id	sid	tid	token	lemma	pos
ejpam-4556	1	1	european	european	PROPN
ejpam-4556	1	2	journal	journal	PROPN
ejpam-4556	1	3	of	of	ADP
ejpam-4556	1	4	pure	pure	ADJ
ejpam-4556	1	5	and	and	CCONJ
ejpam-4556	1	6	applied	apply	VERB
ejpam-4556	1	7	mathematics	mathematic	NOUN
ejpam-4556	1	8	vol	vol	NOUN
ejpam-4556	1	9	.	.	PROPN
ejpam-4556	2	1	15	15	NUM
ejpam-4556	2	2	,	,	PUNCT
ejpam-4556	2	3	no	no	INTJ
ejpam-4556	2	4	.	.	NOUN
ejpam-4556	2	5	4	4	NUM
ejpam-4556	2	6	,	,	PUNCT
ejpam-4556	2	7	2022	2022	NUM
ejpam-4556	2	8	,	,	PUNCT
ejpam-4556	2	9	2054	2054	NUM
ejpam-4556	2	10	-	-	SYM
ejpam-4556	2	11	2073	2073	NUM
ejpam-4556	2	12	issn	issn	VERB
ejpam-4556	2	13	1307	1307	NUM
ejpam-4556	2	14	-	-	SYM
ejpam-4556	2	15	5543	5543	NUM
ejpam-4556	2	16	–	–	PUNCT
ejpam-4556	2	17	ejpam.com	ejpam.com	X
ejpam-4556	2	18	published	publish	VERB
ejpam-4556	2	19	by	by	ADP
ejpam-4556	2	20	new	new	PROPN
ejpam-4556	2	21	york	york	PROPN
ejpam-4556	2	22	business	business	PROPN
ejpam-4556	2	23	global	global	PROPN
ejpam-4556	2	24	mathematical	mathematical	ADJ
ejpam-4556	2	25	analysis	analysis	NOUN
ejpam-4556	2	26	and	and	CCONJ
ejpam-4556	2	27	simulation	simulation	NOUN
ejpam-4556	2	28	of	of	ADP
ejpam-4556	2	29	an	an	DET
ejpam-4556	2	30	age	age	NOUN
ejpam-4556	2	31	-	-	PUNCT
ejpam-4556	2	32	structured	structure	VERB
ejpam-4556	2	33	model	model	NOUN
ejpam-4556	2	34	with	with	ADP
ejpam-4556	2	35	two	two	NUM
ejpam-4556	2	36	-	-	PUNCT
ejpam-4556	2	37	patch	patch	NOUN
ejpam-4556	2	38	and	and	CCONJ
ejpam-4556	2	39	an	an	DET
ejpam-4556	2	40	uncontrolled	uncontrolled	ADJ
ejpam-4556	2	41	migration	migration	NOUN
ejpam-4556	2	42	:	:	PUNCT
ejpam-4556	2	43	application	application	NOUN
ejpam-4556	2	44	to	to	ADP
ejpam-4556	2	45	tuberculosis	tuberculosis	VERB
ejpam-4556	2	46	badjo	badjo	PROPN
ejpam-4556	2	47	kimba	kimba	PROPN
ejpam-4556	2	48	abdoul	abdoul	X
ejpam-4556	2	49	wahid1,∗	wahid1,∗	NOUN
ejpam-4556	2	50	,	,	PUNCT
ejpam-4556	2	51	djibo	djibo	NOUN
ejpam-4556	2	52	moustapha1	moustapha1	NOUN
ejpam-4556	2	53	,	,	PUNCT
ejpam-4556	2	54	saley	saley	ADJ
ejpam-4556	2	55	bisso2	bisso2	NOUN
ejpam-4556	2	56	1	1	NUM
ejpam-4556	2	57	department	department	NOUN
ejpam-4556	2	58	of	of	ADP
ejpam-4556	2	59	applied	apply	VERB
ejpam-4556	2	60	mathematics	mathematic	NOUN
ejpam-4556	2	61	and	and	CCONJ
ejpam-4556	2	62	computer	computer	NOUN
ejpam-4556	2	63	science	science	NOUN
ejpam-4556	2	64	,	,	PUNCT
ejpam-4556	2	65	faculty	faculty	NOUN
ejpam-4556	2	66	of	of	ADP
ejpam-4556	2	67	sciences	science	NOUN
ejpam-4556	2	68	and	and	CCONJ
ejpam-4556	2	69	techniques	technique	NOUN
ejpam-4556	2	70	,	,	PUNCT
ejpam-4556	2	71	dosso	dosso	PROPN
ejpam-4556	2	72	university	university	PROPN
ejpam-4556	2	73	,	,	PUNCT
ejpam-4556	2	74	dosso	dosso	NOUN
ejpam-4556	2	75	,	,	PUNCT
ejpam-4556	2	76	niger	niger	NOUN
ejpam-4556	2	77	2	2	NUM
ejpam-4556	2	78	department	department	NOUN
ejpam-4556	2	79	of	of	ADP
ejpam-4556	2	80	mathematics	mathematic	NOUN
ejpam-4556	2	81	and	and	CCONJ
ejpam-4556	2	82	computer	computer	NOUN
ejpam-4556	2	83	science	science	NOUN
ejpam-4556	2	84	,	,	PUNCT
ejpam-4556	2	85	faculty	faculty	NOUN
ejpam-4556	2	86	of	of	ADP
ejpam-4556	2	87	sciences	science	NOUN
ejpam-4556	2	88	and	and	CCONJ
ejpam-4556	2	89	techniques	technique	NOUN
ejpam-4556	2	90	,	,	PUNCT
ejpam-4556	2	91	abdou	abdou	PROPN
ejpam-4556	2	92	moumouni	moumouni	PROPN
ejpam-4556	2	93	university	university	PROPN
ejpam-4556	2	94	,	,	PUNCT
ejpam-4556	2	95	niamey	niamey	NOUN
ejpam-4556	2	96	,	,	PUNCT
ejpam-4556	2	97	niger	niger	NOUN
ejpam-4556	2	98	abstract	abstract	NOUN
ejpam-4556	2	99	.	.	PUNCT
ejpam-4556	3	1	in	in	ADP
ejpam-4556	3	2	this	this	DET
ejpam-4556	3	3	paper	paper	NOUN
ejpam-4556	3	4	,	,	PUNCT
ejpam-4556	3	5	we	we	PRON
ejpam-4556	3	6	studied	study	VERB
ejpam-4556	3	7	a	a	DET
ejpam-4556	3	8	two	two	NUM
ejpam-4556	3	9	-	-	PUNCT
ejpam-4556	3	10	patch	patch	NOUN
ejpam-4556	3	11	age	age	NOUN
ejpam-4556	3	12	-	-	PUNCT
ejpam-4556	3	13	structured	structure	VERB
ejpam-4556	3	14	model	model	NOUN
ejpam-4556	3	15	of	of	ADP
ejpam-4556	3	16	tuberculosis	tuberculosis	NOUN
ejpam-4556	3	17	in	in	ADP
ejpam-4556	3	18	a	a	DET
ejpam-4556	3	19	context	context	NOUN
ejpam-4556	3	20	where	where	SCONJ
ejpam-4556	3	21	the	the	DET
ejpam-4556	3	22	migration	migration	NOUN
ejpam-4556	3	23	is	be	AUX
ejpam-4556	3	24	not	not	PART
ejpam-4556	3	25	controlled	control	VERB
ejpam-4556	3	26	.	.	PUNCT
ejpam-4556	4	1	motivated	motivate	VERB
ejpam-4556	4	2	by	by	ADP
ejpam-4556	4	3	the	the	DET
ejpam-4556	4	4	fact	fact	NOUN
ejpam-4556	4	5	that	that	SCONJ
ejpam-4556	4	6	no	no	DET
ejpam-4556	4	7	author	author	NOUN
ejpam-4556	4	8	has	have	AUX
ejpam-4556	4	9	highlighted	highlight	VERB
ejpam-4556	4	10	the	the	DET
ejpam-4556	4	11	impact	impact	NOUN
ejpam-4556	4	12	of	of	ADP
ejpam-4556	4	13	migration	migration	NOUN
ejpam-4556	4	14	on	on	ADP
ejpam-4556	4	15	the	the	DET
ejpam-4556	4	16	dynamics	dynamic	NOUN
ejpam-4556	4	17	of	of	ADP
ejpam-4556	4	18	transmission	transmission	NOUN
ejpam-4556	4	19	of	of	ADP
ejpam-4556	4	20	tuberculosis	tuberculosis	NOUN
ejpam-4556	4	21	.	.	PUNCT
ejpam-4556	5	1	each	each	DET
ejpam-4556	5	2	subpopulation	subpopulation	NOUN
ejpam-4556	5	3	is	be	AUX
ejpam-4556	5	4	subdivided	subdivide	VERB
ejpam-4556	5	5	into	into	ADP
ejpam-4556	5	6	five	five	NUM
ejpam-4556	5	7	compartments	compartment	NOUN
ejpam-4556	5	8	:	:	PUNCT
ejpam-4556	5	9	susceptible	susceptible	ADJ
ejpam-4556	5	10	;	;	PUNCT
ejpam-4556	5	11	latent	latent	NOUN
ejpam-4556	5	12	,	,	PUNCT
ejpam-4556	5	13	vaccinated	vaccinate	VERB
ejpam-4556	5	14	,	,	PUNCT
ejpam-4556	5	15	infective	infective	ADJ
ejpam-4556	5	16	and	and	CCONJ
ejpam-4556	5	17	treated	treat	VERB
ejpam-4556	5	18	.	.	PUNCT
ejpam-4556	6	1	after	after	ADP
ejpam-4556	6	2	the	the	DET
ejpam-4556	6	3	determination	determination	NOUN
ejpam-4556	6	4	of	of	ADP
ejpam-4556	6	5	the	the	DET
ejpam-4556	6	6	reproductive	reproductive	ADJ
ejpam-4556	6	7	numbers	number	NOUN
ejpam-4556	6	8	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	6	9	,	,	PUNCT
ejpam-4556	6	10	ρ	ρ	PROPN
ejpam-4556	6	11	)	)	PUNCT
ejpam-4556	6	12	and	and	CCONJ
ejpam-4556	6	13	ℜ0(ρ	ℜ0(ρ	PROPN
ejpam-4556	6	14	)	)	PUNCT
ejpam-4556	6	15	,	,	PUNCT
ejpam-4556	6	16	we	we	PRON
ejpam-4556	6	17	established	establish	VERB
ejpam-4556	6	18	the	the	DET
ejpam-4556	6	19	conditions	condition	NOUN
ejpam-4556	6	20	of	of	ADP
ejpam-4556	6	21	the	the	DET
ejpam-4556	6	22	global	global	ADJ
ejpam-4556	6	23	and	and	CCONJ
ejpam-4556	6	24	local	local	ADJ
ejpam-4556	6	25	stability	stability	NOUN
ejpam-4556	6	26	of	of	ADP
ejpam-4556	6	27	the	the	DET
ejpam-4556	6	28	equilibrium	equilibrium	NOUN
ejpam-4556	6	29	point	point	NOUN
ejpam-4556	6	30	without	without	ADP
ejpam-4556	6	31	disease	disease	NOUN
ejpam-4556	6	32	.	.	PUNCT
ejpam-4556	7	1	it	it	PRON
ejpam-4556	7	2	has	have	AUX
ejpam-4556	7	3	been	be	AUX
ejpam-4556	7	4	shown	show	VERB
ejpam-4556	7	5	that	that	SCONJ
ejpam-4556	7	6	there	there	PRON
ejpam-4556	7	7	is	be	VERB
ejpam-4556	7	8	only	only	ADV
ejpam-4556	7	9	one	one	NUM
ejpam-4556	7	10	point	point	NOUN
ejpam-4556	7	11	of	of	ADP
ejpam-4556	7	12	endemic	endemic	ADJ
ejpam-4556	7	13	equilibrium	equilibrium	NOUN
ejpam-4556	7	14	.	.	PUNCT
ejpam-4556	8	1	numerical	numerical	ADJ
ejpam-4556	8	2	simulations	simulation	NOUN
ejpam-4556	8	3	show	show	VERB
ejpam-4556	8	4	that	that	SCONJ
ejpam-4556	8	5	uncontrolled	uncontrolled	ADJ
ejpam-4556	8	6	migration	migration	NOUN
ejpam-4556	8	7	negatively	negatively	ADV
ejpam-4556	8	8	influences	influence	VERB
ejpam-4556	8	9	the	the	DET
ejpam-4556	8	10	dynamics	dynamic	NOUN
ejpam-4556	8	11	of	of	ADP
ejpam-4556	8	12	tuberculosis	tuberculosis	NOUN
ejpam-4556	8	13	.	.	PUNCT
ejpam-4556	9	1	2020	2020	NUM
ejpam-4556	9	2	mathematics	mathematic	NOUN
ejpam-4556	9	3	subject	subject	NOUN
ejpam-4556	9	4	classifications	classification	NOUN
ejpam-4556	9	5	:	:	PUNCT
ejpam-4556	9	6	92d25	92d25	NUM
ejpam-4556	9	7	,	,	PUNCT
ejpam-4556	9	8	92d30	92d30	NUM
ejpam-4556	9	9	,	,	PUNCT
ejpam-4556	9	10	65p40	65p40	NUM
ejpam-4556	9	11	,	,	PUNCT
ejpam-4556	9	12	93a10	93a10	NUM
ejpam-4556	9	13	key	key	ADJ
ejpam-4556	9	14	words	word	NOUN
ejpam-4556	9	15	and	and	CCONJ
ejpam-4556	9	16	phrases	phrase	NOUN
ejpam-4556	9	17	:	:	PUNCT
ejpam-4556	9	18	age	age	NOUN
ejpam-4556	9	19	-	-	PUNCT
ejpam-4556	9	20	structured	structure	VERB
ejpam-4556	9	21	,	,	PUNCT
ejpam-4556	9	22	reproductive	reproductive	ADJ
ejpam-4556	9	23	number	number	NOUN
ejpam-4556	9	24	,	,	PUNCT
ejpam-4556	9	25	two	two	NUM
ejpam-4556	9	26	-	-	PUNCT
ejpam-4556	9	27	patch	patch	NOUN
ejpam-4556	9	28	,	,	PUNCT
ejpam-4556	9	29	tuberculosis	tuberculosis	NOUN
ejpam-4556	9	30	,	,	PUNCT
ejpam-4556	9	31	stability	stability	NOUN
ejpam-4556	9	32	,	,	PUNCT
ejpam-4556	9	33	migration	migration	NOUN
ejpam-4556	9	34	,	,	PUNCT
ejpam-4556	9	35	simulation	simulation	NOUN
ejpam-4556	9	36	,	,	PUNCT
ejpam-4556	9	37	uncontrolled	uncontrolled	ADJ
ejpam-4556	9	38	,	,	PUNCT
ejpam-4556	9	39	endemic	endemic	ADJ
ejpam-4556	9	40	1	1	NUM
ejpam-4556	9	41	.	.	PUNCT
ejpam-4556	9	42	introduction	introduction	NOUN
ejpam-4556	9	43	tuberculosis	tuberculosis	NOUN
ejpam-4556	9	44	(	(	PUNCT
ejpam-4556	9	45	tb	tb	NOUN
ejpam-4556	9	46	)	)	PUNCT
ejpam-4556	9	47	is	be	AUX
ejpam-4556	9	48	one	one	NUM
ejpam-4556	9	49	of	of	ADP
ejpam-4556	9	50	the	the	DET
ejpam-4556	9	51	oldest	old	ADJ
ejpam-4556	9	52	diseases	disease	NOUN
ejpam-4556	9	53	humanity	humanity	NOUN
ejpam-4556	9	54	has	have	AUX
ejpam-4556	9	55	known	know	VERB
ejpam-4556	9	56	,	,	PUNCT
ejpam-4556	9	57	which	which	PRON
ejpam-4556	9	58	is	be	AUX
ejpam-4556	9	59	still	still	ADV
ejpam-4556	9	60	relevant	relevant	ADJ
ejpam-4556	9	61	today	today	NOUN
ejpam-4556	9	62	;	;	PUNCT
ejpam-4556	9	63	archaeological	archaeological	ADJ
ejpam-4556	9	64	excavations	excavation	NOUN
ejpam-4556	9	65	in	in	ADP
ejpam-4556	9	66	pharaonic	pharaonic	ADJ
ejpam-4556	9	67	egypt	egypt	PROPN
ejpam-4556	9	68	,	,	PUNCT
ejpam-4556	9	69	ancient	ancient	ADJ
ejpam-4556	9	70	india	india	PROPN
ejpam-4556	9	71	and	and	CCONJ
ejpam-4556	9	72	the	the	DET
ejpam-4556	9	73	far	far	PROPN
ejpam-4556	9	74	east	east	NOUN
ejpam-4556	9	75	show	show	VERB
ejpam-4556	9	76	that	that	SCONJ
ejpam-4556	9	77	the	the	DET
ejpam-4556	9	78	date	date	NOUN
ejpam-4556	9	79	of	of	ADP
ejpam-4556	9	80	its	its	PRON
ejpam-4556	9	81	first	first	ADJ
ejpam-4556	9	82	“	"	PUNCT
ejpam-4556	9	83	official	official	ADJ
ejpam-4556	9	84	”	"	PUNCT
ejpam-4556	9	85	recognition	recognition	NOUN
ejpam-4556	9	86	was	be	AUX
ejpam-4556	9	87	2400	2400	NUM
ejpam-4556	9	88	bc	bc	PROPN
ejpam-4556	10	1	[	[	X
ejpam-4556	10	2	8	8	NUM
ejpam-4556	10	3	,	,	PUNCT
ejpam-4556	10	4	10	10	NUM
ejpam-4556	10	5	,	,	PUNCT
ejpam-4556	10	6	16	16	NUM
ejpam-4556	10	7	]	]	PUNCT
ejpam-4556	10	8	.	.	PUNCT
ejpam-4556	11	1	despite	despite	SCONJ
ejpam-4556	11	2	enormous	enormous	ADJ
ejpam-4556	11	3	scientific	scientific	ADJ
ejpam-4556	11	4	advances	advance	NOUN
ejpam-4556	11	5	and	and	CCONJ
ejpam-4556	11	6	the	the	DET
ejpam-4556	11	7	availability	availability	NOUN
ejpam-4556	11	8	of	of	ADP
ejpam-4556	11	9	effective	effective	ADJ
ejpam-4556	11	10	treatment	treatment	NOUN
ejpam-4556	11	11	,	,	PUNCT
ejpam-4556	11	12	tb	tb	X
ejpam-4556	11	13	remains	remain	VERB
ejpam-4556	11	14	one	one	NUM
ejpam-4556	11	15	of	of	ADP
ejpam-4556	11	16	the	the	DET
ejpam-4556	11	17	top	top	ADJ
ejpam-4556	11	18	five	five	NUM
ejpam-4556	11	19	killers	killer	NOUN
ejpam-4556	11	20	worldwide	worldwide	ADV
ejpam-4556	11	21	.	.	PUNCT
ejpam-4556	12	1	understanding	understand	VERB
ejpam-4556	12	2	its	its	PRON
ejpam-4556	12	3	propagation	propagation	NOUN
ejpam-4556	12	4	dynamics	dynamic	NOUN
ejpam-4556	12	5	has	have	AUX
ejpam-4556	12	6	become	become	VERB
ejpam-4556	12	7	a	a	DET
ejpam-4556	12	8	concern	concern	NOUN
ejpam-4556	12	9	for	for	ADP
ejpam-4556	12	10	the	the	DET
ejpam-4556	12	11	entire	entire	ADJ
ejpam-4556	12	12	scientific	scientific	ADJ
ejpam-4556	12	13	community	community	NOUN
ejpam-4556	12	14	.	.	PUNCT
ejpam-4556	13	1	it	it	PRON
ejpam-4556	13	2	is	be	AUX
ejpam-4556	13	3	an	an	DET
ejpam-4556	13	4	infection	infection	NOUN
ejpam-4556	13	5	caused	cause	VERB
ejpam-4556	13	6	by	by	ADP
ejpam-4556	13	7	a	a	DET
ejpam-4556	13	8	bacterium	bacterium	NOUN
ejpam-4556	13	9	called	call	VERB
ejpam-4556	13	10	mycobacterium	mycobacterium	NOUN
ejpam-4556	13	11	tuberculosis	tuberculosis	NOUN
ejpam-4556	13	12	.	.	PUNCT
ejpam-4556	14	1	tuberculosis	tuberculosis	NOUN
ejpam-4556	14	2	most	most	ADV
ejpam-4556	14	3	commonly	commonly	ADV
ejpam-4556	14	4	affects	affect	VERB
ejpam-4556	14	5	the	the	DET
ejpam-4556	14	6	lungs	lung	NOUN
ejpam-4556	14	7	,	,	PUNCT
ejpam-4556	14	8	but	but	CCONJ
ejpam-4556	14	9	can	can	AUX
ejpam-4556	14	10	also	also	ADV
ejpam-4556	14	11	affect	affect	VERB
ejpam-4556	14	12	other	other	ADJ
ejpam-4556	14	13	parts	part	NOUN
ejpam-4556	14	14	of	of	ADP
ejpam-4556	14	15	the	the	DET
ejpam-4556	14	16	body	body	NOUN
ejpam-4556	14	17	,	,	PUNCT
ejpam-4556	14	18	such	such	ADJ
ejpam-4556	14	19	as	as	ADP
ejpam-4556	14	20	the	the	DET
ejpam-4556	14	21	skin	skin	NOUN
ejpam-4556	14	22	,	,	PUNCT
ejpam-4556	14	23	bones	bone	NOUN
ejpam-4556	14	24	,	,	PUNCT
ejpam-4556	14	25	lymph	lymph	NOUN
ejpam-4556	14	26	nodes	node	NOUN
ejpam-4556	14	27	,	,	PUNCT
ejpam-4556	14	28	liver	liver	NOUN
ejpam-4556	14	29	,	,	PUNCT
ejpam-4556	14	30	digestive	digestive	ADJ
ejpam-4556	14	31	tract	tract	NOUN
ejpam-4556	14	32	,	,	PUNCT
ejpam-4556	14	33	and	and	CCONJ
ejpam-4556	14	34	central	central	ADJ
ejpam-4556	14	35	nervous	nervous	ADJ
ejpam-4556	14	36	system	system	NOUN
ejpam-4556	14	37	[	[	X
ejpam-4556	14	38	11	11	NUM
ejpam-4556	14	39	]	]	PUNCT
ejpam-4556	14	40	.	.	PUNCT
ejpam-4556	15	1	tuberculosis	tuberculosis	NOUN
ejpam-4556	15	2	is	be	AUX
ejpam-4556	15	3	transmitted	transmit	VERB
ejpam-4556	15	4	from	from	ADP
ejpam-4556	15	5	one	one	NUM
ejpam-4556	15	6	person	person	NOUN
ejpam-4556	15	7	with	with	ADP
ejpam-4556	15	8	active	active	ADJ
ejpam-4556	15	9	∗corresponding	∗corresponding	NOUN
ejpam-4556	15	10	author	author	NOUN
ejpam-4556	15	11	.	.	PUNCT
ejpam-4556	16	1	doi	doi	NOUN
ejpam-4556	16	2	:	:	PUNCT
ejpam-4556	16	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4556	https://doi.org/10.29020/nybg.ejpam.v15i4.4556	PROPN
ejpam-4556	16	4	email	email	NOUN
ejpam-4556	16	5	addresses	address	NOUN
ejpam-4556	16	6	:	:	PUNCT
ejpam-4556	16	7	abadjokimba@yahoo.fr	abadjokimba@yahoo.fr	NOUN
ejpam-4556	16	8	(	(	PUNCT
ejpam-4556	16	9	b.	b.	PROPN
ejpam-4556	16	10	k.	k.	PROPN
ejpam-4556	16	11	abdoul	abdoul	PROPN
ejpam-4556	16	12	wahid	wahid	PROPN
ejpam-4556	16	13	)	)	PUNCT
ejpam-4556	16	14	,	,	PUNCT
ejpam-4556	16	15	moustaphad530@gmail.com	moustaphad530@gmail.com	X
ejpam-4556	16	16	(	(	PUNCT
ejpam-4556	16	17	d.	d.	PROPN
ejpam-4556	16	18	moustapha	moustapha	PROPN
ejpam-4556	16	19	)	)	PUNCT
ejpam-4556	16	20	,	,	PUNCT
ejpam-4556	16	21	bsaley@yahoo.fr	bsaley@yahoo.fr	PROPN
ejpam-4556	16	22	(	(	PUNCT
ejpam-4556	16	23	s.	s.	PROPN
ejpam-4556	16	24	bisso	bisso	PROPN
ejpam-4556	16	25	)	)	PUNCT
ejpam-4556	16	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4556	16	27	2054	2054	NUM
ejpam-4556	17	1	©	©	ADP
ejpam-4556	17	2	2022	2022	NUM
ejpam-4556	17	3	ejpam	ejpam	VERB
ejpam-4556	17	4	all	all	DET
ejpam-4556	17	5	rights	right	NOUN
ejpam-4556	17	6	reserved	reserve	VERB
ejpam-4556	17	7	.	.	PUNCT
ejpam-4556	18	1	b.	b.	PROPN
ejpam-4556	18	2	k.	k.	PROPN
ejpam-4556	18	3	abdoul	abdoul	PROPN
ejpam-4556	18	4	wahid	wahid	PROPN
ejpam-4556	18	5	,	,	PUNCT
ejpam-4556	18	6	d.moustapha	d.moustapha	PROPN
ejpam-4556	18	7	,	,	PUNCT
ejpam-4556	18	8	s.	s.	PROPN
ejpam-4556	18	9	bisso	bisso	PROPN
ejpam-4556	18	10	/	/	SYM
ejpam-4556	18	11	eur	eur	PROPN
ejpam-4556	18	12	.	.	PUNCT
ejpam-4556	19	1	j.	j.	PROPN
ejpam-4556	19	2	pure	pure	PROPN
ejpam-4556	19	3	appl	appl	PROPN
ejpam-4556	19	4	.	.	PROPN
ejpam-4556	19	5	math	math	PROPN
ejpam-4556	19	6	,	,	PUNCT
ejpam-4556	19	7	15	15	NUM
ejpam-4556	19	8	(	(	PUNCT
ejpam-4556	19	9	4	4	NUM
ejpam-4556	19	10	)	)	PUNCT
ejpam-4556	19	11	(	(	PUNCT
ejpam-4556	19	12	2022	2022	NUM
ejpam-4556	19	13	)	)	PUNCT
ejpam-4556	19	14	,	,	PUNCT
ejpam-4556	19	15	2054	2054	NUM
ejpam-4556	19	16	-	-	SYM
ejpam-4556	19	17	2073	2073	NUM
ejpam-4556	19	18	2055	2055	NUM
ejpam-4556	19	19	pulmonary	pulmonary	ADJ
ejpam-4556	19	20	tuberculosis	tuberculosis	NOUN
ejpam-4556	19	21	to	to	ADP
ejpam-4556	19	22	another	another	PRON
ejpam-4556	19	23	when	when	SCONJ
ejpam-4556	19	24	the	the	DET
ejpam-4556	19	25	latter	latter	ADJ
ejpam-4556	19	26	is	be	AUX
ejpam-4556	19	27	exposed	expose	VERB
ejpam-4556	19	28	to	to	ADP
ejpam-4556	19	29	m.	m.	NOUN
ejpam-4556	19	30	tuberculosis	tuberculosis	NOUN
ejpam-4556	19	31	.	.	PUNCT
ejpam-4556	20	1	living	living	NOUN
ejpam-4556	20	2	conditions	condition	NOUN
ejpam-4556	20	3	that	that	PRON
ejpam-4556	20	4	contribute	contribute	VERB
ejpam-4556	20	5	to	to	ADP
ejpam-4556	20	6	a	a	DET
ejpam-4556	20	7	high	high	ADJ
ejpam-4556	20	8	risk	risk	NOUN
ejpam-4556	20	9	of	of	ADP
ejpam-4556	20	10	exposure	exposure	NOUN
ejpam-4556	20	11	to	to	ADP
ejpam-4556	20	12	tb	tb	PROPN
ejpam-4556	20	13	include	include	VERB
ejpam-4556	20	14	overcrowded	overcrowded	ADJ
ejpam-4556	20	15	housing	housing	NOUN
ejpam-4556	20	16	,	,	PUNCT
ejpam-4556	20	17	homeless	homeless	ADJ
ejpam-4556	20	18	shelters	shelter	NOUN
ejpam-4556	20	19	and	and	CCONJ
ejpam-4556	20	20	correctional	correctional	ADJ
ejpam-4556	20	21	facilities	facility	NOUN
ejpam-4556	20	22	.	.	PUNCT
ejpam-4556	21	1	according	accord	VERB
ejpam-4556	21	2	to	to	ADP
ejpam-4556	21	3	who	who	PRON
ejpam-4556	21	4	reports	report	VERB
ejpam-4556	21	5	,	,	PUNCT
ejpam-4556	21	6	the	the	DET
ejpam-4556	21	7	people	people	NOUN
ejpam-4556	21	8	at	at	ADP
ejpam-4556	21	9	increased	increase	VERB
ejpam-4556	21	10	risk	risk	NOUN
ejpam-4556	21	11	of	of	ADP
ejpam-4556	21	12	exposure	exposure	NOUN
ejpam-4556	21	13	to	to	ADP
ejpam-4556	21	14	tuberculosis	tuberculosis	NOUN
ejpam-4556	21	15	include	include	VERB
ejpam-4556	21	16	those	those	PRON
ejpam-4556	21	17	with	with	ADP
ejpam-4556	21	18	a	a	DET
ejpam-4556	21	19	history	history	NOUN
ejpam-4556	21	20	of	of	ADP
ejpam-4556	21	21	alcohol	alcohol	NOUN
ejpam-4556	21	22	and	and	CCONJ
ejpam-4556	21	23	drug	drug	NOUN
ejpam-4556	21	24	abuse	abuse	NOUN
ejpam-4556	21	25	and	and	CCONJ
ejpam-4556	21	26	those	those	PRON
ejpam-4556	21	27	from	from	ADP
ejpam-4556	21	28	areas	area	NOUN
ejpam-4556	21	29	where	where	SCONJ
ejpam-4556	21	30	tb	tb	NOUN
ejpam-4556	21	31	is	be	AUX
ejpam-4556	21	32	prevalent	prevalent	ADJ
ejpam-4556	21	33	,	,	PUNCT
ejpam-4556	21	34	including	include	VERB
ejpam-4556	21	35	many	many	ADJ
ejpam-4556	21	36	countries	country	NOUN
ejpam-4556	21	37	in	in	ADP
ejpam-4556	21	38	the	the	DET
ejpam-4556	21	39	caribbean	caribbean	PROPN
ejpam-4556	21	40	,	,	PUNCT
ejpam-4556	21	41	africa	africa	PROPN
ejpam-4556	21	42	and	and	CCONJ
ejpam-4556	21	43	asia	asia	PROPN
ejpam-4556	21	44	.	.	PUNCT
ejpam-4556	22	1	until	until	SCONJ
ejpam-4556	22	2	the	the	DET
ejpam-4556	22	3	emergence	emergence	NOUN
ejpam-4556	22	4	of	of	ADP
ejpam-4556	22	5	the	the	DET
ejpam-4556	22	6	covid-19	covid-19	PROPN
ejpam-4556	22	7	pandemic	pandemic	ADJ
ejpam-4556	22	8	(	(	PUNCT
ejpam-4556	22	9	widely	widely	ADV
ejpam-4556	22	10	studied	study	VERB
ejpam-4556	22	11	,	,	PUNCT
ejpam-4556	22	12	among	among	ADP
ejpam-4556	22	13	recent	recent	ADJ
ejpam-4556	22	14	works	work	NOUN
ejpam-4556	22	15	we	we	PRON
ejpam-4556	22	16	can	can	AUX
ejpam-4556	22	17	cite	cite	VERB
ejpam-4556	22	18	[	[	X
ejpam-4556	22	19	1	1	NUM
ejpam-4556	22	20	,	,	PUNCT
ejpam-4556	22	21	17	17	NUM
ejpam-4556	22	22	]	]	PUNCT
ejpam-4556	22	23	)	)	PUNCT
ejpam-4556	22	24	,	,	PUNCT
ejpam-4556	22	25	tuberculosis	tuberculosis	NOUN
ejpam-4556	22	26	was	be	AUX
ejpam-4556	22	27	the	the	DET
ejpam-4556	22	28	leading	lead	VERB
ejpam-4556	22	29	cause	cause	NOUN
ejpam-4556	22	30	of	of	ADP
ejpam-4556	22	31	death	death	NOUN
ejpam-4556	22	32	attributable	attributable	ADJ
ejpam-4556	22	33	to	to	ADP
ejpam-4556	22	34	a	a	DET
ejpam-4556	22	35	single	single	ADJ
ejpam-4556	22	36	infectious	infectious	ADJ
ejpam-4556	22	37	agent	agent	NOUN
ejpam-4556	22	38	,	,	PUNCT
ejpam-4556	22	39	ahead	ahead	ADV
ejpam-4556	22	40	of	of	ADP
ejpam-4556	22	41	hiv	hiv	PROPN
ejpam-4556	22	42	/	/	SYM
ejpam-4556	22	43	aids	aids	PROPN
ejpam-4556	22	44	.	.	PUNCT
ejpam-4556	23	1	according	accord	VERB
ejpam-4556	23	2	to	to	ADP
ejpam-4556	23	3	the	the	DET
ejpam-4556	23	4	2021	2021	NUM
ejpam-4556	23	5	who	who	PRON
ejpam-4556	23	6	report	report	VERB
ejpam-4556	23	7	,	,	PUNCT
ejpam-4556	23	8	most	most	ADJ
ejpam-4556	23	9	people	people	NOUN
ejpam-4556	23	10	(	(	PUNCT
ejpam-4556	23	11	nearly	nearly	ADV
ejpam-4556	23	12	90	90	NUM
ejpam-4556	23	13	%	%	NOUN
ejpam-4556	23	14	)	)	PUNCT
ejpam-4556	23	15	who	who	PRON
ejpam-4556	23	16	develop	develop	VERB
ejpam-4556	23	17	the	the	DET
ejpam-4556	23	18	disease	disease	NOUN
ejpam-4556	23	19	are	be	AUX
ejpam-4556	23	20	adults	adult	NOUN
ejpam-4556	23	21	and	and	CCONJ
ejpam-4556	23	22	more	more	ADV
ejpam-4556	23	23	often	often	ADV
ejpam-4556	23	24	men	man	NOUN
ejpam-4556	23	25	than	than	ADP
ejpam-4556	23	26	women	woman	NOUN
ejpam-4556	23	27	.	.	PUNCT
ejpam-4556	24	1	nearly	nearly	ADV
ejpam-4556	24	2	a	a	DET
ejpam-4556	24	3	quarter	quarter	NOUN
ejpam-4556	24	4	of	of	ADP
ejpam-4556	24	5	the	the	DET
ejpam-4556	24	6	world	world	NOUN
ejpam-4556	24	7	’s	’s	PART
ejpam-4556	24	8	population	population	NOUN
ejpam-4556	24	9	is	be	AUX
ejpam-4556	24	10	infected	infect	VERB
ejpam-4556	24	11	with	with	ADP
ejpam-4556	24	12	m.tuberculosis	m.tuberculosis	NOUN
ejpam-4556	24	13	.	.	PUNCT
ejpam-4556	25	1	despite	despite	SCONJ
ejpam-4556	25	2	the	the	DET
ejpam-4556	25	3	fact	fact	NOUN
ejpam-4556	25	4	tuberculosis	tuberculosis	NOUN
ejpam-4556	25	5	is	be	AUX
ejpam-4556	25	6	a	a	DET
ejpam-4556	25	7	preventable	preventable	ADJ
ejpam-4556	25	8	disease	disease	NOUN
ejpam-4556	25	9	that	that	PRON
ejpam-4556	25	10	can	can	AUX
ejpam-4556	25	11	be	be	AUX
ejpam-4556	25	12	cured	cure	VERB
ejpam-4556	25	13	.	.	PUNCT
ejpam-4556	26	1	several	several	ADJ
ejpam-4556	26	2	mathematical	mathematical	ADJ
ejpam-4556	26	3	models	model	NOUN
ejpam-4556	26	4	have	have	AUX
ejpam-4556	26	5	been	be	AUX
ejpam-4556	26	6	developed	develop	VERB
ejpam-4556	26	7	in	in	ADP
ejpam-4556	26	8	order	order	NOUN
ejpam-4556	26	9	to	to	PART
ejpam-4556	26	10	make	make	VERB
ejpam-4556	26	11	contributions	contribution	NOUN
ejpam-4556	26	12	in	in	ADP
ejpam-4556	26	13	the	the	DET
ejpam-4556	26	14	decision	decision	NOUN
ejpam-4556	26	15	making	making	NOUN
ejpam-4556	26	16	of	of	ADP
ejpam-4556	26	17	the	the	DET
ejpam-4556	26	18	strategies	strategy	NOUN
ejpam-4556	26	19	to	to	PART
ejpam-4556	26	20	carry	carry	VERB
ejpam-4556	26	21	out	out	ADP
ejpam-4556	26	22	the	the	DET
ejpam-4556	26	23	control	control	NOUN
ejpam-4556	26	24	of	of	ADP
ejpam-4556	26	25	this	this	DET
ejpam-4556	26	26	disease	disease	NOUN
ejpam-4556	26	27	.	.	PUNCT
ejpam-4556	27	1	we	we	PRON
ejpam-4556	27	2	must	must	AUX
ejpam-4556	27	3	,	,	PUNCT
ejpam-4556	27	4	the	the	DET
ejpam-4556	27	5	first	first	ADJ
ejpam-4556	27	6	mathematical	mathematical	ADJ
ejpam-4556	27	7	model	model	NOUN
ejpam-4556	27	8	dealing	deal	VERB
ejpam-4556	27	9	with	with	ADP
ejpam-4556	27	10	the	the	DET
ejpam-4556	27	11	case	case	NOUN
ejpam-4556	27	12	of	of	ADP
ejpam-4556	27	13	tuberculosis	tuberculosis	NOUN
ejpam-4556	27	14	to	to	ADP
ejpam-4556	27	15	frost	frost	NOUN
ejpam-4556	27	16	,	,	PUNCT
ejpam-4556	27	17	he	he	PRON
ejpam-4556	27	18	predicted	predict	VERB
ejpam-4556	27	19	that	that	SCONJ
ejpam-4556	27	20	with	with	ADP
ejpam-4556	27	21	the	the	DET
ejpam-4556	27	22	low	low	ADJ
ejpam-4556	27	23	and	and	CCONJ
ejpam-4556	27	24	falling	fall	VERB
ejpam-4556	27	25	rate	rate	NOUN
ejpam-4556	27	26	of	of	ADP
ejpam-4556	27	27	transmission	transmission	NOUN
ejpam-4556	27	28	of	of	ADP
ejpam-4556	27	29	tuberculous	tuberculous	ADJ
ejpam-4556	27	30	infection	infection	NOUN
ejpam-4556	27	31	in	in	ADP
ejpam-4556	27	32	the	the	DET
ejpam-4556	27	33	united	united	PROPN
ejpam-4556	27	34	states	states	PROPN
ejpam-4556	27	35	,	,	PUNCT
ejpam-4556	27	36	it	it	PRON
ejpam-4556	27	37	was	be	AUX
ejpam-4556	27	38	most	most	ADV
ejpam-4556	27	39	likely	likely	ADJ
ejpam-4556	27	40	that	that	SCONJ
ejpam-4556	27	41	the	the	DET
ejpam-4556	27	42	tubercle	tubercle	NOUN
ejpam-4556	27	43	bacilli	bacilli	NOUN
ejpam-4556	27	44	were	be	AUX
ejpam-4556	27	45	fighting	fight	VERB
ejpam-4556	27	46	a	a	DET
ejpam-4556	27	47	losing	lose	VERB
ejpam-4556	27	48	battle	battle	NOUN
ejpam-4556	27	49	,	,	PUNCT
ejpam-4556	27	50	since	since	SCONJ
ejpam-4556	27	51	they	they	PRON
ejpam-4556	27	52	would	would	AUX
ejpam-4556	27	53	be	be	AUX
ejpam-4556	27	54	unable	unable	ADJ
ejpam-4556	27	55	to	to	PART
ejpam-4556	27	56	transmit	transmit	VERB
ejpam-4556	27	57	sufficient	sufficient	ADJ
ejpam-4556	27	58	infection	infection	NOUN
ejpam-4556	27	59	to	to	PART
ejpam-4556	27	60	maintain	maintain	VERB
ejpam-4556	27	61	the	the	DET
ejpam-4556	27	62	balance	balance	NOUN
ejpam-4556	27	63	in	in	ADP
ejpam-4556	27	64	their	their	PRON
ejpam-4556	27	65	own	own	ADJ
ejpam-4556	27	66	favor	favor	NOUN
ejpam-4556	27	67	.	.	PUNCT
ejpam-4556	28	1	(	(	PUNCT
ejpam-4556	28	2	see	see	VERB
ejpam-4556	28	3	[	[	X
ejpam-4556	28	4	21	21	NUM
ejpam-4556	28	5	,	,	PUNCT
ejpam-4556	28	6	22	22	NUM
ejpam-4556	28	7	]	]	PUNCT
ejpam-4556	28	8	.	.	PUNCT
ejpam-4556	29	1	nowadays	nowadays	ADV
ejpam-4556	29	2	,	,	PUNCT
ejpam-4556	29	3	we	we	PRON
ejpam-4556	29	4	have	have	VERB
ejpam-4556	29	5	a	a	DET
ejpam-4556	29	6	fairly	fairly	ADV
ejpam-4556	29	7	broad	broad	ADJ
ejpam-4556	29	8	literature	literature	NOUN
ejpam-4556	29	9	on	on	ADP
ejpam-4556	29	10	the	the	DET
ejpam-4556	29	11	mathematical	mathematical	ADJ
ejpam-4556	29	12	epidemiology	epidemiology	NOUN
ejpam-4556	29	13	of	of	ADP
ejpam-4556	29	14	tuberculosis	tuberculosis	NOUN
ejpam-4556	29	15	(	(	PUNCT
ejpam-4556	29	16	we	we	PRON
ejpam-4556	29	17	refer	refer	VERB
ejpam-4556	29	18	readers	reader	NOUN
ejpam-4556	29	19	to	to	ADP
ejpam-4556	29	20	the	the	DET
ejpam-4556	29	21	documents	document	NOUN
ejpam-4556	29	22	[	[	X
ejpam-4556	29	23	2	2	NUM
ejpam-4556	29	24	,	,	PUNCT
ejpam-4556	29	25	4	4	NUM
ejpam-4556	29	26	,	,	PUNCT
ejpam-4556	29	27	18	18	NUM
ejpam-4556	29	28	]	]	PUNCT
ejpam-4556	29	29	and	and	CCONJ
ejpam-4556	29	30	articles	article	NOUN
ejpam-4556	29	31	cited	cite	VERB
ejpam-4556	29	32	in	in	ADP
ejpam-4556	29	33	these	these	DET
ejpam-4556	29	34	papers	paper	NOUN
ejpam-4556	29	35	for	for	ADP
ejpam-4556	29	36	a	a	DET
ejpam-4556	29	37	good	good	ADJ
ejpam-4556	29	38	overview	overview	NOUN
ejpam-4556	29	39	of	of	ADP
ejpam-4556	29	40	the	the	DET
ejpam-4556	29	41	work	work	NOUN
ejpam-4556	29	42	done	do	VERB
ejpam-4556	29	43	in	in	ADP
ejpam-4556	29	44	this	this	DET
ejpam-4556	29	45	field	field	NOUN
ejpam-4556	29	46	as	as	SCONJ
ejpam-4556	29	47	the	the	DET
ejpam-4556	29	48	list	list	NOUN
ejpam-4556	29	49	is	be	AUX
ejpam-4556	29	50	by	by	ADP
ejpam-4556	29	51	no	no	DET
ejpam-4556	29	52	means	means	NOUN
ejpam-4556	29	53	exhaustive	exhaustive	ADJ
ejpam-4556	29	54	)	)	PUNCT
ejpam-4556	29	55	,	,	PUNCT
ejpam-4556	29	56	but	but	CCONJ
ejpam-4556	29	57	this	this	DET
ejpam-4556	29	58	work	work	NOUN
ejpam-4556	29	59	neglects	neglect	VERB
ejpam-4556	29	60	a	a	DET
ejpam-4556	29	61	number	number	NOUN
ejpam-4556	29	62	of	of	ADP
ejpam-4556	29	63	factors	factor	NOUN
ejpam-4556	29	64	(	(	PUNCT
ejpam-4556	29	65	either	either	CCONJ
ejpam-4556	29	66	all	all	PRON
ejpam-4556	29	67	or	or	CCONJ
ejpam-4556	29	68	some	some	PRON
ejpam-4556	29	69	of	of	ADP
ejpam-4556	29	70	its	its	PRON
ejpam-4556	29	71	parameters	parameter	NOUN
ejpam-4556	29	72	)	)	PUNCT
ejpam-4556	29	73	such	such	ADJ
ejpam-4556	29	74	as	as	ADP
ejpam-4556	29	75	the	the	DET
ejpam-4556	29	76	vaccination	vaccination	NOUN
ejpam-4556	29	77	program	program	NOUN
ejpam-4556	29	78	,	,	PUNCT
ejpam-4556	29	79	the	the	DET
ejpam-4556	29	80	compartment	compartment	NOUN
ejpam-4556	29	81	of	of	ADP
ejpam-4556	29	82	the	the	DET
ejpam-4556	29	83	treaties	treaty	NOUN
ejpam-4556	29	84	,	,	PUNCT
ejpam-4556	29	85	individuals	individual	NOUN
ejpam-4556	29	86	with	with	ADP
ejpam-4556	29	87	rapid	rapid	ADJ
ejpam-4556	29	88	progression	progression	NOUN
ejpam-4556	29	89	to	to	ADP
ejpam-4556	29	90	the	the	DET
ejpam-4556	29	91	state	state	NOUN
ejpam-4556	29	92	of	of	ADP
ejpam-4556	29	93	the	the	DET
ejpam-4556	29	94	disease	disease	NOUN
ejpam-4556	29	95	,	,	PUNCT
ejpam-4556	29	96	the	the	DET
ejpam-4556	29	97	mortality	mortality	NOUN
ejpam-4556	29	98	rate	rate	NOUN
ejpam-4556	29	99	related	relate	VERB
ejpam-4556	29	100	to	to	ADP
ejpam-4556	29	101	the	the	DET
ejpam-4556	29	102	disease	disease	NOUN
ejpam-4556	29	103	,	,	PUNCT
ejpam-4556	29	104	the	the	DET
ejpam-4556	29	105	birth	birth	NOUN
ejpam-4556	29	106	rate	rate	NOUN
ejpam-4556	29	107	of	of	ADP
ejpam-4556	29	108	the	the	DET
ejpam-4556	29	109	population	population	NOUN
ejpam-4556	29	110	in	in	ADP
ejpam-4556	29	111	addition	addition	NOUN
ejpam-4556	29	112	,	,	PUNCT
ejpam-4556	29	113	very	very	ADV
ejpam-4556	29	114	few	few	ADJ
ejpam-4556	29	115	of	of	ADP
ejpam-4556	29	116	these	these	DET
ejpam-4556	29	117	models	model	NOUN
ejpam-4556	29	118	are	be	AUX
ejpam-4556	29	119	structured	structure	VERB
ejpam-4556	29	120	in	in	ADP
ejpam-4556	29	121	age	age	NOUN
ejpam-4556	29	122	and	and	CCONJ
ejpam-4556	29	123	the	the	DET
ejpam-4556	29	124	migration	migration	NOUN
ejpam-4556	29	125	is	be	AUX
ejpam-4556	29	126	considered	consider	VERB
ejpam-4556	29	127	in	in	ADP
ejpam-4556	29	128	very	very	ADV
ejpam-4556	29	129	few	few	ADJ
ejpam-4556	29	130	works	work	NOUN
ejpam-4556	29	131	.	.	PUNCT
ejpam-4556	30	1	on	on	ADP
ejpam-4556	30	2	this	this	DET
ejpam-4556	30	3	subject	subject	ADJ
ejpam-4556	30	4	tewa	tewa	NOUN
ejpam-4556	30	5	j.j	j.j	PROPN
ejpam-4556	30	6	has	have	AUX
ejpam-4556	30	7	dedicated	dedicate	VERB
ejpam-4556	30	8	two	two	NUM
ejpam-4556	30	9	articles	article	NOUN
ejpam-4556	30	10	modeled	model	VERB
ejpam-4556	30	11	by	by	ADP
ejpam-4556	30	12	an	an	DET
ejpam-4556	30	13	edo	edo	PROPN
ejpam-4556	31	1	[	[	X
ejpam-4556	31	2	13	13	NUM
ejpam-4556	31	3	,	,	PUNCT
ejpam-4556	31	4	14	14	NUM
ejpam-4556	31	5	]	]	PUNCT
ejpam-4556	31	6	.	.	PUNCT
ejpam-4556	32	1	these	these	DET
ejpam-4556	32	2	factors	factor	NOUN
ejpam-4556	32	3	are	be	AUX
ejpam-4556	32	4	far	far	ADV
ejpam-4556	32	5	from	from	ADP
ejpam-4556	32	6	negligible	negligible	ADJ
ejpam-4556	32	7	in	in	ADP
ejpam-4556	32	8	african	african	ADJ
ejpam-4556	32	9	countries	country	NOUN
ejpam-4556	32	10	.	.	PUNCT
ejpam-4556	33	1	recently	recently	ADV
ejpam-4556	33	2	marwin	marwin	VERB
ejpam-4556	33	3	ramli	ramli	PROPN
ejpam-4556	33	4	and	and	CCONJ
ejpam-4556	33	5	al	al	PROPN
ejpam-4556	33	6	,	,	PUNCT
ejpam-4556	33	7	studied	study	VERB
ejpam-4556	33	8	the	the	DET
ejpam-4556	33	9	stability	stability	NOUN
ejpam-4556	33	10	of	of	ADP
ejpam-4556	33	11	the	the	DET
ejpam-4556	33	12	endemic	endemic	ADJ
ejpam-4556	33	13	equilibrium	equilibrium	NOUN
ejpam-4556	33	14	of	of	ADP
ejpam-4556	33	15	a	a	DET
ejpam-4556	33	16	sir	sir	NOUN
ejpam-4556	33	17	model	model	NOUN
ejpam-4556	33	18	of	of	ADP
ejpam-4556	33	19	tuberculosis	tuberculosis	NOUN
ejpam-4556	33	20	where	where	SCONJ
ejpam-4556	33	21	the	the	DET
ejpam-4556	33	22	compartment	compartment	NOUN
ejpam-4556	33	23	of	of	ADP
ejpam-4556	33	24	the	the	DET
ejpam-4556	33	25	susceptible	susceptible	ADJ
ejpam-4556	33	26	is	be	AUX
ejpam-4556	33	27	subdivided	subdivide	VERB
ejpam-4556	33	28	into	into	ADP
ejpam-4556	33	29	two	two	NUM
ejpam-4556	33	30	subgroups	subgroup	NOUN
ejpam-4556	33	31	,	,	PUNCT
ejpam-4556	33	32	that	that	PRON
ejpam-4556	33	33	of	of	ADP
ejpam-4556	33	34	susceptible	susceptible	ADJ
ejpam-4556	33	35	vaccinated	vaccinated	ADJ
ejpam-4556	33	36	and	and	CCONJ
ejpam-4556	33	37	those	those	PRON
ejpam-4556	33	38	of	of	ADP
ejpam-4556	33	39	susceptible	susceptible	ADJ
ejpam-4556	33	40	unvaccinated	unvaccinate	VERB
ejpam-4556	33	41	,	,	PUNCT
ejpam-4556	33	42	unstructured	unstructure	VERB
ejpam-4556	33	43	by	by	ADP
ejpam-4556	33	44	age	age	NOUN
ejpam-4556	33	45	[	[	X
ejpam-4556	33	46	12],they	12],they	PRON
ejpam-4556	33	47	made	make	VERB
ejpam-4556	33	48	an	an	DET
ejpam-4556	33	49	extinction	extinction	NOUN
ejpam-4556	33	50	of	of	ADP
ejpam-4556	33	51	this	this	DET
ejpam-4556	33	52	model	model	NOUN
ejpam-4556	33	53	by	by	ADP
ejpam-4556	33	54	adding	add	VERB
ejpam-4556	33	55	the	the	DET
ejpam-4556	33	56	latent	latent	NOUN
ejpam-4556	33	57	compartment[20	compartment[20	PROPN
ejpam-4556	33	58	]	]	PUNCT
ejpam-4556	33	59	;	;	PUNCT
ejpam-4556	33	60	rui	rui	PROPN
ejpam-4556	33	61	xu	xu	PROPN
ejpam-4556	33	62	and	and	CCONJ
ejpam-4556	33	63	al	al	PROPN
ejpam-4556	33	64	motivated	motivate	VERB
ejpam-4556	33	65	by	by	ADP
ejpam-4556	33	66	the	the	DET
ejpam-4556	33	67	work	work	NOUN
ejpam-4556	33	68	of	of	ADP
ejpam-4556	33	69	yang	yang	PROPN
ejpam-4556	33	70	and	and	CCONJ
ejpam-4556	33	71	al	al	PROPN
ejpam-4556	34	1	[	[	X
ejpam-4556	34	2	24	24	NUM
ejpam-4556	34	3	]	]	PUNCT
ejpam-4556	34	4	and	and	CCONJ
ejpam-4556	34	5	mc	mc	PROPN
ejpam-4556	34	6	cluskey	cluskey	NOUN
ejpam-4556	34	7	[	[	X
ejpam-4556	34	8	5	5	NUM
ejpam-4556	34	9	]	]	PUNCT
ejpam-4556	34	10	,	,	PUNCT
ejpam-4556	34	11	in	in	ADP
ejpam-4556	34	12	their	their	PRON
ejpam-4556	34	13	paper	paper	NOUN
ejpam-4556	34	14	,	,	PUNCT
ejpam-4556	34	15	they	they	PRON
ejpam-4556	34	16	investigated	investigate	VERB
ejpam-4556	34	17	the	the	DET
ejpam-4556	34	18	effects	effect	NOUN
ejpam-4556	34	19	of	of	ADP
ejpam-4556	34	20	incomplete	incomplete	ADJ
ejpam-4556	34	21	treatment	treatment	NOUN
ejpam-4556	34	22	and	and	CCONJ
ejpam-4556	34	23	age	age	NOUN
ejpam-4556	34	24	structure	structure	NOUN
ejpam-4556	34	25	in	in	ADP
ejpam-4556	34	26	latently	latently	ADV
ejpam-4556	34	27	infected	infected	ADJ
ejpam-4556	34	28	and	and	CCONJ
ejpam-4556	34	29	infectious	infectious	ADJ
ejpam-4556	34	30	individuals	individual	NOUN
ejpam-4556	34	31	the	the	DET
ejpam-4556	34	32	dynamics	dynamic	NOUN
ejpam-4556	34	33	of	of	ADP
ejpam-4556	34	34	tuberculosis	tuberculosis	NOUN
ejpam-4556	34	35	[	[	X
ejpam-4556	34	36	23].yu	23].yu	NUM
ejpam-4556	34	37	zhao	zhao	NOUN
ejpam-4556	34	38	and	and	CCONJ
ejpam-4556	34	39	al	al	PROPN
ejpam-4556	34	40	.	.	PROPN
ejpam-4556	34	41	analyzed	analyze	VERB
ejpam-4556	34	42	a	a	DET
ejpam-4556	34	43	model	model	NOUN
ejpam-4556	34	44	type	type	NOUN
ejpam-4556	34	45	seir	seir	NOUN
ejpam-4556	34	46	where	where	SCONJ
ejpam-4556	34	47	the	the	DET
ejpam-4556	34	48	compartment	compartment	NOUN
ejpam-4556	34	49	of	of	ADP
ejpam-4556	34	50	susceptible	susceptible	ADJ
ejpam-4556	34	51	is	be	AUX
ejpam-4556	34	52	subdivided	subdivide	VERB
ejpam-4556	34	53	into	into	ADP
ejpam-4556	34	54	three	three	NUM
ejpam-4556	34	55	age	age	NOUN
ejpam-4556	34	56	groups	group	NOUN
ejpam-4556	34	57	:	:	PUNCT
ejpam-4556	34	58	childhood	childhood	NOUN
ejpam-4556	34	59	,	,	PUNCT
ejpam-4556	34	60	middle	middle	ADJ
ejpam-4556	34	61	-	-	PUNCT
ejpam-4556	34	62	age	age	NOUN
ejpam-4556	34	63	and	and	CCONJ
ejpam-4556	34	64	senior	senior	ADJ
ejpam-4556	34	65	.	.	PUNCT
ejpam-4556	35	1	our	our	PRON
ejpam-4556	35	2	model	model	NOUN
ejpam-4556	35	3	is	be	AUX
ejpam-4556	35	4	an	an	DET
ejpam-4556	35	5	extension	extension	NOUN
ejpam-4556	35	6	of	of	ADP
ejpam-4556	35	7	the	the	DET
ejpam-4556	35	8	model	model	NOUN
ejpam-4556	35	9	proposed	propose	VERB
ejpam-4556	35	10	in	in	ADP
ejpam-4556	35	11	[	[	X
ejpam-4556	35	12	19	19	NUM
ejpam-4556	35	13	]	]	PUNCT
ejpam-4556	35	14	,	,	PUNCT
ejpam-4556	35	15	by	by	ADP
ejpam-4556	35	16	the	the	DET
ejpam-4556	35	17	fact	fact	NOUN
ejpam-4556	35	18	that	that	SCONJ
ejpam-4556	35	19	migration	migration	NOUN
ejpam-4556	35	20	is	be	AUX
ejpam-4556	35	21	allowed	allow	VERB
ejpam-4556	35	22	without	without	ADP
ejpam-4556	35	23	distinction	distinction	NOUN
ejpam-4556	35	24	of	of	ADP
ejpam-4556	35	25	the	the	DET
ejpam-4556	35	26	epidemiological	epidemiological	ADJ
ejpam-4556	35	27	status	status	NOUN
ejpam-4556	35	28	of	of	ADP
ejpam-4556	35	29	individuals	individual	NOUN
ejpam-4556	35	30	.	.	PUNCT
ejpam-4556	36	1	this	this	DET
ejpam-4556	36	2	type	type	NOUN
ejpam-4556	36	3	of	of	ADP
ejpam-4556	36	4	migration	migration	NOUN
ejpam-4556	36	5	is	be	AUX
ejpam-4556	36	6	undoubtedly	undoubtedly	ADV
ejpam-4556	36	7	one	one	NUM
ejpam-4556	36	8	of	of	ADP
ejpam-4556	36	9	the	the	DET
ejpam-4556	36	10	factors	factor	NOUN
ejpam-4556	36	11	,	,	PUNCT
ejpam-4556	36	12	delaying	delay	VERB
ejpam-4556	36	13	the	the	DET
ejpam-4556	36	14	process	process	NOUN
ejpam-4556	36	15	of	of	ADP
ejpam-4556	36	16	eradicating	eradicate	VERB
ejpam-4556	36	17	this	this	DET
ejpam-4556	36	18	disease	disease	NOUN
ejpam-4556	36	19	.	.	PUNCT
ejpam-4556	37	1	to	to	PART
ejpam-4556	37	2	evaluate	evaluate	VERB
ejpam-4556	37	3	the	the	DET
ejpam-4556	37	4	impact	impact	NOUN
ejpam-4556	37	5	of	of	ADP
ejpam-4556	37	6	migration	migration	NOUN
ejpam-4556	37	7	on	on	ADP
ejpam-4556	37	8	the	the	DET
ejpam-4556	37	9	propagation	propagation	NOUN
ejpam-4556	37	10	dynamics	dynamic	NOUN
ejpam-4556	37	11	of	of	ADP
ejpam-4556	37	12	this	this	DET
ejpam-4556	37	13	disease	disease	NOUN
ejpam-4556	37	14	,	,	PUNCT
ejpam-4556	37	15	we	we	PRON
ejpam-4556	37	16	expressed	express	VERB
ejpam-4556	37	17	the	the	DET
ejpam-4556	37	18	reproduction	reproduction	NOUN
ejpam-4556	37	19	numbers	number	NOUN
ejpam-4556	37	20	as	as	ADP
ejpam-4556	37	21	a	a	DET
ejpam-4556	37	22	function	function	NOUN
ejpam-4556	37	23	of	of	ADP
ejpam-4556	37	24	the	the	DET
ejpam-4556	37	25	migration	migration	NOUN
ejpam-4556	37	26	rate	rate	NOUN
ejpam-4556	37	27	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	37	28	,	,	PUNCT
ejpam-4556	37	29	ρ	ρ	PROPN
ejpam-4556	37	30	)	)	PUNCT
ejpam-4556	37	31	and	and	CCONJ
ejpam-4556	37	32	ℜ0(ρ	ℜ0(ρ	PROPN
ejpam-4556	37	33	)	)	PUNCT
ejpam-4556	37	34	.	.	PUNCT
ejpam-4556	38	1	after	after	ADP
ejpam-4556	38	2	establishing	establish	VERB
ejpam-4556	38	3	the	the	DET
ejpam-4556	38	4	conditions	condition	NOUN
ejpam-4556	38	5	of	of	ADP
ejpam-4556	38	6	existence	existence	NOUN
ejpam-4556	38	7	and	and	CCONJ
ejpam-4556	38	8	uniqueness	uniqueness	NOUN
ejpam-4556	38	9	of	of	ADP
ejpam-4556	38	10	the	the	DET
ejpam-4556	38	11	positive	positive	ADJ
ejpam-4556	38	12	solutions	solution	NOUN
ejpam-4556	38	13	of	of	ADP
ejpam-4556	38	14	our	our	PRON
ejpam-4556	38	15	model	model	NOUN
ejpam-4556	38	16	by	by	ADP
ejpam-4556	38	17	the	the	DET
ejpam-4556	38	18	semi	semi	ADJ
ejpam-4556	38	19	-	-	ADJ
ejpam-4556	38	20	group	group	ADJ
ejpam-4556	38	21	method	method	NOUN
ejpam-4556	38	22	.	.	PUNCT
ejpam-4556	39	1	we	we	PRON
ejpam-4556	39	2	studied	study	VERB
ejpam-4556	39	3	the	the	DET
ejpam-4556	39	4	global	global	ADJ
ejpam-4556	39	5	and	and	CCONJ
ejpam-4556	39	6	b.	b.	PROPN
ejpam-4556	39	7	k.	k.	PROPN
ejpam-4556	39	8	abdoul	abdoul	PROPN
ejpam-4556	39	9	wahid	wahid	PROPN
ejpam-4556	39	10	,	,	PUNCT
ejpam-4556	39	11	d.moustapha	d.moustapha	PROPN
ejpam-4556	39	12	,	,	PUNCT
ejpam-4556	39	13	s.	s.	PROPN
ejpam-4556	39	14	bisso	bisso	PROPN
ejpam-4556	39	15	/	/	SYM
ejpam-4556	39	16	eur	eur	PROPN
ejpam-4556	39	17	.	.	PUNCT
ejpam-4556	40	1	j.	j.	PROPN
ejpam-4556	40	2	pure	pure	PROPN
ejpam-4556	40	3	appl	appl	PROPN
ejpam-4556	40	4	.	.	PROPN
ejpam-4556	40	5	math	math	PROPN
ejpam-4556	40	6	,	,	PUNCT
ejpam-4556	40	7	15	15	NUM
ejpam-4556	40	8	(	(	PUNCT
ejpam-4556	40	9	4	4	NUM
ejpam-4556	40	10	)	)	PUNCT
ejpam-4556	40	11	(	(	PUNCT
ejpam-4556	40	12	2022	2022	NUM
ejpam-4556	40	13	)	)	PUNCT
ejpam-4556	40	14	,	,	PUNCT
ejpam-4556	40	15	2054	2054	NUM
ejpam-4556	40	16	-	-	SYM
ejpam-4556	40	17	2073	2073	NUM
ejpam-4556	40	18	2056	2056	NUM
ejpam-4556	40	19	local	local	ADJ
ejpam-4556	40	20	stability	stability	NOUN
ejpam-4556	40	21	of	of	ADP
ejpam-4556	40	22	the	the	DET
ejpam-4556	40	23	equilibrium	equilibrium	NOUN
ejpam-4556	40	24	point	point	NOUN
ejpam-4556	40	25	without	without	ADP
ejpam-4556	40	26	disease	disease	NOUN
ejpam-4556	40	27	,	,	PUNCT
ejpam-4556	40	28	showed	show	VERB
ejpam-4556	40	29	the	the	DET
ejpam-4556	40	30	existence	existence	NOUN
ejpam-4556	40	31	of	of	ADP
ejpam-4556	40	32	an	an	DET
ejpam-4556	40	33	endemic	endemic	ADJ
ejpam-4556	40	34	equilibrium	equilibrium	NOUN
ejpam-4556	40	35	point	point	NOUN
ejpam-4556	40	36	and	and	CCONJ
ejpam-4556	40	37	finally	finally	ADV
ejpam-4556	40	38	the	the	DET
ejpam-4556	40	39	results	result	NOUN
ejpam-4556	40	40	of	of	ADP
ejpam-4556	40	41	the	the	DET
ejpam-4556	40	42	numerical	numerical	ADJ
ejpam-4556	40	43	simulations	simulation	NOUN
ejpam-4556	40	44	confirm	confirm	VERB
ejpam-4556	40	45	the	the	DET
ejpam-4556	40	46	negative	negative	ADJ
ejpam-4556	40	47	effects	effect	NOUN
ejpam-4556	40	48	of	of	ADP
ejpam-4556	40	49	the	the	DET
ejpam-4556	40	50	uncontrolled	uncontrolled	ADJ
ejpam-4556	40	51	migration	migration	NOUN
ejpam-4556	40	52	that	that	PRON
ejpam-4556	40	53	would	would	AUX
ejpam-4556	40	54	cause	cause	VERB
ejpam-4556	40	55	tuberculosis	tuberculosis	NOUN
ejpam-4556	40	56	in	in	ADP
ejpam-4556	40	57	our	our	PRON
ejpam-4556	40	58	community.this	community.this	PRON
ejpam-4556	40	59	paper	paper	NOUN
ejpam-4556	40	60	is	be	AUX
ejpam-4556	40	61	organized	organize	VERB
ejpam-4556	40	62	as	as	SCONJ
ejpam-4556	40	63	follows	follow	VERB
ejpam-4556	40	64	:	:	PUNCT
ejpam-4556	40	65	section	section	NOUN
ejpam-4556	40	66	1	1	NUM
ejpam-4556	40	67	introduces	introduce	VERB
ejpam-4556	40	68	the	the	DET
ejpam-4556	40	69	two	two	NUM
ejpam-4556	40	70	-	-	PUNCT
ejpam-4556	40	71	patch	patch	NOUN
ejpam-4556	40	72	model	model	NOUN
ejpam-4556	40	73	structured	structure	VERB
ejpam-4556	40	74	in	in	ADP
ejpam-4556	40	75	age	age	NOUN
ejpam-4556	40	76	to	to	PART
ejpam-4556	40	77	study	study	VERB
ejpam-4556	40	78	the	the	DET
ejpam-4556	40	79	dynamics	dynamic	NOUN
ejpam-4556	40	80	of	of	ADP
ejpam-4556	40	81	tb	tb	ADP
ejpam-4556	40	82	transmission	transmission	NOUN
ejpam-4556	40	83	case	case	NOUN
ejpam-4556	40	84	of	of	ADP
ejpam-4556	40	85	a	a	DET
ejpam-4556	40	86	non	non	NOUN
ejpam-4556	40	87	controlled	control	VERB
ejpam-4556	40	88	migration	migration	NOUN
ejpam-4556	40	89	.the	.the	DET
ejpam-4556	40	90	mathematical	mathematical	ADJ
ejpam-4556	40	91	model	model	NOUN
ejpam-4556	40	92	formulation	formulation	NOUN
ejpam-4556	40	93	is	be	AUX
ejpam-4556	40	94	given	give	VERB
ejpam-4556	40	95	in	in	ADP
ejpam-4556	40	96	the	the	DET
ejpam-4556	40	97	section	section	NOUN
ejpam-4556	40	98	2	2	NUM
ejpam-4556	40	99	.	.	PUNCT
ejpam-4556	41	1	the	the	DET
ejpam-4556	41	2	existence	existence	NOUN
ejpam-4556	41	3	of	of	ADP
ejpam-4556	41	4	positive	positive	ADJ
ejpam-4556	41	5	and	and	CCONJ
ejpam-4556	41	6	unique	unique	ADJ
ejpam-4556	41	7	solutions	solution	NOUN
ejpam-4556	41	8	is	be	AUX
ejpam-4556	41	9	demonstrated	demonstrate	VERB
ejpam-4556	41	10	in	in	ADP
ejpam-4556	41	11	section	section	NOUN
ejpam-4556	41	12	3	3	NUM
ejpam-4556	41	13	.	.	PUNCT
ejpam-4556	42	1	the	the	DET
ejpam-4556	42	2	point	point	NOUN
ejpam-4556	42	3	of	of	ADP
ejpam-4556	42	4	equilibrium	equilibrium	NOUN
ejpam-4556	42	5	without	without	ADP
ejpam-4556	42	6	disease	disease	NOUN
ejpam-4556	42	7	,	,	PUNCT
ejpam-4556	42	8	reproductive	reproductive	ADJ
ejpam-4556	42	9	numbers	number	NOUN
ejpam-4556	42	10	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	42	11	,	,	PUNCT
ejpam-4556	42	12	ρ	ρ	PROPN
ejpam-4556	42	13	)	)	PUNCT
ejpam-4556	42	14	and	and	CCONJ
ejpam-4556	42	15	ℜ0(ρ	ℜ0(ρ	PROPN
ejpam-4556	42	16	)	)	PUNCT
ejpam-4556	42	17	are	be	AUX
ejpam-4556	42	18	defined	define	VERB
ejpam-4556	42	19	in	in	ADP
ejpam-4556	42	20	the	the	DET
ejpam-4556	42	21	section	section	NOUN
ejpam-4556	42	22	4	4	NUM
ejpam-4556	42	23	and	and	CCONJ
ejpam-4556	42	24	the	the	DET
ejpam-4556	42	25	local	local	ADJ
ejpam-4556	42	26	stability	stability	NOUN
ejpam-4556	42	27	of	of	ADP
ejpam-4556	42	28	the	the	DET
ejpam-4556	42	29	disease	disease	NOUN
ejpam-4556	42	30	-	-	PUNCT
ejpam-4556	42	31	free	free	ADJ
ejpam-4556	42	32	equilibrium	equilibrium	NOUN
ejpam-4556	42	33	point	point	NOUN
ejpam-4556	42	34	in	in	ADP
ejpam-4556	42	35	the	the	DET
ejpam-4556	42	36	presence	presence	NOUN
ejpam-4556	42	37	of	of	ADP
ejpam-4556	42	38	vaccine	vaccine	NOUN
ejpam-4556	42	39	.	.	PUNCT
ejpam-4556	43	1	the	the	DET
ejpam-4556	43	2	global	global	ADJ
ejpam-4556	43	3	stability	stability	NOUN
ejpam-4556	43	4	of	of	ADP
ejpam-4556	43	5	the	the	DET
ejpam-4556	43	6	disease	disease	NOUN
ejpam-4556	43	7	-	-	PUNCT
ejpam-4556	43	8	free	free	ADJ
ejpam-4556	43	9	equilibrium	equilibrium	NOUN
ejpam-4556	43	10	point	point	NOUN
ejpam-4556	43	11	to	to	ADP
ejpam-4556	43	12	the	the	DET
ejpam-4556	43	13	absence	absence	NOUN
ejpam-4556	43	14	of	of	ADP
ejpam-4556	43	15	the	the	DET
ejpam-4556	43	16	vaccine	vaccine	NOUN
ejpam-4556	43	17	is	be	AUX
ejpam-4556	43	18	established	establish	VERB
ejpam-4556	43	19	in	in	ADP
ejpam-4556	43	20	section	section	NOUN
ejpam-4556	43	21	5	5	NUM
ejpam-4556	43	22	.	.	PUNCT
ejpam-4556	44	1	the	the	DET
ejpam-4556	44	2	existence	existence	NOUN
ejpam-4556	44	3	of	of	ADP
ejpam-4556	44	4	an	an	DET
ejpam-4556	44	5	endemic	endemic	ADJ
ejpam-4556	44	6	equilibrium	equilibrium	NOUN
ejpam-4556	44	7	is	be	AUX
ejpam-4556	44	8	proven	prove	VERB
ejpam-4556	44	9	in	in	ADP
ejpam-4556	44	10	section	section	NOUN
ejpam-4556	44	11	6	6	NUM
ejpam-4556	44	12	.	.	PUNCT
ejpam-4556	45	1	some	some	DET
ejpam-4556	45	2	numerical	numerical	PROPN
ejpam-4556	45	3	simulation	simulation	PROPN
ejpam-4556	45	4	results	result	NOUN
ejpam-4556	45	5	are	be	AUX
ejpam-4556	45	6	given	give	VERB
ejpam-4556	45	7	in	in	ADP
ejpam-4556	45	8	section	section	NOUN
ejpam-4556	45	9	7	7	NUM
ejpam-4556	45	10	.	.	PUNCT
ejpam-4556	46	1	in	in	ADP
ejpam-4556	46	2	section	section	NOUN
ejpam-4556	46	3	8	8	NUM
ejpam-4556	46	4	,	,	PUNCT
ejpam-4556	46	5	we	we	PRON
ejpam-4556	46	6	have	have	VERB
ejpam-4556	46	7	a	a	DET
ejpam-4556	46	8	discussion	discussion	NOUN
ejpam-4556	46	9	,	,	PUNCT
ejpam-4556	46	10	conclusion	conclusion	NOUN
ejpam-4556	46	11	and	and	CCONJ
ejpam-4556	46	12	further	further	ADJ
ejpam-4556	46	13	work	work	NOUN
ejpam-4556	46	14	.	.	PUNCT
ejpam-4556	47	1	2	2	X
ejpam-4556	47	2	.	.	X
ejpam-4556	47	3	mathematical	mathematical	ADJ
ejpam-4556	47	4	model	model	NOUN
ejpam-4556	47	5	formulation	formulation	NOUN
ejpam-4556	47	6	two	two	NUM
ejpam-4556	47	7	-	-	PUNCT
ejpam-4556	47	8	patch	patch	NOUN
ejpam-4556	47	9	age	age	NOUN
ejpam-4556	47	10	structured	structure	VERB
ejpam-4556	47	11	model	model	NOUN
ejpam-4556	47	12	of	of	ADP
ejpam-4556	47	13	tuberculosis	tuberculosis	NOUN
ejpam-4556	47	14	was	be	AUX
ejpam-4556	47	15	considered	consider	VERB
ejpam-4556	47	16	.	.	PUNCT
ejpam-4556	48	1	the	the	DET
ejpam-4556	48	2	model	model	NOUN
ejpam-4556	48	3	is	be	AUX
ejpam-4556	48	4	to	to	PART
ejpam-4556	48	5	split	split	VERB
ejpam-4556	48	6	the	the	DET
ejpam-4556	48	7	population	population	NOUN
ejpam-4556	48	8	into	into	ADP
ejpam-4556	48	9	two	two	NUM
ejpam-4556	48	10	subpopulations	subpopulation	NOUN
ejpam-4556	48	11	.	.	PUNCT
ejpam-4556	49	1	the	the	DET
ejpam-4556	49	2	recruitment	recruitment	NOUN
ejpam-4556	49	3	is	be	AUX
ejpam-4556	49	4	only	only	ADV
ejpam-4556	49	5	possible	possible	ADJ
ejpam-4556	49	6	in	in	ADP
ejpam-4556	49	7	the	the	DET
ejpam-4556	49	8	class	class	NOUN
ejpam-4556	49	9	of	of	ADP
ejpam-4556	49	10	susceptible	susceptible	ADJ
ejpam-4556	49	11	and	and	CCONJ
ejpam-4556	49	12	the	the	DET
ejpam-4556	49	13	vaccinated	vaccinated	ADJ
ejpam-4556	49	14	individuals	individual	NOUN
ejpam-4556	49	15	were	be	AUX
ejpam-4556	49	16	able	able	ADJ
ejpam-4556	49	17	to	to	PART
ejpam-4556	49	18	migrate	migrate	VERB
ejpam-4556	49	19	between	between	ADP
ejpam-4556	49	20	the	the	DET
ejpam-4556	49	21	two	two	NUM
ejpam-4556	49	22	subpopulations	subpopulation	NOUN
ejpam-4556	49	23	.	.	PUNCT
ejpam-4556	50	1	each	each	DET
ejpam-4556	50	2	subpopulation	subpopulation	NOUN
ejpam-4556	50	3	is	be	AUX
ejpam-4556	50	4	divided	divide	VERB
ejpam-4556	50	5	into	into	ADP
ejpam-4556	50	6	five	five	NUM
ejpam-4556	50	7	classes	class	NOUN
ejpam-4556	50	8	based	base	VERB
ejpam-4556	50	9	on	on	ADP
ejpam-4556	50	10	their	their	PRON
ejpam-4556	50	11	epidemiological	epidemiological	ADJ
ejpam-4556	50	12	status	status	NOUN
ejpam-4556	50	13	:	:	PUNCT
ejpam-4556	50	14	susceptible	susceptible	ADJ
ejpam-4556	50	15	,	,	PUNCT
ejpam-4556	50	16	vaccinated	vaccinated	ADJ
ejpam-4556	50	17	,	,	PUNCT
ejpam-4556	50	18	latent	latent	NOUN
ejpam-4556	50	19	,	,	PUNCT
ejpam-4556	50	20	infectious	infectious	ADJ
ejpam-4556	50	21	or	or	CCONJ
ejpam-4556	50	22	treated	treat	VERB
ejpam-4556	50	23	.	.	PUNCT
ejpam-4556	51	1	we	we	PRON
ejpam-4556	51	2	denote	denote	VERB
ejpam-4556	51	3	these	these	DET
ejpam-4556	51	4	subgroups	subgroup	NOUN
ejpam-4556	51	5	si(t	si(t	VERB
ejpam-4556	51	6	,	,	PUNCT
ejpam-4556	51	7	a	a	PRON
ejpam-4556	51	8	)	)	PUNCT
ejpam-4556	51	9	,	,	PUNCT
ejpam-4556	51	10	vi(t	vi(t	PROPN
ejpam-4556	51	11	,	,	PUNCT
ejpam-4556	51	12	a	a	PRON
ejpam-4556	51	13	)	)	PUNCT
ejpam-4556	51	14	,	,	PUNCT
ejpam-4556	51	15	li(t	li(t	PROPN
ejpam-4556	51	16	,	,	PUNCT
ejpam-4556	51	17	a	a	PRON
ejpam-4556	51	18	)	)	PUNCT
ejpam-4556	51	19	,	,	PUNCT
ejpam-4556	51	20	ii(t	ii(t	NOUN
ejpam-4556	51	21	,	,	PUNCT
ejpam-4556	51	22	a	a	PRON
ejpam-4556	51	23	)	)	PUNCT
ejpam-4556	51	24	and	and	CCONJ
ejpam-4556	51	25	ji(t	ji(t	PROPN
ejpam-4556	51	26	,	,	PUNCT
ejpam-4556	51	27	a	a	PRON
ejpam-4556	51	28	)	)	PUNCT
ejpam-4556	51	29	respectively	respectively	ADV
ejpam-4556	51	30	.	.	PUNCT
ejpam-4556	52	1	the	the	DET
ejpam-4556	52	2	birth	birth	NOUN
ejpam-4556	52	3	rate	rate	NOUN
ejpam-4556	52	4	of	of	ADP
ejpam-4556	52	5	the	the	DET
ejpam-4556	52	6	patch	patch	NOUN
ejpam-4556	52	7	i	i	PRON
ejpam-4556	52	8	is	be	AUX
ejpam-4556	52	9	bi(a	bi(a	ADJ
ejpam-4556	52	10	)	)	PUNCT
ejpam-4556	52	11	;	;	PUNCT
ejpam-4556	52	12	µi(a	µi(a	PUNCT
ejpam-4556	52	13	)	)	PUNCT
ejpam-4556	52	14	and	and	CCONJ
ejpam-4556	52	15	µ(a	µ(a	PROPN
ejpam-4556	52	16	)	)	PUNCT
ejpam-4556	52	17	denote	denote	VERB
ejpam-4556	52	18	the	the	DET
ejpam-4556	52	19	mortality	mortality	NOUN
ejpam-4556	52	20	rate	rate	NOUN
ejpam-4556	52	21	related	relate	VERB
ejpam-4556	52	22	to	to	ADP
ejpam-4556	52	23	the	the	DET
ejpam-4556	52	24	disease	disease	NOUN
ejpam-4556	52	25	relative	relative	ADJ
ejpam-4556	52	26	to	to	ADP
ejpam-4556	52	27	the	the	DET
ejpam-4556	52	28	patch	patch	NOUN
ejpam-4556	52	29	i	i	PRON
ejpam-4556	52	30	and	and	CCONJ
ejpam-4556	52	31	the	the	DET
ejpam-4556	52	32	rate	rate	NOUN
ejpam-4556	52	33	of	of	ADP
ejpam-4556	52	34	natural	natural	ADJ
ejpam-4556	52	35	mortality	mortality	NOUN
ejpam-4556	52	36	.	.	PUNCT
ejpam-4556	53	1	the	the	DET
ejpam-4556	53	2	time	time	NOUN
ejpam-4556	53	3	and	and	CCONJ
ejpam-4556	53	4	age	age	NOUN
ejpam-4556	53	5	depended	depend	VERB
ejpam-4556	53	6	of	of	ADP
ejpam-4556	53	7	the	the	DET
ejpam-4556	53	8	force	force	NOUN
ejpam-4556	53	9	of	of	ADP
ejpam-4556	53	10	infection	infection	NOUN
ejpam-4556	53	11	of	of	ADP
ejpam-4556	53	12	the	the	DET
ejpam-4556	53	13	subpopulation	subpopulation	NOUN
ejpam-4556	53	14	i	i	PRON
ejpam-4556	53	15	is	be	AUX
ejpam-4556	53	16	λi(t	λi(t	NUM
ejpam-4556	53	17	,	,	PUNCT
ejpam-4556	53	18	a	a	PRON
ejpam-4556	53	19	)	)	PUNCT
ejpam-4556	53	20	and	and	CCONJ
ejpam-4556	53	21	vaccination	vaccination	NOUN
ejpam-4556	53	22	rate	rate	NOUN
ejpam-4556	53	23	is	be	AUX
ejpam-4556	53	24	ψi(a	ψi(a	PUNCT
ejpam-4556	53	25	)	)	PUNCT
ejpam-4556	53	26	;	;	PUNCT
ejpam-4556	53	27	pi(a	pi(a	X
ejpam-4556	53	28	,	,	PUNCT
ejpam-4556	53	29	a	a	DET
ejpam-4556	53	30	′	′	NOUN
ejpam-4556	53	31	)	)	PUNCT
ejpam-4556	53	32	is	be	AUX
ejpam-4556	53	33	the	the	DET
ejpam-4556	53	34	probability	probability	NOUN
ejpam-4556	53	35	that	that	SCONJ
ejpam-4556	53	36	an	an	DET
ejpam-4556	53	37	infective	infective	ADJ
ejpam-4556	53	38	individual	individual	NOUN
ejpam-4556	53	39	of	of	ADP
ejpam-4556	53	40	age	age	NOUN
ejpam-4556	53	41	a′	a′	PROPN
ejpam-4556	53	42	will	will	AUX
ejpam-4556	53	43	have	have	AUX
ejpam-4556	53	44	contact	contact	NOUN
ejpam-4556	53	45	with	with	ADP
ejpam-4556	53	46	and	and	CCONJ
ejpam-4556	53	47	successfully	successfully	ADV
ejpam-4556	53	48	infect	infect	VERB
ejpam-4556	53	49	a	a	DET
ejpam-4556	53	50	susceptible	susceptible	ADJ
ejpam-4556	53	51	individual	individual	NOUN
ejpam-4556	53	52	of	of	ADP
ejpam-4556	53	53	age	age	NOUN
ejpam-4556	53	54	a	a	PRON
ejpam-4556	53	55	,	,	PUNCT
ejpam-4556	53	56	ci(a	ci(a	PUNCT
ejpam-4556	53	57	)	)	PUNCT
ejpam-4556	53	58	is	be	AUX
ejpam-4556	53	59	the	the	DET
ejpam-4556	53	60	age	age	NOUN
ejpam-4556	53	61	-	-	PUNCT
ejpam-4556	53	62	specic	specic	NOUN
ejpam-4556	53	63	per	per	ADP
ejpam-4556	53	64	-	-	PUNCT
ejpam-4556	53	65	capita	capita	NOUN
ejpam-4556	53	66	contact	contact	NOUN
ejpam-4556	53	67	/	/	SYM
ejpam-4556	53	68	activity	activity	NOUN
ejpam-4556	53	69	rate	rate	NOUN
ejpam-4556	53	70	(	(	PUNCT
ejpam-4556	53	71	all	all	PRON
ejpam-4556	53	72	of	of	ADP
ejpam-4556	53	73	these	these	DET
ejpam-4556	53	74	functions	function	NOUN
ejpam-4556	53	75	are	be	AUX
ejpam-4556	53	76	assumed	assume	VERB
ejpam-4556	53	77	to	to	PART
ejpam-4556	53	78	be	be	AUX
ejpam-4556	53	79	continuous	continuous	ADJ
ejpam-4556	53	80	and	and	CCONJ
ejpam-4556	53	81	to	to	PART
ejpam-4556	53	82	be	be	AUX
ejpam-4556	53	83	zero	zero	NUM
ejpam-4556	53	84	beyond	beyond	ADP
ejpam-4556	53	85	some	some	DET
ejpam-4556	53	86	maximum	maximum	ADJ
ejpam-4556	53	87	age	age	NOUN
ejpam-4556	53	88	)	)	PUNCT
ejpam-4556	53	89	.	.	PUNCT
ejpam-4556	54	1	a	a	DET
ejpam-4556	54	2	fraction	fraction	NOUN
ejpam-4556	54	3	ϕi	ϕi	ADP
ejpam-4556	54	4	of	of	ADP
ejpam-4556	54	5	newly	newly	ADV
ejpam-4556	54	6	infected	infect	VERB
ejpam-4556	54	7	individuals	individual	NOUN
ejpam-4556	54	8	of	of	ADP
ejpam-4556	54	9	the	the	DET
ejpam-4556	54	10	sub	sub	NOUN
ejpam-4556	54	11	-	-	NOUN
ejpam-4556	54	12	population	population	ADJ
ejpam-4556	54	13	i	i	PRON
ejpam-4556	54	14	is	be	AUX
ejpam-4556	54	15	assumed	assume	VERB
ejpam-4556	54	16	to	to	PART
ejpam-4556	54	17	undergo	undergo	VERB
ejpam-4556	54	18	a	a	DET
ejpam-4556	54	19	fast	fast	ADJ
ejpam-4556	54	20	progression	progression	NOUN
ejpam-4556	54	21	directly	directly	ADV
ejpam-4556	54	22	to	to	ADP
ejpam-4556	54	23	the	the	DET
ejpam-4556	54	24	infectious	infectious	ADJ
ejpam-4556	54	25	class	class	PROPN
ejpam-4556	54	26	ii	ii	PROPN
ejpam-4556	54	27	.	.	PUNCT
ejpam-4556	54	28	rate	rate	NOUN
ejpam-4556	54	29	of	of	ADP
ejpam-4556	54	30	susceptible	susceptible	ADJ
ejpam-4556	54	31	passage	passage	NOUN
ejpam-4556	54	32	to	to	ADP
ejpam-4556	54	33	latent	latent	NOUN
ejpam-4556	54	34	infectious	infectious	ADJ
ejpam-4556	54	35	state	state	NOUN
ejpam-4556	54	36	and	and	CCONJ
ejpam-4556	54	37	treatment	treatment	NOUN
ejpam-4556	54	38	are	be	AUX
ejpam-4556	54	39	respectively	respectively	ADV
ejpam-4556	54	40	ki	ki	PROPN
ejpam-4556	54	41	and	and	CCONJ
ejpam-4556	54	42	ri	ri	PROPN
ejpam-4556	54	43	.	.	PUNCT
ejpam-4556	55	1	σi	σi	PROPN
ejpam-4556	56	1	and	and	CCONJ
ejpam-4556	56	2	δi	δi	PROPN
ejpam-4556	56	3	are	be	AUX
ejpam-4556	56	4	the	the	DET
ejpam-4556	56	5	reductions	reduction	NOUN
ejpam-4556	56	6	in	in	ADP
ejpam-4556	56	7	risk	risk	NOUN
ejpam-4556	56	8	due	due	ADP
ejpam-4556	56	9	to	to	ADP
ejpam-4556	56	10	prior	prior	ADJ
ejpam-4556	56	11	exposure	exposure	NOUN
ejpam-4556	56	12	to	to	ADP
ejpam-4556	56	13	tb	tb	NOUN
ejpam-4556	56	14	and	and	CCONJ
ejpam-4556	56	15	vaccination	vaccination	NOUN
ejpam-4556	56	16	,	,	PUNCT
ejpam-4556	56	17	respectively	respectively	ADV
ejpam-4556	56	18	,	,	PUNCT
ejpam-4556	56	19	0	0	NUM
ejpam-4556	56	20	≤	≤	NUM
ejpam-4556	56	21	σi	σi	X
ejpam-4556	56	22	≤	≤	NUM
ejpam-4556	56	23	(	(	PUNCT
ejpam-4556	56	24	1	1	NUM
ejpam-4556	56	25	−	−	NOUN
ejpam-4556	56	26	ϕi	ϕi	ADP
ejpam-4556	56	27	)	)	PUNCT
ejpam-4556	56	28	,	,	PUNCT
ejpam-4556	56	29	0	0	NUM
ejpam-4556	56	30	≤	≤	NUM
ejpam-4556	56	31	δi	δi	VERB
ejpam-4556	56	32	≤	≤	NUM
ejpam-4556	56	33	(	(	PUNCT
ejpam-4556	56	34	1	1	NUM
ejpam-4556	56	35	−	−	NOUN
ejpam-4556	56	36	ϕi	ϕi	ADP
ejpam-4556	56	37	)	)	PUNCT
ejpam-4556	56	38	.	.	PUNCT
ejpam-4556	57	1	the	the	DET
ejpam-4556	57	2	migration	migration	NOUN
ejpam-4556	57	3	rates	rate	NOUN
ejpam-4556	57	4	of	of	ADP
ejpam-4556	57	5	the	the	DET
ejpam-4556	57	6	susceptible	susceptible	ADJ
ejpam-4556	57	7	,	,	PUNCT
ejpam-4556	57	8	latently	latently	ADV
ejpam-4556	57	9	infected	infect	VERB
ejpam-4556	57	10	,	,	PUNCT
ejpam-4556	57	11	infectious	infectious	ADJ
ejpam-4556	57	12	,	,	PUNCT
ejpam-4556	57	13	treated	treat	VERB
ejpam-4556	57	14	,	,	PUNCT
ejpam-4556	57	15	and	and	CCONJ
ejpam-4556	57	16	vaccinated	vaccinate	VERB
ejpam-4556	57	17	between	between	ADP
ejpam-4556	57	18	the	the	DET
ejpam-4556	57	19	two	two	NUM
ejpam-4556	57	20	populations	population	NOUN
ejpam-4556	57	21	are	be	AUX
ejpam-4556	57	22	respectively	respectively	ADV
ejpam-4556	57	23	ρi1	ρi1	VERB
ejpam-4556	57	24	,	,	PUNCT
ejpam-4556	57	25	ρi2	ρi2	NOUN
ejpam-4556	57	26	,	,	PUNCT
ejpam-4556	57	27	ρi3	ρi3	PROPN
ejpam-4556	57	28	,	,	PUNCT
ejpam-4556	57	29	ρi4	ρi4	PROPN
ejpam-4556	57	30	and	and	CCONJ
ejpam-4556	57	31	ρi5	ρi5	NOUN
ejpam-4556	57	32	,	,	PUNCT
ejpam-4556	57	33	in	in	ADP
ejpam-4556	57	34	this	this	DET
ejpam-4556	57	35	paper	paper	NOUN
ejpam-4556	58	1	i	i	NOUN
ejpam-4556	58	2	=	=	NOUN
ejpam-4556	58	3	1	1	NUM
ejpam-4556	58	4	,	,	PUNCT
ejpam-4556	58	5	2	2	NUM
ejpam-4556	58	6	.	.	X
ejpam-4556	58	7	b.	b.	PROPN
ejpam-4556	58	8	k.	k.	PROPN
ejpam-4556	58	9	abdoul	abdoul	PROPN
ejpam-4556	58	10	wahid	wahid	PROPN
ejpam-4556	58	11	,	,	PUNCT
ejpam-4556	58	12	d.moustapha	d.moustapha	PROPN
ejpam-4556	58	13	,	,	PUNCT
ejpam-4556	58	14	s.	s.	PROPN
ejpam-4556	58	15	bisso	bisso	PROPN
ejpam-4556	58	16	/	/	SYM
ejpam-4556	58	17	eur	eur	PROPN
ejpam-4556	58	18	.	.	PUNCT
ejpam-4556	59	1	j.	j.	PROPN
ejpam-4556	59	2	pure	pure	PROPN
ejpam-4556	59	3	appl	appl	PROPN
ejpam-4556	59	4	.	.	PROPN
ejpam-4556	59	5	math	math	PROPN
ejpam-4556	59	6	,	,	PUNCT
ejpam-4556	59	7	15	15	NUM
ejpam-4556	59	8	(	(	PUNCT
ejpam-4556	59	9	4	4	NUM
ejpam-4556	59	10	)	)	PUNCT
ejpam-4556	59	11	(	(	PUNCT
ejpam-4556	59	12	2022	2022	NUM
ejpam-4556	59	13	)	)	PUNCT
ejpam-4556	59	14	,	,	PUNCT
ejpam-4556	59	15	2054	2054	NUM
ejpam-4556	59	16	-	-	SYM
ejpam-4556	59	17	2073	2073	NUM
ejpam-4556	59	18	2057	2057	NUM
ejpam-4556	59	19	fig.1	fig.1	PROPN
ejpam-4556	59	20	.	.	PUNCT
ejpam-4556	60	1	flow	flow	NOUN
ejpam-4556	60	2	chart	chart	NOUN
ejpam-4556	60	3	of	of	ADP
ejpam-4556	60	4	the	the	DET
ejpam-4556	60	5	two	two	NUM
ejpam-4556	60	6	-	-	PUNCT
ejpam-4556	60	7	patch	patch	NOUN
ejpam-4556	60	8	model	model	NOUN
ejpam-4556	60	9	for	for	ADP
ejpam-4556	60	10	tuberculosis	tuberculosis	NOUN
ejpam-4556	60	11	disease	disease	NOUN
ejpam-4556	60	12	transmission	transmission	NOUN
ejpam-4556	60	13	.	.	PUNCT
ejpam-4556	61	1	the	the	DET
ejpam-4556	61	2	age	age	NOUN
ejpam-4556	61	3	-	-	PUNCT
ejpam-4556	61	4	structured	structure	VERB
ejpam-4556	61	5	model	model	NOUN
ejpam-4556	61	6	for	for	ADP
ejpam-4556	61	7	the	the	DET
ejpam-4556	61	8	transmission	transmission	NOUN
ejpam-4556	61	9	of	of	ADP
ejpam-4556	61	10	tb	tb	NOUN
ejpam-4556	61	11	is	be	AUX
ejpam-4556	61	12	described	describe	VERB
ejpam-4556	61	13	by	by	ADP
ejpam-4556	61	14	the	the	DET
ejpam-4556	61	15	following	follow	VERB
ejpam-4556	61	16	system	system	NOUN
ejpam-4556	61	17	of	of	ADP
ejpam-4556	61	18	partial	partial	ADJ
ejpam-4556	61	19	differential	differential	NOUN
ejpam-4556	61	20	equations	equation	NOUN
ejpam-4556	61	21	:	:	PUNCT
ejpam-4556	61	22			PROPN
ejpam-4556	61	23	(	(	PUNCT
ejpam-4556	61	24	∂	∂	NUM
ejpam-4556	62	1	∂t	∂t	PROPN
ejpam-4556	62	2	+	+	SYM
ejpam-4556	62	3	∂	∂	NUM
ejpam-4556	62	4	∂a	∂a	NOUN
ejpam-4556	62	5	)	)	PUNCT
ejpam-4556	62	6	s1(t	s1(t	PROPN
ejpam-4556	62	7	,	,	PUNCT
ejpam-4556	62	8	a	a	PRON
ejpam-4556	62	9	)	)	PUNCT
ejpam-4556	62	10	=	=	SYM
ejpam-4556	62	11	b1(a)n1(t	b1(a)n1(t	NOUN
ejpam-4556	62	12	,	,	PUNCT
ejpam-4556	62	13	a	a	X
ejpam-4556	62	14	)	)	PUNCT
ejpam-4556	62	15	−	−	PROPN
ejpam-4556	63	1	[	[	X
ejpam-4556	63	2	λ1(t	λ1(t	PROPN
ejpam-4556	63	3	,	,	PUNCT
ejpam-4556	63	4	a	a	PRON
ejpam-4556	63	5	)	)	PUNCT
ejpam-4556	63	6	+	+	PUNCT
ejpam-4556	63	7	ψ1(a	ψ1(a	NOUN
ejpam-4556	63	8	)	)	PUNCT
ejpam-4556	64	1	+	+	CCONJ
ejpam-4556	64	2	µ(a	µ(a	PROPN
ejpam-4556	64	3	)	)	PUNCT
ejpam-4556	65	1	+	+	CCONJ
ejpam-4556	65	2	ρ11]s1(t	ρ11]s1(t	X
ejpam-4556	65	3	,	,	PUNCT
ejpam-4556	65	4	a	a	PRON
ejpam-4556	65	5	)	)	PUNCT
ejpam-4556	66	1	+	+	NOUN
ejpam-4556	66	2	ρ21s2(t	ρ21s2(t	PROPN
ejpam-4556	66	3	,	,	PUNCT
ejpam-4556	66	4	a	a	NOUN
ejpam-4556	66	5	)	)	PUNCT
ejpam-4556	66	6	(	(	PUNCT
ejpam-4556	66	7	∂	∂	NUM
ejpam-4556	66	8	∂t	∂t	PROPN
ejpam-4556	66	9	+	+	SYM
ejpam-4556	66	10	∂	∂	NUM
ejpam-4556	66	11	∂a	∂a	NOUN
ejpam-4556	66	12	)	)	PUNCT
ejpam-4556	66	13	l1(t	l1(t	PROPN
ejpam-4556	66	14	,	,	PUNCT
ejpam-4556	66	15	a	a	PRON
ejpam-4556	66	16	)	)	PUNCT
ejpam-4556	66	17	=	=	SYM
ejpam-4556	67	1	λ1(t	λ1(t	PROPN
ejpam-4556	67	2	,	,	PUNCT
ejpam-4556	67	3	a)[(1	a)[(1	PROPN
ejpam-4556	67	4	−	−	PROPN
ejpam-4556	67	5	ϕ1)s1(t	ϕ1)s1(t	NOUN
ejpam-4556	67	6	,	,	PUNCT
ejpam-4556	67	7	a	a	X
ejpam-4556	67	8	)	)	PUNCT
ejpam-4556	67	9	+	+	CCONJ
ejpam-4556	67	10	σ1j1(t	σ1j1(t	ADJ
ejpam-4556	67	11	,	,	PUNCT
ejpam-4556	67	12	a	a	PRON
ejpam-4556	67	13	)	)	PUNCT
ejpam-4556	67	14	+	+	CCONJ
ejpam-4556	67	15	δ1v1(t	δ1v1(t	PROPN
ejpam-4556	67	16	,	,	PUNCT
ejpam-4556	67	17	a	a	NOUN
ejpam-4556	67	18	)	)	PUNCT
ejpam-4556	67	19	]	]	PUNCT
ejpam-4556	67	20	−	−	PROPN
ejpam-4556	67	21	(	(	PUNCT
ejpam-4556	67	22	k1	k1	NOUN
ejpam-4556	67	23	+	+	CCONJ
ejpam-4556	67	24	µ(a	µ(a	PROPN
ejpam-4556	67	25	)	)	PUNCT
ejpam-4556	68	1	+	+	NUM
ejpam-4556	68	2	ρ12)l1(t	ρ12)l1(t	PROPN
ejpam-4556	68	3	,	,	PUNCT
ejpam-4556	68	4	a	a	PRON
ejpam-4556	68	5	)	)	PUNCT
ejpam-4556	69	1	+	+	CCONJ
ejpam-4556	69	2	ρ22l2(t	ρ22l2(t	PROPN
ejpam-4556	69	3	,	,	PUNCT
ejpam-4556	69	4	a	a	NOUN
ejpam-4556	69	5	)	)	PUNCT
ejpam-4556	69	6	(	(	PUNCT
ejpam-4556	69	7	∂	∂	NUM
ejpam-4556	69	8	∂t	∂t	PROPN
ejpam-4556	69	9	+	+	SYM
ejpam-4556	69	10	∂	∂	NUM
ejpam-4556	70	1	∂a	∂a	NOUN
ejpam-4556	70	2	)	)	PUNCT
ejpam-4556	70	3	i1(t	i1(t	PROPN
ejpam-4556	70	4	,	,	PUNCT
ejpam-4556	70	5	a	a	PRON
ejpam-4556	70	6	)	)	PUNCT
ejpam-4556	70	7	=	=	SYM
ejpam-4556	70	8	k1l1(t	k1l1(t	PROPN
ejpam-4556	70	9	,	,	PUNCT
ejpam-4556	70	10	a	a	NOUN
ejpam-4556	70	11	)	)	PUNCT
ejpam-4556	70	12	−	−	PROPN
ejpam-4556	70	13	(	(	PUNCT
ejpam-4556	70	14	r1	r1	NOUN
ejpam-4556	70	15	+	+	CCONJ
ejpam-4556	70	16	µ(a	µ(a	PROPN
ejpam-4556	70	17	)	)	PUNCT
ejpam-4556	70	18	+	+	PUNCT
ejpam-4556	70	19	µ1(a	µ1(a	ADP
ejpam-4556	70	20	)	)	PUNCT
ejpam-4556	71	1	+	+	CCONJ
ejpam-4556	71	2	ρ13)i1(t	ρ13)i1(t	PROPN
ejpam-4556	71	3	,	,	PUNCT
ejpam-4556	71	4	a	a	PRON
ejpam-4556	71	5	)	)	PUNCT
ejpam-4556	71	6	+	+	CCONJ
ejpam-4556	72	1	ϕ1λ1(t	ϕ1λ1(t	PROPN
ejpam-4556	72	2	,	,	PUNCT
ejpam-4556	72	3	a)s1(t	a)s1(t	PROPN
ejpam-4556	72	4	,	,	PUNCT
ejpam-4556	72	5	a	a	PRON
ejpam-4556	72	6	)	)	PUNCT
ejpam-4556	72	7	+	+	NUM
ejpam-4556	72	8	ρ23i2(t	ρ23i2(t	PROPN
ejpam-4556	72	9	,	,	PUNCT
ejpam-4556	72	10	a	a	NOUN
ejpam-4556	72	11	)	)	PUNCT
ejpam-4556	72	12	(	(	PUNCT
ejpam-4556	72	13	∂	∂	NUM
ejpam-4556	72	14	∂t	∂t	PROPN
ejpam-4556	72	15	+	+	SYM
ejpam-4556	72	16	∂	∂	NUM
ejpam-4556	72	17	∂a	∂a	NOUN
ejpam-4556	72	18	)	)	PUNCT
ejpam-4556	72	19	j1(t	j1(t	PROPN
ejpam-4556	72	20	,	,	PUNCT
ejpam-4556	72	21	a	a	PRON
ejpam-4556	72	22	)	)	PUNCT
ejpam-4556	73	1	=	=	SYM
ejpam-4556	73	2	r1i1(t	r1i1(t	PROPN
ejpam-4556	73	3	,	,	PUNCT
ejpam-4556	73	4	a	a	PRON
ejpam-4556	73	5	)	)	PUNCT
ejpam-4556	73	6	−	−	PROPN
ejpam-4556	73	7	(	(	PUNCT
ejpam-4556	73	8	σ1λ1(t	σ1λ1(t	PROPN
ejpam-4556	73	9	,	,	PUNCT
ejpam-4556	73	10	a	a	PRON
ejpam-4556	73	11	)	)	PUNCT
ejpam-4556	73	12	+	+	NOUN
ejpam-4556	73	13	µ(a	µ(a	PROPN
ejpam-4556	73	14	)	)	PUNCT
ejpam-4556	74	1	+	+	CCONJ
ejpam-4556	74	2	ρ14)j1(t	ρ14)j1(t	PROPN
ejpam-4556	74	3	,	,	PUNCT
ejpam-4556	74	4	a	a	PRON
ejpam-4556	74	5	)	)	PUNCT
ejpam-4556	75	1	+	+	X
ejpam-4556	75	2	ρ24j2(t	ρ24j2(t	PROPN
ejpam-4556	75	3	,	,	PUNCT
ejpam-4556	75	4	a	a	PRON
ejpam-4556	75	5	)	)	PUNCT
ejpam-4556	75	6	(	(	PUNCT
ejpam-4556	75	7	∂	∂	NUM
ejpam-4556	75	8	∂t	∂t	PROPN
ejpam-4556	75	9	+	+	SYM
ejpam-4556	75	10	∂	∂	NUM
ejpam-4556	75	11	∂a	∂a	NOUN
ejpam-4556	75	12	)	)	PUNCT
ejpam-4556	76	1	v1(t	v1(t	ADV
ejpam-4556	76	2	,	,	PUNCT
ejpam-4556	76	3	a	a	X
ejpam-4556	76	4	)	)	PUNCT
ejpam-4556	76	5	=	=	SYM
ejpam-4556	76	6	ψ1(a)s1(t	ψ1(a)s1(t	PROPN
ejpam-4556	76	7	,	,	PUNCT
ejpam-4556	76	8	a	a	X
ejpam-4556	76	9	)	)	PUNCT
ejpam-4556	77	1	+	+	SYM
ejpam-4556	77	2	ρ25v2(t	ρ25v2(t	NUM
ejpam-4556	77	3	,	,	PUNCT
ejpam-4556	77	4	a	a	PRON
ejpam-4556	77	5	)	)	PUNCT
ejpam-4556	77	6	−	−	PROPN
ejpam-4556	77	7	(	(	PUNCT
ejpam-4556	77	8	ρ15	ρ15	PROPN
ejpam-4556	77	9	+	+	CCONJ
ejpam-4556	77	10	µ(a	µ(a	PROPN
ejpam-4556	77	11	)	)	PUNCT
ejpam-4556	77	12	+	+	NUM
ejpam-4556	77	13	δ1λ1(t	δ1λ1(t	NOUN
ejpam-4556	77	14	,	,	PUNCT
ejpam-4556	77	15	a))v1(t	a))v1(t	PROPN
ejpam-4556	77	16	,	,	PUNCT
ejpam-4556	77	17	a	a	PRON
ejpam-4556	77	18	)	)	PUNCT
ejpam-4556	77	19	(	(	PUNCT
ejpam-4556	77	20	∂	∂	NUM
ejpam-4556	77	21	∂t	∂t	PROPN
ejpam-4556	77	22	+	+	SYM
ejpam-4556	77	23	∂	∂	NUM
ejpam-4556	77	24	∂a	∂a	NOUN
ejpam-4556	77	25	)	)	PUNCT
ejpam-4556	77	26	s2(t	s2(t	PROPN
ejpam-4556	77	27	,	,	PUNCT
ejpam-4556	77	28	a	a	PRON
ejpam-4556	77	29	)	)	PUNCT
ejpam-4556	77	30	=	=	SYM
ejpam-4556	77	31	b2(a)n2(t	b2(a)n2(t	PROPN
ejpam-4556	77	32	,	,	PUNCT
ejpam-4556	77	33	a	a	PRON
ejpam-4556	77	34	)	)	PUNCT
ejpam-4556	77	35	−	−	PROPN
ejpam-4556	78	1	[	[	X
ejpam-4556	78	2	λ2(t	λ2(t	X
ejpam-4556	78	3	,	,	PUNCT
ejpam-4556	78	4	a	a	PRON
ejpam-4556	78	5	)	)	PUNCT
ejpam-4556	78	6	+	+	PUNCT
ejpam-4556	78	7	ψ2(a	ψ2(a	X
ejpam-4556	78	8	)	)	PUNCT
ejpam-4556	78	9	+	+	CCONJ
ejpam-4556	78	10	µ(a	µ(a	PROPN
ejpam-4556	78	11	)	)	PUNCT
ejpam-4556	79	1	+	+	CCONJ
ejpam-4556	79	2	ρ21]s2(t	ρ21]s2(t	NOUN
ejpam-4556	79	3	,	,	PUNCT
ejpam-4556	79	4	a	a	PRON
ejpam-4556	79	5	)	)	PUNCT
ejpam-4556	79	6	+	+	NUM
ejpam-4556	79	7	ρ11s1(t	ρ11s1(t	NUM
ejpam-4556	79	8	,	,	PUNCT
ejpam-4556	79	9	a	a	X
ejpam-4556	79	10	)	)	PUNCT
ejpam-4556	79	11	(	(	PUNCT
ejpam-4556	79	12	∂	∂	NUM
ejpam-4556	80	1	∂t	∂t	PROPN
ejpam-4556	80	2	+	+	SYM
ejpam-4556	80	3	∂	∂	NUM
ejpam-4556	80	4	∂a	∂a	NOUN
ejpam-4556	80	5	)	)	PUNCT
ejpam-4556	80	6	l2(t	l2(t	PROPN
ejpam-4556	80	7	,	,	PUNCT
ejpam-4556	80	8	a	a	PRON
ejpam-4556	80	9	)	)	PUNCT
ejpam-4556	80	10	=	=	SYM
ejpam-4556	80	11	λ2(t	λ2(t	PROPN
ejpam-4556	80	12	,	,	PUNCT
ejpam-4556	80	13	a)[(1	a)[(1	PROPN
ejpam-4556	80	14	−	−	PROPN
ejpam-4556	80	15	ϕ2)s2(t	ϕ2)s2(t	PROPN
ejpam-4556	80	16	,	,	PUNCT
ejpam-4556	80	17	a	a	PRON
ejpam-4556	80	18	)	)	PUNCT
ejpam-4556	80	19	+	+	CCONJ
ejpam-4556	80	20	σ2j2(t	σ2j2(t	PROPN
ejpam-4556	80	21	,	,	PUNCT
ejpam-4556	80	22	a	a	PRON
ejpam-4556	80	23	)	)	PUNCT
ejpam-4556	80	24	+	+	CCONJ
ejpam-4556	80	25	δ2v2(t	δ2v2(t	PROPN
ejpam-4556	80	26	,	,	PUNCT
ejpam-4556	80	27	a	a	NOUN
ejpam-4556	80	28	)	)	PUNCT
ejpam-4556	80	29	]	]	PUNCT
ejpam-4556	80	30	−	−	PROPN
ejpam-4556	80	31	(	(	PUNCT
ejpam-4556	80	32	k2	k2	PROPN
ejpam-4556	80	33	+	+	CCONJ
ejpam-4556	80	34	µ(a	µ(a	PROPN
ejpam-4556	80	35	)	)	PUNCT
ejpam-4556	81	1	+	+	CCONJ
ejpam-4556	82	1	ρ22)l2(t	ρ22)l2(t	NOUN
ejpam-4556	82	2	,	,	PUNCT
ejpam-4556	82	3	a	a	PRON
ejpam-4556	82	4	)	)	PUNCT
ejpam-4556	82	5	+	+	CCONJ
ejpam-4556	82	6	ρ12l1(t	ρ12l1(t	NUM
ejpam-4556	82	7	,	,	PUNCT
ejpam-4556	82	8	a	a	X
ejpam-4556	82	9	)	)	PUNCT
ejpam-4556	82	10	(	(	PUNCT
ejpam-4556	82	11	∂	∂	NUM
ejpam-4556	82	12	∂t	∂t	PROPN
ejpam-4556	82	13	+	+	SYM
ejpam-4556	82	14	∂	∂	NUM
ejpam-4556	82	15	∂a	∂a	NOUN
ejpam-4556	82	16	)	)	PUNCT
ejpam-4556	83	1	i2(t	i2(t	PROPN
ejpam-4556	83	2	,	,	PUNCT
ejpam-4556	83	3	a	a	PRON
ejpam-4556	83	4	)	)	PUNCT
ejpam-4556	83	5	=	=	SYM
ejpam-4556	83	6	k2l2(t	k2l2(t	PROPN
ejpam-4556	83	7	,	,	PUNCT
ejpam-4556	83	8	a	a	PRON
ejpam-4556	83	9	)	)	PUNCT
ejpam-4556	83	10	−	−	PROPN
ejpam-4556	83	11	(	(	PUNCT
ejpam-4556	83	12	r2	r2	PROPN
ejpam-4556	83	13	+	+	CCONJ
ejpam-4556	83	14	µ(a	µ(a	PROPN
ejpam-4556	83	15	)	)	PUNCT
ejpam-4556	83	16	+	+	NUM
ejpam-4556	83	17	µ2(a	µ2(a	NOUN
ejpam-4556	83	18	)	)	PUNCT
ejpam-4556	83	19	+	+	X
ejpam-4556	83	20	ρ23)i2(t	ρ23)i2(t	PROPN
ejpam-4556	83	21	,	,	PUNCT
ejpam-4556	83	22	a	a	PRON
ejpam-4556	83	23	)	)	PUNCT
ejpam-4556	83	24	+	+	CCONJ
ejpam-4556	83	25	ρ13i1(t	ρ13i1(t	NUM
ejpam-4556	83	26	,	,	PUNCT
ejpam-4556	83	27	a	a	PRON
ejpam-4556	83	28	)	)	PUNCT
ejpam-4556	83	29	+	+	CCONJ
ejpam-4556	83	30	ϕ2λ2(t	ϕ2λ2(t	NOUN
ejpam-4556	83	31	,	,	PUNCT
ejpam-4556	83	32	a)s2(t	a)s2(t	PROPN
ejpam-4556	83	33	,	,	PUNCT
ejpam-4556	83	34	a	a	NOUN
ejpam-4556	83	35	)	)	PUNCT
ejpam-4556	83	36	(	(	PUNCT
ejpam-4556	83	37	∂	∂	NUM
ejpam-4556	83	38	∂t	∂t	PROPN
ejpam-4556	83	39	+	+	SYM
ejpam-4556	83	40	∂	∂	NUM
ejpam-4556	83	41	∂a	∂a	NOUN
ejpam-4556	83	42	)	)	PUNCT
ejpam-4556	83	43	j2(t	j2(t	PROPN
ejpam-4556	83	44	,	,	PUNCT
ejpam-4556	83	45	a	a	PRON
ejpam-4556	83	46	)	)	PUNCT
ejpam-4556	83	47	=	=	SYM
ejpam-4556	83	48	r2i2(t	r2i2(t	NOUN
ejpam-4556	83	49	,	,	PUNCT
ejpam-4556	83	50	a	a	PRON
ejpam-4556	83	51	)	)	PUNCT
ejpam-4556	83	52	−	−	PROPN
ejpam-4556	83	53	(	(	PUNCT
ejpam-4556	83	54	σ2λ2(t	σ2λ2(t	PROPN
ejpam-4556	83	55	,	,	PUNCT
ejpam-4556	83	56	a	a	PRON
ejpam-4556	83	57	)	)	PUNCT
ejpam-4556	83	58	+	+	NOUN
ejpam-4556	83	59	µ(a	µ(a	PROPN
ejpam-4556	83	60	)	)	PUNCT
ejpam-4556	84	1	+	+	CCONJ
ejpam-4556	84	2	ρ24)j2(t	ρ24)j2(t	PROPN
ejpam-4556	84	3	,	,	PUNCT
ejpam-4556	84	4	a	a	PRON
ejpam-4556	84	5	)	)	PUNCT
ejpam-4556	85	1	+	+	CCONJ
ejpam-4556	85	2	ρ14j2(t	ρ14j2(t	NOUN
ejpam-4556	85	3	,	,	PUNCT
ejpam-4556	85	4	a	a	NOUN
ejpam-4556	85	5	)	)	PUNCT
ejpam-4556	85	6	(	(	PUNCT
ejpam-4556	85	7	∂	∂	NUM
ejpam-4556	86	1	∂t	∂t	PROPN
ejpam-4556	86	2	+	+	SYM
ejpam-4556	86	3	∂	∂	NUM
ejpam-4556	86	4	∂a	∂a	NOUN
ejpam-4556	86	5	)	)	PUNCT
ejpam-4556	86	6	v2(t	v2(t	PROPN
ejpam-4556	86	7	,	,	PUNCT
ejpam-4556	86	8	a	a	PRON
ejpam-4556	86	9	)	)	PUNCT
ejpam-4556	86	10	=	=	SYM
ejpam-4556	86	11	ψ2(a)s2(t	ψ2(a)s2(t	PROPN
ejpam-4556	86	12	,	,	PUNCT
ejpam-4556	86	13	a	a	PRON
ejpam-4556	86	14	)	)	PUNCT
ejpam-4556	86	15	+	+	NUM
ejpam-4556	86	16	ρ15v1(t	ρ15v1(t	NOUN
ejpam-4556	86	17	,	,	PUNCT
ejpam-4556	86	18	a	a	PRON
ejpam-4556	86	19	)	)	PUNCT
ejpam-4556	86	20	−	−	PROPN
ejpam-4556	86	21	(	(	PUNCT
ejpam-4556	86	22	ρ25	ρ25	NOUN
ejpam-4556	86	23	+	+	CCONJ
ejpam-4556	87	1	µ(a	µ(a	PROPN
ejpam-4556	88	1	)	)	PUNCT
ejpam-4556	89	1	+	+	CCONJ
ejpam-4556	89	2	δ2λ2(t	δ2λ2(t	PROPN
ejpam-4556	89	3	,	,	PUNCT
ejpam-4556	89	4	a))v2(t	a))v2(t	PROPN
ejpam-4556	89	5	,	,	PUNCT
ejpam-4556	89	6	a	a	NOUN
ejpam-4556	89	7	)	)	PUNCT
ejpam-4556	89	8	(	(	PUNCT
ejpam-4556	89	9	1	1	X
ejpam-4556	89	10	)	)	PUNCT
ejpam-4556	89	11	with	with	ADP
ejpam-4556	89	12	initial	initial	ADJ
ejpam-4556	89	13	and	and	CCONJ
ejpam-4556	89	14	boundary	boundary	ADJ
ejpam-4556	89	15	conditions	condition	NOUN
ejpam-4556	89	16	:	:	PUNCT
ejpam-4556	89	17			NUM
ejpam-4556	89	18	si(t	si(t	PROPN
ejpam-4556	89	19	,	,	PUNCT
ejpam-4556	89	20	0	0	NUM
ejpam-4556	89	21	)	)	PUNCT
ejpam-4556	89	22	=	=	SYM
ejpam-4556	89	23	∫	∫	PROPN
ejpam-4556	89	24	a2	a2	PROPN
ejpam-4556	89	25	a1	a1	PROPN
ejpam-4556	89	26	bi(a)ni(t	bi(a)ni(t	PROPN
ejpam-4556	89	27	,	,	PUNCT
ejpam-4556	89	28	a)da	a)da	ADJ
ejpam-4556	89	29	li(t	li(t	NOUN
ejpam-4556	89	30	,	,	PUNCT
ejpam-4556	89	31	0	0	NUM
ejpam-4556	89	32	)	)	PUNCT
ejpam-4556	89	33	=	=	PUNCT
ejpam-4556	89	34	vi(t	vi(t	X
ejpam-4556	89	35	,	,	PUNCT
ejpam-4556	89	36	0	0	NUM
ejpam-4556	89	37	)	)	PUNCT
ejpam-4556	89	38	=	=	NOUN
ejpam-4556	89	39	ii(t	ii(t	NOUN
ejpam-4556	89	40	,	,	PUNCT
ejpam-4556	89	41	0	0	NUM
ejpam-4556	89	42	)	)	PUNCT
ejpam-4556	89	43	=	=	SYM
ejpam-4556	89	44	ji(t	ji(t	NOUN
ejpam-4556	89	45	,	,	PUNCT
ejpam-4556	89	46	0	0	NUM
ejpam-4556	89	47	)	)	PUNCT
ejpam-4556	89	48	=	=	SYM
ejpam-4556	90	1	0	0	NUM
ejpam-4556	90	2	si(0	si(0	NOUN
ejpam-4556	90	3	,	,	PUNCT
ejpam-4556	90	4	a	a	PRON
ejpam-4556	90	5	)	)	PUNCT
ejpam-4556	90	6	=	=	SYM
ejpam-4556	90	7	s0i(a);li(0	s0i(a);li(0	PROPN
ejpam-4556	90	8	,	,	PUNCT
ejpam-4556	90	9	a	a	PRON
ejpam-4556	90	10	)	)	PUNCT
ejpam-4556	90	11	=	=	SYM
ejpam-4556	91	1	l0i(a);vi(0	l0i(a);vi(0	PROPN
ejpam-4556	91	2	,	,	PUNCT
ejpam-4556	91	3	a	a	PRON
ejpam-4556	91	4	)	)	PUNCT
ejpam-4556	91	5	=	=	SYM
ejpam-4556	91	6	v0i(a	v0i(a	PROPN
ejpam-4556	91	7	)	)	PUNCT
ejpam-4556	92	1	ii(0	ii(0	NOUN
ejpam-4556	92	2	,	,	PUNCT
ejpam-4556	92	3	a	a	PRON
ejpam-4556	92	4	)	)	PUNCT
ejpam-4556	92	5	=	=	SYM
ejpam-4556	92	6	i0i(a	i0i(a	PROPN
ejpam-4556	92	7	)	)	PUNCT
ejpam-4556	92	8	;	;	PUNCT
ejpam-4556	93	1	ji(0	ji(0	PROPN
ejpam-4556	93	2	,	,	PUNCT
ejpam-4556	93	3	a	a	PRON
ejpam-4556	93	4	)	)	PUNCT
ejpam-4556	93	5	=	=	SYM
ejpam-4556	93	6	j0i(a	j0i(a	PROPN
ejpam-4556	93	7	)	)	PUNCT
ejpam-4556	93	8	.	.	PUNCT
ejpam-4556	94	1	b.	b.	PROPN
ejpam-4556	94	2	k.	k.	PROPN
ejpam-4556	94	3	abdoul	abdoul	PROPN
ejpam-4556	94	4	wahid	wahid	PROPN
ejpam-4556	94	5	,	,	PUNCT
ejpam-4556	94	6	d.moustapha	d.moustapha	PROPN
ejpam-4556	94	7	,	,	PUNCT
ejpam-4556	94	8	s.	s.	PROPN
ejpam-4556	94	9	bisso	bisso	PROPN
ejpam-4556	94	10	/	/	SYM
ejpam-4556	94	11	eur	eur	PROPN
ejpam-4556	94	12	.	.	PUNCT
ejpam-4556	95	1	j.	j.	PROPN
ejpam-4556	95	2	pure	pure	PROPN
ejpam-4556	95	3	appl	appl	PROPN
ejpam-4556	95	4	.	.	PROPN
ejpam-4556	95	5	math	math	PROPN
ejpam-4556	95	6	,	,	PUNCT
ejpam-4556	95	7	15	15	NUM
ejpam-4556	95	8	(	(	PUNCT
ejpam-4556	95	9	4	4	NUM
ejpam-4556	95	10	)	)	PUNCT
ejpam-4556	95	11	(	(	PUNCT
ejpam-4556	95	12	2022	2022	NUM
ejpam-4556	95	13	)	)	PUNCT
ejpam-4556	95	14	,	,	PUNCT
ejpam-4556	95	15	2054	2054	NUM
ejpam-4556	95	16	-	-	SYM
ejpam-4556	95	17	2073	2073	NUM
ejpam-4556	95	18	2058	2058	NUM
ejpam-4556	95	19	and	and	CCONJ
ejpam-4556	95	20	λi(t	λi(t	NOUN
ejpam-4556	95	21	,	,	PUNCT
ejpam-4556	95	22	a	a	PRON
ejpam-4556	95	23	)	)	PUNCT
ejpam-4556	95	24	=	=	SYM
ejpam-4556	95	25	βi(a)ci(a	βi(a)ci(a	ADJ
ejpam-4556	95	26	)	)	PUNCT
ejpam-4556	95	27	∫	∫	PROPN
ejpam-4556	95	28	a+	a+	PUNCT
ejpam-4556	95	29	0	0	NUM
ejpam-4556	95	30	ii(t	ii(t	NOUN
ejpam-4556	95	31	,	,	PUNCT
ejpam-4556	95	32	a	a	DET
ejpam-4556	95	33	′	′	NOUN
ejpam-4556	95	34	)	)	PUNCT
ejpam-4556	95	35	ni(t	ni(t	ADP
ejpam-4556	95	36	,	,	PUNCT
ejpam-4556	95	37	a′	a′	PROPN
ejpam-4556	95	38	)	)	PUNCT
ejpam-4556	95	39	pi(a	pi(a	PROPN
ejpam-4556	95	40	,	,	PUNCT
ejpam-4556	95	41	a	a	DET
ejpam-4556	95	42	′)da′	′)da′	NOUN
ejpam-4556	95	43	,	,	PUNCT
ejpam-4556	95	44	assume	assume	VERB
ejpam-4556	95	45	that	that	SCONJ
ejpam-4556	95	46	pi(a	pi(a	SYM
ejpam-4556	95	47	,	,	PUNCT
ejpam-4556	95	48	a	a	DET
ejpam-4556	95	49	′	′	NOUN
ejpam-4556	95	50	)	)	PUNCT
ejpam-4556	96	1	=	=	SYM
ejpam-4556	96	2	gi(a)β̂i(a	gi(a)β̂i(a	NOUN
ejpam-4556	96	3	′	′	NUM
ejpam-4556	96	4	)	)	PUNCT
ejpam-4556	96	5	(	(	PUNCT
ejpam-4556	96	6	2	2	X
ejpam-4556	96	7	)	)	PUNCT
ejpam-4556	96	8	(	(	PUNCT
ejpam-4556	96	9	see	see	VERB
ejpam-4556	96	10	dietz	dietz	PROPN
ejpam-4556	96	11	and	and	CCONJ
ejpam-4556	96	12	schenzle	schenzle	VERB
ejpam-4556	96	13	1985	1985	NUM
ejpam-4556	96	14	[	[	X
ejpam-4556	96	15	9	9	NUM
ejpam-4556	96	16	]	]	PUNCT
ejpam-4556	96	17	;	;	PUNCT
ejpam-4556	96	18	greenhalgh	greenhalgh	PROPN
ejpam-4556	96	19	1988	1988	NUM
ejpam-4556	96	20	[	[	X
ejpam-4556	96	21	7	7	NUM
ejpam-4556	96	22	]	]	NUM
ejpam-4556	96	23	)	)	PUNCT
ejpam-4556	96	24	.	.	PUNCT
ejpam-4556	97	1	let	let	VERB
ejpam-4556	97	2	n(t	n(t	PROPN
ejpam-4556	97	3	,	,	PUNCT
ejpam-4556	97	4	a	a	PRON
ejpam-4556	97	5	)	)	PUNCT
ejpam-4556	97	6	=	=	SYM
ejpam-4556	97	7	n1(t	n1(t	PROPN
ejpam-4556	97	8	,	,	PUNCT
ejpam-4556	97	9	a	a	PRON
ejpam-4556	97	10	)	)	PUNCT
ejpam-4556	98	1	+	+	NOUN
ejpam-4556	98	2	n2(t	n2(t	PROPN
ejpam-4556	98	3	,	,	PUNCT
ejpam-4556	98	4	a	a	PRON
ejpam-4556	98	5	)	)	PUNCT
ejpam-4556	98	6	and	and	CCONJ
ejpam-4556	98	7	ni(t	ni(t	NOUN
ejpam-4556	98	8	,	,	PUNCT
ejpam-4556	98	9	a	a	PRON
ejpam-4556	98	10	)	)	PUNCT
ejpam-4556	98	11	=	=	SYM
ejpam-4556	98	12	αin(t	αin(t	PROPN
ejpam-4556	98	13	,	,	PUNCT
ejpam-4556	98	14	a	a	PRON
ejpam-4556	98	15	)	)	PUNCT
ejpam-4556	98	16	,	,	PUNCT
ejpam-4556	98	17	with	with	ADP
ejpam-4556	98	18	α1	α1	PROPN
ejpam-4556	98	19	+	+	CCONJ
ejpam-4556	98	20	α2	α2	ADJ
ejpam-4556	98	21	=	=	SYM
ejpam-4556	98	22	1	1	NUM
ejpam-4556	98	23	n(t	n(t	PROPN
ejpam-4556	98	24	,	,	PUNCT
ejpam-4556	98	25	a	a	PRON
ejpam-4556	98	26	)	)	PUNCT
ejpam-4556	98	27	=	=	SYM
ejpam-4556	98	28	s1(t	s1(t	PROPN
ejpam-4556	98	29	,	,	PUNCT
ejpam-4556	98	30	a	a	PRON
ejpam-4556	98	31	)	)	PUNCT
ejpam-4556	98	32	+	+	CCONJ
ejpam-4556	98	33	l1(t	l1(t	PROPN
ejpam-4556	98	34	,	,	PUNCT
ejpam-4556	98	35	a	a	PRON
ejpam-4556	98	36	)	)	PUNCT
ejpam-4556	98	37	+	+	CCONJ
ejpam-4556	98	38	i1(t	i1(t	PROPN
ejpam-4556	98	39	,	,	PUNCT
ejpam-4556	98	40	a	a	PRON
ejpam-4556	98	41	)	)	PUNCT
ejpam-4556	99	1	+	+	CCONJ
ejpam-4556	99	2	j1(t	j1(t	PROPN
ejpam-4556	99	3	,	,	PUNCT
ejpam-4556	99	4	a	a	PRON
ejpam-4556	99	5	)	)	PUNCT
ejpam-4556	99	6	+	+	PROPN
ejpam-4556	99	7	v1(t	v1(t	ADV
ejpam-4556	99	8	,	,	PUNCT
ejpam-4556	99	9	a	a	X
ejpam-4556	99	10	)	)	PUNCT
ejpam-4556	99	11	+	+	CCONJ
ejpam-4556	99	12	s2(t	s2(t	PROPN
ejpam-4556	99	13	,	,	PUNCT
ejpam-4556	99	14	a	a	PRON
ejpam-4556	99	15	)	)	PUNCT
ejpam-4556	99	16	+	+	CCONJ
ejpam-4556	99	17	l2(t	l2(t	PROPN
ejpam-4556	99	18	,	,	PUNCT
ejpam-4556	99	19	a	a	NOUN
ejpam-4556	99	20	)	)	PUNCT
ejpam-4556	100	1	+	+	CCONJ
ejpam-4556	101	1	i2(t	i2(t	PROPN
ejpam-4556	101	2	,	,	PUNCT
ejpam-4556	101	3	a	a	PRON
ejpam-4556	101	4	)	)	PUNCT
ejpam-4556	101	5	+	+	PROPN
ejpam-4556	101	6	j2(t	j2(t	PROPN
ejpam-4556	101	7	,	,	PUNCT
ejpam-4556	101	8	a	a	PRON
ejpam-4556	101	9	)	)	PUNCT
ejpam-4556	101	10	+	+	SYM
ejpam-4556	101	11	v2(t	v2(t	PROPN
ejpam-4556	101	12	,	,	PUNCT
ejpam-4556	101	13	a	a	PRON
ejpam-4556	101	14	)	)	PUNCT
ejpam-4556	101	15	.	.	PUNCT
ejpam-4556	102	1	by	by	ADP
ejpam-4556	102	2	summing	sum	VERB
ejpam-4556	102	3	equations	equation	NOUN
ejpam-4556	102	4	of	of	ADP
ejpam-4556	102	5	system	system	NOUN
ejpam-4556	102	6	(	(	PUNCT
ejpam-4556	102	7	1	1	NUM
ejpam-4556	102	8	)	)	PUNCT
ejpam-4556	102	9	and	and	CCONJ
ejpam-4556	102	10	(	(	PUNCT
ejpam-4556	102	11	2	2	NUM
ejpam-4556	102	12	)	)	PUNCT
ejpam-4556	102	13	,	,	PUNCT
ejpam-4556	102	14	we	we	PRON
ejpam-4556	102	15	obtain	obtain	VERB
ejpam-4556	102	16	the	the	DET
ejpam-4556	102	17	following	follow	VERB
ejpam-4556	102	18	equations	equation	NOUN
ejpam-4556	102	19	for	for	ADP
ejpam-4556	102	20	the	the	DET
ejpam-4556	102	21	total	total	ADJ
ejpam-4556	102	22	population	population	NOUN
ejpam-4556	102	23	n(t	n(t	PROPN
ejpam-4556	102	24	,	,	PUNCT
ejpam-4556	102	25	a):	a):	NOUN
ejpam-4556	102	26	(	(	PUNCT
ejpam-4556	103	1	∂	∂	X
ejpam-4556	103	2	∂t	∂t	PROPN
ejpam-4556	103	3	+	+	SYM
ejpam-4556	103	4	∂	∂	NUM
ejpam-4556	103	5	∂a	∂a	NOUN
ejpam-4556	103	6	)	)	PUNCT
ejpam-4556	103	7	n(t	n(t	PROPN
ejpam-4556	103	8	,	,	PUNCT
ejpam-4556	103	9	a	a	PRON
ejpam-4556	103	10	)	)	PUNCT
ejpam-4556	103	11	=	=	SYM
ejpam-4556	103	12	(	(	PUNCT
ejpam-4556	103	13	b(a)−	b(a)−	VERB
ejpam-4556	103	14	µ(a))n(t	µ(a))n(t	ADV
ejpam-4556	103	15	,	,	PUNCT
ejpam-4556	103	16	a)−	a)−	PROPN
ejpam-4556	103	17	µ1(a)i1(t	µ1(a)i1(t	X
ejpam-4556	103	18	,	,	PUNCT
ejpam-4556	103	19	a)−	a)−	PROPN
ejpam-4556	103	20	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	103	21	,	,	PUNCT
ejpam-4556	103	22	a	a	PRON
ejpam-4556	103	23	)	)	PUNCT
ejpam-4556	103	24	n(t	n(t	PROPN
ejpam-4556	103	25	,	,	PUNCT
ejpam-4556	103	26	0	0	NUM
ejpam-4556	103	27	)	)	PUNCT
ejpam-4556	103	28	=	=	SYM
ejpam-4556	103	29	∫	∫	PROPN
ejpam-4556	103	30	a2	a2	PROPN
ejpam-4556	103	31	a1	a1	PROPN
ejpam-4556	103	32	b(a)n(t	b(a)n(t	PROPN
ejpam-4556	103	33	,	,	PUNCT
ejpam-4556	103	34	a)da	a)da	PROPN
ejpam-4556	103	35	.	.	PUNCT
ejpam-4556	104	1	(	(	PUNCT
ejpam-4556	104	2	3	3	NUM
ejpam-4556	104	3	)	)	PUNCT
ejpam-4556	104	4	where	where	SCONJ
ejpam-4556	104	5	b(a	b(a	NOUN
ejpam-4556	104	6	)	)	PUNCT
ejpam-4556	104	7	=	=	SYM
ejpam-4556	104	8	α1b1(a)+α2b2(a	α1b1(a)+α2b2(a	NOUN
ejpam-4556	104	9	)	)	PUNCT
ejpam-4556	104	10	;	;	PUNCT
ejpam-4556	104	11	a1	a1	NOUN
ejpam-4556	104	12	and	and	CCONJ
ejpam-4556	104	13	a2	a2	PROPN
ejpam-4556	104	14	are	be	AUX
ejpam-4556	104	15	respectively	respectively	ADV
ejpam-4556	104	16	the	the	DET
ejpam-4556	104	17	minimum	minimum	ADJ
ejpam-4556	104	18	and	and	CCONJ
ejpam-4556	104	19	maximum	maximum	ADJ
ejpam-4556	104	20	age	age	NOUN
ejpam-4556	104	21	of	of	ADP
ejpam-4556	104	22	procreation	procreation	NOUN
ejpam-4556	104	23	and	and	CCONJ
ejpam-4556	104	24	a+	a+	PUNCT
ejpam-4556	104	25	is	be	AUX
ejpam-4556	104	26	the	the	DET
ejpam-4556	104	27	maximum	maximum	ADJ
ejpam-4556	104	28	age	age	NOUN
ejpam-4556	104	29	of	of	ADP
ejpam-4556	104	30	an	an	DET
ejpam-4556	104	31	individual	individual	NOUN
ejpam-4556	104	32	,	,	PUNCT
ejpam-4556	104	33	with	with	ADP
ejpam-4556	104	34	a+	a+	PUNCT
ejpam-4556	104	35	<	<	X
ejpam-4556	104	36	+	+	NOUN
ejpam-4556	104	37	∞.	∞.	PROPN
ejpam-4556	104	38	let	let	VERB
ejpam-4556	104	39			PRON
ejpam-4556	104	40	si(t	si(t	VERB
ejpam-4556	104	41	,	,	PUNCT
ejpam-4556	104	42	a	a	PRON
ejpam-4556	105	1	)	)	PUNCT
ejpam-4556	105	2	=	=	SYM
ejpam-4556	105	3	si(t	si(t	NOUN
ejpam-4556	105	4	,	,	PUNCT
ejpam-4556	105	5	a	a	PRON
ejpam-4556	105	6	)	)	PUNCT
ejpam-4556	105	7	n(t	n(t	PROPN
ejpam-4556	105	8	,	,	PUNCT
ejpam-4556	105	9	a	a	PRON
ejpam-4556	105	10	)	)	PUNCT
ejpam-4556	105	11	;	;	PUNCT
ejpam-4556	105	12	li(t	li(t	NOUN
ejpam-4556	105	13	,	,	PUNCT
ejpam-4556	105	14	a	a	PRON
ejpam-4556	105	15	)	)	PUNCT
ejpam-4556	105	16	=	=	SYM
ejpam-4556	105	17	li(t	li(t	NOUN
ejpam-4556	105	18	,	,	PUNCT
ejpam-4556	105	19	a	a	PRON
ejpam-4556	105	20	)	)	PUNCT
ejpam-4556	105	21	n(t	n(t	PROPN
ejpam-4556	105	22	,	,	PUNCT
ejpam-4556	105	23	a	a	PRON
ejpam-4556	105	24	)	)	PUNCT
ejpam-4556	105	25	;	;	PUNCT
ejpam-4556	105	26	ii(t	ii(t	NOUN
ejpam-4556	105	27	,	,	PUNCT
ejpam-4556	105	28	a	a	PRON
ejpam-4556	105	29	)	)	PUNCT
ejpam-4556	105	30	=	=	SYM
ejpam-4556	105	31	ii(t	ii(t	NOUN
ejpam-4556	105	32	,	,	PUNCT
ejpam-4556	105	33	a	a	PRON
ejpam-4556	105	34	)	)	PUNCT
ejpam-4556	105	35	n(t	n(t	PROPN
ejpam-4556	105	36	,	,	PUNCT
ejpam-4556	105	37	a	a	PRON
ejpam-4556	105	38	)	)	PUNCT
ejpam-4556	105	39	ji(t	ji(t	NOUN
ejpam-4556	105	40	,	,	PUNCT
ejpam-4556	105	41	a	a	PRON
ejpam-4556	105	42	)	)	PUNCT
ejpam-4556	105	43	=	=	SYM
ejpam-4556	105	44	ji(t	ji(t	NOUN
ejpam-4556	105	45	,	,	PUNCT
ejpam-4556	105	46	a	a	PRON
ejpam-4556	105	47	)	)	PUNCT
ejpam-4556	105	48	n(t	n(t	PROPN
ejpam-4556	105	49	,	,	PUNCT
ejpam-4556	105	50	a	a	PRON
ejpam-4556	105	51	)	)	PUNCT
ejpam-4556	105	52	;	;	PUNCT
ejpam-4556	105	53	vi(t	vi(t	NUM
ejpam-4556	105	54	,	,	PUNCT
ejpam-4556	105	55	a	a	PRON
ejpam-4556	105	56	)	)	PUNCT
ejpam-4556	105	57	=	=	PUNCT
ejpam-4556	105	58	vi(t	vi(t	PROPN
ejpam-4556	105	59	,	,	PUNCT
ejpam-4556	105	60	a	a	PRON
ejpam-4556	105	61	)	)	PUNCT
ejpam-4556	105	62	n(t	n(t	PROPN
ejpam-4556	105	63	,	,	PUNCT
ejpam-4556	105	64	a	a	PRON
ejpam-4556	105	65	)	)	PUNCT
ejpam-4556	105	66	.	.	PUNCT
ejpam-4556	106	1	(	(	PUNCT
ejpam-4556	106	2	4	4	X
ejpam-4556	106	3	)	)	PUNCT
ejpam-4556	106	4	the	the	DET
ejpam-4556	106	5	system	system	NOUN
ejpam-4556	106	6	(	(	PUNCT
ejpam-4556	106	7	1	1	X
ejpam-4556	106	8	)	)	PUNCT
ejpam-4556	106	9	can	can	AUX
ejpam-4556	106	10	be	be	AUX
ejpam-4556	106	11	normalized	normalize	VERB
ejpam-4556	106	12	as	as	ADP
ejpam-4556	106	13	the	the	DET
ejpam-4556	106	14	following	follow	VERB
ejpam-4556	106	15	system	system	NOUN
ejpam-4556	106	16	:	:	PUNCT
ejpam-4556	106	17			PROPN
ejpam-4556	106	18	(	(	PUNCT
ejpam-4556	106	19	∂	∂	NUM
ejpam-4556	106	20	∂t	∂t	PROPN
ejpam-4556	106	21	+	+	SYM
ejpam-4556	106	22	∂	∂	NUM
ejpam-4556	106	23	∂a	∂a	NOUN
ejpam-4556	106	24	)	)	PUNCT
ejpam-4556	106	25	s1(t	s1(t	PROPN
ejpam-4556	106	26	,	,	PUNCT
ejpam-4556	106	27	a	a	PRON
ejpam-4556	106	28	)	)	PUNCT
ejpam-4556	106	29	=	=	SYM
ejpam-4556	106	30	α1b1(a	α1b1(a	NUM
ejpam-4556	106	31	)	)	PUNCT
ejpam-4556	106	32	−	−	PUNCT
ejpam-4556	107	1	[	[	X
ejpam-4556	107	2	λ1(t	λ1(t	PROPN
ejpam-4556	107	3	,	,	PUNCT
ejpam-4556	107	4	a	a	PRON
ejpam-4556	107	5	)	)	PUNCT
ejpam-4556	107	6	+	+	PUNCT
ejpam-4556	107	7	ψ1(a	ψ1(a	X
ejpam-4556	107	8	)	)	PUNCT
ejpam-4556	108	1	+	+	CCONJ
ejpam-4556	108	2	b(a	b(a	NOUN
ejpam-4556	108	3	)	)	PUNCT
ejpam-4556	108	4	−	−	PROPN
ejpam-4556	109	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	109	2	,	,	PUNCT
ejpam-4556	109	3	a	a	X
ejpam-4556	109	4	)	)	PUNCT
ejpam-4556	109	5	−	−	PROPN
ejpam-4556	110	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	110	2	,	,	PUNCT
ejpam-4556	110	3	a	a	PRON
ejpam-4556	110	4	)	)	PUNCT
ejpam-4556	110	5	+	+	NUM
ejpam-4556	110	6	ρ11]s1(t	ρ11]s1(t	ADJ
ejpam-4556	110	7	,	,	PUNCT
ejpam-4556	110	8	a	a	PRON
ejpam-4556	110	9	)	)	PUNCT
ejpam-4556	111	1	+	+	NOUN
ejpam-4556	111	2	ρ21s2(t	ρ21s2(t	PROPN
ejpam-4556	111	3	,	,	PUNCT
ejpam-4556	111	4	a	a	NOUN
ejpam-4556	111	5	)	)	PUNCT
ejpam-4556	111	6	(	(	PUNCT
ejpam-4556	111	7	∂	∂	NUM
ejpam-4556	111	8	∂t	∂t	PROPN
ejpam-4556	111	9	+	+	SYM
ejpam-4556	111	10	∂	∂	NUM
ejpam-4556	111	11	∂a	∂a	NOUN
ejpam-4556	111	12	)	)	PUNCT
ejpam-4556	111	13	l1(t	l1(t	PROPN
ejpam-4556	111	14	,	,	PUNCT
ejpam-4556	111	15	a	a	PRON
ejpam-4556	111	16	)	)	PUNCT
ejpam-4556	111	17	=	=	SYM
ejpam-4556	112	1	λ1(t	λ1(t	PROPN
ejpam-4556	112	2	,	,	PUNCT
ejpam-4556	112	3	a)[(1	a)[(1	PROPN
ejpam-4556	112	4	−	−	PROPN
ejpam-4556	112	5	ϕ1)s1(t	ϕ1)s1(t	NOUN
ejpam-4556	112	6	,	,	PUNCT
ejpam-4556	112	7	a	a	X
ejpam-4556	112	8	)	)	PUNCT
ejpam-4556	112	9	+	+	CCONJ
ejpam-4556	112	10	σ1j1(t	σ1j1(t	ADJ
ejpam-4556	112	11	,	,	PUNCT
ejpam-4556	112	12	a	a	PRON
ejpam-4556	112	13	)	)	PUNCT
ejpam-4556	112	14	+	+	CCONJ
ejpam-4556	112	15	δ1v1(t	δ1v1(t	PROPN
ejpam-4556	112	16	,	,	PUNCT
ejpam-4556	112	17	a	a	NOUN
ejpam-4556	112	18	)	)	PUNCT
ejpam-4556	112	19	]	]	PUNCT
ejpam-4556	112	20	−(k1	−(k1	SYM
ejpam-4556	112	21	+	+	X
ejpam-4556	112	22	b(a	b(a	NOUN
ejpam-4556	112	23	)	)	PUNCT
ejpam-4556	112	24	−	−	PROPN
ejpam-4556	113	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	113	2	,	,	PUNCT
ejpam-4556	113	3	a	a	X
ejpam-4556	113	4	)	)	PUNCT
ejpam-4556	113	5	−	−	PROPN
ejpam-4556	114	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	114	2	,	,	PUNCT
ejpam-4556	114	3	a	a	PRON
ejpam-4556	114	4	)	)	PUNCT
ejpam-4556	114	5	+	+	NOUN
ejpam-4556	114	6	ρ12)l1(t	ρ12)l1(t	PROPN
ejpam-4556	114	7	,	,	PUNCT
ejpam-4556	114	8	a	a	PRON
ejpam-4556	114	9	)	)	PUNCT
ejpam-4556	114	10	+	+	CCONJ
ejpam-4556	114	11	ρ22l2(t	ρ22l2(t	PROPN
ejpam-4556	114	12	,	,	PUNCT
ejpam-4556	114	13	a	a	NOUN
ejpam-4556	114	14	)	)	PUNCT
ejpam-4556	114	15	(	(	PUNCT
ejpam-4556	114	16	∂	∂	NUM
ejpam-4556	114	17	∂t	∂t	PROPN
ejpam-4556	114	18	+	+	SYM
ejpam-4556	114	19	∂	∂	NUM
ejpam-4556	114	20	∂a	∂a	NOUN
ejpam-4556	114	21	)	)	PUNCT
ejpam-4556	114	22	i1(t	i1(t	PROPN
ejpam-4556	114	23	,	,	PUNCT
ejpam-4556	114	24	a	a	X
ejpam-4556	114	25	)	)	PUNCT
ejpam-4556	114	26	=	=	NOUN
ejpam-4556	114	27	−(r1	−(r1	X
ejpam-4556	114	28	+	+	NOUN
ejpam-4556	114	29	µ1(a	µ1(a	X
ejpam-4556	114	30	)	)	PUNCT
ejpam-4556	115	1	+	+	CCONJ
ejpam-4556	115	2	b(a	b(a	NOUN
ejpam-4556	115	3	)	)	PUNCT
ejpam-4556	115	4	−	−	PROPN
ejpam-4556	116	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	116	2	,	,	PUNCT
ejpam-4556	116	3	a	a	X
ejpam-4556	116	4	)	)	PUNCT
ejpam-4556	116	5	−	−	PROPN
ejpam-4556	117	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	117	2	,	,	PUNCT
ejpam-4556	117	3	a	a	PRON
ejpam-4556	117	4	)	)	PUNCT
ejpam-4556	117	5	+	+	CCONJ
ejpam-4556	117	6	ρ13)i1(t	ρ13)i1(t	PROPN
ejpam-4556	117	7	,	,	PUNCT
ejpam-4556	117	8	a	a	PRON
ejpam-4556	117	9	)	)	PUNCT
ejpam-4556	117	10	+	+	NUM
ejpam-4556	117	11	ρ23i2(t	ρ23i2(t	PROPN
ejpam-4556	117	12	,	,	PUNCT
ejpam-4556	117	13	a	a	PRON
ejpam-4556	117	14	)	)	PUNCT
ejpam-4556	117	15	+	+	NOUN
ejpam-4556	117	16	ϕ1λ1(t	ϕ1λ1(t	PROPN
ejpam-4556	117	17	,	,	PUNCT
ejpam-4556	117	18	a)s1(t	a)s1(t	PROPN
ejpam-4556	117	19	,	,	PUNCT
ejpam-4556	117	20	a	a	PRON
ejpam-4556	117	21	)	)	PUNCT
ejpam-4556	117	22	+	+	CCONJ
ejpam-4556	117	23	k1l1(t	k1l1(t	PROPN
ejpam-4556	117	24	,	,	PUNCT
ejpam-4556	117	25	a	a	NOUN
ejpam-4556	117	26	)	)	PUNCT
ejpam-4556	117	27	(	(	PUNCT
ejpam-4556	117	28	∂	∂	NUM
ejpam-4556	117	29	∂t	∂t	PROPN
ejpam-4556	117	30	+	+	SYM
ejpam-4556	117	31	∂	∂	NUM
ejpam-4556	117	32	∂a	∂a	NOUN
ejpam-4556	117	33	)	)	PUNCT
ejpam-4556	117	34	j1(t	j1(t	PROPN
ejpam-4556	117	35	,	,	PUNCT
ejpam-4556	117	36	a	a	PRON
ejpam-4556	117	37	)	)	PUNCT
ejpam-4556	118	1	=	=	SYM
ejpam-4556	118	2	r1i1(t	r1i1(t	PROPN
ejpam-4556	118	3	,	,	PUNCT
ejpam-4556	118	4	a	a	PRON
ejpam-4556	118	5	)	)	PUNCT
ejpam-4556	118	6	−	−	PROPN
ejpam-4556	118	7	(	(	PUNCT
ejpam-4556	118	8	σ1λ1(t	σ1λ1(t	PROPN
ejpam-4556	118	9	,	,	PUNCT
ejpam-4556	118	10	a	a	PRON
ejpam-4556	118	11	)	)	PUNCT
ejpam-4556	119	1	+	+	CCONJ
ejpam-4556	119	2	b(a	b(a	NOUN
ejpam-4556	119	3	)	)	PUNCT
ejpam-4556	119	4	−	−	PROPN
ejpam-4556	120	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	120	2	,	,	PUNCT
ejpam-4556	120	3	a	a	X
ejpam-4556	120	4	)	)	PUNCT
ejpam-4556	120	5	−	−	PROPN
ejpam-4556	121	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	121	2	,	,	PUNCT
ejpam-4556	121	3	a	a	PRON
ejpam-4556	121	4	)	)	PUNCT
ejpam-4556	121	5	+	+	CCONJ
ejpam-4556	121	6	ρ14)j1(t	ρ14)j1(t	PROPN
ejpam-4556	121	7	,	,	PUNCT
ejpam-4556	121	8	a	a	PRON
ejpam-4556	121	9	)	)	PUNCT
ejpam-4556	121	10	+	+	X
ejpam-4556	121	11	ρ24j2(t	ρ24j2(t	PROPN
ejpam-4556	121	12	,	,	PUNCT
ejpam-4556	121	13	a	a	PRON
ejpam-4556	121	14	)	)	PUNCT
ejpam-4556	121	15	(	(	PUNCT
ejpam-4556	121	16	∂	∂	NUM
ejpam-4556	121	17	∂t	∂t	PROPN
ejpam-4556	121	18	+	+	SYM
ejpam-4556	121	19	∂	∂	NUM
ejpam-4556	121	20	∂a	∂a	NOUN
ejpam-4556	121	21	)	)	PUNCT
ejpam-4556	122	1	v1(t	v1(t	ADV
ejpam-4556	122	2	,	,	PUNCT
ejpam-4556	122	3	a	a	X
ejpam-4556	122	4	)	)	PUNCT
ejpam-4556	122	5	=	=	SYM
ejpam-4556	122	6	ψ1(a)s1(t	ψ1(a)s1(t	PROPN
ejpam-4556	122	7	,	,	PUNCT
ejpam-4556	122	8	a	a	X
ejpam-4556	122	9	)	)	PUNCT
ejpam-4556	123	1	+	+	SYM
ejpam-4556	123	2	ρ25v2(t	ρ25v2(t	NUM
ejpam-4556	123	3	,	,	PUNCT
ejpam-4556	123	4	a	a	PRON
ejpam-4556	123	5	)	)	PUNCT
ejpam-4556	123	6	−	−	PROPN
ejpam-4556	123	7	(	(	PUNCT
ejpam-4556	123	8	b(a	b(a	X
ejpam-4556	123	9	)	)	PUNCT
ejpam-4556	123	10	+	+	CCONJ
ejpam-4556	123	11	ρ15	ρ15	PROPN
ejpam-4556	123	12	+	+	CCONJ
ejpam-4556	123	13	δ1λ1(t	δ1λ1(t	PROPN
ejpam-4556	123	14	,	,	PUNCT
ejpam-4556	123	15	a	a	PRON
ejpam-4556	123	16	)	)	PUNCT
ejpam-4556	123	17	−	−	NOUN
ejpam-4556	123	18	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	123	19	,	,	PUNCT
ejpam-4556	123	20	a	a	X
ejpam-4556	123	21	)	)	PUNCT
ejpam-4556	123	22	−	−	PROPN
ejpam-4556	123	23	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	123	24	,	,	PUNCT
ejpam-4556	123	25	a))v1(t	a))v1(t	PROPN
ejpam-4556	123	26	,	,	PUNCT
ejpam-4556	123	27	a	a	PRON
ejpam-4556	123	28	)	)	PUNCT
ejpam-4556	123	29	(	(	PUNCT
ejpam-4556	123	30	∂	∂	NUM
ejpam-4556	124	1	∂t	∂t	PROPN
ejpam-4556	124	2	+	+	SYM
ejpam-4556	124	3	∂	∂	NUM
ejpam-4556	124	4	∂a	∂a	NOUN
ejpam-4556	124	5	)	)	PUNCT
ejpam-4556	124	6	s2(t	s2(t	PROPN
ejpam-4556	124	7	,	,	PUNCT
ejpam-4556	124	8	a	a	PRON
ejpam-4556	124	9	)	)	PUNCT
ejpam-4556	124	10	=	=	SYM
ejpam-4556	124	11	α2b2(a	α2b2(a	NOUN
ejpam-4556	124	12	)	)	PUNCT
ejpam-4556	124	13	−	−	PUNCT
ejpam-4556	125	1	[	[	X
ejpam-4556	125	2	λ2(t	λ2(t	X
ejpam-4556	125	3	,	,	PUNCT
ejpam-4556	125	4	a	a	PRON
ejpam-4556	125	5	)	)	PUNCT
ejpam-4556	125	6	+	+	PUNCT
ejpam-4556	125	7	ψ2(a	ψ2(a	X
ejpam-4556	125	8	)	)	PUNCT
ejpam-4556	125	9	+	+	CCONJ
ejpam-4556	125	10	b(a	b(a	NOUN
ejpam-4556	125	11	)	)	PUNCT
ejpam-4556	125	12	−	−	PROPN
ejpam-4556	125	13	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	125	14	,	,	PUNCT
ejpam-4556	125	15	a	a	X
ejpam-4556	125	16	)	)	PUNCT
ejpam-4556	125	17	−	−	PROPN
ejpam-4556	126	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	126	2	,	,	PUNCT
ejpam-4556	126	3	a	a	PRON
ejpam-4556	126	4	)	)	PUNCT
ejpam-4556	126	5	+	+	NOUN
ejpam-4556	126	6	ρ21]s2(t	ρ21]s2(t	NOUN
ejpam-4556	126	7	,	,	PUNCT
ejpam-4556	126	8	a	a	PRON
ejpam-4556	126	9	)	)	PUNCT
ejpam-4556	126	10	+	+	NUM
ejpam-4556	126	11	ρ11s1(t	ρ11s1(t	NUM
ejpam-4556	126	12	,	,	PUNCT
ejpam-4556	126	13	a	a	X
ejpam-4556	126	14	)	)	PUNCT
ejpam-4556	126	15	(	(	PUNCT
ejpam-4556	126	16	∂	∂	NUM
ejpam-4556	126	17	∂t	∂t	PROPN
ejpam-4556	126	18	+	+	SYM
ejpam-4556	126	19	∂	∂	NUM
ejpam-4556	126	20	∂a	∂a	NOUN
ejpam-4556	126	21	)	)	PUNCT
ejpam-4556	126	22	l2(t	l2(t	PROPN
ejpam-4556	126	23	,	,	PUNCT
ejpam-4556	126	24	a	a	PRON
ejpam-4556	126	25	)	)	PUNCT
ejpam-4556	126	26	=	=	SYM
ejpam-4556	126	27	λ2(t	λ2(t	PROPN
ejpam-4556	126	28	,	,	PUNCT
ejpam-4556	126	29	a)[(1	a)[(1	PROPN
ejpam-4556	126	30	−	−	PROPN
ejpam-4556	126	31	ϕ2)s2(t	ϕ2)s2(t	PROPN
ejpam-4556	126	32	,	,	PUNCT
ejpam-4556	126	33	a	a	PRON
ejpam-4556	126	34	)	)	PUNCT
ejpam-4556	126	35	+	+	CCONJ
ejpam-4556	126	36	σ2j2(t	σ2j2(t	PROPN
ejpam-4556	126	37	,	,	PUNCT
ejpam-4556	126	38	a	a	PRON
ejpam-4556	126	39	)	)	PUNCT
ejpam-4556	126	40	+	+	CCONJ
ejpam-4556	126	41	δ2v2(t	δ2v2(t	NOUN
ejpam-4556	126	42	,	,	PUNCT
ejpam-4556	126	43	a	a	PRON
ejpam-4556	126	44	)	)	PUNCT
ejpam-4556	126	45	)	)	PUNCT
ejpam-4556	126	46	−(k2	−(k2	NOUN
ejpam-4556	126	47	+	+	CCONJ
ejpam-4556	126	48	b(a	b(a	NOUN
ejpam-4556	126	49	)	)	PUNCT
ejpam-4556	126	50	−	−	PROPN
ejpam-4556	126	51	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	126	52	,	,	PUNCT
ejpam-4556	126	53	a	a	X
ejpam-4556	126	54	)	)	PUNCT
ejpam-4556	126	55	−	−	PROPN
ejpam-4556	127	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	127	2	,	,	PUNCT
ejpam-4556	127	3	a	a	PRON
ejpam-4556	127	4	)	)	PUNCT
ejpam-4556	127	5	+	+	CCONJ
ejpam-4556	127	6	ρ22)l2(t	ρ22)l2(t	NOUN
ejpam-4556	127	7	,	,	PUNCT
ejpam-4556	127	8	a	a	PRON
ejpam-4556	127	9	)	)	PUNCT
ejpam-4556	127	10	+	+	CCONJ
ejpam-4556	127	11	ρ12l1(t	ρ12l1(t	NUM
ejpam-4556	127	12	,	,	PUNCT
ejpam-4556	127	13	a	a	X
ejpam-4556	127	14	)	)	PUNCT
ejpam-4556	127	15	(	(	PUNCT
ejpam-4556	127	16	∂	∂	NUM
ejpam-4556	127	17	∂t	∂t	PROPN
ejpam-4556	127	18	+	+	SYM
ejpam-4556	127	19	∂	∂	NUM
ejpam-4556	127	20	∂a	∂a	NOUN
ejpam-4556	127	21	)	)	PUNCT
ejpam-4556	128	1	i2(t	i2(t	PROPN
ejpam-4556	128	2	,	,	PUNCT
ejpam-4556	128	3	a	a	PRON
ejpam-4556	128	4	)	)	PUNCT
ejpam-4556	128	5	=	=	SYM
ejpam-4556	128	6	−(r2	−(r2	NOUN
ejpam-4556	128	7	+	+	NOUN
ejpam-4556	128	8	µ2(a	µ2(a	NOUN
ejpam-4556	128	9	)	)	PUNCT
ejpam-4556	128	10	+	+	CCONJ
ejpam-4556	128	11	b(a	b(a	NOUN
ejpam-4556	128	12	)	)	PUNCT
ejpam-4556	128	13	−	−	PROPN
ejpam-4556	129	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	129	2	,	,	PUNCT
ejpam-4556	129	3	a	a	X
ejpam-4556	129	4	)	)	PUNCT
ejpam-4556	129	5	−	−	PROPN
ejpam-4556	130	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	130	2	,	,	PUNCT
ejpam-4556	130	3	a	a	PRON
ejpam-4556	130	4	)	)	PUNCT
ejpam-4556	130	5	+	+	CCONJ
ejpam-4556	130	6	ρ23)i2(t	ρ23)i2(t	PROPN
ejpam-4556	130	7	,	,	PUNCT
ejpam-4556	130	8	a	a	PRON
ejpam-4556	130	9	)	)	PUNCT
ejpam-4556	131	1	+	+	CCONJ
ejpam-4556	131	2	ρ13i1(t	ρ13i1(t	NUM
ejpam-4556	131	3	,	,	PUNCT
ejpam-4556	131	4	a	a	PRON
ejpam-4556	131	5	)	)	PUNCT
ejpam-4556	132	1	+	+	NOUN
ejpam-4556	132	2	ϕ2λ2(t	ϕ2λ2(t	NOUN
ejpam-4556	132	3	,	,	PUNCT
ejpam-4556	132	4	a)s2(t	a)s2(t	PROPN
ejpam-4556	132	5	,	,	PUNCT
ejpam-4556	132	6	a	a	PRON
ejpam-4556	132	7	)	)	PUNCT
ejpam-4556	132	8	+	+	CCONJ
ejpam-4556	132	9	k2l2(t	k2l2(t	PROPN
ejpam-4556	132	10	,	,	PUNCT
ejpam-4556	132	11	a	a	NOUN
ejpam-4556	132	12	)	)	PUNCT
ejpam-4556	132	13	(	(	PUNCT
ejpam-4556	132	14	∂	∂	NUM
ejpam-4556	132	15	∂t	∂t	PROPN
ejpam-4556	132	16	+	+	SYM
ejpam-4556	132	17	∂	∂	NUM
ejpam-4556	132	18	∂a	∂a	NOUN
ejpam-4556	132	19	)	)	PUNCT
ejpam-4556	132	20	j2(t	j2(t	PROPN
ejpam-4556	132	21	,	,	PUNCT
ejpam-4556	132	22	a	a	PRON
ejpam-4556	132	23	)	)	PUNCT
ejpam-4556	132	24	=	=	SYM
ejpam-4556	132	25	r2i2(t	r2i2(t	NOUN
ejpam-4556	132	26	,	,	PUNCT
ejpam-4556	132	27	a	a	PRON
ejpam-4556	132	28	)	)	PUNCT
ejpam-4556	132	29	−	−	PROPN
ejpam-4556	132	30	(	(	PUNCT
ejpam-4556	132	31	σ2λ2(t	σ2λ2(t	PROPN
ejpam-4556	132	32	,	,	PUNCT
ejpam-4556	132	33	a	a	PRON
ejpam-4556	132	34	)	)	PUNCT
ejpam-4556	132	35	+	+	CCONJ
ejpam-4556	132	36	b(a	b(a	NOUN
ejpam-4556	132	37	)	)	PUNCT
ejpam-4556	132	38	−	−	PROPN
ejpam-4556	132	39	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	132	40	,	,	PUNCT
ejpam-4556	132	41	a	a	X
ejpam-4556	132	42	)	)	PUNCT
ejpam-4556	133	1	−	−	PROPN
ejpam-4556	133	2	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	133	3	,	,	PUNCT
ejpam-4556	133	4	a	a	PRON
ejpam-4556	133	5	)	)	PUNCT
ejpam-4556	134	1	+	+	CCONJ
ejpam-4556	134	2	ρ24)j2(t	ρ24)j2(t	PROPN
ejpam-4556	134	3	,	,	PUNCT
ejpam-4556	134	4	a	a	PRON
ejpam-4556	134	5	)	)	PUNCT
ejpam-4556	134	6	+	+	CCONJ
ejpam-4556	134	7	ρ14j1(t	ρ14j1(t	NUM
ejpam-4556	134	8	,	,	PUNCT
ejpam-4556	134	9	a	a	X
ejpam-4556	134	10	)	)	PUNCT
ejpam-4556	134	11	(	(	PUNCT
ejpam-4556	134	12	∂	∂	NUM
ejpam-4556	135	1	∂t	∂t	PROPN
ejpam-4556	135	2	+	+	SYM
ejpam-4556	135	3	∂	∂	NUM
ejpam-4556	135	4	∂a	∂a	NOUN
ejpam-4556	135	5	)	)	PUNCT
ejpam-4556	135	6	v2(t	v2(t	PROPN
ejpam-4556	135	7	,	,	PUNCT
ejpam-4556	135	8	a	a	PRON
ejpam-4556	135	9	)	)	PUNCT
ejpam-4556	135	10	=	=	SYM
ejpam-4556	135	11	ψ2(a)s2(t	ψ2(a)s2(t	PROPN
ejpam-4556	135	12	,	,	PUNCT
ejpam-4556	135	13	a	a	PRON
ejpam-4556	135	14	)	)	PUNCT
ejpam-4556	135	15	+	+	NUM
ejpam-4556	135	16	ρ15v1(t	ρ15v1(t	NOUN
ejpam-4556	135	17	,	,	PUNCT
ejpam-4556	135	18	a	a	PRON
ejpam-4556	135	19	)	)	PUNCT
ejpam-4556	135	20	−	−	PROPN
ejpam-4556	135	21	(	(	PUNCT
ejpam-4556	135	22	b(a	b(a	X
ejpam-4556	135	23	)	)	PUNCT
ejpam-4556	135	24	+	+	CCONJ
ejpam-4556	135	25	ρ25	ρ25	ADJ
ejpam-4556	135	26	+	+	CCONJ
ejpam-4556	135	27	δ2λ2(t	δ2λ2(t	PROPN
ejpam-4556	135	28	,	,	PUNCT
ejpam-4556	135	29	a	a	PRON
ejpam-4556	135	30	)	)	PUNCT
ejpam-4556	135	31	−	−	NOUN
ejpam-4556	135	32	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	135	33	,	,	PUNCT
ejpam-4556	135	34	a	a	X
ejpam-4556	135	35	)	)	PUNCT
ejpam-4556	135	36	−	−	PROPN
ejpam-4556	136	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	136	2	,	,	PUNCT
ejpam-4556	136	3	a))v2(t	a))v2(t	PROPN
ejpam-4556	136	4	,	,	PUNCT
ejpam-4556	136	5	a	a	PRON
ejpam-4556	136	6	)	)	PUNCT
ejpam-4556	136	7	(	(	PUNCT
ejpam-4556	136	8	5	5	NUM
ejpam-4556	136	9	)	)	PUNCT
ejpam-4556	136	10	with	with	ADP
ejpam-4556	136	11	boundary	boundary	ADJ
ejpam-4556	136	12	conditions	condition	NOUN
ejpam-4556	136	13	si(t	si(t	VERB
ejpam-4556	136	14	,	,	PUNCT
ejpam-4556	136	15	0	0	NUM
ejpam-4556	136	16	)	)	PUNCT
ejpam-4556	136	17	=	=	SYM
ejpam-4556	136	18	λi	λi	NOUN
ejpam-4556	136	19	;	;	PUNCT
ejpam-4556	136	20	vi(t	vi(t	NUM
ejpam-4556	136	21	,	,	PUNCT
ejpam-4556	136	22	0	0	NUM
ejpam-4556	136	23	)	)	PUNCT
ejpam-4556	136	24	=	=	SYM
ejpam-4556	136	25	li(t	li(t	NOUN
ejpam-4556	136	26	,	,	PUNCT
ejpam-4556	136	27	0	0	NUM
ejpam-4556	136	28	)	)	PUNCT
ejpam-4556	136	29	=	=	NOUN
ejpam-4556	136	30	ii(t	ii(t	NOUN
ejpam-4556	136	31	,	,	PUNCT
ejpam-4556	136	32	0	0	NUM
ejpam-4556	136	33	)	)	PUNCT
ejpam-4556	136	34	=	=	SYM
ejpam-4556	136	35	ji(t	ji(t	NOUN
ejpam-4556	136	36	,	,	PUNCT
ejpam-4556	136	37	0	0	NUM
ejpam-4556	136	38	)	)	PUNCT
ejpam-4556	136	39	=	=	SYM
ejpam-4556	136	40	0	0	PUNCT
ejpam-4556	137	1	with	with	ADP
ejpam-4556	137	2	λ1	λ1	PROPN
ejpam-4556	137	3	+	+	CCONJ
ejpam-4556	137	4	λ2	λ2	NOUN
ejpam-4556	137	5	=	=	SYM
ejpam-4556	137	6	1	1	X
ejpam-4556	137	7	.	.	PUNCT
ejpam-4556	138	1	the	the	DET
ejpam-4556	138	2	problem	problem	NOUN
ejpam-4556	138	3	is	be	AUX
ejpam-4556	138	4	well	well	ADV
ejpam-4556	138	5	possed	posse	VERB
ejpam-4556	138	6	,	,	PUNCT
ejpam-4556	138	7	the	the	DET
ejpam-4556	138	8	methode	methode	NOUN
ejpam-4556	138	9	of	of	ADP
ejpam-4556	138	10	proof	proof	NOUN
ejpam-4556	138	11	is	be	AUX
ejpam-4556	138	12	the	the	DET
ejpam-4556	138	13	same	same	ADJ
ejpam-4556	138	14	used	use	VERB
ejpam-4556	138	15	in	in	ADP
ejpam-4556	138	16	[	[	X
ejpam-4556	138	17	3	3	NUM
ejpam-4556	138	18	]	]	PUNCT
ejpam-4556	138	19	.	.	PUNCT
ejpam-4556	139	1	b.	b.	PROPN
ejpam-4556	139	2	k.	k.	PROPN
ejpam-4556	139	3	abdoul	abdoul	PROPN
ejpam-4556	139	4	wahid	wahid	PROPN
ejpam-4556	139	5	,	,	PUNCT
ejpam-4556	139	6	d.moustapha	d.moustapha	PROPN
ejpam-4556	139	7	,	,	PUNCT
ejpam-4556	139	8	s.	s.	PROPN
ejpam-4556	139	9	bisso	bisso	PROPN
ejpam-4556	139	10	/	/	SYM
ejpam-4556	139	11	eur	eur	PROPN
ejpam-4556	139	12	.	.	PUNCT
ejpam-4556	140	1	j.	j.	PROPN
ejpam-4556	140	2	pure	pure	PROPN
ejpam-4556	140	3	appl	appl	PROPN
ejpam-4556	140	4	.	.	PROPN
ejpam-4556	140	5	math	math	PROPN
ejpam-4556	140	6	,	,	PUNCT
ejpam-4556	140	7	15	15	NUM
ejpam-4556	140	8	(	(	PUNCT
ejpam-4556	140	9	4	4	NUM
ejpam-4556	140	10	)	)	PUNCT
ejpam-4556	140	11	(	(	PUNCT
ejpam-4556	140	12	2022	2022	NUM
ejpam-4556	140	13	)	)	PUNCT
ejpam-4556	140	14	,	,	PUNCT
ejpam-4556	140	15	2054	2054	NUM
ejpam-4556	140	16	-	-	SYM
ejpam-4556	140	17	2073	2073	NUM
ejpam-4556	140	18	2059	2059	NUM
ejpam-4556	140	19	3	3	NUM
ejpam-4556	140	20	.	.	PUNCT
ejpam-4556	141	1	existence	existence	NOUN
ejpam-4556	141	2	of	of	ADP
ejpam-4556	141	3	positive	positive	ADJ
ejpam-4556	141	4	solutions	solution	NOUN
ejpam-4556	141	5	in	in	ADP
ejpam-4556	141	6	this	this	DET
ejpam-4556	141	7	section	section	NOUN
ejpam-4556	141	8	we	we	PRON
ejpam-4556	141	9	will	will	AUX
ejpam-4556	141	10	prove	prove	VERB
ejpam-4556	141	11	that	that	SCONJ
ejpam-4556	141	12	the	the	DET
ejpam-4556	141	13	system	system	NOUN
ejpam-4556	141	14	(	(	PUNCT
ejpam-4556	141	15	5	5	NUM
ejpam-4556	141	16	)	)	PUNCT
ejpam-4556	141	17	has	have	VERB
ejpam-4556	141	18	a	a	DET
ejpam-4556	141	19	unique	unique	ADJ
ejpam-4556	141	20	positive	positive	ADJ
ejpam-4556	141	21	solution	solution	NOUN
ejpam-4556	141	22	,	,	PUNCT
ejpam-4556	141	23	and	and	CCONJ
ejpam-4556	141	24	to	to	PART
ejpam-4556	141	25	achieve	achieve	VERB
ejpam-4556	141	26	this	this	PRON
ejpam-4556	141	27	we	we	PRON
ejpam-4556	141	28	will	will	AUX
ejpam-4556	141	29	write	write	VERB
ejpam-4556	141	30	the	the	DET
ejpam-4556	141	31	system	system	NOUN
ejpam-4556	141	32	(	(	PUNCT
ejpam-4556	141	33	5	5	NUM
ejpam-4556	141	34	)	)	PUNCT
ejpam-4556	141	35	in	in	ADP
ejpam-4556	141	36	compact	compact	ADJ
ejpam-4556	141	37	form	form	NOUN
ejpam-4556	141	38	(	(	PUNCT
ejpam-4556	141	39	abstract	abstract	ADJ
ejpam-4556	141	40	cauchy	cauchy	ADJ
ejpam-4556	141	41	problem	problem	NOUN
ejpam-4556	141	42	)	)	PUNCT
ejpam-4556	141	43	.	.	PUNCT
ejpam-4556	142	1	consider	consider	VERB
ejpam-4556	142	2	the	the	DET
ejpam-4556	142	3	banach	banach	NOUN
ejpam-4556	142	4	space	space	NOUN
ejpam-4556	142	5	x	x	PUNCT
ejpam-4556	142	6	defined	define	VERB
ejpam-4556	142	7	by	by	ADP
ejpam-4556	142	8	x	x	X
ejpam-4556	142	9	=	=	SYM
ejpam-4556	142	10	(	(	PUNCT
ejpam-4556	142	11	l1(0	l1(0	PROPN
ejpam-4556	142	12	,	,	PUNCT
ejpam-4556	142	13	a+	a+	ADJ
ejpam-4556	142	14	)	)	PUNCT
ejpam-4556	142	15	)	)	PUNCT
ejpam-4556	142	16	10	10	NUM
ejpam-4556	142	17	,	,	PUNCT
ejpam-4556	142	18	endowed	endow	VERB
ejpam-4556	142	19	with	with	ADP
ejpam-4556	142	20	the	the	DET
ejpam-4556	142	21	norm	norm	NOUN
ejpam-4556	142	22	∥φ∥	∥φ∥	NOUN
ejpam-4556	143	1	=	=	PUNCT
ejpam-4556	143	2	2∑	2∑	NUM
ejpam-4556	143	3	i=1	i=1	PRON
ejpam-4556	143	4	5∑	5∑	ADJ
ejpam-4556	143	5	j=1	j=1	ADJ
ejpam-4556	143	6	∥φij∥	∥φij∥	PROPN
ejpam-4556	143	7	(	(	PUNCT
ejpam-4556	143	8	6	6	NUM
ejpam-4556	143	9	)	)	PUNCT
ejpam-4556	143	10	where	where	SCONJ
ejpam-4556	143	11	φ(a	φ(a	ADJ
ejpam-4556	143	12	)	)	PUNCT
ejpam-4556	143	13	=	=	SYM
ejpam-4556	143	14	(	(	PUNCT
ejpam-4556	143	15	φ11(a	φ11(a	NOUN
ejpam-4556	143	16	)	)	PUNCT
ejpam-4556	143	17	,	,	PUNCT
ejpam-4556	143	18	φ12(a	φ12(a	NOUN
ejpam-4556	143	19	)	)	PUNCT
ejpam-4556	143	20	,	,	PUNCT
ejpam-4556	143	21	φ13(a	φ13(a	ADJ
ejpam-4556	143	22	)	)	PUNCT
ejpam-4556	143	23	,	,	PUNCT
ejpam-4556	143	24	φ14(a	φ14(a	NUM
ejpam-4556	143	25	)	)	PUNCT
ejpam-4556	143	26	,	,	PUNCT
ejpam-4556	143	27	φ15(a	φ15(a	NOUN
ejpam-4556	143	28	)	)	PUNCT
ejpam-4556	143	29	,	,	PUNCT
ejpam-4556	143	30	φ21(a	φ21(a	NOUN
ejpam-4556	143	31	)	)	PUNCT
ejpam-4556	143	32	,	,	PUNCT
ejpam-4556	143	33	φ22(a	φ22(a	NOUN
ejpam-4556	143	34	)	)	PUNCT
ejpam-4556	143	35	,	,	PUNCT
ejpam-4556	143	36	φ23(a	φ23(a	NUM
ejpam-4556	143	37	)	)	PUNCT
ejpam-4556	143	38	,	,	PUNCT
ejpam-4556	143	39	φ24(a	φ24(a	ADJ
ejpam-4556	143	40	)	)	PUNCT
ejpam-4556	143	41	,	,	PUNCT
ejpam-4556	143	42	φ25(a	φ25(a	NOUN
ejpam-4556	143	43	)	)	PUNCT
ejpam-4556	143	44	)	)	PUNCT
ejpam-4556	143	45	t	t	PROPN
ejpam-4556	143	46	∈	∈	PROPN
ejpam-4556	143	47	x	x	X
ejpam-4556	143	48	and	and	CCONJ
ejpam-4556	143	49	∥.∥	∥.∥	NUM
ejpam-4556	143	50	is	be	AUX
ejpam-4556	143	51	the	the	DET
ejpam-4556	143	52	norm	norm	NOUN
ejpam-4556	143	53	of	of	ADP
ejpam-4556	143	54	l1(0	l1(0	PROPN
ejpam-4556	143	55	,	,	PUNCT
ejpam-4556	143	56	a+	a+	NOUN
ejpam-4556	143	57	)	)	PUNCT
ejpam-4556	143	58	.	.	PUNCT
ejpam-4556	144	1	let	let	AUX
ejpam-4556	144	2	denote	denote	VERB
ejpam-4556	144	3	by	by	ADP
ejpam-4556	144	4	ω	ω	PROPN
ejpam-4556	144	5	=	=	SYM
ejpam-4556	144	6	{	{	PUNCT
ejpam-4556	144	7	(	(	PUNCT
ejpam-4556	144	8	s1	s1	NOUN
ejpam-4556	144	9	,	,	PUNCT
ejpam-4556	144	10	l1	l1	PROPN
ejpam-4556	144	11	,	,	PUNCT
ejpam-4556	144	12	i1	i1	PROPN
ejpam-4556	144	13	,	,	PUNCT
ejpam-4556	144	14	j1	j1	PROPN
ejpam-4556	144	15	,	,	PUNCT
ejpam-4556	144	16	v1	v1	NOUN
ejpam-4556	144	17	,	,	PUNCT
ejpam-4556	144	18	s2	s2	NOUN
ejpam-4556	144	19	,	,	PUNCT
ejpam-4556	144	20	l2	l2	NOUN
ejpam-4556	144	21	,	,	PUNCT
ejpam-4556	144	22	i2	i2	PROPN
ejpam-4556	144	23	,	,	PUNCT
ejpam-4556	144	24	j2	j2	PROPN
ejpam-4556	144	25	,	,	PUNCT
ejpam-4556	144	26	v2	v2	PROPN
ejpam-4556	144	27	)	)	PUNCT
ejpam-4556	144	28	∈	∈	NOUN
ejpam-4556	144	29	x+\0	x+\0	NOUN
ejpam-4556	144	30	≤	≤	NOUN
ejpam-4556	144	31	s1	s1	NOUN
ejpam-4556	144	32	+	+	CCONJ
ejpam-4556	144	33	l1	l1	PROPN
ejpam-4556	144	34	+	+	CCONJ
ejpam-4556	144	35	i1	i1	PROPN
ejpam-4556	144	36	+	+	CCONJ
ejpam-4556	144	37	j1	j1	PROPN
ejpam-4556	144	38	,	,	PUNCT
ejpam-4556	144	39	v1	v1	NOUN
ejpam-4556	144	40	+	+	CCONJ
ejpam-4556	144	41	s2	s2	NOUN
ejpam-4556	144	42	+	+	CCONJ
ejpam-4556	144	43	l2	l2	NOUN
ejpam-4556	144	44	+	+	CCONJ
ejpam-4556	144	45	i2	i2	PROPN
ejpam-4556	144	46	+	+	CCONJ
ejpam-4556	144	47	j2	j2	NOUN
ejpam-4556	144	48	+	+	CCONJ
ejpam-4556	144	49	v2	v2	X
ejpam-4556	144	50	≤	≤	NOUN
ejpam-4556	144	51	1	1	NUM
ejpam-4556	144	52	}	}	PUNCT
ejpam-4556	144	53	(	(	PUNCT
ejpam-4556	144	54	7	7	X
ejpam-4556	144	55	)	)	PUNCT
ejpam-4556	144	56	the	the	DET
ejpam-4556	144	57	state	state	NOUN
ejpam-4556	144	58	space	space	NOUN
ejpam-4556	144	59	of	of	ADP
ejpam-4556	144	60	system	system	NOUN
ejpam-4556	144	61	(	(	PUNCT
ejpam-4556	144	62	5	5	NUM
ejpam-4556	144	63	)	)	PUNCT
ejpam-4556	144	64	.	.	PUNCT
ejpam-4556	145	1	where	where	SCONJ
ejpam-4556	145	2	x+	x+	ADJ
ejpam-4556	145	3	=	=	SYM
ejpam-4556	145	4	(	(	PUNCT
ejpam-4556	145	5	l1	l1	PROPN
ejpam-4556	145	6	+	+	PROPN
ejpam-4556	145	7	(	(	PUNCT
ejpam-4556	145	8	0	0	NUM
ejpam-4556	145	9	,	,	PUNCT
ejpam-4556	145	10	a+	a+	NOUN
ejpam-4556	145	11	)	)	PUNCT
ejpam-4556	145	12	)	)	PUNCT
ejpam-4556	145	13	10	10	NUM
ejpam-4556	145	14	,	,	PUNCT
ejpam-4556	145	15	et	et	PROPN
ejpam-4556	145	16	l1	l1	PROPN
ejpam-4556	145	17	+	+	PROPN
ejpam-4556	145	18	(	(	PUNCT
ejpam-4556	145	19	0	0	NUM
ejpam-4556	145	20	,	,	PUNCT
ejpam-4556	145	21	a+	a+	NOUN
ejpam-4556	145	22	)	)	PUNCT
ejpam-4556	145	23	denotes	denote	VERB
ejpam-4556	145	24	the	the	DET
ejpam-4556	145	25	positive	positive	ADJ
ejpam-4556	145	26	cone	cone	NOUN
ejpam-4556	145	27	of	of	ADP
ejpam-4556	145	28	l1(0	l1(0	PROPN
ejpam-4556	145	29	,	,	PUNCT
ejpam-4556	145	30	a+	a+	NOUN
ejpam-4556	145	31	)	)	PUNCT
ejpam-4556	145	32	.	.	PUNCT
ejpam-4556	146	1	let	let	VERB
ejpam-4556	146	2	a	a	PRON
ejpam-4556	146	3	be	be	AUX
ejpam-4556	146	4	a	a	DET
ejpam-4556	146	5	linear	linear	ADJ
ejpam-4556	146	6	operator	operator	NOUN
ejpam-4556	146	7	defined	define	VERB
ejpam-4556	146	8	by	by	ADP
ejpam-4556	146	9	(	(	PUNCT
ejpam-4556	146	10	aφ)(a	aφ)(a	PROPN
ejpam-4556	146	11	)	)	PUNCT
ejpam-4556	147	1	=	=	PRON
ejpam-4556	147	2	(	(	PUNCT
ejpam-4556	147	3	a11	a11	PROPN
ejpam-4556	147	4	,	,	PUNCT
ejpam-4556	147	5	a12	a12	PROPN
ejpam-4556	147	6	,	,	PUNCT
ejpam-4556	147	7	a13	a13	PROPN
ejpam-4556	147	8	,	,	PUNCT
ejpam-4556	147	9	a14	a14	PROPN
ejpam-4556	147	10	,	,	PUNCT
ejpam-4556	147	11	a15	a15	NOUN
ejpam-4556	147	12	,	,	PUNCT
ejpam-4556	147	13	a21	a21	PROPN
ejpam-4556	147	14	,	,	PUNCT
ejpam-4556	147	15	a22	a22	PROPN
ejpam-4556	147	16	,	,	PUNCT
ejpam-4556	147	17	a23	a23	PROPN
ejpam-4556	147	18	,	,	PUNCT
ejpam-4556	147	19	a24	a24	PROPN
ejpam-4556	147	20	,	,	PUNCT
ejpam-4556	147	21	a25	a25	PROPN
ejpam-4556	147	22	)	)	PUNCT
ejpam-4556	147	23	t	t	PROPN
ejpam-4556	147	24	(	(	PUNCT
ejpam-4556	147	25	8)	8)	NUM
ejpam-4556	147	26			NUM
ejpam-4556	147	27	a11	a11	NOUN
ejpam-4556	147	28	=	=	SYM
ejpam-4556	147	29	(	(	PUNCT
ejpam-4556	147	30	−	−	PROPN
ejpam-4556	147	31	d	d	X
ejpam-4556	147	32	daφ11	daφ11	NOUN
ejpam-4556	147	33	−	−	PROPN
ejpam-4556	147	34	(	(	PUNCT
ejpam-4556	147	35	ψ1(a	ψ1(a	NOUN
ejpam-4556	147	36	)	)	PUNCT
ejpam-4556	148	1	+	+	CCONJ
ejpam-4556	148	2	b(a	b(a	NOUN
ejpam-4556	148	3	)	)	PUNCT
ejpam-4556	148	4	+	+	CCONJ
ejpam-4556	148	5	ρ11)φ11	ρ11)φ11	NUM
ejpam-4556	148	6	,	,	PUNCT
ejpam-4556	148	7	0	0	NUM
ejpam-4556	148	8	,	,	PUNCT
ejpam-4556	148	9	0	0	NUM
ejpam-4556	148	10	,	,	PUNCT
ejpam-4556	148	11	0	0	NUM
ejpam-4556	148	12	,	,	PUNCT
ejpam-4556	148	13	0	0	NUM
ejpam-4556	148	14	,	,	PUNCT
ejpam-4556	148	15	ρ21φ21	ρ21φ21	NOUN
ejpam-4556	148	16	,	,	PUNCT
ejpam-4556	148	17	0	0	NUM
ejpam-4556	148	18	,	,	PUNCT
ejpam-4556	148	19	0	0	NUM
ejpam-4556	148	20	,	,	PUNCT
ejpam-4556	148	21	0	0	NUM
ejpam-4556	148	22	,	,	PUNCT
ejpam-4556	148	23	0	0	NUM
ejpam-4556	148	24	)	)	PUNCT
ejpam-4556	148	25	a12	a12	NOUN
ejpam-4556	148	26	=	=	SYM
ejpam-4556	148	27	(	(	PUNCT
ejpam-4556	148	28	0,−	0,−	NUM
ejpam-4556	148	29	d	d	X
ejpam-4556	148	30	daφ12	daφ12	PROPN
ejpam-4556	148	31	−	−	PROPN
ejpam-4556	148	32	(	(	PUNCT
ejpam-4556	148	33	b(a	b(a	X
ejpam-4556	148	34	)	)	PUNCT
ejpam-4556	148	35	+	+	CCONJ
ejpam-4556	148	36	k1	k1	NOUN
ejpam-4556	148	37	+	+	CCONJ
ejpam-4556	148	38	ρ12)φ12	ρ12)φ12	NUM
ejpam-4556	148	39	,	,	PUNCT
ejpam-4556	148	40	0	0	NUM
ejpam-4556	148	41	,	,	PUNCT
ejpam-4556	148	42	0	0	NUM
ejpam-4556	148	43	,	,	PUNCT
ejpam-4556	148	44	0	0	NUM
ejpam-4556	148	45	,	,	PUNCT
ejpam-4556	148	46	0	0	NUM
ejpam-4556	148	47	,	,	PUNCT
ejpam-4556	148	48	ρ22φ22	ρ22φ22	NUM
ejpam-4556	148	49	,	,	PUNCT
ejpam-4556	148	50	0	0	NUM
ejpam-4556	148	51	,	,	PUNCT
ejpam-4556	148	52	0	0	NUM
ejpam-4556	148	53	,	,	PUNCT
ejpam-4556	148	54	0	0	NUM
ejpam-4556	148	55	)	)	PUNCT
ejpam-4556	148	56	a13	a13	NOUN
ejpam-4556	148	57	=	=	SYM
ejpam-4556	148	58	(	(	PUNCT
ejpam-4556	148	59	0	0	NUM
ejpam-4556	148	60	,	,	PUNCT
ejpam-4556	148	61	k1φ12,−	k1φ12,−	PROPN
ejpam-4556	148	62	d	d	X
ejpam-4556	148	63	daφ13	daφ13	NOUN
ejpam-4556	148	64	−	−	PROPN
ejpam-4556	148	65	(	(	PUNCT
ejpam-4556	148	66	r1	r1	NOUN
ejpam-4556	148	67	+	+	CCONJ
ejpam-4556	148	68	µ1(a	µ1(a	NOUN
ejpam-4556	148	69	)	)	PUNCT
ejpam-4556	149	1	+	+	CCONJ
ejpam-4556	149	2	b(a	b(a	NOUN
ejpam-4556	149	3	)	)	PUNCT
ejpam-4556	150	1	+	+	CCONJ
ejpam-4556	150	2	ρ13)φ13	ρ13)φ13	NUM
ejpam-4556	150	3	,	,	PUNCT
ejpam-4556	150	4	0	0	NUM
ejpam-4556	150	5	,	,	PUNCT
ejpam-4556	150	6	0	0	NUM
ejpam-4556	150	7	,	,	PUNCT
ejpam-4556	150	8	0	0	NUM
ejpam-4556	150	9	,	,	PUNCT
ejpam-4556	150	10	0	0	NUM
ejpam-4556	150	11	,	,	PUNCT
ejpam-4556	150	12	ρ23φ23	ρ23φ23	PROPN
ejpam-4556	150	13	,	,	PUNCT
ejpam-4556	150	14	0	0	NUM
ejpam-4556	150	15	,	,	PUNCT
ejpam-4556	150	16	0	0	NUM
ejpam-4556	150	17	)	)	PUNCT
ejpam-4556	150	18	a14	a14	NOUN
ejpam-4556	150	19	=	=	SYM
ejpam-4556	150	20	(	(	PUNCT
ejpam-4556	150	21	0	0	NUM
ejpam-4556	150	22	,	,	PUNCT
ejpam-4556	150	23	0	0	NUM
ejpam-4556	150	24	,	,	PUNCT
ejpam-4556	151	1	r1φ13,−	r1φ13,−	ADJ
ejpam-4556	151	2	d	d	X
ejpam-4556	151	3	daφ14	daφ14	PROPN
ejpam-4556	151	4	−	−	PROPN
ejpam-4556	151	5	(	(	PUNCT
ejpam-4556	151	6	b(a	b(a	X
ejpam-4556	151	7	)	)	PUNCT
ejpam-4556	151	8	+	+	CCONJ
ejpam-4556	151	9	ρ14)φ14	ρ14)φ14	NUM
ejpam-4556	151	10	,	,	PUNCT
ejpam-4556	151	11	0	0	NUM
ejpam-4556	151	12	,	,	PUNCT
ejpam-4556	151	13	0	0	NUM
ejpam-4556	151	14	,	,	PUNCT
ejpam-4556	151	15	0	0	NUM
ejpam-4556	151	16	,	,	PUNCT
ejpam-4556	151	17	0	0	NUM
ejpam-4556	151	18	,	,	PUNCT
ejpam-4556	151	19	ρ24φ24	ρ24φ24	PROPN
ejpam-4556	151	20	,	,	PUNCT
ejpam-4556	151	21	0	0	NUM
ejpam-4556	151	22	)	)	PUNCT
ejpam-4556	151	23	a15	a15	NOUN
ejpam-4556	151	24	=	=	SYM
ejpam-4556	151	25	(	(	PUNCT
ejpam-4556	151	26	ψ1(a)φ11	ψ1(a)φ11	NOUN
ejpam-4556	151	27	,	,	PUNCT
ejpam-4556	151	28	0	0	NUM
ejpam-4556	151	29	,	,	PUNCT
ejpam-4556	151	30	0	0	NUM
ejpam-4556	151	31	,	,	PUNCT
ejpam-4556	151	32	0,−	0,−	NUM
ejpam-4556	151	33	d	d	PROPN
ejpam-4556	151	34	daφ15	daφ15	PROPN
ejpam-4556	151	35	−	−	PROPN
ejpam-4556	151	36	(	(	PUNCT
ejpam-4556	151	37	ρ15	ρ15	PROPN
ejpam-4556	151	38	+	+	CCONJ
ejpam-4556	151	39	b(a))φ15	b(a))φ15	ADJ
ejpam-4556	151	40	,	,	PUNCT
ejpam-4556	151	41	0	0	NUM
ejpam-4556	151	42	,	,	PUNCT
ejpam-4556	151	43	0	0	NUM
ejpam-4556	151	44	,	,	PUNCT
ejpam-4556	151	45	0	0	NUM
ejpam-4556	151	46	,	,	PUNCT
ejpam-4556	151	47	0	0	NUM
ejpam-4556	151	48	,	,	PUNCT
ejpam-4556	151	49	ρ25φ25	ρ25φ25	NOUN
ejpam-4556	151	50	)	)	PUNCT
ejpam-4556	151	51	a21	a21	NOUN
ejpam-4556	151	52	=	=	SYM
ejpam-4556	151	53	(	(	PUNCT
ejpam-4556	151	54	ρ11φ11	ρ11φ11	PROPN
ejpam-4556	151	55	,	,	PUNCT
ejpam-4556	151	56	0	0	NUM
ejpam-4556	151	57	,	,	PUNCT
ejpam-4556	151	58	0	0	NUM
ejpam-4556	151	59	,	,	PUNCT
ejpam-4556	151	60	0	0	NUM
ejpam-4556	151	61	,	,	PUNCT
ejpam-4556	151	62	0,−	0,−	NUM
ejpam-4556	151	63	d	d	X
ejpam-4556	151	64	daφ21	daφ21	NOUN
ejpam-4556	151	65	−	−	PROPN
ejpam-4556	151	66	(	(	PUNCT
ejpam-4556	151	67	ψ2(a	ψ2(a	NOUN
ejpam-4556	151	68	)	)	PUNCT
ejpam-4556	151	69	+	+	CCONJ
ejpam-4556	151	70	b(a	b(a	NOUN
ejpam-4556	151	71	)	)	PUNCT
ejpam-4556	151	72	+	+	NUM
ejpam-4556	151	73	ρ21)φ21	ρ21)φ21	PROPN
ejpam-4556	151	74	,	,	PUNCT
ejpam-4556	151	75	0	0	NUM
ejpam-4556	151	76	,	,	PUNCT
ejpam-4556	151	77	0	0	NUM
ejpam-4556	151	78	,	,	PUNCT
ejpam-4556	151	79	0	0	NUM
ejpam-4556	151	80	,	,	PUNCT
ejpam-4556	151	81	0	0	NUM
ejpam-4556	151	82	)	)	PUNCT
ejpam-4556	151	83	a22	a22	NOUN
ejpam-4556	151	84	=	=	SYM
ejpam-4556	151	85	(	(	PUNCT
ejpam-4556	151	86	0	0	NUM
ejpam-4556	151	87	,	,	PUNCT
ejpam-4556	151	88	ρ12φ12	ρ12φ12	NOUN
ejpam-4556	151	89	,	,	PUNCT
ejpam-4556	151	90	0	0	NUM
ejpam-4556	151	91	,	,	PUNCT
ejpam-4556	151	92	0	0	NUM
ejpam-4556	151	93	,	,	PUNCT
ejpam-4556	151	94	0	0	NUM
ejpam-4556	151	95	,	,	PUNCT
ejpam-4556	151	96	0,−	0,−	NUM
ejpam-4556	151	97	d	d	PROPN
ejpam-4556	151	98	daφ22	daφ22	PROPN
ejpam-4556	151	99	−	−	PROPN
ejpam-4556	151	100	(	(	PUNCT
ejpam-4556	151	101	b(a	b(a	X
ejpam-4556	151	102	)	)	PUNCT
ejpam-4556	151	103	+	+	CCONJ
ejpam-4556	151	104	k2	k2	X
ejpam-4556	151	105	+	+	CCONJ
ejpam-4556	151	106	ρ22)φ22	ρ22)φ22	PROPN
ejpam-4556	151	107	,	,	PUNCT
ejpam-4556	151	108	0	0	NUM
ejpam-4556	151	109	,	,	PUNCT
ejpam-4556	151	110	0	0	NUM
ejpam-4556	151	111	,	,	PUNCT
ejpam-4556	151	112	0	0	NUM
ejpam-4556	151	113	)	)	PUNCT
ejpam-4556	151	114	a23	a23	NOUN
ejpam-4556	151	115	=	=	SYM
ejpam-4556	151	116	(	(	PUNCT
ejpam-4556	151	117	0	0	NUM
ejpam-4556	151	118	,	,	PUNCT
ejpam-4556	151	119	0	0	NUM
ejpam-4556	151	120	,	,	PUNCT
ejpam-4556	151	121	ρ13φ13	ρ13φ13	NOUN
ejpam-4556	151	122	,	,	PUNCT
ejpam-4556	151	123	0	0	NUM
ejpam-4556	151	124	,	,	PUNCT
ejpam-4556	151	125	0	0	NUM
ejpam-4556	151	126	,	,	PUNCT
ejpam-4556	151	127	0	0	NUM
ejpam-4556	151	128	,	,	PUNCT
ejpam-4556	151	129	k2φ22,−	k2φ22,−	PROPN
ejpam-4556	151	130	d	d	PROPN
ejpam-4556	151	131	daφ23	daφ23	ADV
ejpam-4556	151	132	−	−	PROPN
ejpam-4556	151	133	(	(	PUNCT
ejpam-4556	151	134	r2	r2	PROPN
ejpam-4556	151	135	+	+	CCONJ
ejpam-4556	151	136	µ2(a	µ2(a	NOUN
ejpam-4556	151	137	)	)	PUNCT
ejpam-4556	151	138	+	+	CCONJ
ejpam-4556	151	139	b(a	b(a	NOUN
ejpam-4556	151	140	)	)	PUNCT
ejpam-4556	151	141	+	+	CCONJ
ejpam-4556	152	1	ρ23)φ23	ρ23)φ23	NUM
ejpam-4556	152	2	,	,	PUNCT
ejpam-4556	152	3	0	0	NUM
ejpam-4556	152	4	,	,	PUNCT
ejpam-4556	152	5	0	0	NUM
ejpam-4556	152	6	)	)	PUNCT
ejpam-4556	152	7	a24	a24	PROPN
ejpam-4556	152	8	=	=	SYM
ejpam-4556	152	9	(	(	PUNCT
ejpam-4556	152	10	0	0	NUM
ejpam-4556	152	11	,	,	PUNCT
ejpam-4556	152	12	0	0	NUM
ejpam-4556	152	13	,	,	PUNCT
ejpam-4556	152	14	0	0	NUM
ejpam-4556	152	15	,	,	PUNCT
ejpam-4556	152	16	ρ14φ14	ρ14φ14	NOUN
ejpam-4556	152	17	,	,	PUNCT
ejpam-4556	152	18	0	0	NUM
ejpam-4556	152	19	,	,	PUNCT
ejpam-4556	152	20	0	0	NUM
ejpam-4556	152	21	,	,	PUNCT
ejpam-4556	152	22	0	0	NUM
ejpam-4556	152	23	,	,	PUNCT
ejpam-4556	152	24	r2φ23,−	r2φ23,−	PROPN
ejpam-4556	152	25	d	d	X
ejpam-4556	152	26	daφ24	daφ24	NOUN
ejpam-4556	152	27	−	−	PROPN
ejpam-4556	152	28	(	(	PUNCT
ejpam-4556	152	29	b(a	b(a	X
ejpam-4556	152	30	)	)	PUNCT
ejpam-4556	152	31	+	+	CCONJ
ejpam-4556	152	32	ρ24)φ24	ρ24)φ24	NUM
ejpam-4556	152	33	,	,	PUNCT
ejpam-4556	152	34	0	0	NUM
ejpam-4556	152	35	)	)	PUNCT
ejpam-4556	152	36	a25	a25	NOUN
ejpam-4556	152	37	=	=	SYM
ejpam-4556	152	38	(	(	PUNCT
ejpam-4556	152	39	0	0	NUM
ejpam-4556	152	40	,	,	PUNCT
ejpam-4556	152	41	0	0	NUM
ejpam-4556	152	42	,	,	PUNCT
ejpam-4556	152	43	0	0	NUM
ejpam-4556	152	44	,	,	PUNCT
ejpam-4556	152	45	0	0	NUM
ejpam-4556	152	46	,	,	PUNCT
ejpam-4556	152	47	ρ15φ15	ρ15φ15	NOUN
ejpam-4556	152	48	,	,	PUNCT
ejpam-4556	152	49	ψ2(a)φ21	ψ2(a)φ21	NOUN
ejpam-4556	152	50	,	,	PUNCT
ejpam-4556	152	51	0	0	NUM
ejpam-4556	152	52	,	,	PUNCT
ejpam-4556	152	53	0	0	NUM
ejpam-4556	152	54	,	,	PUNCT
ejpam-4556	152	55	0,−	0,−	NUM
ejpam-4556	152	56	d	d	ADP
ejpam-4556	152	57	daφ25	daφ25	NOUN
ejpam-4556	152	58	−	−	PROPN
ejpam-4556	152	59	(	(	PUNCT
ejpam-4556	152	60	ρ25	ρ25	PROPN
ejpam-4556	152	61	+	+	CCONJ
ejpam-4556	152	62	b(a))φ25	b(a))φ25	NUM
ejpam-4556	152	63	)	)	PUNCT
ejpam-4556	152	64	(	(	PUNCT
ejpam-4556	152	65	9	9	NUM
ejpam-4556	152	66	)	)	PUNCT
ejpam-4556	152	67	with	with	ADP
ejpam-4556	152	68	φ(a	φ(a	ADJ
ejpam-4556	152	69	)	)	PUNCT
ejpam-4556	152	70	=	=	SYM
ejpam-4556	152	71	(	(	PUNCT
ejpam-4556	152	72	φ11(a	φ11(a	NOUN
ejpam-4556	152	73	)	)	PUNCT
ejpam-4556	152	74	,	,	PUNCT
ejpam-4556	152	75	φ12(a	φ12(a	NOUN
ejpam-4556	152	76	)	)	PUNCT
ejpam-4556	152	77	,	,	PUNCT
ejpam-4556	152	78	φ13(a	φ13(a	ADJ
ejpam-4556	152	79	)	)	PUNCT
ejpam-4556	152	80	,	,	PUNCT
ejpam-4556	152	81	φ14(a	φ14(a	NUM
ejpam-4556	152	82	)	)	PUNCT
ejpam-4556	152	83	,	,	PUNCT
ejpam-4556	152	84	φ15(a	φ15(a	NOUN
ejpam-4556	152	85	)	)	PUNCT
ejpam-4556	152	86	,	,	PUNCT
ejpam-4556	152	87	φ21(a	φ21(a	NOUN
ejpam-4556	152	88	)	)	PUNCT
ejpam-4556	152	89	,	,	PUNCT
ejpam-4556	152	90	φ22(a	φ22(a	NOUN
ejpam-4556	152	91	)	)	PUNCT
ejpam-4556	152	92	,	,	PUNCT
ejpam-4556	152	93	φ23(a	φ23(a	NUM
ejpam-4556	152	94	)	)	PUNCT
ejpam-4556	152	95	,	,	PUNCT
ejpam-4556	152	96	φ24(a	φ24(a	ADJ
ejpam-4556	152	97	)	)	PUNCT
ejpam-4556	152	98	,	,	PUNCT
ejpam-4556	152	99	φ25(a	φ25(a	NOUN
ejpam-4556	152	100	)	)	PUNCT
ejpam-4556	152	101	)	)	PUNCT
ejpam-4556	152	102	t	t	PROPN
ejpam-4556	152	103	∈	∈	PROPN
ejpam-4556	152	104	d(a	d(a	PROPN
ejpam-4556	152	105	)	)	PUNCT
ejpam-4556	152	106	b.	b.	PROPN
ejpam-4556	152	107	k.	k.	PROPN
ejpam-4556	152	108	abdoul	abdoul	PROPN
ejpam-4556	152	109	wahid	wahid	PROPN
ejpam-4556	152	110	,	,	PUNCT
ejpam-4556	152	111	d.moustapha	d.moustapha	PROPN
ejpam-4556	152	112	,	,	PUNCT
ejpam-4556	152	113	s.	s.	PROPN
ejpam-4556	152	114	bisso	bisso	PROPN
ejpam-4556	152	115	/	/	SYM
ejpam-4556	152	116	eur	eur	PROPN
ejpam-4556	152	117	.	.	PUNCT
ejpam-4556	153	1	j.	j.	PROPN
ejpam-4556	153	2	pure	pure	PROPN
ejpam-4556	153	3	appl	appl	PROPN
ejpam-4556	153	4	.	.	PROPN
ejpam-4556	153	5	math	math	PROPN
ejpam-4556	153	6	,	,	PUNCT
ejpam-4556	153	7	15	15	NUM
ejpam-4556	153	8	(	(	PUNCT
ejpam-4556	153	9	4	4	NUM
ejpam-4556	153	10	)	)	PUNCT
ejpam-4556	153	11	(	(	PUNCT
ejpam-4556	153	12	2022	2022	NUM
ejpam-4556	153	13	)	)	PUNCT
ejpam-4556	153	14	,	,	PUNCT
ejpam-4556	153	15	2054	2054	NUM
ejpam-4556	153	16	-	-	SYM
ejpam-4556	153	17	2073	2073	NUM
ejpam-4556	153	18	2060	2060	NUM
ejpam-4556	153	19	where	where	SCONJ
ejpam-4556	153	20	d(a	d(a	PROPN
ejpam-4556	153	21	)	)	PUNCT
ejpam-4556	153	22	is	be	AUX
ejpam-4556	153	23	the	the	DET
ejpam-4556	153	24	domain	domain	NOUN
ejpam-4556	153	25	given	give	VERB
ejpam-4556	153	26	by	by	ADP
ejpam-4556	153	27	:	:	PUNCT
ejpam-4556	153	28	d(a	d(a	PROPN
ejpam-4556	153	29	)	)	PUNCT
ejpam-4556	153	30	=	=	PRON
ejpam-4556	153	31	{	{	PUNCT
ejpam-4556	153	32	φ	φ	PROPN
ejpam-4556	153	33	∈	∈	PROPN
ejpam-4556	153	34	x\φij	x\φij	PROPN
ejpam-4556	153	35	∈	∈	PROPN
ejpam-4556	153	36	ac[0	ac[0	NOUN
ejpam-4556	153	37	,	,	PUNCT
ejpam-4556	153	38	a+	a+	ADJ
ejpam-4556	153	39	)	)	PUNCT
ejpam-4556	153	40	,	,	PUNCT
ejpam-4556	153	41	φ(0	φ(0	ADJ
ejpam-4556	153	42	)	)	PUNCT
ejpam-4556	153	43	=	=	SYM
ejpam-4556	153	44	(	(	PUNCT
ejpam-4556	153	45	λ1	λ1	ADJ
ejpam-4556	153	46	,	,	PUNCT
ejpam-4556	153	47	0	0	NUM
ejpam-4556	153	48	,	,	PUNCT
ejpam-4556	153	49	0	0	NUM
ejpam-4556	153	50	,	,	PUNCT
ejpam-4556	153	51	0	0	NUM
ejpam-4556	153	52	,	,	PUNCT
ejpam-4556	153	53	0	0	NUM
ejpam-4556	153	54	,	,	PUNCT
ejpam-4556	153	55	0,λ2	0,λ2	NOUN
ejpam-4556	153	56	,	,	PUNCT
ejpam-4556	153	57	0	0	NUM
ejpam-4556	153	58	,	,	PUNCT
ejpam-4556	153	59	0	0	NUM
ejpam-4556	153	60	,	,	PUNCT
ejpam-4556	153	61	0	0	NUM
ejpam-4556	153	62	,	,	PUNCT
ejpam-4556	153	63	0	0	NUM
ejpam-4556	153	64	)	)	PUNCT
ejpam-4556	153	65	t	t	NOUN
ejpam-4556	153	66	}	}	PUNCT
ejpam-4556	153	67	and	and	CCONJ
ejpam-4556	153	68	ac[0	ac[0	NOUN
ejpam-4556	153	69	,	,	PUNCT
ejpam-4556	153	70	a+	a+	PUNCT
ejpam-4556	153	71	)	)	PUNCT
ejpam-4556	153	72	denotes	denote	VERB
ejpam-4556	153	73	the	the	DET
ejpam-4556	153	74	set	set	NOUN
ejpam-4556	153	75	of	of	ADP
ejpam-4556	153	76	absolutely	absolutely	ADV
ejpam-4556	153	77	continuous	continuous	ADJ
ejpam-4556	153	78	functions	function	NOUN
ejpam-4556	153	79	on	on	ADP
ejpam-4556	153	80	[	[	X
ejpam-4556	153	81	0	0	NUM
ejpam-4556	153	82	,	,	PUNCT
ejpam-4556	153	83	a+	a+	ADJ
ejpam-4556	153	84	)	)	PUNCT
ejpam-4556	153	85	.	.	PUNCT
ejpam-4556	154	1	we	we	PRON
ejpam-4556	154	2	also	also	ADV
ejpam-4556	154	3	define	define	VERB
ejpam-4556	154	4	a	a	DET
ejpam-4556	154	5	nonlinear	nonlinear	ADJ
ejpam-4556	154	6	operator	operator	NOUN
ejpam-4556	154	7	f	f	NOUN
ejpam-4556	154	8	:	:	PUNCT
ejpam-4556	154	9	x	x	PUNCT
ejpam-4556	154	10	−→	−→	NOUN
ejpam-4556	154	11	x	x	SYM
ejpam-4556	154	12	by	by	ADP
ejpam-4556	154	13	:	:	PUNCT
ejpam-4556	154	14	(	(	PUNCT
ejpam-4556	154	15	fφ)(a	fφ)(a	NOUN
ejpam-4556	154	16	)	)	PUNCT
ejpam-4556	155	1	=	=	SYM
ejpam-4556	155	2			NOUN
ejpam-4556	155	3	α1b1(a)−	α1b1(a)−	NUM
ejpam-4556	155	4	(	(	PUNCT
ejpam-4556	155	5	(	(	PUNCT
ejpam-4556	155	6	q1φ13)(a))φ11	q1φ13)(a))φ11	NOUN
ejpam-4556	155	7	+	+	CCONJ
ejpam-4556	155	8	(	(	PUNCT
ejpam-4556	155	9	µ1(a)φ13	µ1(a)φ13	INTJ
ejpam-4556	155	10	+	+	CCONJ
ejpam-4556	155	11	µ2(a)φ23)φ11	µ2(a)φ23)φ11	X
ejpam-4556	155	12	(	(	PUNCT
ejpam-4556	155	13	(	(	PUNCT
ejpam-4556	155	14	q1φ13)(a))((1−	q1φ13)(a))((1−	X
ejpam-4556	155	15	ϕ1)φ11	ϕ1)φ11	NOUN
ejpam-4556	155	16	+	+	CCONJ
ejpam-4556	155	17	σ1φ14	σ1φ14	PROPN
ejpam-4556	155	18	+	+	SYM
ejpam-4556	155	19	δ1φ15	δ1φ15	NOUN
ejpam-4556	155	20	)	)	PUNCT
ejpam-4556	155	21	+	+	CCONJ
ejpam-4556	155	22	(	(	PUNCT
ejpam-4556	155	23	µ1(a)φ13	µ1(a)φ13	INTJ
ejpam-4556	155	24	+	+	CCONJ
ejpam-4556	155	25	µ2(a)φ23)φ12	µ2(a)φ23)φ12	ADJ
ejpam-4556	155	26	ϕ1((q1φ13)(a))φ11	ϕ1((q1φ13)(a))φ11	NOUN
ejpam-4556	155	27	+	+	CCONJ
ejpam-4556	155	28	(	(	PUNCT
ejpam-4556	155	29	µ1(a)φ13	µ1(a)φ13	INTJ
ejpam-4556	155	30	+	+	CCONJ
ejpam-4556	155	31	µ2(a)φ23)φ13	µ2(a)φ23)φ13	PROPN
ejpam-4556	155	32	(	(	PUNCT
ejpam-4556	155	33	µ1(a)φ13	µ1(a)φ13	VERB
ejpam-4556	155	34	+	+	CCONJ
ejpam-4556	155	35	µ2(a)φ23)−	µ2(a)φ23)−	DET
ejpam-4556	155	36	δ1((q1ϕ13)(a))φ14	δ1((q1ϕ13)(a))φ14	NOUN
ejpam-4556	155	37	(	(	PUNCT
ejpam-4556	155	38	µ1(a)φ13	µ1(a)φ13	PROPN
ejpam-4556	155	39	+	+	CCONJ
ejpam-4556	155	40	µ2(a)φ23)−	µ2(a)φ23)−	PROPN
ejpam-4556	155	41	σ1((q1φ13)(a))φ15	σ1((q1φ13)(a))φ15	PROPN
ejpam-4556	155	42	α2b2(a)−	α2b2(a)−	NOUN
ejpam-4556	155	43	(	(	PUNCT
ejpam-4556	155	44	(	(	PUNCT
ejpam-4556	155	45	q2φ23)(a))φ21	q2φ23)(a))φ21	NOUN
ejpam-4556	155	46	+	+	CCONJ
ejpam-4556	155	47	(	(	PUNCT
ejpam-4556	155	48	µ1(a)φ13	µ1(a)φ13	INTJ
ejpam-4556	155	49	+	+	CCONJ
ejpam-4556	155	50	µ2(a)φ23)φ21	µ2(a)φ23)φ21	NOUN
ejpam-4556	155	51	(	(	PUNCT
ejpam-4556	155	52	(	(	PUNCT
ejpam-4556	155	53	q2φ23)(a))((1−	q2φ23)(a))((1−	X
ejpam-4556	155	54	ϕ2)φ21	ϕ2)φ21	X
ejpam-4556	155	55	+	+	CCONJ
ejpam-4556	155	56	σ2φ24	σ2φ24	X
ejpam-4556	155	57	+	+	CCONJ
ejpam-4556	155	58	δ2φ25	δ2φ25	ADJ
ejpam-4556	155	59	)	)	PUNCT
ejpam-4556	155	60	+	+	CCONJ
ejpam-4556	155	61	(	(	PUNCT
ejpam-4556	155	62	µ1(a)φ13	µ1(a)φ13	INTJ
ejpam-4556	155	63	+	+	CCONJ
ejpam-4556	155	64	µ2(a)φ23)φ22	µ2(a)φ23)φ22	ADJ
ejpam-4556	155	65	ϕ2((q2φ23)(a))φ21	ϕ2((q2φ23)(a))φ21	NOUN
ejpam-4556	155	66	+	+	CCONJ
ejpam-4556	155	67	(	(	PUNCT
ejpam-4556	155	68	µ1(a)φ13	µ1(a)φ13	NOUN
ejpam-4556	155	69	+	+	CCONJ
ejpam-4556	155	70	µ2(a)φ23)φ23	µ2(a)φ23)φ23	ADJ
ejpam-4556	155	71	(	(	PUNCT
ejpam-4556	155	72	µ1(a)φ13	µ1(a)φ13	NOUN
ejpam-4556	155	73	+	+	CCONJ
ejpam-4556	155	74	µ2(a)φ23)−	µ2(a)φ23)−	NUM
ejpam-4556	155	75	δ2((q2ϕ23)(a))φ24	δ2((q2ϕ23)(a))φ24	PROPN
ejpam-4556	155	76	(	(	PUNCT
ejpam-4556	155	77	µ1(a)φ13	µ1(a)φ13	PUNCT
ejpam-4556	156	1	+	+	CCONJ
ejpam-4556	156	2	µ2(a)φ23)−	µ2(a)φ23)−	PRON
ejpam-4556	156	3	σ2((q2φ23)(a))φ25	σ2((q2φ23)(a))φ25	NOUN
ejpam-4556	156	4			PROPN
ejpam-4556	156	5	(	(	PUNCT
ejpam-4556	156	6	10	10	NUM
ejpam-4556	156	7	)	)	PUNCT
ejpam-4556	156	8	where	where	SCONJ
ejpam-4556	156	9	qi	qi	PROPN
ejpam-4556	156	10	is	be	AUX
ejpam-4556	156	11	a	a	DET
ejpam-4556	156	12	bounded	bounded	ADJ
ejpam-4556	156	13	linear	linear	ADJ
ejpam-4556	156	14	operator	operator	NOUN
ejpam-4556	156	15	on	on	ADP
ejpam-4556	156	16	l1(0	l1(0	PROPN
ejpam-4556	156	17	,	,	PUNCT
ejpam-4556	156	18	a+	a+	PUNCT
ejpam-4556	156	19	)	)	PUNCT
ejpam-4556	156	20	given	give	VERB
ejpam-4556	156	21	by	by	ADP
ejpam-4556	156	22	(	(	PUNCT
ejpam-4556	156	23	qif)(a	qif)(a	ADV
ejpam-4556	156	24	)	)	PUNCT
ejpam-4556	157	1	=	=	SYM
ejpam-4556	158	1	ci(a)βi(a)gi(a	ci(a)βi(a)gi(a	ADJ
ejpam-4556	158	2	)	)	PUNCT
ejpam-4556	158	3	∫	∫	PROPN
ejpam-4556	158	4	a+	a+	PUNCT
ejpam-4556	158	5	0	0	NUM
ejpam-4556	158	6	β̂i(a	β̂i(a	PROPN
ejpam-4556	158	7	′)f(a′)da′	′)f(a′)da′	X
ejpam-4556	158	8	(	(	PUNCT
ejpam-4556	158	9	11	11	NUM
ejpam-4556	158	10	)	)	PUNCT
ejpam-4556	158	11	let	let	VERB
ejpam-4556	158	12	u(t	u(t	NOUN
ejpam-4556	158	13	)	)	PUNCT
ejpam-4556	158	14	=	=	SYM
ejpam-4556	158	15	(	(	PUNCT
ejpam-4556	158	16	s1	s1	PROPN
ejpam-4556	158	17	(	(	PUNCT
ejpam-4556	158	18	.	.	NUM
ejpam-4556	158	19	,	,	PUNCT
ejpam-4556	158	20	t	t	PROPN
ejpam-4556	158	21	)	)	PUNCT
ejpam-4556	158	22	,	,	PUNCT
ejpam-4556	158	23	l1	l1	PROPN
ejpam-4556	158	24	(	(	PUNCT
ejpam-4556	158	25	.	.	PROPN
ejpam-4556	158	26	,	,	PUNCT
ejpam-4556	158	27	t	t	PROPN
ejpam-4556	158	28	)	)	PUNCT
ejpam-4556	158	29	,	,	PUNCT
ejpam-4556	158	30	i1	i1	PROPN
ejpam-4556	158	31	(	(	PUNCT
ejpam-4556	158	32	.	.	PROPN
ejpam-4556	158	33	,	,	PUNCT
ejpam-4556	158	34	t	t	PROPN
ejpam-4556	158	35	)	)	PUNCT
ejpam-4556	158	36	,	,	PUNCT
ejpam-4556	158	37	j1	j1	PROPN
ejpam-4556	158	38	(	(	PUNCT
ejpam-4556	158	39	.	.	NUM
ejpam-4556	158	40	,	,	PUNCT
ejpam-4556	158	41	t	t	PROPN
ejpam-4556	158	42	)	)	PUNCT
ejpam-4556	158	43	,	,	PUNCT
ejpam-4556	158	44	v1	v1	PROPN
ejpam-4556	158	45	(	(	PUNCT
ejpam-4556	158	46	.	.	PUNCT
ejpam-4556	158	47	,	,	PUNCT
ejpam-4556	158	48	t	t	PROPN
ejpam-4556	158	49	)	)	PUNCT
ejpam-4556	158	50	,	,	PUNCT
ejpam-4556	158	51	s2	s2	PROPN
ejpam-4556	158	52	(	(	PUNCT
ejpam-4556	158	53	.	.	PUNCT
ejpam-4556	158	54	,	,	PUNCT
ejpam-4556	158	55	t	t	PROPN
ejpam-4556	158	56	)	)	PUNCT
ejpam-4556	158	57	,	,	PUNCT
ejpam-4556	158	58	l2	l2	NOUN
ejpam-4556	158	59	(	(	PUNCT
ejpam-4556	158	60	.	.	NUM
ejpam-4556	158	61	,	,	PUNCT
ejpam-4556	158	62	t	t	PROPN
ejpam-4556	158	63	)	)	PUNCT
ejpam-4556	158	64	,	,	PUNCT
ejpam-4556	158	65	i2	i2	PROPN
ejpam-4556	158	66	(	(	PUNCT
ejpam-4556	158	67	.	.	NUM
ejpam-4556	158	68	,	,	PUNCT
ejpam-4556	158	69	t	t	PROPN
ejpam-4556	158	70	)	)	PUNCT
ejpam-4556	158	71	,	,	PUNCT
ejpam-4556	158	72	j2	j2	PROPN
ejpam-4556	158	73	(	(	PUNCT
ejpam-4556	158	74	.	.	PROPN
ejpam-4556	158	75	,	,	PUNCT
ejpam-4556	158	76	t	t	PROPN
ejpam-4556	158	77	)	)	PUNCT
ejpam-4556	158	78	,	,	PUNCT
ejpam-4556	158	79	v2	v2	PROPN
ejpam-4556	158	80	(	(	PUNCT
ejpam-4556	158	81	.	.	NUM
ejpam-4556	158	82	,	,	PUNCT
ejpam-4556	158	83	t	t	PROPN
ejpam-4556	158	84	)	)	PUNCT
ejpam-4556	158	85	)	)	PUNCT
ejpam-4556	159	1	thus	thus	ADV
ejpam-4556	159	2	,	,	PUNCT
ejpam-4556	159	3	we	we	PRON
ejpam-4556	159	4	can	can	AUX
ejpam-4556	159	5	rewrite	rewrite	VERB
ejpam-4556	159	6	the	the	DET
ejpam-4556	159	7	system	system	NOUN
ejpam-4556	159	8	as	as	ADP
ejpam-4556	159	9	an	an	DET
ejpam-4556	159	10	abstract	abstract	ADJ
ejpam-4556	159	11	cauchy	cauchy	ADJ
ejpam-4556	159	12	problem	problem	NOUN
ejpam-4556	159	13	{	{	PUNCT
ejpam-4556	159	14	d	d	X
ejpam-4556	159	15	dtu(t	dtu(t	PROPN
ejpam-4556	159	16	)	)	PUNCT
ejpam-4556	159	17	=	=	SYM
ejpam-4556	159	18	au(t	au(t	PRON
ejpam-4556	159	19	)	)	PUNCT
ejpam-4556	160	1	+	+	NUM
ejpam-4556	160	2	f	f	X
ejpam-4556	160	3	(	(	PUNCT
ejpam-4556	160	4	u(t	u(t	PROPN
ejpam-4556	160	5	)	)	PUNCT
ejpam-4556	160	6	)	)	PUNCT
ejpam-4556	161	1	u(0	u(0	NOUN
ejpam-4556	161	2	)	)	PUNCT
ejpam-4556	161	3	=	=	SYM
ejpam-4556	161	4	u0	u0	ADJ
ejpam-4556	161	5	(	(	PUNCT
ejpam-4556	161	6	12	12	NUM
ejpam-4556	161	7	)	)	PUNCT
ejpam-4556	161	8	where	where	SCONJ
ejpam-4556	161	9	u0(a	u0(a	X
ejpam-4556	161	10	)	)	PUNCT
ejpam-4556	161	11	=	=	SYM
ejpam-4556	161	12	(	(	PUNCT
ejpam-4556	161	13	s01(a	s01(a	NOUN
ejpam-4556	161	14	)	)	PUNCT
ejpam-4556	161	15	,	,	PUNCT
ejpam-4556	161	16	l01(a	l01(a	NOUN
ejpam-4556	161	17	)	)	PUNCT
ejpam-4556	161	18	,	,	PUNCT
ejpam-4556	161	19	i01(a	i01(a	PROPN
ejpam-4556	161	20	)	)	PUNCT
ejpam-4556	161	21	,	,	PUNCT
ejpam-4556	161	22	j01(a	j01(a	NOUN
ejpam-4556	161	23	)	)	PUNCT
ejpam-4556	161	24	,	,	PUNCT
ejpam-4556	161	25	v01(a	v01(a	NOUN
ejpam-4556	161	26	)	)	PUNCT
ejpam-4556	161	27	,	,	PUNCT
ejpam-4556	161	28	s02(a	s02(a	NOUN
ejpam-4556	161	29	)	)	PUNCT
ejpam-4556	161	30	,	,	PUNCT
ejpam-4556	161	31	l02(a	l02(a	NOUN
ejpam-4556	161	32	)	)	PUNCT
ejpam-4556	161	33	,	,	PUNCT
ejpam-4556	161	34	i02(a	i02(a	NOUN
ejpam-4556	161	35	)	)	PUNCT
ejpam-4556	161	36	,	,	PUNCT
ejpam-4556	161	37	j02(a	j02(a	NOUN
ejpam-4556	161	38	)	)	PUNCT
ejpam-4556	161	39	,	,	PUNCT
ejpam-4556	161	40	v02(a	v02(a	NOUN
ejpam-4556	161	41	)	)	PUNCT
ejpam-4556	161	42	)	)	PUNCT
ejpam-4556	161	43	t	t	PROPN
ejpam-4556	161	44	.	.	PUNCT
ejpam-4556	162	1	according	accord	VERB
ejpam-4556	162	2	to	to	ADP
ejpam-4556	162	3	these	these	DET
ejpam-4556	162	4	results	result	NOUN
ejpam-4556	162	5	we	we	PRON
ejpam-4556	162	6	have	have	VERB
ejpam-4556	162	7	the	the	DET
ejpam-4556	162	8	following	follow	VERB
ejpam-4556	162	9	results	result	NOUN
ejpam-4556	162	10	,	,	PUNCT
ejpam-4556	162	11	(	(	PUNCT
ejpam-4556	162	12	see	see	VERB
ejpam-4556	162	13	[	[	X
ejpam-4556	162	14	6	6	NUM
ejpam-4556	162	15	,	,	PUNCT
ejpam-4556	162	16	10	10	NUM
ejpam-4556	162	17	]	]	NUM
ejpam-4556	162	18	)	)	PUNCT
ejpam-4556	162	19	.	.	PUNCT
ejpam-4556	163	1	b.	b.	PROPN
ejpam-4556	163	2	k.	k.	PROPN
ejpam-4556	163	3	abdoul	abdoul	PROPN
ejpam-4556	163	4	wahid	wahid	PROPN
ejpam-4556	163	5	,	,	PUNCT
ejpam-4556	163	6	d.moustapha	d.moustapha	PROPN
ejpam-4556	163	7	,	,	PUNCT
ejpam-4556	163	8	s.	s.	PROPN
ejpam-4556	163	9	bisso	bisso	PROPN
ejpam-4556	163	10	/	/	SYM
ejpam-4556	163	11	eur	eur	PROPN
ejpam-4556	163	12	.	.	PUNCT
ejpam-4556	164	1	j.	j.	PROPN
ejpam-4556	164	2	pure	pure	PROPN
ejpam-4556	164	3	appl	appl	PROPN
ejpam-4556	164	4	.	.	PROPN
ejpam-4556	164	5	math	math	PROPN
ejpam-4556	164	6	,	,	PUNCT
ejpam-4556	164	7	15	15	NUM
ejpam-4556	164	8	(	(	PUNCT
ejpam-4556	164	9	4	4	NUM
ejpam-4556	164	10	)	)	PUNCT
ejpam-4556	164	11	(	(	PUNCT
ejpam-4556	164	12	2022	2022	NUM
ejpam-4556	164	13	)	)	PUNCT
ejpam-4556	164	14	,	,	PUNCT
ejpam-4556	164	15	2054	2054	NUM
ejpam-4556	164	16	-	-	SYM
ejpam-4556	164	17	2073	2073	NUM
ejpam-4556	164	18	2061	2061	NUM
ejpam-4556	164	19	lemma	lemma	PROPN
ejpam-4556	164	20	1	1	NUM
ejpam-4556	164	21	.	.	PUNCT
ejpam-4556	165	1	the	the	DET
ejpam-4556	165	2	operator	operator	NOUN
ejpam-4556	165	3	f	f	PROPN
ejpam-4556	165	4	is	be	AUX
ejpam-4556	165	5	continuously	continuously	ADV
ejpam-4556	165	6	fréchet	fréchet	VERB
ejpam-4556	165	7	differentiable	differentiable	ADJ
ejpam-4556	165	8	on	on	ADP
ejpam-4556	165	9	x.	x.	PROPN
ejpam-4556	165	10	lemma	lemma	PROPN
ejpam-4556	166	1	2	2	X
ejpam-4556	166	2	.	.	PUNCT
ejpam-4556	167	1	the	the	DET
ejpam-4556	167	2	operator	operator	NOUN
ejpam-4556	167	3	a	a	DET
ejpam-4556	167	4	genrates	genrate	NOUN
ejpam-4556	167	5	a	a	DET
ejpam-4556	167	6	c0	c0	NOUN
ejpam-4556	167	7	-	-	PUNCT
ejpam-4556	167	8	semigroup	semigroup	NOUN
ejpam-4556	167	9	of	of	ADP
ejpam-4556	167	10	the	the	DET
ejpam-4556	167	11	bounded	bounded	ADJ
ejpam-4556	167	12	linear	linear	PROPN
ejpam-4556	167	13	operators	operators	PROPN
ejpam-4556	167	14	{	{	PUNCT
ejpam-4556	167	15	t	t	PROPN
ejpam-4556	167	16	(	(	PUNCT
ejpam-4556	167	17	t)}t≥0	t)}t≥0	NOUN
ejpam-4556	167	18	and	and	CCONJ
ejpam-4556	167	19	the	the	DET
ejpam-4556	167	20	space	space	NOUN
ejpam-4556	167	21	ω	ω	NOUN
ejpam-4556	167	22	is	be	AUX
ejpam-4556	167	23	positively	positively	ADV
ejpam-4556	167	24	invariant	invariant	ADJ
ejpam-4556	167	25	by	by	ADP
ejpam-4556	167	26	{	{	PUNCT
ejpam-4556	167	27	t	t	PROPN
ejpam-4556	167	28	(	(	PUNCT
ejpam-4556	167	29	t)}t≥0	t)}t≥0	NOUN
ejpam-4556	167	30	.	.	PUNCT
ejpam-4556	167	31	theorem	theorem	NOUN
ejpam-4556	167	32	1	1	NUM
ejpam-4556	167	33	.	.	X
ejpam-4556	168	1	for	for	ADP
ejpam-4556	168	2	each	each	DET
ejpam-4556	168	3	u0	u0	ADJ
ejpam-4556	168	4	∈	∈	PROPN
ejpam-4556	168	5	x+	x+	PUNCT
ejpam-4556	168	6	there	there	PRON
ejpam-4556	168	7	are	be	VERB
ejpam-4556	168	8	a	a	DET
ejpam-4556	168	9	maximal	maximal	ADJ
ejpam-4556	168	10	interval	interval	NOUN
ejpam-4556	168	11	of	of	ADP
ejpam-4556	168	12	existence	existence	NOUN
ejpam-4556	168	13	[	[	X
ejpam-4556	168	14	0	0	NUM
ejpam-4556	168	15	,	,	PUNCT
ejpam-4556	168	16	tmax	tmax	NUM
ejpam-4556	168	17	)	)	PUNCT
ejpam-4556	168	18	and	and	CCONJ
ejpam-4556	168	19	a	a	DET
ejpam-4556	168	20	unique	unique	ADJ
ejpam-4556	168	21	continous	continous	ADJ
ejpam-4556	168	22	mild	mild	ADJ
ejpam-4556	168	23	solution	solution	NOUN
ejpam-4556	168	24	for	for	ADP
ejpam-4556	168	25	(	(	PUNCT
ejpam-4556	168	26	12	12	NUM
ejpam-4556	168	27	)	)	PUNCT
ejpam-4556	168	28	such	such	ADJ
ejpam-4556	168	29	that	that	SCONJ
ejpam-4556	168	30	u(t	u(t	NOUN
ejpam-4556	168	31	)	)	PUNCT
ejpam-4556	168	32	=	=	PUNCT
ejpam-4556	169	1	u0e	u0e	PROPN
ejpam-4556	169	2	ta	ta	X
ejpam-4556	170	1	+	+	CCONJ
ejpam-4556	170	2	∫	∫	PROPN
ejpam-4556	170	3	t	t	PROPN
ejpam-4556	170	4	0	0	NUM
ejpam-4556	170	5	ea(t−ξ)f	ea(t−ξ)f	PROPN
ejpam-4556	170	6	(	(	PUNCT
ejpam-4556	170	7	u(ξ))dξ	u(ξ))dξ	NOUN
ejpam-4556	170	8	4	4	NUM
ejpam-4556	170	9	.	.	PUNCT
ejpam-4556	171	1	the	the	DET
ejpam-4556	171	2	disease	disease	NOUN
ejpam-4556	171	3	-	-	PUNCT
ejpam-4556	171	4	free	free	ADJ
ejpam-4556	171	5	steady	steady	ADJ
ejpam-4556	171	6	state	state	NOUN
ejpam-4556	171	7	4.1	4.1	NUM
ejpam-4556	171	8	.	.	PUNCT
ejpam-4556	171	9	determination	determination	NOUN
ejpam-4556	171	10	of	of	ADP
ejpam-4556	171	11	the	the	DET
ejpam-4556	171	12	point	point	NOUN
ejpam-4556	171	13	of	of	ADP
ejpam-4556	171	14	disease	disease	NOUN
ejpam-4556	171	15	-	-	PUNCT
ejpam-4556	171	16	free	free	ADJ
ejpam-4556	171	17	equilibrum	equilibrum	NOUN
ejpam-4556	171	18	a	a	DET
ejpam-4556	171	19	steady	steady	ADJ
ejpam-4556	171	20	state	state	NOUN
ejpam-4556	171	21	(	(	PUNCT
ejpam-4556	171	22	s1(a	s1(a	PROPN
ejpam-4556	171	23	)	)	PUNCT
ejpam-4556	171	24	,	,	PUNCT
ejpam-4556	171	25	l1(a	l1(a	NUM
ejpam-4556	171	26	)	)	PUNCT
ejpam-4556	171	27	,	,	PUNCT
ejpam-4556	171	28	i1(a	i1(a	NUM
ejpam-4556	171	29	)	)	PUNCT
ejpam-4556	171	30	,	,	PUNCT
ejpam-4556	171	31	j1(a	j1(a	PROPN
ejpam-4556	171	32	)	)	PUNCT
ejpam-4556	171	33	,	,	PUNCT
ejpam-4556	171	34	v1(a	v1(a	NUM
ejpam-4556	171	35	)	)	PUNCT
ejpam-4556	171	36	,	,	PUNCT
ejpam-4556	171	37	s2(a	s2(a	PROPN
ejpam-4556	171	38	)	)	PUNCT
ejpam-4556	171	39	,	,	PUNCT
ejpam-4556	171	40	l2(a	l2(a	NOUN
ejpam-4556	171	41	)	)	PUNCT
ejpam-4556	171	42	,	,	PUNCT
ejpam-4556	171	43	i2(a	i2(a	NOUN
ejpam-4556	171	44	)	)	PUNCT
ejpam-4556	171	45	,	,	PUNCT
ejpam-4556	171	46	j2(a	j2(a	PROPN
ejpam-4556	171	47	)	)	PUNCT
ejpam-4556	171	48	,	,	PUNCT
ejpam-4556	171	49	v2(a	v2(a	NOUN
ejpam-4556	171	50	)	)	PUNCT
ejpam-4556	171	51	)	)	PUNCT
ejpam-4556	171	52	of	of	ADP
ejpam-4556	171	53	system	system	NOUN
ejpam-4556	171	54	(	(	PUNCT
ejpam-4556	171	55	5	5	NUM
ejpam-4556	171	56	)	)	PUNCT
ejpam-4556	171	57	must	must	AUX
ejpam-4556	171	58	satisfy	satisfy	VERB
ejpam-4556	171	59	the	the	DET
ejpam-4556	171	60	following	following	ADJ
ejpam-4556	171	61	time	time	NOUN
ejpam-4556	171	62	-	-	PUNCT
ejpam-4556	171	63	independent	independent	ADJ
ejpam-4556	171	64	system	system	NOUN
ejpam-4556	171	65	of	of	ADP
ejpam-4556	171	66	ordinary	ordinary	ADJ
ejpam-4556	171	67	differential	differential	ADJ
ejpam-4556	171	68	equations	equation	NOUN
ejpam-4556	171	69	:	:	PUNCT
ejpam-4556	172	1			PROPN
ejpam-4556	172	2	d	d	X
ejpam-4556	172	3	da	da	X
ejpam-4556	172	4	s1(a	s1(a	ADP
ejpam-4556	172	5	)	)	PUNCT
ejpam-4556	172	6	=	=	SYM
ejpam-4556	172	7	α1b1(a	α1b1(a	NUM
ejpam-4556	172	8	)	)	PUNCT
ejpam-4556	172	9	−	−	PROPN
ejpam-4556	173	1	[	[	X
ejpam-4556	173	2	β1(a)c1(a)g1(a)γ1	β1(a)c1(a)g1(a)γ1	X
ejpam-4556	173	3	+	+	CCONJ
ejpam-4556	173	4	ψ1(a	ψ1(a	X
ejpam-4556	173	5	)	)	PUNCT
ejpam-4556	173	6	+	+	CCONJ
ejpam-4556	173	7	b(a	b(a	NOUN
ejpam-4556	173	8	)	)	PUNCT
ejpam-4556	173	9	−	−	PROPN
ejpam-4556	173	10	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	173	11	)	)	PUNCT
ejpam-4556	173	12	−	−	PROPN
ejpam-4556	173	13	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	173	14	)	)	PUNCT
ejpam-4556	173	15	+	+	NUM
ejpam-4556	173	16	ρ11]s1(a	ρ11]s1(a	NOUN
ejpam-4556	173	17	)	)	PUNCT
ejpam-4556	173	18	+	+	CCONJ
ejpam-4556	173	19	ρ21s2(a	ρ21s2(a	NUM
ejpam-4556	173	20	)	)	PUNCT
ejpam-4556	173	21	d	d	X
ejpam-4556	173	22	da	da	X
ejpam-4556	173	23	l1(a	l1(a	PROPN
ejpam-4556	173	24	)	)	PUNCT
ejpam-4556	173	25	=	=	PRON
ejpam-4556	174	1	β1(a)c1(a)g1(a)γ1[(1	β1(a)c1(a)g1(a)γ1[(1	X
ejpam-4556	175	1	−	−	X
ejpam-4556	175	2	ϕ1)s1(a	ϕ1)s1(a	NOUN
ejpam-4556	175	3	)	)	PUNCT
ejpam-4556	175	4	+	+	NUM
ejpam-4556	175	5	δ1v1(a	δ1v1(a	PROPN
ejpam-4556	175	6	)	)	PUNCT
ejpam-4556	175	7	+	+	NUM
ejpam-4556	175	8	σ1j1(a	σ1j1(a	NOUN
ejpam-4556	175	9	)	)	PUNCT
ejpam-4556	175	10	]	]	PUNCT
ejpam-4556	176	1	−(b(a	−(b(a	X
ejpam-4556	176	2	)	)	PUNCT
ejpam-4556	176	3	+	+	NUM
ejpam-4556	176	4	k1	k1	NOUN
ejpam-4556	176	5	−	−	PROPN
ejpam-4556	176	6	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	176	7	)	)	PUNCT
ejpam-4556	176	8	−	−	PROPN
ejpam-4556	176	9	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	176	10	)	)	PUNCT
ejpam-4556	176	11	+	+	CCONJ
ejpam-4556	176	12	ρ12)l1(a	ρ12)l1(a	ADP
ejpam-4556	176	13	)	)	PUNCT
ejpam-4556	177	1	+	+	CCONJ
ejpam-4556	177	2	ρ22l2(a	ρ22l2(a	NOUN
ejpam-4556	177	3	)	)	PUNCT
ejpam-4556	178	1	d	d	X
ejpam-4556	178	2	da	da	NOUN
ejpam-4556	178	3	i1(a	i1(a	PROPN
ejpam-4556	178	4	)	)	PUNCT
ejpam-4556	178	5	=	=	SYM
ejpam-4556	178	6	k1l1(a	k1l1(a	NOUN
ejpam-4556	178	7	)	)	PUNCT
ejpam-4556	179	1	+	+	CCONJ
ejpam-4556	179	2	ϕ1β1(a)c1(a)g1(a)γ1s1(a	ϕ1β1(a)c1(a)g1(a)γ1s1(a	PROPN
ejpam-4556	179	3	)	)	PUNCT
ejpam-4556	179	4	−	−	PROPN
ejpam-4556	180	1	[	[	X
ejpam-4556	180	2	r1	r1	PROPN
ejpam-4556	180	3	+	+	CCONJ
ejpam-4556	180	4	b(a	b(a	NOUN
ejpam-4556	180	5	)	)	PUNCT
ejpam-4556	180	6	+	+	NUM
ejpam-4556	180	7	µ1(a	µ1(a	ADP
ejpam-4556	180	8	)	)	PUNCT
ejpam-4556	180	9	−	−	PROPN
ejpam-4556	180	10	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	180	11	)	)	PUNCT
ejpam-4556	180	12	−	−	PROPN
ejpam-4556	180	13	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	180	14	)	)	PUNCT
ejpam-4556	180	15	+	+	CCONJ
ejpam-4556	180	16	ρ13]i1(a	ρ13]i1(a	NOUN
ejpam-4556	180	17	)	)	PUNCT
ejpam-4556	181	1	+	+	CCONJ
ejpam-4556	181	2	ρ23i2(a	ρ23i2(a	X
ejpam-4556	181	3	)	)	PUNCT
ejpam-4556	182	1	d	d	X
ejpam-4556	182	2	da	da	PROPN
ejpam-4556	182	3	j1(a	j1(a	PROPN
ejpam-4556	182	4	)	)	PUNCT
ejpam-4556	182	5	=	=	SYM
ejpam-4556	182	6	r1i1(a	r1i1(a	NOUN
ejpam-4556	182	7	)	)	PUNCT
ejpam-4556	182	8	−	−	PROPN
ejpam-4556	182	9	(	(	PUNCT
ejpam-4556	182	10	σ1β1(a)c1(a)g1(a)γ1	σ1β1(a)c1(a)g1(a)γ1	VERB
ejpam-4556	182	11	+	+	CCONJ
ejpam-4556	182	12	b(a	b(a	NOUN
ejpam-4556	182	13	)	)	PUNCT
ejpam-4556	182	14	−	−	PROPN
ejpam-4556	182	15	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	182	16	)	)	PUNCT
ejpam-4556	182	17	−	−	PROPN
ejpam-4556	182	18	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	182	19	)	)	PUNCT
ejpam-4556	183	1	+	+	CCONJ
ejpam-4556	183	2	ρ14)j1(a	ρ14)j1(a	NUM
ejpam-4556	183	3	)	)	PUNCT
ejpam-4556	184	1	+	+	CCONJ
ejpam-4556	184	2	ρ24j2(a	ρ24j2(a	NUM
ejpam-4556	184	3	)	)	PUNCT
ejpam-4556	185	1	d	d	X
ejpam-4556	185	2	da	da	PROPN
ejpam-4556	185	3	v1(a	v1(a	PROPN
ejpam-4556	185	4	)	)	PUNCT
ejpam-4556	185	5	=	=	SYM
ejpam-4556	185	6	ψ1(a)s1(a	ψ1(a)s1(a	NOUN
ejpam-4556	185	7	)	)	PUNCT
ejpam-4556	185	8	−	−	PROPN
ejpam-4556	185	9	(	(	PUNCT
ejpam-4556	185	10	δ1β1(a)c1(a)g1(a)γ1	δ1β1(a)c1(a)g1(a)γ1	X
ejpam-4556	185	11	+	+	X
ejpam-4556	185	12	b(a	b(a	NOUN
ejpam-4556	185	13	)	)	PUNCT
ejpam-4556	185	14	−	−	PROPN
ejpam-4556	185	15	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	185	16	)	)	PUNCT
ejpam-4556	185	17	−	−	PROPN
ejpam-4556	185	18	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	185	19	)	)	PUNCT
ejpam-4556	186	1	+	+	CCONJ
ejpam-4556	186	2	ρ15)v1(a	ρ15)v1(a	NUM
ejpam-4556	186	3	)	)	PUNCT
ejpam-4556	186	4	+	+	CCONJ
ejpam-4556	186	5	ρ25v2(a	ρ25v2(a	NOUN
ejpam-4556	186	6	)	)	PUNCT
ejpam-4556	187	1	d	d	X
ejpam-4556	187	2	da	da	PROPN
ejpam-4556	187	3	s2(a	s2(a	PROPN
ejpam-4556	187	4	)	)	PUNCT
ejpam-4556	187	5	=	=	SYM
ejpam-4556	187	6	b2(a	b2(a	NOUN
ejpam-4556	187	7	)	)	PUNCT
ejpam-4556	187	8	−	−	NOUN
ejpam-4556	188	1	[	[	X
ejpam-4556	188	2	β2(a)c2(a)g2(a)γ2	β2(a)c2(a)g2(a)γ2	X
ejpam-4556	188	3	+	+	CCONJ
ejpam-4556	188	4	ψ2(a	ψ2(a	X
ejpam-4556	188	5	)	)	PUNCT
ejpam-4556	188	6	+	+	CCONJ
ejpam-4556	188	7	b(a	b(a	NOUN
ejpam-4556	188	8	)	)	PUNCT
ejpam-4556	188	9	−	−	PROPN
ejpam-4556	188	10	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	188	11	)	)	PUNCT
ejpam-4556	188	12	−	−	PROPN
ejpam-4556	188	13	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	188	14	)	)	PUNCT
ejpam-4556	188	15	+	+	CCONJ
ejpam-4556	188	16	ρ21]s2(a	ρ21]s2(a	NOUN
ejpam-4556	188	17	)	)	PUNCT
ejpam-4556	189	1	+	+	NUM
ejpam-4556	189	2	ρ11s1(a	ρ11s1(a	NUM
ejpam-4556	189	3	)	)	PUNCT
ejpam-4556	190	1	d	d	X
ejpam-4556	190	2	da	da	PROPN
ejpam-4556	190	3	l2(a	l2(a	PROPN
ejpam-4556	190	4	)	)	PUNCT
ejpam-4556	190	5	=	=	SYM
ejpam-4556	191	1	β2(a)c2(a)g2(a)γ2[(1	β2(a)c2(a)g2(a)γ2[(1	ADP
ejpam-4556	191	2	−	−	NOUN
ejpam-4556	191	3	ϕ2)s2(a	ϕ2)s2(a	NOUN
ejpam-4556	191	4	)	)	PUNCT
ejpam-4556	192	1	+	+	CCONJ
ejpam-4556	193	1	δ2v2(a	δ2v2(a	NOUN
ejpam-4556	193	2	)	)	PUNCT
ejpam-4556	194	1	+	+	CCONJ
ejpam-4556	194	2	σ2j2(a	σ2j2(a	NOUN
ejpam-4556	194	3	)	)	PUNCT
ejpam-4556	194	4	]	]	PUNCT
ejpam-4556	195	1	−	−	PROPN
ejpam-4556	195	2	(	(	PUNCT
ejpam-4556	195	3	b(a	b(a	X
ejpam-4556	195	4	)	)	PUNCT
ejpam-4556	195	5	+	+	CCONJ
ejpam-4556	195	6	k2	k2	ADJ
ejpam-4556	195	7	−	−	PROPN
ejpam-4556	195	8	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	195	9	)	)	PUNCT
ejpam-4556	195	10	−	−	PROPN
ejpam-4556	195	11	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	195	12	)	)	PUNCT
ejpam-4556	195	13	+	+	CCONJ
ejpam-4556	195	14	ρ22)l2(a	ρ22)l2(a	NOUN
ejpam-4556	195	15	)	)	PUNCT
ejpam-4556	195	16	+	+	NUM
ejpam-4556	195	17	ρ12l1(a	ρ12l1(a	NUM
ejpam-4556	195	18	)	)	PUNCT
ejpam-4556	196	1	d	d	X
ejpam-4556	196	2	da	da	PROPN
ejpam-4556	196	3	i2(a	i2(a	NOUN
ejpam-4556	196	4	)	)	PUNCT
ejpam-4556	196	5	=	=	SYM
ejpam-4556	196	6	k2l2(a	k2l2(a	NOUN
ejpam-4556	196	7	)	)	PUNCT
ejpam-4556	197	1	+	+	CCONJ
ejpam-4556	197	2	ϕ2β2(a)c2(a)g2(a)γ2s2(a	ϕ2β2(a)c2(a)g2(a)γ2s2(a	NOUN
ejpam-4556	197	3	)	)	PUNCT
ejpam-4556	197	4	−	−	PUNCT
ejpam-4556	198	1	[	[	X
ejpam-4556	198	2	r2	r2	PROPN
ejpam-4556	198	3	+	+	X
ejpam-4556	198	4	b(a	b(a	NOUN
ejpam-4556	198	5	)	)	PUNCT
ejpam-4556	198	6	+	+	CCONJ
ejpam-4556	198	7	µ2(a	µ2(a	NOUN
ejpam-4556	198	8	)	)	PUNCT
ejpam-4556	198	9	−	−	PROPN
ejpam-4556	198	10	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	198	11	)	)	PUNCT
ejpam-4556	198	12	−	−	PROPN
ejpam-4556	198	13	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	198	14	)	)	PUNCT
ejpam-4556	198	15	+	+	CCONJ
ejpam-4556	198	16	ρ23]i2(a	ρ23]i2(a	NOUN
ejpam-4556	198	17	)	)	PUNCT
ejpam-4556	199	1	+	+	CCONJ
ejpam-4556	199	2	ρ13i2(a	ρ13i2(a	NOUN
ejpam-4556	199	3	)	)	PUNCT
ejpam-4556	200	1	d	d	X
ejpam-4556	200	2	da	da	PROPN
ejpam-4556	200	3	j2(a	j2(a	PROPN
ejpam-4556	200	4	)	)	PUNCT
ejpam-4556	200	5	=	=	SYM
ejpam-4556	200	6	r2i2(a	r2i2(a	NOUN
ejpam-4556	200	7	)	)	PUNCT
ejpam-4556	200	8	−	−	PROPN
ejpam-4556	200	9	(	(	PUNCT
ejpam-4556	200	10	σ2β2(a)c2(a)g2(a)γ2	σ2β2(a)c2(a)g2(a)γ2	NOUN
ejpam-4556	200	11	+	+	X
ejpam-4556	200	12	b(a	b(a	NOUN
ejpam-4556	200	13	)	)	PUNCT
ejpam-4556	200	14	−	−	PROPN
ejpam-4556	200	15	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	200	16	)	)	PUNCT
ejpam-4556	200	17	−	−	PROPN
ejpam-4556	200	18	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	200	19	)	)	PUNCT
ejpam-4556	201	1	+	+	CCONJ
ejpam-4556	201	2	ρ24)j2(a	ρ24)j2(a	NOUN
ejpam-4556	201	3	)	)	PUNCT
ejpam-4556	202	1	+	+	CCONJ
ejpam-4556	202	2	ρ14j1(a	ρ14j1(a	NUM
ejpam-4556	202	3	)	)	PUNCT
ejpam-4556	203	1	d	d	X
ejpam-4556	203	2	da	da	PROPN
ejpam-4556	203	3	v2(a	v2(a	NOUN
ejpam-4556	203	4	)	)	PUNCT
ejpam-4556	203	5	=	=	SYM
ejpam-4556	203	6	ψ2(a)s2(a	ψ2(a)s2(a	NOUN
ejpam-4556	203	7	)	)	PUNCT
ejpam-4556	204	1	+	+	CCONJ
ejpam-4556	204	2	ρ15v1(a	ρ15v1(a	NUM
ejpam-4556	204	3	)	)	PUNCT
ejpam-4556	204	4	−	−	PROPN
ejpam-4556	204	5	(	(	PUNCT
ejpam-4556	204	6	δ2β2(a)c2(a)g2(a)γ2	δ2β2(a)c2(a)g2(a)γ2	NOUN
ejpam-4556	204	7	+	+	CCONJ
ejpam-4556	204	8	b(a	b(a	NOUN
ejpam-4556	204	9	)	)	PUNCT
ejpam-4556	204	10	−	−	PROPN
ejpam-4556	204	11	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	204	12	)	)	PUNCT
ejpam-4556	204	13	−	−	PROPN
ejpam-4556	204	14	µ2(a)i2(a	µ2(a)i2(a	NOUN
ejpam-4556	204	15	)	)	PUNCT
ejpam-4556	205	1	+	+	PUNCT
ejpam-4556	205	2	ρ25)v2(a	ρ25)v2(a	NOUN
ejpam-4556	205	3	)	)	PUNCT
ejpam-4556	205	4	γi	γi	NOUN
ejpam-4556	206	1	=	=	SYM
ejpam-4556	206	2	1	1	NUM
ejpam-4556	206	3	αi	αi	VERB
ejpam-4556	206	4	∫	∫	PROPN
ejpam-4556	206	5	a+	a+	X
ejpam-4556	206	6	0	0	NUM
ejpam-4556	206	7	β̂i(a)ii(a)da	β̂i(a)ii(a)da	ADJ
ejpam-4556	206	8	(	(	PUNCT
ejpam-4556	206	9	13	13	NUM
ejpam-4556	206	10	)	)	PUNCT
ejpam-4556	206	11	with	with	ADP
ejpam-4556	206	12	initial	initial	ADJ
ejpam-4556	206	13	value	value	NOUN
ejpam-4556	206	14	conditions	condition	NOUN
ejpam-4556	206	15	si(0	si(0	NOUN
ejpam-4556	206	16	)	)	PUNCT
ejpam-4556	206	17	=	=	SYM
ejpam-4556	207	1	λi	λi	NOUN
ejpam-4556	207	2	;	;	PUNCT
ejpam-4556	207	3	li(0	li(0	PROPN
ejpam-4556	207	4	)	)	PUNCT
ejpam-4556	207	5	=	=	SYM
ejpam-4556	207	6	ii(0	ii(0	NOUN
ejpam-4556	207	7	)	)	PUNCT
ejpam-4556	207	8	=	=	SYM
ejpam-4556	207	9	ji(0	ji(0	NOUN
ejpam-4556	207	10	)	)	PUNCT
ejpam-4556	207	11	=	=	SYM
ejpam-4556	208	1	vi(0	vi(0	PROPN
ejpam-4556	208	2	)	)	PUNCT
ejpam-4556	208	3	=	=	SYM
ejpam-4556	208	4	0	0	PUNCT
ejpam-4556	209	1	therefore	therefore	ADV
ejpam-4556	209	2	,	,	PUNCT
ejpam-4556	209	3	we	we	PRON
ejpam-4556	209	4	obtain	obtain	VERB
ejpam-4556	209	5	the	the	DET
ejpam-4556	209	6	disease	disease	NOUN
ejpam-4556	209	7	-	-	PUNCT
ejpam-4556	209	8	free	free	ADJ
ejpam-4556	209	9	steady	steady	ADJ
ejpam-4556	209	10	state	state	NOUN
ejpam-4556	209	11	s0i	s0i	NOUN
ejpam-4556	209	12	(	(	PUNCT
ejpam-4556	209	13	a	a	X
ejpam-4556	209	14	)	)	PUNCT
ejpam-4556	209	15	=	=	SYM
ejpam-4556	209	16	λie	λie	NOUN
ejpam-4556	209	17	−	−	PROPN
ejpam-4556	209	18	∫	∫	PROPN
ejpam-4556	209	19	a	a	DET
ejpam-4556	209	20	0	0	PROPN
ejpam-4556	209	21	(	(	PUNCT
ejpam-4556	209	22	b(τ)+ψi(τ)+ρi1)dτ	b(τ)+ψi(τ)+ρi1)dτ	NOUN
ejpam-4556	210	1	+	+	CCONJ
ejpam-4556	210	2	∫	∫	PROPN
ejpam-4556	210	3	a	a	DET
ejpam-4556	210	4	0	0	NUM
ejpam-4556	210	5	e	e	NOUN
ejpam-4556	210	6	−	−	PROPN
ejpam-4556	210	7	∫	∫	PROPN
ejpam-4556	210	8	a	a	DET
ejpam-4556	210	9	η	η	PROPN
ejpam-4556	210	10	(	(	PUNCT
ejpam-4556	210	11	b(τ)+ψi(τ)+ρi1)dτ	b(τ)+ψi(τ)+ρi1)dτ	PROPN
ejpam-4556	210	12	(	(	PUNCT
ejpam-4556	210	13	αibi(η	αibi(η	NOUN
ejpam-4556	210	14	)	)	PUNCT
ejpam-4556	210	15	+	+	CCONJ
ejpam-4556	211	1	ρj1s	ρj1s	NOUN
ejpam-4556	211	2	0	0	NUM
ejpam-4556	211	3	j	j	PROPN
ejpam-4556	211	4	(	(	PUNCT
ejpam-4556	211	5	a))dη	a))dη	PROPN
ejpam-4556	211	6	v0i	v0i	PROPN
ejpam-4556	211	7	(	(	PUNCT
ejpam-4556	211	8	a	a	NOUN
ejpam-4556	211	9	)	)	PUNCT
ejpam-4556	211	10	=	=	SYM
ejpam-4556	211	11	λi−s0i	λi−s0i	PROPN
ejpam-4556	211	12	(	(	PUNCT
ejpam-4556	211	13	a)+ρj5v0j	a)+ρj5v0j	NOUN
ejpam-4556	211	14	(	(	PUNCT
ejpam-4556	211	15	a	a	X
ejpam-4556	211	16	)	)	PUNCT
ejpam-4556	211	17	1−ρi5	1−ρi5	NUM
ejpam-4556	211	18	;	;	PUNCT
ejpam-4556	211	19	l0i	l0i	X
ejpam-4556	211	20	(	(	PUNCT
ejpam-4556	211	21	a	a	X
ejpam-4556	211	22	)	)	PUNCT
ejpam-4556	211	23	=	=	SYM
ejpam-4556	211	24	i0i	i0i	NOUN
ejpam-4556	211	25	(	(	PUNCT
ejpam-4556	211	26	a	a	X
ejpam-4556	211	27	)	)	PUNCT
ejpam-4556	212	1	=	=	SYM
ejpam-4556	212	2	j0i	j0i	X
ejpam-4556	212	3	(	(	PUNCT
ejpam-4556	212	4	a	a	X
ejpam-4556	212	5	)	)	PUNCT
ejpam-4556	212	6	=	=	SYM
ejpam-4556	212	7	0	0	NUM
ejpam-4556	212	8	(	(	PUNCT
ejpam-4556	212	9	14	14	NUM
ejpam-4556	212	10	)	)	PUNCT
ejpam-4556	212	11	b.	b.	PROPN
ejpam-4556	212	12	k.	k.	PROPN
ejpam-4556	212	13	abdoul	abdoul	PROPN
ejpam-4556	212	14	wahid	wahid	PROPN
ejpam-4556	212	15	,	,	PUNCT
ejpam-4556	212	16	d.moustapha	d.moustapha	PROPN
ejpam-4556	212	17	,	,	PUNCT
ejpam-4556	212	18	s.	s.	PROPN
ejpam-4556	212	19	bisso	bisso	PROPN
ejpam-4556	212	20	/	/	SYM
ejpam-4556	212	21	eur	eur	PROPN
ejpam-4556	212	22	.	.	PUNCT
ejpam-4556	213	1	j.	j.	PROPN
ejpam-4556	213	2	pure	pure	PROPN
ejpam-4556	213	3	appl	appl	PROPN
ejpam-4556	213	4	.	.	PROPN
ejpam-4556	213	5	math	math	PROPN
ejpam-4556	213	6	,	,	PUNCT
ejpam-4556	213	7	15	15	NUM
ejpam-4556	213	8	(	(	PUNCT
ejpam-4556	213	9	4	4	NUM
ejpam-4556	213	10	)	)	PUNCT
ejpam-4556	213	11	(	(	PUNCT
ejpam-4556	213	12	2022	2022	NUM
ejpam-4556	213	13	)	)	PUNCT
ejpam-4556	213	14	,	,	PUNCT
ejpam-4556	213	15	2054	2054	NUM
ejpam-4556	213	16	-	-	SYM
ejpam-4556	213	17	2073	2073	NUM
ejpam-4556	213	18	2062	2062	NUM
ejpam-4556	213	19	4.2	4.2	NUM
ejpam-4556	213	20	.	.	PUNCT
ejpam-4556	214	1	calculation	calculation	NOUN
ejpam-4556	214	2	of	of	ADP
ejpam-4556	214	3	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	214	4	,	,	PUNCT
ejpam-4556	214	5	ρ)-ℜ0(ρ	ρ)-ℜ0(ρ	ADJ
ejpam-4556	214	6	)	)	PUNCT
ejpam-4556	214	7	and	and	CCONJ
ejpam-4556	214	8	stability	stability	NOUN
ejpam-4556	214	9	of	of	ADP
ejpam-4556	214	10	the	the	DET
ejpam-4556	214	11	infection	infection	NOUN
ejpam-4556	214	12	-	-	PUNCT
ejpam-4556	214	13	free	free	ADJ
ejpam-4556	214	14	state	state	NOUN
ejpam-4556	214	15	to	to	PART
ejpam-4556	214	16	study	study	VERB
ejpam-4556	214	17	the	the	DET
ejpam-4556	214	18	stability	stability	NOUN
ejpam-4556	214	19	of	of	ADP
ejpam-4556	214	20	the	the	DET
ejpam-4556	214	21	disease	disease	NOUN
ejpam-4556	214	22	-	-	PUNCT
ejpam-4556	214	23	free	free	ADJ
ejpam-4556	214	24	steady	steady	ADJ
ejpam-4556	214	25	state	state	NOUN
ejpam-4556	214	26	,	,	PUNCT
ejpam-4556	214	27	we	we	PRON
ejpam-4556	214	28	denote	denote	VERB
ejpam-4556	214	29	the	the	DET
ejpam-4556	214	30	perturbations	perturbation	NOUN
ejpam-4556	214	31	of	of	ADP
ejpam-4556	214	32	system	system	NOUN
ejpam-4556	214	33	by	by	ADP
ejpam-4556	214	34			PROPN
ejpam-4556	214	35	si(t	si(t	VERB
ejpam-4556	214	36	,	,	PUNCT
ejpam-4556	214	37	a	a	PRON
ejpam-4556	214	38	)	)	PUNCT
ejpam-4556	214	39	=	=	SYM
ejpam-4556	214	40	si(t	si(t	X
ejpam-4556	214	41	,	,	PUNCT
ejpam-4556	214	42	a	a	PRON
ejpam-4556	214	43	)	)	PUNCT
ejpam-4556	214	44	+	+	NUM
ejpam-4556	214	45	s0i	s0i	NOUN
ejpam-4556	214	46	(	(	PUNCT
ejpam-4556	214	47	a	a	NOUN
ejpam-4556	214	48	)	)	PUNCT
ejpam-4556	214	49	li(t	li(t	NOUN
ejpam-4556	214	50	,	,	PUNCT
ejpam-4556	214	51	a	a	PRON
ejpam-4556	214	52	)	)	PUNCT
ejpam-4556	214	53	=	=	SYM
ejpam-4556	214	54	li(t	li(t	NOUN
ejpam-4556	214	55	,	,	PUNCT
ejpam-4556	214	56	a	a	PRON
ejpam-4556	214	57	)	)	PUNCT
ejpam-4556	215	1	+	+	NUM
ejpam-4556	215	2	l0i	l0i	X
ejpam-4556	215	3	(	(	PUNCT
ejpam-4556	215	4	a	a	NOUN
ejpam-4556	215	5	)	)	PUNCT
ejpam-4556	215	6	ii(t	ii(t	NOUN
ejpam-4556	215	7	,	,	PUNCT
ejpam-4556	215	8	a	a	PRON
ejpam-4556	215	9	)	)	PUNCT
ejpam-4556	215	10	=	=	SYM
ejpam-4556	215	11	ii(t	ii(t	NOUN
ejpam-4556	215	12	,	,	PUNCT
ejpam-4556	215	13	a	a	PRON
ejpam-4556	215	14	)	)	PUNCT
ejpam-4556	215	15	+	+	NOUN
ejpam-4556	215	16	i0i	i0i	NOUN
ejpam-4556	215	17	(	(	PUNCT
ejpam-4556	215	18	a	a	NOUN
ejpam-4556	215	19	)	)	PUNCT
ejpam-4556	215	20	ji(t	ji(t	NOUN
ejpam-4556	215	21	,	,	PUNCT
ejpam-4556	215	22	a	a	PRON
ejpam-4556	215	23	)	)	PUNCT
ejpam-4556	215	24	=	=	SYM
ejpam-4556	215	25	ji(t	ji(t	NOUN
ejpam-4556	215	26	,	,	PUNCT
ejpam-4556	215	27	a	a	PRON
ejpam-4556	215	28	)	)	PUNCT
ejpam-4556	216	1	+	+	CCONJ
ejpam-4556	216	2	j0i	j0i	X
ejpam-4556	216	3	(	(	PUNCT
ejpam-4556	216	4	a	a	NOUN
ejpam-4556	216	5	)	)	PUNCT
ejpam-4556	216	6	vi(t	vi(t	PUNCT
ejpam-4556	216	7	,	,	PUNCT
ejpam-4556	216	8	a	a	PRON
ejpam-4556	216	9	)	)	PUNCT
ejpam-4556	216	10	=	=	PUNCT
ejpam-4556	216	11	vi(t	vi(t	PROPN
ejpam-4556	216	12	,	,	PUNCT
ejpam-4556	216	13	a	a	PRON
ejpam-4556	216	14	)	)	PUNCT
ejpam-4556	217	1	+	+	CCONJ
ejpam-4556	217	2	v0i	v0i	VERB
ejpam-4556	217	3	(	(	PUNCT
ejpam-4556	217	4	a	a	NOUN
ejpam-4556	217	5	)	)	PUNCT
ejpam-4556	217	6	(	(	PUNCT
ejpam-4556	217	7	15	15	NUM
ejpam-4556	217	8	)	)	PUNCT
ejpam-4556	217	9	the	the	DET
ejpam-4556	217	10	perturbations	perturbation	NOUN
ejpam-4556	217	11	satisfy	satisfy	VERB
ejpam-4556	217	12	the	the	DET
ejpam-4556	217	13	following	follow	VERB
ejpam-4556	217	14	equations	equation	NOUN
ejpam-4556	217	15	:	:	PUNCT
ejpam-4556	217	16			PROPN
ejpam-4556	217	17	(	(	PUNCT
ejpam-4556	217	18	∂	∂	X
ejpam-4556	217	19	∂t	∂t	PROPN
ejpam-4556	217	20	+	+	SYM
ejpam-4556	217	21	∂	∂	NUM
ejpam-4556	217	22	∂a	∂a	NOUN
ejpam-4556	217	23	)	)	PUNCT
ejpam-4556	217	24	s1(t	s1(t	PROPN
ejpam-4556	217	25	,	,	PUNCT
ejpam-4556	217	26	a	a	PRON
ejpam-4556	217	27	)	)	PUNCT
ejpam-4556	217	28	=	=	SYM
ejpam-4556	217	29	ρ21s2(a	ρ21s2(a	NOUN
ejpam-4556	217	30	)	)	PUNCT
ejpam-4556	218	1	−	−	PROPN
ejpam-4556	218	2	(	(	PUNCT
ejpam-4556	218	3	b(a	b(a	X
ejpam-4556	218	4	)	)	PUNCT
ejpam-4556	218	5	+	+	CCONJ
ejpam-4556	218	6	ψ1(a	ψ1(a	X
ejpam-4556	218	7	)	)	PUNCT
ejpam-4556	219	1	+	+	CCONJ
ejpam-4556	219	2	ρ11)s1(t	ρ11)s1(t	PROPN
ejpam-4556	219	3	,	,	PUNCT
ejpam-4556	219	4	a	a	PRON
ejpam-4556	219	5	)	)	PUNCT
ejpam-4556	219	6	−	−	PROPN
ejpam-4556	220	1	[	[	X
ejpam-4556	220	2	γ1(t)β1(a)c1(a)g1(a	γ1(t)β1(a)c1(a)g1(a	NOUN
ejpam-4556	220	3	)	)	PUNCT
ejpam-4556	220	4	−	−	PROPN
ejpam-4556	221	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	221	2	,	,	PUNCT
ejpam-4556	221	3	a	a	X
ejpam-4556	221	4	)	)	PUNCT
ejpam-4556	221	5	−	−	PROPN
ejpam-4556	222	1	µ2i2(t	µ2i2(t	PROPN
ejpam-4556	222	2	,	,	PUNCT
ejpam-4556	222	3	a)]s	a)]s	ADJ
ejpam-4556	222	4	0	0	NUM
ejpam-4556	222	5	1(a	1(a	NUM
ejpam-4556	222	6	)	)	PUNCT
ejpam-4556	222	7	(	(	PUNCT
ejpam-4556	222	8	∂	∂	NUM
ejpam-4556	223	1	∂t	∂t	PROPN
ejpam-4556	223	2	+	+	SYM
ejpam-4556	223	3	∂	∂	NUM
ejpam-4556	223	4	∂a	∂a	NOUN
ejpam-4556	223	5	)	)	PUNCT
ejpam-4556	223	6	l1(t	l1(t	PROPN
ejpam-4556	223	7	,	,	PUNCT
ejpam-4556	223	8	a	a	PRON
ejpam-4556	223	9	)	)	PUNCT
ejpam-4556	223	10	=	=	SYM
ejpam-4556	223	11	ρ22l2(a	ρ22l2(a	NOUN
ejpam-4556	223	12	)	)	PUNCT
ejpam-4556	223	13	−	−	PROPN
ejpam-4556	223	14	(	(	PUNCT
ejpam-4556	223	15	b(a	b(a	X
ejpam-4556	223	16	)	)	PUNCT
ejpam-4556	224	1	+	+	CCONJ
ejpam-4556	224	2	k1	k1	NOUN
ejpam-4556	224	3	+	+	CCONJ
ejpam-4556	224	4	ρ12)l1(t	ρ12)l1(t	PROPN
ejpam-4556	224	5	,	,	PUNCT
ejpam-4556	224	6	a	a	PRON
ejpam-4556	224	7	)	)	PUNCT
ejpam-4556	225	1	+	+	CCONJ
ejpam-4556	225	2	γ1(t)β1(a)c1(a)g1(a)[(1	γ1(t)β1(a)c1(a)g1(a)[(1	ADJ
ejpam-4556	225	3	−	−	PROPN
ejpam-4556	226	1	ϕ1)s	ϕ1)s	NOUN
ejpam-4556	226	2	0	0	NUM
ejpam-4556	226	3	1(a	1(a	NUM
ejpam-4556	226	4	)	)	PUNCT
ejpam-4556	227	1	+	+	CCONJ
ejpam-4556	227	2	δ1v	δ1v	PROPN
ejpam-4556	227	3	0	0	NUM
ejpam-4556	227	4	1(a	1(a	NUM
ejpam-4556	227	5	)	)	PUNCT
ejpam-4556	227	6	]	]	X
ejpam-4556	227	7	(	(	PUNCT
ejpam-4556	227	8	∂	∂	NUM
ejpam-4556	227	9	∂t	∂t	PROPN
ejpam-4556	227	10	+	+	SYM
ejpam-4556	227	11	∂	∂	NUM
ejpam-4556	227	12	∂a	∂a	NOUN
ejpam-4556	227	13	)	)	PUNCT
ejpam-4556	227	14	i1(t	i1(t	PROPN
ejpam-4556	227	15	,	,	PUNCT
ejpam-4556	227	16	a	a	PRON
ejpam-4556	227	17	)	)	PUNCT
ejpam-4556	227	18	=	=	SYM
ejpam-4556	227	19	ρ23i2(a	ρ23i2(a	NOUN
ejpam-4556	227	20	)	)	PUNCT
ejpam-4556	228	1	+	+	CCONJ
ejpam-4556	228	2	k1l1(t	k1l1(t	PROPN
ejpam-4556	228	3	,	,	PUNCT
ejpam-4556	228	4	a	a	PRON
ejpam-4556	228	5	)	)	PUNCT
ejpam-4556	229	1	+	+	CCONJ
ejpam-4556	229	2	ϕ1β1(a)c1(a)g1(a)γ1(t)s	ϕ1β1(a)c1(a)g1(a)γ1(t)s	ADV
ejpam-4556	229	3	0	0	NUM
ejpam-4556	230	1	1(a	1(a	NUM
ejpam-4556	230	2	)	)	PUNCT
ejpam-4556	231	1	−	−	PROPN
ejpam-4556	231	2	(	(	PUNCT
ejpam-4556	231	3	r1	r1	NOUN
ejpam-4556	231	4	+	+	CCONJ
ejpam-4556	231	5	µ1(a	µ1(a	NOUN
ejpam-4556	231	6	)	)	PUNCT
ejpam-4556	232	1	+	+	CCONJ
ejpam-4556	232	2	b(a	b(a	NOUN
ejpam-4556	232	3	)	)	PUNCT
ejpam-4556	233	1	+	+	CCONJ
ejpam-4556	233	2	ρ13)i1(t	ρ13)i1(t	PROPN
ejpam-4556	233	3	,	,	PUNCT
ejpam-4556	233	4	a	a	X
ejpam-4556	233	5	)	)	PUNCT
ejpam-4556	233	6	(	(	PUNCT
ejpam-4556	233	7	∂	∂	NUM
ejpam-4556	234	1	∂t	∂t	PROPN
ejpam-4556	234	2	+	+	SYM
ejpam-4556	234	3	∂	∂	NUM
ejpam-4556	234	4	∂a	∂a	NOUN
ejpam-4556	234	5	)	)	PUNCT
ejpam-4556	234	6	j1(t	j1(t	PROPN
ejpam-4556	234	7	,	,	PUNCT
ejpam-4556	234	8	a	a	PRON
ejpam-4556	234	9	)	)	PUNCT
ejpam-4556	234	10	=	=	SYM
ejpam-4556	234	11	r1i1(t	r1i1(t	PROPN
ejpam-4556	234	12	,	,	PUNCT
ejpam-4556	234	13	a	a	PRON
ejpam-4556	234	14	)	)	PUNCT
ejpam-4556	234	15	+	+	NOUN
ejpam-4556	234	16	ρ24j2(a	ρ24j2(a	NUM
ejpam-4556	234	17	)	)	PUNCT
ejpam-4556	234	18	−	−	PROPN
ejpam-4556	235	1	(	(	PUNCT
ejpam-4556	235	2	ρ14	ρ14	ADV
ejpam-4556	235	3	+	+	CCONJ
ejpam-4556	235	4	b(a))j1(t	b(a))j1(t	NUM
ejpam-4556	235	5	,	,	PUNCT
ejpam-4556	235	6	a	a	X
ejpam-4556	235	7	)	)	PUNCT
ejpam-4556	235	8	(	(	PUNCT
ejpam-4556	235	9	∂	∂	NUM
ejpam-4556	235	10	∂t	∂t	PROPN
ejpam-4556	235	11	+	+	SYM
ejpam-4556	235	12	∂	∂	NUM
ejpam-4556	235	13	∂a	∂a	NOUN
ejpam-4556	235	14	)	)	PUNCT
ejpam-4556	236	1	v1(t	v1(t	ADV
ejpam-4556	236	2	,	,	PUNCT
ejpam-4556	236	3	a	a	X
ejpam-4556	236	4	)	)	PUNCT
ejpam-4556	236	5	=	=	SYM
ejpam-4556	236	6	ψ1(a)s1(t	ψ1(a)s1(t	PROPN
ejpam-4556	236	7	,	,	PUNCT
ejpam-4556	236	8	a	a	X
ejpam-4556	236	9	)	)	PUNCT
ejpam-4556	237	1	+	+	SYM
ejpam-4556	237	2	ρ25v2(t	ρ25v2(t	NUM
ejpam-4556	237	3	,	,	PUNCT
ejpam-4556	237	4	a	a	PRON
ejpam-4556	237	5	)	)	PUNCT
ejpam-4556	237	6	−	−	PROPN
ejpam-4556	238	1	(	(	PUNCT
ejpam-4556	238	2	ρ15	ρ15	PROPN
ejpam-4556	238	3	+	+	CCONJ
ejpam-4556	238	4	b(a))v1(t	b(a))v1(t	PROPN
ejpam-4556	238	5	,	,	PUNCT
ejpam-4556	238	6	a	a	PRON
ejpam-4556	238	7	)	)	PUNCT
ejpam-4556	238	8	−(δ1β1(a)c1(a)g1(a)γ(t	−(δ1β1(a)c1(a)g1(a)γ(t	PROPN
ejpam-4556	238	9	)	)	PUNCT
ejpam-4556	238	10	−	−	PROPN
ejpam-4556	239	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	239	2	,	,	PUNCT
ejpam-4556	239	3	a	a	X
ejpam-4556	239	4	)	)	PUNCT
ejpam-4556	239	5	−	−	PROPN
ejpam-4556	240	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	240	2	,	,	PUNCT
ejpam-4556	240	3	a))v	a))v	NOUN
ejpam-4556	240	4	0	0	PROPN
ejpam-4556	240	5	1(a	1(a	NUM
ejpam-4556	240	6	)	)	PUNCT
ejpam-4556	240	7	(	(	PUNCT
ejpam-4556	240	8	∂	∂	NUM
ejpam-4556	240	9	∂t	∂t	PROPN
ejpam-4556	240	10	+	+	SYM
ejpam-4556	240	11	∂	∂	NUM
ejpam-4556	240	12	∂a	∂a	NOUN
ejpam-4556	240	13	)	)	PUNCT
ejpam-4556	240	14	s2(t	s2(t	PROPN
ejpam-4556	240	15	,	,	PUNCT
ejpam-4556	240	16	a	a	PRON
ejpam-4556	240	17	)	)	PUNCT
ejpam-4556	240	18	=	=	SYM
ejpam-4556	240	19	ρ11s1(a	ρ11s1(a	NOUN
ejpam-4556	240	20	)	)	PUNCT
ejpam-4556	240	21	−	−	PROPN
ejpam-4556	240	22	(	(	PUNCT
ejpam-4556	240	23	b(a	b(a	X
ejpam-4556	240	24	)	)	PUNCT
ejpam-4556	240	25	+	+	PUNCT
ejpam-4556	240	26	ψ2(a	ψ2(a	X
ejpam-4556	240	27	)	)	PUNCT
ejpam-4556	241	1	+	+	CCONJ
ejpam-4556	241	2	ρ21)s2(t	ρ21)s2(t	PROPN
ejpam-4556	241	3	,	,	PUNCT
ejpam-4556	241	4	a	a	NOUN
ejpam-4556	241	5	)	)	PUNCT
ejpam-4556	241	6	−	−	PROPN
ejpam-4556	242	1	[	[	X
ejpam-4556	242	2	γ2(t)β2(a)c2(a)g2(a	γ2(t)β2(a)c2(a)g2(a	NOUN
ejpam-4556	242	3	)	)	PUNCT
ejpam-4556	242	4	−	−	PROPN
ejpam-4556	242	5	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	242	6	,	,	PUNCT
ejpam-4556	242	7	a	a	X
ejpam-4556	242	8	)	)	PUNCT
ejpam-4556	242	9	−	−	PROPN
ejpam-4556	243	1	µ2i2(t	µ2i2(t	PROPN
ejpam-4556	243	2	,	,	PUNCT
ejpam-4556	243	3	a)]s	a)]s	ADJ
ejpam-4556	243	4	0	0	NUM
ejpam-4556	243	5	2(a	2(a	NUM
ejpam-4556	243	6	)	)	PUNCT
ejpam-4556	243	7	(	(	PUNCT
ejpam-4556	243	8	∂	∂	NUM
ejpam-4556	243	9	∂t	∂t	PROPN
ejpam-4556	243	10	+	+	SYM
ejpam-4556	243	11	∂	∂	NUM
ejpam-4556	243	12	∂a	∂a	NOUN
ejpam-4556	243	13	)	)	PUNCT
ejpam-4556	243	14	l2(t	l2(t	PROPN
ejpam-4556	243	15	,	,	PUNCT
ejpam-4556	243	16	a	a	PRON
ejpam-4556	243	17	)	)	PUNCT
ejpam-4556	243	18	=	=	SYM
ejpam-4556	243	19	ρ12l1(a	ρ12l1(a	NUM
ejpam-4556	243	20	)	)	PUNCT
ejpam-4556	243	21	−	−	PROPN
ejpam-4556	243	22	(	(	PUNCT
ejpam-4556	243	23	b(a	b(a	X
ejpam-4556	243	24	)	)	PUNCT
ejpam-4556	243	25	+	+	CCONJ
ejpam-4556	243	26	k2	k2	X
ejpam-4556	243	27	+	+	CCONJ
ejpam-4556	243	28	ρ22)l2(t	ρ22)l2(t	PROPN
ejpam-4556	243	29	,	,	PUNCT
ejpam-4556	243	30	a	a	PRON
ejpam-4556	243	31	)	)	PUNCT
ejpam-4556	243	32	+	+	NUM
ejpam-4556	243	33	γ2(t)β2(a)c2(a)g2(a)[(1	γ2(t)β2(a)c2(a)g2(a)[(1	NOUN
ejpam-4556	243	34	−	−	NOUN
ejpam-4556	243	35	ϕ2)s	ϕ2)s	NOUN
ejpam-4556	243	36	0	0	NUM
ejpam-4556	243	37	2(a	2(a	NUM
ejpam-4556	243	38	)	)	PUNCT
ejpam-4556	244	1	+	+	CCONJ
ejpam-4556	244	2	δ2v	δ2v	ADV
ejpam-4556	244	3	0	0	NUM
ejpam-4556	244	4	2(a	2(a	NUM
ejpam-4556	244	5	)	)	PUNCT
ejpam-4556	244	6	]	]	X
ejpam-4556	244	7	(	(	PUNCT
ejpam-4556	244	8	∂	∂	NUM
ejpam-4556	244	9	∂t	∂t	PROPN
ejpam-4556	244	10	+	+	SYM
ejpam-4556	244	11	∂	∂	NUM
ejpam-4556	244	12	∂a	∂a	NOUN
ejpam-4556	244	13	)	)	PUNCT
ejpam-4556	245	1	i2(t	i2(t	PROPN
ejpam-4556	245	2	,	,	PUNCT
ejpam-4556	245	3	a	a	PRON
ejpam-4556	245	4	)	)	PUNCT
ejpam-4556	245	5	=	=	SYM
ejpam-4556	245	6	ρ13i1(a	ρ13i1(a	PROPN
ejpam-4556	245	7	)	)	PUNCT
ejpam-4556	246	1	+	+	CCONJ
ejpam-4556	246	2	k2l2(t	k2l2(t	PROPN
ejpam-4556	246	3	,	,	PUNCT
ejpam-4556	246	4	a	a	PRON
ejpam-4556	246	5	)	)	PUNCT
ejpam-4556	246	6	+	+	CCONJ
ejpam-4556	247	1	ϕ2β2(a)c2(a)g2(a)γ2(t)s	ϕ2β2(a)c2(a)g2(a)γ2(t)s	PROPN
ejpam-4556	247	2	0	0	NUM
ejpam-4556	247	3	2(a	2(a	NUM
ejpam-4556	247	4	)	)	PUNCT
ejpam-4556	247	5	−	−	PROPN
ejpam-4556	247	6	(	(	PUNCT
ejpam-4556	247	7	r2	r2	PROPN
ejpam-4556	247	8	+	+	CCONJ
ejpam-4556	247	9	µ2(a	µ2(a	NOUN
ejpam-4556	247	10	)	)	PUNCT
ejpam-4556	247	11	+	+	CCONJ
ejpam-4556	247	12	b(a	b(a	NOUN
ejpam-4556	247	13	)	)	PUNCT
ejpam-4556	247	14	+	+	SYM
ejpam-4556	247	15	ρ23)i2(t	ρ23)i2(t	PROPN
ejpam-4556	247	16	,	,	PUNCT
ejpam-4556	247	17	a	a	NOUN
ejpam-4556	247	18	)	)	PUNCT
ejpam-4556	247	19	(	(	PUNCT
ejpam-4556	247	20	∂	∂	NUM
ejpam-4556	247	21	∂t	∂t	PROPN
ejpam-4556	247	22	+	+	SYM
ejpam-4556	247	23	∂	∂	NUM
ejpam-4556	247	24	∂a	∂a	NOUN
ejpam-4556	247	25	)	)	PUNCT
ejpam-4556	247	26	j2(t	j2(t	PROPN
ejpam-4556	247	27	,	,	PUNCT
ejpam-4556	247	28	a	a	PRON
ejpam-4556	247	29	)	)	PUNCT
ejpam-4556	247	30	=	=	SYM
ejpam-4556	247	31	ρ14j1(a	ρ14j1(a	PROPN
ejpam-4556	247	32	)	)	PUNCT
ejpam-4556	247	33	+	+	CCONJ
ejpam-4556	247	34	r2i2(t	r2i2(t	NOUN
ejpam-4556	247	35	,	,	PUNCT
ejpam-4556	247	36	a	a	PRON
ejpam-4556	247	37	)	)	PUNCT
ejpam-4556	247	38	−	−	PROPN
ejpam-4556	247	39	(	(	PUNCT
ejpam-4556	247	40	ρ24	ρ24	NOUN
ejpam-4556	247	41	+	+	CCONJ
ejpam-4556	247	42	b(a))j2(t	b(a))j2(t	ADJ
ejpam-4556	247	43	,	,	PUNCT
ejpam-4556	247	44	a	a	NOUN
ejpam-4556	247	45	)	)	PUNCT
ejpam-4556	247	46	(	(	PUNCT
ejpam-4556	247	47	∂	∂	NUM
ejpam-4556	247	48	∂t	∂t	PROPN
ejpam-4556	247	49	+	+	SYM
ejpam-4556	247	50	∂	∂	NUM
ejpam-4556	247	51	∂a	∂a	NOUN
ejpam-4556	247	52	)	)	PUNCT
ejpam-4556	247	53	v2(t	v2(t	PROPN
ejpam-4556	247	54	,	,	PUNCT
ejpam-4556	247	55	a	a	PRON
ejpam-4556	247	56	)	)	PUNCT
ejpam-4556	247	57	=	=	SYM
ejpam-4556	247	58	ψ2(a)s2(t	ψ2(a)s2(t	PROPN
ejpam-4556	247	59	,	,	PUNCT
ejpam-4556	247	60	a	a	PRON
ejpam-4556	247	61	)	)	PUNCT
ejpam-4556	247	62	+	+	NUM
ejpam-4556	247	63	ρ15v1(t	ρ15v1(t	NOUN
ejpam-4556	247	64	,	,	PUNCT
ejpam-4556	247	65	a	a	PRON
ejpam-4556	247	66	)	)	PUNCT
ejpam-4556	247	67	−	−	PROPN
ejpam-4556	247	68	(	(	PUNCT
ejpam-4556	247	69	ρ25	ρ25	NOUN
ejpam-4556	247	70	+	+	CCONJ
ejpam-4556	247	71	b(a))v2(t	b(a))v2(t	NUM
ejpam-4556	247	72	,	,	PUNCT
ejpam-4556	247	73	a	a	PRON
ejpam-4556	247	74	)	)	PUNCT
ejpam-4556	247	75	−(δ2β2(a)c2(a)g2(a)γ2(t	−(δ2β2(a)c2(a)g2(a)γ2(t	NOUN
ejpam-4556	247	76	)	)	PUNCT
ejpam-4556	247	77	−	−	NOUN
ejpam-4556	248	1	µ1(a)i1(t	µ1(a)i1(t	PROPN
ejpam-4556	248	2	,	,	PUNCT
ejpam-4556	248	3	a	a	X
ejpam-4556	248	4	)	)	PUNCT
ejpam-4556	248	5	−	−	PROPN
ejpam-4556	249	1	µ2(a)i2(t	µ2(a)i2(t	PROPN
ejpam-4556	249	2	,	,	PUNCT
ejpam-4556	249	3	a))v	a))v	NOUN
ejpam-4556	249	4	0	0	NUM
ejpam-4556	249	5	2(a	2(a	NUM
ejpam-4556	249	6	)	)	PUNCT
ejpam-4556	249	7	γi(t	γi(t	PUNCT
ejpam-4556	249	8	)	)	PUNCT
ejpam-4556	249	9	=	=	SYM
ejpam-4556	250	1	1	1	NUM
ejpam-4556	250	2	αi	αi	VERB
ejpam-4556	250	3	∫	∫	PROPN
ejpam-4556	250	4	a+	a+	PUNCT
ejpam-4556	250	5	0	0	NUM
ejpam-4556	250	6	β̂i(a)ii(t	β̂i(a)ii(t	ADJ
ejpam-4556	250	7	,	,	PUNCT
ejpam-4556	250	8	a)da	a)da	PROPN
ejpam-4556	250	9	(	(	PUNCT
ejpam-4556	250	10	16	16	NUM
ejpam-4556	250	11	)	)	PUNCT
ejpam-4556	250	12	with	with	ADP
ejpam-4556	250	13	boundary	boundary	ADJ
ejpam-4556	250	14	conditions	condition	NOUN
ejpam-4556	250	15	:	:	PUNCT
ejpam-4556	250	16	si(t	si(t	NOUN
ejpam-4556	250	17	,	,	PUNCT
ejpam-4556	250	18	0	0	NUM
ejpam-4556	250	19	)	)	PUNCT
ejpam-4556	250	20	=	=	SYM
ejpam-4556	250	21	li(t	li(t	NOUN
ejpam-4556	250	22	,	,	PUNCT
ejpam-4556	250	23	0	0	NUM
ejpam-4556	250	24	)	)	PUNCT
ejpam-4556	250	25	=	=	NOUN
ejpam-4556	250	26	ii(t	ii(t	NOUN
ejpam-4556	250	27	,	,	PUNCT
ejpam-4556	250	28	0	0	NUM
ejpam-4556	250	29	)	)	PUNCT
ejpam-4556	250	30	=	=	SYM
ejpam-4556	250	31	ji(t	ji(t	NOUN
ejpam-4556	250	32	,	,	PUNCT
ejpam-4556	250	33	0	0	NUM
ejpam-4556	250	34	)	)	PUNCT
ejpam-4556	250	35	=	=	PUNCT
ejpam-4556	250	36	vi(t	vi(t	X
ejpam-4556	250	37	,	,	PUNCT
ejpam-4556	250	38	0	0	NUM
ejpam-4556	250	39	)	)	PUNCT
ejpam-4556	250	40	=	=	SYM
ejpam-4556	250	41	0	0	NUM
ejpam-4556	251	1	we	we	PRON
ejpam-4556	251	2	consider	consider	VERB
ejpam-4556	251	3	the	the	DET
ejpam-4556	251	4	exponential	exponential	ADJ
ejpam-4556	251	5	solutions	solution	NOUN
ejpam-4556	251	6	of	of	ADP
ejpam-4556	251	7	system	system	NOUN
ejpam-4556	251	8	(	(	PUNCT
ejpam-4556	251	9	16	16	NUM
ejpam-4556	251	10	)	)	PUNCT
ejpam-4556	251	11	of	of	ADP
ejpam-4556	251	12	the	the	DET
ejpam-4556	251	13	form	form	NOUN
ejpam-4556	251	14	:	:	PUNCT
ejpam-4556	251	15			PUNCT
ejpam-4556	251	16	si(t	si(t	X
ejpam-4556	251	17	,	,	PUNCT
ejpam-4556	251	18	a	a	PRON
ejpam-4556	251	19	)	)	PUNCT
ejpam-4556	251	20	=	=	PUNCT
ejpam-4556	252	1	si(a)e	si(a)e	NUM
ejpam-4556	252	2	λt	λt	ADP
ejpam-4556	252	3	;	;	PUNCT
ejpam-4556	252	4	li(t	li(t	NOUN
ejpam-4556	252	5	,	,	PUNCT
ejpam-4556	252	6	a	a	PRON
ejpam-4556	252	7	)	)	PUNCT
ejpam-4556	252	8	=	=	SYM
ejpam-4556	253	1	li(a)e	li(a)e	PROPN
ejpam-4556	253	2	λt	λt	ADP
ejpam-4556	253	3	;	;	PUNCT
ejpam-4556	253	4	vi(t	vi(t	X
ejpam-4556	253	5	,	,	PUNCT
ejpam-4556	253	6	a	a	PRON
ejpam-4556	253	7	)	)	PUNCT
ejpam-4556	254	1	=	=	PUNCT
ejpam-4556	254	2	vi(a)e	vi(a)e	X
ejpam-4556	254	3	λt	λt	ADP
ejpam-4556	254	4	ii(t	ii(t	NOUN
ejpam-4556	254	5	,	,	PUNCT
ejpam-4556	254	6	a	a	PRON
ejpam-4556	254	7	)	)	PUNCT
ejpam-4556	255	1	=	=	PUNCT
ejpam-4556	255	2	ii(a)e	ii(a)e	PROPN
ejpam-4556	255	3	λt	λt	ADP
ejpam-4556	255	4	;	;	PUNCT
ejpam-4556	255	5	ji(t	ji(t	NOUN
ejpam-4556	255	6	,	,	PUNCT
ejpam-4556	255	7	a	a	PRON
ejpam-4556	255	8	)	)	PUNCT
ejpam-4556	256	1	=	=	SYM
ejpam-4556	256	2	ji(a)e	ji(a)e	PROPN
ejpam-4556	256	3	λt	λt	ADP
ejpam-4556	256	4	(	(	PUNCT
ejpam-4556	256	5	17	17	NUM
ejpam-4556	256	6	)	)	PUNCT
ejpam-4556	256	7	b.	b.	PROPN
ejpam-4556	256	8	k.	k.	PROPN
ejpam-4556	256	9	abdoul	abdoul	PROPN
ejpam-4556	256	10	wahid	wahid	PROPN
ejpam-4556	256	11	,	,	PUNCT
ejpam-4556	256	12	d.moustapha	d.moustapha	PROPN
ejpam-4556	256	13	,	,	PUNCT
ejpam-4556	256	14	s.	s.	PROPN
ejpam-4556	256	15	bisso	bisso	PROPN
ejpam-4556	256	16	/	/	SYM
ejpam-4556	256	17	eur	eur	PROPN
ejpam-4556	256	18	.	.	PUNCT
ejpam-4556	257	1	j.	j.	PROPN
ejpam-4556	257	2	pure	pure	PROPN
ejpam-4556	257	3	appl	appl	PROPN
ejpam-4556	257	4	.	.	PROPN
ejpam-4556	257	5	math	math	PROPN
ejpam-4556	257	6	,	,	PUNCT
ejpam-4556	257	7	15	15	NUM
ejpam-4556	257	8	(	(	PUNCT
ejpam-4556	257	9	4	4	NUM
ejpam-4556	257	10	)	)	PUNCT
ejpam-4556	257	11	(	(	PUNCT
ejpam-4556	257	12	2022	2022	NUM
ejpam-4556	257	13	)	)	PUNCT
ejpam-4556	257	14	,	,	PUNCT
ejpam-4556	257	15	2054	2054	NUM
ejpam-4556	257	16	-	-	SYM
ejpam-4556	257	17	2073	2073	NUM
ejpam-4556	257	18	2063	2063	NUM
ejpam-4556	257	19	the	the	DET
ejpam-4556	257	20	system	system	NOUN
ejpam-4556	257	21	(	(	PUNCT
ejpam-4556	257	22	16	16	NUM
ejpam-4556	257	23	)	)	PUNCT
ejpam-4556	257	24	becomes	become	VERB
ejpam-4556	257	25	:	:	PUNCT
ejpam-4556	257	26			X
ejpam-4556	257	27	d	d	X
ejpam-4556	257	28	da	da	X
ejpam-4556	257	29	s1(a	s1(a	ADP
ejpam-4556	257	30	)	)	PUNCT
ejpam-4556	257	31	=	=	SYM
ejpam-4556	257	32	ρ21s2(a	ρ21s2(a	NOUN
ejpam-4556	257	33	)	)	PUNCT
ejpam-4556	258	1	−	−	PROPN
ejpam-4556	258	2	(	(	PUNCT
ejpam-4556	258	3	b(a	b(a	X
ejpam-4556	258	4	)	)	PUNCT
ejpam-4556	258	5	+	+	CCONJ
ejpam-4556	258	6	ψ1(a	ψ1(a	X
ejpam-4556	258	7	)	)	PUNCT
ejpam-4556	259	1	+	+	NUM
ejpam-4556	259	2	λ	λ	X
ejpam-4556	259	3	+	+	NUM
ejpam-4556	259	4	ρ11)s1(a	ρ11)s1(a	PROPN
ejpam-4556	259	5	)	)	PUNCT
ejpam-4556	259	6	−	−	PUNCT
ejpam-4556	260	1	[	[	X
ejpam-4556	260	2	γ1β1(a)c1(a)g1(a	γ1β1(a)c1(a)g1(a	PROPN
ejpam-4556	260	3	)	)	PUNCT
ejpam-4556	260	4	−	−	PROPN
ejpam-4556	260	5	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	260	6	)	)	PUNCT
ejpam-4556	260	7	−	−	PROPN
ejpam-4556	261	1	µ2(a)i2(a)]s	µ2(a)i2(a)]s	ADV
ejpam-4556	261	2	0	0	NUM
ejpam-4556	262	1	1(a	1(a	NUM
ejpam-4556	262	2	)	)	PUNCT
ejpam-4556	262	3	d	d	X
ejpam-4556	262	4	da	da	PROPN
ejpam-4556	262	5	l1(a	l1(a	PROPN
ejpam-4556	262	6	)	)	PUNCT
ejpam-4556	262	7	=	=	SYM
ejpam-4556	262	8	ρ22l2(a	ρ22l2(a	NOUN
ejpam-4556	262	9	)	)	PUNCT
ejpam-4556	263	1	−	−	PROPN
ejpam-4556	263	2	(	(	PUNCT
ejpam-4556	263	3	b(a	b(a	X
ejpam-4556	263	4	)	)	PUNCT
ejpam-4556	264	1	+	+	CCONJ
ejpam-4556	264	2	k1	k1	NOUN
ejpam-4556	264	3	+	+	CCONJ
ejpam-4556	264	4	λ	λ	X
ejpam-4556	264	5	+	+	NOUN
ejpam-4556	264	6	ρ12)l1(a	ρ12)l1(a	NUM
ejpam-4556	264	7	)	)	PUNCT
ejpam-4556	265	1	+	+	CCONJ
ejpam-4556	265	2	γ1β1(a)c1(a)g1(a)[(1	γ1β1(a)c1(a)g1(a)[(1	PROPN
ejpam-4556	265	3	−	−	PROPN
ejpam-4556	265	4	ϕ1)s	ϕ1)s	NOUN
ejpam-4556	265	5	0	0	NUM
ejpam-4556	265	6	1(a	1(a	NUM
ejpam-4556	265	7	)	)	PUNCT
ejpam-4556	266	1	+	+	CCONJ
ejpam-4556	266	2	δ1v	δ1v	PROPN
ejpam-4556	266	3	0	0	NUM
ejpam-4556	266	4	1(a	1(a	NUM
ejpam-4556	266	5	)	)	PUNCT
ejpam-4556	266	6	]	]	PUNCT
ejpam-4556	267	1	d	d	X
ejpam-4556	267	2	da	da	PROPN
ejpam-4556	267	3	i1(a	i1(a	PROPN
ejpam-4556	267	4	)	)	PUNCT
ejpam-4556	267	5	=	=	PUNCT
ejpam-4556	267	6	ρ23i2(a	ρ23i2(a	NUM
ejpam-4556	267	7	)	)	PUNCT
ejpam-4556	268	1	+	+	CCONJ
ejpam-4556	268	2	ϕ1β1(a)c1(a)g1(a)γ1	ϕ1β1(a)c1(a)g1(a)γ1	INTJ
ejpam-4556	268	3	+	+	NUM
ejpam-4556	268	4	k1l1(a	k1l1(a	NOUN
ejpam-4556	268	5	)	)	PUNCT
ejpam-4556	268	6	−	−	PROPN
ejpam-4556	268	7	(	(	PUNCT
ejpam-4556	268	8	r1	r1	NOUN
ejpam-4556	268	9	+	+	CCONJ
ejpam-4556	268	10	µ1(a	µ1(a	NOUN
ejpam-4556	268	11	)	)	PUNCT
ejpam-4556	269	1	+	+	CCONJ
ejpam-4556	269	2	b(a	b(a	NOUN
ejpam-4556	269	3	)	)	PUNCT
ejpam-4556	270	1	+	+	NUM
ejpam-4556	270	2	λ	λ	X
ejpam-4556	270	3	+	+	NOUN
ejpam-4556	270	4	ρ13)i1(a	ρ13)i1(a	NUM
ejpam-4556	270	5	)	)	PUNCT
ejpam-4556	270	6	d	d	X
ejpam-4556	270	7	da	da	PROPN
ejpam-4556	270	8	j1(a	j1(a	PROPN
ejpam-4556	270	9	)	)	PUNCT
ejpam-4556	270	10	=	=	SYM
ejpam-4556	270	11	ρ24j2(a	ρ24j2(a	NOUN
ejpam-4556	270	12	)	)	PUNCT
ejpam-4556	271	1	+	+	CCONJ
ejpam-4556	271	2	r1i1(a	r1i1(a	NOUN
ejpam-4556	271	3	)	)	PUNCT
ejpam-4556	271	4	−	−	PROPN
ejpam-4556	271	5	(	(	PUNCT
ejpam-4556	271	6	b(a	b(a	X
ejpam-4556	271	7	)	)	PUNCT
ejpam-4556	272	1	+	+	NUM
ejpam-4556	272	2	λ	λ	X
ejpam-4556	272	3	+	+	NUM
ejpam-4556	272	4	ρ14)j1(a	ρ14)j1(a	PROPN
ejpam-4556	272	5	)	)	PUNCT
ejpam-4556	272	6	d	d	X
ejpam-4556	272	7	da	da	PROPN
ejpam-4556	272	8	v1(a	v1(a	PROPN
ejpam-4556	272	9	)	)	PUNCT
ejpam-4556	272	10	=	=	SYM
ejpam-4556	272	11	ψ1(a)s(a	ψ1(a)s(a	NOUN
ejpam-4556	272	12	)	)	PUNCT
ejpam-4556	273	1	+	+	CCONJ
ejpam-4556	273	2	ρ25v2(a	ρ25v2(a	NOUN
ejpam-4556	273	3	)	)	PUNCT
ejpam-4556	274	1	−	−	PROPN
ejpam-4556	274	2	(	(	PUNCT
ejpam-4556	274	3	ρ15	ρ15	PROPN
ejpam-4556	274	4	+	+	CCONJ
ejpam-4556	274	5	b(a	b(a	NOUN
ejpam-4556	274	6	)	)	PUNCT
ejpam-4556	274	7	+	+	PUNCT
ejpam-4556	275	1	λ)v1(a	λ)v1(a	NOUN
ejpam-4556	275	2	)	)	PUNCT
ejpam-4556	276	1	−	−	PROPN
ejpam-4556	276	2	(	(	PUNCT
ejpam-4556	276	3	δ1γβ1(a)c1(a)g1(a	δ1γβ1(a)c1(a)g1(a	PROPN
ejpam-4556	276	4	)	)	PUNCT
ejpam-4556	276	5	−	−	PROPN
ejpam-4556	277	1	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	277	2	)	)	PUNCT
ejpam-4556	278	1	−	−	PROPN
ejpam-4556	278	2	µ2(a)i2(a))v	µ2(a)i2(a))v	NOUN
ejpam-4556	278	3	0	0	NUM
ejpam-4556	278	4	1(a	1(a	NUM
ejpam-4556	278	5	)	)	PUNCT
ejpam-4556	278	6	d	d	X
ejpam-4556	278	7	da	da	PROPN
ejpam-4556	278	8	s2(a	s2(a	PROPN
ejpam-4556	278	9	)	)	PUNCT
ejpam-4556	278	10	=	=	SYM
ejpam-4556	278	11	ρ11s1(a	ρ11s1(a	PROPN
ejpam-4556	278	12	)	)	PUNCT
ejpam-4556	278	13	−	−	PROPN
ejpam-4556	278	14	(	(	PUNCT
ejpam-4556	278	15	b(a	b(a	X
ejpam-4556	278	16	)	)	PUNCT
ejpam-4556	278	17	+	+	PUNCT
ejpam-4556	278	18	ψ2(a	ψ2(a	X
ejpam-4556	278	19	)	)	PUNCT
ejpam-4556	279	1	+	+	NUM
ejpam-4556	279	2	λ	λ	X
ejpam-4556	279	3	+	+	NOUN
ejpam-4556	279	4	ρ21)s2(a	ρ21)s2(a	NOUN
ejpam-4556	279	5	)	)	PUNCT
ejpam-4556	279	6	−	−	PUNCT
ejpam-4556	280	1	[	[	X
ejpam-4556	280	2	γ2β2(a)c2(a)g2(a	γ2β2(a)c2(a)g2(a	PROPN
ejpam-4556	280	3	)	)	PUNCT
ejpam-4556	280	4	−	−	PROPN
ejpam-4556	281	1	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	281	2	)	)	PUNCT
ejpam-4556	281	3	−	−	PROPN
ejpam-4556	282	1	µ2(a)i2(a)]s	µ2(a)i2(a)]s	ADV
ejpam-4556	282	2	0	0	NUM
ejpam-4556	282	3	2(a	2(a	NUM
ejpam-4556	282	4	)	)	PUNCT
ejpam-4556	282	5	d	d	X
ejpam-4556	282	6	da	da	PROPN
ejpam-4556	282	7	l2(a	l2(a	PROPN
ejpam-4556	282	8	)	)	PUNCT
ejpam-4556	282	9	=	=	SYM
ejpam-4556	282	10	ρ12l1(a	ρ12l1(a	NUM
ejpam-4556	282	11	)	)	PUNCT
ejpam-4556	283	1	−	−	PROPN
ejpam-4556	283	2	(	(	PUNCT
ejpam-4556	283	3	b(a	b(a	X
ejpam-4556	283	4	)	)	PUNCT
ejpam-4556	283	5	+	+	CCONJ
ejpam-4556	283	6	k2	k2	X
ejpam-4556	283	7	+	+	CCONJ
ejpam-4556	283	8	λ	λ	PROPN
ejpam-4556	283	9	+	+	CCONJ
ejpam-4556	283	10	ρ22)l2(a	ρ22)l2(a	NOUN
ejpam-4556	283	11	)	)	PUNCT
ejpam-4556	284	1	+	+	CCONJ
ejpam-4556	284	2	γ2β2(a)c2(a)g2(a)[(1	γ2β2(a)c2(a)g2(a)[(1	PROPN
ejpam-4556	284	3	−	−	NOUN
ejpam-4556	284	4	ϕ2)s	ϕ2)s	ADJ
ejpam-4556	284	5	0	0	NUM
ejpam-4556	284	6	2(a	2(a	NUM
ejpam-4556	284	7	)	)	PUNCT
ejpam-4556	285	1	+	+	CCONJ
ejpam-4556	285	2	δ2v	δ2v	ADV
ejpam-4556	285	3	0	0	NUM
ejpam-4556	285	4	2(a	2(a	NUM
ejpam-4556	285	5	)	)	PUNCT
ejpam-4556	285	6	]	]	PUNCT
ejpam-4556	286	1	d	d	X
ejpam-4556	286	2	da	da	PROPN
ejpam-4556	286	3	i2(a	i2(a	NOUN
ejpam-4556	286	4	)	)	PUNCT
ejpam-4556	286	5	=	=	SYM
ejpam-4556	286	6	ρ13i1(a	ρ13i1(a	NUM
ejpam-4556	286	7	)	)	PUNCT
ejpam-4556	287	1	+	+	CCONJ
ejpam-4556	287	2	ϕ2β2(a)c2(a)g2(a)γ2	ϕ2β2(a)c2(a)g2(a)γ2	NOUN
ejpam-4556	287	3	+	+	X
ejpam-4556	287	4	k2l2(a	k2l2(a	NOUN
ejpam-4556	287	5	)	)	PUNCT
ejpam-4556	287	6	−	−	PROPN
ejpam-4556	287	7	(	(	PUNCT
ejpam-4556	287	8	r2	r2	PROPN
ejpam-4556	287	9	+	+	CCONJ
ejpam-4556	287	10	µ2(a	µ2(a	NOUN
ejpam-4556	287	11	)	)	PUNCT
ejpam-4556	287	12	+	+	CCONJ
ejpam-4556	287	13	b(a	b(a	NOUN
ejpam-4556	287	14	)	)	PUNCT
ejpam-4556	288	1	+	+	NUM
ejpam-4556	288	2	λ	λ	X
ejpam-4556	288	3	+	+	NOUN
ejpam-4556	288	4	ρ13)i2(a	ρ13)i2(a	NUM
ejpam-4556	288	5	)	)	PUNCT
ejpam-4556	288	6	d	d	X
ejpam-4556	288	7	da	da	PROPN
ejpam-4556	288	8	j2(a	j2(a	PROPN
ejpam-4556	288	9	)	)	PUNCT
ejpam-4556	288	10	=	=	SYM
ejpam-4556	288	11	ρ14j1(a	ρ14j1(a	PROPN
ejpam-4556	288	12	)	)	PUNCT
ejpam-4556	288	13	+	+	NUM
ejpam-4556	288	14	r2i2(a	r2i2(a	NOUN
ejpam-4556	288	15	)	)	PUNCT
ejpam-4556	288	16	−	−	PROPN
ejpam-4556	288	17	(	(	PUNCT
ejpam-4556	288	18	b(a	b(a	X
ejpam-4556	288	19	)	)	PUNCT
ejpam-4556	289	1	+	+	NUM
ejpam-4556	289	2	λ	λ	X
ejpam-4556	289	3	+	+	NOUN
ejpam-4556	289	4	ρ14)j2(a	ρ14)j2(a	NOUN
ejpam-4556	289	5	)	)	PUNCT
ejpam-4556	289	6	d	d	X
ejpam-4556	289	7	da	da	PROPN
ejpam-4556	289	8	v2(a	v2(a	NOUN
ejpam-4556	289	9	)	)	PUNCT
ejpam-4556	289	10	=	=	SYM
ejpam-4556	289	11	ψ2(a)s2(a	ψ2(a)s2(a	NOUN
ejpam-4556	289	12	)	)	PUNCT
ejpam-4556	290	1	+	+	CCONJ
ejpam-4556	290	2	ρ15v1(a	ρ15v1(a	NUM
ejpam-4556	290	3	)	)	PUNCT
ejpam-4556	291	1	−	−	PROPN
ejpam-4556	292	1	(	(	PUNCT
ejpam-4556	292	2	ρ25	ρ25	NOUN
ejpam-4556	292	3	+	+	X
ejpam-4556	292	4	b(a	b(a	NOUN
ejpam-4556	292	5	)	)	PUNCT
ejpam-4556	293	1	+	+	SYM
ejpam-4556	293	2	λ)v2(a	λ)v2(a	X
ejpam-4556	293	3	)	)	PUNCT
ejpam-4556	293	4	−	−	PROPN
ejpam-4556	293	5	(	(	PUNCT
ejpam-4556	293	6	δ2γβ2(a)c2(a)g2(a	δ2γβ2(a)c2(a)g2(a	PROPN
ejpam-4556	293	7	)	)	PUNCT
ejpam-4556	293	8	−	−	PROPN
ejpam-4556	294	1	µ1(a)i1(a	µ1(a)i1(a	NOUN
ejpam-4556	294	2	)	)	PUNCT
ejpam-4556	295	1	−	−	PROPN
ejpam-4556	296	1	µ2(a)i2(a))v	µ2(a)i2(a))v	NOUN
ejpam-4556	296	2	0	0	NUM
ejpam-4556	296	3	2(a	2(a	NUM
ejpam-4556	296	4	)	)	PUNCT
ejpam-4556	296	5	γi	γi	NOUN
ejpam-4556	297	1	=	=	SYM
ejpam-4556	297	2	1	1	NUM
ejpam-4556	297	3	αi	αi	VERB
ejpam-4556	297	4	∫	∫	PROPN
ejpam-4556	297	5	a+	a+	X
ejpam-4556	297	6	0	0	NUM
ejpam-4556	297	7	β̂i(a)ii(a)da	β̂i(a)ii(a)da	ADJ
ejpam-4556	297	8	(	(	PUNCT
ejpam-4556	297	9	18	18	NUM
ejpam-4556	297	10	)	)	PUNCT
ejpam-4556	297	11	with	with	ADP
ejpam-4556	297	12	boundary	boundary	ADJ
ejpam-4556	297	13	conditions	condition	NOUN
ejpam-4556	297	14	:	:	PUNCT
ejpam-4556	297	15	si(0	si(0	X
ejpam-4556	297	16	)	)	PUNCT
ejpam-4556	297	17	=	=	SYM
ejpam-4556	297	18	li(0	li(0	PROPN
ejpam-4556	297	19	)	)	PUNCT
ejpam-4556	297	20	=	=	SYM
ejpam-4556	297	21	ii(0	ii(0	NOUN
ejpam-4556	297	22	)	)	PUNCT
ejpam-4556	297	23	=	=	SYM
ejpam-4556	297	24	ji(0	ji(0	NOUN
ejpam-4556	297	25	)	)	PUNCT
ejpam-4556	297	26	=	=	SYM
ejpam-4556	297	27	vi(0	vi(0	PROPN
ejpam-4556	297	28	)	)	PUNCT
ejpam-4556	297	29	=	=	SYM
ejpam-4556	297	30	0	0	PUNCT
ejpam-4556	297	31	let	let	VERB
ejpam-4556	297	32	nψi(a	nψi(a	PROPN
ejpam-4556	297	33	)	)	PUNCT
ejpam-4556	297	34	=	=	PUNCT
ejpam-4556	298	1	(	(	PUNCT
ejpam-4556	298	2	1−	1−	NUM
ejpam-4556	298	3	ϕi)s	ϕi)s	NUM
ejpam-4556	298	4	0	0	PUNCT
ejpam-4556	299	1	i	i	PRON
ejpam-4556	299	2	(	(	PUNCT
ejpam-4556	299	3	a	a	X
ejpam-4556	299	4	)	)	PUNCT
ejpam-4556	299	5	+	+	CCONJ
ejpam-4556	299	6	δiv	δiv	VERB
ejpam-4556	299	7	0	0	NUM
ejpam-4556	299	8	i	i	NOUN
ejpam-4556	299	9	(	(	PUNCT
ejpam-4556	299	10	a	a	NOUN
ejpam-4556	299	11	)	)	PUNCT
ejpam-4556	299	12	(	(	PUNCT
ejpam-4556	299	13	19	19	NUM
ejpam-4556	299	14	)	)	PUNCT
ejpam-4556	299	15	ρj2lj(a	ρj2lj(a	PROPN
ejpam-4556	299	16	)	)	PUNCT
ejpam-4556	299	17	=	=	SYM
ejpam-4556	299	18	ρ̂j2li(a	ρ̂j2li(a	PROPN
ejpam-4556	299	19	)	)	PUNCT
ejpam-4556	299	20	and	and	CCONJ
ejpam-4556	299	21	ρj3ij(a	ρj3ij(a	NUM
ejpam-4556	299	22	)	)	PUNCT
ejpam-4556	299	23	=	=	SYM
ejpam-4556	299	24	ρ̂j3ii(a	ρ̂j3ii(a	PROPN
ejpam-4556	299	25	)	)	PUNCT
ejpam-4556	299	26	(	(	PUNCT
ejpam-4556	299	27	20	20	NUM
ejpam-4556	299	28	)	)	PUNCT
ejpam-4556	299	29	from	from	ADP
ejpam-4556	299	30	equation	equation	NOUN
ejpam-4556	299	31	(	(	PUNCT
ejpam-4556	299	32	18	18	NUM
ejpam-4556	299	33	)	)	PUNCT
ejpam-4556	299	34	and	and	CCONJ
ejpam-4556	299	35	(	(	PUNCT
ejpam-4556	299	36	19	19	NUM
ejpam-4556	299	37	)	)	PUNCT
ejpam-4556	299	38	,	,	PUNCT
ejpam-4556	299	39	we	we	PRON
ejpam-4556	299	40	obtain	obtain	VERB
ejpam-4556	299	41	:	:	PUNCT
ejpam-4556	299	42	li(a	li(a	X
ejpam-4556	299	43	)	)	PUNCT
ejpam-4556	299	44	=	=	SYM
ejpam-4556	300	1	γi	γi	NUM
ejpam-4556	300	2	∫	∫	PROPN
ejpam-4556	301	1	a	a	PRON
ejpam-4556	301	2	0	0	NUM
ejpam-4556	302	1	e−	e−	PROPN
ejpam-4556	302	2	∫	∫	PROPN
ejpam-4556	302	3	a	a	DET
ejpam-4556	302	4	η	η	PROPN
ejpam-4556	302	5	(	(	PUNCT
ejpam-4556	302	6	b(τ)+ki+ρi2−ρ̂j2+λ)dτβi(η)ci(η)gi(η)nψi(η)dη	b(τ)+ki+ρi2−ρ̂j2+λ)dτβi(η)ci(η)gi(η)nψi(η)dη	PROPN
ejpam-4556	302	7	(	(	PUNCT
ejpam-4556	302	8	21	21	NUM
ejpam-4556	302	9	)	)	PUNCT
ejpam-4556	302	10	ii(a	ii(a	NOUN
ejpam-4556	302	11	)	)	PUNCT
ejpam-4556	303	1	=	=	SYM
ejpam-4556	303	2	∫	∫	PROPN
ejpam-4556	304	1	a	a	PRON
ejpam-4556	304	2	0	0	NUM
ejpam-4556	305	1	e−	e−	PROPN
ejpam-4556	305	2	∫	∫	PROPN
ejpam-4556	305	3	a	a	DET
ejpam-4556	305	4	η	η	PROPN
ejpam-4556	305	5	(	(	PUNCT
ejpam-4556	305	6	b(τ)+ri+λ+µi(a)+ρi3−ρ̂j3)dτ	b(τ)+ri+λ+µi(a)+ρi3−ρ̂j3)dτ	PROPN
ejpam-4556	305	7	(	(	PUNCT
ejpam-4556	305	8	kili(η	kili(η	NOUN
ejpam-4556	305	9	)	)	PUNCT
ejpam-4556	305	10	+	+	NUM
ejpam-4556	305	11	ϕiγiβi(η)ci(η)gi(η))dη	ϕiγiβi(η)ci(η)gi(η))dη	NUM
ejpam-4556	305	12	(	(	PUNCT
ejpam-4556	305	13	22	22	NUM
ejpam-4556	305	14	)	)	PUNCT
ejpam-4556	305	15	hence	hence	ADV
ejpam-4556	305	16	,	,	PUNCT
ejpam-4556	305	17	by	by	ADP
ejpam-4556	305	18	equations	equation	NOUN
ejpam-4556	305	19	(	(	PUNCT
ejpam-4556	305	20	21	21	NUM
ejpam-4556	305	21	)	)	PUNCT
ejpam-4556	305	22	and	and	CCONJ
ejpam-4556	305	23	(	(	PUNCT
ejpam-4556	305	24	22	22	NUM
ejpam-4556	305	25	)	)	PUNCT
ejpam-4556	305	26	after	after	ADP
ejpam-4556	305	27	changing	change	VERB
ejpam-4556	305	28	order	order	NOUN
ejpam-4556	305	29	of	of	ADP
ejpam-4556	305	30	integration	integration	NOUN
ejpam-4556	305	31	,	,	PUNCT
ejpam-4556	305	32	we	we	PRON
ejpam-4556	305	33	obtain	obtain	VERB
ejpam-4556	305	34	:	:	PUNCT
ejpam-4556	305	35	ii(a	ii(a	X
ejpam-4556	305	36	)	)	PUNCT
ejpam-4556	305	37	=	=	SYM
ejpam-4556	306	1	γi	γi	NUM
ejpam-4556	306	2	∫	∫	PROPN
ejpam-4556	306	3	a	a	DET
ejpam-4556	306	4	0	0	NUM
ejpam-4556	306	5	e	e	NOUN
ejpam-4556	306	6	−	−	PROPN
ejpam-4556	306	7	∫	∫	PROPN
ejpam-4556	306	8	a	a	DET
ejpam-4556	306	9	η	η	PROPN
ejpam-4556	306	10	(	(	PUNCT
ejpam-4556	306	11	b(τ)+µi(τ)+ri+λ+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	b(τ)+µi(τ)+ri+λ+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	NOUN
ejpam-4556	306	12	)	)	PUNCT
ejpam-4556	307	1	[	[	X
ejpam-4556	307	2	ϕis	ϕis	PROPN
ejpam-4556	307	3	0	0	NUM
ejpam-4556	308	1	i	i	NOUN
ejpam-4556	308	2	(	(	PUNCT
ejpam-4556	308	3	η	η	PROPN
ejpam-4556	308	4	)	)	PUNCT
ejpam-4556	308	5	+	+	NUM
ejpam-4556	308	6	kinψi(η	kinψi(η	PROPN
ejpam-4556	308	7	)	)	PUNCT
ejpam-4556	308	8	∫	∫	PROPN
ejpam-4556	308	9	a	a	DET
ejpam-4556	308	10	η	η	PROPN
ejpam-4556	308	11	e−	e−	PROPN
ejpam-4556	308	12	∫	∫	PROPN
ejpam-4556	308	13	η	η	PROPN
ejpam-4556	308	14	x	x	PROPN
ejpam-4556	308	15	(	(	PUNCT
ejpam-4556	308	16	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dη	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dη	PROPN
ejpam-4556	308	17	(	(	PUNCT
ejpam-4556	308	18	23	23	NUM
ejpam-4556	308	19	)	)	PUNCT
ejpam-4556	308	20	b.	b.	PROPN
ejpam-4556	308	21	k.	k.	PROPN
ejpam-4556	308	22	abdoul	abdoul	PROPN
ejpam-4556	308	23	wahid	wahid	PROPN
ejpam-4556	308	24	,	,	PUNCT
ejpam-4556	308	25	d.moustapha	d.moustapha	PROPN
ejpam-4556	308	26	,	,	PUNCT
ejpam-4556	308	27	s.	s.	PROPN
ejpam-4556	308	28	bisso	bisso	PROPN
ejpam-4556	308	29	/	/	SYM
ejpam-4556	308	30	eur	eur	PROPN
ejpam-4556	308	31	.	.	PUNCT
ejpam-4556	309	1	j.	j.	PROPN
ejpam-4556	309	2	pure	pure	PROPN
ejpam-4556	309	3	appl	appl	PROPN
ejpam-4556	309	4	.	.	PROPN
ejpam-4556	309	5	math	math	PROPN
ejpam-4556	309	6	,	,	PUNCT
ejpam-4556	309	7	15	15	NUM
ejpam-4556	309	8	(	(	PUNCT
ejpam-4556	309	9	4	4	NUM
ejpam-4556	309	10	)	)	PUNCT
ejpam-4556	309	11	(	(	PUNCT
ejpam-4556	309	12	2022	2022	NUM
ejpam-4556	309	13	)	)	PUNCT
ejpam-4556	309	14	,	,	PUNCT
ejpam-4556	309	15	2054	2054	NUM
ejpam-4556	309	16	-	-	SYM
ejpam-4556	309	17	2073	2073	NUM
ejpam-4556	309	18	2064	2064	NUM
ejpam-4556	309	19	injecting	inject	VERB
ejpam-4556	309	20	(	(	PUNCT
ejpam-4556	309	21	23	23	NUM
ejpam-4556	309	22	)	)	PUNCT
ejpam-4556	309	23	in	in	ADP
ejpam-4556	309	24	the	the	DET
ejpam-4556	309	25	expression	expression	NOUN
ejpam-4556	309	26	of	of	ADP
ejpam-4556	309	27	γi	γi	NOUN
ejpam-4556	309	28	,	,	PUNCT
ejpam-4556	309	29	and	and	CCONJ
ejpam-4556	309	30	dividing	divide	VERB
ejpam-4556	309	31	both	both	DET
ejpam-4556	309	32	sides	side	NOUN
ejpam-4556	309	33	the	the	DET
ejpam-4556	309	34	expression	expression	NOUN
ejpam-4556	309	35	by	by	ADP
ejpam-4556	309	36	γi	γi	X
ejpam-4556	309	37	(	(	PUNCT
ejpam-4556	309	38	since	since	SCONJ
ejpam-4556	309	39	γi	γi	PROPN
ejpam-4556	309	40	̸=	̸=	PROPN
ejpam-4556	309	41	0	0	NUM
ejpam-4556	309	42	)	)	PUNCT
ejpam-4556	310	1	,	,	PUNCT
ejpam-4556	310	2	we	we	PRON
ejpam-4556	310	3	get	get	VERB
ejpam-4556	310	4	the	the	DET
ejpam-4556	310	5	characteristic	characteristic	ADJ
ejpam-4556	310	6	equation	equation	NOUN
ejpam-4556	310	7	:	:	PUNCT
ejpam-4556	310	8	1	1	NUM
ejpam-4556	310	9	=	=	SYM
ejpam-4556	310	10	1	1	NUM
ejpam-4556	310	11	αi	αi	VERB
ejpam-4556	310	12	∫	∫	PROPN
ejpam-4556	310	13	a+	a+	X
ejpam-4556	310	14	0	0	NUM
ejpam-4556	310	15	β̂i(a	β̂i(a	PROPN
ejpam-4556	310	16	)	)	PUNCT
ejpam-4556	310	17	∫	∫	PROPN
ejpam-4556	311	1	a	a	PRON
ejpam-4556	311	2	0	0	NUM
ejpam-4556	311	3	e	e	NOUN
ejpam-4556	311	4	−	−	PROPN
ejpam-4556	311	5	∫	∫	PROPN
ejpam-4556	311	6	a	a	DET
ejpam-4556	311	7	η	η	PROPN
ejpam-4556	311	8	(	(	PUNCT
ejpam-4556	311	9	b(τ)+µi(τ)+ri+λ+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	b(τ)+µi(τ)+ri+λ+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	NOUN
ejpam-4556	311	10	)	)	PUNCT
ejpam-4556	312	1	[	[	X
ejpam-4556	312	2	ϕis	ϕis	PROPN
ejpam-4556	312	3	0	0	NUM
ejpam-4556	313	1	i	i	NOUN
ejpam-4556	313	2	(	(	PUNCT
ejpam-4556	313	3	η	η	PROPN
ejpam-4556	313	4	)	)	PUNCT
ejpam-4556	313	5	+	+	NUM
ejpam-4556	313	6	kinψi(η	kinψi(η	PROPN
ejpam-4556	313	7	)	)	PUNCT
ejpam-4556	313	8	∫	∫	PROPN
ejpam-4556	313	9	a	a	DET
ejpam-4556	313	10	η	η	PROPN
ejpam-4556	313	11	e−	e−	PROPN
ejpam-4556	313	12	∫	∫	PROPN
ejpam-4556	313	13	η	η	PROPN
ejpam-4556	313	14	x	x	PROPN
ejpam-4556	313	15	(	(	PUNCT
ejpam-4556	313	16	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	ADJ
ejpam-4556	313	17	(	(	PUNCT
ejpam-4556	313	18	24	24	NUM
ejpam-4556	313	19	)	)	PUNCT
ejpam-4556	313	20	denote	denote	VERB
ejpam-4556	313	21	the	the	DET
ejpam-4556	313	22	right	right	ADJ
ejpam-4556	313	23	-	-	PUNCT
ejpam-4556	313	24	hand	hand	NOUN
ejpam-4556	313	25	side	side	NOUN
ejpam-4556	313	26	of	of	ADP
ejpam-4556	313	27	equation	equation	NOUN
ejpam-4556	313	28	(	(	PUNCT
ejpam-4556	313	29	24	24	NUM
ejpam-4556	313	30	)	)	PUNCT
ejpam-4556	313	31	by	by	ADP
ejpam-4556	313	32	gij(λ	gij(λ	PROPN
ejpam-4556	313	33	)	)	PUNCT
ejpam-4556	313	34	i.e	i.e	PROPN
ejpam-4556	313	35	:	:	PUNCT
ejpam-4556	313	36	gij(λ	gij(λ	NOUN
ejpam-4556	313	37	)	)	PUNCT
ejpam-4556	313	38	=	=	SYM
ejpam-4556	314	1	1	1	NUM
ejpam-4556	314	2	αi	αi	VERB
ejpam-4556	314	3	∫	∫	PROPN
ejpam-4556	314	4	a+	a+	X
ejpam-4556	314	5	0	0	NUM
ejpam-4556	314	6	β̂i(a	β̂i(a	PROPN
ejpam-4556	314	7	)	)	PUNCT
ejpam-4556	314	8	∫	∫	PROPN
ejpam-4556	315	1	a	a	PRON
ejpam-4556	315	2	0	0	NUM
ejpam-4556	315	3	e	e	NOUN
ejpam-4556	315	4	−	−	PROPN
ejpam-4556	315	5	∫	∫	PROPN
ejpam-4556	315	6	a	a	DET
ejpam-4556	315	7	η	η	PROPN
ejpam-4556	315	8	(	(	PUNCT
ejpam-4556	315	9	b(τ)+µi(τ)+ri+λ+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	b(τ)+µi(τ)+ri+λ+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	NOUN
ejpam-4556	315	10	)	)	PUNCT
ejpam-4556	316	1	[	[	X
ejpam-4556	316	2	ϕis	ϕis	PROPN
ejpam-4556	316	3	0	0	NUM
ejpam-4556	317	1	i	i	NOUN
ejpam-4556	317	2	(	(	PUNCT
ejpam-4556	317	3	η	η	PROPN
ejpam-4556	317	4	)	)	PUNCT
ejpam-4556	317	5	+	+	NUM
ejpam-4556	317	6	kinψi(η	kinψi(η	PROPN
ejpam-4556	317	7	)	)	PUNCT
ejpam-4556	317	8	∫	∫	PROPN
ejpam-4556	317	9	a	a	DET
ejpam-4556	317	10	η	η	PROPN
ejpam-4556	317	11	e−	e−	PROPN
ejpam-4556	317	12	∫	∫	PROPN
ejpam-4556	317	13	η	η	PROPN
ejpam-4556	317	14	x	x	PROPN
ejpam-4556	317	15	(	(	PUNCT
ejpam-4556	317	16	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	X
ejpam-4556	317	17	(	(	PUNCT
ejpam-4556	317	18	25	25	NUM
ejpam-4556	317	19	)	)	PUNCT
ejpam-4556	317	20	we	we	PRON
ejpam-4556	317	21	define	define	VERB
ejpam-4556	317	22	the	the	DET
ejpam-4556	317	23	net	net	ADJ
ejpam-4556	317	24	reproductive	reproductive	ADJ
ejpam-4556	317	25	number	number	NOUN
ejpam-4556	317	26	as	as	ADP
ejpam-4556	317	27	ℜi(ψ	ℜi(ψ	NOUN
ejpam-4556	317	28	,	,	PUNCT
ejpam-4556	317	29	ρij	ρij	NOUN
ejpam-4556	317	30	)	)	PUNCT
ejpam-4556	317	31	=	=	SYM
ejpam-4556	317	32	gi(0	gi(0	PROPN
ejpam-4556	317	33	)	)	PUNCT
ejpam-4556	317	34	,	,	PUNCT
ejpam-4556	317	35	i.e	i.e	PROPN
ejpam-4556	317	36	ℜi(ψi	ℜi(ψi	PROPN
ejpam-4556	317	37	,	,	PUNCT
ejpam-4556	317	38	ρij	ρij	NOUN
ejpam-4556	317	39	)	)	PUNCT
ejpam-4556	317	40	=	=	SYM
ejpam-4556	317	41	1	1	NUM
ejpam-4556	317	42	αi	αi	VERB
ejpam-4556	317	43	∫	∫	PROPN
ejpam-4556	317	44	a+	a+	X
ejpam-4556	317	45	0	0	NUM
ejpam-4556	317	46	β̂i(a	β̂i(a	PROPN
ejpam-4556	317	47	)	)	PUNCT
ejpam-4556	317	48	∫	∫	PROPN
ejpam-4556	318	1	a	a	PRON
ejpam-4556	318	2	0	0	NUM
ejpam-4556	318	3	e	e	NOUN
ejpam-4556	318	4	−	−	PROPN
ejpam-4556	318	5	∫	∫	PROPN
ejpam-4556	318	6	a	a	DET
ejpam-4556	318	7	η	η	PROPN
ejpam-4556	318	8	(	(	PUNCT
ejpam-4556	318	9	b(τ)+µi(τ)+ri+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	b(τ)+µi(τ)+ri+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	PROPN
ejpam-4556	318	10	)	)	PUNCT
ejpam-4556	319	1	[	[	X
ejpam-4556	319	2	ϕis	ϕis	PROPN
ejpam-4556	319	3	0	0	NUM
ejpam-4556	320	1	i	i	NOUN
ejpam-4556	320	2	(	(	PUNCT
ejpam-4556	320	3	η	η	PROPN
ejpam-4556	320	4	)	)	PUNCT
ejpam-4556	320	5	+	+	NUM
ejpam-4556	320	6	kinψi(η	kinψi(η	PROPN
ejpam-4556	320	7	)	)	PUNCT
ejpam-4556	320	8	∫	∫	PROPN
ejpam-4556	320	9	a	a	DET
ejpam-4556	320	10	η	η	PROPN
ejpam-4556	320	11	e−	e−	PROPN
ejpam-4556	320	12	∫	∫	PROPN
ejpam-4556	320	13	η	η	PROPN
ejpam-4556	320	14	x	x	PROPN
ejpam-4556	320	15	(	(	PUNCT
ejpam-4556	320	16	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	X
ejpam-4556	320	17	(	(	PUNCT
ejpam-4556	320	18	26	26	NUM
ejpam-4556	320	19	)	)	PUNCT
ejpam-4556	320	20	where	where	SCONJ
ejpam-4556	320	21	ρij	ρij	NOUN
ejpam-4556	320	22	=	=	SYM
ejpam-4556	320	23	(	(	PUNCT
ejpam-4556	320	24	ρi2	ρi2	NOUN
ejpam-4556	320	25	,	,	PUNCT
ejpam-4556	320	26	ρ̂j2	ρ̂j2	NOUN
ejpam-4556	320	27	,	,	PUNCT
ejpam-4556	320	28	ρi3	ρi3	PROPN
ejpam-4556	320	29	,	,	PUNCT
ejpam-4556	320	30	ρ̂j3	ρ̂j3	NOUN
ejpam-4556	320	31	)	)	PUNCT
ejpam-4556	320	32	we	we	PRON
ejpam-4556	320	33	can	can	AUX
ejpam-4556	320	34	obtain	obtain	VERB
ejpam-4556	320	35	an	an	DET
ejpam-4556	320	36	expression	expression	NOUN
ejpam-4556	320	37	for	for	ADP
ejpam-4556	320	38	ℜi0(ψi	ℜi0(ψi	NOUN
ejpam-4556	320	39	,	,	PUNCT
ejpam-4556	320	40	ρij	ρij	NOUN
ejpam-4556	320	41	)	)	PUNCT
ejpam-4556	320	42	in	in	ADP
ejpam-4556	320	43	a	a	DET
ejpam-4556	320	44	similar	similar	ADJ
ejpam-4556	320	45	way	way	NOUN
ejpam-4556	320	46	as	as	ADP
ejpam-4556	320	47	the	the	DET
ejpam-4556	320	48	derivation	derivation	NOUN
ejpam-4556	320	49	of	of	ADP
ejpam-4556	320	50	ℜi(ψ	ℜi(ψ	NOUN
ejpam-4556	320	51	,	,	PUNCT
ejpam-4556	320	52	ρij	ρij	NOUN
ejpam-4556	320	53	)	)	PUNCT
ejpam-4556	320	54	by	by	ADP
ejpam-4556	320	55	considering	consider	VERB
ejpam-4556	320	56	equation	equation	NOUN
ejpam-4556	320	57	(	(	PUNCT
ejpam-4556	320	58	1	1	NUM
ejpam-4556	320	59	)	)	PUNCT
ejpam-4556	320	60	without	without	ADP
ejpam-4556	320	61	vaccination	vaccination	NOUN
ejpam-4556	320	62	;	;	PUNCT
ejpam-4556	320	63	i.e.	i.e.	X
ejpam-4556	320	64	,	,	PUNCT
ejpam-4556	320	65	by	by	ADP
ejpam-4556	320	66	assuming	assume	VERB
ejpam-4556	320	67	that	that	SCONJ
ejpam-4556	320	68	ψi(a	ψi(a	PUNCT
ejpam-4556	320	69	)	)	PUNCT
ejpam-4556	320	70	≡	≡	PROPN
ejpam-4556	320	71	0	0	PUNCT
ejpam-4556	320	72	and	and	CCONJ
ejpam-4556	320	73	neglecting	neglect	VERB
ejpam-4556	320	74	the	the	DET
ejpam-4556	320	75	equation	equation	NOUN
ejpam-4556	320	76	of	of	ADP
ejpam-4556	320	77	vaccinated	vaccinated	ADJ
ejpam-4556	320	78	.	.	PUNCT
ejpam-4556	321	1	it	it	PRON
ejpam-4556	321	2	can	can	AUX
ejpam-4556	321	3	be	be	AUX
ejpam-4556	321	4	shown	show	VERB
ejpam-4556	321	5	that	that	SCONJ
ejpam-4556	321	6	ℜi0(ρij	ℜi0(ρij	VERB
ejpam-4556	321	7	)	)	PUNCT
ejpam-4556	321	8	=	=	SYM
ejpam-4556	321	9	ℜi(0	ℜi(0	PROPN
ejpam-4556	321	10	,	,	PUNCT
ejpam-4556	321	11	ρij	ρij	PROPN
ejpam-4556	321	12	)	)	PUNCT
ejpam-4556	321	13	which	which	PRON
ejpam-4556	321	14	is	be	AUX
ejpam-4556	321	15	called	call	VERB
ejpam-4556	321	16	the	the	DET
ejpam-4556	321	17	basic	basic	ADJ
ejpam-4556	321	18	reproductive	reproductive	ADJ
ejpam-4556	321	19	number	number	NOUN
ejpam-4556	321	20	(	(	PUNCT
ejpam-4556	321	21	when	when	SCONJ
ejpam-4556	321	22	a	a	DET
ejpam-4556	321	23	purely	purely	ADV
ejpam-4556	321	24	susceptible	susceptible	ADJ
ejpam-4556	321	25	population	population	NOUN
ejpam-4556	321	26	is	be	AUX
ejpam-4556	321	27	considered	consider	VERB
ejpam-4556	321	28	)	)	PUNCT
ejpam-4556	321	29	(	(	PUNCT
ejpam-4556	321	30	see	see	VERB
ejpam-4556	321	31	[	[	X
ejpam-4556	321	32	3	3	NUM
ejpam-4556	321	33	]	]	NUM
ejpam-4556	321	34	)	)	PUNCT
ejpam-4556	321	35	.	.	PUNCT
ejpam-4556	322	1	ℜi0(ρij	ℜi0(ρij	X
ejpam-4556	322	2	)	)	PUNCT
ejpam-4556	322	3	=	=	PUNCT
ejpam-4556	323	1	λi	λi	NUM
ejpam-4556	323	2	αi	αi	ADV
ejpam-4556	323	3	∫	∫	PROPN
ejpam-4556	323	4	a+	a+	X
ejpam-4556	323	5	0	0	NUM
ejpam-4556	323	6	β̂i(a	β̂i(a	PROPN
ejpam-4556	323	7	)	)	PUNCT
ejpam-4556	323	8	∫	∫	PROPN
ejpam-4556	324	1	a	a	PRON
ejpam-4556	324	2	0	0	NUM
ejpam-4556	324	3	e	e	NOUN
ejpam-4556	324	4	−	−	PROPN
ejpam-4556	324	5	∫	∫	PROPN
ejpam-4556	324	6	a	a	DET
ejpam-4556	324	7	η	η	PROPN
ejpam-4556	324	8	(	(	PUNCT
ejpam-4556	324	9	b(τ)+µi(τ)+ri+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	b(τ)+µi(τ)+ri+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	PROPN
ejpam-4556	324	10	)	)	PUNCT
ejpam-4556	325	1	[	[	X
ejpam-4556	325	2	ϕi	ϕi	ADP
ejpam-4556	325	3	+	+	X
ejpam-4556	325	4	ki(1−	ki(1−	ADJ
ejpam-4556	325	5	ϕi	ϕi	ADJ
ejpam-4556	325	6	)	)	PUNCT
ejpam-4556	325	7	∫	∫	PROPN
ejpam-4556	325	8	a	a	DET
ejpam-4556	325	9	η	η	PROPN
ejpam-4556	325	10	e−	e−	PROPN
ejpam-4556	325	11	∫	∫	PROPN
ejpam-4556	325	12	η	η	PROPN
ejpam-4556	325	13	x	x	PROPN
ejpam-4556	325	14	(	(	PUNCT
ejpam-4556	325	15	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	X
ejpam-4556	325	16	(	(	PUNCT
ejpam-4556	325	17	27	27	NUM
ejpam-4556	325	18	)	)	PUNCT
ejpam-4556	325	19	let	let	VERB
ejpam-4556	325	20	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	325	21	,	,	PUNCT
ejpam-4556	325	22	ρ	ρ	PROPN
ejpam-4556	325	23	)	)	PUNCT
ejpam-4556	325	24	=	=	SYM
ejpam-4556	326	1	max	max	PROPN
ejpam-4556	326	2	i	i	PROPN
ejpam-4556	326	3	,	,	PUNCT
ejpam-4556	326	4	j	j	PROPN
ejpam-4556	326	5	ℜi(ψi	ℜi(ψi	PROPN
ejpam-4556	326	6	,	,	PUNCT
ejpam-4556	326	7	ρij	ρij	NOUN
ejpam-4556	326	8	)	)	PUNCT
ejpam-4556	326	9	and	and	CCONJ
ejpam-4556	326	10	ℜ0(ρ	ℜ0(ρ	PROPN
ejpam-4556	326	11	)	)	PUNCT
ejpam-4556	327	1	=	=	SYM
ejpam-4556	327	2	max	max	PROPN
ejpam-4556	328	1	i	i	PROPN
ejpam-4556	328	2	,	,	PUNCT
ejpam-4556	328	3	j	j	PROPN
ejpam-4556	328	4	ℜi0(ρij	ℜi0(ρij	PROPN
ejpam-4556	328	5	)	)	PUNCT
ejpam-4556	328	6	the	the	DET
ejpam-4556	328	7	infectious	infectious	ADJ
ejpam-4556	328	8	and	and	CCONJ
ejpam-4556	328	9	latent	latent	NOUN
ejpam-4556	328	10	individuals	individual	NOUN
ejpam-4556	328	11	’	'	PUNCT
ejpam-4556	328	12	migration	migration	NOUN
ejpam-4556	328	13	has	have	VERB
ejpam-4556	328	14	a	a	DET
ejpam-4556	328	15	meaningful	meaningful	ADJ
ejpam-4556	328	16	influence	influence	NOUN
ejpam-4556	328	17	on	on	ADP
ejpam-4556	328	18	the	the	DET
ejpam-4556	328	19	spreading	spreading	NOUN
ejpam-4556	328	20	of	of	ADP
ejpam-4556	328	21	the	the	DET
ejpam-4556	328	22	disease	disease	NOUN
ejpam-4556	328	23	because	because	SCONJ
ejpam-4556	328	24	of	of	ADP
ejpam-4556	328	25	the	the	DET
ejpam-4556	328	26	expression	expression	NOUN
ejpam-4556	328	27	of	of	ADP
ejpam-4556	328	28	the	the	DET
ejpam-4556	328	29	so	so	ADV
ejpam-4556	328	30	many	many	ADJ
ejpam-4556	328	31	reproduction	reproduction	NOUN
ejpam-4556	328	32	.	.	PUNCT
ejpam-4556	329	1	4.3	4.3	NUM
ejpam-4556	329	2	.	.	PUNCT
ejpam-4556	330	1	local	local	ADJ
ejpam-4556	330	2	stability	stability	NOUN
ejpam-4556	330	3	of	of	ADP
ejpam-4556	330	4	the	the	DET
ejpam-4556	330	5	infection	infection	NOUN
ejpam-4556	330	6	-	-	PUNCT
ejpam-4556	330	7	free	free	ADJ
ejpam-4556	330	8	equilibrium	equilibrium	NOUN
ejpam-4556	330	9	theorem	theorem	VERB
ejpam-4556	330	10	2	2	NUM
ejpam-4556	330	11	.	.	PUNCT
ejpam-4556	331	1	the	the	DET
ejpam-4556	331	2	infection	infection	NOUN
ejpam-4556	331	3	-	-	PUNCT
ejpam-4556	331	4	free	free	ADJ
ejpam-4556	331	5	steady	steady	ADJ
ejpam-4556	331	6	-	-	PUNCT
ejpam-4556	331	7	state	state	NOUN
ejpam-4556	331	8	(	(	PUNCT
ejpam-4556	331	9	5	5	NUM
ejpam-4556	331	10	)	)	PUNCT
ejpam-4556	331	11	is	be	AUX
ejpam-4556	331	12	locally	locally	ADV
ejpam-4556	331	13	asymptotically	asymptotically	ADV
ejpam-4556	331	14	stable	stable	ADJ
ejpam-4556	331	15	(	(	PUNCT
ejpam-4556	331	16	l.a.s	l.a.s	NOUN
ejpam-4556	331	17	.	.	PUNCT
ejpam-4556	331	18	)	)	PUNCT
ejpam-4556	332	1	if	if	SCONJ
ejpam-4556	332	2	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	332	3	,	,	PUNCT
ejpam-4556	332	4	ρ	ρ	PROPN
ejpam-4556	332	5	)	)	PUNCT
ejpam-4556	332	6	<	<	X
ejpam-4556	332	7	1	1	NUM
ejpam-4556	332	8	and	and	CCONJ
ejpam-4556	332	9	unstable	unstable	ADJ
ejpam-4556	332	10	if	if	SCONJ
ejpam-4556	332	11	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	332	12	,	,	PUNCT
ejpam-4556	332	13	ρ	ρ	PROPN
ejpam-4556	332	14	)	)	PUNCT
ejpam-4556	332	15	>	>	X
ejpam-4556	332	16	1	1	X
ejpam-4556	332	17	.	.	PUNCT
ejpam-4556	332	18	b.	b.	PROPN
ejpam-4556	332	19	k.	k.	PROPN
ejpam-4556	332	20	abdoul	abdoul	PROPN
ejpam-4556	332	21	wahid	wahid	PROPN
ejpam-4556	332	22	,	,	PUNCT
ejpam-4556	332	23	d.moustapha	d.moustapha	PROPN
ejpam-4556	332	24	,	,	PUNCT
ejpam-4556	332	25	s.	s.	PROPN
ejpam-4556	332	26	bisso	bisso	PROPN
ejpam-4556	332	27	/	/	SYM
ejpam-4556	332	28	eur	eur	PROPN
ejpam-4556	332	29	.	.	PUNCT
ejpam-4556	333	1	j.	j.	PROPN
ejpam-4556	333	2	pure	pure	PROPN
ejpam-4556	333	3	appl	appl	PROPN
ejpam-4556	333	4	.	.	PROPN
ejpam-4556	333	5	math	math	PROPN
ejpam-4556	333	6	,	,	PUNCT
ejpam-4556	333	7	15	15	NUM
ejpam-4556	333	8	(	(	PUNCT
ejpam-4556	333	9	4	4	NUM
ejpam-4556	333	10	)	)	PUNCT
ejpam-4556	333	11	(	(	PUNCT
ejpam-4556	333	12	2022	2022	NUM
ejpam-4556	333	13	)	)	PUNCT
ejpam-4556	333	14	,	,	PUNCT
ejpam-4556	333	15	2054	2054	NUM
ejpam-4556	333	16	-	-	SYM
ejpam-4556	333	17	2073	2073	NUM
ejpam-4556	333	18	2065	2065	NUM
ejpam-4556	333	19	proof	proof	NOUN
ejpam-4556	333	20	.	.	PUNCT
ejpam-4556	334	1	noticing	notice	VERB
ejpam-4556	334	2	that	that	DET
ejpam-4556	334	3	g′	g′	NOUN
ejpam-4556	334	4	ij(λ	ij(λ	PUNCT
ejpam-4556	334	5	)	)	PUNCT
ejpam-4556	334	6	<	<	X
ejpam-4556	334	7	0	0	NUM
ejpam-4556	334	8	;	;	PUNCT
ejpam-4556	334	9	lim	lim	PROPN
ejpam-4556	334	10	λ→+∞	λ→+∞	PROPN
ejpam-4556	334	11	gij(λ	gij(λ	PROPN
ejpam-4556	334	12	)	)	PUNCT
ejpam-4556	334	13	=	=	SYM
ejpam-4556	334	14	0	0	NUM
ejpam-4556	334	15	;	;	PUNCT
ejpam-4556	334	16	lim	lim	PROPN
ejpam-4556	334	17	λ→−∞	λ→−∞	PROPN
ejpam-4556	334	18	gij(λ	gij(λ	PROPN
ejpam-4556	334	19	)	)	PUNCT
ejpam-4556	334	20	=	=	PUNCT
ejpam-4556	335	1	+	+	NUM
ejpam-4556	335	2	∞.	∞.	PROPN
ejpam-4556	335	3	we	we	PRON
ejpam-4556	335	4	know	know	VERB
ejpam-4556	335	5	that	that	DET
ejpam-4556	335	6	equation	equation	NOUN
ejpam-4556	335	7	(	(	PUNCT
ejpam-4556	335	8	23	23	NUM
ejpam-4556	335	9	)	)	PUNCT
ejpam-4556	335	10	has	have	VERB
ejpam-4556	335	11	a	a	DET
ejpam-4556	335	12	unique	unique	ADJ
ejpam-4556	335	13	negative	negative	ADJ
ejpam-4556	335	14	real	real	ADJ
ejpam-4556	335	15	solution	solution	NOUN
ejpam-4556	335	16	λ∗	λ∗	PROPN
ejpam-4556	335	17	if	if	SCONJ
ejpam-4556	335	18	,	,	PUNCT
ejpam-4556	335	19	and	and	CCONJ
ejpam-4556	335	20	only	only	ADV
ejpam-4556	335	21	if	if	SCONJ
ejpam-4556	335	22	,	,	PUNCT
ejpam-4556	335	23	gij(0	gij(0	NOUN
ejpam-4556	335	24	)	)	PUNCT
ejpam-4556	335	25	<	<	X
ejpam-4556	335	26	1	1	NUM
ejpam-4556	335	27	,	,	PUNCT
ejpam-4556	335	28	hence	hence	ADV
ejpam-4556	335	29	,	,	PUNCT
ejpam-4556	335	30	ℜi(ψi	ℜi(ψi	PROPN
ejpam-4556	335	31	,	,	PUNCT
ejpam-4556	335	32	ρij	ρij	NOUN
ejpam-4556	335	33	)	)	PUNCT
ejpam-4556	335	34	<	<	X
ejpam-4556	335	35	1	1	NUM
ejpam-4556	335	36	(	(	PUNCT
ejpam-4556	335	37	also	also	ADV
ejpam-4556	335	38	,	,	PUNCT
ejpam-4556	335	39	equation	equation	NOUN
ejpam-4556	335	40	(	(	PUNCT
ejpam-4556	335	41	23	23	NUM
ejpam-4556	335	42	)	)	PUNCT
ejpam-4556	335	43	has	have	VERB
ejpam-4556	335	44	a	a	DET
ejpam-4556	335	45	unique	unique	ADJ
ejpam-4556	335	46	positive	positive	ADJ
ejpam-4556	335	47	(	(	PUNCT
ejpam-4556	335	48	zero	zero	NUM
ejpam-4556	335	49	)	)	PUNCT
ejpam-4556	335	50	real	real	ADJ
ejpam-4556	335	51	solution	solution	NOUN
ejpam-4556	335	52	if	if	SCONJ
ejpam-4556	335	53	ℜi(ψi	ℜi(ψi	NOUN
ejpam-4556	335	54	,	,	PUNCT
ejpam-4556	335	55	ρij	ρij	NOUN
ejpam-4556	335	56	)	)	PUNCT
ejpam-4556	335	57	>	>	X
ejpam-4556	335	58	1	1	NUM
ejpam-4556	335	59	(	(	PUNCT
ejpam-4556	335	60	ℜi(ψi	ℜi(ψi	PROPN
ejpam-4556	335	61	,	,	PUNCT
ejpam-4556	335	62	ρij	ρij	NOUN
ejpam-4556	335	63	)	)	PUNCT
ejpam-4556	335	64	=	=	SYM
ejpam-4556	336	1	1	1	NUM
ejpam-4556	336	2	)	)	PUNCT
ejpam-4556	336	3	.	.	PUNCT
ejpam-4556	337	1	to	to	PART
ejpam-4556	337	2	show	show	VERB
ejpam-4556	337	3	that	that	PRON
ejpam-4556	337	4	λ∗	λ∗	PROPN
ejpam-4556	337	5	is	be	AUX
ejpam-4556	337	6	the	the	DET
ejpam-4556	337	7	dominant	dominant	ADJ
ejpam-4556	337	8	real	real	ADJ
ejpam-4556	337	9	part	part	NOUN
ejpam-4556	337	10	of	of	ADP
ejpam-4556	337	11	roots	root	NOUN
ejpam-4556	337	12	of	of	ADP
ejpam-4556	337	13	gij(λ	gij(λ	PROPN
ejpam-4556	337	14	)	)	PUNCT
ejpam-4556	337	15	,	,	PUNCT
ejpam-4556	337	16	we	we	PRON
ejpam-4556	337	17	let	let	VERB
ejpam-4556	337	18	λ	λ	X
ejpam-4556	337	19	=	=	PRON
ejpam-4556	337	20	x+	x+	PROPN
ejpam-4556	337	21	iy	iy	PROPN
ejpam-4556	337	22	be	be	AUX
ejpam-4556	337	23	an	an	DET
ejpam-4556	337	24	arbitrary	arbitrary	ADJ
ejpam-4556	337	25	complex	complex	ADJ
ejpam-4556	337	26	solution	solution	NOUN
ejpam-4556	337	27	to	to	ADP
ejpam-4556	337	28	equation	equation	NOUN
ejpam-4556	337	29	(	(	PUNCT
ejpam-4556	337	30	23	23	NUM
ejpam-4556	337	31	)	)	PUNCT
ejpam-4556	337	32	.	.	PUNCT
ejpam-4556	338	1	note	note	VERB
ejpam-4556	338	2	that	that	SCONJ
ejpam-4556	338	3	1	1	NUM
ejpam-4556	338	4	=	=	SYM
ejpam-4556	338	5	gij(λ	gij(λ	NOUN
ejpam-4556	338	6	)	)	PUNCT
ejpam-4556	338	7	=|	=|	NOUN
ejpam-4556	339	1	gij(x+	gij(x+	VERB
ejpam-4556	339	2	iy	iy	NOUN
ejpam-4556	339	3	)	)	PUNCT
ejpam-4556	339	4	|≤	|≤	PROPN
ejpam-4556	339	5	gij(x	gij(x	PROPN
ejpam-4556	339	6	)	)	PUNCT
ejpam-4556	339	7	,	,	PUNCT
ejpam-4556	339	8	indicating	indicate	VERB
ejpam-4556	339	9	that	that	SCONJ
ejpam-4556	339	10	re(λ	re(λ	NOUN
ejpam-4556	339	11	)	)	PUNCT
ejpam-4556	339	12	≤	≤	NUM
ejpam-4556	339	13	λ∗	λ∗	NOUN
ejpam-4556	339	14	.	.	PUNCT
ejpam-4556	340	1	it	it	PRON
ejpam-4556	340	2	follows	follow	VERB
ejpam-4556	340	3	that	that	SCONJ
ejpam-4556	340	4	the	the	DET
ejpam-4556	340	5	infection	infection	NOUN
ejpam-4556	340	6	-	-	PUNCT
ejpam-4556	340	7	free	free	ADJ
ejpam-4556	340	8	steady	steady	ADJ
ejpam-4556	340	9	state	state	NOUN
ejpam-4556	340	10	is	be	AUX
ejpam-4556	340	11	l.a.s	l.a.s	ADJ
ejpam-4556	340	12	.	.	PUNCT
ejpam-4556	341	1	if	if	SCONJ
ejpam-4556	341	2	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	341	3	,	,	PUNCT
ejpam-4556	341	4	ρ	ρ	PROPN
ejpam-4556	341	5	)	)	PUNCT
ejpam-4556	341	6	<	<	X
ejpam-4556	341	7	1	1	NUM
ejpam-4556	341	8	,	,	PUNCT
ejpam-4556	341	9	and	and	CCONJ
ejpam-4556	341	10	unstable	unstable	ADJ
ejpam-4556	341	11	if	if	SCONJ
ejpam-4556	341	12	ℜ(ψ	ℜ(ψ	PROPN
ejpam-4556	341	13	,	,	PUNCT
ejpam-4556	341	14	ρ	ρ	PROPN
ejpam-4556	341	15	)	)	PUNCT
ejpam-4556	341	16	>	>	X
ejpam-4556	342	1	1	1	NUM
ejpam-4556	342	2	.	.	X
ejpam-4556	342	3	5	5	NUM
ejpam-4556	342	4	.	.	X
ejpam-4556	342	5	global	global	ADJ
ejpam-4556	342	6	stability	stability	NOUN
ejpam-4556	342	7	of	of	ADP
ejpam-4556	342	8	the	the	DET
ejpam-4556	342	9	infection	infection	NOUN
ejpam-4556	342	10	-	-	PUNCT
ejpam-4556	342	11	free	free	ADJ
ejpam-4556	342	12	state	state	NOUN
ejpam-4556	342	13	since	since	SCONJ
ejpam-4556	342	14	µi(a	µi(a	NUM
ejpam-4556	342	15	)	)	PUNCT
ejpam-4556	342	16	and	and	CCONJ
ejpam-4556	342	17	ii(t	ii(t	NOUN
ejpam-4556	342	18	,	,	PUNCT
ejpam-4556	342	19	a	a	PRON
ejpam-4556	342	20	)	)	PUNCT
ejpam-4556	342	21	are	be	AUX
ejpam-4556	342	22	bounded	bound	VERB
ejpam-4556	342	23	,	,	PUNCT
ejpam-4556	342	24	there	there	PRON
ejpam-4556	342	25	exists	exist	VERB
ejpam-4556	342	26	a	a	DET
ejpam-4556	342	27	positif	positif	PROPN
ejpam-4556	342	28	constant	constant	PROPN
ejpam-4556	342	29	rc	rc	PROPN
ejpam-4556	342	30	that	that	SCONJ
ejpam-4556	342	31	satifies	satifie	NOUN
ejpam-4556	342	32	0	0	NUM
ejpam-4556	342	33	≤	≤	NUM
ejpam-4556	342	34	∫	∫	PROPN
ejpam-4556	342	35	a	a	DET
ejpam-4556	342	36	η	η	PROPN
ejpam-4556	342	37	2∑	2∑	X
ejpam-4556	342	38	i=1	i=1	PROPN
ejpam-4556	342	39	µi(τ)ii(t−	µi(τ)ii(t−	PROPN
ejpam-4556	342	40	a+	a+	PUNCT
ejpam-4556	342	41	τ	τ	PROPN
ejpam-4556	342	42	,	,	PUNCT
ejpam-4556	342	43	τ)dτ	τ)dτ	PROPN
ejpam-4556	342	44	≤	≤	PROPN
ejpam-4556	342	45	rc	rc	PROPN
ejpam-4556	342	46	(	(	PUNCT
ejpam-4556	342	47	28	28	NUM
ejpam-4556	342	48	)	)	PUNCT
ejpam-4556	342	49	theorem	theorem	NOUN
ejpam-4556	342	50	3	3	NUM
ejpam-4556	342	51	.	.	PUNCT
ejpam-4556	343	1	the	the	DET
ejpam-4556	343	2	disease	disease	NOUN
ejpam-4556	343	3	-	-	PUNCT
ejpam-4556	343	4	free	free	ADJ
ejpam-4556	343	5	equilibrium	equilibrium	NOUN
ejpam-4556	343	6	of	of	ADP
ejpam-4556	343	7	system	system	NOUN
ejpam-4556	343	8	(	(	PUNCT
ejpam-4556	343	9	5	5	NUM
ejpam-4556	343	10	)	)	PUNCT
ejpam-4556	343	11	is	be	AUX
ejpam-4556	343	12	globally	globally	ADV
ejpam-4556	343	13	asymptotically	asymptotically	ADV
ejpam-4556	343	14	stable	stable	ADJ
ejpam-4556	343	15	if	if	SCONJ
ejpam-4556	343	16	ℜ0(ρ	ℜ0(ρ	PROPN
ejpam-4556	343	17	)	)	PUNCT
ejpam-4556	344	1	<	<	X
ejpam-4556	344	2	1	1	NUM
ejpam-4556	344	3	and	and	CCONJ
ejpam-4556	344	4	rc	rc	PROPN
ejpam-4556	344	5	<	<	X
ejpam-4556	344	6	ln	ln	PROPN
ejpam-4556	344	7	(	(	PUNCT
ejpam-4556	344	8	1	1	NUM
ejpam-4556	344	9	ℜ0(ρ	ℜ0(ρ	PROPN
ejpam-4556	344	10	)	)	PUNCT
ejpam-4556	344	11	)	)	PUNCT
ejpam-4556	344	12	.	.	PUNCT
ejpam-4556	345	1	proof	proof	NOUN
ejpam-4556	345	2	.	.	PUNCT
ejpam-4556	346	1	the	the	DET
ejpam-4556	346	2	proof	proof	NOUN
ejpam-4556	346	3	consist	consist	VERB
ejpam-4556	346	4	to	to	PART
ejpam-4556	346	5	show	show	VERB
ejpam-4556	346	6	that	that	SCONJ
ejpam-4556	346	7	ii(t	ii(t	NOUN
ejpam-4556	346	8	,	,	PUNCT
ejpam-4556	346	9	a	a	DET
ejpam-4556	346	10	)	)	PUNCT
ejpam-4556	346	11	−→	−→	NOUN
ejpam-4556	346	12	0	0	NUM
ejpam-4556	346	13	;	;	PUNCT
ejpam-4556	346	14	ji(t	ji(t	PROPN
ejpam-4556	346	15	,	,	PUNCT
ejpam-4556	346	16	a	a	DET
ejpam-4556	346	17	)	)	PUNCT
ejpam-4556	346	18	−→	−→	NOUN
ejpam-4556	346	19	0	0	NUM
ejpam-4556	346	20	;	;	PUNCT
ejpam-4556	346	21	li(t	li(t	NOUN
ejpam-4556	346	22	,	,	PUNCT
ejpam-4556	346	23	a	a	PRON
ejpam-4556	346	24	)	)	PUNCT
ejpam-4556	346	25	−→	−→	NOUN
ejpam-4556	346	26	0	0	NUM
ejpam-4556	346	27	;	;	PUNCT
ejpam-4556	346	28	si(t	si(t	X
ejpam-4556	346	29	,	,	PUNCT
ejpam-4556	346	30	a	a	DET
ejpam-4556	346	31	)	)	PUNCT
ejpam-4556	346	32	−→	−→	NOUN
ejpam-4556	346	33	s0i	s0i	NOUN
ejpam-4556	346	34	(	(	PUNCT
ejpam-4556	346	35	a	a	NOUN
ejpam-4556	346	36	)	)	PUNCT
ejpam-4556	346	37	and	and	CCONJ
ejpam-4556	346	38	vi(t	vi(t	NUM
ejpam-4556	346	39	,	,	PUNCT
ejpam-4556	346	40	a	a	DET
ejpam-4556	346	41	)	)	PUNCT
ejpam-4556	346	42	−→	−→	NOUN
ejpam-4556	346	43	λi	λi	ADP
ejpam-4556	346	44	−	−	PROPN
ejpam-4556	346	45	s0i	s0i	NOUN
ejpam-4556	346	46	(	(	PUNCT
ejpam-4556	346	47	a	a	NOUN
ejpam-4556	346	48	)	)	PUNCT
ejpam-4556	346	49	,	,	PUNCT
ejpam-4556	346	50	when	when	SCONJ
ejpam-4556	346	51	t→	t→	PRON
ejpam-4556	346	52	+	+	ADJ
ejpam-4556	346	53	∞	∞	NOUN
ejpam-4556	346	54	integrating	integrating	NOUN
ejpam-4556	346	55	system	system	NOUN
ejpam-4556	346	56	(	(	PUNCT
ejpam-4556	346	57	5	5	NUM
ejpam-4556	346	58	)	)	PUNCT
ejpam-4556	346	59	along	along	ADP
ejpam-4556	346	60	characteristic	characteristic	ADJ
ejpam-4556	346	61	lines	line	NOUN
ejpam-4556	346	62	we	we	PRON
ejpam-4556	346	63	get	get	VERB
ejpam-4556	346	64	li(t	li(t	NOUN
ejpam-4556	346	65	,	,	PUNCT
ejpam-4556	346	66	a	a	PRON
ejpam-4556	346	67	)	)	PUNCT
ejpam-4556	346	68	=	=	SYM
ejpam-4556	347	1	∫	∫	PROPN
ejpam-4556	348	1	a	a	PRON
ejpam-4556	348	2	0	0	NUM
ejpam-4556	349	1	e−	e−	PROPN
ejpam-4556	349	2	∫	∫	PROPN
ejpam-4556	349	3	a	a	DET
ejpam-4556	349	4	η	η	PROPN
ejpam-4556	349	5	(	(	PUNCT
ejpam-4556	349	6	b(τ)−µi(τ)ii(t−a+τ	b(τ)−µi(τ)ii(t−a+τ	PROPN
ejpam-4556	349	7	,	,	PUNCT
ejpam-4556	349	8	τ)−µj(τ)ij(t−a+τ	τ)−µj(τ)ij(t−a+τ	NOUN
ejpam-4556	349	9	,	,	PUNCT
ejpam-4556	349	10	τ)dτ+ki+ρi2−ρ̂j2)dτβi(η)ci(η)gi(η)λi(t−a+η)×	τ)dτ+ki+ρi2−ρ̂j2)dτβi(η)ci(η)gi(η)λi(t−a+η)×	X
ejpam-4556	350	1	[	[	X
ejpam-4556	350	2	σiji(t−	σiji(t−	ADJ
ejpam-4556	350	3	a+	a+	PUNCT
ejpam-4556	350	4	η	η	PROPN
ejpam-4556	350	5	,	,	PUNCT
ejpam-4556	350	6	η	η	PROPN
ejpam-4556	350	7	)	)	PUNCT
ejpam-4556	350	8	+	+	CCONJ
ejpam-4556	350	9	δivi(t−	δivi(t−	PROPN
ejpam-4556	350	10	η	η	PROPN
ejpam-4556	350	11	+	+	PROPN
ejpam-4556	350	12	a	a	DET
ejpam-4556	350	13	,	,	PUNCT
ejpam-4556	350	14	η	η	NOUN
ejpam-4556	350	15	)	)	PUNCT
ejpam-4556	350	16	+	+	CCONJ
ejpam-4556	350	17	(	(	PUNCT
ejpam-4556	350	18	1−	1−	NUM
ejpam-4556	350	19	ϕi)si(t−	ϕi)si(t−	NOUN
ejpam-4556	350	20	a+	a+	PUNCT
ejpam-4556	350	21	η	η	PROPN
ejpam-4556	350	22	,	,	PUNCT
ejpam-4556	350	23	η)]dη	η)]dη	ADJ
ejpam-4556	350	24	,	,	PUNCT
ejpam-4556	350	25	a	a	DET
ejpam-4556	350	26	<	<	X
ejpam-4556	350	27	t	t	X
ejpam-4556	350	28	(	(	PUNCT
ejpam-4556	350	29	29	29	NUM
ejpam-4556	350	30	)	)	PUNCT
ejpam-4556	350	31	ii(t	ii(t	NOUN
ejpam-4556	350	32	,	,	PUNCT
ejpam-4556	350	33	a	a	PRON
ejpam-4556	350	34	)	)	PUNCT
ejpam-4556	350	35	=	=	SYM
ejpam-4556	350	36	∫	∫	PROPN
ejpam-4556	351	1	a	a	PRON
ejpam-4556	351	2	0	0	NUM
ejpam-4556	351	3	e	e	NOUN
ejpam-4556	351	4	−	−	PROPN
ejpam-4556	351	5	∫	∫	PROPN
ejpam-4556	351	6	a	a	DET
ejpam-4556	351	7	ξ	ξ	PROPN
ejpam-4556	351	8	(	(	PUNCT
ejpam-4556	351	9	b(τ)−µi(τ)ii(t−a+τ	b(τ)−µi(τ)ii(t−a+τ	PROPN
ejpam-4556	351	10	,	,	PUNCT
ejpam-4556	351	11	τ)−µj(τ)ij(t−a+τ	τ)−µj(τ)ij(t−a+τ	PROPN
ejpam-4556	351	12	,	,	PUNCT
ejpam-4556	351	13	τ)+ri+µi(τ)+ρi3−ρ̂j3)dτ	τ)+ri+µi(τ)+ρi3−ρ̂j3)dτ	PUNCT
ejpam-4556	352	1	[	[	X
ejpam-4556	352	2	ϕiβi(ξ)ci(ξ)gi(ξ)λi(t−	ϕiβi(ξ)ci(ξ)gi(ξ)λi(t−	INTJ
ejpam-4556	352	3	a+	a+	SYM
ejpam-4556	352	4	ξ	ξ	NOUN
ejpam-4556	352	5	)	)	PUNCT
ejpam-4556	352	6	+	+	CCONJ
ejpam-4556	352	7	kil(t−	kil(t−	PROPN
ejpam-4556	352	8	a+	a+	X
ejpam-4556	352	9	ξ	ξ	NOUN
ejpam-4556	352	10	,	,	PUNCT
ejpam-4556	352	11	ξ)]dξ	ξ)]dξ	NOUN
ejpam-4556	352	12	,	,	PUNCT
ejpam-4556	352	13	a	a	DET
ejpam-4556	352	14	<	<	X
ejpam-4556	352	15	t	t	X
ejpam-4556	352	16	(	(	PUNCT
ejpam-4556	352	17	30	30	NUM
ejpam-4556	352	18	)	)	PUNCT
ejpam-4556	352	19	b.	b.	PROPN
ejpam-4556	352	20	k.	k.	PROPN
ejpam-4556	352	21	abdoul	abdoul	PROPN
ejpam-4556	352	22	wahid	wahid	PROPN
ejpam-4556	352	23	,	,	PUNCT
ejpam-4556	352	24	d.moustapha	d.moustapha	PROPN
ejpam-4556	352	25	,	,	PUNCT
ejpam-4556	352	26	s.	s.	PROPN
ejpam-4556	352	27	bisso	bisso	PROPN
ejpam-4556	352	28	/	/	SYM
ejpam-4556	352	29	eur	eur	PROPN
ejpam-4556	352	30	.	.	PUNCT
ejpam-4556	353	1	j.	j.	PROPN
ejpam-4556	353	2	pure	pure	PROPN
ejpam-4556	353	3	appl	appl	PROPN
ejpam-4556	353	4	.	.	PROPN
ejpam-4556	353	5	math	math	PROPN
ejpam-4556	353	6	,	,	PUNCT
ejpam-4556	353	7	15	15	NUM
ejpam-4556	353	8	(	(	PUNCT
ejpam-4556	353	9	4	4	NUM
ejpam-4556	353	10	)	)	PUNCT
ejpam-4556	353	11	(	(	PUNCT
ejpam-4556	353	12	2022	2022	NUM
ejpam-4556	353	13	)	)	PUNCT
ejpam-4556	353	14	,	,	PUNCT
ejpam-4556	353	15	2054	2054	NUM
ejpam-4556	353	16	-	-	SYM
ejpam-4556	353	17	2073	2073	NUM
ejpam-4556	353	18	2066	2066	NUM
ejpam-4556	353	19	injecting	inject	VERB
ejpam-4556	353	20	(	(	PUNCT
ejpam-4556	353	21	29	29	NUM
ejpam-4556	353	22	)	)	PUNCT
ejpam-4556	353	23	in	in	ADP
ejpam-4556	353	24	(	(	PUNCT
ejpam-4556	353	25	30	30	NUM
ejpam-4556	353	26	)	)	PUNCT
ejpam-4556	353	27	,	,	PUNCT
ejpam-4556	353	28	and	and	CCONJ
ejpam-4556	353	29	changing	change	VERB
ejpam-4556	353	30	order	order	NOUN
ejpam-4556	353	31	of	of	ADP
ejpam-4556	353	32	integration	integration	NOUN
ejpam-4556	353	33	,	,	PUNCT
ejpam-4556	353	34	we	we	PRON
ejpam-4556	353	35	obtain	obtain	VERB
ejpam-4556	353	36	:	:	PUNCT
ejpam-4556	353	37	ii(t	ii(t	NOUN
ejpam-4556	353	38	,	,	PUNCT
ejpam-4556	353	39	a	a	X
ejpam-4556	353	40	)	)	PUNCT
ejpam-4556	353	41	=	=	SYM
ejpam-4556	354	1	∫	∫	PROPN
ejpam-4556	355	1	a	a	PRON
ejpam-4556	355	2	0	0	NUM
ejpam-4556	356	1	e−	e−	PROPN
ejpam-4556	356	2	∫	∫	PROPN
ejpam-4556	356	3	a	a	DET
ejpam-4556	356	4	η	η	PROPN
ejpam-4556	356	5	(	(	PUNCT
ejpam-4556	356	6	µi(τ)−µi(τ)ii(t−a+τ	µi(τ)−µi(τ)ii(t−a+τ	PROPN
ejpam-4556	356	7	,	,	PUNCT
ejpam-4556	356	8	τ)−µj(τ)ij(t−a+τ	τ)−µj(τ)ij(t−a+τ	PRON
ejpam-4556	356	9	,	,	PUNCT
ejpam-4556	356	10	τ)ri+ρi2−ρ̂j2+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η)λi(t−a+η)×	τ)ri+ρi2−ρ̂j2+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η)λi(t−a+η)×	PUNCT
ejpam-4556	357	1	[	[	X
ejpam-4556	357	2	ϕisi(t−	ϕisi(t−	ADJ
ejpam-4556	357	3	a+	a+	PUNCT
ejpam-4556	357	4	η	η	PROPN
ejpam-4556	357	5	,	,	PUNCT
ejpam-4556	357	6	η	η	PROPN
ejpam-4556	357	7	)	)	PUNCT
ejpam-4556	357	8	+	+	CCONJ
ejpam-4556	357	9	ki(σiji(t−	ki(σiji(t−	PROPN
ejpam-4556	357	10	a+	a+	PUNCT
ejpam-4556	357	11	η	η	PROPN
ejpam-4556	357	12	,	,	PUNCT
ejpam-4556	357	13	η	η	PROPN
ejpam-4556	357	14	)	)	PUNCT
ejpam-4556	357	15	+	+	CCONJ
ejpam-4556	357	16	δivi(t−	δivi(t−	PROPN
ejpam-4556	357	17	η	η	PROPN
ejpam-4556	357	18	+	+	PROPN
ejpam-4556	357	19	a	a	DET
ejpam-4556	357	20	,	,	PUNCT
ejpam-4556	357	21	η	η	NOUN
ejpam-4556	357	22	)	)	PUNCT
ejpam-4556	357	23	+	+	PROPN
ejpam-4556	357	24	(	(	PUNCT
ejpam-4556	357	25	1−	1−	NUM
ejpam-4556	357	26	ϕi)si(t−	ϕi)si(t−	NOUN
ejpam-4556	357	27	a+	a+	PUNCT
ejpam-4556	357	28	η	η	PROPN
ejpam-4556	357	29	,	,	PUNCT
ejpam-4556	357	30	η	η	PROPN
ejpam-4556	357	31	)	)	PUNCT
ejpam-4556	357	32	∫	∫	PROPN
ejpam-4556	357	33	a	a	DET
ejpam-4556	357	34	η	η	PROPN
ejpam-4556	357	35	e−	e−	PROPN
ejpam-4556	357	36	∫	∫	PROPN
ejpam-4556	357	37	η	η	PROPN
ejpam-4556	357	38	ξ	ξ	PROPN
ejpam-4556	357	39	(	(	PUNCT
ejpam-4556	357	40	ri+µi(τ)−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dη	ri+µi(τ)−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dη	PROPN
ejpam-4556	357	41	(	(	PUNCT
ejpam-4556	357	42	31	31	NUM
ejpam-4556	357	43	)	)	PUNCT
ejpam-4556	357	44	injecting	inject	VERB
ejpam-4556	357	45	(	(	PUNCT
ejpam-4556	357	46	31	31	NUM
ejpam-4556	357	47	)	)	PUNCT
ejpam-4556	357	48	in	in	ADP
ejpam-4556	357	49	λi(t	λi(t	NUM
ejpam-4556	357	50	)	)	PUNCT
ejpam-4556	357	51	,	,	PUNCT
ejpam-4556	357	52	and	and	CCONJ
ejpam-4556	357	53	changing	change	VERB
ejpam-4556	357	54	order	order	NOUN
ejpam-4556	357	55	of	of	ADP
ejpam-4556	357	56	integration	integration	NOUN
ejpam-4556	357	57	,	,	PUNCT
ejpam-4556	357	58	we	we	PRON
ejpam-4556	357	59	obtain	obtain	VERB
ejpam-4556	357	60	:	:	PUNCT
ejpam-4556	357	61	λi(t	λi(t	NUM
ejpam-4556	357	62	)	)	PUNCT
ejpam-4556	357	63	=	=	SYM
ejpam-4556	358	1	∫	∫	PROPN
ejpam-4556	359	1	a	a	PRON
ejpam-4556	359	2	0	0	NUM
ejpam-4556	360	1	e−	e−	PROPN
ejpam-4556	360	2	∫	∫	PROPN
ejpam-4556	360	3	a	a	DET
ejpam-4556	360	4	η	η	PROPN
ejpam-4556	360	5	(	(	PUNCT
ejpam-4556	360	6	µi(τ)−µi(τ)ii(t−a+τ	µi(τ)−µi(τ)ii(t−a+τ	PROPN
ejpam-4556	360	7	,	,	PUNCT
ejpam-4556	360	8	τ)−µj(τ)ij(t−a+τ	τ)−µj(τ)ij(t−a+τ	PRON
ejpam-4556	360	9	,	,	PUNCT
ejpam-4556	360	10	τ)ri+ρi2−ρ̂j2+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η)λi(t−a+η)×	τ)ri+ρi2−ρ̂j2+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η)λi(t−a+η)×	PUNCT
ejpam-4556	361	1	[	[	X
ejpam-4556	361	2	ϕisi(t−	ϕisi(t−	ADJ
ejpam-4556	361	3	a+	a+	PUNCT
ejpam-4556	361	4	η	η	PROPN
ejpam-4556	361	5	,	,	PUNCT
ejpam-4556	361	6	η	η	PROPN
ejpam-4556	361	7	)	)	PUNCT
ejpam-4556	361	8	+	+	CCONJ
ejpam-4556	361	9	ki(σiji(t−	ki(σiji(t−	PROPN
ejpam-4556	361	10	a+	a+	PUNCT
ejpam-4556	361	11	η	η	PROPN
ejpam-4556	361	12	,	,	PUNCT
ejpam-4556	361	13	η	η	PROPN
ejpam-4556	361	14	)	)	PUNCT
ejpam-4556	361	15	+	+	CCONJ
ejpam-4556	361	16	δivi(t−	δivi(t−	PROPN
ejpam-4556	361	17	η	η	PROPN
ejpam-4556	361	18	+	+	PROPN
ejpam-4556	361	19	a	a	DET
ejpam-4556	361	20	,	,	PUNCT
ejpam-4556	361	21	η	η	NOUN
ejpam-4556	361	22	)	)	PUNCT
ejpam-4556	361	23	+	+	PROPN
ejpam-4556	361	24	(	(	PUNCT
ejpam-4556	361	25	1−	1−	NUM
ejpam-4556	361	26	ϕi)si(t−	ϕi)si(t−	NOUN
ejpam-4556	361	27	a+	a+	PUNCT
ejpam-4556	361	28	η	η	PROPN
ejpam-4556	361	29	,	,	PUNCT
ejpam-4556	361	30	η	η	PROPN
ejpam-4556	361	31	)	)	PUNCT
ejpam-4556	361	32	∫	∫	PROPN
ejpam-4556	361	33	a	a	DET
ejpam-4556	361	34	η	η	PROPN
ejpam-4556	361	35	e−	e−	PROPN
ejpam-4556	361	36	∫	∫	PROPN
ejpam-4556	361	37	η	η	PROPN
ejpam-4556	361	38	ξ	ξ	PROPN
ejpam-4556	361	39	(	(	PUNCT
ejpam-4556	361	40	ri+µi(τ)−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dη	ri+µi(τ)−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dη	PROPN
ejpam-4556	361	41	(	(	PUNCT
ejpam-4556	361	42	32	32	NUM
ejpam-4556	361	43	)	)	PUNCT
ejpam-4556	361	44	it	it	PRON
ejpam-4556	361	45	eassy	eassy	ADV
ejpam-4556	361	46	see	see	VERB
ejpam-4556	361	47	that	that	SCONJ
ejpam-4556	361	48	ϕisi(t−a+η	ϕisi(t−a+η	PROPN
ejpam-4556	361	49	,	,	PUNCT
ejpam-4556	361	50	η)+ki(σiji(t−a+η	η)+ki(σiji(t−a+η	PROPN
ejpam-4556	361	51	,	,	PUNCT
ejpam-4556	361	52	η)+δivi(t−η+a	η)+δivi(t−η+a	PROPN
ejpam-4556	361	53	,	,	PUNCT
ejpam-4556	361	54	η)+(1−ϕi)si(t−a+η	η)+(1−ϕi)si(t−a+η	PROPN
ejpam-4556	361	55	,	,	PUNCT
ejpam-4556	361	56	η	η	NOUN
ejpam-4556	361	57	)	)	PUNCT
ejpam-4556	361	58	≤	≤	NOUN
ejpam-4556	361	59	λi[ϕi+ki(1−ϕi	λi[ϕi+ki(1−ϕi	NUM
ejpam-4556	361	60	)	)	PUNCT
ejpam-4556	361	61	]	]	PUNCT
ejpam-4556	361	62	by	by	ADP
ejpam-4556	361	63	using	use	VERB
ejpam-4556	361	64	inequality	inequality	NOUN
ejpam-4556	361	65	(	(	PUNCT
ejpam-4556	361	66	28	28	NUM
ejpam-4556	361	67	)	)	PUNCT
ejpam-4556	361	68	and	and	CCONJ
ejpam-4556	361	69	fatou	fatou	PROPN
ejpam-4556	361	70	’s	’s	PART
ejpam-4556	361	71	lemma	lemma	PROPN
ejpam-4556	361	72	,	,	PUNCT
ejpam-4556	361	73	we	we	PRON
ejpam-4556	361	74	have	have	VERB
ejpam-4556	361	75	lim	lim	NOUN
ejpam-4556	361	76	t→+∞	t→+∞	PROPN
ejpam-4556	361	77	λi(t	λi(t	NOUN
ejpam-4556	361	78	)	)	PUNCT
ejpam-4556	361	79	≤	≤	NUM
ejpam-4556	361	80	ercℜi0(ρi	ercℜi0(ρi	NOUN
ejpam-4556	361	81	)	)	PUNCT
ejpam-4556	361	82	lim	lim	PROPN
ejpam-4556	361	83	sup	sup	PROPN
ejpam-4556	361	84	t→+∞	t→+∞	PROPN
ejpam-4556	361	85	λi(t	λi(t	NOUN
ejpam-4556	361	86	)	)	PUNCT
ejpam-4556	361	87	.	.	PUNCT
ejpam-4556	362	1	since	since	SCONJ
ejpam-4556	362	2	ercℜi0(ρi	ercℜi0(ρi	VERB
ejpam-4556	362	3	)	)	PUNCT
ejpam-4556	362	4	<	<	X
ejpam-4556	362	5	1	1	NUM
ejpam-4556	362	6	,	,	PUNCT
ejpam-4556	362	7	⇒	⇒	PROPN
ejpam-4556	362	8	lim	lim	PROPN
ejpam-4556	362	9	supt→+∞	supt→+∞	PROPN
ejpam-4556	362	10	λi(t	λi(t	NUM
ejpam-4556	362	11	)	)	PUNCT
ejpam-4556	362	12	=	=	SYM
ejpam-4556	362	13	0	0	NUM
ejpam-4556	362	14	⇒	⇒	NOUN
ejpam-4556	362	15	limt→+∞	limt→+∞	PROPN
ejpam-4556	362	16	ii(t	ii(t	NOUN
ejpam-4556	362	17	,	,	PUNCT
ejpam-4556	362	18	a	a	PRON
ejpam-4556	362	19	)	)	PUNCT
ejpam-4556	362	20	=	=	SYM
ejpam-4556	362	21	limt→+∞ji(t	limt→+∞ji(t	PROPN
ejpam-4556	362	22	,	,	PUNCT
ejpam-4556	362	23	a	a	PRON
ejpam-4556	362	24	)	)	PUNCT
ejpam-4556	362	25	=	=	SYM
ejpam-4556	362	26	limt→+∞	limt→+∞	X
ejpam-4556	362	27	li(t	li(t	PROPN
ejpam-4556	362	28	,	,	PUNCT
ejpam-4556	362	29	a	a	PRON
ejpam-4556	362	30	)	)	PUNCT
ejpam-4556	362	31	=	=	SYM
ejpam-4556	362	32	0	0	X
ejpam-4556	362	33	limt→+∞	limt→+∞	X
ejpam-4556	362	34	si(t	si(t	PROPN
ejpam-4556	362	35	,	,	PUNCT
ejpam-4556	362	36	a	a	PRON
ejpam-4556	362	37	)	)	PUNCT
ejpam-4556	362	38	=	=	SYM
ejpam-4556	362	39	s0i	s0i	NOUN
ejpam-4556	362	40	(	(	PUNCT
ejpam-4556	362	41	a	a	NOUN
ejpam-4556	362	42	)	)	PUNCT
ejpam-4556	362	43	limt→+∞	limt→+∞	X
ejpam-4556	362	44	vi(t	vi(t	PROPN
ejpam-4556	362	45	,	,	PUNCT
ejpam-4556	362	46	a	a	PRON
ejpam-4556	362	47	)	)	PUNCT
ejpam-4556	362	48	=	=	SYM
ejpam-4556	362	49	λi−s0i	λi−s0i	PROPN
ejpam-4556	362	50	(	(	PUNCT
ejpam-4556	362	51	a)+ρj5v0j	a)+ρj5v0j	NOUN
ejpam-4556	362	52	(	(	PUNCT
ejpam-4556	362	53	a	a	X
ejpam-4556	362	54	)	)	PUNCT
ejpam-4556	362	55	1−ρi5	1−ρi5	PROPN
ejpam-4556	362	56	for	for	ADP
ejpam-4556	362	57	this	this	DET
ejpam-4556	362	58	disease	disease	NOUN
ejpam-4556	362	59	can	can	AUX
ejpam-4556	362	60	disappear	disappear	VERB
ejpam-4556	362	61	without	without	ADP
ejpam-4556	362	62	any	any	DET
ejpam-4556	362	63	form	form	NOUN
ejpam-4556	362	64	of	of	ADP
ejpam-4556	362	65	intervention	intervention	NOUN
ejpam-4556	362	66	,	,	PUNCT
ejpam-4556	362	67	according	accord	VERB
ejpam-4556	362	68	to	to	ADP
ejpam-4556	362	69	this	this	DET
ejpam-4556	362	70	result	result	NOUN
ejpam-4556	362	71	we	we	PRON
ejpam-4556	362	72	must	must	AUX
ejpam-4556	362	73	ensure	ensure	VERB
ejpam-4556	362	74	that	that	SCONJ
ejpam-4556	362	75	there	there	PRON
ejpam-4556	362	76	is	be	VERB
ejpam-4556	362	77	no	no	DET
ejpam-4556	362	78	new	new	ADJ
ejpam-4556	362	79	infected	infect	VERB
ejpam-4556	362	80	and	and	CCONJ
ejpam-4556	362	81	the	the	DET
ejpam-4556	362	82	infectious	infectious	ADJ
ejpam-4556	362	83	rate	rate	NOUN
ejpam-4556	362	84	does	do	AUX
ejpam-4556	362	85	not	not	PART
ejpam-4556	362	86	reach	reach	VERB
ejpam-4556	362	87	a	a	DET
ejpam-4556	362	88	certain	certain	ADJ
ejpam-4556	362	89	spread	spread	NOUN
ejpam-4556	362	90	.	.	PUNCT
ejpam-4556	363	1	b.	b.	PROPN
ejpam-4556	363	2	k.	k.	PROPN
ejpam-4556	363	3	abdoul	abdoul	PROPN
ejpam-4556	363	4	wahid	wahid	PROPN
ejpam-4556	363	5	,	,	PUNCT
ejpam-4556	363	6	d.moustapha	d.moustapha	PROPN
ejpam-4556	363	7	,	,	PUNCT
ejpam-4556	363	8	s.	s.	PROPN
ejpam-4556	363	9	bisso	bisso	PROPN
ejpam-4556	363	10	/	/	SYM
ejpam-4556	363	11	eur	eur	PROPN
ejpam-4556	363	12	.	.	PUNCT
ejpam-4556	364	1	j.	j.	PROPN
ejpam-4556	364	2	pure	pure	PROPN
ejpam-4556	364	3	appl	appl	PROPN
ejpam-4556	364	4	.	.	PROPN
ejpam-4556	364	5	math	math	PROPN
ejpam-4556	364	6	,	,	PUNCT
ejpam-4556	364	7	15	15	NUM
ejpam-4556	364	8	(	(	PUNCT
ejpam-4556	364	9	4	4	NUM
ejpam-4556	364	10	)	)	PUNCT
ejpam-4556	364	11	(	(	PUNCT
ejpam-4556	364	12	2022	2022	NUM
ejpam-4556	364	13	)	)	PUNCT
ejpam-4556	364	14	,	,	PUNCT
ejpam-4556	364	15	2054	2054	NUM
ejpam-4556	364	16	-	-	SYM
ejpam-4556	364	17	2073	2073	NUM
ejpam-4556	364	18	2067	2067	NUM
ejpam-4556	364	19	6	6	NUM
ejpam-4556	364	20	.	.	PUNCT
ejpam-4556	365	1	existence	existence	NOUN
ejpam-4556	365	2	of	of	ADP
ejpam-4556	365	3	an	an	DET
ejpam-4556	365	4	endemic	endemic	ADJ
ejpam-4556	365	5	state	state	NOUN
ejpam-4556	365	6	theorem	theorem	NOUN
ejpam-4556	365	7	4	4	NUM
ejpam-4556	365	8	.	.	PUNCT
ejpam-4556	366	1	an	an	DET
ejpam-4556	366	2	interior	interior	ADJ
ejpam-4556	366	3	endemic	endemic	ADJ
ejpam-4556	366	4	equilibrium	equilibrium	NOUN
ejpam-4556	366	5	of	of	ADP
ejpam-4556	366	6	the	the	DET
ejpam-4556	366	7	form	form	NOUN
ejpam-4556	366	8	e∗	e∗	NOUN
ejpam-4556	366	9	=	=	SYM
ejpam-4556	366	10	(	(	PUNCT
ejpam-4556	366	11	s∗1(a	s∗1(a	PROPN
ejpam-4556	366	12	)	)	PUNCT
ejpam-4556	366	13	,	,	PUNCT
ejpam-4556	366	14	l	l	NOUN
ejpam-4556	366	15	∗	∗	NOUN
ejpam-4556	366	16	1(a	1(a	NUM
ejpam-4556	366	17	)	)	PUNCT
ejpam-4556	366	18	,	,	PUNCT
ejpam-4556	366	19	i	i	PRON
ejpam-4556	366	20	∗	∗	VERB
ejpam-4556	366	21	1(a	1(a	NUM
ejpam-4556	366	22	)	)	PUNCT
ejpam-4556	366	23	,	,	PUNCT
ejpam-4556	366	24	j	j	PROPN
ejpam-4556	366	25	∗	∗	NOUN
ejpam-4556	366	26	1(a	1(a	NUM
ejpam-4556	366	27	)	)	PUNCT
ejpam-4556	366	28	,	,	PUNCT
ejpam-4556	366	29	v	v	ADP
ejpam-4556	366	30	∗	∗	NOUN
ejpam-4556	366	31	1(a	1(a	NUM
ejpam-4556	366	32	)	)	PUNCT
ejpam-4556	366	33	,	,	PUNCT
ejpam-4556	366	34	s	s	NOUN
ejpam-4556	366	35	∗	∗	NOUN
ejpam-4556	366	36	2(a	2(a	NUM
ejpam-4556	366	37	)	)	PUNCT
ejpam-4556	366	38	,	,	PUNCT
ejpam-4556	366	39	l	l	NOUN
ejpam-4556	366	40	∗	∗	NOUN
ejpam-4556	366	41	2(a	2(a	NUM
ejpam-4556	366	42	)	)	PUNCT
ejpam-4556	366	43	,	,	PUNCT
ejpam-4556	366	44	i	i	PRON
ejpam-4556	366	45	∗	∗	VERB
ejpam-4556	366	46	2(a	2(a	NUM
ejpam-4556	366	47	)	)	PUNCT
ejpam-4556	366	48	,	,	PUNCT
ejpam-4556	366	49	j	j	PROPN
ejpam-4556	366	50	∗	∗	NOUN
ejpam-4556	366	51	2(a	2(a	NUM
ejpam-4556	366	52	)	)	PUNCT
ejpam-4556	366	53	,	,	PUNCT
ejpam-4556	366	54	v	v	ADP
ejpam-4556	366	55	∗	∗	NOUN
ejpam-4556	366	56	2(a	2(a	NUM
ejpam-4556	366	57	)	)	PUNCT
ejpam-4556	366	58	)	)	PUNCT
ejpam-4556	367	1	whenever	whenever	SCONJ
ejpam-4556	367	2	ℜ1(ψ1	ℜ1(ψ1	NOUN
ejpam-4556	367	3	)	)	PUNCT
ejpam-4556	367	4	>	>	X
ejpam-4556	367	5	1	1	NUM
ejpam-4556	367	6	and	and	CCONJ
ejpam-4556	367	7	ℜ2(ψ2	ℜ2(ψ2	NUM
ejpam-4556	367	8	)	)	PUNCT
ejpam-4556	367	9	>	>	X
ejpam-4556	368	1	1	1	X
ejpam-4556	368	2	.	.	PUNCT
ejpam-4556	368	3	which	which	PRON
ejpam-4556	368	4	corresponds	correspond	VERB
ejpam-4556	368	5	to	to	ADP
ejpam-4556	368	6	case	case	NOUN
ejpam-4556	368	7	when	when	SCONJ
ejpam-4556	368	8	the	the	DET
ejpam-4556	368	9	disease	disease	NOUN
ejpam-4556	368	10	persists	persist	VERB
ejpam-4556	368	11	in	in	ADP
ejpam-4556	368	12	the	the	DET
ejpam-4556	368	13	two	two	NUM
ejpam-4556	368	14	subpopulations	subpopulation	NOUN
ejpam-4556	368	15	.	.	PUNCT
ejpam-4556	369	1	proof	proof	NOUN
ejpam-4556	369	2	.	.	PUNCT
ejpam-4556	370	1	e∗	e∗	PROPN
ejpam-4556	370	2	=	=	SYM
ejpam-4556	370	3	(	(	PUNCT
ejpam-4556	370	4	s∗1(a	s∗1(a	PROPN
ejpam-4556	370	5	)	)	PUNCT
ejpam-4556	370	6	,	,	PUNCT
ejpam-4556	370	7	l	l	NOUN
ejpam-4556	370	8	∗	∗	NOUN
ejpam-4556	370	9	1(a	1(a	NUM
ejpam-4556	370	10	)	)	PUNCT
ejpam-4556	370	11	,	,	PUNCT
ejpam-4556	370	12	i	i	PRON
ejpam-4556	370	13	∗	∗	VERB
ejpam-4556	370	14	1(a	1(a	NUM
ejpam-4556	370	15	)	)	PUNCT
ejpam-4556	370	16	,	,	PUNCT
ejpam-4556	370	17	j	j	PROPN
ejpam-4556	370	18	∗	∗	NOUN
ejpam-4556	370	19	1(a	1(a	NUM
ejpam-4556	370	20	)	)	PUNCT
ejpam-4556	370	21	,	,	PUNCT
ejpam-4556	370	22	v	v	ADP
ejpam-4556	370	23	∗	∗	NOUN
ejpam-4556	370	24	1(a	1(a	NUM
ejpam-4556	370	25	)	)	PUNCT
ejpam-4556	370	26	,	,	PUNCT
ejpam-4556	370	27	s	s	NOUN
ejpam-4556	370	28	∗	∗	NOUN
ejpam-4556	370	29	2(a	2(a	NUM
ejpam-4556	370	30	)	)	PUNCT
ejpam-4556	370	31	,	,	PUNCT
ejpam-4556	370	32	l	l	NOUN
ejpam-4556	370	33	∗	∗	NOUN
ejpam-4556	370	34	2(a	2(a	NUM
ejpam-4556	370	35	)	)	PUNCT
ejpam-4556	370	36	,	,	PUNCT
ejpam-4556	370	37	i	i	PRON
ejpam-4556	370	38	∗	∗	VERB
ejpam-4556	370	39	2(a	2(a	NUM
ejpam-4556	370	40	)	)	PUNCT
ejpam-4556	370	41	,	,	PUNCT
ejpam-4556	370	42	j	j	PROPN
ejpam-4556	370	43	∗	∗	NOUN
ejpam-4556	370	44	2(a	2(a	NUM
ejpam-4556	370	45	)	)	PUNCT
ejpam-4556	370	46	,	,	PUNCT
ejpam-4556	370	47	v	v	ADP
ejpam-4556	370	48	∗	∗	NOUN
ejpam-4556	370	49	2(a	2(a	NUM
ejpam-4556	370	50	)	)	PUNCT
ejpam-4556	370	51	)	)	PUNCT
ejpam-4556	371	1	satifies	satifie	VERB
ejpam-4556	371	2	the	the	DET
ejpam-4556	371	3	following	follow	VERB
ejpam-4556	371	4	equations	equation	NOUN
ejpam-4556	371	5			X
ejpam-4556	371	6	d	d	PROPN
ejpam-4556	371	7	da	da	PROPN
ejpam-4556	371	8	s∗1(a	s∗1(a	PROPN
ejpam-4556	371	9	)	)	PUNCT
ejpam-4556	371	10	=	=	SYM
ejpam-4556	371	11	αib1(a	αib1(a	NUM
ejpam-4556	371	12	)	)	PUNCT
ejpam-4556	371	13	−	−	NOUN
ejpam-4556	372	1	[	[	X
ejpam-4556	372	2	β1(a)c1(a)g1(a)γ	β1(a)c1(a)g1(a)γ	INTJ
ejpam-4556	372	3	∗	∗	NOUN
ejpam-4556	372	4	1	1	NUM
ejpam-4556	372	5	+	+	CCONJ
ejpam-4556	372	6	ψ1(a	ψ1(a	X
ejpam-4556	372	7	)	)	PUNCT
ejpam-4556	373	1	+	+	CCONJ
ejpam-4556	373	2	b(a	b(a	NOUN
ejpam-4556	373	3	)	)	PUNCT
ejpam-4556	374	1	−	−	PROPN
ejpam-4556	374	2	µ1(a)i	µ1(a)i	ADJ
ejpam-4556	374	3	∗	∗	NOUN
ejpam-4556	374	4	1(a	1(a	NUM
ejpam-4556	374	5	)	)	PUNCT
ejpam-4556	374	6	−	−	PROPN
ejpam-4556	374	7	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	374	8	∗	∗	NOUN
ejpam-4556	374	9	2(a	2(a	NUM
ejpam-4556	374	10	)	)	PUNCT
ejpam-4556	375	1	+	+	NUM
ejpam-4556	375	2	ρ11]s	ρ11]s	NOUN
ejpam-4556	375	3	∗	∗	NOUN
ejpam-4556	375	4	1(a	1(a	NUM
ejpam-4556	375	5	)	)	PUNCT
ejpam-4556	376	1	+	+	CCONJ
ejpam-4556	376	2	ρ21s	ρ21s	NUM
ejpam-4556	376	3	∗	∗	NOUN
ejpam-4556	376	4	2(a	2(a	NUM
ejpam-4556	376	5	)	)	PUNCT
ejpam-4556	376	6	d	d	X
ejpam-4556	376	7	da	da	X
ejpam-4556	376	8	l∗1(a	l∗1(a	PROPN
ejpam-4556	376	9	)	)	PUNCT
ejpam-4556	376	10	=	=	PUNCT
ejpam-4556	377	1	β1(a)c1(a)g1(a)γ	β1(a)c1(a)g1(a)γ	ADJ
ejpam-4556	377	2	∗	∗	NOUN
ejpam-4556	377	3	1	1	NUM
ejpam-4556	377	4	[	[	X
ejpam-4556	377	5	(	(	PUNCT
ejpam-4556	377	6	1	1	NUM
ejpam-4556	377	7	−	−	PROPN
ejpam-4556	377	8	ϕ1)s	ϕ1)s	NOUN
ejpam-4556	377	9	∗	∗	NOUN
ejpam-4556	377	10	1(a	1(a	NUM
ejpam-4556	377	11	)	)	PUNCT
ejpam-4556	378	1	+	+	CCONJ
ejpam-4556	379	1	δ1v	δ1v	PROPN
ejpam-4556	379	2	∗	∗	PUNCT
ejpam-4556	379	3	1	1	NUM
ejpam-4556	379	4	(	(	PUNCT
ejpam-4556	379	5	a	a	NOUN
ejpam-4556	379	6	)	)	PUNCT
ejpam-4556	379	7	+	+	NUM
ejpam-4556	379	8	σ1j	σ1j	PROPN
ejpam-4556	379	9	∗	∗	NOUN
ejpam-4556	379	10	1	1	NUM
ejpam-4556	379	11	(	(	PUNCT
ejpam-4556	379	12	a	a	NOUN
ejpam-4556	379	13	)	)	PUNCT
ejpam-4556	379	14	]	]	PUNCT
ejpam-4556	379	15	−(b(a	−(b(a	X
ejpam-4556	379	16	)	)	PUNCT
ejpam-4556	379	17	+	+	CCONJ
ejpam-4556	379	18	k1	k1	PROPN
ejpam-4556	379	19	−	−	PROPN
ejpam-4556	379	20	µ1(a)i	µ1(a)i	PUNCT
ejpam-4556	379	21	∗	∗	NOUN
ejpam-4556	379	22	1(a	1(a	NUM
ejpam-4556	379	23	)	)	PUNCT
ejpam-4556	379	24	−	−	PROPN
ejpam-4556	379	25	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	379	26	∗	∗	NOUN
ejpam-4556	379	27	2(a	2(a	NUM
ejpam-4556	379	28	)	)	PUNCT
ejpam-4556	380	1	+	+	CCONJ
ejpam-4556	380	2	ρ12)l	ρ12)l	PROPN
ejpam-4556	380	3	∗	∗	NOUN
ejpam-4556	380	4	1(a	1(a	NUM
ejpam-4556	380	5	)	)	PUNCT
ejpam-4556	381	1	+	+	CCONJ
ejpam-4556	381	2	ρ22l	ρ22l	NOUN
ejpam-4556	381	3	∗	∗	NOUN
ejpam-4556	381	4	2(a	2(a	NUM
ejpam-4556	381	5	)	)	PUNCT
ejpam-4556	381	6	d	d	X
ejpam-4556	381	7	da	da	PROPN
ejpam-4556	381	8	i∗1(a	i∗1(a	PROPN
ejpam-4556	381	9	)	)	PUNCT
ejpam-4556	381	10	=	=	PUNCT
ejpam-4556	382	1	k1l	k1l	PROPN
ejpam-4556	382	2	∗	∗	NOUN
ejpam-4556	382	3	1(a	1(a	NUM
ejpam-4556	382	4	)	)	PUNCT
ejpam-4556	383	1	+	+	CCONJ
ejpam-4556	383	2	ϕ1β1(a)c1(a)g1(a)γ	ϕ1β1(a)c1(a)g1(a)γ	NOUN
ejpam-4556	383	3	∗	∗	NOUN
ejpam-4556	383	4	1s	1s	NUM
ejpam-4556	383	5	∗	∗	NOUN
ejpam-4556	383	6	1(a	1(a	NUM
ejpam-4556	383	7	)	)	PUNCT
ejpam-4556	383	8	−	−	PROPN
ejpam-4556	384	1	[	[	X
ejpam-4556	384	2	r1	r1	PROPN
ejpam-4556	384	3	+	+	CCONJ
ejpam-4556	384	4	b(a	b(a	NOUN
ejpam-4556	384	5	)	)	PUNCT
ejpam-4556	384	6	+	+	NUM
ejpam-4556	384	7	µ1(a	µ1(a	X
ejpam-4556	384	8	)	)	PUNCT
ejpam-4556	384	9	−	−	PROPN
ejpam-4556	384	10	µ1(a)i	µ1(a)i	ADJ
ejpam-4556	384	11	∗	∗	NOUN
ejpam-4556	384	12	1(a	1(a	NUM
ejpam-4556	384	13	)	)	PUNCT
ejpam-4556	384	14	−	−	PROPN
ejpam-4556	384	15	µ1(a)i	µ1(a)i	VERB
ejpam-4556	384	16	∗	∗	NOUN
ejpam-4556	384	17	2(a	2(a	NUM
ejpam-4556	384	18	)	)	PUNCT
ejpam-4556	385	1	+	+	NUM
ejpam-4556	385	2	ρ13]i	ρ13]i	NUM
ejpam-4556	385	3	∗	∗	NOUN
ejpam-4556	385	4	1(a	1(a	NUM
ejpam-4556	385	5	)	)	PUNCT
ejpam-4556	386	1	+	+	CCONJ
ejpam-4556	387	1	ρ23i	ρ23i	NOUN
ejpam-4556	387	2	∗	∗	NOUN
ejpam-4556	387	3	2(a	2(a	NUM
ejpam-4556	387	4	)	)	PUNCT
ejpam-4556	387	5	d	d	X
ejpam-4556	387	6	da	da	PROPN
ejpam-4556	387	7	j∗1	j∗1	PROPN
ejpam-4556	387	8	(	(	PUNCT
ejpam-4556	387	9	a	a	NOUN
ejpam-4556	387	10	)	)	PUNCT
ejpam-4556	387	11	=	=	SYM
ejpam-4556	387	12	r1i	r1i	NOUN
ejpam-4556	387	13	∗	∗	NOUN
ejpam-4556	387	14	1(a	1(a	NUM
ejpam-4556	387	15	)	)	PUNCT
ejpam-4556	387	16	−	−	PROPN
ejpam-4556	388	1	(	(	PUNCT
ejpam-4556	388	2	σ1β1(a)c1(a)g1(a)γ	σ1β1(a)c1(a)g1(a)γ	PROPN
ejpam-4556	388	3	∗	∗	PROPN
ejpam-4556	388	4	1	1	NUM
ejpam-4556	388	5	+	+	CCONJ
ejpam-4556	388	6	b(a	b(a	NOUN
ejpam-4556	388	7	)	)	PUNCT
ejpam-4556	388	8	−	−	PROPN
ejpam-4556	388	9	µ1(a)i	µ1(a)i	ADJ
ejpam-4556	388	10	∗	∗	NOUN
ejpam-4556	388	11	1(a	1(a	NUM
ejpam-4556	388	12	)	)	PUNCT
ejpam-4556	388	13	−	−	PROPN
ejpam-4556	388	14	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	388	15	∗	∗	NOUN
ejpam-4556	388	16	2(a	2(a	NUM
ejpam-4556	388	17	)	)	PUNCT
ejpam-4556	389	1	+	+	CCONJ
ejpam-4556	389	2	ρ14)j	ρ14)j	NOUN
ejpam-4556	389	3	∗	∗	NOUN
ejpam-4556	389	4	1	1	NUM
ejpam-4556	389	5	(	(	PUNCT
ejpam-4556	389	6	a	a	NOUN
ejpam-4556	389	7	)	)	PUNCT
ejpam-4556	389	8	+	+	CCONJ
ejpam-4556	389	9	ρ24j	ρ24j	NUM
ejpam-4556	389	10	∗(a	∗(a	NOUN
ejpam-4556	389	11	)	)	PUNCT
ejpam-4556	389	12	d	d	X
ejpam-4556	389	13	da	da	PROPN
ejpam-4556	389	14	v∗1	v∗1	NOUN
ejpam-4556	389	15	(	(	PUNCT
ejpam-4556	389	16	a	a	X
ejpam-4556	389	17	)	)	PUNCT
ejpam-4556	389	18	=	=	SYM
ejpam-4556	389	19	ψ1(a)s	ψ1(a)s	NOUN
ejpam-4556	389	20	∗	∗	NOUN
ejpam-4556	389	21	1(a	1(a	NUM
ejpam-4556	389	22	)	)	PUNCT
ejpam-4556	390	1	+	+	CCONJ
ejpam-4556	390	2	ρ25v	ρ25v	NUM
ejpam-4556	390	3	∗	∗	NOUN
ejpam-4556	390	4	2	2	NUM
ejpam-4556	390	5	(	(	PUNCT
ejpam-4556	390	6	a	a	NOUN
ejpam-4556	390	7	)	)	PUNCT
ejpam-4556	390	8	−	−	PROPN
ejpam-4556	390	9	(	(	PUNCT
ejpam-4556	390	10	δ1β1(a)c1(a)g1(a)γ	δ1β1(a)c1(a)g1(a)γ	ADJ
ejpam-4556	390	11	∗	∗	NOUN
ejpam-4556	390	12	1	1	NUM
ejpam-4556	390	13	+	+	ADJ
ejpam-4556	390	14	b(a	b(a	NOUN
ejpam-4556	390	15	)	)	PUNCT
ejpam-4556	390	16	−	−	PROPN
ejpam-4556	390	17	µ1(a)i	µ1(a)i	ADJ
ejpam-4556	390	18	∗	∗	NOUN
ejpam-4556	390	19	1(a	1(a	NUM
ejpam-4556	390	20	)	)	PUNCT
ejpam-4556	390	21	−	−	PROPN
ejpam-4556	390	22	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	390	23	∗	∗	NOUN
ejpam-4556	390	24	2(a	2(a	NUM
ejpam-4556	390	25	)	)	PUNCT
ejpam-4556	391	1	+	+	CCONJ
ejpam-4556	392	1	ρ15)v	ρ15)v	NOUN
ejpam-4556	392	2	∗	∗	NOUN
ejpam-4556	392	3	1	1	NUM
ejpam-4556	392	4	(	(	PUNCT
ejpam-4556	392	5	a	a	NOUN
ejpam-4556	392	6	)	)	PUNCT
ejpam-4556	392	7	d	d	PROPN
ejpam-4556	392	8	da	da	PROPN
ejpam-4556	392	9	s∗2(a	s∗2(a	PROPN
ejpam-4556	392	10	)	)	PUNCT
ejpam-4556	392	11	=	=	SYM
ejpam-4556	392	12	α2b2(a	α2b2(a	NOUN
ejpam-4556	392	13	)	)	PUNCT
ejpam-4556	392	14	−	−	PUNCT
ejpam-4556	393	1	[	[	X
ejpam-4556	393	2	β2(a)c2(a)g2(a)γ	β2(a)c2(a)g2(a)γ	ADJ
ejpam-4556	393	3	∗	∗	NOUN
ejpam-4556	393	4	2	2	NUM
ejpam-4556	393	5	+	+	CCONJ
ejpam-4556	393	6	ψ2(a	ψ2(a	X
ejpam-4556	393	7	)	)	PUNCT
ejpam-4556	394	1	+	+	CCONJ
ejpam-4556	394	2	b(a	b(a	NOUN
ejpam-4556	394	3	)	)	PUNCT
ejpam-4556	395	1	−	−	PROPN
ejpam-4556	395	2	µ1(a)i	µ1(a)i	ADJ
ejpam-4556	395	3	∗	∗	NOUN
ejpam-4556	395	4	1(a	1(a	NUM
ejpam-4556	395	5	)	)	PUNCT
ejpam-4556	395	6	−	−	PROPN
ejpam-4556	396	1	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	396	2	∗	∗	NOUN
ejpam-4556	396	3	2(a	2(a	NUM
ejpam-4556	396	4	)	)	PUNCT
ejpam-4556	397	1	+	+	CCONJ
ejpam-4556	397	2	ρ21]s	ρ21]s	PROPN
ejpam-4556	397	3	∗	∗	NOUN
ejpam-4556	397	4	2(a	2(a	NUM
ejpam-4556	397	5	)	)	PUNCT
ejpam-4556	398	1	+	+	NUM
ejpam-4556	398	2	ρ11s	ρ11s	NOUN
ejpam-4556	398	3	∗	∗	NOUN
ejpam-4556	398	4	1(a	1(a	NUM
ejpam-4556	398	5	)	)	PUNCT
ejpam-4556	398	6	d	d	PRON
ejpam-4556	398	7	da	da	PROPN
ejpam-4556	398	8	l∗2(a	l∗2(a	PROPN
ejpam-4556	398	9	)	)	PUNCT
ejpam-4556	398	10	=	=	PUNCT
ejpam-4556	399	1	β2(a)c2(a)g2(a)γ	β2(a)c2(a)g2(a)γ	NOUN
ejpam-4556	399	2	∗	∗	NOUN
ejpam-4556	399	3	2	2	NUM
ejpam-4556	400	1	[	[	X
ejpam-4556	400	2	(	(	PUNCT
ejpam-4556	400	3	1	1	NUM
ejpam-4556	400	4	−	−	NOUN
ejpam-4556	400	5	ϕ2)s	ϕ2)s	ADJ
ejpam-4556	400	6	∗	∗	NOUN
ejpam-4556	400	7	2(a	2(a	NUM
ejpam-4556	400	8	)	)	PUNCT
ejpam-4556	400	9	+	+	CCONJ
ejpam-4556	400	10	δ2v	δ2v	PROPN
ejpam-4556	400	11	∗	∗	NOUN
ejpam-4556	400	12	2	2	NUM
ejpam-4556	400	13	(	(	PUNCT
ejpam-4556	400	14	a	a	NOUN
ejpam-4556	400	15	)	)	PUNCT
ejpam-4556	400	16	+	+	CCONJ
ejpam-4556	400	17	σ2j	σ2j	PROPN
ejpam-4556	400	18	∗	∗	PROPN
ejpam-4556	400	19	2	2	NUM
ejpam-4556	400	20	(	(	PUNCT
ejpam-4556	400	21	a	a	NOUN
ejpam-4556	400	22	)	)	PUNCT
ejpam-4556	400	23	]	]	PUNCT
ejpam-4556	400	24	−(b(a	−(b(a	ADJ
ejpam-4556	400	25	)	)	PUNCT
ejpam-4556	400	26	+	+	CCONJ
ejpam-4556	400	27	k2	k2	ADJ
ejpam-4556	400	28	−	−	PROPN
ejpam-4556	400	29	µ1(a)i	µ1(a)i	PUNCT
ejpam-4556	400	30	∗	∗	NOUN
ejpam-4556	400	31	1(a	1(a	NUM
ejpam-4556	400	32	)	)	PUNCT
ejpam-4556	400	33	−	−	PROPN
ejpam-4556	400	34	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	400	35	∗	∗	NOUN
ejpam-4556	400	36	2(a	2(a	NUM
ejpam-4556	400	37	)	)	PUNCT
ejpam-4556	401	1	+	+	CCONJ
ejpam-4556	401	2	ρ22)l	ρ22)l	PROPN
ejpam-4556	401	3	∗	∗	NOUN
ejpam-4556	401	4	2(a	2(a	NUM
ejpam-4556	401	5	)	)	PUNCT
ejpam-4556	402	1	+	+	CCONJ
ejpam-4556	402	2	ρ12l	ρ12l	PROPN
ejpam-4556	402	3	∗	∗	NOUN
ejpam-4556	402	4	1(a	1(a	NUM
ejpam-4556	402	5	)	)	PUNCT
ejpam-4556	402	6	d	d	PROPN
ejpam-4556	402	7	da	da	PROPN
ejpam-4556	402	8	i∗2(a	i∗2(a	PROPN
ejpam-4556	402	9	)	)	PUNCT
ejpam-4556	402	10	=	=	PUNCT
ejpam-4556	403	1	k2l	k2l	PROPN
ejpam-4556	403	2	∗	∗	NOUN
ejpam-4556	403	3	2(a	2(a	NUM
ejpam-4556	403	4	)	)	PUNCT
ejpam-4556	404	1	+	+	CCONJ
ejpam-4556	404	2	ϕ2β2(a)c2(a)g2(a)γ	ϕ2β2(a)c2(a)g2(a)γ	NOUN
ejpam-4556	404	3	∗	∗	VERB
ejpam-4556	404	4	2s	2s	NUM
ejpam-4556	404	5	∗	∗	NOUN
ejpam-4556	404	6	2(a	2(a	NUM
ejpam-4556	404	7	)	)	PUNCT
ejpam-4556	404	8	−	−	NOUN
ejpam-4556	405	1	[	[	X
ejpam-4556	405	2	r2	r2	PROPN
ejpam-4556	405	3	+	+	X
ejpam-4556	405	4	b(a	b(a	NOUN
ejpam-4556	405	5	)	)	PUNCT
ejpam-4556	405	6	+	+	CCONJ
ejpam-4556	405	7	µ2(a	µ2(a	NOUN
ejpam-4556	405	8	)	)	PUNCT
ejpam-4556	405	9	−	−	PROPN
ejpam-4556	405	10	µ1(a)i	µ1(a)i	VERB
ejpam-4556	405	11	∗	∗	NOUN
ejpam-4556	405	12	1(a	1(a	NUM
ejpam-4556	405	13	)	)	PUNCT
ejpam-4556	405	14	−	−	PROPN
ejpam-4556	405	15	µ1(a)i	µ1(a)i	VERB
ejpam-4556	405	16	∗	∗	NOUN
ejpam-4556	405	17	2(a	2(a	NUM
ejpam-4556	405	18	)	)	PUNCT
ejpam-4556	406	1	+	+	NUM
ejpam-4556	406	2	ρ23]i	ρ23]i	NUM
ejpam-4556	406	3	∗	∗	NOUN
ejpam-4556	406	4	2(a	2(a	NUM
ejpam-4556	406	5	)	)	PUNCT
ejpam-4556	407	1	+	+	NUM
ejpam-4556	407	2	ρ13i	ρ13i	PROPN
ejpam-4556	407	3	∗	∗	NOUN
ejpam-4556	407	4	1(a	1(a	NUM
ejpam-4556	407	5	)	)	PUNCT
ejpam-4556	407	6	d	d	X
ejpam-4556	407	7	da	da	PROPN
ejpam-4556	407	8	j∗2	j∗2	PROPN
ejpam-4556	407	9	(	(	PUNCT
ejpam-4556	407	10	a	a	X
ejpam-4556	407	11	)	)	PUNCT
ejpam-4556	407	12	=	=	SYM
ejpam-4556	407	13	r2i	r2i	NOUN
ejpam-4556	407	14	∗	∗	NOUN
ejpam-4556	407	15	2(a	2(a	NUM
ejpam-4556	407	16	)	)	PUNCT
ejpam-4556	407	17	−	−	PROPN
ejpam-4556	407	18	(	(	PUNCT
ejpam-4556	407	19	σ2β2(a)c2(a)g2(a)γ	σ2β2(a)c2(a)g2(a)γ	PROPN
ejpam-4556	407	20	∗	∗	NOUN
ejpam-4556	407	21	2	2	NUM
ejpam-4556	407	22	+	+	CCONJ
ejpam-4556	407	23	b(a	b(a	NOUN
ejpam-4556	407	24	)	)	PUNCT
ejpam-4556	407	25	−	−	PROPN
ejpam-4556	407	26	µ1(a)i	µ1(a)i	ADJ
ejpam-4556	407	27	∗	∗	NOUN
ejpam-4556	407	28	1(a	1(a	NUM
ejpam-4556	407	29	)	)	PUNCT
ejpam-4556	407	30	−	−	PROPN
ejpam-4556	407	31	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	407	32	∗	∗	NOUN
ejpam-4556	407	33	2(a	2(a	NUM
ejpam-4556	407	34	)	)	PUNCT
ejpam-4556	408	1	+	+	CCONJ
ejpam-4556	408	2	ρ24)j	ρ24)j	PROPN
ejpam-4556	408	3	∗	∗	X
ejpam-4556	408	4	2	2	NUM
ejpam-4556	408	5	(	(	PUNCT
ejpam-4556	408	6	a	a	NOUN
ejpam-4556	408	7	)	)	PUNCT
ejpam-4556	408	8	+	+	CCONJ
ejpam-4556	408	9	ρ14j	ρ14j	PROPN
ejpam-4556	408	10	∗	∗	NOUN
ejpam-4556	408	11	1	1	NUM
ejpam-4556	408	12	(	(	PUNCT
ejpam-4556	408	13	a	a	NOUN
ejpam-4556	408	14	)	)	PUNCT
ejpam-4556	408	15	d	d	PROPN
ejpam-4556	408	16	da	da	PROPN
ejpam-4556	408	17	v∗2	v∗2	NOUN
ejpam-4556	408	18	(	(	PUNCT
ejpam-4556	408	19	a	a	X
ejpam-4556	408	20	)	)	PUNCT
ejpam-4556	408	21	=	=	PUNCT
ejpam-4556	408	22	ψ2(a)s	ψ2(a)	NOUN
ejpam-4556	408	23	∗	∗	NOUN
ejpam-4556	408	24	2(a	2(a	NUM
ejpam-4556	408	25	)	)	PUNCT
ejpam-4556	409	1	+	+	CCONJ
ejpam-4556	409	2	ρ15v	ρ15v	NUM
ejpam-4556	409	3	∗	∗	NOUN
ejpam-4556	409	4	1	1	NUM
ejpam-4556	409	5	(	(	PUNCT
ejpam-4556	409	6	a	a	NOUN
ejpam-4556	409	7	)	)	PUNCT
ejpam-4556	409	8	−	−	PROPN
ejpam-4556	409	9	(	(	PUNCT
ejpam-4556	409	10	δ2β2(a)c2(a)g2(a)γ	δ2β2(a)c2(a)g2(a)γ	PROPN
ejpam-4556	409	11	∗	∗	NOUN
ejpam-4556	409	12	2	2	NUM
ejpam-4556	409	13	+	+	CCONJ
ejpam-4556	409	14	b(a	b(a	NOUN
ejpam-4556	409	15	)	)	PUNCT
ejpam-4556	409	16	−	−	PROPN
ejpam-4556	409	17	µ1(a)i	µ1(a)i	ADJ
ejpam-4556	409	18	∗	∗	NOUN
ejpam-4556	409	19	1(a	1(a	NUM
ejpam-4556	409	20	)	)	PUNCT
ejpam-4556	409	21	−	−	PROPN
ejpam-4556	409	22	µ2(a)i	µ2(a)i	PROPN
ejpam-4556	409	23	∗	∗	NOUN
ejpam-4556	409	24	2(a	2(a	NUM
ejpam-4556	409	25	)	)	PUNCT
ejpam-4556	409	26	+	+	CCONJ
ejpam-4556	410	1	ρ25)v	ρ25)v	ADV
ejpam-4556	410	2	∗	∗	NOUN
ejpam-4556	410	3	2	2	NUM
ejpam-4556	410	4	(	(	PUNCT
ejpam-4556	410	5	a	a	NOUN
ejpam-4556	410	6	)	)	PUNCT
ejpam-4556	410	7	γ∗	γ∗	NOUN
ejpam-4556	410	8	i	i	NOUN
ejpam-4556	411	1	=	=	PUNCT
ejpam-4556	411	2	∫	∫	PROPN
ejpam-4556	411	3	a+	a+	PUNCT
ejpam-4556	412	1	0	0	NUM
ejpam-4556	412	2	β̂i(a)i	β̂i(a)i	NUM
ejpam-4556	412	3	∗	∗	NOUN
ejpam-4556	412	4	i	i	PRON
ejpam-4556	412	5	(	(	PUNCT
ejpam-4556	412	6	a)da	a)da	PROPN
ejpam-4556	412	7	(	(	PUNCT
ejpam-4556	412	8	33	33	NUM
ejpam-4556	412	9	)	)	PUNCT
ejpam-4556	412	10	s∗i	s∗i	NUM
ejpam-4556	412	11	(	(	PUNCT
ejpam-4556	412	12	0	0	NUM
ejpam-4556	412	13	)	)	PUNCT
ejpam-4556	412	14	=	=	SYM
ejpam-4556	413	1	λi	λi	NOUN
ejpam-4556	413	2	;	;	PUNCT
ejpam-4556	413	3	l∗i	l∗i	NUM
ejpam-4556	413	4	(	(	PUNCT
ejpam-4556	413	5	0	0	NUM
ejpam-4556	413	6	)	)	PUNCT
ejpam-4556	413	7	=	=	PRON
ejpam-4556	413	8	i∗i	i∗i	X
ejpam-4556	413	9	(	(	PUNCT
ejpam-4556	413	10	0	0	NUM
ejpam-4556	413	11	)	)	PUNCT
ejpam-4556	413	12	=	=	PUNCT
ejpam-4556	413	13	j∗i	j∗i	PUNCT
ejpam-4556	413	14	(	(	PUNCT
ejpam-4556	413	15	0	0	NUM
ejpam-4556	413	16	)	)	PUNCT
ejpam-4556	413	17	=	=	NOUN
ejpam-4556	413	18	v∗i	v∗i	X
ejpam-4556	413	19	(	(	PUNCT
ejpam-4556	413	20	0	0	NUM
ejpam-4556	413	21	)	)	PUNCT
ejpam-4556	413	22	=	=	SYM
ejpam-4556	413	23	0	0	NUM
ejpam-4556	413	24	(	(	PUNCT
ejpam-4556	413	25	34	34	NUM
ejpam-4556	413	26	)	)	PUNCT
ejpam-4556	413	27	s∗i	s∗i	NUM
ejpam-4556	413	28	(	(	PUNCT
ejpam-4556	413	29	a	a	NOUN
ejpam-4556	413	30	)	)	PUNCT
ejpam-4556	413	31	=	=	SYM
ejpam-4556	413	32	λie	λie	NOUN
ejpam-4556	413	33	−	−	PROPN
ejpam-4556	414	1	∫	∫	PROPN
ejpam-4556	414	2	a	a	DET
ejpam-4556	414	3	0	0	NUM
ejpam-4556	415	1	[	[	X
ejpam-4556	415	2	βi(τ)ci(τ)gi(τ)γ	βi(τ)ci(τ)gi(τ)γ	X
ejpam-4556	415	3	∗+b(τ)−µ1(τ)i∗1(τ)−µ2(τ)i∗2(τ)+ρi1−ρ̂j1]dτ	∗+b(τ)−µ1(τ)i∗1(τ)−µ2(τ)i∗2(τ)+ρi1−ρ̂j1]dτ	NOUN
ejpam-4556	415	4	+	+	ADV
ejpam-4556	415	5	αi	αi	VERB
ejpam-4556	415	6	∫	∫	PROPN
ejpam-4556	415	7	a	a	DET
ejpam-4556	415	8	0	0	NUM
ejpam-4556	415	9	bi(η)e	bi(η)e	NOUN
ejpam-4556	415	10	−	−	PROPN
ejpam-4556	415	11	∫	∫	PROPN
ejpam-4556	415	12	a	a	DET
ejpam-4556	415	13	η	η	PROPN
ejpam-4556	415	14	[	[	X
ejpam-4556	415	15	βi(τ)ci(τ)gi(τ)γ	βi(τ)ci(τ)gi(τ)γ	PROPN
ejpam-4556	415	16	∗+b(τ)−µ1(τ)i∗1(τ)−µ2(τ)i∗2(τ)+ρi1−ρ̂j1]dτdη	∗+b(τ)−µ1(τ)i∗1(τ)−µ2(τ)i∗2(τ)+ρi1−ρ̂j1]dτdη	NUM
ejpam-4556	415	17	(	(	PUNCT
ejpam-4556	415	18	35	35	NUM
ejpam-4556	415	19	)	)	PUNCT
ejpam-4556	415	20	let	let	VERB
ejpam-4556	415	21	h∗i	h∗i	PROPN
ejpam-4556	415	22	(	(	PUNCT
ejpam-4556	415	23	η	η	PROPN
ejpam-4556	415	24	,	,	PUNCT
ejpam-4556	415	25	γ	γ	PROPN
ejpam-4556	415	26	∗	∗	NOUN
ejpam-4556	415	27	i	i	PRON
ejpam-4556	415	28	)	)	PUNCT
ejpam-4556	416	1	=	=	PUNCT
ejpam-4556	416	2	(	(	PUNCT
ejpam-4556	416	3	1−	1−	NUM
ejpam-4556	416	4	ϕi)s	ϕi)s	PROPN
ejpam-4556	416	5	∗	∗	NOUN
ejpam-4556	417	1	i	i	PRON
ejpam-4556	417	2	(	(	PUNCT
ejpam-4556	417	3	η	η	PROPN
ejpam-4556	417	4	)	)	PUNCT
ejpam-4556	417	5	+	+	CCONJ
ejpam-4556	417	6	δiv	δiv	VERB
ejpam-4556	417	7	∗	∗	NOUN
ejpam-4556	417	8	i	i	PROPN
ejpam-4556	417	9	(	(	PUNCT
ejpam-4556	417	10	η	η	PROPN
ejpam-4556	417	11	)	)	PUNCT
ejpam-4556	417	12	+	+	CCONJ
ejpam-4556	417	13	σij	σij	NOUN
ejpam-4556	417	14	∗	∗	NOUN
ejpam-4556	417	15	i	i	PRON
ejpam-4556	417	16	(	(	PUNCT
ejpam-4556	417	17	η	η	PROPN
ejpam-4556	417	18	)	)	PUNCT
ejpam-4556	417	19	(	(	PUNCT
ejpam-4556	417	20	36	36	NUM
ejpam-4556	417	21	)	)	PUNCT
ejpam-4556	417	22	l∗i	l∗i	PROPN
ejpam-4556	417	23	(	(	PUNCT
ejpam-4556	417	24	a	a	X
ejpam-4556	417	25	)	)	PUNCT
ejpam-4556	418	1	=	=	SYM
ejpam-4556	418	2	γ∗	γ∗	NOUN
ejpam-4556	419	1	i	i	PRON
ejpam-4556	419	2	∫	∫	VERB
ejpam-4556	419	3	a	a	DET
ejpam-4556	419	4	0	0	NUM
ejpam-4556	419	5	βi(η)ci(η)gi(η)hi(η	βi(η)ci(η)gi(η)hi(η	NOUN
ejpam-4556	419	6	,	,	PUNCT
ejpam-4556	419	7	γ	γ	PROPN
ejpam-4556	419	8	∗	∗	NOUN
ejpam-4556	419	9	i	i	PRON
ejpam-4556	419	10	)	)	PUNCT
ejpam-4556	420	1	e	e	X
ejpam-4556	420	2	−	−	PROPN
ejpam-4556	420	3	∫	∫	PROPN
ejpam-4556	420	4	a	a	DET
ejpam-4556	420	5	η	η	PROPN
ejpam-4556	420	6	(	(	PUNCT
ejpam-4556	420	7	b(τ)−µ1(τ)i	b(τ)−µ1(τ)i	PROPN
ejpam-4556	420	8	∗	∗	NOUN
ejpam-4556	420	9	1(τ)−µ2(τ)i∗2(τ)+ρi2−ρ̂j2)dτdη	1(τ)−µ2(τ)i∗2(τ)+ρi2−ρ̂j2)dτdη	PROPN
ejpam-4556	420	10	(	(	PUNCT
ejpam-4556	420	11	37	37	NUM
ejpam-4556	420	12	)	)	PUNCT
ejpam-4556	420	13	i∗i	i∗i	PUNCT
ejpam-4556	420	14	(	(	PUNCT
ejpam-4556	420	15	a	a	X
ejpam-4556	420	16	)	)	PUNCT
ejpam-4556	420	17	=	=	SYM
ejpam-4556	421	1	∫	∫	PROPN
ejpam-4556	422	1	a	a	PRON
ejpam-4556	422	2	0	0	NUM
ejpam-4556	423	1	[	[	X
ejpam-4556	423	2	kil	kil	PROPN
ejpam-4556	423	3	∗	∗	X
ejpam-4556	423	4	i	i	PROPN
ejpam-4556	423	5	(	(	PUNCT
ejpam-4556	423	6	η	η	PROPN
ejpam-4556	423	7	)	)	PUNCT
ejpam-4556	424	1	+	+	NUM
ejpam-4556	424	2	ϕiβi(η)ci(η)gi(η)γ	ϕiβi(η)ci(η)gi(η)γ	PROPN
ejpam-4556	424	3	∗	∗	NOUN
ejpam-4556	424	4	i	i	NOUN
ejpam-4556	424	5	s	s	VERB
ejpam-4556	424	6	∗	∗	NOUN
ejpam-4556	425	1	i	i	PRON
ejpam-4556	425	2	(	(	PUNCT
ejpam-4556	425	3	η)]e	η)]e	NOUN
ejpam-4556	425	4	−	−	PROPN
ejpam-4556	425	5	∫	∫	PROPN
ejpam-4556	425	6	a	a	DET
ejpam-4556	425	7	η	η	PROPN
ejpam-4556	425	8	(	(	PUNCT
ejpam-4556	425	9	b(τ)+ri+µi(τ)−µ1(τ)i	b(τ)+ri+µi(τ)−µ1(τ)i	PROPN
ejpam-4556	425	10	∗	∗	NOUN
ejpam-4556	425	11	1(τ)−µ2(τ)i∗2(τ)+ρi3−ρ̂j3)dτdη(38	1(τ)−µ2(τ)i∗2(τ)+ρi3−ρ̂j3)dτdη(38	NUM
ejpam-4556	425	12	)	)	PUNCT
ejpam-4556	425	13	j∗i	j∗i	NUM
ejpam-4556	425	14	(	(	PUNCT
ejpam-4556	425	15	a	a	X
ejpam-4556	425	16	)	)	PUNCT
ejpam-4556	425	17	=	=	SYM
ejpam-4556	425	18	ri	ri	PROPN
ejpam-4556	425	19	∫	∫	PROPN
ejpam-4556	425	20	a	a	DET
ejpam-4556	425	21	0	0	NUM
ejpam-4556	425	22	i∗i	i∗i	NUM
ejpam-4556	425	23	(	(	PUNCT
ejpam-4556	425	24	η)e	η)e	NOUN
ejpam-4556	425	25	−	−	PROPN
ejpam-4556	425	26	∫	∫	PROPN
ejpam-4556	425	27	a	a	DET
ejpam-4556	425	28	η	η	PROPN
ejpam-4556	425	29	(	(	PUNCT
ejpam-4556	425	30	σiβi(τ)ci(τ)gi(τ)γ	σiβi(τ)ci(τ)gi(τ)γ	PROPN
ejpam-4556	425	31	∗	∗	NOUN
ejpam-4556	425	32	i+b(τ)−µ1(τ)i∗1(τ)−µ2(τ)i∗2(η)+ρi4−ρ̂j4)dτdη	i+b(τ)−µ1(τ)i∗1(τ)−µ2(τ)i∗2(η)+ρi4−ρ̂j4)dτdη	PROPN
ejpam-4556	425	33	(	(	PUNCT
ejpam-4556	425	34	39	39	NUM
ejpam-4556	425	35	)	)	PUNCT
ejpam-4556	425	36	b.	b.	PROPN
ejpam-4556	425	37	k.	k.	PROPN
ejpam-4556	425	38	abdoul	abdoul	PROPN
ejpam-4556	425	39	wahid	wahid	PROPN
ejpam-4556	425	40	,	,	PUNCT
ejpam-4556	425	41	d.moustapha	d.moustapha	PROPN
ejpam-4556	425	42	,	,	PUNCT
ejpam-4556	425	43	s.	s.	PROPN
ejpam-4556	425	44	bisso	bisso	PROPN
ejpam-4556	425	45	/	/	SYM
ejpam-4556	425	46	eur	eur	PROPN
ejpam-4556	425	47	.	.	PUNCT
ejpam-4556	426	1	j.	j.	PROPN
ejpam-4556	426	2	pure	pure	PROPN
ejpam-4556	426	3	appl	appl	PROPN
ejpam-4556	426	4	.	.	PROPN
ejpam-4556	426	5	math	math	PROPN
ejpam-4556	426	6	,	,	PUNCT
ejpam-4556	426	7	15	15	NUM
ejpam-4556	426	8	(	(	PUNCT
ejpam-4556	426	9	4	4	NUM
ejpam-4556	426	10	)	)	PUNCT
ejpam-4556	426	11	(	(	PUNCT
ejpam-4556	426	12	2022	2022	NUM
ejpam-4556	426	13	)	)	PUNCT
ejpam-4556	426	14	,	,	PUNCT
ejpam-4556	426	15	2054	2054	NUM
ejpam-4556	426	16	-	-	SYM
ejpam-4556	426	17	2073	2073	NUM
ejpam-4556	426	18	2068	2068	NUM
ejpam-4556	426	19	v∗i	v∗i	X
ejpam-4556	426	20	(	(	PUNCT
ejpam-4556	426	21	a	a	X
ejpam-4556	426	22	)	)	PUNCT
ejpam-4556	426	23	=	=	SYM
ejpam-4556	427	1	∫	∫	PROPN
ejpam-4556	428	1	a	a	DET
ejpam-4556	428	2	0	0	NUM
ejpam-4556	428	3	(	(	PUNCT
ejpam-4556	428	4	ψi(η)s	ψi(η)	NOUN
ejpam-4556	428	5	∗	∗	NOUN
ejpam-4556	428	6	i	i	PRON
ejpam-4556	428	7	(	(	PUNCT
ejpam-4556	428	8	η))e	η))e	PROPN
ejpam-4556	428	9	−	−	PROPN
ejpam-4556	428	10	∫	∫	PROPN
ejpam-4556	428	11	a	a	DET
ejpam-4556	428	12	η	η	PROPN
ejpam-4556	428	13	(	(	PUNCT
ejpam-4556	428	14	δiβi(τ)ci(τ)gi(τ)γ	δiβi(τ)ci(τ)gi(τ)γ	PROPN
ejpam-4556	428	15	∗	∗	NOUN
ejpam-4556	428	16	i+b(τ)−µi(τ)i∗i	i+b(τ)−µi(τ)i∗i	PRON
ejpam-4556	428	17	(	(	PUNCT
ejpam-4556	428	18	τ)−µj(τ)i∗j	τ)−µj(τ)i∗j	X
ejpam-4556	428	19	(	(	PUNCT
ejpam-4556	428	20	τ)+ρi5−ρ̂j5)dτdη	τ)+ρi5−ρ̂j5)dτdη	NUM
ejpam-4556	428	21	(	(	PUNCT
ejpam-4556	428	22	40	40	NUM
ejpam-4556	428	23	)	)	PUNCT
ejpam-4556	428	24	by	by	ADP
ejpam-4556	428	25	injecting	inject	VERB
ejpam-4556	428	26	(	(	PUNCT
ejpam-4556	428	27	37	37	NUM
ejpam-4556	428	28	)	)	PUNCT
ejpam-4556	428	29	in	in	ADP
ejpam-4556	428	30	(	(	PUNCT
ejpam-4556	428	31	38	38	NUM
ejpam-4556	428	32	)	)	PUNCT
ejpam-4556	428	33	,	,	PUNCT
ejpam-4556	428	34	we	we	PRON
ejpam-4556	428	35	obtain	obtain	VERB
ejpam-4556	428	36	:	:	PUNCT
ejpam-4556	428	37	i∗i	i∗i	X
ejpam-4556	428	38	(	(	PUNCT
ejpam-4556	428	39	a	a	X
ejpam-4556	428	40	)	)	PUNCT
ejpam-4556	428	41	=	=	SYM
ejpam-4556	429	1	γ∗	γ∗	NOUN
ejpam-4556	430	1	i	i	PRON
ejpam-4556	430	2	∫	∫	VERB
ejpam-4556	430	3	a	a	DET
ejpam-4556	430	4	0	0	NUM
ejpam-4556	430	5	βi(η)ci(η)gi(η)e	βi(η)ci(η)gi(η)e	NOUN
ejpam-4556	431	1	−	−	PROPN
ejpam-4556	431	2	∫	∫	PROPN
ejpam-4556	431	3	a	a	DET
ejpam-4556	431	4	η	η	PROPN
ejpam-4556	431	5	(	(	PUNCT
ejpam-4556	431	6	b(τ)−µ1(τ)i	b(τ)−µ1(τ)i	PROPN
ejpam-4556	431	7	∗	∗	NOUN
ejpam-4556	431	8	1(τ)−µ2(τ)i∗2(τ)−ri+µi(τ)+ρi3−ρ̂j3)dτ×	1(τ)−µ2(τ)i∗2(τ)−ri+µi(τ)+ρi3−ρ̂j3)dτ×	NUM
ejpam-4556	432	1	[	[	X
ejpam-4556	432	2	ϕis	ϕis	PROPN
ejpam-4556	432	3	∗	∗	X
ejpam-4556	432	4	i	i	PRON
ejpam-4556	432	5	(	(	PUNCT
ejpam-4556	432	6	η	η	PROPN
ejpam-4556	432	7	)	)	PUNCT
ejpam-4556	432	8	+	+	CCONJ
ejpam-4556	432	9	kihi(η	kihi(η	PROPN
ejpam-4556	432	10	,	,	PUNCT
ejpam-4556	432	11	γ	γ	PROPN
ejpam-4556	432	12	∗	∗	NOUN
ejpam-4556	432	13	i	i	PRON
ejpam-4556	432	14	)	)	PUNCT
ejpam-4556	432	15	∫	∫	PROPN
ejpam-4556	433	1	a	a	DET
ejpam-4556	433	2	η	η	PROPN
ejpam-4556	433	3	e−	e−	PROPN
ejpam-4556	433	4	∫	∫	PROPN
ejpam-4556	433	5	η	η	PROPN
ejpam-4556	433	6	ξ	ξ	PROPN
ejpam-4556	433	7	(	(	PUNCT
ejpam-4556	433	8	ri+µi(τ)−ki)−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dη	ri+µi(τ)−ki)−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dη	NOUN
ejpam-4556	433	9	(	(	PUNCT
ejpam-4556	433	10	41	41	NUM
ejpam-4556	433	11	)	)	PUNCT
ejpam-4556	433	12	by	by	ADP
ejpam-4556	433	13	injecting	inject	VERB
ejpam-4556	433	14	(	(	PUNCT
ejpam-4556	433	15	41	41	NUM
ejpam-4556	433	16	)	)	PUNCT
ejpam-4556	433	17	in	in	ADP
ejpam-4556	433	18	the	the	DET
ejpam-4556	433	19	expression	expression	NOUN
ejpam-4556	433	20	of	of	ADP
ejpam-4556	433	21	γ∗	γ∗	PROPN
ejpam-4556	433	22	i	i	PRON
ejpam-4556	433	23	,	,	PUNCT
ejpam-4556	433	24	and	and	CCONJ
ejpam-4556	433	25	dividing	divide	VERB
ejpam-4556	433	26	by	by	ADP
ejpam-4556	433	27	γ∗	γ∗	PROPN
ejpam-4556	433	28	i	i	PRON
ejpam-4556	433	29	(	(	PUNCT
ejpam-4556	433	30	since	since	SCONJ
ejpam-4556	433	31	γ∗	γ∗	PROPN
ejpam-4556	433	32	i	i	PRON
ejpam-4556	433	33	̸=	̸=	PROPN
ejpam-4556	433	34	0	0	NUM
ejpam-4556	433	35	)	)	PUNCT
ejpam-4556	433	36	we	we	PRON
ejpam-4556	433	37	obtain	obtain	VERB
ejpam-4556	433	38	:	:	PUNCT
ejpam-4556	433	39	1	1	NUM
ejpam-4556	433	40	=	=	SYM
ejpam-4556	433	41	∫	∫	X
ejpam-4556	433	42	a+	a+	X
ejpam-4556	433	43	0	0	NUM
ejpam-4556	433	44	β̂i(a	β̂i(a	PROPN
ejpam-4556	433	45	)	)	PUNCT
ejpam-4556	433	46	∫	∫	PROPN
ejpam-4556	433	47	a	a	DET
ejpam-4556	433	48	0	0	NUM
ejpam-4556	433	49	βi(η)ci(η)gi(η)e	βi(η)ci(η)gi(η)e	NOUN
ejpam-4556	433	50	−	−	PROPN
ejpam-4556	434	1	∫	∫	PROPN
ejpam-4556	435	1	a	a	DET
ejpam-4556	435	2	η	η	PROPN
ejpam-4556	435	3	(	(	PUNCT
ejpam-4556	435	4	b(τ)−µ1(τ)i	b(τ)−µ1(τ)i	PROPN
ejpam-4556	435	5	∗	∗	NOUN
ejpam-4556	435	6	1(τ)−µ2(τ)i∗2(τ)−ri+µi(τ)+ρi3−ρ̂j3)dτ×	1(τ)−µ2(τ)i∗2(τ)−ri+µi(τ)+ρi3−ρ̂j3)dτ×	NUM
ejpam-4556	436	1	[	[	X
ejpam-4556	436	2	ϕis	ϕis	PROPN
ejpam-4556	436	3	∗	∗	X
ejpam-4556	436	4	i	i	PRON
ejpam-4556	436	5	(	(	PUNCT
ejpam-4556	436	6	η	η	PROPN
ejpam-4556	436	7	)	)	PUNCT
ejpam-4556	436	8	+	+	CCONJ
ejpam-4556	436	9	kihi(η	kihi(η	PROPN
ejpam-4556	436	10	,	,	PUNCT
ejpam-4556	436	11	γ	γ	PROPN
ejpam-4556	436	12	∗	∗	NOUN
ejpam-4556	436	13	i	i	PRON
ejpam-4556	436	14	)	)	PUNCT
ejpam-4556	436	15	∫	∫	PROPN
ejpam-4556	437	1	a	a	DET
ejpam-4556	437	2	η	η	PROPN
ejpam-4556	437	3	e−	e−	PROPN
ejpam-4556	437	4	∫	∫	PROPN
ejpam-4556	437	5	η	η	PROPN
ejpam-4556	437	6	ξ	ξ	PROPN
ejpam-4556	437	7	(	(	PUNCT
ejpam-4556	437	8	ri+µi(τ)−ki)−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dηda	ri+µi(τ)−ki)−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dηda	PROPN
ejpam-4556	437	9	(	(	PUNCT
ejpam-4556	437	10	42	42	NUM
ejpam-4556	437	11	)	)	PUNCT
ejpam-4556	437	12	let	let	VERB
ejpam-4556	437	13	hij	hij	NOUN
ejpam-4556	437	14	,	,	PUNCT
ejpam-4556	437	15	the	the	DET
ejpam-4556	437	16	fonction	fonction	NOUN
ejpam-4556	437	17	define	define	VERB
ejpam-4556	437	18	by	by	ADP
ejpam-4556	437	19	:	:	PUNCT
ejpam-4556	437	20	hij(γ	hij(γ	X
ejpam-4556	437	21	∗	∗	NOUN
ejpam-4556	437	22	i	i	PRON
ejpam-4556	437	23	)	)	PUNCT
ejpam-4556	438	1	=	=	SYM
ejpam-4556	438	2	∫	∫	PROPN
ejpam-4556	438	3	a+	a+	X
ejpam-4556	438	4	0	0	NUM
ejpam-4556	438	5	β̂i(a	β̂i(a	PROPN
ejpam-4556	438	6	)	)	PUNCT
ejpam-4556	438	7	∫	∫	PROPN
ejpam-4556	438	8	a	a	DET
ejpam-4556	438	9	0	0	NUM
ejpam-4556	438	10	βi(η)ci(η)gi(η)e	βi(η)ci(η)gi(η)e	NOUN
ejpam-4556	439	1	−	−	PROPN
ejpam-4556	439	2	∫	∫	PROPN
ejpam-4556	439	3	a	a	DET
ejpam-4556	439	4	η	η	PROPN
ejpam-4556	439	5	(	(	PUNCT
ejpam-4556	439	6	b(τ)−µ1(τ)i	b(τ)−µ1(τ)i	PROPN
ejpam-4556	439	7	∗	∗	NOUN
ejpam-4556	439	8	1(τ)−µ2(τ)i∗2(τ)−ri+µi(τ)+ρi3−ρ̂j3)dτ×	1(τ)−µ2(τ)i∗2(τ)−ri+µi(τ)+ρi3−ρ̂j3)dτ×	NUM
ejpam-4556	440	1	[	[	X
ejpam-4556	440	2	ϕis	ϕis	PROPN
ejpam-4556	440	3	∗	∗	X
ejpam-4556	440	4	i	i	PRON
ejpam-4556	440	5	(	(	PUNCT
ejpam-4556	440	6	η	η	PROPN
ejpam-4556	440	7	)	)	PUNCT
ejpam-4556	440	8	+	+	CCONJ
ejpam-4556	440	9	kihi(η	kihi(η	PROPN
ejpam-4556	440	10	,	,	PUNCT
ejpam-4556	440	11	γ	γ	PROPN
ejpam-4556	440	12	∗	∗	NOUN
ejpam-4556	440	13	i	i	PRON
ejpam-4556	440	14	)	)	PUNCT
ejpam-4556	440	15	∫	∫	PROPN
ejpam-4556	441	1	a	a	DET
ejpam-4556	441	2	η	η	PROPN
ejpam-4556	441	3	e−	e−	PROPN
ejpam-4556	441	4	∫	∫	PROPN
ejpam-4556	441	5	η	η	PROPN
ejpam-4556	441	6	ξ	ξ	PROPN
ejpam-4556	441	7	(	(	PUNCT
ejpam-4556	441	8	ri+µi(τ)−ki)−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dηda	ri+µi(τ)−ki)−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdξ]dηda	PROPN
ejpam-4556	441	9	(	(	PUNCT
ejpam-4556	441	10	43	43	NUM
ejpam-4556	441	11	)	)	PUNCT
ejpam-4556	441	12	since	since	SCONJ
ejpam-4556	441	13	hi(η	hi(η	NOUN
ejpam-4556	441	14	,	,	PUNCT
ejpam-4556	441	15	0	0	NUM
ejpam-4556	441	16	)	)	PUNCT
ejpam-4556	441	17	=	=	SYM
ejpam-4556	441	18	nψi(η	nψi(η	PROPN
ejpam-4556	441	19	)	)	PUNCT
ejpam-4556	441	20	i.e	i.e	PROPN
ejpam-4556	441	21	when	when	SCONJ
ejpam-4556	441	22	γ∗	γ∗	PROPN
ejpam-4556	441	23	i	i	NOUN
ejpam-4556	441	24	=	=	NOUN
ejpam-4556	441	25	0	0	NUM
ejpam-4556	441	26	,	,	PUNCT
ejpam-4556	441	27	s∗i	s∗i	X
ejpam-4556	441	28	(	(	PUNCT
ejpam-4556	441	29	a	a	NOUN
ejpam-4556	441	30	)	)	PUNCT
ejpam-4556	441	31	=	=	SYM
ejpam-4556	441	32	s0i	s0i	NOUN
ejpam-4556	441	33	(	(	PUNCT
ejpam-4556	441	34	a	a	NOUN
ejpam-4556	441	35	)	)	PUNCT
ejpam-4556	441	36	and	and	CCONJ
ejpam-4556	441	37	v∗i	v∗i	NUM
ejpam-4556	441	38	(	(	PUNCT
ejpam-4556	441	39	a	a	X
ejpam-4556	441	40	)	)	PUNCT
ejpam-4556	441	41	=	=	SYM
ejpam-4556	442	1	v0i	v0i	X
ejpam-4556	442	2	(	(	PUNCT
ejpam-4556	442	3	a	a	NOUN
ejpam-4556	442	4	)	)	PUNCT
ejpam-4556	442	5	,	,	PUNCT
ejpam-4556	442	6	so	so	CCONJ
ejpam-4556	442	7	the	the	DET
ejpam-4556	442	8	net	net	ADJ
ejpam-4556	442	9	reproductive	reproductive	ADJ
ejpam-4556	442	10	number	number	NOUN
ejpam-4556	442	11	is	be	AUX
ejpam-4556	442	12	given	give	VERB
ejpam-4556	442	13	by	by	ADP
ejpam-4556	442	14	hij(0	hij(0	NOUN
ejpam-4556	442	15	)	)	PUNCT
ejpam-4556	443	1	=	=	SYM
ejpam-4556	443	2	ℜi(ψi	ℜi(ψi	NOUN
ejpam-4556	443	3	,	,	PUNCT
ejpam-4556	443	4	ρij	ρij	NOUN
ejpam-4556	443	5	)	)	PUNCT
ejpam-4556	443	6	,	,	PUNCT
ejpam-4556	443	7	i.e	i.e	PROPN
ejpam-4556	443	8	ℜi(ψi	ℜi(ψi	PROPN
ejpam-4556	443	9	,	,	PUNCT
ejpam-4556	443	10	ρij	ρij	NOUN
ejpam-4556	443	11	)	)	PUNCT
ejpam-4556	443	12	=	=	SYM
ejpam-4556	443	13	∫	∫	PROPN
ejpam-4556	443	14	a+	a+	X
ejpam-4556	443	15	0	0	NUM
ejpam-4556	443	16	β̂i(a	β̂i(a	PROPN
ejpam-4556	443	17	)	)	PUNCT
ejpam-4556	443	18	∫	∫	PROPN
ejpam-4556	444	1	a	a	PRON
ejpam-4556	444	2	0	0	NUM
ejpam-4556	445	1	e−	e−	PROPN
ejpam-4556	445	2	∫	∫	PROPN
ejpam-4556	445	3	a	a	DET
ejpam-4556	445	4	η	η	PROPN
ejpam-4556	445	5	(	(	PUNCT
ejpam-4556	445	6	b(τ)+µi(τ)+ri+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	b(τ)+µi(τ)+ri+ρi3−ρ̂j3)dτβi(η)ci(η)gi(η	PROPN
ejpam-4556	445	7	)	)	PUNCT
ejpam-4556	446	1	[	[	X
ejpam-4556	446	2	ϕis	ϕis	PROPN
ejpam-4556	446	3	0	0	NUM
ejpam-4556	447	1	i	i	NOUN
ejpam-4556	447	2	(	(	PUNCT
ejpam-4556	447	3	η	η	PROPN
ejpam-4556	447	4	)	)	PUNCT
ejpam-4556	447	5	+	+	NUM
ejpam-4556	447	6	kinψi(η	kinψi(η	PROPN
ejpam-4556	447	7	)	)	PUNCT
ejpam-4556	447	8	∫	∫	PROPN
ejpam-4556	447	9	a	a	DET
ejpam-4556	447	10	η	η	PROPN
ejpam-4556	447	11	e−	e−	PROPN
ejpam-4556	447	12	∫	∫	PROPN
ejpam-4556	447	13	η	η	PROPN
ejpam-4556	447	14	x	x	PROPN
ejpam-4556	447	15	(	(	PUNCT
ejpam-4556	447	16	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	µi(τ)+ri−ki−ρi2+ρ̂j2+ρi3−ρ̂j3)dτdx]dηda	X
ejpam-4556	447	17	(	(	PUNCT
ejpam-4556	447	18	44	44	NUM
ejpam-4556	447	19	)	)	PUNCT
ejpam-4556	447	20	we	we	PRON
ejpam-4556	447	21	now	now	ADV
ejpam-4556	447	22	see	see	VERB
ejpam-4556	447	23	that	that	SCONJ
ejpam-4556	447	24	an	an	DET
ejpam-4556	447	25	endemic	endemic	ADJ
ejpam-4556	447	26	steady	steady	ADJ
ejpam-4556	447	27	state	state	NOUN
ejpam-4556	447	28	exists	exist	VERB
ejpam-4556	447	29	if	if	SCONJ
ejpam-4556	447	30	equation	equation	NOUN
ejpam-4556	447	31	(	(	PUNCT
ejpam-4556	447	32	42	42	NUM
ejpam-4556	447	33	)	)	PUNCT
ejpam-4556	447	34	has	have	VERB
ejpam-4556	447	35	a	a	DET
ejpam-4556	447	36	positive	positive	ADJ
ejpam-4556	447	37	solution	solution	NOUN
ejpam-4556	447	38	.	.	PUNCT
ejpam-4556	448	1	since	since	SCONJ
ejpam-4556	448	2	hi(0	hi(0	PROPN
ejpam-4556	448	3	)	)	PUNCT
ejpam-4556	448	4	=	=	SYM
ejpam-4556	448	5	ℜi(ψi	ℜi(ψi	PROPN
ejpam-4556	448	6	)	)	PUNCT
ejpam-4556	448	7	,	,	PUNCT
ejpam-4556	448	8	hence	hence	ADV
ejpam-4556	448	9	hi(0	hi(0	PROPN
ejpam-4556	448	10	)	)	PUNCT
ejpam-4556	448	11	>	>	X
ejpam-4556	449	1	1	1	X
ejpam-4556	449	2	.	.	PUNCT
ejpam-4556	449	3	we	we	PRON
ejpam-4556	449	4	know	know	VERB
ejpam-4556	449	5	that	that	SCONJ
ejpam-4556	449	6	s∗i	s∗i	NUM
ejpam-4556	449	7	(	(	PUNCT
ejpam-4556	449	8	a	a	NOUN
ejpam-4556	449	9	)	)	PUNCT
ejpam-4556	450	1	+	+	CCONJ
ejpam-4556	450	2	l∗i	l∗i	PROPN
ejpam-4556	450	3	(	(	PUNCT
ejpam-4556	450	4	a	a	X
ejpam-4556	450	5	)	)	PUNCT
ejpam-4556	450	6	+	+	CCONJ
ejpam-4556	450	7	i∗i	i∗i	NUM
ejpam-4556	450	8	(	(	PUNCT
ejpam-4556	450	9	a	a	NOUN
ejpam-4556	450	10	)	)	PUNCT
ejpam-4556	450	11	+	+	CCONJ
ejpam-4556	450	12	v∗i	v∗i	NUM
ejpam-4556	450	13	(	(	PUNCT
ejpam-4556	450	14	a	a	NOUN
ejpam-4556	450	15	)	)	PUNCT
ejpam-4556	450	16	+	+	CCONJ
ejpam-4556	450	17	j∗i	j∗i	NUM
ejpam-4556	450	18	(	(	PUNCT
ejpam-4556	450	19	a	a	X
ejpam-4556	450	20	)	)	PUNCT
ejpam-4556	450	21	=	=	PUNCT
ejpam-4556	450	22	λi	λi	X
ejpam-4556	450	23	<	<	X
ejpam-4556	450	24	1	1	NUM
ejpam-4556	450	25	.	.	PUNCT
ejpam-4556	451	1	hence	hence	ADV
ejpam-4556	451	2	i∗i	i∗i	PROPN
ejpam-4556	451	3	(	(	PUNCT
ejpam-4556	451	4	a	a	NOUN
ejpam-4556	451	5	)	)	PUNCT
ejpam-4556	451	6	<	<	X
ejpam-4556	451	7	1	1	NUM
ejpam-4556	451	8	(	(	PUNCT
ejpam-4556	451	9	45	45	NUM
ejpam-4556	451	10	)	)	PUNCT
ejpam-4556	451	11	b.	b.	PROPN
ejpam-4556	451	12	k.	k.	PROPN
ejpam-4556	451	13	abdoul	abdoul	PROPN
ejpam-4556	451	14	wahid	wahid	PROPN
ejpam-4556	451	15	,	,	PUNCT
ejpam-4556	451	16	d.moustapha	d.moustapha	PROPN
ejpam-4556	451	17	,	,	PUNCT
ejpam-4556	451	18	s.	s.	PROPN
ejpam-4556	451	19	bisso	bisso	PROPN
ejpam-4556	451	20	/	/	SYM
ejpam-4556	451	21	eur	eur	PROPN
ejpam-4556	451	22	.	.	PUNCT
ejpam-4556	452	1	j.	j.	PROPN
ejpam-4556	452	2	pure	pure	PROPN
ejpam-4556	452	3	appl	appl	PROPN
ejpam-4556	452	4	.	.	PROPN
ejpam-4556	452	5	math	math	PROPN
ejpam-4556	452	6	,	,	PUNCT
ejpam-4556	452	7	15	15	NUM
ejpam-4556	452	8	(	(	PUNCT
ejpam-4556	452	9	4	4	NUM
ejpam-4556	452	10	)	)	PUNCT
ejpam-4556	452	11	(	(	PUNCT
ejpam-4556	452	12	2022	2022	NUM
ejpam-4556	452	13	)	)	PUNCT
ejpam-4556	452	14	,	,	PUNCT
ejpam-4556	452	15	2054	2054	NUM
ejpam-4556	452	16	-	-	SYM
ejpam-4556	452	17	2073	2073	NUM
ejpam-4556	452	18	2069	2069	NUM
ejpam-4556	452	19	since	since	SCONJ
ejpam-4556	452	20	γ∗	γ∗	PROPN
ejpam-4556	452	21	i	i	X
ejpam-4556	452	22	>	>	X
ejpam-4556	452	23	0	0	NUM
ejpam-4556	452	24	,	,	PUNCT
ejpam-4556	452	25	from	from	ADP
ejpam-4556	452	26	(	(	PUNCT
ejpam-4556	452	27	43	43	NUM
ejpam-4556	452	28	)	)	PUNCT
ejpam-4556	452	29	and	and	CCONJ
ejpam-4556	452	30	(	(	PUNCT
ejpam-4556	452	31	45	45	NUM
ejpam-4556	452	32	)	)	PUNCT
ejpam-4556	452	33	we	we	PRON
ejpam-4556	452	34	obtain	obtain	VERB
ejpam-4556	452	35	:	:	PUNCT
ejpam-4556	452	36	γ∗	γ∗	PROPN
ejpam-4556	452	37	ihi(γ	ihi(γ	PROPN
ejpam-4556	452	38	∗	∗	NOUN
ejpam-4556	452	39	i	i	PRON
ejpam-4556	452	40	)	)	PUNCT
ejpam-4556	453	1	=	=	SYM
ejpam-4556	453	2	∫	∫	PROPN
ejpam-4556	453	3	a+	a+	X
ejpam-4556	453	4	0	0	NUM
ejpam-4556	453	5	β̂i(a	β̂i(a	PROPN
ejpam-4556	453	6	)	)	PUNCT
ejpam-4556	453	7	∫	∫	PROPN
ejpam-4556	453	8	a	a	DET
ejpam-4556	453	9	0	0	NUM
ejpam-4556	453	10	γ∗	γ∗	NOUN
ejpam-4556	453	11	iβi(η)ci(η)gi(η)e	iβi(η)ci(η)gi(η)e	PROPN
ejpam-4556	453	12	−	−	PROPN
ejpam-4556	453	13	∫	∫	PROPN
ejpam-4556	453	14	a	a	DET
ejpam-4556	453	15	η	η	PROPN
ejpam-4556	453	16	(	(	PUNCT
ejpam-4556	453	17	β(τ)−µ1(τ)i	β(τ)−µ1(τ)i	PROPN
ejpam-4556	453	18	∗	∗	NOUN
ejpam-4556	453	19	1(τ)−µ2(τ)i2(τ)+ri+µi(τ))dτ×	1(τ)−µ2(τ)i2(τ)+ri+µi(τ))dτ×	NOUN
ejpam-4556	454	1	[	[	X
ejpam-4556	454	2	ϕis	ϕis	PROPN
ejpam-4556	454	3	∗	∗	X
ejpam-4556	454	4	i	i	PRON
ejpam-4556	454	5	(	(	PUNCT
ejpam-4556	454	6	η	η	PROPN
ejpam-4556	454	7	)	)	PUNCT
ejpam-4556	454	8	+	+	CCONJ
ejpam-4556	454	9	kihi(η	kihi(η	PROPN
ejpam-4556	454	10	,	,	PUNCT
ejpam-4556	454	11	γ	γ	PROPN
ejpam-4556	454	12	∗	∗	NOUN
ejpam-4556	454	13	i	i	PRON
ejpam-4556	454	14	)	)	PUNCT
ejpam-4556	454	15	∫	∫	PROPN
ejpam-4556	454	16	a	a	DET
ejpam-4556	454	17	η	η	PROPN
ejpam-4556	454	18	e−	e−	PROPN
ejpam-4556	454	19	∫	∫	PROPN
ejpam-4556	454	20	η	η	PROPN
ejpam-4556	454	21	ξ	ξ	PROPN
ejpam-4556	454	22	(	(	PUNCT
ejpam-4556	454	23	(	(	PUNCT
ejpam-4556	454	24	ri+µi(τ)−ki)dτdξ]dηda	ri+µi(τ)−ki)dτdξ]dηda	PROPN
ejpam-4556	454	25	<	<	X
ejpam-4556	454	26	∫	∫	PROPN
ejpam-4556	454	27	a+	a+	X
ejpam-4556	454	28	0	0	NUM
ejpam-4556	454	29	β̂i(a)da	β̂i(a)da	NOUN
ejpam-4556	454	30	=	=	PUNCT
ejpam-4556	454	31	β+i	β+i	PUNCT
ejpam-4556	454	32	.	.	PUNCT
ejpam-4556	455	1	in	in	ADP
ejpam-4556	455	2	particular	particular	ADJ
ejpam-4556	455	3	,	,	PUNCT
ejpam-4556	455	4	for	for	ADP
ejpam-4556	455	5	γ∗	γ∗	NOUN
ejpam-4556	455	6	i	i	NOUN
ejpam-4556	455	7	=	=	PUNCT
ejpam-4556	455	8	β+i	β+i	PUNCT
ejpam-4556	455	9	,	,	PUNCT
ejpam-4556	455	10	we	we	PRON
ejpam-4556	455	11	have	have	VERB
ejpam-4556	455	12	hi(β	hi(β	X
ejpam-4556	456	1	+	+	CCONJ
ejpam-4556	456	2	i	i	NOUN
ejpam-4556	456	3	)	)	PUNCT
ejpam-4556	456	4	<	<	X
ejpam-4556	456	5	1	1	NUM
ejpam-4556	456	6	,	,	PUNCT
ejpam-4556	456	7	but	but	CCONJ
ejpam-4556	456	8	hi(0	hi(0	PROPN
ejpam-4556	456	9	)	)	PUNCT
ejpam-4556	456	10	>	>	X
ejpam-4556	457	1	1	1	X
ejpam-4556	457	2	.	.	PUNCT
ejpam-4556	458	1	since	since	SCONJ
ejpam-4556	458	2	hi	hi	PROPN
ejpam-4556	458	3	is	be	VERB
ejpam-4556	458	4	continous	continous	ADJ
ejpam-4556	458	5	fonction	fonction	NOUN
ejpam-4556	458	6	of	of	ADP
ejpam-4556	458	7	γ∗	γ∗	PROPN
ejpam-4556	458	8	i	i	PRON
ejpam-4556	458	9	,	,	PUNCT
ejpam-4556	458	10	we	we	PRON
ejpam-4556	458	11	conclude	conclude	VERB
ejpam-4556	458	12	that	that	SCONJ
ejpam-4556	458	13	h(γ∗	h(γ∗	PROPN
ejpam-4556	458	14	i	i	NOUN
ejpam-4556	458	15	)	)	PUNCT
ejpam-4556	459	1	=	=	SYM
ejpam-4556	459	2	1	1	NUM
ejpam-4556	459	3	,	,	PUNCT
ejpam-4556	459	4	has	have	VERB
ejpam-4556	459	5	a	a	DET
ejpam-4556	459	6	positive	positive	ADJ
ejpam-4556	459	7	solution	solution	NOUN
ejpam-4556	459	8	γ̂∗	γ̂∗	VERB
ejpam-4556	459	9	i	i	PRON
ejpam-4556	459	10	on	on	ADP
ejpam-4556	459	11	]	]	X
ejpam-4556	459	12	0;β+i	0;β+i	ADJ
ejpam-4556	460	1	[	[	X
ejpam-4556	460	2	.	.	PUNCT
ejpam-4556	461	1	this	this	DET
ejpam-4556	461	2	solution	solution	NOUN
ejpam-4556	461	3	may	may	AUX
ejpam-4556	461	4	not	not	PART
ejpam-4556	461	5	be	be	AUX
ejpam-4556	461	6	unique	unique	ADJ
ejpam-4556	461	7	since	since	SCONJ
ejpam-4556	461	8	hi	hi	INTJ
ejpam-4556	461	9	may	may	AUX
ejpam-4556	461	10	not	not	PART
ejpam-4556	461	11	be	be	AUX
ejpam-4556	461	12	monotone	monotone	ADJ
ejpam-4556	461	13	(	(	PUNCT
ejpam-4556	461	14	hi(γ	hi(γ	NOUN
ejpam-4556	461	15	∗	∗	NOUN
ejpam-4556	461	16	i	i	PRON
ejpam-4556	461	17	)	)	PUNCT
ejpam-4556	461	18	depends	depend	VERB
ejpam-4556	461	19	on	on	ADP
ejpam-4556	461	20	h(α	h(α	PROPN
ejpam-4556	461	21	,	,	PUNCT
ejpam-4556	461	22	γ	γ	X
ejpam-4556	461	23	∗	∗	X
ejpam-4556	461	24	i	i	PRON
ejpam-4556	461	25	)	)	PUNCT
ejpam-4556	461	26	which	which	PRON
ejpam-4556	461	27	is	be	AUX
ejpam-4556	461	28	defined	define	VERB
ejpam-4556	461	29	implicitly	implicitly	ADV
ejpam-4556	461	30	)	)	PUNCT
ejpam-4556	461	31	.	.	PUNCT
ejpam-4556	462	1	it	it	PRON
ejpam-4556	462	2	follows	follow	VERB
ejpam-4556	462	3	that	that	SCONJ
ejpam-4556	462	4	when	when	SCONJ
ejpam-4556	462	5	ℜi(ψi	ℜi(ψi	X
ejpam-4556	462	6	)	)	PUNCT
ejpam-4556	462	7	>	>	X
ejpam-4556	463	1	1	1	NUM
ejpam-4556	463	2	,	,	PUNCT
ejpam-4556	463	3	there	there	PRON
ejpam-4556	463	4	exists	exist	VERB
ejpam-4556	463	5	an	an	DET
ejpam-4556	463	6	endemic	endemic	ADJ
ejpam-4556	463	7	steady	steady	ADJ
ejpam-4556	463	8	state	state	NOUN
ejpam-4556	463	9	distribution	distribution	NOUN
ejpam-4556	463	10	which	which	PRON
ejpam-4556	463	11	is	be	AUX
ejpam-4556	463	12	given	give	VERB
ejpam-4556	463	13	by	by	ADP
ejpam-4556	463	14	the	the	DET
ejpam-4556	463	15	unique	unique	ADJ
ejpam-4556	463	16	solution	solution	NOUN
ejpam-4556	463	17	of	of	ADP
ejpam-4556	463	18	equation	equation	NOUN
ejpam-4556	463	19	(	(	PUNCT
ejpam-4556	463	20	42	42	NUM
ejpam-4556	463	21	)	)	PUNCT
ejpam-4556	463	22	corresponding	correspond	VERB
ejpam-4556	463	23	to	to	ADP
ejpam-4556	463	24	γ̂∗	γ̂∗	PROPN
ejpam-4556	463	25	i	i	PROPN
ejpam-4556	463	26	7	7	NUM
ejpam-4556	463	27	.	.	PUNCT
ejpam-4556	463	28	simulation	simulation	NOUN
ejpam-4556	463	29	in	in	ADP
ejpam-4556	463	30	this	this	DET
ejpam-4556	463	31	section	section	NOUN
ejpam-4556	463	32	,	,	PUNCT
ejpam-4556	463	33	the	the	DET
ejpam-4556	463	34	numerical	numerical	ADJ
ejpam-4556	463	35	method	method	NOUN
ejpam-4556	463	36	used	use	VERB
ejpam-4556	463	37	in	in	ADP
ejpam-4556	463	38	our	our	PRON
ejpam-4556	463	39	simulations	simulation	NOUN
ejpam-4556	463	40	is	be	AUX
ejpam-4556	463	41	based	base	VERB
ejpam-4556	463	42	on	on	ADP
ejpam-4556	463	43	the	the	DET
ejpam-4556	463	44	finite	finite	ADJ
ejpam-4556	463	45	difference	difference	NOUN
ejpam-4556	463	46	method	method	NOUN
ejpam-4556	463	47	.	.	PUNCT
ejpam-4556	464	1	forward	forward	ADV
ejpam-4556	464	2	in	in	ADP
ejpam-4556	464	3	time	time	NOUN
ejpam-4556	464	4	-	-	PUNCT
ejpam-4556	464	5	backward	backward	ADJ
ejpam-4556	464	6	in	in	ADP
ejpam-4556	464	7	age	age	NOUN
ejpam-4556	464	8	numerical	numerical	PROPN
ejpam-4556	464	9	scheme	scheme	NOUN
ejpam-4556	464	10	is	be	AUX
ejpam-4556	464	11	used	use	VERB
ejpam-4556	464	12	as	as	ADP
ejpam-4556	464	13	in[36	in[36	NOUN
ejpam-4556	464	14	]	]	PUNCT
ejpam-4556	464	15	.	.	PUNCT
ejpam-4556	465	1	each	each	DET
ejpam-4556	465	2	equation	equation	NOUN
ejpam-4556	465	3	is	be	AUX
ejpam-4556	465	4	system	system	NOUN
ejpam-4556	465	5	(	(	PUNCT
ejpam-4556	465	6	5	5	X
ejpam-4556	465	7	)	)	PUNCT
ejpam-4556	465	8	can	can	AUX
ejpam-4556	465	9	be	be	AUX
ejpam-4556	465	10	rewritten	rewrite	VERB
ejpam-4556	465	11	as	as	ADP
ejpam-4556	465	12	(	(	PUNCT
ejpam-4556	465	13	∂	∂	NUM
ejpam-4556	465	14	∂t	∂t	PROPN
ejpam-4556	465	15	+	+	SYM
ejpam-4556	465	16	∂	∂	NUM
ejpam-4556	465	17	∂a	∂a	NOUN
ejpam-4556	465	18	)	)	PUNCT
ejpam-4556	465	19	f(t	f(t	PROPN
ejpam-4556	465	20	,	,	PUNCT
ejpam-4556	465	21	a	a	PRON
ejpam-4556	465	22	)	)	PUNCT
ejpam-4556	465	23	=	=	SYM
ejpam-4556	465	24	g(t	g(t	PROPN
ejpam-4556	465	25	,	,	PUNCT
ejpam-4556	465	26	a	a	PRON
ejpam-4556	465	27	)	)	PUNCT
ejpam-4556	465	28	can	can	AUX
ejpam-4556	465	29	be	be	AUX
ejpam-4556	465	30	approximated	approximate	VERB
ejpam-4556	465	31	by	by	ADP
ejpam-4556	465	32	f(tk+1	f(tk+1	NOUN
ejpam-4556	465	33	,	,	PUNCT
ejpam-4556	465	34	ai)−	ai)−	NOUN
ejpam-4556	465	35	f(tk	f(tk	NOUN
ejpam-4556	465	36	,	,	PUNCT
ejpam-4556	465	37	ai	ai	VERB
ejpam-4556	465	38	)	)	PUNCT
ejpam-4556	465	39	∆t	∆t	PROPN
ejpam-4556	466	1	+	+	CCONJ
ejpam-4556	466	2	f(tk	f(tk	NOUN
ejpam-4556	466	3	,	,	PUNCT
ejpam-4556	466	4	ai)−	ai)−	NOUN
ejpam-4556	466	5	f(tk	f(tk	NOUN
ejpam-4556	466	6	,	,	PUNCT
ejpam-4556	466	7	ai−1	ai−1	PROPN
ejpam-4556	466	8	)	)	PUNCT
ejpam-4556	466	9	∆a	∆a	PROPN
ejpam-4556	466	10	=	=	PUNCT
ejpam-4556	466	11	g(tk	g(tk	PROPN
ejpam-4556	466	12	,	,	PUNCT
ejpam-4556	466	13	ai	ai	VERB
ejpam-4556	466	14	)	)	PUNCT
ejpam-4556	466	15	in	in	ADP
ejpam-4556	466	16	view	view	NOUN
ejpam-4556	466	17	of	of	ADP
ejpam-4556	466	18	the	the	DET
ejpam-4556	466	19	influence	influence	NOUN
ejpam-4556	466	20	of	of	ADP
ejpam-4556	466	21	migration	migration	NOUN
ejpam-4556	466	22	on	on	ADP
ejpam-4556	466	23	the	the	DET
ejpam-4556	466	24	dynamics	dynamic	NOUN
ejpam-4556	466	25	of	of	ADP
ejpam-4556	466	26	tuberculosis	tuberculosis	NOUN
ejpam-4556	466	27	modeled	model	VERB
ejpam-4556	466	28	by	by	ADP
ejpam-4556	466	29	(	(	PUNCT
ejpam-4556	466	30	5	5	NUM
ejpam-4556	466	31	)	)	PUNCT
ejpam-4556	466	32	,	,	PUNCT
ejpam-4556	466	33	we	we	PRON
ejpam-4556	466	34	considered	consider	VERB
ejpam-4556	466	35	patch2	patch2	NOUN
ejpam-4556	466	36	in	in	ADP
ejpam-4556	466	37	an	an	DET
ejpam-4556	466	38	endemic	endemic	ADJ
ejpam-4556	466	39	situation	situation	NOUN
ejpam-4556	466	40	fig2	fig2	NOUN
ejpam-4556	466	41	and	and	CCONJ
ejpam-4556	466	42	patch1	patch1	NOUN
ejpam-4556	466	43	under	under	ADP
ejpam-4556	466	44	global	global	ADJ
ejpam-4556	466	45	stability	stability	NOUN
ejpam-4556	466	46	conditions	condition	NOUN
ejpam-4556	466	47	.	.	PUNCT
ejpam-4556	467	1	in	in	ADP
ejpam-4556	467	2	absence	absence	NOUN
ejpam-4556	467	3	of	of	ADP
ejpam-4556	467	4	migration	migration	NOUN
ejpam-4556	467	5	,	,	PUNCT
ejpam-4556	467	6	we	we	PRON
ejpam-4556	467	7	obtain	obtain	VERB
ejpam-4556	467	8	the	the	DET
ejpam-4556	467	9	fig	fig	NOUN
ejpam-4556	467	10	3a	3a	NUM
ejpam-4556	467	11	;	;	PUNCT
ejpam-4556	467	12	4a	4a	NUM
ejpam-4556	467	13	;	;	PUNCT
ejpam-4556	467	14	5a	5a	NUM
ejpam-4556	467	15	,	,	PUNCT
ejpam-4556	467	16	which	which	PRON
ejpam-4556	467	17	translate	translate	VERB
ejpam-4556	467	18	the	the	DET
ejpam-4556	467	19	overall	overall	ADJ
ejpam-4556	467	20	stability	stability	NOUN
ejpam-4556	467	21	of	of	ADP
ejpam-4556	467	22	the	the	DET
ejpam-4556	467	23	patch	patch	NOUN
ejpam-4556	467	24	.	.	PUNCT
ejpam-4556	468	1	by	by	ADP
ejpam-4556	468	2	varying	vary	VERB
ejpam-4556	468	3	the	the	DET
ejpam-4556	468	4	migration	migration	NOUN
ejpam-4556	468	5	rates	rate	NOUN
ejpam-4556	468	6	,	,	PUNCT
ejpam-4556	468	7	we	we	PRON
ejpam-4556	468	8	obtain	obtain	VERB
ejpam-4556	468	9	the	the	DET
ejpam-4556	468	10	figure	figure	NOUN
ejpam-4556	468	11	of	of	ADP
ejpam-4556	468	12	the	the	DET
ejpam-4556	468	13	type	type	NOUN
ejpam-4556	468	14	fig	fig	NOUN
ejpam-4556	468	15	3b	3b	NOUN
ejpam-4556	468	16	;	;	PUNCT
ejpam-4556	468	17	4b	4b	X
ejpam-4556	468	18	;	;	PUNCT
ejpam-4556	468	19	5b	5b	NUM
ejpam-4556	468	20	,	,	PUNCT
ejpam-4556	468	21	which	which	PRON
ejpam-4556	468	22	indicate	indicate	VERB
ejpam-4556	468	23	that	that	SCONJ
ejpam-4556	468	24	the	the	DET
ejpam-4556	468	25	migration	migration	NOUN
ejpam-4556	468	26	disrupts	disrupt	VERB
ejpam-4556	468	27	the	the	DET
ejpam-4556	468	28	stability	stability	NOUN
ejpam-4556	468	29	and	and	CCONJ
ejpam-4556	468	30	could	could	AUX
ejpam-4556	468	31	lead	lead	VERB
ejpam-4556	468	32	the	the	DET
ejpam-4556	468	33	patch	patch	NOUN
ejpam-4556	468	34	a	a	DET
ejpam-4556	468	35	dramatic	dramatic	ADJ
ejpam-4556	468	36	situation	situation	NOUN
ejpam-4556	468	37	.	.	PUNCT
ejpam-4556	469	1	b.	b.	PROPN
ejpam-4556	469	2	k.	k.	PROPN
ejpam-4556	469	3	abdoul	abdoul	PROPN
ejpam-4556	469	4	wahid	wahid	PROPN
ejpam-4556	469	5	,	,	PUNCT
ejpam-4556	469	6	d.moustapha	d.moustapha	PROPN
ejpam-4556	469	7	,	,	PUNCT
ejpam-4556	469	8	s.	s.	PROPN
ejpam-4556	469	9	bisso	bisso	PROPN
ejpam-4556	469	10	/	/	SYM
ejpam-4556	469	11	eur	eur	PROPN
ejpam-4556	469	12	.	.	PUNCT
ejpam-4556	470	1	j.	j.	PROPN
ejpam-4556	470	2	pure	pure	PROPN
ejpam-4556	470	3	appl	appl	PROPN
ejpam-4556	470	4	.	.	PROPN
ejpam-4556	470	5	math	math	PROPN
ejpam-4556	470	6	,	,	PUNCT
ejpam-4556	470	7	15	15	NUM
ejpam-4556	470	8	(	(	PUNCT
ejpam-4556	470	9	4	4	NUM
ejpam-4556	470	10	)	)	PUNCT
ejpam-4556	470	11	(	(	PUNCT
ejpam-4556	470	12	2022	2022	NUM
ejpam-4556	470	13	)	)	PUNCT
ejpam-4556	470	14	,	,	PUNCT
ejpam-4556	470	15	2054	2054	NUM
ejpam-4556	470	16	-	-	SYM
ejpam-4556	470	17	2073	2073	NUM
ejpam-4556	470	18	2070	2070	NUM
ejpam-4556	470	19	fig.2	fig.2	PROPN
ejpam-4556	470	20	.	.	PUNCT
ejpam-4556	471	1	infectious	infectious	ADJ
ejpam-4556	471	2	individuals	individual	NOUN
ejpam-4556	471	3	from	from	ADP
ejpam-4556	471	4	path	path	NOUN
ejpam-4556	471	5	2	2	NUM
ejpam-4556	471	6	ℜ2(ψ	ℜ2(ψ	PROPN
ejpam-4556	471	7	,	,	PUNCT
ejpam-4556	471	8	ρ	ρ	PROPN
ejpam-4556	471	9	)	)	PUNCT
ejpam-4556	471	10	>	>	SYM
ejpam-4556	471	11	1	1	NUM
ejpam-4556	471	12	treated	treat	VERB
ejpam-4556	471	13	patch1	patch1	PROPN
ejpam-4556	471	14	-1	-1	PUNCT
ejpam-4556	472	1	-0.5	-0.5	X
ejpam-4556	472	2	0	0	NUM
ejpam-4556	472	3	0.5	0.5	NUM
ejpam-4556	472	4	1	1	NUM
ejpam-4556	472	5	age0	age0	NOUN
ejpam-4556	472	6	50	50	NUM
ejpam-4556	472	7	100	100	NUM
ejpam-4556	472	8	150	150	NUM
ejpam-4556	472	9	time(month	time(month	PROPN
ejpam-4556	472	10	)	)	PUNCT
ejpam-4556	472	11	0	0	NUM
ejpam-4556	472	12	2	2	NUM
ejpam-4556	472	13	4	4	NUM
ejpam-4556	472	14	6	6	NUM
ejpam-4556	472	15	fig.3a	fig.3a	PROPN
ejpam-4556	472	16	.	.	PUNCT
ejpam-4556	472	17	evolution	evolution	NOUN
ejpam-4556	472	18	of	of	ADP
ejpam-4556	472	19	j1	j1	PROPN
ejpam-4556	472	20	when	when	SCONJ
ejpam-4556	472	21	ℜ1	ℜ1	PROPN
ejpam-4556	472	22	0(ρ	0(ρ	NUM
ejpam-4556	472	23	)	)	PUNCT
ejpam-4556	472	24	<	<	X
ejpam-4556	472	25	1	1	NUM
ejpam-4556	472	26	,	,	PUNCT
ejpam-4556	472	27	with	with	ADP
ejpam-4556	472	28	ρ	ρ	PROPN
ejpam-4556	472	29	=	=	SYM
ejpam-4556	472	30	0	0	NUM
ejpam-4556	472	31	fig.3b	fig.3b	NUM
ejpam-4556	472	32	.	.	PUNCT
ejpam-4556	473	1	evolution	evolution	NOUN
ejpam-4556	473	2	of	of	ADP
ejpam-4556	473	3	j1	j1	PROPN
ejpam-4556	473	4	when	when	SCONJ
ejpam-4556	473	5	ℜ1	ℜ1	PROPN
ejpam-4556	473	6	0(ρ	0(ρ	NUM
ejpam-4556	473	7	)	)	PUNCT
ejpam-4556	473	8	<	<	X
ejpam-4556	473	9	1	1	NUM
ejpam-4556	473	10	,	,	PUNCT
ejpam-4556	473	11	with	with	ADP
ejpam-4556	473	12	ρ	ρ	PROPN
ejpam-4556	473	13	̸=	̸=	PROPN
ejpam-4556	473	14	0	0	NUM
ejpam-4556	473	15	b.	b.	PROPN
ejpam-4556	473	16	k.	k.	PROPN
ejpam-4556	473	17	abdoul	abdoul	PROPN
ejpam-4556	473	18	wahid	wahid	PROPN
ejpam-4556	473	19	,	,	PUNCT
ejpam-4556	473	20	d.moustapha	d.moustapha	PROPN
ejpam-4556	473	21	,	,	PUNCT
ejpam-4556	473	22	s.	s.	PROPN
ejpam-4556	473	23	bisso	bisso	PROPN
ejpam-4556	473	24	/	/	SYM
ejpam-4556	473	25	eur	eur	PROPN
ejpam-4556	473	26	.	.	PUNCT
ejpam-4556	474	1	j.	j.	PROPN
ejpam-4556	474	2	pure	pure	PROPN
ejpam-4556	474	3	appl	appl	PROPN
ejpam-4556	474	4	.	.	PROPN
ejpam-4556	474	5	math	math	PROPN
ejpam-4556	474	6	,	,	PUNCT
ejpam-4556	474	7	15	15	NUM
ejpam-4556	474	8	(	(	PUNCT
ejpam-4556	474	9	4	4	NUM
ejpam-4556	474	10	)	)	PUNCT
ejpam-4556	474	11	(	(	PUNCT
ejpam-4556	474	12	2022	2022	NUM
ejpam-4556	474	13	)	)	PUNCT
ejpam-4556	474	14	,	,	PUNCT
ejpam-4556	474	15	2054	2054	NUM
ejpam-4556	474	16	-	-	SYM
ejpam-4556	474	17	2073	2073	NUM
ejpam-4556	474	18	2071	2071	NUM
ejpam-4556	474	19	infectious	infectious	ADJ
ejpam-4556	474	20	patch1	patch1	NOUN
ejpam-4556	474	21	-1	-1	X
ejpam-4556	474	22	-0.5	-0.5	X
ejpam-4556	474	23	0	0	NUM
ejpam-4556	474	24	0.5	0.5	NUM
ejpam-4556	474	25	1	1	NUM
ejpam-4556	474	26	age0	age0	NOUN
ejpam-4556	474	27	50	50	NUM
ejpam-4556	474	28	100	100	NUM
ejpam-4556	474	29	150	150	NUM
ejpam-4556	474	30	time(month	time(month	PROPN
ejpam-4556	474	31	)	)	PUNCT
ejpam-4556	474	32	0	0	NUM
ejpam-4556	475	1	2	2	NUM
ejpam-4556	475	2	4	4	NUM
ejpam-4556	475	3	6	6	NUM
ejpam-4556	475	4	fig.4a	fig.4a	NOUN
ejpam-4556	475	5	.	.	PUNCT
ejpam-4556	476	1	evolution	evolution	NOUN
ejpam-4556	476	2	of	of	ADP
ejpam-4556	476	3	i1	i1	PROPN
ejpam-4556	476	4	when	when	SCONJ
ejpam-4556	476	5	ℜ1	ℜ1	PROPN
ejpam-4556	476	6	0(ρ	0(ρ	NUM
ejpam-4556	476	7	)	)	PUNCT
ejpam-4556	476	8	<	<	X
ejpam-4556	476	9	1	1	NUM
ejpam-4556	476	10	,	,	PUNCT
ejpam-4556	476	11	with	with	ADP
ejpam-4556	476	12	ρ	ρ	PROPN
ejpam-4556	476	13	=	=	SYM
ejpam-4556	476	14	0	0	NUM
ejpam-4556	476	15	fig.4b	fig.4b	NOUN
ejpam-4556	476	16	.	.	PUNCT
ejpam-4556	476	17	evolution	evolution	NOUN
ejpam-4556	476	18	of	of	ADP
ejpam-4556	476	19	i1	i1	PROPN
ejpam-4556	477	1	when	when	SCONJ
ejpam-4556	477	2	ℜ1	ℜ1	PROPN
ejpam-4556	477	3	0(ρ	0(ρ	NUM
ejpam-4556	477	4	)	)	PUNCT
ejpam-4556	477	5	<	<	X
ejpam-4556	477	6	1	1	NUM
ejpam-4556	477	7	,	,	PUNCT
ejpam-4556	477	8	with	with	ADP
ejpam-4556	477	9	ρ	ρ	PROPN
ejpam-4556	477	10	̸=	̸=	PROPN
ejpam-4556	477	11	0	0	NUM
ejpam-4556	477	12	latent	latent	NOUN
ejpam-4556	477	13	patch1	patch1	NOUN
ejpam-4556	477	14	-1	-1	X
ejpam-4556	477	15	-0.5	-0.5	X
ejpam-4556	477	16	0	0	NUM
ejpam-4556	477	17	0.5	0.5	NUM
ejpam-4556	477	18	1	1	NUM
ejpam-4556	477	19	age0	age0	NOUN
ejpam-4556	477	20	50	50	NUM
ejpam-4556	477	21	100	100	NUM
ejpam-4556	477	22	150	150	NUM
ejpam-4556	477	23	time(month	time(month	PROPN
ejpam-4556	477	24	)	)	PUNCT
ejpam-4556	477	25	0	0	NUM
ejpam-4556	477	26	2	2	NUM
ejpam-4556	477	27	4	4	NUM
ejpam-4556	477	28	6	6	NUM
ejpam-4556	477	29	fig.5a	fig.5a	NOUN
ejpam-4556	477	30	.	.	PUNCT
ejpam-4556	478	1	evolution	evolution	NOUN
ejpam-4556	478	2	of	of	ADP
ejpam-4556	478	3	l1	l1	PROPN
ejpam-4556	478	4	when	when	SCONJ
ejpam-4556	478	5	ℜ1	ℜ1	PROPN
ejpam-4556	478	6	0(ρ	0(ρ	NUM
ejpam-4556	478	7	)	)	PUNCT
ejpam-4556	478	8	<	<	X
ejpam-4556	478	9	1	1	NUM
ejpam-4556	478	10	,	,	PUNCT
ejpam-4556	478	11	with	with	ADP
ejpam-4556	478	12	ρ	ρ	PROPN
ejpam-4556	478	13	=	=	SYM
ejpam-4556	478	14	0	0	NUM
ejpam-4556	478	15	fig.5b	fig.5b	NUM
ejpam-4556	478	16	.	.	PUNCT
ejpam-4556	478	17	evolution	evolution	NOUN
ejpam-4556	478	18	of	of	ADP
ejpam-4556	478	19	l1	l1	PROPN
ejpam-4556	478	20	when	when	SCONJ
ejpam-4556	478	21	ℜ1	ℜ1	PROPN
ejpam-4556	478	22	0(ρ	0(ρ	NUM
ejpam-4556	478	23	)	)	PUNCT
ejpam-4556	478	24	<	<	X
ejpam-4556	478	25	1	1	NUM
ejpam-4556	478	26	,	,	PUNCT
ejpam-4556	478	27	with	with	ADP
ejpam-4556	478	28	ρ	ρ	PROPN
ejpam-4556	478	29	̸=	̸=	PROPN
ejpam-4556	478	30	0	0	NUM
ejpam-4556	478	31	8	8	NUM
ejpam-4556	478	32	.	.	PUNCT
ejpam-4556	479	1	conclusion	conclusion	NOUN
ejpam-4556	479	2	in	in	ADP
ejpam-4556	479	3	this	this	DET
ejpam-4556	479	4	paper	paper	NOUN
ejpam-4556	479	5	,	,	PUNCT
ejpam-4556	479	6	we	we	PRON
ejpam-4556	479	7	analyzed	analyze	VERB
ejpam-4556	479	8	a	a	DET
ejpam-4556	479	9	two	two	NUM
ejpam-4556	479	10	-	-	PUNCT
ejpam-4556	479	11	patch	patch	NOUN
ejpam-4556	479	12	age	age	NOUN
ejpam-4556	479	13	-	-	PUNCT
ejpam-4556	479	14	structured	structure	VERB
ejpam-4556	479	15	model	model	NOUN
ejpam-4556	479	16	applied	apply	VERB
ejpam-4556	479	17	to	to	ADP
ejpam-4556	479	18	tuberculosis	tuberculosis	NOUN
ejpam-4556	479	19	in	in	ADP
ejpam-4556	479	20	a	a	DET
ejpam-4556	479	21	context	context	NOUN
ejpam-4556	479	22	where	where	SCONJ
ejpam-4556	479	23	migration	migration	NOUN
ejpam-4556	479	24	is	be	AUX
ejpam-4556	479	25	not	not	PART
ejpam-4556	479	26	controlled	control	VERB
ejpam-4556	479	27	.	.	PUNCT
ejpam-4556	480	1	the	the	DET
ejpam-4556	480	2	aim	aim	NOUN
ejpam-4556	480	3	is	be	AUX
ejpam-4556	480	4	to	to	PART
ejpam-4556	480	5	see	see	VERB
ejpam-4556	480	6	the	the	DET
ejpam-4556	480	7	impact	impact	NOUN
ejpam-4556	480	8	of	of	ADP
ejpam-4556	480	9	migration	migration	NOUN
ejpam-4556	480	10	on	on	ADP
ejpam-4556	480	11	the	the	DET
ejpam-4556	480	12	spread	spread	NOUN
ejpam-4556	480	13	of	of	ADP
ejpam-4556	480	14	tuberculosis	tuberculosis	NOUN
ejpam-4556	480	15	.	.	PUNCT
ejpam-4556	481	1	thus	thus	ADV
ejpam-4556	481	2	,	,	PUNCT
ejpam-4556	481	3	we	we	PRON
ejpam-4556	481	4	allowed	allow	VERB
ejpam-4556	481	5	migration	migration	NOUN
ejpam-4556	481	6	to	to	ADP
ejpam-4556	481	7	all	all	DET
ejpam-4556	481	8	individuals	individual	NOUN
ejpam-4556	481	9	regardless	regardless	ADV
ejpam-4556	481	10	of	of	ADP
ejpam-4556	481	11	their	their	PRON
ejpam-4556	481	12	epidemiological	epidemiological	ADJ
ejpam-4556	481	13	status	status	NOUN
ejpam-4556	481	14	.	.	PUNCT
ejpam-4556	482	1	this	this	DET
ejpam-4556	482	2	study	study	NOUN
ejpam-4556	482	3	shows	show	VERB
ejpam-4556	482	4	that	that	SCONJ
ejpam-4556	482	5	migration	migration	NOUN
ejpam-4556	482	6	has	have	VERB
ejpam-4556	482	7	a	a	DET
ejpam-4556	482	8	negative	negative	ADJ
ejpam-4556	482	9	impact	impact	NOUN
ejpam-4556	482	10	on	on	ADP
ejpam-4556	482	11	the	the	DET
ejpam-4556	482	12	spread	spread	NOUN
ejpam-4556	482	13	of	of	ADP
ejpam-4556	482	14	tb	tb	NOUN
ejpam-4556	482	15	.	.	PUNCT
ejpam-4556	483	1	the	the	DET
ejpam-4556	483	2	results	result	NOUN
ejpam-4556	483	3	of	of	ADP
ejpam-4556	483	4	this	this	DET
ejpam-4556	483	5	analysis	analysis	NOUN
ejpam-4556	483	6	compared	compare	VERB
ejpam-4556	483	7	to	to	ADP
ejpam-4556	483	8	those	those	PRON
ejpam-4556	483	9	obtained	obtain	VERB
ejpam-4556	483	10	in	in	ADP
ejpam-4556	483	11	[	[	X
ejpam-4556	483	12	19	19	NUM
ejpam-4556	483	13	]	]	PUNCT
ejpam-4556	483	14	,	,	PUNCT
ejpam-4556	483	15	allow	allow	VERB
ejpam-4556	483	16	us	we	PRON
ejpam-4556	483	17	to	to	PART
ejpam-4556	483	18	affirm	affirm	VERB
ejpam-4556	483	19	that	that	SCONJ
ejpam-4556	483	20	the	the	DET
ejpam-4556	483	21	control	control	NOUN
ejpam-4556	483	22	of	of	ADP
ejpam-4556	483	23	the	the	DET
ejpam-4556	483	24	migration	migration	NOUN
ejpam-4556	483	25	makes	make	VERB
ejpam-4556	483	26	it	it	PRON
ejpam-4556	483	27	possible	possible	ADJ
ejpam-4556	483	28	to	to	PART
ejpam-4556	483	29	avoid	avoid	VERB
ejpam-4556	483	30	the	the	DET
ejpam-4556	483	31	propagation	propagation	NOUN
ejpam-4556	483	32	of	of	ADP
ejpam-4556	483	33	references	reference	NOUN
ejpam-4556	483	34	2072	2072	NUM
ejpam-4556	483	35	this	this	DET
ejpam-4556	483	36	disease	disease	NOUN
ejpam-4556	483	37	,	,	PUNCT
ejpam-4556	483	38	and	and	CCONJ
ejpam-4556	483	39	reduce	reduce	VERB
ejpam-4556	483	40	the	the	DET
ejpam-4556	483	41	exorbitant	exorbitant	ADJ
ejpam-4556	483	42	cost	cost	NOUN
ejpam-4556	483	43	as	as	ADV
ejpam-4556	483	44	well	well	ADV
ejpam-4556	483	45	as	as	ADP
ejpam-4556	483	46	human	human	ADJ
ejpam-4556	483	47	that	that	SCONJ
ejpam-4556	483	48	the	the	DET
ejpam-4556	483	49	governments	government	NOUN
ejpam-4556	483	50	deploy	deploy	VERB
ejpam-4556	483	51	for	for	ADP
ejpam-4556	483	52	the	the	DET
ejpam-4556	483	53	eradication	eradication	NOUN
ejpam-4556	483	54	of	of	ADP
ejpam-4556	483	55	tuberculosis	tuberculosis	NOUN
ejpam-4556	483	56	.	.	PUNCT
ejpam-4556	484	1	we	we	PRON
ejpam-4556	484	2	intend	intend	VERB
ejpam-4556	484	3	to	to	PART
ejpam-4556	484	4	extend	extend	VERB
ejpam-4556	484	5	this	this	DET
ejpam-4556	484	6	model	model	NOUN
ejpam-4556	484	7	by	by	ADP
ejpam-4556	484	8	introducing	introduce	VERB
ejpam-4556	484	9	the	the	DET
ejpam-4556	484	10	compartments	compartment	NOUN
ejpam-4556	484	11	of	of	ADP
ejpam-4556	484	12	the	the	DET
ejpam-4556	484	13	loss	loss	NOUN
ejpam-4556	484	14	of	of	ADP
ejpam-4556	484	15	seen	see	VERB
ejpam-4556	484	16	otherwise	otherwise	ADV
ejpam-4556	484	17	,	,	PUNCT
ejpam-4556	484	18	the	the	DET
ejpam-4556	484	19	individuals	individual	NOUN
ejpam-4556	484	20	who	who	PRON
ejpam-4556	484	21	leave	leave	VERB
ejpam-4556	484	22	the	the	DET
ejpam-4556	484	23	treatment	treatment	NOUN
ejpam-4556	484	24	and	and	CCONJ
ejpam-4556	484	25	the	the	DET
ejpam-4556	484	26	resistant	resistant	ADJ
ejpam-4556	484	27	to	to	ADP
ejpam-4556	484	28	all	all	DET
ejpam-4556	484	29	the	the	DET
ejpam-4556	484	30	forms	form	NOUN
ejpam-4556	484	31	of	of	ADP
ejpam-4556	484	32	antituberculous	antituberculous	ADJ
ejpam-4556	484	33	drugs	drug	NOUN
ejpam-4556	484	34	that	that	PRON
ejpam-4556	484	35	we	we	PRON
ejpam-4556	484	36	had	have	VERB
ejpam-4556	484	37	,	,	PUNCT
ejpam-4556	484	38	we	we	PRON
ejpam-4556	484	39	also	also	ADV
ejpam-4556	484	40	envisage	envisage	VERB
ejpam-4556	484	41	to	to	PART
ejpam-4556	484	42	study	study	VERB
ejpam-4556	484	43	the	the	DET
ejpam-4556	484	44	stability	stability	NOUN
ejpam-4556	484	45	of	of	ADP
ejpam-4556	484	46	the	the	DET
ejpam-4556	484	47	endemic	endemic	ADJ
ejpam-4556	484	48	equilibrium	equilibrium	NOUN
ejpam-4556	484	49	as	as	ADV
ejpam-4556	484	50	well	well	ADV
ejpam-4556	484	51	as	as	ADP
ejpam-4556	484	52	the	the	DET
ejpam-4556	484	53	possibilities	possibility	NOUN
ejpam-4556	484	54	of	of	ADP
ejpam-4556	484	55	existence	existence	NOUN
ejpam-4556	484	56	of	of	ADP
ejpam-4556	484	57	hopf	hopf	ADJ
ejpam-4556	484	58	bifurcation	bifurcation	NOUN
ejpam-4556	484	59	using	use	VERB
ejpam-4556	484	60	the	the	DET
ejpam-4556	484	61	method	method	NOUN
ejpam-4556	484	62	developed	develop	VERB
ejpam-4556	484	63	by	by	ADP
ejpam-4556	484	64	p.	p.	PROPN
ejpam-4556	484	65	magal	magal	NOUN
ejpam-4556	484	66	,	,	PUNCT
ejpam-4556	484	67	s.	s.	PROPN
ejpam-4556	484	68	ruan	ruan	PROPN
ejpam-4556	485	1	[	[	X
ejpam-4556	485	2	15	15	NUM
ejpam-4556	485	3	]	]	PUNCT
ejpam-4556	485	4	.	.	PUNCT
ejpam-4556	486	1	references	reference	NOUN
ejpam-4556	486	2	[	[	X
ejpam-4556	486	3	1	1	X
ejpam-4556	486	4	]	]	X
ejpam-4556	486	5	o.o	o.o	PROPN
ejpam-4556	486	6	.	.	PROPN
ejpam-4556	486	7	okundalaye	okundalaye	PROPN
ejpam-4556	486	8	a	a	DET
ejpam-4556	486	9	,	,	PUNCT
ejpam-4556	486	10	w.a.m	w.a.m	PROPN
ejpam-4556	486	11	.	.	PROPN
ejpam-4556	486	12	othman	othman	PROPN
ejpam-4556	486	13	,	,	PUNCT
ejpam-4556	486	14	and	and	CCONJ
ejpam-4556	486	15	a.s	a.s	PROPN
ejpam-4556	486	16	.	.	PROPN
ejpam-4556	486	17	oke	oke	PROPN
ejpam-4556	486	18	.	.	PUNCT
ejpam-4556	487	1	an	an	DET
ejpam-4556	487	2	efficient	efficient	ADJ
ejpam-4556	487	3	approximate	approximate	ADJ
ejpam-4556	487	4	analytical	analytical	ADJ
ejpam-4556	487	5	solution	solution	NOUN
ejpam-4556	487	6	for	for	ADP
ejpam-4556	487	7	4	4	NUM
ejpam-4556	487	8	-	-	PUNCT
ejpam-4556	487	9	compartment	compartment	NOUN
ejpam-4556	487	10	covid-19	covid-19	PROPN
ejpam-4556	487	11	fractional	fractional	ADJ
ejpam-4556	487	12	mathematical	mathematical	ADJ
ejpam-4556	487	13	model	model	NOUN
ejpam-4556	487	14	.	.	PUNCT
ejpam-4556	488	1	journal	journal	PROPN
ejpam-4556	488	2	of	of	ADP
ejpam-4556	488	3	computational	computational	ADJ
ejpam-4556	488	4	and	and	CCONJ
ejpam-4556	488	5	applied	applied	ADJ
ejpam-4556	488	6	mathematics	mathematic	NOUN
ejpam-4556	488	7	,	,	PUNCT
ejpam-4556	488	8	419:114506	419:114506	NOUN
ejpam-4556	488	9	,	,	PUNCT
ejpam-4556	488	10	2022	2022	NUM
ejpam-4556	488	11	.	.	PUNCT
ejpam-4556	489	1	[	[	X
ejpam-4556	489	2	2	2	NUM
ejpam-4556	489	3	]	]	PUNCT
ejpam-4556	489	4	a.patel	a.patel	NOUN
ejpam-4556	489	5	,	,	PUNCT
ejpam-4556	489	6	fschofield	fschofield	NOUN
ejpam-4556	489	7	v.siskind	v.siskind	NOUN
ejpam-4556	489	8	,	,	PUNCT
ejpam-4556	489	9	e.abrahams	e.abraham	NOUN
ejpam-4556	489	10	,	,	PUNCT
ejpam-4556	489	11	and	and	CCONJ
ejpam-4556	489	12	j.parker	j.parker	NOUN
ejpam-4556	489	13	.	.	PUNCT
ejpam-4556	490	1	case	case	NOUN
ejpam-4556	490	2	-	-	PUNCT
ejpam-4556	490	3	control	control	NOUN
ejpam-4556	490	4	evaluation	evaluation	NOUN
ejpam-4556	490	5	of	of	ADP
ejpam-4556	490	6	a	a	DET
ejpam-4556	490	7	school	school	NOUN
ejpam-4556	490	8	-	-	PUNCT
ejpam-4556	490	9	age	age	NOUN
ejpam-4556	490	10	bcg	bcg	NOUN
ejpam-4556	490	11	vaccination	vaccination	NOUN
ejpam-4556	490	12	programme	programme	NOUN
ejpam-4556	490	13	in	in	ADP
ejpam-4556	490	14	subtropical	subtropical	ADJ
ejpam-4556	490	15	australia	australia	NOUN
ejpam-4556	490	16	.	.	PUNCT
ejpam-4556	491	1	bullet.who	bullet.who	X
ejpam-4556	491	2	,	,	PUNCT
ejpam-4556	491	3	69(4):424	69(4):424	NUM
ejpam-4556	491	4	,	,	PUNCT
ejpam-4556	491	5	1991	1991	NUM
ejpam-4556	491	6	.	.	PUNCT
ejpam-4556	492	1	[	[	X
ejpam-4556	492	2	3	3	X
ejpam-4556	492	3	]	]	PUNCT
ejpam-4556	492	4	a.zwerling	a.zwerling	NOUN
ejpam-4556	492	5	,	,	PUNCT
ejpam-4556	492	6	s.shrestha	s.shrestha	VERB
ejpam-4556	492	7	,	,	PUNCT
ejpam-4556	492	8	and	and	CCONJ
ejpam-4556	492	9	david.w.d	david.w.d	PROPN
ejpam-4556	492	10	.	.	PUNCT
ejpam-4556	493	1	mathematical	mathematical	ADJ
ejpam-4556	493	2	modeling	modeling	NOUN
ejpam-4556	493	3	and	and	CCONJ
ejpam-4556	493	4	tuberculosis	tuberculosis	NOUN
ejpam-4556	493	5	advances	advance	NOUN
ejpam-4556	493	6	in	in	ADP
ejpam-4556	493	7	diagnostics	diagnostic	NOUN
ejpam-4556	493	8	and	and	CCONJ
ejpam-4556	493	9	novel	novel	ADJ
ejpam-4556	493	10	therapies	therapy	NOUN
ejpam-4556	493	11	.	.	PUNCT
ejpam-4556	494	1	hindawi	hindawi	ADJ
ejpam-4556	494	2	publishing	publishing	NOUN
ejpam-4556	494	3	corporation	corporation	NOUN
ejpam-4556	494	4	advances	advance	VERB
ejpam-4556	494	5	in	in	ADP
ejpam-4556	494	6	medecine	medecine	NOUN
ejpam-4556	494	7	,	,	PUNCT
ejpam-4556	494	8	page	page	NOUN
ejpam-4556	494	9	10	10	NUM
ejpam-4556	494	10	,	,	PUNCT
ejpam-4556	494	11	2015	2015	NUM
ejpam-4556	494	12	.	.	PUNCT
ejpam-4556	495	1	[	[	X
ejpam-4556	495	2	4	4	NUM
ejpam-4556	495	3	]	]	X
ejpam-4556	495	4	b.b.echeng	b.b.echeng	PROPN
ejpam-4556	495	5	and	and	CCONJ
ejpam-4556	495	6	k.a.lebedev	k.a.lebedev	PROPN
ejpam-4556	495	7	.	.	PUNCT
ejpam-4556	496	1	on	on	ADP
ejpam-4556	496	2	mathematical	mathematical	ADJ
ejpam-4556	496	3	modeling	modeling	NOUN
ejpam-4556	496	4	of	of	ADP
ejpam-4556	496	5	the	the	DET
ejpam-4556	496	6	effect	effect	NOUN
ejpam-4556	496	7	of	of	ADP
ejpam-4556	496	8	bitherapeutic	bitherapeutic	ADJ
ejpam-4556	496	9	treatment	treatment	NOUN
ejpam-4556	496	10	of	of	ADP
ejpam-4556	496	11	tuberculosis	tuberculosis	NOUN
ejpam-4556	496	12	epidemic	epidemic	NOUN
ejpam-4556	496	13	.	.	PUNCT
ejpam-4556	497	1	journal	journal	NOUN
ejpam-4556	497	2	of	of	ADP
ejpam-4556	497	3	modern	modern	ADJ
ejpam-4556	497	4	mathematics	mathematic	NOUN
ejpam-4556	497	5	and	and	CCONJ
ejpam-4556	497	6	statistics	statistic	NOUN
ejpam-4556	497	7	,	,	PUNCT
ejpam-4556	497	8	9	9	NUM
ejpam-4556	497	9	(	(	PUNCT
ejpam-4556	497	10	1	1	NUM
ejpam-4556	497	11	-	-	NUM
ejpam-4556	497	12	4):1–7	4):1–7	NUM
ejpam-4556	497	13	,	,	PUNCT
ejpam-4556	497	14	2015	2015	NUM
ejpam-4556	497	15	.	.	PUNCT
ejpam-4556	498	1	[	[	X
ejpam-4556	498	2	5	5	X
ejpam-4556	498	3	]	]	PUNCT
ejpam-4556	498	4	mc	mc	PROPN
ejpam-4556	498	5	cluskey	cluskey	PROPN
ejpam-4556	498	6	cc	cc	PROPN
ejpam-4556	498	7	.	.	PROPN
ejpam-4556	498	8	global	global	ADJ
ejpam-4556	498	9	stability	stability	NOUN
ejpam-4556	498	10	for	for	ADP
ejpam-4556	498	11	an	an	DET
ejpam-4556	498	12	sei	sei	ADJ
ejpam-4556	498	13	epidemiological	epidemiological	ADJ
ejpam-4556	498	14	model	model	NOUN
ejpam-4556	498	15	with	with	ADP
ejpam-4556	498	16	continuous	continuous	ADJ
ejpam-4556	498	17	agestructure	agestructure	NOUN
ejpam-4556	498	18	in	in	ADP
ejpam-4556	498	19	the	the	DET
ejpam-4556	498	20	exposed	expose	VERB
ejpam-4556	498	21	and	and	CCONJ
ejpam-4556	498	22	infectious	infectious	ADJ
ejpam-4556	498	23	classes	class	NOUN
ejpam-4556	498	24	.	.	PUNCT
ejpam-4556	499	1	math.biosci.eng	math.biosci.eng	PROPN
ejpam-4556	499	2	,	,	PUNCT
ejpam-4556	499	3	9:819–841	9:819–841	NUM
ejpam-4556	499	4	,	,	PUNCT
ejpam-4556	499	5	2012	2012	NUM
ejpam-4556	499	6	.	.	PUNCT
ejpam-4556	500	1	[	[	X
ejpam-4556	500	2	6	6	NUM
ejpam-4556	500	3	]	]	SYM
ejpam-4556	500	4	c.c.chavez	c.c.chavez	PROPN
ejpam-4556	500	5	,	,	PUNCT
ejpam-4556	500	6	h.w.hethcotte	h.w.hethcotte	NOUN
ejpam-4556	500	7	,	,	PUNCT
ejpam-4556	500	8	v	v	NOUN
ejpam-4556	500	9	andreasen	andreasen	NOUN
ejpam-4556	500	10	,	,	PUNCT
ejpam-4556	500	11	s.a.levin	s.a.levin	NOUN
ejpam-4556	500	12	,	,	PUNCT
ejpam-4556	500	13	and	and	CCONJ
ejpam-4556	500	14	w.m.liu	w.m.liu	PROPN
ejpam-4556	500	15	.	.	PUNCT
ejpam-4556	501	1	epidemiological	epidemiological	ADJ
ejpam-4556	501	2	models	model	NOUN
ejpam-4556	501	3	with	with	ADP
ejpam-4556	501	4	age	age	NOUN
ejpam-4556	501	5	structure	structure	NOUN
ejpam-4556	501	6	,	,	PUNCT
ejpam-4556	501	7	proportionate	proportionate	ADJ
ejpam-4556	501	8	mixing	mixing	NOUN
ejpam-4556	501	9	,	,	PUNCT
ejpam-4556	501	10	and	and	CCONJ
ejpam-4556	501	11	cross	cross	NOUN
ejpam-4556	501	12	-	-	NOUN
ejpam-4556	501	13	immunity	immunity	NOUN
ejpam-4556	501	14	.	.	PUNCT
ejpam-4556	502	1	j.math.biol	j.math.biol	PROPN
ejpam-4556	502	2	.	.	PROPN
ejpam-4556	502	3	,	,	PUNCT
ejpam-4556	502	4	27:233–258	27:233–258	NUM
ejpam-4556	502	5	,	,	PUNCT
ejpam-4556	502	6	1989	1989	NUM
ejpam-4556	502	7	.	.	PUNCT
ejpam-4556	503	1	[	[	X
ejpam-4556	503	2	7	7	X
ejpam-4556	503	3	]	]	X
ejpam-4556	503	4	c.c.chavez	c.c.chavez	NOUN
ejpam-4556	503	5	and	and	CCONJ
ejpam-4556	503	6	z.feng	z.feng	PROPN
ejpam-4556	503	7	.	.	PUNCT
ejpam-4556	504	1	global	global	ADJ
ejpam-4556	504	2	stability	stability	NOUN
ejpam-4556	504	3	of	of	ADP
ejpam-4556	504	4	an	an	DET
ejpam-4556	504	5	age	age	NOUN
ejpam-4556	504	6	-	-	PUNCT
ejpam-4556	504	7	structure	structure	NOUN
ejpam-4556	504	8	model	model	NOUN
ejpam-4556	504	9	for	for	ADP
ejpam-4556	504	10	tb	tb	NOUN
ejpam-4556	504	11	and	and	CCONJ
ejpam-4556	504	12	its	its	PRON
ejpam-4556	504	13	applications	application	NOUN
ejpam-4556	504	14	to	to	ADP
ejpam-4556	504	15	optimal	optimal	ADJ
ejpam-4556	504	16	vaccination	vaccination	NOUN
ejpam-4556	504	17	strategies	strategy	NOUN
ejpam-4556	504	18	.	.	PUNCT
ejpam-4556	505	1	mathematical	mathematical	ADJ
ejpam-4556	505	2	biosciences	bioscience	NOUN
ejpam-4556	505	3	,	,	PUNCT
ejpam-4556	505	4	151:135	151:135	NUM
ejpam-4556	505	5	–	–	PUNCT
ejpam-4556	505	6	154	154	NUM
ejpam-4556	505	7	,	,	PUNCT
ejpam-4556	505	8	1992	1992	NUM
ejpam-4556	505	9	.	.	PUNCT
ejpam-4556	506	1	[	[	X
ejpam-4556	506	2	8	8	NUM
ejpam-4556	506	3	]	]	X
ejpam-4556	506	4	r.	r.	PROPN
ejpam-4556	506	5	djebbar	djebbar	PROPN
ejpam-4556	506	6	.	.	PUNCT
ejpam-4556	507	1	aperçu	aperçu	NOUN
ejpam-4556	507	2	historique	historique	ADJ
ejpam-4556	507	3	de	de	ADP
ejpam-4556	507	4	l’antiquité	l’antiquité	PROPN
ejpam-4556	507	5	à	à	PROPN
ejpam-4556	507	6	ce	ce	PROPN
ejpam-4556	507	7	jour	jour	X
ejpam-4556	507	8	.	.	PUNCT
ejpam-4556	508	1	[	[	X
ejpam-4556	508	2	9	9	NUM
ejpam-4556	508	3	]	]	SYM
ejpam-4556	508	4	d.p.moualeu	d.p.moualeu	NOUN
ejpam-4556	508	5	,	,	PUNCT
ejpam-4556	508	6	s.bowong	s.bowong	ADJ
ejpam-4556	508	7	andj.j.tewa	andj.j.tewa	PROPN
ejpam-4556	508	8	,	,	PUNCT
ejpam-4556	508	9	and	and	CCONJ
ejpam-4556	508	10	y.emvudu	y.emvudu	NOUN
ejpam-4556	508	11	.	.	PUNCT
ejpam-4556	509	1	analysis	analysis	NOUN
ejpam-4556	509	2	of	of	ADP
ejpam-4556	509	3	the	the	DET
ejpam-4556	509	4	impact	impact	NOUN
ejpam-4556	509	5	of	of	ADP
ejpam-4556	509	6	diabetes	diabetes	NOUN
ejpam-4556	509	7	on	on	ADP
ejpam-4556	509	8	the	the	DET
ejpam-4556	509	9	dynamical	dynamical	ADJ
ejpam-4556	509	10	transmission	transmission	NOUN
ejpam-4556	509	11	of	of	ADP
ejpam-4556	509	12	tuberculosis	tuberculosis	NOUN
ejpam-4556	509	13	.	.	PUNCT
ejpam-4556	510	1	i	i	PRON
ejpam-4556	510	2	m	m	VERB
ejpam-4556	510	3	a	a	PROPN
ejpam-4556	510	4	j.	j.	PROPN
ejpam-4556	510	5	math	math	PROPN
ejpam-4556	510	6	.	.	PUNCT
ejpam-4556	511	1	appl	appl	PROPN
ejpam-4556	511	2	.	.	PROPN
ejpam-4556	512	1	med	med	PROPN
ejpam-4556	512	2	.	.	PUNCT
ejpam-4556	513	1	biol	biol	PROPN
ejpam-4556	513	2	.	.	PUNCT
ejpam-4556	513	3	,	,	PUNCT
ejpam-4556	513	4	7(3):117–146	7(3):117–146	NUM
ejpam-4556	513	5	,	,	PUNCT
ejpam-4556	513	6	2012	2012	NUM
ejpam-4556	513	7	.	.	PUNCT
ejpam-4556	514	1	[	[	X
ejpam-4556	514	2	10	10	NUM
ejpam-4556	514	3	]	]	SYM
ejpam-4556	514	4	d.raoult	d.raoult	NOUN
ejpam-4556	514	5	.	.	PUNCT
ejpam-4556	515	1	epidémie	epidémie	SCONJ
ejpam-4556	515	2	et	et	PROPN
ejpam-4556	515	3	maladies	maladie	VERB
ejpam-4556	515	4	infectieuse	infectieuse	PROPN
ejpam-4556	515	5	dans	dans	PROPN
ejpam-4556	515	6	l’histoire	l’histoire	PROPN
ejpam-4556	515	7	.	.	PUNCT
ejpam-4556	516	1	association	association	PROPN
ejpam-4556	516	2	thucydine	thucydine	NOUN
ejpam-4556	516	3	,	,	PUNCT
ejpam-4556	516	4	page	page	NOUN
ejpam-4556	516	5	16	16	NUM
ejpam-4556	516	6	,	,	PUNCT
ejpam-4556	516	7	18	18	NUM
ejpam-4556	516	8	mars	mar	NOUN
ejpam-4556	516	9	2006	2006	NUM
ejpam-4556	516	10	.	.	PUNCT
ejpam-4556	517	1	[	[	X
ejpam-4556	517	2	11	11	NUM
ejpam-4556	517	3	]	]	PUNCT
ejpam-4556	517	4	e.rohaeti	e.rohaeti	NOUN
ejpam-4556	517	5	,	,	PUNCT
ejpam-4556	517	6	s.wardatun	s.wardatun	NOUN
ejpam-4556	517	7	,	,	PUNCT
ejpam-4556	517	8	and	and	CCONJ
ejpam-4556	517	9	a.andriyati	a.andriyati	NOUN
ejpam-4556	517	10	.	.	PUNCT
ejpam-4556	518	1	stability	stability	NOUN
ejpam-4556	518	2	analysis	analysis	NOUN
ejpam-4556	518	3	model	model	NOUN
ejpam-4556	518	4	of	of	ADP
ejpam-4556	518	5	spreading	spread	VERB
ejpam-4556	518	6	and	and	CCONJ
ejpam-4556	518	7	controlling	controlling	NOUN
ejpam-4556	518	8	of	of	ADP
ejpam-4556	518	9	tuberculosis	tuberculosis	NOUN
ejpam-4556	518	10	.	.	PUNCT
ejpam-4556	519	1	applied	apply	VERB
ejpam-4556	519	2	mathematical	mathematical	ADJ
ejpam-4556	519	3	sciences	science	NOUN
ejpam-4556	519	4	,	,	PUNCT
ejpam-4556	519	5	9(52):2559–2566	9(52):2559–2566	NUM
ejpam-4556	519	6	,	,	PUNCT
ejpam-4556	519	7	2015	2015	NUM
ejpam-4556	519	8	.	.	PUNCT
ejpam-4556	520	1	references	reference	NOUN
ejpam-4556	520	2	2073	2073	NUM
ejpam-4556	520	3	[	[	X
ejpam-4556	520	4	12	12	NUM
ejpam-4556	520	5	]	]	X
ejpam-4556	520	6	taufiq	taufiq	PROPN
ejpam-4556	520	7	iskandar	iskandar	PROPN
ejpam-4556	520	8	,	,	PUNCT
ejpam-4556	520	9	natasya	natasya	PROPN
ejpam-4556	520	10	ayuningtia	ayuningtia	PROPN
ejpam-4556	520	11	chaniago	chaniago	PROPN
ejpam-4556	520	12	,	,	PUNCT
ejpam-4556	520	13	said	say	VERB
ejpam-4556	520	14	munzir	munzir	NOUN
ejpam-4556	520	15	,	,	PUNCT
ejpam-4556	520	16	vera	vera	NOUN
ejpam-4556	520	17	halfiani	halfiani	NOUN
ejpam-4556	520	18	,	,	PUNCT
ejpam-4556	520	19	and	and	CCONJ
ejpam-4556	520	20	marwan	marwan	PROPN
ejpam-4556	520	21	ramli	ramli	PROPN
ejpam-4556	520	22	.	.	PUNCT
ejpam-4556	521	1	mathematical	mathematical	ADJ
ejpam-4556	521	2	model	model	NOUN
ejpam-4556	521	3	of	of	ADP
ejpam-4556	521	4	tuberculosis	tuberculosis	NOUN
ejpam-4556	521	5	epidemic	epidemic	NOUN
ejpam-4556	521	6	with	with	ADP
ejpam-4556	521	7	recovery	recovery	NOUN
ejpam-4556	521	8	time	time	NOUN
ejpam-4556	521	9	delay	delay	NOUN
ejpam-4556	521	10	.	.	PUNCT
ejpam-4556	522	1	international	international	ADJ
ejpam-4556	522	2	conference	conference	NOUN
ejpam-4556	522	3	and	and	CCONJ
ejpam-4556	522	4	workshop	workshop	NOUN
ejpam-4556	522	5	on	on	ADP
ejpam-4556	522	6	mathematical	mathematical	ADJ
ejpam-4556	522	7	analysis	analysis	NOUN
ejpam-4556	522	8	and	and	CCONJ
ejpam-4556	522	9	its	its	PRON
ejpam-4556	522	10	applications	application	NOUN
ejpam-4556	522	11	,	,	PUNCT
ejpam-4556	522	12	(	(	PUNCT
ejpam-4556	522	13	icwomaa	icwomaa	PROPN
ejpam-4556	522	14	2017	2017	NUM
ejpam-4556	522	15	)	)	PUNCT
ejpam-4556	522	16	.	.	PUNCT
ejpam-4556	523	1	[	[	X
ejpam-4556	523	2	13	13	NUM
ejpam-4556	523	3	]	]	X
ejpam-4556	523	4	j.j.tewa	j.j.tewa	PROPN
ejpam-4556	523	5	,	,	PUNCT
ejpam-4556	523	6	s.bowong	s.bowong	NOUN
ejpam-4556	523	7	,	,	PUNCT
ejpam-4556	523	8	and	and	CCONJ
ejpam-4556	523	9	b.mewoli	b.mewoli	NOUN
ejpam-4556	523	10	.	.	PUNCT
ejpam-4556	524	1	mathematical	mathematical	ADJ
ejpam-4556	524	2	analysis	analysis	NOUN
ejpam-4556	524	3	of	of	ADP
ejpam-4556	524	4	two	two	NUM
ejpam-4556	524	5	-	-	PUNCT
ejpam-4556	524	6	patch	patch	NOUN
ejpam-4556	524	7	model	model	NOUN
ejpam-4556	524	8	for	for	ADP
ejpam-4556	524	9	the	the	DET
ejpam-4556	524	10	dynamical	dynamical	ADJ
ejpam-4556	524	11	transmission	transmission	NOUN
ejpam-4556	524	12	of	of	ADP
ejpam-4556	524	13	tuberculosis	tuberculosis	NOUN
ejpam-4556	524	14	.	.	PUNCT
ejpam-4556	525	1	applied	apply	VERB
ejpam-4556	525	2	mathematical	mathematical	ADJ
ejpam-4556	525	3	modelling	modelling	NOUN
ejpam-4556	525	4	,	,	PUNCT
ejpam-4556	525	5	36:2466	36:2466	NUM
ejpam-4556	525	6	–	–	PUNCT
ejpam-4556	525	7	2485	2485	NUM
ejpam-4556	525	8	,	,	PUNCT
ejpam-4556	525	9	2012	2012	NUM
ejpam-4556	525	10	.	.	PUNCT
ejpam-4556	526	1	[	[	X
ejpam-4556	526	2	14	14	NUM
ejpam-4556	526	3	]	]	X
ejpam-4556	526	4	j.j.tewa	j.j.tewa	PROPN
ejpam-4556	526	5	,	,	PUNCT
ejpam-4556	526	6	s.bowong	s.bowong	NOUN
ejpam-4556	526	7	,	,	PUNCT
ejpam-4556	526	8	b.mewoli	b.mewoli	NOUN
ejpam-4556	526	9	,	,	PUNCT
ejpam-4556	526	10	and	and	CCONJ
ejpam-4556	526	11	j.kurths	j.kurth	NOUN
ejpam-4556	526	12	.	.	PUNCT
ejpam-4556	527	1	two	two	NUM
ejpam-4556	527	2	-	-	PUNCT
ejpam-4556	527	3	patch	patch	NOUN
ejpam-4556	527	4	transmission	transmission	NOUN
ejpam-4556	527	5	of	of	ADP
ejpam-4556	527	6	tuberculosis	tuberculosis	NOUN
ejpam-4556	527	7	.	.	PUNCT
ejpam-4556	528	1	mathematical	mathematical	ADJ
ejpam-4556	528	2	population	population	NOUN
ejpam-4556	528	3	studies	study	NOUN
ejpam-4556	528	4	,	,	PUNCT
ejpam-4556	528	5	18(3):189–205	18(3):189–205	NUM
ejpam-4556	528	6	,	,	PUNCT
ejpam-4556	528	7	01	01	NUM
ejpam-4556	528	8	aug	aug	PROPN
ejpam-4556	528	9	2011	2011	NUM
ejpam-4556	528	10	.	.	PUNCT
ejpam-4556	529	1	[	[	X
ejpam-4556	529	2	15	15	NUM
ejpam-4556	529	3	]	]	X
ejpam-4556	529	4	p.	p.	NOUN
ejpam-4556	529	5	magal	magal	PROPN
ejpam-4556	529	6	and	and	CCONJ
ejpam-4556	529	7	s.ruan	s.ruan	PROPN
ejpam-4556	529	8	.	.	PUNCT
ejpam-4556	530	1	center	center	NOUN
ejpam-4556	530	2	manifolds	manifold	NOUN
ejpam-4556	530	3	for	for	ADP
ejpam-4556	530	4	semilinear	semilinear	NOUN
ejpam-4556	530	5	equations	equation	NOUN
ejpam-4556	530	6	with	with	ADP
ejpam-4556	530	7	non	non	ADJ
ejpam-4556	530	8	-	-	ADJ
ejpam-4556	530	9	dense	dense	ADJ
ejpam-4556	530	10	domain	domain	NOUN
ejpam-4556	530	11	and	and	CCONJ
ejpam-4556	530	12	applications	application	NOUN
ejpam-4556	530	13	on	on	ADP
ejpam-4556	530	14	hopf	hopf	ADJ
ejpam-4556	530	15	bifurcation	bifurcation	NOUN
ejpam-4556	530	16	in	in	ADP
ejpam-4556	530	17	age	age	NOUN
ejpam-4556	530	18	structured	structure	VERB
ejpam-4556	530	19	models	model	NOUN
ejpam-4556	530	20	.	.	PUNCT
ejpam-4556	531	1	mem	mem	PROPN
ejpam-4556	531	2	.	.	PUNCT
ejpam-4556	532	1	amer	amer	PROPN
ejpam-4556	532	2	.	.	PUNCT
ejpam-4556	532	3	math	math	PROPN
ejpam-4556	532	4	.	.	PUNCT
ejpam-4556	533	1	soc	soc	PROPN
ejpam-4556	533	2	.	.	PUNCT
ejpam-4556	534	1	,	,	PUNCT
ejpam-4556	534	2	202	202	NUM
ejpam-4556	534	3	(	(	PUNCT
ejpam-4556	534	4	951	951	NUM
ejpam-4556	534	5	)	)	PUNCT
ejpam-4556	534	6	,	,	PUNCT
ejpam-4556	534	7	2009	2009	NUM
ejpam-4556	534	8	.	.	PUNCT
ejpam-4556	535	1	[	[	X
ejpam-4556	535	2	16	16	NUM
ejpam-4556	535	3	]	]	X
ejpam-4556	535	4	m.ananya	m.ananya	PROPN
ejpam-4556	535	5	mandal	mandal	PROPN
ejpam-4556	535	6	.	.	PUNCT
ejpam-4556	536	1	histoire	histoire	PROPN
ejpam-4556	536	2	de	de	PROPN
ejpam-4556	536	3	la	la	PROPN
ejpam-4556	536	4	tuberculose	tuberculose	PROPN
ejpam-4556	536	5	.	.	PUNCT
ejpam-4556	537	1	news	news	NOUN
ejpam-4556	537	2	msdical	msdical	ADJ
ejpam-4556	537	3	life	life	NOUN
ejpam-4556	537	4	sciences	science	NOUN
ejpam-4556	537	5	.	.	PUNCT
ejpam-4556	538	1	[	[	X
ejpam-4556	538	2	17	17	NUM
ejpam-4556	538	3	]	]	PUNCT
ejpam-4556	538	4	abayomi	abayomi	NOUN
ejpam-4556	538	5	samuel	samuel	PROPN
ejpam-4556	538	6	oke	oke	PROPN
ejpam-4556	538	7	,	,	PUNCT
ejpam-4556	538	8	oluwafemi	oluwafemi	PROPN
ejpam-4556	538	9	isaac	isaac	PROPN
ejpam-4556	538	10	bada	bada	PROPN
ejpam-4556	538	11	,	,	PUNCT
ejpam-4556	538	12	ganiyu	ganiyu	NOUN
ejpam-4556	538	13	rasaq	rasaq	NOUN
ejpam-4556	538	14	,	,	PUNCT
ejpam-4556	538	15	and	and	CCONJ
ejpam-4556	538	16	victoria	victoria	PROPN
ejpam-4556	538	17	adodo	adodo	PROPN
ejpam-4556	538	18	.	.	PUNCT
ejpam-4556	539	1	mathematical	mathematical	ADJ
ejpam-4556	539	2	analysis	analysis	NOUN
ejpam-4556	539	3	of	of	ADP
ejpam-4556	539	4	the	the	DET
ejpam-4556	539	5	dynamics	dynamic	NOUN
ejpam-4556	539	6	of	of	ADP
ejpam-4556	539	7	covid-19	covid-19	PROPN
ejpam-4556	539	8	in	in	ADP
ejpam-4556	539	9	africa	africa	PROPN
ejpam-4556	539	10	under	under	ADP
ejpam-4556	539	11	the	the	DET
ejpam-4556	539	12	influence	influence	NOUN
ejpam-4556	539	13	of	of	ADP
ejpam-4556	539	14	asymptomatic	asymptomatic	ADJ
ejpam-4556	539	15	cases	case	NOUN
ejpam-4556	539	16	and	and	CCONJ
ejpam-4556	539	17	re	re	NOUN
ejpam-4556	539	18	-	-	NOUN
ejpam-4556	539	19	infection	infection	NOUN
ejpam-4556	539	20	.	.	PUNCT
ejpam-4556	540	1	math	math	NOUN
ejpam-4556	540	2	meth	meth	PROPN
ejpam-4556	540	3	appl	appl	PROPN
ejpam-4556	540	4	sci	sci	PROPN
ejpam-4556	540	5	,	,	PUNCT
ejpam-4556	540	6	45:137–149	45:137–149	NUM
ejpam-4556	540	7	,	,	PUNCT
ejpam-4556	540	8	2022	2022	NUM
ejpam-4556	540	9	.	.	PUNCT
ejpam-4556	541	1	[	[	X
ejpam-4556	541	2	18	18	NUM
ejpam-4556	541	3	]	]	X
ejpam-4556	541	4	i.a	i.a	PROPN
ejpam-4556	541	5	olapade	olapade	NOUN
ejpam-4556	541	6	,	,	PUNCT
ejpam-4556	541	7	s.o	s.o	PROPN
ejpam-4556	541	8	ajao	ajao	NOUN
ejpam-4556	541	9	,	,	PUNCT
ejpam-4556	541	10	and	and	CCONJ
ejpam-4556	541	11	al	al	PROPN
ejpam-4556	541	12	.	.	PROPN
ejpam-4556	541	13	mathematical	mathematical	ADJ
ejpam-4556	541	14	transmission	transmission	NOUN
ejpam-4556	541	15	of	of	ADP
ejpam-4556	541	16	tuberculose	tuberculose	NOUN
ejpam-4556	541	17	(	(	PUNCT
ejpam-4556	541	18	tb	tb	NOUN
ejpam-4556	541	19	)	)	PUNCT
ejpam-4556	541	20	with	with	ADP
ejpam-4556	541	21	detection	detection	NOUN
ejpam-4556	541	22	of	of	ADP
ejpam-4556	541	23	infected	infected	ADJ
ejpam-4556	541	24	undetected	undetected	ADJ
ejpam-4556	541	25	.	.	PUNCT
ejpam-4556	542	1	asian	asian	ADJ
ejpam-4556	542	2	journal	journal	PROPN
ejpam-4556	542	3	of	of	ADP
ejpam-4556	542	4	research	research	NOUN
ejpam-4556	542	5	in	in	ADP
ejpam-4556	542	6	medecine	medecine	ADJ
ejpam-4556	542	7	and	and	CCONJ
ejpam-4556	542	8	medical	medical	ADJ
ejpam-4556	542	9	science	science	NOUN
ejpam-4556	542	10	,	,	PUNCT
ejpam-4556	542	11	4(1):100–119	4(1):100–119	NUM
ejpam-4556	542	12	,	,	PUNCT
ejpam-4556	542	13	2022	2022	NUM
ejpam-4556	542	14	.	.	PUNCT
ejpam-4556	543	1	[	[	X
ejpam-4556	543	2	19	19	NUM
ejpam-4556	543	3	]	]	X
ejpam-4556	543	4	wahid	wahid	PROPN
ejpam-4556	543	5	b.k.a.and	b.k.a.and	X
ejpam-4556	543	6	bisso	bisso	PROPN
ejpam-4556	543	7	s.	s.	PROPN
ejpam-4556	543	8	mathematical	mathematical	PROPN
ejpam-4556	543	9	analysis	analysis	NOUN
ejpam-4556	543	10	and	and	CCONJ
ejpam-4556	543	11	simulation	simulation	NOUN
ejpam-4556	543	12	of	of	ADP
ejpam-4556	543	13	an	an	DET
ejpam-4556	543	14	age	age	NOUN
ejpam-4556	543	15	-	-	PUNCT
ejpam-4556	543	16	structure	structure	NOUN
ejpam-4556	543	17	of	of	ADP
ejpam-4556	543	18	model	model	NOUN
ejpam-4556	543	19	two	two	NUM
ejpam-4556	543	20	-	-	PUNCT
ejpam-4556	543	21	patch	patch	NOUN
ejpam-4556	543	22	for	for	ADP
ejpam-4556	543	23	tuberculosis	tuberculosis	NOUN
ejpam-4556	543	24	(	(	PUNCT
ejpam-4556	543	25	tb	tb	NOUN
ejpam-4556	543	26	)	)	PUNCT
ejpam-4556	543	27	.	.	PUNCT
ejpam-4556	544	1	applied	apply	VERB
ejpam-4556	544	2	mathematics	mathematic	NOUN
ejpam-4556	544	3	,	,	PUNCT
ejpam-4556	544	4	7:1882–1902	7:1882–1902	NUM
ejpam-4556	544	5	,	,	PUNCT
ejpam-4556	544	6	2016	2016	NUM
ejpam-4556	544	7	.	.	PUNCT
ejpam-4556	545	1	[	[	X
ejpam-4556	545	2	20	20	NUM
ejpam-4556	545	3	]	]	PUNCT
ejpam-4556	545	4	intan	intan	PROPN
ejpam-4556	545	5	syahrini	syahrini	PROPN
ejpam-4556	545	6	,	,	PUNCT
ejpam-4556	545	7	sriwahyuni	sriwahyuni	PROPN
ejpam-4556	545	8	,	,	PUNCT
ejpam-4556	545	9	vera	vera	NOUN
ejpam-4556	545	10	halfini	halfini	PROPN
ejpam-4556	545	11	,	,	PUNCT
ejpam-4556	545	12	syarifah	syarifah	PROPN
ejpam-4556	545	13	meurahyuni	meurahyuni	PROPN
ejpam-4556	545	14	,	,	PUNCT
ejpam-4556	545	15	taufiq	taufiq	PROPN
ejpam-4556	545	16	iskandar	iskandar	PROPN
ejpam-4556	545	17	,	,	PUNCT
ejpam-4556	545	18	rasudin	rasudin	VERB
ejpam-4556	545	19	,	,	PUNCT
ejpam-4556	545	20	and	and	CCONJ
ejpam-4556	545	21	marwan	marwan	PROPN
ejpam-4556	545	22	ramli	ramli	PROPN
ejpam-4556	545	23	.	.	PUNCT
ejpam-4556	546	1	the	the	DET
ejpam-4556	546	2	epidemic	epidemic	NOUN
ejpam-4556	546	3	of	of	ADP
ejpam-4556	546	4	tuberculosis	tuberculosis	NOUN
ejpam-4556	546	5	on	on	ADP
ejpam-4556	546	6	vaccinated	vaccinated	ADJ
ejpam-4556	546	7	population	population	NOUN
ejpam-4556	546	8	.	.	PUNCT
ejpam-4556	547	1	iop	iop	PROPN
ejpam-4556	547	2	conf.sries	conf.sries	PROPN
ejpam-4556	547	3	:	:	PUNCT
ejpam-4556	547	4	journal	journal	PROPN
ejpam-4556	547	5	of	of	ADP
ejpam-4556	547	6	physics	physics	PROPN
ejpam-4556	547	7	,	,	PUNCT
ejpam-4556	547	8	page	page	NOUN
ejpam-4556	547	9	890	890	NUM
ejpam-4556	547	10	,	,	PUNCT
ejpam-4556	547	11	2017	2017	NUM
ejpam-4556	547	12	.	.	PUNCT
ejpam-4556	548	1	[	[	X
ejpam-4556	548	2	21	21	NUM
ejpam-4556	548	3	]	]	X
ejpam-4556	548	4	hans	hans	PROPN
ejpam-4556	548	5	waaler	waaler	PROPN
ejpam-4556	548	6	cand.oecon	cand.oecon	PROPN
ejpam-4556	548	7	,	,	PUNCT
ejpam-4556	548	8	m.d	m.d	PROPN
ejpam-4556	548	9	anton	anton	PROPN
ejpam-4556	548	10	gesser	gesser	PROPN
ejpam-4556	548	11	,	,	PUNCT
ejpam-4556	548	12	stig	stig	PROPN
ejpam-4556	548	13	andersencan	andersencan	PROPN
ejpam-4556	548	14	,	,	PUNCT
ejpam-4556	548	15	and	and	CCONJ
ejpam-4556	548	16	polit	polit	NOUN
ejpam-4556	548	17	.	.	PUNCT
ejpam-4556	549	1	the	the	DET
ejpam-4556	549	2	use	use	NOUN
ejpam-4556	549	3	of	of	ADP
ejpam-4556	549	4	mathematical	mathematical	ADJ
ejpam-4556	549	5	models	model	NOUN
ejpam-4556	549	6	of	of	ADP
ejpam-4556	549	7	the	the	DET
ejpam-4556	549	8	epidemiology	epidemiology	NOUN
ejpam-4556	549	9	of	of	ADP
ejpam-4556	549	10	tuberculosis	tuberculosis	NOUN
ejpam-4556	549	11	.	.	PUNCT
ejpam-4556	550	1	a.j.p.h	a.j.p.h	NOUN
ejpam-4556	550	2	,	,	PUNCT
ejpam-4556	550	3	52(6):1002	52(6):1002	NUM
ejpam-4556	550	4	–	–	PUNCT
ejpam-4556	550	5	1013	1013	NUM
ejpam-4556	550	6	,	,	PUNCT
ejpam-4556	550	7	1962	1962	NUM
ejpam-4556	550	8	.	.	PUNCT
ejpam-4556	551	1	[	[	X
ejpam-4556	551	2	22	22	NUM
ejpam-4556	551	3	]	]	X
ejpam-4556	551	4	frost	frost	NOUN
ejpam-4556	551	5	w.h	w.h	PROPN
ejpam-4556	551	6	.	.	PROPN
ejpam-4556	552	1	how	how	SCONJ
ejpam-4556	552	2	much	much	ADJ
ejpam-4556	552	3	control	control	NOUN
ejpam-4556	552	4	of	of	ADP
ejpam-4556	552	5	tuberculosis	tuberculosis	NOUN
ejpam-4556	552	6	?	?	PUNCT
ejpam-4556	552	7	.	.	PUNCT
ejpam-4556	553	1	a.j.p.h	a.j.p.h	PROPN
ejpam-4556	553	2	.	.	PROPN
ejpam-4556	553	3	,	,	PUNCT
ejpam-4556	553	4	27:759	27:759	NUM
ejpam-4556	553	5	,	,	PUNCT
ejpam-4556	553	6	1937	1937	NUM
ejpam-4556	553	7	.	.	PUNCT
ejpam-4556	554	1	[	[	X
ejpam-4556	554	2	23	23	NUM
ejpam-4556	554	3	]	]	X
ejpam-4556	554	4	rui	rui	PROPN
ejpam-4556	554	5	xu	xu	PROPN
ejpam-4556	554	6	,	,	PUNCT
ejpam-4556	554	7	xiaohong	xiaohong	PROPN
ejpam-4556	554	8	tian	tian	PROPN
ejpam-4556	554	9	,	,	PUNCT
ejpam-4556	554	10	and	and	CCONJ
ejpam-4556	554	11	fengqin	fengqin	PROPN
ejpam-4556	554	12	zang	zang	PROPN
ejpam-4556	554	13	.	.	PUNCT
ejpam-4556	555	1	global	global	ADJ
ejpam-4556	555	2	dynamics	dynamic	NOUN
ejpam-4556	555	3	of	of	ADP
ejpam-4556	555	4	a	a	DET
ejpam-4556	555	5	tuberculosis	tuberculosis	NOUN
ejpam-4556	555	6	transmission	transmission	NOUN
ejpam-4556	555	7	model	model	NOUN
ejpam-4556	555	8	with	with	ADP
ejpam-4556	555	9	age	age	NOUN
ejpam-4556	555	10	of	of	ADP
ejpam-4556	555	11	infection	infection	NOUN
ejpam-4556	555	12	and	and	CCONJ
ejpam-4556	555	13	incomplete	incomplete	ADJ
ejpam-4556	555	14	treatment	treatment	NOUN
ejpam-4556	555	15	.	.	PUNCT
ejpam-4556	556	1	xu	xu	INTJ
ejpam-4556	556	2	and	and	CCONJ
ejpam-4556	556	3	al.advances	al.advance	NOUN
ejpam-4556	556	4	in	in	ADP
ejpam-4556	556	5	difference	difference	NOUN
ejpam-4556	556	6	equations	equation	NOUN
ejpam-4556	556	7	,	,	PUNCT
ejpam-4556	556	8	page	page	NOUN
ejpam-4556	556	9	242	242	NUM
ejpam-4556	556	10	,	,	PUNCT
ejpam-4556	556	11	(	(	PUNCT
ejpam-4556	556	12	2017	2017	NUM
ejpam-4556	556	13	)	)	PUNCT
ejpam-4556	556	14	.	.	PUNCT
ejpam-4556	557	1	[	[	X
ejpam-4556	557	2	24	24	NUM
ejpam-4556	557	3	]	]	X
ejpam-4556	557	4	yang	yang	PROPN
ejpam-4556	557	5	y	y	PROPN
ejpam-4556	557	6	,	,	PUNCT
ejpam-4556	557	7	li	li	PROPN
ejpam-4556	557	8	j	j	PROPN
ejpam-4556	557	9	,	,	PUNCT
ejpam-4556	557	10	ma	ma	PROPN
ejpam-4556	557	11	z	z	PROPN
ejpam-4556	557	12	,	,	PUNCT
ejpam-4556	557	13	and	and	CCONJ
ejpam-4556	557	14	liu	liu	PROPN
ejpam-4556	557	15	l.	l.	PROPN
ejpam-4556	557	16	global	global	PROPN
ejpam-4556	557	17	stability	stability	NOUN
ejpam-4556	557	18	of	of	ADP
ejpam-4556	557	19	two	two	NUM
ejpam-4556	557	20	models	model	NOUN
ejpam-4556	557	21	with	with	ADP
ejpam-4556	557	22	incomplete	incomplete	ADJ
ejpam-4556	557	23	treatment	treatment	NOUN
ejpam-4556	557	24	for	for	ADP
ejpam-4556	557	25	tuberculosis	tuberculosis	NOUN
ejpam-4556	557	26	.	.	PUNCT
ejpam-4556	558	1	chaos	chaos	NOUN
ejpam-4556	558	2	solitons	soliton	NOUN
ejpam-4556	558	3	fractals	fractal	NOUN
ejpam-4556	558	4	,	,	PUNCT
ejpam-4556	558	5	43:79–85	43:79–85	NUM
ejpam-4556	558	6	,	,	PUNCT
ejpam-4556	558	7	2010	2010	NUM
ejpam-4556	558	8	.	.	PUNCT