	25	7	modeled	model	VERB
ejpam-6447	25	8	using	use	VERB
ejpam-6447	25	9	classical	classical	ADJ
ejpam-6447	25	10	integer	integer	NOUN
ejpam-6447	25	11	-	-	PUNCT
ejpam-6447	25	12	order	order	NOUN
ejpam-6447	25	13	differential	differential	ADJ
ejpam-6447	25	14	equations	equation	NOUN
ejpam-6447	25	15	[	[	X
ejpam-6447	25	16	21	21	NUM
ejpam-6447	25	17	,	,	PUNCT
ejpam-6447	25	18	22	22	NUM
ejpam-6447	25	19	]	]	PUNCT
ejpam-6447	25	20	.	.	PUNCT
ejpam-6447	26	1	however	however	ADV
ejpam-6447	26	2	,	,	PUNCT
ejpam-6447	26	3	recent	recent	ADJ
ejpam-6447	26	4	approaches	approach	NOUN
ejpam-6447	26	5	have	have	AUX
ejpam-6447	26	6	employed	employ	VERB
ejpam-6447	26	7	fractional	fractional	ADJ
ejpam-6447	26	8	-	-	PUNCT
ejpam-6447	26	9	order	order	NOUN
ejpam-6447	26	10	differential	differential	ADJ
ejpam-6447	26	11	equations	equation	NOUN
ejpam-6447	26	12	due	due	ADP
ejpam-6447	26	13	to	to	ADP
ejpam-6447	26	14	their	their	PRON
ejpam-6447	26	15	capability	capability	NOUN
ejpam-6447	26	16	to	to	PART
ejpam-6447	26	17	capture	capture	VERB
ejpam-6447	26	18	memory	memory	NOUN
ejpam-6447	26	19	and	and	CCONJ
ejpam-6447	26	20	hereditary	hereditary	ADJ
ejpam-6447	26	21	effects	effect	NOUN
ejpam-6447	26	22	,	,	PUNCT
ejpam-6447	26	23	which	which	PRON
ejpam-6447	26	24	are	be	AUX
ejpam-6447	26	25	especially	especially	ADV
ejpam-6447	26	26	relevant	relevant	ADJ
ejpam-6447	26	27	for	for	ADP
ejpam-6447	26	28	addictive	addictive	ADJ
ejpam-6447	26	29	behaviors	behavior	NOUN
ejpam-6447	26	30	like	like	ADP
ejpam-6447	26	31	smoking	smoke	VERB
ejpam-6447	26	32	[	[	X
ejpam-6447	26	33	23	23	NUM
ejpam-6447	26	34	,	,	PUNCT
ejpam-6447	26	35	24	24	NUM
ejpam-6447	26	36	]	]	PUNCT
ejpam-6447	26	37	.	.	PUNCT
ejpam-6447	27	1	stochastic	stochastic	ADJ
ejpam-6447	27	2	models	model	NOUN
ejpam-6447	27	3	also	also	ADV
ejpam-6447	27	4	contribute	contribute	VERB
ejpam-6447	27	5	to	to	ADP
ejpam-6447	27	6	a	a	DET
ejpam-6447	27	7	more	more	ADV
ejpam-6447	27	8	realistic	realistic	ADJ
ejpam-6447	27	9	representation	representation	NOUN
ejpam-6447	27	10	by	by	ADP
ejpam-6447	27	11	incorporating	incorporate	VERB
ejpam-6447	27	12	randomness	randomness	NOUN
ejpam-6447	27	13	and	and	CCONJ
ejpam-6447	27	14	uncertainty	uncertainty	NOUN
ejpam-6447	27	15	,	,	PUNCT
ejpam-6447	27	16	reflecting	reflect	VERB
ejpam-6447	27	17	population	population	NOUN
ejpam-6447	27	18	-	-	PUNCT
ejpam-6447	27	19	level	level	NOUN
ejpam-6447	27	20	variability	variability	NOUN
ejpam-6447	27	21	in	in	ADP
ejpam-6447	27	22	smoking	smoking	NOUN
ejpam-6447	27	23	tendencies	tendency	NOUN
ejpam-6447	27	24	.	.	PUNCT
ejpam-6447	28	1	additionally	additionally	ADV
ejpam-6447	28	2	,	,	PUNCT
ejpam-6447	28	3	the	the	DET
ejpam-6447	28	4	inclusion	inclusion	NOUN
ejpam-6447	28	5	of	of	ADP
ejpam-6447	28	6	age	age	NOUN
ejpam-6447	28	7	-	-	PUNCT
ejpam-6447	28	8	structured	structure	VERB
ejpam-6447	28	9	modeling	modeling	NOUN
ejpam-6447	28	10	has	have	AUX
ejpam-6447	28	11	gained	gain	VERB
ejpam-6447	28	12	prominence	prominence	NOUN
ejpam-6447	28	13	in	in	ADP
ejpam-6447	28	14	the	the	DET
ejpam-6447	28	15	study	study	NOUN
ejpam-6447	28	16	of	of	ADP
ejpam-6447	28	17	both	both	CCONJ
ejpam-6447	28	18	infectious	infectious	ADJ
ejpam-6447	28	19	and	and	CCONJ
ejpam-6447	28	20	non	non	ADJ
ejpam-6447	28	21	-	-	ADJ
ejpam-6447	28	22	infectious	infectious	ADJ
ejpam-6447	28	23	diseases	disease	NOUN
ejpam-6447	28	24	.	.	PUNCT
ejpam-6447	29	1	age	age	NOUN
ejpam-6447	29	2	-	-	PUNCT
ejpam-6447	29	3	specific	specific	ADJ
ejpam-6447	29	4	modeling	modeling	NOUN
ejpam-6447	29	5	allows	allow	VERB
ejpam-6447	29	6	researchers	researcher	NOUN
ejpam-6447	29	7	to	to	PART
ejpam-6447	29	8	explore	explore	VERB
ejpam-6447	29	9	differences	difference	NOUN
ejpam-6447	29	10	in	in	ADP
ejpam-6447	29	11	susceptibility	susceptibility	NOUN
ejpam-6447	29	12	,	,	PUNCT
ejpam-6447	29	13	behavior	behavior	NOUN
ejpam-6447	29	14	,	,	PUNCT
ejpam-6447	29	15	and	and	CCONJ
ejpam-6447	29	16	exposure	exposure	NOUN
ejpam-6447	29	17	across	across	ADP
ejpam-6447	29	18	age	age	NOUN
ejpam-6447	29	19	groups	group	NOUN
ejpam-6447	29	20	,	,	PUNCT
ejpam-6447	29	21	a	a	DET
ejpam-6447	29	22	feature	feature	NOUN
ejpam-6447	29	23	particularly	particularly	ADV
ejpam-6447	29	24	important	important	ADJ
ejpam-6447	29	25	in	in	ADP
ejpam-6447	29	26	smoking	smoking	NOUN
ejpam-6447	29	27	dynamics	dynamic	NOUN
ejpam-6447	29	28	where	where	SCONJ
ejpam-6447	29	29	younger	young	ADJ
ejpam-6447	29	30	populations	population	NOUN
ejpam-6447	29	31	exhibit	exhibit	VERB
ejpam-6447	29	32	higher	high	ADJ
ejpam-6447	29	33	vulnerability	vulnerability	NOUN
ejpam-6447	29	34	to	to	ADP
ejpam-6447	29	35	addiction	addiction	NOUN
ejpam-6447	29	36	.	.	PUNCT
ejpam-6447	30	1	motivated	motivate	VERB
ejpam-6447	30	2	by	by	ADP
ejpam-6447	30	3	these	these	DET
ejpam-6447	30	4	observations	observation	NOUN
ejpam-6447	30	5	,	,	PUNCT
ejpam-6447	30	6	we	we	PRON
ejpam-6447	30	7	propose	propose	VERB
ejpam-6447	30	8	and	and	CCONJ
ejpam-6447	30	9	study	study	VERB
ejpam-6447	30	10	an	an	DET
ejpam-6447	30	11	age	age	NOUN
ejpam-6447	30	12	-	-	PUNCT
ejpam-6447	30	13	structured	structure	VERB
ejpam-6447	30	14	smoking	smoking	NOUN
ejpam-6447	30	15	model	model	NOUN
ejpam-6447	30	16	.	.	PUNCT
ejpam-6447	31	1	the	the	DET
ejpam-6447	31	2	model	model	NOUN
ejpam-6447	31	3	’s	’s	PART
ejpam-6447	31	4	development	development	NOUN
ejpam-6447	31	5	and	and	CCONJ
ejpam-6447	31	6	analysis	analysis	NOUN
ejpam-6447	31	7	of	of	ADP
ejpam-6447	31	8	the	the	DET
ejpam-6447	31	9	endemic	endemic	ADJ
ejpam-6447	31	10	and	and	CCONJ
ejpam-6447	31	11	smoking	smoking	NOUN
ejpam-6447	31	12	-	-	PUNCT
ejpam-6447	31	13	free	free	ADJ
ejpam-6447	31	14	equilibrium	equilibrium	NOUN
ejpam-6447	31	15	points	point	NOUN
ejpam-6447	31	16	come	come	VERB
ejpam-6447	31	17	first	first	ADV
ejpam-6447	31	18	.	.	PUNCT
ejpam-6447	32	1	the	the	DET
ejpam-6447	32	2	existence	existence	NOUN
ejpam-6447	32	3	and	and	CCONJ
ejpam-6447	32	4	uniqueness	uniqueness	NOUN
ejpam-6447	32	5	of	of	ADP
ejpam-6447	32	6	the	the	DET
ejpam-6447	32	7	model	model	NOUN
ejpam-6447	32	8	solutions	solution	NOUN
ejpam-6447	32	9	are	be	AUX
ejpam-6447	32	10	then	then	ADV
ejpam-6447	32	11	established	establish	VERB
ejpam-6447	32	12	.	.	PUNCT
ejpam-6447	33	1	to	to	PART
ejpam-6447	33	2	investigate	investigate	VERB
ejpam-6447	33	3	long	long	ADJ
ejpam-6447	33	4	-	-	PUNCT
ejpam-6447	33	5	term	term	NOUN
ejpam-6447	33	6	dynamics	dynamic	NOUN
ejpam-6447	33	7	,	,	PUNCT
ejpam-6447	33	8	we	we	PRON
ejpam-6447	33	9	perform	perform	VERB
ejpam-6447	33	10	a	a	DET
ejpam-6447	33	11	global	global	ADJ
ejpam-6447	33	12	stability	stability	NOUN
ejpam-6447	33	13	analysis	analysis	NOUN
ejpam-6447	33	14	of	of	ADP
ejpam-6447	33	15	the	the	DET
ejpam-6447	33	16	equilibrium	equilibrium	NOUN
ejpam-6447	33	17	states	state	NOUN
ejpam-6447	33	18	using	use	VERB
ejpam-6447	33	19	an	an	DET
ejpam-6447	33	20	appropriate	appropriate	ADJ
ejpam-6447	33	21	lyapunov	lyapunov	NOUN
ejpam-6447	33	22	function	function	NOUN
ejpam-6447	33	23	.	.	PUNCT
ejpam-6447	34	1	furthermore	furthermore	ADV
ejpam-6447	34	2	,	,	PUNCT
ejpam-6447	34	3	we	we	PRON
ejpam-6447	34	4	fix	fix	VERB
ejpam-6447	34	5	the	the	DET
ejpam-6447	34	6	age	age	NOUN
ejpam-6447	34	7	variable	variable	NOUN
ejpam-6447	34	8	and	and	CCONJ
ejpam-6447	34	9	implement	implement	VERB
ejpam-6447	34	10	a	a	DET
ejpam-6447	34	11	nonstandard	nonstandard	ADJ
ejpam-6447	34	12	finite	finite	ADJ
ejpam-6447	34	13	difference	difference	NOUN
ejpam-6447	34	14	(	(	PUNCT
ejpam-6447	34	15	nsfd	nsfd	ADJ
ejpam-6447	34	16	)	)	PUNCT
ejpam-6447	34	17	approach	approach	NOUN
ejpam-6447	34	18	to	to	AUX
ejpam-6447	34	19	numerically	numerically	ADV
ejpam-6447	34	20	approximate	approximate	VERB
ejpam-6447	34	21	the	the	DET
ejpam-6447	34	22	model	model	NOUN
ejpam-6447	34	23	’s	’s	PART
ejpam-6447	34	24	solutions	solution	NOUN
ejpam-6447	34	25	,	,	PUNCT
ejpam-6447	34	26	which	which	PRON
ejpam-6447	34	27	are	be	AUX
ejpam-6447	34	28	then	then	ADV
ejpam-6447	34	29	compared	compare	VERB
ejpam-6447	34	30	graphically	graphically	ADV
ejpam-6447	34	31	with	with	ADP
ejpam-6447	34	32	those	those	PRON
ejpam-6447	34	33	obtained	obtain	VERB
ejpam-6447	34	34	using	use	VERB
ejpam-6447	34	35	the	the	DET
ejpam-6447	34	36	classical	classical	ADJ
ejpam-6447	34	37	fourth	fourth	ADJ
ejpam-6447	34	38	-	-	PUNCT
ejpam-6447	34	39	order	order	NOUN
ejpam-6447	34	40	runge	runge	NOUN
ejpam-6447	34	41	–	–	PUNCT
ejpam-6447	34	42	kutta	kutta	NOUN
ejpam-6447	34	43	(	(	PUNCT
ejpam-6447	34	44	rk4	rk4	NOUN
ejpam-6447	34	45	)	)	PUNCT
ejpam-6447	34	46	method	method	NOUN
ejpam-6447	34	47	via	via	ADP
ejpam-6447	34	48	matlab	matlab	PROPN
ejpam-6447	34	49	simulations	simulation	NOUN
ejpam-6447	34	50	.	.	PUNCT
ejpam-6447	35	1	the	the	DET
ejpam-6447	35	2	remainder	remainder	NOUN
ejpam-6447	35	3	of	of	ADP
ejpam-6447	35	4	the	the	DET
ejpam-6447	35	5	paper	paper	NOUN
ejpam-6447	35	6	is	be	AUX
ejpam-6447	35	7	structured	structure	VERB
ejpam-6447	35	8	as	as	SCONJ
ejpam-6447	35	9	follows	follow	VERB
ejpam-6447	35	10	.	.	PUNCT
ejpam-6447	36	1	section	section	NOUN
ejpam-6447	36	2	2	2	NUM
ejpam-6447	36	3	introduces	introduce	VERB
ejpam-6447	36	4	the	the	DET
ejpam-6447	36	5	formulation	formulation	NOUN
ejpam-6447	36	6	of	of	ADP
ejpam-6447	36	7	the	the	DET
ejpam-6447	36	8	age	age	NOUN
ejpam-6447	36	9	-	-	PUNCT
ejpam-6447	36	10	structured	structure	VERB
ejpam-6447	36	11	model	model	NOUN
ejpam-6447	36	12	and	and	CCONJ
ejpam-6447	36	13	discusses	discuss	VERB
ejpam-6447	36	14	the	the	DET
ejpam-6447	36	15	existence	existence	NOUN
ejpam-6447	36	16	and	and	CCONJ
ejpam-6447	36	17	uniqueness	uniqueness	NOUN
ejpam-6447	36	18	of	of	ADP
ejpam-6447	36	19	solutions	solution	NOUN
ejpam-6447	36	20	.	.	PUNCT
ejpam-6447	37	1	section	section	NOUN
ejpam-6447	37	2	3	3	NUM
ejpam-6447	37	3	analyzes	analyze	VERB
ejpam-6447	37	4	the	the	DET
ejpam-6447	37	5	equilibrium	equilibrium	NOUN
ejpam-6447	37	6	points	point	NOUN
ejpam-6447	37	7	and	and	CCONJ
ejpam-6447	37	8	their	their	PRON
ejpam-6447	37	9	local	local	ADJ
ejpam-6447	37	10	stability	stability	NOUN
ejpam-6447	37	11	.	.	PUNCT
ejpam-6447	38	1	section	section	NOUN
ejpam-6447	38	2	4	4	NUM
ejpam-6447	38	3	presents	present	VERB
ejpam-6447	38	4	the	the	DET
ejpam-6447	38	5	global	global	ADJ
ejpam-6447	38	6	stability	stability	NOUN
ejpam-6447	38	7	results	result	NOUN
ejpam-6447	38	8	using	use	VERB
ejpam-6447	38	9	the	the	DET
ejpam-6447	38	10	lyapunov	lyapunov	ADJ
ejpam-6447	38	11	method	method	NOUN
ejpam-6447	38	12	.	.	PUNCT
ejpam-6447	39	1	in	in	ADP
ejpam-6447	39	2	section	section	NOUN
ejpam-6447	39	3	5	5	NUM
ejpam-6447	39	4	,	,	PUNCT
ejpam-6447	39	5	we	we	PRON
ejpam-6447	39	6	employ	employ	VERB
ejpam-6447	39	7	the	the	DET
ejpam-6447	39	8	nsfd	nsfd	ADJ
ejpam-6447	39	9	technique	technique	NOUN
ejpam-6447	39	10	for	for	ADP
ejpam-6447	39	11	numerical	numerical	ADJ
ejpam-6447	39	12	simulations	simulation	NOUN
ejpam-6447	39	13	.	.	PUNCT
ejpam-6447	40	1	finally	finally	ADV
ejpam-6447	40	2	,	,	PUNCT
ejpam-6447	40	3	section	section	NOUN
ejpam-6447	40	4	6	6	NUM
ejpam-6447	40	5	concludes	conclude	VERB
ejpam-6447	40	6	the	the	DET
ejpam-6447	40	7	paper	paper	NOUN
ejpam-6447	40	8	with	with	ADP
ejpam-6447	40	9	key	key	ADJ
ejpam-6447	40	10	findings	finding	NOUN
ejpam-6447	40	11	.	.	PUNCT
ejpam-6447	41	1	2	2	X
ejpam-6447	41	2	.	.	X
ejpam-6447	41	3	model	model	NOUN
ejpam-6447	41	4	formulation	formulation	NOUN
ejpam-6447	41	5	and	and	CCONJ
ejpam-6447	41	6	mathematical	mathematical	ADJ
ejpam-6447	41	7	well	well	ADJ
ejpam-6447	41	8	-	-	PUNCT
ejpam-6447	41	9	posedness	posedness	NOUN
ejpam-6447	41	10	we	we	PRON
ejpam-6447	41	11	introduce	introduce	VERB
ejpam-6447	41	12	an	an	DET
ejpam-6447	41	13	age	age	NOUN
ejpam-6447	41	14	-	-	PUNCT
ejpam-6447	41	15	structured	structure	VERB
ejpam-6447	41	16	smoking	smoking	NOUN
ejpam-6447	41	17	model	model	NOUN
ejpam-6447	41	18	that	that	PRON
ejpam-6447	41	19	incorporates	incorporate	VERB
ejpam-6447	41	20	household	household	NOUN
ejpam-6447	41	21	effects	effect	NOUN
ejpam-6447	41	22	,	,	PUNCT
ejpam-6447	41	23	such	such	ADJ
ejpam-6447	41	24	as	as	ADP
ejpam-6447	41	25	school	school	NOUN
ejpam-6447	41	26	vacations	vacation	NOUN
ejpam-6447	41	27	,	,	PUNCT
ejpam-6447	41	28	that	that	PRON
ejpam-6447	41	29	influence	influence	AUX
ejpam-6447	41	30	smoking	smoke	VERB
ejpam-6447	41	31	initiation	initiation	NOUN
ejpam-6447	41	32	rates	rate	NOUN
ejpam-6447	41	33	.	.	PUNCT
ejpam-6447	42	1	the	the	DET
ejpam-6447	42	2	model	model	NOUN
ejpam-6447	42	3	consists	consist	VERB
ejpam-6447	42	4	of	of	ADP
ejpam-6447	42	5	four	four	NUM
ejpam-6447	42	6	compartments	compartment	NOUN
ejpam-6447	42	7	:	:	PUNCT
ejpam-6447	42	8	susceptible	susceptible	ADJ
ejpam-6447	42	9	(	(	PUNCT
ejpam-6447	42	10	s	s	NOUN
ejpam-6447	42	11	)	)	PUNCT
ejpam-6447	42	12	,	,	PUNCT
ejpam-6447	42	13	exposed	expose	VERB
ejpam-6447	42	14	(	(	PUNCT
ejpam-6447	42	15	e	e	NOUN
ejpam-6447	42	16	)	)	PUNCT
ejpam-6447	42	17	,	,	PUNCT
ejpam-6447	42	18	smokers	smoker	NOUN
ejpam-6447	42	19	(	(	PUNCT
ejpam-6447	42	20	i	i	NOUN
ejpam-6447	42	21	)	)	PUNCT
ejpam-6447	42	22	,	,	PUNCT
ejpam-6447	42	23	and	and	CCONJ
ejpam-6447	42	24	recovered	recover	VERB
ejpam-6447	42	25	(	(	PUNCT
ejpam-6447	42	26	r	r	NOUN
ejpam-6447	42	27	)	)	PUNCT
ejpam-6447	42	28	.	.	PUNCT
ejpam-6447	43	1	the	the	DET
ejpam-6447	43	2	system	system	NOUN
ejpam-6447	43	3	of	of	ADP
ejpam-6447	43	4	ordinary	ordinary	ADJ
ejpam-6447	43	5	differential	differential	ADJ
ejpam-6447	43	6	equations	equation	NOUN
ejpam-6447	43	7	(	(	PUNCT
ejpam-6447	43	8	odes	ode	NOUN
ejpam-6447	43	9	)	)	PUNCT
ejpam-6447	43	10	is	be	AUX
ejpam-6447	43	11	given	give	VERB
ejpam-6447	43	12	by:	by:	NOUN
ejpam-6447	43	13	ds	ds	ADJ
ejpam-6447	43	14	dt	dt	NOUN
ejpam-6447	43	15	=	=	SYM
ejpam-6447	43	16	λ−	λ−	PROPN
ejpam-6447	43	17	β(a	β(a	PROPN
ejpam-6447	43	18	,	,	PUNCT
ejpam-6447	44	1	t)si	t)si	PROPN
ejpam-6447	44	2	−	−	PROPN
ejpam-6447	44	3	µs	µs	NOUN
ejpam-6447	44	4	,	,	PUNCT
ejpam-6447	44	5	de	de	X
ejpam-6447	44	6	dt	dt	NOUN
ejpam-6447	44	7	=	=	SYM
ejpam-6447	44	8	β(a	β(a	PROPN
ejpam-6447	44	9	,	,	PUNCT
ejpam-6447	44	10	t)si	t)si	PROPN
ejpam-6447	44	11	−	−	PROPN
ejpam-6447	44	12	(	(	PUNCT
ejpam-6447	44	13	σ	σ	NOUN
ejpam-6447	44	14	+	+	NUM
ejpam-6447	44	15	µ)e	µ)e	NOUN
ejpam-6447	44	16	,	,	PUNCT
ejpam-6447	44	17	di	di	NOUN
ejpam-6447	44	18	dt	dt	NOUN
ejpam-6447	44	19	=	=	PUNCT
ejpam-6447	44	20	σe	σe	PROPN
ejpam-6447	44	21	−	−	PROPN
ejpam-6447	44	22	(	(	PUNCT
ejpam-6447	44	23	γ	γ	X
ejpam-6447	44	24	+	+	X
ejpam-6447	44	25	µ)i	µ)i	ADJ
ejpam-6447	44	26	,	,	PUNCT
ejpam-6447	44	27	dr	dr	PROPN
ejpam-6447	44	28	dt	dt	PROPN
ejpam-6447	44	29	=	=	PROPN
ejpam-6447	44	30	γi	γi	ADP
ejpam-6447	44	31	−	−	NOUN
ejpam-6447	44	32	µr	µr	ADP
ejpam-6447	44	33	.	.	PUNCT
ejpam-6447	44	34	(	(	PUNCT
ejpam-6447	44	35	1	1	X
ejpam-6447	44	36	)	)	PUNCT
ejpam-6447	44	37	here	here	ADV
ejpam-6447	44	38	,	,	PUNCT
ejpam-6447	44	39	λ	λ	PROPN
ejpam-6447	44	40	is	be	AUX
ejpam-6447	44	41	the	the	DET
ejpam-6447	44	42	recruitment	recruitment	NOUN
ejpam-6447	44	43	rate	rate	NOUN
ejpam-6447	44	44	,	,	PUNCT
ejpam-6447	44	45	µ	µ	X
ejpam-6447	44	46	is	be	AUX
ejpam-6447	44	47	the	the	DET
ejpam-6447	44	48	natural	natural	ADJ
ejpam-6447	44	49	death	death	NOUN
ejpam-6447	44	50	rate	rate	NOUN
ejpam-6447	44	51	,	,	PUNCT
ejpam-6447	44	52	σ	σ	PROPN
ejpam-6447	44	53	is	be	AUX
ejpam-6447	44	54	the	the	DET
ejpam-6447	44	55	transition	transition	NOUN
ejpam-6447	44	56	rate	rate	NOUN
ejpam-6447	44	57	from	from	ADP
ejpam-6447	44	58	the	the	DET
ejpam-6447	44	59	exposed	expose	VERB
ejpam-6447	44	60	class	class	NOUN
ejpam-6447	44	61	to	to	ADP
ejpam-6447	44	62	the	the	DET
ejpam-6447	44	63	infected	infected	ADJ
ejpam-6447	44	64	class	class	NOUN
ejpam-6447	44	65	,	,	PUNCT
ejpam-6447	44	66	γ	γ	X
ejpam-6447	44	67	is	be	AUX
ejpam-6447	44	68	the	the	DET
ejpam-6447	44	69	transition	transition	NOUN
ejpam-6447	44	70	rate	rate	NOUN
ejpam-6447	44	71	from	from	ADP
ejpam-6447	44	72	the	the	DET
ejpam-6447	44	73	infected	infected	ADJ
ejpam-6447	44	74	class	class	NOUN
ejpam-6447	44	75	to	to	ADP
ejpam-6447	44	76	the	the	DET
ejpam-6447	44	77	recovered	recovered	ADJ
ejpam-6447	44	78	class	class	NOUN
ejpam-6447	44	79	,	,	PUNCT
ejpam-6447	44	80	β(a	β(a	PROPN
ejpam-6447	44	81	,	,	PUNCT
ejpam-6447	44	82	t	t	PROPN
ejpam-6447	44	83	)	)	PUNCT
ejpam-6447	44	84	represents	represent	VERB
ejpam-6447	44	85	the	the	DET
ejpam-6447	44	86	transmission	transmission	NOUN
ejpam-6447	44	87	rate	rate	NOUN
ejpam-6447	44	88	,	,	PUNCT
ejpam-6447	44	89	which	which	PRON
ejpam-6447	44	90	varies	vary	VERB
ejpam-6447	44	91	seasonally	seasonally	ADV
ejpam-6447	44	92	according	accord	VERB
ejpam-6447	44	93	to	to	ADP
ejpam-6447	44	94	the	the	DET
ejpam-6447	44	95	effect	effect	NOUN
ejpam-6447	44	96	of	of	ADP
ejpam-6447	44	97	the	the	DET
ejpam-6447	44	98	household	household	NOUN
ejpam-6447	44	99	model	model	NOUN
ejpam-6447	44	100	:	:	PUNCT
ejpam-6447	44	101	s.	s.	PROPN
ejpam-6447	44	102	bushnaq	bushnaq	PROPN
ejpam-6447	44	103	,	,	PUNCT
ejpam-6447	44	104	s.	s.	PROPN
ejpam-6447	44	105	bano	bano	PROPN
ejpam-6447	44	106	,	,	PUNCT
ejpam-6447	44	107	a.	a.	PROPN
ejpam-6447	44	108	zeb	zeb	PROPN
ejpam-6447	44	109	/	/	SYM
ejpam-6447	44	110	eur	eur	PROPN
ejpam-6447	44	111	.	.	PUNCT
ejpam-6447	45	1	j.	j.	PROPN
ejpam-6447	45	2	pure	pure	PROPN
ejpam-6447	45	3	appl	appl	PROPN
ejpam-6447	45	4	.	.	PROPN
ejpam-6447	45	5	math	math	PROPN
ejpam-6447	45	6	,	,	PUNCT
ejpam-6447	45	7	18	18	NUM
ejpam-6447	45	8	(	(	PUNCT
ejpam-6447	45	9	3	3	NUM
ejpam-6447	45	10	)	)	PUNCT
ejpam-6447	45	11	(	(	PUNCT
ejpam-6447	45	12	2025	2025	NUM
ejpam-6447	45	13	)	)	PUNCT
ejpam-6447	45	14	,	,	PUNCT
ejpam-6447	45	15	6447	6447	NUM
ejpam-6447	45	16	3	3	NUM
ejpam-6447	45	17	of	of	ADP
ejpam-6447	45	18	12	12	NUM
ejpam-6447	45	19	β(a	β(a	PROPN
ejpam-6447	45	20	,	,	PUNCT
ejpam-6447	45	21	t	t	PROPN
ejpam-6447	45	22	)	)	PUNCT
ejpam-6447	45	23	=	=	SYM
ejpam-6447	46	1	β0	β0	NOUN
ejpam-6447	46	2	(	(	PUNCT
ejpam-6447	46	3	1	1	NUM
ejpam-6447	46	4	+	+	CCONJ
ejpam-6447	46	5	ϵ	ϵ	X
ejpam-6447	46	6	cos	cos	PROPN
ejpam-6447	46	7	(	(	PUNCT
ejpam-6447	46	8	2πt	2πt	PROPN
ejpam-6447	46	9	t	t	PROPN
ejpam-6447	46	10	)	)	PUNCT
ejpam-6447	46	11	)	)	PUNCT
ejpam-6447	46	12	,	,	PUNCT
ejpam-6447	46	13	where	where	SCONJ
ejpam-6447	46	14	ϵ	ϵ	PROPN
ejpam-6447	46	15	captures	capture	VERB
ejpam-6447	46	16	the	the	DET
ejpam-6447	46	17	strength	strength	NOUN
ejpam-6447	46	18	of	of	ADP
ejpam-6447	46	19	seasonal	seasonal	ADJ
ejpam-6447	46	20	effects	effect	NOUN
ejpam-6447	46	21	(	(	PUNCT
ejpam-6447	46	22	e.g.	e.g.	ADV
ejpam-6447	46	23	,	,	PUNCT
ejpam-6447	46	24	school	school	NOUN
ejpam-6447	46	25	vacations	vacation	NOUN
ejpam-6447	46	26	)	)	PUNCT
ejpam-6447	46	27	,	,	PUNCT
ejpam-6447	46	28	and	and	CCONJ
ejpam-6447	46	29	t	t	PROPN
ejpam-6447	46	30	represents	represent	VERB
ejpam-6447	46	31	the	the	DET
ejpam-6447	46	32	yearly	yearly	ADJ
ejpam-6447	46	33	period	period	NOUN
ejpam-6447	46	34	.	.	PUNCT
ejpam-6447	47	1	by	by	ADP
ejpam-6447	47	2	adding	add	VERB
ejpam-6447	47	3	equations	equation	NOUN
ejpam-6447	47	4	from	from	ADP
ejpam-6447	47	5	1	1	NUM
ejpam-6447	47	6	-	-	SYM
ejpam-6447	47	7	4	4	NUM
ejpam-6447	47	8	of	of	ADP
ejpam-6447	47	9	the	the	DET
ejpam-6447	47	10	model	model	NOUN
ejpam-6447	47	11	(	(	PUNCT
ejpam-6447	47	12	1	1	NUM
ejpam-6447	47	13	)	)	PUNCT
ejpam-6447	47	14	,	,	PUNCT
ejpam-6447	47	15	we	we	PRON
ejpam-6447	47	16	get	get	VERB
ejpam-6447	47	17	figure	figure	NOUN
ejpam-6447	47	18	1	1	NUM
ejpam-6447	47	19	:	:	PUNCT
ejpam-6447	47	20	flow	flow	VERB
ejpam-6447	47	21	chart	chart	NOUN
ejpam-6447	47	22	for	for	ADP
ejpam-6447	47	23	model	model	NOUN
ejpam-6447	47	24	(	(	PUNCT
ejpam-6447	47	25	1	1	X
ejpam-6447	47	26	)	)	PUNCT
ejpam-6447	47	27	dn	dn	NOUN
ejpam-6447	47	28	dt	dt	NOUN
ejpam-6447	48	1	=	=	PUNCT
ejpam-6447	48	2	λ−	λ−	PROPN
ejpam-6447	48	3	µn	µn	PROPN
ejpam-6447	48	4	dn	dn	NOUN
ejpam-6447	48	5	dt	dt	NOUN
ejpam-6447	48	6	+	+	CCONJ
ejpam-6447	48	7	µn	µn	PROPN
ejpam-6447	48	8	=	=	SYM
ejpam-6447	48	9	λ	λ	NOUN
ejpam-6447	48	10	=	=	NOUN
ejpam-6447	48	11	⇒	⇒	NOUN
ejpam-6447	48	12	n	n	NOUN
ejpam-6447	48	13	=	=	SYM
ejpam-6447	48	14	λ	λ	X
ejpam-6447	48	15	µ	µ	X
ejpam-6447	48	16	+	+	CCONJ
ejpam-6447	48	17	(	(	PUNCT
ejpam-6447	48	18	no	no	INTJ
ejpam-6447	48	19	−	−	PROPN
ejpam-6447	48	20	λ	λ	PROPN
ejpam-6447	48	21	µ	µ	X
ejpam-6447	48	22	)	)	PUNCT
ejpam-6447	48	23	exp(−µt	exp(−µt	PROPN
ejpam-6447	48	24	)	)	PUNCT
ejpam-6447	48	25	as	as	ADP
ejpam-6447	48	26	t	t	PROPN
ejpam-6447	48	27	→	→	SYM
ejpam-6447	48	28	∞	∞	PROPN
ejpam-6447	48	29	,	,	PUNCT
ejpam-6447	48	30	we	we	PRON
ejpam-6447	48	31	get	get	VERB
ejpam-6447	48	32	n	n	PRON
ejpam-6447	48	33	=	=	SYM
ejpam-6447	48	34	λ	λ	X
ejpam-6447	48	35	µ	µ	X
ejpam-6447	48	36	,	,	PUNCT
ejpam-6447	48	37	which	which	PRON
ejpam-6447	48	38	implies	imply	VERB
ejpam-6447	48	39	that	that	SCONJ
ejpam-6447	48	40	the	the	DET
ejpam-6447	48	41	given	give	VERB
ejpam-6447	48	42	system	system	NOUN
ejpam-6447	48	43	has	have	VERB
ejpam-6447	48	44	a	a	DET
ejpam-6447	48	45	unique	unique	ADJ
ejpam-6447	48	46	solution	solution	NOUN
ejpam-6447	48	47	.	.	PUNCT
ejpam-6447	49	1	3	3	X
ejpam-6447	49	2	.	.	X
ejpam-6447	49	3	existence	existence	NOUN
ejpam-6447	49	4	of	of	ADP
ejpam-6447	49	5	equilibrium	equilibrium	NOUN
ejpam-6447	49	6	points	point	NOUN
ejpam-6447	49	7	at	at	ADP
ejpam-6447	49	8	equilibrium	equilibrium	NOUN
ejpam-6447	49	9	,	,	PUNCT
ejpam-6447	49	10	the	the	DET
ejpam-6447	49	11	time	time	NOUN
ejpam-6447	49	12	derivatives	derivative	NOUN
ejpam-6447	49	13	are	be	AUX
ejpam-6447	49	14	zero	zero	NUM
ejpam-6447	49	15	.	.	PUNCT
ejpam-6447	50	1	setting	set	VERB
ejpam-6447	50	2	ds	ds	ADJ
ejpam-6447	50	3	dt	dt	NOUN
ejpam-6447	50	4	=	=	SYM
ejpam-6447	50	5	0	0	NUM
ejpam-6447	50	6	,	,	PUNCT
ejpam-6447	50	7	de	de	X
ejpam-6447	50	8	dt	dt	X
ejpam-6447	50	9	=	=	SYM
ejpam-6447	50	10	0	0	NUM
ejpam-6447	50	11	,	,	PUNCT
ejpam-6447	50	12	di	di	NOUN
ejpam-6447	50	13	dt	dt	NOUN
ejpam-6447	50	14	=	=	SYM
ejpam-6447	50	15	0	0	PROPN
ejpam-6447	50	16	,	,	PUNCT
ejpam-6447	50	17	dr	dr	PROPN
ejpam-6447	50	18	dt	dt	PROPN
ejpam-6447	50	19	=	=	SYM
ejpam-6447	50	20	0	0	PROPN
ejpam-6447	50	21	,	,	PUNCT
ejpam-6447	50	22	the	the	DET
ejpam-6447	50	23	equilibrium	equilibrium	NOUN
ejpam-6447	50	24	equations	equation	NOUN
ejpam-6447	50	25	become	become	VERB
ejpam-6447	50	26	λ−	λ−	PROPN
ejpam-6447	50	27	β(a	β(a	PROPN
ejpam-6447	50	28	,	,	PUNCT
ejpam-6447	51	1	t)si	t)si	PROPN
ejpam-6447	51	2	−	−	ADP
ejpam-6447	51	3	µs	µs	NOUN
ejpam-6447	51	4	=	=	NOUN
ejpam-6447	51	5	0	0	NUM
ejpam-6447	51	6	,	,	PUNCT
ejpam-6447	51	7	β(a	β(a	PROPN
ejpam-6447	51	8	,	,	PUNCT
ejpam-6447	51	9	t)si	t)si	PROPN
ejpam-6447	51	10	−	−	PROPN
ejpam-6447	51	11	(	(	PUNCT
ejpam-6447	51	12	σ	σ	NOUN
ejpam-6447	51	13	+	+	NOUN
ejpam-6447	51	14	µ)e	µ)e	NOUN
ejpam-6447	51	15	=	=	SYM
ejpam-6447	51	16	0	0	NUM
ejpam-6447	51	17	,	,	PUNCT
ejpam-6447	51	18	σe	σe	ADP
ejpam-6447	51	19	−	−	PROPN
ejpam-6447	51	20	(	(	PUNCT
ejpam-6447	51	21	γ	γ	X
ejpam-6447	51	22	+	+	X
ejpam-6447	51	23	µ)i	µ)i	X
ejpam-6447	51	24	=	=	SYM
ejpam-6447	51	25	0	0	NUM
ejpam-6447	51	26	,	,	PUNCT
ejpam-6447	51	27	γi	γi	ADP
ejpam-6447	51	28	−	−	NOUN
ejpam-6447	51	29	µr	µr	ADP
ejpam-6447	51	30	=	=	NOUN
ejpam-6447	51	31	0	0	X
ejpam-6447	51	32	.	.	PUNCT
ejpam-6447	52	1	solving	solve	VERB
ejpam-6447	52	2	these	these	DET
ejpam-6447	52	3	equations	equation	NOUN
ejpam-6447	52	4	,	,	PUNCT
ejpam-6447	52	5	we	we	PRON
ejpam-6447	52	6	get	get	VERB
ejpam-6447	52	7	a	a	DET
ejpam-6447	52	8	smoking	smoking	NOUN
ejpam-6447	52	9	-	-	PUNCT
ejpam-6447	52	10	free	free	ADJ
ejpam-6447	52	11	equilibrium	equilibrium	NOUN
ejpam-6447	52	12	point	point	NOUN
ejpam-6447	52	13	d0(s0	d0(s0	PROPN
ejpam-6447	52	14	,	,	PUNCT
ejpam-6447	52	15	e0	e0	PROPN
ejpam-6447	52	16	,	,	PUNCT
ejpam-6447	52	17	i0	i0	PROPN
ejpam-6447	52	18	,	,	PUNCT
ejpam-6447	52	19	r0	r0	NOUN
ejpam-6447	52	20	)	)	PUNCT
ejpam-6447	52	21	,	,	PUNCT
ejpam-6447	52	22	where	where	SCONJ
ejpam-6447	52	23	s0	s0	PROPN
ejpam-6447	52	24	=	=	SYM
ejpam-6447	52	25	λ	λ	X
ejpam-6447	52	26	µ	µ	X
ejpam-6447	52	27	.	.	PUNCT
ejpam-6447	53	1	s.	s.	PROPN
ejpam-6447	53	2	bushnaq	bushnaq	PROPN
ejpam-6447	53	3	,	,	PUNCT
ejpam-6447	53	4	s.	s.	PROPN
ejpam-6447	53	5	bano	bano	PROPN
ejpam-6447	53	6	,	,	PUNCT
ejpam-6447	53	7	a.	a.	PROPN
ejpam-6447	53	8	zeb	zeb	PROPN
ejpam-6447	53	9	/	/	SYM
ejpam-6447	53	10	eur	eur	PROPN
ejpam-6447	53	11	.	.	PUNCT
ejpam-6447	54	1	j.	j.	PROPN
ejpam-6447	54	2	pure	pure	PROPN
ejpam-6447	54	3	appl	appl	PROPN
ejpam-6447	54	4	.	.	PROPN
ejpam-6447	54	5	math	math	PROPN
ejpam-6447	54	6	,	,	PUNCT
ejpam-6447	54	7	18	18	NUM
ejpam-6447	54	8	(	(	PUNCT
ejpam-6447	54	9	3	3	NUM
ejpam-6447	54	10	)	)	PUNCT
ejpam-6447	54	11	(	(	PUNCT
ejpam-6447	54	12	2025	2025	NUM
ejpam-6447	54	13	)	)	PUNCT
ejpam-6447	54	14	,	,	PUNCT
ejpam-6447	54	15	6447	6447	NUM
ejpam-6447	54	16	4	4	NUM
ejpam-6447	54	17	of	of	ADP
ejpam-6447	54	18	12	12	NUM
ejpam-6447	54	19	for	for	ADP
ejpam-6447	54	20	an	an	DET
ejpam-6447	54	21	endemic	endemic	ADJ
ejpam-6447	54	22	equilibrium	equilibrium	NOUN
ejpam-6447	54	23	point	point	NOUN
ejpam-6447	54	24	,	,	PUNCT
ejpam-6447	54	25	we	we	PRON
ejpam-6447	54	26	have	have	VERB
ejpam-6447	54	27	i	i	PRON
ejpam-6447	54	28	>	>	X
ejpam-6447	55	1	0	0	X
ejpam-6447	56	1	.	.	PUNCT
ejpam-6447	57	1	the	the	DET
ejpam-6447	57	2	given	give	VERB
ejpam-6447	57	3	system	system	NOUN
ejpam-6447	57	4	has	have	VERB
ejpam-6447	57	5	an	an	DET
ejpam-6447	57	6	existence	existence	NOUN
ejpam-6447	57	7	of	of	ADP
ejpam-6447	57	8	unique	unique	ADJ
ejpam-6447	57	9	positive	positive	ADJ
ejpam-6447	57	10	equilibrium	equilibrium	NOUN
ejpam-6447	57	11	d∗(s	d∗(s	PROPN
ejpam-6447	57	12	∗	∗	NOUN
ejpam-6447	57	13	,	,	PUNCT
ejpam-6447	57	14	e∗	e∗	NOUN
ejpam-6447	57	15	,	,	PUNCT
ejpam-6447	57	16	i∗	i∗	NOUN
ejpam-6447	57	17	,	,	PUNCT
ejpam-6447	57	18	r∗	r∗	PROPN
ejpam-6447	57	19	)	)	PUNCT
ejpam-6447	57	20	,	,	PUNCT
ejpam-6447	57	21	where	where	SCONJ
ejpam-6447	57	22	s∗	s∗	PROPN
ejpam-6447	57	23	=	=	SYM
ejpam-6447	57	24	(	(	PUNCT
ejpam-6447	57	25	σ	σ	X
ejpam-6447	57	26	+	+	NOUN
ejpam-6447	57	27	µ)(γ	µ)(γ	NOUN
ejpam-6447	57	28	+	+	X
ejpam-6447	57	29	µ	µ	X
ejpam-6447	57	30	)	)	PUNCT
ejpam-6447	57	31	βσ	βσ	PROPN
ejpam-6447	57	32	,	,	PUNCT
ejpam-6447	57	33	e∗	e∗	PROPN
ejpam-6447	57	34	=	=	PUNCT
ejpam-6447	58	1	µ(γ	µ(γ	NOUN
ejpam-6447	58	2	+	+	CCONJ
ejpam-6447	58	3	µ)(r0	µ)(r0	NOUN
ejpam-6447	58	4	−	−	NOUN
ejpam-6447	58	5	1	1	NUM
ejpam-6447	58	6	)	)	PUNCT
ejpam-6447	58	7	σβ	σβ	NOUN
ejpam-6447	58	8	,	,	PUNCT
ejpam-6447	58	9	i∗	i∗	NOUN
ejpam-6447	58	10	=	=	PUNCT
ejpam-6447	58	11	µ(r0	µ(r0	NOUN
ejpam-6447	58	12	−	−	PROPN
ejpam-6447	58	13	1	1	NUM
ejpam-6447	58	14	)	)	PUNCT
ejpam-6447	58	15	β	β	NOUN
ejpam-6447	58	16	,	,	PUNCT
ejpam-6447	58	17	r∗	r∗	PROPN
ejpam-6447	58	18	=	=	PUNCT
ejpam-6447	58	19	γ(r0	γ(r0	NOUN
ejpam-6447	58	20	−	−	PROPN
ejpam-6447	58	21	1	1	X
ejpam-6447	58	22	)	)	PUNCT
ejpam-6447	58	23	β	β	NOUN
ejpam-6447	58	24	.	.	PUNCT
ejpam-6447	59	1	so	so	ADV
ejpam-6447	59	2	there	there	PRON
ejpam-6447	59	3	exists	exist	VERB
ejpam-6447	59	4	an	an	DET
ejpam-6447	59	5	endemic	endemic	ADJ
ejpam-6447	59	6	equilibrium	equilibrium	NOUN
ejpam-6447	59	7	point	point	NOUN
ejpam-6447	59	8	for	for	ADP
ejpam-6447	59	9	r0	r0	NOUN
ejpam-6447	59	10	−	−	PROPN
ejpam-6447	59	11	1	1	NUM
ejpam-6447	59	12	>	>	X
ejpam-6447	59	13	0	0	NUM
ejpam-6447	59	14	.	.	NOUN
ejpam-6447	59	15	3.1	3.1	NUM
ejpam-6447	59	16	.	.	PUNCT
ejpam-6447	60	1	stability	stability	NOUN
ejpam-6447	60	2	and	and	CCONJ
ejpam-6447	60	3	basic	basic	ADJ
ejpam-6447	60	4	reproduction	reproduction	NOUN
ejpam-6447	60	5	number	number	NOUN
ejpam-6447	60	6	the	the	DET
ejpam-6447	60	7	basic	basic	ADJ
ejpam-6447	60	8	reproductive	reproductive	ADJ
ejpam-6447	60	9	number	number	NOUN
ejpam-6447	60	10	,	,	PUNCT
ejpam-6447	60	11	r0	r0	NOUN
ejpam-6447	60	12	,	,	PUNCT
ejpam-6447	60	13	is	be	AUX
ejpam-6447	60	14	calculated	calculate	VERB
ejpam-6447	60	15	as	as	ADP
ejpam-6447	60	16	the	the	DET
ejpam-6447	60	17	spectral	spectral	ADJ
ejpam-6447	60	18	radius	radius	NOUN
ejpam-6447	60	19	of	of	ADP
ejpam-6447	60	20	the	the	DET
ejpam-6447	60	21	next	next	ADJ
ejpam-6447	60	22	-	-	PUNCT
ejpam-6447	60	23	generation	generation	NOUN
ejpam-6447	60	24	matrix	matrix	NOUN
ejpam-6447	60	25	:	:	PUNCT
ejpam-6447	60	26	r0	r0	NOUN
ejpam-6447	60	27	=	=	NOUN
ejpam-6447	60	28	βσλ	βσλ	VERB
ejpam-6447	60	29	µ(σ	µ(σ	NOUN
ejpam-6447	60	30	+	+	CCONJ
ejpam-6447	60	31	µ)(γ	µ)(γ	X
ejpam-6447	60	32	+	+	X
ejpam-6447	60	33	µ	µ	NUM
ejpam-6447	60	34	)	)	PUNCT
ejpam-6447	60	35	.	.	PUNCT
ejpam-6447	61	1	3.2	3.2	NUM
ejpam-6447	61	2	.	.	PUNCT
ejpam-6447	62	1	local	local	ADJ
ejpam-6447	62	2	stability	stability	NOUN
ejpam-6447	62	3	analysis	analysis	NOUN
ejpam-6447	62	4	theorem	theorem	VERB
ejpam-6447	62	5	1	1	NUM
ejpam-6447	62	6	.	.	PUNCT
ejpam-6447	62	7	smoking	smoking	NOUN
ejpam-6447	62	8	-	-	PUNCT
ejpam-6447	62	9	free	free	ADJ
ejpam-6447	62	10	equilibriums	equilibrium	NOUN
ejpam-6447	62	11	are	be	AUX
ejpam-6447	62	12	locally	locally	ADV
ejpam-6447	62	13	asymptotically	asymptotically	ADV
ejpam-6447	62	14	stable	stable	ADJ
ejpam-6447	62	15	when	when	SCONJ
ejpam-6447	62	16	r0	r0	NOUN
ejpam-6447	62	17	<	<	X
ejpam-6447	62	18	1	1	NUM
ejpam-6447	62	19	.	.	PUNCT
ejpam-6447	62	20	proof	proof	NOUN
ejpam-6447	62	21	.	.	PUNCT
ejpam-6447	63	1	the	the	DET
ejpam-6447	63	2	smoking	smoking	NOUN
ejpam-6447	63	3	-	-	PUNCT
ejpam-6447	63	4	free	free	ADJ
ejpam-6447	63	5	equilibrium	equilibrium	NOUN
ejpam-6447	63	6	(	(	PUNCT
ejpam-6447	63	7	sfe	sfe	PROPN
ejpam-6447	63	8	)	)	PUNCT
ejpam-6447	63	9	is	be	AUX
ejpam-6447	63	10	given	give	VERB
ejpam-6447	63	11	by	by	ADP
ejpam-6447	63	12	(	(	PUNCT
ejpam-6447	63	13	s0	s0	PROPN
ejpam-6447	63	14	,	,	PUNCT
ejpam-6447	63	15	e0	e0	PROPN
ejpam-6447	63	16	,	,	PUNCT
ejpam-6447	63	17	i0	i0	PROPN
ejpam-6447	63	18	,	,	PUNCT
ejpam-6447	63	19	r0	r0	NOUN
ejpam-6447	63	20	)	)	PUNCT
ejpam-6447	63	21	=	=	SYM
ejpam-6447	63	22	(	(	PUNCT
ejpam-6447	63	23	λµ	λµ	INTJ
ejpam-6447	63	24	,	,	PUNCT
ejpam-6447	63	25	0	0	NUM
ejpam-6447	63	26	,	,	PUNCT
ejpam-6447	63	27	0	0	NUM
ejpam-6447	63	28	,	,	PUNCT
ejpam-6447	63	29	0	0	NUM
ejpam-6447	63	30	)	)	PUNCT
ejpam-6447	63	31	.	.	PUNCT
ejpam-6447	64	1	the	the	DET
ejpam-6447	64	2	jacobian	jacobian	ADJ
ejpam-6447	64	3	matrix	matrix	NOUN
ejpam-6447	64	4	evaluated	evaluate	VERB
ejpam-6447	64	5	at	at	ADP
ejpam-6447	64	6	sfe	sfe	PROPN
ejpam-6447	64	7	is	be	AUX
ejpam-6447	64	8	as	as	SCONJ
ejpam-6447	64	9	follows	follow	VERB
ejpam-6447	64	10	:	:	PUNCT
ejpam-6447	64	11	j	j	NOUN
ejpam-6447	64	12	=	=	SYM
ejpam-6447	64	13			NOUN
ejpam-6447	64	14	−µ	−µ	NOUN
ejpam-6447	64	15	0	0	PUNCT
ejpam-6447	65	1	−βs0	−βs0	NOUN
ejpam-6447	65	2	0	0	NUM
ejpam-6447	65	3	0	0	NUM
ejpam-6447	65	4	−(σ	−(σ	NOUN
ejpam-6447	65	5	+	+	X
ejpam-6447	65	6	µ	µ	NOUN
ejpam-6447	65	7	)	)	PUNCT
ejpam-6447	65	8	βs0	βs0	NOUN
ejpam-6447	65	9	0	0	NUM
ejpam-6447	65	10	0	0	NUM
ejpam-6447	66	1	σ	σ	NUM
ejpam-6447	66	2	−(γ	−(γ	NOUN
ejpam-6447	66	3	+	+	X
ejpam-6447	66	4	µ	µ	X
ejpam-6447	66	5	)	)	PUNCT
ejpam-6447	66	6	0	0	NUM
ejpam-6447	66	7	0	0	NUM
ejpam-6447	66	8	0	0	NUM
ejpam-6447	66	9	γ	γ	PROPN
ejpam-6447	66	10	−µ	−µ	ADJ
ejpam-6447	66	11			PROPN
ejpam-6447	66	12	.	.	PUNCT
ejpam-6447	67	1	(	(	PUNCT
ejpam-6447	67	2	2	2	X
ejpam-6447	67	3	)	)	PUNCT
ejpam-6447	67	4	for	for	ADP
ejpam-6447	67	5	eigenvalues	eigenvalue	NOUN
ejpam-6447	67	6	,	,	PUNCT
ejpam-6447	67	7	we	we	PRON
ejpam-6447	67	8	solve	solve	VERB
ejpam-6447	67	9	|j	|j	NOUN
ejpam-6447	67	10	−	−	PROPN
ejpam-6447	67	11	λ′i|	λ′i|	NOUN
ejpam-6447	67	12	=	=	SYM
ejpam-6447	67	13	0	0	NUM
ejpam-6447	67	14	,	,	PUNCT
ejpam-6447	67	15	|j	|j	VERB
ejpam-6447	68	1	−	−	PROPN
ejpam-6447	68	2	λ′i|	λ′i|	NOUN
ejpam-6447	68	3	=	=	SYM
ejpam-6447	68	4	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-6447	68	5	−µ−	−µ−	NOUN
ejpam-6447	68	6	λ′	λ′	X
ejpam-6447	68	7	0	0	PUNCT
ejpam-6447	68	8	−βs0	−βs0	NOUN
ejpam-6447	68	9	0	0	NUM
ejpam-6447	68	10	0	0	NUM
ejpam-6447	68	11	−(σ	−(σ	NOUN
ejpam-6447	68	12	+	+	NOUN
ejpam-6447	69	1	µ)−	µ)−	NOUN
ejpam-6447	69	2	λ′	λ′	NUM
ejpam-6447	69	3	βs0	βs0	NOUN
ejpam-6447	69	4	0	0	NUM
ejpam-6447	69	5	0	0	NUM
ejpam-6447	70	1	σ	σ	NUM
ejpam-6447	70	2	−(γ	−(γ	NOUN
ejpam-6447	70	3	+	+	PUNCT
ejpam-6447	70	4	µ)−	µ)−	NOUN
ejpam-6447	70	5	λ′	λ′	PROPN
ejpam-6447	70	6	0	0	NUM
ejpam-6447	70	7	0	0	NUM
ejpam-6447	70	8	0	0	NUM
ejpam-6447	70	9	γ	γ	NOUN
ejpam-6447	70	10	−µ−	−µ−	NOUN
ejpam-6447	70	11	λ′	λ′	NOUN
ejpam-6447	70	12	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-6447	70	13	=	=	SYM
ejpam-6447	70	14	0	0	X
ejpam-6447	70	15	.	.	PUNCT
ejpam-6447	71	1	expanding	expand	VERB
ejpam-6447	71	2	by	by	ADP
ejpam-6447	71	3	c1	c1	PROPN
ejpam-6447	71	4	(	(	PUNCT
ejpam-6447	71	5	−µ−	−µ−	NOUN
ejpam-6447	71	6	λ′	λ′	PROPN
ejpam-6447	71	7	)	)	PUNCT
ejpam-6447	71	8	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6447	71	9	−(σ	−(σ	NOUN
ejpam-6447	71	10	+	+	NOUN
ejpam-6447	71	11	µ)−	µ)−	NOUN
ejpam-6447	71	12	λ′	λ′	X
ejpam-6447	71	13	βs0	βs0	NOUN
ejpam-6447	71	14	0	0	NUM
ejpam-6447	71	15	σ	σ	NUM
ejpam-6447	71	16	−(γ	−(γ	NOUN
ejpam-6447	71	17	+	+	PUNCT
ejpam-6447	72	1	µ)−	µ)−	NOUN
ejpam-6447	72	2	λ′	λ′	PROPN
ejpam-6447	72	3	0	0	NUM
ejpam-6447	72	4	0	0	NUM
ejpam-6447	72	5	γ	γ	X
ejpam-6447	72	6	−µ−	−µ−	NOUN
ejpam-6447	72	7	λ′	λ′	X
ejpam-6447	72	8	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6447	72	9	=	=	SYM
ejpam-6447	72	10	0	0	NUM
ejpam-6447	72	11	,	,	PUNCT
ejpam-6447	72	12	again	again	ADV
ejpam-6447	72	13	expand	expand	VERB
ejpam-6447	72	14	with	with	ADP
ejpam-6447	72	15	c1	c1	PROPN
ejpam-6447	72	16	=	=	PROPN
ejpam-6447	72	17	⇒	⇒	PROPN
ejpam-6447	72	18	(	(	PUNCT
ejpam-6447	72	19	−	−	NUM
ejpam-6447	72	20	µ−	µ−	PROPN
ejpam-6447	72	21	λ′)[(−	λ′)[(−	PROPN
ejpam-6447	72	22	(	(	PUNCT
ejpam-6447	72	23	σ	σ	NOUN
ejpam-6447	72	24	+	+	PUNCT
ejpam-6447	72	25	µ)−	µ)−	PROPN
ejpam-6447	72	26	λ′)(((γ	λ′)(((γ	NOUN
ejpam-6447	72	27	+	+	CCONJ
ejpam-6447	72	28	µ	µ	X
ejpam-6447	72	29	)	)	PUNCT
ejpam-6447	72	30	+	+	NUM
ejpam-6447	72	31	λ′)(µ+	λ′)(µ+	PROPN
ejpam-6447	72	32	λ′	λ′	NUM
ejpam-6447	72	33	)	)	PUNCT
ejpam-6447	72	34	)	)	PUNCT
ejpam-6447	73	1	−	−	PROPN
ejpam-6447	73	2	σ	σ	NOUN
ejpam-6447	73	3	(	(	PUNCT
ejpam-6447	73	4	−	−	PROPN
ejpam-6447	73	5	βs0(µ+	βs0(µ+	X
ejpam-6447	73	6	λ′	λ′	NOUN
ejpam-6447	73	7	)	)	PUNCT
ejpam-6447	73	8	)	)	PUNCT
ejpam-6447	73	9	]	]	PUNCT
ejpam-6447	74	1	=	=	PUNCT
ejpam-6447	74	2	0	0	NUM
ejpam-6447	74	3	,	,	PUNCT
ejpam-6447	74	4	=	=	PRON
ejpam-6447	74	5	⇒	⇒	NOUN
ejpam-6447	74	6	(	(	PUNCT
ejpam-6447	74	7	−	−	NUM
ejpam-6447	74	8	µ−	µ−	PROPN
ejpam-6447	74	9	λ′)[(−	λ′)[(−	PROPN
ejpam-6447	74	10	(	(	PUNCT
ejpam-6447	74	11	σ	σ	NOUN
ejpam-6447	74	12	+	+	PUNCT
ejpam-6447	74	13	µ)−	µ)−	PROPN
ejpam-6447	74	14	λ′)(λ′2	λ′)(λ′2	NOUN
ejpam-6447	74	15	+	+	CCONJ
ejpam-6447	74	16	µλ′	µλ′	X
ejpam-6447	74	17	+	+	PUNCT
ejpam-6447	74	18	µ(γ	µ(γ	NOUN
ejpam-6447	74	19	+	+	CCONJ
ejpam-6447	74	20	µ	µ	X
ejpam-6447	74	21	)	)	PUNCT
ejpam-6447	74	22	+	+	CCONJ
ejpam-6447	74	23	λ′(γ	λ′(γ	PROPN
ejpam-6447	74	24	+	+	X
ejpam-6447	74	25	µ	µ	X
ejpam-6447	74	26	)	)	PUNCT
ejpam-6447	74	27	)	)	PUNCT
ejpam-6447	75	1	+	+	CCONJ
ejpam-6447	75	2	σβs0µ+	σβs0µ+	NOUN
ejpam-6447	75	3	σβs0λ′	σβs0λ′	VERB
ejpam-6447	75	4	]	]	PUNCT
ejpam-6447	75	5	=	=	SYM
ejpam-6447	75	6	0	0	PROPN
ejpam-6447	75	7	,	,	PUNCT
ejpam-6447	75	8	s.	s.	PROPN
ejpam-6447	75	9	bushnaq	bushnaq	PROPN
ejpam-6447	75	10	,	,	PUNCT
ejpam-6447	75	11	s.	s.	PROPN
ejpam-6447	75	12	bano	bano	PROPN
ejpam-6447	75	13	,	,	PUNCT
ejpam-6447	75	14	a.	a.	PROPN
ejpam-6447	75	15	zeb	zeb	PROPN
ejpam-6447	75	16	/	/	SYM
ejpam-6447	75	17	eur	eur	PROPN
ejpam-6447	75	18	.	.	PUNCT
ejpam-6447	76	1	j.	j.	PROPN
ejpam-6447	76	2	pure	pure	PROPN
ejpam-6447	76	3	appl	appl	PROPN
ejpam-6447	76	4	.	.	PROPN
ejpam-6447	76	5	math	math	PROPN
ejpam-6447	76	6	,	,	PUNCT
ejpam-6447	76	7	18	18	NUM
ejpam-6447	76	8	(	(	PUNCT
ejpam-6447	76	9	3	3	NUM
ejpam-6447	76	10	)	)	PUNCT
ejpam-6447	76	11	(	(	PUNCT
ejpam-6447	76	12	2025	2025	NUM
ejpam-6447	76	13	)	)	PUNCT
ejpam-6447	76	14	,	,	PUNCT
ejpam-6447	76	15	6447	6447	NUM
ejpam-6447	76	16	5	5	NUM
ejpam-6447	76	17	of	of	ADP
ejpam-6447	76	18	12	12	NUM
ejpam-6447	76	19	=	=	NOUN
ejpam-6447	76	20	⇒	⇒	NOUN
ejpam-6447	76	21	(	(	PUNCT
ejpam-6447	76	22	−	−	PRON
ejpam-6447	76	23	µ−	µ−	PROPN
ejpam-6447	76	24	λ′)(−	λ′)(−	NOUN
ejpam-6447	76	25	λ′3	λ′3	X
ejpam-6447	76	26	−	−	PROPN
ejpam-6447	76	27	(	(	PUNCT
ejpam-6447	76	28	γ	γ	X
ejpam-6447	76	29	+	+	NOUN
ejpam-6447	76	30	2µ)λ′2	2µ)λ′2	NUM
ejpam-6447	76	31	−	−	NOUN
ejpam-6447	77	1	µ(γ	µ(γ	PRON
ejpam-6447	77	2	+	+	CCONJ
ejpam-6447	77	3	µ)λ′	µ)λ′	PROPN
ejpam-6447	77	4	−	−	PROPN
ejpam-6447	77	5	(	(	PUNCT
ejpam-6447	77	6	σ	σ	PROPN
ejpam-6447	77	7	+	+	PROPN
ejpam-6447	77	8	µ)λ′2	µ)λ′2	PROPN
ejpam-6447	77	9	−	−	PROPN
ejpam-6447	77	10	(	(	PUNCT
ejpam-6447	77	11	σ	σ	NOUN
ejpam-6447	77	12	+	+	NOUN
ejpam-6447	77	13	µ)(γ	µ)(γ	ADJ
ejpam-6447	77	14	+	+	NOUN
ejpam-6447	77	15	2µ)λ′	2µ)λ′	NUM
ejpam-6447	77	16	−	−	NOUN
ejpam-6447	77	17	(	(	PUNCT
ejpam-6447	77	18	σ	σ	NOUN
ejpam-6447	77	19	+	+	CCONJ
ejpam-6447	77	20	µ)µ(γ	µ)µ(γ	NOUN
ejpam-6447	77	21	+	+	ADJ
ejpam-6447	77	22	µ	µ	X
ejpam-6447	77	23	)	)	PUNCT
ejpam-6447	77	24	+	+	NUM
ejpam-6447	77	25	σβs0µ+	σβs0µ+	NOUN
ejpam-6447	77	26	σβs0λ′	σβs0λ′	X
ejpam-6447	77	27	)	)	PUNCT
ejpam-6447	78	1	=	=	PUNCT
ejpam-6447	78	2	0	0	X
ejpam-6447	78	3	.	.	PUNCT
ejpam-6447	79	1	thus	thus	ADV
ejpam-6447	79	2	,	,	PUNCT
ejpam-6447	79	3	it	it	PRON
ejpam-6447	79	4	follows	follow	VERB
ejpam-6447	79	5	the	the	DET
ejpam-6447	79	6	following	follow	VERB
ejpam-6447	79	7	equation	equation	NOUN
ejpam-6447	79	8	,	,	PUNCT
ejpam-6447	79	9	=	=	PRON
ejpam-6447	79	10	⇒	⇒	NOUN
ejpam-6447	79	11	(	(	PUNCT
ejpam-6447	79	12	−	−	PROPN
ejpam-6447	79	13	µ−	µ−	PROPN
ejpam-6447	79	14	λ′)[λ′3	λ′)[λ′3	X
ejpam-6447	79	15	+	+	CCONJ
ejpam-6447	79	16	(	(	PUNCT
ejpam-6447	79	17	γ	γ	X
ejpam-6447	79	18	+	+	X
ejpam-6447	79	19	3µ+	3µ+	NUM
ejpam-6447	79	20	σ)λ′2	σ)λ′2	PROPN
ejpam-6447	80	1	+	+	CCONJ
ejpam-6447	80	2	(	(	PUNCT
ejpam-6447	80	3	µ(γ	µ(γ	NOUN
ejpam-6447	80	4	+	+	CCONJ
ejpam-6447	80	5	µ	µ	X
ejpam-6447	80	6	)	)	PUNCT
ejpam-6447	80	7	+	+	CCONJ
ejpam-6447	80	8	(	(	PUNCT
ejpam-6447	80	9	σ	σ	NOUN
ejpam-6447	80	10	+	+	NOUN
ejpam-6447	80	11	µ)(γ	µ)(γ	ADJ
ejpam-6447	80	12	+	+	CCONJ
ejpam-6447	80	13	2µ)−	2µ)−	NUM
ejpam-6447	80	14	βs0σ	βs0σ	NUM
ejpam-6447	80	15	)	)	PUNCT
ejpam-6447	80	16	λ′	λ′	X
ejpam-6447	81	1	+	+	CCONJ
ejpam-6447	81	2	(	(	PUNCT
ejpam-6447	81	3	σ	σ	NOUN
ejpam-6447	81	4	+	+	NOUN
ejpam-6447	81	5	µ)µ(γ	µ)µ(γ	NOUN
ejpam-6447	81	6	+	+	PUNCT
ejpam-6447	81	7	µ)−	µ)−	NOUN
ejpam-6447	81	8	βs0σµ	βs0σµ	NUM
ejpam-6447	81	9	]	]	PUNCT
ejpam-6447	81	10	=	=	PUNCT
ejpam-6447	81	11	0	0	NUM
ejpam-6447	81	12	,	,	PUNCT
ejpam-6447	81	13	from	from	ADP
ejpam-6447	81	14	the	the	DET
ejpam-6447	81	15	following	follow	VERB
ejpam-6447	81	16	inequalities	inequality	NOUN
ejpam-6447	81	17	:	:	PUNCT
ejpam-6447	81	18	=	=	SYM
ejpam-6447	81	19	⇒	⇒	X
ejpam-6447	81	20	βs0σ	βs0σ	X
ejpam-6447	81	21	<	<	X
ejpam-6447	81	22	(	(	PUNCT
ejpam-6447	81	23	σ	σ	X
ejpam-6447	81	24	+	+	NOUN
ejpam-6447	81	25	µ)(γ	µ)(γ	NOUN
ejpam-6447	81	26	+	+	X
ejpam-6447	81	27	µ	µ	NUM
ejpam-6447	81	28	)	)	PUNCT
ejpam-6447	81	29	,	,	PUNCT
ejpam-6447	81	30	=	=	PRON
ejpam-6447	81	31	⇒	⇒	X
ejpam-6447	81	32	βs0σ	βs0σ	NOUN
ejpam-6447	81	33	<	<	X
ejpam-6447	81	34	(	(	PUNCT
ejpam-6447	81	35	σ	σ	X
ejpam-6447	81	36	+	+	NOUN
ejpam-6447	81	37	µ)(γ	µ)(γ	NOUN
ejpam-6447	81	38	+	+	PRON
ejpam-6447	81	39	2µ	2µ	NUM
ejpam-6447	81	40	)	)	PUNCT
ejpam-6447	81	41	,	,	PUNCT
ejpam-6447	81	42	it	it	PRON
ejpam-6447	81	43	follows	follow	VERB
ejpam-6447	81	44	that	that	SCONJ
ejpam-6447	81	45	r0	r0	NOUN
ejpam-6447	81	46	<	<	X
ejpam-6447	81	47	1	1	NUM
ejpam-6447	81	48	,	,	PUNCT
ejpam-6447	81	49	which	which	PRON
ejpam-6447	81	50	implies	imply	VERB
ejpam-6447	81	51	that	that	SCONJ
ejpam-6447	81	52	the	the	DET
ejpam-6447	81	53	characteristic	characteristic	ADJ
ejpam-6447	81	54	equation	equation	NOUN
ejpam-6447	81	55	associated	associate	VERB
ejpam-6447	81	56	with	with	ADP
ejpam-6447	81	57	the	the	DET
ejpam-6447	81	58	linearized	linearize	VERB
ejpam-6447	81	59	system	system	NOUN
ejpam-6447	81	60	at	at	ADP
ejpam-6447	81	61	the	the	DET
ejpam-6447	81	62	smoking	smoking	NOUN
ejpam-6447	81	63	-	-	PUNCT
ejpam-6447	81	64	free	free	ADJ
ejpam-6447	81	65	equilibrium	equilibrium	NOUN
ejpam-6447	81	66	has	have	VERB
ejpam-6447	81	67	negative	negative	ADJ
ejpam-6447	81	68	roots	root	NOUN
ejpam-6447	81	69	.	.	PUNCT
ejpam-6447	82	1	moreover	moreover	ADV
ejpam-6447	82	2	,	,	PUNCT
ejpam-6447	82	3	the	the	DET
ejpam-6447	82	4	corresponding	corresponding	ADJ
ejpam-6447	82	5	characteristic	characteristic	ADJ
ejpam-6447	82	6	polynomial	polynomial	ADJ
ejpam-6447	82	7	satisfies	satisfie	NOUN
ejpam-6447	82	8	the	the	DET
ejpam-6447	82	9	routh	routh	PROPN
ejpam-6447	82	10	-	-	PUNCT
ejpam-6447	82	11	hurwitz	hurwitz	PROPN
ejpam-6447	82	12	stability	stability	NOUN
ejpam-6447	82	13	criteria	criterion	NOUN
ejpam-6447	82	14	under	under	ADP
ejpam-6447	82	15	the	the	DET
ejpam-6447	82	16	condition	condition	NOUN
ejpam-6447	82	17	r0	r0	NOUN
ejpam-6447	82	18	<	<	X
ejpam-6447	82	19	1	1	NUM
ejpam-6447	82	20	.	.	PUNCT
ejpam-6447	82	21	therefore	therefore	ADV
ejpam-6447	82	22	,	,	PUNCT
ejpam-6447	82	23	all	all	DET
ejpam-6447	82	24	eigenvalues	eigenvalue	VERB
ejpam-6447	82	25	of	of	ADP
ejpam-6447	82	26	the	the	DET
ejpam-6447	82	27	jacobian	jacobian	ADJ
ejpam-6447	82	28	matrix	matrix	NOUN
ejpam-6447	82	29	have	have	VERB
ejpam-6447	82	30	negative	negative	ADJ
ejpam-6447	82	31	real	real	ADJ
ejpam-6447	82	32	parts	part	NOUN
ejpam-6447	82	33	,	,	PUNCT
ejpam-6447	82	34	confirming	confirm	VERB
ejpam-6447	82	35	that	that	SCONJ
ejpam-6447	82	36	the	the	DET
ejpam-6447	82	37	smoking	smoking	NOUN
ejpam-6447	82	38	-	-	PUNCT
ejpam-6447	82	39	free	free	ADJ
ejpam-6447	82	40	equilibrium	equilibrium	NOUN
ejpam-6447	82	41	is	be	AUX
ejpam-6447	82	42	locally	locally	ADV
ejpam-6447	82	43	asymptotically	asymptotically	ADV
ejpam-6447	82	44	stable	stable	ADJ
ejpam-6447	82	45	.	.	PUNCT
ejpam-6447	83	1	theorem	theorem	NOUN
ejpam-6447	83	2	2	2	NUM
ejpam-6447	83	3	.	.	PUNCT
ejpam-6447	84	1	the	the	DET
ejpam-6447	84	2	positive	positive	ADJ
ejpam-6447	84	3	(	(	PUNCT
ejpam-6447	84	4	endemic	endemic	ADJ
ejpam-6447	84	5	)	)	PUNCT
ejpam-6447	84	6	equilibrium	equilibrium	NOUN
ejpam-6447	84	7	is	be	AUX
ejpam-6447	84	8	locally	locally	ADV
ejpam-6447	84	9	asymptotically	asymptotically	ADV
ejpam-6447	84	10	stable	stable	ADJ
ejpam-6447	84	11	if	if	SCONJ
ejpam-6447	84	12	r0	r0	NOUN
ejpam-6447	84	13	>	>	X
ejpam-6447	84	14	1	1	X
ejpam-6447	84	15	.	.	PUNCT
ejpam-6447	85	1	proof	proof	NOUN
ejpam-6447	85	2	.	.	PUNCT
ejpam-6447	86	1	the	the	DET
ejpam-6447	86	2	endemic	endemic	ADJ
ejpam-6447	86	3	equilibrium	equilibrium	NOUN
ejpam-6447	86	4	is	be	AUX
ejpam-6447	86	5	given	give	VERB
ejpam-6447	86	6	by	by	ADP
ejpam-6447	86	7	(	(	PUNCT
ejpam-6447	86	8	s∗	s∗	PROPN
ejpam-6447	86	9	,	,	PUNCT
ejpam-6447	86	10	e∗	e∗	NOUN
ejpam-6447	86	11	,	,	PUNCT
ejpam-6447	86	12	i∗	i∗	NOUN
ejpam-6447	86	13	,	,	PUNCT
ejpam-6447	86	14	r∗	r∗	PROPN
ejpam-6447	86	15	)	)	PUNCT
ejpam-6447	86	16	=	=	SYM
ejpam-6447	87	1	(	(	PUNCT
ejpam-6447	87	2	(	(	PUNCT
ejpam-6447	87	3	σ	σ	X
ejpam-6447	87	4	+	+	NOUN
ejpam-6447	87	5	µ)(γ	µ)(γ	NOUN
ejpam-6447	87	6	+	+	X
ejpam-6447	87	7	µ	µ	X
ejpam-6447	87	8	)	)	PUNCT
ejpam-6447	87	9	βσ	βσ	NOUN
ejpam-6447	87	10	,	,	PUNCT
ejpam-6447	87	11	µ(γ	µ(γ	NOUN
ejpam-6447	87	12	+	+	CCONJ
ejpam-6447	87	13	µ)(r0	µ)(r0	NOUN
ejpam-6447	87	14	−	−	NOUN
ejpam-6447	87	15	1	1	NUM
ejpam-6447	87	16	)	)	PUNCT
ejpam-6447	87	17	σβ	σβ	NOUN
ejpam-6447	87	18	,	,	PUNCT
ejpam-6447	87	19	µ(r0	µ(r0	ADV
ejpam-6447	87	20	−	−	NOUN
ejpam-6447	87	21	1	1	NUM
ejpam-6447	87	22	)	)	PUNCT
ejpam-6447	87	23	β	β	NOUN
ejpam-6447	87	24	,	,	PUNCT
ejpam-6447	87	25	γ(r0	γ(r0	NOUN
ejpam-6447	87	26	−	−	PROPN
ejpam-6447	87	27	1	1	X
ejpam-6447	87	28	)	)	PUNCT
ejpam-6447	87	29	β	β	PROPN
ejpam-6447	87	30	)	)	PUNCT
ejpam-6447	87	31	.	.	PUNCT
ejpam-6447	88	1	the	the	DET
ejpam-6447	88	2	jacobian	jacobian	ADJ
ejpam-6447	88	3	matrix	matrix	NOUN
ejpam-6447	88	4	evaluated	evaluate	VERB
ejpam-6447	88	5	at	at	ADP
ejpam-6447	88	6	the	the	DET
ejpam-6447	88	7	endemic	endemic	ADJ
ejpam-6447	88	8	equilibrium	equilibrium	NOUN
ejpam-6447	88	9	point	point	NOUN
ejpam-6447	88	10	is	be	AUX
ejpam-6447	88	11	j	j	NOUN
ejpam-6447	88	12	=	=	PUNCT
ejpam-6447	88	13			NOUN
ejpam-6447	88	14	−βi∗	−βi∗	X
ejpam-6447	88	15	−	−	X
ejpam-6447	88	16	µ	µ	X
ejpam-6447	88	17	0	0	NUM
ejpam-6447	88	18	−βs∗	−βs∗	SYM
ejpam-6447	88	19	0	0	NUM
ejpam-6447	88	20	βi∗	βi∗	NOUN
ejpam-6447	88	21	−(σ	−(σ	NOUN
ejpam-6447	88	22	+	+	X
ejpam-6447	88	23	µ	µ	X
ejpam-6447	88	24	)	)	PUNCT
ejpam-6447	88	25	βs∗	βs∗	NOUN
ejpam-6447	88	26	0	0	NUM
ejpam-6447	88	27	0	0	NUM
ejpam-6447	89	1	σ	σ	NUM
ejpam-6447	89	2	−(γ	−(γ	NOUN
ejpam-6447	89	3	+	+	X
ejpam-6447	89	4	µ	µ	X
ejpam-6447	89	5	)	)	PUNCT
ejpam-6447	89	6	0	0	NUM
ejpam-6447	89	7	0	0	NUM
ejpam-6447	89	8	0	0	NUM
ejpam-6447	89	9	γ	γ	PROPN
ejpam-6447	89	10	−µ	−µ	ADJ
ejpam-6447	89	11			NOUN
ejpam-6447	89	12	.	.	PUNCT
ejpam-6447	90	1	to	to	PART
ejpam-6447	90	2	determine	determine	VERB
ejpam-6447	90	3	the	the	DET
ejpam-6447	90	4	eigenvalues	eigenvalue	NOUN
ejpam-6447	90	5	,	,	PUNCT
ejpam-6447	90	6	we	we	PRON
ejpam-6447	90	7	solve	solve	VERB
ejpam-6447	90	8	the	the	DET
ejpam-6447	90	9	characteristic	characteristic	ADJ
ejpam-6447	90	10	equation	equation	NOUN
ejpam-6447	90	11	|j	|j	PUNCT
ejpam-6447	91	1	−	−	PROPN
ejpam-6447	91	2	λ′i|	λ′i|	NOUN
ejpam-6447	91	3	=	=	SYM
ejpam-6447	91	4	0	0	NUM
ejpam-6447	91	5	,	,	PUNCT
ejpam-6447	91	6	which	which	PRON
ejpam-6447	91	7	becomes	become	VERB
ejpam-6447	91	8	|j	|j	NOUN
ejpam-6447	91	9	−	−	PROPN
ejpam-6447	91	10	λ′i|	λ′i|	NOUN
ejpam-6447	91	11	=	=	SYM
ejpam-6447	91	12			NOUN
ejpam-6447	92	1	−βi∗	−βi∗	X
ejpam-6447	92	2	−	−	PUNCT
ejpam-6447	92	3	µ−	µ−	PROPN
ejpam-6447	92	4	λ′	λ′	NOUN
ejpam-6447	92	5	0	0	NUM
ejpam-6447	92	6	−βs∗	−βs∗	SYM
ejpam-6447	92	7	0	0	NUM
ejpam-6447	92	8	βi∗	βi∗	NOUN
ejpam-6447	92	9	−(σ	−(σ	NOUN
ejpam-6447	92	10	+	+	NOUN
ejpam-6447	92	11	µ)−	µ)−	NOUN
ejpam-6447	92	12	λ′	λ′	X
ejpam-6447	92	13	βs∗	βs∗	NOUN
ejpam-6447	92	14	0	0	NUM
ejpam-6447	92	15	0	0	NUM
ejpam-6447	93	1	σ	σ	NUM
ejpam-6447	93	2	−(γ	−(γ	NOUN
ejpam-6447	93	3	+	+	PUNCT
ejpam-6447	93	4	µ)−	µ)−	NOUN
ejpam-6447	93	5	λ′	λ′	PROPN
ejpam-6447	93	6	0	0	NUM
ejpam-6447	93	7	0	0	NUM
ejpam-6447	93	8	0	0	NUM
ejpam-6447	93	9	γ	γ	PROPN
ejpam-6447	93	10	−µ−	−µ−	NOUN
ejpam-6447	93	11	λ′	λ′	X
ejpam-6447	93	12			NOUN
ejpam-6447	93	13	=	=	SYM
ejpam-6447	93	14	0	0	X
ejpam-6447	93	15	.	.	PUNCT
ejpam-6447	94	1	expanding	expand	VERB
ejpam-6447	94	2	along	along	ADP
ejpam-6447	94	3	the	the	DET
ejpam-6447	94	4	fourth	fourth	ADJ
ejpam-6447	94	5	column	column	NOUN
ejpam-6447	94	6	c4	c4	NOUN
ejpam-6447	94	7	,	,	PUNCT
ejpam-6447	94	8	we	we	PRON
ejpam-6447	94	9	obtain	obtain	VERB
ejpam-6447	94	10	(	(	PUNCT
ejpam-6447	94	11	−µ−	−µ−	NOUN
ejpam-6447	94	12	λ′	λ′	NOUN
ejpam-6447	94	13	)	)	PUNCT
ejpam-6447	95	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6447	95	2	−βi∗	−βi∗	X
ejpam-6447	96	1	−	−	PUNCT
ejpam-6447	96	2	µ−	µ−	PROPN
ejpam-6447	96	3	λ′	λ′	NOUN
ejpam-6447	96	4	0	0	NUM
ejpam-6447	96	5	−βs∗	−βs∗	NOUN
ejpam-6447	96	6	βi∗	βi∗	NOUN
ejpam-6447	96	7	−(σ	−(σ	NOUN
ejpam-6447	96	8	+	+	NOUN
ejpam-6447	96	9	µ)−	µ)−	NOUN
ejpam-6447	96	10	λ′	λ′	X
ejpam-6447	96	11	βs∗	βs∗	NOUN
ejpam-6447	97	1	0	0	NUM
ejpam-6447	97	2	σ	σ	NUM
ejpam-6447	97	3	−(γ	−(γ	NOUN
ejpam-6447	97	4	+	+	PUNCT
ejpam-6447	97	5	µ)−	µ)−	NOUN
ejpam-6447	97	6	λ′	λ′	X
ejpam-6447	97	7	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6447	97	8	=	=	SYM
ejpam-6447	97	9	0	0	PROPN
ejpam-6447	97	10	.	.	PUNCT
ejpam-6447	98	1	this	this	PRON
ejpam-6447	98	2	yields	yield	VERB
ejpam-6447	98	3	one	one	NUM
ejpam-6447	98	4	eigenvalue	eigenvalue	NOUN
ejpam-6447	98	5	λ′	λ′	X
ejpam-6447	98	6	=	=	PUNCT
ejpam-6447	98	7	−µ.	−µ.	ADV
ejpam-6447	98	8	next	next	ADV
ejpam-6447	98	9	,	,	PUNCT
ejpam-6447	98	10	we	we	PRON
ejpam-6447	98	11	expand	expand	VERB
ejpam-6447	98	12	the	the	DET
ejpam-6447	98	13	remaining	remain	VERB
ejpam-6447	98	14	3×	3×	NUM
ejpam-6447	98	15	3	3	NUM
ejpam-6447	98	16	determinant	determinant	ADJ
ejpam-6447	98	17	along	along	ADP
ejpam-6447	98	18	the	the	DET
ejpam-6447	98	19	first	first	ADJ
ejpam-6447	98	20	column	column	NOUN
ejpam-6447	98	21	c1	c1	NOUN
ejpam-6447	98	22	,	,	PUNCT
ejpam-6447	98	23	leading	lead	VERB
ejpam-6447	98	24	to	to	ADP
ejpam-6447	98	25	:(	:(	PUNCT
ejpam-6447	98	26	−	−	NOUN
ejpam-6447	98	27	βi∗	βi∗	NOUN
ejpam-6447	98	28	−	−	NOUN
ejpam-6447	98	29	µ−	µ−	PROPN
ejpam-6447	98	30	λ′)(((σ	λ′)(((σ	NOUN
ejpam-6447	98	31	+	+	CCONJ
ejpam-6447	98	32	µ	µ	X
ejpam-6447	98	33	)	)	PUNCT
ejpam-6447	98	34	+	+	NUM
ejpam-6447	98	35	λ′)((γ	λ′)((γ	PROPN
ejpam-6447	98	36	+	+	CCONJ
ejpam-6447	98	37	µ	µ	X
ejpam-6447	98	38	)	)	PUNCT
ejpam-6447	98	39	+	+	CCONJ
ejpam-6447	99	1	λ′)−	λ′)−	PROPN
ejpam-6447	99	2	βσs∗	βσs∗	NOUN
ejpam-6447	99	3	)	)	PUNCT
ejpam-6447	100	1	−	−	ADP
ejpam-6447	100	2	β2σi∗s∗	β2σi∗s∗	NUM
ejpam-6447	100	3	=	=	SYM
ejpam-6447	100	4	0	0	NUM
ejpam-6447	100	5	,	,	PUNCT
ejpam-6447	100	6	s.	s.	PROPN
ejpam-6447	100	7	bushnaq	bushnaq	PROPN
ejpam-6447	100	8	,	,	PUNCT
ejpam-6447	100	9	s.	s.	PROPN
ejpam-6447	100	10	bano	bano	PROPN
ejpam-6447	100	11	,	,	PUNCT
ejpam-6447	100	12	a.	a.	PROPN
ejpam-6447	100	13	zeb	zeb	PROPN
ejpam-6447	100	14	/	/	SYM
ejpam-6447	100	15	eur	eur	PROPN
ejpam-6447	100	16	.	.	PUNCT
ejpam-6447	101	1	j.	j.	PROPN
ejpam-6447	101	2	pure	pure	PROPN
ejpam-6447	101	3	appl	appl	PROPN
ejpam-6447	101	4	.	.	PROPN
ejpam-6447	101	5	math	math	PROPN
ejpam-6447	101	6	,	,	PUNCT
ejpam-6447	101	7	18	18	NUM
ejpam-6447	101	8	(	(	PUNCT
ejpam-6447	101	9	3	3	NUM
ejpam-6447	101	10	)	)	PUNCT
ejpam-6447	101	11	(	(	PUNCT
ejpam-6447	101	12	2025	2025	NUM
ejpam-6447	101	13	)	)	PUNCT
ejpam-6447	101	14	,	,	PUNCT
ejpam-6447	101	15	6447	6447	NUM
ejpam-6447	101	16	6	6	NUM
ejpam-6447	101	17	of	of	ADP
ejpam-6447	101	18	12	12	NUM
ejpam-6447	101	19	(	(	PUNCT
ejpam-6447	101	20	−	−	PROPN
ejpam-6447	101	21	βi∗	βi∗	NOUN
ejpam-6447	101	22	−	−	PROPN
ejpam-6447	101	23	µ−	µ−	PROPN
ejpam-6447	101	24	λ′)(λ′2	λ′)(λ′2	NOUN
ejpam-6447	101	25	+	+	CCONJ
ejpam-6447	101	26	(	(	PUNCT
ejpam-6447	101	27	(	(	PUNCT
ejpam-6447	101	28	σ	σ	X
ejpam-6447	101	29	+	+	X
ejpam-6447	101	30	µ	µ	X
ejpam-6447	101	31	)	)	PUNCT
ejpam-6447	102	1	+	+	CCONJ
ejpam-6447	102	2	(	(	PUNCT
ejpam-6447	102	3	γ	γ	X
ejpam-6447	102	4	+	+	X
ejpam-6447	102	5	µ	µ	NUM
ejpam-6447	102	6	)	)	PUNCT
ejpam-6447	102	7	)	)	PUNCT
ejpam-6447	102	8	λ′	λ′	X
ejpam-6447	103	1	+	+	CCONJ
ejpam-6447	103	2	(	(	PUNCT
ejpam-6447	103	3	σ	σ	NOUN
ejpam-6447	103	4	+	+	NOUN
ejpam-6447	103	5	µ)(γ	µ)(γ	ADJ
ejpam-6447	103	6	+	+	CCONJ
ejpam-6447	103	7	µ)−	µ)−	NOUN
ejpam-6447	103	8	βσs∗	βσs∗	NOUN
ejpam-6447	103	9	)	)	PUNCT
ejpam-6447	103	10	−	−	ADP
ejpam-6447	103	11	β2σi∗s∗	β2σi∗s∗	NUM
ejpam-6447	103	12	=	=	SYM
ejpam-6447	103	13	0	0	NUM
ejpam-6447	103	14	,	,	PUNCT
ejpam-6447	103	15	λ′3	λ′3	X
ejpam-6447	103	16	+	+	CCONJ
ejpam-6447	103	17	(	(	PUNCT
ejpam-6447	103	18	(	(	PUNCT
ejpam-6447	103	19	σ	σ	X
ejpam-6447	103	20	+	+	X
ejpam-6447	103	21	µ	µ	X
ejpam-6447	103	22	)	)	PUNCT
ejpam-6447	103	23	+	+	CCONJ
ejpam-6447	103	24	(	(	PUNCT
ejpam-6447	103	25	γ	γ	X
ejpam-6447	103	26	+	+	X
ejpam-6447	103	27	µ	µ	X
ejpam-6447	103	28	)	)	PUNCT
ejpam-6447	103	29	+	+	NUM
ejpam-6447	103	30	βi∗	βi∗	NOUN
ejpam-6447	103	31	+	+	X
ejpam-6447	103	32	µ	µ	X
ejpam-6447	103	33	)	)	PUNCT
ejpam-6447	103	34	λ′2	λ′2	X
ejpam-6447	104	1	+	+	CCONJ
ejpam-6447	104	2	(	(	PUNCT
ejpam-6447	104	3	(	(	PUNCT
ejpam-6447	104	4	(	(	PUNCT
ejpam-6447	104	5	σ	σ	NOUN
ejpam-6447	104	6	+	+	NOUN
ejpam-6447	104	7	µ)(γ	µ)(γ	NOUN
ejpam-6447	104	8	+	+	CCONJ
ejpam-6447	104	9	µ)−	µ)−	PROPN
ejpam-6447	104	10	βσs∗)+	βσs∗)+	NOUN
ejpam-6447	104	11	(	(	PUNCT
ejpam-6447	104	12	βi∗	βi∗	NOUN
ejpam-6447	104	13	+	+	X
ejpam-6447	104	14	µ	µ	X
ejpam-6447	104	15	)	)	PUNCT
ejpam-6447	104	16	(	(	PUNCT
ejpam-6447	104	17	(	(	PUNCT
ejpam-6447	104	18	σ	σ	X
ejpam-6447	104	19	+	+	X
ejpam-6447	104	20	µ	µ	X
ejpam-6447	104	21	)	)	PUNCT
ejpam-6447	104	22	+	+	CCONJ
ejpam-6447	104	23	(	(	PUNCT
ejpam-6447	104	24	γ	γ	X
ejpam-6447	104	25	+	+	X
ejpam-6447	104	26	µ	µ	NUM
ejpam-6447	104	27	)	)	PUNCT
ejpam-6447	104	28	)	)	PUNCT
ejpam-6447	104	29	)	)	PUNCT
ejpam-6447	104	30	λ′	λ′	X
ejpam-6447	105	1	+	+	NOUN
ejpam-6447	105	2	(	(	PUNCT
ejpam-6447	105	3	βi∗	βi∗	NOUN
ejpam-6447	105	4	+	+	X
ejpam-6447	105	5	µ	µ	X
ejpam-6447	105	6	)	)	PUNCT
ejpam-6447	105	7	(	(	PUNCT
ejpam-6447	105	8	(	(	PUNCT
ejpam-6447	105	9	σ	σ	X
ejpam-6447	105	10	+	+	NOUN
ejpam-6447	105	11	µ)(γ	µ)(γ	NOUN
ejpam-6447	105	12	+	+	PUNCT
ejpam-6447	105	13	µ)−	µ)−	NOUN
ejpam-6447	105	14	βσs∗)+	βσs∗)+	NOUN
ejpam-6447	105	15	β2σi∗s∗	β2σi∗s∗	NUM
ejpam-6447	105	16	=	=	SYM
ejpam-6447	105	17	0	0	NUM
ejpam-6447	105	18	.	.	PUNCT
ejpam-6447	106	1	given	give	VERB
ejpam-6447	106	2	that	that	DET
ejpam-6447	106	3	s∗	s∗	PROPN
ejpam-6447	106	4	=	=	SYM
ejpam-6447	106	5	(	(	PUNCT
ejpam-6447	106	6	σ	σ	X
ejpam-6447	106	7	+	+	NOUN
ejpam-6447	106	8	µ)(γ	µ)(γ	NOUN
ejpam-6447	106	9	+	+	X
ejpam-6447	106	10	µ	µ	X
ejpam-6447	106	11	)	)	PUNCT
ejpam-6447	106	12	βσ	βσ	PROPN
ejpam-6447	106	13	,	,	PUNCT
ejpam-6447	106	14	the	the	DET
ejpam-6447	106	15	above	above	ADJ
ejpam-6447	106	16	equation	equation	NOUN
ejpam-6447	106	17	simplifies	simplifie	NOUN
ejpam-6447	106	18	to	to	ADP
ejpam-6447	106	19	the	the	DET
ejpam-6447	106	20	reduced	reduced	ADJ
ejpam-6447	106	21	form	form	NOUN
ejpam-6447	106	22	:	:	PUNCT
ejpam-6447	106	23	λ′3	λ′3	X
ejpam-6447	106	24	+	+	CCONJ
ejpam-6447	106	25	(	(	PUNCT
ejpam-6447	106	26	σ	σ	NOUN
ejpam-6447	106	27	+	+	CCONJ
ejpam-6447	106	28	3µ+	3µ+	NUM
ejpam-6447	106	29	γ	γ	NOUN
ejpam-6447	106	30	+	+	CCONJ
ejpam-6447	106	31	βi∗	βi∗	NOUN
ejpam-6447	106	32	)	)	PUNCT
ejpam-6447	106	33	λ′2	λ′2	X
ejpam-6447	107	1	+	+	CCONJ
ejpam-6447	107	2	(	(	PUNCT
ejpam-6447	107	3	βi∗	βi∗	NOUN
ejpam-6447	107	4	+	+	X
ejpam-6447	107	5	µ	µ	X
ejpam-6447	107	6	)	)	PUNCT
ejpam-6447	107	7	(	(	PUNCT
ejpam-6447	107	8	σ	σ	NOUN
ejpam-6447	107	9	+	+	X
ejpam-6447	107	10	2µ+	2µ+	NUM
ejpam-6447	107	11	γ	γ	NOUN
ejpam-6447	107	12	)	)	PUNCT
ejpam-6447	107	13	λ′	λ′	X
ejpam-6447	108	1	+	+	CCONJ
ejpam-6447	108	2	β2σi∗s∗	β2σi∗s∗	NUM
ejpam-6447	108	3	=	=	SYM
ejpam-6447	108	4	0	0	NUM
ejpam-6447	108	5	,	,	PUNCT
ejpam-6447	108	6	where	where	SCONJ
ejpam-6447	108	7	i∗	i∗	NOUN
ejpam-6447	108	8	=	=	PUNCT
ejpam-6447	108	9	µ(r0	µ(r0	ADV
ejpam-6447	108	10	−	−	PROPN
ejpam-6447	108	11	1	1	NUM
ejpam-6447	108	12	)	)	PUNCT
ejpam-6447	108	13	β	β	NOUN
ejpam-6447	108	14	,	,	PUNCT
ejpam-6447	108	15	for	for	ADP
ejpam-6447	108	16	r0	r0	NOUN
ejpam-6447	108	17	>	>	X
ejpam-6447	108	18	1	1	NUM
ejpam-6447	108	19	.	.	PUNCT
ejpam-6447	109	1	since	since	SCONJ
ejpam-6447	109	2	all	all	DET
ejpam-6447	109	3	the	the	DET
ejpam-6447	109	4	coefficients	coefficient	NOUN
ejpam-6447	109	5	of	of	ADP
ejpam-6447	109	6	the	the	DET
ejpam-6447	109	7	above	above	ADJ
ejpam-6447	109	8	cubic	cubic	ADJ
ejpam-6447	109	9	polynomial	polynomial	NOUN
ejpam-6447	109	10	are	be	AUX
ejpam-6447	109	11	positive	positive	ADJ
ejpam-6447	109	12	forr0	forr0	NOUN
ejpam-6447	109	13	>	>	X
ejpam-6447	109	14	1	1	NUM
ejpam-6447	109	15	,	,	PUNCT
ejpam-6447	109	16	the	the	DET
ejpam-6447	109	17	routh	routh	PROPN
ejpam-6447	109	18	–	–	PUNCT
ejpam-6447	109	19	hurwitz	hurwitz	PROPN
ejpam-6447	109	20	criteria	criterion	NOUN
ejpam-6447	109	21	are	be	AUX
ejpam-6447	109	22	satisfied	satisfied	ADJ
ejpam-6447	109	23	.	.	PUNCT
ejpam-6447	110	1	therefore	therefore	ADV
ejpam-6447	110	2	,	,	PUNCT
ejpam-6447	110	3	all	all	DET
ejpam-6447	110	4	roots	root	NOUN
ejpam-6447	110	5	of	of	ADP
ejpam-6447	110	6	the	the	DET
ejpam-6447	110	7	characteristic	characteristic	ADJ
ejpam-6447	110	8	equation	equation	NOUN
ejpam-6447	110	9	have	have	VERB
ejpam-6447	110	10	negative	negative	ADJ
ejpam-6447	110	11	real	real	ADJ
ejpam-6447	110	12	parts	part	NOUN
ejpam-6447	110	13	.	.	PUNCT
ejpam-6447	111	1	this	this	PRON
ejpam-6447	111	2	confirms	confirm	VERB
ejpam-6447	111	3	that	that	SCONJ
ejpam-6447	111	4	the	the	DET
ejpam-6447	111	5	endemic	endemic	ADJ
ejpam-6447	111	6	equilibrium	equilibrium	NOUN
ejpam-6447	111	7	is	be	AUX
ejpam-6447	111	8	locally	locally	ADV
ejpam-6447	111	9	asymptotically	asymptotically	ADV
ejpam-6447	111	10	stable	stable	ADJ
ejpam-6447	111	11	.	.	PUNCT
ejpam-6447	112	1	4	4	X
ejpam-6447	112	2	.	.	X
ejpam-6447	112	3	global	global	ADJ
ejpam-6447	112	4	stability	stability	NOUN
ejpam-6447	112	5	analysis	analysis	NOUN
ejpam-6447	112	6	using	use	VERB
ejpam-6447	112	7	lyapunov	lyapunov	NOUN
ejpam-6447	112	8	function	function	VERB
ejpam-6447	112	9	4.1	4.1	NUM
ejpam-6447	112	10	.	.	PUNCT
ejpam-6447	113	1	smoking	smoking	NOUN
ejpam-6447	113	2	-	-	PUNCT
ejpam-6447	113	3	free	free	ADJ
ejpam-6447	113	4	equilibrium	equilibrium	NOUN
ejpam-6447	113	5	point	point	NOUN
ejpam-6447	113	6	theorem	theorem	VERB
ejpam-6447	113	7	3	3	NUM
ejpam-6447	113	8	.	.	X
ejpam-6447	113	9	smoking	smoking	NOUN
ejpam-6447	113	10	-	-	PUNCT
ejpam-6447	113	11	free	free	ADJ
ejpam-6447	113	12	equilibrium	equilibrium	NOUN
ejpam-6447	113	13	point	point	NOUN
ejpam-6447	113	14	is	be	AUX
ejpam-6447	113	15	globally	globally	ADV
ejpam-6447	113	16	asymptotically	asymptotically	ADV
ejpam-6447	113	17	stable	stable	ADJ
ejpam-6447	113	18	for	for	ADP
ejpam-6447	113	19	r0	r0	NOUN
ejpam-6447	113	20	<	<	X
ejpam-6447	113	21	1	1	NUM
ejpam-6447	113	22	.	.	PUNCT
ejpam-6447	114	1	proof	proof	NOUN
ejpam-6447	114	2	.	.	PUNCT
ejpam-6447	115	1	to	to	PART
ejpam-6447	115	2	show	show	VERB
ejpam-6447	115	3	global	global	ADJ
ejpam-6447	115	4	stability	stability	NOUN
ejpam-6447	115	5	at	at	ADP
ejpam-6447	115	6	smoking	smoking	NOUN
ejpam-6447	115	7	-	-	PUNCT
ejpam-6447	115	8	free	free	ADJ
ejpam-6447	115	9	equilibrium	equilibrium	NOUN
ejpam-6447	115	10	point	point	NOUN
ejpam-6447	115	11	,	,	PUNCT
ejpam-6447	115	12	we	we	PRON
ejpam-6447	115	13	build	build	VERB
ejpam-6447	115	14	a	a	DET
ejpam-6447	115	15	lyapunov	lyapunov	ADJ
ejpam-6447	115	16	function	function	NOUN
ejpam-6447	115	17	:	:	PUNCT
ejpam-6447	115	18	v	v	X
ejpam-6447	115	19	=	=	SYM
ejpam-6447	115	20	∫	∫	PROPN
ejpam-6447	115	21	a	a	PRON
ejpam-6447	115	22	0	0	NUM
ejpam-6447	116	1	(	(	PUNCT
ejpam-6447	116	2	e2	e2	PROPN
ejpam-6447	116	3	2	2	NUM
ejpam-6447	116	4	+	+	NUM
ejpam-6447	116	5	i2	i2	PROPN
ejpam-6447	116	6	2	2	NUM
ejpam-6447	116	7	)	)	PUNCT
ejpam-6447	116	8	da	da	NOUN
ejpam-6447	116	9	.	.	PUNCT
ejpam-6447	117	1	(	(	PUNCT
ejpam-6447	117	2	3	3	X
ejpam-6447	117	3	)	)	PUNCT
ejpam-6447	117	4	this	this	DET
ejpam-6447	117	5	function	function	NOUN
ejpam-6447	117	6	is	be	AUX
ejpam-6447	117	7	1	1	NUM
ejpam-6447	117	8	)	)	PUNCT
ejpam-6447	117	9	positive	positive	ADJ
ejpam-6447	117	10	definite	definite	ADJ
ejpam-6447	117	11	,	,	PUNCT
ejpam-6447	117	12	i	i	PROPN
ejpam-6447	117	13	-	-	PUNCT
ejpam-6447	117	14	e	e	X
ejpam-6447	117	15	v	v	X
ejpam-6447	117	16	(	(	PUNCT
ejpam-6447	117	17	t	t	PROPN
ejpam-6447	117	18	)	)	PUNCT
ejpam-6447	117	19	>	>	X
ejpam-6447	117	20	0	0	NUM
ejpam-6447	117	21	,	,	PUNCT
ejpam-6447	117	22	when	when	SCONJ
ejpam-6447	117	23	e	e	PROPN
ejpam-6447	117	24	=	=	SYM
ejpam-6447	117	25	i	i	PROPN
ejpam-6447	117	26	=	=	NOUN
ejpam-6447	117	27	0	0	NUM
ejpam-6447	117	28	.	.	NOUN
ejpam-6447	117	29	2	2	NUM
ejpam-6447	117	30	)	)	PUNCT
ejpam-6447	117	31	zero	zero	NUM
ejpam-6447	117	32	only	only	ADV
ejpam-6447	117	33	at	at	ADP
ejpam-6447	117	34	the	the	DET
ejpam-6447	117	35	equilibrium	equilibrium	NOUN
ejpam-6447	117	36	point	point	NOUN
ejpam-6447	117	37	e	e	X
ejpam-6447	118	1	=	=	PUNCT
ejpam-6447	118	2	i	i	NOUN
ejpam-6447	118	3	=	=	NOUN
ejpam-6447	118	4	0	0	NUM
ejpam-6447	118	5	.	.	NOUN
ejpam-6447	118	6	3	3	X
ejpam-6447	118	7	)	)	PUNCT
ejpam-6447	118	8	differentiable	differentiable	ADJ
ejpam-6447	118	9	in	in	ADP
ejpam-6447	118	10	time	time	NOUN
ejpam-6447	118	11	.	.	PUNCT
ejpam-6447	119	1	taking	take	VERB
ejpam-6447	119	2	the	the	DET
ejpam-6447	119	3	time	time	NOUN
ejpam-6447	119	4	derivative	derivative	NOUN
ejpam-6447	119	5	:	:	PUNCT
ejpam-6447	119	6	dv	dv	PROPN
ejpam-6447	119	7	dt	dt	PROPN
ejpam-6447	119	8	=	=	PUNCT
ejpam-6447	119	9	∫	∫	PROPN
ejpam-6447	119	10	a	a	PRON
ejpam-6447	119	11	0	0	NUM
ejpam-6447	120	1	(	(	PUNCT
ejpam-6447	120	2	e	e	X
ejpam-6447	120	3	de	de	X
ejpam-6447	120	4	dt	dt	PROPN
ejpam-6447	121	1	+	+	CCONJ
ejpam-6447	121	2	i	i	PRON
ejpam-6447	121	3	di	di	X
ejpam-6447	121	4	dt	dt	NOUN
ejpam-6447	121	5	)	)	PUNCT
ejpam-6447	121	6	da	da	X
ejpam-6447	121	7	.	.	PUNCT
ejpam-6447	121	8	by	by	ADP
ejpam-6447	121	9	substituting	substitute	VERB
ejpam-6447	121	10	the	the	DET
ejpam-6447	121	11	model	model	NOUN
ejpam-6447	121	12	(	(	PUNCT
ejpam-6447	121	13	1	1	NUM
ejpam-6447	121	14	)	)	PUNCT
ejpam-6447	121	15	equations	equation	NOUN
ejpam-6447	121	16	,	,	PUNCT
ejpam-6447	121	17	we	we	PRON
ejpam-6447	121	18	get	get	VERB
ejpam-6447	121	19	dv	dv	PROPN
ejpam-6447	121	20	dt	dt	PROPN
ejpam-6447	122	1	=	=	SYM
ejpam-6447	122	2	∫	∫	PROPN
ejpam-6447	122	3	a	a	DET
ejpam-6447	122	4	0	0	NUM
ejpam-6447	122	5	(	(	PUNCT
ejpam-6447	122	6	e	e	X
ejpam-6447	122	7	(	(	PUNCT
ejpam-6447	122	8	βsi	βsi	NOUN
ejpam-6447	122	9	−	−	PROPN
ejpam-6447	122	10	(	(	PUNCT
ejpam-6447	122	11	σ	σ	NOUN
ejpam-6447	122	12	+	+	NOUN
ejpam-6447	122	13	µ)e	µ)e	NOUN
ejpam-6447	122	14	)	)	PUNCT
ejpam-6447	123	1	+	+	CCONJ
ejpam-6447	123	2	i	i	PRON
ejpam-6447	123	3	(	(	PUNCT
ejpam-6447	123	4	σe	σe	INTJ
ejpam-6447	123	5	−	−	PROPN
ejpam-6447	123	6	(	(	PUNCT
ejpam-6447	123	7	γ	γ	X
ejpam-6447	123	8	+	+	X
ejpam-6447	123	9	µ)i	µ)i	ADJ
ejpam-6447	123	10	)	)	PUNCT
ejpam-6447	123	11	)	)	PUNCT
ejpam-6447	124	1	da	da	PROPN
ejpam-6447	124	2	,	,	PUNCT
ejpam-6447	124	3	dv	dv	PROPN
ejpam-6447	124	4	dt	dt	PROPN
ejpam-6447	124	5	=	=	PUNCT
ejpam-6447	124	6	∫	∫	PROPN
ejpam-6447	124	7	a	a	DET
ejpam-6447	124	8	0	0	NUM
ejpam-6447	125	1	(	(	PUNCT
ejpam-6447	125	2	β(a	β(a	PROPN
ejpam-6447	125	3	,	,	PUNCT
ejpam-6447	125	4	t)sei	t)sei	ADJ
ejpam-6447	125	5	−	−	PROPN
ejpam-6447	125	6	(	(	PUNCT
ejpam-6447	125	7	σ	σ	PROPN
ejpam-6447	125	8	+	+	X
ejpam-6447	126	1	µ)e2	µ)e2	PROPN
ejpam-6447	126	2	+	+	CCONJ
ejpam-6447	126	3	σei	σei	NOUN
ejpam-6447	126	4	−	−	PROPN
ejpam-6447	126	5	(	(	PUNCT
ejpam-6447	126	6	γ	γ	X
ejpam-6447	126	7	+	+	CCONJ
ejpam-6447	126	8	µ)i2	µ)i2	PROPN
ejpam-6447	126	9	)	)	PUNCT
ejpam-6447	126	10	da	da	PROPN
ejpam-6447	126	11	,	,	PUNCT
ejpam-6447	126	12	dv	dv	PROPN
ejpam-6447	126	13	dt	dt	PROPN
ejpam-6447	126	14	=	=	PUNCT
ejpam-6447	126	15	∫	∫	PROPN
ejpam-6447	127	1	a	a	DET
ejpam-6447	127	2	0	0	NUM
ejpam-6447	127	3	(	(	PUNCT
ejpam-6447	127	4	λ(a	λ(a	PROPN
ejpam-6447	127	5	,	,	PUNCT
ejpam-6447	127	6	t)se	t)se	PROPN
ejpam-6447	127	7	+	+	NUM
ejpam-6447	127	8	σei	σei	NOUN
ejpam-6447	127	9	−	−	PROPN
ejpam-6447	127	10	(	(	PUNCT
ejpam-6447	127	11	σ	σ	PROPN
ejpam-6447	127	12	+	+	PROPN
ejpam-6447	127	13	µ)e2	µ)e2	ADJ
ejpam-6447	127	14	−	−	PROPN
ejpam-6447	127	15	(	(	PUNCT
ejpam-6447	127	16	γ	γ	X
ejpam-6447	127	17	+	+	CCONJ
ejpam-6447	127	18	µ)i2	µ)i2	PROPN
ejpam-6447	127	19	)	)	PUNCT
ejpam-6447	127	20	da	da	PROPN
ejpam-6447	127	21	,	,	PUNCT
ejpam-6447	127	22	where	where	SCONJ
ejpam-6447	127	23	λ	λ	X
ejpam-6447	127	24	=	=	SYM
ejpam-6447	127	25	β(a	β(a	PROPN
ejpam-6447	127	26	,	,	PUNCT
ejpam-6447	127	27	t)i	t)i	PUNCT
ejpam-6447	127	28	dv	dv	PROPN
ejpam-6447	127	29	dt	dt	X
ejpam-6447	127	30	=	=	PUNCT
ejpam-6447	128	1	−	−	PROPN
ejpam-6447	128	2	∫	∫	PROPN
ejpam-6447	128	3	a	a	DET
ejpam-6447	128	4	0	0	NUM
ejpam-6447	128	5	(	(	PUNCT
ejpam-6447	128	6	(	(	PUNCT
ejpam-6447	128	7	σ	σ	X
ejpam-6447	128	8	+	+	X
ejpam-6447	129	1	µ)e2	µ)e2	PROPN
ejpam-6447	129	2	+	+	CCONJ
ejpam-6447	129	3	(	(	PUNCT
ejpam-6447	129	4	γ	γ	X
ejpam-6447	129	5	+	+	NOUN
ejpam-6447	129	6	µ)i2)da+	µ)i2)da+	PROPN
ejpam-6447	129	7	∫	∫	PROPN
ejpam-6447	129	8	a	a	DET
ejpam-6447	129	9	0	0	NUM
ejpam-6447	129	10	(	(	PUNCT
ejpam-6447	129	11	λ(a	λ(a	NOUN
ejpam-6447	129	12	,	,	PUNCT
ejpam-6447	129	13	t)se	t)se	PROPN
ejpam-6447	129	14	+	+	NUM
ejpam-6447	129	15	σeida	σeida	NOUN
ejpam-6447	129	16	)	)	PUNCT
ejpam-6447	129	17	.	.	PUNCT
ejpam-6447	130	1	s.	s.	PROPN
ejpam-6447	130	2	bushnaq	bushnaq	PROPN
ejpam-6447	130	3	,	,	PUNCT
ejpam-6447	130	4	s.	s.	PROPN
ejpam-6447	130	5	bano	bano	PROPN
ejpam-6447	130	6	,	,	PUNCT
ejpam-6447	130	7	a.	a.	PROPN
ejpam-6447	130	8	zeb	zeb	PROPN
ejpam-6447	130	9	/	/	SYM
ejpam-6447	130	10	eur	eur	PROPN
ejpam-6447	130	11	.	.	PUNCT
ejpam-6447	131	1	j.	j.	PROPN
ejpam-6447	131	2	pure	pure	PROPN
ejpam-6447	131	3	appl	appl	PROPN
ejpam-6447	131	4	.	.	PROPN
ejpam-6447	131	5	math	math	PROPN
ejpam-6447	131	6	,	,	PUNCT
ejpam-6447	131	7	18	18	NUM
ejpam-6447	131	8	(	(	PUNCT
ejpam-6447	131	9	3	3	NUM
ejpam-6447	131	10	)	)	PUNCT
ejpam-6447	131	11	(	(	PUNCT
ejpam-6447	131	12	2025	2025	NUM
ejpam-6447	131	13	)	)	PUNCT
ejpam-6447	131	14	,	,	PUNCT
ejpam-6447	131	15	6447	6447	NUM
ejpam-6447	131	16	7	7	NUM
ejpam-6447	131	17	of	of	ADP
ejpam-6447	131	18	12	12	NUM
ejpam-6447	131	19	now	now	ADV
ejpam-6447	131	20	,	,	PUNCT
ejpam-6447	131	21	we	we	PRON
ejpam-6447	131	22	analyze	analyze	VERB
ejpam-6447	131	23	the	the	DET
ejpam-6447	131	24	sign	sign	NOUN
ejpam-6447	131	25	of	of	ADP
ejpam-6447	131	26	dv	dv	PROPN
ejpam-6447	131	27	dt	dt	PROPN
ejpam-6447	131	28	.	.	PUNCT
ejpam-6447	132	1	using	use	VERB
ejpam-6447	132	2	young	young	PROPN
ejpam-6447	132	3	’s	’s	PART
ejpam-6447	132	4	inequality	inequality	PROPN
ejpam-6447	132	5	ab	ab	PROPN
ejpam-6447	132	6	≤	≤	PROPN
ejpam-6447	132	7	a2	a2	PROPN
ejpam-6447	132	8	2	2	NUM
ejpam-6447	132	9	+	+	NUM
ejpam-6447	132	10	b2	b2	NOUN
ejpam-6447	132	11	2	2	NUM
ejpam-6447	132	12	for	for	ADP
ejpam-6447	132	13	cross	cross	NOUN
ejpam-6447	132	14	terms	term	NOUN
ejpam-6447	132	15	.	.	PUNCT
ejpam-6447	133	1	λse	λse	PROPN
ejpam-6447	133	2	≤	≤	NUM
ejpam-6447	133	3	λ2s2	λ2s2	NOUN
ejpam-6447	133	4	2ϵ1	2ϵ1	NUM
ejpam-6447	134	1	+	+	CCONJ
ejpam-6447	134	2	ϵ1e	ϵ1e	PROPN
ejpam-6447	134	3	2	2	NUM
ejpam-6447	134	4	2	2	NUM
ejpam-6447	134	5	,	,	PUNCT
ejpam-6447	134	6	and	and	CCONJ
ejpam-6447	134	7	σei	σei	VERB
ejpam-6447	134	8	≤	≤	NUM
ejpam-6447	135	1	σ2e2	σ2e2	PROPN
ejpam-6447	135	2	2ϵ2	2ϵ2	NUM
ejpam-6447	136	1	+	+	CCONJ
ejpam-6447	136	2	ϵ2i	ϵ2i	PROPN
ejpam-6447	136	3	2	2	NUM
ejpam-6447	136	4	2	2	NUM
ejpam-6447	136	5	.	.	PUNCT
ejpam-6447	137	1	so	so	ADV
ejpam-6447	137	2	dv	dv	PROPN
ejpam-6447	137	3	dt	dt	PROPN
ejpam-6447	137	4	≤	≤	PROPN
ejpam-6447	137	5	−	−	PROPN
ejpam-6447	137	6	∫	∫	PROPN
ejpam-6447	137	7	a	a	PRON
ejpam-6447	137	8	0	0	NUM
ejpam-6447	138	1	(	(	PUNCT
ejpam-6447	138	2	(	(	PUNCT
ejpam-6447	138	3	σ	σ	X
ejpam-6447	138	4	+	+	X
ejpam-6447	139	1	µ)e2	µ)e2	PROPN
ejpam-6447	139	2	+	+	CCONJ
ejpam-6447	139	3	(	(	PUNCT
ejpam-6447	139	4	γ	γ	X
ejpam-6447	139	5	+	+	NOUN
ejpam-6447	139	6	µ)i2)da+	µ)i2)da+	PROPN
ejpam-6447	139	7	∫	∫	PROPN
ejpam-6447	139	8	a	a	DET
ejpam-6447	139	9	0	0	NUM
ejpam-6447	139	10	(	(	PUNCT
ejpam-6447	139	11	λ2s2	λ2s2	NOUN
ejpam-6447	139	12	2ϵ1	2ϵ1	NUM
ejpam-6447	139	13	+	+	CCONJ
ejpam-6447	139	14	ϵ1e	ϵ1e	PROPN
ejpam-6447	139	15	2	2	NUM
ejpam-6447	139	16	2	2	NUM
ejpam-6447	139	17	+	+	CCONJ
ejpam-6447	139	18	σ2e2	σ2e2	PROPN
ejpam-6447	139	19	2ϵ2	2ϵ2	NUM
ejpam-6447	140	1	+	+	CCONJ
ejpam-6447	140	2	ϵ2i	ϵ2i	PROPN
ejpam-6447	140	3	2	2	NUM
ejpam-6447	140	4	2	2	NUM
ejpam-6447	140	5	)	)	PUNCT
ejpam-6447	140	6	da	da	NOUN
ejpam-6447	140	7	.	.	PUNCT
ejpam-6447	141	1	by	by	ADP
ejpam-6447	141	2	rearranging	rearrange	VERB
ejpam-6447	141	3	dv	dv	PROPN
ejpam-6447	141	4	dt	dt	PROPN
ejpam-6447	141	5	≤	≤	PROPN
ejpam-6447	141	6	−	−	PROPN
ejpam-6447	141	7	∫	∫	PROPN
ejpam-6447	141	8	a	a	DET
ejpam-6447	141	9	0	0	NUM
ejpam-6447	141	10	(	(	PUNCT
ejpam-6447	141	11	(	(	PUNCT
ejpam-6447	141	12	σ	σ	X
ejpam-6447	141	13	+	+	CCONJ
ejpam-6447	141	14	µ−	µ−	PROPN
ejpam-6447	141	15	ϵ1	ϵ1	VERB
ejpam-6447	141	16	2	2	NUM
ejpam-6447	141	17	−	−	PROPN
ejpam-6447	141	18	σ2	σ2	PROPN
ejpam-6447	141	19	2ϵ2	2ϵ2	NUM
ejpam-6447	141	20	)	)	PUNCT
ejpam-6447	141	21	e2	e2	PROPN
ejpam-6447	141	22	−	−	PROPN
ejpam-6447	141	23	(	(	PUNCT
ejpam-6447	141	24	γ	γ	PROPN
ejpam-6447	141	25	+	+	CCONJ
ejpam-6447	141	26	µ−	µ−	PROPN
ejpam-6447	141	27	ϵ2	ϵ2	PROPN
ejpam-6447	141	28	2	2	NUM
ejpam-6447	141	29	)	)	PUNCT
ejpam-6447	141	30	i2	i2	PROPN
ejpam-6447	141	31	)	)	PUNCT
ejpam-6447	141	32	da+	da+	VERB
ejpam-6447	141	33	∫	∫	PROPN
ejpam-6447	141	34	a	a	DET
ejpam-6447	141	35	0	0	NUM
ejpam-6447	141	36	λ2s2	λ2s2	NOUN
ejpam-6447	141	37	2ϵ1	2ϵ1	NUM
ejpam-6447	141	38	da	da	NOUN
ejpam-6447	141	39	.	.	PUNCT
ejpam-6447	142	1	if	if	SCONJ
ejpam-6447	142	2	smoking	smoking	NOUN
ejpam-6447	142	3	prevalence	prevalence	NOUN
ejpam-6447	142	4	is	be	AUX
ejpam-6447	142	5	small	small	ADJ
ejpam-6447	142	6	,	,	PUNCT
ejpam-6447	142	7	i	i	PROPN
ejpam-6447	142	8	-	-	PUNCT
ejpam-6447	142	9	e	e	NOUN
ejpam-6447	142	10	λ	λ	PROPN
ejpam-6447	142	11	is	be	AUX
ejpam-6447	142	12	small	small	ADJ
ejpam-6447	142	13	,	,	PUNCT
ejpam-6447	142	14	i	i	PROPN
ejpam-6447	142	15	-	-	PUNCT
ejpam-6447	142	16	e	e	NOUN
ejpam-6447	142	17	λ(t	λ(t	PROPN
ejpam-6447	142	18	)	)	PUNCT
ejpam-6447	142	19	→	→	SYM
ejpam-6447	142	20	0	0	NUM
ejpam-6447	142	21	as	as	ADP
ejpam-6447	142	22	i(t	i(t	NOUN
ejpam-6447	142	23	)	)	PUNCT
ejpam-6447	142	24	→	→	SYM
ejpam-6447	142	25	0	0	NUM
ejpam-6447	142	26	,	,	PUNCT
ejpam-6447	142	27	then	then	ADV
ejpam-6447	142	28	λ2s2	λ2s2	NOUN
ejpam-6447	142	29	is	be	AUX
ejpam-6447	142	30	small	small	ADJ
ejpam-6447	142	31	near	near	ADP
ejpam-6447	142	32	the	the	DET
ejpam-6447	142	33	equilibrium	equilibrium	NOUN
ejpam-6447	142	34	point	point	NOUN
ejpam-6447	142	35	,	,	PUNCT
ejpam-6447	142	36	so	so	CCONJ
ejpam-6447	142	37	the	the	DET
ejpam-6447	142	38	last	last	ADJ
ejpam-6447	142	39	term	term	NOUN
ejpam-6447	142	40	of	of	ADP
ejpam-6447	142	41	the	the	DET
ejpam-6447	142	42	above	above	ADJ
ejpam-6447	142	43	equation	equation	NOUN
ejpam-6447	142	44	is	be	AUX
ejpam-6447	142	45	negligible	negligible	ADJ
ejpam-6447	142	46	.	.	PUNCT
ejpam-6447	143	1	choose	choose	AUX
ejpam-6447	143	2	ϵ1	ϵ1	ADJ
ejpam-6447	143	3	,	,	PUNCT
ejpam-6447	143	4	ϵ2	ϵ2	VERB
ejpam-6447	143	5	such	such	ADJ
ejpam-6447	143	6	that	that	SCONJ
ejpam-6447	143	7	σ	σ	PROPN
ejpam-6447	143	8	−	−	NOUN
ejpam-6447	143	9	ϵ1	ϵ1	ADJ
ejpam-6447	143	10	2	2	NUM
ejpam-6447	143	11	−	−	PROPN
ejpam-6447	143	12	σ2	σ2	PROPN
ejpam-6447	143	13	2ϵ2	2ϵ2	PROPN
ejpam-6447	143	14	>	>	X
ejpam-6447	143	15	0	0	PROPN
ejpam-6447	143	16	,	,	PUNCT
ejpam-6447	143	17	and	and	CCONJ
ejpam-6447	144	1	γ	γ	PROPN
ejpam-6447	144	2	−	−	PROPN
ejpam-6447	144	3	ϵ2	ϵ2	PROPN
ejpam-6447	144	4	2	2	NUM
ejpam-6447	144	5	>	>	X
ejpam-6447	144	6	0	0	NUM
ejpam-6447	144	7	,	,	PUNCT
ejpam-6447	144	8	then	then	ADV
ejpam-6447	144	9	dv	dv	PROPN
ejpam-6447	144	10	dt	dt	PROPN
ejpam-6447	144	11	≤	≤	PROPN
ejpam-6447	144	12	0	0	NUM
ejpam-6447	144	13	.	.	PUNCT
ejpam-6447	145	1	the	the	DET
ejpam-6447	145	2	equality	equality	NOUN
ejpam-6447	145	3	holds	hold	VERB
ejpam-6447	145	4	only	only	ADV
ejpam-6447	145	5	when	when	SCONJ
ejpam-6447	145	6	e	e	PROPN
ejpam-6447	145	7	=	=	SYM
ejpam-6447	145	8	i	i	PROPN
ejpam-6447	145	9	=	=	NOUN
ejpam-6447	145	10	0	0	X
ejpam-6447	145	11	.	.	PUNCT
ejpam-6447	146	1	according	accord	VERB
ejpam-6447	146	2	to	to	ADP
ejpam-6447	146	3	lasalle	lasalle	PROPN
ejpam-6447	146	4	’s	’s	PART
ejpam-6447	146	5	principle	principle	NOUN
ejpam-6447	146	6	of	of	ADP
ejpam-6447	146	7	invariance	invariance	NOUN
ejpam-6447	146	8	,	,	PUNCT
ejpam-6447	146	9	the	the	DET
ejpam-6447	146	10	smoking	smoking	NOUN
ejpam-6447	146	11	-	-	PUNCT
ejpam-6447	146	12	free	free	ADJ
ejpam-6447	146	13	equilibrium	equilibrium	NOUN
ejpam-6447	146	14	point	point	NOUN
ejpam-6447	146	15	is	be	AUX
ejpam-6447	146	16	globally	globally	ADV
ejpam-6447	146	17	asymptotically	asymptotically	ADV
ejpam-6447	146	18	stable	stable	ADJ
ejpam-6447	146	19	.	.	PUNCT
ejpam-6447	147	1	4.2	4.2	NUM
ejpam-6447	147	2	.	.	PUNCT
ejpam-6447	148	1	positive	positive	ADJ
ejpam-6447	148	2	equilibrium	equilibrium	NOUN
ejpam-6447	148	3	point	point	NOUN
ejpam-6447	148	4	theorem	theorem	VERB
ejpam-6447	148	5	4	4	NUM
ejpam-6447	148	6	.	.	NOUN
ejpam-6447	148	7	positive	positive	ADJ
ejpam-6447	148	8	equilibrium	equilibrium	NOUN
ejpam-6447	148	9	point	point	NOUN
ejpam-6447	148	10	is	be	AUX
ejpam-6447	148	11	globally	globally	ADV
ejpam-6447	148	12	asymptotically	asymptotically	ADV
ejpam-6447	148	13	stable	stable	ADJ
ejpam-6447	148	14	.	.	PUNCT
ejpam-6447	149	1	proof	proof	NOUN
ejpam-6447	149	2	.	.	PUNCT
ejpam-6447	150	1	to	to	PART
ejpam-6447	150	2	show	show	VERB
ejpam-6447	150	3	the	the	DET
ejpam-6447	150	4	global	global	ADJ
ejpam-6447	150	5	stability	stability	NOUN
ejpam-6447	150	6	of	of	ADP
ejpam-6447	150	7	the	the	DET
ejpam-6447	150	8	endemic	endemic	ADJ
ejpam-6447	150	9	equilibrium	equilibrium	NOUN
ejpam-6447	150	10	point	point	NOUN
ejpam-6447	150	11	,	,	PUNCT
ejpam-6447	150	12	we	we	PRON
ejpam-6447	150	13	construct	construct	VERB
ejpam-6447	150	14	a	a	DET
ejpam-6447	150	15	lyapunov	lyapunov	NOUN
ejpam-6447	150	16	function	function	NOUN
ejpam-6447	150	17	v	v	ADP
ejpam-6447	150	18	(	(	PUNCT
ejpam-6447	150	19	t	t	NOUN
ejpam-6447	150	20	)	)	PUNCT
ejpam-6447	150	21	=	=	SYM
ejpam-6447	150	22	1	1	NUM
ejpam-6447	150	23	2	2	NUM
ejpam-6447	150	24	(	(	PUNCT
ejpam-6447	150	25	e	e	NOUN
ejpam-6447	150	26	−	−	NOUN
ejpam-6447	150	27	e∗)2	e∗)2	NOUN
ejpam-6447	150	28	+	+	NUM
ejpam-6447	150	29	1	1	NUM
ejpam-6447	150	30	2	2	NUM
ejpam-6447	150	31	(	(	PUNCT
ejpam-6447	150	32	i	i	PRON
ejpam-6447	150	33	−	−	PROPN
ejpam-6447	150	34	i∗)2	i∗)2	NOUN
ejpam-6447	150	35	,	,	PUNCT
ejpam-6447	150	36	=	=	PRON
ejpam-6447	150	37	⇒	⇒	VERB
ejpam-6447	150	38	dv	dv	PROPN
ejpam-6447	150	39	dt	dt	X
ejpam-6447	150	40	=	=	PUNCT
ejpam-6447	150	41	(	(	PUNCT
ejpam-6447	150	42	e	e	NOUN
ejpam-6447	150	43	−	−	PROPN
ejpam-6447	150	44	e∗	e∗	NOUN
ejpam-6447	150	45	)	)	PUNCT
ejpam-6447	150	46	de	de	ADP
ejpam-6447	151	1	dt	dt	X
ejpam-6447	152	1	+	+	CCONJ
ejpam-6447	152	2	(	(	PUNCT
ejpam-6447	152	3	i	i	PRON
ejpam-6447	152	4	−	−	PROPN
ejpam-6447	152	5	i∗	i∗	NOUN
ejpam-6447	152	6	)	)	PUNCT
ejpam-6447	152	7	di	di	NOUN
ejpam-6447	152	8	dt	dt	NOUN
ejpam-6447	152	9	.	.	PUNCT
ejpam-6447	153	1	from	from	ADP
ejpam-6447	153	2	the	the	DET
ejpam-6447	153	3	model	model	NOUN
ejpam-6447	153	4	(	(	PUNCT
ejpam-6447	153	5	1	1	NUM
ejpam-6447	153	6	)	)	PUNCT
ejpam-6447	153	7	equations	equation	NOUN
ejpam-6447	153	8	de	de	X
ejpam-6447	153	9	dt	dt	NOUN
ejpam-6447	153	10	=	=	NOUN
ejpam-6447	153	11	βsi	βsi	NOUN
ejpam-6447	153	12	−	−	PROPN
ejpam-6447	153	13	(	(	PUNCT
ejpam-6447	153	14	σ	σ	NOUN
ejpam-6447	153	15	+	+	NUM
ejpam-6447	153	16	µ)e	µ)e	NOUN
ejpam-6447	153	17	,	,	PUNCT
ejpam-6447	153	18	and	and	CCONJ
ejpam-6447	153	19	di	di	NOUN
ejpam-6447	153	20	dt	dt	NOUN
ejpam-6447	153	21	=	=	PUNCT
ejpam-6447	153	22	σe	σe	PROPN
ejpam-6447	153	23	−	−	PROPN
ejpam-6447	153	24	(	(	PUNCT
ejpam-6447	153	25	γ	γ	X
ejpam-6447	153	26	+	+	X
ejpam-6447	153	27	µ)i	µ)i	ADJ
ejpam-6447	153	28	,	,	PUNCT
ejpam-6447	153	29	=	=	PRON
ejpam-6447	153	30	⇒	⇒	VERB
ejpam-6447	153	31	dv	dv	PROPN
ejpam-6447	153	32	dt	dt	X
ejpam-6447	154	1	=	=	PUNCT
ejpam-6447	154	2	(	(	PUNCT
ejpam-6447	154	3	e	e	NOUN
ejpam-6447	154	4	−	−	PROPN
ejpam-6447	154	5	e∗	e∗	PROPN
ejpam-6447	154	6	)	)	PUNCT
ejpam-6447	154	7	(	(	PUNCT
ejpam-6447	154	8	βsi	βsi	NOUN
ejpam-6447	154	9	−	−	PROPN
ejpam-6447	155	1	(	(	PUNCT
ejpam-6447	155	2	σ	σ	NOUN
ejpam-6447	155	3	+	+	NOUN
ejpam-6447	155	4	µ)e	µ)e	NOUN
ejpam-6447	155	5	)	)	PUNCT
ejpam-6447	156	1	+	+	CCONJ
ejpam-6447	156	2	(	(	PUNCT
ejpam-6447	156	3	i	i	PRON
ejpam-6447	156	4	−	−	PROPN
ejpam-6447	156	5	i∗	i∗	NOUN
ejpam-6447	156	6	)	)	PUNCT
ejpam-6447	156	7	(	(	PUNCT
ejpam-6447	156	8	σe	σe	INTJ
ejpam-6447	156	9	−	−	PROPN
ejpam-6447	156	10	(	(	PUNCT
ejpam-6447	156	11	γ	γ	X
ejpam-6447	156	12	+	+	X
ejpam-6447	156	13	µ)i	µ)i	X
ejpam-6447	156	14	)	)	PUNCT
ejpam-6447	156	15	,	,	PUNCT
ejpam-6447	156	16	=	=	SYM
ejpam-6447	156	17	⇒	⇒	VERB
ejpam-6447	156	18	dv	dv	PROPN
ejpam-6447	156	19	dt	dt	X
ejpam-6447	156	20	=	=	PUNCT
ejpam-6447	156	21	(	(	PUNCT
ejpam-6447	156	22	e	e	NOUN
ejpam-6447	156	23	−	−	PROPN
ejpam-6447	156	24	e∗	e∗	PROPN
ejpam-6447	156	25	)	)	PUNCT
ejpam-6447	156	26	(	(	PUNCT
ejpam-6447	156	27	(	(	PUNCT
ejpam-6447	156	28	σ	σ	X
ejpam-6447	156	29	+	+	PROPN
ejpam-6447	156	30	µ)e∗	µ)e∗	ADJ
ejpam-6447	156	31	−	−	PROPN
ejpam-6447	156	32	(	(	PUNCT
ejpam-6447	156	33	σ	σ	NOUN
ejpam-6447	156	34	+	+	NOUN
ejpam-6447	156	35	µ)e	µ)e	NOUN
ejpam-6447	156	36	)	)	PUNCT
ejpam-6447	157	1	+	+	CCONJ
ejpam-6447	157	2	(	(	PUNCT
ejpam-6447	157	3	e	e	X
ejpam-6447	157	4	−	−	NOUN
ejpam-6447	157	5	e∗)(βsi	e∗)(βsi	NOUN
ejpam-6447	157	6	−	−	NOUN
ejpam-6447	157	7	βs∗i∗	βs∗i∗	NUM
ejpam-6447	157	8	)	)	PUNCT
ejpam-6447	157	9	s.	s.	PROPN
ejpam-6447	157	10	bushnaq	bushnaq	PROPN
ejpam-6447	157	11	,	,	PUNCT
ejpam-6447	157	12	s.	s.	PROPN
ejpam-6447	157	13	bano	bano	PROPN
ejpam-6447	157	14	,	,	PUNCT
ejpam-6447	157	15	a.	a.	PROPN
ejpam-6447	157	16	zeb	zeb	PROPN
ejpam-6447	157	17	/	/	SYM
ejpam-6447	157	18	eur	eur	PROPN
ejpam-6447	157	19	.	.	PUNCT
ejpam-6447	158	1	j.	j.	PROPN
ejpam-6447	158	2	pure	pure	PROPN
ejpam-6447	158	3	appl	appl	PROPN
ejpam-6447	158	4	.	.	PROPN
ejpam-6447	158	5	math	math	PROPN
ejpam-6447	158	6	,	,	PUNCT
ejpam-6447	158	7	18	18	NUM
ejpam-6447	158	8	(	(	PUNCT
ejpam-6447	158	9	3	3	NUM
ejpam-6447	158	10	)	)	PUNCT
ejpam-6447	158	11	(	(	PUNCT
ejpam-6447	158	12	2025	2025	NUM
ejpam-6447	158	13	)	)	PUNCT
ejpam-6447	158	14	,	,	PUNCT
ejpam-6447	158	15	6447	6447	NUM
ejpam-6447	158	16	8	8	NUM
ejpam-6447	158	17	of	of	ADP
ejpam-6447	158	18	12	12	NUM
ejpam-6447	159	1	+	+	NOUN
ejpam-6447	159	2	(	(	PUNCT
ejpam-6447	159	3	i	i	PRON
ejpam-6447	159	4	−	−	PROPN
ejpam-6447	159	5	i∗)(σe	i∗)(σe	NOUN
ejpam-6447	159	6	−	−	PROPN
ejpam-6447	159	7	σe∗	σe∗	PROPN
ejpam-6447	159	8	)	)	PUNCT
ejpam-6447	159	9	+	+	CCONJ
ejpam-6447	159	10	(	(	PUNCT
ejpam-6447	159	11	i	i	PRON
ejpam-6447	159	12	−	−	PROPN
ejpam-6447	159	13	i∗	i∗	NOUN
ejpam-6447	159	14	)	)	PUNCT
ejpam-6447	159	15	(	(	PUNCT
ejpam-6447	159	16	(	(	PUNCT
ejpam-6447	159	17	γ	γ	X
ejpam-6447	159	18	+	+	NOUN
ejpam-6447	159	19	µ)i∗	µ)i∗	DET
ejpam-6447	159	20	−	−	PROPN
ejpam-6447	159	21	(	(	PUNCT
ejpam-6447	159	22	γ	γ	X
ejpam-6447	159	23	+	+	X
ejpam-6447	159	24	µ)i	µ)i	X
ejpam-6447	159	25	)	)	PUNCT
ejpam-6447	159	26	,	,	PUNCT
ejpam-6447	159	27	=	=	SYM
ejpam-6447	159	28	⇒	⇒	VERB
ejpam-6447	159	29	dv	dv	PROPN
ejpam-6447	159	30	dt	dt	X
ejpam-6447	159	31	=	=	PUNCT
ejpam-6447	159	32	−(σ	−(σ	NOUN
ejpam-6447	159	33	+	+	NOUN
ejpam-6447	159	34	µ)(e	µ)(e	NOUN
ejpam-6447	159	35	−	−	NOUN
ejpam-6447	159	36	e∗)2	e∗)2	NOUN
ejpam-6447	159	37	+	+	PUNCT
ejpam-6447	159	38	(	(	PUNCT
ejpam-6447	159	39	e	e	X
ejpam-6447	159	40	−	−	NOUN
ejpam-6447	159	41	e∗)(βsi	e∗)(βsi	NOUN
ejpam-6447	159	42	−	−	NOUN
ejpam-6447	159	43	βs∗i∗	βs∗i∗	NUM
ejpam-6447	159	44	)	)	PUNCT
ejpam-6447	160	1	+	+	NUM
ejpam-6447	160	2	σ(i	σ(i	PROPN
ejpam-6447	160	3	−	−	PROPN
ejpam-6447	160	4	i∗)(e	i∗)(e	NOUN
ejpam-6447	160	5	−	−	PROPN
ejpam-6447	160	6	e∗)−	e∗)−	NOUN
ejpam-6447	160	7	(	(	PUNCT
ejpam-6447	160	8	i	i	PRON
ejpam-6447	160	9	−	−	PROPN
ejpam-6447	160	10	i∗)2(γ	i∗)2(γ	PROPN
ejpam-6447	160	11	+	+	CCONJ
ejpam-6447	160	12	µ	µ	NOUN
ejpam-6447	160	13	)	)	PUNCT
ejpam-6447	160	14	,	,	PUNCT
ejpam-6447	160	15	=	=	PRON
ejpam-6447	160	16	⇒	⇒	VERB
ejpam-6447	160	17	dv	dv	PROPN
ejpam-6447	160	18	dt	dt	X
ejpam-6447	160	19	=	=	PUNCT
ejpam-6447	160	20	−(σ	−(σ	NOUN
ejpam-6447	160	21	+	+	NOUN
ejpam-6447	160	22	µ)(e	µ)(e	NOUN
ejpam-6447	160	23	−	−	PROPN
ejpam-6447	160	24	e∗)2	e∗)2	ADJ
ejpam-6447	160	25	−	−	PROPN
ejpam-6447	161	1	(	(	PUNCT
ejpam-6447	161	2	i	i	PRON
ejpam-6447	161	3	−	−	PROPN
ejpam-6447	161	4	i∗)2(γ	i∗)2(γ	PROPN
ejpam-6447	161	5	+	+	CCONJ
ejpam-6447	161	6	µ	µ	X
ejpam-6447	161	7	)	)	PUNCT
ejpam-6447	161	8	+	+	CCONJ
ejpam-6447	161	9	(	(	PUNCT
ejpam-6447	161	10	e	e	NOUN
ejpam-6447	161	11	−	−	NOUN
ejpam-6447	161	12	e∗)(βsi	e∗)(βsi	NOUN
ejpam-6447	161	13	−	−	NOUN
ejpam-6447	161	14	βs∗i∗	βs∗i∗	NUM
ejpam-6447	161	15	)	)	PUNCT
ejpam-6447	162	1	+	+	NUM
ejpam-6447	162	2	σ(i	σ(i	PROPN
ejpam-6447	162	3	−	−	PROPN
ejpam-6447	162	4	i∗)(e	i∗)(e	ADJ
ejpam-6447	162	5	−	−	PROPN
ejpam-6447	162	6	e∗	e∗	PROPN
ejpam-6447	162	7	)	)	PUNCT
ejpam-6447	162	8	.	.	PUNCT
ejpam-6447	163	1	use	use	VERB
ejpam-6447	163	2	young	young	PROPN
ejpam-6447	163	3	’s	’s	PART
ejpam-6447	163	4	inequality	inequality	NOUN
ejpam-6447	163	5	on	on	ADP
ejpam-6447	163	6	cross	cross	NOUN
ejpam-6447	163	7	terms	term	NOUN
ejpam-6447	163	8	,	,	PUNCT
ejpam-6447	163	9	we	we	PRON
ejpam-6447	163	10	have	have	VERB
ejpam-6447	163	11	(	(	PUNCT
ejpam-6447	163	12	e	e	NOUN
ejpam-6447	163	13	−	−	PROPN
ejpam-6447	163	14	e∗)(i	e∗)(i	NOUN
ejpam-6447	163	15	−	−	PROPN
ejpam-6447	163	16	i∗	i∗	PROPN
ejpam-6447	163	17	)	)	PUNCT
ejpam-6447	163	18	≤	≤	NOUN
ejpam-6447	163	19	1	1	NUM
ejpam-6447	163	20	2	2	NUM
ejpam-6447	163	21	(	(	PUNCT
ejpam-6447	163	22	e	e	NOUN
ejpam-6447	163	23	−	−	NOUN
ejpam-6447	163	24	e∗)2	e∗)2	NOUN
ejpam-6447	163	25	+	+	NUM
ejpam-6447	163	26	1	1	NUM
ejpam-6447	163	27	2	2	NUM
ejpam-6447	163	28	(	(	PUNCT
ejpam-6447	163	29	i	i	PRON
ejpam-6447	163	30	−	−	PROPN
ejpam-6447	163	31	i∗)2	i∗)2	NOUN
ejpam-6447	163	32	,	,	PUNCT
ejpam-6447	163	33	and	and	CCONJ
ejpam-6447	163	34	(	(	PUNCT
ejpam-6447	163	35	e	e	X
ejpam-6447	163	36	−	−	PROPN
ejpam-6447	164	1	e∗)(λs	e∗)(λs	PROPN
ejpam-6447	164	2	−	−	PROPN
ejpam-6447	164	3	λ∗s	λ∗s	NUM
ejpam-6447	164	4	)	)	PUNCT
ejpam-6447	164	5	≤	≤	NUM
ejpam-6447	164	6	1	1	NUM
ejpam-6447	164	7	2ϵ	2ϵ	NOUN
ejpam-6447	164	8	(	(	PUNCT
ejpam-6447	164	9	λs	λs	NOUN
ejpam-6447	164	10	−	−	PROPN
ejpam-6447	165	1	λ∗s∗)2	λ∗s∗)2	PROPN
ejpam-6447	166	1	+	+	NUM
ejpam-6447	166	2	ϵ	ϵ	SYM
ejpam-6447	166	3	2	2	NUM
ejpam-6447	166	4	(	(	PUNCT
ejpam-6447	166	5	e	e	NOUN
ejpam-6447	166	6	−	−	NOUN
ejpam-6447	166	7	e∗)2	e∗)2	ADJ
ejpam-6447	166	8	.	.	PUNCT
ejpam-6447	167	1	thus	thus	ADV
ejpam-6447	167	2	we	we	PRON
ejpam-6447	167	3	can	can	AUX
ejpam-6447	167	4	bound	bind	VERB
ejpam-6447	167	5	dv	dv	PROPN
ejpam-6447	167	6	dt	dt	PUNCT
ejpam-6447	167	7	by	by	ADP
ejpam-6447	167	8	dv	dv	PROPN
ejpam-6447	167	9	dt	dt	PROPN
ejpam-6447	167	10	≤	≤	PROPN
ejpam-6447	167	11	−(σ	−(σ	NOUN
ejpam-6447	167	12	+	+	NOUN
ejpam-6447	167	13	µ)(e	µ)(e	NOUN
ejpam-6447	167	14	−	−	PROPN
ejpam-6447	167	15	e∗)2	e∗)2	ADJ
ejpam-6447	167	16	−	−	PROPN
ejpam-6447	168	1	(	(	PUNCT
ejpam-6447	168	2	i	i	PRON
ejpam-6447	168	3	−	−	PROPN
ejpam-6447	168	4	i∗)2(γ	i∗)2(γ	PROPN
ejpam-6447	168	5	+	+	CCONJ
ejpam-6447	168	6	µ	µ	X
ejpam-6447	168	7	)	)	PUNCT
ejpam-6447	168	8	+	+	CCONJ
ejpam-6447	168	9	1	1	NUM
ejpam-6447	168	10	2ϵ(λs	2ϵ(λs	NUM
ejpam-6447	168	11	−	−	NOUN
ejpam-6447	168	12	λ∗s∗)2	λ∗s∗)2	PROPN
ejpam-6447	169	1	+	+	NOUN
ejpam-6447	169	2	σ	σ	X
ejpam-6447	169	3	2	2	NUM
ejpam-6447	169	4	(	(	PUNCT
ejpam-6447	169	5	e	e	NOUN
ejpam-6447	169	6	−	−	PROPN
ejpam-6447	169	7	e∗)2	e∗)2	PROPN
ejpam-6447	169	8	+	+	NOUN
ejpam-6447	169	9	σ	σ	NOUN
ejpam-6447	169	10	2	2	NUM
ejpam-6447	169	11	(	(	PUNCT
ejpam-6447	169	12	i	i	PRON
ejpam-6447	169	13	−	−	PROPN
ejpam-6447	169	14	i∗)2	i∗)2	NOUN
ejpam-6447	169	15	,	,	PUNCT
ejpam-6447	169	16	=	=	PRON
ejpam-6447	169	17	⇒	⇒	X
ejpam-6447	169	18	dv	dv	PROPN
ejpam-6447	170	1	dt	dt	NOUN
ejpam-6447	170	2	≤	≤	ADV
ejpam-6447	170	3	−	−	PROPN
ejpam-6447	170	4	(	(	PUNCT
ejpam-6447	170	5	σ	σ	PROPN
ejpam-6447	170	6	2	2	NUM
ejpam-6447	170	7	+	+	CCONJ
ejpam-6447	170	8	µ)(e	µ)(e	NOUN
ejpam-6447	170	9	−	−	PROPN
ejpam-6447	170	10	e∗)2	e∗)2	ADJ
ejpam-6447	170	11	−	−	PROPN
ejpam-6447	170	12	(	(	PUNCT
ejpam-6447	170	13	γ	γ	PROPN
ejpam-6447	170	14	+	+	NOUN
ejpam-6447	170	15	µ−	µ−	PROPN
ejpam-6447	170	16	σ	σ	PROPN
ejpam-6447	170	17	2	2	NUM
ejpam-6447	170	18	)	)	PUNCT
ejpam-6447	170	19	(	(	PUNCT
ejpam-6447	170	20	i	i	PRON
ejpam-6447	170	21	−	−	VERB
ejpam-6447	170	22	i∗)2	i∗)2	VERB
ejpam-6447	170	23	+	+	NUM
ejpam-6447	170	24	1	1	NUM
ejpam-6447	170	25	2ϵ	2ϵ	NOUN
ejpam-6447	170	26	(	(	PUNCT
ejpam-6447	170	27	λs	λs	NOUN
ejpam-6447	170	28	−	−	PROPN
ejpam-6447	170	29	λ∗s∗)2	λ∗s∗)2	PROPN
ejpam-6447	170	30	.	.	PUNCT
ejpam-6447	171	1	if	if	SCONJ
ejpam-6447	171	2	(	(	PUNCT
ejpam-6447	171	3	λs−λ∗s∗	λs−λ∗s∗	NUM
ejpam-6447	171	4	)	)	PUNCT
ejpam-6447	171	5	is	be	AUX
ejpam-6447	171	6	small	small	ADJ
ejpam-6447	171	7	near	near	ADP
ejpam-6447	171	8	the	the	DET
ejpam-6447	171	9	equilibrium	equilibrium	NOUN
ejpam-6447	171	10	and	and	CCONJ
ejpam-6447	171	11	if	if	SCONJ
ejpam-6447	171	12	the	the	DET
ejpam-6447	171	13	parameters	parameter	NOUN
ejpam-6447	171	14	satisfy	satisfy	VERB
ejpam-6447	171	15	γ+µ	γ+µ	PROPN
ejpam-6447	171	16	>	>	X
ejpam-6447	171	17	σ	σ	X
ejpam-6447	171	18	2	2	NUM
ejpam-6447	171	19	,	,	PUNCT
ejpam-6447	171	20	then	then	ADV
ejpam-6447	171	21	dv	dv	PROPN
ejpam-6447	171	22	dt	dt	X
ejpam-6447	171	23	<	<	X
ejpam-6447	171	24	0	0	PUNCT
ejpam-6447	171	25	near	near	ADP
ejpam-6447	171	26	the	the	DET
ejpam-6447	171	27	equilibrium	equilibrium	NOUN
ejpam-6447	171	28	.	.	PUNCT
ejpam-6447	172	1	this	this	PRON
ejpam-6447	172	2	implies	imply	VERB
ejpam-6447	172	3	global	global	ADJ
ejpam-6447	172	4	asymptotic	asymptotic	ADJ
ejpam-6447	172	5	stability	stability	NOUN
ejpam-6447	172	6	of	of	ADP
ejpam-6447	172	7	the	the	DET
ejpam-6447	172	8	endemic	endemic	ADJ
ejpam-6447	172	9	equilibrium	equilibrium	NOUN
ejpam-6447	172	10	.	.	PUNCT
ejpam-6447	173	1	s.	s.	PROPN
ejpam-6447	173	2	bushnaq	bushnaq	PROPN
ejpam-6447	173	3	,	,	PUNCT
ejpam-6447	173	4	s.	s.	PROPN
ejpam-6447	173	5	bano	bano	PROPN
ejpam-6447	173	6	,	,	PUNCT
ejpam-6447	173	7	a.	a.	PROPN
ejpam-6447	173	8	zeb	zeb	PROPN
ejpam-6447	173	9	/	/	SYM
ejpam-6447	173	10	eur	eur	PROPN
ejpam-6447	173	11	.	.	PUNCT
ejpam-6447	174	1	j.	j.	PROPN
ejpam-6447	174	2	pure	pure	PROPN
ejpam-6447	174	3	appl	appl	PROPN
ejpam-6447	174	4	.	.	PROPN
ejpam-6447	174	5	math	math	PROPN
ejpam-6447	174	6	,	,	PUNCT
ejpam-6447	174	7	18	18	NUM
ejpam-6447	174	8	(	(	PUNCT
ejpam-6447	174	9	3	3	NUM
ejpam-6447	174	10	)	)	PUNCT
ejpam-6447	174	11	(	(	PUNCT
ejpam-6447	174	12	2025	2025	NUM
ejpam-6447	174	13	)	)	PUNCT
ejpam-6447	174	14	,	,	PUNCT
ejpam-6447	174	15	6447	6447	NUM
ejpam-6447	174	16	9	9	NUM
ejpam-6447	174	17	of	of	ADP
ejpam-6447	174	18	12	12	NUM
ejpam-6447	174	19	5	5	NUM
ejpam-6447	174	20	.	.	PUNCT
ejpam-6447	174	21	numerical	numerical	ADJ
ejpam-6447	174	22	simulations	simulation	NOUN
ejpam-6447	174	23	we	we	PRON
ejpam-6447	174	24	solve	solve	VERB
ejpam-6447	174	25	the	the	DET
ejpam-6447	174	26	system	system	NOUN
ejpam-6447	174	27	numerically	numerically	ADV
ejpam-6447	174	28	using	use	VERB
ejpam-6447	174	29	non	non	ADJ
ejpam-6447	174	30	-	-	ADJ
ejpam-6447	174	31	standard	standard	ADJ
ejpam-6447	174	32	matlab	matlab	NOUN
ejpam-6447	174	33	,	,	PUNCT
ejpam-6447	174	34	employing	employ	VERB
ejpam-6447	174	35	the	the	DET
ejpam-6447	174	36	euler	euler	NOUN
ejpam-6447	174	37	method	method	NOUN
ejpam-6447	174	38	and	and	CCONJ
ejpam-6447	174	39	varying	vary	VERB
ejpam-6447	174	40	β(a	β(a	PROPN
ejpam-6447	174	41	,	,	PUNCT
ejpam-6447	174	42	t	t	PROPN
ejpam-6447	174	43	)	)	PUNCT
ejpam-6447	174	44	to	to	PART
ejpam-6447	174	45	simulate	simulate	VERB
ejpam-6447	174	46	household	household	NOUN
ejpam-6447	174	47	effects	effect	NOUN
ejpam-6447	174	48	.	.	PUNCT
ejpam-6447	175	1	the	the	DET
ejpam-6447	175	2	results	result	NOUN
ejpam-6447	175	3	illustrate	illustrate	VERB
ejpam-6447	175	4	the	the	DET
ejpam-6447	175	5	impact	impact	NOUN
ejpam-6447	175	6	of	of	ADP
ejpam-6447	175	7	seasonal	seasonal	ADJ
ejpam-6447	175	8	variations	variation	NOUN
ejpam-6447	175	9	on	on	ADP
ejpam-6447	175	10	the	the	DET
ejpam-6447	175	11	prevalence	prevalence	NOUN
ejpam-6447	175	12	.	.	PUNCT
ejpam-6447	176	1	the	the	DET
ejpam-6447	176	2	initial	initial	ADJ
ejpam-6447	176	3	conditions	condition	NOUN
ejpam-6447	176	4	are	be	AUX
ejpam-6447	176	5	e(0)=50	e(0)=50	NOUN
ejpam-6447	176	6	,	,	PUNCT
ejpam-6447	176	7	i(0)=30	i(0)=30	NOUN
ejpam-6447	176	8	,	,	PUNCT
ejpam-6447	176	9	r(0)=20	r(0)=20	NOUN
ejpam-6447	176	10	and	and	CCONJ
ejpam-6447	176	11	p(0)=n	p(0)=n	ADV
ejpam-6447	176	12	-	-	PUNCT
ejpam-6447	176	13	e(0)-i(0)-r(0	e(0)-i(0)-r(0	VERB
ejpam-6447	176	14	)	)	PUNCT
ejpam-6447	176	15	.	.	PUNCT
ejpam-6447	177	1	parameters	parameter	NOUN
ejpam-6447	177	2	values	value	NOUN
ejpam-6447	177	3	are	be	AUX
ejpam-6447	177	4	given	give	VERB
ejpam-6447	177	5	in	in	ADP
ejpam-6447	177	6	below	below	ADP
ejpam-6447	177	7	table	table	NOUN
ejpam-6447	177	8	;	;	PUNCT
ejpam-6447	177	9	parameter	parameter	NOUN
ejpam-6447	177	10	values	value	NOUN
ejpam-6447	177	11	λ	λ	PROPN
ejpam-6447	177	12	10.25	10.25	NUM
ejpam-6447	177	13	β0	β0	NOUN
ejpam-6447	177	14	0.005	0.005	NUM
ejpam-6447	177	15	σ	σ	NOUN
ejpam-6447	177	16	0.1	0.1	NUM
ejpam-6447	177	17	γ	γ	NOUN
ejpam-6447	177	18	0.03	0.03	NUM
ejpam-6447	177	19	ϵ	ϵ	NOUN
ejpam-6447	177	20	0,05	0,05	NOUN
ejpam-6447	177	21	n	n	CCONJ
ejpam-6447	177	22	250	250	NUM
ejpam-6447	177	23	table	table	NOUN
ejpam-6447	177	24	1	1	NUM
ejpam-6447	177	25	:	:	PUNCT
ejpam-6447	177	26	parameter	parameter	NOUN
ejpam-6447	177	27	values	value	NOUN
ejpam-6447	177	28	for	for	ADP
ejpam-6447	177	29	the	the	DET
ejpam-6447	177	30	proposed	propose	VERB
ejpam-6447	177	31	model	model	NOUN
ejpam-6447	177	32	(	(	PUNCT
ejpam-6447	177	33	a	a	DET
ejpam-6447	177	34	)	)	PUNCT
ejpam-6447	177	35	comparison	comparison	NOUN
ejpam-6447	177	36	of	of	ADP
ejpam-6447	177	37	susceptible	susceptible	ADJ
ejpam-6447	177	38	population	population	NOUN
ejpam-6447	177	39	with	with	ADP
ejpam-6447	177	40	rk4	rk4	PROPN
ejpam-6447	177	41	,	,	PUNCT
ejpam-6447	177	42	euler	euler	NOUN
ejpam-6447	177	43	,	,	PUNCT
ejpam-6447	177	44	nonstandard	nonstandard	ADJ
ejpam-6447	177	45	finite	finite	ADJ
ejpam-6447	177	46	difference	difference	NOUN
ejpam-6447	177	47	method	method	NOUN
ejpam-6447	177	48	(	(	PUNCT
ejpam-6447	177	49	b	b	NOUN
ejpam-6447	177	50	)	)	PUNCT
ejpam-6447	177	51	comparison	comparison	NOUN
ejpam-6447	177	52	of	of	ADP
ejpam-6447	177	53	exposed	expose	VERB
ejpam-6447	177	54	population	population	NOUN
ejpam-6447	177	55	with	with	ADP
ejpam-6447	177	56	rk4	rk4	PROPN
ejpam-6447	177	57	,	,	PUNCT
ejpam-6447	177	58	euler	euler	NOUN
ejpam-6447	177	59	,	,	PUNCT
ejpam-6447	177	60	nonstandard	nonstandard	ADJ
ejpam-6447	177	61	finite	finite	ADJ
ejpam-6447	177	62	difference	difference	NOUN
ejpam-6447	177	63	method	method	NOUN
ejpam-6447	177	64	(	(	PUNCT
ejpam-6447	177	65	c	c	NOUN
ejpam-6447	177	66	)	)	PUNCT
ejpam-6447	177	67	comparison	comparison	NOUN
ejpam-6447	177	68	of	of	ADP
ejpam-6447	177	69	infected	infected	ADJ
ejpam-6447	177	70	population	population	NOUN
ejpam-6447	177	71	with	with	ADP
ejpam-6447	177	72	rk4	rk4	PROPN
ejpam-6447	177	73	,	,	PUNCT
ejpam-6447	177	74	euler	euler	NOUN
ejpam-6447	177	75	,	,	PUNCT
ejpam-6447	177	76	nonstandard	nonstandard	ADJ
ejpam-6447	177	77	finite	finite	ADJ
ejpam-6447	177	78	difference	difference	NOUN
ejpam-6447	177	79	method	method	NOUN
ejpam-6447	177	80	(	(	PUNCT
ejpam-6447	177	81	d	d	NOUN
ejpam-6447	177	82	)	)	PUNCT
ejpam-6447	177	83	comparison	comparison	NOUN
ejpam-6447	177	84	od	od	PROPN
ejpam-6447	177	85	recovered	recover	VERB
ejpam-6447	177	86	population	population	NOUN
ejpam-6447	177	87	with	with	ADP
ejpam-6447	177	88	rk4,euler	rk4,euler	PROPN
ejpam-6447	177	89	,	,	PUNCT
ejpam-6447	177	90	nonstandard	nonstandard	ADJ
ejpam-6447	177	91	finite	finite	ADJ
ejpam-6447	177	92	difference	difference	NOUN
ejpam-6447	177	93	method	method	NOUN
ejpam-6447	177	94	(	(	PUNCT
ejpam-6447	177	95	e	e	NOUN
ejpam-6447	177	96	)	)	PUNCT
ejpam-6447	177	97	population	population	NOUN
ejpam-6447	177	98	graph	graph	NOUN
ejpam-6447	177	99	with	with	ADP
ejpam-6447	177	100	rk4	rk4	NOUN
ejpam-6447	177	101	(	(	PUNCT
ejpam-6447	177	102	f	f	X
ejpam-6447	177	103	)	)	PUNCT
ejpam-6447	177	104	population	population	NOUN
ejpam-6447	177	105	graph	graph	NOUN
ejpam-6447	177	106	with	with	ADP
ejpam-6447	177	107	euler	euler	PROPN
ejpam-6447	177	108	(	(	PUNCT
ejpam-6447	177	109	g	g	NOUN
ejpam-6447	177	110	)	)	PUNCT
ejpam-6447	177	111	population	population	NOUN
ejpam-6447	177	112	graph	graph	NOUN
ejpam-6447	177	113	with	with	ADP
ejpam-6447	177	114	nsfd	nsfd	ADJ
ejpam-6447	177	115	figure	figure	NOUN
ejpam-6447	177	116	2	2	NUM
ejpam-6447	177	117	:	:	PUNCT
ejpam-6447	177	118	(	(	PUNCT
ejpam-6447	177	119	a	a	X
ejpam-6447	177	120	)	)	PUNCT
ejpam-6447	177	121	plot	plot	NOUN
ejpam-6447	177	122	of	of	ADP
ejpam-6447	177	123	susceptible	susceptible	ADJ
ejpam-6447	177	124	class	class	NOUN
ejpam-6447	177	125	in	in	ADP
ejpam-6447	177	126	which	which	PRON
ejpam-6447	177	127	rk4	rk4	NOUN
ejpam-6447	177	128	,	,	PUNCT
ejpam-6447	177	129	euler	euler	NOUN
ejpam-6447	177	130	and	and	CCONJ
ejpam-6447	177	131	nonstandard	nonstandard	ADJ
ejpam-6447	177	132	finite	finite	ADJ
ejpam-6447	177	133	difference	difference	NOUN
ejpam-6447	177	134	.	.	PUNCT
ejpam-6447	178	1	(	(	PUNCT
ejpam-6447	178	2	b	b	X
ejpam-6447	178	3	)	)	PUNCT
ejpam-6447	178	4	plot	plot	NOUN
ejpam-6447	178	5	of	of	ADP
ejpam-6447	178	6	infected	infected	ADJ
ejpam-6447	178	7	class	class	NOUN
ejpam-6447	178	8	in	in	ADP
ejpam-6447	178	9	which	which	PRON
ejpam-6447	178	10	rk4	rk4	NOUN
ejpam-6447	178	11	,	,	PUNCT
ejpam-6447	178	12	euler	euler	NOUN
ejpam-6447	178	13	and	and	CCONJ
ejpam-6447	178	14	nonstandard	nonstandard	ADJ
ejpam-6447	178	15	finite	finite	ADJ
ejpam-6447	178	16	difference	difference	NOUN
ejpam-6447	178	17	.	.	PUNCT
ejpam-6447	179	1	(	(	PUNCT
ejpam-6447	179	2	c	c	X
ejpam-6447	179	3	)	)	PUNCT
ejpam-6447	179	4	plot	plot	NOUN
ejpam-6447	179	5	of	of	ADP
ejpam-6447	179	6	exposed	expose	VERB
ejpam-6447	179	7	class	class	NOUN
ejpam-6447	179	8	in	in	ADP
ejpam-6447	179	9	which	which	PRON
ejpam-6447	179	10	rk4	rk4	NOUN
ejpam-6447	179	11	,	,	PUNCT
ejpam-6447	179	12	euler	euler	NOUN
ejpam-6447	179	13	and	and	CCONJ
ejpam-6447	179	14	nonstandard	nonstandard	ADJ
ejpam-6447	179	15	finite	finite	ADJ
ejpam-6447	179	16	difference	difference	NOUN
ejpam-6447	179	17	.	.	PUNCT
ejpam-6447	180	1	(	(	PUNCT
ejpam-6447	180	2	d	d	X
ejpam-6447	180	3	)	)	PUNCT
ejpam-6447	180	4	plot	plot	NOUN
ejpam-6447	180	5	of	of	ADP
ejpam-6447	180	6	recovered	recovered	ADJ
ejpam-6447	180	7	class	class	NOUN
ejpam-6447	180	8	in	in	ADP
ejpam-6447	180	9	which	which	PRON
ejpam-6447	180	10	rk4	rk4	NOUN
ejpam-6447	180	11	,	,	PUNCT
ejpam-6447	180	12	euler	euler	NOUN
ejpam-6447	180	13	and	and	CCONJ
ejpam-6447	180	14	nonstandard	nonstandard	ADJ
ejpam-6447	180	15	finite	finite	ADJ
ejpam-6447	180	16	difference	difference	NOUN
ejpam-6447	180	17	(	(	PUNCT
ejpam-6447	180	18	e	e	NOUN
ejpam-6447	180	19	)	)	PUNCT
ejpam-6447	180	20	plot	plot	NOUN
ejpam-6447	180	21	of	of	ADP
ejpam-6447	180	22	population	population	NOUN
ejpam-6447	180	23	with	with	ADP
ejpam-6447	180	24	rk4	rk4	PROPN
ejpam-6447	180	25	method	method	NOUN
ejpam-6447	180	26	.	.	PUNCT
ejpam-6447	181	1	(	(	PUNCT
ejpam-6447	181	2	e	e	NOUN
ejpam-6447	181	3	)	)	PUNCT
ejpam-6447	181	4	plot	plot	NOUN
ejpam-6447	181	5	of	of	ADP
ejpam-6447	181	6	population	population	NOUN
ejpam-6447	181	7	with	with	ADP
ejpam-6447	181	8	euler	euler	NOUN
ejpam-6447	181	9	method	method	NOUN
ejpam-6447	181	10	.	.	PUNCT
ejpam-6447	182	1	(	(	PUNCT
ejpam-6447	182	2	f	f	X
ejpam-6447	182	3	)	)	PUNCT
ejpam-6447	182	4	plot	plot	NOUN
ejpam-6447	182	5	of	of	ADP
ejpam-6447	182	6	population	population	NOUN
ejpam-6447	182	7	with	with	ADP
ejpam-6447	182	8	nonstandard	nonstandard	ADJ
ejpam-6447	182	9	finite	finite	ADJ
ejpam-6447	182	10	difference	difference	NOUN
ejpam-6447	182	11	method	method	NOUN
ejpam-6447	182	12	.	.	PUNCT
ejpam-6447	183	1	for	for	ADP
ejpam-6447	183	2	different	different	ADJ
ejpam-6447	183	3	value	value	NOUN
ejpam-6447	183	4	of	of	ADP
ejpam-6447	183	5	b(a	b(a	PROPN
ejpam-6447	183	6	,	,	PUNCT
ejpam-6447	183	7	t	t	PROPN
ejpam-6447	183	8	)	)	PUNCT
ejpam-6447	183	9	the	the	DET
ejpam-6447	183	10	graph	graph	NOUN
ejpam-6447	183	11	of	of	ADP
ejpam-6447	183	12	all	all	DET
ejpam-6447	183	13	population	population	NOUN
ejpam-6447	183	14	by	by	ADP
ejpam-6447	183	15	using	use	VERB
ejpam-6447	183	16	rk4	rk4	NOUN
ejpam-6447	183	17	,	,	PUNCT
ejpam-6447	183	18	euler	euler	NOUN
ejpam-6447	183	19	,	,	PUNCT
ejpam-6447	183	20	and	and	CCONJ
ejpam-6447	183	21	nonstandard	nonstandard	ADJ
ejpam-6447	183	22	finite	finite	ADJ
ejpam-6447	183	23	difference	difference	NOUN
ejpam-6447	183	24	method	method	NOUN
ejpam-6447	183	25	are	be	AUX
ejpam-6447	183	26	given	give	VERB
ejpam-6447	183	27	below	below	ADV
ejpam-6447	183	28	.	.	PUNCT
ejpam-6447	184	1	s.	s.	PROPN
ejpam-6447	184	2	bushnaq	bushnaq	PROPN
ejpam-6447	184	3	,	,	PUNCT
ejpam-6447	184	4	s.	s.	PROPN
ejpam-6447	184	5	bano	bano	PROPN
ejpam-6447	184	6	,	,	PUNCT
ejpam-6447	184	7	a.	a.	PROPN
ejpam-6447	184	8	zeb	zeb	PROPN
ejpam-6447	184	9	/	/	SYM
ejpam-6447	184	10	eur	eur	PROPN
ejpam-6447	184	11	.	.	PUNCT
ejpam-6447	185	1	j.	j.	PROPN
ejpam-6447	185	2	pure	pure	PROPN
ejpam-6447	185	3	appl	appl	PROPN
ejpam-6447	185	4	.	.	PROPN
ejpam-6447	185	5	math	math	PROPN
ejpam-6447	185	6	,	,	PUNCT
ejpam-6447	185	7	18	18	NUM
ejpam-6447	185	8	(	(	PUNCT
ejpam-6447	185	9	3	3	NUM
ejpam-6447	185	10	)	)	PUNCT
ejpam-6447	185	11	(	(	PUNCT
ejpam-6447	185	12	2025	2025	NUM
ejpam-6447	185	13	)	)	PUNCT
ejpam-6447	185	14	,	,	PUNCT
ejpam-6447	185	15	6447	6447	NUM
ejpam-6447	185	16	10	10	NUM
ejpam-6447	185	17	of	of	ADP
ejpam-6447	185	18	12	12	NUM
ejpam-6447	185	19	(	(	PUNCT
ejpam-6447	185	20	a	a	NOUN
ejpam-6447	185	21	)	)	PUNCT
ejpam-6447	185	22	susceptible	susceptible	ADJ
ejpam-6447	185	23	population	population	NOUN
ejpam-6447	185	24	using	use	VERB
ejpam-6447	185	25	the	the	DET
ejpam-6447	185	26	rk4	rk4	NOUN
ejpam-6447	185	27	technique	technique	NOUN
ejpam-6447	185	28	with	with	ADP
ejpam-6447	185	29	various	various	ADJ
ejpam-6447	185	30	numbers	number	NOUN
ejpam-6447	185	31	of	of	ADP
ejpam-6447	185	32	β(a	β(a	PROPN
ejpam-6447	185	33	,	,	PUNCT
ejpam-6447	185	34	t	t	PROPN
ejpam-6447	185	35	)	)	PUNCT
ejpam-6447	185	36	(	(	PUNCT
ejpam-6447	185	37	b	b	X
ejpam-6447	185	38	)	)	PUNCT
ejpam-6447	185	39	infected	infected	ADJ
ejpam-6447	185	40	population	population	NOUN
ejpam-6447	185	41	using	use	VERB
ejpam-6447	185	42	the	the	DET
ejpam-6447	185	43	rk4	rk4	NOUN
ejpam-6447	185	44	technique	technique	NOUN
ejpam-6447	185	45	with	with	ADP
ejpam-6447	185	46	various	various	ADJ
ejpam-6447	185	47	numbers	number	NOUN
ejpam-6447	185	48	of	of	ADP
ejpam-6447	185	49	β(a	β(a	PROPN
ejpam-6447	185	50	,	,	PUNCT
ejpam-6447	185	51	t	t	PROPN
ejpam-6447	185	52	)	)	PUNCT
ejpam-6447	185	53	(	(	PUNCT
ejpam-6447	185	54	c	c	X
ejpam-6447	185	55	)	)	PUNCT
ejpam-6447	185	56	exposed	expose	VERB
ejpam-6447	185	57	population	population	NOUN
ejpam-6447	185	58	using	use	VERB
ejpam-6447	185	59	the	the	DET
ejpam-6447	185	60	rk4	rk4	NOUN
ejpam-6447	185	61	technique	technique	NOUN
ejpam-6447	185	62	with	with	ADP
ejpam-6447	185	63	various	various	ADJ
ejpam-6447	185	64	numbers	number	NOUN
ejpam-6447	185	65	of	of	ADP
ejpam-6447	185	66	β(a	β(a	PROPN
ejpam-6447	185	67	,	,	PUNCT
ejpam-6447	185	68	t	t	PROPN
ejpam-6447	185	69	)	)	PUNCT
ejpam-6447	185	70	(	(	PUNCT
ejpam-6447	185	71	d	d	X
ejpam-6447	185	72	)	)	PUNCT
ejpam-6447	185	73	recovered	recover	VERB
ejpam-6447	185	74	population	population	NOUN
ejpam-6447	185	75	using	use	VERB
ejpam-6447	185	76	the	the	DET
ejpam-6447	185	77	rk4	rk4	NOUN
ejpam-6447	185	78	technique	technique	NOUN
ejpam-6447	185	79	with	with	ADP
ejpam-6447	185	80	various	various	ADJ
ejpam-6447	185	81	numbers	number	NOUN
ejpam-6447	185	82	of	of	ADP
ejpam-6447	185	83	β(a	β(a	PROPN
ejpam-6447	185	84	,	,	PUNCT
ejpam-6447	185	85	t	t	PROPN
ejpam-6447	185	86	)	)	PUNCT
ejpam-6447	185	87	(	(	PUNCT
ejpam-6447	185	88	e	e	NOUN
ejpam-6447	185	89	)	)	PUNCT
ejpam-6447	185	90	susceptible	susceptible	ADJ
ejpam-6447	185	91	population	population	NOUN
ejpam-6447	185	92	using	use	VERB
ejpam-6447	185	93	the	the	DET
ejpam-6447	185	94	euler	euler	NOUN
ejpam-6447	185	95	technique	technique	NOUN
ejpam-6447	185	96	with	with	ADP
ejpam-6447	185	97	various	various	ADJ
ejpam-6447	185	98	numbers	number	NOUN
ejpam-6447	185	99	of	of	ADP
ejpam-6447	185	100	β(a	β(a	PROPN
ejpam-6447	185	101	,	,	PUNCT
ejpam-6447	185	102	t	t	PROPN
ejpam-6447	185	103	)	)	PUNCT
ejpam-6447	185	104	(	(	PUNCT
ejpam-6447	185	105	f	f	X
ejpam-6447	185	106	)	)	PUNCT
ejpam-6447	185	107	exposed	expose	VERB
ejpam-6447	185	108	population	population	NOUN
ejpam-6447	185	109	using	use	VERB
ejpam-6447	185	110	the	the	DET
ejpam-6447	185	111	euler	euler	NOUN
ejpam-6447	185	112	technique	technique	NOUN
ejpam-6447	185	113	with	with	ADP
ejpam-6447	185	114	various	various	ADJ
ejpam-6447	185	115	numbers	number	NOUN
ejpam-6447	185	116	of	of	ADP
ejpam-6447	185	117	β(a	β(a	PROPN
ejpam-6447	185	118	,	,	PUNCT
ejpam-6447	185	119	t	t	PROPN
ejpam-6447	185	120	)	)	PUNCT
ejpam-6447	185	121	(	(	PUNCT
ejpam-6447	185	122	g	g	NOUN
ejpam-6447	185	123	)	)	PUNCT
ejpam-6447	185	124	infected	infected	ADJ
ejpam-6447	185	125	population	population	NOUN
ejpam-6447	185	126	using	use	VERB
ejpam-6447	185	127	the	the	DET
ejpam-6447	185	128	euler	euler	NOUN
ejpam-6447	185	129	technique	technique	NOUN
ejpam-6447	185	130	with	with	ADP
ejpam-6447	185	131	various	various	ADJ
ejpam-6447	185	132	numbers	number	NOUN
ejpam-6447	185	133	of	of	ADP
ejpam-6447	185	134	β(a	β(a	PROPN
ejpam-6447	185	135	,	,	PUNCT
ejpam-6447	185	136	t	t	PROPN
ejpam-6447	185	137	)	)	PUNCT
ejpam-6447	185	138	(	(	PUNCT
ejpam-6447	185	139	h	h	NOUN
ejpam-6447	185	140	)	)	PUNCT
ejpam-6447	185	141	recovered	recover	VERB
ejpam-6447	185	142	population	population	NOUN
ejpam-6447	185	143	using	use	VERB
ejpam-6447	185	144	the	the	DET
ejpam-6447	185	145	euler	euler	NOUN
ejpam-6447	185	146	technique	technique	NOUN
ejpam-6447	185	147	with	with	ADP
ejpam-6447	185	148	various	various	ADJ
ejpam-6447	185	149	numbers	number	NOUN
ejpam-6447	185	150	of	of	ADP
ejpam-6447	185	151	β(a	β(a	PROPN
ejpam-6447	185	152	,	,	PUNCT
ejpam-6447	185	153	t	t	PROPN
ejpam-6447	185	154	)	)	PUNCT
ejpam-6447	185	155	(	(	PUNCT
ejpam-6447	185	156	i	i	NOUN
ejpam-6447	185	157	)	)	PUNCT
ejpam-6447	185	158	susceptible	susceptible	ADJ
ejpam-6447	185	159	population	population	NOUN
ejpam-6447	185	160	using	use	VERB
ejpam-6447	185	161	the	the	DET
ejpam-6447	185	162	nsfd	nsfd	ADJ
ejpam-6447	185	163	technique	technique	NOUN
ejpam-6447	185	164	with	with	ADP
ejpam-6447	185	165	various	various	ADJ
ejpam-6447	185	166	numbers	number	NOUN
ejpam-6447	185	167	of	of	ADP
ejpam-6447	185	168	β(a	β(a	PROPN
ejpam-6447	185	169	,	,	PUNCT
ejpam-6447	185	170	t	t	PROPN
ejpam-6447	185	171	)	)	PUNCT
ejpam-6447	185	172	(	(	PUNCT
ejpam-6447	185	173	j	j	NOUN
ejpam-6447	185	174	)	)	PUNCT
ejpam-6447	185	175	exposed	expose	VERB
ejpam-6447	185	176	population	population	NOUN
ejpam-6447	185	177	using	use	VERB
ejpam-6447	185	178	the	the	DET
ejpam-6447	185	179	nsfd	nsfd	ADJ
ejpam-6447	185	180	technique	technique	NOUN
ejpam-6447	185	181	with	with	ADP
ejpam-6447	185	182	various	various	ADJ
ejpam-6447	185	183	numbers	number	NOUN
ejpam-6447	185	184	of	of	ADP
ejpam-6447	185	185	β(a	β(a	PROPN
ejpam-6447	185	186	,	,	PUNCT
ejpam-6447	185	187	t	t	PROPN
ejpam-6447	185	188	)	)	PUNCT
ejpam-6447	185	189	(	(	PUNCT
ejpam-6447	185	190	k	k	X
ejpam-6447	185	191	)	)	PUNCT
ejpam-6447	185	192	infected	infected	ADJ
ejpam-6447	185	193	population	population	NOUN
ejpam-6447	185	194	using	use	VERB
ejpam-6447	185	195	the	the	DET
ejpam-6447	185	196	nsfd	nsfd	ADJ
ejpam-6447	185	197	technique	technique	NOUN
ejpam-6447	185	198	with	with	ADP
ejpam-6447	185	199	various	various	ADJ
ejpam-6447	185	200	numbers	number	NOUN
ejpam-6447	185	201	of	of	ADP
ejpam-6447	185	202	β(a	β(a	PROPN
ejpam-6447	185	203	,	,	PUNCT
ejpam-6447	185	204	t	t	PROPN
ejpam-6447	185	205	)	)	PUNCT
ejpam-6447	185	206	(	(	PUNCT
ejpam-6447	185	207	l	l	NOUN
ejpam-6447	185	208	)	)	PUNCT
ejpam-6447	185	209	recovered	recover	VERB
ejpam-6447	185	210	population	population	NOUN
ejpam-6447	185	211	using	use	VERB
ejpam-6447	185	212	the	the	DET
ejpam-6447	185	213	nsfd	nsfd	ADJ
ejpam-6447	185	214	technique	technique	NOUN
ejpam-6447	185	215	with	with	ADP
ejpam-6447	185	216	various	various	ADJ
ejpam-6447	185	217	numbers	number	NOUN
ejpam-6447	185	218	of	of	ADP
ejpam-6447	185	219	β(a	β(a	PROPN
ejpam-6447	185	220	,	,	PUNCT
ejpam-6447	185	221	t	t	PROPN
ejpam-6447	185	222	)	)	PUNCT
ejpam-6447	185	223	figure	figure	NOUN
ejpam-6447	185	224	3	3	NUM
ejpam-6447	185	225	:	:	PUNCT
ejpam-6447	185	226	(	(	PUNCT
ejpam-6447	185	227	a	a	X
ejpam-6447	185	228	)	)	PUNCT
ejpam-6447	185	229	plot	plot	NOUN
ejpam-6447	185	230	of	of	ADP
ejpam-6447	185	231	susceptible	susceptible	ADJ
ejpam-6447	185	232	class	class	NOUN
ejpam-6447	185	233	in	in	ADP
ejpam-6447	185	234	which	which	PRON
ejpam-6447	185	235	rk4	rk4	NOUN
ejpam-6447	185	236	method	method	NOUN
ejpam-6447	185	237	is	be	AUX
ejpam-6447	185	238	used	use	VERB
ejpam-6447	185	239	for	for	ADP
ejpam-6447	185	240	different	different	ADJ
ejpam-6447	185	241	value	value	NOUN
ejpam-6447	185	242	of	of	ADP
ejpam-6447	185	243	β(a	β(a	PROPN
ejpam-6447	185	244	,	,	PUNCT
ejpam-6447	185	245	t	t	PROPN
ejpam-6447	185	246	)	)	PUNCT
ejpam-6447	185	247	.	.	PUNCT
ejpam-6447	186	1	(	(	PUNCT
ejpam-6447	186	2	b)plot	b)plot	PROPN
ejpam-6447	186	3	of	of	ADP
ejpam-6447	186	4	exposed	expose	VERB
ejpam-6447	186	5	class	class	NOUN
ejpam-6447	186	6	in	in	ADP
ejpam-6447	186	7	which	which	PRON
ejpam-6447	186	8	rk4	rk4	NOUN
ejpam-6447	186	9	method	method	NOUN
ejpam-6447	186	10	is	be	AUX
ejpam-6447	186	11	used	use	VERB
ejpam-6447	186	12	for	for	ADP
ejpam-6447	186	13	different	different	ADJ
ejpam-6447	186	14	value	value	NOUN
ejpam-6447	186	15	of	of	ADP
ejpam-6447	186	16	β(a	β(a	PROPN
ejpam-6447	186	17	,	,	PUNCT
ejpam-6447	186	18	t	t	PROPN
ejpam-6447	186	19	)	)	PUNCT
ejpam-6447	186	20	.	.	PUNCT
ejpam-6447	187	1	(	(	PUNCT
ejpam-6447	187	2	c	c	X
ejpam-6447	187	3	)	)	PUNCT
ejpam-6447	187	4	plot	plot	NOUN
ejpam-6447	187	5	of	of	ADP
ejpam-6447	187	6	infected	infected	ADJ
ejpam-6447	187	7	class	class	NOUN
ejpam-6447	187	8	in	in	ADP
ejpam-6447	187	9	which	which	PRON
ejpam-6447	187	10	rk4	rk4	NOUN
ejpam-6447	187	11	method	method	NOUN
ejpam-6447	187	12	is	be	AUX
ejpam-6447	187	13	used	use	VERB
ejpam-6447	187	14	for	for	ADP
ejpam-6447	187	15	different	different	ADJ
ejpam-6447	187	16	value	value	NOUN
ejpam-6447	187	17	of	of	ADP
ejpam-6447	187	18	β(a	β(a	PROPN
ejpam-6447	187	19	,	,	PUNCT
ejpam-6447	187	20	t	t	PROPN
ejpam-6447	187	21	)	)	PUNCT
ejpam-6447	187	22	(	(	PUNCT
ejpam-6447	187	23	d	d	X
ejpam-6447	187	24	)	)	PUNCT
ejpam-6447	187	25	plot	plot	NOUN
ejpam-6447	187	26	of	of	ADP
ejpam-6447	187	27	recovered	recovered	ADJ
ejpam-6447	187	28	class	class	NOUN
ejpam-6447	187	29	in	in	ADP
ejpam-6447	187	30	which	which	PRON
ejpam-6447	187	31	rk4	rk4	NOUN
ejpam-6447	187	32	method	method	NOUN
ejpam-6447	187	33	is	be	AUX
ejpam-6447	187	34	used	use	VERB
ejpam-6447	187	35	for	for	ADP
ejpam-6447	187	36	different	different	ADJ
ejpam-6447	187	37	value	value	NOUN
ejpam-6447	187	38	of	of	ADP
ejpam-6447	187	39	β(a	β(a	PROPN
ejpam-6447	187	40	,	,	PUNCT
ejpam-6447	187	41	t	t	PROPN
ejpam-6447	187	42	)	)	PUNCT
ejpam-6447	187	43	.	.	PUNCT
ejpam-6447	188	1	(	(	PUNCT
ejpam-6447	188	2	e	e	NOUN
ejpam-6447	188	3	)	)	PUNCT
ejpam-6447	188	4	plot	plot	NOUN
ejpam-6447	188	5	of	of	ADP
ejpam-6447	188	6	susceptible	susceptible	ADJ
ejpam-6447	188	7	class	class	NOUN
ejpam-6447	188	8	in	in	ADP
ejpam-6447	188	9	which	which	PRON
ejpam-6447	188	10	euler	euler	NOUN
ejpam-6447	188	11	method	method	NOUN
ejpam-6447	188	12	is	be	AUX
ejpam-6447	188	13	used	use	VERB
ejpam-6447	188	14	for	for	ADP
ejpam-6447	188	15	different	different	ADJ
ejpam-6447	188	16	value	value	NOUN
ejpam-6447	188	17	of	of	ADP
ejpam-6447	188	18	β(a	β(a	PROPN
ejpam-6447	188	19	,	,	PUNCT
ejpam-6447	188	20	t	t	PROPN
ejpam-6447	188	21	)	)	PUNCT
ejpam-6447	188	22	.	.	PUNCT
ejpam-6447	189	1	(	(	PUNCT
ejpam-6447	189	2	f	f	X
ejpam-6447	189	3	)	)	PUNCT
ejpam-6447	189	4	plot	plot	NOUN
ejpam-6447	189	5	of	of	ADP
ejpam-6447	189	6	exposed	expose	VERB
ejpam-6447	189	7	class	class	NOUN
ejpam-6447	189	8	in	in	ADP
ejpam-6447	189	9	which	which	PRON
ejpam-6447	189	10	euler	euler	NOUN
ejpam-6447	189	11	method	method	NOUN
ejpam-6447	189	12	is	be	AUX
ejpam-6447	189	13	used	use	VERB
ejpam-6447	189	14	for	for	ADP
ejpam-6447	189	15	different	different	ADJ
ejpam-6447	189	16	value	value	NOUN
ejpam-6447	189	17	of	of	ADP
ejpam-6447	189	18	β(a	β(a	PROPN
ejpam-6447	189	19	,	,	PUNCT
ejpam-6447	189	20	t	t	PROPN
ejpam-6447	189	21	)	)	PUNCT
ejpam-6447	189	22	.	.	PUNCT
ejpam-6447	190	1	(	(	PUNCT
ejpam-6447	190	2	g	g	NOUN
ejpam-6447	190	3	)	)	PUNCT
ejpam-6447	190	4	plot	plot	NOUN
ejpam-6447	190	5	of	of	ADP
ejpam-6447	190	6	infected	infected	ADJ
ejpam-6447	190	7	class	class	NOUN
ejpam-6447	190	8	in	in	ADP
ejpam-6447	190	9	which	which	PRON
ejpam-6447	190	10	euler	euler	NOUN
ejpam-6447	190	11	method	method	NOUN
ejpam-6447	190	12	is	be	AUX
ejpam-6447	190	13	used	use	VERB
ejpam-6447	190	14	for	for	ADP
ejpam-6447	190	15	different	different	ADJ
ejpam-6447	190	16	value	value	NOUN
ejpam-6447	190	17	of	of	ADP
ejpam-6447	190	18	β(a	β(a	PROPN
ejpam-6447	190	19	,	,	PUNCT
ejpam-6447	190	20	t	t	PROPN
ejpam-6447	190	21	)	)	PUNCT
ejpam-6447	190	22	.	.	PUNCT
ejpam-6447	191	1	(	(	PUNCT
ejpam-6447	191	2	h	h	NOUN
ejpam-6447	191	3	)	)	PUNCT
ejpam-6447	191	4	plot	plot	NOUN
ejpam-6447	191	5	of	of	ADP
ejpam-6447	191	6	recovered	recovered	ADJ
ejpam-6447	191	7	class	class	NOUN
ejpam-6447	191	8	in	in	ADP
ejpam-6447	191	9	which	which	PRON
ejpam-6447	191	10	euler	euler	NOUN
ejpam-6447	191	11	method	method	NOUN
ejpam-6447	191	12	is	be	AUX
ejpam-6447	191	13	used	use	VERB
ejpam-6447	191	14	for	for	ADP
ejpam-6447	191	15	different	different	ADJ
ejpam-6447	191	16	value	value	NOUN
ejpam-6447	191	17	of	of	ADP
ejpam-6447	191	18	β(a	β(a	PROPN
ejpam-6447	191	19	,	,	PUNCT
ejpam-6447	191	20	t	t	PROPN
ejpam-6447	191	21	)	)	PUNCT
ejpam-6447	191	22	.	.	PUNCT
ejpam-6447	192	1	(	(	PUNCT
ejpam-6447	192	2	i	i	NOUN
ejpam-6447	192	3	)	)	PUNCT
ejpam-6447	192	4	plot	plot	NOUN
ejpam-6447	192	5	of	of	ADP
ejpam-6447	192	6	susceptible	susceptible	ADJ
ejpam-6447	192	7	class	class	NOUN
ejpam-6447	192	8	in	in	ADP
ejpam-6447	192	9	which	which	PRON
ejpam-6447	192	10	nonstandard	nonstandard	ADJ
ejpam-6447	192	11	finite	finite	ADJ
ejpam-6447	192	12	difference	difference	NOUN
ejpam-6447	192	13	method	method	NOUN
ejpam-6447	192	14	is	be	AUX
ejpam-6447	192	15	used	use	VERB
ejpam-6447	192	16	for	for	ADP
ejpam-6447	192	17	different	different	ADJ
ejpam-6447	192	18	value	value	NOUN
ejpam-6447	192	19	of	of	ADP
ejpam-6447	192	20	β(a	β(a	PROPN
ejpam-6447	192	21	,	,	PUNCT
ejpam-6447	192	22	t).(j	t).(j	PROPN
ejpam-6447	192	23	)	)	PUNCT
ejpam-6447	192	24	plot	plot	NOUN
ejpam-6447	192	25	of	of	ADP
ejpam-6447	192	26	exposed	expose	VERB
ejpam-6447	192	27	class	class	NOUN
ejpam-6447	192	28	in	in	ADP
ejpam-6447	192	29	which	which	PRON
ejpam-6447	192	30	nonstandard	nonstandard	ADJ
ejpam-6447	192	31	finite	finite	ADJ
ejpam-6447	192	32	difference	difference	NOUN
ejpam-6447	192	33	method	method	NOUN
ejpam-6447	192	34	is	be	AUX
ejpam-6447	192	35	used	use	VERB
ejpam-6447	192	36	for	for	ADP
ejpam-6447	192	37	different	different	ADJ
ejpam-6447	192	38	value	value	NOUN
ejpam-6447	192	39	of	of	ADP
ejpam-6447	192	40	β(a	β(a	PROPN
ejpam-6447	192	41	,	,	PUNCT
ejpam-6447	192	42	t	t	PROPN
ejpam-6447	192	43	)	)	PUNCT
ejpam-6447	192	44	.	.	PUNCT
ejpam-6447	193	1	(	(	PUNCT
ejpam-6447	193	2	k	k	X
ejpam-6447	193	3	)	)	PUNCT
ejpam-6447	193	4	plot	plot	NOUN
ejpam-6447	193	5	of	of	ADP
ejpam-6447	193	6	infected	infected	ADJ
ejpam-6447	193	7	class	class	NOUN
ejpam-6447	193	8	in	in	ADP
ejpam-6447	193	9	which	which	PRON
ejpam-6447	193	10	nonstandard	nonstandard	ADJ
ejpam-6447	193	11	finite	finite	ADJ
ejpam-6447	193	12	difference	difference	NOUN
ejpam-6447	193	13	method	method	NOUN
ejpam-6447	193	14	is	be	AUX
ejpam-6447	193	15	used	use	VERB
ejpam-6447	193	16	for	for	ADP
ejpam-6447	193	17	different	different	ADJ
ejpam-6447	193	18	value	value	NOUN
ejpam-6447	193	19	of	of	ADP
ejpam-6447	193	20	β(a	β(a	PROPN
ejpam-6447	193	21	,	,	PUNCT
ejpam-6447	193	22	t).(l	t).(l	PROPN
ejpam-6447	193	23	)	)	PUNCT
ejpam-6447	193	24	plot	plot	NOUN
ejpam-6447	193	25	of	of	ADP
ejpam-6447	193	26	recovered	recovered	ADJ
ejpam-6447	193	27	class	class	NOUN
ejpam-6447	193	28	in	in	ADP
ejpam-6447	193	29	which	which	PRON
ejpam-6447	193	30	nonstandard	nonstandard	ADJ
ejpam-6447	193	31	finite	finite	ADJ
ejpam-6447	193	32	difference	difference	NOUN
ejpam-6447	193	33	method	method	NOUN
ejpam-6447	193	34	is	be	AUX
ejpam-6447	193	35	used	use	VERB
ejpam-6447	193	36	for	for	ADP
ejpam-6447	193	37	different	different	ADJ
ejpam-6447	193	38	value	value	NOUN
ejpam-6447	193	39	of	of	ADP
ejpam-6447	193	40	β(a	β(a	PROPN
ejpam-6447	193	41	,	,	PUNCT
ejpam-6447	193	42	t	t	PROPN
ejpam-6447	193	43	)	)	PUNCT
ejpam-6447	193	44	.	.	PUNCT
ejpam-6447	194	1	6	6	X
ejpam-6447	194	2	.	.	X
ejpam-6447	194	3	conclusions	conclusion	NOUN
ejpam-6447	194	4	and	and	CCONJ
ejpam-6447	194	5	discussions	discussion	NOUN
ejpam-6447	194	6	the	the	DET
ejpam-6447	194	7	current	current	ADJ
ejpam-6447	194	8	paper	paper	NOUN
ejpam-6447	194	9	investigated	investigate	VERB
ejpam-6447	194	10	the	the	DET
ejpam-6447	194	11	global	global	ADJ
ejpam-6447	194	12	asymptotic	asymptotic	ADJ
ejpam-6447	194	13	dynamics	dynamic	NOUN
ejpam-6447	194	14	of	of	ADP
ejpam-6447	194	15	an	an	DET
ejpam-6447	194	16	age	age	NOUN
ejpam-6447	194	17	-	-	PUNCT
ejpam-6447	194	18	structured	structure	VERB
ejpam-6447	194	19	smoking	smoking	NOUN
ejpam-6447	194	20	model	model	NOUN
ejpam-6447	194	21	.	.	PUNCT
ejpam-6447	195	1	our	our	PRON
ejpam-6447	195	2	initial	initial	ADJ
ejpam-6447	195	3	step	step	NOUN
ejpam-6447	195	4	involved	involve	VERB
ejpam-6447	195	5	formulating	formulate	VERB
ejpam-6447	195	6	the	the	DET
ejpam-6447	195	7	model	model	NOUN
ejpam-6447	195	8	and	and	CCONJ
ejpam-6447	195	9	verifying	verifying	NOUN
ejpam-6447	195	10	that	that	SCONJ
ejpam-6447	195	11	it	it	PRON
ejpam-6447	195	12	admits	admit	VERB
ejpam-6447	195	13	a	a	DET
ejpam-6447	195	14	unique	unique	ADJ
ejpam-6447	195	15	solution	solution	NOUN
ejpam-6447	195	16	.	.	PUNCT
ejpam-6447	196	1	we	we	PRON
ejpam-6447	196	2	then	then	ADV
ejpam-6447	196	3	analyzed	analyze	VERB
ejpam-6447	196	4	the	the	DET
ejpam-6447	196	5	equilibrium	equilibrium	NOUN
ejpam-6447	196	6	points	point	NOUN
ejpam-6447	196	7	,	,	PUNCT
ejpam-6447	196	8	including	include	VERB
ejpam-6447	196	9	the	the	DET
ejpam-6447	196	10	smoking	smoking	NOUN
ejpam-6447	196	11	-	-	PUNCT
ejpam-6447	196	12	free	free	ADJ
ejpam-6447	196	13	and	and	CCONJ
ejpam-6447	196	14	endemic	endemic	ADJ
ejpam-6447	196	15	equilibria	equilibrium	NOUN
ejpam-6447	196	16	.	.	PUNCT
ejpam-6447	197	1	to	to	PART
ejpam-6447	197	2	establish	establish	VERB
ejpam-6447	197	3	the	the	DET
ejpam-6447	197	4	global	global	ADJ
ejpam-6447	197	5	asymptotic	asymptotic	ADJ
ejpam-6447	197	6	stability	stability	NOUN
ejpam-6447	197	7	of	of	ADP
ejpam-6447	197	8	these	these	DET
ejpam-6447	197	9	points	point	NOUN
ejpam-6447	197	10	,	,	PUNCT
ejpam-6447	197	11	we	we	PRON
ejpam-6447	197	12	constructed	construct	VERB
ejpam-6447	197	13	an	an	DET
ejpam-6447	197	14	appropriate	appropriate	ADJ
ejpam-6447	197	15	lyapunov	lyapunov	NOUN
ejpam-6447	197	16	function	function	NOUN
ejpam-6447	197	17	.	.	PUNCT
ejpam-6447	198	1	the	the	DET
ejpam-6447	198	2	analytical	analytical	ADJ
ejpam-6447	198	3	results	result	NOUN
ejpam-6447	198	4	were	be	AUX
ejpam-6447	198	5	supported	support	VERB
ejpam-6447	198	6	by	by	ADP
ejpam-6447	198	7	numerical	numerical	ADJ
ejpam-6447	198	8	simulations	simulation	NOUN
ejpam-6447	198	9	,	,	PUNCT
ejpam-6447	198	10	s.	s.	PROPN
ejpam-6447	198	11	bushnaq	bushnaq	PROPN
ejpam-6447	198	12	,	,	PUNCT
ejpam-6447	198	13	s.	s.	PROPN
ejpam-6447	198	14	bano	bano	PROPN
ejpam-6447	198	15	,	,	PUNCT
ejpam-6447	198	16	a.	a.	PROPN
ejpam-6447	198	17	zeb	zeb	PROPN
ejpam-6447	198	18	/	/	SYM
ejpam-6447	198	19	eur	eur	PROPN
ejpam-6447	198	20	.	.	PUNCT
ejpam-6447	199	1	j.	j.	PROPN
ejpam-6447	199	2	pure	pure	PROPN
ejpam-6447	199	3	appl	appl	PROPN
ejpam-6447	199	4	.	.	PROPN
ejpam-6447	199	5	math	math	PROPN
ejpam-6447	199	6	,	,	PUNCT
ejpam-6447	199	7	18	18	NUM
ejpam-6447	199	8	(	(	PUNCT
ejpam-6447	199	9	3	3	NUM
ejpam-6447	199	10	)	)	PUNCT
ejpam-6447	199	11	(	(	PUNCT
ejpam-6447	199	12	2025	2025	NUM
ejpam-6447	199	13	)	)	PUNCT
ejpam-6447	199	14	,	,	PUNCT
ejpam-6447	199	15	6447	6447	NUM
ejpam-6447	199	16	11	11	NUM
ejpam-6447	199	17	of	of	ADP
ejpam-6447	199	18	12	12	NUM
ejpam-6447	199	19	which	which	PRON
ejpam-6447	199	20	validated	validate	VERB
ejpam-6447	199	21	the	the	DET
ejpam-6447	199	22	model	model	NOUN
ejpam-6447	199	23	behavior	behavior	NOUN
ejpam-6447	199	24	for	for	ADP
ejpam-6447	199	25	different	different	ADJ
ejpam-6447	199	26	parameter	parameter	NOUN
ejpam-6447	199	27	values	value	NOUN
ejpam-6447	199	28	.	.	PUNCT
ejpam-6447	200	1	the	the	DET
ejpam-6447	200	2	impact	impact	NOUN
ejpam-6447	200	3	of	of	ADP
ejpam-6447	200	4	the	the	DET
ejpam-6447	200	5	incremental	incremental	ADJ
ejpam-6447	200	6	rate	rate	NOUN
ejpam-6447	200	7	was	be	AUX
ejpam-6447	200	8	examined	examine	VERB
ejpam-6447	200	9	through	through	ADP
ejpam-6447	200	10	graphical	graphical	ADJ
ejpam-6447	200	11	results	result	NOUN
ejpam-6447	200	12	,	,	PUNCT
ejpam-6447	200	13	highlighting	highlight	VERB
ejpam-6447	200	14	the	the	DET
ejpam-6447	200	15	sensitivity	sensitivity	NOUN
ejpam-6447	200	16	of	of	ADP
ejpam-6447	200	17	the	the	DET
ejpam-6447	200	18	model	model	NOUN
ejpam-6447	200	19	to	to	ADP
ejpam-6447	200	20	behavioral	behavioral	ADJ
ejpam-6447	200	21	transitions	transition	NOUN
ejpam-6447	200	22	across	across	ADP
ejpam-6447	200	23	age	age	NOUN
ejpam-6447	200	24	groups	group	NOUN
ejpam-6447	200	25	.	.	PUNCT
ejpam-6447	201	1	compared	compare	VERB
ejpam-6447	201	2	to	to	ADP
ejpam-6447	201	3	previous	previous	ADJ
ejpam-6447	201	4	models	model	NOUN
ejpam-6447	201	5	in	in	ADP
ejpam-6447	201	6	the	the	DET
ejpam-6447	201	7	literature	literature	NOUN
ejpam-6447	201	8	,	,	PUNCT
ejpam-6447	201	9	our	our	PRON
ejpam-6447	201	10	age	age	NOUN
ejpam-6447	201	11	-	-	PUNCT
ejpam-6447	201	12	structured	structure	VERB
ejpam-6447	201	13	formulation	formulation	NOUN
ejpam-6447	201	14	adds	add	VERB
ejpam-6447	201	15	a	a	DET
ejpam-6447	201	16	significant	significant	ADJ
ejpam-6447	201	17	layer	layer	NOUN
ejpam-6447	201	18	of	of	ADP
ejpam-6447	201	19	realism	realism	NOUN
ejpam-6447	201	20	,	,	PUNCT
ejpam-6447	201	21	especially	especially	ADV
ejpam-6447	201	22	in	in	ADP
ejpam-6447	201	23	modeling	model	VERB
ejpam-6447	201	24	differential	differential	ADJ
ejpam-6447	201	25	susceptibility	susceptibility	NOUN
ejpam-6447	201	26	and	and	CCONJ
ejpam-6447	201	27	recovery	recovery	NOUN
ejpam-6447	201	28	rates	rate	NOUN
ejpam-6447	201	29	among	among	ADP
ejpam-6447	201	30	distinct	distinct	ADJ
ejpam-6447	201	31	age	age	NOUN
ejpam-6447	201	32	cohorts	cohort	NOUN
ejpam-6447	201	33	.	.	PUNCT
ejpam-6447	202	1	this	this	PRON
ejpam-6447	202	2	provides	provide	VERB
ejpam-6447	202	3	a	a	DET
ejpam-6447	202	4	refined	refined	ADJ
ejpam-6447	202	5	framework	framework	NOUN
ejpam-6447	202	6	for	for	ADP
ejpam-6447	202	7	analyzing	analyze	VERB
ejpam-6447	202	8	the	the	DET
ejpam-6447	202	9	spread	spread	NOUN
ejpam-6447	202	10	and	and	CCONJ
ejpam-6447	202	11	persistence	persistence	NOUN
ejpam-6447	202	12	of	of	ADP
ejpam-6447	202	13	smoking	smoking	NOUN
ejpam-6447	202	14	behaviors	behavior	NOUN
ejpam-6447	202	15	in	in	ADP
ejpam-6447	202	16	populations	population	NOUN
ejpam-6447	202	17	.	.	PUNCT
ejpam-6447	203	1	in	in	ADP
ejpam-6447	203	2	line	line	NOUN
ejpam-6447	203	3	with	with	ADP
ejpam-6447	203	4	the	the	DET
ejpam-6447	203	5	reviewer	reviewer	NOUN
ejpam-6447	203	6	’s	’s	PART
ejpam-6447	203	7	recommendation	recommendation	NOUN
ejpam-6447	203	8	,	,	PUNCT
ejpam-6447	203	9	this	this	DET
ejpam-6447	203	10	work	work	NOUN
ejpam-6447	203	11	opens	open	VERB
ejpam-6447	203	12	several	several	ADJ
ejpam-6447	203	13	promising	promising	ADJ
ejpam-6447	203	14	avenues	avenue	NOUN
ejpam-6447	203	15	for	for	ADP
ejpam-6447	203	16	future	future	ADJ
ejpam-6447	203	17	research	research	NOUN
ejpam-6447	203	18	.	.	PUNCT
ejpam-6447	204	1	one	one	NUM
ejpam-6447	204	2	natural	natural	ADJ
ejpam-6447	204	3	extension	extension	NOUN
ejpam-6447	204	4	is	be	AUX
ejpam-6447	204	5	to	to	PART
ejpam-6447	204	6	incorporate	incorporate	VERB
ejpam-6447	204	7	*	*	NOUN
ejpam-6447	204	8	*	*	NOUN
ejpam-6447	204	9	relapse	relapse	NOUN
ejpam-6447	204	10	dynamics	dynamic	NOUN
ejpam-6447	204	11	*	*	PUNCT
ejpam-6447	204	12	*	*	PUNCT
ejpam-6447	204	13	,	,	PUNCT
ejpam-6447	204	14	allowing	allow	VERB
ejpam-6447	204	15	former	former	ADJ
ejpam-6447	204	16	smokers	smoker	NOUN
ejpam-6447	204	17	to	to	PART
ejpam-6447	204	18	return	return	VERB
ejpam-6447	204	19	to	to	ADP
ejpam-6447	204	20	smoking	smoke	VERB
ejpam-6447	204	21	under	under	ADP
ejpam-6447	204	22	certain	certain	ADJ
ejpam-6447	204	23	behavioral	behavioral	ADJ
ejpam-6447	204	24	or	or	CCONJ
ejpam-6447	204	25	social	social	ADJ
ejpam-6447	204	26	conditions	condition	NOUN
ejpam-6447	204	27	.	.	PUNCT
ejpam-6447	205	1	moreover	moreover	ADV
ejpam-6447	205	2	,	,	PUNCT
ejpam-6447	205	3	integrating	integrate	VERB
ejpam-6447	205	4	*	*	PUNCT
ejpam-6447	205	5	*	*	NOUN
ejpam-6447	205	6	intervention	intervention	NOUN
ejpam-6447	205	7	strategies	strategy	NOUN
ejpam-6447	205	8	*	*	PUNCT
ejpam-6447	205	9	*	*	NOUN
ejpam-6447	205	10	,	,	PUNCT
ejpam-6447	205	11	such	such	ADJ
ejpam-6447	205	12	as	as	ADP
ejpam-6447	205	13	public	public	ADJ
ejpam-6447	205	14	health	health	NOUN
ejpam-6447	205	15	campaigns	campaign	NOUN
ejpam-6447	205	16	or	or	CCONJ
ejpam-6447	205	17	medical	medical	ADJ
ejpam-6447	205	18	treatments	treatment	NOUN
ejpam-6447	205	19	,	,	PUNCT
ejpam-6447	205	20	could	could	AUX
ejpam-6447	205	21	enhance	enhance	VERB
ejpam-6447	205	22	the	the	DET
ejpam-6447	205	23	practical	practical	ADJ
ejpam-6447	205	24	relevance	relevance	NOUN
ejpam-6447	205	25	of	of	ADP
ejpam-6447	205	26	the	the	DET
ejpam-6447	205	27	model	model	NOUN
ejpam-6447	205	28	.	.	PUNCT
ejpam-6447	206	1	additionally	additionally	ADV
ejpam-6447	206	2	,	,	PUNCT
ejpam-6447	206	3	the	the	DET
ejpam-6447	206	4	inclusion	inclusion	NOUN
ejpam-6447	206	5	of	of	ADP
ejpam-6447	206	6	*	*	NOUN
ejpam-6447	206	7	*	*	NOUN
ejpam-6447	206	8	stochastic	stochastic	ADJ
ejpam-6447	206	9	effects	effect	NOUN
ejpam-6447	206	10	*	*	PUNCT
ejpam-6447	206	11	*	*	PUNCT
ejpam-6447	206	12	would	would	AUX
ejpam-6447	206	13	enable	enable	VERB
ejpam-6447	206	14	the	the	DET
ejpam-6447	206	15	modeling	modeling	NOUN
ejpam-6447	206	16	of	of	ADP
ejpam-6447	206	17	randomness	randomness	NOUN
ejpam-6447	206	18	and	and	CCONJ
ejpam-6447	206	19	uncertainty	uncertainty	NOUN
ejpam-6447	206	20	in	in	ADP
ejpam-6447	206	21	smoking	smoking	NOUN
ejpam-6447	206	22	behaviors	behavior	NOUN
ejpam-6447	206	23	and	and	CCONJ
ejpam-6447	206	24	policy	policy	NOUN
ejpam-6447	206	25	outcomes	outcome	NOUN
ejpam-6447	206	26	,	,	PUNCT
ejpam-6447	206	27	which	which	PRON
ejpam-6447	206	28	is	be	AUX
ejpam-6447	206	29	particularly	particularly	ADV
ejpam-6447	206	30	important	important	ADJ
ejpam-6447	206	31	for	for	ADP
ejpam-6447	206	32	small	small	ADJ
ejpam-6447	206	33	populations	population	NOUN
ejpam-6447	206	34	or	or	CCONJ
ejpam-6447	206	35	individual	individual	ADJ
ejpam-6447	206	36	-	-	PUNCT
ejpam-6447	206	37	level	level	NOUN
ejpam-6447	206	38	modeling	modeling	NOUN
ejpam-6447	206	39	.	.	PUNCT
ejpam-6447	207	1	these	these	DET
ejpam-6447	207	2	enhancements	enhancement	NOUN
ejpam-6447	207	3	can	can	AUX
ejpam-6447	207	4	lead	lead	VERB
ejpam-6447	207	5	to	to	ADP
ejpam-6447	207	6	more	more	ADV
ejpam-6447	207	7	comprehensive	comprehensive	ADJ
ejpam-6447	207	8	insights	insight	NOUN
ejpam-6447	207	9	and	and	CCONJ
ejpam-6447	207	10	provide	provide	VERB
ejpam-6447	207	11	policymakers	policymaker	NOUN
ejpam-6447	207	12	with	with	ADP
ejpam-6447	207	13	robust	robust	ADJ
ejpam-6447	207	14	tools	tool	NOUN
ejpam-6447	207	15	to	to	PART
ejpam-6447	207	16	design	design	VERB
ejpam-6447	207	17	targeted	target	VERB
ejpam-6447	207	18	anti	anti	ADJ
ejpam-6447	207	19	-	-	ADJ
ejpam-6447	207	20	smoking	smoking	ADJ
ejpam-6447	207	21	strategies	strategy	NOUN
ejpam-6447	207	22	.	.	PUNCT
ejpam-6447	208	1	references	reference	NOUN
ejpam-6447	208	2	[	[	X
ejpam-6447	208	3	1	1	NUM
ejpam-6447	208	4	]	]	PUNCT
ejpam-6447	208	5	r.	r.	PROPN
ejpam-6447	208	6	m.	m.	PROPN
ejpam-6447	208	7	anderson	anderson	PROPN
ejpam-6447	208	8	and	and	CCONJ
ejpam-6447	208	9	r.	r.	PROPN
ejpam-6447	208	10	m.	m.	PROPN
ejpam-6447	208	11	may	may	AUX
ejpam-6447	208	12	.	.	PUNCT
ejpam-6447	209	1	infectious	infectious	ADJ
ejpam-6447	209	2	diseases	disease	NOUN
ejpam-6447	209	3	of	of	ADP
ejpam-6447	209	4	humans	human	NOUN
ejpam-6447	209	5	:	:	PUNCT
ejpam-6447	209	6	dynamics	dynamic	NOUN
ejpam-6447	209	7	and	and	CCONJ
ejpam-6447	209	8	control	control	NOUN
ejpam-6447	209	9	.	.	PUNCT
ejpam-6447	210	1	oxford	oxford	PROPN
ejpam-6447	210	2	university	university	PROPN
ejpam-6447	210	3	press	press	NOUN
ejpam-6447	210	4	,	,	PUNCT
ejpam-6447	210	5	1991	1991	NUM
ejpam-6447	210	6	.	.	PUNCT
ejpam-6447	211	1	[	[	X
ejpam-6447	211	2	2	2	X
ejpam-6447	211	3	]	]	PUNCT
ejpam-6447	211	4	h.	h.	PROPN
ejpam-6447	211	5	w.	w.	PROPN
ejpam-6447	211	6	hethcote	hethcote	PROPN
ejpam-6447	211	7	.	.	PUNCT
ejpam-6447	212	1	the	the	DET
ejpam-6447	212	2	mathematics	mathematic	NOUN
ejpam-6447	212	3	of	of	ADP
ejpam-6447	212	4	infectious	infectious	ADJ
ejpam-6447	212	5	diseases	disease	NOUN
ejpam-6447	212	6	.	.	PUNCT
ejpam-6447	213	1	siam	siam	PROPN
ejpam-6447	213	2	review	review	PROPN
ejpam-6447	213	3	,	,	PUNCT
ejpam-6447	213	4	42(4):599–653	42(4):599–653	PROPN
ejpam-6447	213	5	,	,	PUNCT
ejpam-6447	213	6	2000	2000	NUM
ejpam-6447	213	7	.	.	PUNCT
ejpam-6447	214	1	[	[	X
ejpam-6447	214	2	3	3	NUM
ejpam-6447	214	3	]	]	X
ejpam-6447	214	4	f.	f.	PROPN
ejpam-6447	214	5	brauer	brauer	PROPN
ejpam-6447	214	6	,	,	PUNCT
ejpam-6447	214	7	c.	c.	PROPN
ejpam-6447	214	8	castillo	castillo	PROPN
ejpam-6447	214	9	-	-	PUNCT
ejpam-6447	214	10	chavez	chavez	PROPN
ejpam-6447	214	11	,	,	PUNCT
ejpam-6447	214	12	and	and	CCONJ
ejpam-6447	214	13	z.	z.	PROPN
ejpam-6447	214	14	feng	feng	PROPN
ejpam-6447	214	15	.	.	PUNCT
ejpam-6447	215	1	mathematical	mathematical	ADJ
ejpam-6447	215	2	models	model	NOUN
ejpam-6447	215	3	in	in	ADP
ejpam-6447	215	4	epidemiology	epidemiology	NOUN
ejpam-6447	215	5	.	.	PUNCT
ejpam-6447	216	1	springer	springer	NOUN
ejpam-6447	216	2	,	,	PUNCT
ejpam-6447	216	3	2019	2019	NUM
ejpam-6447	216	4	.	.	PUNCT
ejpam-6447	217	1	[	[	X
ejpam-6447	217	2	4	4	X
ejpam-6447	217	3	]	]	X
ejpam-6447	217	4	o.	o.	NOUN
ejpam-6447	217	5	diekmann	diekmann	PROPN
ejpam-6447	217	6	,	,	PUNCT
ejpam-6447	217	7	j.	j.	PROPN
ejpam-6447	217	8	a.	a.	PROPN
ejpam-6447	217	9	p.	p.	PROPN
ejpam-6447	217	10	heesterbeek	heesterbeek	PROPN
ejpam-6447	217	11	,	,	PUNCT
ejpam-6447	217	12	and	and	CCONJ
ejpam-6447	217	13	t.	t.	PROPN
ejpam-6447	217	14	britton	britton	PROPN
ejpam-6447	217	15	.	.	PUNCT
ejpam-6447	218	1	mathematical	mathematical	ADJ
ejpam-6447	218	2	tools	tool	NOUN
ejpam-6447	218	3	for	for	ADP
ejpam-6447	218	4	understanding	understand	VERB
ejpam-6447	218	5	infectious	infectious	ADJ
ejpam-6447	218	6	disease	disease	NOUN
ejpam-6447	218	7	dynamics	dynamic	NOUN
ejpam-6447	218	8	.	.	PUNCT
ejpam-6447	219	1	princeton	princeton	PROPN
ejpam-6447	219	2	university	university	PROPN
ejpam-6447	219	3	press	press	NOUN
ejpam-6447	219	4	,	,	PUNCT
ejpam-6447	219	5	2013	2013	NUM
ejpam-6447	219	6	.	.	PUNCT
ejpam-6447	220	1	[	[	X
ejpam-6447	220	2	5	5	X
ejpam-6447	220	3	]	]	PUNCT
ejpam-6447	220	4	l.	l.	PROPN
ejpam-6447	220	5	g.	g.	PROPN
ejpam-6447	220	6	de	de	PROPN
ejpam-6447	220	7	pillis	pillis	PROPN
ejpam-6447	220	8	and	and	CCONJ
ejpam-6447	220	9	a.	a.	PROPN
ejpam-6447	220	10	e.	e.	PROPN
ejpam-6447	220	11	radunskaya	radunskaya	PROPN
ejpam-6447	220	12	.	.	PUNCT
ejpam-6447	221	1	a	a	DET
ejpam-6447	221	2	mathematical	mathematical	ADJ
ejpam-6447	221	3	tumor	tumor	NOUN
ejpam-6447	221	4	model	model	NOUN
ejpam-6447	221	5	with	with	ADP
ejpam-6447	221	6	immune	immune	ADJ
ejpam-6447	221	7	resistance	resistance	NOUN
ejpam-6447	221	8	and	and	CCONJ
ejpam-6447	221	9	drug	drug	NOUN
ejpam-6447	221	10	therapy	therapy	NOUN
ejpam-6447	221	11	:	:	PUNCT
ejpam-6447	221	12	an	an	DET
ejpam-6447	221	13	optimal	optimal	ADJ
ejpam-6447	221	14	control	control	NOUN
ejpam-6447	221	15	approach	approach	NOUN
ejpam-6447	221	16	.	.	PUNCT
ejpam-6447	222	1	journal	journal	NOUN
ejpam-6447	222	2	of	of	ADP
ejpam-6447	222	3	theoretical	theoretical	ADJ
ejpam-6447	222	4	biology	biology	NOUN
ejpam-6447	222	5	,	,	PUNCT
ejpam-6447	222	6	238(4):841	238(4):841	NUM
ejpam-6447	222	7	–	–	PUNCT
ejpam-6447	222	8	862	862	NUM
ejpam-6447	222	9	,	,	PUNCT
ejpam-6447	222	10	2006	2006	NUM
ejpam-6447	222	11	.	.	PUNCT
ejpam-6447	223	1	[	[	X
ejpam-6447	223	2	6	6	NUM
ejpam-6447	223	3	]	]	PUNCT
ejpam-6447	223	4	m.	m.	NOUN
ejpam-6447	223	5	gümüs	gümüs	PROPN
ejpam-6447	223	6	and	and	CCONJ
ejpam-6447	223	7	ö.	ö.	PROPN
ejpam-6447	223	8	öcalan	öcalan	PROPN
ejpam-6447	223	9	.	.	PUNCT
ejpam-6447	224	1	global	global	ADJ
ejpam-6447	224	2	asymptotic	asymptotic	ADJ
ejpam-6447	224	3	stability	stability	NOUN
ejpam-6447	224	4	of	of	ADP
ejpam-6447	224	5	a	a	DET
ejpam-6447	224	6	nonautonomous	nonautonomous	ADJ
ejpam-6447	224	7	difference	difference	NOUN
ejpam-6447	224	8	equation	equation	NOUN
ejpam-6447	224	9	.	.	PUNCT
ejpam-6447	225	1	journal	journal	PROPN
ejpam-6447	225	2	of	of	ADP
ejpam-6447	225	3	applied	apply	VERB
ejpam-6447	225	4	mathematics	mathematic	NOUN
ejpam-6447	225	5	,	,	PUNCT
ejpam-6447	225	6	2014	2014	NUM
ejpam-6447	225	7	:	:	PUNCT
ejpam-6447	225	8	article	article	NOUN
ejpam-6447	225	9	i	i	PROPN
ejpam-6447	225	10	d	d	PROPN
ejpam-6447	225	11	395954	395954	NUM
ejpam-6447	225	12	,	,	PUNCT
ejpam-6447	225	13	5	5	NUM
ejpam-6447	225	14	pages	page	NOUN
ejpam-6447	225	15	,	,	PUNCT
ejpam-6447	225	16	2014	2014	NUM
ejpam-6447	225	17	.	.	PUNCT
ejpam-6447	226	1	[	[	X
ejpam-6447	226	2	7	7	X
ejpam-6447	226	3	]	]	PUNCT
ejpam-6447	226	4	m.	m.	NOUN
ejpam-6447	226	5	y.	y.	PROPN
ejpam-6447	226	6	li	li	PROPN
ejpam-6447	226	7	and	and	CCONJ
ejpam-6447	226	8	j.	j.	PROPN
ejpam-6447	226	9	s.	s.	PROPN
ejpam-6447	226	10	muldowney	muldowney	PROPN
ejpam-6447	226	11	.	.	PUNCT
ejpam-6447	227	1	global	global	ADJ
ejpam-6447	227	2	stability	stability	NOUN
ejpam-6447	227	3	for	for	ADP
ejpam-6447	227	4	the	the	DET
ejpam-6447	227	5	seir	seir	ADJ
ejpam-6447	227	6	model	model	NOUN
ejpam-6447	227	7	in	in	ADP
ejpam-6447	227	8	epidemiology	epidemiology	NOUN
ejpam-6447	227	9	.	.	PUNCT
ejpam-6447	228	1	mathematical	mathematical	ADJ
ejpam-6447	228	2	biosciences	bioscience	NOUN
ejpam-6447	228	3	,	,	PUNCT
ejpam-6447	228	4	125(2):155–164	125(2):155–164	NUM
ejpam-6447	228	5	,	,	PUNCT
ejpam-6447	228	6	1995	1995	NUM
ejpam-6447	228	7	.	.	PUNCT
ejpam-6447	229	1	[	[	X
ejpam-6447	229	2	8	8	X
ejpam-6447	229	3	]	]	PUNCT
ejpam-6447	229	4	j.	j.	PROPN
ejpam-6447	229	5	wang	wang	PROPN
ejpam-6447	229	6	,	,	PUNCT
ejpam-6447	229	7	m.	m.	PROPN
ejpam-6447	229	8	zhang	zhang	PROPN
ejpam-6447	229	9	,	,	PUNCT
ejpam-6447	229	10	and	and	CCONJ
ejpam-6447	229	11	w.	w.	PROPN
ejpam-6447	229	12	yang	yang	PROPN
ejpam-6447	229	13	.	.	PUNCT
ejpam-6447	229	14	dynamics	dynamic	NOUN
ejpam-6447	229	15	and	and	CCONJ
ejpam-6447	229	16	asymptotic	asymptotic	ADJ
ejpam-6447	229	17	profiles	profile	NOUN
ejpam-6447	229	18	of	of	ADP
ejpam-6447	229	19	a	a	DET
ejpam-6447	229	20	local	local	ADJ
ejpam-6447	229	21	-	-	PUNCT
ejpam-6447	229	22	nonlocal	nonlocal	ADJ
ejpam-6447	229	23	dispersal	dispersal	NOUN
ejpam-6447	229	24	sir	sir	NOUN
ejpam-6447	229	25	epidemic	epidemic	NOUN
ejpam-6447	229	26	model	model	NOUN
ejpam-6447	229	27	with	with	ADP
ejpam-6447	229	28	spatial	spatial	ADJ
ejpam-6447	229	29	heterogeneity	heterogeneity	NOUN
ejpam-6447	229	30	.	.	PUNCT
ejpam-6447	230	1	journal	journal	PROPN
ejpam-6447	230	2	of	of	ADP
ejpam-6447	230	3	differential	differential	ADJ
ejpam-6447	230	4	equations	equation	NOUN
ejpam-6447	230	5	,	,	PUNCT
ejpam-6447	230	6	313:1–34	313:1–34	NUM
ejpam-6447	230	7	,	,	PUNCT
ejpam-6447	230	8	2022	2022	NUM
ejpam-6447	230	9	.	.	PUNCT
ejpam-6447	231	1	[	[	X
ejpam-6447	231	2	9	9	NUM
ejpam-6447	231	3	]	]	PUNCT
ejpam-6447	231	4	c.	c.	PROPN
ejpam-6447	231	5	liu	liu	PROPN
ejpam-6447	231	6	and	and	CCONJ
ejpam-6447	231	7	j.	j.	PROPN
ejpam-6447	231	8	shi	shi	PROPN
ejpam-6447	231	9	.	.	PUNCT
ejpam-6447	232	1	traveling	travel	VERB
ejpam-6447	232	2	wave	wave	NOUN
ejpam-6447	232	3	solution	solution	NOUN
ejpam-6447	232	4	for	for	ADP
ejpam-6447	232	5	a	a	DET
ejpam-6447	232	6	delayed	delay	VERB
ejpam-6447	232	7	reaction	reaction	NOUN
ejpam-6447	232	8	-	-	PUNCT
ejpam-6447	232	9	diffusion	diffusion	NOUN
ejpam-6447	232	10	two	two	NUM
ejpam-6447	232	11	-	-	PUNCT
ejpam-6447	232	12	group	group	NOUN
ejpam-6447	232	13	sir	sir	NOUN
ejpam-6447	232	14	epidemic	epidemic	NOUN
ejpam-6447	232	15	model	model	NOUN
ejpam-6447	232	16	with	with	ADP
ejpam-6447	232	17	a	a	DET
ejpam-6447	232	18	generalized	generalized	ADJ
ejpam-6447	232	19	nonlinear	nonlinear	ADJ
ejpam-6447	232	20	incidence	incidence	NOUN
ejpam-6447	232	21	function	function	NOUN
ejpam-6447	232	22	.	.	PUNCT
ejpam-6447	233	1	nonlinear	nonlinear	ADJ
ejpam-6447	233	2	analysis	analysis	NOUN
ejpam-6447	233	3	:	:	PUNCT
ejpam-6447	233	4	real	real	ADJ
ejpam-6447	233	5	world	world	NOUN
ejpam-6447	233	6	applications	application	NOUN
ejpam-6447	233	7	,	,	PUNCT
ejpam-6447	233	8	65:103434	65:103434	NUM
ejpam-6447	233	9	,	,	PUNCT
ejpam-6447	233	10	2022	2022	NUM
ejpam-6447	233	11	.	.	PUNCT
ejpam-6447	234	1	[	[	X
ejpam-6447	234	2	10	10	NUM
ejpam-6447	234	3	]	]	X
ejpam-6447	234	4	e.	e.	PROPN
ejpam-6447	234	5	alzahrani	alzahrani	PROPN
ejpam-6447	234	6	and	and	CCONJ
ejpam-6447	234	7	a.	a.	PROPN
ejpam-6447	234	8	zeb	zeb	PROPN
ejpam-6447	234	9	.	.	PUNCT
ejpam-6447	235	1	stability	stability	NOUN
ejpam-6447	235	2	analysis	analysis	NOUN
ejpam-6447	235	3	and	and	CCONJ
ejpam-6447	235	4	prevention	prevention	NOUN
ejpam-6447	235	5	strategies	strategy	NOUN
ejpam-6447	235	6	of	of	ADP
ejpam-6447	235	7	tobacco	tobacco	NOUN
ejpam-6447	235	8	smoking	smoking	NOUN
ejpam-6447	235	9	model	model	NOUN
ejpam-6447	235	10	.	.	PUNCT
ejpam-6447	236	1	boundary	boundary	ADJ
ejpam-6447	236	2	value	value	NOUN
ejpam-6447	236	3	problems	problem	NOUN
ejpam-6447	236	4	,	,	PUNCT
ejpam-6447	236	5	2020:1–13	2020:1–13	NUM
ejpam-6447	236	6	,	,	PUNCT
ejpam-6447	236	7	2020	2020	NUM
ejpam-6447	236	8	.	.	PUNCT
ejpam-6447	237	1	[	[	X
ejpam-6447	237	2	11	11	NUM
ejpam-6447	237	3	]	]	PUNCT
ejpam-6447	237	4	a.	a.	NOUN
ejpam-6447	237	5	zeb	zeb	PROPN
ejpam-6447	237	6	,	,	PUNCT
ejpam-6447	237	7	s.	s.	PROPN
ejpam-6447	237	8	kumar	kumar	PROPN
ejpam-6447	237	9	,	,	PUNCT
ejpam-6447	237	10	a.	a.	NOUN
ejpam-6447	237	11	tesfay	tesfay	PROPN
ejpam-6447	237	12	,	,	PUNCT
ejpam-6447	237	13	and	and	CCONJ
ejpam-6447	237	14	a.	a.	PROPN
ejpam-6447	237	15	kumar	kumar	PROPN
ejpam-6447	237	16	.	.	PUNCT
ejpam-6447	238	1	a	a	DET
ejpam-6447	238	2	stability	stability	NOUN
ejpam-6447	238	3	analysis	analysis	NOUN
ejpam-6447	238	4	on	on	ADP
ejpam-6447	238	5	a	a	DET
ejpam-6447	238	6	smoking	smoking	NOUN
ejpam-6447	238	7	model	model	NOUN
ejpam-6447	238	8	with	with	ADP
ejpam-6447	238	9	stochastic	stochastic	ADJ
ejpam-6447	238	10	perturbation	perturbation	NOUN
ejpam-6447	238	11	.	.	PUNCT
ejpam-6447	239	1	international	international	ADJ
ejpam-6447	239	2	journal	journal	PROPN
ejpam-6447	239	3	of	of	ADP
ejpam-6447	239	4	numerical	numerical	ADJ
ejpam-6447	239	5	methods	method	NOUN
ejpam-6447	239	6	for	for	ADP
ejpam-6447	239	7	heat	heat	NOUN
ejpam-6447	239	8	and	and	CCONJ
ejpam-6447	239	9	fluid	fluid	ADJ
ejpam-6447	239	10	flow	flow	NOUN
ejpam-6447	239	11	,	,	PUNCT
ejpam-6447	239	12	32(3):915–930	32(3):915–930	NUM
ejpam-6447	239	13	,	,	PUNCT
ejpam-6447	239	14	2022	2022	NUM
ejpam-6447	239	15	.	.	PUNCT
ejpam-6447	240	1	[	[	X
ejpam-6447	240	2	12	12	NUM
ejpam-6447	240	3	]	]	X
ejpam-6447	240	4	s.	s.	PROPN
ejpam-6447	240	5	m.	m.	PROPN
ejpam-6447	240	6	lestari	lestari	PROPN
ejpam-6447	240	7	,	,	PUNCT
ejpam-6447	240	8	y.	y.	PROPN
ejpam-6447	240	9	yulida	yulida	PROPN
ejpam-6447	240	10	,	,	PUNCT
ejpam-6447	240	11	a.	a.	PROPN
ejpam-6447	240	12	s.	s.	PROPN
ejpam-6447	240	13	lestia	lestia	PROPN
ejpam-6447	240	14	,	,	PUNCT
ejpam-6447	240	15	and	and	CCONJ
ejpam-6447	240	16	m.	m.	NOUN
ejpam-6447	240	17	a.	a.	PROPN
ejpam-6447	240	18	karim	karim	PROPN
ejpam-6447	240	19	.	.	PUNCT
ejpam-6447	241	1	stability	stability	NOUN
ejpam-6447	241	2	analysis	analysis	NOUN
ejpam-6447	241	3	of	of	ADP
ejpam-6447	241	4	a	a	DET
ejpam-6447	241	5	smoking	smoking	NOUN
ejpam-6447	241	6	behavior	behavior	NOUN
ejpam-6447	241	7	model	model	NOUN
ejpam-6447	241	8	.	.	PUNCT
ejpam-6447	242	1	journal	journal	PROPN
ejpam-6447	242	2	of	of	ADP
ejpam-6447	242	3	physics	physics	PROPN
ejpam-6447	242	4	:	:	PUNCT
ejpam-6447	242	5	conference	conference	NOUN
ejpam-6447	242	6	series	series	NOUN
ejpam-6447	242	7	,	,	PUNCT
ejpam-6447	242	8	2106(1):012025	2106(1):012025	NUM
ejpam-6447	242	9	,	,	PUNCT
ejpam-6447	242	10	2021	2021	NUM
ejpam-6447	242	11	.	.	PUNCT
ejpam-6447	243	1	[	[	X
ejpam-6447	243	2	13	13	NUM
ejpam-6447	243	3	]	]	PUNCT
ejpam-6447	243	4	a.	a.	NOUN
ejpam-6447	243	5	m.	m.	PROPN
ejpam-6447	243	6	pulecio	pulecio	PROPN
ejpam-6447	243	7	-	-	PUNCT
ejpam-6447	243	8	montoya	montoya	PROPN
ejpam-6447	243	9	,	,	PUNCT
ejpam-6447	243	10	l.	l.	PROPN
ejpam-6447	243	11	e.	e.	PROPN
ejpam-6447	243	12	lópez	lópez	PROPN
ejpam-6447	243	13	-	-	PUNCT
ejpam-6447	243	14	montenegro	montenegro	PROPN
ejpam-6447	243	15	,	,	PUNCT
ejpam-6447	243	16	and	and	CCONJ
ejpam-6447	243	17	l.	l.	PROPN
ejpam-6447	243	18	m.	m.	PROPN
ejpam-6447	243	19	benavides	benavides	PROPN
ejpam-6447	243	20	.	.	PUNCT
ejpam-6447	244	1	analysis	analysis	NOUN
ejpam-6447	244	2	of	of	ADP
ejpam-6447	244	3	a	a	DET
ejpam-6447	244	4	mathematical	mathematical	ADJ
ejpam-6447	244	5	model	model	NOUN
ejpam-6447	244	6	of	of	ADP
ejpam-6447	244	7	smoking	smoking	NOUN
ejpam-6447	244	8	.	.	PUNCT
ejpam-6447	245	1	contemporary	contemporary	ADJ
ejpam-6447	245	2	engineering	engineering	PROPN
ejpam-6447	245	3	sciences	sciences	PROPN
ejpam-6447	245	4	,	,	PUNCT
ejpam-6447	245	5	12(3):117–129	12(3):117–129	NUM
ejpam-6447	245	6	,	,	PUNCT
ejpam-6447	245	7	2019	2019	NUM
ejpam-6447	245	8	.	.	PUNCT
ejpam-6447	246	1	[	[	X
ejpam-6447	246	2	14	14	NUM
ejpam-6447	246	3	]	]	PUNCT
ejpam-6447	246	4	z.	z.	PROPN
ejpam-6447	246	5	alkhudari	alkhudari	PROPN
ejpam-6447	246	6	,	,	PUNCT
ejpam-6447	246	7	s.	s.	PROPN
ejpam-6447	246	8	al	al	PROPN
ejpam-6447	246	9	-	-	PUNCT
ejpam-6447	246	10	sheikh	sheikh	PROPN
ejpam-6447	246	11	,	,	PUNCT
ejpam-6447	246	12	and	and	CCONJ
ejpam-6447	246	13	s.	s.	PROPN
ejpam-6447	246	14	al	al	PROPN
ejpam-6447	246	15	-	-	PUNCT
ejpam-6447	246	16	tuwairqi	tuwairqi	PROPN
ejpam-6447	246	17	.	.	PUNCT
ejpam-6447	247	1	the	the	DET
ejpam-6447	247	2	effect	effect	NOUN
ejpam-6447	247	3	of	of	ADP
ejpam-6447	247	4	occasional	occasional	ADJ
ejpam-6447	247	5	smokers	smoker	NOUN
ejpam-6447	247	6	on	on	ADP
ejpam-6447	247	7	the	the	DET
ejpam-6447	247	8	dynamics	dynamic	NOUN
ejpam-6447	247	9	of	of	ADP
ejpam-6447	247	10	a	a	DET
ejpam-6447	247	11	smoking	smoking	NOUN
ejpam-6447	247	12	model	model	NOUN
ejpam-6447	247	13	.	.	PUNCT
ejpam-6447	248	1	international	international	ADJ
ejpam-6447	248	2	mathematical	mathematical	PROPN
ejpam-6447	248	3	forum	forum	PROPN
ejpam-6447	248	4	,	,	PUNCT
ejpam-6447	248	5	9(25):1207–1222	9(25):1207–1222	NOUN
ejpam-6447	248	6	,	,	PUNCT
ejpam-6447	248	7	2014	2014	NUM
ejpam-6447	248	8	.	.	PUNCT
ejpam-6447	249	1	s.	s.	PROPN
ejpam-6447	249	2	bushnaq	bushnaq	PROPN
ejpam-6447	249	3	,	,	PUNCT
ejpam-6447	249	4	s.	s.	PROPN
ejpam-6447	249	5	bano	bano	PROPN
ejpam-6447	249	6	,	,	PUNCT
ejpam-6447	249	7	a.	a.	PROPN
ejpam-6447	249	8	zeb	zeb	PROPN
ejpam-6447	249	9	/	/	SYM
ejpam-6447	249	10	eur	eur	PROPN
ejpam-6447	249	11	.	.	PUNCT
ejpam-6447	250	1	j.	j.	PROPN
ejpam-6447	250	2	pure	pure	PROPN
ejpam-6447	250	3	appl	appl	PROPN
ejpam-6447	250	4	.	.	PROPN
ejpam-6447	250	5	math	math	PROPN
ejpam-6447	250	6	,	,	PUNCT
ejpam-6447	250	7	18	18	NUM
ejpam-6447	250	8	(	(	PUNCT
ejpam-6447	250	9	3	3	NUM
ejpam-6447	250	10	)	)	PUNCT
ejpam-6447	250	11	(	(	PUNCT
ejpam-6447	250	12	2025	2025	NUM
ejpam-6447	250	13	)	)	PUNCT
ejpam-6447	250	14	,	,	PUNCT
ejpam-6447	250	15	6447	6447	NUM
ejpam-6447	250	16	12	12	NUM
ejpam-6447	250	17	of	of	ADP
ejpam-6447	250	18	12	12	NUM
ejpam-6447	251	1	[	[	SYM
ejpam-6447	251	2	15	15	NUM
ejpam-6447	251	3	]	]	X
ejpam-6447	251	4	g.	g.	PROPN
ejpam-6447	251	5	zaman	zaman	PROPN
ejpam-6447	251	6	and	and	CCONJ
ejpam-6447	251	7	s.	s.	PROPN
ejpam-6447	251	8	gul	gul	PROPN
ejpam-6447	251	9	.	.	PUNCT
ejpam-6447	252	1	qualitative	qualitative	ADJ
ejpam-6447	252	2	behavior	behavior	NOUN
ejpam-6447	252	3	of	of	ADP
ejpam-6447	252	4	giving	give	VERB
ejpam-6447	252	5	up	up	ADP
ejpam-6447	252	6	smoking	smoking	NOUN
ejpam-6447	252	7	models	model	NOUN
ejpam-6447	252	8	.	.	PUNCT
ejpam-6447	253	1	bulletin	bulletin	NOUN
ejpam-6447	253	2	of	of	ADP
ejpam-6447	253	3	the	the	DET
ejpam-6447	253	4	malaysian	malaysian	PROPN
ejpam-6447	253	5	mathematical	mathematical	PROPN
ejpam-6447	253	6	sciences	sciences	PROPN
ejpam-6447	253	7	society	society	NOUN
ejpam-6447	253	8	.	.	PUNCT
ejpam-6447	254	1	second	second	ADJ
ejpam-6447	254	2	series	series	NOUN
ejpam-6447	254	3	,	,	PUNCT
ejpam-6447	254	4	34(2):403–415	34(2):403–415	PROPN
ejpam-6447	254	5	,	,	PUNCT
ejpam-6447	254	6	2011	2011	NUM
ejpam-6447	254	7	.	.	PUNCT
ejpam-6447	255	1	[	[	X
ejpam-6447	255	2	16	16	NUM
ejpam-6447	255	3	]	]	PUNCT
ejpam-6447	255	4	z.	z.	PROPN
ejpam-6447	255	5	alkhudhari	alkhudhari	PROPN
ejpam-6447	255	6	,	,	PUNCT
ejpam-6447	255	7	s.	s.	PROPN
ejpam-6447	255	8	al	al	PROPN
ejpam-6447	255	9	-	-	PUNCT
ejpam-6447	255	10	sheikh	sheikh	PROPN
ejpam-6447	255	11	,	,	PUNCT
ejpam-6447	255	12	and	and	CCONJ
ejpam-6447	255	13	s.	s.	PROPN
ejpam-6447	255	14	al	al	PROPN
ejpam-6447	255	15	-	-	PUNCT
ejpam-6447	255	16	tuwairqi	tuwairqi	PROPN
ejpam-6447	255	17	.	.	PUNCT
ejpam-6447	256	1	global	global	ADJ
ejpam-6447	256	2	dynamics	dynamic	NOUN
ejpam-6447	256	3	of	of	ADP
ejpam-6447	256	4	a	a	DET
ejpam-6447	256	5	mathematical	mathematical	ADJ
ejpam-6447	256	6	model	model	NOUN
ejpam-6447	256	7	on	on	ADP
ejpam-6447	256	8	smoking	smoking	NOUN
ejpam-6447	256	9	.	.	PUNCT
ejpam-6447	257	1	international	international	ADJ
ejpam-6447	257	2	scholarly	scholarly	ADJ
ejpam-6447	257	3	research	research	NOUN
ejpam-6447	257	4	notices	notice	NOUN
ejpam-6447	257	5	,	,	PUNCT
ejpam-6447	257	6	2014(1):847075	2014(1):847075	NUM
ejpam-6447	257	7	,	,	PUNCT
ejpam-6447	257	8	2014	2014	NUM
ejpam-6447	257	9	.	.	PUNCT
ejpam-6447	258	1	[	[	X
ejpam-6447	258	2	17	17	NUM
ejpam-6447	258	3	]	]	PUNCT
ejpam-6447	258	4	a.	a.	NOUN
ejpam-6447	258	5	zeb	zeb	PROPN
ejpam-6447	258	6	,	,	PUNCT
ejpam-6447	258	7	g.	g.	PROPN
ejpam-6447	258	8	zaman	zaman	PROPN
ejpam-6447	258	9	,	,	PUNCT
ejpam-6447	258	10	s.	s.	PROPN
ejpam-6447	258	11	momani	momani	PROPN
ejpam-6447	258	12	,	,	PUNCT
ejpam-6447	258	13	and	and	CCONJ
ejpam-6447	258	14	s.	s.	PROPN
ejpam-6447	258	15	shaher	shaher	PROPN
ejpam-6447	258	16	.	.	PUNCT
ejpam-6447	259	1	square	square	ADJ
ejpam-6447	259	2	-	-	PUNCT
ejpam-6447	259	3	root	root	NOUN
ejpam-6447	259	4	dynamics	dynamic	NOUN
ejpam-6447	259	5	of	of	ADP
ejpam-6447	259	6	a	a	DET
ejpam-6447	259	7	giving	giving	NOUN
ejpam-6447	259	8	up	up	ADP
ejpam-6447	259	9	smoking	smoking	NOUN
ejpam-6447	259	10	model	model	NOUN
ejpam-6447	259	11	.	.	PUNCT
ejpam-6447	260	1	applied	apply	VERB
ejpam-6447	260	2	mathematical	mathematical	ADJ
ejpam-6447	260	3	modelling	modelling	NOUN
ejpam-6447	260	4	,	,	PUNCT
ejpam-6447	260	5	37(7):5326–5334	37(7):5326–5334	NUM
ejpam-6447	260	6	,	,	PUNCT
ejpam-6447	260	7	2013	2013	NUM
ejpam-6447	260	8	.	.	PUNCT
ejpam-6447	261	1	[	[	X
ejpam-6447	261	2	18	18	NUM
ejpam-6447	261	3	]	]	PUNCT
ejpam-6447	261	4	a.	a.	NOUN
ejpam-6447	261	5	zeb	zeb	PROPN
ejpam-6447	261	6	,	,	PUNCT
ejpam-6447	261	7	a.	a.	PROPN
ejpam-6447	261	8	bano	bano	PROPN
ejpam-6447	261	9	,	,	PUNCT
ejpam-6447	261	10	e.	e.	PROPN
ejpam-6447	261	11	alzahrani	alzahrani	PROPN
ejpam-6447	261	12	,	,	PUNCT
ejpam-6447	261	13	and	and	CCONJ
ejpam-6447	261	14	g.	g.	PROPN
ejpam-6447	261	15	zaman	zaman	PROPN
ejpam-6447	261	16	.	.	PUNCT
ejpam-6447	262	1	dynamical	dynamical	ADJ
ejpam-6447	262	2	analysis	analysis	NOUN
ejpam-6447	262	3	of	of	ADP
ejpam-6447	262	4	cigarette	cigarette	NOUN
ejpam-6447	262	5	smoking	smoking	NOUN
ejpam-6447	262	6	model	model	NOUN
ejpam-6447	262	7	with	with	ADP
ejpam-6447	262	8	a	a	DET
ejpam-6447	262	9	saturated	saturate	VERB
ejpam-6447	262	10	incidence	incidence	NOUN
ejpam-6447	262	11	rate	rate	NOUN
ejpam-6447	262	12	.	.	PUNCT
ejpam-6447	263	1	aip	aip	PROPN
ejpam-6447	263	2	advances	advance	NOUN
ejpam-6447	263	3	,	,	PUNCT
ejpam-6447	263	4	8(4	8(4	NUM
ejpam-6447	263	5	)	)	PUNCT
ejpam-6447	263	6	,	,	PUNCT
ejpam-6447	263	7	2018	2018	NUM
ejpam-6447	263	8	.	.	PUNCT
ejpam-6447	264	1	[	[	X
ejpam-6447	264	2	19	19	NUM
ejpam-6447	264	3	]	]	X
ejpam-6447	264	4	y.	y.	PROPN
ejpam-6447	264	5	s.	s.	PROPN
ejpam-6447	264	6	tan	tan	PROPN
ejpam-6447	264	7	,	,	PUNCT
ejpam-6447	264	8	x.	x.	PROPN
ejpam-6447	264	9	x.	x.	PROPN
ejpam-6447	264	10	li	li	PROPN
ejpam-6447	264	11	,	,	PUNCT
ejpam-6447	264	12	j.	j.	PROPN
ejpam-6447	264	13	yang	yang	PROPN
ejpam-6447	264	14	,	,	PUNCT
ejpam-6447	264	15	and	and	CCONJ
ejpam-6447	264	16	r.	r.	PROPN
ejpam-6447	264	17	a.	a.	PROPN
ejpam-6447	264	18	cheke	cheke	PROPN
ejpam-6447	264	19	.	.	PUNCT
ejpam-6447	265	1	global	global	ADJ
ejpam-6447	265	2	stability	stability	NOUN
ejpam-6447	265	3	of	of	ADP
ejpam-6447	265	4	an	an	DET
ejpam-6447	265	5	age	age	NOUN
ejpam-6447	265	6	-	-	PUNCT
ejpam-6447	265	7	structured	structure	VERB
ejpam-6447	265	8	model	model	NOUN
ejpam-6447	265	9	of	of	ADP
ejpam-6447	265	10	smoking	smoking	NOUN
ejpam-6447	265	11	and	and	CCONJ
ejpam-6447	265	12	its	its	PRON
ejpam-6447	265	13	treatment	treatment	NOUN
ejpam-6447	265	14	.	.	PUNCT
ejpam-6447	266	1	international	international	ADJ
ejpam-6447	266	2	journal	journal	NOUN
ejpam-6447	266	3	of	of	ADP
ejpam-6447	266	4	biomathematics	biomathematic	NOUN
ejpam-6447	266	5	,	,	PUNCT
ejpam-6447	266	6	16(01):2250063	16(01):2250063	NUM
ejpam-6447	266	7	,	,	PUNCT
ejpam-6447	266	8	2023	2023	NUM
ejpam-6447	266	9	.	.	PUNCT
ejpam-6447	267	1	[	[	X
ejpam-6447	267	2	20	20	NUM
ejpam-6447	267	3	]	]	PUNCT
ejpam-6447	267	4	a.	a.	NOUN
ejpam-6447	267	5	zeb	zeb	PROPN
ejpam-6447	267	6	,	,	PUNCT
ejpam-6447	267	7	s.	s.	PROPN
ejpam-6447	267	8	hussain	hussain	PROPN
ejpam-6447	267	9	,	,	PUNCT
ejpam-6447	267	10	o.	o.	PROPN
ejpam-6447	267	11	j.	j.	PROPN
ejpam-6447	267	12	algahtani	algahtani	PROPN
ejpam-6447	267	13	,	,	PUNCT
ejpam-6447	267	14	and	and	CCONJ
ejpam-6447	267	15	g.	g.	PROPN
ejpam-6447	267	16	zaman	zaman	PROPN
ejpam-6447	267	17	.	.	PUNCT
ejpam-6447	268	1	global	global	ADJ
ejpam-6447	268	2	aspects	aspect	NOUN
ejpam-6447	268	3	of	of	ADP
ejpam-6447	268	4	age	age	NOUN
ejpam-6447	268	5	-	-	PUNCT
ejpam-6447	268	6	structured	structure	VERB
ejpam-6447	268	7	cigarette	cigarette	NOUN
ejpam-6447	268	8	smoking	smoking	NOUN
ejpam-6447	268	9	model	model	NOUN
ejpam-6447	268	10	.	.	PUNCT
ejpam-6447	269	1	mediterranean	mediterranean	PROPN
ejpam-6447	269	2	journal	journal	PROPN
ejpam-6447	269	3	of	of	ADP
ejpam-6447	269	4	mathematics	mathematic	NOUN
ejpam-6447	269	5	,	,	PUNCT
ejpam-6447	269	6	15:1–11	15:1–11	NUM
ejpam-6447	269	7	,	,	PUNCT
ejpam-6447	269	8	2018	2018	NUM
ejpam-6447	269	9	.	.	PUNCT
ejpam-6447	270	1	[	[	X
ejpam-6447	270	2	21	21	NUM
ejpam-6447	270	3	]	]	X
ejpam-6447	270	4	e.	e.	PROPN
ejpam-6447	270	5	addai	addai	PROPN
ejpam-6447	270	6	,	,	PUNCT
ejpam-6447	270	7	a.	a.	PROPN
ejpam-6447	270	8	adeniji	adeniji	PROPN
ejpam-6447	270	9	,	,	PUNCT
ejpam-6447	270	10	o.	o.	PROPN
ejpam-6447	270	11	j.	j.	PROPN
ejpam-6447	270	12	peter	peter	PROPN
ejpam-6447	270	13	,	,	PUNCT
ejpam-6447	270	14	j.	j.	PROPN
ejpam-6447	270	15	o.	o.	PROPN
ejpam-6447	270	16	agbaje	agbaje	NOUN
ejpam-6447	270	17	,	,	PUNCT
ejpam-6447	270	18	and	and	CCONJ
ejpam-6447	270	19	k.	k.	PROPN
ejpam-6447	270	20	oshinubi	oshinubi	PROPN
ejpam-6447	270	21	.	.	PUNCT
ejpam-6447	271	1	dynamics	dynamic	NOUN
ejpam-6447	271	2	of	of	ADP
ejpam-6447	271	3	agestructure	agestructure	ADJ
ejpam-6447	271	4	smoking	smoking	NOUN
ejpam-6447	271	5	models	model	NOUN
ejpam-6447	271	6	with	with	ADP
ejpam-6447	271	7	government	government	NOUN
ejpam-6447	271	8	intervention	intervention	NOUN
ejpam-6447	271	9	coverage	coverage	NOUN
ejpam-6447	271	10	under	under	ADP
ejpam-6447	271	11	fractal	fractal	ADJ
ejpam-6447	271	12	-	-	PUNCT
ejpam-6447	271	13	fractional	fractional	ADJ
ejpam-6447	271	14	order	order	NOUN
ejpam-6447	271	15	derivatives	derivative	NOUN
ejpam-6447	271	16	.	.	PUNCT
ejpam-6447	272	1	fractal	fractal	ADJ
ejpam-6447	272	2	and	and	CCONJ
ejpam-6447	272	3	fractional	fractional	ADJ
ejpam-6447	272	4	,	,	PUNCT
ejpam-6447	272	5	7(5):370	7(5):370	NUM
ejpam-6447	272	6	,	,	PUNCT
ejpam-6447	272	7	2023	2023	NUM
ejpam-6447	272	8	.	.	PUNCT
ejpam-6447	273	1	[	[	X
ejpam-6447	273	2	22	22	NUM
ejpam-6447	273	3	]	]	X
ejpam-6447	273	4	s.	s.	PROPN
ejpam-6447	273	5	djilali	djilali	PROPN
ejpam-6447	273	6	,	,	PUNCT
ejpam-6447	273	7	s.	s.	PROPN
ejpam-6447	273	8	bentout	bentout	PROPN
ejpam-6447	273	9	,	,	PUNCT
ejpam-6447	273	10	a.	a.	PROPN
ejpam-6447	273	11	zeb	zeb	PROPN
ejpam-6447	273	12	,	,	PUNCT
ejpam-6447	273	13	s.	s.	PROPN
ejpam-6447	273	14	saeed	saeed	PROPN
ejpam-6447	273	15	,	,	PUNCT
ejpam-6447	273	16	and	and	CCONJ
ejpam-6447	273	17	t.	t.	PROPN
ejpam-6447	273	18	tareq	tareq	PROPN
ejpam-6447	273	19	.	.	PUNCT
ejpam-6447	274	1	global	global	ADJ
ejpam-6447	274	2	stability	stability	NOUN
ejpam-6447	274	3	of	of	ADP
ejpam-6447	274	4	hybrid	hybrid	ADJ
ejpam-6447	274	5	smoking	smoking	NOUN
ejpam-6447	274	6	model	model	NOUN
ejpam-6447	274	7	with	with	ADP
ejpam-6447	274	8	nonlocal	nonlocal	ADJ
ejpam-6447	274	9	diffusion	diffusion	NOUN
ejpam-6447	274	10	.	.	PUNCT
ejpam-6447	275	1	fractals	fractal	NOUN
ejpam-6447	275	2	,	,	PUNCT
ejpam-6447	275	3	30(08):2240224	30(08):2240224	NUM
ejpam-6447	275	4	,	,	PUNCT
ejpam-6447	275	5	2022	2022	NUM
ejpam-6447	275	6	.	.	PUNCT
ejpam-6447	276	1	[	[	X
ejpam-6447	276	2	23	23	NUM
ejpam-6447	276	3	]	]	PUNCT
ejpam-6447	276	4	a.	a.	NOUN
ejpam-6447	276	5	lahrouz	lahrouz	PROPN
ejpam-6447	276	6	,	,	PUNCT
ejpam-6447	276	7	l.	l.	PROPN
ejpam-6447	276	8	omari	omari	PROPN
ejpam-6447	276	9	,	,	PUNCT
ejpam-6447	276	10	d.	d.	PROPN
ejpam-6447	276	11	kiouach	kiouach	PROPN
ejpam-6447	276	12	,	,	PUNCT
ejpam-6447	276	13	and	and	CCONJ
ejpam-6447	276	14	a.	a.	PROPN
ejpam-6447	276	15	belmaâti	belmaâti	PROPN
ejpam-6447	276	16	.	.	PUNCT
ejpam-6447	277	1	deterministic	deterministic	ADJ
ejpam-6447	277	2	and	and	CCONJ
ejpam-6447	277	3	stochastic	stochastic	ADJ
ejpam-6447	277	4	stability	stability	NOUN
ejpam-6447	277	5	of	of	ADP
ejpam-6447	277	6	a	a	DET
ejpam-6447	277	7	mathematical	mathematical	ADJ
ejpam-6447	277	8	model	model	NOUN
ejpam-6447	277	9	of	of	ADP
ejpam-6447	277	10	smoking	smoking	NOUN
ejpam-6447	277	11	.	.	PUNCT
ejpam-6447	278	1	statistics	statistic	NOUN
ejpam-6447	278	2	&	&	CCONJ
ejpam-6447	278	3	probability	probability	NOUN
ejpam-6447	278	4	letters	letter	NOUN
ejpam-6447	278	5	,	,	PUNCT
ejpam-6447	278	6	81(8):1276–1284	81(8):1276–1284	NUM
ejpam-6447	278	7	,	,	PUNCT
ejpam-6447	278	8	2011	2011	NUM
ejpam-6447	278	9	.	.	PUNCT
ejpam-6447	279	1	[	[	X
ejpam-6447	279	2	24	24	NUM
ejpam-6447	279	3	]	]	PUNCT
ejpam-6447	279	4	a.	a.	NOUN
ejpam-6447	279	5	zeb	zeb	PROPN
ejpam-6447	279	6	,	,	PUNCT
ejpam-6447	279	7	g.	g.	PROPN
ejpam-6447	279	8	zaman	zaman	PROPN
ejpam-6447	279	9	,	,	PUNCT
ejpam-6447	279	10	i.	i.	PROPN
ejpam-6447	279	11	h.	h.	PROPN
ejpam-6447	279	12	jung	jung	PROPN
ejpam-6447	279	13	,	,	PUNCT
ejpam-6447	279	14	and	and	CCONJ
ejpam-6447	279	15	m.	m.	PROPN
ejpam-6447	279	16	khan	khan	PROPN
ejpam-6447	279	17	.	.	PUNCT
ejpam-6447	280	1	optimal	optimal	ADJ
ejpam-6447	280	2	campaign	campaign	NOUN
ejpam-6447	280	3	strategies	strategy	NOUN
ejpam-6447	280	4	in	in	ADP
ejpam-6447	280	5	fractionalorder	fractionalorder	ADJ
ejpam-6447	280	6	smoking	smoking	NOUN
ejpam-6447	280	7	dynamics	dynamic	NOUN
ejpam-6447	280	8	.	.	PUNCT
ejpam-6447	281	1	zeitschrift	zeitschrift	NOUN
ejpam-6447	281	2	für	für	PROPN
ejpam-6447	281	3	naturforschung	naturforschung	VERB
ejpam-6447	281	4	a	a	DET
ejpam-6447	281	5	,	,	PUNCT
ejpam-6447	281	6	69(5	69(5	PROPN
ejpam-6447	281	7	-	-	SYM
ejpam-6447	281	8	6):225–231	6):225–231	NUM
ejpam-6447	281	9	,	,	PUNCT
ejpam-6447	281	10	2014	2014	NUM
ejpam-6447	281	11	.	.	PUNCT