id	sid	tid	token	lemma	pos
ejpam-6082	1	1	european	european	PROPN
ejpam-6082	1	2	journal	journal	PROPN
ejpam-6082	1	3	of	of	ADP
ejpam-6082	1	4	pure	pure	ADJ
ejpam-6082	1	5	and	and	CCONJ
ejpam-6082	1	6	applied	applied	ADJ
ejpam-6082	1	7	mathematics	mathematic	NOUN
ejpam-6082	1	8	2025	2025	NUM
ejpam-6082	1	9	,	,	PUNCT
ejpam-6082	1	10	vol	vol	NOUN
ejpam-6082	1	11	.	.	PROPN
ejpam-6082	1	12	18	18	NUM
ejpam-6082	1	13	,	,	PUNCT
ejpam-6082	1	14	issue	issue	NOUN
ejpam-6082	1	15	2	2	NUM
ejpam-6082	1	16	,	,	PUNCT
ejpam-6082	1	17	article	article	NOUN
ejpam-6082	1	18	number	number	NOUN
ejpam-6082	1	19	6082	6082	NUM
ejpam-6082	1	20	issn	issn	PROPN
ejpam-6082	1	21	1307	1307	NUM
ejpam-6082	1	22	-	-	SYM
ejpam-6082	1	23	5543	5543	NUM
ejpam-6082	1	24	–	–	PUNCT
ejpam-6082	1	25	ejpam.com	ejpam.com	X
ejpam-6082	1	26	published	publish	VERB
ejpam-6082	1	27	by	by	ADP
ejpam-6082	1	28	new	new	PROPN
ejpam-6082	1	29	york	york	PROPN
ejpam-6082	1	30	business	business	PROPN
ejpam-6082	1	31	global	global	ADJ
ejpam-6082	1	32	advanced	advance	VERB
ejpam-6082	1	33	fractional	fractional	ADJ
ejpam-6082	1	34	reaction	reaction	NOUN
ejpam-6082	1	35	-	-	PUNCT
ejpam-6082	1	36	diffusion	diffusion	NOUN
ejpam-6082	1	37	modeling	modeling	NOUN
ejpam-6082	1	38	for	for	ADP
ejpam-6082	1	39	spatio	spatio	NOUN
ejpam-6082	1	40	-	-	PUNCT
ejpam-6082	1	41	temporal	temporal	ADJ
ejpam-6082	1	42	dynamics	dynamic	NOUN
ejpam-6082	1	43	of	of	ADP
ejpam-6082	1	44	poliovirus	poliovirus	NOUN
ejpam-6082	1	45	transmission	transmission	NOUN
ejpam-6082	1	46	with	with	ADP
ejpam-6082	1	47	disability	disability	NOUN
ejpam-6082	1	48	outcomes	outcome	NOUN
ejpam-6082	1	49	and	and	CCONJ
ejpam-6082	1	50	vaccination	vaccination	NOUN
ejpam-6082	1	51	impacts	impact	NOUN
ejpam-6082	1	52	kamel	kamel	PROPN
ejpam-6082	1	53	guedri1	guedri1	PROPN
ejpam-6082	1	54	,	,	PUNCT
ejpam-6082	1	55	rahat	rahat	PROPN
ejpam-6082	1	56	zarin2,∗	zarin2,∗	PROPN
ejpam-6082	1	57	,	,	PUNCT
ejpam-6082	1	58	basim	basim	PROPN
ejpam-6082	1	59	m.	m.	PROPN
ejpam-6082	1	60	makhdoum1,3	makhdoum1,3	PROPN
ejpam-6082	1	61	,	,	PUNCT
ejpam-6082	1	62	hatoon	hatoon	ADJ
ejpam-6082	1	63	a.	a.	NOUN
ejpam-6082	1	64	niyazi4	niyazi4	PROPN
ejpam-6082	1	65	1	1	NUM
ejpam-6082	1	66	mechanical	mechanical	ADJ
ejpam-6082	1	67	engineering	engineering	NOUN
ejpam-6082	1	68	department	department	NOUN
ejpam-6082	1	69	,	,	PUNCT
ejpam-6082	1	70	college	college	NOUN
ejpam-6082	1	71	of	of	ADP
ejpam-6082	1	72	engineering	engineering	NOUN
ejpam-6082	1	73	and	and	CCONJ
ejpam-6082	1	74	architecture	architecture	NOUN
ejpam-6082	1	75	,	,	PUNCT
ejpam-6082	1	76	umm	umm	INTJ
ejpam-6082	1	77	al	al	PROPN
ejpam-6082	1	78	-	-	PUNCT
ejpam-6082	1	79	qura	qura	PROPN
ejpam-6082	1	80	university	university	PROPN
ejpam-6082	1	81	,	,	PUNCT
ejpam-6082	1	82	p.o	p.o	PROPN
ejpam-6082	1	83	.	.	PROPN
ejpam-6082	1	84	box	box	PROPN
ejpam-6082	1	85	5555	5555	NUM
ejpam-6082	1	86	,	,	PUNCT
ejpam-6082	1	87	makkah	makkah	PROPN
ejpam-6082	1	88	21955	21955	NUM
ejpam-6082	1	89	,	,	PUNCT
ejpam-6082	1	90	saudi	saudi	PROPN
ejpam-6082	1	91	arabia	arabia	PROPN
ejpam-6082	1	92	2	2	NUM
ejpam-6082	1	93	department	department	NOUN
ejpam-6082	1	94	of	of	ADP
ejpam-6082	1	95	mathematics	mathematic	NOUN
ejpam-6082	1	96	,	,	PUNCT
ejpam-6082	1	97	faculty	faculty	NOUN
ejpam-6082	1	98	of	of	ADP
ejpam-6082	1	99	science	science	NOUN
ejpam-6082	1	100	,	,	PUNCT
ejpam-6082	1	101	king	king	PROPN
ejpam-6082	1	102	mongkut	mongkut	PROPN
ejpam-6082	1	103	’s	’s	PROPN
ejpam-6082	1	104	university	university	PROPN
ejpam-6082	1	105	of	of	ADP
ejpam-6082	1	106	technology	technology	NOUN
ejpam-6082	1	107	,	,	PUNCT
ejpam-6082	1	108	thonburi	thonburi	NOUN
ejpam-6082	1	109	(	(	PUNCT
ejpam-6082	1	110	kmutt	kmutt	PROPN
ejpam-6082	1	111	)	)	PUNCT
ejpam-6082	1	112	,	,	PUNCT
ejpam-6082	1	113	bangkok	bangkok	PROPN
ejpam-6082	1	114	10140	10140	NUM
ejpam-6082	1	115	,	,	PUNCT
ejpam-6082	1	116	thailand	thailand	PROPN
ejpam-6082	1	117	3	3	NUM
ejpam-6082	1	118	king	king	PROPN
ejpam-6082	1	119	salman	salman	PROPN
ejpam-6082	1	120	center	center	PROPN
ejpam-6082	1	121	for	for	ADP
ejpam-6082	1	122	disability	disability	NOUN
ejpam-6082	1	123	research	research	NOUN
ejpam-6082	1	124	,	,	PUNCT
ejpam-6082	1	125	riyadh	riyadh	PROPN
ejpam-6082	1	126	11614	11614	NUM
ejpam-6082	1	127	,	,	PUNCT
ejpam-6082	1	128	saudi	saudi	PROPN
ejpam-6082	1	129	arabia	arabia	PROPN
ejpam-6082	1	130	4	4	NUM
ejpam-6082	1	131	department	department	NOUN
ejpam-6082	1	132	of	of	ADP
ejpam-6082	1	133	clinical	clinical	ADJ
ejpam-6082	1	134	microbiology	microbiology	NOUN
ejpam-6082	1	135	and	and	CCONJ
ejpam-6082	1	136	immunology	immunology	NOUN
ejpam-6082	1	137	,	,	PUNCT
ejpam-6082	1	138	faculty	faculty	NOUN
ejpam-6082	1	139	of	of	ADP
ejpam-6082	1	140	medicine	medicine	NOUN
ejpam-6082	1	141	,	,	PUNCT
ejpam-6082	1	142	king	king	PROPN
ejpam-6082	1	143	abdulaziz	abdulaziz	PROPN
ejpam-6082	1	144	university	university	PROPN
ejpam-6082	1	145	,	,	PUNCT
ejpam-6082	1	146	jeddah	jeddah	PROPN
ejpam-6082	1	147	21589	21589	NUM
ejpam-6082	1	148	,	,	PUNCT
ejpam-6082	1	149	saudi	saudi	PROPN
ejpam-6082	1	150	arabia	arabia	PROPN
ejpam-6082	1	151	abstract	abstract	NOUN
ejpam-6082	1	152	.	.	PUNCT
ejpam-6082	2	1	this	this	DET
ejpam-6082	2	2	work	work	NOUN
ejpam-6082	2	3	presents	present	VERB
ejpam-6082	2	4	a	a	DET
ejpam-6082	2	5	novel	novel	ADJ
ejpam-6082	2	6	fractional	fractional	ADJ
ejpam-6082	2	7	reaction	reaction	NOUN
ejpam-6082	2	8	-	-	PUNCT
ejpam-6082	2	9	diffusion	diffusion	NOUN
ejpam-6082	2	10	model	model	NOUN
ejpam-6082	2	11	to	to	PART
ejpam-6082	2	12	analyze	analyze	VERB
ejpam-6082	2	13	the	the	DET
ejpam-6082	2	14	spatiotemporal	spatiotemporal	ADJ
ejpam-6082	2	15	dynamics	dynamic	NOUN
ejpam-6082	2	16	of	of	ADP
ejpam-6082	2	17	poliovirus	poliovirus	NOUN
ejpam-6082	2	18	transmission	transmission	NOUN
ejpam-6082	2	19	.	.	PUNCT
ejpam-6082	3	1	polio	polio	NOUN
ejpam-6082	3	2	,	,	PUNCT
ejpam-6082	3	3	a	a	DET
ejpam-6082	3	4	highly	highly	ADV
ejpam-6082	3	5	contagious	contagious	ADJ
ejpam-6082	3	6	viral	viral	ADJ
ejpam-6082	3	7	infection	infection	NOUN
ejpam-6082	3	8	that	that	PRON
ejpam-6082	3	9	primarily	primarily	ADV
ejpam-6082	3	10	affects	affect	VERB
ejpam-6082	3	11	children	child	NOUN
ejpam-6082	3	12	under	under	ADP
ejpam-6082	3	13	five	five	NUM
ejpam-6082	3	14	and	and	CCONJ
ejpam-6082	3	15	can	can	AUX
ejpam-6082	3	16	lead	lead	VERB
ejpam-6082	3	17	to	to	ADP
ejpam-6082	3	18	permanent	permanent	ADJ
ejpam-6082	3	19	disability	disability	NOUN
ejpam-6082	3	20	,	,	PUNCT
ejpam-6082	3	21	spreads	spread	VERB
ejpam-6082	3	22	through	through	ADP
ejpam-6082	3	23	fecal	fecal	ADJ
ejpam-6082	3	24	-	-	PUNCT
ejpam-6082	3	25	oral	oral	ADJ
ejpam-6082	3	26	and	and	CCONJ
ejpam-6082	3	27	airborne	airborne	ADJ
ejpam-6082	3	28	transmission	transmission	NOUN
ejpam-6082	3	29	,	,	PUNCT
ejpam-6082	3	30	often	often	ADV
ejpam-6082	3	31	exacerbated	exacerbate	VERB
ejpam-6082	3	32	by	by	ADP
ejpam-6082	3	33	poor	poor	ADJ
ejpam-6082	3	34	sanitation	sanitation	NOUN
ejpam-6082	3	35	and	and	CCONJ
ejpam-6082	3	36	environmental	environmental	ADJ
ejpam-6082	3	37	conditions	condition	NOUN
ejpam-6082	3	38	.	.	PUNCT
ejpam-6082	4	1	traditional	traditional	ADJ
ejpam-6082	4	2	polio	polio	NOUN
ejpam-6082	4	3	models	model	NOUN
ejpam-6082	4	4	,	,	PUNCT
ejpam-6082	4	5	predominantly	predominantly	ADV
ejpam-6082	4	6	based	base	VERB
ejpam-6082	4	7	on	on	ADP
ejpam-6082	4	8	ordinary	ordinary	ADJ
ejpam-6082	4	9	differential	differential	ADJ
ejpam-6082	4	10	equations	equation	NOUN
ejpam-6082	4	11	(	(	PUNCT
ejpam-6082	4	12	odes	ode	NOUN
ejpam-6082	4	13	)	)	PUNCT
ejpam-6082	4	14	,	,	PUNCT
ejpam-6082	4	15	have	have	AUX
ejpam-6082	4	16	assumed	assume	VERB
ejpam-6082	4	17	spatial	spatial	ADJ
ejpam-6082	4	18	uniformity	uniformity	NOUN
ejpam-6082	4	19	an	an	DET
ejpam-6082	4	20	oversimplification	oversimplification	NOUN
ejpam-6082	4	21	of	of	ADP
ejpam-6082	4	22	real	real	ADJ
ejpam-6082	4	23	-	-	PUNCT
ejpam-6082	4	24	world	world	NOUN
ejpam-6082	4	25	scenarios	scenario	NOUN
ejpam-6082	4	26	influenced	influence	VERB
ejpam-6082	4	27	by	by	ADP
ejpam-6082	4	28	population	population	NOUN
ejpam-6082	4	29	density	density	NOUN
ejpam-6082	4	30	,	,	PUNCT
ejpam-6082	4	31	environmental	environmental	ADJ
ejpam-6082	4	32	heterogeneity	heterogeneity	NOUN
ejpam-6082	4	33	,	,	PUNCT
ejpam-6082	4	34	and	and	CCONJ
ejpam-6082	4	35	mobility	mobility	NOUN
ejpam-6082	4	36	.	.	PUNCT
ejpam-6082	5	1	our	our	PRON
ejpam-6082	5	2	study	study	NOUN
ejpam-6082	5	3	extends	extend	VERB
ejpam-6082	5	4	classical	classical	ADJ
ejpam-6082	5	5	models	model	NOUN
ejpam-6082	5	6	by	by	ADP
ejpam-6082	5	7	incorporating	incorporate	VERB
ejpam-6082	5	8	spatial	spatial	ADJ
ejpam-6082	5	9	heterogeneity	heterogeneity	NOUN
ejpam-6082	5	10	and	and	CCONJ
ejpam-6082	5	11	memory	memory	NOUN
ejpam-6082	5	12	effects	effect	NOUN
ejpam-6082	5	13	using	use	VERB
ejpam-6082	5	14	caputo	caputo	PROPN
ejpam-6082	5	15	fractional	fractional	ADJ
ejpam-6082	5	16	derivatives	derivative	NOUN
ejpam-6082	5	17	and	and	CCONJ
ejpam-6082	5	18	reaction	reaction	NOUN
ejpam-6082	5	19	-	-	PUNCT
ejpam-6082	5	20	diffusion	diffusion	NOUN
ejpam-6082	5	21	dynamics	dynamic	NOUN
ejpam-6082	5	22	.	.	PUNCT
ejpam-6082	6	1	the	the	DET
ejpam-6082	6	2	model	model	NOUN
ejpam-6082	6	3	divides	divide	VERB
ejpam-6082	6	4	the	the	DET
ejpam-6082	6	5	population	population	NOUN
ejpam-6082	6	6	into	into	ADP
ejpam-6082	6	7	seven	seven	NUM
ejpam-6082	6	8	epidemiological	epidemiological	ADJ
ejpam-6082	6	9	compartments	compartment	NOUN
ejpam-6082	6	10	:	:	PUNCT
ejpam-6082	6	11	susceptible	susceptible	ADJ
ejpam-6082	6	12	(	(	PUNCT
ejpam-6082	6	13	s	s	NOUN
ejpam-6082	6	14	)	)	PUNCT
ejpam-6082	6	15	,	,	PUNCT
ejpam-6082	6	16	vaccinated	vaccinate	VERB
ejpam-6082	6	17	(	(	PUNCT
ejpam-6082	6	18	v	v	NOUN
ejpam-6082	6	19	)	)	PUNCT
ejpam-6082	6	20	,	,	PUNCT
ejpam-6082	6	21	exposed	expose	VERB
ejpam-6082	6	22	(	(	PUNCT
ejpam-6082	6	23	e	e	NOUN
ejpam-6082	6	24	)	)	PUNCT
ejpam-6082	6	25	,	,	PUNCT
ejpam-6082	6	26	non	non	ADJ
ejpam-6082	6	27	-	-	ADJ
ejpam-6082	6	28	paralytic	paralytic	ADJ
ejpam-6082	6	29	infected	infect	VERB
ejpam-6082	6	30	(	(	PUNCT
ejpam-6082	6	31	np	np	INTJ
ejpam-6082	6	32	)	)	PUNCT
ejpam-6082	6	33	,	,	PUNCT
ejpam-6082	6	34	paralytic	paralytic	ADJ
ejpam-6082	6	35	infected	infected	ADJ
ejpam-6082	6	36	(	(	PUNCT
ejpam-6082	6	37	p	p	NOUN
ejpam-6082	6	38	)	)	PUNCT
ejpam-6082	6	39	,	,	PUNCT
ejpam-6082	6	40	recovered	recover	VERB
ejpam-6082	6	41	(	(	PUNCT
ejpam-6082	6	42	r	r	NOUN
ejpam-6082	6	43	)	)	PUNCT
ejpam-6082	6	44	,	,	PUNCT
ejpam-6082	6	45	and	and	CCONJ
ejpam-6082	6	46	post	post	ADJ
ejpam-6082	6	47	-	-	ADJ
ejpam-6082	6	48	paralytic	paralytic	ADJ
ejpam-6082	6	49	(	(	PUNCT
ejpam-6082	6	50	a	a	NOUN
ejpam-6082	6	51	)	)	PUNCT
ejpam-6082	6	52	,	,	PUNCT
ejpam-6082	6	53	with	with	ADP
ejpam-6082	6	54	corresponding	correspond	VERB
ejpam-6082	6	55	diffusion	diffusion	NOUN
ejpam-6082	6	56	terms	term	NOUN
ejpam-6082	6	57	to	to	PART
ejpam-6082	6	58	capture	capture	VERB
ejpam-6082	6	59	spatial	spatial	ADJ
ejpam-6082	6	60	mobility	mobility	NOUN
ejpam-6082	6	61	.	.	PUNCT
ejpam-6082	7	1	the	the	DET
ejpam-6082	7	2	inclusion	inclusion	NOUN
ejpam-6082	7	3	of	of	ADP
ejpam-6082	7	4	fractional	fractional	ADJ
ejpam-6082	7	5	derivatives	derivative	NOUN
ejpam-6082	7	6	accounts	account	NOUN
ejpam-6082	7	7	for	for	ADP
ejpam-6082	7	8	the	the	DET
ejpam-6082	7	9	memory	memory	NOUN
ejpam-6082	7	10	-	-	PUNCT
ejpam-6082	7	11	dependent	dependent	ADJ
ejpam-6082	7	12	nature	nature	NOUN
ejpam-6082	7	13	of	of	ADP
ejpam-6082	7	14	disease	disease	NOUN
ejpam-6082	7	15	progression	progression	NOUN
ejpam-6082	7	16	,	,	PUNCT
ejpam-6082	7	17	offering	offer	VERB
ejpam-6082	7	18	a	a	DET
ejpam-6082	7	19	more	more	ADV
ejpam-6082	7	20	realistic	realistic	ADJ
ejpam-6082	7	21	depiction	depiction	NOUN
ejpam-6082	7	22	of	of	ADP
ejpam-6082	7	23	poliovirus	poliovirus	NOUN
ejpam-6082	7	24	dynamics	dynamic	NOUN
ejpam-6082	7	25	.	.	PUNCT
ejpam-6082	8	1	key	key	ADJ
ejpam-6082	8	2	contributions	contribution	NOUN
ejpam-6082	8	3	include	include	VERB
ejpam-6082	8	4	proving	prove	VERB
ejpam-6082	8	5	the	the	DET
ejpam-6082	8	6	existence	existence	NOUN
ejpam-6082	8	7	and	and	CCONJ
ejpam-6082	8	8	uniqueness	uniqueness	NOUN
ejpam-6082	8	9	of	of	ADP
ejpam-6082	8	10	positively	positively	ADV
ejpam-6082	8	11	bounded	bound	VERB
ejpam-6082	8	12	solutions	solution	NOUN
ejpam-6082	8	13	,	,	PUNCT
ejpam-6082	8	14	identifying	identify	VERB
ejpam-6082	8	15	equilibrium	equilibrium	NOUN
ejpam-6082	8	16	points	point	NOUN
ejpam-6082	8	17	,	,	PUNCT
ejpam-6082	8	18	and	and	CCONJ
ejpam-6082	8	19	assessing	assess	VERB
ejpam-6082	8	20	their	their	PRON
ejpam-6082	8	21	local	local	ADJ
ejpam-6082	8	22	and	and	CCONJ
ejpam-6082	8	23	global	global	ADJ
ejpam-6082	8	24	stability	stability	NOUN
ejpam-6082	8	25	using	use	VERB
ejpam-6082	8	26	the	the	DET
ejpam-6082	8	27	basic	basic	ADJ
ejpam-6082	8	28	reproduction	reproduction	NOUN
ejpam-6082	8	29	number	number	NOUN
ejpam-6082	8	30	(	(	PUNCT
ejpam-6082	8	31	r0	r0	NOUN
ejpam-6082	8	32	)	)	PUNCT
ejpam-6082	8	33	and	and	CCONJ
ejpam-6082	8	34	lyapunov	lyapunov	ADJ
ejpam-6082	8	35	functions	function	NOUN
ejpam-6082	8	36	under	under	ADP
ejpam-6082	8	37	fractional	fractional	ADJ
ejpam-6082	8	38	dynamics	dynamic	NOUN
ejpam-6082	8	39	.	.	PUNCT
ejpam-6082	9	1	sensitivity	sensitivity	NOUN
ejpam-6082	9	2	analysis	analysis	NOUN
ejpam-6082	9	3	is	be	AUX
ejpam-6082	9	4	conducted	conduct	VERB
ejpam-6082	9	5	to	to	PART
ejpam-6082	9	6	find	find	VERB
ejpam-6082	9	7	the	the	DET
ejpam-6082	9	8	most	most	ADV
ejpam-6082	9	9	sensitive	sensitive	ADJ
ejpam-6082	9	10	parameters	parameter	NOUN
ejpam-6082	9	11	using	use	VERB
ejpam-6082	9	12	the	the	DET
ejpam-6082	9	13	direct	direct	ADJ
ejpam-6082	9	14	differentiation	differentiation	NOUN
ejpam-6082	9	15	method	method	NOUN
ejpam-6082	9	16	.	.	PUNCT
ejpam-6082	10	1	sensitivity	sensitivity	NOUN
ejpam-6082	10	2	analysis	analysis	NOUN
ejpam-6082	10	3	highlights	highlight	NOUN
ejpam-6082	10	4	critical	critical	ADJ
ejpam-6082	10	5	parameters	parameter	NOUN
ejpam-6082	10	6	influencing	influence	VERB
ejpam-6082	10	7	disease	disease	NOUN
ejpam-6082	10	8	propagation	propagation	NOUN
ejpam-6082	10	9	,	,	PUNCT
ejpam-6082	10	10	while	while	SCONJ
ejpam-6082	10	11	numerical	numerical	ADJ
ejpam-6082	10	12	simulations	simulation	NOUN
ejpam-6082	10	13	validate	validate	VERB
ejpam-6082	10	14	the	the	DET
ejpam-6082	10	15	theoretical	theoretical	ADJ
ejpam-6082	10	16	findings	finding	NOUN
ejpam-6082	10	17	.	.	PUNCT
ejpam-6082	11	1	graphical	graphical	ADJ
ejpam-6082	11	2	results	result	NOUN
ejpam-6082	11	3	demonstrate	demonstrate	VERB
ejpam-6082	11	4	the	the	DET
ejpam-6082	11	5	impact	impact	NOUN
ejpam-6082	11	6	of	of	ADP
ejpam-6082	11	7	fractional	fractional	ADJ
ejpam-6082	11	8	order	order	NOUN
ejpam-6082	11	9	(	(	PUNCT
ejpam-6082	11	10	α	α	NOUN
ejpam-6082	11	11	)	)	PUNCT
ejpam-6082	11	12	and	and	CCONJ
ejpam-6082	11	13	vaccination	vaccination	NOUN
ejpam-6082	11	14	on	on	ADP
ejpam-6082	11	15	disease	disease	NOUN
ejpam-6082	11	16	spread	spread	VERB
ejpam-6082	11	17	,	,	PUNCT
ejpam-6082	11	18	illustrating	illustrate	VERB
ejpam-6082	11	19	how	how	SCONJ
ejpam-6082	11	20	memory	memory	NOUN
ejpam-6082	11	21	effects	effect	NOUN
ejpam-6082	11	22	influence	influence	NOUN
ejpam-6082	11	23	convergence	convergence	NOUN
ejpam-6082	11	24	to	to	ADP
ejpam-6082	11	25	steady	steady	ADJ
ejpam-6082	11	26	states	state	NOUN
ejpam-6082	11	27	.	.	PUNCT
ejpam-6082	12	1	this	this	DET
ejpam-6082	12	2	fractional	fractional	ADJ
ejpam-6082	12	3	reaction	reaction	NOUN
ejpam-6082	12	4	-	-	PUNCT
ejpam-6082	12	5	diffusion	diffusion	NOUN
ejpam-6082	12	6	framework	framework	NOUN
ejpam-6082	12	7	provides	provide	VERB
ejpam-6082	12	8	valuable	valuable	ADJ
ejpam-6082	12	9	insights	insight	NOUN
ejpam-6082	12	10	into	into	ADP
ejpam-6082	12	11	poliovirus	poliovirus	NOUN
ejpam-6082	12	12	transmission	transmission	NOUN
ejpam-6082	12	13	,	,	PUNCT
ejpam-6082	12	14	offering	offer	VERB
ejpam-6082	12	15	a	a	DET
ejpam-6082	12	16	robust	robust	ADJ
ejpam-6082	12	17	tool	tool	NOUN
ejpam-6082	12	18	for	for	ADP
ejpam-6082	12	19	predicting	predict	VERB
ejpam-6082	12	20	outbreaks	outbreak	NOUN
ejpam-6082	12	21	and	and	CCONJ
ejpam-6082	12	22	guiding	guide	VERB
ejpam-6082	12	23	effective	effective	ADJ
ejpam-6082	12	24	intervention	intervention	NOUN
ejpam-6082	12	25	strategies	strategy	NOUN
ejpam-6082	12	26	in	in	ADP
ejpam-6082	12	27	diverse	diverse	ADJ
ejpam-6082	12	28	populations	population	NOUN
ejpam-6082	12	29	.	.	PUNCT
ejpam-6082	13	1	2020	2020	NUM
ejpam-6082	13	2	mathematics	mathematic	NOUN
ejpam-6082	13	3	subject	subject	NOUN
ejpam-6082	13	4	classifications	classification	NOUN
ejpam-6082	13	5	:	:	PUNCT
ejpam-6082	13	6	35r11	35r11	NUM
ejpam-6082	13	7	,	,	PUNCT
ejpam-6082	13	8	92d30	92d30	NUM
ejpam-6082	13	9	,	,	PUNCT
ejpam-6082	13	10	35k57	35k57	NUM
ejpam-6082	13	11	,	,	PUNCT
ejpam-6082	13	12	65m70	65m70	NUM
ejpam-6082	13	13	∗corresponding	∗corresponde	VERB
ejpam-6082	13	14	author	author	NOUN
ejpam-6082	13	15	.	.	PUNCT
ejpam-6082	14	1	doi	doi	NOUN
ejpam-6082	14	2	:	:	PUNCT
ejpam-6082	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6082	https://doi.org/10.29020/nybg.ejpam.v18i2.6082	PROPN
ejpam-6082	14	4	email	email	NOUN
ejpam-6082	14	5	address	address	NOUN
ejpam-6082	14	6	:	:	PUNCT
ejpam-6082	14	7	rahat.zari@mail.kmutt.ac.th	rahat.zari@mail.kmutt.ac.th	NOUN
ejpam-6082	14	8	(	(	PUNCT
ejpam-6082	14	9	r.	r.	PROPN
ejpam-6082	14	10	zarin	zarin	PROPN
ejpam-6082	14	11	)	)	PUNCT
ejpam-6082	14	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6082	15	1	1	1	NUM
ejpam-6082	15	2	copyright	copyright	NOUN
ejpam-6082	15	3	:	:	PUNCT
ejpam-6082	15	4	©	©	PROPN
ejpam-6082	15	5	2025	2025	NUM
ejpam-6082	15	6	the	the	DET
ejpam-6082	15	7	author(s	author(s	NOUN
ejpam-6082	15	8	)	)	PUNCT
ejpam-6082	15	9	.	.	PUNCT
ejpam-6082	16	1	(	(	PUNCT
ejpam-6082	16	2	cc	cc	NOUN
ejpam-6082	16	3	by	by	ADP
ejpam-6082	16	4	-	-	PUNCT
ejpam-6082	16	5	nc	nc	PROPN
ejpam-6082	16	6	4.0	4.0	NUM
ejpam-6082	16	7	)	)	PUNCT
ejpam-6082	16	8	k.	k.	PROPN
ejpam-6082	16	9	guedri	guedri	PROPN
ejpam-6082	17	1	et	et	PROPN
ejpam-6082	17	2	al	al	PROPN
ejpam-6082	17	3	.	.	PUNCT
ejpam-6082	17	4	/	/	SYM
ejpam-6082	17	5	eur	eur	PROPN
ejpam-6082	17	6	.	.	PUNCT
ejpam-6082	18	1	j.	j.	PROPN
ejpam-6082	18	2	pure	pure	PROPN
ejpam-6082	18	3	appl	appl	PROPN
ejpam-6082	18	4	.	.	PROPN
ejpam-6082	18	5	math	math	PROPN
ejpam-6082	18	6	,	,	PUNCT
ejpam-6082	18	7	18	18	NUM
ejpam-6082	18	8	(	(	PUNCT
ejpam-6082	18	9	2	2	NUM
ejpam-6082	18	10	)	)	PUNCT
ejpam-6082	18	11	(	(	PUNCT
ejpam-6082	18	12	2025	2025	NUM
ejpam-6082	18	13	)	)	PUNCT
ejpam-6082	18	14	,	,	PUNCT
ejpam-6082	18	15	6082	6082	NUM
ejpam-6082	18	16	2	2	NUM
ejpam-6082	18	17	of	of	ADP
ejpam-6082	18	18	39	39	NUM
ejpam-6082	18	19	key	key	ADJ
ejpam-6082	18	20	words	word	NOUN
ejpam-6082	18	21	and	and	CCONJ
ejpam-6082	18	22	phrases	phrase	NOUN
ejpam-6082	18	23	:	:	PUNCT
ejpam-6082	18	24	fractional	fractional	ADJ
ejpam-6082	18	25	reaction	reaction	NOUN
ejpam-6082	18	26	-	-	PUNCT
ejpam-6082	18	27	diffusion	diffusion	NOUN
ejpam-6082	18	28	,	,	PUNCT
ejpam-6082	18	29	polio	polio	NOUN
ejpam-6082	18	30	virus	virus	NOUN
ejpam-6082	18	31	,	,	PUNCT
ejpam-6082	18	32	sensitivity	sensitivity	NOUN
ejpam-6082	18	33	analysis	analysis	NOUN
ejpam-6082	18	34	,	,	PUNCT
ejpam-6082	18	35	disability	disability	NOUN
ejpam-6082	18	36	outcomes	outcome	NOUN
ejpam-6082	18	37	,	,	PUNCT
ejpam-6082	18	38	global	global	ADJ
ejpam-6082	18	39	stability	stability	NOUN
ejpam-6082	18	40	,	,	PUNCT
ejpam-6082	18	41	numerical	numerical	PROPN
ejpam-6082	18	42	simulation	simulation	PROPN
ejpam-6082	18	43	1	1	NUM
ejpam-6082	18	44	.	.	PUNCT
ejpam-6082	19	1	introduction	introduction	NOUN
ejpam-6082	19	2	poliomyelitis	poliomyelitis	PROPN
ejpam-6082	19	3	,	,	PUNCT
ejpam-6082	19	4	commonly	commonly	ADV
ejpam-6082	19	5	referred	refer	VERB
ejpam-6082	19	6	to	to	ADP
ejpam-6082	19	7	as	as	ADP
ejpam-6082	19	8	polio	polio	NOUN
ejpam-6082	19	9	,	,	PUNCT
ejpam-6082	19	10	is	be	AUX
ejpam-6082	19	11	a	a	DET
ejpam-6082	19	12	viral	viral	ADJ
ejpam-6082	19	13	infection	infection	NOUN
ejpam-6082	19	14	that	that	PRON
ejpam-6082	19	15	primarily	primarily	ADV
ejpam-6082	19	16	affects	affect	VERB
ejpam-6082	19	17	the	the	DET
ejpam-6082	19	18	nervous	nervous	ADJ
ejpam-6082	19	19	system	system	NOUN
ejpam-6082	19	20	.	.	PUNCT
ejpam-6082	20	1	children	child	NOUN
ejpam-6082	20	2	under	under	ADP
ejpam-6082	20	3	the	the	DET
ejpam-6082	20	4	age	age	NOUN
ejpam-6082	20	5	of	of	ADP
ejpam-6082	20	6	five	five	NUM
ejpam-6082	20	7	are	be	AUX
ejpam-6082	20	8	considered	consider	VERB
ejpam-6082	20	9	particularly	particularly	ADV
ejpam-6082	20	10	vulnerable	vulnerable	ADJ
ejpam-6082	20	11	,	,	PUNCT
ejpam-6082	20	12	although	although	SCONJ
ejpam-6082	20	13	individuals	individual	NOUN
ejpam-6082	20	14	of	of	ADP
ejpam-6082	20	15	all	all	DET
ejpam-6082	20	16	age	age	NOUN
ejpam-6082	20	17	groups	group	NOUN
ejpam-6082	20	18	can	can	AUX
ejpam-6082	20	19	contract	contract	VERB
ejpam-6082	20	20	the	the	DET
ejpam-6082	20	21	disease	disease	NOUN
ejpam-6082	20	22	.	.	PUNCT
ejpam-6082	21	1	polio	polio	NOUN
ejpam-6082	21	2	is	be	AUX
ejpam-6082	21	3	typically	typically	ADV
ejpam-6082	21	4	transmitted	transmit	VERB
ejpam-6082	21	5	through	through	ADP
ejpam-6082	21	6	the	the	DET
ejpam-6082	21	7	ingestion	ingestion	NOUN
ejpam-6082	21	8	of	of	ADP
ejpam-6082	21	9	material	material	NOUN
ejpam-6082	21	10	contaminated	contaminate	VERB
ejpam-6082	21	11	with	with	ADP
ejpam-6082	21	12	feces	fece	NOUN
ejpam-6082	21	13	from	from	ADP
ejpam-6082	21	14	an	an	DET
ejpam-6082	21	15	infected	infected	ADJ
ejpam-6082	21	16	person	person	NOUN
ejpam-6082	21	17	.	.	PUNCT
ejpam-6082	22	1	it	it	PRON
ejpam-6082	22	2	may	may	AUX
ejpam-6082	22	3	also	also	ADV
ejpam-6082	22	4	spread	spread	VERB
ejpam-6082	22	5	through	through	ADP
ejpam-6082	22	6	airborne	airborne	ADJ
ejpam-6082	22	7	droplets	droplet	NOUN
ejpam-6082	22	8	released	release	VERB
ejpam-6082	22	9	when	when	SCONJ
ejpam-6082	22	10	an	an	DET
ejpam-6082	22	11	infected	infected	ADJ
ejpam-6082	22	12	individual	individual	ADJ
ejpam-6082	22	13	coughs	cough	NOUN
ejpam-6082	22	14	or	or	CCONJ
ejpam-6082	22	15	sneezes	sneeze	VERB
ejpam-6082	22	16	.	.	PUNCT
ejpam-6082	23	1	the	the	DET
ejpam-6082	23	2	virus	virus	NOUN
ejpam-6082	23	3	primarily	primarily	ADV
ejpam-6082	23	4	resides	reside	VERB
ejpam-6082	23	5	in	in	ADP
ejpam-6082	23	6	the	the	DET
ejpam-6082	23	7	throat	throat	NOUN
ejpam-6082	23	8	and	and	CCONJ
ejpam-6082	23	9	intestinal	intestinal	ADJ
ejpam-6082	23	10	tract	tract	NOUN
ejpam-6082	23	11	of	of	ADP
ejpam-6082	23	12	the	the	DET
ejpam-6082	23	13	host	host	NOUN
ejpam-6082	23	14	.	.	PUNCT
ejpam-6082	24	1	communities	community	NOUN
ejpam-6082	24	2	where	where	SCONJ
ejpam-6082	24	3	open	open	ADJ
ejpam-6082	24	4	defecation	defecation	NOUN
ejpam-6082	24	5	is	be	AUX
ejpam-6082	24	6	prevalent	prevalent	ADJ
ejpam-6082	24	7	are	be	AUX
ejpam-6082	24	8	at	at	ADP
ejpam-6082	24	9	higher	high	ADJ
ejpam-6082	24	10	risk	risk	NOUN
ejpam-6082	24	11	of	of	ADP
ejpam-6082	24	12	polio	polio	NOUN
ejpam-6082	24	13	outbreaks	outbreak	NOUN
ejpam-6082	24	14	.	.	PUNCT
ejpam-6082	25	1	cultural	cultural	ADJ
ejpam-6082	25	2	traditions	tradition	NOUN
ejpam-6082	25	3	,	,	PUNCT
ejpam-6082	25	4	a	a	DET
ejpam-6082	25	5	lack	lack	NOUN
ejpam-6082	25	6	of	of	ADP
ejpam-6082	25	7	access	access	NOUN
ejpam-6082	25	8	to	to	ADP
ejpam-6082	25	9	sanitation	sanitation	NOUN
ejpam-6082	25	10	facilities	facility	NOUN
ejpam-6082	25	11	,	,	PUNCT
ejpam-6082	25	12	or	or	CCONJ
ejpam-6082	25	13	both	both	PRON
ejpam-6082	25	14	,	,	PUNCT
ejpam-6082	25	15	often	often	ADV
ejpam-6082	25	16	contribute	contribute	VERB
ejpam-6082	25	17	to	to	PART
ejpam-6082	25	18	open	open	VERB
ejpam-6082	25	19	defecation	defecation	NOUN
ejpam-6082	25	20	practices	practice	NOUN
ejpam-6082	25	21	.	.	PUNCT
ejpam-6082	26	1	additionally	additionally	ADV
ejpam-6082	26	2	,	,	PUNCT
ejpam-6082	26	3	improper	improper	ADJ
ejpam-6082	26	4	waste	waste	NOUN
ejpam-6082	26	5	disposal	disposal	NOUN
ejpam-6082	26	6	and	and	CCONJ
ejpam-6082	26	7	unsanitary	unsanitary	ADJ
ejpam-6082	26	8	environmental	environmental	ADJ
ejpam-6082	26	9	conditions	condition	NOUN
ejpam-6082	26	10	can	can	AUX
ejpam-6082	26	11	facilitate	facilitate	VERB
ejpam-6082	26	12	the	the	DET
ejpam-6082	26	13	persistence	persistence	NOUN
ejpam-6082	26	14	and	and	CCONJ
ejpam-6082	26	15	spread	spread	NOUN
ejpam-6082	26	16	of	of	ADP
ejpam-6082	26	17	the	the	DET
ejpam-6082	26	18	virus	virus	NOUN
ejpam-6082	26	19	within	within	ADP
ejpam-6082	26	20	a	a	DET
ejpam-6082	26	21	community	community	NOUN
ejpam-6082	26	22	.	.	PUNCT
ejpam-6082	27	1	once	once	SCONJ
ejpam-6082	27	2	the	the	DET
ejpam-6082	27	3	virus	virus	NOUN
ejpam-6082	27	4	enters	enter	VERB
ejpam-6082	27	5	the	the	DET
ejpam-6082	27	6	body	body	NOUN
ejpam-6082	27	7	,	,	PUNCT
ejpam-6082	27	8	it	it	PRON
ejpam-6082	27	9	targets	target	VERB
ejpam-6082	27	10	the	the	DET
ejpam-6082	27	11	nervous	nervous	ADJ
ejpam-6082	27	12	system	system	NOUN
ejpam-6082	27	13	,	,	PUNCT
ejpam-6082	27	14	including	include	VERB
ejpam-6082	27	15	the	the	DET
ejpam-6082	27	16	brain	brain	NOUN
ejpam-6082	27	17	.	.	PUNCT
ejpam-6082	28	1	the	the	DET
ejpam-6082	28	2	incubation	incubation	NOUN
ejpam-6082	28	3	period	period	NOUN
ejpam-6082	28	4	for	for	ADP
ejpam-6082	28	5	polio	polio	NOUN
ejpam-6082	28	6	ranges	range	VERB
ejpam-6082	28	7	from	from	ADP
ejpam-6082	28	8	as	as	ADV
ejpam-6082	28	9	few	few	ADJ
ejpam-6082	28	10	as	as	ADP
ejpam-6082	28	11	four	four	NUM
ejpam-6082	28	12	days	day	NOUN
ejpam-6082	28	13	to	to	ADP
ejpam-6082	28	14	up	up	ADP
ejpam-6082	28	15	to	to	PART
ejpam-6082	28	16	35	35	NUM
ejpam-6082	28	17	days	day	NOUN
ejpam-6082	28	18	[	[	X
ejpam-6082	28	19	1	1	NUM
ejpam-6082	28	20	]	]	PUNCT
ejpam-6082	28	21	.	.	PUNCT
ejpam-6082	29	1	currently	currently	ADV
ejpam-6082	29	2	,	,	PUNCT
ejpam-6082	29	3	there	there	PRON
ejpam-6082	29	4	is	be	VERB
ejpam-6082	29	5	no	no	DET
ejpam-6082	29	6	known	know	VERB
ejpam-6082	29	7	cure	cure	NOUN
ejpam-6082	29	8	for	for	ADP
ejpam-6082	29	9	this	this	DET
ejpam-6082	29	10	disease	disease	NOUN
ejpam-6082	29	11	.	.	PUNCT
ejpam-6082	30	1	while	while	SCONJ
ejpam-6082	30	2	many	many	ADJ
ejpam-6082	30	3	individuals	individual	NOUN
ejpam-6082	30	4	infected	infect	VERB
ejpam-6082	30	5	with	with	ADP
ejpam-6082	30	6	the	the	DET
ejpam-6082	30	7	poliovirus	poliovirus	NOUN
ejpam-6082	30	8	do	do	AUX
ejpam-6082	30	9	not	not	PART
ejpam-6082	30	10	exhibit	exhibit	VERB
ejpam-6082	30	11	symptoms	symptom	NOUN
ejpam-6082	30	12	,	,	PUNCT
ejpam-6082	30	13	they	they	PRON
ejpam-6082	30	14	remain	remain	VERB
ejpam-6082	30	15	capable	capable	ADJ
ejpam-6082	30	16	of	of	ADP
ejpam-6082	30	17	transmitting	transmit	VERB
ejpam-6082	30	18	the	the	DET
ejpam-6082	30	19	virus	virus	NOUN
ejpam-6082	30	20	to	to	ADP
ejpam-6082	30	21	others	other	NOUN
ejpam-6082	30	22	.	.	PUNCT
ejpam-6082	31	1	in	in	ADP
ejpam-6082	31	2	cases	case	NOUN
ejpam-6082	31	3	where	where	SCONJ
ejpam-6082	31	4	symptoms	symptom	NOUN
ejpam-6082	31	5	do	do	AUX
ejpam-6082	31	6	appear	appear	VERB
ejpam-6082	31	7	,	,	PUNCT
ejpam-6082	31	8	they	they	PRON
ejpam-6082	31	9	can	can	AUX
ejpam-6082	31	10	include	include	VERB
ejpam-6082	31	11	fever	fever	NOUN
ejpam-6082	31	12	,	,	PUNCT
ejpam-6082	31	13	sore	sore	ADJ
ejpam-6082	31	14	throat	throat	NOUN
ejpam-6082	31	15	,	,	PUNCT
ejpam-6082	31	16	headache	headache	NOUN
ejpam-6082	31	17	,	,	PUNCT
ejpam-6082	31	18	vomiting	vomiting	NOUN
ejpam-6082	31	19	,	,	PUNCT
ejpam-6082	31	20	and	and	CCONJ
ejpam-6082	31	21	fatigue	fatigue	NOUN
ejpam-6082	31	22	.	.	PUNCT
ejpam-6082	32	1	severe	severe	ADJ
ejpam-6082	32	2	cases	case	NOUN
ejpam-6082	32	3	may	may	AUX
ejpam-6082	32	4	progress	progress	VERB
ejpam-6082	32	5	to	to	ADP
ejpam-6082	32	6	paralysis	paralysis	NOUN
ejpam-6082	32	7	,	,	PUNCT
ejpam-6082	32	8	resulting	result	VERB
ejpam-6082	32	9	in	in	ADP
ejpam-6082	32	10	reduced	reduced	ADJ
ejpam-6082	32	11	reflexes	reflex	NOUN
ejpam-6082	32	12	,	,	PUNCT
ejpam-6082	32	13	weakened	weaken	VERB
ejpam-6082	32	14	or	or	CCONJ
ejpam-6082	32	15	deformed	deform	VERB
ejpam-6082	32	16	limbs	limb	NOUN
ejpam-6082	32	17	,	,	PUNCT
ejpam-6082	32	18	and	and	CCONJ
ejpam-6082	32	19	other	other	ADJ
ejpam-6082	32	20	motor	motor	NOUN
ejpam-6082	32	21	impairments	impairment	NOUN
ejpam-6082	32	22	.	.	PUNCT
ejpam-6082	33	1	recovery	recovery	NOUN
ejpam-6082	33	2	from	from	ADP
ejpam-6082	33	3	polio	polio	NOUN
ejpam-6082	33	4	is	be	AUX
ejpam-6082	33	5	possible	possible	ADJ
ejpam-6082	33	6	,	,	PUNCT
ejpam-6082	33	7	but	but	CCONJ
ejpam-6082	33	8	some	some	DET
ejpam-6082	33	9	individuals	individual	NOUN
ejpam-6082	33	10	may	may	AUX
ejpam-6082	33	11	experience	experience	VERB
ejpam-6082	33	12	a	a	DET
ejpam-6082	33	13	recurrence	recurrence	NOUN
ejpam-6082	33	14	of	of	ADP
ejpam-6082	33	15	symptoms	symptom	NOUN
ejpam-6082	33	16	years	year	NOUN
ejpam-6082	33	17	later	later	ADV
ejpam-6082	33	18	,	,	PUNCT
ejpam-6082	33	19	a	a	DET
ejpam-6082	33	20	condition	condition	NOUN
ejpam-6082	33	21	known	know	VERB
ejpam-6082	33	22	as	as	ADP
ejpam-6082	33	23	post	post	ADJ
ejpam-6082	33	24	-	-	ADJ
ejpam-6082	33	25	polio	polio	ADJ
ejpam-6082	33	26	syndrome	syndrome	NOUN
ejpam-6082	33	27	(	(	PUNCT
ejpam-6082	33	28	pps	pps	PROPN
ejpam-6082	33	29	)	)	PUNCT
ejpam-6082	33	30	.	.	PUNCT
ejpam-6082	34	1	pps	pps	PROPN
ejpam-6082	34	2	typically	typically	ADV
ejpam-6082	34	3	affects	affect	VERB
ejpam-6082	34	4	polio	polio	NOUN
ejpam-6082	34	5	survivors	survivor	NOUN
ejpam-6082	34	6	15	15	NUM
ejpam-6082	34	7	to	to	PART
ejpam-6082	34	8	40	40	NUM
ejpam-6082	34	9	years	year	NOUN
ejpam-6082	34	10	after	after	ADP
ejpam-6082	34	11	their	their	PRON
ejpam-6082	34	12	initial	initial	ADJ
ejpam-6082	34	13	recovery	recovery	NOUN
ejpam-6082	34	14	.	.	PUNCT
ejpam-6082	35	1	the	the	DET
ejpam-6082	35	2	exact	exact	ADJ
ejpam-6082	35	3	prevalence	prevalence	NOUN
ejpam-6082	35	4	and	and	CCONJ
ejpam-6082	35	5	mechanisms	mechanism	NOUN
ejpam-6082	35	6	of	of	ADP
ejpam-6082	35	7	pps	pps	NOUN
ejpam-6082	35	8	remain	remain	VERB
ejpam-6082	35	9	uncertain	uncertain	ADJ
ejpam-6082	35	10	,	,	PUNCT
ejpam-6082	35	11	with	with	ADP
ejpam-6082	35	12	proposed	propose	VERB
ejpam-6082	35	13	explanations	explanation	NOUN
ejpam-6082	35	14	including	include	VERB
ejpam-6082	35	15	overuse	overuse	NOUN
ejpam-6082	35	16	of	of	ADP
ejpam-6082	35	17	surviving	survive	VERB
ejpam-6082	35	18	nerve	nerve	NOUN
ejpam-6082	35	19	cells	cell	NOUN
ejpam-6082	35	20	and	and	CCONJ
ejpam-6082	35	21	potential	potential	ADJ
ejpam-6082	35	22	brain	brain	NOUN
ejpam-6082	35	23	damage	damage	NOUN
ejpam-6082	35	24	.	.	PUNCT
ejpam-6082	36	1	the	the	DET
ejpam-6082	36	2	first	first	ADJ
ejpam-6082	36	3	documented	document	VERB
ejpam-6082	36	4	polio	polio	NOUN
ejpam-6082	36	5	outbreak	outbreak	NOUN
ejpam-6082	36	6	in	in	ADP
ejpam-6082	36	7	the	the	DET
ejpam-6082	36	8	united	united	PROPN
ejpam-6082	36	9	states	states	PROPN
ejpam-6082	36	10	occurred	occur	VERB
ejpam-6082	36	11	in	in	ADP
ejpam-6082	36	12	vermont	vermont	PROPN
ejpam-6082	36	13	in	in	ADP
ejpam-6082	36	14	1894	1894	NUM
ejpam-6082	36	15	,	,	PUNCT
ejpam-6082	36	16	resulting	result	VERB
ejpam-6082	36	17	in	in	ADP
ejpam-6082	36	18	132	132	NUM
ejpam-6082	36	19	cases	case	NOUN
ejpam-6082	36	20	.	.	PUNCT
ejpam-6082	37	1	since	since	SCONJ
ejpam-6082	37	2	that	that	DET
ejpam-6082	37	3	time	time	NOUN
ejpam-6082	37	4	,	,	PUNCT
ejpam-6082	37	5	significant	significant	ADJ
ejpam-6082	37	6	efforts	effort	NOUN
ejpam-6082	37	7	have	have	AUX
ejpam-6082	37	8	been	be	AUX
ejpam-6082	37	9	made	make	VERB
ejpam-6082	37	10	by	by	ADP
ejpam-6082	37	11	medical	medical	ADJ
ejpam-6082	37	12	researchers	researcher	NOUN
ejpam-6082	37	13	to	to	PART
ejpam-6082	37	14	address	address	VERB
ejpam-6082	37	15	the	the	DET
ejpam-6082	37	16	devastating	devastating	ADJ
ejpam-6082	37	17	effects	effect	NOUN
ejpam-6082	37	18	of	of	ADP
ejpam-6082	37	19	the	the	DET
ejpam-6082	37	20	virus	virus	NOUN
ejpam-6082	37	21	.	.	PUNCT
ejpam-6082	38	1	in	in	ADP
ejpam-6082	38	2	1988	1988	NUM
ejpam-6082	38	3	,	,	PUNCT
ejpam-6082	38	4	the	the	DET
ejpam-6082	38	5	world	world	PROPN
ejpam-6082	38	6	health	health	NOUN
ejpam-6082	38	7	assembly	assembly	NOUN
ejpam-6082	38	8	adopted	adopt	VERB
ejpam-6082	38	9	a	a	DET
ejpam-6082	38	10	resolution	resolution	NOUN
ejpam-6082	38	11	aimed	aim	VERB
ejpam-6082	38	12	at	at	ADP
ejpam-6082	38	13	eradicating	eradicate	VERB
ejpam-6082	38	14	poliomyelitis	poliomyelitis	NOUN
ejpam-6082	38	15	globally	globally	ADV
ejpam-6082	38	16	,	,	PUNCT
ejpam-6082	38	17	leading	lead	VERB
ejpam-6082	38	18	to	to	ADP
ejpam-6082	38	19	the	the	DET
ejpam-6082	38	20	establishment	establishment	NOUN
ejpam-6082	38	21	of	of	ADP
ejpam-6082	38	22	the	the	DET
ejpam-6082	38	23	global	global	ADJ
ejpam-6082	38	24	polio	polio	NOUN
ejpam-6082	38	25	eradication	eradication	NOUN
ejpam-6082	38	26	initiative	initiative	NOUN
ejpam-6082	38	27	(	(	PUNCT
ejpam-6082	38	28	gpei	gpei	PROPN
ejpam-6082	38	29	)	)	PUNCT
ejpam-6082	38	30	.	.	PUNCT
ejpam-6082	39	1	this	this	DET
ejpam-6082	39	2	initiative	initiative	NOUN
ejpam-6082	39	3	has	have	AUX
ejpam-6082	39	4	significantly	significantly	ADV
ejpam-6082	39	5	reduced	reduce	VERB
ejpam-6082	39	6	the	the	DET
ejpam-6082	39	7	prevalence	prevalence	NOUN
ejpam-6082	39	8	and	and	CCONJ
ejpam-6082	39	9	incidence	incidence	NOUN
ejpam-6082	39	10	of	of	ADP
ejpam-6082	39	11	polio	polio	NOUN
ejpam-6082	39	12	in	in	ADP
ejpam-6082	39	13	many	many	ADJ
ejpam-6082	39	14	parts	part	NOUN
ejpam-6082	39	15	of	of	ADP
ejpam-6082	39	16	the	the	DET
ejpam-6082	39	17	world	world	NOUN
ejpam-6082	39	18	[	[	X
ejpam-6082	39	19	2	2	NUM
ejpam-6082	39	20	]	]	PUNCT
ejpam-6082	39	21	.	.	PUNCT
ejpam-6082	40	1	despite	despite	SCONJ
ejpam-6082	40	2	these	these	DET
ejpam-6082	40	3	efforts	effort	NOUN
ejpam-6082	40	4	,	,	PUNCT
ejpam-6082	40	5	countries	country	NOUN
ejpam-6082	40	6	such	such	ADJ
ejpam-6082	40	7	as	as	ADP
ejpam-6082	40	8	afghanistan	afghanistan	PROPN
ejpam-6082	40	9	,	,	PUNCT
ejpam-6082	40	10	nigeria	nigeria	PROPN
ejpam-6082	40	11	,	,	PUNCT
ejpam-6082	40	12	and	and	CCONJ
ejpam-6082	40	13	pakistan	pakistan	PROPN
ejpam-6082	40	14	continue	continue	VERB
ejpam-6082	40	15	to	to	PART
ejpam-6082	40	16	report	report	VERB
ejpam-6082	40	17	cases	case	NOUN
ejpam-6082	40	18	of	of	ADP
ejpam-6082	40	19	the	the	DET
ejpam-6082	40	20	disease	disease	NOUN
ejpam-6082	40	21	.	.	PUNCT
ejpam-6082	41	1	as	as	ADV
ejpam-6082	41	2	long	long	ADV
ejpam-6082	41	3	as	as	SCONJ
ejpam-6082	41	4	the	the	DET
ejpam-6082	41	5	poliovirus	poliovirus	NOUN
ejpam-6082	41	6	persists	persist	VERB
ejpam-6082	41	7	in	in	ADP
ejpam-6082	41	8	even	even	ADV
ejpam-6082	41	9	one	one	NUM
ejpam-6082	41	10	individual	individual	NOUN
ejpam-6082	41	11	,	,	PUNCT
ejpam-6082	41	12	there	there	PRON
ejpam-6082	41	13	is	be	VERB
ejpam-6082	41	14	a	a	DET
ejpam-6082	41	15	risk	risk	NOUN
ejpam-6082	41	16	of	of	ADP
ejpam-6082	41	17	further	further	ADJ
ejpam-6082	41	18	transmission	transmission	NOUN
ejpam-6082	41	19	.	.	PUNCT
ejpam-6082	42	1	polio	polio	NOUN
ejpam-6082	42	2	remains	remain	VERB
ejpam-6082	42	3	a	a	DET
ejpam-6082	42	4	global	global	ADJ
ejpam-6082	42	5	health	health	NOUN
ejpam-6082	42	6	concern	concern	NOUN
ejpam-6082	42	7	due	due	ADP
ejpam-6082	42	8	to	to	ADP
ejpam-6082	42	9	its	its	PRON
ejpam-6082	42	10	ability	ability	NOUN
ejpam-6082	42	11	to	to	PART
ejpam-6082	42	12	spread	spread	VERB
ejpam-6082	42	13	silently	silently	ADV
ejpam-6082	42	14	over	over	ADP
ejpam-6082	42	15	several	several	ADJ
ejpam-6082	42	16	weeks	week	NOUN
ejpam-6082	42	17	and	and	CCONJ
ejpam-6082	42	18	its	its	PRON
ejpam-6082	42	19	potential	potential	NOUN
ejpam-6082	42	20	to	to	PART
ejpam-6082	42	21	travel	travel	VERB
ejpam-6082	42	22	long	long	ADJ
ejpam-6082	42	23	distances	distance	NOUN
ejpam-6082	42	24	via	via	ADP
ejpam-6082	42	25	land	land	NOUN
ejpam-6082	42	26	,	,	PUNCT
ejpam-6082	42	27	air	air	NOUN
ejpam-6082	42	28	,	,	PUNCT
ejpam-6082	42	29	or	or	CCONJ
ejpam-6082	42	30	sea	sea	NOUN
ejpam-6082	42	31	.	.	PUNCT
ejpam-6082	42	32	vaccination	vaccination	NOUN
ejpam-6082	42	33	plays	play	VERB
ejpam-6082	42	34	a	a	DET
ejpam-6082	42	35	crucial	crucial	ADJ
ejpam-6082	42	36	role	role	NOUN
ejpam-6082	42	37	in	in	ADP
ejpam-6082	42	38	helping	help	VERB
ejpam-6082	42	39	individuals	individual	NOUN
ejpam-6082	42	40	develop	develop	VERB
ejpam-6082	42	41	immunity	immunity	NOUN
ejpam-6082	42	42	against	against	ADP
ejpam-6082	42	43	the	the	DET
ejpam-6082	42	44	poliovirus	poliovirus	NOUN
ejpam-6082	42	45	.	.	PUNCT
ejpam-6082	43	1	however	however	ADV
ejpam-6082	43	2	,	,	PUNCT
ejpam-6082	43	3	administering	administer	VERB
ejpam-6082	43	4	a	a	DET
ejpam-6082	43	5	vaccine	vaccine	NOUN
ejpam-6082	43	6	during	during	ADP
ejpam-6082	43	7	the	the	DET
ejpam-6082	43	8	virus	virus	NOUN
ejpam-6082	43	9	’s	’s	PART
ejpam-6082	43	10	incubation	incubation	NOUN
ejpam-6082	43	11	period	period	NOUN
ejpam-6082	43	12	can	can	AUX
ejpam-6082	43	13	have	have	VERB
ejpam-6082	43	14	harmful	harmful	ADJ
ejpam-6082	43	15	effects	effect	NOUN
ejpam-6082	43	16	,	,	PUNCT
ejpam-6082	43	17	as	as	SCONJ
ejpam-6082	43	18	it	it	PRON
ejpam-6082	43	19	may	may	AUX
ejpam-6082	43	20	increase	increase	VERB
ejpam-6082	43	21	the	the	DET
ejpam-6082	43	22	viral	viral	ADJ
ejpam-6082	43	23	load	load	NOUN
ejpam-6082	43	24	in	in	ADP
ejpam-6082	43	25	the	the	DET
ejpam-6082	43	26	individual	individual	NOUN
ejpam-6082	43	27	.	.	PUNCT
ejpam-6082	44	1	agarwal	agarwal	PROPN
ejpam-6082	44	2	and	and	CCONJ
ejpam-6082	44	3	bhadauria	bhadauria	PROPN
ejpam-6082	45	1	[	[	X
ejpam-6082	45	2	3	3	X
ejpam-6082	45	3	]	]	PUNCT
ejpam-6082	45	4	observed	observe	VERB
ejpam-6082	45	5	that	that	SCONJ
ejpam-6082	45	6	receiving	receive	VERB
ejpam-6082	45	7	an	an	DET
ejpam-6082	45	8	inactivated	inactivated	ADJ
ejpam-6082	45	9	polio	polio	NOUN
ejpam-6082	45	10	vaccine	vaccine	NOUN
ejpam-6082	45	11	(	(	PUNCT
ejpam-6082	45	12	ipv	ipv	PROPN
ejpam-6082	45	13	)	)	PUNCT
ejpam-6082	45	14	during	during	ADP
ejpam-6082	45	15	the	the	DET
ejpam-6082	45	16	incubation	incubation	NOUN
ejpam-6082	45	17	phase	phase	NOUN
ejpam-6082	45	18	k.	k.	PROPN
ejpam-6082	45	19	guedri	guedri	PROPN
ejpam-6082	45	20	et	et	PROPN
ejpam-6082	45	21	al	al	PROPN
ejpam-6082	45	22	.	.	PUNCT
ejpam-6082	45	23	/	/	SYM
ejpam-6082	45	24	eur	eur	PROPN
ejpam-6082	45	25	.	.	PUNCT
ejpam-6082	46	1	j.	j.	PROPN
ejpam-6082	46	2	pure	pure	PROPN
ejpam-6082	46	3	appl	appl	PROPN
ejpam-6082	46	4	.	.	PROPN
ejpam-6082	46	5	math	math	PROPN
ejpam-6082	46	6	,	,	PUNCT
ejpam-6082	46	7	18	18	NUM
ejpam-6082	46	8	(	(	PUNCT
ejpam-6082	46	9	2	2	NUM
ejpam-6082	46	10	)	)	PUNCT
ejpam-6082	46	11	(	(	PUNCT
ejpam-6082	46	12	2025	2025	NUM
ejpam-6082	46	13	)	)	PUNCT
ejpam-6082	46	14	,	,	PUNCT
ejpam-6082	46	15	6082	6082	NUM
ejpam-6082	46	16	3	3	NUM
ejpam-6082	46	17	of	of	ADP
ejpam-6082	46	18	39	39	NUM
ejpam-6082	46	19	could	could	AUX
ejpam-6082	46	20	lead	lead	VERB
ejpam-6082	46	21	to	to	ADP
ejpam-6082	46	22	a	a	DET
ejpam-6082	46	23	progression	progression	NOUN
ejpam-6082	46	24	from	from	ADP
ejpam-6082	46	25	the	the	DET
ejpam-6082	46	26	incubation	incubation	NOUN
ejpam-6082	46	27	stage	stage	NOUN
ejpam-6082	46	28	to	to	ADP
ejpam-6082	46	29	paralysis	paralysis	NOUN
ejpam-6082	46	30	.	.	PUNCT
ejpam-6082	47	1	for	for	ADP
ejpam-6082	47	2	this	this	DET
ejpam-6082	47	3	reason	reason	NOUN
ejpam-6082	47	4	,	,	PUNCT
ejpam-6082	47	5	it	it	PRON
ejpam-6082	47	6	is	be	AUX
ejpam-6082	47	7	recommended	recommend	VERB
ejpam-6082	47	8	to	to	PART
ejpam-6082	47	9	conduct	conduct	VERB
ejpam-6082	47	10	appropriate	appropriate	ADJ
ejpam-6082	47	11	screening	screening	NOUN
ejpam-6082	47	12	before	before	ADP
ejpam-6082	47	13	administering	administer	VERB
ejpam-6082	47	14	the	the	DET
ejpam-6082	47	15	vaccine	vaccine	NOUN
ejpam-6082	47	16	.	.	PUNCT
ejpam-6082	48	1	compartmental	compartmental	ADJ
ejpam-6082	48	2	models	model	NOUN
ejpam-6082	48	3	address	address	VERB
ejpam-6082	48	4	refined	refine	VERB
ejpam-6082	48	5	numerical	numerical	ADJ
ejpam-6082	48	6	structures	structure	NOUN
ejpam-6082	48	7	intended	intend	VERB
ejpam-6082	48	8	to	to	PART
ejpam-6082	48	9	give	give	VERB
ejpam-6082	48	10	an	an	DET
ejpam-6082	48	11	itemized	itemize	VERB
ejpam-6082	48	12	comprehension	comprehension	NOUN
ejpam-6082	48	13	of	of	ADP
ejpam-6082	48	14	the	the	DET
ejpam-6082	48	15	transmission	transmission	NOUN
ejpam-6082	48	16	elements	element	NOUN
ejpam-6082	48	17	of	of	ADP
ejpam-6082	48	18	infectious	infectious	ADJ
ejpam-6082	48	19	diseases	disease	NOUN
ejpam-6082	48	20	inside	inside	ADP
ejpam-6082	48	21	human	human	ADJ
ejpam-6082	48	22	population	population	NOUN
ejpam-6082	49	1	[	[	X
ejpam-6082	49	2	4–9	4–9	X
ejpam-6082	49	3	]	]	PUNCT
ejpam-6082	49	4	.	.	PUNCT
ejpam-6082	50	1	the	the	DET
ejpam-6082	50	2	starting	starting	NOUN
ejpam-6082	50	3	points	point	NOUN
ejpam-6082	50	4	of	of	ADP
ejpam-6082	50	5	these	these	DET
ejpam-6082	50	6	models	model	NOUN
ejpam-6082	50	7	can	can	AUX
ejpam-6082	50	8	be	be	AUX
ejpam-6082	50	9	followed	follow	VERB
ejpam-6082	50	10	back	back	ADV
ejpam-6082	50	11	to	to	ADP
ejpam-6082	50	12	1760	1760	NUM
ejpam-6082	50	13	,	,	PUNCT
ejpam-6082	50	14	when	when	SCONJ
ejpam-6082	50	15	daniel	daniel	PROPN
ejpam-6082	50	16	bernoulli	bernoulli	PROPN
ejpam-6082	50	17	fostered	foster	VERB
ejpam-6082	50	18	the	the	DET
ejpam-6082	50	19	principal	principal	ADJ
ejpam-6082	50	20	numerical	numerical	PROPN
ejpam-6082	50	21	compartmental	compartmental	PROPN
ejpam-6082	50	22	model	model	NOUN
ejpam-6082	51	1	[	[	X
ejpam-6082	51	2	10	10	NUM
ejpam-6082	51	3	]	]	PUNCT
ejpam-6082	51	4	.	.	PUNCT
ejpam-6082	52	1	from	from	ADP
ejpam-6082	52	2	that	that	DET
ejpam-6082	52	3	point	point	NOUN
ejpam-6082	52	4	forward	forward	ADV
ejpam-6082	52	5	,	,	PUNCT
ejpam-6082	52	6	various	various	ADJ
ejpam-6082	52	7	compartmental	compartmental	ADJ
ejpam-6082	52	8	models	model	NOUN
ejpam-6082	52	9	have	have	AUX
ejpam-6082	52	10	been	be	AUX
ejpam-6082	52	11	planned	plan	VERB
ejpam-6082	52	12	to	to	PART
ejpam-6082	52	13	portray	portray	VERB
ejpam-6082	52	14	the	the	DET
ejpam-6082	52	15	spread	spread	NOUN
ejpam-6082	52	16	of	of	ADP
ejpam-6082	52	17	different	different	ADJ
ejpam-6082	52	18	scourges	scourge	NOUN
ejpam-6082	52	19	and	and	CCONJ
ejpam-6082	52	20	irresistible	irresistible	ADJ
ejpam-6082	52	21	specialists	specialist	NOUN
ejpam-6082	52	22	,	,	PUNCT
ejpam-6082	52	23	frequently	frequently	ADV
ejpam-6082	52	24	using	use	VERB
ejpam-6082	52	25	old	old	ADJ
ejpam-6082	52	26	style	style	NOUN
ejpam-6082	52	27	whole	whole	ADJ
ejpam-6082	52	28	number	number	NOUN
ejpam-6082	52	29	request	request	NOUN
ejpam-6082	52	30	subsidiaries	subsidiary	NOUN
ejpam-6082	52	31	[	[	X
ejpam-6082	52	32	11	11	NUM
ejpam-6082	52	33	,	,	PUNCT
ejpam-6082	52	34	12	12	NUM
ejpam-6082	52	35	]	]	PUNCT
ejpam-6082	52	36	.	.	PUNCT
ejpam-6082	53	1	a	a	DET
ejpam-6082	53	2	few	few	ADJ
ejpam-6082	53	3	compartmental	compartmental	ADJ
ejpam-6082	53	4	models	model	NOUN
ejpam-6082	53	5	explicitly	explicitly	ADV
ejpam-6082	53	6	address	address	VERB
ejpam-6082	53	7	the	the	DET
ejpam-6082	53	8	transmission	transmission	NOUN
ejpam-6082	53	9	elements	element	NOUN
ejpam-6082	53	10	of	of	ADP
ejpam-6082	53	11	poliomyelitis	poliomyelitis	NOUN
ejpam-6082	53	12	.	.	PUNCT
ejpam-6082	54	1	for	for	ADP
ejpam-6082	54	2	example	example	NOUN
ejpam-6082	54	3	,	,	PUNCT
ejpam-6082	54	4	duque	duque	ADJ
ejpam-6082	54	5	-	-	PUNCT
ejpam-6082	54	6	marin	marin	NOUN
ejpam-6082	54	7	et	et	PROPN
ejpam-6082	54	8	al	al	PROPN
ejpam-6082	54	9	.	.	PUNCT
ejpam-6082	55	1	[	[	X
ejpam-6082	55	2	13	13	NUM
ejpam-6082	55	3	]	]	PUNCT
ejpam-6082	55	4	fostered	foster	VERB
ejpam-6082	55	5	a	a	DET
ejpam-6082	55	6	model	model	NOUN
ejpam-6082	55	7	that	that	PRON
ejpam-6082	55	8	catches	catch	VERB
ejpam-6082	55	9	the	the	DET
ejpam-6082	55	10	elements	element	NOUN
ejpam-6082	55	11	of	of	ADP
ejpam-6082	55	12	polio	polio	NOUN
ejpam-6082	55	13	contaminations	contamination	NOUN
ejpam-6082	55	14	inside	inside	ADP
ejpam-6082	55	15	a	a	DET
ejpam-6082	55	16	populace	populace	NOUN
ejpam-6082	55	17	,	,	PUNCT
ejpam-6082	55	18	consolidating	consolidate	VERB
ejpam-6082	55	19	two	two	NUM
ejpam-6082	55	20	kinds	kind	NOUN
ejpam-6082	55	21	of	of	ADP
ejpam-6082	55	22	immunizations	immunization	NOUN
ejpam-6082	55	23	,	,	PUNCT
ejpam-6082	55	24	delineation	delineation	NOUN
ejpam-6082	55	25	by	by	ADP
ejpam-6082	55	26	age	age	NOUN
ejpam-6082	55	27	gatherings	gathering	NOUN
ejpam-6082	55	28	,	,	PUNCT
ejpam-6082	55	29	and	and	CCONJ
ejpam-6082	55	30	transient	transient	ADJ
ejpam-6082	55	31	impacts	impact	NOUN
ejpam-6082	55	32	.	.	PUNCT
ejpam-6082	56	1	browne	browne	PROPN
ejpam-6082	56	2	et	et	PROPN
ejpam-6082	56	3	al	al	PROPN
ejpam-6082	56	4	.	.	PUNCT
ejpam-6082	57	1	[	[	X
ejpam-6082	57	2	14	14	NUM
ejpam-6082	57	3	]	]	PUNCT
ejpam-6082	57	4	proposed	propose	VERB
ejpam-6082	57	5	a	a	DET
ejpam-6082	57	6	model	model	NOUN
ejpam-6082	57	7	that	that	PRON
ejpam-6082	57	8	records	record	VERB
ejpam-6082	57	9	for	for	ADP
ejpam-6082	57	10	sickness	sickness	NOUN
ejpam-6082	57	11	elements	element	NOUN
ejpam-6082	57	12	across	across	ADP
ejpam-6082	57	13	interconnected	interconnected	ADJ
ejpam-6082	57	14	locales	locale	NOUN
ejpam-6082	57	15	,	,	PUNCT
ejpam-6082	57	16	incorporating	incorporate	VERB
ejpam-6082	57	17	variables	variable	NOUN
ejpam-6082	57	18	like	like	ADP
ejpam-6082	57	19	occasional	occasional	ADJ
ejpam-6082	57	20	varieties	variety	NOUN
ejpam-6082	57	21	,	,	PUNCT
ejpam-6082	57	22	ecological	ecological	ADJ
ejpam-6082	57	23	repositories	repository	NOUN
ejpam-6082	57	24	,	,	PUNCT
ejpam-6082	57	25	and	and	CCONJ
ejpam-6082	57	26	district	district	NOUN
ejpam-6082	57	27	explicit	explicit	ADJ
ejpam-6082	57	28	intermittent	intermittent	ADJ
ejpam-6082	57	29	heartbeat	heartbeat	NOUN
ejpam-6082	57	30	immunization	immunization	NOUN
ejpam-6082	57	31	techniques	technique	NOUN
ejpam-6082	57	32	.	.	PUNCT
ejpam-6082	58	1	dénes	dénes	PROPN
ejpam-6082	58	2	et	et	PROPN
ejpam-6082	58	3	al	al	PROPN
ejpam-6082	58	4	.	.	PUNCT
ejpam-6082	59	1	[	[	X
ejpam-6082	59	2	15	15	NUM
ejpam-6082	59	3	]	]	PUNCT
ejpam-6082	59	4	presented	present	VERB
ejpam-6082	59	5	a	a	DET
ejpam-6082	59	6	compartmental	compartmental	ADJ
ejpam-6082	59	7	model	model	NOUN
ejpam-6082	59	8	inspecting	inspect	VERB
ejpam-6082	59	9	the	the	DET
ejpam-6082	59	10	expected	expect	VERB
ejpam-6082	59	11	effect	effect	NOUN
ejpam-6082	59	12	of	of	ADP
ejpam-6082	59	13	unvaccinated	unvaccinated	ADJ
ejpam-6082	59	14	people	people	NOUN
ejpam-6082	59	15	relocating	relocate	VERB
ejpam-6082	59	16	into	into	ADP
ejpam-6082	59	17	regions	region	NOUN
ejpam-6082	59	18	with	with	ADP
ejpam-6082	59	19	low	low	ADJ
ejpam-6082	59	20	immunization	immunization	NOUN
ejpam-6082	59	21	inclusion	inclusion	NOUN
ejpam-6082	59	22	.	.	PUNCT
ejpam-6082	60	1	various	various	ADJ
ejpam-6082	60	2	extra	extra	ADJ
ejpam-6082	60	3	investigations	investigation	NOUN
ejpam-6082	60	4	have	have	AUX
ejpam-6082	60	5	investigated	investigate	VERB
ejpam-6082	60	6	different	different	ADJ
ejpam-6082	60	7	elements	element	NOUN
ejpam-6082	60	8	of	of	ADP
ejpam-6082	60	9	polio	polio	NOUN
ejpam-6082	60	10	transmission	transmission	NOUN
ejpam-6082	60	11	elements	element	NOUN
ejpam-6082	60	12	,	,	PUNCT
ejpam-6082	60	13	adding	add	VERB
ejpam-6082	60	14	to	to	ADP
ejpam-6082	60	15	a	a	DET
ejpam-6082	60	16	more	more	ADV
ejpam-6082	60	17	profound	profound	ADJ
ejpam-6082	60	18	comprehension	comprehension	NOUN
ejpam-6082	60	19	of	of	ADP
ejpam-6082	60	20	the	the	DET
ejpam-6082	60	21	infection	infection	NOUN
ejpam-6082	60	22	’s	’s	PART
ejpam-6082	60	23	spread	spread	VERB
ejpam-6082	60	24	and	and	CCONJ
ejpam-6082	60	25	control	control	NOUN
ejpam-6082	60	26	systems	system	NOUN
ejpam-6082	60	27	[	[	X
ejpam-6082	60	28	16–18	16–18	NUM
ejpam-6082	60	29	]	]	PUNCT
ejpam-6082	60	30	.	.	PUNCT
ejpam-6082	61	1	in	in	ADP
ejpam-6082	61	2	recent	recent	ADJ
ejpam-6082	61	3	years	year	NOUN
ejpam-6082	61	4	,	,	PUNCT
ejpam-6082	61	5	reaction	reaction	NOUN
ejpam-6082	61	6	-	-	PUNCT
ejpam-6082	61	7	diffusion	diffusion	NOUN
ejpam-6082	61	8	models	model	NOUN
ejpam-6082	61	9	have	have	AUX
ejpam-6082	61	10	been	be	AUX
ejpam-6082	61	11	widely	widely	ADV
ejpam-6082	61	12	utilized	utilize	VERB
ejpam-6082	61	13	to	to	PART
ejpam-6082	61	14	depict	depict	VERB
ejpam-6082	61	15	the	the	DET
ejpam-6082	61	16	spatial	spatial	ADJ
ejpam-6082	61	17	and	and	CCONJ
ejpam-6082	61	18	temporal	temporal	ADJ
ejpam-6082	61	19	dynamics	dynamic	NOUN
ejpam-6082	61	20	of	of	ADP
ejpam-6082	61	21	infection	infection	NOUN
ejpam-6082	61	22	transmission	transmission	NOUN
ejpam-6082	61	23	,	,	PUNCT
ejpam-6082	61	24	both	both	CCONJ
ejpam-6082	61	25	in	in	ADP
ejpam-6082	61	26	vitro	vitro	X
ejpam-6082	61	27	and	and	CCONJ
ejpam-6082	61	28	in	in	ADP
ejpam-6082	61	29	vivo	vivo	NOUN
ejpam-6082	61	30	[	[	X
ejpam-6082	61	31	19–23	19–23	NUM
ejpam-6082	61	32	]	]	PUNCT
ejpam-6082	61	33	.	.	PUNCT
ejpam-6082	62	1	these	these	DET
ejpam-6082	62	2	models	model	NOUN
ejpam-6082	62	3	normally	normally	ADV
ejpam-6082	62	4	expect	expect	VERB
ejpam-6082	62	5	that	that	SCONJ
ejpam-6082	62	6	all	all	DET
ejpam-6082	62	7	elements	element	NOUN
ejpam-6082	62	8	engaged	engage	VERB
ejpam-6082	62	9	with	with	ADP
ejpam-6082	62	10	the	the	DET
ejpam-6082	62	11	disease	disease	NOUN
ejpam-6082	62	12	interaction	interaction	NOUN
ejpam-6082	62	13	like	like	ADP
ejpam-6082	62	14	target	target	NOUN
ejpam-6082	62	15	cells	cell	NOUN
ejpam-6082	62	16	,	,	PUNCT
ejpam-6082	62	17	contaminated	contaminate	VERB
ejpam-6082	62	18	cells	cell	NOUN
ejpam-6082	62	19	,	,	PUNCT
ejpam-6082	62	20	and	and	CCONJ
ejpam-6082	62	21	viral	viral	ADJ
ejpam-6082	62	22	particles	particle	NOUN
ejpam-6082	62	23	follow	follow	VERB
ejpam-6082	62	24	old	old	ADJ
ejpam-6082	62	25	style	style	NOUN
ejpam-6082	62	26	fickian	fickian	ADJ
ejpam-6082	62	27	dissemination	dissemination	NOUN
ejpam-6082	62	28	with	with	ADP
ejpam-6082	62	29	steady	steady	ADJ
ejpam-6082	62	30	dispersion	dispersion	NOUN
ejpam-6082	62	31	rates	rate	NOUN
ejpam-6082	62	32	.	.	PUNCT
ejpam-6082	63	1	notwithstanding	notwithstanding	ADV
ejpam-6082	63	2	,	,	PUNCT
ejpam-6082	63	3	trial	trial	NOUN
ejpam-6082	63	4	discoveries	discovery	NOUN
ejpam-6082	63	5	,	,	PUNCT
ejpam-6082	63	6	for	for	ADP
ejpam-6082	63	7	example	example	NOUN
ejpam-6082	63	8	,	,	PUNCT
ejpam-6082	63	9	those	those	PRON
ejpam-6082	63	10	detailed	detailed	ADJ
ejpam-6082	63	11	in	in	ADP
ejpam-6082	63	12	[	[	X
ejpam-6082	63	13	24	24	NUM
ejpam-6082	63	14	]	]	PUNCT
ejpam-6082	63	15	,	,	PUNCT
ejpam-6082	63	16	propose	propose	VERB
ejpam-6082	63	17	that	that	SCONJ
ejpam-6082	63	18	the	the	DET
ejpam-6082	63	19	dissemination	dissemination	NOUN
ejpam-6082	63	20	properties	property	NOUN
ejpam-6082	63	21	of	of	ADP
ejpam-6082	63	22	cells	cell	NOUN
ejpam-6082	63	23	and	and	CCONJ
ejpam-6082	63	24	infections	infection	NOUN
ejpam-6082	63	25	can	can	AUX
ejpam-6082	63	26	fluctuate	fluctuate	VERB
ejpam-6082	63	27	altogether	altogether	ADV
ejpam-6082	63	28	contingent	contingent	ADJ
ejpam-6082	63	29	upon	upon	SCONJ
ejpam-6082	63	30	the	the	DET
ejpam-6082	63	31	encompassing	encompass	VERB
ejpam-6082	63	32	tissues	tissue	NOUN
ejpam-6082	63	33	or	or	CCONJ
ejpam-6082	63	34	natural	natural	ADJ
ejpam-6082	63	35	circumstances	circumstance	NOUN
ejpam-6082	63	36	.	.	PUNCT
ejpam-6082	64	1	for	for	ADP
ejpam-6082	64	2	instance	instance	NOUN
ejpam-6082	64	3	,	,	PUNCT
ejpam-6082	64	4	with	with	ADP
ejpam-6082	64	5	regards	regard	NOUN
ejpam-6082	64	6	to	to	ADP
ejpam-6082	64	7	poliovirus	poliovirus	NOUN
ejpam-6082	64	8	,	,	PUNCT
ejpam-6082	64	9	its	its	PRON
ejpam-6082	64	10	portability	portability	NOUN
ejpam-6082	64	11	and	and	CCONJ
ejpam-6082	64	12	determination	determination	NOUN
ejpam-6082	64	13	are	be	AUX
ejpam-6082	64	14	intensely	intensely	ADV
ejpam-6082	64	15	affected	affect	VERB
ejpam-6082	64	16	by	by	ADP
ejpam-6082	64	17	the	the	DET
ejpam-6082	64	18	digestive	digestive	ADJ
ejpam-6082	64	19	system	system	NOUN
ejpam-6082	64	20	,	,	PUNCT
ejpam-6082	64	21	brain	brain	NOUN
ejpam-6082	64	22	tissues	tissue	NOUN
ejpam-6082	64	23	,	,	PUNCT
ejpam-6082	64	24	or	or	CCONJ
ejpam-6082	64	25	ecological	ecological	ADJ
ejpam-6082	64	26	repositories	repository	NOUN
ejpam-6082	64	27	,	,	PUNCT
ejpam-6082	64	28	for	for	ADP
ejpam-6082	64	29	example	example	NOUN
ejpam-6082	64	30	,	,	PUNCT
ejpam-6082	64	31	water	water	NOUN
ejpam-6082	64	32	and	and	CCONJ
ejpam-6082	64	33	soil	soil	NOUN
ejpam-6082	64	34	,	,	PUNCT
ejpam-6082	64	35	which	which	PRON
ejpam-6082	64	36	are	be	AUX
ejpam-6082	64	37	normal	normal	ADJ
ejpam-6082	64	38	transmission	transmission	NOUN
ejpam-6082	64	39	pathways	pathway	NOUN
ejpam-6082	64	40	.	.	PUNCT
ejpam-6082	65	1	to	to	PART
ejpam-6082	65	2	investigate	investigate	VERB
ejpam-6082	65	3	the	the	DET
ejpam-6082	65	4	effect	effect	NOUN
ejpam-6082	65	5	of	of	ADP
ejpam-6082	65	6	spatial	spatial	ADJ
ejpam-6082	65	7	heterogeneity	heterogeneity	NOUN
ejpam-6082	65	8	on	on	ADP
ejpam-6082	65	9	viral	viral	ADJ
ejpam-6082	65	10	elements	element	NOUN
ejpam-6082	65	11	,	,	PUNCT
ejpam-6082	65	12	scientists	scientist	NOUN
ejpam-6082	65	13	have	have	AUX
ejpam-6082	65	14	researched	research	VERB
ejpam-6082	65	15	response	response	NOUN
ejpam-6082	65	16	dispersion	dispersion	NOUN
ejpam-6082	65	17	models	model	NOUN
ejpam-6082	65	18	custom	custom	NOUN
ejpam-6082	65	19	fitted	fit	VERB
ejpam-6082	65	20	to	to	ADP
ejpam-6082	65	21	explicit	explicit	ADJ
ejpam-6082	65	22	infections	infection	NOUN
ejpam-6082	65	23	.	.	PUNCT
ejpam-6082	66	1	for	for	ADP
ejpam-6082	66	2	example	example	NOUN
ejpam-6082	66	3	,	,	PUNCT
ejpam-6082	66	4	pankavich	pankavich	PROPN
ejpam-6082	66	5	and	and	CCONJ
ejpam-6082	66	6	parkinson	parkinson	NOUN
ejpam-6082	67	1	[	[	X
ejpam-6082	67	2	25	25	NUM
ejpam-6082	67	3	]	]	PUNCT
ejpam-6082	67	4	broke	break	VERB
ejpam-6082	67	5	down	down	ADP
ejpam-6082	67	6	a	a	DET
ejpam-6082	67	7	response	response	NOUN
ejpam-6082	67	8	dissemination	dissemination	NOUN
ejpam-6082	67	9	model	model	NOUN
ejpam-6082	67	10	for	for	ADP
ejpam-6082	67	11	hiv	hiv	PROPN
ejpam-6082	67	12	contamination	contamination	NOUN
ejpam-6082	67	13	,	,	PUNCT
ejpam-6082	67	14	representing	represent	VERB
ejpam-6082	67	15	different	different	ADJ
ejpam-6082	67	16	dispersion	dispersion	NOUN
ejpam-6082	67	17	rates	rate	NOUN
ejpam-6082	67	18	among	among	ADP
ejpam-6082	67	19	target	target	NOUN
ejpam-6082	67	20	and	and	CCONJ
ejpam-6082	67	21	tainted	tainted	ADJ
ejpam-6082	67	22	cells	cell	NOUN
ejpam-6082	67	23	,	,	PUNCT
ejpam-6082	67	24	and	and	CCONJ
ejpam-6082	67	25	concentrated	concentrate	VERB
ejpam-6082	67	26	on	on	ADP
ejpam-6082	67	27	the	the	DET
ejpam-6082	67	28	worldwide	worldwide	ADJ
ejpam-6082	67	29	security	security	NOUN
ejpam-6082	67	30	of	of	ADP
ejpam-6082	67	31	the	the	DET
ejpam-6082	67	32	sickness	sickness	NOUN
ejpam-6082	67	33	free	free	ADJ
ejpam-6082	67	34	balance	balance	NOUN
ejpam-6082	67	35	.	.	PUNCT
ejpam-6082	68	1	likewise	likewise	ADV
ejpam-6082	68	2	,	,	PUNCT
ejpam-6082	68	3	cai	cai	PROPN
ejpam-6082	68	4	et	et	PROPN
ejpam-6082	68	5	al	al	PROPN
ejpam-6082	68	6	.	.	PUNCT
ejpam-6082	69	1	[	[	X
ejpam-6082	69	2	26	26	NUM
ejpam-6082	69	3	]	]	PUNCT
ejpam-6082	69	4	inspected	inspect	VERB
ejpam-6082	69	5	the	the	DET
ejpam-6082	69	6	spatial	spatial	ADJ
ejpam-6082	69	7	elements	element	NOUN
ejpam-6082	69	8	of	of	ADP
ejpam-6082	69	9	the	the	DET
ejpam-6082	69	10	zika	zika	NOUN
ejpam-6082	69	11	infection	infection	NOUN
ejpam-6082	69	12	,	,	PUNCT
ejpam-6082	69	13	consolidating	consolidate	VERB
ejpam-6082	69	14	particular	particular	ADJ
ejpam-6082	69	15	dissemination	dissemination	NOUN
ejpam-6082	69	16	coefficients	coefficient	NOUN
ejpam-6082	69	17	for	for	ADP
ejpam-6082	69	18	different	different	ADJ
ejpam-6082	69	19	specialists	specialist	NOUN
ejpam-6082	69	20	.	.	PUNCT
ejpam-6082	70	1	applying	apply	VERB
ejpam-6082	70	2	this	this	DET
ejpam-6082	70	3	way	way	NOUN
ejpam-6082	70	4	to	to	PART
ejpam-6082	70	5	deal	deal	VERB
ejpam-6082	70	6	with	with	ADP
ejpam-6082	70	7	poliovirus	poliovirus	NOUN
ejpam-6082	70	8	,	,	PUNCT
ejpam-6082	70	9	figuring	figure	VERB
ejpam-6082	70	10	out	out	ADP
ejpam-6082	70	11	the	the	DET
ejpam-6082	70	12	heterogeneous	heterogeneous	ADJ
ejpam-6082	70	13	dissemination	dissemination	NOUN
ejpam-6082	70	14	of	of	ADP
ejpam-6082	70	15	viral	viral	ADJ
ejpam-6082	70	16	particles	particle	NOUN
ejpam-6082	70	17	through	through	ADP
ejpam-6082	70	18	various	various	ADJ
ejpam-6082	70	19	mediums	medium	NOUN
ejpam-6082	70	20	like	like	ADP
ejpam-6082	70	21	feces	fece	NOUN
ejpam-6082	70	22	,	,	PUNCT
ejpam-6082	70	23	water	water	NOUN
ejpam-6082	70	24	,	,	PUNCT
ejpam-6082	70	25	or	or	CCONJ
ejpam-6082	70	26	air	air	NOUN
ejpam-6082	70	27	is	be	AUX
ejpam-6082	70	28	critical	critical	ADJ
ejpam-6082	70	29	for	for	ADP
ejpam-6082	70	30	precisely	precisely	ADV
ejpam-6082	70	31	displaying	display	VERB
ejpam-6082	70	32	its	its	PRON
ejpam-6082	70	33	spatial	spatial	ADJ
ejpam-6082	70	34	spread	spread	NOUN
ejpam-6082	70	35	.	.	PUNCT
ejpam-6082	71	1	fractional	fractional	ADJ
ejpam-6082	71	2	derivatives	derivative	NOUN
ejpam-6082	71	3	(	(	PUNCT
ejpam-6082	71	4	fds	fds	NOUN
ejpam-6082	71	5	)	)	PUNCT
ejpam-6082	71	6	,	,	PUNCT
ejpam-6082	71	7	representing	represent	VERB
ejpam-6082	71	8	derivatives	derivative	NOUN
ejpam-6082	71	9	of	of	ADP
ejpam-6082	71	10	non	non	ADJ
ejpam-6082	71	11	-	-	ADJ
ejpam-6082	71	12	integer	integer	ADJ
ejpam-6082	71	13	order	order	NOUN
ejpam-6082	71	14	,	,	PUNCT
ejpam-6082	71	15	have	have	AUX
ejpam-6082	71	16	emerged	emerge	VERB
ejpam-6082	71	17	as	as	ADP
ejpam-6082	71	18	a	a	DET
ejpam-6082	71	19	vital	vital	ADJ
ejpam-6082	71	20	component	component	NOUN
ejpam-6082	71	21	in	in	ADP
ejpam-6082	71	22	mathematical	mathematical	ADJ
ejpam-6082	71	23	models	model	NOUN
ejpam-6082	71	24	(	(	PUNCT
ejpam-6082	71	25	mms	mms	NOUN
ejpam-6082	71	26	)	)	PUNCT
ejpam-6082	71	27	due	due	ADP
ejpam-6082	71	28	to	to	ADP
ejpam-6082	71	29	their	their	PRON
ejpam-6082	71	30	ability	ability	NOUN
ejpam-6082	71	31	to	to	PART
ejpam-6082	71	32	incorporate	incorporate	VERB
ejpam-6082	71	33	k.	k.	PROPN
ejpam-6082	71	34	guedri	guedri	PROPN
ejpam-6082	71	35	et	et	PROPN
ejpam-6082	71	36	al	al	PROPN
ejpam-6082	71	37	.	.	PUNCT
ejpam-6082	71	38	/	/	SYM
ejpam-6082	71	39	eur	eur	PROPN
ejpam-6082	71	40	.	.	PUNCT
ejpam-6082	72	1	j.	j.	PROPN
ejpam-6082	72	2	pure	pure	PROPN
ejpam-6082	72	3	appl	appl	PROPN
ejpam-6082	72	4	.	.	PROPN
ejpam-6082	72	5	math	math	PROPN
ejpam-6082	72	6	,	,	PUNCT
ejpam-6082	72	7	18	18	NUM
ejpam-6082	72	8	(	(	PUNCT
ejpam-6082	72	9	2	2	NUM
ejpam-6082	72	10	)	)	PUNCT
ejpam-6082	72	11	(	(	PUNCT
ejpam-6082	72	12	2025	2025	NUM
ejpam-6082	72	13	)	)	PUNCT
ejpam-6082	72	14	,	,	PUNCT
ejpam-6082	72	15	6082	6082	NUM
ejpam-6082	72	16	4	4	NUM
ejpam-6082	72	17	of	of	ADP
ejpam-6082	72	18	39	39	NUM
ejpam-6082	72	19	memory	memory	NOUN
ejpam-6082	72	20	and	and	CCONJ
ejpam-6082	72	21	hereditary	hereditary	ADJ
ejpam-6082	72	22	effects	effect	NOUN
ejpam-6082	72	23	.	.	PUNCT
ejpam-6082	73	1	these	these	DET
ejpam-6082	73	2	properties	property	NOUN
ejpam-6082	73	3	are	be	AUX
ejpam-6082	73	4	particularly	particularly	ADV
ejpam-6082	73	5	advantageous	advantageous	ADJ
ejpam-6082	73	6	for	for	ADP
ejpam-6082	73	7	modeling	modeling	NOUN
ejpam-6082	73	8	processes	process	NOUN
ejpam-6082	73	9	where	where	SCONJ
ejpam-6082	73	10	the	the	DET
ejpam-6082	73	11	current	current	ADJ
ejpam-6082	73	12	state	state	NOUN
ejpam-6082	73	13	depends	depend	VERB
ejpam-6082	73	14	on	on	ADP
ejpam-6082	73	15	historical	historical	ADJ
ejpam-6082	73	16	influences	influence	NOUN
ejpam-6082	73	17	,	,	PUNCT
ejpam-6082	73	18	such	such	ADJ
ejpam-6082	73	19	as	as	ADP
ejpam-6082	73	20	in	in	ADP
ejpam-6082	73	21	infectious	infectious	ADJ
ejpam-6082	73	22	disease	disease	NOUN
ejpam-6082	73	23	dynamics	dynamic	NOUN
ejpam-6082	73	24	and	and	CCONJ
ejpam-6082	73	25	ecological	ecological	ADJ
ejpam-6082	73	26	systems	system	NOUN
ejpam-6082	73	27	.	.	PUNCT
ejpam-6082	74	1	unlike	unlike	ADP
ejpam-6082	74	2	classical	classical	ADJ
ejpam-6082	74	3	derivatives	derivative	NOUN
ejpam-6082	74	4	,	,	PUNCT
ejpam-6082	74	5	fds	fds	NOUN
ejpam-6082	74	6	offer	offer	VERB
ejpam-6082	74	7	greater	great	ADJ
ejpam-6082	74	8	flexibility	flexibility	NOUN
ejpam-6082	74	9	and	and	CCONJ
ejpam-6082	74	10	a	a	DET
ejpam-6082	74	11	higher	high	ADJ
ejpam-6082	74	12	degree	degree	NOUN
ejpam-6082	74	13	of	of	ADP
ejpam-6082	74	14	freedom	freedom	NOUN
ejpam-6082	74	15	,	,	PUNCT
ejpam-6082	74	16	enabling	enable	VERB
ejpam-6082	74	17	a	a	DET
ejpam-6082	74	18	more	more	ADV
ejpam-6082	74	19	precise	precise	ADJ
ejpam-6082	74	20	representation	representation	NOUN
ejpam-6082	74	21	of	of	ADP
ejpam-6082	74	22	complex	complex	ADJ
ejpam-6082	74	23	system	system	NOUN
ejpam-6082	74	24	dynamics	dynamic	NOUN
ejpam-6082	74	25	.	.	PUNCT
ejpam-6082	75	1	consequently	consequently	ADV
ejpam-6082	75	2	,	,	PUNCT
ejpam-6082	75	3	fractional	fractional	ADJ
ejpam-6082	75	4	-	-	PUNCT
ejpam-6082	75	5	order	order	NOUN
ejpam-6082	75	6	models	model	NOUN
ejpam-6082	75	7	(	(	PUNCT
ejpam-6082	75	8	foms	fom	NOUN
ejpam-6082	75	9	)	)	PUNCT
ejpam-6082	75	10	have	have	AUX
ejpam-6082	75	11	been	be	AUX
ejpam-6082	75	12	extensively	extensively	ADV
ejpam-6082	75	13	applied	apply	VERB
ejpam-6082	75	14	in	in	ADP
ejpam-6082	75	15	various	various	ADJ
ejpam-6082	75	16	domains	domain	NOUN
ejpam-6082	75	17	,	,	PUNCT
ejpam-6082	75	18	including	include	VERB
ejpam-6082	75	19	the	the	DET
ejpam-6082	75	20	study	study	NOUN
ejpam-6082	75	21	of	of	ADP
ejpam-6082	75	22	infectious	infectious	ADJ
ejpam-6082	75	23	diseases	disease	NOUN
ejpam-6082	75	24	[	[	X
ejpam-6082	75	25	27–33	27–33	NUM
ejpam-6082	75	26	]	]	X
ejpam-6082	75	27	,	,	PUNCT
ejpam-6082	75	28	physical	physical	ADJ
ejpam-6082	75	29	processes	process	NOUN
ejpam-6082	75	30	[	[	X
ejpam-6082	75	31	34	34	NUM
ejpam-6082	75	32	]	]	PUNCT
ejpam-6082	75	33	,	,	PUNCT
ejpam-6082	75	34	control	control	NOUN
ejpam-6082	75	35	theory	theory	NOUN
ejpam-6082	75	36	[	[	X
ejpam-6082	75	37	35	35	NUM
ejpam-6082	75	38	,	,	PUNCT
ejpam-6082	75	39	36	36	NUM
ejpam-6082	75	40	]	]	PUNCT
ejpam-6082	75	41	,	,	PUNCT
ejpam-6082	75	42	biology	biology	NOUN
ejpam-6082	75	43	[	[	X
ejpam-6082	75	44	37	37	NUM
ejpam-6082	75	45	]	]	PUNCT
ejpam-6082	75	46	,	,	PUNCT
ejpam-6082	75	47	viscoelastic	viscoelastic	ADJ
ejpam-6082	75	48	materials	material	NOUN
ejpam-6082	75	49	[	[	X
ejpam-6082	75	50	38	38	NUM
ejpam-6082	75	51	]	]	PUNCT
ejpam-6082	75	52	,	,	PUNCT
ejpam-6082	75	53	and	and	CCONJ
ejpam-6082	75	54	engineering	engineer	VERB
ejpam-6082	75	55	[	[	X
ejpam-6082	75	56	39	39	NUM
ejpam-6082	75	57	]	]	PUNCT
ejpam-6082	75	58	.	.	PUNCT
ejpam-6082	76	1	foms	fom	NOUN
ejpam-6082	76	2	possess	possess	VERB
ejpam-6082	76	3	unique	unique	ADJ
ejpam-6082	76	4	features	feature	NOUN
ejpam-6082	76	5	such	such	ADJ
ejpam-6082	76	6	as	as	ADP
ejpam-6082	76	7	the	the	DET
ejpam-6082	76	8	ability	ability	NOUN
ejpam-6082	76	9	to	to	PART
ejpam-6082	76	10	model	model	VERB
ejpam-6082	76	11	anomalous	anomalous	ADJ
ejpam-6082	76	12	diffusion	diffusion	NOUN
ejpam-6082	76	13	,	,	PUNCT
ejpam-6082	76	14	account	account	VERB
ejpam-6082	76	15	for	for	ADP
ejpam-6082	76	16	intrinsic	intrinsic	ADJ
ejpam-6082	76	17	memory	memory	NOUN
ejpam-6082	76	18	effects	effect	NOUN
ejpam-6082	76	19	,	,	PUNCT
ejpam-6082	76	20	capture	capture	VERB
ejpam-6082	76	21	fractal	fractal	ADJ
ejpam-6082	76	22	structures	structure	NOUN
ejpam-6082	76	23	,	,	PUNCT
ejpam-6082	76	24	fit	fit	ADJ
ejpam-6082	76	25	data	datum	NOUN
ejpam-6082	76	26	more	more	ADV
ejpam-6082	76	27	effectively	effectively	ADV
ejpam-6082	76	28	,	,	PUNCT
ejpam-6082	76	29	and	and	CCONJ
ejpam-6082	76	30	handle	handle	VERB
ejpam-6082	76	31	multiscale	multiscale	ADJ
ejpam-6082	76	32	phenomena	phenomenon	NOUN
ejpam-6082	76	33	.	.	PUNCT
ejpam-6082	77	1	these	these	DET
ejpam-6082	77	2	characteristics	characteristic	NOUN
ejpam-6082	77	3	make	make	VERB
ejpam-6082	77	4	foms	fom	NOUN
ejpam-6082	77	5	a	a	DET
ejpam-6082	77	6	powerful	powerful	ADJ
ejpam-6082	77	7	framework	framework	NOUN
ejpam-6082	77	8	for	for	ADP
ejpam-6082	77	9	incorporating	incorporate	VERB
ejpam-6082	77	10	memory	memory	NOUN
ejpam-6082	77	11	and	and	CCONJ
ejpam-6082	77	12	hereditary	hereditary	ADJ
ejpam-6082	77	13	properties	property	NOUN
ejpam-6082	77	14	into	into	ADP
ejpam-6082	77	15	infectious	infectious	ADJ
ejpam-6082	77	16	disease	disease	NOUN
ejpam-6082	77	17	models	model	NOUN
ejpam-6082	77	18	,	,	PUNCT
ejpam-6082	77	19	surpassing	surpass	VERB
ejpam-6082	77	20	the	the	DET
ejpam-6082	77	21	capabilities	capability	NOUN
ejpam-6082	77	22	of	of	ADP
ejpam-6082	77	23	integer	integer	NOUN
ejpam-6082	77	24	-	-	PUNCT
ejpam-6082	77	25	order	order	NOUN
ejpam-6082	77	26	models	model	NOUN
ejpam-6082	77	27	,	,	PUNCT
ejpam-6082	77	28	which	which	PRON
ejpam-6082	77	29	lack	lack	VERB
ejpam-6082	77	30	non	non	ADJ
ejpam-6082	77	31	-	-	ADJ
ejpam-6082	77	32	local	local	ADJ
ejpam-6082	77	33	interactions	interaction	NOUN
ejpam-6082	77	34	and	and	CCONJ
ejpam-6082	77	35	memory	memory	NOUN
ejpam-6082	77	36	effects	effect	NOUN
ejpam-6082	77	37	.	.	PUNCT
ejpam-6082	78	1	the	the	DET
ejpam-6082	78	2	growing	grow	VERB
ejpam-6082	78	3	interest	interest	NOUN
ejpam-6082	78	4	in	in	ADP
ejpam-6082	78	5	fractional	fractional	ADJ
ejpam-6082	78	6	calculus	calculus	NOUN
ejpam-6082	78	7	(	(	PUNCT
ejpam-6082	78	8	fc	fc	X
ejpam-6082	78	9	)	)	PUNCT
ejpam-6082	78	10	has	have	AUX
ejpam-6082	78	11	led	lead	VERB
ejpam-6082	78	12	to	to	ADP
ejpam-6082	78	13	the	the	DET
ejpam-6082	78	14	development	development	NOUN
ejpam-6082	78	15	of	of	ADP
ejpam-6082	78	16	multiple	multiple	ADJ
ejpam-6082	78	17	definitions	definition	NOUN
ejpam-6082	78	18	of	of	ADP
ejpam-6082	78	19	fds	fds	NOUN
ejpam-6082	78	20	,	,	PUNCT
ejpam-6082	78	21	each	each	PRON
ejpam-6082	78	22	with	with	ADP
ejpam-6082	78	23	distinct	distinct	ADJ
ejpam-6082	78	24	advantages	advantage	NOUN
ejpam-6082	78	25	.	.	PUNCT
ejpam-6082	79	1	among	among	ADP
ejpam-6082	79	2	these	these	PRON
ejpam-6082	79	3	,	,	PUNCT
ejpam-6082	79	4	the	the	DET
ejpam-6082	79	5	caputo	caputo	PROPN
ejpam-6082	79	6	and	and	CCONJ
ejpam-6082	79	7	riemann	riemann	PROPN
ejpam-6082	79	8	–	–	PUNCT
ejpam-6082	79	9	liouville	liouville	VERB
ejpam-6082	79	10	derivatives	derivative	NOUN
ejpam-6082	79	11	remain	remain	VERB
ejpam-6082	79	12	the	the	PRON
ejpam-6082	79	13	most	most	ADV
ejpam-6082	79	14	commonly	commonly	ADV
ejpam-6082	79	15	used	use	VERB
ejpam-6082	79	16	[	[	X
ejpam-6082	79	17	40	40	NUM
ejpam-6082	79	18	,	,	PUNCT
ejpam-6082	79	19	41	41	NUM
ejpam-6082	79	20	]	]	PUNCT
ejpam-6082	79	21	.	.	PUNCT
ejpam-6082	80	1	fractional	fractional	ADJ
ejpam-6082	80	2	-	-	PUNCT
ejpam-6082	80	3	order	order	NOUN
ejpam-6082	80	4	models	model	NOUN
ejpam-6082	80	5	based	base	VERB
ejpam-6082	80	6	on	on	ADP
ejpam-6082	80	7	these	these	DET
ejpam-6082	80	8	derivatives	derivative	NOUN
ejpam-6082	80	9	have	have	AUX
ejpam-6082	80	10	demonstrated	demonstrate	VERB
ejpam-6082	80	11	superior	superior	ADJ
ejpam-6082	80	12	accuracy	accuracy	NOUN
ejpam-6082	80	13	in	in	ADP
ejpam-6082	80	14	describing	describe	VERB
ejpam-6082	80	15	disease	disease	NOUN
ejpam-6082	80	16	progression	progression	NOUN
ejpam-6082	80	17	compared	compare	VERB
ejpam-6082	80	18	to	to	ADP
ejpam-6082	80	19	classical	classical	ADJ
ejpam-6082	80	20	models	model	NOUN
ejpam-6082	80	21	[	[	X
ejpam-6082	80	22	42	42	NUM
ejpam-6082	80	23	]	]	PUNCT
ejpam-6082	80	24	.	.	PUNCT
ejpam-6082	81	1	traditional	traditional	ADJ
ejpam-6082	81	2	ordinary	ordinary	ADJ
ejpam-6082	81	3	differential	differential	ADJ
ejpam-6082	81	4	equations	equation	NOUN
ejpam-6082	81	5	(	(	PUNCT
ejpam-6082	81	6	odes	ode	NOUN
ejpam-6082	81	7	)	)	PUNCT
ejpam-6082	81	8	often	often	ADV
ejpam-6082	81	9	fail	fail	VERB
ejpam-6082	81	10	to	to	PART
ejpam-6082	81	11	adequately	adequately	ADV
ejpam-6082	81	12	capture	capture	VERB
ejpam-6082	81	13	the	the	DET
ejpam-6082	81	14	discontinuous	discontinuous	ADJ
ejpam-6082	81	15	nature	nature	NOUN
ejpam-6082	81	16	of	of	ADP
ejpam-6082	81	17	disease	disease	NOUN
ejpam-6082	81	18	spread	spread	VERB
ejpam-6082	81	19	,	,	PUNCT
ejpam-6082	81	20	whereas	whereas	SCONJ
ejpam-6082	81	21	fractional	fractional	ADJ
ejpam-6082	81	22	-	-	PUNCT
ejpam-6082	81	23	order	order	NOUN
ejpam-6082	81	24	models	model	NOUN
ejpam-6082	81	25	effectively	effectively	ADV
ejpam-6082	81	26	address	address	VERB
ejpam-6082	81	27	these	these	DET
ejpam-6082	81	28	limitations	limitation	NOUN
ejpam-6082	81	29	[	[	X
ejpam-6082	81	30	43	43	NUM
ejpam-6082	81	31	]	]	PUNCT
ejpam-6082	81	32	.	.	PUNCT
ejpam-6082	82	1	the	the	DET
ejpam-6082	82	2	use	use	NOUN
ejpam-6082	82	3	of	of	ADP
ejpam-6082	82	4	fractional	fractional	ADJ
ejpam-6082	82	5	derivatives	derivative	NOUN
ejpam-6082	82	6	,	,	PUNCT
ejpam-6082	82	7	particularly	particularly	ADV
ejpam-6082	82	8	the	the	DET
ejpam-6082	82	9	caputo	caputo	PROPN
ejpam-6082	82	10	fd	fd	PROPN
ejpam-6082	82	11	,	,	PUNCT
ejpam-6082	82	12	in	in	ADP
ejpam-6082	82	13	mathematical	mathematical	ADJ
ejpam-6082	82	14	epidemiology	epidemiology	NOUN
ejpam-6082	82	15	has	have	AUX
ejpam-6082	82	16	been	be	AUX
ejpam-6082	82	17	shown	show	VERB
ejpam-6082	82	18	to	to	PART
ejpam-6082	82	19	improve	improve	VERB
ejpam-6082	82	20	the	the	DET
ejpam-6082	82	21	realism	realism	NOUN
ejpam-6082	82	22	and	and	CCONJ
ejpam-6082	82	23	accuracy	accuracy	NOUN
ejpam-6082	82	24	of	of	ADP
ejpam-6082	82	25	infectious	infectious	ADJ
ejpam-6082	82	26	disease	disease	NOUN
ejpam-6082	82	27	dynamics	dynamic	NOUN
ejpam-6082	82	28	[	[	X
ejpam-6082	82	29	40	40	NUM
ejpam-6082	82	30	,	,	PUNCT
ejpam-6082	82	31	44	44	NUM
ejpam-6082	82	32	]	]	PUNCT
ejpam-6082	82	33	.	.	PUNCT
ejpam-6082	83	1	the	the	DET
ejpam-6082	83	2	novelty	novelty	NOUN
ejpam-6082	83	3	of	of	ADP
ejpam-6082	83	4	this	this	DET
ejpam-6082	83	5	research	research	NOUN
ejpam-6082	83	6	lies	lie	VERB
ejpam-6082	83	7	in	in	ADP
ejpam-6082	83	8	extending	extend	VERB
ejpam-6082	83	9	the	the	DET
ejpam-6082	83	10	classical	classical	ADJ
ejpam-6082	83	11	ordinary	ordinary	ADJ
ejpam-6082	83	12	differential	differential	ADJ
ejpam-6082	83	13	equation	equation	NOUN
ejpam-6082	83	14	(	(	PUNCT
ejpam-6082	83	15	ode)-based	ode)-base	VERB
ejpam-6082	83	16	polio	polio	NOUN
ejpam-6082	83	17	transmission	transmission	NOUN
ejpam-6082	83	18	models	model	NOUN
ejpam-6082	83	19	to	to	ADP
ejpam-6082	83	20	a	a	DET
ejpam-6082	83	21	more	more	ADV
ejpam-6082	83	22	comprehensive	comprehensive	ADJ
ejpam-6082	83	23	fractional	fractional	ADJ
ejpam-6082	83	24	reactiondiffusion	reactiondiffusion	NOUN
ejpam-6082	83	25	framework	framework	NOUN
ejpam-6082	83	26	.	.	PUNCT
ejpam-6082	84	1	while	while	SCONJ
ejpam-6082	84	2	traditional	traditional	ADJ
ejpam-6082	84	3	ode	ode	ADJ
ejpam-6082	84	4	models	model	NOUN
ejpam-6082	84	5	effectively	effectively	ADV
ejpam-6082	84	6	describe	describe	VERB
ejpam-6082	84	7	temporal	temporal	ADJ
ejpam-6082	84	8	dynamics	dynamic	NOUN
ejpam-6082	84	9	,	,	PUNCT
ejpam-6082	84	10	they	they	PRON
ejpam-6082	84	11	assume	assume	VERB
ejpam-6082	84	12	spatial	spatial	ADJ
ejpam-6082	84	13	uniformity	uniformity	NOUN
ejpam-6082	84	14	,	,	PUNCT
ejpam-6082	84	15	an	an	DET
ejpam-6082	84	16	oversimplification	oversimplification	NOUN
ejpam-6082	84	17	in	in	ADP
ejpam-6082	84	18	the	the	DET
ejpam-6082	84	19	context	context	NOUN
ejpam-6082	84	20	of	of	ADP
ejpam-6082	84	21	real	real	ADJ
ejpam-6082	84	22	-	-	PUNCT
ejpam-6082	84	23	world	world	NOUN
ejpam-6082	84	24	disease	disease	NOUN
ejpam-6082	84	25	transmission	transmission	NOUN
ejpam-6082	84	26	influenced	influence	VERB
ejpam-6082	84	27	by	by	ADP
ejpam-6082	84	28	environmental	environmental	ADJ
ejpam-6082	84	29	heterogeneity	heterogeneity	NOUN
ejpam-6082	84	30	and	and	CCONJ
ejpam-6082	84	31	human	human	ADJ
ejpam-6082	84	32	mobility	mobility	NOUN
ejpam-6082	84	33	.	.	PUNCT
ejpam-6082	85	1	by	by	ADP
ejpam-6082	85	2	incorporating	incorporate	VERB
ejpam-6082	85	3	diffusion	diffusion	NOUN
ejpam-6082	85	4	terms	term	NOUN
ejpam-6082	85	5	into	into	ADP
ejpam-6082	85	6	the	the	DET
ejpam-6082	85	7	model	model	NOUN
ejpam-6082	85	8	,	,	PUNCT
ejpam-6082	85	9	this	this	DET
ejpam-6082	85	10	study	study	NOUN
ejpam-6082	85	11	accounts	account	VERB
ejpam-6082	85	12	for	for	ADP
ejpam-6082	85	13	spatial	spatial	ADJ
ejpam-6082	85	14	heterogeneity	heterogeneity	NOUN
ejpam-6082	85	15	,	,	PUNCT
ejpam-6082	85	16	reflecting	reflect	VERB
ejpam-6082	85	17	the	the	DET
ejpam-6082	85	18	localized	localize	VERB
ejpam-6082	85	19	impact	impact	NOUN
ejpam-6082	85	20	of	of	ADP
ejpam-6082	85	21	population	population	NOUN
ejpam-6082	85	22	density	density	NOUN
ejpam-6082	85	23	,	,	PUNCT
ejpam-6082	85	24	sanitation	sanitation	NOUN
ejpam-6082	85	25	conditions	condition	NOUN
ejpam-6082	85	26	,	,	PUNCT
ejpam-6082	85	27	and	and	CCONJ
ejpam-6082	85	28	vaccination	vaccination	NOUN
ejpam-6082	85	29	efforts	effort	NOUN
ejpam-6082	85	30	on	on	ADP
ejpam-6082	85	31	poliovirus	poliovirus	NOUN
ejpam-6082	85	32	dynamics	dynamic	NOUN
ejpam-6082	85	33	.	.	PUNCT
ejpam-6082	86	1	furthermore	furthermore	ADV
ejpam-6082	86	2	,	,	PUNCT
ejpam-6082	86	3	replacing	replace	VERB
ejpam-6082	86	4	classical	classical	ADJ
ejpam-6082	86	5	time	time	NOUN
ejpam-6082	86	6	derivatives	derivative	NOUN
ejpam-6082	86	7	with	with	ADP
ejpam-6082	86	8	caputo	caputo	PROPN
ejpam-6082	86	9	fractional	fractional	ADJ
ejpam-6082	86	10	derivatives	derivative	NOUN
ejpam-6082	86	11	introduces	introduce	VERB
ejpam-6082	86	12	memory	memory	NOUN
ejpam-6082	86	13	effects	effect	NOUN
ejpam-6082	86	14	and	and	CCONJ
ejpam-6082	86	15	non	non	ADJ
ejpam-6082	86	16	-	-	ADJ
ejpam-6082	86	17	local	local	ADJ
ejpam-6082	86	18	temporal	temporal	ADJ
ejpam-6082	86	19	interactions	interaction	NOUN
ejpam-6082	86	20	into	into	ADP
ejpam-6082	86	21	the	the	DET
ejpam-6082	86	22	model	model	NOUN
ejpam-6082	86	23	,	,	PUNCT
ejpam-6082	86	24	which	which	PRON
ejpam-6082	86	25	are	be	AUX
ejpam-6082	86	26	crucial	crucial	ADJ
ejpam-6082	86	27	for	for	ADP
ejpam-6082	86	28	accurately	accurately	ADV
ejpam-6082	86	29	capturing	capture	VERB
ejpam-6082	86	30	the	the	DET
ejpam-6082	86	31	history	history	NOUN
ejpam-6082	86	32	-	-	PUNCT
ejpam-6082	86	33	dependent	dependent	ADJ
ejpam-6082	86	34	nature	nature	NOUN
ejpam-6082	86	35	of	of	ADP
ejpam-6082	86	36	disease	disease	NOUN
ejpam-6082	86	37	progression	progression	NOUN
ejpam-6082	86	38	.	.	PUNCT
ejpam-6082	87	1	this	this	DET
ejpam-6082	87	2	combined	combine	VERB
ejpam-6082	87	3	fractional	fractional	ADJ
ejpam-6082	87	4	reaction	reaction	NOUN
ejpam-6082	87	5	-	-	PUNCT
ejpam-6082	87	6	diffusion	diffusion	NOUN
ejpam-6082	87	7	framework	framework	NOUN
ejpam-6082	87	8	offers	offer	VERB
ejpam-6082	87	9	significant	significant	ADJ
ejpam-6082	87	10	advantages	advantage	NOUN
ejpam-6082	87	11	over	over	ADP
ejpam-6082	87	12	fractional	fractional	ADJ
ejpam-6082	87	13	odes	ode	NOUN
ejpam-6082	87	14	by	by	ADP
ejpam-6082	87	15	integrating	integrate	VERB
ejpam-6082	87	16	both	both	CCONJ
ejpam-6082	87	17	spatial	spatial	ADJ
ejpam-6082	87	18	and	and	CCONJ
ejpam-6082	87	19	temporal	temporal	ADJ
ejpam-6082	87	20	complexity	complexity	NOUN
ejpam-6082	87	21	,	,	PUNCT
ejpam-6082	87	22	providing	provide	VERB
ejpam-6082	87	23	a	a	DET
ejpam-6082	87	24	more	more	ADV
ejpam-6082	87	25	realistic	realistic	ADJ
ejpam-6082	87	26	and	and	CCONJ
ejpam-6082	87	27	precise	precise	ADJ
ejpam-6082	87	28	depiction	depiction	NOUN
ejpam-6082	87	29	of	of	ADP
ejpam-6082	87	30	poliovirus	poliovirus	NOUN
ejpam-6082	87	31	spread	spread	NOUN
ejpam-6082	87	32	.	.	PUNCT
ejpam-6082	88	1	the	the	DET
ejpam-6082	88	2	proposed	propose	VERB
ejpam-6082	88	3	model	model	NOUN
ejpam-6082	88	4	not	not	PART
ejpam-6082	88	5	only	only	ADV
ejpam-6082	88	6	enhances	enhance	VERB
ejpam-6082	88	7	our	our	PRON
ejpam-6082	88	8	understanding	understanding	NOUN
ejpam-6082	88	9	of	of	ADP
ejpam-6082	88	10	spatially	spatially	ADV
ejpam-6082	88	11	heterogeneous	heterogeneous	ADJ
ejpam-6082	88	12	disease	disease	NOUN
ejpam-6082	88	13	dynamics	dynamic	NOUN
ejpam-6082	88	14	but	but	CCONJ
ejpam-6082	88	15	also	also	ADV
ejpam-6082	88	16	offers	offer	VERB
ejpam-6082	88	17	a	a	DET
ejpam-6082	88	18	valuable	valuable	ADJ
ejpam-6082	88	19	tool	tool	NOUN
ejpam-6082	88	20	for	for	ADP
ejpam-6082	88	21	informing	inform	VERB
ejpam-6082	88	22	effective	effective	ADJ
ejpam-6082	88	23	intervention	intervention	NOUN
ejpam-6082	88	24	strategies	strategy	NOUN
ejpam-6082	88	25	and	and	CCONJ
ejpam-6082	88	26	predicting	predict	VERB
ejpam-6082	88	27	outbreak	outbreak	NOUN
ejpam-6082	88	28	scenarios	scenario	NOUN
ejpam-6082	88	29	in	in	ADP
ejpam-6082	88	30	diverse	diverse	ADJ
ejpam-6082	88	31	populations	population	NOUN
ejpam-6082	88	32	.	.	PUNCT
ejpam-6082	89	1	k.	k.	PROPN
ejpam-6082	89	2	guedri	guedri	PROPN
ejpam-6082	89	3	et	et	PROPN
ejpam-6082	89	4	al	al	PROPN
ejpam-6082	89	5	.	.	PUNCT
ejpam-6082	89	6	/	/	SYM
ejpam-6082	89	7	eur	eur	PROPN
ejpam-6082	89	8	.	.	PUNCT
ejpam-6082	90	1	j.	j.	PROPN
ejpam-6082	90	2	pure	pure	PROPN
ejpam-6082	90	3	appl	appl	PROPN
ejpam-6082	90	4	.	.	PROPN
ejpam-6082	90	5	math	math	PROPN
ejpam-6082	90	6	,	,	PUNCT
ejpam-6082	90	7	18	18	NUM
ejpam-6082	90	8	(	(	PUNCT
ejpam-6082	90	9	2	2	NUM
ejpam-6082	90	10	)	)	PUNCT
ejpam-6082	90	11	(	(	PUNCT
ejpam-6082	90	12	2025	2025	NUM
ejpam-6082	90	13	)	)	PUNCT
ejpam-6082	90	14	,	,	PUNCT
ejpam-6082	90	15	6082	6082	NUM
ejpam-6082	90	16	5	5	NUM
ejpam-6082	90	17	of	of	ADP
ejpam-6082	90	18	39	39	NUM
ejpam-6082	90	19	2	2	NUM
ejpam-6082	90	20	.	.	PUNCT
ejpam-6082	90	21	model	model	NOUN
ejpam-6082	90	22	formulation	formulation	NOUN
ejpam-6082	90	23	the	the	DET
ejpam-6082	90	24	population	population	NOUN
ejpam-6082	90	25	under	under	ADP
ejpam-6082	90	26	study	study	NOUN
ejpam-6082	90	27	is	be	AUX
ejpam-6082	90	28	categorized	categorize	VERB
ejpam-6082	90	29	into	into	ADP
ejpam-6082	90	30	seven	seven	NUM
ejpam-6082	90	31	distinct	distinct	ADJ
ejpam-6082	90	32	compartments	compartment	NOUN
ejpam-6082	90	33	based	base	VERB
ejpam-6082	90	34	on	on	ADP
ejpam-6082	90	35	the	the	DET
ejpam-6082	90	36	epidemiological	epidemiological	ADJ
ejpam-6082	90	37	state	state	NOUN
ejpam-6082	90	38	of	of	ADP
ejpam-6082	90	39	individuals	individual	NOUN
ejpam-6082	90	40	.	.	PUNCT
ejpam-6082	91	1	these	these	DET
ejpam-6082	91	2	compartments	compartment	NOUN
ejpam-6082	91	3	are	be	AUX
ejpam-6082	91	4	:	:	PUNCT
ejpam-6082	91	5	susceptible	susceptible	ADJ
ejpam-6082	91	6	(	(	PUNCT
ejpam-6082	91	7	s(t	s(t	PROPN
ejpam-6082	91	8	)	)	PUNCT
ejpam-6082	91	9	)	)	PUNCT
ejpam-6082	91	10	,	,	PUNCT
ejpam-6082	91	11	vaccinated	vaccinate	VERB
ejpam-6082	91	12	(	(	PUNCT
ejpam-6082	91	13	v	v	NOUN
ejpam-6082	91	14	(	(	PUNCT
ejpam-6082	91	15	t	t	PROPN
ejpam-6082	91	16	)	)	PUNCT
ejpam-6082	91	17	)	)	PUNCT
ejpam-6082	91	18	,	,	PUNCT
ejpam-6082	91	19	exposed	expose	VERB
ejpam-6082	91	20	(	(	PUNCT
ejpam-6082	91	21	e(t	e(t	NOUN
ejpam-6082	91	22	)	)	PUNCT
ejpam-6082	91	23	)	)	PUNCT
ejpam-6082	91	24	,	,	PUNCT
ejpam-6082	91	25	infected	infect	VERB
ejpam-6082	91	26	non	non	ADJ
ejpam-6082	91	27	-	-	ADJ
ejpam-6082	91	28	paralytic	paralytic	ADJ
ejpam-6082	91	29	(	(	PUNCT
ejpam-6082	91	30	np(t	np(t	NOUN
ejpam-6082	91	31	)	)	PUNCT
ejpam-6082	91	32	)	)	PUNCT
ejpam-6082	91	33	,	,	PUNCT
ejpam-6082	91	34	infected	infect	VERB
ejpam-6082	91	35	paralytic	paralytic	NOUN
ejpam-6082	91	36	(	(	PUNCT
ejpam-6082	91	37	p	p	X
ejpam-6082	91	38	(	(	PUNCT
ejpam-6082	91	39	t	t	PROPN
ejpam-6082	91	40	)	)	PUNCT
ejpam-6082	91	41	)	)	PUNCT
ejpam-6082	91	42	,	,	PUNCT
ejpam-6082	91	43	recovered	recover	VERB
ejpam-6082	91	44	(	(	PUNCT
ejpam-6082	91	45	r(t	r(t	NOUN
ejpam-6082	91	46	)	)	PUNCT
ejpam-6082	91	47	)	)	PUNCT
ejpam-6082	91	48	,	,	PUNCT
ejpam-6082	91	49	and	and	CCONJ
ejpam-6082	91	50	post	post	ADJ
ejpam-6082	91	51	-	-	ADJ
ejpam-6082	91	52	paralytic	paralytic	ADJ
ejpam-6082	91	53	(	(	PUNCT
ejpam-6082	91	54	a(t	a(t	NOUN
ejpam-6082	91	55	)	)	PUNCT
ejpam-6082	91	56	)	)	PUNCT
ejpam-6082	91	57	.	.	PUNCT
ejpam-6082	92	1	the	the	DET
ejpam-6082	92	2	total	total	ADJ
ejpam-6082	92	3	population	population	NOUN
ejpam-6082	92	4	size	size	NOUN
ejpam-6082	92	5	is	be	AUX
ejpam-6082	92	6	expressed	express	VERB
ejpam-6082	92	7	as	as	ADP
ejpam-6082	92	8	:	:	PUNCT
ejpam-6082	92	9	n	n	PROPN
ejpam-6082	92	10	=	=	SYM
ejpam-6082	92	11	s	s	PART
ejpam-6082	92	12	+	+	X
ejpam-6082	92	13	v	v	NOUN
ejpam-6082	92	14	+	+	CCONJ
ejpam-6082	92	15	e	e	NOUN
ejpam-6082	92	16	+	+	NOUN
ejpam-6082	92	17	np	np	VERB
ejpam-6082	92	18	+	+	NOUN
ejpam-6082	92	19	p	p	X
ejpam-6082	92	20	+	+	PROPN
ejpam-6082	92	21	r+a	r+a	PROPN
ejpam-6082	92	22	.	.	PUNCT
ejpam-6082	92	23	susceptible	susceptible	ADJ
ejpam-6082	92	24	individuals	individual	NOUN
ejpam-6082	92	25	increase	increase	VERB
ejpam-6082	92	26	in	in	ADP
ejpam-6082	92	27	number	number	NOUN
ejpam-6082	92	28	due	due	ADP
ejpam-6082	92	29	to	to	ADP
ejpam-6082	92	30	recruitment	recruitment	NOUN
ejpam-6082	92	31	through	through	ADP
ejpam-6082	92	32	births	birth	NOUN
ejpam-6082	92	33	and	and	CCONJ
ejpam-6082	92	34	immigration	immigration	NOUN
ejpam-6082	92	35	at	at	ADP
ejpam-6082	92	36	a	a	DET
ejpam-6082	92	37	constant	constant	ADJ
ejpam-6082	92	38	rate	rate	NOUN
ejpam-6082	92	39	λ	λ	PROPN
ejpam-6082	92	40	.	.	PUNCT
ejpam-6082	93	1	they	they	PRON
ejpam-6082	93	2	are	be	AUX
ejpam-6082	93	3	exposed	expose	VERB
ejpam-6082	93	4	to	to	ADP
ejpam-6082	93	5	the	the	DET
ejpam-6082	93	6	polio	polio	NOUN
ejpam-6082	93	7	virus	virus	NOUN
ejpam-6082	93	8	via	via	ADP
ejpam-6082	93	9	contact	contact	NOUN
ejpam-6082	93	10	with	with	ADP
ejpam-6082	93	11	environmental	environmental	ADJ
ejpam-6082	93	12	contamination	contamination	NOUN
ejpam-6082	93	13	originating	originate	VERB
ejpam-6082	93	14	from	from	ADP
ejpam-6082	93	15	sources	source	NOUN
ejpam-6082	93	16	such	such	ADJ
ejpam-6082	93	17	as	as	ADP
ejpam-6082	93	18	infected	infected	ADJ
ejpam-6082	93	19	individuals	individual	NOUN
ejpam-6082	93	20	(	(	PUNCT
ejpam-6082	93	21	e	e	NOUN
ejpam-6082	93	22	,	,	PUNCT
ejpam-6082	93	23	np	np	INTJ
ejpam-6082	93	24	,	,	PUNCT
ejpam-6082	93	25	p	p	NOUN
ejpam-6082	93	26	)	)	PUNCT
ejpam-6082	93	27	.	.	PUNCT
ejpam-6082	94	1	the	the	DET
ejpam-6082	94	2	rate	rate	NOUN
ejpam-6082	94	3	of	of	ADP
ejpam-6082	94	4	exposure	exposure	NOUN
ejpam-6082	94	5	to	to	ADP
ejpam-6082	94	6	the	the	DET
ejpam-6082	94	7	virus	virus	NOUN
ejpam-6082	94	8	is	be	AUX
ejpam-6082	94	9	represented	represent	VERB
ejpam-6082	94	10	by	by	ADP
ejpam-6082	94	11	:	:	PUNCT
ejpam-6082	94	12	λ	λ	X
ejpam-6082	94	13	=	=	VERB
ejpam-6082	94	14	βcτ	βcτ	NOUN
ejpam-6082	94	15	(	(	PUNCT
ejpam-6082	94	16	e	e	X
ejpam-6082	94	17	+	+	NOUN
ejpam-6082	94	18	np	np	NOUN
ejpam-6082	94	19	+	+	X
ejpam-6082	94	20	p	p	NOUN
ejpam-6082	94	21	)	)	PUNCT
ejpam-6082	94	22	n	n	NOUN
ejpam-6082	94	23	,	,	PUNCT
ejpam-6082	94	24	where	where	SCONJ
ejpam-6082	94	25	β	β	PROPN
ejpam-6082	94	26	denotes	denote	VERB
ejpam-6082	94	27	the	the	DET
ejpam-6082	94	28	likelihood	likelihood	NOUN
ejpam-6082	94	29	of	of	ADP
ejpam-6082	94	30	transmission	transmission	NOUN
ejpam-6082	94	31	from	from	ADP
ejpam-6082	94	32	an	an	DET
ejpam-6082	94	33	infectious	infectious	ADJ
ejpam-6082	94	34	source	source	NOUN
ejpam-6082	94	35	,	,	PUNCT
ejpam-6082	94	36	c	c	PROPN
ejpam-6082	94	37	represents	represent	VERB
ejpam-6082	94	38	the	the	DET
ejpam-6082	94	39	average	average	ADJ
ejpam-6082	94	40	contact	contact	NOUN
ejpam-6082	94	41	rate	rate	NOUN
ejpam-6082	94	42	with	with	ADP
ejpam-6082	94	43	contaminated	contaminate	VERB
ejpam-6082	94	44	fecal	fecal	ADJ
ejpam-6082	94	45	waste	waste	NOUN
ejpam-6082	94	46	per	per	ADP
ejpam-6082	94	47	unit	unit	NOUN
ejpam-6082	94	48	time	time	NOUN
ejpam-6082	94	49	,	,	PUNCT
ejpam-6082	94	50	and	and	CCONJ
ejpam-6082	94	51	τ	τ	X
ejpam-6082	94	52	>	>	X
ejpam-6082	94	53	1	1	NUM
ejpam-6082	94	54	is	be	AUX
ejpam-6082	94	55	a	a	DET
ejpam-6082	94	56	factor	factor	NOUN
ejpam-6082	94	57	accounting	account	VERB
ejpam-6082	94	58	for	for	ADP
ejpam-6082	94	59	enhanced	enhanced	ADJ
ejpam-6082	94	60	environmental	environmental	ADJ
ejpam-6082	94	61	contamination	contamination	NOUN
ejpam-6082	94	62	due	due	ADP
ejpam-6082	94	63	to	to	ADP
ejpam-6082	94	64	poor	poor	ADJ
ejpam-6082	94	65	sanitation	sanitation	NOUN
ejpam-6082	94	66	practices	practice	NOUN
ejpam-6082	94	67	,	,	PUNCT
ejpam-6082	94	68	such	such	ADJ
ejpam-6082	94	69	as	as	ADP
ejpam-6082	94	70	open	open	ADJ
ejpam-6082	94	71	defecation	defecation	NOUN
ejpam-6082	94	72	.	.	PUNCT
ejpam-6082	95	1	individuals	individual	NOUN
ejpam-6082	95	2	in	in	ADP
ejpam-6082	95	3	the	the	DET
ejpam-6082	95	4	susceptible	susceptible	ADJ
ejpam-6082	95	5	compartment	compartment	NOUN
ejpam-6082	95	6	(	(	PUNCT
ejpam-6082	95	7	s	s	NOUN
ejpam-6082	95	8	)	)	PUNCT
ejpam-6082	95	9	transition	transition	NOUN
ejpam-6082	95	10	to	to	ADP
ejpam-6082	95	11	the	the	DET
ejpam-6082	95	12	exposed	expose	VERB
ejpam-6082	95	13	compartment	compartment	NOUN
ejpam-6082	95	14	upon	upon	SCONJ
ejpam-6082	95	15	infection	infection	NOUN
ejpam-6082	95	16	,	,	PUNCT
ejpam-6082	95	17	driven	drive	VERB
ejpam-6082	95	18	by	by	ADP
ejpam-6082	95	19	the	the	DET
ejpam-6082	95	20	force	force	NOUN
ejpam-6082	95	21	of	of	ADP
ejpam-6082	95	22	infection	infection	NOUN
ejpam-6082	95	23	λ	λ	PROPN
ejpam-6082	95	24	.	.	PUNCT
ejpam-6082	95	25	additionally	additionally	ADV
ejpam-6082	95	26	,	,	PUNCT
ejpam-6082	95	27	it	it	PRON
ejpam-6082	95	28	is	be	AUX
ejpam-6082	95	29	assumed	assume	VERB
ejpam-6082	95	30	that	that	SCONJ
ejpam-6082	95	31	a	a	DET
ejpam-6082	95	32	proportion	proportion	NOUN
ejpam-6082	95	33	of	of	ADP
ejpam-6082	95	34	the	the	DET
ejpam-6082	95	35	susceptible	susceptible	ADJ
ejpam-6082	95	36	population	population	NOUN
ejpam-6082	95	37	is	be	AUX
ejpam-6082	95	38	vaccinated	vaccinate	VERB
ejpam-6082	95	39	at	at	ADP
ejpam-6082	95	40	a	a	DET
ejpam-6082	95	41	rate	rate	NOUN
ejpam-6082	95	42	δ	δ	PROPN
ejpam-6082	95	43	.	.	PUNCT
ejpam-6082	96	1	once	once	ADV
ejpam-6082	96	2	vaccinated	vaccinate	VERB
ejpam-6082	96	3	,	,	PUNCT
ejpam-6082	96	4	individuals	individual	NOUN
ejpam-6082	96	5	gain	gain	VERB
ejpam-6082	96	6	temporary	temporary	ADJ
ejpam-6082	96	7	immunity	immunity	NOUN
ejpam-6082	96	8	and	and	CCONJ
ejpam-6082	96	9	eventually	eventually	ADV
ejpam-6082	96	10	move	move	VERB
ejpam-6082	96	11	to	to	ADP
ejpam-6082	96	12	the	the	DET
ejpam-6082	96	13	recovered	recover	VERB
ejpam-6082	96	14	compartment	compartment	NOUN
ejpam-6082	96	15	(	(	PUNCT
ejpam-6082	96	16	r	r	NOUN
ejpam-6082	96	17	)	)	PUNCT
ejpam-6082	96	18	at	at	ADP
ejpam-6082	96	19	a	a	DET
ejpam-6082	96	20	recovery	recovery	NOUN
ejpam-6082	96	21	rate	rate	NOUN
ejpam-6082	96	22	γ	γ	PROPN
ejpam-6082	96	23	.	.	PUNCT
ejpam-6082	97	1	however	however	ADV
ejpam-6082	97	2	,	,	PUNCT
ejpam-6082	97	3	vaccine	vaccine	NOUN
ejpam-6082	97	4	failure	failure	NOUN
ejpam-6082	97	5	may	may	AUX
ejpam-6082	97	6	occur	occur	VERB
ejpam-6082	97	7	.	.	PUNCT
ejpam-6082	98	1	this	this	PRON
ejpam-6082	98	2	can	can	AUX
ejpam-6082	98	3	happen	happen	VERB
ejpam-6082	98	4	if	if	SCONJ
ejpam-6082	98	5	the	the	DET
ejpam-6082	98	6	body	body	NOUN
ejpam-6082	98	7	either	either	ADV
ejpam-6082	98	8	:	:	PUNCT
ejpam-6082	98	9	•	•	NOUN
ejpam-6082	98	10	fails	fail	VERB
ejpam-6082	98	11	to	to	PART
ejpam-6082	98	12	fight	fight	VERB
ejpam-6082	98	13	the	the	DET
ejpam-6082	98	14	virus	virus	NOUN
ejpam-6082	98	15	introduced	introduce	VERB
ejpam-6082	98	16	by	by	ADP
ejpam-6082	98	17	vaccination	vaccination	NOUN
ejpam-6082	98	18	and	and	CCONJ
ejpam-6082	98	19	becomes	become	VERB
ejpam-6082	98	20	infected	infect	VERB
ejpam-6082	98	21	.	.	PUNCT
ejpam-6082	99	1	•	•	NUM
ejpam-6082	99	2	successfully	successfully	ADV
ejpam-6082	99	3	fights	fight	VERB
ejpam-6082	99	4	the	the	DET
ejpam-6082	99	5	introduced	introduce	VERB
ejpam-6082	99	6	virus	virus	NOUN
ejpam-6082	99	7	but	but	CCONJ
ejpam-6082	99	8	does	do	AUX
ejpam-6082	99	9	not	not	PART
ejpam-6082	99	10	gain	gain	VERB
ejpam-6082	99	11	immunity	immunity	NOUN
ejpam-6082	99	12	,	,	PUNCT
ejpam-6082	99	13	becoming	become	VERB
ejpam-6082	99	14	susceptible	susceptible	ADJ
ejpam-6082	99	15	to	to	ADP
ejpam-6082	99	16	infection	infection	NOUN
ejpam-6082	99	17	upon	upon	SCONJ
ejpam-6082	99	18	contact	contact	NOUN
ejpam-6082	99	19	with	with	ADP
ejpam-6082	99	20	the	the	DET
ejpam-6082	99	21	virus	virus	NOUN
ejpam-6082	99	22	source	source	NOUN
ejpam-6082	99	23	.	.	PUNCT
ejpam-6082	100	1	in	in	ADP
ejpam-6082	100	2	such	such	ADJ
ejpam-6082	100	3	cases	case	NOUN
ejpam-6082	100	4	,	,	PUNCT
ejpam-6082	100	5	individuals	individual	NOUN
ejpam-6082	100	6	with	with	ADP
ejpam-6082	100	7	vaccination	vaccination	NOUN
ejpam-6082	100	8	failure	failure	NOUN
ejpam-6082	100	9	move	move	VERB
ejpam-6082	100	10	from	from	ADP
ejpam-6082	100	11	the	the	DET
ejpam-6082	100	12	vaccinated	vaccinated	ADJ
ejpam-6082	100	13	class	class	NOUN
ejpam-6082	100	14	into	into	ADP
ejpam-6082	100	15	the	the	DET
ejpam-6082	100	16	exposed	expose	VERB
ejpam-6082	100	17	class	class	NOUN
ejpam-6082	100	18	with	with	ADP
ejpam-6082	100	19	a	a	DET
ejpam-6082	100	20	probability	probability	NOUN
ejpam-6082	100	21	of	of	ADP
ejpam-6082	100	22	(	(	PUNCT
ejpam-6082	100	23	1−	1−	NUM
ejpam-6082	100	24	δ	δ	PROPN
ejpam-6082	100	25	)	)	PUNCT
ejpam-6082	100	26	.	.	PUNCT
ejpam-6082	101	1	the	the	DET
ejpam-6082	101	2	natural	natural	ADJ
ejpam-6082	101	3	and	and	CCONJ
ejpam-6082	101	4	polio	polio	NOUN
ejpam-6082	101	5	-	-	PUNCT
ejpam-6082	101	6	induced	induce	VERB
ejpam-6082	101	7	death	death	NOUN
ejpam-6082	101	8	rates	rate	NOUN
ejpam-6082	101	9	are	be	AUX
ejpam-6082	101	10	µ	µ	NOUN
ejpam-6082	101	11	and	and	CCONJ
ejpam-6082	101	12	σ	σ	PROPN
ejpam-6082	101	13	,	,	PUNCT
ejpam-6082	101	14	respectively	respectively	ADV
ejpam-6082	101	15	.	.	PUNCT
ejpam-6082	102	1	the	the	DET
ejpam-6082	102	2	rates	rate	NOUN
ejpam-6082	102	3	of	of	ADP
ejpam-6082	102	4	progression	progression	NOUN
ejpam-6082	102	5	of	of	ADP
ejpam-6082	102	6	exposed	expose	VERB
ejpam-6082	102	7	individuals	individual	NOUN
ejpam-6082	102	8	to	to	ADP
ejpam-6082	102	9	the	the	DET
ejpam-6082	102	10	non	non	ADJ
ejpam-6082	102	11	-	-	ADJ
ejpam-6082	102	12	paralytic	paralytic	ADJ
ejpam-6082	102	13	and	and	CCONJ
ejpam-6082	102	14	paralytic	paralytic	ADJ
ejpam-6082	102	15	stages	stage	NOUN
ejpam-6082	102	16	are	be	AUX
ejpam-6082	102	17	α1	α1	ADJ
ejpam-6082	102	18	and	and	CCONJ
ejpam-6082	102	19	α2	α2	ADJ
ejpam-6082	102	20	,	,	PUNCT
ejpam-6082	102	21	respectively	respectively	ADV
ejpam-6082	102	22	.	.	PUNCT
ejpam-6082	103	1	recovery	recovery	NOUN
ejpam-6082	103	2	rates	rate	NOUN
ejpam-6082	103	3	for	for	ADP
ejpam-6082	103	4	individuals	individual	NOUN
ejpam-6082	103	5	in	in	ADP
ejpam-6082	103	6	the	the	DET
ejpam-6082	103	7	exposed	expose	VERB
ejpam-6082	103	8	,	,	PUNCT
ejpam-6082	103	9	non	non	ADJ
ejpam-6082	103	10	-	-	ADJ
ejpam-6082	103	11	paralytic	paralytic	ADJ
ejpam-6082	103	12	,	,	PUNCT
ejpam-6082	103	13	and	and	CCONJ
ejpam-6082	103	14	paralytic	paralytic	ADJ
ejpam-6082	103	15	classes	class	NOUN
ejpam-6082	103	16	are	be	AUX
ejpam-6082	103	17	ω	ω	NOUN
ejpam-6082	103	18	,	,	PUNCT
ejpam-6082	103	19	ω1	ω1	PROPN
ejpam-6082	103	20	,	,	PUNCT
ejpam-6082	103	21	and	and	CCONJ
ejpam-6082	103	22	ω2	ω2	ADJ
ejpam-6082	103	23	,	,	PUNCT
ejpam-6082	103	24	respectively	respectively	ADV
ejpam-6082	103	25	.	.	PUNCT
ejpam-6082	104	1	individuals	individual	NOUN
ejpam-6082	104	2	in	in	ADP
ejpam-6082	104	3	the	the	DET
ejpam-6082	104	4	recovered	recovered	ADJ
ejpam-6082	104	5	class	class	NOUN
ejpam-6082	104	6	may	may	AUX
ejpam-6082	104	7	progress	progress	VERB
ejpam-6082	104	8	to	to	ADP
ejpam-6082	104	9	the	the	DET
ejpam-6082	104	10	post	post	ADJ
ejpam-6082	104	11	-	-	ADJ
ejpam-6082	104	12	paralytic	paralytic	ADJ
ejpam-6082	104	13	class	class	NOUN
ejpam-6082	104	14	at	at	ADP
ejpam-6082	104	15	rate	rate	NOUN
ejpam-6082	104	16	ρ	ρ	PROPN
ejpam-6082	104	17	,	,	PUNCT
ejpam-6082	104	18	while	while	SCONJ
ejpam-6082	104	19	a	a	DET
ejpam-6082	104	20	fraction	fraction	NOUN
ejpam-6082	104	21	of	of	ADP
ejpam-6082	104	22	them	they	PRON
ejpam-6082	104	23	may	may	AUX
ejpam-6082	104	24	lose	lose	VERB
ejpam-6082	104	25	immunity	immunity	NOUN
ejpam-6082	104	26	and	and	CCONJ
ejpam-6082	104	27	re	re	VERB
ejpam-6082	104	28	-	-	VERB
ejpam-6082	104	29	enter	enter	VERB
ejpam-6082	104	30	the	the	DET
ejpam-6082	104	31	susceptible	susceptible	ADJ
ejpam-6082	104	32	class	class	NOUN
ejpam-6082	104	33	at	at	ADP
ejpam-6082	104	34	a	a	DET
ejpam-6082	104	35	rate	rate	NOUN
ejpam-6082	104	36	ρ1	ρ1	NOUN
ejpam-6082	104	37	.	.	PUNCT
ejpam-6082	105	1	under	under	ADP
ejpam-6082	105	2	these	these	DET
ejpam-6082	105	3	assumptions	assumption	NOUN
ejpam-6082	105	4	,	,	PUNCT
ejpam-6082	105	5	and	and	CCONJ
ejpam-6082	105	6	following	follow	VERB
ejpam-6082	105	7	the	the	DET
ejpam-6082	105	8	flow	flow	NOUN
ejpam-6082	105	9	diagram	diagram	NOUN
ejpam-6082	105	10	in	in	ADP
ejpam-6082	105	11	figure	figure	NOUN
ejpam-6082	105	12	1	1	NUM
ejpam-6082	105	13	,	,	PUNCT
ejpam-6082	105	14	the	the	DET
ejpam-6082	105	15	dynamics	dynamic	NOUN
ejpam-6082	105	16	of	of	ADP
ejpam-6082	105	17	polio	polio	NOUN
ejpam-6082	105	18	infection	infection	NOUN
ejpam-6082	105	19	are	be	AUX
ejpam-6082	105	20	governed	govern	VERB
ejpam-6082	105	21	by	by	ADP
ejpam-6082	105	22	the	the	DET
ejpam-6082	105	23	following	follow	VERB
ejpam-6082	105	24	system	system	NOUN
ejpam-6082	105	25	of	of	ADP
ejpam-6082	105	26	differential	differential	ADJ
ejpam-6082	105	27	equations	equation	NOUN
ejpam-6082	105	28	,	,	PUNCT
ejpam-6082	105	29	as	as	SCONJ
ejpam-6082	105	30	proposed	propose	VERB
ejpam-6082	105	31	k.	k.	PROPN
ejpam-6082	105	32	guedri	guedri	PROPN
ejpam-6082	105	33	et	et	PROPN
ejpam-6082	105	34	al	al	PROPN
ejpam-6082	105	35	.	.	PUNCT
ejpam-6082	105	36	/	/	SYM
ejpam-6082	105	37	eur	eur	PROPN
ejpam-6082	105	38	.	.	PUNCT
ejpam-6082	106	1	j.	j.	PROPN
ejpam-6082	106	2	pure	pure	PROPN
ejpam-6082	106	3	appl	appl	PROPN
ejpam-6082	106	4	.	.	PROPN
ejpam-6082	106	5	math	math	PROPN
ejpam-6082	106	6	,	,	PUNCT
ejpam-6082	106	7	18	18	NUM
ejpam-6082	106	8	(	(	PUNCT
ejpam-6082	106	9	2	2	NUM
ejpam-6082	106	10	)	)	PUNCT
ejpam-6082	106	11	(	(	PUNCT
ejpam-6082	106	12	2025	2025	NUM
ejpam-6082	106	13	)	)	PUNCT
ejpam-6082	106	14	,	,	PUNCT
ejpam-6082	106	15	6082	6082	NUM
ejpam-6082	106	16	6	6	NUM
ejpam-6082	106	17	of	of	ADP
ejpam-6082	106	18	39	39	NUM
ejpam-6082	106	19	in	in	ADP
ejpam-6082	106	20	[	[	X
ejpam-6082	106	21	1	1	NUM
ejpam-6082	106	22	]	]	NOUN
ejpam-6082	106	23	:	:	PUNCT
ejpam-6082	106	24			NOUN
ejpam-6082	106	25	ds	ds	ADJ
ejpam-6082	106	26	dt	dt	NOUN
ejpam-6082	106	27	=	=	PUNCT
ejpam-6082	106	28	λ+	λ+	PUNCT
ejpam-6082	106	29	ρ1r−	ρ1r−	PRON
ejpam-6082	106	30	(	(	PUNCT
ejpam-6082	106	31	λ+	λ+	PUNCT
ejpam-6082	106	32	δ	δ	NOUN
ejpam-6082	106	33	+	+	NOUN
ejpam-6082	106	34	µ)s	µ)s	NOUN
ejpam-6082	106	35	,	,	PUNCT
ejpam-6082	106	36	dv	dv	PROPN
ejpam-6082	106	37	dt	dt	X
ejpam-6082	106	38	=	=	SYM
ejpam-6082	106	39	δs	δs	PROPN
ejpam-6082	106	40	−	−	PROPN
ejpam-6082	106	41	(	(	PUNCT
ejpam-6082	106	42	1−	1−	NUM
ejpam-6082	106	43	δ)λv	δ)λv	PROPN
ejpam-6082	106	44	−	−	PROPN
ejpam-6082	106	45	(	(	PUNCT
ejpam-6082	106	46	γ	γ	X
ejpam-6082	106	47	+	+	NOUN
ejpam-6082	106	48	µ)v	µ)v	ADJ
ejpam-6082	106	49	,	,	PUNCT
ejpam-6082	106	50	de	de	X
ejpam-6082	106	51	dt	dt	NOUN
ejpam-6082	106	52	=	=	PUNCT
ejpam-6082	106	53	λs	λs	PROPN
ejpam-6082	106	54	+	+	CCONJ
ejpam-6082	106	55	(	(	PUNCT
ejpam-6082	106	56	1−	1−	NUM
ejpam-6082	106	57	δ)λv	δ)λv	PROPN
ejpam-6082	106	58	−	−	PROPN
ejpam-6082	106	59	(	(	PUNCT
ejpam-6082	106	60	α1	α1	PROPN
ejpam-6082	106	61	+	+	CCONJ
ejpam-6082	106	62	α2	α2	ADJ
ejpam-6082	106	63	+	+	CCONJ
ejpam-6082	106	64	ω	ω	PROPN
ejpam-6082	106	65	+	+	CCONJ
ejpam-6082	106	66	µ)e	µ)e	NOUN
ejpam-6082	106	67	,	,	PUNCT
ejpam-6082	106	68	dnp	dnp	PROPN
ejpam-6082	106	69	dt	dt	NOUN
ejpam-6082	106	70	=	=	SYM
ejpam-6082	106	71	α1e	α1e	PROPN
ejpam-6082	106	72	−	−	PROPN
ejpam-6082	106	73	(	(	PUNCT
ejpam-6082	106	74	σ	σ	PROPN
ejpam-6082	106	75	+	+	X
ejpam-6082	106	76	µ+	µ+	X
ejpam-6082	106	77	ω1)np	ω1)np	PROPN
ejpam-6082	106	78	,	,	PUNCT
ejpam-6082	106	79	dp	dp	NOUN
ejpam-6082	106	80	dt	dt	NOUN
ejpam-6082	106	81	=	=	SYM
ejpam-6082	106	82	α2e	α2e	X
ejpam-6082	106	83	−	−	PROPN
ejpam-6082	107	1	(	(	PUNCT
ejpam-6082	107	2	σ	σ	PROPN
ejpam-6082	107	3	+	+	X
ejpam-6082	107	4	µ+	µ+	PROPN
ejpam-6082	107	5	ω2)p	ω2)p	NOUN
ejpam-6082	107	6	,	,	PUNCT
ejpam-6082	107	7	dr	dr	PROPN
ejpam-6082	107	8	dt	dt	NOUN
ejpam-6082	107	9	=	=	PUNCT
ejpam-6082	107	10	γv	γv	X
ejpam-6082	108	1	+	+	CCONJ
ejpam-6082	108	2	ωe	ωe	ADV
ejpam-6082	108	3	+	+	NUM
ejpam-6082	108	4	ω1np	ω1np	NOUN
ejpam-6082	108	5	+	+	CCONJ
ejpam-6082	108	6	ω2p	ω2p	NOUN
ejpam-6082	108	7	−	−	X
ejpam-6082	108	8	(	(	PUNCT
ejpam-6082	108	9	ρ+	ρ+	NUM
ejpam-6082	108	10	ρ1	ρ1	NOUN
ejpam-6082	108	11	+	+	CCONJ
ejpam-6082	108	12	µ)r	µ)r	NOUN
ejpam-6082	108	13	,	,	PUNCT
ejpam-6082	108	14	da	da	ADJ
ejpam-6082	108	15	dt	dt	NOUN
ejpam-6082	109	1	=	=	SYM
ejpam-6082	109	2	ρr−	ρr−	PROPN
ejpam-6082	109	3	(	(	PUNCT
ejpam-6082	109	4	σ	σ	NOUN
ejpam-6082	109	5	+	+	NOUN
ejpam-6082	109	6	µ)a	µ)a	NOUN
ejpam-6082	109	7	.	.	PUNCT
ejpam-6082	110	1	(	(	PUNCT
ejpam-6082	110	2	1	1	X
ejpam-6082	110	3	)	)	PUNCT
ejpam-6082	110	4	2.1	2.1	NUM
ejpam-6082	110	5	.	.	PUNCT
ejpam-6082	111	1	fractional	fractional	ADJ
ejpam-6082	111	2	reaction	reaction	NOUN
ejpam-6082	111	3	-	-	PUNCT
ejpam-6082	111	4	diffusion	diffusion	NOUN
ejpam-6082	111	5	polio	polio	NOUN
ejpam-6082	111	6	model	model	VERB
ejpam-6082	111	7	the	the	DET
ejpam-6082	111	8	classical	classical	ADJ
ejpam-6082	111	9	models	model	NOUN
ejpam-6082	111	10	for	for	ADP
ejpam-6082	111	11	the	the	DET
ejpam-6082	111	12	dynamics	dynamic	NOUN
ejpam-6082	111	13	of	of	ADP
ejpam-6082	111	14	polio	polio	NOUN
ejpam-6082	111	15	virus	virus	NOUN
ejpam-6082	111	16	infection	infection	NOUN
ejpam-6082	111	17	predominantly	predominantly	ADV
ejpam-6082	111	18	focus	focus	VERB
ejpam-6082	111	19	on	on	ADP
ejpam-6082	111	20	temporal	temporal	ADJ
ejpam-6082	111	21	changes	change	NOUN
ejpam-6082	111	22	in	in	ADP
ejpam-6082	111	23	the	the	DET
ejpam-6082	111	24	population	population	NOUN
ejpam-6082	111	25	compartments	compartment	NOUN
ejpam-6082	111	26	(	(	PUNCT
ejpam-6082	111	27	e.g.	e.g.	ADV
ejpam-6082	111	28	,	,	PUNCT
ejpam-6082	111	29	[	[	X
ejpam-6082	111	30	1–3	1–3	NOUN
ejpam-6082	111	31	]	]	X
ejpam-6082	111	32	)	)	PUNCT
ejpam-6082	111	33	.	.	PUNCT
ejpam-6082	112	1	these	these	DET
ejpam-6082	112	2	models	model	NOUN
ejpam-6082	112	3	are	be	AUX
ejpam-6082	112	4	often	often	ADV
ejpam-6082	112	5	based	base	VERB
ejpam-6082	112	6	on	on	ADP
ejpam-6082	112	7	lumped	lump	VERB
ejpam-6082	112	8	parameters	parameter	NOUN
ejpam-6082	112	9	,	,	PUNCT
ejpam-6082	112	10	assuming	assume	VERB
ejpam-6082	112	11	a	a	DET
ejpam-6082	112	12	homogeneously	homogeneously	ADV
ejpam-6082	112	13	mixed	mixed	ADJ
ejpam-6082	112	14	population	population	NOUN
ejpam-6082	112	15	.	.	PUNCT
ejpam-6082	113	1	however	however	ADV
ejpam-6082	113	2	,	,	PUNCT
ejpam-6082	113	3	this	this	DET
ejpam-6082	113	4	assumption	assumption	NOUN
ejpam-6082	113	5	oversimplifies	oversimplify	VERB
ejpam-6082	113	6	the	the	DET
ejpam-6082	113	7	real	real	ADJ
ejpam-6082	113	8	-	-	PUNCT
ejpam-6082	113	9	world	world	NOUN
ejpam-6082	113	10	scenario	scenario	NOUN
ejpam-6082	113	11	where	where	SCONJ
ejpam-6082	113	12	spatial	spatial	ADJ
ejpam-6082	113	13	factors	factor	NOUN
ejpam-6082	113	14	,	,	PUNCT
ejpam-6082	113	15	such	such	ADJ
ejpam-6082	113	16	as	as	ADP
ejpam-6082	113	17	population	population	NOUN
ejpam-6082	113	18	mobility	mobility	NOUN
ejpam-6082	113	19	,	,	PUNCT
ejpam-6082	113	20	environmental	environmental	ADJ
ejpam-6082	113	21	heterogeneity	heterogeneity	NOUN
ejpam-6082	113	22	,	,	PUNCT
ejpam-6082	113	23	and	and	CCONJ
ejpam-6082	113	24	local	local	ADJ
ejpam-6082	113	25	climatic	climatic	ADJ
ejpam-6082	113	26	conditions	condition	NOUN
ejpam-6082	113	27	,	,	PUNCT
ejpam-6082	113	28	significantly	significantly	ADV
ejpam-6082	113	29	influence	influence	NOUN
ejpam-6082	113	30	disease	disease	NOUN
ejpam-6082	113	31	transmission	transmission	NOUN
ejpam-6082	113	32	dynamics	dynamic	NOUN
ejpam-6082	113	33	.	.	PUNCT
ejpam-6082	114	1	incorporating	incorporate	VERB
ejpam-6082	114	2	spatial	spatial	ADJ
ejpam-6082	114	3	heterogeneity	heterogeneity	NOUN
ejpam-6082	114	4	the	the	DET
ejpam-6082	114	5	baseline	baseline	NOUN
ejpam-6082	114	6	model	model	NOUN
ejpam-6082	114	7	(	(	PUNCT
ejpam-6082	114	8	1	1	X
ejpam-6082	114	9	)	)	PUNCT
ejpam-6082	114	10	assumes	assume	VERB
ejpam-6082	114	11	a	a	DET
ejpam-6082	114	12	homogeneous	homogeneous	ADJ
ejpam-6082	114	13	population	population	NOUN
ejpam-6082	114	14	where	where	SCONJ
ejpam-6082	114	15	individuals	individual	NOUN
ejpam-6082	114	16	are	be	AUX
ejpam-6082	114	17	uniformly	uniformly	ADV
ejpam-6082	114	18	distributed	distribute	VERB
ejpam-6082	114	19	across	across	ADP
ejpam-6082	114	20	the	the	DET
ejpam-6082	114	21	domain	domain	NOUN
ejpam-6082	114	22	.	.	PUNCT
ejpam-6082	115	1	this	this	PRON
ejpam-6082	115	2	implies	imply	VERB
ejpam-6082	115	3	that	that	SCONJ
ejpam-6082	115	4	the	the	DET
ejpam-6082	115	5	infection	infection	NOUN
ejpam-6082	115	6	spreads	spread	VERB
ejpam-6082	115	7	uniformly	uniformly	ADV
ejpam-6082	115	8	without	without	ADP
ejpam-6082	115	9	spatial	spatial	ADJ
ejpam-6082	115	10	variation	variation	NOUN
ejpam-6082	115	11	.	.	PUNCT
ejpam-6082	116	1	however	however	ADV
ejpam-6082	116	2	,	,	PUNCT
ejpam-6082	116	3	in	in	ADP
ejpam-6082	116	4	practice	practice	NOUN
ejpam-6082	116	5	,	,	PUNCT
ejpam-6082	116	6	disease	disease	NOUN
ejpam-6082	116	7	spread	spread	NOUN
ejpam-6082	116	8	can	can	AUX
ejpam-6082	116	9	vary	vary	VERB
ejpam-6082	116	10	significantly	significantly	ADV
ejpam-6082	116	11	due	due	ADP
ejpam-6082	116	12	to	to	ADP
ejpam-6082	116	13	:	:	PUNCT
ejpam-6082	116	14	•	•	NUM
ejpam-6082	116	15	environmental	environmental	ADJ
ejpam-6082	116	16	factors	factor	NOUN
ejpam-6082	116	17	(	(	PUNCT
ejpam-6082	116	18	e.g.	e.g.	ADV
ejpam-6082	116	19	,	,	PUNCT
ejpam-6082	116	20	climate	climate	NOUN
ejpam-6082	116	21	and	and	CCONJ
ejpam-6082	116	22	sanitation	sanitation	NOUN
ejpam-6082	116	23	conditions	condition	NOUN
ejpam-6082	116	24	)	)	PUNCT
ejpam-6082	116	25	,	,	PUNCT
ejpam-6082	116	26	•	•	NUM
ejpam-6082	116	27	population	population	NOUN
ejpam-6082	116	28	density	density	NOUN
ejpam-6082	116	29	,	,	PUNCT
ejpam-6082	116	30	•	•	ADP
ejpam-6082	116	31	localized	localized	ADJ
ejpam-6082	116	32	interventions	intervention	NOUN
ejpam-6082	116	33	(	(	PUNCT
ejpam-6082	116	34	e.g.	e.g.	ADV
ejpam-6082	116	35	,	,	PUNCT
ejpam-6082	116	36	vaccination	vaccination	NOUN
ejpam-6082	116	37	campaigns	campaign	NOUN
ejpam-6082	116	38	)	)	PUNCT
ejpam-6082	116	39	.	.	PUNCT
ejpam-6082	117	1	to	to	PART
ejpam-6082	117	2	address	address	VERB
ejpam-6082	117	3	these	these	DET
ejpam-6082	117	4	complexities	complexity	NOUN
ejpam-6082	117	5	,	,	PUNCT
ejpam-6082	117	6	we	we	PRON
ejpam-6082	117	7	introduce	introduce	VERB
ejpam-6082	117	8	spatial	spatial	ADJ
ejpam-6082	117	9	dependence	dependence	NOUN
ejpam-6082	117	10	into	into	ADP
ejpam-6082	117	11	the	the	DET
ejpam-6082	117	12	model	model	NOUN
ejpam-6082	117	13	by	by	ADP
ejpam-6082	117	14	adding	add	VERB
ejpam-6082	117	15	a	a	DET
ejpam-6082	117	16	diffusion	diffusion	NOUN
ejpam-6082	117	17	term	term	NOUN
ejpam-6082	117	18	to	to	PART
ejpam-6082	117	19	represent	represent	VERB
ejpam-6082	117	20	the	the	DET
ejpam-6082	117	21	mobility	mobility	NOUN
ejpam-6082	117	22	of	of	ADP
ejpam-6082	117	23	individuals	individual	NOUN
ejpam-6082	117	24	within	within	ADP
ejpam-6082	117	25	the	the	DET
ejpam-6082	117	26	domain	domain	NOUN
ejpam-6082	117	27	[	[	X
ejpam-6082	117	28	45–48	45–48	NUM
ejpam-6082	117	29	]	]	PUNCT
ejpam-6082	117	30	.	.	PUNCT
ejpam-6082	118	1	the	the	DET
ejpam-6082	118	2	k.	k.	PROPN
ejpam-6082	118	3	guedri	guedri	PROPN
ejpam-6082	118	4	et	et	PROPN
ejpam-6082	118	5	al	al	PROPN
ejpam-6082	118	6	.	.	PUNCT
ejpam-6082	118	7	/	/	SYM
ejpam-6082	118	8	eur	eur	PROPN
ejpam-6082	118	9	.	.	PUNCT
ejpam-6082	119	1	j.	j.	PROPN
ejpam-6082	119	2	pure	pure	PROPN
ejpam-6082	119	3	appl	appl	PROPN
ejpam-6082	119	4	.	.	PROPN
ejpam-6082	119	5	math	math	PROPN
ejpam-6082	119	6	,	,	PUNCT
ejpam-6082	119	7	18	18	NUM
ejpam-6082	119	8	(	(	PUNCT
ejpam-6082	119	9	2	2	NUM
ejpam-6082	119	10	)	)	PUNCT
ejpam-6082	119	11	(	(	PUNCT
ejpam-6082	119	12	2025	2025	NUM
ejpam-6082	119	13	)	)	PUNCT
ejpam-6082	119	14	,	,	PUNCT
ejpam-6082	119	15	6082	6082	NUM
ejpam-6082	119	16	7	7	NUM
ejpam-6082	119	17	of	of	ADP
ejpam-6082	119	18	39	39	NUM
ejpam-6082	119	19	resulting	result	VERB
ejpam-6082	119	20	reaction	reaction	NOUN
ejpam-6082	119	21	-	-	PUNCT
ejpam-6082	119	22	diffusion	diffusion	NOUN
ejpam-6082	119	23	system	system	NOUN
ejpam-6082	119	24	is	be	AUX
ejpam-6082	119	25	as	as	SCONJ
ejpam-6082	119	26	follows	follow	VERB
ejpam-6082	119	27	:	:	PUNCT
ejpam-6082	119	28	∂s(t	∂s(t	NOUN
ejpam-6082	119	29	,	,	PUNCT
ejpam-6082	119	30	x	x	NOUN
ejpam-6082	119	31	)	)	PUNCT
ejpam-6082	120	1	∂t	∂t	PROPN
ejpam-6082	120	2	−	−	PROPN
ejpam-6082	120	3	d1∆s(t	d1∆s(t	PROPN
ejpam-6082	120	4	,	,	PUNCT
ejpam-6082	120	5	x	x	X
ejpam-6082	120	6	)	)	PUNCT
ejpam-6082	120	7	=	=	SYM
ejpam-6082	121	1	λ	λ	NOUN
ejpam-6082	121	2	+	+	CCONJ
ejpam-6082	121	3	ρ1r(t	ρ1r(t	PROPN
ejpam-6082	121	4	,	,	PUNCT
ejpam-6082	121	5	x)−	x)−	PROPN
ejpam-6082	121	6	(	(	PUNCT
ejpam-6082	121	7	λ+	λ+	NUM
ejpam-6082	121	8	δ	δ	PROPN
ejpam-6082	121	9	+	+	CCONJ
ejpam-6082	121	10	µ)s(t	µ)s(t	PROPN
ejpam-6082	121	11	,	,	PUNCT
ejpam-6082	121	12	x	x	NOUN
ejpam-6082	121	13	)	)	PUNCT
ejpam-6082	121	14	,	,	PUNCT
ejpam-6082	121	15	∂v	∂v	PROPN
ejpam-6082	121	16	(	(	PUNCT
ejpam-6082	121	17	t	t	PROPN
ejpam-6082	121	18	,	,	PUNCT
ejpam-6082	121	19	x	x	NOUN
ejpam-6082	121	20	)	)	PUNCT
ejpam-6082	122	1	∂t	∂t	PROPN
ejpam-6082	122	2	−	−	PROPN
ejpam-6082	123	1	d2∆v	d2∆v	X
ejpam-6082	123	2	(	(	PUNCT
ejpam-6082	123	3	t	t	PROPN
ejpam-6082	123	4	,	,	PUNCT
ejpam-6082	123	5	x	x	NOUN
ejpam-6082	123	6	)	)	PUNCT
ejpam-6082	123	7	=	=	SYM
ejpam-6082	123	8	δs(t	δs(t	PROPN
ejpam-6082	123	9	,	,	PUNCT
ejpam-6082	123	10	x)−	x)−	PROPN
ejpam-6082	123	11	(	(	PUNCT
ejpam-6082	123	12	1−	1−	NUM
ejpam-6082	123	13	δ)λv	δ)λv	PROPN
ejpam-6082	123	14	(	(	PUNCT
ejpam-6082	123	15	t	t	PROPN
ejpam-6082	123	16	,	,	PUNCT
ejpam-6082	123	17	x)−	x)−	PROPN
ejpam-6082	123	18	(	(	PUNCT
ejpam-6082	123	19	γ	γ	X
ejpam-6082	123	20	+	+	NOUN
ejpam-6082	123	21	µ)v	µ)v	ADJ
ejpam-6082	123	22	(	(	PUNCT
ejpam-6082	123	23	t	t	PROPN
ejpam-6082	123	24	,	,	PUNCT
ejpam-6082	123	25	x	x	NOUN
ejpam-6082	123	26	)	)	PUNCT
ejpam-6082	123	27	,	,	PUNCT
ejpam-6082	123	28	∂e(t	∂e(t	PROPN
ejpam-6082	123	29	,	,	PUNCT
ejpam-6082	123	30	x	x	NOUN
ejpam-6082	123	31	)	)	PUNCT
ejpam-6082	123	32	∂t	∂t	PROPN
ejpam-6082	123	33	−	−	PROPN
ejpam-6082	123	34	d3∆e(t	d3∆e(t	NOUN
ejpam-6082	123	35	,	,	PUNCT
ejpam-6082	123	36	x	x	NOUN
ejpam-6082	123	37	)	)	PUNCT
ejpam-6082	123	38	=	=	SYM
ejpam-6082	123	39	λs(t	λs(t	PROPN
ejpam-6082	123	40	,	,	PUNCT
ejpam-6082	123	41	x	x	PRON
ejpam-6082	123	42	)	)	PUNCT
ejpam-6082	123	43	+	+	CCONJ
ejpam-6082	123	44	(	(	PUNCT
ejpam-6082	123	45	1−	1−	NUM
ejpam-6082	123	46	δ)λv	δ)λv	PROPN
ejpam-6082	123	47	(	(	PUNCT
ejpam-6082	123	48	t	t	PROPN
ejpam-6082	123	49	,	,	PUNCT
ejpam-6082	123	50	x)−	x)−	PROPN
ejpam-6082	123	51	(	(	PUNCT
ejpam-6082	123	52	α1	α1	PROPN
ejpam-6082	123	53	+	+	CCONJ
ejpam-6082	123	54	α2	α2	ADJ
ejpam-6082	123	55	+	+	CCONJ
ejpam-6082	123	56	ω	ω	PROPN
ejpam-6082	124	1	+	+	CCONJ
ejpam-6082	124	2	µ)e(t	µ)e(t	NOUN
ejpam-6082	124	3	,	,	PUNCT
ejpam-6082	124	4	x	x	NOUN
ejpam-6082	124	5	)	)	PUNCT
ejpam-6082	124	6	,	,	PUNCT
ejpam-6082	124	7	∂np(t	∂np(t	PROPN
ejpam-6082	124	8	,	,	PUNCT
ejpam-6082	124	9	x	x	X
ejpam-6082	124	10	)	)	PUNCT
ejpam-6082	124	11	∂t	∂t	PROPN
ejpam-6082	124	12	−	−	PROPN
ejpam-6082	124	13	d4∆np(t	d4∆np(t	PROPN
ejpam-6082	124	14	,	,	PUNCT
ejpam-6082	124	15	x	x	NOUN
ejpam-6082	124	16	)	)	PUNCT
ejpam-6082	124	17	=	=	SYM
ejpam-6082	124	18	α1e(t	α1e(t	PROPN
ejpam-6082	124	19	,	,	PUNCT
ejpam-6082	124	20	x)−	x)−	PROPN
ejpam-6082	124	21	(	(	PUNCT
ejpam-6082	124	22	σ	σ	PROPN
ejpam-6082	124	23	+	+	X
ejpam-6082	124	24	µ+	µ+	PROPN
ejpam-6082	124	25	ω1)np(t	ω1)np(t	NUM
ejpam-6082	124	26	,	,	PUNCT
ejpam-6082	124	27	x	x	NOUN
ejpam-6082	124	28	)	)	PUNCT
ejpam-6082	124	29	,	,	PUNCT
ejpam-6082	124	30	∂p	∂p	PROPN
ejpam-6082	124	31	(	(	PUNCT
ejpam-6082	124	32	t	t	PROPN
ejpam-6082	124	33	,	,	PUNCT
ejpam-6082	124	34	x	x	NOUN
ejpam-6082	124	35	)	)	PUNCT
ejpam-6082	124	36	∂t	∂t	PROPN
ejpam-6082	124	37	−	−	PROPN
ejpam-6082	124	38	d5∆p	d5∆p	PROPN
ejpam-6082	124	39	(	(	PUNCT
ejpam-6082	124	40	t	t	PROPN
ejpam-6082	124	41	,	,	PUNCT
ejpam-6082	124	42	x	x	NOUN
ejpam-6082	124	43	)	)	PUNCT
ejpam-6082	124	44	=	=	SYM
ejpam-6082	124	45	α2e(t	α2e(t	PROPN
ejpam-6082	124	46	,	,	PUNCT
ejpam-6082	124	47	x)−	x)−	PROPN
ejpam-6082	124	48	(	(	PUNCT
ejpam-6082	124	49	σ	σ	PROPN
ejpam-6082	124	50	+	+	X
ejpam-6082	124	51	µ+	µ+	PUNCT
ejpam-6082	124	52	ω2)p	ω2)p	PROPN
ejpam-6082	124	53	(	(	PUNCT
ejpam-6082	124	54	t	t	PROPN
ejpam-6082	124	55	,	,	PUNCT
ejpam-6082	124	56	x	x	NOUN
ejpam-6082	124	57	)	)	PUNCT
ejpam-6082	124	58	,	,	PUNCT
ejpam-6082	124	59	∂r(t	∂r(t	PROPN
ejpam-6082	124	60	,	,	PUNCT
ejpam-6082	124	61	x	x	NOUN
ejpam-6082	124	62	)	)	PUNCT
ejpam-6082	124	63	∂t	∂t	PROPN
ejpam-6082	124	64	−	−	PROPN
ejpam-6082	124	65	d6∆r(t	d6∆r(t	NOUN
ejpam-6082	124	66	,	,	PUNCT
ejpam-6082	124	67	x	x	X
ejpam-6082	124	68	)	)	PUNCT
ejpam-6082	124	69	=	=	SYM
ejpam-6082	124	70	γv	γv	X
ejpam-6082	124	71	(	(	PUNCT
ejpam-6082	124	72	t	t	PROPN
ejpam-6082	124	73	,	,	PUNCT
ejpam-6082	124	74	x	x	NOUN
ejpam-6082	124	75	)	)	PUNCT
ejpam-6082	125	1	+	+	CCONJ
ejpam-6082	125	2	ωe	ωe	ADV
ejpam-6082	125	3	+	+	CCONJ
ejpam-6082	125	4	ω1np(t	ω1np(t	NOUN
ejpam-6082	125	5	,	,	PUNCT
ejpam-6082	125	6	x	x	PRON
ejpam-6082	125	7	)	)	PUNCT
ejpam-6082	126	1	+	+	NUM
ejpam-6082	126	2	ω2p	ω2p	NOUN
ejpam-6082	126	3	(	(	PUNCT
ejpam-6082	126	4	t	t	PROPN
ejpam-6082	126	5	,	,	PUNCT
ejpam-6082	126	6	x)−	x)−	PROPN
ejpam-6082	126	7	(	(	PUNCT
ejpam-6082	126	8	ρ+	ρ+	NUM
ejpam-6082	126	9	ρ1	ρ1	NOUN
ejpam-6082	126	10	+	+	CCONJ
ejpam-6082	126	11	µ)r(t	µ)r(t	ADJ
ejpam-6082	126	12	,	,	PUNCT
ejpam-6082	126	13	x	x	NOUN
ejpam-6082	126	14	)	)	PUNCT
ejpam-6082	126	15	,	,	PUNCT
ejpam-6082	126	16	∂a(t	∂a(t	PROPN
ejpam-6082	126	17	,	,	PUNCT
ejpam-6082	126	18	x	x	NOUN
ejpam-6082	126	19	)	)	PUNCT
ejpam-6082	126	20	∂t	∂t	PROPN
ejpam-6082	126	21	−	−	PROPN
ejpam-6082	126	22	d7∆a(t	d7∆a(t	PROPN
ejpam-6082	126	23	,	,	PUNCT
ejpam-6082	126	24	x	x	NOUN
ejpam-6082	126	25	)	)	PUNCT
ejpam-6082	126	26	=	=	SYM
ejpam-6082	126	27	ρr(t	ρr(t	NUM
ejpam-6082	126	28	,	,	PUNCT
ejpam-6082	126	29	x)−	x)−	PROPN
ejpam-6082	126	30	(	(	PUNCT
ejpam-6082	126	31	σ	σ	PROPN
ejpam-6082	126	32	+	+	CCONJ
ejpam-6082	126	33	µ)a(t	µ)a(t	PROPN
ejpam-6082	126	34	,	,	PUNCT
ejpam-6082	126	35	x	x	NOUN
ejpam-6082	126	36	)	)	PUNCT
ejpam-6082	126	37	,	,	PUNCT
ejpam-6082	126	38	where	where	SCONJ
ejpam-6082	126	39	di	di	X
ejpam-6082	126	40	(	(	PUNCT
ejpam-6082	126	41	i	i	NOUN
ejpam-6082	126	42	=	=	NOUN
ejpam-6082	126	43	1	1	NUM
ejpam-6082	126	44	,	,	PUNCT
ejpam-6082	126	45	2	2	NUM
ejpam-6082	126	46	,	,	PUNCT
ejpam-6082	126	47	.	.	PUNCT
ejpam-6082	126	48	.	.	PUNCT
ejpam-6082	126	49	.	.	PUNCT
ejpam-6082	127	1	,	,	PUNCT
ejpam-6082	127	2	7	7	X
ejpam-6082	127	3	)	)	PUNCT
ejpam-6082	127	4	are	be	AUX
ejpam-6082	127	5	the	the	DET
ejpam-6082	127	6	diffusion	diffusion	NOUN
ejpam-6082	127	7	coefficients	coefficient	NOUN
ejpam-6082	127	8	corresponding	correspond	VERB
ejpam-6082	127	9	to	to	ADP
ejpam-6082	127	10	each	each	DET
ejpam-6082	127	11	compartment	compartment	NOUN
ejpam-6082	127	12	,	,	PUNCT
ejpam-6082	127	13	and	and	CCONJ
ejpam-6082	127	14	∆	∆	PROPN
ejpam-6082	127	15	is	be	AUX
ejpam-6082	127	16	the	the	DET
ejpam-6082	127	17	laplacian	laplacian	ADJ
ejpam-6082	127	18	operator	operator	NOUN
ejpam-6082	127	19	capturing	capture	VERB
ejpam-6082	127	20	spatial	spatial	ADJ
ejpam-6082	127	21	mobility	mobility	NOUN
ejpam-6082	127	22	.	.	PUNCT
ejpam-6082	128	1	incorporating	incorporate	VERB
ejpam-6082	128	2	fractional	fractional	ADJ
ejpam-6082	128	3	dynamics	dynamic	NOUN
ejpam-6082	128	4	recent	recent	ADJ
ejpam-6082	128	5	advancements	advancement	NOUN
ejpam-6082	128	6	in	in	ADP
ejpam-6082	128	7	mathematical	mathematical	ADJ
ejpam-6082	128	8	modeling	modeling	NOUN
ejpam-6082	128	9	emphasize	emphasize	VERB
ejpam-6082	128	10	the	the	DET
ejpam-6082	128	11	utility	utility	NOUN
ejpam-6082	128	12	of	of	ADP
ejpam-6082	128	13	fractional	fractional	ADJ
ejpam-6082	128	14	calculus	calculus	NOUN
ejpam-6082	128	15	for	for	ADP
ejpam-6082	128	16	capturing	capture	VERB
ejpam-6082	128	17	memory	memory	NOUN
ejpam-6082	128	18	effects	effect	NOUN
ejpam-6082	128	19	and	and	CCONJ
ejpam-6082	128	20	non	non	ADJ
ejpam-6082	128	21	-	-	ADJ
ejpam-6082	128	22	local	local	ADJ
ejpam-6082	128	23	dynamics	dynamic	NOUN
ejpam-6082	128	24	in	in	ADP
ejpam-6082	128	25	complex	complex	ADJ
ejpam-6082	128	26	systems	system	NOUN
ejpam-6082	128	27	.	.	PUNCT
ejpam-6082	129	1	fractional	fractional	ADJ
ejpam-6082	129	2	derivatives	derivative	NOUN
ejpam-6082	129	3	allow	allow	VERB
ejpam-6082	129	4	for	for	ADP
ejpam-6082	129	5	more	more	ADV
ejpam-6082	129	6	accurate	accurate	ADJ
ejpam-6082	129	7	modeling	modeling	NOUN
ejpam-6082	129	8	of	of	ADP
ejpam-6082	129	9	biological	biological	ADJ
ejpam-6082	129	10	processes	process	NOUN
ejpam-6082	129	11	,	,	PUNCT
ejpam-6082	129	12	as	as	SCONJ
ejpam-6082	129	13	they	they	PRON
ejpam-6082	129	14	incorporate	incorporate	VERB
ejpam-6082	129	15	the	the	DET
ejpam-6082	129	16	history	history	NOUN
ejpam-6082	129	17	-	-	PUNCT
ejpam-6082	129	18	dependent	dependent	ADJ
ejpam-6082	129	19	nature	nature	NOUN
ejpam-6082	129	20	of	of	ADP
ejpam-6082	129	21	the	the	DET
ejpam-6082	129	22	disease	disease	NOUN
ejpam-6082	129	23	spread	spread	VERB
ejpam-6082	129	24	and	and	CCONJ
ejpam-6082	129	25	population	population	NOUN
ejpam-6082	129	26	interactions	interaction	NOUN
ejpam-6082	129	27	.	.	PUNCT
ejpam-6082	130	1	to	to	PART
ejpam-6082	130	2	further	far	ADV
ejpam-6082	130	3	generalize	generalize	VERB
ejpam-6082	130	4	the	the	DET
ejpam-6082	130	5	model	model	NOUN
ejpam-6082	130	6	,	,	PUNCT
ejpam-6082	130	7	we	we	PRON
ejpam-6082	130	8	replace	replace	VERB
ejpam-6082	130	9	the	the	DET
ejpam-6082	130	10	classical	classical	ADJ
ejpam-6082	130	11	time	time	NOUN
ejpam-6082	130	12	derivative	derivative	ADJ
ejpam-6082	130	13	with	with	ADP
ejpam-6082	130	14	the	the	DET
ejpam-6082	130	15	caputo	caputo	PROPN
ejpam-6082	130	16	fractional	fractional	PROPN
ejpam-6082	130	17	derivative	derivative	NOUN
ejpam-6082	130	18	of	of	ADP
ejpam-6082	130	19	order	order	NOUN
ejpam-6082	130	20	α	α	X
ejpam-6082	130	21	(	(	PUNCT
ejpam-6082	130	22	0	0	NUM
ejpam-6082	130	23	<	<	X
ejpam-6082	130	24	α	α	PROPN
ejpam-6082	130	25	≤	≤	NUM
ejpam-6082	130	26	1	1	NUM
ejpam-6082	130	27	)	)	PUNCT
ejpam-6082	130	28	and	and	CCONJ
ejpam-6082	130	29	retain	retain	VERB
ejpam-6082	130	30	the	the	DET
ejpam-6082	130	31	diffusion	diffusion	NOUN
ejpam-6082	130	32	term	term	NOUN
ejpam-6082	130	33	.	.	PUNCT
ejpam-6082	131	1	the	the	DET
ejpam-6082	131	2	resulting	result	VERB
ejpam-6082	131	3	fractional	fractional	ADJ
ejpam-6082	131	4	reaction	reaction	NOUN
ejpam-6082	131	5	-	-	PUNCT
ejpam-6082	131	6	diffusion	diffusion	NOUN
ejpam-6082	131	7	system	system	NOUN
ejpam-6082	131	8	is	be	AUX
ejpam-6082	131	9	given	give	VERB
ejpam-6082	131	10	by:	by:	PROPN
ejpam-6082	131	11	c	c	NOUN
ejpam-6082	131	12	0	0	NUM
ejpam-6082	131	13	d	d	NOUN
ejpam-6082	131	14	α	α	PROPN
ejpam-6082	131	15	t	t	PROPN
ejpam-6082	131	16	s(t	s(t	PROPN
ejpam-6082	131	17	,	,	PUNCT
ejpam-6082	131	18	x)−	x)−	PROPN
ejpam-6082	131	19	d1∆s(t	d1∆s(t	PROPN
ejpam-6082	131	20	,	,	PUNCT
ejpam-6082	131	21	x	x	X
ejpam-6082	131	22	)	)	PUNCT
ejpam-6082	131	23	=	=	SYM
ejpam-6082	131	24	λ	λ	NOUN
ejpam-6082	131	25	+	+	CCONJ
ejpam-6082	131	26	ρ1r(t	ρ1r(t	PROPN
ejpam-6082	131	27	,	,	PUNCT
ejpam-6082	131	28	x)−	x)−	PROPN
ejpam-6082	131	29	(	(	PUNCT
ejpam-6082	131	30	λ+	λ+	NUM
ejpam-6082	131	31	δ	δ	PROPN
ejpam-6082	131	32	+	+	CCONJ
ejpam-6082	131	33	µ)s(t	µ)s(t	PROPN
ejpam-6082	131	34	,	,	PUNCT
ejpam-6082	131	35	x	x	NOUN
ejpam-6082	131	36	)	)	PUNCT
ejpam-6082	131	37	,	,	PUNCT
ejpam-6082	131	38	c	c	NOUN
ejpam-6082	131	39	0	0	PUNCT
ejpam-6082	132	1	d	d	NOUN
ejpam-6082	132	2	α	α	PROPN
ejpam-6082	132	3	t	t	NOUN
ejpam-6082	132	4	v	v	PROPN
ejpam-6082	132	5	(	(	PUNCT
ejpam-6082	132	6	t	t	PROPN
ejpam-6082	132	7	,	,	PUNCT
ejpam-6082	132	8	x)−	x)−	PROPN
ejpam-6082	132	9	d2∆v	d2∆v	X
ejpam-6082	132	10	(	(	PUNCT
ejpam-6082	132	11	t	t	PROPN
ejpam-6082	132	12	,	,	PUNCT
ejpam-6082	132	13	x	x	NOUN
ejpam-6082	132	14	)	)	PUNCT
ejpam-6082	132	15	=	=	SYM
ejpam-6082	132	16	δs(t	δs(t	PROPN
ejpam-6082	132	17	,	,	PUNCT
ejpam-6082	132	18	x)−	x)−	PROPN
ejpam-6082	132	19	(	(	PUNCT
ejpam-6082	132	20	1−	1−	NUM
ejpam-6082	132	21	δ)λv	δ)λv	PROPN
ejpam-6082	132	22	(	(	PUNCT
ejpam-6082	132	23	t	t	PROPN
ejpam-6082	132	24	,	,	PUNCT
ejpam-6082	132	25	x)−	x)−	PROPN
ejpam-6082	132	26	(	(	PUNCT
ejpam-6082	132	27	γ	γ	X
ejpam-6082	132	28	+	+	NOUN
ejpam-6082	132	29	µ)v	µ)v	ADJ
ejpam-6082	132	30	(	(	PUNCT
ejpam-6082	132	31	t	t	PROPN
ejpam-6082	132	32	,	,	PUNCT
ejpam-6082	132	33	x	x	NOUN
ejpam-6082	132	34	)	)	PUNCT
ejpam-6082	132	35	,	,	PUNCT
ejpam-6082	132	36	c	c	NOUN
ejpam-6082	132	37	0	0	PUNCT
ejpam-6082	133	1	d	d	NOUN
ejpam-6082	133	2	α	α	PROPN
ejpam-6082	133	3	t	t	PROPN
ejpam-6082	133	4	e(t	e(t	PROPN
ejpam-6082	133	5	,	,	PUNCT
ejpam-6082	133	6	x)−	x)−	PROPN
ejpam-6082	133	7	d3∆e(t	d3∆e(t	NOUN
ejpam-6082	133	8	,	,	PUNCT
ejpam-6082	133	9	x	x	NOUN
ejpam-6082	133	10	)	)	PUNCT
ejpam-6082	133	11	=	=	SYM
ejpam-6082	133	12	λs(t	λs(t	PROPN
ejpam-6082	133	13	,	,	PUNCT
ejpam-6082	133	14	x	x	PRON
ejpam-6082	133	15	)	)	PUNCT
ejpam-6082	134	1	+	+	CCONJ
ejpam-6082	134	2	(	(	PUNCT
ejpam-6082	134	3	1−	1−	NUM
ejpam-6082	134	4	δ)λv	δ)λv	PROPN
ejpam-6082	134	5	(	(	PUNCT
ejpam-6082	134	6	t	t	PROPN
ejpam-6082	134	7	,	,	PUNCT
ejpam-6082	134	8	x)−	x)−	PROPN
ejpam-6082	134	9	(	(	PUNCT
ejpam-6082	134	10	α1	α1	PROPN
ejpam-6082	134	11	+	+	CCONJ
ejpam-6082	134	12	α2	α2	ADJ
ejpam-6082	134	13	+	+	CCONJ
ejpam-6082	134	14	ω	ω	PROPN
ejpam-6082	134	15	+	+	CCONJ
ejpam-6082	134	16	µ)e(t	µ)e(t	NOUN
ejpam-6082	134	17	,	,	PUNCT
ejpam-6082	134	18	x	x	NOUN
ejpam-6082	134	19	)	)	PUNCT
ejpam-6082	134	20	,	,	PUNCT
ejpam-6082	134	21	c	c	NOUN
ejpam-6082	134	22	0	0	PUNCT
ejpam-6082	135	1	d	d	NOUN
ejpam-6082	135	2	α	α	PROPN
ejpam-6082	135	3	t	t	NOUN
ejpam-6082	135	4	np(t	np(t	NOUN
ejpam-6082	135	5	,	,	PUNCT
ejpam-6082	135	6	x)−	x)−	PROPN
ejpam-6082	135	7	d4∆np(t	d4∆np(t	PROPN
ejpam-6082	135	8	,	,	PUNCT
ejpam-6082	135	9	x	x	NOUN
ejpam-6082	135	10	)	)	PUNCT
ejpam-6082	135	11	=	=	SYM
ejpam-6082	135	12	α1e(t	α1e(t	PROPN
ejpam-6082	135	13	,	,	PUNCT
ejpam-6082	135	14	x)−	x)−	PROPN
ejpam-6082	135	15	(	(	PUNCT
ejpam-6082	135	16	σ	σ	PROPN
ejpam-6082	135	17	+	+	X
ejpam-6082	135	18	µ+	µ+	PROPN
ejpam-6082	135	19	ω1)np(t	ω1)np(t	NUM
ejpam-6082	135	20	,	,	PUNCT
ejpam-6082	135	21	x	x	NOUN
ejpam-6082	135	22	)	)	PUNCT
ejpam-6082	135	23	,	,	PUNCT
ejpam-6082	135	24	c	c	NOUN
ejpam-6082	135	25	0	0	PUNCT
ejpam-6082	136	1	d	d	NOUN
ejpam-6082	136	2	α	α	NOUN
ejpam-6082	137	1	t	t	X
ejpam-6082	137	2	p	p	X
ejpam-6082	137	3	(	(	PUNCT
ejpam-6082	137	4	t	t	PROPN
ejpam-6082	137	5	,	,	PUNCT
ejpam-6082	137	6	x)−	x)−	PROPN
ejpam-6082	137	7	d5∆p	d5∆p	PROPN
ejpam-6082	137	8	(	(	PUNCT
ejpam-6082	137	9	t	t	PROPN
ejpam-6082	137	10	,	,	PUNCT
ejpam-6082	137	11	x	x	NOUN
ejpam-6082	137	12	)	)	PUNCT
ejpam-6082	137	13	=	=	SYM
ejpam-6082	137	14	α2e(t	α2e(t	PROPN
ejpam-6082	137	15	,	,	PUNCT
ejpam-6082	137	16	x)−	x)−	PROPN
ejpam-6082	137	17	(	(	PUNCT
ejpam-6082	137	18	σ	σ	PROPN
ejpam-6082	137	19	+	+	X
ejpam-6082	137	20	µ+	µ+	PUNCT
ejpam-6082	137	21	ω2)p	ω2)p	PROPN
ejpam-6082	137	22	(	(	PUNCT
ejpam-6082	137	23	t	t	PROPN
ejpam-6082	137	24	,	,	PUNCT
ejpam-6082	137	25	x	x	NOUN
ejpam-6082	137	26	)	)	PUNCT
ejpam-6082	137	27	,	,	PUNCT
ejpam-6082	137	28	c	c	NOUN
ejpam-6082	137	29	0	0	PROPN
ejpam-6082	138	1	d	d	NOUN
ejpam-6082	138	2	α	α	PROPN
ejpam-6082	138	3	t	t	NOUN
ejpam-6082	138	4	r(t	r(t	NOUN
ejpam-6082	138	5	,	,	PUNCT
ejpam-6082	138	6	x)−	x)−	PROPN
ejpam-6082	138	7	d6∆r(t	d6∆r(t	NOUN
ejpam-6082	138	8	,	,	PUNCT
ejpam-6082	138	9	x	x	NOUN
ejpam-6082	138	10	)	)	PUNCT
ejpam-6082	138	11	=	=	SYM
ejpam-6082	139	1	γv	γv	X
ejpam-6082	139	2	(	(	PUNCT
ejpam-6082	139	3	t	t	PROPN
ejpam-6082	139	4	,	,	PUNCT
ejpam-6082	139	5	x	x	NOUN
ejpam-6082	139	6	)	)	PUNCT
ejpam-6082	139	7	+	+	CCONJ
ejpam-6082	139	8	ωe(t	ωe(t	NUM
ejpam-6082	139	9	,	,	PUNCT
ejpam-6082	139	10	x	x	X
ejpam-6082	139	11	)	)	PUNCT
ejpam-6082	139	12	+	+	NUM
ejpam-6082	139	13	ω1np(t	ω1np(t	NOUN
ejpam-6082	139	14	,	,	PUNCT
ejpam-6082	139	15	x	x	PRON
ejpam-6082	139	16	)	)	PUNCT
ejpam-6082	140	1	+	+	NUM
ejpam-6082	140	2	ω2p	ω2p	NOUN
ejpam-6082	140	3	(	(	PUNCT
ejpam-6082	140	4	t	t	PROPN
ejpam-6082	140	5	,	,	PUNCT
ejpam-6082	140	6	x)−	x)−	PROPN
ejpam-6082	140	7	(	(	PUNCT
ejpam-6082	140	8	ρ+	ρ+	NUM
ejpam-6082	140	9	ρ1	ρ1	NOUN
ejpam-6082	140	10	+	+	CCONJ
ejpam-6082	140	11	µ)r(t	µ)r(t	ADJ
ejpam-6082	140	12	,	,	PUNCT
ejpam-6082	140	13	x	x	NOUN
ejpam-6082	140	14	)	)	PUNCT
ejpam-6082	140	15	,	,	PUNCT
ejpam-6082	140	16	c	c	NOUN
ejpam-6082	140	17	0	0	PUNCT
ejpam-6082	141	1	d	d	NOUN
ejpam-6082	141	2	α	α	NOUN
ejpam-6082	141	3	t	t	NOUN
ejpam-6082	141	4	a(t	a(t	NOUN
ejpam-6082	141	5	,	,	PUNCT
ejpam-6082	141	6	x)−	x)−	PROPN
ejpam-6082	141	7	d7∆a(t	d7∆a(t	NOUN
ejpam-6082	141	8	,	,	PUNCT
ejpam-6082	141	9	x	x	NOUN
ejpam-6082	141	10	)	)	PUNCT
ejpam-6082	141	11	=	=	SYM
ejpam-6082	141	12	ρr(t	ρr(t	NUM
ejpam-6082	141	13	,	,	PUNCT
ejpam-6082	141	14	x)−	x)−	PROPN
ejpam-6082	141	15	(	(	PUNCT
ejpam-6082	141	16	σ	σ	PROPN
ejpam-6082	141	17	+	+	CCONJ
ejpam-6082	141	18	µ)a(t	µ)a(t	PROPN
ejpam-6082	141	19	,	,	PUNCT
ejpam-6082	141	20	x	x	NOUN
ejpam-6082	141	21	)	)	PUNCT
ejpam-6082	141	22	,	,	PUNCT
ejpam-6082	141	23	(	(	PUNCT
ejpam-6082	141	24	2	2	X
ejpam-6082	141	25	)	)	PUNCT
ejpam-6082	141	26	here	here	ADV
ejpam-6082	141	27	,	,	PUNCT
ejpam-6082	141	28	c	c	PROPN
ejpam-6082	141	29	0	0	PROPN
ejpam-6082	142	1	d	d	NOUN
ejpam-6082	142	2	α	α	PROPN
ejpam-6082	142	3	t	t	PROPN
ejpam-6082	142	4	denotes	denote	VERB
ejpam-6082	142	5	the	the	DET
ejpam-6082	142	6	caputo	caputo	PROPN
ejpam-6082	142	7	fractional	fractional	PROPN
ejpam-6082	142	8	derivative	derivative	NOUN
ejpam-6082	142	9	of	of	ADP
ejpam-6082	142	10	order	order	NOUN
ejpam-6082	142	11	α	α	NOUN
ejpam-6082	142	12	.	.	PUNCT
ejpam-6082	143	1	the	the	DET
ejpam-6082	143	2	combination	combination	NOUN
ejpam-6082	143	3	of	of	ADP
ejpam-6082	143	4	fractional	fractional	ADJ
ejpam-6082	143	5	derivatives	derivative	NOUN
ejpam-6082	143	6	and	and	CCONJ
ejpam-6082	143	7	diffusion	diffusion	NOUN
ejpam-6082	143	8	terms	term	NOUN
ejpam-6082	143	9	enhances	enhance	VERB
ejpam-6082	143	10	the	the	DET
ejpam-6082	143	11	model	model	NOUN
ejpam-6082	143	12	’s	’s	PART
ejpam-6082	143	13	capability	capability	NOUN
ejpam-6082	143	14	to	to	PART
ejpam-6082	143	15	capture	capture	VERB
ejpam-6082	143	16	both	both	DET
ejpam-6082	143	17	temporal	temporal	ADJ
ejpam-6082	143	18	and	and	CCONJ
ejpam-6082	143	19	spatial	spatial	ADJ
ejpam-6082	143	20	heterogeneity	heterogeneity	NOUN
ejpam-6082	143	21	in	in	ADP
ejpam-6082	143	22	disease	disease	NOUN
ejpam-6082	143	23	dynamics	dynamic	NOUN
ejpam-6082	143	24	.	.	PUNCT
ejpam-6082	144	1	the	the	DET
ejpam-6082	144	2	initial	initial	ADJ
ejpam-6082	144	3	conditions	condition	NOUN
ejpam-6082	144	4	(	(	PUNCT
ejpam-6082	144	5	ics	ics	NOUN
ejpam-6082	144	6	)	)	PUNCT
ejpam-6082	144	7	for	for	ADP
ejpam-6082	144	8	the	the	DET
ejpam-6082	144	9	above	above	ADJ
ejpam-6082	144	10	model	model	NOUN
ejpam-6082	144	11	are	be	AUX
ejpam-6082	144	12	as	as	SCONJ
ejpam-6082	144	13	follows	follow	VERB
ejpam-6082	144	14	:	:	PUNCT
ejpam-6082	144	15	s(x	s(x	NOUN
ejpam-6082	144	16	,	,	PUNCT
ejpam-6082	144	17	0	0	NUM
ejpam-6082	144	18	)	)	PUNCT
ejpam-6082	144	19	=	=	SYM
ejpam-6082	144	20	ψ1(x	ψ1(x	PROPN
ejpam-6082	144	21	)	)	PUNCT
ejpam-6082	144	22	,	,	PUNCT
ejpam-6082	144	23	v	v	X
ejpam-6082	144	24	(	(	PUNCT
ejpam-6082	144	25	x	x	NOUN
ejpam-6082	144	26	,	,	PUNCT
ejpam-6082	144	27	0	0	NUM
ejpam-6082	144	28	)	)	PUNCT
ejpam-6082	144	29	=	=	SYM
ejpam-6082	144	30	ψ2(x	ψ2(x	PROPN
ejpam-6082	144	31	)	)	PUNCT
ejpam-6082	144	32	,	,	PUNCT
ejpam-6082	144	33	e(x	e(x	NUM
ejpam-6082	144	34	,	,	PUNCT
ejpam-6082	144	35	0	0	NUM
ejpam-6082	144	36	)	)	PUNCT
ejpam-6082	144	37	=	=	SYM
ejpam-6082	144	38	ψ3(x	ψ3(x	PROPN
ejpam-6082	144	39	)	)	PUNCT
ejpam-6082	144	40	,	,	PUNCT
ejpam-6082	144	41	np(x	np(x	PROPN
ejpam-6082	144	42	,	,	PUNCT
ejpam-6082	144	43	0	0	NUM
ejpam-6082	144	44	)	)	PUNCT
ejpam-6082	144	45	=	=	PUNCT
ejpam-6082	145	1	ψ4(x	ψ4(x	NOUN
ejpam-6082	145	2	)	)	PUNCT
ejpam-6082	145	3	,	,	PUNCT
ejpam-6082	145	4	p(x	p(x	NOUN
ejpam-6082	145	5	,	,	PUNCT
ejpam-6082	145	6	0	0	NUM
ejpam-6082	145	7	)	)	PUNCT
ejpam-6082	145	8	=	=	PUNCT
ejpam-6082	145	9	ψ5(x	ψ5(x	NUM
ejpam-6082	145	10	)	)	PUNCT
ejpam-6082	145	11	,	,	PUNCT
ejpam-6082	145	12	r(x	r(x	PROPN
ejpam-6082	145	13	,	,	PUNCT
ejpam-6082	145	14	0	0	NUM
ejpam-6082	145	15	)	)	PUNCT
ejpam-6082	145	16	=	=	SYM
ejpam-6082	145	17	ψ6(x	ψ6(x	PROPN
ejpam-6082	145	18	)	)	PUNCT
ejpam-6082	145	19	,	,	PUNCT
ejpam-6082	145	20	a(x	a(x	PROPN
ejpam-6082	145	21	,	,	PUNCT
ejpam-6082	145	22	0	0	NUM
ejpam-6082	145	23	)	)	PUNCT
ejpam-6082	145	24	=	=	SYM
ejpam-6082	145	25	ψ7(x	ψ7(x	NUM
ejpam-6082	145	26	)	)	PUNCT
ejpam-6082	145	27	,	,	PUNCT
ejpam-6082	145	28	x	x	PUNCT
ejpam-6082	145	29	∈	∈	PROPN
ejpam-6082	145	30	ω	ω	PROPN
ejpam-6082	145	31	.	.	PUNCT
ejpam-6082	146	1	(	(	PUNCT
ejpam-6082	146	2	3	3	X
ejpam-6082	146	3	)	)	PUNCT
ejpam-6082	146	4	k.	k.	NOUN
ejpam-6082	146	5	guedri	guedri	PROPN
ejpam-6082	147	1	et	et	PROPN
ejpam-6082	147	2	al	al	PROPN
ejpam-6082	147	3	.	.	PUNCT
ejpam-6082	147	4	/	/	SYM
ejpam-6082	147	5	eur	eur	PROPN
ejpam-6082	147	6	.	.	PUNCT
ejpam-6082	148	1	j.	j.	PROPN
ejpam-6082	148	2	pure	pure	PROPN
ejpam-6082	148	3	appl	appl	PROPN
ejpam-6082	148	4	.	.	PROPN
ejpam-6082	148	5	math	math	PROPN
ejpam-6082	148	6	,	,	PUNCT
ejpam-6082	148	7	18	18	NUM
ejpam-6082	148	8	(	(	PUNCT
ejpam-6082	148	9	2	2	NUM
ejpam-6082	148	10	)	)	PUNCT
ejpam-6082	148	11	(	(	PUNCT
ejpam-6082	148	12	2025	2025	NUM
ejpam-6082	148	13	)	)	PUNCT
ejpam-6082	148	14	,	,	PUNCT
ejpam-6082	148	15	6082	6082	NUM
ejpam-6082	148	16	8	8	NUM
ejpam-6082	148	17	of	of	ADP
ejpam-6082	148	18	39	39	NUM
ejpam-6082	148	19	no	no	DET
ejpam-6082	148	20	-	-	PUNCT
ejpam-6082	148	21	flux	flux	NOUN
ejpam-6082	148	22	boundary	boundary	ADJ
ejpam-6082	148	23	conditions	condition	NOUN
ejpam-6082	148	24	(	(	PUNCT
ejpam-6082	148	25	bcs	bcs	NOUN
ejpam-6082	148	26	)	)	PUNCT
ejpam-6082	148	27	for	for	ADP
ejpam-6082	148	28	the	the	DET
ejpam-6082	148	29	model	model	NOUN
ejpam-6082	148	30	(	(	PUNCT
ejpam-6082	148	31	2	2	NUM
ejpam-6082	148	32	)	)	PUNCT
ejpam-6082	148	33	∂	∂	NUM
ejpam-6082	148	34	∂n	∂n	PROPN
ejpam-6082	148	35	s(x	s(x	PROPN
ejpam-6082	148	36	,	,	PUNCT
ejpam-6082	148	37	t	t	PROPN
ejpam-6082	148	38	)	)	PUNCT
ejpam-6082	148	39	=	=	SYM
ejpam-6082	148	40	∂	∂	NUM
ejpam-6082	148	41	∂n	∂n	PROPN
ejpam-6082	148	42	v	v	NOUN
ejpam-6082	148	43	(	(	PUNCT
ejpam-6082	148	44	x	x	NOUN
ejpam-6082	148	45	,	,	PUNCT
ejpam-6082	148	46	t	t	PROPN
ejpam-6082	148	47	)	)	PUNCT
ejpam-6082	148	48	=	=	SYM
ejpam-6082	148	49	∂	∂	NUM
ejpam-6082	148	50	∂n	∂n	PROPN
ejpam-6082	148	51	e(x	e(x	NUM
ejpam-6082	148	52	,	,	PUNCT
ejpam-6082	148	53	t	t	PROPN
ejpam-6082	148	54	)	)	PUNCT
ejpam-6082	148	55	=	=	SYM
ejpam-6082	148	56	∂	∂	NUM
ejpam-6082	148	57	∂n	∂n	PROPN
ejpam-6082	148	58	np(x	np(x	NUM
ejpam-6082	148	59	,	,	PUNCT
ejpam-6082	148	60	t	t	PROPN
ejpam-6082	148	61	)	)	PUNCT
ejpam-6082	148	62	=	=	SYM
ejpam-6082	148	63	0	0	NUM
ejpam-6082	148	64	,	,	PUNCT
ejpam-6082	148	65	∂	∂	NOUN
ejpam-6082	148	66	∂n	∂n	PROPN
ejpam-6082	148	67	p	p	PROPN
ejpam-6082	148	68	(	(	PUNCT
ejpam-6082	148	69	x	x	PROPN
ejpam-6082	148	70	,	,	PUNCT
ejpam-6082	148	71	t	t	PROPN
ejpam-6082	148	72	)	)	PUNCT
ejpam-6082	148	73	=	=	SYM
ejpam-6082	148	74	∂	∂	NUM
ejpam-6082	148	75	∂n	∂n	PROPN
ejpam-6082	148	76	r(x	r(x	PROPN
ejpam-6082	148	77	,	,	PUNCT
ejpam-6082	148	78	t	t	PROPN
ejpam-6082	148	79	)	)	PUNCT
ejpam-6082	148	80	=	=	SYM
ejpam-6082	148	81	∂	∂	NUM
ejpam-6082	148	82	∂n	∂n	PROPN
ejpam-6082	148	83	a(x	a(x	PROPN
ejpam-6082	148	84	,	,	PUNCT
ejpam-6082	148	85	t	t	PROPN
ejpam-6082	148	86	)	)	PUNCT
ejpam-6082	148	87	=	=	SYM
ejpam-6082	149	1	0	0	NUM
ejpam-6082	149	2	,	,	PUNCT
ejpam-6082	149	3	t	t	PROPN
ejpam-6082	149	4	≥	≥	NUM
ejpam-6082	149	5	0	0	NUM
ejpam-6082	149	6	,	,	PUNCT
ejpam-6082	149	7	x	x	SYM
ejpam-6082	149	8	∈	∈	PROPN
ejpam-6082	149	9	∂ω	∂ω	PROPN
ejpam-6082	149	10	(	(	PUNCT
ejpam-6082	149	11	4	4	NUM
ejpam-6082	149	12	)	)	PUNCT
ejpam-6082	149	13	where	where	SCONJ
ejpam-6082	149	14	∂ω	∂ω	PROPN
ejpam-6082	149	15	represent	represent	VERB
ejpam-6082	149	16	the	the	DET
ejpam-6082	149	17	smooth	smooth	ADJ
ejpam-6082	149	18	boundary	boundary	NOUN
ejpam-6082	149	19	with	with	ADP
ejpam-6082	149	20	a	a	DET
ejpam-6082	149	21	bounded	bounded	ADJ
ejpam-6082	149	22	domain	domain	NOUN
ejpam-6082	149	23	ω	ω	X
ejpam-6082	149	24	⊂	⊂	X
ejpam-6082	149	25	r	r	NOUN
ejpam-6082	149	26	,	,	PUNCT
ejpam-6082	149	27	and	and	CCONJ
ejpam-6082	149	28	the	the	DET
ejpam-6082	149	29	homogeneous	homogeneous	ADJ
ejpam-6082	149	30	neumann	neumann	PROPN
ejpam-6082	149	31	boundary	boundary	PROPN
ejpam-6082	149	32	conditions	condition	NOUN
ejpam-6082	149	33	mean	mean	VERB
ejpam-6082	149	34	that	that	SCONJ
ejpam-6082	149	35	no	no	DET
ejpam-6082	149	36	individual	individual	ADJ
ejpam-6082	149	37	crosses	cross	VERB
ejpam-6082	149	38	the	the	DET
ejpam-6082	149	39	boundary	boundary	ADJ
ejpam-6082	149	40	∂ω	∂ω	PROPN
ejpam-6082	149	41	.	.	PUNCT
ejpam-6082	150	1	the	the	DET
ejpam-6082	150	2	coefficients	coefficient	NOUN
ejpam-6082	150	3	d1	d1	PROPN
ejpam-6082	150	4	,	,	PUNCT
ejpam-6082	150	5	...	...	PUNCT
ejpam-6082	150	6	,	,	PUNCT
ejpam-6082	150	7	d7	d7	PROPN
ejpam-6082	150	8	are	be	AUX
ejpam-6082	150	9	positive	positive	ADJ
ejpam-6082	150	10	constants	constant	NOUN
ejpam-6082	150	11	which	which	PRON
ejpam-6082	150	12	control	control	VERB
ejpam-6082	150	13	the	the	DET
ejpam-6082	150	14	movement	movement	NOUN
ejpam-6082	150	15	or	or	CCONJ
ejpam-6082	150	16	migration	migration	NOUN
ejpam-6082	150	17	of	of	ADP
ejpam-6082	150	18	classes	class	NOUN
ejpam-6082	150	19	of	of	ADP
ejpam-6082	150	20	population	population	NOUN
ejpam-6082	150	21	,	,	PUNCT
ejpam-6082	150	22	respectively	respectively	ADV
ejpam-6082	150	23	.	.	PUNCT
ejpam-6082	151	1	s	s	PART
ejpam-6082	152	1	e	e	NOUN
ejpam-6082	152	2	p	p	NOUN
ejpam-6082	152	3	np	np	INTJ
ejpam-6082	152	4	v	v	NOUN
ejpam-6082	152	5	r	r	NOUN
ejpam-6082	152	6	a	a	PRON
ejpam-6082	152	7	λ	λ	NOUN
ejpam-6082	152	8	λ	λ	X
ejpam-6082	152	9	δ	δ	NOUN
ejpam-6082	152	10	γ	γ	X
ejpam-6082	152	11	α2	α2	PROPN
ejpam-6082	152	12	(	(	PUNCT
ejpam-6082	152	13	1−	1−	NUM
ejpam-6082	152	14	δ)λ	δ)λ	NOUN
ejpam-6082	152	15	ω	ω	PROPN
ejpam-6082	152	16	ω2	ω2	PROPN
ejpam-6082	152	17	ω1	ω1	PROPN
ejpam-6082	152	18	ρ	ρ	PROPN
ejpam-6082	152	19	µ	µ	PROPN
ejpam-6082	152	20	µ	µ	X
ejpam-6082	152	21	µ+	µ+	X
ejpam-6082	152	22	σ	σ	PROPN
ejpam-6082	152	23	µ+	µ+	PROPN
ejpam-6082	152	24	σ	σ	PROPN
ejpam-6082	152	25	µ+	µ+	PROPN
ejpam-6082	152	26	σ	σ	PROPN
ejpam-6082	152	27	µ	µ	PROPN
ejpam-6082	152	28	µ	µ	PROPN
ejpam-6082	152	29	ρ1	ρ1	NOUN
ejpam-6082	152	30	α1	α1	PROPN
ejpam-6082	152	31	figure	figure	NOUN
ejpam-6082	152	32	1	1	NUM
ejpam-6082	152	33	:	:	PUNCT
ejpam-6082	152	34	flow	flow	NOUN
ejpam-6082	152	35	diagram	diagram	NOUN
ejpam-6082	152	36	of	of	ADP
ejpam-6082	152	37	polio	polio	NOUN
ejpam-6082	152	38	virus	virus	NOUN
ejpam-6082	152	39	dynamics	dynamic	NOUN
ejpam-6082	152	40	3	3	NUM
ejpam-6082	152	41	.	.	PUNCT
ejpam-6082	152	42	preliminaries	preliminary	NOUN
ejpam-6082	152	43	we	we	PRON
ejpam-6082	152	44	recall	recall	VERB
ejpam-6082	152	45	the	the	DET
ejpam-6082	152	46	definitions	definition	NOUN
ejpam-6082	152	47	of	of	ADP
ejpam-6082	152	48	the	the	DET
ejpam-6082	152	49	caputo	caputo	PROPN
ejpam-6082	152	50	fractional	fractional	PROPN
ejpam-6082	152	51	partial	partial	ADJ
ejpam-6082	152	52	derivative	derivative	NOUN
ejpam-6082	152	53	(	(	PUNCT
ejpam-6082	152	54	cfpd	cfpd	PROPN
ejpam-6082	152	55	)	)	PUNCT
ejpam-6082	152	56	,	,	PUNCT
ejpam-6082	152	57	laplace	laplace	NOUN
ejpam-6082	152	58	transform	transform	NOUN
ejpam-6082	152	59	(	(	PUNCT
ejpam-6082	152	60	lt	lt	NOUN
ejpam-6082	152	61	)	)	PUNCT
ejpam-6082	152	62	,	,	PUNCT
ejpam-6082	152	63	and	and	CCONJ
ejpam-6082	152	64	mittag	mittag	ADJ
ejpam-6082	152	65	-	-	PUNCT
ejpam-6082	152	66	leffler	leffler	NOUN
ejpam-6082	152	67	function	function	NOUN
ejpam-6082	152	68	(	(	PUNCT
ejpam-6082	152	69	see	see	VERB
ejpam-6082	152	70	,	,	PUNCT
ejpam-6082	152	71	e.g.	e.g.	ADV
ejpam-6082	152	72	,	,	PUNCT
ejpam-6082	152	73	[	[	X
ejpam-6082	152	74	49–51	49–51	NUM
ejpam-6082	152	75	]	]	PUNCT
ejpam-6082	152	76	)	)	PUNCT
ejpam-6082	152	77	.	.	PUNCT
ejpam-6082	153	1	definition	definition	NOUN
ejpam-6082	153	2	1	1	NUM
ejpam-6082	153	3	(	(	PUNCT
ejpam-6082	153	4	riemann	riemann	PROPN
ejpam-6082	153	5	-	-	PUNCT
ejpam-6082	153	6	liouville	liouville	VERB
ejpam-6082	153	7	fractional	fractional	ADJ
ejpam-6082	153	8	integral	integral	ADJ
ejpam-6082	153	9	)	)	PUNCT
ejpam-6082	153	10	.	.	PUNCT
ejpam-6082	154	1	let	let	VERB
ejpam-6082	154	2	g(t	g(t	PROPN
ejpam-6082	154	3	)	)	PUNCT
ejpam-6082	154	4	∈	∈	PROPN
ejpam-6082	154	5	l1	l1	PROPN
ejpam-6082	154	6	(	(	PUNCT
ejpam-6082	154	7	r+	r+	X
ejpam-6082	154	8	)	)	PUNCT
ejpam-6082	154	9	.	.	PUNCT
ejpam-6082	155	1	the	the	DET
ejpam-6082	155	2	riemannliouville	riemannliouville	NOUN
ejpam-6082	155	3	fractional	fractional	ADJ
ejpam-6082	155	4	integral	integral	ADJ
ejpam-6082	155	5	is	be	AUX
ejpam-6082	155	6	defined	define	VERB
ejpam-6082	155	7	as	as	ADP
ejpam-6082	155	8	:	:	PUNCT
ejpam-6082	155	9	ℑα	ℑα	PROPN
ejpam-6082	155	10	t	t	PROPN
ejpam-6082	155	11	g(t	g(t	PROPN
ejpam-6082	155	12	)	)	PUNCT
ejpam-6082	156	1	=	=	SYM
ejpam-6082	156	2	1	1	NUM
ejpam-6082	156	3	γ(α	γ(α	NOUN
ejpam-6082	156	4	)	)	PUNCT
ejpam-6082	157	1	∫	∫	PROPN
ejpam-6082	157	2	t	t	PROPN
ejpam-6082	157	3	0	0	NUM
ejpam-6082	157	4	(	(	PUNCT
ejpam-6082	157	5	t−	t−	PROPN
ejpam-6082	157	6	ζ)α−1g(ζ	ζ)α−1g(ζ	NOUN
ejpam-6082	157	7	)	)	PUNCT
ejpam-6082	157	8	dζ	dζ	PROPN
ejpam-6082	157	9	,	,	PUNCT
ejpam-6082	157	10	t	t	X
ejpam-6082	157	11	>	>	X
ejpam-6082	157	12	0	0	PROPN
ejpam-6082	157	13	,	,	PUNCT
ejpam-6082	157	14	α	α	NOUN
ejpam-6082	157	15	>	>	X
ejpam-6082	157	16	0	0	NUM
ejpam-6082	157	17	,	,	PUNCT
ejpam-6082	157	18	(	(	PUNCT
ejpam-6082	157	19	5	5	X
ejpam-6082	157	20	)	)	PUNCT
ejpam-6082	157	21	k.	k.	NOUN
ejpam-6082	157	22	guedri	guedri	PROPN
ejpam-6082	157	23	et	et	PROPN
ejpam-6082	157	24	al	al	PROPN
ejpam-6082	157	25	.	.	PUNCT
ejpam-6082	157	26	/	/	SYM
ejpam-6082	157	27	eur	eur	PROPN
ejpam-6082	157	28	.	.	PUNCT
ejpam-6082	158	1	j.	j.	PROPN
ejpam-6082	158	2	pure	pure	PROPN
ejpam-6082	158	3	appl	appl	PROPN
ejpam-6082	158	4	.	.	PROPN
ejpam-6082	158	5	math	math	PROPN
ejpam-6082	158	6	,	,	PUNCT
ejpam-6082	158	7	18	18	NUM
ejpam-6082	158	8	(	(	PUNCT
ejpam-6082	158	9	2	2	NUM
ejpam-6082	158	10	)	)	PUNCT
ejpam-6082	158	11	(	(	PUNCT
ejpam-6082	158	12	2025	2025	NUM
ejpam-6082	158	13	)	)	PUNCT
ejpam-6082	158	14	,	,	PUNCT
ejpam-6082	158	15	6082	6082	NUM
ejpam-6082	158	16	9	9	NUM
ejpam-6082	158	17	of	of	ADP
ejpam-6082	158	18	39	39	NUM
ejpam-6082	158	19	with	with	ADP
ejpam-6082	158	20	the	the	DET
ejpam-6082	158	21	special	special	ADJ
ejpam-6082	158	22	case	case	NOUN
ejpam-6082	158	23	:	:	PUNCT
ejpam-6082	158	24	ℑ0	ℑ0	PROPN
ejpam-6082	158	25	t	t	PROPN
ejpam-6082	158	26	g(t	g(t	PROPN
ejpam-6082	158	27	)	)	PUNCT
ejpam-6082	158	28	=	=	PUNCT
ejpam-6082	158	29	g(t	g(t	PROPN
ejpam-6082	158	30	)	)	PUNCT
ejpam-6082	158	31	.	.	PUNCT
ejpam-6082	159	1	(	(	PUNCT
ejpam-6082	159	2	6	6	X
ejpam-6082	159	3	)	)	PUNCT
ejpam-6082	159	4	definition	definition	NOUN
ejpam-6082	159	5	2	2	NUM
ejpam-6082	159	6	(	(	PUNCT
ejpam-6082	159	7	caputo	caputo	PROPN
ejpam-6082	159	8	fractional	fractional	ADJ
ejpam-6082	159	9	partial	partial	ADJ
ejpam-6082	159	10	derivative	derivative	NOUN
ejpam-6082	159	11	)	)	PUNCT
ejpam-6082	159	12	.	.	PUNCT
ejpam-6082	160	1	let	let	VERB
ejpam-6082	160	2	g(x	g(x	NOUN
ejpam-6082	160	3	,	,	PUNCT
ejpam-6082	160	4	t	t	PROPN
ejpam-6082	160	5	)	)	PUNCT
ejpam-6082	160	6	∈	∈	PROPN
ejpam-6082	160	7	acn	acn	PROPN
ejpam-6082	160	8	(	(	PUNCT
ejpam-6082	160	9	[	[	X
ejpam-6082	160	10	0,+∞),r+	0,+∞),r+	NOUN
ejpam-6082	160	11	)	)	PUNCT
ejpam-6082	160	12	.	.	PUNCT
ejpam-6082	161	1	the	the	DET
ejpam-6082	161	2	caputo	caputo	PROPN
ejpam-6082	161	3	fractional	fractional	PROPN
ejpam-6082	161	4	derivative	derivative	NOUN
ejpam-6082	161	5	of	of	ADP
ejpam-6082	161	6	order	order	NOUN
ejpam-6082	161	7	α	α	NOUN
ejpam-6082	161	8	is	be	AUX
ejpam-6082	161	9	defined	define	VERB
ejpam-6082	161	10	as	as	ADP
ejpam-6082	161	11	:	:	PUNCT
ejpam-6082	161	12	cdα	cdα	NOUN
ejpam-6082	161	13	t	t	PROPN
ejpam-6082	161	14	g(x	g(x	PROPN
ejpam-6082	161	15	,	,	PUNCT
ejpam-6082	161	16	t	t	PROPN
ejpam-6082	161	17	)	)	PUNCT
ejpam-6082	161	18	=	=	PRON
ejpam-6082	161	19	{	{	PUNCT
ejpam-6082	161	20	1	1	NUM
ejpam-6082	161	21	γ(n−α	γ(n−α	NOUN
ejpam-6082	161	22	)	)	PUNCT
ejpam-6082	162	1	∫	∫	PROPN
ejpam-6082	162	2	t	t	PROPN
ejpam-6082	162	3	0	0	NUM
ejpam-6082	162	4	(	(	PUNCT
ejpam-6082	162	5	t−	t−	PROPN
ejpam-6082	162	6	ζ)n−α−1	ζ)n−α−1	PROPN
ejpam-6082	162	7	∂	∂	NUM
ejpam-6082	162	8	ng(x	ng(x	NUM
ejpam-6082	162	9	,	,	PUNCT
ejpam-6082	162	10	ζ	ζ	NOUN
ejpam-6082	162	11	)	)	PUNCT
ejpam-6082	162	12	∂ζn	∂ζn	PROPN
ejpam-6082	162	13	dζ	dζ	PROPN
ejpam-6082	162	14	,	,	PUNCT
ejpam-6082	162	15	n−	n−	NOUN
ejpam-6082	162	16	1	1	NUM
ejpam-6082	162	17	<	<	X
ejpam-6082	162	18	α	α	X
ejpam-6082	162	19	<	<	X
ejpam-6082	162	20	n	n	CCONJ
ejpam-6082	162	21	,	,	PUNCT
ejpam-6082	162	22	∂ng(x	∂ng(x	ADJ
ejpam-6082	162	23	,	,	PUNCT
ejpam-6082	162	24	t	t	PROPN
ejpam-6082	162	25	)	)	PUNCT
ejpam-6082	162	26	∂tn	∂tn	PROPN
ejpam-6082	162	27	,	,	PUNCT
ejpam-6082	162	28	α	α	NOUN
ejpam-6082	162	29	=	=	SYM
ejpam-6082	162	30	n	n	CCONJ
ejpam-6082	162	31	∈	∈	PROPN
ejpam-6082	162	32	n.	n.	NOUN
ejpam-6082	162	33	(	(	PUNCT
ejpam-6082	162	34	7	7	NUM
ejpam-6082	162	35	)	)	PUNCT
ejpam-6082	162	36	definition	definition	NOUN
ejpam-6082	162	37	3	3	NUM
ejpam-6082	162	38	(	(	PUNCT
ejpam-6082	162	39	laplace	laplace	NOUN
ejpam-6082	162	40	transform	transform	NOUN
ejpam-6082	162	41	of	of	ADP
ejpam-6082	162	42	cfpd	cfpd	NOUN
ejpam-6082	162	43	)	)	PUNCT
ejpam-6082	162	44	.	.	PUNCT
ejpam-6082	163	1	let	let	VERB
ejpam-6082	163	2	g(s	g(	NOUN
ejpam-6082	163	3	)	)	PUNCT
ejpam-6082	163	4	be	be	AUX
ejpam-6082	163	5	the	the	DET
ejpam-6082	163	6	laplace	laplace	NOUN
ejpam-6082	163	7	transform	transform	NOUN
ejpam-6082	163	8	of	of	ADP
ejpam-6082	163	9	the	the	DET
ejpam-6082	163	10	function	function	NOUN
ejpam-6082	163	11	g(t	g(t	PROPN
ejpam-6082	163	12	)	)	PUNCT
ejpam-6082	163	13	.	.	PUNCT
ejpam-6082	164	1	then	then	ADV
ejpam-6082	164	2	,	,	PUNCT
ejpam-6082	164	3	the	the	DET
ejpam-6082	164	4	lt	lt	NOUN
ejpam-6082	164	5	of	of	ADP
ejpam-6082	164	6	cfpd	cfpd	PROPN
ejpam-6082	164	7	is	be	AUX
ejpam-6082	164	8	given	give	VERB
ejpam-6082	164	9	by	by	ADP
ejpam-6082	164	10	:	:	PUNCT
ejpam-6082	164	11	l{dα	l{dα	PROPN
ejpam-6082	164	12	t	t	PROPN
ejpam-6082	164	13	g(x	g(x	PROPN
ejpam-6082	164	14	,	,	PUNCT
ejpam-6082	164	15	t	t	PROPN
ejpam-6082	164	16	)	)	PUNCT
ejpam-6082	164	17	;	;	PUNCT
ejpam-6082	164	18	s	s	X
ejpam-6082	164	19	}	}	PUNCT
ejpam-6082	164	20	=	=	SYM
ejpam-6082	164	21	sαg(x	sαg(x	PROPN
ejpam-6082	164	22	,	,	PUNCT
ejpam-6082	164	23	s)−	s)−	PROPN
ejpam-6082	164	24	n−1∑	n−1∑	NUM
ejpam-6082	164	25	i=0	i=0	PROPN
ejpam-6082	164	26	sα−i−1g(i)(x	sα−i−1g(i)(x	PROPN
ejpam-6082	164	27	,	,	PUNCT
ejpam-6082	164	28	0	0	NUM
ejpam-6082	164	29	)	)	PUNCT
ejpam-6082	164	30	,	,	PUNCT
ejpam-6082	164	31	(	(	PUNCT
ejpam-6082	164	32	8)	8)	NUM
ejpam-6082	164	33	where	where	SCONJ
ejpam-6082	164	34	α	α	PROPN
ejpam-6082	164	35	∈	∈	PROPN
ejpam-6082	164	36	(	(	PUNCT
ejpam-6082	164	37	n−	n−	NOUN
ejpam-6082	164	38	1	1	NUM
ejpam-6082	164	39	,	,	PUNCT
ejpam-6082	164	40	n	n	CCONJ
ejpam-6082	164	41	]	]	PUNCT
ejpam-6082	164	42	,	,	PUNCT
ejpam-6082	164	43	n	n	PROPN
ejpam-6082	164	44	∈	∈	PROPN
ejpam-6082	164	45	n.	n.	NOUN
ejpam-6082	164	46	definition	definition	NOUN
ejpam-6082	164	47	4	4	NUM
ejpam-6082	164	48	(	(	PUNCT
ejpam-6082	164	49	mittag	mittag	ADJ
ejpam-6082	164	50	-	-	PUNCT
ejpam-6082	164	51	leffler	leffler	NOUN
ejpam-6082	164	52	function	function	NOUN
ejpam-6082	164	53	)	)	PUNCT
ejpam-6082	164	54	.	.	PUNCT
ejpam-6082	165	1	the	the	DET
ejpam-6082	165	2	two	two	NUM
ejpam-6082	165	3	-	-	PUNCT
ejpam-6082	165	4	parameter	parameter	NOUN
ejpam-6082	165	5	mittag	mittag	ADJ
ejpam-6082	165	6	-	-	PUNCT
ejpam-6082	165	7	leffler	leffler	NOUN
ejpam-6082	165	8	function	function	NOUN
ejpam-6082	165	9	ma	ma	PROPN
ejpam-6082	165	10	,	,	PUNCT
ejpam-6082	165	11	b(x	b(x	NOUN
ejpam-6082	165	12	)	)	PUNCT
ejpam-6082	165	13	is	be	AUX
ejpam-6082	165	14	defined	define	VERB
ejpam-6082	165	15	as	as	ADP
ejpam-6082	165	16	:	:	PUNCT
ejpam-6082	165	17	ma	ma	PROPN
ejpam-6082	165	18	,	,	PUNCT
ejpam-6082	165	19	b(x	b(x	NOUN
ejpam-6082	165	20	)	)	PUNCT
ejpam-6082	165	21	=	=	SYM
ejpam-6082	166	1	∞∑	∞∑	NUM
ejpam-6082	166	2	m=0	m=0	PROPN
ejpam-6082	166	3	xm	xm	PROPN
ejpam-6082	166	4	γ(am+	γ(am+	NUM
ejpam-6082	166	5	b	b	X
ejpam-6082	166	6	)	)	PUNCT
ejpam-6082	166	7	,	,	PUNCT
ejpam-6082	166	8	x	x	PUNCT
ejpam-6082	166	9	∈	∈	PROPN
ejpam-6082	166	10	r	r	NOUN
ejpam-6082	166	11	,	,	PUNCT
ejpam-6082	166	12	a	a	DET
ejpam-6082	166	13	>	>	X
ejpam-6082	166	14	0	0	NUM
ejpam-6082	166	15	,	,	PUNCT
ejpam-6082	166	16	b	b	X
ejpam-6082	166	17	>	>	X
ejpam-6082	166	18	0	0	NUM
ejpam-6082	166	19	.	.	PUNCT
ejpam-6082	166	20	(	(	PUNCT
ejpam-6082	166	21	9	9	X
ejpam-6082	166	22	)	)	PUNCT
ejpam-6082	166	23	the	the	DET
ejpam-6082	166	24	following	follow	VERB
ejpam-6082	166	25	properties	property	NOUN
ejpam-6082	166	26	of	of	ADP
ejpam-6082	166	27	ma	ma	PROPN
ejpam-6082	166	28	,	,	PUNCT
ejpam-6082	166	29	b(x	b(x	NOUN
ejpam-6082	166	30	)	)	PUNCT
ejpam-6082	166	31	hold	hold	VERB
ejpam-6082	166	32	[	[	X
ejpam-6082	166	33	49	49	NUM
ejpam-6082	166	34	]	]	X
ejpam-6082	166	35	:	:	PUNCT
ejpam-6082	166	36	ma	ma	PROPN
ejpam-6082	166	37	,	,	PUNCT
ejpam-6082	166	38	b(x	b(x	NOUN
ejpam-6082	166	39	)	)	PUNCT
ejpam-6082	166	40	=	=	SYM
ejpam-6082	166	41	xma	xma	NOUN
ejpam-6082	166	42	,	,	PUNCT
ejpam-6082	166	43	a+b(x	a+b(x	NOUN
ejpam-6082	166	44	)	)	PUNCT
ejpam-6082	166	45	+	+	CCONJ
ejpam-6082	166	46	1	1	NUM
ejpam-6082	166	47	γ(b	γ(b	NOUN
ejpam-6082	166	48	)	)	PUNCT
ejpam-6082	166	49	,	,	PUNCT
ejpam-6082	166	50	(	(	PUNCT
ejpam-6082	166	51	10	10	NUM
ejpam-6082	166	52	)	)	PUNCT
ejpam-6082	166	53	l	l	NOUN
ejpam-6082	166	54	[	[	PUNCT
ejpam-6082	166	55	tb−1ma	tb−1ma	NUM
ejpam-6082	166	56	,	,	PUNCT
ejpam-6082	166	57	b	b	NOUN
ejpam-6082	166	58	(	(	PUNCT
ejpam-6082	166	59	±κta	±κta	NOUN
ejpam-6082	166	60	)	)	PUNCT
ejpam-6082	166	61	]	]	PUNCT
ejpam-6082	167	1	=	=	PUNCT
ejpam-6082	167	2	sa−b	sa−b	NOUN
ejpam-6082	167	3	sa	sa	PROPN
ejpam-6082	167	4	∓	∓	PROPN
ejpam-6082	167	5	κ	κ	PROPN
ejpam-6082	167	6	.	.	PUNCT
ejpam-6082	168	1	(	(	PUNCT
ejpam-6082	168	2	11	11	NUM
ejpam-6082	168	3	)	)	PUNCT
ejpam-6082	168	4	proposition	proposition	NOUN
ejpam-6082	168	5	1	1	NUM
ejpam-6082	168	6	(	(	PUNCT
ejpam-6082	168	7	green	green	NOUN
ejpam-6082	168	8	’s	’s	PART
ejpam-6082	168	9	formula	formula	NOUN
ejpam-6082	168	10	[	[	X
ejpam-6082	168	11	50	50	NUM
ejpam-6082	168	12	]	]	NUM
ejpam-6082	168	13	)	)	PUNCT
ejpam-6082	168	14	.	.	PUNCT
ejpam-6082	169	1	let	let	VERB
ejpam-6082	169	2	d	d	PRON
ejpam-6082	169	3	be	be	AUX
ejpam-6082	169	4	a	a	DET
ejpam-6082	169	5	domain	domain	NOUN
ejpam-6082	169	6	of	of	ADP
ejpam-6082	169	7	rn	rn	PROPN
ejpam-6082	169	8	and	and	CCONJ
ejpam-6082	169	9	v(x	v(x	PROPN
ejpam-6082	169	10	)	)	PUNCT
ejpam-6082	169	11	its	its	PRON
ejpam-6082	169	12	exterior	exterior	NOUN
ejpam-6082	169	13	normal	normal	ADJ
ejpam-6082	169	14	.	.	PUNCT
ejpam-6082	170	1	then	then	ADV
ejpam-6082	170	2	,	,	PUNCT
ejpam-6082	170	3	for	for	ADP
ejpam-6082	170	4	two	two	NUM
ejpam-6082	170	5	regular	regular	ADJ
ejpam-6082	170	6	functions	function	NOUN
ejpam-6082	170	7	v	v	ADP
ejpam-6082	170	8	and	and	CCONJ
ejpam-6082	170	9	w	w	NOUN
ejpam-6082	170	10	,	,	PUNCT
ejpam-6082	170	11	green	green	ADJ
ejpam-6082	170	12	’s	’s	PART
ejpam-6082	170	13	formula	formula	NOUN
ejpam-6082	170	14	is	be	AUX
ejpam-6082	170	15	expressed	express	VERB
ejpam-6082	170	16	as:∫	as:∫	PROPN
ejpam-6082	170	17	d	d	PROPN
ejpam-6082	170	18	(	(	PUNCT
ejpam-6082	170	19	∆v)w	∆v)w	PROPN
ejpam-6082	170	20	dx	dx	PROPN
ejpam-6082	171	1	=	=	PUNCT
ejpam-6082	172	1	−	−	PROPN
ejpam-6082	172	2	∫	∫	PROPN
ejpam-6082	173	1	d	d	X
ejpam-6082	173	2	∇v	∇v	PROPN
ejpam-6082	173	3	·	·	PUNCT
ejpam-6082	173	4	∇w	∇w	ADV
ejpam-6082	173	5	dx+	dx+	ADJ
ejpam-6082	173	6	∫	∫	PROPN
ejpam-6082	173	7	∂d	∂d	PROPN
ejpam-6082	173	8	∂v	∂v	PROPN
ejpam-6082	173	9	∂n	∂n	PROPN
ejpam-6082	173	10	w	w	PROPN
ejpam-6082	173	11	dσ	dσ	PROPN
ejpam-6082	173	12	,	,	PUNCT
ejpam-6082	173	13	(	(	PUNCT
ejpam-6082	173	14	12	12	NUM
ejpam-6082	173	15	)	)	PUNCT
ejpam-6082	173	16	where	where	SCONJ
ejpam-6082	173	17	∂d	∂d	PROPN
ejpam-6082	173	18	is	be	AUX
ejpam-6082	173	19	the	the	DET
ejpam-6082	173	20	boundary	boundary	NOUN
ejpam-6082	173	21	of	of	ADP
ejpam-6082	173	22	region	region	NOUN
ejpam-6082	173	23	d.	d.	PROPN
ejpam-6082	173	24	we	we	PRON
ejpam-6082	173	25	now	now	ADV
ejpam-6082	173	26	introduce	introduce	VERB
ejpam-6082	173	27	the	the	DET
ejpam-6082	173	28	following	follow	VERB
ejpam-6082	173	29	definition	definition	NOUN
ejpam-6082	173	30	of	of	ADP
ejpam-6082	173	31	the	the	DET
ejpam-6082	173	32	lyapunov	lyapunov	ADJ
ejpam-6082	173	33	function	function	NOUN
ejpam-6082	173	34	and	and	CCONJ
ejpam-6082	173	35	some	some	DET
ejpam-6082	173	36	lemmas	lemmas	ADJ
ejpam-6082	173	37	[	[	X
ejpam-6082	173	38	49–51	49–51	X
ejpam-6082	173	39	]	]	PUNCT
ejpam-6082	173	40	to	to	PART
ejpam-6082	173	41	prove	prove	VERB
ejpam-6082	173	42	the	the	DET
ejpam-6082	173	43	stability	stability	NOUN
ejpam-6082	173	44	of	of	ADP
ejpam-6082	173	45	equilibrium	equilibrium	NOUN
ejpam-6082	173	46	points	point	NOUN
ejpam-6082	173	47	.	.	PUNCT
ejpam-6082	174	1	definition	definition	NOUN
ejpam-6082	174	2	5	5	NUM
ejpam-6082	174	3	(	(	PUNCT
ejpam-6082	174	4	lyapunov	lyapunov	NOUN
ejpam-6082	174	5	function	function	NOUN
ejpam-6082	174	6	)	)	PUNCT
ejpam-6082	174	7	.	.	PUNCT
ejpam-6082	175	1	let	let	VERB
ejpam-6082	175	2	θ(ξ	θ(ξ	PROPN
ejpam-6082	175	3	)	)	PUNCT
ejpam-6082	175	4	be	be	AUX
ejpam-6082	175	5	a	a	DET
ejpam-6082	175	6	neighborhood	neighborhood	NOUN
ejpam-6082	175	7	of	of	ADP
ejpam-6082	175	8	ξ	ξ	PROPN
ejpam-6082	175	9	.	.	PUNCT
ejpam-6082	176	1	a	a	DET
ejpam-6082	176	2	real	real	ADV
ejpam-6082	176	3	-	-	PUNCT
ejpam-6082	176	4	valued	value	VERB
ejpam-6082	176	5	differentiable	differentiable	ADJ
ejpam-6082	176	6	function	function	NOUN
ejpam-6082	176	7	v	v	NUM
ejpam-6082	176	8	defined	define	VERB
ejpam-6082	176	9	on	on	ADP
ejpam-6082	176	10	θ(ξ	θ(ξ	PROPN
ejpam-6082	176	11	)	)	PUNCT
ejpam-6082	176	12	is	be	AUX
ejpam-6082	176	13	said	say	VERB
ejpam-6082	176	14	to	to	PART
ejpam-6082	176	15	be	be	AUX
ejpam-6082	176	16	a	a	DET
ejpam-6082	176	17	lyapunov	lyapunov	ADJ
ejpam-6082	176	18	function	function	NOUN
ejpam-6082	176	19	for	for	ADP
ejpam-6082	176	20	system	system	NOUN
ejpam-6082	176	21	(	(	PUNCT
ejpam-6082	176	22	2	2	X
ejpam-6082	176	23	)	)	PUNCT
ejpam-6082	176	24	if	if	SCONJ
ejpam-6082	176	25	:	:	PUNCT
ejpam-6082	176	26	1	1	X
ejpam-6082	176	27	.	.	X
ejpam-6082	176	28	v(ξ	v(ξ	NOUN
ejpam-6082	176	29	)	)	PUNCT
ejpam-6082	177	1	=	=	SYM
ejpam-6082	177	2	0	0	NUM
ejpam-6082	177	3	,	,	PUNCT
ejpam-6082	177	4	2	2	NUM
ejpam-6082	177	5	.	.	NOUN
ejpam-6082	177	6	v	v	X
ejpam-6082	177	7	(	(	PUNCT
ejpam-6082	177	8	ξ1	ξ1	PROPN
ejpam-6082	177	9	)	)	PUNCT
ejpam-6082	177	10	>	>	X
ejpam-6082	177	11	0	0	PUNCT
ejpam-6082	177	12	in	in	ADP
ejpam-6082	177	13	θ(ξ	θ(ξ	PROPN
ejpam-6082	177	14	)	)	PUNCT
ejpam-6082	177	15	,	,	PUNCT
ejpam-6082	177	16	∀ξ	∀ξ	X
ejpam-6082	177	17	̸=	̸=	PROPN
ejpam-6082	177	18	ξ1	ξ1	NOUN
ejpam-6082	177	19	.	.	PUNCT
ejpam-6082	178	1	k.	k.	PROPN
ejpam-6082	178	2	guedri	guedri	PROPN
ejpam-6082	178	3	et	et	PROPN
ejpam-6082	178	4	al	al	PROPN
ejpam-6082	178	5	.	.	PUNCT
ejpam-6082	178	6	/	/	SYM
ejpam-6082	178	7	eur	eur	PROPN
ejpam-6082	178	8	.	.	PUNCT
ejpam-6082	179	1	j.	j.	PROPN
ejpam-6082	179	2	pure	pure	PROPN
ejpam-6082	179	3	appl	appl	PROPN
ejpam-6082	179	4	.	.	PROPN
ejpam-6082	179	5	math	math	PROPN
ejpam-6082	179	6	,	,	PUNCT
ejpam-6082	179	7	18	18	NUM
ejpam-6082	179	8	(	(	PUNCT
ejpam-6082	179	9	2	2	NUM
ejpam-6082	179	10	)	)	PUNCT
ejpam-6082	179	11	(	(	PUNCT
ejpam-6082	179	12	2025	2025	NUM
ejpam-6082	179	13	)	)	PUNCT
ejpam-6082	179	14	,	,	PUNCT
ejpam-6082	179	15	6082	6082	NUM
ejpam-6082	179	16	10	10	NUM
ejpam-6082	179	17	of	of	ADP
ejpam-6082	179	18	39	39	NUM
ejpam-6082	179	19	lemma	lemma	PROPN
ejpam-6082	179	20	1	1	NUM
ejpam-6082	179	21	.	.	PUNCT
ejpam-6082	180	1	let	let	VERB
ejpam-6082	180	2	ω	ω	PRON
ejpam-6082	180	3	be	be	AUX
ejpam-6082	180	4	a	a	DET
ejpam-6082	180	5	positively	positively	ADV
ejpam-6082	180	6	invariant	invariant	ADJ
ejpam-6082	180	7	subset	subset	NOUN
ejpam-6082	180	8	of	of	ADP
ejpam-6082	180	9	π	π	PROPN
ejpam-6082	180	10	,	,	PUNCT
ejpam-6082	180	11	where	where	SCONJ
ejpam-6082	180	12	π	π	PROPN
ejpam-6082	180	13	⊆	⊆	NUM
ejpam-6082	180	14	rn	rn	NOUN
ejpam-6082	180	15	.	.	PUNCT
ejpam-6082	181	1	if	if	SCONJ
ejpam-6082	181	2	y	y	PRON
ejpam-6082	181	3	:	:	PUNCT
ejpam-6082	181	4	π	π	X
ejpam-6082	181	5	→	→	PUNCT
ejpam-6082	181	6	r	r	NOUN
ejpam-6082	181	7	is	be	AUX
ejpam-6082	181	8	continuously	continuously	ADV
ejpam-6082	181	9	differentiable	differentiable	ADJ
ejpam-6082	181	10	and	and	CCONJ
ejpam-6082	181	11	y(x	y(x	NOUN
ejpam-6082	181	12	)	)	PUNCT
ejpam-6082	181	13	>	>	X
ejpam-6082	181	14	0	0	NUM
ejpam-6082	181	15	,	,	PUNCT
ejpam-6082	181	16	and	and	CCONJ
ejpam-6082	181	17	cdα	cdα	PROPN
ejpam-6082	181	18	t	t	PROPN
ejpam-6082	181	19	y(x(t	y(x(t	PROPN
ejpam-6082	181	20	)	)	PUNCT
ejpam-6082	181	21	)	)	PUNCT
ejpam-6082	182	1	≤	≤	ADV
ejpam-6082	182	2	0	0	NUM
ejpam-6082	182	3	in	in	ADP
ejpam-6082	182	4	ω	ω	NUM
ejpam-6082	182	5	,	,	PUNCT
ejpam-6082	182	6	then	then	ADV
ejpam-6082	182	7	:	:	PUNCT
ejpam-6082	182	8	•	•	ADP
ejpam-6082	182	9	the	the	DET
ejpam-6082	182	10	set	set	NOUN
ejpam-6082	182	11	f	f	PROPN
ejpam-6082	182	12	contains	contain	VERB
ejpam-6082	182	13	all	all	DET
ejpam-6082	182	14	points	point	NOUN
ejpam-6082	182	15	in	in	ADP
ejpam-6082	182	16	ω	ω	NUM
ejpam-6082	182	17	where	where	SCONJ
ejpam-6082	182	18	cdα	cdα	NOUN
ejpam-6082	182	19	t	t	PROPN
ejpam-6082	182	20	y(x(t	y(x(t	PROPN
ejpam-6082	182	21	)	)	PUNCT
ejpam-6082	182	22	)	)	PUNCT
ejpam-6082	183	1	=	=	PUNCT
ejpam-6082	183	2	0	0	NUM
ejpam-6082	183	3	,	,	PUNCT
ejpam-6082	183	4	•	•	NUM
ejpam-6082	183	5	σ	σ	PROPN
ejpam-6082	183	6	is	be	AUX
ejpam-6082	183	7	the	the	DET
ejpam-6082	183	8	largest	large	ADJ
ejpam-6082	183	9	invariant	invariant	ADJ
ejpam-6082	183	10	set	set	NOUN
ejpam-6082	183	11	in	in	ADP
ejpam-6082	183	12	f	f	PROPN
ejpam-6082	183	13	,	,	PUNCT
ejpam-6082	183	14	•	•	NUM
ejpam-6082	183	15	every	every	DET
ejpam-6082	183	16	bounded	bounded	ADJ
ejpam-6082	183	17	solution	solution	NOUN
ejpam-6082	183	18	starting	start	VERB
ejpam-6082	183	19	in	in	ADP
ejpam-6082	183	20	ω	ω	PROPN
ejpam-6082	183	21	→	→	SYM
ejpam-6082	183	22	σ	σ	PROPN
ejpam-6082	183	23	as	as	ADP
ejpam-6082	183	24	t→	t→	NUM
ejpam-6082	183	25	∞.	∞.	PROPN
ejpam-6082	183	26	lemma	lemma	PROPN
ejpam-6082	183	27	2	2	X
ejpam-6082	183	28	.	.	PUNCT
ejpam-6082	184	1	let	let	VERB
ejpam-6082	185	1	y(t	y(t	NUM
ejpam-6082	185	2	)	)	PUNCT
ejpam-6082	185	3	∈	∈	PROPN
ejpam-6082	185	4	r+	r+	PUNCT
ejpam-6082	185	5	be	be	AUX
ejpam-6082	185	6	a	a	DET
ejpam-6082	185	7	continuously	continuously	ADV
ejpam-6082	185	8	differentiable	differentiable	ADJ
ejpam-6082	185	9	function	function	NOUN
ejpam-6082	185	10	.	.	PUNCT
ejpam-6082	186	1	for	for	ADP
ejpam-6082	186	2	t	t	PROPN
ejpam-6082	186	3	≥	≥	NOUN
ejpam-6082	186	4	0	0	NUM
ejpam-6082	186	5	and	and	CCONJ
ejpam-6082	186	6	α	α	PRON
ejpam-6082	186	7	∈	∈	PROPN
ejpam-6082	186	8	(	(	PUNCT
ejpam-6082	186	9	0	0	NUM
ejpam-6082	186	10	,	,	PUNCT
ejpam-6082	186	11	1	1	NUM
ejpam-6082	186	12	):	):	PUNCT
ejpam-6082	186	13	cdα	cdα	PROPN
ejpam-6082	186	14	t	t	PROPN
ejpam-6082	186	15	[	[	PUNCT
ejpam-6082	186	16	y∗φ	y∗φ	NUM
ejpam-6082	186	17	(	(	PUNCT
ejpam-6082	186	18	y(t	y(t	PROPN
ejpam-6082	186	19	)	)	PUNCT
ejpam-6082	186	20	y∗	y∗	ADV
ejpam-6082	186	21	)	)	PUNCT
ejpam-6082	186	22	]	]	PUNCT
ejpam-6082	186	23	≤	≤	NUM
ejpam-6082	186	24	(	(	PUNCT
ejpam-6082	186	25	1−	1−	NUM
ejpam-6082	186	26	y∗	y∗	ADV
ejpam-6082	186	27	y(t	y(t	NUM
ejpam-6082	186	28	)	)	PUNCT
ejpam-6082	186	29	)	)	PUNCT
ejpam-6082	186	30	cdα	cdα	NOUN
ejpam-6082	186	31	t	t	PROPN
ejpam-6082	186	32	y(t	y(t	PROPN
ejpam-6082	186	33	)	)	PUNCT
ejpam-6082	186	34	,	,	PUNCT
ejpam-6082	186	35	y∗	y∗	PROPN
ejpam-6082	186	36	∈	∈	PROPN
ejpam-6082	186	37	r+	r+	NOUN
ejpam-6082	186	38	,	,	PUNCT
ejpam-6082	186	39	(	(	PUNCT
ejpam-6082	186	40	13	13	NUM
ejpam-6082	186	41	)	)	PUNCT
ejpam-6082	186	42	where	where	SCONJ
ejpam-6082	186	43	φ(y	φ(y	NOUN
ejpam-6082	186	44	)	)	PUNCT
ejpam-6082	186	45	=	=	PUNCT
ejpam-6082	187	1	(	(	PUNCT
ejpam-6082	187	2	y	y	PROPN
ejpam-6082	187	3	−	−	PROPN
ejpam-6082	187	4	1−	1−	NUM
ejpam-6082	187	5	ln(y	ln(y	PUNCT
ejpam-6082	187	6	)	)	PUNCT
ejpam-6082	187	7	)	)	PUNCT
ejpam-6082	187	8	≥	≥	NOUN
ejpam-6082	187	9	0	0	NUM
ejpam-6082	187	10	for	for	ADP
ejpam-6082	187	11	any	any	DET
ejpam-6082	187	12	y	y	PROPN
ejpam-6082	187	13	>	>	X
ejpam-6082	187	14	0	0	NUM
ejpam-6082	187	15	.	.	NOUN
ejpam-6082	187	16	4	4	NUM
ejpam-6082	187	17	.	.	NOUN
ejpam-6082	187	18	qualitative	qualitative	ADJ
ejpam-6082	187	19	analysis	analysis	NOUN
ejpam-6082	187	20	of	of	ADP
ejpam-6082	187	21	model	model	NOUN
ejpam-6082	187	22	dynamics	dynamic	NOUN
ejpam-6082	187	23	in	in	ADP
ejpam-6082	187	24	this	this	DET
ejpam-6082	187	25	section	section	NOUN
ejpam-6082	187	26	,	,	PUNCT
ejpam-6082	187	27	we	we	PRON
ejpam-6082	187	28	analyze	analyze	VERB
ejpam-6082	187	29	the	the	DET
ejpam-6082	187	30	behavior	behavior	NOUN
ejpam-6082	187	31	of	of	ADP
ejpam-6082	187	32	the	the	DET
ejpam-6082	187	33	proposed	propose	VERB
ejpam-6082	187	34	fractional	fractional	ADJ
ejpam-6082	187	35	-	-	PUNCT
ejpam-6082	187	36	order	order	NOUN
ejpam-6082	187	37	model	model	NOUN
ejpam-6082	187	38	(	(	PUNCT
ejpam-6082	187	39	2	2	NUM
ejpam-6082	187	40	)	)	PUNCT
ejpam-6082	187	41	to	to	PART
ejpam-6082	187	42	understand	understand	VERB
ejpam-6082	187	43	its	its	PRON
ejpam-6082	187	44	general	general	ADJ
ejpam-6082	187	45	characteristics	characteristic	NOUN
ejpam-6082	187	46	.	.	PUNCT
ejpam-6082	188	1	these	these	DET
ejpam-6082	188	2	analyses	analysis	NOUN
ejpam-6082	188	3	allow	allow	VERB
ejpam-6082	188	4	us	we	PRON
ejpam-6082	188	5	to	to	PART
ejpam-6082	188	6	establish	establish	VERB
ejpam-6082	188	7	the	the	DET
ejpam-6082	188	8	positivity	positivity	NOUN
ejpam-6082	188	9	and	and	CCONJ
ejpam-6082	188	10	boundedness	boundedness	NOUN
ejpam-6082	188	11	of	of	ADP
ejpam-6082	188	12	the	the	DET
ejpam-6082	188	13	solutions	solution	NOUN
ejpam-6082	188	14	,	,	PUNCT
ejpam-6082	188	15	describe	describe	VERB
ejpam-6082	188	16	solution	solution	NOUN
ejpam-6082	188	17	trends	trend	NOUN
ejpam-6082	188	18	by	by	ADP
ejpam-6082	188	19	evaluating	evaluate	VERB
ejpam-6082	188	20	equilibrium	equilibrium	NOUN
ejpam-6082	188	21	points	point	NOUN
ejpam-6082	188	22	(	(	PUNCT
ejpam-6082	188	23	eps	eps	PROPN
ejpam-6082	188	24	)	)	PUNCT
ejpam-6082	188	25	,	,	PUNCT
ejpam-6082	188	26	investigate	investigate	VERB
ejpam-6082	188	27	their	their	PRON
ejpam-6082	188	28	stability	stability	NOUN
ejpam-6082	188	29	,	,	PUNCT
ejpam-6082	188	30	and	and	CCONJ
ejpam-6082	188	31	perform	perform	VERB
ejpam-6082	188	32	sensitivity	sensitivity	NOUN
ejpam-6082	188	33	analysis	analysis	NOUN
ejpam-6082	188	34	.	.	PUNCT
ejpam-6082	189	1	4.1	4.1	NUM
ejpam-6082	189	2	.	.	PUNCT
ejpam-6082	190	1	existence	existence	NOUN
ejpam-6082	190	2	,	,	PUNCT
ejpam-6082	190	3	positivity	positivity	NOUN
ejpam-6082	190	4	,	,	PUNCT
ejpam-6082	190	5	and	and	CCONJ
ejpam-6082	190	6	boundedness	boundedness	NOUN
ejpam-6082	190	7	of	of	ADP
ejpam-6082	190	8	solutions	solution	NOUN
ejpam-6082	190	9	to	to	PART
ejpam-6082	190	10	ensure	ensure	VERB
ejpam-6082	190	11	that	that	SCONJ
ejpam-6082	190	12	the	the	DET
ejpam-6082	190	13	proposed	propose	VERB
ejpam-6082	190	14	fractional	fractional	ADJ
ejpam-6082	190	15	-	-	PUNCT
ejpam-6082	190	16	order	order	NOUN
ejpam-6082	190	17	reaction	reaction	NOUN
ejpam-6082	190	18	-	-	PUNCT
ejpam-6082	190	19	diffusion	diffusion	NOUN
ejpam-6082	190	20	model	model	NOUN
ejpam-6082	190	21	(	(	PUNCT
ejpam-6082	190	22	2	2	NUM
ejpam-6082	190	23	)	)	PUNCT
ejpam-6082	190	24	reflects	reflect	VERB
ejpam-6082	190	25	biological	biological	ADJ
ejpam-6082	190	26	reality	reality	NOUN
ejpam-6082	190	27	,	,	PUNCT
ejpam-6082	190	28	we	we	PRON
ejpam-6082	190	29	analyze	analyze	VERB
ejpam-6082	190	30	the	the	DET
ejpam-6082	190	31	existence	existence	NOUN
ejpam-6082	190	32	,	,	PUNCT
ejpam-6082	190	33	positivity	positivity	NOUN
ejpam-6082	190	34	,	,	PUNCT
ejpam-6082	190	35	and	and	CCONJ
ejpam-6082	190	36	boundedness	boundedness	NOUN
ejpam-6082	190	37	of	of	ADP
ejpam-6082	190	38	its	its	PRON
ejpam-6082	190	39	solutions	solution	NOUN
ejpam-6082	190	40	.	.	PUNCT
ejpam-6082	191	1	let	let	VERB
ejpam-6082	191	2	x	x	SYM
ejpam-6082	191	3	=	=	SYM
ejpam-6082	191	4	c(0̄,r	c(0̄,r	NOUN
ejpam-6082	191	5	)	)	PUNCT
ejpam-6082	191	6	be	be	VERB
ejpam-6082	191	7	a	a	DET
ejpam-6082	191	8	banach	banach	NOUN
ejpam-6082	191	9	space	space	NOUN
ejpam-6082	191	10	equipped	equip	VERB
ejpam-6082	191	11	with	with	ADP
ejpam-6082	191	12	the	the	DET
ejpam-6082	191	13	usual	usual	ADJ
ejpam-6082	191	14	norms	norm	NOUN
ejpam-6082	191	15	.	.	PUNCT
ejpam-6082	192	1	the	the	DET
ejpam-6082	192	2	system	system	NOUN
ejpam-6082	192	3	(	(	PUNCT
ejpam-6082	192	4	2	2	X
ejpam-6082	192	5	)	)	PUNCT
ejpam-6082	192	6	can	can	AUX
ejpam-6082	192	7	be	be	AUX
ejpam-6082	192	8	rewritten	rewrite	VERB
ejpam-6082	192	9	in	in	ADP
ejpam-6082	192	10	a	a	DET
ejpam-6082	192	11	compact	compact	ADJ
ejpam-6082	192	12	form	form	NOUN
ejpam-6082	192	13	as	as	ADP
ejpam-6082	192	14	:	:	PUNCT
ejpam-6082	192	15	{	{	PUNCT
ejpam-6082	192	16	c	c	NOUN
ejpam-6082	192	17	0	0	PUNCT
ejpam-6082	193	1	d	d	NOUN
ejpam-6082	193	2	α	α	PROPN
ejpam-6082	193	3	t	t	PROPN
ejpam-6082	193	4	λ(t	λ(t	PROPN
ejpam-6082	193	5	,	,	PUNCT
ejpam-6082	193	6	x)−aλ(t	x)−aλ(t	PROPN
ejpam-6082	193	7	,	,	PUNCT
ejpam-6082	193	8	x	x	X
ejpam-6082	193	9	)	)	PUNCT
ejpam-6082	193	10	=	=	SYM
ejpam-6082	193	11	f	f	PROPN
ejpam-6082	193	12	(	(	PUNCT
ejpam-6082	193	13	t	t	PROPN
ejpam-6082	193	14	,	,	PUNCT
ejpam-6082	193	15	x	x	NOUN
ejpam-6082	193	16	)	)	PUNCT
ejpam-6082	193	17	,	,	PUNCT
ejpam-6082	193	18	λ(0	λ(0	NOUN
ejpam-6082	193	19	,	,	PUNCT
ejpam-6082	193	20	x	x	NOUN
ejpam-6082	193	21	)	)	PUNCT
ejpam-6082	193	22	=	=	SYM
ejpam-6082	193	23	λ0	λ0	NOUN
ejpam-6082	193	24	,	,	PUNCT
ejpam-6082	193	25	(	(	PUNCT
ejpam-6082	193	26	14	14	NUM
ejpam-6082	193	27	)	)	PUNCT
ejpam-6082	194	1	where	where	SCONJ
ejpam-6082	194	2	λ	λ	X
ejpam-6082	194	3	=	=	PRON
ejpam-6082	194	4	(	(	PUNCT
ejpam-6082	194	5	s	s	PROPN
ejpam-6082	194	6	,	,	PUNCT
ejpam-6082	194	7	v	v	NOUN
ejpam-6082	194	8	,	,	PUNCT
ejpam-6082	194	9	e	e	NOUN
ejpam-6082	194	10	,	,	PUNCT
ejpam-6082	194	11	np	np	INTJ
ejpam-6082	194	12	,	,	PUNCT
ejpam-6082	194	13	p	p	X
ejpam-6082	194	14	,	,	PUNCT
ejpam-6082	194	15	r	r	NOUN
ejpam-6082	194	16	,	,	PUNCT
ejpam-6082	194	17	a	a	PRON
ejpam-6082	194	18	)	)	PUNCT
ejpam-6082	194	19	t	t	NOUN
ejpam-6082	194	20	,	,	PUNCT
ejpam-6082	194	21	λ0	λ0	NOUN
ejpam-6082	194	22	=	=	SYM
ejpam-6082	194	23	(	(	PUNCT
ejpam-6082	194	24	s0	s0	PROPN
ejpam-6082	194	25	,	,	PUNCT
ejpam-6082	194	26	v0	v0	PROPN
ejpam-6082	194	27	,	,	PUNCT
ejpam-6082	194	28	e0	e0	PROPN
ejpam-6082	194	29	,	,	PUNCT
ejpam-6082	194	30	np,0	np,0	PROPN
ejpam-6082	194	31	,	,	PUNCT
ejpam-6082	194	32	p0	p0	NOUN
ejpam-6082	194	33	,	,	PUNCT
ejpam-6082	194	34	r0	r0	NOUN
ejpam-6082	194	35	,	,	PUNCT
ejpam-6082	194	36	a0	a0	PROPN
ejpam-6082	194	37	)	)	PUNCT
ejpam-6082	194	38	t	t	PROPN
ejpam-6082	194	39	,	,	PUNCT
ejpam-6082	194	40	and	and	CCONJ
ejpam-6082	194	41	aλ(t	aλ(t	NUM
ejpam-6082	194	42	,	,	PUNCT
ejpam-6082	194	43	x	x	NOUN
ejpam-6082	194	44	)	)	PUNCT
ejpam-6082	194	45	=	=	SYM
ejpam-6082	194	46	(	(	PUNCT
ejpam-6082	194	47	d1∆s	d1∆s	ADJ
ejpam-6082	194	48	,	,	PUNCT
ejpam-6082	194	49	d2∆v	d2∆v	ADJ
ejpam-6082	194	50	,	,	PUNCT
ejpam-6082	194	51	d3∆e	d3∆e	ADJ
ejpam-6082	194	52	,	,	PUNCT
ejpam-6082	194	53	d4∆np	d4∆np	PROPN
ejpam-6082	194	54	,	,	PUNCT
ejpam-6082	194	55	d5∆p	d5∆p	NOUN
ejpam-6082	194	56	,	,	PUNCT
ejpam-6082	194	57	d6∆r	d6∆r	NOUN
ejpam-6082	194	58	,	,	PUNCT
ejpam-6082	194	59	d7∆a	d7∆a	ADJ
ejpam-6082	194	60	)	)	PUNCT
ejpam-6082	194	61	t	t	NOUN
ejpam-6082	194	62	.	.	PUNCT
ejpam-6082	195	1	here	here	ADV
ejpam-6082	195	2	,	,	PUNCT
ejpam-6082	195	3	a	a	DET
ejpam-6082	195	4	:	:	PUNCT
ejpam-6082	195	5	d(a	d(a	PROPN
ejpam-6082	195	6	)	)	PUNCT
ejpam-6082	196	1	⊂	⊂	PROPN
ejpam-6082	196	2	x7	x7	NOUN
ejpam-6082	196	3	→	→	SYM
ejpam-6082	196	4	x7	x7	NOUN
ejpam-6082	196	5	is	be	AUX
ejpam-6082	196	6	a	a	DET
ejpam-6082	196	7	linear	linear	ADJ
ejpam-6082	196	8	diffusion	diffusion	NOUN
ejpam-6082	196	9	operator	operator	NOUN
ejpam-6082	196	10	with	with	ADP
ejpam-6082	196	11	domain	domain	NOUN
ejpam-6082	196	12	:	:	PUNCT
ejpam-6082	196	13	d(a	d(a	PROPN
ejpam-6082	196	14	)	)	PUNCT
ejpam-6082	197	1	=	=	PRON
ejpam-6082	197	2	{	{	PUNCT
ejpam-6082	197	3	λ	λ	X
ejpam-6082	197	4	∈	∈	NOUN
ejpam-6082	197	5	x7	x7	NOUN
ejpam-6082	197	6	:	:	PUNCT
ejpam-6082	197	7	∆λ	∆λ	PROPN
ejpam-6082	197	8	∈	∈	PROPN
ejpam-6082	197	9	x7	x7	NOUN
ejpam-6082	197	10	,	,	PUNCT
ejpam-6082	197	11	∂λ	∂λ	PROPN
ejpam-6082	197	12	∂n	∂n	PROPN
ejpam-6082	197	13	=	=	PUNCT
ejpam-6082	197	14	0r7	0r7	NUM
ejpam-6082	197	15	for	for	ADP
ejpam-6082	197	16	x	x	PROPN
ejpam-6082	197	17	∈	∈	PROPN
ejpam-6082	197	18	∂0	∂0	NOUN
ejpam-6082	197	19	}	}	PUNCT
ejpam-6082	197	20	.	.	PUNCT
ejpam-6082	198	1	k.	k.	PROPN
ejpam-6082	198	2	guedri	guedri	PROPN
ejpam-6082	198	3	et	et	PROPN
ejpam-6082	198	4	al	al	PROPN
ejpam-6082	198	5	.	.	PUNCT
ejpam-6082	198	6	/	/	SYM
ejpam-6082	198	7	eur	eur	PROPN
ejpam-6082	198	8	.	.	PUNCT
ejpam-6082	199	1	j.	j.	PROPN
ejpam-6082	199	2	pure	pure	PROPN
ejpam-6082	199	3	appl	appl	PROPN
ejpam-6082	199	4	.	.	PROPN
ejpam-6082	199	5	math	math	PROPN
ejpam-6082	199	6	,	,	PUNCT
ejpam-6082	199	7	18	18	NUM
ejpam-6082	199	8	(	(	PUNCT
ejpam-6082	199	9	2	2	NUM
ejpam-6082	199	10	)	)	PUNCT
ejpam-6082	199	11	(	(	PUNCT
ejpam-6082	199	12	2025	2025	NUM
ejpam-6082	199	13	)	)	PUNCT
ejpam-6082	199	14	,	,	PUNCT
ejpam-6082	199	15	6082	6082	NUM
ejpam-6082	199	16	11	11	NUM
ejpam-6082	199	17	of	of	ADP
ejpam-6082	199	18	39	39	NUM
ejpam-6082	199	19	the	the	DET
ejpam-6082	199	20	nonlinear	nonlinear	ADJ
ejpam-6082	199	21	function	function	NOUN
ejpam-6082	199	22	f	f	NOUN
ejpam-6082	200	1	:	:	PUNCT
ejpam-6082	200	2	[	[	X
ejpam-6082	200	3	0	0	NUM
ejpam-6082	200	4	,	,	PUNCT
ejpam-6082	200	5	t	t	X
ejpam-6082	200	6	]	]	X
ejpam-6082	200	7	×x7	×x7	NOUN
ejpam-6082	200	8	→	→	SYM
ejpam-6082	200	9	x7	x7	NOUN
ejpam-6082	200	10	is	be	AUX
ejpam-6082	200	11	defined	define	VERB
ejpam-6082	200	12	as	as	ADP
ejpam-6082	200	13	:	:	PUNCT
ejpam-6082	200	14	f	f	PROPN
ejpam-6082	200	15	(	(	PUNCT
ejpam-6082	200	16	λ(t	λ(t	PROPN
ejpam-6082	200	17	,	,	PUNCT
ejpam-6082	200	18	x	x	NOUN
ejpam-6082	200	19	)	)	PUNCT
ejpam-6082	200	20	)	)	PUNCT
ejpam-6082	201	1	=	=	PUNCT
ejpam-6082	201	2			ADJ
ejpam-6082	201	3	λ	λ	X
ejpam-6082	202	1	+	+	CCONJ
ejpam-6082	202	2	ρ1r−	ρ1r−	PRON
ejpam-6082	202	3	(	(	PUNCT
ejpam-6082	202	4	λ+	λ+	VERB
ejpam-6082	202	5	δ	δ	NOUN
ejpam-6082	202	6	+	+	NOUN
ejpam-6082	202	7	µ)s	µ)s	NOUN
ejpam-6082	202	8	δs	δs	NOUN
ejpam-6082	202	9	−	−	PROPN
ejpam-6082	202	10	(	(	PUNCT
ejpam-6082	202	11	1−	1−	NUM
ejpam-6082	202	12	δ)λv	δ)λv	PROPN
ejpam-6082	202	13	−	−	PROPN
ejpam-6082	202	14	(	(	PUNCT
ejpam-6082	202	15	γ	γ	X
ejpam-6082	202	16	+	+	NOUN
ejpam-6082	202	17	µ)v	µ)v	ADJ
ejpam-6082	202	18	λs	λs	X
ejpam-6082	202	19	+	+	CCONJ
ejpam-6082	202	20	(	(	PUNCT
ejpam-6082	202	21	1−	1−	NUM
ejpam-6082	202	22	δ)λv	δ)λv	PROPN
ejpam-6082	202	23	−	−	PROPN
ejpam-6082	202	24	(	(	PUNCT
ejpam-6082	202	25	α1	α1	PROPN
ejpam-6082	202	26	+	+	CCONJ
ejpam-6082	202	27	α2	α2	ADJ
ejpam-6082	202	28	+	+	CCONJ
ejpam-6082	202	29	ω	ω	NUM
ejpam-6082	202	30	+	+	CCONJ
ejpam-6082	202	31	µ)e	µ)e	SYM
ejpam-6082	202	32	α1e	α1e	NOUN
ejpam-6082	202	33	−	−	PROPN
ejpam-6082	202	34	(	(	PUNCT
ejpam-6082	202	35	σ	σ	PROPN
ejpam-6082	202	36	+	+	CCONJ
ejpam-6082	202	37	µ+	µ+	X
ejpam-6082	202	38	ω1)np	ω1)np	PROPN
ejpam-6082	202	39	α2e	α2e	NOUN
ejpam-6082	202	40	−	−	PROPN
ejpam-6082	202	41	(	(	PUNCT
ejpam-6082	202	42	σ	σ	PROPN
ejpam-6082	202	43	+	+	X
ejpam-6082	202	44	µ+	µ+	PUNCT
ejpam-6082	202	45	ω2)p	ω2)p	NOUN
ejpam-6082	202	46	γv	γv	X
ejpam-6082	202	47	+	+	CCONJ
ejpam-6082	202	48	ωe	ωe	ADV
ejpam-6082	202	49	+	+	NUM
ejpam-6082	202	50	ω1np	ω1np	NOUN
ejpam-6082	202	51	+	+	CCONJ
ejpam-6082	202	52	ω2p	ω2p	NOUN
ejpam-6082	202	53	−	−	X
ejpam-6082	202	54	(	(	PUNCT
ejpam-6082	202	55	ρ+	ρ+	NUM
ejpam-6082	202	56	ρ1	ρ1	NOUN
ejpam-6082	202	57	+	+	CCONJ
ejpam-6082	202	58	µ)r	µ)r	NOUN
ejpam-6082	202	59	ρr−	ρr−	NUM
ejpam-6082	202	60	(	(	PUNCT
ejpam-6082	202	61	σ	σ	NOUN
ejpam-6082	202	62	+	+	CCONJ
ejpam-6082	202	63	µ)a	µ)a	NOUN
ejpam-6082	202	64			PROPN
ejpam-6082	202	65	.	.	PUNCT
ejpam-6082	203	1	theorem	theorem	NOUN
ejpam-6082	203	2	1	1	NUM
ejpam-6082	203	3	.	.	PUNCT
ejpam-6082	204	1	the	the	DET
ejpam-6082	204	2	problem	problem	NOUN
ejpam-6082	204	3	(	(	PUNCT
ejpam-6082	204	4	14	14	NUM
ejpam-6082	204	5	)	)	PUNCT
ejpam-6082	204	6	has	have	VERB
ejpam-6082	204	7	a	a	DET
ejpam-6082	204	8	unique	unique	ADJ
ejpam-6082	204	9	positive	positive	ADJ
ejpam-6082	204	10	solution	solution	NOUN
ejpam-6082	204	11	for	for	ADP
ejpam-6082	204	12	all	all	DET
ejpam-6082	204	13	α	α	PRON
ejpam-6082	204	14	∈	∈	NOUN
ejpam-6082	204	15	(	(	PUNCT
ejpam-6082	204	16	0	0	NUM
ejpam-6082	204	17	,	,	PUNCT
ejpam-6082	204	18	1	1	NUM
ejpam-6082	204	19	]	]	PUNCT
ejpam-6082	204	20	.	.	PUNCT
ejpam-6082	205	1	proof	proof	NOUN
ejpam-6082	205	2	.	.	PUNCT
ejpam-6082	206	1	the	the	DET
ejpam-6082	206	2	operator	operator	NOUN
ejpam-6082	206	3	a	a	PRON
ejpam-6082	206	4	is	be	AUX
ejpam-6082	206	5	linear	linear	ADJ
ejpam-6082	206	6	and	and	CCONJ
ejpam-6082	206	7	densely	densely	ADV
ejpam-6082	206	8	defined	define	VERB
ejpam-6082	206	9	on	on	ADP
ejpam-6082	206	10	d(a	d(a	PROPN
ejpam-6082	206	11	)	)	PUNCT
ejpam-6082	206	12	,	,	PUNCT
ejpam-6082	206	13	and	and	CCONJ
ejpam-6082	206	14	the	the	DET
ejpam-6082	206	15	function	function	NOUN
ejpam-6082	206	16	f	f	PROPN
ejpam-6082	206	17	is	be	AUX
ejpam-6082	206	18	lipschitz	lipschitz	VERB
ejpam-6082	206	19	continuous	continuous	ADJ
ejpam-6082	206	20	in	in	ADP
ejpam-6082	206	21	x.	x.	NOUN
ejpam-6082	206	22	by	by	ADP
ejpam-6082	206	23	the	the	DET
ejpam-6082	206	24	fixed	fix	VERB
ejpam-6082	206	25	-	-	PUNCT
ejpam-6082	206	26	point	point	NOUN
ejpam-6082	206	27	theorem	theorem	NOUN
ejpam-6082	206	28	for	for	ADP
ejpam-6082	206	29	fractional	fractional	ADJ
ejpam-6082	206	30	differential	differential	ADJ
ejpam-6082	206	31	equations	equation	NOUN
ejpam-6082	206	32	(	(	PUNCT
ejpam-6082	206	33	see	see	VERB
ejpam-6082	206	34	[	[	X
ejpam-6082	206	35	52	52	NUM
ejpam-6082	206	36	]	]	NUM
ejpam-6082	206	37	)	)	PUNCT
ejpam-6082	206	38	,	,	PUNCT
ejpam-6082	206	39	there	there	PRON
ejpam-6082	206	40	exists	exist	VERB
ejpam-6082	206	41	a	a	DET
ejpam-6082	206	42	unique	unique	ADJ
ejpam-6082	206	43	solution	solution	NOUN
ejpam-6082	206	44	λ(t	λ(t	PRON
ejpam-6082	206	45	,	,	PUNCT
ejpam-6082	206	46	x	x	NOUN
ejpam-6082	206	47	)	)	PUNCT
ejpam-6082	206	48	for	for	ADP
ejpam-6082	206	49	the	the	DET
ejpam-6082	206	50	problem	problem	NOUN
ejpam-6082	206	51	(	(	PUNCT
ejpam-6082	206	52	14	14	NUM
ejpam-6082	206	53	)	)	PUNCT
ejpam-6082	206	54	.	.	PUNCT
ejpam-6082	207	1	furthermore	furthermore	ADV
ejpam-6082	207	2	,	,	PUNCT
ejpam-6082	207	3	the	the	DET
ejpam-6082	207	4	positivity	positivity	NOUN
ejpam-6082	207	5	of	of	ADP
ejpam-6082	207	6	the	the	DET
ejpam-6082	207	7	initial	initial	ADJ
ejpam-6082	207	8	conditions	condition	NOUN
ejpam-6082	207	9	λ0	λ0	VERB
ejpam-6082	207	10	≥	≥	NOUN
ejpam-6082	207	11	0	0	NUM
ejpam-6082	207	12	ensures	ensure	VERB
ejpam-6082	207	13	that	that	SCONJ
ejpam-6082	207	14	all	all	DET
ejpam-6082	207	15	components	component	NOUN
ejpam-6082	207	16	of	of	ADP
ejpam-6082	207	17	the	the	DET
ejpam-6082	207	18	solution	solution	NOUN
ejpam-6082	207	19	remain	remain	VERB
ejpam-6082	207	20	non	non	ADJ
ejpam-6082	207	21	-	-	ADJ
ejpam-6082	207	22	negative	negative	ADJ
ejpam-6082	207	23	due	due	ADP
ejpam-6082	207	24	to	to	ADP
ejpam-6082	207	25	the	the	DET
ejpam-6082	207	26	structure	structure	NOUN
ejpam-6082	207	27	of	of	ADP
ejpam-6082	207	28	f	f	PROPN
ejpam-6082	207	29	,	,	PUNCT
ejpam-6082	207	30	which	which	PRON
ejpam-6082	207	31	reflects	reflect	VERB
ejpam-6082	207	32	biological	biological	ADJ
ejpam-6082	207	33	constraints	constraint	NOUN
ejpam-6082	207	34	.	.	PUNCT
ejpam-6082	208	1	hence	hence	ADV
ejpam-6082	208	2	,	,	PUNCT
ejpam-6082	208	3	the	the	DET
ejpam-6082	208	4	solution	solution	NOUN
ejpam-6082	208	5	is	be	AUX
ejpam-6082	208	6	positive	positive	ADJ
ejpam-6082	208	7	for	for	ADP
ejpam-6082	208	8	all	all	DET
ejpam-6082	208	9	t	t	NOUN
ejpam-6082	208	10	>	>	X
ejpam-6082	208	11	0	0	PUNCT
ejpam-6082	209	1	and	and	CCONJ
ejpam-6082	209	2	x	x	SYM
ejpam-6082	209	3	∈	∈	PROPN
ejpam-6082	209	4	0	0	X
ejpam-6082	209	5	.	.	PUNCT
ejpam-6082	209	6	theorem	theorem	NOUN
ejpam-6082	209	7	2	2	NUM
ejpam-6082	209	8	.	.	PUNCT
ejpam-6082	210	1	the	the	DET
ejpam-6082	210	2	solution	solution	NOUN
ejpam-6082	210	3	of	of	ADP
ejpam-6082	210	4	the	the	DET
ejpam-6082	210	5	fractional	fractional	ADJ
ejpam-6082	210	6	-	-	PUNCT
ejpam-6082	210	7	order	order	NOUN
ejpam-6082	210	8	system	system	NOUN
ejpam-6082	210	9	(	(	PUNCT
ejpam-6082	210	10	2	2	X
ejpam-6082	210	11	)	)	PUNCT
ejpam-6082	210	12	is	be	AUX
ejpam-6082	210	13	bounded	bound	VERB
ejpam-6082	210	14	on	on	ADP
ejpam-6082	210	15	0	0	NUM
ejpam-6082	210	16	×	×	NOUN
ejpam-6082	210	17	[	[	X
ejpam-6082	210	18	0,+∞	0,+∞	NUM
ejpam-6082	210	19	)	)	PUNCT
ejpam-6082	210	20	for	for	ADP
ejpam-6082	210	21	all	all	DET
ejpam-6082	210	22	t	t	PROPN
ejpam-6082	210	23	≥	≥	NOUN
ejpam-6082	210	24	0	0	NUM
ejpam-6082	210	25	.	.	PUNCT
ejpam-6082	211	1	proof	proof	NOUN
ejpam-6082	211	2	.	.	PUNCT
ejpam-6082	212	1	the	the	DET
ejpam-6082	212	2	total	total	ADJ
ejpam-6082	212	3	population	population	NOUN
ejpam-6082	212	4	at	at	ADP
ejpam-6082	212	5	time	time	NOUN
ejpam-6082	212	6	t	t	PROPN
ejpam-6082	212	7	is	be	AUX
ejpam-6082	212	8	given	give	VERB
ejpam-6082	212	9	by	by	ADP
ejpam-6082	212	10	:	:	PUNCT
ejpam-6082	212	11	n(t	n(t	PROPN
ejpam-6082	212	12	)	)	PUNCT
ejpam-6082	212	13	=	=	PUNCT
ejpam-6082	213	1	∫	∫	PROPN
ejpam-6082	213	2	0	0	PUNCT
ejpam-6082	214	1	[	[	X
ejpam-6082	214	2	s(t	s(t	PROPN
ejpam-6082	214	3	,	,	PUNCT
ejpam-6082	214	4	x	x	X
ejpam-6082	214	5	)	)	PUNCT
ejpam-6082	214	6	+	+	CCONJ
ejpam-6082	214	7	v	v	X
ejpam-6082	214	8	(	(	PUNCT
ejpam-6082	214	9	t	t	PROPN
ejpam-6082	214	10	,	,	PUNCT
ejpam-6082	214	11	x	x	NOUN
ejpam-6082	214	12	)	)	PUNCT
ejpam-6082	214	13	+	+	CCONJ
ejpam-6082	214	14	e(t	e(t	NOUN
ejpam-6082	214	15	,	,	PUNCT
ejpam-6082	214	16	x	x	X
ejpam-6082	214	17	)	)	PUNCT
ejpam-6082	215	1	+	+	ADV
ejpam-6082	215	2	np(t	np(t	NOUN
ejpam-6082	215	3	,	,	PUNCT
ejpam-6082	215	4	x	x	PRON
ejpam-6082	215	5	)	)	PUNCT
ejpam-6082	216	1	+	+	CCONJ
ejpam-6082	216	2	p	p	X
ejpam-6082	216	3	(	(	PUNCT
ejpam-6082	216	4	t	t	PROPN
ejpam-6082	216	5	,	,	PUNCT
ejpam-6082	216	6	x	x	NOUN
ejpam-6082	216	7	)	)	PUNCT
ejpam-6082	217	1	+	+	NOUN
ejpam-6082	217	2	r(t	r(t	NOUN
ejpam-6082	217	3	,	,	PUNCT
ejpam-6082	217	4	x	x	X
ejpam-6082	217	5	)	)	PUNCT
ejpam-6082	218	1	+	+	NOUN
ejpam-6082	218	2	a(t	a(t	NOUN
ejpam-6082	218	3	,	,	PUNCT
ejpam-6082	218	4	x	x	NOUN
ejpam-6082	218	5	)	)	PUNCT
ejpam-6082	218	6	]	]	PUNCT
ejpam-6082	218	7	dx	dx	PROPN
ejpam-6082	218	8	.	.	PUNCT
ejpam-6082	219	1	(	(	PUNCT
ejpam-6082	219	2	15	15	X
ejpam-6082	219	3	)	)	PUNCT
ejpam-6082	219	4	adding	add	VERB
ejpam-6082	219	5	the	the	DET
ejpam-6082	219	6	equations	equation	NOUN
ejpam-6082	219	7	in	in	ADP
ejpam-6082	219	8	(	(	PUNCT
ejpam-6082	219	9	2	2	NUM
ejpam-6082	219	10	)	)	PUNCT
ejpam-6082	219	11	and	and	CCONJ
ejpam-6082	219	12	integrating	integrate	VERB
ejpam-6082	219	13	over	over	ADP
ejpam-6082	219	14	0	0	NUM
ejpam-6082	219	15	,	,	PUNCT
ejpam-6082	219	16	we	we	PRON
ejpam-6082	219	17	have:∫	have:∫	VERB
ejpam-6082	219	18	0	0	NUM
ejpam-6082	220	1	7∑	7∑	NUM
ejpam-6082	220	2	i=1	i=1	PROPN
ejpam-6082	220	3	c	c	NOUN
ejpam-6082	220	4	0	0	PUNCT
ejpam-6082	221	1	d	d	NOUN
ejpam-6082	221	2	α	α	PROPN
ejpam-6082	221	3	t	t	PROPN
ejpam-6082	221	4	λi	λi	X
ejpam-6082	221	5	dx	dx	PROPN
ejpam-6082	221	6	=	=	SYM
ejpam-6082	221	7	∫	∫	PROPN
ejpam-6082	221	8	0	0	NUM
ejpam-6082	222	1	7∑	7∑	NUM
ejpam-6082	222	2	i=1	i=1	PRON
ejpam-6082	222	3	di∆λi	di∆λi	PUNCT
ejpam-6082	222	4	dx+	dx+	NOUN
ejpam-6082	222	5	∫	∫	NOUN
ejpam-6082	222	6	0	0	NUM
ejpam-6082	223	1	7∑	7∑	NUM
ejpam-6082	223	2	i=1	i=1	PROPN
ejpam-6082	223	3	fi	fi	PROPN
ejpam-6082	223	4	dx	dx	PROPN
ejpam-6082	223	5	.	.	PUNCT
ejpam-6082	224	1	using	use	VERB
ejpam-6082	224	2	green	green	PROPN
ejpam-6082	224	3	’s	’s	PART
ejpam-6082	224	4	formula	formula	NOUN
ejpam-6082	224	5	and	and	CCONJ
ejpam-6082	224	6	the	the	DET
ejpam-6082	224	7	boundary	boundary	ADJ
ejpam-6082	224	8	conditions	condition	NOUN
ejpam-6082	224	9	,	,	PUNCT
ejpam-6082	224	10	we	we	PRON
ejpam-6082	224	11	get:∫	get:∫	VERB
ejpam-6082	224	12	0	0	NUM
ejpam-6082	225	1	7∑	7∑	NUM
ejpam-6082	225	2	i=1	i=1	PRON
ejpam-6082	225	3	di∆λi	di∆λi	ADJ
ejpam-6082	225	4	dx	dx	PROPN
ejpam-6082	225	5	=	=	SYM
ejpam-6082	225	6	0	0	PROPN
ejpam-6082	225	7	.	.	PUNCT
ejpam-6082	226	1	hence	hence	ADV
ejpam-6082	226	2	:	:	PUNCT
ejpam-6082	226	3	c	c	NOUN
ejpam-6082	226	4	0	0	PUNCT
ejpam-6082	227	1	d	d	NOUN
ejpam-6082	227	2	α	α	PROPN
ejpam-6082	227	3	t	t	PROPN
ejpam-6082	227	4	n(t	n(t	PROPN
ejpam-6082	227	5	)	)	PUNCT
ejpam-6082	227	6	+	+	NUM
ejpam-6082	227	7	ηn(t	ηn(t	X
ejpam-6082	227	8	)	)	PUNCT
ejpam-6082	227	9	≤	≤	NUM
ejpam-6082	227	10	λ∥0∥.	λ∥0∥.	VERB
ejpam-6082	227	11	taking	take	VERB
ejpam-6082	227	12	the	the	DET
ejpam-6082	227	13	laplace	laplace	NOUN
ejpam-6082	227	14	transform	transform	NOUN
ejpam-6082	227	15	of	of	ADP
ejpam-6082	227	16	the	the	DET
ejpam-6082	227	17	above	above	ADJ
ejpam-6082	227	18	inequality	inequality	NOUN
ejpam-6082	227	19	,	,	PUNCT
ejpam-6082	227	20	we	we	PRON
ejpam-6082	227	21	obtain	obtain	VERB
ejpam-6082	227	22	:	:	PUNCT
ejpam-6082	227	23	sαl{n	sαl{n	ADJ
ejpam-6082	227	24	}	}	PUNCT
ejpam-6082	227	25	−	−	PROPN
ejpam-6082	227	26	sα−1n(0	sα−1n(0	PROPN
ejpam-6082	227	27	)	)	PUNCT
ejpam-6082	227	28	+	+	PUNCT
ejpam-6082	228	1	ηl{n	ηl{n	ADJ
ejpam-6082	228	2	}	}	PUNCT
ejpam-6082	228	3	≤	≤	NUM
ejpam-6082	228	4	λ	λ	PROPN
ejpam-6082	228	5	s	s	PART
ejpam-6082	228	6	.	.	PUNCT
ejpam-6082	228	7	solving	solve	VERB
ejpam-6082	228	8	for	for	ADP
ejpam-6082	228	9	l{n	l{n	PROPN
ejpam-6082	228	10	}	}	PUNCT
ejpam-6082	228	11	,	,	PUNCT
ejpam-6082	228	12	we	we	PRON
ejpam-6082	228	13	get	get	VERB
ejpam-6082	228	14	:	:	PUNCT
ejpam-6082	228	15	l{n	l{n	NOUN
ejpam-6082	228	16	}	}	PUNCT
ejpam-6082	228	17	≤	≤	NUM
ejpam-6082	229	1	λ	λ	ADP
ejpam-6082	229	2	s(sα	s(sα	PROPN
ejpam-6082	229	3	+	+	CCONJ
ejpam-6082	229	4	η	η	NOUN
ejpam-6082	229	5	)	)	PUNCT
ejpam-6082	229	6	+	+	SYM
ejpam-6082	229	7	sα−1n(0	sα−1n(0	NOUN
ejpam-6082	229	8	)	)	PUNCT
ejpam-6082	229	9	sα	sα	ADV
ejpam-6082	229	10	+	+	PROPN
ejpam-6082	229	11	η	η	PROPN
ejpam-6082	229	12	.	.	PUNCT
ejpam-6082	229	13	k.	k.	PROPN
ejpam-6082	229	14	guedri	guedri	PROPN
ejpam-6082	229	15	et	et	PROPN
ejpam-6082	229	16	al	al	PROPN
ejpam-6082	229	17	.	.	PUNCT
ejpam-6082	229	18	/	/	SYM
ejpam-6082	229	19	eur	eur	PROPN
ejpam-6082	229	20	.	.	PUNCT
ejpam-6082	230	1	j.	j.	PROPN
ejpam-6082	230	2	pure	pure	PROPN
ejpam-6082	230	3	appl	appl	PROPN
ejpam-6082	230	4	.	.	PROPN
ejpam-6082	230	5	math	math	PROPN
ejpam-6082	230	6	,	,	PUNCT
ejpam-6082	230	7	18	18	NUM
ejpam-6082	230	8	(	(	PUNCT
ejpam-6082	230	9	2	2	NUM
ejpam-6082	230	10	)	)	PUNCT
ejpam-6082	230	11	(	(	PUNCT
ejpam-6082	230	12	2025	2025	NUM
ejpam-6082	230	13	)	)	PUNCT
ejpam-6082	230	14	,	,	PUNCT
ejpam-6082	230	15	6082	6082	NUM
ejpam-6082	230	16	12	12	NUM
ejpam-6082	230	17	of	of	ADP
ejpam-6082	230	18	39	39	NUM
ejpam-6082	230	19	using	use	VERB
ejpam-6082	230	20	the	the	DET
ejpam-6082	230	21	inverse	inverse	ADJ
ejpam-6082	230	22	laplace	laplace	NOUN
ejpam-6082	230	23	transform	transform	NOUN
ejpam-6082	230	24	and	and	CCONJ
ejpam-6082	230	25	the	the	DET
ejpam-6082	230	26	properties	property	NOUN
ejpam-6082	230	27	of	of	ADP
ejpam-6082	230	28	the	the	DET
ejpam-6082	230	29	mittag	mittag	ADJ
ejpam-6082	230	30	-	-	PUNCT
ejpam-6082	230	31	leffler	leffler	NOUN
ejpam-6082	230	32	function	function	NOUN
ejpam-6082	230	33	,	,	PUNCT
ejpam-6082	230	34	we	we	PRON
ejpam-6082	230	35	have	have	VERB
ejpam-6082	230	36	:	:	PUNCT
ejpam-6082	230	37	n(t	n(t	X
ejpam-6082	230	38	)	)	PUNCT
ejpam-6082	230	39	≤	≤	NUM
ejpam-6082	231	1	max	max	PROPN
ejpam-6082	231	2	{	{	PUNCT
ejpam-6082	231	3	λ	λ	PROPN
ejpam-6082	231	4	η	η	PROPN
ejpam-6082	231	5	,	,	PUNCT
ejpam-6082	231	6	n(0	n(0	PROPN
ejpam-6082	231	7	)	)	PUNCT
ejpam-6082	231	8	}	}	PUNCT
ejpam-6082	232	1	[	[	X
ejpam-6082	232	2	ηtαmα	ηtαmα	NOUN
ejpam-6082	232	3	,	,	PUNCT
ejpam-6082	232	4	α+1(−ηtα	α+1(−ηtα	NUM
ejpam-6082	232	5	)	)	PUNCT
ejpam-6082	232	6	+	+	NOUN
ejpam-6082	232	7	mα,1(−ηtα	mα,1(−ηtα	NOUN
ejpam-6082	232	8	)	)	PUNCT
ejpam-6082	232	9	]	]	PUNCT
ejpam-6082	232	10	.	.	PUNCT
ejpam-6082	233	1	since	since	SCONJ
ejpam-6082	233	2	mα	mα	PROPN
ejpam-6082	233	3	,	,	PUNCT
ejpam-6082	233	4	α+1	α+1	NUM
ejpam-6082	233	5	and	and	CCONJ
ejpam-6082	233	6	mα,1	mα,1	PROPN
ejpam-6082	233	7	are	be	AUX
ejpam-6082	233	8	bounded	bound	VERB
ejpam-6082	233	9	for	for	ADP
ejpam-6082	233	10	all	all	DET
ejpam-6082	233	11	t	t	PROPN
ejpam-6082	233	12	,	,	PUNCT
ejpam-6082	233	13	it	it	PRON
ejpam-6082	233	14	follows	follow	VERB
ejpam-6082	233	15	that	that	SCONJ
ejpam-6082	233	16	:	:	PUNCT
ejpam-6082	233	17	n(t	n(t	NUM
ejpam-6082	233	18	)	)	PUNCT
ejpam-6082	233	19	≤	≤	PUNCT
ejpam-6082	234	1	λ	λ	PROPN
ejpam-6082	234	2	η	η	PROPN
ejpam-6082	234	3	,	,	PUNCT
ejpam-6082	234	4	ensuring	ensure	VERB
ejpam-6082	234	5	boundedness	boundedness	NOUN
ejpam-6082	234	6	of	of	ADP
ejpam-6082	234	7	the	the	DET
ejpam-6082	234	8	solution	solution	NOUN
ejpam-6082	234	9	.	.	PUNCT
ejpam-6082	235	1	this	this	PRON
ejpam-6082	235	2	completes	complete	VERB
ejpam-6082	235	3	the	the	DET
ejpam-6082	235	4	proof	proof	NOUN
ejpam-6082	235	5	.	.	PUNCT
ejpam-6082	236	1	5	5	X
ejpam-6082	236	2	.	.	X
ejpam-6082	236	3	equilibria	equilibrium	NOUN
ejpam-6082	236	4	of	of	ADP
ejpam-6082	236	5	the	the	DET
ejpam-6082	236	6	model	model	NOUN
ejpam-6082	236	7	model	model	NOUN
ejpam-6082	236	8	(	(	PUNCT
ejpam-6082	236	9	2	2	X
ejpam-6082	236	10	)	)	PUNCT
ejpam-6082	236	11	exhibits	exhibit	VERB
ejpam-6082	236	12	two	two	NUM
ejpam-6082	236	13	types	type	NOUN
ejpam-6082	236	14	of	of	ADP
ejpam-6082	236	15	equilibrium	equilibrium	NOUN
ejpam-6082	236	16	states	state	NOUN
ejpam-6082	236	17	.	.	PUNCT
ejpam-6082	237	1	the	the	DET
ejpam-6082	237	2	first	first	ADJ
ejpam-6082	237	3	is	be	AUX
ejpam-6082	237	4	the	the	DET
ejpam-6082	237	5	polio	polio	NOUN
ejpam-6082	237	6	-	-	PUNCT
ejpam-6082	237	7	free	free	ADJ
ejpam-6082	237	8	equilibrium	equilibrium	NOUN
ejpam-6082	237	9	,	,	PUNCT
ejpam-6082	237	10	expressed	express	VERB
ejpam-6082	237	11	as	as	ADP
ejpam-6082	237	12	:	:	PUNCT
ejpam-6082	237	13	ε0	ε0	NOUN
ejpam-6082	237	14	=	=	SYM
ejpam-6082	237	15	(	(	PUNCT
ejpam-6082	237	16	λk5k6	λk5k6	PROPN
ejpam-6082	237	17	ξ	ξ	PROPN
ejpam-6082	237	18	,	,	PUNCT
ejpam-6082	237	19	δλk6	δλk6	PROPN
ejpam-6082	237	20	k1k5k7	k1k5k7	PROPN
ejpam-6082	237	21	−	−	PROPN
ejpam-6082	237	22	δγρ1	δγρ1	PROPN
ejpam-6082	237	23	,	,	PUNCT
ejpam-6082	237	24	0	0	NUM
ejpam-6082	237	25	,	,	PUNCT
ejpam-6082	237	26	0	0	NUM
ejpam-6082	237	27	,	,	PUNCT
ejpam-6082	237	28	0	0	NUM
ejpam-6082	237	29	,	,	PUNCT
ejpam-6082	237	30	σγλ	σγλ	PRON
ejpam-6082	237	31	k1k5k7	k1k5k7	PROPN
ejpam-6082	237	32	−	−	PROPN
ejpam-6082	237	33	δγρ1	δγρ1	PROPN
ejpam-6082	237	34	,	,	PUNCT
ejpam-6082	237	35	ρσγλ	ρσγλ	NOUN
ejpam-6082	237	36	k6(k1k5k7	k6(k1k5k7	PROPN
ejpam-6082	237	37	−	−	PROPN
ejpam-6082	237	38	δγρ1	δγρ1	PROPN
ejpam-6082	237	39	)	)	PUNCT
ejpam-6082	237	40	)	)	PUNCT
ejpam-6082	237	41	,	,	PUNCT
ejpam-6082	237	42	along	along	ADP
ejpam-6082	237	43	with	with	ADP
ejpam-6082	237	44	a	a	DET
ejpam-6082	237	45	second	second	ADJ
ejpam-6082	237	46	equilibrium	equilibrium	NOUN
ejpam-6082	237	47	,	,	PUNCT
ejpam-6082	237	48	referred	refer	VERB
ejpam-6082	237	49	to	to	ADP
ejpam-6082	237	50	as	as	SCONJ
ejpam-6082	237	51	the	the	DET
ejpam-6082	237	52	polio	polio	NOUN
ejpam-6082	237	53	-	-	PUNCT
ejpam-6082	237	54	endemic	endemic	ADJ
ejpam-6082	237	55	equilibrium	equilibrium	NOUN
ejpam-6082	237	56	ξ∗.	ξ∗.	AUX
ejpam-6082	237	57	utilizing	utilize	VERB
ejpam-6082	237	58	the	the	DET
ejpam-6082	237	59	next	next	ADJ
ejpam-6082	237	60	-	-	PUNCT
ejpam-6082	237	61	generation	generation	NOUN
ejpam-6082	237	62	matrix	matrix	NOUN
ejpam-6082	237	63	approach	approach	NOUN
ejpam-6082	237	64	as	as	SCONJ
ejpam-6082	237	65	described	describe	VERB
ejpam-6082	237	66	by	by	ADP
ejpam-6082	237	67	shuai	shuai	PROPN
ejpam-6082	237	68	and	and	CCONJ
ejpam-6082	237	69	van	van	PROPN
ejpam-6082	237	70	den	den	PROPN
ejpam-6082	237	71	driessche	driessche	NOUN
ejpam-6082	238	1	[	[	X
ejpam-6082	238	2	53	53	NUM
ejpam-6082	238	3	]	]	PUNCT
ejpam-6082	238	4	,	,	PUNCT
ejpam-6082	238	5	the	the	DET
ejpam-6082	238	6	transmission	transmission	NOUN
ejpam-6082	238	7	and	and	CCONJ
ejpam-6082	238	8	transition	transition	NOUN
ejpam-6082	238	9	matrices	matrix	NOUN
ejpam-6082	238	10	for	for	ADP
ejpam-6082	238	11	model	model	NOUN
ejpam-6082	238	12	(	(	PUNCT
ejpam-6082	238	13	2	2	NUM
ejpam-6082	238	14	)	)	PUNCT
ejpam-6082	238	15	at	at	ADP
ejpam-6082	238	16	the	the	DET
ejpam-6082	238	17	equilibrium	equilibrium	NOUN
ejpam-6082	238	18	point	point	NOUN
ejpam-6082	238	19	e0	e0	PROPN
ejpam-6082	238	20	are	be	AUX
ejpam-6082	238	21	determined	determine	VERB
ejpam-6082	238	22	as	as	SCONJ
ejpam-6082	238	23	follows	follow	VERB
ejpam-6082	238	24	:	:	PUNCT
ejpam-6082	238	25	f	f	PROPN
ejpam-6082	238	26	=	=	SYM
ejpam-6082	238	27	βcr(s0+(1−δ)v0	βcr(s0+(1−δ)v0	NOUN
ejpam-6082	238	28	)	)	PUNCT
ejpam-6082	238	29	n0	n0	NOUN
ejpam-6082	238	30	βcr(s0+(1−δ)v0	βcr(s0+(1−δ)v0	NOUN
ejpam-6082	238	31	)	)	PUNCT
ejpam-6082	238	32	n0	n0	NOUN
ejpam-6082	238	33	βcr(s0+(1−δ)v0	βcr(s0+(1−δ)v0	NOUN
ejpam-6082	238	34	)	)	PUNCT
ejpam-6082	238	35	n0	n0	NOUN
ejpam-6082	238	36	0	0	NUM
ejpam-6082	238	37	0	0	NUM
ejpam-6082	238	38	0	0	NUM
ejpam-6082	238	39	0	0	NUM
ejpam-6082	238	40	0	0	NUM
ejpam-6082	238	41	0	0	NUM
ejpam-6082	238	42			NOUN
ejpam-6082	238	43	,	,	PUNCT
ejpam-6082	238	44	where	where	SCONJ
ejpam-6082	238	45	s0	s0	PROPN
ejpam-6082	238	46	,	,	PUNCT
ejpam-6082	238	47	v0	v0	PROPN
ejpam-6082	238	48	,	,	PUNCT
ejpam-6082	238	49	and	and	CCONJ
ejpam-6082	238	50	n0	n0	NUM
ejpam-6082	238	51	are	be	AUX
ejpam-6082	238	52	the	the	DET
ejpam-6082	238	53	values	value	NOUN
ejpam-6082	238	54	of	of	ADP
ejpam-6082	238	55	s	s	PROPN
ejpam-6082	238	56	,	,	PUNCT
ejpam-6082	238	57	v	v	NOUN
ejpam-6082	238	58	,	,	PUNCT
ejpam-6082	238	59	and	and	CCONJ
ejpam-6082	238	60	n	n	CCONJ
ejpam-6082	238	61	at	at	ADP
ejpam-6082	238	62	e0	e0	PROPN
ejpam-6082	238	63	,	,	PUNCT
ejpam-6082	238	64	and	and	CCONJ
ejpam-6082	239	1	v	v	X
ejpam-6082	239	2	=	=	SYM
ejpam-6082	239	3	−k2	−k2	NUM
ejpam-6082	239	4	0	0	NUM
ejpam-6082	239	5	0	0	NUM
ejpam-6082	239	6	α1	α1	PROPN
ejpam-6082	239	7	−k3	−k3	PROPN
ejpam-6082	239	8	0	0	NUM
ejpam-6082	239	9	α2	α2	ADJ
ejpam-6082	239	10	0	0	PUNCT
ejpam-6082	240	1	−k4	−k4	VERB
ejpam-6082	240	2			NOUN
ejpam-6082	240	3	.	.	PUNCT
ejpam-6082	241	1	by	by	ADP
ejpam-6082	241	2	applying	apply	VERB
ejpam-6082	241	3	the	the	DET
ejpam-6082	241	4	approach	approach	NOUN
ejpam-6082	241	5	outlined	outline	VERB
ejpam-6082	241	6	in	in	ADP
ejpam-6082	241	7	[	[	X
ejpam-6082	241	8	53	53	NUM
ejpam-6082	241	9	]	]	PUNCT
ejpam-6082	241	10	,	,	PUNCT
ejpam-6082	241	11	the	the	DET
ejpam-6082	241	12	basic	basic	ADJ
ejpam-6082	241	13	reproduction	reproduction	NOUN
ejpam-6082	241	14	number	number	NOUN
ejpam-6082	241	15	is	be	AUX
ejpam-6082	241	16	derived	derive	VERB
ejpam-6082	241	17	as	as	ADP
ejpam-6082	241	18	the	the	DET
ejpam-6082	241	19	spectral	spectral	ADJ
ejpam-6082	241	20	radius	radius	NOUN
ejpam-6082	241	21	of	of	ADP
ejpam-6082	241	22	the	the	DET
ejpam-6082	241	23	next	next	ADJ
ejpam-6082	241	24	-	-	PUNCT
ejpam-6082	241	25	generation	generation	NOUN
ejpam-6082	241	26	matrix	matrix	NOUN
ejpam-6082	241	27	fv−1	fv−1	NOUN
ejpam-6082	241	28	.	.	PUNCT
ejpam-6082	242	1	consequently	consequently	ADV
ejpam-6082	242	2	,	,	PUNCT
ejpam-6082	242	3	the	the	DET
ejpam-6082	242	4	basic	basic	ADJ
ejpam-6082	242	5	reproduction	reproduction	NOUN
ejpam-6082	242	6	number	number	NOUN
ejpam-6082	242	7	is	be	AUX
ejpam-6082	242	8	expressed	express	VERB
ejpam-6082	242	9	as	as	ADP
ejpam-6082	242	10	:	:	PUNCT
ejpam-6082	242	11	r0	r0	NOUN
ejpam-6082	242	12	=	=	SYM
ejpam-6082	242	13	βcrk5	βcrk5	NOUN
ejpam-6082	242	14	(	(	PUNCT
ejpam-6082	242	15	k1	k1	NOUN
ejpam-6082	242	16	+	+	CCONJ
ejpam-6082	242	17	δ(1−	δ(1−	PROPN
ejpam-6082	242	18	δ	δ	PROPN
ejpam-6082	242	19	)	)	PUNCT
ejpam-6082	242	20	)	)	PUNCT
ejpam-6082	243	1	(	(	PUNCT
ejpam-6082	243	2	α1k4	α1k4	PROPN
ejpam-6082	243	3	+	+	SYM
ejpam-6082	243	4	α2k3	α2k3	PROPN
ejpam-6082	243	5	+	+	CCONJ
ejpam-6082	243	6	k3k4	k3k4	NOUN
ejpam-6082	243	7	)	)	PUNCT
ejpam-6082	243	8	ηk2k3k4	ηk2k3k4	PROPN
ejpam-6082	243	9	,	,	PUNCT
ejpam-6082	243	10	where	where	SCONJ
ejpam-6082	243	11	η	η	PROPN
ejpam-6082	243	12	=	=	SYM
ejpam-6082	243	13	k1k5	k1k5	PROPN
ejpam-6082	243	14	+	+	PROPN
ejpam-6082	243	15	δ	δ	PROPN
ejpam-6082	243	16	(	(	PUNCT
ejpam-6082	243	17	k5	k5	PROPN
ejpam-6082	243	18	+	+	CCONJ
ejpam-6082	243	19	γ	γ	X
ejpam-6082	243	20	+	+	CCONJ
ejpam-6082	243	21	ργ	ργ	ADJ
ejpam-6082	243	22	k6	k6	NOUN
ejpam-6082	243	23	)	)	PUNCT
ejpam-6082	243	24	.	.	PUNCT
ejpam-6082	244	1	k1	k1	NOUN
ejpam-6082	244	2	=	=	PUNCT
ejpam-6082	244	3	γ	γ	PROPN
ejpam-6082	244	4	+	+	X
ejpam-6082	244	5	µ	µ	NUM
ejpam-6082	244	6	,	,	PUNCT
ejpam-6082	244	7	k2	k2	ADJ
ejpam-6082	244	8	=	=	SYM
ejpam-6082	244	9	α1	α1	PROPN
ejpam-6082	244	10	+	+	CCONJ
ejpam-6082	244	11	α2	α2	ADJ
ejpam-6082	244	12	+	+	CCONJ
ejpam-6082	244	13	µ+	µ+	PROPN
ejpam-6082	244	14	ω	ω	PROPN
ejpam-6082	244	15	,	,	PUNCT
ejpam-6082	244	16	k3	k3	PROPN
ejpam-6082	244	17	=	=	PROPN
ejpam-6082	244	18	σ	σ	PROPN
ejpam-6082	244	19	+	+	PROPN
ejpam-6082	244	20	µ+	µ+	PROPN
ejpam-6082	244	21	ω1	ω1	PROPN
ejpam-6082	244	22	,	,	PUNCT
ejpam-6082	244	23	k5	k5	PROPN
ejpam-6082	244	24	=	=	PUNCT
ejpam-6082	244	25	ρ+	ρ+	PROPN
ejpam-6082	244	26	ρ1	ρ1	NOUN
ejpam-6082	244	27	+	+	CCONJ
ejpam-6082	244	28	µ	µ	NOUN
ejpam-6082	244	29	,	,	PUNCT
ejpam-6082	244	30	k6	k6	NOUN
ejpam-6082	244	31	=	=	SYM
ejpam-6082	244	32	σ	σ	PROPN
ejpam-6082	244	33	+	+	X
ejpam-6082	244	34	µ	µ	NOUN
ejpam-6082	244	35	,	,	PUNCT
ejpam-6082	244	36	k7	k7	PROPN
ejpam-6082	244	37	=	=	PROPN
ejpam-6082	244	38	δ	δ	PROPN
ejpam-6082	244	39	+	+	PROPN
ejpam-6082	244	40	µ.	µ.	PROPN
ejpam-6082	244	41	k.	k.	PROPN
ejpam-6082	244	42	guedri	guedri	PROPN
ejpam-6082	244	43	et	et	PROPN
ejpam-6082	244	44	al	al	PROPN
ejpam-6082	244	45	.	.	PUNCT
ejpam-6082	244	46	/	/	SYM
ejpam-6082	244	47	eur	eur	PROPN
ejpam-6082	244	48	.	.	PUNCT
ejpam-6082	245	1	j.	j.	PROPN
ejpam-6082	245	2	pure	pure	PROPN
ejpam-6082	245	3	appl	appl	PROPN
ejpam-6082	245	4	.	.	PROPN
ejpam-6082	245	5	math	math	PROPN
ejpam-6082	245	6	,	,	PUNCT
ejpam-6082	245	7	18	18	NUM
ejpam-6082	245	8	(	(	PUNCT
ejpam-6082	245	9	2	2	NUM
ejpam-6082	245	10	)	)	PUNCT
ejpam-6082	245	11	(	(	PUNCT
ejpam-6082	245	12	2025	2025	NUM
ejpam-6082	245	13	)	)	PUNCT
ejpam-6082	245	14	,	,	PUNCT
ejpam-6082	245	15	6082	6082	NUM
ejpam-6082	245	16	13	13	NUM
ejpam-6082	245	17	of	of	ADP
ejpam-6082	245	18	39	39	NUM
ejpam-6082	245	19	the	the	DET
ejpam-6082	245	20	polio	polio	NOUN
ejpam-6082	245	21	-	-	PUNCT
ejpam-6082	245	22	endemic	endemic	ADJ
ejpam-6082	245	23	equilibrium	equilibrium	NOUN
ejpam-6082	245	24	is	be	AUX
ejpam-6082	245	25	represented	represent	VERB
ejpam-6082	245	26	as	as	ADP
ejpam-6082	245	27	ξ∗	ξ∗	NOUN
ejpam-6082	245	28	=	=	SYM
ejpam-6082	245	29	(	(	PUNCT
ejpam-6082	245	30	s∗	s∗	PROPN
ejpam-6082	245	31	,	,	PUNCT
ejpam-6082	245	32	v	v	NOUN
ejpam-6082	245	33	∗	∗	NOUN
ejpam-6082	245	34	,	,	PUNCT
ejpam-6082	245	35	e∗	e∗	PROPN
ejpam-6082	245	36	,	,	PUNCT
ejpam-6082	245	37	n∗	n∗	PROPN
ejpam-6082	245	38	p	p	NOUN
ejpam-6082	245	39	,	,	PUNCT
ejpam-6082	245	40	p	p	NOUN
ejpam-6082	245	41	∗	∗	NOUN
ejpam-6082	245	42	,	,	PUNCT
ejpam-6082	245	43	r∗	r∗	PROPN
ejpam-6082	245	44	,	,	PUNCT
ejpam-6082	245	45	a∗	a∗	NOUN
ejpam-6082	245	46	)	)	PUNCT
ejpam-6082	245	47	,	,	PUNCT
ejpam-6082	245	48	with	with	ADP
ejpam-6082	245	49	the	the	DET
ejpam-6082	245	50	components	component	NOUN
ejpam-6082	245	51	defined	define	VERB
ejpam-6082	245	52	as	as	SCONJ
ejpam-6082	245	53	follows	follow	VERB
ejpam-6082	245	54	:	:	PUNCT
ejpam-6082	246	1	s∗	s∗	PROPN
ejpam-6082	246	2	=	=	SYM
ejpam-6082	246	3	λk5	λk5	PROPN
ejpam-6082	246	4	(	(	PUNCT
ejpam-6082	246	5	k5	k5	PROPN
ejpam-6082	246	6	−	−	PROPN
ejpam-6082	246	7	γ1ρ1	γ1ρ1	PROPN
ejpam-6082	246	8	)	)	PUNCT
ejpam-6082	246	9	(	(	PUNCT
ejpam-6082	246	10	λ∗	λ∗	NOUN
ejpam-6082	246	11	+	+	CCONJ
ejpam-6082	246	12	k7	k7	PROPN
ejpam-6082	246	13	)	)	PUNCT
ejpam-6082	246	14	,	,	PUNCT
ejpam-6082	246	15	v	v	NOUN
ejpam-6082	246	16	∗	∗	NOUN
ejpam-6082	246	17	=	=	SYM
ejpam-6082	246	18	k5δλ	k5δλ	PUNCT
ejpam-6082	246	19	(	(	PUNCT
ejpam-6082	246	20	k5	k5	PROPN
ejpam-6082	246	21	−	−	PROPN
ejpam-6082	246	22	γ1ρ1	γ1ρ1	PROPN
ejpam-6082	246	23	)	)	PUNCT
ejpam-6082	246	24	(	(	PUNCT
ejpam-6082	246	25	λ∗	λ∗	NOUN
ejpam-6082	246	26	+	+	CCONJ
ejpam-6082	246	27	k7	k7	PROPN
ejpam-6082	246	28	)	)	PUNCT
ejpam-6082	246	29	(	(	PUNCT
ejpam-6082	246	30	(	(	PUNCT
ejpam-6082	246	31	1−	1−	NUM
ejpam-6082	246	32	δ)λ∗	δ)λ∗	NOUN
ejpam-6082	246	33	+	+	NUM
ejpam-6082	246	34	k1	k1	NOUN
ejpam-6082	246	35	)	)	PUNCT
ejpam-6082	246	36	,	,	PUNCT
ejpam-6082	246	37	e∗	e∗	NOUN
ejpam-6082	246	38	=	=	SYM
ejpam-6082	246	39	λ∗k5λ	λ∗k5λ	PROPN
ejpam-6082	246	40	(	(	PUNCT
ejpam-6082	246	41	k5	k5	PROPN
ejpam-6082	246	42	−	−	PROPN
ejpam-6082	246	43	γ1ρ1	γ1ρ1	PROPN
ejpam-6082	246	44	)	)	PUNCT
ejpam-6082	246	45	(	(	PUNCT
ejpam-6082	246	46	λ∗	λ∗	NOUN
ejpam-6082	246	47	+	+	CCONJ
ejpam-6082	246	48	k7	k7	PROPN
ejpam-6082	246	49	)	)	PUNCT
ejpam-6082	246	50	k2	k2	PROPN
ejpam-6082	246	51	(	(	PUNCT
ejpam-6082	246	52	1	1	NUM
ejpam-6082	246	53	+	+	CCONJ
ejpam-6082	246	54	δ(1−	δ(1−	PROPN
ejpam-6082	246	55	δ	δ	PROPN
ejpam-6082	246	56	)	)	PUNCT
ejpam-6082	246	57	(	(	PUNCT
ejpam-6082	246	58	1−	1−	NUM
ejpam-6082	246	59	δ)λ∗	δ)λ∗	NOUN
ejpam-6082	246	60	+	+	CCONJ
ejpam-6082	246	61	k1	k1	PROPN
ejpam-6082	246	62	)	)	PUNCT
ejpam-6082	246	63	,	,	PUNCT
ejpam-6082	246	64	n∗	n∗	VERB
ejpam-6082	246	65	p	p	NOUN
ejpam-6082	246	66	=	=	X
ejpam-6082	247	1	λ∗k5λα1	λ∗k5λα1	X
ejpam-6082	247	2	(	(	PUNCT
ejpam-6082	247	3	k5	k5	PROPN
ejpam-6082	247	4	−	−	PROPN
ejpam-6082	247	5	γ1ρ1	γ1ρ1	PROPN
ejpam-6082	247	6	)	)	PUNCT
ejpam-6082	247	7	(	(	PUNCT
ejpam-6082	247	8	λ∗	λ∗	NOUN
ejpam-6082	247	9	+	+	CCONJ
ejpam-6082	247	10	k7	k7	PROPN
ejpam-6082	247	11	)	)	PUNCT
ejpam-6082	247	12	k2k3	k2k3	NOUN
ejpam-6082	247	13	(	(	PUNCT
ejpam-6082	247	14	1	1	NUM
ejpam-6082	247	15	+	+	CCONJ
ejpam-6082	247	16	δ(1−	δ(1−	PROPN
ejpam-6082	247	17	δ	δ	PROPN
ejpam-6082	247	18	)	)	PUNCT
ejpam-6082	247	19	(	(	PUNCT
ejpam-6082	247	20	1−	1−	NUM
ejpam-6082	247	21	δ)λ∗	δ)λ∗	NOUN
ejpam-6082	247	22	+	+	CCONJ
ejpam-6082	247	23	k1	k1	NOUN
ejpam-6082	247	24	)	)	PUNCT
ejpam-6082	247	25	,	,	PUNCT
ejpam-6082	247	26	p	p	NOUN
ejpam-6082	247	27	∗	∗	NOUN
ejpam-6082	247	28	=	=	SYM
ejpam-6082	247	29	λ∗k5λα2	λ∗k5λα2	PROPN
ejpam-6082	247	30	(	(	PUNCT
ejpam-6082	247	31	k5	k5	PROPN
ejpam-6082	247	32	−	−	PROPN
ejpam-6082	247	33	γ1ρ1	γ1ρ1	PROPN
ejpam-6082	247	34	)	)	PUNCT
ejpam-6082	247	35	(	(	PUNCT
ejpam-6082	247	36	λ∗	λ∗	NOUN
ejpam-6082	247	37	+	+	CCONJ
ejpam-6082	247	38	k7	k7	PROPN
ejpam-6082	247	39	)	)	PUNCT
ejpam-6082	248	1	k2k4	k2k4	NOUN
ejpam-6082	248	2	(	(	PUNCT
ejpam-6082	248	3	1	1	NUM
ejpam-6082	248	4	+	+	CCONJ
ejpam-6082	248	5	δ(1−	δ(1−	PROPN
ejpam-6082	248	6	δ	δ	PROPN
ejpam-6082	248	7	)	)	PUNCT
ejpam-6082	248	8	(	(	PUNCT
ejpam-6082	248	9	1−	1−	NUM
ejpam-6082	248	10	δ)λ∗	δ)λ∗	NOUN
ejpam-6082	248	11	+	+	CCONJ
ejpam-6082	248	12	k1	k1	PROPN
ejpam-6082	248	13	)	)	PUNCT
ejpam-6082	248	14	,	,	PUNCT
ejpam-6082	248	15	a∗	a∗	PROPN
ejpam-6082	248	16	=	=	SYM
ejpam-6082	248	17	ργ1λ	ργ1λ	PROPN
ejpam-6082	248	18	k5	k5	PROPN
ejpam-6082	248	19	(	(	PUNCT
ejpam-6082	248	20	k6	k6	PROPN
ejpam-6082	248	21	(	(	PUNCT
ejpam-6082	248	22	λ∗	λ∗	PROPN
ejpam-6082	248	23	+	+	CCONJ
ejpam-6082	248	24	k7)−	k7)−	PROPN
ejpam-6082	248	25	ρ1γ1	ρ1γ1	NOUN
ejpam-6082	248	26	)	)	PUNCT
ejpam-6082	248	27	,	,	PUNCT
ejpam-6082	248	28	r∗	r∗	PROPN
ejpam-6082	248	29	=	=	SYM
ejpam-6082	248	30	γ1λ	γ1λ	NOUN
ejpam-6082	248	31	k6	k6	NOUN
ejpam-6082	248	32	(	(	PUNCT
ejpam-6082	248	33	λ∗	λ∗	PROPN
ejpam-6082	248	34	+	+	CCONJ
ejpam-6082	248	35	k7)−	k7)−	PROPN
ejpam-6082	249	1	ρ1γ1	ρ1γ1	INTJ
ejpam-6082	249	2	.	.	PUNCT
ejpam-6082	250	1	here	here	ADV
ejpam-6082	250	2	,	,	PUNCT
ejpam-6082	250	3	γ1	γ1	PROPN
ejpam-6082	250	4	is	be	AUX
ejpam-6082	250	5	given	give	VERB
ejpam-6082	250	6	by	by	ADP
ejpam-6082	250	7	γ1	γ1	NOUN
ejpam-6082	250	8	=	=	SYM
ejpam-6082	250	9	1	1	NUM
ejpam-6082	250	10	(	(	PUNCT
ejpam-6082	250	11	x∗	x∗	PROPN
ejpam-6082	250	12	+	+	CCONJ
ejpam-6082	250	13	k1	k1	NOUN
ejpam-6082	250	14	)	)	PUNCT
ejpam-6082	250	15	[	[	PUNCT
ejpam-6082	250	16	x∗	x∗	X
ejpam-6082	250	17	(	(	PUNCT
ejpam-6082	250	18	ωk6k4	ωk6k4	PROPN
ejpam-6082	250	19	+	+	NUM
ejpam-6082	250	20	α1k6	α1k6	NUM
ejpam-6082	250	21	+	+	NUM
ejpam-6082	250	22	α2k5	α2k5	X
ejpam-6082	250	23	)	)	PUNCT
ejpam-6082	251	1	+	+	NUM
ejpam-6082	251	2	δ	δ	PROPN
ejpam-6082	251	3	(	(	PUNCT
ejpam-6082	251	4	1−	1−	NUM
ejpam-6082	251	5	δ	δ	NOUN
ejpam-6082	251	6	)	)	PUNCT
ejpam-6082	251	7	(	(	PUNCT
ejpam-6082	251	8	1−	1−	NUM
ejpam-6082	251	9	δ)x∗	δ)x∗	NOUN
ejpam-6082	251	10	+	+	NUM
ejpam-6082	251	11	k1	k1	NOUN
ejpam-6082	251	12	+	+	CCONJ
ejpam-6082	251	13	γ	γ	X
ejpam-6082	251	14	(	(	PUNCT
ejpam-6082	251	15	(	(	PUNCT
ejpam-6082	251	16	1−	1−	NUM
ejpam-6082	251	17	δ)x∗	δ)x∗	NOUN
ejpam-6082	251	18	+	+	NUM
ejpam-6082	251	19	k1	k1	NOUN
ejpam-6082	251	20	)	)	PUNCT
ejpam-6082	251	21	]	]	PUNCT
ejpam-6082	251	22	.	.	PUNCT
ejpam-6082	252	1	substituting	substitute	VERB
ejpam-6082	252	2	the	the	DET
ejpam-6082	252	3	appropriate	appropriate	ADJ
ejpam-6082	252	4	variables	variable	NOUN
ejpam-6082	252	5	into	into	ADP
ejpam-6082	252	6	the	the	DET
ejpam-6082	252	7	expression	expression	NOUN
ejpam-6082	252	8	for	for	ADP
ejpam-6082	252	9	λ	λ	PROPN
ejpam-6082	252	10	and	and	CCONJ
ejpam-6082	252	11	simplifying	simplifying	NOUN
ejpam-6082	252	12	shows	show	VERB
ejpam-6082	252	13	that	that	SCONJ
ejpam-6082	252	14	at	at	ADP
ejpam-6082	252	15	equilibrium	equilibrium	NOUN
ejpam-6082	252	16	,	,	PUNCT
ejpam-6082	252	17	x∗	x∗	PROPN
ejpam-6082	252	18	satisfies	satisfy	VERB
ejpam-6082	252	19	the	the	DET
ejpam-6082	252	20	following	follow	VERB
ejpam-6082	252	21	equation	equation	NOUN
ejpam-6082	252	22	:	:	PUNCT
ejpam-6082	252	23	x∗	x∗	PROPN
ejpam-6082	252	24	(	(	PUNCT
ejpam-6082	252	25	φ2(x	φ2(x	X
ejpam-6082	252	26	∗)2	∗)2	ADV
ejpam-6082	253	1	+	+	ADP
ejpam-6082	253	2	φ1x	φ1x	ADJ
ejpam-6082	253	3	∗	∗	NOUN
ejpam-6082	253	4	+	+	NOUN
ejpam-6082	253	5	φ0	φ0	ADJ
ejpam-6082	253	6	)	)	PUNCT
ejpam-6082	253	7	=	=	SYM
ejpam-6082	253	8	0	0	NUM
ejpam-6082	253	9	,	,	PUNCT
ejpam-6082	253	10	(	(	PUNCT
ejpam-6082	253	11	16	16	NUM
ejpam-6082	253	12	)	)	PUNCT
ejpam-6082	253	13	where	where	SCONJ
ejpam-6082	253	14	φ2	φ2	NOUN
ejpam-6082	253	15	=	=	SYM
ejpam-6082	253	16	(	(	PUNCT
ejpam-6082	253	17	1−	1−	NUM
ejpam-6082	253	18	δ	δ	NOUN
ejpam-6082	253	19	)	)	PUNCT
ejpam-6082	253	20	[	[	PUNCT
ejpam-6082	253	21	k5	k5	PROPN
ejpam-6082	253	22	−	−	PROPN
ejpam-6082	253	23	k6	k6	PROPN
ejpam-6082	253	24	k4	k4	PROPN
ejpam-6082	253	25	(	(	PUNCT
ejpam-6082	253	26	γ	γ	X
ejpam-6082	253	27	+	+	CCONJ
ejpam-6082	253	28	δ	δ	PROPN
ejpam-6082	253	29	k1	k1	NOUN
ejpam-6082	253	30	)	)	PUNCT
ejpam-6082	253	31	−	−	ADP
ejpam-6082	254	1	ωk6	ωk6	NOUN
ejpam-6082	254	2	k4k3	k4k3	X
ejpam-6082	254	3	(	(	PUNCT
ejpam-6082	254	4	α1k4	α1k4	X
ejpam-6082	254	5	+	+	CCONJ
ejpam-6082	254	6	α2k5	α2k5	NOUN
ejpam-6082	254	7	)	)	PUNCT
ejpam-6082	254	8	]	]	PUNCT
ejpam-6082	254	9	,	,	PUNCT
ejpam-6082	254	10	φ1	φ1	PROPN
ejpam-6082	254	11	=	=	SYM
ejpam-6082	254	12	k4k5	k4k5	PROPN
ejpam-6082	254	13	(	(	PUNCT
ejpam-6082	254	14	1−	1−	NUM
ejpam-6082	254	15	δ	δ	NOUN
ejpam-6082	254	16	)	)	PUNCT
ejpam-6082	255	1	[	[	X
ejpam-6082	255	2	1−	1−	NUM
ejpam-6082	255	3	k1(k6(1−	k1(k6(1−	PROPN
ejpam-6082	255	4	δ))]−	δ))]−	PROPN
ejpam-6082	255	5	ωk6k4k5	ωk6k4k5	PROPN
ejpam-6082	255	6	k3k4k5	k3k4k5	PROPN
ejpam-6082	255	7	(	(	PUNCT
ejpam-6082	255	8	α1k4	α1k4	X
ejpam-6082	255	9	+	+	CCONJ
ejpam-6082	255	10	α2k5	α2k5	NOUN
ejpam-6082	255	11	)	)	PUNCT
ejpam-6082	255	12	,	,	PUNCT
ejpam-6082	255	13	φ0	φ0	PROPN
ejpam-6082	255	14	=	=	SYM
ejpam-6082	255	15	k4k5	k4k5	PROPN
ejpam-6082	255	16	[	[	X
ejpam-6082	255	17	γ	γ	X
ejpam-6082	255	18	+	+	X
ejpam-6082	255	19	ρr∗	ρr∗	NOUN
ejpam-6082	255	20	−	−	PROPN
ejpam-6082	256	1	ρ1r	ρ1r	NUM
ejpam-6082	256	2	∗	∗	NOUN
ejpam-6082	256	3	]	]	PUNCT
ejpam-6082	256	4	.	.	PUNCT
ejpam-6082	257	1	equation	equation	NOUN
ejpam-6082	257	2	(	(	PUNCT
ejpam-6082	257	3	16	16	NUM
ejpam-6082	257	4	)	)	PUNCT
ejpam-6082	257	5	describes	describe	VERB
ejpam-6082	257	6	the	the	DET
ejpam-6082	257	7	equilibrium	equilibrium	NOUN
ejpam-6082	257	8	states	state	NOUN
ejpam-6082	257	9	of	of	ADP
ejpam-6082	257	10	model	model	NOUN
ejpam-6082	257	11	(	(	PUNCT
ejpam-6082	257	12	2	2	NUM
ejpam-6082	257	13	)	)	PUNCT
ejpam-6082	257	14	,	,	PUNCT
ejpam-6082	257	15	where	where	SCONJ
ejpam-6082	257	16	the	the	DET
ejpam-6082	257	17	condition	condition	NOUN
ejpam-6082	257	18	x∗	x∗	VERB
ejpam-6082	257	19	=	=	SYM
ejpam-6082	258	1	0	0	PUNCT
ejpam-6082	258	2	represents	represent	VERB
ejpam-6082	258	3	the	the	DET
ejpam-6082	258	4	polio	polio	NOUN
ejpam-6082	258	5	-	-	PUNCT
ejpam-6082	258	6	free	free	ADJ
ejpam-6082	258	7	equilibrium	equilibrium	NOUN
ejpam-6082	258	8	.	.	PUNCT
ejpam-6082	259	1	the	the	DET
ejpam-6082	259	2	non	non	ADJ
ejpam-6082	259	3	-	-	ADJ
ejpam-6082	259	4	trivial	trivial	ADJ
ejpam-6082	259	5	solution	solution	NOUN
ejpam-6082	259	6	x∗	x∗	PROPN
ejpam-6082	259	7	=	=	SYM
ejpam-6082	260	1	√	√	ADP
ejpam-6082	260	2	−	−	PROPN
ejpam-6082	260	3	φ1	φ1	PROPN
ejpam-6082	260	4	2φ2	2φ2	NUM
ejpam-6082	260	5	+	+	CCONJ
ejpam-6082	260	6	√	√	PROPN
ejpam-6082	260	7	φ2	φ2	PROPN
ejpam-6082	260	8	1	1	NUM
ejpam-6082	260	9	4φ2	4φ2	NUM
ejpam-6082	260	10	2	2	NUM
ejpam-6082	260	11	−	−	PROPN
ejpam-6082	260	12	φ0	φ0	ADJ
ejpam-6082	260	13	φ2	φ2	PROPN
ejpam-6082	260	14	represents	represent	VERB
ejpam-6082	260	15	the	the	DET
ejpam-6082	260	16	polio	polio	NOUN
ejpam-6082	260	17	-	-	PUNCT
ejpam-6082	260	18	endemic	endemic	ADJ
ejpam-6082	260	19	equilibrium	equilibrium	NOUN
ejpam-6082	260	20	.	.	PUNCT
ejpam-6082	261	1	the	the	DET
ejpam-6082	261	2	number	number	NOUN
ejpam-6082	261	3	of	of	ADP
ejpam-6082	261	4	endemic	endemic	ADJ
ejpam-6082	261	5	equilibria	equilibrium	NOUN
ejpam-6082	261	6	in	in	ADP
ejpam-6082	261	7	model	model	NOUN
ejpam-6082	261	8	(	(	PUNCT
ejpam-6082	261	9	1	1	NUM
ejpam-6082	261	10	)	)	PUNCT
ejpam-6082	261	11	is	be	AUX
ejpam-6082	261	12	determined	determine	VERB
ejpam-6082	261	13	by	by	ADP
ejpam-6082	261	14	the	the	DET
ejpam-6082	261	15	positive	positive	ADJ
ejpam-6082	261	16	roots	root	NOUN
ejpam-6082	261	17	of	of	ADP
ejpam-6082	261	18	eq	eq	PROPN
ejpam-6082	261	19	.	.	PUNCT
ejpam-6082	262	1	(	(	PUNCT
ejpam-6082	262	2	16	16	NUM
ejpam-6082	262	3	)	)	PUNCT
ejpam-6082	262	4	.	.	PUNCT
ejpam-6082	263	1	these	these	DET
ejpam-6082	263	2	positive	positive	ADJ
ejpam-6082	263	3	roots	root	NOUN
ejpam-6082	263	4	depend	depend	VERB
ejpam-6082	263	5	on	on	ADP
ejpam-6082	263	6	the	the	DET
ejpam-6082	263	7	signs	sign	NOUN
ejpam-6082	263	8	of	of	ADP
ejpam-6082	263	9	the	the	DET
ejpam-6082	263	10	coefficients	coefficient	NOUN
ejpam-6082	263	11	φ0	φ0	ADJ
ejpam-6082	263	12	,	,	PUNCT
ejpam-6082	263	13	φ1	φ1	PROPN
ejpam-6082	263	14	,	,	PUNCT
ejpam-6082	263	15	and	and	CCONJ
ejpam-6082	263	16	φ2	φ2	PROPN
ejpam-6082	263	17	,	,	PUNCT
ejpam-6082	263	18	and	and	CCONJ
ejpam-6082	263	19	each	each	DET
ejpam-6082	263	20	positive	positive	ADJ
ejpam-6082	263	21	root	root	NOUN
ejpam-6082	263	22	corresponds	correspond	VERB
ejpam-6082	263	23	to	to	ADP
ejpam-6082	263	24	an	an	DET
ejpam-6082	263	25	endemic	endemic	ADJ
ejpam-6082	263	26	k.	k.	PROPN
ejpam-6082	263	27	guedri	guedri	PROPN
ejpam-6082	263	28	et	et	PROPN
ejpam-6082	263	29	al	al	PROPN
ejpam-6082	263	30	.	.	PUNCT
ejpam-6082	263	31	/	/	SYM
ejpam-6082	263	32	eur	eur	PROPN
ejpam-6082	263	33	.	.	PUNCT
ejpam-6082	264	1	j.	j.	PROPN
ejpam-6082	264	2	pure	pure	PROPN
ejpam-6082	264	3	appl	appl	PROPN
ejpam-6082	264	4	.	.	PROPN
ejpam-6082	264	5	math	math	PROPN
ejpam-6082	264	6	,	,	PUNCT
ejpam-6082	264	7	18	18	NUM
ejpam-6082	264	8	(	(	PUNCT
ejpam-6082	264	9	2	2	NUM
ejpam-6082	264	10	)	)	PUNCT
ejpam-6082	264	11	(	(	PUNCT
ejpam-6082	264	12	2025	2025	NUM
ejpam-6082	264	13	)	)	PUNCT
ejpam-6082	264	14	,	,	PUNCT
ejpam-6082	264	15	6082	6082	NUM
ejpam-6082	264	16	14	14	NUM
ejpam-6082	264	17	of	of	ADP
ejpam-6082	264	18	39	39	NUM
ejpam-6082	264	19	equilibrium	equilibrium	NOUN
ejpam-6082	264	20	point	point	NOUN
ejpam-6082	264	21	.	.	PUNCT
ejpam-6082	265	1	it	it	PRON
ejpam-6082	265	2	can	can	AUX
ejpam-6082	265	3	be	be	AUX
ejpam-6082	265	4	shown	show	VERB
ejpam-6082	265	5	that	that	SCONJ
ejpam-6082	265	6	φ2	φ2	PROPN
ejpam-6082	265	7	>	>	X
ejpam-6082	265	8	0	0	NUM
ejpam-6082	265	9	,	,	PUNCT
ejpam-6082	265	10	meaning	mean	VERB
ejpam-6082	265	11	the	the	DET
ejpam-6082	265	12	number	number	NOUN
ejpam-6082	265	13	of	of	ADP
ejpam-6082	265	14	positive	positive	ADJ
ejpam-6082	265	15	roots	root	NOUN
ejpam-6082	265	16	(	(	PUNCT
ejpam-6082	265	17	and	and	CCONJ
ejpam-6082	265	18	therefore	therefore	ADV
ejpam-6082	265	19	the	the	DET
ejpam-6082	265	20	number	number	NOUN
ejpam-6082	265	21	of	of	ADP
ejpam-6082	265	22	endemic	endemic	ADJ
ejpam-6082	265	23	equilibria	equilibrium	NOUN
ejpam-6082	265	24	)	)	PUNCT
ejpam-6082	265	25	is	be	AUX
ejpam-6082	265	26	influenced	influence	VERB
ejpam-6082	265	27	only	only	ADV
ejpam-6082	265	28	by	by	ADP
ejpam-6082	265	29	the	the	DET
ejpam-6082	265	30	signs	sign	NOUN
ejpam-6082	265	31	of	of	ADP
ejpam-6082	265	32	φ0	φ0	PROPN
ejpam-6082	265	33	and	and	CCONJ
ejpam-6082	265	34	φ1	φ1	PROPN
ejpam-6082	265	35	.	.	PUNCT
ejpam-6082	266	1	using	use	VERB
ejpam-6082	266	2	descartes	descarte	NOUN
ejpam-6082	266	3	’	'	PUNCT
ejpam-6082	266	4	rule	rule	NOUN
ejpam-6082	266	5	of	of	ADP
ejpam-6082	266	6	signs	sign	NOUN
ejpam-6082	266	7	,	,	PUNCT
ejpam-6082	266	8	the	the	DET
ejpam-6082	266	9	following	follow	VERB
ejpam-6082	266	10	conclusions	conclusion	NOUN
ejpam-6082	266	11	can	can	AUX
ejpam-6082	266	12	be	be	AUX
ejpam-6082	266	13	drawn	draw	VERB
ejpam-6082	266	14	:	:	PUNCT
ejpam-6082	266	15	theorem	theorem	NOUN
ejpam-6082	266	16	3	3	NUM
ejpam-6082	266	17	.	.	X
ejpam-6082	266	18	for	for	ADP
ejpam-6082	266	19	model	model	NOUN
ejpam-6082	266	20	(	(	PUNCT
ejpam-6082	266	21	2	2	NUM
ejpam-6082	266	22	)	)	PUNCT
ejpam-6082	266	23	,	,	PUNCT
ejpam-6082	266	24	the	the	DET
ejpam-6082	266	25	following	follow	VERB
ejpam-6082	266	26	conditions	condition	NOUN
ejpam-6082	266	27	apply	apply	VERB
ejpam-6082	266	28	:	:	PUNCT
ejpam-6082	267	1	1	1	X
ejpam-6082	267	2	.	.	X
ejpam-6082	268	1	no	no	DET
ejpam-6082	268	2	endemic	endemic	ADJ
ejpam-6082	268	3	equilibria	equilibrium	NOUN
ejpam-6082	268	4	exist	exist	VERB
ejpam-6082	268	5	(	(	PUNCT
ejpam-6082	268	6	i.e.	i.e.	X
ejpam-6082	268	7	,	,	PUNCT
ejpam-6082	268	8	only	only	ADV
ejpam-6082	268	9	x∗	x∗	PROPN
ejpam-6082	269	1	=	=	SYM
ejpam-6082	269	2	0	0	NUM
ejpam-6082	269	3	is	be	AUX
ejpam-6082	269	4	valid	valid	ADJ
ejpam-6082	269	5	)	)	PUNCT
ejpam-6082	269	6	if	if	SCONJ
ejpam-6082	269	7	φ0	φ0	PROPN
ejpam-6082	269	8	>	>	X
ejpam-6082	269	9	0	0	PROPN
ejpam-6082	269	10	.	.	PROPN
ejpam-6082	270	1	2	2	NUM
ejpam-6082	270	2	.	.	X
ejpam-6082	270	3	a	a	DET
ejpam-6082	270	4	unique	unique	ADJ
ejpam-6082	270	5	endemic	endemic	ADJ
ejpam-6082	270	6	equilibrium	equilibrium	NOUN
ejpam-6082	270	7	exists	exist	VERB
ejpam-6082	270	8	when	when	SCONJ
ejpam-6082	270	9	φ0	φ0	ADJ
ejpam-6082	270	10	<	<	X
ejpam-6082	270	11	0	0	NUM
ejpam-6082	270	12	.	.	NOUN
ejpam-6082	271	1	3	3	NUM
ejpam-6082	271	2	.	.	X
ejpam-6082	271	3	two	two	NUM
ejpam-6082	271	4	endemic	endemic	ADJ
ejpam-6082	271	5	equilibria	equilibrium	NOUN
ejpam-6082	271	6	exist	exist	VERB
ejpam-6082	271	7	if	if	SCONJ
ejpam-6082	271	8	φ1	φ1	PROPN
ejpam-6082	271	9	<	<	X
ejpam-6082	271	10	0	0	PUNCT
ejpam-6082	271	11	and	and	CCONJ
ejpam-6082	271	12	φ0	φ0	PROPN
ejpam-6082	271	13	>	>	X
ejpam-6082	271	14	0	0	PROPN
ejpam-6082	271	15	.	.	PUNCT
ejpam-6082	272	1	the	the	DET
ejpam-6082	272	2	next	next	ADJ
ejpam-6082	272	3	section	section	NOUN
ejpam-6082	272	4	focuses	focus	VERB
ejpam-6082	272	5	on	on	ADP
ejpam-6082	272	6	analyzing	analyze	VERB
ejpam-6082	272	7	the	the	DET
ejpam-6082	272	8	stability	stability	NOUN
ejpam-6082	272	9	of	of	ADP
ejpam-6082	272	10	the	the	DET
ejpam-6082	272	11	model	model	NOUN
ejpam-6082	272	12	’s	’s	PART
ejpam-6082	272	13	equilibrium	equilibrium	NOUN
ejpam-6082	272	14	states	state	NOUN
ejpam-6082	272	15	.	.	PUNCT
ejpam-6082	273	1	6	6	X
ejpam-6082	273	2	.	.	X
ejpam-6082	273	3	global	global	ADJ
ejpam-6082	273	4	stability	stability	NOUN
ejpam-6082	273	5	of	of	ADP
ejpam-6082	273	6	the	the	DET
ejpam-6082	273	7	endemic	endemic	ADJ
ejpam-6082	273	8	equilibrium	equilibrium	NOUN
ejpam-6082	273	9	theorem	theorem	VERB
ejpam-6082	273	10	4	4	NUM
ejpam-6082	273	11	.	.	PUNCT
ejpam-6082	274	1	the	the	DET
ejpam-6082	274	2	endemic	endemic	ADJ
ejpam-6082	274	3	equilibrium	equilibrium	NOUN
ejpam-6082	274	4	ξ∗	ξ∗	NOUN
ejpam-6082	274	5	is	be	AUX
ejpam-6082	274	6	globally	globally	ADV
ejpam-6082	274	7	asymptotically	asymptotically	ADV
ejpam-6082	274	8	stable	stable	ADJ
ejpam-6082	274	9	(	(	PUNCT
ejpam-6082	274	10	gas	gas	NOUN
ejpam-6082	274	11	)	)	PUNCT
ejpam-6082	274	12	if	if	SCONJ
ejpam-6082	274	13	r0	r0	NOUN
ejpam-6082	274	14	>	>	X
ejpam-6082	274	15	1	1	X
ejpam-6082	274	16	.	.	PUNCT
ejpam-6082	274	17	proof	proof	NOUN
ejpam-6082	274	18	.	.	PUNCT
ejpam-6082	275	1	assuming	assume	VERB
ejpam-6082	275	2	the	the	DET
ejpam-6082	275	3	lyapunov	lyapunov	ADJ
ejpam-6082	275	4	function	function	NOUN
ejpam-6082	275	5	as	as	SCONJ
ejpam-6082	275	6	follows	follow	VERB
ejpam-6082	275	7	:	:	PUNCT
ejpam-6082	275	8	v2(t	v2(t	NOUN
ejpam-6082	275	9	,	,	PUNCT
ejpam-6082	275	10	x	x	NOUN
ejpam-6082	275	11	)	)	PUNCT
ejpam-6082	275	12	=	=	SYM
ejpam-6082	275	13	∫	∫	PROPN
ejpam-6082	275	14	ω	ω	PROPN
ejpam-6082	275	15	[	[	PUNCT
ejpam-6082	275	16	s∗φ	s∗φ	X
ejpam-6082	275	17	(	(	PUNCT
ejpam-6082	275	18	s	s	X
ejpam-6082	275	19	s∗	s∗	PROPN
ejpam-6082	275	20	)	)	PUNCT
ejpam-6082	276	1	+	+	CCONJ
ejpam-6082	276	2	e∗φ	e∗φ	PROPN
ejpam-6082	276	3	(	(	PUNCT
ejpam-6082	276	4	e	e	NOUN
ejpam-6082	276	5	e∗	e∗	PROPN
ejpam-6082	276	6	)	)	PUNCT
ejpam-6082	277	1	+	+	CCONJ
ejpam-6082	277	2	η	η	PROPN
ejpam-6082	277	3	+	+	PROPN
ejpam-6082	277	4	δ	δ	PROPN
ejpam-6082	277	5	δ	δ	PROPN
ejpam-6082	277	6	n∗	n∗	VERB
ejpam-6082	277	7	pφ	pφ	INTJ
ejpam-6082	277	8	(	(	PUNCT
ejpam-6082	277	9	np	np	INTJ
ejpam-6082	277	10	n∗	n∗	PROPN
ejpam-6082	277	11	p	p	PROPN
ejpam-6082	277	12	)	)	PUNCT
ejpam-6082	277	13	+	+	CCONJ
ejpam-6082	277	14	.	.	PUNCT
ejpam-6082	277	15	.	.	PUNCT
ejpam-6082	277	16	.	.	PUNCT
ejpam-6082	278	1	]	]	PUNCT
ejpam-6082	279	1	dx	dx	PROPN
ejpam-6082	279	2	,	,	PUNCT
ejpam-6082	279	3	where	where	SCONJ
ejpam-6082	279	4	φ(z	φ(z	NOUN
ejpam-6082	279	5	)	)	PUNCT
ejpam-6082	279	6	=	=	SYM
ejpam-6082	279	7	z	z	NOUN
ejpam-6082	280	1	−	−	PROPN
ejpam-6082	280	2	1−	1−	NUM
ejpam-6082	280	3	ln(z	ln(z	PROPN
ejpam-6082	280	4	)	)	PUNCT
ejpam-6082	280	5	satisfies	satisfie	NOUN
ejpam-6082	280	6	φ(z	φ(z	PROPN
ejpam-6082	280	7	)	)	PUNCT
ejpam-6082	280	8	≥	≥	NOUN
ejpam-6082	280	9	0	0	NUM
ejpam-6082	280	10	,	,	PUNCT
ejpam-6082	280	11	with	with	ADP
ejpam-6082	280	12	equality	equality	NOUN
ejpam-6082	280	13	only	only	ADV
ejpam-6082	280	14	if	if	SCONJ
ejpam-6082	280	15	z	z	NOUN
ejpam-6082	280	16	=	=	NOUN
ejpam-6082	280	17	1	1	X
ejpam-6082	280	18	.	.	X
ejpam-6082	280	19	using	use	VERB
ejpam-6082	280	20	lemma	lemma	PROPN
ejpam-6082	280	21	2	2	NUM
ejpam-6082	280	22	and	and	CCONJ
ejpam-6082	280	23	the	the	DET
ejpam-6082	280	24	system	system	NOUN
ejpam-6082	280	25	of	of	ADP
ejpam-6082	280	26	equations	equation	NOUN
ejpam-6082	280	27	,	,	PUNCT
ejpam-6082	280	28	we	we	PRON
ejpam-6082	280	29	calculate	calculate	VERB
ejpam-6082	280	30	:	:	PUNCT
ejpam-6082	280	31	c	c	NOUN
ejpam-6082	280	32	0	0	PUNCT
ejpam-6082	281	1	d	d	NOUN
ejpam-6082	281	2	α	α	X
ejpam-6082	281	3	t	t	PROPN
ejpam-6082	281	4	v2(t	v2(t	PROPN
ejpam-6082	281	5	,	,	PUNCT
ejpam-6082	281	6	x	x	X
ejpam-6082	281	7	)	)	PUNCT
ejpam-6082	281	8	=	=	SYM
ejpam-6082	282	1	∫	∫	PROPN
ejpam-6082	282	2	ω	ω	PROPN
ejpam-6082	282	3	[	[	PUNCT
ejpam-6082	282	4	c	c	NOUN
ejpam-6082	282	5	0	0	PUNCT
ejpam-6082	283	1	d	d	NOUN
ejpam-6082	283	2	α	α	PROPN
ejpam-6082	283	3	t	t	PROPN
ejpam-6082	283	4	(	(	PUNCT
ejpam-6082	283	5	s∗φ	s∗φ	X
ejpam-6082	283	6	(	(	PUNCT
ejpam-6082	283	7	s	s	VERB
ejpam-6082	283	8	s∗	s∗	PROPN
ejpam-6082	283	9	)	)	PUNCT
ejpam-6082	283	10	)	)	PUNCT
ejpam-6082	284	1	+	+	CCONJ
ejpam-6082	285	1	c	c	NOUN
ejpam-6082	285	2	0	0	PUNCT
ejpam-6082	286	1	d	d	NOUN
ejpam-6082	286	2	α	α	PROPN
ejpam-6082	286	3	t	t	PROPN
ejpam-6082	286	4	(	(	PUNCT
ejpam-6082	286	5	e∗φ	e∗φ	PROPN
ejpam-6082	286	6	(	(	PUNCT
ejpam-6082	286	7	e	e	NOUN
ejpam-6082	286	8	e∗	e∗	PROPN
ejpam-6082	286	9	)	)	PUNCT
ejpam-6082	286	10	)	)	PUNCT
ejpam-6082	287	1	+	+	CCONJ
ejpam-6082	287	2	η	η	PROPN
ejpam-6082	287	3	+	+	PROPN
ejpam-6082	287	4	δ	δ	PROPN
ejpam-6082	287	5	δ	δ	X
ejpam-6082	287	6	c	c	NOUN
ejpam-6082	287	7	0	0	PUNCT
ejpam-6082	288	1	d	d	NOUN
ejpam-6082	288	2	α	α	PROPN
ejpam-6082	288	3	t	t	PROPN
ejpam-6082	288	4	(	(	PUNCT
ejpam-6082	288	5	n∗	n∗	PROPN
ejpam-6082	288	6	pφ	pφ	X
ejpam-6082	288	7	(	(	PUNCT
ejpam-6082	288	8	np	np	INTJ
ejpam-6082	288	9	n∗	n∗	PROPN
ejpam-6082	288	10	p	p	PROPN
ejpam-6082	288	11	)	)	PUNCT
ejpam-6082	288	12	)	)	PUNCT
ejpam-6082	289	1	+	+	CCONJ
ejpam-6082	289	2	.	.	PUNCT
ejpam-6082	289	3	.	.	PUNCT
ejpam-6082	289	4	.	.	PUNCT
ejpam-6082	290	1	]	]	PUNCT
ejpam-6082	291	1	dx	dx	PROPN
ejpam-6082	291	2	.	.	PUNCT
ejpam-6082	292	1	using	use	VERB
ejpam-6082	292	2	the	the	DET
ejpam-6082	292	3	equation	equation	NOUN
ejpam-6082	292	4	for	for	ADP
ejpam-6082	292	5	s	s	NOUN
ejpam-6082	292	6	:	:	PUNCT
ejpam-6082	292	7	c	c	NOUN
ejpam-6082	292	8	0	0	PUNCT
ejpam-6082	293	1	d	d	NOUN
ejpam-6082	293	2	α	α	NOUN
ejpam-6082	293	3	t	t	NOUN
ejpam-6082	293	4	s	s	PART
ejpam-6082	293	5	=	=	PUNCT
ejpam-6082	293	6	λ+	λ+	PUNCT
ejpam-6082	293	7	ρ1r−	ρ1r−	PRON
ejpam-6082	293	8	(	(	PUNCT
ejpam-6082	293	9	λ+	λ+	PUNCT
ejpam-6082	293	10	δ	δ	NOUN
ejpam-6082	293	11	+	+	NOUN
ejpam-6082	293	12	µ)s	µ)s	NOUN
ejpam-6082	293	13	−	−	NOUN
ejpam-6082	293	14	d1∆s	d1∆s	ADJ
ejpam-6082	293	15	,	,	PUNCT
ejpam-6082	293	16	we	we	PRON
ejpam-6082	293	17	compute	compute	VERB
ejpam-6082	293	18	:	:	PUNCT
ejpam-6082	294	1	c	c	NOUN
ejpam-6082	294	2	0	0	PUNCT
ejpam-6082	295	1	d	d	NOUN
ejpam-6082	295	2	α	α	PROPN
ejpam-6082	295	3	t	t	PROPN
ejpam-6082	295	4	(	(	PUNCT
ejpam-6082	295	5	s∗φ	s∗φ	X
ejpam-6082	295	6	(	(	PUNCT
ejpam-6082	295	7	s	s	VERB
ejpam-6082	295	8	s∗	s∗	PROPN
ejpam-6082	295	9	)	)	PUNCT
ejpam-6082	295	10	)	)	PUNCT
ejpam-6082	296	1	=	=	PRON
ejpam-6082	296	2	s∗	s∗	PROPN
ejpam-6082	296	3	(	(	PUNCT
ejpam-6082	296	4	1−	1−	NUM
ejpam-6082	296	5	s∗	s∗	PROPN
ejpam-6082	296	6	s	s	PART
ejpam-6082	296	7	)	)	PUNCT
ejpam-6082	297	1	[	[	X
ejpam-6082	297	2	λ	λ	X
ejpam-6082	297	3	+	+	CCONJ
ejpam-6082	297	4	ρ1r−	ρ1r−	PRON
ejpam-6082	297	5	(	(	PUNCT
ejpam-6082	297	6	λ+	λ+	PUNCT
ejpam-6082	297	7	δ	δ	NOUN
ejpam-6082	297	8	+	+	NOUN
ejpam-6082	297	9	µ)s	µ)s	NOUN
ejpam-6082	297	10	−	−	NOUN
ejpam-6082	297	11	d1∆s	d1∆s	NOUN
ejpam-6082	297	12	]	]	PUNCT
ejpam-6082	297	13	.	.	PUNCT
ejpam-6082	298	1	expanding	expand	VERB
ejpam-6082	298	2	and	and	CCONJ
ejpam-6082	298	3	simplifying	simplifying	NOUN
ejpam-6082	298	4	,	,	PUNCT
ejpam-6082	298	5	we	we	PRON
ejpam-6082	298	6	get	get	VERB
ejpam-6082	298	7	:	:	PUNCT
ejpam-6082	298	8	c	c	NOUN
ejpam-6082	298	9	0	0	PUNCT
ejpam-6082	299	1	d	d	NOUN
ejpam-6082	299	2	α	α	PROPN
ejpam-6082	299	3	t	t	PROPN
ejpam-6082	299	4	(	(	PUNCT
ejpam-6082	299	5	s∗φ	s∗φ	X
ejpam-6082	299	6	(	(	PUNCT
ejpam-6082	299	7	s	s	VERB
ejpam-6082	299	8	s∗	s∗	PROPN
ejpam-6082	299	9	)	)	PUNCT
ejpam-6082	299	10	)	)	PUNCT
ejpam-6082	300	1	≤	≤	NUM
ejpam-6082	300	2	∫	∫	PROPN
ejpam-6082	300	3	ω	ω	PROPN
ejpam-6082	300	4	[	[	PUNCT
ejpam-6082	300	5	d1∆s	d1∆s	ADJ
ejpam-6082	300	6	−	−	NOUN
ejpam-6082	300	7	d1s	d1s	X
ejpam-6082	300	8	∗∆s	∗∆s	X
ejpam-6082	300	9	s	s	PART
ejpam-6082	300	10	+	+	NUM
ejpam-6082	300	11	source	source	NOUN
ejpam-6082	300	12	terms	term	NOUN
ejpam-6082	300	13	]	]	PUNCT
ejpam-6082	300	14	dx	dx	PROPN
ejpam-6082	300	15	.	.	PUNCT
ejpam-6082	301	1	using	use	VERB
ejpam-6082	301	2	the	the	DET
ejpam-6082	301	3	equation	equation	NOUN
ejpam-6082	301	4	for	for	ADP
ejpam-6082	301	5	e	e	NOUN
ejpam-6082	301	6	:	:	PUNCT
ejpam-6082	301	7	c	c	NOUN
ejpam-6082	301	8	0	0	PUNCT
ejpam-6082	302	1	d	d	NOUN
ejpam-6082	302	2	α	α	NOUN
ejpam-6082	302	3	t	t	X
ejpam-6082	302	4	e	e	X
ejpam-6082	302	5	=	=	PUNCT
ejpam-6082	302	6	λs	λs	PROPN
ejpam-6082	302	7	+	+	CCONJ
ejpam-6082	302	8	(	(	PUNCT
ejpam-6082	302	9	1−	1−	NUM
ejpam-6082	302	10	δ)λv	δ)λv	PROPN
ejpam-6082	302	11	−	−	PROPN
ejpam-6082	302	12	(	(	PUNCT
ejpam-6082	302	13	α1	α1	PROPN
ejpam-6082	302	14	+	+	CCONJ
ejpam-6082	302	15	α2	α2	ADJ
ejpam-6082	302	16	+	+	CCONJ
ejpam-6082	302	17	ω	ω	NUM
ejpam-6082	302	18	+	+	CCONJ
ejpam-6082	302	19	µ)e	µ)e	NOUN
ejpam-6082	302	20	−	−	PROPN
ejpam-6082	302	21	d3∆e	d3∆e	PROPN
ejpam-6082	302	22	,	,	PUNCT
ejpam-6082	302	23	k.	k.	PROPN
ejpam-6082	302	24	guedri	guedri	PROPN
ejpam-6082	302	25	et	et	PROPN
ejpam-6082	302	26	al	al	PROPN
ejpam-6082	302	27	.	.	PUNCT
ejpam-6082	302	28	/	/	SYM
ejpam-6082	302	29	eur	eur	PROPN
ejpam-6082	302	30	.	.	PUNCT
ejpam-6082	303	1	j.	j.	PROPN
ejpam-6082	303	2	pure	pure	PROPN
ejpam-6082	303	3	appl	appl	PROPN
ejpam-6082	303	4	.	.	PROPN
ejpam-6082	303	5	math	math	PROPN
ejpam-6082	303	6	,	,	PUNCT
ejpam-6082	303	7	18	18	NUM
ejpam-6082	303	8	(	(	PUNCT
ejpam-6082	303	9	2	2	NUM
ejpam-6082	303	10	)	)	PUNCT
ejpam-6082	303	11	(	(	PUNCT
ejpam-6082	303	12	2025	2025	NUM
ejpam-6082	303	13	)	)	PUNCT
ejpam-6082	303	14	,	,	PUNCT
ejpam-6082	303	15	6082	6082	NUM
ejpam-6082	303	16	15	15	NUM
ejpam-6082	303	17	of	of	ADP
ejpam-6082	303	18	39	39	NUM
ejpam-6082	303	19	we	we	PRON
ejpam-6082	303	20	compute	compute	VERB
ejpam-6082	303	21	:	:	PUNCT
ejpam-6082	303	22	c	c	NOUN
ejpam-6082	303	23	0	0	PUNCT
ejpam-6082	304	1	d	d	NOUN
ejpam-6082	304	2	α	α	PROPN
ejpam-6082	304	3	t	t	PROPN
ejpam-6082	304	4	(	(	PUNCT
ejpam-6082	304	5	e∗φ	e∗φ	PROPN
ejpam-6082	304	6	(	(	PUNCT
ejpam-6082	304	7	e	e	NOUN
ejpam-6082	304	8	e∗	e∗	PROPN
ejpam-6082	304	9	)	)	PUNCT
ejpam-6082	304	10	)	)	PUNCT
ejpam-6082	305	1	=	=	SYM
ejpam-6082	305	2	e∗	e∗	NOUN
ejpam-6082	305	3	(	(	PUNCT
ejpam-6082	305	4	1−	1−	NUM
ejpam-6082	305	5	e∗	e∗	PROPN
ejpam-6082	305	6	e	e	NOUN
ejpam-6082	305	7	)	)	PUNCT
ejpam-6082	306	1	[	[	X
ejpam-6082	306	2	λs	λs	X
ejpam-6082	306	3	+	+	CCONJ
ejpam-6082	306	4	(	(	PUNCT
ejpam-6082	306	5	1−	1−	NUM
ejpam-6082	306	6	δ)λv	δ)λv	PROPN
ejpam-6082	306	7	−	−	PROPN
ejpam-6082	306	8	(	(	PUNCT
ejpam-6082	306	9	α1	α1	PROPN
ejpam-6082	306	10	+	+	CCONJ
ejpam-6082	306	11	α2	α2	ADJ
ejpam-6082	306	12	+	+	CCONJ
ejpam-6082	306	13	ω	ω	NUM
ejpam-6082	306	14	+	+	CCONJ
ejpam-6082	306	15	µ)e	µ)e	NOUN
ejpam-6082	306	16	−	−	PROPN
ejpam-6082	306	17	d3∆e	d3∆e	NOUN
ejpam-6082	306	18	]	]	PUNCT
ejpam-6082	306	19	.	.	PUNCT
ejpam-6082	307	1	this	this	PRON
ejpam-6082	307	2	leads	lead	VERB
ejpam-6082	307	3	to	to	ADP
ejpam-6082	307	4	:	:	PUNCT
ejpam-6082	307	5	c	c	NOUN
ejpam-6082	307	6	0	0	PUNCT
ejpam-6082	308	1	d	d	NOUN
ejpam-6082	308	2	α	α	PROPN
ejpam-6082	308	3	t	t	PROPN
ejpam-6082	308	4	(	(	PUNCT
ejpam-6082	308	5	e∗φ	e∗φ	PROPN
ejpam-6082	308	6	(	(	PUNCT
ejpam-6082	308	7	e	e	NOUN
ejpam-6082	308	8	e∗	e∗	PROPN
ejpam-6082	308	9	)	)	PUNCT
ejpam-6082	308	10	)	)	PUNCT
ejpam-6082	309	1	≤	≤	NUM
ejpam-6082	310	1	∫	∫	PROPN
ejpam-6082	310	2	ω	ω	PROPN
ejpam-6082	310	3	[	[	PUNCT
ejpam-6082	310	4	d3∆e	d3∆e	NOUN
ejpam-6082	310	5	−	−	PROPN
ejpam-6082	311	1	d3e	d3e	PROPN
ejpam-6082	311	2	∗∆e	∗∆e	SYM
ejpam-6082	311	3	e	e	X
ejpam-6082	311	4	+	+	NUM
ejpam-6082	311	5	source	source	NOUN
ejpam-6082	311	6	terms	term	NOUN
ejpam-6082	311	7	]	]	PUNCT
ejpam-6082	311	8	dx	dx	PROPN
ejpam-6082	311	9	.	.	PUNCT
ejpam-6082	312	1	using	use	VERB
ejpam-6082	312	2	the	the	DET
ejpam-6082	312	3	equation	equation	NOUN
ejpam-6082	312	4	for	for	ADP
ejpam-6082	312	5	np	np	NOUN
ejpam-6082	312	6	:	:	PUNCT
ejpam-6082	312	7	c	c	NOUN
ejpam-6082	312	8	0	0	PUNCT
ejpam-6082	313	1	d	d	NOUN
ejpam-6082	313	2	α	α	NOUN
ejpam-6082	313	3	t	t	NOUN
ejpam-6082	313	4	np	np	INTJ
ejpam-6082	313	5	=	=	SYM
ejpam-6082	313	6	α1e	α1e	PROPN
ejpam-6082	313	7	−	−	PROPN
ejpam-6082	313	8	(	(	PUNCT
ejpam-6082	313	9	σ	σ	PROPN
ejpam-6082	313	10	+	+	CCONJ
ejpam-6082	313	11	µ+	µ+	X
ejpam-6082	313	12	ω1)np	ω1)np	PROPN
ejpam-6082	313	13	−	−	PROPN
ejpam-6082	313	14	d4∆np	d4∆np	PROPN
ejpam-6082	313	15	,	,	PUNCT
ejpam-6082	313	16	we	we	PRON
ejpam-6082	313	17	compute	compute	VERB
ejpam-6082	313	18	:	:	PUNCT
ejpam-6082	313	19	c	c	NOUN
ejpam-6082	313	20	0	0	PUNCT
ejpam-6082	314	1	d	d	NOUN
ejpam-6082	314	2	α	α	PROPN
ejpam-6082	314	3	t	t	PROPN
ejpam-6082	314	4	(	(	PUNCT
ejpam-6082	314	5	n∗	n∗	PROPN
ejpam-6082	314	6	pφ	pφ	X
ejpam-6082	314	7	(	(	PUNCT
ejpam-6082	314	8	np	np	INTJ
ejpam-6082	314	9	n∗	n∗	PROPN
ejpam-6082	314	10	p	p	NOUN
ejpam-6082	314	11	)	)	PUNCT
ejpam-6082	314	12	)	)	PUNCT
ejpam-6082	315	1	=	=	PUNCT
ejpam-6082	315	2	n∗	n∗	VERB
ejpam-6082	315	3	p	p	X
ejpam-6082	315	4	(	(	PUNCT
ejpam-6082	315	5	1−	1−	NUM
ejpam-6082	315	6	n∗	n∗	PROPN
ejpam-6082	315	7	p	p	PROPN
ejpam-6082	315	8	np	np	INTJ
ejpam-6082	315	9	)	)	PUNCT
ejpam-6082	316	1	[	[	X
ejpam-6082	316	2	α1e	α1e	X
ejpam-6082	316	3	−	−	PROPN
ejpam-6082	316	4	(	(	PUNCT
ejpam-6082	316	5	σ	σ	PROPN
ejpam-6082	316	6	+	+	CCONJ
ejpam-6082	316	7	µ+	µ+	X
ejpam-6082	316	8	ω1)np	ω1)np	PROPN
ejpam-6082	316	9	−	−	PROPN
ejpam-6082	316	10	d4∆np	d4∆np	PROPN
ejpam-6082	316	11	]	]	PUNCT
ejpam-6082	316	12	.	.	PUNCT
ejpam-6082	317	1	simplifying	simplify	VERB
ejpam-6082	317	2	:	:	PUNCT
ejpam-6082	318	1	c	c	NOUN
ejpam-6082	318	2	0	0	PUNCT
ejpam-6082	319	1	d	d	NOUN
ejpam-6082	319	2	α	α	PROPN
ejpam-6082	319	3	t	t	PROPN
ejpam-6082	319	4	(	(	PUNCT
ejpam-6082	319	5	n∗	n∗	PROPN
ejpam-6082	319	6	pφ	pφ	X
ejpam-6082	319	7	(	(	PUNCT
ejpam-6082	319	8	np	np	INTJ
ejpam-6082	319	9	n∗	n∗	PROPN
ejpam-6082	319	10	p	p	PROPN
ejpam-6082	319	11	)	)	PUNCT
ejpam-6082	319	12	)	)	PUNCT
ejpam-6082	320	1	≤	≤	NUM
ejpam-6082	320	2	∫	∫	PROPN
ejpam-6082	320	3	ω	ω	PROPN
ejpam-6082	320	4	[	[	PUNCT
ejpam-6082	320	5	d4∆np	d4∆np	PROPN
ejpam-6082	320	6	−	−	PROPN
ejpam-6082	320	7	d4n	d4n	PROPN
ejpam-6082	320	8	∗	∗	VERB
ejpam-6082	320	9	p	p	NOUN
ejpam-6082	320	10	∆np	∆np	PROPN
ejpam-6082	320	11	np	np	INTJ
ejpam-6082	320	12	+	+	NUM
ejpam-6082	320	13	source	source	NOUN
ejpam-6082	320	14	terms	term	NOUN
ejpam-6082	320	15	]	]	PUNCT
ejpam-6082	320	16	dx	dx	PROPN
ejpam-6082	320	17	.	.	PUNCT
ejpam-6082	321	1	adding	add	VERB
ejpam-6082	321	2	the	the	DET
ejpam-6082	321	3	contributions	contribution	NOUN
ejpam-6082	321	4	of	of	ADP
ejpam-6082	321	5	all	all	DET
ejpam-6082	321	6	terms	term	NOUN
ejpam-6082	321	7	:	:	PUNCT
ejpam-6082	321	8	c	c	NOUN
ejpam-6082	321	9	0	0	PUNCT
ejpam-6082	322	1	d	d	NOUN
ejpam-6082	322	2	α	α	X
ejpam-6082	322	3	t	t	PROPN
ejpam-6082	323	1	v2(t	v2(t	PROPN
ejpam-6082	323	2	,	,	PUNCT
ejpam-6082	323	3	x	x	NOUN
ejpam-6082	323	4	)	)	PUNCT
ejpam-6082	323	5	≤	≤	NOUN
ejpam-6082	323	6	−	−	PROPN
ejpam-6082	324	1	∫	∫	PROPN
ejpam-6082	324	2	ω	ω	PROPN
ejpam-6082	324	3	[	[	PUNCT
ejpam-6082	324	4	d1s	d1s	NOUN
ejpam-6082	324	5	∗	∗	NOUN
ejpam-6082	324	6	|∇s|2	|∇s|2	NUM
ejpam-6082	324	7	s2	s2	PROPN
ejpam-6082	324	8	+	+	CCONJ
ejpam-6082	324	9	d3e	d3e	PROPN
ejpam-6082	324	10	∗	∗	NOUN
ejpam-6082	324	11	|∇e|2	|∇e|2	X
ejpam-6082	324	12	e2	e2	PROPN
ejpam-6082	324	13	+	+	CCONJ
ejpam-6082	324	14	d4n	d4n	PROPN
ejpam-6082	324	15	∗	∗	NOUN
ejpam-6082	324	16	p	p	NOUN
ejpam-6082	324	17	|∇np|2	|∇np|2	NOUN
ejpam-6082	324	18	n2	n2	NOUN
ejpam-6082	324	19	p	p	PROPN
ejpam-6082	324	20	+	+	X
ejpam-6082	324	21	.	.	PUNCT
ejpam-6082	324	22	.	.	PUNCT
ejpam-6082	324	23	.	.	PUNCT
ejpam-6082	324	24	]	]	PUNCT
ejpam-6082	325	1	dx	dx	PROPN
ejpam-6082	325	2	.	.	PUNCT
ejpam-6082	326	1	the	the	DET
ejpam-6082	326	2	terms	term	NOUN
ejpam-6082	326	3	involving	involve	VERB
ejpam-6082	326	4	(	(	PUNCT
ejpam-6082	326	5	1−x∗/x	1−x∗/x	NOUN
ejpam-6082	326	6	)	)	PUNCT
ejpam-6082	326	7	simplify	simplify	NOUN
ejpam-6082	326	8	using	use	VERB
ejpam-6082	326	9	equilibrium	equilibrium	NOUN
ejpam-6082	326	10	relations:∫	relations:∫	PROPN
ejpam-6082	326	11	ω	ω	PROPN
ejpam-6082	327	1	[	[	X
ejpam-6082	327	2	λs∗	λs∗	X
ejpam-6082	327	3	−	−	PROPN
ejpam-6082	327	4	ρ1r	ρ1r	NUM
ejpam-6082	327	5	∗	∗	NOUN
ejpam-6082	327	6	+	+	X
ejpam-6082	327	7	.	.	PUNCT
ejpam-6082	327	8	.	.	PUNCT
ejpam-6082	327	9	.	.	PUNCT
ejpam-6082	328	1	]	]	PUNCT
ejpam-6082	329	1	dx	dx	PROPN
ejpam-6082	329	2	,	,	PUNCT
ejpam-6082	329	3	which	which	PRON
ejpam-6082	329	4	are	be	AUX
ejpam-6082	329	5	all	all	PRON
ejpam-6082	329	6	non	non	ADJ
ejpam-6082	329	7	-	-	ADJ
ejpam-6082	329	8	positive	positive	ADJ
ejpam-6082	329	9	due	due	ADP
ejpam-6082	329	10	to	to	ADP
ejpam-6082	329	11	the	the	DET
ejpam-6082	329	12	equilibrium	equilibrium	NOUN
ejpam-6082	329	13	relations	relation	NOUN
ejpam-6082	329	14	and	and	CCONJ
ejpam-6082	329	15	the	the	DET
ejpam-6082	329	16	properties	property	NOUN
ejpam-6082	329	17	of	of	ADP
ejpam-6082	329	18	φ(z	φ(z	PROPN
ejpam-6082	329	19	)	)	PUNCT
ejpam-6082	329	20	.	.	PUNCT
ejpam-6082	330	1	apply	apply	VERB
ejpam-6082	330	2	fractional	fractional	PROPN
ejpam-6082	330	3	lasalle	lasalle	PROPN
ejpam-6082	330	4	invariance	invariance	PROPN
ejpam-6082	330	5	principle	principle	NOUN
ejpam-6082	330	6	since	since	SCONJ
ejpam-6082	330	7	c	c	PROPN
ejpam-6082	330	8	0	0	NUM
ejpam-6082	331	1	d	d	NOUN
ejpam-6082	331	2	α	α	X
ejpam-6082	331	3	t	t	PROPN
ejpam-6082	331	4	v2(t	v2(t	PROPN
ejpam-6082	331	5	,	,	PUNCT
ejpam-6082	331	6	x	x	NOUN
ejpam-6082	331	7	)	)	PUNCT
ejpam-6082	331	8	≤	≤	NUM
ejpam-6082	331	9	0	0	NUM
ejpam-6082	331	10	and	and	CCONJ
ejpam-6082	331	11	equality	equality	NOUN
ejpam-6082	331	12	holds	hold	VERB
ejpam-6082	331	13	only	only	ADV
ejpam-6082	331	14	when	when	SCONJ
ejpam-6082	331	15	s	s	NOUN
ejpam-6082	331	16	=	=	SYM
ejpam-6082	331	17	s∗	s∗	PROPN
ejpam-6082	331	18	,	,	PUNCT
ejpam-6082	331	19	e	e	PROPN
ejpam-6082	331	20	=	=	SYM
ejpam-6082	331	21	e∗	e∗	PROPN
ejpam-6082	331	22	,	,	PUNCT
ejpam-6082	331	23	.	.	PUNCT
ejpam-6082	331	24	.	.	PUNCT
ejpam-6082	332	1	.	.	PUNCT
ejpam-6082	332	2	,	,	PUNCT
ejpam-6082	332	3	the	the	DET
ejpam-6082	332	4	largest	large	ADJ
ejpam-6082	332	5	invariant	invariant	ADJ
ejpam-6082	332	6	set	set	NOUN
ejpam-6082	332	7	is	be	AUX
ejpam-6082	332	8	{	{	PUNCT
ejpam-6082	332	9	ξ∗	ξ∗	ADJ
ejpam-6082	332	10	}	}	PUNCT
ejpam-6082	332	11	.	.	PUNCT
ejpam-6082	333	1	by	by	ADP
ejpam-6082	333	2	the	the	DET
ejpam-6082	333	3	fractional	fractional	PROPN
ejpam-6082	333	4	lasalle	lasalle	PROPN
ejpam-6082	333	5	invariance	invariance	PROPN
ejpam-6082	333	6	principle	principle	NOUN
ejpam-6082	333	7	,	,	PUNCT
ejpam-6082	333	8	ξ∗	ξ∗	PROPN
ejpam-6082	333	9	is	be	AUX
ejpam-6082	333	10	gas	gas	NOUN
ejpam-6082	333	11	when	when	SCONJ
ejpam-6082	333	12	r0	r0	NOUN
ejpam-6082	333	13	>	>	X
ejpam-6082	333	14	1	1	NUM
ejpam-6082	333	15	.	.	X
ejpam-6082	333	16	7	7	X
ejpam-6082	333	17	.	.	X
ejpam-6082	333	18	global	global	ADJ
ejpam-6082	333	19	stability	stability	NOUN
ejpam-6082	333	20	of	of	ADP
ejpam-6082	333	21	the	the	DET
ejpam-6082	333	22	disease	disease	NOUN
ejpam-6082	333	23	-	-	PUNCT
ejpam-6082	333	24	free	free	ADJ
ejpam-6082	333	25	equilibrium	equilibrium	NOUN
ejpam-6082	333	26	to	to	PART
ejpam-6082	333	27	analyze	analyze	VERB
ejpam-6082	333	28	the	the	DET
ejpam-6082	333	29	global	global	ADJ
ejpam-6082	333	30	stability	stability	NOUN
ejpam-6082	333	31	of	of	ADP
ejpam-6082	333	32	the	the	DET
ejpam-6082	333	33	disease	disease	NOUN
ejpam-6082	333	34	-	-	PUNCT
ejpam-6082	333	35	free	free	ADJ
ejpam-6082	333	36	equilibrium	equilibrium	NOUN
ejpam-6082	333	37	(	(	PUNCT
ejpam-6082	333	38	dfe	dfe	PROPN
ejpam-6082	333	39	)	)	PUNCT
ejpam-6082	333	40	of	of	ADP
ejpam-6082	333	41	the	the	DET
ejpam-6082	333	42	model	model	NOUN
ejpam-6082	333	43	at	at	ADP
ejpam-6082	333	44	ε0	ε0	PROPN
ejpam-6082	333	45	,	,	PUNCT
ejpam-6082	333	46	we	we	PRON
ejpam-6082	333	47	proceed	proceed	VERB
ejpam-6082	333	48	with	with	ADP
ejpam-6082	333	49	the	the	DET
ejpam-6082	333	50	following	follow	VERB
ejpam-6082	333	51	steps	step	NOUN
ejpam-6082	333	52	.	.	PUNCT
ejpam-6082	334	1	the	the	DET
ejpam-6082	334	2	disease	disease	NOUN
ejpam-6082	334	3	-	-	PUNCT
ejpam-6082	334	4	free	free	ADJ
ejpam-6082	334	5	equilibrium	equilibrium	NOUN
ejpam-6082	334	6	of	of	ADP
ejpam-6082	334	7	the	the	DET
ejpam-6082	334	8	model	model	NOUN
ejpam-6082	334	9	is	be	AUX
ejpam-6082	334	10	given	give	VERB
ejpam-6082	334	11	by	by	ADP
ejpam-6082	334	12	:	:	PUNCT
ejpam-6082	334	13	ε0	ε0	PROPN
ejpam-6082	334	14	=	=	SYM
ejpam-6082	334	15	(	(	PUNCT
ejpam-6082	334	16	s∗	s∗	PROPN
ejpam-6082	334	17	,	,	PUNCT
ejpam-6082	334	18	v	v	NOUN
ejpam-6082	334	19	∗	∗	NOUN
ejpam-6082	334	20	,	,	PUNCT
ejpam-6082	334	21	0	0	NUM
ejpam-6082	334	22	,	,	PUNCT
ejpam-6082	334	23	0	0	NUM
ejpam-6082	334	24	,	,	PUNCT
ejpam-6082	334	25	0	0	NUM
ejpam-6082	334	26	,	,	PUNCT
ejpam-6082	334	27	r∗	r∗	PROPN
ejpam-6082	334	28	,	,	PUNCT
ejpam-6082	334	29	a∗	a∗	NOUN
ejpam-6082	334	30	)	)	PUNCT
ejpam-6082	334	31	,	,	PUNCT
ejpam-6082	334	32	where	where	SCONJ
ejpam-6082	334	33	:	:	PUNCT
ejpam-6082	334	34	s∗	s∗	PROPN
ejpam-6082	334	35	=	=	SYM
ejpam-6082	334	36	λk5k6	λk5k6	PROPN
ejpam-6082	334	37	ξ	ξ	PROPN
ejpam-6082	334	38	,	,	PUNCT
ejpam-6082	334	39	v	v	NOUN
ejpam-6082	334	40	∗	∗	NOUN
ejpam-6082	334	41	=	=	SYM
ejpam-6082	334	42	δλk6	δλk6	PROPN
ejpam-6082	334	43	ξ	ξ	PROPN
ejpam-6082	334	44	,	,	PUNCT
ejpam-6082	334	45	r∗	r∗	PROPN
ejpam-6082	334	46	=	=	PUNCT
ejpam-6082	334	47	σγλ	σγλ	NOUN
ejpam-6082	334	48	ξ	ξ	PROPN
ejpam-6082	334	49	,	,	PUNCT
ejpam-6082	334	50	a∗	a∗	PROPN
ejpam-6082	334	51	=	=	SYM
ejpam-6082	334	52	ρσγλ	ρσγλ	NOUN
ejpam-6082	334	53	k6ξ	k6ξ	PROPN
ejpam-6082	334	54	,	,	PUNCT
ejpam-6082	334	55	and	and	CCONJ
ejpam-6082	334	56	ξ	ξ	X
ejpam-6082	334	57	=	=	SYM
ejpam-6082	334	58	k1k5k7	k1k5k7	PROPN
ejpam-6082	334	59	−	−	PROPN
ejpam-6082	334	60	δγρ1	δγρ1	PROPN
ejpam-6082	334	61	.	.	PUNCT
ejpam-6082	335	1	k.	k.	PROPN
ejpam-6082	335	2	guedri	guedri	PROPN
ejpam-6082	335	3	et	et	PROPN
ejpam-6082	335	4	al	al	PROPN
ejpam-6082	335	5	.	.	PUNCT
ejpam-6082	335	6	/	/	SYM
ejpam-6082	335	7	eur	eur	PROPN
ejpam-6082	335	8	.	.	PUNCT
ejpam-6082	336	1	j.	j.	PROPN
ejpam-6082	336	2	pure	pure	PROPN
ejpam-6082	336	3	appl	appl	PROPN
ejpam-6082	336	4	.	.	PROPN
ejpam-6082	336	5	math	math	PROPN
ejpam-6082	336	6	,	,	PUNCT
ejpam-6082	336	7	18	18	NUM
ejpam-6082	336	8	(	(	PUNCT
ejpam-6082	336	9	2	2	NUM
ejpam-6082	336	10	)	)	PUNCT
ejpam-6082	336	11	(	(	PUNCT
ejpam-6082	336	12	2025	2025	NUM
ejpam-6082	336	13	)	)	PUNCT
ejpam-6082	336	14	,	,	PUNCT
ejpam-6082	336	15	6082	6082	NUM
ejpam-6082	336	16	16	16	NUM
ejpam-6082	336	17	of	of	ADP
ejpam-6082	336	18	39	39	NUM
ejpam-6082	336	19	theorem	theorem	NOUN
ejpam-6082	336	20	5	5	NUM
ejpam-6082	336	21	.	.	PUNCT
ejpam-6082	337	1	the	the	DET
ejpam-6082	337	2	disease	disease	NOUN
ejpam-6082	337	3	-	-	PUNCT
ejpam-6082	337	4	free	free	ADJ
ejpam-6082	337	5	equilibrium	equilibrium	NOUN
ejpam-6082	337	6	ε0	ε0	NOUN
ejpam-6082	337	7	of	of	ADP
ejpam-6082	337	8	the	the	DET
ejpam-6082	337	9	system	system	NOUN
ejpam-6082	337	10	is	be	AUX
ejpam-6082	337	11	globally	globally	ADV
ejpam-6082	337	12	asymptotically	asymptotically	ADV
ejpam-6082	337	13	stable	stable	ADJ
ejpam-6082	337	14	if	if	SCONJ
ejpam-6082	337	15	r0	r0	NOUN
ejpam-6082	337	16	<	<	X
ejpam-6082	337	17	1	1	NUM
ejpam-6082	337	18	.	.	PUNCT
ejpam-6082	337	19	proof	proof	NOUN
ejpam-6082	337	20	.	.	PUNCT
ejpam-6082	338	1	we	we	PRON
ejpam-6082	338	2	define	define	VERB
ejpam-6082	338	3	the	the	DET
ejpam-6082	338	4	lyapunov	lyapunov	ADJ
ejpam-6082	338	5	function	function	NOUN
ejpam-6082	338	6	:	:	PUNCT
ejpam-6082	338	7	v(t	v(t	NOUN
ejpam-6082	338	8	,	,	PUNCT
ejpam-6082	338	9	x	x	NOUN
ejpam-6082	338	10	)	)	PUNCT
ejpam-6082	338	11	=	=	SYM
ejpam-6082	338	12	∫	∫	PROPN
ejpam-6082	338	13	ω	ω	PROPN
ejpam-6082	338	14	[	[	PUNCT
ejpam-6082	338	15	s∗φ	s∗φ	X
ejpam-6082	338	16	(	(	PUNCT
ejpam-6082	338	17	s	s	X
ejpam-6082	338	18	s∗	s∗	PROPN
ejpam-6082	338	19	)	)	PUNCT
ejpam-6082	339	1	+	+	CCONJ
ejpam-6082	339	2	e∗φ	e∗φ	PROPN
ejpam-6082	339	3	(	(	PUNCT
ejpam-6082	339	4	e	e	NOUN
ejpam-6082	339	5	e∗	e∗	PROPN
ejpam-6082	339	6	)	)	PUNCT
ejpam-6082	340	1	+	+	NUM
ejpam-6082	340	2	n∗	n∗	NOUN
ejpam-6082	340	3	pφ	pφ	VERB
ejpam-6082	340	4	(	(	PUNCT
ejpam-6082	340	5	np	np	INTJ
ejpam-6082	340	6	n∗	n∗	PROPN
ejpam-6082	340	7	p	p	PROPN
ejpam-6082	340	8	)	)	PUNCT
ejpam-6082	341	1	+	+	CCONJ
ejpam-6082	341	2	p	p	VERB
ejpam-6082	341	3	∗φ	∗φ	NOUN
ejpam-6082	341	4	(	(	PUNCT
ejpam-6082	341	5	p	p	X
ejpam-6082	341	6	p	p	NOUN
ejpam-6082	341	7	∗	∗	NOUN
ejpam-6082	341	8	)	)	PUNCT
ejpam-6082	341	9	]	]	PUNCT
ejpam-6082	342	1	dx	dx	PROPN
ejpam-6082	342	2	,	,	PUNCT
ejpam-6082	342	3	where	where	SCONJ
ejpam-6082	342	4	φ(z	φ(z	NOUN
ejpam-6082	342	5	)	)	PUNCT
ejpam-6082	342	6	=	=	SYM
ejpam-6082	342	7	z	z	NOUN
ejpam-6082	342	8	−	−	PROPN
ejpam-6082	342	9	1−	1−	NUM
ejpam-6082	342	10	ln(z	ln(z	NOUN
ejpam-6082	342	11	)	)	PUNCT
ejpam-6082	342	12	,	,	PUNCT
ejpam-6082	342	13	which	which	PRON
ejpam-6082	342	14	satisfies	satisfy	VERB
ejpam-6082	342	15	φ(z	φ(z	PROPN
ejpam-6082	342	16	)	)	PUNCT
ejpam-6082	342	17	≥	≥	NOUN
ejpam-6082	342	18	0	0	NUM
ejpam-6082	342	19	and	and	CCONJ
ejpam-6082	342	20	is	be	AUX
ejpam-6082	342	21	equal	equal	ADJ
ejpam-6082	342	22	to	to	ADP
ejpam-6082	342	23	0	0	NUM
ejpam-6082	342	24	only	only	ADV
ejpam-6082	342	25	if	if	SCONJ
ejpam-6082	342	26	z	z	NOUN
ejpam-6082	342	27	=	=	NOUN
ejpam-6082	342	28	1	1	X
ejpam-6082	342	29	.	.	PUNCT
ejpam-6082	343	1	here	here	ADV
ejpam-6082	343	2	,	,	PUNCT
ejpam-6082	343	3	e∗	e∗	PROPN
ejpam-6082	343	4	=	=	PUNCT
ejpam-6082	343	5	n∗	n∗	VERB
ejpam-6082	343	6	p	p	NOUN
ejpam-6082	343	7	=	=	PUNCT
ejpam-6082	343	8	p	p	NOUN
ejpam-6082	343	9	∗	∗	NOUN
ejpam-6082	343	10	=	=	SYM
ejpam-6082	343	11	0	0	NUM
ejpam-6082	344	1	at	at	ADP
ejpam-6082	344	2	the	the	DET
ejpam-6082	344	3	dfe	dfe	PROPN
ejpam-6082	344	4	(	(	PUNCT
ejpam-6082	344	5	ε0	ε0	PROPN
ejpam-6082	344	6	)	)	PUNCT
ejpam-6082	344	7	.	.	PUNCT
ejpam-6082	345	1	time	time	NOUN
ejpam-6082	345	2	derivative	derivative	NOUN
ejpam-6082	345	3	of	of	ADP
ejpam-6082	345	4	v	v	NOUN
ejpam-6082	345	5	,	,	PUNCT
ejpam-6082	345	6	using	use	VERB
ejpam-6082	345	7	the	the	DET
ejpam-6082	345	8	system	system	NOUN
ejpam-6082	345	9	of	of	ADP
ejpam-6082	345	10	equations	equation	NOUN
ejpam-6082	345	11	,	,	PUNCT
ejpam-6082	345	12	compute	compute	VERB
ejpam-6082	345	13	the	the	DET
ejpam-6082	345	14	fractional	fractional	ADJ
ejpam-6082	345	15	derivative	derivative	NOUN
ejpam-6082	345	16	of	of	ADP
ejpam-6082	345	17	v	v	NOUN
ejpam-6082	345	18	:	:	PUNCT
ejpam-6082	345	19	c	c	NOUN
ejpam-6082	345	20	0	0	PUNCT
ejpam-6082	346	1	d	d	NOUN
ejpam-6082	346	2	α	α	PROPN
ejpam-6082	346	3	t	t	NOUN
ejpam-6082	346	4	v(t	v(t	PROPN
ejpam-6082	346	5	,	,	PUNCT
ejpam-6082	346	6	x	x	X
ejpam-6082	346	7	)	)	PUNCT
ejpam-6082	346	8	=	=	SYM
ejpam-6082	347	1	∫	∫	PROPN
ejpam-6082	347	2	ω	ω	PROPN
ejpam-6082	347	3	[	[	PUNCT
ejpam-6082	347	4	c	c	NOUN
ejpam-6082	347	5	0	0	PUNCT
ejpam-6082	348	1	d	d	NOUN
ejpam-6082	348	2	α	α	PROPN
ejpam-6082	348	3	t	t	PROPN
ejpam-6082	348	4	(	(	PUNCT
ejpam-6082	348	5	s∗φ	s∗φ	X
ejpam-6082	348	6	(	(	PUNCT
ejpam-6082	348	7	s	s	VERB
ejpam-6082	348	8	s∗	s∗	PROPN
ejpam-6082	348	9	)	)	PUNCT
ejpam-6082	348	10	)	)	PUNCT
ejpam-6082	349	1	+	+	PUNCT
ejpam-6082	349	2	c	c	NOUN
ejpam-6082	349	3	0	0	PUNCT
ejpam-6082	349	4	d	d	NOUN
ejpam-6082	349	5	α	α	PROPN
ejpam-6082	349	6	t	t	PROPN
ejpam-6082	349	7	(	(	PUNCT
ejpam-6082	349	8	e∗φ	e∗φ	PROPN
ejpam-6082	349	9	(	(	PUNCT
ejpam-6082	349	10	e	e	NOUN
ejpam-6082	349	11	e∗	e∗	PROPN
ejpam-6082	349	12	)	)	PUNCT
ejpam-6082	349	13	)	)	PUNCT
ejpam-6082	350	1	+	+	PUNCT
ejpam-6082	350	2	c	c	NOUN
ejpam-6082	350	3	0	0	PUNCT
ejpam-6082	351	1	d	d	NOUN
ejpam-6082	351	2	α	α	PROPN
ejpam-6082	351	3	t	t	PROPN
ejpam-6082	351	4	(	(	PUNCT
ejpam-6082	351	5	n∗	n∗	PROPN
ejpam-6082	351	6	pφ	pφ	X
ejpam-6082	351	7	(	(	PUNCT
ejpam-6082	351	8	np	np	INTJ
ejpam-6082	351	9	n∗	n∗	PROPN
ejpam-6082	351	10	p	p	PROPN
ejpam-6082	351	11	)	)	PUNCT
ejpam-6082	351	12	)	)	PUNCT
ejpam-6082	352	1	+	+	ADP
ejpam-6082	352	2	c	c	NOUN
ejpam-6082	352	3	0	0	PUNCT
ejpam-6082	353	1	d	d	NOUN
ejpam-6082	353	2	α	α	NOUN
ejpam-6082	353	3	t	t	NOUN
ejpam-6082	353	4	(	(	PUNCT
ejpam-6082	353	5	p	p	NOUN
ejpam-6082	353	6	∗φ	∗φ	PROPN
ejpam-6082	353	7	(	(	PUNCT
ejpam-6082	353	8	p	p	X
ejpam-6082	353	9	p	p	NOUN
ejpam-6082	353	10	∗	∗	NOUN
ejpam-6082	353	11	)	)	PUNCT
ejpam-6082	353	12	)	)	PUNCT
ejpam-6082	353	13	]	]	PUNCT
ejpam-6082	354	1	dx	dx	PROPN
ejpam-6082	354	2	.	.	PROPN
ejpam-6082	354	3	evaluate	evaluate	VERB
ejpam-6082	354	4	each	each	DET
ejpam-6082	354	5	compartment	compartment	NOUN
ejpam-6082	354	6	.	.	PUNCT
ejpam-6082	355	1	the	the	DET
ejpam-6082	355	2	equation	equation	NOUN
ejpam-6082	355	3	for	for	ADP
ejpam-6082	355	4	s	s	NOUN
ejpam-6082	355	5	is	be	AUX
ejpam-6082	355	6	:	:	PUNCT
ejpam-6082	355	7	c	c	NOUN
ejpam-6082	355	8	0	0	PUNCT
ejpam-6082	356	1	d	d	NOUN
ejpam-6082	356	2	α	α	NOUN
ejpam-6082	356	3	t	t	NOUN
ejpam-6082	356	4	s	s	PART
ejpam-6082	356	5	=	=	PUNCT
ejpam-6082	356	6	λ+	λ+	PUNCT
ejpam-6082	356	7	ρ1r−	ρ1r−	PRON
ejpam-6082	356	8	(	(	PUNCT
ejpam-6082	356	9	λ+	λ+	PUNCT
ejpam-6082	356	10	δ	δ	NOUN
ejpam-6082	356	11	+	+	NOUN
ejpam-6082	356	12	µ)s	µ)s	NOUN
ejpam-6082	356	13	−	−	NOUN
ejpam-6082	356	14	d1∆s	d1∆s	PROPN
ejpam-6082	356	15	.	.	PUNCT
ejpam-6082	356	16	substitute	substitute	PROPN
ejpam-6082	356	17	into	into	ADP
ejpam-6082	356	18	the	the	DET
ejpam-6082	356	19	lyapunov	lyapunov	ADJ
ejpam-6082	356	20	derivative	derivative	NOUN
ejpam-6082	356	21	:	:	PUNCT
ejpam-6082	357	1	c	c	NOUN
ejpam-6082	357	2	0	0	PUNCT
ejpam-6082	358	1	d	d	NOUN
ejpam-6082	358	2	α	α	PROPN
ejpam-6082	358	3	t	t	PROPN
ejpam-6082	358	4	(	(	PUNCT
ejpam-6082	358	5	s∗φ	s∗φ	X
ejpam-6082	358	6	(	(	PUNCT
ejpam-6082	358	7	s	s	VERB
ejpam-6082	358	8	s∗	s∗	PROPN
ejpam-6082	358	9	)	)	PUNCT
ejpam-6082	358	10	)	)	PUNCT
ejpam-6082	359	1	=	=	PRON
ejpam-6082	359	2	s∗	s∗	PROPN
ejpam-6082	359	3	(	(	PUNCT
ejpam-6082	359	4	1−	1−	NUM
ejpam-6082	359	5	s∗	s∗	PROPN
ejpam-6082	359	6	s	s	PART
ejpam-6082	359	7	)	)	PUNCT
ejpam-6082	359	8	[	[	PUNCT
ejpam-6082	359	9	λ	λ	X
ejpam-6082	359	10	+	+	CCONJ
ejpam-6082	359	11	ρ1r−	ρ1r−	PRON
ejpam-6082	359	12	(	(	PUNCT
ejpam-6082	359	13	λ+	λ+	PUNCT
ejpam-6082	359	14	δ	δ	NOUN
ejpam-6082	359	15	+	+	NOUN
ejpam-6082	359	16	µ)s	µ)s	NOUN
ejpam-6082	359	17	−	−	NOUN
ejpam-6082	359	18	d1∆s	d1∆s	NOUN
ejpam-6082	359	19	]	]	PUNCT
ejpam-6082	359	20	.	.	PUNCT
ejpam-6082	360	1	at	at	ADP
ejpam-6082	360	2	the	the	DET
ejpam-6082	360	3	dfe	dfe	PROPN
ejpam-6082	360	4	(	(	PUNCT
ejpam-6082	360	5	s	s	NOUN
ejpam-6082	360	6	=	=	SYM
ejpam-6082	360	7	s∗	s∗	PROPN
ejpam-6082	360	8	):	):	PUNCT
ejpam-6082	360	9	c	c	NOUN
ejpam-6082	360	10	0	0	PUNCT
ejpam-6082	361	1	d	d	NOUN
ejpam-6082	361	2	α	α	PROPN
ejpam-6082	361	3	t	t	PROPN
ejpam-6082	361	4	(	(	PUNCT
ejpam-6082	361	5	s∗φ	s∗φ	X
ejpam-6082	361	6	(	(	PUNCT
ejpam-6082	361	7	s	s	VERB
ejpam-6082	361	8	s∗	s∗	PROPN
ejpam-6082	361	9	)	)	PUNCT
ejpam-6082	361	10	)	)	PUNCT
ejpam-6082	361	11	≤	≤	PUNCT
ejpam-6082	362	1	−d1s∗	−d1s∗	PROPN
ejpam-6082	362	2	|∇s|2	|∇s|2	NUM
ejpam-6082	362	3	s2	s2	NOUN
ejpam-6082	362	4	.	.	PUNCT
ejpam-6082	363	1	the	the	DET
ejpam-6082	363	2	equation	equation	NOUN
ejpam-6082	363	3	for	for	ADP
ejpam-6082	363	4	e	e	PROPN
ejpam-6082	363	5	is	be	AUX
ejpam-6082	363	6	:	:	PUNCT
ejpam-6082	363	7	c	c	NOUN
ejpam-6082	363	8	0	0	PUNCT
ejpam-6082	364	1	d	d	NOUN
ejpam-6082	364	2	α	α	NOUN
ejpam-6082	364	3	t	t	X
ejpam-6082	364	4	e	e	X
ejpam-6082	364	5	=	=	PUNCT
ejpam-6082	364	6	λs	λs	PROPN
ejpam-6082	364	7	+	+	CCONJ
ejpam-6082	364	8	(	(	PUNCT
ejpam-6082	364	9	1−	1−	NUM
ejpam-6082	364	10	δ)λv	δ)λv	PROPN
ejpam-6082	364	11	−	−	PROPN
ejpam-6082	364	12	(	(	PUNCT
ejpam-6082	364	13	α1	α1	PROPN
ejpam-6082	364	14	+	+	CCONJ
ejpam-6082	364	15	α2	α2	ADJ
ejpam-6082	364	16	+	+	CCONJ
ejpam-6082	364	17	ω	ω	NUM
ejpam-6082	364	18	+	+	CCONJ
ejpam-6082	364	19	µ)e	µ)e	NOUN
ejpam-6082	364	20	−	−	PROPN
ejpam-6082	364	21	d3∆e	d3∆e	PROPN
ejpam-6082	364	22	.	.	PUNCT
ejpam-6082	364	23	substitute	substitute	PROPN
ejpam-6082	364	24	into	into	ADP
ejpam-6082	364	25	the	the	DET
ejpam-6082	364	26	lyapunov	lyapunov	ADJ
ejpam-6082	364	27	derivative	derivative	NOUN
ejpam-6082	364	28	:	:	PUNCT
ejpam-6082	365	1	c	c	NOUN
ejpam-6082	365	2	0	0	PUNCT
ejpam-6082	366	1	d	d	NOUN
ejpam-6082	366	2	α	α	PROPN
ejpam-6082	366	3	t	t	PROPN
ejpam-6082	366	4	(	(	PUNCT
ejpam-6082	366	5	e∗φ	e∗φ	PROPN
ejpam-6082	366	6	(	(	PUNCT
ejpam-6082	366	7	e	e	NOUN
ejpam-6082	366	8	e∗	e∗	PROPN
ejpam-6082	366	9	)	)	PUNCT
ejpam-6082	366	10	)	)	PUNCT
ejpam-6082	367	1	=	=	SYM
ejpam-6082	367	2	e∗	e∗	NOUN
ejpam-6082	367	3	(	(	PUNCT
ejpam-6082	367	4	1−	1−	NUM
ejpam-6082	367	5	e∗	e∗	PROPN
ejpam-6082	367	6	e	e	PROPN
ejpam-6082	367	7	)	)	PUNCT
ejpam-6082	367	8	[	[	PUNCT
ejpam-6082	367	9	λs	λs	X
ejpam-6082	367	10	+	+	CCONJ
ejpam-6082	367	11	(	(	PUNCT
ejpam-6082	367	12	1−	1−	NUM
ejpam-6082	367	13	δ)λv	δ)λv	PROPN
ejpam-6082	367	14	−	−	PROPN
ejpam-6082	367	15	(	(	PUNCT
ejpam-6082	367	16	α1	α1	PROPN
ejpam-6082	367	17	+	+	CCONJ
ejpam-6082	367	18	α2	α2	ADJ
ejpam-6082	367	19	+	+	CCONJ
ejpam-6082	367	20	ω	ω	NUM
ejpam-6082	367	21	+	+	CCONJ
ejpam-6082	367	22	µ)e	µ)e	NOUN
ejpam-6082	367	23	−	−	PROPN
ejpam-6082	367	24	d3∆e	d3∆e	NOUN
ejpam-6082	367	25	]	]	PUNCT
ejpam-6082	367	26	.	.	PUNCT
ejpam-6082	368	1	at	at	ADP
ejpam-6082	368	2	the	the	DET
ejpam-6082	368	3	dfe	dfe	PROPN
ejpam-6082	368	4	(	(	PUNCT
ejpam-6082	368	5	e	e	NOUN
ejpam-6082	368	6	=	=	SYM
ejpam-6082	368	7	0	0	NUM
ejpam-6082	368	8	):	):	PUNCT
ejpam-6082	368	9	c	c	NOUN
ejpam-6082	368	10	0	0	PUNCT
ejpam-6082	369	1	d	d	NOUN
ejpam-6082	369	2	α	α	PROPN
ejpam-6082	369	3	t	t	PROPN
ejpam-6082	369	4	(	(	PUNCT
ejpam-6082	369	5	e∗φ	e∗φ	PROPN
ejpam-6082	369	6	(	(	PUNCT
ejpam-6082	369	7	e	e	NOUN
ejpam-6082	369	8	e∗	e∗	PROPN
ejpam-6082	369	9	)	)	PUNCT
ejpam-6082	369	10	)	)	PUNCT
ejpam-6082	370	1	≤	≤	X
ejpam-6082	371	1	−d3e∗	−d3e∗	NOUN
ejpam-6082	371	2	|∇e|2	|∇e|2	ADP
ejpam-6082	371	3	e2	e2	PROPN
ejpam-6082	371	4	.	.	PUNCT
ejpam-6082	372	1	the	the	DET
ejpam-6082	372	2	equation	equation	NOUN
ejpam-6082	372	3	for	for	ADP
ejpam-6082	372	4	np	np	INTJ
ejpam-6082	372	5	is	be	AUX
ejpam-6082	372	6	:	:	PUNCT
ejpam-6082	372	7	c	c	NOUN
ejpam-6082	372	8	0	0	PUNCT
ejpam-6082	373	1	d	d	NOUN
ejpam-6082	373	2	α	α	NOUN
ejpam-6082	373	3	t	t	NOUN
ejpam-6082	373	4	np	np	INTJ
ejpam-6082	373	5	=	=	SYM
ejpam-6082	373	6	α1e	α1e	PROPN
ejpam-6082	373	7	−	−	PROPN
ejpam-6082	373	8	(	(	PUNCT
ejpam-6082	373	9	σ	σ	PROPN
ejpam-6082	373	10	+	+	CCONJ
ejpam-6082	373	11	µ+	µ+	X
ejpam-6082	373	12	ω1)np	ω1)np	PROPN
ejpam-6082	373	13	−	−	PROPN
ejpam-6082	373	14	d4∆np	d4∆np	PROPN
ejpam-6082	373	15	.	.	PUNCT
ejpam-6082	373	16	substitute	substitute	PROPN
ejpam-6082	373	17	into	into	ADP
ejpam-6082	373	18	the	the	DET
ejpam-6082	373	19	lyapunov	lyapunov	ADJ
ejpam-6082	373	20	derivative	derivative	NOUN
ejpam-6082	373	21	:	:	PUNCT
ejpam-6082	373	22	c	c	NOUN
ejpam-6082	373	23	0	0	PUNCT
ejpam-6082	374	1	d	d	NOUN
ejpam-6082	374	2	α	α	PROPN
ejpam-6082	374	3	t	t	PROPN
ejpam-6082	374	4	(	(	PUNCT
ejpam-6082	374	5	n∗	n∗	PROPN
ejpam-6082	374	6	pφ	pφ	X
ejpam-6082	374	7	(	(	PUNCT
ejpam-6082	374	8	np	np	INTJ
ejpam-6082	374	9	n∗	n∗	PROPN
ejpam-6082	374	10	p	p	NOUN
ejpam-6082	374	11	)	)	PUNCT
ejpam-6082	374	12	)	)	PUNCT
ejpam-6082	375	1	=	=	PUNCT
ejpam-6082	375	2	n∗	n∗	VERB
ejpam-6082	375	3	p	p	X
ejpam-6082	375	4	(	(	PUNCT
ejpam-6082	375	5	1−	1−	NUM
ejpam-6082	375	6	n∗	n∗	PROPN
ejpam-6082	375	7	p	p	PROPN
ejpam-6082	375	8	np	np	INTJ
ejpam-6082	375	9	)	)	PUNCT
ejpam-6082	375	10	[	[	PUNCT
ejpam-6082	375	11	α1e	α1e	PROPN
ejpam-6082	375	12	−	−	PROPN
ejpam-6082	375	13	(	(	PUNCT
ejpam-6082	375	14	σ	σ	PROPN
ejpam-6082	375	15	+	+	CCONJ
ejpam-6082	375	16	µ+	µ+	X
ejpam-6082	375	17	ω1)np	ω1)np	PROPN
ejpam-6082	375	18	−	−	PROPN
ejpam-6082	375	19	d4∆np	d4∆np	PROPN
ejpam-6082	375	20	]	]	PUNCT
ejpam-6082	375	21	.	.	PUNCT
ejpam-6082	376	1	k.	k.	PROPN
ejpam-6082	376	2	guedri	guedri	PROPN
ejpam-6082	376	3	et	et	PROPN
ejpam-6082	376	4	al	al	PROPN
ejpam-6082	376	5	.	.	PUNCT
ejpam-6082	376	6	/	/	SYM
ejpam-6082	376	7	eur	eur	PROPN
ejpam-6082	376	8	.	.	PUNCT
ejpam-6082	377	1	j.	j.	PROPN
ejpam-6082	377	2	pure	pure	PROPN
ejpam-6082	377	3	appl	appl	PROPN
ejpam-6082	377	4	.	.	PROPN
ejpam-6082	377	5	math	math	PROPN
ejpam-6082	377	6	,	,	PUNCT
ejpam-6082	377	7	18	18	NUM
ejpam-6082	377	8	(	(	PUNCT
ejpam-6082	377	9	2	2	NUM
ejpam-6082	377	10	)	)	PUNCT
ejpam-6082	377	11	(	(	PUNCT
ejpam-6082	377	12	2025	2025	NUM
ejpam-6082	377	13	)	)	PUNCT
ejpam-6082	377	14	,	,	PUNCT
ejpam-6082	377	15	6082	6082	NUM
ejpam-6082	377	16	17	17	NUM
ejpam-6082	377	17	of	of	ADP
ejpam-6082	377	18	39	39	NUM
ejpam-6082	377	19	at	at	ADP
ejpam-6082	377	20	the	the	DET
ejpam-6082	377	21	dfe	dfe	PROPN
ejpam-6082	377	22	(	(	PUNCT
ejpam-6082	377	23	np	np	NOUN
ejpam-6082	377	24	=	=	NOUN
ejpam-6082	377	25	0	0	NUM
ejpam-6082	377	26	):	):	PUNCT
ejpam-6082	377	27	c	c	NOUN
ejpam-6082	377	28	0	0	PUNCT
ejpam-6082	378	1	d	d	NOUN
ejpam-6082	378	2	α	α	PROPN
ejpam-6082	378	3	t	t	PROPN
ejpam-6082	378	4	(	(	PUNCT
ejpam-6082	378	5	n∗	n∗	PROPN
ejpam-6082	378	6	pφ	pφ	X
ejpam-6082	378	7	(	(	PUNCT
ejpam-6082	378	8	np	np	INTJ
ejpam-6082	378	9	n∗	n∗	PROPN
ejpam-6082	378	10	p	p	PROPN
ejpam-6082	378	11	)	)	PUNCT
ejpam-6082	378	12	)	)	PUNCT
ejpam-6082	379	1	≤	≤	NUM
ejpam-6082	379	2	−d4n∗	−d4n∗	PROPN
ejpam-6082	379	3	p	p	NOUN
ejpam-6082	379	4	|∇np|2	|∇np|2	NOUN
ejpam-6082	379	5	n2	n2	PROPN
ejpam-6082	379	6	p	p	PROPN
ejpam-6082	379	7	.	.	PUNCT
ejpam-6082	380	1	the	the	DET
ejpam-6082	380	2	equation	equation	NOUN
ejpam-6082	380	3	for	for	ADP
ejpam-6082	380	4	p	p	NOUN
ejpam-6082	380	5	is	be	AUX
ejpam-6082	380	6	:	:	PUNCT
ejpam-6082	380	7	c	c	NOUN
ejpam-6082	380	8	0	0	PUNCT
ejpam-6082	381	1	d	d	NOUN
ejpam-6082	381	2	α	α	NOUN
ejpam-6082	381	3	t	t	NOUN
ejpam-6082	381	4	p	p	X
ejpam-6082	381	5	=	=	X
ejpam-6082	381	6	α2e	α2e	X
ejpam-6082	381	7	−	−	PROPN
ejpam-6082	382	1	(	(	PUNCT
ejpam-6082	382	2	σ	σ	PROPN
ejpam-6082	382	3	+	+	CCONJ
ejpam-6082	382	4	µ+	µ+	PUNCT
ejpam-6082	382	5	ω2)p	ω2)p	ADJ
ejpam-6082	382	6	−	−	PROPN
ejpam-6082	382	7	d5∆p	d5∆p	PROPN
ejpam-6082	382	8	.	.	PUNCT
ejpam-6082	383	1	substitute	substitute	PROPN
ejpam-6082	383	2	into	into	ADP
ejpam-6082	383	3	the	the	DET
ejpam-6082	383	4	lyapunov	lyapunov	ADJ
ejpam-6082	383	5	derivative	derivative	NOUN
ejpam-6082	383	6	:	:	PUNCT
ejpam-6082	384	1	c	c	NOUN
ejpam-6082	384	2	0	0	PUNCT
ejpam-6082	385	1	d	d	NOUN
ejpam-6082	385	2	α	α	NOUN
ejpam-6082	385	3	t	t	NOUN
ejpam-6082	385	4	(	(	PUNCT
ejpam-6082	385	5	p	p	NOUN
ejpam-6082	385	6	∗φ	∗φ	PROPN
ejpam-6082	385	7	(	(	PUNCT
ejpam-6082	385	8	p	p	X
ejpam-6082	385	9	p	p	NOUN
ejpam-6082	385	10	∗	∗	NOUN
ejpam-6082	385	11	)	)	PUNCT
ejpam-6082	385	12	)	)	PUNCT
ejpam-6082	386	1	=	=	PUNCT
ejpam-6082	387	1	p	p	NOUN
ejpam-6082	387	2	∗	∗	NOUN
ejpam-6082	387	3	(	(	PUNCT
ejpam-6082	387	4	1−	1−	NUM
ejpam-6082	387	5	p	p	NOUN
ejpam-6082	387	6	∗	∗	X
ejpam-6082	387	7	p	p	NOUN
ejpam-6082	387	8	)	)	PUNCT
ejpam-6082	387	9	[	[	PUNCT
ejpam-6082	387	10	α2e	α2e	NUM
ejpam-6082	387	11	−	−	PROPN
ejpam-6082	387	12	(	(	PUNCT
ejpam-6082	387	13	σ	σ	PROPN
ejpam-6082	387	14	+	+	CCONJ
ejpam-6082	387	15	µ+	µ+	PUNCT
ejpam-6082	387	16	ω2)p	ω2)p	ADJ
ejpam-6082	387	17	−	−	PROPN
ejpam-6082	387	18	d5∆p	d5∆p	PROPN
ejpam-6082	387	19	]	]	PUNCT
ejpam-6082	387	20	.	.	PUNCT
ejpam-6082	388	1	at	at	ADP
ejpam-6082	388	2	the	the	DET
ejpam-6082	388	3	dfe	dfe	PROPN
ejpam-6082	389	1	(	(	PUNCT
ejpam-6082	389	2	p	p	NOUN
ejpam-6082	389	3	=	=	NOUN
ejpam-6082	389	4	0	0	NUM
ejpam-6082	389	5	):	):	PUNCT
ejpam-6082	389	6	c	c	NOUN
ejpam-6082	389	7	0	0	PUNCT
ejpam-6082	390	1	d	d	NOUN
ejpam-6082	390	2	α	α	NOUN
ejpam-6082	390	3	t	t	NOUN
ejpam-6082	390	4	(	(	PUNCT
ejpam-6082	390	5	p	p	NOUN
ejpam-6082	390	6	∗φ	∗φ	PROPN
ejpam-6082	390	7	(	(	PUNCT
ejpam-6082	390	8	p	p	X
ejpam-6082	390	9	p	p	NOUN
ejpam-6082	390	10	∗	∗	NOUN
ejpam-6082	390	11	)	)	PUNCT
ejpam-6082	390	12	)	)	PUNCT
ejpam-6082	391	1	≤	≤	NUM
ejpam-6082	391	2	−d5p	−d5p	PROPN
ejpam-6082	391	3	∗	∗	NOUN
ejpam-6082	391	4	|∇p	|∇p	PROPN
ejpam-6082	391	5	|2	|2	NUM
ejpam-6082	391	6	p	p	X
ejpam-6082	391	7	2	2	NUM
ejpam-6082	391	8	.	.	PUNCT
ejpam-6082	391	9	combine	combine	VERB
ejpam-6082	391	10	the	the	DET
ejpam-6082	391	11	contributions	contribution	NOUN
ejpam-6082	391	12	of	of	ADP
ejpam-6082	391	13	all	all	DET
ejpam-6082	391	14	compartments	compartment	NOUN
ejpam-6082	391	15	:	:	PUNCT
ejpam-6082	391	16	c	c	NOUN
ejpam-6082	391	17	0	0	PUNCT
ejpam-6082	392	1	d	d	NOUN
ejpam-6082	392	2	α	α	PROPN
ejpam-6082	392	3	t	t	NOUN
ejpam-6082	392	4	v(t	v(t	PROPN
ejpam-6082	392	5	,	,	PUNCT
ejpam-6082	392	6	x	x	NOUN
ejpam-6082	392	7	)	)	PUNCT
ejpam-6082	392	8	≤	≤	NOUN
ejpam-6082	392	9	−	−	PROPN
ejpam-6082	393	1	∫	∫	PROPN
ejpam-6082	393	2	ω	ω	PROPN
ejpam-6082	393	3	[	[	PUNCT
ejpam-6082	393	4	d1s	d1s	NOUN
ejpam-6082	393	5	∗	∗	NOUN
ejpam-6082	393	6	|∇s|2	|∇s|2	NUM
ejpam-6082	393	7	s2	s2	PROPN
ejpam-6082	393	8	+	+	CCONJ
ejpam-6082	393	9	d3e	d3e	PROPN
ejpam-6082	393	10	∗	∗	NOUN
ejpam-6082	393	11	|∇e|2	|∇e|2	X
ejpam-6082	393	12	e2	e2	PROPN
ejpam-6082	393	13	+	+	CCONJ
ejpam-6082	393	14	d4n	d4n	PROPN
ejpam-6082	393	15	∗	∗	NOUN
ejpam-6082	393	16	p	p	NOUN
ejpam-6082	393	17	|∇np|2	|∇np|2	NOUN
ejpam-6082	393	18	n2	n2	NOUN
ejpam-6082	393	19	p	p	PROPN
ejpam-6082	393	20	+	+	PUNCT
ejpam-6082	393	21	d5p	d5p	ADJ
ejpam-6082	393	22	∗	∗	NOUN
ejpam-6082	393	23	|∇p	|∇p	PROPN
ejpam-6082	393	24	|2	|2	NUM
ejpam-6082	393	25	p	p	X
ejpam-6082	393	26	2	2	NUM
ejpam-6082	393	27	]	]	PUNCT
ejpam-6082	393	28	dx	dx	PROPN
ejpam-6082	393	29	.	.	PUNCT
ejpam-6082	394	1	all	all	DET
ejpam-6082	394	2	terms	term	NOUN
ejpam-6082	394	3	are	be	AUX
ejpam-6082	394	4	non	non	ADJ
ejpam-6082	394	5	-	-	ADJ
ejpam-6082	394	6	positive	positive	ADJ
ejpam-6082	394	7	,	,	PUNCT
ejpam-6082	394	8	with	with	ADP
ejpam-6082	394	9	equality	equality	NOUN
ejpam-6082	394	10	only	only	ADV
ejpam-6082	394	11	when	when	SCONJ
ejpam-6082	394	12	s	s	X
ejpam-6082	394	13	=	=	SYM
ejpam-6082	394	14	s∗	s∗	PROPN
ejpam-6082	394	15	,	,	PUNCT
ejpam-6082	394	16	e	e	X
ejpam-6082	394	17	=	=	SYM
ejpam-6082	394	18	0	0	NUM
ejpam-6082	394	19	,	,	PUNCT
ejpam-6082	394	20	np	np	NOUN
ejpam-6082	394	21	=	=	NOUN
ejpam-6082	394	22	0	0	NUM
ejpam-6082	394	23	,	,	PUNCT
ejpam-6082	394	24	and	and	CCONJ
ejpam-6082	394	25	p	p	X
ejpam-6082	394	26	=	=	NOUN
ejpam-6082	394	27	0	0	PROPN
ejpam-6082	394	28	.	.	PUNCT
ejpam-6082	395	1	the	the	DET
ejpam-6082	395	2	basic	basic	ADJ
ejpam-6082	395	3	reproduction	reproduction	NOUN
ejpam-6082	395	4	number	number	NOUN
ejpam-6082	395	5	r0	r0	NOUN
ejpam-6082	395	6	is	be	AUX
ejpam-6082	395	7	derived	derive	VERB
ejpam-6082	395	8	using	use	VERB
ejpam-6082	395	9	the	the	DET
ejpam-6082	395	10	next	next	ADJ
ejpam-6082	395	11	-	-	PUNCT
ejpam-6082	395	12	generation	generation	NOUN
ejpam-6082	395	13	matrix	matrix	NOUN
ejpam-6082	395	14	method	method	NOUN
ejpam-6082	395	15	:	:	PUNCT
ejpam-6082	395	16	r0	r0	NOUN
ejpam-6082	395	17	=	=	SYM
ejpam-6082	395	18	βcrk5	βcrk5	NOUN
ejpam-6082	395	19	(	(	PUNCT
ejpam-6082	395	20	k1	k1	NOUN
ejpam-6082	395	21	+	+	CCONJ
ejpam-6082	395	22	δ(1−	δ(1−	PROPN
ejpam-6082	395	23	δ	δ	PROPN
ejpam-6082	395	24	)	)	PUNCT
ejpam-6082	395	25	)	)	PUNCT
ejpam-6082	395	26	(	(	PUNCT
ejpam-6082	395	27	α1k4	α1k4	PROPN
ejpam-6082	395	28	+	+	SYM
ejpam-6082	395	29	α2k3	α2k3	PROPN
ejpam-6082	395	30	+	+	CCONJ
ejpam-6082	395	31	k3k4	k3k4	NOUN
ejpam-6082	395	32	)	)	PUNCT
ejpam-6082	395	33	ηk2k3k4	ηk2k3k4	PROPN
ejpam-6082	395	34	,	,	PUNCT
ejpam-6082	395	35	where	where	SCONJ
ejpam-6082	395	36	:	:	PUNCT
ejpam-6082	396	1	η	η	PROPN
ejpam-6082	396	2	=	=	SYM
ejpam-6082	396	3	k1k5	k1k5	PROPN
ejpam-6082	396	4	+	+	PROPN
ejpam-6082	396	5	δ	δ	PROPN
ejpam-6082	396	6	(	(	PUNCT
ejpam-6082	396	7	k5	k5	PROPN
ejpam-6082	396	8	+	+	CCONJ
ejpam-6082	396	9	γ	γ	X
ejpam-6082	396	10	+	+	CCONJ
ejpam-6082	396	11	ργ	ργ	ADJ
ejpam-6082	396	12	k6	k6	NOUN
ejpam-6082	396	13	)	)	PUNCT
ejpam-6082	396	14	.	.	PUNCT
ejpam-6082	397	1	if	if	SCONJ
ejpam-6082	397	2	r0	r0	NOUN
ejpam-6082	397	3	<	<	X
ejpam-6082	397	4	1	1	NUM
ejpam-6082	397	5	,	,	PUNCT
ejpam-6082	397	6	the	the	DET
ejpam-6082	397	7	disease	disease	NOUN
ejpam-6082	397	8	dies	die	VERB
ejpam-6082	397	9	out	out	ADV
ejpam-6082	397	10	,	,	PUNCT
ejpam-6082	397	11	and	and	CCONJ
ejpam-6082	397	12	the	the	DET
ejpam-6082	397	13	lyapunov	lyapunov	ADJ
ejpam-6082	397	14	derivative	derivative	NOUN
ejpam-6082	397	15	is	be	AUX
ejpam-6082	397	16	strictly	strictly	ADV
ejpam-6082	397	17	negative	negative	ADJ
ejpam-6082	397	18	.	.	PUNCT
ejpam-6082	398	1	by	by	ADP
ejpam-6082	398	2	the	the	DET
ejpam-6082	398	3	fractional	fractional	PROPN
ejpam-6082	398	4	lasalle	lasalle	PROPN
ejpam-6082	398	5	invariance	invariance	PROPN
ejpam-6082	398	6	principle	principle	NOUN
ejpam-6082	398	7	,	,	PUNCT
ejpam-6082	398	8	the	the	DET
ejpam-6082	398	9	dfe	dfe	PROPN
ejpam-6082	398	10	is	be	AUX
ejpam-6082	398	11	globally	globally	ADV
ejpam-6082	398	12	asymptotically	asymptotically	ADV
ejpam-6082	398	13	stable	stable	ADJ
ejpam-6082	398	14	when	when	SCONJ
ejpam-6082	398	15	r0	r0	NOUN
ejpam-6082	398	16	<	<	X
ejpam-6082	398	17	1	1	NUM
ejpam-6082	398	18	.	.	NOUN
ejpam-6082	398	19	8	8	NUM
ejpam-6082	398	20	.	.	X
ejpam-6082	399	1	sensitivity	sensitivity	NOUN
ejpam-6082	399	2	analysis	analysis	NOUN
ejpam-6082	399	3	determining	determine	VERB
ejpam-6082	399	4	the	the	DET
ejpam-6082	399	5	parameters	parameter	NOUN
ejpam-6082	399	6	that	that	PRON
ejpam-6082	399	7	help	help	VERB
ejpam-6082	399	8	reduce	reduce	VERB
ejpam-6082	399	9	the	the	DET
ejpam-6082	399	10	spread	spread	NOUN
ejpam-6082	399	11	of	of	ADP
ejpam-6082	399	12	infectious	infectious	ADJ
ejpam-6082	399	13	diseases	disease	NOUN
ejpam-6082	399	14	is	be	AUX
ejpam-6082	399	15	carried	carry	VERB
ejpam-6082	399	16	out	out	ADP
ejpam-6082	399	17	through	through	ADP
ejpam-6082	399	18	sensitivity	sensitivity	NOUN
ejpam-6082	399	19	analysis	analysis	NOUN
ejpam-6082	399	20	.	.	PUNCT
ejpam-6082	400	1	forward	forward	ADJ
ejpam-6082	400	2	sensitivity	sensitivity	NOUN
ejpam-6082	400	3	analysis	analysis	NOUN
ejpam-6082	400	4	is	be	AUX
ejpam-6082	400	5	considered	consider	VERB
ejpam-6082	400	6	a	a	DET
ejpam-6082	400	7	vital	vital	ADJ
ejpam-6082	400	8	component	component	NOUN
ejpam-6082	400	9	of	of	ADP
ejpam-6082	400	10	disease	disease	NOUN
ejpam-6082	400	11	modeling	modeling	NOUN
ejpam-6082	400	12	,	,	PUNCT
ejpam-6082	400	13	though	though	SCONJ
ejpam-6082	400	14	its	its	PRON
ejpam-6082	400	15	computation	computation	NOUN
ejpam-6082	400	16	becomes	become	VERB
ejpam-6082	400	17	tedious	tedious	ADJ
ejpam-6082	400	18	for	for	ADP
ejpam-6082	400	19	complex	complex	ADJ
ejpam-6082	400	20	biological	biological	ADJ
ejpam-6082	400	21	models	model	NOUN
ejpam-6082	400	22	.	.	PUNCT
ejpam-6082	401	1	sensitivity	sensitivity	NOUN
ejpam-6082	401	2	analysis	analysis	NOUN
ejpam-6082	401	3	of	of	ADP
ejpam-6082	401	4	r0	r0	NOUN
ejpam-6082	401	5	has	have	AUX
ejpam-6082	401	6	received	receive	VERB
ejpam-6082	401	7	much	much	ADJ
ejpam-6082	401	8	attention	attention	NOUN
ejpam-6082	401	9	from	from	ADP
ejpam-6082	401	10	ecologists	ecologist	NOUN
ejpam-6082	401	11	and	and	CCONJ
ejpam-6082	401	12	epidemiologists	epidemiologist	NOUN
ejpam-6082	401	13	.	.	PUNCT
ejpam-6082	402	1	definition	definition	NOUN
ejpam-6082	402	2	6	6	NUM
ejpam-6082	402	3	.	.	PUNCT
ejpam-6082	403	1	the	the	PRON
ejpam-6082	403	2	normalized	normalize	VERB
ejpam-6082	403	3	forward	forward	ADJ
ejpam-6082	403	4	sensitivity	sensitivity	NOUN
ejpam-6082	403	5	index	index	NOUN
ejpam-6082	403	6	of	of	ADP
ejpam-6082	403	7	r0	r0	NOUN
ejpam-6082	403	8	that	that	PRON
ejpam-6082	403	9	depends	depend	VERB
ejpam-6082	403	10	differentiably	differentiably	ADV
ejpam-6082	403	11	on	on	ADP
ejpam-6082	403	12	a	a	DET
ejpam-6082	403	13	parameter	parameter	NOUN
ejpam-6082	403	14	ω	ω	PROPN
ejpam-6082	403	15	is	be	AUX
ejpam-6082	403	16	defined	define	VERB
ejpam-6082	403	17	as	as	ADP
ejpam-6082	403	18	k.	k.	PROPN
ejpam-6082	403	19	guedri	guedri	PROPN
ejpam-6082	403	20	et	et	PROPN
ejpam-6082	403	21	al	al	PROPN
ejpam-6082	403	22	.	.	PUNCT
ejpam-6082	403	23	/	/	SYM
ejpam-6082	403	24	eur	eur	PROPN
ejpam-6082	403	25	.	.	PUNCT
ejpam-6082	404	1	j.	j.	PROPN
ejpam-6082	404	2	pure	pure	PROPN
ejpam-6082	404	3	appl	appl	PROPN
ejpam-6082	404	4	.	.	PROPN
ejpam-6082	404	5	math	math	PROPN
ejpam-6082	404	6	,	,	PUNCT
ejpam-6082	404	7	18	18	NUM
ejpam-6082	404	8	(	(	PUNCT
ejpam-6082	404	9	2	2	NUM
ejpam-6082	404	10	)	)	PUNCT
ejpam-6082	404	11	(	(	PUNCT
ejpam-6082	404	12	2025	2025	NUM
ejpam-6082	404	13	)	)	PUNCT
ejpam-6082	404	14	,	,	PUNCT
ejpam-6082	404	15	6082	6082	NUM
ejpam-6082	404	16	18	18	NUM
ejpam-6082	404	17	of	of	ADP
ejpam-6082	404	18	39	39	NUM
ejpam-6082	404	19	sω	sω	NOUN
ejpam-6082	404	20	=	=	SYM
ejpam-6082	404	21	ω	ω	NUM
ejpam-6082	404	22	r0	r0	NOUN
ejpam-6082	404	23	∂r0	∂r0	ADP
ejpam-6082	404	24	∂ω	∂ω	PROPN
ejpam-6082	404	25	.	.	PUNCT
ejpam-6082	405	1	three	three	NUM
ejpam-6082	405	2	methods	method	NOUN
ejpam-6082	405	3	are	be	AUX
ejpam-6082	405	4	commonly	commonly	ADV
ejpam-6082	405	5	used	use	VERB
ejpam-6082	405	6	to	to	PART
ejpam-6082	405	7	calculate	calculate	VERB
ejpam-6082	405	8	sensitivity	sensitivity	NOUN
ejpam-6082	405	9	indices	index	NOUN
ejpam-6082	405	10	:	:	PUNCT
ejpam-6082	405	11	(	(	PUNCT
ejpam-6082	405	12	i	i	NOUN
ejpam-6082	405	13	)	)	PUNCT
ejpam-6082	405	14	by	by	ADP
ejpam-6082	405	15	direct	direct	ADJ
ejpam-6082	405	16	differentiation	differentiation	NOUN
ejpam-6082	405	17	,	,	PUNCT
ejpam-6082	405	18	(	(	PUNCT
ejpam-6082	405	19	ii	ii	NOUN
ejpam-6082	405	20	)	)	PUNCT
ejpam-6082	405	21	by	by	ADP
ejpam-6082	405	22	a	a	DET
ejpam-6082	405	23	latin	latin	ADJ
ejpam-6082	405	24	hypercube	hypercube	NOUN
ejpam-6082	405	25	sampling	sample	VERB
ejpam-6082	405	26	method	method	NOUN
ejpam-6082	405	27	,	,	PUNCT
ejpam-6082	405	28	and	and	CCONJ
ejpam-6082	405	29	(	(	PUNCT
ejpam-6082	405	30	iii	iii	NOUN
ejpam-6082	405	31	)	)	PUNCT
ejpam-6082	405	32	by	by	ADP
ejpam-6082	405	33	linearizing	linearize	VERB
ejpam-6082	405	34	the	the	DET
ejpam-6082	405	35	system	system	NOUN
ejpam-6082	405	36	(	(	PUNCT
ejpam-6082	405	37	2	2	NUM
ejpam-6082	405	38	)	)	PUNCT
ejpam-6082	405	39	and	and	CCONJ
ejpam-6082	405	40	then	then	ADV
ejpam-6082	405	41	solving	solve	VERB
ejpam-6082	405	42	the	the	DET
ejpam-6082	405	43	obtained	obtain	VERB
ejpam-6082	405	44	set	set	NOUN
ejpam-6082	405	45	of	of	ADP
ejpam-6082	405	46	linear	linear	PROPN
ejpam-6082	405	47	algebraic	algebraic	ADJ
ejpam-6082	405	48	equations	equation	NOUN
ejpam-6082	405	49	.	.	PUNCT
ejpam-6082	406	1	we	we	PRON
ejpam-6082	406	2	will	will	AUX
ejpam-6082	406	3	apply	apply	VERB
ejpam-6082	406	4	the	the	DET
ejpam-6082	406	5	direct	direct	ADJ
ejpam-6082	406	6	differentiation	differentiation	NOUN
ejpam-6082	406	7	method	method	NOUN
ejpam-6082	406	8	as	as	SCONJ
ejpam-6082	406	9	it	it	PRON
ejpam-6082	406	10	provides	provide	VERB
ejpam-6082	406	11	analytical	analytical	ADJ
ejpam-6082	406	12	expressions	expression	NOUN
ejpam-6082	406	13	for	for	ADP
ejpam-6082	406	14	the	the	DET
ejpam-6082	406	15	indices	index	NOUN
ejpam-6082	406	16	.	.	PUNCT
ejpam-6082	407	1	the	the	DET
ejpam-6082	407	2	indices	index	NOUN
ejpam-6082	407	3	not	not	PART
ejpam-6082	407	4	only	only	ADV
ejpam-6082	407	5	show	show	VERB
ejpam-6082	407	6	us	we	PRON
ejpam-6082	407	7	the	the	DET
ejpam-6082	407	8	influence	influence	NOUN
ejpam-6082	407	9	of	of	ADP
ejpam-6082	407	10	various	various	ADJ
ejpam-6082	407	11	aspects	aspect	NOUN
ejpam-6082	407	12	associated	associate	VERB
ejpam-6082	407	13	with	with	ADP
ejpam-6082	407	14	the	the	DET
ejpam-6082	407	15	spread	spread	NOUN
ejpam-6082	407	16	of	of	ADP
ejpam-6082	407	17	infectious	infectious	ADJ
ejpam-6082	407	18	diseases	disease	NOUN
ejpam-6082	407	19	but	but	CCONJ
ejpam-6082	407	20	also	also	ADV
ejpam-6082	407	21	provide	provide	VERB
ejpam-6082	407	22	important	important	ADJ
ejpam-6082	407	23	information	information	NOUN
ejpam-6082	407	24	regarding	regard	VERB
ejpam-6082	407	25	the	the	DET
ejpam-6082	407	26	comparative	comparative	ADJ
ejpam-6082	407	27	change	change	NOUN
ejpam-6082	407	28	between	between	ADP
ejpam-6082	407	29	r0	r0	NOUN
ejpam-6082	407	30	and	and	CCONJ
ejpam-6082	407	31	different	different	ADJ
ejpam-6082	407	32	parameters	parameter	NOUN
ejpam-6082	407	33	.	.	PUNCT
ejpam-6082	408	1	consequently	consequently	ADV
ejpam-6082	408	2	,	,	PUNCT
ejpam-6082	408	3	it	it	PRON
ejpam-6082	408	4	helps	help	VERB
ejpam-6082	408	5	in	in	ADP
ejpam-6082	408	6	developing	develop	VERB
ejpam-6082	408	7	effective	effective	ADJ
ejpam-6082	408	8	control	control	NOUN
ejpam-6082	408	9	strategies	strategy	NOUN
ejpam-6082	408	10	.	.	PUNCT
ejpam-6082	409	1	table	table	NOUN
ejpam-6082	409	2	1	1	NUM
ejpam-6082	409	3	shows	show	VERB
ejpam-6082	409	4	that	that	SCONJ
ejpam-6082	409	5	the	the	DET
ejpam-6082	409	6	parameters	parameter	NOUN
ejpam-6082	409	7	β	β	VERB
ejpam-6082	409	8	,	,	PUNCT
ejpam-6082	409	9	c	c	X
ejpam-6082	409	10	,	,	PUNCT
ejpam-6082	409	11	r	r	NOUN
ejpam-6082	409	12	,	,	PUNCT
ejpam-6082	409	13	ρ1	ρ1	NOUN
ejpam-6082	409	14	,	,	PUNCT
ejpam-6082	409	15	γ	γ	X
ejpam-6082	409	16	,	,	PUNCT
ejpam-6082	409	17	and	and	CCONJ
ejpam-6082	409	18	γ1	γ1	PROPN
ejpam-6082	409	19	positively	positively	ADV
ejpam-6082	409	20	influence	influence	VERB
ejpam-6082	409	21	the	the	DET
ejpam-6082	409	22	reproduction	reproduction	NOUN
ejpam-6082	409	23	number	number	NOUN
ejpam-6082	409	24	r0	r0	NOUN
ejpam-6082	409	25	.	.	PUNCT
ejpam-6082	410	1	this	this	PRON
ejpam-6082	410	2	implies	imply	VERB
ejpam-6082	410	3	that	that	SCONJ
ejpam-6082	410	4	an	an	DET
ejpam-6082	410	5	increase	increase	NOUN
ejpam-6082	410	6	or	or	CCONJ
ejpam-6082	410	7	decrease	decrease	NOUN
ejpam-6082	410	8	in	in	ADP
ejpam-6082	410	9	these	these	DET
ejpam-6082	410	10	parameters	parameter	NOUN
ejpam-6082	410	11	by	by	ADP
ejpam-6082	410	12	10	10	NUM
ejpam-6082	410	13	%	%	NOUN
ejpam-6082	410	14	will	will	AUX
ejpam-6082	410	15	proportionally	proportionally	ADV
ejpam-6082	410	16	increase	increase	VERB
ejpam-6082	410	17	or	or	CCONJ
ejpam-6082	410	18	decrease	decrease	VERB
ejpam-6082	410	19	r0	r0	NOUN
ejpam-6082	410	20	by	by	ADP
ejpam-6082	410	21	10	10	NUM
ejpam-6082	410	22	%	%	NOUN
ejpam-6082	410	23	,	,	PUNCT
ejpam-6082	410	24	10	10	NUM
ejpam-6082	410	25	%	%	NOUN
ejpam-6082	410	26	,	,	PUNCT
ejpam-6082	410	27	10	10	NUM
ejpam-6082	410	28	%	%	NOUN
ejpam-6082	410	29	,	,	PUNCT
ejpam-6082	410	30	2.2384	2.2384	NUM
ejpam-6082	410	31	%	%	NOUN
ejpam-6082	410	32	,	,	PUNCT
ejpam-6082	410	33	7.283	7.283	NUM
ejpam-6082	410	34	%	%	NOUN
ejpam-6082	410	35	,	,	PUNCT
ejpam-6082	410	36	and	and	CCONJ
ejpam-6082	410	37	9.347	9.347	NUM
ejpam-6082	410	38	%	%	NOUN
ejpam-6082	410	39	,	,	PUNCT
ejpam-6082	410	40	respectively	respectively	ADV
ejpam-6082	410	41	.	.	PUNCT
ejpam-6082	411	1	on	on	ADP
ejpam-6082	411	2	the	the	DET
ejpam-6082	411	3	other	other	ADJ
ejpam-6082	411	4	hand	hand	NOUN
ejpam-6082	411	5	,	,	PUNCT
ejpam-6082	411	6	the	the	DET
ejpam-6082	411	7	indices	index	NOUN
ejpam-6082	411	8	for	for	ADP
ejpam-6082	411	9	parameters	parameter	NOUN
ejpam-6082	411	10	ρ	ρ	PROPN
ejpam-6082	411	11	,	,	PUNCT
ejpam-6082	411	12	µ	µ	NOUN
ejpam-6082	411	13	,	,	PUNCT
ejpam-6082	411	14	δ	δ	PROPN
ejpam-6082	411	15	,	,	PUNCT
ejpam-6082	411	16	σ	σ	PROPN
ejpam-6082	411	17	,	,	PUNCT
ejpam-6082	411	18	ω	ω	PROPN
ejpam-6082	411	19	,	,	PUNCT
ejpam-6082	411	20	ω1	ω1	PROPN
ejpam-6082	411	21	,	,	PUNCT
ejpam-6082	411	22	and	and	CCONJ
ejpam-6082	411	23	ω2	ω2	ADV
ejpam-6082	411	24	show	show	VERB
ejpam-6082	411	25	that	that	SCONJ
ejpam-6082	411	26	increasing	increase	VERB
ejpam-6082	411	27	their	their	PRON
ejpam-6082	411	28	values	value	NOUN
ejpam-6082	411	29	by	by	ADP
ejpam-6082	411	30	10	10	NUM
ejpam-6082	411	31	%	%	NOUN
ejpam-6082	411	32	will	will	AUX
ejpam-6082	411	33	decrease	decrease	VERB
ejpam-6082	411	34	r0	r0	VERB
ejpam-6082	411	35	by	by	ADP
ejpam-6082	411	36	0.25475	0.25475	NUM
ejpam-6082	411	37	%	%	NOUN
ejpam-6082	411	38	,	,	PUNCT
ejpam-6082	411	39	0.46834	0.46834	NUM
ejpam-6082	411	40	%	%	NOUN
ejpam-6082	411	41	,	,	PUNCT
ejpam-6082	411	42	5.4797	5.4797	NUM
ejpam-6082	411	43	%	%	NOUN
ejpam-6082	411	44	,	,	PUNCT
ejpam-6082	411	45	7.725	7.725	NUM
ejpam-6082	411	46	%	%	NOUN
ejpam-6082	411	47	,	,	PUNCT
ejpam-6082	411	48	0.10323	0.10323	NUM
ejpam-6082	411	49	%	%	NOUN
ejpam-6082	411	50	,	,	PUNCT
ejpam-6082	411	51	0.034112	0.034112	NUM
ejpam-6082	411	52	%	%	NOUN
ejpam-6082	411	53	,	,	PUNCT
ejpam-6082	411	54	and	and	CCONJ
ejpam-6082	411	55	0.0031115	0.0031115	NUM
ejpam-6082	411	56	%	%	NOUN
ejpam-6082	411	57	,	,	PUNCT
ejpam-6082	411	58	respectively	respectively	ADV
ejpam-6082	411	59	.	.	PUNCT
ejpam-6082	412	1	parameters	parameter	NOUN
ejpam-6082	412	2	α1	α1	PROPN
ejpam-6082	412	3	and	and	CCONJ
ejpam-6082	412	4	α2	α2	PROPN
ejpam-6082	412	5	also	also	ADV
ejpam-6082	412	6	have	have	VERB
ejpam-6082	412	7	a	a	DET
ejpam-6082	412	8	negative	negative	ADJ
ejpam-6082	412	9	impact	impact	NOUN
ejpam-6082	412	10	,	,	PUNCT
ejpam-6082	412	11	with	with	ADP
ejpam-6082	412	12	r0	r0	NOUN
ejpam-6082	412	13	decreasing	decrease	VERB
ejpam-6082	412	14	by	by	ADP
ejpam-6082	412	15	0.56475	0.56475	NUM
ejpam-6082	412	16	%	%	NOUN
ejpam-6082	412	17	and	and	CCONJ
ejpam-6082	412	18	0.48046	0.48046	NUM
ejpam-6082	412	19	%	%	NOUN
ejpam-6082	412	20	,	,	PUNCT
ejpam-6082	412	21	respectively	respectively	ADV
ejpam-6082	412	22	,	,	PUNCT
ejpam-6082	412	23	for	for	ADP
ejpam-6082	412	24	a	a	DET
ejpam-6082	412	25	10	10	NUM
ejpam-6082	412	26	%	%	NOUN
ejpam-6082	412	27	increase	increase	NOUN
ejpam-6082	412	28	in	in	ADP
ejpam-6082	412	29	these	these	DET
ejpam-6082	412	30	parameters	parameter	NOUN
ejpam-6082	412	31	.	.	PUNCT
ejpam-6082	413	1	figs	fig	NOUN
ejpam-6082	413	2	.	.	PUNCT
ejpam-6082	414	1	3(a	3(a	NUM
ejpam-6082	414	2	,	,	PUNCT
ejpam-6082	414	3	b	b	NOUN
ejpam-6082	414	4	,	,	PUNCT
ejpam-6082	414	5	c	c	NOUN
ejpam-6082	414	6	,	,	PUNCT
ejpam-6082	414	7	d	d	NOUN
ejpam-6082	414	8	,	,	PUNCT
ejpam-6082	414	9	e	e	NOUN
ejpam-6082	414	10	,	,	PUNCT
ejpam-6082	414	11	f	f	NOUN
ejpam-6082	414	12	)	)	PUNCT
ejpam-6082	414	13	and	and	CCONJ
ejpam-6082	414	14	figs	fig	NOUN
ejpam-6082	414	15	.	.	PUNCT
ejpam-6082	415	1	4(a	4(a	NUM
ejpam-6082	415	2	,	,	PUNCT
ejpam-6082	415	3	b	b	NOUN
ejpam-6082	415	4	,	,	PUNCT
ejpam-6082	415	5	c	c	NOUN
ejpam-6082	415	6	,	,	PUNCT
ejpam-6082	415	7	d	d	NOUN
ejpam-6082	415	8	,	,	PUNCT
ejpam-6082	415	9	e	e	NOUN
ejpam-6082	415	10	,	,	PUNCT
ejpam-6082	415	11	f	f	X
ejpam-6082	415	12	)	)	PUNCT
ejpam-6082	415	13	depict	depict	VERB
ejpam-6082	415	14	the	the	DET
ejpam-6082	415	15	sensitivity	sensitivity	NOUN
ejpam-6082	415	16	of	of	ADP
ejpam-6082	415	17	various	various	ADJ
ejpam-6082	415	18	parameters	parameter	NOUN
ejpam-6082	415	19	.	.	PUNCT
ejpam-6082	416	1	these	these	DET
ejpam-6082	416	2	results	result	NOUN
ejpam-6082	416	3	underline	underline	VERB
ejpam-6082	416	4	the	the	DET
ejpam-6082	416	5	importance	importance	NOUN
ejpam-6082	416	6	of	of	ADP
ejpam-6082	416	7	prioritizing	prioritize	VERB
ejpam-6082	416	8	interventions	intervention	NOUN
ejpam-6082	416	9	targeting	target	VERB
ejpam-6082	416	10	the	the	DET
ejpam-6082	416	11	most	most	ADV
ejpam-6082	416	12	sensitive	sensitive	ADJ
ejpam-6082	416	13	parameters	parameter	NOUN
ejpam-6082	416	14	to	to	PART
ejpam-6082	416	15	effectively	effectively	ADV
ejpam-6082	416	16	control	control	VERB
ejpam-6082	416	17	the	the	DET
ejpam-6082	416	18	disease	disease	NOUN
ejpam-6082	416	19	.	.	PUNCT
ejpam-6082	417	1	parameter	parameter	PROPN
ejpam-6082	417	2	sindex	sindex	PROPN
ejpam-6082	417	3	value	value	PROPN
ejpam-6082	417	4	parameter	parameter	PROPN
ejpam-6082	417	5	sindex	sindex	PROPN
ejpam-6082	417	6	value	value	NOUN
ejpam-6082	417	7	β	β	X
ejpam-6082	417	8	sβ	sβ	NUM
ejpam-6082	417	9	1.00	1.00	NUM
ejpam-6082	417	10	c	c	X
ejpam-6082	417	11	sc	sc	PROPN
ejpam-6082	417	12	1.00	1.00	NUM
ejpam-6082	417	13	r	r	NOUN
ejpam-6082	417	14	sr	sr	PROPN
ejpam-6082	417	15	1.00	1.00	NUM
ejpam-6082	417	16	ρ	ρ	NOUN
ejpam-6082	417	17	sρ	sρ	ADP
ejpam-6082	417	18	-0.025475	-0.025475	PROPN
ejpam-6082	417	19	ρ1	ρ1	NOUN
ejpam-6082	417	20	sρ1	sρ1	NOUN
ejpam-6082	417	21	0.22384	0.22384	NUM
ejpam-6082	417	22	µ	µ	PROPN
ejpam-6082	417	23	sµ	sµ	NOUN
ejpam-6082	417	24	-0.046834	-0.046834	NOUN
ejpam-6082	418	1	γ	γ	PROPN
ejpam-6082	418	2	sγ	sγ	PROPN
ejpam-6082	418	3	-0.084718	-0.084718	VERB
ejpam-6082	418	4	δ	δ	PROPN
ejpam-6082	418	5	sδ	sδ	ADJ
ejpam-6082	418	6	-0.54797	-0.54797	NOUN
ejpam-6082	418	7	σ	σ	PROPN
ejpam-6082	418	8	sσ	sσ	PROPN
ejpam-6082	418	9	-0.7725	-0.7725	PROPN
ejpam-6082	418	10	ω	ω	PROPN
ejpam-6082	418	11	sω	sω	PRON
ejpam-6082	418	12	-0.010323	-0.010323	PROPN
ejpam-6082	418	13	ω1	ω1	PROPN
ejpam-6082	419	1	sω1	sω1	PROPN
ejpam-6082	419	2	-0.0034112	-0.0034112	PROPN
ejpam-6082	419	3	ω2	ω2	PROPN
ejpam-6082	419	4	sω2	sω2	PROPN
ejpam-6082	419	5	-0.00031115	-0.00031115	PROPN
ejpam-6082	419	6	α1	α1	PROPN
ejpam-6082	419	7	sα1	sα1	NOUN
ejpam-6082	419	8	-0.056475	-0.056475	PROPN
ejpam-6082	419	9	α2	α2	PROPN
ejpam-6082	419	10	sα2	sα2	PROPN
ejpam-6082	419	11	-0.048046	-0.048046	PROPN
ejpam-6082	419	12	table	table	NOUN
ejpam-6082	419	13	1	1	NUM
ejpam-6082	419	14	:	:	PUNCT
ejpam-6082	419	15	sensitivity	sensitivity	NOUN
ejpam-6082	419	16	indices	index	NOUN
ejpam-6082	419	17	of	of	ADP
ejpam-6082	419	18	the	the	DET
ejpam-6082	419	19	reproduction	reproduction	NOUN
ejpam-6082	419	20	number	number	NOUN
ejpam-6082	419	21	r0	r0	NOUN
ejpam-6082	419	22	against	against	ADP
ejpam-6082	419	23	mentioned	mention	VERB
ejpam-6082	419	24	parameters	parameter	NOUN
ejpam-6082	419	25	.	.	PUNCT
ejpam-6082	420	1	k.	k.	PROPN
ejpam-6082	420	2	guedri	guedri	PROPN
ejpam-6082	420	3	et	et	PROPN
ejpam-6082	420	4	al	al	PROPN
ejpam-6082	420	5	.	.	PUNCT
ejpam-6082	420	6	/	/	SYM
ejpam-6082	420	7	eur	eur	PROPN
ejpam-6082	420	8	.	.	PUNCT
ejpam-6082	421	1	j.	j.	PROPN
ejpam-6082	421	2	pure	pure	PROPN
ejpam-6082	421	3	appl	appl	PROPN
ejpam-6082	421	4	.	.	PROPN
ejpam-6082	421	5	math	math	PROPN
ejpam-6082	421	6	,	,	PUNCT
ejpam-6082	421	7	18	18	NUM
ejpam-6082	421	8	(	(	PUNCT
ejpam-6082	421	9	2	2	NUM
ejpam-6082	421	10	)	)	PUNCT
ejpam-6082	421	11	(	(	PUNCT
ejpam-6082	421	12	2025	2025	NUM
ejpam-6082	421	13	)	)	PUNCT
ejpam-6082	421	14	,	,	PUNCT
ejpam-6082	421	15	6082	6082	NUM
ejpam-6082	421	16	19	19	NUM
ejpam-6082	421	17	of	of	ADP
ejpam-6082	421	18	39	39	NUM
ejpam-6082	421	19	sensitivity	sensitivity	NOUN
ejpam-6082	421	20	analysis	analysis	NOUN
ejpam-6082	421	21	of	of	ADP
ejpam-6082	421	22	r	r	NOUN
ejpam-6082	421	23	0	0	NUM
ejpam-6082	421	24	1	1	NUM
ejpam-6082	421	25	2	2	NUM
ejpam-6082	421	26	3	3	NUM
ejpam-6082	421	27	4	4	NUM
ejpam-6082	421	28	5	5	NUM
ejpam-6082	421	29	6	6	NUM
ejpam-6082	421	30	7	7	NUM
ejpam-6082	421	31	8	8	NUM
ejpam-6082	421	32	9	9	NUM
ejpam-6082	421	33	10	10	NUM
ejpam-6082	421	34	11	11	NUM
ejpam-6082	421	35	12	12	NUM
ejpam-6082	421	36	13	13	NUM
ejpam-6082	421	37	14	14	NUM
ejpam-6082	421	38	c	c	NOUN
ejpam-6082	421	39	r	r	NOUN
ejpam-6082	421	40	1	1	NUM
ejpam-6082	421	41	1	1	NUM
ejpam-6082	421	42	2	2	NUM
ejpam-6082	421	43	1	1	NUM
ejpam-6082	421	44	2	2	NUM
ejpam-6082	421	45	-1	-1	SYM
ejpam-6082	421	46	-0.8	-0.8	PROPN
ejpam-6082	421	47	-0.6	-0.6	X
ejpam-6082	421	48	-0.4	-0.4	X
ejpam-6082	421	49	-0.2	-0.2	PROPN
ejpam-6082	421	50	0	0	NUM
ejpam-6082	421	51	0.2	0.2	NUM
ejpam-6082	421	52	0.4	0.4	NUM
ejpam-6082	421	53	0.6	0.6	NUM
ejpam-6082	421	54	0.8	0.8	NUM
ejpam-6082	421	55	1	1	NUM
ejpam-6082	421	56	figure	figure	NOUN
ejpam-6082	421	57	2	2	NUM
ejpam-6082	421	58	:	:	PUNCT
ejpam-6082	421	59	sensitivity	sensitivity	NOUN
ejpam-6082	421	60	bar	bar	NOUN
ejpam-6082	421	61	chart	chart	NOUN
ejpam-6082	421	62	related	relate	VERB
ejpam-6082	421	63	to	to	ADP
ejpam-6082	421	64	model	model	NOUN
ejpam-6082	421	65	parameters	parameter	NOUN
ejpam-6082	421	66	.	.	PUNCT
ejpam-6082	422	1	k.	k.	PROPN
ejpam-6082	422	2	guedri	guedri	PROPN
ejpam-6082	422	3	et	et	PROPN
ejpam-6082	422	4	al	al	PROPN
ejpam-6082	422	5	.	.	PUNCT
ejpam-6082	422	6	/	/	SYM
ejpam-6082	422	7	eur	eur	PROPN
ejpam-6082	422	8	.	.	PUNCT
ejpam-6082	423	1	j.	j.	PROPN
ejpam-6082	423	2	pure	pure	PROPN
ejpam-6082	423	3	appl	appl	PROPN
ejpam-6082	423	4	.	.	PROPN
ejpam-6082	423	5	math	math	PROPN
ejpam-6082	423	6	,	,	PUNCT
ejpam-6082	423	7	18	18	NUM
ejpam-6082	423	8	(	(	PUNCT
ejpam-6082	423	9	2	2	NUM
ejpam-6082	423	10	)	)	PUNCT
ejpam-6082	423	11	(	(	PUNCT
ejpam-6082	423	12	2025	2025	NUM
ejpam-6082	423	13	)	)	PUNCT
ejpam-6082	423	14	,	,	PUNCT
ejpam-6082	423	15	6082	6082	NUM
ejpam-6082	423	16	20	20	NUM
ejpam-6082	423	17	of	of	ADP
ejpam-6082	423	18	39	39	NUM
ejpam-6082	423	19	(	(	PUNCT
ejpam-6082	423	20	a	a	PRON
ejpam-6082	423	21	)	)	PUNCT
ejpam-6082	423	22	r0	r0	NOUN
ejpam-6082	423	23	vs	vs	ADP
ejpam-6082	423	24	σ	σ	PROPN
ejpam-6082	423	25	and	and	CCONJ
ejpam-6082	423	26	µ	µ	PRON
ejpam-6082	423	27	contour	contour	NOUN
ejpam-6082	423	28	plot	plot	NOUN
ejpam-6082	423	29	of	of	ADP
ejpam-6082	423	30	r0	r0	NOUN
ejpam-6082	423	31	for	for	ADP
ejpam-6082	423	32	vs	vs	ADP
ejpam-6082	423	33	0.0026639	0.0026639	NUM
ejpam-6082	423	34	0.0028231	0.0028231	NUM
ejpam-6082	423	35	0.0028231	0.0028231	NUM
ejpam-6082	423	36	0.0029823	0.0029823	NUM
ejpam-6082	423	37	0.0029823	0.0029823	NUM
ejpam-6082	423	38	0.0031415	0.0031415	NUM
ejpam-6082	423	39	0.0031415	0.0031415	NUM
ejpam-6082	423	40	0.0033007	0.0033007	NUM
ejpam-6082	423	41	0.0033007	0.0033007	NUM
ejpam-6082	423	42	0.0034599	0.0034599	NUM
ejpam-6082	423	43	0.0034599	0.0034599	NUM
ejpam-6082	423	44	0.00361910.0037783	0.00361910.0037783	NOUN
ejpam-6082	423	45	0.1	0.1	NUM
ejpam-6082	423	46	0.12	0.12	NUM
ejpam-6082	423	47	0.14	0.14	NUM
ejpam-6082	423	48	0.16	0.16	NUM
ejpam-6082	423	49	0.18	0.18	NUM
ejpam-6082	423	50	0.2	0.2	NUM
ejpam-6082	423	51	0.05	0.05	NUM
ejpam-6082	423	52	0.06	0.06	NUM
ejpam-6082	423	53	0.07	0.07	NUM
ejpam-6082	423	54	0.08	0.08	NUM
ejpam-6082	423	55	0.09	0.09	NUM
ejpam-6082	423	56	0.1	0.1	NUM
ejpam-6082	423	57	0	0	NUM
ejpam-6082	423	58	0.1	0.1	NUM
ejpam-6082	423	59	0.2	0.2	NUM
ejpam-6082	423	60	0.3	0.3	NUM
ejpam-6082	423	61	0.4	0.4	NUM
ejpam-6082	423	62	0.5	0.5	NUM
ejpam-6082	423	63	0.6	0.6	NUM
ejpam-6082	423	64	0.7	0.7	NUM
ejpam-6082	423	65	0.8	0.8	NUM
ejpam-6082	423	66	0.9	0.9	NUM
ejpam-6082	423	67	1	1	NUM
ejpam-6082	423	68	(	(	PUNCT
ejpam-6082	423	69	b	b	NOUN
ejpam-6082	423	70	)	)	PUNCT
ejpam-6082	423	71	r0	r0	NOUN
ejpam-6082	423	72	vs	vs	ADP
ejpam-6082	423	73	σ	σ	PROPN
ejpam-6082	423	74	and	and	CCONJ
ejpam-6082	423	75	µ	µ	PROPN
ejpam-6082	423	76	(	(	PUNCT
ejpam-6082	423	77	c	c	NOUN
ejpam-6082	423	78	)	)	PUNCT
ejpam-6082	423	79	r0	r0	NOUN
ejpam-6082	423	80	vs	vs	ADP
ejpam-6082	423	81	σ	σ	PROPN
ejpam-6082	423	82	and	and	CCONJ
ejpam-6082	423	83	β	β	X
ejpam-6082	423	84	contour	contour	NOUN
ejpam-6082	423	85	plot	plot	NOUN
ejpam-6082	423	86	of	of	ADP
ejpam-6082	423	87	r0	r0	NOUN
ejpam-6082	423	88	for	for	ADP
ejpam-6082	423	89	vs	vs	ADP
ejpam-6082	423	90	1	1	NUM
ejpam-6082	423	91	.	.	NOUN
ejpam-6082	423	92	64	64	NUM
ejpam-6082	423	93	38	38	NUM
ejpam-6082	423	94	1	1	NUM
ejpam-6082	423	95	.	.	NUM
ejpam-6082	423	96	64	64	NUM
ejpam-6082	423	97	38	38	NUM
ejpam-6082	423	98	2	2	NUM
ejpam-6082	423	99	.	.	NUM
ejpam-6082	423	100	18	18	NUM
ejpam-6082	423	101	26	26	NUM
ejpam-6082	423	102	2	2	NUM
ejpam-6082	423	103	.	.	NUM
ejpam-6082	423	104	18	18	NUM
ejpam-6082	423	105	26	26	NUM
ejpam-6082	423	106	2	2	NUM
ejpam-6082	423	107	.	.	X
ejpam-6082	423	108	72	72	NUM
ejpam-6082	423	109	14	14	NUM
ejpam-6082	423	110	2	2	NUM
ejpam-6082	423	111	.	.	X
ejpam-6082	423	112	72	72	NUM
ejpam-6082	423	113	14	14	NUM
ejpam-6082	423	114	3	3	NUM
ejpam-6082	423	115	.	.	X
ejpam-6082	423	116	26	26	NUM
ejpam-6082	423	117	02	02	NUM
ejpam-6082	423	118	3	3	NUM
ejpam-6082	423	119	.	.	X
ejpam-6082	423	120	26	26	NUM
ejpam-6082	423	121	02	02	NUM
ejpam-6082	423	122	3	3	NUM
ejpam-6082	423	123	.	.	X
ejpam-6082	423	124	79	79	NUM
ejpam-6082	423	125	9	9	NUM
ejpam-6082	423	126	3	3	NUM
ejpam-6082	423	127	.	.	NOUN
ejpam-6082	423	128	79	79	NUM
ejpam-6082	423	129	9	9	NUM
ejpam-6082	423	130	4	4	NUM
ejpam-6082	423	131	.	.	PUNCT
ejpam-6082	424	1	33	33	NUM
ejpam-6082	424	2	78	78	NUM
ejpam-6082	424	3	4	4	NUM
ejpam-6082	424	4	.	.	PUNCT
ejpam-6082	424	5	33	33	NUM
ejpam-6082	424	6	78	78	NUM
ejpam-6082	424	7	4	4	NUM
ejpam-6082	424	8	.	.	PUNCT
ejpam-6082	425	1	87	87	NUM
ejpam-6082	425	2	66	66	NUM
ejpam-6082	425	3	4	4	NUM
ejpam-6082	425	4	.	.	PUNCT
ejpam-6082	426	1	87	87	NUM
ejpam-6082	426	2	66	66	NUM
ejpam-6082	426	3	5	5	NUM
ejpam-6082	426	4	.	.	PUNCT
ejpam-6082	427	1	41	41	NUM
ejpam-6082	427	2	53	53	NUM
ejpam-6082	427	3	5	5	NUM
ejpam-6082	427	4	.	.	PUNCT
ejpam-6082	428	1	95	95	NUM
ejpam-6082	429	1	41	41	NUM
ejpam-6082	429	2	0.1	0.1	NUM
ejpam-6082	429	3	0.15	0.15	NUM
ejpam-6082	429	4	0.2	0.2	NUM
ejpam-6082	429	5	0.25	0.25	NUM
ejpam-6082	429	6	0.3	0.3	NUM
ejpam-6082	429	7	0.35	0.35	NUM
ejpam-6082	429	8	0.4	0.4	NUM
ejpam-6082	429	9	0	0	NUM
ejpam-6082	429	10	0.002	0.002	NUM
ejpam-6082	429	11	0.004	0.004	NUM
ejpam-6082	429	12	0.006	0.006	NUM
ejpam-6082	429	13	0.008	0.008	NUM
ejpam-6082	429	14	0.01	0.01	NUM
ejpam-6082	429	15	1	1	NUM
ejpam-6082	429	16	2	2	NUM
ejpam-6082	429	17	3	3	NUM
ejpam-6082	429	18	4	4	NUM
ejpam-6082	429	19	5	5	NUM
ejpam-6082	429	20	6	6	NUM
ejpam-6082	429	21	7	7	NUM
ejpam-6082	429	22	8	8	NUM
ejpam-6082	429	23	(	(	PUNCT
ejpam-6082	429	24	d	d	NOUN
ejpam-6082	429	25	)	)	PUNCT
ejpam-6082	429	26	r0	r0	NOUN
ejpam-6082	429	27	vs	vs	ADP
ejpam-6082	429	28	σ	σ	PROPN
ejpam-6082	429	29	and	and	CCONJ
ejpam-6082	429	30	β	β	X
ejpam-6082	429	31	(	(	PUNCT
ejpam-6082	429	32	e	e	NOUN
ejpam-6082	429	33	)	)	PUNCT
ejpam-6082	429	34	r0	r0	NOUN
ejpam-6082	429	35	vs	vs	ADP
ejpam-6082	429	36	µ	µ	NOUN
ejpam-6082	429	37	and	and	CCONJ
ejpam-6082	429	38	β	β	X
ejpam-6082	429	39	contour	contour	NOUN
ejpam-6082	429	40	plot	plot	NOUN
ejpam-6082	429	41	of	of	ADP
ejpam-6082	429	42	r0	r0	NOUN
ejpam-6082	429	43	for	for	ADP
ejpam-6082	429	44	vs	vs	ADP
ejpam-6082	429	45	0	0	NUM
ejpam-6082	429	46	.	.	NOUN
ejpam-6082	429	47	08	08	NUM
ejpam-6082	429	48	59	59	NUM
ejpam-6082	429	49	15	15	NUM
ejpam-6082	429	50	0	0	NUM
ejpam-6082	429	51	.	.	PUNCT
ejpam-6082	429	52	08	08	NUM
ejpam-6082	430	1	59	59	NUM
ejpam-6082	430	2	15	15	NUM
ejpam-6082	430	3	0	0	NUM
ejpam-6082	430	4	.	.	PUNCT
ejpam-6082	431	1	17	17	NUM
ejpam-6082	431	2	02	02	NUM
ejpam-6082	431	3	7	7	NUM
ejpam-6082	431	4	0	0	NUM
ejpam-6082	431	5	.	.	PUNCT
ejpam-6082	432	1	17	17	NUM
ejpam-6082	432	2	02	02	NUM
ejpam-6082	432	3	7	7	NUM
ejpam-6082	432	4	0	0	NUM
ejpam-6082	432	5	.	.	PUNCT
ejpam-6082	433	1	25	25	NUM
ejpam-6082	433	2	46	46	NUM
ejpam-6082	433	3	2	2	NUM
ejpam-6082	433	4	0	0	NUM
ejpam-6082	433	5	.	.	PUNCT
ejpam-6082	434	1	25	25	NUM
ejpam-6082	434	2	46	46	NUM
ejpam-6082	434	3	2	2	NUM
ejpam-6082	434	4	0	0	NUM
ejpam-6082	434	5	.	.	PUNCT
ejpam-6082	435	1	33	33	NUM
ejpam-6082	435	2	89	89	NUM
ejpam-6082	435	3	8	8	NUM
ejpam-6082	435	4	0	0	NUM
ejpam-6082	435	5	.	.	PUNCT
ejpam-6082	436	1	33	33	NUM
ejpam-6082	436	2	89	89	NUM
ejpam-6082	436	3	8	8	NUM
ejpam-6082	436	4	0	0	NUM
ejpam-6082	436	5	.	.	PUNCT
ejpam-6082	437	1	42	42	NUM
ejpam-6082	437	2	33	33	NUM
ejpam-6082	437	3	3	3	NUM
ejpam-6082	437	4	0	0	NUM
ejpam-6082	437	5	.	.	PUNCT
ejpam-6082	438	1	42	42	NUM
ejpam-6082	438	2	33	33	NUM
ejpam-6082	438	3	3	3	NUM
ejpam-6082	438	4	0	0	NUM
ejpam-6082	438	5	.	.	PUNCT
ejpam-6082	438	6	50	50	NUM
ejpam-6082	438	7	76	76	NUM
ejpam-6082	438	8	9	9	NUM
ejpam-6082	438	9	0	0	NUM
ejpam-6082	438	10	.	.	PUNCT
ejpam-6082	438	11	50	50	NUM
ejpam-6082	438	12	76	76	NUM
ejpam-6082	438	13	9	9	NUM
ejpam-6082	438	14	0	0	NUM
ejpam-6082	438	15	.	.	PUNCT
ejpam-6082	439	1	59	59	NUM
ejpam-6082	439	2	20	20	NUM
ejpam-6082	439	3	4	4	NUM
ejpam-6082	439	4	0	0	NUM
ejpam-6082	439	5	.	.	PUNCT
ejpam-6082	440	1	59	59	NUM
ejpam-6082	440	2	20	20	NUM
ejpam-6082	440	3	4	4	NUM
ejpam-6082	440	4	0	0	NUM
ejpam-6082	440	5	.	.	PUNCT
ejpam-6082	441	1	67	67	NUM
ejpam-6082	441	2	63	63	NUM
ejpam-6082	441	3	9	9	NUM
ejpam-6082	441	4	0	0	NUM
ejpam-6082	441	5	.	.	PUNCT
ejpam-6082	442	1	76	76	NUM
ejpam-6082	443	1	07	07	NUM
ejpam-6082	443	2	5	5	NUM
ejpam-6082	443	3	0.05	0.05	NUM
ejpam-6082	443	4	0.1	0.1	NUM
ejpam-6082	443	5	0.15	0.15	NUM
ejpam-6082	443	6	0.2	0.2	NUM
ejpam-6082	443	7	0.25	0.25	NUM
ejpam-6082	443	8	0.3	0.3	NUM
ejpam-6082	443	9	0.35	0.35	NUM
ejpam-6082	443	10	0.4	0.4	NUM
ejpam-6082	443	11	0.02	0.02	NUM
ejpam-6082	443	12	0.04	0.04	NUM
ejpam-6082	443	13	0.06	0.06	NUM
ejpam-6082	443	14	0.08	0.08	NUM
ejpam-6082	443	15	0.1	0.1	NUM
ejpam-6082	443	16	0	0	NUM
ejpam-6082	443	17	0.1	0.1	NUM
ejpam-6082	443	18	0.2	0.2	NUM
ejpam-6082	443	19	0.3	0.3	NUM
ejpam-6082	443	20	0.4	0.4	NUM
ejpam-6082	443	21	0.5	0.5	NUM
ejpam-6082	443	22	0.6	0.6	NUM
ejpam-6082	443	23	0.7	0.7	NUM
ejpam-6082	443	24	0.8	0.8	NUM
ejpam-6082	443	25	0.9	0.9	NUM
ejpam-6082	443	26	1	1	NUM
ejpam-6082	443	27	(	(	PUNCT
ejpam-6082	443	28	f	f	X
ejpam-6082	443	29	)	)	PUNCT
ejpam-6082	443	30	r0	r0	NOUN
ejpam-6082	443	31	vs	vs	ADP
ejpam-6082	443	32	µ	µ	NOUN
ejpam-6082	443	33	and	and	CCONJ
ejpam-6082	443	34	β	β	NOUN
ejpam-6082	443	35	figure	figure	NOUN
ejpam-6082	443	36	3	3	NUM
ejpam-6082	443	37	:	:	PUNCT
ejpam-6082	443	38	3d	3d	NUM
ejpam-6082	443	39	sensitivity	sensitivity	NOUN
ejpam-6082	443	40	analysis	analysis	NOUN
ejpam-6082	443	41	profiles	profile	NOUN
ejpam-6082	443	42	showing	show	VERB
ejpam-6082	443	43	the	the	DET
ejpam-6082	443	44	impact	impact	NOUN
ejpam-6082	443	45	of	of	ADP
ejpam-6082	443	46	various	various	ADJ
ejpam-6082	443	47	parameter	parameter	NOUN
ejpam-6082	443	48	pairs	pair	NOUN
ejpam-6082	443	49	(	(	PUNCT
ejpam-6082	443	50	σ	σ	NOUN
ejpam-6082	443	51	,	,	PUNCT
ejpam-6082	443	52	β	β	X
ejpam-6082	443	53	,	,	PUNCT
ejpam-6082	443	54	µ	µ	NOUN
ejpam-6082	443	55	)	)	PUNCT
ejpam-6082	443	56	on	on	ADP
ejpam-6082	443	57	the	the	DET
ejpam-6082	443	58	basic	basic	ADJ
ejpam-6082	443	59	reproduction	reproduction	NOUN
ejpam-6082	443	60	number	number	NOUN
ejpam-6082	443	61	r0	r0	NOUN
ejpam-6082	443	62	.	.	PUNCT
ejpam-6082	444	1	k.	k.	PROPN
ejpam-6082	444	2	guedri	guedri	PROPN
ejpam-6082	444	3	et	et	PROPN
ejpam-6082	444	4	al	al	PROPN
ejpam-6082	444	5	.	.	PUNCT
ejpam-6082	444	6	/	/	SYM
ejpam-6082	444	7	eur	eur	PROPN
ejpam-6082	444	8	.	.	PUNCT
ejpam-6082	445	1	j.	j.	PROPN
ejpam-6082	445	2	pure	pure	PROPN
ejpam-6082	445	3	appl	appl	PROPN
ejpam-6082	445	4	.	.	PROPN
ejpam-6082	445	5	math	math	PROPN
ejpam-6082	445	6	,	,	PUNCT
ejpam-6082	445	7	18	18	NUM
ejpam-6082	445	8	(	(	PUNCT
ejpam-6082	445	9	2	2	NUM
ejpam-6082	445	10	)	)	PUNCT
ejpam-6082	445	11	(	(	PUNCT
ejpam-6082	445	12	2025	2025	NUM
ejpam-6082	445	13	)	)	PUNCT
ejpam-6082	445	14	,	,	PUNCT
ejpam-6082	445	15	6082	6082	NUM
ejpam-6082	445	16	21	21	NUM
ejpam-6082	445	17	of	of	ADP
ejpam-6082	445	18	39	39	NUM
ejpam-6082	445	19	(	(	PUNCT
ejpam-6082	445	20	a	a	PRON
ejpam-6082	445	21	)	)	PUNCT
ejpam-6082	445	22	r0	r0	NOUN
ejpam-6082	445	23	vs	vs	ADP
ejpam-6082	445	24	ω1	ω1	PROPN
ejpam-6082	445	25	and	and	CCONJ
ejpam-6082	445	26	α2	α2	ADJ
ejpam-6082	445	27	contour	contour	NOUN
ejpam-6082	445	28	plot	plot	NOUN
ejpam-6082	445	29	of	of	ADP
ejpam-6082	445	30	r0	r0	NOUN
ejpam-6082	445	31	for	for	ADP
ejpam-6082	445	32	1	1	NUM
ejpam-6082	445	33	vs	vs	ADP
ejpam-6082	445	34	2	2	NUM
ejpam-6082	445	35	0.002902	0.002902	NUM
ejpam-6082	445	36	0	0	NUM
ejpam-6082	445	37	.	.	PUNCT
ejpam-6082	445	38	00	00	NUM
ejpam-6082	446	1	31	31	NUM
ejpam-6082	446	2	04	04	NUM
ejpam-6082	446	3	9	9	NUM
ejpam-6082	446	4	0.0031049	0.0031049	NUM
ejpam-6082	446	5	0	0	NUM
ejpam-6082	446	6	.	.	PUNCT
ejpam-6082	446	7	00	00	NUM
ejpam-6082	447	1	33	33	NUM
ejpam-6082	447	2	07	07	NUM
ejpam-6082	447	3	8	8	NUM
ejpam-6082	447	4	0.0033078	0.0033078	NUM
ejpam-6082	447	5	0	0	NUM
ejpam-6082	447	6	.	.	PUNCT
ejpam-6082	447	7	00	00	NUM
ejpam-6082	447	8	35	35	NUM
ejpam-6082	447	9	10	10	NUM
ejpam-6082	447	10	7	7	NUM
ejpam-6082	447	11	0	0	NUM
ejpam-6082	447	12	.	.	PUNCT
ejpam-6082	447	13	00	00	NUM
ejpam-6082	447	14	35	35	NUM
ejpam-6082	447	15	10	10	NUM
ejpam-6082	447	16	7	7	NUM
ejpam-6082	447	17	0	0	NUM
ejpam-6082	447	18	.	.	PUNCT
ejpam-6082	447	19	00	00	NUM
ejpam-6082	448	1	37	37	NUM
ejpam-6082	448	2	13	13	NUM
ejpam-6082	448	3	5	5	NUM
ejpam-6082	448	4	0	0	NUM
ejpam-6082	448	5	.	.	PUNCT
ejpam-6082	448	6	00	00	NUM
ejpam-6082	449	1	37	37	NUM
ejpam-6082	449	2	13	13	NUM
ejpam-6082	449	3	5	5	NUM
ejpam-6082	449	4	0	0	NUM
ejpam-6082	449	5	.	.	PUNCT
ejpam-6082	449	6	00	00	NUM
ejpam-6082	450	1	39	39	NUM
ejpam-6082	450	2	16	16	NUM
ejpam-6082	450	3	4	4	NUM
ejpam-6082	450	4	0	0	NUM
ejpam-6082	450	5	.	.	PUNCT
ejpam-6082	450	6	00	00	NUM
ejpam-6082	451	1	39	39	NUM
ejpam-6082	452	1	16	16	NUM
ejpam-6082	452	2	4	4	NUM
ejpam-6082	452	3	0.0041193	0.0041193	NUM
ejpam-6082	452	4	0.0041193	0.0041193	NUM
ejpam-6082	452	5	0.0043222	0.0043222	NUM
ejpam-6082	452	6	0.0043222	0.0043222	NUM
ejpam-6082	452	7	0.0045251	0.0045251	NUM
ejpam-6082	452	8	0.1	0.1	NUM
ejpam-6082	452	9	0.2	0.2	NUM
ejpam-6082	452	10	0.3	0.3	NUM
ejpam-6082	452	11	0.4	0.4	NUM
ejpam-6082	452	12	0.5	0.5	NUM
ejpam-6082	452	13	1	1	NUM
ejpam-6082	452	14	0.2	0.2	NUM
ejpam-6082	452	15	0.3	0.3	NUM
ejpam-6082	452	16	0.4	0.4	NUM
ejpam-6082	452	17	0.5	0.5	NUM
ejpam-6082	452	18	0.6	0.6	NUM
ejpam-6082	452	19	0.7	0.7	NUM
ejpam-6082	452	20	0.8	0.8	NUM
ejpam-6082	452	21	0.9	0.9	NUM
ejpam-6082	452	22	2	2	NUM
ejpam-6082	452	23	0	0	NUM
ejpam-6082	452	24	0.2	0.2	NUM
ejpam-6082	452	25	0.4	0.4	NUM
ejpam-6082	452	26	0.6	0.6	NUM
ejpam-6082	452	27	0.8	0.8	NUM
ejpam-6082	452	28	1	1	NUM
ejpam-6082	452	29	(	(	PUNCT
ejpam-6082	452	30	b	b	NOUN
ejpam-6082	452	31	)	)	PUNCT
ejpam-6082	452	32	r0	r0	NOUN
ejpam-6082	452	33	vs	vs	ADP
ejpam-6082	452	34	ω1	ω1	PROPN
ejpam-6082	452	35	and	and	CCONJ
ejpam-6082	452	36	α2	α2	PROPN
ejpam-6082	452	37	(	(	PUNCT
ejpam-6082	452	38	c	c	NOUN
ejpam-6082	452	39	)	)	PUNCT
ejpam-6082	452	40	r0	r0	NOUN
ejpam-6082	452	41	vs	vs	ADP
ejpam-6082	452	42	µ	µ	NOUN
ejpam-6082	452	43	and	and	CCONJ
ejpam-6082	452	44	α1	α1	PROPN
ejpam-6082	452	45	contour	contour	NOUN
ejpam-6082	452	46	plot	plot	NOUN
ejpam-6082	452	47	of	of	ADP
ejpam-6082	452	48	r0	r0	NOUN
ejpam-6082	452	49	for	for	ADP
ejpam-6082	452	50	1	1	NUM
ejpam-6082	452	51	vs	vs	ADP
ejpam-6082	452	52	0.00407750.004185	0.00407750.004185	NOUN
ejpam-6082	452	53	0.0042925	0.0042925	NUM
ejpam-6082	452	54	0.0042925	0.0042925	NUM
ejpam-6082	452	55	0.0044	0.0044	NUM
ejpam-6082	452	56	0.0044	0.0044	NUM
ejpam-6082	452	57	0.0045075	0.0045075	NUM
ejpam-6082	453	1	0.0045075	0.0045075	NUM
ejpam-6082	453	2	0.004615	0.004615	NUM
ejpam-6082	453	3	0.004615	0.004615	NUM
ejpam-6082	453	4	0.00472260.0048301	0.00472260.0048301	NUM
ejpam-6082	453	5	0.1	0.1	NUM
ejpam-6082	453	6	0.2	0.2	NUM
ejpam-6082	453	7	0.3	0.3	NUM
ejpam-6082	453	8	0.4	0.4	NUM
ejpam-6082	453	9	0.5	0.5	NUM
ejpam-6082	453	10	0.6	0.6	NUM
ejpam-6082	453	11	0.7	0.7	NUM
ejpam-6082	453	12	0.8	0.8	NUM
ejpam-6082	453	13	1	1	NUM
ejpam-6082	453	14	0.005	0.005	NUM
ejpam-6082	453	15	0.01	0.01	NUM
ejpam-6082	453	16	0.015	0.015	NUM
ejpam-6082	453	17	0.02	0.02	NUM
ejpam-6082	453	18	0.025	0.025	NUM
ejpam-6082	453	19	0.03	0.03	NUM
ejpam-6082	453	20	0	0	NUM
ejpam-6082	453	21	0.2	0.2	NUM
ejpam-6082	453	22	0.4	0.4	NUM
ejpam-6082	453	23	0.6	0.6	NUM
ejpam-6082	453	24	0.8	0.8	NUM
ejpam-6082	453	25	1	1	NUM
ejpam-6082	453	26	(	(	PUNCT
ejpam-6082	453	27	d	d	NOUN
ejpam-6082	453	28	)	)	PUNCT
ejpam-6082	453	29	r0	r0	NOUN
ejpam-6082	453	30	vs	vs	ADP
ejpam-6082	453	31	µ	µ	NOUN
ejpam-6082	453	32	and	and	CCONJ
ejpam-6082	453	33	α1	α1	PROPN
ejpam-6082	453	34	(	(	PUNCT
ejpam-6082	453	35	e	e	NOUN
ejpam-6082	453	36	)	)	PUNCT
ejpam-6082	453	37	r0	r0	NOUN
ejpam-6082	453	38	vs	vs	ADP
ejpam-6082	453	39	α2	α2	ADJ
ejpam-6082	453	40	and	and	CCONJ
ejpam-6082	453	41	α1	α1	PROPN
ejpam-6082	453	42	contour	contour	NOUN
ejpam-6082	453	43	plot	plot	NOUN
ejpam-6082	453	44	of	of	ADP
ejpam-6082	453	45	r0	r0	NOUN
ejpam-6082	453	46	for	for	ADP
ejpam-6082	453	47	2	2	NUM
ejpam-6082	453	48	vs	vs	ADP
ejpam-6082	453	49	1	1	NUM
ejpam-6082	453	50	0.004333	0.004333	NUM
ejpam-6082	453	51	0.004364	0.004364	NUM
ejpam-6082	453	52	0.004364	0.004364	NUM
ejpam-6082	453	53	0.004395	0.004395	NUM
ejpam-6082	453	54	0.004395	0.004395	NUM
ejpam-6082	453	55	0.0044261	0.0044261	NUM
ejpam-6082	453	56	0.0044261	0.0044261	NUM
ejpam-6082	453	57	0.0044571	0.0044571	NUM
ejpam-6082	453	58	0.0044571	0.0044571	NUM
ejpam-6082	453	59	0.00448810.0045192	0.00448810.0045192	NUM
ejpam-6082	453	60	0.4	0.4	NUM
ejpam-6082	453	61	0.5	0.5	NUM
ejpam-6082	453	62	0.6	0.6	NUM
ejpam-6082	453	63	0.7	0.7	NUM
ejpam-6082	453	64	0.8	0.8	NUM
ejpam-6082	453	65	0.9	0.9	NUM
ejpam-6082	453	66	1	1	NUM
ejpam-6082	453	67	2	2	NUM
ejpam-6082	453	68	0.4	0.4	NUM
ejpam-6082	453	69	0.5	0.5	NUM
ejpam-6082	453	70	0.6	0.6	NUM
ejpam-6082	453	71	0.7	0.7	NUM
ejpam-6082	453	72	0.8	0.8	NUM
ejpam-6082	453	73	0.9	0.9	NUM
ejpam-6082	453	74	1	1	NUM
ejpam-6082	453	75	1	1	NUM
ejpam-6082	453	76	0	0	NUM
ejpam-6082	453	77	0.2	0.2	NUM
ejpam-6082	453	78	0.4	0.4	NUM
ejpam-6082	453	79	0.6	0.6	NUM
ejpam-6082	453	80	0.8	0.8	NUM
ejpam-6082	453	81	1	1	NUM
ejpam-6082	453	82	(	(	PUNCT
ejpam-6082	453	83	f	f	X
ejpam-6082	453	84	)	)	PUNCT
ejpam-6082	453	85	r0	r0	NOUN
ejpam-6082	453	86	vs	vs	ADP
ejpam-6082	453	87	α2	α2	ADJ
ejpam-6082	453	88	and	and	CCONJ
ejpam-6082	453	89	α1	α1	PROPN
ejpam-6082	453	90	figure	figure	NOUN
ejpam-6082	453	91	4	4	NUM
ejpam-6082	453	92	:	:	PUNCT
ejpam-6082	453	93	3d	3d	NUM
ejpam-6082	453	94	sensitivity	sensitivity	NOUN
ejpam-6082	453	95	analysis	analysis	NOUN
ejpam-6082	453	96	profiles	profile	NOUN
ejpam-6082	453	97	showing	show	VERB
ejpam-6082	453	98	the	the	DET
ejpam-6082	453	99	impact	impact	NOUN
ejpam-6082	453	100	of	of	ADP
ejpam-6082	453	101	various	various	ADJ
ejpam-6082	453	102	parameter	parameter	NOUN
ejpam-6082	453	103	pairs	pair	NOUN
ejpam-6082	453	104	(	(	PUNCT
ejpam-6082	453	105	ω1	ω1	PROPN
ejpam-6082	453	106	,	,	PUNCT
ejpam-6082	453	107	α1	α1	PROPN
ejpam-6082	453	108	,	,	PUNCT
ejpam-6082	453	109	α2	α2	ADJ
ejpam-6082	453	110	)	)	PUNCT
ejpam-6082	453	111	on	on	ADP
ejpam-6082	453	112	the	the	DET
ejpam-6082	453	113	basic	basic	ADJ
ejpam-6082	453	114	reproduction	reproduction	NOUN
ejpam-6082	453	115	number	number	NOUN
ejpam-6082	453	116	r0	r0	NOUN
ejpam-6082	453	117	.	.	PUNCT
ejpam-6082	454	1	k.	k.	PROPN
ejpam-6082	454	2	guedri	guedri	PROPN
ejpam-6082	454	3	et	et	PROPN
ejpam-6082	454	4	al	al	PROPN
ejpam-6082	454	5	.	.	PUNCT
ejpam-6082	454	6	/	/	SYM
ejpam-6082	454	7	eur	eur	PROPN
ejpam-6082	454	8	.	.	PUNCT
ejpam-6082	455	1	j.	j.	PROPN
ejpam-6082	455	2	pure	pure	PROPN
ejpam-6082	455	3	appl	appl	PROPN
ejpam-6082	455	4	.	.	PROPN
ejpam-6082	455	5	math	math	PROPN
ejpam-6082	455	6	,	,	PUNCT
ejpam-6082	455	7	18	18	NUM
ejpam-6082	455	8	(	(	PUNCT
ejpam-6082	455	9	2	2	NUM
ejpam-6082	455	10	)	)	PUNCT
ejpam-6082	455	11	(	(	PUNCT
ejpam-6082	455	12	2025	2025	NUM
ejpam-6082	455	13	)	)	PUNCT
ejpam-6082	455	14	,	,	PUNCT
ejpam-6082	455	15	6082	6082	NUM
ejpam-6082	455	16	22	22	NUM
ejpam-6082	455	17	of	of	ADP
ejpam-6082	455	18	39	39	NUM
ejpam-6082	455	19	9	9	NUM
ejpam-6082	455	20	.	.	PUNCT
ejpam-6082	455	21	numerical	numerical	ADJ
ejpam-6082	455	22	scheme	scheme	NOUN
ejpam-6082	455	23	in	in	ADP
ejpam-6082	455	24	this	this	DET
ejpam-6082	455	25	section	section	NOUN
ejpam-6082	455	26	,	,	PUNCT
ejpam-6082	455	27	we	we	PRON
ejpam-6082	455	28	present	present	VERB
ejpam-6082	455	29	the	the	DET
ejpam-6082	455	30	numerical	numerical	ADJ
ejpam-6082	455	31	simulations	simulation	NOUN
ejpam-6082	455	32	of	of	ADP
ejpam-6082	455	33	the	the	DET
ejpam-6082	455	34	fractional	fractional	ADJ
ejpam-6082	455	35	-	-	PUNCT
ejpam-6082	455	36	order	order	NOUN
ejpam-6082	455	37	reaction	reaction	NOUN
ejpam-6082	455	38	diffusion	diffusion	NOUN
ejpam-6082	455	39	model	model	NOUN
ejpam-6082	455	40	(	(	PUNCT
ejpam-6082	455	41	2	2	NUM
ejpam-6082	455	42	)	)	PUNCT
ejpam-6082	455	43	.	.	PUNCT
ejpam-6082	456	1	the	the	DET
ejpam-6082	456	2	fractional	fractional	ADJ
ejpam-6082	456	3	-	-	PUNCT
ejpam-6082	456	4	order	order	NOUN
ejpam-6082	456	5	derivatives	derivative	NOUN
ejpam-6082	456	6	are	be	AUX
ejpam-6082	456	7	approximated	approximate	VERB
ejpam-6082	456	8	using	use	VERB
ejpam-6082	456	9	a	a	DET
ejpam-6082	456	10	forward	forward	ADJ
ejpam-6082	456	11	finite	finite	ADJ
ejpam-6082	456	12	difference	difference	NOUN
ejpam-6082	456	13	scheme	scheme	NOUN
ejpam-6082	456	14	,	,	PUNCT
ejpam-6082	456	15	while	while	SCONJ
ejpam-6082	456	16	the	the	DET
ejpam-6082	456	17	diffusion	diffusion	NOUN
ejpam-6082	456	18	operator	operator	NOUN
ejpam-6082	456	19	is	be	AUX
ejpam-6082	456	20	discretized	discretize	VERB
ejpam-6082	456	21	using	use	VERB
ejpam-6082	456	22	a	a	DET
ejpam-6082	456	23	centered	center	VERB
ejpam-6082	456	24	finite	finite	ADJ
ejpam-6082	456	25	difference	difference	NOUN
ejpam-6082	456	26	approach	approach	NOUN
ejpam-6082	456	27	.	.	PUNCT
ejpam-6082	457	1	the	the	DET
ejpam-6082	457	2	domain	domain	NOUN
ejpam-6082	457	3	is	be	AUX
ejpam-6082	457	4	given	give	VERB
ejpam-6082	457	5	by	by	ADP
ejpam-6082	457	6	u	u	NOUN
ejpam-6082	457	7	=	=	PUNCT
ejpam-6082	458	1	[	[	X
ejpam-6082	458	2	0	0	NUM
ejpam-6082	458	3	,	,	PUNCT
ejpam-6082	458	4	l	l	NOUN
ejpam-6082	458	5	]	]	X
ejpam-6082	458	6	,	,	PUNCT
ejpam-6082	458	7	with	with	ADP
ejpam-6082	458	8	temporal	temporal	ADJ
ejpam-6082	458	9	and	and	CCONJ
ejpam-6082	458	10	spatial	spatial	ADJ
ejpam-6082	458	11	step	step	NOUN
ejpam-6082	458	12	sizes	size	NOUN
ejpam-6082	458	13	ht	ht	PROPN
ejpam-6082	458	14	=	=	SYM
ejpam-6082	458	15	t	t	PROPN
ejpam-6082	458	16	n	n	PROPN
ejpam-6082	458	17	and	and	CCONJ
ejpam-6082	458	18	hx	hx	PROPN
ejpam-6082	458	19	=	=	SYM
ejpam-6082	458	20	l	l	PROPN
ejpam-6082	458	21	n	n	CCONJ
ejpam-6082	458	22	,	,	PUNCT
ejpam-6082	458	23	respectively	respectively	ADV
ejpam-6082	458	24	.	.	PUNCT
ejpam-6082	459	1	here	here	ADV
ejpam-6082	459	2	,	,	PUNCT
ejpam-6082	459	3	ti	ti	X
ejpam-6082	459	4	=	=	NOUN
ejpam-6082	459	5	iht	iht	NOUN
ejpam-6082	459	6	for	for	ADP
ejpam-6082	459	7	i	i	PRON
ejpam-6082	459	8	=	=	NOUN
ejpam-6082	459	9	0	0	NUM
ejpam-6082	459	10	,	,	PUNCT
ejpam-6082	459	11	1	1	NUM
ejpam-6082	459	12	,	,	PUNCT
ejpam-6082	459	13	.	.	PUNCT
ejpam-6082	459	14	.	.	PUNCT
ejpam-6082	460	1	.	.	PUNCT
ejpam-6082	461	1	,	,	PUNCT
ejpam-6082	461	2	n	n	PROPN
ejpam-6082	461	3	and	and	CCONJ
ejpam-6082	461	4	xj	xj	PROPN
ejpam-6082	461	5	=	=	PRON
ejpam-6082	461	6	jhx	jhx	VERB
ejpam-6082	461	7	for	for	ADP
ejpam-6082	461	8	j	j	PROPN
ejpam-6082	461	9	=	=	SYM
ejpam-6082	461	10	0	0	PROPN
ejpam-6082	461	11	,	,	PUNCT
ejpam-6082	461	12	1	1	NUM
ejpam-6082	461	13	,	,	PUNCT
ejpam-6082	461	14	.	.	PUNCT
ejpam-6082	461	15	.	.	PUNCT
ejpam-6082	462	1	.	.	PUNCT
ejpam-6082	463	1	,	,	PUNCT
ejpam-6082	463	2	n.	n.	NOUN
ejpam-6082	463	3	for	for	ADP
ejpam-6082	463	4	simplicity	simplicity	NOUN
ejpam-6082	463	5	,	,	PUNCT
ejpam-6082	463	6	the	the	DET
ejpam-6082	463	7	approximate	approximate	ADJ
ejpam-6082	463	8	solutions	solution	NOUN
ejpam-6082	463	9	for	for	ADP
ejpam-6082	463	10	s(ti	s(ti	PROPN
ejpam-6082	463	11	,	,	PUNCT
ejpam-6082	463	12	xj	xj	PROPN
ejpam-6082	463	13	)	)	PUNCT
ejpam-6082	463	14	,	,	PUNCT
ejpam-6082	463	15	v	v	X
ejpam-6082	463	16	(	(	PUNCT
ejpam-6082	463	17	ti	ti	PROPN
ejpam-6082	463	18	,	,	PUNCT
ejpam-6082	463	19	xj	xj	PROPN
ejpam-6082	463	20	)	)	PUNCT
ejpam-6082	463	21	,	,	PUNCT
ejpam-6082	463	22	e(ti	e(ti	PROPN
ejpam-6082	463	23	,	,	PUNCT
ejpam-6082	463	24	xj	xj	PROPN
ejpam-6082	463	25	)	)	PUNCT
ejpam-6082	463	26	,	,	PUNCT
ejpam-6082	463	27	np(ti	np(ti	PROPN
ejpam-6082	463	28	,	,	PUNCT
ejpam-6082	463	29	xj	xj	PROPN
ejpam-6082	463	30	)	)	PUNCT
ejpam-6082	463	31	,	,	PUNCT
ejpam-6082	463	32	p	p	X
ejpam-6082	463	33	(	(	PUNCT
ejpam-6082	463	34	ti	ti	PROPN
ejpam-6082	463	35	,	,	PUNCT
ejpam-6082	463	36	xj	xj	PROPN
ejpam-6082	463	37	)	)	PUNCT
ejpam-6082	463	38	,	,	PUNCT
ejpam-6082	463	39	r(ti	r(ti	PROPN
ejpam-6082	463	40	,	,	PUNCT
ejpam-6082	463	41	xj	xj	PROPN
ejpam-6082	463	42	)	)	PUNCT
ejpam-6082	463	43	,	,	PUNCT
ejpam-6082	463	44	and	and	CCONJ
ejpam-6082	463	45	a(ti	a(ti	NOUN
ejpam-6082	463	46	,	,	PUNCT
ejpam-6082	463	47	xj	xj	NOUN
ejpam-6082	463	48	)	)	PUNCT
ejpam-6082	463	49	are	be	AUX
ejpam-6082	463	50	denoted	denote	VERB
ejpam-6082	463	51	as	as	ADP
ejpam-6082	463	52	si	si	PROPN
ejpam-6082	463	53	j	j	PROPN
ejpam-6082	463	54	,	,	PUNCT
ejpam-6082	463	55	v	v	INTJ
ejpam-6082	463	56	i	i	PRON
ejpam-6082	463	57	j	j	PROPN
ejpam-6082	463	58	,	,	PUNCT
ejpam-6082	464	1	e	e	PROPN
ejpam-6082	464	2	i	i	PRON
ejpam-6082	464	3	j	j	PROPN
ejpam-6082	464	4	,	,	PUNCT
ejpam-6082	464	5	n	n	PROPN
ejpam-6082	465	1	i	i	PRON
ejpam-6082	465	2	p	p	PROPN
ejpam-6082	465	3	,	,	PUNCT
ejpam-6082	465	4	j	j	PROPN
ejpam-6082	465	5	,	,	PUNCT
ejpam-6082	465	6	p	p	X
ejpam-6082	466	1	i	i	PRON
ejpam-6082	466	2	j	j	PROPN
ejpam-6082	466	3	,	,	PUNCT
ejpam-6082	467	1	r	r	VERB
ejpam-6082	467	2	i	i	PRON
ejpam-6082	467	3	j	j	PROPN
ejpam-6082	467	4	,	,	PUNCT
ejpam-6082	467	5	and	and	CCONJ
ejpam-6082	467	6	a	a	DET
ejpam-6082	467	7	i	i	PROPN
ejpam-6082	467	8	j	j	PROPN
ejpam-6082	467	9	,	,	PUNCT
ejpam-6082	467	10	respectively	respectively	ADV
ejpam-6082	467	11	.	.	PUNCT
ejpam-6082	468	1	we	we	PRON
ejpam-6082	468	2	can	can	AUX
ejpam-6082	468	3	write	write	VERB
ejpam-6082	468	4	,	,	PUNCT
ejpam-6082	468	5	for	for	ADP
ejpam-6082	468	6	example	example	NOUN
ejpam-6082	468	7	,	,	PUNCT
ejpam-6082	468	8	the	the	DET
ejpam-6082	468	9	approximation	approximation	NOUN
ejpam-6082	468	10	of	of	ADP
ejpam-6082	468	11	c	c	PROPN
ejpam-6082	468	12	0	0	PUNCT
ejpam-6082	469	1	d	d	NOUN
ejpam-6082	469	2	α	α	PROPN
ejpam-6082	469	3	t	t	PROPN
ejpam-6082	469	4	s(ti	s(ti	PROPN
ejpam-6082	469	5	,	,	PUNCT
ejpam-6082	469	6	xj	xj	PROPN
ejpam-6082	469	7	)	)	PUNCT
ejpam-6082	469	8	and	and	CCONJ
ejpam-6082	469	9	∆s(ti	∆s(ti	PROPN
ejpam-6082	469	10	,	,	PUNCT
ejpam-6082	469	11	xj	xj	PROPN
ejpam-6082	469	12	)	)	PUNCT
ejpam-6082	469	13	,	,	PUNCT
ejpam-6082	469	14	respectively	respectively	ADV
ejpam-6082	469	15	,	,	PUNCT
ejpam-6082	469	16	as	as	SCONJ
ejpam-6082	469	17	follows	follow	VERB
ejpam-6082	469	18	:	:	PUNCT
ejpam-6082	469	19	c	c	NOUN
ejpam-6082	469	20	0	0	PUNCT
ejpam-6082	470	1	d	d	NOUN
ejpam-6082	470	2	α	α	PROPN
ejpam-6082	470	3	t	t	PROPN
ejpam-6082	470	4	s(ti	s(ti	PROPN
ejpam-6082	470	5	,	,	PUNCT
ejpam-6082	470	6	xj	xj	PROPN
ejpam-6082	470	7	)	)	PUNCT
ejpam-6082	471	1	≈	≈	PROPN
ejpam-6082	471	2	1	1	NUM
ejpam-6082	471	3	γ(2−	γ(2−	PROPN
ejpam-6082	471	4	α	α	NOUN
ejpam-6082	471	5	)	)	PUNCT
ejpam-6082	471	6	i∑	i∑	PROPN
ejpam-6082	471	7	l=0	l=0	PROPN
ejpam-6082	471	8	(	(	PUNCT
ejpam-6082	471	9	l	l	NOUN
ejpam-6082	471	10	+	+	CCONJ
ejpam-6082	471	11	1)1−α	1)1−α	NUM
ejpam-6082	471	12	−	−	NOUN
ejpam-6082	471	13	l1−α	l1−α	PROPN
ejpam-6082	471	14	hαt	hαt	PROPN
ejpam-6082	471	15	(	(	PUNCT
ejpam-6082	471	16	si+1−l	si+1−l	NOUN
ejpam-6082	471	17	j	j	NOUN
ejpam-6082	471	18	−	−	PROPN
ejpam-6082	471	19	si−l	si−l	PROPN
ejpam-6082	471	20	j	j	PROPN
ejpam-6082	471	21	)	)	PUNCT
ejpam-6082	471	22	,	,	PUNCT
ejpam-6082	471	23	and	and	CCONJ
ejpam-6082	471	24	∆s(ti	∆s(ti	NOUN
ejpam-6082	471	25	,	,	PUNCT
ejpam-6082	471	26	xj	xj	PROPN
ejpam-6082	471	27	)	)	PUNCT
ejpam-6082	472	1	≈	≈	PROPN
ejpam-6082	472	2	si	si	NOUN
ejpam-6082	473	1	j+1	j+1	ADV
ejpam-6082	473	2	−	−	PROPN
ejpam-6082	473	3	2si	2si	ADJ
ejpam-6082	473	4	j	j	PROPN
ejpam-6082	473	5	+	+	CCONJ
ejpam-6082	473	6	si	si	X
ejpam-6082	473	7	j−1	j−1	PROPN
ejpam-6082	473	8	h2x	h2x	PROPN
ejpam-6082	473	9	.	.	PUNCT
ejpam-6082	474	1	using	use	VERB
ejpam-6082	474	2	the	the	DET
ejpam-6082	474	3	discretization	discretization	NOUN
ejpam-6082	474	4	,	,	PUNCT
ejpam-6082	474	5	we	we	PRON
ejpam-6082	474	6	derive	derive	VERB
ejpam-6082	474	7	the	the	DET
ejpam-6082	474	8	following	follow	VERB
ejpam-6082	474	9	numerical	numerical	ADJ
ejpam-6082	474	10	schemes	scheme	NOUN
ejpam-6082	474	11	for	for	ADP
ejpam-6082	474	12	each	each	DET
ejpam-6082	474	13	compartment	compartment	NOUN
ejpam-6082	474	14	of	of	ADP
ejpam-6082	474	15	the	the	DET
ejpam-6082	474	16	model	model	NOUN
ejpam-6082	474	17	:	:	PUNCT
ejpam-6082	474	18	si+1	si+1	PROPN
ejpam-6082	474	19	j	j	NOUN
ejpam-6082	474	20	=	=	PUNCT
ejpam-6082	474	21	si	si	PROPN
ejpam-6082	474	22	j	j	PROPN
ejpam-6082	474	23	−	−	PROPN
ejpam-6082	474	24	i∑	i∑	PROPN
ejpam-6082	475	1	l=1	l=1	PROPN
ejpam-6082	475	2	(	(	PUNCT
ejpam-6082	475	3	l	l	NOUN
ejpam-6082	475	4	+	+	SYM
ejpam-6082	475	5	1)1−α	1)1−α	NUM
ejpam-6082	475	6	−	−	NOUN
ejpam-6082	475	7	l1−α	l1−α	PROPN
ejpam-6082	475	8	γ(2−	γ(2−	NOUN
ejpam-6082	475	9	α)hαt	α)hαt	PROPN
ejpam-6082	475	10	(	(	PUNCT
ejpam-6082	475	11	si+1−l	si+1−l	NOUN
ejpam-6082	475	12	j	j	NOUN
ejpam-6082	475	13	−	−	PROPN
ejpam-6082	475	14	si−l	si−l	PROPN
ejpam-6082	475	15	j	j	PROPN
ejpam-6082	475	16	)	)	PUNCT
ejpam-6082	476	1	+	+	CCONJ
ejpam-6082	476	2	ds	ds	PRON
ejpam-6082	476	3	γ(2−	γ(2−	NOUN
ejpam-6082	476	4	α)hαt	α)hαt	NUM
ejpam-6082	476	5	h2x	h2x	PROPN
ejpam-6082	476	6	(	(	PUNCT
ejpam-6082	476	7	si	si	NOUN
ejpam-6082	476	8	j+1	j+1	PROPN
ejpam-6082	476	9	−	−	PROPN
ejpam-6082	476	10	2si	2si	ADJ
ejpam-6082	476	11	j	j	PROPN
ejpam-6082	477	1	+	+	CCONJ
ejpam-6082	477	2	si	si	X
ejpam-6082	477	3	j−1	j−1	PROPN
ejpam-6082	477	4	)	)	PUNCT
ejpam-6082	478	1	+	+	NOUN
ejpam-6082	478	2	γ(2−	γ(2−	NOUN
ejpam-6082	478	3	α)hαt	α)hαt	NUM
ejpam-6082	478	4	[	[	PUNCT
ejpam-6082	478	5	λ	λ	X
ejpam-6082	479	1	+	+	CCONJ
ejpam-6082	480	1	ρ1r	ρ1r	NUM
ejpam-6082	481	1	i	i	PRON
ejpam-6082	481	2	j	j	PROPN
ejpam-6082	482	1	−	−	PROPN
ejpam-6082	482	2	(	(	PUNCT
ejpam-6082	482	3	λ+	λ+	PUNCT
ejpam-6082	482	4	δ	δ	NOUN
ejpam-6082	482	5	+	+	PROPN
ejpam-6082	482	6	µ)si	µ)si	PROPN
ejpam-6082	482	7	j	j	PROPN
ejpam-6082	482	8	]	]	PUNCT
ejpam-6082	482	9	,	,	PUNCT
ejpam-6082	482	10	v	v	ADP
ejpam-6082	482	11	i+1	i+1	PRON
ejpam-6082	483	1	j	j	PROPN
ejpam-6082	483	2	=	=	SYM
ejpam-6082	483	3	v	v	PROPN
ejpam-6082	484	1	i	i	PRON
ejpam-6082	484	2	j	j	PROPN
ejpam-6082	484	3	−	−	PROPN
ejpam-6082	484	4	i∑	i∑	PROPN
ejpam-6082	485	1	l=1	l=1	PROPN
ejpam-6082	485	2	(	(	PUNCT
ejpam-6082	485	3	l	l	NOUN
ejpam-6082	485	4	+	+	SYM
ejpam-6082	485	5	1)1−α	1)1−α	NUM
ejpam-6082	485	6	−	−	NOUN
ejpam-6082	485	7	l1−α	l1−α	PROPN
ejpam-6082	485	8	γ(2−	γ(2−	NOUN
ejpam-6082	485	9	α)hαt	α)hαt	PROPN
ejpam-6082	485	10	(	(	PUNCT
ejpam-6082	485	11	v	v	NUM
ejpam-6082	485	12	i+1−l	i+1−l	PROPN
ejpam-6082	486	1	j	j	PROPN
ejpam-6082	487	1	−	−	PROPN
ejpam-6082	487	2	v	v	PROPN
ejpam-6082	487	3	i−l	i−l	PROPN
ejpam-6082	487	4	j	j	PROPN
ejpam-6082	487	5	)	)	PUNCT
ejpam-6082	488	1	+	+	CCONJ
ejpam-6082	488	2	dv	dv	PROPN
ejpam-6082	488	3	γ(2−	γ(2−	PROPN
ejpam-6082	488	4	α)hαt	α)hαt	NUM
ejpam-6082	488	5	h2x	h2x	PROPN
ejpam-6082	489	1	(	(	PUNCT
ejpam-6082	489	2	v	v	NOUN
ejpam-6082	489	3	i	i	PRON
ejpam-6082	489	4	j+1	j+1	ADV
ejpam-6082	489	5	−	−	PROPN
ejpam-6082	489	6	2v	2v	NUM
ejpam-6082	489	7	i	i	PRON
ejpam-6082	489	8	j	j	PROPN
ejpam-6082	490	1	+	+	CCONJ
ejpam-6082	490	2	v	v	NOUN
ejpam-6082	490	3	i	i	PROPN
ejpam-6082	490	4	j−1	j−1	PROPN
ejpam-6082	490	5	)	)	PUNCT
ejpam-6082	491	1	+	+	NOUN
ejpam-6082	491	2	γ(2−	γ(2−	NOUN
ejpam-6082	491	3	α)hαt	α)hαt	PROPN
ejpam-6082	491	4	[	[	PUNCT
ejpam-6082	491	5	δsi	δsi	NOUN
ejpam-6082	491	6	j	j	PROPN
ejpam-6082	491	7	−	−	PROPN
ejpam-6082	492	1	(	(	PUNCT
ejpam-6082	492	2	1−	1−	NUM
ejpam-6082	492	3	δ)λv	δ)λv	PROPN
ejpam-6082	492	4	i	i	PRON
ejpam-6082	492	5	j	j	PROPN
ejpam-6082	493	1	−	−	PROPN
ejpam-6082	493	2	(	(	PUNCT
ejpam-6082	493	3	γ	γ	X
ejpam-6082	493	4	+	+	NOUN
ejpam-6082	493	5	µ)v	µ)v	ADJ
ejpam-6082	494	1	i	i	NOUN
ejpam-6082	494	2	j	j	X
ejpam-6082	494	3	]	]	PUNCT
ejpam-6082	494	4	,	,	PUNCT
ejpam-6082	494	5	ei+1	ei+1	PROPN
ejpam-6082	494	6	j	j	PROPN
ejpam-6082	494	7	=	=	PUNCT
ejpam-6082	494	8	ei	ei	PROPN
ejpam-6082	494	9	j	j	PROPN
ejpam-6082	494	10	−	−	PROPN
ejpam-6082	494	11	i∑	i∑	PROPN
ejpam-6082	494	12	l=1	l=1	PROPN
ejpam-6082	494	13	(	(	PUNCT
ejpam-6082	494	14	l	l	NOUN
ejpam-6082	494	15	+	+	SYM
ejpam-6082	494	16	1)1−α	1)1−α	NUM
ejpam-6082	494	17	−	−	NOUN
ejpam-6082	494	18	l1−α	l1−α	PROPN
ejpam-6082	494	19	γ(2−	γ(2−	NOUN
ejpam-6082	494	20	α)hαt	α)hαt	PROPN
ejpam-6082	494	21	(	(	PUNCT
ejpam-6082	494	22	ei+1−l	ei+1−l	ADV
ejpam-6082	494	23	j	j	PROPN
ejpam-6082	494	24	−	−	PROPN
ejpam-6082	494	25	ei−l	ei−l	PROPN
ejpam-6082	494	26	j	j	PROPN
ejpam-6082	494	27	)	)	PUNCT
ejpam-6082	495	1	+	+	CCONJ
ejpam-6082	495	2	de	de	X
ejpam-6082	495	3	γ(2−	γ(2−	NOUN
ejpam-6082	495	4	α)hαt	α)hαt	PROPN
ejpam-6082	495	5	h2x	h2x	PROPN
ejpam-6082	495	6	(	(	PUNCT
ejpam-6082	495	7	ei	ei	ADP
ejpam-6082	495	8	j+1	j+1	CCONJ
ejpam-6082	495	9	−	−	NUM
ejpam-6082	495	10	2ei	2ei	ADJ
ejpam-6082	495	11	j	j	NOUN
ejpam-6082	496	1	+	+	CCONJ
ejpam-6082	496	2	ei	ei	X
ejpam-6082	496	3	j−1	j−1	PROPN
ejpam-6082	496	4	)	)	PUNCT
ejpam-6082	497	1	+	+	NOUN
ejpam-6082	497	2	γ(2−	γ(2−	NOUN
ejpam-6082	497	3	α)hαt	α)hαt	NUM
ejpam-6082	497	4	[	[	PUNCT
ejpam-6082	497	5	λsi	λsi	PUNCT
ejpam-6082	497	6	j	j	NOUN
ejpam-6082	497	7	+	+	CCONJ
ejpam-6082	497	8	(	(	PUNCT
ejpam-6082	497	9	1−	1−	NUM
ejpam-6082	497	10	δ)λv	δ)λv	PROPN
ejpam-6082	497	11	i	i	PRON
ejpam-6082	497	12	j	j	PROPN
ejpam-6082	498	1	−	−	PROPN
ejpam-6082	498	2	(	(	PUNCT
ejpam-6082	498	3	α1	α1	PROPN
ejpam-6082	498	4	+	+	CCONJ
ejpam-6082	498	5	α2	α2	ADJ
ejpam-6082	498	6	+	+	CCONJ
ejpam-6082	498	7	ω	ω	NUM
ejpam-6082	498	8	+	+	CCONJ
ejpam-6082	499	1	µ)ei	µ)ei	PROPN
ejpam-6082	499	2	j	j	PROPN
ejpam-6082	499	3	]	]	PUNCT
ejpam-6082	499	4	,	,	PUNCT
ejpam-6082	499	5	n	n	PROPN
ejpam-6082	499	6	i+1	i+1	SYM
ejpam-6082	499	7	p	p	X
ejpam-6082	499	8	,	,	PUNCT
ejpam-6082	499	9	j	j	PROPN
ejpam-6082	499	10	=	=	SYM
ejpam-6082	499	11	n	n	PROPN
ejpam-6082	499	12	i	i	PRON
ejpam-6082	499	13	p	p	NOUN
ejpam-6082	499	14	,	,	PUNCT
ejpam-6082	499	15	j−	j−	VERB
ejpam-6082	499	16	i∑	i∑	PROPN
ejpam-6082	500	1	l=1	l=1	PROPN
ejpam-6082	500	2	(	(	PUNCT
ejpam-6082	500	3	l	l	NOUN
ejpam-6082	500	4	+	+	SYM
ejpam-6082	500	5	1)1−α	1)1−α	NUM
ejpam-6082	500	6	−	−	NOUN
ejpam-6082	500	7	l1−α	l1−α	PROPN
ejpam-6082	500	8	γ(2−	γ(2−	NOUN
ejpam-6082	500	9	α)hαt	α)hαt	PROPN
ejpam-6082	500	10	(	(	PUNCT
ejpam-6082	500	11	n	n	CCONJ
ejpam-6082	500	12	i+1−l	i+1−l	PROPN
ejpam-6082	500	13	p	p	NOUN
ejpam-6082	500	14	,	,	PUNCT
ejpam-6082	500	15	j	j	PROPN
ejpam-6082	500	16	−n	−n	ADJ
ejpam-6082	500	17	i−l	i−l	VERB
ejpam-6082	500	18	p	p	NOUN
ejpam-6082	500	19	,	,	PUNCT
ejpam-6082	500	20	j	j	PROPN
ejpam-6082	500	21	)	)	PUNCT
ejpam-6082	501	1	+	+	PROPN
ejpam-6082	501	2	dnp	dnp	PROPN
ejpam-6082	501	3	γ(2−	γ(2−	PROPN
ejpam-6082	501	4	α)hαt	α)hαt	NUM
ejpam-6082	501	5	h2x	h2x	PROPN
ejpam-6082	502	1	(	(	PUNCT
ejpam-6082	502	2	n	n	NOUN
ejpam-6082	502	3	i	i	PRON
ejpam-6082	502	4	p	p	NOUN
ejpam-6082	502	5	,	,	PUNCT
ejpam-6082	502	6	j+1−2n	j+1−2n	NOUN
ejpam-6082	502	7	i	i	PRON
ejpam-6082	502	8	p	p	NOUN
ejpam-6082	502	9	,	,	PUNCT
ejpam-6082	502	10	j+n	j+n	PROPN
ejpam-6082	502	11	i	i	PRON
ejpam-6082	502	12	p	p	NOUN
ejpam-6082	502	13	,	,	PUNCT
ejpam-6082	502	14	j−1	j−1	PROPN
ejpam-6082	502	15	)	)	PUNCT
ejpam-6082	503	1	+	+	NOUN
ejpam-6082	503	2	γ(2−	γ(2−	NOUN
ejpam-6082	503	3	α)hαt	α)hαt	NUM
ejpam-6082	503	4	[	[	PUNCT
ejpam-6082	503	5	α1e	α1e	NOUN
ejpam-6082	503	6	i	i	NOUN
ejpam-6082	503	7	j	j	PROPN
ejpam-6082	504	1	−	−	PROPN
ejpam-6082	504	2	(	(	PUNCT
ejpam-6082	504	3	σ	σ	PROPN
ejpam-6082	504	4	+	+	CCONJ
ejpam-6082	504	5	µ+	µ+	X
ejpam-6082	504	6	ω1)n	ω1)n	NOUN
ejpam-6082	505	1	i	i	PRON
ejpam-6082	505	2	p	p	PROPN
ejpam-6082	505	3	,	,	PUNCT
ejpam-6082	505	4	j	j	PROPN
ejpam-6082	505	5	]	]	PUNCT
ejpam-6082	505	6	,	,	PUNCT
ejpam-6082	505	7	p	p	X
ejpam-6082	505	8	i+1	i+1	PRON
ejpam-6082	505	9	j	j	NOUN
ejpam-6082	506	1	=	=	PUNCT
ejpam-6082	506	2	p	p	X
ejpam-6082	507	1	i	i	PRON
ejpam-6082	507	2	j	j	PROPN
ejpam-6082	507	3	−	−	PROPN
ejpam-6082	507	4	i∑	i∑	PROPN
ejpam-6082	508	1	l=1	l=1	PROPN
ejpam-6082	508	2	(	(	PUNCT
ejpam-6082	508	3	l	l	NOUN
ejpam-6082	508	4	+	+	SYM
ejpam-6082	508	5	1)1−α	1)1−α	NUM
ejpam-6082	508	6	−	−	NOUN
ejpam-6082	508	7	l1−α	l1−α	PROPN
ejpam-6082	508	8	γ(2−	γ(2−	NOUN
ejpam-6082	508	9	α)hαt	α)hαt	PROPN
ejpam-6082	508	10	(	(	PUNCT
ejpam-6082	508	11	p	p	NOUN
ejpam-6082	508	12	i+1−l	i+1−l	PROPN
ejpam-6082	508	13	j	j	PROPN
ejpam-6082	509	1	−	−	PROPN
ejpam-6082	509	2	p	p	PROPN
ejpam-6082	509	3	i−l	i−l	PROPN
ejpam-6082	509	4	j	j	PROPN
ejpam-6082	509	5	)	)	PUNCT
ejpam-6082	510	1	+	+	CCONJ
ejpam-6082	510	2	dp	dp	NOUN
ejpam-6082	510	3	γ(2−	γ(2−	NOUN
ejpam-6082	510	4	α)hαt	α)hαt	NUM
ejpam-6082	510	5	h2x	h2x	PROPN
ejpam-6082	511	1	(	(	PUNCT
ejpam-6082	511	2	p	p	X
ejpam-6082	511	3	i	i	NOUN
ejpam-6082	511	4	j+1	j+1	ADV
ejpam-6082	511	5	−	−	NUM
ejpam-6082	511	6	2p	2p	NUM
ejpam-6082	512	1	i	i	PRON
ejpam-6082	512	2	j	j	PROPN
ejpam-6082	513	1	+	+	CCONJ
ejpam-6082	513	2	p	p	X
ejpam-6082	513	3	i	i	PROPN
ejpam-6082	513	4	j−1	j−1	PROPN
ejpam-6082	513	5	)	)	PUNCT
ejpam-6082	513	6	k.	k.	PROPN
ejpam-6082	513	7	guedri	guedri	PROPN
ejpam-6082	513	8	et	et	PROPN
ejpam-6082	513	9	al	al	PROPN
ejpam-6082	513	10	.	.	PUNCT
ejpam-6082	513	11	/	/	SYM
ejpam-6082	513	12	eur	eur	PROPN
ejpam-6082	513	13	.	.	PUNCT
ejpam-6082	514	1	j.	j.	PROPN
ejpam-6082	514	2	pure	pure	PROPN
ejpam-6082	514	3	appl	appl	PROPN
ejpam-6082	514	4	.	.	PROPN
ejpam-6082	514	5	math	math	PROPN
ejpam-6082	514	6	,	,	PUNCT
ejpam-6082	514	7	18	18	NUM
ejpam-6082	514	8	(	(	PUNCT
ejpam-6082	514	9	2	2	NUM
ejpam-6082	514	10	)	)	PUNCT
ejpam-6082	514	11	(	(	PUNCT
ejpam-6082	514	12	2025	2025	NUM
ejpam-6082	514	13	)	)	PUNCT
ejpam-6082	514	14	,	,	PUNCT
ejpam-6082	514	15	6082	6082	NUM
ejpam-6082	514	16	23	23	NUM
ejpam-6082	514	17	of	of	ADP
ejpam-6082	514	18	39	39	NUM
ejpam-6082	514	19	+	+	NOUN
ejpam-6082	514	20	γ(2−	γ(2−	NOUN
ejpam-6082	514	21	α)hαt	α)hαt	PROPN
ejpam-6082	514	22	[	[	PUNCT
ejpam-6082	514	23	α2e	α2e	PUNCT
ejpam-6082	514	24	i	i	PRON
ejpam-6082	514	25	j	j	PROPN
ejpam-6082	515	1	−	−	PROPN
ejpam-6082	515	2	(	(	PUNCT
ejpam-6082	515	3	σ	σ	PROPN
ejpam-6082	515	4	+	+	CCONJ
ejpam-6082	515	5	µ+	µ+	PUNCT
ejpam-6082	515	6	ω2)p	ω2)p	ADJ
ejpam-6082	515	7	i	i	NOUN
ejpam-6082	515	8	j	j	PROPN
ejpam-6082	515	9	]	]	PUNCT
ejpam-6082	515	10	,	,	PUNCT
ejpam-6082	515	11	ri+1	ri+1	PROPN
ejpam-6082	515	12	j	j	PROPN
ejpam-6082	515	13	=	=	PROPN
ejpam-6082	515	14	ri	ri	PROPN
ejpam-6082	515	15	j	j	PROPN
ejpam-6082	515	16	−	−	PROPN
ejpam-6082	515	17	i∑	i∑	PROPN
ejpam-6082	516	1	l=1	l=1	PROPN
ejpam-6082	516	2	(	(	PUNCT
ejpam-6082	516	3	l	l	NOUN
ejpam-6082	516	4	+	+	SYM
ejpam-6082	516	5	1)1−α	1)1−α	NUM
ejpam-6082	516	6	−	−	NOUN
ejpam-6082	516	7	l1−α	l1−α	PROPN
ejpam-6082	516	8	γ(2−	γ(2−	NOUN
ejpam-6082	516	9	α)hαt	α)hαt	PROPN
ejpam-6082	516	10	(	(	PUNCT
ejpam-6082	516	11	ri+1−l	ri+1−l	ADP
ejpam-6082	516	12	j	j	PROPN
ejpam-6082	516	13	−ri−l	−ri−l	PROPN
ejpam-6082	516	14	j	j	PROPN
ejpam-6082	516	15	)	)	PUNCT
ejpam-6082	517	1	+	+	CCONJ
ejpam-6082	517	2	dr	dr	PROPN
ejpam-6082	517	3	γ(2−	γ(2−	PROPN
ejpam-6082	517	4	α)hαt	α)hαt	PROPN
ejpam-6082	517	5	h2x	h2x	PROPN
ejpam-6082	517	6	(	(	PUNCT
ejpam-6082	517	7	ri	ri	NOUN
ejpam-6082	517	8	j+1	j+1	ADV
ejpam-6082	518	1	−	−	PROPN
ejpam-6082	518	2	2ri	2ri	ADJ
ejpam-6082	518	3	j	j	PROPN
ejpam-6082	519	1	+	+	NOUN
ejpam-6082	519	2	ri	ri	PROPN
ejpam-6082	519	3	j−1	j−1	PROPN
ejpam-6082	519	4	)	)	PUNCT
ejpam-6082	520	1	+	+	NOUN
ejpam-6082	520	2	γ(2−	γ(2−	NOUN
ejpam-6082	520	3	α)hαt	α)hαt	PROPN
ejpam-6082	520	4	[	[	PUNCT
ejpam-6082	520	5	γv	γv	X
ejpam-6082	520	6	i	i	PROPN
ejpam-6082	520	7	j	j	PROPN
ejpam-6082	521	1	+	+	CCONJ
ejpam-6082	521	2	ωei	ωei	ADJ
ejpam-6082	521	3	j	j	PROPN
ejpam-6082	521	4	+	+	CCONJ
ejpam-6082	521	5	ω1n	ω1n	PROPN
ejpam-6082	521	6	i	i	PRON
ejpam-6082	521	7	p	p	X
ejpam-6082	521	8	,	,	PUNCT
ejpam-6082	521	9	j	j	PROPN
ejpam-6082	522	1	+	+	NUM
ejpam-6082	522	2	ω2p	ω2p	X
ejpam-6082	522	3	i	i	PRON
ejpam-6082	522	4	j	j	PROPN
ejpam-6082	523	1	−	−	PROPN
ejpam-6082	523	2	(	(	PUNCT
ejpam-6082	523	3	ρ+	ρ+	NUM
ejpam-6082	523	4	ρ1	ρ1	NOUN
ejpam-6082	523	5	+	+	PROPN
ejpam-6082	524	1	µ)ri	µ)ri	PROPN
ejpam-6082	524	2	j	j	PROPN
ejpam-6082	524	3	]	]	PUNCT
ejpam-6082	524	4	,	,	PUNCT
ejpam-6082	524	5	ai+1	ai+1	NUM
ejpam-6082	524	6	j	j	PROPN
ejpam-6082	525	1	=	=	PRON
ejpam-6082	525	2	ai	ai	VERB
ejpam-6082	525	3	j	j	PROPN
ejpam-6082	525	4	−	−	PROPN
ejpam-6082	525	5	i∑	i∑	PROPN
ejpam-6082	525	6	l=1	l=1	PROPN
ejpam-6082	525	7	(	(	PUNCT
ejpam-6082	525	8	l	l	NOUN
ejpam-6082	525	9	+	+	SYM
ejpam-6082	525	10	1)1−α	1)1−α	NUM
ejpam-6082	525	11	−	−	NOUN
ejpam-6082	525	12	l1−α	l1−α	PROPN
ejpam-6082	525	13	γ(2−	γ(2−	NOUN
ejpam-6082	525	14	α)hαt	α)hαt	PROPN
ejpam-6082	525	15	(	(	PUNCT
ejpam-6082	525	16	ai+1−l	ai+1−l	PROPN
ejpam-6082	525	17	j	j	PROPN
ejpam-6082	525	18	−ai−l	−ai−l	X
ejpam-6082	525	19	j	j	PROPN
ejpam-6082	525	20	)	)	PUNCT
ejpam-6082	526	1	+	+	CCONJ
ejpam-6082	526	2	da	da	PROPN
ejpam-6082	526	3	γ(2−	γ(2−	NOUN
ejpam-6082	526	4	α)hαt	α)hαt	NUM
ejpam-6082	526	5	h2x	h2x	PROPN
ejpam-6082	526	6	(	(	PUNCT
ejpam-6082	526	7	ai	ai	VERB
ejpam-6082	526	8	j+1	j+1	PROPN
ejpam-6082	526	9	−	−	PROPN
ejpam-6082	526	10	2ai	2ai	ADJ
ejpam-6082	526	11	j	j	PUNCT
ejpam-6082	527	1	+	+	NOUN
ejpam-6082	527	2	ai	ai	ADJ
ejpam-6082	527	3	j−1	j−1	PROPN
ejpam-6082	527	4	)	)	PUNCT
ejpam-6082	528	1	+	+	NOUN
ejpam-6082	528	2	γ(2−	γ(2−	NOUN
ejpam-6082	528	3	α)hαt	α)hαt	NUM
ejpam-6082	528	4	[	[	PUNCT
ejpam-6082	528	5	ρri	ρri	NOUN
ejpam-6082	528	6	j	j	NOUN
ejpam-6082	528	7	−	−	PROPN
ejpam-6082	529	1	(	(	PUNCT
ejpam-6082	529	2	σ	σ	PROPN
ejpam-6082	529	3	+	+	NUM
ejpam-6082	529	4	µ)ai	µ)ai	PROPN
ejpam-6082	529	5	j	j	PROPN
ejpam-6082	529	6	]	]	PUNCT
ejpam-6082	529	7	.	.	PUNCT
ejpam-6082	530	1	this	this	DET
ejpam-6082	530	2	numerical	numerical	ADJ
ejpam-6082	530	3	scheme	scheme	NOUN
ejpam-6082	530	4	allows	allow	VERB
ejpam-6082	530	5	for	for	ADP
ejpam-6082	530	6	a	a	DET
ejpam-6082	530	7	detailed	detailed	ADJ
ejpam-6082	530	8	investigation	investigation	NOUN
ejpam-6082	530	9	of	of	ADP
ejpam-6082	530	10	the	the	DET
ejpam-6082	530	11	spatiotemporal	spatiotemporal	ADJ
ejpam-6082	530	12	behavior	behavior	NOUN
ejpam-6082	530	13	of	of	ADP
ejpam-6082	530	14	the	the	DET
ejpam-6082	530	15	model	model	NOUN
ejpam-6082	530	16	under	under	ADP
ejpam-6082	530	17	various	various	ADJ
ejpam-6082	530	18	parameter	parameter	NOUN
ejpam-6082	530	19	configurations	configuration	NOUN
ejpam-6082	530	20	and	and	CCONJ
ejpam-6082	530	21	initial	initial	ADJ
ejpam-6082	530	22	conditions	condition	NOUN
ejpam-6082	530	23	.	.	PUNCT
ejpam-6082	531	1	10	10	NUM
ejpam-6082	531	2	.	.	PUNCT
ejpam-6082	531	3	numerical	numerical	ADJ
ejpam-6082	531	4	results	result	NOUN
ejpam-6082	531	5	and	and	CCONJ
ejpam-6082	531	6	discussion	discussion	NOUN
ejpam-6082	531	7	in	in	ADP
ejpam-6082	531	8	this	this	DET
ejpam-6082	531	9	section	section	NOUN
ejpam-6082	531	10	,	,	PUNCT
ejpam-6082	531	11	we	we	PRON
ejpam-6082	531	12	analyze	analyze	VERB
ejpam-6082	531	13	the	the	DET
ejpam-6082	531	14	numerical	numerical	ADJ
ejpam-6082	531	15	results	result	NOUN
ejpam-6082	531	16	obtained	obtain	VERB
ejpam-6082	531	17	from	from	ADP
ejpam-6082	531	18	the	the	DET
ejpam-6082	531	19	fractional	fractional	ADJ
ejpam-6082	531	20	-	-	PUNCT
ejpam-6082	531	21	order	order	NOUN
ejpam-6082	531	22	reaction	reaction	NOUN
ejpam-6082	531	23	-	-	PUNCT
ejpam-6082	531	24	diffusion	diffusion	NOUN
ejpam-6082	531	25	model	model	NOUN
ejpam-6082	531	26	.	.	PUNCT
ejpam-6082	532	1	the	the	DET
ejpam-6082	532	2	simulations	simulation	NOUN
ejpam-6082	532	3	are	be	AUX
ejpam-6082	532	4	conducted	conduct	VERB
ejpam-6082	532	5	using	use	VERB
ejpam-6082	532	6	the	the	DET
ejpam-6082	532	7	parameter	parameter	NOUN
ejpam-6082	532	8	values	value	NOUN
ejpam-6082	532	9	listed	list	VERB
ejpam-6082	532	10	in	in	ADP
ejpam-6082	532	11	table	table	NOUN
ejpam-6082	532	12	?	?	PUNCT
ejpam-6082	532	13	?	?	PUNCT
ejpam-6082	532	14	.	.	PUNCT
ejpam-6082	533	1	for	for	ADP
ejpam-6082	533	2	the	the	DET
ejpam-6082	533	3	spatial	spatial	ADJ
ejpam-6082	533	4	domain	domain	NOUN
ejpam-6082	533	5	,	,	PUNCT
ejpam-6082	533	6	we	we	PRON
ejpam-6082	533	7	consider	consider	VERB
ejpam-6082	533	8	the	the	DET
ejpam-6082	533	9	one	one	NUM
ejpam-6082	533	10	-	-	PUNCT
ejpam-6082	533	11	dimensional	dimensional	ADJ
ejpam-6082	533	12	interval	interval	NOUN
ejpam-6082	533	13	0	0	NUM
ejpam-6082	533	14	≤	≤	NUM
ejpam-6082	533	15	x	x	SYM
ejpam-6082	533	16	≤	≤	NUM
ejpam-6082	533	17	l	l	NOUN
ejpam-6082	533	18	,	,	PUNCT
ejpam-6082	533	19	while	while	SCONJ
ejpam-6082	533	20	for	for	ADP
ejpam-6082	533	21	the	the	DET
ejpam-6082	533	22	temporal	temporal	ADJ
ejpam-6082	533	23	domain	domain	NOUN
ejpam-6082	533	24	,	,	PUNCT
ejpam-6082	533	25	we	we	PRON
ejpam-6082	533	26	have	have	VERB
ejpam-6082	533	27	0	0	NUM
ejpam-6082	533	28	≤	≤	NUM
ejpam-6082	533	29	t	t	PROPN
ejpam-6082	533	30	≤	≤	PROPN
ejpam-6082	533	31	t	t	PROPN
ejpam-6082	533	32	.	.	PUNCT
ejpam-6082	534	1	the	the	DET
ejpam-6082	534	2	diffusion	diffusion	NOUN
ejpam-6082	534	3	coefficients	coefficient	NOUN
ejpam-6082	534	4	used	use	VERB
ejpam-6082	534	5	in	in	ADP
ejpam-6082	534	6	the	the	DET
ejpam-6082	534	7	model	model	NOUN
ejpam-6082	534	8	are	be	AUX
ejpam-6082	534	9	specified	specify	VERB
ejpam-6082	534	10	as	as	SCONJ
ejpam-6082	534	11	follows	follow	VERB
ejpam-6082	534	12	:	:	PUNCT
ejpam-6082	534	13	ds	ds	ADJ
ejpam-6082	534	14	=	=	NOUN
ejpam-6082	534	15	0.01	0.01	NUM
ejpam-6082	534	16	,	,	PUNCT
ejpam-6082	534	17	dv	dv	PROPN
ejpam-6082	534	18	=	=	PROPN
ejpam-6082	534	19	0.2	0.2	NUM
ejpam-6082	534	20	,	,	PUNCT
ejpam-6082	534	21	de	de	X
ejpam-6082	534	22	=	=	X
ejpam-6082	534	23	0.2	0.2	NUM
ejpam-6082	534	24	,	,	PUNCT
ejpam-6082	534	25	dnp	dnp	PROPN
ejpam-6082	534	26	=	=	PROPN
ejpam-6082	534	27	0.2	0.2	NUM
ejpam-6082	534	28	,	,	PUNCT
ejpam-6082	534	29	dp	dp	NOUN
ejpam-6082	534	30	=	=	NOUN
ejpam-6082	534	31	0.01	0.01	NUM
ejpam-6082	534	32	,	,	PUNCT
ejpam-6082	534	33	dr	dr	PROPN
ejpam-6082	534	34	=	=	PROPN
ejpam-6082	534	35	0.2	0.2	NUM
ejpam-6082	534	36	,	,	PUNCT
ejpam-6082	534	37	and	and	CCONJ
ejpam-6082	534	38	da	da	NOUN
ejpam-6082	534	39	=	=	SYM
ejpam-6082	534	40	0.1	0.1	NUM
ejpam-6082	534	41	(	(	PUNCT
ejpam-6082	534	42	all	all	PRON
ejpam-6082	534	43	in	in	ADP
ejpam-6082	534	44	km	km	NOUN
ejpam-6082	534	45	per	per	ADP
ejpam-6082	534	46	day	day	NOUN
ejpam-6082	534	47	)	)	PUNCT
ejpam-6082	534	48	.	.	PUNCT
ejpam-6082	535	1	the	the	DET
ejpam-6082	535	2	numerical	numerical	ADJ
ejpam-6082	535	3	solutions	solution	NOUN
ejpam-6082	535	4	for	for	ADP
ejpam-6082	535	5	the	the	DET
ejpam-6082	535	6	compartments	compartment	NOUN
ejpam-6082	535	7	s	s	PART
ejpam-6082	535	8	,	,	PUNCT
ejpam-6082	535	9	v	v	NOUN
ejpam-6082	535	10	,	,	PUNCT
ejpam-6082	535	11	e	e	NOUN
ejpam-6082	535	12	,	,	PUNCT
ejpam-6082	535	13	np	np	INTJ
ejpam-6082	535	14	,	,	PUNCT
ejpam-6082	535	15	p	p	X
ejpam-6082	535	16	,	,	PUNCT
ejpam-6082	535	17	r	r	NOUN
ejpam-6082	535	18	,	,	PUNCT
ejpam-6082	535	19	and	and	CCONJ
ejpam-6082	535	20	a	a	DET
ejpam-6082	535	21	demonstrate	demonstrate	NOUN
ejpam-6082	535	22	complex	complex	ADJ
ejpam-6082	535	23	spatiotemporal	spatiotemporal	ADJ
ejpam-6082	535	24	behaviors	behavior	NOUN
ejpam-6082	535	25	under	under	ADP
ejpam-6082	535	26	varying	vary	VERB
ejpam-6082	535	27	parameter	parameter	NOUN
ejpam-6082	535	28	configurations	configuration	NOUN
ejpam-6082	535	29	.	.	PUNCT
ejpam-6082	536	1	these	these	DET
ejpam-6082	536	2	solutions	solution	NOUN
ejpam-6082	536	3	reveal	reveal	VERB
ejpam-6082	536	4	the	the	DET
ejpam-6082	536	5	interactions	interaction	NOUN
ejpam-6082	536	6	among	among	ADP
ejpam-6082	536	7	susceptible	susceptible	ADJ
ejpam-6082	536	8	,	,	PUNCT
ejpam-6082	536	9	exposed	expose	VERB
ejpam-6082	536	10	,	,	PUNCT
ejpam-6082	536	11	vaccinated	vaccinated	ADJ
ejpam-6082	536	12	,	,	PUNCT
ejpam-6082	536	13	and	and	CCONJ
ejpam-6082	536	14	infected	infected	ADJ
ejpam-6082	536	15	individuals	individual	NOUN
ejpam-6082	536	16	over	over	ADP
ejpam-6082	536	17	time	time	NOUN
ejpam-6082	536	18	and	and	CCONJ
ejpam-6082	536	19	space	space	NOUN
ejpam-6082	536	20	.	.	PUNCT
ejpam-6082	537	1	the	the	DET
ejpam-6082	537	2	choice	choice	NOUN
ejpam-6082	537	3	of	of	ADP
ejpam-6082	537	4	diffusion	diffusion	NOUN
ejpam-6082	537	5	coefficients	coefficient	NOUN
ejpam-6082	537	6	significantly	significantly	ADV
ejpam-6082	537	7	influences	influence	VERB
ejpam-6082	537	8	the	the	DET
ejpam-6082	537	9	spatial	spatial	ADJ
ejpam-6082	537	10	spread	spread	NOUN
ejpam-6082	537	11	of	of	ADP
ejpam-6082	537	12	the	the	DET
ejpam-6082	537	13	disease	disease	NOUN
ejpam-6082	537	14	.	.	PUNCT
ejpam-6082	538	1	higher	high	ADJ
ejpam-6082	538	2	diffusion	diffusion	NOUN
ejpam-6082	538	3	coefficients	coefficient	NOUN
ejpam-6082	538	4	,	,	PUNCT
ejpam-6082	538	5	such	such	ADJ
ejpam-6082	538	6	as	as	ADP
ejpam-6082	538	7	de	de	PROPN
ejpam-6082	538	8	,	,	PUNCT
ejpam-6082	538	9	dnp	dnp	PROPN
ejpam-6082	538	10	,	,	PUNCT
ejpam-6082	538	11	and	and	CCONJ
ejpam-6082	538	12	dr	dr	PROPN
ejpam-6082	538	13	,	,	PUNCT
ejpam-6082	538	14	result	result	VERB
ejpam-6082	538	15	in	in	ADP
ejpam-6082	538	16	faster	fast	ADJ
ejpam-6082	538	17	spatial	spatial	ADJ
ejpam-6082	538	18	propagation	propagation	NOUN
ejpam-6082	538	19	of	of	ADP
ejpam-6082	538	20	the	the	DET
ejpam-6082	538	21	disease	disease	NOUN
ejpam-6082	538	22	,	,	PUNCT
ejpam-6082	538	23	leading	lead	VERB
ejpam-6082	538	24	to	to	ADP
ejpam-6082	538	25	more	more	ADV
ejpam-6082	538	26	homogeneous	homogeneous	ADJ
ejpam-6082	538	27	distributions	distribution	NOUN
ejpam-6082	538	28	of	of	ADP
ejpam-6082	538	29	infected	infect	VERB
ejpam-6082	538	30	individuals	individual	NOUN
ejpam-6082	538	31	across	across	ADP
ejpam-6082	538	32	the	the	DET
ejpam-6082	538	33	domain	domain	NOUN
ejpam-6082	538	34	.	.	PUNCT
ejpam-6082	539	1	conversely	conversely	ADV
ejpam-6082	539	2	,	,	PUNCT
ejpam-6082	539	3	smaller	small	ADJ
ejpam-6082	539	4	diffusion	diffusion	NOUN
ejpam-6082	539	5	coefficients	coefficient	NOUN
ejpam-6082	539	6	,	,	PUNCT
ejpam-6082	539	7	such	such	ADJ
ejpam-6082	539	8	as	as	ADP
ejpam-6082	539	9	ds	ds	ADJ
ejpam-6082	539	10	and	and	CCONJ
ejpam-6082	539	11	dp	dp	NOUN
ejpam-6082	539	12	,	,	PUNCT
ejpam-6082	539	13	create	create	VERB
ejpam-6082	539	14	localized	localized	ADJ
ejpam-6082	539	15	variations	variation	NOUN
ejpam-6082	539	16	,	,	PUNCT
ejpam-6082	539	17	maintaining	maintain	VERB
ejpam-6082	539	18	higher	high	ADJ
ejpam-6082	539	19	concentrations	concentration	NOUN
ejpam-6082	539	20	of	of	ADP
ejpam-6082	539	21	susceptible	susceptible	ADJ
ejpam-6082	539	22	and	and	CCONJ
ejpam-6082	539	23	infected	infected	ADJ
ejpam-6082	539	24	individuals	individual	NOUN
ejpam-6082	539	25	in	in	ADP
ejpam-6082	539	26	specific	specific	ADJ
ejpam-6082	539	27	regions	region	NOUN
ejpam-6082	539	28	.	.	PUNCT
ejpam-6082	540	1	the	the	DET
ejpam-6082	540	2	recovery	recovery	NOUN
ejpam-6082	540	3	rates	rate	NOUN
ejpam-6082	540	4	(	(	PUNCT
ejpam-6082	540	5	ω	ω	PROPN
ejpam-6082	540	6	,	,	PUNCT
ejpam-6082	540	7	ω1	ω1	PROPN
ejpam-6082	540	8	,	,	PUNCT
ejpam-6082	540	9	ω2	ω2	ADJ
ejpam-6082	540	10	)	)	PUNCT
ejpam-6082	540	11	and	and	CCONJ
ejpam-6082	540	12	the	the	PRON
ejpam-6082	540	13	of	of	ADP
ejpam-6082	540	14	progression	progression	NOUN
ejpam-6082	540	15	rates	rate	NOUN
ejpam-6082	540	16	(	(	PUNCT
ejpam-6082	540	17	α1	α1	PROPN
ejpam-6082	540	18	,	,	PUNCT
ejpam-6082	540	19	α2	α2	ADJ
ejpam-6082	540	20	)	)	PUNCT
ejpam-6082	540	21	decide	decide	VERB
ejpam-6082	540	22	the	the	DET
ejpam-6082	540	23	elements	element	NOUN
ejpam-6082	540	24	of	of	ADP
ejpam-6082	540	25	changes	change	NOUN
ejpam-6082	540	26	between	between	ADP
ejpam-6082	540	27	various	various	ADJ
ejpam-6082	540	28	compartments	compartment	NOUN
ejpam-6082	540	29	.	.	PUNCT
ejpam-6082	541	1	higher	high	ADJ
ejpam-6082	541	2	recovery	recovery	NOUN
ejpam-6082	541	3	rates	rate	NOUN
ejpam-6082	541	4	(	(	PUNCT
ejpam-6082	541	5	ω1	ω1	PROPN
ejpam-6082	541	6	,	,	PUNCT
ejpam-6082	541	7	ω2	ω2	ADJ
ejpam-6082	541	8	)	)	PUNCT
ejpam-6082	541	9	decline	decline	VERB
ejpam-6082	541	10	the	the	DET
ejpam-6082	541	11	span	span	NOUN
ejpam-6082	541	12	people	people	NOUN
ejpam-6082	541	13	spend	spend	VERB
ejpam-6082	541	14	in	in	ADP
ejpam-6082	541	15	the	the	DET
ejpam-6082	541	16	infected	infected	ADJ
ejpam-6082	541	17	class	class	NOUN
ejpam-6082	541	18	,	,	PUNCT
ejpam-6082	541	19	in	in	ADP
ejpam-6082	541	20	this	this	DET
ejpam-6082	541	21	way	way	NOUN
ejpam-6082	541	22	decreasing	decrease	VERB
ejpam-6082	541	23	the	the	DET
ejpam-6082	541	24	spread	spread	NOUN
ejpam-6082	541	25	of	of	ADP
ejpam-6082	541	26	the	the	DET
ejpam-6082	541	27	illness	illness	NOUN
ejpam-6082	541	28	.	.	PUNCT
ejpam-6082	542	1	interestingly	interestingly	ADV
ejpam-6082	542	2	,	,	PUNCT
ejpam-6082	542	3	higher	high	ADJ
ejpam-6082	542	4	movement	movement	NOUN
ejpam-6082	542	5	rates	rate	NOUN
ejpam-6082	542	6	(	(	PUNCT
ejpam-6082	542	7	α1	α1	PROPN
ejpam-6082	542	8	,	,	PUNCT
ejpam-6082	542	9	α2	α2	ADJ
ejpam-6082	542	10	)	)	PUNCT
ejpam-6082	542	11	speed	speed	VERB
ejpam-6082	542	12	up	up	ADP
ejpam-6082	542	13	the	the	DET
ejpam-6082	542	14	development	development	NOUN
ejpam-6082	542	15	of	of	ADP
ejpam-6082	542	16	uncovered	uncovered	ADJ
ejpam-6082	542	17	people	people	NOUN
ejpam-6082	542	18	into	into	ADP
ejpam-6082	542	19	tainted	tainted	ADJ
ejpam-6082	542	20	compartments	compartment	NOUN
ejpam-6082	542	21	,	,	PUNCT
ejpam-6082	542	22	prompting	prompt	VERB
ejpam-6082	542	23	an	an	DET
ejpam-6082	542	24	expanded	expand	VERB
ejpam-6082	542	25	infection	infection	NOUN
ejpam-6082	542	26	trouble	trouble	NOUN
ejpam-6082	542	27	.	.	PUNCT
ejpam-6082	543	1	these	these	DET
ejpam-6082	543	2	elements	element	NOUN
ejpam-6082	543	3	highlight	highlight	VERB
ejpam-6082	543	4	the	the	DET
ejpam-6082	543	5	significance	significance	NOUN
ejpam-6082	543	6	of	of	ADP
ejpam-6082	543	7	recuperation	recuperation	NOUN
ejpam-6082	543	8	and	and	CCONJ
ejpam-6082	543	9	movement	movement	NOUN
ejpam-6082	543	10	boundaries	boundary	NOUN
ejpam-6082	543	11	in	in	ADP
ejpam-6082	543	12	forming	form	VERB
ejpam-6082	543	13	the	the	DET
ejpam-6082	543	14	overall	overall	ADJ
ejpam-6082	543	15	disease	disease	NOUN
ejpam-6082	543	16	trajectory	trajectory	NOUN
ejpam-6082	543	17	.	.	PUNCT
ejpam-6082	544	1	to	to	PART
ejpam-6082	544	2	approve	approve	VERB
ejpam-6082	544	3	the	the	DET
ejpam-6082	544	4	model	model	NOUN
ejpam-6082	544	5	’s	’s	PART
ejpam-6082	544	6	precision	precision	NOUN
ejpam-6082	544	7	,	,	PUNCT
ejpam-6082	544	8	we	we	PRON
ejpam-6082	544	9	simulated	simulate	VERB
ejpam-6082	544	10	different	different	ADJ
ejpam-6082	544	11	situations	situation	NOUN
ejpam-6082	544	12	utilizing	utilize	VERB
ejpam-6082	544	13	different	different	ADJ
ejpam-6082	544	14	initial	initial	ADJ
ejpam-6082	544	15	conditions	condition	NOUN
ejpam-6082	544	16	and	and	CCONJ
ejpam-6082	544	17	parameter	parameter	NOUN
ejpam-6082	544	18	values	value	NOUN
ejpam-6082	544	19	.	.	PUNCT
ejpam-6082	545	1	the	the	DET
ejpam-6082	545	2	outcomes	outcome	NOUN
ejpam-6082	545	3	,	,	PUNCT
ejpam-6082	545	4	illustrated	illustrate	VERB
ejpam-6082	545	5	in	in	ADP
ejpam-6082	545	6	figures	figure	NOUN
ejpam-6082	545	7	,	,	PUNCT
ejpam-6082	545	8	portray	portray	VERB
ejpam-6082	545	9	the	the	DET
ejpam-6082	545	10	temporal	temporal	ADJ
ejpam-6082	545	11	evolution	evolution	NOUN
ejpam-6082	545	12	of	of	ADP
ejpam-6082	545	13	the	the	DET
ejpam-6082	545	14	compartments	compartment	NOUN
ejpam-6082	545	15	over	over	ADP
ejpam-6082	545	16	the	the	DET
ejpam-6082	545	17	time	time	NOUN
ejpam-6082	545	18	interval	interval	NOUN
ejpam-6082	545	19	0	0	NUM
ejpam-6082	545	20	≤	≤	NUM
ejpam-6082	545	21	t	t	PROPN
ejpam-6082	545	22	≤	≤	PROPN
ejpam-6082	545	23	t	t	PROPN
ejpam-6082	545	24	.	.	PUNCT
ejpam-6082	546	1	the	the	DET
ejpam-6082	546	2	simulations	simulation	NOUN
ejpam-6082	546	3	result	result	VERB
ejpam-6082	546	4	show	show	VERB
ejpam-6082	546	5	that	that	SCONJ
ejpam-6082	546	6	the	the	DET
ejpam-6082	546	7	model	model	NOUN
ejpam-6082	546	8	effectively	effectively	ADV
ejpam-6082	546	9	catches	catch	VERB
ejpam-6082	546	10	fundamental	fundamental	ADJ
ejpam-6082	546	11	elements	element	NOUN
ejpam-6082	546	12	of	of	ADP
ejpam-6082	546	13	illness	illness	NOUN
ejpam-6082	546	14	elements	element	NOUN
ejpam-6082	546	15	,	,	PUNCT
ejpam-6082	546	16	including	include	VERB
ejpam-6082	546	17	beginning	begin	VERB
ejpam-6082	546	18	dramatic	dramatic	ADJ
ejpam-6082	546	19	development	development	NOUN
ejpam-6082	546	20	,	,	PUNCT
ejpam-6082	546	21	top	top	ADJ
ejpam-6082	546	22	contamination	contamination	NOUN
ejpam-6082	546	23	levels	level	NOUN
ejpam-6082	546	24	,	,	PUNCT
ejpam-6082	546	25	and	and	CCONJ
ejpam-6082	546	26	k.	k.	PROPN
ejpam-6082	546	27	guedri	guedri	PROPN
ejpam-6082	546	28	et	et	PROPN
ejpam-6082	546	29	al	al	PROPN
ejpam-6082	546	30	.	.	PUNCT
ejpam-6082	546	31	/	/	SYM
ejpam-6082	546	32	eur	eur	PROPN
ejpam-6082	546	33	.	.	PUNCT
ejpam-6082	547	1	j.	j.	PROPN
ejpam-6082	547	2	pure	pure	PROPN
ejpam-6082	547	3	appl	appl	PROPN
ejpam-6082	547	4	.	.	PROPN
ejpam-6082	547	5	math	math	PROPN
ejpam-6082	547	6	,	,	PUNCT
ejpam-6082	547	7	18	18	NUM
ejpam-6082	547	8	(	(	PUNCT
ejpam-6082	547	9	2	2	NUM
ejpam-6082	547	10	)	)	PUNCT
ejpam-6082	547	11	(	(	PUNCT
ejpam-6082	547	12	2025	2025	NUM
ejpam-6082	547	13	)	)	PUNCT
ejpam-6082	547	14	,	,	PUNCT
ejpam-6082	547	15	6082	6082	NUM
ejpam-6082	547	16	24	24	NUM
ejpam-6082	547	17	of	of	ADP
ejpam-6082	547	18	39	39	NUM
ejpam-6082	547	19	inevitable	inevitable	ADJ
ejpam-6082	547	20	decay	decay	NOUN
ejpam-6082	547	21	because	because	SCONJ
ejpam-6082	547	22	of	of	ADP
ejpam-6082	547	23	recuperation	recuperation	NOUN
ejpam-6082	547	24	and	and	CCONJ
ejpam-6082	547	25	inoculation	inoculation	NOUN
ejpam-6082	547	26	endeavors	endeavor	NOUN
ejpam-6082	547	27	.	.	PUNCT
ejpam-6082	548	1	the	the	DET
ejpam-6082	548	2	transaction	transaction	NOUN
ejpam-6082	548	3	of	of	ADP
ejpam-6082	548	4	boundary	boundary	ADJ
ejpam-6082	548	5	values	value	NOUN
ejpam-6082	548	6	,	,	PUNCT
ejpam-6082	548	7	for	for	ADP
ejpam-6082	548	8	example	example	NOUN
ejpam-6082	548	9	,	,	PUNCT
ejpam-6082	548	10	immunization	immunization	NOUN
ejpam-6082	548	11	rate	rate	NOUN
ejpam-6082	548	12	(	(	PUNCT
ejpam-6082	548	13	δ	δ	NOUN
ejpam-6082	548	14	)	)	PUNCT
ejpam-6082	548	15	and	and	CCONJ
ejpam-6082	548	16	disappearing	disappear	VERB
ejpam-6082	548	17	resistance	resistance	NOUN
ejpam-6082	548	18	rate	rate	NOUN
ejpam-6082	548	19	(	(	PUNCT
ejpam-6082	548	20	ρ1	ρ1	NOUN
ejpam-6082	548	21	)	)	PUNCT
ejpam-6082	548	22	,	,	PUNCT
ejpam-6082	548	23	was	be	AUX
ejpam-6082	548	24	basic	basic	ADJ
ejpam-6082	548	25	in	in	ADP
ejpam-6082	548	26	deciding	decide	VERB
ejpam-6082	548	27	the	the	DET
ejpam-6082	548	28	elements	element	NOUN
ejpam-6082	548	29	of	of	ADP
ejpam-6082	548	30	the	the	DET
ejpam-6082	548	31	powerless	powerless	ADJ
ejpam-6082	548	32	and	and	CCONJ
ejpam-6082	548	33	recuperated	recuperated	ADJ
ejpam-6082	548	34	populaces	populace	NOUN
ejpam-6082	548	35	over	over	ADP
ejpam-6082	548	36	time	time	NOUN
ejpam-6082	548	37	.	.	PUNCT
ejpam-6082	549	1	the	the	DET
ejpam-6082	549	2	results	result	NOUN
ejpam-6082	549	3	of	of	ADP
ejpam-6082	549	4	our	our	PRON
ejpam-6082	549	5	simulations	simulation	NOUN
ejpam-6082	549	6	propose	propose	VERB
ejpam-6082	549	7	a	a	DET
ejpam-6082	549	8	few	few	ADJ
ejpam-6082	549	9	significant	significant	ADJ
ejpam-6082	549	10	experiences	experience	NOUN
ejpam-6082	549	11	.	.	PUNCT
ejpam-6082	550	1	expanding	expand	VERB
ejpam-6082	550	2	inoculation	inoculation	ADJ
ejpam-6082	550	3	rates	rate	NOUN
ejpam-6082	550	4	(	(	PUNCT
ejpam-6082	550	5	δ	δ	NOUN
ejpam-6082	550	6	)	)	PUNCT
ejpam-6082	550	7	significantly	significantly	ADV
ejpam-6082	550	8	reduces	reduce	VERB
ejpam-6082	550	9	the	the	DET
ejpam-6082	550	10	quantity	quantity	NOUN
ejpam-6082	550	11	of	of	ADP
ejpam-6082	550	12	susceptible	susceptible	ADJ
ejpam-6082	550	13	people	people	NOUN
ejpam-6082	550	14	,	,	PUNCT
ejpam-6082	550	15	which	which	PRON
ejpam-6082	550	16	by	by	ADP
ejpam-6082	550	17	implication	implication	NOUN
ejpam-6082	550	18	brings	bring	VERB
ejpam-6082	550	19	down	down	ADP
ejpam-6082	550	20	the	the	DET
ejpam-6082	550	21	disease	disease	NOUN
ejpam-6082	550	22	rate	rate	NOUN
ejpam-6082	550	23	.	.	PUNCT
ejpam-6082	551	1	moreover	moreover	ADV
ejpam-6082	551	2	,	,	PUNCT
ejpam-6082	551	3	the	the	DET
ejpam-6082	551	4	waning	wane	VERB
ejpam-6082	551	5	immunity	immunity	NOUN
ejpam-6082	551	6	rate	rate	NOUN
ejpam-6082	551	7	(	(	PUNCT
ejpam-6082	551	8	ρ1	ρ1	NOUN
ejpam-6082	551	9	)	)	PUNCT
ejpam-6082	551	10	assumes	assume	VERB
ejpam-6082	551	11	a	a	DET
ejpam-6082	551	12	vital	vital	ADJ
ejpam-6082	551	13	part	part	NOUN
ejpam-6082	551	14	in	in	ADP
ejpam-6082	551	15	deciding	decide	VERB
ejpam-6082	551	16	the	the	DET
ejpam-6082	551	17	drawn	draw	VERB
ejpam-6082	551	18	out	out	ADP
ejpam-6082	551	19	dynamics	dynamic	NOUN
ejpam-6082	551	20	of	of	ADP
ejpam-6082	551	21	the	the	DET
ejpam-6082	551	22	recovered	recover	VERB
ejpam-6082	551	23	compartment	compartment	NOUN
ejpam-6082	551	24	,	,	PUNCT
ejpam-6082	551	25	as	as	ADP
ejpam-6082	551	26	higher	high	ADJ
ejpam-6082	551	27	upsides	upside	NOUN
ejpam-6082	551	28	of	of	ADP
ejpam-6082	551	29	ρ1	ρ1	NOUN
ejpam-6082	551	30	lead	lead	VERB
ejpam-6082	551	31	to	to	ADP
ejpam-6082	551	32	quicker	quick	ADJ
ejpam-6082	551	33	changes	change	NOUN
ejpam-6082	551	34	of	of	ADP
ejpam-6082	551	35	recuperated	recuperated	ADJ
ejpam-6082	551	36	people	people	NOUN
ejpam-6082	551	37	back	back	ADV
ejpam-6082	551	38	to	to	ADP
ejpam-6082	551	39	the	the	DET
ejpam-6082	551	40	powerless	powerless	ADJ
ejpam-6082	551	41	class	class	NOUN
ejpam-6082	551	42	.	.	PUNCT
ejpam-6082	552	1	moreover	moreover	ADV
ejpam-6082	552	2	,	,	PUNCT
ejpam-6082	552	3	the	the	DET
ejpam-6082	552	4	boundary	boundary	ADJ
ejpam-6082	552	5	c	c	NOUN
ejpam-6082	552	6	,	,	PUNCT
ejpam-6082	552	7	addressing	address	VERB
ejpam-6082	552	8	the	the	DET
ejpam-6082	552	9	typical	typical	ADJ
ejpam-6082	552	10	pace	pace	NOUN
ejpam-6082	552	11	of	of	ADP
ejpam-6082	552	12	contact	contact	NOUN
ejpam-6082	552	13	with	with	ADP
ejpam-6082	552	14	waste	waste	NOUN
ejpam-6082	552	15	,	,	PUNCT
ejpam-6082	552	16	firmly	firmly	ADV
ejpam-6082	552	17	impacts	impact	VERB
ejpam-6082	552	18	the	the	DET
ejpam-6082	552	19	underlying	underlie	VERB
ejpam-6082	552	20	spread	spread	NOUN
ejpam-6082	552	21	of	of	ADP
ejpam-6082	552	22	the	the	DET
ejpam-6082	552	23	illness	illness	NOUN
ejpam-6082	552	24	.	.	PUNCT
ejpam-6082	553	1	reducing	reduce	VERB
ejpam-6082	553	2	c	c	NOUN
ejpam-6082	553	3	through	through	ADP
ejpam-6082	553	4	improved	improve	VERB
ejpam-6082	553	5	sanitation	sanitation	NOUN
ejpam-6082	553	6	measures	measure	NOUN
ejpam-6082	553	7	can	can	AUX
ejpam-6082	553	8	effectively	effectively	ADV
ejpam-6082	553	9	control	control	VERB
ejpam-6082	553	10	the	the	DET
ejpam-6082	553	11	outbreak	outbreak	NOUN
ejpam-6082	553	12	,	,	PUNCT
ejpam-6082	553	13	highlighting	highlight	VERB
ejpam-6082	553	14	the	the	DET
ejpam-6082	553	15	importance	importance	NOUN
ejpam-6082	553	16	of	of	ADP
ejpam-6082	553	17	environmental	environmental	ADJ
ejpam-6082	553	18	interventions	intervention	NOUN
ejpam-6082	553	19	in	in	ADP
ejpam-6082	553	20	disease	disease	NOUN
ejpam-6082	553	21	management	management	NOUN
ejpam-6082	553	22	.	.	PUNCT
ejpam-6082	554	1	table	table	NOUN
ejpam-6082	554	2	2	2	NUM
ejpam-6082	554	3	:	:	PUNCT
ejpam-6082	554	4	descriptions	description	NOUN
ejpam-6082	554	5	of	of	ADP
ejpam-6082	554	6	model	model	NOUN
ejpam-6082	554	7	parameters	parameter	NOUN
ejpam-6082	554	8	and	and	CCONJ
ejpam-6082	554	9	their	their	PRON
ejpam-6082	554	10	values	value	NOUN
ejpam-6082	554	11	used	use	VERB
ejpam-6082	554	12	for	for	ADP
ejpam-6082	554	13	simulation	simulation	NOUN
ejpam-6082	554	14	.	.	PUNCT
ejpam-6082	555	1	parameter	parameter	NOUN
ejpam-6082	555	2	description	description	NOUN
ejpam-6082	555	3	value	value	NOUN
ejpam-6082	555	4	ref	ref	NOUN
ejpam-6082	555	5	.	.	PUNCT
ejpam-6082	556	1	µ	µ	PRON
ejpam-6082	556	2	natural	natural	ADJ
ejpam-6082	556	3	death	death	NOUN
ejpam-6082	556	4	rate	rate	NOUN
ejpam-6082	556	5	8.75×	8.75×	NUM
ejpam-6082	556	6	10−3	10−3	NUM
ejpam-6082	556	7	[	[	X
ejpam-6082	556	8	1	1	NUM
ejpam-6082	556	9	]	]	PUNCT
ejpam-6082	556	10	σ	σ	X
ejpam-6082	556	11	polio	polio	NOUN
ejpam-6082	556	12	-	-	PUNCT
ejpam-6082	556	13	induced	induce	VERB
ejpam-6082	556	14	death	death	NOUN
ejpam-6082	556	15	rate	rate	NOUN
ejpam-6082	556	16	0.125	0.125	NUM
ejpam-6082	556	17	[	[	X
ejpam-6082	556	18	1	1	NUM
ejpam-6082	556	19	]	]	PUNCT
ejpam-6082	556	20	β	β	NOUN
ejpam-6082	556	21	transmission	transmission	NOUN
ejpam-6082	556	22	probability	probability	NOUN
ejpam-6082	556	23	0.002	0.002	NUM
ejpam-6082	556	24	[	[	X
ejpam-6082	556	25	1	1	NUM
ejpam-6082	556	26	]	]	PUNCT
ejpam-6082	556	27	ρ	ρ	NUM
ejpam-6082	556	28	rate	rate	NOUN
ejpam-6082	556	29	of	of	ADP
ejpam-6082	556	30	development	development	NOUN
ejpam-6082	556	31	of	of	ADP
ejpam-6082	556	32	pps	pps	NOUN
ejpam-6082	556	33	0.030	0.030	NUM
ejpam-6082	556	34	[	[	X
ejpam-6082	556	35	1	1	NUM
ejpam-6082	556	36	]	]	X
ejpam-6082	556	37	λ	λ	PROPN
ejpam-6082	556	38	recruitment	recruitment	NOUN
ejpam-6082	556	39	rate	rate	NOUN
ejpam-6082	556	40	1000	1000	NUM
ejpam-6082	556	41	[	[	X
ejpam-6082	556	42	1	1	NUM
ejpam-6082	556	43	]	]	PUNCT
ejpam-6082	556	44	ω	ω	NUM
ejpam-6082	556	45	recovery	recovery	NOUN
ejpam-6082	556	46	rate	rate	NOUN
ejpam-6082	556	47	of	of	ADP
ejpam-6082	556	48	exposed	expose	VERB
ejpam-6082	556	49	individuals	individual	NOUN
ejpam-6082	556	50	0.010	0.010	NUM
ejpam-6082	556	51	[	[	X
ejpam-6082	556	52	1	1	NUM
ejpam-6082	556	53	]	]	PUNCT
ejpam-6082	556	54	ρ1	ρ1	NOUN
ejpam-6082	556	55	waning	wane	VERB
ejpam-6082	556	56	rate	rate	NOUN
ejpam-6082	556	57	of	of	ADP
ejpam-6082	556	58	post	post	ADJ
ejpam-6082	556	59	-	-	NOUN
ejpam-6082	556	60	recovery	recovery	NOUN
ejpam-6082	556	61	immunity	immunity	NOUN
ejpam-6082	556	62	0.330	0.330	NUM
ejpam-6082	556	63	[	[	SYM
ejpam-6082	556	64	1	1	NUM
ejpam-6082	556	65	]	]	PUNCT
ejpam-6082	556	66	γ	γ	PROPN
ejpam-6082	556	67	recovery	recovery	NOUN
ejpam-6082	556	68	rate	rate	NOUN
ejpam-6082	556	69	of	of	ADP
ejpam-6082	556	70	vaccinated	vaccinated	ADJ
ejpam-6082	556	71	individuals	individual	NOUN
ejpam-6082	556	72	0.140	0.140	NUM
ejpam-6082	556	73	[	[	SYM
ejpam-6082	556	74	1	1	NUM
ejpam-6082	556	75	]	]	PUNCT
ejpam-6082	556	76	δ	δ	NOUN
ejpam-6082	556	77	vaccination	vaccination	NOUN
ejpam-6082	556	78	rate	rate	NOUN
ejpam-6082	556	79	of	of	ADP
ejpam-6082	556	80	susceptibles	susceptible	NOUN
ejpam-6082	556	81	0.378	0.378	NUM
ejpam-6082	556	82	[	[	X
ejpam-6082	556	83	1	1	NUM
ejpam-6082	556	84	]	]	PUNCT
ejpam-6082	556	85	ω2	ω2	ADJ
ejpam-6082	556	86	recovery	recovery	NOUN
ejpam-6082	556	87	rate	rate	NOUN
ejpam-6082	556	88	in	in	ADP
ejpam-6082	556	89	paralytic	paralytic	ADJ
ejpam-6082	556	90	class	class	NOUN
ejpam-6082	556	91	10−4	10−4	NUM
ejpam-6082	556	92	[	[	X
ejpam-6082	556	93	1	1	NUM
ejpam-6082	556	94	]	]	X
ejpam-6082	556	95	ω1	ω1	PROPN
ejpam-6082	556	96	recovery	recovery	NOUN
ejpam-6082	556	97	rate	rate	NOUN
ejpam-6082	556	98	in	in	ADP
ejpam-6082	556	99	non	non	ADJ
ejpam-6082	556	100	-	-	ADJ
ejpam-6082	556	101	paralytic	paralytic	ADJ
ejpam-6082	556	102	class	class	NOUN
ejpam-6082	556	103	0.001	0.001	NUM
ejpam-6082	556	104	[	[	X
ejpam-6082	556	105	1	1	NUM
ejpam-6082	556	106	]	]	X
ejpam-6082	556	107	α2	α2	ADJ
ejpam-6082	556	108	progression	progression	NOUN
ejpam-6082	556	109	rate	rate	NOUN
ejpam-6082	556	110	to	to	ADP
ejpam-6082	556	111	paralytic	paralytic	ADJ
ejpam-6082	556	112	class	class	NOUN
ejpam-6082	556	113	0.450	0.450	NUM
ejpam-6082	556	114	[	[	X
ejpam-6082	556	115	1	1	NUM
ejpam-6082	556	116	]	]	X
ejpam-6082	556	117	α1	α1	PROPN
ejpam-6082	556	118	progression	progression	NOUN
ejpam-6082	556	119	rate	rate	NOUN
ejpam-6082	556	120	to	to	ADP
ejpam-6082	556	121	non	non	ADJ
ejpam-6082	556	122	-	-	ADJ
ejpam-6082	556	123	paralytic	paralytic	ADJ
ejpam-6082	556	124	class	class	NOUN
ejpam-6082	556	125	0.500	0.500	NUM
ejpam-6082	556	126	[	[	X
ejpam-6082	556	127	1	1	NUM
ejpam-6082	556	128	]	]	PUNCT
ejpam-6082	556	129	c	c	NOUN
ejpam-6082	556	130	contact	contact	NOUN
ejpam-6082	556	131	rate	rate	NOUN
ejpam-6082	556	132	with	with	ADP
ejpam-6082	556	133	faecal	faecal	ADJ
ejpam-6082	556	134	waste	waste	NOUN
ejpam-6082	556	135	0.500	0.500	NUM
ejpam-6082	557	1	[	[	X
ejpam-6082	557	2	1	1	NUM
ejpam-6082	557	3	]	]	PUNCT
ejpam-6082	557	4	k.	k.	PROPN
ejpam-6082	557	5	guedri	guedri	PROPN
ejpam-6082	557	6	et	et	PROPN
ejpam-6082	557	7	al	al	PROPN
ejpam-6082	557	8	.	.	PUNCT
ejpam-6082	557	9	/	/	SYM
ejpam-6082	557	10	eur	eur	PROPN
ejpam-6082	557	11	.	.	PUNCT
ejpam-6082	558	1	j.	j.	PROPN
ejpam-6082	558	2	pure	pure	PROPN
ejpam-6082	558	3	appl	appl	PROPN
ejpam-6082	558	4	.	.	PROPN
ejpam-6082	558	5	math	math	PROPN
ejpam-6082	558	6	,	,	PUNCT
ejpam-6082	558	7	18	18	NUM
ejpam-6082	558	8	(	(	PUNCT
ejpam-6082	558	9	2	2	NUM
ejpam-6082	558	10	)	)	PUNCT
ejpam-6082	558	11	(	(	PUNCT
ejpam-6082	558	12	2025	2025	NUM
ejpam-6082	558	13	)	)	PUNCT
ejpam-6082	558	14	,	,	PUNCT
ejpam-6082	558	15	6082	6082	NUM
ejpam-6082	558	16	25	25	NUM
ejpam-6082	558	17	of	of	ADP
ejpam-6082	558	18	39	39	NUM
ejpam-6082	558	19	(	(	PUNCT
ejpam-6082	558	20	a	a	NOUN
ejpam-6082	558	21	)	)	PUNCT
ejpam-6082	558	22	0	0	NUM
ejpam-6082	559	1	50	50	NUM
ejpam-6082	559	2	100	100	NUM
ejpam-6082	559	3	150	150	NUM
ejpam-6082	559	4	200	200	NUM
ejpam-6082	559	5	250	250	NUM
ejpam-6082	559	6	300	300	NUM
ejpam-6082	559	7	350	350	NUM
ejpam-6082	559	8	400	400	NUM
ejpam-6082	559	9	time	time	NOUN
ejpam-6082	559	10	in	in	ADP
ejpam-6082	559	11	days	day	NOUN
ejpam-6082	559	12	0.2	0.2	NUM
ejpam-6082	559	13	0.4	0.4	NUM
ejpam-6082	559	14	0.6	0.6	NUM
ejpam-6082	559	15	0.8	0.8	NUM
ejpam-6082	559	16	1	1	NUM
ejpam-6082	559	17	1.2	1.2	NUM
ejpam-6082	559	18	1.4	1.4	NUM
ejpam-6082	559	19	1.6	1.6	NUM
ejpam-6082	559	20	1.8	1.8	NUM
ejpam-6082	559	21	2	2	NUM
ejpam-6082	559	22	s	s	PART
ejpam-6082	559	23	(	(	PUNCT
ejpam-6082	559	24	t	t	PROPN
ejpam-6082	559	25	)	)	PUNCT
ejpam-6082	559	26	s	s	PROPN
ejpam-6082	559	27	us	us	PROPN
ejpam-6082	559	28	ce	ce	PROPN
ejpam-6082	559	29	pt	pt	X
ejpam-6082	559	30	ib	ib	PROPN
ejpam-6082	559	31	le	le	PROPN
ejpam-6082	559	32	p	p	PROPN
ejpam-6082	559	33	op	op	NOUN
ejpam-6082	559	34	ul	ul	NOUN
ejpam-6082	559	35	at	at	ADP
ejpam-6082	559	36	io	io	PROPN
ejpam-6082	559	37	n	n	CCONJ
ejpam-6082	559	38	109	109	NUM
ejpam-6082	559	39	susceptible	susceptible	ADJ
ejpam-6082	559	40	population	population	NOUN
ejpam-6082	559	41	over	over	ADP
ejpam-6082	559	42	time	time	NOUN
ejpam-6082	559	43	for	for	ADP
ejpam-6082	559	44	different	different	ADJ
ejpam-6082	559	45	=	=	SYM
ejpam-6082	559	46	0.7	0.7	NUM
ejpam-6082	559	47	=	=	SYM
ejpam-6082	559	48	0.75	0.75	NUM
ejpam-6082	559	49	=	=	SYM
ejpam-6082	559	50	0.8	0.8	NUM
ejpam-6082	559	51	=	=	SYM
ejpam-6082	559	52	0.85	0.85	NUM
ejpam-6082	559	53	=	=	SYM
ejpam-6082	559	54	0.9	0.9	NUM
ejpam-6082	559	55	(	(	PUNCT
ejpam-6082	559	56	b	b	NOUN
ejpam-6082	559	57	)	)	PUNCT
ejpam-6082	559	58	figure	figure	NOUN
ejpam-6082	559	59	5	5	NUM
ejpam-6082	559	60	:	:	PUNCT
ejpam-6082	559	61	simulation	simulation	NOUN
ejpam-6082	559	62	results	result	NOUN
ejpam-6082	559	63	of	of	ADP
ejpam-6082	559	64	the	the	DET
ejpam-6082	559	65	susceptible	susceptible	ADJ
ejpam-6082	559	66	population	population	NOUN
ejpam-6082	559	67	for	for	ADP
ejpam-6082	559	68	different	different	ADJ
ejpam-6082	559	69	fractional	fractional	ADJ
ejpam-6082	559	70	orders	order	NOUN
ejpam-6082	559	71	α	α	X
ejpam-6082	559	72	.	.	PUNCT
ejpam-6082	560	1	(	(	PUNCT
ejpam-6082	560	2	a	a	X
ejpam-6082	560	3	)	)	PUNCT
ejpam-6082	560	4	0	0	NUM
ejpam-6082	560	5	100	100	NUM
ejpam-6082	560	6	200	200	NUM
ejpam-6082	560	7	300	300	NUM
ejpam-6082	560	8	400	400	NUM
ejpam-6082	560	9	500	500	NUM
ejpam-6082	560	10	600	600	NUM
ejpam-6082	560	11	700	700	NUM
ejpam-6082	560	12	800	800	NUM
ejpam-6082	560	13	time	time	NOUN
ejpam-6082	560	14	in	in	ADP
ejpam-6082	560	15	days	day	NOUN
ejpam-6082	560	16	0	0	NUM
ejpam-6082	560	17	0.2	0.2	NUM
ejpam-6082	560	18	0.4	0.4	NUM
ejpam-6082	560	19	0.6	0.6	NUM
ejpam-6082	560	20	0.8	0.8	NUM
ejpam-6082	560	21	1	1	NUM
ejpam-6082	560	22	1.2	1.2	NUM
ejpam-6082	560	23	1.4	1.4	NUM
ejpam-6082	560	24	1.6	1.6	NUM
ejpam-6082	560	25	1.8	1.8	NUM
ejpam-6082	560	26	2	2	NUM
ejpam-6082	560	27	s	s	PART
ejpam-6082	560	28	(	(	PUNCT
ejpam-6082	560	29	t	t	PROPN
ejpam-6082	560	30	)	)	PUNCT
ejpam-6082	560	31	s	s	PROPN
ejpam-6082	560	32	us	us	PROPN
ejpam-6082	560	33	ce	ce	PROPN
ejpam-6082	560	34	pt	pt	X
ejpam-6082	560	35	ib	ib	PROPN
ejpam-6082	560	36	le	le	PROPN
ejpam-6082	560	37	p	p	PROPN
ejpam-6082	560	38	op	op	NOUN
ejpam-6082	560	39	ul	ul	NOUN
ejpam-6082	560	40	at	at	ADP
ejpam-6082	560	41	io	io	PROPN
ejpam-6082	560	42	n	n	CCONJ
ejpam-6082	560	43	109	109	NUM
ejpam-6082	560	44	susceptible	susceptible	ADJ
ejpam-6082	560	45	population	population	NOUN
ejpam-6082	560	46	over	over	ADP
ejpam-6082	560	47	time	time	NOUN
ejpam-6082	560	48	for	for	ADP
ejpam-6082	560	49	different	different	ADJ
ejpam-6082	560	50	=	=	SYM
ejpam-6082	560	51	0.8	0.8	NUM
ejpam-6082	560	52	=	=	SYM
ejpam-6082	560	53	0.85	0.85	NUM
ejpam-6082	560	54	=	=	SYM
ejpam-6082	560	55	0.9	0.9	NUM
ejpam-6082	560	56	=	=	SYM
ejpam-6082	560	57	0.95	0.95	NUM
ejpam-6082	560	58	=	=	SYM
ejpam-6082	560	59	1	1	NUM
ejpam-6082	560	60	(	(	PUNCT
ejpam-6082	560	61	b	b	NOUN
ejpam-6082	560	62	)	)	PUNCT
ejpam-6082	560	63	figure	figure	NOUN
ejpam-6082	560	64	6	6	NUM
ejpam-6082	560	65	:	:	PUNCT
ejpam-6082	560	66	long	long	ADJ
ejpam-6082	560	67	term	term	NOUN
ejpam-6082	560	68	behavior	behavior	NOUN
ejpam-6082	560	69	of	of	ADP
ejpam-6082	560	70	susceptible	susceptible	ADJ
ejpam-6082	560	71	population	population	NOUN
ejpam-6082	560	72	for	for	ADP
ejpam-6082	560	73	different	different	ADJ
ejpam-6082	560	74	fractional	fractional	ADJ
ejpam-6082	560	75	orders	order	NOUN
ejpam-6082	560	76	α	α	NOUN
ejpam-6082	560	77	.	.	PUNCT
ejpam-6082	561	1	the	the	DET
ejpam-6082	561	2	simulation	simulation	NOUN
ejpam-6082	561	3	results	result	VERB
ejpam-6082	561	4	in	in	ADP
ejpam-6082	561	5	figure	figure	NOUN
ejpam-6082	561	6	5	5	NUM
ejpam-6082	561	7	illustrate	illustrate	VERB
ejpam-6082	561	8	the	the	DET
ejpam-6082	561	9	impact	impact	NOUN
ejpam-6082	561	10	of	of	ADP
ejpam-6082	561	11	fractional	fractional	ADJ
ejpam-6082	561	12	-	-	PUNCT
ejpam-6082	561	13	order	order	NOUN
ejpam-6082	561	14	derivatives	derivative	NOUN
ejpam-6082	561	15	and	and	CCONJ
ejpam-6082	561	16	spatial	spatial	ADJ
ejpam-6082	561	17	heterogeneity	heterogeneity	NOUN
ejpam-6082	561	18	on	on	ADP
ejpam-6082	561	19	the	the	DET
ejpam-6082	561	20	dynamics	dynamic	NOUN
ejpam-6082	561	21	of	of	ADP
ejpam-6082	561	22	the	the	DET
ejpam-6082	561	23	susceptible	susceptible	ADJ
ejpam-6082	561	24	population	population	NOUN
ejpam-6082	561	25	s(t	s(t	PROPN
ejpam-6082	561	26	,	,	PUNCT
ejpam-6082	561	27	x	x	X
ejpam-6082	561	28	)	)	PUNCT
ejpam-6082	561	29	in	in	ADP
ejpam-6082	561	30	the	the	DET
ejpam-6082	561	31	fractional	fractional	ADJ
ejpam-6082	561	32	-	-	PUNCT
ejpam-6082	561	33	order	order	NOUN
ejpam-6082	561	34	reaction	reaction	NOUN
ejpam-6082	561	35	-	-	PUNCT
ejpam-6082	561	36	diffusion	diffusion	NOUN
ejpam-6082	561	37	polio	polio	NOUN
ejpam-6082	561	38	model	model	NOUN
ejpam-6082	561	39	.	.	PUNCT
ejpam-6082	562	1	the	the	DET
ejpam-6082	562	2	fractional	fractional	ADJ
ejpam-6082	562	3	order	order	NOUN
ejpam-6082	562	4	α	α	NOUN
ejpam-6082	562	5	introduces	introduce	NOUN
ejpam-6082	562	6	memory	memory	NOUN
ejpam-6082	562	7	effects	effect	NOUN
ejpam-6082	562	8	,	,	PUNCT
ejpam-6082	562	9	influencing	influence	VERB
ejpam-6082	562	10	the	the	DET
ejpam-6082	562	11	depletion	depletion	NOUN
ejpam-6082	562	12	rate	rate	NOUN
ejpam-6082	562	13	of	of	ADP
ejpam-6082	562	14	susceptibles	susceptible	NOUN
ejpam-6082	562	15	.	.	PUNCT
ejpam-6082	563	1	lower	low	ADJ
ejpam-6082	563	2	values	value	NOUN
ejpam-6082	563	3	of	of	ADP
ejpam-6082	563	4	α	α	NOUN
ejpam-6082	563	5	(	(	PUNCT
ejpam-6082	563	6	e.g.	e.g.	ADV
ejpam-6082	563	7	,	,	PUNCT
ejpam-6082	563	8	α	α	NOUN
ejpam-6082	563	9	=	=	SYM
ejpam-6082	563	10	0.7	0.7	NUM
ejpam-6082	563	11	)	)	PUNCT
ejpam-6082	563	12	correspond	correspond	VERB
ejpam-6082	563	13	to	to	ADP
ejpam-6082	563	14	stronger	strong	ADJ
ejpam-6082	563	15	memory	memory	NOUN
ejpam-6082	563	16	effects	effect	NOUN
ejpam-6082	563	17	,	,	PUNCT
ejpam-6082	563	18	accelerating	accelerate	VERB
ejpam-6082	563	19	the	the	DET
ejpam-6082	563	20	depletion	depletion	NOUN
ejpam-6082	563	21	due	due	ADP
ejpam-6082	563	22	to	to	ADP
ejpam-6082	563	23	the	the	DET
ejpam-6082	563	24	cumulative	cumulative	ADJ
ejpam-6082	563	25	influence	influence	NOUN
ejpam-6082	563	26	of	of	ADP
ejpam-6082	563	27	historical	historical	ADJ
ejpam-6082	563	28	interactions	interaction	NOUN
ejpam-6082	563	29	.	.	PUNCT
ejpam-6082	564	1	higher	high	ADJ
ejpam-6082	564	2	α	α	NOUN
ejpam-6082	564	3	values	value	NOUN
ejpam-6082	564	4	(	(	PUNCT
ejpam-6082	564	5	e.g.	e.g.	ADV
ejpam-6082	564	6	,	,	PUNCT
ejpam-6082	564	7	α	α	NOUN
ejpam-6082	564	8	=	=	SYM
ejpam-6082	564	9	0.9	0.9	NUM
ejpam-6082	564	10	)	)	PUNCT
ejpam-6082	564	11	result	result	NOUN
ejpam-6082	564	12	in	in	ADP
ejpam-6082	564	13	a	a	DET
ejpam-6082	564	14	slower	slow	ADJ
ejpam-6082	564	15	depletion	depletion	NOUN
ejpam-6082	564	16	,	,	PUNCT
ejpam-6082	564	17	reflecting	reflect	VERB
ejpam-6082	564	18	behavior	behavior	NOUN
ejpam-6082	564	19	closer	close	ADV
ejpam-6082	564	20	to	to	ADP
ejpam-6082	564	21	classical	classical	ADJ
ejpam-6082	564	22	models	model	NOUN
ejpam-6082	564	23	with	with	ADP
ejpam-6082	564	24	limited	limited	ADJ
ejpam-6082	564	25	memory	memory	NOUN
ejpam-6082	564	26	effects	effect	NOUN
ejpam-6082	564	27	.	.	PUNCT
ejpam-6082	565	1	the	the	DET
ejpam-6082	565	2	three	three	NUM
ejpam-6082	565	3	-	-	PUNCT
ejpam-6082	565	4	dimensional	dimensional	ADJ
ejpam-6082	565	5	plot	plot	NOUN
ejpam-6082	565	6	shows	show	VERB
ejpam-6082	565	7	significant	significant	ADJ
ejpam-6082	565	8	spatial	spatial	ADJ
ejpam-6082	565	9	heterogeneity	heterogeneity	NOUN
ejpam-6082	565	10	,	,	PUNCT
ejpam-6082	565	11	where	where	SCONJ
ejpam-6082	565	12	regions	region	NOUN
ejpam-6082	565	13	with	with	ADP
ejpam-6082	565	14	higher	high	ADJ
ejpam-6082	565	15	k.	k.	PROPN
ejpam-6082	565	16	guedri	guedri	PROPN
ejpam-6082	565	17	et	et	PROPN
ejpam-6082	565	18	al	al	PROPN
ejpam-6082	565	19	.	.	PUNCT
ejpam-6082	565	20	/	/	SYM
ejpam-6082	565	21	eur	eur	PROPN
ejpam-6082	565	22	.	.	PUNCT
ejpam-6082	566	1	j.	j.	PROPN
ejpam-6082	566	2	pure	pure	PROPN
ejpam-6082	566	3	appl	appl	PROPN
ejpam-6082	566	4	.	.	PROPN
ejpam-6082	566	5	math	math	PROPN
ejpam-6082	566	6	,	,	PUNCT
ejpam-6082	566	7	18	18	NUM
ejpam-6082	566	8	(	(	PUNCT
ejpam-6082	566	9	2	2	NUM
ejpam-6082	566	10	)	)	PUNCT
ejpam-6082	566	11	(	(	PUNCT
ejpam-6082	566	12	2025	2025	NUM
ejpam-6082	566	13	)	)	PUNCT
ejpam-6082	566	14	,	,	PUNCT
ejpam-6082	566	15	6082	6082	NUM
ejpam-6082	566	16	26	26	NUM
ejpam-6082	566	17	of	of	ADP
ejpam-6082	566	18	39	39	NUM
ejpam-6082	566	19	initial	initial	ADJ
ejpam-6082	566	20	densities	density	NOUN
ejpam-6082	566	21	of	of	ADP
ejpam-6082	566	22	susceptibles	susceptible	NOUN
ejpam-6082	566	23	experience	experience	NOUN
ejpam-6082	566	24	faster	fast	ADJ
ejpam-6082	566	25	depletion	depletion	NOUN
ejpam-6082	566	26	due	due	ADP
ejpam-6082	566	27	to	to	ADP
ejpam-6082	566	28	localized	localize	VERB
ejpam-6082	566	29	transmission	transmission	NOUN
ejpam-6082	566	30	dynamics	dynamic	NOUN
ejpam-6082	566	31	.	.	PUNCT
ejpam-6082	567	1	these	these	DET
ejpam-6082	567	2	findings	finding	NOUN
ejpam-6082	567	3	underscore	underscore	VERB
ejpam-6082	567	4	the	the	DET
ejpam-6082	567	5	importance	importance	NOUN
ejpam-6082	567	6	of	of	ADP
ejpam-6082	567	7	spatially	spatially	ADV
ejpam-6082	567	8	targeted	target	VERB
ejpam-6082	567	9	interventions	intervention	NOUN
ejpam-6082	567	10	,	,	PUNCT
ejpam-6082	567	11	such	such	ADJ
ejpam-6082	567	12	as	as	ADP
ejpam-6082	567	13	vaccination	vaccination	NOUN
ejpam-6082	567	14	campaigns	campaign	NOUN
ejpam-6082	567	15	and	and	CCONJ
ejpam-6082	567	16	improved	improved	ADJ
ejpam-6082	567	17	sanitation	sanitation	NOUN
ejpam-6082	567	18	,	,	PUNCT
ejpam-6082	567	19	particularly	particularly	ADV
ejpam-6082	567	20	in	in	ADP
ejpam-6082	567	21	high	high	ADJ
ejpam-6082	567	22	-	-	PUNCT
ejpam-6082	567	23	density	density	NOUN
ejpam-6082	567	24	regions	region	NOUN
ejpam-6082	567	25	.	.	PUNCT
ejpam-6082	568	1	the	the	DET
ejpam-6082	568	2	interplay	interplay	NOUN
ejpam-6082	568	3	of	of	ADP
ejpam-6082	568	4	diffusion	diffusion	NOUN
ejpam-6082	568	5	and	and	CCONJ
ejpam-6082	568	6	memory	memory	NOUN
ejpam-6082	568	7	effects	effect	NOUN
ejpam-6082	568	8	highlights	highlight	VERB
ejpam-6082	568	9	the	the	DET
ejpam-6082	568	10	need	need	NOUN
ejpam-6082	568	11	to	to	PART
ejpam-6082	568	12	account	account	VERB
ejpam-6082	568	13	for	for	ADP
ejpam-6082	568	14	both	both	PRON
ejpam-6082	568	15	mobility	mobility	NOUN
ejpam-6082	568	16	and	and	CCONJ
ejpam-6082	568	17	historical	historical	ADJ
ejpam-6082	568	18	interactions	interaction	NOUN
ejpam-6082	568	19	in	in	ADP
ejpam-6082	568	20	control	control	NOUN
ejpam-6082	568	21	strategies	strategy	NOUN
ejpam-6082	568	22	,	,	PUNCT
ejpam-6082	568	23	emphasizing	emphasize	VERB
ejpam-6082	568	24	the	the	DET
ejpam-6082	568	25	utility	utility	NOUN
ejpam-6082	568	26	of	of	ADP
ejpam-6082	568	27	fractional	fractional	ADJ
ejpam-6082	568	28	models	model	NOUN
ejpam-6082	568	29	in	in	ADP
ejpam-6082	568	30	capturing	capture	VERB
ejpam-6082	568	31	the	the	DET
ejpam-6082	568	32	complex	complex	ADJ
ejpam-6082	568	33	temporal	temporal	ADJ
ejpam-6082	568	34	and	and	CCONJ
ejpam-6082	568	35	spatial	spatial	ADJ
ejpam-6082	568	36	dynamics	dynamic	NOUN
ejpam-6082	568	37	of	of	ADP
ejpam-6082	568	38	polio	polio	NOUN
ejpam-6082	568	39	outbreaks	outbreak	NOUN
ejpam-6082	568	40	.	.	PUNCT
ejpam-6082	569	1	(	(	PUNCT
ejpam-6082	569	2	a	a	X
ejpam-6082	569	3	)	)	PUNCT
ejpam-6082	569	4	0	0	NUM
ejpam-6082	569	5	50	50	NUM
ejpam-6082	569	6	100	100	NUM
ejpam-6082	569	7	150	150	NUM
ejpam-6082	569	8	200	200	NUM
ejpam-6082	569	9	250	250	NUM
ejpam-6082	569	10	300	300	NUM
ejpam-6082	569	11	350	350	NUM
ejpam-6082	569	12	400	400	NUM
ejpam-6082	569	13	time	time	NOUN
ejpam-6082	569	14	in	in	ADP
ejpam-6082	569	15	days	day	NOUN
ejpam-6082	569	16	0	0	NUM
ejpam-6082	569	17	0.5	0.5	NUM
ejpam-6082	569	18	1	1	NUM
ejpam-6082	569	19	1.5	1.5	NUM
ejpam-6082	569	20	2	2	NUM
ejpam-6082	569	21	2.5	2.5	NUM
ejpam-6082	569	22	3	3	NUM
ejpam-6082	569	23	3.5	3.5	NUM
ejpam-6082	569	24	v	v	NOUN
ejpam-6082	569	25	(	(	PUNCT
ejpam-6082	569	26	t	t	PROPN
ejpam-6082	569	27	)	)	PUNCT
ejpam-6082	569	28	v	v	ADP
ejpam-6082	569	29	a	a	DET
ejpam-6082	569	30	c	c	NOUN
ejpam-6082	569	31	c	c	NOUN
ejpam-6082	569	32	in	in	ADP
ejpam-6082	569	33	a	a	DET
ejpam-6082	569	34	te	te	X
ejpam-6082	570	1	d	d	X
ejpam-6082	570	2	p	p	X
ejpam-6082	570	3	o	o	X
ejpam-6082	570	4	p	p	X
ejpam-6082	570	5	u	u	X
ejpam-6082	570	6	la	la	X
ejpam-6082	570	7	ti	ti	X
ejpam-6082	570	8	o	o	NOUN
ejpam-6082	570	9	n	n	PROPN
ejpam-6082	570	10	108	108	NUM
ejpam-6082	570	11	vaccinated	vaccinated	ADJ
ejpam-6082	570	12	population	population	NOUN
ejpam-6082	570	13	over	over	ADP
ejpam-6082	570	14	time	time	NOUN
ejpam-6082	570	15	for	for	ADP
ejpam-6082	570	16	different	different	ADJ
ejpam-6082	571	1	=	=	SYM
ejpam-6082	571	2	0.7	0.7	NUM
ejpam-6082	571	3	=	=	SYM
ejpam-6082	571	4	0.75	0.75	NUM
ejpam-6082	571	5	=	=	SYM
ejpam-6082	571	6	0.8	0.8	NUM
ejpam-6082	571	7	=	=	SYM
ejpam-6082	571	8	0.85	0.85	NUM
ejpam-6082	571	9	=	=	SYM
ejpam-6082	571	10	0.9	0.9	NUM
ejpam-6082	571	11	(	(	PUNCT
ejpam-6082	571	12	b	b	NOUN
ejpam-6082	571	13	)	)	PUNCT
ejpam-6082	571	14	figure	figure	NOUN
ejpam-6082	571	15	7	7	NUM
ejpam-6082	571	16	:	:	PUNCT
ejpam-6082	571	17	simulation	simulation	NOUN
ejpam-6082	571	18	results	result	NOUN
ejpam-6082	571	19	of	of	ADP
ejpam-6082	571	20	the	the	DET
ejpam-6082	571	21	vaccinated	vaccinated	ADJ
ejpam-6082	571	22	population	population	NOUN
ejpam-6082	571	23	for	for	ADP
ejpam-6082	571	24	different	different	ADJ
ejpam-6082	571	25	fractional	fractional	ADJ
ejpam-6082	571	26	orders	order	NOUN
ejpam-6082	571	27	α	α	NOUN
ejpam-6082	571	28	.	.	PUNCT
ejpam-6082	572	1	k.	k.	PROPN
ejpam-6082	572	2	guedri	guedri	PROPN
ejpam-6082	572	3	et	et	PROPN
ejpam-6082	572	4	al	al	PROPN
ejpam-6082	572	5	.	.	PUNCT
ejpam-6082	572	6	/	/	SYM
ejpam-6082	572	7	eur	eur	PROPN
ejpam-6082	572	8	.	.	PUNCT
ejpam-6082	573	1	j.	j.	PROPN
ejpam-6082	573	2	pure	pure	PROPN
ejpam-6082	573	3	appl	appl	PROPN
ejpam-6082	573	4	.	.	PROPN
ejpam-6082	573	5	math	math	PROPN
ejpam-6082	573	6	,	,	PUNCT
ejpam-6082	573	7	18	18	NUM
ejpam-6082	573	8	(	(	PUNCT
ejpam-6082	573	9	2	2	NUM
ejpam-6082	573	10	)	)	PUNCT
ejpam-6082	573	11	(	(	PUNCT
ejpam-6082	573	12	2025	2025	NUM
ejpam-6082	573	13	)	)	PUNCT
ejpam-6082	573	14	,	,	PUNCT
ejpam-6082	573	15	6082	6082	NUM
ejpam-6082	573	16	27	27	NUM
ejpam-6082	573	17	of	of	ADP
ejpam-6082	573	18	39	39	NUM
ejpam-6082	573	19	(	(	PUNCT
ejpam-6082	573	20	a	a	NOUN
ejpam-6082	573	21	)	)	PUNCT
ejpam-6082	573	22	0	0	NUM
ejpam-6082	573	23	100	100	NUM
ejpam-6082	573	24	200	200	NUM
ejpam-6082	573	25	300	300	NUM
ejpam-6082	573	26	400	400	NUM
ejpam-6082	573	27	500	500	NUM
ejpam-6082	573	28	600	600	NUM
ejpam-6082	573	29	700	700	NUM
ejpam-6082	573	30	800	800	NUM
ejpam-6082	573	31	time	time	NOUN
ejpam-6082	573	32	in	in	ADP
ejpam-6082	573	33	days	day	NOUN
ejpam-6082	573	34	0	0	NUM
ejpam-6082	573	35	0.5	0.5	NUM
ejpam-6082	573	36	1	1	NUM
ejpam-6082	573	37	1.5	1.5	NUM
ejpam-6082	573	38	2	2	NUM
ejpam-6082	573	39	2.5	2.5	NUM
ejpam-6082	573	40	3	3	NUM
ejpam-6082	573	41	3.5	3.5	NUM
ejpam-6082	573	42	4	4	NUM
ejpam-6082	573	43	v	v	NOUN
ejpam-6082	573	44	(	(	PUNCT
ejpam-6082	573	45	t	t	PROPN
ejpam-6082	573	46	)	)	PUNCT
ejpam-6082	573	47	v	v	ADP
ejpam-6082	573	48	a	a	DET
ejpam-6082	573	49	c	c	NOUN
ejpam-6082	573	50	c	c	NOUN
ejpam-6082	573	51	in	in	ADP
ejpam-6082	573	52	a	a	DET
ejpam-6082	573	53	te	te	X
ejpam-6082	574	1	d	d	X
ejpam-6082	574	2	p	p	X
ejpam-6082	574	3	o	o	X
ejpam-6082	574	4	p	p	X
ejpam-6082	574	5	u	u	X
ejpam-6082	574	6	la	la	X
ejpam-6082	574	7	ti	ti	X
ejpam-6082	574	8	o	o	NOUN
ejpam-6082	574	9	n	n	PROPN
ejpam-6082	574	10	108	108	NUM
ejpam-6082	574	11	vaccinated	vaccinated	ADJ
ejpam-6082	574	12	population	population	NOUN
ejpam-6082	574	13	over	over	ADP
ejpam-6082	574	14	time	time	NOUN
ejpam-6082	574	15	for	for	ADP
ejpam-6082	574	16	different	different	ADJ
ejpam-6082	574	17	=	=	SYM
ejpam-6082	574	18	0.8	0.8	NUM
ejpam-6082	574	19	=	=	SYM
ejpam-6082	574	20	0.85	0.85	NUM
ejpam-6082	574	21	=	=	SYM
ejpam-6082	574	22	0.9	0.9	NUM
ejpam-6082	574	23	=	=	SYM
ejpam-6082	574	24	0.95	0.95	NUM
ejpam-6082	574	25	=	=	SYM
ejpam-6082	574	26	1	1	NUM
ejpam-6082	574	27	(	(	PUNCT
ejpam-6082	574	28	b	b	NOUN
ejpam-6082	574	29	)	)	PUNCT
ejpam-6082	574	30	figure	figure	NOUN
ejpam-6082	574	31	8	8	NUM
ejpam-6082	574	32	:	:	PUNCT
ejpam-6082	574	33	long	long	ADJ
ejpam-6082	574	34	term	term	NOUN
ejpam-6082	574	35	behavior	behavior	NOUN
ejpam-6082	574	36	of	of	ADP
ejpam-6082	574	37	vaccinated	vaccinated	ADJ
ejpam-6082	574	38	population	population	NOUN
ejpam-6082	574	39	for	for	ADP
ejpam-6082	574	40	different	different	ADJ
ejpam-6082	574	41	fractional	fractional	ADJ
ejpam-6082	574	42	orders	order	NOUN
ejpam-6082	574	43	α	α	NOUN
ejpam-6082	574	44	.	.	PUNCT
ejpam-6082	575	1	the	the	DET
ejpam-6082	575	2	dynamics	dynamic	NOUN
ejpam-6082	575	3	of	of	ADP
ejpam-6082	575	4	the	the	DET
ejpam-6082	575	5	vaccinated	vaccinated	ADJ
ejpam-6082	575	6	population	population	NOUN
ejpam-6082	575	7	v	v	ADP
ejpam-6082	575	8	(	(	PUNCT
ejpam-6082	575	9	t	t	PROPN
ejpam-6082	575	10	,	,	PUNCT
ejpam-6082	575	11	x	x	NOUN
ejpam-6082	575	12	)	)	PUNCT
ejpam-6082	575	13	,	,	PUNCT
ejpam-6082	575	14	depicted	depict	VERB
ejpam-6082	575	15	in	in	ADP
ejpam-6082	575	16	figure	figure	NOUN
ejpam-6082	575	17	7	7	NUM
ejpam-6082	575	18	,	,	PUNCT
ejpam-6082	575	19	are	be	AUX
ejpam-6082	575	20	significantly	significantly	ADV
ejpam-6082	575	21	influenced	influence	VERB
ejpam-6082	575	22	by	by	ADP
ejpam-6082	575	23	fractional	fractional	ADJ
ejpam-6082	575	24	-	-	PUNCT
ejpam-6082	575	25	order	order	NOUN
ejpam-6082	575	26	memory	memory	NOUN
ejpam-6082	575	27	effects	effect	NOUN
ejpam-6082	575	28	and	and	CCONJ
ejpam-6082	575	29	spatial	spatial	ADJ
ejpam-6082	575	30	heterogeneity	heterogeneity	NOUN
ejpam-6082	575	31	.	.	PUNCT
ejpam-6082	576	1	lower	low	ADJ
ejpam-6082	576	2	α	α	NOUN
ejpam-6082	576	3	values	value	NOUN
ejpam-6082	576	4	(	(	PUNCT
ejpam-6082	576	5	e.g.	e.g.	ADV
ejpam-6082	576	6	,	,	PUNCT
ejpam-6082	576	7	α	α	NOUN
ejpam-6082	576	8	=	=	SYM
ejpam-6082	576	9	0.7	0.7	NUM
ejpam-6082	576	10	)	)	PUNCT
ejpam-6082	576	11	lead	lead	NOUN
ejpam-6082	576	12	to	to	ADP
ejpam-6082	576	13	a	a	DET
ejpam-6082	576	14	prior	prior	ADJ
ejpam-6082	576	15	and	and	CCONJ
ejpam-6082	576	16	more	more	ADV
ejpam-6082	576	17	keen	keen	ADJ
ejpam-6082	576	18	top	top	NOUN
ejpam-6082	576	19	in	in	ADP
ejpam-6082	576	20	the	the	DET
ejpam-6082	576	21	vaccinated	vaccinated	ADJ
ejpam-6082	576	22	individuals	individual	NOUN
ejpam-6082	576	23	,	,	PUNCT
ejpam-6082	576	24	reflecting	reflect	VERB
ejpam-6082	576	25	quick	quick	ADJ
ejpam-6082	576	26	take	take	VERB
ejpam-6082	576	27	-	-	PUNCT
ejpam-6082	576	28	up	up	NOUN
ejpam-6082	576	29	driven	drive	VERB
ejpam-6082	576	30	by	by	ADP
ejpam-6082	576	31	more	more	ADJ
ejpam-6082	576	32	grounded	ground	VERB
ejpam-6082	576	33	memory	memory	NOUN
ejpam-6082	576	34	impacts	impact	NOUN
ejpam-6082	576	35	.	.	PUNCT
ejpam-6082	577	1	conversely	conversely	ADV
ejpam-6082	577	2	,	,	PUNCT
ejpam-6082	577	3	higher	high	ADJ
ejpam-6082	577	4	α	α	NOUN
ejpam-6082	577	5	values	value	NOUN
ejpam-6082	577	6	(	(	PUNCT
ejpam-6082	577	7	e.g.	e.g.	ADV
ejpam-6082	577	8	,	,	PUNCT
ejpam-6082	577	9	α	α	NOUN
ejpam-6082	577	10	=	=	SYM
ejpam-6082	577	11	0.9	0.9	NUM
ejpam-6082	577	12	)	)	PUNCT
ejpam-6082	577	13	bring	bring	VERB
ejpam-6082	577	14	about	about	ADV
ejpam-6082	577	15	deferred	deferred	ADJ
ejpam-6082	577	16	and	and	CCONJ
ejpam-6082	577	17	continuous	continuous	ADJ
ejpam-6082	577	18	immunization	immunization	NOUN
ejpam-6082	577	19	elements	element	NOUN
ejpam-6082	577	20	,	,	PUNCT
ejpam-6082	577	21	similar	similar	ADJ
ejpam-6082	577	22	to	to	ADP
ejpam-6082	577	23	old	old	ADJ
ejpam-6082	577	24	style	style	NOUN
ejpam-6082	577	25	models	model	NOUN
ejpam-6082	577	26	.	.	PUNCT
ejpam-6082	578	1	the	the	DET
ejpam-6082	578	2	three	three	NUM
ejpam-6082	578	3	-	-	PUNCT
ejpam-6082	578	4	layered	layer	VERB
ejpam-6082	578	5	plot	plot	NOUN
ejpam-6082	578	6	uncovers	uncover	NOUN
ejpam-6082	578	7	spatial	spatial	ADJ
ejpam-6082	578	8	changeability	changeability	NOUN
ejpam-6082	578	9	in	in	ADP
ejpam-6082	578	10	immunization	immunization	NOUN
ejpam-6082	578	11	inclusion	inclusion	NOUN
ejpam-6082	578	12	,	,	PUNCT
ejpam-6082	578	13	with	with	ADP
ejpam-6082	578	14	longer	long	ADJ
ejpam-6082	578	15	times	time	NOUN
ejpam-6082	578	16	expected	expect	VERB
ejpam-6082	578	17	to	to	PART
ejpam-6082	578	18	accomplish	accomplish	VERB
ejpam-6082	578	19	immersion	immersion	NOUN
ejpam-6082	578	20	in	in	ADP
ejpam-6082	578	21	certain	certain	ADJ
ejpam-6082	578	22	areas	area	NOUN
ejpam-6082	578	23	.	.	PUNCT
ejpam-6082	579	1	this	this	PRON
ejpam-6082	579	2	stresses	stress	VERB
ejpam-6082	579	3	the	the	DET
ejpam-6082	579	4	requirement	requirement	NOUN
ejpam-6082	579	5	for	for	ADP
ejpam-6082	579	6	geologically	geologically	ADV
ejpam-6082	579	7	designated	designate	VERB
ejpam-6082	579	8	endeavors	endeavor	NOUN
ejpam-6082	579	9	to	to	PART
ejpam-6082	579	10	accomplish	accomplish	VERB
ejpam-6082	579	11	uniform	uniform	ADJ
ejpam-6082	579	12	immunization	immunization	NOUN
ejpam-6082	579	13	inclusion	inclusion	NOUN
ejpam-6082	579	14	.	.	PUNCT
ejpam-6082	580	1	the	the	DET
ejpam-6082	580	2	cooperation	cooperation	NOUN
ejpam-6082	580	3	among	among	ADP
ejpam-6082	580	4	dissemination	dissemination	NOUN
ejpam-6082	580	5	and	and	CCONJ
ejpam-6082	580	6	memory	memory	NOUN
ejpam-6082	580	7	impacts	impact	NOUN
ejpam-6082	580	8	proposes	propose	VERB
ejpam-6082	580	9	that	that	SCONJ
ejpam-6082	580	10	areas	area	NOUN
ejpam-6082	580	11	with	with	ADP
ejpam-6082	580	12	high	high	ADJ
ejpam-6082	580	13	populace	populace	NOUN
ejpam-6082	580	14	thickness	thickness	NOUN
ejpam-6082	580	15	or	or	CCONJ
ejpam-6082	580	16	more	more	ADV
ejpam-6082	580	17	prominent	prominent	ADJ
ejpam-6082	580	18	openness	openness	NOUN
ejpam-6082	580	19	to	to	ADP
ejpam-6082	580	20	the	the	DET
ejpam-6082	580	21	infection	infection	NOUN
ejpam-6082	580	22	accomplish	accomplish	VERB
ejpam-6082	580	23	quicker	quick	ADJ
ejpam-6082	580	24	immunization	immunization	NOUN
ejpam-6082	580	25	tops	top	NOUN
ejpam-6082	580	26	however	however	ADV
ejpam-6082	580	27	may	may	AUX
ejpam-6082	580	28	likewise	likewise	ADV
ejpam-6082	580	29	encounter	encounter	VERB
ejpam-6082	580	30	more	more	ADV
ejpam-6082	580	31	fast	fast	ADJ
ejpam-6082	580	32	downfalls	downfall	NOUN
ejpam-6082	580	33	because	because	SCONJ
ejpam-6082	580	34	of	of	ADP
ejpam-6082	580	35	fading	fade	VERB
ejpam-6082	580	36	resistance	resistance	NOUN
ejpam-6082	580	37	or	or	CCONJ
ejpam-6082	580	38	antibody	antibody	NOUN
ejpam-6082	580	39	disappointment	disappointment	NOUN
ejpam-6082	580	40	.	.	PUNCT
ejpam-6082	581	1	these	these	DET
ejpam-6082	581	2	outcomes	outcome	NOUN
ejpam-6082	581	3	highlight	highlight	VERB
ejpam-6082	581	4	the	the	DET
ejpam-6082	581	5	worth	worth	NOUN
ejpam-6082	581	6	of	of	ADP
ejpam-6082	581	7	fragmentary	fragmentary	ADJ
ejpam-6082	581	8	request	request	NOUN
ejpam-6082	581	9	models	model	NOUN
ejpam-6082	581	10	in	in	ADP
ejpam-6082	581	11	improving	improve	VERB
ejpam-6082	581	12	vaccination	vaccination	NOUN
ejpam-6082	581	13	methodologies	methodology	NOUN
ejpam-6082	581	14	for	for	ADP
ejpam-6082	581	15	polio	polio	NOUN
ejpam-6082	581	16	control	control	NOUN
ejpam-6082	581	17	in	in	ADP
ejpam-6082	581	18	heterogeneous	heterogeneous	ADJ
ejpam-6082	581	19	populations	population	NOUN
ejpam-6082	581	20	.	.	PUNCT
ejpam-6082	582	1	k.	k.	PROPN
ejpam-6082	582	2	guedri	guedri	PROPN
ejpam-6082	582	3	et	et	PROPN
ejpam-6082	582	4	al	al	PROPN
ejpam-6082	582	5	.	.	PUNCT
ejpam-6082	582	6	/	/	SYM
ejpam-6082	582	7	eur	eur	PROPN
ejpam-6082	582	8	.	.	PUNCT
ejpam-6082	583	1	j.	j.	PROPN
ejpam-6082	583	2	pure	pure	PROPN
ejpam-6082	583	3	appl	appl	PROPN
ejpam-6082	583	4	.	.	PROPN
ejpam-6082	583	5	math	math	PROPN
ejpam-6082	583	6	,	,	PUNCT
ejpam-6082	583	7	18	18	NUM
ejpam-6082	583	8	(	(	PUNCT
ejpam-6082	583	9	2	2	NUM
ejpam-6082	583	10	)	)	PUNCT
ejpam-6082	583	11	(	(	PUNCT
ejpam-6082	583	12	2025	2025	NUM
ejpam-6082	583	13	)	)	PUNCT
ejpam-6082	583	14	,	,	PUNCT
ejpam-6082	583	15	6082	6082	NUM
ejpam-6082	583	16	28	28	NUM
ejpam-6082	583	17	of	of	ADP
ejpam-6082	583	18	39	39	NUM
ejpam-6082	583	19	(	(	PUNCT
ejpam-6082	583	20	a	a	NOUN
ejpam-6082	583	21	)	)	PUNCT
ejpam-6082	583	22	0	0	NUM
ejpam-6082	584	1	50	50	NUM
ejpam-6082	584	2	100	100	NUM
ejpam-6082	584	3	150	150	NUM
ejpam-6082	584	4	200	200	NUM
ejpam-6082	584	5	250	250	NUM
ejpam-6082	584	6	300	300	NUM
ejpam-6082	584	7	350	350	NUM
ejpam-6082	584	8	400	400	NUM
ejpam-6082	584	9	time	time	NOUN
ejpam-6082	584	10	in	in	ADP
ejpam-6082	584	11	days	day	NOUN
ejpam-6082	584	12	0	0	NUM
ejpam-6082	584	13	2	2	NUM
ejpam-6082	584	14	4	4	NUM
ejpam-6082	584	15	6	6	NUM
ejpam-6082	584	16	8	8	NUM
ejpam-6082	584	17	10	10	NUM
ejpam-6082	584	18	12	12	NUM
ejpam-6082	584	19	14	14	NUM
ejpam-6082	584	20	16	16	NUM
ejpam-6082	584	21	18	18	NUM
ejpam-6082	584	22	e	e	NOUN
ejpam-6082	584	23	(	(	PUNCT
ejpam-6082	584	24	t	t	PROPN
ejpam-6082	584	25	)	)	PUNCT
ejpam-6082	585	1	e	e	NOUN
ejpam-6082	586	1	x	x	PUNCT
ejpam-6082	586	2	p	p	X
ejpam-6082	586	3	o	o	X
ejpam-6082	586	4	s	s	X
ejpam-6082	586	5	e	e	NOUN
ejpam-6082	586	6	d	d	NOUN
ejpam-6082	586	7	p	p	X
ejpam-6082	586	8	o	o	X
ejpam-6082	586	9	p	p	X
ejpam-6082	586	10	u	u	X
ejpam-6082	586	11	la	la	X
ejpam-6082	586	12	ti	ti	X
ejpam-6082	586	13	o	o	NOUN
ejpam-6082	586	14	n	n	CCONJ
ejpam-6082	586	15	107	107	NUM
ejpam-6082	586	16	exposed	expose	VERB
ejpam-6082	586	17	population	population	NOUN
ejpam-6082	586	18	over	over	ADP
ejpam-6082	586	19	time	time	NOUN
ejpam-6082	586	20	for	for	ADP
ejpam-6082	586	21	different	different	ADJ
ejpam-6082	586	22	=	=	SYM
ejpam-6082	586	23	0.7	0.7	NUM
ejpam-6082	586	24	=	=	SYM
ejpam-6082	586	25	0.75	0.75	NUM
ejpam-6082	586	26	=	=	SYM
ejpam-6082	586	27	0.8	0.8	NUM
ejpam-6082	586	28	=	=	SYM
ejpam-6082	586	29	0.85	0.85	NUM
ejpam-6082	586	30	=	=	SYM
ejpam-6082	586	31	0.9	0.9	NUM
ejpam-6082	586	32	(	(	PUNCT
ejpam-6082	586	33	b	b	NOUN
ejpam-6082	586	34	)	)	PUNCT
ejpam-6082	586	35	figure	figure	NOUN
ejpam-6082	586	36	9	9	NUM
ejpam-6082	586	37	:	:	PUNCT
ejpam-6082	586	38	simulation	simulation	NOUN
ejpam-6082	586	39	results	result	NOUN
ejpam-6082	586	40	of	of	ADP
ejpam-6082	586	41	the	the	DET
ejpam-6082	586	42	exposed	expose	VERB
ejpam-6082	586	43	population	population	NOUN
ejpam-6082	586	44	for	for	ADP
ejpam-6082	586	45	different	different	ADJ
ejpam-6082	586	46	fractional	fractional	ADJ
ejpam-6082	586	47	orders	order	NOUN
ejpam-6082	586	48	α	α	X
ejpam-6082	586	49	.	.	PUNCT
ejpam-6082	587	1	(	(	PUNCT
ejpam-6082	587	2	a	a	X
ejpam-6082	587	3	)	)	PUNCT
ejpam-6082	587	4	0	0	NUM
ejpam-6082	587	5	100	100	NUM
ejpam-6082	587	6	200	200	NUM
ejpam-6082	587	7	300	300	NUM
ejpam-6082	587	8	400	400	NUM
ejpam-6082	587	9	500	500	NUM
ejpam-6082	587	10	600	600	NUM
ejpam-6082	587	11	700	700	NUM
ejpam-6082	587	12	800	800	NUM
ejpam-6082	587	13	time	time	NOUN
ejpam-6082	587	14	in	in	ADP
ejpam-6082	587	15	days	day	NOUN
ejpam-6082	587	16	0	0	NUM
ejpam-6082	587	17	2	2	NUM
ejpam-6082	587	18	4	4	NUM
ejpam-6082	587	19	6	6	NUM
ejpam-6082	587	20	8	8	NUM
ejpam-6082	587	21	10	10	NUM
ejpam-6082	587	22	12	12	NUM
ejpam-6082	587	23	14	14	NUM
ejpam-6082	587	24	16	16	NUM
ejpam-6082	587	25	18	18	NUM
ejpam-6082	587	26	e	e	NOUN
ejpam-6082	587	27	(	(	PUNCT
ejpam-6082	587	28	t	t	PROPN
ejpam-6082	587	29	)	)	PUNCT
ejpam-6082	588	1	e	e	NOUN
ejpam-6082	589	1	x	x	PUNCT
ejpam-6082	589	2	p	p	X
ejpam-6082	589	3	o	o	X
ejpam-6082	589	4	s	s	X
ejpam-6082	589	5	e	e	NOUN
ejpam-6082	589	6	d	d	NOUN
ejpam-6082	589	7	p	p	X
ejpam-6082	589	8	o	o	X
ejpam-6082	589	9	p	p	X
ejpam-6082	589	10	u	u	X
ejpam-6082	589	11	la	la	X
ejpam-6082	589	12	ti	ti	X
ejpam-6082	589	13	o	o	NOUN
ejpam-6082	589	14	n	n	CCONJ
ejpam-6082	589	15	107	107	NUM
ejpam-6082	589	16	exposed	expose	VERB
ejpam-6082	589	17	population	population	NOUN
ejpam-6082	589	18	over	over	ADP
ejpam-6082	589	19	time	time	NOUN
ejpam-6082	589	20	for	for	ADP
ejpam-6082	589	21	different	different	ADJ
ejpam-6082	589	22	=	=	SYM
ejpam-6082	589	23	0.8	0.8	NUM
ejpam-6082	589	24	=	=	SYM
ejpam-6082	589	25	0.85	0.85	NUM
ejpam-6082	589	26	=	=	SYM
ejpam-6082	589	27	0.9	0.9	NUM
ejpam-6082	589	28	=	=	SYM
ejpam-6082	589	29	0.95	0.95	NUM
ejpam-6082	589	30	=	=	SYM
ejpam-6082	589	31	1	1	NUM
ejpam-6082	589	32	(	(	PUNCT
ejpam-6082	589	33	b	b	NOUN
ejpam-6082	589	34	)	)	PUNCT
ejpam-6082	589	35	figure	figure	NOUN
ejpam-6082	589	36	10	10	NUM
ejpam-6082	589	37	:	:	PUNCT
ejpam-6082	589	38	long	long	ADJ
ejpam-6082	589	39	term	term	NOUN
ejpam-6082	589	40	behavior	behavior	NOUN
ejpam-6082	589	41	of	of	ADP
ejpam-6082	589	42	exposed	expose	VERB
ejpam-6082	589	43	population	population	NOUN
ejpam-6082	589	44	for	for	ADP
ejpam-6082	589	45	different	different	ADJ
ejpam-6082	589	46	fractional	fractional	ADJ
ejpam-6082	589	47	orders	order	NOUN
ejpam-6082	589	48	α	α	X
ejpam-6082	589	49	.	.	PUNCT
ejpam-6082	589	50	figure	figure	NOUN
ejpam-6082	589	51	10	10	NUM
ejpam-6082	589	52	illustrates	illustrate	VERB
ejpam-6082	589	53	the	the	DET
ejpam-6082	589	54	dynamics	dynamic	NOUN
ejpam-6082	589	55	of	of	ADP
ejpam-6082	589	56	the	the	DET
ejpam-6082	589	57	exposed	expose	VERB
ejpam-6082	589	58	population	population	NOUN
ejpam-6082	589	59	e(t	e(t	NOUN
ejpam-6082	589	60	,	,	PUNCT
ejpam-6082	589	61	x	x	NOUN
ejpam-6082	589	62	)	)	PUNCT
ejpam-6082	589	63	,	,	PUNCT
ejpam-6082	589	64	reflecting	reflect	VERB
ejpam-6082	589	65	the	the	DET
ejpam-6082	589	66	influence	influence	NOUN
ejpam-6082	589	67	of	of	ADP
ejpam-6082	589	68	memory	memory	NOUN
ejpam-6082	589	69	effects	effect	NOUN
ejpam-6082	589	70	and	and	CCONJ
ejpam-6082	589	71	spatial	spatial	ADJ
ejpam-6082	589	72	heterogeneity	heterogeneity	NOUN
ejpam-6082	589	73	on	on	ADP
ejpam-6082	589	74	disease	disease	NOUN
ejpam-6082	589	75	progression	progression	NOUN
ejpam-6082	589	76	.	.	PUNCT
ejpam-6082	590	1	smaller	small	ADJ
ejpam-6082	590	2	k.	k.	PROPN
ejpam-6082	590	3	guedri	guedri	PROPN
ejpam-6082	590	4	et	et	PROPN
ejpam-6082	590	5	al	al	PROPN
ejpam-6082	590	6	.	.	PUNCT
ejpam-6082	590	7	/	/	SYM
ejpam-6082	590	8	eur	eur	PROPN
ejpam-6082	590	9	.	.	PUNCT
ejpam-6082	591	1	j.	j.	PROPN
ejpam-6082	591	2	pure	pure	PROPN
ejpam-6082	591	3	appl	appl	PROPN
ejpam-6082	591	4	.	.	PROPN
ejpam-6082	591	5	math	math	PROPN
ejpam-6082	591	6	,	,	PUNCT
ejpam-6082	591	7	18	18	NUM
ejpam-6082	591	8	(	(	PUNCT
ejpam-6082	591	9	2	2	NUM
ejpam-6082	591	10	)	)	PUNCT
ejpam-6082	591	11	(	(	PUNCT
ejpam-6082	591	12	2025	2025	NUM
ejpam-6082	591	13	)	)	PUNCT
ejpam-6082	591	14	,	,	PUNCT
ejpam-6082	591	15	6082	6082	NUM
ejpam-6082	591	16	29	29	NUM
ejpam-6082	591	17	of	of	ADP
ejpam-6082	591	18	39	39	NUM
ejpam-6082	591	19	α	α	NOUN
ejpam-6082	591	20	values	value	NOUN
ejpam-6082	591	21	(	(	PUNCT
ejpam-6082	591	22	e.g.	e.g.	ADV
ejpam-6082	591	23	,	,	PUNCT
ejpam-6082	591	24	α	α	NOUN
ejpam-6082	591	25	=	=	SYM
ejpam-6082	591	26	0.7	0.7	NUM
ejpam-6082	591	27	)	)	PUNCT
ejpam-6082	591	28	result	result	NOUN
ejpam-6082	591	29	in	in	ADP
ejpam-6082	591	30	earlier	early	ADV
ejpam-6082	591	31	and	and	CCONJ
ejpam-6082	591	32	sharper	sharp	ADJ
ejpam-6082	591	33	peaks	peak	NOUN
ejpam-6082	591	34	,	,	PUNCT
ejpam-6082	591	35	driven	drive	VERB
ejpam-6082	591	36	by	by	ADP
ejpam-6082	591	37	enhanced	enhanced	ADJ
ejpam-6082	591	38	memory	memory	NOUN
ejpam-6082	591	39	effects	effect	NOUN
ejpam-6082	591	40	,	,	PUNCT
ejpam-6082	591	41	which	which	PRON
ejpam-6082	591	42	amplify	amplify	VERB
ejpam-6082	591	43	historical	historical	ADJ
ejpam-6082	591	44	exposure	exposure	NOUN
ejpam-6082	591	45	and	and	CCONJ
ejpam-6082	591	46	infection	infection	NOUN
ejpam-6082	591	47	dynamics	dynamic	NOUN
ejpam-6082	591	48	.	.	PUNCT
ejpam-6082	592	1	larger	large	ADJ
ejpam-6082	592	2	α	α	NOUN
ejpam-6082	592	3	values	value	NOUN
ejpam-6082	592	4	(	(	PUNCT
ejpam-6082	592	5	e.g.	e.g.	ADV
ejpam-6082	592	6	,	,	PUNCT
ejpam-6082	592	7	α	α	NOUN
ejpam-6082	592	8	=	=	SYM
ejpam-6082	592	9	0.9	0.9	NUM
ejpam-6082	592	10	)	)	PUNCT
ejpam-6082	592	11	lead	lead	VERB
ejpam-6082	592	12	to	to	ADP
ejpam-6082	592	13	slower	slow	ADJ
ejpam-6082	592	14	and	and	CCONJ
ejpam-6082	592	15	later	later	ADJ
ejpam-6082	592	16	peaks	peak	NOUN
ejpam-6082	592	17	,	,	PUNCT
ejpam-6082	592	18	reflecting	reflect	VERB
ejpam-6082	592	19	weaker	weak	ADJ
ejpam-6082	592	20	memory	memory	NOUN
ejpam-6082	592	21	effects	effect	NOUN
ejpam-6082	592	22	.	.	PUNCT
ejpam-6082	593	1	spatial	spatial	ADJ
ejpam-6082	593	2	heterogeneity	heterogeneity	NOUN
ejpam-6082	593	3	,	,	PUNCT
ejpam-6082	593	4	shown	show	VERB
ejpam-6082	593	5	in	in	ADP
ejpam-6082	593	6	the	the	DET
ejpam-6082	593	7	three	three	NUM
ejpam-6082	593	8	-	-	PUNCT
ejpam-6082	593	9	dimensional	dimensional	ADJ
ejpam-6082	593	10	plot	plot	NOUN
ejpam-6082	593	11	,	,	PUNCT
ejpam-6082	593	12	highlights	highlight	NOUN
ejpam-6082	593	13	areas	area	NOUN
ejpam-6082	593	14	with	with	ADP
ejpam-6082	593	15	concentrated	concentrated	ADJ
ejpam-6082	593	16	transmission	transmission	NOUN
ejpam-6082	593	17	potential	potential	NOUN
ejpam-6082	593	18	.	.	PUNCT
ejpam-6082	594	1	diffusion	diffusion	NOUN
ejpam-6082	594	2	redistributes	redistribute	NOUN
ejpam-6082	594	3	exposed	expose	VERB
ejpam-6082	594	4	individuals	individual	NOUN
ejpam-6082	594	5	,	,	PUNCT
ejpam-6082	594	6	amplifying	amplify	VERB
ejpam-6082	594	7	localized	localized	ADJ
ejpam-6082	594	8	outbreaks	outbreak	NOUN
ejpam-6082	594	9	in	in	ADP
ejpam-6082	594	10	regions	region	NOUN
ejpam-6082	594	11	with	with	ADP
ejpam-6082	594	12	high	high	ADJ
ejpam-6082	594	13	susceptibility	susceptibility	NOUN
ejpam-6082	594	14	or	or	CCONJ
ejpam-6082	594	15	insufficient	insufficient	ADJ
ejpam-6082	594	16	vaccination	vaccination	NOUN
ejpam-6082	594	17	.	.	PUNCT
ejpam-6082	595	1	these	these	DET
ejpam-6082	595	2	results	result	NOUN
ejpam-6082	595	3	emphasize	emphasize	VERB
ejpam-6082	595	4	the	the	DET
ejpam-6082	595	5	importance	importance	NOUN
ejpam-6082	595	6	of	of	ADP
ejpam-6082	595	7	region	region	NOUN
ejpam-6082	595	8	-	-	PUNCT
ejpam-6082	595	9	specific	specific	ADJ
ejpam-6082	595	10	interventions	intervention	NOUN
ejpam-6082	595	11	to	to	PART
ejpam-6082	595	12	mitigate	mitigate	VERB
ejpam-6082	595	13	exposure	exposure	NOUN
ejpam-6082	595	14	and	and	CCONJ
ejpam-6082	595	15	control	control	NOUN
ejpam-6082	595	16	disease	disease	NOUN
ejpam-6082	595	17	progression	progression	NOUN
ejpam-6082	595	18	,	,	PUNCT
ejpam-6082	595	19	showcasing	showcase	VERB
ejpam-6082	595	20	the	the	DET
ejpam-6082	595	21	utility	utility	NOUN
ejpam-6082	595	22	of	of	ADP
ejpam-6082	595	23	fractional	fractional	ADJ
ejpam-6082	595	24	-	-	PUNCT
ejpam-6082	595	25	order	order	NOUN
ejpam-6082	595	26	models	model	NOUN
ejpam-6082	595	27	in	in	ADP
ejpam-6082	595	28	designing	design	VERB
ejpam-6082	595	29	effective	effective	ADJ
ejpam-6082	595	30	strategies	strategy	NOUN
ejpam-6082	595	31	.	.	PUNCT
ejpam-6082	596	1	(	(	PUNCT
ejpam-6082	596	2	a	a	X
ejpam-6082	596	3	)	)	PUNCT
ejpam-6082	596	4	0	0	NUM
ejpam-6082	596	5	50	50	NUM
ejpam-6082	596	6	100	100	NUM
ejpam-6082	596	7	150	150	NUM
ejpam-6082	596	8	200	200	NUM
ejpam-6082	596	9	250	250	NUM
ejpam-6082	596	10	300	300	NUM
ejpam-6082	596	11	350	350	NUM
ejpam-6082	596	12	400	400	NUM
ejpam-6082	596	13	time	time	NOUN
ejpam-6082	596	14	in	in	ADP
ejpam-6082	596	15	days	day	NOUN
ejpam-6082	596	16	0	0	NUM
ejpam-6082	596	17	1	1	NUM
ejpam-6082	596	18	2	2	NUM
ejpam-6082	596	19	3	3	NUM
ejpam-6082	596	20	4	4	NUM
ejpam-6082	596	21	5	5	NUM
ejpam-6082	596	22	6	6	NUM
ejpam-6082	596	23	7	7	NUM
ejpam-6082	596	24	8	8	NUM
ejpam-6082	596	25	9	9	NUM
ejpam-6082	596	26	n	n	NOUN
ejpam-6082	596	27	p	p	X
ejpam-6082	596	28	(	(	PUNCT
ejpam-6082	596	29	t	t	PROPN
ejpam-6082	596	30	)	)	PUNCT
ejpam-6082	596	31	in	in	ADP
ejpam-6082	596	32	fe	fe	X
ejpam-6082	596	33	c	c	X
ejpam-6082	596	34	te	te	PROPN
ejpam-6082	596	35	d	d	PROPN
ejpam-6082	596	36	n	n	NOUN
ejpam-6082	596	37	o	o	NOUN
ejpam-6082	596	38	n	n	INTJ
ejpam-6082	596	39	-p	-p	ADV
ejpam-6082	596	40	a	a	DET
ejpam-6082	596	41	ra	ra	NOUN
ejpam-6082	596	42	ly	ly	X
ejpam-6082	596	43	ti	ti	NOUN
ejpam-6082	596	44	c	c	NOUN
ejpam-6082	596	45	p	p	NOUN
ejpam-6082	596	46	o	o	X
ejpam-6082	596	47	p	p	X
ejpam-6082	596	48	u	u	X
ejpam-6082	596	49	la	la	X
ejpam-6082	596	50	ti	ti	X
ejpam-6082	596	51	o	o	NOUN
ejpam-6082	596	52	n	n	PROPN
ejpam-6082	596	53	107infected	107infected	PROPN
ejpam-6082	596	54	non	non	ADJ
ejpam-6082	596	55	-	-	ADJ
ejpam-6082	596	56	paralytic	paralytic	ADJ
ejpam-6082	596	57	population	population	NOUN
ejpam-6082	596	58	over	over	ADP
ejpam-6082	596	59	time	time	NOUN
ejpam-6082	596	60	for	for	ADP
ejpam-6082	596	61	different	different	ADJ
ejpam-6082	596	62	=	=	SYM
ejpam-6082	596	63	0.7	0.7	NUM
ejpam-6082	596	64	=	=	SYM
ejpam-6082	596	65	0.75	0.75	NUM
ejpam-6082	596	66	=	=	SYM
ejpam-6082	596	67	0.8	0.8	NUM
ejpam-6082	596	68	=	=	SYM
ejpam-6082	596	69	0.85	0.85	NUM
ejpam-6082	596	70	=	=	SYM
ejpam-6082	596	71	0.9	0.9	NUM
ejpam-6082	596	72	(	(	PUNCT
ejpam-6082	596	73	b	b	NOUN
ejpam-6082	596	74	)	)	PUNCT
ejpam-6082	596	75	figure	figure	NOUN
ejpam-6082	596	76	11	11	NUM
ejpam-6082	596	77	:	:	PUNCT
ejpam-6082	596	78	simulation	simulation	NOUN
ejpam-6082	596	79	results	result	NOUN
ejpam-6082	596	80	of	of	ADP
ejpam-6082	596	81	the	the	DET
ejpam-6082	596	82	infected	infected	ADJ
ejpam-6082	596	83	non	non	ADJ
ejpam-6082	596	84	-	-	ADJ
ejpam-6082	596	85	paralytic	paralytic	ADJ
ejpam-6082	596	86	population	population	NOUN
ejpam-6082	596	87	for	for	ADP
ejpam-6082	596	88	different	different	ADJ
ejpam-6082	596	89	fractional	fractional	ADJ
ejpam-6082	596	90	orders	order	NOUN
ejpam-6082	596	91	α	α	NOUN
ejpam-6082	596	92	.	.	PUNCT
ejpam-6082	597	1	k.	k.	PROPN
ejpam-6082	597	2	guedri	guedri	PROPN
ejpam-6082	597	3	et	et	PROPN
ejpam-6082	597	4	al	al	PROPN
ejpam-6082	597	5	.	.	PUNCT
ejpam-6082	597	6	/	/	SYM
ejpam-6082	597	7	eur	eur	PROPN
ejpam-6082	597	8	.	.	PUNCT
ejpam-6082	598	1	j.	j.	PROPN
ejpam-6082	598	2	pure	pure	PROPN
ejpam-6082	598	3	appl	appl	PROPN
ejpam-6082	598	4	.	.	PROPN
ejpam-6082	598	5	math	math	PROPN
ejpam-6082	598	6	,	,	PUNCT
ejpam-6082	598	7	18	18	NUM
ejpam-6082	598	8	(	(	PUNCT
ejpam-6082	598	9	2	2	NUM
ejpam-6082	598	10	)	)	PUNCT
ejpam-6082	598	11	(	(	PUNCT
ejpam-6082	598	12	2025	2025	NUM
ejpam-6082	598	13	)	)	PUNCT
ejpam-6082	598	14	,	,	PUNCT
ejpam-6082	598	15	6082	6082	NUM
ejpam-6082	598	16	30	30	NUM
ejpam-6082	598	17	of	of	ADP
ejpam-6082	598	18	39	39	NUM
ejpam-6082	598	19	(	(	PUNCT
ejpam-6082	598	20	a	a	NOUN
ejpam-6082	598	21	)	)	PUNCT
ejpam-6082	598	22	0	0	NUM
ejpam-6082	598	23	100	100	NUM
ejpam-6082	598	24	200	200	NUM
ejpam-6082	598	25	300	300	NUM
ejpam-6082	598	26	400	400	NUM
ejpam-6082	598	27	500	500	NUM
ejpam-6082	598	28	600	600	NUM
ejpam-6082	598	29	700	700	NUM
ejpam-6082	598	30	800	800	NUM
ejpam-6082	598	31	time	time	NOUN
ejpam-6082	598	32	in	in	ADP
ejpam-6082	598	33	days	day	NOUN
ejpam-6082	598	34	-1	-1	SYM
ejpam-6082	598	35	0	0	NUM
ejpam-6082	598	36	1	1	NUM
ejpam-6082	598	37	2	2	NUM
ejpam-6082	598	38	3	3	NUM
ejpam-6082	598	39	4	4	NUM
ejpam-6082	598	40	5	5	NUM
ejpam-6082	598	41	6	6	NUM
ejpam-6082	598	42	7	7	NUM
ejpam-6082	598	43	8	8	NUM
ejpam-6082	598	44	9	9	NUM
ejpam-6082	598	45	n	n	NOUN
ejpam-6082	598	46	p	p	X
ejpam-6082	598	47	(	(	PUNCT
ejpam-6082	598	48	t	t	PROPN
ejpam-6082	598	49	)	)	PUNCT
ejpam-6082	598	50	in	in	ADP
ejpam-6082	598	51	fe	fe	X
ejpam-6082	598	52	c	c	X
ejpam-6082	598	53	te	te	PROPN
ejpam-6082	598	54	d	d	PROPN
ejpam-6082	598	55	n	n	NOUN
ejpam-6082	598	56	o	o	NOUN
ejpam-6082	598	57	n	n	INTJ
ejpam-6082	598	58	-p	-p	ADV
ejpam-6082	598	59	a	a	DET
ejpam-6082	598	60	ra	ra	NOUN
ejpam-6082	598	61	ly	ly	X
ejpam-6082	598	62	ti	ti	NOUN
ejpam-6082	598	63	c	c	NOUN
ejpam-6082	598	64	p	p	NOUN
ejpam-6082	598	65	o	o	X
ejpam-6082	598	66	p	p	X
ejpam-6082	598	67	u	u	X
ejpam-6082	598	68	la	la	X
ejpam-6082	598	69	ti	ti	X
ejpam-6082	598	70	o	o	NOUN
ejpam-6082	598	71	n	n	PROPN
ejpam-6082	598	72	107infected	107infected	PROPN
ejpam-6082	598	73	non	non	ADJ
ejpam-6082	598	74	-	-	ADJ
ejpam-6082	598	75	paralytic	paralytic	ADJ
ejpam-6082	598	76	population	population	NOUN
ejpam-6082	598	77	over	over	ADP
ejpam-6082	598	78	time	time	NOUN
ejpam-6082	598	79	for	for	ADP
ejpam-6082	598	80	different	different	ADJ
ejpam-6082	598	81	=	=	SYM
ejpam-6082	598	82	0.8	0.8	NUM
ejpam-6082	598	83	=	=	SYM
ejpam-6082	598	84	0.85	0.85	NUM
ejpam-6082	598	85	=	=	SYM
ejpam-6082	598	86	0.9	0.9	NUM
ejpam-6082	598	87	=	=	SYM
ejpam-6082	598	88	0.95	0.95	NUM
ejpam-6082	598	89	=	=	SYM
ejpam-6082	598	90	1	1	NUM
ejpam-6082	598	91	(	(	PUNCT
ejpam-6082	598	92	b	b	NOUN
ejpam-6082	598	93	)	)	PUNCT
ejpam-6082	598	94	figure	figure	NOUN
ejpam-6082	598	95	12	12	NUM
ejpam-6082	598	96	:	:	PUNCT
ejpam-6082	598	97	long	long	ADJ
ejpam-6082	598	98	term	term	NOUN
ejpam-6082	598	99	behavior	behavior	NOUN
ejpam-6082	598	100	of	of	ADP
ejpam-6082	598	101	infected	infected	ADJ
ejpam-6082	598	102	non	non	ADJ
ejpam-6082	598	103	-	-	ADJ
ejpam-6082	598	104	paralytic	paralytic	ADJ
ejpam-6082	598	105	population	population	NOUN
ejpam-6082	598	106	for	for	ADP
ejpam-6082	598	107	different	different	ADJ
ejpam-6082	598	108	fractional	fractional	ADJ
ejpam-6082	598	109	orders	order	NOUN
ejpam-6082	598	110	α	α	NOUN
ejpam-6082	598	111	.	.	PUNCT
ejpam-6082	599	1	the	the	DET
ejpam-6082	599	2	infected	infected	ADJ
ejpam-6082	599	3	non	non	ADJ
ejpam-6082	599	4	-	-	ADJ
ejpam-6082	599	5	paralytic	paralytic	ADJ
ejpam-6082	599	6	population	population	NOUN
ejpam-6082	599	7	np(t	np(t	ADP
ejpam-6082	599	8	,	,	PUNCT
ejpam-6082	599	9	x	x	NOUN
ejpam-6082	599	10	)	)	PUNCT
ejpam-6082	599	11	,	,	PUNCT
ejpam-6082	599	12	shown	show	VERB
ejpam-6082	599	13	in	in	ADP
ejpam-6082	599	14	figure	figure	NOUN
ejpam-6082	599	15	12	12	NUM
ejpam-6082	599	16	,	,	PUNCT
ejpam-6082	599	17	highlights	highlight	VERB
ejpam-6082	599	18	the	the	DET
ejpam-6082	599	19	effects	effect	NOUN
ejpam-6082	599	20	of	of	ADP
ejpam-6082	599	21	fractional	fractional	ADJ
ejpam-6082	599	22	orders	order	NOUN
ejpam-6082	599	23	and	and	CCONJ
ejpam-6082	599	24	spatial	spatial	ADJ
ejpam-6082	599	25	factors	factor	NOUN
ejpam-6082	599	26	on	on	ADP
ejpam-6082	599	27	disease	disease	NOUN
ejpam-6082	599	28	dynamics	dynamic	NOUN
ejpam-6082	599	29	.	.	PUNCT
ejpam-6082	600	1	smaller	small	ADJ
ejpam-6082	600	2	α	α	NOUN
ejpam-6082	600	3	values	value	NOUN
ejpam-6082	600	4	(	(	PUNCT
ejpam-6082	600	5	e.g.	e.g.	ADV
ejpam-6082	600	6	,	,	PUNCT
ejpam-6082	600	7	α	α	NOUN
ejpam-6082	600	8	=	=	SYM
ejpam-6082	600	9	0.7	0.7	NUM
ejpam-6082	600	10	)	)	PUNCT
ejpam-6082	600	11	produce	produce	VERB
ejpam-6082	600	12	earlier	early	ADV
ejpam-6082	600	13	and	and	CCONJ
ejpam-6082	600	14	sharper	sharp	ADJ
ejpam-6082	600	15	peaks	peak	NOUN
ejpam-6082	600	16	,	,	PUNCT
ejpam-6082	600	17	reflecting	reflect	VERB
ejpam-6082	600	18	accelerated	accelerate	VERB
ejpam-6082	600	19	disease	disease	NOUN
ejpam-6082	600	20	progression	progression	NOUN
ejpam-6082	600	21	due	due	ADP
ejpam-6082	600	22	to	to	ADP
ejpam-6082	600	23	memory	memory	NOUN
ejpam-6082	600	24	effects	effect	NOUN
ejpam-6082	600	25	.	.	PUNCT
ejpam-6082	601	1	conversely	conversely	ADV
ejpam-6082	601	2	,	,	PUNCT
ejpam-6082	601	3	larger	large	ADJ
ejpam-6082	601	4	α	α	NOUN
ejpam-6082	601	5	values	value	NOUN
ejpam-6082	601	6	(	(	PUNCT
ejpam-6082	601	7	e.g.	e.g.	ADV
ejpam-6082	601	8	,	,	PUNCT
ejpam-6082	601	9	α	α	NOUN
ejpam-6082	601	10	=	=	SYM
ejpam-6082	601	11	0.9	0.9	NUM
ejpam-6082	601	12	)	)	PUNCT
ejpam-6082	601	13	lead	lead	VERB
ejpam-6082	601	14	to	to	ADP
ejpam-6082	601	15	delayed	delay	VERB
ejpam-6082	601	16	peaks	peak	NOUN
ejpam-6082	601	17	and	and	CCONJ
ejpam-6082	601	18	gradual	gradual	ADJ
ejpam-6082	601	19	transitions	transition	NOUN
ejpam-6082	601	20	.	.	PUNCT
ejpam-6082	602	1	the	the	DET
ejpam-6082	602	2	spatial	spatial	ADJ
ejpam-6082	602	3	plot	plot	NOUN
ejpam-6082	602	4	underscores	underscore	VERB
ejpam-6082	602	5	localized	localized	ADJ
ejpam-6082	602	6	transmission	transmission	NOUN
ejpam-6082	602	7	influenced	influence	VERB
ejpam-6082	602	8	by	by	ADP
ejpam-6082	602	9	high	high	ADJ
ejpam-6082	602	10	population	population	NOUN
ejpam-6082	602	11	densities	density	NOUN
ejpam-6082	602	12	and	and	CCONJ
ejpam-6082	602	13	environmental	environmental	ADJ
ejpam-6082	602	14	factors	factor	NOUN
ejpam-6082	602	15	,	,	PUNCT
ejpam-6082	602	16	necessitating	necessitate	VERB
ejpam-6082	602	17	targeted	target	VERB
ejpam-6082	602	18	public	public	ADJ
ejpam-6082	602	19	health	health	NOUN
ejpam-6082	602	20	measures	measure	NOUN
ejpam-6082	602	21	.	.	PUNCT
ejpam-6082	603	1	fractional	fractional	ADJ
ejpam-6082	603	2	-	-	PUNCT
ejpam-6082	603	3	order	order	NOUN
ejpam-6082	603	4	models	model	NOUN
ejpam-6082	603	5	provide	provide	VERB
ejpam-6082	603	6	critical	critical	ADJ
ejpam-6082	603	7	insights	insight	NOUN
ejpam-6082	603	8	into	into	ADP
ejpam-6082	603	9	managing	manage	VERB
ejpam-6082	603	10	non	non	ADJ
ejpam-6082	603	11	-	-	ADJ
ejpam-6082	603	12	paralytic	paralytic	ADJ
ejpam-6082	603	13	infections	infection	NOUN
ejpam-6082	603	14	and	and	CCONJ
ejpam-6082	603	15	mitigating	mitigate	VERB
ejpam-6082	603	16	transmission	transmission	NOUN
ejpam-6082	603	17	risks	risk	NOUN
ejpam-6082	603	18	.	.	PUNCT
ejpam-6082	604	1	k.	k.	PROPN
ejpam-6082	604	2	guedri	guedri	PROPN
ejpam-6082	604	3	et	et	PROPN
ejpam-6082	604	4	al	al	PROPN
ejpam-6082	604	5	.	.	PUNCT
ejpam-6082	604	6	/	/	SYM
ejpam-6082	604	7	eur	eur	PROPN
ejpam-6082	604	8	.	.	PUNCT
ejpam-6082	605	1	j.	j.	PROPN
ejpam-6082	605	2	pure	pure	PROPN
ejpam-6082	605	3	appl	appl	PROPN
ejpam-6082	605	4	.	.	PROPN
ejpam-6082	605	5	math	math	PROPN
ejpam-6082	605	6	,	,	PUNCT
ejpam-6082	605	7	18	18	NUM
ejpam-6082	605	8	(	(	PUNCT
ejpam-6082	605	9	2	2	NUM
ejpam-6082	605	10	)	)	PUNCT
ejpam-6082	605	11	(	(	PUNCT
ejpam-6082	605	12	2025	2025	NUM
ejpam-6082	605	13	)	)	PUNCT
ejpam-6082	605	14	,	,	PUNCT
ejpam-6082	605	15	6082	6082	NUM
ejpam-6082	605	16	31	31	NUM
ejpam-6082	605	17	of	of	ADP
ejpam-6082	605	18	39	39	NUM
ejpam-6082	605	19	(	(	PUNCT
ejpam-6082	605	20	a	a	NOUN
ejpam-6082	605	21	)	)	PUNCT
ejpam-6082	605	22	0	0	NUM
ejpam-6082	605	23	50	50	NUM
ejpam-6082	605	24	100	100	NUM
ejpam-6082	605	25	150	150	NUM
ejpam-6082	605	26	200	200	NUM
ejpam-6082	605	27	250	250	NUM
ejpam-6082	605	28	300	300	NUM
ejpam-6082	605	29	350	350	NUM
ejpam-6082	605	30	400	400	NUM
ejpam-6082	605	31	time	time	NOUN
ejpam-6082	605	32	in	in	ADP
ejpam-6082	605	33	days	day	NOUN
ejpam-6082	605	34	0	0	NUM
ejpam-6082	605	35	0.5	0.5	NUM
ejpam-6082	605	36	1	1	NUM
ejpam-6082	605	37	1.5	1.5	NUM
ejpam-6082	605	38	2	2	NUM
ejpam-6082	605	39	2.5	2.5	NUM
ejpam-6082	605	40	3	3	NUM
ejpam-6082	605	41	3.5	3.5	NUM
ejpam-6082	605	42	4	4	NUM
ejpam-6082	605	43	p	p	NOUN
ejpam-6082	605	44	(	(	PUNCT
ejpam-6082	605	45	t	t	PROPN
ejpam-6082	605	46	)	)	PUNCT
ejpam-6082	605	47	in	in	ADP
ejpam-6082	605	48	fe	fe	X
ejpam-6082	605	49	c	c	X
ejpam-6082	605	50	te	te	PROPN
ejpam-6082	606	1	d	d	X
ejpam-6082	606	2	p	p	X
ejpam-6082	606	3	a	a	DET
ejpam-6082	606	4	ra	ra	NOUN
ejpam-6082	606	5	ly	ly	ADP
ejpam-6082	606	6	ti	ti	NOUN
ejpam-6082	607	1	c	c	NOUN
ejpam-6082	607	2	p	p	NOUN
ejpam-6082	607	3	o	o	X
ejpam-6082	607	4	p	p	X
ejpam-6082	607	5	u	u	X
ejpam-6082	607	6	la	la	X
ejpam-6082	607	7	ti	ti	X
ejpam-6082	607	8	o	o	NOUN
ejpam-6082	607	9	n	n	CCONJ
ejpam-6082	607	10	107	107	NUM
ejpam-6082	607	11	infected	infect	VERB
ejpam-6082	607	12	paralytic	paralytic	ADJ
ejpam-6082	607	13	population	population	NOUN
ejpam-6082	607	14	over	over	ADP
ejpam-6082	607	15	time	time	NOUN
ejpam-6082	607	16	for	for	ADP
ejpam-6082	607	17	different	different	ADJ
ejpam-6082	608	1	=	=	SYM
ejpam-6082	608	2	0.7	0.7	NUM
ejpam-6082	608	3	=	=	SYM
ejpam-6082	608	4	0.75	0.75	NUM
ejpam-6082	608	5	=	=	SYM
ejpam-6082	608	6	0.8	0.8	NUM
ejpam-6082	608	7	=	=	SYM
ejpam-6082	608	8	0.85	0.85	NUM
ejpam-6082	608	9	=	=	SYM
ejpam-6082	608	10	0.9	0.9	NUM
ejpam-6082	608	11	(	(	PUNCT
ejpam-6082	608	12	b	b	NOUN
ejpam-6082	608	13	)	)	PUNCT
ejpam-6082	608	14	figure	figure	NOUN
ejpam-6082	608	15	13	13	NUM
ejpam-6082	608	16	:	:	PUNCT
ejpam-6082	608	17	simulation	simulation	NOUN
ejpam-6082	608	18	results	result	NOUN
ejpam-6082	608	19	of	of	ADP
ejpam-6082	608	20	the	the	DET
ejpam-6082	608	21	infected	infected	ADJ
ejpam-6082	608	22	paralytic	paralytic	ADJ
ejpam-6082	608	23	population	population	NOUN
ejpam-6082	608	24	for	for	ADP
ejpam-6082	608	25	different	different	ADJ
ejpam-6082	608	26	fractional	fractional	ADJ
ejpam-6082	608	27	orders	order	NOUN
ejpam-6082	608	28	α	α	X
ejpam-6082	608	29	.	.	PUNCT
ejpam-6082	609	1	(	(	PUNCT
ejpam-6082	609	2	a	a	X
ejpam-6082	609	3	)	)	PUNCT
ejpam-6082	609	4	0	0	NUM
ejpam-6082	609	5	100	100	NUM
ejpam-6082	609	6	200	200	NUM
ejpam-6082	609	7	300	300	NUM
ejpam-6082	609	8	400	400	NUM
ejpam-6082	609	9	500	500	NUM
ejpam-6082	609	10	600	600	NUM
ejpam-6082	609	11	700	700	NUM
ejpam-6082	609	12	800	800	NUM
ejpam-6082	609	13	time	time	NOUN
ejpam-6082	609	14	in	in	ADP
ejpam-6082	609	15	days	day	NOUN
ejpam-6082	609	16	-0.5	-0.5	X
ejpam-6082	609	17	0	0	NUM
ejpam-6082	609	18	0.5	0.5	NUM
ejpam-6082	609	19	1	1	NUM
ejpam-6082	609	20	1.5	1.5	NUM
ejpam-6082	609	21	2	2	NUM
ejpam-6082	609	22	2.5	2.5	NUM
ejpam-6082	609	23	3	3	NUM
ejpam-6082	609	24	3.5	3.5	NUM
ejpam-6082	609	25	4	4	NUM
ejpam-6082	609	26	4.5	4.5	NUM
ejpam-6082	609	27	p	p	NOUN
ejpam-6082	609	28	(	(	PUNCT
ejpam-6082	609	29	t	t	PROPN
ejpam-6082	609	30	)	)	PUNCT
ejpam-6082	609	31	in	in	ADP
ejpam-6082	609	32	fe	fe	X
ejpam-6082	610	1	c	c	X
ejpam-6082	610	2	te	te	PROPN
ejpam-6082	611	1	d	d	X
ejpam-6082	611	2	p	p	X
ejpam-6082	611	3	a	a	DET
ejpam-6082	611	4	ra	ra	NOUN
ejpam-6082	611	5	ly	ly	ADP
ejpam-6082	611	6	ti	ti	NOUN
ejpam-6082	612	1	c	c	NOUN
ejpam-6082	612	2	p	p	NOUN
ejpam-6082	612	3	o	o	X
ejpam-6082	612	4	p	p	X
ejpam-6082	612	5	u	u	X
ejpam-6082	612	6	la	la	X
ejpam-6082	612	7	ti	ti	X
ejpam-6082	612	8	o	o	NOUN
ejpam-6082	612	9	n	n	CCONJ
ejpam-6082	612	10	107	107	NUM
ejpam-6082	612	11	infected	infect	VERB
ejpam-6082	612	12	paralytic	paralytic	ADJ
ejpam-6082	612	13	population	population	NOUN
ejpam-6082	612	14	over	over	ADP
ejpam-6082	612	15	time	time	NOUN
ejpam-6082	612	16	for	for	ADP
ejpam-6082	612	17	different	different	ADJ
ejpam-6082	612	18	=	=	SYM
ejpam-6082	612	19	0.8	0.8	NUM
ejpam-6082	612	20	=	=	SYM
ejpam-6082	612	21	0.85	0.85	NUM
ejpam-6082	612	22	=	=	SYM
ejpam-6082	612	23	0.9	0.9	NUM
ejpam-6082	612	24	=	=	SYM
ejpam-6082	612	25	0.95	0.95	NUM
ejpam-6082	612	26	=	=	SYM
ejpam-6082	612	27	1	1	NUM
ejpam-6082	612	28	(	(	PUNCT
ejpam-6082	612	29	b	b	NOUN
ejpam-6082	612	30	)	)	PUNCT
ejpam-6082	612	31	figure	figure	NOUN
ejpam-6082	612	32	14	14	NUM
ejpam-6082	612	33	:	:	PUNCT
ejpam-6082	612	34	long	long	ADJ
ejpam-6082	612	35	term	term	NOUN
ejpam-6082	612	36	behavior	behavior	NOUN
ejpam-6082	612	37	of	of	ADP
ejpam-6082	612	38	infected	infected	ADJ
ejpam-6082	612	39	paralytic	paralytic	ADJ
ejpam-6082	612	40	population	population	NOUN
ejpam-6082	612	41	for	for	ADP
ejpam-6082	612	42	different	different	ADJ
ejpam-6082	612	43	fractional	fractional	ADJ
ejpam-6082	612	44	orders	order	NOUN
ejpam-6082	612	45	α	α	NOUN
ejpam-6082	612	46	.	.	PUNCT
ejpam-6082	613	1	k.	k.	PROPN
ejpam-6082	613	2	guedri	guedri	PROPN
ejpam-6082	613	3	et	et	PROPN
ejpam-6082	613	4	al	al	PROPN
ejpam-6082	613	5	.	.	PUNCT
ejpam-6082	613	6	/	/	SYM
ejpam-6082	613	7	eur	eur	PROPN
ejpam-6082	613	8	.	.	PUNCT
ejpam-6082	614	1	j.	j.	PROPN
ejpam-6082	614	2	pure	pure	PROPN
ejpam-6082	614	3	appl	appl	PROPN
ejpam-6082	614	4	.	.	PROPN
ejpam-6082	614	5	math	math	PROPN
ejpam-6082	614	6	,	,	PUNCT
ejpam-6082	614	7	18	18	NUM
ejpam-6082	614	8	(	(	PUNCT
ejpam-6082	614	9	2	2	NUM
ejpam-6082	614	10	)	)	PUNCT
ejpam-6082	614	11	(	(	PUNCT
ejpam-6082	614	12	2025	2025	NUM
ejpam-6082	614	13	)	)	PUNCT
ejpam-6082	614	14	,	,	PUNCT
ejpam-6082	614	15	6082	6082	NUM
ejpam-6082	614	16	32	32	NUM
ejpam-6082	614	17	of	of	ADP
ejpam-6082	614	18	39	39	NUM
ejpam-6082	614	19	the	the	DET
ejpam-6082	614	20	dynamics	dynamic	NOUN
ejpam-6082	614	21	of	of	ADP
ejpam-6082	614	22	the	the	DET
ejpam-6082	614	23	infected	infected	ADJ
ejpam-6082	614	24	paralytic	paralytic	ADJ
ejpam-6082	614	25	population	population	NOUN
ejpam-6082	614	26	p	p	X
ejpam-6082	614	27	(	(	PUNCT
ejpam-6082	614	28	t	t	PROPN
ejpam-6082	614	29	,	,	PUNCT
ejpam-6082	614	30	x	x	NOUN
ejpam-6082	614	31	)	)	PUNCT
ejpam-6082	614	32	,	,	PUNCT
ejpam-6082	614	33	shown	show	VERB
ejpam-6082	614	34	in	in	ADP
ejpam-6082	614	35	figure	figure	NOUN
ejpam-6082	614	36	14	14	NUM
ejpam-6082	614	37	,	,	PUNCT
ejpam-6082	614	38	reveal	reveal	VERB
ejpam-6082	614	39	critical	critical	ADJ
ejpam-6082	614	40	insights	insight	NOUN
ejpam-6082	614	41	into	into	ADP
ejpam-6082	614	42	severe	severe	ADJ
ejpam-6082	614	43	polio	polio	NOUN
ejpam-6082	614	44	manifestations	manifestation	NOUN
ejpam-6082	614	45	.	.	PUNCT
ejpam-6082	615	1	smaller	small	ADJ
ejpam-6082	615	2	α	α	NOUN
ejpam-6082	615	3	values	value	NOUN
ejpam-6082	615	4	(	(	PUNCT
ejpam-6082	615	5	e.g.	e.g.	ADV
ejpam-6082	615	6	,	,	PUNCT
ejpam-6082	615	7	α	α	NOUN
ejpam-6082	615	8	=	=	SYM
ejpam-6082	615	9	0.7	0.7	NUM
ejpam-6082	615	10	)	)	PUNCT
ejpam-6082	615	11	yield	yield	VERB
ejpam-6082	615	12	faster	fast	ADJ
ejpam-6082	615	13	progression	progression	NOUN
ejpam-6082	615	14	to	to	ADP
ejpam-6082	615	15	paralysis	paralysis	NOUN
ejpam-6082	615	16	,	,	PUNCT
ejpam-6082	615	17	while	while	SCONJ
ejpam-6082	615	18	larger	large	ADJ
ejpam-6082	615	19	α	α	NOUN
ejpam-6082	615	20	values	value	NOUN
ejpam-6082	615	21	(	(	PUNCT
ejpam-6082	615	22	e.g.	e.g.	ADV
ejpam-6082	615	23	,	,	PUNCT
ejpam-6082	615	24	α	α	NOUN
ejpam-6082	615	25	=	=	SYM
ejpam-6082	615	26	0.9	0.9	NUM
ejpam-6082	615	27	)	)	PUNCT
ejpam-6082	615	28	result	result	NOUN
ejpam-6082	615	29	in	in	ADP
ejpam-6082	615	30	delayed	delay	VERB
ejpam-6082	615	31	but	but	CCONJ
ejpam-6082	615	32	more	more	ADJ
ejpam-6082	615	33	prolonged	prolonged	ADJ
ejpam-6082	615	34	peaks	peak	NOUN
ejpam-6082	615	35	.	.	PUNCT
ejpam-6082	616	1	spatial	spatial	ADJ
ejpam-6082	616	2	heterogeneity	heterogeneity	NOUN
ejpam-6082	616	3	highlights	highlight	NOUN
ejpam-6082	616	4	regions	region	NOUN
ejpam-6082	616	5	with	with	ADP
ejpam-6082	616	6	concentrated	concentrated	ADJ
ejpam-6082	616	7	severe	severe	ADJ
ejpam-6082	616	8	cases	case	NOUN
ejpam-6082	616	9	,	,	PUNCT
ejpam-6082	616	10	driven	drive	VERB
ejpam-6082	616	11	by	by	ADP
ejpam-6082	616	12	diffusion	diffusion	NOUN
ejpam-6082	616	13	and	and	CCONJ
ejpam-6082	616	14	clustering	clustering	ADJ
ejpam-6082	616	15	effects	effect	NOUN
ejpam-6082	616	16	.	.	PUNCT
ejpam-6082	617	1	these	these	DET
ejpam-6082	617	2	results	result	NOUN
ejpam-6082	617	3	emphasize	emphasize	VERB
ejpam-6082	617	4	the	the	DET
ejpam-6082	617	5	need	need	NOUN
ejpam-6082	617	6	for	for	ADP
ejpam-6082	617	7	targeted	target	VERB
ejpam-6082	617	8	medical	medical	ADJ
ejpam-6082	617	9	interventions	intervention	NOUN
ejpam-6082	617	10	and	and	CCONJ
ejpam-6082	617	11	enhanced	enhance	VERB
ejpam-6082	617	12	sanitation	sanitation	NOUN
ejpam-6082	617	13	in	in	ADP
ejpam-6082	617	14	high	high	ADJ
ejpam-6082	617	15	-	-	PUNCT
ejpam-6082	617	16	incidence	incidence	NOUN
ejpam-6082	617	17	regions	region	NOUN
ejpam-6082	617	18	,	,	PUNCT
ejpam-6082	617	19	demonstrating	demonstrate	VERB
ejpam-6082	617	20	the	the	DET
ejpam-6082	617	21	model	model	NOUN
ejpam-6082	617	22	’s	’s	PART
ejpam-6082	617	23	value	value	NOUN
ejpam-6082	617	24	in	in	ADP
ejpam-6082	617	25	understanding	understand	VERB
ejpam-6082	617	26	paralytic	paralytic	ADJ
ejpam-6082	617	27	polio	polio	NOUN
ejpam-6082	617	28	dynamics	dynamic	NOUN
ejpam-6082	617	29	.	.	PUNCT
ejpam-6082	618	1	(	(	PUNCT
ejpam-6082	618	2	a	a	X
ejpam-6082	618	3	)	)	PUNCT
ejpam-6082	618	4	0	0	NUM
ejpam-6082	618	5	50	50	NUM
ejpam-6082	618	6	100	100	NUM
ejpam-6082	618	7	150	150	NUM
ejpam-6082	618	8	200	200	NUM
ejpam-6082	618	9	250	250	NUM
ejpam-6082	618	10	300	300	NUM
ejpam-6082	618	11	350	350	NUM
ejpam-6082	618	12	400	400	NUM
ejpam-6082	618	13	time	time	NOUN
ejpam-6082	618	14	in	in	ADP
ejpam-6082	618	15	days	day	NOUN
ejpam-6082	618	16	0	0	NUM
ejpam-6082	618	17	5	5	NUM
ejpam-6082	618	18	10	10	NUM
ejpam-6082	618	19	15	15	NUM
ejpam-6082	618	20	r	r	NOUN
ejpam-6082	618	21	(	(	PUNCT
ejpam-6082	618	22	t	t	NOUN
ejpam-6082	618	23	)	)	PUNCT
ejpam-6082	619	1	r	r	NOUN
ejpam-6082	619	2	e	e	NOUN
ejpam-6082	619	3	c	c	NOUN
ejpam-6082	619	4	o	o	X
ejpam-6082	619	5	v	v	X
ejpam-6082	619	6	e	e	X
ejpam-6082	619	7	re	re	NOUN
ejpam-6082	619	8	d	d	NOUN
ejpam-6082	619	9	p	p	X
ejpam-6082	619	10	o	o	X
ejpam-6082	619	11	p	p	X
ejpam-6082	619	12	u	u	X
ejpam-6082	619	13	la	la	X
ejpam-6082	619	14	ti	ti	X
ejpam-6082	619	15	o	o	NOUN
ejpam-6082	619	16	n	n	CCONJ
ejpam-6082	619	17	108	108	NUM
ejpam-6082	619	18	recovered	recover	VERB
ejpam-6082	619	19	population	population	NOUN
ejpam-6082	619	20	over	over	ADP
ejpam-6082	619	21	time	time	NOUN
ejpam-6082	619	22	for	for	ADP
ejpam-6082	619	23	different	different	ADJ
ejpam-6082	620	1	=	=	SYM
ejpam-6082	620	2	0.7	0.7	NUM
ejpam-6082	620	3	=	=	SYM
ejpam-6082	620	4	0.75	0.75	NUM
ejpam-6082	620	5	=	=	SYM
ejpam-6082	620	6	0.8	0.8	NUM
ejpam-6082	620	7	=	=	SYM
ejpam-6082	620	8	0.85	0.85	NUM
ejpam-6082	620	9	=	=	SYM
ejpam-6082	620	10	0.9	0.9	NUM
ejpam-6082	620	11	(	(	PUNCT
ejpam-6082	620	12	b	b	NOUN
ejpam-6082	620	13	)	)	PUNCT
ejpam-6082	620	14	figure	figure	NOUN
ejpam-6082	620	15	15	15	NUM
ejpam-6082	620	16	:	:	PUNCT
ejpam-6082	620	17	simulation	simulation	NOUN
ejpam-6082	620	18	results	result	NOUN
ejpam-6082	620	19	of	of	ADP
ejpam-6082	620	20	the	the	DET
ejpam-6082	620	21	recovered	recovered	ADJ
ejpam-6082	620	22	population	population	NOUN
ejpam-6082	620	23	for	for	ADP
ejpam-6082	620	24	different	different	ADJ
ejpam-6082	620	25	fractional	fractional	ADJ
ejpam-6082	620	26	orders	order	NOUN
ejpam-6082	620	27	α	α	NOUN
ejpam-6082	620	28	.	.	PUNCT
ejpam-6082	621	1	k.	k.	PROPN
ejpam-6082	621	2	guedri	guedri	PROPN
ejpam-6082	621	3	et	et	PROPN
ejpam-6082	621	4	al	al	PROPN
ejpam-6082	621	5	.	.	PUNCT
ejpam-6082	621	6	/	/	SYM
ejpam-6082	621	7	eur	eur	PROPN
ejpam-6082	621	8	.	.	PUNCT
ejpam-6082	622	1	j.	j.	PROPN
ejpam-6082	622	2	pure	pure	PROPN
ejpam-6082	622	3	appl	appl	PROPN
ejpam-6082	622	4	.	.	PROPN
ejpam-6082	622	5	math	math	PROPN
ejpam-6082	622	6	,	,	PUNCT
ejpam-6082	622	7	18	18	NUM
ejpam-6082	622	8	(	(	PUNCT
ejpam-6082	622	9	2	2	NUM
ejpam-6082	622	10	)	)	PUNCT
ejpam-6082	622	11	(	(	PUNCT
ejpam-6082	622	12	2025	2025	NUM
ejpam-6082	622	13	)	)	PUNCT
ejpam-6082	622	14	,	,	PUNCT
ejpam-6082	622	15	6082	6082	NUM
ejpam-6082	622	16	33	33	NUM
ejpam-6082	622	17	of	of	ADP
ejpam-6082	622	18	39	39	NUM
ejpam-6082	622	19	(	(	PUNCT
ejpam-6082	622	20	a	a	NOUN
ejpam-6082	622	21	)	)	PUNCT
ejpam-6082	622	22	0	0	NUM
ejpam-6082	623	1	100	100	NUM
ejpam-6082	623	2	200	200	NUM
ejpam-6082	623	3	300	300	NUM
ejpam-6082	623	4	400	400	NUM
ejpam-6082	623	5	500	500	NUM
ejpam-6082	623	6	600	600	NUM
ejpam-6082	623	7	700	700	NUM
ejpam-6082	623	8	800	800	NUM
ejpam-6082	623	9	time	time	NOUN
ejpam-6082	623	10	in	in	ADP
ejpam-6082	623	11	days	day	NOUN
ejpam-6082	623	12	0	0	NUM
ejpam-6082	623	13	2	2	NUM
ejpam-6082	623	14	4	4	NUM
ejpam-6082	623	15	6	6	NUM
ejpam-6082	623	16	8	8	NUM
ejpam-6082	623	17	10	10	NUM
ejpam-6082	623	18	12	12	NUM
ejpam-6082	623	19	14	14	NUM
ejpam-6082	623	20	16	16	NUM
ejpam-6082	623	21	18	18	NUM
ejpam-6082	623	22	r	r	NOUN
ejpam-6082	623	23	(	(	PUNCT
ejpam-6082	623	24	t	t	NOUN
ejpam-6082	623	25	)	)	PUNCT
ejpam-6082	624	1	r	r	NOUN
ejpam-6082	624	2	e	e	NOUN
ejpam-6082	624	3	c	c	NOUN
ejpam-6082	624	4	o	o	X
ejpam-6082	624	5	v	v	X
ejpam-6082	624	6	e	e	X
ejpam-6082	624	7	re	re	NOUN
ejpam-6082	624	8	d	d	NOUN
ejpam-6082	624	9	p	p	X
ejpam-6082	624	10	o	o	X
ejpam-6082	624	11	p	p	X
ejpam-6082	624	12	u	u	X
ejpam-6082	624	13	la	la	X
ejpam-6082	624	14	ti	ti	X
ejpam-6082	624	15	o	o	NOUN
ejpam-6082	624	16	n	n	CCONJ
ejpam-6082	624	17	108	108	NUM
ejpam-6082	624	18	recovered	recover	VERB
ejpam-6082	624	19	population	population	NOUN
ejpam-6082	624	20	over	over	ADP
ejpam-6082	624	21	time	time	NOUN
ejpam-6082	624	22	for	for	ADP
ejpam-6082	624	23	different	different	ADJ
ejpam-6082	624	24	=	=	SYM
ejpam-6082	624	25	0.8	0.8	NUM
ejpam-6082	624	26	=	=	SYM
ejpam-6082	624	27	0.85	0.85	NUM
ejpam-6082	624	28	=	=	SYM
ejpam-6082	624	29	0.9	0.9	NUM
ejpam-6082	624	30	=	=	SYM
ejpam-6082	624	31	0.95	0.95	NUM
ejpam-6082	624	32	=	=	SYM
ejpam-6082	624	33	1	1	NUM
ejpam-6082	624	34	(	(	PUNCT
ejpam-6082	624	35	b	b	NOUN
ejpam-6082	624	36	)	)	PUNCT
ejpam-6082	624	37	figure	figure	NOUN
ejpam-6082	624	38	16	16	NUM
ejpam-6082	624	39	:	:	PUNCT
ejpam-6082	624	40	long	long	ADJ
ejpam-6082	624	41	term	term	NOUN
ejpam-6082	624	42	behavior	behavior	NOUN
ejpam-6082	624	43	of	of	ADP
ejpam-6082	624	44	recovered	recovered	ADJ
ejpam-6082	624	45	population	population	NOUN
ejpam-6082	624	46	for	for	ADP
ejpam-6082	624	47	different	different	ADJ
ejpam-6082	624	48	fractional	fractional	ADJ
ejpam-6082	624	49	orders	order	NOUN
ejpam-6082	624	50	α	α	NOUN
ejpam-6082	624	51	.	.	PUNCT
ejpam-6082	625	1	the	the	DET
ejpam-6082	625	2	recovered	recovered	ADJ
ejpam-6082	625	3	population	population	NOUN
ejpam-6082	625	4	r(t	r(t	NOUN
ejpam-6082	625	5	,	,	PUNCT
ejpam-6082	625	6	x	x	NOUN
ejpam-6082	625	7	)	)	PUNCT
ejpam-6082	625	8	,	,	PUNCT
ejpam-6082	625	9	depicted	depict	VERB
ejpam-6082	625	10	in	in	ADP
ejpam-6082	625	11	figure	figure	NOUN
ejpam-6082	625	12	16	16	NUM
ejpam-6082	625	13	,	,	PUNCT
ejpam-6082	625	14	increases	increase	VERB
ejpam-6082	625	15	consistently	consistently	ADV
ejpam-6082	625	16	over	over	ADP
ejpam-6082	625	17	time	time	NOUN
ejpam-6082	625	18	across	across	ADP
ejpam-6082	625	19	all	all	DET
ejpam-6082	625	20	α	α	PRON
ejpam-6082	625	21	values	value	NOUN
ejpam-6082	625	22	.	.	PUNCT
ejpam-6082	626	1	smaller	small	ADJ
ejpam-6082	626	2	α	α	NOUN
ejpam-6082	626	3	values	value	NOUN
ejpam-6082	626	4	(	(	PUNCT
ejpam-6082	626	5	e.g.	e.g.	ADV
ejpam-6082	626	6	,	,	PUNCT
ejpam-6082	626	7	α	α	NOUN
ejpam-6082	626	8	=	=	SYM
ejpam-6082	626	9	0.7	0.7	NUM
ejpam-6082	626	10	)	)	PUNCT
ejpam-6082	626	11	result	result	NOUN
ejpam-6082	626	12	in	in	ADP
ejpam-6082	626	13	slower	slow	ADJ
ejpam-6082	626	14	recovery	recovery	NOUN
ejpam-6082	626	15	rates	rate	NOUN
ejpam-6082	626	16	,	,	PUNCT
ejpam-6082	626	17	while	while	SCONJ
ejpam-6082	626	18	larger	large	ADJ
ejpam-6082	626	19	α	α	NOUN
ejpam-6082	626	20	values	value	NOUN
ejpam-6082	626	21	(	(	PUNCT
ejpam-6082	626	22	e.g.	e.g.	ADV
ejpam-6082	626	23	,	,	PUNCT
ejpam-6082	626	24	α	α	NOUN
ejpam-6082	626	25	=	=	SYM
ejpam-6082	626	26	0.9	0.9	NUM
ejpam-6082	626	27	)	)	PUNCT
ejpam-6082	626	28	show	show	VERB
ejpam-6082	626	29	rapid	rapid	ADJ
ejpam-6082	626	30	recovery	recovery	NOUN
ejpam-6082	626	31	and	and	CCONJ
ejpam-6082	626	32	earlier	early	ADJ
ejpam-6082	626	33	saturation	saturation	NOUN
ejpam-6082	626	34	.	.	PUNCT
ejpam-6082	627	1	spatial	spatial	ADJ
ejpam-6082	627	2	analysis	analysis	NOUN
ejpam-6082	627	3	highlights	highlight	VERB
ejpam-6082	627	4	regional	regional	ADJ
ejpam-6082	627	5	disparities	disparity	NOUN
ejpam-6082	627	6	influenced	influence	VERB
ejpam-6082	627	7	by	by	ADP
ejpam-6082	627	8	vaccination	vaccination	NOUN
ejpam-6082	627	9	and	and	CCONJ
ejpam-6082	627	10	intervention	intervention	NOUN
ejpam-6082	627	11	efforts	effort	NOUN
ejpam-6082	627	12	.	.	PUNCT
ejpam-6082	628	1	these	these	DET
ejpam-6082	628	2	results	result	NOUN
ejpam-6082	628	3	guide	guide	VERB
ejpam-6082	628	4	the	the	DET
ejpam-6082	628	5	allocation	allocation	NOUN
ejpam-6082	628	6	of	of	ADP
ejpam-6082	628	7	resources	resource	NOUN
ejpam-6082	628	8	to	to	PART
ejpam-6082	628	9	optimize	optimize	VERB
ejpam-6082	628	10	recovery	recovery	NOUN
ejpam-6082	628	11	outcomes	outcome	NOUN
ejpam-6082	628	12	and	and	CCONJ
ejpam-6082	628	13	reduce	reduce	VERB
ejpam-6082	628	14	disease	disease	NOUN
ejpam-6082	628	15	burdens	burden	NOUN
ejpam-6082	628	16	.	.	PUNCT
ejpam-6082	629	1	k.	k.	PROPN
ejpam-6082	629	2	guedri	guedri	PROPN
ejpam-6082	629	3	et	et	PROPN
ejpam-6082	629	4	al	al	PROPN
ejpam-6082	629	5	.	.	PUNCT
ejpam-6082	629	6	/	/	SYM
ejpam-6082	629	7	eur	eur	PROPN
ejpam-6082	629	8	.	.	PUNCT
ejpam-6082	630	1	j.	j.	PROPN
ejpam-6082	630	2	pure	pure	PROPN
ejpam-6082	630	3	appl	appl	PROPN
ejpam-6082	630	4	.	.	PROPN
ejpam-6082	630	5	math	math	PROPN
ejpam-6082	630	6	,	,	PUNCT
ejpam-6082	630	7	18	18	NUM
ejpam-6082	630	8	(	(	PUNCT
ejpam-6082	630	9	2	2	NUM
ejpam-6082	630	10	)	)	PUNCT
ejpam-6082	630	11	(	(	PUNCT
ejpam-6082	630	12	2025	2025	NUM
ejpam-6082	630	13	)	)	PUNCT
ejpam-6082	630	14	,	,	PUNCT
ejpam-6082	630	15	6082	6082	NUM
ejpam-6082	630	16	34	34	NUM
ejpam-6082	630	17	of	of	ADP
ejpam-6082	630	18	39	39	NUM
ejpam-6082	630	19	(	(	PUNCT
ejpam-6082	630	20	a	a	NOUN
ejpam-6082	630	21	)	)	PUNCT
ejpam-6082	630	22	0	0	NUM
ejpam-6082	630	23	50	50	NUM
ejpam-6082	630	24	100	100	NUM
ejpam-6082	630	25	150	150	NUM
ejpam-6082	630	26	200	200	NUM
ejpam-6082	630	27	250	250	NUM
ejpam-6082	630	28	300	300	NUM
ejpam-6082	630	29	350	350	NUM
ejpam-6082	630	30	400	400	NUM
ejpam-6082	630	31	time	time	NOUN
ejpam-6082	630	32	in	in	ADP
ejpam-6082	630	33	days	day	NOUN
ejpam-6082	630	34	0	0	NUM
ejpam-6082	630	35	0.5	0.5	NUM
ejpam-6082	630	36	1	1	NUM
ejpam-6082	630	37	1.5	1.5	NUM
ejpam-6082	630	38	2	2	NUM
ejpam-6082	630	39	2.5	2.5	NUM
ejpam-6082	630	40	a	a	DET
ejpam-6082	630	41	(	(	PUNCT
ejpam-6082	630	42	t	t	NOUN
ejpam-6082	630	43	)	)	PUNCT
ejpam-6082	631	1	p	p	X
ejpam-6082	631	2	o	o	NOUN
ejpam-6082	631	3	s	s	X
ejpam-6082	631	4	tp	tp	NOUN
ejpam-6082	631	5	a	a	DET
ejpam-6082	631	6	ra	ra	NOUN
ejpam-6082	631	7	ly	ly	ADP
ejpam-6082	631	8	ti	ti	NOUN
ejpam-6082	631	9	c	c	NOUN
ejpam-6082	631	10	o	o	NOUN
ejpam-6082	631	11	r	r	NOUN
ejpam-6082	631	12	d	d	NOUN
ejpam-6082	631	13	is	be	AUX
ejpam-6082	632	1	a	a	DET
ejpam-6082	632	2	b	b	X
ejpam-6082	632	3	le	le	ADP
ejpam-6082	632	4	d	d	NOUN
ejpam-6082	632	5	p	p	X
ejpam-6082	632	6	o	o	X
ejpam-6082	632	7	p	p	X
ejpam-6082	632	8	u	u	X
ejpam-6082	632	9	la	la	X
ejpam-6082	632	10	ti	ti	X
ejpam-6082	632	11	o	o	NOUN
ejpam-6082	632	12	n	n	CCONJ
ejpam-6082	632	13	107	107	NUM
ejpam-6082	632	14	post	post	ADJ
ejpam-6082	632	15	-	-	ADJ
ejpam-6082	632	16	paralytic	paralytic	ADJ
ejpam-6082	632	17	population	population	NOUN
ejpam-6082	632	18	over	over	ADP
ejpam-6082	632	19	time	time	NOUN
ejpam-6082	632	20	for	for	ADP
ejpam-6082	632	21	different	different	ADJ
ejpam-6082	633	1	=	=	SYM
ejpam-6082	633	2	0.7	0.7	NUM
ejpam-6082	633	3	=	=	SYM
ejpam-6082	633	4	0.75	0.75	NUM
ejpam-6082	633	5	=	=	SYM
ejpam-6082	633	6	0.8	0.8	NUM
ejpam-6082	633	7	=	=	SYM
ejpam-6082	633	8	0.85	0.85	NUM
ejpam-6082	633	9	=	=	SYM
ejpam-6082	633	10	0.9	0.9	NUM
ejpam-6082	633	11	(	(	PUNCT
ejpam-6082	633	12	b	b	NOUN
ejpam-6082	633	13	)	)	PUNCT
ejpam-6082	633	14	figure	figure	NOUN
ejpam-6082	633	15	17	17	NUM
ejpam-6082	633	16	:	:	PUNCT
ejpam-6082	633	17	simulation	simulation	NOUN
ejpam-6082	633	18	results	result	NOUN
ejpam-6082	633	19	of	of	ADP
ejpam-6082	633	20	the	the	DET
ejpam-6082	633	21	post	post	ADJ
ejpam-6082	633	22	-	-	ADJ
ejpam-6082	633	23	paralytic	paralytic	ADJ
ejpam-6082	633	24	population	population	NOUN
ejpam-6082	633	25	for	for	ADP
ejpam-6082	633	26	different	different	ADJ
ejpam-6082	633	27	fractional	fractional	ADJ
ejpam-6082	633	28	orders	order	NOUN
ejpam-6082	633	29	α	α	X
ejpam-6082	633	30	.	.	PUNCT
ejpam-6082	634	1	(	(	PUNCT
ejpam-6082	634	2	a	a	X
ejpam-6082	634	3	)	)	PUNCT
ejpam-6082	634	4	0	0	NUM
ejpam-6082	634	5	100	100	NUM
ejpam-6082	634	6	200	200	NUM
ejpam-6082	634	7	300	300	NUM
ejpam-6082	634	8	400	400	NUM
ejpam-6082	634	9	500	500	NUM
ejpam-6082	634	10	600	600	NUM
ejpam-6082	634	11	700	700	NUM
ejpam-6082	634	12	800	800	NUM
ejpam-6082	634	13	time	time	NOUN
ejpam-6082	634	14	in	in	ADP
ejpam-6082	634	15	days	day	NOUN
ejpam-6082	634	16	0	0	NUM
ejpam-6082	634	17	2	2	NUM
ejpam-6082	634	18	4	4	NUM
ejpam-6082	634	19	6	6	NUM
ejpam-6082	634	20	8	8	NUM
ejpam-6082	634	21	10	10	NUM
ejpam-6082	634	22	12	12	NUM
ejpam-6082	634	23	a	a	DET
ejpam-6082	634	24	(	(	PUNCT
ejpam-6082	634	25	t	t	NOUN
ejpam-6082	634	26	)	)	PUNCT
ejpam-6082	635	1	p	p	X
ejpam-6082	635	2	o	o	NOUN
ejpam-6082	635	3	s	s	X
ejpam-6082	635	4	tp	tp	NOUN
ejpam-6082	635	5	a	a	DET
ejpam-6082	635	6	ra	ra	NOUN
ejpam-6082	635	7	ly	ly	ADP
ejpam-6082	635	8	ti	ti	NOUN
ejpam-6082	635	9	c	c	NOUN
ejpam-6082	635	10	o	o	NOUN
ejpam-6082	635	11	r	r	NOUN
ejpam-6082	635	12	d	d	NOUN
ejpam-6082	635	13	is	be	AUX
ejpam-6082	636	1	a	a	DET
ejpam-6082	636	2	b	b	X
ejpam-6082	636	3	le	le	ADP
ejpam-6082	636	4	d	d	NOUN
ejpam-6082	636	5	p	p	X
ejpam-6082	636	6	o	o	X
ejpam-6082	636	7	p	p	X
ejpam-6082	636	8	u	u	X
ejpam-6082	636	9	la	la	X
ejpam-6082	636	10	ti	ti	X
ejpam-6082	636	11	o	o	NOUN
ejpam-6082	636	12	n	n	CCONJ
ejpam-6082	636	13	107	107	NUM
ejpam-6082	636	14	post	post	ADJ
ejpam-6082	636	15	-	-	ADJ
ejpam-6082	636	16	paralytic	paralytic	ADJ
ejpam-6082	636	17	population	population	NOUN
ejpam-6082	636	18	over	over	ADP
ejpam-6082	636	19	time	time	NOUN
ejpam-6082	636	20	for	for	ADP
ejpam-6082	636	21	different	different	ADJ
ejpam-6082	636	22	=	=	SYM
ejpam-6082	636	23	0.8	0.8	NUM
ejpam-6082	636	24	=	=	SYM
ejpam-6082	636	25	0.85	0.85	NUM
ejpam-6082	636	26	=	=	SYM
ejpam-6082	636	27	0.9	0.9	NUM
ejpam-6082	636	28	=	=	SYM
ejpam-6082	636	29	0.95	0.95	NUM
ejpam-6082	636	30	=	=	SYM
ejpam-6082	636	31	1	1	NUM
ejpam-6082	636	32	(	(	PUNCT
ejpam-6082	636	33	b	b	NOUN
ejpam-6082	636	34	)	)	PUNCT
ejpam-6082	636	35	figure	figure	NOUN
ejpam-6082	636	36	18	18	NUM
ejpam-6082	636	37	:	:	PUNCT
ejpam-6082	636	38	long	long	ADJ
ejpam-6082	636	39	term	term	NOUN
ejpam-6082	636	40	behavior	behavior	NOUN
ejpam-6082	636	41	of	of	ADP
ejpam-6082	636	42	post	post	ADJ
ejpam-6082	636	43	-	-	ADJ
ejpam-6082	636	44	paralytic	paralytic	ADJ
ejpam-6082	636	45	population	population	NOUN
ejpam-6082	636	46	for	for	ADP
ejpam-6082	636	47	different	different	ADJ
ejpam-6082	636	48	fractional	fractional	ADJ
ejpam-6082	636	49	orders	order	NOUN
ejpam-6082	636	50	α	α	NOUN
ejpam-6082	636	51	.	.	PUNCT
ejpam-6082	637	1	k.	k.	PROPN
ejpam-6082	637	2	guedri	guedri	PROPN
ejpam-6082	637	3	et	et	PROPN
ejpam-6082	637	4	al	al	PROPN
ejpam-6082	637	5	.	.	PUNCT
ejpam-6082	637	6	/	/	SYM
ejpam-6082	637	7	eur	eur	PROPN
ejpam-6082	637	8	.	.	PUNCT
ejpam-6082	638	1	j.	j.	PROPN
ejpam-6082	638	2	pure	pure	PROPN
ejpam-6082	638	3	appl	appl	PROPN
ejpam-6082	638	4	.	.	PROPN
ejpam-6082	638	5	math	math	PROPN
ejpam-6082	638	6	,	,	PUNCT
ejpam-6082	638	7	18	18	NUM
ejpam-6082	638	8	(	(	PUNCT
ejpam-6082	638	9	2	2	NUM
ejpam-6082	638	10	)	)	PUNCT
ejpam-6082	638	11	(	(	PUNCT
ejpam-6082	638	12	2025	2025	NUM
ejpam-6082	638	13	)	)	PUNCT
ejpam-6082	638	14	,	,	PUNCT
ejpam-6082	638	15	6082	6082	NUM
ejpam-6082	638	16	35	35	NUM
ejpam-6082	638	17	of	of	ADP
ejpam-6082	638	18	39	39	NUM
ejpam-6082	638	19	figure	figure	NOUN
ejpam-6082	638	20	18	18	NUM
ejpam-6082	638	21	highlights	highlight	NOUN
ejpam-6082	638	22	the	the	DET
ejpam-6082	638	23	dynamics	dynamic	NOUN
ejpam-6082	638	24	of	of	ADP
ejpam-6082	638	25	the	the	DET
ejpam-6082	638	26	post	post	ADJ
ejpam-6082	638	27	-	-	ADJ
ejpam-6082	638	28	paralytic	paralytic	ADJ
ejpam-6082	638	29	population	population	NOUN
ejpam-6082	638	30	a(t	a(t	NOUN
ejpam-6082	638	31	,	,	PUNCT
ejpam-6082	638	32	x	x	NOUN
ejpam-6082	638	33	)	)	PUNCT
ejpam-6082	638	34	,	,	PUNCT
ejpam-6082	638	35	representing	represent	VERB
ejpam-6082	638	36	individuals	individual	NOUN
ejpam-6082	638	37	with	with	ADP
ejpam-6082	638	38	long	long	ADJ
ejpam-6082	638	39	-	-	PUNCT
ejpam-6082	638	40	term	term	NOUN
ejpam-6082	638	41	effects	effect	NOUN
ejpam-6082	638	42	of	of	ADP
ejpam-6082	638	43	polio	polio	NOUN
ejpam-6082	638	44	.	.	PUNCT
ejpam-6082	639	1	smaller	small	ADJ
ejpam-6082	639	2	α	α	NOUN
ejpam-6082	639	3	values	value	NOUN
ejpam-6082	639	4	(	(	PUNCT
ejpam-6082	639	5	e.g.	e.g.	ADV
ejpam-6082	639	6	,	,	PUNCT
ejpam-6082	639	7	α	α	NOUN
ejpam-6082	639	8	=	=	SYM
ejpam-6082	639	9	0.7	0.7	NUM
ejpam-6082	639	10	)	)	PUNCT
ejpam-6082	639	11	lead	lead	NOUN
ejpam-6082	639	12	to	to	ADP
ejpam-6082	639	13	slower	slow	ADJ
ejpam-6082	639	14	growth	growth	NOUN
ejpam-6082	639	15	,	,	PUNCT
ejpam-6082	639	16	while	while	SCONJ
ejpam-6082	639	17	larger	large	ADJ
ejpam-6082	639	18	values	value	NOUN
ejpam-6082	639	19	(	(	PUNCT
ejpam-6082	639	20	e.g.	e.g.	ADV
ejpam-6082	639	21	,	,	PUNCT
ejpam-6082	639	22	α	α	NOUN
ejpam-6082	639	23	=	=	SYM
ejpam-6082	639	24	0.9	0.9	NUM
ejpam-6082	639	25	)	)	PUNCT
ejpam-6082	639	26	show	show	VERB
ejpam-6082	639	27	rapid	rapid	ADJ
ejpam-6082	639	28	accumulation	accumulation	NOUN
ejpam-6082	639	29	.	.	PUNCT
ejpam-6082	640	1	spatial	spatial	ADJ
ejpam-6082	640	2	heterogeneity	heterogeneity	NOUN
ejpam-6082	640	3	emphasizes	emphasize	VERB
ejpam-6082	640	4	regions	region	NOUN
ejpam-6082	640	5	with	with	ADP
ejpam-6082	640	6	higher	high	ADJ
ejpam-6082	640	7	densities	density	NOUN
ejpam-6082	640	8	of	of	ADP
ejpam-6082	640	9	disabled	disabled	ADJ
ejpam-6082	640	10	individuals	individual	NOUN
ejpam-6082	640	11	,	,	PUNCT
ejpam-6082	640	12	necessitating	necessitate	VERB
ejpam-6082	640	13	targeted	target	VERB
ejpam-6082	640	14	healthcare	healthcare	NOUN
ejpam-6082	640	15	and	and	CCONJ
ejpam-6082	640	16	rehabilitation	rehabilitation	NOUN
ejpam-6082	640	17	efforts	effort	NOUN
ejpam-6082	640	18	.	.	PUNCT
ejpam-6082	641	1	these	these	DET
ejpam-6082	641	2	results	result	NOUN
ejpam-6082	641	3	underscore	underscore	VERB
ejpam-6082	641	4	the	the	DET
ejpam-6082	641	5	importance	importance	NOUN
ejpam-6082	641	6	of	of	ADP
ejpam-6082	641	7	fractional	fractional	ADJ
ejpam-6082	641	8	models	model	NOUN
ejpam-6082	641	9	in	in	ADP
ejpam-6082	641	10	addressing	address	VERB
ejpam-6082	641	11	chronic	chronic	ADJ
ejpam-6082	641	12	disease	disease	NOUN
ejpam-6082	641	13	burdens	burden	NOUN
ejpam-6082	641	14	and	and	CCONJ
ejpam-6082	641	15	guiding	guide	VERB
ejpam-6082	641	16	long	long	ADJ
ejpam-6082	641	17	-	-	PUNCT
ejpam-6082	641	18	term	term	NOUN
ejpam-6082	641	19	interventions	intervention	NOUN
ejpam-6082	641	20	.	.	PUNCT
ejpam-6082	642	1	11	11	X
ejpam-6082	642	2	.	.	X
ejpam-6082	642	3	conclusion	conclusion	NOUN
ejpam-6082	642	4	this	this	DET
ejpam-6082	642	5	study	study	NOUN
ejpam-6082	642	6	presents	present	VERB
ejpam-6082	642	7	a	a	DET
ejpam-6082	642	8	novel	novel	ADJ
ejpam-6082	642	9	fractional	fractional	ADJ
ejpam-6082	642	10	reaction	reaction	NOUN
ejpam-6082	642	11	-	-	PUNCT
ejpam-6082	642	12	diffusion	diffusion	NOUN
ejpam-6082	642	13	model	model	NOUN
ejpam-6082	642	14	tailored	tailor	VERB
ejpam-6082	642	15	to	to	ADP
ejpam-6082	642	16	the	the	DET
ejpam-6082	642	17	spatiotemporal	spatiotemporal	ADJ
ejpam-6082	642	18	dynamics	dynamic	NOUN
ejpam-6082	642	19	of	of	ADP
ejpam-6082	642	20	poliovirus	poliovirus	NOUN
ejpam-6082	642	21	transmission	transmission	NOUN
ejpam-6082	642	22	,	,	PUNCT
ejpam-6082	642	23	integrating	integrate	VERB
ejpam-6082	642	24	the	the	DET
ejpam-6082	642	25	effects	effect	NOUN
ejpam-6082	642	26	of	of	ADP
ejpam-6082	642	27	vaccination	vaccination	NOUN
ejpam-6082	642	28	and	and	CCONJ
ejpam-6082	642	29	post	post	ADJ
ejpam-6082	642	30	-	-	ADJ
ejpam-6082	642	31	paralytic	paralytic	ADJ
ejpam-6082	642	32	outcomes	outcome	NOUN
ejpam-6082	642	33	.	.	PUNCT
ejpam-6082	643	1	unlike	unlike	ADP
ejpam-6082	643	2	traditional	traditional	ADJ
ejpam-6082	643	3	models	model	NOUN
ejpam-6082	643	4	,	,	PUNCT
ejpam-6082	643	5	which	which	PRON
ejpam-6082	643	6	often	often	ADV
ejpam-6082	643	7	assume	assume	VERB
ejpam-6082	643	8	spatial	spatial	ADJ
ejpam-6082	643	9	homogeneity	homogeneity	NOUN
ejpam-6082	643	10	and	and	CCONJ
ejpam-6082	643	11	classical	classical	ADJ
ejpam-6082	643	12	derivatives	derivative	NOUN
ejpam-6082	643	13	,	,	PUNCT
ejpam-6082	643	14	this	this	DET
ejpam-6082	643	15	research	research	NOUN
ejpam-6082	643	16	incorporates	incorporate	VERB
ejpam-6082	643	17	caputo	caputo	PROPN
ejpam-6082	643	18	fractional	fractional	ADJ
ejpam-6082	643	19	derivatives	derivative	NOUN
ejpam-6082	643	20	to	to	PART
ejpam-6082	643	21	model	model	VERB
ejpam-6082	643	22	memory	memory	NOUN
ejpam-6082	643	23	-	-	PUNCT
ejpam-6082	643	24	dependent	dependent	ADJ
ejpam-6082	643	25	disease	disease	NOUN
ejpam-6082	643	26	progression	progression	NOUN
ejpam-6082	643	27	and	and	CCONJ
ejpam-6082	643	28	heterogeneous	heterogeneous	ADJ
ejpam-6082	643	29	diffusion	diffusion	NOUN
ejpam-6082	643	30	terms	term	NOUN
ejpam-6082	643	31	to	to	PART
ejpam-6082	643	32	capture	capture	VERB
ejpam-6082	643	33	population	population	NOUN
ejpam-6082	643	34	mobility	mobility	NOUN
ejpam-6082	643	35	and	and	CCONJ
ejpam-6082	643	36	environmental	environmental	ADJ
ejpam-6082	643	37	influences	influence	NOUN
ejpam-6082	643	38	.	.	PUNCT
ejpam-6082	644	1	the	the	DET
ejpam-6082	644	2	model	model	NOUN
ejpam-6082	644	3	divides	divide	VERB
ejpam-6082	644	4	the	the	DET
ejpam-6082	644	5	population	population	NOUN
ejpam-6082	644	6	into	into	ADP
ejpam-6082	644	7	seven	seven	NUM
ejpam-6082	644	8	distinct	distinct	ADJ
ejpam-6082	644	9	compartments	compartment	NOUN
ejpam-6082	644	10	,	,	PUNCT
ejpam-6082	644	11	addressing	address	VERB
ejpam-6082	644	12	the	the	DET
ejpam-6082	644	13	intricate	intricate	ADJ
ejpam-6082	644	14	transitions	transition	NOUN
ejpam-6082	644	15	from	from	ADP
ejpam-6082	644	16	susceptibility	susceptibility	NOUN
ejpam-6082	644	17	to	to	ADP
ejpam-6082	644	18	post	post	ADJ
ejpam-6082	644	19	-	-	ADJ
ejpam-6082	644	20	paralytic	paralytic	ADJ
ejpam-6082	644	21	disability	disability	NOUN
ejpam-6082	644	22	.	.	PUNCT
ejpam-6082	645	1	rigorous	rigorous	ADJ
ejpam-6082	645	2	mathematical	mathematical	ADJ
ejpam-6082	645	3	analysis	analysis	NOUN
ejpam-6082	645	4	demonstrates	demonstrate	VERB
ejpam-6082	645	5	the	the	DET
ejpam-6082	645	6	existence	existence	NOUN
ejpam-6082	645	7	,	,	PUNCT
ejpam-6082	645	8	positivity	positivity	NOUN
ejpam-6082	645	9	,	,	PUNCT
ejpam-6082	645	10	and	and	CCONJ
ejpam-6082	645	11	boundedness	boundedness	NOUN
ejpam-6082	645	12	of	of	ADP
ejpam-6082	645	13	solutions	solution	NOUN
ejpam-6082	645	14	,	,	PUNCT
ejpam-6082	645	15	ensuring	ensure	VERB
ejpam-6082	645	16	the	the	DET
ejpam-6082	645	17	biological	biological	ADJ
ejpam-6082	645	18	realism	realism	NOUN
ejpam-6082	645	19	of	of	ADP
ejpam-6082	645	20	the	the	DET
ejpam-6082	645	21	model	model	NOUN
ejpam-6082	645	22	.	.	PUNCT
ejpam-6082	646	1	stability	stability	NOUN
ejpam-6082	646	2	assessments	assessment	NOUN
ejpam-6082	646	3	of	of	ADP
ejpam-6082	646	4	equilibrium	equilibrium	NOUN
ejpam-6082	646	5	points	point	NOUN
ejpam-6082	646	6	,	,	PUNCT
ejpam-6082	646	7	using	use	VERB
ejpam-6082	646	8	tools	tool	NOUN
ejpam-6082	646	9	such	such	ADJ
ejpam-6082	646	10	as	as	ADP
ejpam-6082	646	11	lyapunov	lyapunov	ADJ
ejpam-6082	646	12	functions	function	NOUN
ejpam-6082	646	13	and	and	CCONJ
ejpam-6082	646	14	reproduction	reproduction	NOUN
ejpam-6082	646	15	number	number	NOUN
ejpam-6082	646	16	(	(	PUNCT
ejpam-6082	646	17	r0	r0	NOUN
ejpam-6082	646	18	)	)	PUNCT
ejpam-6082	646	19	,	,	PUNCT
ejpam-6082	646	20	reveal	reveal	VERB
ejpam-6082	646	21	conditions	condition	NOUN
ejpam-6082	646	22	for	for	ADP
ejpam-6082	646	23	both	both	CCONJ
ejpam-6082	646	24	the	the	DET
ejpam-6082	646	25	eradication	eradication	NOUN
ejpam-6082	646	26	and	and	CCONJ
ejpam-6082	646	27	persistence	persistence	NOUN
ejpam-6082	646	28	of	of	ADP
ejpam-6082	646	29	poliovirus	poliovirus	NOUN
ejpam-6082	646	30	.	.	PUNCT
ejpam-6082	647	1	sensitivity	sensitivity	NOUN
ejpam-6082	647	2	analysis	analysis	NOUN
ejpam-6082	647	3	identifies	identify	VERB
ejpam-6082	647	4	critical	critical	ADJ
ejpam-6082	647	5	factors	factor	NOUN
ejpam-6082	647	6	,	,	PUNCT
ejpam-6082	647	7	such	such	ADJ
ejpam-6082	647	8	as	as	ADP
ejpam-6082	647	9	the	the	DET
ejpam-6082	647	10	fractional	fractional	ADJ
ejpam-6082	647	11	order	order	NOUN
ejpam-6082	647	12	(	(	PUNCT
ejpam-6082	647	13	α	α	NOUN
ejpam-6082	647	14	)	)	PUNCT
ejpam-6082	647	15	and	and	CCONJ
ejpam-6082	647	16	vaccination	vaccination	NOUN
ejpam-6082	647	17	rates	rate	NOUN
ejpam-6082	647	18	,	,	PUNCT
ejpam-6082	647	19	that	that	SCONJ
ejpam-6082	647	20	strongly	strongly	ADV
ejpam-6082	647	21	influence	influence	NOUN
ejpam-6082	647	22	disease	disease	NOUN
ejpam-6082	647	23	dynamics	dynamic	NOUN
ejpam-6082	647	24	.	.	PUNCT
ejpam-6082	648	1	numerical	numerical	ADJ
ejpam-6082	648	2	simulations	simulation	NOUN
ejpam-6082	648	3	provide	provide	VERB
ejpam-6082	648	4	practical	practical	ADJ
ejpam-6082	648	5	insights	insight	NOUN
ejpam-6082	648	6	into	into	ADP
ejpam-6082	648	7	how	how	SCONJ
ejpam-6082	648	8	fractional	fractional	ADJ
ejpam-6082	648	9	memory	memory	NOUN
ejpam-6082	648	10	effects	effect	NOUN
ejpam-6082	648	11	alter	alter	VERB
ejpam-6082	648	12	the	the	DET
ejpam-6082	648	13	pace	pace	NOUN
ejpam-6082	648	14	of	of	ADP
ejpam-6082	648	15	disease	disease	NOUN
ejpam-6082	648	16	spread	spread	VERB
ejpam-6082	648	17	and	and	CCONJ
ejpam-6082	648	18	recovery	recovery	NOUN
ejpam-6082	648	19	.	.	PUNCT
ejpam-6082	649	1	lower	low	ADJ
ejpam-6082	649	2	values	value	NOUN
ejpam-6082	649	3	of	of	ADP
ejpam-6082	649	4	α	α	PRON
ejpam-6082	649	5	correlate	correlate	VERB
ejpam-6082	649	6	with	with	ADP
ejpam-6082	649	7	accelerated	accelerate	VERB
ejpam-6082	649	8	depletion	depletion	NOUN
ejpam-6082	649	9	of	of	ADP
ejpam-6082	649	10	susceptibles	susceptible	NOUN
ejpam-6082	649	11	and	and	CCONJ
ejpam-6082	649	12	earlier	early	ADJ
ejpam-6082	649	13	peaks	peak	NOUN
ejpam-6082	649	14	in	in	ADP
ejpam-6082	649	15	infected	infected	ADJ
ejpam-6082	649	16	populations	population	NOUN
ejpam-6082	649	17	,	,	PUNCT
ejpam-6082	649	18	underscoring	underscore	VERB
ejpam-6082	649	19	the	the	DET
ejpam-6082	649	20	importance	importance	NOUN
ejpam-6082	649	21	of	of	ADP
ejpam-6082	649	22	incorporating	incorporate	VERB
ejpam-6082	649	23	memory	memory	NOUN
ejpam-6082	649	24	effects	effect	NOUN
ejpam-6082	649	25	in	in	ADP
ejpam-6082	649	26	outbreak	outbreak	NOUN
ejpam-6082	649	27	predictions	prediction	NOUN
ejpam-6082	649	28	.	.	PUNCT
ejpam-6082	650	1	furthermore	furthermore	ADV
ejpam-6082	650	2	,	,	PUNCT
ejpam-6082	650	3	the	the	DET
ejpam-6082	650	4	spatial	spatial	ADJ
ejpam-6082	650	5	distribution	distribution	NOUN
ejpam-6082	650	6	of	of	ADP
ejpam-6082	650	7	disease	disease	NOUN
ejpam-6082	650	8	burden	burden	NOUN
ejpam-6082	650	9	,	,	PUNCT
ejpam-6082	650	10	as	as	SCONJ
ejpam-6082	650	11	revealed	reveal	VERB
ejpam-6082	650	12	by	by	ADP
ejpam-6082	650	13	the	the	DET
ejpam-6082	650	14	reaction	reaction	NOUN
ejpam-6082	650	15	-	-	PUNCT
ejpam-6082	650	16	diffusion	diffusion	NOUN
ejpam-6082	650	17	framework	framework	NOUN
ejpam-6082	650	18	,	,	PUNCT
ejpam-6082	650	19	highlights	highlight	VERB
ejpam-6082	650	20	the	the	DET
ejpam-6082	650	21	necessity	necessity	NOUN
ejpam-6082	650	22	of	of	ADP
ejpam-6082	650	23	regionspecific	regionspecific	ADJ
ejpam-6082	650	24	public	public	ADJ
ejpam-6082	650	25	health	health	NOUN
ejpam-6082	650	26	interventions	intervention	NOUN
ejpam-6082	650	27	,	,	PUNCT
ejpam-6082	650	28	particularly	particularly	ADV
ejpam-6082	650	29	in	in	ADP
ejpam-6082	650	30	high	high	ADJ
ejpam-6082	650	31	-	-	PUNCT
ejpam-6082	650	32	density	density	NOUN
ejpam-6082	650	33	or	or	CCONJ
ejpam-6082	650	34	sanitation	sanitation	NOUN
ejpam-6082	650	35	-	-	PUNCT
ejpam-6082	650	36	compromised	compromise	VERB
ejpam-6082	650	37	areas	area	NOUN
ejpam-6082	650	38	.	.	PUNCT
ejpam-6082	651	1	this	this	DET
ejpam-6082	651	2	study	study	NOUN
ejpam-6082	651	3	’s	’s	PART
ejpam-6082	651	4	fractional	fractional	ADJ
ejpam-6082	651	5	reaction	reaction	NOUN
ejpam-6082	651	6	-	-	PUNCT
ejpam-6082	651	7	diffusion	diffusion	NOUN
ejpam-6082	651	8	approach	approach	NOUN
ejpam-6082	651	9	significantly	significantly	ADV
ejpam-6082	651	10	enhances	enhance	VERB
ejpam-6082	651	11	the	the	DET
ejpam-6082	651	12	predictive	predictive	ADJ
ejpam-6082	651	13	power	power	NOUN
ejpam-6082	651	14	of	of	ADP
ejpam-6082	651	15	mathematical	mathematical	ADJ
ejpam-6082	651	16	models	model	NOUN
ejpam-6082	651	17	in	in	ADP
ejpam-6082	651	18	epidemiology	epidemiology	NOUN
ejpam-6082	651	19	,	,	PUNCT
ejpam-6082	651	20	offering	offer	VERB
ejpam-6082	651	21	actionable	actionable	ADJ
ejpam-6082	651	22	insights	insight	NOUN
ejpam-6082	651	23	into	into	ADP
ejpam-6082	651	24	poliovirus	poliovirus	NOUN
ejpam-6082	651	25	control	control	NOUN
ejpam-6082	651	26	.	.	PUNCT
ejpam-6082	652	1	by	by	ADP
ejpam-6082	652	2	addressing	address	VERB
ejpam-6082	652	3	both	both	CCONJ
ejpam-6082	652	4	spatial	spatial	ADJ
ejpam-6082	652	5	and	and	CCONJ
ejpam-6082	652	6	temporal	temporal	ADJ
ejpam-6082	652	7	complexities	complexity	NOUN
ejpam-6082	652	8	,	,	PUNCT
ejpam-6082	652	9	it	it	PRON
ejpam-6082	652	10	provides	provide	VERB
ejpam-6082	652	11	a	a	DET
ejpam-6082	652	12	robust	robust	ADJ
ejpam-6082	652	13	tool	tool	NOUN
ejpam-6082	652	14	for	for	ADP
ejpam-6082	652	15	optimizing	optimize	VERB
ejpam-6082	652	16	vaccination	vaccination	NOUN
ejpam-6082	652	17	campaigns	campaign	NOUN
ejpam-6082	652	18	,	,	PUNCT
ejpam-6082	652	19	improving	improve	VERB
ejpam-6082	652	20	sanitation	sanitation	NOUN
ejpam-6082	652	21	strategies	strategy	NOUN
ejpam-6082	652	22	,	,	PUNCT
ejpam-6082	652	23	and	and	CCONJ
ejpam-6082	652	24	mitigating	mitigate	VERB
ejpam-6082	652	25	long	long	ADJ
ejpam-6082	652	26	-	-	PUNCT
ejpam-6082	652	27	term	term	NOUN
ejpam-6082	652	28	disability	disability	NOUN
ejpam-6082	652	29	outcomes	outcome	NOUN
ejpam-6082	652	30	,	,	PUNCT
ejpam-6082	652	31	paving	pave	VERB
ejpam-6082	652	32	the	the	DET
ejpam-6082	652	33	way	way	NOUN
ejpam-6082	652	34	for	for	ADP
ejpam-6082	652	35	more	more	ADV
ejpam-6082	652	36	effective	effective	ADJ
ejpam-6082	652	37	public	public	ADJ
ejpam-6082	652	38	health	health	NOUN
ejpam-6082	652	39	responses	response	NOUN
ejpam-6082	652	40	to	to	ADP
ejpam-6082	652	41	poliovirus	poliovirus	NOUN
ejpam-6082	652	42	outbreaks	outbreak	NOUN
ejpam-6082	652	43	.	.	PUNCT
ejpam-6082	653	1	acknowledgements	acknowledgement	NOUN
ejpam-6082	653	2	the	the	DET
ejpam-6082	653	3	authors	author	NOUN
ejpam-6082	653	4	extend	extend	VERB
ejpam-6082	653	5	their	their	PRON
ejpam-6082	653	6	appreciation	appreciation	NOUN
ejpam-6082	653	7	to	to	ADP
ejpam-6082	653	8	the	the	DET
ejpam-6082	653	9	king	king	NOUN
ejpam-6082	653	10	salman	salman	PROPN
ejpam-6082	653	11	center	center	PROPN
ejpam-6082	653	12	for	for	ADP
ejpam-6082	653	13	disability	disability	NOUN
ejpam-6082	653	14	research	research	NOUN
ejpam-6082	653	15	for	for	ADP
ejpam-6082	653	16	funding	fund	VERB
ejpam-6082	653	17	this	this	DET
ejpam-6082	653	18	work	work	NOUN
ejpam-6082	653	19	through	through	ADP
ejpam-6082	653	20	research	research	NOUN
ejpam-6082	653	21	group	group	NOUN
ejpam-6082	653	22	no	no	DET
ejpam-6082	653	23	ksrg-2024	ksrg-2024	NOUN
ejpam-6082	653	24	-	-	PUNCT
ejpam-6082	653	25	200	200	NUM
ejpam-6082	653	26	.	.	PUNCT
ejpam-6082	654	1	k.	k.	PROPN
ejpam-6082	654	2	guedri	guedri	PROPN
ejpam-6082	654	3	et	et	PROPN
ejpam-6082	654	4	al	al	PROPN
ejpam-6082	654	5	.	.	PUNCT
ejpam-6082	654	6	/	/	SYM
ejpam-6082	654	7	eur	eur	PROPN
ejpam-6082	654	8	.	.	PUNCT
ejpam-6082	655	1	j.	j.	PROPN
ejpam-6082	655	2	pure	pure	PROPN
ejpam-6082	655	3	appl	appl	PROPN
ejpam-6082	655	4	.	.	PROPN
ejpam-6082	655	5	math	math	PROPN
ejpam-6082	655	6	,	,	PUNCT
ejpam-6082	655	7	18	18	NUM
ejpam-6082	655	8	(	(	PUNCT
ejpam-6082	655	9	2	2	NUM
ejpam-6082	655	10	)	)	PUNCT
ejpam-6082	655	11	(	(	PUNCT
ejpam-6082	655	12	2025	2025	NUM
ejpam-6082	655	13	)	)	PUNCT
ejpam-6082	655	14	,	,	PUNCT
ejpam-6082	655	15	6082	6082	NUM
ejpam-6082	655	16	36	36	NUM
ejpam-6082	655	17	of	of	ADP
ejpam-6082	655	18	39	39	NUM
ejpam-6082	655	19	funding	funding	NOUN
ejpam-6082	655	20	the	the	DET
ejpam-6082	655	21	authors	author	NOUN
ejpam-6082	655	22	extend	extend	VERB
ejpam-6082	655	23	their	their	PRON
ejpam-6082	655	24	appreciation	appreciation	NOUN
ejpam-6082	655	25	to	to	ADP
ejpam-6082	655	26	the	the	DET
ejpam-6082	655	27	king	king	NOUN
ejpam-6082	655	28	salman	salman	PROPN
ejpam-6082	655	29	center	center	PROPN
ejpam-6082	655	30	for	for	ADP
ejpam-6082	655	31	disability	disability	NOUN
ejpam-6082	655	32	research	research	NOUN
ejpam-6082	655	33	for	for	ADP
ejpam-6082	655	34	funding	fund	VERB
ejpam-6082	655	35	this	this	DET
ejpam-6082	655	36	work	work	NOUN
ejpam-6082	655	37	through	through	ADP
ejpam-6082	655	38	research	research	NOUN
ejpam-6082	655	39	group	group	NOUN
ejpam-6082	655	40	no	no	DET
ejpam-6082	655	41	ksrg-2024	ksrg-2024	NOUN
ejpam-6082	655	42	-	-	PUNCT
ejpam-6082	655	43	200	200	NUM
ejpam-6082	655	44	.	.	PUNCT
ejpam-6082	656	1	conflict	conflict	NOUN
ejpam-6082	656	2	of	of	ADP
ejpam-6082	656	3	interest	interest	NOUN
ejpam-6082	656	4	the	the	DET
ejpam-6082	656	5	authors	author	NOUN
ejpam-6082	656	6	declare	declare	VERB
ejpam-6082	656	7	that	that	SCONJ
ejpam-6082	656	8	they	they	PRON
ejpam-6082	656	9	have	have	VERB
ejpam-6082	656	10	no	no	DET
ejpam-6082	656	11	conflict	conflict	NOUN
ejpam-6082	656	12	of	of	ADP
ejpam-6082	656	13	interest	interest	NOUN
ejpam-6082	656	14	.	.	PUNCT
ejpam-6082	657	1	data	datum	NOUN
ejpam-6082	657	2	availability	availability	NOUN
ejpam-6082	657	3	statement	statement	NOUN
ejpam-6082	657	4	“	"	PUNCT
ejpam-6082	657	5	all	all	DET
ejpam-6082	657	6	data	datum	NOUN
ejpam-6082	657	7	generated	generate	VERB
ejpam-6082	657	8	or	or	CCONJ
ejpam-6082	657	9	analyzed	analyze	VERB
ejpam-6082	657	10	during	during	ADP
ejpam-6082	657	11	this	this	DET
ejpam-6082	657	12	study	study	NOUN
ejpam-6082	657	13	are	be	AUX
ejpam-6082	657	14	included	include	VERB
ejpam-6082	657	15	in	in	ADP
ejpam-6082	657	16	this	this	DET
ejpam-6082	657	17	article	article	NOUN
ejpam-6082	657	18	”	"	PUNCT
ejpam-6082	657	19	.	.	PUNCT
ejpam-6082	658	1	references	reference	NOUN
ejpam-6082	658	2	[	[	X
ejpam-6082	658	3	1	1	NUM
ejpam-6082	658	4	]	]	PUNCT
ejpam-6082	658	5	c.	c.	PROPN
ejpam-6082	658	6	s.	s.	PROPN
ejpam-6082	658	7	bornaa	bornaa	PROPN
ejpam-6082	658	8	,	,	PUNCT
ejpam-6082	658	9	b.	b.	PROPN
ejpam-6082	658	10	seidu	seidu	PROPN
ejpam-6082	658	11	,	,	PUNCT
ejpam-6082	658	12	and	and	CCONJ
ejpam-6082	658	13	o.	o.	PROPN
ejpam-6082	658	14	d.	d.	PROPN
ejpam-6082	658	15	makinde	makinde	PROPN
ejpam-6082	658	16	.	.	PUNCT
ejpam-6082	659	1	mathematical	mathematical	ADJ
ejpam-6082	659	2	analysis	analysis	NOUN
ejpam-6082	659	3	of	of	ADP
ejpam-6082	659	4	the	the	DET
ejpam-6082	659	5	impact	impact	NOUN
ejpam-6082	659	6	of	of	ADP
ejpam-6082	659	7	vaccination	vaccination	NOUN
ejpam-6082	659	8	and	and	CCONJ
ejpam-6082	659	9	poor	poor	ADJ
ejpam-6082	659	10	sanitation	sanitation	NOUN
ejpam-6082	659	11	on	on	ADP
ejpam-6082	659	12	the	the	DET
ejpam-6082	659	13	dynamics	dynamic	NOUN
ejpam-6082	659	14	of	of	ADP
ejpam-6082	659	15	poliomyelitis	poliomyelitis	PROPN
ejpam-6082	659	16	.	.	PUNCT
ejpam-6082	660	1	international	international	ADJ
ejpam-6082	660	2	journal	journal	PROPN
ejpam-6082	660	3	of	of	ADP
ejpam-6082	660	4	nonlinear	nonlinear	PROPN
ejpam-6082	660	5	sciences	sciences	PROPN
ejpam-6082	660	6	and	and	CCONJ
ejpam-6082	660	7	numerical	numerical	PROPN
ejpam-6082	660	8	simulation	simulation	PROPN
ejpam-6082	660	9	,	,	PUNCT
ejpam-6082	660	10	24(1):161–169	24(1):161–169	PROPN
ejpam-6082	660	11	,	,	PUNCT
ejpam-6082	660	12	2023	2023	NUM
ejpam-6082	660	13	.	.	PUNCT
ejpam-6082	661	1	[	[	X
ejpam-6082	661	2	2	2	X
ejpam-6082	661	3	]	]	PUNCT
ejpam-6082	661	4	j.	j.	PROPN
ejpam-6082	661	5	radboud	radboud	PROPN
ejpam-6082	661	6	d.	d.	PROPN
ejpam-6082	661	7	tebbens	tebbens	PROPN
ejpam-6082	661	8	,	,	PUNCT
ejpam-6082	661	9	m.	m.	NOUN
ejpam-6082	661	10	a.	a.	PROPN
ejpam-6082	661	11	pallansch	pallansch	PROPN
ejpam-6082	661	12	,	,	PUNCT
ejpam-6082	661	13	et	et	PROPN
ejpam-6082	661	14	al	al	PROPN
ejpam-6082	661	15	.	.	PUNCT
ejpam-6082	662	1	a	a	DET
ejpam-6082	662	2	dynamic	dynamic	ADJ
ejpam-6082	662	3	model	model	NOUN
ejpam-6082	662	4	of	of	ADP
ejpam-6082	662	5	poliomyelitis	poliomyelitis	NOUN
ejpam-6082	662	6	outbreaks	outbreak	NOUN
ejpam-6082	662	7	:	:	PUNCT
ejpam-6082	662	8	learning	learn	VERB
ejpam-6082	662	9	from	from	ADP
ejpam-6082	662	10	the	the	DET
ejpam-6082	662	11	past	past	NOUN
ejpam-6082	662	12	to	to	PART
ejpam-6082	662	13	help	help	VERB
ejpam-6082	662	14	inform	inform	VERB
ejpam-6082	662	15	the	the	DET
ejpam-6082	662	16	future	future	NOUN
ejpam-6082	662	17	.	.	PUNCT
ejpam-6082	663	1	american	american	ADJ
ejpam-6082	663	2	journal	journal	PROPN
ejpam-6082	663	3	of	of	ADP
ejpam-6082	663	4	epidemiology	epidemiology	NOUN
ejpam-6082	663	5	,	,	PUNCT
ejpam-6082	663	6	162(4):223–241	162(4):223–241	NUM
ejpam-6082	663	7	,	,	PUNCT
ejpam-6082	663	8	2005	2005	NUM
ejpam-6082	663	9	.	.	PUNCT
ejpam-6082	664	1	[	[	X
ejpam-6082	664	2	3	3	NUM
ejpam-6082	664	3	]	]	X
ejpam-6082	664	4	m.	m.	NOUN
ejpam-6082	664	5	agarwal	agarwal	PROPN
ejpam-6082	664	6	and	and	CCONJ
ejpam-6082	664	7	a.	a.	PROPN
ejpam-6082	664	8	s.	s.	PROPN
ejpam-6082	664	9	bhadauria	bhadauria	PROPN
ejpam-6082	664	10	.	.	PUNCT
ejpam-6082	665	1	modeling	model	VERB
ejpam-6082	665	2	spread	spread	NOUN
ejpam-6082	665	3	of	of	ADP
ejpam-6082	665	4	polio	polio	NOUN
ejpam-6082	665	5	with	with	ADP
ejpam-6082	665	6	the	the	DET
ejpam-6082	665	7	role	role	NOUN
ejpam-6082	665	8	of	of	ADP
ejpam-6082	665	9	vaccination	vaccination	NOUN
ejpam-6082	665	10	.	.	PUNCT
ejpam-6082	666	1	applications	application	NOUN
ejpam-6082	666	2	and	and	CCONJ
ejpam-6082	666	3	applied	apply	VERB
ejpam-6082	666	4	mathematics	mathematic	NOUN
ejpam-6082	666	5	:	:	PUNCT
ejpam-6082	666	6	an	an	DET
ejpam-6082	666	7	international	international	ADJ
ejpam-6082	666	8	journal	journal	NOUN
ejpam-6082	666	9	,	,	PUNCT
ejpam-6082	666	10	6(2):552–571	6(2):552–571	NUM
ejpam-6082	666	11	,	,	PUNCT
ejpam-6082	666	12	2011	2011	NUM
ejpam-6082	666	13	.	.	PUNCT
ejpam-6082	667	1	[	[	X
ejpam-6082	667	2	4	4	X
ejpam-6082	667	3	]	]	X
ejpam-6082	667	4	y.	y.	NOUN
ejpam-6082	667	5	sabbar	sabbar	PROPN
ejpam-6082	667	6	and	and	CCONJ
ejpam-6082	667	7	a.	a.	NOUN
ejpam-6082	667	8	a.	a.	NOUN
ejpam-6082	667	9	raezah	raezah	NOUN
ejpam-6082	667	10	.	.	PUNCT
ejpam-6082	668	1	the	the	DET
ejpam-6082	668	2	influence	influence	NOUN
ejpam-6082	668	3	of	of	ADP
ejpam-6082	668	4	independent	independent	ADJ
ejpam-6082	668	5	jumps	jump	NOUN
ejpam-6082	668	6	on	on	ADP
ejpam-6082	668	7	the	the	DET
ejpam-6082	668	8	dynamics	dynamic	NOUN
ejpam-6082	668	9	of	of	ADP
ejpam-6082	668	10	a	a	DET
ejpam-6082	668	11	perturbed	perturb	VERB
ejpam-6082	668	12	sirs	sirs	PROPN
ejpam-6082	668	13	epidemic	epidemic	NOUN
ejpam-6082	668	14	model	model	NOUN
ejpam-6082	668	15	with	with	ADP
ejpam-6082	668	16	altered	altered	ADJ
ejpam-6082	668	17	behavior	behavior	NOUN
ejpam-6082	668	18	.	.	PUNCT
ejpam-6082	669	1	international	international	ADJ
ejpam-6082	669	2	journal	journal	PROPN
ejpam-6082	669	3	of	of	ADP
ejpam-6082	669	4	dynamics	dynamic	NOUN
ejpam-6082	669	5	and	and	CCONJ
ejpam-6082	669	6	control	control	NOUN
ejpam-6082	669	7	,	,	PUNCT
ejpam-6082	669	8	13(1):1–16	13(1):1–16	NUM
ejpam-6082	669	9	,	,	PUNCT
ejpam-6082	669	10	2025	2025	NUM
ejpam-6082	669	11	.	.	PUNCT
ejpam-6082	670	1	[	[	X
ejpam-6082	670	2	5	5	NUM
ejpam-6082	670	3	]	]	X
ejpam-6082	670	4	y.	y.	PROPN
ejpam-6082	670	5	sabbar	sabbar	PROPN
ejpam-6082	670	6	.	.	PUNCT
ejpam-6082	671	1	exploring	explore	VERB
ejpam-6082	671	2	threshold	threshold	NOUN
ejpam-6082	671	3	dynamics	dynamic	NOUN
ejpam-6082	671	4	of	of	ADP
ejpam-6082	671	5	a	a	DET
ejpam-6082	671	6	behavioral	behavioral	ADJ
ejpam-6082	671	7	epidemic	epidemic	NOUN
ejpam-6082	671	8	model	model	NOUN
ejpam-6082	671	9	featuring	feature	VERB
ejpam-6082	671	10	two	two	NUM
ejpam-6082	671	11	susceptible	susceptible	ADJ
ejpam-6082	671	12	classes	class	NOUN
ejpam-6082	671	13	and	and	CCONJ
ejpam-6082	671	14	second	second	ADJ
ejpam-6082	671	15	-	-	PUNCT
ejpam-6082	671	16	order	order	NOUN
ejpam-6082	671	17	jump	jump	NOUN
ejpam-6082	671	18	-	-	PUNCT
ejpam-6082	671	19	diffusion	diffusion	NOUN
ejpam-6082	671	20	.	.	PUNCT
ejpam-6082	672	1	chaos	chaos	NOUN
ejpam-6082	672	2	,	,	PUNCT
ejpam-6082	672	3	solitons	soliton	NOUN
ejpam-6082	672	4	&	&	CCONJ
ejpam-6082	672	5	fractals	fractal	NOUN
ejpam-6082	672	6	,	,	PUNCT
ejpam-6082	672	7	186:115216	186:115216	NUM
ejpam-6082	672	8	,	,	PUNCT
ejpam-6082	672	9	2024	2024	NUM
ejpam-6082	672	10	.	.	PUNCT
ejpam-6082	673	1	[	[	X
ejpam-6082	673	2	6	6	NUM
ejpam-6082	673	3	]	]	PUNCT
ejpam-6082	673	4	a.	a.	NOUN
ejpam-6082	673	5	din	din	PROPN
ejpam-6082	673	6	,	,	PUNCT
ejpam-6082	673	7	y.	y.	PROPN
ejpam-6082	673	8	sabbar	sabbar	PROPN
ejpam-6082	673	9	,	,	PUNCT
ejpam-6082	673	10	and	and	CCONJ
ejpam-6082	673	11	p.	p.	PROPN
ejpam-6082	673	12	wu	wu	PROPN
ejpam-6082	673	13	.	.	PUNCT
ejpam-6082	674	1	a	a	DET
ejpam-6082	674	2	novel	novel	ADJ
ejpam-6082	674	3	stochastic	stochastic	NOUN
ejpam-6082	674	4	hepatitis	hepatitis	PROPN
ejpam-6082	674	5	b	b	PROPN
ejpam-6082	674	6	virus	virus	NOUN
ejpam-6082	674	7	epidemic	epidemic	NOUN
ejpam-6082	674	8	model	model	NOUN
ejpam-6082	674	9	with	with	ADP
ejpam-6082	674	10	second	second	ADJ
ejpam-6082	674	11	-	-	PUNCT
ejpam-6082	674	12	order	order	NOUN
ejpam-6082	674	13	multiplicative	multiplicative	ADJ
ejpam-6082	674	14	α	α	ADJ
ejpam-6082	674	15	-	-	ADJ
ejpam-6082	674	16	stable	stable	ADJ
ejpam-6082	674	17	noise	noise	NOUN
ejpam-6082	674	18	and	and	CCONJ
ejpam-6082	674	19	real	real	ADJ
ejpam-6082	674	20	data	datum	NOUN
ejpam-6082	674	21	.	.	PUNCT
ejpam-6082	675	1	acta	acta	PROPN
ejpam-6082	675	2	mathematica	mathematica	PROPN
ejpam-6082	675	3	scientia	scientia	PROPN
ejpam-6082	675	4	,	,	PUNCT
ejpam-6082	675	5	44(2):752–788	44(2):752–788	PROPN
ejpam-6082	675	6	,	,	PUNCT
ejpam-6082	675	7	2024	2024	NUM
ejpam-6082	675	8	.	.	PUNCT
ejpam-6082	676	1	[	[	X
ejpam-6082	676	2	7	7	X
ejpam-6082	676	3	]	]	X
ejpam-6082	676	4	y.	y.	NOUN
ejpam-6082	676	5	sabbar	sabbar	PROPN
ejpam-6082	676	6	and	and	CCONJ
ejpam-6082	676	7	a.	a.	NOUN
ejpam-6082	676	8	a.	a.	NOUN
ejpam-6082	676	9	raezah	raezah	NOUN
ejpam-6082	676	10	.	.	PUNCT
ejpam-6082	677	1	modeling	model	VERB
ejpam-6082	677	2	mosquito	mosquito	NOUN
ejpam-6082	677	3	-	-	PUNCT
ejpam-6082	677	4	borne	bear	VERB
ejpam-6082	677	5	disease	disease	NOUN
ejpam-6082	677	6	dynamics	dynamic	NOUN
ejpam-6082	677	7	via	via	ADP
ejpam-6082	677	8	stochastic	stochastic	ADJ
ejpam-6082	677	9	differential	differential	ADJ
ejpam-6082	677	10	equations	equation	NOUN
ejpam-6082	677	11	and	and	CCONJ
ejpam-6082	677	12	generalized	generalize	VERB
ejpam-6082	677	13	tempered	temper	VERB
ejpam-6082	677	14	stable	stable	ADJ
ejpam-6082	677	15	distribution	distribution	NOUN
ejpam-6082	677	16	.	.	PUNCT
ejpam-6082	678	1	aims	aim	VERB
ejpam-6082	678	2	mathematics	mathematic	NOUN
ejpam-6082	678	3	,	,	PUNCT
ejpam-6082	678	4	9(8):22454–22485	9(8):22454–22485	NOUN
ejpam-6082	678	5	,	,	PUNCT
ejpam-6082	678	6	2024	2024	NUM
ejpam-6082	678	7	.	.	PUNCT
ejpam-6082	679	1	[	[	X
ejpam-6082	679	2	8	8	NUM
ejpam-6082	679	3	]	]	PUNCT
ejpam-6082	679	4	k.	k.	PROPN
ejpam-6082	679	5	s.	s.	PROPN
ejpam-6082	679	6	nisar	nisar	PROPN
ejpam-6082	679	7	and	and	CCONJ
ejpam-6082	679	8	y.	y.	PROPN
ejpam-6082	679	9	sabbar	sabbar	PROPN
ejpam-6082	679	10	.	.	PUNCT
ejpam-6082	680	1	long	long	ADV
ejpam-6082	680	2	-	-	PUNCT
ejpam-6082	680	3	run	run	NOUN
ejpam-6082	680	4	analysis	analysis	NOUN
ejpam-6082	680	5	of	of	ADP
ejpam-6082	680	6	a	a	DET
ejpam-6082	680	7	perturbed	perturb	VERB
ejpam-6082	680	8	hiv	hiv	PROPN
ejpam-6082	680	9	/	/	SYM
ejpam-6082	680	10	aids	aids	PROPN
ejpam-6082	680	11	model	model	NOUN
ejpam-6082	680	12	with	with	ADP
ejpam-6082	680	13	antiretroviral	antiretroviral	ADJ
ejpam-6082	680	14	therapy	therapy	NOUN
ejpam-6082	680	15	and	and	CCONJ
ejpam-6082	680	16	heavy	heavy	ADJ
ejpam-6082	680	17	-	-	PUNCT
ejpam-6082	680	18	tailed	tail	VERB
ejpam-6082	680	19	increments	increment	NOUN
ejpam-6082	680	20	performed	perform	VERB
ejpam-6082	680	21	by	by	ADP
ejpam-6082	680	22	tempered	temper	VERB
ejpam-6082	680	23	stable	stable	ADJ
ejpam-6082	680	24	lévy	lévy	X
ejpam-6082	680	25	jumps	jump	VERB
ejpam-6082	680	26	.	.	PUNCT
ejpam-6082	681	1	alexandria	alexandria	PROPN
ejpam-6082	681	2	engineering	engineering	PROPN
ejpam-6082	681	3	journal	journal	PROPN
ejpam-6082	681	4	,	,	PUNCT
ejpam-6082	681	5	78:498–516	78:498–516	PROPN
ejpam-6082	681	6	,	,	PUNCT
ejpam-6082	681	7	2023	2023	NUM
ejpam-6082	681	8	.	.	PUNCT
ejpam-6082	682	1	[	[	X
ejpam-6082	682	2	9	9	NUM
ejpam-6082	682	3	]	]	PUNCT
ejpam-6082	682	4	a.	a.	NOUN
ejpam-6082	682	5	khan	khan	PROPN
ejpam-6082	682	6	,	,	PUNCT
ejpam-6082	682	7	y.	y.	PROPN
ejpam-6082	682	8	sabbar	sabbar	PROPN
ejpam-6082	682	9	,	,	PUNCT
ejpam-6082	682	10	and	and	CCONJ
ejpam-6082	682	11	a.	a.	PROPN
ejpam-6082	682	12	din	din	PROPN
ejpam-6082	682	13	.	.	PROPN
ejpam-6082	682	14	stochastic	stochastic	ADJ
ejpam-6082	682	15	modeling	modeling	NOUN
ejpam-6082	682	16	of	of	ADP
ejpam-6082	682	17	the	the	DET
ejpam-6082	682	18	monkeypox	monkeypox	NOUN
ejpam-6082	682	19	2022	2022	NUM
ejpam-6082	682	20	epidemic	epidemic	NOUN
ejpam-6082	682	21	with	with	ADP
ejpam-6082	682	22	cross	cross	ADJ
ejpam-6082	682	23	-	-	ADJ
ejpam-6082	682	24	infection	infection	ADJ
ejpam-6082	682	25	hypothesis	hypothesis	NOUN
ejpam-6082	682	26	in	in	ADP
ejpam-6082	682	27	a	a	DET
ejpam-6082	682	28	highly	highly	ADV
ejpam-6082	682	29	disturbed	disturbed	ADJ
ejpam-6082	682	30	environment	environment	NOUN
ejpam-6082	682	31	.	.	PUNCT
ejpam-6082	683	1	mathematical	mathematical	ADJ
ejpam-6082	683	2	biosciences	bioscience	NOUN
ejpam-6082	683	3	and	and	CCONJ
ejpam-6082	683	4	engineering	engineering	NOUN
ejpam-6082	683	5	,	,	PUNCT
ejpam-6082	683	6	19(12):13560–13581	19(12):13560–13581	NUM
ejpam-6082	683	7	,	,	PUNCT
ejpam-6082	683	8	2022	2022	NUM
ejpam-6082	683	9	.	.	PUNCT
ejpam-6082	684	1	k.	k.	PROPN
ejpam-6082	684	2	guedri	guedri	PROPN
ejpam-6082	684	3	et	et	PROPN
ejpam-6082	684	4	al	al	PROPN
ejpam-6082	684	5	.	.	PUNCT
ejpam-6082	684	6	/	/	SYM
ejpam-6082	684	7	eur	eur	PROPN
ejpam-6082	684	8	.	.	PUNCT
ejpam-6082	685	1	j.	j.	PROPN
ejpam-6082	685	2	pure	pure	PROPN
ejpam-6082	685	3	appl	appl	PROPN
ejpam-6082	685	4	.	.	PROPN
ejpam-6082	685	5	math	math	PROPN
ejpam-6082	685	6	,	,	PUNCT
ejpam-6082	685	7	18	18	NUM
ejpam-6082	685	8	(	(	PUNCT
ejpam-6082	685	9	2	2	NUM
ejpam-6082	685	10	)	)	PUNCT
ejpam-6082	685	11	(	(	PUNCT
ejpam-6082	685	12	2025	2025	NUM
ejpam-6082	685	13	)	)	PUNCT
ejpam-6082	685	14	,	,	PUNCT
ejpam-6082	685	15	6082	6082	NUM
ejpam-6082	685	16	37	37	NUM
ejpam-6082	685	17	of	of	ADP
ejpam-6082	685	18	39	39	NUM
ejpam-6082	686	1	[	[	SYM
ejpam-6082	686	2	10	10	NUM
ejpam-6082	686	3	]	]	PUNCT
ejpam-6082	686	4	k.	k.	PROPN
ejpam-6082	686	5	dietz	dietz	PROPN
ejpam-6082	686	6	and	and	CCONJ
ejpam-6082	686	7	j.	j.	PROPN
ejpam-6082	686	8	a.	a.	PROPN
ejpam-6082	686	9	p.	p.	PROPN
ejpam-6082	686	10	heesterbeek	heesterbeek	PROPN
ejpam-6082	686	11	.	.	PUNCT
ejpam-6082	687	1	daniel	daniel	PROPN
ejpam-6082	687	2	bernoulli	bernoulli	PROPN
ejpam-6082	687	3	’s	’s	PART
ejpam-6082	687	4	epidemiological	epidemiological	ADJ
ejpam-6082	687	5	model	model	NOUN
ejpam-6082	687	6	revisited	revisit	VERB
ejpam-6082	687	7	.	.	PUNCT
ejpam-6082	688	1	mathematical	mathematical	ADJ
ejpam-6082	688	2	biosciences	bioscience	NOUN
ejpam-6082	688	3	,	,	PUNCT
ejpam-6082	688	4	180(1	180(1	NUM
ejpam-6082	688	5	-	-	SYM
ejpam-6082	688	6	2):1–21	2):1–21	NUM
ejpam-6082	688	7	,	,	PUNCT
ejpam-6082	688	8	2002	2002	NUM
ejpam-6082	688	9	.	.	PUNCT
ejpam-6082	689	1	[	[	X
ejpam-6082	689	2	11	11	NUM
ejpam-6082	689	3	]	]	X
ejpam-6082	689	4	fred	fred	PROPN
ejpam-6082	689	5	brauer	brauer	PROPN
ejpam-6082	689	6	.	.	PUNCT
ejpam-6082	690	1	compartmental	compartmental	PROPN
ejpam-6082	690	2	models	model	NOUN
ejpam-6082	690	3	in	in	ADP
ejpam-6082	690	4	epidemiology	epidemiology	NOUN
ejpam-6082	690	5	.	.	PUNCT
ejpam-6082	691	1	mathematical	mathematical	ADJ
ejpam-6082	691	2	epidemiology	epidemiology	NOUN
ejpam-6082	691	3	,	,	PUNCT
ejpam-6082	691	4	1945:19–79	1945:19–79	ADV
ejpam-6082	691	5	,	,	PUNCT
ejpam-6082	691	6	2008	2008	NUM
ejpam-6082	691	7	.	.	PUNCT
ejpam-6082	692	1	[	[	X
ejpam-6082	692	2	12	12	NUM
ejpam-6082	692	3	]	]	X
ejpam-6082	692	4	i.	i.	PROPN
ejpam-6082	692	5	nali	nali	PROPN
ejpam-6082	692	6	and	and	CCONJ
ejpam-6082	692	7	a.	a.	PROPN
ejpam-6082	692	8	dénes	dénes	PROPN
ejpam-6082	692	9	.	.	PUNCT
ejpam-6082	693	1	global	global	ADJ
ejpam-6082	693	2	dynamics	dynamic	NOUN
ejpam-6082	693	3	of	of	ADP
ejpam-6082	693	4	a	a	DET
ejpam-6082	693	5	within	within	ADP
ejpam-6082	693	6	-	-	PUNCT
ejpam-6082	693	7	host	host	NOUN
ejpam-6082	693	8	model	model	NOUN
ejpam-6082	693	9	for	for	ADP
ejpam-6082	693	10	usutu	usutu	PROPN
ejpam-6082	693	11	virus	virus	PROPN
ejpam-6082	693	12	.	.	PUNCT
ejpam-6082	694	1	computation	computation	NOUN
ejpam-6082	694	2	,	,	PUNCT
ejpam-6082	694	3	11(11):226	11(11):226	PRON
ejpam-6082	694	4	,	,	PUNCT
ejpam-6082	694	5	2023	2023	NUM
ejpam-6082	694	6	.	.	PUNCT
ejpam-6082	695	1	[	[	X
ejpam-6082	695	2	13	13	NUM
ejpam-6082	695	3	]	]	X
ejpam-6082	695	4	e.	e.	PROPN
ejpam-6082	695	5	duque	duque	PROPN
ejpam-6082	695	6	-	-	PUNCT
ejpam-6082	695	7	maŕın	maŕın	PROPN
ejpam-6082	695	8	,	,	PUNCT
ejpam-6082	695	9	j.	j.	PROPN
ejpam-6082	695	10	g.	g.	PROPN
ejpam-6082	695	11	vergaño	vergaño	PROPN
ejpam-6082	695	12	-	-	PUNCT
ejpam-6082	695	13	salazar	salazar	PROPN
ejpam-6082	695	14	,	,	PUNCT
ejpam-6082	695	15	i.	i.	PROPN
ejpam-6082	695	16	duarte	duarte	PROPN
ejpam-6082	695	17	-	-	PUNCT
ejpam-6082	695	18	gandica	gandica	PROPN
ejpam-6082	695	19	,	,	PUNCT
ejpam-6082	695	20	and	and	CCONJ
ejpam-6082	695	21	k.	k.	PROPN
ejpam-6082	695	22	vilches	vilches	PROPN
ejpam-6082	695	23	.	.	PUNCT
ejpam-6082	696	1	mathematical	mathematical	ADJ
ejpam-6082	696	2	modelling	modelling	NOUN
ejpam-6082	696	3	of	of	ADP
ejpam-6082	696	4	some	some	DET
ejpam-6082	696	5	poliomyelitis	poliomyelitis	NOUN
ejpam-6082	696	6	vaccination	vaccination	NOUN
ejpam-6082	696	7	and	and	CCONJ
ejpam-6082	696	8	migration	migration	NOUN
ejpam-6082	696	9	scenarios	scenario	NOUN
ejpam-6082	696	10	in	in	ADP
ejpam-6082	696	11	colombia	colombia	PROPN
ejpam-6082	696	12	.	.	PUNCT
ejpam-6082	697	1	journal	journal	PROPN
ejpam-6082	697	2	of	of	ADP
ejpam-6082	697	3	physics	physics	PROPN
ejpam-6082	697	4	:	:	PUNCT
ejpam-6082	697	5	conference	conference	NOUN
ejpam-6082	697	6	series	series	NOUN
ejpam-6082	697	7	,	,	PUNCT
ejpam-6082	697	8	1160:012021	1160:012021	NUM
ejpam-6082	697	9	,	,	PUNCT
ejpam-6082	697	10	2019	2019	NUM
ejpam-6082	697	11	.	.	PUNCT
ejpam-6082	698	1	[	[	X
ejpam-6082	698	2	14	14	NUM
ejpam-6082	698	3	]	]	X
ejpam-6082	698	4	c.	c.	PROPN
ejpam-6082	698	5	j.	j.	PROPN
ejpam-6082	698	6	browne	browne	PROPN
ejpam-6082	698	7	,	,	PUNCT
ejpam-6082	698	8	r.	r.	PROPN
ejpam-6082	698	9	j.	j.	PROPN
ejpam-6082	698	10	smith	smith	PROPN
ejpam-6082	698	11	,	,	PUNCT
ejpam-6082	698	12	and	and	CCONJ
ejpam-6082	698	13	l.	l.	PROPN
ejpam-6082	698	14	bourouiba	bourouiba	PROPN
ejpam-6082	698	15	.	.	PUNCT
ejpam-6082	699	1	from	from	ADP
ejpam-6082	699	2	regional	regional	ADJ
ejpam-6082	699	3	pulse	pulse	NOUN
ejpam-6082	699	4	vaccination	vaccination	NOUN
ejpam-6082	699	5	to	to	ADP
ejpam-6082	699	6	global	global	ADJ
ejpam-6082	699	7	disease	disease	NOUN
ejpam-6082	699	8	eradication	eradication	NOUN
ejpam-6082	699	9	:	:	PUNCT
ejpam-6082	699	10	insights	insight	NOUN
ejpam-6082	699	11	from	from	ADP
ejpam-6082	699	12	a	a	DET
ejpam-6082	699	13	mathematical	mathematical	ADJ
ejpam-6082	699	14	model	model	NOUN
ejpam-6082	699	15	of	of	ADP
ejpam-6082	699	16	poliomyelitis	poliomyelitis	PROPN
ejpam-6082	699	17	.	.	PUNCT
ejpam-6082	700	1	journal	journal	PROPN
ejpam-6082	700	2	of	of	ADP
ejpam-6082	700	3	mathematical	mathematical	ADJ
ejpam-6082	700	4	biology	biology	NOUN
ejpam-6082	700	5	,	,	PUNCT
ejpam-6082	700	6	71(1):215–253	71(1):215–253	NUM
ejpam-6082	700	7	,	,	PUNCT
ejpam-6082	700	8	2015	2015	NUM
ejpam-6082	700	9	.	.	PUNCT
ejpam-6082	701	1	[	[	X
ejpam-6082	701	2	15	15	NUM
ejpam-6082	701	3	]	]	X
ejpam-6082	701	4	a.	a.	NOUN
ejpam-6082	701	5	dénes	dénes	PROPN
ejpam-6082	701	6	and	and	CCONJ
ejpam-6082	701	7	l.	l.	PROPN
ejpam-6082	701	8	székely	székely	ADV
ejpam-6082	701	9	.	.	PUNCT
ejpam-6082	702	1	global	global	ADJ
ejpam-6082	702	2	dynamics	dynamic	NOUN
ejpam-6082	702	3	of	of	ADP
ejpam-6082	702	4	a	a	DET
ejpam-6082	702	5	mathematical	mathematical	ADJ
ejpam-6082	702	6	model	model	NOUN
ejpam-6082	702	7	for	for	ADP
ejpam-6082	702	8	the	the	DET
ejpam-6082	702	9	possible	possible	ADJ
ejpam-6082	702	10	re	re	NOUN
ejpam-6082	702	11	-	-	NOUN
ejpam-6082	702	12	emergence	emergence	NOUN
ejpam-6082	702	13	of	of	ADP
ejpam-6082	702	14	polio	polio	NOUN
ejpam-6082	702	15	.	.	PUNCT
ejpam-6082	703	1	mathematical	mathematical	ADJ
ejpam-6082	703	2	biosciences	bioscience	NOUN
ejpam-6082	703	3	,	,	PUNCT
ejpam-6082	703	4	293:64–74	293:64–74	NUM
ejpam-6082	703	5	,	,	PUNCT
ejpam-6082	703	6	2017	2017	NUM
ejpam-6082	703	7	.	.	PUNCT
ejpam-6082	704	1	[	[	X
ejpam-6082	704	2	16	16	NUM
ejpam-6082	704	3	]	]	PUNCT
ejpam-6082	704	4	f.	f.	PROPN
ejpam-6082	704	5	a.	a.	PROPN
ejpam-6082	704	6	alrawajeh	alrawajeh	PROPN
ejpam-6082	704	7	,	,	PUNCT
ejpam-6082	704	8	f.	f.	PROPN
ejpam-6082	704	9	m.	m.	PROPN
ejpam-6082	704	10	allehiany	allehiany	PROPN
ejpam-6082	704	11	,	,	PUNCT
ejpam-6082	704	12	a.	a.	NOUN
ejpam-6082	704	13	raza	raza	PROPN
ejpam-6082	704	14	,	,	PUNCT
ejpam-6082	704	15	s.	s.	PROPN
ejpam-6082	704	16	a.	a.	PROPN
ejpam-6082	704	17	m.	m.	PROPN
ejpam-6082	704	18	abdelmohsen	abdelmohsen	PROPN
ejpam-6082	704	19	,	,	PUNCT
ejpam-6082	704	20	t.	t.	PROPN
ejpam-6082	704	21	n.	n.	PROPN
ejpam-6082	704	22	cheema	cheema	PROPN
ejpam-6082	704	23	,	,	PUNCT
ejpam-6082	704	24	m.	m.	PROPN
ejpam-6082	704	25	rafiq	rafiq	PROPN
ejpam-6082	704	26	,	,	PUNCT
ejpam-6082	704	27	and	and	CCONJ
ejpam-6082	704	28	m.	m.	PROPN
ejpam-6082	704	29	mohsin	mohsin	PROPN
ejpam-6082	704	30	.	.	PUNCT
ejpam-6082	705	1	bio	bio	PROPN
ejpam-6082	705	2	-	-	PUNCT
ejpam-6082	705	3	inspired	inspire	VERB
ejpam-6082	705	4	computational	computational	ADJ
ejpam-6082	705	5	methods	method	NOUN
ejpam-6082	705	6	for	for	ADP
ejpam-6082	705	7	the	the	DET
ejpam-6082	705	8	polio	polio	NOUN
ejpam-6082	705	9	virus	virus	NOUN
ejpam-6082	705	10	epidemic	epidemic	NOUN
ejpam-6082	705	11	model	model	NOUN
ejpam-6082	705	12	.	.	PUNCT
ejpam-6082	706	1	computers	computer	NOUN
ejpam-6082	706	2	,	,	PUNCT
ejpam-6082	706	3	materials	material	NOUN
ejpam-6082	706	4	&	&	CCONJ
ejpam-6082	706	5	continua	continua	PROPN
ejpam-6082	706	6	,	,	PUNCT
ejpam-6082	706	7	72(2):2351–2374	72(2):2351–2374	NUM
ejpam-6082	706	8	,	,	PUNCT
ejpam-6082	706	9	2022	2022	NUM
ejpam-6082	706	10	.	.	PUNCT
ejpam-6082	707	1	[	[	X
ejpam-6082	707	2	17	17	NUM
ejpam-6082	707	3	]	]	PUNCT
ejpam-6082	707	4	a.	a.	NOUN
ejpam-6082	707	5	raza	raza	PROPN
ejpam-6082	707	6	,	,	PUNCT
ejpam-6082	707	7	d.	d.	PROPN
ejpam-6082	707	8	baleanu	baleanu	PROPN
ejpam-6082	707	9	,	,	PUNCT
ejpam-6082	707	10	z.	z.	PROPN
ejpam-6082	707	11	u.	u.	PROPN
ejpam-6082	707	12	khan	khan	PROPN
ejpam-6082	707	13	,	,	PUNCT
ejpam-6082	707	14	m.	m.	NOUN
ejpam-6082	707	15	mohsin	mohsin	PROPN
ejpam-6082	707	16	,	,	PUNCT
ejpam-6082	707	17	n.	n.	PROPN
ejpam-6082	707	18	ahmad	ahmad	PROPN
ejpam-6082	707	19	,	,	PUNCT
ejpam-6082	707	20	m.	m.	NOUN
ejpam-6082	707	21	rafiq	rafiq	PROPN
ejpam-6082	707	22	,	,	PUNCT
ejpam-6082	707	23	and	and	CCONJ
ejpam-6082	707	24	p.	p.	PROPN
ejpam-6082	707	25	anwar	anwar	PROPN
ejpam-6082	707	26	.	.	PUNCT
ejpam-6082	708	1	stochastic	stochastic	ADJ
ejpam-6082	708	2	analysis	analysis	NOUN
ejpam-6082	708	3	for	for	ADP
ejpam-6082	708	4	the	the	DET
ejpam-6082	708	5	dynamics	dynamic	NOUN
ejpam-6082	708	6	of	of	ADP
ejpam-6082	708	7	a	a	DET
ejpam-6082	708	8	poliovirus	poliovirus	NOUN
ejpam-6082	708	9	epidemic	epidemic	NOUN
ejpam-6082	708	10	model	model	NOUN
ejpam-6082	708	11	,	,	PUNCT
ejpam-6082	708	12	2023	2023	NUM
ejpam-6082	708	13	.	.	PUNCT
ejpam-6082	709	1	preprint	preprint	NOUN
ejpam-6082	709	2	,	,	PUNCT
ejpam-6082	709	3	no	no	DET
ejpam-6082	709	4	journal	journal	NOUN
ejpam-6082	709	5	specified	specify	VERB
ejpam-6082	709	6	.	.	PUNCT
ejpam-6082	710	1	[	[	X
ejpam-6082	710	2	18	18	NUM
ejpam-6082	710	3	]	]	PUNCT
ejpam-6082	710	4	m.	m.	NOUN
ejpam-6082	710	5	agarwal	agarwal	PROPN
ejpam-6082	710	6	and	and	CCONJ
ejpam-6082	710	7	a.	a.	PROPN
ejpam-6082	710	8	s.	s.	PROPN
ejpam-6082	710	9	bhadauria	bhadauria	PROPN
ejpam-6082	710	10	.	.	PUNCT
ejpam-6082	711	1	modeling	model	VERB
ejpam-6082	711	2	spread	spread	NOUN
ejpam-6082	711	3	of	of	ADP
ejpam-6082	711	4	polio	polio	NOUN
ejpam-6082	711	5	with	with	ADP
ejpam-6082	711	6	the	the	DET
ejpam-6082	711	7	role	role	NOUN
ejpam-6082	711	8	of	of	ADP
ejpam-6082	711	9	vaccination	vaccination	NOUN
ejpam-6082	711	10	.	.	PUNCT
ejpam-6082	712	1	applications	application	NOUN
ejpam-6082	712	2	and	and	CCONJ
ejpam-6082	712	3	applied	apply	VERB
ejpam-6082	712	4	mathematics	mathematic	NOUN
ejpam-6082	712	5	:	:	PUNCT
ejpam-6082	712	6	an	an	DET
ejpam-6082	712	7	international	international	ADJ
ejpam-6082	712	8	journal	journal	NOUN
ejpam-6082	712	9	,	,	PUNCT
ejpam-6082	712	10	6(2):552–571	6(2):552–571	NUM
ejpam-6082	712	11	,	,	PUNCT
ejpam-6082	712	12	2011	2011	NUM
ejpam-6082	712	13	.	.	PUNCT
ejpam-6082	713	1	[	[	X
ejpam-6082	713	2	19	19	NUM
ejpam-6082	713	3	]	]	X
ejpam-6082	713	4	h.	h.	PROPN
ejpam-6082	713	5	miao	miao	PROPN
ejpam-6082	713	6	,	,	PUNCT
ejpam-6082	713	7	z.	z.	PROPN
ejpam-6082	713	8	teng	teng	PROPN
ejpam-6082	713	9	,	,	PUNCT
ejpam-6082	713	10	x.	x.	PROPN
ejpam-6082	713	11	abdurahman	abdurahman	NOUN
ejpam-6082	713	12	,	,	PUNCT
ejpam-6082	713	13	and	and	CCONJ
ejpam-6082	713	14	z.	z.	PROPN
ejpam-6082	713	15	li	li	PROPN
ejpam-6082	713	16	.	.	PROPN
ejpam-6082	714	1	global	global	ADJ
ejpam-6082	714	2	stability	stability	NOUN
ejpam-6082	714	3	of	of	ADP
ejpam-6082	714	4	a	a	DET
ejpam-6082	714	5	diffusive	diffusive	ADJ
ejpam-6082	714	6	and	and	CCONJ
ejpam-6082	714	7	delayed	delay	VERB
ejpam-6082	714	8	virus	virus	NOUN
ejpam-6082	714	9	infection	infection	NOUN
ejpam-6082	714	10	model	model	NOUN
ejpam-6082	714	11	with	with	ADP
ejpam-6082	714	12	general	general	ADJ
ejpam-6082	714	13	incidence	incidence	NOUN
ejpam-6082	714	14	function	function	NOUN
ejpam-6082	714	15	and	and	CCONJ
ejpam-6082	714	16	adaptive	adaptive	ADJ
ejpam-6082	714	17	immune	immune	ADJ
ejpam-6082	714	18	response	response	NOUN
ejpam-6082	714	19	.	.	PUNCT
ejpam-6082	715	1	journal	journal	NOUN
ejpam-6082	715	2	of	of	ADP
ejpam-6082	715	3	computational	computational	ADJ
ejpam-6082	715	4	and	and	CCONJ
ejpam-6082	715	5	applied	applied	ADJ
ejpam-6082	715	6	mathematics	mathematic	NOUN
ejpam-6082	715	7	,	,	PUNCT
ejpam-6082	715	8	37(12):3780–3805	37(12):3780–3805	PROPN
ejpam-6082	715	9	,	,	PUNCT
ejpam-6082	715	10	2018	2018	NUM
ejpam-6082	715	11	.	.	PUNCT
ejpam-6082	716	1	[	[	X
ejpam-6082	716	2	20	20	NUM
ejpam-6082	716	3	]	]	X
ejpam-6082	716	4	n.	n.	PROPN
ejpam-6082	716	5	ahmed	ahmed	PROPN
ejpam-6082	716	6	,	,	PUNCT
ejpam-6082	716	7	j.	j.	PROPN
ejpam-6082	716	8	e.	e.	PROPN
ejpam-6082	716	9	macias	macias	PROPN
ejpam-6082	716	10	-	-	PUNCT
ejpam-6082	716	11	diaz	diaz	PROPN
ejpam-6082	716	12	,	,	PUNCT
ejpam-6082	716	13	n.	n.	PROPN
ejpam-6082	716	14	shahid	shahid	PROPN
ejpam-6082	716	15	,	,	PUNCT
ejpam-6082	716	16	a.	a.	NOUN
ejpam-6082	716	17	raza	raza	PROPN
ejpam-6082	716	18	,	,	PUNCT
ejpam-6082	716	19	and	and	CCONJ
ejpam-6082	716	20	m.	m.	PROPN
ejpam-6082	716	21	rafiq	rafiq	PROPN
ejpam-6082	716	22	.	.	PUNCT
ejpam-6082	717	1	on	on	ADP
ejpam-6082	717	2	the	the	DET
ejpam-6082	717	3	computational	computational	ADJ
ejpam-6082	717	4	simulation	simulation	NOUN
ejpam-6082	717	5	of	of	ADP
ejpam-6082	717	6	a	a	DET
ejpam-6082	717	7	temporally	temporally	ADV
ejpam-6082	717	8	non	non	ADJ
ejpam-6082	717	9	-	-	ADJ
ejpam-6082	717	10	local	local	ADJ
ejpam-6082	717	11	and	and	CCONJ
ejpam-6082	717	12	nonlinear	nonlinear	ADJ
ejpam-6082	717	13	diffusive	diffusive	ADJ
ejpam-6082	717	14	epidemic	epidemic	NOUN
ejpam-6082	717	15	model	model	NOUN
ejpam-6082	717	16	of	of	ADP
ejpam-6082	717	17	disease	disease	NOUN
ejpam-6082	717	18	transmission	transmission	NOUN
ejpam-6082	717	19	.	.	PUNCT
ejpam-6082	718	1	international	international	ADJ
ejpam-6082	718	2	journal	journal	NOUN
ejpam-6082	718	3	of	of	ADP
ejpam-6082	718	4	modern	modern	ADJ
ejpam-6082	718	5	physics	physic	NOUN
ejpam-6082	718	6	c	c	NOUN
ejpam-6082	718	7	,	,	PUNCT
ejpam-6082	718	8	2024	2024	NUM
ejpam-6082	718	9	.	.	PUNCT
ejpam-6082	719	1	[	[	X
ejpam-6082	719	2	21	21	NUM
ejpam-6082	719	3	]	]	X
ejpam-6082	719	4	e.	e.	PROPN
ejpam-6082	719	5	fadhal	fadhal	PROPN
ejpam-6082	719	6	,	,	PUNCT
ejpam-6082	719	7	m.	m.	NOUN
ejpam-6082	719	8	m.	m.	PROPN
ejpam-6082	719	9	al	al	PROPN
ejpam-6082	719	10	-	-	PUNCT
ejpam-6082	719	11	shamiri	shamiri	PROPN
ejpam-6082	719	12	,	,	PUNCT
ejpam-6082	719	13	m.	m.	PROPN
ejpam-6082	719	14	w.	w.	PROPN
ejpam-6082	719	15	yasin	yasin	PROPN
ejpam-6082	719	16	,	,	PUNCT
ejpam-6082	719	17	s.	s.	PROPN
ejpam-6082	719	18	m.	m.	PROPN
ejpam-6082	719	19	h.	h.	PROPN
ejpam-6082	719	20	ashfaq	ashfaq	PROPN
ejpam-6082	719	21	,	,	PUNCT
ejpam-6082	719	22	n.	n.	PROPN
ejpam-6082	719	23	ahmed	ahmed	PROPN
ejpam-6082	719	24	,	,	PUNCT
ejpam-6082	719	25	a.	a.	NOUN
ejpam-6082	719	26	raza	raza	PROPN
ejpam-6082	719	27	,	,	PUNCT
ejpam-6082	719	28	and	and	CCONJ
ejpam-6082	719	29	m.	m.	PROPN
ejpam-6082	719	30	rafiq	rafiq	PROPN
ejpam-6082	719	31	.	.	PUNCT
ejpam-6082	720	1	spatio	spatio	PROPN
ejpam-6082	720	2	-	-	PUNCT
ejpam-6082	720	3	temporal	temporal	ADJ
ejpam-6082	720	4	dynamics	dynamic	NOUN
ejpam-6082	720	5	of	of	ADP
ejpam-6082	720	6	the	the	DET
ejpam-6082	720	7	vector	vector	NOUN
ejpam-6082	720	8	-	-	PUNCT
ejpam-6082	720	9	borne	borne	ADJ
ejpam-6082	720	10	plant	plant	NOUN
ejpam-6082	720	11	disease	disease	NOUN
ejpam-6082	720	12	model	model	NOUN
ejpam-6082	720	13	.	.	PUNCT
ejpam-6082	721	1	modeling	model	VERB
ejpam-6082	721	2	earth	earth	NOUN
ejpam-6082	721	3	systems	system	NOUN
ejpam-6082	721	4	and	and	CCONJ
ejpam-6082	721	5	environment	environment	NOUN
ejpam-6082	721	6	,	,	PUNCT
ejpam-6082	721	7	10(6):6417–6430	10(6):6417–6430	NUM
ejpam-6082	721	8	,	,	PUNCT
ejpam-6082	721	9	2024	2024	NUM
ejpam-6082	721	10	.	.	PUNCT
ejpam-6082	722	1	[	[	X
ejpam-6082	722	2	22	22	NUM
ejpam-6082	722	3	]	]	PUNCT
ejpam-6082	722	4	m.	m.	PROPN
ejpam-6082	722	5	w.	w.	PROPN
ejpam-6082	722	6	yasin	yasin	PROPN
ejpam-6082	722	7	,	,	PUNCT
ejpam-6082	722	8	n.	n.	PROPN
ejpam-6082	722	9	ahmed	ahmed	PROPN
ejpam-6082	722	10	,	,	PUNCT
ejpam-6082	722	11	m.	m.	PROPN
ejpam-6082	722	12	s.	s.	PROPN
ejpam-6082	722	13	iqbal	iqbal	PROPN
ejpam-6082	722	14	,	,	PUNCT
ejpam-6082	722	15	a.	a.	NOUN
ejpam-6082	722	16	raza	raza	PROPN
ejpam-6082	722	17	,	,	PUNCT
ejpam-6082	722	18	m.	m.	PROPN
ejpam-6082	722	19	rafiq	rafiq	PROPN
ejpam-6082	722	20	,	,	PUNCT
ejpam-6082	722	21	e.	e.	PROPN
ejpam-6082	722	22	m.	m.	PROPN
ejpam-6082	722	23	t.	t.	PROPN
ejpam-6082	722	24	eldin	eldin	PROPN
ejpam-6082	722	25	,	,	PUNCT
ejpam-6082	722	26	and	and	CCONJ
ejpam-6082	722	27	i.	i.	PROPN
ejpam-6082	722	28	khan	khan	PROPN
ejpam-6082	722	29	.	.	PUNCT
ejpam-6082	723	1	spatio	spatio	PROPN
ejpam-6082	723	2	-	-	PUNCT
ejpam-6082	723	3	temporal	temporal	ADJ
ejpam-6082	723	4	numerical	numerical	ADJ
ejpam-6082	723	5	modeling	modeling	NOUN
ejpam-6082	723	6	of	of	ADP
ejpam-6082	723	7	stochastic	stochastic	ADJ
ejpam-6082	723	8	predator	predator	NOUN
ejpam-6082	723	9	-	-	PUNCT
ejpam-6082	723	10	prey	prey	NOUN
ejpam-6082	723	11	model	model	NOUN
ejpam-6082	723	12	.	.	PUNCT
ejpam-6082	724	1	scientific	scientific	ADJ
ejpam-6082	724	2	reports	report	NOUN
ejpam-6082	724	3	,	,	PUNCT
ejpam-6082	724	4	13(1):1990	13(1):1990	NUM
ejpam-6082	724	5	,	,	PUNCT
ejpam-6082	724	6	2023	2023	NUM
ejpam-6082	724	7	.	.	PUNCT
ejpam-6082	725	1	[	[	X
ejpam-6082	725	2	23	23	NUM
ejpam-6082	725	3	]	]	X
ejpam-6082	725	4	r.	r.	PROPN
ejpam-6082	725	5	zarin	zarin	PROPN
ejpam-6082	725	6	.	.	PUNCT
ejpam-6082	726	1	a	a	DET
ejpam-6082	726	2	robust	robust	ADJ
ejpam-6082	726	3	study	study	NOUN
ejpam-6082	726	4	of	of	ADP
ejpam-6082	726	5	dual	dual	ADJ
ejpam-6082	726	6	variants	variant	NOUN
ejpam-6082	726	7	of	of	ADP
ejpam-6082	726	8	sars	sar	NOUN
ejpam-6082	726	9	-	-	PUNCT
ejpam-6082	726	10	cov-2	cov-2	PART
ejpam-6082	726	11	using	use	VERB
ejpam-6082	726	12	a	a	DET
ejpam-6082	726	13	reaction	reaction	NOUN
ejpam-6082	726	14	-	-	PUNCT
ejpam-6082	726	15	diffusion	diffusion	NOUN
ejpam-6082	726	16	mathematical	mathematical	ADJ
ejpam-6082	726	17	model	model	NOUN
ejpam-6082	726	18	with	with	ADP
ejpam-6082	726	19	real	real	ADJ
ejpam-6082	726	20	data	datum	NOUN
ejpam-6082	726	21	from	from	ADP
ejpam-6082	726	22	the	the	DET
ejpam-6082	726	23	usa	usa	PROPN
ejpam-6082	726	24	.	.	PUNCT
ejpam-6082	727	1	the	the	DET
ejpam-6082	727	2	european	european	PROPN
ejpam-6082	727	3	physical	physical	PROPN
ejpam-6082	727	4	journal	journal	PROPN
ejpam-6082	727	5	plus	plus	CCONJ
ejpam-6082	727	6	,	,	PUNCT
ejpam-6082	727	7	138(11):1011	138(11):1011	NUM
ejpam-6082	727	8	,	,	PUNCT
ejpam-6082	727	9	2023	2023	NUM
ejpam-6082	727	10	.	.	PUNCT
ejpam-6082	728	1	[	[	X
ejpam-6082	728	2	24	24	NUM
ejpam-6082	728	3	]	]	PUNCT
ejpam-6082	728	4	x.	x.	NOUN
ejpam-6082	728	5	ren	ren	PROPN
ejpam-6082	728	6	,	,	PUNCT
ejpam-6082	728	7	y.	y.	PROPN
ejpam-6082	728	8	tian	tian	PROPN
ejpam-6082	728	9	,	,	PUNCT
ejpam-6082	728	10	l.	l.	PROPN
ejpam-6082	728	11	liu	liu	PROPN
ejpam-6082	728	12	,	,	PUNCT
ejpam-6082	728	13	and	and	CCONJ
ejpam-6082	728	14	x.	x.	PROPN
ejpam-6082	728	15	liu	liu	PROPN
ejpam-6082	728	16	.	.	PUNCT
ejpam-6082	729	1	a	a	DET
ejpam-6082	729	2	reaction	reaction	NOUN
ejpam-6082	729	3	–	–	PUNCT
ejpam-6082	729	4	diffusion	diffusion	NOUN
ejpam-6082	729	5	within	within	ADP
ejpam-6082	729	6	-	-	PUNCT
ejpam-6082	729	7	host	host	NOUN
ejpam-6082	729	8	hiv	hiv	PROPN
ejpam-6082	729	9	model	model	NOUN
ejpam-6082	729	10	with	with	ADP
ejpam-6082	729	11	cell	cell	NOUN
ejpam-6082	729	12	-	-	PUNCT
ejpam-6082	729	13	to	to	ADP
ejpam-6082	729	14	-	-	PUNCT
ejpam-6082	729	15	cell	cell	NOUN
ejpam-6082	729	16	transmission	transmission	NOUN
ejpam-6082	729	17	.	.	PUNCT
ejpam-6082	730	1	journal	journal	PROPN
ejpam-6082	730	2	of	of	ADP
ejpam-6082	730	3	mathematical	mathematical	ADJ
ejpam-6082	730	4	biology	biology	NOUN
ejpam-6082	730	5	,	,	PUNCT
ejpam-6082	730	6	76(7):1831–1872	76(7):1831–1872	NUM
ejpam-6082	730	7	,	,	PUNCT
ejpam-6082	730	8	2018	2018	NUM
ejpam-6082	730	9	.	.	PUNCT
ejpam-6082	731	1	[	[	X
ejpam-6082	731	2	25	25	NUM
ejpam-6082	731	3	]	]	X
ejpam-6082	731	4	s.	s.	PROPN
ejpam-6082	731	5	pankavich	pankavich	PROPN
ejpam-6082	731	6	and	and	CCONJ
ejpam-6082	731	7	c.	c.	PROPN
ejpam-6082	731	8	parkinson	parkinson	PROPN
ejpam-6082	731	9	.	.	PUNCT
ejpam-6082	732	1	mathematical	mathematical	ADJ
ejpam-6082	732	2	analysis	analysis	NOUN
ejpam-6082	732	3	of	of	ADP
ejpam-6082	732	4	an	an	DET
ejpam-6082	732	5	in	in	ADP
ejpam-6082	732	6	-	-	PUNCT
ejpam-6082	732	7	host	host	NOUN
ejpam-6082	732	8	model	model	NOUN
ejpam-6082	732	9	of	of	ADP
ejpam-6082	732	10	viral	viral	ADJ
ejpam-6082	732	11	dynamics	dynamic	NOUN
ejpam-6082	732	12	with	with	ADP
ejpam-6082	732	13	spatial	spatial	ADJ
ejpam-6082	732	14	heterogeneity	heterogeneity	NOUN
ejpam-6082	732	15	.	.	PUNCT
ejpam-6082	733	1	discrete	discrete	VERB
ejpam-6082	733	2	and	and	CCONJ
ejpam-6082	733	3	continuous	continuous	ADJ
ejpam-6082	733	4	dynamical	dynamical	ADJ
ejpam-6082	733	5	systems	system	NOUN
ejpam-6082	733	6	k.	k.	PROPN
ejpam-6082	733	7	guedri	guedri	PROPN
ejpam-6082	733	8	et	et	PROPN
ejpam-6082	733	9	al	al	PROPN
ejpam-6082	733	10	.	.	PUNCT
ejpam-6082	733	11	/	/	SYM
ejpam-6082	733	12	eur	eur	PROPN
ejpam-6082	733	13	.	.	PUNCT
ejpam-6082	734	1	j.	j.	PROPN
ejpam-6082	734	2	pure	pure	PROPN
ejpam-6082	734	3	appl	appl	PROPN
ejpam-6082	734	4	.	.	PROPN
ejpam-6082	734	5	math	math	PROPN
ejpam-6082	734	6	,	,	PUNCT
ejpam-6082	734	7	18	18	NUM
ejpam-6082	734	8	(	(	PUNCT
ejpam-6082	734	9	2	2	NUM
ejpam-6082	734	10	)	)	PUNCT
ejpam-6082	734	11	(	(	PUNCT
ejpam-6082	734	12	2025	2025	NUM
ejpam-6082	734	13	)	)	PUNCT
ejpam-6082	734	14	,	,	PUNCT
ejpam-6082	734	15	6082	6082	NUM
ejpam-6082	734	16	38	38	NUM
ejpam-6082	734	17	of	of	ADP
ejpam-6082	734	18	39	39	NUM
ejpam-6082	734	19	series	series	NOUN
ejpam-6082	734	20	b	b	PROPN
ejpam-6082	734	21	,	,	PUNCT
ejpam-6082	734	22	21(4):1237–1257	21(4):1237–1257	NUM
ejpam-6082	734	23	,	,	PUNCT
ejpam-6082	734	24	2016	2016	NUM
ejpam-6082	734	25	.	.	PUNCT
ejpam-6082	735	1	[	[	X
ejpam-6082	735	2	26	26	NUM
ejpam-6082	735	3	]	]	X
ejpam-6082	735	4	y.	y.	PROPN
ejpam-6082	735	5	cai	cai	PROPN
ejpam-6082	735	6	,	,	PUNCT
ejpam-6082	735	7	z.	z.	PROPN
ejpam-6082	735	8	ding	ding	PROPN
ejpam-6082	735	9	,	,	PUNCT
ejpam-6082	735	10	and	and	CCONJ
ejpam-6082	735	11	w.	w.	PROPN
ejpam-6082	735	12	wang	wang	PROPN
ejpam-6082	735	13	.	.	PUNCT
ejpam-6082	736	1	transmission	transmission	NOUN
ejpam-6082	736	2	dynamics	dynamic	NOUN
ejpam-6082	736	3	of	of	ADP
ejpam-6082	736	4	zika	zika	X
ejpam-6082	736	5	virus	virus	NOUN
ejpam-6082	736	6	with	with	ADP
ejpam-6082	736	7	spatial	spatial	ADJ
ejpam-6082	736	8	structure	structure	NOUN
ejpam-6082	736	9	—	—	PUNCT
ejpam-6082	736	10	a	a	DET
ejpam-6082	736	11	case	case	NOUN
ejpam-6082	736	12	study	study	NOUN
ejpam-6082	736	13	in	in	ADP
ejpam-6082	736	14	rio	rio	PROPN
ejpam-6082	736	15	de	de	PROPN
ejpam-6082	736	16	janeiro	janeiro	PROPN
ejpam-6082	736	17	,	,	PUNCT
ejpam-6082	736	18	brazil	brazil	PROPN
ejpam-6082	736	19	.	.	PUNCT
ejpam-6082	737	1	physica	physica	PROPN
ejpam-6082	737	2	a	a	DET
ejpam-6082	737	3	:	:	PUNCT
ejpam-6082	737	4	statistical	statistical	ADJ
ejpam-6082	737	5	mechanics	mechanic	NOUN
ejpam-6082	737	6	and	and	CCONJ
ejpam-6082	737	7	its	its	PRON
ejpam-6082	737	8	applications	application	NOUN
ejpam-6082	737	9	,	,	PUNCT
ejpam-6082	737	10	514:729–740	514:729–740	NUM
ejpam-6082	737	11	,	,	PUNCT
ejpam-6082	737	12	2019	2019	NUM
ejpam-6082	737	13	.	.	PUNCT
ejpam-6082	738	1	[	[	X
ejpam-6082	738	2	27	27	NUM
ejpam-6082	738	3	]	]	X
ejpam-6082	738	4	rashid	rashid	PROPN
ejpam-6082	738	5	jan	jan	PROPN
ejpam-6082	738	6	and	and	CCONJ
ejpam-6082	738	7	asif	asif	PROPN
ejpam-6082	738	8	jan	jan	PROPN
ejpam-6082	738	9	.	.	PROPN
ejpam-6082	738	10	msgdtm	msgdtm	PROPN
ejpam-6082	738	11	for	for	ADP
ejpam-6082	738	12	solution	solution	NOUN
ejpam-6082	738	13	of	of	ADP
ejpam-6082	738	14	fractional	fractional	ADJ
ejpam-6082	738	15	order	order	NOUN
ejpam-6082	738	16	dengue	dengue	NOUN
ejpam-6082	738	17	disease	disease	NOUN
ejpam-6082	738	18	model	model	NOUN
ejpam-6082	738	19	.	.	PUNCT
ejpam-6082	739	1	international	international	ADJ
ejpam-6082	739	2	journal	journal	PROPN
ejpam-6082	739	3	of	of	ADP
ejpam-6082	739	4	science	science	NOUN
ejpam-6082	739	5	and	and	CCONJ
ejpam-6082	739	6	research	research	NOUN
ejpam-6082	739	7	,	,	PUNCT
ejpam-6082	739	8	6(3):1140–1144	6(3):1140–1144	NUM
ejpam-6082	739	9	,	,	PUNCT
ejpam-6082	739	10	2017	2017	NUM
ejpam-6082	739	11	.	.	PUNCT
ejpam-6082	740	1	[	[	X
ejpam-6082	740	2	28	28	NUM
ejpam-6082	740	3	]	]	X
ejpam-6082	740	4	i.	i.	PROPN
ejpam-6082	740	5	ahmad	ahmad	PROPN
ejpam-6082	740	6	,	,	PUNCT
ejpam-6082	740	7	i.	i.	PROPN
ejpam-6082	740	8	ali	ali	PROPN
ejpam-6082	740	9	,	,	PUNCT
ejpam-6082	740	10	rashid	rashid	PROPN
ejpam-6082	740	11	jan	jan	PROPN
ejpam-6082	740	12	,	,	PUNCT
ejpam-6082	740	13	s.	s.	PROPN
ejpam-6082	740	14	a.	a.	PROPN
ejpam-6082	740	15	idris	idris	PROPN
ejpam-6082	740	16	,	,	PUNCT
ejpam-6082	740	17	and	and	CCONJ
ejpam-6082	740	18	m.	m.	NOUN
ejpam-6082	740	19	mousa	mousa	PROPN
ejpam-6082	740	20	.	.	PUNCT
ejpam-6082	741	1	solutions	solution	NOUN
ejpam-6082	741	2	of	of	ADP
ejpam-6082	741	3	a	a	DET
ejpam-6082	741	4	threedimensional	threedimensional	ADJ
ejpam-6082	741	5	multi	multi	ADJ
ejpam-6082	741	6	-	-	ADJ
ejpam-6082	741	7	term	term	ADJ
ejpam-6082	741	8	fractional	fractional	ADJ
ejpam-6082	741	9	anomalous	anomalous	ADJ
ejpam-6082	741	10	solute	solute	NOUN
ejpam-6082	741	11	transport	transport	NOUN
ejpam-6082	741	12	model	model	NOUN
ejpam-6082	741	13	for	for	ADP
ejpam-6082	741	14	contamination	contamination	NOUN
ejpam-6082	741	15	in	in	ADP
ejpam-6082	741	16	groundwater	groundwater	NOUN
ejpam-6082	741	17	.	.	PUNCT
ejpam-6082	742	1	plos	plos	PROPN
ejpam-6082	742	2	one	one	NUM
ejpam-6082	742	3	,	,	PUNCT
ejpam-6082	742	4	18(12):e0294348	18(12):e0294348	PROPN
ejpam-6082	742	5	,	,	PUNCT
ejpam-6082	742	6	2023	2023	NUM
ejpam-6082	742	7	.	.	PUNCT
ejpam-6082	743	1	[	[	X
ejpam-6082	743	2	29	29	NUM
ejpam-6082	743	3	]	]	X
ejpam-6082	743	4	r.	r.	PROPN
ejpam-6082	743	5	zarin	zarin	PROPN
ejpam-6082	743	6	,	,	PUNCT
ejpam-6082	743	7	a.	a.	PROPN
ejpam-6082	743	8	khan	khan	PROPN
ejpam-6082	743	9	,	,	PUNCT
ejpam-6082	743	10	and	and	CCONJ
ejpam-6082	743	11	p.	p.	PROPN
ejpam-6082	743	12	kumar	kumar	PROPN
ejpam-6082	743	13	.	.	PUNCT
ejpam-6082	744	1	fractional	fractional	ADJ
ejpam-6082	744	2	-	-	PUNCT
ejpam-6082	744	3	order	order	NOUN
ejpam-6082	744	4	dynamics	dynamic	NOUN
ejpam-6082	744	5	of	of	ADP
ejpam-6082	744	6	chagas	chagas	NOUN
ejpam-6082	744	7	-	-	PUNCT
ejpam-6082	744	8	hiv	hiv	PROPN
ejpam-6082	744	9	epidemic	epidemic	NOUN
ejpam-6082	744	10	model	model	NOUN
ejpam-6082	744	11	with	with	ADP
ejpam-6082	744	12	different	different	ADJ
ejpam-6082	744	13	fractional	fractional	ADJ
ejpam-6082	744	14	operators	operator	NOUN
ejpam-6082	744	15	.	.	PUNCT
ejpam-6082	745	1	aims	aim	VERB
ejpam-6082	745	2	mathematics	mathematic	NOUN
ejpam-6082	745	3	,	,	PUNCT
ejpam-6082	745	4	7(10):18897–18924	7(10):18897–18924	NUM
ejpam-6082	745	5	,	,	PUNCT
ejpam-6082	745	6	2022	2022	NUM
ejpam-6082	745	7	.	.	PUNCT
ejpam-6082	746	1	[	[	X
ejpam-6082	746	2	30	30	NUM
ejpam-6082	746	3	]	]	X
ejpam-6082	746	4	m.	m.	NOUN
ejpam-6082	746	5	c.	c.	PROPN
ejpam-6082	746	6	bahi	bahi	PROPN
ejpam-6082	746	7	,	,	PUNCT
ejpam-6082	746	8	s.	s.	PROPN
ejpam-6082	746	9	bahramand	bahramand	PROPN
ejpam-6082	746	10	,	,	PUNCT
ejpam-6082	746	11	rashid	rashid	PROPN
ejpam-6082	746	12	jan	jan	PROPN
ejpam-6082	746	13	,	,	PUNCT
ejpam-6082	746	14	s.	s.	PROPN
ejpam-6082	746	15	boulaaras	boulaaras	PROPN
ejpam-6082	746	16	,	,	PUNCT
ejpam-6082	746	17	h.	h.	PROPN
ejpam-6082	746	18	ahmad	ahmad	PROPN
ejpam-6082	746	19	,	,	PUNCT
ejpam-6082	746	20	and	and	CCONJ
ejpam-6082	746	21	r.	r.	PROPN
ejpam-6082	746	22	guefaifia	guefaifia	PROPN
ejpam-6082	746	23	.	.	PUNCT
ejpam-6082	747	1	fractional	fractional	ADJ
ejpam-6082	747	2	view	view	NOUN
ejpam-6082	747	3	analysis	analysis	NOUN
ejpam-6082	747	4	of	of	ADP
ejpam-6082	747	5	sexual	sexual	ADJ
ejpam-6082	747	6	transmitted	transmit	VERB
ejpam-6082	747	7	human	human	ADJ
ejpam-6082	747	8	papilloma	papilloma	NOUN
ejpam-6082	747	9	virus	virus	NOUN
ejpam-6082	747	10	infection	infection	NOUN
ejpam-6082	747	11	for	for	ADP
ejpam-6082	747	12	public	public	ADJ
ejpam-6082	747	13	health	health	NOUN
ejpam-6082	747	14	.	.	PUNCT
ejpam-6082	748	1	scientific	scientific	ADJ
ejpam-6082	748	2	reports	report	NOUN
ejpam-6082	748	3	,	,	PUNCT
ejpam-6082	748	4	14(1):3048	14(1):3048	NUM
ejpam-6082	748	5	,	,	PUNCT
ejpam-6082	748	6	2024	2024	NUM
ejpam-6082	748	7	.	.	PUNCT
ejpam-6082	749	1	[	[	X
ejpam-6082	749	2	31	31	NUM
ejpam-6082	749	3	]	]	X
ejpam-6082	749	4	rashid	rashid	PROPN
ejpam-6082	749	5	jan	jan	PROPN
ejpam-6082	749	6	,	,	PUNCT
ejpam-6082	749	7	mona	mona	PROPN
ejpam-6082	749	8	alsulami	alsulami	PROPN
ejpam-6082	749	9	,	,	PUNCT
ejpam-6082	749	10	and	and	CCONJ
ejpam-6082	749	11	n.	n.	PROPN
ejpam-6082	749	12	n.	n.	PROPN
ejpam-6082	749	13	a.	a.	PROPN
ejpam-6082	749	14	razak	razak	PROPN
ejpam-6082	749	15	.	.	PUNCT
ejpam-6082	750	1	modeling	model	VERB
ejpam-6082	750	2	the	the	DET
ejpam-6082	750	3	response	response	NOUN
ejpam-6082	750	4	of	of	ADP
ejpam-6082	750	5	the	the	DET
ejpam-6082	750	6	immune	immune	ADJ
ejpam-6082	750	7	system	system	NOUN
ejpam-6082	750	8	to	to	ADP
ejpam-6082	750	9	hiv	hiv	PROPN
ejpam-6082	750	10	-	-	PUNCT
ejpam-6082	750	11	tumor	tumor	NOUN
ejpam-6082	750	12	interaction	interaction	NOUN
ejpam-6082	750	13	via	via	ADP
ejpam-6082	750	14	a	a	DET
ejpam-6082	750	15	fractional	fractional	ADJ
ejpam-6082	750	16	framework	framework	NOUN
ejpam-6082	750	17	.	.	PUNCT
ejpam-6082	751	1	european	european	ADJ
ejpam-6082	751	2	journal	journal	PROPN
ejpam-6082	751	3	of	of	ADP
ejpam-6082	751	4	pure	pure	ADJ
ejpam-6082	751	5	and	and	CCONJ
ejpam-6082	751	6	applied	applied	ADJ
ejpam-6082	751	7	mathematics	mathematic	NOUN
ejpam-6082	751	8	,	,	PUNCT
ejpam-6082	751	9	18(1):5670	18(1):5670	NUM
ejpam-6082	751	10	,	,	PUNCT
ejpam-6082	751	11	2025	2025	NUM
ejpam-6082	751	12	.	.	PUNCT
ejpam-6082	752	1	[	[	X
ejpam-6082	752	2	32	32	NUM
ejpam-6082	752	3	]	]	X
ejpam-6082	752	4	rashid	rashid	PROPN
ejpam-6082	752	5	jan	jan	PROPN
ejpam-6082	752	6	,	,	PUNCT
ejpam-6082	752	7	s.	s.	PROPN
ejpam-6082	752	8	boulaaras	boulaaras	PROPN
ejpam-6082	752	9	,	,	PUNCT
ejpam-6082	752	10	a.	a.	NOUN
ejpam-6082	752	11	alharbi	alharbi	PROPN
ejpam-6082	752	12	,	,	PUNCT
ejpam-6082	752	13	and	and	CCONJ
ejpam-6082	752	14	n.	n.	PROPN
ejpam-6082	752	15	n.	n.	PROPN
ejpam-6082	752	16	a.	a.	PROPN
ejpam-6082	752	17	razak	razak	PROPN
ejpam-6082	752	18	.	.	PUNCT
ejpam-6082	753	1	nonlinear	nonlinear	ADJ
ejpam-6082	753	2	dynamics	dynamic	NOUN
ejpam-6082	753	3	of	of	ADP
ejpam-6082	753	4	a	a	DET
ejpam-6082	753	5	zoonotic	zoonotic	ADJ
ejpam-6082	753	6	disease	disease	NOUN
ejpam-6082	753	7	with	with	ADP
ejpam-6082	753	8	control	control	NOUN
ejpam-6082	753	9	interventions	intervention	NOUN
ejpam-6082	753	10	through	through	ADP
ejpam-6082	753	11	fractional	fractional	ADJ
ejpam-6082	753	12	derivative	derivative	NOUN
ejpam-6082	753	13	.	.	PUNCT
ejpam-6082	754	1	european	european	PROPN
ejpam-6082	754	2	journal	journal	PROPN
ejpam-6082	754	3	of	of	ADP
ejpam-6082	754	4	pure	pure	ADJ
ejpam-6082	754	5	and	and	CCONJ
ejpam-6082	754	6	applied	applied	ADJ
ejpam-6082	754	7	mathematics	mathematic	NOUN
ejpam-6082	754	8	,	,	PUNCT
ejpam-6082	754	9	17(4):3781–3800	17(4):3781–3800	NUM
ejpam-6082	754	10	,	,	PUNCT
ejpam-6082	754	11	2024	2024	NUM
ejpam-6082	754	12	.	.	PUNCT
ejpam-6082	755	1	[	[	X
ejpam-6082	755	2	33	33	NUM
ejpam-6082	755	3	]	]	PUNCT
ejpam-6082	755	4	i.	i.	PROPN
ejpam-6082	755	5	ahmad	ahmad	PROPN
ejpam-6082	755	6	,	,	PUNCT
ejpam-6082	755	7	rashid	rashid	PROPN
ejpam-6082	755	8	jan	jan	PROPN
ejpam-6082	755	9	,	,	PUNCT
ejpam-6082	755	10	n.	n.	PROPN
ejpam-6082	755	11	n.	n.	PROPN
ejpam-6082	755	12	a.	a.	PROPN
ejpam-6082	755	13	razak	razak	PROPN
ejpam-6082	755	14	,	,	PUNCT
ejpam-6082	755	15	a.	a.	PROPN
ejpam-6082	755	16	khan	khan	PROPN
ejpam-6082	755	17	,	,	PUNCT
ejpam-6082	755	18	and	and	CCONJ
ejpam-6082	755	19	t.	t.	PROPN
ejpam-6082	755	20	abdeljawad	abdeljawad	PROPN
ejpam-6082	755	21	.	.	PUNCT
ejpam-6082	756	1	numerical	numerical	PROPN
ejpam-6082	756	2	investigation	investigation	NOUN
ejpam-6082	756	3	of	of	ADP
ejpam-6082	756	4	the	the	DET
ejpam-6082	756	5	dynamical	dynamical	ADJ
ejpam-6082	756	6	behavior	behavior	NOUN
ejpam-6082	756	7	of	of	ADP
ejpam-6082	756	8	hepatitis	hepatitis	PROPN
ejpam-6082	756	9	b	b	PROPN
ejpam-6082	756	10	virus	virus	NOUN
ejpam-6082	756	11	via	via	ADP
ejpam-6082	756	12	caputo	caputo	PROPN
ejpam-6082	756	13	-	-	PUNCT
ejpam-6082	756	14	fabrizio	fabrizio	PROPN
ejpam-6082	756	15	fractional	fractional	PROPN
ejpam-6082	756	16	derivative	derivative	NOUN
ejpam-6082	756	17	.	.	PUNCT
ejpam-6082	757	1	european	european	PROPN
ejpam-6082	757	2	journal	journal	PROPN
ejpam-6082	757	3	of	of	ADP
ejpam-6082	757	4	pure	pure	ADJ
ejpam-6082	757	5	and	and	CCONJ
ejpam-6082	757	6	applied	applied	ADJ
ejpam-6082	757	7	mathematics	mathematic	NOUN
ejpam-6082	757	8	,	,	PUNCT
ejpam-6082	757	9	18(1):5509	18(1):5509	NUM
ejpam-6082	757	10	,	,	PUNCT
ejpam-6082	757	11	2025	2025	NUM
ejpam-6082	757	12	.	.	PUNCT
ejpam-6082	758	1	[	[	X
ejpam-6082	758	2	34	34	NUM
ejpam-6082	758	3	]	]	PUNCT
ejpam-6082	758	4	a.	a.	PROPN
ejpam-6082	758	5	e.	e.	PROPN
ejpam-6082	758	6	matouk	matouk	PROPN
ejpam-6082	758	7	and	and	CCONJ
ejpam-6082	758	8	i.	i.	PROPN
ejpam-6082	758	9	khan	khan	PROPN
ejpam-6082	758	10	.	.	PUNCT
ejpam-6082	759	1	complex	complex	ADJ
ejpam-6082	759	2	dynamics	dynamic	NOUN
ejpam-6082	759	3	and	and	CCONJ
ejpam-6082	759	4	control	control	NOUN
ejpam-6082	759	5	of	of	ADP
ejpam-6082	759	6	a	a	DET
ejpam-6082	759	7	novel	novel	ADJ
ejpam-6082	759	8	physical	physical	ADJ
ejpam-6082	759	9	model	model	NOUN
ejpam-6082	759	10	using	use	VERB
ejpam-6082	759	11	nonlocal	nonlocal	ADJ
ejpam-6082	759	12	fractional	fractional	ADJ
ejpam-6082	759	13	differential	differential	NOUN
ejpam-6082	759	14	operator	operator	NOUN
ejpam-6082	759	15	with	with	ADP
ejpam-6082	759	16	singular	singular	ADJ
ejpam-6082	759	17	kernel	kernel	PROPN
ejpam-6082	759	18	.	.	PUNCT
ejpam-6082	760	1	journal	journal	PROPN
ejpam-6082	760	2	of	of	ADP
ejpam-6082	760	3	advanced	advanced	ADJ
ejpam-6082	760	4	research	research	NOUN
ejpam-6082	760	5	,	,	PUNCT
ejpam-6082	760	6	24:463–474	24:463–474	PROPN
ejpam-6082	760	7	,	,	PUNCT
ejpam-6082	760	8	2020	2020	NUM
ejpam-6082	760	9	.	.	PUNCT
ejpam-6082	761	1	[	[	X
ejpam-6082	761	2	35	35	NUM
ejpam-6082	761	3	]	]	PUNCT
ejpam-6082	761	4	a.	a.	PROPN
ejpam-6082	761	5	al	al	PROPN
ejpam-6082	761	6	-	-	PUNCT
ejpam-6082	761	7	khedhairi	khedhairi	PROPN
ejpam-6082	761	8	,	,	PUNCT
ejpam-6082	761	9	a.	a.	PROPN
ejpam-6082	761	10	e.	e.	PROPN
ejpam-6082	761	11	matouk	matouk	PROPN
ejpam-6082	761	12	,	,	PUNCT
ejpam-6082	761	13	and	and	CCONJ
ejpam-6082	761	14	i.	i.	PROPN
ejpam-6082	761	15	khan	khan	PROPN
ejpam-6082	761	16	.	.	PUNCT
ejpam-6082	762	1	chaotic	chaotic	ADJ
ejpam-6082	762	2	dynamics	dynamic	NOUN
ejpam-6082	762	3	and	and	CCONJ
ejpam-6082	762	4	chaos	chaos	NOUN
ejpam-6082	762	5	control	control	NOUN
ejpam-6082	762	6	for	for	ADP
ejpam-6082	762	7	the	the	DET
ejpam-6082	762	8	fractional	fractional	ADJ
ejpam-6082	762	9	-	-	PUNCT
ejpam-6082	762	10	order	order	NOUN
ejpam-6082	762	11	geomagnetic	geomagnetic	ADJ
ejpam-6082	762	12	field	field	NOUN
ejpam-6082	762	13	model	model	NOUN
ejpam-6082	762	14	.	.	PUNCT
ejpam-6082	763	1	chaos	chaos	NOUN
ejpam-6082	763	2	,	,	PUNCT
ejpam-6082	763	3	solitons	soliton	NOUN
ejpam-6082	763	4	&	&	CCONJ
ejpam-6082	763	5	fractals	fractal	NOUN
ejpam-6082	763	6	,	,	PUNCT
ejpam-6082	763	7	128:390	128:390	NOUN
ejpam-6082	763	8	–	–	PUNCT
ejpam-6082	763	9	401	401	NUM
ejpam-6082	763	10	,	,	PUNCT
ejpam-6082	763	11	2019	2019	NUM
ejpam-6082	763	12	.	.	PUNCT
ejpam-6082	764	1	[	[	X
ejpam-6082	764	2	36	36	NUM
ejpam-6082	764	3	]	]	X
ejpam-6082	764	4	r.	r.	PROPN
ejpam-6082	764	5	p.	p.	PROPN
ejpam-6082	764	6	agarwal	agarwal	PROPN
ejpam-6082	764	7	,	,	PUNCT
ejpam-6082	764	8	d.	d.	PROPN
ejpam-6082	764	9	baleanu	baleanu	PROPN
ejpam-6082	764	10	,	,	PUNCT
ejpam-6082	764	11	j.	j.	PROPN
ejpam-6082	764	12	j.	j.	PROPN
ejpam-6082	764	13	nieto	nieto	PROPN
ejpam-6082	764	14	,	,	PUNCT
ejpam-6082	764	15	d.	d.	PROPN
ejpam-6082	764	16	f.	f.	PROPN
ejpam-6082	764	17	m.	m.	PROPN
ejpam-6082	764	18	torres	torres	PROPN
ejpam-6082	764	19	,	,	PUNCT
ejpam-6082	764	20	and	and	CCONJ
ejpam-6082	764	21	y.	y.	PROPN
ejpam-6082	764	22	zhou	zhou	PROPN
ejpam-6082	764	23	.	.	PUNCT
ejpam-6082	765	1	a	a	DET
ejpam-6082	765	2	survey	survey	NOUN
ejpam-6082	765	3	on	on	ADP
ejpam-6082	765	4	fuzzy	fuzzy	ADJ
ejpam-6082	765	5	fractional	fractional	ADJ
ejpam-6082	765	6	differential	differential	NOUN
ejpam-6082	765	7	,	,	PUNCT
ejpam-6082	765	8	and	and	CCONJ
ejpam-6082	765	9	optimal	optimal	ADJ
ejpam-6082	765	10	control	control	NOUN
ejpam-6082	765	11	nonlocal	nonlocal	ADJ
ejpam-6082	765	12	evolution	evolution	NOUN
ejpam-6082	765	13	equations	equation	NOUN
ejpam-6082	765	14	.	.	PUNCT
ejpam-6082	766	1	journal	journal	NOUN
ejpam-6082	766	2	of	of	ADP
ejpam-6082	766	3	computational	computational	ADJ
ejpam-6082	766	4	and	and	CCONJ
ejpam-6082	766	5	applied	applied	ADJ
ejpam-6082	766	6	mathematics	mathematic	NOUN
ejpam-6082	766	7	,	,	PUNCT
ejpam-6082	766	8	339:3–29	339:3–29	NUM
ejpam-6082	766	9	,	,	PUNCT
ejpam-6082	766	10	2018	2018	NUM
ejpam-6082	766	11	.	.	PUNCT
ejpam-6082	767	1	[	[	X
ejpam-6082	767	2	37	37	NUM
ejpam-6082	767	3	]	]	PUNCT
ejpam-6082	767	4	a.	a.	PROPN
ejpam-6082	767	5	e.	e.	PROPN
ejpam-6082	767	6	matouk	matouk	PROPN
ejpam-6082	767	7	and	and	CCONJ
ejpam-6082	767	8	b.	b.	PROPN
ejpam-6082	767	9	lahcene	lahcene	PROPN
ejpam-6082	767	10	.	.	PUNCT
ejpam-6082	768	1	chaotic	chaotic	ADJ
ejpam-6082	768	2	dynamics	dynamic	NOUN
ejpam-6082	768	3	in	in	ADP
ejpam-6082	768	4	some	some	DET
ejpam-6082	768	5	fractional	fractional	ADJ
ejpam-6082	768	6	predator	predator	NOUN
ejpam-6082	768	7	-	-	PUNCT
ejpam-6082	768	8	prey	prey	NOUN
ejpam-6082	768	9	models	model	NOUN
ejpam-6082	768	10	via	via	ADP
ejpam-6082	768	11	a	a	DET
ejpam-6082	768	12	new	new	ADJ
ejpam-6082	768	13	caputo	caputo	NOUN
ejpam-6082	768	14	operator	operator	NOUN
ejpam-6082	768	15	based	base	VERB
ejpam-6082	768	16	on	on	ADP
ejpam-6082	768	17	the	the	DET
ejpam-6082	768	18	generalised	generalise	VERB
ejpam-6082	768	19	gamma	gamma	NOUN
ejpam-6082	768	20	function	function	NOUN
ejpam-6082	768	21	.	.	PUNCT
ejpam-6082	769	1	chaos	chaos	NOUN
ejpam-6082	769	2	,	,	PUNCT
ejpam-6082	769	3	solitons	soliton	NOUN
ejpam-6082	769	4	&	&	CCONJ
ejpam-6082	769	5	fractals	fractal	NOUN
ejpam-6082	769	6	,	,	PUNCT
ejpam-6082	769	7	166:112946	166:112946	NUM
ejpam-6082	769	8	,	,	PUNCT
ejpam-6082	769	9	2023	2023	NUM
ejpam-6082	769	10	.	.	PUNCT
ejpam-6082	770	1	[	[	X
ejpam-6082	770	2	38	38	NUM
ejpam-6082	770	3	]	]	PUNCT
ejpam-6082	770	4	r.	r.	PROPN
ejpam-6082	770	5	almeida	almeida	PROPN
ejpam-6082	770	6	,	,	PUNCT
ejpam-6082	770	7	d.	d.	PROPN
ejpam-6082	770	8	tavares	tavares	PROPN
ejpam-6082	770	9	,	,	PUNCT
ejpam-6082	770	10	and	and	CCONJ
ejpam-6082	770	11	d.	d.	PROPN
ejpam-6082	770	12	f.	f.	PROPN
ejpam-6082	770	13	m.	m.	PROPN
ejpam-6082	770	14	torres	torre	VERB
ejpam-6082	770	15	.	.	PUNCT
ejpam-6082	771	1	the	the	DET
ejpam-6082	771	2	variable	variable	ADJ
ejpam-6082	771	3	-	-	PUNCT
ejpam-6082	771	4	order	order	NOUN
ejpam-6082	771	5	fractional	fractional	ADJ
ejpam-6082	771	6	calculus	calculus	NOUN
ejpam-6082	771	7	of	of	ADP
ejpam-6082	771	8	variations	variation	NOUN
ejpam-6082	771	9	.	.	PUNCT
ejpam-6082	772	1	springer	springer	NOUN
ejpam-6082	772	2	,	,	PUNCT
ejpam-6082	772	3	cham	cham	PROPN
ejpam-6082	772	4	,	,	PUNCT
ejpam-6082	772	5	2019	2019	NUM
ejpam-6082	772	6	.	.	PUNCT
ejpam-6082	773	1	[	[	X
ejpam-6082	773	2	39	39	NUM
ejpam-6082	773	3	]	]	PUNCT
ejpam-6082	773	4	l.	l.	PROPN
ejpam-6082	773	5	debnath	debnath	PROPN
ejpam-6082	773	6	.	.	PUNCT
ejpam-6082	774	1	recent	recent	ADJ
ejpam-6082	774	2	applications	application	NOUN
ejpam-6082	774	3	of	of	ADP
ejpam-6082	774	4	fractional	fractional	ADJ
ejpam-6082	774	5	calculus	calculus	NOUN
ejpam-6082	774	6	to	to	ADP
ejpam-6082	774	7	science	science	NOUN
ejpam-6082	774	8	and	and	CCONJ
ejpam-6082	774	9	engineering	engineering	NOUN
ejpam-6082	774	10	.	.	PUNCT
ejpam-6082	775	1	international	international	ADJ
ejpam-6082	775	2	journal	journal	PROPN
ejpam-6082	775	3	of	of	ADP
ejpam-6082	775	4	mathematics	mathematics	PROPN
ejpam-6082	775	5	and	and	CCONJ
ejpam-6082	775	6	mathematical	mathematical	ADJ
ejpam-6082	775	7	sciences	science	NOUN
ejpam-6082	775	8	,	,	PUNCT
ejpam-6082	775	9	2003(54):3413–3442	2003(54):3413–3442	NUM
ejpam-6082	775	10	,	,	PUNCT
ejpam-6082	775	11	2003	2003	NUM
ejpam-6082	775	12	.	.	PUNCT
ejpam-6082	776	1	[	[	X
ejpam-6082	776	2	40	40	NUM
ejpam-6082	776	3	]	]	PUNCT
ejpam-6082	776	4	m.	m.	NOUN
ejpam-6082	776	5	awadalla	awadalla	PROPN
ejpam-6082	776	6	,	,	PUNCT
ejpam-6082	776	7	j.	j.	PROPN
ejpam-6082	776	8	alahmadi	alahmadi	PROPN
ejpam-6082	776	9	,	,	PUNCT
ejpam-6082	776	10	k.	k.	PROPN
ejpam-6082	776	11	r.	r.	PROPN
ejpam-6082	776	12	cheneke	cheneke	PROPN
ejpam-6082	776	13	,	,	PUNCT
ejpam-6082	776	14	and	and	CCONJ
ejpam-6082	776	15	s.	s.	PROPN
ejpam-6082	776	16	qureshi	qureshi	PROPN
ejpam-6082	776	17	.	.	PUNCT
ejpam-6082	777	1	fractional	fractional	ADJ
ejpam-6082	777	2	optimal	optimal	ADJ
ejpam-6082	777	3	control	control	PROPN
ejpam-6082	777	4	k.	k.	PROPN
ejpam-6082	777	5	guedri	guedri	PROPN
ejpam-6082	777	6	et	et	PROPN
ejpam-6082	777	7	al	al	PROPN
ejpam-6082	777	8	.	.	PUNCT
ejpam-6082	777	9	/	/	SYM
ejpam-6082	777	10	eur	eur	PROPN
ejpam-6082	777	11	.	.	PUNCT
ejpam-6082	778	1	j.	j.	PROPN
ejpam-6082	778	2	pure	pure	PROPN
ejpam-6082	778	3	appl	appl	PROPN
ejpam-6082	778	4	.	.	PROPN
ejpam-6082	778	5	math	math	PROPN
ejpam-6082	778	6	,	,	PUNCT
ejpam-6082	778	7	18	18	NUM
ejpam-6082	778	8	(	(	PUNCT
ejpam-6082	778	9	2	2	NUM
ejpam-6082	778	10	)	)	PUNCT
ejpam-6082	778	11	(	(	PUNCT
ejpam-6082	778	12	2025	2025	NUM
ejpam-6082	778	13	)	)	PUNCT
ejpam-6082	778	14	,	,	PUNCT
ejpam-6082	778	15	6082	6082	NUM
ejpam-6082	778	16	39	39	NUM
ejpam-6082	778	17	of	of	ADP
ejpam-6082	778	18	39	39	NUM
ejpam-6082	778	19	model	model	NOUN
ejpam-6082	778	20	and	and	CCONJ
ejpam-6082	778	21	bifurcation	bifurcation	NOUN
ejpam-6082	778	22	analysis	analysis	NOUN
ejpam-6082	778	23	of	of	ADP
ejpam-6082	778	24	human	human	ADJ
ejpam-6082	778	25	syncytial	syncytial	ADJ
ejpam-6082	778	26	respiratory	respiratory	ADJ
ejpam-6082	778	27	virus	virus	NOUN
ejpam-6082	778	28	transmission	transmission	NOUN
ejpam-6082	778	29	dynamics	dynamic	NOUN
ejpam-6082	778	30	.	.	PUNCT
ejpam-6082	779	1	fractal	fractal	ADJ
ejpam-6082	779	2	and	and	CCONJ
ejpam-6082	779	3	fractional	fractional	ADJ
ejpam-6082	779	4	,	,	PUNCT
ejpam-6082	779	5	8(1):44	8(1):44	NUM
ejpam-6082	779	6	,	,	PUNCT
ejpam-6082	779	7	2024	2024	NUM
ejpam-6082	779	8	.	.	PUNCT
ejpam-6082	780	1	[	[	X
ejpam-6082	780	2	41	41	NUM
ejpam-6082	780	3	]	]	PUNCT
ejpam-6082	780	4	k.	k.	PROPN
ejpam-6082	780	5	diethelm	diethelm	PROPN
ejpam-6082	780	6	.	.	PUNCT
ejpam-6082	781	1	a	a	DET
ejpam-6082	781	2	fractional	fractional	ADJ
ejpam-6082	781	3	calculus	calculus	NOUN
ejpam-6082	781	4	based	base	VERB
ejpam-6082	781	5	model	model	NOUN
ejpam-6082	781	6	for	for	ADP
ejpam-6082	781	7	the	the	DET
ejpam-6082	781	8	simulation	simulation	NOUN
ejpam-6082	781	9	of	of	ADP
ejpam-6082	781	10	an	an	DET
ejpam-6082	781	11	outbreak	outbreak	NOUN
ejpam-6082	781	12	of	of	ADP
ejpam-6082	781	13	dengue	dengue	NOUN
ejpam-6082	781	14	fever	fever	NOUN
ejpam-6082	781	15	.	.	PUNCT
ejpam-6082	782	1	nonlinear	nonlinear	ADJ
ejpam-6082	782	2	dynamics	dynamic	NOUN
ejpam-6082	782	3	,	,	PUNCT
ejpam-6082	782	4	71(4):613–619	71(4):613–619	NUM
ejpam-6082	782	5	,	,	PUNCT
ejpam-6082	782	6	2013	2013	NUM
ejpam-6082	782	7	.	.	PUNCT
ejpam-6082	783	1	[	[	X
ejpam-6082	783	2	42	42	NUM
ejpam-6082	783	3	]	]	PUNCT
ejpam-6082	783	4	s.	s.	PROPN
ejpam-6082	783	5	rosa	rosa	PROPN
ejpam-6082	783	6	and	and	CCONJ
ejpam-6082	783	7	d.	d.	PROPN
ejpam-6082	783	8	f.	f.	PROPN
ejpam-6082	783	9	m.	m.	PROPN
ejpam-6082	783	10	torres	torre	VERB
ejpam-6082	783	11	.	.	PUNCT
ejpam-6082	784	1	optimal	optimal	ADJ
ejpam-6082	784	2	control	control	NOUN
ejpam-6082	784	3	of	of	ADP
ejpam-6082	784	4	a	a	DET
ejpam-6082	784	5	fractional	fractional	ADJ
ejpam-6082	784	6	order	order	NOUN
ejpam-6082	784	7	epidemic	epidemic	NOUN
ejpam-6082	784	8	model	model	NOUN
ejpam-6082	784	9	with	with	ADP
ejpam-6082	784	10	application	application	NOUN
ejpam-6082	784	11	to	to	ADP
ejpam-6082	784	12	human	human	ADJ
ejpam-6082	784	13	respiratory	respiratory	ADJ
ejpam-6082	784	14	syncytial	syncytial	ADJ
ejpam-6082	784	15	virus	virus	NOUN
ejpam-6082	784	16	infection	infection	NOUN
ejpam-6082	784	17	.	.	PUNCT
ejpam-6082	785	1	chaos	chaos	NOUN
ejpam-6082	785	2	,	,	PUNCT
ejpam-6082	785	3	solitons	soliton	NOUN
ejpam-6082	785	4	&	&	CCONJ
ejpam-6082	785	5	fractals	fractal	NOUN
ejpam-6082	785	6	,	,	PUNCT
ejpam-6082	785	7	117:142–149	117:142–149	NUM
ejpam-6082	785	8	,	,	PUNCT
ejpam-6082	785	9	2018	2018	NUM
ejpam-6082	785	10	.	.	PUNCT
ejpam-6082	786	1	[	[	X
ejpam-6082	786	2	43	43	NUM
ejpam-6082	786	3	]	]	X
ejpam-6082	786	4	a.	a.	PROPN
ejpam-6082	786	5	b.	b.	PROPN
ejpam-6082	786	6	salati	salati	PROPN
ejpam-6082	786	7	and	and	CCONJ
ejpam-6082	786	8	m.	m.	NOUN
ejpam-6082	786	9	shamsi	shamsi	PROPN
ejpam-6082	786	10	.	.	PUNCT
ejpam-6082	787	1	direct	direct	ADJ
ejpam-6082	787	2	transcription	transcription	NOUN
ejpam-6082	787	3	methods	method	NOUN
ejpam-6082	787	4	based	base	VERB
ejpam-6082	787	5	on	on	ADP
ejpam-6082	787	6	fractional	fractional	ADJ
ejpam-6082	787	7	integral	integral	ADJ
ejpam-6082	787	8	approximation	approximation	NOUN
ejpam-6082	787	9	formulas	formula	NOUN
ejpam-6082	787	10	for	for	ADP
ejpam-6082	787	11	solving	solve	VERB
ejpam-6082	787	12	nonlinear	nonlinear	ADJ
ejpam-6082	787	13	fractional	fractional	ADJ
ejpam-6082	787	14	optimal	optimal	ADJ
ejpam-6082	787	15	control	control	NOUN
ejpam-6082	787	16	problems	problem	NOUN
ejpam-6082	787	17	.	.	PUNCT
ejpam-6082	788	1	communications	communication	NOUN
ejpam-6082	788	2	in	in	ADP
ejpam-6082	788	3	nonlinear	nonlinear	ADJ
ejpam-6082	788	4	science	science	NOUN
ejpam-6082	788	5	and	and	CCONJ
ejpam-6082	788	6	numerical	numerical	PROPN
ejpam-6082	788	7	simulation	simulation	PROPN
ejpam-6082	788	8	,	,	PUNCT
ejpam-6082	788	9	67:334–350	67:334–350	PROPN
ejpam-6082	788	10	,	,	PUNCT
ejpam-6082	788	11	2019	2019	NUM
ejpam-6082	788	12	.	.	PUNCT
ejpam-6082	789	1	[	[	X
ejpam-6082	789	2	44	44	NUM
ejpam-6082	789	3	]	]	PUNCT
ejpam-6082	789	4	s.	s.	PROPN
ejpam-6082	789	5	qureshi	qureshi	PROPN
ejpam-6082	789	6	and	and	CCONJ
ejpam-6082	789	7	a.	a.	PROPN
ejpam-6082	789	8	yusuf	yusuf	PROPN
ejpam-6082	789	9	.	.	PUNCT
ejpam-6082	790	1	fractional	fractional	ADJ
ejpam-6082	790	2	derivatives	derivative	NOUN
ejpam-6082	790	3	applied	apply	VERB
ejpam-6082	790	4	to	to	ADP
ejpam-6082	790	5	mseir	mseir	NOUN
ejpam-6082	790	6	problems	problem	NOUN
ejpam-6082	790	7	:	:	PUNCT
ejpam-6082	790	8	comparative	comparative	ADJ
ejpam-6082	790	9	study	study	NOUN
ejpam-6082	790	10	with	with	ADP
ejpam-6082	790	11	real	real	ADJ
ejpam-6082	790	12	world	world	NOUN
ejpam-6082	790	13	data	datum	NOUN
ejpam-6082	790	14	.	.	PUNCT
ejpam-6082	791	1	the	the	DET
ejpam-6082	791	2	european	european	PROPN
ejpam-6082	791	3	physical	physical	PROPN
ejpam-6082	791	4	journal	journal	PROPN
ejpam-6082	791	5	plus	plus	CCONJ
ejpam-6082	791	6	,	,	PUNCT
ejpam-6082	791	7	134(4):171	134(4):171	NUM
ejpam-6082	791	8	,	,	PUNCT
ejpam-6082	791	9	2019	2019	NUM
ejpam-6082	791	10	.	.	PUNCT
ejpam-6082	792	1	[	[	X
ejpam-6082	792	2	45	45	NUM
ejpam-6082	792	3	]	]	PUNCT
ejpam-6082	792	4	r.	r.	PROPN
ejpam-6082	792	5	zarin	zarin	PROPN
ejpam-6082	792	6	.	.	PUNCT
ejpam-6082	793	1	artificial	artificial	ADJ
ejpam-6082	793	2	neural	neural	ADJ
ejpam-6082	793	3	network	network	NOUN
ejpam-6082	793	4	-	-	PUNCT
ejpam-6082	793	5	based	base	VERB
ejpam-6082	793	6	approach	approach	NOUN
ejpam-6082	793	7	for	for	ADP
ejpam-6082	793	8	simulating	simulate	VERB
ejpam-6082	793	9	influenza	influenza	ADJ
ejpam-6082	793	10	dynamics	dynamic	NOUN
ejpam-6082	793	11	:	:	PUNCT
ejpam-6082	793	12	a	a	DET
ejpam-6082	793	13	nonlinear	nonlinear	ADJ
ejpam-6082	793	14	sveir	sveir	ADJ
ejpam-6082	793	15	model	model	NOUN
ejpam-6082	793	16	with	with	ADP
ejpam-6082	793	17	spatial	spatial	ADJ
ejpam-6082	793	18	diffusion	diffusion	NOUN
ejpam-6082	793	19	.	.	PUNCT
ejpam-6082	794	1	engineering	engineering	NOUN
ejpam-6082	794	2	analysis	analysis	NOUN
ejpam-6082	794	3	with	with	ADP
ejpam-6082	794	4	boundary	boundary	ADJ
ejpam-6082	794	5	elements	element	NOUN
ejpam-6082	794	6	,	,	PUNCT
ejpam-6082	794	7	176:106230	176:106230	NUM
ejpam-6082	794	8	,	,	PUNCT
ejpam-6082	794	9	2025	2025	NUM
ejpam-6082	794	10	.	.	PUNCT
ejpam-6082	795	1	[	[	X
ejpam-6082	795	2	46	46	NUM
ejpam-6082	795	3	]	]	PUNCT
ejpam-6082	795	4	r.	r.	PROPN
ejpam-6082	795	5	zarin	zarin	PROPN
ejpam-6082	795	6	and	and	CCONJ
ejpam-6082	795	7	u.	u.	PROPN
ejpam-6082	795	8	w.	w.	PROPN
ejpam-6082	795	9	humphries	humphries	PROPN
ejpam-6082	795	10	.	.	PUNCT
ejpam-6082	796	1	analyzing	analyze	VERB
ejpam-6082	796	2	spatial	spatial	ADJ
ejpam-6082	796	3	diffusion	diffusion	NOUN
ejpam-6082	796	4	and	and	CCONJ
ejpam-6082	796	5	vaccination	vaccination	NOUN
ejpam-6082	796	6	strategies	strategy	NOUN
ejpam-6082	796	7	in	in	ADP
ejpam-6082	796	8	malaria	malaria	NOUN
ejpam-6082	796	9	epidemics	epidemic	NOUN
ejpam-6082	796	10	:	:	PUNCT
ejpam-6082	796	11	a	a	DET
ejpam-6082	796	12	numerical	numerical	ADJ
ejpam-6082	796	13	approach	approach	NOUN
ejpam-6082	796	14	.	.	PUNCT
ejpam-6082	797	1	modeling	model	VERB
ejpam-6082	797	2	earth	earth	NOUN
ejpam-6082	797	3	systems	system	NOUN
ejpam-6082	797	4	and	and	CCONJ
ejpam-6082	797	5	environment	environment	NOUN
ejpam-6082	797	6	,	,	PUNCT
ejpam-6082	797	7	11(3):1587–1605	11(3):1587–1605	NUM
ejpam-6082	797	8	,	,	PUNCT
ejpam-6082	797	9	2025	2025	NUM
ejpam-6082	797	10	.	.	PUNCT
ejpam-6082	798	1	[	[	X
ejpam-6082	798	2	47	47	NUM
ejpam-6082	798	3	]	]	PUNCT
ejpam-6082	798	4	k.	k.	PROPN
ejpam-6082	798	5	guedri	guedri	PROPN
ejpam-6082	798	6	,	,	PUNCT
ejpam-6082	798	7	r.	r.	PROPN
ejpam-6082	798	8	zarin	zarin	PROPN
ejpam-6082	798	9	,	,	PUNCT
ejpam-6082	798	10	a.	a.	PROPN
ejpam-6082	798	11	khan	khan	PROPN
ejpam-6082	798	12	,	,	PUNCT
ejpam-6082	798	13	a.	a.	PROPN
ejpam-6082	798	14	khan	khan	PROPN
ejpam-6082	798	15	,	,	PUNCT
ejpam-6082	798	16	b.	b.	PROPN
ejpam-6082	798	17	m.	m.	PROPN
ejpam-6082	798	18	makhdoum	makhdoum	PROPN
ejpam-6082	798	19	,	,	PUNCT
ejpam-6082	798	20	and	and	CCONJ
ejpam-6082	798	21	h.	h.	PROPN
ejpam-6082	798	22	a.	a.	PROPN
ejpam-6082	798	23	niyazi	niyazi	PROPN
ejpam-6082	798	24	.	.	PUNCT
ejpam-6082	799	1	modeling	model	VERB
ejpam-6082	799	2	hepatitis	hepatitis	PROPN
ejpam-6082	799	3	b	b	NOUN
ejpam-6082	799	4	transmission	transmission	NOUN
ejpam-6082	799	5	dynamics	dynamic	NOUN
ejpam-6082	799	6	with	with	ADP
ejpam-6082	799	7	spatial	spatial	ADJ
ejpam-6082	799	8	diffusion	diffusion	NOUN
ejpam-6082	799	9	and	and	CCONJ
ejpam-6082	799	10	disability	disability	NOUN
ejpam-6082	799	11	potential	potential	NOUN
ejpam-6082	799	12	in	in	ADP
ejpam-6082	799	13	the	the	DET
ejpam-6082	799	14	chronic	chronic	ADJ
ejpam-6082	799	15	stage	stage	NOUN
ejpam-6082	799	16	.	.	PUNCT
ejpam-6082	800	1	aims	aim	VERB
ejpam-6082	800	2	mathematics	mathematic	NOUN
ejpam-6082	800	3	,	,	PUNCT
ejpam-6082	800	4	10(1):1322–1349	10(1):1322–1349	NUM
ejpam-6082	800	5	,	,	PUNCT
ejpam-6082	800	6	2025	2025	NUM
ejpam-6082	800	7	.	.	PUNCT
ejpam-6082	801	1	[	[	X
ejpam-6082	801	2	48	48	NUM
ejpam-6082	801	3	]	]	PUNCT
ejpam-6082	801	4	k.	k.	PROPN
ejpam-6082	801	5	guedri	guedri	PROPN
ejpam-6082	801	6	,	,	PUNCT
ejpam-6082	801	7	r.	r.	PROPN
ejpam-6082	801	8	zarin	zarin	PROPN
ejpam-6082	801	9	,	,	PUNCT
ejpam-6082	801	10	a.	a.	PROPN
ejpam-6082	801	11	zeb	zeb	PROPN
ejpam-6082	801	12	,	,	PUNCT
ejpam-6082	801	13	b.	b.	PROPN
ejpam-6082	801	14	m.	m.	PROPN
ejpam-6082	801	15	makhdoum	makhdoum	PROPN
ejpam-6082	801	16	,	,	PUNCT
ejpam-6082	801	17	h.	h.	PROPN
ejpam-6082	801	18	a.	a.	PROPN
ejpam-6082	801	19	niyazi	niyazi	PROPN
ejpam-6082	801	20	,	,	PUNCT
ejpam-6082	801	21	and	and	CCONJ
ejpam-6082	801	22	a.	a.	PROPN
ejpam-6082	801	23	khan	khan	PROPN
ejpam-6082	801	24	.	.	PUNCT
ejpam-6082	802	1	a	a	DET
ejpam-6082	802	2	numerical	numerical	ADJ
ejpam-6082	802	3	study	study	NOUN
ejpam-6082	802	4	of	of	ADP
ejpam-6082	802	5	hiv	hiv	PROPN
ejpam-6082	802	6	/	/	SYM
ejpam-6082	802	7	aids	aids	PROPN
ejpam-6082	802	8	transmission	transmission	NOUN
ejpam-6082	802	9	dynamics	dynamic	NOUN
ejpam-6082	802	10	and	and	CCONJ
ejpam-6082	802	11	the	the	DET
ejpam-6082	802	12	onset	onset	NOUN
ejpam-6082	802	13	of	of	ADP
ejpam-6082	802	14	long	long	ADJ
ejpam-6082	802	15	-	-	PUNCT
ejpam-6082	802	16	term	term	NOUN
ejpam-6082	802	17	disability	disability	NOUN
ejpam-6082	802	18	in	in	ADP
ejpam-6082	802	19	chronic	chronic	ADJ
ejpam-6082	802	20	infection	infection	NOUN
ejpam-6082	802	21	.	.	PUNCT
ejpam-6082	803	1	the	the	DET
ejpam-6082	803	2	european	european	PROPN
ejpam-6082	803	3	physical	physical	PROPN
ejpam-6082	803	4	journal	journal	PROPN
ejpam-6082	803	5	plus	plus	CCONJ
ejpam-6082	803	6	,	,	PUNCT
ejpam-6082	803	7	139(12):1089	139(12):1089	NUM
ejpam-6082	803	8	,	,	PUNCT
ejpam-6082	803	9	2024	2024	NUM
ejpam-6082	803	10	.	.	PUNCT
ejpam-6082	804	1	[	[	X
ejpam-6082	804	2	49	49	NUM
ejpam-6082	804	3	]	]	X
ejpam-6082	804	4	kai	kai	PROPN
ejpam-6082	804	5	diethelm	diethelm	PROPN
ejpam-6082	804	6	.	.	PUNCT
ejpam-6082	805	1	the	the	DET
ejpam-6082	805	2	analysis	analysis	NOUN
ejpam-6082	805	3	of	of	ADP
ejpam-6082	805	4	fractional	fractional	ADJ
ejpam-6082	805	5	differential	differential	ADJ
ejpam-6082	805	6	equations	equation	NOUN
ejpam-6082	805	7	:	:	PUNCT
ejpam-6082	805	8	an	an	DET
ejpam-6082	805	9	applicationoriented	applicationoriente	VERB
ejpam-6082	805	10	exposition	exposition	NOUN
ejpam-6082	805	11	using	use	VERB
ejpam-6082	805	12	operators	operator	NOUN
ejpam-6082	805	13	of	of	ADP
ejpam-6082	805	14	caputo	caputo	PROPN
ejpam-6082	805	15	type	type	PROPN
ejpam-6082	805	16	.	.	PUNCT
ejpam-6082	806	1	2010	2010	NUM
ejpam-6082	806	2	.	.	PUNCT
ejpam-6082	807	1	[	[	X
ejpam-6082	807	2	50	50	NUM
ejpam-6082	807	3	]	]	PUNCT
ejpam-6082	807	4	s.	s.	PROPN
ejpam-6082	807	5	a.	a.	PROPN
ejpam-6082	807	6	khuri	khuri	PROPN
ejpam-6082	807	7	.	.	PUNCT
ejpam-6082	808	1	a	a	DET
ejpam-6082	808	2	laplace	laplace	NOUN
ejpam-6082	808	3	decomposition	decomposition	NOUN
ejpam-6082	808	4	algorithm	algorithm	NOUN
ejpam-6082	808	5	applied	apply	VERB
ejpam-6082	808	6	to	to	ADP
ejpam-6082	808	7	a	a	DET
ejpam-6082	808	8	class	class	NOUN
ejpam-6082	808	9	of	of	ADP
ejpam-6082	808	10	nonlinear	nonlinear	ADJ
ejpam-6082	808	11	differential	differential	ADJ
ejpam-6082	808	12	equations	equation	NOUN
ejpam-6082	808	13	.	.	PUNCT
ejpam-6082	809	1	journal	journal	PROPN
ejpam-6082	809	2	of	of	ADP
ejpam-6082	809	3	applied	apply	VERB
ejpam-6082	809	4	mathematics	mathematic	NOUN
ejpam-6082	809	5	,	,	PUNCT
ejpam-6082	809	6	1(4):141–155	1(4):141–155	NUM
ejpam-6082	809	7	,	,	PUNCT
ejpam-6082	809	8	2001	2001	NUM
ejpam-6082	809	9	.	.	PUNCT
ejpam-6082	810	1	[	[	X
ejpam-6082	810	2	51	51	NUM
ejpam-6082	810	3	]	]	SYM
ejpam-6082	810	4	roland	roland	PROPN
ejpam-6082	810	5	duduchava	duduchava	NOUN
ejpam-6082	810	6	.	.	PUNCT
ejpam-6082	811	1	the	the	DET
ejpam-6082	811	2	green	green	ADJ
ejpam-6082	811	3	formula	formula	NOUN
ejpam-6082	811	4	and	and	CCONJ
ejpam-6082	811	5	layer	layer	NOUN
ejpam-6082	811	6	potentials	potential	NOUN
ejpam-6082	811	7	.	.	PUNCT
ejpam-6082	812	1	integral	integral	ADJ
ejpam-6082	812	2	equations	equation	NOUN
ejpam-6082	812	3	and	and	CCONJ
ejpam-6082	812	4	operator	operator	NOUN
ejpam-6082	812	5	theory	theory	NOUN
ejpam-6082	812	6	,	,	PUNCT
ejpam-6082	812	7	41(2):127–178	41(2):127–178	PROPN
ejpam-6082	812	8	,	,	PUNCT
ejpam-6082	812	9	2001	2001	NUM
ejpam-6082	812	10	.	.	PUNCT
ejpam-6082	813	1	[	[	X
ejpam-6082	813	2	52	52	NUM
ejpam-6082	813	3	]	]	PUNCT
ejpam-6082	813	4	m.	m.	NOUN
ejpam-6082	813	5	m.	m.	PROPN
ejpam-6082	813	6	el	el	PROPN
ejpam-6082	813	7	-	-	PUNCT
ejpam-6082	813	8	borai	borai	NOUN
ejpam-6082	813	9	.	.	PUNCT
ejpam-6082	814	1	some	some	DET
ejpam-6082	814	2	probability	probability	NOUN
ejpam-6082	814	3	density	density	NOUN
ejpam-6082	814	4	and	and	CCONJ
ejpam-6082	814	5	fundamental	fundamental	ADJ
ejpam-6082	814	6	solutions	solution	NOUN
ejpam-6082	814	7	of	of	ADP
ejpam-6082	814	8	fractional	fractional	ADJ
ejpam-6082	814	9	evolution	evolution	NOUN
ejpam-6082	814	10	equations	equation	NOUN
ejpam-6082	814	11	.	.	PUNCT
ejpam-6082	815	1	chaos	chaos	NOUN
ejpam-6082	815	2	,	,	PUNCT
ejpam-6082	815	3	solitons	soliton	NOUN
ejpam-6082	815	4	&	&	CCONJ
ejpam-6082	815	5	fractals	fractal	NOUN
ejpam-6082	815	6	,	,	PUNCT
ejpam-6082	815	7	14(3):433–440	14(3):433–440	NUM
ejpam-6082	815	8	,	,	PUNCT
ejpam-6082	815	9	2002	2002	NUM
ejpam-6082	815	10	.	.	PUNCT
ejpam-6082	816	1	[	[	X
ejpam-6082	816	2	53	53	NUM
ejpam-6082	816	3	]	]	PUNCT
ejpam-6082	816	4	zhisheng	zhisheng	PROPN
ejpam-6082	816	5	shuai	shuai	PROPN
ejpam-6082	816	6	and	and	CCONJ
ejpam-6082	816	7	p.	p.	PROPN
ejpam-6082	816	8	van	van	PROPN
ejpam-6082	816	9	den	den	PROPN
ejpam-6082	816	10	driessche	driessche	PROPN
ejpam-6082	816	11	.	.	PUNCT
ejpam-6082	817	1	global	global	ADJ
ejpam-6082	817	2	stability	stability	NOUN
ejpam-6082	817	3	of	of	ADP
ejpam-6082	817	4	infectious	infectious	ADJ
ejpam-6082	817	5	disease	disease	NOUN
ejpam-6082	817	6	models	model	NOUN
ejpam-6082	817	7	using	use	VERB
ejpam-6082	817	8	lyapunov	lyapunov	ADJ
ejpam-6082	817	9	functions	function	NOUN
ejpam-6082	817	10	.	.	PUNCT
ejpam-6082	818	1	siam	siam	PROPN
ejpam-6082	818	2	journal	journal	PROPN
ejpam-6082	818	3	on	on	ADP
ejpam-6082	818	4	applied	apply	VERB
ejpam-6082	818	5	mathematics	mathematic	NOUN
ejpam-6082	818	6	,	,	PUNCT
ejpam-6082	818	7	73(4):1513–1532	73(4):1513–1532	NUM
ejpam-6082	818	8	,	,	PUNCT
ejpam-6082	818	9	2013	2013	NUM
ejpam-6082	818	10	.	.	PUNCT