id	sid	tid	token	lemma	pos
ejpam-3454	1	1	european	european	PROPN
ejpam-3454	1	2	journal	journal	PROPN
ejpam-3454	1	3	of	of	ADP
ejpam-3454	1	4	pure	pure	ADJ
ejpam-3454	1	5	and	and	CCONJ
ejpam-3454	1	6	applied	apply	VERB
ejpam-3454	1	7	mathematics	mathematic	NOUN
ejpam-3454	1	8	vol	vol	NOUN
ejpam-3454	1	9	.	.	PROPN
ejpam-3454	2	1	12	12	NUM
ejpam-3454	2	2	,	,	PUNCT
ejpam-3454	2	3	no	no	INTJ
ejpam-3454	2	4	.	.	NOUN
ejpam-3454	2	5	3	3	NUM
ejpam-3454	2	6	,	,	PUNCT
ejpam-3454	2	7	2019	2019	NUM
ejpam-3454	2	8	,	,	PUNCT
ejpam-3454	2	9	944	944	NUM
ejpam-3454	2	10	-	-	SYM
ejpam-3454	2	11	959	959	NUM
ejpam-3454	2	12	issn	issn	PROPN
ejpam-3454	2	13	1307	1307	NUM
ejpam-3454	2	14	-	-	SYM
ejpam-3454	2	15	5543	5543	NUM
ejpam-3454	2	16	–	–	PUNCT
ejpam-3454	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3454	2	18	published	publish	VERB
ejpam-3454	2	19	by	by	ADP
ejpam-3454	2	20	new	new	PROPN
ejpam-3454	2	21	york	york	PROPN
ejpam-3454	2	22	business	business	PROPN
ejpam-3454	2	23	global	global	ADJ
ejpam-3454	2	24	global	global	ADJ
ejpam-3454	2	25	dynamics	dynamic	NOUN
ejpam-3454	2	26	of	of	ADP
ejpam-3454	2	27	an	an	DET
ejpam-3454	2	28	hepatitis	hepatitis	NOUN
ejpam-3454	2	29	c	c	PROPN
ejpam-3454	2	30	virus	virus	PROPN
ejpam-3454	2	31	mathematical	mathematical	ADJ
ejpam-3454	2	32	cellular	cellular	ADJ
ejpam-3454	2	33	model	model	NOUN
ejpam-3454	2	34	with	with	ADP
ejpam-3454	2	35	a	a	DET
ejpam-3454	2	36	logistic	logistic	ADJ
ejpam-3454	2	37	term	term	NOUN
ejpam-3454	2	38	alexis	alexis	PROPN
ejpam-3454	2	39	nangue1,∗	nangue1,∗	PROPN
ejpam-3454	2	40	,	,	PUNCT
ejpam-3454	2	41	thiery	thiery	VERB
ejpam-3454	2	42	donfack1	donfack1	PROPN
ejpam-3454	2	43	,	,	PUNCT
ejpam-3454	2	44	david	david	PROPN
ejpam-3454	2	45	avava	avava	PROPN
ejpam-3454	2	46	ndode	ndode	PROPN
ejpam-3454	2	47	yafago1	yafago1	PROPN
ejpam-3454	2	48	1	1	NUM
ejpam-3454	2	49	department	department	NOUN
ejpam-3454	2	50	of	of	ADP
ejpam-3454	2	51	mathematics	mathematic	NOUN
ejpam-3454	2	52	,	,	PUNCT
ejpam-3454	2	53	higher	high	ADJ
ejpam-3454	2	54	teacher	teacher	NOUN
ejpam-3454	2	55	’s	’s	PART
ejpam-3454	2	56	training	training	NOUN
ejpam-3454	2	57	college	college	NOUN
ejpam-3454	2	58	,	,	PUNCT
ejpam-3454	2	59	university	university	NOUN
ejpam-3454	2	60	of	of	ADP
ejpam-3454	2	61	maroua	maroua	PROPN
ejpam-3454	2	62	,	,	PUNCT
ejpam-3454	2	63	cameroon	cameroon	PROPN
ejpam-3454	2	64	abstract	abstract	NOUN
ejpam-3454	2	65	.	.	PUNCT
ejpam-3454	3	1	in	in	ADP
ejpam-3454	3	2	this	this	DET
ejpam-3454	3	3	paper	paper	NOUN
ejpam-3454	3	4	,	,	PUNCT
ejpam-3454	3	5	the	the	DET
ejpam-3454	3	6	aim	aim	NOUN
ejpam-3454	3	7	is	be	AUX
ejpam-3454	3	8	to	to	PART
ejpam-3454	3	9	analyze	analyze	VERB
ejpam-3454	3	10	the	the	DET
ejpam-3454	3	11	global	global	ADJ
ejpam-3454	3	12	dynamics	dynamic	NOUN
ejpam-3454	3	13	of	of	ADP
ejpam-3454	3	14	hepatitis	hepatitis	PROPN
ejpam-3454	3	15	c	c	PROPN
ejpam-3454	3	16	virus	virus	NOUN
ejpam-3454	3	17	(	(	PUNCT
ejpam-3454	3	18	hcv	hcv	NOUN
ejpam-3454	3	19	)	)	PUNCT
ejpam-3454	3	20	cellular	cellular	ADJ
ejpam-3454	3	21	mathematical	mathematical	ADJ
ejpam-3454	3	22	model	model	NOUN
ejpam-3454	3	23	under	under	ADP
ejpam-3454	3	24	therapy	therapy	NOUN
ejpam-3454	3	25	with	with	ADP
ejpam-3454	3	26	uninfected	uninfected	ADJ
ejpam-3454	3	27	hepatocytes	hepatocyte	NOUN
ejpam-3454	3	28	proliferation	proliferation	NOUN
ejpam-3454	3	29	.	.	PUNCT
ejpam-3454	4	1	we	we	PRON
ejpam-3454	4	2	prove	prove	VERB
ejpam-3454	4	3	that	that	SCONJ
ejpam-3454	4	4	the	the	DET
ejpam-3454	4	5	solution	solution	NOUN
ejpam-3454	4	6	of	of	ADP
ejpam-3454	4	7	the	the	DET
ejpam-3454	4	8	model	model	NOUN
ejpam-3454	4	9	with	with	ADP
ejpam-3454	4	10	positive	positive	ADJ
ejpam-3454	4	11	initial	initial	ADJ
ejpam-3454	4	12	values	value	NOUN
ejpam-3454	4	13	are	be	AUX
ejpam-3454	4	14	global	global	ADJ
ejpam-3454	4	15	,	,	PUNCT
ejpam-3454	4	16	positive	positive	ADJ
ejpam-3454	4	17	and	and	CCONJ
ejpam-3454	4	18	bounded	bound	VERB
ejpam-3454	4	19	.	.	PUNCT
ejpam-3454	5	1	in	in	ADP
ejpam-3454	5	2	addition	addition	NOUN
ejpam-3454	5	3	,	,	PUNCT
ejpam-3454	5	4	firstly	firstly	ADV
ejpam-3454	5	5	we	we	PRON
ejpam-3454	5	6	show	show	VERB
ejpam-3454	5	7	that	that	SCONJ
ejpam-3454	5	8	the	the	DET
ejpam-3454	5	9	model	model	NOUN
ejpam-3454	5	10	is	be	AUX
ejpam-3454	5	11	locally	locally	ADV
ejpam-3454	5	12	asymptotically	asymptotically	ADV
ejpam-3454	5	13	stable	stable	ADJ
ejpam-3454	5	14	at	at	ADP
ejpam-3454	5	15	free	free	PROPN
ejpam-3454	5	16	virus	virus	NOUN
ejpam-3454	5	17	equilibrium	equilibrium	NOUN
ejpam-3454	5	18	and	and	CCONJ
ejpam-3454	5	19	also	also	ADV
ejpam-3454	5	20	at	at	ADP
ejpam-3454	5	21	infected	infected	ADJ
ejpam-3454	5	22	equilibrium	equilibrium	NOUN
ejpam-3454	5	23	.	.	PUNCT
ejpam-3454	6	1	secondly	secondly	ADV
ejpam-3454	6	2	we	we	PRON
ejpam-3454	6	3	show	show	VERB
ejpam-3454	6	4	that	that	SCONJ
ejpam-3454	6	5	the	the	DET
ejpam-3454	6	6	model	model	NOUN
ejpam-3454	6	7	is	be	AUX
ejpam-3454	6	8	globally	globally	ADV
ejpam-3454	6	9	asymptotically	asymptotically	ADV
ejpam-3454	6	10	stable	stable	ADJ
ejpam-3454	6	11	at	at	ADP
ejpam-3454	6	12	the	the	DET
ejpam-3454	6	13	free	free	PROPN
ejpam-3454	6	14	virus	virus	NOUN
ejpam-3454	6	15	equilibrium	equilibrium	NOUN
ejpam-3454	6	16	by	by	ADP
ejpam-3454	6	17	using	use	VERB
ejpam-3454	6	18	an	an	DET
ejpam-3454	6	19	appropriate	appropriate	ADJ
ejpam-3454	6	20	lyapunov	lyapunov	NOUN
ejpam-3454	6	21	function	function	NOUN
ejpam-3454	6	22	.	.	PUNCT
ejpam-3454	7	1	2010	2010	NUM
ejpam-3454	7	2	mathematics	mathematic	NOUN
ejpam-3454	7	3	subject	subject	NOUN
ejpam-3454	7	4	classifications	classification	NOUN
ejpam-3454	7	5	:	:	PUNCT
ejpam-3454	7	6	92b99	92b99	NUM
ejpam-3454	7	7	,	,	PUNCT
ejpam-3454	7	8	34d23	34d23	NUM
ejpam-3454	7	9	,	,	PUNCT
ejpam-3454	7	10	92d25	92d25	NUM
ejpam-3454	7	11	key	key	ADJ
ejpam-3454	7	12	words	word	NOUN
ejpam-3454	7	13	and	and	CCONJ
ejpam-3454	7	14	phrases	phrase	NOUN
ejpam-3454	7	15	:	:	PUNCT
ejpam-3454	7	16	hcv	hcv	VERB
ejpam-3454	7	17	cellular	cellular	ADJ
ejpam-3454	7	18	model	model	NOUN
ejpam-3454	7	19	,	,	PUNCT
ejpam-3454	7	20	local	local	ADJ
ejpam-3454	7	21	and	and	CCONJ
ejpam-3454	7	22	global	global	ADJ
ejpam-3454	7	23	solution	solution	NOUN
ejpam-3454	7	24	,	,	PUNCT
ejpam-3454	7	25	invariant	invariant	ADJ
ejpam-3454	7	26	set	set	NOUN
ejpam-3454	7	27	,	,	PUNCT
ejpam-3454	7	28	stability	stability	NOUN
ejpam-3454	7	29	,	,	PUNCT
ejpam-3454	7	30	basic	basic	ADJ
ejpam-3454	7	31	reproduction	reproduction	NOUN
ejpam-3454	7	32	ratio	ratio	NOUN
ejpam-3454	8	1	,	,	PUNCT
ejpam-3454	8	2	lyapunov	lyapunov	NOUN
ejpam-3454	8	3	function	function	VERB
ejpam-3454	8	4	1	1	NUM
ejpam-3454	8	5	.	.	PUNCT
ejpam-3454	9	1	introduction	introduction	NOUN
ejpam-3454	9	2	viral	viral	ADJ
ejpam-3454	9	3	hepatitis	hepatitis	NOUN
ejpam-3454	9	4	c	c	PROPN
ejpam-3454	9	5	is	be	AUX
ejpam-3454	9	6	an	an	DET
ejpam-3454	9	7	infectious	infectious	ADJ
ejpam-3454	9	8	disease	disease	NOUN
ejpam-3454	9	9	caused	cause	VERB
ejpam-3454	9	10	by	by	ADP
ejpam-3454	9	11	the	the	DET
ejpam-3454	9	12	hepatitis	hepatitis	PROPN
ejpam-3454	9	13	c	c	PROPN
ejpam-3454	9	14	virus	virus	NOUN
ejpam-3454	9	15	(	(	PUNCT
ejpam-3454	9	16	hcv	hcv	PROPN
ejpam-3454	9	17	)	)	PUNCT
ejpam-3454	9	18	.	.	PUNCT
ejpam-3454	10	1	it	it	PRON
ejpam-3454	10	2	is	be	AUX
ejpam-3454	10	3	among	among	ADP
ejpam-3454	10	4	the	the	DET
ejpam-3454	10	5	causes	cause	NOUN
ejpam-3454	10	6	of	of	ADP
ejpam-3454	10	7	liver	liver	NOUN
ejpam-3454	10	8	cancer	cancer	NOUN
ejpam-3454	10	9	,	,	PUNCT
ejpam-3454	10	10	the	the	DET
ejpam-3454	10	11	latter	latter	ADJ
ejpam-3454	10	12	being	be	AUX
ejpam-3454	10	13	one	one	NUM
ejpam-3454	10	14	of	of	ADP
ejpam-3454	10	15	the	the	DET
ejpam-3454	10	16	biggest	big	ADJ
ejpam-3454	10	17	causes	cause	NOUN
ejpam-3454	10	18	of	of	ADP
ejpam-3454	10	19	death	death	NOUN
ejpam-3454	10	20	in	in	ADP
ejpam-3454	10	21	the	the	DET
ejpam-3454	10	22	world	world	NOUN
ejpam-3454	10	23	.	.	PUNCT
ejpam-3454	11	1	in	in	ADP
ejpam-3454	11	2	particular	particular	ADJ
ejpam-3454	11	3	,	,	PUNCT
ejpam-3454	11	4	according	accord	VERB
ejpam-3454	11	5	to	to	ADP
ejpam-3454	11	6	the	the	DET
ejpam-3454	11	7	2018	2018	NUM
ejpam-3454	11	8	who	who	PRON
ejpam-3454	11	9	report	report	VERB
ejpam-3454	11	10	,	,	PUNCT
ejpam-3454	11	11	10,000	10,000	NUM
ejpam-3454	11	12	people	people	NOUN
ejpam-3454	11	13	die	die	VERB
ejpam-3454	11	14	each	each	DET
ejpam-3454	11	15	year	year	NOUN
ejpam-3454	11	16	from	from	ADP
ejpam-3454	11	17	hepatitis	hepatitis	NOUN
ejpam-3454	11	18	with	with	ADP
ejpam-3454	11	19	a	a	DET
ejpam-3454	11	20	prevalence	prevalence	NOUN
ejpam-3454	11	21	rate	rate	NOUN
ejpam-3454	11	22	of	of	ADP
ejpam-3454	11	23	around	around	ADP
ejpam-3454	11	24	13	13	NUM
ejpam-3454	11	25	%	%	NOUN
ejpam-3454	11	26	for	for	ADP
ejpam-3454	11	27	hepatitis	hepatitis	PROPN
ejpam-3454	11	28	c	c	PROPN
ejpam-3454	11	29	versus	versus	ADP
ejpam-3454	11	30	10	10	NUM
ejpam-3454	11	31	%	%	NOUN
ejpam-3454	11	32	for	for	ADP
ejpam-3454	11	33	hepatitis	hepatitis	PROPN
ejpam-3454	11	34	b.	b.	PROPN
ejpam-3454	11	35	mathematical	mathematical	PROPN
ejpam-3454	11	36	and	and	CCONJ
ejpam-3454	11	37	computer	computer	NOUN
ejpam-3454	11	38	models	model	NOUN
ejpam-3454	11	39	have	have	AUX
ejpam-3454	11	40	become	become	VERB
ejpam-3454	11	41	essential	essential	ADJ
ejpam-3454	11	42	tools	tool	NOUN
ejpam-3454	11	43	for	for	ADP
ejpam-3454	11	44	analyzing	analyze	VERB
ejpam-3454	11	45	,	,	PUNCT
ejpam-3454	11	46	predicting	predict	VERB
ejpam-3454	11	47	and	and	CCONJ
ejpam-3454	11	48	controlling	control	VERB
ejpam-3454	11	49	infectious	infectious	ADJ
ejpam-3454	11	50	diseases	disease	NOUN
ejpam-3454	11	51	(	(	PUNCT
ejpam-3454	11	52	hepatitis	hepatitis	NOUN
ejpam-3454	11	53	,	,	PUNCT
ejpam-3454	11	54	hiv	hiv	PROPN
ejpam-3454	11	55	,	,	PUNCT
ejpam-3454	11	56	ebola	ebola	PROPN
ejpam-3454	11	57	,	,	PUNCT
ejpam-3454	11	58	dengue	dengue	NOUN
ejpam-3454	11	59	,	,	PUNCT
ejpam-3454	11	60	chikungunya	chikungunya	NOUN
ejpam-3454	11	61	...	...	PUNCT
ejpam-3454	11	62	)	)	PUNCT
ejpam-3454	11	63	,	,	PUNCT
ejpam-3454	11	64	both	both	CCONJ
ejpam-3454	11	65	at	at	ADP
ejpam-3454	11	66	the	the	DET
ejpam-3454	11	67	population	population	NOUN
ejpam-3454	11	68	level	level	NOUN
ejpam-3454	11	69	and	and	CCONJ
ejpam-3454	11	70	at	at	ADP
ejpam-3454	11	71	the	the	DET
ejpam-3454	11	72	individual	individual	ADJ
ejpam-3454	11	73	level	level	NOUN
ejpam-3454	11	74	.	.	PUNCT
ejpam-3454	12	1	these	these	DET
ejpam-3454	12	2	models	model	NOUN
ejpam-3454	12	3	can	can	AUX
ejpam-3454	12	4	be	be	AUX
ejpam-3454	12	5	used	use	VERB
ejpam-3454	12	6	to	to	PART
ejpam-3454	12	7	construct	construct	VERB
ejpam-3454	12	8	and	and	CCONJ
ejpam-3454	12	9	test	test	NOUN
ejpam-3454	12	10	hypotheses	hypothesis	NOUN
ejpam-3454	12	11	,	,	PUNCT
ejpam-3454	12	12	make	make	VERB
ejpam-3454	12	13	predictions	prediction	NOUN
ejpam-3454	12	14	and	and	CCONJ
ejpam-3454	12	15	evaluate	evaluate	VERB
ejpam-3454	12	16	effective	effective	ADJ
ejpam-3454	12	17	measures	measure	NOUN
ejpam-3454	12	18	to	to	PART
ejpam-3454	12	19	make	make	VERB
ejpam-3454	12	20	drugs	drug	NOUN
ejpam-3454	12	21	effective	effective	ADJ
ejpam-3454	12	22	.	.	PUNCT
ejpam-3454	13	1	numerous	numerous	ADJ
ejpam-3454	13	2	mathematical	mathematical	ADJ
ejpam-3454	13	3	models	model	NOUN
ejpam-3454	13	4	describing	describe	VERB
ejpam-3454	13	5	the	the	DET
ejpam-3454	13	6	temporal	temporal	ADJ
ejpam-3454	13	7	dynamics	dynamic	NOUN
ejpam-3454	13	8	of	of	ADP
ejpam-3454	13	9	hepatitis	hepatitis	PROPN
ejpam-3454	13	10	c	c	PROPN
ejpam-3454	13	11	virus	virus	NOUN
ejpam-3454	13	12	(	(	PUNCT
ejpam-3454	13	13	hcv	hcv	PROPN
ejpam-3454	13	14	)	)	PUNCT
ejpam-3454	13	15	have	have	AUX
ejpam-3454	13	16	been	be	AUX
ejpam-3454	13	17	proposed	propose	VERB
ejpam-3454	13	18	by	by	ADP
ejpam-3454	13	19	various	various	ADJ
ejpam-3454	13	20	authors	author	NOUN
ejpam-3454	13	21	,	,	PUNCT
ejpam-3454	13	22	such	such	ADJ
ejpam-3454	13	23	as	as	ADP
ejpam-3454	13	24	:	:	PUNCT
ejpam-3454	13	25	neumann	neumann	PROPN
ejpam-3454	13	26	et	et	PROPN
ejpam-3454	13	27	al	al	PROPN
ejpam-3454	13	28	.	.	PUNCT
ejpam-3454	14	1	[	[	X
ejpam-3454	14	2	8	8	NUM
ejpam-3454	14	3	]	]	PUNCT
ejpam-3454	14	4	in	in	ADP
ejpam-3454	14	5	1998	1998	NUM
ejpam-3454	14	6	;	;	PUNCT
ejpam-3454	14	7	guedj	guedj	NOUN
ejpam-3454	14	8	and	and	CCONJ
ejpam-3454	14	9	neumann	neumann	PROPN
ejpam-3454	15	1	[	[	X
ejpam-3454	15	2	5	5	NUM
ejpam-3454	15	3	]	]	PUNCT
ejpam-3454	15	4	in	in	ADP
ejpam-3454	15	5	2010	2010	NUM
ejpam-3454	15	6	;	;	PUNCT
ejpam-3454	15	7	chatterjee	chatterjee	PROPN
ejpam-3454	15	8	et	et	PROPN
ejpam-3454	15	9	al	al	PROPN
ejpam-3454	15	10	.	.	PUNCT
ejpam-3454	16	1	[	[	X
ejpam-3454	16	2	1	1	X
ejpam-3454	16	3	]	]	PUNCT
ejpam-3454	16	4	in	in	ADP
ejpam-3454	16	5	2012	2012	NUM
ejpam-3454	16	6	and	and	CCONJ
ejpam-3454	16	7	j.	j.	PROPN
ejpam-3454	16	8	rong	rong	PROPN
ejpam-3454	16	9	and	and	CCONJ
ejpam-3454	16	10	al	al	PROPN
ejpam-3454	16	11	.	.	PUNCT
ejpam-3454	17	1	[	[	X
ejpam-3454	17	2	6	6	NUM
ejpam-3454	17	3	]	]	PUNCT
ejpam-3454	17	4	in	in	ADP
ejpam-3454	17	5	2013	2013	NUM
ejpam-3454	17	6	.	.	PUNCT
ejpam-3454	18	1	our	our	PRON
ejpam-3454	18	2	model	model	NOUN
ejpam-3454	18	3	is	be	AUX
ejpam-3454	18	4	inspired	inspire	VERB
ejpam-3454	18	5	by	by	ADP
ejpam-3454	18	6	the	the	DET
ejpam-3454	18	7	model	model	NOUN
ejpam-3454	18	8	of	of	ADP
ejpam-3454	18	9	guedj	guedj	PROPN
ejpam-3454	18	10	and	and	CCONJ
ejpam-3454	18	11	neumann	neumann	PROPN
ejpam-3454	19	1	[	[	X
ejpam-3454	19	2	5	5	NUM
ejpam-3454	19	3	]	]	PUNCT
ejpam-3454	19	4	which	which	PRON
ejpam-3454	19	5	considers	consider	VERB
ejpam-3454	19	6	two	two	NUM
ejpam-3454	19	7	levels	level	NOUN
ejpam-3454	19	8	of	of	ADP
ejpam-3454	19	9	the	the	DET
ejpam-3454	19	10	infection	infection	NOUN
ejpam-3454	19	11	namely	namely	ADV
ejpam-3454	19	12	:	:	PUNCT
ejpam-3454	19	13	extracellular	extracellular	ADJ
ejpam-3454	19	14	infection	infection	NOUN
ejpam-3454	19	15	and	and	CCONJ
ejpam-3454	19	16	intracellular	intracellular	ADJ
ejpam-3454	19	17	infection	infection	NOUN
ejpam-3454	19	18	.	.	PUNCT
ejpam-3454	20	1	stability	stability	NOUN
ejpam-3454	20	2	is	be	AUX
ejpam-3454	20	3	a	a	DET
ejpam-3454	20	4	∗corresponding	∗corresponde	VERB
ejpam-3454	20	5	author	author	NOUN
ejpam-3454	20	6	.	.	PUNCT
ejpam-3454	21	1	doi	doi	NOUN
ejpam-3454	21	2	:	:	PUNCT
ejpam-3454	21	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3454	https://doi.org/10.29020/nybg.ejpam.v12i3.3454	DET
ejpam-3454	21	4	email	email	NOUN
ejpam-3454	21	5	addresses	address	VERB
ejpam-3454	21	6	:	:	PUNCT
ejpam-3454	21	7	alexnanga02@yahoo.fr	alexnanga02@yahoo.fr	PROPN
ejpam-3454	21	8	(	(	PUNCT
ejpam-3454	21	9	a.	a.	NOUN
ejpam-3454	21	10	nangue	nangue	PROPN
ejpam-3454	21	11	)	)	PUNCT
ejpam-3454	21	12	,	,	PUNCT
ejpam-3454	21	13	thierytd@yahoo.fr	thierytd@yahoo.fr	PROPN
ejpam-3454	21	14	(	(	PUNCT
ejpam-3454	21	15	t.	t.	PROPN
ejpam-3454	21	16	donfack	donfack	PROPN
ejpam-3454	21	17	)	)	PUNCT
ejpam-3454	21	18	,	,	PUNCT
ejpam-3454	21	19	avavadavid@gmail.com	avavadavid@gmail.com	X
ejpam-3454	22	1	(	(	PUNCT
ejpam-3454	22	2	d.	d.	PROPN
ejpam-3454	22	3	a.	a.	PROPN
ejpam-3454	22	4	yafago	yafago	PROPN
ejpam-3454	22	5	)	)	PUNCT
ejpam-3454	22	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3454	23	1	944	944	NUM
ejpam-3454	23	2	c	c	AUX
ejpam-3454	23	3	©	©	PROPN
ejpam-3454	23	4	2019	2019	NUM
ejpam-3454	23	5	ejpam	ejpam	NOUN
ejpam-3454	23	6	all	all	DET
ejpam-3454	23	7	rights	right	NOUN
ejpam-3454	23	8	reserved	reserve	VERB
ejpam-3454	23	9	.	.	PUNCT
ejpam-3454	24	1	a.	a.	NOUN
ejpam-3454	24	2	nangue	nangue	PROPN
ejpam-3454	24	3	,	,	PUNCT
ejpam-3454	24	4	t.	t.	PROPN
ejpam-3454	24	5	donfack	donfack	PROPN
ejpam-3454	24	6	,	,	PUNCT
ejpam-3454	24	7	d.	d.	PROPN
ejpam-3454	24	8	a.	a.	PROPN
ejpam-3454	24	9	ndode	ndode	PROPN
ejpam-3454	24	10	yafago	yafago	PROPN
ejpam-3454	24	11	/	/	SYM
ejpam-3454	24	12	eur	eur	PROPN
ejpam-3454	24	13	.	.	PUNCT
ejpam-3454	25	1	j.	j.	PROPN
ejpam-3454	25	2	pure	pure	PROPN
ejpam-3454	25	3	appl	appl	PROPN
ejpam-3454	25	4	.	.	PROPN
ejpam-3454	25	5	math	math	PROPN
ejpam-3454	25	6	,	,	PUNCT
ejpam-3454	25	7	12	12	NUM
ejpam-3454	25	8	(	(	PUNCT
ejpam-3454	25	9	3	3	NUM
ejpam-3454	25	10	)	)	PUNCT
ejpam-3454	25	11	(	(	PUNCT
ejpam-3454	25	12	2019	2019	NUM
ejpam-3454	25	13	)	)	PUNCT
ejpam-3454	25	14	,	,	PUNCT
ejpam-3454	25	15	944	944	NUM
ejpam-3454	25	16	-	-	SYM
ejpam-3454	25	17	959	959	NUM
ejpam-3454	25	18	945	945	NUM
ejpam-3454	25	19	central	central	ADJ
ejpam-3454	25	20	issue	issue	NOUN
ejpam-3454	25	21	in	in	ADP
ejpam-3454	25	22	the	the	DET
ejpam-3454	25	23	study	study	NOUN
ejpam-3454	25	24	of	of	ADP
ejpam-3454	25	25	the	the	DET
ejpam-3454	25	26	dynamics	dynamic	NOUN
ejpam-3454	25	27	of	of	ADP
ejpam-3454	25	28	cellular	cellular	ADJ
ejpam-3454	25	29	models	model	NOUN
ejpam-3454	25	30	.	.	PUNCT
ejpam-3454	26	1	our	our	PRON
ejpam-3454	26	2	work	work	NOUN
ejpam-3454	26	3	will	will	AUX
ejpam-3454	26	4	consist	consist	VERB
ejpam-3454	26	5	to	to	PART
ejpam-3454	26	6	study	study	VERB
ejpam-3454	26	7	the	the	DET
ejpam-3454	26	8	global	global	ADJ
ejpam-3454	26	9	dynamics	dynamic	NOUN
ejpam-3454	26	10	of	of	ADP
ejpam-3454	26	11	the	the	DET
ejpam-3454	26	12	model	model	NOUN
ejpam-3454	26	13	(	(	PUNCT
ejpam-3454	26	14	1	1	NUM
ejpam-3454	26	15	)	)	PUNCT
ejpam-3454	26	16	.	.	PUNCT
ejpam-3454	27	1	the	the	DET
ejpam-3454	27	2	mathematical	mathematical	ADJ
ejpam-3454	27	3	properties	property	NOUN
ejpam-3454	27	4	of	of	ADP
ejpam-3454	27	5	a	a	DET
ejpam-3454	27	6	certain	certain	ADJ
ejpam-3454	27	7	number	number	NOUN
ejpam-3454	27	8	of	of	ADP
ejpam-3454	27	9	models	model	NOUN
ejpam-3454	27	10	of	of	ADP
ejpam-3454	27	11	hepatitis	hepatitis	PROPN
ejpam-3454	27	12	c	c	PROPN
ejpam-3454	27	13	virus	virus	NOUN
ejpam-3454	27	14	infection	infection	NOUN
ejpam-3454	27	15	have	have	AUX
ejpam-3454	27	16	already	already	ADV
ejpam-3454	27	17	been	be	AUX
ejpam-3454	27	18	studied	study	VERB
ejpam-3454	27	19	,	,	PUNCT
ejpam-3454	27	20	for	for	ADP
ejpam-3454	27	21	example	example	NOUN
ejpam-3454	27	22	in	in	ADP
ejpam-3454	27	23	[	[	X
ejpam-3454	27	24	2	2	NUM
ejpam-3454	27	25	]	]	PUNCT
ejpam-3454	27	26	.	.	PUNCT
ejpam-3454	28	1	the	the	DET
ejpam-3454	28	2	neumann	neumann	PROPN
ejpam-3454	28	3	et	et	PROPN
ejpam-3454	28	4	al	al	PROPN
ejpam-3454	28	5	.	.	PUNCT
ejpam-3454	29	1	[	[	X
ejpam-3454	29	2	8	8	NUM
ejpam-3454	29	3	]	]	SYM
ejpam-3454	29	4	model	model	NOUN
ejpam-3454	29	5	of	of	ADP
ejpam-3454	29	6	viral	viral	ADJ
ejpam-3454	29	7	dynamics	dynamic	NOUN
ejpam-3454	29	8	,	,	PUNCT
ejpam-3454	29	9	named	name	VERB
ejpam-3454	29	10	here	here	ADV
ejpam-3454	29	11	the	the	DET
ejpam-3454	29	12	cell	cell	NOUN
ejpam-3454	29	13	infection(ci	infection(ci	ADJ
ejpam-3454	29	14	)	)	PUNCT
ejpam-3454	29	15	model	model	NOUN
ejpam-3454	29	16	is	be	AUX
ejpam-3454	29	17	the	the	DET
ejpam-3454	29	18	standard	standard	ADJ
ejpam-3454	29	19	description	description	NOUN
ejpam-3454	29	20	for	for	ADP
ejpam-3454	29	21	hcv	hcv	NOUN
ejpam-3454	29	22	kinetics	kinetic	NOUN
ejpam-3454	29	23	during	during	ADP
ejpam-3454	29	24	treatment	treatment	NOUN
ejpam-3454	29	25	.	.	PUNCT
ejpam-3454	30	1	in	in	ADP
ejpam-3454	30	2	this	this	DET
ejpam-3454	30	3	model	model	NOUN
ejpam-3454	30	4	,	,	PUNCT
ejpam-3454	30	5	the	the	DET
ejpam-3454	30	6	change	change	NOUN
ejpam-3454	30	7	in	in	ADP
ejpam-3454	30	8	viral	viral	ADJ
ejpam-3454	30	9	load	load	NOUN
ejpam-3454	30	10	,	,	PUNCT
ejpam-3454	30	11	v	v	X
ejpam-3454	30	12	(	(	PUNCT
ejpam-3454	30	13	t	t	PROPN
ejpam-3454	30	14	)	)	PUNCT
ejpam-3454	30	15	,	,	PUNCT
ejpam-3454	30	16	is	be	AUX
ejpam-3454	30	17	occurring	occur	VERB
ejpam-3454	30	18	on	on	ADP
ejpam-3454	30	19	the	the	DET
ejpam-3454	30	20	level	level	NOUN
ejpam-3454	30	21	of	of	ADP
ejpam-3454	30	22	cell	cell	NOUN
ejpam-3454	30	23	infection	infection	NOUN
ejpam-3454	30	24	and	and	CCONJ
ejpam-3454	30	25	involves	involve	VERB
ejpam-3454	30	26	de	de	X
ejpam-3454	30	27	novo	novo	NOUN
ejpam-3454	30	28	infection	infection	NOUN
ejpam-3454	30	29	(	(	PUNCT
ejpam-3454	30	30	with	with	ADP
ejpam-3454	30	31	constant	constant	ADJ
ejpam-3454	30	32	rate	rate	NOUN
ejpam-3454	30	33	β	β	NOUN
ejpam-3454	30	34	)	)	PUNCT
ejpam-3454	30	35	,	,	PUNCT
ejpam-3454	30	36	infected	infected	ADJ
ejpam-3454	30	37	cell	cell	NOUN
ejpam-3454	30	38	loss	loss	NOUN
ejpam-3454	30	39	(	(	PUNCT
ejpam-3454	30	40	with	with	ADP
ejpam-3454	30	41	constant	constant	ADJ
ejpam-3454	30	42	rate	rate	NOUN
ejpam-3454	30	43	d	d	PROPN
ejpam-3454	30	44	)	)	PUNCT
ejpam-3454	30	45	,	,	PUNCT
ejpam-3454	30	46	virus	virus	NOUN
ejpam-3454	30	47	particle	particle	NOUN
ejpam-3454	30	48	production	production	NOUN
ejpam-3454	30	49	(	(	PUNCT
ejpam-3454	30	50	with	with	ADP
ejpam-3454	30	51	constant	constant	ADJ
ejpam-3454	30	52	rate	rate	NOUN
ejpam-3454	30	53	per	per	ADP
ejpam-3454	30	54	infected	infect	VERB
ejpam-3454	30	55	cell	cell	NOUN
ejpam-3454	30	56	p	p	NOUN
ejpam-3454	30	57	)	)	PUNCT
ejpam-3454	30	58	,	,	PUNCT
ejpam-3454	30	59	and	and	CCONJ
ejpam-3454	30	60	virus	virus	NOUN
ejpam-3454	30	61	clearance	clearance	NOUN
ejpam-3454	30	62	from	from	ADP
ejpam-3454	30	63	circulation	circulation	NOUN
ejpam-3454	30	64	(	(	PUNCT
ejpam-3454	30	65	with	with	ADP
ejpam-3454	30	66	rate	rate	NOUN
ejpam-3454	30	67	constant	constant	ADJ
ejpam-3454	30	68	c	c	NOUN
ejpam-3454	30	69	)	)	PUNCT
ejpam-3454	30	70	,	,	PUNCT
ejpam-3454	30	71	in	in	ADP
ejpam-3454	30	72	figure	figure	NOUN
ejpam-3454	30	73	1	1	NUM
ejpam-3454	31	1	[	[	X
ejpam-3454	31	2	8	8	NUM
ejpam-3454	31	3	]	]	PUNCT
ejpam-3454	31	4	by	by	ADP
ejpam-3454	31	5	the	the	DET
ejpam-3454	31	6	following	follow	VERB
ejpam-3454	31	7	compartmental	compartmental	ADJ
ejpam-3454	31	8	model	model	NOUN
ejpam-3454	31	9	:	:	PUNCT
ejpam-3454	31	10	figure	figure	NOUN
ejpam-3454	31	11	1	1	NUM
ejpam-3454	31	12	:	:	PUNCT
ejpam-3454	31	13	the	the	DET
ejpam-3454	31	14	ci	ci	PROPN
ejpam-3454	31	15	model	model	NOUN
ejpam-3454	31	16	(	(	PUNCT
ejpam-3454	31	17	1)comprises	1)comprises	NUM
ejpam-3454	31	18	of	of	ADP
ejpam-3454	31	19	de	de	X
ejpam-3454	31	20	novo	novo	PROPN
ejpam-3454	31	21	infection	infection	NOUN
ejpam-3454	31	22	and	and	CCONJ
ejpam-3454	31	23	loss	loss	NOUN
ejpam-3454	31	24	of	of	ADP
ejpam-3454	31	25	infected	infected	ADJ
ejpam-3454	31	26	cells	cell	NOUN
ejpam-3454	31	27	(	(	PUNCT
ejpam-3454	31	28	i	i	NOUN
ejpam-3454	31	29	)	)	PUNCT
ejpam-3454	31	30	,	,	PUNCT
ejpam-3454	31	31	production	production	NOUN
ejpam-3454	31	32	and	and	CCONJ
ejpam-3454	31	33	clearance	clearance	NOUN
ejpam-3454	31	34	of	of	ADP
ejpam-3454	31	35	virus	virus	NOUN
ejpam-3454	31	36	in	in	ADP
ejpam-3454	31	37	circulation	circulation	NOUN
ejpam-3454	31	38	(	(	PUNCT
ejpam-3454	31	39	v	v	NOUN
ejpam-3454	31	40	)	)	PUNCT
ejpam-3454	31	41	and	and	CCONJ
ejpam-3454	31	42	target	target	NOUN
ejpam-3454	31	43	cell	cell	NOUN
ejpam-3454	31	44	(	(	PUNCT
ejpam-3454	31	45	t	t	NOUN
ejpam-3454	31	46	)	)	PUNCT
ejpam-3454	31	47	dynamics	dynamic	NOUN
ejpam-3454	31	48	.	.	PUNCT
ejpam-3454	32	1	in	in	ADP
ejpam-3454	32	2	the	the	DET
ejpam-3454	32	3	original	original	ADJ
ejpam-3454	32	4	model	model	NOUN
ejpam-3454	32	5	,	,	PUNCT
ejpam-3454	32	6	the	the	DET
ejpam-3454	32	7	target	target	NOUN
ejpam-3454	32	8	cells	cell	NOUN
ejpam-3454	32	9	t	t	PROPN
ejpam-3454	32	10	(	(	PUNCT
ejpam-3454	32	11	t	t	PROPN
ejpam-3454	32	12	)	)	PUNCT
ejpam-3454	32	13	are	be	AUX
ejpam-3454	32	14	produced	produce	VERB
ejpam-3454	32	15	at	at	ADP
ejpam-3454	32	16	a	a	DET
ejpam-3454	32	17	constant	constant	ADJ
ejpam-3454	32	18	rate	rate	NOUN
ejpam-3454	32	19	s	s	PART
ejpam-3454	32	20	and	and	CCONJ
ejpam-3454	32	21	die	die	VERB
ejpam-3454	32	22	with	with	ADP
ejpam-3454	32	23	death	death	NOUN
ejpam-3454	32	24	rate	rate	NOUN
ejpam-3454	32	25	constant	constant	ADJ
ejpam-3454	32	26	d.	d.	NOUN
ejpam-3454	32	27	in	in	ADP
ejpam-3454	32	28	this	this	DET
ejpam-3454	32	29	new	new	ADJ
ejpam-3454	32	30	model	model	NOUN
ejpam-3454	32	31	we	we	PRON
ejpam-3454	32	32	taking	take	VERB
ejpam-3454	32	33	into	into	ADP
ejpam-3454	32	34	account	account	NOUN
ejpam-3454	32	35	a	a	DET
ejpam-3454	32	36	logistic	logistic	ADJ
ejpam-3454	32	37	rate	rate	NOUN
ejpam-3454	32	38	,	,	PUNCT
ejpam-3454	32	39	r	r	NOUN
ejpam-3454	32	40	(	(	PUNCT
ejpam-3454	32	41	1−	1−	NUM
ejpam-3454	32	42	t+i	t+i	PROPN
ejpam-3454	32	43	tmax	tmax	ADV
ejpam-3454	32	44	)	)	PUNCT
ejpam-3454	32	45	,	,	PUNCT
ejpam-3454	32	46	that	that	PRON
ejpam-3454	32	47	allows	allow	VERB
ejpam-3454	32	48	for	for	ADP
ejpam-3454	32	49	a	a	DET
ejpam-3454	32	50	more	more	ADV
ejpam-3454	32	51	realistic	realistic	ADJ
ejpam-3454	32	52	growth	growth	NOUN
ejpam-3454	32	53	of	of	ADP
ejpam-3454	32	54	hepatocytes	hepatocyte	NOUN
ejpam-3454	32	55	by	by	ADP
ejpam-3454	32	56	proliferation	proliferation	NOUN
ejpam-3454	32	57	.	.	PUNCT
ejpam-3454	33	1	it	it	PRON
ejpam-3454	33	2	should	should	AUX
ejpam-3454	33	3	be	be	AUX
ejpam-3454	33	4	noted	note	VERB
ejpam-3454	33	5	that	that	SCONJ
ejpam-3454	33	6	tmax	tmax	ADJ
ejpam-3454	33	7	is	be	AUX
ejpam-3454	33	8	the	the	DET
ejpam-3454	33	9	maximum	maximum	ADJ
ejpam-3454	33	10	hepatocyte	hepatocyte	NOUN
ejpam-3454	33	11	density	density	NOUN
ejpam-3454	33	12	or	or	CCONJ
ejpam-3454	33	13	’	'	PUNCT
ejpam-3454	33	14	carrying	carry	VERB
ejpam-3454	33	15	capacity	capacity	NOUN
ejpam-3454	33	16	’	'	PUNCT
ejpam-3454	33	17	which	which	PRON
ejpam-3454	33	18	is	be	AUX
ejpam-3454	33	19	based	base	VERB
ejpam-3454	33	20	on	on	ADP
ejpam-3454	33	21	both	both	CCONJ
ejpam-3454	33	22	uninfected	uninfected	ADJ
ejpam-3454	33	23	and	and	CCONJ
ejpam-3454	33	24	infected	infected	ADJ
ejpam-3454	33	25	hepatocyte	hepatocyte	NOUN
ejpam-3454	33	26	in	in	ADP
ejpam-3454	33	27	the	the	DET
ejpam-3454	33	28	liver	liver	NOUN
ejpam-3454	33	29	.	.	PUNCT
ejpam-3454	34	1	it	it	PRON
ejpam-3454	34	2	is	be	AUX
ejpam-3454	34	3	implicitly	implicitly	ADV
ejpam-3454	34	4	assumed	assume	VERB
ejpam-3454	34	5	that	that	SCONJ
ejpam-3454	34	6	the	the	DET
ejpam-3454	34	7	vast	vast	ADJ
ejpam-3454	34	8	majority	majority	NOUN
ejpam-3454	34	9	of	of	ADP
ejpam-3454	34	10	hepatocytes	hepatocyte	NOUN
ejpam-3454	34	11	are	be	AUX
ejpam-3454	34	12	susceptible	susceptible	ADJ
ejpam-3454	34	13	to	to	ADP
ejpam-3454	34	14	infection	infection	NOUN
ejpam-3454	34	15	,	,	PUNCT
ejpam-3454	34	16	consistent	consistent	ADJ
ejpam-3454	34	17	with	with	ADP
ejpam-3454	34	18	experimental	experimental	ADJ
ejpam-3454	34	19	findings	finding	NOUN
ejpam-3454	34	20	that	that	SCONJ
ejpam-3454	34	21	a	a	DET
ejpam-3454	34	22	large	large	ADJ
ejpam-3454	34	23	proportion	proportion	NOUN
ejpam-3454	34	24	of	of	ADP
ejpam-3454	34	25	hepatocytes	hepatocyte	NOUN
ejpam-3454	34	26	can	can	AUX
ejpam-3454	34	27	be	be	AUX
ejpam-3454	34	28	infected	infect	VERB
ejpam-3454	34	29	(	(	PUNCT
ejpam-3454	34	30	rodriguez	rodriguez	NOUN
ejpam-3454	34	31	-	-	PUNCT
ejpam-3454	34	32	inigo	inigo	PROPN
ejpam-3454	34	33	et	et	PROPN
ejpam-3454	34	34	al	al	PROPN
ejpam-3454	34	35	.	.	PUNCT
ejpam-3454	35	1	[	[	X
ejpam-3454	35	2	9	9	NUM
ejpam-3454	35	3	]	]	PUNCT
ejpam-3454	35	4	;	;	PUNCT
ejpam-3454	35	5	stiffler	stiffler	PROPN
ejpam-3454	35	6	et	et	PROPN
ejpam-3454	35	7	al	al	PROPN
ejpam-3454	35	8	.	.	PUNCT
ejpam-3454	36	1	[	[	X
ejpam-3454	36	2	10	10	NUM
ejpam-3454	36	3	]	]	NUM
ejpam-3454	36	4	)	)	PUNCT
ejpam-3454	36	5	.	.	PUNCT
ejpam-3454	37	1	initially	initially	ADV
ejpam-3454	37	2	,	,	PUNCT
ejpam-3454	37	3	the	the	DET
ejpam-3454	37	4	model	model	NOUN
ejpam-3454	37	5	neglects	neglect	VERB
ejpam-3454	37	6	the	the	DET
ejpam-3454	37	7	fact	fact	NOUN
ejpam-3454	37	8	that	that	SCONJ
ejpam-3454	37	9	when	when	SCONJ
ejpam-3454	37	10	a	a	DET
ejpam-3454	37	11	cell	cell	NOUN
ejpam-3454	37	12	is	be	AUX
ejpam-3454	37	13	infected	infect	VERB
ejpam-3454	37	14	the	the	DET
ejpam-3454	37	15	number	number	NOUN
ejpam-3454	37	16	of	of	ADP
ejpam-3454	37	17	virions	virion	NOUN
ejpam-3454	37	18	outside	outside	ADP
ejpam-3454	37	19	the	the	DET
ejpam-3454	37	20	cells	cell	NOUN
ejpam-3454	37	21	is	be	AUX
ejpam-3454	37	22	reduced	reduce	VERB
ejpam-3454	37	23	by	by	ADP
ejpam-3454	37	24	one	one	NUM
ejpam-3454	37	25	.	.	PUNCT
ejpam-3454	38	1	for	for	ADP
ejpam-3454	38	2	this	this	DET
ejpam-3454	38	3	reason	reason	NOUN
ejpam-3454	38	4	the	the	DET
ejpam-3454	38	5	equation	equation	NOUN
ejpam-3454	38	6	for	for	ADP
ejpam-3454	38	7	dv	dv	PROPN
ejpam-3454	38	8	dt	dt	PROPN
ejpam-3454	38	9	should	should	AUX
ejpam-3454	38	10	contain	contain	VERB
ejpam-3454	38	11	an	an	DET
ejpam-3454	38	12	extra	extra	ADJ
ejpam-3454	38	13	term	term	NOUN
ejpam-3454	38	14	−(1−	−(1−	NOUN
ejpam-3454	38	15	η)βv	η)βv	PROPN
ejpam-3454	38	16	t	t	PROPN
ejpam-3454	38	17	.	.	PUNCT
ejpam-3454	39	1	it	it	PRON
ejpam-3454	39	2	is	be	AUX
ejpam-3454	39	3	argued	argue	VERB
ejpam-3454	39	4	,	,	PUNCT
ejpam-3454	39	5	however	however	ADV
ejpam-3454	39	6	,	,	PUNCT
ejpam-3454	39	7	that	that	SCONJ
ejpam-3454	39	8	this	this	DET
ejpam-3454	39	9	term	term	NOUN
ejpam-3454	39	10	is	be	AUX
ejpam-3454	39	11	small	small	ADJ
ejpam-3454	39	12	in	in	ADP
ejpam-3454	39	13	comparison	comparison	NOUN
ejpam-3454	39	14	to	to	ADP
ejpam-3454	39	15	other	other	ADJ
ejpam-3454	39	16	terms	term	NOUN
ejpam-3454	39	17	in	in	ADP
ejpam-3454	39	18	the	the	DET
ejpam-3454	39	19	same	same	ADJ
ejpam-3454	39	20	equation	equation	NOUN
ejpam-3454	39	21	,	,	PUNCT
ejpam-3454	39	22	so	so	SCONJ
ejpam-3454	39	23	that	that	SCONJ
ejpam-3454	39	24	it	it	PRON
ejpam-3454	39	25	is	be	AUX
ejpam-3454	39	26	justified	justify	VERB
ejpam-3454	39	27	to	to	PART
ejpam-3454	39	28	omit	omit	VERB
ejpam-3454	39	29	it	it	PRON
ejpam-3454	39	30	.	.	PUNCT
ejpam-3454	40	1	from	from	ADP
ejpam-3454	40	2	a	a	DET
ejpam-3454	40	3	mathematical	mathematical	ADJ
ejpam-3454	40	4	point	point	NOUN
ejpam-3454	40	5	of	of	ADP
ejpam-3454	40	6	view	view	NOUN
ejpam-3454	40	7	including	include	VERB
ejpam-3454	40	8	this	this	DET
ejpam-3454	40	9	effect	effect	NOUN
ejpam-3454	40	10	leads	lead	VERB
ejpam-3454	40	11	to	to	ADP
ejpam-3454	40	12	a	a	DET
ejpam-3454	40	13	new	new	ADJ
ejpam-3454	40	14	system	system	NOUN
ejpam-3454	40	15	which	which	PRON
ejpam-3454	40	16	we	we	PRON
ejpam-3454	40	17	call	call	VERB
ejpam-3454	40	18	the	the	DET
ejpam-3454	40	19	‘	'	PUNCT
ejpam-3454	40	20	modified	modified	ADJ
ejpam-3454	40	21	fundamental	fundamental	ADJ
ejpam-3454	40	22	model	model	NOUN
ejpam-3454	40	23	of	of	ADP
ejpam-3454	40	24	virus	virus	NOUN
ejpam-3454	40	25	dynamics	dynamic	NOUN
ejpam-3454	40	26	’	'	PUNCT
ejpam-3454	40	27	.	.	PUNCT
ejpam-3454	41	1	the	the	DET
ejpam-3454	41	2	additional	additional	ADJ
ejpam-3454	41	3	term	term	NOUN
ejpam-3454	41	4	can	can	AUX
ejpam-3454	41	5	be	be	AUX
ejpam-3454	41	6	written	write	VERB
ejpam-3454	41	7	as	as	ADP
ejpam-3454	41	8	−α(1−	−α(1−	PROPN
ejpam-3454	41	9	η)βv	η)βv	PROPN
ejpam-3454	41	10	t	t	PROPN
ejpam-3454	41	11	,	,	PUNCT
ejpam-3454	41	12	where	where	SCONJ
ejpam-3454	41	13	the	the	DET
ejpam-3454	41	14	parameter	parameter	NOUN
ejpam-3454	41	15	α	α	PROPN
ejpam-3454	41	16	takes	take	VERB
ejpam-3454	41	17	the	the	DET
ejpam-3454	41	18	value	value	NOUN
ejpam-3454	41	19	zero	zero	NUM
ejpam-3454	41	20	or	or	CCONJ
ejpam-3454	41	21	one	one	NUM
ejpam-3454	41	22	.	.	PUNCT
ejpam-3454	42	1	the	the	DET
ejpam-3454	42	2	phenomenon	phenomenon	NOUN
ejpam-3454	42	3	described	describe	VERB
ejpam-3454	42	4	above	above	ADV
ejpam-3454	42	5	is	be	AUX
ejpam-3454	42	6	governed	govern	VERB
ejpam-3454	42	7	according	accord	VERB
ejpam-3454	42	8	to	to	ADP
ejpam-3454	42	9	j.	j.	PROPN
ejpam-3454	42	10	guedj	guedj	PROPN
ejpam-3454	42	11	and	and	CCONJ
ejpam-3454	42	12	a.	a.	NOUN
ejpam-3454	42	13	u.	u.	PROPN
ejpam-3454	42	14	neumann	neumann	PROPN
ejpam-3454	43	1	[	[	X
ejpam-3454	43	2	5	5	NUM
ejpam-3454	43	3	]	]	PUNCT
ejpam-3454	43	4	by	by	ADP
ejpam-3454	43	5	a	a	DET
ejpam-3454	43	6	set	set	NOUN
ejpam-3454	43	7	of	of	ADP
ejpam-3454	43	8	three	three	NUM
ejpam-3454	43	9	autonomous	autonomous	ADJ
ejpam-3454	43	10	ordinary	ordinary	ADJ
ejpam-3454	43	11	differential	differential	ADJ
ejpam-3454	43	12	equations	equation	NOUN
ejpam-3454	43	13	:	:	PUNCT
ejpam-3454	43	14	a.	a.	NOUN
ejpam-3454	43	15	nangue	nangue	NOUN
ejpam-3454	43	16	,	,	PUNCT
ejpam-3454	43	17	t.	t.	PROPN
ejpam-3454	43	18	donfack	donfack	PROPN
ejpam-3454	43	19	,	,	PUNCT
ejpam-3454	43	20	d.	d.	PROPN
ejpam-3454	43	21	a.	a.	PROPN
ejpam-3454	43	22	ndode	ndode	PROPN
ejpam-3454	43	23	yafago	yafago	PROPN
ejpam-3454	43	24	/	/	SYM
ejpam-3454	43	25	eur	eur	PROPN
ejpam-3454	43	26	.	.	PUNCT
ejpam-3454	44	1	j.	j.	PROPN
ejpam-3454	44	2	pure	pure	PROPN
ejpam-3454	44	3	appl	appl	PROPN
ejpam-3454	44	4	.	.	PROPN
ejpam-3454	44	5	math	math	PROPN
ejpam-3454	44	6	,	,	PUNCT
ejpam-3454	44	7	12	12	NUM
ejpam-3454	44	8	(	(	PUNCT
ejpam-3454	44	9	3	3	NUM
ejpam-3454	44	10	)	)	PUNCT
ejpam-3454	44	11	(	(	PUNCT
ejpam-3454	44	12	2019	2019	NUM
ejpam-3454	44	13	)	)	PUNCT
ejpam-3454	44	14	,	,	PUNCT
ejpam-3454	44	15	944	944	NUM
ejpam-3454	44	16	-	-	SYM
ejpam-3454	44	17	959	959	NUM
ejpam-3454	44	18	946	946	NUM
ejpam-3454	44	19	dt	dt	NOUN
ejpam-3454	44	20	dt	dt	PROPN
ejpam-3454	44	21	=	=	PUNCT
ejpam-3454	44	22	rt	rt	PROPN
ejpam-3454	44	23	(	(	PUNCT
ejpam-3454	44	24	1−	1−	NUM
ejpam-3454	44	25	t	t	NOUN
ejpam-3454	45	1	+	+	CCONJ
ejpam-3454	45	2	i	i	PRON
ejpam-3454	45	3	tmax	tmax	ADJ
ejpam-3454	45	4	)	)	PUNCT
ejpam-3454	45	5	−	−	PROPN
ejpam-3454	46	1	(	(	PUNCT
ejpam-3454	46	2	1−	1−	NUM
ejpam-3454	46	3	η)βv	η)βv	PROPN
ejpam-3454	46	4	t	t	PROPN
ejpam-3454	46	5	−	−	PROPN
ejpam-3454	46	6	dt	dt	NOUN
ejpam-3454	46	7	;	;	PUNCT
ejpam-3454	46	8	(	(	PUNCT
ejpam-3454	46	9	1a	1a	X
ejpam-3454	46	10	)	)	PUNCT
ejpam-3454	46	11	di	di	NOUN
ejpam-3454	46	12	dt	dt	NOUN
ejpam-3454	46	13	=	=	PUNCT
ejpam-3454	46	14	(	(	PUNCT
ejpam-3454	46	15	1−	1−	NUM
ejpam-3454	46	16	η)βv	η)βv	PROPN
ejpam-3454	46	17	t	t	VERB
ejpam-3454	46	18	−	−	PROPN
ejpam-3454	46	19	δi	δi	ADV
ejpam-3454	46	20	;	;	PUNCT
ejpam-3454	46	21	(	(	PUNCT
ejpam-3454	46	22	1b	1b	NUM
ejpam-3454	46	23	)	)	PUNCT
ejpam-3454	47	1	dv	dv	PROPN
ejpam-3454	47	2	dt	dt	X
ejpam-3454	47	3	=	=	SYM
ejpam-3454	47	4	(	(	PUNCT
ejpam-3454	47	5	1−	1−	NUM
ejpam-3454	47	6	ε)pi	ε)pi	PROPN
ejpam-3454	47	7	−	−	PROPN
ejpam-3454	47	8	cv	cv	PROPN
ejpam-3454	47	9	−	−	PROPN
ejpam-3454	47	10	α(1−	α(1−	PROPN
ejpam-3454	47	11	η)βv	η)βv	PROPN
ejpam-3454	47	12	t	t	PROPN
ejpam-3454	47	13	;	;	PUNCT
ejpam-3454	47	14	(	(	PUNCT
ejpam-3454	47	15	1c	1c	X
ejpam-3454	47	16	)	)	PUNCT
ejpam-3454	47	17	where	where	SCONJ
ejpam-3454	47	18	the	the	DET
ejpam-3454	47	19	equations	equation	NOUN
ejpam-3454	47	20	relate	relate	VERB
ejpam-3454	47	21	the	the	DET
ejpam-3454	47	22	dynamics	dynamic	NOUN
ejpam-3454	47	23	relationship	relationship	NOUN
ejpam-3454	47	24	between	between	ADP
ejpam-3454	47	25	,	,	PUNCT
ejpam-3454	47	26	t	t	PROPN
ejpam-3454	47	27	as	as	ADP
ejpam-3454	47	28	the	the	DET
ejpam-3454	47	29	uninfected	uninfected	ADJ
ejpam-3454	47	30	target	target	NOUN
ejpam-3454	47	31	cells	cell	NOUN
ejpam-3454	47	32	(	(	PUNCT
ejpam-3454	47	33	hepatocytes	hepatocytes	PROPN
ejpam-3454	47	34	)	)	PUNCT
ejpam-3454	47	35	,	,	PUNCT
ejpam-3454	47	36	i	i	PRON
ejpam-3454	47	37	as	as	ADP
ejpam-3454	47	38	the	the	DET
ejpam-3454	47	39	infected	infected	ADJ
ejpam-3454	47	40	cells	cell	NOUN
ejpam-3454	47	41	and	and	CCONJ
ejpam-3454	47	42	v	v	NOUN
ejpam-3454	47	43	as	as	ADP
ejpam-3454	47	44	the	the	DET
ejpam-3454	47	45	viral	viral	ADJ
ejpam-3454	47	46	load	load	NOUN
ejpam-3454	47	47	(	(	PUNCT
ejpam-3454	47	48	amount	amount	NOUN
ejpam-3454	47	49	of	of	ADP
ejpam-3454	47	50	viruses	virus	NOUN
ejpam-3454	47	51	present	present	ADJ
ejpam-3454	47	52	in	in	ADP
ejpam-3454	47	53	the	the	DET
ejpam-3454	47	54	blood	blood	NOUN
ejpam-3454	47	55	)	)	PUNCT
ejpam-3454	47	56	.	.	PUNCT
ejpam-3454	48	1	the	the	DET
ejpam-3454	48	2	efficacy	efficacy	NOUN
ejpam-3454	48	3	of	of	ADP
ejpam-3454	48	4	treatment	treatment	NOUN
ejpam-3454	48	5	in	in	ADP
ejpam-3454	48	6	blocking	block	VERB
ejpam-3454	48	7	virion	virion	NOUN
ejpam-3454	48	8	production	production	NOUN
ejpam-3454	48	9	and	and	CCONJ
ejpam-3454	48	10	reducing	reduce	VERB
ejpam-3454	48	11	new	new	ADJ
ejpam-3454	48	12	infections	infection	NOUN
ejpam-3454	48	13	is	be	AUX
ejpam-3454	48	14	described	describe	VERB
ejpam-3454	48	15	by	by	ADP
ejpam-3454	48	16	the	the	DET
ejpam-3454	48	17	parameters	parameter	NOUN
ejpam-3454	48	18	,	,	PUNCT
ejpam-3454	48	19	ε	ε	PROPN
ejpam-3454	48	20	and	and	CCONJ
ejpam-3454	48	21	η	η	PROPN
ejpam-3454	48	22	,	,	PUNCT
ejpam-3454	48	23	respectively	respectively	ADV
ejpam-3454	48	24	,	,	PUNCT
ejpam-3454	48	25	which	which	DET
ejpam-3454	48	26	values	value	NOUN
ejpam-3454	48	27	are	be	AUX
ejpam-3454	48	28	nonnegative	nonnegative	ADJ
ejpam-3454	48	29	and	and	CCONJ
ejpam-3454	48	30	less	less	ADJ
ejpam-3454	48	31	than	than	ADP
ejpam-3454	48	32	one	one	NUM
ejpam-3454	48	33	.	.	PUNCT
ejpam-3454	49	1	for	for	ADP
ejpam-3454	49	2	biological	biological	ADJ
ejpam-3454	49	3	significance	significance	NOUN
ejpam-3454	49	4	of	of	ADP
ejpam-3454	49	5	the	the	DET
ejpam-3454	49	6	parameters	parameter	NOUN
ejpam-3454	49	7	,	,	PUNCT
ejpam-3454	49	8	one	one	NUM
ejpam-3454	49	9	assumption	assumption	NOUN
ejpam-3454	49	10	is	be	AUX
ejpam-3454	49	11	employed	employ	VERB
ejpam-3454	49	12	.	.	PUNCT
ejpam-3454	50	1	infected	infected	ADJ
ejpam-3454	50	2	cells	cell	NOUN
ejpam-3454	50	3	have	have	VERB
ejpam-3454	50	4	a	a	DET
ejpam-3454	50	5	higher	high	ADJ
ejpam-3454	50	6	turnover	turnover	NOUN
ejpam-3454	50	7	rate	rate	NOUN
ejpam-3454	50	8	than	than	ADP
ejpam-3454	50	9	uninfected	uninfected	ADJ
ejpam-3454	50	10	cells	cell	NOUN
ejpam-3454	50	11	,	,	PUNCT
ejpam-3454	50	12	i.e.	i.e.	X
ejpam-3454	50	13	d	d	X
ejpam-3454	50	14	≤	≤	ADJ
ejpam-3454	50	15	δ	δ	PROPN
ejpam-3454	51	1	and	and	CCONJ
ejpam-3454	51	2	we	we	PRON
ejpam-3454	51	3	also	also	ADV
ejpam-3454	51	4	suppose	suppose	VERB
ejpam-3454	51	5	that	that	SCONJ
ejpam-3454	51	6	r	r	NOUN
ejpam-3454	51	7	≥	≥	PROPN
ejpam-3454	51	8	d.	d.	NOUN
ejpam-3454	51	9	let	let	VERB
ejpam-3454	51	10	t0	t0	PROPN
ejpam-3454	51	11	,	,	PUNCT
ejpam-3454	51	12	i0	i0	PROPN
ejpam-3454	51	13	,	,	PUNCT
ejpam-3454	51	14	v0	v0	PROPN
ejpam-3454	51	15	∈	∈	NOUN
ejpam-3454	51	16	r	r	NOUN
ejpam-3454	51	17	be	be	AUX
ejpam-3454	51	18	given	give	VERB
ejpam-3454	51	19	real	real	ADJ
ejpam-3454	51	20	numbers	number	NOUN
ejpam-3454	51	21	.	.	PUNCT
ejpam-3454	52	1	we	we	PRON
ejpam-3454	52	2	look	look	VERB
ejpam-3454	52	3	for	for	ADP
ejpam-3454	52	4	solutions	solution	NOUN
ejpam-3454	52	5	t	t	PROPN
ejpam-3454	52	6	,	,	PUNCT
ejpam-3454	52	7	i	i	PRON
ejpam-3454	52	8	and	and	CCONJ
ejpam-3454	52	9	v	v	NOUN
ejpam-3454	52	10	of	of	ADP
ejpam-3454	52	11	the	the	DET
ejpam-3454	52	12	mathematical	mathematical	ADJ
ejpam-3454	52	13	model	model	NOUN
ejpam-3454	52	14	(	(	PUNCT
ejpam-3454	52	15	1	1	NUM
ejpam-3454	52	16	)	)	PUNCT
ejpam-3454	52	17	over	over	ADP
ejpam-3454	52	18	[	[	X
ejpam-3454	52	19	t0,+∞	t0,+∞	PROPN
ejpam-3454	52	20	[	[	X
ejpam-3454	52	21	,	,	PUNCT
ejpam-3454	52	22	t	t	NOUN
ejpam-3454	52	23	≤	≤	X
ejpam-3454	53	1	+	+	PUNCT
ejpam-3454	53	2	∞	∞	NUM
ejpam-3454	53	3	satisfying	satisfying	ADJ
ejpam-3454	53	4	:	:	PUNCT
ejpam-3454	53	5	t	t	PROPN
ejpam-3454	53	6	(	(	PUNCT
ejpam-3454	53	7	t0	t0	PROPN
ejpam-3454	53	8	)	)	PUNCT
ejpam-3454	53	9	=	=	SYM
ejpam-3454	53	10	t0	t0	PROPN
ejpam-3454	53	11	,	,	PUNCT
ejpam-3454	53	12	i(t0	i(t0	NOUN
ejpam-3454	53	13	)	)	PUNCT
ejpam-3454	53	14	=	=	SYM
ejpam-3454	53	15	i0	i0	PROPN
ejpam-3454	53	16	,	,	PUNCT
ejpam-3454	53	17	and	and	CCONJ
ejpam-3454	53	18	v	v	NOUN
ejpam-3454	53	19	(	(	PUNCT
ejpam-3454	53	20	t0	t0	NOUN
ejpam-3454	53	21	)	)	PUNCT
ejpam-3454	53	22	=	=	SYM
ejpam-3454	53	23	v0	v0	PROPN
ejpam-3454	53	24	,	,	PUNCT
ejpam-3454	53	25	t0	t0	PROPN
ejpam-3454	53	26	∈	∈	PROPN
ejpam-3454	54	1	[	[	X
ejpam-3454	54	2	0,+∞	0,+∞	NUM
ejpam-3454	55	1	[	[	X
ejpam-3454	55	2	.	.	PUNCT
ejpam-3454	56	1	(	(	PUNCT
ejpam-3454	56	2	2	2	NUM
ejpam-3454	56	3	)	)	PUNCT
ejpam-3454	56	4	(	(	PUNCT
ejpam-3454	56	5	2	2	X
ejpam-3454	56	6	)	)	PUNCT
ejpam-3454	56	7	are	be	AUX
ejpam-3454	56	8	called	call	VERB
ejpam-3454	56	9	initial	initial	ADJ
ejpam-3454	56	10	conditions	condition	NOUN
ejpam-3454	56	11	and	and	CCONJ
ejpam-3454	56	12	the	the	DET
ejpam-3454	56	13	given	give	VERB
ejpam-3454	56	14	numbers	number	NOUN
ejpam-3454	56	15	t0	t0	PROPN
ejpam-3454	56	16	,	,	PUNCT
ejpam-3454	56	17	i0	i0	PROPN
ejpam-3454	56	18	,	,	PUNCT
ejpam-3454	56	19	v0	v0	NOUN
ejpam-3454	56	20	being	be	AUX
ejpam-3454	56	21	the	the	DET
ejpam-3454	56	22	initial	initial	ADJ
ejpam-3454	56	23	data	datum	NOUN
ejpam-3454	56	24	.	.	PUNCT
ejpam-3454	57	1	the	the	DET
ejpam-3454	57	2	aim	aim	NOUN
ejpam-3454	57	3	of	of	ADP
ejpam-3454	57	4	this	this	DET
ejpam-3454	57	5	paper	paper	NOUN
ejpam-3454	57	6	is	be	AUX
ejpam-3454	57	7	to	to	PART
ejpam-3454	57	8	analyze	analyze	VERB
ejpam-3454	57	9	the	the	DET
ejpam-3454	57	10	global	global	ADJ
ejpam-3454	57	11	dynamics	dynamic	NOUN
ejpam-3454	57	12	of	of	ADP
ejpam-3454	57	13	hepatitis	hepatitis	PROPN
ejpam-3454	57	14	c	c	PROPN
ejpam-3454	57	15	virus	virus	NOUN
ejpam-3454	57	16	(	(	PUNCT
ejpam-3454	57	17	hcv	hcv	NOUN
ejpam-3454	57	18	)	)	PUNCT
ejpam-3454	57	19	cellular	cellular	ADJ
ejpam-3454	57	20	mathematical	mathematical	ADJ
ejpam-3454	57	21	model	model	NOUN
ejpam-3454	57	22	under	under	ADP
ejpam-3454	57	23	therapy	therapy	NOUN
ejpam-3454	57	24	with	with	ADP
ejpam-3454	57	25	uninfected	uninfected	ADJ
ejpam-3454	57	26	hepatocytes	hepatocytes	ADJ
ejpam-3454	57	27	proliferation	proliferation	NOUN
ejpam-3454	57	28	described	describe	VERB
ejpam-3454	57	29	by	by	ADP
ejpam-3454	57	30	system	system	NOUN
ejpam-3454	57	31	(	(	PUNCT
ejpam-3454	57	32	1	1	NUM
ejpam-3454	57	33	)	)	PUNCT
ejpam-3454	57	34	.	.	PUNCT
ejpam-3454	58	1	to	to	PART
ejpam-3454	58	2	achieve	achieve	VERB
ejpam-3454	58	3	this	this	PRON
ejpam-3454	58	4	,	,	PUNCT
ejpam-3454	58	5	we	we	PRON
ejpam-3454	58	6	will	will	AUX
ejpam-3454	58	7	organized	organize	VERB
ejpam-3454	58	8	the	the	DET
ejpam-3454	58	9	paper	paper	NOUN
ejpam-3454	58	10	as	as	SCONJ
ejpam-3454	58	11	follows	follow	VERB
ejpam-3454	58	12	:	:	PUNCT
ejpam-3454	58	13	we	we	PRON
ejpam-3454	58	14	study	study	VERB
ejpam-3454	58	15	in	in	ADP
ejpam-3454	58	16	section	section	NOUN
ejpam-3454	58	17	1	1	NUM
ejpam-3454	58	18	some	some	DET
ejpam-3454	58	19	properties	property	NOUN
ejpam-3454	58	20	of	of	ADP
ejpam-3454	58	21	the	the	DET
ejpam-3454	58	22	solutions	solution	NOUN
ejpam-3454	58	23	of	of	ADP
ejpam-3454	58	24	the	the	DET
ejpam-3454	58	25	studied	studied	ADJ
ejpam-3454	58	26	model	model	NOUN
ejpam-3454	58	27	.	.	PUNCT
ejpam-3454	59	1	section	section	NOUN
ejpam-3454	59	2	2	2	NUM
ejpam-3454	59	3	is	be	AUX
ejpam-3454	59	4	devoted	devote	VERB
ejpam-3454	59	5	to	to	ADP
ejpam-3454	59	6	the	the	DET
ejpam-3454	59	7	study	study	NOUN
ejpam-3454	59	8	of	of	ADP
ejpam-3454	59	9	the	the	DET
ejpam-3454	59	10	local	local	ADJ
ejpam-3454	59	11	stability	stability	NOUN
ejpam-3454	59	12	of	of	ADP
ejpam-3454	59	13	equilibrium	equilibrium	NOUN
ejpam-3454	59	14	points	point	NOUN
ejpam-3454	59	15	and	and	CCONJ
ejpam-3454	59	16	we	we	PRON
ejpam-3454	59	17	end	end	VERB
ejpam-3454	59	18	with	with	ADP
ejpam-3454	59	19	the	the	DET
ejpam-3454	59	20	global	global	ADJ
ejpam-3454	59	21	stability	stability	NOUN
ejpam-3454	59	22	of	of	ADP
ejpam-3454	59	23	the	the	DET
ejpam-3454	59	24	uninfected	uninfected	ADJ
ejpam-3454	59	25	equilibrium	equilibrium	NOUN
ejpam-3454	59	26	point	point	NOUN
ejpam-3454	59	27	in	in	ADP
ejpam-3454	59	28	section	section	NOUN
ejpam-3454	59	29	3	3	NUM
ejpam-3454	59	30	2	2	NUM
ejpam-3454	59	31	.	.	PUNCT
ejpam-3454	59	32	properties	property	NOUN
ejpam-3454	59	33	of	of	ADP
ejpam-3454	59	34	solutions	solution	NOUN
ejpam-3454	59	35	to	to	ADP
ejpam-3454	59	36	the	the	DET
ejpam-3454	59	37	cauchy	cauchy	ADJ
ejpam-3454	59	38	problem	problem	NOUN
ejpam-3454	59	39	(	(	PUNCT
ejpam-3454	59	40	1	1	NUM
ejpam-3454	59	41	)	)	PUNCT
ejpam-3454	59	42	,	,	PUNCT
ejpam-3454	59	43	(	(	PUNCT
ejpam-3454	59	44	2	2	X
ejpam-3454	59	45	)	)	PUNCT
ejpam-3454	59	46	2.1	2.1	NUM
ejpam-3454	59	47	.	.	PUNCT
ejpam-3454	60	1	existence	existence	NOUN
ejpam-3454	60	2	of	of	ADP
ejpam-3454	60	3	local	local	ADJ
ejpam-3454	60	4	and	and	CCONJ
ejpam-3454	60	5	global	global	ADJ
ejpam-3454	60	6	solutions	solution	NOUN
ejpam-3454	60	7	,	,	PUNCT
ejpam-3454	60	8	positivity	positivity	NOUN
ejpam-3454	60	9	our	our	PRON
ejpam-3454	60	10	objective	objective	NOUN
ejpam-3454	60	11	is	be	AUX
ejpam-3454	60	12	to	to	PART
ejpam-3454	60	13	prove	prove	VERB
ejpam-3454	60	14	the	the	DET
ejpam-3454	60	15	existence	existence	NOUN
ejpam-3454	60	16	of	of	ADP
ejpam-3454	60	17	global	global	ADJ
ejpam-3454	60	18	solution	solution	NOUN
ejpam-3454	60	19	t	t	PROPN
ejpam-3454	60	20	,	,	PUNCT
ejpam-3454	60	21	i	i	PRON
ejpam-3454	60	22	v	v	NUM
ejpam-3454	60	23	defined	define	VERB
ejpam-3454	60	24	over	over	ADP
ejpam-3454	60	25	the	the	DET
ejpam-3454	60	26	whole	whole	ADJ
ejpam-3454	60	27	interval	interval	NOUN
ejpam-3454	61	1	[	[	X
ejpam-3454	61	2	t0,+∞	t0,+∞	X
ejpam-3454	61	3	[	[	PUNCT
ejpam-3454	61	4	and	and	CCONJ
ejpam-3454	61	5	satisfying	satisfying	ADJ
ejpam-3454	61	6	(	(	PUNCT
ejpam-3454	61	7	2	2	NUM
ejpam-3454	61	8	)	)	PUNCT
ejpam-3454	61	9	.	.	PUNCT
ejpam-3454	62	1	the	the	DET
ejpam-3454	62	2	first	first	ADJ
ejpam-3454	62	3	step	step	NOUN
ejpam-3454	62	4	in	in	ADP
ejpam-3454	62	5	examining	examine	VERB
ejpam-3454	62	6	model	model	NOUN
ejpam-3454	62	7	(	(	PUNCT
ejpam-3454	62	8	1	1	NUM
ejpam-3454	62	9	)	)	PUNCT
ejpam-3454	62	10	is	be	AUX
ejpam-3454	62	11	to	to	PART
ejpam-3454	62	12	prove	prove	VERB
ejpam-3454	62	13	that	that	SCONJ
ejpam-3454	62	14	local	local	ADJ
ejpam-3454	62	15	solution	solution	NOUN
ejpam-3454	62	16	to	to	ADP
ejpam-3454	62	17	the	the	DET
ejpam-3454	62	18	initial	initial	ADJ
ejpam-3454	62	19	-	-	PUNCT
ejpam-3454	62	20	value	value	NOUN
ejpam-3454	62	21	problem	problem	NOUN
ejpam-3454	62	22	does	do	AUX
ejpam-3454	62	23	,	,	PUNCT
ejpam-3454	62	24	in	in	ADP
ejpam-3454	62	25	fact	fact	NOUN
ejpam-3454	62	26	,	,	PUNCT
ejpam-3454	62	27	exist	exist	VERB
ejpam-3454	62	28	,	,	PUNCT
ejpam-3454	62	29	and	and	CCONJ
ejpam-3454	62	30	that	that	SCONJ
ejpam-3454	62	31	this	this	DET
ejpam-3454	62	32	solution	solution	NOUN
ejpam-3454	62	33	is	be	AUX
ejpam-3454	62	34	unique	unique	ADJ
ejpam-3454	62	35	.	.	PUNCT
ejpam-3454	63	1	proposition	proposition	NOUN
ejpam-3454	63	2	1	1	NUM
ejpam-3454	63	3	.	.	PUNCT
ejpam-3454	64	1	let	let	VERB
ejpam-3454	64	2	t0	t0	PROPN
ejpam-3454	64	3	,	,	PUNCT
ejpam-3454	64	4	i0	i0	PROPN
ejpam-3454	64	5	,	,	PUNCT
ejpam-3454	64	6	v0	v0	PROPN
ejpam-3454	64	7	∈	∈	PROPN
ejpam-3454	64	8	r	r	NOUN
ejpam-3454	64	9	be	be	AUX
ejpam-3454	64	10	given	give	VERB
ejpam-3454	64	11	.	.	PUNCT
ejpam-3454	65	1	there	there	PRON
ejpam-3454	65	2	exists	exist	VERB
ejpam-3454	65	3	t1	t1	NOUN
ejpam-3454	65	4	>	>	X
ejpam-3454	65	5	t0	t0	X
ejpam-3454	65	6	>	>	X
ejpam-3454	65	7	0	0	PUNCT
ejpam-3454	66	1	and	and	CCONJ
ejpam-3454	66	2	continuously	continuously	ADV
ejpam-3454	66	3	differentiable	differentiable	ADJ
ejpam-3454	66	4	functions	function	NOUN
ejpam-3454	66	5	t	t	PROPN
ejpam-3454	66	6	,	,	PUNCT
ejpam-3454	66	7	i	i	PRON
ejpam-3454	66	8	,	,	PUNCT
ejpam-3454	66	9	v	v	NOUN
ejpam-3454	66	10	:	:	PUNCT
ejpam-3454	66	11	[	[	X
ejpam-3454	66	12	0	0	NUM
ejpam-3454	66	13	,	,	PUNCT
ejpam-3454	66	14	t0	t0	NOUN
ejpam-3454	66	15	)	)	PUNCT
ejpam-3454	66	16	−→	−→	NOUN
ejpam-3454	66	17	r	r	NOUN
ejpam-3454	66	18	such	such	ADJ
ejpam-3454	66	19	that	that	SCONJ
ejpam-3454	66	20	the	the	DET
ejpam-3454	66	21	ordered	ordered	ADJ
ejpam-3454	66	22	triple	triple	ADJ
ejpam-3454	66	23	(	(	PUNCT
ejpam-3454	66	24	t	t	PROPN
ejpam-3454	66	25	,	,	PUNCT
ejpam-3454	66	26	i	i	PRON
ejpam-3454	66	27	,	,	PUNCT
ejpam-3454	66	28	v	v	NOUN
ejpam-3454	66	29	)	)	PUNCT
ejpam-3454	66	30	satisfies	satisfie	NOUN
ejpam-3454	66	31	(	(	PUNCT
ejpam-3454	66	32	1	1	NUM
ejpam-3454	66	33	)	)	PUNCT
ejpam-3454	66	34	and	and	CCONJ
ejpam-3454	66	35	(	(	PUNCT
ejpam-3454	66	36	t	t	PROPN
ejpam-3454	66	37	(	(	PUNCT
ejpam-3454	66	38	t0	t0	PROPN
ejpam-3454	66	39	)	)	PUNCT
ejpam-3454	66	40	,	,	PUNCT
ejpam-3454	66	41	i(t0	i(t0	NOUN
ejpam-3454	66	42	)	)	PUNCT
ejpam-3454	66	43	,	,	PUNCT
ejpam-3454	66	44	v	v	X
ejpam-3454	66	45	(	(	PUNCT
ejpam-3454	66	46	t0	t0	NOUN
ejpam-3454	66	47	)	)	PUNCT
ejpam-3454	66	48	)	)	PUNCT
ejpam-3454	67	1	=	=	PRON
ejpam-3454	67	2	(	(	PUNCT
ejpam-3454	67	3	t0	t0	PROPN
ejpam-3454	67	4	,	,	PUNCT
ejpam-3454	67	5	i0	i0	PROPN
ejpam-3454	67	6	,	,	PUNCT
ejpam-3454	67	7	v0	v0	PROPN
ejpam-3454	67	8	)	)	PUNCT
ejpam-3454	67	9	.	.	PUNCT
ejpam-3454	68	1	proof	proof	NOUN
ejpam-3454	68	2	.	.	PUNCT
ejpam-3454	69	1	to	to	PART
ejpam-3454	69	2	prove	prove	VERB
ejpam-3454	69	3	the	the	DET
ejpam-3454	69	4	result	result	NOUN
ejpam-3454	69	5	,	,	PUNCT
ejpam-3454	69	6	we	we	PRON
ejpam-3454	69	7	use	use	VERB
ejpam-3454	69	8	the	the	DET
ejpam-3454	69	9	classical	classical	ADJ
ejpam-3454	69	10	cauchy	cauchy	NOUN
ejpam-3454	69	11	-	-	PUNCT
ejpam-3454	69	12	lipschitz	lipschitz	NOUN
ejpam-3454	69	13	theorem	theorem	VERB
ejpam-3454	69	14	.	.	PUNCT
ejpam-3454	70	1	since	since	SCONJ
ejpam-3454	70	2	the	the	DET
ejpam-3454	70	3	first	first	ADJ
ejpam-3454	70	4	order	order	NOUN
ejpam-3454	70	5	system	system	NOUN
ejpam-3454	70	6	of	of	ADP
ejpam-3454	70	7	ordinary	ordinary	ADJ
ejpam-3454	70	8	differential	differential	ADJ
ejpam-3454	70	9	equations	equation	NOUN
ejpam-3454	70	10	(	(	PUNCT
ejpam-3454	70	11	1	1	X
ejpam-3454	70	12	)	)	PUNCT
ejpam-3454	70	13	is	be	AUX
ejpam-3454	70	14	autonomous	autonomous	ADJ
ejpam-3454	70	15	,	,	PUNCT
ejpam-3454	70	16	it	it	PRON
ejpam-3454	70	17	is	be	AUX
ejpam-3454	70	18	enough	enough	ADJ
ejpam-3454	70	19	to	to	PART
ejpam-3454	70	20	show	show	VERB
ejpam-3454	70	21	a.	a.	NOUN
ejpam-3454	70	22	nangue	nangue	NOUN
ejpam-3454	70	23	,	,	PUNCT
ejpam-3454	70	24	t.	t.	PROPN
ejpam-3454	70	25	donfack	donfack	PROPN
ejpam-3454	70	26	,	,	PUNCT
ejpam-3454	70	27	d.	d.	PROPN
ejpam-3454	70	28	a.	a.	PROPN
ejpam-3454	70	29	ndode	ndode	PROPN
ejpam-3454	70	30	yafago	yafago	PROPN
ejpam-3454	70	31	/	/	SYM
ejpam-3454	70	32	eur	eur	PROPN
ejpam-3454	70	33	.	.	PUNCT
ejpam-3454	71	1	j.	j.	PROPN
ejpam-3454	71	2	pure	pure	PROPN
ejpam-3454	71	3	appl	appl	PROPN
ejpam-3454	71	4	.	.	PROPN
ejpam-3454	71	5	math	math	PROPN
ejpam-3454	71	6	,	,	PUNCT
ejpam-3454	71	7	12	12	NUM
ejpam-3454	71	8	(	(	PUNCT
ejpam-3454	71	9	3	3	NUM
ejpam-3454	71	10	)	)	PUNCT
ejpam-3454	71	11	(	(	PUNCT
ejpam-3454	71	12	2019	2019	NUM
ejpam-3454	71	13	)	)	PUNCT
ejpam-3454	71	14	,	,	PUNCT
ejpam-3454	71	15	944	944	NUM
ejpam-3454	71	16	-	-	SYM
ejpam-3454	71	17	959	959	NUM
ejpam-3454	71	18	947	947	NUM
ejpam-3454	71	19	that	that	SCONJ
ejpam-3454	71	20	the	the	DET
ejpam-3454	71	21	function	function	NOUN
ejpam-3454	71	22	f	f	NOUN
ejpam-3454	71	23	:	:	PUNCT
ejpam-3454	71	24	r3	r3	PROPN
ejpam-3454	71	25	−→	−→	NOUN
ejpam-3454	71	26	r3	r3	PROPN
ejpam-3454	71	27	defined	define	VERB
ejpam-3454	71	28	by	by	ADP
ejpam-3454	71	29	:	:	PUNCT
ejpam-3454	71	30	f(x	f(x	PROPN
ejpam-3454	71	31	,	,	PUNCT
ejpam-3454	71	32	y	y	PROPN
ejpam-3454	71	33	,	,	PUNCT
ejpam-3454	71	34	z	z	NOUN
ejpam-3454	71	35	)	)	PUNCT
ejpam-3454	71	36	=	=	SYM
ejpam-3454	72	1			PROPN
ejpam-3454	72	2	f1(x	f1(x	PROPN
ejpam-3454	72	3	,	,	PUNCT
ejpam-3454	72	4	y	y	PROPN
ejpam-3454	72	5	,	,	PUNCT
ejpam-3454	72	6	z	z	NOUN
ejpam-3454	72	7	)	)	PUNCT
ejpam-3454	72	8	f2(x	f2(x	PROPN
ejpam-3454	72	9	,	,	PUNCT
ejpam-3454	72	10	y	y	PROPN
ejpam-3454	72	11	,	,	PUNCT
ejpam-3454	72	12	z	z	NOUN
ejpam-3454	72	13	)	)	PUNCT
ejpam-3454	72	14	f3(x	f3(x	PROPN
ejpam-3454	72	15	,	,	PUNCT
ejpam-3454	72	16	y	y	PROPN
ejpam-3454	72	17	,	,	PUNCT
ejpam-3454	72	18	z	z	NOUN
ejpam-3454	72	19	)	)	PUNCT
ejpam-3454	72	20			PROPN
ejpam-3454	72	21	=	=	SYM
ejpam-3454	73	1			PROPN
ejpam-3454	73	2	rx(1−	rx(1−	PROPN
ejpam-3454	73	3	x+y	x+y	NUM
ejpam-3454	73	4	tmax	tmax	ADP
ejpam-3454	73	5	)	)	PUNCT
ejpam-3454	73	6	−	−	PROPN
ejpam-3454	73	7	dx−	dx−	NUM
ejpam-3454	73	8	(	(	PUNCT
ejpam-3454	73	9	1−	1−	NUM
ejpam-3454	73	10	η)βzx	η)βzx	NOUN
ejpam-3454	73	11	(	(	PUNCT
ejpam-3454	73	12	1−	1−	NUM
ejpam-3454	73	13	η)βzx−	η)βzx−	PROPN
ejpam-3454	73	14	δy	δy	NOUN
ejpam-3454	73	15	(	(	PUNCT
ejpam-3454	73	16	1−	1−	NUM
ejpam-3454	73	17	ε)py	ε)py	PROPN
ejpam-3454	73	18	−	−	PROPN
ejpam-3454	73	19	cz	cz	NOUN
ejpam-3454	73	20	−	−	PROPN
ejpam-3454	73	21	α(1−	α(1−	PROPN
ejpam-3454	73	22	η)βzx	η)βzx	PROPN
ejpam-3454	73	23			PROPN
ejpam-3454	73	24	is	be	AUX
ejpam-3454	73	25	locally	locally	ADV
ejpam-3454	73	26	lipschitz	lipschitz	NOUN
ejpam-3454	73	27	in	in	ADP
ejpam-3454	73	28	its	its	PRON
ejpam-3454	73	29	u	u	NOUN
ejpam-3454	73	30	=	=	PUNCT
ejpam-3454	73	31	(	(	PUNCT
ejpam-3454	73	32	x	x	X
ejpam-3454	73	33	,	,	PUNCT
ejpam-3454	73	34	y	y	PROPN
ejpam-3454	73	35	,	,	PUNCT
ejpam-3454	73	36	z	z	NOUN
ejpam-3454	73	37	)	)	PUNCT
ejpam-3454	73	38	argument	argument	NOUN
ejpam-3454	73	39	.	.	PUNCT
ejpam-3454	74	1	in	in	ADP
ejpam-3454	74	2	fact	fact	NOUN
ejpam-3454	74	3	,	,	PUNCT
ejpam-3454	74	4	it	it	PRON
ejpam-3454	74	5	suffices	suffice	VERB
ejpam-3454	74	6	to	to	PART
ejpam-3454	74	7	notice	notice	VERB
ejpam-3454	74	8	that	that	SCONJ
ejpam-3454	74	9	the	the	DET
ejpam-3454	74	10	jacobian	jacobian	ADJ
ejpam-3454	74	11	matrix	matrix	NOUN
ejpam-3454	74	12	∇f(x	∇f(x	PROPN
ejpam-3454	74	13	,	,	PUNCT
ejpam-3454	74	14	y	y	PROPN
ejpam-3454	74	15	,	,	PUNCT
ejpam-3454	74	16	z	z	NOUN
ejpam-3454	74	17	)	)	PUNCT
ejpam-3454	74	18	=	=	SYM
ejpam-3454	74	19			PROPN
ejpam-3454	74	20	r(1−	r(1−	NOUN
ejpam-3454	74	21	2x+y	2x+y	NUM
ejpam-3454	74	22	tmax	tmax	NOUN
ejpam-3454	74	23	)	)	PUNCT
ejpam-3454	74	24	−	−	ADP
ejpam-3454	74	25	rx	rx	VERB
ejpam-3454	74	26	tmax	tmax	ADV
ejpam-3454	74	27	−(1−	−(1−	ADP
ejpam-3454	74	28	η)βx	η)βx	PROPN
ejpam-3454	74	29	(	(	PUNCT
ejpam-3454	74	30	1−	1−	NUM
ejpam-3454	74	31	η)βz	η)βz	PROPN
ejpam-3454	74	32	−δ	−δ	NOUN
ejpam-3454	74	33	(	(	PUNCT
ejpam-3454	74	34	1−	1−	NUM
ejpam-3454	74	35	η)βx	η)βx	PROPN
ejpam-3454	74	36	−α(1−	−α(1−	PROPN
ejpam-3454	75	1	η)βx	η)βx	PROPN
ejpam-3454	75	2	(	(	PUNCT
ejpam-3454	75	3	1−	1−	NUM
ejpam-3454	75	4	ε)p	ε)p	PUNCT
ejpam-3454	75	5	−c−	−c−	NOUN
ejpam-3454	75	6	α(1−	α(1−	PUNCT
ejpam-3454	76	1	η)βx	η)βx	ADJ
ejpam-3454	76	2			NOUN
ejpam-3454	76	3	is	be	AUX
ejpam-3454	76	4	locally	locally	ADV
ejpam-3454	76	5	bounded	bound	VERB
ejpam-3454	76	6	for	for	ADP
ejpam-3454	76	7	every	every	DET
ejpam-3454	76	8	u	u	NOUN
ejpam-3454	76	9	=	=	PUNCT
ejpam-3454	76	10	(	(	PUNCT
ejpam-3454	76	11	x	x	X
ejpam-3454	76	12	,	,	PUNCT
ejpam-3454	76	13	y	y	PROPN
ejpam-3454	76	14	,	,	PUNCT
ejpam-3454	76	15	z	z	NOUN
ejpam-3454	76	16	)	)	PUNCT
ejpam-3454	76	17	∈	∈	PROPN
ejpam-3454	76	18	r3	r3	PROPN
ejpam-3454	76	19	.	.	PUNCT
ejpam-3454	77	1	hence	hence	ADV
ejpam-3454	77	2	,	,	PUNCT
ejpam-3454	77	3	f	f	PROPN
ejpam-3454	77	4	has	have	VERB
ejpam-3454	77	5	a	a	DET
ejpam-3454	77	6	continuous	continuous	ADJ
ejpam-3454	77	7	,	,	PUNCT
ejpam-3454	77	8	bounded	bound	VERB
ejpam-3454	77	9	derivative	derivative	NOUN
ejpam-3454	77	10	on	on	ADP
ejpam-3454	77	11	any	any	DET
ejpam-3454	77	12	compact	compact	ADJ
ejpam-3454	77	13	subset	subset	NOUN
ejpam-3454	77	14	of	of	ADP
ejpam-3454	77	15	r3	r3	PROPN
ejpam-3454	77	16	and	and	CCONJ
ejpam-3454	77	17	though	though	SCONJ
ejpam-3454	77	18	f	f	PROPN
ejpam-3454	77	19	is	be	AUX
ejpam-3454	77	20	locally	locally	ADV
ejpam-3454	77	21	lipschitz	lipschitz	NOUN
ejpam-3454	77	22	in	in	ADP
ejpam-3454	77	23	u	u	NOUN
ejpam-3454	77	24	=	=	PUNCT
ejpam-3454	77	25	(	(	PUNCT
ejpam-3454	77	26	x	x	X
ejpam-3454	77	27	,	,	PUNCT
ejpam-3454	77	28	y	y	PROPN
ejpam-3454	77	29	,	,	PUNCT
ejpam-3454	77	30	z	z	NOUN
ejpam-3454	77	31	)	)	PUNCT
ejpam-3454	77	32	;	;	PUNCT
ejpam-3454	77	33	in	in	ADP
ejpam-3454	77	34	addition	addition	NOUN
ejpam-3454	77	35	f	f	PROPN
ejpam-3454	77	36	is	be	AUX
ejpam-3454	77	37	continuous	continuous	ADJ
ejpam-3454	77	38	.	.	PUNCT
ejpam-3454	78	1	by	by	ADP
ejpam-3454	78	2	cauchy	cauchy	NOUN
ejpam-3454	78	3	-	-	PUNCT
ejpam-3454	78	4	lipschitz	lipschitz	NOUN
ejpam-3454	78	5	theorem	theorem	NOUN
ejpam-3454	78	6	,	,	PUNCT
ejpam-3454	78	7	there	there	PRON
ejpam-3454	78	8	exists	exist	VERB
ejpam-3454	78	9	a	a	DET
ejpam-3454	78	10	unique	unique	ADJ
ejpam-3454	78	11	solution	solution	NOUN
ejpam-3454	78	12	,	,	PUNCT
ejpam-3454	78	13	x(t	x(t	PROPN
ejpam-3454	78	14	)	)	PUNCT
ejpam-3454	78	15	,	,	PUNCT
ejpam-3454	78	16	to	to	ADP
ejpam-3454	78	17	the	the	DET
ejpam-3454	78	18	ordinary	ordinary	ADJ
ejpam-3454	78	19	differential	differential	ADJ
ejpam-3454	78	20	equation	equation	NOUN
ejpam-3454	78	21	u′(t	u′(t	NOUN
ejpam-3454	78	22	)	)	PUNCT
ejpam-3454	79	1	=	=	SYM
ejpam-3454	79	2	f(x(t	f(x(t	NOUN
ejpam-3454	79	3	)	)	PUNCT
ejpam-3454	79	4	)	)	PUNCT
ejpam-3454	79	5	with	with	ADP
ejpam-3454	79	6	initial	initial	ADJ
ejpam-3454	79	7	value	value	NOUN
ejpam-3454	79	8	u(t0	u(t0	NOUN
ejpam-3454	79	9	)	)	PUNCT
ejpam-3454	80	1	=	=	SYM
ejpam-3454	80	2	u0	u0	NOUN
ejpam-3454	80	3	=	=	X
ejpam-3454	80	4	(	(	PUNCT
ejpam-3454	80	5	x0	x0	PROPN
ejpam-3454	80	6	,	,	PUNCT
ejpam-3454	80	7	y0	y0	PROPN
ejpam-3454	80	8	,	,	PUNCT
ejpam-3454	80	9	z0	z0	PROPN
ejpam-3454	80	10	)	)	PUNCT
ejpam-3454	80	11	on	on	ADP
ejpam-3454	80	12	[	[	X
ejpam-3454	80	13	t0	t0	NOUN
ejpam-3454	80	14	,	,	PUNCT
ejpam-3454	80	15	t1	t1	PROPN
ejpam-3454	80	16	]	]	PUNCT
ejpam-3454	80	17	for	for	ADP
ejpam-3454	80	18	some	some	DET
ejpam-3454	80	19	time	time	NOUN
ejpam-3454	80	20	t1	t1	NOUN
ejpam-3454	80	21	>	>	X
ejpam-3454	80	22	t0	t0	PROPN
ejpam-3454	80	23	≥	≥	NUM
ejpam-3454	80	24	0	0	NUM
ejpam-3454	80	25	.	.	PUNCT
ejpam-3454	81	1	this	this	PRON
ejpam-3454	81	2	completes	complete	VERB
ejpam-3454	81	3	the	the	DET
ejpam-3454	81	4	proof	proof	NOUN
ejpam-3454	81	5	of	of	ADP
ejpam-3454	81	6	the	the	DET
ejpam-3454	81	7	proposition	proposition	NOUN
ejpam-3454	81	8	.	.	PUNCT
ejpam-3454	82	1	remark	remark	PROPN
ejpam-3454	82	2	1	1	NUM
ejpam-3454	82	3	.	.	PUNCT
ejpam-3454	83	1	since	since	SCONJ
ejpam-3454	83	2	f	f	PROPN
ejpam-3454	83	3	is	be	AUX
ejpam-3454	83	4	a	a	DET
ejpam-3454	83	5	continuously	continuously	ADV
ejpam-3454	83	6	differentiable	differentiable	ADJ
ejpam-3454	83	7	function	function	NOUN
ejpam-3454	83	8	,	,	PUNCT
ejpam-3454	83	9	we	we	PRON
ejpam-3454	83	10	deduce	deduce	VERB
ejpam-3454	83	11	a	a	DET
ejpam-3454	83	12	unique	unique	ADJ
ejpam-3454	83	13	maximal	maximal	ADJ
ejpam-3454	83	14	solution	solution	NOUN
ejpam-3454	83	15	of	of	ADP
ejpam-3454	83	16	initial	initial	ADJ
ejpam-3454	83	17	value	value	NOUN
ejpam-3454	83	18	problem	problem	NOUN
ejpam-3454	83	19	(	(	PUNCT
ejpam-3454	83	20	1	1	NUM
ejpam-3454	83	21	)	)	PUNCT
ejpam-3454	83	22	,	,	PUNCT
ejpam-3454	83	23	(	(	PUNCT
ejpam-3454	83	24	2	2	NUM
ejpam-3454	83	25	)	)	PUNCT
ejpam-3454	83	26	.	.	PUNCT
ejpam-3454	84	1	in	in	ADP
ejpam-3454	84	2	addition	addition	NOUN
ejpam-3454	84	3	,	,	PUNCT
ejpam-3454	84	4	f	f	X
ejpam-3454	84	5	,	,	PUNCT
ejpam-3454	84	6	being	be	AUX
ejpam-3454	84	7	indefinitely	indefinitely	ADV
ejpam-3454	84	8	continuously	continuously	ADV
ejpam-3454	84	9	differentiable	differentiable	ADJ
ejpam-3454	84	10	,	,	PUNCT
ejpam-3454	84	11	we	we	PRON
ejpam-3454	84	12	can	can	AUX
ejpam-3454	84	13	also	also	ADV
ejpam-3454	84	14	deduce	deduce	VERB
ejpam-3454	84	15	that	that	SCONJ
ejpam-3454	84	16	this	this	DET
ejpam-3454	84	17	solution	solution	NOUN
ejpam-3454	84	18	is	be	AUX
ejpam-3454	84	19	indefinitely	indefinitely	ADV
ejpam-3454	84	20	continuously	continuously	ADV
ejpam-3454	84	21	differentiable	differentiable	ADJ
ejpam-3454	84	22	.	.	PUNCT
ejpam-3454	85	1	additionally	additionally	ADV
ejpam-3454	85	2	,	,	PUNCT
ejpam-3454	85	3	we	we	PRON
ejpam-3454	85	4	may	may	AUX
ejpam-3454	85	5	show	show	VERB
ejpam-3454	85	6	that	that	SCONJ
ejpam-3454	85	7	for	for	ADP
ejpam-3454	85	8	positive	positive	ADJ
ejpam-3454	85	9	initial	initial	ADJ
ejpam-3454	85	10	data	datum	NOUN
ejpam-3454	85	11	,	,	PUNCT
ejpam-3454	85	12	solutions	solution	NOUN
ejpam-3454	85	13	of	of	ADP
ejpam-3454	85	14	cauchy	cauchy	PROPN
ejpam-3454	85	15	problem	problem	NOUN
ejpam-3454	85	16	(	(	PUNCT
ejpam-3454	85	17	1	1	NUM
ejpam-3454	85	18	)	)	PUNCT
ejpam-3454	85	19	,	,	PUNCT
ejpam-3454	85	20	(	(	PUNCT
ejpam-3454	85	21	2	2	X
ejpam-3454	85	22	)	)	PUNCT
ejpam-3454	85	23	remain	remain	VERB
ejpam-3454	85	24	positive	positive	ADJ
ejpam-3454	85	25	as	as	ADV
ejpam-3454	85	26	long	long	ADV
ejpam-3454	85	27	as	as	SCONJ
ejpam-3454	85	28	they	they	PRON
ejpam-3454	85	29	exist	exist	VERB
ejpam-3454	85	30	.	.	PUNCT
ejpam-3454	86	1	theorem	theorem	NOUN
ejpam-3454	86	2	1	1	NUM
ejpam-3454	86	3	.	.	PUNCT
ejpam-3454	87	1	let	let	AUX
ejpam-3454	87	2	(	(	PUNCT
ejpam-3454	87	3	t	t	PROPN
ejpam-3454	87	4	,	,	PUNCT
ejpam-3454	87	5	i	i	PRON
ejpam-3454	87	6	,	,	PUNCT
ejpam-3454	87	7	v	v	NOUN
ejpam-3454	87	8	)	)	PUNCT
ejpam-3454	87	9	be	be	AUX
ejpam-3454	87	10	a	a	DET
ejpam-3454	87	11	solution	solution	NOUN
ejpam-3454	87	12	of	of	ADP
ejpam-3454	87	13	the	the	DET
ejpam-3454	87	14	cauchy	cauchy	ADJ
ejpam-3454	87	15	problem	problem	NOUN
ejpam-3454	87	16	(	(	PUNCT
ejpam-3454	87	17	1	1	NUM
ejpam-3454	87	18	)	)	PUNCT
ejpam-3454	87	19	,	,	PUNCT
ejpam-3454	87	20	(	(	PUNCT
ejpam-3454	87	21	2	2	X
ejpam-3454	87	22	)	)	PUNCT
ejpam-3454	87	23	on	on	ADP
ejpam-3454	87	24	an	an	DET
ejpam-3454	87	25	interval	interval	NOUN
ejpam-3454	87	26	[	[	X
ejpam-3454	87	27	t0	t0	NOUN
ejpam-3454	87	28	,	,	PUNCT
ejpam-3454	87	29	t1	t1	PROPN
ejpam-3454	87	30	[	[	X
ejpam-3454	87	31	.	.	PUNCT
ejpam-3454	88	1	assume	assume	VERB
ejpam-3454	88	2	the	the	DET
ejpam-3454	88	3	initial	initial	ADJ
ejpam-3454	88	4	data	datum	NOUN
ejpam-3454	88	5	of	of	ADP
ejpam-3454	88	6	(	(	PUNCT
ejpam-3454	88	7	1	1	NUM
ejpam-3454	88	8	)	)	PUNCT
ejpam-3454	88	9	,	,	PUNCT
ejpam-3454	88	10	(	(	PUNCT
ejpam-3454	88	11	2	2	X
ejpam-3454	88	12	)	)	PUNCT
ejpam-3454	88	13	satisfy	satisfy	NOUN
ejpam-3454	88	14	t0	t0	PROPN
ejpam-3454	88	15	>	>	X
ejpam-3454	88	16	0	0	PROPN
ejpam-3454	88	17	,	,	PUNCT
ejpam-3454	88	18	i0	i0	PROPN
ejpam-3454	88	19	>	>	X
ejpam-3454	88	20	0	0	PROPN
ejpam-3454	88	21	,	,	PUNCT
ejpam-3454	88	22	and	and	CCONJ
ejpam-3454	88	23	v0	v0	VERB
ejpam-3454	88	24	>	>	X
ejpam-3454	88	25	0	0	PUNCT
ejpam-3454	89	1	then	then	ADV
ejpam-3454	89	2	t	t	PROPN
ejpam-3454	89	3	(	(	PUNCT
ejpam-3454	89	4	t	t	PROPN
ejpam-3454	89	5	)	)	PUNCT
ejpam-3454	89	6	,	,	PUNCT
ejpam-3454	89	7	t	t	PROPN
ejpam-3454	89	8	(	(	PUNCT
ejpam-3454	89	9	t	t	PROPN
ejpam-3454	89	10	)	)	PUNCT
ejpam-3454	89	11	and	and	CCONJ
ejpam-3454	89	12	v	v	NOUN
ejpam-3454	89	13	(	(	PUNCT
ejpam-3454	89	14	t	t	NOUN
ejpam-3454	89	15	)	)	PUNCT
ejpam-3454	89	16	remain	remain	VERB
ejpam-3454	89	17	positive	positive	ADJ
ejpam-3454	89	18	for	for	ADP
ejpam-3454	89	19	all	all	DET
ejpam-3454	89	20	t	t	NOUN
ejpam-3454	89	21	∈	∈	PROPN
ejpam-3454	90	1	[	[	X
ejpam-3454	90	2	t0	t0	NOUN
ejpam-3454	90	3	,	,	PUNCT
ejpam-3454	90	4	t1	t1	PROPN
ejpam-3454	90	5	[	[	X
ejpam-3454	90	6	.	.	PUNCT
ejpam-3454	91	1	proof	proof	NOUN
ejpam-3454	91	2	.	.	PUNCT
ejpam-3454	92	1	call	call	VERB
ejpam-3454	92	2	the	the	DET
ejpam-3454	92	3	variables	variable	NOUN
ejpam-3454	92	4	xi	xi	X
ejpam-3454	92	5	.	.	PUNCT
ejpam-3454	93	1	if	if	SCONJ
ejpam-3454	93	2	there	there	PRON
ejpam-3454	93	3	is	be	VERB
ejpam-3454	93	4	an	an	DET
ejpam-3454	93	5	index	index	NOUN
ejpam-3454	93	6	i	i	PRON
ejpam-3454	93	7	and	and	CCONJ
ejpam-3454	93	8	a	a	DET
ejpam-3454	93	9	time	time	NOUN
ejpam-3454	93	10	t	t	NOUN
ejpam-3454	93	11	for	for	ADP
ejpam-3454	93	12	which	which	PRON
ejpam-3454	93	13	xi(t	xi(t	PUNCT
ejpam-3454	93	14	)	)	PUNCT
ejpam-3454	93	15	=	=	SYM
ejpam-3454	93	16	0	0	NUM
ejpam-3454	93	17	,	,	PUNCT
ejpam-3454	93	18	let	let	VERB
ejpam-3454	93	19	t∗	t∗	NOUN
ejpam-3454	93	20	be	be	AUX
ejpam-3454	93	21	the	the	DET
ejpam-3454	93	22	infimum	infimum	NOUN
ejpam-3454	93	23	of	of	ADP
ejpam-3454	93	24	all	all	DET
ejpam-3454	93	25	such	such	ADJ
ejpam-3454	93	26	t	t	NOUN
ejpam-3454	93	27	for	for	ADP
ejpam-3454	93	28	any	any	DET
ejpam-3454	93	29	i.	i.	NOUN
ejpam-3454	93	30	then	then	ADV
ejpam-3454	93	31	the	the	DET
ejpam-3454	93	32	restriction	restriction	NOUN
ejpam-3454	93	33	of	of	ADP
ejpam-3454	93	34	the	the	DET
ejpam-3454	93	35	solution	solution	NOUN
ejpam-3454	93	36	to	to	ADP
ejpam-3454	93	37	the	the	DET
ejpam-3454	93	38	interval	interval	NOUN
ejpam-3454	94	1	[	[	X
ejpam-3454	94	2	t0	t0	NOUN
ejpam-3454	94	3	;	;	PUNCT
ejpam-3454	94	4	t∗	t∗	PROPN
ejpam-3454	94	5	[	[	PUNCT
ejpam-3454	94	6	is	be	AUX
ejpam-3454	94	7	positive	positive	ADJ
ejpam-3454	94	8	and	and	CCONJ
ejpam-3454	94	9	xi(t∗	xi(t∗	NUM
ejpam-3454	94	10	)	)	PUNCT
ejpam-3454	95	1	=	=	SYM
ejpam-3454	95	2	0	0	NUM
ejpam-3454	95	3	for	for	ADP
ejpam-3454	95	4	a	a	DET
ejpam-3454	95	5	certain	certain	ADJ
ejpam-3454	95	6	value	value	NOUN
ejpam-3454	95	7	of	of	ADP
ejpam-3454	95	8	i.	i.	NOUN
ejpam-3454	95	9	the	the	DET
ejpam-3454	95	10	equation	equation	NOUN
ejpam-3454	95	11	for	for	ADP
ejpam-3454	95	12	xi	xi	PROPN
ejpam-3454	95	13	in	in	ADP
ejpam-3454	95	14	the	the	DET
ejpam-3454	95	15	system	system	NOUN
ejpam-3454	95	16	(	(	PUNCT
ejpam-3454	95	17	1	1	X
ejpam-3454	95	18	)	)	PUNCT
ejpam-3454	95	19	can	can	AUX
ejpam-3454	95	20	be	be	AUX
ejpam-3454	95	21	written	write	VERB
ejpam-3454	95	22	in	in	ADP
ejpam-3454	95	23	the	the	DET
ejpam-3454	95	24	form	form	NOUN
ejpam-3454	95	25	:	:	PUNCT
ejpam-3454	95	26	dxi(t	dxi(t	X
ejpam-3454	95	27	)	)	PUNCT
ejpam-3454	95	28	dt	dt	NOUN
ejpam-3454	96	1	=	=	SYM
ejpam-3454	96	2	−xif(x	−xif(x	PROPN
ejpam-3454	96	3	)	)	PUNCT
ejpam-3454	97	1	+	+	CCONJ
ejpam-3454	97	2	g(x	g(x	NOUN
ejpam-3454	97	3	)	)	PUNCT
ejpam-3454	98	1	,	,	PUNCT
ejpam-3454	98	2	where	where	SCONJ
ejpam-3454	98	3	g(x	g(x	NOUN
ejpam-3454	98	4	)	)	PUNCT
ejpam-3454	98	5	is	be	AUX
ejpam-3454	98	6	non	non	ADJ
ejpam-3454	98	7	-	-	ADJ
ejpam-3454	98	8	negative	negative	ADJ
ejpam-3454	98	9	.	.	PUNCT
ejpam-3454	99	1	as	as	ADP
ejpam-3454	99	2	a	a	DET
ejpam-3454	99	3	consequence	consequence	NOUN
ejpam-3454	99	4	dxi(t	dxi(t	NOUN
ejpam-3454	99	5	)	)	PUNCT
ejpam-3454	99	6	dt	dt	X
ejpam-3454	99	7	≥	≥	PROPN
ejpam-3454	99	8	−xif(x	−xif(x	PROPN
ejpam-3454	99	9	)	)	PUNCT
ejpam-3454	99	10	and	and	CCONJ
ejpam-3454	99	11	xi(t	xi(t	NOUN
ejpam-3454	99	12	)	)	PUNCT
ejpam-3454	99	13	>	>	X
ejpam-3454	99	14	0	0	NUM
ejpam-3454	99	15	,	,	PUNCT
ejpam-3454	99	16	∀t	∀t	PROPN
ejpam-3454	99	17	∈	∈	PROPN
ejpam-3454	99	18	[	[	X
ejpam-3454	99	19	t0	t0	NOUN
ejpam-3454	99	20	,	,	PUNCT
ejpam-3454	99	21	t∗	t∗	PROPN
ejpam-3454	99	22	]	]	PUNCT
ejpam-3454	99	23	.	.	PUNCT
ejpam-3454	100	1	a	a	DET
ejpam-3454	100	2	contradiction	contradiction	NOUN
ejpam-3454	100	3	.	.	PUNCT
ejpam-3454	101	1	this	this	PRON
ejpam-3454	101	2	completes	complete	VERB
ejpam-3454	101	3	the	the	DET
ejpam-3454	101	4	proof	proof	NOUN
ejpam-3454	101	5	of	of	ADP
ejpam-3454	101	6	the	the	DET
ejpam-3454	101	7	theorem	theorem	PROPN
ejpam-3454	101	8	.	.	PUNCT
ejpam-3454	101	9	a.	a.	NOUN
ejpam-3454	101	10	nangue	nangue	PROPN
ejpam-3454	101	11	,	,	PUNCT
ejpam-3454	101	12	t.	t.	PROPN
ejpam-3454	101	13	donfack	donfack	PROPN
ejpam-3454	101	14	,	,	PUNCT
ejpam-3454	101	15	d.	d.	PROPN
ejpam-3454	101	16	a.	a.	PROPN
ejpam-3454	101	17	ndode	ndode	PROPN
ejpam-3454	101	18	yafago	yafago	PROPN
ejpam-3454	101	19	/	/	SYM
ejpam-3454	101	20	eur	eur	PROPN
ejpam-3454	101	21	.	.	PUNCT
ejpam-3454	102	1	j.	j.	PROPN
ejpam-3454	102	2	pure	pure	PROPN
ejpam-3454	102	3	appl	appl	PROPN
ejpam-3454	102	4	.	.	PROPN
ejpam-3454	102	5	math	math	PROPN
ejpam-3454	102	6	,	,	PUNCT
ejpam-3454	102	7	12	12	NUM
ejpam-3454	102	8	(	(	PUNCT
ejpam-3454	102	9	3	3	NUM
ejpam-3454	102	10	)	)	PUNCT
ejpam-3454	102	11	(	(	PUNCT
ejpam-3454	102	12	2019	2019	NUM
ejpam-3454	102	13	)	)	PUNCT
ejpam-3454	102	14	,	,	PUNCT
ejpam-3454	102	15	944	944	NUM
ejpam-3454	102	16	-	-	SYM
ejpam-3454	102	17	959	959	NUM
ejpam-3454	102	18	948	948	NUM
ejpam-3454	102	19	remark	remark	NOUN
ejpam-3454	102	20	2	2	NUM
ejpam-3454	102	21	.	.	PUNCT
ejpam-3454	103	1	with	with	ADP
ejpam-3454	103	2	this	this	PRON
ejpam-3454	103	3	,	,	PUNCT
ejpam-3454	103	4	we	we	PRON
ejpam-3454	103	5	have	have	VERB
ejpam-3454	103	6	a	a	DET
ejpam-3454	103	7	general	general	ADJ
ejpam-3454	103	8	idea	idea	NOUN
ejpam-3454	103	9	that	that	SCONJ
ejpam-3454	103	10	the	the	DET
ejpam-3454	103	11	model	model	NOUN
ejpam-3454	103	12	is	be	AUX
ejpam-3454	103	13	sustainable	sustainable	ADJ
ejpam-3454	103	14	,	,	PUNCT
ejpam-3454	103	15	and	and	CCONJ
ejpam-3454	103	16	can	can	AUX
ejpam-3454	103	17	say	say	VERB
ejpam-3454	103	18	with	with	ADP
ejpam-3454	103	19	assurance	assurance	NOUN
ejpam-3454	103	20	that	that	SCONJ
ejpam-3454	103	21	it	it	PRON
ejpam-3454	103	22	remains	remain	VERB
ejpam-3454	103	23	biologically	biologically	ADV
ejpam-3454	103	24	valid	valid	ADJ
ejpam-3454	103	25	as	as	ADV
ejpam-3454	103	26	long	long	ADV
ejpam-3454	103	27	as	as	SCONJ
ejpam-3454	103	28	it	it	PRON
ejpam-3454	103	29	began	begin	VERB
ejpam-3454	103	30	with	with	ADP
ejpam-3454	103	31	biologicallyreasonable	biologicallyreasonable	NOUN
ejpam-3454	103	32	(	(	PUNCT
ejpam-3454	103	33	i.e	i.e	ADJ
ejpam-3454	103	34	,	,	PUNCT
ejpam-3454	103	35	positive	positive	ADJ
ejpam-3454	103	36	)	)	PUNCT
ejpam-3454	103	37	data	datum	NOUN
ejpam-3454	103	38	.	.	PUNCT
ejpam-3454	104	1	this	this	PRON
ejpam-3454	104	2	also	also	ADV
ejpam-3454	104	3	shows	show	VERB
ejpam-3454	104	4	that	that	SCONJ
ejpam-3454	104	5	once	once	ADV
ejpam-3454	104	6	infected	infect	VERB
ejpam-3454	104	7	,	,	PUNCT
ejpam-3454	104	8	it	it	PRON
ejpam-3454	104	9	is	be	AUX
ejpam-3454	104	10	entirely	entirely	ADV
ejpam-3454	104	11	possible	possible	ADJ
ejpam-3454	104	12	that	that	SCONJ
ejpam-3454	104	13	the	the	DET
ejpam-3454	104	14	virus	virus	NOUN
ejpam-3454	104	15	may	may	AUX
ejpam-3454	104	16	continue	continue	VERB
ejpam-3454	104	17	to	to	PART
ejpam-3454	104	18	exist	exist	VERB
ejpam-3454	104	19	beneath	beneath	ADP
ejpam-3454	104	20	a	a	DET
ejpam-3454	104	21	detectable	detectable	ADJ
ejpam-3454	104	22	threshold	threshold	NOUN
ejpam-3454	104	23	without	without	ADP
ejpam-3454	104	24	doing	do	VERB
ejpam-3454	104	25	any	any	DET
ejpam-3454	104	26	damage	damage	NOUN
ejpam-3454	104	27	.	.	PUNCT
ejpam-3454	105	1	remark	remark	NOUN
ejpam-3454	105	2	3	3	NUM
ejpam-3454	105	3	.	.	PUNCT
ejpam-3454	106	1	one	one	NUM
ejpam-3454	106	2	reason	reason	NOUN
ejpam-3454	106	3	why	why	SCONJ
ejpam-3454	106	4	we	we	PRON
ejpam-3454	106	5	choose	choose	VERB
ejpam-3454	106	6	the	the	DET
ejpam-3454	106	7	strict	strict	ADJ
ejpam-3454	106	8	inequalities	inequality	NOUN
ejpam-3454	106	9	for	for	ADP
ejpam-3454	106	10	the	the	DET
ejpam-3454	106	11	initial	initial	ADJ
ejpam-3454	106	12	data	data	NOUN
ejpam-3454	106	13	is	be	AUX
ejpam-3454	106	14	that	that	SCONJ
ejpam-3454	106	15	often	often	ADV
ejpam-3454	106	16	in	in	ADP
ejpam-3454	106	17	biological	biological	ADJ
ejpam-3454	106	18	(	(	PUNCT
ejpam-3454	106	19	or	or	CCONJ
ejpam-3454	106	20	chemical	chemical	ADJ
ejpam-3454	106	21	)	)	PUNCT
ejpam-3454	106	22	applications	application	NOUN
ejpam-3454	106	23	we	we	PRON
ejpam-3454	106	24	are	be	AUX
ejpam-3454	106	25	interested	interested	ADJ
ejpam-3454	106	26	in	in	ADP
ejpam-3454	106	27	the	the	DET
ejpam-3454	106	28	case	case	NOUN
ejpam-3454	106	29	of	of	ADP
ejpam-3454	106	30	solutions	solution	NOUN
ejpam-3454	106	31	where	where	SCONJ
ejpam-3454	106	32	all	all	DET
ejpam-3454	106	33	unknowns	unknown	NOUN
ejpam-3454	106	34	are	be	AUX
ejpam-3454	106	35	positive	positive	ADJ
ejpam-3454	106	36	.	.	PUNCT
ejpam-3454	107	1	this	this	PRON
ejpam-3454	107	2	means	mean	VERB
ejpam-3454	107	3	intuitively	intuitively	ADV
ejpam-3454	107	4	that	that	SCONJ
ejpam-3454	107	5	all	all	DET
ejpam-3454	107	6	elements	element	NOUN
ejpam-3454	107	7	of	of	ADP
ejpam-3454	107	8	the	the	DET
ejpam-3454	107	9	model	model	NOUN
ejpam-3454	107	10	are	be	AUX
ejpam-3454	107	11	’	'	PUNCT
ejpam-3454	107	12	active	active	ADJ
ejpam-3454	107	13	’	'	PUNCT
ejpam-3454	107	14	.	.	PUNCT
ejpam-3454	108	1	on	on	ADP
ejpam-3454	108	2	the	the	DET
ejpam-3454	108	3	other	other	ADJ
ejpam-3454	108	4	hand	hand	NOUN
ejpam-3454	108	5	it	it	PRON
ejpam-3454	108	6	is	be	AUX
ejpam-3454	108	7	sometimes	sometimes	ADV
ejpam-3454	108	8	relevant	relevant	ADJ
ejpam-3454	108	9	to	to	PART
ejpam-3454	108	10	consider	consider	VERB
ejpam-3454	108	11	solutions	solution	NOUN
ejpam-3454	108	12	with	with	ADP
ejpam-3454	108	13	non	non	ADJ
ejpam-3454	108	14	-	-	ADJ
ejpam-3454	108	15	strict	strict	ADJ
ejpam-3454	108	16	inequalities	inequality	NOUN
ejpam-3454	108	17	.	.	PUNCT
ejpam-3454	109	1	the	the	DET
ejpam-3454	109	2	fact	fact	NOUN
ejpam-3454	109	3	the	the	DET
ejpam-3454	109	4	statement	statement	NOUN
ejpam-3454	109	5	of	of	ADP
ejpam-3454	109	6	the	the	DET
ejpam-3454	109	7	theorem	theorem	NOUN
ejpam-3454	109	8	with	with	ADP
ejpam-3454	109	9	strict	strict	ADJ
ejpam-3454	109	10	inequalities	inequality	NOUN
ejpam-3454	109	11	implies	imply	VERB
ejpam-3454	109	12	the	the	DET
ejpam-3454	109	13	corresponding	correspond	VERB
ejpam-3454	109	14	statement	statement	NOUN
ejpam-3454	109	15	with	with	ADP
ejpam-3454	109	16	non	non	ADJ
ejpam-3454	109	17	-	-	ADJ
ejpam-3454	109	18	strict	strict	ADJ
ejpam-3454	109	19	inequalities	inequality	NOUN
ejpam-3454	109	20	is	be	AUX
ejpam-3454	109	21	based	base	VERB
ejpam-3454	109	22	on	on	ADP
ejpam-3454	109	23	continuous	continuous	ADJ
ejpam-3454	109	24	dependence	dependence	NOUN
ejpam-3454	109	25	of	of	ADP
ejpam-3454	109	26	the	the	DET
ejpam-3454	109	27	solution	solution	NOUN
ejpam-3454	109	28	on	on	ADP
ejpam-3454	109	29	initial	initial	ADJ
ejpam-3454	109	30	data	datum	NOUN
ejpam-3454	109	31	.	.	PUNCT
ejpam-3454	110	1	it	it	PRON
ejpam-3454	110	2	will	will	AUX
ejpam-3454	110	3	now	now	ADV
ejpam-3454	110	4	be	be	AUX
ejpam-3454	110	5	shown	show	VERB
ejpam-3454	110	6	,	,	PUNCT
ejpam-3454	110	7	with	with	ADP
ejpam-3454	110	8	the	the	DET
ejpam-3454	110	9	help	help	NOUN
ejpam-3454	110	10	of	of	ADP
ejpam-3454	110	11	the	the	DET
ejpam-3454	110	12	continuation	continuation	NOUN
ejpam-3454	110	13	criterion	criterion	NOUN
ejpam-3454	110	14	the	the	DET
ejpam-3454	110	15	existence	existence	NOUN
ejpam-3454	110	16	of	of	ADP
ejpam-3454	110	17	global	global	ADJ
ejpam-3454	110	18	solutions	solution	NOUN
ejpam-3454	110	19	.	.	PUNCT
ejpam-3454	111	1	theorem	theorem	NOUN
ejpam-3454	111	2	2	2	NUM
ejpam-3454	111	3	.	.	PUNCT
ejpam-3454	112	1	if	if	SCONJ
ejpam-3454	112	2	(	(	PUNCT
ejpam-3454	112	3	1	1	NUM
ejpam-3454	112	4	−	−	NOUN
ejpam-3454	112	5	ε)p	ε)p	PUNCT
ejpam-3454	112	6	−	−	PROPN
ejpam-3454	112	7	δ	δ	PROPN
ejpam-3454	112	8	>	>	X
ejpam-3454	112	9	0	0	PUNCT
ejpam-3454	113	1	the	the	DET
ejpam-3454	113	2	solution	solution	NOUN
ejpam-3454	113	3	of	of	ADP
ejpam-3454	113	4	the	the	DET
ejpam-3454	113	5	initial	initial	ADJ
ejpam-3454	113	6	value	value	NOUN
ejpam-3454	113	7	problem	problem	NOUN
ejpam-3454	113	8	(	(	PUNCT
ejpam-3454	113	9	1	1	NUM
ejpam-3454	113	10	)	)	PUNCT
ejpam-3454	113	11	,	,	PUNCT
ejpam-3454	113	12	(	(	PUNCT
ejpam-3454	113	13	2	2	NUM
ejpam-3454	113	14	)	)	PUNCT
ejpam-3454	113	15	,	,	PUNCT
ejpam-3454	113	16	with	with	ADP
ejpam-3454	113	17	positive	positive	ADJ
ejpam-3454	113	18	initial	initial	ADJ
ejpam-3454	113	19	data	datum	NOUN
ejpam-3454	113	20	,	,	PUNCT
ejpam-3454	113	21	exists	exist	VERB
ejpam-3454	113	22	globally	globally	ADV
ejpam-3454	113	23	in	in	ADP
ejpam-3454	113	24	time	time	NOUN
ejpam-3454	113	25	in	in	ADP
ejpam-3454	113	26	the	the	DET
ejpam-3454	113	27	future	future	NOUN
ejpam-3454	113	28	,	,	PUNCT
ejpam-3454	113	29	i.e.	i.e.	X
ejpam-3454	113	30	on	on	ADP
ejpam-3454	113	31	[	[	X
ejpam-3454	113	32	t0,+∞	t0,+∞	PROPN
ejpam-3454	113	33	[	[	NOUN
ejpam-3454	113	34	.	.	PUNCT
ejpam-3454	113	35	proof	proof	NOUN
ejpam-3454	113	36	.	.	PUNCT
ejpam-3454	114	1	to	to	PART
ejpam-3454	114	2	prove	prove	VERB
ejpam-3454	114	3	this	this	PRON
ejpam-3454	114	4	,	,	PUNCT
ejpam-3454	114	5	it	it	PRON
ejpam-3454	114	6	is	be	AUX
ejpam-3454	114	7	enough	enough	ADJ
ejpam-3454	114	8	to	to	PART
ejpam-3454	114	9	show	show	VERB
ejpam-3454	114	10	that	that	SCONJ
ejpam-3454	114	11	all	all	DET
ejpam-3454	114	12	variables	variable	NOUN
ejpam-3454	114	13	are	be	AUX
ejpam-3454	114	14	bounded	bound	VERB
ejpam-3454	114	15	on	on	ADP
ejpam-3454	114	16	an	an	DET
ejpam-3454	114	17	arbitrary	arbitrary	ADJ
ejpam-3454	114	18	finite	finite	ADJ
ejpam-3454	114	19	interval	interval	NOUN
ejpam-3454	114	20	[	[	X
ejpam-3454	114	21	t0	t0	NOUN
ejpam-3454	114	22	;	;	PUNCT
ejpam-3454	114	23	t	t	PROPN
ejpam-3454	114	24	)	)	PUNCT
ejpam-3454	114	25	.	.	PUNCT
ejpam-3454	115	1	using	use	VERB
ejpam-3454	115	2	the	the	DET
ejpam-3454	115	3	positivity	positivity	NOUN
ejpam-3454	115	4	of	of	ADP
ejpam-3454	115	5	the	the	DET
ejpam-3454	115	6	solutions	solution	NOUN
ejpam-3454	115	7	,	,	PUNCT
ejpam-3454	115	8	is	be	AUX
ejpam-3454	115	9	suffices	suffice	NOUN
ejpam-3454	115	10	to	to	PART
ejpam-3454	115	11	show	show	VERB
ejpam-3454	115	12	that	that	SCONJ
ejpam-3454	115	13	all	all	DET
ejpam-3454	115	14	variables	variable	NOUN
ejpam-3454	115	15	are	be	AUX
ejpam-3454	115	16	bounded	bound	VERB
ejpam-3454	115	17	above	above	ADV
ejpam-3454	115	18	.	.	PUNCT
ejpam-3454	116	1	the	the	DET
ejpam-3454	116	2	sum	sum	NOUN
ejpam-3454	116	3	of	of	ADP
ejpam-3454	116	4	equations	equation	NOUN
ejpam-3454	116	5	(	(	PUNCT
ejpam-3454	116	6	1a	1a	NUM
ejpam-3454	116	7	)	)	PUNCT
ejpam-3454	116	8	,	,	PUNCT
ejpam-3454	116	9	(	(	PUNCT
ejpam-3454	116	10	1b	1b	NUM
ejpam-3454	116	11	)	)	PUNCT
ejpam-3454	116	12	and	and	CCONJ
ejpam-3454	116	13	(	(	PUNCT
ejpam-3454	116	14	1c	1c	X
ejpam-3454	116	15	)	)	PUNCT
ejpam-3454	116	16	leads	lead	VERB
ejpam-3454	116	17	to	to	ADP
ejpam-3454	116	18	:	:	PUNCT
ejpam-3454	117	1	d	d	X
ejpam-3454	117	2	dt	dt	X
ejpam-3454	117	3	(	(	PUNCT
ejpam-3454	117	4	t	t	PROPN
ejpam-3454	117	5	+	+	CCONJ
ejpam-3454	117	6	i	i	PRON
ejpam-3454	117	7	+	+	CCONJ
ejpam-3454	117	8	v	v	NOUN
ejpam-3454	117	9	)	)	PUNCT
ejpam-3454	117	10	=	=	SYM
ejpam-3454	117	11	rt	rt	PROPN
ejpam-3454	117	12	(	(	PUNCT
ejpam-3454	117	13	1−	1−	NUM
ejpam-3454	117	14	t	t	NOUN
ejpam-3454	117	15	+	+	CCONJ
ejpam-3454	117	16	i	i	PRON
ejpam-3454	117	17	tmax	tmax	ADJ
ejpam-3454	117	18	)	)	PUNCT
ejpam-3454	117	19	−	−	NOUN
ejpam-3454	118	1	dt	dt	X
ejpam-3454	119	1	+	+	CCONJ
ejpam-3454	119	2	(	(	PUNCT
ejpam-3454	119	3	(	(	PUNCT
ejpam-3454	119	4	1−	1−	NUM
ejpam-3454	119	5	ε)p−	ε)p−	PROPN
ejpam-3454	119	6	δ)i	δ)i	PUNCT
ejpam-3454	119	7	−	−	PROPN
ejpam-3454	119	8	cv	cv	NOUN
ejpam-3454	119	9	−	−	NOUN
ejpam-3454	119	10	α(1−	α(1−	PROPN
ejpam-3454	119	11	η)βv	η)βv	PROPN
ejpam-3454	119	12	t.	t.	NOUN
ejpam-3454	120	1	hence	hence	ADV
ejpam-3454	120	2	d	d	X
ejpam-3454	120	3	dt	dt	X
ejpam-3454	120	4	(	(	PUNCT
ejpam-3454	120	5	t	t	PROPN
ejpam-3454	121	1	+	+	CCONJ
ejpam-3454	121	2	i	i	PRON
ejpam-3454	121	3	+	+	CCONJ
ejpam-3454	121	4	v	v	NOUN
ejpam-3454	121	5	)	)	PUNCT
ejpam-3454	121	6	≤	≤	NOUN
ejpam-3454	121	7	rtmax	rtmax	VERB
ejpam-3454	121	8	4	4	NUM
ejpam-3454	121	9	−	−	PROPN
ejpam-3454	121	10	(	(	PUNCT
ejpam-3454	121	11	√	√	INTJ
ejpam-3454	121	12	rt√	rt√	NOUN
ejpam-3454	121	13	tmax	tmax	ADV
ejpam-3454	121	14	−	−	PROPN
ejpam-3454	121	15	√	√	NUM
ejpam-3454	121	16	rtmax	rtmax	VERB
ejpam-3454	121	17	2	2	NUM
ejpam-3454	121	18	)	)	PUNCT
ejpam-3454	121	19	2	2	NUM
ejpam-3454	122	1	+	+	NOUN
ejpam-3454	122	2	a	a	DET
ejpam-3454	122	3	(	(	PUNCT
ejpam-3454	122	4	t	t	NOUN
ejpam-3454	122	5	+	+	CCONJ
ejpam-3454	122	6	i	i	PRON
ejpam-3454	122	7	+	+	CCONJ
ejpam-3454	122	8	v	v	NOUN
ejpam-3454	122	9	)	)	PUNCT
ejpam-3454	122	10	where	where	SCONJ
ejpam-3454	122	11	a	a	DET
ejpam-3454	122	12	=	=	NOUN
ejpam-3454	122	13	max{c	max{c	NOUN
ejpam-3454	122	14	,	,	PUNCT
ejpam-3454	122	15	d	d	PROPN
ejpam-3454	122	16	,	,	PUNCT
ejpam-3454	122	17	(	(	PUNCT
ejpam-3454	122	18	1−	1−	NUM
ejpam-3454	122	19	ε)p−	ε)p−	PROPN
ejpam-3454	122	20	δ	δ	PROPN
ejpam-3454	122	21	}	}	PUNCT
ejpam-3454	122	22	.	.	PUNCT
ejpam-3454	123	1	it	it	PRON
ejpam-3454	123	2	follows	follow	VERB
ejpam-3454	123	3	that	that	PRON
ejpam-3454	123	4	:	:	PUNCT
ejpam-3454	124	1	d	d	X
ejpam-3454	124	2	dt	dt	X
ejpam-3454	124	3	(	(	PUNCT
ejpam-3454	124	4	t	t	PROPN
ejpam-3454	124	5	+	+	CCONJ
ejpam-3454	124	6	i	i	PRON
ejpam-3454	124	7	+	+	CCONJ
ejpam-3454	124	8	v	v	NOUN
ejpam-3454	124	9	)	)	PUNCT
ejpam-3454	124	10	≤	≤	NOUN
ejpam-3454	124	11	rtmax	rtmax	VERB
ejpam-3454	124	12	4	4	NUM
ejpam-3454	124	13	+	+	NOUN
ejpam-3454	124	14	a	a	DET
ejpam-3454	124	15	(	(	PUNCT
ejpam-3454	124	16	t	t	NOUN
ejpam-3454	125	1	+	+	CCONJ
ejpam-3454	125	2	i	i	PRON
ejpam-3454	125	3	+	+	CCONJ
ejpam-3454	125	4	v	v	NOUN
ejpam-3454	125	5	)	)	PUNCT
ejpam-3454	125	6	.	.	PUNCT
ejpam-3454	126	1	(	(	PUNCT
ejpam-3454	126	2	3	3	X
ejpam-3454	126	3	)	)	PUNCT
ejpam-3454	126	4	from	from	ADP
ejpam-3454	126	5	differential	differential	ADJ
ejpam-3454	126	6	inequation	inequation	NOUN
ejpam-3454	126	7	(	(	PUNCT
ejpam-3454	126	8	3	3	NUM
ejpam-3454	126	9	)	)	PUNCT
ejpam-3454	126	10	,	,	PUNCT
ejpam-3454	126	11	t	t	PROPN
ejpam-3454	126	12	(	(	PUNCT
ejpam-3454	126	13	t	t	PROPN
ejpam-3454	126	14	)	)	PUNCT
ejpam-3454	126	15	+	+	CCONJ
ejpam-3454	126	16	i(t	i(t	NOUN
ejpam-3454	126	17	)	)	PUNCT
ejpam-3454	127	1	+	+	NUM
ejpam-3454	127	2	v	v	X
ejpam-3454	127	3	(	(	PUNCT
ejpam-3454	127	4	t	t	NOUN
ejpam-3454	127	5	)	)	PUNCT
ejpam-3454	127	6	should	should	AUX
ejpam-3454	127	7	verify	verify	VERB
ejpam-3454	127	8	:	:	PUNCT
ejpam-3454	127	9	t	t	PROPN
ejpam-3454	127	10	(	(	PUNCT
ejpam-3454	127	11	t	t	PROPN
ejpam-3454	127	12	)	)	PUNCT
ejpam-3454	127	13	+	+	CCONJ
ejpam-3454	127	14	i(t	i(t	NOUN
ejpam-3454	127	15	)	)	PUNCT
ejpam-3454	128	1	+	+	NUM
ejpam-3454	128	2	v	v	X
ejpam-3454	128	3	(	(	PUNCT
ejpam-3454	128	4	t	t	NOUN
ejpam-3454	128	5	)	)	PUNCT
ejpam-3454	128	6	≤	≤	NOUN
ejpam-3454	128	7	n(t	n(t	PROPN
ejpam-3454	128	8	)	)	PUNCT
ejpam-3454	128	9	,	,	PUNCT
ejpam-3454	128	10	where	where	SCONJ
ejpam-3454	128	11	the	the	DET
ejpam-3454	128	12	function	function	NOUN
ejpam-3454	128	13	n	n	VERB
ejpam-3454	128	14	is	be	AUX
ejpam-3454	128	15	the	the	DET
ejpam-3454	128	16	solution	solution	NOUN
ejpam-3454	128	17	of	of	ADP
ejpam-3454	128	18	the	the	DET
ejpam-3454	128	19	following	following	ADJ
ejpam-3454	128	20	initial	initial	ADJ
ejpam-3454	128	21	value	value	NOUN
ejpam-3454	128	22	problem	problem	NOUN
ejpam-3454	128	23	(	(	PUNCT
ejpam-3454	128	24	4	4	NUM
ejpam-3454	128	25	)	)	PUNCT
ejpam-3454	128	26	,	,	PUNCT
ejpam-3454	128	27	(	(	PUNCT
ejpam-3454	128	28	5	5	NUM
ejpam-3454	128	29	):	):	PUNCT
ejpam-3454	128	30	dn	dn	NOUN
ejpam-3454	128	31	dt	dt	NOUN
ejpam-3454	128	32	=	=	PUNCT
ejpam-3454	129	1	an	an	DET
ejpam-3454	129	2	+	+	NUM
ejpam-3454	129	3	rtmax	rtmax	VERB
ejpam-3454	129	4	4	4	NUM
ejpam-3454	129	5	(	(	PUNCT
ejpam-3454	129	6	4	4	NUM
ejpam-3454	129	7	)	)	PUNCT
ejpam-3454	129	8	n(t0	n(t0	NOUN
ejpam-3454	129	9	)	)	PUNCT
ejpam-3454	129	10	=	=	SYM
ejpam-3454	129	11	n0	n0	NUM
ejpam-3454	129	12	=	=	SYM
ejpam-3454	129	13	t0	t0	PROPN
ejpam-3454	129	14	+	+	CCONJ
ejpam-3454	130	1	i0	i0	PROPN
ejpam-3454	130	2	+	+	PROPN
ejpam-3454	130	3	v0	v0	PROPN
ejpam-3454	130	4	.	.	PUNCT
ejpam-3454	131	1	(	(	PUNCT
ejpam-3454	131	2	5	5	X
ejpam-3454	131	3	)	)	PUNCT
ejpam-3454	131	4	a.	a.	NOUN
ejpam-3454	131	5	nangue	nangue	NOUN
ejpam-3454	131	6	,	,	PUNCT
ejpam-3454	131	7	t.	t.	PROPN
ejpam-3454	131	8	donfack	donfack	PROPN
ejpam-3454	131	9	,	,	PUNCT
ejpam-3454	131	10	d.	d.	PROPN
ejpam-3454	131	11	a.	a.	PROPN
ejpam-3454	131	12	ndode	ndode	PROPN
ejpam-3454	131	13	yafago	yafago	PROPN
ejpam-3454	131	14	/	/	SYM
ejpam-3454	131	15	eur	eur	PROPN
ejpam-3454	131	16	.	.	PUNCT
ejpam-3454	132	1	j.	j.	PROPN
ejpam-3454	132	2	pure	pure	PROPN
ejpam-3454	132	3	appl	appl	PROPN
ejpam-3454	132	4	.	.	PROPN
ejpam-3454	132	5	math	math	PROPN
ejpam-3454	132	6	,	,	PUNCT
ejpam-3454	132	7	12	12	NUM
ejpam-3454	132	8	(	(	PUNCT
ejpam-3454	132	9	3	3	NUM
ejpam-3454	132	10	)	)	PUNCT
ejpam-3454	132	11	(	(	PUNCT
ejpam-3454	132	12	2019	2019	NUM
ejpam-3454	132	13	)	)	PUNCT
ejpam-3454	132	14	,	,	PUNCT
ejpam-3454	132	15	944	944	NUM
ejpam-3454	132	16	-	-	SYM
ejpam-3454	132	17	959	959	NUM
ejpam-3454	132	18	949	949	NUM
ejpam-3454	132	19	the	the	DET
ejpam-3454	132	20	solution	solution	NOUN
ejpam-3454	132	21	of	of	ADP
ejpam-3454	132	22	the	the	DET
ejpam-3454	132	23	initial	initial	ADJ
ejpam-3454	132	24	value	value	NOUN
ejpam-3454	132	25	problem	problem	NOUN
ejpam-3454	132	26	(	(	PUNCT
ejpam-3454	132	27	4	4	NUM
ejpam-3454	132	28	)	)	PUNCT
ejpam-3454	132	29	,	,	PUNCT
ejpam-3454	132	30	(	(	PUNCT
ejpam-3454	132	31	5	5	X
ejpam-3454	132	32	)	)	PUNCT
ejpam-3454	132	33	is	be	AUX
ejpam-3454	132	34	given	give	VERB
ejpam-3454	132	35	by	by	ADP
ejpam-3454	132	36	:	:	PUNCT
ejpam-3454	132	37	n(t	n(t	PROPN
ejpam-3454	132	38	)	)	PUNCT
ejpam-3454	132	39	=	=	SYM
ejpam-3454	133	1	−rtmax	−rtmax	NUM
ejpam-3454	133	2	4a	4a	NUM
ejpam-3454	133	3	+	+	CCONJ
ejpam-3454	133	4	(	(	PUNCT
ejpam-3454	133	5	n0	n0	X
ejpam-3454	133	6	+	+	CCONJ
ejpam-3454	133	7	rtmax	rtmax	X
ejpam-3454	133	8	4a	4a	NUM
ejpam-3454	133	9	)	)	PUNCT
ejpam-3454	133	10	ea(t−t0	ea(t−t0	PROPN
ejpam-3454	133	11	)	)	PUNCT
ejpam-3454	133	12	.	.	PUNCT
ejpam-3454	134	1	it	it	PRON
ejpam-3454	134	2	follows	follow	VERB
ejpam-3454	134	3	that	that	PRON
ejpam-3454	134	4	,	,	PUNCT
ejpam-3454	134	5	t	t	PROPN
ejpam-3454	134	6	(	(	PUNCT
ejpam-3454	134	7	t	t	PROPN
ejpam-3454	134	8	)	)	PUNCT
ejpam-3454	134	9	+	+	CCONJ
ejpam-3454	135	1	i(t	i(t	NOUN
ejpam-3454	135	2	)	)	PUNCT
ejpam-3454	136	1	+	+	NUM
ejpam-3454	136	2	v	v	X
ejpam-3454	136	3	(	(	PUNCT
ejpam-3454	136	4	t	t	NOUN
ejpam-3454	136	5	)	)	PUNCT
ejpam-3454	136	6	≤	≤	NUM
ejpam-3454	136	7	−rtmax	−rtmax	NUM
ejpam-3454	136	8	4a	4a	NUM
ejpam-3454	137	1	+	+	CCONJ
ejpam-3454	137	2	(	(	PUNCT
ejpam-3454	137	3	t0	t0	X
ejpam-3454	137	4	+	+	CCONJ
ejpam-3454	137	5	i0	i0	PROPN
ejpam-3454	137	6	+	+	CCONJ
ejpam-3454	137	7	v0	v0	PROPN
ejpam-3454	137	8	+	+	CCONJ
ejpam-3454	137	9	rtmax	rtmax	X
ejpam-3454	137	10	4a	4a	NUM
ejpam-3454	137	11	)	)	PUNCT
ejpam-3454	137	12	ea(t−t0	ea(t−t0	PROPN
ejpam-3454	137	13	)	)	PUNCT
ejpam-3454	137	14	.	.	PUNCT
ejpam-3454	138	1	this	this	DET
ejpam-3454	138	2	last	last	ADJ
ejpam-3454	138	3	equation	equation	NOUN
ejpam-3454	138	4	leads	lead	VERB
ejpam-3454	138	5	to	to	ADP
ejpam-3454	138	6	:	:	PUNCT
ejpam-3454	138	7	t	t	PROPN
ejpam-3454	138	8	(	(	PUNCT
ejpam-3454	138	9	t	t	PROPN
ejpam-3454	138	10	)	)	PUNCT
ejpam-3454	139	1	+	+	CCONJ
ejpam-3454	139	2	i(t	i(t	NOUN
ejpam-3454	139	3	)	)	PUNCT
ejpam-3454	140	1	+	+	NUM
ejpam-3454	140	2	v	v	X
ejpam-3454	140	3	(	(	PUNCT
ejpam-3454	140	4	t	t	NOUN
ejpam-3454	140	5	)	)	PUNCT
ejpam-3454	140	6	≤	≤	NOUN
ejpam-3454	140	7	(	(	PUNCT
ejpam-3454	140	8	t0	t0	NOUN
ejpam-3454	140	9	+	+	CCONJ
ejpam-3454	140	10	i0	i0	PROPN
ejpam-3454	140	11	+	+	CCONJ
ejpam-3454	140	12	v0	v0	PROPN
ejpam-3454	140	13	+	+	CCONJ
ejpam-3454	140	14	rtmax	rtmax	X
ejpam-3454	140	15	4a	4a	NUM
ejpam-3454	140	16	)	)	PUNCT
ejpam-3454	140	17	ea(t−t0	ea(t−t0	PROPN
ejpam-3454	140	18	)	)	PUNCT
ejpam-3454	140	19	.	.	PUNCT
ejpam-3454	141	1	therefore	therefore	ADV
ejpam-3454	141	2	,	,	PUNCT
ejpam-3454	141	3	t	t	PROPN
ejpam-3454	141	4	(	(	PUNCT
ejpam-3454	141	5	t	t	PROPN
ejpam-3454	141	6	)	)	PUNCT
ejpam-3454	141	7	+	+	CCONJ
ejpam-3454	141	8	i(t	i(t	NOUN
ejpam-3454	141	9	)	)	PUNCT
ejpam-3454	142	1	+	+	NUM
ejpam-3454	142	2	v	v	X
ejpam-3454	142	3	(	(	PUNCT
ejpam-3454	142	4	t	t	NOUN
ejpam-3454	142	5	)	)	PUNCT
ejpam-3454	142	6	≤	≤	NUM
ejpam-3454	142	7	g(t	g(t	PROPN
ejpam-3454	142	8	)	)	PUNCT
ejpam-3454	142	9	(	(	PUNCT
ejpam-3454	142	10	6	6	NUM
ejpam-3454	142	11	)	)	PUNCT
ejpam-3454	142	12	where	where	SCONJ
ejpam-3454	142	13	:	:	PUNCT
ejpam-3454	142	14	g(t	g(t	PROPN
ejpam-3454	142	15	)	)	PUNCT
ejpam-3454	142	16	=	=	PRON
ejpam-3454	142	17	(	(	PUNCT
ejpam-3454	142	18	t0	t0	X
ejpam-3454	142	19	+	+	CCONJ
ejpam-3454	142	20	i0	i0	PROPN
ejpam-3454	142	21	+	+	CCONJ
ejpam-3454	142	22	v0	v0	PROPN
ejpam-3454	142	23	+	+	CCONJ
ejpam-3454	142	24	rtmax	rtmax	X
ejpam-3454	142	25	4a	4a	NUM
ejpam-3454	142	26	)	)	PUNCT
ejpam-3454	142	27	ea(t−t0	ea(t−t0	PROPN
ejpam-3454	142	28	)	)	PUNCT
ejpam-3454	142	29	.	.	PUNCT
ejpam-3454	143	1	g	g	PROPN
ejpam-3454	143	2	is	be	AUX
ejpam-3454	143	3	a	a	DET
ejpam-3454	143	4	continuous	continuous	ADJ
ejpam-3454	143	5	function	function	NOUN
ejpam-3454	143	6	thus	thus	ADV
ejpam-3454	143	7	g	g	PROPN
ejpam-3454	143	8	is	be	AUX
ejpam-3454	143	9	bounded	bound	VERB
ejpam-3454	143	10	function	function	NOUN
ejpam-3454	143	11	on	on	ADP
ejpam-3454	143	12	[	[	X
ejpam-3454	143	13	t0	t0	PROPN
ejpam-3454	143	14	,	,	PUNCT
ejpam-3454	143	15	t	t	X
ejpam-3454	143	16	]	]	PUNCT
ejpam-3454	143	17	.	.	PUNCT
ejpam-3454	144	1	furthermore	furthermore	ADV
ejpam-3454	144	2	according	accord	VERB
ejpam-3454	144	3	to	to	ADP
ejpam-3454	144	4	the	the	DET
ejpam-3454	144	5	positivity	positivity	NOUN
ejpam-3454	144	6	result	result	NOUN
ejpam-3454	144	7	and	and	CCONJ
ejpam-3454	144	8	inequation	inequation	NOUN
ejpam-3454	144	9	(	(	PUNCT
ejpam-3454	144	10	6	6	NUM
ejpam-3454	144	11	)	)	PUNCT
ejpam-3454	144	12	,	,	PUNCT
ejpam-3454	144	13	we	we	PRON
ejpam-3454	144	14	have	have	VERB
ejpam-3454	144	15	:	:	PUNCT
ejpam-3454	144	16	0	0	PUNCT
ejpam-3454	144	17	<	<	X
ejpam-3454	144	18	n(t	n(t	PROPN
ejpam-3454	144	19	)	)	PUNCT
ejpam-3454	144	20	≤	≤	NUM
ejpam-3454	144	21	g(t	g(t	PROPN
ejpam-3454	144	22	)	)	PUNCT
ejpam-3454	144	23	on	on	ADP
ejpam-3454	144	24	[	[	X
ejpam-3454	144	25	t0	t0	NOUN
ejpam-3454	144	26	,	,	PUNCT
ejpam-3454	144	27	t	t	PROPN
ejpam-3454	144	28	]	]	PUNCT
ejpam-3454	144	29	.	.	PUNCT
ejpam-3454	145	1	therefore	therefore	ADV
ejpam-3454	145	2	,	,	PUNCT
ejpam-3454	145	3	since	since	SCONJ
ejpam-3454	145	4	n	n	ADV
ejpam-3454	145	5	is	be	AUX
ejpam-3454	145	6	bounded	bound	VERB
ejpam-3454	145	7	on	on	ADP
ejpam-3454	145	8	any	any	DET
ejpam-3454	145	9	finite	finite	ADJ
ejpam-3454	145	10	interval	interval	NOUN
ejpam-3454	145	11	,	,	PUNCT
ejpam-3454	145	12	t	t	PROPN
ejpam-3454	145	13	,	,	PUNCT
ejpam-3454	145	14	i	i	PRON
ejpam-3454	145	15	,	,	PUNCT
ejpam-3454	145	16	v	v	NOUN
ejpam-3454	145	17	are	be	AUX
ejpam-3454	145	18	also	also	ADV
ejpam-3454	145	19	bounded	bound	VERB
ejpam-3454	145	20	.	.	PUNCT
ejpam-3454	146	1	this	this	PRON
ejpam-3454	146	2	completes	complete	VERB
ejpam-3454	146	3	the	the	DET
ejpam-3454	146	4	proof	proof	NOUN
ejpam-3454	146	5	of	of	ADP
ejpam-3454	146	6	the	the	DET
ejpam-3454	146	7	theorem	theorem	NOUN
ejpam-3454	146	8	.	.	PROPN
ejpam-3454	146	9	2.2	2.2	NUM
ejpam-3454	146	10	.	.	PUNCT
ejpam-3454	147	1	asymptotic	asymptotic	ADJ
ejpam-3454	147	2	behaviour	behaviour	NOUN
ejpam-3454	147	3	and	and	CCONJ
ejpam-3454	147	4	invariant	invariant	PROPN
ejpam-3454	147	5	set	set	VERB
ejpam-3454	147	6	the	the	DET
ejpam-3454	147	7	following	follow	VERB
ejpam-3454	147	8	theorem	theorem	NOUN
ejpam-3454	147	9	shows	show	VERB
ejpam-3454	147	10	that	that	SCONJ
ejpam-3454	147	11	all	all	DET
ejpam-3454	147	12	solutions	solution	NOUN
ejpam-3454	147	13	of	of	ADP
ejpam-3454	147	14	model	model	NOUN
ejpam-3454	147	15	(	(	PUNCT
ejpam-3454	147	16	1	1	NUM
ejpam-3454	147	17	)	)	PUNCT
ejpam-3454	147	18	in	in	ADP
ejpam-3454	147	19	r3	r3	PROPN
ejpam-3454	147	20	+	+	CCONJ
ejpam-3454	147	21	are	be	AUX
ejpam-3454	147	22	ultimately	ultimately	ADV
ejpam-3454	147	23	bounded	bound	VERB
ejpam-3454	147	24	and	and	CCONJ
ejpam-3454	147	25	that	that	SCONJ
ejpam-3454	147	26	solutions	solution	NOUN
ejpam-3454	147	27	with	with	ADP
ejpam-3454	147	28	positive	positive	ADJ
ejpam-3454	147	29	initial	initial	ADJ
ejpam-3454	147	30	value	value	NOUN
ejpam-3454	147	31	conditions	condition	NOUN
ejpam-3454	147	32	are	be	AUX
ejpam-3454	147	33	positive	positive	ADJ
ejpam-3454	147	34	,	,	PUNCT
ejpam-3454	147	35	which	which	PRON
ejpam-3454	147	36	indicates	indicate	VERB
ejpam-3454	147	37	that	that	DET
ejpam-3454	147	38	model	model	NOUN
ejpam-3454	147	39	(	(	PUNCT
ejpam-3454	147	40	1	1	X
ejpam-3454	147	41	)	)	PUNCT
ejpam-3454	147	42	is	be	AUX
ejpam-3454	147	43	well	well	ADV
ejpam-3454	147	44	-	-	PUNCT
ejpam-3454	147	45	posed	pose	VERB
ejpam-3454	147	46	.	.	PUNCT
ejpam-3454	148	1	otherwise	otherwise	ADV
ejpam-3454	148	2	for	for	ADP
ejpam-3454	148	3	biological	biological	ADJ
ejpam-3454	148	4	reasons	reason	NOUN
ejpam-3454	148	5	only	only	ADV
ejpam-3454	148	6	initial	initial	ADJ
ejpam-3454	148	7	data	datum	NOUN
ejpam-3454	148	8	are	be	AUX
ejpam-3454	148	9	considered	consider	VERB
ejpam-3454	148	10	for	for	ADP
ejpam-3454	148	11	which	which	PRON
ejpam-3454	148	12	at	at	ADP
ejpam-3454	148	13	the	the	DET
ejpam-3454	148	14	initial	initial	ADJ
ejpam-3454	148	15	time	time	NOUN
ejpam-3454	148	16	t	t	PROPN
ejpam-3454	149	1	+	+	CCONJ
ejpam-3454	149	2	i	i	PRON
ejpam-3454	149	3	≤	≤	ADV
ejpam-3454	149	4	tmax	tmax	ADV
ejpam-3454	149	5	.	.	PUNCT
ejpam-3454	150	1	then	then	ADV
ejpam-3454	150	2	we	we	PRON
ejpam-3454	150	3	will	will	AUX
ejpam-3454	150	4	prove	prove	VERB
ejpam-3454	150	5	that	that	SCONJ
ejpam-3454	150	6	if	if	SCONJ
ejpam-3454	150	7	the	the	DET
ejpam-3454	150	8	initial	initial	ADJ
ejpam-3454	150	9	data	datum	NOUN
ejpam-3454	150	10	satisfy	satisfy	VERB
ejpam-3454	150	11	this	this	DET
ejpam-3454	150	12	previous	previous	ADJ
ejpam-3454	150	13	inequality	inequality	NOUN
ejpam-3454	150	14	the	the	DET
ejpam-3454	150	15	solution	solution	NOUN
ejpam-3454	150	16	also	also	ADV
ejpam-3454	150	17	does	do	VERB
ejpam-3454	150	18	so	so	ADV
ejpam-3454	150	19	.	.	PUNCT
ejpam-3454	151	1	theorem	theorem	NOUN
ejpam-3454	151	2	3	3	NUM
ejpam-3454	151	3	.	.	X
ejpam-3454	152	1	for	for	ADP
ejpam-3454	152	2	any	any	DET
ejpam-3454	152	3	positive	positive	ADJ
ejpam-3454	152	4	initial	initial	ADJ
ejpam-3454	152	5	data	datum	NOUN
ejpam-3454	152	6	t0	t0	PROPN
ejpam-3454	152	7	,	,	PUNCT
ejpam-3454	152	8	i0	i0	PROPN
ejpam-3454	152	9	and	and	CCONJ
ejpam-3454	152	10	v0	v0	PROPN
ejpam-3454	152	11	of	of	ADP
ejpam-3454	152	12	the	the	DET
ejpam-3454	152	13	cauchy	cauchy	ADJ
ejpam-3454	152	14	problem	problem	NOUN
ejpam-3454	152	15	(	(	PUNCT
ejpam-3454	152	16	1	1	NUM
ejpam-3454	152	17	)	)	PUNCT
ejpam-3454	152	18	,	,	PUNCT
ejpam-3454	152	19	we	we	PRON
ejpam-3454	152	20	have	have	VERB
ejpam-3454	152	21	:	:	PUNCT
ejpam-3454	152	22	t	t	PROPN
ejpam-3454	152	23	(	(	PUNCT
ejpam-3454	152	24	t	t	PROPN
ejpam-3454	152	25	)	)	PUNCT
ejpam-3454	152	26	≤	≤	PROPN
ejpam-3454	152	27	c1	c1	PROPN
ejpam-3454	152	28	,	,	PUNCT
ejpam-3454	152	29	i(t	i(t	PROPN
ejpam-3454	152	30	)	)	PUNCT
ejpam-3454	152	31	≤	≤	NOUN
ejpam-3454	152	32	c1	c1	NOUN
ejpam-3454	152	33	and	and	CCONJ
ejpam-3454	152	34	v	v	PROPN
ejpam-3454	152	35	(	(	PUNCT
ejpam-3454	152	36	t	t	NOUN
ejpam-3454	152	37	)	)	PUNCT
ejpam-3454	152	38	≤	≤	PROPN
ejpam-3454	152	39	c2	c2	PROPN
ejpam-3454	152	40	,	,	PUNCT
ejpam-3454	152	41	where	where	SCONJ
ejpam-3454	152	42	c1	c1	PROPN
ejpam-3454	152	43	=	=	PUNCT
ejpam-3454	152	44	(	(	PUNCT
ejpam-3454	152	45	r	r	NOUN
ejpam-3454	152	46	−	−	PROPN
ejpam-3454	152	47	d)tmax	d)tmax	NOUN
ejpam-3454	152	48	r	r	NOUN
ejpam-3454	152	49	,	,	PUNCT
ejpam-3454	152	50	c2	c2	PROPN
ejpam-3454	152	51	=	=	SYM
ejpam-3454	152	52	max	max	PROPN
ejpam-3454	152	53	(	(	PUNCT
ejpam-3454	152	54	(	(	PUNCT
ejpam-3454	152	55	1−	1−	NUM
ejpam-3454	152	56	ε)p	ε)p	X
ejpam-3454	152	57	c	c	PROPN
ejpam-3454	152	58	c1	c1	PROPN
ejpam-3454	152	59	,	,	PUNCT
ejpam-3454	152	60	v0	v0	PROPN
ejpam-3454	152	61	)	)	PUNCT
ejpam-3454	152	62	when	when	SCONJ
ejpam-3454	152	63	t	t	PROPN
ejpam-3454	152	64	tends	tend	VERB
ejpam-3454	152	65	to	to	ADP
ejpam-3454	152	66	+	+	NOUN
ejpam-3454	152	67	∞.	∞.	PROPN
ejpam-3454	152	68	a.	a.	NOUN
ejpam-3454	152	69	nangue	nangue	NOUN
ejpam-3454	152	70	,	,	PUNCT
ejpam-3454	152	71	t.	t.	PROPN
ejpam-3454	152	72	donfack	donfack	PROPN
ejpam-3454	152	73	,	,	PUNCT
ejpam-3454	152	74	d.	d.	PROPN
ejpam-3454	152	75	a.	a.	PROPN
ejpam-3454	152	76	ndode	ndode	PROPN
ejpam-3454	152	77	yafago	yafago	PROPN
ejpam-3454	152	78	/	/	SYM
ejpam-3454	152	79	eur	eur	PROPN
ejpam-3454	152	80	.	.	PUNCT
ejpam-3454	153	1	j.	j.	PROPN
ejpam-3454	153	2	pure	pure	PROPN
ejpam-3454	153	3	appl	appl	PROPN
ejpam-3454	153	4	.	.	PROPN
ejpam-3454	153	5	math	math	PROPN
ejpam-3454	153	6	,	,	PUNCT
ejpam-3454	153	7	12	12	NUM
ejpam-3454	153	8	(	(	PUNCT
ejpam-3454	153	9	3	3	NUM
ejpam-3454	153	10	)	)	PUNCT
ejpam-3454	153	11	(	(	PUNCT
ejpam-3454	153	12	2019	2019	NUM
ejpam-3454	153	13	)	)	PUNCT
ejpam-3454	153	14	,	,	PUNCT
ejpam-3454	153	15	944	944	NUM
ejpam-3454	153	16	-	-	SYM
ejpam-3454	153	17	959	959	NUM
ejpam-3454	153	18	950	950	NUM
ejpam-3454	153	19	proof	proof	NOUN
ejpam-3454	153	20	.	.	PUNCT
ejpam-3454	154	1	adding	add	VERB
ejpam-3454	154	2	equations	equation	NOUN
ejpam-3454	154	3	(	(	PUNCT
ejpam-3454	154	4	1a	1a	X
ejpam-3454	154	5	)	)	PUNCT
ejpam-3454	154	6	and	and	CCONJ
ejpam-3454	154	7	(	(	PUNCT
ejpam-3454	154	8	1b	1b	NUM
ejpam-3454	154	9	)	)	PUNCT
ejpam-3454	154	10	implies	imply	VERB
ejpam-3454	154	11	,	,	PUNCT
ejpam-3454	154	12	since	since	SCONJ
ejpam-3454	154	13	d	d	PROPN
ejpam-3454	154	14	≤	≤	X
ejpam-3454	154	15	δ	δ	NOUN
ejpam-3454	154	16	:	:	PUNCT
ejpam-3454	155	1	d	d	X
ejpam-3454	155	2	dt	dt	X
ejpam-3454	155	3	(	(	PUNCT
ejpam-3454	155	4	t	t	PROPN
ejpam-3454	155	5	+	+	CCONJ
ejpam-3454	155	6	i	i	NOUN
ejpam-3454	155	7	)	)	PUNCT
ejpam-3454	156	1	=	=	SYM
ejpam-3454	156	2	r	r	NOUN
ejpam-3454	156	3	(	(	PUNCT
ejpam-3454	156	4	1−	1−	NUM
ejpam-3454	156	5	t	t	NOUN
ejpam-3454	156	6	+	+	CCONJ
ejpam-3454	156	7	i	i	PRON
ejpam-3454	156	8	tmax	tmax	ADV
ejpam-3454	156	9	)	)	PUNCT
ejpam-3454	156	10	t	t	NOUN
ejpam-3454	156	11	−	−	PROPN
ejpam-3454	156	12	dt	dt	NOUN
ejpam-3454	156	13	−	−	NOUN
ejpam-3454	156	14	δi	δi	VERB
ejpam-3454	156	15	≤	≤	ADJ
ejpam-3454	156	16	r	r	NOUN
ejpam-3454	156	17	(	(	PUNCT
ejpam-3454	156	18	1−	1−	NUM
ejpam-3454	156	19	t	t	NOUN
ejpam-3454	156	20	+	+	CCONJ
ejpam-3454	156	21	i	i	PRON
ejpam-3454	156	22	tmax	tmax	ADV
ejpam-3454	156	23	)	)	PUNCT
ejpam-3454	156	24	t	t	PROPN
ejpam-3454	156	25	−	−	PROPN
ejpam-3454	156	26	d(t	d(t	PROPN
ejpam-3454	156	27	+	+	PROPN
ejpam-3454	156	28	i	i	PROPN
ejpam-3454	156	29	)	)	PUNCT
ejpam-3454	156	30	≤	≤	NOUN
ejpam-3454	157	1	r	r	NOUN
ejpam-3454	157	2	(	(	PUNCT
ejpam-3454	157	3	1−	1−	NUM
ejpam-3454	157	4	t	t	NOUN
ejpam-3454	157	5	+	+	CCONJ
ejpam-3454	157	6	i	i	PRON
ejpam-3454	157	7	tmax	tmax	ADV
ejpam-3454	157	8	)	)	PUNCT
ejpam-3454	157	9	t	t	NOUN
ejpam-3454	158	1	+	+	CCONJ
ejpam-3454	158	2	r	r	NOUN
ejpam-3454	158	3	(	(	PUNCT
ejpam-3454	158	4	1−	1−	NUM
ejpam-3454	158	5	t	t	NOUN
ejpam-3454	159	1	+	+	CCONJ
ejpam-3454	159	2	i	i	PRON
ejpam-3454	159	3	tmax	tmax	ADV
ejpam-3454	159	4	)	)	PUNCT
ejpam-3454	160	1	i	i	PRON
ejpam-3454	160	2	−	−	PROPN
ejpam-3454	160	3	d(t	d(t	PROPN
ejpam-3454	160	4	+	+	PROPN
ejpam-3454	160	5	i	i	PROPN
ejpam-3454	160	6	)	)	PUNCT
ejpam-3454	161	1	d	d	NOUN
ejpam-3454	161	2	dt	dt	X
ejpam-3454	161	3	(	(	PUNCT
ejpam-3454	161	4	t	t	PROPN
ejpam-3454	161	5	+	+	CCONJ
ejpam-3454	161	6	i	i	NOUN
ejpam-3454	161	7	)	)	PUNCT
ejpam-3454	161	8	≤	≤	NOUN
ejpam-3454	162	1	r	r	NOUN
ejpam-3454	162	2	(	(	PUNCT
ejpam-3454	162	3	1−	1−	NUM
ejpam-3454	162	4	t	t	NOUN
ejpam-3454	162	5	+	+	CCONJ
ejpam-3454	162	6	i	i	PRON
ejpam-3454	162	7	tmax	tmax	ADV
ejpam-3454	162	8	)	)	PUNCT
ejpam-3454	162	9	(	(	PUNCT
ejpam-3454	162	10	t	t	PROPN
ejpam-3454	162	11	+	+	CCONJ
ejpam-3454	162	12	i)−	i)−	PROPN
ejpam-3454	162	13	d(t	d(t	PROPN
ejpam-3454	162	14	+	+	CCONJ
ejpam-3454	162	15	i	i	PROPN
ejpam-3454	162	16	)	)	PUNCT
ejpam-3454	162	17	.	.	PUNCT
ejpam-3454	163	1	(	(	PUNCT
ejpam-3454	163	2	7	7	X
ejpam-3454	163	3	)	)	PUNCT
ejpam-3454	163	4	we	we	PRON
ejpam-3454	163	5	know	know	VERB
ejpam-3454	163	6	that	that	SCONJ
ejpam-3454	163	7	t	t	PROPN
ejpam-3454	163	8	(	(	PUNCT
ejpam-3454	163	9	t	t	PROPN
ejpam-3454	163	10	)	)	PUNCT
ejpam-3454	163	11	+	+	CCONJ
ejpam-3454	163	12	i(t	i(t	NOUN
ejpam-3454	163	13	)	)	PUNCT
ejpam-3454	163	14	≤m(t	≤m(t	NOUN
ejpam-3454	163	15	)	)	PUNCT
ejpam-3454	163	16	,	,	PUNCT
ejpam-3454	163	17	where	where	SCONJ
ejpam-3454	163	18	m	m	NOUN
ejpam-3454	163	19	satisfies	satisfy	VERB
ejpam-3454	163	20	:	:	PUNCT
ejpam-3454	164	1	dm	dm	INTJ
ejpam-3454	164	2	dt	dt	NOUN
ejpam-3454	164	3	=	=	PUNCT
ejpam-3454	164	4	(	(	PUNCT
ejpam-3454	164	5	r	r	NOUN
ejpam-3454	164	6	−	−	PROPN
ejpam-3454	164	7	d)m	d)m	NOUN
ejpam-3454	164	8	−	−	PROPN
ejpam-3454	164	9	r	r	NOUN
ejpam-3454	164	10	tmax	tmax	ADP
ejpam-3454	164	11	m2	m2	PROPN
ejpam-3454	164	12	(	(	PUNCT
ejpam-3454	164	13	8)	8)	NUM
ejpam-3454	164	14	m(t0	m(t0	NOUN
ejpam-3454	164	15	)	)	PUNCT
ejpam-3454	165	1	=	=	SYM
ejpam-3454	165	2	t	t	PROPN
ejpam-3454	165	3	(	(	PUNCT
ejpam-3454	165	4	t0	t0	PROPN
ejpam-3454	165	5	)	)	PUNCT
ejpam-3454	165	6	+	+	X
ejpam-3454	165	7	i(t0	i(t0	NOUN
ejpam-3454	165	8	)	)	PUNCT
ejpam-3454	165	9	=	=	SYM
ejpam-3454	165	10	t0	t0	PROPN
ejpam-3454	165	11	+	+	CCONJ
ejpam-3454	165	12	i0	i0	PROPN
ejpam-3454	165	13	.	.	PUNCT
ejpam-3454	166	1	(	(	PUNCT
ejpam-3454	166	2	9	9	NUM
ejpam-3454	166	3	)	)	PUNCT
ejpam-3454	166	4	(	(	PUNCT
ejpam-3454	166	5	8)	8)	NUM
ejpam-3454	166	6	is	be	AUX
ejpam-3454	166	7	a	a	DET
ejpam-3454	166	8	first	first	ADJ
ejpam-3454	166	9	order	order	NOUN
ejpam-3454	166	10	differential	differential	ADJ
ejpam-3454	166	11	equation	equation	NOUN
ejpam-3454	166	12	of	of	ADP
ejpam-3454	166	13	bernoulli	bernoulli	PROPN
ejpam-3454	166	14	type	type	NOUN
ejpam-3454	166	15	.	.	PUNCT
ejpam-3454	167	1	hence	hence	ADV
ejpam-3454	167	2	,	,	PUNCT
ejpam-3454	167	3	by	by	ADP
ejpam-3454	167	4	direct	direct	ADJ
ejpam-3454	167	5	calculation	calculation	NOUN
ejpam-3454	167	6	,	,	PUNCT
ejpam-3454	167	7	using	use	VERB
ejpam-3454	167	8	(	(	PUNCT
ejpam-3454	167	9	9	9	NUM
ejpam-3454	167	10	)	)	PUNCT
ejpam-3454	167	11	,	,	PUNCT
ejpam-3454	167	12	we	we	PRON
ejpam-3454	167	13	obtain	obtain	VERB
ejpam-3454	167	14	the	the	DET
ejpam-3454	167	15	following	follow	VERB
ejpam-3454	167	16	expression	expression	NOUN
ejpam-3454	167	17	of	of	ADP
ejpam-3454	167	18	m	m	PROPN
ejpam-3454	167	19	:	:	PUNCT
ejpam-3454	167	20	m(t	m(t	X
ejpam-3454	167	21	)	)	PUNCT
ejpam-3454	167	22	=	=	PRON
ejpam-3454	168	1	(	(	PUNCT
ejpam-3454	168	2	r	r	NOUN
ejpam-3454	168	3	−	−	PROPN
ejpam-3454	168	4	d)tmax	d)tmax	NOUN
ejpam-3454	168	5	r	r	NOUN
ejpam-3454	169	1	+	+	CCONJ
ejpam-3454	169	2	(	(	PUNCT
ejpam-3454	169	3	r	r	NOUN
ejpam-3454	169	4	−	−	PROPN
ejpam-3454	169	5	d)tmax	d)tmax	NOUN
ejpam-3454	169	6	(	(	PUNCT
ejpam-3454	169	7	z0	z0	NOUN
ejpam-3454	169	8	−	−	PROPN
ejpam-3454	169	9	r	r	NOUN
ejpam-3454	169	10	(	(	PUNCT
ejpam-3454	169	11	r−d)tmax	r−d)tmax	X
ejpam-3454	169	12	)	)	PUNCT
ejpam-3454	169	13	e−(r−d)(t−t0	e−(r−d)(t−t0	PROPN
ejpam-3454	169	14	)	)	PUNCT
ejpam-3454	169	15	which	which	PRON
ejpam-3454	169	16	shows	show	VERB
ejpam-3454	169	17	that	that	SCONJ
ejpam-3454	169	18	m(t	m(t	NOUN
ejpam-3454	169	19	)	)	PUNCT
ejpam-3454	169	20	−→	−→	NOUN
ejpam-3454	169	21	(	(	PUNCT
ejpam-3454	169	22	r−d)tmax	r−d)tmax	NOUN
ejpam-3454	169	23	r	r	NOUN
ejpam-3454	169	24	as	as	ADP
ejpam-3454	169	25	t	t	NOUN
ejpam-3454	169	26	−→	−→	NOUN
ejpam-3454	170	1	+	+	PROPN
ejpam-3454	170	2	∞	∞	PROPN
ejpam-3454	170	3	and	and	CCONJ
ejpam-3454	170	4	hence	hence	ADV
ejpam-3454	170	5	,	,	PUNCT
ejpam-3454	170	6	m	m	VERB
ejpam-3454	170	7	is	be	AUX
ejpam-3454	170	8	bounded	bound	VERB
ejpam-3454	170	9	.	.	PUNCT
ejpam-3454	171	1	since	since	SCONJ
ejpam-3454	171	2	0	0	NUM
ejpam-3454	171	3	≤	≤	PROPN
ejpam-3454	171	4	t	t	PROPN
ejpam-3454	171	5	(	(	PUNCT
ejpam-3454	171	6	t	t	PROPN
ejpam-3454	171	7	)	)	PUNCT
ejpam-3454	171	8	+	+	CCONJ
ejpam-3454	171	9	i(t	i(t	NOUN
ejpam-3454	171	10	)	)	PUNCT
ejpam-3454	171	11	≤m(t	≤m(t	NOUN
ejpam-3454	171	12	)	)	PUNCT
ejpam-3454	171	13	,	,	PUNCT
ejpam-3454	171	14	t	t	PROPN
ejpam-3454	171	15	+	+	CCONJ
ejpam-3454	171	16	i	i	PRON
ejpam-3454	171	17	is	be	AUX
ejpam-3454	171	18	bounded	bound	VERB
ejpam-3454	171	19	and	and	CCONJ
ejpam-3454	171	20	therefore	therefore	ADV
ejpam-3454	171	21	t	t	PROPN
ejpam-3454	171	22	(	(	PUNCT
ejpam-3454	171	23	t	t	PROPN
ejpam-3454	171	24	)	)	PUNCT
ejpam-3454	171	25	≤	≤	NUM
ejpam-3454	171	26	(	(	PUNCT
ejpam-3454	171	27	r−d)tmax	r−d)tmax	NOUN
ejpam-3454	171	28	r	r	NOUN
ejpam-3454	171	29	,	,	PUNCT
ejpam-3454	171	30	i(t	i(t	PROPN
ejpam-3454	171	31	)	)	PUNCT
ejpam-3454	171	32	≤	≤	NUM
ejpam-3454	171	33	(	(	PUNCT
ejpam-3454	171	34	r−d)tmax	r−d)tmax	X
ejpam-3454	172	1	r	r	NOUN
ejpam-3454	172	2	.	.	PUNCT
ejpam-3454	173	1	moreover	moreover	ADV
ejpam-3454	173	2	,	,	PUNCT
ejpam-3454	173	3	as	as	ADV
ejpam-3454	173	4	far	far	ADV
ejpam-3454	173	5	as	as	SCONJ
ejpam-3454	173	6	v	v	NOUN
ejpam-3454	173	7	is	be	AUX
ejpam-3454	173	8	concerned	concern	VERB
ejpam-3454	173	9	,	,	PUNCT
ejpam-3454	173	10	according	accord	VERB
ejpam-3454	173	11	to	to	ADP
ejpam-3454	173	12	1c	1c	NUM
ejpam-3454	173	13	,	,	PUNCT
ejpam-3454	173	14	we	we	PRON
ejpam-3454	173	15	have	have	VERB
ejpam-3454	173	16	:	:	PUNCT
ejpam-3454	173	17	dv	dv	PROPN
ejpam-3454	173	18	dt	dt	X
ejpam-3454	173	19	=	=	SYM
ejpam-3454	173	20	(	(	PUNCT
ejpam-3454	173	21	1−	1−	NUM
ejpam-3454	173	22	ε)pi	ε)pi	PROPN
ejpam-3454	173	23	−	−	PROPN
ejpam-3454	174	1	cv	cv	PROPN
ejpam-3454	174	2	−	−	PROPN
ejpam-3454	174	3	α(1−	α(1−	PROPN
ejpam-3454	174	4	η)βv	η)βv	PROPN
ejpam-3454	174	5	t	t	PROPN
ejpam-3454	174	6	≤	≤	NUM
ejpam-3454	174	7	(	(	PUNCT
ejpam-3454	174	8	1−	1−	NUM
ejpam-3454	174	9	ε)pi	ε)pi	PROPN
ejpam-3454	174	10	−	−	PROPN
ejpam-3454	174	11	cv	cv	PROPN
ejpam-3454	174	12	≤	≤	PROPN
ejpam-3454	174	13	(	(	PUNCT
ejpam-3454	174	14	1−	1−	NUM
ejpam-3454	175	1	ε)pc1	ε)pc1	ADV
ejpam-3454	175	2	−	−	PROPN
ejpam-3454	175	3	cv	cv	PROPN
ejpam-3454	175	4	i.e.	i.e.	X
ejpam-3454	175	5	dv	dv	PROPN
ejpam-3454	175	6	dt	dt	X
ejpam-3454	175	7	≤	≤	PROPN
ejpam-3454	175	8	−cv	−cv	NOUN
ejpam-3454	175	9	+	+	CCONJ
ejpam-3454	175	10	(	(	PUNCT
ejpam-3454	175	11	1−	1−	NUM
ejpam-3454	175	12	ε)pc1	ε)pc1	ADV
ejpam-3454	175	13	(	(	PUNCT
ejpam-3454	175	14	10	10	NUM
ejpam-3454	175	15	)	)	PUNCT
ejpam-3454	175	16	we	we	PRON
ejpam-3454	175	17	know	know	VERB
ejpam-3454	175	18	,	,	PUNCT
ejpam-3454	175	19	by	by	ADP
ejpam-3454	175	20	differential	differential	NOUN
ejpam-3454	175	21	calculus	calculus	NOUN
ejpam-3454	175	22	,	,	PUNCT
ejpam-3454	175	23	that	that	DET
ejpam-3454	175	24	v	v	NOUN
ejpam-3454	175	25	(	(	PUNCT
ejpam-3454	175	26	t	t	PROPN
ejpam-3454	175	27	)	)	PUNCT
ejpam-3454	175	28	≤	≤	NOUN
ejpam-3454	176	1	n(t	n(t	PROPN
ejpam-3454	176	2	)	)	PUNCT
ejpam-3454	176	3	,	,	PUNCT
ejpam-3454	176	4	where	where	SCONJ
ejpam-3454	176	5	n	n	PRON
ejpam-3454	176	6	satisfies	satisfy	VERB
ejpam-3454	176	7	:	:	PUNCT
ejpam-3454	177	1	dn	dn	NOUN
ejpam-3454	177	2	dt	dt	NOUN
ejpam-3454	177	3	≤	≤	ADJ
ejpam-3454	177	4	−cv	−cv	NOUN
ejpam-3454	177	5	+	+	CCONJ
ejpam-3454	177	6	(	(	PUNCT
ejpam-3454	177	7	1−	1−	NUM
ejpam-3454	177	8	ε)pc1	ε)pc1	ADV
ejpam-3454	177	9	,	,	PUNCT
ejpam-3454	177	10	(	(	PUNCT
ejpam-3454	177	11	11	11	NUM
ejpam-3454	177	12	)	)	PUNCT
ejpam-3454	177	13	n(t0	n(t0	NOUN
ejpam-3454	177	14	)	)	PUNCT
ejpam-3454	177	15	=	=	SYM
ejpam-3454	177	16	v	v	X
ejpam-3454	177	17	(	(	PUNCT
ejpam-3454	177	18	t0	t0	NOUN
ejpam-3454	177	19	)	)	PUNCT
ejpam-3454	177	20	)	)	PUNCT
ejpam-3454	178	1	=	=	SYM
ejpam-3454	178	2	v0	v0	NOUN
ejpam-3454	178	3	.	.	PUNCT
ejpam-3454	179	1	(	(	PUNCT
ejpam-3454	179	2	12	12	NUM
ejpam-3454	179	3	)	)	PUNCT
ejpam-3454	179	4	a.	a.	NOUN
ejpam-3454	179	5	nangue	nangue	NOUN
ejpam-3454	179	6	,	,	PUNCT
ejpam-3454	179	7	t.	t.	PROPN
ejpam-3454	179	8	donfack	donfack	PROPN
ejpam-3454	179	9	,	,	PUNCT
ejpam-3454	179	10	d.	d.	PROPN
ejpam-3454	179	11	a.	a.	PROPN
ejpam-3454	179	12	ndode	ndode	PROPN
ejpam-3454	179	13	yafago	yafago	PROPN
ejpam-3454	179	14	/	/	SYM
ejpam-3454	179	15	eur	eur	PROPN
ejpam-3454	179	16	.	.	PUNCT
ejpam-3454	180	1	j.	j.	PROPN
ejpam-3454	180	2	pure	pure	PROPN
ejpam-3454	180	3	appl	appl	PROPN
ejpam-3454	180	4	.	.	PROPN
ejpam-3454	180	5	math	math	PROPN
ejpam-3454	180	6	,	,	PUNCT
ejpam-3454	180	7	12	12	NUM
ejpam-3454	180	8	(	(	PUNCT
ejpam-3454	180	9	3	3	NUM
ejpam-3454	180	10	)	)	PUNCT
ejpam-3454	180	11	(	(	PUNCT
ejpam-3454	180	12	2019	2019	NUM
ejpam-3454	180	13	)	)	PUNCT
ejpam-3454	180	14	,	,	PUNCT
ejpam-3454	180	15	944	944	NUM
ejpam-3454	180	16	-	-	SYM
ejpam-3454	180	17	959	959	NUM
ejpam-3454	180	18	951	951	NUM
ejpam-3454	180	19	(	(	PUNCT
ejpam-3454	180	20	11	11	NUM
ejpam-3454	180	21	)	)	PUNCT
ejpam-3454	180	22	is	be	AUX
ejpam-3454	180	23	a	a	DET
ejpam-3454	180	24	non	non	ADJ
ejpam-3454	180	25	homogeneous	homogeneous	ADJ
ejpam-3454	180	26	first	first	ADJ
ejpam-3454	180	27	order	order	NOUN
ejpam-3454	180	28	differential	differential	ADJ
ejpam-3454	180	29	equation	equation	NOUN
ejpam-3454	180	30	.	.	PUNCT
ejpam-3454	181	1	hence	hence	ADV
ejpam-3454	181	2	,	,	PUNCT
ejpam-3454	181	3	by	by	ADP
ejpam-3454	181	4	direct	direct	ADJ
ejpam-3454	181	5	calculation	calculation	NOUN
ejpam-3454	181	6	,	,	PUNCT
ejpam-3454	181	7	using	use	VERB
ejpam-3454	181	8	(	(	PUNCT
ejpam-3454	181	9	12	12	NUM
ejpam-3454	181	10	)	)	PUNCT
ejpam-3454	181	11	,	,	PUNCT
ejpam-3454	181	12	we	we	PRON
ejpam-3454	181	13	obtain	obtain	VERB
ejpam-3454	181	14	the	the	DET
ejpam-3454	181	15	following	follow	VERB
ejpam-3454	181	16	expression	expression	NOUN
ejpam-3454	181	17	of	of	ADP
ejpam-3454	181	18	n	n	PROPN
ejpam-3454	181	19	:	:	PUNCT
ejpam-3454	181	20	n(t	n(t	PROPN
ejpam-3454	181	21	)	)	PUNCT
ejpam-3454	181	22	=	=	PUNCT
ejpam-3454	182	1	(	(	PUNCT
ejpam-3454	182	2	1−	1−	NUM
ejpam-3454	182	3	ε)pc1	ε)pc1	ADV
ejpam-3454	182	4	c	c	AUX
ejpam-3454	182	5	+	+	CCONJ
ejpam-3454	182	6	e−c(t−t0	e−c(t−t0	PROPN
ejpam-3454	182	7	)	)	PUNCT
ejpam-3454	182	8	(	(	PUNCT
ejpam-3454	182	9	v0	v0	NOUN
ejpam-3454	182	10	−	−	PROPN
ejpam-3454	183	1	(	(	PUNCT
ejpam-3454	183	2	1−	1−	NUM
ejpam-3454	183	3	ε)pc1	ε)pc1	ADV
ejpam-3454	183	4	c	c	NOUN
ejpam-3454	183	5	)	)	PUNCT
ejpam-3454	183	6	;	;	PUNCT
ejpam-3454	183	7	=	=	SYM
ejpam-3454	183	8	max	max	X
ejpam-3454	183	9	(	(	PUNCT
ejpam-3454	183	10	(	(	PUNCT
ejpam-3454	183	11	1−	1−	NUM
ejpam-3454	183	12	ε)p	ε)p	X
ejpam-3454	183	13	c	c	PROPN
ejpam-3454	183	14	c1	c1	PROPN
ejpam-3454	183	15	,	,	PUNCT
ejpam-3454	183	16	v0	v0	PROPN
ejpam-3454	183	17	)	)	PUNCT
ejpam-3454	183	18	(	(	PUNCT
ejpam-3454	183	19	1	1	NUM
ejpam-3454	183	20	+	+	NUM
ejpam-3454	183	21	e−c(t−t0	e−c(t−t0	PROPN
ejpam-3454	183	22	)	)	PUNCT
ejpam-3454	183	23	−	−	PROPN
ejpam-3454	183	24	e−c(t−t0	e−c(t−t0	PROPN
ejpam-3454	183	25	)	)	PUNCT
ejpam-3454	183	26	)	)	PUNCT
ejpam-3454	183	27	,	,	PUNCT
ejpam-3454	183	28	which	which	PRON
ejpam-3454	183	29	shows	show	VERB
ejpam-3454	183	30	that	that	SCONJ
ejpam-3454	183	31	:	:	PUNCT
ejpam-3454	183	32	n(t	n(t	X
ejpam-3454	183	33	)	)	PUNCT
ejpam-3454	183	34	≤	≤	NUM
ejpam-3454	183	35	max	max	NOUN
ejpam-3454	183	36	(	(	PUNCT
ejpam-3454	183	37	(	(	PUNCT
ejpam-3454	183	38	1−	1−	NUM
ejpam-3454	183	39	ε)p	ε)p	X
ejpam-3454	183	40	c	c	PROPN
ejpam-3454	183	41	c1	c1	PROPN
ejpam-3454	183	42	,	,	PUNCT
ejpam-3454	183	43	v0	v0	PROPN
ejpam-3454	183	44	)	)	PUNCT
ejpam-3454	183	45	and	and	CCONJ
ejpam-3454	183	46	therefore	therefore	ADV
ejpam-3454	183	47	,	,	PUNCT
ejpam-3454	183	48	n	n	PRON
ejpam-3454	183	49	is	be	AUX
ejpam-3454	183	50	bounded	bound	VERB
ejpam-3454	183	51	as	as	SCONJ
ejpam-3454	183	52	t	t	PROPN
ejpam-3454	183	53	tends	tend	VERB
ejpam-3454	183	54	to	to	ADP
ejpam-3454	183	55	+	+	PROPN
ejpam-3454	183	56	∞.	∞.	PROPN
ejpam-3454	183	57	since	since	SCONJ
ejpam-3454	183	58	0	0	NUM
ejpam-3454	183	59	≤	≤	NUM
ejpam-3454	183	60	v	v	NOUN
ejpam-3454	183	61	(	(	PUNCT
ejpam-3454	183	62	t	t	PROPN
ejpam-3454	183	63	)	)	PUNCT
ejpam-3454	183	64	≤	≤	NOUN
ejpam-3454	183	65	n(t	n(t	PROPN
ejpam-3454	183	66	)	)	PUNCT
ejpam-3454	183	67	,	,	PUNCT
ejpam-3454	183	68	v	v	NOUN
ejpam-3454	183	69	is	be	AUX
ejpam-3454	183	70	bounded	bound	VERB
ejpam-3454	183	71	and	and	CCONJ
ejpam-3454	183	72	hence	hence	ADV
ejpam-3454	183	73	v	v	NOUN
ejpam-3454	183	74	(	(	PUNCT
ejpam-3454	183	75	t	t	NOUN
ejpam-3454	183	76	)	)	PUNCT
ejpam-3454	183	77	≤	≤	NUM
ejpam-3454	183	78	max	max	NOUN
ejpam-3454	183	79	(	(	PUNCT
ejpam-3454	183	80	(	(	PUNCT
ejpam-3454	183	81	1−ε)p	1−ε)p	PROPN
ejpam-3454	183	82	c	c	PROPN
ejpam-3454	183	83	c1	c1	PROPN
ejpam-3454	183	84	,	,	PUNCT
ejpam-3454	183	85	v0	v0	PROPN
ejpam-3454	183	86	)	)	PUNCT
ejpam-3454	183	87	.	.	PUNCT
ejpam-3454	184	1	at	at	ADP
ejpam-3454	184	2	the	the	DET
ejpam-3454	184	3	end	end	NOUN
ejpam-3454	184	4	we	we	PRON
ejpam-3454	184	5	achieve	achieve	VERB
ejpam-3454	184	6	the	the	DET
ejpam-3454	184	7	proof	proof	NOUN
ejpam-3454	184	8	of	of	ADP
ejpam-3454	184	9	theorem	theorem	ADJ
ejpam-3454	184	10	3	3	NUM
ejpam-3454	184	11	.	.	PUNCT
ejpam-3454	185	1	as	as	ADP
ejpam-3454	185	2	consequences	consequence	NOUN
ejpam-3454	185	3	of	of	ADP
ejpam-3454	185	4	theorem	theorem	NOUN
ejpam-3454	185	5	3	3	NUM
ejpam-3454	185	6	we	we	PRON
ejpam-3454	185	7	have	have	VERB
ejpam-3454	185	8	the	the	DET
ejpam-3454	185	9	followings	following	NOUN
ejpam-3454	185	10	:	:	PUNCT
ejpam-3454	185	11	remark	remark	VERB
ejpam-3454	185	12	4	4	NUM
ejpam-3454	185	13	.	.	PUNCT
ejpam-3454	186	1	let	let	VERB
ejpam-3454	186	2	s	s	PRON
ejpam-3454	186	3	be	be	AUX
ejpam-3454	186	4	a	a	DET
ejpam-3454	186	5	solution	solution	NOUN
ejpam-3454	186	6	of	of	ADP
ejpam-3454	186	7	system	system	NOUN
ejpam-3454	186	8	(	(	PUNCT
ejpam-3454	186	9	1	1	NUM
ejpam-3454	186	10	)	)	PUNCT
ejpam-3454	186	11	.	.	PUNCT
ejpam-3454	187	1	if	if	SCONJ
ejpam-3454	187	2	s0	s0	PROPN
ejpam-3454	187	3	∈	∈	PROPN
ejpam-3454	187	4	r	r	NOUN
ejpam-3454	187	5	×	×	PROPN
ejpam-3454	187	6	r3	r3	PROPN
ejpam-3454	187	7	+	+	CCONJ
ejpam-3454	187	8	then	then	ADV
ejpam-3454	187	9	,	,	PUNCT
ejpam-3454	187	10	the	the	DET
ejpam-3454	187	11	limit	limit	NOUN
ejpam-3454	187	12	of	of	ADP
ejpam-3454	187	13	s(t	s(t	PROPN
ejpam-3454	187	14	)	)	PUNCT
ejpam-3454	187	15	exits	exit	VERB
ejpam-3454	187	16	when	when	SCONJ
ejpam-3454	187	17	t	t	NOUN
ejpam-3454	187	18	−→	−→	NOUN
ejpam-3454	187	19	+	+	NOUN
ejpam-3454	187	20	∞	∞	NUM
ejpam-3454	187	21	.	.	PUNCT
ejpam-3454	188	1	in	in	ADP
ejpam-3454	188	2	other	other	ADJ
ejpam-3454	188	3	words	word	NOUN
ejpam-3454	188	4	the	the	DET
ejpam-3454	188	5	solution	solution	NOUN
ejpam-3454	188	6	is	be	AUX
ejpam-3454	188	7	globally	globally	ADV
ejpam-3454	188	8	bounded	bound	VERB
ejpam-3454	188	9	in	in	ADP
ejpam-3454	188	10	the	the	DET
ejpam-3454	188	11	future	future	NOUN
ejpam-3454	188	12	.	.	PUNCT
ejpam-3454	189	1	in	in	ADP
ejpam-3454	189	2	particular	particular	ADJ
ejpam-3454	189	3	,	,	PUNCT
ejpam-3454	189	4	s	s	VERB
ejpam-3454	189	5	is	be	AUX
ejpam-3454	189	6	periodic	periodic	ADJ
ejpam-3454	189	7	if	if	SCONJ
ejpam-3454	189	8	and	and	CCONJ
ejpam-3454	189	9	only	only	ADV
ejpam-3454	189	10	if	if	SCONJ
ejpam-3454	189	11	s	s	NOUN
ejpam-3454	189	12	is	be	AUX
ejpam-3454	189	13	stationary	stationary	ADJ
ejpam-3454	189	14	under	under	ADP
ejpam-3454	189	15	the	the	DET
ejpam-3454	189	16	condition	condition	NOUN
ejpam-3454	189	17	that	that	PRON
ejpam-3454	189	18	s(t	s(t	PROPN
ejpam-3454	189	19	)	)	PUNCT
ejpam-3454	189	20	admits	admit	VERB
ejpam-3454	189	21	a	a	DET
ejpam-3454	189	22	finite	finite	ADJ
ejpam-3454	189	23	limit	limit	NOUN
ejpam-3454	189	24	when	when	SCONJ
ejpam-3454	189	25	t	t	PROPN
ejpam-3454	189	26	tends	tend	VERB
ejpam-3454	189	27	to	to	PART
ejpam-3454	189	28	infinity	infinity	VERB
ejpam-3454	189	29	.	.	PUNCT
ejpam-3454	190	1	theorem	theorem	ADJ
ejpam-3454	190	2	4	4	NUM
ejpam-3454	190	3	.	.	PUNCT
ejpam-3454	191	1	let	let	VERB
ejpam-3454	191	2	(	(	PUNCT
ejpam-3454	191	3	t0	t0	NOUN
ejpam-3454	191	4	,	,	PUNCT
ejpam-3454	191	5	s0	s0	PROPN
ejpam-3454	191	6	=	=	SYM
ejpam-3454	191	7	(	(	PUNCT
ejpam-3454	191	8	t0	t0	PROPN
ejpam-3454	191	9	,	,	PUNCT
ejpam-3454	191	10	i0	i0	PROPN
ejpam-3454	191	11	,	,	PUNCT
ejpam-3454	191	12	v0	v0	PROPN
ejpam-3454	191	13	)	)	PUNCT
ejpam-3454	191	14	)	)	PUNCT
ejpam-3454	192	1	∈	∈	PROPN
ejpam-3454	192	2	r×r3	r×r3	NOUN
ejpam-3454	192	3	+	+	CCONJ
ejpam-3454	193	1	and	and	CCONJ
ejpam-3454	193	2	(	(	PUNCT
ejpam-3454	193	3	[	[	X
ejpam-3454	193	4	t0	t0	NOUN
ejpam-3454	193	5	,	,	PUNCT
ejpam-3454	193	6	t	t	X
ejpam-3454	194	1	[	[	X
ejpam-3454	194	2	,	,	PUNCT
ejpam-3454	194	3	s	s	X
ejpam-3454	194	4	=	=	SYM
ejpam-3454	194	5	(	(	PUNCT
ejpam-3454	194	6	t	t	PROPN
ejpam-3454	194	7	,	,	PUNCT
ejpam-3454	194	8	i	i	PRON
ejpam-3454	194	9	,	,	PUNCT
ejpam-3454	194	10	v	v	NOUN
ejpam-3454	194	11	)	)	PUNCT
ejpam-3454	194	12	)	)	PUNCT
ejpam-3454	194	13	be	be	AUX
ejpam-3454	194	14	a	a	DET
ejpam-3454	194	15	maximal	maximal	ADJ
ejpam-3454	194	16	solution	solution	NOUN
ejpam-3454	194	17	of	of	ADP
ejpam-3454	194	18	the	the	DET
ejpam-3454	194	19	cauchy	cauchy	ADJ
ejpam-3454	194	20	problem	problem	NOUN
ejpam-3454	194	21	(	(	PUNCT
ejpam-3454	194	22	1	1	NUM
ejpam-3454	194	23	)	)	PUNCT
ejpam-3454	194	24	,	,	PUNCT
ejpam-3454	194	25	(	(	PUNCT
ejpam-3454	194	26	2	2	X
ejpam-3454	194	27	)	)	PUNCT
ejpam-3454	194	28	(	(	PUNCT
ejpam-3454	194	29	t	t	PROPN
ejpam-3454	194	30	∈]t0,+∞	∈]t0,+∞	PROPN
ejpam-3454	194	31	[	[	X
ejpam-3454	194	32	)	)	PUNCT
ejpam-3454	194	33	.	.	PUNCT
ejpam-3454	195	1	if	if	SCONJ
ejpam-3454	195	2	t	t	PROPN
ejpam-3454	195	3	(	(	PUNCT
ejpam-3454	195	4	t0	t0	PROPN
ejpam-3454	195	5	)	)	PUNCT
ejpam-3454	195	6	+	+	CCONJ
ejpam-3454	195	7	i(t0	i(t0	ADJ
ejpam-3454	195	8	)	)	PUNCT
ejpam-3454	195	9	≤	≤	NOUN
ejpam-3454	195	10	c1	c1	NOUN
ejpam-3454	195	11	and	and	CCONJ
ejpam-3454	195	12	v	v	PROPN
ejpam-3454	195	13	(	(	PUNCT
ejpam-3454	195	14	t0	t0	NOUN
ejpam-3454	195	15	)	)	PUNCT
ejpam-3454	195	16	≤	≤	NOUN
ejpam-3454	195	17	c2	c2	PROPN
ejpam-3454	195	18	then	then	ADV
ejpam-3454	195	19	the	the	DET
ejpam-3454	195	20	set	set	NOUN
ejpam-3454	195	21	:	:	PUNCT
ejpam-3454	195	22	ω	ω	X
ejpam-3454	195	23	=	=	SYM
ejpam-3454	195	24	{	{	PUNCT
ejpam-3454	195	25	(	(	PUNCT
ejpam-3454	195	26	t	t	PROPN
ejpam-3454	195	27	(	(	PUNCT
ejpam-3454	195	28	t	t	PROPN
ejpam-3454	195	29	)	)	PUNCT
ejpam-3454	195	30	,	,	PUNCT
ejpam-3454	195	31	i(t	i(t	PROPN
ejpam-3454	195	32	)	)	PUNCT
ejpam-3454	195	33	,	,	PUNCT
ejpam-3454	195	34	v	v	X
ejpam-3454	195	35	(	(	PUNCT
ejpam-3454	195	36	t	t	NOUN
ejpam-3454	195	37	)	)	PUNCT
ejpam-3454	195	38	)	)	PUNCT
ejpam-3454	196	1	∈	∈	PROPN
ejpam-3454	196	2	r3	r3	PROPN
ejpam-3454	196	3	+	+	CCONJ
ejpam-3454	196	4	:	:	PUNCT
ejpam-3454	196	5	t	t	PROPN
ejpam-3454	196	6	(	(	PUNCT
ejpam-3454	196	7	t	t	PROPN
ejpam-3454	196	8	)	)	PUNCT
ejpam-3454	196	9	+	+	CCONJ
ejpam-3454	196	10	i(t	i(t	PROPN
ejpam-3454	196	11	)	)	PUNCT
ejpam-3454	196	12	≤	≤	NOUN
ejpam-3454	196	13	c1	c1	PROPN
ejpam-3454	196	14	,	,	PUNCT
ejpam-3454	196	15	v	v	PROPN
ejpam-3454	196	16	(	(	PUNCT
ejpam-3454	196	17	t	t	NOUN
ejpam-3454	196	18	)	)	PUNCT
ejpam-3454	196	19	≤	≤	NOUN
ejpam-3454	196	20	c2	c2	PROPN
ejpam-3454	196	21	}	}	PUNCT
ejpam-3454	196	22	,	,	PUNCT
ejpam-3454	196	23	where	where	SCONJ
ejpam-3454	196	24	c1	c1	PROPN
ejpam-3454	196	25	=	=	PUNCT
ejpam-3454	196	26	(	(	PUNCT
ejpam-3454	196	27	r	r	NOUN
ejpam-3454	196	28	−	−	PROPN
ejpam-3454	196	29	d)tmax	d)tmax	NOUN
ejpam-3454	196	30	r	r	NOUN
ejpam-3454	196	31	,	,	PUNCT
ejpam-3454	196	32	c2	c2	PROPN
ejpam-3454	196	33	=	=	SYM
ejpam-3454	196	34	max	max	PROPN
ejpam-3454	196	35	(	(	PUNCT
ejpam-3454	196	36	(	(	PUNCT
ejpam-3454	196	37	1−	1−	NUM
ejpam-3454	196	38	ε)p	ε)p	X
ejpam-3454	196	39	c	c	PROPN
ejpam-3454	196	40	c1	c1	PROPN
ejpam-3454	196	41	,	,	PUNCT
ejpam-3454	196	42	v0	v0	PROPN
ejpam-3454	196	43	)	)	PUNCT
ejpam-3454	196	44	,	,	PUNCT
ejpam-3454	196	45	is	be	AUX
ejpam-3454	196	46	a	a	DET
ejpam-3454	196	47	positively	positively	ADV
ejpam-3454	196	48	invariant	invariant	ADJ
ejpam-3454	196	49	set	set	VERB
ejpam-3454	196	50	by	by	ADP
ejpam-3454	196	51	system	system	NOUN
ejpam-3454	196	52	(	(	PUNCT
ejpam-3454	196	53	1	1	NUM
ejpam-3454	196	54	)	)	PUNCT
ejpam-3454	196	55	.	.	PUNCT
ejpam-3454	197	1	3	3	X
ejpam-3454	197	2	.	.	X
ejpam-3454	197	3	equilibria	equilibrium	NOUN
ejpam-3454	197	4	and	and	CCONJ
ejpam-3454	197	5	basic	basic	ADJ
ejpam-3454	197	6	reproduction	reproduction	NOUN
ejpam-3454	197	7	number	number	NOUN
ejpam-3454	197	8	r0	r0	NOUN
ejpam-3454	197	9	in	in	ADP
ejpam-3454	197	10	this	this	DET
ejpam-3454	197	11	section	section	NOUN
ejpam-3454	197	12	,	,	PUNCT
ejpam-3454	197	13	we	we	PRON
ejpam-3454	197	14	will	will	AUX
ejpam-3454	197	15	derive	derive	VERB
ejpam-3454	197	16	the	the	DET
ejpam-3454	197	17	basic	basic	ADJ
ejpam-3454	197	18	reproduction	reproduction	NOUN
ejpam-3454	197	19	number	number	NOUN
ejpam-3454	197	20	,	,	PUNCT
ejpam-3454	197	21	and	and	CCONJ
ejpam-3454	197	22	compute	compute	VERB
ejpam-3454	197	23	the	the	DET
ejpam-3454	197	24	equilibria	equilibrium	NOUN
ejpam-3454	197	25	of	of	ADP
ejpam-3454	197	26	model	model	NOUN
ejpam-3454	197	27	(	(	PUNCT
ejpam-3454	197	28	1	1	NUM
ejpam-3454	197	29	)	)	PUNCT
ejpam-3454	197	30	.	.	PUNCT
ejpam-3454	198	1	when	when	SCONJ
ejpam-3454	198	2	there	there	PRON
ejpam-3454	198	3	is	be	VERB
ejpam-3454	198	4	no	no	DET
ejpam-3454	198	5	viral	viral	ADJ
ejpam-3454	198	6	infection	infection	NOUN
ejpam-3454	198	7	,	,	PUNCT
ejpam-3454	198	8	the	the	DET
ejpam-3454	198	9	uninfected	uninfected	ADJ
ejpam-3454	198	10	hepatocytes	hepatocyte	NOUN
ejpam-3454	198	11	dynamics	dynamic	NOUN
ejpam-3454	198	12	is	be	AUX
ejpam-3454	198	13	determined	determine	VERB
ejpam-3454	198	14	by	by	ADP
ejpam-3454	198	15	:	:	PUNCT
ejpam-3454	198	16	dt	dt	ADP
ejpam-3454	198	17	dt	dt	X
ejpam-3454	199	1	=	=	PUNCT
ejpam-3454	199	2	rt	rt	PROPN
ejpam-3454	199	3	(	(	PUNCT
ejpam-3454	199	4	1−	1−	NUM
ejpam-3454	199	5	t	t	NOUN
ejpam-3454	199	6	tmax	tmax	ADV
ejpam-3454	199	7	)	)	PUNCT
ejpam-3454	199	8	−	−	PROPN
ejpam-3454	200	1	dt	dt	X
ejpam-3454	200	2	.	.	PUNCT
ejpam-3454	201	1	(	(	PUNCT
ejpam-3454	201	2	13	13	NUM
ejpam-3454	201	3	)	)	PUNCT
ejpam-3454	201	4	a.	a.	NOUN
ejpam-3454	201	5	nangue	nangue	NOUN
ejpam-3454	201	6	,	,	PUNCT
ejpam-3454	201	7	t.	t.	PROPN
ejpam-3454	201	8	donfack	donfack	PROPN
ejpam-3454	201	9	,	,	PUNCT
ejpam-3454	201	10	d.	d.	PROPN
ejpam-3454	201	11	a.	a.	PROPN
ejpam-3454	201	12	ndode	ndode	PROPN
ejpam-3454	201	13	yafago	yafago	PROPN
ejpam-3454	201	14	/	/	SYM
ejpam-3454	201	15	eur	eur	PROPN
ejpam-3454	201	16	.	.	PUNCT
ejpam-3454	202	1	j.	j.	PROPN
ejpam-3454	202	2	pure	pure	PROPN
ejpam-3454	202	3	appl	appl	PROPN
ejpam-3454	202	4	.	.	PROPN
ejpam-3454	202	5	math	math	PROPN
ejpam-3454	202	6	,	,	PUNCT
ejpam-3454	202	7	12	12	NUM
ejpam-3454	202	8	(	(	PUNCT
ejpam-3454	202	9	3	3	NUM
ejpam-3454	202	10	)	)	PUNCT
ejpam-3454	202	11	(	(	PUNCT
ejpam-3454	202	12	2019	2019	NUM
ejpam-3454	202	13	)	)	PUNCT
ejpam-3454	202	14	,	,	PUNCT
ejpam-3454	202	15	944	944	NUM
ejpam-3454	202	16	-	-	SYM
ejpam-3454	202	17	959	959	NUM
ejpam-3454	202	18	952	952	NUM
ejpam-3454	202	19	thus	thus	ADV
ejpam-3454	202	20	,	,	PUNCT
ejpam-3454	202	21	in	in	ADP
ejpam-3454	202	22	the	the	DET
ejpam-3454	202	23	absence	absence	NOUN
ejpam-3454	202	24	of	of	ADP
ejpam-3454	202	25	viral	viral	ADJ
ejpam-3454	202	26	infection	infection	NOUN
ejpam-3454	202	27	,	,	PUNCT
ejpam-3454	202	28	the	the	DET
ejpam-3454	202	29	amount	amount	NOUN
ejpam-3454	202	30	of	of	ADP
ejpam-3454	202	31	susceptible	susceptible	ADJ
ejpam-3454	202	32	cells	cell	NOUN
ejpam-3454	202	33	will	will	AUX
ejpam-3454	202	34	attend	attend	VERB
ejpam-3454	202	35	to	to	ADP
ejpam-3454	202	36	a	a	DET
ejpam-3454	202	37	positive	positive	ADJ
ejpam-3454	202	38	constant	constant	ADJ
ejpam-3454	202	39	level	level	NOUN
ejpam-3454	202	40	t	t	PROPN
ejpam-3454	202	41	0	0	NUM
ejpam-3454	202	42	,	,	PUNCT
ejpam-3454	202	43	which	which	PRON
ejpam-3454	202	44	is	be	AUX
ejpam-3454	202	45	:	:	PUNCT
ejpam-3454	202	46	t	t	NOUN
ejpam-3454	202	47	0	0	NUM
ejpam-3454	203	1	=	=	SYM
ejpam-3454	203	2	r	r	NOUN
ejpam-3454	203	3	−	−	NOUN
ejpam-3454	204	1	d	d	NOUN
ejpam-3454	204	2	r	r	NOUN
ejpam-3454	204	3	tmax	tmax	VERB
ejpam-3454	204	4	≤	≤	ADJ
ejpam-3454	204	5	tmax	tmax	ADV
ejpam-3454	204	6	.	.	PUNCT
ejpam-3454	205	1	(	(	PUNCT
ejpam-3454	205	2	14	14	NUM
ejpam-3454	205	3	)	)	PUNCT
ejpam-3454	205	4	now	now	ADV
ejpam-3454	205	5	,	,	PUNCT
ejpam-3454	205	6	using	use	VERB
ejpam-3454	205	7	the	the	DET
ejpam-3454	205	8	idea	idea	NOUN
ejpam-3454	205	9	of	of	ADP
ejpam-3454	205	10	next	next	ADJ
ejpam-3454	205	11	generation	generation	NOUN
ejpam-3454	205	12	matrix	matrix	NOUN
ejpam-3454	205	13	for	for	ADP
ejpam-3454	205	14	a	a	DET
ejpam-3454	205	15	general	general	ADJ
ejpam-3454	205	16	compartmental	compartmental	ADJ
ejpam-3454	205	17	disease	disease	NOUN
ejpam-3454	205	18	transmission	transmission	NOUN
ejpam-3454	205	19	model	model	NOUN
ejpam-3454	205	20	in	in	ADP
ejpam-3454	205	21	[	[	X
ejpam-3454	205	22	4	4	NUM
ejpam-3454	205	23	]	]	PUNCT
ejpam-3454	205	24	,	,	PUNCT
ejpam-3454	205	25	we	we	PRON
ejpam-3454	205	26	can	can	AUX
ejpam-3454	205	27	obtain	obtain	VERB
ejpam-3454	205	28	the	the	DET
ejpam-3454	205	29	basic	basic	ADJ
ejpam-3454	205	30	reproduction	reproduction	NOUN
ejpam-3454	205	31	ratio	ratio	NOUN
ejpam-3454	205	32	of	of	ADP
ejpam-3454	205	33	(	(	PUNCT
ejpam-3454	205	34	1	1	NUM
ejpam-3454	205	35	)	)	PUNCT
ejpam-3454	205	36	.	.	PUNCT
ejpam-3454	206	1	proposition	proposition	NOUN
ejpam-3454	206	2	2	2	NUM
ejpam-3454	206	3	.	.	PUNCT
ejpam-3454	207	1	the	the	DET
ejpam-3454	207	2	basic	basic	ADJ
ejpam-3454	207	3	reproduction	reproduction	NOUN
ejpam-3454	207	4	ratio	ratio	NOUN
ejpam-3454	207	5	r0	r0	NOUN
ejpam-3454	207	6	of	of	ADP
ejpam-3454	207	7	model	model	NOUN
ejpam-3454	207	8	(	(	PUNCT
ejpam-3454	207	9	1	1	NUM
ejpam-3454	207	10	)	)	PUNCT
ejpam-3454	207	11	is	be	AUX
ejpam-3454	207	12	given	give	VERB
ejpam-3454	207	13	by	by	ADP
ejpam-3454	207	14	:	:	PUNCT
ejpam-3454	207	15	r0	r0	NOUN
ejpam-3454	207	16	=	=	SYM
ejpam-3454	207	17	(	(	PUNCT
ejpam-3454	207	18	1−	1−	NUM
ejpam-3454	207	19	ε)(1−	ε)(1−	PROPN
ejpam-3454	207	20	η)pβt	η)pβt	PROPN
ejpam-3454	207	21	0	0	NUM
ejpam-3454	207	22	δ(c+	δ(c+	NOUN
ejpam-3454	207	23	(	(	PUNCT
ejpam-3454	207	24	1−	1−	NUM
ejpam-3454	207	25	η)αβt	η)αβt	NOUN
ejpam-3454	207	26	0	0	NUM
ejpam-3454	207	27	)	)	PUNCT
ejpam-3454	207	28	.	.	PUNCT
ejpam-3454	208	1	proof	proof	NOUN
ejpam-3454	208	2	.	.	PUNCT
ejpam-3454	209	1	using	use	VERB
ejpam-3454	209	2	(	(	PUNCT
ejpam-3454	209	3	13	13	NUM
ejpam-3454	209	4	)	)	PUNCT
ejpam-3454	209	5	and	and	CCONJ
ejpam-3454	209	6	(	(	PUNCT
ejpam-3454	209	7	14	14	NUM
ejpam-3454	209	8	)	)	PUNCT
ejpam-3454	209	9	,	,	PUNCT
ejpam-3454	209	10	we	we	PRON
ejpam-3454	209	11	know	know	VERB
ejpam-3454	209	12	that	that	SCONJ
ejpam-3454	209	13	e0	e0	PROPN
ejpam-3454	209	14	=	=	PUNCT
ejpam-3454	209	15	(	(	PUNCT
ejpam-3454	209	16	t	t	PROPN
ejpam-3454	209	17	0	0	NUM
ejpam-3454	209	18	,	,	PUNCT
ejpam-3454	209	19	0	0	NUM
ejpam-3454	209	20	,	,	PUNCT
ejpam-3454	209	21	0	0	NUM
ejpam-3454	209	22	)	)	PUNCT
ejpam-3454	209	23	is	be	AUX
ejpam-3454	209	24	the	the	DET
ejpam-3454	209	25	virus	virus	NOUN
ejpam-3454	209	26	-	-	PUNCT
ejpam-3454	209	27	free	free	ADJ
ejpam-3454	209	28	equilibrium	equilibrium	NOUN
ejpam-3454	209	29	or	or	CCONJ
ejpam-3454	209	30	uninfected	uninfected	ADJ
ejpam-3454	209	31	equilibrium	equilibrium	NOUN
ejpam-3454	209	32	,	,	PUNCT
ejpam-3454	209	33	which	which	PRON
ejpam-3454	209	34	exists	exist	VERB
ejpam-3454	209	35	for	for	ADP
ejpam-3454	209	36	all	all	DET
ejpam-3454	209	37	positive	positive	ADJ
ejpam-3454	209	38	parameter	parameter	NOUN
ejpam-3454	209	39	values	value	NOUN
ejpam-3454	209	40	.	.	PUNCT
ejpam-3454	210	1	based	base	VERB
ejpam-3454	210	2	on	on	ADP
ejpam-3454	210	3	the	the	DET
ejpam-3454	210	4	notations	notation	NOUN
ejpam-3454	210	5	in	in	ADP
ejpam-3454	210	6	[	[	X
ejpam-3454	210	7	4	4	NUM
ejpam-3454	210	8	]	]	PUNCT
ejpam-3454	210	9	,	,	PUNCT
ejpam-3454	210	10	we	we	PRON
ejpam-3454	210	11	have	have	VERB
ejpam-3454	210	12	df	df	NOUN
ejpam-3454	210	13	=	=	SYM
ejpam-3454	210	14			PROPN
ejpam-3454	210	15	0	0	PUNCT
ejpam-3454	210	16	(	(	PUNCT
ejpam-3454	210	17	1−	1−	NUM
ejpam-3454	210	18	η)βt	η)βt	PROPN
ejpam-3454	210	19	0	0	NUM
ejpam-3454	210	20	(	(	PUNCT
ejpam-3454	210	21	1−	1−	NUM
ejpam-3454	210	22	ε)p	ε)p	X
ejpam-3454	210	23	0	0	NUM
ejpam-3454	210	24			NOUN
ejpam-3454	210	25	,	,	PUNCT
ejpam-3454	210	26	dv	dv	PROPN
ejpam-3454	210	27	=	=	PROPN
ejpam-3454	210	28			PROPN
ejpam-3454	210	29	δ	δ	NOUN
ejpam-3454	210	30	0	0	NUM
ejpam-3454	210	31	0	0	NUM
ejpam-3454	210	32	c+	c+	VERB
ejpam-3454	210	33	α(1−	α(1−	PUNCT
ejpam-3454	211	1	η)βt	η)βt	PROPN
ejpam-3454	211	2	0	0	NUM
ejpam-3454	211	3			NOUN
ejpam-3454	211	4	and	and	CCONJ
ejpam-3454	211	5	dv	dv	PROPN
ejpam-3454	211	6	−1	−1	NOUN
ejpam-3454	211	7	=	=	SYM
ejpam-3454	211	8			PROPN
ejpam-3454	211	9	1	1	NUM
ejpam-3454	211	10	δ	δ	NOUN
ejpam-3454	211	11	0	0	NUM
ejpam-3454	211	12	0	0	NUM
ejpam-3454	211	13	1	1	NUM
ejpam-3454	211	14	c+α(1−η)βt	c+α(1−η)βt	ADV
ejpam-3454	211	15	0	0	NUM
ejpam-3454	211	16			NOUN
ejpam-3454	211	17	.	.	PUNCT
ejpam-3454	212	1	and	and	CCONJ
ejpam-3454	212	2	the	the	DET
ejpam-3454	212	3	next	next	ADJ
ejpam-3454	212	4	generation	generation	NOUN
ejpam-3454	212	5	matrix	matrix	NOUN
ejpam-3454	212	6	is	be	AUX
ejpam-3454	212	7	:	:	PUNCT
ejpam-3454	212	8	df.dv	df.dv	PROPN
ejpam-3454	212	9	−1	−1	NOUN
ejpam-3454	212	10	=	=	SYM
ejpam-3454	212	11			PROPN
ejpam-3454	212	12	0	0	PUNCT
ejpam-3454	212	13	(	(	PUNCT
ejpam-3454	212	14	1−	1−	NUM
ejpam-3454	212	15	η)βt	η)βt	PROPN
ejpam-3454	212	16	0	0	NUM
ejpam-3454	212	17	(	(	PUNCT
ejpam-3454	212	18	1−	1−	NUM
ejpam-3454	212	19	ε)p	ε)p	X
ejpam-3454	212	20	0	0	NUM
ejpam-3454	212	21			SYM
ejpam-3454	212	22	1	1	NUM
ejpam-3454	212	23	δ	δ	NOUN
ejpam-3454	212	24	0	0	NUM
ejpam-3454	212	25	0	0	NUM
ejpam-3454	212	26	1	1	NUM
ejpam-3454	212	27	c+α(1−η)βt	c+α(1−η)βt	ADV
ejpam-3454	212	28	0	0	NUM
ejpam-3454	212	29			NOUN
ejpam-3454	212	30	=	=	VERB
ejpam-3454	212	31			X
ejpam-3454	212	32	0	0	PUNCT
ejpam-3454	213	1	(	(	PUNCT
ejpam-3454	213	2	1−η)βt	1−η)βt	NUM
ejpam-3454	213	3	0	0	SYM
ejpam-3454	214	1	c+α(1−η)βt	c+α(1−η)βt	NUM
ejpam-3454	214	2	0	0	NUM
ejpam-3454	215	1	(	(	PUNCT
ejpam-3454	215	2	1−ε)p	1−ε)p	NUM
ejpam-3454	215	3	δ	δ	NOUN
ejpam-3454	215	4	0	0	NUM
ejpam-3454	215	5			NUM
ejpam-3454	215	6	.	.	PUNCT
ejpam-3454	216	1	according	accord	VERB
ejpam-3454	216	2	to	to	ADP
ejpam-3454	216	3	[	[	X
ejpam-3454	216	4	4	4	NUM
ejpam-3454	216	5	,	,	PUNCT
ejpam-3454	216	6	theorem	theorem	VERB
ejpam-3454	216	7	2	2	NUM
ejpam-3454	216	8	]	]	PUNCT
ejpam-3454	216	9	,	,	PUNCT
ejpam-3454	216	10	the	the	DET
ejpam-3454	216	11	basic	basic	ADJ
ejpam-3454	216	12	reproduction	reproduction	NOUN
ejpam-3454	216	13	number	number	NOUN
ejpam-3454	216	14	of	of	ADP
ejpam-3454	216	15	(	(	PUNCT
ejpam-3454	216	16	1	1	NUM
ejpam-3454	216	17	)	)	PUNCT
ejpam-3454	216	18	is	be	AUX
ejpam-3454	216	19	defined	define	VERB
ejpam-3454	216	20	by	by	ADP
ejpam-3454	216	21	r0	r0	NOUN
ejpam-3454	216	22	=	=	SYM
ejpam-3454	216	23	ρ(df.dv	ρ(df.dv	NUM
ejpam-3454	216	24	−1	−1	NOUN
ejpam-3454	216	25	)	)	PUNCT
ejpam-3454	216	26	=	=	PUNCT
ejpam-3454	217	1	(	(	PUNCT
ejpam-3454	217	2	1−	1−	NUM
ejpam-3454	217	3	θ)pβt	θ)pβt	ADV
ejpam-3454	217	4	0	0	NUM
ejpam-3454	217	5	δ(c+	δ(c+	NOUN
ejpam-3454	217	6	(	(	PUNCT
ejpam-3454	217	7	1−	1−	NUM
ejpam-3454	217	8	η)αβt	η)αβt	NOUN
ejpam-3454	217	9	0	0	NUM
ejpam-3454	217	10	)	)	PUNCT
ejpam-3454	217	11	,	,	PUNCT
ejpam-3454	217	12	where	where	SCONJ
ejpam-3454	217	13	ρ(a	ρ(a	NOUN
ejpam-3454	217	14	)	)	PUNCT
ejpam-3454	217	15	denotes	denote	VERB
ejpam-3454	217	16	the	the	DET
ejpam-3454	217	17	spectral	spectral	ADJ
ejpam-3454	217	18	radius	radius	NOUN
ejpam-3454	217	19	of	of	ADP
ejpam-3454	217	20	a	a	DET
ejpam-3454	217	21	matrix	matrix	NOUN
ejpam-3454	217	22	a	a	PRON
ejpam-3454	217	23	and	and	CCONJ
ejpam-3454	217	24	1−	1−	NUM
ejpam-3454	217	25	θ	θ	NOUN
ejpam-3454	217	26	=	=	SYM
ejpam-3454	217	27	(	(	PUNCT
ejpam-3454	217	28	1−	1−	NUM
ejpam-3454	217	29	ε)(1−	ε)(1−	PROPN
ejpam-3454	217	30	η	η	PROPN
ejpam-3454	217	31	)	)	PUNCT
ejpam-3454	217	32	.	.	PUNCT
ejpam-3454	218	1	remark	remark	PROPN
ejpam-3454	218	2	5	5	NUM
ejpam-3454	218	3	.	.	PUNCT
ejpam-3454	219	1	henceforth	henceforth	ADV
ejpam-3454	219	2	(	(	PUNCT
ejpam-3454	219	3	1−ε)(1−η	1−ε)(1−η	X
ejpam-3454	219	4	)	)	PUNCT
ejpam-3454	219	5	=	=	PUNCT
ejpam-3454	219	6	(	(	PUNCT
ejpam-3454	219	7	1−θ	1−θ	NUM
ejpam-3454	219	8	)	)	PUNCT
ejpam-3454	219	9	and	and	CCONJ
ejpam-3454	219	10	θ	θ	PROPN
ejpam-3454	219	11	denotes	denote	VERB
ejpam-3454	219	12	the	the	DET
ejpam-3454	219	13	overall	overall	ADJ
ejpam-3454	219	14	drug	drug	NOUN
ejpam-3454	219	15	effectiveness	effectiveness	NOUN
ejpam-3454	219	16	[	[	X
ejpam-3454	219	17	3	3	NUM
ejpam-3454	219	18	]	]	PUNCT
ejpam-3454	219	19	.	.	PUNCT
ejpam-3454	220	1	besides	besides	SCONJ
ejpam-3454	220	2	the	the	DET
ejpam-3454	220	3	virus	virus	NOUN
ejpam-3454	220	4	-	-	PUNCT
ejpam-3454	220	5	free	free	ADJ
ejpam-3454	220	6	equilibrium	equilibrium	NOUN
ejpam-3454	220	7	point	point	NOUN
ejpam-3454	220	8	e0	e0	PROPN
ejpam-3454	220	9	,	,	PUNCT
ejpam-3454	220	10	we	we	PRON
ejpam-3454	220	11	now	now	ADV
ejpam-3454	220	12	discuss	discuss	VERB
ejpam-3454	220	13	the	the	DET
ejpam-3454	220	14	existence	existence	NOUN
ejpam-3454	220	15	of	of	ADP
ejpam-3454	220	16	the	the	DET
ejpam-3454	220	17	infected	infected	ADJ
ejpam-3454	220	18	equilibrium	equilibrium	NOUN
ejpam-3454	220	19	point	point	NOUN
ejpam-3454	220	20	e+	e+	PUNCT
ejpam-3454	220	21	=	=	SYM
ejpam-3454	220	22	(	(	PUNCT
ejpam-3454	220	23	t	t	NOUN
ejpam-3454	220	24	∗	∗	NOUN
ejpam-3454	220	25	,	,	PUNCT
ejpam-3454	220	26	i∗	i∗	NOUN
ejpam-3454	220	27	,	,	PUNCT
ejpam-3454	220	28	v	v	NOUN
ejpam-3454	220	29	∗	∗	NOUN
ejpam-3454	220	30	)	)	PUNCT
ejpam-3454	220	31	,	,	PUNCT
ejpam-3454	220	32	in	in	ADP
ejpam-3454	220	33	which	which	PRON
ejpam-3454	220	34	x∗	x∗	PROPN
ejpam-3454	220	35	means	mean	VERB
ejpam-3454	220	36	a	a	DET
ejpam-3454	220	37	positive	positive	ADJ
ejpam-3454	220	38	constant	constant	NOUN
ejpam-3454	220	39	.	.	PUNCT
ejpam-3454	221	1	to	to	PART
ejpam-3454	221	2	determine	determine	VERB
ejpam-3454	221	3	t	t	PROPN
ejpam-3454	221	4	∗	∗	NOUN
ejpam-3454	221	5	,	,	PUNCT
ejpam-3454	221	6	i∗	i∗	NOUN
ejpam-3454	221	7	and	and	CCONJ
ejpam-3454	221	8	v	v	NOUN
ejpam-3454	221	9	∗	∗	NOUN
ejpam-3454	221	10	we	we	PRON
ejpam-3454	221	11	should	should	AUX
ejpam-3454	221	12	solve	solve	VERB
ejpam-3454	221	13	the	the	DET
ejpam-3454	221	14	following	follow	VERB
ejpam-3454	221	15	algebraic	algebraic	ADJ
ejpam-3454	221	16	system	system	NOUN
ejpam-3454	221	17	:	:	PUNCT
ejpam-3454	221	18			PROPN
ejpam-3454	221	19	rt	rt	PROPN
ejpam-3454	221	20	(	(	PUNCT
ejpam-3454	221	21	1−	1−	NUM
ejpam-3454	221	22	t	t	NOUN
ejpam-3454	221	23	+	+	CCONJ
ejpam-3454	221	24	i	i	PRON
ejpam-3454	221	25	tmax	tmax	ADJ
ejpam-3454	221	26	)	)	PUNCT
ejpam-3454	221	27	−	−	PROPN
ejpam-3454	222	1	(	(	PUNCT
ejpam-3454	222	2	1−	1−	NUM
ejpam-3454	222	3	η)βv	η)βv	PROPN
ejpam-3454	222	4	t	t	PROPN
ejpam-3454	222	5	−	−	NOUN
ejpam-3454	222	6	dt	dt	NOUN
ejpam-3454	222	7	=	=	SYM
ejpam-3454	222	8	0	0	NUM
ejpam-3454	222	9	;	;	PUNCT
ejpam-3454	222	10	(	(	PUNCT
ejpam-3454	222	11	1−	1−	NUM
ejpam-3454	222	12	η)βv	η)βv	PROPN
ejpam-3454	222	13	t	t	VERB
ejpam-3454	222	14	−	−	NOUN
ejpam-3454	222	15	δi	δi	VERB
ejpam-3454	222	16	=	=	SYM
ejpam-3454	222	17	0	0	NUM
ejpam-3454	222	18	;	;	PUNCT
ejpam-3454	222	19	(	(	PUNCT
ejpam-3454	222	20	15	15	NUM
ejpam-3454	222	21	)	)	PUNCT
ejpam-3454	222	22	(	(	PUNCT
ejpam-3454	223	1	1−	1−	NUM
ejpam-3454	223	2	ε)pi	ε)pi	PROPN
ejpam-3454	223	3	−	−	PROPN
ejpam-3454	223	4	cv	cv	PROPN
ejpam-3454	223	5	−	−	PROPN
ejpam-3454	223	6	α(1−	α(1−	PROPN
ejpam-3454	223	7	η)βv	η)βv	PROPN
ejpam-3454	223	8	t	t	PROPN
ejpam-3454	223	9	=	=	SYM
ejpam-3454	223	10	0	0	X
ejpam-3454	223	11	.	.	PUNCT
ejpam-3454	224	1	we	we	PRON
ejpam-3454	224	2	have	have	VERB
ejpam-3454	224	3	the	the	DET
ejpam-3454	224	4	following	follow	VERB
ejpam-3454	224	5	result	result	NOUN
ejpam-3454	224	6	by	by	ADP
ejpam-3454	224	7	easy	easy	ADJ
ejpam-3454	224	8	way	way	NOUN
ejpam-3454	224	9	:	:	PUNCT
ejpam-3454	224	10	a.	a.	NOUN
ejpam-3454	224	11	nangue	nangue	NOUN
ejpam-3454	224	12	,	,	PUNCT
ejpam-3454	224	13	t.	t.	PROPN
ejpam-3454	224	14	donfack	donfack	PROPN
ejpam-3454	224	15	,	,	PUNCT
ejpam-3454	224	16	d.	d.	PROPN
ejpam-3454	224	17	a.	a.	PROPN
ejpam-3454	224	18	ndode	ndode	PROPN
ejpam-3454	224	19	yafago	yafago	PROPN
ejpam-3454	224	20	/	/	SYM
ejpam-3454	224	21	eur	eur	PROPN
ejpam-3454	224	22	.	.	PUNCT
ejpam-3454	225	1	j.	j.	PROPN
ejpam-3454	225	2	pure	pure	PROPN
ejpam-3454	225	3	appl	appl	PROPN
ejpam-3454	225	4	.	.	PROPN
ejpam-3454	225	5	math	math	PROPN
ejpam-3454	225	6	,	,	PUNCT
ejpam-3454	225	7	12	12	NUM
ejpam-3454	225	8	(	(	PUNCT
ejpam-3454	225	9	3	3	NUM
ejpam-3454	225	10	)	)	PUNCT
ejpam-3454	225	11	(	(	PUNCT
ejpam-3454	225	12	2019	2019	NUM
ejpam-3454	225	13	)	)	PUNCT
ejpam-3454	225	14	,	,	PUNCT
ejpam-3454	225	15	944	944	NUM
ejpam-3454	225	16	-	-	SYM
ejpam-3454	225	17	959	959	NUM
ejpam-3454	225	18	953	953	NUM
ejpam-3454	225	19	proposition	proposition	NOUN
ejpam-3454	225	20	3	3	NUM
ejpam-3454	225	21	.	.	PUNCT
ejpam-3454	226	1	if	if	SCONJ
ejpam-3454	226	2	r0	r0	NOUN
ejpam-3454	226	3	>	>	X
ejpam-3454	226	4	1	1	NUM
ejpam-3454	226	5	and	and	CCONJ
ejpam-3454	226	6	(	(	PUNCT
ejpam-3454	226	7	1−	1−	NUM
ejpam-3454	226	8	ε)p−αδ	ε)p−αδ	SYM
ejpam-3454	226	9	>	>	SYM
ejpam-3454	226	10	0	0	PUNCT
ejpam-3454	227	1	then	then	ADV
ejpam-3454	227	2	the	the	DET
ejpam-3454	227	3	mathematical	mathematical	ADJ
ejpam-3454	227	4	model	model	NOUN
ejpam-3454	227	5	(	(	PUNCT
ejpam-3454	227	6	1	1	X
ejpam-3454	227	7	)	)	PUNCT
ejpam-3454	227	8	admits	admit	VERB
ejpam-3454	227	9	an	an	DET
ejpam-3454	227	10	infected	infected	ADJ
ejpam-3454	227	11	equilibrium	equilibrium	NOUN
ejpam-3454	227	12	point	point	NOUN
ejpam-3454	227	13	e+	e+	PUNCT
ejpam-3454	227	14	=	=	SYM
ejpam-3454	227	15	(	(	PUNCT
ejpam-3454	227	16	t	t	NOUN
ejpam-3454	227	17	∗	∗	NOUN
ejpam-3454	227	18	,	,	PUNCT
ejpam-3454	227	19	i∗	i∗	NOUN
ejpam-3454	227	20	,	,	PUNCT
ejpam-3454	227	21	v	v	NOUN
ejpam-3454	227	22	∗	∗	NOUN
ejpam-3454	227	23	)	)	PUNCT
ejpam-3454	227	24	where	where	SCONJ
ejpam-3454	227	25	t	t	NOUN
ejpam-3454	227	26	∗	∗	NOUN
ejpam-3454	227	27	=	=	PUNCT
ejpam-3454	227	28	cδ	cδ	NOUN
ejpam-3454	227	29	(	(	PUNCT
ejpam-3454	227	30	1−	1−	NUM
ejpam-3454	227	31	η)β[(1−	η)β[(1−	PROPN
ejpam-3454	227	32	ε)p−	ε)p−	PROPN
ejpam-3454	227	33	αδ	αδ	ADP
ejpam-3454	227	34	]	]	PUNCT
ejpam-3454	227	35	;	;	PUNCT
ejpam-3454	228	1	v	v	X
ejpam-3454	228	2	∗	∗	NOUN
ejpam-3454	228	3	=	=	SYM
ejpam-3454	228	4	c	c	X
ejpam-3454	228	5	(	(	PUNCT
ejpam-3454	228	6	1−	1−	NUM
ejpam-3454	228	7	ε)p−	ε)p−	PROPN
ejpam-3454	228	8	αδ	αδ	ADP
ejpam-3454	228	9	{	{	PUNCT
ejpam-3454	228	10	(	(	PUNCT
ejpam-3454	228	11	1−	1−	NUM
ejpam-3454	228	12	η)kβ[(1−	η)kβ[(1−	PROPN
ejpam-3454	228	13	ε)p−	ε)p−	PROPN
ejpam-3454	228	14	αδ](r	αδ](r	PROPN
ejpam-3454	228	15	−	−	PUNCT
ejpam-3454	228	16	d)−	d)−	ADJ
ejpam-3454	228	17	crδ	crδ	NOUN
ejpam-3454	228	18	(	(	PUNCT
ejpam-3454	228	19	1−	1−	NUM
ejpam-3454	228	20	η)βcr	η)βcr	PROPN
ejpam-3454	228	21	+	+	CCONJ
ejpam-3454	228	22	(	(	PUNCT
ejpam-3454	228	23	1−	1−	NUM
ejpam-3454	228	24	η)2kβ2[(1−	η)2kβ2[(1−	PROPN
ejpam-3454	228	25	ε)p−	ε)p−	PROPN
ejpam-3454	228	26	αδ	αδ	ADP
ejpam-3454	228	27	]	]	PUNCT
ejpam-3454	228	28	}	}	PUNCT
ejpam-3454	228	29	=	=	SYM
ejpam-3454	228	30	c	c	X
ejpam-3454	228	31	(	(	PUNCT
ejpam-3454	228	32	1−	1−	NUM
ejpam-3454	228	33	ε)p−	ε)p−	PROPN
ejpam-3454	228	34	αδ	αδ	ADP
ejpam-3454	228	35	i∗	i∗	NOUN
ejpam-3454	228	36	and	and	CCONJ
ejpam-3454	228	37	i∗	i∗	NOUN
ejpam-3454	228	38	=	=	SYM
ejpam-3454	228	39	(	(	PUNCT
ejpam-3454	228	40	1−	1−	NUM
ejpam-3454	228	41	η)kβ[(1−	η)kβ[(1−	PROPN
ejpam-3454	228	42	ε)p−	ε)p−	PROPN
ejpam-3454	228	43	αδ](r	αδ](r	PROPN
ejpam-3454	228	44	−	−	PUNCT
ejpam-3454	228	45	d)−	d)−	ADJ
ejpam-3454	228	46	crδ	crδ	NOUN
ejpam-3454	228	47	(	(	PUNCT
ejpam-3454	228	48	1−	1−	NUM
ejpam-3454	228	49	η)βcr	η)βcr	PROPN
ejpam-3454	228	50	+	+	CCONJ
ejpam-3454	228	51	(	(	PUNCT
ejpam-3454	228	52	1−	1−	NUM
ejpam-3454	228	53	η)2kβ2[(1−	η)2kβ2[(1−	PROPN
ejpam-3454	228	54	ε)p−	ε)p−	PROPN
ejpam-3454	228	55	αδ	αδ	ADP
ejpam-3454	228	56	]	]	PUNCT
ejpam-3454	228	57	.	.	PUNCT
ejpam-3454	229	1	remark	remark	PROPN
ejpam-3454	229	2	6	6	NUM
ejpam-3454	229	3	.	.	PUNCT
ejpam-3454	230	1	(	(	PUNCT
ejpam-3454	230	2	i	i	NOUN
ejpam-3454	230	3	)	)	PUNCT
ejpam-3454	230	4	the	the	DET
ejpam-3454	230	5	point	point	NOUN
ejpam-3454	230	6	(	(	PUNCT
ejpam-3454	230	7	0	0	NUM
ejpam-3454	230	8	,	,	PUNCT
ejpam-3454	230	9	0	0	NUM
ejpam-3454	230	10	,	,	PUNCT
ejpam-3454	230	11	0	0	NUM
ejpam-3454	230	12	)	)	PUNCT
ejpam-3454	230	13	is	be	AUX
ejpam-3454	230	14	also	also	ADV
ejpam-3454	230	15	an	an	DET
ejpam-3454	230	16	equilibrium	equilibrium	NOUN
ejpam-3454	230	17	of	of	ADP
ejpam-3454	230	18	the	the	DET
ejpam-3454	230	19	model	model	NOUN
ejpam-3454	230	20	(	(	PUNCT
ejpam-3454	230	21	1	1	NUM
ejpam-3454	230	22	)	)	PUNCT
ejpam-3454	230	23	.	.	PUNCT
ejpam-3454	231	1	(	(	PUNCT
ejpam-3454	231	2	ii	ii	NOUN
ejpam-3454	231	3	)	)	PUNCT
ejpam-3454	231	4	t	t	PROPN
ejpam-3454	231	5	∗	∗	NOUN
ejpam-3454	231	6	can	can	AUX
ejpam-3454	231	7	be	be	AUX
ejpam-3454	231	8	expressed	express	VERB
ejpam-3454	231	9	with	with	ADP
ejpam-3454	231	10	respect	respect	NOUN
ejpam-3454	231	11	to	to	ADP
ejpam-3454	231	12	r0	r0	NOUN
ejpam-3454	231	13	,	,	PUNCT
ejpam-3454	231	14	thus	thus	ADV
ejpam-3454	231	15	we	we	PRON
ejpam-3454	231	16	have	have	VERB
ejpam-3454	231	17	:	:	PUNCT
ejpam-3454	231	18	t	t	NOUN
ejpam-3454	231	19	∗	∗	NOUN
ejpam-3454	231	20	=	=	SYM
ejpam-3454	232	1	cδt0	cδt0	PROPN
ejpam-3454	232	2	r0δc+	r0δc+	PROPN
ejpam-3454	232	3	(	(	PUNCT
ejpam-3454	232	4	1−	1−	NUM
ejpam-3454	232	5	η)αβt0(r0	η)αβt0(r0	INTJ
ejpam-3454	232	6	−	−	NUM
ejpam-3454	232	7	1	1	X
ejpam-3454	232	8	)	)	PUNCT
ejpam-3454	232	9	this	this	PRON
ejpam-3454	232	10	means	mean	VERB
ejpam-3454	232	11	that	that	SCONJ
ejpam-3454	232	12	t	t	PROPN
ejpam-3454	232	13	∗	∗	NOUN
ejpam-3454	232	14	exists	exist	VERB
ejpam-3454	232	15	if	if	SCONJ
ejpam-3454	232	16	and	and	CCONJ
ejpam-3454	232	17	only	only	ADV
ejpam-3454	232	18	if	if	SCONJ
ejpam-3454	232	19	r0	r0	NOUN
ejpam-3454	232	20	>	>	X
ejpam-3454	232	21	1	1	NUM
ejpam-3454	232	22	.	.	NOUN
ejpam-3454	232	23	4	4	NUM
ejpam-3454	232	24	.	.	X
ejpam-3454	232	25	local	local	ADJ
ejpam-3454	232	26	stability	stability	NOUN
ejpam-3454	232	27	analysis	analysis	NOUN
ejpam-3454	232	28	in	in	ADP
ejpam-3454	232	29	this	this	DET
ejpam-3454	232	30	subsection	subsection	NOUN
ejpam-3454	232	31	,	,	PUNCT
ejpam-3454	232	32	we	we	PRON
ejpam-3454	232	33	investigate	investigate	VERB
ejpam-3454	232	34	the	the	DET
ejpam-3454	232	35	local	local	ADJ
ejpam-3454	232	36	stability	stability	NOUN
ejpam-3454	232	37	of	of	ADP
ejpam-3454	232	38	the	the	DET
ejpam-3454	232	39	equilibria	equilibrium	NOUN
ejpam-3454	232	40	e0	e0	PROPN
ejpam-3454	232	41	and	and	CCONJ
ejpam-3454	232	42	e+	e+	VERB
ejpam-3454	232	43	by	by	ADP
ejpam-3454	232	44	finding	find	VERB
ejpam-3454	232	45	the	the	DET
ejpam-3454	232	46	eigenvalues	eigenvalue	NOUN
ejpam-3454	232	47	of	of	ADP
ejpam-3454	232	48	the	the	DET
ejpam-3454	232	49	associated	associated	ADJ
ejpam-3454	232	50	jacobian	jacobian	ADJ
ejpam-3454	232	51	matrices	matrix	NOUN
ejpam-3454	232	52	.	.	PUNCT
ejpam-3454	233	1	the	the	DET
ejpam-3454	233	2	jacobian	jacobian	ADJ
ejpam-3454	233	3	matrix	matrix	NOUN
ejpam-3454	233	4	j	j	PROPN
ejpam-3454	233	5	(	(	PUNCT
ejpam-3454	233	6	t	t	PROPN
ejpam-3454	233	7	,	,	PUNCT
ejpam-3454	233	8	i	i	PRON
ejpam-3454	233	9	,	,	PUNCT
ejpam-3454	233	10	v	v	NOUN
ejpam-3454	233	11	)	)	PUNCT
ejpam-3454	233	12	of	of	ADP
ejpam-3454	233	13	model	model	NOUN
ejpam-3454	233	14	(	(	PUNCT
ejpam-3454	233	15	1	1	X
ejpam-3454	233	16	)	)	PUNCT
ejpam-3454	233	17	is	be	AUX
ejpam-3454	233	18	given	give	VERB
ejpam-3454	233	19	by	by	ADP
ejpam-3454	233	20	:	:	PUNCT
ejpam-3454	233	21	j	j	PROPN
ejpam-3454	233	22	(	(	PUNCT
ejpam-3454	233	23	t	t	PROPN
ejpam-3454	233	24	,	,	PUNCT
ejpam-3454	233	25	i	i	PRON
ejpam-3454	233	26	,	,	PUNCT
ejpam-3454	233	27	v	v	NOUN
ejpam-3454	233	28	)	)	PUNCT
ejpam-3454	233	29	=	=	SYM
ejpam-3454	233	30			NOUN
ejpam-3454	233	31	p1	p1	PROPN
ejpam-3454	233	32	rt	rt	PROPN
ejpam-3454	233	33	tmax	tmax	ADP
ejpam-3454	233	34	−(1−	−(1−	ADP
ejpam-3454	233	35	η)βt	η)βt	PROPN
ejpam-3454	233	36	(	(	PUNCT
ejpam-3454	233	37	1−	1−	NUM
ejpam-3454	233	38	η)βv	η)βv	PROPN
ejpam-3454	233	39	−δ	−δ	NOUN
ejpam-3454	233	40	(	(	PUNCT
ejpam-3454	233	41	1−	1−	NUM
ejpam-3454	233	42	η)βt	η)βt	PROPN
ejpam-3454	233	43	−α(1−	−α(1−	PROPN
ejpam-3454	233	44	η)βv	η)βv	PROPN
ejpam-3454	233	45	(	(	PUNCT
ejpam-3454	233	46	1−	1−	NUM
ejpam-3454	233	47	ε)p	ε)p	X
ejpam-3454	233	48	p2	p2	PROPN
ejpam-3454	233	49			NUM
ejpam-3454	233	50	(	(	PUNCT
ejpam-3454	233	51	16	16	NUM
ejpam-3454	233	52	)	)	PUNCT
ejpam-3454	233	53	where	where	SCONJ
ejpam-3454	233	54	p1	p1	NOUN
ejpam-3454	233	55	=	=	SYM
ejpam-3454	233	56	r	r	PROPN
ejpam-3454	233	57	(	(	PUNCT
ejpam-3454	233	58	1−	1−	NUM
ejpam-3454	233	59	2	2	NUM
ejpam-3454	233	60	t	t	NOUN
ejpam-3454	233	61	+	+	NUM
ejpam-3454	233	62	i	i	PRON
ejpam-3454	233	63	tmax	tmax	ADJ
ejpam-3454	233	64	)	)	PUNCT
ejpam-3454	233	65	−	−	PROPN
ejpam-3454	234	1	d−	d−	PROPN
ejpam-3454	234	2	(	(	PUNCT
ejpam-3454	234	3	1−	1−	NUM
ejpam-3454	234	4	η)βv	η)βv	PROPN
ejpam-3454	234	5	and	and	CCONJ
ejpam-3454	234	6	p2	p2	PROPN
ejpam-3454	234	7	=	=	SYM
ejpam-3454	234	8	−	−	PROPN
ejpam-3454	234	9	(	(	PUNCT
ejpam-3454	234	10	c+	c+	PROPN
ejpam-3454	234	11	α(1−	α(1−	PROPN
ejpam-3454	234	12	η))βt	η))βt	PROPN
ejpam-3454	234	13	.	.	PUNCT
ejpam-3454	235	1	first	first	ADV
ejpam-3454	235	2	,	,	PUNCT
ejpam-3454	235	3	we	we	PRON
ejpam-3454	235	4	have	have	AUX
ejpam-3454	235	5	theorem	theorem	VERB
ejpam-3454	235	6	5	5	NUM
ejpam-3454	235	7	.	.	X
ejpam-3454	235	8	for	for	ADP
ejpam-3454	235	9	model	model	NOUN
ejpam-3454	235	10	(	(	PUNCT
ejpam-3454	235	11	1	1	NUM
ejpam-3454	235	12	)	)	PUNCT
ejpam-3454	235	13	,	,	PUNCT
ejpam-3454	235	14	the	the	DET
ejpam-3454	235	15	virus	virus	NOUN
ejpam-3454	235	16	-	-	PUNCT
ejpam-3454	235	17	free	free	ADJ
ejpam-3454	235	18	equilibrium	equilibrium	NOUN
ejpam-3454	235	19	point	point	NOUN
ejpam-3454	235	20	e0	e0	PROPN
ejpam-3454	235	21	=	=	PUNCT
ejpam-3454	235	22	(	(	PUNCT
ejpam-3454	235	23	t	t	PROPN
ejpam-3454	235	24	0	0	NUM
ejpam-3454	235	25	,	,	PUNCT
ejpam-3454	235	26	0	0	NUM
ejpam-3454	235	27	,	,	PUNCT
ejpam-3454	235	28	0	0	NUM
ejpam-3454	235	29	)	)	PUNCT
ejpam-3454	235	30	is	be	AUX
ejpam-3454	235	31	locally	locally	ADV
ejpam-3454	235	32	asymptotically	asymptotically	ADV
ejpam-3454	235	33	stable	stable	ADJ
ejpam-3454	235	34	if	if	SCONJ
ejpam-3454	235	35	r0	r0	NOUN
ejpam-3454	235	36	<	<	X
ejpam-3454	235	37	1	1	NUM
ejpam-3454	235	38	and	and	CCONJ
ejpam-3454	235	39	unstable	unstable	ADJ
ejpam-3454	235	40	if	if	SCONJ
ejpam-3454	235	41	r0	r0	NOUN
ejpam-3454	235	42	>	>	X
ejpam-3454	235	43	1	1	NUM
ejpam-3454	235	44	a.	a.	NOUN
ejpam-3454	235	45	nangue	nangue	NOUN
ejpam-3454	235	46	,	,	PUNCT
ejpam-3454	235	47	t.	t.	PROPN
ejpam-3454	235	48	donfack	donfack	PROPN
ejpam-3454	235	49	,	,	PUNCT
ejpam-3454	235	50	d.	d.	PROPN
ejpam-3454	235	51	a.	a.	PROPN
ejpam-3454	235	52	ndode	ndode	PROPN
ejpam-3454	235	53	yafago	yafago	PROPN
ejpam-3454	235	54	/	/	SYM
ejpam-3454	235	55	eur	eur	PROPN
ejpam-3454	235	56	.	.	PUNCT
ejpam-3454	236	1	j.	j.	PROPN
ejpam-3454	236	2	pure	pure	PROPN
ejpam-3454	236	3	appl	appl	PROPN
ejpam-3454	236	4	.	.	PROPN
ejpam-3454	236	5	math	math	PROPN
ejpam-3454	236	6	,	,	PUNCT
ejpam-3454	236	7	12	12	NUM
ejpam-3454	236	8	(	(	PUNCT
ejpam-3454	236	9	3	3	NUM
ejpam-3454	236	10	)	)	PUNCT
ejpam-3454	236	11	(	(	PUNCT
ejpam-3454	236	12	2019	2019	NUM
ejpam-3454	236	13	)	)	PUNCT
ejpam-3454	236	14	,	,	PUNCT
ejpam-3454	236	15	944	944	NUM
ejpam-3454	236	16	-	-	SYM
ejpam-3454	236	17	959	959	NUM
ejpam-3454	236	18	954	954	NUM
ejpam-3454	236	19	proof	proof	NOUN
ejpam-3454	236	20	.	.	PUNCT
ejpam-3454	237	1	the	the	DET
ejpam-3454	237	2	local	local	ADJ
ejpam-3454	237	3	stability	stability	NOUN
ejpam-3454	237	4	of	of	ADP
ejpam-3454	237	5	the	the	DET
ejpam-3454	237	6	uninfected	uninfected	ADJ
ejpam-3454	237	7	steady	steady	ADJ
ejpam-3454	237	8	state	state	NOUN
ejpam-3454	237	9	e0	e0	NOUN
ejpam-3454	237	10	=	=	PUNCT
ejpam-3454	237	11	(	(	PUNCT
ejpam-3454	237	12	t	t	PROPN
ejpam-3454	237	13	0	0	NUM
ejpam-3454	237	14	,	,	PUNCT
ejpam-3454	237	15	0	0	NUM
ejpam-3454	237	16	,	,	PUNCT
ejpam-3454	237	17	0	0	NUM
ejpam-3454	237	18	)	)	PUNCT
ejpam-3454	237	19	is	be	AUX
ejpam-3454	237	20	governed	govern	VERB
ejpam-3454	237	21	by	by	ADP
ejpam-3454	237	22	the	the	DET
ejpam-3454	237	23	eigenvalues	eigenvalue	NOUN
ejpam-3454	237	24	of	of	ADP
ejpam-3454	237	25	the	the	DET
ejpam-3454	237	26	matrix	matrix	NOUN
ejpam-3454	237	27	j	j	PROPN
ejpam-3454	237	28	(	(	PUNCT
ejpam-3454	237	29	e0	e0	PROPN
ejpam-3454	237	30	)	)	PUNCT
ejpam-3454	238	1	=	=	SYM
ejpam-3454	238	2			NOUN
ejpam-3454	238	3	−(r	−(r	NOUN
ejpam-3454	238	4	−	−	PROPN
ejpam-3454	239	1	d	d	NOUN
ejpam-3454	239	2	)	)	PUNCT
ejpam-3454	239	3	0	0	NUM
ejpam-3454	240	1	−	−	PROPN
ejpam-3454	240	2	(	(	PUNCT
ejpam-3454	240	3	1−η)(r−d)β	1−η)(r−d)β	NOUN
ejpam-3454	240	4	r	r	NOUN
ejpam-3454	240	5	0	0	NUM
ejpam-3454	240	6	−δ	−δ	ADJ
ejpam-3454	240	7	(	(	PUNCT
ejpam-3454	240	8	1−η)(r−d)β	1−η)(r−d)β	NOUN
ejpam-3454	240	9	r	r	NOUN
ejpam-3454	240	10	0	0	NUM
ejpam-3454	240	11	(	(	PUNCT
ejpam-3454	240	12	1−	1−	NUM
ejpam-3454	240	13	ε)p	ε)p	ADJ
ejpam-3454	240	14	b2	b2	NOUN
ejpam-3454	240	15			VERB
ejpam-3454	240	16	where	where	SCONJ
ejpam-3454	240	17	b2	b2	NOUN
ejpam-3454	240	18	=	=	SYM
ejpam-3454	240	19	−	−	PROPN
ejpam-3454	240	20	(	(	PUNCT
ejpam-3454	240	21	c+	c+	VERB
ejpam-3454	240	22	α	α	X
ejpam-3454	240	23	(	(	PUNCT
ejpam-3454	240	24	1−	1−	NUM
ejpam-3454	240	25	η)(r	η)(r	NOUN
ejpam-3454	240	26	−	−	PROPN
ejpam-3454	240	27	d)β	d)β	NOUN
ejpam-3454	240	28	r	r	NOUN
ejpam-3454	240	29	)	)	PUNCT
ejpam-3454	240	30	.	.	PUNCT
ejpam-3454	241	1	the	the	DET
ejpam-3454	241	2	characteristic	characteristic	ADJ
ejpam-3454	241	3	equation	equation	NOUN
ejpam-3454	241	4	of	of	ADP
ejpam-3454	241	5	the	the	DET
ejpam-3454	241	6	linearised	linearise	VERB
ejpam-3454	241	7	system	system	NOUN
ejpam-3454	241	8	is	be	AUX
ejpam-3454	241	9	given	give	VERB
ejpam-3454	241	10	by	by	ADP
ejpam-3454	241	11	the	the	DET
ejpam-3454	241	12	following	follow	VERB
ejpam-3454	241	13	equation	equation	NOUN
ejpam-3454	241	14	:	:	PUNCT
ejpam-3454	242	1	[	[	X
ejpam-3454	242	2	−λ−	−λ−	X
ejpam-3454	242	3	(	(	PUNCT
ejpam-3454	242	4	r−d)][λ2	r−d)][λ2	PROPN
ejpam-3454	242	5	+	+	PUNCT
ejpam-3454	242	6	λ	λ	X
ejpam-3454	242	7	r	r	NOUN
ejpam-3454	242	8	[	[	X
ejpam-3454	242	9	cr+	cr+	ADJ
ejpam-3454	242	10	δr+αβ(1−	δr+αβ(1−	ADJ
ejpam-3454	242	11	η)(r−d)]−	η)(r−d)]−	PROPN
ejpam-3454	242	12	β	β	NOUN
ejpam-3454	242	13	r	r	NOUN
ejpam-3454	242	14	(	(	PUNCT
ejpam-3454	242	15	1−	1−	NUM
ejpam-3454	242	16	η)(r−d)[(1−	η)(r−d)[(1−	NUM
ejpam-3454	242	17	ε)p−	ε)p−	PROPN
ejpam-3454	242	18	δα	δα	PRON
ejpam-3454	242	19	]	]	X
ejpam-3454	242	20	+	+	CCONJ
ejpam-3454	242	21	crδ	crδ	X
ejpam-3454	242	22	]	]	X
ejpam-3454	242	23	=	=	SYM
ejpam-3454	242	24	0	0	NUM
ejpam-3454	242	25	i.e.	i.e.	X
ejpam-3454	242	26	[	[	X
ejpam-3454	242	27	−λ−	−λ−	NOUN
ejpam-3454	242	28	(	(	PUNCT
ejpam-3454	242	29	r	r	NOUN
ejpam-3454	242	30	−	−	NOUN
ejpam-3454	242	31	d)][λ2	d)][λ2	NOUN
ejpam-3454	242	32	+	+	CCONJ
ejpam-3454	242	33	λa1	λa1	PROPN
ejpam-3454	242	34	+	+	NUM
ejpam-3454	242	35	a2	a2	PROPN
ejpam-3454	242	36	]	]	X
ejpam-3454	242	37	=	=	SYM
ejpam-3454	242	38	0	0	NUM
ejpam-3454	242	39	where	where	SCONJ
ejpam-3454	242	40	coefficients	coefficient	NOUN
ejpam-3454	242	41	are	be	AUX
ejpam-3454	242	42	given	give	VERB
ejpam-3454	242	43	by	by	ADP
ejpam-3454	242	44	:	:	PUNCT
ejpam-3454	242	45	a1	a1	NOUN
ejpam-3454	242	46	=	=	SYM
ejpam-3454	242	47	1	1	NUM
ejpam-3454	242	48	r	r	NOUN
ejpam-3454	242	49	[	[	X
ejpam-3454	242	50	cr	cr	NOUN
ejpam-3454	242	51	+	+	NUM
ejpam-3454	242	52	δr	δr	ADP
ejpam-3454	242	53	+	+	CCONJ
ejpam-3454	242	54	αβ(1−	αβ(1−	PROPN
ejpam-3454	242	55	η)(r	η)(r	NOUN
ejpam-3454	242	56	−	−	NOUN
ejpam-3454	242	57	d	d	NOUN
ejpam-3454	242	58	)	)	PUNCT
ejpam-3454	242	59	]	]	PUNCT
ejpam-3454	242	60	a2	a2	PROPN
ejpam-3454	242	61	=	=	SYM
ejpam-3454	242	62	−β	−β	PROPN
ejpam-3454	242	63	r	r	NOUN
ejpam-3454	242	64	(	(	PUNCT
ejpam-3454	242	65	1−	1−	NUM
ejpam-3454	242	66	η)(r	η)(r	NOUN
ejpam-3454	242	67	−	−	PROPN
ejpam-3454	242	68	d)[(1−	d)[(1−	NUM
ejpam-3454	242	69	ε)p−	ε)p−	PROPN
ejpam-3454	242	70	δα	δα	PRON
ejpam-3454	242	71	]	]	X
ejpam-3454	242	72	+	+	CCONJ
ejpam-3454	242	73	cδ	cδ	NOUN
ejpam-3454	242	74	.	.	PUNCT
ejpam-3454	243	1	λ	λ	X
ejpam-3454	243	2	=	=	PUNCT
ejpam-3454	243	3	−(r−d	−(r−d	X
ejpam-3454	243	4	)	)	PUNCT
ejpam-3454	243	5	is	be	AUX
ejpam-3454	243	6	already	already	ADV
ejpam-3454	243	7	a	a	DET
ejpam-3454	243	8	negative	negative	ADJ
ejpam-3454	243	9	eigenvalue	eigenvalue	NOUN
ejpam-3454	243	10	of	of	ADP
ejpam-3454	243	11	the	the	DET
ejpam-3454	243	12	jacobian	jacobian	ADJ
ejpam-3454	243	13	matrix	matrix	NOUN
ejpam-3454	243	14	j	j	PROPN
ejpam-3454	243	15	(	(	PUNCT
ejpam-3454	243	16	e0	e0	PROPN
ejpam-3454	243	17	)	)	PUNCT
ejpam-3454	243	18	and	and	CCONJ
ejpam-3454	243	19	to	to	PART
ejpam-3454	243	20	achieve	achieve	VERB
ejpam-3454	243	21	the	the	DET
ejpam-3454	243	22	study	study	NOUN
ejpam-3454	243	23	we	we	PRON
ejpam-3454	243	24	will	will	AUX
ejpam-3454	243	25	use	use	VERB
ejpam-3454	243	26	the	the	DET
ejpam-3454	243	27	routh	routh	PROPN
ejpam-3454	243	28	-	-	PUNCT
ejpam-3454	243	29	hurwitz	hurwitz	PROPN
ejpam-3454	243	30	criterion	criterion	NOUN
ejpam-3454	243	31	.	.	PUNCT
ejpam-3454	244	1	if	if	SCONJ
ejpam-3454	244	2	a1	a1	NOUN
ejpam-3454	244	3	and	and	CCONJ
ejpam-3454	244	4	a2	a2	PROPN
ejpam-3454	244	5	are	be	AUX
ejpam-3454	244	6	all	all	ADV
ejpam-3454	244	7	positive	positive	ADJ
ejpam-3454	244	8	,	,	PUNCT
ejpam-3454	244	9	then	then	ADV
ejpam-3454	244	10	applying	apply	VERB
ejpam-3454	244	11	the	the	DET
ejpam-3454	244	12	routh	routh	PROPN
ejpam-3454	244	13	-	-	PUNCT
ejpam-3454	244	14	hurwitz	hurwitz	PROPN
ejpam-3454	244	15	criterion	criterion	NOUN
ejpam-3454	244	16	to	to	ADP
ejpam-3454	244	17	the	the	DET
ejpam-3454	244	18	quadratic	quadratic	ADJ
ejpam-3454	244	19	equation	equation	NOUN
ejpam-3454	244	20	guarantees	guarantee	VERB
ejpam-3454	244	21	the	the	DET
ejpam-3454	244	22	eigenvalues	eigenvalue	NOUN
ejpam-3454	244	23	to	to	PART
ejpam-3454	244	24	have	have	VERB
ejpam-3454	244	25	negative	negative	ADJ
ejpam-3454	244	26	real	real	ADJ
ejpam-3454	244	27	part	part	NOUN
ejpam-3454	244	28	,	,	PUNCT
ejpam-3454	244	29	and	and	CCONJ
ejpam-3454	244	30	that	that	SCONJ
ejpam-3454	244	31	two	two	NUM
ejpam-3454	244	32	conditions	condition	NOUN
ejpam-3454	244	33	must	must	AUX
ejpam-3454	244	34	be	be	AUX
ejpam-3454	244	35	satisfied	satisfied	ADJ
ejpam-3454	244	36	for	for	ADP
ejpam-3454	244	37	local	local	ADJ
ejpam-3454	244	38	asymptotic	asymptotic	ADJ
ejpam-3454	244	39	stability	stability	NOUN
ejpam-3454	244	40	of	of	ADP
ejpam-3454	244	41	the	the	DET
ejpam-3454	244	42	uninfected	uninfected	ADJ
ejpam-3454	244	43	steady	steady	ADJ
ejpam-3454	244	44	state	state	NOUN
ejpam-3454	244	45	:	:	PUNCT
ejpam-3454	244	46	a1	a1	VERB
ejpam-3454	244	47	>	>	X
ejpam-3454	244	48	0	0	PUNCT
ejpam-3454	245	1	i.e.	i.e.	X
ejpam-3454	245	2	1	1	NUM
ejpam-3454	245	3	r	r	NOUN
ejpam-3454	245	4	[	[	X
ejpam-3454	245	5	cr	cr	NOUN
ejpam-3454	245	6	+	+	NUM
ejpam-3454	245	7	δr	δr	ADP
ejpam-3454	245	8	+	+	CCONJ
ejpam-3454	245	9	αβ(1−	αβ(1−	PROPN
ejpam-3454	245	10	η)(r	η)(r	NOUN
ejpam-3454	245	11	−	−	NOUN
ejpam-3454	245	12	d	d	NOUN
ejpam-3454	245	13	)	)	PUNCT
ejpam-3454	245	14	]	]	PUNCT
ejpam-3454	246	1	>	>	X
ejpam-3454	246	2	0	0	PUNCT
ejpam-3454	246	3	is	be	AUX
ejpam-3454	246	4	satisfied	satisfied	ADJ
ejpam-3454	246	5	.	.	PUNCT
ejpam-3454	247	1	a2	a2	PROPN
ejpam-3454	247	2	>	>	X
ejpam-3454	247	3	0	0	PUNCT
ejpam-3454	248	1	i.e.	i.e.	X
ejpam-3454	248	2	−β	−β	ADJ
ejpam-3454	248	3	r	r	NOUN
ejpam-3454	248	4	(	(	PUNCT
ejpam-3454	248	5	1−	1−	NUM
ejpam-3454	248	6	η)(r	η)(r	NOUN
ejpam-3454	248	7	−	−	PROPN
ejpam-3454	248	8	d)[(1−	d)[(1−	NUM
ejpam-3454	248	9	ε)p−	ε)p−	PROPN
ejpam-3454	248	10	δα	δα	PRON
ejpam-3454	248	11	]	]	X
ejpam-3454	248	12	+	+	CCONJ
ejpam-3454	248	13	cδ	cδ	NOUN
ejpam-3454	248	14	>	>	X
ejpam-3454	248	15	0	0	PUNCT
ejpam-3454	249	1	i.e.	i.e.	X
ejpam-3454	249	2	β	β	X
ejpam-3454	249	3	r	r	X
ejpam-3454	249	4	(	(	PUNCT
ejpam-3454	249	5	1−	1−	NUM
ejpam-3454	249	6	η)(r	η)(r	NOUN
ejpam-3454	249	7	−	−	NOUN
ejpam-3454	249	8	d)[(1−	d)[(1−	NUM
ejpam-3454	249	9	ε)p+	ε)p+	NOUN
ejpam-3454	249	10	αδ	αδ	NUM
ejpam-3454	249	11	]	]	PUNCT
ejpam-3454	249	12	<	<	X
ejpam-3454	249	13	cδ	cδ	NOUN
ejpam-3454	249	14	it	it	PRON
ejpam-3454	249	15	follows	follow	VERB
ejpam-3454	249	16	that	that	PRON
ejpam-3454	249	17	:	:	PUNCT
ejpam-3454	249	18	β	β	X
ejpam-3454	249	19	r	r	X
ejpam-3454	249	20	(	(	PUNCT
ejpam-3454	249	21	1−	1−	NUM
ejpam-3454	249	22	η)(r	η)(r	NOUN
ejpam-3454	249	23	−	−	PROPN
ejpam-3454	249	24	d)(1−	d)(1−	NOUN
ejpam-3454	249	25	ε)p	ε)p	PUNCT
ejpam-3454	249	26	<	<	X
ejpam-3454	249	27	cδ	cδ	X
ejpam-3454	250	1	+	+	CCONJ
ejpam-3454	250	2	αδβ	αδβ	NOUN
ejpam-3454	250	3	r	r	NOUN
ejpam-3454	250	4	(	(	PUNCT
ejpam-3454	250	5	1−	1−	NUM
ejpam-3454	250	6	η)(r	η)(r	NOUN
ejpam-3454	250	7	−	−	NOUN
ejpam-3454	250	8	d	d	NOUN
ejpam-3454	250	9	)	)	PUNCT
ejpam-3454	250	10	a.	a.	NOUN
ejpam-3454	250	11	nangue	nangue	NOUN
ejpam-3454	250	12	,	,	PUNCT
ejpam-3454	250	13	t.	t.	PROPN
ejpam-3454	250	14	donfack	donfack	PROPN
ejpam-3454	250	15	,	,	PUNCT
ejpam-3454	250	16	d.	d.	PROPN
ejpam-3454	250	17	a.	a.	PROPN
ejpam-3454	250	18	ndode	ndode	PROPN
ejpam-3454	251	1	yafago	yafago	PROPN
ejpam-3454	251	2	/	/	SYM
ejpam-3454	251	3	eur	eur	PROPN
ejpam-3454	251	4	.	.	PUNCT
ejpam-3454	252	1	j.	j.	PROPN
ejpam-3454	252	2	pure	pure	PROPN
ejpam-3454	252	3	appl	appl	PROPN
ejpam-3454	252	4	.	.	PROPN
ejpam-3454	252	5	math	math	PROPN
ejpam-3454	252	6	,	,	PUNCT
ejpam-3454	252	7	12	12	NUM
ejpam-3454	252	8	(	(	PUNCT
ejpam-3454	252	9	3	3	NUM
ejpam-3454	252	10	)	)	PUNCT
ejpam-3454	252	11	(	(	PUNCT
ejpam-3454	252	12	2019	2019	NUM
ejpam-3454	252	13	)	)	PUNCT
ejpam-3454	252	14	,	,	PUNCT
ejpam-3454	252	15	944	944	NUM
ejpam-3454	252	16	-	-	SYM
ejpam-3454	252	17	959	959	NUM
ejpam-3454	252	18	955	955	NUM
ejpam-3454	252	19	which	which	PRON
ejpam-3454	252	20	yields	yield	VERB
ejpam-3454	252	21	pβ(1−	pβ(1−	ADJ
ejpam-3454	252	22	η)(r	η)(r	NOUN
ejpam-3454	252	23	−	−	ADP
ejpam-3454	252	24	d)(1−	d)(1−	PROPN
ejpam-3454	252	25	ε	ε	PROPN
ejpam-3454	252	26	)	)	PUNCT
ejpam-3454	252	27	<	<	X
ejpam-3454	252	28	δ(cr	δ(cr	PROPN
ejpam-3454	252	29	+	+	CCONJ
ejpam-3454	252	30	αβ(1−	αβ(1−	PROPN
ejpam-3454	252	31	η)(r	η)(r	NOUN
ejpam-3454	252	32	−	−	NOUN
ejpam-3454	252	33	d	d	NOUN
ejpam-3454	252	34	)	)	PUNCT
ejpam-3454	252	35	)	)	PUNCT
ejpam-3454	252	36	.	.	PUNCT
ejpam-3454	253	1	that	that	PRON
ejpam-3454	253	2	leads	lead	VERB
ejpam-3454	253	3	to	to	ADP
ejpam-3454	253	4	:	:	PUNCT
ejpam-3454	253	5	pβ(1−	pβ(1−	ADJ
ejpam-3454	253	6	η)(r	η)(r	NOUN
ejpam-3454	253	7	−	−	ADP
ejpam-3454	253	8	d)(1−	d)(1−	PROPN
ejpam-3454	253	9	ε	ε	PROPN
ejpam-3454	253	10	)	)	PUNCT
ejpam-3454	253	11	δ(cr	δ(cr	PROPN
ejpam-3454	253	12	+	+	CCONJ
ejpam-3454	253	13	αβ(1−	αβ(1−	PROPN
ejpam-3454	253	14	η)(r	η)(r	NOUN
ejpam-3454	253	15	−	−	NOUN
ejpam-3454	253	16	d	d	NOUN
ejpam-3454	253	17	)	)	PUNCT
ejpam-3454	253	18	)	)	PUNCT
ejpam-3454	253	19	<	<	X
ejpam-3454	253	20	1	1	NUM
ejpam-3454	253	21	⇒	⇒	NOUN
ejpam-3454	253	22	r0	r0	NOUN
ejpam-3454	253	23	<	<	X
ejpam-3454	253	24	1	1	NUM
ejpam-3454	253	25	.	.	PUNCT
ejpam-3454	254	1	all	all	DET
ejpam-3454	254	2	conditions	condition	NOUN
ejpam-3454	254	3	are	be	AUX
ejpam-3454	254	4	satisfied	satisfied	ADJ
ejpam-3454	254	5	if	if	SCONJ
ejpam-3454	254	6	and	and	CCONJ
ejpam-3454	254	7	only	only	ADV
ejpam-3454	254	8	if	if	SCONJ
ejpam-3454	254	9	r0	r0	NOUN
ejpam-3454	254	10	<	<	X
ejpam-3454	254	11	1	1	NUM
ejpam-3454	254	12	for	for	ADP
ejpam-3454	254	13	local	local	ADJ
ejpam-3454	254	14	asymptotic	asymptotic	ADJ
ejpam-3454	254	15	stability	stability	NOUN
ejpam-3454	254	16	of	of	ADP
ejpam-3454	254	17	the	the	DET
ejpam-3454	254	18	uninfected	uninfected	ADJ
ejpam-3454	254	19	steady	steady	ADJ
ejpam-3454	254	20	state	state	NOUN
ejpam-3454	254	21	.	.	PUNCT
ejpam-3454	255	1	this	this	PRON
ejpam-3454	255	2	completes	complete	VERB
ejpam-3454	255	3	the	the	DET
ejpam-3454	255	4	proof	proof	NOUN
ejpam-3454	255	5	.	.	PUNCT
ejpam-3454	256	1	next	next	ADV
ejpam-3454	256	2	we	we	PRON
ejpam-3454	256	3	consider	consider	VERB
ejpam-3454	256	4	the	the	DET
ejpam-3454	256	5	local	local	ADJ
ejpam-3454	256	6	stability	stability	NOUN
ejpam-3454	256	7	of	of	ADP
ejpam-3454	256	8	the	the	DET
ejpam-3454	256	9	unique	unique	ADJ
ejpam-3454	256	10	infected	infect	VERB
ejpam-3454	256	11	equilibrium	equilibrium	NOUN
ejpam-3454	256	12	pont	pont	NOUN
ejpam-3454	256	13	e+	e+	VERB
ejpam-3454	256	14	when	when	SCONJ
ejpam-3454	256	15	r0	r0	NOUN
ejpam-3454	256	16	>	>	X
ejpam-3454	256	17	1	1	NUM
ejpam-3454	256	18	and	and	CCONJ
ejpam-3454	256	19	(	(	PUNCT
ejpam-3454	256	20	1−	1−	NUM
ejpam-3454	256	21	ε)p−	ε)p−	PROPN
ejpam-3454	256	22	αδ	αδ	ADP
ejpam-3454	256	23	>	>	X
ejpam-3454	256	24	0	0	PROPN
ejpam-3454	256	25	.	.	PUNCT
ejpam-3454	257	1	using	use	VERB
ejpam-3454	257	2	(	(	PUNCT
ejpam-3454	257	3	16	16	NUM
ejpam-3454	257	4	)	)	PUNCT
ejpam-3454	257	5	and	and	CCONJ
ejpam-3454	257	6	the	the	DET
ejpam-3454	257	7	following	follow	VERB
ejpam-3454	257	8	equation	equation	NOUN
ejpam-3454	257	9	:	:	PUNCT
ejpam-3454	257	10	rt	rt	NOUN
ejpam-3454	257	11	∗	∗	NOUN
ejpam-3454	257	12	(	(	PUNCT
ejpam-3454	257	13	1−	1−	NUM
ejpam-3454	257	14	t	t	NOUN
ejpam-3454	257	15	∗	∗	NOUN
ejpam-3454	257	16	+	+	CCONJ
ejpam-3454	257	17	i∗	i∗	NOUN
ejpam-3454	257	18	tmax	tmax	NOUN
ejpam-3454	257	19	)	)	PUNCT
ejpam-3454	257	20	−	−	PROPN
ejpam-3454	258	1	(	(	PUNCT
ejpam-3454	258	2	1−	1−	NUM
ejpam-3454	258	3	η)βv	η)βv	PROPN
ejpam-3454	258	4	∗t	∗t	PROPN
ejpam-3454	258	5	∗	∗	NOUN
ejpam-3454	258	6	−	−	PROPN
ejpam-3454	258	7	dt	dt	NOUN
ejpam-3454	258	8	∗	∗	NOUN
ejpam-3454	258	9	=	=	SYM
ejpam-3454	258	10	0	0	NUM
ejpam-3454	258	11	,	,	PUNCT
ejpam-3454	258	12	the	the	DET
ejpam-3454	258	13	jacobian	jacobian	ADJ
ejpam-3454	258	14	matrix	matrix	NOUN
ejpam-3454	258	15	of	of	ADP
ejpam-3454	258	16	model	model	NOUN
ejpam-3454	258	17	(	(	PUNCT
ejpam-3454	258	18	1	1	NUM
ejpam-3454	258	19	)	)	PUNCT
ejpam-3454	258	20	at	at	ADP
ejpam-3454	258	21	infected	infect	VERB
ejpam-3454	258	22	equilibrium	equilibrium	NOUN
ejpam-3454	258	23	point	point	NOUN
ejpam-3454	258	24	e+	e+	NUM
ejpam-3454	258	25	is	be	AUX
ejpam-3454	258	26	:	:	PUNCT
ejpam-3454	258	27	j(e+	j(e+	X
ejpam-3454	258	28	)	)	PUNCT
ejpam-3454	259	1	=	=	PUNCT
ejpam-3454	259	2			PROPN
ejpam-3454	259	3	−	−	X
ejpam-3454	259	4	rt	rt	PROPN
ejpam-3454	259	5	tmax	tmax	ADP
ejpam-3454	259	6	−	−	PROPN
ejpam-3454	259	7	rt	rt	PROPN
ejpam-3454	259	8	tmax	tmax	ADV
ejpam-3454	259	9	−(1−	−(1−	ADP
ejpam-3454	259	10	η)βt	η)βt	PROPN
ejpam-3454	259	11	(	(	PUNCT
ejpam-3454	259	12	1−	1−	NUM
ejpam-3454	259	13	η)βv	η)βv	PROPN
ejpam-3454	259	14	−δ	−δ	NOUN
ejpam-3454	259	15	(	(	PUNCT
ejpam-3454	259	16	1−	1−	NUM
ejpam-3454	259	17	η)βt	η)βt	PROPN
ejpam-3454	259	18	−α(1−	−α(1−	PROPN
ejpam-3454	259	19	η)βv	η)βv	PROPN
ejpam-3454	259	20	(	(	PUNCT
ejpam-3454	259	21	1−	1−	NUM
ejpam-3454	259	22	ε)p	ε)p	X
ejpam-3454	259	23	−c−	−c−	NOUN
ejpam-3454	259	24	α(1−	α(1−	PROPN
ejpam-3454	259	25	η)βt	η)βt	PROPN
ejpam-3454	259	26	.	.	PUNCT
ejpam-3454	259	27			NOUN
ejpam-3454	259	28	.	.	PUNCT
ejpam-3454	260	1	we	we	PRON
ejpam-3454	260	2	have	have	VERB
ejpam-3454	260	3	the	the	DET
ejpam-3454	260	4	following	follow	VERB
ejpam-3454	260	5	characteristic	characteristic	ADJ
ejpam-3454	260	6	equation	equation	NOUN
ejpam-3454	260	7	associated	associate	VERB
ejpam-3454	260	8	with	with	ADP
ejpam-3454	260	9	the	the	DET
ejpam-3454	260	10	above	above	ADJ
ejpam-3454	260	11	jacobian	jacobian	ADJ
ejpam-3454	260	12	matrix	matrix	NOUN
ejpam-3454	260	13	j(e+	j(e+	PROPN
ejpam-3454	260	14	)	)	PUNCT
ejpam-3454	260	15	:	:	PUNCT
ejpam-3454	260	16	|j(e+)−	|j(e+)−	VERB
ejpam-3454	261	1	λi|	λi|	NOUN
ejpam-3454	261	2	=	=	PUNCT
ejpam-3454	261	3	λ3	λ3	PROPN
ejpam-3454	261	4	+	+	PROPN
ejpam-3454	261	5	a1λ	a1λ	PROPN
ejpam-3454	261	6	2	2	NUM
ejpam-3454	261	7	+	+	NOUN
ejpam-3454	261	8	a2λ+a3	a2λ+a3	NOUN
ejpam-3454	261	9	=	=	SYM
ejpam-3454	261	10	0	0	NUM
ejpam-3454	261	11	,	,	PUNCT
ejpam-3454	261	12	where	where	SCONJ
ejpam-3454	261	13	:	:	PUNCT
ejpam-3454	261	14	a1	a1	NOUN
ejpam-3454	261	15	=	=	SYM
ejpam-3454	261	16	α	α	PROPN
ejpam-3454	261	17	(	(	PUNCT
ejpam-3454	261	18	1−	1−	NUM
ejpam-3454	261	19	η)βt	η)βt	PROPN
ejpam-3454	261	20	∗	∗	NOUN
ejpam-3454	261	21	+	+	CCONJ
ejpam-3454	261	22	c+	c+	X
ejpam-3454	261	23	δ	δ	PROPN
ejpam-3454	261	24	+	+	ADP
ejpam-3454	261	25	t	t	PROPN
ejpam-3454	261	26	∗r	∗r	PROPN
ejpam-3454	261	27	tmax	tmax	PROPN
ejpam-3454	261	28	,	,	PUNCT
ejpam-3454	261	29	a2	a2	PROPN
ejpam-3454	261	30	=	=	SYM
ejpam-3454	261	31	α	α	PROPN
ejpam-3454	261	32	(	(	PUNCT
ejpam-3454	261	33	−η	−η	NOUN
ejpam-3454	261	34	+	+	CCONJ
ejpam-3454	261	35	1)t	1)t	PROPN
ejpam-3454	261	36	∗v	∗v	NOUN
ejpam-3454	261	37	∗β2η	∗β2η	PROPN
ejpam-3454	261	38	−	−	PROPN
ejpam-3454	261	39	α	α	PROPN
ejpam-3454	261	40	(	(	PUNCT
ejpam-3454	261	41	−η	−η	NOUN
ejpam-3454	261	42	+	+	CCONJ
ejpam-3454	261	43	1)t	1)t	PROPN
ejpam-3454	261	44	∗v	∗v	NOUN
ejpam-3454	261	45	∗β2	∗β2	NOUN
ejpam-3454	261	46	−	−	PROPN
ejpam-3454	262	1	t	t	PROPN
ejpam-3454	262	2	∗β	∗β	PROPN
ejpam-3454	262	3	εηp+	εηp+	PROPN
ejpam-3454	262	4	α	α	PROPN
ejpam-3454	262	5	(	(	PUNCT
ejpam-3454	262	6	1−	1−	NUM
ejpam-3454	262	7	η)t	η)t	NOUN
ejpam-3454	262	8	∗βδ	∗βδ	VERB
ejpam-3454	262	9	+	+	NUM
ejpam-3454	262	10	t	t	NOUN
ejpam-3454	262	11	∗βε	∗βε	PROPN
ejpam-3454	262	12	p	p	X
ejpam-3454	262	13	+	+	PROPN
ejpam-3454	262	14	t	t	PROPN
ejpam-3454	262	15	∗βηp−	∗βηp−	PUNCT
ejpam-3454	262	16	t	t	PROPN
ejpam-3454	262	17	∗βp+	∗βp+	NOUN
ejpam-3454	262	18	cδ	cδ	NOUN
ejpam-3454	262	19	+	+	CCONJ
ejpam-3454	262	20	1	1	NUM
ejpam-3454	262	21	tmax	tmax	ADP
ejpam-3454	262	22	(	(	PUNCT
ejpam-3454	262	23	t	t	NOUN
ejpam-3454	262	24	∗2βrα	∗2βrα	PROPN
ejpam-3454	262	25	(	(	PUNCT
ejpam-3454	262	26	1−	1−	NUM
ejpam-3454	262	27	η)−	η)−	PROPN
ejpam-3454	262	28	t	t	NOUN
ejpam-3454	262	29	∗v	∗v	NOUN
ejpam-3454	262	30	∗βηr	∗βηr	PUNCT
ejpam-3454	262	31	+	+	NUM
ejpam-3454	262	32	t	t	NOUN
ejpam-3454	262	33	∗v	∗v	NOUN
ejpam-3454	262	34	∗βr	∗βr	PROPN
ejpam-3454	262	35	+	+	NUM
ejpam-3454	262	36	t	t	X
ejpam-3454	262	37	∗cr	∗cr	PUNCT
ejpam-3454	262	38	+	+	NUM
ejpam-3454	262	39	t	t	PROPN
ejpam-3454	262	40	∗δ	∗δ	NOUN
ejpam-3454	262	41	r	r	NOUN
ejpam-3454	262	42	)	)	PUNCT
ejpam-3454	262	43	,	,	PUNCT
ejpam-3454	262	44	i.e.	i.e.	X
ejpam-3454	262	45	a2	a2	PROPN
ejpam-3454	262	46	=	=	SYM
ejpam-3454	262	47	α(1−	α(1−	PROPN
ejpam-3454	263	1	η)βt	η)βt	PROPN
ejpam-3454	263	2	∗	∗	NOUN
ejpam-3454	263	3	(	(	PUNCT
ejpam-3454	263	4	δ	δ	PROPN
ejpam-3454	263	5	−	−	PROPN
ejpam-3454	263	6	(	(	PUNCT
ejpam-3454	263	7	1−	1−	PROPN
ejpam-3454	263	8	η)βv	η)βv	PROPN
ejpam-3454	263	9	∗	∗	NOUN
ejpam-3454	263	10	)	)	PUNCT
ejpam-3454	264	1	+	+	NUM
ejpam-3454	264	2	rt	rt	PROPN
ejpam-3454	264	3	∗	∗	NOUN
ejpam-3454	264	4	tmax	tmax	PROPN
ejpam-3454	264	5	(	(	PUNCT
ejpam-3454	264	6	1−	1−	NUM
ejpam-3454	264	7	η)βv	η)βv	PROPN
ejpam-3454	264	8	∗	∗	NOUN
ejpam-3454	264	9	+	+	CCONJ
ejpam-3454	264	10	(	(	PUNCT
ejpam-3454	264	11	1−	1−	NUM
ejpam-3454	264	12	η)βt	η)βt	PROPN
ejpam-3454	264	13	∗	∗	NOUN
ejpam-3454	264	14	(	(	PUNCT
ejpam-3454	264	15	α	α	PROPN
ejpam-3454	264	16	rt	rt	PROPN
ejpam-3454	264	17	∗	∗	NOUN
ejpam-3454	264	18	tmax	tmax	ADP
ejpam-3454	264	19	−	−	PROPN
ejpam-3454	264	20	(	(	PUNCT
ejpam-3454	264	21	1−	1−	NUM
ejpam-3454	264	22	ε)p	ε)p	X
ejpam-3454	264	23	)	)	PUNCT
ejpam-3454	265	1	+	+	CCONJ
ejpam-3454	265	2	rt	rt	PROPN
ejpam-3454	265	3	∗	∗	NOUN
ejpam-3454	265	4	tmax	tmax	PROPN
ejpam-3454	265	5	(	(	PUNCT
ejpam-3454	265	6	c+	c+	X
ejpam-3454	265	7	δ	δ	PROPN
ejpam-3454	265	8	)	)	PUNCT
ejpam-3454	265	9	+	+	CCONJ
ejpam-3454	265	10	δc	δc	NOUN
ejpam-3454	265	11	a3	a3	NOUN
ejpam-3454	265	12	=	=	PUNCT
ejpam-3454	265	13	(	(	PUNCT
ejpam-3454	265	14	−v	−v	NOUN
ejpam-3454	265	15	∗β2εη2p+	∗β2εη2p+	PROPN
ejpam-3454	265	16	α	α	PROPN
ejpam-3454	265	17	(	(	PUNCT
ejpam-3454	265	18	1−	1−	NUM
ejpam-3454	265	19	η)v	η)v	NOUN
ejpam-3454	265	20	∗β2δη	∗β2δη	X
ejpam-3454	265	21	+	+	NUM
ejpam-3454	265	22	2v	2v	PROPN
ejpam-3454	265	23	∗β2εηp+	∗β2εηp+	NOUN
ejpam-3454	265	24	v	v	ADP
ejpam-3454	265	25	∗β2η2p−	∗β2η2p−	NOUN
ejpam-3454	265	26	α	α	NOUN
ejpam-3454	265	27	(	(	PUNCT
ejpam-3454	265	28	1−	1−	NUM
ejpam-3454	265	29	η)v	η)v	NOUN
ejpam-3454	265	30	∗β2δ	∗β2δ	NOUN
ejpam-3454	265	31	−	−	PROPN
ejpam-3454	265	32	v	v	NOUN
ejpam-3454	265	33	∗β2εp	∗β2εp	PUNCT
ejpam-3454	265	34	)	)	PUNCT
ejpam-3454	265	35	t	t	PROPN
ejpam-3454	265	36	∗	∗	NOUN
ejpam-3454	265	37	a.	a.	NOUN
ejpam-3454	265	38	nangue	nangue	NOUN
ejpam-3454	265	39	,	,	PUNCT
ejpam-3454	265	40	t.	t.	PROPN
ejpam-3454	265	41	donfack	donfack	PROPN
ejpam-3454	265	42	,	,	PUNCT
ejpam-3454	265	43	d.	d.	PROPN
ejpam-3454	265	44	a.	a.	PROPN
ejpam-3454	265	45	ndode	ndode	PROPN
ejpam-3454	265	46	yafago	yafago	PROPN
ejpam-3454	265	47	/	/	SYM
ejpam-3454	265	48	eur	eur	PROPN
ejpam-3454	265	49	.	.	PUNCT
ejpam-3454	266	1	j.	j.	PROPN
ejpam-3454	266	2	pure	pure	PROPN
ejpam-3454	266	3	appl	appl	PROPN
ejpam-3454	266	4	.	.	PROPN
ejpam-3454	266	5	math	math	PROPN
ejpam-3454	266	6	,	,	PUNCT
ejpam-3454	266	7	12	12	NUM
ejpam-3454	266	8	(	(	PUNCT
ejpam-3454	266	9	3	3	NUM
ejpam-3454	266	10	)	)	PUNCT
ejpam-3454	266	11	(	(	PUNCT
ejpam-3454	266	12	2019	2019	NUM
ejpam-3454	266	13	)	)	PUNCT
ejpam-3454	266	14	,	,	PUNCT
ejpam-3454	266	15	944	944	NUM
ejpam-3454	266	16	-	-	SYM
ejpam-3454	266	17	959	959	NUM
ejpam-3454	266	18	956	956	NUM
ejpam-3454	266	19	+	+	SYM
ejpam-3454	266	20	t	t	NOUN
ejpam-3454	266	21	∗	∗	NOUN
ejpam-3454	266	22	tmax	tmax	PROPN
ejpam-3454	266	23	(	(	PUNCT
ejpam-3454	266	24	−t	−t	PROPN
ejpam-3454	266	25	∗βεηpr	∗βεηpr	NOUN
ejpam-3454	266	26	+	+	NUM
ejpam-3454	266	27	t	t	PROPN
ejpam-3454	266	28	∗βδrα	∗βδrα	PROPN
ejpam-3454	266	29	(	(	PUNCT
ejpam-3454	266	30	1−	1−	NUM
ejpam-3454	266	31	η	η	NOUN
ejpam-3454	266	32	)	)	PUNCT
ejpam-3454	267	1	+	+	NUM
ejpam-3454	267	2	t	t	NOUN
ejpam-3454	267	3	∗βεpr	∗βεpr	NOUN
ejpam-3454	268	1	+	+	CCONJ
ejpam-3454	268	2	t	t	PROPN
ejpam-3454	268	3	∗βηpr	∗βηpr	NOUN
ejpam-3454	268	4	−	−	PROPN
ejpam-3454	268	5	v	v	ADP
ejpam-3454	268	6	∗βcηr	∗βcηr	NUM
ejpam-3454	268	7	−	−	PROPN
ejpam-3454	268	8	t	t	NOUN
ejpam-3454	268	9	∗βpr	∗βpr	PROPN
ejpam-3454	269	1	+	+	CCONJ
ejpam-3454	269	2	v	v	ADP
ejpam-3454	269	3	∗βcr	∗βcr	PROPN
ejpam-3454	269	4	+	+	NUM
ejpam-3454	269	5	cδr	cδr	NOUN
ejpam-3454	269	6	)	)	PUNCT
ejpam-3454	269	7	−	−	PROPN
ejpam-3454	270	1	(	(	PUNCT
ejpam-3454	270	2	2v	2v	PROPN
ejpam-3454	270	3	∗β2ηp−	∗β2ηp−	PROPN
ejpam-3454	270	4	v	v	PROPN
ejpam-3454	270	5	∗β2p	∗β2p	PROPN
ejpam-3454	270	6	)	)	PUNCT
ejpam-3454	270	7	t	t	PROPN
ejpam-3454	270	8	∗.	∗.	PUNCT
ejpam-3454	270	9	obviously	obviously	ADV
ejpam-3454	270	10	we	we	PRON
ejpam-3454	270	11	have	have	AUX
ejpam-3454	270	12	:	:	PUNCT
ejpam-3454	270	13	a1	a1	VERB
ejpam-3454	270	14	>	>	X
ejpam-3454	270	15	0	0	PUNCT
ejpam-3454	270	16	and	and	CCONJ
ejpam-3454	270	17	a2	a2	PROPN
ejpam-3454	270	18	>	>	X
ejpam-3454	270	19	0	0	PUNCT
ejpam-3454	271	1	if	if	SCONJ
ejpam-3454	271	2	and	and	CCONJ
ejpam-3454	271	3	only	only	ADV
ejpam-3454	271	4	if	if	SCONJ
ejpam-3454	271	5	α	α	PROPN
ejpam-3454	271	6	rt	rt	PROPN
ejpam-3454	271	7	∗	∗	NOUN
ejpam-3454	271	8	tmax	tmax	ADP
ejpam-3454	271	9	−	−	PROPN
ejpam-3454	271	10	(	(	PUNCT
ejpam-3454	271	11	1−	1−	NUM
ejpam-3454	271	12	ε)p	ε)p	X
ejpam-3454	271	13	>	>	X
ejpam-3454	271	14	0	0	PUNCT
ejpam-3454	271	15	and	and	CCONJ
ejpam-3454	271	16	δ	δ	PROPN
ejpam-3454	271	17	−	−	PROPN
ejpam-3454	271	18	(	(	PUNCT
ejpam-3454	271	19	1−	1−	NUM
ejpam-3454	271	20	η)βv	η)βv	PROPN
ejpam-3454	271	21	∗	∗	VERB
ejpam-3454	271	22	>	>	X
ejpam-3454	271	23	0	0	X
ejpam-3454	271	24	.	.	PUNCT
ejpam-3454	272	1	let	let	VERB
ejpam-3454	272	2	∆	∆	PROPN
ejpam-3454	272	3	=	=	PUNCT
ejpam-3454	272	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3454	272	5	a1	a1	NOUN
ejpam-3454	272	6	1	1	NUM
ejpam-3454	272	7	a3	a3	NOUN
ejpam-3454	272	8	a2	a2	PROPN
ejpam-3454	272	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3454	272	10	=	=	PUNCT
ejpam-3454	272	11	a1a2	a1a2	PROPN
ejpam-3454	272	12	−a3	−a3	PROPN
ejpam-3454	272	13	.	.	PUNCT
ejpam-3454	273	1	then	then	ADV
ejpam-3454	273	2	,	,	PUNCT
ejpam-3454	273	3	by	by	ADP
ejpam-3454	273	4	routh	routh	PROPN
ejpam-3454	273	5	-	-	PUNCT
ejpam-3454	273	6	hurwitz	hurwitz	PROPN
ejpam-3454	273	7	criterion	criterion	NOUN
ejpam-3454	273	8	,	,	PUNCT
ejpam-3454	273	9	we	we	PRON
ejpam-3454	273	10	have	have	VERB
ejpam-3454	273	11	the	the	DET
ejpam-3454	273	12	following	follow	VERB
ejpam-3454	273	13	result	result	NOUN
ejpam-3454	273	14	.	.	PUNCT
ejpam-3454	274	1	theorem	theorem	ADJ
ejpam-3454	274	2	6	6	NUM
ejpam-3454	274	3	.	.	X
ejpam-3454	274	4	for	for	ADP
ejpam-3454	274	5	model	model	NOUN
ejpam-3454	274	6	(	(	PUNCT
ejpam-3454	274	7	1	1	NUM
ejpam-3454	274	8	)	)	PUNCT
ejpam-3454	274	9	,	,	PUNCT
ejpam-3454	274	10	when	when	SCONJ
ejpam-3454	274	11	α	α	PROPN
ejpam-3454	274	12	rt	rt	PROPN
ejpam-3454	274	13	∗	∗	NOUN
ejpam-3454	274	14	tmax	tmax	ADP
ejpam-3454	274	15	−	−	PROPN
ejpam-3454	274	16	(	(	PUNCT
ejpam-3454	274	17	1	1	NUM
ejpam-3454	274	18	−	−	NOUN
ejpam-3454	274	19	ε)p	ε)p	X
ejpam-3454	274	20	>	>	X
ejpam-3454	274	21	0	0	PUNCT
ejpam-3454	274	22	and	and	CCONJ
ejpam-3454	274	23	δ	δ	PROPN
ejpam-3454	274	24	−	−	PROPN
ejpam-3454	274	25	(	(	PUNCT
ejpam-3454	274	26	1	1	NUM
ejpam-3454	274	27	−	−	PROPN
ejpam-3454	274	28	η)βv	η)βv	PROPN
ejpam-3454	275	1	∗	∗	NOUN
ejpam-3454	275	2	>	>	X
ejpam-3454	275	3	0	0	NUM
ejpam-3454	275	4	are	be	AUX
ejpam-3454	275	5	valid	valid	ADJ
ejpam-3454	275	6	,	,	PUNCT
ejpam-3454	275	7	then	then	ADV
ejpam-3454	275	8	the	the	DET
ejpam-3454	275	9	unique	unique	ADJ
ejpam-3454	275	10	infected	infected	ADJ
ejpam-3454	275	11	equilibrium	equilibrium	NOUN
ejpam-3454	275	12	e+	e+	VERB
ejpam-3454	275	13	is	be	AUX
ejpam-3454	275	14	locally	locally	ADV
ejpam-3454	275	15	asymptotically	asymptotically	ADV
ejpam-3454	275	16	stable	stable	ADJ
ejpam-3454	275	17	if	if	SCONJ
ejpam-3454	275	18	∆	∆	PROPN
ejpam-3454	275	19	>	>	X
ejpam-3454	275	20	0	0	PUNCT
ejpam-3454	275	21	and	and	CCONJ
ejpam-3454	275	22	unstable	unstable	ADJ
ejpam-3454	275	23	if	if	SCONJ
ejpam-3454	275	24	∆	∆	PROPN
ejpam-3454	275	25	<	<	X
ejpam-3454	275	26	0	0	X
ejpam-3454	275	27	.	.	PUNCT
ejpam-3454	276	1	especially	especially	ADV
ejpam-3454	276	2	we	we	PRON
ejpam-3454	276	3	have	have	AUX
ejpam-3454	276	4	:	:	PUNCT
ejpam-3454	276	5	corollary	corollary	ADJ
ejpam-3454	276	6	1	1	X
ejpam-3454	276	7	.	.	PUNCT
ejpam-3454	276	8	suppose	suppose	VERB
ejpam-3454	276	9	that	that	SCONJ
ejpam-3454	276	10	rt	rt	PROPN
ejpam-3454	276	11	∗	∗	NOUN
ejpam-3454	276	12	tmax	tmax	ADP
ejpam-3454	276	13	c−	c−	NOUN
ejpam-3454	276	14	(	(	PUNCT
ejpam-3454	276	15	1−	1−	NUM
ejpam-3454	276	16	η)βt	η)βt	PROPN
ejpam-3454	276	17	∗(αδ	∗(αδ	PART
ejpam-3454	276	18	+	+	CCONJ
ejpam-3454	276	19	(	(	PUNCT
ejpam-3454	276	20	1−	1−	NUM
ejpam-3454	276	21	ε)p	ε)p	ADV
ejpam-3454	276	22	)	)	PUNCT
ejpam-3454	276	23	>	>	X
ejpam-3454	276	24	0	0	NUM
ejpam-3454	276	25	,	,	PUNCT
ejpam-3454	276	26	then	then	ADV
ejpam-3454	276	27	∆	∆	PROPN
ejpam-3454	276	28	>	>	X
ejpam-3454	276	29	0	0	PUNCT
ejpam-3454	276	30	is	be	AUX
ejpam-3454	276	31	always	always	ADV
ejpam-3454	276	32	valid	valid	ADJ
ejpam-3454	276	33	,	,	PUNCT
ejpam-3454	276	34	i.e.	i.e.	X
ejpam-3454	276	35	e+	e+	X
ejpam-3454	276	36	is	be	AUX
ejpam-3454	276	37	locally	locally	ADV
ejpam-3454	276	38	asymptotically	asymptotically	ADV
ejpam-3454	276	39	stable	stable	ADJ
ejpam-3454	276	40	only	only	ADV
ejpam-3454	276	41	if	if	SCONJ
ejpam-3454	276	42	it	it	PRON
ejpam-3454	276	43	exists	exist	VERB
ejpam-3454	276	44	in	in	ADP
ejpam-3454	276	45	this	this	DET
ejpam-3454	276	46	case	case	NOUN
ejpam-3454	276	47	.	.	PUNCT
ejpam-3454	277	1	proof	proof	NOUN
ejpam-3454	277	2	.	.	PUNCT
ejpam-3454	278	1	we	we	PRON
ejpam-3454	278	2	have	have	VERB
ejpam-3454	278	3	:	:	PUNCT
ejpam-3454	278	4	∆	∆	PROPN
ejpam-3454	278	5	=	=	PUNCT
ejpam-3454	278	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3454	278	7	a1	a1	NOUN
ejpam-3454	278	8	1	1	NUM
ejpam-3454	278	9	a3	a3	NOUN
ejpam-3454	278	10	a2	a2	PROPN
ejpam-3454	278	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3454	278	12	=	=	PUNCT
ejpam-3454	278	13	a1a2	a1a2	PROPN
ejpam-3454	278	14	−a3	−a3	PROPN
ejpam-3454	278	15	=	=	SYM
ejpam-3454	278	16	t	t	PROPN
ejpam-3454	278	17	∗βδηp−	∗βδηp−	NOUN
ejpam-3454	278	18	t	t	PROPN
ejpam-3454	278	19	∗v	∗v	PROPN
ejpam-3454	278	20	∗β2η2p+	∗β2η2p+	PROPN
ejpam-3454	278	21	t	t	NOUN
ejpam-3454	278	22	∗v	∗v	NOUN
ejpam-3454	278	23	∗β2εp+	∗β2εp+	NUM
ejpam-3454	278	24	2	2	NUM
ejpam-3454	278	25	t	t	NOUN
ejpam-3454	278	26	∗v	∗v	NOUN
ejpam-3454	278	27	∗β2ηp+	∗β2ηp+	PROPN
ejpam-3454	278	28	t	t	PROPN
ejpam-3454	278	29	∗βcεp+	∗βcεp+	NOUN
ejpam-3454	278	30	t	t	PROPN
ejpam-3454	278	31	∗β	∗β	PROPN
ejpam-3454	278	32	cηp+	cηp+	PROPN
ejpam-3454	278	33	t	t	NOUN
ejpam-3454	278	34	∗βδεp+	∗βδεp+	X
ejpam-3454	278	35	c2δ	c2δ	PUNCT
ejpam-3454	279	1	+	+	CCONJ
ejpam-3454	279	2	cδ2	cδ2	PROPN
ejpam-3454	279	3	+	+	NUM
ejpam-3454	279	4	t	t	NOUN
ejpam-3454	279	5	∗	∗	NOUN
ejpam-3454	279	6	(	(	PUNCT
ejpam-3454	279	7	α	α	PROPN
ejpam-3454	279	8	(	(	PUNCT
ejpam-3454	279	9	1−	1−	NUM
ejpam-3454	279	10	η)t	η)t	NOUN
ejpam-3454	279	11	∗β2ε	∗β2ε	NOUN
ejpam-3454	279	12	p+	p+	VERB
ejpam-3454	279	13	α	α	X
ejpam-3454	279	14	(	(	PUNCT
ejpam-3454	279	15	1−	1−	NUM
ejpam-3454	279	16	η)t	η)t	NOUN
ejpam-3454	279	17	∗β2ηp−	∗β2ηp−	PROPN
ejpam-3454	279	18	α	α	PROPN
ejpam-3454	279	19	(	(	PUNCT
ejpam-3454	279	20	1−	1−	NUM
ejpam-3454	279	21	η)v	η)v	NOUN
ejpam-3454	279	22	∗β2c+	∗β2c+	ADJ
ejpam-3454	279	23	2α	2α	NOUN
ejpam-3454	279	24	(	(	PUNCT
ejpam-3454	279	25	1−	1−	NUM
ejpam-3454	279	26	η)βcδ	η)βcδ	NOUN
ejpam-3454	279	27	+	+	CCONJ
ejpam-3454	279	28	(	(	PUNCT
ejpam-3454	279	29	α	α	PROPN
ejpam-3454	279	30	(	(	PUNCT
ejpam-3454	279	31	1−	1−	NUM
ejpam-3454	279	32	η))2	η))2	NOUN
ejpam-3454	279	33	t	t	PROPN
ejpam-3454	279	34	∗v	∗v	PROPN
ejpam-3454	279	35	∗β3η	∗β3η	PROPN
ejpam-3454	279	36	)	)	PUNCT
ejpam-3454	280	1	+	+	NUM
ejpam-3454	280	2	t	t	NOUN
ejpam-3454	280	3	∗	∗	NOUN
ejpam-3454	280	4	(	(	PUNCT
ejpam-3454	280	5	α	α	PROPN
ejpam-3454	280	6	(	(	PUNCT
ejpam-3454	280	7	1−	1−	NUM
ejpam-3454	280	8	η)v	η)v	X
ejpam-3454	280	9	∗β2cη	∗β2cη	PUNCT
ejpam-3454	281	1	+	+	CCONJ
ejpam-3454	281	2	v	v	NUM
ejpam-3454	281	3	∗β2εη2p−	∗β2εη2p−	NOUN
ejpam-3454	281	4	2v	2v	PROPN
ejpam-3454	281	5	β2εηp−	β2εηp−	NOUN
ejpam-3454	281	6	βcεηp−	βcεηp−	NOUN
ejpam-3454	281	7	βδεηp−	βδεηp−	NOUN
ejpam-3454	281	8	α	α	NOUN
ejpam-3454	281	9	(	(	PUNCT
ejpam-3454	281	10	1−	1−	NUM
ejpam-3454	281	11	η)t	η)t	X
ejpam-3454	281	12	∗β2εηp	∗β2εηp	PROPN
ejpam-3454	281	13	)	)	PUNCT
ejpam-3454	282	1	+	+	NUM
ejpam-3454	282	2	t	t	NOUN
ejpam-3454	282	3	∗	∗	NOUN
ejpam-3454	282	4	tmax	tmax	PROPN
ejpam-3454	282	5	(	(	PUNCT
ejpam-3454	282	6	(	(	PUNCT
ejpam-3454	282	7	α	α	X
ejpam-3454	282	8	(	(	PUNCT
ejpam-3454	282	9	1−	1−	NUM
ejpam-3454	282	10	η))2	η))2	NOUN
ejpam-3454	282	11	t	t	NOUN
ejpam-3454	282	12	∗2β2r	∗2β2r	NOUN
ejpam-3454	282	13	+	+	CCONJ
ejpam-3454	282	14	2α	2α	NOUN
ejpam-3454	282	15	(	(	PUNCT
ejpam-3454	282	16	1−	1−	NUM
ejpam-3454	282	17	η)t	η)t	NOUN
ejpam-3454	282	18	∗βcr	∗βcr	PROPN
ejpam-3454	282	19	+	+	NUM
ejpam-3454	282	20	2α	2α	NOUN
ejpam-3454	282	21	(	(	PUNCT
ejpam-3454	282	22	1−	1−	NUM
ejpam-3454	282	23	η)t	η)t	NOUN
ejpam-3454	283	1	∗βδr	∗βδr	PROPN
ejpam-3454	283	2	−	−	PROPN
ejpam-3454	283	3	v	v	PROPN
ejpam-3454	283	4	∗βδηr	∗βδηr	NOUN
ejpam-3454	283	5	+	+	CCONJ
ejpam-3454	283	6	v	v	ADP
ejpam-3454	283	7	∗βδr	∗βδr	PROPN
ejpam-3454	283	8	+	+	CCONJ
ejpam-3454	283	9	c2r	c2r	NOUN
ejpam-3454	283	10	)	)	PUNCT
ejpam-3454	284	1	+	+	CCONJ
ejpam-3454	284	2	t	t	NOUN
ejpam-3454	284	3	∗	∗	NOUN
ejpam-3454	284	4	tmax	tmax	PROPN
ejpam-3454	284	5	(	(	PUNCT
ejpam-3454	284	6	α	α	PROPN
ejpam-3454	284	7	(	(	PUNCT
ejpam-3454	284	8	1−	1−	NUM
ejpam-3454	284	9	η)t	η)t	NOUN
ejpam-3454	284	10	∗2βr2	∗2βr2	X
ejpam-3454	284	11	−	−	PROPN
ejpam-3454	284	12	t	t	NOUN
ejpam-3454	285	1	∗v	∗v	PROPN
ejpam-3454	285	2	∗βηr2	∗βηr2	PROPN
ejpam-3454	285	3	+	+	NUM
ejpam-3454	285	4	t	t	PROPN
ejpam-3454	285	5	∗v	∗v	PROPN
ejpam-3454	285	6	∗βr2	∗βr2	PROPN
ejpam-3454	286	1	+	+	CCONJ
ejpam-3454	286	2	t	t	NOUN
ejpam-3454	286	3	∗cr2	∗cr2	VERB
ejpam-3454	286	4	+	+	CCONJ
ejpam-3454	286	5	t	t	X
ejpam-3454	286	6	∗δr2	∗δr2	NOUN
ejpam-3454	287	1	+	+	CCONJ
ejpam-3454	288	1	2cδr	2cδr	PROPN
ejpam-3454	288	2	+	+	CCONJ
ejpam-3454	288	3	δ2r	δ2r	NOUN
ejpam-3454	288	4	)	)	PUNCT
ejpam-3454	288	5	−	−	PROPN
ejpam-3454	289	1	(	(	PUNCT
ejpam-3454	289	2	α	α	X
ejpam-3454	289	3	(	(	PUNCT
ejpam-3454	289	4	1−	1−	NUM
ejpam-3454	289	5	η))2	η))2	NOUN
ejpam-3454	289	6	t	t	PROPN
ejpam-3454	289	7	∗2v	∗2v	PROPN
ejpam-3454	289	8	∗β3	∗β3	PROPN
ejpam-3454	290	1	+	+	CCONJ
ejpam-3454	290	2	(	(	PUNCT
ejpam-3454	290	3	α	α	PROPN
ejpam-3454	290	4	(	(	PUNCT
ejpam-3454	290	5	1−	1−	NUM
ejpam-3454	290	6	η))2	η))2	NOUN
ejpam-3454	290	7	t	t	X
ejpam-3454	290	8	∗2β2δ	∗2β2δ	NOUN
ejpam-3454	290	9	−	−	PROPN
ejpam-3454	290	10	α	α	PROPN
ejpam-3454	290	11	(	(	PUNCT
ejpam-3454	290	12	1−	1−	NUM
ejpam-3454	290	13	η)t	η)t	NOUN
ejpam-3454	290	14	∗2β2p+	∗2β2p+	NOUN
ejpam-3454	290	15	α	α	X
ejpam-3454	290	16	(	(	PUNCT
ejpam-3454	290	17	1−	1−	NUM
ejpam-3454	290	18	η)t	η)t	NOUN
ejpam-3454	290	19	∗βδ2	∗βδ2	NOUN
ejpam-3454	290	20	−	−	PROPN
ejpam-3454	290	21	t	t	PROPN
ejpam-3454	290	22	∗v	∗v	NOUN
ejpam-3454	290	23	∗β2p	∗β2p	NOUN
ejpam-3454	290	24	−	−	PROPN
ejpam-3454	290	25	t	t	PROPN
ejpam-3454	290	26	∗βcp−	∗βcp−	PROPN
ejpam-3454	290	27	t	t	PROPN
ejpam-3454	290	28	∗βδp	∗βδp	PROPN
ejpam-3454	290	29	,	,	PUNCT
ejpam-3454	290	30	i.e	i.e	ADJ
ejpam-3454	290	31	,	,	PUNCT
ejpam-3454	290	32	∆	∆	X
ejpam-3454	290	33	=	=	SYM
ejpam-3454	290	34	(	(	PUNCT
ejpam-3454	290	35	1−	1−	NUM
ejpam-3454	290	36	η)βt	η)βt	PROPN
ejpam-3454	290	37	∗	∗	NOUN
ejpam-3454	290	38	(	(	PUNCT
ejpam-3454	290	39	α	α	PROPN
ejpam-3454	290	40	rt	rt	PROPN
ejpam-3454	290	41	∗	∗	NOUN
ejpam-3454	290	42	tmax	tmax	ADP
ejpam-3454	290	43	−	−	PROPN
ejpam-3454	290	44	(	(	PUNCT
ejpam-3454	290	45	1−	1−	NUM
ejpam-3454	290	46	ε)p	ε)p	X
ejpam-3454	290	47	)	)	PUNCT
ejpam-3454	290	48	(	(	PUNCT
ejpam-3454	290	49	c+	c+	X
ejpam-3454	290	50	α(1−	α(1−	X
ejpam-3454	291	1	η)βt	η)βt	PROPN
ejpam-3454	291	2	∗	∗	NOUN
ejpam-3454	291	3	+	+	CCONJ
ejpam-3454	291	4	δ	δ	NOUN
ejpam-3454	291	5	)	)	PUNCT
ejpam-3454	292	1	+	+	NUM
ejpam-3454	292	2	δc2	δc2	NOUN
ejpam-3454	292	3	+	+	CCONJ
ejpam-3454	292	4	δ2c+	δ2c+	X
ejpam-3454	292	5	(	(	PUNCT
ejpam-3454	292	6	1−	1−	NUM
ejpam-3454	292	7	η)βt	η)βt	PROPN
ejpam-3454	292	8	∗αδc	∗αδc	PUNCT
ejpam-3454	292	9	+	+	NOUN
ejpam-3454	292	10	(	(	PUNCT
ejpam-3454	292	11	c+	c+	PROPN
ejpam-3454	292	12	δ	δ	PROPN
ejpam-3454	292	13	)	)	PUNCT
ejpam-3454	292	14	rt	rt	PROPN
ejpam-3454	292	15	∗	∗	NOUN
ejpam-3454	292	16	tmax	tmax	PROPN
ejpam-3454	292	17	(	(	PUNCT
ejpam-3454	292	18	rt	rt	PROPN
ejpam-3454	292	19	∗	∗	X
ejpam-3454	292	20	tmax	tmax	ADV
ejpam-3454	292	21	+	+	CCONJ
ejpam-3454	292	22	c+	c+	X
ejpam-3454	292	23	α(1−	α(1−	PUNCT
ejpam-3454	293	1	η)βt	η)βt	PROPN
ejpam-3454	293	2	∗	∗	NOUN
ejpam-3454	293	3	+	+	NUM
ejpam-3454	293	4	δ	δ	NOUN
ejpam-3454	293	5	)	)	PUNCT
ejpam-3454	294	1	+	+	CCONJ
ejpam-3454	294	2	(	(	PUNCT
ejpam-3454	294	3	1−	1−	NUM
ejpam-3454	294	4	η)βv	η)βv	PROPN
ejpam-3454	294	5	∗	∗	NOUN
ejpam-3454	294	6	(	(	PUNCT
ejpam-3454	294	7	rt	rt	NOUN
ejpam-3454	294	8	∗	∗	NOUN
ejpam-3454	294	9	tmax	tmax	ADP
ejpam-3454	294	10	c−	c−	NOUN
ejpam-3454	294	11	(	(	PUNCT
ejpam-3454	294	12	1−	1−	NUM
ejpam-3454	294	13	η)βt	η)βt	PROPN
ejpam-3454	294	14	∗(αδ	∗(αδ	PART
ejpam-3454	294	15	+	+	CCONJ
ejpam-3454	294	16	(	(	PUNCT
ejpam-3454	294	17	1−	1−	NUM
ejpam-3454	294	18	ε)p	ε)p	ADV
ejpam-3454	294	19	)	)	PUNCT
ejpam-3454	294	20	)	)	PUNCT
ejpam-3454	295	1	+	+	NUM
ejpam-3454	295	2	α(1−	α(1−	PROPN
ejpam-3454	295	3	η)βt	η)βt	PROPN
ejpam-3454	295	4	∗(δ	∗(δ	NOUN
ejpam-3454	295	5	−	−	PROPN
ejpam-3454	295	6	(	(	PUNCT
ejpam-3454	295	7	1−	1−	NUM
ejpam-3454	295	8	η)βv	η)βv	PROPN
ejpam-3454	295	9	∗	∗	NOUN
ejpam-3454	295	10	)	)	PUNCT
ejpam-3454	295	11	(	(	PUNCT
ejpam-3454	295	12	rt	rt	NOUN
ejpam-3454	295	13	∗	∗	X
ejpam-3454	295	14	tmax	tmax	ADV
ejpam-3454	295	15	+	+	CCONJ
ejpam-3454	295	16	c+	c+	X
ejpam-3454	295	17	α(1−	α(1−	PUNCT
ejpam-3454	296	1	η)βt	η)βt	PROPN
ejpam-3454	296	2	∗	∗	NOUN
ejpam-3454	296	3	+	+	NUM
ejpam-3454	296	4	δ	δ	NOUN
ejpam-3454	296	5	)	)	PUNCT
ejpam-3454	296	6	.	.	PUNCT
ejpam-3454	297	1	clearly	clearly	ADV
ejpam-3454	297	2	∆	∆	VERB
ejpam-3454	297	3	>	>	X
ejpam-3454	297	4	0	0	PUNCT
ejpam-3454	298	1	if	if	SCONJ
ejpam-3454	298	2	and	and	CCONJ
ejpam-3454	298	3	only	only	ADV
ejpam-3454	298	4	if	if	SCONJ
ejpam-3454	298	5	rt	rt	PROPN
ejpam-3454	298	6	∗	∗	VERB
ejpam-3454	298	7	tmax	tmax	ADP
ejpam-3454	298	8	c−	c−	NOUN
ejpam-3454	298	9	(	(	PUNCT
ejpam-3454	298	10	1−	1−	NUM
ejpam-3454	298	11	η)βt	η)βt	PROPN
ejpam-3454	298	12	∗(αδ	∗(αδ	PART
ejpam-3454	298	13	+	+	CCONJ
ejpam-3454	298	14	(	(	PUNCT
ejpam-3454	298	15	1−	1−	NUM
ejpam-3454	298	16	ε)p	ε)p	ADV
ejpam-3454	298	17	)	)	PUNCT
ejpam-3454	298	18	>	>	X
ejpam-3454	299	1	0	0	X
ejpam-3454	299	2	.	.	PUNCT
ejpam-3454	300	1	as	as	ADP
ejpam-3454	300	2	a	a	DET
ejpam-3454	300	3	result	result	NOUN
ejpam-3454	300	4	,	,	PUNCT
ejpam-3454	300	5	∆	∆	PROPN
ejpam-3454	300	6	>	>	X
ejpam-3454	300	7	0	0	PUNCT
ejpam-3454	300	8	is	be	AUX
ejpam-3454	300	9	always	always	ADV
ejpam-3454	300	10	valid	valid	ADJ
ejpam-3454	300	11	.	.	PUNCT
ejpam-3454	301	1	this	this	PRON
ejpam-3454	301	2	completes	complete	VERB
ejpam-3454	301	3	the	the	DET
ejpam-3454	301	4	proof	proof	NOUN
ejpam-3454	301	5	of	of	ADP
ejpam-3454	301	6	this	this	DET
ejpam-3454	301	7	corollary	corollary	NOUN
ejpam-3454	301	8	.	.	PUNCT
ejpam-3454	302	1	a.	a.	NOUN
ejpam-3454	302	2	nangue	nangue	PROPN
ejpam-3454	302	3	,	,	PUNCT
ejpam-3454	302	4	t.	t.	PROPN
ejpam-3454	302	5	donfack	donfack	PROPN
ejpam-3454	302	6	,	,	PUNCT
ejpam-3454	302	7	d.	d.	PROPN
ejpam-3454	302	8	a.	a.	PROPN
ejpam-3454	302	9	ndode	ndode	PROPN
ejpam-3454	302	10	yafago	yafago	PROPN
ejpam-3454	302	11	/	/	SYM
ejpam-3454	302	12	eur	eur	PROPN
ejpam-3454	302	13	.	.	PUNCT
ejpam-3454	303	1	j.	j.	PROPN
ejpam-3454	303	2	pure	pure	PROPN
ejpam-3454	303	3	appl	appl	PROPN
ejpam-3454	303	4	.	.	PROPN
ejpam-3454	303	5	math	math	PROPN
ejpam-3454	303	6	,	,	PUNCT
ejpam-3454	303	7	12	12	NUM
ejpam-3454	303	8	(	(	PUNCT
ejpam-3454	303	9	3	3	NUM
ejpam-3454	303	10	)	)	PUNCT
ejpam-3454	303	11	(	(	PUNCT
ejpam-3454	303	12	2019	2019	NUM
ejpam-3454	303	13	)	)	PUNCT
ejpam-3454	303	14	,	,	PUNCT
ejpam-3454	303	15	944	944	NUM
ejpam-3454	303	16	-	-	SYM
ejpam-3454	303	17	959	959	NUM
ejpam-3454	303	18	957	957	NUM
ejpam-3454	303	19	5	5	NUM
ejpam-3454	303	20	.	.	PUNCT
ejpam-3454	303	21	global	global	ADJ
ejpam-3454	303	22	stability	stability	NOUN
ejpam-3454	303	23	analysis	analysis	NOUN
ejpam-3454	303	24	of	of	ADP
ejpam-3454	303	25	the	the	DET
ejpam-3454	303	26	model	model	NOUN
ejpam-3454	303	27	(	(	PUNCT
ejpam-3454	303	28	1	1	NUM
ejpam-3454	303	29	)	)	PUNCT
ejpam-3454	303	30	at	at	ADP
ejpam-3454	303	31	uninfected	uninfected	ADJ
ejpam-3454	303	32	steady	steady	ADJ
ejpam-3454	303	33	state	state	NOUN
ejpam-3454	303	34	for	for	ADP
ejpam-3454	303	35	the	the	DET
ejpam-3454	303	36	global	global	ADJ
ejpam-3454	303	37	stability	stability	NOUN
ejpam-3454	303	38	of	of	ADP
ejpam-3454	303	39	the	the	DET
ejpam-3454	303	40	equilibria	equilibrium	NOUN
ejpam-3454	303	41	,	,	PUNCT
ejpam-3454	303	42	we	we	PRON
ejpam-3454	303	43	have	have	AUX
ejpam-3454	303	44	:	:	PUNCT
ejpam-3454	303	45	theorem	theorem	VERB
ejpam-3454	303	46	7	7	NUM
ejpam-3454	303	47	.	.	PUNCT
ejpam-3454	304	1	the	the	DET
ejpam-3454	304	2	infection	infection	NOUN
ejpam-3454	304	3	-	-	PUNCT
ejpam-3454	304	4	free	free	ADJ
ejpam-3454	304	5	steady	steady	ADJ
ejpam-3454	304	6	state	state	NOUN
ejpam-3454	304	7	e0	e0	PROPN
ejpam-3454	304	8	of	of	ADP
ejpam-3454	304	9	model	model	NOUN
ejpam-3454	304	10	(	(	PUNCT
ejpam-3454	304	11	1	1	NUM
ejpam-3454	304	12	)	)	PUNCT
ejpam-3454	304	13	is	be	AUX
ejpam-3454	304	14	globally	globally	ADV
ejpam-3454	304	15	asymptotically	asymptotically	ADV
ejpam-3454	304	16	stable	stable	ADJ
ejpam-3454	304	17	if	if	SCONJ
ejpam-3454	304	18	the	the	DET
ejpam-3454	304	19	basic	basic	ADJ
ejpam-3454	304	20	reproduction	reproduction	NOUN
ejpam-3454	304	21	number	number	NOUN
ejpam-3454	304	22	r0	r0	NOUN
ejpam-3454	304	23	<	<	X
ejpam-3454	304	24	c	c	PROPN
ejpam-3454	304	25	c+α(1−η)βt	c+α(1−η)βt	PROPN
ejpam-3454	304	26	0	0	NUM
ejpam-3454	304	27	.	.	PUNCT
ejpam-3454	305	1	remark	remark	PROPN
ejpam-3454	305	2	7	7	NUM
ejpam-3454	305	3	.	.	PUNCT
ejpam-3454	306	1	since	since	SCONJ
ejpam-3454	306	2	r0	r0	NOUN
ejpam-3454	306	3	=	=	PUNCT
ejpam-3454	306	4	(	(	PUNCT
ejpam-3454	306	5	1−	1−	NUM
ejpam-3454	306	6	ε)(1−	ε)(1−	PROPN
ejpam-3454	306	7	η)pβt	η)pβt	PROPN
ejpam-3454	306	8	0	0	NUM
ejpam-3454	306	9	δ(c+	δ(c+	NOUN
ejpam-3454	306	10	(	(	PUNCT
ejpam-3454	306	11	1−	1−	NUM
ejpam-3454	306	12	η)αβt	η)αβt	NOUN
ejpam-3454	306	13	0	0	NUM
ejpam-3454	306	14	)	)	PUNCT
ejpam-3454	306	15	=	=	SYM
ejpam-3454	306	16	(	(	PUNCT
ejpam-3454	306	17	1−	1−	NUM
ejpam-3454	306	18	θ)pβt	θ)pβt	ADV
ejpam-3454	306	19	0	0	NUM
ejpam-3454	306	20	δ(c+	δ(c+	NOUN
ejpam-3454	306	21	(	(	PUNCT
ejpam-3454	306	22	1−	1−	NUM
ejpam-3454	306	23	η)αβt	η)αβt	NOUN
ejpam-3454	306	24	0	0	NUM
ejpam-3454	306	25	)	)	PUNCT
ejpam-3454	306	26	and	and	CCONJ
ejpam-3454	306	27	(	(	PUNCT
ejpam-3454	306	28	1−	1−	NUM
ejpam-3454	306	29	ε)(1−	ε)(1−	PROPN
ejpam-3454	306	30	η	η	PROPN
ejpam-3454	306	31	)	)	PUNCT
ejpam-3454	306	32	=	=	PUNCT
ejpam-3454	306	33	(	(	PUNCT
ejpam-3454	306	34	1−	1−	NUM
ejpam-3454	306	35	θ	θ	NOUN
ejpam-3454	306	36	)	)	PUNCT
ejpam-3454	306	37	.	.	PUNCT
ejpam-3454	307	1	then	then	ADV
ejpam-3454	307	2	(	(	PUNCT
ejpam-3454	307	3	1−	1−	NUM
ejpam-3454	307	4	θ)pβt	θ)pβt	ADV
ejpam-3454	307	5	0	0	NUM
ejpam-3454	308	1	=	=	SYM
ejpam-3454	308	2	r0δ(c+	r0δ(c+	NOUN
ejpam-3454	308	3	(	(	PUNCT
ejpam-3454	308	4	1−	1−	NUM
ejpam-3454	308	5	η)αβt	η)αβt	NOUN
ejpam-3454	308	6	0	0	NUM
ejpam-3454	308	7	)	)	PUNCT
ejpam-3454	308	8	)	)	PUNCT
ejpam-3454	308	9	.	.	PUNCT
ejpam-3454	309	1	therefore	therefore	ADV
ejpam-3454	309	2	(	(	PUNCT
ejpam-3454	309	3	1−	1−	NUM
ejpam-3454	309	4	θ)pβt	θ)pβt	ADV
ejpam-3454	309	5	0i	0i	X
ejpam-3454	309	6	c	c	PROPN
ejpam-3454	310	1	−	−	PROPN
ejpam-3454	310	2	δ	δ	PROPN
ejpam-3454	310	3	<	<	X
ejpam-3454	310	4	0	0	NUM
ejpam-3454	310	5	⇐	⇐	ADJ
ejpam-3454	310	6	⇒	⇒	PROPN
ejpam-3454	310	7	r0δ(c+	r0δ(c+	NOUN
ejpam-3454	310	8	α(1−	α(1−	PUNCT
ejpam-3454	310	9	η)βt	η)βt	PROPN
ejpam-3454	310	10	0	0	NUM
ejpam-3454	310	11	)	)	PUNCT
ejpam-3454	310	12	c	c	NOUN
ejpam-3454	310	13	−	−	PROPN
ejpam-3454	310	14	δ	δ	PROPN
ejpam-3454	310	15	<	<	X
ejpam-3454	310	16	0	0	NUM
ejpam-3454	310	17	⇐	⇐	ADJ
ejpam-3454	310	18	⇒	⇒	NOUN
ejpam-3454	310	19	r0	r0	NOUN
ejpam-3454	310	20	<	<	X
ejpam-3454	310	21	c	c	X
ejpam-3454	310	22	c+	c+	VERB
ejpam-3454	310	23	α(1−	α(1−	PUNCT
ejpam-3454	311	1	η)βt	η)βt	PROPN
ejpam-3454	311	2	0	0	NUM
ejpam-3454	311	3	.	.	PUNCT
ejpam-3454	312	1	proof	proof	NOUN
ejpam-3454	312	2	.	.	PUNCT
ejpam-3454	313	1	consider	consider	VERB
ejpam-3454	313	2	the	the	DET
ejpam-3454	313	3	lyapunov	lyapunov	ADJ
ejpam-3454	313	4	function	function	NOUN
ejpam-3454	313	5	:	:	PUNCT
ejpam-3454	314	1	l1(t	l1(t	PROPN
ejpam-3454	314	2	,	,	PUNCT
ejpam-3454	314	3	i	i	PRON
ejpam-3454	314	4	,	,	PUNCT
ejpam-3454	314	5	v	v	NOUN
ejpam-3454	314	6	)	)	PUNCT
ejpam-3454	314	7	=	=	SYM
ejpam-3454	314	8	t	t	PROPN
ejpam-3454	314	9	−	−	PROPN
ejpam-3454	314	10	t	t	PROPN
ejpam-3454	314	11	0	0	NUM
ejpam-3454	315	1	−	−	PROPN
ejpam-3454	315	2	t	t	NOUN
ejpam-3454	315	3	0	0	NUM
ejpam-3454	315	4	ln	ln	PROPN
ejpam-3454	315	5	t	t	PROPN
ejpam-3454	315	6	t	t	NOUN
ejpam-3454	315	7	0	0	PUNCT
ejpam-3454	316	1	+	+	CCONJ
ejpam-3454	316	2	i	i	PRON
ejpam-3454	316	3	+	+	CCONJ
ejpam-3454	316	4	(	(	PUNCT
ejpam-3454	316	5	1−	1−	NUM
ejpam-3454	316	6	η)βt	η)βt	PROPN
ejpam-3454	316	7	0	0	PUNCT
ejpam-3454	316	8	c	c	PROPN
ejpam-3454	316	9	v	v	PROPN
ejpam-3454	316	10	l1	l1	PROPN
ejpam-3454	316	11	is	be	AUX
ejpam-3454	316	12	defined	define	VERB
ejpam-3454	316	13	,	,	PUNCT
ejpam-3454	316	14	continuous	continuous	ADJ
ejpam-3454	316	15	and	and	CCONJ
ejpam-3454	316	16	positive	positive	ADJ
ejpam-3454	316	17	definite	definite	ADJ
ejpam-3454	316	18	for	for	ADP
ejpam-3454	316	19	all	all	DET
ejpam-3454	316	20	t	t	PROPN
ejpam-3454	316	21	>	>	X
ejpam-3454	316	22	0	0	PROPN
ejpam-3454	316	23	,	,	PUNCT
ejpam-3454	316	24	i	i	PRON
ejpam-3454	316	25	>	>	X
ejpam-3454	316	26	0	0	PROPN
ejpam-3454	316	27	,	,	PUNCT
ejpam-3454	316	28	v	v	ADP
ejpam-3454	316	29	>	>	X
ejpam-3454	316	30	0	0	NUM
ejpam-3454	316	31	.	.	PUNCT
ejpam-3454	317	1	also	also	ADV
ejpam-3454	317	2	,	,	PUNCT
ejpam-3454	317	3	the	the	DET
ejpam-3454	317	4	global	global	ADJ
ejpam-3454	317	5	minimum	minimum	NOUN
ejpam-3454	317	6	l1	l1	PROPN
ejpam-3454	317	7	=	=	SYM
ejpam-3454	317	8	0	0	NUM
ejpam-3454	317	9	occurs	occur	VERB
ejpam-3454	317	10	at	at	ADP
ejpam-3454	317	11	the	the	DET
ejpam-3454	317	12	infection	infection	NOUN
ejpam-3454	317	13	free	free	ADJ
ejpam-3454	317	14	equilibrium	equilibrium	NOUN
ejpam-3454	317	15	e0	e0	PROPN
ejpam-3454	317	16	.	.	PUNCT
ejpam-3454	318	1	further	far	ADV
ejpam-3454	318	2	,	,	PUNCT
ejpam-3454	318	3	function	function	PROPN
ejpam-3454	318	4	l1	l1	PROPN
ejpam-3454	318	5	,	,	PUNCT
ejpam-3454	318	6	along	along	ADP
ejpam-3454	318	7	the	the	DET
ejpam-3454	318	8	solutions	solution	NOUN
ejpam-3454	318	9	of	of	ADP
ejpam-3454	318	10	system	system	NOUN
ejpam-3454	318	11	(	(	PUNCT
ejpam-3454	318	12	1	1	X
ejpam-3454	318	13	)	)	PUNCT
ejpam-3454	318	14	at	at	ADP
ejpam-3454	318	15	e0	e0	PROPN
ejpam-3454	318	16	,	,	PUNCT
ejpam-3454	318	17	satisfies	satisfy	VERB
ejpam-3454	318	18	:	:	PUNCT
ejpam-3454	318	19	dl1	dl1	NOUN
ejpam-3454	318	20	dt	dt	X
ejpam-3454	319	1	=	=	SYM
ejpam-3454	319	2	∂l1	∂l1	NOUN
ejpam-3454	319	3	∂t	∂t	PROPN
ejpam-3454	319	4	dt	dt	X
ejpam-3454	319	5	dt	dt	X
ejpam-3454	320	1	+	+	CCONJ
ejpam-3454	320	2	∂l1	∂l1	PROPN
ejpam-3454	320	3	∂i	∂i	PROPN
ejpam-3454	320	4	di	di	NOUN
ejpam-3454	320	5	dt	dt	PROPN
ejpam-3454	320	6	+	+	PROPN
ejpam-3454	320	7	∂l1	∂l1	PROPN
ejpam-3454	320	8	∂v	∂v	PROPN
ejpam-3454	320	9	dv	dv	PROPN
ejpam-3454	320	10	dt	dt	PROPN
ejpam-3454	321	1	=	=	PUNCT
ejpam-3454	321	2	dt	dt	X
ejpam-3454	321	3	dt	dt	INTJ
ejpam-3454	322	1	−	−	PROPN
ejpam-3454	322	2	dt	dt	X
ejpam-3454	322	3	0	0	NUM
ejpam-3454	322	4	dt	dt	NOUN
ejpam-3454	322	5	dt	dt	X
ejpam-3454	322	6	dt	dt	X
ejpam-3454	323	1	+	+	CCONJ
ejpam-3454	323	2	di	di	X
ejpam-3454	323	3	dt	dt	NOUN
ejpam-3454	323	4	+	+	CCONJ
ejpam-3454	323	5	(	(	PUNCT
ejpam-3454	323	6	1−	1−	NUM
ejpam-3454	323	7	η)βt0	η)βt0	VERB
ejpam-3454	323	8	c	c	X
ejpam-3454	323	9	dv	dv	PROPN
ejpam-3454	323	10	dt	dt	X
ejpam-3454	323	11	=	=	PUNCT
ejpam-3454	323	12	(	(	PUNCT
ejpam-3454	323	13	1−	1−	NUM
ejpam-3454	323	14	dt	dt	NOUN
ejpam-3454	323	15	0	0	NUM
ejpam-3454	323	16	dt	dt	NOUN
ejpam-3454	323	17	)	)	PUNCT
ejpam-3454	323	18	ṫ	ṫ	PROPN
ejpam-3454	323	19	+	+	CCONJ
ejpam-3454	323	20	i̇	i̇	ADJ
ejpam-3454	324	1	+	+	CCONJ
ejpam-3454	324	2	(	(	PUNCT
ejpam-3454	324	3	1−	1−	NUM
ejpam-3454	324	4	η)βt0	η)βt0	VERB
ejpam-3454	324	5	c	c	X
ejpam-3454	324	6	v̇	v̇	NOUN
ejpam-3454	324	7	.	.	PUNCT
ejpam-3454	325	1	further	far	ADV
ejpam-3454	325	2	collecting	collect	VERB
ejpam-3454	325	3	terms	term	NOUN
ejpam-3454	325	4	,	,	PUNCT
ejpam-3454	325	5	we	we	PRON
ejpam-3454	325	6	have	have	VERB
ejpam-3454	325	7	dl1	dl1	NOUN
ejpam-3454	325	8	dt	dt	NOUN
ejpam-3454	325	9	=	=	PUNCT
ejpam-3454	325	10	(	(	PUNCT
ejpam-3454	325	11	t	t	PROPN
ejpam-3454	325	12	−	−	PROPN
ejpam-3454	325	13	t0	t0	PROPN
ejpam-3454	325	14	)	)	PUNCT
ejpam-3454	326	1	[	[	PUNCT
ejpam-3454	326	2	r	r	NOUN
ejpam-3454	326	3	−	−	NOUN
ejpam-3454	326	4	r(t	r(t	NOUN
ejpam-3454	326	5	+	+	CCONJ
ejpam-3454	326	6	i	i	NOUN
ejpam-3454	326	7	)	)	PUNCT
ejpam-3454	326	8	tmax	tmax	ADP
ejpam-3454	326	9	−	−	NUM
ejpam-3454	326	10	d−	d−	PROPN
ejpam-3454	326	11	(	(	PUNCT
ejpam-3454	326	12	1−	1−	NUM
ejpam-3454	326	13	η)βv	η)βv	PROPN
ejpam-3454	326	14	]	]	PUNCT
ejpam-3454	327	1	+	+	CCONJ
ejpam-3454	327	2	(	(	PUNCT
ejpam-3454	327	3	1−	1−	NUM
ejpam-3454	327	4	η)βv	η)βv	PROPN
ejpam-3454	327	5	t	t	VERB
ejpam-3454	327	6	−	−	NOUN
ejpam-3454	328	1	δi	δi	NOUN
ejpam-3454	329	1	+	+	CCONJ
ejpam-3454	330	1	(	(	PUNCT
ejpam-3454	330	2	1−	1−	NUM
ejpam-3454	330	3	η)βt0	η)βt0	VERB
ejpam-3454	330	4	c	c	NOUN
ejpam-3454	331	1	[	[	X
ejpam-3454	331	2	(	(	PUNCT
ejpam-3454	331	3	1−	1−	NUM
ejpam-3454	331	4	ε)pi	ε)pi	PROPN
ejpam-3454	331	5	−	−	PROPN
ejpam-3454	331	6	cv	cv	PROPN
ejpam-3454	331	7	−	−	PROPN
ejpam-3454	331	8	α(1−	α(1−	PROPN
ejpam-3454	331	9	η)βv	η)βv	PROPN
ejpam-3454	331	10	t	t	PROPN
ejpam-3454	331	11	]	]	PUNCT
ejpam-3454	331	12	.	.	PUNCT
ejpam-3454	332	1	a.	a.	NOUN
ejpam-3454	332	2	nangue	nangue	PROPN
ejpam-3454	332	3	,	,	PUNCT
ejpam-3454	332	4	t.	t.	PROPN
ejpam-3454	332	5	donfack	donfack	PROPN
ejpam-3454	332	6	,	,	PUNCT
ejpam-3454	332	7	d.	d.	PROPN
ejpam-3454	332	8	a.	a.	PROPN
ejpam-3454	332	9	ndode	ndode	PROPN
ejpam-3454	332	10	yafago	yafago	PROPN
ejpam-3454	332	11	/	/	SYM
ejpam-3454	332	12	eur	eur	PROPN
ejpam-3454	332	13	.	.	PUNCT
ejpam-3454	333	1	j.	j.	PROPN
ejpam-3454	333	2	pure	pure	PROPN
ejpam-3454	333	3	appl	appl	PROPN
ejpam-3454	333	4	.	.	PROPN
ejpam-3454	333	5	math	math	PROPN
ejpam-3454	333	6	,	,	PUNCT
ejpam-3454	333	7	12	12	NUM
ejpam-3454	333	8	(	(	PUNCT
ejpam-3454	333	9	3	3	NUM
ejpam-3454	333	10	)	)	PUNCT
ejpam-3454	333	11	(	(	PUNCT
ejpam-3454	333	12	2019	2019	NUM
ejpam-3454	333	13	)	)	PUNCT
ejpam-3454	333	14	,	,	PUNCT
ejpam-3454	333	15	944	944	NUM
ejpam-3454	333	16	-	-	SYM
ejpam-3454	333	17	959	959	NUM
ejpam-3454	333	18	958	958	NUM
ejpam-3454	333	19	hence	hence	ADV
ejpam-3454	333	20	:	:	PUNCT
ejpam-3454	333	21	dl1	dl1	NOUN
ejpam-3454	333	22	dt	dt	NOUN
ejpam-3454	333	23	=	=	PUNCT
ejpam-3454	333	24	(	(	PUNCT
ejpam-3454	333	25	t	t	PROPN
ejpam-3454	333	26	−	−	PROPN
ejpam-3454	333	27	t	t	PROPN
ejpam-3454	333	28	0	0	NUM
ejpam-3454	333	29	)	)	PUNCT
ejpam-3454	334	1	[	[	PUNCT
ejpam-3454	334	2	−	−	NOUN
ejpam-3454	334	3	r	r	NOUN
ejpam-3454	334	4	tmax	tmax	NOUN
ejpam-3454	334	5	(	(	PUNCT
ejpam-3454	334	6	t	t	PROPN
ejpam-3454	334	7	−	−	PROPN
ejpam-3454	334	8	t	t	PROPN
ejpam-3454	334	9	0)−	0)−	PUNCT
ejpam-3454	335	1	r	r	NOUN
ejpam-3454	335	2	tmax	tmax	ADV
ejpam-3454	336	1	i	i	PRON
ejpam-3454	336	2	]	]	PUNCT
ejpam-3454	336	3	−	−	PUNCT
ejpam-3454	336	4	δi	δi	X
ejpam-3454	337	1	+	+	CCONJ
ejpam-3454	337	2	(	(	PUNCT
ejpam-3454	337	3	1−	1−	NUM
ejpam-3454	337	4	η)(1−	η)(1−	NUM
ejpam-3454	337	5	ε)pβt	ε)pβt	PROPN
ejpam-3454	337	6	0i	0i	X
ejpam-3454	337	7	c	c	PROPN
ejpam-3454	338	1	−α(1−	−α(1−	NOUN
ejpam-3454	338	2	η)2β2v	η)2β2v	PROPN
ejpam-3454	338	3	tt	tt	PROPN
ejpam-3454	338	4	0	0	PUNCT
ejpam-3454	338	5	c	c	PROPN
ejpam-3454	338	6	=	=	SYM
ejpam-3454	339	1	−	−	NOUN
ejpam-3454	339	2	r	r	NOUN
ejpam-3454	339	3	tmax	tmax	ADP
ejpam-3454	339	4	[	[	X
ejpam-3454	339	5	(	(	PUNCT
ejpam-3454	339	6	t	t	PROPN
ejpam-3454	339	7	−	−	PROPN
ejpam-3454	339	8	t	t	PROPN
ejpam-3454	339	9	0)2	0)2	NUM
ejpam-3454	340	1	−	−	PROPN
ejpam-3454	341	1	(	(	PUNCT
ejpam-3454	341	2	t	t	PROPN
ejpam-3454	341	3	−	−	PROPN
ejpam-3454	341	4	t	t	NOUN
ejpam-3454	341	5	0)i	0)i	NOUN
ejpam-3454	341	6	]	]	X
ejpam-3454	342	1	+	+	CCONJ
ejpam-3454	342	2	(	(	PUNCT
ejpam-3454	342	3	(	(	PUNCT
ejpam-3454	342	4	1−	1−	NUM
ejpam-3454	342	5	η)(1−	η)(1−	NUM
ejpam-3454	342	6	ε)pβt	ε)pβt	PROPN
ejpam-3454	342	7	0i	0i	X
ejpam-3454	342	8	c	c	PROPN
ejpam-3454	343	1	−	−	PROPN
ejpam-3454	343	2	δ	δ	PROPN
ejpam-3454	343	3	)	)	PUNCT
ejpam-3454	344	1	i	i	PRON
ejpam-3454	344	2	−α(1−	−α(1−	NOUN
ejpam-3454	344	3	η)2β2v	η)2β2v	PROPN
ejpam-3454	344	4	tt	tt	PROPN
ejpam-3454	344	5	0	0	PUNCT
ejpam-3454	345	1	c	c	PROPN
ejpam-3454	345	2	this	this	PRON
ejpam-3454	345	3	leads	lead	VERB
ejpam-3454	345	4	to	to	ADP
ejpam-3454	345	5	:	:	PUNCT
ejpam-3454	345	6	dl1	dl1	NOUN
ejpam-3454	345	7	dt	dt	NOUN
ejpam-3454	346	1	=	=	PUNCT
ejpam-3454	347	1	−	−	PROPN
ejpam-3454	347	2	r	r	NOUN
ejpam-3454	347	3	tmax	tmax	ADP
ejpam-3454	347	4	[	[	X
ejpam-3454	347	5	(	(	PUNCT
ejpam-3454	347	6	t	t	PROPN
ejpam-3454	347	7	−	−	PROPN
ejpam-3454	347	8	t	t	PROPN
ejpam-3454	347	9	0)(t	0)(t	PROPN
ejpam-3454	348	1	+	+	CCONJ
ejpam-3454	349	1	i	i	PRON
ejpam-3454	349	2	−	−	VERB
ejpam-3454	349	3	t	t	NOUN
ejpam-3454	349	4	0	0	NUM
ejpam-3454	349	5	)	)	PUNCT
ejpam-3454	349	6	]	]	PUNCT
ejpam-3454	350	1	+	+	CCONJ
ejpam-3454	350	2	(	(	PUNCT
ejpam-3454	350	3	(	(	PUNCT
ejpam-3454	350	4	1−	1−	NUM
ejpam-3454	350	5	θ)pβt	θ)pβt	ADV
ejpam-3454	350	6	0i	0i	X
ejpam-3454	350	7	c	c	PROPN
ejpam-3454	351	1	−	−	PROPN
ejpam-3454	351	2	δ	δ	PROPN
ejpam-3454	351	3	)	)	PUNCT
ejpam-3454	352	1	i	i	PRON
ejpam-3454	352	2	−	−	VERB
ejpam-3454	352	3	α(1−	α(1−	PROPN
ejpam-3454	352	4	η)2β2v	η)2β2v	PROPN
ejpam-3454	352	5	tt	tt	PROPN
ejpam-3454	352	6	0	0	NUM
ejpam-3454	352	7	c	c	NOUN
ejpam-3454	352	8	,	,	PUNCT
ejpam-3454	352	9	since	since	SCONJ
ejpam-3454	352	10	1−	1−	NUM
ejpam-3454	352	11	θ	θ	NOUN
ejpam-3454	352	12	=	=	SYM
ejpam-3454	352	13	(	(	PUNCT
ejpam-3454	352	14	1−	1−	NUM
ejpam-3454	352	15	η)(1−	η)(1−	PROPN
ejpam-3454	352	16	ε	ε	PROPN
ejpam-3454	352	17	)	)	PUNCT
ejpam-3454	352	18	.	.	PUNCT
ejpam-3454	353	1	furthermore	furthermore	ADV
ejpam-3454	353	2	,	,	PUNCT
ejpam-3454	353	3	we	we	PRON
ejpam-3454	353	4	have	have	VERB
ejpam-3454	353	5	:	:	PUNCT
ejpam-3454	353	6	dl1	dl1	NOUN
ejpam-3454	353	7	dt	dt	X
ejpam-3454	354	1	≤	≤	NUM
ejpam-3454	354	2	−	−	NOUN
ejpam-3454	354	3	r	r	NOUN
ejpam-3454	354	4	tmax	tmax	ADP
ejpam-3454	354	5	[	[	X
ejpam-3454	354	6	(	(	PUNCT
ejpam-3454	354	7	t	t	PROPN
ejpam-3454	354	8	−	−	PROPN
ejpam-3454	354	9	t	t	PROPN
ejpam-3454	354	10	0)(t	0)(t	PROPN
ejpam-3454	355	1	+	+	CCONJ
ejpam-3454	356	1	i	i	PRON
ejpam-3454	356	2	−	−	VERB
ejpam-3454	356	3	t	t	NOUN
ejpam-3454	356	4	0	0	NUM
ejpam-3454	356	5	)	)	PUNCT
ejpam-3454	356	6	]	]	PUNCT
ejpam-3454	357	1	+	+	CCONJ
ejpam-3454	357	2	i(r0	i(r0	NOUN
ejpam-3454	357	3	−	−	PROPN
ejpam-3454	357	4	c	c	NOUN
ejpam-3454	357	5	c+	c+	VERB
ejpam-3454	357	6	α(1−	α(1−	PUNCT
ejpam-3454	358	1	η)βt	η)βt	PROPN
ejpam-3454	358	2	0	0	NUM
ejpam-3454	358	3	)	)	PUNCT
ejpam-3454	358	4	−	−	PROPN
ejpam-3454	358	5	α(1−	α(1−	PROPN
ejpam-3454	358	6	η)2β2v	η)2β2v	PROPN
ejpam-3454	358	7	tt	tt	PROPN
ejpam-3454	358	8	0	0	NUM
ejpam-3454	358	9	c	c	X
ejpam-3454	358	10	.	.	PUNCT
ejpam-3454	359	1	r0	r0	NOUN
ejpam-3454	359	2	≤	≤	NUM
ejpam-3454	359	3	c	c	PUNCT
ejpam-3454	360	1	c+α(1−η)βt	c+α(1−η)βt	NUM
ejpam-3454	360	2	0	0	NUM
ejpam-3454	361	1	and	and	CCONJ
ejpam-3454	361	2	theorem	theorem	VERB
ejpam-3454	361	3	4	4	NUM
ejpam-3454	361	4	ensure	ensure	VERB
ejpam-3454	361	5	dl1	dl1	NOUN
ejpam-3454	361	6	dt	dt	NOUN
ejpam-3454	361	7	≤	≤	NUM
ejpam-3454	361	8	0	0	NUM
ejpam-3454	361	9	for	for	ADP
ejpam-3454	361	10	all	all	DET
ejpam-3454	361	11	t	t	PROPN
ejpam-3454	361	12	>	>	X
ejpam-3454	361	13	0	0	PROPN
ejpam-3454	361	14	,	,	PUNCT
ejpam-3454	361	15	i	i	PRON
ejpam-3454	361	16	>	>	X
ejpam-3454	361	17	0	0	NUM
ejpam-3454	361	18	,	,	PUNCT
ejpam-3454	361	19	v	v	PART
ejpam-3454	361	20	>	>	X
ejpam-3454	361	21	0	0	NUM
ejpam-3454	361	22	.	.	PUNCT
ejpam-3454	362	1	the	the	DET
ejpam-3454	362	2	equality	equality	NOUN
ejpam-3454	362	3	dl1	dl1	NOUN
ejpam-3454	362	4	dt	dt	X
ejpam-3454	362	5	=	=	SYM
ejpam-3454	362	6	0	0	NUM
ejpam-3454	362	7	holds	hold	VERB
ejpam-3454	362	8	only	only	ADV
ejpam-3454	362	9	at	at	ADP
ejpam-3454	362	10	the	the	DET
ejpam-3454	362	11	free	free	ADJ
ejpam-3454	362	12	equilibrium	equilibrium	NOUN
ejpam-3454	362	13	e0	e0	PROPN
ejpam-3454	362	14	.	.	PUNCT
ejpam-3454	363	1	therefore	therefore	ADV
ejpam-3454	363	2	,	,	PUNCT
ejpam-3454	363	3	the	the	DET
ejpam-3454	363	4	largest	large	ADJ
ejpam-3454	363	5	compact	compact	ADJ
ejpam-3454	363	6	invariant	invariant	ADJ
ejpam-3454	363	7	subset	subset	NOUN
ejpam-3454	363	8	of	of	ADP
ejpam-3454	363	9	the	the	DET
ejpam-3454	363	10	set	set	NOUN
ejpam-3454	363	11	m	m	NOUN
ejpam-3454	363	12	=	=	SYM
ejpam-3454	363	13	{	{	PUNCT
ejpam-3454	363	14	(	(	PUNCT
ejpam-3454	363	15	t	t	PROPN
ejpam-3454	363	16	,	,	PUNCT
ejpam-3454	363	17	i	i	PRON
ejpam-3454	363	18	,	,	PUNCT
ejpam-3454	363	19	v	v	NOUN
ejpam-3454	363	20	)	)	PUNCT
ejpam-3454	363	21	∈	∈	PROPN
ejpam-3454	363	22	ω	ω	NOUN
ejpam-3454	363	23	:	:	PUNCT
ejpam-3454	363	24	dl1	dl1	NOUN
ejpam-3454	363	25	dt	dt	NOUN
ejpam-3454	364	1	=	=	SYM
ejpam-3454	364	2	0	0	NUM
ejpam-3454	364	3	}	}	PUNCT
ejpam-3454	364	4	is	be	AUX
ejpam-3454	364	5	the	the	DET
ejpam-3454	364	6	singleton	singleton	PROPN
ejpam-3454	364	7	{	{	PUNCT
ejpam-3454	364	8	e0	e0	PROPN
ejpam-3454	364	9	}	}	PUNCT
ejpam-3454	364	10	.	.	PUNCT
ejpam-3454	365	1	by	by	ADP
ejpam-3454	365	2	the	the	DET
ejpam-3454	365	3	lasalle	lasalle	PROPN
ejpam-3454	365	4	invariance	invariance	PROPN
ejpam-3454	365	5	principle	principle	NOUN
ejpam-3454	365	6	,	,	PUNCT
ejpam-3454	365	7	the	the	DET
ejpam-3454	365	8	infection	infection	NOUN
ejpam-3454	365	9	-	-	PUNCT
ejpam-3454	365	10	free	free	ADJ
ejpam-3454	365	11	equilibrium	equilibrium	NOUN
ejpam-3454	365	12	is	be	AUX
ejpam-3454	365	13	globally	globally	ADV
ejpam-3454	365	14	asymptotically	asymptotically	ADV
ejpam-3454	365	15	stable	stable	ADJ
ejpam-3454	365	16	if	if	SCONJ
ejpam-3454	365	17	r0	r0	NOUN
ejpam-3454	365	18	≤	≤	NOUN
ejpam-3454	365	19	c	c	NOUN
ejpam-3454	366	1	c+α(1−η)βt	c+α(1−η)βt	PROPN
ejpam-3454	366	2	0	0	NUM
ejpam-3454	366	3	.	.	PUNCT
ejpam-3454	367	1	this	this	PRON
ejpam-3454	367	2	completes	complete	VERB
ejpam-3454	367	3	the	the	DET
ejpam-3454	367	4	proof	proof	NOUN
ejpam-3454	367	5	of	of	ADP
ejpam-3454	367	6	theorem	theorem	ADJ
ejpam-3454	367	7	7	7	NUM
ejpam-3454	367	8	.	.	NOUN
ejpam-3454	367	9	6	6	NUM
ejpam-3454	367	10	.	.	X
ejpam-3454	367	11	concluding	conclude	VERB
ejpam-3454	367	12	remark	remark	NOUN
ejpam-3454	367	13	it	it	PRON
ejpam-3454	367	14	is	be	AUX
ejpam-3454	367	15	clear	clear	ADJ
ejpam-3454	367	16	that	that	SCONJ
ejpam-3454	367	17	this	this	DET
ejpam-3454	367	18	paper	paper	NOUN
ejpam-3454	367	19	is	be	AUX
ejpam-3454	367	20	a	a	DET
ejpam-3454	367	21	starting	starting	NOUN
ejpam-3454	367	22	point	point	NOUN
ejpam-3454	367	23	for	for	ADP
ejpam-3454	367	24	further	further	ADJ
ejpam-3454	367	25	investigations	investigation	NOUN
ejpam-3454	367	26	.	.	PUNCT
ejpam-3454	368	1	in	in	ADP
ejpam-3454	368	2	a	a	DET
ejpam-3454	368	3	very	very	ADV
ejpam-3454	368	4	near	near	ADJ
ejpam-3454	368	5	future	future	NOUN
ejpam-3454	368	6	we	we	PRON
ejpam-3454	368	7	will	will	AUX
ejpam-3454	368	8	attempt	attempt	VERB
ejpam-3454	368	9	to	to	PART
ejpam-3454	368	10	solve	solve	VERB
ejpam-3454	368	11	the	the	DET
ejpam-3454	368	12	case	case	NOUN
ejpam-3454	368	13	of	of	ADP
ejpam-3454	368	14	the	the	DET
ejpam-3454	368	15	global	global	ADJ
ejpam-3454	368	16	asymptotic	asymptotic	ADJ
ejpam-3454	368	17	stability	stability	NOUN
ejpam-3454	368	18	of	of	ADP
ejpam-3454	368	19	the	the	DET
ejpam-3454	368	20	infected	infected	ADJ
ejpam-3454	368	21	equilibrium	equilibrium	NOUN
ejpam-3454	368	22	point	point	NOUN
ejpam-3454	368	23	.	.	PUNCT
ejpam-3454	369	1	constructing	construct	VERB
ejpam-3454	369	2	a	a	DET
ejpam-3454	369	3	lyapunov	lyapunov	ADJ
ejpam-3454	369	4	function	function	NOUN
ejpam-3454	369	5	for	for	ADP
ejpam-3454	369	6	this	this	DET
ejpam-3454	369	7	infected	infect	VERB
ejpam-3454	369	8	equilibrium	equilibrium	NOUN
ejpam-3454	369	9	model	model	NOUN
ejpam-3454	369	10	appears	appear	VERB
ejpam-3454	369	11	to	to	PART
ejpam-3454	369	12	be	be	AUX
ejpam-3454	369	13	very	very	ADV
ejpam-3454	369	14	complex	complex	ADJ
ejpam-3454	369	15	.	.	PUNCT
ejpam-3454	370	1	we	we	PRON
ejpam-3454	370	2	will	will	AUX
ejpam-3454	370	3	think	think	VERB
ejpam-3454	370	4	about	about	ADP
ejpam-3454	370	5	li	li	NOUN
ejpam-3454	370	6	-	-	PUNCT
ejpam-3454	370	7	muldowney	muldowney	ADJ
ejpam-3454	370	8	global	global	ADJ
ejpam-3454	370	9	-	-	PUNCT
ejpam-3454	370	10	stability	stability	NOUN
ejpam-3454	370	11	criterion	criterion	NOUN
ejpam-3454	370	12	[	[	X
ejpam-3454	370	13	7	7	X
ejpam-3454	370	14	]	]	PUNCT
ejpam-3454	370	15	for	for	ADP
ejpam-3454	370	16	example	example	NOUN
ejpam-3454	370	17	.	.	PUNCT
ejpam-3454	371	1	acknowledgements	acknowledgement	NOUN
ejpam-3454	371	2	we	we	PRON
ejpam-3454	371	3	are	be	AUX
ejpam-3454	371	4	grateful	grateful	ADJ
ejpam-3454	371	5	to	to	ADP
ejpam-3454	371	6	professor	professor	PROPN
ejpam-3454	371	7	alan	alan	PROPN
ejpam-3454	371	8	rendall	rendall	PROPN
ejpam-3454	371	9	for	for	ADP
ejpam-3454	371	10	valuable	valuable	ADJ
ejpam-3454	371	11	and	and	CCONJ
ejpam-3454	371	12	tremendous	tremendous	ADJ
ejpam-3454	371	13	discussions	discussion	NOUN
ejpam-3454	371	14	about	about	ADP
ejpam-3454	371	15	this	this	DET
ejpam-3454	371	16	paper	paper	NOUN
ejpam-3454	371	17	.	.	PUNCT
ejpam-3454	372	1	we	we	PRON
ejpam-3454	372	2	also	also	ADV
ejpam-3454	372	3	thank	thank	VERB
ejpam-3454	372	4	the	the	DET
ejpam-3454	372	5	higher	high	ADJ
ejpam-3454	372	6	teachers	teacher	NOUN
ejpam-3454	372	7	’	’	PART
ejpam-3454	372	8	training	training	NOUN
ejpam-3454	372	9	college	college	NOUN
ejpam-3454	372	10	of	of	ADP
ejpam-3454	372	11	the	the	DET
ejpam-3454	372	12	university	university	NOUN
ejpam-3454	372	13	of	of	ADP
ejpam-3454	372	14	maroua	maroua	PROPN
ejpam-3454	372	15	were	be	AUX
ejpam-3454	372	16	this	this	DET
ejpam-3454	372	17	paper	paper	NOUN
ejpam-3454	372	18	were	be	AUX
ejpam-3454	372	19	initiated	initiate	VERB
ejpam-3454	372	20	.	.	PUNCT
ejpam-3454	373	1	references	reference	NOUN
ejpam-3454	373	2	959	959	NUM
ejpam-3454	373	3	references	reference	NOUN
ejpam-3454	373	4	[	[	X
ejpam-3454	373	5	1	1	NUM
ejpam-3454	373	6	]	]	X
ejpam-3454	373	7	chatterjee	chatterjee	PROPN
ejpam-3454	373	8	a	a	X
ejpam-3454	373	9	,	,	PUNCT
ejpam-3454	373	10	guedj	guedj	PROPN
ejpam-3454	373	11	j	j	PROPN
ejpam-3454	373	12	,	,	PUNCT
ejpam-3454	373	13	and	and	CCONJ
ejpam-3454	373	14	perelson	perelson	VERB
ejpam-3454	373	15	a	a	DET
ejpam-3454	373	16	s.	s.	PROPN
ejpam-3454	373	17	mathematical	mathematical	PROPN
ejpam-3454	373	18	modelling	modelling	NOUN
ejpam-3454	373	19	of	of	ADP
ejpam-3454	373	20	hcv	hcv	NOUN
ejpam-3454	373	21	infection	infection	NOUN
ejpam-3454	373	22	:	:	PUNCT
ejpam-3454	373	23	what	what	PRON
ejpam-3454	373	24	can	can	AUX
ejpam-3454	373	25	it	it	PRON
ejpam-3454	373	26	teach	teach	VERB
ejpam-3454	373	27	us	we	PRON
ejpam-3454	373	28	in	in	ADP
ejpam-3454	373	29	the	the	DET
ejpam-3454	373	30	era	era	NOUN
ejpam-3454	373	31	of	of	ADP
ejpam-3454	373	32	direct	direct	ADJ
ejpam-3454	373	33	-	-	PUNCT
ejpam-3454	373	34	acting	act	VERB
ejpam-3454	373	35	antiviral	antiviral	ADJ
ejpam-3454	373	36	agents	agent	NOUN
ejpam-3454	373	37	?	?	PUNCT
ejpam-3454	374	1	antivir	antivir	NOUN
ejpam-3454	374	2	.	.	PUNCT
ejpam-3454	375	1	ther	ther	PROPN
ejpam-3454	375	2	.	.	PUNCT
ejpam-3454	375	3	,	,	PUNCT
ejpam-3454	375	4	17(6):1171–1182	17(6):1171–1182	NUM
ejpam-3454	375	5	,	,	PUNCT
ejpam-3454	375	6	2012	2012	NUM
ejpam-3454	375	7	.	.	PUNCT
ejpam-3454	376	1	[	[	X
ejpam-3454	376	2	2	2	NUM
ejpam-3454	376	3	]	]	X
ejpam-3454	376	4	m	m	PROPN
ejpam-3454	376	5	s	s	PROPN
ejpam-3454	376	6	f	f	PROPN
ejpam-3454	376	7	chong	chong	PROPN
ejpam-3454	376	8	,	,	PUNCT
ejpam-3454	376	9	m	m	PROPN
ejpam-3454	376	10	c	c	NOUN
ejpam-3454	376	11	l	l	NOUN
ejpam-3454	376	12	shahrill	shahrill	NOUN
ejpam-3454	376	13	,	,	PUNCT
ejpam-3454	376	14	and	and	CCONJ
ejpam-3454	376	15	a	a	DET
ejpam-3454	376	16	madzvamuse	madzvamuse	NOUN
ejpam-3454	376	17	.	.	PUNCT
ejpam-3454	377	1	the	the	DET
ejpam-3454	377	2	stability	stability	NOUN
ejpam-3454	377	3	analyses	analyse	VERB
ejpam-3454	377	4	of	of	ADP
ejpam-3454	377	5	the	the	DET
ejpam-3454	377	6	mathematical	mathematical	ADJ
ejpam-3454	377	7	models	model	NOUN
ejpam-3454	377	8	of	of	ADP
ejpam-3454	377	9	hepatitis	hepatitis	PROPN
ejpam-3454	377	10	c	c	PROPN
ejpam-3454	377	11	virus	virus	NOUN
ejpam-3454	377	12	infection	infection	NOUN
ejpam-3454	377	13	.	.	PUNCT
ejpam-3454	378	1	modern	modern	ADJ
ejpam-3454	378	2	.	.	PUNCT
ejpam-3454	379	1	applied	apply	VERB
ejpam-3454	379	2	science	science	NOUN
ejpam-3454	379	3	,	,	PUNCT
ejpam-3454	379	4	9(3):250–271	9(3):250–271	NUM
ejpam-3454	379	5	,	,	PUNCT
ejpam-3454	379	6	2015	2015	NUM
ejpam-3454	379	7	.	.	PUNCT
ejpam-3454	380	1	[	[	X
ejpam-3454	380	2	3	3	X
ejpam-3454	380	3	]	]	X
ejpam-3454	380	4	h	h	NOUN
ejpam-3454	380	5	dahari	dahari	PROPN
ejpam-3454	380	6	,	,	PUNCT
ejpam-3454	380	7	j	j	PROPN
ejpam-3454	380	8	e	e	SYM
ejpam-3454	380	9	layden	layden	PROPN
ejpam-3454	380	10	-	-	PUNCT
ejpam-3454	380	11	almer	almer	PROPN
ejpam-3454	380	12	,	,	PUNCT
ejpam-3454	380	13	e	e	NOUN
ejpam-3454	380	14	kallwitz	kallwitz	PROPN
ejpam-3454	380	15	,	,	PUNCT
ejpam-3454	380	16	r	r	PROPN
ejpam-3454	380	17	m	m	PROPN
ejpam-3454	380	18	ribeiro	ribeiro	PROPN
ejpam-3454	380	19	,	,	PUNCT
ejpam-3454	380	20	s	s	PART
ejpam-3454	380	21	j	j	NOUN
ejpam-3454	380	22	cotler	cotler	NOUN
ejpam-3454	380	23	,	,	PUNCT
ejpam-3454	380	24	t	t	PROPN
ejpam-3454	380	25	j	j	PROPN
ejpam-3454	380	26	layden	layden	PROPN
ejpam-3454	380	27	,	,	PUNCT
ejpam-3454	380	28	and	and	CCONJ
ejpam-3454	380	29	a	a	DET
ejpam-3454	380	30	s	s	NOUN
ejpam-3454	380	31	perelson	perelson	NOUN
ejpam-3454	380	32	.	.	PUNCT
ejpam-3454	381	1	a	a	DET
ejpam-3454	381	2	mathematical	mathematical	ADJ
ejpam-3454	381	3	model	model	NOUN
ejpam-3454	381	4	of	of	ADP
ejpam-3454	381	5	hepatitis	hepatitis	PROPN
ejpam-3454	381	6	c	c	PROPN
ejpam-3454	381	7	virus	virus	NOUN
ejpam-3454	381	8	dynamics	dynamic	NOUN
ejpam-3454	381	9	in	in	ADP
ejpam-3454	381	10	patients	patient	NOUN
ejpam-3454	381	11	with	with	ADP
ejpam-3454	381	12	high	high	ADJ
ejpam-3454	381	13	baseline	baseline	ADJ
ejpam-3454	381	14	viral	viral	ADJ
ejpam-3454	381	15	loads	load	NOUN
ejpam-3454	381	16	or	or	CCONJ
ejpam-3454	381	17	advanced	advanced	ADJ
ejpam-3454	381	18	liver	liver	NOUN
ejpam-3454	381	19	disease	disease	NOUN
ejpam-3454	381	20	.	.	PUNCT
ejpam-3454	382	1	gastroenterology	gastroenterology	NOUN
ejpam-3454	382	2	,	,	PUNCT
ejpam-3454	382	3	136:1402–1409	136:1402–1409	NUM
ejpam-3454	382	4	,	,	PUNCT
ejpam-3454	382	5	2009	2009	NUM
ejpam-3454	382	6	.	.	PUNCT
ejpam-3454	383	1	[	[	X
ejpam-3454	383	2	4	4	X
ejpam-3454	383	3	]	]	X
ejpam-3454	383	4	p	p	PROPN
ejpam-3454	383	5	van	van	PROPN
ejpam-3454	383	6	den	den	PROPN
ejpam-3454	383	7	driessche	driessche	NOUN
ejpam-3454	383	8	and	and	CCONJ
ejpam-3454	383	9	j	j	PROPN
ejpam-3454	383	10	watmough	watmough	PROPN
ejpam-3454	383	11	.	.	PUNCT
ejpam-3454	384	1	reproduction	reproduction	NOUN
ejpam-3454	384	2	numbers	number	NOUN
ejpam-3454	384	3	and	and	CCONJ
ejpam-3454	384	4	sub	sub	ADJ
ejpam-3454	384	5	-	-	ADJ
ejpam-3454	384	6	threshold	threshold	ADJ
ejpam-3454	384	7	endemic	endemic	ADJ
ejpam-3454	384	8	equilibria	equilibrium	NOUN
ejpam-3454	384	9	for	for	ADP
ejpam-3454	384	10	compartmental	compartmental	ADJ
ejpam-3454	384	11	models	model	NOUN
ejpam-3454	384	12	of	of	ADP
ejpam-3454	384	13	disease	disease	NOUN
ejpam-3454	384	14	transmission	transmission	NOUN
ejpam-3454	384	15	.	.	PUNCT
ejpam-3454	385	1	math	math	NOUN
ejpam-3454	385	2	.	.	PUNCT
ejpam-3454	386	1	biosci	biosci	PROPN
ejpam-3454	386	2	.	.	PUNCT
ejpam-3454	386	3	,	,	PUNCT
ejpam-3454	386	4	180:29–48	180:29–48	NUM
ejpam-3454	386	5	,	,	PUNCT
ejpam-3454	386	6	2002	2002	NUM
ejpam-3454	386	7	.	.	PUNCT
ejpam-3454	387	1	[	[	X
ejpam-3454	387	2	5	5	NUM
ejpam-3454	387	3	]	]	PUNCT
ejpam-3454	387	4	j	j	PROPN
ejpam-3454	387	5	guedj	guedj	PROPN
ejpam-3454	387	6	and	and	CCONJ
ejpam-3454	387	7	a	a	DET
ejpam-3454	387	8	u	u	X
ejpam-3454	387	9	neumann	neumann	PROPN
ejpam-3454	387	10	.	.	PUNCT
ejpam-3454	388	1	understanding	understand	VERB
ejpam-3454	388	2	hepatitis	hepatitis	PROPN
ejpam-3454	388	3	c	c	PROPN
ejpam-3454	388	4	viral	viral	ADJ
ejpam-3454	388	5	dynamics	dynamic	NOUN
ejpam-3454	388	6	with	with	ADP
ejpam-3454	388	7	directacting	directacting	NOUN
ejpam-3454	388	8	antiviral	antiviral	ADJ
ejpam-3454	388	9	agents	agent	NOUN
ejpam-3454	388	10	due	due	ADP
ejpam-3454	388	11	to	to	ADP
ejpam-3454	388	12	the	the	DET
ejpam-3454	388	13	interplay	interplay	NOUN
ejpam-3454	388	14	between	between	ADP
ejpam-3454	388	15	intracellular	intracellular	ADJ
ejpam-3454	388	16	replication	replication	NOUN
ejpam-3454	388	17	and	and	CCONJ
ejpam-3454	388	18	cellular	cellular	ADJ
ejpam-3454	388	19	infection	infection	NOUN
ejpam-3454	388	20	dynamics	dynamic	NOUN
ejpam-3454	388	21	.	.	PUNCT
ejpam-3454	389	1	j.theo.bio	j.theo.bio	INTJ
ejpam-3454	389	2	,	,	PUNCT
ejpam-3454	389	3	267:330–340	267:330–340	NUM
ejpam-3454	389	4	,	,	PUNCT
ejpam-3454	389	5	2010	2010	NUM
ejpam-3454	389	6	.	.	PUNCT
ejpam-3454	390	1	[	[	X
ejpam-3454	390	2	6	6	NUM
ejpam-3454	390	3	]	]	PUNCT
ejpam-3454	390	4	rong	rong	PROPN
ejpam-3454	390	5	j	j	PROPN
ejpam-3454	390	6	,	,	PUNCT
ejpam-3454	390	7	guedj	guedj	PROPN
ejpam-3454	390	8	j	j	PROPN
ejpam-3454	390	9	,	,	PUNCT
ejpam-3454	390	10	dahari	dahari	ADJ
ejpam-3454	390	11	h	h	NOUN
ejpam-3454	390	12	,	,	PUNCT
ejpam-3454	390	13	coffield	coffield	VERB
ejpam-3454	390	14	d	d	PROPN
ejpam-3454	390	15	j	j	PROPN
ejpam-3454	390	16	,	,	PUNCT
ejpam-3454	390	17	levi	levi	PROPN
ejpam-3454	390	18	m	m	PROPN
ejpam-3454	390	19	,	,	PUNCT
ejpam-3454	390	20	smith	smith	PROPN
ejpam-3454	390	21	p	p	X
ejpam-3454	390	22	,	,	PUNCT
ejpam-3454	390	23	and	and	CCONJ
ejpam-3454	390	24	perelson	perelson	VERB
ejpam-3454	390	25	a	a	DET
ejpam-3454	390	26	s.	s.	PROPN
ejpam-3454	390	27	analysis	analysis	NOUN
ejpam-3454	390	28	of	of	ADP
ejpam-3454	390	29	hepatitis	hepatitis	PROPN
ejpam-3454	390	30	c	c	PROPN
ejpam-3454	390	31	virus	virus	NOUN
ejpam-3454	390	32	decline	decline	VERB
ejpam-3454	390	33	during	during	ADP
ejpam-3454	390	34	treatment	treatment	NOUN
ejpam-3454	390	35	with	with	ADP
ejpam-3454	390	36	the	the	DET
ejpam-3454	390	37	protease	protease	NOUN
ejpam-3454	390	38	inhibitor	inhibitor	NOUN
ejpam-3454	390	39	danoprevir	danoprevir	PROPN
ejpam-3454	390	40	using	use	VERB
ejpam-3454	390	41	a	a	DET
ejpam-3454	390	42	multiscale	multiscale	ADJ
ejpam-3454	390	43	model	model	NOUN
ejpam-3454	390	44	.	.	PUNCT
ejpam-3454	391	1	plos	plos	PROPN
ejpam-3454	391	2	.	.	PROPN
ejpam-3454	391	3	comput	comput	PROPN
ejpam-3454	391	4	.	.	PUNCT
ejpam-3454	392	1	biol	biol	PROPN
ejpam-3454	392	2	,	,	PUNCT
ejpam-3454	392	3	9(3):e1002959	9(3):e1002959	NUM
ejpam-3454	392	4	,	,	PUNCT
ejpam-3454	392	5	2013	2013	NUM
ejpam-3454	392	6	.	.	PUNCT
ejpam-3454	393	1	[	[	X
ejpam-3454	393	2	7	7	NUM
ejpam-3454	393	3	]	]	X
ejpam-3454	393	4	m	m	VERB
ejpam-3454	393	5	y	y	PROPN
ejpam-3454	393	6	li	li	PROPN
ejpam-3454	393	7	and	and	CCONJ
ejpam-3454	393	8	j	j	PROPN
ejpam-3454	393	9	s	s	PROPN
ejpam-3454	393	10	muldowney	muldowney	PROPN
ejpam-3454	393	11	.	.	PUNCT
ejpam-3454	394	1	a	a	DET
ejpam-3454	394	2	geometric	geometric	ADJ
ejpam-3454	394	3	approach	approach	NOUN
ejpam-3454	394	4	to	to	ADP
ejpam-3454	394	5	the	the	DET
ejpam-3454	394	6	global	global	ADJ
ejpam-3454	394	7	-	-	PUNCT
ejpam-3454	394	8	stability	stability	NOUN
ejpam-3454	394	9	problems	problem	NOUN
ejpam-3454	394	10	.	.	PUNCT
ejpam-3454	395	1	siam	siam	PROPN
ejpam-3454	395	2	j.	j.	PROPN
ejpam-3454	395	3	math	math	PROPN
ejpam-3454	395	4	.	.	PUNCT
ejpam-3454	396	1	anal	anal	PROPN
ejpam-3454	396	2	.	.	PROPN
ejpam-3454	396	3	,	,	PUNCT
ejpam-3454	396	4	27:1070–1083	27:1070–1083	NUM
ejpam-3454	396	5	,	,	PUNCT
ejpam-3454	396	6	1996	1996	NUM
ejpam-3454	396	7	.	.	PUNCT
ejpam-3454	397	1	[	[	X
ejpam-3454	397	2	8	8	NUM
ejpam-3454	397	3	]	]	X
ejpam-3454	397	4	a	a	DET
ejpam-3454	397	5	u	u	X
ejpam-3454	397	6	neumann	neumann	PROPN
ejpam-3454	397	7	,	,	PUNCT
ejpam-3454	397	8	n	n	PROPN
ejpam-3454	397	9	p	p	PROPN
ejpam-3454	397	10	lam	lam	PROPN
ejpam-3454	397	11	,	,	PUNCT
ejpam-3454	397	12	h	h	PROPN
ejpam-3454	397	13	dahari	dahari	ADJ
ejpam-3454	397	14	,	,	PUNCT
ejpam-3454	397	15	d	d	PROPN
ejpam-3454	397	16	r	r	PROPN
ejpam-3454	397	17	gretch	gretch	PROPN
ejpam-3454	397	18	,	,	PUNCT
ejpam-3454	397	19	t	t	PROPN
ejpam-3454	397	20	e	e	PROPN
ejpam-3454	397	21	wiley	wiley	PROPN
ejpam-3454	397	22	,	,	PUNCT
ejpam-3454	397	23	t	t	PROPN
ejpam-3454	397	24	j	j	PROPN
ejpam-3454	397	25	layden	layden	PROPN
ejpam-3454	397	26	,	,	PUNCT
ejpam-3454	397	27	and	and	CCONJ
ejpam-3454	397	28	a	a	DET
ejpam-3454	397	29	s	s	NOUN
ejpam-3454	397	30	perelson	perelson	NOUN
ejpam-3454	397	31	.	.	PUNCT
ejpam-3454	398	1	hepatitis	hepatitis	PROPN
ejpam-3454	398	2	c	c	PROPN
ejpam-3454	398	3	viral	viral	ADJ
ejpam-3454	398	4	dynamics	dynamic	NOUN
ejpam-3454	398	5	in	in	ADP
ejpam-3454	398	6	vivo	vivo	NOUN
ejpam-3454	398	7	and	and	CCONJ
ejpam-3454	398	8	the	the	DET
ejpam-3454	398	9	antiviral	antiviral	ADJ
ejpam-3454	398	10	efficacy	efficacy	NOUN
ejpam-3454	398	11	of	of	ADP
ejpam-3454	398	12	interferonalpha	interferonalpha	NOUN
ejpam-3454	398	13	therapy	therapy	NOUN
ejpam-3454	398	14	.	.	PUNCT
ejpam-3454	399	1	science	science	NOUN
ejpam-3454	399	2	,	,	PUNCT
ejpam-3454	399	3	282:103–107	282:103–107	NUM
ejpam-3454	399	4	,	,	PUNCT
ejpam-3454	399	5	1998	1998	NUM
ejpam-3454	399	6	.	.	PUNCT
ejpam-3454	400	1	[	[	X
ejpam-3454	400	2	9	9	NUM
ejpam-3454	400	3	]	]	X
ejpam-3454	400	4	e	e	X
ejpam-3454	400	5	rodriguez	rodriguez	PROPN
ejpam-3454	400	6	-	-	PUNCT
ejpam-3454	400	7	inigo	inigo	PROPN
ejpam-3454	400	8	,	,	PUNCT
ejpam-3454	400	9	j	j	PROPN
ejpam-3454	400	10	lopez	lopez	PROPN
ejpam-3454	400	11	-	-	PUNCT
ejpam-3454	400	12	alcorocho	alcorocho	PROPN
ejpam-3454	400	13	,	,	PUNCT
ejpam-3454	400	14	j	j	PROPN
ejpam-3454	400	15	bartolome	bartolome	PROPN
ejpam-3454	400	16	,	,	PUNCT
ejpam-3454	400	17	n	n	CCONJ
ejpam-3454	400	18	ortiz	ortiz	NOUN
ejpam-3454	400	19	-	-	PUNCT
ejpam-3454	400	20	movilla	movilla	NOUN
ejpam-3454	400	21	,	,	PUNCT
ejpam-3454	400	22	m	m	VERB
ejpam-3454	400	23	pardoand	pardoand	ADJ
ejpam-3454	400	24	,	,	PUNCT
ejpam-3454	400	25	and	and	CCONJ
ejpam-3454	400	26	v	v	ADP
ejpam-3454	400	27	carreno	carreno	NOUN
ejpam-3454	400	28	.	.	PUNCT
ejpam-3454	401	1	percentage	percentage	NOUN
ejpam-3454	401	2	of	of	ADP
ejpam-3454	401	3	hepatitis	hepatitis	PROPN
ejpam-3454	401	4	c	c	PROPN
ejpam-3454	401	5	virus	virus	NOUN
ejpam-3454	401	6	-	-	PUNCT
ejpam-3454	401	7	infected	infect	VERB
ejpam-3454	401	8	hepatocytes	hepatocyte	NOUN
ejpam-3454	401	9	is	be	AUX
ejpam-3454	401	10	a	a	DET
ejpam-3454	401	11	better	well	ADJ
ejpam-3454	401	12	predictor	predictor	NOUN
ejpam-3454	401	13	of	of	ADP
ejpam-3454	401	14	response	response	NOUN
ejpam-3454	401	15	than	than	ADP
ejpam-3454	401	16	serum	serum	NOUN
ejpam-3454	401	17	viremia	viremia	NOUN
ejpam-3454	401	18	levels	level	NOUN
ejpam-3454	401	19	.	.	PUNCT
ejpam-3454	402	1	j.mol.diag	j.mol.diag	PROPN
ejpam-3454	402	2	,	,	PUNCT
ejpam-3454	402	3	4:535–543	4:535–543	NUM
ejpam-3454	402	4	,	,	PUNCT
ejpam-3454	402	5	2005	2005	NUM
ejpam-3454	402	6	.	.	PUNCT
ejpam-3454	403	1	[	[	X
ejpam-3454	403	2	10	10	NUM
ejpam-3454	403	3	]	]	X
ejpam-3454	403	4	j	j	PROPN
ejpam-3454	403	5	stiffler	stiffler	PROPN
ejpam-3454	403	6	,	,	PUNCT
ejpam-3454	403	7	m	m	PROPN
ejpam-3454	403	8	nguyen	nguyen	NOUN
ejpam-3454	403	9	,	,	PUNCT
ejpam-3454	403	10	j	j	PROPN
ejpam-3454	403	11	sohn	sohn	PROPN
ejpam-3454	403	12	,	,	PUNCT
ejpam-3454	403	13	c	c	PROPN
ejpam-3454	403	14	liu	liu	PROPN
ejpam-3454	403	15	,	,	PUNCT
ejpam-3454	403	16	d	d	PROPN
ejpam-3454	403	17	kaplan	kaplan	PROPN
ejpam-3454	403	18	,	,	PUNCT
ejpam-3454	403	19	and	and	CCONJ
ejpam-3454	403	20	c	c	PROPN
ejpam-3454	403	21	seeger	seeger	PROPN
ejpam-3454	403	22	.	.	PUNCT
ejpam-3454	404	1	focal	focal	ADJ
ejpam-3454	404	2	distribution	distribution	NOUN
ejpam-3454	404	3	of	of	ADP
ejpam-3454	404	4	hepatitis	hepatitis	PROPN
ejpam-3454	404	5	c	c	PROPN
ejpam-3454	404	6	virus	virus	PROPN
ejpam-3454	404	7	rna	rna	PROPN
ejpam-3454	404	8	in	in	ADP
ejpam-3454	404	9	infected	infected	ADJ
ejpam-3454	404	10	livers	liver	NOUN
ejpam-3454	404	11	.	.	PUNCT
ejpam-3454	405	1	bios	bio	NOUN
ejpam-3454	405	2	,	,	PUNCT
ejpam-3454	405	3	4(8):e6661	4(8):e6661	NOUN
ejpam-3454	405	4	,	,	PUNCT
ejpam-3454	405	5	2009	2009	NUM
ejpam-3454	405	6	.	.	PUNCT