id	sid	tid	token	lemma	pos
ejpam-4550	1	1	european	european	PROPN
ejpam-4550	1	2	journal	journal	PROPN
ejpam-4550	1	3	of	of	ADP
ejpam-4550	1	4	pure	pure	ADJ
ejpam-4550	1	5	and	and	CCONJ
ejpam-4550	1	6	applied	apply	VERB
ejpam-4550	1	7	mathematics	mathematic	NOUN
ejpam-4550	1	8	vol	vol	NOUN
ejpam-4550	1	9	.	.	PUNCT
ejpam-4550	2	1	16	16	NUM
ejpam-4550	2	2	,	,	PUNCT
ejpam-4550	2	3	no	no	INTJ
ejpam-4550	2	4	.	.	NOUN
ejpam-4550	2	5	1	1	NUM
ejpam-4550	2	6	,	,	PUNCT
ejpam-4550	2	7	2023	2023	NUM
ejpam-4550	2	8	,	,	PUNCT
ejpam-4550	2	9	207	207	NUM
ejpam-4550	2	10	-	-	SYM
ejpam-4550	2	11	232	232	NUM
ejpam-4550	2	12	issn	issn	PROPN
ejpam-4550	2	13	1307	1307	NUM
ejpam-4550	2	14	-	-	SYM
ejpam-4550	2	15	5543	5543	NUM
ejpam-4550	2	16	–	–	PUNCT
ejpam-4550	2	17	ejpam.com	ejpam.com	X
ejpam-4550	2	18	published	publish	VERB
ejpam-4550	2	19	by	by	ADP
ejpam-4550	2	20	new	new	PROPN
ejpam-4550	2	21	york	york	PROPN
ejpam-4550	2	22	business	business	PROPN
ejpam-4550	2	23	global	global	PROPN
ejpam-4550	2	24	a	a	DET
ejpam-4550	2	25	mathematical	mathematical	ADJ
ejpam-4550	2	26	framework	framework	NOUN
ejpam-4550	2	27	for	for	ADP
ejpam-4550	2	28	modeling	model	VERB
ejpam-4550	2	29	the	the	DET
ejpam-4550	2	30	spread	spread	NOUN
ejpam-4550	2	31	of	of	ADP
ejpam-4550	2	32	hiv	hiv	PROPN
ejpam-4550	2	33	-	-	PUNCT
ejpam-4550	2	34	disease	disease	NOUN
ejpam-4550	2	35	within	within	ADP
ejpam-4550	2	36	two	two	NUM
ejpam-4550	2	37	different	different	ADJ
ejpam-4550	2	38	age	age	NOUN
ejpam-4550	2	39	classes	class	NOUN
ejpam-4550	2	40	mahamadou	mahamadou	VERB
ejpam-4550	2	41	alassane1,∗	alassane1,∗	PROPN
ejpam-4550	2	42	,	,	PUNCT
ejpam-4550	2	43	abdoulaye	abdoulaye	VERB
ejpam-4550	2	44	samaké1	samaké1	PROPN
ejpam-4550	2	45	,	,	PUNCT
ejpam-4550	2	46	amadou	amadou	NOUN
ejpam-4550	2	47	mahamane1	mahamane1	PROPN
ejpam-4550	2	48	,	,	PUNCT
ejpam-4550	2	49	ouaténi	ouaténi	NOUN
ejpam-4550	2	50	diallo1	diallo1	NOUN
ejpam-4550	2	51	1	1	NUM
ejpam-4550	2	52	université	université	NOUN
ejpam-4550	2	53	des	des	X
ejpam-4550	2	54	sciences	sciences	PROPN
ejpam-4550	2	55	,	,	PUNCT
ejpam-4550	2	56	des	des	X
ejpam-4550	2	57	techniques	technique	NOUN
ejpam-4550	2	58	et	et	PROPN
ejpam-4550	2	59	des	des	PROPN
ejpam-4550	2	60	technologies	technologies	PROPN
ejpam-4550	2	61	de	de	X
ejpam-4550	2	62	bamako	bamako	PROPN
ejpam-4550	2	63	,	,	PUNCT
ejpam-4550	2	64	bpe	bpe	PROPN
ejpam-4550	2	65	423	423	NUM
ejpam-4550	2	66	,	,	PUNCT
ejpam-4550	2	67	bamako	bamako	PROPN
ejpam-4550	2	68	,	,	PUNCT
ejpam-4550	2	69	mali	mali	PROPN
ejpam-4550	2	70	abstract	abstract	NOUN
ejpam-4550	2	71	.	.	PUNCT
ejpam-4550	3	1	in	in	ADP
ejpam-4550	3	2	this	this	DET
ejpam-4550	3	3	paper	paper	NOUN
ejpam-4550	3	4	,	,	PUNCT
ejpam-4550	3	5	we	we	PRON
ejpam-4550	3	6	propose	propose	VERB
ejpam-4550	3	7	a	a	DET
ejpam-4550	3	8	mathematical	mathematical	ADJ
ejpam-4550	3	9	model	model	NOUN
ejpam-4550	3	10	for	for	ADP
ejpam-4550	3	11	the	the	DET
ejpam-4550	3	12	spread	spread	NOUN
ejpam-4550	3	13	of	of	ADP
ejpam-4550	3	14	hiv	hiv	PROPN
ejpam-4550	3	15	disease	disease	NOUN
ejpam-4550	3	16	within	within	ADP
ejpam-4550	3	17	two	two	NUM
ejpam-4550	3	18	different	different	ADJ
ejpam-4550	3	19	age	age	NOUN
ejpam-4550	3	20	classes	class	NOUN
ejpam-4550	3	21	.	.	PUNCT
ejpam-4550	4	1	we	we	PRON
ejpam-4550	4	2	define	define	VERB
ejpam-4550	4	3	a	a	DET
ejpam-4550	4	4	basic	basic	ADJ
ejpam-4550	4	5	reproduction	reproduction	NOUN
ejpam-4550	4	6	number	number	NOUN
ejpam-4550	4	7	r0	r0	NOUN
ejpam-4550	4	8	that	that	PRON
ejpam-4550	4	9	depends	depend	VERB
ejpam-4550	4	10	on	on	ADP
ejpam-4550	4	11	the	the	DET
ejpam-4550	4	12	characteristics	characteristic	NOUN
ejpam-4550	4	13	of	of	ADP
ejpam-4550	4	14	the	the	DET
ejpam-4550	4	15	two	two	NUM
ejpam-4550	4	16	age	age	NOUN
ejpam-4550	4	17	classes	class	NOUN
ejpam-4550	4	18	.	.	PUNCT
ejpam-4550	5	1	we	we	PRON
ejpam-4550	5	2	prove	prove	VERB
ejpam-4550	5	3	that	that	SCONJ
ejpam-4550	5	4	if	if	SCONJ
ejpam-4550	5	5	r0	r0	NOUN
ejpam-4550	5	6	<	<	X
ejpam-4550	5	7	1	1	NUM
ejpam-4550	5	8	,	,	PUNCT
ejpam-4550	5	9	then	then	ADV
ejpam-4550	5	10	the	the	DET
ejpam-4550	5	11	disease	disease	NOUN
ejpam-4550	5	12	is	be	AUX
ejpam-4550	5	13	extinct	extinct	ADJ
ejpam-4550	5	14	in	in	ADP
ejpam-4550	5	15	both	both	DET
ejpam-4550	5	16	age	age	NOUN
ejpam-4550	5	17	classes	class	NOUN
ejpam-4550	5	18	.	.	PUNCT
ejpam-4550	6	1	in	in	ADP
ejpam-4550	6	2	contrast	contrast	NOUN
ejpam-4550	6	3	,	,	PUNCT
ejpam-4550	6	4	we	we	PRON
ejpam-4550	6	5	prove	prove	VERB
ejpam-4550	6	6	that	that	SCONJ
ejpam-4550	6	7	if	if	SCONJ
ejpam-4550	6	8	r0	r0	NOUN
ejpam-4550	6	9	>	>	X
ejpam-4550	6	10	1	1	NUM
ejpam-4550	6	11	,	,	PUNCT
ejpam-4550	6	12	then	then	ADV
ejpam-4550	6	13	the	the	DET
ejpam-4550	6	14	disease	disease	NOUN
ejpam-4550	6	15	is	be	AUX
ejpam-4550	6	16	endemic	endemic	ADJ
ejpam-4550	6	17	in	in	ADP
ejpam-4550	6	18	both	both	DET
ejpam-4550	6	19	age	age	NOUN
ejpam-4550	6	20	classes	class	NOUN
ejpam-4550	6	21	.	.	PUNCT
ejpam-4550	7	1	2020	2020	NUM
ejpam-4550	7	2	mathematics	mathematic	NOUN
ejpam-4550	7	3	subject	subject	NOUN
ejpam-4550	7	4	classifications	classification	NOUN
ejpam-4550	7	5	:	:	PUNCT
ejpam-4550	7	6	34a12,37n25,65l05,92b05	34a12,37n25,65l05,92b05	NUM
ejpam-4550	7	7	key	key	ADJ
ejpam-4550	7	8	words	word	NOUN
ejpam-4550	7	9	and	and	CCONJ
ejpam-4550	7	10	phrases	phrase	NOUN
ejpam-4550	7	11	:	:	PUNCT
ejpam-4550	7	12	hiv	hiv	PROPN
ejpam-4550	7	13	-	-	PUNCT
ejpam-4550	7	14	aids	aids	PROPN
ejpam-4550	7	15	,	,	PUNCT
ejpam-4550	7	16	epidemic	epidemic	NOUN
ejpam-4550	7	17	model	model	NOUN
ejpam-4550	7	18	,	,	PUNCT
ejpam-4550	7	19	basic	basic	ADJ
ejpam-4550	7	20	reproduction	reproduction	NOUN
ejpam-4550	7	21	number	number	NOUN
ejpam-4550	7	22	,	,	PUNCT
ejpam-4550	7	23	asymptotic	asymptotic	ADJ
ejpam-4550	7	24	stability	stability	NOUN
ejpam-4550	7	25	,	,	PUNCT
ejpam-4550	7	26	global	global	ADJ
ejpam-4550	7	27	stability	stability	NOUN
ejpam-4550	7	28	,	,	PUNCT
ejpam-4550	7	29	numerical	numerical	ADJ
ejpam-4550	7	30	simulations	simulation	NOUN
ejpam-4550	7	31	1	1	NUM
ejpam-4550	7	32	.	.	PUNCT
ejpam-4550	8	1	introduction	introduction	NOUN
ejpam-4550	8	2	acquired	acquire	VERB
ejpam-4550	8	3	immunodeficiency	immunodeficiency	NOUN
ejpam-4550	8	4	syndrome	syndrome	NOUN
ejpam-4550	8	5	(	(	PUNCT
ejpam-4550	8	6	aids	aids	PROPN
ejpam-4550	8	7	)	)	PUNCT
ejpam-4550	8	8	is	be	AUX
ejpam-4550	8	9	one	one	NUM
ejpam-4550	8	10	the	the	DET
ejpam-4550	8	11	most	most	ADV
ejpam-4550	8	12	deadly	deadly	ADJ
ejpam-4550	8	13	disease	disease	NOUN
ejpam-4550	8	14	caused	cause	VERB
ejpam-4550	8	15	by	by	ADP
ejpam-4550	8	16	a	a	DET
ejpam-4550	8	17	human	human	ADJ
ejpam-4550	8	18	immunodeficiency	immunodeficiency	NOUN
ejpam-4550	8	19	virus	virus	NOUN
ejpam-4550	8	20	(	(	PUNCT
ejpam-4550	8	21	hiv	hiv	PROPN
ejpam-4550	8	22	)	)	PUNCT
ejpam-4550	8	23	.	.	PUNCT
ejpam-4550	9	1	the	the	DET
ejpam-4550	9	2	virus	virus	NOUN
ejpam-4550	9	3	destroys	destroy	VERB
ejpam-4550	9	4	all	all	DET
ejpam-4550	9	5	the	the	DET
ejpam-4550	9	6	immune	immune	ADJ
ejpam-4550	9	7	system	system	NOUN
ejpam-4550	9	8	,	,	PUNCT
ejpam-4550	9	9	in	in	ADP
ejpam-4550	9	10	particular	particular	ADJ
ejpam-4550	9	11	the	the	DET
ejpam-4550	9	12	cd4	cd4	PROPN
ejpam-4550	9	13	t	t	PROPN
ejpam-4550	9	14	-	-	PUNCT
ejpam-4550	9	15	lymphocytes	lymphocyte	NOUN
ejpam-4550	9	16	,	,	PUNCT
ejpam-4550	9	17	and	and	CCONJ
ejpam-4550	9	18	leaves	leave	VERB
ejpam-4550	9	19	individuals	individual	NOUN
ejpam-4550	9	20	susceptible	susceptible	ADJ
ejpam-4550	9	21	to	to	ADP
ejpam-4550	9	22	any	any	DET
ejpam-4550	9	23	other	other	ADJ
ejpam-4550	9	24	infections	infection	NOUN
ejpam-4550	9	25	.	.	PUNCT
ejpam-4550	10	1	it	it	PRON
ejpam-4550	10	2	multiplies	multiply	VERB
ejpam-4550	10	3	within	within	ADP
ejpam-4550	10	4	those	those	DET
ejpam-4550	10	5	lymphocytes	lymphocyte	NOUN
ejpam-4550	10	6	and	and	CCONJ
ejpam-4550	10	7	eventually	eventually	ADV
ejpam-4550	10	8	destroys	destroy	VERB
ejpam-4550	10	9	them	they	PRON
ejpam-4550	10	10	.	.	PUNCT
ejpam-4550	11	1	once	once	SCONJ
ejpam-4550	11	2	the	the	DET
ejpam-4550	11	3	lymphocytes	lymphocyte	NOUN
ejpam-4550	11	4	are	be	AUX
ejpam-4550	11	5	depleted	deplete	VERB
ejpam-4550	11	6	,	,	PUNCT
ejpam-4550	11	7	then	then	ADV
ejpam-4550	11	8	the	the	DET
ejpam-4550	11	9	immune	immune	ADJ
ejpam-4550	11	10	system	system	NOUN
ejpam-4550	11	11	stops	stop	VERB
ejpam-4550	11	12	functioning	function	VERB
ejpam-4550	11	13	properly	properly	ADV
ejpam-4550	11	14	.	.	PUNCT
ejpam-4550	12	1	as	as	ADP
ejpam-4550	12	2	a	a	DET
ejpam-4550	12	3	result	result	NOUN
ejpam-4550	12	4	,	,	PUNCT
ejpam-4550	12	5	the	the	DET
ejpam-4550	12	6	individual	individual	NOUN
ejpam-4550	12	7	can	can	AUX
ejpam-4550	12	8	catch	catch	VERB
ejpam-4550	12	9	any	any	DET
ejpam-4550	12	10	kind	kind	NOUN
ejpam-4550	12	11	of	of	ADP
ejpam-4550	12	12	disease	disease	NOUN
ejpam-4550	12	13	that	that	PRON
ejpam-4550	12	14	might	might	AUX
ejpam-4550	12	15	kill	kill	VERB
ejpam-4550	12	16	him	he	PRON
ejpam-4550	12	17	easily	easily	ADV
ejpam-4550	12	18	because	because	SCONJ
ejpam-4550	12	19	of	of	ADP
ejpam-4550	12	20	the	the	DET
ejpam-4550	12	21	failure	failure	NOUN
ejpam-4550	12	22	of	of	ADP
ejpam-4550	12	23	its	its	PRON
ejpam-4550	12	24	immune	immune	ADJ
ejpam-4550	12	25	system	system	NOUN
ejpam-4550	12	26	.	.	PUNCT
ejpam-4550	13	1	however	however	ADV
ejpam-4550	13	2	,	,	PUNCT
ejpam-4550	13	3	there	there	PRON
ejpam-4550	13	4	are	be	VERB
ejpam-4550	13	5	drugs	drug	NOUN
ejpam-4550	13	6	that	that	PRON
ejpam-4550	13	7	can	can	AUX
ejpam-4550	13	8	slow	slow	VERB
ejpam-4550	13	9	down	down	ADP
ejpam-4550	13	10	the	the	DET
ejpam-4550	13	11	progression	progression	NOUN
ejpam-4550	13	12	of	of	ADP
ejpam-4550	13	13	the	the	DET
ejpam-4550	13	14	virus	virus	NOUN
ejpam-4550	13	15	.	.	PUNCT
ejpam-4550	14	1	hiv	hiv	PROPN
ejpam-4550	14	2	-	-	PUNCT
ejpam-4550	14	3	aids	aids	PROPN
ejpam-4550	14	4	is	be	AUX
ejpam-4550	14	5	usually	usually	ADV
ejpam-4550	14	6	transmitted	transmit	VERB
ejpam-4550	14	7	in	in	ADP
ejpam-4550	14	8	three	three	NUM
ejpam-4550	14	9	different	different	ADJ
ejpam-4550	14	10	ways	way	NOUN
ejpam-4550	14	11	,	,	PUNCT
ejpam-4550	14	12	namely	namely	ADV
ejpam-4550	14	13	the	the	DET
ejpam-4550	14	14	sexual	sexual	ADJ
ejpam-4550	14	15	contact	contact	NOUN
ejpam-4550	14	16	,	,	PUNCT
ejpam-4550	14	17	blood	blood	NOUN
ejpam-4550	14	18	transfusion	transfusion	NOUN
ejpam-4550	14	19	,	,	PUNCT
ejpam-4550	14	20	mother	mother	NOUN
ejpam-4550	14	21	-	-	PUNCT
ejpam-4550	14	22	to	to	ADP
ejpam-4550	14	23	-	-	PUNCT
ejpam-4550	14	24	child	child	NOUN
ejpam-4550	14	25	exchanges	exchange	NOUN
ejpam-4550	14	26	during	during	ADP
ejpam-4550	14	27	pregnancy	pregnancy	NOUN
ejpam-4550	14	28	,	,	PUNCT
ejpam-4550	14	29	childbirth	childbirth	NOUN
ejpam-4550	14	30	and	and	CCONJ
ejpam-4550	14	31	breastfeeding	breastfeeding	NOUN
ejpam-4550	14	32	.	.	PUNCT
ejpam-4550	15	1	many	many	ADJ
ejpam-4550	15	2	mathematical	mathematical	ADJ
ejpam-4550	15	3	models	model	NOUN
ejpam-4550	15	4	are	be	AUX
ejpam-4550	15	5	used	use	VERB
ejpam-4550	15	6	to	to	PART
ejpam-4550	15	7	study	study	VERB
ejpam-4550	15	8	the	the	DET
ejpam-4550	15	9	impact	impact	NOUN
ejpam-4550	15	10	of	of	ADP
ejpam-4550	15	11	preventive	preventive	ADJ
ejpam-4550	15	12	control	control	NOUN
ejpam-4550	15	13	strategies	strategy	NOUN
ejpam-4550	15	14	on	on	ADP
ejpam-4550	15	15	the	the	DET
ejpam-4550	15	16	spread	spread	NOUN
ejpam-4550	15	17	of	of	ADP
ejpam-4550	15	18	hiv	hiv	PROPN
ejpam-4550	15	19	-	-	PUNCT
ejpam-4550	15	20	aids	aids	PROPN
ejpam-4550	15	21	in	in	ADP
ejpam-4550	15	22	given	give	VERB
ejpam-4550	15	23	populations	population	NOUN
ejpam-4550	15	24	[	[	X
ejpam-4550	15	25	1	1	NUM
ejpam-4550	15	26	,	,	PUNCT
ejpam-4550	15	27	3	3	NUM
ejpam-4550	15	28	,	,	PUNCT
ejpam-4550	15	29	5	5	NUM
ejpam-4550	15	30	,	,	PUNCT
ejpam-4550	15	31	6	6	NUM
ejpam-4550	15	32	,	,	PUNCT
ejpam-4550	15	33	9–14	9–14	PROPN
ejpam-4550	15	34	]	]	X
ejpam-4550	15	35	.	.	PUNCT
ejpam-4550	16	1	some	some	PRON
ejpam-4550	16	2	of	of	ADP
ejpam-4550	16	3	these	these	DET
ejpam-4550	16	4	models	model	NOUN
ejpam-4550	16	5	have	have	AUX
ejpam-4550	16	6	shown	show	VERB
ejpam-4550	16	7	that	that	SCONJ
ejpam-4550	16	8	a	a	DET
ejpam-4550	16	9	change	change	NOUN
ejpam-4550	16	10	in	in	ADP
ejpam-4550	16	11	risky	risky	ADJ
ejpam-4550	16	12	behavior	behavior	NOUN
ejpam-4550	16	13	is	be	AUX
ejpam-4550	16	14	necessary	necessary	ADJ
ejpam-4550	16	15	to	to	PART
ejpam-4550	16	16	prevent	prevent	VERB
ejpam-4550	16	17	the	the	DET
ejpam-4550	16	18	spread	spread	NOUN
ejpam-4550	16	19	of	of	ADP
ejpam-4550	16	20	hiv	hiv	PROPN
ejpam-4550	16	21	-	-	PUNCT
ejpam-4550	16	22	aids	aids	PROPN
ejpam-4550	16	23	,	,	PUNCT
ejpam-4550	16	24	even	even	ADV
ejpam-4550	16	25	in	in	ADP
ejpam-4550	16	26	the	the	DET
ejpam-4550	16	27	presence	presence	NOUN
ejpam-4550	16	28	of	of	ADP
ejpam-4550	16	29	a	a	DET
ejpam-4550	16	30	treatment	treatment	NOUN
ejpam-4550	16	31	[	[	X
ejpam-4550	16	32	2	2	NUM
ejpam-4550	16	33	,	,	PUNCT
ejpam-4550	16	34	8	8	NUM
ejpam-4550	16	35	]	]	PUNCT
ejpam-4550	16	36	.	.	PUNCT
ejpam-4550	17	1	in	in	ADP
ejpam-4550	17	2	this	this	DET
ejpam-4550	17	3	paper	paper	NOUN
ejpam-4550	17	4	,	,	PUNCT
ejpam-4550	17	5	we	we	PRON
ejpam-4550	17	6	study	study	VERB
ejpam-4550	17	7	the	the	DET
ejpam-4550	17	8	spread	spread	NOUN
ejpam-4550	17	9	of	of	ADP
ejpam-4550	17	10	hiv	hiv	PROPN
ejpam-4550	17	11	-	-	PUNCT
ejpam-4550	17	12	aids	aids	PROPN
ejpam-4550	17	13	in	in	ADP
ejpam-4550	17	14	the	the	DET
ejpam-4550	17	15	age	age	NOUN
ejpam-4550	17	16	structured	structure	VERB
ejpam-4550	17	17	populations	population	NOUN
ejpam-4550	17	18	.	.	PUNCT
ejpam-4550	18	1	in	in	ADP
ejpam-4550	18	2	fact	fact	NOUN
ejpam-4550	18	3	,	,	PUNCT
ejpam-4550	18	4	we	we	PRON
ejpam-4550	18	5	consider	consider	VERB
ejpam-4550	18	6	two	two	NUM
ejpam-4550	18	7	different	different	ADJ
ejpam-4550	18	8	age	age	NOUN
ejpam-4550	18	9	classes	class	NOUN
ejpam-4550	18	10	:	:	PUNCT
ejpam-4550	18	11	a	a	DET
ejpam-4550	18	12	first	first	ADJ
ejpam-4550	18	13	class	class	NOUN
ejpam-4550	18	14	that	that	PRON
ejpam-4550	18	15	corresponds	correspond	VERB
ejpam-4550	18	16	to	to	ADP
ejpam-4550	18	17	individuals	individual	NOUN
ejpam-4550	18	18	aged	age	VERB
ejpam-4550	18	19	∗corresponding	∗corresponde	VERB
ejpam-4550	18	20	author	author	NOUN
ejpam-4550	18	21	.	.	PUNCT
ejpam-4550	19	1	doi	doi	NOUN
ejpam-4550	19	2	:	:	PUNCT
ejpam-4550	19	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4550	https://doi.org/10.29020/nybg.ejpam.v16i1.4550	X
ejpam-4550	19	4	email	email	NOUN
ejpam-4550	19	5	addresses	address	NOUN
ejpam-4550	19	6	:	:	PUNCT
ejpam-4550	19	7	alassanemaiga@yahoo.fr	alassanemaiga@yahoo.fr	PROPN
ejpam-4550	19	8	(	(	PUNCT
ejpam-4550	19	9	m.	m.	NOUN
ejpam-4550	19	10	alassane	alassane	PROPN
ejpam-4550	19	11	)	)	PUNCT
ejpam-4550	19	12	,	,	PUNCT
ejpam-4550	19	13	abdoulaye.samake@usttb.edu.ml	abdoulaye.samake@usttb.edu.ml	PROPN
ejpam-4550	19	14	(	(	PUNCT
ejpam-4550	19	15	a.	a.	NOUN
ejpam-4550	19	16	samaké	samaké	NOUN
ejpam-4550	19	17	)	)	PUNCT
ejpam-4550	19	18	,	,	PUNCT
ejpam-4550	19	19	moulaye.ahmad@gmail.com	moulaye.ahmad@gmail.com	X
ejpam-4550	19	20	(	(	PUNCT
ejpam-4550	19	21	a.	a.	NOUN
ejpam-4550	19	22	mahamane	mahamane	NOUN
ejpam-4550	19	23	)	)	PUNCT
ejpam-4550	19	24	,	,	PUNCT
ejpam-4550	19	25	ouateni@yahoo.fr	ouateni@yahoo.fr	PROPN
ejpam-4550	19	26	(	(	PUNCT
ejpam-4550	19	27	o.	o.	PROPN
ejpam-4550	19	28	diallo	diallo	PROPN
ejpam-4550	19	29	)	)	PUNCT
ejpam-4550	19	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4550	19	31	207	207	NUM
ejpam-4550	20	1	©	©	PROPN
ejpam-4550	20	2	2023	2023	NUM
ejpam-4550	20	3	ejpam	ejpam	NOUN
ejpam-4550	20	4	all	all	DET
ejpam-4550	20	5	rights	right	NOUN
ejpam-4550	20	6	reserved	reserve	VERB
ejpam-4550	20	7	.	.	PUNCT
ejpam-4550	21	1	m.	m.	NOUN
ejpam-4550	21	2	alassane	alassane	PROPN
ejpam-4550	21	3	et	et	PROPN
ejpam-4550	21	4	al	al	PROPN
ejpam-4550	21	5	.	.	PUNCT
ejpam-4550	21	6	/	/	SYM
ejpam-4550	21	7	eur	eur	PROPN
ejpam-4550	21	8	.	.	PUNCT
ejpam-4550	22	1	j.	j.	PROPN
ejpam-4550	22	2	pure	pure	PROPN
ejpam-4550	22	3	appl	appl	PROPN
ejpam-4550	22	4	.	.	PROPN
ejpam-4550	22	5	math	math	PROPN
ejpam-4550	22	6	,	,	PUNCT
ejpam-4550	22	7	16	16	NUM
ejpam-4550	22	8	(	(	PUNCT
ejpam-4550	22	9	1	1	NUM
ejpam-4550	22	10	)	)	PUNCT
ejpam-4550	22	11	(	(	PUNCT
ejpam-4550	22	12	2023	2023	NUM
ejpam-4550	22	13	)	)	PUNCT
ejpam-4550	22	14	,	,	PUNCT
ejpam-4550	22	15	207	207	NUM
ejpam-4550	22	16	-	-	SYM
ejpam-4550	22	17	232	232	NUM
ejpam-4550	22	18	208	208	NUM
ejpam-4550	22	19	25	25	NUM
ejpam-4550	22	20	years	year	NOUN
ejpam-4550	22	21	or	or	CCONJ
ejpam-4550	22	22	less	less	ADJ
ejpam-4550	22	23	and	and	CCONJ
ejpam-4550	22	24	a	a	DET
ejpam-4550	22	25	second	second	ADJ
ejpam-4550	22	26	class	class	NOUN
ejpam-4550	22	27	that	that	PRON
ejpam-4550	22	28	corresponds	correspond	VERB
ejpam-4550	22	29	to	to	ADP
ejpam-4550	22	30	individuals	individual	NOUN
ejpam-4550	22	31	aged	age	VERB
ejpam-4550	22	32	over	over	ADP
ejpam-4550	22	33	25	25	NUM
ejpam-4550	22	34	years	year	NOUN
ejpam-4550	22	35	.	.	PUNCT
ejpam-4550	23	1	we	we	PRON
ejpam-4550	23	2	suppose	suppose	VERB
ejpam-4550	23	3	that	that	SCONJ
ejpam-4550	23	4	each	each	DET
ejpam-4550	23	5	age	age	NOUN
ejpam-4550	23	6	class	class	NOUN
ejpam-4550	23	7	is	be	AUX
ejpam-4550	23	8	composed	compose	VERB
ejpam-4550	23	9	of	of	ADP
ejpam-4550	23	10	susceptible	susceptible	ADJ
ejpam-4550	23	11	and	and	CCONJ
ejpam-4550	23	12	infected	infected	ADJ
ejpam-4550	23	13	individuals	individual	NOUN
ejpam-4550	23	14	.	.	PUNCT
ejpam-4550	24	1	according	accord	VERB
ejpam-4550	24	2	to	to	ADP
ejpam-4550	24	3	the	the	DET
ejpam-4550	24	4	center	center	NOUN
ejpam-4550	24	5	of	of	ADP
ejpam-4550	24	6	disease	disease	NOUN
ejpam-4550	24	7	control	control	NOUN
ejpam-4550	24	8	(	(	PUNCT
ejpam-4550	24	9	cdc	cdc	PROPN
ejpam-4550	24	10	)	)	PUNCT
ejpam-4550	24	11	,	,	PUNCT
ejpam-4550	24	12	there	there	PRON
ejpam-4550	24	13	are	be	VERB
ejpam-4550	24	14	three	three	NUM
ejpam-4550	24	15	main	main	ADJ
ejpam-4550	24	16	classes	class	NOUN
ejpam-4550	24	17	of	of	ADP
ejpam-4550	24	18	hiv	hiv	PROPN
ejpam-4550	24	19	-	-	PUNCT
ejpam-4550	24	20	aids	aids	PROPN
ejpam-4550	24	21	infected	infect	VERB
ejpam-4550	24	22	individuals	individual	NOUN
ejpam-4550	24	23	based	base	VERB
ejpam-4550	24	24	on	on	ADP
ejpam-4550	24	25	cd4	cd4	PROPN
ejpam-4550	24	26	t	t	PROPN
ejpam-4550	24	27	-	-	PUNCT
ejpam-4550	24	28	lymphocyte	lymphocyte	ADJ
ejpam-4550	24	29	counts	count	NOUN
ejpam-4550	24	30	,	,	PUNCT
ejpam-4550	24	31	see	see	VERB
ejpam-4550	24	32	table	table	NOUN
ejpam-4550	24	33	1	1	NUM
ejpam-4550	24	34	.	.	PUNCT
ejpam-4550	24	35	table	table	NOUN
ejpam-4550	24	36	1	1	NUM
ejpam-4550	24	37	:	:	PUNCT
ejpam-4550	24	38	main	main	ADJ
ejpam-4550	24	39	classes	class	NOUN
ejpam-4550	24	40	of	of	ADP
ejpam-4550	24	41	hiv	hiv	PROPN
ejpam-4550	24	42	-	-	PUNCT
ejpam-4550	24	43	aids	aids	PROPN
ejpam-4550	24	44	infected	infect	VERB
ejpam-4550	24	45	individuals	individual	NOUN
ejpam-4550	24	46	stages	stage	NOUN
ejpam-4550	24	47	of	of	ADP
ejpam-4550	24	48	infection	infection	NOUN
ejpam-4550	24	49	cd4	cd4	PROPN
ejpam-4550	24	50	t	t	PROPN
ejpam-4550	24	51	-	-	PUNCT
ejpam-4550	24	52	lymphocytes	lymphocyte	NOUN
ejpam-4550	24	53	/	/	SYM
ejpam-4550	24	54	mm3	mm3	NOUN
ejpam-4550	24	55	stage	stage	NOUN
ejpam-4550	24	56	1	1	NUM
ejpam-4550	24	57	>	>	SYM
ejpam-4550	24	58	500	500	NUM
ejpam-4550	24	59	stage	stage	NOUN
ejpam-4550	24	60	2	2	NUM
ejpam-4550	24	61	200	200	NUM
ejpam-4550	24	62	<	<	X
ejpam-4550	24	63	cd4	cd4	PROPN
ejpam-4550	24	64	t	t	PROPN
ejpam-4550	24	65	<	<	X
ejpam-4550	24	66	500	500	NUM
ejpam-4550	24	67	stage	stage	NOUN
ejpam-4550	24	68	3	3	NUM
ejpam-4550	24	69	<	<	SYM
ejpam-4550	24	70	200	200	NUM
ejpam-4550	24	71	the	the	DET
ejpam-4550	24	72	first	first	ADJ
ejpam-4550	24	73	stage	stage	NOUN
ejpam-4550	24	74	of	of	ADP
ejpam-4550	24	75	infection	infection	NOUN
ejpam-4550	24	76	occurs	occur	VERB
ejpam-4550	24	77	between	between	ADP
ejpam-4550	24	78	two	two	NUM
ejpam-4550	24	79	and	and	CCONJ
ejpam-4550	24	80	six	six	NUM
ejpam-4550	24	81	weeks	week	NOUN
ejpam-4550	24	82	after	after	ADP
ejpam-4550	24	83	hiv	hiv	PROPN
ejpam-4550	24	84	infection	infection	NOUN
ejpam-4550	24	85	.	.	PUNCT
ejpam-4550	25	1	the	the	DET
ejpam-4550	25	2	infected	infected	ADJ
ejpam-4550	25	3	individual	individual	NOUN
ejpam-4550	25	4	begins	begin	VERB
ejpam-4550	25	5	to	to	PART
ejpam-4550	25	6	produce	produce	VERB
ejpam-4550	25	7	antibodies	antibody	NOUN
ejpam-4550	25	8	that	that	PRON
ejpam-4550	25	9	are	be	AUX
ejpam-4550	25	10	detectable	detectable	ADJ
ejpam-4550	25	11	by	by	ADP
ejpam-4550	25	12	hiv	hiv	PROPN
ejpam-4550	25	13	tests	test	NOUN
ejpam-4550	25	14	.	.	PUNCT
ejpam-4550	26	1	the	the	DET
ejpam-4550	26	2	individual	individual	NOUN
ejpam-4550	26	3	is	be	AUX
ejpam-4550	26	4	then	then	ADV
ejpam-4550	26	5	called	call	VERB
ejpam-4550	26	6	hiv	hiv	PROPN
ejpam-4550	26	7	-	-	PUNCT
ejpam-4550	26	8	positive	positive	ADJ
ejpam-4550	26	9	.	.	PUNCT
ejpam-4550	27	1	the	the	DET
ejpam-4550	27	2	second	second	ADJ
ejpam-4550	27	3	stage	stage	NOUN
ejpam-4550	27	4	of	of	ADP
ejpam-4550	27	5	infection	infection	NOUN
ejpam-4550	27	6	is	be	AUX
ejpam-4550	27	7	characterized	characterize	VERB
ejpam-4550	27	8	by	by	ADP
ejpam-4550	27	9	a	a	DET
ejpam-4550	27	10	reduction	reduction	NOUN
ejpam-4550	27	11	in	in	ADP
ejpam-4550	27	12	the	the	DET
ejpam-4550	27	13	number	number	NOUN
ejpam-4550	27	14	of	of	ADP
ejpam-4550	27	15	viral	viral	ADJ
ejpam-4550	27	16	particles	particle	NOUN
ejpam-4550	27	17	in	in	ADP
ejpam-4550	27	18	the	the	DET
ejpam-4550	27	19	blood	blood	NOUN
ejpam-4550	27	20	,	,	PUNCT
ejpam-4550	27	21	marking	mark	VERB
ejpam-4550	27	22	the	the	DET
ejpam-4550	27	23	beginning	beginning	NOUN
ejpam-4550	27	24	of	of	ADP
ejpam-4550	27	25	the	the	DET
ejpam-4550	27	26	clinical	clinical	ADJ
ejpam-4550	27	27	latency	latency	NOUN
ejpam-4550	27	28	phase	phase	NOUN
ejpam-4550	27	29	of	of	ADP
ejpam-4550	27	30	the	the	DET
ejpam-4550	27	31	infection	infection	NOUN
ejpam-4550	27	32	.	.	PUNCT
ejpam-4550	28	1	finally	finally	ADV
ejpam-4550	28	2	,	,	PUNCT
ejpam-4550	28	3	the	the	DET
ejpam-4550	28	4	third	third	ADJ
ejpam-4550	28	5	stage	stage	NOUN
ejpam-4550	28	6	of	of	ADP
ejpam-4550	28	7	infection	infection	NOUN
ejpam-4550	28	8	is	be	AUX
ejpam-4550	28	9	characterized	characterize	VERB
ejpam-4550	28	10	by	by	ADP
ejpam-4550	28	11	the	the	DET
ejpam-4550	28	12	presence	presence	NOUN
ejpam-4550	28	13	of	of	ADP
ejpam-4550	28	14	major	major	ADJ
ejpam-4550	28	15	infections	infection	NOUN
ejpam-4550	28	16	.	.	PUNCT
ejpam-4550	29	1	we	we	PRON
ejpam-4550	29	2	aim	aim	VERB
ejpam-4550	29	3	to	to	PART
ejpam-4550	29	4	capture	capture	VERB
ejpam-4550	29	5	the	the	DET
ejpam-4550	29	6	spread	spread	NOUN
ejpam-4550	29	7	of	of	ADP
ejpam-4550	29	8	hiv	hiv	PROPN
ejpam-4550	29	9	-	-	PUNCT
ejpam-4550	29	10	aids	aids	PROPN
ejpam-4550	29	11	in	in	ADP
ejpam-4550	29	12	a	a	DET
ejpam-4550	29	13	population	population	NOUN
ejpam-4550	29	14	divided	divide	VERB
ejpam-4550	29	15	into	into	ADP
ejpam-4550	29	16	two	two	NUM
ejpam-4550	29	17	different	different	ADJ
ejpam-4550	29	18	age	age	NOUN
ejpam-4550	29	19	classes	class	NOUN
ejpam-4550	29	20	by	by	ADP
ejpam-4550	29	21	a	a	DET
ejpam-4550	29	22	system	system	NOUN
ejpam-4550	29	23	of	of	ADP
ejpam-4550	29	24	ordinary	ordinary	ADJ
ejpam-4550	29	25	differential	differential	ADJ
ejpam-4550	29	26	equations	equation	NOUN
ejpam-4550	29	27	.	.	PUNCT
ejpam-4550	30	1	the	the	DET
ejpam-4550	30	2	paper	paper	NOUN
ejpam-4550	30	3	is	be	AUX
ejpam-4550	30	4	organized	organize	VERB
ejpam-4550	30	5	as	as	SCONJ
ejpam-4550	30	6	follows	follow	VERB
ejpam-4550	30	7	.	.	PUNCT
ejpam-4550	31	1	in	in	ADP
ejpam-4550	31	2	section	section	NOUN
ejpam-4550	31	3	2	2	NUM
ejpam-4550	31	4	,	,	PUNCT
ejpam-4550	31	5	we	we	PRON
ejpam-4550	31	6	formulate	formulate	VERB
ejpam-4550	31	7	a	a	DET
ejpam-4550	31	8	mathematical	mathematical	ADJ
ejpam-4550	31	9	model	model	NOUN
ejpam-4550	31	10	for	for	ADP
ejpam-4550	31	11	hiv	hiv	PROPN
ejpam-4550	31	12	-	-	PUNCT
ejpam-4550	31	13	aids	aids	PROPN
ejpam-4550	31	14	.	.	PUNCT
ejpam-4550	32	1	the	the	DET
ejpam-4550	32	2	basic	basic	ADJ
ejpam-4550	32	3	properties	property	NOUN
ejpam-4550	32	4	of	of	ADP
ejpam-4550	32	5	the	the	DET
ejpam-4550	32	6	model	model	NOUN
ejpam-4550	32	7	are	be	AUX
ejpam-4550	32	8	given	give	VERB
ejpam-4550	32	9	in	in	ADP
ejpam-4550	32	10	section	section	NOUN
ejpam-4550	32	11	3	3	NUM
ejpam-4550	32	12	.	.	PUNCT
ejpam-4550	33	1	in	in	ADP
ejpam-4550	33	2	section	section	NOUN
ejpam-4550	33	3	4	4	NUM
ejpam-4550	33	4	,	,	PUNCT
ejpam-4550	33	5	the	the	DET
ejpam-4550	33	6	disease	disease	NOUN
ejpam-4550	33	7	-	-	PUNCT
ejpam-4550	33	8	free	free	ADJ
ejpam-4550	33	9	equilibrium	equilibrium	NOUN
ejpam-4550	33	10	point	point	NOUN
ejpam-4550	33	11	(	(	PUNCT
ejpam-4550	33	12	dfe	dfe	PROPN
ejpam-4550	33	13	)	)	PUNCT
ejpam-4550	33	14	and	and	CCONJ
ejpam-4550	33	15	the	the	DET
ejpam-4550	33	16	basic	basic	ADJ
ejpam-4550	33	17	reproduction	reproduction	NOUN
ejpam-4550	33	18	number	number	NOUN
ejpam-4550	33	19	r0	r0	NOUN
ejpam-4550	33	20	are	be	AUX
ejpam-4550	33	21	calculated	calculate	VERB
ejpam-4550	33	22	.	.	PUNCT
ejpam-4550	34	1	in	in	ADP
ejpam-4550	34	2	section	section	NOUN
ejpam-4550	34	3	5	5	NUM
ejpam-4550	34	4	,	,	PUNCT
ejpam-4550	34	5	we	we	PRON
ejpam-4550	34	6	prove	prove	VERB
ejpam-4550	34	7	the	the	DET
ejpam-4550	34	8	local	local	ADJ
ejpam-4550	34	9	extinction	extinction	NOUN
ejpam-4550	34	10	of	of	ADP
ejpam-4550	34	11	the	the	DET
ejpam-4550	34	12	infected	infected	ADJ
ejpam-4550	34	13	populations	population	NOUN
ejpam-4550	34	14	in	in	ADP
ejpam-4550	34	15	both	both	DET
ejpam-4550	34	16	age	age	NOUN
ejpam-4550	34	17	classes	class	NOUN
ejpam-4550	34	18	when	when	SCONJ
ejpam-4550	34	19	r0	r0	VERB
ejpam-4550	34	20	<	<	X
ejpam-4550	34	21	1	1	NUM
ejpam-4550	34	22	.	.	PUNCT
ejpam-4550	35	1	in	in	ADP
ejpam-4550	35	2	section	section	NOUN
ejpam-4550	35	3	6	6	NUM
ejpam-4550	35	4	,	,	PUNCT
ejpam-4550	35	5	the	the	DET
ejpam-4550	35	6	global	global	ADJ
ejpam-4550	35	7	extinction	extinction	NOUN
ejpam-4550	35	8	of	of	ADP
ejpam-4550	35	9	the	the	DET
ejpam-4550	35	10	disease	disease	NOUN
ejpam-4550	35	11	in	in	ADP
ejpam-4550	35	12	both	both	DET
ejpam-4550	35	13	age	age	NOUN
ejpam-4550	35	14	classes	class	NOUN
ejpam-4550	35	15	is	be	AUX
ejpam-4550	35	16	studied	study	VERB
ejpam-4550	35	17	and	and	CCONJ
ejpam-4550	35	18	followed	follow	VERB
ejpam-4550	35	19	by	by	ADP
ejpam-4550	35	20	some	some	DET
ejpam-4550	35	21	concluding	concluding	NOUN
ejpam-4550	35	22	results	result	NOUN
ejpam-4550	35	23	.	.	PUNCT
ejpam-4550	36	1	sections	section	NOUN
ejpam-4550	36	2	7	7	NUM
ejpam-4550	36	3	and	and	CCONJ
ejpam-4550	36	4	8	8	NUM
ejpam-4550	36	5	deal	deal	NOUN
ejpam-4550	36	6	with	with	ADP
ejpam-4550	36	7	the	the	DET
ejpam-4550	36	8	persistence	persistence	NOUN
ejpam-4550	36	9	of	of	ADP
ejpam-4550	36	10	the	the	DET
ejpam-4550	36	11	disease	disease	NOUN
ejpam-4550	36	12	in	in	ADP
ejpam-4550	36	13	both	both	DET
ejpam-4550	36	14	classes	class	NOUN
ejpam-4550	36	15	when	when	SCONJ
ejpam-4550	36	16	r0	r0	VERB
ejpam-4550	36	17	>	>	X
ejpam-4550	36	18	1	1	X
ejpam-4550	36	19	.	.	PUNCT
ejpam-4550	37	1	in	in	ADP
ejpam-4550	37	2	section	section	NOUN
ejpam-4550	37	3	9	9	NUM
ejpam-4550	37	4	,	,	PUNCT
ejpam-4550	37	5	some	some	DET
ejpam-4550	37	6	numerical	numerical	ADJ
ejpam-4550	37	7	results	result	NOUN
ejpam-4550	37	8	are	be	AUX
ejpam-4550	37	9	presented	present	VERB
ejpam-4550	37	10	.	.	PUNCT
ejpam-4550	38	1	the	the	DET
ejpam-4550	38	2	main	main	ADJ
ejpam-4550	38	3	conclusions	conclusion	NOUN
ejpam-4550	38	4	are	be	AUX
ejpam-4550	38	5	recapped	recap	VERB
ejpam-4550	38	6	in	in	ADP
ejpam-4550	38	7	section	section	NOUN
ejpam-4550	38	8	10	10	NUM
ejpam-4550	38	9	.	.	PUNCT
ejpam-4550	39	1	2	2	NUM
ejpam-4550	39	2	.	.	NOUN
ejpam-4550	39	3	mathematical	mathematical	ADJ
ejpam-4550	39	4	model	model	NOUN
ejpam-4550	39	5	for	for	ADP
ejpam-4550	39	6	hiv	hiv	PROPN
ejpam-4550	39	7	-	-	PUNCT
ejpam-4550	39	8	aids	aids	PROPN
ejpam-4550	39	9	in	in	ADP
ejpam-4550	39	10	this	this	DET
ejpam-4550	39	11	section	section	NOUN
ejpam-4550	39	12	,	,	PUNCT
ejpam-4550	39	13	we	we	PRON
ejpam-4550	39	14	formulate	formulate	VERB
ejpam-4550	39	15	a	a	DET
ejpam-4550	39	16	mathematical	mathematical	ADJ
ejpam-4550	39	17	model	model	NOUN
ejpam-4550	39	18	for	for	ADP
ejpam-4550	39	19	hiv	hiv	PROPN
ejpam-4550	39	20	-	-	PUNCT
ejpam-4550	39	21	aids	aids	PROPN
ejpam-4550	39	22	.	.	PUNCT
ejpam-4550	40	1	we	we	PRON
ejpam-4550	40	2	divide	divide	VERB
ejpam-4550	40	3	the	the	DET
ejpam-4550	40	4	total	total	ADJ
ejpam-4550	40	5	population	population	NOUN
ejpam-4550	40	6	n	n	NOUN
ejpam-4550	40	7	into	into	ADP
ejpam-4550	40	8	two	two	NUM
ejpam-4550	40	9	age	age	NOUN
ejpam-4550	40	10	classes	class	NOUN
ejpam-4550	40	11	.	.	PUNCT
ejpam-4550	41	1	the	the	DET
ejpam-4550	41	2	first	first	ADJ
ejpam-4550	41	3	age	age	NOUN
ejpam-4550	41	4	class	class	NOUN
ejpam-4550	41	5	is	be	AUX
ejpam-4550	41	6	denoted	denote	VERB
ejpam-4550	41	7	by	by	ADP
ejpam-4550	41	8	c1	c1	PROPN
ejpam-4550	41	9	and	and	CCONJ
ejpam-4550	41	10	the	the	DET
ejpam-4550	41	11	second	second	ADJ
ejpam-4550	41	12	by	by	ADP
ejpam-4550	41	13	c2	c2	PROPN
ejpam-4550	41	14	.	.	PUNCT
ejpam-4550	42	1	in	in	ADP
ejpam-4550	42	2	each	each	DET
ejpam-4550	42	3	age	age	NOUN
ejpam-4550	42	4	class	class	NOUN
ejpam-4550	42	5	,	,	PUNCT
ejpam-4550	42	6	there	there	PRON
ejpam-4550	42	7	is	be	VERB
ejpam-4550	42	8	one	one	NUM
ejpam-4550	42	9	compartment	compartment	NOUN
ejpam-4550	42	10	of	of	ADP
ejpam-4550	42	11	susceptible	susceptible	ADJ
ejpam-4550	42	12	individuals	individual	NOUN
ejpam-4550	42	13	and	and	CCONJ
ejpam-4550	42	14	three	three	NUM
ejpam-4550	42	15	compartments	compartment	NOUN
ejpam-4550	42	16	of	of	ADP
ejpam-4550	42	17	infected	infected	ADJ
ejpam-4550	42	18	individuals	individual	NOUN
ejpam-4550	42	19	.	.	PUNCT
ejpam-4550	43	1	in	in	ADP
ejpam-4550	43	2	the	the	DET
ejpam-4550	43	3	class	class	NOUN
ejpam-4550	43	4	c1	c1	NOUN
ejpam-4550	43	5	,	,	PUNCT
ejpam-4550	43	6	s1	s1	PROPN
ejpam-4550	43	7	represents	represent	VERB
ejpam-4550	43	8	the	the	DET
ejpam-4550	43	9	compartment	compartment	NOUN
ejpam-4550	43	10	of	of	ADP
ejpam-4550	43	11	susceptible	susceptible	ADJ
ejpam-4550	43	12	individuals	individual	NOUN
ejpam-4550	43	13	and	and	CCONJ
ejpam-4550	43	14	i11	i11	ADJ
ejpam-4550	43	15	,	,	PUNCT
ejpam-4550	43	16	i	i	NOUN
ejpam-4550	43	17	2	2	NUM
ejpam-4550	43	18	1	1	NUM
ejpam-4550	43	19	and	and	CCONJ
ejpam-4550	43	20	i31	i31	NOUN
ejpam-4550	43	21	are	be	AUX
ejpam-4550	43	22	the	the	DET
ejpam-4550	43	23	compartments	compartment	NOUN
ejpam-4550	43	24	of	of	ADP
ejpam-4550	43	25	infected	infect	VERB
ejpam-4550	43	26	individuals	individual	NOUN
ejpam-4550	43	27	at	at	ADP
ejpam-4550	43	28	stage	stage	NOUN
ejpam-4550	43	29	1	1	NUM
ejpam-4550	43	30	,	,	PUNCT
ejpam-4550	43	31	2	2	NUM
ejpam-4550	43	32	and	and	CCONJ
ejpam-4550	43	33	3	3	NUM
ejpam-4550	43	34	of	of	ADP
ejpam-4550	43	35	infection	infection	NOUN
ejpam-4550	43	36	,	,	PUNCT
ejpam-4550	43	37	respectively	respectively	ADV
ejpam-4550	43	38	.	.	PUNCT
ejpam-4550	44	1	similarly	similarly	ADV
ejpam-4550	44	2	,	,	PUNCT
ejpam-4550	44	3	in	in	ADP
ejpam-4550	44	4	the	the	DET
ejpam-4550	44	5	class	class	NOUN
ejpam-4550	44	6	c2	c2	PROPN
ejpam-4550	44	7	,	,	PUNCT
ejpam-4550	44	8	s2	s2	PROPN
ejpam-4550	44	9	is	be	AUX
ejpam-4550	44	10	the	the	DET
ejpam-4550	44	11	compartment	compartment	NOUN
ejpam-4550	44	12	of	of	ADP
ejpam-4550	44	13	susceptible	susceptible	ADJ
ejpam-4550	44	14	individuals	individual	NOUN
ejpam-4550	44	15	and	and	CCONJ
ejpam-4550	44	16	i12	i12	NOUN
ejpam-4550	44	17	,	,	PUNCT
ejpam-4550	44	18	i	i	NOUN
ejpam-4550	44	19	2	2	NUM
ejpam-4550	44	20	2	2	NUM
ejpam-4550	44	21	and	and	CCONJ
ejpam-4550	44	22	i32	i32	PROPN
ejpam-4550	44	23	represent	represent	VERB
ejpam-4550	44	24	the	the	DET
ejpam-4550	44	25	compartments	compartment	NOUN
ejpam-4550	44	26	of	of	ADP
ejpam-4550	44	27	infected	infect	VERB
ejpam-4550	44	28	individuals	individual	NOUN
ejpam-4550	44	29	at	at	ADP
ejpam-4550	44	30	stage	stage	NOUN
ejpam-4550	44	31	1	1	NUM
ejpam-4550	44	32	,	,	PUNCT
ejpam-4550	44	33	2	2	NUM
ejpam-4550	44	34	and	and	CCONJ
ejpam-4550	44	35	3	3	NUM
ejpam-4550	44	36	of	of	ADP
ejpam-4550	44	37	infection	infection	NOUN
ejpam-4550	44	38	,	,	PUNCT
ejpam-4550	44	39	respectively	respectively	ADV
ejpam-4550	44	40	.	.	PUNCT
ejpam-4550	45	1	the	the	DET
ejpam-4550	45	2	total	total	ADJ
ejpam-4550	45	3	population	population	NOUN
ejpam-4550	45	4	n	n	CCONJ
ejpam-4550	45	5	can	can	AUX
ejpam-4550	45	6	be	be	AUX
ejpam-4550	45	7	expressed	express	VERB
ejpam-4550	45	8	as	as	ADP
ejpam-4550	45	9	the	the	DET
ejpam-4550	45	10	following	following	ADJ
ejpam-4550	45	11	sum	sum	NOUN
ejpam-4550	45	12	:	:	PUNCT
ejpam-4550	45	13	n	n	PROPN
ejpam-4550	45	14	=	=	SYM
ejpam-4550	45	15	2∑	2∑	NOUN
ejpam-4550	45	16	j=1	j=1	NOUN
ejpam-4550	45	17	sj	sj	PROPN
ejpam-4550	46	1	+	+	NOUN
ejpam-4550	46	2	3∑	3∑	NUM
ejpam-4550	46	3	j=1	j=1	NOUN
ejpam-4550	46	4	ij1	ij1	NOUN
ejpam-4550	46	5	+	+	CCONJ
ejpam-4550	46	6	3∑	3∑	NUM
ejpam-4550	46	7	j=1	j=1	ADJ
ejpam-4550	46	8	ij2	ij2	PROPN
ejpam-4550	46	9	.	.	PUNCT
ejpam-4550	47	1	m.	m.	NOUN
ejpam-4550	47	2	alassane	alassane	NOUN
ejpam-4550	47	3	et	et	PROPN
ejpam-4550	47	4	al	al	PROPN
ejpam-4550	47	5	.	.	PUNCT
ejpam-4550	47	6	/	/	SYM
ejpam-4550	47	7	eur	eur	PROPN
ejpam-4550	47	8	.	.	PUNCT
ejpam-4550	48	1	j.	j.	PROPN
ejpam-4550	48	2	pure	pure	PROPN
ejpam-4550	48	3	appl	appl	PROPN
ejpam-4550	48	4	.	.	PROPN
ejpam-4550	48	5	math	math	PROPN
ejpam-4550	48	6	,	,	PUNCT
ejpam-4550	48	7	16	16	NUM
ejpam-4550	48	8	(	(	PUNCT
ejpam-4550	48	9	1	1	NUM
ejpam-4550	48	10	)	)	PUNCT
ejpam-4550	48	11	(	(	PUNCT
ejpam-4550	48	12	2023	2023	NUM
ejpam-4550	48	13	)	)	PUNCT
ejpam-4550	48	14	,	,	PUNCT
ejpam-4550	48	15	207	207	NUM
ejpam-4550	48	16	-	-	SYM
ejpam-4550	48	17	232	232	NUM
ejpam-4550	48	18	209	209	NUM
ejpam-4550	48	19	the	the	DET
ejpam-4550	48	20	spread	spread	NOUN
ejpam-4550	48	21	of	of	ADP
ejpam-4550	48	22	hiv	hiv	PROPN
ejpam-4550	48	23	-	-	PUNCT
ejpam-4550	48	24	aids	aids	PROPN
ejpam-4550	48	25	within	within	ADP
ejpam-4550	48	26	two	two	NUM
ejpam-4550	48	27	different	different	ADJ
ejpam-4550	48	28	age	age	NOUN
ejpam-4550	48	29	classes	class	NOUN
ejpam-4550	48	30	in	in	ADP
ejpam-4550	48	31	the	the	DET
ejpam-4550	48	32	population	population	NOUN
ejpam-4550	48	33	is	be	AUX
ejpam-4550	48	34	illustrated	illustrate	VERB
ejpam-4550	48	35	in	in	ADP
ejpam-4550	48	36	figure	figure	NOUN
ejpam-4550	48	37	1	1	NUM
ejpam-4550	48	38	.	.	PUNCT
ejpam-4550	49	1	s2	s2	PROPN
ejpam-4550	49	2	m	m	VERB
ejpam-4550	49	3	i12	i12	PROPN
ejpam-4550	49	4	m	m	PROPN
ejpam-4550	49	5	i22	i22	NOUN
ejpam-4550	49	6	m	m	PROPN
ejpam-4550	49	7	i32	i32	PROPN
ejpam-4550	49	8	m	m	PROPN
ejpam-4550	49	9	s1	s1	PROPN
ejpam-4550	49	10	m	m	PROPN
ejpam-4550	49	11	i11	i11	ADJ
ejpam-4550	49	12	m	m	PROPN
ejpam-4550	49	13	i21	i21	NOUN
ejpam-4550	49	14	m	m	PROPN
ejpam-4550	49	15	i31	i31	PROPN
ejpam-4550	49	16	m	m	PROPN
ejpam-4550	49	17	β2	β2	NOUN
ejpam-4550	49	18	a3	a3	NOUN
ejpam-4550	49	19	a4	a4	PROPN
ejpam-4550	49	20	γ	γ	PROPN
ejpam-4550	49	21	β1	β1	PROPN
ejpam-4550	49	22	a1	a1	NOUN
ejpam-4550	49	23	a2	a2	PROPN
ejpam-4550	49	24	c1	c1	PROPN
ejpam-4550	49	25	c2	c2	PROPN
ejpam-4550	49	26	c3	c3	PROPN
ejpam-4550	49	27	bn	bn	PROPN
ejpam-4550	49	28	figure	figure	NOUN
ejpam-4550	49	29	1	1	NUM
ejpam-4550	49	30	:	:	PUNCT
ejpam-4550	49	31	flow	flow	NOUN
ejpam-4550	49	32	diagram	diagram	NOUN
ejpam-4550	49	33	of	of	ADP
ejpam-4550	49	34	hiv	hiv	PROPN
ejpam-4550	49	35	-	-	PUNCT
ejpam-4550	49	36	aids	aids	PROPN
ejpam-4550	49	37	transmission	transmission	NOUN
ejpam-4550	49	38	dynamics	dynamic	NOUN
ejpam-4550	49	39	using	use	VERB
ejpam-4550	49	40	the	the	DET
ejpam-4550	49	41	above	above	ADJ
ejpam-4550	49	42	representation	representation	NOUN
ejpam-4550	49	43	,	,	PUNCT
ejpam-4550	49	44	we	we	PRON
ejpam-4550	49	45	formulate	formulate	VERB
ejpam-4550	49	46	the	the	DET
ejpam-4550	49	47	corresponding	corresponding	ADJ
ejpam-4550	49	48	dynamical	dynamical	ADJ
ejpam-4550	49	49	model	model	NOUN
ejpam-4550	49	50	as	as	SCONJ
ejpam-4550	49	51	follows	follow	VERB
ejpam-4550	49	52	:	:	PUNCT
ejpam-4550	50	1	m.	m.	NOUN
ejpam-4550	50	2	alassane	alassane	NOUN
ejpam-4550	50	3	et	et	PROPN
ejpam-4550	50	4	al	al	PROPN
ejpam-4550	50	5	.	.	PUNCT
ejpam-4550	50	6	/	/	SYM
ejpam-4550	50	7	eur	eur	PROPN
ejpam-4550	50	8	.	.	PUNCT
ejpam-4550	51	1	j.	j.	PROPN
ejpam-4550	51	2	pure	pure	PROPN
ejpam-4550	51	3	appl	appl	PROPN
ejpam-4550	51	4	.	.	PROPN
ejpam-4550	51	5	math	math	PROPN
ejpam-4550	51	6	,	,	PUNCT
ejpam-4550	51	7	16	16	NUM
ejpam-4550	51	8	(	(	PUNCT
ejpam-4550	51	9	1	1	NUM
ejpam-4550	51	10	)	)	PUNCT
ejpam-4550	51	11	(	(	PUNCT
ejpam-4550	51	12	2023	2023	NUM
ejpam-4550	51	13	)	)	PUNCT
ejpam-4550	51	14	,	,	PUNCT
ejpam-4550	51	15	207	207	NUM
ejpam-4550	51	16	-	-	SYM
ejpam-4550	51	17	232	232	NUM
ejpam-4550	51	18	210	210	NUM
ejpam-4550	51	19			NOUN
ejpam-4550	51	20	d	d	NOUN
ejpam-4550	51	21	s1	s1	NOUN
ejpam-4550	51	22	dt	dt	X
ejpam-4550	51	23	=	=	SYM
ejpam-4550	51	24	bn−	bn−	PUNCT
ejpam-4550	51	25	s1	s1	NOUN
ejpam-4550	51	26	n	n	CCONJ
ejpam-4550	51	27	β1	β1	VERB
ejpam-4550	51	28	3∑	3∑	NUM
ejpam-4550	51	29	j=1	j=1	NOUN
ejpam-4550	51	30	ij1	ij1	NOUN
ejpam-4550	51	31	+	+	CCONJ
ejpam-4550	51	32	β2	β2	NOUN
ejpam-4550	51	33	3∑	3∑	NUM
ejpam-4550	51	34	j=1	j=1	NOUN
ejpam-4550	51	35	ij2	ij2	PROPN
ejpam-4550	52	1	−	−	ADV
ejpam-4550	52	2	(	(	PUNCT
ejpam-4550	52	3	m	m	PROPN
ejpam-4550	52	4	+	+	X
ejpam-4550	52	5	γ)s1	γ)s1	PROPN
ejpam-4550	52	6	d	d	PROPN
ejpam-4550	52	7	i11	i11	ADJ
ejpam-4550	52	8	dt	dt	NOUN
ejpam-4550	52	9	=	=	SYM
ejpam-4550	52	10	s1	s1	PROPN
ejpam-4550	52	11	n	n	CCONJ
ejpam-4550	52	12	β1	β1	VERB
ejpam-4550	52	13	3∑	3∑	NUM
ejpam-4550	52	14	j=1	j=1	NOUN
ejpam-4550	52	15	ij1	ij1	NOUN
ejpam-4550	52	16	+	+	CCONJ
ejpam-4550	52	17	β2	β2	NOUN
ejpam-4550	52	18	3∑	3∑	NUM
ejpam-4550	52	19	j=1	j=1	NOUN
ejpam-4550	52	20	ij2	ij2	PROPN
ejpam-4550	52	21	−	−	ADV
ejpam-4550	53	1	(	(	PUNCT
ejpam-4550	53	2	m	m	AUX
ejpam-4550	53	3	+	+	CCONJ
ejpam-4550	53	4	a1	a1	NOUN
ejpam-4550	53	5	+	+	CCONJ
ejpam-4550	53	6	c1)i	c1)i	ADJ
ejpam-4550	53	7	1	1	NUM
ejpam-4550	53	8	1	1	NUM
ejpam-4550	53	9	d	d	NOUN
ejpam-4550	53	10	i21	i21	NOUN
ejpam-4550	53	11	dt	dt	NOUN
ejpam-4550	53	12	=	=	PUNCT
ejpam-4550	53	13	a1i	a1i	VERB
ejpam-4550	53	14	1	1	NUM
ejpam-4550	53	15	1	1	NUM
ejpam-4550	53	16	−	−	PROPN
ejpam-4550	54	1	(	(	PUNCT
ejpam-4550	54	2	m	m	PROPN
ejpam-4550	54	3	+	+	NUM
ejpam-4550	54	4	a2	a2	PROPN
ejpam-4550	54	5	+	+	CCONJ
ejpam-4550	54	6	c2)i	c2)i	NOUN
ejpam-4550	54	7	2	2	NUM
ejpam-4550	54	8	1	1	NUM
ejpam-4550	54	9	d	d	NOUN
ejpam-4550	54	10	i31	i31	NOUN
ejpam-4550	54	11	dt	dt	NOUN
ejpam-4550	55	1	=	=	NOUN
ejpam-4550	55	2	a2i	a2i	NOUN
ejpam-4550	55	3	2	2	NUM
ejpam-4550	55	4	1	1	NUM
ejpam-4550	55	5	−	−	PROPN
ejpam-4550	55	6	(	(	PUNCT
ejpam-4550	55	7	m	m	VERB
ejpam-4550	55	8	+	+	X
ejpam-4550	55	9	c3)i	c3)i	VERB
ejpam-4550	55	10	3	3	NUM
ejpam-4550	55	11	1	1	NUM
ejpam-4550	55	12	d	d	PROPN
ejpam-4550	55	13	s2	s2	NOUN
ejpam-4550	55	14	dt	dt	X
ejpam-4550	56	1	=	=	SYM
ejpam-4550	56	2	γs1	γs1	PROPN
ejpam-4550	56	3	−	−	PROPN
ejpam-4550	56	4	s2	s2	PROPN
ejpam-4550	56	5	n	n	CCONJ
ejpam-4550	56	6	β1	β1	VERB
ejpam-4550	56	7	3∑	3∑	NUM
ejpam-4550	56	8	j=1	j=1	NOUN
ejpam-4550	56	9	ij1	ij1	NOUN
ejpam-4550	56	10	+	+	CCONJ
ejpam-4550	56	11	β2	β2	NOUN
ejpam-4550	56	12	3∑	3∑	NUM
ejpam-4550	56	13	j=1	j=1	NOUN
ejpam-4550	56	14	ij2	ij2	PROPN
ejpam-4550	56	15	−ms2	−ms2	PROPN
ejpam-4550	57	1	d	d	X
ejpam-4550	57	2	i12	i12	NOUN
ejpam-4550	57	3	dt	dt	NOUN
ejpam-4550	58	1	=	=	SYM
ejpam-4550	58	2	s2	s2	PROPN
ejpam-4550	58	3	n	n	PRON
ejpam-4550	58	4	β1	β1	VERB
ejpam-4550	58	5	3∑	3∑	NUM
ejpam-4550	58	6	j=1	j=1	NOUN
ejpam-4550	58	7	ij1	ij1	NOUN
ejpam-4550	58	8	+	+	CCONJ
ejpam-4550	58	9	β2	β2	NOUN
ejpam-4550	58	10	3∑	3∑	NUM
ejpam-4550	58	11	j=1	j=1	NOUN
ejpam-4550	58	12	ij2	ij2	PROPN
ejpam-4550	59	1	−	−	ADV
ejpam-4550	59	2	(	(	PUNCT
ejpam-4550	59	3	m	m	VERB
ejpam-4550	59	4	+	+	X
ejpam-4550	59	5	a3)i	a3)i	NOUN
ejpam-4550	59	6	1	1	NUM
ejpam-4550	59	7	2	2	NUM
ejpam-4550	59	8	+	+	CCONJ
ejpam-4550	59	9	c1i	c1i	ADJ
ejpam-4550	59	10	1	1	NUM
ejpam-4550	59	11	1	1	NUM
ejpam-4550	59	12	d	d	NOUN
ejpam-4550	59	13	i22	i22	NOUN
ejpam-4550	59	14	dt	dt	NOUN
ejpam-4550	59	15	=	=	SYM
ejpam-4550	59	16	a3i	a3i	ADP
ejpam-4550	59	17	1	1	NUM
ejpam-4550	59	18	2	2	NUM
ejpam-4550	59	19	−	−	NOUN
ejpam-4550	59	20	(	(	PUNCT
ejpam-4550	59	21	m	m	PROPN
ejpam-4550	59	22	+	+	X
ejpam-4550	59	23	a4)i	a4)i	ADJ
ejpam-4550	59	24	2	2	NUM
ejpam-4550	59	25	2	2	NUM
ejpam-4550	59	26	+	+	CCONJ
ejpam-4550	59	27	c2i	c2i	X
ejpam-4550	59	28	2	2	NUM
ejpam-4550	59	29	1	1	NUM
ejpam-4550	59	30	d	d	NOUN
ejpam-4550	59	31	i32	i32	NOUN
ejpam-4550	59	32	dt	dt	PROPN
ejpam-4550	60	1	=	=	SYM
ejpam-4550	60	2	a4i	a4i	PROPN
ejpam-4550	60	3	2	2	NUM
ejpam-4550	60	4	2	2	NUM
ejpam-4550	60	5	−mi32	−mi32	NOUN
ejpam-4550	60	6	+	+	CCONJ
ejpam-4550	60	7	c3i	c3i	NOUN
ejpam-4550	60	8	3	3	NUM
ejpam-4550	60	9	1	1	NUM
ejpam-4550	60	10	(	(	PUNCT
ejpam-4550	60	11	1	1	NUM
ejpam-4550	60	12	)	)	PUNCT
ejpam-4550	60	13	the	the	DET
ejpam-4550	60	14	system	system	NOUN
ejpam-4550	60	15	(	(	PUNCT
ejpam-4550	60	16	1	1	X
ejpam-4550	60	17	)	)	PUNCT
ejpam-4550	60	18	is	be	AUX
ejpam-4550	60	19	completed	complete	VERB
ejpam-4550	60	20	with	with	ADP
ejpam-4550	60	21	the	the	DET
ejpam-4550	60	22	following	follow	VERB
ejpam-4550	60	23	initial	initial	ADJ
ejpam-4550	60	24	conditions	condition	NOUN
ejpam-4550	60	25	:	:	PUNCT
ejpam-4550	60	26	s1	s1	NOUN
ejpam-4550	60	27	≥	≥	NUM
ejpam-4550	60	28	0	0	NUM
ejpam-4550	60	29	,	,	PUNCT
ejpam-4550	60	30	i11	i11	ADJ
ejpam-4550	60	31	≥	≥	NOUN
ejpam-4550	60	32	0	0	NUM
ejpam-4550	60	33	,	,	PUNCT
ejpam-4550	60	34	i21	i21	NOUN
ejpam-4550	60	35	≥	≥	NOUN
ejpam-4550	60	36	0	0	NUM
ejpam-4550	60	37	,	,	PUNCT
ejpam-4550	60	38	i31	i31	NOUN
ejpam-4550	60	39	≥	≥	NOUN
ejpam-4550	60	40	0	0	NUM
ejpam-4550	60	41	,	,	PUNCT
ejpam-4550	60	42	s2	s2	VERB
ejpam-4550	60	43	≥	≥	NUM
ejpam-4550	60	44	0	0	NUM
ejpam-4550	60	45	,	,	PUNCT
ejpam-4550	60	46	i12	i12	PROPN
ejpam-4550	60	47	≥	≥	PROPN
ejpam-4550	60	48	0	0	NUM
ejpam-4550	60	49	,	,	PUNCT
ejpam-4550	60	50	i22	i22	NOUN
ejpam-4550	60	51	≥	≥	NOUN
ejpam-4550	60	52	0	0	NUM
ejpam-4550	60	53	,	,	PUNCT
ejpam-4550	60	54	i32	i32	PROPN
ejpam-4550	60	55	≥	≥	PROPN
ejpam-4550	60	56	0	0	NUM
ejpam-4550	60	57	.	.	PUNCT
ejpam-4550	61	1	(	(	PUNCT
ejpam-4550	61	2	2	2	X
ejpam-4550	61	3	)	)	PUNCT
ejpam-4550	61	4	summing	sum	VERB
ejpam-4550	61	5	the	the	DET
ejpam-4550	61	6	equations	equation	NOUN
ejpam-4550	61	7	of	of	ADP
ejpam-4550	61	8	system	system	NOUN
ejpam-4550	61	9	(	(	PUNCT
ejpam-4550	61	10	1	1	NUM
ejpam-4550	61	11	)	)	PUNCT
ejpam-4550	61	12	,	,	PUNCT
ejpam-4550	61	13	we	we	PRON
ejpam-4550	61	14	obtain	obtain	VERB
ejpam-4550	61	15	:	:	PUNCT
ejpam-4550	61	16	d	d	NOUN
ejpam-4550	61	17	n	n	PRON
ejpam-4550	61	18	dt	dt	NOUN
ejpam-4550	61	19	=	=	SYM
ejpam-4550	61	20	(	(	PUNCT
ejpam-4550	61	21	b−m)n	b−m)n	PROPN
ejpam-4550	61	22	.	.	PUNCT
ejpam-4550	62	1	the	the	DET
ejpam-4550	62	2	parameters	parameter	NOUN
ejpam-4550	62	3	of	of	ADP
ejpam-4550	62	4	the	the	DET
ejpam-4550	62	5	model	model	NOUN
ejpam-4550	62	6	are	be	AUX
ejpam-4550	62	7	reported	report	VERB
ejpam-4550	62	8	in	in	ADP
ejpam-4550	62	9	table	table	NOUN
ejpam-4550	62	10	2	2	NUM
ejpam-4550	62	11	.	.	PUNCT
ejpam-4550	63	1	they	they	PRON
ejpam-4550	63	2	are	be	AUX
ejpam-4550	63	3	all	all	ADV
ejpam-4550	63	4	positive	positive	ADJ
ejpam-4550	63	5	.	.	PUNCT
ejpam-4550	64	1	the	the	DET
ejpam-4550	64	2	parameter	parameter	PROPN
ejpam-4550	64	3	b	b	PROPN
ejpam-4550	64	4	represents	represent	VERB
ejpam-4550	64	5	the	the	DET
ejpam-4550	64	6	rate	rate	NOUN
ejpam-4550	64	7	at	at	ADP
ejpam-4550	64	8	which	which	PRON
ejpam-4550	64	9	young	young	ADJ
ejpam-4550	64	10	begin	begin	VERB
ejpam-4550	64	11	sexual	sexual	ADJ
ejpam-4550	64	12	activity	activity	NOUN
ejpam-4550	64	13	.	.	PUNCT
ejpam-4550	65	1	the	the	DET
ejpam-4550	65	2	parameter	parameter	NOUN
ejpam-4550	65	3	m	m	VERB
ejpam-4550	65	4	is	be	AUX
ejpam-4550	65	5	the	the	DET
ejpam-4550	65	6	death	death	NOUN
ejpam-4550	65	7	rate	rate	NOUN
ejpam-4550	65	8	.	.	PUNCT
ejpam-4550	66	1	the	the	DET
ejpam-4550	66	2	parameters	parameter	NOUN
ejpam-4550	66	3	β1	β1	PROPN
ejpam-4550	66	4	and	and	CCONJ
ejpam-4550	66	5	β2	β2	NOUN
ejpam-4550	66	6	are	be	AUX
ejpam-4550	66	7	infection	infection	NOUN
ejpam-4550	66	8	rates	rate	NOUN
ejpam-4550	66	9	in	in	ADP
ejpam-4550	66	10	c1	c1	PROPN
ejpam-4550	66	11	and	and	CCONJ
ejpam-4550	66	12	c2	c2	PROPN
ejpam-4550	66	13	,	,	PUNCT
ejpam-4550	66	14	respectively	respectively	ADV
ejpam-4550	66	15	.	.	PUNCT
ejpam-4550	67	1	the	the	DET
ejpam-4550	67	2	rate	rate	NOUN
ejpam-4550	67	3	at	at	ADP
ejpam-4550	67	4	which	which	PRON
ejpam-4550	67	5	susceptible	susceptible	ADJ
ejpam-4550	67	6	individuals	individual	NOUN
ejpam-4550	67	7	in	in	ADP
ejpam-4550	67	8	c1	c1	PROPN
ejpam-4550	67	9	get	get	VERB
ejpam-4550	67	10	older	old	ADJ
ejpam-4550	67	11	and	and	CCONJ
ejpam-4550	67	12	reach	reach	VERB
ejpam-4550	67	13	the	the	DET
ejpam-4550	67	14	age	age	NOUN
ejpam-4550	67	15	of	of	ADP
ejpam-4550	67	16	becoming	become	VERB
ejpam-4550	67	17	susceptible	susceptible	ADJ
ejpam-4550	67	18	individuals	individual	NOUN
ejpam-4550	67	19	in	in	ADP
ejpam-4550	67	20	c2	c2	PROPN
ejpam-4550	67	21	is	be	AUX
ejpam-4550	67	22	given	give	VERB
ejpam-4550	67	23	by	by	ADP
ejpam-4550	67	24	γ	γ	PROPN
ejpam-4550	67	25	.	.	PUNCT
ejpam-4550	68	1	the	the	DET
ejpam-4550	68	2	parameters	parameter	NOUN
ejpam-4550	68	3	a1	a1	VERB
ejpam-4550	68	4	and	and	CCONJ
ejpam-4550	68	5	a2	a2	PROPN
ejpam-4550	68	6	are	be	AUX
ejpam-4550	68	7	the	the	DET
ejpam-4550	68	8	rates	rate	NOUN
ejpam-4550	68	9	at	at	ADP
ejpam-4550	68	10	which	which	PRON
ejpam-4550	68	11	infected	infect	VERB
ejpam-4550	68	12	individuals	individual	NOUN
ejpam-4550	68	13	in	in	ADP
ejpam-4550	68	14	the	the	DET
ejpam-4550	68	15	class	class	NOUN
ejpam-4550	68	16	c1	c1	PROPN
ejpam-4550	68	17	move	move	VERB
ejpam-4550	68	18	from	from	ADP
ejpam-4550	68	19	stage	stage	NOUN
ejpam-4550	68	20	1	1	NUM
ejpam-4550	68	21	to	to	PART
ejpam-4550	68	22	stage	stage	VERB
ejpam-4550	68	23	2	2	NUM
ejpam-4550	68	24	and	and	CCONJ
ejpam-4550	68	25	from	from	ADP
ejpam-4550	68	26	stage	stage	NOUN
ejpam-4550	68	27	2	2	NUM
ejpam-4550	68	28	to	to	PART
ejpam-4550	68	29	stage	stage	VERB
ejpam-4550	68	30	3	3	NUM
ejpam-4550	68	31	,	,	PUNCT
ejpam-4550	68	32	respectively	respectively	ADV
ejpam-4550	68	33	,	,	PUNCT
ejpam-4550	68	34	within	within	ADP
ejpam-4550	68	35	this	this	DET
ejpam-4550	68	36	class	class	NOUN
ejpam-4550	68	37	.	.	PUNCT
ejpam-4550	69	1	similarly	similarly	ADV
ejpam-4550	69	2	,	,	PUNCT
ejpam-4550	69	3	the	the	DET
ejpam-4550	69	4	parameters	parameter	NOUN
ejpam-4550	69	5	a3	a3	VERB
ejpam-4550	69	6	and	and	CCONJ
ejpam-4550	69	7	m.	m.	NOUN
ejpam-4550	69	8	alassane	alassane	PROPN
ejpam-4550	69	9	et	et	PROPN
ejpam-4550	69	10	al	al	PROPN
ejpam-4550	69	11	.	.	PUNCT
ejpam-4550	69	12	/	/	SYM
ejpam-4550	69	13	eur	eur	PROPN
ejpam-4550	69	14	.	.	PUNCT
ejpam-4550	70	1	j.	j.	PROPN
ejpam-4550	70	2	pure	pure	PROPN
ejpam-4550	70	3	appl	appl	PROPN
ejpam-4550	70	4	.	.	PROPN
ejpam-4550	70	5	math	math	PROPN
ejpam-4550	70	6	,	,	PUNCT
ejpam-4550	70	7	16	16	NUM
ejpam-4550	70	8	(	(	PUNCT
ejpam-4550	70	9	1	1	NUM
ejpam-4550	70	10	)	)	PUNCT
ejpam-4550	70	11	(	(	PUNCT
ejpam-4550	70	12	2023	2023	NUM
ejpam-4550	70	13	)	)	PUNCT
ejpam-4550	70	14	,	,	PUNCT
ejpam-4550	70	15	207	207	NUM
ejpam-4550	70	16	-	-	SYM
ejpam-4550	70	17	232	232	NUM
ejpam-4550	70	18	211	211	NUM
ejpam-4550	70	19	table	table	NOUN
ejpam-4550	70	20	2	2	NUM
ejpam-4550	70	21	:	:	PUNCT
ejpam-4550	70	22	description	description	NOUN
ejpam-4550	70	23	of	of	ADP
ejpam-4550	70	24	the	the	DET
ejpam-4550	70	25	model	model	NOUN
ejpam-4550	70	26	parameters	parameter	NOUN
ejpam-4550	70	27	parameters	parameter	NOUN
ejpam-4550	70	28	description	description	NOUN
ejpam-4550	70	29	b	b	X
ejpam-4550	70	30	,	,	PUNCT
ejpam-4550	70	31	m	m	NOUN
ejpam-4550	70	32	recruitment	recruitment	NOUN
ejpam-4550	70	33	rate	rate	NOUN
ejpam-4550	70	34	,	,	PUNCT
ejpam-4550	70	35	natural	natural	ADJ
ejpam-4550	70	36	mortality	mortality	NOUN
ejpam-4550	70	37	rate	rate	NOUN
ejpam-4550	70	38	γ	γ	PROPN
ejpam-4550	70	39	,	,	PUNCT
ejpam-4550	70	40	c1	c1	PROPN
ejpam-4550	70	41	,	,	PUNCT
ejpam-4550	70	42	c2	c2	PROPN
ejpam-4550	70	43	,	,	PUNCT
ejpam-4550	70	44	c3	c3	NOUN
ejpam-4550	70	45	transfer	transfer	NOUN
ejpam-4550	70	46	rates	rate	NOUN
ejpam-4550	70	47	from	from	ADP
ejpam-4550	70	48	c1	c1	PROPN
ejpam-4550	70	49	to	to	ADP
ejpam-4550	70	50	c2	c2	PROPN
ejpam-4550	70	51	a1	a1	PROPN
ejpam-4550	70	52	,	,	PUNCT
ejpam-4550	70	53	a2	a2	NOUN
ejpam-4550	70	54	transfer	transfer	NOUN
ejpam-4550	70	55	rates	rate	NOUN
ejpam-4550	70	56	within	within	ADP
ejpam-4550	70	57	c1	c1	PROPN
ejpam-4550	70	58	a3	a3	NOUN
ejpam-4550	70	59	,	,	PUNCT
ejpam-4550	70	60	a4	a4	NOUN
ejpam-4550	70	61	transfer	transfer	NOUN
ejpam-4550	70	62	rates	rate	NOUN
ejpam-4550	70	63	within	within	ADP
ejpam-4550	70	64	c2	c2	PROPN
ejpam-4550	70	65	β1	β1	PROPN
ejpam-4550	70	66	,	,	PUNCT
ejpam-4550	70	67	β2	β2	NOUN
ejpam-4550	70	68	transmission	transmission	NOUN
ejpam-4550	70	69	rates	rate	NOUN
ejpam-4550	70	70	a4	a4	INTJ
ejpam-4550	70	71	describe	describe	VERB
ejpam-4550	70	72	the	the	DET
ejpam-4550	70	73	rates	rate	NOUN
ejpam-4550	70	74	at	at	ADP
ejpam-4550	70	75	which	which	PRON
ejpam-4550	70	76	infected	infect	VERB
ejpam-4550	70	77	individuals	individual	NOUN
ejpam-4550	70	78	in	in	ADP
ejpam-4550	70	79	the	the	DET
ejpam-4550	70	80	class	class	NOUN
ejpam-4550	70	81	c2	c2	PROPN
ejpam-4550	70	82	move	move	VERB
ejpam-4550	70	83	from	from	ADP
ejpam-4550	70	84	stage	stage	NOUN
ejpam-4550	70	85	1	1	NUM
ejpam-4550	70	86	to	to	PART
ejpam-4550	70	87	stage	stage	VERB
ejpam-4550	70	88	2	2	NUM
ejpam-4550	70	89	and	and	CCONJ
ejpam-4550	70	90	from	from	ADP
ejpam-4550	70	91	stage	stage	NOUN
ejpam-4550	70	92	2	2	NUM
ejpam-4550	70	93	to	to	PART
ejpam-4550	70	94	stage	stage	VERB
ejpam-4550	70	95	3	3	NUM
ejpam-4550	70	96	,	,	PUNCT
ejpam-4550	70	97	respectively	respectively	ADV
ejpam-4550	70	98	,	,	PUNCT
ejpam-4550	70	99	within	within	ADP
ejpam-4550	70	100	this	this	DET
ejpam-4550	70	101	class	class	NOUN
ejpam-4550	70	102	.	.	PUNCT
ejpam-4550	71	1	the	the	DET
ejpam-4550	71	2	parameters	parameter	NOUN
ejpam-4550	71	3	ck	ck	PRON
ejpam-4550	71	4	,	,	PUNCT
ejpam-4550	71	5	k	k	PROPN
ejpam-4550	72	1	=	=	SYM
ejpam-4550	73	1	1	1	NUM
ejpam-4550	73	2	,	,	PUNCT
ejpam-4550	73	3	2	2	NUM
ejpam-4550	73	4	,	,	PUNCT
ejpam-4550	73	5	3	3	NUM
ejpam-4550	73	6	,	,	PUNCT
ejpam-4550	73	7	denote	denote	VERB
ejpam-4550	73	8	the	the	DET
ejpam-4550	73	9	rates	rate	NOUN
ejpam-4550	73	10	at	at	ADP
ejpam-4550	73	11	which	which	PRON
ejpam-4550	73	12	infected	infect	VERB
ejpam-4550	73	13	individuals	individual	NOUN
ejpam-4550	73	14	in	in	ADP
ejpam-4550	73	15	the	the	DET
ejpam-4550	73	16	stage	stage	NOUN
ejpam-4550	73	17	k	k	PROPN
ejpam-4550	73	18	of	of	ADP
ejpam-4550	73	19	c1	c1	PROPN
ejpam-4550	73	20	get	get	VERB
ejpam-4550	73	21	older	old	ADJ
ejpam-4550	73	22	and	and	CCONJ
ejpam-4550	73	23	reach	reach	VERB
ejpam-4550	73	24	the	the	DET
ejpam-4550	73	25	age	age	NOUN
ejpam-4550	73	26	of	of	ADP
ejpam-4550	73	27	becoming	become	VERB
ejpam-4550	73	28	infected	infect	VERB
ejpam-4550	73	29	individuals	individual	NOUN
ejpam-4550	73	30	in	in	ADP
ejpam-4550	73	31	the	the	DET
ejpam-4550	73	32	stage	stage	NOUN
ejpam-4550	73	33	k	k	PROPN
ejpam-4550	73	34	of	of	ADP
ejpam-4550	73	35	c2	c2	PROPN
ejpam-4550	73	36	.	.	PUNCT
ejpam-4550	74	1	for	for	ADP
ejpam-4550	74	2	the	the	DET
ejpam-4550	74	3	mathematical	mathematical	ADJ
ejpam-4550	74	4	analysis	analysis	NOUN
ejpam-4550	74	5	of	of	ADP
ejpam-4550	74	6	the	the	DET
ejpam-4550	74	7	model	model	NOUN
ejpam-4550	74	8	,	,	PUNCT
ejpam-4550	74	9	we	we	PRON
ejpam-4550	74	10	introduce	introduce	VERB
ejpam-4550	74	11	the	the	DET
ejpam-4550	74	12	following	follow	VERB
ejpam-4550	74	13	scalings	scaling	NOUN
ejpam-4550	74	14	:	:	PUNCT
ejpam-4550	74	15	s1	s1	NOUN
ejpam-4550	74	16	=	=	SYM
ejpam-4550	74	17	s1	s1	PROPN
ejpam-4550	74	18	n	n	NOUN
ejpam-4550	74	19	,	,	PUNCT
ejpam-4550	74	20	i11	i11	ADJ
ejpam-4550	74	21	=	=	SYM
ejpam-4550	74	22	i11	i11	ADJ
ejpam-4550	74	23	n	n	NOUN
ejpam-4550	74	24	,	,	PUNCT
ejpam-4550	74	25	i21	i21	NOUN
ejpam-4550	74	26	=	=	SYM
ejpam-4550	74	27	i21	i21	NOUN
ejpam-4550	74	28	n	n	NOUN
ejpam-4550	74	29	,	,	PUNCT
ejpam-4550	74	30	i31	i31	NOUN
ejpam-4550	74	31	=	=	SYM
ejpam-4550	74	32	i11	i11	ADJ
ejpam-4550	74	33	n	n	NOUN
ejpam-4550	74	34	,	,	PUNCT
ejpam-4550	74	35	s2	s2	NOUN
ejpam-4550	74	36	=	=	SYM
ejpam-4550	74	37	s2	s2	PROPN
ejpam-4550	74	38	n	n	NOUN
ejpam-4550	74	39	,	,	PUNCT
ejpam-4550	74	40	i12	i12	PROPN
ejpam-4550	74	41	=	=	NOUN
ejpam-4550	74	42	i12	i12	NUM
ejpam-4550	74	43	n	n	NOUN
ejpam-4550	74	44	,	,	PUNCT
ejpam-4550	74	45	i22	i22	NOUN
ejpam-4550	74	46	=	=	SYM
ejpam-4550	74	47	i22	i22	NOUN
ejpam-4550	74	48	n	n	NOUN
ejpam-4550	74	49	,	,	PUNCT
ejpam-4550	74	50	i32	i32	NOUN
ejpam-4550	74	51	=	=	PROPN
ejpam-4550	74	52	i32	i32	PROPN
ejpam-4550	74	53	n	n	PROPN
ejpam-4550	74	54	.	.	PUNCT
ejpam-4550	75	1	(	(	PUNCT
ejpam-4550	75	2	3	3	X
ejpam-4550	75	3	)	)	PUNCT
ejpam-4550	75	4	from	from	ADP
ejpam-4550	75	5	the	the	DET
ejpam-4550	75	6	equation	equation	NOUN
ejpam-4550	75	7	3	3	NUM
ejpam-4550	75	8	,	,	PUNCT
ejpam-4550	75	9	it	it	PRON
ejpam-4550	75	10	holds	hold	VERB
ejpam-4550	75	11	:	:	PUNCT
ejpam-4550	76	1	2∑	2∑	NUM
ejpam-4550	76	2	j=1	j=1	NOUN
ejpam-4550	76	3	sj	sj	PROPN
ejpam-4550	76	4	+	+	NOUN
ejpam-4550	76	5	3∑	3∑	NUM
ejpam-4550	76	6	j=1	j=1	NOUN
ejpam-4550	76	7	ij1	ij1	NOUN
ejpam-4550	76	8	+	+	CCONJ
ejpam-4550	76	9	3∑	3∑	NUM
ejpam-4550	76	10	j=1	j=1	NOUN
ejpam-4550	76	11	ij2	ij2	NOUN
ejpam-4550	76	12	=	=	NOUN
ejpam-4550	76	13	1	1	X
ejpam-4550	76	14	.	.	PUNCT
ejpam-4550	76	15	(	(	PUNCT
ejpam-4550	76	16	4	4	X
ejpam-4550	76	17	)	)	PUNCT
ejpam-4550	76	18	m.	m.	NOUN
ejpam-4550	76	19	alassane	alassane	NOUN
ejpam-4550	76	20	et	et	PROPN
ejpam-4550	76	21	al	al	PROPN
ejpam-4550	76	22	.	.	PUNCT
ejpam-4550	76	23	/	/	SYM
ejpam-4550	76	24	eur	eur	PROPN
ejpam-4550	76	25	.	.	PUNCT
ejpam-4550	77	1	j.	j.	PROPN
ejpam-4550	77	2	pure	pure	PROPN
ejpam-4550	77	3	appl	appl	PROPN
ejpam-4550	77	4	.	.	PROPN
ejpam-4550	77	5	math	math	PROPN
ejpam-4550	77	6	,	,	PUNCT
ejpam-4550	77	7	16	16	NUM
ejpam-4550	77	8	(	(	PUNCT
ejpam-4550	77	9	1	1	NUM
ejpam-4550	77	10	)	)	PUNCT
ejpam-4550	77	11	(	(	PUNCT
ejpam-4550	77	12	2023	2023	NUM
ejpam-4550	77	13	)	)	PUNCT
ejpam-4550	77	14	,	,	PUNCT
ejpam-4550	77	15	207	207	NUM
ejpam-4550	77	16	-	-	SYM
ejpam-4550	77	17	232	232	NUM
ejpam-4550	77	18	212	212	NUM
ejpam-4550	77	19	according	accord	VERB
ejpam-4550	77	20	to	to	ADP
ejpam-4550	77	21	the	the	DET
ejpam-4550	77	22	new	new	ADJ
ejpam-4550	77	23	variables	variable	NOUN
ejpam-4550	77	24	,	,	PUNCT
ejpam-4550	77	25	the	the	DET
ejpam-4550	77	26	system	system	NOUN
ejpam-4550	77	27	(	(	PUNCT
ejpam-4550	77	28	1	1	X
ejpam-4550	77	29	)	)	PUNCT
ejpam-4550	77	30	can	can	AUX
ejpam-4550	77	31	be	be	AUX
ejpam-4550	77	32	rewritten	rewrite	VERB
ejpam-4550	77	33	as	as	ADP
ejpam-4550	77	34	follows:	follows:	NOUN
ejpam-4550	77	35	d	d	NOUN
ejpam-4550	77	36	s1	s1	NOUN
ejpam-4550	77	37	dt	dt	X
ejpam-4550	77	38	=	=	SYM
ejpam-4550	77	39	b	b	PROPN
ejpam-4550	77	40	s1	s1	PROPN
ejpam-4550	77	41	β1	β1	VERB
ejpam-4550	77	42	3∑	3∑	NUM
ejpam-4550	77	43	j=1	j=1	NOUN
ejpam-4550	77	44	ij1	ij1	NOUN
ejpam-4550	77	45	+	+	CCONJ
ejpam-4550	77	46	β2	β2	NOUN
ejpam-4550	77	47	3∑	3∑	NUM
ejpam-4550	77	48	j=1	j=1	NOUN
ejpam-4550	77	49	ij2	ij2	NOUN
ejpam-4550	77	50	−	−	PRON
ejpam-4550	77	51	κ1s1	κ1s1	NOUN
ejpam-4550	78	1	d	d	X
ejpam-4550	78	2	i11	i11	ADJ
ejpam-4550	78	3	dt	dt	X
ejpam-4550	78	4	=	=	SYM
ejpam-4550	78	5	s1	s1	PROPN
ejpam-4550	78	6	β1	β1	VERB
ejpam-4550	78	7	3∑	3∑	NUM
ejpam-4550	78	8	j=1	j=1	NOUN
ejpam-4550	78	9	ij1	ij1	NOUN
ejpam-4550	78	10	+	+	CCONJ
ejpam-4550	78	11	β2	β2	NOUN
ejpam-4550	78	12	3∑	3∑	NUM
ejpam-4550	78	13	j=1	j=1	NOUN
ejpam-4550	78	14	ij2	ij2	X
ejpam-4550	79	1	−	−	ADP
ejpam-4550	79	2	κ2i	κ2i	PROPN
ejpam-4550	79	3	1	1	NUM
ejpam-4550	79	4	1	1	NUM
ejpam-4550	79	5	d	d	NOUN
ejpam-4550	79	6	i21	i21	NOUN
ejpam-4550	79	7	dt	dt	NOUN
ejpam-4550	79	8	=	=	PUNCT
ejpam-4550	79	9	a1i	a1i	VERB
ejpam-4550	79	10	1	1	NUM
ejpam-4550	79	11	1	1	NUM
ejpam-4550	79	12	−	−	NUM
ejpam-4550	79	13	κ3i	κ3i	NOUN
ejpam-4550	79	14	2	2	NUM
ejpam-4550	79	15	1	1	NUM
ejpam-4550	79	16	d	d	NOUN
ejpam-4550	79	17	i31	i31	NOUN
ejpam-4550	79	18	dt	dt	NOUN
ejpam-4550	80	1	=	=	NOUN
ejpam-4550	80	2	a2i	a2i	NOUN
ejpam-4550	80	3	2	2	NUM
ejpam-4550	80	4	1	1	NUM
ejpam-4550	80	5	−	−	NOUN
ejpam-4550	80	6	κ4i	κ4i	NOUN
ejpam-4550	80	7	3	3	NUM
ejpam-4550	80	8	1	1	NUM
ejpam-4550	80	9	d	d	PROPN
ejpam-4550	80	10	s2	s2	NOUN
ejpam-4550	80	11	dt	dt	X
ejpam-4550	81	1	=	=	SYM
ejpam-4550	81	2	γs1	γs1	PROPN
ejpam-4550	81	3	−	−	PROPN
ejpam-4550	81	4	s2	s2	PROPN
ejpam-4550	81	5	β1	β1	VERB
ejpam-4550	81	6	3∑	3∑	NUM
ejpam-4550	81	7	j=1	j=1	NOUN
ejpam-4550	81	8	ij1	ij1	NOUN
ejpam-4550	81	9	+	+	CCONJ
ejpam-4550	81	10	β2	β2	NOUN
ejpam-4550	82	1	3∑	3∑	NUM
ejpam-4550	82	2	j=1	j=1	NOUN
ejpam-4550	82	3	ij2	ij2	PROPN
ejpam-4550	82	4	−	−	ADV
ejpam-4550	83	1	bs2	bs2	PROPN
ejpam-4550	84	1	d	d	NOUN
ejpam-4550	84	2	i12	i12	NOUN
ejpam-4550	84	3	dt	dt	PROPN
ejpam-4550	84	4	=	=	NOUN
ejpam-4550	84	5	s2	s2	PROPN
ejpam-4550	84	6	β1	β1	VERB
ejpam-4550	84	7	3∑	3∑	NUM
ejpam-4550	84	8	j=1	j=1	NOUN
ejpam-4550	84	9	ij1	ij1	NOUN
ejpam-4550	84	10	+	+	CCONJ
ejpam-4550	84	11	β2	β2	NOUN
ejpam-4550	85	1	3∑	3∑	NUM
ejpam-4550	85	2	j=1	j=1	NOUN
ejpam-4550	85	3	ij2	ij2	NOUN
ejpam-4550	85	4	−	−	PUNCT
ejpam-4550	86	1	κ5i	κ5i	PUNCT
ejpam-4550	87	1	1	1	NUM
ejpam-4550	87	2	2	2	NUM
ejpam-4550	87	3	+	+	CCONJ
ejpam-4550	87	4	c1i	c1i	ADJ
ejpam-4550	87	5	1	1	NUM
ejpam-4550	87	6	1	1	NUM
ejpam-4550	87	7	d	d	NOUN
ejpam-4550	87	8	i22	i22	NOUN
ejpam-4550	87	9	dt	dt	NOUN
ejpam-4550	88	1	=	=	SYM
ejpam-4550	88	2	a3i	a3i	SYM
ejpam-4550	88	3	1	1	NUM
ejpam-4550	88	4	2	2	NUM
ejpam-4550	88	5	−	−	NOUN
ejpam-4550	88	6	κ6i	κ6i	PROPN
ejpam-4550	88	7	2	2	NUM
ejpam-4550	88	8	2	2	NUM
ejpam-4550	88	9	+	+	CCONJ
ejpam-4550	88	10	c2i	c2i	X
ejpam-4550	88	11	2	2	NUM
ejpam-4550	88	12	1	1	NUM
ejpam-4550	88	13	d	d	NOUN
ejpam-4550	88	14	i32	i32	NOUN
ejpam-4550	88	15	dt	dt	PROPN
ejpam-4550	89	1	=	=	SYM
ejpam-4550	89	2	a4i	a4i	PROPN
ejpam-4550	89	3	2	2	NUM
ejpam-4550	89	4	2	2	NUM
ejpam-4550	89	5	−	−	PROPN
ejpam-4550	89	6	b	b	PROPN
ejpam-4550	89	7	i32	i32	NOUN
ejpam-4550	89	8	+	+	CCONJ
ejpam-4550	89	9	c3i	c3i	NOUN
ejpam-4550	89	10	3	3	NUM
ejpam-4550	89	11	1	1	NUM
ejpam-4550	89	12	(	(	PUNCT
ejpam-4550	89	13	5	5	NUM
ejpam-4550	89	14	)	)	PUNCT
ejpam-4550	89	15	where	where	SCONJ
ejpam-4550	89	16	κ1	κ1	NOUN
ejpam-4550	89	17	=	=	SYM
ejpam-4550	89	18	b+γ	b+γ	PROPN
ejpam-4550	89	19	,	,	PUNCT
ejpam-4550	89	20	κ2	κ2	NOUN
ejpam-4550	89	21	=	=	PUNCT
ejpam-4550	89	22	b+a1+c1	b+a1+c1	NOUN
ejpam-4550	89	23	,	,	PUNCT
ejpam-4550	89	24	κ3	κ3	PROPN
ejpam-4550	89	25	=	=	PUNCT
ejpam-4550	89	26	b+a2+c2	b+a2+c2	PROPN
ejpam-4550	89	27	,	,	PUNCT
ejpam-4550	89	28	κ4	κ4	PROPN
ejpam-4550	89	29	=	=	SYM
ejpam-4550	89	30	b+c3	b+c3	PROPN
ejpam-4550	89	31	,	,	PUNCT
ejpam-4550	89	32	κ5	κ5	NOUN
ejpam-4550	89	33	=	=	SYM
ejpam-4550	89	34	b+a3	b+a3	NOUN
ejpam-4550	89	35	,	,	PUNCT
ejpam-4550	89	36	κ6	κ6	NOUN
ejpam-4550	89	37	=	=	PUNCT
ejpam-4550	89	38	b+a4	b+a4	PROPN
ejpam-4550	89	39	.	.	PUNCT
ejpam-4550	90	1	after	after	ADP
ejpam-4550	90	2	normalization	normalization	NOUN
ejpam-4550	90	3	of	of	ADP
ejpam-4550	90	4	the	the	DET
ejpam-4550	90	5	initial	initial	ADJ
ejpam-4550	90	6	data	datum	NOUN
ejpam-4550	90	7	,	,	PUNCT
ejpam-4550	90	8	we	we	PRON
ejpam-4550	90	9	obtain	obtain	VERB
ejpam-4550	90	10	:	:	PUNCT
ejpam-4550	90	11	2∑	2∑	NUM
ejpam-4550	90	12	j=1	j=1	PROPN
ejpam-4550	90	13	sj(0	sj(0	NOUN
ejpam-4550	90	14	)	)	PUNCT
ejpam-4550	91	1	+	+	NOUN
ejpam-4550	91	2	3∑	3∑	NUM
ejpam-4550	91	3	j=1	j=1	PROPN
ejpam-4550	91	4	ij1(0	ij1(0	PRON
ejpam-4550	91	5	)	)	PUNCT
ejpam-4550	92	1	+	+	NUM
ejpam-4550	92	2	3∑	3∑	NUM
ejpam-4550	92	3	j=1	j=1	NOUN
ejpam-4550	92	4	ij2(0	ij2(0	NOUN
ejpam-4550	92	5	)	)	PUNCT
ejpam-4550	92	6	=	=	SYM
ejpam-4550	92	7	1	1	NUM
ejpam-4550	92	8	(	(	PUNCT
ejpam-4550	92	9	6	6	NUM
ejpam-4550	92	10	)	)	PUNCT
ejpam-4550	92	11	and	and	CCONJ
ejpam-4550	92	12	s1(0	s1(0	PROPN
ejpam-4550	92	13	)	)	PUNCT
ejpam-4550	92	14	≥	≥	NOUN
ejpam-4550	92	15	0	0	NUM
ejpam-4550	92	16	,	,	PUNCT
ejpam-4550	92	17	i11(0	i11(0	PROPN
ejpam-4550	92	18	)	)	PUNCT
ejpam-4550	92	19	≥	≥	NOUN
ejpam-4550	92	20	0	0	NUM
ejpam-4550	92	21	,	,	PUNCT
ejpam-4550	92	22	i21(0	i21(0	PROPN
ejpam-4550	92	23	)	)	PUNCT
ejpam-4550	92	24	≥	≥	NOUN
ejpam-4550	92	25	0	0	NUM
ejpam-4550	92	26	,	,	PUNCT
ejpam-4550	92	27	i31(0	i31(0	PROPN
ejpam-4550	92	28	)	)	PUNCT
ejpam-4550	92	29	≥	≥	NOUN
ejpam-4550	92	30	0	0	NUM
ejpam-4550	92	31	,	,	PUNCT
ejpam-4550	92	32	s2(0	s2(0	PROPN
ejpam-4550	92	33	)	)	PUNCT
ejpam-4550	92	34	≥	≥	NOUN
ejpam-4550	92	35	0	0	NUM
ejpam-4550	92	36	,	,	PUNCT
ejpam-4550	92	37	i12(0	i12(0	ADJ
ejpam-4550	92	38	)	)	PUNCT
ejpam-4550	92	39	≥	≥	NOUN
ejpam-4550	92	40	0	0	NUM
ejpam-4550	92	41	,	,	PUNCT
ejpam-4550	92	42	i22(0	i22(0	PROPN
ejpam-4550	92	43	)	)	PUNCT
ejpam-4550	92	44	≥	≥	NOUN
ejpam-4550	92	45	0	0	NUM
ejpam-4550	92	46	,	,	PUNCT
ejpam-4550	92	47	i32(0	i32(0	PROPN
ejpam-4550	92	48	)	)	PUNCT
ejpam-4550	92	49	≥	≥	NOUN
ejpam-4550	92	50	0	0	NUM
ejpam-4550	92	51	.	.	PUNCT
ejpam-4550	93	1	(	(	PUNCT
ejpam-4550	93	2	7	7	X
ejpam-4550	93	3	)	)	PUNCT
ejpam-4550	93	4	the	the	DET
ejpam-4550	93	5	variables	variable	NOUN
ejpam-4550	93	6	of	of	ADP
ejpam-4550	93	7	the	the	DET
ejpam-4550	93	8	model	model	NOUN
ejpam-4550	93	9	(	(	PUNCT
ejpam-4550	93	10	5	5	NUM
ejpam-4550	93	11	)	)	PUNCT
ejpam-4550	93	12	are	be	AUX
ejpam-4550	93	13	reported	report	VERB
ejpam-4550	93	14	in	in	ADP
ejpam-4550	93	15	table	table	NOUN
ejpam-4550	93	16	3	3	NUM
ejpam-4550	93	17	.	.	PUNCT
ejpam-4550	93	18	m.	m.	NOUN
ejpam-4550	93	19	alassane	alassane	NOUN
ejpam-4550	93	20	et	et	PROPN
ejpam-4550	93	21	al	al	PROPN
ejpam-4550	93	22	.	.	PUNCT
ejpam-4550	93	23	/	/	SYM
ejpam-4550	93	24	eur	eur	PROPN
ejpam-4550	93	25	.	.	PUNCT
ejpam-4550	94	1	j.	j.	PROPN
ejpam-4550	94	2	pure	pure	PROPN
ejpam-4550	94	3	appl	appl	PROPN
ejpam-4550	94	4	.	.	PROPN
ejpam-4550	94	5	math	math	PROPN
ejpam-4550	94	6	,	,	PUNCT
ejpam-4550	94	7	16	16	NUM
ejpam-4550	94	8	(	(	PUNCT
ejpam-4550	94	9	1	1	NUM
ejpam-4550	94	10	)	)	PUNCT
ejpam-4550	94	11	(	(	PUNCT
ejpam-4550	94	12	2023	2023	NUM
ejpam-4550	94	13	)	)	PUNCT
ejpam-4550	94	14	,	,	PUNCT
ejpam-4550	94	15	207	207	NUM
ejpam-4550	94	16	-	-	SYM
ejpam-4550	94	17	232	232	NUM
ejpam-4550	94	18	213	213	NUM
ejpam-4550	94	19	table	table	NOUN
ejpam-4550	94	20	3	3	NUM
ejpam-4550	94	21	:	:	PUNCT
ejpam-4550	94	22	variables	variable	NOUN
ejpam-4550	94	23	for	for	ADP
ejpam-4550	94	24	the	the	DET
ejpam-4550	94	25	re	re	ADJ
ejpam-4550	94	26	-	-	VERB
ejpam-4550	94	27	scaled	scaled	ADJ
ejpam-4550	94	28	hiv	hiv	PROPN
ejpam-4550	94	29	-	-	PUNCT
ejpam-4550	94	30	aids	aids	PROPN
ejpam-4550	94	31	model	model	NOUN
ejpam-4550	94	32	variables	variable	VERB
ejpam-4550	94	33	description	description	NOUN
ejpam-4550	94	34	s1	s1	NOUN
ejpam-4550	94	35	proportion	proportion	NOUN
ejpam-4550	94	36	of	of	ADP
ejpam-4550	94	37	susceptible	susceptible	ADJ
ejpam-4550	94	38	individuals	individual	NOUN
ejpam-4550	94	39	in	in	ADP
ejpam-4550	94	40	class	class	NOUN
ejpam-4550	94	41	c1	c1	NOUN
ejpam-4550	94	42	s2	s2	NOUN
ejpam-4550	94	43	proportion	proportion	NOUN
ejpam-4550	94	44	of	of	ADP
ejpam-4550	94	45	susceptible	susceptible	ADJ
ejpam-4550	94	46	individuals	individual	NOUN
ejpam-4550	94	47	in	in	ADP
ejpam-4550	94	48	class	class	NOUN
ejpam-4550	94	49	c2	c2	PROPN
ejpam-4550	94	50	i11	i11	ADJ
ejpam-4550	94	51	proportion	proportion	NOUN
ejpam-4550	94	52	of	of	ADP
ejpam-4550	94	53	individuals	individual	NOUN
ejpam-4550	94	54	at	at	ADP
ejpam-4550	94	55	stage	stage	NOUN
ejpam-4550	94	56	1	1	NUM
ejpam-4550	94	57	of	of	ADP
ejpam-4550	94	58	infection	infection	NOUN
ejpam-4550	94	59	in	in	ADP
ejpam-4550	94	60	c1	c1	PROPN
ejpam-4550	94	61	i21	i21	NOUN
ejpam-4550	94	62	proportion	proportion	NOUN
ejpam-4550	94	63	of	of	ADP
ejpam-4550	94	64	individuals	individual	NOUN
ejpam-4550	94	65	at	at	ADP
ejpam-4550	94	66	stage	stage	NOUN
ejpam-4550	94	67	2	2	NUM
ejpam-4550	94	68	of	of	ADP
ejpam-4550	94	69	infection	infection	NOUN
ejpam-4550	94	70	in	in	ADP
ejpam-4550	94	71	c1	c1	PROPN
ejpam-4550	94	72	i31	i31	NOUN
ejpam-4550	94	73	proportion	proportion	NOUN
ejpam-4550	94	74	of	of	ADP
ejpam-4550	94	75	individuals	individual	NOUN
ejpam-4550	94	76	at	at	ADP
ejpam-4550	94	77	stage	stage	NOUN
ejpam-4550	94	78	3	3	NUM
ejpam-4550	94	79	of	of	ADP
ejpam-4550	94	80	infection	infection	NOUN
ejpam-4550	94	81	in	in	ADP
ejpam-4550	94	82	c1	c1	PROPN
ejpam-4550	94	83	i12	i12	PROPN
ejpam-4550	94	84	proportion	proportion	NOUN
ejpam-4550	94	85	of	of	ADP
ejpam-4550	94	86	individuals	individual	NOUN
ejpam-4550	94	87	at	at	ADP
ejpam-4550	94	88	stage	stage	NOUN
ejpam-4550	94	89	1	1	NUM
ejpam-4550	94	90	of	of	ADP
ejpam-4550	94	91	infection	infection	NOUN
ejpam-4550	94	92	in	in	ADP
ejpam-4550	94	93	c2	c2	PROPN
ejpam-4550	94	94	i22	i22	NOUN
ejpam-4550	94	95	proportion	proportion	NOUN
ejpam-4550	94	96	of	of	ADP
ejpam-4550	94	97	individuals	individual	NOUN
ejpam-4550	94	98	at	at	ADP
ejpam-4550	94	99	stage	stage	NOUN
ejpam-4550	94	100	2	2	NUM
ejpam-4550	94	101	of	of	ADP
ejpam-4550	94	102	infection	infection	NOUN
ejpam-4550	94	103	in	in	ADP
ejpam-4550	94	104	c2	c2	PROPN
ejpam-4550	94	105	i32	i32	PROPN
ejpam-4550	94	106	proportion	proportion	NOUN
ejpam-4550	94	107	of	of	ADP
ejpam-4550	94	108	individuals	individual	NOUN
ejpam-4550	94	109	at	at	ADP
ejpam-4550	94	110	stage	stage	NOUN
ejpam-4550	94	111	3	3	NUM
ejpam-4550	94	112	of	of	ADP
ejpam-4550	94	113	infection	infection	NOUN
ejpam-4550	94	114	in	in	ADP
ejpam-4550	94	115	c2	c2	PROPN
ejpam-4550	94	116	3	3	NUM
ejpam-4550	94	117	.	.	PUNCT
ejpam-4550	94	118	basic	basic	ADJ
ejpam-4550	94	119	properties	property	NOUN
ejpam-4550	94	120	theorem	theorem	VERB
ejpam-4550	94	121	1	1	NUM
ejpam-4550	94	122	.	.	PUNCT
ejpam-4550	95	1	the	the	DET
ejpam-4550	95	2	feasible	feasible	ADJ
ejpam-4550	95	3	region	region	NOUN
ejpam-4550	95	4	γ	γ	NOUN
ejpam-4550	95	5	defined	define	VERB
ejpam-4550	95	6	by	by	ADP
ejpam-4550	95	7	γ	γ	X
ejpam-4550	95	8	=	=	SYM
ejpam-4550	95	9	e	e	PROPN
ejpam-4550	95	10	=	=	SYM
ejpam-4550	95	11	(	(	PUNCT
ejpam-4550	95	12	s1	s1	NOUN
ejpam-4550	95	13	,	,	PUNCT
ejpam-4550	95	14	i11	i11	NOUN
ejpam-4550	95	15	,	,	PUNCT
ejpam-4550	95	16	i21	i21	NOUN
ejpam-4550	95	17	,	,	PUNCT
ejpam-4550	95	18	i31	i31	NOUN
ejpam-4550	95	19	,	,	PUNCT
ejpam-4550	95	20	s2	s2	PROPN
ejpam-4550	95	21	,	,	PUNCT
ejpam-4550	95	22	i12	i12	NOUN
ejpam-4550	95	23	,	,	PUNCT
ejpam-4550	95	24	i22	i22	NOUN
ejpam-4550	95	25	,	,	PUNCT
ejpam-4550	95	26	i32	i32	PROPN
ejpam-4550	95	27	)	)	PUNCT
ejpam-4550	95	28	∈	∈	PROPN
ejpam-4550	95	29	r8	r8	PROPN
ejpam-4550	95	30	+	+	CCONJ
ejpam-4550	95	31	:	:	SYM
ejpam-4550	95	32	0	0	NUM
ejpam-4550	95	33	≤	≤	NUM
ejpam-4550	96	1	2∑	2∑	NUM
ejpam-4550	96	2	j=1	j=1	NOUN
ejpam-4550	96	3	sj	sj	PROPN
ejpam-4550	96	4	+	+	NOUN
ejpam-4550	96	5	3∑	3∑	NUM
ejpam-4550	96	6	j=1	j=1	NOUN
ejpam-4550	96	7	ij1	ij1	NOUN
ejpam-4550	96	8	+	+	NOUN
ejpam-4550	96	9	3∑	3∑	NUM
ejpam-4550	96	10	j=1	j=1	NOUN
ejpam-4550	96	11	ij2	ij2	NOUN
ejpam-4550	96	12	≤	≤	ADJ
ejpam-4550	96	13	1	1	NUM
ejpam-4550	96	14			NOUN
ejpam-4550	96	15	with	with	ADP
ejpam-4550	96	16	the	the	DET
ejpam-4550	96	17	initial	initial	ADJ
ejpam-4550	96	18	conditions	condition	NOUN
ejpam-4550	96	19	s1(0	s1(0	PROPN
ejpam-4550	96	20	)	)	PUNCT
ejpam-4550	96	21	≥	≥	NOUN
ejpam-4550	96	22	0	0	NUM
ejpam-4550	96	23	,	,	PUNCT
ejpam-4550	96	24	i11(0	i11(0	PROPN
ejpam-4550	96	25	)	)	PUNCT
ejpam-4550	96	26	≥	≥	NOUN
ejpam-4550	96	27	0	0	NUM
ejpam-4550	96	28	,	,	PUNCT
ejpam-4550	96	29	i21(0	i21(0	PROPN
ejpam-4550	96	30	)	)	PUNCT
ejpam-4550	96	31	≥	≥	NOUN
ejpam-4550	96	32	0	0	NUM
ejpam-4550	96	33	,	,	PUNCT
ejpam-4550	96	34	i31(0	i31(0	PROPN
ejpam-4550	96	35	)	)	PUNCT
ejpam-4550	96	36	≥	≥	NOUN
ejpam-4550	96	37	0	0	NUM
ejpam-4550	96	38	,	,	PUNCT
ejpam-4550	96	39	s2(0	s2(0	PROPN
ejpam-4550	96	40	)	)	PUNCT
ejpam-4550	96	41	≥	≥	NOUN
ejpam-4550	96	42	0	0	NUM
ejpam-4550	96	43	,	,	PUNCT
ejpam-4550	96	44	i12(0	i12(0	ADJ
ejpam-4550	96	45	)	)	PUNCT
ejpam-4550	96	46	≥	≥	NOUN
ejpam-4550	96	47	0	0	NUM
ejpam-4550	96	48	,	,	PUNCT
ejpam-4550	96	49	i22(0	i22(0	PROPN
ejpam-4550	96	50	)	)	PUNCT
ejpam-4550	96	51	≥	≥	NOUN
ejpam-4550	96	52	0	0	NUM
ejpam-4550	96	53	,	,	PUNCT
ejpam-4550	96	54	i32(0	i32(0	PROPN
ejpam-4550	96	55	)	)	PUNCT
ejpam-4550	96	56	≥	≥	X
ejpam-4550	96	57	0	0	NUM
ejpam-4550	96	58	is	be	AUX
ejpam-4550	96	59	a	a	DET
ejpam-4550	96	60	positively	positively	ADV
ejpam-4550	96	61	invariant	invariant	ADJ
ejpam-4550	96	62	set	set	NOUN
ejpam-4550	96	63	for	for	ADP
ejpam-4550	96	64	the	the	DET
ejpam-4550	96	65	system	system	NOUN
ejpam-4550	96	66	(	(	PUNCT
ejpam-4550	96	67	5	5	NUM
ejpam-4550	96	68	)	)	PUNCT
ejpam-4550	96	69	.	.	PUNCT
ejpam-4550	97	1	proof	proof	NOUN
ejpam-4550	97	2	.	.	PUNCT
ejpam-4550	98	1	1	1	X
ejpam-4550	98	2	.	.	X
ejpam-4550	98	3	positivity	positivity	NOUN
ejpam-4550	98	4	of	of	ADP
ejpam-4550	98	5	solutions	solution	NOUN
ejpam-4550	98	6	we	we	PRON
ejpam-4550	98	7	show	show	VERB
ejpam-4550	98	8	by	by	ADP
ejpam-4550	98	9	absurd	absurd	ADJ
ejpam-4550	98	10	that	that	SCONJ
ejpam-4550	98	11	for	for	ADP
ejpam-4550	98	12	all	all	DET
ejpam-4550	98	13	t	t	PROPN
ejpam-4550	98	14	≥	≥	NOUN
ejpam-4550	98	15	0	0	NUM
ejpam-4550	98	16	,	,	PUNCT
ejpam-4550	98	17	e(t	e(t	PROPN
ejpam-4550	98	18	)	)	PUNCT
ejpam-4550	98	19	≥	≥	NOUN
ejpam-4550	98	20	0	0	NUM
ejpam-4550	98	21	.	.	PUNCT
ejpam-4550	98	22	suppose	suppose	VERB
ejpam-4550	98	23	that	that	SCONJ
ejpam-4550	98	24	for	for	ADP
ejpam-4550	98	25	a	a	DET
ejpam-4550	98	26	time	time	NOUN
ejpam-4550	98	27	t′	t′	NUM
ejpam-4550	98	28	>	>	SYM
ejpam-4550	98	29	0	0	PROPN
ejpam-4550	98	30	,	,	PUNCT
ejpam-4550	98	31	we	we	PRON
ejpam-4550	98	32	have	have	VERB
ejpam-4550	98	33	e(t	e(t	NOUN
ejpam-4550	98	34	’	'	PUNCT
ejpam-4550	98	35	)	)	PUNCT
ejpam-4550	99	1	<	<	X
ejpam-4550	100	1	0	0	X
ejpam-4550	100	2	.	.	PUNCT
ejpam-4550	101	1	the	the	DET
ejpam-4550	101	2	function	function	NOUN
ejpam-4550	101	3	e	e	VERB
ejpam-4550	101	4	being	be	AUX
ejpam-4550	101	5	continuous	continuous	ADJ
ejpam-4550	101	6	,	,	PUNCT
ejpam-4550	101	7	from	from	ADP
ejpam-4550	101	8	the	the	DET
ejpam-4550	101	9	intermediate	intermediate	ADJ
ejpam-4550	101	10	value	value	NOUN
ejpam-4550	101	11	theorem	theorem	VERB
ejpam-4550	101	12	,	,	PUNCT
ejpam-4550	101	13	there	there	PRON
ejpam-4550	101	14	exists	exist	VERB
ejpam-4550	101	15	a	a	DET
ejpam-4550	101	16	time	time	NOUN
ejpam-4550	101	17	t1	t1	NOUN
ejpam-4550	101	18	∈]0	∈]0	NOUN
ejpam-4550	101	19	,	,	PUNCT
ejpam-4550	101	20	t	t	PROPN
ejpam-4550	101	21	’	'	PUNCT
ejpam-4550	101	22	[	[	PUNCT
ejpam-4550	101	23	such	such	ADJ
ejpam-4550	101	24	that	that	DET
ejpam-4550	101	25	e(t1	e(t1	NOUN
ejpam-4550	101	26	)	)	PUNCT
ejpam-4550	102	1	=	=	SYM
ejpam-4550	102	2	0	0	X
ejpam-4550	102	3	.	.	PUNCT
ejpam-4550	102	4	consider	consider	VERB
ejpam-4550	102	5	the	the	DET
ejpam-4550	102	6	equations	equation	NOUN
ejpam-4550	102	7	of	of	ADP
ejpam-4550	102	8	system	system	NOUN
ejpam-4550	102	9	(	(	PUNCT
ejpam-4550	102	10	5	5	NUM
ejpam-4550	102	11	)	)	PUNCT
ejpam-4550	102	12	and	and	CCONJ
ejpam-4550	102	13	let	let	VERB
ejpam-4550	102	14	:	:	PUNCT
ejpam-4550	102	15	ξ1(t	ξ1(t	X
ejpam-4550	102	16	)	)	PUNCT
ejpam-4550	102	17	=	=	SYM
ejpam-4550	102	18	exp	exp	NOUN
ejpam-4550	102	19	∫	∫	PROPN
ejpam-4550	102	20	t	t	NOUN
ejpam-4550	102	21	0	0	NUM
ejpam-4550	102	22	β1	β1	NOUN
ejpam-4550	103	1	3∑	3∑	NUM
ejpam-4550	103	2	j=1	j=1	NOUN
ejpam-4550	103	3	ij1	ij1	NOUN
ejpam-4550	103	4	+	+	CCONJ
ejpam-4550	103	5	β2	β2	NOUN
ejpam-4550	103	6	3∑	3∑	NUM
ejpam-4550	103	7	j=1	j=1	NOUN
ejpam-4550	103	8	ij2	ij2	PROPN
ejpam-4550	104	1	+	+	CCONJ
ejpam-4550	104	2	κ1	κ1	NOUN
ejpam-4550	104	3	dτ	dτ	PRON
ejpam-4550	104	4			NOUN
ejpam-4550	104	5	,	,	PUNCT
ejpam-4550	104	6	ξ3(t	ξ3(t	X
ejpam-4550	104	7	)	)	PUNCT
ejpam-4550	104	8	=	=	SYM
ejpam-4550	104	9	exp	exp	NOUN
ejpam-4550	104	10	(	(	PUNCT
ejpam-4550	104	11	∫	∫	PROPN
ejpam-4550	104	12	t	t	PROPN
ejpam-4550	104	13	0	0	NUM
ejpam-4550	104	14	(	(	PUNCT
ejpam-4550	104	15	κ2	κ2	NOUN
ejpam-4550	104	16	−	−	NOUN
ejpam-4550	104	17	β1s1	β1s1	SYM
ejpam-4550	104	18	)	)	PUNCT
ejpam-4550	104	19	dτ	dτ	NOUN
ejpam-4550	104	20	)	)	PUNCT
ejpam-4550	104	21	,	,	PUNCT
ejpam-4550	104	22	ξ2(t	ξ2(t	PROPN
ejpam-4550	104	23	)	)	PUNCT
ejpam-4550	104	24	=	=	SYM
ejpam-4550	104	25	exp	exp	NOUN
ejpam-4550	104	26	(	(	PUNCT
ejpam-4550	104	27	κ3	κ3	PROPN
ejpam-4550	104	28	t	t	PROPN
ejpam-4550	104	29	)	)	PUNCT
ejpam-4550	104	30	,	,	PUNCT
ejpam-4550	104	31	ξ4(t	ξ4(t	X
ejpam-4550	104	32	)	)	PUNCT
ejpam-4550	104	33	=	=	NOUN
ejpam-4550	104	34	exp	exp	NOUN
ejpam-4550	104	35	(	(	PUNCT
ejpam-4550	104	36	κ4	κ4	PROPN
ejpam-4550	104	37	t	t	PROPN
ejpam-4550	104	38	)	)	PUNCT
ejpam-4550	104	39	,	,	PUNCT
ejpam-4550	104	40	ξ5(t	ξ5(t	X
ejpam-4550	104	41	)	)	PUNCT
ejpam-4550	104	42	=	=	NOUN
ejpam-4550	104	43	exp	exp	NOUN
ejpam-4550	104	44	(	(	PUNCT
ejpam-4550	104	45	κ6	κ6	PROPN
ejpam-4550	104	46	t	t	PROPN
ejpam-4550	104	47	)	)	PUNCT
ejpam-4550	104	48	,	,	PUNCT
ejpam-4550	104	49	ξ7(t	ξ7(t	X
ejpam-4550	104	50	)	)	PUNCT
ejpam-4550	104	51	=	=	NOUN
ejpam-4550	104	52	exp	exp	X
ejpam-4550	104	53	(	(	PUNCT
ejpam-4550	104	54	bt	bt	NOUN
ejpam-4550	104	55	)	)	PUNCT
ejpam-4550	104	56	,	,	PUNCT
ejpam-4550	104	57	ξ6(t	ξ6(t	NOUN
ejpam-4550	104	58	)	)	PUNCT
ejpam-4550	104	59	=	=	NOUN
ejpam-4550	104	60	exp	exp	NOUN
ejpam-4550	104	61	(	(	PUNCT
ejpam-4550	104	62	∫	∫	PROPN
ejpam-4550	104	63	t	t	PROPN
ejpam-4550	104	64	0	0	NUM
ejpam-4550	104	65	(	(	PUNCT
ejpam-4550	104	66	κ5	κ5	VERB
ejpam-4550	104	67	−	−	NOUN
ejpam-4550	104	68	β2s2	β2s2	NOUN
ejpam-4550	104	69	)	)	PUNCT
ejpam-4550	104	70	dτ	dτ	NOUN
ejpam-4550	104	71	)	)	PUNCT
ejpam-4550	104	72	,	,	PUNCT
ejpam-4550	104	73	ξ8(t	ξ8(t	PROPN
ejpam-4550	104	74	)	)	PUNCT
ejpam-4550	104	75	=	=	PUNCT
ejpam-4550	104	76	exp	exp	NOUN
ejpam-4550	104	77	∫	∫	PROPN
ejpam-4550	104	78	t	t	NOUN
ejpam-4550	104	79	0	0	NUM
ejpam-4550	104	80	β1	β1	NOUN
ejpam-4550	104	81	3∑	3∑	NUM
ejpam-4550	104	82	j=1	j=1	NOUN
ejpam-4550	104	83	ij1	ij1	NOUN
ejpam-4550	104	84	+	+	CCONJ
ejpam-4550	104	85	β2	β2	NOUN
ejpam-4550	104	86	3∑	3∑	NUM
ejpam-4550	104	87	j=1	j=1	NOUN
ejpam-4550	104	88	ij2	ij2	PROPN
ejpam-4550	105	1	+	+	NUM
ejpam-4550	105	2	b	b	PROPN
ejpam-4550	105	3			PROPN
ejpam-4550	105	4	dτ	dτ	NOUN
ejpam-4550	105	5			NOUN
ejpam-4550	105	6	.	.	PUNCT
ejpam-4550	106	1	m.	m.	NOUN
ejpam-4550	106	2	alassane	alassane	NOUN
ejpam-4550	106	3	et	et	PROPN
ejpam-4550	106	4	al	al	PROPN
ejpam-4550	106	5	.	.	PUNCT
ejpam-4550	106	6	/	/	SYM
ejpam-4550	106	7	eur	eur	PROPN
ejpam-4550	106	8	.	.	PUNCT
ejpam-4550	107	1	j.	j.	PROPN
ejpam-4550	107	2	pure	pure	PROPN
ejpam-4550	107	3	appl	appl	PROPN
ejpam-4550	107	4	.	.	PROPN
ejpam-4550	107	5	math	math	PROPN
ejpam-4550	107	6	,	,	PUNCT
ejpam-4550	107	7	16	16	NUM
ejpam-4550	107	8	(	(	PUNCT
ejpam-4550	107	9	1	1	NUM
ejpam-4550	107	10	)	)	PUNCT
ejpam-4550	107	11	(	(	PUNCT
ejpam-4550	107	12	2023	2023	NUM
ejpam-4550	107	13	)	)	PUNCT
ejpam-4550	107	14	,	,	PUNCT
ejpam-4550	107	15	207	207	NUM
ejpam-4550	107	16	-	-	SYM
ejpam-4550	107	17	232	232	NUM
ejpam-4550	107	18	214	214	NUM
ejpam-4550	107	19	by	by	ADP
ejpam-4550	107	20	differentiating	differentiate	VERB
ejpam-4550	107	21	each	each	PRON
ejpam-4550	107	22	of	of	ADP
ejpam-4550	107	23	the	the	DET
ejpam-4550	107	24	expressions	expression	NOUN
ejpam-4550	107	25	s1ξ1	s1ξ1	PROPN
ejpam-4550	107	26	,	,	PUNCT
ejpam-4550	107	27	i	i	PROPN
ejpam-4550	107	28	1	1	NUM
ejpam-4550	107	29	1ξ3	1ξ3	NUM
ejpam-4550	107	30	,	,	PUNCT
ejpam-4550	107	31	i	i	NOUN
ejpam-4550	107	32	2	2	NUM
ejpam-4550	107	33	1ξ2	1ξ2	NUM
ejpam-4550	107	34	,	,	PUNCT
ejpam-4550	107	35	i	i	PRON
ejpam-4550	107	36	3	3	NUM
ejpam-4550	107	37	1ξ4	1ξ4	NUM
ejpam-4550	107	38	,	,	PUNCT
ejpam-4550	107	39	s2ξ8	s2ξ8	X
ejpam-4550	107	40	,	,	PUNCT
ejpam-4550	107	41	i	i	PROPN
ejpam-4550	107	42	1	1	NUM
ejpam-4550	107	43	2ξ5	2ξ5	NUM
ejpam-4550	107	44	,	,	PUNCT
ejpam-4550	107	45	i	i	NOUN
ejpam-4550	107	46	2	2	NUM
ejpam-4550	107	47	2ξ6	2ξ6	NUM
ejpam-4550	107	48	and	and	CCONJ
ejpam-4550	107	49	i32ξ7	i32ξ7	NOUN
ejpam-4550	107	50	with	with	ADP
ejpam-4550	107	51	respect	respect	NOUN
ejpam-4550	107	52	to	to	ADP
ejpam-4550	107	53	time	time	NOUN
ejpam-4550	107	54	t	t	PROPN
ejpam-4550	107	55	,	,	PUNCT
ejpam-4550	107	56	we	we	PRON
ejpam-4550	107	57	obtain	obtain	VERB
ejpam-4550	107	58	:	:	PUNCT
ejpam-4550	107	59	ds1ξ1	ds1ξ1	PROPN
ejpam-4550	107	60	dt	dt	X
ejpam-4550	107	61	=	=	SYM
ejpam-4550	107	62	bξ1	bξ1	NOUN
ejpam-4550	107	63	(	(	PUNCT
ejpam-4550	107	64	8a	8a	NUM
ejpam-4550	107	65	)	)	PUNCT
ejpam-4550	107	66	di11ξ3	di11ξ3	PROPN
ejpam-4550	107	67	dt	dt	NOUN
ejpam-4550	107	68	=	=	PUNCT
ejpam-4550	107	69	s1ξ3	s1ξ3	PROPN
ejpam-4550	107	70	β1	β1	VERB
ejpam-4550	107	71	3∑	3∑	NUM
ejpam-4550	107	72	j=2	j=2	NOUN
ejpam-4550	107	73	ij1	ij1	NOUN
ejpam-4550	107	74	+	+	CCONJ
ejpam-4550	107	75	β2	β2	NOUN
ejpam-4550	107	76	3∑	3∑	NUM
ejpam-4550	107	77	j=1	j=1	NOUN
ejpam-4550	107	78	ij2	ij2	PROPN
ejpam-4550	108	1			PROPN
ejpam-4550	108	2	(	(	PUNCT
ejpam-4550	108	3	8b	8b	NUM
ejpam-4550	108	4	)	)	PUNCT
ejpam-4550	108	5	di21ξ2	di21ξ2	NOUN
ejpam-4550	108	6	dt	dt	NOUN
ejpam-4550	108	7	=	=	PUNCT
ejpam-4550	108	8	a1i	a1i	VERB
ejpam-4550	108	9	1	1	NUM
ejpam-4550	108	10	1ξ2	1ξ2	NUM
ejpam-4550	108	11	(	(	PUNCT
ejpam-4550	108	12	8c	8c	NUM
ejpam-4550	108	13	)	)	PUNCT
ejpam-4550	108	14	di31ξ4	di31ξ4	ADP
ejpam-4550	108	15	dt	dt	PUNCT
ejpam-4550	108	16	=	=	PUNCT
ejpam-4550	109	1	a2i	a2i	NOUN
ejpam-4550	109	2	2	2	NUM
ejpam-4550	109	3	1ξ4	1ξ4	NUM
ejpam-4550	109	4	(	(	PUNCT
ejpam-4550	109	5	8d	8d	NUM
ejpam-4550	109	6	)	)	PUNCT
ejpam-4550	110	1	ds2ξ8	ds2ξ8	NOUN
ejpam-4550	110	2	dt	dt	NOUN
ejpam-4550	110	3	=	=	SYM
ejpam-4550	110	4	γs1ξ8	γs1ξ8	PROPN
ejpam-4550	110	5	(	(	PUNCT
ejpam-4550	110	6	8e	8e	NUM
ejpam-4550	110	7	)	)	PUNCT
ejpam-4550	110	8	di12ξ6	di12ξ6	NOUN
ejpam-4550	110	9	dt	dt	NOUN
ejpam-4550	110	10	=	=	SYM
ejpam-4550	110	11	ξ6	ξ6	NOUN
ejpam-4550	110	12	β1s2	β1s2	PROPN
ejpam-4550	110	13	3∑	3∑	NOUN
ejpam-4550	110	14	j=1	j=1	NOUN
ejpam-4550	110	15	ij1	ij1	NOUN
ejpam-4550	110	16	+	+	CCONJ
ejpam-4550	110	17	β2s2	β2s2	PROPN
ejpam-4550	110	18	3∑	3∑	NUM
ejpam-4550	110	19	j=2	j=2	NOUN
ejpam-4550	110	20	ij2	ij2	NOUN
ejpam-4550	111	1	+	+	CCONJ
ejpam-4550	111	2	c1i	c1i	ADJ
ejpam-4550	111	3	1	1	NUM
ejpam-4550	111	4	1	1	NUM
ejpam-4550	111	5			PROPN
ejpam-4550	111	6	(	(	PUNCT
ejpam-4550	111	7	8f	8f	NOUN
ejpam-4550	111	8	)	)	PUNCT
ejpam-4550	111	9	di22ξ5	di22ξ5	NOUN
ejpam-4550	111	10	dt	dt	NOUN
ejpam-4550	111	11	=	=	PUNCT
ejpam-4550	111	12	(	(	PUNCT
ejpam-4550	111	13	a3i	a3i	SYM
ejpam-4550	111	14	1	1	NUM
ejpam-4550	111	15	2	2	NUM
ejpam-4550	111	16	+	+	CCONJ
ejpam-4550	111	17	c2i	c2i	X
ejpam-4550	111	18	2	2	NUM
ejpam-4550	111	19	1	1	NUM
ejpam-4550	111	20	)	)	PUNCT
ejpam-4550	111	21	ξ5	ξ5	NOUN
ejpam-4550	111	22	(	(	PUNCT
ejpam-4550	111	23	8	8	NUM
ejpam-4550	111	24	g	g	NOUN
ejpam-4550	111	25	)	)	PUNCT
ejpam-4550	111	26	di32ξ7	di32ξ7	NOUN
ejpam-4550	111	27	dt	dt	NOUN
ejpam-4550	112	1	=	=	PUNCT
ejpam-4550	113	1	(	(	PUNCT
ejpam-4550	113	2	a4i	a4i	NOUN
ejpam-4550	113	3	2	2	NUM
ejpam-4550	113	4	2	2	NUM
ejpam-4550	113	5	+	+	NUM
ejpam-4550	113	6	c3i	c3i	NOUN
ejpam-4550	113	7	3	3	NUM
ejpam-4550	113	8	1	1	NUM
ejpam-4550	113	9	)	)	PUNCT
ejpam-4550	113	10	ξ7	ξ7	NOUN
ejpam-4550	113	11	(	(	PUNCT
ejpam-4550	113	12	8h	8h	NUM
ejpam-4550	113	13	)	)	PUNCT
ejpam-4550	113	14	by	by	ADP
ejpam-4550	113	15	integrating	integrate	VERB
ejpam-4550	113	16	the	the	DET
ejpam-4550	113	17	equations	equation	NOUN
ejpam-4550	113	18	(	(	PUNCT
ejpam-4550	113	19	8a)-(8h	8a)-(8h	NUM
ejpam-4550	113	20	)	)	PUNCT
ejpam-4550	113	21	between	between	ADP
ejpam-4550	113	22	0	0	NUM
ejpam-4550	113	23	and	and	CCONJ
ejpam-4550	113	24	t1	t1	NOUN
ejpam-4550	113	25	,	,	PUNCT
ejpam-4550	113	26	it	it	PRON
ejpam-4550	113	27	holds	hold	VERB
ejpam-4550	113	28	:	:	PUNCT
ejpam-4550	113	29	s1(t1	s1(t1	X
ejpam-4550	113	30	)	)	PUNCT
ejpam-4550	113	31	=	=	SYM
ejpam-4550	113	32	1	1	NUM
ejpam-4550	113	33	ξ1(t1	ξ1(t1	NUM
ejpam-4550	113	34	)	)	PUNCT
ejpam-4550	113	35	[	[	PUNCT
ejpam-4550	113	36	s1(0	s1(0	PROPN
ejpam-4550	113	37	)	)	PUNCT
ejpam-4550	114	1	+	+	CCONJ
ejpam-4550	114	2	∫	∫	PROPN
ejpam-4550	114	3	t1	t1	NOUN
ejpam-4550	114	4	0	0	NUM
ejpam-4550	115	1	bξ1dt	bξ1dt	X
ejpam-4550	115	2	]	]	PUNCT
ejpam-4550	115	3	>	>	X
ejpam-4550	115	4	0	0	PUNCT
ejpam-4550	115	5	(	(	PUNCT
ejpam-4550	115	6	9a	9a	NOUN
ejpam-4550	115	7	)	)	PUNCT
ejpam-4550	115	8	i11(t1	i11(t1	PROPN
ejpam-4550	115	9	)	)	PUNCT
ejpam-4550	116	1	=	=	SYM
ejpam-4550	116	2	1	1	NUM
ejpam-4550	116	3	ξ3(t1	ξ3(t1	NUM
ejpam-4550	116	4	)	)	PUNCT
ejpam-4550	116	5	i11(0	i11(0	NOUN
ejpam-4550	116	6	)	)	PUNCT
ejpam-4550	117	1	+	+	NUM
ejpam-4550	117	2	∫	∫	PROPN
ejpam-4550	117	3	t1	t1	NOUN
ejpam-4550	117	4	0	0	NUM
ejpam-4550	118	1	s1ξ3	s1ξ3	PROPN
ejpam-4550	118	2	β1	β1	VERB
ejpam-4550	118	3	3∑	3∑	NUM
ejpam-4550	118	4	j=2	j=2	NOUN
ejpam-4550	118	5	ij1	ij1	NOUN
ejpam-4550	118	6	+	+	CCONJ
ejpam-4550	118	7	β2	β2	NOUN
ejpam-4550	118	8	3∑	3∑	NUM
ejpam-4550	118	9	j=1	j=1	NOUN
ejpam-4550	118	10	ij2	ij2	NOUN
ejpam-4550	118	11	dt	dt	PUNCT
ejpam-4550	118	12			NOUN
ejpam-4550	118	13	>	>	X
ejpam-4550	118	14	0	0	NUM
ejpam-4550	118	15	(	(	PUNCT
ejpam-4550	118	16	9b	9b	NUM
ejpam-4550	118	17	)	)	PUNCT
ejpam-4550	118	18	i21(t1	i21(t1	NOUN
ejpam-4550	118	19	)	)	PUNCT
ejpam-4550	118	20	=	=	SYM
ejpam-4550	118	21	1	1	NUM
ejpam-4550	118	22	ξ2(t1	ξ2(t1	NOUN
ejpam-4550	118	23	)	)	PUNCT
ejpam-4550	118	24	[	[	PUNCT
ejpam-4550	118	25	i21(0	i21(0	NOUN
ejpam-4550	118	26	)	)	PUNCT
ejpam-4550	118	27	+	+	CCONJ
ejpam-4550	119	1	∫	∫	PROPN
ejpam-4550	119	2	t1	t1	NOUN
ejpam-4550	119	3	0	0	NUM
ejpam-4550	119	4	a1ξ2i	a1ξ2i	NUM
ejpam-4550	119	5	1	1	NUM
ejpam-4550	119	6	1dt	1dt	NOUN
ejpam-4550	119	7	]	]	PUNCT
ejpam-4550	119	8	>	>	X
ejpam-4550	119	9	0	0	PUNCT
ejpam-4550	119	10	(	(	PUNCT
ejpam-4550	119	11	9c	9c	NUM
ejpam-4550	119	12	)	)	PUNCT
ejpam-4550	119	13	i31(t1	i31(t1	PROPN
ejpam-4550	119	14	)	)	PUNCT
ejpam-4550	119	15	=	=	SYM
ejpam-4550	119	16	1	1	NUM
ejpam-4550	119	17	ξ4(t1	ξ4(t1	NUM
ejpam-4550	119	18	)	)	PUNCT
ejpam-4550	119	19	[	[	PUNCT
ejpam-4550	119	20	i31(0	i31(0	NOUN
ejpam-4550	119	21	)	)	PUNCT
ejpam-4550	119	22	+	+	CCONJ
ejpam-4550	120	1	∫	∫	PROPN
ejpam-4550	120	2	t1	t1	NOUN
ejpam-4550	120	3	0	0	NUM
ejpam-4550	120	4	a2ξ4i	a2ξ4i	SYM
ejpam-4550	120	5	2	2	NUM
ejpam-4550	120	6	1dt	1dt	NOUN
ejpam-4550	120	7	]	]	PUNCT
ejpam-4550	120	8	>	>	X
ejpam-4550	120	9	0	0	PUNCT
ejpam-4550	120	10	(	(	PUNCT
ejpam-4550	120	11	9d	9d	NUM
ejpam-4550	120	12	)	)	PUNCT
ejpam-4550	120	13	s2(t1	s2(t1	NOUN
ejpam-4550	120	14	)	)	PUNCT
ejpam-4550	120	15	=	=	PUNCT
ejpam-4550	121	1	1	1	NUM
ejpam-4550	121	2	ξ8(t1	ξ8(t1	ADV
ejpam-4550	121	3	)	)	PUNCT
ejpam-4550	121	4	[	[	PUNCT
ejpam-4550	121	5	s2(0	s2(0	NOUN
ejpam-4550	121	6	)	)	PUNCT
ejpam-4550	121	7	+	+	CCONJ
ejpam-4550	121	8	∫	∫	PROPN
ejpam-4550	121	9	t1	t1	NOUN
ejpam-4550	121	10	0	0	NUM
ejpam-4550	122	1	γs1ξ8dt	γs1ξ8dt	PROPN
ejpam-4550	122	2	]	]	PUNCT
ejpam-4550	122	3	>	>	X
ejpam-4550	122	4	0	0	PUNCT
ejpam-4550	122	5	(	(	PUNCT
ejpam-4550	122	6	9e	9e	NOUN
ejpam-4550	122	7	)	)	PUNCT
ejpam-4550	122	8	i12(t1	i12(t1	PROPN
ejpam-4550	122	9	)	)	PUNCT
ejpam-4550	122	10	=	=	SYM
ejpam-4550	122	11	1	1	NUM
ejpam-4550	122	12	ξ6(t1	ξ6(t1	NUM
ejpam-4550	122	13	)	)	PUNCT
ejpam-4550	122	14	i12(0	i12(0	NOUN
ejpam-4550	122	15	)	)	PUNCT
ejpam-4550	123	1	+	+	CCONJ
ejpam-4550	124	1	∫	∫	PROPN
ejpam-4550	124	2	t1	t1	NOUN
ejpam-4550	124	3	0	0	NUM
ejpam-4550	124	4	ξ6	ξ6	NOUN
ejpam-4550	124	5	β1s2	β1s2	NOUN
ejpam-4550	124	6	3∑	3∑	NOUN
ejpam-4550	124	7	j=1	j=1	NOUN
ejpam-4550	124	8	ij1	ij1	NOUN
ejpam-4550	124	9	+	+	CCONJ
ejpam-4550	124	10	β2s2	β2s2	PROPN
ejpam-4550	124	11	3∑	3∑	NUM
ejpam-4550	124	12	j=2	j=2	NOUN
ejpam-4550	124	13	ij2	ij2	NOUN
ejpam-4550	125	1	+	+	CCONJ
ejpam-4550	125	2	c1i	c1i	ADV
ejpam-4550	125	3	1	1	NUM
ejpam-4550	125	4	1	1	NUM
ejpam-4550	125	5	dt	dt	ADP
ejpam-4550	125	6			NOUN
ejpam-4550	125	7	>	>	X
ejpam-4550	125	8	0	0	NUM
ejpam-4550	126	1	(	(	PUNCT
ejpam-4550	126	2	9f	9f	NUM
ejpam-4550	126	3	)	)	PUNCT
ejpam-4550	126	4	i22(t1	i22(t1	PROPN
ejpam-4550	126	5	)	)	PUNCT
ejpam-4550	126	6	=	=	SYM
ejpam-4550	126	7	1	1	NUM
ejpam-4550	126	8	ξ5(t1	ξ5(t1	NOUN
ejpam-4550	126	9	)	)	PUNCT
ejpam-4550	126	10	[	[	PUNCT
ejpam-4550	126	11	i22(0	i22(0	PROPN
ejpam-4550	126	12	)	)	PUNCT
ejpam-4550	127	1	+	+	NUM
ejpam-4550	127	2	∫	∫	PROPN
ejpam-4550	127	3	t1	t1	NOUN
ejpam-4550	127	4	0	0	NUM
ejpam-4550	128	1	(	(	PUNCT
ejpam-4550	128	2	a3i	a3i	ADP
ejpam-4550	128	3	1	1	NUM
ejpam-4550	128	4	2	2	NUM
ejpam-4550	128	5	+	+	CCONJ
ejpam-4550	128	6	c2i	c2i	X
ejpam-4550	128	7	2	2	NUM
ejpam-4550	128	8	1	1	NUM
ejpam-4550	128	9	)	)	PUNCT
ejpam-4550	128	10	ξ5dt	ξ5dt	PUNCT
ejpam-4550	128	11	]	]	PUNCT
ejpam-4550	129	1	>	>	X
ejpam-4550	129	2	0	0	PUNCT
ejpam-4550	130	1	(	(	PUNCT
ejpam-4550	130	2	9	9	NUM
ejpam-4550	130	3	g	g	NOUN
ejpam-4550	130	4	)	)	PUNCT
ejpam-4550	130	5	i32(t1	i32(t1	NOUN
ejpam-4550	130	6	)	)	PUNCT
ejpam-4550	130	7	=	=	SYM
ejpam-4550	130	8	1	1	NUM
ejpam-4550	130	9	ξ7(t1	ξ7(t1	NUM
ejpam-4550	130	10	)	)	PUNCT
ejpam-4550	130	11	[	[	PUNCT
ejpam-4550	130	12	i32(0	i32(0	NOUN
ejpam-4550	130	13	)	)	PUNCT
ejpam-4550	130	14	+	+	CCONJ
ejpam-4550	130	15	∫	∫	PROPN
ejpam-4550	130	16	t1	t1	NOUN
ejpam-4550	130	17	0	0	NUM
ejpam-4550	131	1	(	(	PUNCT
ejpam-4550	131	2	a4i	a4i	NOUN
ejpam-4550	131	3	2	2	NUM
ejpam-4550	131	4	2	2	NUM
ejpam-4550	131	5	+	+	NUM
ejpam-4550	131	6	c3i	c3i	NOUN
ejpam-4550	131	7	3	3	NUM
ejpam-4550	131	8	1	1	NUM
ejpam-4550	131	9	)	)	PUNCT
ejpam-4550	131	10	ξ7dt	ξ7dt	NUM
ejpam-4550	131	11	]	]	PUNCT
ejpam-4550	131	12	>	>	X
ejpam-4550	131	13	0	0	PUNCT
ejpam-4550	131	14	(	(	PUNCT
ejpam-4550	131	15	9h	9h	NUM
ejpam-4550	131	16	)	)	PUNCT
ejpam-4550	131	17	m.	m.	NOUN
ejpam-4550	131	18	alassane	alassane	NOUN
ejpam-4550	131	19	et	et	PROPN
ejpam-4550	131	20	al	al	PROPN
ejpam-4550	131	21	.	.	PUNCT
ejpam-4550	131	22	/	/	SYM
ejpam-4550	131	23	eur	eur	PROPN
ejpam-4550	131	24	.	.	PUNCT
ejpam-4550	132	1	j.	j.	PROPN
ejpam-4550	132	2	pure	pure	PROPN
ejpam-4550	132	3	appl	appl	PROPN
ejpam-4550	132	4	.	.	PROPN
ejpam-4550	132	5	math	math	PROPN
ejpam-4550	132	6	,	,	PUNCT
ejpam-4550	132	7	16	16	NUM
ejpam-4550	132	8	(	(	PUNCT
ejpam-4550	132	9	1	1	NUM
ejpam-4550	132	10	)	)	PUNCT
ejpam-4550	132	11	(	(	PUNCT
ejpam-4550	132	12	2023	2023	NUM
ejpam-4550	132	13	)	)	PUNCT
ejpam-4550	132	14	,	,	PUNCT
ejpam-4550	132	15	207	207	NUM
ejpam-4550	132	16	-	-	SYM
ejpam-4550	132	17	232	232	NUM
ejpam-4550	132	18	215	215	NUM
ejpam-4550	132	19	from	from	ADP
ejpam-4550	132	20	(	(	PUNCT
ejpam-4550	132	21	9a)-(9h	9a)-(9h	NUM
ejpam-4550	132	22	)	)	PUNCT
ejpam-4550	133	1	,	,	PUNCT
ejpam-4550	133	2	it	it	PRON
ejpam-4550	133	3	follows	follow	VERB
ejpam-4550	133	4	that	that	SCONJ
ejpam-4550	133	5	e(t1	e(t1	NOUN
ejpam-4550	133	6	)	)	PUNCT
ejpam-4550	133	7	>	>	X
ejpam-4550	134	1	0	0	X
ejpam-4550	134	2	.	.	PUNCT
ejpam-4550	135	1	this	this	PRON
ejpam-4550	135	2	is	be	AUX
ejpam-4550	135	3	a	a	DET
ejpam-4550	135	4	contradiction	contradiction	NOUN
ejpam-4550	135	5	according	accord	VERB
ejpam-4550	135	6	to	to	ADP
ejpam-4550	135	7	the	the	DET
ejpam-4550	135	8	starting	starting	NOUN
ejpam-4550	135	9	hypothesis	hypothesis	NOUN
ejpam-4550	135	10	.	.	PUNCT
ejpam-4550	136	1	then	then	ADV
ejpam-4550	136	2	,	,	PUNCT
ejpam-4550	136	3	∀t	∀t	PROPN
ejpam-4550	136	4	≥	≥	NUM
ejpam-4550	136	5	0	0	NUM
ejpam-4550	136	6	,	,	PUNCT
ejpam-4550	136	7	e(t	e(t	PROPN
ejpam-4550	136	8	)	)	PUNCT
ejpam-4550	136	9	≥	≥	NOUN
ejpam-4550	136	10	0	0	NUM
ejpam-4550	136	11	.	.	PUNCT
ejpam-4550	136	12	therefore	therefore	ADV
ejpam-4550	136	13	,	,	PUNCT
ejpam-4550	136	14	all	all	DET
ejpam-4550	136	15	solutions	solution	NOUN
ejpam-4550	136	16	initiated	initiate	VERB
ejpam-4550	136	17	in	in	ADP
ejpam-4550	136	18	r8	r8	PROPN
ejpam-4550	136	19	+	+	CCONJ
ejpam-4550	136	20	are	be	AUX
ejpam-4550	136	21	positive	positive	ADJ
ejpam-4550	136	22	.	.	PUNCT
ejpam-4550	137	1	2	2	X
ejpam-4550	137	2	.	.	X
ejpam-4550	137	3	invariant	invariant	ADJ
ejpam-4550	137	4	region	region	NOUN
ejpam-4550	137	5	summing	sum	VERB
ejpam-4550	137	6	the	the	DET
ejpam-4550	137	7	equations	equation	NOUN
ejpam-4550	137	8	of	of	ADP
ejpam-4550	137	9	system	system	NOUN
ejpam-4550	137	10	(	(	PUNCT
ejpam-4550	137	11	5	5	NUM
ejpam-4550	137	12	)	)	PUNCT
ejpam-4550	137	13	,	,	PUNCT
ejpam-4550	137	14	we	we	PRON
ejpam-4550	137	15	obtain	obtain	VERB
ejpam-4550	137	16	:	:	PUNCT
ejpam-4550	137	17	d	d	NOUN
ejpam-4550	137	18	dt	dt	PUNCT
ejpam-4550	137	19	s1	s1	NOUN
ejpam-4550	138	1	+	+	CCONJ
ejpam-4550	138	2	3∑	3∑	NUM
ejpam-4550	138	3	j=1	j=1	NOUN
ejpam-4550	138	4	ij1	ij1	NOUN
ejpam-4550	138	5	+	+	CCONJ
ejpam-4550	138	6	s2	s2	VERB
ejpam-4550	138	7	+	+	CCONJ
ejpam-4550	138	8	3∑	3∑	NUM
ejpam-4550	138	9	j=1	j=1	NOUN
ejpam-4550	138	10	ij2	ij2	NOUN
ejpam-4550	138	11			PROPN
ejpam-4550	138	12	=	=	SYM
ejpam-4550	138	13	0	0	PROPN
ejpam-4550	138	14	.	.	PUNCT
ejpam-4550	139	1	(	(	PUNCT
ejpam-4550	139	2	10	10	NUM
ejpam-4550	139	3	)	)	PUNCT
ejpam-4550	139	4	integrating	integrating	NOUN
ejpam-4550	139	5	(	(	PUNCT
ejpam-4550	139	6	10	10	NUM
ejpam-4550	139	7	)	)	PUNCT
ejpam-4550	139	8	using	use	VERB
ejpam-4550	139	9	initial	initial	ADJ
ejpam-4550	139	10	conditions	condition	NOUN
ejpam-4550	139	11	,	,	PUNCT
ejpam-4550	139	12	it	it	PRON
ejpam-4550	139	13	holds	hold	VERB
ejpam-4550	139	14	:	:	PUNCT
ejpam-4550	139	15	∀t	∀t	PROPN
ejpam-4550	139	16	≥	≥	NOUN
ejpam-4550	139	17	0	0	NUM
ejpam-4550	139	18	,	,	PUNCT
ejpam-4550	139	19	s1(t	s1(t	X
ejpam-4550	139	20	)	)	PUNCT
ejpam-4550	139	21	+	+	NUM
ejpam-4550	139	22	3∑	3∑	NUM
ejpam-4550	139	23	j=1	j=1	NOUN
ejpam-4550	139	24	ij1(t	ij1(t	PROPN
ejpam-4550	139	25	)	)	PUNCT
ejpam-4550	140	1	+	+	NUM
ejpam-4550	140	2	s2	s2	PROPN
ejpam-4550	140	3	t	t	NOUN
ejpam-4550	140	4	+	+	NOUN
ejpam-4550	140	5	3∑	3∑	NUM
ejpam-4550	140	6	j=1	j=1	NOUN
ejpam-4550	140	7	ij2(t	ij2(t	PROPN
ejpam-4550	140	8	)	)	PUNCT
ejpam-4550	140	9	≤	≤	NUM
ejpam-4550	140	10	1	1	NUM
ejpam-4550	140	11	.	.	PUNCT
ejpam-4550	141	1	this	this	PRON
ejpam-4550	141	2	achieves	achieve	VERB
ejpam-4550	141	3	the	the	DET
ejpam-4550	141	4	proof	proof	NOUN
ejpam-4550	141	5	.	.	PUNCT
ejpam-4550	142	1	consequently	consequently	ADV
ejpam-4550	142	2	,	,	PUNCT
ejpam-4550	142	3	in	in	ADP
ejpam-4550	142	4	γ	γ	PROPN
ejpam-4550	142	5	,	,	PUNCT
ejpam-4550	142	6	the	the	DET
ejpam-4550	142	7	model	model	NOUN
ejpam-4550	142	8	(	(	PUNCT
ejpam-4550	142	9	5	5	NUM
ejpam-4550	142	10	)	)	PUNCT
ejpam-4550	142	11	is	be	AUX
ejpam-4550	142	12	epidemiologically	epidemiologically	ADV
ejpam-4550	142	13	and	and	CCONJ
ejpam-4550	142	14	mathematically	mathematically	ADV
ejpam-4550	142	15	well	well	ADV
ejpam-4550	142	16	-	-	PUNCT
ejpam-4550	142	17	posed	pose	VERB
ejpam-4550	142	18	.	.	PUNCT
ejpam-4550	143	1	therefore	therefore	ADV
ejpam-4550	143	2	,	,	PUNCT
ejpam-4550	143	3	it	it	PRON
ejpam-4550	143	4	is	be	AUX
ejpam-4550	143	5	sufficient	sufficient	ADJ
ejpam-4550	143	6	to	to	PART
ejpam-4550	143	7	study	study	VERB
ejpam-4550	143	8	the	the	DET
ejpam-4550	143	9	dynamics	dynamic	NOUN
ejpam-4550	143	10	of	of	ADP
ejpam-4550	143	11	the	the	DET
ejpam-4550	143	12	model	model	NOUN
ejpam-4550	143	13	in	in	ADP
ejpam-4550	143	14	γ	γ	PROPN
ejpam-4550	143	15	.	.	PROPN
ejpam-4550	143	16	m.	m.	NOUN
ejpam-4550	143	17	alassane	alassane	PROPN
ejpam-4550	143	18	et	et	PROPN
ejpam-4550	143	19	al	al	PROPN
ejpam-4550	143	20	.	.	PUNCT
ejpam-4550	143	21	/	/	SYM
ejpam-4550	143	22	eur	eur	PROPN
ejpam-4550	143	23	.	.	PUNCT
ejpam-4550	144	1	j.	j.	PROPN
ejpam-4550	144	2	pure	pure	PROPN
ejpam-4550	144	3	appl	appl	PROPN
ejpam-4550	144	4	.	.	PROPN
ejpam-4550	144	5	math	math	PROPN
ejpam-4550	144	6	,	,	PUNCT
ejpam-4550	144	7	16	16	NUM
ejpam-4550	144	8	(	(	PUNCT
ejpam-4550	144	9	1	1	NUM
ejpam-4550	144	10	)	)	PUNCT
ejpam-4550	144	11	(	(	PUNCT
ejpam-4550	144	12	2023	2023	NUM
ejpam-4550	144	13	)	)	PUNCT
ejpam-4550	144	14	,	,	PUNCT
ejpam-4550	144	15	207	207	NUM
ejpam-4550	144	16	-	-	SYM
ejpam-4550	144	17	232	232	NUM
ejpam-4550	144	18	216	216	NUM
ejpam-4550	144	19	4	4	NUM
ejpam-4550	144	20	.	.	PUNCT
ejpam-4550	144	21	disease	disease	NOUN
ejpam-4550	144	22	-	-	PUNCT
ejpam-4550	144	23	free	free	ADJ
ejpam-4550	144	24	equilibrium	equilibrium	NOUN
ejpam-4550	144	25	(	(	PUNCT
ejpam-4550	144	26	dfe	dfe	PROPN
ejpam-4550	144	27	)	)	PUNCT
ejpam-4550	144	28	e0	e0	PROPN
ejpam-4550	144	29	and	and	CCONJ
ejpam-4550	144	30	reproduction	reproduction	NOUN
ejpam-4550	144	31	number	number	NOUN
ejpam-4550	144	32	r0	r0	VERB
ejpam-4550	144	33	the	the	DET
ejpam-4550	144	34	disease	disease	NOUN
ejpam-4550	144	35	-	-	PUNCT
ejpam-4550	144	36	free	free	ADJ
ejpam-4550	144	37	equilibrium	equilibrium	NOUN
ejpam-4550	144	38	(	(	PUNCT
ejpam-4550	144	39	dfe	dfe	PROPN
ejpam-4550	144	40	)	)	PUNCT
ejpam-4550	144	41	e0	e0	PROPN
ejpam-4550	144	42	of	of	ADP
ejpam-4550	144	43	the	the	DET
ejpam-4550	144	44	model	model	NOUN
ejpam-4550	144	45	(	(	PUNCT
ejpam-4550	144	46	5	5	NUM
ejpam-4550	144	47	)	)	PUNCT
ejpam-4550	144	48	is	be	AUX
ejpam-4550	144	49	determined	determine	VERB
ejpam-4550	144	50	by	by	ADP
ejpam-4550	144	51	solving	solve	VERB
ejpam-4550	144	52	the	the	DET
ejpam-4550	144	53	following	follow	VERB
ejpam-4550	144	54	system	system	NOUN
ejpam-4550	144	55	:	:	PUNCT
ejpam-4550	144	56			PROPN
ejpam-4550	144	57	d	d	NOUN
ejpam-4550	144	58	s1	s1	NOUN
ejpam-4550	144	59	dt	dt	X
ejpam-4550	145	1	=	=	SYM
ejpam-4550	145	2	0	0	PUNCT
ejpam-4550	145	3	d	d	NOUN
ejpam-4550	145	4	i11	i11	ADJ
ejpam-4550	145	5	dt	dt	X
ejpam-4550	145	6	=	=	SYM
ejpam-4550	145	7	0	0	PUNCT
ejpam-4550	146	1	d	d	NOUN
ejpam-4550	146	2	i21	i21	NOUN
ejpam-4550	146	3	dt	dt	NOUN
ejpam-4550	146	4	=	=	SYM
ejpam-4550	146	5	0	0	PUNCT
ejpam-4550	147	1	d	d	NOUN
ejpam-4550	147	2	i31	i31	NOUN
ejpam-4550	147	3	dt	dt	NOUN
ejpam-4550	147	4	=	=	SYM
ejpam-4550	147	5	0	0	PUNCT
ejpam-4550	147	6	d	d	NUM
ejpam-4550	147	7	s2	s2	NOUN
ejpam-4550	147	8	dt	dt	NOUN
ejpam-4550	148	1	=	=	SYM
ejpam-4550	148	2	0	0	PUNCT
ejpam-4550	148	3	d	d	NOUN
ejpam-4550	148	4	i12	i12	NOUN
ejpam-4550	149	1	dt	dt	X
ejpam-4550	149	2	=	=	SYM
ejpam-4550	149	3	0	0	PUNCT
ejpam-4550	149	4	d	d	NOUN
ejpam-4550	149	5	i22	i22	NOUN
ejpam-4550	149	6	dt	dt	NOUN
ejpam-4550	149	7	=	=	SYM
ejpam-4550	149	8	0	0	PUNCT
ejpam-4550	150	1	d	d	NOUN
ejpam-4550	150	2	i32	i32	NOUN
ejpam-4550	150	3	dt	dt	NOUN
ejpam-4550	150	4	=	=	SYM
ejpam-4550	150	5	0	0	NUM
ejpam-4550	151	1	(	(	PUNCT
ejpam-4550	151	2	11	11	NUM
ejpam-4550	151	3	)	)	PUNCT
ejpam-4550	151	4	in	in	ADP
ejpam-4550	151	5	the	the	DET
ejpam-4550	151	6	case	case	NOUN
ejpam-4550	151	7	of	of	ADP
ejpam-4550	151	8	absence	absence	NOUN
ejpam-4550	151	9	of	of	ADP
ejpam-4550	151	10	disease	disease	NOUN
ejpam-4550	151	11	,	,	PUNCT
ejpam-4550	151	12	i.e.	i.e.	X
ejpam-4550	151	13	the	the	DET
ejpam-4550	151	14	population	population	NOUN
ejpam-4550	151	15	size	size	NOUN
ejpam-4550	151	16	is	be	AUX
ejpam-4550	151	17	zero	zero	NUM
ejpam-4550	151	18	in	in	ADP
ejpam-4550	151	19	all	all	DET
ejpam-4550	151	20	compartments	compartment	NOUN
ejpam-4550	151	21	except	except	SCONJ
ejpam-4550	151	22	the	the	DET
ejpam-4550	151	23	susceptible	susceptible	ADJ
ejpam-4550	151	24	compartment	compartment	NOUN
ejpam-4550	151	25	,	,	PUNCT
ejpam-4550	151	26	the	the	DET
ejpam-4550	151	27	solution	solution	NOUN
ejpam-4550	151	28	of	of	ADP
ejpam-4550	151	29	(	(	PUNCT
ejpam-4550	151	30	11	11	NUM
ejpam-4550	151	31	)	)	PUNCT
ejpam-4550	151	32	is	be	AUX
ejpam-4550	151	33	given	give	VERB
ejpam-4550	151	34	by	by	ADP
ejpam-4550	151	35	:	:	PUNCT
ejpam-4550	151	36	e0	e0	PROPN
ejpam-4550	151	37	(	(	PUNCT
ejpam-4550	151	38	b	b	PROPN
ejpam-4550	151	39	κ1	κ1	NOUN
ejpam-4550	151	40	,	,	PUNCT
ejpam-4550	151	41	0	0	NUM
ejpam-4550	151	42	,	,	PUNCT
ejpam-4550	151	43	0	0	NUM
ejpam-4550	151	44	,	,	PUNCT
ejpam-4550	151	45	0	0	NUM
ejpam-4550	151	46	,	,	PUNCT
ejpam-4550	151	47	γ	γ	NOUN
ejpam-4550	151	48	κ1	κ1	NOUN
ejpam-4550	151	49	,	,	PUNCT
ejpam-4550	151	50	0	0	NUM
ejpam-4550	151	51	,	,	PUNCT
ejpam-4550	151	52	0	0	NUM
ejpam-4550	151	53	,	,	PUNCT
ejpam-4550	151	54	0	0	NUM
ejpam-4550	151	55	)	)	PUNCT
ejpam-4550	151	56	.	.	PUNCT
ejpam-4550	152	1	we	we	PRON
ejpam-4550	152	2	determine	determine	VERB
ejpam-4550	152	3	the	the	DET
ejpam-4550	152	4	basic	basic	ADJ
ejpam-4550	152	5	reproduction	reproduction	NOUN
ejpam-4550	152	6	number	number	NOUN
ejpam-4550	152	7	r0	r0	NOUN
ejpam-4550	152	8	using	use	VERB
ejpam-4550	152	9	the	the	DET
ejpam-4550	152	10	next	next	ADJ
ejpam-4550	152	11	generation	generation	NOUN
ejpam-4550	152	12	matrix	matrix	NOUN
ejpam-4550	152	13	method	method	NOUN
ejpam-4550	152	14	at	at	ADP
ejpam-4550	152	15	disease	disease	NOUN
ejpam-4550	152	16	-	-	PUNCT
ejpam-4550	152	17	free	free	ADJ
ejpam-4550	152	18	equilibrium	equilibrium	NOUN
ejpam-4550	152	19	[	[	X
ejpam-4550	152	20	12	12	NUM
ejpam-4550	152	21	]	]	PUNCT
ejpam-4550	152	22	.	.	PUNCT
ejpam-4550	153	1	according	accord	VERB
ejpam-4550	153	2	to	to	ADP
ejpam-4550	153	3	this	this	DET
ejpam-4550	153	4	method	method	NOUN
ejpam-4550	153	5	,	,	PUNCT
ejpam-4550	153	6	r0	r0	NOUN
ejpam-4550	153	7	is	be	AUX
ejpam-4550	153	8	defined	define	VERB
ejpam-4550	153	9	as	as	ADP
ejpam-4550	153	10	the	the	DET
ejpam-4550	153	11	effective	effective	ADJ
ejpam-4550	153	12	number	number	NOUN
ejpam-4550	153	13	of	of	ADP
ejpam-4550	153	14	secondary	secondary	ADJ
ejpam-4550	153	15	infections	infection	NOUN
ejpam-4550	153	16	caused	cause	VERB
ejpam-4550	153	17	by	by	ADP
ejpam-4550	153	18	typical	typical	ADJ
ejpam-4550	153	19	infected	infected	ADJ
ejpam-4550	153	20	individual	individual	NOUN
ejpam-4550	153	21	during	during	ADP
ejpam-4550	153	22	his	his	PRON
ejpam-4550	153	23	/	/	SYM
ejpam-4550	153	24	her	her	PRON
ejpam-4550	153	25	entire	entire	ADJ
ejpam-4550	153	26	period	period	NOUN
ejpam-4550	153	27	of	of	ADP
ejpam-4550	153	28	infectioussness	infectioussness	NOUN
ejpam-4550	153	29	[	[	X
ejpam-4550	153	30	1	1	NUM
ejpam-4550	153	31	,	,	PUNCT
ejpam-4550	153	32	4	4	NUM
ejpam-4550	153	33	]	]	PUNCT
ejpam-4550	153	34	.	.	PUNCT
ejpam-4550	154	1	let	let	VERB
ejpam-4550	154	2	x	x	PRON
ejpam-4550	154	3	be	be	AUX
ejpam-4550	154	4	the	the	DET
ejpam-4550	154	5	vector	vector	NOUN
ejpam-4550	154	6	of	of	ADP
ejpam-4550	154	7	infected	infected	ADJ
ejpam-4550	154	8	classes	class	NOUN
ejpam-4550	154	9	:	:	PUNCT
ejpam-4550	154	10	x	x	SYM
ejpam-4550	154	11	=	=	SYM
ejpam-4550	154	12	(	(	PUNCT
ejpam-4550	154	13	i11	i11	NOUN
ejpam-4550	154	14	,	,	PUNCT
ejpam-4550	154	15	i21	i21	NOUN
ejpam-4550	154	16	,	,	PUNCT
ejpam-4550	154	17	i31	i31	NOUN
ejpam-4550	154	18	,	,	PUNCT
ejpam-4550	154	19	i12	i12	NOUN
ejpam-4550	154	20	,	,	PUNCT
ejpam-4550	154	21	i22	i22	NOUN
ejpam-4550	154	22	,	,	PUNCT
ejpam-4550	154	23	i32	i32	PROPN
ejpam-4550	154	24	)	)	PUNCT
ejpam-4550	154	25	t	t	PROPN
ejpam-4550	154	26	.	.	PUNCT
ejpam-4550	155	1	f	f	X
ejpam-4550	155	2	=	=	PUNCT
ejpam-4550	155	3	s1	s1	NOUN
ejpam-4550	155	4	(	(	PUNCT
ejpam-4550	155	5	β1	β1	PROPN
ejpam-4550	155	6	3∑	3∑	NUM
ejpam-4550	155	7	j=1	j=1	NOUN
ejpam-4550	155	8	ij1	ij1	NOUN
ejpam-4550	155	9	+	+	CCONJ
ejpam-4550	155	10	β2	β2	NOUN
ejpam-4550	155	11	3∑	3∑	NUM
ejpam-4550	155	12	j=1	j=1	NOUN
ejpam-4550	155	13	ij2	ij2	PROPN
ejpam-4550	155	14	)	)	PUNCT
ejpam-4550	155	15	,	,	PUNCT
ejpam-4550	155	16	0	0	NUM
ejpam-4550	155	17	,	,	PUNCT
ejpam-4550	155	18	0	0	NUM
ejpam-4550	155	19	,	,	PUNCT
ejpam-4550	155	20	s2	s2	PROPN
ejpam-4550	155	21	(	(	PUNCT
ejpam-4550	155	22	β1	β1	PROPN
ejpam-4550	155	23	3∑	3∑	NUM
ejpam-4550	155	24	j=1	j=1	NOUN
ejpam-4550	155	25	ij1	ij1	NOUN
ejpam-4550	155	26	+	+	CCONJ
ejpam-4550	155	27	β2	β2	NOUN
ejpam-4550	155	28	3∑	3∑	NUM
ejpam-4550	155	29	j=1	j=1	NOUN
ejpam-4550	155	30	ij2	ij2	PROPN
ejpam-4550	155	31	)	)	PUNCT
ejpam-4550	155	32	,	,	PUNCT
ejpam-4550	155	33	0	0	NUM
ejpam-4550	155	34	,	,	PUNCT
ejpam-4550	155	35	0	0	NUM
ejpam-4550	155	36	t	t	PUNCT
ejpam-4550	155	37	m.	m.	NOUN
ejpam-4550	155	38	alassane	alassane	NOUN
ejpam-4550	155	39	et	et	PROPN
ejpam-4550	155	40	al	al	PROPN
ejpam-4550	155	41	.	.	PUNCT
ejpam-4550	155	42	/	/	SYM
ejpam-4550	155	43	eur	eur	PROPN
ejpam-4550	155	44	.	.	PUNCT
ejpam-4550	156	1	j.	j.	PROPN
ejpam-4550	156	2	pure	pure	PROPN
ejpam-4550	156	3	appl	appl	PROPN
ejpam-4550	156	4	.	.	PROPN
ejpam-4550	156	5	math	math	PROPN
ejpam-4550	156	6	,	,	PUNCT
ejpam-4550	156	7	16	16	NUM
ejpam-4550	156	8	(	(	PUNCT
ejpam-4550	156	9	1	1	NUM
ejpam-4550	156	10	)	)	PUNCT
ejpam-4550	156	11	(	(	PUNCT
ejpam-4550	156	12	2023	2023	NUM
ejpam-4550	156	13	)	)	PUNCT
ejpam-4550	156	14	,	,	PUNCT
ejpam-4550	156	15	207	207	NUM
ejpam-4550	156	16	-	-	SYM
ejpam-4550	156	17	232	232	NUM
ejpam-4550	156	18	217	217	NUM
ejpam-4550	156	19	denotes	denote	NOUN
ejpam-4550	156	20	the	the	DET
ejpam-4550	156	21	vector	vector	NOUN
ejpam-4550	156	22	of	of	ADP
ejpam-4550	156	23	terms	term	NOUN
ejpam-4550	156	24	corresponding	correspond	VERB
ejpam-4550	156	25	to	to	ADP
ejpam-4550	156	26	new	new	ADJ
ejpam-4550	156	27	infections	infection	NOUN
ejpam-4550	156	28	.	.	PUNCT
ejpam-4550	157	1	v	v	X
ejpam-4550	157	2	=	=	SYM
ejpam-4550	157	3	(	(	PUNCT
ejpam-4550	157	4	κ2i	κ2i	PROPN
ejpam-4550	157	5	1	1	NUM
ejpam-4550	157	6	1	1	NUM
ejpam-4550	157	7	,	,	PUNCT
ejpam-4550	157	8	κ3i	κ3i	PROPN
ejpam-4550	157	9	2	2	NUM
ejpam-4550	157	10	1	1	NUM
ejpam-4550	157	11	−	−	NOUN
ejpam-4550	157	12	a1i	a1i	VERB
ejpam-4550	157	13	1	1	NUM
ejpam-4550	157	14	1	1	NUM
ejpam-4550	157	15	,	,	PUNCT
ejpam-4550	157	16	κ4i	κ4i	NOUN
ejpam-4550	157	17	3	3	NUM
ejpam-4550	157	18	1	1	NUM
ejpam-4550	157	19	−	−	NOUN
ejpam-4550	157	20	a2i	a2i	NOUN
ejpam-4550	157	21	2	2	NUM
ejpam-4550	157	22	1	1	NUM
ejpam-4550	157	23	,	,	PUNCT
ejpam-4550	157	24	κ5i	κ5i	X
ejpam-4550	157	25	1	1	NUM
ejpam-4550	157	26	2	2	NUM
ejpam-4550	157	27	−	−	NOUN
ejpam-4550	157	28	c1i	c1i	ADJ
ejpam-4550	157	29	1	1	NUM
ejpam-4550	157	30	1	1	NUM
ejpam-4550	157	31	,	,	PUNCT
ejpam-4550	157	32	κ6i	κ6i	PROPN
ejpam-4550	157	33	2	2	NUM
ejpam-4550	157	34	2	2	NUM
ejpam-4550	157	35	−	−	NOUN
ejpam-4550	157	36	c2i	c2i	PROPN
ejpam-4550	157	37	2	2	NUM
ejpam-4550	157	38	1	1	NUM
ejpam-4550	157	39	−	−	NOUN
ejpam-4550	157	40	a3i	a3i	ADP
ejpam-4550	157	41	1	1	NUM
ejpam-4550	157	42	2	2	NUM
ejpam-4550	157	43	,	,	PUNCT
ejpam-4550	157	44	b	b	PROPN
ejpam-4550	157	45	i32	i32	PROPN
ejpam-4550	157	46	−	−	PROPN
ejpam-4550	157	47	c3i	c3i	NOUN
ejpam-4550	157	48	3	3	NUM
ejpam-4550	157	49	1	1	NUM
ejpam-4550	157	50	−	−	NOUN
ejpam-4550	157	51	a4i	a4i	NOUN
ejpam-4550	157	52	2	2	NUM
ejpam-4550	157	53	2	2	NUM
ejpam-4550	157	54	)	)	PUNCT
ejpam-4550	157	55	t	t	PROPN
ejpam-4550	157	56	refers	refer	VERB
ejpam-4550	157	57	to	to	ADP
ejpam-4550	157	58	the	the	DET
ejpam-4550	157	59	vector	vector	NOUN
ejpam-4550	157	60	of	of	ADP
ejpam-4550	157	61	terms	term	NOUN
ejpam-4550	157	62	corresponding	correspond	VERB
ejpam-4550	157	63	to	to	ADP
ejpam-4550	157	64	individuals	individual	NOUN
ejpam-4550	157	65	entering	enter	VERB
ejpam-4550	157	66	a	a	DET
ejpam-4550	157	67	given	give	VERB
ejpam-4550	157	68	compartment	compartment	NOUN
ejpam-4550	157	69	and	and	CCONJ
ejpam-4550	157	70	individuals	individual	NOUN
ejpam-4550	157	71	leaving	leave	VERB
ejpam-4550	157	72	.	.	PUNCT
ejpam-4550	158	1	the	the	DET
ejpam-4550	158	2	partial	partial	ADJ
ejpam-4550	158	3	derivatives	derivative	NOUN
ejpam-4550	158	4	of	of	ADP
ejpam-4550	158	5	f	f	PROPN
ejpam-4550	158	6	and	and	CCONJ
ejpam-4550	158	7	v	v	X
ejpam-4550	158	8	with	with	ADP
ejpam-4550	158	9	respect	respect	NOUN
ejpam-4550	158	10	to	to	ADP
ejpam-4550	158	11	i11	i11	NOUN
ejpam-4550	158	12	,	,	PUNCT
ejpam-4550	158	13	i	i	NOUN
ejpam-4550	158	14	2	2	NUM
ejpam-4550	158	15	1	1	NUM
ejpam-4550	158	16	,	,	PUNCT
ejpam-4550	158	17	i	i	PRON
ejpam-4550	158	18	3	3	NUM
ejpam-4550	158	19	1	1	NUM
ejpam-4550	158	20	,	,	PUNCT
ejpam-4550	158	21	i	i	PRON
ejpam-4550	158	22	1	1	NUM
ejpam-4550	158	23	2	2	NUM
ejpam-4550	158	24	,	,	PUNCT
ejpam-4550	158	25	i	i	NOUN
ejpam-4550	158	26	2	2	NUM
ejpam-4550	158	27	2	2	NUM
ejpam-4550	158	28	and	and	CCONJ
ejpam-4550	158	29	i32	i32	NOUN
ejpam-4550	158	30	are	be	AUX
ejpam-4550	158	31	given	give	VERB
ejpam-4550	158	32	by	by	ADP
ejpam-4550	158	33	the	the	DET
ejpam-4550	158	34	following	follow	VERB
ejpam-4550	158	35	matrices	matrix	NOUN
ejpam-4550	158	36	f	f	PROPN
ejpam-4550	158	37	and	and	CCONJ
ejpam-4550	158	38	v	v	ADP
ejpam-4550	158	39	:	:	PUNCT
ejpam-4550	158	40	f	f	PROPN
ejpam-4550	158	41	=	=	SYM
ejpam-4550	158	42			NOUN
ejpam-4550	158	43	β1	β1	PROPN
ejpam-4550	158	44	b	b	PROPN
ejpam-4550	158	45	κ1	κ1	PROPN
ejpam-4550	158	46	β1	β1	PROPN
ejpam-4550	158	47	b	b	PROPN
ejpam-4550	158	48	κ1	κ1	PROPN
ejpam-4550	158	49	β1	β1	PROPN
ejpam-4550	158	50	b	b	PROPN
ejpam-4550	158	51	κ1	κ1	PROPN
ejpam-4550	158	52	β2	β2	PROPN
ejpam-4550	158	53	b	b	PROPN
ejpam-4550	158	54	κ1	κ1	PROPN
ejpam-4550	158	55	β2	β2	PROPN
ejpam-4550	158	56	b	b	PROPN
ejpam-4550	158	57	κ1	κ1	PROPN
ejpam-4550	158	58	β2	β2	PROPN
ejpam-4550	158	59	b	b	PROPN
ejpam-4550	158	60	κ1	κ1	NOUN
ejpam-4550	158	61	0	0	NUM
ejpam-4550	158	62	0	0	NUM
ejpam-4550	158	63	0	0	NUM
ejpam-4550	158	64	0	0	NUM
ejpam-4550	158	65	0	0	NUM
ejpam-4550	158	66	0	0	NUM
ejpam-4550	158	67	0	0	NUM
ejpam-4550	158	68	0	0	NUM
ejpam-4550	158	69	0	0	NUM
ejpam-4550	158	70	0	0	NUM
ejpam-4550	158	71	0	0	SYM
ejpam-4550	158	72	0	0	NUM
ejpam-4550	159	1	β1	β1	PROPN
ejpam-4550	159	2	γ	γ	PROPN
ejpam-4550	159	3	κ1	κ1	PROPN
ejpam-4550	159	4	β1	β1	PROPN
ejpam-4550	159	5	γ	γ	PROPN
ejpam-4550	159	6	κ1	κ1	PROPN
ejpam-4550	159	7	β1	β1	PROPN
ejpam-4550	159	8	γ	γ	PROPN
ejpam-4550	159	9	κ1	κ1	PROPN
ejpam-4550	159	10	β2	β2	PROPN
ejpam-4550	159	11	γ	γ	PROPN
ejpam-4550	159	12	κ1	κ1	PROPN
ejpam-4550	159	13	β2	β2	PROPN
ejpam-4550	159	14	γ	γ	PROPN
ejpam-4550	159	15	κ1	κ1	PROPN
ejpam-4550	159	16	β2	β2	PROPN
ejpam-4550	159	17	γ	γ	PROPN
ejpam-4550	159	18	κ1	κ1	PROPN
ejpam-4550	159	19	0	0	NUM
ejpam-4550	159	20	0	0	NUM
ejpam-4550	159	21	0	0	NUM
ejpam-4550	159	22	0	0	NUM
ejpam-4550	159	23	0	0	NUM
ejpam-4550	159	24	0	0	NUM
ejpam-4550	159	25	0	0	NUM
ejpam-4550	159	26	0	0	NUM
ejpam-4550	159	27	0	0	NUM
ejpam-4550	159	28	0	0	NUM
ejpam-4550	159	29	0	0	NUM
ejpam-4550	159	30	0	0	NUM
ejpam-4550	159	31			NOUN
ejpam-4550	159	32	,	,	PUNCT
ejpam-4550	159	33	v	v	NOUN
ejpam-4550	159	34	=	=	SYM
ejpam-4550	159	35			NOUN
ejpam-4550	159	36	κ2	κ2	NOUN
ejpam-4550	159	37	0	0	NUM
ejpam-4550	159	38	0	0	NUM
ejpam-4550	159	39	0	0	NUM
ejpam-4550	159	40	0	0	NUM
ejpam-4550	159	41	0	0	NUM
ejpam-4550	159	42	−a1	−a1	PROPN
ejpam-4550	159	43	κ3	κ3	PROPN
ejpam-4550	159	44	0	0	NUM
ejpam-4550	159	45	0	0	NUM
ejpam-4550	159	46	0	0	NUM
ejpam-4550	159	47	0	0	NUM
ejpam-4550	159	48	0	0	NUM
ejpam-4550	159	49	−a2	−a2	NOUN
ejpam-4550	159	50	κ4	κ4	NOUN
ejpam-4550	159	51	0	0	NUM
ejpam-4550	159	52	0	0	NUM
ejpam-4550	159	53	0	0	NUM
ejpam-4550	160	1	−c1	−c1	NOUN
ejpam-4550	160	2	0	0	NUM
ejpam-4550	160	3	0	0	NUM
ejpam-4550	160	4	κ5	κ5	NOUN
ejpam-4550	160	5	0	0	NUM
ejpam-4550	160	6	0	0	NUM
ejpam-4550	160	7	0	0	NUM
ejpam-4550	161	1	−c2	−c2	PROPN
ejpam-4550	161	2	0	0	NUM
ejpam-4550	161	3	−a3	−a3	NOUN
ejpam-4550	161	4	κ6	κ6	NOUN
ejpam-4550	161	5	0	0	NUM
ejpam-4550	161	6	0	0	SYM
ejpam-4550	161	7	0	0	NUM
ejpam-4550	162	1	−c3	−c3	NOUN
ejpam-4550	162	2	0	0	PUNCT
ejpam-4550	163	1	−a4	−a4	ADV
ejpam-4550	163	2	b	b	NOUN
ejpam-4550	163	3			SCONJ
ejpam-4550	163	4	the	the	DET
ejpam-4550	163	5	next	next	ADJ
ejpam-4550	163	6	-	-	PUNCT
ejpam-4550	163	7	generation	generation	NOUN
ejpam-4550	163	8	matrix	matrix	NOUN
ejpam-4550	163	9	is	be	AUX
ejpam-4550	163	10	defined	define	VERB
ejpam-4550	163	11	by	by	ADP
ejpam-4550	163	12	:	:	PUNCT
ejpam-4550	163	13	k	k	X
ejpam-4550	163	14	=	=	PUNCT
ejpam-4550	163	15	fv−1	fv−1	NOUN
ejpam-4550	163	16	=	=	SYM
ejpam-4550	163	17	1	1	NUM
ejpam-4550	163	18	m7	m7	PROPN
ejpam-4550	163	19			PROPN
ejpam-4550	163	20	m1b	m1b	PROPN
ejpam-4550	163	21	m2b	m2b	PROPN
ejpam-4550	163	22	m3b	m3b	PROPN
ejpam-4550	163	23	m4b	m4b	VERB
ejpam-4550	163	24	m5b	m5b	NOUN
ejpam-4550	163	25	m6b	m6b	NOUN
ejpam-4550	163	26	0	0	NUM
ejpam-4550	163	27	0	0	NUM
ejpam-4550	163	28	0	0	NUM
ejpam-4550	163	29	0	0	NUM
ejpam-4550	163	30	0	0	NUM
ejpam-4550	163	31	0	0	NUM
ejpam-4550	163	32	0	0	NUM
ejpam-4550	163	33	0	0	NUM
ejpam-4550	163	34	0	0	NUM
ejpam-4550	163	35	0	0	NUM
ejpam-4550	163	36	0	0	NUM
ejpam-4550	163	37	0	0	NUM
ejpam-4550	163	38	m1γ	m1γ	NUM
ejpam-4550	163	39	m2γ	m2γ	PRON
ejpam-4550	163	40	m3γ	m3γ	ADJ
ejpam-4550	163	41	m4γ	m4γ	PROPN
ejpam-4550	163	42	m5γ	m5γ	NOUN
ejpam-4550	163	43	m6γ	m6γ	PROPN
ejpam-4550	163	44	0	0	NUM
ejpam-4550	163	45	0	0	NUM
ejpam-4550	163	46	0	0	NUM
ejpam-4550	163	47	0	0	NUM
ejpam-4550	163	48	0	0	NUM
ejpam-4550	163	49	0	0	NUM
ejpam-4550	163	50	0	0	NUM
ejpam-4550	163	51	0	0	NUM
ejpam-4550	163	52	0	0	NUM
ejpam-4550	163	53	0	0	NUM
ejpam-4550	163	54	0	0	NUM
ejpam-4550	163	55	0	0	NUM
ejpam-4550	163	56			ADP
ejpam-4550	163	57	where	where	SCONJ
ejpam-4550	163	58	m1	m1	PROPN
ejpam-4550	163	59	=	=	SYM
ejpam-4550	163	60	β1bκ3κ4κ5κ6	β1bκ3κ4κ5κ6	PROPN
ejpam-4550	164	1	+	+	NUM
ejpam-4550	164	2	a1β1bκ4κ5κ6	a1β1bκ4κ5κ6	NOUN
ejpam-4550	165	1	+	+	CCONJ
ejpam-4550	165	2	β1a1a2bκ5κ6	β1a1a2bκ5κ6	PROPN
ejpam-4550	165	3	+	+	CCONJ
ejpam-4550	165	4	β2c1bκ3κ4κ6	β2c1bκ3κ4κ6	NUM
ejpam-4550	166	1	+	+	CCONJ
ejpam-4550	166	2	β2c2a1bκ4κ5	β2c2a1bκ4κ5	PROPN
ejpam-4550	166	3	+	+	ADJ
ejpam-4550	166	4	β2a3c1bκ3κ4	β2a3c1bκ3κ4	ADJ
ejpam-4550	166	5	+	+	NUM
ejpam-4550	166	6	β2c3a2a1κ5κ6	β2c3a2a1κ5κ6	X
ejpam-4550	167	1	+	+	X
ejpam-4550	167	2	β2a4a1c2κ4κ5	β2a4a1c2κ4κ5	ADJ
ejpam-4550	167	3	+	+	CCONJ
ejpam-4550	167	4	β2a4a3c1κ3κ4	β2a4a3c1κ3κ4	PROPN
ejpam-4550	167	5	(	(	PUNCT
ejpam-4550	167	6	12	12	NUM
ejpam-4550	167	7	)	)	PUNCT
ejpam-4550	167	8	m2	m2	PROPN
ejpam-4550	167	9	=	=	PROPN
ejpam-4550	167	10	β1bκ2κ4κ5κ6	β1bκ2κ4κ5κ6	PROPN
ejpam-4550	168	1	+	+	CCONJ
ejpam-4550	168	2	β1a2bκ2κ5κ6	β1a2bκ2κ5κ6	PUNCT
ejpam-4550	168	3	+	+	CCONJ
ejpam-4550	168	4	β2c2bκ2κ4κ5	β2c2bκ2κ4κ5	PUNCT
ejpam-4550	169	1	+	+	CCONJ
ejpam-4550	169	2	β2c3a2κ2κ5κ6	β2c3a2κ2κ5κ6	PRON
ejpam-4550	170	1	+	+	ADV
ejpam-4550	170	2	β2a4c2κ2κ4κ5	β2a4c2κ2κ4κ5	ADJ
ejpam-4550	170	3	(	(	PUNCT
ejpam-4550	170	4	13	13	NUM
ejpam-4550	170	5	)	)	PUNCT
ejpam-4550	170	6	m3	m3	PROPN
ejpam-4550	170	7	=	=	SYM
ejpam-4550	170	8	β1bκ2κ3κ5κ6	β1bκ2κ3κ5κ6	PROPN
ejpam-4550	170	9	+	+	CCONJ
ejpam-4550	170	10	β2c3κ2κ3κ5κ6	β2c3κ2κ3κ5κ6	PROPN
ejpam-4550	170	11	(	(	PUNCT
ejpam-4550	170	12	14	14	NUM
ejpam-4550	170	13	)	)	PUNCT
ejpam-4550	170	14	m4	m4	PROPN
ejpam-4550	170	15	=	=	PUNCT
ejpam-4550	171	1	β2bκ2κ3κ4κ6	β2bκ2κ3κ4κ6	PROPN
ejpam-4550	172	1	+	+	NUM
ejpam-4550	172	2	β2a3bκ2κ3κ4	β2a3bκ2κ3κ4	NUM
ejpam-4550	173	1	+	+	NUM
ejpam-4550	173	2	β2a3a4κ2κ3κ4	β2a3a4κ2κ3κ4	PROPN
ejpam-4550	173	3	(	(	PUNCT
ejpam-4550	173	4	15	15	NUM
ejpam-4550	173	5	)	)	PUNCT
ejpam-4550	173	6	m5	m5	NOUN
ejpam-4550	173	7	=	=	SYM
ejpam-4550	173	8	β2bκ2κ3κ4κ5	β2bκ2κ3κ4κ5	PROPN
ejpam-4550	173	9	+	+	CCONJ
ejpam-4550	173	10	β2a4κ2κ3κ4κ5	β2a4κ2κ3κ4κ5	PROPN
ejpam-4550	173	11	(	(	PUNCT
ejpam-4550	173	12	16	16	NUM
ejpam-4550	173	13	)	)	PUNCT
ejpam-4550	173	14	m6	m6	PROPN
ejpam-4550	173	15	=	=	PUNCT
ejpam-4550	173	16	β2κ2κ3κ4κ5κ6	β2κ2κ3κ4κ5κ6	X
ejpam-4550	173	17	(	(	PUNCT
ejpam-4550	173	18	17	17	NUM
ejpam-4550	173	19	)	)	PUNCT
ejpam-4550	173	20	m7	m7	NOUN
ejpam-4550	173	21	=	=	SYM
ejpam-4550	173	22	bκ1κ2κ3κ4κ5κ6	bκ1κ2κ3κ4κ5κ6	X
ejpam-4550	173	23	(	(	PUNCT
ejpam-4550	173	24	18	18	NUM
ejpam-4550	173	25	)	)	PUNCT
ejpam-4550	173	26	the	the	DET
ejpam-4550	173	27	basic	basic	ADJ
ejpam-4550	173	28	reproduction	reproduction	NOUN
ejpam-4550	173	29	number	number	NOUN
ejpam-4550	173	30	r0	r0	NOUN
ejpam-4550	173	31	,	,	PUNCT
ejpam-4550	173	32	computed	compute	VERB
ejpam-4550	173	33	from	from	ADP
ejpam-4550	173	34	the	the	DET
ejpam-4550	173	35	spectral	spectral	ADJ
ejpam-4550	173	36	raduis	raduis	NOUN
ejpam-4550	173	37	of	of	ADP
ejpam-4550	173	38	the	the	DET
ejpam-4550	173	39	nextgeneration	nextgeneration	NOUN
ejpam-4550	173	40	matrix	matrix	NOUN
ejpam-4550	173	41	k	k	PROPN
ejpam-4550	173	42	,	,	PUNCT
ejpam-4550	173	43	is	be	AUX
ejpam-4550	173	44	given	give	VERB
ejpam-4550	173	45	by	by	ADP
ejpam-4550	173	46	:	:	PUNCT
ejpam-4550	173	47	r0	r0	NOUN
ejpam-4550	173	48	=	=	SYM
ejpam-4550	173	49	b	b	PROPN
ejpam-4550	173	50	m1	m1	PROPN
ejpam-4550	173	51	+	+	CCONJ
ejpam-4550	173	52	γm4	γm4	X
ejpam-4550	173	53	m7	m7	NOUN
ejpam-4550	173	54	(	(	PUNCT
ejpam-4550	173	55	19	19	NUM
ejpam-4550	173	56	)	)	PUNCT
ejpam-4550	173	57	where	where	SCONJ
ejpam-4550	173	58	m1	m1	PROPN
ejpam-4550	173	59	,	,	PUNCT
ejpam-4550	173	60	m4	m4	PROPN
ejpam-4550	173	61	and	and	CCONJ
ejpam-4550	173	62	m7	m7	PROPN
ejpam-4550	173	63	are	be	AUX
ejpam-4550	173	64	explicitly	explicitly	ADV
ejpam-4550	173	65	defined	define	VERB
ejpam-4550	173	66	by	by	ADP
ejpam-4550	173	67	(	(	PUNCT
ejpam-4550	173	68	12	12	NUM
ejpam-4550	173	69	)	)	PUNCT
ejpam-4550	173	70	,	,	PUNCT
ejpam-4550	173	71	(	(	PUNCT
ejpam-4550	173	72	15	15	NUM
ejpam-4550	173	73	)	)	PUNCT
ejpam-4550	173	74	and	and	CCONJ
ejpam-4550	173	75	(	(	PUNCT
ejpam-4550	173	76	18	18	NUM
ejpam-4550	173	77	)	)	PUNCT
ejpam-4550	173	78	.	.	PUNCT
ejpam-4550	174	1	m.	m.	NOUN
ejpam-4550	174	2	alassane	alassane	NOUN
ejpam-4550	174	3	et	et	PROPN
ejpam-4550	174	4	al	al	PROPN
ejpam-4550	174	5	.	.	PUNCT
ejpam-4550	174	6	/	/	SYM
ejpam-4550	174	7	eur	eur	PROPN
ejpam-4550	174	8	.	.	PUNCT
ejpam-4550	175	1	j.	j.	PROPN
ejpam-4550	175	2	pure	pure	PROPN
ejpam-4550	175	3	appl	appl	PROPN
ejpam-4550	175	4	.	.	PROPN
ejpam-4550	175	5	math	math	PROPN
ejpam-4550	175	6	,	,	PUNCT
ejpam-4550	175	7	16	16	NUM
ejpam-4550	175	8	(	(	PUNCT
ejpam-4550	175	9	1	1	NUM
ejpam-4550	175	10	)	)	PUNCT
ejpam-4550	175	11	(	(	PUNCT
ejpam-4550	175	12	2023	2023	NUM
ejpam-4550	175	13	)	)	PUNCT
ejpam-4550	175	14	,	,	PUNCT
ejpam-4550	175	15	207	207	NUM
ejpam-4550	175	16	-	-	SYM
ejpam-4550	175	17	232	232	NUM
ejpam-4550	175	18	218	218	NUM
ejpam-4550	175	19	5	5	NUM
ejpam-4550	175	20	.	.	PUNCT
ejpam-4550	176	1	local	local	ADJ
ejpam-4550	176	2	stability	stability	NOUN
ejpam-4550	176	3	of	of	ADP
ejpam-4550	176	4	disease	disease	NOUN
ejpam-4550	176	5	-	-	PUNCT
ejpam-4550	176	6	free	free	ADJ
ejpam-4550	176	7	equilibrium	equilibrium	NOUN
ejpam-4550	176	8	(	(	PUNCT
ejpam-4550	176	9	dfe	dfe	PROPN
ejpam-4550	176	10	)	)	PUNCT
ejpam-4550	176	11	theorem	theorem	NOUN
ejpam-4550	176	12	2	2	NUM
ejpam-4550	176	13	.	.	PUNCT
ejpam-4550	177	1	if	if	SCONJ
ejpam-4550	177	2	r0	r0	NOUN
ejpam-4550	177	3	<	<	X
ejpam-4550	177	4	1	1	NUM
ejpam-4550	177	5	,	,	PUNCT
ejpam-4550	177	6	then	then	ADV
ejpam-4550	177	7	the	the	DET
ejpam-4550	177	8	disease	disease	NOUN
ejpam-4550	177	9	-	-	PUNCT
ejpam-4550	177	10	free	free	ADJ
ejpam-4550	177	11	equilibrium	equilibrium	NOUN
ejpam-4550	177	12	point	point	NOUN
ejpam-4550	177	13	e0	e0	PROPN
ejpam-4550	177	14	(	(	PUNCT
ejpam-4550	177	15	b	b	PROPN
ejpam-4550	177	16	κ1	κ1	NOUN
ejpam-4550	177	17	,	,	PUNCT
ejpam-4550	177	18	0	0	NUM
ejpam-4550	177	19	,	,	PUNCT
ejpam-4550	177	20	0	0	NUM
ejpam-4550	177	21	,	,	PUNCT
ejpam-4550	177	22	0	0	NUM
ejpam-4550	177	23	,	,	PUNCT
ejpam-4550	177	24	γ	γ	NOUN
ejpam-4550	177	25	κ1	κ1	NOUN
ejpam-4550	177	26	,	,	PUNCT
ejpam-4550	177	27	0	0	NUM
ejpam-4550	177	28	,	,	PUNCT
ejpam-4550	177	29	0	0	NUM
ejpam-4550	177	30	,	,	PUNCT
ejpam-4550	177	31	0	0	NUM
ejpam-4550	177	32	)	)	PUNCT
ejpam-4550	177	33	is	be	AUX
ejpam-4550	177	34	locally	locally	ADV
ejpam-4550	177	35	asymptotically	asymptotically	ADV
ejpam-4550	177	36	stable	stable	ADJ
ejpam-4550	177	37	.	.	PUNCT
ejpam-4550	178	1	proof	proof	NOUN
ejpam-4550	178	2	.	.	PUNCT
ejpam-4550	179	1	consider	consider	VERB
ejpam-4550	179	2	the	the	DET
ejpam-4550	179	3	system	system	NOUN
ejpam-4550	179	4	(	(	PUNCT
ejpam-4550	179	5	5	5	NUM
ejpam-4550	179	6	)	)	PUNCT
ejpam-4550	179	7	.	.	PUNCT
ejpam-4550	180	1	the	the	DET
ejpam-4550	180	2	jacobian	jacobian	NOUN
ejpam-4550	180	3	of	of	ADP
ejpam-4550	180	4	this	this	DET
ejpam-4550	180	5	system	system	NOUN
ejpam-4550	180	6	at	at	ADP
ejpam-4550	180	7	e0	e0	PROPN
ejpam-4550	180	8	is	be	AUX
ejpam-4550	180	9	denoted	denote	VERB
ejpam-4550	180	10	by	by	ADP
ejpam-4550	180	11	j(e0	j(e0	NOUN
ejpam-4550	180	12	)	)	PUNCT
ejpam-4550	180	13	and	and	CCONJ
ejpam-4550	180	14	its	its	PRON
ejpam-4550	180	15	eigenvalues	eigenvalue	NOUN
ejpam-4550	180	16	are	be	AUX
ejpam-4550	180	17	the	the	DET
ejpam-4550	180	18	solutions	solution	NOUN
ejpam-4550	180	19	of	of	ADP
ejpam-4550	180	20	the	the	DET
ejpam-4550	180	21	following	follow	VERB
ejpam-4550	180	22	equations	equation	NOUN
ejpam-4550	180	23	:	:	PUNCT
ejpam-4550	180	24	r8x	r8x	PROPN
ejpam-4550	180	25	8	8	NUM
ejpam-4550	181	1	+	+	CCONJ
ejpam-4550	181	2	r7x	r7x	PROPN
ejpam-4550	181	3	7	7	NUM
ejpam-4550	182	1	+	+	CCONJ
ejpam-4550	182	2	r6x	r6x	ADP
ejpam-4550	182	3	6	6	NUM
ejpam-4550	182	4	+	+	NUM
ejpam-4550	182	5	r5x	r5x	NOUN
ejpam-4550	182	6	5	5	NUM
ejpam-4550	182	7	+	+	NOUN
ejpam-4550	182	8	r4x	r4x	ADV
ejpam-4550	182	9	4	4	NUM
ejpam-4550	182	10	+	+	NUM
ejpam-4550	182	11	r3x	r3x	NOUN
ejpam-4550	182	12	3	3	NUM
ejpam-4550	182	13	+	+	CCONJ
ejpam-4550	182	14	r2x	r2x	PROPN
ejpam-4550	182	15	2	2	NUM
ejpam-4550	182	16	+	+	NUM
ejpam-4550	182	17	r1x+	r1x+	PROPN
ejpam-4550	182	18	r0	r0	NOUN
ejpam-4550	182	19	=	=	NOUN
ejpam-4550	182	20	0	0	X
ejpam-4550	182	21	.	.	PUNCT
ejpam-4550	182	22	let	let	VERB
ejpam-4550	182	23	us	we	PRON
ejpam-4550	182	24	define	define	VERB
ejpam-4550	182	25	:	:	PUNCT
ejpam-4550	182	26	f1	f1	NOUN
ejpam-4550	182	27	=	=	SYM
ejpam-4550	182	28	−a1κ5a4c2κ4β2b−	−a1κ5a4c2κ4β2b−	NUM
ejpam-4550	183	1	a1a2κ5κ6b	a1a2κ5κ6b	CCONJ
ejpam-4550	183	2	2β1	2β1	NUM
ejpam-4550	184	1	−	−	NOUN
ejpam-4550	184	2	γβ2κ6bκ4κ3κ2	γβ2κ6bκ4κ3κ2	NOUN
ejpam-4550	184	3	−	−	PROPN
ejpam-4550	184	4	a3γa4κ4κ3κ2β2a1κ5κ6b	a3γa4κ4κ3κ2β2a1κ5κ6b	NOUN
ejpam-4550	184	5	2κ4β1	2κ4β1	NUM
ejpam-4550	184	6	−a3a4κ4κ3c1β2b	−a3a4κ4κ3c1β2b	ADP
ejpam-4550	184	7	f2	f2	PROPN
ejpam-4550	184	8	=	=	SYM
ejpam-4550	184	9	−β2b	−β2b	PROPN
ejpam-4550	184	10	2κ6κ4κ3c1	2κ6κ4κ3c1	NUM
ejpam-4550	184	11	−	−	NOUN
ejpam-4550	184	12	a1a2c3κ5κ6β2b−	a1a2c3κ5κ6β2b−	ADP
ejpam-4550	184	13	a3β2b	a3β2b	ADP
ejpam-4550	184	14	2κ4κ3c1	2κ4κ3c1	NUM
ejpam-4550	184	15	−	−	NOUN
ejpam-4550	184	16	κ5κ6b	κ5κ6b	NUM
ejpam-4550	184	17	2κ4κ3β1	2κ4κ3β1	NUM
ejpam-4550	184	18	−	−	NOUN
ejpam-4550	184	19	a3γβ2bκ4κ3κ2	a3γβ2bκ4κ3κ2	NOUN
ejpam-4550	184	20	−a1κ5b	−a1κ5b	PROPN
ejpam-4550	184	21	2c2κ4β2	2c2κ4β2	NUM
ejpam-4550	184	22	f3	f3	NOUN
ejpam-4550	184	23	=	=	SYM
ejpam-4550	184	24	bκ1κ2κ3κ4κ5κ6	bκ1κ2κ3κ4κ5κ6	X
ejpam-4550	184	25	f4	f4	NOUN
ejpam-4550	184	26	=	=	SYM
ejpam-4550	184	27	−a1κ5a4c2β2b−	−a1κ5a4c2β2b−	X
ejpam-4550	184	28	β2b	β2b	NUM
ejpam-4550	184	29	2κ6κ3c1	2κ6κ3c1	NUM
ejpam-4550	184	30	−	−	NOUN
ejpam-4550	184	31	a3β2b	a3β2b	ADP
ejpam-4550	184	32	2κ3c1	2κ3c1	NUM
ejpam-4550	184	33	−	−	NUM
ejpam-4550	184	34	κ5κ6b	κ5κ6b	PUNCT
ejpam-4550	184	35	2κ3β1	2κ3β1	NUM
ejpam-4550	184	36	−	−	NOUN
ejpam-4550	184	37	a3γβ2bκ3κ2	a3γβ2bκ3κ2	NOUN
ejpam-4550	184	38	−	−	NOUN
ejpam-4550	184	39	a1κ5b	a1κ5b	SYM
ejpam-4550	184	40	2c2β2	2c2β2	NUM
ejpam-4550	184	41	f5	f5	NOUN
ejpam-4550	184	42	=	=	SYM
ejpam-4550	184	43	−γβ2κ6bκ3κ2	−γβ2κ6bκ3κ2	NOUN
ejpam-4550	184	44	−	−	PROPN
ejpam-4550	184	45	a3γa4κ3κ2β2	a3γa4κ3κ2β2	PROPN
ejpam-4550	184	46	−	−	PROPN
ejpam-4550	185	1	a1κ5κ6b	a1κ5κ6b	PROPN
ejpam-4550	185	2	2β1	2β1	NUM
ejpam-4550	185	3	−	−	PROPN
ejpam-4550	185	4	a3a4κ3c1β2b	a3a4κ3c1β2b	NOUN
ejpam-4550	185	5	+	+	CCONJ
ejpam-4550	185	6	κ1κ5κ6bκ3κ2	κ1κ5κ6bκ3κ2	NOUN
ejpam-4550	185	7	f6	f6	NUM
ejpam-4550	186	1	=	=	PUNCT
ejpam-4550	186	2	−a3γβ2bκ4κ3	−a3γβ2bκ4κ3	NOUN
ejpam-4550	187	1	−	−	PROPN
ejpam-4550	187	2	γβ2κ6bκ4κ3	γβ2κ6bκ4κ3	VERB
ejpam-4550	187	3	−	−	NOUN
ejpam-4550	187	4	a3γa4κ4κ3β2	a3γa4κ4κ3β2	NOUN
ejpam-4550	187	5	+	+	CCONJ
ejpam-4550	187	6	κ1κ5κ6bκ4κ3	κ1κ5κ6bκ4κ3	PROPN
ejpam-4550	187	7	f7	f7	PROPN
ejpam-4550	187	8	=	=	SYM
ejpam-4550	187	9	−β2b	−β2b	PROPN
ejpam-4550	187	10	2κ6κ4c1	2κ6κ4c1	NUM
ejpam-4550	187	11	−	−	NOUN
ejpam-4550	187	12	a3β2b	a3β2b	ADP
ejpam-4550	187	13	2κ4c1	2κ4c1	NUM
ejpam-4550	187	14	−	−	PROPN
ejpam-4550	187	15	κ5κ6b	κ5κ6b	NUM
ejpam-4550	187	16	2κ4β1	2κ4β1	NUM
ejpam-4550	187	17	−	−	ADP
ejpam-4550	187	18	a3γβ2bκ4κ2	a3γβ2bκ4κ2	PROPN
ejpam-4550	187	19	f8	f8	PROPN
ejpam-4550	187	20	=	=	PUNCT
ejpam-4550	187	21	−γβ2κ6bκ4κ2	−γβ2κ6bκ4κ2	PART
ejpam-4550	188	1	−	−	PROPN
ejpam-4550	188	2	a3γa4κ4κ2β2	a3γa4κ4κ2β2	NOUN
ejpam-4550	188	3	−	−	NOUN
ejpam-4550	188	4	a3a4κ4c1β2b	a3a4κ4c1β2b	NOUN
ejpam-4550	188	5	+	+	CCONJ
ejpam-4550	189	1	κ1κ5κ6bκ4κ2	κ1κ5κ6bκ4κ2	X
ejpam-4550	189	2	f9	f9	PROPN
ejpam-4550	189	3	=	=	SYM
ejpam-4550	189	4	−a1a4c2κ4β2b−	−a1a4c2κ4β2b−	PUNCT
ejpam-4550	189	5	a1a2c3κ6β2b−	a1a2c3κ6β2b−	NOUN
ejpam-4550	189	6	κ6b	κ6b	NOUN
ejpam-4550	189	7	2κ4κ3β1	2κ4κ3β1	NUM
ejpam-4550	189	8	−	−	NOUN
ejpam-4550	189	9	a1b	a1b	PROPN
ejpam-4550	189	10	2c2κ4β2	2c2κ4β2	NUM
ejpam-4550	189	11	−	−	NOUN
ejpam-4550	190	1	a1a2κ6b	a1a2κ6b	NUM
ejpam-4550	190	2	2β1	2β1	NUM
ejpam-4550	190	3	−	−	NOUN
ejpam-4550	190	4	a1κ6b	a1κ6b	NUM
ejpam-4550	190	5	2κ4β1	2κ4β1	NUM
ejpam-4550	191	1	+	+	NOUN
ejpam-4550	191	2	κ1κ6bκ4κ3κ2	κ1κ6bκ4κ3κ2	NOUN
ejpam-4550	191	3	f10	f10	NOUN
ejpam-4550	191	4	=	=	SYM
ejpam-4550	191	5	−β2b	−β2b	ADP
ejpam-4550	191	6	2κ4κ3c1	2κ4κ3c1	NUM
ejpam-4550	191	7	−	−	NOUN
ejpam-4550	191	8	a1a2c3κ5β2b−	a1a2c3κ5β2b−	NOUN
ejpam-4550	191	9	κ5b	κ5b	PROPN
ejpam-4550	191	10	2κ4κ3β1	2κ4κ3β1	NUM
ejpam-4550	191	11	−	−	PUNCT
ejpam-4550	191	12	a1a2κ5b	a1a2κ5b	PROPN
ejpam-4550	191	13	2β1	2β1	NUM
ejpam-4550	192	1	−	−	NOUN
ejpam-4550	192	2	γβ2bκ4κ3κ2	γβ2bκ4κ3κ2	NOUN
ejpam-4550	192	3	−	−	PROPN
ejpam-4550	192	4	a1κ5b	a1κ5b	NUM
ejpam-4550	192	5	2κ4β1	2κ4β1	NUM
ejpam-4550	193	1	+	+	ADP
ejpam-4550	193	2	κ1κ5bκ4κ3κ2	κ1κ5bκ4κ3κ2	ADJ
ejpam-4550	193	3	f11	f11	X
ejpam-4550	193	4	=	=	SYM
ejpam-4550	193	5	−a1a2κ5κ6β1b−	−a1a2κ5κ6β1b−	NUM
ejpam-4550	193	6	a3β2bκ4κ3c1	a3β2bκ4κ3c1	NOUN
ejpam-4550	193	7	−	−	PROPN
ejpam-4550	193	8	κ5κ6bκ4κ3β1	κ5κ6bκ4κ3β1	VERB
ejpam-4550	193	9	−	−	PROPN
ejpam-4550	193	10	a3γβ2κ4κ3κ2	a3γβ2κ4κ3κ2	NOUN
ejpam-4550	193	11	−	−	PROPN
ejpam-4550	193	12	a1κ5c2κ4β2b	a1κ5c2κ4β2b	ADJ
ejpam-4550	193	13	f12	f12	NOUN
ejpam-4550	193	14	=	=	PUNCT
ejpam-4550	193	15	−β2bκ6κ4κ3c1	−β2bκ6κ4κ3c1	PROPN
ejpam-4550	193	16	−	−	PROPN
ejpam-4550	193	17	a1κ5κ6κ4β1b−	a1κ5κ6κ4β1b−	NOUN
ejpam-4550	193	18	γβ2κ6κ4κ3κ2	γβ2κ6κ4κ3κ2	NOUN
ejpam-4550	194	1	+	+	CCONJ
ejpam-4550	194	2	κ1κ5κ6κ4κ3κ2	κ1κ5κ6κ4κ3κ2	X
ejpam-4550	194	3	f13	f13	X
ejpam-4550	194	4	=	=	SYM
ejpam-4550	194	5	−β2b	−β2b	PROPN
ejpam-4550	194	6	2κ6c1	2κ6c1	NUM
ejpam-4550	194	7	−	−	NOUN
ejpam-4550	194	8	a3β2b	a3β2b	ADP
ejpam-4550	194	9	2c1	2c1	NUM
ejpam-4550	194	10	−	−	NOUN
ejpam-4550	194	11	κ5κ6b	κ5κ6b	PUNCT
ejpam-4550	194	12	2β1	2β1	NUM
ejpam-4550	194	13	−	−	NOUN
ejpam-4550	194	14	a3γβ2bκ2	a3γβ2bκ2	NUM
ejpam-4550	194	15	−	−	PROPN
ejpam-4550	194	16	γβ2κ6bκ2	γβ2κ6bκ2	NOUN
ejpam-4550	194	17	−	−	PROPN
ejpam-4550	194	18	a3γa4κ2β2	a3γa4κ2β2	NOUN
ejpam-4550	194	19	−	−	PROPN
ejpam-4550	195	1	a3a4c1β2b	a3a4c1β2b	INTJ
ejpam-4550	195	2	+	+	ADJ
ejpam-4550	195	3	κ1κ5κ6bκ2	κ1κ5κ6bκ2	ADJ
ejpam-4550	195	4	f14	f14	NOUN
ejpam-4550	195	5	=	=	PUNCT
ejpam-4550	195	6	−a3γβ2bκ3	−a3γβ2bκ3	ADJ
ejpam-4550	195	7	−	−	PROPN
ejpam-4550	195	8	γβ2κ6bκ3	γβ2κ6bκ3	NOUN
ejpam-4550	195	9	−	−	PROPN
ejpam-4550	196	1	a3γa4κ3β2	a3γa4κ3β2	PROPN
ejpam-4550	197	1	+	+	CCONJ
ejpam-4550	197	2	κ1κ5κ6bκ3	κ1κ5κ6bκ3	PROPN
ejpam-4550	197	3	f15	f15	PROPN
ejpam-4550	197	4	=	=	SYM
ejpam-4550	197	5	−β2bκ4κ3c1	−β2bκ4κ3c1	PROPN
ejpam-4550	197	6	−	−	PROPN
ejpam-4550	197	7	κ5bκ4κ3β1	κ5bκ4κ3β1	PROPN
ejpam-4550	197	8	−	−	PROPN
ejpam-4550	197	9	a1a2κ5β1b−	a1a2κ5β1b−	PROPN
ejpam-4550	197	10	γβ2κ4κ3κ2	γβ2κ4κ3κ2	NOUN
ejpam-4550	197	11	−	−	PROPN
ejpam-4550	197	12	a1κ5κ4β1b	a1κ5κ4β1b	NOUN
ejpam-4550	197	13	+	+	CCONJ
ejpam-4550	197	14	κ1κ5κ4κ3κ2	κ1κ5κ4κ3κ2	NUM
ejpam-4550	197	15	f16	f16	PROPN
ejpam-4550	197	16	=	=	SYM
ejpam-4550	197	17	−β2bκ6κ4c1	−β2bκ6κ4c1	NOUN
ejpam-4550	197	18	−	−	NOUN
ejpam-4550	197	19	a3β2bκ4c1	a3β2bκ4c1	NOUN
ejpam-4550	197	20	−	−	NUM
ejpam-4550	197	21	κ5κ6bκ4β1	κ5κ6bκ4β1	NOUN
ejpam-4550	197	22	−	−	PROPN
ejpam-4550	197	23	a3γβ2κ4κ2	a3γβ2κ4κ2	VERB
ejpam-4550	197	24	−	−	PROPN
ejpam-4550	197	25	γβ2κ6κ4κ2	γβ2κ6κ4κ2	NOUN
ejpam-4550	198	1	+	+	CCONJ
ejpam-4550	198	2	κ1κ5κ6κ4κ2	κ1κ5κ6κ4κ2	X
ejpam-4550	198	3	f17	f17	NOUN
ejpam-4550	198	4	=	=	NOUN
ejpam-4550	198	5	−β2bκ6κ3c1	−β2bκ6κ3c1	PUNCT
ejpam-4550	198	6	−	−	NOUN
ejpam-4550	198	7	a3β2bκ3c1	a3β2bκ3c1	SYM
ejpam-4550	198	8	−	−	NOUN
ejpam-4550	198	9	κ5κ6bκ3β1	κ5κ6bκ3β1	VERB
ejpam-4550	198	10	−	−	PROPN
ejpam-4550	198	11	a3γβ2κ3κ2	a3γβ2κ3κ2	NOUN
ejpam-4550	198	12	−	−	NOUN
ejpam-4550	198	13	a1κ5c2β2b−	a1κ5c2β2b−	ADV
ejpam-4550	198	14	γβ2κ6κ3κ2	γβ2κ6κ3κ2	ADV
ejpam-4550	198	15	−a1κ5κ6β1b	−a1κ5κ6β1b	NOUN
ejpam-4550	199	1	+	+	CCONJ
ejpam-4550	199	2	κ1κ5κ6κ3κ2	κ1κ5κ6κ3κ2	VERB
ejpam-4550	199	3	m.	m.	NOUN
ejpam-4550	199	4	alassane	alassane	PROPN
ejpam-4550	199	5	et	et	PROPN
ejpam-4550	199	6	al	al	PROPN
ejpam-4550	199	7	.	.	PUNCT
ejpam-4550	199	8	/	/	SYM
ejpam-4550	199	9	eur	eur	PROPN
ejpam-4550	199	10	.	.	PUNCT
ejpam-4550	200	1	j.	j.	PROPN
ejpam-4550	200	2	pure	pure	PROPN
ejpam-4550	200	3	appl	appl	PROPN
ejpam-4550	200	4	.	.	PROPN
ejpam-4550	200	5	math	math	PROPN
ejpam-4550	200	6	,	,	PUNCT
ejpam-4550	200	7	16	16	NUM
ejpam-4550	200	8	(	(	PUNCT
ejpam-4550	200	9	1	1	NUM
ejpam-4550	200	10	)	)	PUNCT
ejpam-4550	200	11	(	(	PUNCT
ejpam-4550	200	12	2023	2023	NUM
ejpam-4550	200	13	)	)	PUNCT
ejpam-4550	200	14	,	,	PUNCT
ejpam-4550	200	15	207	207	NUM
ejpam-4550	200	16	-	-	SYM
ejpam-4550	200	17	232	232	NUM
ejpam-4550	200	18	219	219	NUM
ejpam-4550	200	19	f18	f18	NOUN
ejpam-4550	200	20	=	=	PUNCT
ejpam-4550	200	21	−a1a4c2β2b−	−a1a4c2β2b−	ADP
ejpam-4550	200	22	κ6b	κ6b	VERB
ejpam-4550	200	23	2κ3β1	2κ3β1	NUM
ejpam-4550	200	24	−	−	NOUN
ejpam-4550	200	25	a1b	a1b	NOUN
ejpam-4550	200	26	2c2β2	2c2β2	NUM
ejpam-4550	200	27	−	−	NOUN
ejpam-4550	200	28	a1κ6b	a1κ6b	NUM
ejpam-4550	200	29	2β1	2β1	NUM
ejpam-4550	201	1	+	+	CCONJ
ejpam-4550	201	2	κ1κ6bκ3κ2	κ1κ6bκ3κ2	PROPN
ejpam-4550	201	3	f19	f19	PROPN
ejpam-4550	201	4	=	=	NOUN
ejpam-4550	201	5	−a3γβ2bκ4	−a3γβ2bκ4	ADV
ejpam-4550	201	6	−	−	NOUN
ejpam-4550	201	7	γβ2κ6bκ4	γβ2κ6bκ4	NOUN
ejpam-4550	201	8	−	−	PROPN
ejpam-4550	201	9	a3γa4κ4β2	a3γa4κ4β2	PROPN
ejpam-4550	202	1	+	+	CCONJ
ejpam-4550	202	2	κ1κ5κ6bκ4	κ1κ5κ6bκ4	PROPN
ejpam-4550	202	3	f20	f20	NOUN
ejpam-4550	202	4	=	=	PUNCT
ejpam-4550	202	5	−κ6b	−κ6b	PROPN
ejpam-4550	202	6	2κ4β1	2κ4β1	NUM
ejpam-4550	202	7	+	+	CCONJ
ejpam-4550	202	8	κ1κ6bκ4κ2	κ1κ6bκ4κ2	X
ejpam-4550	202	9	f21	f21	NOUN
ejpam-4550	202	10	=	=	SYM
ejpam-4550	202	11	−a3γβ2κ4κ3	−a3γβ2κ4κ3	VERB
ejpam-4550	202	12	−	−	PROPN
ejpam-4550	202	13	γβ2κ6κ4κ3	γβ2κ6κ4κ3	NOUN
ejpam-4550	202	14	+	+	CCONJ
ejpam-4550	202	15	κ1κ5κ6κ4κ3	κ1κ5κ6κ4κ3	X
ejpam-4550	202	16	f22	f22	NOUN
ejpam-4550	202	17	=	=	SYM
ejpam-4550	202	18	−γβ2bκ4κ3	−γβ2bκ4κ3	PROPN
ejpam-4550	202	19	+	+	NUM
ejpam-4550	202	20	κ1κ5bκ4κ3	κ1κ5bκ4κ3	PROPN
ejpam-4550	202	21	f23	f23	PROPN
ejpam-4550	202	22	=	=	SYM
ejpam-4550	202	23	−β2b	−β2b	PROPN
ejpam-4550	202	24	2κ3c1	2κ3c1	NUM
ejpam-4550	202	25	−	−	PROPN
ejpam-4550	203	1	κ5b	κ5b	PROPN
ejpam-4550	203	2	2κ3β1	2κ3β1	NUM
ejpam-4550	203	3	−	−	NOUN
ejpam-4550	203	4	γβ2bκ3κ2	γβ2bκ3κ2	NOUN
ejpam-4550	203	5	−	−	PROPN
ejpam-4550	203	6	a1κ5b	a1κ5b	NUM
ejpam-4550	203	7	2β1	2β1	NUM
ejpam-4550	204	1	+	+	CCONJ
ejpam-4550	204	2	κ1κ6bκ4κ3	κ1κ6bκ4κ3	ADJ
ejpam-4550	204	3	+	+	NUM
ejpam-4550	204	4	κ1κ5bκ3κ2	κ1κ5bκ3κ2	NUM
ejpam-4550	204	5	f24	f24	NOUN
ejpam-4550	204	6	=	=	PUNCT
ejpam-4550	204	7	−κ6bκ4κ3β1	−κ6bκ4κ3β1	PROPN
ejpam-4550	204	8	−	−	NOUN
ejpam-4550	204	9	a1c2κ4β2b−	a1c2κ4β2b−	NOUN
ejpam-4550	204	10	a1a2κ6β1b−	a1a2κ6β1b−	PROPN
ejpam-4550	204	11	a1κ6κ4β1b	a1κ6κ4β1b	PROPN
ejpam-4550	204	12	+	+	PUNCT
ejpam-4550	204	13	κ1κ6κ4κ3κ2	κ1κ6κ4κ3κ2	NUM
ejpam-4550	204	14	f25	f25	NOUN
ejpam-4550	204	15	=	=	PUNCT
ejpam-4550	204	16	−b2κ4κ3β1	−b2κ4κ3β1	PROPN
ejpam-4550	204	17	−	−	PROPN
ejpam-4550	204	18	a1a2b	a1a2b	NUM
ejpam-4550	204	19	2β1	2β1	NUM
ejpam-4550	204	20	−	−	NOUN
ejpam-4550	204	21	a1b	a1b	PROPN
ejpam-4550	204	22	2κ4β1	2κ4β1	NUM
ejpam-4550	204	23	−	−	PROPN
ejpam-4550	205	1	a1a2c3β2b	a1a2c3β2b	NOUN
ejpam-4550	205	2	+	+	NUM
ejpam-4550	205	3	κ1bκ4κ3κ2	κ1bκ4κ3κ2	PROPN
ejpam-4550	205	4	f26	f26	VERB
ejpam-4550	205	5	=	=	SYM
ejpam-4550	205	6	−κ5b	−κ5b	PROPN
ejpam-4550	205	7	2κ4β1	2κ4β1	NUM
ejpam-4550	205	8	−	−	NUM
ejpam-4550	206	1	γβ2bκ4κ2	γβ2bκ4κ2	NUM
ejpam-4550	207	1	−	−	PRON
ejpam-4550	207	2	β2b	β2b	SYM
ejpam-4550	207	3	2κ4c1	2κ4c1	NUM
ejpam-4550	207	4	+	+	CCONJ
ejpam-4550	207	5	κ1κ5bκ4κ2	κ1κ5bκ4κ2	NUM
ejpam-4550	207	6	f27	f27	NOUN
ejpam-4550	208	1	=	=	PROPN
ejpam-4550	209	1	−γβ2bκ4	−γβ2bκ4	NOUN
ejpam-4550	210	1	+	+	CCONJ
ejpam-4550	210	2	κ1κ5bκ4	κ1κ5bκ4	VERB
ejpam-4550	210	3	−	−	NOUN
ejpam-4550	211	1	κ6b	κ6b	VERB
ejpam-4550	211	2	2β1	2β1	NUM
ejpam-4550	212	1	+	+	CCONJ
ejpam-4550	212	2	κ1κ6bκ2	κ1κ6bκ2	X
ejpam-4550	212	3	−	−	PROPN
ejpam-4550	212	4	κ4κ3β1b−	κ4κ3β1b−	PROPN
ejpam-4550	212	5	a1a2β1b−	a1a2β1b−	PROPN
ejpam-4550	212	6	a1κ4β1b	a1κ4β1b	PUNCT
ejpam-4550	213	1	+	+	CCONJ
ejpam-4550	213	2	κ1κ4κ3κ2	κ1κ4κ3κ2	PROPN
ejpam-4550	213	3	f28	f28	PROPN
ejpam-4550	213	4	=	=	SYM
ejpam-4550	213	5	−b2κ3β1	−b2κ3β1	NUM
ejpam-4550	213	6	−	−	NOUN
ejpam-4550	213	7	a1b	a1b	PROPN
ejpam-4550	213	8	2β1	2β1	NUM
ejpam-4550	214	1	+	+	CCONJ
ejpam-4550	214	2	κ1bκ3κ2	κ1bκ3κ2	NOUN
ejpam-4550	214	3	−	−	NOUN
ejpam-4550	214	4	κ6bκ3β1	κ6bκ3β1	ADV
ejpam-4550	214	5	−	−	PUNCT
ejpam-4550	214	6	a1c2β2b−	a1c2β2b−	PROPN
ejpam-4550	214	7	a1κ6β1b	a1κ6β1b	PROPN
ejpam-4550	214	8	+	+	NUM
ejpam-4550	214	9	κ1κ6κ3κ2	κ1κ6κ3κ2	NOUN
ejpam-4550	214	10	f29	f29	NOUN
ejpam-4550	214	11	=	=	SYM
ejpam-4550	214	12	−κ6bκ4β1	−κ6bκ4β1	NOUN
ejpam-4550	214	13	+	+	PROPN
ejpam-4550	214	14	κ1κ6κ4κ2	κ1κ6κ4κ2	NOUN
ejpam-4550	214	15	−	−	PROPN
ejpam-4550	214	16	β2b	β2b	PUNCT
ejpam-4550	214	17	2c1	2c1	NUM
ejpam-4550	215	1	−	−	PROPN
ejpam-4550	216	1	κ5b	κ5b	PROPN
ejpam-4550	216	2	2β1	2β1	NUM
ejpam-4550	217	1	−	−	NOUN
ejpam-4550	217	2	γβ2bκ2	γβ2bκ2	NOUN
ejpam-4550	217	3	+	+	CCONJ
ejpam-4550	217	4	κ1κ5bκ2	κ1κ5bκ2	VERB
ejpam-4550	217	5	f30	f30	NOUN
ejpam-4550	217	6	=	=	SYM
ejpam-4550	217	7	−β2bκ6c1	−β2bκ6c1	NOUN
ejpam-4550	217	8	−	−	NOUN
ejpam-4550	218	1	a3β2bc1	a3β2bc1	ADP
ejpam-4550	218	2	−	−	PUNCT
ejpam-4550	218	3	κ5κ6bβ1	κ5κ6bβ1	NOUN
ejpam-4550	218	4	−	−	PROPN
ejpam-4550	218	5	a3γβ2κ2	a3γβ2κ2	NOUN
ejpam-4550	218	6	−	−	X
ejpam-4550	218	7	γβ2κ6κ2	γβ2κ6κ2	PUNCT
ejpam-4550	218	8	+	+	NUM
ejpam-4550	218	9	κ1κ5κ6κ2	κ1κ5κ6κ2	PROPN
ejpam-4550	218	10	f31	f31	NOUN
ejpam-4550	218	11	=	=	NOUN
ejpam-4550	218	12	−a3γβ2κ3	−a3γβ2κ3	NOUN
ejpam-4550	218	13	−	−	PROPN
ejpam-4550	218	14	γβ2κ6κ3	γβ2κ6κ3	NOUN
ejpam-4550	219	1	+	+	CCONJ
ejpam-4550	219	2	κ1κ5κ6κ3	κ1κ5κ6κ3	PROPN
ejpam-4550	219	3	−	−	PROPN
ejpam-4550	219	4	a3γβ2b−	a3γβ2b−	X
ejpam-4550	219	5	γβ2κ6b−	γβ2κ6b−	X
ejpam-4550	219	6	a3γa4β2	a3γa4β2	AUX
ejpam-4550	219	7	+	+	CCONJ
ejpam-4550	219	8	κ1κ5κ6b	κ1κ5κ6b	PROPN
ejpam-4550	219	9	f32	f32	NOUN
ejpam-4550	219	10	=	=	SYM
ejpam-4550	219	11	−γβ2κ4κ3	−γβ2κ4κ3	NOUN
ejpam-4550	219	12	+	+	CCONJ
ejpam-4550	219	13	κ1κ5κ4κ3	κ1κ5κ4κ3	NOUN
ejpam-4550	219	14	−	−	NOUN
ejpam-4550	219	15	β2bκ4c1	β2bκ4c1	NUM
ejpam-4550	219	16	−	−	NOUN
ejpam-4550	219	17	κ5bκ4β1	κ5bκ4β1	NUM
ejpam-4550	219	18	−	−	PROPN
ejpam-4550	220	1	γβ2κ4κ2	γβ2κ4κ2	PROPN
ejpam-4550	220	2	+	+	NUM
ejpam-4550	220	3	κ1κ5κ4κ2	κ1κ5κ4κ2	PROPN
ejpam-4550	220	4	f33	f33	NOUN
ejpam-4550	220	5	=	=	PUNCT
ejpam-4550	220	6	−β2bκ3c1	−β2bκ3c1	NOUN
ejpam-4550	221	1	−	−	NOUN
ejpam-4550	221	2	κ5bκ3β1	κ5bκ3β1	ADV
ejpam-4550	221	3	−	−	PROPN
ejpam-4550	221	4	γβ2κ3κ2	γβ2κ3κ2	PROPN
ejpam-4550	221	5	−	−	PROPN
ejpam-4550	221	6	a1κ5β1b	a1κ5β1b	PUNCT
ejpam-4550	222	1	+	+	NUM
ejpam-4550	222	2	κ1κ5κ3κ2	κ1κ5κ3κ2	NOUN
ejpam-4550	222	3	−	−	PROPN
ejpam-4550	222	4	a3γβ2κ4	a3γβ2κ4	NOUN
ejpam-4550	222	5	−	−	PROPN
ejpam-4550	222	6	γβ2κ6κ4	γβ2κ6κ4	PUNCT
ejpam-4550	223	1	+	+	CCONJ
ejpam-4550	223	2	κ1κ5κ6κ4	κ1κ5κ6κ4	NOUN
ejpam-4550	223	3	f34	f34	NOUN
ejpam-4550	224	1	=	=	SYM
ejpam-4550	224	2	−γβ2bκ3	−γβ2bκ3	VERB
ejpam-4550	225	1	+	+	PUNCT
ejpam-4550	226	1	κ1κ5bκ3	κ1κ5bκ3	VERB
ejpam-4550	226	2	−	−	NOUN
ejpam-4550	226	3	b2κ4β1	b2κ4β1	PROPN
ejpam-4550	226	4	+	+	CCONJ
ejpam-4550	226	5	κ1bκ4κ2	κ1bκ4κ2	PROPN
ejpam-4550	226	6	f35	f35	NOUN
ejpam-4550	226	7	=	=	PUNCT
ejpam-4550	226	8	−b2β1	−b2β1	PROPN
ejpam-4550	226	9	+	+	CCONJ
ejpam-4550	226	10	κ1bκ2	κ1bκ2	NOUN
ejpam-4550	226	11	−	−	NOUN
ejpam-4550	226	12	κ4β1b	κ4β1b	SYM
ejpam-4550	226	13	+	+	PUNCT
ejpam-4550	226	14	κ1κ4κ2	κ1κ4κ2	NOUN
ejpam-4550	226	15	−	−	PROPN
ejpam-4550	226	16	γβ2b	γβ2b	NOUN
ejpam-4550	226	17	+	+	CCONJ
ejpam-4550	226	18	κ1κ5b−	κ1κ5b−	PRON
ejpam-4550	226	19	a3γβ2	a3γβ2	VERB
ejpam-4550	226	20	−	−	PROPN
ejpam-4550	226	21	γβ2κ6	γβ2κ6	PUNCT
ejpam-4550	226	22	+	+	NUM
ejpam-4550	226	23	κ1κ5κ6	κ1κ5κ6	NOUN
ejpam-4550	226	24	−	−	NOUN
ejpam-4550	226	25	γβ2κ4	γβ2κ4	NOUN
ejpam-4550	226	26	+	+	ADJ
ejpam-4550	226	27	κ1κ5κ4	κ1κ5κ4	PROPN
ejpam-4550	226	28	f36	f36	NOUN
ejpam-4550	226	29	=	=	SYM
ejpam-4550	226	30	−κ6bβ1	−κ6bβ1	PROPN
ejpam-4550	226	31	+	+	CCONJ
ejpam-4550	226	32	κ1κ6κ2	κ1κ6κ2	VERB
ejpam-4550	226	33	−	−	NOUN
ejpam-4550	226	34	κ3β1b−	κ3β1b−	X
ejpam-4550	226	35	β1ba1	β1ba1	NOUN
ejpam-4550	226	36	+	+	CCONJ
ejpam-4550	226	37	κ1κ3κ2	κ1κ3κ2	PROPN
ejpam-4550	226	38	−	−	PROPN
ejpam-4550	226	39	β2bc1	β2bc1	NOUN
ejpam-4550	226	40	−	−	NOUN
ejpam-4550	226	41	κ5bβ1	κ5bβ1	VERB
ejpam-4550	226	42	−	−	NOUN
ejpam-4550	226	43	γβ2κ2	γβ2κ2	NOUN
ejpam-4550	226	44	+	+	NUM
ejpam-4550	226	45	κ1κ5κ2	κ1κ5κ2	NOUN
ejpam-4550	226	46	−	−	PUNCT
ejpam-4550	226	47	γβ2κ3	γβ2κ3	PUNCT
ejpam-4550	226	48	+	+	PROPN
ejpam-4550	226	49	κ1κ5κ3	κ1κ5κ3	ADJ
ejpam-4550	226	50	f37	f37	NOUN
ejpam-4550	226	51	=	=	PUNCT
ejpam-4550	227	1	κ1κ6	κ1κ6	PROPN
ejpam-4550	227	2	−	−	PROPN
ejpam-4550	227	3	β1b	β1b	PUNCT
ejpam-4550	228	1	+	+	CCONJ
ejpam-4550	228	2	κ1κ5	κ1κ5	PROPN
ejpam-4550	228	3	−	−	PROPN
ejpam-4550	228	4	γβ2	γβ2	VERB
ejpam-4550	228	5	+	+	NUM
ejpam-4550	228	6	κ1b	κ1b	PROPN
ejpam-4550	228	7	+	+	CCONJ
ejpam-4550	228	8	κ1κ4	κ1κ4	PROPN
ejpam-4550	228	9	+	+	NUM
ejpam-4550	228	10	κ2κ1	κ2κ1	X
ejpam-4550	228	11	+	+	X
ejpam-4550	228	12	κ1κ3	κ1κ3	NOUN
ejpam-4550	228	13	and	and	CCONJ
ejpam-4550	228	14	f1	f1	NOUN
ejpam-4550	228	15	=	=	SYM
ejpam-4550	228	16	f1	f1	PROPN
ejpam-4550	228	17	+	+	CCONJ
ejpam-4550	228	18	f2	f2	PROPN
ejpam-4550	228	19	+	+	CCONJ
ejpam-4550	228	20	f3	f3	ADJ
ejpam-4550	228	21	;	;	PUNCT
ejpam-4550	228	22	f2	f2	PROPN
ejpam-4550	228	23	=	=	SYM
ejpam-4550	228	24	f13	f13	X
ejpam-4550	228	25	+	+	CCONJ
ejpam-4550	228	26	f14	f14	PROPN
ejpam-4550	228	27	+	+	NUM
ejpam-4550	228	28	f15	f15	NOUN
ejpam-4550	228	29	+	+	CCONJ
ejpam-4550	228	30	f16	f16	PROPN
ejpam-4550	228	31	+	+	CCONJ
ejpam-4550	228	32	f17	f17	ADJ
ejpam-4550	228	33	+	+	CCONJ
ejpam-4550	228	34	f18	f18	NOUN
ejpam-4550	228	35	+	+	CCONJ
ejpam-4550	228	36	f19	f19	PROPN
ejpam-4550	228	37	+	+	CCONJ
ejpam-4550	228	38	f20	f20	NOUN
ejpam-4550	228	39	+	+	CCONJ
ejpam-4550	228	40	f21	f21	NOUN
ejpam-4550	228	41	+	+	CCONJ
ejpam-4550	228	42	f22	f22	NOUN
ejpam-4550	228	43	+	+	CCONJ
ejpam-4550	228	44	f23	f23	NOUN
ejpam-4550	228	45	+	+	CCONJ
ejpam-4550	228	46	f24	f24	NOUN
ejpam-4550	228	47	+	+	CCONJ
ejpam-4550	228	48	f25	f25	NOUN
ejpam-4550	228	49	+	+	CCONJ
ejpam-4550	228	50	f26	f26	ADP
ejpam-4550	228	51	f3	f3	NOUN
ejpam-4550	228	52	=	=	PUNCT
ejpam-4550	228	53	f4	f4	PROPN
ejpam-4550	228	54	+	+	PUNCT
ejpam-4550	228	55	f5	f5	NOUN
ejpam-4550	228	56	+	+	NUM
ejpam-4550	228	57	f6	f6	NOUN
ejpam-4550	228	58	+	+	CCONJ
ejpam-4550	228	59	f7	f7	PROPN
ejpam-4550	228	60	+	+	CCONJ
ejpam-4550	228	61	f8	f8	PROPN
ejpam-4550	228	62	+	+	CCONJ
ejpam-4550	228	63	f9	f9	PROPN
ejpam-4550	228	64	+	+	CCONJ
ejpam-4550	228	65	f10	f10	PROPN
ejpam-4550	228	66	+	+	CCONJ
ejpam-4550	228	67	f11	f11	NOUN
ejpam-4550	228	68	+	+	NUM
ejpam-4550	228	69	f12	f12	NOUN
ejpam-4550	228	70	;	;	PUNCT
ejpam-4550	228	71	f4	f4	PROPN
ejpam-4550	228	72	=	=	SYM
ejpam-4550	228	73	f27	f27	NOUN
ejpam-4550	228	74	+	+	CCONJ
ejpam-4550	228	75	f28	f28	PROPN
ejpam-4550	228	76	+	+	CCONJ
ejpam-4550	228	77	f29	f29	ADJ
ejpam-4550	228	78	+	+	NUM
ejpam-4550	228	79	f30	f30	NOUN
ejpam-4550	228	80	+	+	X
ejpam-4550	228	81	f31	f31	NOUN
ejpam-4550	228	82	+	+	CCONJ
ejpam-4550	228	83	f32	f32	X
ejpam-4550	228	84	+	+	X
ejpam-4550	228	85	f33	f33	NOUN
ejpam-4550	228	86	+	+	CCONJ
ejpam-4550	228	87	f34	f34	NOUN
ejpam-4550	228	88	f5	f5	NOUN
ejpam-4550	228	89	=	=	SYM
ejpam-4550	228	90	f35	f35	NOUN
ejpam-4550	228	91	+	+	CCONJ
ejpam-4550	228	92	f36	f36	NOUN
ejpam-4550	228	93	;	;	PUNCT
ejpam-4550	228	94	f6	f6	PROPN
ejpam-4550	228	95	=	=	PUNCT
ejpam-4550	228	96	f37	f37	PROPN
ejpam-4550	228	97	.	.	PUNCT
ejpam-4550	229	1	then	then	ADV
ejpam-4550	229	2	r8	r8	NOUN
ejpam-4550	229	3	=	=	SYM
ejpam-4550	229	4	1	1	NUM
ejpam-4550	229	5	,	,	PUNCT
ejpam-4550	229	6	r7	r7	NOUN
ejpam-4550	229	7	=	=	SYM
ejpam-4550	229	8	1	1	NUM
ejpam-4550	229	9	κ1	κ1	NOUN
ejpam-4550	229	10	(	(	PUNCT
ejpam-4550	229	11	f6	f6	PROPN
ejpam-4550	229	12	+	+	CCONJ
ejpam-4550	229	13	κ1b	κ1b	PROPN
ejpam-4550	229	14	+	+	CCONJ
ejpam-4550	229	15	κ21	κ21	PROPN
ejpam-4550	229	16	)	)	PUNCT
ejpam-4550	229	17	,	,	PUNCT
ejpam-4550	229	18	r6	r6	NOUN
ejpam-4550	229	19	=	=	SYM
ejpam-4550	229	20	1	1	NUM
ejpam-4550	229	21	κ1	κ1	NOUN
ejpam-4550	229	22	[	[	PUNCT
ejpam-4550	229	23	f5	f5	PROPN
ejpam-4550	229	24	+	+	CCONJ
ejpam-4550	229	25	f6	f6	PROPN
ejpam-4550	229	26	(	(	PUNCT
ejpam-4550	229	27	κ1	κ1	NOUN
ejpam-4550	229	28	+	+	CCONJ
ejpam-4550	229	29	b	b	NOUN
ejpam-4550	229	30	)	)	PUNCT
ejpam-4550	230	1	+	+	CCONJ
ejpam-4550	230	2	κ21b	κ21b	PROPN
ejpam-4550	230	3	]	]	PUNCT
ejpam-4550	230	4	,	,	PUNCT
ejpam-4550	230	5	r5	r5	PROPN
ejpam-4550	230	6	=	=	SYM
ejpam-4550	230	7	1	1	NUM
ejpam-4550	230	8	κ1	κ1	NOUN
ejpam-4550	230	9	[	[	X
ejpam-4550	230	10	f4	f4	NOUN
ejpam-4550	230	11	+	+	CCONJ
ejpam-4550	230	12	f5	f5	NOUN
ejpam-4550	230	13	(	(	PUNCT
ejpam-4550	230	14	κ1	κ1	NOUN
ejpam-4550	230	15	+	+	CCONJ
ejpam-4550	230	16	b	b	NOUN
ejpam-4550	230	17	)	)	PUNCT
ejpam-4550	230	18	+	+	CCONJ
ejpam-4550	230	19	f6κ1b	f6κ1b	X
ejpam-4550	230	20	]	]	PUNCT
ejpam-4550	230	21	,	,	PUNCT
ejpam-4550	230	22	r4	r4	NOUN
ejpam-4550	230	23	=	=	SYM
ejpam-4550	230	24	1	1	NUM
ejpam-4550	230	25	κ1	κ1	NOUN
ejpam-4550	230	26	[	[	X
ejpam-4550	230	27	f2	f2	PROPN
ejpam-4550	230	28	+	+	CCONJ
ejpam-4550	230	29	f4	f4	PROPN
ejpam-4550	230	30	(	(	PUNCT
ejpam-4550	230	31	κ1	κ1	NOUN
ejpam-4550	230	32	+	+	CCONJ
ejpam-4550	230	33	b	b	NOUN
ejpam-4550	230	34	)	)	PUNCT
ejpam-4550	230	35	+	+	NUM
ejpam-4550	230	36	f5κ1b	f5κ1b	NUM
ejpam-4550	230	37	]	]	X
ejpam-4550	230	38	,	,	PUNCT
ejpam-4550	230	39	r3	r3	PROPN
ejpam-4550	230	40	=	=	SYM
ejpam-4550	230	41	1	1	NUM
ejpam-4550	230	42	κ1	κ1	NOUN
ejpam-4550	230	43	[	[	X
ejpam-4550	230	44	f3	f3	PROPN
ejpam-4550	230	45	+	+	CCONJ
ejpam-4550	230	46	f2	f2	PROPN
ejpam-4550	230	47	(	(	PUNCT
ejpam-4550	230	48	κ1	κ1	NOUN
ejpam-4550	230	49	+	+	CCONJ
ejpam-4550	230	50	b	b	NOUN
ejpam-4550	230	51	)	)	PUNCT
ejpam-4550	230	52	+	+	CCONJ
ejpam-4550	230	53	f4κ1b	f4κ1b	NUM
ejpam-4550	230	54	]	]	PUNCT
ejpam-4550	230	55	,	,	PUNCT
ejpam-4550	230	56	r2	r2	PROPN
ejpam-4550	230	57	=	=	SYM
ejpam-4550	230	58	1	1	NUM
ejpam-4550	230	59	κ1	κ1	NOUN
ejpam-4550	230	60	[	[	X
ejpam-4550	230	61	f1	f1	NOUN
ejpam-4550	230	62	+	+	CCONJ
ejpam-4550	230	63	f3	f3	ADJ
ejpam-4550	230	64	(	(	PUNCT
ejpam-4550	230	65	κ1	κ1	NOUN
ejpam-4550	230	66	+	+	CCONJ
ejpam-4550	230	67	b	b	NOUN
ejpam-4550	230	68	)	)	PUNCT
ejpam-4550	230	69	+	+	CCONJ
ejpam-4550	230	70	f2κ1b	f2κ1b	NOUN
ejpam-4550	230	71	]	]	PUNCT
ejpam-4550	230	72	,	,	PUNCT
ejpam-4550	230	73	r1	r1	NOUN
ejpam-4550	230	74	=	=	SYM
ejpam-4550	230	75	1	1	NUM
ejpam-4550	230	76	κ1	κ1	NOUN
ejpam-4550	230	77	[	[	X
ejpam-4550	230	78	f1	f1	NOUN
ejpam-4550	230	79	(	(	PUNCT
ejpam-4550	230	80	κ1	κ1	NOUN
ejpam-4550	230	81	+	+	CCONJ
ejpam-4550	230	82	b	b	NOUN
ejpam-4550	230	83	)	)	PUNCT
ejpam-4550	230	84	+	+	CCONJ
ejpam-4550	230	85	f3κ1b	f3κ1b	X
ejpam-4550	230	86	]	]	PUNCT
ejpam-4550	230	87	,	,	PUNCT
ejpam-4550	230	88	r0	r0	NOUN
ejpam-4550	230	89	=	=	SYM
ejpam-4550	230	90	f1b	f1b	PROPN
ejpam-4550	230	91	.	.	PUNCT
ejpam-4550	231	1	m.	m.	PROPN
ejpam-4550	231	2	alassane	alassane	PROPN
ejpam-4550	231	3	et	et	PROPN
ejpam-4550	231	4	al	al	PROPN
ejpam-4550	231	5	.	.	PUNCT
ejpam-4550	231	6	/	/	SYM
ejpam-4550	231	7	eur	eur	PROPN
ejpam-4550	231	8	.	.	PUNCT
ejpam-4550	232	1	j.	j.	PROPN
ejpam-4550	232	2	pure	pure	PROPN
ejpam-4550	232	3	appl	appl	PROPN
ejpam-4550	232	4	.	.	PROPN
ejpam-4550	232	5	math	math	PROPN
ejpam-4550	232	6	,	,	PUNCT
ejpam-4550	232	7	16	16	NUM
ejpam-4550	232	8	(	(	PUNCT
ejpam-4550	232	9	1	1	NUM
ejpam-4550	232	10	)	)	PUNCT
ejpam-4550	232	11	(	(	PUNCT
ejpam-4550	232	12	2023	2023	NUM
ejpam-4550	232	13	)	)	PUNCT
ejpam-4550	232	14	,	,	PUNCT
ejpam-4550	232	15	207	207	NUM
ejpam-4550	232	16	-	-	SYM
ejpam-4550	232	17	232	232	NUM
ejpam-4550	232	18	220	220	NUM
ejpam-4550	232	19	we	we	PRON
ejpam-4550	232	20	now	now	ADV
ejpam-4550	232	21	need	need	VERB
ejpam-4550	232	22	to	to	PART
ejpam-4550	232	23	verify	verify	VERB
ejpam-4550	232	24	that	that	SCONJ
ejpam-4550	232	25	all	all	DET
ejpam-4550	232	26	the	the	DET
ejpam-4550	232	27	coefficients	coefficient	NOUN
ejpam-4550	232	28	r0	r0	NOUN
ejpam-4550	232	29	,	,	PUNCT
ejpam-4550	232	30	r1	r1	NOUN
ejpam-4550	232	31	,	,	PUNCT
ejpam-4550	232	32	r2	r2	PROPN
ejpam-4550	232	33	,	,	PUNCT
ejpam-4550	232	34	r3	r3	PROPN
ejpam-4550	232	35	,	,	PUNCT
ejpam-4550	232	36	r4	r4	NOUN
ejpam-4550	232	37	,	,	PUNCT
ejpam-4550	232	38	r5	r5	PROPN
ejpam-4550	232	39	and	and	CCONJ
ejpam-4550	232	40	r6	r6	NOUN
ejpam-4550	232	41	are	be	AUX
ejpam-4550	232	42	positive	positive	ADJ
ejpam-4550	232	43	.	.	PUNCT
ejpam-4550	233	1	for	for	ADP
ejpam-4550	233	2	this	this	PRON
ejpam-4550	233	3	,	,	PUNCT
ejpam-4550	233	4	it	it	PRON
ejpam-4550	233	5	is	be	AUX
ejpam-4550	233	6	sufficient	sufficient	ADJ
ejpam-4550	233	7	to	to	PART
ejpam-4550	233	8	prove	prove	VERB
ejpam-4550	233	9	that	that	DET
ejpam-4550	233	10	f1	f1	NOUN
ejpam-4550	233	11	,	,	PUNCT
ejpam-4550	233	12	f2	f2	PROPN
ejpam-4550	233	13	,	,	PUNCT
ejpam-4550	233	14	f3	f3	PROPN
ejpam-4550	233	15	,	,	PUNCT
ejpam-4550	233	16	f4	f4	PROPN
ejpam-4550	233	17	,	,	PUNCT
ejpam-4550	233	18	f5	f5	PROPN
ejpam-4550	233	19	and	and	CCONJ
ejpam-4550	233	20	f6	f6	PROPN
ejpam-4550	233	21	are	be	AUX
ejpam-4550	233	22	positive	positive	ADJ
ejpam-4550	233	23	.	.	PUNCT
ejpam-4550	234	1	we	we	PRON
ejpam-4550	234	2	can	can	AUX
ejpam-4550	234	3	clearly	clearly	ADV
ejpam-4550	234	4	see	see	VERB
ejpam-4550	234	5	that	that	SCONJ
ejpam-4550	234	6	all	all	DET
ejpam-4550	234	7	the	the	DET
ejpam-4550	234	8	fj	fj	PROPN
ejpam-4550	234	9	,	,	PUNCT
ejpam-4550	234	10	j	j	PROPN
ejpam-4550	234	11	=	=	NOUN
ejpam-4550	234	12	1	1	NUM
ejpam-4550	234	13	to	to	PART
ejpam-4550	234	14	6	6	NUM
ejpam-4550	234	15	,	,	PUNCT
ejpam-4550	234	16	are	be	AUX
ejpam-4550	234	17	positive	positive	ADJ
ejpam-4550	234	18	when	when	SCONJ
ejpam-4550	234	19	r0	r0	NOUN
ejpam-4550	234	20	<	<	X
ejpam-4550	234	21	1	1	NUM
ejpam-4550	234	22	.	.	PUNCT
ejpam-4550	235	1	therefore	therefore	ADV
ejpam-4550	235	2	,	,	PUNCT
ejpam-4550	235	3	all	all	DET
ejpam-4550	235	4	the	the	DET
ejpam-4550	235	5	rj	rj	PROPN
ejpam-4550	235	6	,	,	PUNCT
ejpam-4550	235	7	j	j	PROPN
ejpam-4550	235	8	=	=	NOUN
ejpam-4550	235	9	1	1	NUM
ejpam-4550	235	10	to	to	PART
ejpam-4550	235	11	6	6	NUM
ejpam-4550	235	12	,	,	PUNCT
ejpam-4550	235	13	are	be	AUX
ejpam-4550	235	14	positive	positive	ADJ
ejpam-4550	235	15	when	when	SCONJ
ejpam-4550	235	16	r0	r0	NOUN
ejpam-4550	235	17	<	<	X
ejpam-4550	235	18	1	1	NUM
ejpam-4550	235	19	.	.	PUNCT
ejpam-4550	236	1	therefore	therefore	ADV
ejpam-4550	236	2	,	,	PUNCT
ejpam-4550	236	3	from	from	ADP
ejpam-4550	236	4	routh	routh	PROPN
ejpam-4550	236	5	hurwitz	hurwitz	PROPN
ejpam-4550	236	6	criterion	criterion	NOUN
ejpam-4550	236	7	,	,	PUNCT
ejpam-4550	236	8	e0	e0	PROPN
ejpam-4550	236	9	is	be	AUX
ejpam-4550	236	10	locally	locally	ADV
ejpam-4550	236	11	asymptotically	asymptotically	ADV
ejpam-4550	236	12	stable	stable	ADJ
ejpam-4550	236	13	if	if	SCONJ
ejpam-4550	236	14	r0	r0	NOUN
ejpam-4550	236	15	<	<	X
ejpam-4550	236	16	1	1	NUM
ejpam-4550	236	17	.	.	NOUN
ejpam-4550	236	18	6	6	NUM
ejpam-4550	236	19	.	.	X
ejpam-4550	236	20	global	global	ADJ
ejpam-4550	236	21	stability	stability	NOUN
ejpam-4550	236	22	in	in	ADP
ejpam-4550	236	23	theorem	theorem	NOUN
ejpam-4550	236	24	2	2	NUM
ejpam-4550	236	25	,	,	PUNCT
ejpam-4550	236	26	we	we	PRON
ejpam-4550	236	27	have	have	AUX
ejpam-4550	236	28	proved	prove	VERB
ejpam-4550	236	29	that	that	SCONJ
ejpam-4550	236	30	the	the	DET
ejpam-4550	236	31	disease	disease	NOUN
ejpam-4550	236	32	-	-	PUNCT
ejpam-4550	236	33	free	free	ADJ
ejpam-4550	236	34	equilibrium	equilibrium	NOUN
ejpam-4550	236	35	point	point	NOUN
ejpam-4550	236	36	e0	e0	PROPN
ejpam-4550	236	37	is	be	AUX
ejpam-4550	236	38	locally	locally	ADV
ejpam-4550	236	39	asymptotically	asymptotically	ADV
ejpam-4550	236	40	stable	stable	ADJ
ejpam-4550	236	41	if	if	SCONJ
ejpam-4550	236	42	r0	r0	NOUN
ejpam-4550	236	43	<	<	X
ejpam-4550	236	44	1	1	NUM
ejpam-4550	236	45	.	.	PUNCT
ejpam-4550	237	1	we	we	PRON
ejpam-4550	237	2	will	will	AUX
ejpam-4550	237	3	now	now	ADV
ejpam-4550	237	4	prove	prove	VERB
ejpam-4550	237	5	that	that	SCONJ
ejpam-4550	237	6	,	,	PUNCT
ejpam-4550	237	7	independently	independently	ADV
ejpam-4550	237	8	of	of	ADP
ejpam-4550	237	9	the	the	DET
ejpam-4550	237	10	initial	initial	ADJ
ejpam-4550	237	11	population	population	NOUN
ejpam-4550	237	12	size	size	NOUN
ejpam-4550	237	13	,	,	PUNCT
ejpam-4550	237	14	if	if	SCONJ
ejpam-4550	237	15	r0	r0	NOUN
ejpam-4550	237	16	<	<	X
ejpam-4550	237	17	1	1	NUM
ejpam-4550	237	18	,	,	PUNCT
ejpam-4550	237	19	then	then	ADV
ejpam-4550	237	20	the	the	DET
ejpam-4550	237	21	disease	disease	NOUN
ejpam-4550	237	22	will	will	AUX
ejpam-4550	237	23	die	die	VERB
ejpam-4550	237	24	out	out	ADP
ejpam-4550	237	25	.	.	PUNCT
ejpam-4550	238	1	let	let	VERB
ejpam-4550	238	2	us	we	PRON
ejpam-4550	238	3	define	define	VERB
ejpam-4550	238	4	:	:	PUNCT
ejpam-4550	239	1	x1	x1	PROPN
ejpam-4550	239	2	=	=	SYM
ejpam-4550	239	3	b	b	PROPN
ejpam-4550	239	4	κ1	κ1	NOUN
ejpam-4550	239	5	−	−	PROPN
ejpam-4550	239	6	s1	s1	NOUN
ejpam-4550	239	7	and	and	CCONJ
ejpam-4550	239	8	x2	x2	NOUN
ejpam-4550	239	9	=	=	PUNCT
ejpam-4550	239	10	γ	γ	PROPN
ejpam-4550	239	11	κ2	κ2	PROPN
ejpam-4550	239	12	−	−	PROPN
ejpam-4550	239	13	s2	s2	PROPN
ejpam-4550	239	14	.	.	PUNCT
ejpam-4550	240	1	the	the	DET
ejpam-4550	240	2	system	system	NOUN
ejpam-4550	240	3	(	(	PUNCT
ejpam-4550	240	4	5	5	X
ejpam-4550	240	5	)	)	PUNCT
ejpam-4550	240	6	becomes	become	VERB
ejpam-4550	240	7	:	:	PUNCT
ejpam-4550	240	8	m.	m.	NOUN
ejpam-4550	240	9	alassane	alassane	NOUN
ejpam-4550	240	10	et	et	PROPN
ejpam-4550	240	11	al	al	PROPN
ejpam-4550	240	12	.	.	PUNCT
ejpam-4550	240	13	/	/	SYM
ejpam-4550	240	14	eur	eur	PROPN
ejpam-4550	240	15	.	.	PUNCT
ejpam-4550	241	1	j.	j.	PROPN
ejpam-4550	241	2	pure	pure	PROPN
ejpam-4550	241	3	appl	appl	PROPN
ejpam-4550	241	4	.	.	PROPN
ejpam-4550	241	5	math	math	PROPN
ejpam-4550	241	6	,	,	PUNCT
ejpam-4550	241	7	16	16	NUM
ejpam-4550	241	8	(	(	PUNCT
ejpam-4550	241	9	1	1	NUM
ejpam-4550	241	10	)	)	PUNCT
ejpam-4550	241	11	(	(	PUNCT
ejpam-4550	241	12	2023	2023	NUM
ejpam-4550	241	13	)	)	PUNCT
ejpam-4550	241	14	,	,	PUNCT
ejpam-4550	241	15	207	207	NUM
ejpam-4550	241	16	-	-	SYM
ejpam-4550	241	17	232	232	NUM
ejpam-4550	241	18	221	221	NUM
ejpam-4550	241	19			PROPN
ejpam-4550	242	1	d	d	NOUN
ejpam-4550	242	2	x1	x1	NOUN
ejpam-4550	243	1	dt	dt	X
ejpam-4550	244	1	=	=	PUNCT
ejpam-4550	245	1	(	(	PUNCT
ejpam-4550	245	2	b	b	NUM
ejpam-4550	245	3	κ1	κ1	NOUN
ejpam-4550	245	4	−	−	PROPN
ejpam-4550	245	5	x1	x1	PROPN
ejpam-4550	245	6	)	)	PUNCT
ejpam-4550	245	7	β1	β1	VERB
ejpam-4550	245	8	3∑	3∑	NUM
ejpam-4550	246	1	j=1	j=1	NOUN
ejpam-4550	246	2	ij1	ij1	NOUN
ejpam-4550	246	3	+	+	CCONJ
ejpam-4550	246	4	β2	β2	NOUN
ejpam-4550	246	5	3∑	3∑	NUM
ejpam-4550	246	6	j=1	j=1	NOUN
ejpam-4550	246	7	ij2	ij2	NOUN
ejpam-4550	246	8	−	−	ADP
ejpam-4550	246	9	κ1x1	κ1x1	NOUN
ejpam-4550	246	10	d	d	NOUN
ejpam-4550	246	11	i11	i11	NOUN
ejpam-4550	246	12	dt	dt	X
ejpam-4550	246	13	=	=	PUNCT
ejpam-4550	246	14	(	(	PUNCT
ejpam-4550	246	15	b	b	NUM
ejpam-4550	246	16	κ1	κ1	NOUN
ejpam-4550	246	17	−	−	PROPN
ejpam-4550	246	18	x1	x1	PROPN
ejpam-4550	246	19	)	)	PUNCT
ejpam-4550	246	20	β1	β1	VERB
ejpam-4550	247	1	3∑	3∑	NUM
ejpam-4550	247	2	j=1	j=1	NOUN
ejpam-4550	247	3	ij1	ij1	NOUN
ejpam-4550	247	4	+	+	CCONJ
ejpam-4550	247	5	β2	β2	NOUN
ejpam-4550	247	6	3∑	3∑	NUM
ejpam-4550	247	7	j=1	j=1	NOUN
ejpam-4550	247	8	ij2	ij2	X
ejpam-4550	247	9	−	−	ADP
ejpam-4550	247	10	κ2i	κ2i	PROPN
ejpam-4550	247	11	1	1	NUM
ejpam-4550	247	12	1	1	NUM
ejpam-4550	247	13	d	d	NOUN
ejpam-4550	247	14	i21	i21	NOUN
ejpam-4550	247	15	dt	dt	NOUN
ejpam-4550	247	16	=	=	PUNCT
ejpam-4550	247	17	a1i	a1i	VERB
ejpam-4550	247	18	1	1	NUM
ejpam-4550	247	19	1	1	NUM
ejpam-4550	247	20	−	−	NUM
ejpam-4550	247	21	κ3i	κ3i	NOUN
ejpam-4550	247	22	2	2	NUM
ejpam-4550	247	23	1	1	NUM
ejpam-4550	247	24	d	d	NOUN
ejpam-4550	247	25	i31	i31	NOUN
ejpam-4550	247	26	dt	dt	NOUN
ejpam-4550	247	27	=	=	NOUN
ejpam-4550	248	1	a2i	a2i	NOUN
ejpam-4550	248	2	2	2	NUM
ejpam-4550	248	3	1	1	NUM
ejpam-4550	248	4	−	−	NOUN
ejpam-4550	248	5	κ4i	κ4i	NOUN
ejpam-4550	248	6	3	3	NUM
ejpam-4550	248	7	1	1	NUM
ejpam-4550	248	8	d	d	NOUN
ejpam-4550	248	9	x2	x2	NOUN
ejpam-4550	248	10	dt	dt	NOUN
ejpam-4550	248	11	=	=	SYM
ejpam-4550	248	12	−γ	−γ	NOUN
ejpam-4550	248	13	(	(	PUNCT
ejpam-4550	248	14	b	b	NUM
ejpam-4550	248	15	κ1	κ1	NOUN
ejpam-4550	248	16	−	−	PROPN
ejpam-4550	248	17	x1	x1	PROPN
ejpam-4550	248	18	)	)	PUNCT
ejpam-4550	249	1	+	+	CCONJ
ejpam-4550	249	2	(	(	PUNCT
ejpam-4550	249	3	γ	γ	X
ejpam-4550	249	4	κ1	κ1	NOUN
ejpam-4550	249	5	−	−	PROPN
ejpam-4550	249	6	x2	x2	PROPN
ejpam-4550	249	7	)	)	PUNCT
ejpam-4550	249	8	β1	β1	VERB
ejpam-4550	250	1	3∑	3∑	NUM
ejpam-4550	250	2	j=1	j=1	NOUN
ejpam-4550	250	3	ij1	ij1	NOUN
ejpam-4550	250	4	+	+	CCONJ
ejpam-4550	250	5	β2	β2	NOUN
ejpam-4550	250	6	3∑	3∑	NUM
ejpam-4550	250	7	j=1	j=1	NOUN
ejpam-4550	250	8	ij2	ij2	PROPN
ejpam-4550	250	9	−	−	ADV
ejpam-4550	250	10	bx2	bx2	PROPN
ejpam-4550	251	1	d	d	X
ejpam-4550	251	2	i12	i12	NOUN
ejpam-4550	252	1	dt	dt	PROPN
ejpam-4550	253	1	=	=	PUNCT
ejpam-4550	253	2	(	(	PUNCT
ejpam-4550	253	3	γ	γ	X
ejpam-4550	253	4	κ1	κ1	NOUN
ejpam-4550	253	5	−	−	PROPN
ejpam-4550	253	6	x2	x2	PROPN
ejpam-4550	253	7	)	)	PUNCT
ejpam-4550	253	8	β1	β1	VERB
ejpam-4550	253	9	3∑	3∑	NUM
ejpam-4550	253	10	j=1	j=1	NOUN
ejpam-4550	253	11	ij1	ij1	NOUN
ejpam-4550	253	12	+	+	CCONJ
ejpam-4550	253	13	β2	β2	NOUN
ejpam-4550	254	1	3∑	3∑	NUM
ejpam-4550	254	2	j=1	j=1	NOUN
ejpam-4550	254	3	ij2	ij2	NOUN
ejpam-4550	254	4	−	−	PUNCT
ejpam-4550	255	1	κ5i	κ5i	PUNCT
ejpam-4550	256	1	1	1	NUM
ejpam-4550	256	2	2	2	NUM
ejpam-4550	256	3	+	+	CCONJ
ejpam-4550	256	4	c1i	c1i	ADJ
ejpam-4550	256	5	1	1	NUM
ejpam-4550	256	6	1	1	NUM
ejpam-4550	256	7	d	d	NOUN
ejpam-4550	256	8	i22	i22	NOUN
ejpam-4550	256	9	dt	dt	NOUN
ejpam-4550	257	1	=	=	SYM
ejpam-4550	257	2	a3i	a3i	SYM
ejpam-4550	257	3	1	1	NUM
ejpam-4550	257	4	2	2	NUM
ejpam-4550	257	5	−	−	NOUN
ejpam-4550	257	6	κ6i	κ6i	PROPN
ejpam-4550	257	7	2	2	NUM
ejpam-4550	257	8	2	2	NUM
ejpam-4550	257	9	+	+	CCONJ
ejpam-4550	257	10	c2i	c2i	X
ejpam-4550	257	11	2	2	NUM
ejpam-4550	257	12	1	1	NUM
ejpam-4550	257	13	d	d	NOUN
ejpam-4550	257	14	i32	i32	NOUN
ejpam-4550	257	15	dt	dt	PROPN
ejpam-4550	258	1	=	=	SYM
ejpam-4550	258	2	a4i	a4i	PROPN
ejpam-4550	258	3	2	2	NUM
ejpam-4550	258	4	2	2	NUM
ejpam-4550	258	5	−	−	PROPN
ejpam-4550	258	6	b	b	PROPN
ejpam-4550	258	7	i32	i32	NOUN
ejpam-4550	258	8	+	+	CCONJ
ejpam-4550	258	9	c3i	c3i	NOUN
ejpam-4550	258	10	3	3	NUM
ejpam-4550	258	11	1	1	NUM
ejpam-4550	258	12	(	(	PUNCT
ejpam-4550	258	13	20	20	NUM
ejpam-4550	258	14	)	)	PUNCT
ejpam-4550	258	15	e0	e0	PROPN
ejpam-4550	258	16	(	(	PUNCT
ejpam-4550	258	17	b	b	PROPN
ejpam-4550	258	18	κ1	κ1	NOUN
ejpam-4550	258	19	,	,	PUNCT
ejpam-4550	258	20	0	0	NUM
ejpam-4550	258	21	,	,	PUNCT
ejpam-4550	258	22	0	0	NUM
ejpam-4550	258	23	,	,	PUNCT
ejpam-4550	258	24	0	0	NUM
ejpam-4550	258	25	,	,	PUNCT
ejpam-4550	258	26	γ	γ	NOUN
ejpam-4550	258	27	κ1	κ1	NOUN
ejpam-4550	258	28	,	,	PUNCT
ejpam-4550	258	29	0	0	NUM
ejpam-4550	258	30	,	,	PUNCT
ejpam-4550	258	31	0	0	NUM
ejpam-4550	258	32	,	,	PUNCT
ejpam-4550	258	33	0	0	NUM
ejpam-4550	258	34	)	)	PUNCT
ejpam-4550	258	35	is	be	AUX
ejpam-4550	258	36	globally	globally	ADV
ejpam-4550	258	37	asymptotically	asymptotically	ADV
ejpam-4550	258	38	stable	stable	ADJ
ejpam-4550	258	39	for	for	ADP
ejpam-4550	258	40	system	system	NOUN
ejpam-4550	258	41	(	(	PUNCT
ejpam-4550	258	42	5	5	NUM
ejpam-4550	258	43	)	)	PUNCT
ejpam-4550	258	44	if	if	SCONJ
ejpam-4550	259	1	and	and	CCONJ
ejpam-4550	259	2	only	only	ADV
ejpam-4550	259	3	if	if	SCONJ
ejpam-4550	259	4	e0	e0	PROPN
ejpam-4550	259	5	(	(	PUNCT
ejpam-4550	259	6	0	0	NUM
ejpam-4550	259	7	,	,	PUNCT
ejpam-4550	259	8	0	0	NUM
ejpam-4550	259	9	,	,	PUNCT
ejpam-4550	259	10	0	0	NUM
ejpam-4550	259	11	,	,	PUNCT
ejpam-4550	259	12	0	0	NUM
ejpam-4550	259	13	,	,	PUNCT
ejpam-4550	259	14	0	0	NUM
ejpam-4550	259	15	,	,	PUNCT
ejpam-4550	259	16	0	0	NUM
ejpam-4550	259	17	,	,	PUNCT
ejpam-4550	259	18	0	0	NUM
ejpam-4550	259	19	,	,	PUNCT
ejpam-4550	259	20	0	0	NUM
ejpam-4550	259	21	)	)	PUNCT
ejpam-4550	259	22	is	be	AUX
ejpam-4550	259	23	globally	globally	ADV
ejpam-4550	259	24	asymptotically	asymptotically	ADV
ejpam-4550	259	25	stable	stable	ADJ
ejpam-4550	259	26	for	for	ADP
ejpam-4550	259	27	system	system	NOUN
ejpam-4550	259	28	(	(	PUNCT
ejpam-4550	259	29	20	20	NUM
ejpam-4550	259	30	)	)	PUNCT
ejpam-4550	259	31	.	.	PUNCT
ejpam-4550	260	1	theorem	theorem	VERB
ejpam-4550	260	2	3	3	X
ejpam-4550	260	3	.	.	PUNCT
ejpam-4550	261	1	if	if	SCONJ
ejpam-4550	261	2	r0	r0	NOUN
ejpam-4550	261	3	<	<	X
ejpam-4550	261	4	1	1	NUM
ejpam-4550	261	5	,	,	PUNCT
ejpam-4550	261	6	then	then	ADV
ejpam-4550	261	7	the	the	DET
ejpam-4550	261	8	disease	disease	NOUN
ejpam-4550	261	9	-	-	PUNCT
ejpam-4550	261	10	free	free	ADJ
ejpam-4550	261	11	equilibrium	equilibrium	NOUN
ejpam-4550	261	12	point	point	NOUN
ejpam-4550	261	13	e0	e0	PROPN
ejpam-4550	261	14	(	(	PUNCT
ejpam-4550	261	15	0	0	NUM
ejpam-4550	261	16	,	,	PUNCT
ejpam-4550	261	17	0	0	NUM
ejpam-4550	261	18	,	,	PUNCT
ejpam-4550	261	19	0	0	NUM
ejpam-4550	261	20	,	,	PUNCT
ejpam-4550	261	21	0	0	NUM
ejpam-4550	261	22	,	,	PUNCT
ejpam-4550	261	23	0	0	NUM
ejpam-4550	261	24	,	,	PUNCT
ejpam-4550	261	25	0	0	NUM
ejpam-4550	261	26	,	,	PUNCT
ejpam-4550	261	27	0	0	NUM
ejpam-4550	261	28	,	,	PUNCT
ejpam-4550	261	29	0	0	NUM
ejpam-4550	261	30	)	)	PUNCT
ejpam-4550	261	31	is	be	AUX
ejpam-4550	261	32	globally	globally	ADV
ejpam-4550	261	33	asymptotically	asymptotically	ADV
ejpam-4550	261	34	stable	stable	ADJ
ejpam-4550	261	35	for	for	ADP
ejpam-4550	261	36	the	the	DET
ejpam-4550	261	37	system	system	NOUN
ejpam-4550	261	38	(	(	PUNCT
ejpam-4550	261	39	20	20	NUM
ejpam-4550	261	40	)	)	PUNCT
ejpam-4550	261	41	.	.	PUNCT
ejpam-4550	262	1	proof	proof	NOUN
ejpam-4550	262	2	.	.	PUNCT
ejpam-4550	263	1	consider	consider	VERB
ejpam-4550	263	2	the	the	DET
ejpam-4550	263	3	following	follow	VERB
ejpam-4550	263	4	function	function	NOUN
ejpam-4550	263	5	v	v	NOUN
ejpam-4550	263	6	:	:	PUNCT
ejpam-4550	264	1	γ	γ	X
ejpam-4550	264	2	−→	−→	NOUN
ejpam-4550	264	3	r+	r+	NOUN
ejpam-4550	264	4	defined	define	VERB
ejpam-4550	264	5	by	by	ADP
ejpam-4550	264	6	:	:	PUNCT
ejpam-4550	264	7	v	v	NOUN
ejpam-4550	264	8	=	=	SYM
ejpam-4550	264	9	κ−1	κ−1	PROPN
ejpam-4550	264	10	2	2	NUM
ejpam-4550	264	11	(m7	(m7	NOUN
ejpam-4550	264	12	−	−	NOUN
ejpam-4550	264	13	γm4	γm4	NOUN
ejpam-4550	264	14	)	)	PUNCT
ejpam-4550	264	15	i	i	NOUN
ejpam-4550	264	16	1	1	NUM
ejpam-4550	264	17	1	1	NUM
ejpam-4550	264	18	+	+	SYM
ejpam-4550	264	19	b	b	PROPN
ejpam-4550	264	20	m2i	m2i	PROPN
ejpam-4550	264	21	2	2	NUM
ejpam-4550	264	22	1	1	NUM
ejpam-4550	264	23	+	+	ADV
ejpam-4550	264	24	m4i	m4i	NOUN
ejpam-4550	264	25	1	1	NUM
ejpam-4550	264	26	2	2	NUM
ejpam-4550	264	27	+	+	NOUN
ejpam-4550	264	28	m5i	m5i	NOUN
ejpam-4550	264	29	2	2	NUM
ejpam-4550	264	30	2	2	NUM
ejpam-4550	264	31	+	+	CCONJ
ejpam-4550	264	32	(	(	PUNCT
ejpam-4550	264	33	m3	m3	PROPN
ejpam-4550	264	34	+	+	PROPN
ejpam-4550	264	35	m6	m6	ADJ
ejpam-4550	264	36	)	)	PUNCT
ejpam-4550	264	37			PROPN
ejpam-4550	264	38	2∑	2∑	PROPN
ejpam-4550	264	39	j=1	j=1	PROPN
ejpam-4550	264	40	xj	xj	PROPN
ejpam-4550	265	1	−	−	PROPN
ejpam-4550	265	2	3∑	3∑	NUM
ejpam-4550	265	3	j=1	j=1	NOUN
ejpam-4550	265	4	ij1	ij1	NOUN
ejpam-4550	265	5	−	−	NOUN
ejpam-4550	265	6	2∑	2∑	NUM
ejpam-4550	265	7	j=1	j=1	PROPN
ejpam-4550	265	8	ij2	ij2	PROPN
ejpam-4550	265	9			PROPN
ejpam-4550	266	1	m.	m.	NOUN
ejpam-4550	266	2	alassane	alassane	NOUN
ejpam-4550	266	3	et	et	PROPN
ejpam-4550	266	4	al	al	PROPN
ejpam-4550	266	5	.	.	PUNCT
ejpam-4550	266	6	/	/	SYM
ejpam-4550	266	7	eur	eur	PROPN
ejpam-4550	266	8	.	.	PUNCT
ejpam-4550	267	1	j.	j.	PROPN
ejpam-4550	267	2	pure	pure	PROPN
ejpam-4550	267	3	appl	appl	PROPN
ejpam-4550	267	4	.	.	PROPN
ejpam-4550	267	5	math	math	PROPN
ejpam-4550	267	6	,	,	PUNCT
ejpam-4550	267	7	16	16	NUM
ejpam-4550	267	8	(	(	PUNCT
ejpam-4550	267	9	1	1	NUM
ejpam-4550	267	10	)	)	PUNCT
ejpam-4550	267	11	(	(	PUNCT
ejpam-4550	267	12	2023	2023	NUM
ejpam-4550	267	13	)	)	PUNCT
ejpam-4550	267	14	,	,	PUNCT
ejpam-4550	267	15	207	207	NUM
ejpam-4550	267	16	-	-	SYM
ejpam-4550	267	17	232	232	NUM
ejpam-4550	267	18	222	222	NUM
ejpam-4550	267	19	if	if	SCONJ
ejpam-4550	267	20	r0	r0	VERB
ejpam-4550	267	21	<	<	X
ejpam-4550	267	22	1	1	NUM
ejpam-4550	267	23	,	,	PUNCT
ejpam-4550	267	24	then	then	ADV
ejpam-4550	267	25	m7	m7	PROPN
ejpam-4550	267	26	−	−	PROPN
ejpam-4550	267	27	γm4	γm4	NOUN
ejpam-4550	267	28	,	,	PUNCT
ejpam-4550	267	29	m2	m2	PROPN
ejpam-4550	267	30	,	,	PUNCT
ejpam-4550	267	31	m3	m3	PROPN
ejpam-4550	267	32	,	,	PUNCT
ejpam-4550	267	33	m4	m4	PROPN
ejpam-4550	267	34	,	,	PUNCT
ejpam-4550	267	35	m5	m5	PROPN
ejpam-4550	267	36	and	and	CCONJ
ejpam-4550	267	37	m6	m6	PROPN
ejpam-4550	267	38	are	be	AUX
ejpam-4550	267	39	positive	positive	ADJ
ejpam-4550	267	40	.	.	PUNCT
ejpam-4550	268	1	consequently	consequently	ADV
ejpam-4550	268	2	,	,	PUNCT
ejpam-4550	268	3	the	the	DET
ejpam-4550	268	4	function	function	NOUN
ejpam-4550	268	5	v	v	NOUN
ejpam-4550	268	6	is	be	AUX
ejpam-4550	268	7	positive	positive	ADJ
ejpam-4550	268	8	and	and	CCONJ
ejpam-4550	268	9	vanishes	vanish	VERB
ejpam-4550	268	10	at	at	ADP
ejpam-4550	268	11	the	the	DET
ejpam-4550	268	12	disease	disease	NOUN
ejpam-4550	268	13	-	-	PUNCT
ejpam-4550	268	14	free	free	ADJ
ejpam-4550	268	15	equilibrium	equilibrium	NOUN
ejpam-4550	268	16	.	.	PUNCT
ejpam-4550	269	1	the	the	DET
ejpam-4550	269	2	derivative	derivative	NOUN
ejpam-4550	269	3	of	of	ADP
ejpam-4550	269	4	this	this	PRON
ejpam-4550	269	5	lyapunov	lyapunov	NOUN
ejpam-4550	269	6	function	function	VERB
ejpam-4550	269	7	v	v	ADP
ejpam-4550	269	8	along	along	ADP
ejpam-4550	269	9	the	the	DET
ejpam-4550	269	10	trajectories	trajectory	NOUN
ejpam-4550	269	11	of	of	ADP
ejpam-4550	269	12	the	the	DET
ejpam-4550	269	13	ordinary	ordinary	ADJ
ejpam-4550	269	14	differential	differential	NOUN
ejpam-4550	269	15	system	system	NOUN
ejpam-4550	269	16	is	be	AUX
ejpam-4550	269	17	v̇	v̇	NOUN
ejpam-4550	269	18	=	=	PUNCT
ejpam-4550	269	19	κ−1	κ−1	PROPN
ejpam-4550	269	20	2	2	NUM
ejpam-4550	269	21	(	(	PUNCT
ejpam-4550	269	22	m7	m7	PROPN
ejpam-4550	269	23	−	−	PROPN
ejpam-4550	269	24	κγm4	κγm4	PROPN
ejpam-4550	269	25	)	)	PUNCT
ejpam-4550	269	26	(bκ−1	(bκ−1	NOUN
ejpam-4550	269	27	1	1	NUM
ejpam-4550	270	1	−	−	NOUN
ejpam-4550	271	1	x1	x1	PROPN
ejpam-4550	271	2	)	)	PUNCT
ejpam-4550	271	3	β1	β1	VERB
ejpam-4550	271	4	3∑	3∑	NUM
ejpam-4550	272	1	j=1	j=1	NOUN
ejpam-4550	272	2	ij1	ij1	NOUN
ejpam-4550	272	3	+	+	CCONJ
ejpam-4550	272	4	β2	β2	NOUN
ejpam-4550	272	5	3∑	3∑	NUM
ejpam-4550	272	6	j=1	j=1	NOUN
ejpam-4550	272	7	ij2	ij2	X
ejpam-4550	272	8	−	−	ADP
ejpam-4550	272	9	κ2i	κ2i	PROPN
ejpam-4550	272	10	1	1	NUM
ejpam-4550	272	11	1	1	NUM
ejpam-4550	272	12	+	+	PROPN
ejpam-4550	272	13	bκ−1	bκ−1	PROPN
ejpam-4550	272	14	2	2	NUM
ejpam-4550	272	15	m2	m2	PROPN
ejpam-4550	272	16	(	(	PUNCT
ejpam-4550	272	17	a1i	a1i	VERB
ejpam-4550	272	18	1	1	NUM
ejpam-4550	272	19	1	1	NUM
ejpam-4550	272	20	−	−	NUM
ejpam-4550	272	21	κ3i	κ3i	NOUN
ejpam-4550	272	22	2	2	NUM
ejpam-4550	272	23	1	1	NUM
ejpam-4550	272	24	)	)	PUNCT
ejpam-4550	272	25	+	+	CCONJ
ejpam-4550	272	26	bκ−1	bκ−1	PROPN
ejpam-4550	272	27	2	2	NUM
ejpam-4550	272	28	m3	m3	PROPN
ejpam-4550	272	29	(	(	PUNCT
ejpam-4550	272	30	a2i	a2i	NOUN
ejpam-4550	272	31	2	2	NUM
ejpam-4550	272	32	1	1	NUM
ejpam-4550	272	33	−	−	NOUN
ejpam-4550	272	34	κ4i	κ4i	NOUN
ejpam-4550	272	35	3	3	NUM
ejpam-4550	272	36	1	1	NUM
ejpam-4550	272	37	)	)	PUNCT
ejpam-4550	272	38	+	+	CCONJ
ejpam-4550	272	39	bκ−1	bκ−1	PROPN
ejpam-4550	272	40	2	2	NUM
ejpam-4550	272	41	m4	m4	PROPN
ejpam-4550	272	42	(γκ−1	(γκ−1	NOUN
ejpam-4550	272	43	1	1	NUM
ejpam-4550	272	44	−	−	PROPN
ejpam-4550	272	45	x2	x2	PROPN
ejpam-4550	272	46	)	)	PUNCT
ejpam-4550	272	47	β1	β1	NOUN
ejpam-4550	272	48	3∑	3∑	NUM
ejpam-4550	272	49	j=1	j=1	NOUN
ejpam-4550	272	50	ij1	ij1	NOUN
ejpam-4550	272	51	+	+	CCONJ
ejpam-4550	272	52	β2	β2	NOUN
ejpam-4550	273	1	3∑	3∑	NUM
ejpam-4550	273	2	j=1	j=1	NOUN
ejpam-4550	273	3	ij2	ij2	NOUN
ejpam-4550	273	4	−	−	PUNCT
ejpam-4550	274	1	κ5i	κ5i	PUNCT
ejpam-4550	275	1	1	1	NUM
ejpam-4550	275	2	2	2	NUM
ejpam-4550	275	3	+	+	CCONJ
ejpam-4550	275	4	c1i	c1i	ADJ
ejpam-4550	275	5	1	1	NUM
ejpam-4550	275	6	1	1	NUM
ejpam-4550	275	7			NOUN
ejpam-4550	275	8	+	+	CCONJ
ejpam-4550	275	9	bκ−1	bκ−1	PROPN
ejpam-4550	275	10	2	2	NUM
ejpam-4550	275	11	m5	m5	PROPN
ejpam-4550	275	12	(	(	PUNCT
ejpam-4550	275	13	a3ii	a3ii	NOUN
ejpam-4550	275	14	1	1	NUM
ejpam-4550	275	15	2	2	NUM
ejpam-4550	275	16	−	−	NOUN
ejpam-4550	275	17	κ6i	κ6i	PROPN
ejpam-4550	275	18	2	2	NUM
ejpam-4550	275	19	2	2	NUM
ejpam-4550	275	20	+	+	CCONJ
ejpam-4550	275	21	c2i	c2i	X
ejpam-4550	275	22	2	2	NUM
ejpam-4550	275	23	1	1	NUM
ejpam-4550	275	24	)	)	PUNCT
ejpam-4550	275	25	+	+	CCONJ
ejpam-4550	275	26	bκ−1	bκ−1	PROPN
ejpam-4550	275	27	2	2	PROPN
ejpam-4550	275	28	m6	m6	PROPN
ejpam-4550	275	29	(	(	PUNCT
ejpam-4550	275	30	a4i	a4i	PROPN
ejpam-4550	275	31	2	2	NUM
ejpam-4550	275	32	2	2	NUM
ejpam-4550	275	33	−	−	ADP
ejpam-4550	275	34	bi32	bi32	PROPN
ejpam-4550	275	35	+	+	NUM
ejpam-4550	275	36	c3i	c3i	NOUN
ejpam-4550	275	37	3	3	NUM
ejpam-4550	275	38	1	1	NUM
ejpam-4550	275	39	)	)	PUNCT
ejpam-4550	275	40	.	.	PUNCT
ejpam-4550	276	1	we	we	PRON
ejpam-4550	276	2	can	can	AUX
ejpam-4550	276	3	also	also	ADV
ejpam-4550	276	4	write	write	VERB
ejpam-4550	276	5	v̇	v̇	NOUN
ejpam-4550	276	6	=	=	PUNCT
ejpam-4550	276	7	κ−1	κ−1	PROPN
ejpam-4550	276	8	2	2	NUM
ejpam-4550	276	9	(	(	PUNCT
ejpam-4550	276	10	m7	m7	NOUN
ejpam-4550	276	11	−	−	PROPN
ejpam-4550	276	12	γm4	γm4	PROPN
ejpam-4550	276	13	)	)	PUNCT
ejpam-4550	276	14	b	b	NOUN
ejpam-4550	276	15	κ1	κ1	NOUN
ejpam-4550	276	16	β1	β1	VERB
ejpam-4550	276	17	3∑	3∑	NUM
ejpam-4550	277	1	j=1	j=1	NOUN
ejpam-4550	277	2	ij1	ij1	NOUN
ejpam-4550	277	3	+	+	CCONJ
ejpam-4550	277	4	β2	β2	NOUN
ejpam-4550	277	5	3∑	3∑	NUM
ejpam-4550	277	6	j=1	j=1	NOUN
ejpam-4550	277	7	ij2	ij2	NOUN
ejpam-4550	277	8	−	−	ADP
ejpam-4550	278	1	κ−1	κ−1	PROPN
ejpam-4550	278	2	2	2	NUM
ejpam-4550	278	3	(	(	PUNCT
ejpam-4550	278	4	m7	m7	NOUN
ejpam-4550	278	5	−	−	PROPN
ejpam-4550	278	6	γm4	γm4	PROPN
ejpam-4550	278	7	)	)	PUNCT
ejpam-4550	278	8	β1	β1	VERB
ejpam-4550	278	9	3∑	3∑	NUM
ejpam-4550	278	10	j=1	j=1	NOUN
ejpam-4550	278	11	ij1	ij1	NOUN
ejpam-4550	278	12	+	+	CCONJ
ejpam-4550	278	13	β2	β2	NOUN
ejpam-4550	278	14	3∑	3∑	NUM
ejpam-4550	278	15	j=1	j=1	NOUN
ejpam-4550	278	16	ij2	ij2	NOUN
ejpam-4550	279	1			PROPN
ejpam-4550	279	2	x1	x1	PRON
ejpam-4550	279	3	−	−	PROPN
ejpam-4550	280	1	(	(	PUNCT
ejpam-4550	280	2	m7	m7	PROPN
ejpam-4550	280	3	−	−	PROPN
ejpam-4550	280	4	γm4	γm4	PROPN
ejpam-4550	280	5	)	)	PUNCT
ejpam-4550	281	1	i	i	NOUN
ejpam-4550	281	2	1	1	NUM
ejpam-4550	281	3	1	1	NUM
ejpam-4550	281	4	+	+	CCONJ
ejpam-4550	281	5	bκ−1	bκ−1	PROPN
ejpam-4550	281	6	2	2	NUM
ejpam-4550	281	7	m2a1i	m2a1i	NUM
ejpam-4550	281	8	1	1	NUM
ejpam-4550	281	9	1	1	NUM
ejpam-4550	281	10	−	−	NOUN
ejpam-4550	281	11	bκ−1	bκ−1	PROPN
ejpam-4550	281	12	2	2	NUM
ejpam-4550	281	13	m2κ3i	m2κ3i	NUM
ejpam-4550	281	14	2	2	NUM
ejpam-4550	281	15	1	1	NUM
ejpam-4550	281	16	+	+	CCONJ
ejpam-4550	281	17	bκ−1	bκ−1	PROPN
ejpam-4550	281	18	2	2	NUM
ejpam-4550	281	19	m3a2i	m3a2i	SYM
ejpam-4550	281	20	2	2	NUM
ejpam-4550	281	21	1	1	NUM
ejpam-4550	281	22	−	−	NOUN
ejpam-4550	281	23	bκ−1	bκ−1	PROPN
ejpam-4550	281	24	2	2	NUM
ejpam-4550	281	25	m3κ4i	m3κ4i	NUM
ejpam-4550	281	26	3	3	NUM
ejpam-4550	281	27	1	1	NUM
ejpam-4550	281	28	−	−	NOUN
ejpam-4550	281	29	bκ−1	bκ−1	PROPN
ejpam-4550	281	30	2	2	NUM
ejpam-4550	281	31	m4κ5i	m4κ5i	SYM
ejpam-4550	281	32	1	1	NUM
ejpam-4550	281	33	2	2	NUM
ejpam-4550	281	34	+	+	NOUN
ejpam-4550	281	35	bκ−1	bκ−1	PROPN
ejpam-4550	281	36	2	2	NUM
ejpam-4550	281	37	γm4κ1	γm4κ1	PROPN
ejpam-4550	281	38	−1	−1	NOUN
ejpam-4550	281	39	β1	β1	VERB
ejpam-4550	281	40	3∑	3∑	NUM
ejpam-4550	281	41	j=1	j=1	NOUN
ejpam-4550	281	42	ij1	ij1	NOUN
ejpam-4550	281	43	+	+	CCONJ
ejpam-4550	281	44	β2	β2	NOUN
ejpam-4550	281	45	3∑	3∑	NUM
ejpam-4550	281	46	j=1	j=1	NOUN
ejpam-4550	281	47	ij2	ij2	PROPN
ejpam-4550	281	48	−	−	ADP
ejpam-4550	281	49	bκ−1	bκ−1	PROPN
ejpam-4550	281	50	2	2	NUM
ejpam-4550	281	51	m4	m4	PROPN
ejpam-4550	281	52	β1	β1	NOUN
ejpam-4550	281	53	3∑	3∑	NUM
ejpam-4550	281	54	j=1	j=1	NOUN
ejpam-4550	281	55	ij1	ij1	NOUN
ejpam-4550	281	56	+	+	CCONJ
ejpam-4550	281	57	β2	β2	NOUN
ejpam-4550	282	1	3∑	3∑	NUM
ejpam-4550	282	2	j=1	j=1	NOUN
ejpam-4550	282	3	ij2	ij2	NOUN
ejpam-4550	282	4			PROPN
ejpam-4550	283	1	x2	x2	PROPN
ejpam-4550	284	1	+	+	CCONJ
ejpam-4550	284	2	bκ−1	bκ−1	PROPN
ejpam-4550	284	3	2	2	NUM
ejpam-4550	284	4	m4c1i	m4c1i	NUM
ejpam-4550	284	5	1	1	NUM
ejpam-4550	284	6	1	1	NUM
ejpam-4550	284	7	+	+	NOUN
ejpam-4550	284	8	bκ−1	bκ−1	PROPN
ejpam-4550	284	9	2	2	NUM
ejpam-4550	284	10	m5a3i	m5a3i	NUM
ejpam-4550	284	11	1	1	NUM
ejpam-4550	284	12	2	2	NUM
ejpam-4550	284	13	−	−	NOUN
ejpam-4550	284	14	bκ−1	bκ−1	PROPN
ejpam-4550	284	15	2	2	NUM
ejpam-4550	284	16	m5κ6i	m5κ6i	NUM
ejpam-4550	284	17	2	2	NUM
ejpam-4550	284	18	2	2	NUM
ejpam-4550	284	19	+	+	CCONJ
ejpam-4550	284	20	bκ−1	bκ−1	PROPN
ejpam-4550	284	21	2	2	NUM
ejpam-4550	284	22	m5c2i	m5c2i	NUM
ejpam-4550	284	23	2	2	NUM
ejpam-4550	284	24	1	1	NUM
ejpam-4550	284	25	+	+	CCONJ
ejpam-4550	284	26	bκ−1	bκ−1	PROPN
ejpam-4550	284	27	2	2	NUM
ejpam-4550	284	28	m6a4i	m6a4i	NUM
ejpam-4550	284	29	2	2	NUM
ejpam-4550	284	30	2	2	NUM
ejpam-4550	284	31	−	−	NOUN
ejpam-4550	284	32	bκ−1	bκ−1	PROPN
ejpam-4550	284	33	2	2	NUM
ejpam-4550	284	34	m6bi	m6bi	SYM
ejpam-4550	284	35	3	3	NUM
ejpam-4550	284	36	2	2	NUM
ejpam-4550	284	37	+	+	CCONJ
ejpam-4550	284	38	bκ−1	bκ−1	PROPN
ejpam-4550	284	39	2	2	NUM
ejpam-4550	284	40	m6γ3i	m6γ3i	NOUN
ejpam-4550	284	41	3	3	NUM
ejpam-4550	284	42	2	2	NUM
ejpam-4550	284	43	.	.	PUNCT
ejpam-4550	285	1	following	follow	VERB
ejpam-4550	285	2	algebraic	algebraic	ADJ
ejpam-4550	285	3	manipulations	manipulation	NOUN
ejpam-4550	285	4	,	,	PUNCT
ejpam-4550	285	5	it	it	PRON
ejpam-4550	285	6	holds	hold	VERB
ejpam-4550	285	7	:	:	PUNCT
ejpam-4550	286	1	v̇	v̇	NOUN
ejpam-4550	286	2	=	=	SYM
ejpam-4550	286	3	−κ−1	−κ−1	NUM
ejpam-4550	286	4	2	2	NUM
ejpam-4550	286	5	(	(	PUNCT
ejpam-4550	286	6	m7	m7	NOUN
ejpam-4550	286	7	−	−	PROPN
ejpam-4550	286	8	γm4	γm4	PROPN
ejpam-4550	286	9	)	)	PUNCT
ejpam-4550	286	10	β1	β1	VERB
ejpam-4550	286	11	3∑	3∑	NUM
ejpam-4550	286	12	j=1	j=1	NOUN
ejpam-4550	286	13	ij1	ij1	NOUN
ejpam-4550	286	14	+	+	CCONJ
ejpam-4550	286	15	β2	β2	NOUN
ejpam-4550	286	16	3∑	3∑	NUM
ejpam-4550	286	17	j=1	j=1	NOUN
ejpam-4550	286	18	ij2	ij2	NOUN
ejpam-4550	287	1			PROPN
ejpam-4550	288	1	x1	x1	DET
ejpam-4550	288	2	−	−	PROPN
ejpam-4550	288	3	bκ−1	bκ−1	PROPN
ejpam-4550	288	4	2	2	NUM
ejpam-4550	288	5	m4	m4	PROPN
ejpam-4550	288	6	β1	β1	NOUN
ejpam-4550	288	7	3∑	3∑	NUM
ejpam-4550	288	8	j=1	j=1	NOUN
ejpam-4550	288	9	ij1	ij1	NOUN
ejpam-4550	288	10	+	+	CCONJ
ejpam-4550	288	11	β2	β2	NOUN
ejpam-4550	288	12	3∑	3∑	NUM
ejpam-4550	288	13	j=1	j=1	NOUN
ejpam-4550	288	14	ij2	ij2	NOUN
ejpam-4550	289	1			PROPN
ejpam-4550	289	2	x2	x2	INTJ
ejpam-4550	290	1	+	+	CCONJ
ejpam-4550	290	2	(	(	PUNCT
ejpam-4550	290	3	−m7	−m7	NOUN
ejpam-4550	290	4	+	+	NUM
ejpam-4550	290	5	γm4	γm4	NOUN
ejpam-4550	290	6	+	+	CCONJ
ejpam-4550	290	7	bκ−1	bκ−1	PROPN
ejpam-4550	290	8	2	2	NUM
ejpam-4550	290	9	m2a1	m2a1	NOUN
ejpam-4550	290	10	+	+	CCONJ
ejpam-4550	290	11	bκ−1	bκ−1	NOUN
ejpam-4550	290	12	2	2	NUM
ejpam-4550	290	13	m4c1	m4c1	NOUN
ejpam-4550	290	14	+	+	CCONJ
ejpam-4550	290	15	β1bκ	β1bκ	PUNCT
ejpam-4550	290	16	−1	−1	NOUN
ejpam-4550	290	17	1	1	NUM
ejpam-4550	290	18	κ−1	κ−1	PROPN
ejpam-4550	290	19	2	2	NUM
ejpam-4550	290	20	m7	m7	NOUN
ejpam-4550	290	21	)	)	PUNCT
ejpam-4550	290	22	i11	i11	NOUN
ejpam-4550	290	23	or	or	CCONJ
ejpam-4550	290	24	v̇	v̇	NOUN
ejpam-4550	290	25	=	=	SYM
ejpam-4550	290	26	−κ−1	−κ−1	NUM
ejpam-4550	290	27	2	2	NUM
ejpam-4550	290	28	(	(	PUNCT
ejpam-4550	290	29	m7	m7	NOUN
ejpam-4550	290	30	−	−	PROPN
ejpam-4550	290	31	γm4	γm4	PROPN
ejpam-4550	290	32	)	)	PUNCT
ejpam-4550	290	33	β1	β1	VERB
ejpam-4550	290	34	3∑	3∑	NUM
ejpam-4550	290	35	j=1	j=1	NOUN
ejpam-4550	290	36	ij1	ij1	NOUN
ejpam-4550	290	37	+	+	CCONJ
ejpam-4550	290	38	β2	β2	NOUN
ejpam-4550	290	39	3∑	3∑	NUM
ejpam-4550	290	40	j=1	j=1	NOUN
ejpam-4550	290	41	ij2	ij2	NOUN
ejpam-4550	291	1			PROPN
ejpam-4550	291	2	x1−bκ−1	x1−bκ−1	PROPN
ejpam-4550	291	3	2	2	NUM
ejpam-4550	291	4	m4	m4	PROPN
ejpam-4550	291	5	(	(	PUNCT
ejpam-4550	291	6	kh	kh	PROPN
ejpam-4550	291	7	+	+	PROPN
ejpam-4550	291	8	kf	kf	PROPN
ejpam-4550	291	9	)	)	PUNCT
ejpam-4550	291	10	x2−(m7	x2−(m7	PROPN
ejpam-4550	291	11	−	−	NOUN
ejpam-4550	291	12	γm4	γm4	ADV
ejpam-4550	291	13	−	−	PROPN
ejpam-4550	292	1	bm1	bm1	PROPN
ejpam-4550	292	2	)	)	PUNCT
ejpam-4550	293	1	i	i	NOUN
ejpam-4550	293	2	1	1	NUM
ejpam-4550	293	3	1	1	NUM
ejpam-4550	293	4	.	.	PUNCT
ejpam-4550	294	1	if	if	SCONJ
ejpam-4550	294	2	r0	r0	NOUN
ejpam-4550	294	3	<	<	X
ejpam-4550	294	4	1	1	NUM
ejpam-4550	294	5	,	,	PUNCT
ejpam-4550	294	6	then	then	ADV
ejpam-4550	294	7	m7	m7	PROPN
ejpam-4550	294	8	−	−	PROPN
ejpam-4550	294	9	κθm4	κθm4	PROPN
ejpam-4550	294	10	and	and	CCONJ
ejpam-4550	294	11	m7	m7	PROPN
ejpam-4550	294	12	−	−	PROPN
ejpam-4550	294	13	κθm4	κθm4	PROPN
ejpam-4550	294	14	−	−	PROPN
ejpam-4550	294	15	bm1	bm1	NOUN
ejpam-4550	294	16	are	be	AUX
ejpam-4550	294	17	positive	positive	ADJ
ejpam-4550	294	18	,	,	PUNCT
ejpam-4550	294	19	consequently	consequently	ADV
ejpam-4550	294	20	,	,	PUNCT
ejpam-4550	294	21	v̇	v̇	NOUN
ejpam-4550	294	22	is	be	AUX
ejpam-4550	294	23	negative	negative	ADJ
ejpam-4550	294	24	definite	definite	ADJ
ejpam-4550	294	25	along	along	ADP
ejpam-4550	294	26	the	the	DET
ejpam-4550	294	27	trajectories	trajectory	NOUN
ejpam-4550	294	28	of	of	ADP
ejpam-4550	294	29	the	the	DET
ejpam-4550	294	30	system	system	NOUN
ejpam-4550	294	31	(	(	PUNCT
ejpam-4550	294	32	5	5	NUM
ejpam-4550	294	33	)	)	PUNCT
ejpam-4550	294	34	.	.	PUNCT
ejpam-4550	295	1	therefore	therefore	ADV
ejpam-4550	295	2	,	,	PUNCT
ejpam-4550	295	3	the	the	DET
ejpam-4550	295	4	dfe	dfe	PROPN
ejpam-4550	295	5	e0	e0	PROPN
ejpam-4550	295	6	is	be	AUX
ejpam-4550	295	7	globally	globally	ADV
ejpam-4550	295	8	asymptotically	asymptotically	ADV
ejpam-4550	295	9	stable	stable	ADJ
ejpam-4550	295	10	for	for	ADP
ejpam-4550	295	11	the	the	DET
ejpam-4550	295	12	system	system	NOUN
ejpam-4550	295	13	(	(	PUNCT
ejpam-4550	295	14	5	5	NUM
ejpam-4550	295	15	)	)	PUNCT
ejpam-4550	295	16	if	if	SCONJ
ejpam-4550	295	17	r0	r0	NOUN
ejpam-4550	295	18	<	<	X
ejpam-4550	295	19	1	1	NUM
ejpam-4550	295	20	.	.	PUNCT
ejpam-4550	296	1	this	this	PRON
ejpam-4550	296	2	ends	end	VERB
ejpam-4550	296	3	the	the	DET
ejpam-4550	296	4	proof	proof	NOUN
ejpam-4550	296	5	of	of	ADP
ejpam-4550	296	6	theorem	theorem	ADJ
ejpam-4550	296	7	3	3	NUM
ejpam-4550	296	8	.	.	NOUN
ejpam-4550	296	9	7	7	NUM
ejpam-4550	296	10	.	.	NOUN
ejpam-4550	296	11	existence	existence	NOUN
ejpam-4550	296	12	of	of	ADP
ejpam-4550	296	13	endemic	endemic	ADJ
ejpam-4550	296	14	equilibrium	equilibrium	NOUN
ejpam-4550	296	15	in	in	ADP
ejpam-4550	296	16	this	this	DET
ejpam-4550	296	17	section	section	NOUN
ejpam-4550	296	18	,	,	PUNCT
ejpam-4550	296	19	we	we	PRON
ejpam-4550	296	20	analyze	analyze	VERB
ejpam-4550	296	21	the	the	DET
ejpam-4550	296	22	existence	existence	NOUN
ejpam-4550	296	23	of	of	ADP
ejpam-4550	296	24	non	non	ADJ
ejpam-4550	296	25	-	-	ADJ
ejpam-4550	296	26	trivial	trivial	ADJ
ejpam-4550	296	27	endemic	endemic	ADJ
ejpam-4550	296	28	equilibrium	equilibrium	NOUN
ejpam-4550	296	29	e∗	e∗	NOUN
ejpam-4550	296	30	(	(	PUNCT
ejpam-4550	296	31	s∗1	s∗1	NOUN
ejpam-4550	296	32	,	,	PUNCT
ejpam-4550	296	33	i11∗	i11∗	NOUN
ejpam-4550	296	34	,	,	PUNCT
ejpam-4550	296	35	i21∗	i21∗	PROPN
ejpam-4550	296	36	,	,	PUNCT
ejpam-4550	296	37	i31∗	i31∗	NOUN
ejpam-4550	296	38	,	,	PUNCT
ejpam-4550	296	39	s∗2	s∗2	PROPN
ejpam-4550	296	40	,	,	PUNCT
ejpam-4550	296	41	i12∗	i12∗	NOUN
ejpam-4550	296	42	,	,	PUNCT
ejpam-4550	296	43	i22∗	i22∗	PROPN
ejpam-4550	296	44	,	,	PUNCT
ejpam-4550	296	45	i32∗	i32∗	PROPN
ejpam-4550	296	46	)	)	PUNCT
ejpam-4550	296	47	of	of	ADP
ejpam-4550	296	48	the	the	DET
ejpam-4550	296	49	system	system	NOUN
ejpam-4550	296	50	(	(	PUNCT
ejpam-4550	296	51	5	5	NUM
ejpam-4550	296	52	)	)	PUNCT
ejpam-4550	296	53	.	.	PUNCT
ejpam-4550	297	1	m.	m.	NOUN
ejpam-4550	297	2	alassane	alassane	NOUN
ejpam-4550	297	3	et	et	PROPN
ejpam-4550	297	4	al	al	PROPN
ejpam-4550	297	5	.	.	PUNCT
ejpam-4550	297	6	/	/	SYM
ejpam-4550	297	7	eur	eur	PROPN
ejpam-4550	297	8	.	.	PUNCT
ejpam-4550	298	1	j.	j.	PROPN
ejpam-4550	298	2	pure	pure	PROPN
ejpam-4550	298	3	appl	appl	PROPN
ejpam-4550	298	4	.	.	PROPN
ejpam-4550	298	5	math	math	PROPN
ejpam-4550	298	6	,	,	PUNCT
ejpam-4550	298	7	16	16	NUM
ejpam-4550	298	8	(	(	PUNCT
ejpam-4550	298	9	1	1	NUM
ejpam-4550	298	10	)	)	PUNCT
ejpam-4550	298	11	(	(	PUNCT
ejpam-4550	298	12	2023	2023	NUM
ejpam-4550	298	13	)	)	PUNCT
ejpam-4550	298	14	,	,	PUNCT
ejpam-4550	298	15	207	207	NUM
ejpam-4550	298	16	-	-	SYM
ejpam-4550	298	17	232	232	NUM
ejpam-4550	298	18	223	223	NUM
ejpam-4550	298	19	theorem	theorem	NOUN
ejpam-4550	298	20	4	4	NUM
ejpam-4550	298	21	.	.	PUNCT
ejpam-4550	299	1	if	if	SCONJ
ejpam-4550	299	2	r0	r0	NOUN
ejpam-4550	299	3	>	>	X
ejpam-4550	299	4	1	1	NUM
ejpam-4550	299	5	,	,	PUNCT
ejpam-4550	299	6	then	then	ADV
ejpam-4550	299	7	there	there	PRON
ejpam-4550	299	8	exists	exist	VERB
ejpam-4550	299	9	an	an	DET
ejpam-4550	299	10	endemic	endemic	ADJ
ejpam-4550	299	11	equilibrium	equilibrium	NOUN
ejpam-4550	299	12	point	point	NOUN
ejpam-4550	299	13	e∗	e∗	NOUN
ejpam-4550	299	14	for	for	ADP
ejpam-4550	299	15	the	the	DET
ejpam-4550	299	16	system	system	NOUN
ejpam-4550	299	17	(	(	PUNCT
ejpam-4550	299	18	5	5	NUM
ejpam-4550	299	19	)	)	PUNCT
ejpam-4550	299	20	.	.	PUNCT
ejpam-4550	300	1	proof	proof	NOUN
ejpam-4550	300	2	.	.	PUNCT
ejpam-4550	301	1	solving	solve	VERB
ejpam-4550	301	2	the	the	DET
ejpam-4550	301	3	equations	equation	NOUN
ejpam-4550	301	4	of	of	ADP
ejpam-4550	301	5	system	system	NOUN
ejpam-4550	301	6	(	(	PUNCT
ejpam-4550	301	7	5	5	NUM
ejpam-4550	301	8	)	)	PUNCT
ejpam-4550	301	9	at	at	ADP
ejpam-4550	301	10	equilibrium	equilibrium	NOUN
ejpam-4550	301	11	state	state	NOUN
ejpam-4550	301	12	,	,	PUNCT
ejpam-4550	301	13	we	we	PRON
ejpam-4550	301	14	obtain	obtain	VERB
ejpam-4550	301	15	:	:	PUNCT
ejpam-4550	301	16	s1	s1	NOUN
ejpam-4550	301	17	=	=	PUNCT
ejpam-4550	301	18	κ2i	κ2i	PROPN
ejpam-4550	301	19	1	1	NUM
ejpam-4550	301	20	1	1	NUM
ejpam-4550	301	21	β1	β1	NOUN
ejpam-4550	301	22	3∑	3∑	NUM
ejpam-4550	301	23	j=1	j=1	NOUN
ejpam-4550	301	24	ij1	ij1	NOUN
ejpam-4550	301	25	+	+	CCONJ
ejpam-4550	301	26	β2	β2	NOUN
ejpam-4550	301	27	3∑	3∑	NUM
ejpam-4550	301	28	j=1	j=1	NOUN
ejpam-4550	301	29	ij2	ij2	PROPN
ejpam-4550	301	30	(	(	PUNCT
ejpam-4550	301	31	21a	21a	ADJ
ejpam-4550	301	32	)	)	PUNCT
ejpam-4550	301	33	s2	s2	NOUN
ejpam-4550	301	34	=	=	PUNCT
ejpam-4550	302	1	κ5i	κ5i	X
ejpam-4550	302	2	1	1	NUM
ejpam-4550	302	3	2	2	NUM
ejpam-4550	302	4	−	−	NOUN
ejpam-4550	302	5	c1i	c1i	ADJ
ejpam-4550	302	6	1	1	NUM
ejpam-4550	302	7	1	1	NUM
ejpam-4550	302	8	β1	β1	NOUN
ejpam-4550	302	9	3∑	3∑	NUM
ejpam-4550	302	10	j=1	j=1	NOUN
ejpam-4550	302	11	ij1	ij1	NOUN
ejpam-4550	302	12	+	+	CCONJ
ejpam-4550	302	13	β2	β2	NOUN
ejpam-4550	302	14	3∑	3∑	NUM
ejpam-4550	302	15	j=1	j=1	NOUN
ejpam-4550	302	16	ij2	ij2	PROPN
ejpam-4550	302	17	(	(	PUNCT
ejpam-4550	302	18	21b	21b	NOUN
ejpam-4550	302	19	)	)	PUNCT
ejpam-4550	302	20	i21	i21	NOUN
ejpam-4550	302	21	=	=	SYM
ejpam-4550	302	22	a1	a1	NOUN
ejpam-4550	302	23	κ3	κ3	PROPN
ejpam-4550	302	24	i11	i11	NOUN
ejpam-4550	302	25	(	(	PUNCT
ejpam-4550	302	26	21c	21c	NOUN
ejpam-4550	302	27	)	)	PUNCT
ejpam-4550	302	28	i31	i31	NOUN
ejpam-4550	302	29	=	=	SYM
ejpam-4550	302	30	a1a2	a1a2	PROPN
ejpam-4550	302	31	κ3κ4	κ3κ4	NOUN
ejpam-4550	302	32	i11	i11	NOUN
ejpam-4550	302	33	(	(	PUNCT
ejpam-4550	302	34	21d	21d	NOUN
ejpam-4550	302	35	)	)	PUNCT
ejpam-4550	302	36	i22	i22	NOUN
ejpam-4550	302	37	=	=	SYM
ejpam-4550	302	38	a3	a3	PROPN
ejpam-4550	302	39	κ6	κ6	PROPN
ejpam-4550	302	40	i12	i12	PROPN
ejpam-4550	303	1	+	+	CCONJ
ejpam-4550	304	1	a1c2	a1c2	INTJ
ejpam-4550	304	2	κ6κ3	κ6κ3	PRON
ejpam-4550	304	3	i11	i11	ADJ
ejpam-4550	304	4	(	(	PUNCT
ejpam-4550	304	5	21e	21e	NUM
ejpam-4550	304	6	)	)	PUNCT
ejpam-4550	304	7	i32	i32	NOUN
ejpam-4550	304	8	=	=	PUNCT
ejpam-4550	304	9	a3a4	a3a4	PROPN
ejpam-4550	304	10	bκ6	bκ6	PROPN
ejpam-4550	304	11	i12	i12	NOUN
ejpam-4550	305	1	+	+	CCONJ
ejpam-4550	305	2	(	(	PUNCT
ejpam-4550	305	3	a4a1c2	a4a1c2	NOUN
ejpam-4550	305	4	bκ6κ3	bκ6κ3	PROPN
ejpam-4550	305	5	+	+	CCONJ
ejpam-4550	305	6	a1a2c3	a1a2c3	PROPN
ejpam-4550	305	7	bκ4κ3	bκ4κ3	PROPN
ejpam-4550	305	8	)	)	PUNCT
ejpam-4550	305	9	i11	i11	NOUN
ejpam-4550	305	10	(	(	PUNCT
ejpam-4550	305	11	21f	21f	NOUN
ejpam-4550	305	12	)	)	PUNCT
ejpam-4550	305	13	i12	i12	NOUN
ejpam-4550	305	14	=	=	SYM
ejpam-4550	306	1	−i11	−i11	PROPN
ejpam-4550	306	2	f38	f38	NOUN
ejpam-4550	307	1	+	+	CCONJ
ejpam-4550	307	2	f39i	f39i	NUM
ejpam-4550	307	3	1	1	NUM
ejpam-4550	307	4	1	1	NUM
ejpam-4550	307	5	β2κ3κ4	β2κ3κ4	ADP
ejpam-4550	307	6	(	(	PUNCT
ejpam-4550	307	7	−f40	−f40	PROPN
ejpam-4550	307	8	+	+	NUM
ejpam-4550	307	9	f41i	f41i	NOUN
ejpam-4550	307	10	1	1	NUM
ejpam-4550	307	11	1	1	NUM
ejpam-4550	307	12	)	)	PUNCT
ejpam-4550	307	13	(	(	PUNCT
ejpam-4550	307	14	21	21	NUM
ejpam-4550	307	15	g	g	NOUN
ejpam-4550	307	16	)	)	PUNCT
ejpam-4550	307	17	β1	β1	NOUN
ejpam-4550	308	1	3∑	3∑	NUM
ejpam-4550	308	2	j=1	j=1	NOUN
ejpam-4550	308	3	ij1	ij1	NOUN
ejpam-4550	308	4	+	+	CCONJ
ejpam-4550	308	5	β2	β2	NOUN
ejpam-4550	308	6	3∑	3∑	NUM
ejpam-4550	308	7	j=1	j=1	NOUN
ejpam-4550	308	8	ij2	ij2	PROPN
ejpam-4550	308	9	=	=	SYM
ejpam-4550	308	10	b−	b−	PROPN
ejpam-4550	308	11	κ1s1	κ1s1	PUNCT
ejpam-4550	308	12	s1	s1	PROPN
ejpam-4550	308	13	(	(	PUNCT
ejpam-4550	308	14	21h	21h	PROPN
ejpam-4550	308	15	)	)	PUNCT
ejpam-4550	308	16	where	where	SCONJ
ejpam-4550	308	17	f38	f38	NOUN
ejpam-4550	308	18	=	=	SYM
ejpam-4550	308	19	−β1κ6b	−β1κ6b	NOUN
ejpam-4550	308	20	2κ4κ3	2κ4κ3	NUM
ejpam-4550	308	21	−	−	NOUN
ejpam-4550	308	22	β1κ6b	β1κ6b	SYM
ejpam-4550	308	23	2a1κ4	2a1κ4	NUM
ejpam-4550	308	24	−	−	NUM
ejpam-4550	308	25	β1κ6b	β1κ6b	SYM
ejpam-4550	308	26	2a1a2	2a1a2	NUM
ejpam-4550	308	27	−	−	ADP
ejpam-4550	308	28	β2a1c2b	β2a1c2b	PROPN
ejpam-4550	308	29	2κ4	2κ4	NUM
ejpam-4550	308	30	−	−	NOUN
ejpam-4550	308	31	bβ2a1a4c2κ4	bβ2a1a4c2κ4	NOUN
ejpam-4550	308	32	−	−	NOUN
ejpam-4550	308	33	bβ2a1a2c3κ6	bβ2a1a2c3κ6	NOUN
ejpam-4550	309	1	+	+	PROPN
ejpam-4550	309	2	κ1κ2κ6κ3bκ4	κ1κ2κ6κ3bκ4	PROPN
ejpam-4550	309	3	f39	f39	NOUN
ejpam-4550	309	4	=	=	PUNCT
ejpam-4550	309	5	κ2β1κ6bκ4κ3	κ2β1κ6bκ4κ3	VERB
ejpam-4550	309	6	+	+	CCONJ
ejpam-4550	309	7	κ2β1κ6ba1κ4	κ2β1κ6ba1κ4	PROPN
ejpam-4550	309	8	+	+	CCONJ
ejpam-4550	309	9	κ2β1κ6ba1a2	κ2β1κ6ba1a2	PROPN
ejpam-4550	309	10	+	+	CCONJ
ejpam-4550	309	11	κ2β2a1c2bκ4	κ2β2a1c2bκ4	PRON
ejpam-4550	309	12	+	+	CCONJ
ejpam-4550	309	13	κ2β2a1a4c2κ4	κ2β2a1a4c2κ4	NOUN
ejpam-4550	309	14	+	+	CCONJ
ejpam-4550	309	15	κ2β2a1a2c3κ6	κ2β2a1a2c3κ6	NOUN
ejpam-4550	309	16	f40	f40	NOUN
ejpam-4550	309	17	=	=	SYM
ejpam-4550	309	18	b2κ6	b2κ6	VERB
ejpam-4550	309	19	+	+	CCONJ
ejpam-4550	309	20	a3b	a3b	ADJ
ejpam-4550	309	21	2	2	NUM
ejpam-4550	309	22	+	+	CCONJ
ejpam-4550	309	23	ba3a4	ba3a4	PROPN
ejpam-4550	309	24	f41	f41	NOUN
ejpam-4550	309	25	=	=	SYM
ejpam-4550	309	26	κ2bκ6	κ2bκ6	NOUN
ejpam-4550	309	27	+	+	CCONJ
ejpam-4550	309	28	κ2a3b	κ2a3b	NUM
ejpam-4550	309	29	+	+	NUM
ejpam-4550	309	30	κ2a3a4	κ2a3a4	NOUN
ejpam-4550	309	31	.	.	PUNCT
ejpam-4550	310	1	from	from	ADP
ejpam-4550	310	2	(	(	PUNCT
ejpam-4550	310	3	21b)-(21	21b)-(21	NOUN
ejpam-4550	310	4	g	g	NOUN
ejpam-4550	310	5	)	)	PUNCT
ejpam-4550	310	6	,	,	PUNCT
ejpam-4550	310	7	let	let	VERB
ejpam-4550	310	8	f44	f44	X
ejpam-4550	310	9	(	(	PUNCT
ejpam-4550	310	10	i11	i11	ADJ
ejpam-4550	310	11	)	)	PUNCT
ejpam-4550	310	12	2	2	NUM
ejpam-4550	310	13	+	+	CCONJ
ejpam-4550	310	14	f43i	f43i	SYM
ejpam-4550	310	15	1	1	NUM
ejpam-4550	310	16	1	1	NUM
ejpam-4550	310	17	+	+	NUM
ejpam-4550	310	18	f42	f42	X
ejpam-4550	310	19	=	=	SYM
ejpam-4550	310	20	0	0	NUM
ejpam-4550	310	21	(	(	PUNCT
ejpam-4550	310	22	22	22	NUM
ejpam-4550	310	23	)	)	PUNCT
ejpam-4550	310	24	where	where	SCONJ
ejpam-4550	310	25	f42	f42	PROPN
ejpam-4550	310	26	=	=	PROPN
ejpam-4550	310	27	b2	b2	PROPN
ejpam-4550	310	28	(	(	PUNCT
ejpam-4550	310	29	1−	1−	NUM
ejpam-4550	310	30	r0	r0	NOUN
ejpam-4550	310	31	)	)	PUNCT
ejpam-4550	310	32	bκ1κ2κ3κ4κ5κ6	bκ1κ2κ3κ4κ5κ6	NOUN
ejpam-4550	310	33	f43	f43	NOUN
ejpam-4550	310	34	=	=	SYM
ejpam-4550	310	35	κ2b	κ2b	PROPN
ejpam-4550	310	36	(	(	PUNCT
ejpam-4550	310	37	2b2κ6κ5β1a1κ4	2b2κ6κ5β1a1κ4	NUM
ejpam-4550	310	38	+	+	CCONJ
ejpam-4550	310	39	2b2κ6κ5β1a1a2	2b2κ6κ5β1a1a2	NUM
ejpam-4550	310	40	+	+	CCONJ
ejpam-4550	310	41	2b2κ6κ5β1κ4κ3	2b2κ6κ5β1κ4κ3	NUM
ejpam-4550	310	42	+	+	X
ejpam-4550	310	43	2b2κ6β2κ3κ4c1	2b2κ6β2κ3κ4c1	NUM
ejpam-4550	310	44	+	+	CCONJ
ejpam-4550	310	45	2b2κ5β2a1c2κ4	2b2κ5β2a1c2κ4	NUM
ejpam-4550	310	46	+2b2β2κ3κ4c1a3	+2b2β2κ3κ4c1a3	NOUN
ejpam-4550	310	47	+	+	CCONJ
ejpam-4550	310	48	2bβ2κ3κ4c1a3a4	2bβ2κ3κ4c1a3a4	NUM
ejpam-4550	310	49	+	+	SYM
ejpam-4550	310	50	2bκ6κ5β2a1a2c3	2bκ6κ5β2a1a2c3	NUM
ejpam-4550	310	51	−	−	NOUN
ejpam-4550	310	52	bκ6c1β2κ3κ4κ1	bκ6c1β2κ3κ4κ1	ADJ
ejpam-4550	310	53	−	−	PROPN
ejpam-4550	310	54	bc1β2κ3κ4κ1a3	bc1β2κ3κ4κ1a3	NOUN
ejpam-4550	310	55	m.	m.	NOUN
ejpam-4550	310	56	alassane	alassane	NOUN
ejpam-4550	310	57	et	et	PROPN
ejpam-4550	310	58	al	al	PROPN
ejpam-4550	310	59	.	.	PUNCT
ejpam-4550	310	60	/	/	SYM
ejpam-4550	310	61	eur	eur	PROPN
ejpam-4550	310	62	.	.	PUNCT
ejpam-4550	311	1	j.	j.	PROPN
ejpam-4550	311	2	pure	pure	PROPN
ejpam-4550	311	3	appl	appl	PROPN
ejpam-4550	311	4	.	.	PROPN
ejpam-4550	311	5	math	math	PROPN
ejpam-4550	311	6	,	,	PUNCT
ejpam-4550	311	7	16	16	NUM
ejpam-4550	311	8	(	(	PUNCT
ejpam-4550	311	9	1	1	NUM
ejpam-4550	311	10	)	)	PUNCT
ejpam-4550	311	11	(	(	PUNCT
ejpam-4550	311	12	2023	2023	NUM
ejpam-4550	311	13	)	)	PUNCT
ejpam-4550	311	14	,	,	PUNCT
ejpam-4550	311	15	207	207	NUM
ejpam-4550	311	16	-	-	SYM
ejpam-4550	311	17	232	232	NUM
ejpam-4550	311	18	224	224	NUM
ejpam-4550	311	19	−bκ6κ5κ1β1κ4κ3	−bκ6κ5κ1β1κ4κ3	NUM
ejpam-4550	312	1	+	+	CCONJ
ejpam-4550	313	1	2bκ2β2κ3κ4γa3	2bκ2β2κ3κ4γa3	NUM
ejpam-4550	313	2	−	−	NOUN
ejpam-4550	313	3	bκ6κ5κ1β1a1κ4	bκ6κ5κ1β1a1κ4	NOUN
ejpam-4550	313	4	−	−	PROPN
ejpam-4550	313	5	bκ6κ5κ1β1a1a2	bκ6κ5κ1β1a1a2	NOUN
ejpam-4550	313	6	−	−	NOUN
ejpam-4550	313	7	bκ2κ6κ5κ1κ3κ4	bκ2κ6κ5κ1κ3κ4	NOUN
ejpam-4550	313	8	+2bκ5β2a1a4c2κ4	+2bκ5β2a1a4c2κ4	NOUN
ejpam-4550	313	9	−	−	NOUN
ejpam-4550	313	10	bκ5κ1β2a1c2κ4	bκ5κ1β2a1c2κ4	NOUN
ejpam-4550	313	11	+	+	CCONJ
ejpam-4550	313	12	2bκ2κ6β2κ3κ4γ	2bκ2κ6β2κ3κ4γ	NUM
ejpam-4550	313	13	−	−	NOUN
ejpam-4550	313	14	κ6κ5κ1β2a1a2c3	κ6κ5κ1β2a1a2c3	X
ejpam-4550	313	15	+	+	NOUN
ejpam-4550	313	16	2κ2β2κ3κ4γa3a4	2κ2β2κ3κ4γa3a4	NOUN
ejpam-4550	313	17	+	+	NOUN
ejpam-4550	313	18	κ2κ6κ5κ	κ2κ6κ5κ	NOUN
ejpam-4550	313	19	2	2	NUM
ejpam-4550	313	20	1κ3κ4	1κ3κ4	NUM
ejpam-4550	313	21	−	−	NOUN
ejpam-4550	314	1	c1β2κ3κ4κ1a3a4	c1β2κ3κ4κ1a3a4	NOUN
ejpam-4550	314	2	−	−	NOUN
ejpam-4550	314	3	κ5κ1β2a1a4c2κ4	κ5κ1β2a1a4c2κ4	NOUN
ejpam-4550	314	4	)	)	PUNCT
ejpam-4550	314	5	f44	f44	NOUN
ejpam-4550	314	6	=	=	SYM
ejpam-4550	314	7	κ22	κ22	NOUN
ejpam-4550	314	8	(	(	PUNCT
ejpam-4550	314	9	−	−	NOUN
ejpam-4550	314	10	κ2β2κ3κ4γa3a4	κ2β2κ3κ4γa3a4	NOUN
ejpam-4550	314	11	−	−	NOUN
ejpam-4550	314	12	bκ2κ6β2κ3κ4γ	bκ2κ6β2κ3κ4γ	PRON
ejpam-4550	314	13	−	−	PROPN
ejpam-4550	314	14	bκ2β2κ3κ4γa3	bκ2β2κ3κ4γa3	ADJ
ejpam-4550	314	15	+	+	CCONJ
ejpam-4550	314	16	bκ6c1β2κ3κ4κ1	bκ6c1β2κ3κ4κ1	ADJ
ejpam-4550	314	17	+	+	NUM
ejpam-4550	314	18	bc1β2κ3κ4κ1a3	bc1β2κ3κ4κ1a3	X
ejpam-4550	314	19	+	+	NOUN
ejpam-4550	314	20	c1β2κ3κ4κ1a3a4	c1β2κ3κ4κ1a3a4	PROPN
ejpam-4550	314	21	−	−	NOUN
ejpam-4550	314	22	b2κ6κ5β1κ4κ3	b2κ6κ5β1κ4κ3	NOUN
ejpam-4550	314	23	−	−	PROPN
ejpam-4550	314	24	b2κ6κ5β1a1a2	b2κ6κ5β1a1a2	PROPN
ejpam-4550	314	25	+	+	CCONJ
ejpam-4550	314	26	bκ6κ5κ1β1a1κ4	bκ6κ5κ1β1a1κ4	NOUN
ejpam-4550	314	27	+	+	X
ejpam-4550	314	28	κ6κ5κ1β2a1a2c3	κ6κ5κ1β2a1a2c3	ADJ
ejpam-4550	314	29	−b2κ6κ5β1a1κ4	−b2κ6κ5β1a1κ4	NOUN
ejpam-4550	314	30	+	+	CCONJ
ejpam-4550	314	31	bκ6κ5κ1β1a1a2	bκ6κ5κ1β1a1a2	NOUN
ejpam-4550	314	32	+	+	CCONJ
ejpam-4550	314	33	κ5κ1β2a1a4c2κ4	κ5κ1β2a1a4c2κ4	VERB
ejpam-4550	314	34	−	−	NOUN
ejpam-4550	314	35	b2β2κ3κ4c1a3	b2β2κ3κ4c1a3	NOUN
ejpam-4550	314	36	+	+	CCONJ
ejpam-4550	314	37	bκ6κ5κ1β1κ4κ3	bκ6κ5κ1β1κ4κ3	ADJ
ejpam-4550	314	38	−bβ2κ3κ4c1a3a4	−bβ2κ3κ4c1a3a4	NOUN
ejpam-4550	314	39	−	−	PROPN
ejpam-4550	314	40	b2κ6β2κ3κ4c1	b2κ6β2κ3κ4c1	NOUN
ejpam-4550	314	41	−	−	PROPN
ejpam-4550	314	42	b2κ5β2a1c2κ4	b2κ5β2a1c2κ4	NOUN
ejpam-4550	314	43	−	−	NOUN
ejpam-4550	314	44	bκ6κ5β2a1a2c3	bκ6κ5β2a1a2c3	NOUN
ejpam-4550	314	45	−	−	NOUN
ejpam-4550	314	46	bκ5β2a1a4c2κ4	bκ5β2a1a4c2κ4	NOUN
ejpam-4550	314	47	+	+	NOUN
ejpam-4550	314	48	bκ5κ1β2a1c2κ4	bκ5κ1β2a1c2κ4	NOUN
ejpam-4550	314	49	)	)	PUNCT
ejpam-4550	315	1	.	.	PUNCT
ejpam-4550	316	1	by	by	ADP
ejpam-4550	316	2	replacing	replace	VERB
ejpam-4550	316	3	κ1	κ1	NOUN
ejpam-4550	316	4	,	,	PUNCT
ejpam-4550	316	5	κ2	κ2	PROPN
ejpam-4550	316	6	,	,	PUNCT
ejpam-4550	316	7	κ3	κ3	PROPN
ejpam-4550	316	8	,	,	PUNCT
ejpam-4550	316	9	κ4	κ4	NOUN
ejpam-4550	316	10	,	,	PUNCT
ejpam-4550	316	11	κ5	κ5	NOUN
ejpam-4550	316	12	and	and	CCONJ
ejpam-4550	316	13	κ6	κ6	ADV
ejpam-4550	316	14	by	by	ADP
ejpam-4550	316	15	their	their	PRON
ejpam-4550	316	16	expressions	expression	NOUN
ejpam-4550	316	17	into	into	ADP
ejpam-4550	316	18	f44	f44	NOUN
ejpam-4550	316	19	,	,	PUNCT
ejpam-4550	316	20	we	we	PRON
ejpam-4550	316	21	get	get	VERB
ejpam-4550	316	22	:	:	PUNCT
ejpam-4550	316	23	f44	f44	X
ejpam-4550	316	24	=	=	SYM
ejpam-4550	316	25	(	(	PUNCT
ejpam-4550	316	26	a1	a1	NOUN
ejpam-4550	316	27	+	+	CCONJ
ejpam-4550	316	28	c1	c1	NOUN
ejpam-4550	316	29	+	+	CCONJ
ejpam-4550	316	30	b)2	b)2	PROPN
ejpam-4550	316	31	bγ	bγ	PROPN
ejpam-4550	316	32	(	(	PUNCT
ejpam-4550	316	33	−β2	−β2	PROPN
ejpam-4550	316	34	+	+	CCONJ
ejpam-4550	316	35	β1	β1	PROPN
ejpam-4550	316	36	)	)	PUNCT
ejpam-4550	316	37	(	(	PUNCT
ejpam-4550	316	38	b	b	X
ejpam-4550	316	39	+	+	SYM
ejpam-4550	316	40	a4	a4	NUM
ejpam-4550	316	41	)	)	PUNCT
ejpam-4550	316	42	(	(	PUNCT
ejpam-4550	316	43	b	b	X
ejpam-4550	316	44	+	+	NUM
ejpam-4550	316	45	a3	a3	NOUN
ejpam-4550	316	46	)	)	PUNCT
ejpam-4550	316	47	(	(	PUNCT
ejpam-4550	316	48	b2	b2	NOUN
ejpam-4550	316	49	+	+	CCONJ
ejpam-4550	316	50	ba2	ba2	PROPN
ejpam-4550	316	51	+	+	CCONJ
ejpam-4550	316	52	bc2	bc2	VERB
ejpam-4550	317	1	+	+	NOUN
ejpam-4550	317	2	bc3	bc3	NOUN
ejpam-4550	317	3	+	+	CCONJ
ejpam-4550	317	4	a1b	a1b	PROPN
ejpam-4550	317	5	+	+	CCONJ
ejpam-4550	317	6	a1c3	a1c3	X
ejpam-4550	318	1	+	+	CCONJ
ejpam-4550	318	2	a1a2	a1a2	PROPN
ejpam-4550	318	3	+	+	PUNCT
ejpam-4550	318	4	c2c3	c2c3	X
ejpam-4550	318	5	+	+	NOUN
ejpam-4550	318	6	a2c3	a2c3	PRON
ejpam-4550	318	7	)	)	PUNCT
ejpam-4550	318	8	.	.	PUNCT
ejpam-4550	319	1	if	if	SCONJ
ejpam-4550	319	2	r0	r0	NOUN
ejpam-4550	319	3	>	>	X
ejpam-4550	319	4	1	1	NUM
ejpam-4550	319	5	,	,	PUNCT
ejpam-4550	319	6	we	we	PRON
ejpam-4550	319	7	clearly	clearly	ADV
ejpam-4550	319	8	see	see	VERB
ejpam-4550	319	9	that	that	SCONJ
ejpam-4550	319	10	f42	f42	PROPN
ejpam-4550	319	11	<	<	X
ejpam-4550	319	12	0	0	NUM
ejpam-4550	319	13	.	.	PUNCT
ejpam-4550	320	1	we	we	PRON
ejpam-4550	320	2	also	also	ADV
ejpam-4550	320	3	note	note	VERB
ejpam-4550	320	4	that	that	SCONJ
ejpam-4550	320	5	:	:	PUNCT
ejpam-4550	320	6	(	(	PUNCT
ejpam-4550	320	7	i	i	NOUN
ejpam-4550	320	8	)	)	PUNCT
ejpam-4550	320	9	if	if	SCONJ
ejpam-4550	320	10	β1	β1	PROPN
ejpam-4550	320	11	>	>	X
ejpam-4550	320	12	β2	β2	PROPN
ejpam-4550	320	13	,	,	PUNCT
ejpam-4550	320	14	then	then	ADV
ejpam-4550	320	15	f44	f44	VERB
ejpam-4550	320	16	>	>	X
ejpam-4550	320	17	0	0	X
ejpam-4550	320	18	.	.	PUNCT
ejpam-4550	321	1	consequently	consequently	ADV
ejpam-4550	321	2	,	,	PUNCT
ejpam-4550	321	3	the	the	DET
ejpam-4550	321	4	discriminant	discriminant	NOUN
ejpam-4550	321	5	of	of	ADP
ejpam-4550	321	6	(	(	PUNCT
ejpam-4550	321	7	22	22	NUM
ejpam-4550	321	8	)	)	PUNCT
ejpam-4550	321	9	is	be	AUX
ejpam-4550	321	10	positive	positive	ADJ
ejpam-4550	321	11	and	and	CCONJ
ejpam-4550	321	12	the	the	DET
ejpam-4550	321	13	product	product	NOUN
ejpam-4550	321	14	of	of	ADP
ejpam-4550	321	15	the	the	DET
ejpam-4550	321	16	solutions	solution	NOUN
ejpam-4550	321	17	is	be	AUX
ejpam-4550	321	18	negative	negative	ADJ
ejpam-4550	321	19	.	.	PUNCT
ejpam-4550	322	1	so	so	ADV
ejpam-4550	322	2	,	,	PUNCT
ejpam-4550	322	3	there	there	PRON
ejpam-4550	322	4	exists	exist	VERB
ejpam-4550	322	5	a	a	DET
ejpam-4550	322	6	positive	positive	ADJ
ejpam-4550	322	7	solution	solution	NOUN
ejpam-4550	322	8	i11	i11	NOUN
ejpam-4550	322	9	for	for	ADP
ejpam-4550	322	10	(	(	PUNCT
ejpam-4550	322	11	22	22	NUM
ejpam-4550	322	12	)	)	PUNCT
ejpam-4550	322	13	.	.	PUNCT
ejpam-4550	323	1	(	(	PUNCT
ejpam-4550	323	2	ii	ii	NOUN
ejpam-4550	323	3	)	)	PUNCT
ejpam-4550	323	4	if	if	SCONJ
ejpam-4550	323	5	β1	β1	PROPN
ejpam-4550	323	6	<	<	X
ejpam-4550	323	7	β2	β2	PROPN
ejpam-4550	323	8	,	,	PUNCT
ejpam-4550	323	9	then	then	ADV
ejpam-4550	323	10	f44	f44	VERB
ejpam-4550	323	11	<	<	X
ejpam-4550	323	12	0	0	NUM
ejpam-4550	323	13	and	and	CCONJ
ejpam-4550	323	14	f43	f43	NOUN
ejpam-4550	323	15	>	>	X
ejpam-4550	323	16	0	0	X
ejpam-4550	323	17	.	.	PUNCT
ejpam-4550	324	1	consequently	consequently	ADV
ejpam-4550	324	2	,	,	PUNCT
ejpam-4550	324	3	the	the	DET
ejpam-4550	324	4	discriminant	discriminant	NOUN
ejpam-4550	324	5	of	of	ADP
ejpam-4550	324	6	(	(	PUNCT
ejpam-4550	324	7	22	22	NUM
ejpam-4550	324	8	)	)	PUNCT
ejpam-4550	324	9	is	be	AUX
ejpam-4550	324	10	positive	positive	ADJ
ejpam-4550	324	11	,	,	PUNCT
ejpam-4550	324	12	the	the	DET
ejpam-4550	324	13	sum	sum	NOUN
ejpam-4550	324	14	and	and	CCONJ
ejpam-4550	324	15	the	the	DET
ejpam-4550	324	16	product	product	NOUN
ejpam-4550	324	17	of	of	ADP
ejpam-4550	324	18	the	the	DET
ejpam-4550	324	19	solutions	solution	NOUN
ejpam-4550	324	20	of	of	ADP
ejpam-4550	324	21	(	(	PUNCT
ejpam-4550	324	22	22	22	NUM
ejpam-4550	324	23	)	)	PUNCT
ejpam-4550	324	24	are	be	AUX
ejpam-4550	324	25	positive	positive	ADJ
ejpam-4550	324	26	.	.	PUNCT
ejpam-4550	325	1	therefore	therefore	ADV
ejpam-4550	325	2	,	,	PUNCT
ejpam-4550	325	3	there	there	PRON
ejpam-4550	325	4	exist	exist	VERB
ejpam-4550	325	5	two	two	NUM
ejpam-4550	325	6	distinct	distinct	ADJ
ejpam-4550	325	7	solutions	solution	NOUN
ejpam-4550	325	8	.	.	PUNCT
ejpam-4550	326	1	(	(	PUNCT
ejpam-4550	326	2	iii	iii	X
ejpam-4550	326	3	)	)	PUNCT
ejpam-4550	327	1	if	if	SCONJ
ejpam-4550	327	2	β1	β1	PROPN
ejpam-4550	327	3	=	=	SYM
ejpam-4550	327	4	β2	β2	PROPN
ejpam-4550	327	5	,	,	PUNCT
ejpam-4550	327	6	then	then	ADV
ejpam-4550	327	7	f44	f44	VERB
ejpam-4550	327	8	=	=	SYM
ejpam-4550	327	9	0	0	NUM
ejpam-4550	327	10	and	and	CCONJ
ejpam-4550	327	11	f43	f43	NOUN
ejpam-4550	327	12	>	>	X
ejpam-4550	327	13	0	0	X
ejpam-4550	327	14	.	.	PUNCT
ejpam-4550	328	1	so	so	ADV
ejpam-4550	328	2	,	,	PUNCT
ejpam-4550	328	3	(	(	PUNCT
ejpam-4550	328	4	22	22	NUM
ejpam-4550	328	5	)	)	PUNCT
ejpam-4550	328	6	becomes	become	VERB
ejpam-4550	328	7	:	:	PUNCT
ejpam-4550	328	8	f43i	f43i	NOUN
ejpam-4550	328	9	1	1	NUM
ejpam-4550	328	10	1	1	NUM
ejpam-4550	328	11	+	+	NUM
ejpam-4550	328	12	f42	f42	X
ejpam-4550	328	13	=	=	SYM
ejpam-4550	328	14	0	0	PROPN
ejpam-4550	328	15	.	.	PUNCT
ejpam-4550	329	1	(	(	PUNCT
ejpam-4550	329	2	23	23	NUM
ejpam-4550	329	3	)	)	PUNCT
ejpam-4550	329	4	therefore	therefore	ADV
ejpam-4550	329	5	,	,	PUNCT
ejpam-4550	329	6	there	there	PRON
ejpam-4550	329	7	exists	exist	VERB
ejpam-4550	329	8	a	a	DET
ejpam-4550	329	9	unique	unique	ADJ
ejpam-4550	329	10	positive	positive	ADJ
ejpam-4550	329	11	solution	solution	NOUN
ejpam-4550	329	12	i11	i11	NOUN
ejpam-4550	329	13	.	.	PUNCT
ejpam-4550	330	1	in	in	ADP
ejpam-4550	330	2	all	all	DET
ejpam-4550	330	3	the	the	DET
ejpam-4550	330	4	cases	case	NOUN
ejpam-4550	330	5	discussed	discuss	VERB
ejpam-4550	330	6	above	above	ADV
ejpam-4550	330	7	,	,	PUNCT
ejpam-4550	330	8	there	there	PRON
ejpam-4550	330	9	exists	exist	VERB
ejpam-4550	330	10	at	at	ADP
ejpam-4550	330	11	least	least	ADJ
ejpam-4550	330	12	a	a	DET
ejpam-4550	330	13	positive	positive	ADJ
ejpam-4550	330	14	solution	solution	NOUN
ejpam-4550	330	15	i11	i11	NOUN
ejpam-4550	330	16	of	of	ADP
ejpam-4550	330	17	(	(	PUNCT
ejpam-4550	330	18	22	22	NUM
ejpam-4550	330	19	)	)	PUNCT
ejpam-4550	330	20	.	.	PUNCT
ejpam-4550	331	1	let	let	VERB
ejpam-4550	331	2	us	we	PRON
ejpam-4550	331	3	denote	denote	VERB
ejpam-4550	331	4	by	by	ADP
ejpam-4550	331	5	i11	i11	ADJ
ejpam-4550	331	6	∗	∗	NOUN
ejpam-4550	331	7	this	this	DET
ejpam-4550	331	8	positive	positive	ADJ
ejpam-4550	331	9	solution	solution	NOUN
ejpam-4550	331	10	.	.	PUNCT
ejpam-4550	332	1	we	we	PRON
ejpam-4550	332	2	will	will	AUX
ejpam-4550	332	3	now	now	ADV
ejpam-4550	332	4	define	define	VERB
ejpam-4550	332	5	and	and	CCONJ
ejpam-4550	332	6	prove	prove	VERB
ejpam-4550	332	7	the	the	DET
ejpam-4550	332	8	positivity	positivity	NOUN
ejpam-4550	332	9	of	of	ADP
ejpam-4550	332	10	i12	i12	PROPN
ejpam-4550	332	11	∗	∗	NOUN
ejpam-4550	332	12	,	,	PUNCT
ejpam-4550	332	13	i31	i31	NOUN
ejpam-4550	332	14	∗	∗	NOUN
ejpam-4550	332	15	,	,	PUNCT
ejpam-4550	332	16	i22	i22	NOUN
ejpam-4550	332	17	∗	∗	NOUN
ejpam-4550	332	18	,	,	PUNCT
ejpam-4550	332	19	i32	i32	NOUN
ejpam-4550	332	20	∗	∗	NOUN
ejpam-4550	332	21	,	,	PUNCT
ejpam-4550	332	22	s1	s1	NOUN
ejpam-4550	332	23	∗	∗	NOUN
ejpam-4550	332	24	and	and	CCONJ
ejpam-4550	332	25	s2	s2	PROPN
ejpam-4550	332	26	∗	∗	NOUN
ejpam-4550	332	27	if	if	SCONJ
ejpam-4550	332	28	r0	r0	NOUN
ejpam-4550	332	29	>	>	X
ejpam-4550	332	30	1	1	NUM
ejpam-4550	332	31	.	.	PUNCT
ejpam-4550	332	32	from	from	ADP
ejpam-4550	332	33	equation	equation	NOUN
ejpam-4550	332	34	(	(	PUNCT
ejpam-4550	332	35	21	21	NUM
ejpam-4550	332	36	g	g	NOUN
ejpam-4550	332	37	)	)	PUNCT
ejpam-4550	332	38	,	,	PUNCT
ejpam-4550	332	39	we	we	PRON
ejpam-4550	332	40	get	get	VERB
ejpam-4550	332	41	:	:	PUNCT
ejpam-4550	332	42	i12	i12	NOUN
ejpam-4550	332	43	∗	∗	NOUN
ejpam-4550	332	44	=	=	PUNCT
ejpam-4550	333	1	−i11	−i11	NOUN
ejpam-4550	333	2	∗	∗	NOUN
ejpam-4550	333	3	f38	f38	NOUN
ejpam-4550	333	4	+	+	CCONJ
ejpam-4550	333	5	f39i	f39i	ADJ
ejpam-4550	333	6	1	1	NUM
ejpam-4550	333	7	1	1	NUM
ejpam-4550	333	8	∗	∗	NOUN
ejpam-4550	333	9	β2κ3κ4	β2κ3κ4	PUNCT
ejpam-4550	333	10	(	(	PUNCT
ejpam-4550	333	11	−f40	−f40	PROPN
ejpam-4550	333	12	+	+	NUM
ejpam-4550	333	13	f41i	f41i	NOUN
ejpam-4550	333	14	1	1	NUM
ejpam-4550	333	15	1	1	NUM
ejpam-4550	333	16	∗	∗	NOUN
ejpam-4550	333	17	)	)	PUNCT
ejpam-4550	333	18	if	if	SCONJ
ejpam-4550	333	19	r0	r0	NOUN
ejpam-4550	333	20	>	>	X
ejpam-4550	333	21	1	1	NUM
ejpam-4550	333	22	,	,	PUNCT
ejpam-4550	333	23	then	then	ADV
ejpam-4550	333	24	f38	f38	ADP
ejpam-4550	333	25	>	>	X
ejpam-4550	333	26	0	0	X
ejpam-4550	333	27	.	.	PUNCT
ejpam-4550	334	1	from	from	ADP
ejpam-4550	334	2	(	(	PUNCT
ejpam-4550	334	3	21a	21a	NUM
ejpam-4550	334	4	)	)	PUNCT
ejpam-4550	334	5	and	and	CCONJ
ejpam-4550	334	6	(	(	PUNCT
ejpam-4550	334	7	21h	21h	NUM
ejpam-4550	334	8	)	)	PUNCT
ejpam-4550	334	9	,	,	PUNCT
ejpam-4550	334	10	it	it	PRON
ejpam-4550	334	11	follows	follow	VERB
ejpam-4550	334	12	that	that	SCONJ
ejpam-4550	334	13	−f40	−f40	PROPN
ejpam-4550	335	1	+	+	NUM
ejpam-4550	335	2	f41i	f41i	NOUN
ejpam-4550	335	3	1	1	NUM
ejpam-4550	335	4	1	1	NUM
ejpam-4550	335	5	∗	∗	NOUN
ejpam-4550	335	6	<	<	X
ejpam-4550	335	7	0	0	NUM
ejpam-4550	335	8	,	,	PUNCT
ejpam-4550	335	9	hence	hence	ADV
ejpam-4550	335	10	i12	i12	PROPN
ejpam-4550	335	11	∗	∗	NOUN
ejpam-4550	335	12	>	>	X
ejpam-4550	335	13	0	0	X
ejpam-4550	335	14	.	.	PUNCT
ejpam-4550	335	15	from	from	ADP
ejpam-4550	335	16	equation	equation	NOUN
ejpam-4550	335	17	(	(	PUNCT
ejpam-4550	335	18	21c	21c	NUM
ejpam-4550	335	19	)	)	PUNCT
ejpam-4550	335	20	,	,	PUNCT
ejpam-4550	335	21	it	it	PRON
ejpam-4550	335	22	follows	follow	VERB
ejpam-4550	335	23	that	that	SCONJ
ejpam-4550	335	24	i21	i21	NOUN
ejpam-4550	335	25	∗	∗	NOUN
ejpam-4550	335	26	=	=	SYM
ejpam-4550	335	27	a1	a1	NOUN
ejpam-4550	335	28	κ3	κ3	PROPN
ejpam-4550	335	29	i11	i11	ADJ
ejpam-4550	335	30	∗	∗	NOUN
ejpam-4550	335	31	,	,	PUNCT
ejpam-4550	335	32	hence	hence	ADV
ejpam-4550	335	33	i21	i21	VERB
ejpam-4550	335	34	∗	∗	NOUN
ejpam-4550	335	35	>	>	X
ejpam-4550	335	36	0	0	X
ejpam-4550	335	37	.	.	PUNCT
ejpam-4550	335	38	m.	m.	NOUN
ejpam-4550	335	39	alassane	alassane	NOUN
ejpam-4550	335	40	et	et	PROPN
ejpam-4550	335	41	al	al	PROPN
ejpam-4550	335	42	.	.	PUNCT
ejpam-4550	335	43	/	/	SYM
ejpam-4550	335	44	eur	eur	PROPN
ejpam-4550	335	45	.	.	PUNCT
ejpam-4550	336	1	j.	j.	PROPN
ejpam-4550	336	2	pure	pure	PROPN
ejpam-4550	336	3	appl	appl	PROPN
ejpam-4550	336	4	.	.	PROPN
ejpam-4550	336	5	math	math	PROPN
ejpam-4550	336	6	,	,	PUNCT
ejpam-4550	336	7	16	16	NUM
ejpam-4550	336	8	(	(	PUNCT
ejpam-4550	336	9	1	1	NUM
ejpam-4550	336	10	)	)	PUNCT
ejpam-4550	336	11	(	(	PUNCT
ejpam-4550	336	12	2023	2023	NUM
ejpam-4550	336	13	)	)	PUNCT
ejpam-4550	336	14	,	,	PUNCT
ejpam-4550	336	15	207	207	NUM
ejpam-4550	336	16	-	-	SYM
ejpam-4550	336	17	232	232	NUM
ejpam-4550	336	18	225	225	NUM
ejpam-4550	336	19	from	from	ADP
ejpam-4550	336	20	equation	equation	NOUN
ejpam-4550	336	21	(	(	PUNCT
ejpam-4550	336	22	21d	21d	NOUN
ejpam-4550	336	23	)	)	PUNCT
ejpam-4550	336	24	,	,	PUNCT
ejpam-4550	336	25	it	it	PRON
ejpam-4550	336	26	follows	follow	VERB
ejpam-4550	336	27	that	that	SCONJ
ejpam-4550	336	28	,	,	PUNCT
ejpam-4550	336	29	i31	i31	NOUN
ejpam-4550	336	30	∗	∗	NOUN
ejpam-4550	336	31	=	=	PUNCT
ejpam-4550	336	32	a1a2	a1a2	ADP
ejpam-4550	336	33	κ3κ4	κ3κ4	NOUN
ejpam-4550	336	34	i11	i11	ADJ
ejpam-4550	336	35	∗	∗	NOUN
ejpam-4550	336	36	,	,	PUNCT
ejpam-4550	336	37	hence	hence	ADV
ejpam-4550	336	38	i31	i31	NOUN
ejpam-4550	336	39	∗	∗	NOUN
ejpam-4550	336	40	>	>	X
ejpam-4550	336	41	0	0	X
ejpam-4550	336	42	.	.	PUNCT
ejpam-4550	337	1	from	from	ADP
ejpam-4550	337	2	equation	equation	NOUN
ejpam-4550	337	3	(	(	PUNCT
ejpam-4550	337	4	21e	21e	NUM
ejpam-4550	337	5	)	)	PUNCT
ejpam-4550	337	6	,	,	PUNCT
ejpam-4550	337	7	it	it	PRON
ejpam-4550	337	8	follows	follow	VERB
ejpam-4550	337	9	that	that	SCONJ
ejpam-4550	337	10	,	,	PUNCT
ejpam-4550	337	11	i22	i22	NOUN
ejpam-4550	337	12	∗	∗	NOUN
ejpam-4550	337	13	=	=	SYM
ejpam-4550	337	14	a3	a3	PROPN
ejpam-4550	337	15	κ6	κ6	PROPN
ejpam-4550	337	16	i12	i12	PROPN
ejpam-4550	337	17	∗	∗	NOUN
ejpam-4550	338	1	+	+	CCONJ
ejpam-4550	339	1	a1c2	a1c2	INTJ
ejpam-4550	339	2	κ6κ3	κ6κ3	PRON
ejpam-4550	339	3	i11	i11	ADJ
ejpam-4550	339	4	∗	∗	NOUN
ejpam-4550	339	5	,	,	PUNCT
ejpam-4550	339	6	hence	hence	ADV
ejpam-4550	339	7	i22	i22	VERB
ejpam-4550	339	8	∗	∗	NOUN
ejpam-4550	339	9	>	>	X
ejpam-4550	339	10	0	0	X
ejpam-4550	339	11	.	.	PUNCT
ejpam-4550	340	1	from	from	ADP
ejpam-4550	340	2	equation	equation	NOUN
ejpam-4550	340	3	(	(	PUNCT
ejpam-4550	340	4	21f	21f	NOUN
ejpam-4550	340	5	)	)	PUNCT
ejpam-4550	340	6	,	,	PUNCT
ejpam-4550	340	7	it	it	PRON
ejpam-4550	340	8	follows	follow	VERB
ejpam-4550	340	9	that	that	SCONJ
ejpam-4550	340	10	,	,	PUNCT
ejpam-4550	340	11	i32	i32	NOUN
ejpam-4550	340	12	∗	∗	X
ejpam-4550	340	13	=	=	PUNCT
ejpam-4550	340	14	a3a4	a3a4	PROPN
ejpam-4550	340	15	bκ6	bκ6	PROPN
ejpam-4550	340	16	i12	i12	PROPN
ejpam-4550	340	17	∗	∗	NOUN
ejpam-4550	341	1	+	+	CCONJ
ejpam-4550	341	2	(	(	PUNCT
ejpam-4550	341	3	a4a1c2	a4a1c2	NOUN
ejpam-4550	341	4	bκ6κ3	bκ6κ3	PROPN
ejpam-4550	341	5	+	+	CCONJ
ejpam-4550	341	6	a1a2c3	a1a2c3	PROPN
ejpam-4550	341	7	bκ4κ3	bκ4κ3	PROPN
ejpam-4550	341	8	)	)	PUNCT
ejpam-4550	341	9	i11	i11	ADJ
ejpam-4550	341	10	∗	∗	NOUN
ejpam-4550	341	11	,	,	PUNCT
ejpam-4550	341	12	hence	hence	ADV
ejpam-4550	341	13	i32	i32	PROPN
ejpam-4550	341	14	∗	∗	NOUN
ejpam-4550	341	15	>	>	X
ejpam-4550	341	16	0	0	X
ejpam-4550	341	17	.	.	PUNCT
ejpam-4550	341	18	from	from	ADP
ejpam-4550	341	19	equation	equation	NOUN
ejpam-4550	341	20	(	(	PUNCT
ejpam-4550	341	21	21a	21a	NUM
ejpam-4550	341	22	)	)	PUNCT
ejpam-4550	341	23	,	,	PUNCT
ejpam-4550	341	24	it	it	PRON
ejpam-4550	341	25	follows	follow	VERB
ejpam-4550	341	26	that	that	SCONJ
ejpam-4550	341	27	,	,	PUNCT
ejpam-4550	341	28	s∗1	s∗1	NOUN
ejpam-4550	341	29	=	=	PUNCT
ejpam-4550	341	30	κ2i	κ2i	PROPN
ejpam-4550	341	31	1	1	NUM
ejpam-4550	341	32	1	1	NUM
ejpam-4550	341	33	∗	∗	NOUN
ejpam-4550	341	34	β1	β1	NOUN
ejpam-4550	341	35	3∑	3∑	NUM
ejpam-4550	341	36	j=1	j=1	NOUN
ejpam-4550	341	37	ij1	ij1	NOUN
ejpam-4550	341	38	∗	∗	NOUN
ejpam-4550	341	39	+	+	CCONJ
ejpam-4550	341	40	β2	β2	VERB
ejpam-4550	341	41	3∑	3∑	NUM
ejpam-4550	341	42	j=1	j=1	NOUN
ejpam-4550	341	43	ij2	ij2	PROPN
ejpam-4550	341	44	∗	∗	NOUN
ejpam-4550	341	45	,	,	PUNCT
ejpam-4550	341	46	hence	hence	ADV
ejpam-4550	341	47	s∗1	s∗1	VERB
ejpam-4550	341	48	>	>	X
ejpam-4550	341	49	0	0	X
ejpam-4550	341	50	.	.	PUNCT
ejpam-4550	342	1	from	from	ADP
ejpam-4550	342	2	equation	equation	NOUN
ejpam-4550	342	3	(	(	PUNCT
ejpam-4550	342	4	21b	21b	NUM
ejpam-4550	342	5	)	)	PUNCT
ejpam-4550	342	6	,	,	PUNCT
ejpam-4550	342	7	it	it	PRON
ejpam-4550	342	8	follows	follow	VERB
ejpam-4550	342	9	that	that	SCONJ
ejpam-4550	342	10	,	,	PUNCT
ejpam-4550	342	11	s∗2	s∗2	PROPN
ejpam-4550	342	12	=	=	SYM
ejpam-4550	342	13	κ5i	κ5i	PROPN
ejpam-4550	342	14	1	1	NUM
ejpam-4550	342	15	2	2	NUM
ejpam-4550	342	16	∗	∗	NOUN
ejpam-4550	342	17	−	−	VERB
ejpam-4550	343	1	c1i	c1i	ADV
ejpam-4550	343	2	1	1	NUM
ejpam-4550	343	3	1	1	NUM
ejpam-4550	343	4	∗	∗	NOUN
ejpam-4550	343	5	β1	β1	NOUN
ejpam-4550	343	6	3∑	3∑	NUM
ejpam-4550	343	7	j=1	j=1	NOUN
ejpam-4550	343	8	ij1	ij1	NOUN
ejpam-4550	343	9	∗	∗	NOUN
ejpam-4550	343	10	+	+	CCONJ
ejpam-4550	343	11	β2	β2	VERB
ejpam-4550	343	12	3∑	3∑	NUM
ejpam-4550	343	13	j=1	j=1	NOUN
ejpam-4550	343	14	ij2	ij2	PROPN
ejpam-4550	343	15	∗	∗	NOUN
ejpam-4550	343	16	,	,	PUNCT
ejpam-4550	343	17	hence	hence	ADV
ejpam-4550	343	18	s∗2	s∗2	VERB
ejpam-4550	343	19	>	>	X
ejpam-4550	343	20	0	0	X
ejpam-4550	343	21	.	.	PUNCT
ejpam-4550	344	1	therefore	therefore	ADV
ejpam-4550	344	2	,	,	PUNCT
ejpam-4550	344	3	if	if	SCONJ
ejpam-4550	344	4	r0	r0	NOUN
ejpam-4550	344	5	>	>	X
ejpam-4550	344	6	1	1	NUM
ejpam-4550	344	7	,	,	PUNCT
ejpam-4550	344	8	there	there	PRON
ejpam-4550	344	9	exists	exist	VERB
ejpam-4550	344	10	a	a	DET
ejpam-4550	344	11	positive	positive	ADJ
ejpam-4550	344	12	solution	solution	NOUN
ejpam-4550	344	13	e∗	e∗	NOUN
ejpam-4550	344	14	(	(	PUNCT
ejpam-4550	344	15	s∗1	s∗1	NOUN
ejpam-4550	344	16	,	,	PUNCT
ejpam-4550	344	17	i11∗	i11∗	NOUN
ejpam-4550	344	18	,	,	PUNCT
ejpam-4550	344	19	i21∗	i21∗	PROPN
ejpam-4550	344	20	,	,	PUNCT
ejpam-4550	344	21	i31∗	i31∗	NOUN
ejpam-4550	344	22	,	,	PUNCT
ejpam-4550	344	23	s∗2	s∗2	PROPN
ejpam-4550	344	24	,	,	PUNCT
ejpam-4550	344	25	i12∗	i12∗	NOUN
ejpam-4550	344	26	,	,	PUNCT
ejpam-4550	344	27	i22∗	i22∗	PROPN
ejpam-4550	344	28	,	,	PUNCT
ejpam-4550	344	29	i32∗	i32∗	PROPN
ejpam-4550	344	30	)	)	PUNCT
ejpam-4550	344	31	for	for	ADP
ejpam-4550	344	32	the	the	DET
ejpam-4550	344	33	system	system	NOUN
ejpam-4550	344	34	(	(	PUNCT
ejpam-4550	344	35	5	5	NUM
ejpam-4550	344	36	)	)	PUNCT
ejpam-4550	344	37	.	.	PUNCT
ejpam-4550	345	1	8	8	X
ejpam-4550	345	2	.	.	X
ejpam-4550	346	1	stability	stability	NOUN
ejpam-4550	346	2	analysis	analysis	NOUN
ejpam-4550	346	3	of	of	ADP
ejpam-4550	346	4	endemic	endemic	ADJ
ejpam-4550	346	5	equilibrium	equilibrium	NOUN
ejpam-4550	346	6	theorem	theorem	NOUN
ejpam-4550	346	7	5	5	NUM
ejpam-4550	346	8	.	.	PUNCT
ejpam-4550	347	1	if	if	SCONJ
ejpam-4550	347	2	r0	r0	NOUN
ejpam-4550	347	3	>	>	X
ejpam-4550	347	4	1	1	NUM
ejpam-4550	347	5	,	,	PUNCT
ejpam-4550	347	6	then	then	ADV
ejpam-4550	347	7	the	the	DET
ejpam-4550	347	8	endemic	endemic	ADJ
ejpam-4550	347	9	equilibrium	equilibrium	NOUN
ejpam-4550	347	10	point	point	NOUN
ejpam-4550	347	11	e∗	e∗	PROPN
ejpam-4550	347	12	(	(	PUNCT
ejpam-4550	347	13	s∗1	s∗1	PROPN
ejpam-4550	347	14	,	,	PUNCT
ejpam-4550	347	15	i	i	NOUN
ejpam-4550	347	16	1	1	NUM
ejpam-4550	347	17	1	1	NUM
ejpam-4550	347	18	∗	∗	NOUN
ejpam-4550	347	19	,	,	PUNCT
ejpam-4550	347	20	i21	i21	NOUN
ejpam-4550	347	21	∗	∗	NOUN
ejpam-4550	347	22	,	,	PUNCT
ejpam-4550	347	23	i31	i31	NOUN
ejpam-4550	347	24	∗	∗	NOUN
ejpam-4550	347	25	,	,	PUNCT
ejpam-4550	347	26	s∗2	s∗2	PROPN
ejpam-4550	347	27	,	,	PUNCT
ejpam-4550	347	28	i	i	NOUN
ejpam-4550	347	29	1	1	NUM
ejpam-4550	347	30	2	2	NUM
ejpam-4550	347	31	∗	∗	NOUN
ejpam-4550	347	32	,	,	PUNCT
ejpam-4550	347	33	i22	i22	NOUN
ejpam-4550	347	34	∗	∗	NOUN
ejpam-4550	347	35	,	,	PUNCT
ejpam-4550	347	36	i32	i32	PROPN
ejpam-4550	347	37	∗	∗	NOUN
ejpam-4550	347	38	)	)	PUNCT
ejpam-4550	347	39	is	be	AUX
ejpam-4550	347	40	locally	locally	ADV
ejpam-4550	347	41	asymptotically	asymptotically	ADV
ejpam-4550	347	42	stable	stable	ADJ
ejpam-4550	347	43	.	.	PUNCT
ejpam-4550	348	1	proof	proof	NOUN
ejpam-4550	348	2	.	.	PUNCT
ejpam-4550	349	1	let	let	VERB
ejpam-4550	349	2	us	we	PRON
ejpam-4550	349	3	compute	compute	VERB
ejpam-4550	349	4	the	the	DET
ejpam-4550	349	5	jacobian	jacobian	NOUN
ejpam-4550	349	6	of	of	ADP
ejpam-4550	349	7	the	the	DET
ejpam-4550	349	8	system	system	NOUN
ejpam-4550	349	9	at	at	ADP
ejpam-4550	349	10	the	the	DET
ejpam-4550	349	11	point	point	NOUN
ejpam-4550	349	12	e∗	e∗	PROPN
ejpam-4550	349	13	(	(	PUNCT
ejpam-4550	349	14	s∗1	s∗1	NOUN
ejpam-4550	349	15	,	,	PUNCT
ejpam-4550	349	16	i11∗	i11∗	NOUN
ejpam-4550	349	17	,	,	PUNCT
ejpam-4550	349	18	i21∗	i21∗	PROPN
ejpam-4550	349	19	,	,	PUNCT
ejpam-4550	349	20	i31∗	i31∗	NOUN
ejpam-4550	349	21	,	,	PUNCT
ejpam-4550	349	22	s∗2	s∗2	PROPN
ejpam-4550	349	23	,	,	PUNCT
ejpam-4550	349	24	i12∗	i12∗	NOUN
ejpam-4550	349	25	,	,	PUNCT
ejpam-4550	349	26	i22∗	i22∗	PROPN
ejpam-4550	349	27	,	,	PUNCT
ejpam-4550	349	28	i32∗	i32∗	PROPN
ejpam-4550	349	29	)	)	PUNCT
ejpam-4550	349	30	.	.	PUNCT
ejpam-4550	350	1	m.	m.	NOUN
ejpam-4550	350	2	alassane	alassane	NOUN
ejpam-4550	350	3	et	et	PROPN
ejpam-4550	350	4	al	al	PROPN
ejpam-4550	350	5	.	.	PUNCT
ejpam-4550	350	6	/	/	SYM
ejpam-4550	350	7	eur	eur	PROPN
ejpam-4550	350	8	.	.	PUNCT
ejpam-4550	351	1	j.	j.	PROPN
ejpam-4550	351	2	pure	pure	PROPN
ejpam-4550	351	3	appl	appl	PROPN
ejpam-4550	351	4	.	.	PROPN
ejpam-4550	351	5	math	math	PROPN
ejpam-4550	351	6	,	,	PUNCT
ejpam-4550	351	7	16	16	NUM
ejpam-4550	351	8	(	(	PUNCT
ejpam-4550	351	9	1	1	NUM
ejpam-4550	351	10	)	)	PUNCT
ejpam-4550	351	11	(	(	PUNCT
ejpam-4550	351	12	2023	2023	NUM
ejpam-4550	351	13	)	)	PUNCT
ejpam-4550	351	14	,	,	PUNCT
ejpam-4550	351	15	207	207	NUM
ejpam-4550	351	16	-	-	SYM
ejpam-4550	351	17	232	232	NUM
ejpam-4550	351	18	226	226	NUM
ejpam-4550	351	19	j(e∗	j(e∗	NOUN
ejpam-4550	351	20	)	)	PUNCT
ejpam-4550	352	1	=	=	VERB
ejpam-4550	352	2			NOUN
ejpam-4550	352	3	−h∗	−h∗	ADP
ejpam-4550	352	4	−	−	PROPN
ejpam-4550	352	5	κ1	κ1	NOUN
ejpam-4550	352	6	−β1s	−β1s	NOUN
ejpam-4550	352	7	∗	∗	NOUN
ejpam-4550	352	8	1	1	NUM
ejpam-4550	352	9	−β1s	−β1s	NOUN
ejpam-4550	352	10	∗	∗	NOUN
ejpam-4550	352	11	1	1	NUM
ejpam-4550	352	12	−β1s	−β1s	NOUN
ejpam-4550	352	13	∗	∗	NOUN
ejpam-4550	352	14	1	1	NUM
ejpam-4550	352	15	0	0	NUM
ejpam-4550	352	16	−β2s	−β2s	NUM
ejpam-4550	352	17	∗	∗	NOUN
ejpam-4550	352	18	1	1	NUM
ejpam-4550	352	19	−β2s	−β2s	NUM
ejpam-4550	352	20	∗	∗	NOUN
ejpam-4550	352	21	1	1	NUM
ejpam-4550	352	22	−β2s	−β2s	NUM
ejpam-4550	352	23	∗	∗	NOUN
ejpam-4550	352	24	1	1	NUM
ejpam-4550	352	25	h∗	h∗	NOUN
ejpam-4550	352	26	β1s	β1s	PROPN
ejpam-4550	352	27	∗	∗	PROPN
ejpam-4550	352	28	1	1	NUM
ejpam-4550	352	29	−	−	PROPN
ejpam-4550	352	30	κ2	κ2	NOUN
ejpam-4550	352	31	β1s	β1s	PUNCT
ejpam-4550	352	32	∗	∗	PROPN
ejpam-4550	352	33	1	1	NUM
ejpam-4550	352	34	β1s	β1s	PUNCT
ejpam-4550	352	35	∗	∗	NOUN
ejpam-4550	352	36	1	1	NUM
ejpam-4550	352	37	0	0	NUM
ejpam-4550	352	38	β2s	β2	NOUN
ejpam-4550	352	39	∗	∗	NOUN
ejpam-4550	352	40	1	1	NUM
ejpam-4550	352	41	β2s	β2	NOUN
ejpam-4550	352	42	∗	∗	NOUN
ejpam-4550	352	43	1	1	NUM
ejpam-4550	352	44	β2s	β2	NOUN
ejpam-4550	352	45	∗	∗	NOUN
ejpam-4550	352	46	1	1	NUM
ejpam-4550	352	47	0	0	NUM
ejpam-4550	352	48	a1	a1	NOUN
ejpam-4550	352	49	−κ3	−κ3	PROPN
ejpam-4550	352	50	0	0	NUM
ejpam-4550	353	1	0	0	NUM
ejpam-4550	353	2	0	0	NUM
ejpam-4550	353	3	0	0	NUM
ejpam-4550	353	4	0	0	NUM
ejpam-4550	353	5	0	0	NUM
ejpam-4550	353	6	0	0	NUM
ejpam-4550	353	7	a2	a2	PROPN
ejpam-4550	353	8	−κ4	−κ4	PROPN
ejpam-4550	353	9	0	0	NUM
ejpam-4550	353	10	0	0	NUM
ejpam-4550	353	11	0	0	NUM
ejpam-4550	353	12	0	0	NUM
ejpam-4550	353	13	γ	γ	PROPN
ejpam-4550	353	14	−β1s	−β1s	NOUN
ejpam-4550	353	15	∗	∗	NOUN
ejpam-4550	353	16	2	2	NUM
ejpam-4550	353	17	−β1s	−β1s	NOUN
ejpam-4550	353	18	∗	∗	NOUN
ejpam-4550	353	19	2	2	NUM
ejpam-4550	353	20	−β1s	−β1s	NOUN
ejpam-4550	353	21	∗	∗	NOUN
ejpam-4550	353	22	2	2	NUM
ejpam-4550	353	23	−h∗	−h∗	NOUN
ejpam-4550	353	24	−	−	PROPN
ejpam-4550	353	25	b	b	NOUN
ejpam-4550	353	26	−β2s	−β2s	NUM
ejpam-4550	353	27	∗	∗	X
ejpam-4550	353	28	2	2	NUM
ejpam-4550	353	29	−β2s	−β2s	NUM
ejpam-4550	353	30	∗	∗	NOUN
ejpam-4550	353	31	2	2	NUM
ejpam-4550	353	32	−β2s	−β2s	NUM
ejpam-4550	353	33	∗	∗	NOUN
ejpam-4550	353	34	2	2	NUM
ejpam-4550	353	35	0	0	NUM
ejpam-4550	353	36	β1s	β1s	PUNCT
ejpam-4550	353	37	∗	∗	NOUN
ejpam-4550	353	38	2	2	NUM
ejpam-4550	353	39	+	+	NUM
ejpam-4550	353	40	c1	c1	NOUN
ejpam-4550	353	41	β1s	β1s	PROPN
ejpam-4550	353	42	∗	∗	PROPN
ejpam-4550	353	43	2	2	NUM
ejpam-4550	353	44	h∗	h∗	PROPN
ejpam-4550	353	45	β2s	β2s	PROPN
ejpam-4550	353	46	∗	∗	X
ejpam-4550	353	47	2	2	NUM
ejpam-4550	353	48	−	−	NOUN
ejpam-4550	353	49	κ5	κ5	NOUN
ejpam-4550	353	50	β2s	β2s	PUNCT
ejpam-4550	353	51	∗	∗	NOUN
ejpam-4550	353	52	2	2	NUM
ejpam-4550	353	53	β2s	β2s	X
ejpam-4550	353	54	∗	∗	NOUN
ejpam-4550	353	55	2	2	NUM
ejpam-4550	353	56	0	0	NUM
ejpam-4550	353	57	0	0	NUM
ejpam-4550	353	58	c2	c2	PROPN
ejpam-4550	353	59	0	0	NUM
ejpam-4550	353	60	0	0	NUM
ejpam-4550	353	61	a3	a3	NOUN
ejpam-4550	353	62	−κ6	−κ6	PROPN
ejpam-4550	353	63	0	0	NUM
ejpam-4550	353	64	0	0	NUM
ejpam-4550	353	65	0	0	NUM
ejpam-4550	353	66	0	0	NUM
ejpam-4550	354	1	c3	c3	NOUN
ejpam-4550	354	2	0	0	NUM
ejpam-4550	354	3	0	0	NUM
ejpam-4550	354	4	a4	a4	NOUN
ejpam-4550	354	5	−b	−b	ADP
ejpam-4550	354	6			PROPN
ejpam-4550	354	7	where	where	SCONJ
ejpam-4550	354	8	h∗	h∗	PROPN
ejpam-4550	354	9	=	=	PROPN
ejpam-4550	354	10	β1	β1	PROPN
ejpam-4550	354	11	3∑	3∑	NUM
ejpam-4550	354	12	j=1	j=1	NOUN
ejpam-4550	354	13	ij1	ij1	NOUN
ejpam-4550	354	14	∗	∗	NOUN
ejpam-4550	354	15	+	+	CCONJ
ejpam-4550	354	16	β2	β2	VERB
ejpam-4550	354	17	3∑	3∑	NUM
ejpam-4550	354	18	j=1	j=1	NOUN
ejpam-4550	354	19	ij2	ij2	PROPN
ejpam-4550	354	20	∗	∗	NOUN
ejpam-4550	354	21	.	.	PUNCT
ejpam-4550	355	1	the	the	DET
ejpam-4550	355	2	characteristic	characteristic	ADJ
ejpam-4550	355	3	equation	equation	NOUN
ejpam-4550	355	4	of	of	ADP
ejpam-4550	355	5	j(e∗	j(e∗	NOUN
ejpam-4550	355	6	)	)	PUNCT
ejpam-4550	355	7	is	be	AUX
ejpam-4550	355	8	given	give	VERB
ejpam-4550	355	9	by	by	ADP
ejpam-4550	355	10	:	:	PUNCT
ejpam-4550	355	11	a8x	a8x	NOUN
ejpam-4550	355	12	8	8	NUM
ejpam-4550	356	1	+	+	ADJ
ejpam-4550	356	2	a7x	a7x	PROPN
ejpam-4550	356	3	7	7	NUM
ejpam-4550	356	4	+	+	NOUN
ejpam-4550	356	5	a6x	a6x	PROPN
ejpam-4550	356	6	6	6	NUM
ejpam-4550	356	7	+	+	ADJ
ejpam-4550	356	8	a5x	a5x	ADP
ejpam-4550	356	9	5	5	NUM
ejpam-4550	356	10	+	+	ADV
ejpam-4550	356	11	a4x	a4x	ADJ
ejpam-4550	356	12	4	4	NUM
ejpam-4550	357	1	+	+	NOUN
ejpam-4550	357	2	a3x	a3x	NOUN
ejpam-4550	357	3	2	2	NUM
ejpam-4550	357	4	+	+	NOUN
ejpam-4550	357	5	a2x	a2x	PROPN
ejpam-4550	357	6	2	2	NUM
ejpam-4550	357	7	+	+	NOUN
ejpam-4550	357	8	a1x+a0	a1x+a0	NOUN
ejpam-4550	357	9	=	=	SYM
ejpam-4550	357	10	0	0	NUM
ejpam-4550	357	11	(	(	PUNCT
ejpam-4550	357	12	24	24	NUM
ejpam-4550	357	13	)	)	PUNCT
ejpam-4550	357	14	where	where	SCONJ
ejpam-4550	357	15	a0	a0	PROPN
ejpam-4550	357	16	,	,	PUNCT
ejpam-4550	357	17	a1	a1	PROPN
ejpam-4550	357	18	,	,	PUNCT
ejpam-4550	357	19	a2	a2	PROPN
ejpam-4550	357	20	,	,	PUNCT
ejpam-4550	357	21	a3	a3	NOUN
ejpam-4550	357	22	,	,	PUNCT
ejpam-4550	357	23	a4	a4	PROPN
ejpam-4550	357	24	,	,	PUNCT
ejpam-4550	357	25	a5	a5	NOUN
ejpam-4550	357	26	,	,	PUNCT
ejpam-4550	357	27	a6	a6	NOUN
ejpam-4550	357	28	,	,	PUNCT
ejpam-4550	357	29	a7	a7	PROPN
ejpam-4550	357	30	,	,	PUNCT
ejpam-4550	357	31	a8	a8	PROPN
ejpam-4550	357	32	are	be	AUX
ejpam-4550	357	33	obtained	obtain	VERB
ejpam-4550	357	34	as	as	ADP
ejpam-4550	357	35	a	a	DET
ejpam-4550	357	36	result	result	NOUN
ejpam-4550	357	37	of	of	ADP
ejpam-4550	357	38	a	a	DET
ejpam-4550	357	39	boring	boring	ADJ
ejpam-4550	357	40	calculation	calculation	NOUN
ejpam-4550	357	41	.	.	PUNCT
ejpam-4550	358	1	they	they	PRON
ejpam-4550	358	2	are	be	AUX
ejpam-4550	358	3	all	all	ADV
ejpam-4550	358	4	positive	positive	ADJ
ejpam-4550	358	5	.	.	PUNCT
ejpam-4550	359	1	applying	apply	VERB
ejpam-4550	359	2	the	the	DET
ejpam-4550	359	3	routh	routh	PROPN
ejpam-4550	359	4	-	-	PUNCT
ejpam-4550	359	5	hurwitz	hurwitz	PROPN
ejpam-4550	359	6	criterion	criterion	NOUN
ejpam-4550	360	1	[	[	X
ejpam-4550	360	2	7	7	NUM
ejpam-4550	360	3	]	]	PUNCT
ejpam-4550	360	4	,	,	PUNCT
ejpam-4550	360	5	it	it	PRON
ejpam-4550	360	6	follows	follow	VERB
ejpam-4550	360	7	that	that	SCONJ
ejpam-4550	360	8	all	all	DET
ejpam-4550	360	9	eigenvalues	eigenvalue	NOUN
ejpam-4550	360	10	of	of	ADP
ejpam-4550	360	11	the	the	DET
ejpam-4550	360	12	characteristic	characteristic	ADJ
ejpam-4550	360	13	equation	equation	NOUN
ejpam-4550	360	14	(	(	PUNCT
ejpam-4550	360	15	24	24	NUM
ejpam-4550	360	16	)	)	PUNCT
ejpam-4550	360	17	have	have	VERB
ejpam-4550	360	18	negative	negative	ADJ
ejpam-4550	360	19	real	real	ADJ
ejpam-4550	360	20	part	part	NOUN
ejpam-4550	360	21	if	if	SCONJ
ejpam-4550	360	22	r0	r0	NOUN
ejpam-4550	360	23	>	>	X
ejpam-4550	361	1	1	1	X
ejpam-4550	361	2	.	.	PUNCT
ejpam-4550	362	1	therefore	therefore	ADV
ejpam-4550	362	2	,	,	PUNCT
ejpam-4550	362	3	the	the	DET
ejpam-4550	362	4	endemic	endemic	ADJ
ejpam-4550	362	5	solution	solution	NOUN
ejpam-4550	362	6	e∗	e∗	NOUN
ejpam-4550	362	7	is	be	AUX
ejpam-4550	362	8	locally	locally	ADV
ejpam-4550	362	9	asymptotically	asymptotically	ADV
ejpam-4550	362	10	stable	stable	ADJ
ejpam-4550	362	11	if	if	SCONJ
ejpam-4550	362	12	r0	r0	NOUN
ejpam-4550	362	13	>	>	X
ejpam-4550	362	14	1	1	NUM
ejpam-4550	362	15	.	.	NOUN
ejpam-4550	362	16	9	9	NUM
ejpam-4550	362	17	.	.	X
ejpam-4550	362	18	numerical	numerical	ADJ
ejpam-4550	362	19	simulations	simulation	NOUN
ejpam-4550	362	20	and	and	CCONJ
ejpam-4550	362	21	discussion	discussion	NOUN
ejpam-4550	362	22	in	in	ADP
ejpam-4550	362	23	this	this	DET
ejpam-4550	362	24	section	section	NOUN
ejpam-4550	362	25	,	,	PUNCT
ejpam-4550	362	26	we	we	PRON
ejpam-4550	362	27	perform	perform	VERB
ejpam-4550	362	28	numerical	numerical	ADJ
ejpam-4550	362	29	simulations	simulation	NOUN
ejpam-4550	362	30	to	to	PART
ejpam-4550	362	31	support	support	VERB
ejpam-4550	362	32	the	the	DET
ejpam-4550	362	33	theoretical	theoretical	ADJ
ejpam-4550	362	34	results	result	NOUN
ejpam-4550	362	35	from	from	ADP
ejpam-4550	362	36	the	the	DET
ejpam-4550	362	37	mathematical	mathematical	ADJ
ejpam-4550	362	38	analysis	analysis	NOUN
ejpam-4550	362	39	of	of	ADP
ejpam-4550	362	40	model	model	NOUN
ejpam-4550	362	41	(	(	PUNCT
ejpam-4550	362	42	5	5	NUM
ejpam-4550	362	43	)	)	PUNCT
ejpam-4550	362	44	.	.	PUNCT
ejpam-4550	363	1	in	in	ADP
ejpam-4550	363	2	addition	addition	NOUN
ejpam-4550	363	3	to	to	ADP
ejpam-4550	363	4	the	the	DET
ejpam-4550	363	5	verification	verification	NOUN
ejpam-4550	363	6	of	of	ADP
ejpam-4550	363	7	the	the	DET
ejpam-4550	363	8	theoretical	theoretical	ADJ
ejpam-4550	363	9	results	result	NOUN
ejpam-4550	363	10	,	,	PUNCT
ejpam-4550	363	11	these	these	DET
ejpam-4550	363	12	numerical	numerical	ADJ
ejpam-4550	363	13	solutions	solution	NOUN
ejpam-4550	363	14	are	be	AUX
ejpam-4550	363	15	very	very	ADV
ejpam-4550	363	16	important	important	ADJ
ejpam-4550	363	17	from	from	ADP
ejpam-4550	363	18	a	a	DET
ejpam-4550	363	19	practical	practical	ADJ
ejpam-4550	363	20	point	point	NOUN
ejpam-4550	363	21	of	of	ADP
ejpam-4550	363	22	view	view	NOUN
ejpam-4550	363	23	.	.	PUNCT
ejpam-4550	364	1	we	we	PRON
ejpam-4550	364	2	first	first	ADV
ejpam-4550	364	3	consider	consider	VERB
ejpam-4550	364	4	the	the	DET
ejpam-4550	364	5	case	case	NOUN
ejpam-4550	364	6	where	where	SCONJ
ejpam-4550	364	7	r0	r0	NOUN
ejpam-4550	364	8	=	=	PROPN
ejpam-4550	364	9	0.67893	0.67893	NUM
ejpam-4550	364	10	<	<	X
ejpam-4550	364	11	1	1	NUM
ejpam-4550	364	12	using	use	VERB
ejpam-4550	364	13	the	the	DET
ejpam-4550	364	14	parameter	parameter	NOUN
ejpam-4550	364	15	values	value	NOUN
ejpam-4550	364	16	reported	report	VERB
ejpam-4550	364	17	in	in	ADP
ejpam-4550	364	18	table	table	NOUN
ejpam-4550	364	19	4	4	NUM
ejpam-4550	364	20	.	.	PUNCT
ejpam-4550	364	21	using	use	VERB
ejpam-4550	364	22	different	different	ADJ
ejpam-4550	364	23	initial	initial	ADJ
ejpam-4550	364	24	conditions	condition	NOUN
ejpam-4550	364	25	,	,	PUNCT
ejpam-4550	364	26	the	the	DET
ejpam-4550	364	27	dynamics	dynamic	NOUN
ejpam-4550	364	28	of	of	ADP
ejpam-4550	364	29	the	the	DET
ejpam-4550	364	30	susceptible	susceptible	ADJ
ejpam-4550	364	31	and	and	CCONJ
ejpam-4550	364	32	infected	infected	ADJ
ejpam-4550	364	33	populations	population	NOUN
ejpam-4550	364	34	of	of	ADP
ejpam-4550	364	35	the	the	DET
ejpam-4550	364	36	model	model	NOUN
ejpam-4550	364	37	are	be	AUX
ejpam-4550	364	38	plotted	plot	VERB
ejpam-4550	364	39	in	in	ADP
ejpam-4550	364	40	figures	figure	NOUN
ejpam-4550	364	41	2	2	NUM
ejpam-4550	364	42	,	,	PUNCT
ejpam-4550	364	43	3	3	NUM
ejpam-4550	364	44	,	,	PUNCT
ejpam-4550	364	45	4	4	NUM
ejpam-4550	364	46	and	and	CCONJ
ejpam-4550	364	47	5	5	NUM
ejpam-4550	364	48	.	.	PUNCT
ejpam-4550	365	1	in	in	ADP
ejpam-4550	365	2	figure	figure	NOUN
ejpam-4550	365	3	2	2	NUM
ejpam-4550	365	4	,	,	PUNCT
ejpam-4550	365	5	we	we	PRON
ejpam-4550	365	6	can	can	AUX
ejpam-4550	365	7	observe	observe	VERB
ejpam-4550	365	8	that	that	SCONJ
ejpam-4550	365	9	the	the	DET
ejpam-4550	365	10	proportions	proportion	NOUN
ejpam-4550	365	11	of	of	ADP
ejpam-4550	365	12	susceptible	susceptible	ADJ
ejpam-4550	365	13	individuals	individual	NOUN
ejpam-4550	365	14	in	in	ADP
ejpam-4550	365	15	classes	class	NOUN
ejpam-4550	365	16	c1	c1	PROPN
ejpam-4550	365	17	and	and	CCONJ
ejpam-4550	365	18	c2	c2	PROPN
ejpam-4550	365	19	are	be	AUX
ejpam-4550	365	20	consistent	consistent	ADJ
ejpam-4550	365	21	,	,	PUNCT
ejpam-4550	365	22	(	(	PUNCT
ejpam-4550	365	23	s1	s1	PROPN
ejpam-4550	365	24	=	=	SYM
ejpam-4550	365	25	0.63343	0.63343	NUM
ejpam-4550	365	26	,	,	PUNCT
ejpam-4550	365	27	s2	s2	X
ejpam-4550	365	28	=	=	PUNCT
ejpam-4550	365	29	0.36657	0.36657	NUM
ejpam-4550	365	30	)	)	PUNCT
ejpam-4550	365	31	.	.	PUNCT
ejpam-4550	366	1	in	in	ADP
ejpam-4550	366	2	contrast	contrast	NOUN
ejpam-4550	366	3	,	,	PUNCT
ejpam-4550	366	4	as	as	SCONJ
ejpam-4550	366	5	shown	show	VERB
ejpam-4550	366	6	in	in	ADP
ejpam-4550	366	7	figures	figure	NOUN
ejpam-4550	366	8	3	3	NUM
ejpam-4550	366	9	,	,	PUNCT
ejpam-4550	366	10	4	4	NUM
ejpam-4550	366	11	and	and	CCONJ
ejpam-4550	366	12	5	5	NUM
ejpam-4550	366	13	,	,	PUNCT
ejpam-4550	366	14	the	the	DET
ejpam-4550	366	15	proportions	proportion	NOUN
ejpam-4550	366	16	of	of	ADP
ejpam-4550	366	17	infected	infected	ADJ
ejpam-4550	366	18	individuals	individual	NOUN
ejpam-4550	366	19	in	in	ADP
ejpam-4550	366	20	classes	class	NOUN
ejpam-4550	366	21	c1	c1	PROPN
ejpam-4550	366	22	and	and	CCONJ
ejpam-4550	366	23	c2	c2	PROPN
ejpam-4550	366	24	decline	decline	VERB
ejpam-4550	366	25	to	to	ADP
ejpam-4550	366	26	zero	zero	NUM
ejpam-4550	366	27	(	(	PUNCT
ejpam-4550	366	28	i11	i11	NOUN
ejpam-4550	366	29	=	=	SYM
ejpam-4550	366	30	0	0	NUM
ejpam-4550	366	31	,	,	PUNCT
ejpam-4550	366	32	i21	i21	NOUN
ejpam-4550	366	33	=	=	SYM
ejpam-4550	366	34	0	0	NUM
ejpam-4550	366	35	,	,	PUNCT
ejpam-4550	366	36	i31	i31	NOUN
ejpam-4550	366	37	=	=	SYM
ejpam-4550	366	38	0	0	NUM
ejpam-4550	366	39	,	,	PUNCT
ejpam-4550	366	40	i12	i12	NOUN
ejpam-4550	366	41	=	=	SYM
ejpam-4550	366	42	0	0	NUM
ejpam-4550	366	43	,	,	PUNCT
ejpam-4550	366	44	i22	i22	NOUN
ejpam-4550	366	45	=	=	SYM
ejpam-4550	366	46	0	0	NUM
ejpam-4550	366	47	,	,	PUNCT
ejpam-4550	366	48	i32	i32	NOUN
ejpam-4550	366	49	=	=	NOUN
ejpam-4550	366	50	0	0	NUM
ejpam-4550	366	51	)	)	PUNCT
ejpam-4550	366	52	,	,	PUNCT
ejpam-4550	366	53	i.e.	i.e.	X
ejpam-4550	366	54	approach	approach	VERB
ejpam-4550	366	55	the	the	DET
ejpam-4550	366	56	disease	disease	NOUN
ejpam-4550	366	57	-	-	PUNCT
ejpam-4550	366	58	free	free	ADJ
ejpam-4550	366	59	equilibrium	equilibrium	NOUN
ejpam-4550	366	60	m.	m.	NOUN
ejpam-4550	366	61	alassane	alassane	NOUN
ejpam-4550	366	62	et	et	PROPN
ejpam-4550	366	63	al	al	PROPN
ejpam-4550	366	64	.	.	PUNCT
ejpam-4550	366	65	/	/	SYM
ejpam-4550	366	66	eur	eur	PROPN
ejpam-4550	366	67	.	.	PUNCT
ejpam-4550	367	1	j.	j.	PROPN
ejpam-4550	367	2	pure	pure	PROPN
ejpam-4550	367	3	appl	appl	PROPN
ejpam-4550	367	4	.	.	PROPN
ejpam-4550	367	5	math	math	PROPN
ejpam-4550	367	6	,	,	PUNCT
ejpam-4550	367	7	16	16	NUM
ejpam-4550	367	8	(	(	PUNCT
ejpam-4550	367	9	1	1	NUM
ejpam-4550	367	10	)	)	PUNCT
ejpam-4550	367	11	(	(	PUNCT
ejpam-4550	367	12	2023	2023	NUM
ejpam-4550	367	13	)	)	PUNCT
ejpam-4550	367	14	,	,	PUNCT
ejpam-4550	367	15	207	207	NUM
ejpam-4550	367	16	-	-	SYM
ejpam-4550	367	17	232	232	NUM
ejpam-4550	367	18	227	227	NUM
ejpam-4550	367	19	table	table	NOUN
ejpam-4550	367	20	4	4	NUM
ejpam-4550	367	21	:	:	PUNCT
ejpam-4550	367	22	parameter	parameter	NOUN
ejpam-4550	367	23	values	value	NOUN
ejpam-4550	367	24	parameter	parameter	PROPN
ejpam-4550	367	25	value	value	NOUN
ejpam-4550	367	26	source	source	NOUN
ejpam-4550	367	27	parameter	parameter	NOUN
ejpam-4550	367	28	value	value	NOUN
ejpam-4550	367	29	source	source	NOUN
ejpam-4550	367	30	b	b	PROPN
ejpam-4550	367	31	0.0432	0.0432	NUM
ejpam-4550	367	32	estimated	estimate	VERB
ejpam-4550	367	33	a2	a2	PROPN
ejpam-4550	367	34	0.01	0.01	NUM
ejpam-4550	367	35	estimated	estimate	VERB
ejpam-4550	367	36	m	m	PROPN
ejpam-4550	367	37	0.0096	0.0096	NUM
ejpam-4550	367	38	estimated	estimate	VERB
ejpam-4550	367	39	a3	a3	NOUN
ejpam-4550	367	40	0.01	0.01	NUM
ejpam-4550	367	41	estimated	estimate	VERB
ejpam-4550	367	42	γ	γ	X
ejpam-4550	367	43	0.025	0.025	NUM
ejpam-4550	367	44	estimated	estimate	VERB
ejpam-4550	367	45	a4	a4	NOUN
ejpam-4550	367	46	0.01	0.01	NUM
ejpam-4550	367	47	estimated	estimate	VERB
ejpam-4550	367	48	β1	β1	PROPN
ejpam-4550	367	49	0.035	0.035	NUM
ejpam-4550	367	50	estimated	estimate	VERB
ejpam-4550	367	51	c1	c1	PROPN
ejpam-4550	367	52	0.02	0.02	NUM
ejpam-4550	367	53	estimated	estimate	VERB
ejpam-4550	367	54	β2	β2	NOUN
ejpam-4550	367	55	0.025	0.025	NUM
ejpam-4550	367	56	estimated	estimate	VERB
ejpam-4550	367	57	c2	c2	PROPN
ejpam-4550	367	58	0.02	0.02	NUM
ejpam-4550	367	59	estimated	estimate	VERB
ejpam-4550	367	60	a1	a1	NOUN
ejpam-4550	367	61	0.01	0.01	NUM
ejpam-4550	367	62	estimated	estimate	VERB
ejpam-4550	367	63	c3	c3	PROPN
ejpam-4550	367	64	0.02	0.02	NUM
ejpam-4550	367	65	estimated	estimate	VERB
ejpam-4550	367	66	0	0	NUM
ejpam-4550	367	67	200	200	NUM
ejpam-4550	367	68	400	400	NUM
ejpam-4550	367	69	600	600	NUM
ejpam-4550	367	70	800	800	NUM
ejpam-4550	367	71	1000	1000	NUM
ejpam-4550	367	72	1200	1200	NUM
ejpam-4550	367	73	1400	1400	NUM
ejpam-4550	367	74	1600	1600	NUM
ejpam-4550	367	75	time	time	NOUN
ejpam-4550	367	76	(	(	PUNCT
ejpam-4550	367	77	t	t	NOUN
ejpam-4550	367	78	)	)	PUNCT
ejpam-4550	367	79	0.2	0.2	NUM
ejpam-4550	367	80	0.3	0.3	NUM
ejpam-4550	367	81	0.4	0.4	NUM
ejpam-4550	367	82	0.5	0.5	NUM
ejpam-4550	367	83	0.6	0.6	NUM
ejpam-4550	367	84	0.7	0.7	NUM
ejpam-4550	367	85	0.8	0.8	NUM
ejpam-4550	367	86	p	p	NOUN
ejpam-4550	368	1	ro	ro	NOUN
ejpam-4550	369	1	p	p	X
ejpam-4550	369	2	o	o	X
ejpam-4550	369	3	rt	rt	PROPN
ejpam-4550	369	4	io	io	PROPN
ejpam-4550	369	5	n	n	ADV
ejpam-4550	370	1	o	o	X
ejpam-4550	370	2	f	f	X
ejpam-4550	370	3	s	s	PROPN
ejpam-4550	370	4	u	u	NOUN
ejpam-4550	370	5	s	s	PRON
ejpam-4550	370	6	c	c	NOUN
ejpam-4550	370	7	e	e	NOUN
ejpam-4550	370	8	p	p	X
ejpam-4550	370	9	ti	ti	PROPN
ejpam-4550	370	10	b	b	X
ejpam-4550	370	11	le	le	X
ejpam-4550	370	12	i	i	PRON
ejpam-4550	371	1	n	n	VERB
ejpam-4550	371	2	d	d	NOUN
ejpam-4550	371	3	iv	iv	X
ejpam-4550	372	1	i	i	PROPN
ejpam-4550	372	2	d	d	PROPN
ejpam-4550	372	3	u	u	PROPN
ejpam-4550	372	4	a	a	DET
ejpam-4550	372	5	ls	ls	ADJ
ejpam-4550	372	6	o	o	X
ejpam-4550	372	7	f	f	X
ejpam-4550	372	8	c	c	X
ejpam-4550	372	9	la	la	PROPN
ejpam-4550	372	10	s	s	PROPN
ejpam-4550	372	11	s	s	X
ejpam-4550	372	12	c	c	NOUN
ejpam-4550	372	13	1	1	NUM
ejpam-4550	372	14	(	(	PUNCT
ejpam-4550	372	15	a	a	DET
ejpam-4550	372	16	)	)	PUNCT
ejpam-4550	372	17	proportion	proportion	NOUN
ejpam-4550	372	18	of	of	ADP
ejpam-4550	372	19	susceptible	susceptible	ADJ
ejpam-4550	372	20	individuals	individual	NOUN
ejpam-4550	372	21	in	in	ADP
ejpam-4550	372	22	c1	c1	PROPN
ejpam-4550	372	23	0	0	NUM
ejpam-4550	372	24	200	200	NUM
ejpam-4550	372	25	400	400	NUM
ejpam-4550	372	26	600	600	NUM
ejpam-4550	372	27	800	800	NUM
ejpam-4550	372	28	1000	1000	NUM
ejpam-4550	372	29	1200	1200	NUM
ejpam-4550	372	30	1400	1400	NUM
ejpam-4550	372	31	1600	1600	NUM
ejpam-4550	372	32	time	time	NOUN
ejpam-4550	372	33	(	(	PUNCT
ejpam-4550	372	34	t	t	NOUN
ejpam-4550	372	35	)	)	PUNCT
ejpam-4550	372	36	0.1	0.1	NUM
ejpam-4550	372	37	0.15	0.15	NUM
ejpam-4550	372	38	0.2	0.2	NUM
ejpam-4550	372	39	0.25	0.25	NUM
ejpam-4550	372	40	0.3	0.3	NUM
ejpam-4550	372	41	0.35	0.35	NUM
ejpam-4550	372	42	0.4	0.4	NUM
ejpam-4550	372	43	p	p	NOUN
ejpam-4550	372	44	ro	ro	NOUN
ejpam-4550	373	1	p	p	X
ejpam-4550	373	2	o	o	X
ejpam-4550	373	3	rt	rt	PROPN
ejpam-4550	373	4	io	io	PROPN
ejpam-4550	373	5	n	n	ADV
ejpam-4550	374	1	o	o	X
ejpam-4550	374	2	f	f	X
ejpam-4550	374	3	s	s	PROPN
ejpam-4550	374	4	u	u	NOUN
ejpam-4550	374	5	s	s	PRON
ejpam-4550	374	6	c	c	NOUN
ejpam-4550	374	7	e	e	NOUN
ejpam-4550	374	8	p	p	X
ejpam-4550	374	9	ti	ti	PROPN
ejpam-4550	374	10	b	b	X
ejpam-4550	374	11	le	le	X
ejpam-4550	374	12	i	i	PRON
ejpam-4550	375	1	n	n	VERB
ejpam-4550	375	2	d	d	NOUN
ejpam-4550	375	3	iv	iv	X
ejpam-4550	376	1	i	i	PROPN
ejpam-4550	376	2	d	d	PROPN
ejpam-4550	376	3	u	u	PROPN
ejpam-4550	376	4	a	a	DET
ejpam-4550	376	5	ls	ls	ADJ
ejpam-4550	376	6	o	o	X
ejpam-4550	376	7	f	f	X
ejpam-4550	376	8	c	c	X
ejpam-4550	376	9	la	la	PROPN
ejpam-4550	376	10	s	s	PROPN
ejpam-4550	376	11	s	s	X
ejpam-4550	376	12	c	c	NOUN
ejpam-4550	376	13	2	2	NUM
ejpam-4550	376	14	(	(	PUNCT
ejpam-4550	376	15	b	b	NOUN
ejpam-4550	376	16	)	)	PUNCT
ejpam-4550	376	17	proportion	proportion	NOUN
ejpam-4550	376	18	of	of	ADP
ejpam-4550	376	19	susceptible	susceptible	ADJ
ejpam-4550	376	20	individuals	individual	NOUN
ejpam-4550	376	21	in	in	ADP
ejpam-4550	376	22	c2	c2	PROPN
ejpam-4550	376	23	figure	figure	NOUN
ejpam-4550	376	24	2	2	NUM
ejpam-4550	376	25	:	:	PUNCT
ejpam-4550	376	26	time	time	NOUN
ejpam-4550	376	27	series	series	NOUN
ejpam-4550	376	28	plots	plot	NOUN
ejpam-4550	376	29	of	of	ADP
ejpam-4550	376	30	the	the	DET
ejpam-4550	376	31	proportions	proportion	NOUN
ejpam-4550	376	32	of	of	ADP
ejpam-4550	376	33	susceptible	susceptible	ADJ
ejpam-4550	376	34	individuals	individual	NOUN
ejpam-4550	376	35	in	in	ADP
ejpam-4550	376	36	classes	class	NOUN
ejpam-4550	376	37	c1	c1	PROPN
ejpam-4550	376	38	and	and	CCONJ
ejpam-4550	376	39	c2	c2	PROPN
ejpam-4550	376	40	for	for	ADP
ejpam-4550	376	41	r0	r0	NOUN
ejpam-4550	376	42	=	=	PUNCT
ejpam-4550	376	43	0.67893	0.67893	NUM
ejpam-4550	376	44	<	<	X
ejpam-4550	376	45	1	1	NUM
ejpam-4550	376	46	using	use	VERB
ejpam-4550	376	47	various	various	ADJ
ejpam-4550	376	48	initial	initial	ADJ
ejpam-4550	376	49	conditions	condition	NOUN
ejpam-4550	376	50	and	and	CCONJ
ejpam-4550	376	51	parameter	parameter	NOUN
ejpam-4550	376	52	values	value	NOUN
ejpam-4550	376	53	reported	report	VERB
ejpam-4550	376	54	in	in	ADP
ejpam-4550	376	55	table	table	NOUN
ejpam-4550	376	56	4	4	NUM
ejpam-4550	376	57	.	.	NOUN
ejpam-4550	376	58	0	0	NUM
ejpam-4550	377	1	200	200	NUM
ejpam-4550	377	2	400	400	NUM
ejpam-4550	377	3	600	600	NUM
ejpam-4550	377	4	800	800	NUM
ejpam-4550	377	5	1000	1000	NUM
ejpam-4550	377	6	1200	1200	NUM
ejpam-4550	377	7	1400	1400	NUM
ejpam-4550	377	8	1600	1600	NUM
ejpam-4550	377	9	time	time	NOUN
ejpam-4550	377	10	(	(	PUNCT
ejpam-4550	377	11	t	t	NOUN
ejpam-4550	377	12	)	)	PUNCT
ejpam-4550	377	13	0	0	NUM
ejpam-4550	377	14	0.01	0.01	NUM
ejpam-4550	377	15	0.02	0.02	NUM
ejpam-4550	377	16	0.03	0.03	NUM
ejpam-4550	377	17	0.04	0.04	NUM
ejpam-4550	377	18	0.05	0.05	NUM
ejpam-4550	377	19	0.06	0.06	NUM
ejpam-4550	377	20	p	p	NOUN
ejpam-4550	377	21	ro	ro	NOUN
ejpam-4550	378	1	p	p	X
ejpam-4550	378	2	o	o	X
ejpam-4550	378	3	rt	rt	PROPN
ejpam-4550	378	4	io	io	PROPN
ejpam-4550	378	5	n	n	PROPN
ejpam-4550	378	6	o	o	X
ejpam-4550	378	7	f	f	X
ejpam-4550	379	1	in	in	ADP
ejpam-4550	379	2	d	d	PROPN
ejpam-4550	379	3	iv	iv	INTJ
ejpam-4550	379	4	i	i	PROPN
ejpam-4550	379	5	d	d	PROPN
ejpam-4550	379	6	u	u	PROPN
ejpam-4550	379	7	a	a	DET
ejpam-4550	379	8	ls	ls	X
ejpam-4550	379	9	i	i	PRON
ejpam-4550	379	10	n	n	X
ejpam-4550	379	11	fe	fe	X
ejpam-4550	379	12	c	c	X
ejpam-4550	379	13	te	te	PROPN
ejpam-4550	379	14	d	d	X
ejpam-4550	379	15	a	a	DET
ejpam-4550	379	16	t	t	NOUN
ejpam-4550	379	17	s	s	X
ejpam-4550	379	18	ta	ta	ADP
ejpam-4550	379	19	g	g	PROPN
ejpam-4550	379	20	e	e	PROPN
ejpam-4550	380	1	1	1	NUM
ejpam-4550	380	2	o	o	NOUN
ejpam-4550	380	3	f	f	X
ejpam-4550	380	4	c	c	X
ejpam-4550	380	5	la	la	PROPN
ejpam-4550	380	6	s	s	PROPN
ejpam-4550	380	7	s	s	X
ejpam-4550	380	8	c	c	NOUN
ejpam-4550	380	9	1	1	NUM
ejpam-4550	380	10	(	(	PUNCT
ejpam-4550	380	11	a	a	DET
ejpam-4550	380	12	)	)	PUNCT
ejpam-4550	380	13	proportion	proportion	NOUN
ejpam-4550	380	14	of	of	ADP
ejpam-4550	380	15	individuals	individual	NOUN
ejpam-4550	380	16	infected	infect	VERB
ejpam-4550	380	17	at	at	ADP
ejpam-4550	380	18	stage	stage	NOUN
ejpam-4550	380	19	1	1	NUM
ejpam-4550	380	20	in	in	ADP
ejpam-4550	380	21	c1	c1	PROPN
ejpam-4550	380	22	0	0	NUM
ejpam-4550	380	23	200	200	NUM
ejpam-4550	380	24	400	400	NUM
ejpam-4550	380	25	600	600	NUM
ejpam-4550	380	26	800	800	NUM
ejpam-4550	380	27	1000	1000	NUM
ejpam-4550	380	28	1200	1200	NUM
ejpam-4550	380	29	1400	1400	NUM
ejpam-4550	380	30	1600	1600	NUM
ejpam-4550	380	31	time	time	NOUN
ejpam-4550	380	32	(	(	PUNCT
ejpam-4550	380	33	t	t	NOUN
ejpam-4550	380	34	)	)	PUNCT
ejpam-4550	380	35	0	0	NUM
ejpam-4550	380	36	0.01	0.01	NUM
ejpam-4550	380	37	0.02	0.02	NUM
ejpam-4550	380	38	0.03	0.03	NUM
ejpam-4550	380	39	0.04	0.04	NUM
ejpam-4550	380	40	0.05	0.05	NUM
ejpam-4550	380	41	0.06	0.06	NUM
ejpam-4550	380	42	0.07	0.07	NUM
ejpam-4550	380	43	p	p	NOUN
ejpam-4550	380	44	ro	ro	NOUN
ejpam-4550	381	1	p	p	X
ejpam-4550	382	1	o	o	X
ejpam-4550	383	1	rt	rt	PROPN
ejpam-4550	384	1	io	io	PROPN
ejpam-4550	385	1	n	n	PROPN
ejpam-4550	385	2	o	o	X
ejpam-4550	385	3	f	f	X
ejpam-4550	385	4	in	in	ADP
ejpam-4550	385	5	d	d	PROPN
ejpam-4550	385	6	iv	iv	INTJ
ejpam-4550	385	7	i	i	PROPN
ejpam-4550	385	8	d	d	PROPN
ejpam-4550	385	9	u	u	PROPN
ejpam-4550	385	10	a	a	DET
ejpam-4550	385	11	ls	ls	X
ejpam-4550	385	12	i	i	PRON
ejpam-4550	385	13	n	n	X
ejpam-4550	385	14	fe	fe	X
ejpam-4550	385	15	c	c	X
ejpam-4550	385	16	te	te	PROPN
ejpam-4550	385	17	d	d	X
ejpam-4550	385	18	a	a	DET
ejpam-4550	385	19	t	t	NOUN
ejpam-4550	385	20	s	s	X
ejpam-4550	385	21	ta	ta	ADP
ejpam-4550	385	22	g	g	PROPN
ejpam-4550	385	23	e	e	PROPN
ejpam-4550	385	24	1	1	NUM
ejpam-4550	385	25	o	o	NOUN
ejpam-4550	385	26	f	f	X
ejpam-4550	385	27	c	c	X
ejpam-4550	385	28	la	la	PROPN
ejpam-4550	385	29	s	s	PROPN
ejpam-4550	385	30	s	s	X
ejpam-4550	385	31	c	c	NOUN
ejpam-4550	385	32	2	2	NUM
ejpam-4550	385	33	(	(	PUNCT
ejpam-4550	385	34	b	b	NOUN
ejpam-4550	385	35	)	)	PUNCT
ejpam-4550	385	36	proportion	proportion	NOUN
ejpam-4550	385	37	of	of	ADP
ejpam-4550	385	38	individuals	individual	NOUN
ejpam-4550	385	39	infected	infect	VERB
ejpam-4550	385	40	at	at	ADP
ejpam-4550	385	41	stage	stage	NOUN
ejpam-4550	385	42	1	1	NUM
ejpam-4550	385	43	in	in	ADP
ejpam-4550	385	44	c2	c2	PROPN
ejpam-4550	385	45	figure	figure	VERB
ejpam-4550	385	46	3	3	NUM
ejpam-4550	385	47	:	:	PUNCT
ejpam-4550	385	48	time	time	NOUN
ejpam-4550	385	49	series	series	NOUN
ejpam-4550	385	50	plots	plot	NOUN
ejpam-4550	385	51	of	of	ADP
ejpam-4550	385	52	the	the	DET
ejpam-4550	385	53	proportions	proportion	NOUN
ejpam-4550	385	54	of	of	ADP
ejpam-4550	385	55	infected	infected	ADJ
ejpam-4550	385	56	individuals	individual	NOUN
ejpam-4550	385	57	at	at	ADP
ejpam-4550	385	58	stage	stage	NOUN
ejpam-4550	385	59	1	1	NUM
ejpam-4550	385	60	in	in	ADP
ejpam-4550	385	61	classes	class	NOUN
ejpam-4550	385	62	c1	c1	PROPN
ejpam-4550	385	63	and	and	CCONJ
ejpam-4550	385	64	c2	c2	PROPN
ejpam-4550	385	65	for	for	ADP
ejpam-4550	385	66	r0	r0	NOUN
ejpam-4550	385	67	=	=	PUNCT
ejpam-4550	385	68	0.67893	0.67893	NUM
ejpam-4550	385	69	<	<	X
ejpam-4550	385	70	1	1	NUM
ejpam-4550	385	71	using	use	VERB
ejpam-4550	385	72	various	various	ADJ
ejpam-4550	385	73	initial	initial	ADJ
ejpam-4550	385	74	conditions	condition	NOUN
ejpam-4550	385	75	and	and	CCONJ
ejpam-4550	385	76	parameter	parameter	NOUN
ejpam-4550	385	77	values	value	NOUN
ejpam-4550	385	78	reported	report	VERB
ejpam-4550	385	79	in	in	ADP
ejpam-4550	385	80	table	table	NOUN
ejpam-4550	385	81	4	4	NUM
ejpam-4550	385	82	.	.	PUNCT
ejpam-4550	385	83	(	(	PUNCT
ejpam-4550	385	84	dfe	dfe	PROPN
ejpam-4550	385	85	)	)	PUNCT
ejpam-4550	385	86	.	.	PUNCT
ejpam-4550	386	1	they	they	PRON
ejpam-4550	386	2	show	show	VERB
ejpam-4550	386	3	that	that	SCONJ
ejpam-4550	386	4	dfe	dfe	PROPN
ejpam-4550	386	5	is	be	AUX
ejpam-4550	386	6	locally	locally	ADV
ejpam-4550	386	7	asymptotically	asymptotically	ADV
ejpam-4550	386	8	stable	stable	ADJ
ejpam-4550	386	9	when	when	SCONJ
ejpam-4550	386	10	r0	r0	NOUN
ejpam-4550	386	11	<	<	X
ejpam-4550	386	12	1	1	NUM
ejpam-4550	386	13	.	.	PUNCT
ejpam-4550	387	1	these	these	DET
ejpam-4550	387	2	numerical	numerical	ADJ
ejpam-4550	387	3	simulations	simulation	NOUN
ejpam-4550	387	4	support	support	VERB
ejpam-4550	387	5	the	the	DET
ejpam-4550	387	6	result	result	NOUN
ejpam-4550	387	7	stated	state	VERB
ejpam-4550	387	8	in	in	ADP
ejpam-4550	387	9	theorem	theorem	NOUN
ejpam-4550	387	10	2	2	NUM
ejpam-4550	387	11	on	on	ADP
ejpam-4550	387	12	the	the	DET
ejpam-4550	387	13	stability	stability	NOUN
ejpam-4550	387	14	of	of	ADP
ejpam-4550	387	15	dfe	dfe	PROPN
ejpam-4550	387	16	.	.	PUNCT
ejpam-4550	388	1	further	far	ADV
ejpam-4550	388	2	using	use	VERB
ejpam-4550	388	3	the	the	DET
ejpam-4550	388	4	parameter	parameter	NOUN
ejpam-4550	388	5	values	value	NOUN
ejpam-4550	388	6	given	give	VERB
ejpam-4550	388	7	in	in	ADP
ejpam-4550	388	8	table	table	NOUN
ejpam-4550	388	9	5	5	NUM
ejpam-4550	388	10	,	,	PUNCT
ejpam-4550	388	11	we	we	PRON
ejpam-4550	388	12	consider	consider	VERB
ejpam-4550	388	13	the	the	DET
ejpam-4550	388	14	case	case	NOUN
ejpam-4550	389	1	when	when	SCONJ
ejpam-4550	389	2	r0	r0	NOUN
ejpam-4550	389	3	=	=	SYM
ejpam-4550	389	4	m.	m.	NOUN
ejpam-4550	389	5	alassane	alassane	NOUN
ejpam-4550	389	6	et	et	PROPN
ejpam-4550	389	7	al	al	PROPN
ejpam-4550	389	8	.	.	PUNCT
ejpam-4550	389	9	/	/	SYM
ejpam-4550	389	10	eur	eur	PROPN
ejpam-4550	389	11	.	.	PUNCT
ejpam-4550	390	1	j.	j.	PROPN
ejpam-4550	390	2	pure	pure	PROPN
ejpam-4550	390	3	appl	appl	PROPN
ejpam-4550	390	4	.	.	PROPN
ejpam-4550	390	5	math	math	PROPN
ejpam-4550	390	6	,	,	PUNCT
ejpam-4550	390	7	16	16	NUM
ejpam-4550	390	8	(	(	PUNCT
ejpam-4550	390	9	1	1	NUM
ejpam-4550	390	10	)	)	PUNCT
ejpam-4550	390	11	(	(	PUNCT
ejpam-4550	390	12	2023	2023	NUM
ejpam-4550	390	13	)	)	PUNCT
ejpam-4550	390	14	,	,	PUNCT
ejpam-4550	390	15	207	207	NUM
ejpam-4550	390	16	-	-	SYM
ejpam-4550	390	17	232	232	NUM
ejpam-4550	390	18	228	228	NUM
ejpam-4550	390	19	0	0	NUM
ejpam-4550	391	1	200	200	NUM
ejpam-4550	391	2	400	400	NUM
ejpam-4550	391	3	600	600	NUM
ejpam-4550	391	4	800	800	NUM
ejpam-4550	391	5	1000	1000	NUM
ejpam-4550	391	6	1200	1200	NUM
ejpam-4550	391	7	1400	1400	NUM
ejpam-4550	391	8	1600	1600	NUM
ejpam-4550	391	9	time	time	NOUN
ejpam-4550	391	10	(	(	PUNCT
ejpam-4550	391	11	t	t	NOUN
ejpam-4550	391	12	)	)	PUNCT
ejpam-4550	391	13	0	0	NUM
ejpam-4550	391	14	0.01	0.01	NUM
ejpam-4550	391	15	0.02	0.02	NUM
ejpam-4550	391	16	0.03	0.03	NUM
ejpam-4550	391	17	0.04	0.04	NUM
ejpam-4550	391	18	0.05	0.05	NUM
ejpam-4550	391	19	0.06	0.06	NUM
ejpam-4550	391	20	0.07	0.07	NUM
ejpam-4550	391	21	0.08	0.08	NUM
ejpam-4550	391	22	0.09	0.09	NUM
ejpam-4550	391	23	0.1	0.1	NUM
ejpam-4550	391	24	p	p	NOUN
ejpam-4550	391	25	ro	ro	NOUN
ejpam-4550	392	1	p	p	X
ejpam-4550	392	2	o	o	X
ejpam-4550	392	3	rt	rt	PROPN
ejpam-4550	392	4	io	io	PROPN
ejpam-4550	392	5	n	n	PROPN
ejpam-4550	392	6	o	o	X
ejpam-4550	392	7	f	f	X
ejpam-4550	392	8	in	in	ADP
ejpam-4550	392	9	d	d	PROPN
ejpam-4550	392	10	iv	iv	INTJ
ejpam-4550	392	11	i	i	PROPN
ejpam-4550	392	12	d	d	PROPN
ejpam-4550	392	13	u	u	PROPN
ejpam-4550	392	14	a	a	DET
ejpam-4550	392	15	ls	ls	X
ejpam-4550	392	16	i	i	PRON
ejpam-4550	392	17	n	n	X
ejpam-4550	392	18	fe	fe	X
ejpam-4550	393	1	c	c	X
ejpam-4550	393	2	te	te	PROPN
ejpam-4550	393	3	d	d	X
ejpam-4550	393	4	a	a	DET
ejpam-4550	393	5	t	t	NOUN
ejpam-4550	393	6	s	s	X
ejpam-4550	393	7	ta	ta	ADP
ejpam-4550	393	8	g	g	PROPN
ejpam-4550	393	9	e	e	PROPN
ejpam-4550	393	10	2	2	NUM
ejpam-4550	393	11	o	o	NOUN
ejpam-4550	393	12	f	f	X
ejpam-4550	393	13	c	c	X
ejpam-4550	393	14	la	la	PROPN
ejpam-4550	393	15	s	s	PROPN
ejpam-4550	393	16	s	s	X
ejpam-4550	393	17	c	c	NOUN
ejpam-4550	393	18	1	1	NUM
ejpam-4550	393	19	(	(	PUNCT
ejpam-4550	393	20	a	a	DET
ejpam-4550	393	21	)	)	PUNCT
ejpam-4550	393	22	proportion	proportion	NOUN
ejpam-4550	393	23	of	of	ADP
ejpam-4550	393	24	individuals	individual	NOUN
ejpam-4550	393	25	infected	infect	VERB
ejpam-4550	393	26	at	at	ADP
ejpam-4550	393	27	stage	stage	NOUN
ejpam-4550	393	28	2	2	NUM
ejpam-4550	393	29	in	in	ADP
ejpam-4550	393	30	c1	c1	PROPN
ejpam-4550	393	31	0	0	NUM
ejpam-4550	393	32	200	200	NUM
ejpam-4550	393	33	400	400	NUM
ejpam-4550	393	34	600	600	NUM
ejpam-4550	393	35	800	800	NUM
ejpam-4550	393	36	1000	1000	NUM
ejpam-4550	393	37	1200	1200	NUM
ejpam-4550	393	38	1400	1400	NUM
ejpam-4550	393	39	1600	1600	NUM
ejpam-4550	393	40	time	time	NOUN
ejpam-4550	393	41	(	(	PUNCT
ejpam-4550	393	42	t	t	NOUN
ejpam-4550	393	43	)	)	PUNCT
ejpam-4550	393	44	0	0	NUM
ejpam-4550	393	45	0.02	0.02	NUM
ejpam-4550	393	46	0.04	0.04	NUM
ejpam-4550	393	47	0.06	0.06	NUM
ejpam-4550	393	48	0.08	0.08	NUM
ejpam-4550	393	49	0.1	0.1	NUM
ejpam-4550	393	50	0.12	0.12	NUM
ejpam-4550	393	51	p	p	NOUN
ejpam-4550	394	1	ro	ro	NOUN
ejpam-4550	395	1	p	p	X
ejpam-4550	395	2	o	o	X
ejpam-4550	395	3	rt	rt	PROPN
ejpam-4550	395	4	io	io	PROPN
ejpam-4550	395	5	n	n	PROPN
ejpam-4550	395	6	o	o	X
ejpam-4550	395	7	f	f	X
ejpam-4550	396	1	in	in	ADP
ejpam-4550	396	2	d	d	PROPN
ejpam-4550	396	3	iv	iv	INTJ
ejpam-4550	396	4	i	i	PROPN
ejpam-4550	396	5	d	d	PROPN
ejpam-4550	396	6	u	u	PROPN
ejpam-4550	396	7	a	a	DET
ejpam-4550	396	8	ls	ls	X
ejpam-4550	396	9	i	i	PRON
ejpam-4550	396	10	n	n	X
ejpam-4550	396	11	fe	fe	X
ejpam-4550	396	12	c	c	X
ejpam-4550	396	13	te	te	PROPN
ejpam-4550	396	14	d	d	X
ejpam-4550	396	15	a	a	DET
ejpam-4550	396	16	t	t	NOUN
ejpam-4550	396	17	s	s	X
ejpam-4550	396	18	ta	ta	ADP
ejpam-4550	396	19	g	g	PROPN
ejpam-4550	396	20	e	e	PROPN
ejpam-4550	396	21	2	2	NUM
ejpam-4550	396	22	o	o	NOUN
ejpam-4550	396	23	f	f	X
ejpam-4550	396	24	c	c	X
ejpam-4550	396	25	la	la	PROPN
ejpam-4550	396	26	s	s	PROPN
ejpam-4550	396	27	s	s	X
ejpam-4550	396	28	c	c	NOUN
ejpam-4550	396	29	2	2	NUM
ejpam-4550	396	30	(	(	PUNCT
ejpam-4550	396	31	b	b	NOUN
ejpam-4550	396	32	)	)	PUNCT
ejpam-4550	396	33	proportion	proportion	NOUN
ejpam-4550	396	34	of	of	ADP
ejpam-4550	396	35	individuals	individual	NOUN
ejpam-4550	396	36	infected	infect	VERB
ejpam-4550	396	37	at	at	ADP
ejpam-4550	396	38	stage	stage	NOUN
ejpam-4550	396	39	2	2	NUM
ejpam-4550	396	40	in	in	ADP
ejpam-4550	396	41	c2	c2	PROPN
ejpam-4550	396	42	figure	figure	VERB
ejpam-4550	396	43	4	4	NUM
ejpam-4550	396	44	:	:	PUNCT
ejpam-4550	396	45	time	time	NOUN
ejpam-4550	396	46	series	series	NOUN
ejpam-4550	396	47	plots	plot	NOUN
ejpam-4550	396	48	of	of	ADP
ejpam-4550	396	49	the	the	DET
ejpam-4550	396	50	proportions	proportion	NOUN
ejpam-4550	396	51	of	of	ADP
ejpam-4550	396	52	infected	infected	ADJ
ejpam-4550	396	53	individuals	individual	NOUN
ejpam-4550	396	54	at	at	ADP
ejpam-4550	396	55	stage	stage	NOUN
ejpam-4550	396	56	2	2	NUM
ejpam-4550	396	57	in	in	ADP
ejpam-4550	396	58	classes	class	NOUN
ejpam-4550	396	59	c1	c1	PROPN
ejpam-4550	396	60	and	and	CCONJ
ejpam-4550	396	61	c2	c2	PROPN
ejpam-4550	396	62	for	for	ADP
ejpam-4550	396	63	r0	r0	NOUN
ejpam-4550	396	64	=	=	PUNCT
ejpam-4550	396	65	0.67893	0.67893	NUM
ejpam-4550	396	66	<	<	X
ejpam-4550	396	67	1	1	NUM
ejpam-4550	396	68	using	use	VERB
ejpam-4550	396	69	various	various	ADJ
ejpam-4550	396	70	initial	initial	ADJ
ejpam-4550	396	71	conditions	condition	NOUN
ejpam-4550	396	72	and	and	CCONJ
ejpam-4550	396	73	parameter	parameter	NOUN
ejpam-4550	396	74	values	value	NOUN
ejpam-4550	396	75	reported	report	VERB
ejpam-4550	396	76	in	in	ADP
ejpam-4550	396	77	table	table	NOUN
ejpam-4550	396	78	4	4	NUM
ejpam-4550	396	79	.	.	NOUN
ejpam-4550	396	80	0	0	NUM
ejpam-4550	396	81	200	200	NUM
ejpam-4550	396	82	400	400	NUM
ejpam-4550	396	83	600	600	NUM
ejpam-4550	396	84	800	800	NUM
ejpam-4550	396	85	1000	1000	NUM
ejpam-4550	396	86	1200	1200	NUM
ejpam-4550	396	87	1400	1400	NUM
ejpam-4550	396	88	1600	1600	NUM
ejpam-4550	396	89	time	time	NOUN
ejpam-4550	396	90	(	(	PUNCT
ejpam-4550	396	91	t	t	NOUN
ejpam-4550	396	92	)	)	PUNCT
ejpam-4550	396	93	0	0	NUM
ejpam-4550	396	94	0.01	0.01	NUM
ejpam-4550	396	95	0.02	0.02	NUM
ejpam-4550	396	96	0.03	0.03	NUM
ejpam-4550	396	97	0.04	0.04	NUM
ejpam-4550	396	98	0.05	0.05	NUM
ejpam-4550	396	99	0.06	0.06	NUM
ejpam-4550	396	100	0.07	0.07	NUM
ejpam-4550	396	101	0.08	0.08	NUM
ejpam-4550	396	102	p	p	NOUN
ejpam-4550	396	103	ro	ro	NOUN
ejpam-4550	396	104	p	p	X
ejpam-4550	396	105	o	o	X
ejpam-4550	396	106	rt	rt	PROPN
ejpam-4550	396	107	io	io	PROPN
ejpam-4550	396	108	n	n	PROPN
ejpam-4550	396	109	o	o	X
ejpam-4550	396	110	f	f	X
ejpam-4550	397	1	in	in	ADP
ejpam-4550	397	2	d	d	PROPN
ejpam-4550	397	3	iv	iv	INTJ
ejpam-4550	397	4	i	i	PROPN
ejpam-4550	397	5	d	d	PROPN
ejpam-4550	397	6	u	u	PROPN
ejpam-4550	397	7	a	a	DET
ejpam-4550	397	8	ls	ls	X
ejpam-4550	397	9	i	i	PRON
ejpam-4550	397	10	n	n	X
ejpam-4550	397	11	fe	fe	X
ejpam-4550	397	12	c	c	X
ejpam-4550	397	13	te	te	PROPN
ejpam-4550	397	14	d	d	X
ejpam-4550	397	15	a	a	DET
ejpam-4550	397	16	t	t	NOUN
ejpam-4550	397	17	s	s	X
ejpam-4550	397	18	ta	ta	ADP
ejpam-4550	397	19	g	g	PROPN
ejpam-4550	397	20	e	e	PROPN
ejpam-4550	397	21	3	3	NUM
ejpam-4550	397	22	o	o	NOUN
ejpam-4550	397	23	f	f	X
ejpam-4550	397	24	c	c	X
ejpam-4550	397	25	la	la	PROPN
ejpam-4550	397	26	s	s	PROPN
ejpam-4550	397	27	s	s	X
ejpam-4550	397	28	c	c	NOUN
ejpam-4550	397	29	1	1	NUM
ejpam-4550	397	30	(	(	PUNCT
ejpam-4550	397	31	a	a	DET
ejpam-4550	397	32	)	)	PUNCT
ejpam-4550	397	33	proportion	proportion	NOUN
ejpam-4550	397	34	of	of	ADP
ejpam-4550	397	35	individuals	individual	NOUN
ejpam-4550	397	36	infected	infect	VERB
ejpam-4550	397	37	at	at	ADP
ejpam-4550	397	38	stage	stage	NOUN
ejpam-4550	397	39	3	3	NUM
ejpam-4550	397	40	in	in	ADP
ejpam-4550	397	41	c1	c1	PROPN
ejpam-4550	397	42	0	0	NUM
ejpam-4550	397	43	200	200	NUM
ejpam-4550	397	44	400	400	NUM
ejpam-4550	397	45	600	600	NUM
ejpam-4550	397	46	800	800	NUM
ejpam-4550	397	47	1000	1000	NUM
ejpam-4550	397	48	1200	1200	NUM
ejpam-4550	397	49	1400	1400	NUM
ejpam-4550	397	50	1600	1600	NUM
ejpam-4550	397	51	time	time	NOUN
ejpam-4550	397	52	(	(	PUNCT
ejpam-4550	397	53	t	t	NOUN
ejpam-4550	397	54	)	)	PUNCT
ejpam-4550	397	55	0	0	NUM
ejpam-4550	397	56	0.01	0.01	NUM
ejpam-4550	397	57	0.02	0.02	NUM
ejpam-4550	397	58	0.03	0.03	NUM
ejpam-4550	397	59	0.04	0.04	NUM
ejpam-4550	397	60	0.05	0.05	NUM
ejpam-4550	397	61	0.06	0.06	NUM
ejpam-4550	397	62	0.07	0.07	NUM
ejpam-4550	397	63	0.08	0.08	NUM
ejpam-4550	397	64	p	p	NOUN
ejpam-4550	397	65	ro	ro	NOUN
ejpam-4550	398	1	p	p	X
ejpam-4550	399	1	o	o	X
ejpam-4550	400	1	rt	rt	PROPN
ejpam-4550	401	1	io	io	PROPN
ejpam-4550	402	1	n	n	PROPN
ejpam-4550	402	2	o	o	X
ejpam-4550	402	3	f	f	X
ejpam-4550	402	4	in	in	ADP
ejpam-4550	402	5	d	d	PROPN
ejpam-4550	402	6	iv	iv	INTJ
ejpam-4550	402	7	i	i	PROPN
ejpam-4550	402	8	d	d	PROPN
ejpam-4550	402	9	u	u	PROPN
ejpam-4550	402	10	a	a	DET
ejpam-4550	402	11	ls	ls	X
ejpam-4550	402	12	i	i	PRON
ejpam-4550	402	13	n	n	X
ejpam-4550	402	14	fe	fe	X
ejpam-4550	402	15	c	c	X
ejpam-4550	402	16	te	te	PROPN
ejpam-4550	402	17	d	d	X
ejpam-4550	402	18	a	a	DET
ejpam-4550	402	19	t	t	NOUN
ejpam-4550	402	20	s	s	X
ejpam-4550	402	21	ta	ta	ADP
ejpam-4550	402	22	g	g	PROPN
ejpam-4550	402	23	e	e	PROPN
ejpam-4550	402	24	3	3	NUM
ejpam-4550	402	25	o	o	NOUN
ejpam-4550	402	26	f	f	X
ejpam-4550	402	27	c	c	X
ejpam-4550	402	28	la	la	PROPN
ejpam-4550	402	29	s	s	PROPN
ejpam-4550	402	30	s	s	X
ejpam-4550	402	31	c	c	NOUN
ejpam-4550	402	32	2	2	NUM
ejpam-4550	402	33	(	(	PUNCT
ejpam-4550	402	34	b	b	NOUN
ejpam-4550	402	35	)	)	PUNCT
ejpam-4550	402	36	proportion	proportion	NOUN
ejpam-4550	402	37	of	of	ADP
ejpam-4550	402	38	individuals	individual	NOUN
ejpam-4550	402	39	infected	infect	VERB
ejpam-4550	402	40	at	at	ADP
ejpam-4550	402	41	stage	stage	NOUN
ejpam-4550	402	42	3	3	NUM
ejpam-4550	402	43	in	in	ADP
ejpam-4550	402	44	c2	c2	PROPN
ejpam-4550	402	45	figure	figure	NOUN
ejpam-4550	402	46	5	5	NUM
ejpam-4550	402	47	:	:	PUNCT
ejpam-4550	402	48	time	time	NOUN
ejpam-4550	402	49	series	series	NOUN
ejpam-4550	402	50	plots	plot	NOUN
ejpam-4550	402	51	of	of	ADP
ejpam-4550	402	52	the	the	DET
ejpam-4550	402	53	proportions	proportion	NOUN
ejpam-4550	402	54	of	of	ADP
ejpam-4550	402	55	infected	infected	ADJ
ejpam-4550	402	56	individuals	individual	NOUN
ejpam-4550	402	57	at	at	ADP
ejpam-4550	402	58	stage	stage	NOUN
ejpam-4550	402	59	3	3	NUM
ejpam-4550	402	60	in	in	ADP
ejpam-4550	402	61	classes	class	NOUN
ejpam-4550	402	62	c1	c1	PROPN
ejpam-4550	402	63	and	and	CCONJ
ejpam-4550	402	64	c2	c2	PROPN
ejpam-4550	402	65	for	for	ADP
ejpam-4550	402	66	r0	r0	NOUN
ejpam-4550	402	67	=	=	PUNCT
ejpam-4550	402	68	0.67893	0.67893	NUM
ejpam-4550	402	69	<	<	X
ejpam-4550	402	70	1	1	NUM
ejpam-4550	402	71	using	use	VERB
ejpam-4550	402	72	various	various	ADJ
ejpam-4550	402	73	initial	initial	ADJ
ejpam-4550	402	74	conditions	condition	NOUN
ejpam-4550	402	75	and	and	CCONJ
ejpam-4550	402	76	parameter	parameter	NOUN
ejpam-4550	402	77	values	value	NOUN
ejpam-4550	402	78	reported	report	VERB
ejpam-4550	402	79	in	in	ADP
ejpam-4550	402	80	table	table	NOUN
ejpam-4550	402	81	4	4	NUM
ejpam-4550	402	82	.	.	NOUN
ejpam-4550	402	83	1.408	1.408	NUM
ejpam-4550	402	84	>	>	SYM
ejpam-4550	402	85	1	1	NUM
ejpam-4550	402	86	.	.	PUNCT
ejpam-4550	402	87	table	table	NOUN
ejpam-4550	402	88	5	5	NUM
ejpam-4550	402	89	:	:	PUNCT
ejpam-4550	402	90	parameter	parameter	NOUN
ejpam-4550	402	91	values	value	NOUN
ejpam-4550	402	92	parameter	parameter	PROPN
ejpam-4550	402	93	value	value	NOUN
ejpam-4550	402	94	source	source	NOUN
ejpam-4550	402	95	parameter	parameter	NOUN
ejpam-4550	402	96	value	value	NOUN
ejpam-4550	402	97	source	source	NOUN
ejpam-4550	402	98	b	b	PROPN
ejpam-4550	402	99	0.0432	0.0432	NUM
ejpam-4550	402	100	estimated	estimate	VERB
ejpam-4550	402	101	a2	a2	PROPN
ejpam-4550	402	102	0.01	0.01	NUM
ejpam-4550	402	103	estimated	estimate	VERB
ejpam-4550	402	104	m	m	PROPN
ejpam-4550	402	105	0.0096	0.0096	NUM
ejpam-4550	402	106	estimated	estimate	VERB
ejpam-4550	402	107	a3	a3	NOUN
ejpam-4550	402	108	0.01	0.01	NUM
ejpam-4550	402	109	estimated	estimate	VERB
ejpam-4550	402	110	γ	γ	X
ejpam-4550	402	111	0.025	0.025	NUM
ejpam-4550	402	112	estimated	estimate	VERB
ejpam-4550	402	113	a4	a4	NOUN
ejpam-4550	402	114	0.01	0.01	NUM
ejpam-4550	402	115	estimated	estimate	VERB
ejpam-4550	402	116	β1	β1	PROPN
ejpam-4550	402	117	0.075	0.075	NUM
ejpam-4550	402	118	estimated	estimate	VERB
ejpam-4550	402	119	c1	c1	PROPN
ejpam-4550	402	120	0.02	0.02	NUM
ejpam-4550	402	121	estimated	estimate	VERB
ejpam-4550	402	122	β2	β2	NOUN
ejpam-4550	402	123	0.05	0.05	NUM
ejpam-4550	402	124	estimated	estimate	VERB
ejpam-4550	402	125	c2	c2	PROPN
ejpam-4550	402	126	0.02	0.02	NUM
ejpam-4550	402	127	estimated	estimate	VERB
ejpam-4550	402	128	a1	a1	NOUN
ejpam-4550	402	129	0.01	0.01	NUM
ejpam-4550	402	130	estimated	estimate	VERB
ejpam-4550	402	131	c3	c3	PROPN
ejpam-4550	402	132	0.02	0.02	NUM
ejpam-4550	402	133	estimated	estimate	VERB
ejpam-4550	402	134	using	use	VERB
ejpam-4550	402	135	different	different	ADJ
ejpam-4550	402	136	initial	initial	ADJ
ejpam-4550	402	137	conditions	condition	NOUN
ejpam-4550	402	138	,	,	PUNCT
ejpam-4550	402	139	the	the	DET
ejpam-4550	402	140	dynamics	dynamic	NOUN
ejpam-4550	402	141	of	of	ADP
ejpam-4550	402	142	the	the	DET
ejpam-4550	402	143	susceptible	susceptible	ADJ
ejpam-4550	402	144	and	and	CCONJ
ejpam-4550	402	145	infected	infected	ADJ
ejpam-4550	402	146	popum	popum	PROPN
ejpam-4550	402	147	.	.	PUNCT
ejpam-4550	403	1	alassane	alassane	PROPN
ejpam-4550	403	2	et	et	PROPN
ejpam-4550	403	3	al	al	PROPN
ejpam-4550	403	4	.	.	PUNCT
ejpam-4550	403	5	/	/	SYM
ejpam-4550	403	6	eur	eur	PROPN
ejpam-4550	403	7	.	.	PUNCT
ejpam-4550	404	1	j.	j.	PROPN
ejpam-4550	404	2	pure	pure	PROPN
ejpam-4550	404	3	appl	appl	PROPN
ejpam-4550	404	4	.	.	PROPN
ejpam-4550	404	5	math	math	PROPN
ejpam-4550	404	6	,	,	PUNCT
ejpam-4550	404	7	16	16	NUM
ejpam-4550	404	8	(	(	PUNCT
ejpam-4550	404	9	1	1	NUM
ejpam-4550	404	10	)	)	PUNCT
ejpam-4550	404	11	(	(	PUNCT
ejpam-4550	404	12	2023	2023	NUM
ejpam-4550	404	13	)	)	PUNCT
ejpam-4550	404	14	,	,	PUNCT
ejpam-4550	404	15	207	207	NUM
ejpam-4550	404	16	-	-	SYM
ejpam-4550	404	17	232	232	NUM
ejpam-4550	404	18	229	229	NUM
ejpam-4550	404	19	lations	lation	NOUN
ejpam-4550	404	20	of	of	ADP
ejpam-4550	404	21	the	the	DET
ejpam-4550	404	22	model	model	NOUN
ejpam-4550	404	23	are	be	AUX
ejpam-4550	404	24	plotted	plot	VERB
ejpam-4550	404	25	in	in	ADP
ejpam-4550	404	26	figures	figure	NOUN
ejpam-4550	404	27	6	6	NUM
ejpam-4550	404	28	,	,	PUNCT
ejpam-4550	404	29	7	7	NUM
ejpam-4550	404	30	,	,	PUNCT
ejpam-4550	404	31	8	8	NUM
ejpam-4550	404	32	and	and	CCONJ
ejpam-4550	404	33	9	9	NUM
ejpam-4550	404	34	.	.	NOUN
ejpam-4550	404	35	0	0	NUM
ejpam-4550	405	1	200	200	NUM
ejpam-4550	405	2	400	400	NUM
ejpam-4550	405	3	600	600	NUM
ejpam-4550	405	4	800	800	NUM
ejpam-4550	405	5	1000	1000	NUM
ejpam-4550	405	6	1200	1200	NUM
ejpam-4550	405	7	1400	1400	NUM
ejpam-4550	405	8	1600	1600	NUM
ejpam-4550	405	9	time	time	NOUN
ejpam-4550	405	10	(	(	PUNCT
ejpam-4550	405	11	t	t	NOUN
ejpam-4550	405	12	)	)	PUNCT
ejpam-4550	405	13	0.2	0.2	NUM
ejpam-4550	405	14	0.3	0.3	NUM
ejpam-4550	405	15	0.4	0.4	NUM
ejpam-4550	405	16	0.5	0.5	NUM
ejpam-4550	405	17	0.6	0.6	NUM
ejpam-4550	405	18	0.7	0.7	NUM
ejpam-4550	405	19	0.8	0.8	NUM
ejpam-4550	405	20	p	p	NOUN
ejpam-4550	405	21	ro	ro	NOUN
ejpam-4550	406	1	p	p	X
ejpam-4550	406	2	o	o	X
ejpam-4550	406	3	rt	rt	PROPN
ejpam-4550	406	4	io	io	PROPN
ejpam-4550	406	5	n	n	ADV
ejpam-4550	407	1	o	o	X
ejpam-4550	407	2	f	f	X
ejpam-4550	407	3	s	s	PROPN
ejpam-4550	407	4	u	u	NOUN
ejpam-4550	407	5	s	s	PRON
ejpam-4550	407	6	c	c	NOUN
ejpam-4550	407	7	e	e	NOUN
ejpam-4550	407	8	p	p	X
ejpam-4550	407	9	ti	ti	PROPN
ejpam-4550	407	10	b	b	X
ejpam-4550	407	11	le	le	X
ejpam-4550	407	12	i	i	PRON
ejpam-4550	408	1	n	n	VERB
ejpam-4550	408	2	d	d	NOUN
ejpam-4550	408	3	iv	iv	X
ejpam-4550	409	1	i	i	PROPN
ejpam-4550	409	2	d	d	PROPN
ejpam-4550	409	3	u	u	PROPN
ejpam-4550	409	4	a	a	DET
ejpam-4550	409	5	ls	ls	ADJ
ejpam-4550	409	6	o	o	X
ejpam-4550	409	7	f	f	X
ejpam-4550	409	8	c	c	X
ejpam-4550	409	9	la	la	PROPN
ejpam-4550	409	10	s	s	PROPN
ejpam-4550	409	11	s	s	X
ejpam-4550	409	12	c	c	NOUN
ejpam-4550	409	13	1	1	NUM
ejpam-4550	409	14	(	(	PUNCT
ejpam-4550	409	15	a	a	DET
ejpam-4550	409	16	)	)	PUNCT
ejpam-4550	409	17	proportion	proportion	NOUN
ejpam-4550	409	18	of	of	ADP
ejpam-4550	409	19	susceptible	susceptible	ADJ
ejpam-4550	409	20	individuals	individual	NOUN
ejpam-4550	409	21	in	in	ADP
ejpam-4550	409	22	c1	c1	PROPN
ejpam-4550	409	23	0	0	NUM
ejpam-4550	409	24	200	200	NUM
ejpam-4550	409	25	400	400	NUM
ejpam-4550	409	26	600	600	NUM
ejpam-4550	409	27	800	800	NUM
ejpam-4550	409	28	1000	1000	NUM
ejpam-4550	409	29	1200	1200	NUM
ejpam-4550	409	30	1400	1400	NUM
ejpam-4550	409	31	1600	1600	NUM
ejpam-4550	409	32	time	time	NOUN
ejpam-4550	409	33	(	(	PUNCT
ejpam-4550	409	34	t	t	NOUN
ejpam-4550	409	35	)	)	PUNCT
ejpam-4550	409	36	0.1	0.1	NUM
ejpam-4550	409	37	0.15	0.15	NUM
ejpam-4550	409	38	0.2	0.2	NUM
ejpam-4550	409	39	0.25	0.25	NUM
ejpam-4550	409	40	0.3	0.3	NUM
ejpam-4550	409	41	0.35	0.35	NUM
ejpam-4550	409	42	0.4	0.4	NUM
ejpam-4550	409	43	p	p	NOUN
ejpam-4550	409	44	ro	ro	NOUN
ejpam-4550	410	1	p	p	X
ejpam-4550	410	2	o	o	X
ejpam-4550	410	3	rt	rt	PROPN
ejpam-4550	410	4	io	io	PROPN
ejpam-4550	410	5	n	n	ADV
ejpam-4550	411	1	o	o	X
ejpam-4550	411	2	f	f	X
ejpam-4550	411	3	s	s	PROPN
ejpam-4550	411	4	u	u	NOUN
ejpam-4550	411	5	s	s	PRON
ejpam-4550	411	6	c	c	NOUN
ejpam-4550	411	7	e	e	NOUN
ejpam-4550	411	8	p	p	X
ejpam-4550	411	9	ti	ti	PROPN
ejpam-4550	411	10	b	b	X
ejpam-4550	411	11	le	le	X
ejpam-4550	411	12	i	i	PRON
ejpam-4550	412	1	n	n	VERB
ejpam-4550	412	2	d	d	NOUN
ejpam-4550	412	3	iv	iv	X
ejpam-4550	413	1	i	i	PROPN
ejpam-4550	413	2	d	d	PROPN
ejpam-4550	413	3	u	u	PROPN
ejpam-4550	413	4	a	a	DET
ejpam-4550	413	5	ls	ls	ADJ
ejpam-4550	413	6	o	o	X
ejpam-4550	413	7	f	f	X
ejpam-4550	413	8	c	c	X
ejpam-4550	413	9	la	la	PROPN
ejpam-4550	413	10	s	s	PROPN
ejpam-4550	413	11	s	s	X
ejpam-4550	413	12	c	c	NOUN
ejpam-4550	413	13	2	2	NUM
ejpam-4550	413	14	(	(	PUNCT
ejpam-4550	413	15	b	b	NOUN
ejpam-4550	413	16	)	)	PUNCT
ejpam-4550	413	17	proportion	proportion	NOUN
ejpam-4550	413	18	of	of	ADP
ejpam-4550	413	19	susceptible	susceptible	ADJ
ejpam-4550	413	20	individuals	individual	NOUN
ejpam-4550	413	21	in	in	ADP
ejpam-4550	413	22	c2	c2	PROPN
ejpam-4550	413	23	figure	figure	VERB
ejpam-4550	413	24	6	6	NUM
ejpam-4550	413	25	:	:	PUNCT
ejpam-4550	413	26	time	time	NOUN
ejpam-4550	413	27	series	series	PROPN
ejpam-4550	413	28	plot	plot	NOUN
ejpam-4550	413	29	of	of	ADP
ejpam-4550	413	30	the	the	DET
ejpam-4550	413	31	proportions	proportion	NOUN
ejpam-4550	413	32	of	of	ADP
ejpam-4550	413	33	susceptible	susceptible	ADJ
ejpam-4550	413	34	individuals	individual	NOUN
ejpam-4550	413	35	in	in	ADP
ejpam-4550	413	36	classes	class	NOUN
ejpam-4550	413	37	c1	c1	PROPN
ejpam-4550	413	38	and	and	CCONJ
ejpam-4550	413	39	c2	c2	PROPN
ejpam-4550	413	40	for	for	ADP
ejpam-4550	413	41	r0	r0	NOUN
ejpam-4550	413	42	=	=	PUNCT
ejpam-4550	413	43	1.408	1.408	NUM
ejpam-4550	413	44	>	>	X
ejpam-4550	413	45	1	1	NUM
ejpam-4550	413	46	using	use	VERB
ejpam-4550	413	47	various	various	ADJ
ejpam-4550	413	48	initial	initial	ADJ
ejpam-4550	413	49	conditions	condition	NOUN
ejpam-4550	413	50	and	and	CCONJ
ejpam-4550	413	51	parameter	parameter	NOUN
ejpam-4550	413	52	values	value	NOUN
ejpam-4550	413	53	reported	report	VERB
ejpam-4550	413	54	in	in	ADP
ejpam-4550	413	55	table	table	NOUN
ejpam-4550	413	56	5	5	NUM
ejpam-4550	413	57	.	.	NOUN
ejpam-4550	413	58	0	0	NUM
ejpam-4550	414	1	200	200	NUM
ejpam-4550	414	2	400	400	NUM
ejpam-4550	414	3	600	600	NUM
ejpam-4550	414	4	800	800	NUM
ejpam-4550	414	5	1000	1000	NUM
ejpam-4550	414	6	1200	1200	NUM
ejpam-4550	414	7	1400	1400	NUM
ejpam-4550	414	8	1600	1600	NUM
ejpam-4550	414	9	time	time	NOUN
ejpam-4550	414	10	(	(	PUNCT
ejpam-4550	414	11	t	t	NOUN
ejpam-4550	414	12	)	)	PUNCT
ejpam-4550	414	13	0.02	0.02	NUM
ejpam-4550	414	14	0.04	0.04	NUM
ejpam-4550	414	15	0.06	0.06	NUM
ejpam-4550	414	16	0.08	0.08	NUM
ejpam-4550	414	17	0.1	0.1	NUM
ejpam-4550	414	18	0.12	0.12	NUM
ejpam-4550	414	19	0.14	0.14	NUM
ejpam-4550	414	20	p	p	NOUN
ejpam-4550	415	1	ro	ro	NOUN
ejpam-4550	416	1	p	p	X
ejpam-4550	416	2	o	o	X
ejpam-4550	416	3	rt	rt	PROPN
ejpam-4550	416	4	io	io	PROPN
ejpam-4550	416	5	n	n	PROPN
ejpam-4550	416	6	o	o	X
ejpam-4550	416	7	f	f	X
ejpam-4550	416	8	in	in	ADP
ejpam-4550	416	9	d	d	PROPN
ejpam-4550	416	10	iv	iv	INTJ
ejpam-4550	416	11	i	i	PROPN
ejpam-4550	416	12	d	d	PROPN
ejpam-4550	416	13	u	u	PROPN
ejpam-4550	416	14	a	a	DET
ejpam-4550	416	15	ls	ls	X
ejpam-4550	416	16	i	i	PRON
ejpam-4550	416	17	n	n	X
ejpam-4550	416	18	fe	fe	X
ejpam-4550	417	1	c	c	X
ejpam-4550	417	2	te	te	PROPN
ejpam-4550	417	3	d	d	X
ejpam-4550	417	4	a	a	DET
ejpam-4550	417	5	t	t	NOUN
ejpam-4550	417	6	s	s	X
ejpam-4550	417	7	ta	ta	ADP
ejpam-4550	417	8	g	g	PROPN
ejpam-4550	417	9	e	e	PROPN
ejpam-4550	418	1	1	1	NUM
ejpam-4550	418	2	o	o	NOUN
ejpam-4550	418	3	f	f	X
ejpam-4550	418	4	c	c	X
ejpam-4550	418	5	la	la	PROPN
ejpam-4550	418	6	s	s	PROPN
ejpam-4550	418	7	s	s	X
ejpam-4550	418	8	c	c	NOUN
ejpam-4550	418	9	1	1	NUM
ejpam-4550	418	10	(	(	PUNCT
ejpam-4550	418	11	a	a	DET
ejpam-4550	418	12	)	)	PUNCT
ejpam-4550	418	13	proportion	proportion	NOUN
ejpam-4550	418	14	of	of	ADP
ejpam-4550	418	15	individuals	individual	NOUN
ejpam-4550	418	16	infected	infect	VERB
ejpam-4550	418	17	at	at	ADP
ejpam-4550	418	18	stage	stage	NOUN
ejpam-4550	418	19	1	1	NUM
ejpam-4550	418	20	in	in	ADP
ejpam-4550	418	21	c1	c1	PROPN
ejpam-4550	418	22	0	0	NUM
ejpam-4550	418	23	200	200	NUM
ejpam-4550	418	24	400	400	NUM
ejpam-4550	418	25	600	600	NUM
ejpam-4550	418	26	800	800	NUM
ejpam-4550	418	27	1000	1000	NUM
ejpam-4550	418	28	1200	1200	NUM
ejpam-4550	418	29	1400	1400	NUM
ejpam-4550	418	30	1600	1600	NUM
ejpam-4550	418	31	time	time	NOUN
ejpam-4550	418	32	(	(	PUNCT
ejpam-4550	418	33	t	t	NOUN
ejpam-4550	418	34	)	)	PUNCT
ejpam-4550	418	35	0	0	NUM
ejpam-4550	418	36	0.02	0.02	NUM
ejpam-4550	418	37	0.04	0.04	NUM
ejpam-4550	418	38	0.06	0.06	NUM
ejpam-4550	418	39	0.08	0.08	NUM
ejpam-4550	418	40	0.1	0.1	NUM
ejpam-4550	418	41	0.12	0.12	NUM
ejpam-4550	418	42	0.14	0.14	NUM
ejpam-4550	418	43	p	p	NOUN
ejpam-4550	419	1	ro	ro	NOUN
ejpam-4550	420	1	p	p	X
ejpam-4550	420	2	o	o	X
ejpam-4550	420	3	rt	rt	PROPN
ejpam-4550	420	4	io	io	PROPN
ejpam-4550	420	5	n	n	PROPN
ejpam-4550	420	6	o	o	X
ejpam-4550	420	7	f	f	X
ejpam-4550	420	8	in	in	ADP
ejpam-4550	420	9	d	d	PROPN
ejpam-4550	420	10	iv	iv	INTJ
ejpam-4550	420	11	i	i	PROPN
ejpam-4550	420	12	d	d	PROPN
ejpam-4550	420	13	u	u	PROPN
ejpam-4550	420	14	a	a	DET
ejpam-4550	420	15	ls	ls	X
ejpam-4550	420	16	i	i	PRON
ejpam-4550	420	17	n	n	X
ejpam-4550	420	18	fe	fe	X
ejpam-4550	421	1	c	c	X
ejpam-4550	421	2	te	te	PROPN
ejpam-4550	421	3	d	d	X
ejpam-4550	421	4	a	a	DET
ejpam-4550	421	5	t	t	NOUN
ejpam-4550	421	6	s	s	X
ejpam-4550	421	7	ta	ta	ADP
ejpam-4550	421	8	g	g	PROPN
ejpam-4550	421	9	e	e	PROPN
ejpam-4550	422	1	1	1	NUM
ejpam-4550	422	2	o	o	NOUN
ejpam-4550	422	3	f	f	X
ejpam-4550	422	4	c	c	X
ejpam-4550	422	5	la	la	PROPN
ejpam-4550	422	6	s	s	PROPN
ejpam-4550	422	7	s	s	X
ejpam-4550	422	8	c	c	NOUN
ejpam-4550	422	9	2	2	NUM
ejpam-4550	422	10	(	(	PUNCT
ejpam-4550	422	11	b	b	NOUN
ejpam-4550	422	12	)	)	PUNCT
ejpam-4550	422	13	proportion	proportion	NOUN
ejpam-4550	422	14	of	of	ADP
ejpam-4550	422	15	individuals	individual	NOUN
ejpam-4550	422	16	infected	infect	VERB
ejpam-4550	422	17	at	at	ADP
ejpam-4550	422	18	stage	stage	NOUN
ejpam-4550	422	19	1	1	NUM
ejpam-4550	422	20	in	in	ADP
ejpam-4550	422	21	c2	c2	PROPN
ejpam-4550	422	22	figure	figure	VERB
ejpam-4550	422	23	7	7	NUM
ejpam-4550	422	24	:	:	PUNCT
ejpam-4550	422	25	time	time	NOUN
ejpam-4550	422	26	series	series	PROPN
ejpam-4550	422	27	plot	plot	NOUN
ejpam-4550	422	28	of	of	ADP
ejpam-4550	422	29	the	the	DET
ejpam-4550	422	30	proportions	proportion	NOUN
ejpam-4550	422	31	of	of	ADP
ejpam-4550	422	32	individuals	individual	NOUN
ejpam-4550	422	33	infected	infect	VERB
ejpam-4550	422	34	at	at	ADP
ejpam-4550	422	35	stage	stage	NOUN
ejpam-4550	422	36	1	1	NUM
ejpam-4550	422	37	in	in	ADP
ejpam-4550	422	38	classes	class	NOUN
ejpam-4550	422	39	c1	c1	PROPN
ejpam-4550	422	40	and	and	CCONJ
ejpam-4550	422	41	c2	c2	PROPN
ejpam-4550	422	42	for	for	ADP
ejpam-4550	422	43	r0	r0	NOUN
ejpam-4550	422	44	=	=	PUNCT
ejpam-4550	422	45	1.408	1.408	NUM
ejpam-4550	422	46	>	>	X
ejpam-4550	422	47	1	1	NUM
ejpam-4550	422	48	using	use	VERB
ejpam-4550	422	49	various	various	ADJ
ejpam-4550	422	50	initial	initial	ADJ
ejpam-4550	422	51	conditions	condition	NOUN
ejpam-4550	422	52	and	and	CCONJ
ejpam-4550	422	53	parameter	parameter	NOUN
ejpam-4550	422	54	values	value	NOUN
ejpam-4550	422	55	reported	report	VERB
ejpam-4550	422	56	in	in	ADP
ejpam-4550	422	57	table	table	NOUN
ejpam-4550	422	58	5	5	NUM
ejpam-4550	422	59	.	.	PUNCT
ejpam-4550	422	60	as	as	SCONJ
ejpam-4550	422	61	shown	show	VERB
ejpam-4550	422	62	in	in	ADP
ejpam-4550	422	63	figures	figure	NOUN
ejpam-4550	422	64	6	6	NUM
ejpam-4550	422	65	,	,	PUNCT
ejpam-4550	422	66	7	7	NUM
ejpam-4550	422	67	,	,	PUNCT
ejpam-4550	422	68	8	8	NUM
ejpam-4550	422	69	and	and	CCONJ
ejpam-4550	422	70	9	9	NUM
ejpam-4550	422	71	,	,	PUNCT
ejpam-4550	422	72	the	the	DET
ejpam-4550	422	73	proportions	proportion	NOUN
ejpam-4550	422	74	of	of	ADP
ejpam-4550	422	75	susceptible	susceptible	ADJ
ejpam-4550	422	76	and	and	CCONJ
ejpam-4550	422	77	infected	infected	ADJ
ejpam-4550	422	78	individuals	individual	NOUN
ejpam-4550	422	79	in	in	ADP
ejpam-4550	422	80	classes	class	NOUN
ejpam-4550	422	81	c1	c1	PROPN
ejpam-4550	422	82	and	and	CCONJ
ejpam-4550	422	83	c2	c2	PROPN
ejpam-4550	422	84	are	be	AUX
ejpam-4550	422	85	consistent	consistent	ADJ
ejpam-4550	422	86	,	,	PUNCT
ejpam-4550	422	87	[	[	X
ejpam-4550	422	88	(	(	PUNCT
ejpam-4550	422	89	s1	s1	NOUN
ejpam-4550	422	90	∗	∗	NOUN
ejpam-4550	422	91	,	,	PUNCT
ejpam-4550	422	92	i11	i11	ADJ
ejpam-4550	422	93	∗	∗	NOUN
ejpam-4550	422	94	,	,	PUNCT
ejpam-4550	422	95	i21	i21	NOUN
ejpam-4550	422	96	∗	∗	NOUN
ejpam-4550	422	97	,	,	PUNCT
ejpam-4550	422	98	i31	i31	NOUN
ejpam-4550	422	99	∗	∗	NOUN
ejpam-4550	422	100	,	,	PUNCT
ejpam-4550	422	101	s2	s2	NOUN
ejpam-4550	422	102	∗	∗	NOUN
ejpam-4550	422	103	,	,	PUNCT
ejpam-4550	422	104	i12	i12	PROPN
ejpam-4550	422	105	∗	∗	NOUN
ejpam-4550	422	106	,	,	PUNCT
ejpam-4550	422	107	i22	i22	NOUN
ejpam-4550	422	108	,	,	PUNCT
ejpam-4550	422	109	i32	i32	PROPN
ejpam-4550	422	110	∗	∗	NOUN
ejpam-4550	422	111	)	)	PUNCT
ejpam-4550	422	112	=(	=(	NOUN
ejpam-4550	422	113	0.49548	0.49548	NUM
ejpam-4550	422	114	,	,	PUNCT
ejpam-4550	422	115	0.12853	0.12853	NUM
ejpam-4550	422	116	,	,	PUNCT
ejpam-4550	422	117	0.017559	0.017559	NUM
ejpam-4550	422	118	,	,	PUNCT
ejpam-4550	422	119	0.0027783	0.0027783	NUM
ejpam-4550	422	120	,	,	PUNCT
ejpam-4550	422	121	0.19918	0.19918	NUM
ejpam-4550	422	122	,	,	PUNCT
ejpam-4550	422	123	0.11941	0.11941	NUM
ejpam-4550	422	124	,	,	PUNCT
ejpam-4550	422	125	0.029047	0.029047	NUM
ejpam-4550	422	126	,	,	PUNCT
ejpam-4550	422	127	0.0080157	0.0080157	NUM
ejpam-4550	422	128	)	)	PUNCT
ejpam-4550	422	129	]	]	PUNCT
ejpam-4550	422	130	,	,	PUNCT
ejpam-4550	422	131	i.e.	i.e.	X
ejpam-4550	422	132	,	,	PUNCT
ejpam-4550	422	133	the	the	DET
ejpam-4550	422	134	population	population	NOUN
ejpam-4550	422	135	tends	tend	VERB
ejpam-4550	422	136	to	to	ADP
ejpam-4550	422	137	endemic	endemic	ADJ
ejpam-4550	422	138	equilibrium	equilibrium	NOUN
ejpam-4550	422	139	e∗	e∗	NOUN
ejpam-4550	422	140	when	when	SCONJ
ejpam-4550	422	141	r0	r0	NOUN
ejpam-4550	422	142	>	>	X
ejpam-4550	422	143	1	1	X
ejpam-4550	422	144	.	.	PUNCT
ejpam-4550	423	1	this	this	PRON
ejpam-4550	423	2	indicates	indicate	VERB
ejpam-4550	423	3	that	that	SCONJ
ejpam-4550	423	4	,	,	PUNCT
ejpam-4550	423	5	regardless	regardless	ADV
ejpam-4550	423	6	of	of	ADP
ejpam-4550	423	7	initial	initial	ADJ
ejpam-4550	423	8	conditions	condition	NOUN
ejpam-4550	423	9	,	,	PUNCT
ejpam-4550	423	10	the	the	DET
ejpam-4550	423	11	infected	infected	ADJ
ejpam-4550	423	12	population	population	NOUN
ejpam-4550	423	13	eventually	eventually	ADV
ejpam-4550	423	14	reaches	reach	VERB
ejpam-4550	423	15	endemic	endemic	ADJ
ejpam-4550	423	16	equilibrium	equilibrium	NOUN
ejpam-4550	423	17	over	over	ADP
ejpam-4550	423	18	time	time	NOUN
ejpam-4550	423	19	and	and	CCONJ
ejpam-4550	423	20	the	the	DET
ejpam-4550	423	21	disease	disease	NOUN
ejpam-4550	423	22	-	-	PUNCT
ejpam-4550	423	23	free	free	ADJ
ejpam-4550	423	24	equilibrium	equilibrium	NOUN
ejpam-4550	423	25	point	point	NOUN
ejpam-4550	423	26	becomes	become	VERB
ejpam-4550	423	27	unstable	unstable	ADJ
ejpam-4550	423	28	when	when	SCONJ
ejpam-4550	423	29	r0	r0	NOUN
ejpam-4550	423	30	>	>	X
ejpam-4550	423	31	1	1	X
ejpam-4550	423	32	.	.	PUNCT
ejpam-4550	424	1	these	these	DET
ejpam-4550	424	2	numerical	numerical	ADJ
ejpam-4550	424	3	simulations	simulation	NOUN
ejpam-4550	424	4	support	support	VERB
ejpam-4550	424	5	our	our	PRON
ejpam-4550	424	6	theoretical	theoretical	ADJ
ejpam-4550	424	7	results	result	NOUN
ejpam-4550	424	8	.	.	PUNCT
ejpam-4550	425	1	10	10	NUM
ejpam-4550	425	2	.	.	PUNCT
ejpam-4550	425	3	conclusions	conclusion	NOUN
ejpam-4550	425	4	in	in	ADP
ejpam-4550	425	5	this	this	DET
ejpam-4550	425	6	paper	paper	NOUN
ejpam-4550	425	7	,	,	PUNCT
ejpam-4550	425	8	we	we	PRON
ejpam-4550	425	9	have	have	AUX
ejpam-4550	425	10	developed	develop	VERB
ejpam-4550	425	11	a	a	DET
ejpam-4550	425	12	mathematical	mathematical	ADJ
ejpam-4550	425	13	model	model	NOUN
ejpam-4550	425	14	for	for	ADP
ejpam-4550	425	15	the	the	DET
ejpam-4550	425	16	spread	spread	NOUN
ejpam-4550	425	17	of	of	ADP
ejpam-4550	425	18	hiv	hiv	PROPN
ejpam-4550	425	19	disease	disease	NOUN
ejpam-4550	425	20	within	within	ADP
ejpam-4550	425	21	two	two	NUM
ejpam-4550	425	22	different	different	ADJ
ejpam-4550	425	23	age	age	NOUN
ejpam-4550	425	24	classes	class	NOUN
ejpam-4550	425	25	.	.	PUNCT
ejpam-4550	426	1	we	we	PRON
ejpam-4550	426	2	proposed	propose	VERB
ejpam-4550	426	3	a	a	DET
ejpam-4550	426	4	basic	basic	ADJ
ejpam-4550	426	5	reproduction	reproduction	NOUN
ejpam-4550	426	6	number	number	NOUN
ejpam-4550	426	7	that	that	PRON
ejpam-4550	426	8	depends	depend	VERB
ejpam-4550	426	9	m.	m.	NOUN
ejpam-4550	426	10	alassane	alassane	PROPN
ejpam-4550	426	11	et	et	PROPN
ejpam-4550	426	12	al	al	PROPN
ejpam-4550	426	13	.	.	PUNCT
ejpam-4550	426	14	/	/	SYM
ejpam-4550	426	15	eur	eur	PROPN
ejpam-4550	426	16	.	.	PUNCT
ejpam-4550	427	1	j.	j.	PROPN
ejpam-4550	427	2	pure	pure	PROPN
ejpam-4550	427	3	appl	appl	PROPN
ejpam-4550	427	4	.	.	PROPN
ejpam-4550	427	5	math	math	PROPN
ejpam-4550	427	6	,	,	PUNCT
ejpam-4550	427	7	16	16	NUM
ejpam-4550	427	8	(	(	PUNCT
ejpam-4550	427	9	1	1	NUM
ejpam-4550	427	10	)	)	PUNCT
ejpam-4550	427	11	(	(	PUNCT
ejpam-4550	427	12	2023	2023	NUM
ejpam-4550	427	13	)	)	PUNCT
ejpam-4550	427	14	,	,	PUNCT
ejpam-4550	427	15	207	207	NUM
ejpam-4550	427	16	-	-	SYM
ejpam-4550	427	17	232	232	NUM
ejpam-4550	427	18	230	230	NUM
ejpam-4550	427	19	0	0	NUM
ejpam-4550	427	20	200	200	NUM
ejpam-4550	427	21	400	400	NUM
ejpam-4550	427	22	600	600	NUM
ejpam-4550	427	23	800	800	NUM
ejpam-4550	427	24	1000	1000	NUM
ejpam-4550	427	25	1200	1200	NUM
ejpam-4550	427	26	1400	1400	NUM
ejpam-4550	427	27	1600	1600	NUM
ejpam-4550	427	28	time	time	NOUN
ejpam-4550	427	29	(	(	PUNCT
ejpam-4550	427	30	t	t	NOUN
ejpam-4550	427	31	)	)	PUNCT
ejpam-4550	427	32	0	0	NUM
ejpam-4550	428	1	0.01	0.01	NUM
ejpam-4550	428	2	0.02	0.02	NUM
ejpam-4550	428	3	0.03	0.03	NUM
ejpam-4550	428	4	0.04	0.04	NUM
ejpam-4550	428	5	0.05	0.05	NUM
ejpam-4550	428	6	0.06	0.06	NUM
ejpam-4550	428	7	0.07	0.07	NUM
ejpam-4550	428	8	0.08	0.08	NUM
ejpam-4550	428	9	0.09	0.09	NUM
ejpam-4550	428	10	0.1	0.1	NUM
ejpam-4550	428	11	p	p	NOUN
ejpam-4550	428	12	ro	ro	NOUN
ejpam-4550	429	1	p	p	X
ejpam-4550	429	2	o	o	X
ejpam-4550	429	3	rt	rt	PROPN
ejpam-4550	429	4	io	io	PROPN
ejpam-4550	429	5	n	n	PROPN
ejpam-4550	429	6	o	o	X
ejpam-4550	429	7	f	f	X
ejpam-4550	429	8	in	in	ADP
ejpam-4550	429	9	d	d	PROPN
ejpam-4550	429	10	iv	iv	INTJ
ejpam-4550	429	11	i	i	PROPN
ejpam-4550	429	12	d	d	PROPN
ejpam-4550	429	13	u	u	PROPN
ejpam-4550	429	14	a	a	DET
ejpam-4550	429	15	ls	ls	X
ejpam-4550	429	16	i	i	PRON
ejpam-4550	429	17	n	n	X
ejpam-4550	429	18	fe	fe	X
ejpam-4550	430	1	c	c	X
ejpam-4550	430	2	te	te	PROPN
ejpam-4550	430	3	d	d	X
ejpam-4550	430	4	a	a	DET
ejpam-4550	430	5	t	t	NOUN
ejpam-4550	430	6	s	s	X
ejpam-4550	430	7	ta	ta	ADP
ejpam-4550	430	8	g	g	PROPN
ejpam-4550	430	9	e	e	PROPN
ejpam-4550	430	10	2	2	NUM
ejpam-4550	430	11	o	o	NOUN
ejpam-4550	430	12	f	f	X
ejpam-4550	430	13	c	c	X
ejpam-4550	430	14	la	la	PROPN
ejpam-4550	430	15	s	s	PROPN
ejpam-4550	430	16	s	s	X
ejpam-4550	430	17	c	c	NOUN
ejpam-4550	430	18	1	1	NUM
ejpam-4550	430	19	(	(	PUNCT
ejpam-4550	430	20	a	a	DET
ejpam-4550	430	21	)	)	PUNCT
ejpam-4550	430	22	proportion	proportion	NOUN
ejpam-4550	430	23	of	of	ADP
ejpam-4550	430	24	individuals	individual	NOUN
ejpam-4550	430	25	infected	infect	VERB
ejpam-4550	430	26	at	at	ADP
ejpam-4550	430	27	stage	stage	NOUN
ejpam-4550	430	28	2	2	NUM
ejpam-4550	430	29	in	in	ADP
ejpam-4550	430	30	c1	c1	PROPN
ejpam-4550	430	31	0	0	NUM
ejpam-4550	430	32	200	200	NUM
ejpam-4550	430	33	400	400	NUM
ejpam-4550	430	34	600	600	NUM
ejpam-4550	430	35	800	800	NUM
ejpam-4550	430	36	1000	1000	NUM
ejpam-4550	430	37	1200	1200	NUM
ejpam-4550	430	38	1400	1400	NUM
ejpam-4550	430	39	1600	1600	NUM
ejpam-4550	430	40	time	time	NOUN
ejpam-4550	430	41	(	(	PUNCT
ejpam-4550	430	42	t	t	NOUN
ejpam-4550	430	43	)	)	PUNCT
ejpam-4550	430	44	0.01	0.01	NUM
ejpam-4550	430	45	0.02	0.02	NUM
ejpam-4550	430	46	0.03	0.03	NUM
ejpam-4550	430	47	0.04	0.04	NUM
ejpam-4550	430	48	0.05	0.05	NUM
ejpam-4550	430	49	0.06	0.06	NUM
ejpam-4550	430	50	0.07	0.07	NUM
ejpam-4550	430	51	0.08	0.08	NUM
ejpam-4550	430	52	0.09	0.09	NUM
ejpam-4550	430	53	0.1	0.1	NUM
ejpam-4550	430	54	0.11	0.11	NUM
ejpam-4550	430	55	p	p	NOUN
ejpam-4550	431	1	ro	ro	NOUN
ejpam-4550	432	1	p	p	X
ejpam-4550	433	1	o	o	X
ejpam-4550	434	1	rt	rt	PROPN
ejpam-4550	435	1	io	io	PROPN
ejpam-4550	436	1	n	n	PROPN
ejpam-4550	436	2	o	o	X
ejpam-4550	436	3	f	f	X
ejpam-4550	436	4	in	in	ADP
ejpam-4550	436	5	d	d	PROPN
ejpam-4550	436	6	iv	iv	INTJ
ejpam-4550	436	7	i	i	PROPN
ejpam-4550	436	8	d	d	PROPN
ejpam-4550	436	9	u	u	PROPN
ejpam-4550	436	10	a	a	DET
ejpam-4550	436	11	ls	ls	X
ejpam-4550	436	12	i	i	PRON
ejpam-4550	436	13	n	n	X
ejpam-4550	436	14	fe	fe	X
ejpam-4550	436	15	c	c	X
ejpam-4550	436	16	te	te	PROPN
ejpam-4550	436	17	d	d	X
ejpam-4550	436	18	a	a	DET
ejpam-4550	436	19	t	t	NOUN
ejpam-4550	436	20	s	s	X
ejpam-4550	436	21	ta	ta	ADP
ejpam-4550	436	22	g	g	PROPN
ejpam-4550	436	23	e	e	PROPN
ejpam-4550	436	24	2	2	NUM
ejpam-4550	436	25	o	o	NOUN
ejpam-4550	436	26	f	f	X
ejpam-4550	436	27	c	c	X
ejpam-4550	436	28	la	la	PROPN
ejpam-4550	436	29	s	s	PROPN
ejpam-4550	436	30	s	s	X
ejpam-4550	436	31	c	c	NOUN
ejpam-4550	436	32	2	2	NUM
ejpam-4550	436	33	(	(	PUNCT
ejpam-4550	436	34	b	b	NOUN
ejpam-4550	436	35	)	)	PUNCT
ejpam-4550	436	36	proportion	proportion	NOUN
ejpam-4550	436	37	of	of	ADP
ejpam-4550	436	38	individuals	individual	NOUN
ejpam-4550	436	39	infected	infect	VERB
ejpam-4550	436	40	at	at	ADP
ejpam-4550	436	41	stage	stage	NOUN
ejpam-4550	436	42	2	2	NUM
ejpam-4550	436	43	in	in	ADP
ejpam-4550	436	44	c2	c2	PROPN
ejpam-4550	436	45	figure	figure	VERB
ejpam-4550	436	46	8	8	NUM
ejpam-4550	436	47	:	:	PUNCT
ejpam-4550	436	48	time	time	NOUN
ejpam-4550	436	49	series	series	PROPN
ejpam-4550	436	50	plot	plot	NOUN
ejpam-4550	436	51	of	of	ADP
ejpam-4550	436	52	the	the	DET
ejpam-4550	436	53	proportions	proportion	NOUN
ejpam-4550	436	54	of	of	ADP
ejpam-4550	436	55	individuals	individual	NOUN
ejpam-4550	436	56	infected	infect	VERB
ejpam-4550	436	57	at	at	ADP
ejpam-4550	436	58	stage	stage	NOUN
ejpam-4550	436	59	2	2	NUM
ejpam-4550	436	60	in	in	ADP
ejpam-4550	436	61	classes	class	NOUN
ejpam-4550	436	62	c1	c1	PROPN
ejpam-4550	436	63	and	and	CCONJ
ejpam-4550	436	64	c2	c2	PROPN
ejpam-4550	436	65	for	for	ADP
ejpam-4550	436	66	r0	r0	NOUN
ejpam-4550	436	67	=	=	PUNCT
ejpam-4550	436	68	1.408	1.408	NUM
ejpam-4550	436	69	>	>	X
ejpam-4550	436	70	1	1	NUM
ejpam-4550	436	71	using	use	VERB
ejpam-4550	436	72	various	various	ADJ
ejpam-4550	436	73	initial	initial	ADJ
ejpam-4550	436	74	conditions	condition	NOUN
ejpam-4550	436	75	and	and	CCONJ
ejpam-4550	436	76	parameter	parameter	NOUN
ejpam-4550	436	77	values	value	NOUN
ejpam-4550	436	78	reported	report	VERB
ejpam-4550	436	79	in	in	ADP
ejpam-4550	436	80	table	table	NOUN
ejpam-4550	436	81	5	5	NUM
ejpam-4550	436	82	.	.	NOUN
ejpam-4550	436	83	0	0	NUM
ejpam-4550	437	1	200	200	NUM
ejpam-4550	437	2	400	400	NUM
ejpam-4550	437	3	600	600	NUM
ejpam-4550	437	4	800	800	NUM
ejpam-4550	437	5	1000	1000	NUM
ejpam-4550	437	6	1200	1200	NUM
ejpam-4550	437	7	1400	1400	NUM
ejpam-4550	437	8	1600	1600	NUM
ejpam-4550	437	9	time	time	NOUN
ejpam-4550	437	10	(	(	PUNCT
ejpam-4550	437	11	t	t	NOUN
ejpam-4550	437	12	)	)	PUNCT
ejpam-4550	437	13	0	0	NUM
ejpam-4550	437	14	0.01	0.01	NUM
ejpam-4550	437	15	0.02	0.02	NUM
ejpam-4550	437	16	0.03	0.03	NUM
ejpam-4550	437	17	0.04	0.04	NUM
ejpam-4550	437	18	0.05	0.05	NUM
ejpam-4550	437	19	0.06	0.06	NUM
ejpam-4550	437	20	0.07	0.07	NUM
ejpam-4550	437	21	0.08	0.08	NUM
ejpam-4550	437	22	p	p	NOUN
ejpam-4550	437	23	ro	ro	NOUN
ejpam-4550	438	1	p	p	X
ejpam-4550	439	1	o	o	X
ejpam-4550	440	1	rt	rt	PROPN
ejpam-4550	441	1	io	io	PROPN
ejpam-4550	442	1	n	n	PROPN
ejpam-4550	442	2	o	o	X
ejpam-4550	442	3	f	f	X
ejpam-4550	442	4	in	in	ADP
ejpam-4550	442	5	d	d	PROPN
ejpam-4550	442	6	iv	iv	INTJ
ejpam-4550	442	7	i	i	PROPN
ejpam-4550	442	8	d	d	PROPN
ejpam-4550	442	9	u	u	PROPN
ejpam-4550	442	10	a	a	DET
ejpam-4550	442	11	ls	ls	X
ejpam-4550	442	12	i	i	PRON
ejpam-4550	442	13	n	n	X
ejpam-4550	442	14	fe	fe	X
ejpam-4550	442	15	c	c	X
ejpam-4550	442	16	te	te	PROPN
ejpam-4550	442	17	d	d	X
ejpam-4550	442	18	a	a	DET
ejpam-4550	442	19	t	t	NOUN
ejpam-4550	442	20	s	s	X
ejpam-4550	442	21	ta	ta	ADP
ejpam-4550	442	22	g	g	PROPN
ejpam-4550	442	23	e	e	PROPN
ejpam-4550	442	24	3	3	NUM
ejpam-4550	442	25	o	o	NOUN
ejpam-4550	442	26	f	f	X
ejpam-4550	442	27	c	c	X
ejpam-4550	442	28	la	la	PROPN
ejpam-4550	442	29	s	s	PROPN
ejpam-4550	442	30	s	s	X
ejpam-4550	442	31	c	c	NOUN
ejpam-4550	442	32	1	1	NUM
ejpam-4550	442	33	(	(	PUNCT
ejpam-4550	442	34	a	a	DET
ejpam-4550	442	35	)	)	PUNCT
ejpam-4550	442	36	proportion	proportion	NOUN
ejpam-4550	442	37	of	of	ADP
ejpam-4550	442	38	individuals	individual	NOUN
ejpam-4550	442	39	infected	infect	VERB
ejpam-4550	442	40	at	at	ADP
ejpam-4550	442	41	stage	stage	NOUN
ejpam-4550	442	42	3	3	NUM
ejpam-4550	442	43	in	in	ADP
ejpam-4550	442	44	c1	c1	PROPN
ejpam-4550	442	45	0	0	NUM
ejpam-4550	442	46	200	200	NUM
ejpam-4550	442	47	400	400	NUM
ejpam-4550	442	48	600	600	NUM
ejpam-4550	442	49	800	800	NUM
ejpam-4550	442	50	1000	1000	NUM
ejpam-4550	442	51	1200	1200	NUM
ejpam-4550	442	52	1400	1400	NUM
ejpam-4550	442	53	1600	1600	NUM
ejpam-4550	442	54	time	time	NOUN
ejpam-4550	442	55	(	(	PUNCT
ejpam-4550	442	56	t	t	NOUN
ejpam-4550	442	57	)	)	PUNCT
ejpam-4550	442	58	0	0	NUM
ejpam-4550	443	1	0.01	0.01	NUM
ejpam-4550	443	2	0.02	0.02	NUM
ejpam-4550	443	3	0.03	0.03	NUM
ejpam-4550	443	4	0.04	0.04	NUM
ejpam-4550	443	5	0.05	0.05	NUM
ejpam-4550	443	6	0.06	0.06	NUM
ejpam-4550	443	7	0.07	0.07	NUM
ejpam-4550	443	8	0.08	0.08	NUM
ejpam-4550	443	9	p	p	NOUN
ejpam-4550	443	10	ro	ro	NOUN
ejpam-4550	444	1	p	p	X
ejpam-4550	445	1	o	o	X
ejpam-4550	446	1	rt	rt	PROPN
ejpam-4550	447	1	io	io	PROPN
ejpam-4550	448	1	n	n	PROPN
ejpam-4550	448	2	o	o	X
ejpam-4550	448	3	f	f	X
ejpam-4550	448	4	in	in	ADP
ejpam-4550	448	5	d	d	PROPN
ejpam-4550	448	6	iv	iv	INTJ
ejpam-4550	448	7	i	i	PROPN
ejpam-4550	448	8	d	d	PROPN
ejpam-4550	448	9	u	u	PROPN
ejpam-4550	448	10	a	a	DET
ejpam-4550	448	11	ls	ls	X
ejpam-4550	448	12	i	i	PRON
ejpam-4550	448	13	n	n	X
ejpam-4550	448	14	fe	fe	X
ejpam-4550	448	15	c	c	X
ejpam-4550	448	16	te	te	PROPN
ejpam-4550	448	17	d	d	X
ejpam-4550	448	18	a	a	DET
ejpam-4550	448	19	t	t	NOUN
ejpam-4550	448	20	s	s	X
ejpam-4550	448	21	ta	ta	ADP
ejpam-4550	448	22	g	g	PROPN
ejpam-4550	448	23	e	e	PROPN
ejpam-4550	448	24	3	3	NUM
ejpam-4550	448	25	o	o	NOUN
ejpam-4550	448	26	f	f	X
ejpam-4550	448	27	c	c	X
ejpam-4550	448	28	la	la	PROPN
ejpam-4550	448	29	s	s	PROPN
ejpam-4550	448	30	s	s	X
ejpam-4550	448	31	c	c	NOUN
ejpam-4550	448	32	2	2	NUM
ejpam-4550	448	33	(	(	PUNCT
ejpam-4550	448	34	b	b	NOUN
ejpam-4550	448	35	)	)	PUNCT
ejpam-4550	448	36	proportion	proportion	NOUN
ejpam-4550	448	37	of	of	ADP
ejpam-4550	448	38	individuals	individual	NOUN
ejpam-4550	448	39	infected	infect	VERB
ejpam-4550	448	40	at	at	ADP
ejpam-4550	448	41	stage	stage	NOUN
ejpam-4550	448	42	3	3	NUM
ejpam-4550	448	43	in	in	ADP
ejpam-4550	448	44	c2	c2	PROPN
ejpam-4550	448	45	figure	figure	NOUN
ejpam-4550	448	46	9	9	NUM
ejpam-4550	448	47	:	:	PUNCT
ejpam-4550	448	48	time	time	NOUN
ejpam-4550	448	49	series	series	PROPN
ejpam-4550	448	50	plot	plot	NOUN
ejpam-4550	448	51	of	of	ADP
ejpam-4550	448	52	the	the	DET
ejpam-4550	448	53	proportions	proportion	NOUN
ejpam-4550	448	54	of	of	ADP
ejpam-4550	448	55	individuals	individual	NOUN
ejpam-4550	448	56	infected	infect	VERB
ejpam-4550	448	57	at	at	ADP
ejpam-4550	448	58	stage	stage	NOUN
ejpam-4550	448	59	3	3	NUM
ejpam-4550	448	60	in	in	ADP
ejpam-4550	448	61	classes	class	NOUN
ejpam-4550	448	62	c1	c1	PROPN
ejpam-4550	448	63	and	and	CCONJ
ejpam-4550	448	64	c2	c2	PROPN
ejpam-4550	448	65	for	for	ADP
ejpam-4550	448	66	r0	r0	NOUN
ejpam-4550	448	67	=	=	PUNCT
ejpam-4550	448	68	1.408	1.408	NUM
ejpam-4550	448	69	>	>	X
ejpam-4550	448	70	1	1	NUM
ejpam-4550	448	71	using	use	VERB
ejpam-4550	448	72	various	various	ADJ
ejpam-4550	448	73	initial	initial	ADJ
ejpam-4550	448	74	conditions	condition	NOUN
ejpam-4550	448	75	and	and	CCONJ
ejpam-4550	448	76	parameter	parameter	NOUN
ejpam-4550	448	77	values	value	NOUN
ejpam-4550	448	78	reported	report	VERB
ejpam-4550	448	79	in	in	ADP
ejpam-4550	448	80	table	table	NOUN
ejpam-4550	448	81	5	5	NUM
ejpam-4550	448	82	.	.	PUNCT
ejpam-4550	449	1	on	on	ADP
ejpam-4550	449	2	the	the	DET
ejpam-4550	449	3	characteristics	characteristic	NOUN
ejpam-4550	449	4	of	of	ADP
ejpam-4550	449	5	the	the	DET
ejpam-4550	449	6	two	two	NUM
ejpam-4550	449	7	age	age	NOUN
ejpam-4550	449	8	classes	class	NOUN
ejpam-4550	449	9	.	.	PUNCT
ejpam-4550	450	1	we	we	PRON
ejpam-4550	450	2	have	have	AUX
ejpam-4550	450	3	proved	prove	VERB
ejpam-4550	450	4	that	that	SCONJ
ejpam-4550	450	5	if	if	SCONJ
ejpam-4550	450	6	the	the	DET
ejpam-4550	450	7	routh	routh	PROPN
ejpam-4550	450	8	-	-	PUNCT
ejpam-4550	450	9	hurwitz	hurwitz	PROPN
ejpam-4550	450	10	criterion	criterion	NOUN
ejpam-4550	450	11	are	be	AUX
ejpam-4550	450	12	satisfied	satisfied	ADJ
ejpam-4550	450	13	,	,	PUNCT
ejpam-4550	450	14	then	then	ADV
ejpam-4550	450	15	the	the	DET
ejpam-4550	450	16	disease	disease	NOUN
ejpam-4550	450	17	-	-	PUNCT
ejpam-4550	450	18	free	free	ADJ
ejpam-4550	450	19	equilibrium	equilibrium	NOUN
ejpam-4550	450	20	(	(	PUNCT
ejpam-4550	450	21	dfe	dfe	PROPN
ejpam-4550	450	22	)	)	PUNCT
ejpam-4550	450	23	e0	e0	PROPN
ejpam-4550	450	24	is	be	AUX
ejpam-4550	450	25	locally	locally	ADV
ejpam-4550	450	26	asymptotically	asymptotically	ADV
ejpam-4550	450	27	stable	stable	ADJ
ejpam-4550	450	28	.	.	PUNCT
ejpam-4550	451	1	we	we	PRON
ejpam-4550	451	2	constructed	construct	VERB
ejpam-4550	451	3	a	a	DET
ejpam-4550	451	4	lyapunov	lyapunov	ADJ
ejpam-4550	451	5	function	function	NOUN
ejpam-4550	451	6	to	to	PART
ejpam-4550	451	7	prove	prove	VERB
ejpam-4550	451	8	that	that	SCONJ
ejpam-4550	451	9	the	the	DET
ejpam-4550	451	10	disease	disease	NOUN
ejpam-4550	451	11	-	-	PUNCT
ejpam-4550	451	12	free	free	ADJ
ejpam-4550	451	13	equilibrium	equilibrium	NOUN
ejpam-4550	451	14	(	(	PUNCT
ejpam-4550	451	15	dfe	dfe	PROPN
ejpam-4550	451	16	)	)	PUNCT
ejpam-4550	451	17	e0	e0	PROPN
ejpam-4550	451	18	is	be	AUX
ejpam-4550	451	19	globally	globally	ADV
ejpam-4550	451	20	stable	stable	ADJ
ejpam-4550	451	21	when	when	SCONJ
ejpam-4550	451	22	r0	r0	NOUN
ejpam-4550	451	23	<	<	X
ejpam-4550	451	24	1	1	NUM
ejpam-4550	451	25	.	.	PUNCT
ejpam-4550	452	1	for	for	ADP
ejpam-4550	452	2	r0	r0	PROPN
ejpam-4550	452	3	>	>	X
ejpam-4550	452	4	1	1	NUM
ejpam-4550	452	5	,	,	PUNCT
ejpam-4550	452	6	we	we	PRON
ejpam-4550	452	7	obtain	obtain	VERB
ejpam-4550	452	8	from	from	ADP
ejpam-4550	452	9	mathematical	mathematical	ADJ
ejpam-4550	452	10	analysis	analysis	NOUN
ejpam-4550	452	11	a	a	DET
ejpam-4550	452	12	quadratic	quadratic	ADJ
ejpam-4550	452	13	equation	equation	NOUN
ejpam-4550	452	14	in	in	ADP
ejpam-4550	452	15	i11	i11	NOUN
ejpam-4550	452	16	.	.	PUNCT
ejpam-4550	453	1	it	it	PRON
ejpam-4550	453	2	has	have	AUX
ejpam-4550	453	3	been	be	AUX
ejpam-4550	453	4	proven	prove	VERB
ejpam-4550	453	5	that	that	SCONJ
ejpam-4550	453	6	the	the	DET
ejpam-4550	453	7	existence	existence	NOUN
ejpam-4550	453	8	of	of	ADP
ejpam-4550	453	9	an	an	DET
ejpam-4550	453	10	endemic	endemic	ADJ
ejpam-4550	453	11	equilibrium	equilibrium	NOUN
ejpam-4550	453	12	depends	depend	VERB
ejpam-4550	453	13	on	on	ADP
ejpam-4550	453	14	the	the	DET
ejpam-4550	453	15	existence	existence	NOUN
ejpam-4550	453	16	of	of	ADP
ejpam-4550	453	17	at	at	ADV
ejpam-4550	453	18	least	least	ADV
ejpam-4550	453	19	one	one	NUM
ejpam-4550	453	20	real	real	ADV
ejpam-4550	453	21	positive	positive	ADJ
ejpam-4550	453	22	value	value	NOUN
ejpam-4550	453	23	for	for	ADP
ejpam-4550	453	24	i11	i11	NOUN
ejpam-4550	453	25	.	.	PUNCT
ejpam-4550	454	1	the	the	DET
ejpam-4550	454	2	stability	stability	NOUN
ejpam-4550	454	3	analysis	analysis	NOUN
ejpam-4550	454	4	of	of	ADP
ejpam-4550	454	5	endemic	endemic	ADJ
ejpam-4550	454	6	equilibrium	equilibrium	NOUN
ejpam-4550	454	7	produces	produce	VERB
ejpam-4550	454	8	that	that	SCONJ
ejpam-4550	454	9	if	if	SCONJ
ejpam-4550	454	10	the	the	DET
ejpam-4550	454	11	routh	routh	PROPN
ejpam-4550	454	12	-	-	PUNCT
ejpam-4550	454	13	hurwitz	hurwitz	PROPN
ejpam-4550	454	14	criterion	criterion	NOUN
ejpam-4550	454	15	are	be	AUX
ejpam-4550	454	16	satisfied	satisfied	ADJ
ejpam-4550	454	17	,	,	PUNCT
ejpam-4550	454	18	then	then	ADV
ejpam-4550	454	19	the	the	DET
ejpam-4550	454	20	endemic	endemic	ADJ
ejpam-4550	454	21	equilibrium	equilibrium	NOUN
ejpam-4550	454	22	e∗	e∗	NOUN
ejpam-4550	454	23	is	be	AUX
ejpam-4550	454	24	locally	locally	ADV
ejpam-4550	454	25	asymptotically	asymptotically	ADV
ejpam-4550	454	26	stable	stable	ADJ
ejpam-4550	454	27	.	.	PUNCT
ejpam-4550	455	1	the	the	DET
ejpam-4550	455	2	important	important	ADJ
ejpam-4550	455	3	mathematical	mathematical	ADJ
ejpam-4550	455	4	results	result	NOUN
ejpam-4550	455	5	in	in	ADP
ejpam-4550	455	6	this	this	DET
ejpam-4550	455	7	paper	paper	NOUN
ejpam-4550	455	8	were	be	AUX
ejpam-4550	455	9	all	all	PRON
ejpam-4550	455	10	corroborated	corroborate	VERB
ejpam-4550	455	11	by	by	ADP
ejpam-4550	455	12	numerical	numerical	ADJ
ejpam-4550	455	13	simulations	simulation	NOUN
ejpam-4550	455	14	performed	perform	VERB
ejpam-4550	455	15	using	use	VERB
ejpam-4550	455	16	matlab	matlab	PROPN
ejpam-4550	455	17	.	.	PUNCT
ejpam-4550	456	1	indeed	indeed	ADV
ejpam-4550	456	2	,	,	PUNCT
ejpam-4550	456	3	we	we	PRON
ejpam-4550	456	4	verified	verify	VERB
ejpam-4550	456	5	through	through	ADP
ejpam-4550	456	6	numerical	numerical	ADJ
ejpam-4550	456	7	experiments	experiment	NOUN
ejpam-4550	456	8	that	that	SCONJ
ejpam-4550	456	9	the	the	DET
ejpam-4550	456	10	disease	disease	NOUN
ejpam-4550	456	11	-	-	PUNCT
ejpam-4550	456	12	free	free	ADJ
ejpam-4550	456	13	equilibrium	equilibrium	NOUN
ejpam-4550	456	14	e0	e0	PROPN
ejpam-4550	456	15	is	be	AUX
ejpam-4550	456	16	stable	stable	ADJ
ejpam-4550	456	17	when	when	SCONJ
ejpam-4550	456	18	r0	r0	NOUN
ejpam-4550	456	19	<	<	X
ejpam-4550	456	20	1	1	NUM
ejpam-4550	456	21	.	.	PUNCT
ejpam-4550	457	1	on	on	ADP
ejpam-4550	457	2	the	the	DET
ejpam-4550	457	3	other	other	ADJ
ejpam-4550	457	4	hand	hand	NOUN
ejpam-4550	457	5	,	,	PUNCT
ejpam-4550	457	6	we	we	PRON
ejpam-4550	457	7	numerically	numerically	ADV
ejpam-4550	457	8	verified	verify	VERB
ejpam-4550	457	9	that	that	SCONJ
ejpam-4550	457	10	,	,	PUNCT
ejpam-4550	457	11	if	if	SCONJ
ejpam-4550	457	12	r0	r0	NOUN
ejpam-4550	457	13	>	>	X
ejpam-4550	457	14	1	1	NUM
ejpam-4550	457	15	,	,	PUNCT
ejpam-4550	457	16	then	then	ADV
ejpam-4550	457	17	the	the	DET
ejpam-4550	457	18	endemic	endemic	ADJ
ejpam-4550	457	19	equilibrium	equilibrium	NOUN
ejpam-4550	457	20	e∗	e∗	NOUN
ejpam-4550	457	21	becomes	become	VERB
ejpam-4550	457	22	stable	stable	ADJ
ejpam-4550	457	23	.	.	PUNCT
ejpam-4550	458	1	references	reference	NOUN
ejpam-4550	458	2	231	231	NUM
ejpam-4550	458	3	references	reference	NOUN
ejpam-4550	458	4	[	[	X
ejpam-4550	458	5	1	1	NUM
ejpam-4550	458	6	]	]	PUNCT
ejpam-4550	458	7	neterindwa	neterindwa	PROPN
ejpam-4550	458	8	ainea	ainea	PROPN
ejpam-4550	458	9	,	,	PUNCT
ejpam-4550	458	10	estomih	estomih	PROPN
ejpam-4550	458	11	s	s	PART
ejpam-4550	458	12	massawe	massawe	NOUN
ejpam-4550	458	13	,	,	PUNCT
ejpam-4550	458	14	and	and	CCONJ
ejpam-4550	458	15	oluwole	oluwole	PROPN
ejpam-4550	458	16	daniel	daniel	PROPN
ejpam-4550	458	17	makinde	makinde	PROPN
ejpam-4550	458	18	.	.	PUNCT
ejpam-4550	459	1	modelling	model	VERB
ejpam-4550	459	2	the	the	DET
ejpam-4550	459	3	effect	effect	NOUN
ejpam-4550	459	4	of	of	ADP
ejpam-4550	459	5	treatment	treatment	NOUN
ejpam-4550	459	6	and	and	CCONJ
ejpam-4550	459	7	infected	infected	ADJ
ejpam-4550	459	8	immigrants	immigrant	NOUN
ejpam-4550	459	9	on	on	ADP
ejpam-4550	459	10	the	the	DET
ejpam-4550	459	11	spread	spread	NOUN
ejpam-4550	459	12	of	of	ADP
ejpam-4550	459	13	hepatitis	hepatitis	PROPN
ejpam-4550	459	14	c	c	PROPN
ejpam-4550	459	15	virus	virus	NOUN
ejpam-4550	459	16	disease	disease	NOUN
ejpam-4550	459	17	with	with	ADP
ejpam-4550	459	18	acute	acute	ADJ
ejpam-4550	459	19	and	and	CCONJ
ejpam-4550	459	20	chronic	chronic	ADJ
ejpam-4550	459	21	stages	stage	NOUN
ejpam-4550	459	22	.	.	PUNCT
ejpam-4550	460	1	american	american	ADJ
ejpam-4550	460	2	journal	journal	PROPN
ejpam-4550	460	3	of	of	ADP
ejpam-4550	460	4	computational	computational	ADJ
ejpam-4550	460	5	and	and	CCONJ
ejpam-4550	460	6	applied	applied	ADJ
ejpam-4550	460	7	mathematics	mathematic	NOUN
ejpam-4550	460	8	,	,	PUNCT
ejpam-4550	460	9	2(1):10–20	2(1):10–20	NUM
ejpam-4550	460	10	,	,	PUNCT
ejpam-4550	460	11	2012	2012	NUM
ejpam-4550	460	12	.	.	PUNCT
ejpam-4550	461	1	[	[	X
ejpam-4550	461	2	2	2	NUM
ejpam-4550	461	3	]	]	PUNCT
ejpam-4550	461	4	mahamadou	mahamadou	NOUN
ejpam-4550	461	5	alassane	alassane	NOUN
ejpam-4550	461	6	,	,	PUNCT
ejpam-4550	461	7	ouaténi	ouaténi	PROPN
ejpam-4550	461	8	diallo	diallo	PROPN
ejpam-4550	461	9	,	,	PUNCT
ejpam-4550	461	10	and	and	CCONJ
ejpam-4550	461	11	jérôme	jérôme	PROPN
ejpam-4550	461	12	pousin	pousin	NOUN
ejpam-4550	461	13	.	.	PUNCT
ejpam-4550	462	1	individual	individual	ADJ
ejpam-4550	462	2	behavior	behavior	NOUN
ejpam-4550	462	3	and	and	CCONJ
ejpam-4550	462	4	epidemiological	epidemiological	ADJ
ejpam-4550	462	5	model	model	NOUN
ejpam-4550	462	6	.	.	PUNCT
ejpam-4550	463	1	journal	journal	PROPN
ejpam-4550	463	2	of	of	ADP
ejpam-4550	463	3	applied	apply	VERB
ejpam-4550	463	4	mathematics	mathematic	NOUN
ejpam-4550	463	5	and	and	CCONJ
ejpam-4550	463	6	bioinformatics	bioinformatics	NOUN
ejpam-4550	463	7	,	,	PUNCT
ejpam-4550	463	8	1(2):57	1(2):57	NUM
ejpam-4550	463	9	,	,	PUNCT
ejpam-4550	463	10	2011	2011	NUM
ejpam-4550	463	11	.	.	PUNCT
ejpam-4550	464	1	[	[	X
ejpam-4550	464	2	3	3	X
ejpam-4550	464	3	]	]	X
ejpam-4550	464	4	rm	rm	PROPN
ejpam-4550	464	5	anderson	anderson	PROPN
ejpam-4550	464	6	,	,	PUNCT
ejpam-4550	464	7	gf	gf	PROPN
ejpam-4550	464	8	medley	medley	NOUN
ejpam-4550	464	9	,	,	PUNCT
ejpam-4550	464	10	rm	rm	PROPN
ejpam-4550	464	11	may	may	AUX
ejpam-4550	464	12	,	,	PUNCT
ejpam-4550	464	13	and	and	CCONJ
ejpam-4550	464	14	am	be	AUX
ejpam-4550	464	15	johnson	johnson	PROPN
ejpam-4550	464	16	.	.	PUNCT
ejpam-4550	465	1	a	a	DET
ejpam-4550	465	2	preliminary	preliminary	ADJ
ejpam-4550	465	3	study	study	NOUN
ejpam-4550	465	4	of	of	ADP
ejpam-4550	465	5	the	the	DET
ejpam-4550	465	6	transmission	transmission	NOUN
ejpam-4550	465	7	dynamics	dynamic	NOUN
ejpam-4550	465	8	of	of	ADP
ejpam-4550	465	9	the	the	DET
ejpam-4550	465	10	human	human	ADJ
ejpam-4550	465	11	immunodeficiency	immunodeficiency	NOUN
ejpam-4550	465	12	virus	virus	NOUN
ejpam-4550	465	13	(	(	PUNCT
ejpam-4550	465	14	hiv	hiv	PROPN
ejpam-4550	465	15	)	)	PUNCT
ejpam-4550	465	16	,	,	PUNCT
ejpam-4550	465	17	the	the	DET
ejpam-4550	465	18	causative	causative	ADJ
ejpam-4550	465	19	agent	agent	NOUN
ejpam-4550	465	20	of	of	ADP
ejpam-4550	465	21	aids	aids	PROPN
ejpam-4550	465	22	.	.	PUNCT
ejpam-4550	466	1	mathematical	mathematical	ADJ
ejpam-4550	466	2	medicine	medicine	NOUN
ejpam-4550	466	3	and	and	CCONJ
ejpam-4550	466	4	biology	biology	NOUN
ejpam-4550	466	5	:	:	PUNCT
ejpam-4550	466	6	a	a	DET
ejpam-4550	466	7	journal	journal	NOUN
ejpam-4550	466	8	of	of	ADP
ejpam-4550	466	9	the	the	DET
ejpam-4550	466	10	i	i	PROPN
ejpam-4550	466	11	m	m	PROPN
ejpam-4550	466	12	a	a	PROPN
ejpam-4550	466	13	,	,	PUNCT
ejpam-4550	466	14	3(4):229	3(4):229	NUM
ejpam-4550	466	15	–	–	PUNCT
ejpam-4550	466	16	263	263	NUM
ejpam-4550	466	17	,	,	PUNCT
ejpam-4550	466	18	1986	1986	NUM
ejpam-4550	466	19	.	.	PUNCT
ejpam-4550	467	1	[	[	X
ejpam-4550	467	2	4	4	X
ejpam-4550	467	3	]	]	X
ejpam-4550	467	4	o.	o.	NOUN
ejpam-4550	467	5	diekmann	diekmann	PROPN
ejpam-4550	467	6	,	,	PUNCT
ejpam-4550	467	7	j.	j.	PROPN
ejpam-4550	467	8	a.	a.	PROPN
ejpam-4550	467	9	p.	p.	PROPN
ejpam-4550	467	10	heesterbeek	heesterbeek	PROPN
ejpam-4550	467	11	,	,	PUNCT
ejpam-4550	467	12	and	and	CCONJ
ejpam-4550	467	13	j.	j.	PROPN
ejpam-4550	467	14	a.	a.	PROPN
ejpam-4550	467	15	j.	j.	PROPN
ejpam-4550	467	16	metz	metz	PROPN
ejpam-4550	467	17	.	.	PUNCT
ejpam-4550	468	1	on	on	ADP
ejpam-4550	468	2	the	the	DET
ejpam-4550	468	3	definition	definition	NOUN
ejpam-4550	468	4	and	and	CCONJ
ejpam-4550	468	5	the	the	DET
ejpam-4550	468	6	computation	computation	NOUN
ejpam-4550	468	7	of	of	ADP
ejpam-4550	468	8	the	the	DET
ejpam-4550	468	9	basic	basic	ADJ
ejpam-4550	468	10	reproduction	reproduction	NOUN
ejpam-4550	468	11	ratio	ratio	NOUN
ejpam-4550	468	12	r0	r0	NOUN
ejpam-4550	468	13	in	in	ADP
ejpam-4550	468	14	models	model	NOUN
ejpam-4550	468	15	for	for	ADP
ejpam-4550	468	16	infectious	infectious	ADJ
ejpam-4550	468	17	diseases	disease	NOUN
ejpam-4550	468	18	in	in	ADP
ejpam-4550	468	19	heterogeneous	heterogeneous	ADJ
ejpam-4550	468	20	populations	population	NOUN
ejpam-4550	468	21	.	.	PUNCT
ejpam-4550	469	1	journal	journal	PROPN
ejpam-4550	469	2	of	of	ADP
ejpam-4550	469	3	mathematical	mathematical	ADJ
ejpam-4550	469	4	biology	biology	NOUN
ejpam-4550	469	5	,	,	PUNCT
ejpam-4550	469	6	28(4):365–382	28(4):365–382	PROPN
ejpam-4550	469	7	,	,	PUNCT
ejpam-4550	469	8	1990	1990	NUM
ejpam-4550	469	9	.	.	PUNCT
ejpam-4550	470	1	[	[	X
ejpam-4550	470	2	5	5	NUM
ejpam-4550	470	3	]	]	X
ejpam-4550	470	4	ab	ab	PROPN
ejpam-4550	470	5	gumel	gumel	PROPN
ejpam-4550	470	6	,	,	PUNCT
ejpam-4550	470	7	connell	connell	PROPN
ejpam-4550	470	8	c	c	PROPN
ejpam-4550	470	9	mccluskey	mccluskey	PROPN
ejpam-4550	470	10	,	,	PUNCT
ejpam-4550	470	11	and	and	CCONJ
ejpam-4550	470	12	pauline	pauline	PROPN
ejpam-4550	470	13	van	van	PROPN
ejpam-4550	470	14	den	den	PROPN
ejpam-4550	470	15	driessche	driessche	PROPN
ejpam-4550	470	16	.	.	PUNCT
ejpam-4550	471	1	mathematical	mathematical	ADJ
ejpam-4550	471	2	study	study	NOUN
ejpam-4550	471	3	of	of	ADP
ejpam-4550	471	4	a	a	DET
ejpam-4550	471	5	staged	stage	VERB
ejpam-4550	471	6	-	-	PUNCT
ejpam-4550	471	7	progression	progression	NOUN
ejpam-4550	471	8	hiv	hiv	PROPN
ejpam-4550	471	9	model	model	NOUN
ejpam-4550	471	10	with	with	ADP
ejpam-4550	471	11	imperfect	imperfect	ADJ
ejpam-4550	471	12	vaccine	vaccine	NOUN
ejpam-4550	471	13	.	.	PUNCT
ejpam-4550	472	1	bulletin	bulletin	NOUN
ejpam-4550	472	2	of	of	ADP
ejpam-4550	472	3	mathematical	mathematical	ADJ
ejpam-4550	472	4	biology	biology	NOUN
ejpam-4550	472	5	,	,	PUNCT
ejpam-4550	472	6	68(8):2105–2128	68(8):2105–2128	NOUN
ejpam-4550	472	7	,	,	PUNCT
ejpam-4550	472	8	2006	2006	NUM
ejpam-4550	472	9	.	.	PUNCT
ejpam-4550	473	1	[	[	X
ejpam-4550	473	2	6	6	NUM
ejpam-4550	473	3	]	]	X
ejpam-4550	473	4	james	james	PROPN
ejpam-4550	473	5	m	m	PROPN
ejpam-4550	473	6	hyman	hyman	PROPN
ejpam-4550	473	7	and	and	CCONJ
ejpam-4550	473	8	e	e	PROPN
ejpam-4550	473	9	ann	ann	PROPN
ejpam-4550	473	10	stanley	stanley	PROPN
ejpam-4550	473	11	.	.	PUNCT
ejpam-4550	474	1	using	use	VERB
ejpam-4550	474	2	mathematical	mathematical	ADJ
ejpam-4550	474	3	models	model	NOUN
ejpam-4550	474	4	to	to	PART
ejpam-4550	474	5	understand	understand	VERB
ejpam-4550	474	6	the	the	DET
ejpam-4550	474	7	aids	aids	PROPN
ejpam-4550	474	8	epidemic	epidemic	NOUN
ejpam-4550	474	9	.	.	PUNCT
ejpam-4550	475	1	mathematical	mathematical	ADJ
ejpam-4550	475	2	biosciences	bioscience	NOUN
ejpam-4550	475	3	,	,	PUNCT
ejpam-4550	475	4	90(1	90(1	NUM
ejpam-4550	475	5	-	-	SYM
ejpam-4550	475	6	2):415–473	2):415–473	NUM
ejpam-4550	475	7	,	,	PUNCT
ejpam-4550	475	8	1988	1988	NUM
ejpam-4550	475	9	.	.	PUNCT
ejpam-4550	476	1	[	[	X
ejpam-4550	476	2	7	7	X
ejpam-4550	476	3	]	]	PUNCT
ejpam-4550	476	4	mark	mark	PROPN
ejpam-4550	476	5	kot	kot	PROPN
ejpam-4550	476	6	.	.	PUNCT
ejpam-4550	477	1	elements	element	NOUN
ejpam-4550	477	2	of	of	ADP
ejpam-4550	477	3	mathematical	mathematical	ADJ
ejpam-4550	477	4	ecology	ecology	NOUN
ejpam-4550	477	5	.	.	PUNCT
ejpam-4550	478	1	cambridge	cambridge	PROPN
ejpam-4550	478	2	university	university	PROPN
ejpam-4550	478	3	press	press	NOUN
ejpam-4550	478	4	,	,	PUNCT
ejpam-4550	478	5	2001	2001	NUM
ejpam-4550	478	6	.	.	PUNCT
ejpam-4550	479	1	[	[	X
ejpam-4550	479	2	8	8	NUM
ejpam-4550	479	3	]	]	X
ejpam-4550	479	4	christopher	christopher	PROPN
ejpam-4550	479	5	m	m	PROPN
ejpam-4550	479	6	kribs	kribs	PROPN
ejpam-4550	479	7	-	-	PROPN
ejpam-4550	479	8	zaleta	zaleta	PROPN
ejpam-4550	479	9	and	and	CCONJ
ejpam-4550	479	10	jorge	jorge	NOUN
ejpam-4550	479	11	x	x	PROPN
ejpam-4550	479	12	velasco	velasco	PROPN
ejpam-4550	479	13	-	-	PUNCT
ejpam-4550	479	14	hernández	hernández	PROPN
ejpam-4550	479	15	.	.	PUNCT
ejpam-4550	480	1	a	a	DET
ejpam-4550	480	2	simple	simple	ADJ
ejpam-4550	480	3	vaccination	vaccination	NOUN
ejpam-4550	480	4	model	model	NOUN
ejpam-4550	480	5	with	with	ADP
ejpam-4550	480	6	multiple	multiple	ADJ
ejpam-4550	480	7	endemic	endemic	ADJ
ejpam-4550	480	8	states	state	NOUN
ejpam-4550	480	9	.	.	PUNCT
ejpam-4550	481	1	mathematical	mathematical	ADJ
ejpam-4550	481	2	biosciences	bioscience	NOUN
ejpam-4550	481	3	,	,	PUNCT
ejpam-4550	481	4	164(2):183–201	164(2):183–201	NUM
ejpam-4550	481	5	,	,	PUNCT
ejpam-4550	481	6	2000	2000	NUM
ejpam-4550	481	7	.	.	PUNCT
ejpam-4550	482	1	[	[	X
ejpam-4550	482	2	9	9	NUM
ejpam-4550	482	3	]	]	X
ejpam-4550	482	4	rachid	rachid	PROPN
ejpam-4550	482	5	lounès	lounès	PROPN
ejpam-4550	482	6	and	and	CCONJ
ejpam-4550	482	7	héctor	héctor	PROPN
ejpam-4550	482	8	de	de	PROPN
ejpam-4550	482	9	arazoza	arazoza	PROPN
ejpam-4550	482	10	.	.	PUNCT
ejpam-4550	483	1	a	a	DET
ejpam-4550	483	2	two	two	NUM
ejpam-4550	483	3	-	-	PUNCT
ejpam-4550	483	4	type	type	NOUN
ejpam-4550	483	5	model	model	NOUN
ejpam-4550	483	6	for	for	ADP
ejpam-4550	483	7	the	the	DET
ejpam-4550	483	8	cuban	cuban	ADJ
ejpam-4550	483	9	national	national	ADJ
ejpam-4550	483	10	programme	programme	PROPN
ejpam-4550	483	11	on	on	ADP
ejpam-4550	483	12	hiv	hiv	PROPN
ejpam-4550	483	13	/	/	SYM
ejpam-4550	483	14	aids	aids	PROPN
ejpam-4550	483	15	.	.	PUNCT
ejpam-4550	484	1	mathematical	mathematical	ADJ
ejpam-4550	484	2	medicine	medicine	NOUN
ejpam-4550	484	3	and	and	CCONJ
ejpam-4550	484	4	biology	biology	NOUN
ejpam-4550	484	5	:	:	PUNCT
ejpam-4550	484	6	a	a	DET
ejpam-4550	484	7	journal	journal	NOUN
ejpam-4550	484	8	of	of	ADP
ejpam-4550	484	9	the	the	DET
ejpam-4550	484	10	i	i	PROPN
ejpam-4550	484	11	m	m	PROPN
ejpam-4550	484	12	a	a	PROPN
ejpam-4550	484	13	,	,	PUNCT
ejpam-4550	484	14	16(2):143–154	16(2):143–154	PROPN
ejpam-4550	484	15	,	,	PUNCT
ejpam-4550	484	16	1999	1999	NUM
ejpam-4550	484	17	.	.	PUNCT
ejpam-4550	485	1	[	[	X
ejpam-4550	485	2	10	10	NUM
ejpam-4550	485	3	]	]	X
ejpam-4550	485	4	c	c	PROPN
ejpam-4550	485	5	connell	connell	PROPN
ejpam-4550	485	6	mccluskey	mccluskey	PROPN
ejpam-4550	485	7	.	.	PUNCT
ejpam-4550	486	1	a	a	DET
ejpam-4550	486	2	model	model	NOUN
ejpam-4550	486	3	of	of	ADP
ejpam-4550	486	4	hiv	hiv	PROPN
ejpam-4550	486	5	/	/	SYM
ejpam-4550	486	6	aids	aids	PROPN
ejpam-4550	486	7	with	with	ADP
ejpam-4550	486	8	staged	stage	VERB
ejpam-4550	486	9	progression	progression	NOUN
ejpam-4550	486	10	and	and	CCONJ
ejpam-4550	486	11	amelioration	amelioration	NOUN
ejpam-4550	486	12	.	.	PUNCT
ejpam-4550	487	1	mathematical	mathematical	ADJ
ejpam-4550	487	2	biosciences	bioscience	NOUN
ejpam-4550	487	3	,	,	PUNCT
ejpam-4550	487	4	181(1):1–16	181(1):1–16	NUM
ejpam-4550	487	5	,	,	PUNCT
ejpam-4550	487	6	2003	2003	NUM
ejpam-4550	487	7	.	.	PUNCT
ejpam-4550	488	1	[	[	X
ejpam-4550	488	2	11	11	NUM
ejpam-4550	488	3	]	]	PUNCT
ejpam-4550	488	4	jyt	jyt	PROPN
ejpam-4550	488	5	mugisha	mugisha	PROPN
ejpam-4550	488	6	.	.	PUNCT
ejpam-4550	489	1	the	the	DET
ejpam-4550	489	2	mathematical	mathematical	ADJ
ejpam-4550	489	3	dynamics	dynamic	NOUN
ejpam-4550	489	4	of	of	ADP
ejpam-4550	489	5	hiv	hiv	PROPN
ejpam-4550	489	6	/	/	SYM
ejpam-4550	489	7	aids	aids	PROPN
ejpam-4550	489	8	epidemic	epidemic	NOUN
ejpam-4550	489	9	in	in	ADP
ejpam-4550	489	10	age	age	NOUN
ejpam-4550	489	11	-	-	PUNCT
ejpam-4550	489	12	structured	structure	VERB
ejpam-4550	489	13	population	population	NOUN
ejpam-4550	489	14	.	.	PUNCT
ejpam-4550	490	1	in	in	ADP
ejpam-4550	490	2	proceedings	proceeding	NOUN
ejpam-4550	490	3	of	of	ADP
ejpam-4550	490	4	xi	xi	PROPN
ejpam-4550	490	5	samsa	samsa	PROPN
ejpam-4550	490	6	symposium	symposium	NOUN
ejpam-4550	490	7	on	on	ADP
ejpam-4550	490	8	the	the	DET
ejpam-4550	490	9	potential	potential	NOUN
ejpam-4550	490	10	of	of	ADP
ejpam-4550	490	11	mathematical	mathematical	ADJ
ejpam-4550	490	12	modeling	modeling	NOUN
ejpam-4550	490	13	of	of	ADP
ejpam-4550	490	14	problems	problem	NOUN
ejpam-4550	490	15	from	from	ADP
ejpam-4550	490	16	the	the	DET
ejpam-4550	490	17	samsa	samsa	PROPN
ejpam-4550	490	18	region	region	NOUN
ejpam-4550	490	19	,	,	PUNCT
ejpam-4550	490	20	pages	page	NOUN
ejpam-4550	490	21	8–23	8–23	PROPN
ejpam-4550	490	22	,	,	PUNCT
ejpam-4550	490	23	1997	1997	NUM
ejpam-4550	490	24	.	.	PUNCT
ejpam-4550	491	1	[	[	X
ejpam-4550	491	2	12	12	NUM
ejpam-4550	491	3	]	]	X
ejpam-4550	491	4	z	z	NOUN
ejpam-4550	491	5	mukandavire	mukandavire	NOUN
ejpam-4550	491	6	,	,	PUNCT
ejpam-4550	491	7	w	w	PROPN
ejpam-4550	491	8	garira	garira	PROPN
ejpam-4550	491	9	,	,	PUNCT
ejpam-4550	491	10	and	and	CCONJ
ejpam-4550	491	11	c	c	X
ejpam-4550	491	12	chiyaka	chiyaka	ADV
ejpam-4550	491	13	.	.	PUNCT
ejpam-4550	492	1	asymptotic	asymptotic	ADJ
ejpam-4550	492	2	properties	property	NOUN
ejpam-4550	492	3	of	of	ADP
ejpam-4550	492	4	an	an	DET
ejpam-4550	492	5	hiv	hiv	PROPN
ejpam-4550	492	6	/	/	SYM
ejpam-4550	492	7	aids	aids	PROPN
ejpam-4550	492	8	model	model	NOUN
ejpam-4550	492	9	with	with	ADP
ejpam-4550	492	10	a	a	DET
ejpam-4550	492	11	time	time	NOUN
ejpam-4550	492	12	delay	delay	NOUN
ejpam-4550	492	13	.	.	PUNCT
ejpam-4550	493	1	journal	journal	PROPN
ejpam-4550	493	2	of	of	ADP
ejpam-4550	493	3	mathematical	mathematical	ADJ
ejpam-4550	493	4	analysis	analysis	NOUN
ejpam-4550	493	5	and	and	CCONJ
ejpam-4550	493	6	applications	application	NOUN
ejpam-4550	493	7	,	,	PUNCT
ejpam-4550	493	8	330(2):916–933	330(2):916–933	NUM
ejpam-4550	493	9	,	,	PUNCT
ejpam-4550	493	10	2007	2007	NUM
ejpam-4550	493	11	.	.	PUNCT
ejpam-4550	494	1	references	reference	NOUN
ejpam-4550	494	2	232	232	NUM
ejpam-4550	495	1	[	[	X
ejpam-4550	495	2	13	13	NUM
ejpam-4550	495	3	]	]	X
ejpam-4550	495	4	arni	arni	PROPN
ejpam-4550	495	5	sr	sr	PROPN
ejpam-4550	495	6	srinivasa	srinivasa	PROPN
ejpam-4550	495	7	rao	rao	PROPN
ejpam-4550	495	8	.	.	PUNCT
ejpam-4550	496	1	mathematical	mathematical	ADJ
ejpam-4550	496	2	modelling	modelling	NOUN
ejpam-4550	496	3	of	of	ADP
ejpam-4550	496	4	aids	aids	PROPN
ejpam-4550	496	5	epidemic	epidemic	NOUN
ejpam-4550	496	6	in	in	ADP
ejpam-4550	496	7	india	india	PROPN
ejpam-4550	496	8	.	.	PUNCT
ejpam-4550	497	1	current	current	ADJ
ejpam-4550	497	2	science	science	NOUN
ejpam-4550	497	3	,	,	PUNCT
ejpam-4550	497	4	84(9):1192–1197	84(9):1192–1197	NUM
ejpam-4550	497	5	,	,	PUNCT
ejpam-4550	497	6	2003	2003	NUM
ejpam-4550	497	7	.	.	PUNCT
ejpam-4550	498	1	[	[	X
ejpam-4550	498	2	14	14	NUM
ejpam-4550	498	3	]	]	X
ejpam-4550	498	4	robert	robert	PROPN
ejpam-4550	498	5	j	j	PROPN
ejpam-4550	498	6	smith	smith	PROPN
ejpam-4550	498	7	,	,	PUNCT
ejpam-4550	498	8	jing	jing	PROPN
ejpam-4550	498	9	li	li	PROPN
ejpam-4550	498	10	,	,	PUNCT
ejpam-4550	498	11	richard	richard	PROPN
ejpam-4550	498	12	gordon	gordon	PROPN
ejpam-4550	498	13	,	,	PUNCT
ejpam-4550	498	14	and	and	CCONJ
ejpam-4550	498	15	jane	jane	PROPN
ejpam-4550	498	16	m	m	PROPN
ejpam-4550	498	17	heffernan	heffernan	PROPN
ejpam-4550	498	18	.	.	PUNCT
ejpam-4550	499	1	can	can	AUX
ejpam-4550	499	2	we	we	PRON
ejpam-4550	499	3	spend	spend	VERB
ejpam-4550	499	4	our	our	PRON
ejpam-4550	499	5	way	way	NOUN
ejpam-4550	499	6	out	out	ADP
ejpam-4550	499	7	of	of	ADP
ejpam-4550	499	8	the	the	DET
ejpam-4550	499	9	aids	aids	PROPN
ejpam-4550	499	10	epidemic	epidemic	NOUN
ejpam-4550	499	11	?	?	PUNCT
ejpam-4550	500	1	a	a	DET
ejpam-4550	500	2	world	world	NOUN
ejpam-4550	500	3	halting	halting	ADJ
ejpam-4550	500	4	aids	aids	PROPN
ejpam-4550	500	5	model	model	NOUN
ejpam-4550	500	6	.	.	PUNCT
ejpam-4550	501	1	bmc	bmc	ADJ
ejpam-4550	501	2	public	public	ADJ
ejpam-4550	501	3	health	health	NOUN
ejpam-4550	501	4	,	,	PUNCT
ejpam-4550	501	5	9(1):1–17	9(1):1–17	NUM
ejpam-4550	501	6	,	,	PUNCT
ejpam-4550	501	7	2009	2009	NUM
ejpam-4550	501	8	.	.	PUNCT