id	sid	tid	token	lemma	pos
ejpam-3822	1	1	european	european	PROPN
ejpam-3822	1	2	journal	journal	PROPN
ejpam-3822	1	3	of	of	ADP
ejpam-3822	1	4	pure	pure	ADJ
ejpam-3822	1	5	and	and	CCONJ
ejpam-3822	1	6	applied	apply	VERB
ejpam-3822	1	7	mathematics	mathematic	NOUN
ejpam-3822	1	8	vol	vol	NOUN
ejpam-3822	1	9	.	.	PROPN
ejpam-3822	2	1	13	13	NUM
ejpam-3822	2	2	,	,	PUNCT
ejpam-3822	2	3	no	no	INTJ
ejpam-3822	2	4	.	.	NOUN
ejpam-3822	2	5	4	4	NUM
ejpam-3822	2	6	,	,	PUNCT
ejpam-3822	2	7	2020	2020	NUM
ejpam-3822	2	8	,	,	PUNCT
ejpam-3822	2	9	840	840	NUM
ejpam-3822	2	10	-	-	SYM
ejpam-3822	2	11	851	851	NUM
ejpam-3822	2	12	issn	issn	PROPN
ejpam-3822	2	13	1307	1307	NUM
ejpam-3822	2	14	-	-	SYM
ejpam-3822	2	15	5543	5543	NUM
ejpam-3822	2	16	–	–	PUNCT
ejpam-3822	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3822	2	18	published	publish	VERB
ejpam-3822	2	19	by	by	ADP
ejpam-3822	2	20	new	new	PROPN
ejpam-3822	2	21	york	york	PROPN
ejpam-3822	2	22	business	business	PROPN
ejpam-3822	3	1	global	global	PROPN
ejpam-3822	3	2	a	a	DET
ejpam-3822	3	3	delayed	delay	VERB
ejpam-3822	3	4	vaccination	vaccination	NOUN
ejpam-3822	3	5	model	model	NOUN
ejpam-3822	3	6	for	for	ADP
ejpam-3822	3	7	rotavirus	rotavirus	NOUN
ejpam-3822	3	8	infection	infection	NOUN
ejpam-3822	3	9	florence	florence	NOUN
ejpam-3822	3	10	a.	a.	PROPN
ejpam-3822	3	11	adongo1	adongo1	PROPN
ejpam-3822	3	12	,	,	PUNCT
ejpam-3822	3	13	lawrence	lawrence	PROPN
ejpam-3822	3	14	o.	o.	PROPN
ejpam-3822	3	15	onyango2,∗	onyango2,∗	PROPN
ejpam-3822	3	16	,	,	PUNCT
ejpam-3822	3	17	job	job	NOUN
ejpam-3822	3	18	bonyo3	bonyo3	NOUN
ejpam-3822	3	19	,	,	PUNCT
ejpam-3822	3	20	g.o	g.o	PROPN
ejpam-3822	3	21	.	.	PROPN
ejpam-3822	3	22	lawi4	lawi4	PROPN
ejpam-3822	3	23	,	,	PUNCT
ejpam-3822	4	1	ogada	ogada	NOUN
ejpam-3822	4	2	a.	a.	NOUN
ejpam-3822	4	3	elisha5	elisha5	PROPN
ejpam-3822	4	4	2,5	2,5	NUM
ejpam-3822	4	5	mathematics	mathematic	NOUN
ejpam-3822	4	6	department	department	NOUN
ejpam-3822	4	7	,	,	PUNCT
ejpam-3822	4	8	faculty	faculty	NOUN
ejpam-3822	4	9	of	of	ADP
ejpam-3822	4	10	science	science	NOUN
ejpam-3822	4	11	,	,	PUNCT
ejpam-3822	4	12	egerton	egerton	PROPN
ejpam-3822	4	13	university	university	PROPN
ejpam-3822	4	14	,	,	PUNCT
ejpam-3822	4	15	nakuru	nakuru	PROPN
ejpam-3822	4	16	,	,	PUNCT
ejpam-3822	4	17	kenya	kenya	PROPN
ejpam-3822	4	18	1,3	1,3	NUM
ejpam-3822	4	19	mathematics	mathematics	PROPN
ejpam-3822	4	20	department	department	NOUN
ejpam-3822	4	21	,	,	PUNCT
ejpam-3822	4	22	faculty	faculty	NOUN
ejpam-3822	4	23	of	of	ADP
ejpam-3822	4	24	science	science	NOUN
ejpam-3822	4	25	,	,	PUNCT
ejpam-3822	4	26	maseno	maseno	NOUN
ejpam-3822	4	27	university	university	PROPN
ejpam-3822	4	28	,	,	PUNCT
ejpam-3822	4	29	kisumu	kisumu	PROPN
ejpam-3822	4	30	,	,	PUNCT
ejpam-3822	4	31	kenya	kenya	PROPN
ejpam-3822	4	32	4	4	NUM
ejpam-3822	4	33	mathematics	mathematics	PROPN
ejpam-3822	4	34	department	department	NOUN
ejpam-3822	4	35	,	,	PUNCT
ejpam-3822	4	36	faculty	faculty	NOUN
ejpam-3822	4	37	of	of	ADP
ejpam-3822	4	38	science	science	NOUN
ejpam-3822	4	39	,	,	PUNCT
ejpam-3822	4	40	masinde	masinde	VERB
ejpam-3822	4	41	muliro	muliro	PROPN
ejpam-3822	4	42	university	university	PROPN
ejpam-3822	4	43	of	of	ADP
ejpam-3822	4	44	science	science	NOUN
ejpam-3822	4	45	and	and	CCONJ
ejpam-3822	4	46	technology	technology	NOUN
ejpam-3822	4	47	,	,	PUNCT
ejpam-3822	4	48	kakamega	kakamega	PROPN
ejpam-3822	4	49	,	,	PUNCT
ejpam-3822	4	50	kenya	kenya	PROPN
ejpam-3822	4	51	abstract	abstract	NOUN
ejpam-3822	4	52	.	.	PUNCT
ejpam-3822	5	1	in	in	ADP
ejpam-3822	5	2	this	this	DET
ejpam-3822	5	3	work	work	NOUN
ejpam-3822	5	4	,	,	PUNCT
ejpam-3822	5	5	a	a	DET
ejpam-3822	5	6	mathematical	mathematical	ADJ
ejpam-3822	5	7	model	model	NOUN
ejpam-3822	5	8	for	for	ADP
ejpam-3822	5	9	rotavirus	rotavirus	NOUN
ejpam-3822	5	10	infection	infection	NOUN
ejpam-3822	5	11	incorporating	incorporate	VERB
ejpam-3822	5	12	delay	delay	NOUN
ejpam-3822	5	13	differential	differential	ADJ
ejpam-3822	5	14	equations	equation	NOUN
ejpam-3822	5	15	has	have	AUX
ejpam-3822	5	16	been	be	AUX
ejpam-3822	5	17	formulated	formulate	VERB
ejpam-3822	5	18	.	.	PUNCT
ejpam-3822	6	1	stability	stability	NOUN
ejpam-3822	6	2	analysis	analysis	NOUN
ejpam-3822	6	3	of	of	ADP
ejpam-3822	6	4	the	the	DET
ejpam-3822	6	5	model	model	NOUN
ejpam-3822	6	6	has	have	AUX
ejpam-3822	6	7	been	be	AUX
ejpam-3822	6	8	performed	perform	VERB
ejpam-3822	6	9	.	.	PUNCT
ejpam-3822	7	1	the	the	DET
ejpam-3822	7	2	result	result	NOUN
ejpam-3822	7	3	shows	show	VERB
ejpam-3822	7	4	that	that	SCONJ
ejpam-3822	7	5	the	the	DET
ejpam-3822	7	6	disease	disease	NOUN
ejpam-3822	7	7	free	free	ADJ
ejpam-3822	7	8	equilibrium	equilibrium	NOUN
ejpam-3822	7	9	is	be	AUX
ejpam-3822	7	10	globally	globally	ADV
ejpam-3822	7	11	asymptotically	asymptotically	ADV
ejpam-3822	7	12	stable	stable	ADJ
ejpam-3822	7	13	and	and	CCONJ
ejpam-3822	7	14	the	the	DET
ejpam-3822	7	15	endemic	endemic	ADJ
ejpam-3822	7	16	equilibrium	equilibrium	NOUN
ejpam-3822	7	17	undergoes	undergo	VERB
ejpam-3822	7	18	a	a	DET
ejpam-3822	7	19	hopf	hopf	ADJ
ejpam-3822	7	20	bifurcation	bifurcation	NOUN
ejpam-3822	7	21	.	.	PUNCT
ejpam-3822	8	1	numerical	numerical	ADJ
ejpam-3822	8	2	analysis	analysis	NOUN
ejpam-3822	8	3	has	have	AUX
ejpam-3822	8	4	been	be	AUX
ejpam-3822	8	5	performed	perform	VERB
ejpam-3822	8	6	to	to	PART
ejpam-3822	8	7	validate	validate	VERB
ejpam-3822	8	8	the	the	DET
ejpam-3822	8	9	analysis	analysis	NOUN
ejpam-3822	8	10	.	.	PUNCT
ejpam-3822	9	1	2020	2020	NUM
ejpam-3822	9	2	mathematics	mathematic	NOUN
ejpam-3822	9	3	subject	subject	NOUN
ejpam-3822	9	4	classifications	classification	NOUN
ejpam-3822	9	5	:	:	PUNCT
ejpam-3822	9	6	34c60	34c60	NUM
ejpam-3822	9	7	,	,	PUNCT
ejpam-3822	9	8	34xx	34xx	ADJ
ejpam-3822	9	9	,	,	PUNCT
ejpam-3822	9	10	37nxx	37nxx	ADJ
ejpam-3822	9	11	key	key	ADJ
ejpam-3822	9	12	words	word	NOUN
ejpam-3822	9	13	and	and	CCONJ
ejpam-3822	9	14	phrases	phrase	NOUN
ejpam-3822	9	15	:	:	PUNCT
ejpam-3822	9	16	rotavirus	rotaviru	NOUN
ejpam-3822	9	17	,	,	PUNCT
ejpam-3822	9	18	hopf	hopf	ADJ
ejpam-3822	9	19	bifurcation	bifurcation	NOUN
ejpam-3822	9	20	,	,	PUNCT
ejpam-3822	9	21	global	global	ADJ
ejpam-3822	9	22	asymptotic	asymptotic	ADJ
ejpam-3822	9	23	stability	stability	NOUN
ejpam-3822	9	24	,	,	PUNCT
ejpam-3822	9	25	endemic	endemic	ADJ
ejpam-3822	9	26	equilibrium	equilibrium	NOUN
ejpam-3822	9	27	1	1	NUM
ejpam-3822	9	28	.	.	PUNCT
ejpam-3822	10	1	introduction	introduction	NOUN
ejpam-3822	10	2	this	this	DET
ejpam-3822	10	3	work	work	NOUN
ejpam-3822	10	4	is	be	AUX
ejpam-3822	10	5	an	an	DET
ejpam-3822	10	6	extension	extension	NOUN
ejpam-3822	10	7	of	of	ADP
ejpam-3822	10	8	the	the	DET
ejpam-3822	10	9	work	work	NOUN
ejpam-3822	10	10	done	do	VERB
ejpam-3822	10	11	by	by	ADP
ejpam-3822	10	12	onyango	onyango	NOUN
ejpam-3822	10	13	et.al	et.al	PROPN
ejpam-3822	10	14	[	[	X
ejpam-3822	10	15	8	8	NUM
ejpam-3822	10	16	]	]	PUNCT
ejpam-3822	10	17	.	.	PUNCT
ejpam-3822	11	1	in	in	ADP
ejpam-3822	11	2	their	their	PRON
ejpam-3822	11	3	work	work	NOUN
ejpam-3822	11	4	,	,	PUNCT
ejpam-3822	11	5	they	they	PRON
ejpam-3822	11	6	assumed	assume	VERB
ejpam-3822	11	7	that	that	SCONJ
ejpam-3822	11	8	the	the	DET
ejpam-3822	11	9	effects	effect	NOUN
ejpam-3822	11	10	of	of	ADP
ejpam-3822	11	11	vaccines	vaccine	NOUN
ejpam-3822	11	12	are	be	AUX
ejpam-3822	11	13	immediate	immediate	ADJ
ejpam-3822	11	14	.	.	PUNCT
ejpam-3822	12	1	this	this	PRON
ejpam-3822	12	2	has	have	AUX
ejpam-3822	12	3	not	not	PART
ejpam-3822	12	4	been	be	AUX
ejpam-3822	12	5	the	the	DET
ejpam-3822	12	6	case	case	NOUN
ejpam-3822	12	7	since	since	SCONJ
ejpam-3822	12	8	there	there	PRON
ejpam-3822	12	9	must	must	AUX
ejpam-3822	12	10	be	be	AUX
ejpam-3822	12	11	time	time	NOUN
ejpam-3822	12	12	lapse	lapse	NOUN
ejpam-3822	12	13	.	.	PUNCT
ejpam-3822	13	1	it	it	PRON
ejpam-3822	13	2	is	be	AUX
ejpam-3822	13	3	therefore	therefore	ADV
ejpam-3822	13	4	necessary	necessary	ADJ
ejpam-3822	13	5	to	to	PART
ejpam-3822	13	6	investigate	investigate	VERB
ejpam-3822	13	7	how	how	SCONJ
ejpam-3822	13	8	this	this	DET
ejpam-3822	13	9	time	time	NOUN
ejpam-3822	13	10	lapse	lapse	NOUN
ejpam-3822	13	11	impact	impact	NOUN
ejpam-3822	13	12	on	on	ADP
ejpam-3822	13	13	the	the	DET
ejpam-3822	13	14	effectiveness	effectiveness	NOUN
ejpam-3822	13	15	of	of	ADP
ejpam-3822	13	16	the	the	DET
ejpam-3822	13	17	vaccine	vaccine	NOUN
ejpam-3822	13	18	.	.	PUNCT
ejpam-3822	14	1	for	for	ADP
ejpam-3822	14	2	the	the	DET
ejpam-3822	14	3	literature	literature	PROPN
ejpam-3822	14	4	review	review	NOUN
ejpam-3822	14	5	,	,	PUNCT
ejpam-3822	14	6	proof	proof	NOUN
ejpam-3822	14	7	of	of	ADP
ejpam-3822	14	8	existence	existence	NOUN
ejpam-3822	14	9	of	of	ADP
ejpam-3822	14	10	both	both	DET
ejpam-3822	14	11	disease	disease	NOUN
ejpam-3822	14	12	free	free	ADJ
ejpam-3822	14	13	and	and	CCONJ
ejpam-3822	14	14	endemic	endemic	ADJ
ejpam-3822	14	15	equilibrium	equilibrium	NOUN
ejpam-3822	14	16	,	,	PUNCT
ejpam-3822	14	17	the	the	DET
ejpam-3822	14	18	establishment	establishment	NOUN
ejpam-3822	14	19	of	of	ADP
ejpam-3822	14	20	basic	basic	ADJ
ejpam-3822	14	21	reproduction	reproduction	NOUN
ejpam-3822	14	22	number	number	NOUN
ejpam-3822	14	23	of	of	ADP
ejpam-3822	14	24	the	the	DET
ejpam-3822	14	25	model	model	NOUN
ejpam-3822	14	26	,	,	PUNCT
ejpam-3822	14	27	see	see	VERB
ejpam-3822	14	28	[	[	X
ejpam-3822	14	29	8	8	NUM
ejpam-3822	14	30	]	]	PUNCT
ejpam-3822	14	31	.	.	PUNCT
ejpam-3822	15	1	this	this	DET
ejpam-3822	15	2	work	work	NOUN
ejpam-3822	15	3	is	be	AUX
ejpam-3822	15	4	organized	organize	VERB
ejpam-3822	15	5	as	as	SCONJ
ejpam-3822	15	6	follows	follow	VERB
ejpam-3822	15	7	.	.	PUNCT
ejpam-3822	16	1	the	the	DET
ejpam-3822	16	2	model	model	NOUN
ejpam-3822	16	3	is	be	AUX
ejpam-3822	16	4	formulated	formulate	VERB
ejpam-3822	16	5	in	in	ADP
ejpam-3822	16	6	section	section	NOUN
ejpam-3822	16	7	2	2	NUM
ejpam-3822	16	8	,	,	PUNCT
ejpam-3822	16	9	in	in	ADP
ejpam-3822	16	10	section	section	NOUN
ejpam-3822	16	11	3	3	NUM
ejpam-3822	16	12	,	,	PUNCT
ejpam-3822	16	13	the	the	DET
ejpam-3822	16	14	model	model	NOUN
ejpam-3822	16	15	is	be	AUX
ejpam-3822	16	16	analyzed	analyze	VERB
ejpam-3822	16	17	.	.	PUNCT
ejpam-3822	17	1	in	in	ADP
ejpam-3822	17	2	section	section	NOUN
ejpam-3822	17	3	4	4	NUM
ejpam-3822	17	4	,	,	PUNCT
ejpam-3822	17	5	the	the	DET
ejpam-3822	17	6	numerical	numerical	PROPN
ejpam-3822	17	7	simulation	simulation	NOUN
ejpam-3822	17	8	and	and	CCONJ
ejpam-3822	17	9	discussion	discussion	NOUN
ejpam-3822	17	10	is	be	AUX
ejpam-3822	17	11	performed	perform	VERB
ejpam-3822	17	12	.	.	PUNCT
ejpam-3822	18	1	conclusion	conclusion	NOUN
ejpam-3822	18	2	and	and	CCONJ
ejpam-3822	18	3	discussion	discussion	NOUN
ejpam-3822	18	4	is	be	AUX
ejpam-3822	18	5	done	do	VERB
ejpam-3822	18	6	in	in	ADP
ejpam-3822	18	7	section	section	NOUN
ejpam-3822	18	8	5	5	NUM
ejpam-3822	18	9	.	.	PUNCT
ejpam-3822	18	10	∗corresponding	∗corresponde	VERB
ejpam-3822	18	11	author	author	NOUN
ejpam-3822	18	12	.	.	PUNCT
ejpam-3822	19	1	doi	doi	NOUN
ejpam-3822	19	2	:	:	PUNCT
ejpam-3822	19	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3822	https://doi.org/10.29020/nybg.ejpam.v13i4.3822	NOUN
ejpam-3822	19	4	email	email	NOUN
ejpam-3822	19	5	addresses	address	VERB
ejpam-3822	19	6	:	:	PUNCT
ejpam-3822	19	7	florenceeadongo@gmail.com	florenceeadongo@gmail.com	X
ejpam-3822	19	8	(	(	PUNCT
ejpam-3822	19	9	f.a	f.a	PROPN
ejpam-3822	19	10	.	.	PROPN
ejpam-3822	19	11	adongoi	adongoi	PROPN
ejpam-3822	19	12	)	)	PUNCT
ejpam-3822	19	13	,	,	PUNCT
ejpam-3822	19	14	lawionyi@gmail.com	lawionyi@gmail.com	X
ejpam-3822	20	1	(	(	PUNCT
ejpam-3822	20	2	o.l	o.l	PROPN
ejpam-3822	20	3	.	.	PROPN
ejpam-3822	20	4	onyango	onyango	PROPN
ejpam-3822	20	5	)	)	PUNCT
ejpam-3822	21	1	,	,	PUNCT
ejpam-3822	21	2	jobbonyo@maseno.ac.ke	jobbonyo@maseno.ac.ke	PROPN
ejpam-3822	21	3	(	(	PUNCT
ejpam-3822	21	4	j.	j.	PROPN
ejpam-3822	21	5	bonyo	bonyo	PROPN
ejpam-3822	21	6	)	)	PUNCT
ejpam-3822	21	7	,	,	PUNCT
ejpam-3822	21	8	achiengelisha@gmail.com	achiengelisha@gmail.com	X
ejpam-3822	22	1	(	(	PUNCT
ejpam-3822	22	2	e.a	e.a	PROPN
ejpam-3822	22	3	.	.	PROPN
ejpam-3822	22	4	ogada	ogada	PROPN
ejpam-3822	22	5	)	)	PUNCT
ejpam-3822	22	6	,	,	PUNCT
ejpam-3822	22	7	glawi@mmust.ac.ke	glawi@mmust.ac.ke	PROPN
ejpam-3822	22	8	(	(	PUNCT
ejpam-3822	22	9	g.lawi	g.lawi	ADJ
ejpam-3822	22	10	)	)	PUNCT
ejpam-3822	22	11	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3822	23	1	840	840	NUM
ejpam-3822	23	2	c	c	NOUN
ejpam-3822	23	3	©	©	NOUN
ejpam-3822	23	4	2020	2020	NUM
ejpam-3822	23	5	ejpam	ejpam	VERB
ejpam-3822	23	6	all	all	DET
ejpam-3822	23	7	rights	right	NOUN
ejpam-3822	23	8	reserved	reserve	VERB
ejpam-3822	23	9	.	.	PUNCT
ejpam-3822	24	1	l.	l.	PROPN
ejpam-3822	24	2	o.	o.	PROPN
ejpam-3822	24	3	onyango	onyango	PROPN
ejpam-3822	24	4	et	et	PROPN
ejpam-3822	25	1	al	al	PROPN
ejpam-3822	25	2	.	.	PUNCT
ejpam-3822	25	3	/	/	SYM
ejpam-3822	25	4	eur	eur	PROPN
ejpam-3822	25	5	.	.	PUNCT
ejpam-3822	26	1	j.	j.	PROPN
ejpam-3822	26	2	pure	pure	PROPN
ejpam-3822	26	3	appl	appl	PROPN
ejpam-3822	26	4	.	.	PROPN
ejpam-3822	26	5	math	math	PROPN
ejpam-3822	26	6	,	,	PUNCT
ejpam-3822	26	7	13	13	NUM
ejpam-3822	26	8	(	(	PUNCT
ejpam-3822	26	9	4	4	NUM
ejpam-3822	26	10	)	)	PUNCT
ejpam-3822	26	11	(	(	PUNCT
ejpam-3822	26	12	2020	2020	NUM
ejpam-3822	26	13	)	)	PUNCT
ejpam-3822	26	14	,	,	PUNCT
ejpam-3822	26	15	840	840	NUM
ejpam-3822	26	16	-	-	SYM
ejpam-3822	26	17	851	851	NUM
ejpam-3822	26	18	841	841	NUM
ejpam-3822	26	19	2	2	NUM
ejpam-3822	26	20	.	.	PUNCT
ejpam-3822	26	21	model	model	NOUN
ejpam-3822	26	22	description	description	NOUN
ejpam-3822	26	23	and	and	CCONJ
ejpam-3822	26	24	formulation	formulation	NOUN
ejpam-3822	26	25	.	.	PUNCT
ejpam-3822	27	1	we	we	PRON
ejpam-3822	27	2	achieve	achieve	VERB
ejpam-3822	27	3	the	the	DET
ejpam-3822	27	4	objective	objective	NOUN
ejpam-3822	27	5	of	of	ADP
ejpam-3822	27	6	this	this	DET
ejpam-3822	27	7	study	study	NOUN
ejpam-3822	27	8	,	,	PUNCT
ejpam-3822	27	9	by	by	ADP
ejpam-3822	27	10	formulating	formulate	VERB
ejpam-3822	27	11	a	a	DET
ejpam-3822	27	12	mathematical	mathematical	ADJ
ejpam-3822	27	13	model	model	NOUN
ejpam-3822	27	14	based	base	VERB
ejpam-3822	27	15	on	on	ADP
ejpam-3822	27	16	a	a	DET
ejpam-3822	27	17	system	system	NOUN
ejpam-3822	27	18	of	of	ADP
ejpam-3822	27	19	delay	delay	NOUN
ejpam-3822	27	20	differential	differential	ADJ
ejpam-3822	27	21	equation	equation	NOUN
ejpam-3822	27	22	for	for	ADP
ejpam-3822	27	23	rota	rota	NOUN
ejpam-3822	27	24	-	-	PUNCT
ejpam-3822	27	25	virus	virus	NOUN
ejpam-3822	27	26	incorporating	incorporate	VERB
ejpam-3822	27	27	time	time	NOUN
ejpam-3822	27	28	delay	delay	NOUN
ejpam-3822	27	29	in	in	ADP
ejpam-3822	27	30	the	the	DET
ejpam-3822	27	31	effects	effect	NOUN
ejpam-3822	27	32	of	of	ADP
ejpam-3822	27	33	vaccination	vaccination	NOUN
ejpam-3822	27	34	.	.	PUNCT
ejpam-3822	28	1	the	the	DET
ejpam-3822	28	2	total	total	ADJ
ejpam-3822	28	3	human	human	ADJ
ejpam-3822	28	4	population	population	NOUN
ejpam-3822	28	5	size	size	NOUN
ejpam-3822	28	6	understudy	understudy	NOUN
ejpam-3822	28	7	,	,	PUNCT
ejpam-3822	28	8	n(t	n(t	PROPN
ejpam-3822	28	9	)	)	PUNCT
ejpam-3822	28	10	,	,	PUNCT
ejpam-3822	28	11	at	at	ADP
ejpam-3822	28	12	any	any	DET
ejpam-3822	28	13	time	time	NOUN
ejpam-3822	28	14	is	be	AUX
ejpam-3822	28	15	subdivided	subdivide	VERB
ejpam-3822	28	16	into	into	ADP
ejpam-3822	28	17	classes	class	NOUN
ejpam-3822	28	18	such	such	ADJ
ejpam-3822	28	19	as	as	ADP
ejpam-3822	28	20	susceptible	susceptible	ADJ
ejpam-3822	28	21	s	s	NOUN
ejpam-3822	28	22	,	,	PUNCT
ejpam-3822	28	23	infectious	infectious	ADJ
ejpam-3822	28	24	with	with	ADP
ejpam-3822	28	25	rotavirus	rotaviru	NOUN
ejpam-3822	28	26	i	i	PRON
ejpam-3822	28	27	,	,	PUNCT
ejpam-3822	28	28	vaccinated	vaccinate	VERB
ejpam-3822	28	29	v	v	ADP
ejpam-3822	28	30	and	and	CCONJ
ejpam-3822	28	31	recovered	recover	VERB
ejpam-3822	28	32	r.	r.	PROPN
ejpam-3822	28	33	the	the	DET
ejpam-3822	28	34	total	total	ADJ
ejpam-3822	28	35	population	population	NOUN
ejpam-3822	28	36	n(t	n(t	NOUN
ejpam-3822	28	37	)	)	PUNCT
ejpam-3822	28	38	=	=	PUNCT
ejpam-3822	28	39	s(t	s(t	PROPN
ejpam-3822	28	40	)	)	PUNCT
ejpam-3822	28	41	+	+	CCONJ
ejpam-3822	28	42	v(t	v(t	VERB
ejpam-3822	28	43	)	)	PUNCT
ejpam-3822	28	44	+	+	CCONJ
ejpam-3822	28	45	i(t	i(t	NOUN
ejpam-3822	28	46	)	)	PUNCT
ejpam-3822	28	47	+	+	NUM
ejpam-3822	28	48	r(t	r(t	NOUN
ejpam-3822	28	49	)	)	PUNCT
ejpam-3822	28	50	.	.	PUNCT
ejpam-3822	29	1	assuming	assume	VERB
ejpam-3822	29	2	that	that	SCONJ
ejpam-3822	29	3	the	the	DET
ejpam-3822	29	4	mass	mass	ADJ
ejpam-3822	29	5	action	action	NOUN
ejpam-3822	29	6	incidence	incidence	NOUN
ejpam-3822	29	7	transmission	transmission	NOUN
ejpam-3822	29	8	is	be	AUX
ejpam-3822	29	9	defined	define	VERB
ejpam-3822	29	10	by	by	ADP
ejpam-3822	29	11	βsi	βsi	NOUN
ejpam-3822	29	12	,	,	PUNCT
ejpam-3822	29	13	where	where	SCONJ
ejpam-3822	29	14	β	β	PROPN
ejpam-3822	29	15	is	be	AUX
ejpam-3822	29	16	the	the	DET
ejpam-3822	29	17	effective	effective	ADJ
ejpam-3822	29	18	contact	contact	NOUN
ejpam-3822	29	19	rate	rate	NOUN
ejpam-3822	29	20	for	for	ADP
ejpam-3822	29	21	disease	disease	NOUN
ejpam-3822	29	22	transmission	transmission	NOUN
ejpam-3822	29	23	and	and	CCONJ
ejpam-3822	29	24	the	the	DET
ejpam-3822	29	25	initial	initial	ADJ
ejpam-3822	29	26	conditions	condition	NOUN
ejpam-3822	29	27	are	be	AUX
ejpam-3822	29	28	such	such	ADJ
ejpam-3822	29	29	that	that	SCONJ
ejpam-3822	29	30	the	the	DET
ejpam-3822	29	31	parameter	parameter	NOUN
ejpam-3822	29	32	s	s	PROPN
ejpam-3822	29	33	,	,	PUNCT
ejpam-3822	29	34	v	v	NOUN
ejpam-3822	29	35	,	,	PUNCT
ejpam-3822	29	36	i	i	PRON
ejpam-3822	29	37	,	,	PUNCT
ejpam-3822	29	38	r	r	NOUN
ejpam-3822	29	39	remain	remain	VERB
ejpam-3822	29	40	non	non	ADJ
ejpam-3822	29	41	-	-	ADJ
ejpam-3822	29	42	negative	negative	ADJ
ejpam-3822	29	43	for	for	ADP
ejpam-3822	29	44	all	all	DET
ejpam-3822	29	45	time	time	NOUN
ejpam-3822	29	46	t	t	PROPN
ejpam-3822	29	47	≥	≥	NOUN
ejpam-3822	29	48	0	0	NUM
ejpam-3822	29	49	.	.	PUNCT
ejpam-3822	30	1	stability	stability	NOUN
ejpam-3822	30	2	analysis	analysis	NOUN
ejpam-3822	30	3	of	of	ADP
ejpam-3822	30	4	the	the	DET
ejpam-3822	30	5	model	model	NOUN
ejpam-3822	30	6	is	be	AUX
ejpam-3822	30	7	done	do	VERB
ejpam-3822	30	8	to	to	PART
ejpam-3822	30	9	determine	determine	VERB
ejpam-3822	30	10	the	the	DET
ejpam-3822	30	11	conditions	condition	NOUN
ejpam-3822	30	12	for	for	ADP
ejpam-3822	30	13	the	the	DET
ejpam-3822	30	14	spread	spread	NOUN
ejpam-3822	30	15	of	of	ADP
ejpam-3822	30	16	disease	disease	NOUN
ejpam-3822	30	17	in	in	ADP
ejpam-3822	30	18	a	a	DET
ejpam-3822	30	19	given	give	VERB
ejpam-3822	30	20	population	population	NOUN
ejpam-3822	30	21	.	.	PUNCT
ejpam-3822	31	1	rotavirus	rotavirus	NOUN
ejpam-3822	31	2	spreads	spread	VERB
ejpam-3822	31	3	by	by	ADP
ejpam-3822	31	4	contact	contact	NOUN
ejpam-3822	31	5	with	with	ADP
ejpam-3822	31	6	infected	infected	ADJ
ejpam-3822	31	7	faeces	faece	NOUN
ejpam-3822	31	8	and	and	CCONJ
ejpam-3822	31	9	might	might	AUX
ejpam-3822	31	10	also	also	ADV
ejpam-3822	31	11	be	be	AUX
ejpam-3822	31	12	transmitted	transmit	VERB
ejpam-3822	31	13	through	through	ADP
ejpam-3822	31	14	faecally	faecally	ADV
ejpam-3822	31	15	-	-	PUNCT
ejpam-3822	31	16	contaminated	contaminate	VERB
ejpam-3822	31	17	;	;	PUNCT
ejpam-3822	31	18	food	food	NOUN
ejpam-3822	31	19	,	,	PUNCT
ejpam-3822	31	20	water	water	NOUN
ejpam-3822	31	21	and	and	CCONJ
ejpam-3822	31	22	respiratory	respiratory	ADJ
ejpam-3822	31	23	droplets	droplet	NOUN
ejpam-3822	31	24	[	[	X
ejpam-3822	31	25	1	1	NUM
ejpam-3822	31	26	]	]	PUNCT
ejpam-3822	31	27	.	.	PUNCT
ejpam-3822	32	1	since	since	SCONJ
ejpam-3822	32	2	the	the	DET
ejpam-3822	32	3	incubation	incubation	NOUN
ejpam-3822	32	4	period	period	NOUN
ejpam-3822	32	5	is	be	AUX
ejpam-3822	32	6	very	very	ADV
ejpam-3822	32	7	short	short	ADJ
ejpam-3822	32	8	[	[	X
ejpam-3822	32	9	8	8	NUM
ejpam-3822	32	10	]	]	PUNCT
ejpam-3822	32	11	,	,	PUNCT
ejpam-3822	32	12	we	we	PRON
ejpam-3822	32	13	assume	assume	VERB
ejpam-3822	32	14	that	that	SCONJ
ejpam-3822	32	15	the	the	DET
ejpam-3822	32	16	probability	probability	NOUN
ejpam-3822	32	17	of	of	ADP
ejpam-3822	32	18	survival	survival	NOUN
ejpam-3822	32	19	till	till	SCONJ
ejpam-3822	32	20	the	the	DET
ejpam-3822	32	21	infectious	infectious	ADJ
ejpam-3822	32	22	state	state	NOUN
ejpam-3822	32	23	for	for	ADP
ejpam-3822	32	24	the	the	DET
ejpam-3822	32	25	individuals	individual	NOUN
ejpam-3822	32	26	exposed	expose	VERB
ejpam-3822	32	27	to	to	ADP
ejpam-3822	32	28	rotavirus	rotavirus	NOUN
ejpam-3822	32	29	is	be	AUX
ejpam-3822	32	30	unity	unity	NOUN
ejpam-3822	32	31	and	and	CCONJ
ejpam-3822	32	32	therefore	therefore	ADV
ejpam-3822	32	33	exclude	exclude	VERB
ejpam-3822	32	34	the	the	DET
ejpam-3822	32	35	exposure	exposure	NOUN
ejpam-3822	32	36	stage	stage	NOUN
ejpam-3822	32	37	.	.	PUNCT
ejpam-3822	33	1	the	the	DET
ejpam-3822	33	2	individuals	individual	NOUN
ejpam-3822	33	3	infected	infect	VERB
ejpam-3822	33	4	with	with	ADP
ejpam-3822	33	5	rotavirus	rotavirus	NOUN
ejpam-3822	33	6	include	include	VERB
ejpam-3822	33	7	both	both	CCONJ
ejpam-3822	33	8	symptomatic	symptomatic	ADJ
ejpam-3822	33	9	and	and	CCONJ
ejpam-3822	33	10	asymptomatic	asymptomatic	ADJ
ejpam-3822	33	11	cases	case	NOUN
ejpam-3822	33	12	because	because	SCONJ
ejpam-3822	33	13	they	they	PRON
ejpam-3822	33	14	are	be	AUX
ejpam-3822	33	15	capable	capable	ADJ
ejpam-3822	33	16	of	of	ADP
ejpam-3822	33	17	infecting	infect	VERB
ejpam-3822	33	18	others	other	NOUN
ejpam-3822	34	1	[	[	X
ejpam-3822	34	2	9	9	NUM
ejpam-3822	34	3	]	]	PUNCT
ejpam-3822	34	4	.	.	PUNCT
ejpam-3822	35	1	the	the	DET
ejpam-3822	35	2	recovery	recovery	NOUN
ejpam-3822	35	3	class	class	NOUN
ejpam-3822	35	4	comprises	comprise	NOUN
ejpam-3822	35	5	of	of	ADP
ejpam-3822	35	6	those	those	PRON
ejpam-3822	35	7	who	who	PRON
ejpam-3822	35	8	have	have	AUX
ejpam-3822	35	9	been	be	AUX
ejpam-3822	35	10	removed	remove	VERB
ejpam-3822	35	11	from	from	ADP
ejpam-3822	35	12	the	the	DET
ejpam-3822	35	13	scene	scene	NOUN
ejpam-3822	35	14	of	of	ADP
ejpam-3822	35	15	infection	infection	NOUN
ejpam-3822	35	16	by	by	ADP
ejpam-3822	35	17	such	such	ADJ
ejpam-3822	35	18	means	mean	NOUN
ejpam-3822	35	19	as	as	SCONJ
ejpam-3822	35	20	infection	infection	NOUN
ejpam-3822	35	21	acquired	acquire	VERB
ejpam-3822	35	22	immunity	immunity	NOUN
ejpam-3822	35	23	and	and	CCONJ
ejpam-3822	35	24	death	death	NOUN
ejpam-3822	35	25	.	.	PUNCT
ejpam-3822	36	1	it	it	PRON
ejpam-3822	36	2	is	be	AUX
ejpam-3822	36	3	possible	possible	ADJ
ejpam-3822	36	4	children	child	NOUN
ejpam-3822	36	5	can	can	AUX
ejpam-3822	36	6	develop	develop	VERB
ejpam-3822	36	7	some	some	DET
ejpam-3822	36	8	level	level	NOUN
ejpam-3822	36	9	of	of	ADP
ejpam-3822	36	10	immunity	immunity	NOUN
ejpam-3822	36	11	to	to	ADP
ejpam-3822	36	12	rotavirus	rotavirus	NOUN
ejpam-3822	36	13	from	from	ADP
ejpam-3822	36	14	maternal	maternal	ADJ
ejpam-3822	36	15	antibody	antibody	NOUN
ejpam-3822	36	16	due	due	ADP
ejpam-3822	36	17	to	to	ADP
ejpam-3822	36	18	breastfeeding	breastfeeding	NOUN
ejpam-3822	36	19	but	but	CCONJ
ejpam-3822	36	20	this	this	DET
ejpam-3822	36	21	immunity	immunity	NOUN
ejpam-3822	36	22	does	do	AUX
ejpam-3822	36	23	not	not	PART
ejpam-3822	36	24	last	last	VERB
ejpam-3822	36	25	for	for	ADP
ejpam-3822	36	26	long	long	ADV
ejpam-3822	36	27	hence	hence	ADV
ejpam-3822	36	28	we	we	PRON
ejpam-3822	36	29	consider	consider	VERB
ejpam-3822	36	30	the	the	DET
ejpam-3822	36	31	effect	effect	NOUN
ejpam-3822	36	32	of	of	ADP
ejpam-3822	36	33	vaccination	vaccination	NOUN
ejpam-3822	36	34	at	at	ADP
ejpam-3822	36	35	birth	birth	NOUN
ejpam-3822	36	36	and	and	CCONJ
ejpam-3822	36	37	vaccination	vaccination	NOUN
ejpam-3822	36	38	of	of	ADP
ejpam-3822	36	39	susceptibles	susceptible	NOUN
ejpam-3822	36	40	[	[	X
ejpam-3822	36	41	8	8	NUM
ejpam-3822	36	42	]	]	PUNCT
ejpam-3822	36	43	.	.	PUNCT
ejpam-3822	37	1	the	the	DET
ejpam-3822	37	2	human	human	ADJ
ejpam-3822	37	3	population	population	NOUN
ejpam-3822	37	4	is	be	AUX
ejpam-3822	37	5	not	not	PART
ejpam-3822	37	6	assumed	assume	VERB
ejpam-3822	37	7	to	to	PART
ejpam-3822	37	8	be	be	AUX
ejpam-3822	37	9	constant	constant	ADJ
ejpam-3822	37	10	,	,	PUNCT
ejpam-3822	37	11	since	since	SCONJ
ejpam-3822	37	12	birth	birth	NOUN
ejpam-3822	37	13	,	,	PUNCT
ejpam-3822	37	14	immigration	immigration	NOUN
ejpam-3822	37	15	,	,	PUNCT
ejpam-3822	37	16	emigration	emigration	NOUN
ejpam-3822	37	17	and	and	CCONJ
ejpam-3822	37	18	death	death	NOUN
ejpam-3822	37	19	occur	occur	VERB
ejpam-3822	37	20	.	.	PUNCT
ejpam-3822	38	1	assumed	assume	VERB
ejpam-3822	38	2	a	a	DET
ejpam-3822	38	3	constant	constant	ADJ
ejpam-3822	38	4	recruitment	recruitment	NOUN
ejpam-3822	38	5	ρ	ρ	NOUN
ejpam-3822	38	6	out	out	ADP
ejpam-3822	38	7	of	of	ADP
ejpam-3822	38	8	which	which	PRON
ejpam-3822	38	9	(	(	PUNCT
ejpam-3822	38	10	1	1	NUM
ejpam-3822	38	11	−	−	NOUN
ejpam-3822	38	12	ρ)λ	ρ)λ	ADJ
ejpam-3822	38	13	is	be	AUX
ejpam-3822	38	14	into	into	ADP
ejpam-3822	38	15	susceptible	susceptible	ADJ
ejpam-3822	38	16	class	class	NOUN
ejpam-3822	38	17	and	and	CCONJ
ejpam-3822	38	18	ρλ	ρλ	NOUN
ejpam-3822	38	19	is	be	AUX
ejpam-3822	38	20	into	into	ADP
ejpam-3822	38	21	the	the	DET
ejpam-3822	38	22	vaccinated	vaccinated	ADJ
ejpam-3822	38	23	class	class	NOUN
ejpam-3822	38	24	.	.	PUNCT
ejpam-3822	39	1	susceptibles	susceptible	NOUN
ejpam-3822	39	2	are	be	AUX
ejpam-3822	39	3	vaccinated	vaccinate	VERB
ejpam-3822	39	4	at	at	ADP
ejpam-3822	39	5	the	the	DET
ejpam-3822	39	6	rate	rate	NOUN
ejpam-3822	39	7	γ	γ	NOUN
ejpam-3822	39	8	and	and	CCONJ
ejpam-3822	39	9	the	the	DET
ejpam-3822	39	10	vaccine	vaccine	NOUN
ejpam-3822	39	11	efficacy	efficacy	NOUN
ejpam-3822	39	12	which	which	PRON
ejpam-3822	39	13	has	have	AUX
ejpam-3822	39	14	been	be	AUX
ejpam-3822	39	15	shown	show	VERB
ejpam-3822	39	16	to	to	PART
ejpam-3822	39	17	wane	wane	NOUN
ejpam-3822	39	18	is	be	AUX
ejpam-3822	39	19	assumed	assume	VERB
ejpam-3822	39	20	to	to	PART
ejpam-3822	39	21	take	take	VERB
ejpam-3822	39	22	place	place	NOUN
ejpam-3822	39	23	at	at	ADP
ejpam-3822	39	24	the	the	PRON
ejpam-3822	39	25	of	of	ADP
ejpam-3822	39	26	ω	ω	PROPN
ejpam-3822	40	1	[	[	X
ejpam-3822	40	2	6	6	NUM
ejpam-3822	40	3	]	]	PUNCT
ejpam-3822	40	4	.	.	PUNCT
ejpam-3822	41	1	the	the	DET
ejpam-3822	41	2	parameter	parameter	NOUN
ejpam-3822	41	3	0	0	NUM
ejpam-3822	41	4	≤	≤	NUM
ejpam-3822	41	5	1−ε	1−ε	NUM
ejpam-3822	41	6	<	<	SYM
ejpam-3822	41	7	1	1	NUM
ejpam-3822	41	8	models	model	NOUN
ejpam-3822	41	9	the	the	DET
ejpam-3822	41	10	decrease	decrease	NOUN
ejpam-3822	41	11	in	in	ADP
ejpam-3822	41	12	the	the	DET
ejpam-3822	41	13	risk	risk	NOUN
ejpam-3822	41	14	of	of	ADP
ejpam-3822	41	15	infection	infection	NOUN
ejpam-3822	41	16	as	as	ADP
ejpam-3822	41	17	a	a	DET
ejpam-3822	41	18	result	result	NOUN
ejpam-3822	41	19	of	of	ADP
ejpam-3822	41	20	vaccination	vaccination	NOUN
ejpam-3822	41	21	.	.	PUNCT
ejpam-3822	42	1	disease	disease	NOUN
ejpam-3822	42	2	mortality	mortality	NOUN
ejpam-3822	42	3	takes	take	VERB
ejpam-3822	42	4	place	place	NOUN
ejpam-3822	42	5	at	at	ADP
ejpam-3822	42	6	the	the	DET
ejpam-3822	42	7	rate	rate	NOUN
ejpam-3822	42	8	δ	δ	PROPN
ejpam-3822	42	9	and	and	CCONJ
ejpam-3822	42	10	recovery	recovery	NOUN
ejpam-3822	42	11	from	from	ADP
ejpam-3822	42	12	infection	infection	NOUN
ejpam-3822	42	13	takes	take	VERB
ejpam-3822	42	14	place	place	NOUN
ejpam-3822	42	15	at	at	ADP
ejpam-3822	42	16	the	the	DET
ejpam-3822	42	17	rate	rate	NOUN
ejpam-3822	42	18	κ	κ	NOUN
ejpam-3822	42	19	,	,	PUNCT
ejpam-3822	42	20	it	it	PRON
ejpam-3822	42	21	therefore	therefore	ADV
ejpam-3822	42	22	natural	natural	ADJ
ejpam-3822	42	23	that	that	SCONJ
ejpam-3822	42	24	after	after	SCONJ
ejpam-3822	42	25	a	a	DET
ejpam-3822	42	26	single	single	ADJ
ejpam-3822	42	27	natural	natural	ADJ
ejpam-3822	42	28	infection	infection	NOUN
ejpam-3822	42	29	immunity	immunity	NOUN
ejpam-3822	42	30	is	be	AUX
ejpam-3822	42	31	developed	develop	VERB
ejpam-3822	42	32	,	,	PUNCT
ejpam-3822	42	33	subsequent	subsequent	ADJ
ejpam-3822	42	34	infections	infection	NOUN
ejpam-3822	42	35	are	be	AUX
ejpam-3822	42	36	less	less	ADV
ejpam-3822	42	37	severe	severe	ADJ
ejpam-3822	42	38	[	[	X
ejpam-3822	42	39	8	8	NUM
ejpam-3822	42	40	]	]	PUNCT
ejpam-3822	42	41	.	.	PUNCT
ejpam-3822	43	1	the	the	DET
ejpam-3822	43	2	population	population	NOUN
ejpam-3822	43	3	decreases	decrease	VERB
ejpam-3822	43	4	due	due	ADJ
ejpam-3822	43	5	to	to	ADP
ejpam-3822	43	6	natural	natural	ADJ
ejpam-3822	43	7	deaths	death	NOUN
ejpam-3822	43	8	at	at	ADP
ejpam-3822	43	9	a	a	DET
ejpam-3822	43	10	rate	rate	NOUN
ejpam-3822	43	11	µ.	µ.	NOUN
ejpam-3822	43	12	most	most	ADJ
ejpam-3822	43	13	vaccines	vaccine	NOUN
ejpam-3822	43	14	take	take	VERB
ejpam-3822	43	15	time	time	NOUN
ejpam-3822	43	16	in	in	ADP
ejpam-3822	43	17	the	the	DET
ejpam-3822	43	18	body	body	NOUN
ejpam-3822	43	19	to	to	PART
ejpam-3822	43	20	become	become	VERB
ejpam-3822	43	21	effective	effective	ADJ
ejpam-3822	43	22	,	,	PUNCT
ejpam-3822	43	23	this	this	PRON
ejpam-3822	43	24	is	be	AUX
ejpam-3822	43	25	because	because	SCONJ
ejpam-3822	43	26	immunity	immunity	NOUN
ejpam-3822	43	27	has	have	VERB
ejpam-3822	43	28	to	to	PART
ejpam-3822	43	29	be	be	AUX
ejpam-3822	43	30	developed	develop	VERB
ejpam-3822	43	31	to	to	PART
ejpam-3822	43	32	protect	protect	VERB
ejpam-3822	43	33	the	the	DET
ejpam-3822	43	34	body	body	NOUN
ejpam-3822	43	35	against	against	ADP
ejpam-3822	43	36	infection	infection	NOUN
ejpam-3822	43	37	.	.	PUNCT
ejpam-3822	44	1	the	the	DET
ejpam-3822	44	2	time	time	NOUN
ejpam-3822	44	3	the	the	DET
ejpam-3822	44	4	vaccine	vaccine	NOUN
ejpam-3822	44	5	is	be	AUX
ejpam-3822	44	6	administered	administer	VERB
ejpam-3822	44	7	and	and	CCONJ
ejpam-3822	44	8	the	the	DET
ejpam-3822	44	9	time	time	NOUN
ejpam-3822	44	10	it	it	PRON
ejpam-3822	44	11	becomes	become	VERB
ejpam-3822	44	12	effective	effective	ADJ
ejpam-3822	44	13	is	be	AUX
ejpam-3822	44	14	defined	define	VERB
ejpam-3822	44	15	as	as	ADP
ejpam-3822	44	16	time	time	NOUN
ejpam-3822	44	17	delay	delay	NOUN
ejpam-3822	44	18	denoted	denote	VERB
ejpam-3822	44	19	by	by	ADP
ejpam-3822	44	20	τ	τ	PROPN
ejpam-3822	44	21	.	.	PUNCT
ejpam-3822	45	1	these	these	DET
ejpam-3822	45	2	parameter	parameter	NOUN
ejpam-3822	45	3	values	value	NOUN
ejpam-3822	45	4	are	be	AUX
ejpam-3822	45	5	summarized	summarize	VERB
ejpam-3822	45	6	in	in	ADP
ejpam-3822	45	7	table	table	NOUN
ejpam-3822	45	8	1	1	NUM
ejpam-3822	45	9	below	below	ADV
ejpam-3822	45	10	.	.	PUNCT
ejpam-3822	46	1	the	the	DET
ejpam-3822	46	2	flow	flow	NOUN
ejpam-3822	46	3	chart	chart	NOUN
ejpam-3822	46	4	for	for	ADP
ejpam-3822	46	5	the	the	DET
ejpam-3822	46	6	proposed	propose	VERB
ejpam-3822	46	7	model	model	NOUN
ejpam-3822	46	8	is	be	AUX
ejpam-3822	46	9	shown	show	VERB
ejpam-3822	46	10	in	in	ADP
ejpam-3822	46	11	fig.1	fig.1	PROPN
ejpam-3822	46	12	finally	finally	ADV
ejpam-3822	46	13	,	,	PUNCT
ejpam-3822	46	14	from	from	ADP
ejpam-3822	46	15	the	the	DET
ejpam-3822	46	16	above	above	ADJ
ejpam-3822	46	17	definition	definition	NOUN
ejpam-3822	46	18	and	and	CCONJ
ejpam-3822	46	19	assumptions	assumption	NOUN
ejpam-3822	46	20	,	,	PUNCT
ejpam-3822	46	21	the	the	DET
ejpam-3822	46	22	proposed	propose	VERB
ejpam-3822	46	23	mathematical	mathematical	ADJ
ejpam-3822	46	24	model	model	NOUN
ejpam-3822	46	25	and	and	CCONJ
ejpam-3822	46	26	the	the	DET
ejpam-3822	46	27	parameters	parameter	NOUN
ejpam-3822	46	28	are	be	AUX
ejpam-3822	46	29	described	describe	VERB
ejpam-3822	46	30	below	below	ADP
ejpam-3822	46	31	:	:	PUNCT
ejpam-3822	46	32	ds	ds	ADP
ejpam-3822	46	33	dt	dt	NOUN
ejpam-3822	46	34	=	=	SYM
ejpam-3822	46	35	(	(	PUNCT
ejpam-3822	46	36	1−	1−	NUM
ejpam-3822	46	37	ρ)λ−	ρ)λ−	NOUN
ejpam-3822	46	38	βsi	βsi	NOUN
ejpam-3822	46	39	−	−	NOUN
ejpam-3822	46	40	γs	γ	VERB
ejpam-3822	46	41	+	+	X
ejpam-3822	46	42	ωv	ωv	ADP
ejpam-3822	46	43	−	−	PROPN
ejpam-3822	46	44	µs	µs	NOUN
ejpam-3822	46	45	,	,	PUNCT
ejpam-3822	46	46	dv	dv	PROPN
ejpam-3822	46	47	dt	dt	PROPN
ejpam-3822	46	48	=	=	SYM
ejpam-3822	46	49	ρλ	ρλ	PROPN
ejpam-3822	46	50	+	+	CCONJ
ejpam-3822	46	51	γs	γs	X
ejpam-3822	46	52	−	−	PROPN
ejpam-3822	46	53	(	(	PUNCT
ejpam-3822	46	54	1−	1−	NUM
ejpam-3822	46	55	ε)βv	ε)βv	PROPN
ejpam-3822	46	56	(	(	PUNCT
ejpam-3822	46	57	t−	t−	PROPN
ejpam-3822	46	58	τ)i	τ)i	NOUN
ejpam-3822	46	59	−	−	PROPN
ejpam-3822	47	1	(	(	PUNCT
ejpam-3822	47	2	ω	ω	NOUN
ejpam-3822	47	3	+	+	SYM
ejpam-3822	47	4	µ)v	µ)v	ADJ
ejpam-3822	47	5	,	,	PUNCT
ejpam-3822	47	6	di	di	NOUN
ejpam-3822	47	7	dt	dt	NOUN
ejpam-3822	47	8	=	=	NOUN
ejpam-3822	47	9	βsi	βsi	NOUN
ejpam-3822	47	10	+	+	CCONJ
ejpam-3822	47	11	(	(	PUNCT
ejpam-3822	47	12	1−	1−	NUM
ejpam-3822	47	13	ε)βv	ε)βv	PROPN
ejpam-3822	47	14	(	(	PUNCT
ejpam-3822	47	15	t−	t−	PROPN
ejpam-3822	47	16	τ)i	τ)i	NOUN
ejpam-3822	47	17	−	−	PROPN
ejpam-3822	47	18	(	(	PUNCT
ejpam-3822	47	19	δ	δ	PROPN
ejpam-3822	47	20	+	+	CCONJ
ejpam-3822	47	21	κ+	κ+	NOUN
ejpam-3822	47	22	µ)i	µ)i	ADJ
ejpam-3822	47	23	,	,	PUNCT
ejpam-3822	47	24	l.	l.	PROPN
ejpam-3822	47	25	o.	o.	PROPN
ejpam-3822	47	26	onyango	onyango	PROPN
ejpam-3822	47	27	et	et	PROPN
ejpam-3822	47	28	al	al	PROPN
ejpam-3822	47	29	.	.	PUNCT
ejpam-3822	47	30	/	/	SYM
ejpam-3822	47	31	eur	eur	PROPN
ejpam-3822	47	32	.	.	PUNCT
ejpam-3822	48	1	j.	j.	PROPN
ejpam-3822	48	2	pure	pure	PROPN
ejpam-3822	48	3	appl	appl	PROPN
ejpam-3822	48	4	.	.	PROPN
ejpam-3822	48	5	math	math	PROPN
ejpam-3822	48	6	,	,	PUNCT
ejpam-3822	48	7	13	13	NUM
ejpam-3822	48	8	(	(	PUNCT
ejpam-3822	48	9	4	4	NUM
ejpam-3822	48	10	)	)	PUNCT
ejpam-3822	48	11	(	(	PUNCT
ejpam-3822	48	12	2020	2020	NUM
ejpam-3822	48	13	)	)	PUNCT
ejpam-3822	48	14	,	,	PUNCT
ejpam-3822	48	15	840	840	NUM
ejpam-3822	48	16	-	-	SYM
ejpam-3822	48	17	851	851	NUM
ejpam-3822	48	18	842	842	NUM
ejpam-3822	48	19	table	table	NOUN
ejpam-3822	48	20	1	1	NUM
ejpam-3822	48	21	:	:	PUNCT
ejpam-3822	48	22	parameter	parameter	NOUN
ejpam-3822	48	23	values	value	NOUN
ejpam-3822	48	24	parameter	parameter	NOUN
ejpam-3822	48	25	symbol	symbol	NOUN
ejpam-3822	48	26	recruitment	recruitment	NOUN
ejpam-3822	48	27	rate	rate	NOUN
ejpam-3822	48	28	into	into	ADP
ejpam-3822	48	29	susceptible	susceptible	ADJ
ejpam-3822	48	30	(	(	PUNCT
ejpam-3822	48	31	1−	1−	NUM
ejpam-3822	48	32	ρ)λ	ρ)λ	ADJ
ejpam-3822	48	33	recruitment	recruitment	NOUN
ejpam-3822	48	34	rate	rate	NOUN
ejpam-3822	48	35	into	into	ADP
ejpam-3822	48	36	vaccination	vaccination	NOUN
ejpam-3822	48	37	ρλ	ρλ	NOUN
ejpam-3822	48	38	vaccination	vaccination	NOUN
ejpam-3822	48	39	rate	rate	NOUN
ejpam-3822	48	40	of	of	ADP
ejpam-3822	48	41	susceptible	susceptible	ADJ
ejpam-3822	48	42	γ	γ	NOUN
ejpam-3822	48	43	vaccine	vaccine	NOUN
ejpam-3822	48	44	efficacy	efficacy	NOUN
ejpam-3822	48	45	waning	wane	VERB
ejpam-3822	48	46	rate	rate	NOUN
ejpam-3822	48	47	ω	ω	PROPN
ejpam-3822	48	48	expected	expect	VERB
ejpam-3822	48	49	decrease	decrease	NOUN
ejpam-3822	48	50	in	in	ADP
ejpam-3822	48	51	the	the	DET
ejpam-3822	48	52	risk	risk	NOUN
ejpam-3822	48	53	of	of	ADP
ejpam-3822	48	54	infection	infection	NOUN
ejpam-3822	48	55	ε	ε	PROPN
ejpam-3822	48	56	rate	rate	NOUN
ejpam-3822	48	57	of	of	ADP
ejpam-3822	48	58	flow	flow	NOUN
ejpam-3822	48	59	into	into	ADP
ejpam-3822	48	60	the	the	DET
ejpam-3822	48	61	removed	remove	VERB
ejpam-3822	48	62	class	class	NOUN
ejpam-3822	48	63	κ	κ	NOUN
ejpam-3822	48	64	transmission	transmission	NOUN
ejpam-3822	48	65	rate	rate	NOUN
ejpam-3822	48	66	β	β	X
ejpam-3822	48	67	natural	natural	ADJ
ejpam-3822	48	68	death	death	NOUN
ejpam-3822	48	69	rate	rate	NOUN
ejpam-3822	48	70	of	of	ADP
ejpam-3822	48	71	human	human	ADJ
ejpam-3822	48	72	µ	µ	PROPN
ejpam-3822	48	73	rotavirus	rotavirus	NOUN
ejpam-3822	48	74	induced	induce	VERB
ejpam-3822	48	75	deaths	death	NOUN
ejpam-3822	48	76	δ	δ	PROPN
ejpam-3822	48	77	vaccinated	vaccinate	VERB
ejpam-3822	48	78	individual	individual	ADJ
ejpam-3822	48	79	ρ	ρ	PROPN
ejpam-3822	48	80	delay	delay	NOUN
ejpam-3822	48	81	time	time	NOUN
ejpam-3822	48	82	in	in	ADP
ejpam-3822	48	83	vaccination	vaccination	NOUN
ejpam-3822	48	84	τ	τ	X
ejpam-3822	48	85	dr	dr	PROPN
ejpam-3822	48	86	dt	dt	PROPN
ejpam-3822	48	87	=	=	PUNCT
ejpam-3822	48	88	κi	κi	NOUN
ejpam-3822	48	89	−	−	NOUN
ejpam-3822	49	1	µr	µr	ADP
ejpam-3822	49	2	(	(	PUNCT
ejpam-3822	49	3	1	1	X
ejpam-3822	49	4	)	)	PUNCT
ejpam-3822	49	5	we	we	PRON
ejpam-3822	49	6	set	set	VERB
ejpam-3822	49	7	the	the	DET
ejpam-3822	49	8	initial	initial	ADJ
ejpam-3822	49	9	conditions	condition	NOUN
ejpam-3822	49	10	for	for	ADP
ejpam-3822	49	11	system	system	NOUN
ejpam-3822	49	12	(	(	PUNCT
ejpam-3822	49	13	1	1	NUM
ejpam-3822	49	14	)	)	PUNCT
ejpam-3822	49	15	as	as	ADP
ejpam-3822	49	16	s(θ	s(θ	NOUN
ejpam-3822	49	17	)	)	PUNCT
ejpam-3822	49	18	=	=	SYM
ejpam-3822	49	19	φ1(θ	φ1(θ	PROPN
ejpam-3822	49	20	)	)	PUNCT
ejpam-3822	49	21	,	,	PUNCT
ejpam-3822	49	22	v	v	NOUN
ejpam-3822	49	23	(	(	PUNCT
ejpam-3822	49	24	θ	θ	NOUN
ejpam-3822	49	25	)	)	PUNCT
ejpam-3822	49	26	=	=	SYM
ejpam-3822	49	27	φ2(θ	φ2(θ	PROPN
ejpam-3822	49	28	)	)	PUNCT
ejpam-3822	49	29	,	,	PUNCT
ejpam-3822	49	30	i(θ	i(θ	PROPN
ejpam-3822	49	31	)	)	PUNCT
ejpam-3822	49	32	=	=	SYM
ejpam-3822	49	33	φ3(θ	φ3(θ	PROPN
ejpam-3822	49	34	)	)	PUNCT
ejpam-3822	49	35	,	,	PUNCT
ejpam-3822	49	36	r(θ	r(θ	NOUN
ejpam-3822	49	37	)	)	PUNCT
ejpam-3822	49	38	=	=	PUNCT
ejpam-3822	49	39	φ4(θ	φ4(θ	NOUN
ejpam-3822	49	40	)	)	PUNCT
ejpam-3822	49	41	,	,	PUNCT
ejpam-3822	49	42	where	where	SCONJ
ejpam-3822	49	43	φi(θ	φi(θ	NOUN
ejpam-3822	49	44	)	)	PUNCT
ejpam-3822	49	45	≥	≥	NOUN
ejpam-3822	49	46	0	0	NUM
ejpam-3822	49	47	,	,	PUNCT
ejpam-3822	49	48	θ	θ	PROPN
ejpam-3822	49	49	∈	∈	PROPN
ejpam-3822	50	1	[	[	X
ejpam-3822	50	2	−τ	−τ	NOUN
ejpam-3822	50	3	,	,	PUNCT
ejpam-3822	50	4	0	0	NUM
ejpam-3822	50	5	]	]	PUNCT
ejpam-3822	50	6	,	,	PUNCT
ejpam-3822	50	7	φ(0	φ(0	ADJ
ejpam-3822	50	8	)	)	PUNCT
ejpam-3822	50	9	>	>	X
ejpam-3822	50	10	0	0	NUM
ejpam-3822	50	11	,	,	PUNCT
ejpam-3822	50	12	for	for	ADP
ejpam-3822	50	13	i	i	PROPN
ejpam-3822	50	14	=	=	SYM
ejpam-3822	50	15	1	1	NUM
ejpam-3822	50	16	,	,	PUNCT
ejpam-3822	50	17	2	2	NUM
ejpam-3822	50	18	,	,	PUNCT
ejpam-3822	50	19	3	3	NUM
ejpam-3822	50	20	·	·	PUNCT
ejpam-3822	50	21	·	·	PUNCT
ejpam-3822	50	22	·	·	PUNCT
ejpam-3822	50	23	such	such	ADJ
ejpam-3822	50	24	that	that	SCONJ
ejpam-3822	50	25	φ	φ	PROPN
ejpam-3822	50	26	=	=	SYM
ejpam-3822	50	27	(	(	PUNCT
ejpam-3822	50	28	φ1	φ1	PROPN
ejpam-3822	50	29	,	,	PUNCT
ejpam-3822	50	30	φ2	φ2	PROPN
ejpam-3822	50	31	,	,	PUNCT
ejpam-3822	50	32	φ3	φ3	NOUN
ejpam-3822	50	33	,	,	PUNCT
ejpam-3822	50	34	φ4	φ4	NOUN
ejpam-3822	50	35	)	)	PUNCT
ejpam-3822	50	36	are	be	AUX
ejpam-3822	50	37	defined	define	VERB
ejpam-3822	50	38	in	in	ADP
ejpam-3822	50	39	the	the	DET
ejpam-3822	50	40	banach	banach	NOUN
ejpam-3822	50	41	space	space	NOUN
ejpam-3822	50	42	of	of	ADP
ejpam-3822	50	43	continuous	continuous	ADJ
ejpam-3822	50	44	functions	function	NOUN
ejpam-3822	50	45	mapping	mapping	NOUN
ejpam-3822	50	46	in	in	ADP
ejpam-3822	50	47	the	the	DET
ejpam-3822	50	48	interval	interval	NOUN
ejpam-3822	50	49	[	[	X
ejpam-3822	50	50	−τ	−τ	NOUN
ejpam-3822	50	51	,	,	PUNCT
ejpam-3822	50	52	0]⇒	0]⇒	PROPN
ejpam-3822	50	53	r4	r4	NOUN
ejpam-3822	50	54	.	.	PUNCT
ejpam-3822	51	1	3	3	X
ejpam-3822	51	2	.	.	X
ejpam-3822	51	3	model	model	NOUN
ejpam-3822	51	4	analysis	analysis	NOUN
ejpam-3822	51	5	since	since	SCONJ
ejpam-3822	51	6	the	the	DET
ejpam-3822	51	7	model	model	NOUN
ejpam-3822	51	8	has	have	AUX
ejpam-3822	51	9	been	be	AUX
ejpam-3822	51	10	analysed	analyse	VERB
ejpam-3822	51	11	by	by	ADP
ejpam-3822	51	12	onyango	onyango	NOUN
ejpam-3822	51	13	et.al	et.al	PROPN
ejpam-3822	51	14	[	[	X
ejpam-3822	51	15	8	8	NUM
ejpam-3822	51	16	]	]	PUNCT
ejpam-3822	51	17	when	when	SCONJ
ejpam-3822	51	18	delay	delay	NOUN
ejpam-3822	51	19	has	have	AUX
ejpam-3822	51	20	not	not	PART
ejpam-3822	51	21	been	be	AUX
ejpam-3822	51	22	incorporated	incorporate	VERB
ejpam-3822	51	23	,	,	PUNCT
ejpam-3822	51	24	it	it	PRON
ejpam-3822	51	25	is	be	AUX
ejpam-3822	51	26	in	in	ADP
ejpam-3822	51	27	order	order	NOUN
ejpam-3822	51	28	that	that	SCONJ
ejpam-3822	51	29	we	we	PRON
ejpam-3822	51	30	analyse	analyse	VERB
ejpam-3822	51	31	only	only	ADV
ejpam-3822	51	32	the	the	DET
ejpam-3822	51	33	effect	effect	NOUN
ejpam-3822	51	34	of	of	ADP
ejpam-3822	51	35	delay	delay	NOUN
ejpam-3822	51	36	on	on	ADP
ejpam-3822	51	37	both	both	CCONJ
ejpam-3822	51	38	the	the	DET
ejpam-3822	51	39	disease	disease	NOUN
ejpam-3822	51	40	free	free	ADJ
ejpam-3822	51	41	equilibrium	equilibrium	NOUN
ejpam-3822	51	42	and	and	CCONJ
ejpam-3822	51	43	local	local	ADJ
ejpam-3822	51	44	stability	stability	NOUN
ejpam-3822	51	45	of	of	ADP
ejpam-3822	51	46	the	the	DET
ejpam-3822	51	47	endemic	endemic	ADJ
ejpam-3822	51	48	equilibrium	equilibrium	NOUN
ejpam-3822	51	49	.	.	PUNCT
ejpam-3822	52	1	3.1	3.1	NUM
ejpam-3822	52	2	.	.	PUNCT
ejpam-3822	53	1	the	the	DET
ejpam-3822	53	2	global	global	ADJ
ejpam-3822	53	3	stability	stability	NOUN
ejpam-3822	53	4	of	of	ADP
ejpam-3822	53	5	disease	disease	NOUN
ejpam-3822	53	6	free	free	ADJ
ejpam-3822	53	7	equilibrium	equilibrium	NOUN
ejpam-3822	53	8	to	to	PART
ejpam-3822	53	9	prove	prove	VERB
ejpam-3822	53	10	the	the	DET
ejpam-3822	53	11	global	global	ADJ
ejpam-3822	53	12	stability	stability	NOUN
ejpam-3822	53	13	,	,	PUNCT
ejpam-3822	53	14	we	we	PRON
ejpam-3822	53	15	use	use	VERB
ejpam-3822	53	16	rv	rv	PROPN
ejpam-3822	53	17	as	as	SCONJ
ejpam-3822	53	18	derived	derive	VERB
ejpam-3822	53	19	and	and	CCONJ
ejpam-3822	53	20	explained	explain	VERB
ejpam-3822	53	21	by	by	ADP
ejpam-3822	53	22	onyango	onyango	NOUN
ejpam-3822	53	23	et.al	et.al	PROPN
ejpam-3822	53	24	,	,	PUNCT
ejpam-3822	53	25	see	see	VERB
ejpam-3822	53	26	[	[	X
ejpam-3822	53	27	8	8	NUM
ejpam-3822	53	28	]	]	PUNCT
ejpam-3822	53	29	.	.	PUNCT
ejpam-3822	54	1	the	the	DET
ejpam-3822	54	2	global	global	ADJ
ejpam-3822	54	3	stability	stability	NOUN
ejpam-3822	54	4	of	of	ADP
ejpam-3822	54	5	equilibrium	equilibrium	NOUN
ejpam-3822	54	6	is	be	AUX
ejpam-3822	54	7	globally	globally	ADV
ejpam-3822	54	8	asymptotically	asymptotically	ADV
ejpam-3822	54	9	stable	stable	ADJ
ejpam-3822	54	10	if	if	SCONJ
ejpam-3822	54	11	rv	rv	PROPN
ejpam-3822	54	12	≤	≤	ADV
ejpam-3822	54	13	1	1	NUM
ejpam-3822	54	14	.	.	PUNCT
ejpam-3822	55	1	we	we	PRON
ejpam-3822	55	2	use	use	VERB
ejpam-3822	55	3	the	the	DET
ejpam-3822	55	4	technique	technique	NOUN
ejpam-3822	55	5	by	by	ADP
ejpam-3822	55	6	castillo	castillo	PROPN
ejpam-3822	55	7	chavez	chavez	PROPN
ejpam-3822	56	1	[	[	X
ejpam-3822	56	2	4	4	NUM
ejpam-3822	56	3	]	]	PUNCT
ejpam-3822	56	4	.	.	PUNCT
ejpam-3822	57	1	we	we	PRON
ejpam-3822	57	2	write	write	VERB
ejpam-3822	57	3	system	system	NOUN
ejpam-3822	57	4	(	(	PUNCT
ejpam-3822	57	5	1	1	NUM
ejpam-3822	57	6	)	)	PUNCT
ejpam-3822	57	7	in	in	ADP
ejpam-3822	57	8	the	the	DET
ejpam-3822	57	9	form	form	NOUN
ejpam-3822	57	10	;	;	PUNCT
ejpam-3822	57	11	dx	dx	PROPN
ejpam-3822	57	12	dt	dt	PROPN
ejpam-3822	58	1	=	=	SYM
ejpam-3822	58	2	h(x	h(x	PROPN
ejpam-3822	58	3	,	,	PUNCT
ejpam-3822	58	4	z	z	NOUN
ejpam-3822	58	5	)	)	PUNCT
ejpam-3822	58	6	dz	dz	NOUN
ejpam-3822	58	7	dt	dt	NOUN
ejpam-3822	59	1	=	=	SYM
ejpam-3822	59	2	g(x	g(x	PROPN
ejpam-3822	59	3	,	,	PUNCT
ejpam-3822	59	4	z	z	NOUN
ejpam-3822	59	5	)	)	PUNCT
ejpam-3822	59	6	,	,	PUNCT
ejpam-3822	59	7	g(x	g(x	NOUN
ejpam-3822	59	8	,	,	PUNCT
ejpam-3822	59	9	0	0	NUM
ejpam-3822	59	10	)	)	PUNCT
ejpam-3822	59	11	=	=	SYM
ejpam-3822	59	12	0	0	NUM
ejpam-3822	59	13	where	where	SCONJ
ejpam-3822	59	14	x	x	PUNCT
ejpam-3822	59	15	∈	∈	PROPN
ejpam-3822	59	16	r2	r2	NOUN
ejpam-3822	59	17	denotes	denote	NOUN
ejpam-3822	59	18	uninfected	uninfected	ADJ
ejpam-3822	59	19	compartments	compartment	NOUN
ejpam-3822	59	20	(	(	PUNCT
ejpam-3822	59	21	s	s	X
ejpam-3822	59	22	,	,	PUNCT
ejpam-3822	59	23	v	v	NOUN
ejpam-3822	59	24	)	)	PUNCT
ejpam-3822	59	25	and	and	CCONJ
ejpam-3822	59	26	z	z	NOUN
ejpam-3822	59	27	∈	∈	PROPN
ejpam-3822	59	28	r1	r1	NOUN
ejpam-3822	59	29	denotes	denote	VERB
ejpam-3822	59	30	infected	infect	VERB
ejpam-3822	59	31	compartment	compartment	NOUN
ejpam-3822	59	32	(	(	PUNCT
ejpam-3822	59	33	i	i	NOUN
ejpam-3822	59	34	)	)	PUNCT
ejpam-3822	59	35	.	.	PUNCT
ejpam-3822	60	1	the	the	DET
ejpam-3822	60	2	disease	disease	NOUN
ejpam-3822	60	3	free	free	ADJ
ejpam-3822	60	4	equilibrium	equilibrium	NOUN
ejpam-3822	60	5	is	be	AUX
ejpam-3822	60	6	now	now	ADV
ejpam-3822	60	7	denoted	denote	VERB
ejpam-3822	60	8	as	as	ADP
ejpam-3822	60	9	e0	e0	PROPN
ejpam-3822	60	10	1	1	NUM
ejpam-3822	60	11	=	=	SYM
ejpam-3822	60	12	(	(	PUNCT
ejpam-3822	60	13	x0	x0	PROPN
ejpam-3822	60	14	,	,	PUNCT
ejpam-3822	60	15	0	0	NUM
ejpam-3822	60	16	)	)	PUNCT
ejpam-3822	60	17	,	,	PUNCT
ejpam-3822	60	18	x0	x0	PROPN
ejpam-3822	60	19	=	=	PRON
ejpam-3822	60	20	(	(	PUNCT
ejpam-3822	60	21	ωλ+(1−ρ)µλ	ωλ+(1−ρ)µλ	NUM
ejpam-3822	60	22	µ(ω+γ+µ	µ(ω+γ+µ	ADJ
ejpam-3822	60	23	)	)	PUNCT
ejpam-3822	60	24	,	,	PUNCT
ejpam-3822	60	25	(	(	PUNCT
ejpam-3822	60	26	γ+µρ)λ	γ+µρ)λ	NOUN
ejpam-3822	60	27	µ(µ+ω+γ	µ(µ+ω+γ	NOUN
ejpam-3822	60	28	)	)	PUNCT
ejpam-3822	60	29	)	)	PUNCT
ejpam-3822	61	1	the	the	DET
ejpam-3822	61	2	technique	technique	NOUN
ejpam-3822	61	3	stipulates	stipulate	VERB
ejpam-3822	61	4	that	that	SCONJ
ejpam-3822	61	5	the	the	DET
ejpam-3822	61	6	following	follow	VERB
ejpam-3822	61	7	conditions	condition	NOUN
ejpam-3822	61	8	h1	h1	VERB
ejpam-3822	61	9	and	and	CCONJ
ejpam-3822	61	10	h2	h2	PROPN
ejpam-3822	61	11	must	must	AUX
ejpam-3822	61	12	be	be	AUX
ejpam-3822	61	13	met	meet	VERB
ejpam-3822	61	14	to	to	PART
ejpam-3822	61	15	guarantee	guarantee	VERB
ejpam-3822	61	16	global	global	ADJ
ejpam-3822	61	17	asymptotically	asymptotically	ADJ
ejpam-3822	61	18	stability	stability	NOUN
ejpam-3822	61	19	:	:	PUNCT
ejpam-3822	61	20	h1	h1	X
ejpam-3822	61	21	:	:	PUNCT
ejpam-3822	61	22	for	for	ADP
ejpam-3822	61	23	dx	dx	PROPN
ejpam-3822	61	24	dt	dt	PROPN
ejpam-3822	62	1	=	=	SYM
ejpam-3822	62	2	h(x	h(x	PROPN
ejpam-3822	62	3	,	,	PUNCT
ejpam-3822	62	4	0	0	NUM
ejpam-3822	62	5	)	)	PUNCT
ejpam-3822	63	1	,	,	PUNCT
ejpam-3822	63	2	x0	x0	PROPN
ejpam-3822	63	3	is	be	AUX
ejpam-3822	63	4	globally	globally	ADV
ejpam-3822	63	5	asymptotically	asymptotically	ADV
ejpam-3822	63	6	stable	stable	ADJ
ejpam-3822	63	7	.	.	PUNCT
ejpam-3822	64	1	h2	h2	NOUN
ejpam-3822	64	2	:	:	PUNCT
ejpam-3822	65	1	g(x	g(x	NOUN
ejpam-3822	65	2	,	,	PUNCT
ejpam-3822	65	3	z	z	NOUN
ejpam-3822	65	4	)	)	PUNCT
ejpam-3822	65	5	=	=	SYM
ejpam-3822	65	6	pz	pz	NOUN
ejpam-3822	65	7	−	−	NOUN
ejpam-3822	65	8	ĝ(x	ĝ(x	NOUN
ejpam-3822	65	9	,	,	PUNCT
ejpam-3822	65	10	z	z	NOUN
ejpam-3822	65	11	)	)	PUNCT
ejpam-3822	65	12	,	,	PUNCT
ejpam-3822	65	13	ĝ(x	ĝ(x	NOUN
ejpam-3822	65	14	,	,	PUNCT
ejpam-3822	65	15	z	z	NOUN
ejpam-3822	65	16	)	)	PUNCT
ejpam-3822	65	17	≥	≥	NOUN
ejpam-3822	65	18	0	0	NUM
ejpam-3822	65	19	for	for	ADP
ejpam-3822	65	20	(	(	PUNCT
ejpam-3822	65	21	x	x	NOUN
ejpam-3822	65	22	,	,	PUNCT
ejpam-3822	65	23	z	z	NOUN
ejpam-3822	65	24	)	)	PUNCT
ejpam-3822	65	25	∈	∈	PROPN
ejpam-3822	65	26	ω	ω	PROPN
ejpam-3822	65	27	,	,	PUNCT
ejpam-3822	65	28	l.	l.	PROPN
ejpam-3822	65	29	o.	o.	PROPN
ejpam-3822	65	30	onyango	onyango	PROPN
ejpam-3822	65	31	et	et	PROPN
ejpam-3822	65	32	al	al	PROPN
ejpam-3822	65	33	.	.	PUNCT
ejpam-3822	65	34	/	/	SYM
ejpam-3822	65	35	eur	eur	PROPN
ejpam-3822	65	36	.	.	PUNCT
ejpam-3822	66	1	j.	j.	PROPN
ejpam-3822	66	2	pure	pure	PROPN
ejpam-3822	66	3	appl	appl	PROPN
ejpam-3822	66	4	.	.	PROPN
ejpam-3822	66	5	math	math	PROPN
ejpam-3822	66	6	,	,	PUNCT
ejpam-3822	66	7	13	13	NUM
ejpam-3822	66	8	(	(	PUNCT
ejpam-3822	66	9	4	4	NUM
ejpam-3822	66	10	)	)	PUNCT
ejpam-3822	66	11	(	(	PUNCT
ejpam-3822	66	12	2020	2020	NUM
ejpam-3822	66	13	)	)	PUNCT
ejpam-3822	66	14	,	,	PUNCT
ejpam-3822	66	15	840	840	NUM
ejpam-3822	66	16	-	-	SYM
ejpam-3822	66	17	851	851	NUM
ejpam-3822	66	18	843	843	NUM
ejpam-3822	66	19	figure	figure	NOUN
ejpam-3822	66	20	1	1	NUM
ejpam-3822	66	21	:	:	PUNCT
ejpam-3822	66	22	model	model	NOUN
ejpam-3822	66	23	flow	flow	NOUN
ejpam-3822	66	24	chart	chart	NOUN
ejpam-3822	66	25	where	where	SCONJ
ejpam-3822	66	26	x0	x0	PROPN
ejpam-3822	66	27	is	be	AUX
ejpam-3822	66	28	the	the	DET
ejpam-3822	66	29	disease	disease	NOUN
ejpam-3822	66	30	free	free	ADJ
ejpam-3822	66	31	equilibrium	equilibrium	NOUN
ejpam-3822	66	32	,	,	PUNCT
ejpam-3822	66	33	p	p	NOUN
ejpam-3822	66	34	=	=	NOUN
ejpam-3822	66	35	dzg(x	dzg(x	PROPN
ejpam-3822	66	36	,	,	PUNCT
ejpam-3822	66	37	0	0	NUM
ejpam-3822	66	38	)	)	PUNCT
ejpam-3822	66	39	is	be	AUX
ejpam-3822	66	40	an	an	DET
ejpam-3822	66	41	m	m	NOUN
ejpam-3822	66	42	-	-	NOUN
ejpam-3822	66	43	matrix	matrix	NOUN
ejpam-3822	66	44	(	(	PUNCT
ejpam-3822	66	45	the	the	DET
ejpam-3822	66	46	offdiagonal	offdiagonal	ADJ
ejpam-3822	66	47	element	element	NOUN
ejpam-3822	66	48	of	of	ADP
ejpam-3822	66	49	p	p	PROPN
ejpam-3822	66	50	are	be	AUX
ejpam-3822	66	51	non	non	ADJ
ejpam-3822	66	52	-	-	ADJ
ejpam-3822	66	53	negative	negative	ADJ
ejpam-3822	66	54	)	)	PUNCT
ejpam-3822	66	55	and	and	CCONJ
ejpam-3822	66	56	ω	ω	PROPN
ejpam-3822	66	57	is	be	AUX
ejpam-3822	66	58	the	the	DET
ejpam-3822	66	59	region	region	NOUN
ejpam-3822	66	60	where	where	SCONJ
ejpam-3822	66	61	the	the	DET
ejpam-3822	66	62	model	model	NOUN
ejpam-3822	66	63	(	(	PUNCT
ejpam-3822	66	64	1	1	X
ejpam-3822	66	65	)	)	PUNCT
ejpam-3822	66	66	is	be	AUX
ejpam-3822	66	67	biologically	biologically	ADV
ejpam-3822	66	68	feasible	feasible	ADJ
ejpam-3822	66	69	.	.	PUNCT
ejpam-3822	67	1	theorem	theorem	NOUN
ejpam-3822	67	2	1	1	NUM
ejpam-3822	67	3	.	.	PUNCT
ejpam-3822	68	1	the	the	DET
ejpam-3822	68	2	disease	disease	NOUN
ejpam-3822	68	3	free	free	VERB
ejpam-3822	68	4	equilibrium	equilibrium	NOUN
ejpam-3822	68	5	e0	e0	PROPN
ejpam-3822	68	6	of	of	ADP
ejpam-3822	68	7	system	system	NOUN
ejpam-3822	68	8	(	(	PUNCT
ejpam-3822	68	9	1	1	X
ejpam-3822	68	10	)	)	PUNCT
ejpam-3822	68	11	is	be	AUX
ejpam-3822	68	12	globally	globally	ADV
ejpam-3822	68	13	stable	stable	ADJ
ejpam-3822	68	14	if	if	SCONJ
ejpam-3822	68	15	rv	rv	PROPN
ejpam-3822	68	16	<	<	X
ejpam-3822	68	17	1	1	NUM
ejpam-3822	68	18	and	and	CCONJ
ejpam-3822	68	19	unstable	unstable	ADJ
ejpam-3822	68	20	whenever	whenever	SCONJ
ejpam-3822	68	21	rv	rv	PROPN
ejpam-3822	68	22	>	>	X
ejpam-3822	68	23	1	1	NUM
ejpam-3822	68	24	,	,	PUNCT
ejpam-3822	68	25	provided	provide	VERB
ejpam-3822	68	26	that	that	SCONJ
ejpam-3822	68	27	the	the	DET
ejpam-3822	68	28	conditions	condition	NOUN
ejpam-3822	68	29	h1	h1	VERB
ejpam-3822	68	30	and	and	CCONJ
ejpam-3822	68	31	h2	h2	PROPN
ejpam-3822	68	32	above	above	ADV
ejpam-3822	68	33	are	be	AUX
ejpam-3822	68	34	satisfied	satisfied	ADJ
ejpam-3822	68	35	.	.	PUNCT
ejpam-3822	69	1	proof	proof	NOUN
ejpam-3822	69	2	.	.	PUNCT
ejpam-3822	70	1	from	from	ADP
ejpam-3822	70	2	system	system	NOUN
ejpam-3822	70	3	(	(	PUNCT
ejpam-3822	70	4	1	1	NUM
ejpam-3822	70	5	)	)	PUNCT
ejpam-3822	70	6	,	,	PUNCT
ejpam-3822	70	7	we	we	PRON
ejpam-3822	70	8	can	can	AUX
ejpam-3822	70	9	clearly	clearly	ADV
ejpam-3822	70	10	see	see	VERB
ejpam-3822	70	11	that	that	SCONJ
ejpam-3822	70	12	h(x	h(x	PROPN
ejpam-3822	70	13	,	,	PUNCT
ejpam-3822	70	14	0	0	NUM
ejpam-3822	70	15	)	)	PUNCT
ejpam-3822	70	16	=	=	PRON
ejpam-3822	70	17	(	(	PUNCT
ejpam-3822	70	18	(	(	PUNCT
ejpam-3822	70	19	1−	1−	NUM
ejpam-3822	70	20	ρ)λ−	ρ)λ−	NOUN
ejpam-3822	70	21	(	(	PUNCT
ejpam-3822	70	22	γ	γ	NOUN
ejpam-3822	70	23	+	+	NOUN
ejpam-3822	70	24	µ)s	µ)s	NOUN
ejpam-3822	70	25	+	+	CCONJ
ejpam-3822	70	26	ωv	ωv	PRON
ejpam-3822	70	27	ρλ	ρλ	NOUN
ejpam-3822	70	28	+	+	CCONJ
ejpam-3822	70	29	γs	γs	AUX
ejpam-3822	70	30	−	−	PROPN
ejpam-3822	70	31	(	(	PUNCT
ejpam-3822	70	32	ω	ω	NOUN
ejpam-3822	70	33	+	+	NOUN
ejpam-3822	70	34	µ)v	µ)v	ADJ
ejpam-3822	70	35	)	)	PUNCT
ejpam-3822	70	36	and	and	CCONJ
ejpam-3822	70	37	g(x	g(x	NOUN
ejpam-3822	70	38	,	,	PUNCT
ejpam-3822	70	39	z	z	NOUN
ejpam-3822	70	40	)	)	PUNCT
ejpam-3822	70	41	=	=	SYM
ejpam-3822	70	42	pz	pz	NOUN
ejpam-3822	70	43	−	−	NOUN
ejpam-3822	70	44	ĝ(x	ĝ(x	NOUN
ejpam-3822	70	45	,	,	PUNCT
ejpam-3822	70	46	z	z	NOUN
ejpam-3822	70	47	)	)	PUNCT
ejpam-3822	70	48	differentiating	differentiate	VERB
ejpam-3822	70	49	the	the	DET
ejpam-3822	70	50	right	right	ADJ
ejpam-3822	70	51	hand	hand	NOUN
ejpam-3822	70	52	side	side	NOUN
ejpam-3822	70	53	of	of	ADP
ejpam-3822	70	54	equation	equation	NOUN
ejpam-3822	70	55	3	3	NUM
ejpam-3822	70	56	of	of	ADP
ejpam-3822	70	57	system	system	NOUN
ejpam-3822	70	58	(	(	PUNCT
ejpam-3822	70	59	1	1	NUM
ejpam-3822	70	60	)	)	PUNCT
ejpam-3822	70	61	with	with	ADP
ejpam-3822	70	62	respect	respect	NOUN
ejpam-3822	70	63	to	to	ADP
ejpam-3822	70	64	i	i	PRON
ejpam-3822	70	65	,	,	PUNCT
ejpam-3822	70	66	we	we	PRON
ejpam-3822	70	67	obtain	obtain	VERB
ejpam-3822	70	68	p	p	NOUN
ejpam-3822	70	69	=	=	PUNCT
ejpam-3822	70	70	βs	βs	X
ejpam-3822	71	1	+	+	CCONJ
ejpam-3822	71	2	(	(	PUNCT
ejpam-3822	71	3	1−	1−	NUM
ejpam-3822	71	4	ε)βv	ε)βv	PROPN
ejpam-3822	71	5	(	(	PUNCT
ejpam-3822	71	6	t−	t−	PROPN
ejpam-3822	71	7	τ)−	τ)−	PROPN
ejpam-3822	71	8	(	(	PUNCT
ejpam-3822	71	9	δ	δ	PROPN
ejpam-3822	71	10	+	+	CCONJ
ejpam-3822	71	11	κ+	κ+	PROPN
ejpam-3822	71	12	µ	µ	NUM
ejpam-3822	71	13	)	)	PUNCT
ejpam-3822	71	14	.	.	PUNCT
ejpam-3822	72	1	therefore	therefore	ADV
ejpam-3822	72	2	pz	pz	NOUN
ejpam-3822	72	3	=	=	NOUN
ejpam-3822	72	4	βsi	βsi	NOUN
ejpam-3822	72	5	+	+	CCONJ
ejpam-3822	72	6	(	(	PUNCT
ejpam-3822	72	7	1−	1−	NUM
ejpam-3822	72	8	ε)βv	ε)βv	PROPN
ejpam-3822	72	9	(	(	PUNCT
ejpam-3822	72	10	t−	t−	PROPN
ejpam-3822	72	11	τ)i	τ)i	NOUN
ejpam-3822	72	12	−	−	PROPN
ejpam-3822	72	13	(	(	PUNCT
ejpam-3822	72	14	δ	δ	PROPN
ejpam-3822	72	15	+	+	CCONJ
ejpam-3822	72	16	κ+	κ+	PROPN
ejpam-3822	72	17	µ)i	µ)i	ADJ
ejpam-3822	72	18	and	and	CCONJ
ejpam-3822	72	19	ĝz	ĝz	NOUN
ejpam-3822	72	20	=	=	SYM
ejpam-3822	72	21	pz	pz	NOUN
ejpam-3822	72	22	−gz	−gz	NOUN
ejpam-3822	72	23	=	=	NOUN
ejpam-3822	72	24	βsi	βsi	NOUN
ejpam-3822	72	25	+	+	CCONJ
ejpam-3822	72	26	(	(	PUNCT
ejpam-3822	72	27	1−	1−	NUM
ejpam-3822	72	28	ε)βv	ε)βv	PROPN
ejpam-3822	72	29	(	(	PUNCT
ejpam-3822	72	30	t−	t−	PROPN
ejpam-3822	72	31	τ)i	τ)i	NOUN
ejpam-3822	72	32	−	−	PROPN
ejpam-3822	72	33	(	(	PUNCT
ejpam-3822	72	34	δ	δ	PROPN
ejpam-3822	72	35	+	+	CCONJ
ejpam-3822	72	36	κ+	κ+	PROPN
ejpam-3822	72	37	µ)i	µ)i	ADJ
ejpam-3822	72	38	−	−	PROPN
ejpam-3822	72	39	(	(	PUNCT
ejpam-3822	72	40	βsi	βsi	NOUN
ejpam-3822	72	41	+	+	CCONJ
ejpam-3822	72	42	(	(	PUNCT
ejpam-3822	72	43	1−	1−	NUM
ejpam-3822	72	44	ε)βv	ε)βv	PROPN
ejpam-3822	72	45	(	(	PUNCT
ejpam-3822	72	46	t−	t−	PROPN
ejpam-3822	72	47	τ)i	τ)i	NOUN
ejpam-3822	72	48	−	−	PROPN
ejpam-3822	72	49	(	(	PUNCT
ejpam-3822	72	50	δ	δ	PROPN
ejpam-3822	72	51	+	+	CCONJ
ejpam-3822	72	52	κ+	κ+	NOUN
ejpam-3822	72	53	µ)i	µ)i	ADJ
ejpam-3822	72	54	)	)	PUNCT
ejpam-3822	73	1	=	=	SYM
ejpam-3822	73	2	0	0	PUNCT
ejpam-3822	74	1	since	since	SCONJ
ejpam-3822	74	2	conditions	condition	NOUN
ejpam-3822	74	3	h1	h1	PROPN
ejpam-3822	74	4	and	and	CCONJ
ejpam-3822	74	5	h2	h2	NOUN
ejpam-3822	74	6	are	be	AUX
ejpam-3822	74	7	satisfied	satisfied	ADJ
ejpam-3822	74	8	,	,	PUNCT
ejpam-3822	74	9	the	the	DET
ejpam-3822	74	10	disease	disease	NOUN
ejpam-3822	74	11	free	free	ADJ
ejpam-3822	74	12	equilibrium	equilibrium	NOUN
ejpam-3822	74	13	is	be	AUX
ejpam-3822	74	14	therefore	therefore	ADV
ejpam-3822	74	15	globally	globally	ADV
ejpam-3822	74	16	asymptotically	asymptotically	ADV
ejpam-3822	74	17	stable	stable	ADJ
ejpam-3822	74	18	when	when	SCONJ
ejpam-3822	74	19	rv	rv	PROPN
ejpam-3822	74	20	<	<	X
ejpam-3822	74	21	1	1	NUM
ejpam-3822	74	22	and	and	CCONJ
ejpam-3822	74	23	unstable	unstable	ADJ
ejpam-3822	74	24	whenever	whenever	SCONJ
ejpam-3822	74	25	rv	rv	PROPN
ejpam-3822	74	26	>	>	X
ejpam-3822	74	27	1	1	X
ejpam-3822	74	28	.	.	PUNCT
ejpam-3822	74	29	l.	l.	PROPN
ejpam-3822	74	30	o.	o.	PROPN
ejpam-3822	74	31	onyango	onyango	PROPN
ejpam-3822	75	1	et	et	PROPN
ejpam-3822	75	2	al	al	PROPN
ejpam-3822	75	3	.	.	PUNCT
ejpam-3822	75	4	/	/	SYM
ejpam-3822	75	5	eur	eur	PROPN
ejpam-3822	75	6	.	.	PUNCT
ejpam-3822	76	1	j.	j.	PROPN
ejpam-3822	76	2	pure	pure	PROPN
ejpam-3822	76	3	appl	appl	PROPN
ejpam-3822	76	4	.	.	PROPN
ejpam-3822	76	5	math	math	PROPN
ejpam-3822	76	6	,	,	PUNCT
ejpam-3822	76	7	13	13	NUM
ejpam-3822	76	8	(	(	PUNCT
ejpam-3822	76	9	4	4	NUM
ejpam-3822	76	10	)	)	PUNCT
ejpam-3822	76	11	(	(	PUNCT
ejpam-3822	76	12	2020	2020	NUM
ejpam-3822	76	13	)	)	PUNCT
ejpam-3822	76	14	,	,	PUNCT
ejpam-3822	76	15	840	840	NUM
ejpam-3822	76	16	-	-	SYM
ejpam-3822	76	17	851	851	NUM
ejpam-3822	76	18	844	844	NUM
ejpam-3822	76	19	3.2	3.2	NUM
ejpam-3822	76	20	.	.	PUNCT
ejpam-3822	77	1	the	the	DET
ejpam-3822	77	2	local	local	ADJ
ejpam-3822	77	3	stability	stability	NOUN
ejpam-3822	77	4	of	of	ADP
ejpam-3822	77	5	endemic	endemic	ADJ
ejpam-3822	77	6	equilibrium	equilibrium	NOUN
ejpam-3822	77	7	(	(	PUNCT
ejpam-3822	77	8	e.e	e.e	PROPN
ejpam-3822	77	9	.	.	PROPN
ejpam-3822	77	10	)	)	PUNCT
ejpam-3822	78	1	the	the	DET
ejpam-3822	78	2	jacobian	jacobian	ADJ
ejpam-3822	78	3	matrix	matrix	NOUN
ejpam-3822	78	4	at	at	ADP
ejpam-3822	78	5	the	the	DET
ejpam-3822	78	6	endemic	endemic	ADJ
ejpam-3822	78	7	equilibrium	equilibrium	NOUN
ejpam-3822	78	8	e∗	e∗	NOUN
ejpam-3822	78	9	can	can	AUX
ejpam-3822	78	10	be	be	AUX
ejpam-3822	78	11	expressed	express	VERB
ejpam-3822	78	12	as	as	ADP
ejpam-3822	78	13	j	j	PROPN
ejpam-3822	78	14	=	=	SYM
ejpam-3822	78	15	a1	a1	X
ejpam-3822	78	16	a2	a2	PROPN
ejpam-3822	78	17	a3	a3	PROPN
ejpam-3822	78	18	a4	a4	PROPN
ejpam-3822	78	19	a5e	a5e	NOUN
ejpam-3822	78	20	−λτ	−λτ	PROPN
ejpam-3822	79	1	+	+	CCONJ
ejpam-3822	79	2	a6	a6	PROPN
ejpam-3822	79	3	a7	a7	PROPN
ejpam-3822	79	4	a8	a8	PROPN
ejpam-3822	79	5	a5e	a5e	NOUN
ejpam-3822	79	6	−λτ	−λτ	PROPN
ejpam-3822	79	7	a9	a9	PROPN
ejpam-3822	79	8			PROPN
ejpam-3822	79	9	where	where	SCONJ
ejpam-3822	79	10	,	,	PUNCT
ejpam-3822	79	11	a1	a1	NOUN
ejpam-3822	79	12	=	=	SYM
ejpam-3822	79	13	−(βi∗	−(βi∗	NOUN
ejpam-3822	79	14	+	+	CCONJ
ejpam-3822	79	15	γ	γ	PROPN
ejpam-3822	79	16	+	+	X
ejpam-3822	79	17	µ	µ	X
ejpam-3822	79	18	)	)	PUNCT
ejpam-3822	79	19	a2	a2	PROPN
ejpam-3822	79	20	=	=	SYM
ejpam-3822	79	21	ω	ω	PROPN
ejpam-3822	79	22	a3	a3	NOUN
ejpam-3822	79	23	=	=	SYM
ejpam-3822	79	24	−βs∗	−βs∗	X
ejpam-3822	79	25	a4	a4	NOUN
ejpam-3822	79	26	=	=	SYM
ejpam-3822	79	27	γ	γ	X
ejpam-3822	79	28	a5	a5	NOUN
ejpam-3822	79	29	=	=	PUNCT
ejpam-3822	79	30	−(1−	−(1−	ADP
ejpam-3822	79	31	ε)βi∗	ε)βi∗	NOUN
ejpam-3822	79	32	a6	a6	NOUN
ejpam-3822	79	33	=	=	SYM
ejpam-3822	79	34	−(ω	−(ω	PROPN
ejpam-3822	79	35	+	+	CCONJ
ejpam-3822	79	36	µ	µ	X
ejpam-3822	79	37	)	)	PUNCT
ejpam-3822	79	38	a7	a7	NOUN
ejpam-3822	79	39	=	=	PUNCT
ejpam-3822	79	40	(	(	PUNCT
ejpam-3822	79	41	1−	1−	NUM
ejpam-3822	79	42	ε)βv	ε)βv	PROPN
ejpam-3822	79	43	∗(t−	∗(t−	PROPN
ejpam-3822	79	44	τ	τ	PROPN
ejpam-3822	79	45	)	)	PUNCT
ejpam-3822	79	46	a8	a8	PROPN
ejpam-3822	79	47	=	=	SYM
ejpam-3822	79	48	βi∗	βi∗	NOUN
ejpam-3822	79	49	a9	a9	NOUN
ejpam-3822	79	50	=	=	PUNCT
ejpam-3822	79	51	βs∗	βs∗	X
ejpam-3822	80	1	+	+	CCONJ
ejpam-3822	80	2	(	(	PUNCT
ejpam-3822	80	3	1−	1−	NUM
ejpam-3822	80	4	ε)v	ε)v	X
ejpam-3822	80	5	∗(t−	∗(t−	PROPN
ejpam-3822	81	1	τ)−	τ)−	PROPN
ejpam-3822	81	2	(	(	PUNCT
ejpam-3822	81	3	δ	δ	PROPN
ejpam-3822	81	4	+	+	CCONJ
ejpam-3822	81	5	κ+	κ+	PROPN
ejpam-3822	81	6	µ	µ	NUM
ejpam-3822	81	7	)	)	PUNCT
ejpam-3822	81	8	to	to	PART
ejpam-3822	81	9	find	find	VERB
ejpam-3822	81	10	the	the	DET
ejpam-3822	81	11	characteristic	characteristic	ADJ
ejpam-3822	81	12	equation	equation	NOUN
ejpam-3822	81	13	of	of	ADP
ejpam-3822	81	14	the	the	DET
ejpam-3822	81	15	linearized	linearize	VERB
ejpam-3822	81	16	system	system	NOUN
ejpam-3822	81	17	(	(	PUNCT
ejpam-3822	81	18	1	1	NUM
ejpam-3822	81	19	)	)	PUNCT
ejpam-3822	81	20	at	at	ADP
ejpam-3822	81	21	steady	steady	ADJ
ejpam-3822	81	22	states	state	NOUN
ejpam-3822	81	23	,	,	PUNCT
ejpam-3822	81	24	we	we	PRON
ejpam-3822	81	25	compute	compute	VERB
ejpam-3822	81	26	the	the	DET
ejpam-3822	81	27	eigenvalues	eigenvalue	NOUN
ejpam-3822	81	28	of	of	ADP
ejpam-3822	81	29	the	the	DET
ejpam-3822	81	30	following	follow	VERB
ejpam-3822	81	31	matrix∣∣∣∣∣∣	matrix∣∣∣∣∣∣	NOUN
ejpam-3822	81	32	λ−	λ−	PROPN
ejpam-3822	81	33	a1	a1	NOUN
ejpam-3822	81	34	a2	a2	PROPN
ejpam-3822	81	35	a3	a3	PROPN
ejpam-3822	81	36	a4	a4	PROPN
ejpam-3822	82	1	λ−	λ−	PROPN
ejpam-3822	83	1	[	[	X
ejpam-3822	83	2	a5e	a5e	NOUN
ejpam-3822	83	3	−λτ	−λτ	PROPN
ejpam-3822	83	4	+	+	CCONJ
ejpam-3822	83	5	a6	a6	X
ejpam-3822	83	6	]	]	X
ejpam-3822	83	7	a7	a7	PROPN
ejpam-3822	83	8	a8	a8	PROPN
ejpam-3822	83	9	a5e	a5e	NOUN
ejpam-3822	83	10	−λτ	−λτ	NOUN
ejpam-3822	83	11	λ−	λ−	PROPN
ejpam-3822	83	12	a9	a9	PROPN
ejpam-3822	83	13	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3822	84	1	=	=	SYM
ejpam-3822	84	2	0	0	PROPN
ejpam-3822	85	1	this	this	PRON
ejpam-3822	85	2	gives	give	VERB
ejpam-3822	85	3	λ3	λ3	PROPN
ejpam-3822	85	4	+	+	PROPN
ejpam-3822	85	5	m2λ	m2λ	PROPN
ejpam-3822	85	6	2	2	NUM
ejpam-3822	85	7	+	+	NOUN
ejpam-3822	85	8	m1λ+m0	m1λ+m0	NOUN
ejpam-3822	85	9	+	+	CCONJ
ejpam-3822	85	10	(	(	PUNCT
ejpam-3822	85	11	n2λ	n2λ	PROPN
ejpam-3822	85	12	2	2	NUM
ejpam-3822	85	13	+	+	NOUN
ejpam-3822	85	14	n1λ+n0)e−λτ	n1λ+n0)e−λτ	NOUN
ejpam-3822	85	15	=	=	SYM
ejpam-3822	85	16	0	0	NUM
ejpam-3822	85	17	,	,	PUNCT
ejpam-3822	85	18	(	(	PUNCT
ejpam-3822	85	19	2	2	X
ejpam-3822	85	20	)	)	PUNCT
ejpam-3822	85	21	where	where	SCONJ
ejpam-3822	85	22	m2	m2	PROPN
ejpam-3822	85	23	=	=	PROPN
ejpam-3822	85	24	−(a1	−(a1	X
ejpam-3822	85	25	+	+	X
ejpam-3822	85	26	a6	a6	NOUN
ejpam-3822	85	27	+	+	CCONJ
ejpam-3822	85	28	a9	a9	NOUN
ejpam-3822	85	29	)	)	PUNCT
ejpam-3822	85	30	m1	m1	NOUN
ejpam-3822	85	31	=	=	SYM
ejpam-3822	85	32	(	(	PUNCT
ejpam-3822	85	33	a6a9	a6a9	X
ejpam-3822	85	34	+	+	NUM
ejpam-3822	85	35	a1a6	a1a6	NOUN
ejpam-3822	86	1	+	+	NUM
ejpam-3822	86	2	a1a9	a1a9	ADJ
ejpam-3822	86	3	−	−	NOUN
ejpam-3822	86	4	a2a4	a2a4	ADP
ejpam-3822	86	5	−	−	DET
ejpam-3822	86	6	a3a8	a3a8	NOUN
ejpam-3822	86	7	)	)	PUNCT
ejpam-3822	86	8	m0	m0	NOUN
ejpam-3822	86	9	=	=	PUNCT
ejpam-3822	86	10	(	(	PUNCT
ejpam-3822	86	11	−a1a6a9	−a1a6a9	X
ejpam-3822	86	12	−	−	PROPN
ejpam-3822	86	13	a2a4a9	a2a4a9	PROPN
ejpam-3822	86	14	−	−	PROPN
ejpam-3822	86	15	a2a7a8	a2a7a8	PROPN
ejpam-3822	86	16	+	+	CCONJ
ejpam-3822	86	17	a3a6a8	a3a6a8	ADJ
ejpam-3822	86	18	)	)	PUNCT
ejpam-3822	86	19	n2	n2	NOUN
ejpam-3822	86	20	=	=	PUNCT
ejpam-3822	86	21	−a5	−a5	PROPN
ejpam-3822	86	22	n1	n1	NOUN
ejpam-3822	86	23	=	=	SYM
ejpam-3822	86	24	(	(	PUNCT
ejpam-3822	86	25	a5a9	a5a9	INTJ
ejpam-3822	86	26	−	−	PROPN
ejpam-3822	86	27	a5a7	a5a7	NOUN
ejpam-3822	86	28	+	+	CCONJ
ejpam-3822	86	29	a1a5	a1a5	NOUN
ejpam-3822	86	30	)	)	PUNCT
ejpam-3822	86	31	n0	n0	NOUN
ejpam-3822	86	32	=	=	SYM
ejpam-3822	86	33	(	(	PUNCT
ejpam-3822	86	34	a1a5a7	a1a5a7	PROPN
ejpam-3822	86	35	−	−	PROPN
ejpam-3822	86	36	a1a5a9	a1a5a9	NOUN
ejpam-3822	86	37	+	+	CCONJ
ejpam-3822	86	38	a3a4a5	a3a4a5	ADP
ejpam-3822	86	39	+	+	CCONJ
ejpam-3822	86	40	a3a5a8	a3a5a8	NOUN
ejpam-3822	86	41	)	)	PUNCT
ejpam-3822	86	42	.	.	PUNCT
ejpam-3822	87	1	multiplying	multiply	VERB
ejpam-3822	87	2	both	both	DET
ejpam-3822	87	3	sides	side	NOUN
ejpam-3822	87	4	of	of	ADP
ejpam-3822	87	5	equation	equation	NOUN
ejpam-3822	87	6	(	(	PUNCT
ejpam-3822	87	7	2	2	NUM
ejpam-3822	87	8	)	)	PUNCT
ejpam-3822	87	9	by	by	ADP
ejpam-3822	87	10	eλτ	eλτ	NOUN
ejpam-3822	87	11	,	,	PUNCT
ejpam-3822	87	12	we	we	PRON
ejpam-3822	87	13	obtain	obtain	VERB
ejpam-3822	87	14	(	(	PUNCT
ejpam-3822	87	15	λ3	λ3	PROPN
ejpam-3822	87	16	+	+	PROPN
ejpam-3822	87	17	m2λ	m2λ	PROPN
ejpam-3822	87	18	2	2	NUM
ejpam-3822	87	19	+	+	NOUN
ejpam-3822	87	20	m1λ+m0)eλτ	m1λ+m0)eλτ	ADJ
ejpam-3822	87	21	+	+	ADJ
ejpam-3822	87	22	n2λ	n2λ	PROPN
ejpam-3822	87	23	2	2	NUM
ejpam-3822	87	24	+	+	NOUN
ejpam-3822	87	25	n1λ+n0	n1λ+n0	NOUN
ejpam-3822	87	26	=	=	SYM
ejpam-3822	87	27	0	0	PUNCT
ejpam-3822	87	28	(	(	PUNCT
ejpam-3822	87	29	3	3	NUM
ejpam-3822	87	30	)	)	PUNCT
ejpam-3822	87	31	when	when	SCONJ
ejpam-3822	87	32	τ	τ	PROPN
ejpam-3822	87	33	=	=	SYM
ejpam-3822	87	34	0	0	NUM
ejpam-3822	87	35	,	,	PUNCT
ejpam-3822	87	36	equation	equation	NOUN
ejpam-3822	87	37	(	(	PUNCT
ejpam-3822	87	38	3	3	X
ejpam-3822	87	39	)	)	PUNCT
ejpam-3822	87	40	can	can	AUX
ejpam-3822	87	41	be	be	AUX
ejpam-3822	87	42	expressed	express	VERB
ejpam-3822	87	43	as	as	ADP
ejpam-3822	87	44	λ3	λ3	PROPN
ejpam-3822	87	45	+	+	PROPN
ejpam-3822	87	46	m02λ	m02λ	PROPN
ejpam-3822	87	47	2	2	NUM
ejpam-3822	87	48	+	+	NOUN
ejpam-3822	87	49	m01λ+m00	m01λ+m00	NOUN
ejpam-3822	87	50	=	=	SYM
ejpam-3822	87	51	0	0	NUM
ejpam-3822	87	52	,	,	PUNCT
ejpam-3822	87	53	(	(	PUNCT
ejpam-3822	87	54	4	4	X
ejpam-3822	87	55	)	)	PUNCT
ejpam-3822	87	56	l.	l.	PROPN
ejpam-3822	87	57	o.	o.	PROPN
ejpam-3822	87	58	onyango	onyango	PROPN
ejpam-3822	87	59	et	et	PROPN
ejpam-3822	87	60	al	al	PROPN
ejpam-3822	87	61	.	.	PUNCT
ejpam-3822	87	62	/	/	SYM
ejpam-3822	87	63	eur	eur	PROPN
ejpam-3822	87	64	.	.	PUNCT
ejpam-3822	88	1	j.	j.	PROPN
ejpam-3822	88	2	pure	pure	PROPN
ejpam-3822	88	3	appl	appl	PROPN
ejpam-3822	88	4	.	.	PROPN
ejpam-3822	88	5	math	math	PROPN
ejpam-3822	88	6	,	,	PUNCT
ejpam-3822	88	7	13	13	NUM
ejpam-3822	88	8	(	(	PUNCT
ejpam-3822	88	9	4	4	NUM
ejpam-3822	88	10	)	)	PUNCT
ejpam-3822	88	11	(	(	PUNCT
ejpam-3822	88	12	2020	2020	NUM
ejpam-3822	88	13	)	)	PUNCT
ejpam-3822	88	14	,	,	PUNCT
ejpam-3822	88	15	840	840	NUM
ejpam-3822	88	16	-	-	SYM
ejpam-3822	88	17	851	851	NUM
ejpam-3822	88	18	845	845	NUM
ejpam-3822	88	19	where	where	SCONJ
ejpam-3822	88	20	m02	m02	PROPN
ejpam-3822	88	21	=(	=(	NOUN
ejpam-3822	88	22	m2	m2	PROPN
ejpam-3822	88	23	+	+	PROPN
ejpam-3822	88	24	n2	n2	ADJ
ejpam-3822	88	25	)	)	PUNCT
ejpam-3822	88	26	m01	m01	PROPN
ejpam-3822	88	27	=(	=(	PROPN
ejpam-3822	88	28	m1	m1	PROPN
ejpam-3822	88	29	+	+	PROPN
ejpam-3822	88	30	n1	n1	ADJ
ejpam-3822	88	31	)	)	PUNCT
ejpam-3822	88	32	m00	m00	NOUN
ejpam-3822	88	33	=(	=(	PROPN
ejpam-3822	88	34	m0	m0	PROPN
ejpam-3822	88	35	+	+	PROPN
ejpam-3822	88	36	n0	n0	NUM
ejpam-3822	88	37	)	)	PUNCT
ejpam-3822	88	38	.	.	PUNCT
ejpam-3822	89	1	based	base	VERB
ejpam-3822	89	2	on	on	ADP
ejpam-3822	89	3	routh	routh	PROPN
ejpam-3822	89	4	hurwitz	hurwitz	PROPN
ejpam-3822	89	5	theorem	theorem	PROPN
ejpam-3822	89	6	[	[	X
ejpam-3822	89	7	10	10	NUM
ejpam-3822	89	8	]	]	PUNCT
ejpam-3822	89	9	,	,	PUNCT
ejpam-3822	89	10	it	it	PRON
ejpam-3822	89	11	can	can	AUX
ejpam-3822	89	12	be	be	AUX
ejpam-3822	89	13	concluded	conclude	VERB
ejpam-3822	89	14	that	that	SCONJ
ejpam-3822	89	15	all	all	DET
ejpam-3822	89	16	the	the	DET
ejpam-3822	89	17	roots	root	NOUN
ejpam-3822	89	18	of	of	ADP
ejpam-3822	89	19	equation	equation	NOUN
ejpam-3822	89	20	(	(	PUNCT
ejpam-3822	89	21	4	4	X
ejpam-3822	89	22	)	)	PUNCT
ejpam-3822	89	23	are	be	AUX
ejpam-3822	89	24	in	in	ADP
ejpam-3822	89	25	the	the	DET
ejpam-3822	89	26	open	open	ADJ
ejpam-3822	89	27	left	left	ADJ
ejpam-3822	89	28	half	half	DET
ejpam-3822	89	29	plane	plane	NOUN
ejpam-3822	89	30	if	if	SCONJ
ejpam-3822	89	31	and	and	CCONJ
ejpam-3822	89	32	only	only	ADV
ejpam-3822	89	33	if	if	SCONJ
ejpam-3822	89	34	the	the	DET
ejpam-3822	89	35	following	follow	VERB
ejpam-3822	89	36	condition	condition	NOUN
ejpam-3822	89	37	holds	hold	VERB
ejpam-3822	89	38	:	:	PUNCT
ejpam-3822	89	39	c1	c1	NOUN
ejpam-3822	89	40	:	:	PUNCT
ejpam-3822	89	41	m02	m02	PROPN
ejpam-3822	89	42	>	>	X
ejpam-3822	90	1	0,m00	0,m00	PUNCT
ejpam-3822	90	2	>	>	X
ejpam-3822	90	3	0	0	PUNCT
ejpam-3822	90	4	and	and	CCONJ
ejpam-3822	90	5	m02m01	m02m01	ADJ
ejpam-3822	90	6	>	>	X
ejpam-3822	90	7	m00	m00	NOUN
ejpam-3822	90	8	.	.	PUNCT
ejpam-3822	91	1	if	if	SCONJ
ejpam-3822	91	2	τ	τ	PROPN
ejpam-3822	91	3	=	=	SYM
ejpam-3822	91	4	0	0	PUNCT
ejpam-3822	91	5	and	and	CCONJ
ejpam-3822	91	6	c1	c1	PROPN
ejpam-3822	91	7	holds	hold	VERB
ejpam-3822	91	8	then	then	ADV
ejpam-3822	91	9	equation	equation	NOUN
ejpam-3822	91	10	(	(	PUNCT
ejpam-3822	91	11	2	2	X
ejpam-3822	91	12	)	)	PUNCT
ejpam-3822	91	13	is	be	AUX
ejpam-3822	91	14	locally	locally	ADV
ejpam-3822	91	15	asymptotically	asymptotically	ADV
ejpam-3822	91	16	stable	stable	ADJ
ejpam-3822	91	17	.	.	PUNCT
ejpam-3822	92	1	for	for	ADP
ejpam-3822	92	2	τ	τ	PROPN
ejpam-3822	92	3	>	>	X
ejpam-3822	92	4	0	0	PROPN
ejpam-3822	92	5	,	,	PUNCT
ejpam-3822	92	6	we	we	PRON
ejpam-3822	92	7	let	let	VERB
ejpam-3822	92	8	λ	λ	X
ejpam-3822	92	9	=	=	VERB
ejpam-3822	92	10	iw	iw	PROPN
ejpam-3822	92	11	,	,	PUNCT
ejpam-3822	92	12	for	for	ADP
ejpam-3822	92	13	w	w	PROPN
ejpam-3822	92	14	>	>	X
ejpam-3822	92	15	0	0	PUNCT
ejpam-3822	92	16	be	be	AUX
ejpam-3822	92	17	a	a	DET
ejpam-3822	92	18	root	root	NOUN
ejpam-3822	92	19	of	of	ADP
ejpam-3822	92	20	equation	equation	NOUN
ejpam-3822	92	21	(	(	PUNCT
ejpam-3822	92	22	3	3	NUM
ejpam-3822	92	23	)	)	PUNCT
ejpam-3822	92	24	.	.	PUNCT
ejpam-3822	93	1	substituting	substitute	VERB
ejpam-3822	93	2	λ	λ	PROPN
ejpam-3822	93	3	=	=	SYM
ejpam-3822	93	4	iw	iw	PROPN
ejpam-3822	93	5	into	into	ADP
ejpam-3822	93	6	(	(	PUNCT
ejpam-3822	93	7	2	2	X
ejpam-3822	93	8	)	)	PUNCT
ejpam-3822	93	9	we	we	PRON
ejpam-3822	93	10	obtain	obtain	VERB
ejpam-3822	93	11	(	(	PUNCT
ejpam-3822	93	12	−iw3	−iw3	NOUN
ejpam-3822	93	13	−m2w	−m2w	PROPN
ejpam-3822	93	14	2	2	NUM
ejpam-3822	93	15	+	+	CCONJ
ejpam-3822	93	16	im1w	im1w	ADJ
ejpam-3822	93	17	+	+	NOUN
ejpam-3822	93	18	m0)((cos(wτ	m0)((cos(wτ	NOUN
ejpam-3822	93	19	)	)	PUNCT
ejpam-3822	94	1	+	+	CCONJ
ejpam-3822	94	2	isin(wτ))−n2w	isin(wτ))−n2w	NOUN
ejpam-3822	94	3	2	2	NUM
ejpam-3822	94	4	+	+	CCONJ
ejpam-3822	94	5	in1w	in1w	PROPN
ejpam-3822	94	6	+	+	PROPN
ejpam-3822	94	7	n0	n0	X
ejpam-3822	94	8	=	=	SYM
ejpam-3822	94	9	0	0	NUM
ejpam-3822	94	10	(	(	PUNCT
ejpam-3822	94	11	5	5	NUM
ejpam-3822	94	12	)	)	PUNCT
ejpam-3822	94	13	on	on	ADP
ejpam-3822	94	14	separating	separate	VERB
ejpam-3822	94	15	the	the	DET
ejpam-3822	94	16	real	real	ADJ
ejpam-3822	94	17	and	and	CCONJ
ejpam-3822	94	18	imaginary	imaginary	ADJ
ejpam-3822	94	19	parts	part	NOUN
ejpam-3822	94	20	of	of	ADP
ejpam-3822	94	21	equation	equation	NOUN
ejpam-3822	94	22	(	(	PUNCT
ejpam-3822	94	23	5	5	X
ejpam-3822	94	24	)	)	PUNCT
ejpam-3822	94	25	gives	give	VERB
ejpam-3822	94	26	p1(w)cos(wτ)−	p1(w)cos(wτ)−	PROPN
ejpam-3822	94	27	p2(w)sin(wτ	p2(w)sin(wτ	NOUN
ejpam-3822	94	28	)	)	PUNCT
ejpam-3822	95	1	=	=	SYM
ejpam-3822	95	2	p3(w	p3(w	X
ejpam-3822	95	3	)	)	PUNCT
ejpam-3822	95	4	p4(w)sin(wτ	p4(w)sin(wτ	NOUN
ejpam-3822	95	5	)	)	PUNCT
ejpam-3822	96	1	+	+	NUM
ejpam-3822	96	2	p5(w)cos(wτ	p5(w)cos(wτ	NOUN
ejpam-3822	96	3	)	)	PUNCT
ejpam-3822	97	1	=	=	SYM
ejpam-3822	97	2	p6(w	p6(w	ADJ
ejpam-3822	97	3	)	)	PUNCT
ejpam-3822	97	4	,	,	PUNCT
ejpam-3822	97	5	(	(	PUNCT
ejpam-3822	97	6	6	6	NUM
ejpam-3822	97	7	)	)	PUNCT
ejpam-3822	97	8	where	where	SCONJ
ejpam-3822	97	9	p1(w	p1(w	NOUN
ejpam-3822	97	10	)	)	PUNCT
ejpam-3822	97	11	=	=	SYM
ejpam-3822	97	12	−m2w	−m2w	PROPN
ejpam-3822	97	13	2	2	NUM
ejpam-3822	98	1	+	+	NOUN
ejpam-3822	98	2	m0	m0	NOUN
ejpam-3822	98	3	p2(w	p2(w	NUM
ejpam-3822	98	4	)	)	PUNCT
ejpam-3822	98	5	=	=	SYM
ejpam-3822	99	1	m1w	m1w	PROPN
ejpam-3822	99	2	−	−	PROPN
ejpam-3822	99	3	w3	w3	PROPN
ejpam-3822	99	4	p3(w	p3(w	PROPN
ejpam-3822	99	5	)	)	PUNCT
ejpam-3822	99	6	=	=	SYM
ejpam-3822	99	7	n2w	n2w	PROPN
ejpam-3822	99	8	2	2	NUM
ejpam-3822	99	9	−n0	−n0	NOUN
ejpam-3822	99	10	p4(w	p4(w	NOUN
ejpam-3822	99	11	)	)	PUNCT
ejpam-3822	99	12	=	=	SYM
ejpam-3822	99	13	m0	m0	NOUN
ejpam-3822	99	14	−m2w	−m2w	PROPN
ejpam-3822	99	15	2	2	NUM
ejpam-3822	99	16	p5(w	p5(w	NOUN
ejpam-3822	99	17	)	)	PUNCT
ejpam-3822	99	18	=	=	SYM
ejpam-3822	99	19	m1w	m1w	PROPN
ejpam-3822	99	20	−	−	PROPN
ejpam-3822	99	21	w3	w3	PROPN
ejpam-3822	99	22	p6(w	p6(w	PROPN
ejpam-3822	99	23	)	)	PUNCT
ejpam-3822	99	24	=	=	SYM
ejpam-3822	99	25	−n1w	−n1w	PROPN
ejpam-3822	99	26	solving	solve	VERB
ejpam-3822	99	27	equation	equation	NOUN
ejpam-3822	99	28	(	(	PUNCT
ejpam-3822	99	29	6	6	NUM
ejpam-3822	99	30	)	)	PUNCT
ejpam-3822	99	31	,	,	PUNCT
ejpam-3822	99	32	we	we	PRON
ejpam-3822	99	33	obtain	obtain	VERB
ejpam-3822	99	34	cos(wτ	cos(wτ	NOUN
ejpam-3822	99	35	)	)	PUNCT
ejpam-3822	99	36	=	=	SYM
ejpam-3822	99	37	p01(w	p01(w	ADJ
ejpam-3822	99	38	)	)	PUNCT
ejpam-3822	99	39	p00(w	p00(w	NOUN
ejpam-3822	99	40	)	)	PUNCT
ejpam-3822	99	41	sin(wτ	sin(wτ	NOUN
ejpam-3822	99	42	)	)	PUNCT
ejpam-3822	99	43	=	=	SYM
ejpam-3822	99	44	p02(w	p02(w	NOUN
ejpam-3822	99	45	)	)	PUNCT
ejpam-3822	99	46	p00(w	p00(w	NOUN
ejpam-3822	99	47	)	)	PUNCT
ejpam-3822	99	48	,	,	PUNCT
ejpam-3822	99	49	(	(	PUNCT
ejpam-3822	99	50	7	7	X
ejpam-3822	99	51	)	)	PUNCT
ejpam-3822	99	52	where	where	SCONJ
ejpam-3822	99	53	p00	p00	NOUN
ejpam-3822	99	54	=	=	SYM
ejpam-3822	99	55	m2w	m2w	PROPN
ejpam-3822	99	56	4	4	NUM
ejpam-3822	99	57	−	−	NOUN
ejpam-3822	99	58	(	(	PUNCT
ejpam-3822	99	59	2m0m2	2m0m2	PROPN
ejpam-3822	99	60	−m2	−m2	NOUN
ejpam-3822	99	61	1	1	NUM
ejpam-3822	99	62	)	)	PUNCT
ejpam-3822	99	63	w2	w2	NOUN
ejpam-3822	99	64	−	−	PROPN
ejpam-3822	99	65	w6	w6	PROPN
ejpam-3822	99	66	+	+	PROPN
ejpam-3822	99	67	m0	m0	PROPN
ejpam-3822	99	68	+	+	CCONJ
ejpam-3822	99	69	2m1w	2m1w	ADJ
ejpam-3822	99	70	4	4	NUM
ejpam-3822	99	71	p01	p01	NOUN
ejpam-3822	99	72	=	=	SYM
ejpam-3822	99	73	(	(	PUNCT
ejpam-3822	99	74	m0n2	m0n2	PROPN
ejpam-3822	99	75	+	+	PROPN
ejpam-3822	99	76	n0m2	n0m2	NOUN
ejpam-3822	99	77	−m1n1)w2	−m1n1)w2	ADJ
ejpam-3822	99	78	−	−	PROPN
ejpam-3822	99	79	(	(	PUNCT
ejpam-3822	99	80	m2n2	m2n2	VERB
ejpam-3822	99	81	−n1)w4	−n1)w4	PROPN
ejpam-3822	99	82	−n0m0	−n0m0	PROPN
ejpam-3822	99	83	p02	p02	X
ejpam-3822	99	84	=	=	SYM
ejpam-3822	99	85	(	(	PUNCT
ejpam-3822	99	86	m1n2	m1n2	NOUN
ejpam-3822	99	87	−n0)w3	−n0)w3	NOUN
ejpam-3822	99	88	−n2w	−n2w	X
ejpam-3822	99	89	5	5	NUM
ejpam-3822	99	90	−n0m1w	−n0m1w	ADJ
ejpam-3822	99	91	squaring	squaring	NOUN
ejpam-3822	99	92	and	and	CCONJ
ejpam-3822	99	93	adding	add	VERB
ejpam-3822	99	94	the	the	DET
ejpam-3822	99	95	two	two	NUM
ejpam-3822	99	96	equations	equation	NOUN
ejpam-3822	99	97	in	in	ADP
ejpam-3822	99	98	equation	equation	NOUN
ejpam-3822	99	99	(	(	PUNCT
ejpam-3822	99	100	7	7	NUM
ejpam-3822	99	101	)	)	PUNCT
ejpam-3822	99	102	,	,	PUNCT
ejpam-3822	99	103	we	we	PRON
ejpam-3822	99	104	get	get	VERB
ejpam-3822	99	105	p2	p2	NOUN
ejpam-3822	99	106	01(w	01(w	NUM
ejpam-3822	99	107	)	)	PUNCT
ejpam-3822	100	1	+	+	CCONJ
ejpam-3822	100	2	p2	p2	X
ejpam-3822	100	3	02(w)−	02(w)−	NUM
ejpam-3822	100	4	p2	p2	X
ejpam-3822	100	5	00(w	00(w	NUM
ejpam-3822	100	6	)	)	PUNCT
ejpam-3822	101	1	=	=	SYM
ejpam-3822	101	2	0	0	PUNCT
ejpam-3822	102	1	(	(	PUNCT
ejpam-3822	102	2	8)	8)	NUM
ejpam-3822	102	3	l.	l.	PROPN
ejpam-3822	102	4	o.	o.	PROPN
ejpam-3822	102	5	onyango	onyango	PROPN
ejpam-3822	102	6	et	et	PROPN
ejpam-3822	102	7	al	al	PROPN
ejpam-3822	102	8	.	.	PUNCT
ejpam-3822	102	9	/	/	SYM
ejpam-3822	102	10	eur	eur	PROPN
ejpam-3822	102	11	.	.	PUNCT
ejpam-3822	103	1	j.	j.	PROPN
ejpam-3822	103	2	pure	pure	PROPN
ejpam-3822	103	3	appl	appl	PROPN
ejpam-3822	103	4	.	.	PROPN
ejpam-3822	103	5	math	math	PROPN
ejpam-3822	103	6	,	,	PUNCT
ejpam-3822	103	7	13	13	NUM
ejpam-3822	103	8	(	(	PUNCT
ejpam-3822	103	9	4	4	NUM
ejpam-3822	103	10	)	)	PUNCT
ejpam-3822	103	11	(	(	PUNCT
ejpam-3822	103	12	2020	2020	NUM
ejpam-3822	103	13	)	)	PUNCT
ejpam-3822	103	14	,	,	PUNCT
ejpam-3822	103	15	840	840	NUM
ejpam-3822	103	16	-	-	SYM
ejpam-3822	103	17	851	851	NUM
ejpam-3822	103	18	846	846	NUM
ejpam-3822	103	19	suppose	suppose	VERB
ejpam-3822	103	20	that	that	SCONJ
ejpam-3822	103	21	c2	c2	PROPN
ejpam-3822	103	22	:	:	PUNCT
ejpam-3822	103	23	equation	equation	NOUN
ejpam-3822	103	24	(	(	PUNCT
ejpam-3822	103	25	8)	8)	NUM
ejpam-3822	103	26	has	have	AUX
ejpam-3822	103	27	at	at	ADV
ejpam-3822	103	28	least	least	ADV
ejpam-3822	103	29	one	one	NUM
ejpam-3822	103	30	positive	positive	ADJ
ejpam-3822	103	31	root	root	NOUN
ejpam-3822	103	32	,	,	PUNCT
ejpam-3822	103	33	w0	w0	PROPN
ejpam-3822	103	34	,	,	PUNCT
ejpam-3822	103	35	then	then	ADV
ejpam-3822	103	36	equation	equation	NOUN
ejpam-3822	103	37	(	(	PUNCT
ejpam-3822	103	38	4	4	X
ejpam-3822	103	39	)	)	PUNCT
ejpam-3822	103	40	will	will	AUX
ejpam-3822	103	41	definitely	definitely	ADV
ejpam-3822	103	42	have	have	VERB
ejpam-3822	103	43	pure	pure	ADJ
ejpam-3822	103	44	imaginary	imaginary	ADJ
ejpam-3822	103	45	roots	root	NOUN
ejpam-3822	103	46	±iw0	±iw0	NOUN
ejpam-3822	103	47	.	.	PUNCT
ejpam-3822	104	1	for	for	ADP
ejpam-3822	104	2	w0	w0	PROPN
ejpam-3822	104	3	we	we	PRON
ejpam-3822	104	4	obtain	obtain	VERB
ejpam-3822	104	5	the	the	DET
ejpam-3822	104	6	critical	critical	ADJ
ejpam-3822	104	7	value	value	NOUN
ejpam-3822	104	8	of	of	ADP
ejpam-3822	104	9	time	time	NOUN
ejpam-3822	104	10	delay	delay	NOUN
ejpam-3822	104	11	as	as	SCONJ
ejpam-3822	104	12	shown	show	VERB
ejpam-3822	104	13	below	below	ADP
ejpam-3822	104	14	τ0	τ0	NOUN
ejpam-3822	104	15	=	=	SYM
ejpam-3822	104	16	1	1	NUM
ejpam-3822	104	17	w0	w0	PROPN
ejpam-3822	104	18	arccos	arccos	X
ejpam-3822	104	19	{	{	PUNCT
ejpam-3822	104	20	p01(w0	p01(w0	NOUN
ejpam-3822	104	21	)	)	PUNCT
ejpam-3822	104	22	p00(w0	p00(w0	PROPN
ejpam-3822	104	23	)	)	PUNCT
ejpam-3822	104	24	}	}	PUNCT
ejpam-3822	104	25	(	(	PUNCT
ejpam-3822	104	26	9	9	X
ejpam-3822	104	27	)	)	PUNCT
ejpam-3822	104	28	differentiating	differentiate	VERB
ejpam-3822	104	29	equation	equation	NOUN
ejpam-3822	104	30	(	(	PUNCT
ejpam-3822	104	31	3	3	NUM
ejpam-3822	104	32	)	)	PUNCT
ejpam-3822	104	33	implicitly	implicitly	ADV
ejpam-3822	104	34	with	with	ADP
ejpam-3822	104	35	respect	respect	NOUN
ejpam-3822	104	36	to	to	ADP
ejpam-3822	104	37	τ	τ	PROPN
ejpam-3822	104	38	we	we	PRON
ejpam-3822	104	39	obtain	obtain	VERB
ejpam-3822	104	40	(	(	PUNCT
ejpam-3822	104	41	3λ2	3λ2	NUM
ejpam-3822	104	42	+	+	CCONJ
ejpam-3822	104	43	2m2λ+m1	2m2λ+m1	NUM
ejpam-3822	104	44	)	)	PUNCT
ejpam-3822	104	45	eλτ	eλτ	ADP
ejpam-3822	104	46	dλ	dλ	PROPN
ejpam-3822	104	47	dτ	dτ	PROPN
ejpam-3822	104	48	+	+	CCONJ
ejpam-3822	104	49	(	(	PUNCT
ejpam-3822	104	50	λ+	λ+	PUNCT
ejpam-3822	104	51	τ	τ	PROPN
ejpam-3822	104	52	dλ	dλ	PROPN
ejpam-3822	104	53	dτ	dτ	PROPN
ejpam-3822	104	54	)	)	PUNCT
ejpam-3822	104	55	(	(	PUNCT
ejpam-3822	104	56	λ3	λ3	PROPN
ejpam-3822	104	57	+	+	PROPN
ejpam-3822	104	58	m2λ	m2λ	PROPN
ejpam-3822	104	59	2	2	NUM
ejpam-3822	104	60	+	+	NOUN
ejpam-3822	104	61	m1λ+m0	m1λ+m0	NOUN
ejpam-3822	104	62	)	)	PUNCT
ejpam-3822	104	63	eλτ+(2n2λ+n1	eλτ+(2n2λ+n1	PROPN
ejpam-3822	104	64	)	)	PUNCT
ejpam-3822	104	65	dλ	dλ	NOUN
ejpam-3822	104	66	dτ	dτ	NOUN
ejpam-3822	104	67	=	=	NOUN
ejpam-3822	104	68	0	0	PROPN
ejpam-3822	104	69	,	,	PUNCT
ejpam-3822	104	70	(	(	PUNCT
ejpam-3822	104	71	10	10	NUM
ejpam-3822	104	72	)	)	PUNCT
ejpam-3822	104	73	which	which	PRON
ejpam-3822	104	74	can	can	AUX
ejpam-3822	104	75	be	be	AUX
ejpam-3822	104	76	arranged	arrange	VERB
ejpam-3822	104	77	in	in	ADP
ejpam-3822	104	78	the	the	DET
ejpam-3822	104	79	form	form	NOUN
ejpam-3822	104	80	of	of	ADP
ejpam-3822	104	81	(	(	PUNCT
ejpam-3822	104	82	dλ	dλ	INTJ
ejpam-3822	104	83	dτ	dτ	INTJ
ejpam-3822	104	84	)	)	PUNCT
ejpam-3822	104	85	−1	−1	NOUN
ejpam-3822	104	86	=	=	SYM
ejpam-3822	104	87	q1(λ	q1(λ	PROPN
ejpam-3822	104	88	)	)	PUNCT
ejpam-3822	104	89	q2(λ	q2(λ	NOUN
ejpam-3822	104	90	)	)	PUNCT
ejpam-3822	104	91	−	−	PROPN
ejpam-3822	105	1	τ	τ	PROPN
ejpam-3822	105	2	λ	λ	PROPN
ejpam-3822	105	3	,	,	PUNCT
ejpam-3822	105	4	(	(	PUNCT
ejpam-3822	105	5	11	11	NUM
ejpam-3822	105	6	)	)	PUNCT
ejpam-3822	105	7	where	where	SCONJ
ejpam-3822	105	8	q1	q1	NOUN
ejpam-3822	105	9	=	=	PUNCT
ejpam-3822	105	10	(	(	PUNCT
ejpam-3822	105	11	3λ2	3λ2	NUM
ejpam-3822	105	12	+	+	CCONJ
ejpam-3822	105	13	2m2λ+m1	2m2λ+m1	NUM
ejpam-3822	105	14	)	)	PUNCT
ejpam-3822	105	15	eλτ	eλτ	ADV
ejpam-3822	105	16	+	+	CCONJ
ejpam-3822	105	17	2n2λ+n1	2n2λ+n1	NUM
ejpam-3822	105	18	q2	q2	NOUN
ejpam-3822	105	19	=	=	SYM
ejpam-3822	105	20	λ	λ	PROPN
ejpam-3822	105	21	(	(	PUNCT
ejpam-3822	105	22	λ3	λ3	PROPN
ejpam-3822	105	23	+	+	PROPN
ejpam-3822	105	24	m2λ	m2λ	PROPN
ejpam-3822	105	25	2	2	NUM
ejpam-3822	105	26	+	+	NOUN
ejpam-3822	105	27	m1λ+m0	m1λ+m0	NOUN
ejpam-3822	105	28	)	)	PUNCT
ejpam-3822	105	29	eλτ	eλτ	ADV
ejpam-3822	105	30	taking	take	VERB
ejpam-3822	105	31	real	real	ADJ
ejpam-3822	105	32	component	component	NOUN
ejpam-3822	105	33	of	of	ADP
ejpam-3822	105	34	(	(	PUNCT
ejpam-3822	105	35	dλ	dλ	PROPN
ejpam-3822	105	36	dτ	dτ	INTJ
ejpam-3822	105	37	)	)	PUNCT
ejpam-3822	105	38	−1	−1	NOUN
ejpam-3822	105	39	at	at	ADP
ejpam-3822	105	40	τ	τ	X
ejpam-3822	105	41	=	=	SYM
ejpam-3822	105	42	τ0	τ0	NOUN
ejpam-3822	105	43	,	,	PUNCT
ejpam-3822	105	44	with	with	ADP
ejpam-3822	105	45	λ	λ	PROPN
ejpam-3822	105	46	=	=	SYM
ejpam-3822	105	47	iw	iw	PROPN
ejpam-3822	105	48	,	,	PUNCT
ejpam-3822	105	49	we	we	PRON
ejpam-3822	105	50	have	have	AUX
ejpam-3822	105	51	re	re	VERB
ejpam-3822	105	52	[	[	PUNCT
ejpam-3822	105	53	dλ	dλ	INTJ
ejpam-3822	105	54	dτ	dτ	INTJ
ejpam-3822	105	55	]	]	X
ejpam-3822	105	56	−1	−1	NOUN
ejpam-3822	105	57	τ	τ	X
ejpam-3822	105	58	=	=	NOUN
ejpam-3822	105	59	τ0	τ0	NOUN
ejpam-3822	105	60	=	=	SYM
ejpam-3822	105	61	brnr	brnr	PROPN
ejpam-3822	106	1	+	+	ADJ
ejpam-3822	106	2	bini	bini	PROPN
ejpam-3822	106	3	n2	n2	PROPN
ejpam-3822	106	4	r	r	PROPN
ejpam-3822	106	5	+	+	PROPN
ejpam-3822	106	6	n2	n2	ADJ
ejpam-3822	106	7	i	i	PRON
ejpam-3822	106	8	,	,	PUNCT
ejpam-3822	106	9	where	where	SCONJ
ejpam-3822	106	10	br	br	NOUN
ejpam-3822	106	11	=	=	SYM
ejpam-3822	106	12	3w2cosτ0w0	3w2cosτ0w0	NUM
ejpam-3822	106	13	−	−	NOUN
ejpam-3822	106	14	2m2w	2m2w	NOUN
ejpam-3822	106	15	2cosτ0w0	2cosτ0w0	NUM
ejpam-3822	106	16	−m1sinτ0w0	−m1sinτ0w0	PROPN
ejpam-3822	106	17	−	−	PROPN
ejpam-3822	106	18	2n2w	2n2w	NOUN
ejpam-3822	106	19	2	2	NUM
ejpam-3822	106	20	−	−	NOUN
ejpam-3822	106	21	τw4cosτ0w0	τw4cosτ0w0	PUNCT
ejpam-3822	106	22	−m2w	−m2w	PROPN
ejpam-3822	106	23	2cosτ0w0	2cosτ0w0	NUM
ejpam-3822	106	24	+	+	NUM
ejpam-3822	106	25	m2w	m2w	NOUN
ejpam-3822	106	26	3sinτ0w0	3sinτ0w0	NUM
ejpam-3822	106	27	−m0wsinτ0w0	−m0wsinτ0w0	PROPN
ejpam-3822	106	28	;	;	PUNCT
ejpam-3822	106	29	bi	bi	NOUN
ejpam-3822	106	30	=	=	PROPN
ejpam-3822	106	31	3w3cosτ0w0	3w3cosτ0w0	PROPN
ejpam-3822	106	32	+	+	NUM
ejpam-3822	106	33	2m2w	2m2w	NOUN
ejpam-3822	106	34	2sinτ0w0	2sinτ0w0	NUM
ejpam-3822	106	35	−m1wcosτ0w0	−m1wcosτ0w0	PROPN
ejpam-3822	106	36	−n1w	−n1w	PUNCT
ejpam-3822	106	37	+	+	CCONJ
ejpam-3822	106	38	τw4sinτ0w0	τw4sinτ0w0	NOUN
ejpam-3822	106	39	+	+	ADJ
ejpam-3822	106	40	m2w	m2w	NOUN
ejpam-3822	106	41	3cosτ0w0	3cosτ0w0	NUM
ejpam-3822	106	42	+	+	SYM
ejpam-3822	106	43	m2	m2	PROPN
ejpam-3822	106	44	wsinτ0w0	wsinτ0w0	PROPN
ejpam-3822	106	45	−m0wcosτ0w0	−m0wcosτ0w0	PROPN
ejpam-3822	106	46	;	;	PUNCT
ejpam-3822	106	47	nr	nr	X
ejpam-3822	106	48	=	=	SYM
ejpam-3822	106	49	−w5sinτ0w0	−w5sinτ0w0	PROPN
ejpam-3822	106	50	+	+	NUM
ejpam-3822	106	51	m2w	m2w	NOUN
ejpam-3822	106	52	4cosτ0w0	4cosτ0w0	NOUN
ejpam-3822	106	53	+	+	PROPN
ejpam-3822	106	54	m1w	m1w	PROPN
ejpam-3822	106	55	3sinτ0w0	3sinτ0w0	NUM
ejpam-3822	106	56	−m0cosτ0w0	−m0cosτ0w0	PROPN
ejpam-3822	106	57	ni	ni	PROPN
ejpam-3822	106	58	=	=	PROPN
ejpam-3822	106	59	w5cosτ0w0	w5cosτ0w0	PROPN
ejpam-3822	106	60	+	+	NUM
ejpam-3822	106	61	m2w	m2w	NOUN
ejpam-3822	106	62	4sinτ0w0	4sinτ0w0	NOUN
ejpam-3822	106	63	−m1w	−m1w	NUM
ejpam-3822	106	64	3cosτ0w0	3cosτ0w0	NUM
ejpam-3822	106	65	−m0w	−m0w	NUM
ejpam-3822	106	66	2sinτ0w0	2sinτ0w0	NUM
ejpam-3822	106	67	observe	observe	VERB
ejpam-3822	106	68	that	that	SCONJ
ejpam-3822	106	69	if	if	SCONJ
ejpam-3822	106	70	c3	c3	PROPN
ejpam-3822	106	71	:	:	PUNCT
ejpam-3822	106	72	brnr	brnr	PROPN
ejpam-3822	106	73	+	+	CCONJ
ejpam-3822	106	74	bini	bini	PROPN
ejpam-3822	106	75	6=	6=	ADP
ejpam-3822	106	76	0	0	NUM
ejpam-3822	106	77	holds	hold	NOUN
ejpam-3822	106	78	,	,	PUNCT
ejpam-3822	106	79	then	then	ADV
ejpam-3822	106	80	re	re	ADP
ejpam-3822	106	81	[	[	PUNCT
ejpam-3822	106	82	dλ	dλ	INTJ
ejpam-3822	106	83	dτ	dτ	INTJ
ejpam-3822	106	84	]	]	X
ejpam-3822	106	85	−1	−1	NOUN
ejpam-3822	106	86	τ	τ	X
ejpam-3822	106	87	=	=	NOUN
ejpam-3822	106	88	τ0	τ0	NOUN
ejpam-3822	106	89	6=	6=	ADP
ejpam-3822	106	90	0	0	NUM
ejpam-3822	106	91	.	.	PUNCT
ejpam-3822	107	1	following	follow	VERB
ejpam-3822	107	2	the	the	DET
ejpam-3822	107	3	workings	working	NOUN
ejpam-3822	107	4	above	above	ADV
ejpam-3822	107	5	and	and	CCONJ
ejpam-3822	107	6	the	the	DET
ejpam-3822	107	7	hopf	hopf	ADJ
ejpam-3822	107	8	bifurcation	bifurcation	NOUN
ejpam-3822	107	9	theory	theory	NOUN
ejpam-3822	107	10	in	in	ADP
ejpam-3822	107	11	[	[	X
ejpam-3822	107	12	2	2	NUM
ejpam-3822	107	13	,	,	PUNCT
ejpam-3822	107	14	3	3	NUM
ejpam-3822	107	15	,	,	PUNCT
ejpam-3822	107	16	5	5	NUM
ejpam-3822	107	17	,	,	PUNCT
ejpam-3822	107	18	7	7	NUM
ejpam-3822	107	19	]	]	PUNCT
ejpam-3822	107	20	,	,	PUNCT
ejpam-3822	107	21	we	we	PRON
ejpam-3822	107	22	have	have	VERB
ejpam-3822	107	23	the	the	DET
ejpam-3822	107	24	theorem	theorem	NOUN
ejpam-3822	107	25	below	below	ADP
ejpam-3822	107	26	theorem	theorem	NOUN
ejpam-3822	107	27	2	2	NUM
ejpam-3822	107	28	.	.	PUNCT
ejpam-3822	107	29	.	.	PUNCT
ejpam-3822	108	1	if	if	SCONJ
ejpam-3822	108	2	conditions	condition	NOUN
ejpam-3822	108	3	c1	c1	PROPN
ejpam-3822	108	4	−	−	PROPN
ejpam-3822	108	5	c3	c3	PROPN
ejpam-3822	108	6	hold	hold	VERB
ejpam-3822	108	7	,	,	PUNCT
ejpam-3822	108	8	then	then	ADV
ejpam-3822	108	9	the	the	DET
ejpam-3822	108	10	endemic	endemic	ADJ
ejpam-3822	108	11	equilibrium	equilibrium	NOUN
ejpam-3822	108	12	e∗(s∗	e∗(s∗	NOUN
ejpam-3822	108	13	,	,	PUNCT
ejpam-3822	108	14	v	v	NOUN
ejpam-3822	108	15	∗	∗	NOUN
ejpam-3822	108	16	,	,	PUNCT
ejpam-3822	108	17	i∗	i∗	NOUN
ejpam-3822	108	18	)	)	PUNCT
ejpam-3822	108	19	of	of	ADP
ejpam-3822	108	20	the	the	DET
ejpam-3822	108	21	system	system	NOUN
ejpam-3822	108	22	(	(	PUNCT
ejpam-3822	108	23	1	1	X
ejpam-3822	108	24	)	)	PUNCT
ejpam-3822	108	25	is	be	AUX
ejpam-3822	108	26	locally	locally	ADV
ejpam-3822	108	27	asymptotically	asymptotically	ADV
ejpam-3822	108	28	stable	stable	ADJ
ejpam-3822	108	29	when	when	SCONJ
ejpam-3822	108	30	τ	τ	PROPN
ejpam-3822	108	31	∈	∈	PROPN
ejpam-3822	109	1	[	[	X
ejpam-3822	109	2	0	0	NUM
ejpam-3822	109	3	,	,	PUNCT
ejpam-3822	109	4	τ0	τ0	NOUN
ejpam-3822	109	5	]	]	PUNCT
ejpam-3822	109	6	;	;	PUNCT
ejpam-3822	109	7	the	the	DET
ejpam-3822	109	8	system	system	NOUN
ejpam-3822	109	9	undergoes	undergo	VERB
ejpam-3822	109	10	a	a	DET
ejpam-3822	109	11	hopf	hopf	ADJ
ejpam-3822	109	12	bifurcation	bifurcation	NOUN
ejpam-3822	109	13	at	at	ADP
ejpam-3822	109	14	e∗(s∗	e∗(s∗	NOUN
ejpam-3822	109	15	,	,	PUNCT
ejpam-3822	109	16	v	v	NOUN
ejpam-3822	109	17	∗	∗	NOUN
ejpam-3822	109	18	,	,	PUNCT
ejpam-3822	109	19	i∗	i∗	NOUN
ejpam-3822	109	20	)	)	PUNCT
ejpam-3822	109	21	when	when	SCONJ
ejpam-3822	109	22	τ	τ	PROPN
ejpam-3822	109	23	=	=	PROPN
ejpam-3822	109	24	τ0	τ0	NOUN
ejpam-3822	109	25	and	and	CCONJ
ejpam-3822	109	26	a	a	DET
ejpam-3822	109	27	family	family	NOUN
ejpam-3822	109	28	of	of	ADP
ejpam-3822	109	29	periodic	periodic	ADJ
ejpam-3822	109	30	solutions	solution	NOUN
ejpam-3822	109	31	bifurcate	bifurcate	NOUN
ejpam-3822	109	32	from	from	ADP
ejpam-3822	109	33	e∗(s∗	e∗(s∗	NOUN
ejpam-3822	109	34	,	,	PUNCT
ejpam-3822	109	35	v	v	NOUN
ejpam-3822	109	36	∗	∗	NOUN
ejpam-3822	109	37	,	,	PUNCT
ejpam-3822	109	38	i∗	i∗	NOUN
ejpam-3822	109	39	)	)	PUNCT
ejpam-3822	109	40	.	.	PUNCT
ejpam-3822	110	1	l.	l.	PROPN
ejpam-3822	110	2	o.	o.	PROPN
ejpam-3822	110	3	onyango	onyango	PROPN
ejpam-3822	110	4	et	et	PROPN
ejpam-3822	110	5	al	al	PROPN
ejpam-3822	110	6	.	.	PUNCT
ejpam-3822	110	7	/	/	SYM
ejpam-3822	110	8	eur	eur	PROPN
ejpam-3822	110	9	.	.	PUNCT
ejpam-3822	111	1	j.	j.	PROPN
ejpam-3822	111	2	pure	pure	PROPN
ejpam-3822	111	3	appl	appl	PROPN
ejpam-3822	111	4	.	.	PROPN
ejpam-3822	111	5	math	math	PROPN
ejpam-3822	111	6	,	,	PUNCT
ejpam-3822	111	7	13	13	NUM
ejpam-3822	111	8	(	(	PUNCT
ejpam-3822	111	9	4	4	NUM
ejpam-3822	111	10	)	)	PUNCT
ejpam-3822	111	11	(	(	PUNCT
ejpam-3822	111	12	2020	2020	NUM
ejpam-3822	111	13	)	)	PUNCT
ejpam-3822	111	14	,	,	PUNCT
ejpam-3822	111	15	840	840	NUM
ejpam-3822	111	16	-	-	SYM
ejpam-3822	111	17	851	851	NUM
ejpam-3822	111	18	847	847	NUM
ejpam-3822	111	19	4	4	NUM
ejpam-3822	111	20	.	.	PUNCT
ejpam-3822	111	21	numerical	numerical	ADJ
ejpam-3822	111	22	simulations	simulation	NOUN
ejpam-3822	111	23	and	and	CCONJ
ejpam-3822	111	24	discussions	discussion	NOUN
ejpam-3822	111	25	in	in	ADP
ejpam-3822	111	26	this	this	DET
ejpam-3822	111	27	section	section	NOUN
ejpam-3822	111	28	we	we	PRON
ejpam-3822	111	29	have	have	AUX
ejpam-3822	111	30	carried	carry	VERB
ejpam-3822	111	31	out	out	ADP
ejpam-3822	111	32	the	the	DET
ejpam-3822	111	33	simulations	simulation	NOUN
ejpam-3822	111	34	to	to	PART
ejpam-3822	111	35	validate	validate	VERB
ejpam-3822	111	36	the	the	DET
ejpam-3822	111	37	analytical	analytical	ADJ
ejpam-3822	111	38	findings	finding	NOUN
ejpam-3822	111	39	and	and	CCONJ
ejpam-3822	111	40	illustrate	illustrate	VERB
ejpam-3822	111	41	the	the	DET
ejpam-3822	111	42	long	long	ADJ
ejpam-3822	111	43	term	term	NOUN
ejpam-3822	111	44	dynamics	dynamic	NOUN
ejpam-3822	111	45	of	of	ADP
ejpam-3822	111	46	system	system	NOUN
ejpam-3822	111	47	(	(	PUNCT
ejpam-3822	111	48	1	1	NUM
ejpam-3822	111	49	)	)	PUNCT
ejpam-3822	111	50	.	.	PUNCT
ejpam-3822	112	1	the	the	DET
ejpam-3822	112	2	parameter	parameter	NOUN
ejpam-3822	112	3	values	value	NOUN
ejpam-3822	112	4	are	be	AUX
ejpam-3822	112	5	the	the	DET
ejpam-3822	112	6	same	same	ADJ
ejpam-3822	112	7	as	as	ADP
ejpam-3822	112	8	the	the	DET
ejpam-3822	112	9	ones	one	NOUN
ejpam-3822	112	10	used	use	VERB
ejpam-3822	112	11	in	in	ADP
ejpam-3822	112	12	[	[	X
ejpam-3822	112	13	8	8	NUM
ejpam-3822	112	14	]	]	PUNCT
ejpam-3822	112	15	with	with	ADP
ejpam-3822	112	16	only	only	ADV
ejpam-3822	112	17	τ	τ	PROPN
ejpam-3822	112	18	being	be	AUX
ejpam-3822	112	19	varied	varied	ADJ
ejpam-3822	112	20	with	with	ADP
ejpam-3822	112	21	time	time	NOUN
ejpam-3822	112	22	as	as	SCONJ
ejpam-3822	112	23	indicated	indicate	VERB
ejpam-3822	112	24	in	in	ADP
ejpam-3822	112	25	the	the	DET
ejpam-3822	112	26	figures	figure	NOUN
ejpam-3822	112	27	.	.	PUNCT
ejpam-3822	113	1	figure	figure	NOUN
ejpam-3822	113	2	(	(	PUNCT
ejpam-3822	113	3	2	2	NUM
ejpam-3822	113	4	)	)	PUNCT
ejpam-3822	113	5	shows	show	VERB
ejpam-3822	113	6	that	that	SCONJ
ejpam-3822	113	7	the	the	DET
ejpam-3822	113	8	disease	disease	NOUN
ejpam-3822	113	9	free	free	ADJ
ejpam-3822	113	10	equilibrium	equilibrium	NOUN
ejpam-3822	113	11	is	be	AUX
ejpam-3822	113	12	globally	globally	ADV
ejpam-3822	113	13	asymptotically	asymptotically	ADV
ejpam-3822	113	14	stable	stable	ADJ
ejpam-3822	113	15	when	when	SCONJ
ejpam-3822	113	16	rv	rv	PROPN
ejpam-3822	113	17	=	=	PROPN
ejpam-3822	113	18	0.7692	0.7692	NUM
ejpam-3822	113	19	which	which	PRON
ejpam-3822	113	20	is	be	AUX
ejpam-3822	113	21	clearly	clearly	ADV
ejpam-3822	113	22	less	less	ADJ
ejpam-3822	113	23	than	than	ADP
ejpam-3822	113	24	unity	unity	NOUN
ejpam-3822	113	25	.	.	PUNCT
ejpam-3822	114	1	from	from	ADP
ejpam-3822	114	2	the	the	DET
ejpam-3822	114	3	figure	figure	NOUN
ejpam-3822	114	4	,	,	PUNCT
ejpam-3822	114	5	it	it	PRON
ejpam-3822	114	6	can	can	AUX
ejpam-3822	114	7	be	be	AUX
ejpam-3822	114	8	clearly	clearly	ADV
ejpam-3822	114	9	seen	see	VERB
ejpam-3822	114	10	that	that	SCONJ
ejpam-3822	114	11	i0	i0	PROPN
ejpam-3822	114	12	=	=	PROPN
ejpam-3822	114	13	0	0	X
ejpam-3822	114	14	.	.	PUNCT
ejpam-3822	115	1	figure	figure	NOUN
ejpam-3822	115	2	(	(	PUNCT
ejpam-3822	115	3	3	3	X
ejpam-3822	115	4	)	)	PUNCT
ejpam-3822	115	5	shows	show	VERB
ejpam-3822	115	6	that	that	SCONJ
ejpam-3822	115	7	the	the	DET
ejpam-3822	115	8	endemic	endemic	ADJ
ejpam-3822	115	9	equilibrium	equilibrium	NOUN
ejpam-3822	115	10	e∗(35.7321	e∗(35.7321	PROPN
ejpam-3822	115	11	,	,	PUNCT
ejpam-3822	115	12	45.5913	45.5913	NUM
ejpam-3822	115	13	,	,	PUNCT
ejpam-3822	115	14	6.3217	6.3217	NUM
ejpam-3822	115	15	)	)	PUNCT
ejpam-3822	115	16	figure	figure	NOUN
ejpam-3822	115	17	2	2	NUM
ejpam-3822	115	18	:	:	PUNCT
ejpam-3822	115	19	simulation	simulation	NOUN
ejpam-3822	115	20	of	of	ADP
ejpam-3822	115	21	system	system	NOUN
ejpam-3822	115	22	(	(	PUNCT
ejpam-3822	115	23	1	1	X
ejpam-3822	115	24	)	)	PUNCT
ejpam-3822	115	25	shows	show	VERB
ejpam-3822	115	26	the	the	DET
ejpam-3822	115	27	global	global	ADJ
ejpam-3822	115	28	stability	stability	NOUN
ejpam-3822	115	29	of	of	ADP
ejpam-3822	115	30	the	the	DET
ejpam-3822	115	31	disease	disease	NOUN
ejpam-3822	115	32	-	-	PUNCT
ejpam-3822	115	33	free	free	ADJ
ejpam-3822	115	34	equilibrium	equilibrium	NOUN
ejpam-3822	115	35	when	when	SCONJ
ejpam-3822	115	36	rv	rv	PROPN
ejpam-3822	115	37	=	=	PROPN
ejpam-3822	115	38	0.7692	0.7692	NUM
ejpam-3822	115	39	is	be	AUX
ejpam-3822	115	40	locally	locally	ADV
ejpam-3822	115	41	asymptotically	asymptotically	ADV
ejpam-3822	115	42	stable	stable	ADJ
ejpam-3822	115	43	when	when	SCONJ
ejpam-3822	115	44	τ	τ	PROPN
ejpam-3822	115	45	∈	∈	PROPN
ejpam-3822	116	1	[	[	X
ejpam-3822	116	2	0	0	NUM
ejpam-3822	116	3	,	,	PUNCT
ejpam-3822	116	4	τ0	τ0	NOUN
ejpam-3822	116	5	=	=	PUNCT
ejpam-3822	116	6	31.1725	31.1725	NUM
ejpam-3822	116	7	]	]	PUNCT
ejpam-3822	116	8	.	.	PUNCT
ejpam-3822	117	1	this	this	PRON
ejpam-3822	117	2	is	be	AUX
ejpam-3822	117	3	in	in	ADP
ejpam-3822	117	4	line	line	NOUN
ejpam-3822	117	5	with	with	ADP
ejpam-3822	117	6	theorem	theorem	ADJ
ejpam-3822	117	7	2	2	NUM
ejpam-3822	117	8	above	above	ADV
ejpam-3822	117	9	.	.	PUNCT
ejpam-3822	118	1	l.	l.	PROPN
ejpam-3822	118	2	o.	o.	PROPN
ejpam-3822	118	3	onyango	onyango	PROPN
ejpam-3822	118	4	et	et	PROPN
ejpam-3822	119	1	al	al	PROPN
ejpam-3822	119	2	.	.	PUNCT
ejpam-3822	119	3	/	/	SYM
ejpam-3822	119	4	eur	eur	PROPN
ejpam-3822	119	5	.	.	PUNCT
ejpam-3822	120	1	j.	j.	PROPN
ejpam-3822	120	2	pure	pure	PROPN
ejpam-3822	120	3	appl	appl	PROPN
ejpam-3822	120	4	.	.	PROPN
ejpam-3822	120	5	math	math	PROPN
ejpam-3822	120	6	,	,	PUNCT
ejpam-3822	120	7	13	13	NUM
ejpam-3822	120	8	(	(	PUNCT
ejpam-3822	120	9	4	4	NUM
ejpam-3822	120	10	)	)	PUNCT
ejpam-3822	120	11	(	(	PUNCT
ejpam-3822	120	12	2020	2020	NUM
ejpam-3822	120	13	)	)	PUNCT
ejpam-3822	120	14	,	,	PUNCT
ejpam-3822	120	15	840	840	NUM
ejpam-3822	120	16	-	-	SYM
ejpam-3822	120	17	851	851	NUM
ejpam-3822	120	18	848	848	NUM
ejpam-3822	120	19	figure	figure	NOUN
ejpam-3822	120	20	3	3	NUM
ejpam-3822	120	21	:	:	PUNCT
ejpam-3822	120	22	the	the	DET
ejpam-3822	120	23	effects	effect	NOUN
ejpam-3822	120	24	of	of	ADP
ejpam-3822	120	25	ε	ε	PROPN
ejpam-3822	120	26	on	on	ADP
ejpam-3822	120	27	all	all	DET
ejpam-3822	120	28	classes	class	NOUN
ejpam-3822	120	29	with	with	ADP
ejpam-3822	120	30	(	(	PUNCT
ejpam-3822	120	31	a	a	X
ejpam-3822	120	32	)	)	PUNCT
ejpam-3822	120	33	ε	ε	PROPN
ejpam-3822	120	34	=	=	SYM
ejpam-3822	120	35	0.0127	0.0127	NUM
ejpam-3822	120	36	,	,	PUNCT
ejpam-3822	120	37	τ	τ	PROPN
ejpam-3822	120	38	=	=	SYM
ejpam-3822	120	39	5.76	5.76	NUM
ejpam-3822	120	40	and	and	CCONJ
ejpam-3822	120	41	rv	rv	NOUN
ejpam-3822	120	42	=	=	SYM
ejpam-3822	120	43	4.5672	4.5672	NUM
ejpam-3822	120	44	,	,	PUNCT
ejpam-3822	120	45	(	(	PUNCT
ejpam-3822	120	46	b	b	X
ejpam-3822	120	47	)	)	PUNCT
ejpam-3822	120	48	ε	ε	PROPN
ejpam-3822	120	49	=	=	SYM
ejpam-3822	120	50	0.91855	0.91855	NUM
ejpam-3822	120	51	,	,	PUNCT
ejpam-3822	120	52	τ	τ	PROPN
ejpam-3822	120	53	=	=	NUM
ejpam-3822	120	54	1.257	1.257	NUM
ejpam-3822	120	55	,	,	PUNCT
ejpam-3822	120	56	rv	rv	PROPN
ejpam-3822	120	57	=	=	SYM
ejpam-3822	120	58	1.7261	1.7261	NUM
ejpam-3822	120	59	and	and	CCONJ
ejpam-3822	120	60	(	(	PUNCT
ejpam-3822	120	61	c	c	NOUN
ejpam-3822	120	62	)	)	PUNCT
ejpam-3822	120	63	ε	ε	PROPN
ejpam-3822	120	64	=	=	SYM
ejpam-3822	120	65	0.4123	0.4123	NUM
ejpam-3822	120	66	,	,	PUNCT
ejpam-3822	120	67	τ	τ	PROPN
ejpam-3822	120	68	=	=	SYM
ejpam-3822	120	69	3.1267	3.1267	NUM
ejpam-3822	120	70	,	,	PUNCT
ejpam-3822	120	71	rv	rv	PROPN
ejpam-3822	120	72	=	=	PROPN
ejpam-3822	120	73	3.1672	3.1672	NUM
ejpam-3822	120	74	.	.	PUNCT
ejpam-3822	121	1	in	in	ADP
ejpam-3822	121	2	figure	figure	NOUN
ejpam-3822	121	3	(	(	PUNCT
ejpam-3822	121	4	3)(a	3)(a	NUM
ejpam-3822	121	5	)	)	PUNCT
ejpam-3822	121	6	,	,	PUNCT
ejpam-3822	121	7	we	we	PRON
ejpam-3822	121	8	can	can	AUX
ejpam-3822	121	9	clearly	clearly	ADV
ejpam-3822	121	10	see	see	VERB
ejpam-3822	121	11	that	that	SCONJ
ejpam-3822	121	12	when	when	SCONJ
ejpam-3822	121	13	ε	ε	PROPN
ejpam-3822	121	14	=	=	PROPN
ejpam-3822	121	15	0.0127	0.0127	NUM
ejpam-3822	121	16	,	,	PUNCT
ejpam-3822	121	17	τ	τ	PROPN
ejpam-3822	121	18	=	=	SYM
ejpam-3822	121	19	5.76	5.76	NUM
ejpam-3822	121	20	and	and	CCONJ
ejpam-3822	121	21	rv	rv	NOUN
ejpam-3822	121	22	=	=	SYM
ejpam-3822	121	23	4.5672	4.5672	NUM
ejpam-3822	121	24	,	,	PUNCT
ejpam-3822	121	25	the	the	DET
ejpam-3822	121	26	rate	rate	NOUN
ejpam-3822	121	27	of	of	ADP
ejpam-3822	121	28	infectives	infective	NOUN
ejpam-3822	121	29	are	be	AUX
ejpam-3822	121	30	quite	quite	ADV
ejpam-3822	121	31	high	high	ADJ
ejpam-3822	121	32	as	as	SCONJ
ejpam-3822	121	33	compared	compare	VERB
ejpam-3822	121	34	to	to	ADP
ejpam-3822	121	35	figures	figure	NOUN
ejpam-3822	121	36	(	(	PUNCT
ejpam-3822	121	37	3)(b	3)(b	NUM
ejpam-3822	121	38	)	)	PUNCT
ejpam-3822	121	39	and	and	CCONJ
ejpam-3822	121	40	(	(	PUNCT
ejpam-3822	121	41	c	c	X
ejpam-3822	121	42	)	)	PUNCT
ejpam-3822	121	43	when	when	SCONJ
ejpam-3822	121	44	ε	ε	PROPN
ejpam-3822	121	45	=	=	SYM
ejpam-3822	121	46	0.91855	0.91855	NUM
ejpam-3822	121	47	,	,	PUNCT
ejpam-3822	121	48	τ	τ	PROPN
ejpam-3822	121	49	=	=	NUM
ejpam-3822	121	50	1.257	1.257	NUM
ejpam-3822	121	51	,	,	PUNCT
ejpam-3822	121	52	rv	rv	PROPN
ejpam-3822	121	53	=	=	SYM
ejpam-3822	121	54	1.7261	1.7261	NUM
ejpam-3822	121	55	and	and	CCONJ
ejpam-3822	121	56	ε	ε	PROPN
ejpam-3822	121	57	=	=	SYM
ejpam-3822	121	58	0.4123	0.4123	NUM
ejpam-3822	121	59	,	,	PUNCT
ejpam-3822	121	60	τ	τ	PROPN
ejpam-3822	121	61	=	=	SYM
ejpam-3822	121	62	3.1267	3.1267	NUM
ejpam-3822	121	63	,	,	PUNCT
ejpam-3822	121	64	rv	rv	PROPN
ejpam-3822	122	1	=	=	PROPN
ejpam-3822	122	2	3.1672	3.1672	NUM
ejpam-3822	122	3	respectively	respectively	ADV
ejpam-3822	122	4	.	.	PUNCT
ejpam-3822	123	1	this	this	PRON
ejpam-3822	123	2	is	be	AUX
ejpam-3822	123	3	a	a	DET
ejpam-3822	123	4	proof	proof	NOUN
ejpam-3822	123	5	enough	enough	ADV
ejpam-3822	123	6	that	that	SCONJ
ejpam-3822	123	7	rotavirus	rotavirus	NOUN
ejpam-3822	123	8	infections	infection	NOUN
ejpam-3822	123	9	can	can	AUX
ejpam-3822	123	10	be	be	AUX
ejpam-3822	123	11	easily	easily	ADV
ejpam-3822	123	12	contained	contain	VERB
ejpam-3822	123	13	by	by	ADP
ejpam-3822	123	14	introducing	introduce	VERB
ejpam-3822	123	15	very	very	ADV
ejpam-3822	123	16	strong	strong	ADJ
ejpam-3822	123	17	vaccines	vaccine	NOUN
ejpam-3822	123	18	and	and	CCONJ
ejpam-3822	123	19	reducing	reduce	VERB
ejpam-3822	123	20	the	the	DET
ejpam-3822	123	21	vaccine	vaccine	NOUN
ejpam-3822	123	22	delay	delay	VERB
ejpam-3822	123	23	time	time	NOUN
ejpam-3822	123	24	.	.	PUNCT
ejpam-3822	124	1	l.	l.	PROPN
ejpam-3822	124	2	o.	o.	PROPN
ejpam-3822	124	3	onyango	onyango	PROPN
ejpam-3822	124	4	et	et	PROPN
ejpam-3822	125	1	al	al	PROPN
ejpam-3822	125	2	.	.	PUNCT
ejpam-3822	125	3	/	/	SYM
ejpam-3822	125	4	eur	eur	PROPN
ejpam-3822	125	5	.	.	PUNCT
ejpam-3822	126	1	j.	j.	PROPN
ejpam-3822	126	2	pure	pure	PROPN
ejpam-3822	126	3	appl	appl	PROPN
ejpam-3822	126	4	.	.	PROPN
ejpam-3822	126	5	math	math	PROPN
ejpam-3822	126	6	,	,	PUNCT
ejpam-3822	126	7	13	13	NUM
ejpam-3822	126	8	(	(	PUNCT
ejpam-3822	126	9	4	4	NUM
ejpam-3822	126	10	)	)	PUNCT
ejpam-3822	126	11	(	(	PUNCT
ejpam-3822	126	12	2020	2020	NUM
ejpam-3822	126	13	)	)	PUNCT
ejpam-3822	126	14	,	,	PUNCT
ejpam-3822	126	15	840	840	NUM
ejpam-3822	126	16	-	-	SYM
ejpam-3822	126	17	851	851	NUM
ejpam-3822	126	18	849	849	NUM
ejpam-3822	126	19	figure	figure	NOUN
ejpam-3822	126	20	4	4	NUM
ejpam-3822	126	21	:	:	PUNCT
ejpam-3822	126	22	time	time	NOUN
ejpam-3822	126	23	plots	plot	NOUN
ejpam-3822	126	24	of	of	ADP
ejpam-3822	126	25	s	s	PROPN
ejpam-3822	126	26	,	,	PUNCT
ejpam-3822	126	27	v	v	NOUN
ejpam-3822	126	28	and	and	CCONJ
ejpam-3822	126	29	i	i	PRON
ejpam-3822	126	30	with	with	ADP
ejpam-3822	126	31	τ	τ	X
ejpam-3822	126	32	=	=	PROPN
ejpam-3822	127	1	36.125	36.125	NUM
ejpam-3822	127	2	>	>	X
ejpam-3822	127	3	τ0	τ0	NOUN
ejpam-3822	127	4	=	=	SYM
ejpam-3822	127	5	31.1725	31.1725	NUM
ejpam-3822	127	6	figure	figure	NOUN
ejpam-3822	127	7	5	5	NUM
ejpam-3822	127	8	:	:	PUNCT
ejpam-3822	127	9	bifurcation	bifurcation	NOUN
ejpam-3822	127	10	diagrams	diagram	NOUN
ejpam-3822	127	11	of	of	ADP
ejpam-3822	127	12	system	system	NOUN
ejpam-3822	127	13	(	(	PUNCT
ejpam-3822	127	14	1	1	NUM
ejpam-3822	127	15	)	)	PUNCT
ejpam-3822	127	16	with	with	ADP
ejpam-3822	127	17	respect	respect	NOUN
ejpam-3822	127	18	to	to	ADP
ejpam-3822	127	19	τ	τ	PROPN
ejpam-3822	127	20	(	(	PUNCT
ejpam-3822	127	21	a)s	a)s	NOUN
ejpam-3822	127	22	,	,	PUNCT
ejpam-3822	127	23	(	(	PUNCT
ejpam-3822	127	24	b	b	X
ejpam-3822	127	25	)	)	PUNCT
ejpam-3822	127	26	v	v	NOUN
ejpam-3822	127	27	and	and	CCONJ
ejpam-3822	127	28	(	(	PUNCT
ejpam-3822	127	29	c	c	X
ejpam-3822	127	30	)	)	PUNCT
ejpam-3822	127	31	i	i	PROPN
ejpam-3822	127	32	l.	l.	PROPN
ejpam-3822	127	33	o.	o.	PROPN
ejpam-3822	127	34	onyango	onyango	PROPN
ejpam-3822	127	35	et	et	PROPN
ejpam-3822	127	36	al	al	PROPN
ejpam-3822	127	37	.	.	PUNCT
ejpam-3822	127	38	/	/	SYM
ejpam-3822	127	39	eur	eur	PROPN
ejpam-3822	127	40	.	.	PUNCT
ejpam-3822	128	1	j.	j.	PROPN
ejpam-3822	128	2	pure	pure	PROPN
ejpam-3822	128	3	appl	appl	PROPN
ejpam-3822	128	4	.	.	PROPN
ejpam-3822	128	5	math	math	PROPN
ejpam-3822	128	6	,	,	PUNCT
ejpam-3822	128	7	13	13	NUM
ejpam-3822	128	8	(	(	PUNCT
ejpam-3822	128	9	4	4	NUM
ejpam-3822	128	10	)	)	PUNCT
ejpam-3822	128	11	(	(	PUNCT
ejpam-3822	128	12	2020	2020	NUM
ejpam-3822	128	13	)	)	PUNCT
ejpam-3822	128	14	,	,	PUNCT
ejpam-3822	128	15	840	840	NUM
ejpam-3822	128	16	-	-	SYM
ejpam-3822	128	17	851	851	NUM
ejpam-3822	128	18	850	850	NUM
ejpam-3822	128	19	figure	figure	NOUN
ejpam-3822	128	20	4	4	NUM
ejpam-3822	128	21	that	that	SCONJ
ejpam-3822	128	22	a	a	DET
ejpam-3822	128	23	family	family	NOUN
ejpam-3822	128	24	of	of	ADP
ejpam-3822	128	25	periodic	periodic	ADJ
ejpam-3822	128	26	solutions	solution	NOUN
ejpam-3822	128	27	bifurcate	bifurcate	NOUN
ejpam-3822	128	28	at	at	ADP
ejpam-3822	128	29	e∗(35.7321	e∗(35.7321	PROPN
ejpam-3822	128	30	,	,	PUNCT
ejpam-3822	128	31	45.5913	45.5913	NUM
ejpam-3822	128	32	,	,	PUNCT
ejpam-3822	128	33	6.3217	6.3217	NUM
ejpam-3822	128	34	)	)	PUNCT
ejpam-3822	128	35	.	.	PUNCT
ejpam-3822	129	1	this	this	DET
ejpam-3822	129	2	phenomenon	phenomenon	NOUN
ejpam-3822	129	3	is	be	AUX
ejpam-3822	129	4	also	also	ADV
ejpam-3822	129	5	illustrated	illustrate	VERB
ejpam-3822	129	6	by	by	ADP
ejpam-3822	129	7	figure	figure	NOUN
ejpam-3822	129	8	5	5	NUM
ejpam-3822	129	9	5	5	NUM
ejpam-3822	129	10	.	.	PUNCT
ejpam-3822	129	11	conclusion	conclusion	NOUN
ejpam-3822	129	12	and	and	CCONJ
ejpam-3822	129	13	recommendation	recommendation	NOUN
ejpam-3822	129	14	in	in	ADP
ejpam-3822	129	15	this	this	DET
ejpam-3822	129	16	work	work	NOUN
ejpam-3822	129	17	,	,	PUNCT
ejpam-3822	129	18	we	we	PRON
ejpam-3822	129	19	have	have	AUX
ejpam-3822	129	20	formulated	formulate	VERB
ejpam-3822	129	21	a	a	DET
ejpam-3822	129	22	mathematical	mathematical	ADJ
ejpam-3822	129	23	model	model	NOUN
ejpam-3822	129	24	for	for	ADP
ejpam-3822	129	25	rotavirus	rotaviru	NOUN
ejpam-3822	129	26	incorporating	incorporate	VERB
ejpam-3822	129	27	time	time	NOUN
ejpam-3822	129	28	delay	delay	NOUN
ejpam-3822	129	29	in	in	ADP
ejpam-3822	129	30	vaccination	vaccination	NOUN
ejpam-3822	129	31	.	.	PUNCT
ejpam-3822	130	1	the	the	DET
ejpam-3822	130	2	disease	disease	NOUN
ejpam-3822	130	3	free	free	ADJ
ejpam-3822	130	4	equilibrium	equilibrium	NOUN
ejpam-3822	130	5	has	have	AUX
ejpam-3822	130	6	been	be	AUX
ejpam-3822	130	7	proved	prove	VERB
ejpam-3822	130	8	to	to	PART
ejpam-3822	130	9	be	be	AUX
ejpam-3822	130	10	globally	globally	ADV
ejpam-3822	130	11	stable	stable	ADJ
ejpam-3822	130	12	.	.	PUNCT
ejpam-3822	131	1	the	the	DET
ejpam-3822	131	2	endemic	endemic	ADJ
ejpam-3822	131	3	equilibria	equilibrium	NOUN
ejpam-3822	131	4	is	be	AUX
ejpam-3822	131	5	proved	prove	VERB
ejpam-3822	131	6	to	to	PART
ejpam-3822	131	7	be	be	AUX
ejpam-3822	131	8	locally	locally	ADV
ejpam-3822	131	9	stable	stable	ADJ
ejpam-3822	131	10	whenever	whenever	SCONJ
ejpam-3822	131	11	τ	τ	PROPN
ejpam-3822	131	12	=	=	SYM
ejpam-3822	131	13	0	0	PUNCT
ejpam-3822	131	14	and	and	CCONJ
ejpam-3822	131	15	undergoes	undergo	VERB
ejpam-3822	131	16	a	a	DET
ejpam-3822	131	17	hopf	hopf	ADJ
ejpam-3822	131	18	bifurcation	bifurcation	NOUN
ejpam-3822	131	19	if	if	SCONJ
ejpam-3822	131	20	τ	τ	PROPN
ejpam-3822	131	21	>	>	X
ejpam-3822	131	22	0	0	NUM
ejpam-3822	131	23	.	.	PUNCT
ejpam-3822	132	1	from	from	ADP
ejpam-3822	132	2	the	the	DET
ejpam-3822	132	3	analytical	analytical	ADJ
ejpam-3822	132	4	and	and	CCONJ
ejpam-3822	132	5	simulation	simulation	NOUN
ejpam-3822	132	6	results	result	NOUN
ejpam-3822	132	7	,	,	PUNCT
ejpam-3822	132	8	we	we	PRON
ejpam-3822	132	9	recommend	recommend	VERB
ejpam-3822	132	10	that	that	SCONJ
ejpam-3822	132	11	a	a	DET
ejpam-3822	132	12	strong	strong	ADJ
ejpam-3822	132	13	vaccine	vaccine	NOUN
ejpam-3822	132	14	with	with	ADP
ejpam-3822	132	15	a	a	DET
ejpam-3822	132	16	short	short	ADJ
ejpam-3822	132	17	delay	delay	NOUN
ejpam-3822	132	18	time	time	NOUN
ejpam-3822	132	19	should	should	AUX
ejpam-3822	132	20	be	be	AUX
ejpam-3822	132	21	introduced	introduce	VERB
ejpam-3822	132	22	in	in	ADP
ejpam-3822	132	23	order	order	NOUN
ejpam-3822	132	24	to	to	PART
ejpam-3822	132	25	effectively	effectively	ADV
ejpam-3822	132	26	control	control	VERB
ejpam-3822	132	27	rotavirus	rotavirus	NOUN
ejpam-3822	132	28	infections	infection	NOUN
ejpam-3822	132	29	.	.	PUNCT
ejpam-3822	133	1	as	as	ADP
ejpam-3822	133	2	a	a	DET
ejpam-3822	133	3	future	future	ADJ
ejpam-3822	133	4	work	work	NOUN
ejpam-3822	133	5	,	,	PUNCT
ejpam-3822	133	6	we	we	PRON
ejpam-3822	133	7	propose	propose	VERB
ejpam-3822	133	8	that	that	SCONJ
ejpam-3822	133	9	the	the	DET
ejpam-3822	133	10	stability	stability	NOUN
ejpam-3822	133	11	and	and	CCONJ
ejpam-3822	133	12	directions	direction	NOUN
ejpam-3822	133	13	of	of	ADP
ejpam-3822	133	14	hopf	hopf	ADJ
ejpam-3822	133	15	bifurcations	bifurcation	NOUN
ejpam-3822	133	16	derived	derive	VERB
ejpam-3822	133	17	in	in	ADP
ejpam-3822	133	18	this	this	DET
ejpam-3822	133	19	work	work	NOUN
ejpam-3822	133	20	should	should	AUX
ejpam-3822	133	21	be	be	AUX
ejpam-3822	133	22	established	establish	VERB
ejpam-3822	133	23	.	.	PUNCT
ejpam-3822	134	1	6	6	X
ejpam-3822	134	2	.	.	X
ejpam-3822	134	3	declarations	declaration	NOUN
ejpam-3822	134	4	6.1	6.1	NUM
ejpam-3822	134	5	.	.	PUNCT
ejpam-3822	135	1	competing	compete	VERB
ejpam-3822	135	2	interests	interest	NOUN
ejpam-3822	135	3	the	the	DET
ejpam-3822	135	4	authors	author	NOUN
ejpam-3822	135	5	declare	declare	VERB
ejpam-3822	135	6	that	that	SCONJ
ejpam-3822	135	7	they	they	PRON
ejpam-3822	135	8	have	have	VERB
ejpam-3822	135	9	no	no	DET
ejpam-3822	135	10	competing	compete	VERB
ejpam-3822	135	11	interests	interest	NOUN
ejpam-3822	135	12	.	.	PUNCT
ejpam-3822	136	1	6.2	6.2	NUM
ejpam-3822	136	2	.	.	PUNCT
ejpam-3822	136	3	authorial	authorial	ADJ
ejpam-3822	136	4	contribution	contribution	NOUN
ejpam-3822	136	5	the	the	DET
ejpam-3822	136	6	authors	author	NOUN
ejpam-3822	136	7	have	have	AUX
ejpam-3822	136	8	contributed	contribute	VERB
ejpam-3822	136	9	as	as	SCONJ
ejpam-3822	136	10	follows	follow	VERB
ejpam-3822	136	11	:	:	PUNCT
ejpam-3822	136	12	(	(	PUNCT
ejpam-3822	136	13	i	i	NOUN
ejpam-3822	136	14	)	)	PUNCT
ejpam-3822	136	15	florence	florence	PROPN
ejpam-3822	136	16	adongo	adongo	PROPN
ejpam-3822	136	17	:	:	PUNCT
ejpam-3822	136	18	formulated	formulate	VERB
ejpam-3822	136	19	the	the	DET
ejpam-3822	136	20	model	model	NOUN
ejpam-3822	136	21	(	(	PUNCT
ejpam-3822	136	22	ii	ii	NOUN
ejpam-3822	136	23	)	)	PUNCT
ejpam-3822	136	24	lawrence	lawrence	PROPN
ejpam-3822	136	25	onyango	onyango	PROPN
ejpam-3822	136	26	:	:	PUNCT
ejpam-3822	136	27	analyzed	analyze	VERB
ejpam-3822	136	28	the	the	DET
ejpam-3822	136	29	model	model	NOUN
ejpam-3822	136	30	(	(	PUNCT
ejpam-3822	136	31	iii	iii	NOUN
ejpam-3822	136	32	)	)	PUNCT
ejpam-3822	136	33	job	job	NOUN
ejpam-3822	136	34	bonyo	bonyo	NOUN
ejpam-3822	136	35	:	:	PUNCT
ejpam-3822	136	36	performed	perform	VERB
ejpam-3822	136	37	numerical	numerical	ADJ
ejpam-3822	136	38	analysis	analysis	NOUN
ejpam-3822	136	39	(	(	PUNCT
ejpam-3822	136	40	iv	iv	NUM
ejpam-3822	136	41	)	)	PUNCT
ejpam-3822	136	42	:	:	PUNCT
ejpam-3822	137	1	ogada	ogada	PROPN
ejpam-3822	137	2	a.	a.	PROPN
ejpam-3822	137	3	elisha	elisha	PROPN
ejpam-3822	137	4	:	:	PUNCT
ejpam-3822	137	5	performed	perform	VERB
ejpam-3822	137	6	numerical	numerical	ADJ
ejpam-3822	137	7	simulations	simulation	NOUN
ejpam-3822	137	8	(	(	PUNCT
ejpam-3822	137	9	v	v	NOUN
ejpam-3822	137	10	)	)	PUNCT
ejpam-3822	137	11	george	george	PROPN
ejpam-3822	137	12	lawi	lawi	PROPN
ejpam-3822	137	13	:	:	PUNCT
ejpam-3822	137	14	proof	proof	NOUN
ejpam-3822	137	15	read	read	VERB
ejpam-3822	137	16	the	the	DET
ejpam-3822	137	17	manuscript	manuscript	NOUN
ejpam-3822	137	18	6.3	6.3	NUM
ejpam-3822	137	19	.	.	PUNCT
ejpam-3822	138	1	source	source	NOUN
ejpam-3822	138	2	of	of	ADP
ejpam-3822	138	3	data	datum	NOUN
ejpam-3822	138	4	the	the	DET
ejpam-3822	138	5	data	datum	NOUN
ejpam-3822	138	6	used	use	VERB
ejpam-3822	138	7	to	to	PART
ejpam-3822	138	8	perform	perform	VERB
ejpam-3822	138	9	numerical	numerical	ADJ
ejpam-3822	138	10	simulation	simulation	NOUN
ejpam-3822	138	11	is	be	AUX
ejpam-3822	138	12	from	from	ADP
ejpam-3822	138	13	onyango	onyango	NOUN
ejpam-3822	138	14	et.al	et.al	PROPN
ejpam-3822	138	15	[	[	X
ejpam-3822	138	16	8	8	NUM
ejpam-3822	138	17	]	]	ADJ
ejpam-3822	138	18	acknowledgements	acknowledgement	NOUN
ejpam-3822	138	19	we	we	PRON
ejpam-3822	138	20	the	the	DET
ejpam-3822	138	21	authors	author	NOUN
ejpam-3822	138	22	would	would	AUX
ejpam-3822	138	23	like	like	VERB
ejpam-3822	138	24	to	to	ADP
ejpam-3822	138	25	sincere	sincere	VERB
ejpam-3822	138	26	thank	thank	PROPN
ejpam-3822	138	27	dr	dr	PROPN
ejpam-3822	138	28	.	.	PROPN
ejpam-3822	138	29	patriciah	patriciah	PROPN
ejpam-3822	138	30	gathia	gathia	NOUN
ejpam-3822	138	31	for	for	ADP
ejpam-3822	138	32	the	the	DET
ejpam-3822	138	33	support	support	NOUN
ejpam-3822	138	34	and	and	CCONJ
ejpam-3822	138	35	encouragement	encouragement	NOUN
ejpam-3822	138	36	she	she	PRON
ejpam-3822	138	37	gave	give	VERB
ejpam-3822	138	38	to	to	ADP
ejpam-3822	138	39	us	we	PRON
ejpam-3822	138	40	during	during	ADP
ejpam-3822	138	41	the	the	DET
ejpam-3822	138	42	time	time	NOUN
ejpam-3822	138	43	we	we	PRON
ejpam-3822	138	44	were	be	AUX
ejpam-3822	138	45	busy	busy	ADJ
ejpam-3822	138	46	doing	do	VERB
ejpam-3822	138	47	the	the	DET
ejpam-3822	138	48	research	research	NOUN
ejpam-3822	138	49	.	.	PUNCT
ejpam-3822	139	1	we	we	PRON
ejpam-3822	139	2	ca	can	AUX
ejpam-3822	139	3	n’t	not	PART
ejpam-3822	139	4	fail	fail	VERB
ejpam-3822	139	5	to	to	PART
ejpam-3822	139	6	appreciate	appreciate	VERB
ejpam-3822	139	7	the	the	DET
ejpam-3822	139	8	many	many	ADJ
ejpam-3822	139	9	lunches	lunch	NOUN
ejpam-3822	139	10	you	you	PRON
ejpam-3822	139	11	bought	buy	VERB
ejpam-3822	139	12	to	to	ADP
ejpam-3822	139	13	us	we	PRON
ejpam-3822	139	14	during	during	ADP
ejpam-3822	139	15	this	this	DET
ejpam-3822	139	16	time	time	NOUN
ejpam-3822	139	17	.	.	PUNCT
ejpam-3822	140	1	may	may	AUX
ejpam-3822	140	2	the	the	DET
ejpam-3822	140	3	almighty	almighty	PROPN
ejpam-3822	140	4	bless	bless	VERB
ejpam-3822	140	5	you	you	PRON
ejpam-3822	140	6	doctor	doctor	NOUN
ejpam-3822	140	7	.	.	PUNCT
ejpam-3822	141	1	references	reference	NOUN
ejpam-3822	141	2	851	851	NUM
ejpam-3822	141	3	references	reference	NOUN
ejpam-3822	141	4	[	[	X
ejpam-3822	141	5	1	1	NUM
ejpam-3822	141	6	]	]	ADJ
ejpam-3822	141	7	rotavirus	rotavirus	NOUN
ejpam-3822	141	8	and	and	CCONJ
ejpam-3822	141	9	symptoms	symptom	NOUN
ejpam-3822	141	10	.	.	PUNCT
ejpam-3822	142	1	center	center	NOUN
ejpam-3822	142	2	for	for	ADP
ejpam-3822	142	3	disease	disease	NOUN
ejpam-3822	142	4	control	control	NOUN
ejpam-3822	142	5	,	,	PUNCT
ejpam-3822	142	6	sep	sep	PROPN
ejpam-3822	142	7	2016	2016	NUM
ejpam-3822	142	8	.	.	PUNCT
ejpam-3822	143	1	[	[	X
ejpam-3822	143	2	2	2	NUM
ejpam-3822	143	3	]	]	X
ejpam-3822	143	4	omar	omar	PROPN
ejpam-3822	143	5	bazighifan	bazighifan	PROPN
ejpam-3822	143	6	and	and	CCONJ
ejpam-3822	143	7	clemente	clemente	PROPN
ejpam-3822	143	8	cesarano	cesarano	PROPN
ejpam-3822	143	9	.	.	PUNCT
ejpam-3822	144	1	some	some	DET
ejpam-3822	144	2	new	new	ADJ
ejpam-3822	144	3	oscillation	oscillation	NOUN
ejpam-3822	144	4	criteria	criterion	NOUN
ejpam-3822	144	5	for	for	ADP
ejpam-3822	144	6	second	second	ADJ
ejpam-3822	144	7	order	order	NOUN
ejpam-3822	144	8	neutral	neutral	ADJ
ejpam-3822	144	9	differential	differential	ADJ
ejpam-3822	144	10	equations	equation	NOUN
ejpam-3822	144	11	with	with	ADP
ejpam-3822	144	12	delayed	delay	VERB
ejpam-3822	144	13	arguments	argument	NOUN
ejpam-3822	144	14	.	.	PUNCT
ejpam-3822	145	1	mathematics	mathematic	NOUN
ejpam-3822	145	2	,	,	PUNCT
ejpam-3822	145	3	7(7):619	7(7):619	NUM
ejpam-3822	145	4	,	,	PUNCT
ejpam-3822	145	5	2019	2019	NUM
ejpam-3822	145	6	.	.	PUNCT
ejpam-3822	146	1	[	[	X
ejpam-3822	146	2	3	3	X
ejpam-3822	146	3	]	]	X
ejpam-3822	146	4	omar	omar	PROPN
ejpam-3822	146	5	bazighifan	bazighifan	PROPN
ejpam-3822	146	6	and	and	CCONJ
ejpam-3822	146	7	clemente	clemente	PROPN
ejpam-3822	146	8	cesarano	cesarano	PROPN
ejpam-3822	146	9	.	.	PUNCT
ejpam-3822	147	1	a	a	DET
ejpam-3822	147	2	philos	philos	NOUN
ejpam-3822	147	3	-	-	PUNCT
ejpam-3822	147	4	type	type	NOUN
ejpam-3822	147	5	oscillation	oscillation	NOUN
ejpam-3822	147	6	criteria	criterion	NOUN
ejpam-3822	147	7	for	for	ADP
ejpam-3822	147	8	fourthorder	fourthorder	NOUN
ejpam-3822	147	9	neutral	neutral	ADJ
ejpam-3822	147	10	differential	differential	NOUN
ejpam-3822	147	11	equations	equation	NOUN
ejpam-3822	147	12	.	.	PUNCT
ejpam-3822	148	1	symmetry	symmetry	PROPN
ejpam-3822	148	2	,	,	PUNCT
ejpam-3822	148	3	12(3):379	12(3):379	NUM
ejpam-3822	148	4	,	,	PUNCT
ejpam-3822	148	5	2020	2020	NUM
ejpam-3822	148	6	.	.	PUNCT
ejpam-3822	149	1	[	[	X
ejpam-3822	149	2	4	4	NUM
ejpam-3822	149	3	]	]	X
ejpam-3822	149	4	c	c	PROPN
ejpam-3822	149	5	carlos	carlos	PROPN
ejpam-3822	149	6	-	-	PUNCT
ejpam-3822	149	7	chavez	chavez	PROPN
ejpam-3822	149	8	,	,	PUNCT
ejpam-3822	149	9	f	f	PROPN
ejpam-3822	149	10	zhilan	zhilan	NOUN
ejpam-3822	149	11	,	,	PUNCT
ejpam-3822	149	12	and	and	CCONJ
ejpam-3822	149	13	w	w	PROPN
ejpam-3822	149	14	huang	huang	PROPN
ejpam-3822	149	15	.	.	PUNCT
ejpam-3822	150	1	on	on	ADP
ejpam-3822	150	2	the	the	DET
ejpam-3822	150	3	computation	computation	NOUN
ejpam-3822	150	4	of	of	ADP
ejpam-3822	150	5	and	and	CCONJ
ejpam-3822	150	6	its	its	PRON
ejpam-3822	150	7	role	role	NOUN
ejpam-3822	150	8	on	on	ADP
ejpam-3822	150	9	global	global	ADJ
ejpam-3822	150	10	stability	stability	NOUN
ejpam-3822	150	11	.	.	PUNCT
ejpam-3822	151	1	institute	institute	PROPN
ejpam-3822	151	2	for	for	ADP
ejpam-3822	151	3	mathematics	mathematic	NOUN
ejpam-3822	151	4	and	and	CCONJ
ejpam-3822	151	5	its	its	PRON
ejpam-3822	151	6	application	application	NOUN
ejpam-3822	151	7	,	,	PUNCT
ejpam-3822	151	8	125	125	NUM
ejpam-3822	151	9	,	,	PUNCT
ejpam-3822	151	10	2001	2001	NUM
ejpam-3822	151	11	.	.	PUNCT
ejpam-3822	152	1	[	[	X
ejpam-3822	152	2	5	5	NUM
ejpam-3822	152	3	]	]	X
ejpam-3822	152	4	brian	brian	PROPN
ejpam-3822	152	5	d	d	PROPN
ejpam-3822	152	6	hassard	hassard	NOUN
ejpam-3822	152	7	,	,	PUNCT
ejpam-3822	152	8	db	db	ADP
ejpam-3822	152	9	hassard	hassard	NOUN
ejpam-3822	152	10	,	,	PUNCT
ejpam-3822	152	11	nicholas	nicholas	PROPN
ejpam-3822	152	12	d	d	PROPN
ejpam-3822	152	13	kazarinoff	kazarinoff	PROPN
ejpam-3822	152	14	,	,	PUNCT
ejpam-3822	152	15	y	y	PROPN
ejpam-3822	152	16	-	-	PUNCT
ejpam-3822	152	17	h	h	NOUN
ejpam-3822	152	18	wan	wan	PROPN
ejpam-3822	152	19	,	,	PUNCT
ejpam-3822	152	20	and	and	CCONJ
ejpam-3822	152	21	y	y	PROPN
ejpam-3822	152	22	wah	wah	PROPN
ejpam-3822	152	23	wan	wan	PROPN
ejpam-3822	152	24	.	.	PROPN
ejpam-3822	152	25	theory	theory	NOUN
ejpam-3822	152	26	and	and	CCONJ
ejpam-3822	152	27	applications	application	NOUN
ejpam-3822	152	28	of	of	ADP
ejpam-3822	152	29	hopf	hopf	ADJ
ejpam-3822	152	30	bifurcation	bifurcation	NOUN
ejpam-3822	152	31	,	,	PUNCT
ejpam-3822	152	32	volume	volume	NOUN
ejpam-3822	152	33	41	41	NUM
ejpam-3822	152	34	.	.	PUNCT
ejpam-3822	153	1	cup	cup	NOUN
ejpam-3822	153	2	archive	archive	NOUN
ejpam-3822	153	3	,	,	PUNCT
ejpam-3822	153	4	1981	1981	NUM
ejpam-3822	153	5	.	.	PUNCT
ejpam-3822	154	1	[	[	X
ejpam-3822	154	2	6	6	NUM
ejpam-3822	154	3	]	]	PUNCT
ejpam-3822	154	4	benjamin	benjamin	PROPN
ejpam-3822	154	5	a	a	DET
ejpam-3822	154	6	lopman	lopman	NOUN
ejpam-3822	154	7	,	,	PUNCT
ejpam-3822	154	8	virginia	virginia	PROPN
ejpam-3822	154	9	e	e	PROPN
ejpam-3822	154	10	pitzer	pitzer	PROPN
ejpam-3822	154	11	,	,	PUNCT
ejpam-3822	154	12	rajiv	rajiv	PROPN
ejpam-3822	154	13	sarkar	sarkar	PROPN
ejpam-3822	154	14	,	,	PUNCT
ejpam-3822	154	15	beryl	beryl	PROPN
ejpam-3822	154	16	gladstone	gladstone	PROPN
ejpam-3822	154	17	,	,	PUNCT
ejpam-3822	154	18	manish	manish	PROPN
ejpam-3822	154	19	patel	patel	PROPN
ejpam-3822	154	20	,	,	PUNCT
ejpam-3822	154	21	john	john	PROPN
ejpam-3822	154	22	glasser	glasser	PROPN
ejpam-3822	154	23	,	,	PUNCT
ejpam-3822	154	24	manoj	manoj	PROPN
ejpam-3822	154	25	gambhir	gambhir	PROPN
ejpam-3822	154	26	,	,	PUNCT
ejpam-3822	154	27	christina	christina	PROPN
ejpam-3822	154	28	atchison	atchison	PROPN
ejpam-3822	154	29	,	,	PUNCT
ejpam-3822	154	30	bryan	bryan	PROPN
ejpam-3822	154	31	t	t	PROPN
ejpam-3822	154	32	grenfell	grenfell	PROPN
ejpam-3822	154	33	,	,	PUNCT
ejpam-3822	154	34	w	w	PROPN
ejpam-3822	154	35	john	john	PROPN
ejpam-3822	154	36	edmunds	edmunds	PROPN
ejpam-3822	154	37	,	,	PUNCT
ejpam-3822	154	38	et	et	PROPN
ejpam-3822	154	39	al	al	PROPN
ejpam-3822	154	40	.	.	PUNCT
ejpam-3822	154	41	understanding	understand	VERB
ejpam-3822	154	42	reduced	reduce	VERB
ejpam-3822	154	43	rotavirus	rotavirus	NOUN
ejpam-3822	154	44	vaccine	vaccine	NOUN
ejpam-3822	154	45	efficacy	efficacy	NOUN
ejpam-3822	154	46	in	in	ADP
ejpam-3822	154	47	low	low	ADJ
ejpam-3822	154	48	socio	socio	NOUN
ejpam-3822	154	49	-	-	PUNCT
ejpam-3822	154	50	economic	economic	ADJ
ejpam-3822	154	51	settings	setting	NOUN
ejpam-3822	154	52	.	.	PUNCT
ejpam-3822	155	1	plos	plos	PROPN
ejpam-3822	155	2	one	one	NUM
ejpam-3822	155	3	,	,	PUNCT
ejpam-3822	155	4	7(8):e41720	7(8):e41720	NUM
ejpam-3822	155	5	,	,	PUNCT
ejpam-3822	155	6	2012	2012	NUM
ejpam-3822	155	7	.	.	PUNCT
ejpam-3822	156	1	[	[	X
ejpam-3822	156	2	7	7	X
ejpam-3822	156	3	]	]	X
ejpam-3822	156	4	jerrold	jerrold	PROPN
ejpam-3822	156	5	e	e	PROPN
ejpam-3822	156	6	marsden	marsden	PROPN
ejpam-3822	156	7	and	and	CCONJ
ejpam-3822	156	8	marjorie	marjorie	PROPN
ejpam-3822	156	9	mccracken	mccracken	PROPN
ejpam-3822	156	10	.	.	PUNCT
ejpam-3822	157	1	the	the	DET
ejpam-3822	157	2	hopf	hopf	ADJ
ejpam-3822	157	3	bifurcation	bifurcation	NOUN
ejpam-3822	157	4	and	and	CCONJ
ejpam-3822	157	5	its	its	PRON
ejpam-3822	157	6	applications	application	NOUN
ejpam-3822	157	7	,	,	PUNCT
ejpam-3822	157	8	volume	volume	NOUN
ejpam-3822	157	9	19	19	NUM
ejpam-3822	157	10	.	.	PUNCT
ejpam-3822	157	11	springer	springer	PROPN
ejpam-3822	157	12	science	science	PROPN
ejpam-3822	157	13	&	&	CCONJ
ejpam-3822	157	14	business	business	NOUN
ejpam-3822	157	15	media	medium	NOUN
ejpam-3822	157	16	,	,	PUNCT
ejpam-3822	157	17	2012	2012	NUM
ejpam-3822	157	18	.	.	PUNCT
ejpam-3822	158	1	[	[	X
ejpam-3822	158	2	8	8	NUM
ejpam-3822	158	3	]	]	PUNCT
ejpam-3822	158	4	onyango	onyango	PROPN
ejpam-3822	158	5	lawrence	lawrence	PROPN
ejpam-3822	158	6	omondi	omondi	PROPN
ejpam-3822	158	7	,	,	PUNCT
ejpam-3822	158	8	chuncheng	chuncheng	PROPN
ejpam-3822	158	9	wang	wang	PROPN
ejpam-3822	158	10	,	,	PUNCT
ejpam-3822	158	11	xiaoping	xiaoping	PROPN
ejpam-3822	158	12	xue	xue	PROPN
ejpam-3822	158	13	,	,	PUNCT
ejpam-3822	158	14	and	and	CCONJ
ejpam-3822	158	15	owuor	owuor	PROPN
ejpam-3822	158	16	george	george	PROPN
ejpam-3822	158	17	lawi	lawi	PROPN
ejpam-3822	158	18	.	.	PUNCT
ejpam-3822	159	1	modeling	model	VERB
ejpam-3822	159	2	the	the	DET
ejpam-3822	159	3	effects	effect	NOUN
ejpam-3822	159	4	of	of	ADP
ejpam-3822	159	5	vaccination	vaccination	NOUN
ejpam-3822	159	6	on	on	ADP
ejpam-3822	159	7	rotavirus	rotavirus	NOUN
ejpam-3822	159	8	infection	infection	NOUN
ejpam-3822	159	9	.	.	PUNCT
ejpam-3822	160	1	advances	advance	NOUN
ejpam-3822	160	2	in	in	ADP
ejpam-3822	160	3	difference	difference	NOUN
ejpam-3822	160	4	equations	equation	NOUN
ejpam-3822	160	5	,	,	PUNCT
ejpam-3822	160	6	2015(1):381	2015(1):381	NUM
ejpam-3822	160	7	,	,	PUNCT
ejpam-3822	160	8	2015	2015	NUM
ejpam-3822	160	9	.	.	PUNCT
ejpam-3822	161	1	[	[	X
ejpam-3822	161	2	9	9	NUM
ejpam-3822	161	3	]	]	SYM
ejpam-3822	161	4	virginia	virginia	PROPN
ejpam-3822	161	5	e	e	PROPN
ejpam-3822	161	6	pitzer	pitzer	PROPN
ejpam-3822	161	7	,	,	PUNCT
ejpam-3822	161	8	katherine	katherine	PROPN
ejpam-3822	161	9	e	e	PROPN
ejpam-3822	161	10	atkins	atkins	PROPN
ejpam-3822	161	11	,	,	PUNCT
ejpam-3822	161	12	birgitte	birgitte	NOUN
ejpam-3822	161	13	freiesleben	freiesleben	NOUN
ejpam-3822	161	14	de	de	X
ejpam-3822	161	15	blasio	blasio	ADJ
ejpam-3822	161	16	,	,	PUNCT
ejpam-3822	161	17	thierry	thierry	PROPN
ejpam-3822	161	18	van	van	PROPN
ejpam-3822	161	19	effelterre	effelterre	PROPN
ejpam-3822	161	20	,	,	PUNCT
ejpam-3822	161	21	christina	christina	PROPN
ejpam-3822	161	22	j	j	PROPN
ejpam-3822	161	23	atchison	atchison	PROPN
ejpam-3822	161	24	,	,	PUNCT
ejpam-3822	161	25	john	john	PROPN
ejpam-3822	161	26	p	p	PROPN
ejpam-3822	161	27	harris	harris	PROPN
ejpam-3822	161	28	,	,	PUNCT
ejpam-3822	161	29	eunha	eunha	VERB
ejpam-3822	161	30	shim	shim	NOUN
ejpam-3822	161	31	,	,	PUNCT
ejpam-3822	161	32	alison	alison	PROPN
ejpam-3822	161	33	p	p	PROPN
ejpam-3822	161	34	galvani	galvani	PROPN
ejpam-3822	161	35	,	,	PUNCT
ejpam-3822	161	36	w	w	PROPN
ejpam-3822	161	37	john	john	PROPN
ejpam-3822	161	38	edmunds	edmunds	PROPN
ejpam-3822	161	39	,	,	PUNCT
ejpam-3822	161	40	cecile	cecile	PROPN
ejpam-3822	161	41	viboud	viboud	PROPN
ejpam-3822	161	42	,	,	PUNCT
ejpam-3822	161	43	et	et	PROPN
ejpam-3822	161	44	al	al	PROPN
ejpam-3822	161	45	.	.	PROPN
ejpam-3822	162	1	direct	direct	ADJ
ejpam-3822	162	2	and	and	CCONJ
ejpam-3822	162	3	indirect	indirect	ADJ
ejpam-3822	162	4	effects	effect	NOUN
ejpam-3822	162	5	of	of	ADP
ejpam-3822	162	6	rotavirus	rotavirus	NOUN
ejpam-3822	162	7	vaccination	vaccination	NOUN
ejpam-3822	162	8	:	:	PUNCT
ejpam-3822	162	9	comparing	compare	VERB
ejpam-3822	162	10	predictions	prediction	NOUN
ejpam-3822	162	11	from	from	ADP
ejpam-3822	162	12	transmission	transmission	NOUN
ejpam-3822	162	13	dynamic	dynamic	ADJ
ejpam-3822	162	14	models	model	NOUN
ejpam-3822	162	15	.	.	PUNCT
ejpam-3822	163	1	plos	plos	PROPN
ejpam-3822	163	2	one	one	NUM
ejpam-3822	163	3	,	,	PUNCT
ejpam-3822	163	4	7(8):e42320	7(8):e42320	NUM
ejpam-3822	163	5	,	,	PUNCT
ejpam-3822	163	6	2012	2012	NUM
ejpam-3822	163	7	.	.	PUNCT
ejpam-3822	164	1	[	[	X
ejpam-3822	164	2	10	10	NUM
ejpam-3822	164	3	]	]	PUNCT
ejpam-3822	164	4	sine	sine	ADJ
ejpam-3822	164	5	leergaard	leergaard	PROPN
ejpam-3822	164	6	wiggers	wiggers	PROPN
ejpam-3822	164	7	and	and	CCONJ
ejpam-3822	164	8	pauli	pauli	PROPN
ejpam-3822	164	9	pedersen	pedersen	PROPN
ejpam-3822	164	10	.	.	PUNCT
ejpam-3822	165	1	routh	routh	PROPN
ejpam-3822	165	2	–	–	PUNCT
ejpam-3822	165	3	hurwitz	hurwitz	PROPN
ejpam-3822	165	4	-	-	PUNCT
ejpam-3822	165	5	liénard	liénard	PROPN
ejpam-3822	165	6	–	–	PUNCT
ejpam-3822	165	7	chipart	chipart	NOUN
ejpam-3822	165	8	criteria	criterion	NOUN
ejpam-3822	165	9	.	.	PUNCT
ejpam-3822	166	1	in	in	ADP
ejpam-3822	166	2	structural	structural	ADJ
ejpam-3822	166	3	stability	stability	NOUN
ejpam-3822	166	4	and	and	CCONJ
ejpam-3822	166	5	vibration	vibration	NOUN
ejpam-3822	166	6	,	,	PUNCT
ejpam-3822	166	7	pages	page	NOUN
ejpam-3822	166	8	133–140	133–140	NUM
ejpam-3822	166	9	.	.	PUNCT
ejpam-3822	166	10	springer	springer	NOUN
ejpam-3822	166	11	,	,	PUNCT
ejpam-3822	166	12	2018	2018	NUM
ejpam-3822	166	13	.	.	PUNCT