id	sid	tid	token	lemma	pos
ejpam-6682	1	1	european	european	PROPN
ejpam-6682	1	2	journal	journal	PROPN
ejpam-6682	1	3	of	of	ADP
ejpam-6682	1	4	pure	pure	ADJ
ejpam-6682	1	5	and	and	CCONJ
ejpam-6682	1	6	applied	applied	ADJ
ejpam-6682	1	7	mathematics	mathematic	NOUN
ejpam-6682	1	8	2025	2025	NUM
ejpam-6682	1	9	,	,	PUNCT
ejpam-6682	1	10	vol	vol	NOUN
ejpam-6682	1	11	.	.	PROPN
ejpam-6682	1	12	18	18	NUM
ejpam-6682	1	13	,	,	PUNCT
ejpam-6682	1	14	issue	issue	NOUN
ejpam-6682	1	15	4	4	NUM
ejpam-6682	1	16	,	,	PUNCT
ejpam-6682	1	17	article	article	NOUN
ejpam-6682	1	18	number	number	NOUN
ejpam-6682	1	19	6682	6682	NUM
ejpam-6682	1	20	issn	issn	VERB
ejpam-6682	1	21	1307	1307	NUM
ejpam-6682	1	22	-	-	SYM
ejpam-6682	1	23	5543	5543	NUM
ejpam-6682	1	24	–	–	PUNCT
ejpam-6682	1	25	ejpam.com	ejpam.com	X
ejpam-6682	1	26	published	publish	VERB
ejpam-6682	1	27	by	by	ADP
ejpam-6682	1	28	new	new	PROPN
ejpam-6682	1	29	york	york	PROPN
ejpam-6682	1	30	business	business	PROPN
ejpam-6682	1	31	global	global	PROPN
ejpam-6682	1	32	modeling	modeling	NOUN
ejpam-6682	1	33	dengue	dengue	NOUN
ejpam-6682	1	34	dynamics	dynamic	NOUN
ejpam-6682	1	35	using	use	VERB
ejpam-6682	1	36	classical	classical	NOUN
ejpam-6682	1	37	,	,	PUNCT
ejpam-6682	1	38	caputo	caputo	PROPN
ejpam-6682	1	39	fractional	fractional	NOUN
ejpam-6682	1	40	,	,	PUNCT
ejpam-6682	1	41	and	and	CCONJ
ejpam-6682	1	42	fractal	fractal	ADJ
ejpam-6682	1	43	derivatives	derivative	NOUN
ejpam-6682	1	44	rania	rania	PROPN
ejpam-6682	1	45	saadeh1,∗	saadeh1,∗	PROPN
ejpam-6682	1	46	,	,	PUNCT
ejpam-6682	1	47	naseam	naseam	PROPN
ejpam-6682	1	48	al	al	PROPN
ejpam-6682	1	49	-	-	PUNCT
ejpam-6682	1	50	kuleab2	kuleab2	PROPN
ejpam-6682	1	51	,	,	PUNCT
ejpam-6682	1	52	maha	maha	PROPN
ejpam-6682	1	53	s.	s.	PROPN
ejpam-6682	1	54	al	al	PROPN
ejpam-6682	1	55	soudi3	soudi3	PROPN
ejpam-6682	1	56	,	,	PUNCT
ejpam-6682	1	57	khadeeja	khadeeja	PROPN
ejpam-6682	1	58	a.	a.	PROPN
ejpam-6682	1	59	a.	a.	PROPN
ejpam-6682	1	60	helal4	helal4	PROPN
ejpam-6682	1	61	,	,	PUNCT
ejpam-6682	1	62	aymen	aymen	PROPN
ejpam-6682	1	63	imam4	imam4	PROPN
ejpam-6682	1	64	,	,	PUNCT
ejpam-6682	1	65	ibrahim	ibrahim	PROPN
ejpam-6682	1	66	elshamy4,5	elshamy4,5	PROPN
ejpam-6682	1	67	,	,	PUNCT
ejpam-6682	1	68	suliman	suliman	NOUN
ejpam-6682	1	69	jamiel	jamiel	PROPN
ejpam-6682	1	70	m.	m.	PROPN
ejpam-6682	1	71	abdalla6	abdalla6	PROPN
ejpam-6682	2	1	1	1	NUM
ejpam-6682	2	2	department	department	NOUN
ejpam-6682	2	3	of	of	ADP
ejpam-6682	2	4	applied	apply	VERB
ejpam-6682	2	5	science	science	NOUN
ejpam-6682	2	6	,	,	PUNCT
ejpam-6682	2	7	ajloun	ajloun	PROPN
ejpam-6682	2	8	college	college	PROPN
ejpam-6682	2	9	,	,	PUNCT
ejpam-6682	2	10	al	al	PROPN
ejpam-6682	2	11	-	-	PUNCT
ejpam-6682	2	12	balqa	balqa	NOUN
ejpam-6682	2	13	applied	apply	VERB
ejpam-6682	2	14	university	university	NOUN
ejpam-6682	2	15	,	,	PUNCT
ejpam-6682	2	16	ajloun	ajloun	PROPN
ejpam-6682	2	17	,	,	PUNCT
ejpam-6682	2	18	jordan	jordan	PROPN
ejpam-6682	2	19	2	2	NUM
ejpam-6682	2	20	department	department	NOUN
ejpam-6682	2	21	of	of	ADP
ejpam-6682	2	22	mathematics	mathematic	NOUN
ejpam-6682	2	23	and	and	CCONJ
ejpam-6682	2	24	statistics	statistic	NOUN
ejpam-6682	2	25	,	,	PUNCT
ejpam-6682	2	26	college	college	NOUN
ejpam-6682	2	27	of	of	ADP
ejpam-6682	2	28	science	science	NOUN
ejpam-6682	2	29	,	,	PUNCT
ejpam-6682	2	30	king	king	NOUN
ejpam-6682	2	31	faisal	faisal	PROPN
ejpam-6682	2	32	university	university	PROPN
ejpam-6682	2	33	,	,	PUNCT
ejpam-6682	2	34	al	al	PROPN
ejpam-6682	2	35	-	-	PUNCT
ejpam-6682	2	36	ahsa	ahsa	NOUN
ejpam-6682	2	37	31982	31982	NUM
ejpam-6682	2	38	,	,	PUNCT
ejpam-6682	2	39	saudi	saudi	PROPN
ejpam-6682	2	40	arabia	arabia	PROPN
ejpam-6682	2	41	3	3	NUM
ejpam-6682	2	42	department	department	NOUN
ejpam-6682	2	43	of	of	ADP
ejpam-6682	2	44	basic	basic	ADJ
ejpam-6682	2	45	scientific	scientific	ADJ
ejpam-6682	2	46	sciences	science	NOUN
ejpam-6682	2	47	,	,	PUNCT
ejpam-6682	2	48	applied	apply	VERB
ejpam-6682	2	49	science	science	NOUN
ejpam-6682	2	50	private	private	ADJ
ejpam-6682	2	51	university	university	NOUN
ejpam-6682	2	52	,	,	PUNCT
ejpam-6682	2	53	amman	amman	PROPN
ejpam-6682	2	54	11931	11931	NUM
ejpam-6682	2	55	,	,	PUNCT
ejpam-6682	2	56	jordan	jordan	PROPN
ejpam-6682	2	57	4	4	NUM
ejpam-6682	2	58	department	department	NOUN
ejpam-6682	2	59	of	of	ADP
ejpam-6682	2	60	mathematics	mathematic	NOUN
ejpam-6682	2	61	,	,	PUNCT
ejpam-6682	2	62	faculty	faculty	NOUN
ejpam-6682	2	63	of	of	ADP
ejpam-6682	2	64	science	science	NOUN
ejpam-6682	2	65	,	,	PUNCT
ejpam-6682	2	66	al	al	PROPN
ejpam-6682	2	67	-	-	PUNCT
ejpam-6682	2	68	baha	baha	PROPN
ejpam-6682	2	69	university	university	PROPN
ejpam-6682	2	70	,	,	PUNCT
ejpam-6682	2	71	albaha	albaha	PROPN
ejpam-6682	2	72	,	,	PUNCT
ejpam-6682	2	73	saudi	saudi	PROPN
ejpam-6682	2	74	arabia	arabia	PROPN
ejpam-6682	2	75	5	5	NUM
ejpam-6682	2	76	higher	high	ADJ
ejpam-6682	2	77	institute	institute	NOUN
ejpam-6682	2	78	of	of	ADP
ejpam-6682	2	79	engineering	engineering	PROPN
ejpam-6682	2	80	technology	technology	NOUN
ejpam-6682	2	81	,	,	PUNCT
ejpam-6682	2	82	almanzala	almanzala	PROPN
ejpam-6682	2	83	,	,	PUNCT
ejpam-6682	2	84	egypt	egypt	PROPN
ejpam-6682	2	85	6	6	NUM
ejpam-6682	2	86	department	department	NOUN
ejpam-6682	2	87	of	of	ADP
ejpam-6682	2	88	mathematics	mathematic	NOUN
ejpam-6682	2	89	and	and	CCONJ
ejpam-6682	2	90	applied	applied	ADJ
ejpam-6682	2	91	mathematics	mathematic	NOUN
ejpam-6682	2	92	,	,	PUNCT
ejpam-6682	2	93	university	university	PROPN
ejpam-6682	2	94	of	of	ADP
ejpam-6682	2	95	johannesburg	johannesburg	PROPN
ejpam-6682	2	96	,	,	PUNCT
ejpam-6682	2	97	po	po	PROPN
ejpam-6682	2	98	box	box	PROPN
ejpam-6682	2	99	524	524	NUM
ejpam-6682	2	100	,	,	PUNCT
ejpam-6682	2	101	auckland	auckland	PROPN
ejpam-6682	2	102	park	park	PROPN
ejpam-6682	2	103	2006	2006	NUM
ejpam-6682	2	104	,	,	PUNCT
ejpam-6682	2	105	johannesburg	johannesburg	PROPN
ejpam-6682	2	106	,	,	PUNCT
ejpam-6682	2	107	south	south	PROPN
ejpam-6682	2	108	africa	africa	PROPN
ejpam-6682	2	109	abstract	abstract	PROPN
ejpam-6682	2	110	.	.	PUNCT
ejpam-6682	3	1	dengue	dengue	NOUN
ejpam-6682	3	2	is	be	AUX
ejpam-6682	3	3	a	a	DET
ejpam-6682	3	4	major	major	ADJ
ejpam-6682	3	5	problem	problem	NOUN
ejpam-6682	3	6	in	in	ADP
ejpam-6682	3	7	sudan	sudan	PROPN
ejpam-6682	3	8	.	.	PUNCT
ejpam-6682	4	1	dengue	dengue	NOUN
ejpam-6682	4	2	spreads	spread	VERB
ejpam-6682	4	3	in	in	ADP
ejpam-6682	4	4	gedaref	gedaref	NOUN
ejpam-6682	4	5	,	,	PUNCT
ejpam-6682	4	6	sudan	sudan	PROPN
ejpam-6682	4	7	.	.	PUNCT
ejpam-6682	5	1	in	in	ADP
ejpam-6682	5	2	this	this	DET
ejpam-6682	5	3	work	work	NOUN
ejpam-6682	5	4	,	,	PUNCT
ejpam-6682	5	5	we	we	PRON
ejpam-6682	5	6	compare	compare	VERB
ejpam-6682	5	7	classical	classical	ADJ
ejpam-6682	5	8	,	,	PUNCT
ejpam-6682	5	9	caputo	caputo	PROPN
ejpam-6682	5	10	fractional	fractional	PROPN
ejpam-6682	5	11	derivative	derivative	PROPN
ejpam-6682	5	12	,	,	PUNCT
ejpam-6682	5	13	and	and	CCONJ
ejpam-6682	5	14	fractal	fractal	ADJ
ejpam-6682	5	15	siar	siar	PROPN
ejpam-6682	5	16	-	-	PUNCT
ejpam-6682	5	17	si	si	X
ejpam-6682	5	18	pandemic	pandemic	ADJ
ejpam-6682	5	19	models	model	NOUN
ejpam-6682	5	20	.	.	PUNCT
ejpam-6682	6	1	we	we	PRON
ejpam-6682	6	2	investigate	investigate	VERB
ejpam-6682	6	3	the	the	DET
ejpam-6682	6	4	disease	disease	NOUN
ejpam-6682	6	5	-	-	PUNCT
ejpam-6682	6	6	free	free	ADJ
ejpam-6682	6	7	and	and	CCONJ
ejpam-6682	6	8	endemic	endemic	ADJ
ejpam-6682	6	9	equilibrium	equilibrium	NOUN
ejpam-6682	6	10	stability	stability	NOUN
ejpam-6682	6	11	,	,	PUNCT
ejpam-6682	6	12	two	two	NUM
ejpam-6682	6	13	important	important	ADJ
ejpam-6682	6	14	stable	stable	ADJ
ejpam-6682	6	15	states	state	NOUN
ejpam-6682	6	16	of	of	ADP
ejpam-6682	6	17	the	the	DET
ejpam-6682	6	18	proposed	propose	VERB
ejpam-6682	6	19	dynamical	dynamical	ADJ
ejpam-6682	6	20	model	model	NOUN
ejpam-6682	6	21	.	.	PUNCT
ejpam-6682	7	1	this	this	DET
ejpam-6682	7	2	study	study	NOUN
ejpam-6682	7	3	identifies	identify	VERB
ejpam-6682	7	4	the	the	DET
ejpam-6682	7	5	factors	factor	NOUN
ejpam-6682	7	6	guiding	guide	VERB
ejpam-6682	7	7	a	a	DET
ejpam-6682	7	8	disease	disease	NOUN
ejpam-6682	7	9	’s	’s	PART
ejpam-6682	7	10	persistence	persistence	NOUN
ejpam-6682	7	11	or	or	CCONJ
ejpam-6682	7	12	extinction	extinction	NOUN
ejpam-6682	7	13	in	in	ADP
ejpam-6682	7	14	the	the	DET
ejpam-6682	7	15	population	population	NOUN
ejpam-6682	7	16	.	.	PUNCT
ejpam-6682	8	1	the	the	DET
ejpam-6682	8	2	model	model	NOUN
ejpam-6682	8	3	is	be	AUX
ejpam-6682	8	4	fitted	fit	VERB
ejpam-6682	8	5	using	use	VERB
ejpam-6682	8	6	real	real	ADJ
ejpam-6682	8	7	data	datum	NOUN
ejpam-6682	8	8	from	from	ADP
ejpam-6682	8	9	gedaref	gedaref	NOUN
ejpam-6682	8	10	,	,	PUNCT
ejpam-6682	8	11	sudan	sudan	PROPN
ejpam-6682	8	12	,	,	PUNCT
ejpam-6682	8	13	and	and	CCONJ
ejpam-6682	8	14	the	the	DET
ejpam-6682	8	15	markov	markov	NOUN
ejpam-6682	8	16	chain	chain	NOUN
ejpam-6682	8	17	monte	monte	PROPN
ejpam-6682	8	18	carlo	carlo	PROPN
ejpam-6682	8	19	method	method	NOUN
ejpam-6682	8	20	is	be	AUX
ejpam-6682	8	21	used	use	VERB
ejpam-6682	8	22	for	for	ADP
ejpam-6682	8	23	estimating	estimate	VERB
ejpam-6682	8	24	parameters	parameter	NOUN
ejpam-6682	8	25	.	.	PUNCT
ejpam-6682	9	1	the	the	DET
ejpam-6682	9	2	computed	compute	VERB
ejpam-6682	9	3	r0	r0	NOUN
ejpam-6682	9	4	=	=	PUNCT
ejpam-6682	9	5	3.27	3.27	NUM
ejpam-6682	9	6	,	,	PUNCT
ejpam-6682	9	7	indicating	indicate	VERB
ejpam-6682	9	8	that	that	SCONJ
ejpam-6682	9	9	the	the	DET
ejpam-6682	9	10	disease	disease	NOUN
ejpam-6682	9	11	is	be	AUX
ejpam-6682	9	12	endemic	endemic	ADJ
ejpam-6682	9	13	.	.	PUNCT
ejpam-6682	10	1	the	the	DET
ejpam-6682	10	2	classical	classical	ADJ
ejpam-6682	10	3	model	model	NOUN
ejpam-6682	10	4	fits	fit	VERB
ejpam-6682	10	5	the	the	DET
ejpam-6682	10	6	real	real	ADJ
ejpam-6682	10	7	data	datum	NOUN
ejpam-6682	10	8	better	well	ADV
ejpam-6682	10	9	than	than	ADP
ejpam-6682	10	10	the	the	DET
ejpam-6682	10	11	other	other	ADJ
ejpam-6682	10	12	methods	method	NOUN
ejpam-6682	10	13	.	.	PUNCT
ejpam-6682	11	1	the	the	DET
ejpam-6682	11	2	fractional	fractional	ADJ
ejpam-6682	11	3	model	model	NOUN
ejpam-6682	11	4	,	,	PUNCT
ejpam-6682	11	5	involving	involve	VERB
ejpam-6682	11	6	caputo	caputo	PROPN
ejpam-6682	11	7	derivatives	derivative	NOUN
ejpam-6682	11	8	,	,	PUNCT
ejpam-6682	11	9	explains	explain	VERB
ejpam-6682	11	10	memory	memory	NOUN
ejpam-6682	11	11	effects	effect	NOUN
ejpam-6682	11	12	.	.	PUNCT
ejpam-6682	12	1	thus	thus	ADV
ejpam-6682	12	2	,	,	PUNCT
ejpam-6682	12	3	they	they	PRON
ejpam-6682	12	4	provide	provide	VERB
ejpam-6682	12	5	a	a	DET
ejpam-6682	12	6	more	more	ADV
ejpam-6682	12	7	realistic	realistic	ADJ
ejpam-6682	12	8	formulation	formulation	NOUN
ejpam-6682	12	9	of	of	ADP
ejpam-6682	12	10	disease	disease	NOUN
ejpam-6682	12	11	transmission	transmission	NOUN
ejpam-6682	12	12	.	.	PUNCT
ejpam-6682	13	1	the	the	DET
ejpam-6682	13	2	fractal	fractal	ADJ
ejpam-6682	13	3	model	model	NOUN
ejpam-6682	13	4	with	with	ADP
ejpam-6682	13	5	hausdorff	hausdorff	NOUN
ejpam-6682	13	6	derivatives	derivative	NOUN
ejpam-6682	13	7	offers	offer	VERB
ejpam-6682	13	8	a	a	DET
ejpam-6682	13	9	new	new	ADJ
ejpam-6682	13	10	direction	direction	NOUN
ejpam-6682	13	11	for	for	ADP
ejpam-6682	13	12	complicated	complicated	ADJ
ejpam-6682	13	13	transmission	transmission	NOUN
ejpam-6682	13	14	dynamics	dynamic	NOUN
ejpam-6682	13	15	and	and	CCONJ
ejpam-6682	13	16	is	be	AUX
ejpam-6682	13	17	worthy	worthy	ADJ
ejpam-6682	13	18	of	of	ADP
ejpam-6682	13	19	further	further	ADJ
ejpam-6682	13	20	research	research	NOUN
ejpam-6682	13	21	.	.	PUNCT
ejpam-6682	14	1	the	the	DET
ejpam-6682	14	2	fractional	fractional	ADJ
ejpam-6682	14	3	and	and	CCONJ
ejpam-6682	14	4	fractal	fractal	ADJ
ejpam-6682	14	5	models	model	NOUN
ejpam-6682	14	6	outperform	outperform	VERB
ejpam-6682	14	7	the	the	DET
ejpam-6682	14	8	classical	classical	ADJ
ejpam-6682	14	9	model	model	NOUN
ejpam-6682	14	10	by	by	ADP
ejpam-6682	14	11	treating	treat	VERB
ejpam-6682	14	12	long	long	ADJ
ejpam-6682	14	13	-	-	PUNCT
ejpam-6682	14	14	term	term	NOUN
ejpam-6682	14	15	dependency	dependency	NOUN
ejpam-6682	14	16	with	with	ADP
ejpam-6682	14	17	fractional	fractional	ADJ
ejpam-6682	14	18	derivatives	derivative	NOUN
ejpam-6682	14	19	and	and	CCONJ
ejpam-6682	14	20	disease	disease	NOUN
ejpam-6682	14	21	spread	spread	VERB
ejpam-6682	14	22	accurately	accurately	ADV
ejpam-6682	14	23	with	with	ADP
ejpam-6682	14	24	fractal	fractal	ADJ
ejpam-6682	14	25	operators	operator	NOUN
ejpam-6682	14	26	.	.	PUNCT
ejpam-6682	15	1	2020	2020	NUM
ejpam-6682	15	2	mathematics	mathematic	NOUN
ejpam-6682	15	3	subject	subject	NOUN
ejpam-6682	15	4	classifications	classification	NOUN
ejpam-6682	15	5	:	:	PUNCT
ejpam-6682	15	6	26a33	26a33	NUM
ejpam-6682	15	7	,	,	PUNCT
ejpam-6682	15	8	34a08	34a08	NUM
ejpam-6682	15	9	,	,	PUNCT
ejpam-6682	15	10	92d30	92d30	NUM
ejpam-6682	15	11	key	key	ADJ
ejpam-6682	15	12	words	word	NOUN
ejpam-6682	15	13	and	and	CCONJ
ejpam-6682	15	14	phrases	phrase	NOUN
ejpam-6682	15	15	:	:	PUNCT
ejpam-6682	15	16	dengue	dengue	NOUN
ejpam-6682	15	17	fever	fever	NOUN
ejpam-6682	15	18	,	,	PUNCT
ejpam-6682	15	19	mathematical	mathematical	ADJ
ejpam-6682	15	20	modeling	modeling	NOUN
ejpam-6682	15	21	,	,	PUNCT
ejpam-6682	15	22	fractional	fractional	ADJ
ejpam-6682	15	23	derivatives	derivative	NOUN
ejpam-6682	15	24	,	,	PUNCT
ejpam-6682	15	25	fractals	fractal	NOUN
ejpam-6682	15	26	,	,	PUNCT
ejpam-6682	15	27	epidemiology	epidemiology	NOUN
ejpam-6682	15	28	,	,	PUNCT
ejpam-6682	15	29	forecasting	forecasting	NOUN
ejpam-6682	15	30	∗corresponding	∗corresponde	VERB
ejpam-6682	15	31	author	author	NOUN
ejpam-6682	15	32	.	.	PUNCT
ejpam-6682	16	1	doi	doi	NOUN
ejpam-6682	16	2	:	:	PUNCT
ejpam-6682	16	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6682	https://doi.org/10.29020/nybg.ejpam.v18i4.6682	ADJ
ejpam-6682	16	4	email	email	NOUN
ejpam-6682	16	5	addresses	address	NOUN
ejpam-6682	16	6	:	:	PUNCT
ejpam-6682	16	7	r.saadeh@bau.edu.jo	r.saadeh@bau.edu.jo	PROPN
ejpam-6682	16	8	(	(	PUNCT
ejpam-6682	16	9	r.	r.	PROPN
ejpam-6682	16	10	saadeh	saadeh	PROPN
ejpam-6682	16	11	)	)	PUNCT
ejpam-6682	16	12	,	,	PUNCT
ejpam-6682	16	13	nkuleab@ksu.edu.sa	nkuleab@ksu.edu.sa	PROPN
ejpam-6682	16	14	(	(	PUNCT
ejpam-6682	16	15	n.	n.	PROPN
ejpam-6682	16	16	al	al	PROPN
ejpam-6682	16	17	-	-	PUNCT
ejpam-6682	16	18	kuleab	kuleab	PROPN
ejpam-6682	16	19	)	)	PUNCT
ejpam-6682	16	20	,	,	PUNCT
ejpam-6682	16	21	m	m	VERB
ejpam-6682	16	22	alsoudi@asu.edu.jo	alsoudi@asu.edu.jo	ADJ
ejpam-6682	16	23	(	(	PUNCT
ejpam-6682	16	24	m.	m.	PROPN
ejpam-6682	16	25	s.	s.	PROPN
ejpam-6682	16	26	al	al	PROPN
ejpam-6682	16	27	soudi	soudi	PROPN
ejpam-6682	16	28	)	)	PUNCT
ejpam-6682	16	29	,	,	PUNCT
ejpam-6682	16	30	khilal@bu.edu.sa	khilal@bu.edu.sa	PROPN
ejpam-6682	16	31	(	(	PUNCT
ejpam-6682	16	32	k.	k.	PROPN
ejpam-6682	16	33	a.	a.	PROPN
ejpam-6682	16	34	a.	a.	PROPN
ejpam-6682	16	35	helal	helal	PROPN
ejpam-6682	16	36	)	)	PUNCT
ejpam-6682	16	37	,	,	PUNCT
ejpam-6682	16	38	aimam@bu.edu.sa	aimam@bu.edu.sa	PROPN
ejpam-6682	16	39	(	(	PUNCT
ejpam-6682	16	40	a.	a.	NOUN
ejpam-6682	16	41	imam	imam	PROPN
ejpam-6682	16	42	)	)	PUNCT
ejpam-6682	16	43	,	,	PUNCT
ejpam-6682	16	44	elshamyii@hotmail.com	elshamyii@hotmail.com	X
ejpam-6682	16	45	(	(	PUNCT
ejpam-6682	16	46	i.	i.	PROPN
ejpam-6682	16	47	elshamy	elshamy	PROPN
ejpam-6682	16	48	)	)	PUNCT
ejpam-6682	16	49	,	,	PUNCT
ejpam-6682	16	50	jamiel@aims.ac.za	jamiel@aims.ac.za	PROPN
ejpam-6682	16	51	(	(	PUNCT
ejpam-6682	16	52	s.	s.	PROPN
ejpam-6682	16	53	j.	j.	PROPN
ejpam-6682	16	54	m.	m.	PROPN
ejpam-6682	16	55	abdalla	abdalla	PROPN
ejpam-6682	16	56	)	)	PUNCT
ejpam-6682	16	57	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6682	16	58	1	1	NUM
ejpam-6682	16	59	copyright	copyright	NOUN
ejpam-6682	16	60	:	:	PUNCT
ejpam-6682	17	1	©	©	PROPN
ejpam-6682	17	2	2025	2025	NUM
ejpam-6682	17	3	the	the	DET
ejpam-6682	17	4	author(s	author(s	NOUN
ejpam-6682	17	5	)	)	PUNCT
ejpam-6682	17	6	.	.	PUNCT
ejpam-6682	18	1	(	(	PUNCT
ejpam-6682	18	2	cc	cc	NOUN
ejpam-6682	18	3	by	by	ADP
ejpam-6682	18	4	-	-	PUNCT
ejpam-6682	18	5	nc	nc	PROPN
ejpam-6682	18	6	4.0	4.0	NUM
ejpam-6682	18	7	)	)	PUNCT
ejpam-6682	18	8	r.	r.	PROPN
ejpam-6682	18	9	saadeh	saadeh	PROPN
ejpam-6682	18	10	et	et	PROPN
ejpam-6682	18	11	al	al	PROPN
ejpam-6682	18	12	.	.	PUNCT
ejpam-6682	18	13	/	/	SYM
ejpam-6682	18	14	eur	eur	PROPN
ejpam-6682	18	15	.	.	PUNCT
ejpam-6682	19	1	j.	j.	PROPN
ejpam-6682	19	2	pure	pure	PROPN
ejpam-6682	19	3	appl	appl	PROPN
ejpam-6682	19	4	.	.	PROPN
ejpam-6682	19	5	math	math	PROPN
ejpam-6682	19	6	,	,	PUNCT
ejpam-6682	19	7	18	18	NUM
ejpam-6682	19	8	(	(	PUNCT
ejpam-6682	19	9	4	4	NUM
ejpam-6682	19	10	)	)	PUNCT
ejpam-6682	19	11	(	(	PUNCT
ejpam-6682	19	12	2025	2025	NUM
ejpam-6682	19	13	)	)	PUNCT
ejpam-6682	19	14	,	,	PUNCT
ejpam-6682	19	15	6682	6682	NUM
ejpam-6682	19	16	2	2	NUM
ejpam-6682	19	17	of	of	ADP
ejpam-6682	19	18	21	21	NUM
ejpam-6682	19	19	1	1	NUM
ejpam-6682	19	20	.	.	PUNCT
ejpam-6682	20	1	introduction	introduction	NOUN
ejpam-6682	20	2	dengue	dengue	NOUN
ejpam-6682	20	3	fever	fever	NOUN
ejpam-6682	20	4	is	be	AUX
ejpam-6682	20	5	a	a	DET
ejpam-6682	20	6	viral	viral	ADJ
ejpam-6682	20	7	infection	infection	NOUN
ejpam-6682	20	8	spread	spread	VERB
ejpam-6682	20	9	by	by	ADP
ejpam-6682	20	10	mosquitoes	mosquito	NOUN
ejpam-6682	20	11	.	.	PUNCT
ejpam-6682	21	1	the	the	DET
ejpam-6682	21	2	infection	infection	NOUN
ejpam-6682	21	3	usually	usually	ADV
ejpam-6682	21	4	occurs	occur	VERB
ejpam-6682	21	5	in	in	ADP
ejpam-6682	21	6	warm	warm	ADJ
ejpam-6682	21	7	and	and	CCONJ
ejpam-6682	21	8	subtropical	subtropical	ADJ
ejpam-6682	21	9	regions	region	NOUN
ejpam-6682	21	10	with	with	ADP
ejpam-6682	21	11	a	a	DET
ejpam-6682	21	12	high	high	ADJ
ejpam-6682	21	13	population	population	NOUN
ejpam-6682	21	14	density	density	NOUN
ejpam-6682	21	15	.	.	PUNCT
ejpam-6682	22	1	the	the	DET
ejpam-6682	22	2	virus	virus	NOUN
ejpam-6682	22	3	has	have	VERB
ejpam-6682	22	4	four	four	NUM
ejpam-6682	22	5	serotypes	serotype	NOUN
ejpam-6682	22	6	:	:	PUNCT
ejpam-6682	22	7	denv-1	denv-1	NUM
ejpam-6682	22	8	,	,	PUNCT
ejpam-6682	22	9	denv-2	denv-2	PROPN
ejpam-6682	22	10	,	,	PUNCT
ejpam-6682	22	11	denv-3	denv-3	NOUN
ejpam-6682	22	12	,	,	PUNCT
ejpam-6682	22	13	and	and	CCONJ
ejpam-6682	23	1	denv-4	denv-4	PROPN
ejpam-6682	23	2	.	.	PUNCT
ejpam-6682	24	1	dengue	dengue	NOUN
ejpam-6682	24	2	fever	fever	NOUN
ejpam-6682	24	3	can	can	AUX
ejpam-6682	24	4	appear	appear	VERB
ejpam-6682	24	5	in	in	ADP
ejpam-6682	24	6	various	various	ADJ
ejpam-6682	24	7	ways	way	NOUN
ejpam-6682	24	8	,	,	PUNCT
ejpam-6682	24	9	ranging	range	VERB
ejpam-6682	24	10	from	from	ADP
ejpam-6682	24	11	minor	minor	ADJ
ejpam-6682	24	12	signs	sign	NOUN
ejpam-6682	24	13	such	such	ADJ
ejpam-6682	24	14	as	as	ADP
ejpam-6682	24	15	fever	fever	NOUN
ejpam-6682	24	16	,	,	PUNCT
ejpam-6682	24	17	headache	headache	NOUN
ejpam-6682	24	18	,	,	PUNCT
ejpam-6682	24	19	and	and	CCONJ
ejpam-6682	24	20	joint	joint	ADJ
ejpam-6682	24	21	pain	pain	NOUN
ejpam-6682	24	22	to	to	ADP
ejpam-6682	24	23	severe	severe	ADJ
ejpam-6682	24	24	complications	complication	NOUN
ejpam-6682	24	25	such	such	ADJ
ejpam-6682	24	26	as	as	ADP
ejpam-6682	24	27	dengue	dengue	NOUN
ejpam-6682	24	28	hemorrhagic	hemorrhagic	NOUN
ejpam-6682	24	29	fever	fever	NOUN
ejpam-6682	24	30	and	and	CCONJ
ejpam-6682	24	31	dengue	dengue	NOUN
ejpam-6682	24	32	shock	shock	NOUN
ejpam-6682	24	33	syndrome	syndrome	NOUN
ejpam-6682	24	34	[	[	X
ejpam-6682	24	35	1–5	1–5	X
ejpam-6682	24	36	]	]	X
ejpam-6682	24	37	.	.	PUNCT
ejpam-6682	25	1	dengue	dengue	NOUN
ejpam-6682	25	2	fever	fever	NOUN
ejpam-6682	25	3	is	be	AUX
ejpam-6682	25	4	a	a	DET
ejpam-6682	25	5	worldwide	worldwide	ADJ
ejpam-6682	25	6	health	health	NOUN
ejpam-6682	25	7	issue	issue	NOUN
ejpam-6682	25	8	.	.	PUNCT
ejpam-6682	26	1	it	it	PRON
ejpam-6682	26	2	causes	cause	VERB
ejpam-6682	26	3	millions	million	NOUN
ejpam-6682	26	4	of	of	ADP
ejpam-6682	26	5	reported	report	VERB
ejpam-6682	26	6	cases	case	NOUN
ejpam-6682	26	7	annually	annually	ADV
ejpam-6682	26	8	in	in	ADP
ejpam-6682	26	9	asia	asia	PROPN
ejpam-6682	26	10	,	,	PUNCT
ejpam-6682	26	11	africa	africa	PROPN
ejpam-6682	26	12	,	,	PUNCT
ejpam-6682	26	13	and	and	CCONJ
ejpam-6682	26	14	south	south	PROPN
ejpam-6682	26	15	america	america	PROPN
ejpam-6682	27	1	[	[	X
ejpam-6682	27	2	6	6	NUM
ejpam-6682	27	3	]	]	PUNCT
ejpam-6682	27	4	.	.	PUNCT
ejpam-6682	28	1	weather	weather	NOUN
ejpam-6682	28	2	factors	factor	NOUN
ejpam-6682	28	3	like	like	ADP
ejpam-6682	28	4	temperature	temperature	NOUN
ejpam-6682	28	5	,	,	PUNCT
ejpam-6682	28	6	humidity	humidity	NOUN
ejpam-6682	28	7	,	,	PUNCT
ejpam-6682	28	8	and	and	CCONJ
ejpam-6682	28	9	rainfall	rainfall	NOUN
ejpam-6682	28	10	influence	influence	NOUN
ejpam-6682	28	11	viral	viral	ADJ
ejpam-6682	28	12	spread	spread	NOUN
ejpam-6682	28	13	due	due	ADP
ejpam-6682	28	14	to	to	ADP
ejpam-6682	28	15	their	their	PRON
ejpam-6682	28	16	direct	direct	ADJ
ejpam-6682	28	17	effect	effect	NOUN
ejpam-6682	28	18	on	on	ADP
ejpam-6682	28	19	the	the	DET
ejpam-6682	28	20	breeding	breeding	NOUN
ejpam-6682	28	21	of	of	ADP
ejpam-6682	28	22	mosquitoes	mosquito	NOUN
ejpam-6682	28	23	and	and	CCONJ
ejpam-6682	28	24	virus	virus	NOUN
ejpam-6682	28	25	reproduction	reproduction	NOUN
ejpam-6682	28	26	.	.	PUNCT
ejpam-6682	29	1	dengue	dengue	NOUN
ejpam-6682	29	2	fever	fever	NOUN
ejpam-6682	29	3	burst	burst	VERB
ejpam-6682	29	4	into	into	ADP
ejpam-6682	29	5	epidemic	epidemic	NOUN
ejpam-6682	29	6	proportions	proportion	NOUN
ejpam-6682	29	7	in	in	ADP
ejpam-6682	29	8	eastern	eastern	PROPN
ejpam-6682	29	9	sudan	sudan	PROPN
ejpam-6682	29	10	in	in	ADP
ejpam-6682	29	11	2023	2023	NUM
ejpam-6682	29	12	,	,	PUNCT
ejpam-6682	29	13	specifically	specifically	ADV
ejpam-6682	29	14	in	in	ADP
ejpam-6682	29	15	gedaref	gedaref	NOUN
ejpam-6682	29	16	state	state	NOUN
ejpam-6682	29	17	,	,	PUNCT
ejpam-6682	29	18	with	with	ADP
ejpam-6682	29	19	morbidity	morbidity	NOUN
ejpam-6682	29	20	and	and	CCONJ
ejpam-6682	29	21	mortality	mortality	NOUN
ejpam-6682	29	22	[	[	X
ejpam-6682	29	23	7	7	NUM
ejpam-6682	29	24	]	]	PUNCT
ejpam-6682	29	25	.	.	PUNCT
ejpam-6682	30	1	the	the	DET
ejpam-6682	30	2	extremely	extremely	ADV
ejpam-6682	30	3	high	high	ADJ
ejpam-6682	30	4	dengue	dengue	NOUN
ejpam-6682	30	5	fever	fever	NOUN
ejpam-6682	30	6	epidemics	epidemic	NOUN
ejpam-6682	30	7	in	in	ADP
ejpam-6682	30	8	gedaref	gedaref	NOUN
ejpam-6682	30	9	are	be	AUX
ejpam-6682	30	10	due	due	ADJ
ejpam-6682	30	11	to	to	ADP
ejpam-6682	30	12	the	the	DET
ejpam-6682	30	13	interaction	interaction	NOUN
ejpam-6682	30	14	between	between	ADP
ejpam-6682	30	15	social	social	ADJ
ejpam-6682	30	16	,	,	PUNCT
ejpam-6682	30	17	environmental	environmental	ADJ
ejpam-6682	30	18	,	,	PUNCT
ejpam-6682	30	19	and	and	CCONJ
ejpam-6682	30	20	economic	economic	ADJ
ejpam-6682	30	21	determinants	determinant	NOUN
ejpam-6682	30	22	.	.	PUNCT
ejpam-6682	31	1	climate	climate	NOUN
ejpam-6682	31	2	change	change	NOUN
ejpam-6682	31	3	and	and	CCONJ
ejpam-6682	31	4	the	the	DET
ejpam-6682	31	5	intensification	intensification	NOUN
ejpam-6682	31	6	of	of	ADP
ejpam-6682	31	7	seasonal	seasonal	ADJ
ejpam-6682	31	8	rains	rain	NOUN
ejpam-6682	31	9	create	create	VERB
ejpam-6682	31	10	favorable	favorable	ADJ
ejpam-6682	31	11	breeding	breeding	NOUN
ejpam-6682	31	12	conditions	condition	NOUN
ejpam-6682	31	13	for	for	ADP
ejpam-6682	31	14	mosquitoes	mosquito	NOUN
ejpam-6682	31	15	.	.	PUNCT
ejpam-6682	32	1	however	however	ADV
ejpam-6682	32	2	,	,	PUNCT
ejpam-6682	32	3	water	water	NOUN
ejpam-6682	32	4	courses	course	NOUN
ejpam-6682	32	5	and	and	CCONJ
ejpam-6682	32	6	wetland	wetland	NOUN
ejpam-6682	32	7	areas	area	NOUN
ejpam-6682	32	8	represent	represent	VERB
ejpam-6682	32	9	breeding	breeding	NOUN
ejpam-6682	32	10	sites	site	NOUN
ejpam-6682	32	11	that	that	PRON
ejpam-6682	32	12	contribute	contribute	VERB
ejpam-6682	32	13	to	to	ADP
ejpam-6682	32	14	the	the	DET
ejpam-6682	32	15	spread	spread	NOUN
ejpam-6682	32	16	of	of	ADP
ejpam-6682	32	17	the	the	DET
ejpam-6682	32	18	epidemic	epidemic	NOUN
ejpam-6682	32	19	.	.	PUNCT
ejpam-6682	33	1	inadequate	inadequate	ADJ
ejpam-6682	33	2	healthcare	healthcare	NOUN
ejpam-6682	33	3	impacts	impact	VERB
ejpam-6682	33	4	the	the	DET
ejpam-6682	33	5	timely	timely	ADJ
ejpam-6682	33	6	detection	detection	NOUN
ejpam-6682	33	7	and	and	CCONJ
ejpam-6682	33	8	care	care	NOUN
ejpam-6682	33	9	of	of	ADP
ejpam-6682	33	10	new	new	ADJ
ejpam-6682	33	11	cases	case	NOUN
ejpam-6682	33	12	,	,	PUNCT
ejpam-6682	33	13	increasing	increase	VERB
ejpam-6682	33	14	outbreaks	outbreak	NOUN
ejpam-6682	33	15	’	'	PUNCT
ejpam-6682	33	16	severity	severity	NOUN
ejpam-6682	33	17	.	.	PUNCT
ejpam-6682	34	1	these	these	DET
ejpam-6682	34	2	linked	link	VERB
ejpam-6682	34	3	determinants	determinant	NOUN
ejpam-6682	34	4	explain	explain	VERB
ejpam-6682	34	5	the	the	DET
ejpam-6682	34	6	region	region	NOUN
ejpam-6682	34	7	’s	’s	PART
ejpam-6682	34	8	chronic	chronic	ADJ
ejpam-6682	34	9	and	and	CCONJ
ejpam-6682	34	10	endemic	endemic	ADJ
ejpam-6682	34	11	dengue	dengue	NOUN
ejpam-6682	34	12	fever	fever	NOUN
ejpam-6682	34	13	epidemic	epidemic	NOUN
ejpam-6682	34	14	.	.	PUNCT
ejpam-6682	35	1	in	in	ADP
ejpam-6682	35	2	2023	2023	NUM
ejpam-6682	35	3	,	,	PUNCT
ejpam-6682	35	4	gedaref	gedaref	NOUN
ejpam-6682	35	5	state	state	NOUN
ejpam-6682	35	6	recorded	record	VERB
ejpam-6682	35	7	one	one	NUM
ejpam-6682	35	8	of	of	ADP
ejpam-6682	35	9	sudan	sudan	PROPN
ejpam-6682	35	10	’s	’s	PART
ejpam-6682	35	11	highest	high	ADJ
ejpam-6682	35	12	dengue	dengue	NOUN
ejpam-6682	35	13	fever	fever	NOUN
ejpam-6682	35	14	incidence	incidence	NOUN
ejpam-6682	35	15	rates	rate	NOUN
ejpam-6682	35	16	.	.	PUNCT
ejpam-6682	36	1	thus	thus	ADV
ejpam-6682	36	2	,	,	PUNCT
ejpam-6682	36	3	it	it	PRON
ejpam-6682	36	4	is	be	AUX
ejpam-6682	36	5	critical	critical	ADJ
ejpam-6682	36	6	to	to	PART
ejpam-6682	36	7	investigate	investigate	VERB
ejpam-6682	36	8	epidemiological	epidemiological	ADJ
ejpam-6682	36	9	characteristics	characteristic	NOUN
ejpam-6682	36	10	of	of	ADP
ejpam-6682	36	11	the	the	DET
ejpam-6682	36	12	disease	disease	NOUN
ejpam-6682	36	13	spread	spread	VERB
ejpam-6682	36	14	in	in	ADP
ejpam-6682	36	15	the	the	DET
ejpam-6682	36	16	region	region	NOUN
ejpam-6682	37	1	[	[	X
ejpam-6682	37	2	8–11	8–11	X
ejpam-6682	37	3	]	]	PUNCT
ejpam-6682	37	4	.	.	PUNCT
ejpam-6682	38	1	mathematical	mathematical	ADJ
ejpam-6682	38	2	models	model	NOUN
ejpam-6682	38	3	are	be	AUX
ejpam-6682	38	4	of	of	ADP
ejpam-6682	38	5	central	central	ADJ
ejpam-6682	38	6	importance	importance	NOUN
ejpam-6682	38	7	to	to	ADP
ejpam-6682	38	8	comprehending	comprehend	VERB
ejpam-6682	38	9	and	and	CCONJ
ejpam-6682	38	10	predicting	predict	VERB
ejpam-6682	38	11	infectious	infectious	ADJ
ejpam-6682	38	12	disease	disease	NOUN
ejpam-6682	38	13	transmission	transmission	NOUN
ejpam-6682	38	14	to	to	PART
ejpam-6682	38	15	enable	enable	VERB
ejpam-6682	38	16	public	public	ADJ
ejpam-6682	38	17	health	health	NOUN
ejpam-6682	38	18	authorities	authority	NOUN
ejpam-6682	38	19	to	to	PART
ejpam-6682	38	20	design	design	VERB
ejpam-6682	38	21	effective	effective	ADJ
ejpam-6682	38	22	disease	disease	NOUN
ejpam-6682	38	23	surveillance	surveillance	NOUN
ejpam-6682	38	24	systems	system	NOUN
ejpam-6682	38	25	,	,	PUNCT
ejpam-6682	38	26	respond	respond	VERB
ejpam-6682	38	27	to	to	ADP
ejpam-6682	38	28	outbreaks	outbreak	NOUN
ejpam-6682	38	29	,	,	PUNCT
ejpam-6682	38	30	and	and	CCONJ
ejpam-6682	38	31	formulate	formulate	ADJ
ejpam-6682	38	32	policy	policy	NOUN
ejpam-6682	38	33	.	.	PUNCT
ejpam-6682	39	1	the	the	DET
ejpam-6682	39	2	models	model	NOUN
ejpam-6682	39	3	utilize	utilize	VERB
ejpam-6682	39	4	accurate	accurate	ADJ
ejpam-6682	39	5	data	datum	NOUN
ejpam-6682	39	6	and	and	CCONJ
ejpam-6682	39	7	computer	computer	NOUN
ejpam-6682	39	8	methods	method	NOUN
ejpam-6682	39	9	to	to	PART
ejpam-6682	39	10	understand	understand	VERB
ejpam-6682	39	11	infection	infection	NOUN
ejpam-6682	39	12	transmission	transmission	NOUN
ejpam-6682	39	13	,	,	PUNCT
ejpam-6682	39	14	intervention	intervention	NOUN
ejpam-6682	39	15	effectiveness	effectiveness	NOUN
ejpam-6682	39	16	,	,	PUNCT
ejpam-6682	39	17	and	and	CCONJ
ejpam-6682	39	18	environmental	environmental	ADJ
ejpam-6682	39	19	factors	factor	NOUN
ejpam-6682	39	20	that	that	PRON
ejpam-6682	39	21	affect	affect	VERB
ejpam-6682	39	22	disease	disease	NOUN
ejpam-6682	39	23	transmission	transmission	NOUN
ejpam-6682	40	1	[	[	X
ejpam-6682	40	2	12	12	NUM
ejpam-6682	40	3	–	–	PUNCT
ejpam-6682	40	4	14	14	NUM
ejpam-6682	40	5	]	]	PUNCT
ejpam-6682	40	6	.	.	PUNCT
ejpam-6682	41	1	scientists	scientist	NOUN
ejpam-6682	41	2	have	have	AUX
ejpam-6682	41	3	devised	devise	VERB
ejpam-6682	41	4	various	various	ADJ
ejpam-6682	41	5	modelling	modelling	NOUN
ejpam-6682	41	6	methods	method	NOUN
ejpam-6682	41	7	,	,	PUNCT
ejpam-6682	41	8	each	each	PRON
ejpam-6682	41	9	with	with	ADP
ejpam-6682	41	10	advantages	advantage	NOUN
ejpam-6682	41	11	and	and	CCONJ
ejpam-6682	41	12	disadvantages	disadvantage	NOUN
ejpam-6682	41	13	.	.	PUNCT
ejpam-6682	42	1	classical	classical	ADJ
ejpam-6682	42	2	susceptible	susceptible	ADJ
ejpam-6682	42	3	-	-	PUNCT
ejpam-6682	42	4	infected	infect	VERB
ejpam-6682	42	5	-	-	PUNCT
ejpam-6682	42	6	recovered	recover	VERB
ejpam-6682	42	7	(	(	PUNCT
ejpam-6682	42	8	sir	sir	NOUN
ejpam-6682	42	9	)	)	PUNCT
ejpam-6682	42	10	and	and	CCONJ
ejpam-6682	42	11	susceptible	susceptible	ADJ
ejpam-6682	42	12	-	-	PUNCT
ejpam-6682	42	13	exposed	expose	VERB
ejpam-6682	42	14	-	-	PUNCT
ejpam-6682	42	15	infectedrecovered	infectedrecovere	VERB
ejpam-6682	42	16	(	(	PUNCT
ejpam-6682	42	17	seir	seir	NOUN
ejpam-6682	42	18	)	)	PUNCT
ejpam-6682	42	19	are	be	AUX
ejpam-6682	42	20	among	among	ADP
ejpam-6682	42	21	the	the	DET
ejpam-6682	42	22	most	most	ADV
ejpam-6682	42	23	commonly	commonly	ADV
ejpam-6682	42	24	used	use	VERB
ejpam-6682	42	25	integer	integer	NOUN
ejpam-6682	42	26	-	-	PUNCT
ejpam-6682	42	27	order	order	NOUN
ejpam-6682	42	28	models	model	NOUN
ejpam-6682	42	29	.	.	PUNCT
ejpam-6682	43	1	while	while	SCONJ
ejpam-6682	43	2	providing	provide	VERB
ejpam-6682	43	3	a	a	DET
ejpam-6682	43	4	straightforward	straightforward	ADJ
ejpam-6682	43	5	framework	framework	NOUN
ejpam-6682	43	6	for	for	ADP
ejpam-6682	43	7	understanding	understand	VERB
ejpam-6682	43	8	disease	disease	NOUN
ejpam-6682	43	9	spread	spread	VERB
ejpam-6682	43	10	,	,	PUNCT
ejpam-6682	43	11	these	these	DET
ejpam-6682	43	12	models	model	NOUN
ejpam-6682	43	13	fail	fail	VERB
ejpam-6682	43	14	to	to	PART
ejpam-6682	43	15	capture	capture	VERB
ejpam-6682	43	16	the	the	DET
ejpam-6682	43	17	complexity	complexity	NOUN
ejpam-6682	43	18	of	of	ADP
ejpam-6682	43	19	actual	actual	ADJ
ejpam-6682	43	20	epidemics	epidemic	NOUN
ejpam-6682	43	21	[	[	X
ejpam-6682	43	22	15	15	NUM
ejpam-6682	43	23	]	]	PUNCT
ejpam-6682	43	24	.	.	PUNCT
ejpam-6682	44	1	fractional	fractional	ADJ
ejpam-6682	44	2	and	and	CCONJ
ejpam-6682	44	3	fractal	fractal	ADJ
ejpam-6682	44	4	models	model	NOUN
ejpam-6682	44	5	emerged	emerge	VERB
ejpam-6682	44	6	and	and	CCONJ
ejpam-6682	44	7	are	be	AUX
ejpam-6682	44	8	used	use	VERB
ejpam-6682	44	9	to	to	PART
ejpam-6682	44	10	address	address	VERB
ejpam-6682	44	11	these	these	DET
ejpam-6682	44	12	limitations	limitation	NOUN
ejpam-6682	44	13	.	.	PUNCT
ejpam-6682	45	1	these	these	DET
ejpam-6682	45	2	models	model	NOUN
ejpam-6682	45	3	incorporate	incorporate	VERB
ejpam-6682	45	4	memory	memory	NOUN
ejpam-6682	45	5	effects	effect	NOUN
ejpam-6682	45	6	and	and	CCONJ
ejpam-6682	45	7	improve	improve	VERB
ejpam-6682	45	8	prediction	prediction	NOUN
ejpam-6682	45	9	accuracy	accuracy	NOUN
ejpam-6682	46	1	[	[	X
ejpam-6682	46	2	16	16	NUM
ejpam-6682	46	3	,	,	PUNCT
ejpam-6682	46	4	17	17	NUM
ejpam-6682	46	5	]	]	PUNCT
ejpam-6682	46	6	.	.	PUNCT
ejpam-6682	47	1	fractional	fractional	ADJ
ejpam-6682	47	2	-	-	PUNCT
ejpam-6682	47	3	order	order	NOUN
ejpam-6682	47	4	models	model	NOUN
ejpam-6682	47	5	enhance	enhance	VERB
ejpam-6682	47	6	conventional	conventional	ADJ
ejpam-6682	47	7	frameworks	framework	NOUN
ejpam-6682	47	8	by	by	ADP
ejpam-6682	47	9	incorporating	incorporate	VERB
ejpam-6682	47	10	non	non	ADJ
ejpam-6682	47	11	-	-	ADJ
ejpam-6682	47	12	integer	integer	ADJ
ejpam-6682	47	13	derivatives	derivative	NOUN
ejpam-6682	47	14	.	.	PUNCT
ejpam-6682	48	1	they	they	PRON
ejpam-6682	48	2	are	be	AUX
ejpam-6682	48	3	of	of	ADP
ejpam-6682	48	4	special	special	ADJ
ejpam-6682	48	5	use	use	NOUN
ejpam-6682	48	6	in	in	ADP
ejpam-6682	48	7	long	long	ADJ
ejpam-6682	48	8	-	-	PUNCT
ejpam-6682	48	9	term	term	NOUN
ejpam-6682	48	10	epidemic	epidemic	NOUN
ejpam-6682	48	11	forecasting	forecasting	NOUN
ejpam-6682	48	12	,	,	PUNCT
ejpam-6682	48	13	particularly	particularly	ADV
ejpam-6682	48	14	for	for	ADP
ejpam-6682	48	15	diseases	disease	NOUN
ejpam-6682	48	16	with	with	ADP
ejpam-6682	48	17	latency	latency	NOUN
ejpam-6682	48	18	in	in	ADP
ejpam-6682	48	19	immune	immune	ADJ
ejpam-6682	48	20	response	response	NOUN
ejpam-6682	48	21	or	or	CCONJ
ejpam-6682	48	22	with	with	ADP
ejpam-6682	48	23	long	long	ADJ
ejpam-6682	48	24	incubation	incubation	NOUN
ejpam-6682	48	25	periods	period	NOUN
ejpam-6682	48	26	[	[	X
ejpam-6682	48	27	16	16	NUM
ejpam-6682	48	28	]	]	PUNCT
ejpam-6682	48	29	.	.	PUNCT
ejpam-6682	49	1	fractionalorder	fractionalorder	PROPN
ejpam-6682	49	2	models	model	NOUN
ejpam-6682	49	3	were	be	AUX
ejpam-6682	49	4	found	find	VERB
ejpam-6682	49	5	to	to	PART
ejpam-6682	49	6	increase	increase	VERB
ejpam-6682	49	7	accuracy	accuracy	NOUN
ejpam-6682	49	8	in	in	ADP
ejpam-6682	49	9	prediction	prediction	NOUN
ejpam-6682	49	10	,	,	PUNCT
ejpam-6682	49	11	particularly	particularly	ADV
ejpam-6682	49	12	for	for	ADP
ejpam-6682	49	13	vector	vector	NOUN
ejpam-6682	49	14	-	-	PUNCT
ejpam-6682	49	15	borne	bear	VERB
ejpam-6682	49	16	disease	disease	NOUN
ejpam-6682	49	17	,	,	PUNCT
ejpam-6682	49	18	which	which	PRON
ejpam-6682	49	19	is	be	AUX
ejpam-6682	49	20	influenced	influence	VERB
ejpam-6682	49	21	by	by	ADP
ejpam-6682	49	22	changing	change	VERB
ejpam-6682	49	23	mosquito	mosquito	ADJ
ejpam-6682	49	24	populations	population	NOUN
ejpam-6682	49	25	and	and	CCONJ
ejpam-6682	49	26	environmental	environmental	ADJ
ejpam-6682	49	27	conditions	condition	NOUN
ejpam-6682	49	28	[	[	X
ejpam-6682	49	29	18	18	NUM
ejpam-6682	49	30	,	,	PUNCT
ejpam-6682	49	31	19	19	NUM
ejpam-6682	49	32	]	]	PUNCT
ejpam-6682	49	33	.	.	PUNCT
ejpam-6682	50	1	studies	study	NOUN
ejpam-6682	50	2	on	on	ADP
ejpam-6682	50	3	dengue	dengue	NOUN
ejpam-6682	50	4	showed	show	VERB
ejpam-6682	50	5	that	that	SCONJ
ejpam-6682	50	6	fractional	fractional	ADJ
ejpam-6682	50	7	order	order	NOUN
ejpam-6682	50	8	predicted	predict	VERB
ejpam-6682	50	9	epidemic	epidemic	NOUN
ejpam-6682	50	10	patterns	pattern	NOUN
ejpam-6682	50	11	more	more	ADV
ejpam-6682	50	12	precisely	precisely	ADV
ejpam-6682	50	13	than	than	ADP
ejpam-6682	50	14	traditional	traditional	ADJ
ejpam-6682	50	15	models	model	NOUN
ejpam-6682	50	16	[	[	X
ejpam-6682	50	17	20	20	NUM
ejpam-6682	50	18	]	]	PUNCT
ejpam-6682	50	19	.	.	PUNCT
ejpam-6682	51	1	fractional	fractional	ADJ
ejpam-6682	51	2	models	model	NOUN
ejpam-6682	51	3	,	,	PUNCT
ejpam-6682	51	4	however	however	ADV
ejpam-6682	51	5	,	,	PUNCT
ejpam-6682	51	6	can	can	AUX
ejpam-6682	51	7	not	not	PART
ejpam-6682	51	8	account	account	VERB
ejpam-6682	51	9	for	for	ADP
ejpam-6682	51	10	time	time	NOUN
ejpam-6682	51	11	variations	variation	NOUN
ejpam-6682	51	12	[	[	X
ejpam-6682	51	13	21–23	21–23	NUM
ejpam-6682	51	14	]	]	X
ejpam-6682	51	15	.	.	PUNCT
ejpam-6682	52	1	fractal	fractal	PROPN
ejpam-6682	52	2	models	model	NOUN
ejpam-6682	52	3	account	account	VERB
ejpam-6682	52	4	for	for	ADP
ejpam-6682	52	5	time	time	NOUN
ejpam-6682	52	6	variations	variation	NOUN
ejpam-6682	52	7	,	,	PUNCT
ejpam-6682	52	8	assuming	assume	VERB
ejpam-6682	52	9	that	that	SCONJ
ejpam-6682	52	10	disease	disease	NOUN
ejpam-6682	52	11	transmission	transmission	NOUN
ejpam-6682	52	12	occurs	occur	VERB
ejpam-6682	52	13	in	in	ADP
ejpam-6682	52	14	irregular	irregular	ADJ
ejpam-6682	52	15	patterns	pattern	NOUN
ejpam-6682	52	16	influenced	influence	VERB
ejpam-6682	52	17	by	by	ADP
ejpam-6682	52	18	population	population	NOUN
ejpam-6682	52	19	density	density	NOUN
ejpam-6682	52	20	and	and	CCONJ
ejpam-6682	52	21	vector	vector	NOUN
ejpam-6682	52	22	mobility	mobility	NOUN
ejpam-6682	52	23	.	.	PUNCT
ejpam-6682	53	1	expanding	expand	VERB
ejpam-6682	53	2	epidemiological	epidemiological	ADJ
ejpam-6682	53	3	modeling	modeling	NOUN
ejpam-6682	53	4	into	into	ADP
ejpam-6682	53	5	non	non	ADJ
ejpam-6682	53	6	-	-	ADJ
ejpam-6682	53	7	euclidean	euclidean	ADJ
ejpam-6682	53	8	space	space	NOUN
ejpam-6682	53	9	allows	allow	VERB
ejpam-6682	53	10	fractal	fractal	PROPN
ejpam-6682	53	11	r.	r.	PROPN
ejpam-6682	53	12	saadeh	saadeh	PROPN
ejpam-6682	53	13	et	et	PROPN
ejpam-6682	53	14	al	al	PROPN
ejpam-6682	53	15	.	.	PUNCT
ejpam-6682	53	16	/	/	SYM
ejpam-6682	53	17	eur	eur	PROPN
ejpam-6682	53	18	.	.	PUNCT
ejpam-6682	54	1	j.	j.	PROPN
ejpam-6682	54	2	pure	pure	PROPN
ejpam-6682	54	3	appl	appl	PROPN
ejpam-6682	54	4	.	.	PROPN
ejpam-6682	54	5	math	math	PROPN
ejpam-6682	54	6	,	,	PUNCT
ejpam-6682	54	7	18	18	NUM
ejpam-6682	54	8	(	(	PUNCT
ejpam-6682	54	9	4	4	NUM
ejpam-6682	54	10	)	)	PUNCT
ejpam-6682	54	11	(	(	PUNCT
ejpam-6682	54	12	2025	2025	NUM
ejpam-6682	54	13	)	)	PUNCT
ejpam-6682	54	14	,	,	PUNCT
ejpam-6682	54	15	6682	6682	NUM
ejpam-6682	54	16	3	3	NUM
ejpam-6682	54	17	of	of	ADP
ejpam-6682	54	18	21	21	NUM
ejpam-6682	54	19	models	model	NOUN
ejpam-6682	54	20	to	to	PART
ejpam-6682	54	21	represent	represent	VERB
ejpam-6682	54	22	disease	disease	NOUN
ejpam-6682	54	23	transmission	transmission	NOUN
ejpam-6682	54	24	in	in	ADP
ejpam-6682	54	25	complex	complex	ADJ
ejpam-6682	54	26	ecosystems	ecosystem	NOUN
ejpam-6682	54	27	accurately	accurately	ADV
ejpam-6682	54	28	[	[	X
ejpam-6682	54	29	24	24	NUM
ejpam-6682	54	30	]	]	PUNCT
ejpam-6682	54	31	.	.	PUNCT
ejpam-6682	55	1	fractal	fractal	PROPN
ejpam-6682	55	2	models	model	NOUN
ejpam-6682	55	3	improved	improve	VERB
ejpam-6682	55	4	epidemic	epidemic	NOUN
ejpam-6682	55	5	predictions	prediction	NOUN
ejpam-6682	55	6	,	,	PUNCT
ejpam-6682	55	7	particularly	particularly	ADV
ejpam-6682	55	8	in	in	ADP
ejpam-6682	55	9	densely	densely	ADV
ejpam-6682	55	10	populated	populated	ADJ
ejpam-6682	55	11	urban	urban	ADJ
ejpam-6682	55	12	areas	area	NOUN
ejpam-6682	55	13	where	where	SCONJ
ejpam-6682	55	14	human	human	ADJ
ejpam-6682	55	15	mobility	mobility	NOUN
ejpam-6682	55	16	and	and	CCONJ
ejpam-6682	55	17	clustering	clustering	NOUN
ejpam-6682	55	18	are	be	AUX
ejpam-6682	55	19	critical	critical	ADJ
ejpam-6682	55	20	elements	element	NOUN
ejpam-6682	55	21	in	in	ADP
ejpam-6682	55	22	disease	disease	NOUN
ejpam-6682	55	23	spread	spread	VERB
ejpam-6682	55	24	[	[	X
ejpam-6682	55	25	23	23	NUM
ejpam-6682	55	26	]	]	PUNCT
ejpam-6682	55	27	.	.	PUNCT
ejpam-6682	56	1	fractal	fractal	PROPN
ejpam-6682	56	2	surpassed	surpass	VERB
ejpam-6682	56	3	traditional	traditional	ADJ
ejpam-6682	56	4	models	model	NOUN
ejpam-6682	56	5	in	in	ADP
ejpam-6682	56	6	forecasting	forecasting	NOUN
ejpam-6682	56	7	infection	infection	NOUN
ejpam-6682	56	8	,	,	PUNCT
ejpam-6682	56	9	as	as	SCONJ
ejpam-6682	56	10	indicated	indicate	VERB
ejpam-6682	56	11	by	by	ADP
ejpam-6682	56	12	the	the	DET
ejpam-6682	56	13	study	study	NOUN
ejpam-6682	56	14	of	of	ADP
ejpam-6682	56	15	the	the	DET
ejpam-6682	56	16	influenza	influenza	NOUN
ejpam-6682	56	17	epidemic	epidemic	NOUN
ejpam-6682	56	18	that	that	PRON
ejpam-6682	56	19	showed	show	VERB
ejpam-6682	56	20	more	more	ADJ
ejpam-6682	56	21	congruence	congruence	NOUN
ejpam-6682	56	22	with	with	ADP
ejpam-6682	56	23	empirical	empirical	ADJ
ejpam-6682	56	24	data	datum	NOUN
ejpam-6682	56	25	[	[	X
ejpam-6682	56	26	25	25	NUM
ejpam-6682	56	27	]	]	PUNCT
ejpam-6682	56	28	.	.	PUNCT
ejpam-6682	57	1	the	the	DET
ejpam-6682	57	2	advantages	advantage	NOUN
ejpam-6682	57	3	of	of	ADP
ejpam-6682	57	4	each	each	DET
ejpam-6682	57	5	modelling	modelling	NOUN
ejpam-6682	57	6	technique	technique	NOUN
ejpam-6682	57	7	,	,	PUNCT
ejpam-6682	57	8	integer	integer	NOUN
ejpam-6682	57	9	,	,	PUNCT
ejpam-6682	57	10	fractional	fractional	ADJ
ejpam-6682	57	11	,	,	PUNCT
ejpam-6682	57	12	and	and	CCONJ
ejpam-6682	57	13	fractal	fractal	ADJ
ejpam-6682	57	14	,	,	PUNCT
ejpam-6682	57	15	are	be	AUX
ejpam-6682	57	16	distinct	distinct	ADJ
ejpam-6682	57	17	.	.	PUNCT
ejpam-6682	58	1	the	the	DET
ejpam-6682	58	2	integer	integer	NOUN
ejpam-6682	58	3	models	model	NOUN
ejpam-6682	58	4	give	give	VERB
ejpam-6682	58	5	a	a	DET
ejpam-6682	58	6	simple	simple	ADJ
ejpam-6682	58	7	and	and	CCONJ
ejpam-6682	58	8	practical	practical	ADJ
ejpam-6682	58	9	foundation	foundation	NOUN
ejpam-6682	58	10	,	,	PUNCT
ejpam-6682	58	11	whereas	whereas	SCONJ
ejpam-6682	58	12	fractional	fractional	ADJ
ejpam-6682	58	13	models	model	NOUN
ejpam-6682	58	14	increase	increase	VERB
ejpam-6682	58	15	accuracy	accuracy	NOUN
ejpam-6682	58	16	by	by	ADP
ejpam-6682	58	17	incorporating	incorporate	VERB
ejpam-6682	58	18	memory	memory	NOUN
ejpam-6682	58	19	effects	effect	NOUN
ejpam-6682	58	20	,	,	PUNCT
ejpam-6682	58	21	and	and	CCONJ
ejpam-6682	58	22	fractal	fractal	ADJ
ejpam-6682	58	23	models	model	NOUN
ejpam-6682	58	24	introduce	introduce	VERB
ejpam-6682	58	25	consciousness	consciousness	NOUN
ejpam-6682	58	26	to	to	PART
ejpam-6682	58	27	improve	improve	VERB
ejpam-6682	58	28	predictions	prediction	NOUN
ejpam-6682	58	29	[	[	X
ejpam-6682	58	30	26	26	NUM
ejpam-6682	58	31	]	]	PUNCT
ejpam-6682	58	32	.	.	PUNCT
ejpam-6682	59	1	due	due	ADP
ejpam-6682	59	2	to	to	ADP
ejpam-6682	59	3	these	these	DET
ejpam-6682	59	4	complementary	complementary	ADJ
ejpam-6682	59	5	qualities	quality	NOUN
ejpam-6682	59	6	,	,	PUNCT
ejpam-6682	59	7	there	there	PRON
ejpam-6682	59	8	is	be	VERB
ejpam-6682	59	9	an	an	DET
ejpam-6682	59	10	increasing	increase	VERB
ejpam-6682	59	11	interest	interest	NOUN
ejpam-6682	59	12	in	in	ADP
ejpam-6682	59	13	developing	develop	VERB
ejpam-6682	59	14	better	well	ADJ
ejpam-6682	59	15	and	and	CCONJ
ejpam-6682	59	16	more	more	ADV
ejpam-6682	59	17	flexible	flexible	ADJ
ejpam-6682	59	18	epidemiological	epidemiological	ADJ
ejpam-6682	59	19	models	model	NOUN
ejpam-6682	59	20	by	by	ADP
ejpam-6682	59	21	incorporating	incorporate	VERB
ejpam-6682	59	22	integer	integer	NOUN
ejpam-6682	59	23	,	,	PUNCT
ejpam-6682	59	24	fractional	fractional	ADJ
ejpam-6682	59	25	,	,	PUNCT
ejpam-6682	59	26	and	and	CCONJ
ejpam-6682	59	27	fractal	fractal	ADJ
ejpam-6682	59	28	components	component	NOUN
ejpam-6682	59	29	in	in	ADP
ejpam-6682	59	30	hybrid	hybrid	ADJ
ejpam-6682	59	31	modelling	modelling	NOUN
ejpam-6682	59	32	strategies	strategy	NOUN
ejpam-6682	59	33	.	.	PUNCT
ejpam-6682	60	1	in	in	ADP
ejpam-6682	60	2	this	this	DET
ejpam-6682	60	3	study	study	NOUN
ejpam-6682	60	4	,	,	PUNCT
ejpam-6682	60	5	we	we	PRON
ejpam-6682	60	6	aim	aim	VERB
ejpam-6682	60	7	to	to	PART
ejpam-6682	60	8	compare	compare	VERB
ejpam-6682	60	9	the	the	DET
ejpam-6682	60	10	performance	performance	NOUN
ejpam-6682	60	11	of	of	ADP
ejpam-6682	60	12	three	three	NUM
ejpam-6682	60	13	modelling	modelling	NOUN
ejpam-6682	60	14	approaches	approach	NOUN
ejpam-6682	60	15	in	in	ADP
ejpam-6682	60	16	forecasting	forecast	VERB
ejpam-6682	60	17	dengue	dengue	NOUN
ejpam-6682	60	18	fever	fever	NOUN
ejpam-6682	60	19	outbreaks	outbreak	NOUN
ejpam-6682	60	20	in	in	ADP
ejpam-6682	60	21	gedaref	gedaref	NOUN
ejpam-6682	60	22	,	,	PUNCT
ejpam-6682	60	23	sudan	sudan	PROPN
ejpam-6682	60	24	,	,	PUNCT
ejpam-6682	60	25	by	by	ADP
ejpam-6682	60	26	integrating	integrate	VERB
ejpam-6682	60	27	actual	actual	ADJ
ejpam-6682	60	28	epidemiological	epidemiological	ADJ
ejpam-6682	60	29	data	datum	NOUN
ejpam-6682	60	30	with	with	ADP
ejpam-6682	60	31	computational	computational	ADJ
ejpam-6682	60	32	approaches	approach	NOUN
ejpam-6682	60	33	to	to	PART
ejpam-6682	60	34	determine	determine	VERB
ejpam-6682	60	35	the	the	DET
ejpam-6682	60	36	most	most	ADV
ejpam-6682	60	37	accurate	accurate	ADJ
ejpam-6682	60	38	model	model	NOUN
ejpam-6682	60	39	.	.	PUNCT
ejpam-6682	61	1	specifically	specifically	ADV
ejpam-6682	61	2	,	,	PUNCT
ejpam-6682	61	3	we	we	PRON
ejpam-6682	61	4	explore	explore	VERB
ejpam-6682	61	5	how	how	SCONJ
ejpam-6682	61	6	the	the	DET
ejpam-6682	61	7	role	role	NOUN
ejpam-6682	61	8	of	of	ADP
ejpam-6682	61	9	memory	memory	NOUN
ejpam-6682	61	10	effects	effect	NOUN
ejpam-6682	61	11	in	in	ADP
ejpam-6682	61	12	fractional	fractional	ADJ
ejpam-6682	61	13	models	model	NOUN
ejpam-6682	61	14	and	and	CCONJ
ejpam-6682	61	15	spatial	spatial	ADJ
ejpam-6682	61	16	heterogeneity	heterogeneity	NOUN
ejpam-6682	61	17	in	in	ADP
ejpam-6682	61	18	fractal	fractal	ADJ
ejpam-6682	61	19	models	model	NOUN
ejpam-6682	61	20	influence	influence	NOUN
ejpam-6682	61	21	disease	disease	NOUN
ejpam-6682	61	22	transmission	transmission	NOUN
ejpam-6682	61	23	dynamics	dynamic	NOUN
ejpam-6682	61	24	and	and	CCONJ
ejpam-6682	61	25	outbreak	outbreak	NOUN
ejpam-6682	61	26	generation	generation	NOUN
ejpam-6682	61	27	.	.	PUNCT
ejpam-6682	62	1	furthermore	furthermore	ADV
ejpam-6682	62	2	,	,	PUNCT
ejpam-6682	62	3	the	the	DET
ejpam-6682	62	4	study	study	NOUN
ejpam-6682	62	5	assesses	assess	VERB
ejpam-6682	62	6	the	the	DET
ejpam-6682	62	7	predictability	predictability	NOUN
ejpam-6682	62	8	and	and	CCONJ
ejpam-6682	62	9	applicability	applicability	NOUN
ejpam-6682	62	10	of	of	ADP
ejpam-6682	62	11	integer	integer	NOUN
ejpam-6682	62	12	,	,	PUNCT
ejpam-6682	62	13	fractional	fractional	ADJ
ejpam-6682	62	14	,	,	PUNCT
ejpam-6682	62	15	and	and	CCONJ
ejpam-6682	62	16	fractal	fractal	ADJ
ejpam-6682	62	17	models	model	NOUN
ejpam-6682	62	18	in	in	ADP
ejpam-6682	62	19	enhancing	enhance	VERB
ejpam-6682	62	20	disease	disease	NOUN
ejpam-6682	62	21	control	control	NOUN
ejpam-6682	62	22	interventions	intervention	NOUN
ejpam-6682	62	23	.	.	PUNCT
ejpam-6682	63	1	this	this	DET
ejpam-6682	63	2	research	research	NOUN
ejpam-6682	63	3	has	have	VERB
ejpam-6682	63	4	six	six	NUM
ejpam-6682	63	5	chapters	chapter	NOUN
ejpam-6682	63	6	,	,	PUNCT
ejpam-6682	63	7	starting	start	VERB
ejpam-6682	63	8	with	with	ADP
ejpam-6682	63	9	the	the	DET
ejpam-6682	63	10	introduction	introduction	NOUN
ejpam-6682	63	11	,	,	PUNCT
ejpam-6682	63	12	which	which	PRON
ejpam-6682	63	13	discusses	discuss	VERB
ejpam-6682	63	14	dengue	dengue	NOUN
ejpam-6682	63	15	fever	fever	NOUN
ejpam-6682	63	16	and	and	CCONJ
ejpam-6682	63	17	its	its	PRON
ejpam-6682	63	18	public	public	ADJ
ejpam-6682	63	19	health	health	NOUN
ejpam-6682	63	20	impact	impact	NOUN
ejpam-6682	63	21	in	in	ADP
ejpam-6682	63	22	gedaref	gedaref	NOUN
ejpam-6682	63	23	,	,	PUNCT
ejpam-6682	63	24	sudan	sudan	PROPN
ejpam-6682	63	25	,	,	PUNCT
ejpam-6682	63	26	which	which	PRON
ejpam-6682	63	27	was	be	AUX
ejpam-6682	63	28	chosen	choose	VERB
ejpam-6682	63	29	for	for	ADP
ejpam-6682	63	30	the	the	DET
ejpam-6682	63	31	investigation	investigation	NOUN
ejpam-6682	63	32	.	.	PUNCT
ejpam-6682	64	1	in	in	ADP
ejpam-6682	64	2	the	the	DET
ejpam-6682	64	3	classical	classical	ADJ
ejpam-6682	64	4	describe	describe	NOUN
ejpam-6682	64	5	chapter	chapter	NOUN
ejpam-6682	64	6	,	,	PUNCT
ejpam-6682	64	7	integer	integer	NOUN
ejpam-6682	64	8	-	-	PUNCT
ejpam-6682	64	9	order	order	NOUN
ejpam-6682	64	10	differential	differential	ADJ
ejpam-6682	64	11	equations	equation	NOUN
ejpam-6682	64	12	have	have	AUX
ejpam-6682	64	13	been	be	AUX
ejpam-6682	64	14	utilized	utilize	VERB
ejpam-6682	64	15	to	to	PART
ejpam-6682	64	16	describe	describe	VERB
ejpam-6682	64	17	disease	disease	NOUN
ejpam-6682	64	18	transmission	transmission	NOUN
ejpam-6682	64	19	.	.	PUNCT
ejpam-6682	65	1	theoretical	theoretical	ADJ
ejpam-6682	65	2	analysis	analysis	NOUN
ejpam-6682	65	3	analyzes	analyze	VERB
ejpam-6682	65	4	the	the	DET
ejpam-6682	65	5	model	model	NOUN
ejpam-6682	65	6	’s	’s	PART
ejpam-6682	65	7	behaviour	behaviour	NOUN
ejpam-6682	65	8	and	and	CCONJ
ejpam-6682	65	9	stability	stability	NOUN
ejpam-6682	65	10	to	to	PART
ejpam-6682	65	11	understand	understand	VERB
ejpam-6682	65	12	the	the	DET
ejpam-6682	65	13	disease	disease	NOUN
ejpam-6682	65	14	’s	’s	PART
ejpam-6682	65	15	dynamics	dynamic	NOUN
ejpam-6682	65	16	.	.	PUNCT
ejpam-6682	66	1	the	the	DET
ejpam-6682	66	2	chapter	chapter	NOUN
ejpam-6682	66	3	on	on	ADP
ejpam-6682	66	4	fractional	fractional	ADJ
ejpam-6682	66	5	and	and	CCONJ
ejpam-6682	66	6	fractal	fractal	ADJ
ejpam-6682	66	7	models	model	NOUN
ejpam-6682	66	8	is	be	AUX
ejpam-6682	66	9	called	call	VERB
ejpam-6682	66	10	non	non	ADJ
ejpam-6682	66	11	-	-	ADJ
ejpam-6682	66	12	integer	integer	ADJ
ejpam-6682	66	13	calculus	calculus	NOUN
ejpam-6682	66	14	.	.	PUNCT
ejpam-6682	67	1	in	in	ADP
ejpam-6682	67	2	the	the	DET
ejpam-6682	67	3	discussion	discussion	NOUN
ejpam-6682	67	4	,	,	PUNCT
ejpam-6682	67	5	classical	classical	ADJ
ejpam-6682	67	6	,	,	PUNCT
ejpam-6682	67	7	fractional	fractional	ADJ
ejpam-6682	67	8	,	,	PUNCT
ejpam-6682	67	9	and	and	CCONJ
ejpam-6682	67	10	fractal	fractal	ADJ
ejpam-6682	67	11	models	model	NOUN
ejpam-6682	67	12	are	be	AUX
ejpam-6682	67	13	compared	compare	VERB
ejpam-6682	67	14	to	to	ADP
ejpam-6682	67	15	actual	actual	ADJ
ejpam-6682	67	16	data	datum	NOUN
ejpam-6682	67	17	.	.	PUNCT
ejpam-6682	68	1	finally	finally	ADV
ejpam-6682	68	2	,	,	PUNCT
ejpam-6682	68	3	the	the	DET
ejpam-6682	68	4	conclusion	conclusion	NOUN
ejpam-6682	68	5	summarises	summarise	VERB
ejpam-6682	68	6	key	key	ADJ
ejpam-6682	68	7	findings	finding	NOUN
ejpam-6682	68	8	and	and	CCONJ
ejpam-6682	68	9	emphasizes	emphasize	VERB
ejpam-6682	68	10	the	the	DET
ejpam-6682	68	11	importance	importance	NOUN
ejpam-6682	68	12	of	of	ADP
ejpam-6682	68	13	sophisticated	sophisticated	ADJ
ejpam-6682	68	14	modeling	modeling	NOUN
ejpam-6682	68	15	in	in	ADP
ejpam-6682	68	16	predicting	predict	VERB
ejpam-6682	68	17	illnesses	illness	NOUN
ejpam-6682	68	18	.	.	PUNCT
ejpam-6682	69	1	2	2	X
ejpam-6682	69	2	.	.	X
ejpam-6682	69	3	classical	classical	ADJ
ejpam-6682	69	4	model	model	NOUN
ejpam-6682	69	5	let	let	VERB
ejpam-6682	69	6	n1	n1	NOUN
ejpam-6682	69	7	and	and	CCONJ
ejpam-6682	69	8	n2	n2	PROPN
ejpam-6682	69	9	denote	denote	VERB
ejpam-6682	69	10	the	the	DET
ejpam-6682	69	11	total	total	ADJ
ejpam-6682	69	12	populations	population	NOUN
ejpam-6682	69	13	of	of	ADP
ejpam-6682	69	14	humans	human	NOUN
ejpam-6682	69	15	and	and	CCONJ
ejpam-6682	69	16	mosquitoes	mosquito	NOUN
ejpam-6682	69	17	,	,	PUNCT
ejpam-6682	69	18	respectively	respectively	ADV
ejpam-6682	69	19	.	.	PUNCT
ejpam-6682	70	1	dengue	dengue	NOUN
ejpam-6682	70	2	,	,	PUNCT
ejpam-6682	70	3	transmitted	transmit	VERB
ejpam-6682	70	4	by	by	ADP
ejpam-6682	70	5	aedes	aedes	PROPN
ejpam-6682	70	6	aegypti	aegypti	PROPN
ejpam-6682	70	7	,	,	PUNCT
ejpam-6682	70	8	has	have	VERB
ejpam-6682	70	9	four	four	NUM
ejpam-6682	70	10	distinct	distinct	ADJ
ejpam-6682	70	11	serotypes	serotype	NOUN
ejpam-6682	70	12	(	(	PUNCT
ejpam-6682	70	13	denv-1	denv-1	NUM
ejpam-6682	70	14	to	to	ADP
ejpam-6682	70	15	denv-4	denv-4	NUM
ejpam-6682	70	16	)	)	PUNCT
ejpam-6682	70	17	.	.	PUNCT
ejpam-6682	71	1	infection	infection	NOUN
ejpam-6682	71	2	grants	grant	NOUN
ejpam-6682	71	3	serotype	serotype	NOUN
ejpam-6682	71	4	-	-	PUNCT
ejpam-6682	71	5	specific	specific	NOUN
ejpam-6682	71	6	immunity	immunity	NOUN
ejpam-6682	71	7	,	,	PUNCT
ejpam-6682	71	8	but	but	CCONJ
ejpam-6682	71	9	reinfection	reinfection	NOUN
ejpam-6682	71	10	with	with	ADP
ejpam-6682	71	11	a	a	DET
ejpam-6682	71	12	different	different	ADJ
ejpam-6682	71	13	serotype	serotype	NOUN
ejpam-6682	71	14	increases	increase	VERB
ejpam-6682	71	15	the	the	DET
ejpam-6682	71	16	risk	risk	NOUN
ejpam-6682	71	17	of	of	ADP
ejpam-6682	71	18	severe	severe	ADJ
ejpam-6682	71	19	complications	complication	NOUN
ejpam-6682	71	20	due	due	ADJ
ejpam-6682	71	21	to	to	ADP
ejpam-6682	71	22	antibody	antibody	NOUN
ejpam-6682	71	23	-	-	PUNCT
ejpam-6682	71	24	dependent	dependent	ADJ
ejpam-6682	71	25	enhancement	enhancement	NOUN
ejpam-6682	71	26	(	(	PUNCT
ejpam-6682	71	27	ade	ade	PROPN
ejpam-6682	71	28	)	)	PUNCT
ejpam-6682	71	29	.	.	PUNCT
ejpam-6682	72	1	the	the	DET
ejpam-6682	72	2	human	human	ADJ
ejpam-6682	72	3	population	population	NOUN
ejpam-6682	72	4	is	be	AUX
ejpam-6682	72	5	divided	divide	VERB
ejpam-6682	72	6	into	into	ADP
ejpam-6682	72	7	:	:	PUNCT
ejpam-6682	72	8	s1	s1	NOUN
ejpam-6682	72	9	(	(	PUNCT
ejpam-6682	72	10	susceptible	susceptible	ADJ
ejpam-6682	72	11	)	)	PUNCT
ejpam-6682	72	12	,	,	PUNCT
ejpam-6682	72	13	i1	i1	PROPN
ejpam-6682	72	14	(	(	PUNCT
ejpam-6682	72	15	infected	infected	ADJ
ejpam-6682	72	16	and	and	CCONJ
ejpam-6682	72	17	infectious	infectious	ADJ
ejpam-6682	72	18	)	)	PUNCT
ejpam-6682	72	19	,	,	PUNCT
ejpam-6682	72	20	a1	a1	NOUN
ejpam-6682	72	21	(	(	PUNCT
ejpam-6682	72	22	partially	partially	ADV
ejpam-6682	72	23	immune	immune	ADJ
ejpam-6682	72	24	)	)	PUNCT
ejpam-6682	72	25	,	,	PUNCT
ejpam-6682	72	26	and	and	CCONJ
ejpam-6682	72	27	r1	r1	PROPN
ejpam-6682	72	28	(	(	PUNCT
ejpam-6682	72	29	fully	fully	ADV
ejpam-6682	72	30	immune	immune	ADJ
ejpam-6682	72	31	)	)	PUNCT
ejpam-6682	72	32	.	.	PUNCT
ejpam-6682	73	1	for	for	ADP
ejpam-6682	73	2	mosquitoes	mosquito	NOUN
ejpam-6682	73	3	:	:	PUNCT
ejpam-6682	73	4	s2	s2	NOUN
ejpam-6682	73	5	(	(	PUNCT
ejpam-6682	73	6	susceptible	susceptible	ADJ
ejpam-6682	73	7	)	)	PUNCT
ejpam-6682	73	8	and	and	CCONJ
ejpam-6682	73	9	i2	i2	PROPN
ejpam-6682	73	10	(	(	PUNCT
ejpam-6682	73	11	infected	infected	ADJ
ejpam-6682	73	12	and	and	CCONJ
ejpam-6682	73	13	infectious	infectious	ADJ
ejpam-6682	73	14	)	)	PUNCT
ejpam-6682	73	15	.	.	PUNCT
ejpam-6682	74	1	we	we	PRON
ejpam-6682	74	2	assume	assume	VERB
ejpam-6682	74	3	constant	constant	ADJ
ejpam-6682	74	4	total	total	ADJ
ejpam-6682	74	5	populations	population	NOUN
ejpam-6682	74	6	for	for	ADP
ejpam-6682	74	7	humans	human	NOUN
ejpam-6682	74	8	and	and	CCONJ
ejpam-6682	74	9	mosquitoes	mosquito	NOUN
ejpam-6682	74	10	,	,	PUNCT
ejpam-6682	74	11	i.e.	i.e.	X
ejpam-6682	74	12	,	,	PUNCT
ejpam-6682	74	13	n1	n1	ADJ
ejpam-6682	74	14	=	=	SYM
ejpam-6682	74	15	s1	s1	PROPN
ejpam-6682	74	16	+	+	CCONJ
ejpam-6682	74	17	i1	i1	PROPN
ejpam-6682	75	1	+	+	CCONJ
ejpam-6682	75	2	a1	a1	PROPN
ejpam-6682	75	3	+	+	SYM
ejpam-6682	75	4	r1	r1	NOUN
ejpam-6682	75	5	,	,	PUNCT
ejpam-6682	75	6	n2	n2	NOUN
ejpam-6682	75	7	=	=	PROPN
ejpam-6682	75	8	s2	s2	PROPN
ejpam-6682	75	9	+	+	CCONJ
ejpam-6682	75	10	i2	i2	PROPN
ejpam-6682	75	11	,	,	PUNCT
ejpam-6682	75	12	with	with	ADP
ejpam-6682	75	13	natural	natural	ADJ
ejpam-6682	75	14	births	birth	NOUN
ejpam-6682	75	15	balancing	balance	VERB
ejpam-6682	75	16	natural	natural	ADJ
ejpam-6682	75	17	deaths	death	NOUN
ejpam-6682	75	18	.	.	PUNCT
ejpam-6682	76	1	the	the	DET
ejpam-6682	76	2	parameters	parameter	NOUN
ejpam-6682	76	3	of	of	ADP
ejpam-6682	76	4	the	the	DET
ejpam-6682	76	5	model	model	NOUN
ejpam-6682	76	6	in	in	ADP
ejpam-6682	76	7	table	table	NOUN
ejpam-6682	76	8	(	(	PUNCT
ejpam-6682	76	9	1	1	NUM
ejpam-6682	76	10	)	)	PUNCT
ejpam-6682	76	11	and	and	CCONJ
ejpam-6682	76	12	figure((1	figure((1	NUM
ejpam-6682	76	13	)	)	PUNCT
ejpam-6682	76	14	)	)	PUNCT
ejpam-6682	76	15	.	.	PUNCT
ejpam-6682	77	1	the	the	DET
ejpam-6682	77	2	model	model	NOUN
ejpam-6682	77	3	equations	equation	NOUN
ejpam-6682	77	4	are	be	AUX
ejpam-6682	77	5	described	describe	VERB
ejpam-6682	77	6	below	below	ADP
ejpam-6682	77	7	,	,	PUNCT
ejpam-6682	77	8	where	where	SCONJ
ejpam-6682	77	9	β1	β1	PROPN
ejpam-6682	77	10	represents	represent	VERB
ejpam-6682	77	11	the	the	DET
ejpam-6682	77	12	transmission	transmission	NOUN
ejpam-6682	77	13	rate	rate	NOUN
ejpam-6682	77	14	at	at	ADP
ejpam-6682	77	15	which	which	PRON
ejpam-6682	77	16	an	an	DET
ejpam-6682	77	17	infected	infect	VERB
ejpam-6682	77	18	mosquito	mosquito	NOUN
ejpam-6682	77	19	infects	infect	NOUN
ejpam-6682	77	20	susceptible	susceptible	ADJ
ejpam-6682	77	21	humans	human	NOUN
ejpam-6682	77	22	.	.	PUNCT
ejpam-6682	78	1	r.	r.	PROPN
ejpam-6682	78	2	saadeh	saadeh	PROPN
ejpam-6682	78	3	et	et	PROPN
ejpam-6682	78	4	al	al	PROPN
ejpam-6682	78	5	.	.	PUNCT
ejpam-6682	78	6	/	/	SYM
ejpam-6682	78	7	eur	eur	PROPN
ejpam-6682	78	8	.	.	PUNCT
ejpam-6682	79	1	j.	j.	PROPN
ejpam-6682	79	2	pure	pure	PROPN
ejpam-6682	79	3	appl	appl	PROPN
ejpam-6682	79	4	.	.	PROPN
ejpam-6682	79	5	math	math	PROPN
ejpam-6682	79	6	,	,	PUNCT
ejpam-6682	79	7	18	18	NUM
ejpam-6682	79	8	(	(	PUNCT
ejpam-6682	79	9	4	4	NUM
ejpam-6682	79	10	)	)	PUNCT
ejpam-6682	79	11	(	(	PUNCT
ejpam-6682	79	12	2025	2025	NUM
ejpam-6682	79	13	)	)	PUNCT
ejpam-6682	79	14	,	,	PUNCT
ejpam-6682	79	15	6682	6682	NUM
ejpam-6682	79	16	4	4	NUM
ejpam-6682	79	17	of	of	ADP
ejpam-6682	79	18	21	21	NUM
ejpam-6682	79	19	ds1	ds1	NOUN
ejpam-6682	79	20	dt	dt	NOUN
ejpam-6682	80	1	=	=	PUNCT
ejpam-6682	80	2	µ1n1	µ1n1	PRON
ejpam-6682	80	3	−	−	PUNCT
ejpam-6682	80	4	β1	β1	PROPN
ejpam-6682	80	5	s1i2	s1i2	INTJ
ejpam-6682	80	6	n1	n1	PROPN
ejpam-6682	80	7	−	−	PROPN
ejpam-6682	80	8	µ1s1	µ1s1	NOUN
ejpam-6682	80	9	,	,	PUNCT
ejpam-6682	80	10	di1	di1	INTJ
ejpam-6682	80	11	dt	dt	NOUN
ejpam-6682	80	12	=	=	PUNCT
ejpam-6682	80	13	β1i2	β1i2	PUNCT
ejpam-6682	80	14	n1	n1	PROPN
ejpam-6682	80	15	s1	s1	NOUN
ejpam-6682	80	16	+	+	CCONJ
ejpam-6682	80	17	δ1a1	δ1a1	NOUN
ejpam-6682	80	18	−	−	PROPN
ejpam-6682	80	19	(	(	PUNCT
ejpam-6682	80	20	µ1	µ1	PROPN
ejpam-6682	80	21	+	+	CCONJ
ejpam-6682	80	22	γ)i1	γ)i1	PROPN
ejpam-6682	80	23	,	,	PUNCT
ejpam-6682	80	24	da1	da1	PROPN
ejpam-6682	80	25	dt	dt	AUX
ejpam-6682	81	1	=	=	PUNCT
ejpam-6682	81	2	pγi1	pγi1	NOUN
ejpam-6682	81	3	−	−	PROPN
ejpam-6682	82	1	(	(	PUNCT
ejpam-6682	82	2	µ1	µ1	PROPN
ejpam-6682	82	3	+	+	X
ejpam-6682	82	4	δ1)a1	δ1)a1	PROPN
ejpam-6682	82	5	,	,	PUNCT
ejpam-6682	82	6	dr1	dr1	PROPN
ejpam-6682	82	7	dt	dt	NOUN
ejpam-6682	83	1	=	=	PUNCT
ejpam-6682	83	2	(	(	PUNCT
ejpam-6682	83	3	1−	1−	NUM
ejpam-6682	83	4	p)γi1	p)γi1	NOUN
ejpam-6682	83	5	−	−	NOUN
ejpam-6682	83	6	µ1r1	µ1r1	NOUN
ejpam-6682	83	7	.	.	PUNCT
ejpam-6682	83	8	ds2	ds2	PROPN
ejpam-6682	83	9	dt	dt	X
ejpam-6682	84	1	=	=	PUNCT
ejpam-6682	84	2	µ2n2	µ2n2	NOUN
ejpam-6682	84	3	−	−	NOUN
ejpam-6682	84	4	β2	β2	ADJ
ejpam-6682	84	5	s2i1	s2i1	CCONJ
ejpam-6682	84	6	n1	n1	NOUN
ejpam-6682	84	7	−	−	PROPN
ejpam-6682	84	8	µ2s2	µ2s2	PROPN
ejpam-6682	84	9	,	,	PUNCT
ejpam-6682	84	10	di2	di2	PROPN
ejpam-6682	84	11	dt	dt	PROPN
ejpam-6682	85	1	=	=	SYM
ejpam-6682	85	2	β2	β2	VERB
ejpam-6682	85	3	s2i1	s2i1	PROPN
ejpam-6682	85	4	n1	n1	NOUN
ejpam-6682	85	5	−	−	NUM
ejpam-6682	85	6	µ2i2	µ2i2	X
ejpam-6682	85	7	.	.	PUNCT
ejpam-6682	86	1	(	(	PUNCT
ejpam-6682	86	2	1	1	X
ejpam-6682	86	3	)	)	PUNCT
ejpam-6682	86	4	system	system	NOUN
ejpam-6682	86	5	(	(	PUNCT
ejpam-6682	86	6	1	1	X
ejpam-6682	86	7	)	)	PUNCT
ejpam-6682	86	8	is	be	AUX
ejpam-6682	86	9	naturally	naturally	ADV
ejpam-6682	86	10	appended	append	VERB
ejpam-6682	86	11	with	with	ADP
ejpam-6682	86	12	initial	initial	ADJ
ejpam-6682	86	13	conditions	condition	NOUN
ejpam-6682	86	14	:	:	PUNCT
ejpam-6682	86	15	s1(0	s1(0	PROPN
ejpam-6682	86	16	)	)	PUNCT
ejpam-6682	86	17	=	=	SYM
ejpam-6682	86	18	n1−i1(0)−a1(0)−r1(0	n1−i1(0)−a1(0)−r1(0	PROPN
ejpam-6682	86	19	)	)	PUNCT
ejpam-6682	86	20	,	,	PUNCT
ejpam-6682	86	21	i1(0	i1(0	PROPN
ejpam-6682	86	22	)	)	PUNCT
ejpam-6682	86	23	=	=	SYM
ejpam-6682	86	24	8	8	NUM
ejpam-6682	86	25	,	,	PUNCT
ejpam-6682	86	26	a1(0	a1(0	PROPN
ejpam-6682	86	27	)	)	PUNCT
ejpam-6682	86	28	=	=	SYM
ejpam-6682	87	1	0	0	NUM
ejpam-6682	87	2	,	,	PUNCT
ejpam-6682	87	3	r1(0	r1(0	PROPN
ejpam-6682	87	4	)	)	PUNCT
ejpam-6682	87	5	=	=	SYM
ejpam-6682	87	6	0	0	NUM
ejpam-6682	87	7	,	,	PUNCT
ejpam-6682	87	8	s2(0	s2(0	NOUN
ejpam-6682	87	9	)	)	PUNCT
ejpam-6682	87	10	=	=	PUNCT
ejpam-6682	87	11	n2−i2(0	n2−i2(0	NOUN
ejpam-6682	87	12	)	)	PUNCT
ejpam-6682	87	13	,	,	PUNCT
ejpam-6682	87	14	i2(0	i2(0	NOUN
ejpam-6682	87	15	)	)	PUNCT
ejpam-6682	87	16	=	=	PUNCT
ejpam-6682	88	1	10	10	NUM
ejpam-6682	88	2	.	.	PUNCT
ejpam-6682	89	1	figure	figure	NOUN
ejpam-6682	89	2	1	1	NUM
ejpam-6682	89	3	:	:	PUNCT
ejpam-6682	89	4	enhanced	enhance	VERB
ejpam-6682	89	5	schematic	schematic	ADJ
ejpam-6682	89	6	of	of	ADP
ejpam-6682	89	7	dengue	dengue	NOUN
ejpam-6682	89	8	transmission	transmission	NOUN
ejpam-6682	89	9	dynamics	dynamic	NOUN
ejpam-6682	89	10	.	.	PUNCT
ejpam-6682	90	1	r.	r.	PROPN
ejpam-6682	90	2	saadeh	saadeh	PROPN
ejpam-6682	90	3	et	et	PROPN
ejpam-6682	90	4	al	al	PROPN
ejpam-6682	90	5	.	.	PUNCT
ejpam-6682	90	6	/	/	SYM
ejpam-6682	90	7	eur	eur	PROPN
ejpam-6682	90	8	.	.	PUNCT
ejpam-6682	91	1	j.	j.	PROPN
ejpam-6682	91	2	pure	pure	PROPN
ejpam-6682	91	3	appl	appl	PROPN
ejpam-6682	91	4	.	.	PROPN
ejpam-6682	91	5	math	math	PROPN
ejpam-6682	91	6	,	,	PUNCT
ejpam-6682	91	7	18	18	NUM
ejpam-6682	91	8	(	(	PUNCT
ejpam-6682	91	9	4	4	NUM
ejpam-6682	91	10	)	)	PUNCT
ejpam-6682	91	11	(	(	PUNCT
ejpam-6682	91	12	2025	2025	NUM
ejpam-6682	91	13	)	)	PUNCT
ejpam-6682	91	14	,	,	PUNCT
ejpam-6682	91	15	6682	6682	NUM
ejpam-6682	91	16	5	5	NUM
ejpam-6682	91	17	of	of	ADP
ejpam-6682	91	18	21	21	NUM
ejpam-6682	91	19	table	table	NOUN
ejpam-6682	91	20	1	1	NUM
ejpam-6682	91	21	:	:	PUNCT
ejpam-6682	91	22	model	model	NOUN
ejpam-6682	91	23	parameters	parameter	NOUN
ejpam-6682	91	24	,	,	PUNCT
ejpam-6682	91	25	values	value	NOUN
ejpam-6682	91	26	,	,	PUNCT
ejpam-6682	91	27	and	and	CCONJ
ejpam-6682	91	28	sources	source	NOUN
ejpam-6682	91	29	.	.	PUNCT
ejpam-6682	92	1	parameter	parameter	PROPN
ejpam-6682	92	2	interpretation	interpretation	NOUN
ejpam-6682	92	3	value	value	NOUN
ejpam-6682	92	4	source	source	NOUN
ejpam-6682	92	5	µ1	µ1	NOUN
ejpam-6682	92	6	birth	birth	NOUN
ejpam-6682	92	7	/	/	SYM
ejpam-6682	92	8	death	death	NOUN
ejpam-6682	92	9	rate	rate	NOUN
ejpam-6682	92	10	(	(	PUNCT
ejpam-6682	92	11	humans	human	NOUN
ejpam-6682	92	12	)	)	PUNCT
ejpam-6682	92	13	.	.	PUNCT
ejpam-6682	93	1	0.0000391	0.0000391	NUM
ejpam-6682	93	2	fixed	fix	VERB
ejpam-6682	93	3	µ2	µ2	PROPN
ejpam-6682	93	4	birth	birth	NOUN
ejpam-6682	93	5	/	/	SYM
ejpam-6682	93	6	death	death	NOUN
ejpam-6682	93	7	rate	rate	NOUN
ejpam-6682	93	8	(	(	PUNCT
ejpam-6682	93	9	mosquitoes	mosquito	NOUN
ejpam-6682	93	10	)	)	PUNCT
ejpam-6682	93	11	.	.	PUNCT
ejpam-6682	94	1	0.1	0.1	NUM
ejpam-6682	94	2	fixed	fix	VERB
ejpam-6682	94	3	β1	β1	PROPN
ejpam-6682	94	4	mosquito	mosquito	NOUN
ejpam-6682	94	5	to	to	ADP
ejpam-6682	94	6	human	human	ADJ
ejpam-6682	94	7	transmission	transmission	NOUN
ejpam-6682	94	8	rate	rate	NOUN
ejpam-6682	94	9	.	.	PUNCT
ejpam-6682	95	1	0.1003	0.1003	NUM
ejpam-6682	95	2	fitted	fit	VERB
ejpam-6682	95	3	β2	β2	NOUN
ejpam-6682	95	4	human	human	ADJ
ejpam-6682	95	5	to	to	AUX
ejpam-6682	95	6	mosquito	mosquito	VERB
ejpam-6682	95	7	transmission	transmission	NOUN
ejpam-6682	95	8	rate	rate	NOUN
ejpam-6682	95	9	.	.	PUNCT
ejpam-6682	96	1	0.1001	0.1001	NUM
ejpam-6682	96	2	fitted	fit	VERB
ejpam-6682	96	3	γ	γ	PROPN
ejpam-6682	96	4	human	human	ADJ
ejpam-6682	96	5	recovery	recovery	NOUN
ejpam-6682	96	6	rate	rate	NOUN
ejpam-6682	96	7	.	.	PUNCT
ejpam-6682	97	1	0.2101	0.2101	NUM
ejpam-6682	97	2	fitted	fit	VERB
ejpam-6682	97	3	p	p	NOUN
ejpam-6682	97	4	proportion	proportion	NOUN
ejpam-6682	97	5	of	of	ADP
ejpam-6682	97	6	partial	partial	ADJ
ejpam-6682	97	7	immunity	immunity	NOUN
ejpam-6682	97	8	.	.	PUNCT
ejpam-6682	98	1	0.8452	0.8452	NUM
ejpam-6682	98	2	fitted	fit	VERB
ejpam-6682	98	3	δ1	δ1	NOUN
ejpam-6682	98	4	reinfection	reinfection	NOUN
ejpam-6682	98	5	rate	rate	NOUN
ejpam-6682	98	6	.	.	PUNCT
ejpam-6682	99	1	0.0250	0.0250	NUM
ejpam-6682	99	2	fitted	fit	VERB
ejpam-6682	99	3	n1	n1	ADJ
ejpam-6682	99	4	total	total	ADJ
ejpam-6682	99	5	humans	human	NOUN
ejpam-6682	99	6	.	.	PUNCT
ejpam-6682	100	1	2,208,385	2,208,385	NUM
ejpam-6682	100	2	fixed	fix	VERB
ejpam-6682	100	3	n2	n2	ADJ
ejpam-6682	100	4	total	total	ADJ
ejpam-6682	100	5	mosquitoes	mosquito	NOUN
ejpam-6682	100	6	.	.	PUNCT
ejpam-6682	101	1	3.5×n1	3.5×n1	NOUN
ejpam-6682	101	2	assumed	assume	VERB
ejpam-6682	101	3	precise	precise	ADJ
ejpam-6682	101	4	estimation	estimation	NOUN
ejpam-6682	101	5	of	of	ADP
ejpam-6682	101	6	model	model	NOUN
ejpam-6682	101	7	parameters	parameter	NOUN
ejpam-6682	101	8	is	be	AUX
ejpam-6682	101	9	crucial	crucial	ADJ
ejpam-6682	101	10	for	for	ADP
ejpam-6682	101	11	adequately	adequately	ADV
ejpam-6682	101	12	delineating	delineate	VERB
ejpam-6682	101	13	dengue	dengue	NOUN
ejpam-6682	101	14	transmission	transmission	NOUN
ejpam-6682	101	15	patterns	pattern	NOUN
ejpam-6682	101	16	and	and	CCONJ
ejpam-6682	101	17	forecasting	forecasting	NOUN
ejpam-6682	101	18	capacities	capacity	NOUN
ejpam-6682	101	19	.	.	PUNCT
ejpam-6682	102	1	this	this	DET
ejpam-6682	102	2	study	study	NOUN
ejpam-6682	102	3	applied	apply	VERB
ejpam-6682	102	4	the	the	DET
ejpam-6682	102	5	markov	markov	NOUN
ejpam-6682	102	6	chain	chain	NOUN
ejpam-6682	102	7	monte	monte	PROPN
ejpam-6682	102	8	carlo	carlo	PROPN
ejpam-6682	102	9	(	(	PUNCT
ejpam-6682	102	10	mcmc	mcmc	PROPN
ejpam-6682	102	11	)	)	PUNCT
ejpam-6682	102	12	technique	technique	NOUN
ejpam-6682	102	13	[	[	X
ejpam-6682	102	14	27	27	NUM
ejpam-6682	102	15	,	,	PUNCT
ejpam-6682	102	16	28	28	NUM
ejpam-6682	102	17	]	]	PUNCT
ejpam-6682	102	18	to	to	PART
ejpam-6682	102	19	estimate	estimate	VERB
ejpam-6682	102	20	parameter	parameter	NOUN
ejpam-6682	102	21	values	value	NOUN
ejpam-6682	102	22	derived	derive	VERB
ejpam-6682	102	23	from	from	ADP
ejpam-6682	102	24	daily	daily	ADJ
ejpam-6682	102	25	data	datum	NOUN
ejpam-6682	102	26	about	about	ADP
ejpam-6682	102	27	the	the	DET
ejpam-6682	102	28	dengue	dengue	NOUN
ejpam-6682	102	29	outbreak	outbreak	NOUN
ejpam-6682	102	30	in	in	ADP
ejpam-6682	102	31	gedaref	gedaref	NOUN
ejpam-6682	102	32	state	state	NOUN
ejpam-6682	102	33	,	,	PUNCT
ejpam-6682	102	34	eastern	eastern	PROPN
ejpam-6682	102	35	sudan	sudan	PROPN
ejpam-6682	102	36	,	,	PUNCT
ejpam-6682	102	37	reported	report	VERB
ejpam-6682	102	38	in	in	ADP
ejpam-6682	102	39	2023	2023	NUM
ejpam-6682	102	40	.	.	PUNCT
ejpam-6682	103	1	the	the	DET
ejpam-6682	103	2	data	datum	NOUN
ejpam-6682	103	3	were	be	AUX
ejpam-6682	103	4	obtained	obtain	VERB
ejpam-6682	103	5	from	from	ADP
ejpam-6682	103	6	the	the	DET
ejpam-6682	103	7	reports	report	NOUN
ejpam-6682	103	8	of	of	ADP
ejpam-6682	103	9	the	the	DET
ejpam-6682	103	10	ministry	ministry	PROPN
ejpam-6682	103	11	of	of	ADP
ejpam-6682	103	12	health	health	PROPN
ejpam-6682	103	13	in	in	ADP
ejpam-6682	103	14	gedaref	gedaref	NOUN
ejpam-6682	103	15	state	state	NOUN
ejpam-6682	103	16	,	,	PUNCT
ejpam-6682	103	17	sudan	sudan	PROPN
ejpam-6682	103	18	.	.	PUNCT
ejpam-6682	104	1	the	the	DET
ejpam-6682	104	2	use	use	NOUN
ejpam-6682	104	3	of	of	ADP
ejpam-6682	104	4	mcmc	mcmc	PROPN
ejpam-6682	104	5	provides	provide	VERB
ejpam-6682	104	6	excellent	excellent	ADJ
ejpam-6682	104	7	accuracy	accuracy	NOUN
ejpam-6682	104	8	in	in	ADP
ejpam-6682	104	9	obtaining	obtain	VERB
ejpam-6682	104	10	parameter	parameter	NOUN
ejpam-6682	104	11	values	value	NOUN
ejpam-6682	104	12	,	,	PUNCT
ejpam-6682	104	13	enabling	enable	VERB
ejpam-6682	104	14	a	a	DET
ejpam-6682	104	15	more	more	ADV
ejpam-6682	104	16	reliable	reliable	ADJ
ejpam-6682	104	17	assessment	assessment	NOUN
ejpam-6682	104	18	of	of	ADP
ejpam-6682	104	19	dengue	dengue	NOUN
ejpam-6682	104	20	management	management	NOUN
ejpam-6682	104	21	efforts	effort	NOUN
ejpam-6682	104	22	.	.	PUNCT
ejpam-6682	105	1	table	table	NOUN
ejpam-6682	105	2	1	1	NUM
ejpam-6682	105	3	presents	present	VERB
ejpam-6682	105	4	the	the	DET
ejpam-6682	105	5	estimated	estimate	VERB
ejpam-6682	105	6	values	value	NOUN
ejpam-6682	105	7	.	.	PUNCT
ejpam-6682	106	1	3	3	X
ejpam-6682	106	2	.	.	X
ejpam-6682	106	3	analysis	analysis	NOUN
ejpam-6682	106	4	of	of	ADP
ejpam-6682	106	5	model	model	NOUN
ejpam-6682	106	6	in	in	ADP
ejpam-6682	106	7	this	this	DET
ejpam-6682	106	8	part	part	NOUN
ejpam-6682	106	9	,	,	PUNCT
ejpam-6682	106	10	we	we	PRON
ejpam-6682	106	11	verify	verify	VERB
ejpam-6682	106	12	that	that	SCONJ
ejpam-6682	106	13	all	all	DET
ejpam-6682	106	14	state	state	NOUN
ejpam-6682	106	15	variables	variable	NOUN
ejpam-6682	106	16	are	be	AUX
ejpam-6682	106	17	nonnegative	nonnegative	ADJ
ejpam-6682	106	18	and	and	CCONJ
ejpam-6682	106	19	bounded	bound	VERB
ejpam-6682	106	20	for	for	ADP
ejpam-6682	106	21	all	all	DET
ejpam-6682	106	22	time	time	NOUN
ejpam-6682	106	23	.	.	PUNCT
ejpam-6682	107	1	we	we	PRON
ejpam-6682	107	2	also	also	ADV
ejpam-6682	107	3	obtain	obtain	VERB
ejpam-6682	107	4	the	the	DET
ejpam-6682	107	5	model	model	NOUN
ejpam-6682	107	6	equilibrium	equilibrium	NOUN
ejpam-6682	107	7	points	point	NOUN
ejpam-6682	107	8	and	and	CCONJ
ejpam-6682	107	9	compute	compute	VERB
ejpam-6682	107	10	the	the	DET
ejpam-6682	107	11	basic	basic	ADJ
ejpam-6682	107	12	reproduction	reproduction	NOUN
ejpam-6682	107	13	number	number	NOUN
ejpam-6682	107	14	.	.	PUNCT
ejpam-6682	108	1	further	far	ADV
ejpam-6682	108	2	,	,	PUNCT
ejpam-6682	108	3	we	we	PRON
ejpam-6682	108	4	explore	explore	VERB
ejpam-6682	108	5	bifurcation	bifurcation	NOUN
ejpam-6682	108	6	and	and	CCONJ
ejpam-6682	108	7	stability	stability	NOUN
ejpam-6682	108	8	properties	property	NOUN
ejpam-6682	108	9	.	.	PUNCT
ejpam-6682	109	1	3.1	3.1	NUM
ejpam-6682	109	2	.	.	PUNCT
ejpam-6682	109	3	model	model	PROPN
ejpam-6682	109	4	non	non	ADJ
ejpam-6682	109	5	-	-	ADJ
ejpam-6682	109	6	negativity	negativity	ADJ
ejpam-6682	109	7	and	and	CCONJ
ejpam-6682	109	8	boundedness	boundedness	NOUN
ejpam-6682	109	9	proposition	proposition	NOUN
ejpam-6682	109	10	1	1	NUM
ejpam-6682	109	11	.	.	PUNCT
ejpam-6682	110	1	let	let	VERB
ejpam-6682	110	2	s1,0	s1,0	PROPN
ejpam-6682	110	3	,	,	PUNCT
ejpam-6682	110	4	i1,0	i1,0	PROPN
ejpam-6682	110	5	,	,	PUNCT
ejpam-6682	110	6	a1,0	a1,0	PROPN
ejpam-6682	110	7	,	,	PUNCT
ejpam-6682	110	8	r1,0	r1,0	PROPN
ejpam-6682	110	9	,	,	PUNCT
ejpam-6682	110	10	s2,0	s2,0	PROPN
ejpam-6682	110	11	,	,	PUNCT
ejpam-6682	110	12	i2,0	i2,0	NOUN
ejpam-6682	110	13	be	be	AUX
ejpam-6682	110	14	non	non	ADJ
ejpam-6682	110	15	-	-	ADJ
ejpam-6682	110	16	negative	negative	ADJ
ejpam-6682	110	17	initial	initial	ADJ
ejpam-6682	110	18	conditions	condition	NOUN
ejpam-6682	110	19	.	.	PUNCT
ejpam-6682	111	1	then	then	ADV
ejpam-6682	111	2	the	the	DET
ejpam-6682	111	3	solution	solution	NOUN
ejpam-6682	111	4	of	of	ADP
ejpam-6682	111	5	(	(	PUNCT
ejpam-6682	111	6	1	1	NUM
ejpam-6682	111	7	)	)	PUNCT
ejpam-6682	111	8	is	be	AUX
ejpam-6682	111	9	non	non	ADJ
ejpam-6682	111	10	-	-	ADJ
ejpam-6682	111	11	negative	negative	ADJ
ejpam-6682	111	12	for	for	ADP
ejpam-6682	111	13	all	all	DET
ejpam-6682	111	14	t	t	PROPN
ejpam-6682	111	15	≥	≥	NOUN
ejpam-6682	111	16	0	0	NUM
ejpam-6682	111	17	.	.	PUNCT
ejpam-6682	112	1	proof	proof	NOUN
ejpam-6682	112	2	.	.	PUNCT
ejpam-6682	113	1	for	for	ADP
ejpam-6682	113	2	y	y	PROPN
ejpam-6682	113	3	∈	∈	PROPN
ejpam-6682	113	4	{	{	PUNCT
ejpam-6682	113	5	s1	s1	PROPN
ejpam-6682	113	6	,	,	PUNCT
ejpam-6682	113	7	i1	i1	PROPN
ejpam-6682	113	8	,	,	PUNCT
ejpam-6682	113	9	a1	a1	PROPN
ejpam-6682	113	10	,	,	PUNCT
ejpam-6682	113	11	r1	r1	NOUN
ejpam-6682	113	12	,	,	PUNCT
ejpam-6682	113	13	s2	s2	PROPN
ejpam-6682	113	14	,	,	PUNCT
ejpam-6682	113	15	i2	i2	PROPN
ejpam-6682	113	16	}	}	PUNCT
ejpam-6682	113	17	,	,	PUNCT
ejpam-6682	113	18	dy	dy	X
ejpam-6682	113	19	dt	dt	NOUN
ejpam-6682	113	20	∣∣∣	∣∣∣	NOUN
ejpam-6682	113	21	y=0	y=0	X
ejpam-6682	113	22	≥	≥	NOUN
ejpam-6682	113	23	0	0	NUM
ejpam-6682	113	24	ensures	ensure	VERB
ejpam-6682	113	25	non	non	ADJ
ejpam-6682	113	26	-	-	ADJ
ejpam-6682	113	27	negativity	negativity	ADJ
ejpam-6682	113	28	.	.	PUNCT
ejpam-6682	114	1	proposition	proposition	NOUN
ejpam-6682	114	2	2	2	NUM
ejpam-6682	114	3	.	.	PUNCT
ejpam-6682	115	1	the	the	DET
ejpam-6682	115	2	solution	solution	NOUN
ejpam-6682	115	3	of	of	ADP
ejpam-6682	115	4	(	(	PUNCT
ejpam-6682	115	5	1	1	NUM
ejpam-6682	115	6	)	)	PUNCT
ejpam-6682	115	7	is	be	AUX
ejpam-6682	115	8	bounded	bound	VERB
ejpam-6682	115	9	for	for	ADP
ejpam-6682	115	10	all	all	DET
ejpam-6682	115	11	t.	t.	PROPN
ejpam-6682	115	12	r.	r.	PROPN
ejpam-6682	115	13	saadeh	saadeh	PROPN
ejpam-6682	115	14	et	et	PROPN
ejpam-6682	115	15	al	al	PROPN
ejpam-6682	115	16	.	.	PUNCT
ejpam-6682	115	17	/	/	SYM
ejpam-6682	115	18	eur	eur	PROPN
ejpam-6682	115	19	.	.	PUNCT
ejpam-6682	116	1	j.	j.	PROPN
ejpam-6682	116	2	pure	pure	PROPN
ejpam-6682	116	3	appl	appl	PROPN
ejpam-6682	116	4	.	.	PROPN
ejpam-6682	116	5	math	math	PROPN
ejpam-6682	116	6	,	,	PUNCT
ejpam-6682	116	7	18	18	NUM
ejpam-6682	116	8	(	(	PUNCT
ejpam-6682	116	9	4	4	NUM
ejpam-6682	116	10	)	)	PUNCT
ejpam-6682	116	11	(	(	PUNCT
ejpam-6682	116	12	2025	2025	NUM
ejpam-6682	116	13	)	)	PUNCT
ejpam-6682	116	14	,	,	PUNCT
ejpam-6682	116	15	6682	6682	NUM
ejpam-6682	116	16	6	6	NUM
ejpam-6682	116	17	of	of	ADP
ejpam-6682	116	18	21	21	NUM
ejpam-6682	116	19	proof	proof	NOUN
ejpam-6682	116	20	.	.	PUNCT
ejpam-6682	117	1	if	if	SCONJ
ejpam-6682	117	2	n1	n1	PROPN
ejpam-6682	117	3	and	and	CCONJ
ejpam-6682	117	4	n2	n2	PROPN
ejpam-6682	117	5	are	be	AUX
ejpam-6682	117	6	bounded	bound	VERB
ejpam-6682	117	7	,	,	PUNCT
ejpam-6682	117	8	all	all	DET
ejpam-6682	117	9	state	state	NOUN
ejpam-6682	117	10	variables	variable	NOUN
ejpam-6682	117	11	remain	remain	VERB
ejpam-6682	117	12	bounded	bound	VERB
ejpam-6682	117	13	.	.	PUNCT
ejpam-6682	118	1	thus	thus	ADV
ejpam-6682	118	2	,	,	PUNCT
ejpam-6682	118	3	system	system	NOUN
ejpam-6682	118	4	(	(	PUNCT
ejpam-6682	118	5	1	1	X
ejpam-6682	118	6	)	)	PUNCT
ejpam-6682	118	7	remains	remain	VERB
ejpam-6682	118	8	in	in	ADP
ejpam-6682	118	9	the	the	DET
ejpam-6682	118	10	compact	compact	ADJ
ejpam-6682	118	11	biologically	biologically	ADV
ejpam-6682	118	12	feasible	feasible	ADJ
ejpam-6682	118	13	set	set	NOUN
ejpam-6682	118	14	:	:	PUNCT
ejpam-6682	118	15	ω	ω	NUM
ejpam-6682	118	16	=	=	SYM
ejpam-6682	118	17	{	{	PUNCT
ejpam-6682	118	18	(	(	PUNCT
ejpam-6682	118	19	s1(t	s1(t	NOUN
ejpam-6682	118	20	)	)	PUNCT
ejpam-6682	118	21	,	,	PUNCT
ejpam-6682	118	22	i1(t	i1(t	PROPN
ejpam-6682	118	23	)	)	PUNCT
ejpam-6682	118	24	,	,	PUNCT
ejpam-6682	118	25	a1(t	a1(t	PROPN
ejpam-6682	118	26	)	)	PUNCT
ejpam-6682	118	27	,	,	PUNCT
ejpam-6682	118	28	r1(t	r1(t	PROPN
ejpam-6682	118	29	)	)	PUNCT
ejpam-6682	118	30	,	,	PUNCT
ejpam-6682	118	31	s2(t	s2(t	PROPN
ejpam-6682	118	32	)	)	PUNCT
ejpam-6682	118	33	,	,	PUNCT
ejpam-6682	118	34	i2(t	i2(t	NOUN
ejpam-6682	118	35	)	)	PUNCT
ejpam-6682	118	36	)	)	PUNCT
ejpam-6682	119	1	⊂	⊂	PROPN
ejpam-6682	119	2	r6	r6	NOUN
ejpam-6682	119	3	+	+	CCONJ
ejpam-6682	119	4	:	:	PUNCT
ejpam-6682	119	5	n1(t	n1(t	X
ejpam-6682	119	6	)	)	PUNCT
ejpam-6682	119	7	+	+	NOUN
ejpam-6682	119	8	n2(t	n2(t	NOUN
ejpam-6682	119	9	)	)	PUNCT
ejpam-6682	119	10	=	=	PUNCT
ejpam-6682	120	1	n1,0	n1,0	NOUN
ejpam-6682	120	2	+	+	PROPN
ejpam-6682	120	3	n2,0	n2,0	PROPN
ejpam-6682	120	4	}	}	PUNCT
ejpam-6682	120	5	.	.	PUNCT
ejpam-6682	121	1	3.2	3.2	NUM
ejpam-6682	121	2	.	.	PUNCT
ejpam-6682	121	3	model	model	NOUN
ejpam-6682	121	4	equilibria	equilibrium	NOUN
ejpam-6682	121	5	and	and	CCONJ
ejpam-6682	121	6	basic	basic	ADJ
ejpam-6682	121	7	reproduction	reproduction	NOUN
ejpam-6682	121	8	number	number	NOUN
ejpam-6682	121	9	as	as	ADP
ejpam-6682	121	10	the	the	DET
ejpam-6682	121	11	total	total	ADJ
ejpam-6682	121	12	population	population	NOUN
ejpam-6682	121	13	n1(t	n1(t	PART
ejpam-6682	121	14	)	)	PUNCT
ejpam-6682	121	15	=	=	PUNCT
ejpam-6682	121	16	s1(t)+	s1(t)+	NUM
ejpam-6682	121	17	i1(t)+a1(t)+r1(t	i1(t)+a1(t)+r1(t	PROPN
ejpam-6682	121	18	)	)	PUNCT
ejpam-6682	121	19	and	and	CCONJ
ejpam-6682	121	20	n2(t	n2(t	NUM
ejpam-6682	121	21	)	)	PUNCT
ejpam-6682	121	22	=	=	SYM
ejpam-6682	121	23	s2(t)+	s2(t)+	PROPN
ejpam-6682	121	24	i2(t	i2(t	PROPN
ejpam-6682	121	25	)	)	PUNCT
ejpam-6682	121	26	are	be	AUX
ejpam-6682	121	27	constants	constant	NOUN
ejpam-6682	121	28	,	,	PUNCT
ejpam-6682	121	29	system	system	NOUN
ejpam-6682	121	30	(	(	PUNCT
ejpam-6682	121	31	1	1	X
ejpam-6682	121	32	)	)	PUNCT
ejpam-6682	121	33	simplifies	simplifie	NOUN
ejpam-6682	121	34	to	to	PART
ejpam-6682	121	35	:	:	PUNCT
ejpam-6682	122	1	ds1	ds1	PROPN
ejpam-6682	122	2	dt	dt	X
ejpam-6682	123	1	=	=	PUNCT
ejpam-6682	123	2	µ1n1	µ1n1	PRON
ejpam-6682	123	3	−	−	PUNCT
ejpam-6682	123	4	β1	β1	PROPN
ejpam-6682	123	5	n1	n1	PROPN
ejpam-6682	123	6	s1i2	s1i2	NOUN
ejpam-6682	123	7	−	−	PROPN
ejpam-6682	123	8	µ1s1	µ1s1	NOUN
ejpam-6682	123	9	,	,	PUNCT
ejpam-6682	123	10	di1	di1	INTJ
ejpam-6682	123	11	dt	dt	NOUN
ejpam-6682	123	12	=	=	SYM
ejpam-6682	123	13	β1	β1	PROPN
ejpam-6682	123	14	n1	n1	PROPN
ejpam-6682	123	15	s1i2	s1i2	NOUN
ejpam-6682	123	16	−	−	PROPN
ejpam-6682	123	17	(	(	PUNCT
ejpam-6682	123	18	µ1	µ1	PROPN
ejpam-6682	123	19	+	+	CCONJ
ejpam-6682	123	20	γ)i1	γ)i1	PROPN
ejpam-6682	123	21	+	+	CCONJ
ejpam-6682	123	22	δ1a1	δ1a1	PROPN
ejpam-6682	123	23	,	,	PUNCT
ejpam-6682	123	24	da1	da1	PROPN
ejpam-6682	123	25	dt	dt	AUX
ejpam-6682	124	1	=	=	PUNCT
ejpam-6682	124	2	pγi1	pγi1	NOUN
ejpam-6682	124	3	−	−	PROPN
ejpam-6682	125	1	(	(	PUNCT
ejpam-6682	125	2	µ1	µ1	PROPN
ejpam-6682	125	3	+	+	X
ejpam-6682	125	4	δ1)a1	δ1)a1	ADJ
ejpam-6682	125	5	,	,	PUNCT
ejpam-6682	125	6	di2	di2	NOUN
ejpam-6682	125	7	dt	dt	X
ejpam-6682	126	1	=	=	SYM
ejpam-6682	126	2	β2	β2	PROPN
ejpam-6682	126	3	n1	n1	PROPN
ejpam-6682	126	4	(	(	PUNCT
ejpam-6682	126	5	n2	n2	ADJ
ejpam-6682	126	6	−	−	PROPN
ejpam-6682	126	7	i2)i1	i2)i1	PROPN
ejpam-6682	126	8	−	−	PROPN
ejpam-6682	126	9	µ2i2	µ2i2	X
ejpam-6682	126	10	.	.	PUNCT
ejpam-6682	127	1	(	(	PUNCT
ejpam-6682	127	2	2	2	X
ejpam-6682	127	3	)	)	PUNCT
ejpam-6682	127	4	this	this	DET
ejpam-6682	127	5	system	system	NOUN
ejpam-6682	127	6	has	have	VERB
ejpam-6682	127	7	two	two	NUM
ejpam-6682	127	8	equilibrium	equilibrium	NOUN
ejpam-6682	127	9	points	point	NOUN
ejpam-6682	127	10	:	:	PUNCT
ejpam-6682	127	11	the	the	DET
ejpam-6682	127	12	disease	disease	NOUN
ejpam-6682	127	13	-	-	PUNCT
ejpam-6682	127	14	free	free	ADJ
ejpam-6682	127	15	equilibrium	equilibrium	NOUN
ejpam-6682	127	16	(	(	PUNCT
ejpam-6682	127	17	dfe	dfe	PROPN
ejpam-6682	127	18	)	)	PUNCT
ejpam-6682	127	19	p0	p0	NOUN
ejpam-6682	127	20	=	=	SYM
ejpam-6682	127	21	(	(	PUNCT
ejpam-6682	127	22	n1	n1	PROPN
ejpam-6682	127	23	,	,	PUNCT
ejpam-6682	127	24	0	0	NUM
ejpam-6682	127	25	,	,	PUNCT
ejpam-6682	127	26	0	0	NUM
ejpam-6682	127	27	,	,	PUNCT
ejpam-6682	127	28	0	0	NUM
ejpam-6682	127	29	)	)	PUNCT
ejpam-6682	127	30	and	and	CCONJ
ejpam-6682	127	31	the	the	DET
ejpam-6682	127	32	endemic	endemic	ADJ
ejpam-6682	127	33	equilibrium	equilibrium	NOUN
ejpam-6682	127	34	(	(	PUNCT
ejpam-6682	127	35	ee	ee	NOUN
ejpam-6682	127	36	)	)	PUNCT
ejpam-6682	127	37	p	p	NOUN
ejpam-6682	127	38	∗	∗	NOUN
ejpam-6682	127	39	=	=	PUNCT
ejpam-6682	127	40	(	(	PUNCT
ejpam-6682	127	41	s∗	s∗	PROPN
ejpam-6682	127	42	1	1	NUM
ejpam-6682	127	43	,	,	PUNCT
ejpam-6682	127	44	i	i	PRON
ejpam-6682	127	45	∗	∗	VERB
ejpam-6682	127	46	1	1	NUM
ejpam-6682	127	47	,	,	PUNCT
ejpam-6682	127	48	a	a	DET
ejpam-6682	127	49	∗	∗	NOUN
ejpam-6682	127	50	1	1	NUM
ejpam-6682	127	51	,	,	PUNCT
ejpam-6682	127	52	s	s	NOUN
ejpam-6682	127	53	∗	∗	NOUN
ejpam-6682	127	54	2	2	NUM
ejpam-6682	127	55	,	,	PUNCT
ejpam-6682	127	56	i	i	PRON
ejpam-6682	127	57	∗	∗	NOUN
ejpam-6682	127	58	2	2	NUM
ejpam-6682	127	59	)	)	PUNCT
ejpam-6682	127	60	with	with	ADP
ejpam-6682	127	61	:	:	PUNCT
ejpam-6682	127	62	s∗	s∗	PROPN
ejpam-6682	127	63	1	1	NUM
ejpam-6682	127	64	=	=	SYM
ejpam-6682	127	65	n1(n1n	n1(n1n	SYM
ejpam-6682	127	66	−1	−1	NOUN
ejpam-6682	127	67	2	2	NUM
ejpam-6682	127	68	µ1r̂0	µ1r̂0	NOUN
ejpam-6682	127	69	+	+	CCONJ
ejpam-6682	127	70	β1	β1	NOUN
ejpam-6682	127	71	)	)	PUNCT
ejpam-6682	127	72	r̂0(n1n	r̂0(n1n	X
ejpam-6682	127	73	−1	−1	NOUN
ejpam-6682	127	74	2	2	NUM
ejpam-6682	127	75	µ1	µ1	NOUN
ejpam-6682	127	76	+	+	SYM
ejpam-6682	127	77	β1	β1	PROPN
ejpam-6682	127	78	)	)	PUNCT
ejpam-6682	127	79	,	,	PUNCT
ejpam-6682	127	80	i∗1	i∗1	NOUN
ejpam-6682	127	81	=	=	PUNCT
ejpam-6682	127	82	(	(	PUNCT
ejpam-6682	127	83	µ1n1(µ1	µ1n1(µ1	X
ejpam-6682	127	84	+	+	CCONJ
ejpam-6682	127	85	δ1)β1	δ1)β1	NOUN
ejpam-6682	127	86	(	(	PUNCT
ejpam-6682	127	87	µ1	µ1	PROPN
ejpam-6682	127	88	+	+	SYM
ejpam-6682	127	89	γ)(µ1	γ)(µ1	PROPN
ejpam-6682	127	90	+	+	CCONJ
ejpam-6682	127	91	δ1)−	δ1)−	NOUN
ejpam-6682	127	92	δ1pγ	δ1pγ	X
ejpam-6682	127	93	)	)	PUNCT
ejpam-6682	127	94	(	(	PUNCT
ejpam-6682	127	95	r̂0	r̂0	VERB
ejpam-6682	127	96	−	−	NOUN
ejpam-6682	127	97	1	1	NUM
ejpam-6682	127	98	r̂0(n1n	r̂0(n1n	NOUN
ejpam-6682	127	99	−1	−1	NOUN
ejpam-6682	127	100	2	2	NUM
ejpam-6682	127	101	µ1	µ1	NOUN
ejpam-6682	127	102	+	+	SYM
ejpam-6682	127	103	β1	β1	NOUN
ejpam-6682	127	104	)	)	PUNCT
ejpam-6682	127	105	)	)	PUNCT
ejpam-6682	127	106	,	,	PUNCT
ejpam-6682	127	107	a∗	a∗	PROPN
ejpam-6682	127	108	1	1	NUM
ejpam-6682	127	109	=	=	SYM
ejpam-6682	127	110	(	(	PUNCT
ejpam-6682	127	111	µ1n1β1pγ	µ1n1β1pγ	PROPN
ejpam-6682	127	112	(	(	PUNCT
ejpam-6682	127	113	µ1	µ1	PROPN
ejpam-6682	127	114	+	+	SYM
ejpam-6682	127	115	γ)(µ1	γ)(µ1	PROPN
ejpam-6682	127	116	+	+	CCONJ
ejpam-6682	127	117	δ1)−	δ1)−	NOUN
ejpam-6682	127	118	δ1pγ	δ1pγ	X
ejpam-6682	127	119	)	)	PUNCT
ejpam-6682	127	120	(	(	PUNCT
ejpam-6682	127	121	r̂0	r̂0	VERB
ejpam-6682	127	122	−	−	NOUN
ejpam-6682	127	123	1	1	NUM
ejpam-6682	127	124	r̂0(n1n	r̂0(n1n	NOUN
ejpam-6682	127	125	−1	−1	NOUN
ejpam-6682	127	126	2	2	NUM
ejpam-6682	127	127	µ1	µ1	NOUN
ejpam-6682	127	128	+	+	SYM
ejpam-6682	127	129	β1	β1	NOUN
ejpam-6682	127	130	)	)	PUNCT
ejpam-6682	127	131	)	)	PUNCT
ejpam-6682	127	132	,	,	PUNCT
ejpam-6682	127	133	i∗2	i∗2	NOUN
ejpam-6682	127	134	=	=	PUNCT
ejpam-6682	127	135	µ1n1(r̂0	µ1n1(r̂0	ADV
ejpam-6682	127	136	−	−	NOUN
ejpam-6682	127	137	1	1	NUM
ejpam-6682	127	138	)	)	PUNCT
ejpam-6682	127	139	n1n	n1n	PRON
ejpam-6682	127	140	−1	−1	NOUN
ejpam-6682	127	141	2	2	NUM
ejpam-6682	127	142	µ1r̂0	µ1r̂0	NOUN
ejpam-6682	127	143	+	+	CCONJ
ejpam-6682	127	144	β1	β1	NOUN
ejpam-6682	127	145	.	.	PUNCT
ejpam-6682	128	1	(	(	PUNCT
ejpam-6682	128	2	3	3	X
ejpam-6682	128	3	)	)	PUNCT
ejpam-6682	128	4	where	where	SCONJ
ejpam-6682	128	5	r̂0	r̂0	NOUN
ejpam-6682	128	6	is	be	AUX
ejpam-6682	128	7	:	:	PUNCT
ejpam-6682	128	8	r̂0	r̂0	NOUN
ejpam-6682	128	9	=	=	PUNCT
ejpam-6682	128	10	β1β2n2(µ1	β1β2n2(µ1	NOUN
ejpam-6682	128	11	+	+	CCONJ
ejpam-6682	128	12	δ1	δ1	NOUN
ejpam-6682	128	13	)	)	PUNCT
ejpam-6682	128	14	n1µ2[(µ1	n1µ2[(µ1	VERB
ejpam-6682	128	15	+	+	X
ejpam-6682	128	16	γ)(µ1	γ)(µ1	ADJ
ejpam-6682	128	17	+	+	CCONJ
ejpam-6682	128	18	δ1)−	δ1)−	NOUN
ejpam-6682	128	19	δ1pγ	δ1pγ	X
ejpam-6682	128	20	]	]	PUNCT
ejpam-6682	128	21	.	.	PUNCT
ejpam-6682	129	1	(	(	PUNCT
ejpam-6682	129	2	4	4	X
ejpam-6682	129	3	)	)	PUNCT
ejpam-6682	129	4	we	we	PRON
ejpam-6682	129	5	calculate	calculate	VERB
ejpam-6682	129	6	the	the	DET
ejpam-6682	129	7	basic	basic	ADJ
ejpam-6682	129	8	reproductive	reproductive	ADJ
ejpam-6682	129	9	number	number	NOUN
ejpam-6682	129	10	,	,	PUNCT
ejpam-6682	129	11	r0	r0	NOUN
ejpam-6682	129	12	,	,	PUNCT
ejpam-6682	129	13	using	use	VERB
ejpam-6682	129	14	the	the	DET
ejpam-6682	129	15	next	next	ADJ
ejpam-6682	129	16	-	-	PUNCT
ejpam-6682	129	17	generation	generation	NOUN
ejpam-6682	129	18	matrix	matrix	NOUN
ejpam-6682	129	19	method	method	NOUN
ejpam-6682	129	20	.	.	PUNCT
ejpam-6682	130	1	the	the	DET
ejpam-6682	130	2	jacobian	jacobian	ADJ
ejpam-6682	130	3	matrices	matrix	NOUN
ejpam-6682	130	4	are	be	AUX
ejpam-6682	130	5	:	:	PUNCT
ejpam-6682	130	6	f	f	X
ejpam-6682	130	7	=	=	PUNCT
ejpam-6682	130	8			PROPN
ejpam-6682	130	9	0	0	NUM
ejpam-6682	130	10	0	0	NUM
ejpam-6682	131	1	β1	β1	NOUN
ejpam-6682	131	2	0	0	NUM
ejpam-6682	131	3	0	0	NUM
ejpam-6682	131	4	0	0	NUM
ejpam-6682	131	5	β2n2	β2n2	NOUN
ejpam-6682	131	6	n1	n1	PROPN
ejpam-6682	131	7	0	0	NUM
ejpam-6682	131	8	0	0	NUM
ejpam-6682	132	1			PROPN
ejpam-6682	132	2	,	,	PUNCT
ejpam-6682	132	3	v	v	NOUN
ejpam-6682	132	4	=	=	PUNCT
ejpam-6682	132	5	µ1	µ1	ADP
ejpam-6682	132	6	+	+	CCONJ
ejpam-6682	132	7	γ	γ	X
ejpam-6682	132	8	−δ1	−δ1	PROPN
ejpam-6682	132	9	0	0	NUM
ejpam-6682	132	10	−pγ	−pγ	PROPN
ejpam-6682	132	11	µ1	µ1	PROPN
ejpam-6682	132	12	+	+	NOUN
ejpam-6682	132	13	δ1	δ1	NOUN
ejpam-6682	132	14	0	0	NUM
ejpam-6682	132	15	0	0	NUM
ejpam-6682	132	16	0	0	NUM
ejpam-6682	133	1	µ2	µ2	PROPN
ejpam-6682	133	2			PROPN
ejpam-6682	133	3	.	.	PUNCT
ejpam-6682	134	1	the	the	DET
ejpam-6682	134	2	basic	basic	ADJ
ejpam-6682	134	3	reproduction	reproduction	NOUN
ejpam-6682	134	4	number	number	NOUN
ejpam-6682	134	5	is	be	AUX
ejpam-6682	134	6	the	the	DET
ejpam-6682	134	7	dominant	dominant	ADJ
ejpam-6682	134	8	eigenvalue	eigenvalue	PROPN
ejpam-6682	134	9	of	of	ADP
ejpam-6682	134	10	fv	fv	PROPN
ejpam-6682	134	11	−1	−1	PROPN
ejpam-6682	134	12	:	:	PUNCT
ejpam-6682	135	1	r.	r.	PROPN
ejpam-6682	135	2	saadeh	saadeh	PROPN
ejpam-6682	135	3	et	et	PROPN
ejpam-6682	135	4	al	al	PROPN
ejpam-6682	135	5	.	.	PUNCT
ejpam-6682	135	6	/	/	SYM
ejpam-6682	135	7	eur	eur	PROPN
ejpam-6682	135	8	.	.	PUNCT
ejpam-6682	136	1	j.	j.	PROPN
ejpam-6682	136	2	pure	pure	PROPN
ejpam-6682	136	3	appl	appl	PROPN
ejpam-6682	136	4	.	.	PROPN
ejpam-6682	136	5	math	math	PROPN
ejpam-6682	136	6	,	,	PUNCT
ejpam-6682	136	7	18	18	NUM
ejpam-6682	136	8	(	(	PUNCT
ejpam-6682	136	9	4	4	NUM
ejpam-6682	136	10	)	)	PUNCT
ejpam-6682	136	11	(	(	PUNCT
ejpam-6682	136	12	2025	2025	NUM
ejpam-6682	136	13	)	)	PUNCT
ejpam-6682	136	14	,	,	PUNCT
ejpam-6682	136	15	6682	6682	NUM
ejpam-6682	136	16	7	7	NUM
ejpam-6682	136	17	of	of	ADP
ejpam-6682	136	18	21	21	NUM
ejpam-6682	136	19	r0	r0	NOUN
ejpam-6682	136	20	=	=	SYM
ejpam-6682	136	21	√	√	NUM
ejpam-6682	136	22	r̂0	r̂0	NOUN
ejpam-6682	136	23	.	.	PUNCT
ejpam-6682	137	1	(	(	PUNCT
ejpam-6682	137	2	5	5	NUM
ejpam-6682	137	3	)	)	PUNCT
ejpam-6682	137	4	3.3	3.3	NUM
ejpam-6682	137	5	.	.	PUNCT
ejpam-6682	138	1	stability	stability	NOUN
ejpam-6682	138	2	analysis	analysis	NOUN
ejpam-6682	138	3	theorem	theorem	VERB
ejpam-6682	138	4	1	1	NUM
ejpam-6682	138	5	.	.	PUNCT
ejpam-6682	139	1	(	(	PUNCT
ejpam-6682	139	2	i	i	NOUN
ejpam-6682	139	3	)	)	PUNCT
ejpam-6682	139	4	if	if	SCONJ
ejpam-6682	139	5	r0	r0	NOUN
ejpam-6682	139	6	<	<	X
ejpam-6682	139	7	1	1	NUM
ejpam-6682	139	8	,	,	PUNCT
ejpam-6682	139	9	the	the	DET
ejpam-6682	139	10	disease	disease	NOUN
ejpam-6682	139	11	-	-	PUNCT
ejpam-6682	139	12	free	free	ADJ
ejpam-6682	139	13	equilibrium	equilibrium	NOUN
ejpam-6682	139	14	(	(	PUNCT
ejpam-6682	139	15	dfe	dfe	PROPN
ejpam-6682	139	16	)	)	PUNCT
ejpam-6682	139	17	of	of	ADP
ejpam-6682	139	18	system	system	NOUN
ejpam-6682	139	19	(	(	PUNCT
ejpam-6682	139	20	2	2	X
ejpam-6682	139	21	)	)	PUNCT
ejpam-6682	139	22	is	be	AUX
ejpam-6682	139	23	locally	locally	ADV
ejpam-6682	139	24	asymptotically	asymptotically	ADV
ejpam-6682	139	25	stable	stable	ADJ
ejpam-6682	139	26	.	.	PUNCT
ejpam-6682	140	1	(	(	PUNCT
ejpam-6682	140	2	ii	ii	NOUN
ejpam-6682	140	3	)	)	PUNCT
ejpam-6682	140	4	if	if	SCONJ
ejpam-6682	140	5	r0	r0	NOUN
ejpam-6682	140	6	>	>	X
ejpam-6682	140	7	1	1	NUM
ejpam-6682	140	8	,	,	PUNCT
ejpam-6682	140	9	the	the	DET
ejpam-6682	140	10	dfe	dfe	PROPN
ejpam-6682	140	11	is	be	AUX
ejpam-6682	140	12	unstable	unstable	ADJ
ejpam-6682	140	13	.	.	PUNCT
ejpam-6682	141	1	proof	proof	NOUN
ejpam-6682	141	2	.	.	PUNCT
ejpam-6682	142	1	the	the	DET
ejpam-6682	142	2	jacobian	jacobian	ADJ
ejpam-6682	142	3	matrix	matrix	NOUN
ejpam-6682	142	4	of	of	ADP
ejpam-6682	142	5	system	system	NOUN
ejpam-6682	142	6	(	(	PUNCT
ejpam-6682	142	7	2	2	NUM
ejpam-6682	142	8	)	)	PUNCT
ejpam-6682	142	9	,	,	PUNCT
ejpam-6682	142	10	denoted	denote	VERB
ejpam-6682	142	11	by	by	ADP
ejpam-6682	142	12	j	j	PROPN
ejpam-6682	142	13	,	,	PUNCT
ejpam-6682	142	14	is	be	AUX
ejpam-6682	142	15	expressed	express	VERB
ejpam-6682	142	16	as	as	ADP
ejpam-6682	142	17	:	:	PUNCT
ejpam-6682	142	18	j	j	PROPN
ejpam-6682	142	19	=	=	PUNCT
ejpam-6682	142	20			PROPN
ejpam-6682	142	21	−	−	PROPN
ejpam-6682	142	22	β1	β1	PROPN
ejpam-6682	142	23	n1	n1	PROPN
ejpam-6682	142	24	i2	i2	PROPN
ejpam-6682	142	25	−	−	PROPN
ejpam-6682	142	26	µ1	µ1	PROPN
ejpam-6682	142	27	0	0	NUM
ejpam-6682	142	28	0	0	NUM
ejpam-6682	143	1	−	−	PROPN
ejpam-6682	143	2	β1	β1	PROPN
ejpam-6682	143	3	n1	n1	PROPN
ejpam-6682	143	4	s1	s1	PROPN
ejpam-6682	143	5	β1	β1	PROPN
ejpam-6682	143	6	n1	n1	PROPN
ejpam-6682	143	7	i2	i2	PROPN
ejpam-6682	143	8	−(µ1	−(µ1	X
ejpam-6682	143	9	+	+	CCONJ
ejpam-6682	143	10	γ	γ	X
ejpam-6682	143	11	)	)	PUNCT
ejpam-6682	143	12	δ1	δ1	NOUN
ejpam-6682	143	13	β1	β1	NOUN
ejpam-6682	143	14	n1	n1	PROPN
ejpam-6682	143	15	s1	s1	PROPN
ejpam-6682	143	16	0	0	NUM
ejpam-6682	143	17	pγ	pγ	VERB
ejpam-6682	143	18	−(µ1	−(µ1	PRON
ejpam-6682	143	19	+	+	CCONJ
ejpam-6682	143	20	δ1	δ1	NOUN
ejpam-6682	143	21	)	)	PUNCT
ejpam-6682	143	22	0	0	NUM
ejpam-6682	143	23	0	0	NUM
ejpam-6682	143	24	β2	β2	NOUN
ejpam-6682	143	25	n1	n1	PROPN
ejpam-6682	143	26	(	(	PUNCT
ejpam-6682	143	27	n2	n2	PROPN
ejpam-6682	143	28	−	−	PROPN
ejpam-6682	143	29	i2	i2	PROPN
ejpam-6682	143	30	)	)	PUNCT
ejpam-6682	143	31	0	0	NUM
ejpam-6682	144	1	−	−	PROPN
ejpam-6682	144	2	β2	β2	PROPN
ejpam-6682	144	3	n1	n1	PROPN
ejpam-6682	144	4	i1	i1	PROPN
ejpam-6682	144	5	−	−	PROPN
ejpam-6682	144	6	µ2	µ2	PROPN
ejpam-6682	144	7			VERB
ejpam-6682	144	8	.	.	PUNCT
ejpam-6682	145	1	at	at	ADP
ejpam-6682	145	2	the	the	DET
ejpam-6682	145	3	disease	disease	NOUN
ejpam-6682	145	4	-	-	PUNCT
ejpam-6682	145	5	free	free	ADJ
ejpam-6682	145	6	equilibrium	equilibrium	NOUN
ejpam-6682	145	7	p0	p0	NOUN
ejpam-6682	145	8	,	,	PUNCT
ejpam-6682	145	9	where	where	SCONJ
ejpam-6682	145	10	i1	i1	PROPN
ejpam-6682	145	11	=	=	PROPN
ejpam-6682	145	12	i2	i2	PROPN
ejpam-6682	145	13	=	=	SYM
ejpam-6682	145	14	0	0	NUM
ejpam-6682	145	15	,	,	PUNCT
ejpam-6682	145	16	s1	s1	NOUN
ejpam-6682	145	17	=	=	SYM
ejpam-6682	145	18	n1	n1	PROPN
ejpam-6682	145	19	,	,	PUNCT
ejpam-6682	145	20	and	and	CCONJ
ejpam-6682	145	21	s2	s2	PROPN
ejpam-6682	145	22	=	=	SYM
ejpam-6682	145	23	n2	n2	PROPN
ejpam-6682	145	24	,	,	PUNCT
ejpam-6682	145	25	the	the	DET
ejpam-6682	145	26	jacobian	jacobian	ADJ
ejpam-6682	145	27	matrix	matrix	NOUN
ejpam-6682	145	28	simplifies	simplifie	NOUN
ejpam-6682	145	29	to	to	ADP
ejpam-6682	145	30	:	:	PUNCT
ejpam-6682	145	31	jp0	jp0	PROPN
ejpam-6682	145	32	=	=	PUNCT
ejpam-6682	145	33			PROPN
ejpam-6682	145	34	−µ1	−µ1	ADJ
ejpam-6682	145	35	0	0	NUM
ejpam-6682	145	36	0	0	NUM
ejpam-6682	146	1	−β1	−β1	NOUN
ejpam-6682	146	2	0	0	PUNCT
ejpam-6682	146	3	−(µ1	−(µ1	X
ejpam-6682	146	4	+	+	CCONJ
ejpam-6682	146	5	γ	γ	X
ejpam-6682	146	6	)	)	PUNCT
ejpam-6682	146	7	δ1	δ1	NOUN
ejpam-6682	146	8	β1	β1	PROPN
ejpam-6682	146	9	0	0	NUM
ejpam-6682	146	10	pγ	pγ	PROPN
ejpam-6682	146	11	−(µ1	−(µ1	PRON
ejpam-6682	146	12	+	+	CCONJ
ejpam-6682	146	13	δ1	δ1	NOUN
ejpam-6682	146	14	)	)	PUNCT
ejpam-6682	146	15	0	0	NUM
ejpam-6682	146	16	0	0	NUM
ejpam-6682	146	17	β2n2	β2n2	NOUN
ejpam-6682	146	18	n1	n1	PROPN
ejpam-6682	146	19	0	0	NUM
ejpam-6682	147	1	−µ2	−µ2	NOUN
ejpam-6682	147	2			VERB
ejpam-6682	147	3	.	.	PUNCT
ejpam-6682	148	1	the	the	DET
ejpam-6682	148	2	eigenvalues	eigenvalue	NOUN
ejpam-6682	148	3	of	of	ADP
ejpam-6682	148	4	jp0	jp0	PROPN
ejpam-6682	148	5	are	be	AUX
ejpam-6682	148	6	{	{	PUNCT
ejpam-6682	148	7	λ1	λ1	ADJ
ejpam-6682	148	8	,	,	PUNCT
ejpam-6682	148	9	λ2	λ2	PROPN
ejpam-6682	148	10	,	,	PUNCT
ejpam-6682	148	11	λ3	λ3	PROPN
ejpam-6682	148	12	,	,	PUNCT
ejpam-6682	148	13	λ4	λ4	PROPN
ejpam-6682	148	14	}	}	PUNCT
ejpam-6682	148	15	,	,	PUNCT
ejpam-6682	148	16	where	where	SCONJ
ejpam-6682	148	17	:	:	PUNCT
ejpam-6682	148	18	λ1	λ1	ADJ
ejpam-6682	148	19	=	=	SYM
ejpam-6682	148	20	−µ1	−µ1	PROPN
ejpam-6682	148	21	,	,	PUNCT
ejpam-6682	148	22	λ2	λ2	NOUN
ejpam-6682	148	23	=	=	SYM
ejpam-6682	148	24	−(µ1	−(µ1	X
ejpam-6682	148	25	+	+	X
ejpam-6682	148	26	γ	γ	NOUN
ejpam-6682	148	27	)	)	PUNCT
ejpam-6682	148	28	.	.	PUNCT
ejpam-6682	149	1	the	the	DET
ejpam-6682	149	2	remaining	remain	VERB
ejpam-6682	149	3	eigenvalues	eigenvalue	NOUN
ejpam-6682	149	4	,	,	PUNCT
ejpam-6682	149	5	λ3	λ3	PROPN
ejpam-6682	149	6	and	and	CCONJ
ejpam-6682	149	7	λ4	λ4	PROPN
ejpam-6682	149	8	,	,	PUNCT
ejpam-6682	149	9	are	be	AUX
ejpam-6682	149	10	determined	determine	VERB
ejpam-6682	149	11	by	by	ADP
ejpam-6682	149	12	solving	solve	VERB
ejpam-6682	149	13	the	the	DET
ejpam-6682	149	14	following	follow	VERB
ejpam-6682	149	15	characteristic	characteristic	ADJ
ejpam-6682	149	16	equations	equation	NOUN
ejpam-6682	149	17	:	:	PUNCT
ejpam-6682	150	1	1	1	X
ejpam-6682	150	2	.	.	X
ejpam-6682	150	3	for	for	ADP
ejpam-6682	150	4	λ3	λ3	PROPN
ejpam-6682	150	5	,	,	PUNCT
ejpam-6682	150	6	we	we	PRON
ejpam-6682	150	7	have	have	VERB
ejpam-6682	150	8	:	:	PUNCT
ejpam-6682	150	9	λ2	λ2	NOUN
ejpam-6682	150	10	3	3	NUM
ejpam-6682	150	11	+	+	CCONJ
ejpam-6682	150	12	(	(	PUNCT
ejpam-6682	150	13	γ	γ	X
ejpam-6682	150	14	+	+	NUM
ejpam-6682	150	15	2µ1	2µ1	NUM
ejpam-6682	150	16	+	+	CCONJ
ejpam-6682	150	17	δ1)λ3	δ1)λ3	NOUN
ejpam-6682	150	18	+	+	CCONJ
ejpam-6682	150	19	γδ1(1−	γδ1(1−	PROPN
ejpam-6682	150	20	p	p	X
ejpam-6682	150	21	)	)	PUNCT
ejpam-6682	150	22	+	+	CCONJ
ejpam-6682	150	23	γµ1	γµ1	ADJ
ejpam-6682	150	24	+	+	CCONJ
ejpam-6682	150	25	µ1(δ1	µ1(δ1	X
ejpam-6682	150	26	+	+	CCONJ
ejpam-6682	150	27	µ1	µ1	NOUN
ejpam-6682	150	28	)	)	PUNCT
ejpam-6682	150	29	=	=	SYM
ejpam-6682	151	1	0	0	X
ejpam-6682	151	2	.	.	PUNCT
ejpam-6682	151	3	r.	r.	PROPN
ejpam-6682	151	4	saadeh	saadeh	PROPN
ejpam-6682	151	5	et	et	PROPN
ejpam-6682	151	6	al	al	PROPN
ejpam-6682	151	7	.	.	PUNCT
ejpam-6682	151	8	/	/	SYM
ejpam-6682	151	9	eur	eur	PROPN
ejpam-6682	151	10	.	.	PUNCT
ejpam-6682	152	1	j.	j.	PROPN
ejpam-6682	152	2	pure	pure	PROPN
ejpam-6682	152	3	appl	appl	PROPN
ejpam-6682	152	4	.	.	PROPN
ejpam-6682	152	5	math	math	PROPN
ejpam-6682	152	6	,	,	PUNCT
ejpam-6682	152	7	18	18	NUM
ejpam-6682	152	8	(	(	PUNCT
ejpam-6682	152	9	4	4	NUM
ejpam-6682	152	10	)	)	PUNCT
ejpam-6682	152	11	(	(	PUNCT
ejpam-6682	152	12	2025	2025	NUM
ejpam-6682	152	13	)	)	PUNCT
ejpam-6682	152	14	,	,	PUNCT
ejpam-6682	152	15	6682	6682	NUM
ejpam-6682	152	16	8	8	NUM
ejpam-6682	152	17	of	of	ADP
ejpam-6682	152	18	21	21	NUM
ejpam-6682	152	19	2	2	NUM
ejpam-6682	152	20	.	.	PUNCT
ejpam-6682	153	1	for	for	ADP
ejpam-6682	153	2	λ4	λ4	PROPN
ejpam-6682	153	3	,	,	PUNCT
ejpam-6682	153	4	we	we	PRON
ejpam-6682	153	5	solve	solve	VERB
ejpam-6682	153	6	:	:	PUNCT
ejpam-6682	153	7	λ3	λ3	PROPN
ejpam-6682	153	8	4	4	NUM
ejpam-6682	153	9	+	+	CCONJ
ejpam-6682	153	10	(	(	PUNCT
ejpam-6682	153	11	δ1	δ1	NOUN
ejpam-6682	153	12	+	+	CCONJ
ejpam-6682	153	13	γ	γ	PROPN
ejpam-6682	153	14	+	+	NUM
ejpam-6682	153	15	2µ1	2µ1	NUM
ejpam-6682	153	16	+	+	CCONJ
ejpam-6682	153	17	µ2)λ	µ2)λ	NOUN
ejpam-6682	153	18	2	2	NUM
ejpam-6682	153	19	4	4	NUM
ejpam-6682	153	20	+	+	CCONJ
ejpam-6682	153	21	[	[	PUNCT
ejpam-6682	153	22	µ2(δ1	µ2(δ1	X
ejpam-6682	153	23	+	+	CCONJ
ejpam-6682	153	24	µ1	µ1	NUM
ejpam-6682	153	25	)	)	PUNCT
ejpam-6682	153	26	+	+	CCONJ
ejpam-6682	153	27	(	(	PUNCT
ejpam-6682	153	28	δ1	δ1	NOUN
ejpam-6682	153	29	+	+	CCONJ
ejpam-6682	153	30	µ1)(γ	µ1)(γ	PROPN
ejpam-6682	153	31	+	+	ADP
ejpam-6682	153	32	µ1)−	µ1)−	ADJ
ejpam-6682	153	33	pγδ1	pγδ1	NOUN
ejpam-6682	153	34	+	+	CCONJ
ejpam-6682	153	35	µ2(µ1	µ2(µ1	NOUN
ejpam-6682	153	36	+	+	CCONJ
ejpam-6682	153	37	γ)−	γ)−	PROPN
ejpam-6682	153	38	n2β1β2	n2β1β2	AUX
ejpam-6682	153	39	n1	n1	VERB
ejpam-6682	153	40	]	]	PUNCT
ejpam-6682	154	1	λ4	λ4	PROPN
ejpam-6682	155	1	+	+	CCONJ
ejpam-6682	155	2	1	1	NUM
ejpam-6682	155	3	µ2	µ2	NOUN
ejpam-6682	155	4	(	(	PUNCT
ejpam-6682	155	5	(	(	PUNCT
ejpam-6682	155	6	δ1	δ1	NOUN
ejpam-6682	155	7	+	+	CCONJ
ejpam-6682	155	8	µ1)(γ	µ1)(γ	PROPN
ejpam-6682	155	9	+	+	CCONJ
ejpam-6682	155	10	µ1)−	µ1)−	ADJ
ejpam-6682	155	11	pγδ1	pγδ1	NOUN
ejpam-6682	155	12	)	)	PUNCT
ejpam-6682	156	1	[	[	PUNCT
ejpam-6682	156	2	1−	1−	NUM
ejpam-6682	156	3	r̂0	r̂0	NOUN
ejpam-6682	156	4	]	]	PUNCT
ejpam-6682	157	1	=	=	PUNCT
ejpam-6682	157	2	0	0	X
ejpam-6682	157	3	.	.	PUNCT
ejpam-6682	157	4	to	to	PART
ejpam-6682	157	5	analyze	analyze	VERB
ejpam-6682	157	6	the	the	DET
ejpam-6682	157	7	stability	stability	NOUN
ejpam-6682	157	8	of	of	ADP
ejpam-6682	157	9	the	the	DET
ejpam-6682	157	10	dfe	dfe	PROPN
ejpam-6682	157	11	,	,	PUNCT
ejpam-6682	157	12	we	we	PRON
ejpam-6682	157	13	examine	examine	VERB
ejpam-6682	157	14	the	the	DET
ejpam-6682	157	15	condition.r0	condition.r0	PROPN
ejpam-6682	157	16	<	<	X
ejpam-6682	157	17	1	1	NUM
ejpam-6682	157	18	.	.	PUNCT
ejpam-6682	157	19	from	from	ADP
ejpam-6682	157	20	the	the	DET
ejpam-6682	157	21	definition	definition	NOUN
ejpam-6682	157	22	of	of	ADP
ejpam-6682	157	23	r0	r0	NOUN
ejpam-6682	157	24	,	,	PUNCT
ejpam-6682	157	25	r0	r0	NOUN
ejpam-6682	157	26	=	=	PUNCT
ejpam-6682	157	27	√	√	NUM
ejpam-6682	157	28	r̂0	r̂0	PROPN
ejpam-6682	157	29	,	,	PUNCT
ejpam-6682	157	30	where	where	SCONJ
ejpam-6682	157	31	:	:	PUNCT
ejpam-6682	157	32	r̂0	r̂0	NOUN
ejpam-6682	157	33	=	=	PUNCT
ejpam-6682	158	1	β1β2n2(µ1	β1β2n2(µ1	NOUN
ejpam-6682	158	2	+	+	CCONJ
ejpam-6682	158	3	δ1	δ1	NOUN
ejpam-6682	158	4	)	)	PUNCT
ejpam-6682	158	5	n1µ2[(µ1	n1µ2[(µ1	VERB
ejpam-6682	158	6	+	+	X
ejpam-6682	158	7	γ)(µ1	γ)(µ1	ADJ
ejpam-6682	158	8	+	+	CCONJ
ejpam-6682	158	9	δ1)−	δ1)−	NOUN
ejpam-6682	158	10	δ1pγ	δ1pγ	X
ejpam-6682	158	11	]	]	PUNCT
ejpam-6682	158	12	.	.	PUNCT
ejpam-6682	159	1	if	if	SCONJ
ejpam-6682	159	2	r0	r0	NOUN
ejpam-6682	159	3	<	<	X
ejpam-6682	159	4	1	1	NUM
ejpam-6682	159	5	,	,	PUNCT
ejpam-6682	159	6	it	it	PRON
ejpam-6682	159	7	follows	follow	VERB
ejpam-6682	159	8	that	that	SCONJ
ejpam-6682	159	9	β1β2n2	β1β2n2	NOUN
ejpam-6682	159	10	n1	n1	NOUN
ejpam-6682	159	11	<	<	X
ejpam-6682	159	12	µ2(µ1	µ2(µ1	NOUN
ejpam-6682	159	13	+	+	CCONJ
ejpam-6682	159	14	γ	γ	NOUN
ejpam-6682	159	15	)	)	PUNCT
ejpam-6682	159	16	.	.	PUNCT
ejpam-6682	160	1	this	this	PRON
ejpam-6682	160	2	ensures	ensure	VERB
ejpam-6682	160	3	that	that	SCONJ
ejpam-6682	160	4	all	all	DET
ejpam-6682	160	5	coefficients	coefficient	NOUN
ejpam-6682	160	6	of	of	ADP
ejpam-6682	160	7	the	the	DET
ejpam-6682	160	8	characteristic	characteristic	ADJ
ejpam-6682	160	9	equations	equation	NOUN
ejpam-6682	160	10	are	be	AUX
ejpam-6682	160	11	positive	positive	ADJ
ejpam-6682	160	12	,	,	PUNCT
ejpam-6682	160	13	and	and	CCONJ
ejpam-6682	160	14	using	use	VERB
ejpam-6682	160	15	the	the	DET
ejpam-6682	160	16	routh	routh	PROPN
ejpam-6682	160	17	-	-	PUNCT
ejpam-6682	160	18	hurwitz	hurwitz	PROPN
ejpam-6682	160	19	criterion	criterion	NOUN
ejpam-6682	160	20	,	,	PUNCT
ejpam-6682	160	21	all	all	DET
ejpam-6682	160	22	eigenvalues	eigenvalue	NOUN
ejpam-6682	160	23	have	have	VERB
ejpam-6682	160	24	negative	negative	ADJ
ejpam-6682	160	25	real	real	ADJ
ejpam-6682	160	26	parts	part	NOUN
ejpam-6682	160	27	.	.	PUNCT
ejpam-6682	161	1	thus	thus	ADV
ejpam-6682	161	2	,	,	PUNCT
ejpam-6682	161	3	the	the	DET
ejpam-6682	161	4	dfe	dfe	PROPN
ejpam-6682	161	5	is	be	AUX
ejpam-6682	161	6	locally	locally	ADV
ejpam-6682	161	7	asymptotically	asymptotically	ADV
ejpam-6682	161	8	stable	stable	ADJ
ejpam-6682	161	9	when	when	SCONJ
ejpam-6682	161	10	r0	r0	NOUN
ejpam-6682	161	11	<	<	X
ejpam-6682	161	12	1	1	NUM
ejpam-6682	161	13	.	.	PUNCT
ejpam-6682	162	1	in	in	ADP
ejpam-6682	162	2	contrast	contrast	NOUN
ejpam-6682	162	3	,	,	PUNCT
ejpam-6682	162	4	if	if	SCONJ
ejpam-6682	162	5	r0	r0	NOUN
ejpam-6682	162	6	>	>	X
ejpam-6682	162	7	1	1	NUM
ejpam-6682	162	8	,	,	PUNCT
ejpam-6682	162	9	according	accord	VERB
ejpam-6682	162	10	to	to	ADP
ejpam-6682	162	11	descartes	descartes	PROPN
ejpam-6682	162	12	’	'	PUNCT
ejpam-6682	162	13	sign	sign	PROPN
ejpam-6682	162	14	rule	rule	NOUN
ejpam-6682	162	15	,	,	PUNCT
ejpam-6682	162	16	the	the	DET
ejpam-6682	162	17	characteristic	characteristic	ADJ
ejpam-6682	162	18	equation	equation	NOUN
ejpam-6682	162	19	for	for	ADP
ejpam-6682	162	20	λ4	λ4	PROPN
ejpam-6682	162	21	has	have	VERB
ejpam-6682	162	22	at	at	ADV
ejpam-6682	162	23	least	least	ADV
ejpam-6682	162	24	one	one	NUM
ejpam-6682	162	25	positive	positive	ADJ
ejpam-6682	162	26	root	root	NOUN
ejpam-6682	162	27	.	.	PUNCT
ejpam-6682	163	1	it	it	PRON
ejpam-6682	163	2	causes	cause	VERB
ejpam-6682	163	3	the	the	DET
ejpam-6682	163	4	dfe	dfe	PROPN
ejpam-6682	163	5	to	to	PART
ejpam-6682	163	6	be	be	AUX
ejpam-6682	163	7	unstable	unstable	ADJ
ejpam-6682	163	8	.	.	PUNCT
ejpam-6682	164	1	theorem	theorem	NOUN
ejpam-6682	164	2	2	2	NUM
ejpam-6682	164	3	.	.	PUNCT
ejpam-6682	165	1	the	the	DET
ejpam-6682	165	2	disease	disease	NOUN
ejpam-6682	165	3	-	-	PUNCT
ejpam-6682	165	4	free	free	ADJ
ejpam-6682	165	5	equilibrium	equilibrium	NOUN
ejpam-6682	165	6	(	(	PUNCT
ejpam-6682	165	7	dfe	dfe	PROPN
ejpam-6682	165	8	)	)	PUNCT
ejpam-6682	165	9	is	be	AUX
ejpam-6682	165	10	globally	globally	ADV
ejpam-6682	165	11	asymptotically	asymptotically	ADV
ejpam-6682	165	12	stable	stable	ADJ
ejpam-6682	165	13	when	when	SCONJ
ejpam-6682	165	14	r0	r0	NOUN
ejpam-6682	165	15	<	<	X
ejpam-6682	165	16	1	1	NUM
ejpam-6682	165	17	.	.	PUNCT
ejpam-6682	165	18	proof	proof	NOUN
ejpam-6682	165	19	.	.	PUNCT
ejpam-6682	166	1	to	to	PART
ejpam-6682	166	2	establish	establish	VERB
ejpam-6682	166	3	the	the	DET
ejpam-6682	166	4	global	global	ADJ
ejpam-6682	166	5	stability	stability	NOUN
ejpam-6682	166	6	of	of	ADP
ejpam-6682	166	7	the	the	DET
ejpam-6682	166	8	dfe	dfe	PROPN
ejpam-6682	166	9	,	,	PUNCT
ejpam-6682	166	10	we	we	PRON
ejpam-6682	166	11	analyze	analyze	VERB
ejpam-6682	166	12	the	the	DET
ejpam-6682	166	13	subsystem	subsystem	NOUN
ejpam-6682	166	14	corresponding	correspond	VERB
ejpam-6682	166	15	to	to	ADP
ejpam-6682	166	16	the	the	DET
ejpam-6682	166	17	disease	disease	NOUN
ejpam-6682	166	18	-	-	PUNCT
ejpam-6682	166	19	free	free	ADJ
ejpam-6682	166	20	state	state	NOUN
ejpam-6682	166	21	variables	variable	NOUN
ejpam-6682	166	22	(	(	PUNCT
ejpam-6682	166	23	s1	s1	NOUN
ejpam-6682	166	24	,	,	PUNCT
ejpam-6682	166	25	a1	a1	NOUN
ejpam-6682	166	26	,	,	PUNCT
ejpam-6682	166	27	r1	r1	NOUN
ejpam-6682	166	28	,	,	PUNCT
ejpam-6682	166	29	s2	s2	PROPN
ejpam-6682	166	30	)	)	PUNCT
ejpam-6682	166	31	and	and	CCONJ
ejpam-6682	166	32	rewrite	rewrite	VERB
ejpam-6682	166	33	the	the	DET
ejpam-6682	166	34	full	full	ADJ
ejpam-6682	166	35	system	system	NOUN
ejpam-6682	166	36	(	(	PUNCT
ejpam-6682	166	37	1	1	NUM
ejpam-6682	166	38	)	)	PUNCT
ejpam-6682	166	39	in	in	ADP
ejpam-6682	166	40	the	the	DET
ejpam-6682	166	41	following	follow	VERB
ejpam-6682	166	42	form	form	NOUN
ejpam-6682	166	43	:	:	PUNCT
ejpam-6682	166	44	dx	dx	PROPN
ejpam-6682	166	45	dt	dt	NOUN
ejpam-6682	167	1	=	=	PUNCT
ejpam-6682	167	2	p	p	X
ejpam-6682	167	3	(	(	PUNCT
ejpam-6682	167	4	x	x	X
ejpam-6682	167	5	,	,	PUNCT
ejpam-6682	167	6	y	y	PROPN
ejpam-6682	167	7	)	)	PUNCT
ejpam-6682	167	8	,	,	PUNCT
ejpam-6682	167	9	dy	dy	NOUN
ejpam-6682	167	10	dt	dt	NOUN
ejpam-6682	167	11	=	=	SYM
ejpam-6682	167	12	g(x	g(x	PROPN
ejpam-6682	167	13	,	,	PUNCT
ejpam-6682	167	14	y	y	PROPN
ejpam-6682	167	15	)	)	PUNCT
ejpam-6682	167	16	,	,	PUNCT
ejpam-6682	167	17	with	with	ADP
ejpam-6682	167	18	g(x	g(x	NOUN
ejpam-6682	167	19	,	,	PUNCT
ejpam-6682	167	20	0	0	NUM
ejpam-6682	167	21	)	)	PUNCT
ejpam-6682	167	22	=	=	SYM
ejpam-6682	167	23	0	0	NUM
ejpam-6682	167	24	,	,	PUNCT
ejpam-6682	167	25	(	(	PUNCT
ejpam-6682	167	26	6	6	NUM
ejpam-6682	167	27	)	)	PUNCT
ejpam-6682	167	28	where	where	SCONJ
ejpam-6682	167	29	x	x	SYM
ejpam-6682	167	30	=	=	PRON
ejpam-6682	167	31	(	(	PUNCT
ejpam-6682	167	32	s1	s1	NOUN
ejpam-6682	167	33	,	,	PUNCT
ejpam-6682	167	34	a1	a1	NOUN
ejpam-6682	167	35	,	,	PUNCT
ejpam-6682	167	36	r1	r1	NOUN
ejpam-6682	167	37	,	,	PUNCT
ejpam-6682	167	38	s2	s2	PROPN
ejpam-6682	167	39	)	)	PUNCT
ejpam-6682	167	40	∈	∈	PROPN
ejpam-6682	167	41	r4	r4	NOUN
ejpam-6682	167	42	+	+	CCONJ
ejpam-6682	167	43	and	and	CCONJ
ejpam-6682	167	44	y	y	PROPN
ejpam-6682	167	45	=	=	SYM
ejpam-6682	167	46	(	(	PUNCT
ejpam-6682	167	47	i1	i1	PROPN
ejpam-6682	167	48	,	,	PUNCT
ejpam-6682	167	49	i2	i2	PROPN
ejpam-6682	167	50	)	)	PUNCT
ejpam-6682	167	51	∈	∈	PROPN
ejpam-6682	167	52	r2	r2	NOUN
ejpam-6682	168	1	+	+	PROPN
ejpam-6682	168	2	.	.	PUNCT
ejpam-6682	169	1	we	we	PRON
ejpam-6682	169	2	use	use	VERB
ejpam-6682	169	3	castillo	castillo	PROPN
ejpam-6682	169	4	-	-	PUNCT
ejpam-6682	169	5	chavez	chavez	PROPN
ejpam-6682	169	6	’s	’s	PART
ejpam-6682	169	7	method	method	NOUN
ejpam-6682	169	8	to	to	PART
ejpam-6682	169	9	determine	determine	VERB
ejpam-6682	169	10	the	the	DET
ejpam-6682	169	11	dfe	dfe	PROPN
ejpam-6682	169	12	’s	’s	PART
ejpam-6682	169	13	global	global	ADJ
ejpam-6682	169	14	stability	stability	NOUN
ejpam-6682	169	15	.	.	PUNCT
ejpam-6682	170	1	(	(	PUNCT
ejpam-6682	170	2	p0	p0	NOUN
ejpam-6682	170	3	)	)	PUNCT
ejpam-6682	170	4	.	.	PUNCT
ejpam-6682	171	1	specifically	specifically	ADV
ejpam-6682	171	2	,	,	PUNCT
ejpam-6682	171	3	we	we	PRON
ejpam-6682	171	4	define	define	VERB
ejpam-6682	171	5	:	:	PUNCT
ejpam-6682	171	6	ĝ(x	ĝ(x	NOUN
ejpam-6682	171	7	,	,	PUNCT
ejpam-6682	171	8	y	y	PROPN
ejpam-6682	171	9	)	)	PUNCT
ejpam-6682	172	1	=	=	PUNCT
ejpam-6682	172	2	a3|p0y	a3|p0y	NUM
ejpam-6682	172	3	−g(x	−g(x	PROPN
ejpam-6682	172	4	,	,	PUNCT
ejpam-6682	172	5	y	y	PROPN
ejpam-6682	172	6	)	)	PUNCT
ejpam-6682	172	7	,	,	PUNCT
ejpam-6682	172	8	(	(	PUNCT
ejpam-6682	172	9	7	7	X
ejpam-6682	172	10	)	)	PUNCT
ejpam-6682	172	11	r.	r.	PROPN
ejpam-6682	172	12	saadeh	saadeh	PROPN
ejpam-6682	172	13	et	et	PROPN
ejpam-6682	172	14	al	al	PROPN
ejpam-6682	172	15	.	.	PUNCT
ejpam-6682	172	16	/	/	SYM
ejpam-6682	172	17	eur	eur	PROPN
ejpam-6682	172	18	.	.	PUNCT
ejpam-6682	173	1	j.	j.	PROPN
ejpam-6682	173	2	pure	pure	PROPN
ejpam-6682	173	3	appl	appl	PROPN
ejpam-6682	173	4	.	.	PROPN
ejpam-6682	173	5	math	math	PROPN
ejpam-6682	173	6	,	,	PUNCT
ejpam-6682	173	7	18	18	NUM
ejpam-6682	173	8	(	(	PUNCT
ejpam-6682	173	9	4	4	NUM
ejpam-6682	173	10	)	)	PUNCT
ejpam-6682	173	11	(	(	PUNCT
ejpam-6682	173	12	2025	2025	NUM
ejpam-6682	173	13	)	)	PUNCT
ejpam-6682	173	14	,	,	PUNCT
ejpam-6682	173	15	6682	6682	NUM
ejpam-6682	173	16	9	9	NUM
ejpam-6682	173	17	of	of	ADP
ejpam-6682	173	18	21	21	NUM
ejpam-6682	173	19	where	where	SCONJ
ejpam-6682	173	20	g(x	g(x	NOUN
ejpam-6682	173	21	,	,	PUNCT
ejpam-6682	173	22	y	y	PROPN
ejpam-6682	173	23	)	)	PUNCT
ejpam-6682	173	24	is	be	AUX
ejpam-6682	173	25	given	give	VERB
ejpam-6682	173	26	by	by	ADP
ejpam-6682	173	27	g(x	g(x	PROPN
ejpam-6682	173	28	,	,	PUNCT
ejpam-6682	173	29	y	y	PROPN
ejpam-6682	173	30	)	)	PUNCT
ejpam-6682	174	1	=	=	PUNCT
ejpam-6682	174	2	β1s1i2	β1s1i2	PROPN
ejpam-6682	174	3	n1	n1	NOUN
ejpam-6682	174	4	−	−	PROPN
ejpam-6682	174	5	(	(	PUNCT
ejpam-6682	174	6	µ1	µ1	PROPN
ejpam-6682	174	7	+	+	CCONJ
ejpam-6682	174	8	γ)i1	γ)i1	PROPN
ejpam-6682	174	9	β2s2i1	β2s2i1	ADJ
ejpam-6682	174	10	n1	n1	NOUN
ejpam-6682	174	11	−	−	NOUN
ejpam-6682	174	12	µ2i2	µ2i2	NOUN
ejpam-6682	174	13			NOUN
ejpam-6682	174	14	.	.	PUNCT
ejpam-6682	175	1	here	here	ADV
ejpam-6682	175	2	a3|p0	a3|p0	PROPN
ejpam-6682	175	3	is	be	AUX
ejpam-6682	175	4	the	the	DET
ejpam-6682	175	5	jacobian	jacobian	ADJ
ejpam-6682	175	6	matrix	matrix	NOUN
ejpam-6682	175	7	g(x	g(x	PROPN
ejpam-6682	175	8	,	,	PUNCT
ejpam-6682	175	9	y	y	PROPN
ejpam-6682	175	10	)	)	PUNCT
ejpam-6682	175	11	evaluated	evaluate	VERB
ejpam-6682	175	12	at	at	ADP
ejpam-6682	175	13	the	the	DET
ejpam-6682	175	14	dfe	dfe	PROPN
ejpam-6682	175	15	p0	p0	NOUN
ejpam-6682	175	16	.	.	PUNCT
ejpam-6682	176	1	the	the	DET
ejpam-6682	176	2	jacobian	jacobian	PROPN
ejpam-6682	176	3	a3|p0	a3|p0	PROPN
ejpam-6682	176	4	is	be	AUX
ejpam-6682	176	5	expressed	express	VERB
ejpam-6682	176	6	as	as	ADP
ejpam-6682	176	7	:	:	PUNCT
ejpam-6682	176	8	a3|p0	a3|p0	X
ejpam-6682	176	9	=	=	SYM
ejpam-6682	177	1	−(µ1	−(µ1	NOUN
ejpam-6682	177	2	+	+	CCONJ
ejpam-6682	177	3	γ	γ	X
ejpam-6682	177	4	)	)	PUNCT
ejpam-6682	177	5	β1	β1	NOUN
ejpam-6682	177	6	β2n2	β2n2	ADP
ejpam-6682	177	7	n1	n1	NOUN
ejpam-6682	177	8	−µ2	−µ2	NOUN
ejpam-6682	177	9			NOUN
ejpam-6682	177	10	.	.	PUNCT
ejpam-6682	178	1	substituting	substitute	VERB
ejpam-6682	178	2	g(x	g(x	PROPN
ejpam-6682	178	3	,	,	PUNCT
ejpam-6682	178	4	y	y	PROPN
ejpam-6682	178	5	)	)	PUNCT
ejpam-6682	178	6	and	and	CCONJ
ejpam-6682	178	7	a3|p0	a3|p0	VERB
ejpam-6682	178	8	into	into	ADP
ejpam-6682	178	9	equation	equation	NOUN
ejpam-6682	178	10	(	(	PUNCT
ejpam-6682	178	11	7	7	NUM
ejpam-6682	178	12	)	)	PUNCT
ejpam-6682	178	13	,	,	PUNCT
ejpam-6682	178	14	we	we	PRON
ejpam-6682	178	15	obtain	obtain	VERB
ejpam-6682	178	16	:	:	PUNCT
ejpam-6682	178	17	ĝ(x	ĝ(x	NOUN
ejpam-6682	178	18	,	,	PUNCT
ejpam-6682	178	19	y	y	NOUN
ejpam-6682	178	20	)	)	PUNCT
ejpam-6682	178	21	=	=	PUNCT
ejpam-6682	179	1			NOUN
ejpam-6682	179	2	β1	β1	PROPN
ejpam-6682	179	3	n1	n1	NOUN
ejpam-6682	179	4	i2(n1	i2(n1	VERB
ejpam-6682	179	5	−	−	PROPN
ejpam-6682	179	6	s1	s1	NOUN
ejpam-6682	179	7	)	)	PUNCT
ejpam-6682	179	8	β2	β2	NOUN
ejpam-6682	179	9	n1	n1	NOUN
ejpam-6682	179	10	i1(n2	i1(n2	DET
ejpam-6682	179	11	−	−	PROPN
ejpam-6682	179	12	s2	s2	NOUN
ejpam-6682	179	13	)	)	PUNCT
ejpam-6682	179	14			NOUN
ejpam-6682	179	15	.	.	PUNCT
ejpam-6682	180	1	consequently	consequently	ADV
ejpam-6682	180	2	,	,	PUNCT
ejpam-6682	180	3	ĝ(x	ĝ(x	NOUN
ejpam-6682	180	4	,	,	PUNCT
ejpam-6682	180	5	y	y	PROPN
ejpam-6682	180	6	)	)	PUNCT
ejpam-6682	180	7	≥	≥	NOUN
ejpam-6682	180	8	0	0	NUM
ejpam-6682	180	9	,	,	PUNCT
ejpam-6682	180	10	(	(	PUNCT
ejpam-6682	180	11	x	x	X
ejpam-6682	180	12	,	,	PUNCT
ejpam-6682	180	13	y	y	PROPN
ejpam-6682	180	14	)	)	PUNCT
ejpam-6682	180	15	∈	∈	PROPN
ejpam-6682	180	16	ω	ω	PROPN
ejpam-6682	180	17	.	.	PUNCT
ejpam-6682	181	1	therefore	therefore	ADV
ejpam-6682	181	2	,	,	PUNCT
ejpam-6682	181	3	p0	p0	NOUN
ejpam-6682	181	4	is	be	AUX
ejpam-6682	181	5	globally	globally	ADV
ejpam-6682	181	6	asymptotically	asymptotically	ADV
ejpam-6682	181	7	stable	stable	ADJ
ejpam-6682	181	8	when	when	SCONJ
ejpam-6682	181	9	r0	r0	NOUN
ejpam-6682	181	10	<	<	X
ejpam-6682	181	11	1	1	NUM
ejpam-6682	181	12	.	.	PUNCT
ejpam-6682	181	13	theorem	theorem	NOUN
ejpam-6682	181	14	3	3	NUM
ejpam-6682	181	15	.	.	PUNCT
ejpam-6682	182	1	the	the	DET
ejpam-6682	182	2	endemic	endemic	ADJ
ejpam-6682	182	3	equilibrium	equilibrium	NOUN
ejpam-6682	182	4	point	point	NOUN
ejpam-6682	182	5	p	p	NOUN
ejpam-6682	182	6	∗	∗	NOUN
ejpam-6682	182	7	of	of	ADP
ejpam-6682	182	8	system	system	NOUN
ejpam-6682	182	9	(	(	PUNCT
ejpam-6682	182	10	1	1	X
ejpam-6682	182	11	)	)	PUNCT
ejpam-6682	182	12	is	be	AUX
ejpam-6682	182	13	globally	globally	ADV
ejpam-6682	182	14	asymptotically	asymptotically	ADV
ejpam-6682	182	15	stable	stable	ADJ
ejpam-6682	182	16	.	.	PUNCT
ejpam-6682	183	1	proof	proof	NOUN
ejpam-6682	183	2	.	.	PUNCT
ejpam-6682	184	1	first	first	ADV
ejpam-6682	184	2	,	,	PUNCT
ejpam-6682	184	3	we	we	PRON
ejpam-6682	184	4	normalize	normalize	VERB
ejpam-6682	184	5	state	state	NOUN
ejpam-6682	184	6	variables	variable	NOUN
ejpam-6682	184	7	:	:	PUNCT
ejpam-6682	184	8	s1	s1	NOUN
ejpam-6682	184	9	=	=	SYM
ejpam-6682	184	10	s1	s1	PROPN
ejpam-6682	184	11	n1	n1	PROPN
ejpam-6682	184	12	,	,	PUNCT
ejpam-6682	184	13	i1	i1	PROPN
ejpam-6682	184	14	=	=	PROPN
ejpam-6682	184	15	i1	i1	PROPN
ejpam-6682	184	16	n1	n1	PROPN
ejpam-6682	184	17	,	,	PUNCT
ejpam-6682	184	18	a1	a1	NOUN
ejpam-6682	184	19	=	=	SYM
ejpam-6682	184	20	a1	a1	NOUN
ejpam-6682	184	21	n1	n1	NOUN
ejpam-6682	184	22	,	,	PUNCT
ejpam-6682	184	23	r1	r1	PROPN
ejpam-6682	184	24	=	=	SYM
ejpam-6682	184	25	r1	r1	PROPN
ejpam-6682	184	26	n1	n1	PROPN
ejpam-6682	184	27	,	,	PUNCT
ejpam-6682	184	28	s2	s2	NOUN
ejpam-6682	184	29	=	=	SYM
ejpam-6682	184	30	s2	s2	PROPN
ejpam-6682	184	31	n2	n2	NOUN
ejpam-6682	184	32	,	,	PUNCT
ejpam-6682	184	33	i2	i2	PROPN
ejpam-6682	184	34	=	=	PROPN
ejpam-6682	184	35	i2	i2	PROPN
ejpam-6682	184	36	n2	n2	NOUN
ejpam-6682	184	37	.	.	PUNCT
ejpam-6682	185	1	under	under	ADP
ejpam-6682	185	2	this	this	DET
ejpam-6682	185	3	normalization	normalization	NOUN
ejpam-6682	185	4	,	,	PUNCT
ejpam-6682	185	5	the	the	DET
ejpam-6682	185	6	total	total	ADJ
ejpam-6682	185	7	human	human	ADJ
ejpam-6682	185	8	and	and	CCONJ
ejpam-6682	185	9	mosquito	mosquito	ADJ
ejpam-6682	185	10	populations	population	NOUN
ejpam-6682	185	11	satisfy	satisfy	VERB
ejpam-6682	185	12	:	:	PUNCT
ejpam-6682	185	13	s1	s1	PROPN
ejpam-6682	185	14	+	+	CCONJ
ejpam-6682	185	15	i1	i1	PROPN
ejpam-6682	185	16	+	+	CCONJ
ejpam-6682	185	17	a1	a1	NOUN
ejpam-6682	185	18	+	+	CCONJ
ejpam-6682	185	19	r1	r1	NOUN
ejpam-6682	185	20	=	=	SYM
ejpam-6682	185	21	1	1	NUM
ejpam-6682	185	22	,	,	PUNCT
ejpam-6682	185	23	s2	s2	NOUN
ejpam-6682	185	24	+	+	CCONJ
ejpam-6682	185	25	i2	i2	PROPN
ejpam-6682	185	26	=	=	SYM
ejpam-6682	185	27	1	1	X
ejpam-6682	185	28	.	.	PUNCT
ejpam-6682	186	1	furthermore	furthermore	ADV
ejpam-6682	186	2	,	,	PUNCT
ejpam-6682	186	3	the	the	DET
ejpam-6682	186	4	endemic	endemic	ADJ
ejpam-6682	186	5	equilibrium	equilibrium	NOUN
ejpam-6682	186	6	p	p	NOUN
ejpam-6682	186	7	∗	∗	NOUN
ejpam-6682	186	8	corresponds	correspond	NOUN
ejpam-6682	186	9	to	to	ADP
ejpam-6682	186	10	the	the	DET
ejpam-6682	186	11	equilibrium	equilibrium	NOUN
ejpam-6682	186	12	point	point	NOUN
ejpam-6682	186	13	(	(	PUNCT
ejpam-6682	186	14	s∗1	s∗1	NOUN
ejpam-6682	186	15	,	,	PUNCT
ejpam-6682	186	16	i	i	PRON
ejpam-6682	186	17	∗	∗	NOUN
ejpam-6682	186	18	1	1	NUM
ejpam-6682	186	19	,	,	PUNCT
ejpam-6682	186	20	a	a	DET
ejpam-6682	186	21	∗	∗	NOUN
ejpam-6682	186	22	1	1	NUM
ejpam-6682	186	23	,	,	PUNCT
ejpam-6682	186	24	r	r	NOUN
ejpam-6682	186	25	∗	∗	NOUN
ejpam-6682	186	26	1	1	NUM
ejpam-6682	186	27	,	,	PUNCT
ejpam-6682	186	28	s	s	NOUN
ejpam-6682	186	29	∗	∗	NOUN
ejpam-6682	186	30	2	2	NUM
ejpam-6682	186	31	,	,	PUNCT
ejpam-6682	186	32	i	i	PRON
ejpam-6682	186	33	∗	∗	NOUN
ejpam-6682	186	34	2	2	NUM
ejpam-6682	186	35	)	)	PUNCT
ejpam-6682	186	36	.	.	PUNCT
ejpam-6682	187	1	to	to	PART
ejpam-6682	187	2	prove	prove	VERB
ejpam-6682	187	3	global	global	ADJ
ejpam-6682	187	4	stability	stability	NOUN
ejpam-6682	187	5	,	,	PUNCT
ejpam-6682	187	6	we	we	PRON
ejpam-6682	187	7	construct	construct	VERB
ejpam-6682	187	8	the	the	DET
ejpam-6682	187	9	following	follow	VERB
ejpam-6682	187	10	lyapunov	lyapunov	ADJ
ejpam-6682	187	11	function	function	NOUN
ejpam-6682	187	12	:	:	PUNCT
ejpam-6682	187	13	v	v	X
ejpam-6682	187	14	(	(	PUNCT
ejpam-6682	187	15	s1	s1	PROPN
ejpam-6682	187	16	,	,	PUNCT
ejpam-6682	187	17	i1	i1	PROPN
ejpam-6682	187	18	,	,	PUNCT
ejpam-6682	187	19	a1	a1	PROPN
ejpam-6682	187	20	,	,	PUNCT
ejpam-6682	187	21	r1	r1	NOUN
ejpam-6682	187	22	,	,	PUNCT
ejpam-6682	187	23	s2	s2	PROPN
ejpam-6682	187	24	,	,	PUNCT
ejpam-6682	187	25	i2	i2	PROPN
ejpam-6682	187	26	)	)	PUNCT
ejpam-6682	187	27	=	=	SYM
ejpam-6682	187	28	1	1	NUM
ejpam-6682	187	29	2	2	NUM
ejpam-6682	187	30	[	[	PUNCT
ejpam-6682	187	31	(	(	PUNCT
ejpam-6682	187	32	s1	s1	PROPN
ejpam-6682	187	33	−	−	PROPN
ejpam-6682	187	34	s∗1	s∗1	NOUN
ejpam-6682	187	35	)	)	PUNCT
ejpam-6682	187	36	2	2	NUM
ejpam-6682	188	1	+	+	CCONJ
ejpam-6682	188	2	(	(	PUNCT
ejpam-6682	188	3	i1	i1	PROPN
ejpam-6682	188	4	−	−	PROPN
ejpam-6682	188	5	i∗1	i∗1	PROPN
ejpam-6682	188	6	)	)	PUNCT
ejpam-6682	188	7	2	2	NUM
ejpam-6682	189	1	+	+	CCONJ
ejpam-6682	189	2	(	(	PUNCT
ejpam-6682	189	3	a1	a1	NOUN
ejpam-6682	189	4	−	−	PROPN
ejpam-6682	189	5	a∗1	a∗1	NOUN
ejpam-6682	189	6	)	)	PUNCT
ejpam-6682	189	7	2	2	NUM
ejpam-6682	190	1	+	+	CCONJ
ejpam-6682	190	2	(	(	PUNCT
ejpam-6682	190	3	r1	r1	PROPN
ejpam-6682	190	4	−	−	PROPN
ejpam-6682	190	5	r∗1	r∗1	PROPN
ejpam-6682	190	6	)	)	PUNCT
ejpam-6682	190	7	2	2	NUM
ejpam-6682	191	1	+	+	CCONJ
ejpam-6682	191	2	(	(	PUNCT
ejpam-6682	191	3	s2	s2	PROPN
ejpam-6682	191	4	−	−	PROPN
ejpam-6682	191	5	s∗2	s∗2	PROPN
ejpam-6682	191	6	)	)	PUNCT
ejpam-6682	191	7	2	2	NUM
ejpam-6682	191	8	+	+	CCONJ
ejpam-6682	191	9	(	(	PUNCT
ejpam-6682	191	10	i2	i2	PROPN
ejpam-6682	191	11	−	−	PROPN
ejpam-6682	191	12	i∗2	i∗2	NOUN
ejpam-6682	191	13	)	)	PUNCT
ejpam-6682	191	14	2	2	NUM
ejpam-6682	191	15	]	]	PUNCT
ejpam-6682	191	16	.	.	PUNCT
ejpam-6682	192	1	the	the	DET
ejpam-6682	192	2	derivative	derivative	NOUN
ejpam-6682	192	3	of	of	ADP
ejpam-6682	192	4	v	v	NOUN
ejpam-6682	192	5	in	in	ADP
ejpam-6682	192	6	(	(	PUNCT
ejpam-6682	192	7	1	1	NUM
ejpam-6682	192	8	)	)	PUNCT
ejpam-6682	192	9	is	be	AUX
ejpam-6682	192	10	:	:	PUNCT
ejpam-6682	192	11	dv	dv	PROPN
ejpam-6682	192	12	dt	dt	X
ejpam-6682	193	1	=	=	PUNCT
ejpam-6682	193	2	[	[	PUNCT
ejpam-6682	193	3	(	(	PUNCT
ejpam-6682	193	4	s1	s1	PROPN
ejpam-6682	193	5	−	−	PROPN
ejpam-6682	193	6	s∗1	s∗1	NOUN
ejpam-6682	193	7	)	)	PUNCT
ejpam-6682	194	1	ds1	ds1	PROPN
ejpam-6682	194	2	dt	dt	X
ejpam-6682	195	1	+	+	CCONJ
ejpam-6682	195	2	(	(	PUNCT
ejpam-6682	195	3	i1	i1	PROPN
ejpam-6682	195	4	−	−	PROPN
ejpam-6682	195	5	i∗1	i∗1	PROPN
ejpam-6682	195	6	)	)	PUNCT
ejpam-6682	195	7	di1	di1	NOUN
ejpam-6682	195	8	dt	dt	NOUN
ejpam-6682	196	1	+	+	CCONJ
ejpam-6682	196	2	(	(	PUNCT
ejpam-6682	196	3	a1	a1	NOUN
ejpam-6682	196	4	−	−	PROPN
ejpam-6682	196	5	a∗1	a∗1	NOUN
ejpam-6682	196	6	)	)	PUNCT
ejpam-6682	197	1	da1	da1	PROPN
ejpam-6682	197	2	dt	dt	X
ejpam-6682	198	1	+	+	CCONJ
ejpam-6682	198	2	(	(	PUNCT
ejpam-6682	198	3	r1	r1	PROPN
ejpam-6682	198	4	−	−	PROPN
ejpam-6682	198	5	r∗1	r∗1	PROPN
ejpam-6682	198	6	)	)	PUNCT
ejpam-6682	199	1	dr1	dr1	PROPN
ejpam-6682	199	2	dt	dt	PROPN
ejpam-6682	200	1	+	+	CCONJ
ejpam-6682	200	2	(	(	PUNCT
ejpam-6682	200	3	s2	s2	PROPN
ejpam-6682	200	4	−	−	PROPN
ejpam-6682	200	5	s∗2	s∗2	PROPN
ejpam-6682	200	6	)	)	PUNCT
ejpam-6682	200	7	ds2	ds2	PROPN
ejpam-6682	200	8	dt	dt	X
ejpam-6682	201	1	+	+	CCONJ
ejpam-6682	201	2	(	(	PUNCT
ejpam-6682	201	3	i2	i2	PROPN
ejpam-6682	201	4	−	−	PROPN
ejpam-6682	201	5	i∗2	i∗2	NOUN
ejpam-6682	201	6	)	)	PUNCT
ejpam-6682	201	7	di2	di2	PROPN
ejpam-6682	201	8	dt	dt	X
ejpam-6682	201	9	]	]	PUNCT
ejpam-6682	201	10	.	.	PUNCT
ejpam-6682	202	1	r.	r.	PROPN
ejpam-6682	202	2	saadeh	saadeh	PROPN
ejpam-6682	202	3	et	et	PROPN
ejpam-6682	202	4	al	al	PROPN
ejpam-6682	202	5	.	.	PUNCT
ejpam-6682	202	6	/	/	SYM
ejpam-6682	202	7	eur	eur	PROPN
ejpam-6682	202	8	.	.	PUNCT
ejpam-6682	203	1	j.	j.	PROPN
ejpam-6682	203	2	pure	pure	PROPN
ejpam-6682	203	3	appl	appl	PROPN
ejpam-6682	203	4	.	.	PROPN
ejpam-6682	203	5	math	math	PROPN
ejpam-6682	203	6	,	,	PUNCT
ejpam-6682	203	7	18	18	NUM
ejpam-6682	203	8	(	(	PUNCT
ejpam-6682	203	9	4	4	NUM
ejpam-6682	203	10	)	)	PUNCT
ejpam-6682	203	11	(	(	PUNCT
ejpam-6682	203	12	2025	2025	NUM
ejpam-6682	203	13	)	)	PUNCT
ejpam-6682	203	14	,	,	PUNCT
ejpam-6682	203	15	6682	6682	NUM
ejpam-6682	203	16	10	10	NUM
ejpam-6682	203	17	of	of	ADP
ejpam-6682	203	18	21	21	NUM
ejpam-6682	203	19	since	since	SCONJ
ejpam-6682	203	20	all	all	DET
ejpam-6682	203	21	normalized	normalize	VERB
ejpam-6682	203	22	states	state	NOUN
ejpam-6682	203	23	are	be	AUX
ejpam-6682	203	24	in	in	ADP
ejpam-6682	203	25	[	[	X
ejpam-6682	203	26	0	0	NUM
ejpam-6682	203	27	,	,	PUNCT
ejpam-6682	203	28	1	1	NUM
ejpam-6682	203	29	]	]	PUNCT
ejpam-6682	203	30	,	,	PUNCT
ejpam-6682	203	31	we	we	PRON
ejpam-6682	203	32	obtain	obtain	VERB
ejpam-6682	203	33	dv	dv	PROPN
ejpam-6682	203	34	dt	dt	PROPN
ejpam-6682	203	35	=	=	PUNCT
ejpam-6682	203	36	[	[	PUNCT
ejpam-6682	203	37	(	(	PUNCT
ejpam-6682	203	38	s1	s1	PROPN
ejpam-6682	203	39	−	−	PROPN
ejpam-6682	203	40	s∗1	s∗1	NOUN
ejpam-6682	203	41	)	)	PUNCT
ejpam-6682	204	1	ds1	ds1	PROPN
ejpam-6682	204	2	dt	dt	X
ejpam-6682	205	1	+	+	CCONJ
ejpam-6682	205	2	(	(	PUNCT
ejpam-6682	205	3	i1	i1	PROPN
ejpam-6682	205	4	−	−	PROPN
ejpam-6682	205	5	i∗1	i∗1	PROPN
ejpam-6682	205	6	)	)	PUNCT
ejpam-6682	205	7	di1	di1	NOUN
ejpam-6682	205	8	dt	dt	NOUN
ejpam-6682	206	1	+	+	CCONJ
ejpam-6682	206	2	(	(	PUNCT
ejpam-6682	206	3	a1	a1	NOUN
ejpam-6682	206	4	−	−	PROPN
ejpam-6682	206	5	a∗1	a∗1	NOUN
ejpam-6682	206	6	)	)	PUNCT
ejpam-6682	207	1	da1	da1	PROPN
ejpam-6682	207	2	dt	dt	X
ejpam-6682	208	1	+	+	CCONJ
ejpam-6682	208	2	(	(	PUNCT
ejpam-6682	208	3	r1	r1	PROPN
ejpam-6682	208	4	−	−	PROPN
ejpam-6682	208	5	r∗1	r∗1	PROPN
ejpam-6682	208	6	)	)	PUNCT
ejpam-6682	209	1	dr1	dr1	PROPN
ejpam-6682	209	2	dt	dt	PROPN
ejpam-6682	210	1	+	+	CCONJ
ejpam-6682	210	2	(	(	PUNCT
ejpam-6682	210	3	s2	s2	PROPN
ejpam-6682	210	4	−	−	PROPN
ejpam-6682	210	5	s∗2	s∗2	PROPN
ejpam-6682	210	6	)	)	PUNCT
ejpam-6682	210	7	ds2	ds2	PROPN
ejpam-6682	210	8	dt	dt	X
ejpam-6682	211	1	+	+	CCONJ
ejpam-6682	211	2	(	(	PUNCT
ejpam-6682	211	3	i2	i2	PROPN
ejpam-6682	211	4	−	−	PROPN
ejpam-6682	211	5	i∗2	i∗2	NOUN
ejpam-6682	211	6	)	)	PUNCT
ejpam-6682	211	7	di2	di2	PROPN
ejpam-6682	211	8	dt	dt	X
ejpam-6682	211	9	]	]	PUNCT
ejpam-6682	211	10	≤	≤	NUM
ejpam-6682	212	1	d	d	NOUN
ejpam-6682	212	2	dt	dt	X
ejpam-6682	212	3	(	(	PUNCT
ejpam-6682	212	4	s1	s1	PROPN
ejpam-6682	212	5	+	+	CCONJ
ejpam-6682	212	6	i1	i1	PROPN
ejpam-6682	212	7	+	+	CCONJ
ejpam-6682	212	8	a1	a1	NOUN
ejpam-6682	212	9	+	+	CCONJ
ejpam-6682	212	10	r1	r1	NOUN
ejpam-6682	212	11	+	+	CCONJ
ejpam-6682	212	12	s2	s2	PROPN
ejpam-6682	212	13	+	+	CCONJ
ejpam-6682	212	14	i2	i2	NOUN
ejpam-6682	212	15	)	)	PUNCT
ejpam-6682	212	16	=	=	SYM
ejpam-6682	212	17	0	0	X
ejpam-6682	212	18	.	.	PUNCT
ejpam-6682	213	1	thus	thus	ADV
ejpam-6682	213	2	dv	dv	PROPN
ejpam-6682	213	3	dt	dt	PROPN
ejpam-6682	213	4	≤	≤	PROPN
ejpam-6682	213	5	0	0	NUM
ejpam-6682	213	6	.	.	PUNCT
ejpam-6682	214	1	furthermore	furthermore	ADV
ejpam-6682	214	2	,	,	PUNCT
ejpam-6682	214	3	it	it	PRON
ejpam-6682	214	4	dv	dv	INTJ
ejpam-6682	214	5	dt	dt	X
ejpam-6682	214	6	=	=	SYM
ejpam-6682	214	7	0	0	NUM
ejpam-6682	214	8	occurs	occur	VERB
ejpam-6682	214	9	only	only	ADV
ejpam-6682	214	10	at	at	ADP
ejpam-6682	214	11	p	p	PROPN
ejpam-6682	214	12	∗.	∗.	PROPN
ejpam-6682	214	13	by	by	ADP
ejpam-6682	214	14	lasalle	lasalle	PROPN
ejpam-6682	214	15	’s	’s	PART
ejpam-6682	214	16	invariance	invariance	NOUN
ejpam-6682	214	17	principle	principle	NOUN
ejpam-6682	214	18	,	,	PUNCT
ejpam-6682	214	19	all	all	DET
ejpam-6682	214	20	trajectories	trajectory	NOUN
ejpam-6682	214	21	asymptotically	asymptotically	ADV
ejpam-6682	214	22	approach	approach	VERB
ejpam-6682	214	23	.	.	PUNCT
ejpam-6682	215	1	p	p	X
ejpam-6682	215	2	∗.	∗.	PROPN
ejpam-6682	215	3	thus	thus	ADV
ejpam-6682	215	4	,	,	PUNCT
ejpam-6682	215	5	the	the	DET
ejpam-6682	215	6	endemic	endemic	ADJ
ejpam-6682	215	7	equilibrium	equilibrium	NOUN
ejpam-6682	215	8	is	be	AUX
ejpam-6682	215	9	globally	globally	ADV
ejpam-6682	215	10	asymptotically	asymptotically	ADV
ejpam-6682	215	11	stable	stable	ADJ
ejpam-6682	215	12	.	.	PUNCT
ejpam-6682	216	1	4	4	X
ejpam-6682	216	2	.	.	X
ejpam-6682	216	3	non	non	ADJ
ejpam-6682	216	4	-	-	ADJ
ejpam-6682	216	5	integer	integer	ADJ
ejpam-6682	216	6	calculus	calculus	NOUN
ejpam-6682	216	7	research	research	NOUN
ejpam-6682	216	8	of	of	ADP
ejpam-6682	216	9	differential	differential	ADJ
ejpam-6682	216	10	operators	operator	NOUN
ejpam-6682	216	11	of	of	ADP
ejpam-6682	216	12	fractional	fractional	ADJ
ejpam-6682	216	13	orders	order	NOUN
ejpam-6682	216	14	dates	date	VERB
ejpam-6682	216	15	back	back	ADV
ejpam-6682	216	16	to	to	ADP
ejpam-6682	216	17	1695	1695	NUM
ejpam-6682	216	18	when	when	SCONJ
ejpam-6682	216	19	l’hospital	l’hospital	PROPN
ejpam-6682	216	20	asked	ask	VERB
ejpam-6682	216	21	leibniz	leibniz	PROPN
ejpam-6682	216	22	the	the	DET
ejpam-6682	216	23	meaning	meaning	NOUN
ejpam-6682	216	24	of	of	ADP
ejpam-6682	216	25	duy	duy	PROPN
ejpam-6682	216	26	dxu	dxu	NOUN
ejpam-6682	216	27	for	for	ADP
ejpam-6682	216	28	u	u	NOUN
ejpam-6682	216	29	=	=	NOUN
ejpam-6682	216	30	1/2	1/2	NUM
ejpam-6682	217	1	[	[	X
ejpam-6682	217	2	29	29	NUM
ejpam-6682	217	3	]	]	PUNCT
ejpam-6682	217	4	.	.	PUNCT
ejpam-6682	218	1	this	this	PRON
ejpam-6682	218	2	led	lead	VERB
ejpam-6682	218	3	to	to	ADP
ejpam-6682	218	4	the	the	DET
ejpam-6682	218	5	investigation	investigation	NOUN
ejpam-6682	218	6	of	of	ADP
ejpam-6682	218	7	fractional	fractional	ADJ
ejpam-6682	218	8	calculus	calculus	NOUN
ejpam-6682	218	9	,	,	PUNCT
ejpam-6682	218	10	and	and	CCONJ
ejpam-6682	218	11	mathematicians	mathematician	NOUN
ejpam-6682	218	12	like	like	ADP
ejpam-6682	218	13	euler	euler	PROPN
ejpam-6682	218	14	,	,	PUNCT
ejpam-6682	218	15	lagrange	lagrange	NOUN
ejpam-6682	218	16	,	,	PUNCT
ejpam-6682	218	17	and	and	CCONJ
ejpam-6682	218	18	fourier	fourier	NOUN
ejpam-6682	218	19	took	take	VERB
ejpam-6682	218	20	an	an	DET
ejpam-6682	218	21	interest	interest	NOUN
ejpam-6682	218	22	in	in	ADP
ejpam-6682	218	23	it	it	PRON
ejpam-6682	218	24	[	[	X
ejpam-6682	218	25	30	30	NUM
ejpam-6682	218	26	]	]	PUNCT
ejpam-6682	218	27	.	.	PUNCT
ejpam-6682	219	1	the	the	DET
ejpam-6682	219	2	fractional	fractional	ADJ
ejpam-6682	219	3	calculus	calculus	NOUN
ejpam-6682	219	4	was	be	AUX
ejpam-6682	219	5	later	later	ADV
ejpam-6682	219	6	used	use	VERB
ejpam-6682	219	7	in	in	ADP
ejpam-6682	219	8	various	various	ADJ
ejpam-6682	219	9	fields	field	NOUN
ejpam-6682	219	10	such	such	ADJ
ejpam-6682	219	11	as	as	ADP
ejpam-6682	219	12	electrical	electrical	ADJ
ejpam-6682	219	13	spectroscopy	spectroscopy	NOUN
ejpam-6682	219	14	,	,	PUNCT
ejpam-6682	219	15	wave	wave	NOUN
ejpam-6682	219	16	propagation	propagation	NOUN
ejpam-6682	219	17	,	,	PUNCT
ejpam-6682	219	18	quantum	quantum	NOUN
ejpam-6682	219	19	mechanics	mechanic	NOUN
ejpam-6682	219	20	,	,	PUNCT
ejpam-6682	219	21	fluid	fluid	ADJ
ejpam-6682	219	22	mechanics	mechanic	NOUN
ejpam-6682	219	23	,	,	PUNCT
ejpam-6682	219	24	and	and	CCONJ
ejpam-6682	219	25	epidemiology	epidemiology	NOUN
ejpam-6682	220	1	[	[	X
ejpam-6682	220	2	31–34	31–34	NUM
ejpam-6682	220	3	]	]	PUNCT
ejpam-6682	220	4	.	.	PUNCT
ejpam-6682	221	1	fractal	fractal	ADJ
ejpam-6682	221	2	derivatives	derivative	NOUN
ejpam-6682	221	3	and	and	CCONJ
ejpam-6682	221	4	hybrid	hybrid	ADJ
ejpam-6682	221	5	fractal	fractal	ADJ
ejpam-6682	221	6	-	-	PUNCT
ejpam-6682	221	7	fractional	fractional	ADJ
ejpam-6682	221	8	models	model	NOUN
ejpam-6682	221	9	were	be	AUX
ejpam-6682	221	10	also	also	ADV
ejpam-6682	221	11	studied	study	VERB
ejpam-6682	221	12	[	[	PUNCT
ejpam-6682	221	13	35–37	35–37	NOUN
ejpam-6682	221	14	]	]	X
ejpam-6682	221	15	.	.	PUNCT
ejpam-6682	222	1	in	in	ADP
ejpam-6682	222	2	this	this	DET
ejpam-6682	222	3	paper	paper	NOUN
ejpam-6682	222	4	,	,	PUNCT
ejpam-6682	222	5	the	the	DET
ejpam-6682	222	6	effects	effect	NOUN
ejpam-6682	222	7	of	of	ADP
ejpam-6682	222	8	noninteger	noninteger	NOUN
ejpam-6682	222	9	-	-	PUNCT
ejpam-6682	222	10	order	order	NOUN
ejpam-6682	222	11	derivatives	derivative	NOUN
ejpam-6682	222	12	on	on	ADP
ejpam-6682	222	13	the	the	DET
ejpam-6682	222	14	dengue	dengue	NOUN
ejpam-6682	222	15	fever	fever	NOUN
ejpam-6682	222	16	epidemic	epidemic	NOUN
ejpam-6682	222	17	model	model	NOUN
ejpam-6682	222	18	are	be	AUX
ejpam-6682	222	19	considered	consider	VERB
ejpam-6682	222	20	.	.	PUNCT
ejpam-6682	223	1	4.1	4.1	NUM
ejpam-6682	223	2	.	.	PUNCT
ejpam-6682	223	3	fractional	fractional	ADJ
ejpam-6682	223	4	operators	operator	NOUN
ejpam-6682	223	5	here	here	ADV
ejpam-6682	223	6	,	,	PUNCT
ejpam-6682	223	7	we	we	PRON
ejpam-6682	223	8	introduce	introduce	VERB
ejpam-6682	223	9	fundamental	fundamental	ADJ
ejpam-6682	223	10	concepts	concept	NOUN
ejpam-6682	223	11	of	of	ADP
ejpam-6682	223	12	fractional	fractional	ADJ
ejpam-6682	223	13	calculus	calculus	NOUN
ejpam-6682	223	14	[	[	X
ejpam-6682	223	15	38–41	38–41	NUM
ejpam-6682	223	16	]	]	PUNCT
ejpam-6682	223	17	,	,	PUNCT
ejpam-6682	223	18	which	which	PRON
ejpam-6682	223	19	will	will	AUX
ejpam-6682	223	20	be	be	AUX
ejpam-6682	223	21	used	use	VERB
ejpam-6682	223	22	to	to	PART
ejpam-6682	223	23	develop	develop	VERB
ejpam-6682	223	24	our	our	PRON
ejpam-6682	223	25	analysis	analysis	NOUN
ejpam-6682	223	26	.	.	PUNCT
ejpam-6682	224	1	due	due	ADP
ejpam-6682	224	2	to	to	ADP
ejpam-6682	224	3	the	the	DET
ejpam-6682	224	4	non	non	NOUN
ejpam-6682	224	5	-	-	NOUN
ejpam-6682	224	6	linearity	linearity	NOUN
ejpam-6682	224	7	of	of	ADP
ejpam-6682	224	8	the	the	DET
ejpam-6682	224	9	epidemiological	epidemiological	ADJ
ejpam-6682	224	10	equations	equation	NOUN
ejpam-6682	224	11	,	,	PUNCT
ejpam-6682	224	12	obtaining	obtain	VERB
ejpam-6682	224	13	analytical	analytical	ADJ
ejpam-6682	224	14	solutions	solution	NOUN
ejpam-6682	224	15	is	be	AUX
ejpam-6682	224	16	usually	usually	ADV
ejpam-6682	224	17	very	very	ADV
ejpam-6682	224	18	difficult	difficult	ADJ
ejpam-6682	224	19	or	or	CCONJ
ejpam-6682	224	20	,	,	PUNCT
ejpam-6682	224	21	in	in	ADP
ejpam-6682	224	22	most	most	ADJ
ejpam-6682	224	23	cases	case	NOUN
ejpam-6682	224	24	,	,	PUNCT
ejpam-6682	224	25	impossible	impossible	ADJ
ejpam-6682	224	26	.	.	PUNCT
ejpam-6682	225	1	to	to	PART
ejpam-6682	225	2	overcome	overcome	VERB
ejpam-6682	225	3	this	this	DET
ejpam-6682	225	4	challenge	challenge	NOUN
ejpam-6682	225	5	,	,	PUNCT
ejpam-6682	225	6	we	we	PRON
ejpam-6682	225	7	present	present	VERB
ejpam-6682	225	8	the	the	DET
ejpam-6682	225	9	system	system	NOUN
ejpam-6682	225	10	1	1	NUM
ejpam-6682	225	11	under	under	ADP
ejpam-6682	225	12	the	the	DET
ejpam-6682	225	13	caputo	caputo	PROPN
ejpam-6682	225	14	operator	operator	NOUN
ejpam-6682	225	15	:	:	PUNCT
ejpam-6682	225	16	cdα	cdα	PROPN
ejpam-6682	225	17	t	t	PROPN
ejpam-6682	225	18	s1	s1	PROPN
ejpam-6682	225	19	=	=	PUNCT
ejpam-6682	225	20	µ1n1	µ1n1	PRON
ejpam-6682	225	21	−	−	PUNCT
ejpam-6682	225	22	β1	β1	PROPN
ejpam-6682	225	23	s1i2	s1i2	INTJ
ejpam-6682	225	24	n1	n1	PROPN
ejpam-6682	225	25	−	−	PROPN
ejpam-6682	225	26	µ1s1	µ1s1	NOUN
ejpam-6682	225	27	,	,	PUNCT
ejpam-6682	225	28	cdα	cdα	PROPN
ejpam-6682	225	29	t	t	PROPN
ejpam-6682	225	30	i1	i1	PROPN
ejpam-6682	225	31	=	=	PUNCT
ejpam-6682	225	32	β1i2	β1i2	PUNCT
ejpam-6682	225	33	n1	n1	PROPN
ejpam-6682	225	34	s1	s1	NOUN
ejpam-6682	225	35	+	+	CCONJ
ejpam-6682	225	36	δ1a1	δ1a1	NOUN
ejpam-6682	225	37	−	−	PROPN
ejpam-6682	225	38	(	(	PUNCT
ejpam-6682	225	39	µ1	µ1	PROPN
ejpam-6682	225	40	+	+	CCONJ
ejpam-6682	225	41	γ)i1	γ)i1	PROPN
ejpam-6682	225	42	,	,	PUNCT
ejpam-6682	225	43	cdα	cdα	NOUN
ejpam-6682	225	44	t	t	PROPN
ejpam-6682	225	45	a1	a1	NOUN
ejpam-6682	225	46	=	=	PROPN
ejpam-6682	225	47	pγi1	pγi1	NOUN
ejpam-6682	225	48	−	−	PROPN
ejpam-6682	226	1	(	(	PUNCT
ejpam-6682	226	2	µ1	µ1	PROPN
ejpam-6682	226	3	+	+	X
ejpam-6682	226	4	δ1)a1	δ1)a1	ADJ
ejpam-6682	226	5	,	,	PUNCT
ejpam-6682	226	6	cdα	cdα	NOUN
ejpam-6682	226	7	t	t	PROPN
ejpam-6682	226	8	r1	r1	PROPN
ejpam-6682	226	9	=	=	PUNCT
ejpam-6682	226	10	(	(	PUNCT
ejpam-6682	226	11	1−	1−	NUM
ejpam-6682	226	12	p)γi1	p)γi1	NOUN
ejpam-6682	226	13	−	−	PROPN
ejpam-6682	226	14	µ1r1	µ1r1	PROPN
ejpam-6682	226	15	,	,	PUNCT
ejpam-6682	226	16	cdα	cdα	PROPN
ejpam-6682	226	17	t	t	PROPN
ejpam-6682	226	18	s2	s2	PROPN
ejpam-6682	226	19	=	=	PUNCT
ejpam-6682	226	20	µ2n2	µ2n2	NOUN
ejpam-6682	226	21	−	−	NOUN
ejpam-6682	226	22	β2	β2	ADJ
ejpam-6682	226	23	s2i1	s2i1	CCONJ
ejpam-6682	226	24	n1	n1	NOUN
ejpam-6682	226	25	−	−	PROPN
ejpam-6682	226	26	µ2s2	µ2s2	NOUN
ejpam-6682	226	27	,	,	PUNCT
ejpam-6682	226	28	cdα	cdα	PROPN
ejpam-6682	226	29	t	t	PROPN
ejpam-6682	226	30	i2	i2	PROPN
ejpam-6682	226	31	=	=	PUNCT
ejpam-6682	226	32	β2	β2	VERB
ejpam-6682	226	33	s2i1	s2i1	PROPN
ejpam-6682	226	34	n1	n1	NOUN
ejpam-6682	226	35	−	−	NUM
ejpam-6682	226	36	µ2i2	µ2i2	X
ejpam-6682	226	37	.	.	PUNCT
ejpam-6682	227	1	(	(	PUNCT
ejpam-6682	227	2	8)	8)	NUM
ejpam-6682	227	3	now	now	ADV
ejpam-6682	227	4	,	,	PUNCT
ejpam-6682	227	5	we	we	PRON
ejpam-6682	227	6	present	present	VERB
ejpam-6682	227	7	a	a	DET
ejpam-6682	227	8	numerical	numerical	ADJ
ejpam-6682	227	9	method	method	NOUN
ejpam-6682	227	10	for	for	ADP
ejpam-6682	227	11	solving	solve	VERB
ejpam-6682	227	12	fractional	fractional	ADJ
ejpam-6682	227	13	differential	differential	ADJ
ejpam-6682	227	14	equations	equation	NOUN
ejpam-6682	227	15	,	,	PUNCT
ejpam-6682	227	16	referred	refer	VERB
ejpam-6682	227	17	to	to	ADP
ejpam-6682	227	18	as	as	ADP
ejpam-6682	227	19	the	the	DET
ejpam-6682	227	20	fractional	fractional	PROPN
ejpam-6682	227	21	euler	euler	NOUN
ejpam-6682	227	22	method	method	NOUN
ejpam-6682	227	23	.	.	PUNCT
ejpam-6682	228	1	the	the	DET
ejpam-6682	228	2	method	method	NOUN
ejpam-6682	228	3	is	be	AUX
ejpam-6682	228	4	based	base	VERB
ejpam-6682	228	5	on	on	ADP
ejpam-6682	228	6	the	the	DET
ejpam-6682	228	7	following	follow	VERB
ejpam-6682	228	8	formula	formula	NOUN
ejpam-6682	228	9	:	:	PUNCT
ejpam-6682	228	10	r.	r.	PROPN
ejpam-6682	228	11	saadeh	saadeh	PROPN
ejpam-6682	228	12	et	et	PROPN
ejpam-6682	228	13	al	al	PROPN
ejpam-6682	228	14	.	.	PUNCT
ejpam-6682	228	15	/	/	SYM
ejpam-6682	228	16	eur	eur	PROPN
ejpam-6682	228	17	.	.	PUNCT
ejpam-6682	229	1	j.	j.	PROPN
ejpam-6682	229	2	pure	pure	PROPN
ejpam-6682	229	3	appl	appl	PROPN
ejpam-6682	229	4	.	.	PROPN
ejpam-6682	229	5	math	math	PROPN
ejpam-6682	229	6	,	,	PUNCT
ejpam-6682	229	7	18	18	NUM
ejpam-6682	229	8	(	(	PUNCT
ejpam-6682	229	9	4	4	NUM
ejpam-6682	229	10	)	)	PUNCT
ejpam-6682	229	11	(	(	PUNCT
ejpam-6682	229	12	2025	2025	NUM
ejpam-6682	229	13	)	)	PUNCT
ejpam-6682	229	14	,	,	PUNCT
ejpam-6682	229	15	6682	6682	NUM
ejpam-6682	229	16	11	11	NUM
ejpam-6682	229	17	of	of	ADP
ejpam-6682	229	18	21	21	NUM
ejpam-6682	229	19	yk+1	yk+1	NOUN
ejpam-6682	229	20	=	=	NOUN
ejpam-6682	229	21	y0	y0	PROPN
ejpam-6682	229	22	+	+	CCONJ
ejpam-6682	229	23	hα	hα	ADP
ejpam-6682	229	24	γ(α+	γ(α+	DET
ejpam-6682	229	25	1	1	NUM
ejpam-6682	229	26	)	)	PUNCT
ejpam-6682	229	27	k∑	k∑	NOUN
ejpam-6682	229	28	j=0	j=0	PROPN
ejpam-6682	230	1	[	[	X
ejpam-6682	230	2	(	(	PUNCT
ejpam-6682	230	3	k	k	X
ejpam-6682	230	4	+	+	PROPN
ejpam-6682	230	5	1−	1−	NUM
ejpam-6682	230	6	j)α	j)α	X
ejpam-6682	230	7	−	−	PROPN
ejpam-6682	231	1	(	(	PUNCT
ejpam-6682	231	2	k	k	X
ejpam-6682	231	3	−	−	PROPN
ejpam-6682	231	4	j)α	j)α	NOUN
ejpam-6682	231	5	]	]	X
ejpam-6682	232	1	f(tj	f(tj	PROPN
ejpam-6682	232	2	,	,	PUNCT
ejpam-6682	232	3	yj	yj	PROPN
ejpam-6682	232	4	)	)	PUNCT
ejpam-6682	232	5	,	,	PUNCT
ejpam-6682	232	6	(	(	PUNCT
ejpam-6682	232	7	9	9	X
ejpam-6682	232	8	)	)	PUNCT
ejpam-6682	232	9	when	when	SCONJ
ejpam-6682	232	10	α	α	NOUN
ejpam-6682	232	11	=	=	SYM
ejpam-6682	232	12	1	1	NUM
ejpam-6682	232	13	,	,	PUNCT
ejpam-6682	232	14	equation	equation	NOUN
ejpam-6682	232	15	9	9	NUM
ejpam-6682	232	16	reduces	reduce	VERB
ejpam-6682	232	17	to	to	ADP
ejpam-6682	232	18	the	the	DET
ejpam-6682	232	19	euler	euler	NOUN
ejpam-6682	232	20	method	method	NOUN
ejpam-6682	232	21	for	for	ADP
ejpam-6682	232	22	odes	ode	NOUN
ejpam-6682	232	23	.	.	PUNCT
ejpam-6682	233	1	this	this	DET
ejpam-6682	233	2	scheme	scheme	NOUN
ejpam-6682	233	3	is	be	AUX
ejpam-6682	233	4	used	use	VERB
ejpam-6682	233	5	for	for	ADP
ejpam-6682	233	6	solving	solve	VERB
ejpam-6682	233	7	fractional	fractional	ADJ
ejpam-6682	233	8	differential	differential	ADJ
ejpam-6682	233	9	equations	equation	NOUN
ejpam-6682	233	10	with	with	ADP
ejpam-6682	233	11	h	h	NOUN
ejpam-6682	233	12	=	=	NOUN
ejpam-6682	233	13	0.01	0.01	NUM
ejpam-6682	233	14	in	in	ADP
ejpam-6682	233	15	simulations	simulation	NOUN
ejpam-6682	233	16	.	.	PUNCT
ejpam-6682	234	1	convergence	convergence	NOUN
ejpam-6682	234	2	is	be	AUX
ejpam-6682	234	3	ensured	ensure	VERB
ejpam-6682	234	4	if	if	SCONJ
ejpam-6682	234	5	f(t	f(t	NOUN
ejpam-6682	234	6	,	,	PUNCT
ejpam-6682	234	7	y	y	NOUN
ejpam-6682	234	8	)	)	PUNCT
ejpam-6682	234	9	satisfies	satisfy	VERB
ejpam-6682	234	10	the	the	DET
ejpam-6682	234	11	lipschitz	lipschitz	NOUN
ejpam-6682	234	12	condition	condition	NOUN
ejpam-6682	234	13	,	,	PUNCT
ejpam-6682	234	14	guaranteeing	guarantee	VERB
ejpam-6682	234	15	uniqueness	uniqueness	NOUN
ejpam-6682	234	16	and	and	CCONJ
ejpam-6682	234	17	stability	stability	NOUN
ejpam-6682	234	18	of	of	ADP
ejpam-6682	234	19	the	the	DET
ejpam-6682	234	20	solution	solution	NOUN
ejpam-6682	234	21	.	.	PUNCT
ejpam-6682	235	1	(	(	PUNCT
ejpam-6682	235	2	a	a	X
ejpam-6682	235	3	)	)	PUNCT
ejpam-6682	235	4	s1	s1	NOUN
ejpam-6682	235	5	(	(	PUNCT
ejpam-6682	235	6	b	b	NOUN
ejpam-6682	235	7	)	)	PUNCT
ejpam-6682	235	8	i1	i1	NOUN
ejpam-6682	235	9	(	(	PUNCT
ejpam-6682	235	10	c	c	NOUN
ejpam-6682	235	11	)	)	PUNCT
ejpam-6682	235	12	a1	a1	NOUN
ejpam-6682	235	13	(	(	PUNCT
ejpam-6682	235	14	d	d	NOUN
ejpam-6682	235	15	)	)	PUNCT
ejpam-6682	235	16	r1	r1	NOUN
ejpam-6682	235	17	(	(	PUNCT
ejpam-6682	235	18	e	e	NOUN
ejpam-6682	235	19	)	)	PUNCT
ejpam-6682	235	20	s2	s2	NOUN
ejpam-6682	235	21	(	(	PUNCT
ejpam-6682	235	22	f	f	X
ejpam-6682	235	23	)	)	PUNCT
ejpam-6682	235	24	i2	i2	NOUN
ejpam-6682	235	25	figure	figure	NOUN
ejpam-6682	235	26	2	2	NUM
ejpam-6682	235	27	:	:	PUNCT
ejpam-6682	235	28	fractional	fractional	ADJ
ejpam-6682	235	29	-	-	PUNCT
ejpam-6682	235	30	order	order	NOUN
ejpam-6682	235	31	dynamics	dynamic	NOUN
ejpam-6682	235	32	of	of	ADP
ejpam-6682	235	33	the	the	DET
ejpam-6682	235	34	compartmental	compartmental	ADJ
ejpam-6682	235	35	variables	variable	NOUN
ejpam-6682	235	36	s1(t	s1(t	PART
ejpam-6682	235	37	)	)	PUNCT
ejpam-6682	235	38	,	,	PUNCT
ejpam-6682	235	39	i1(t	i1(t	PROPN
ejpam-6682	235	40	)	)	PUNCT
ejpam-6682	235	41	,	,	PUNCT
ejpam-6682	235	42	a1(t	a1(t	PROPN
ejpam-6682	235	43	)	)	PUNCT
ejpam-6682	235	44	,	,	PUNCT
ejpam-6682	235	45	r1(t	r1(t	PROPN
ejpam-6682	235	46	)	)	PUNCT
ejpam-6682	235	47	,	,	PUNCT
ejpam-6682	235	48	s2(t	s2(t	PROPN
ejpam-6682	235	49	)	)	PUNCT
ejpam-6682	235	50	,	,	PUNCT
ejpam-6682	235	51	and	and	CCONJ
ejpam-6682	235	52	i2(t	i2(t	PROPN
ejpam-6682	235	53	)	)	PUNCT
ejpam-6682	235	54	under	under	ADP
ejpam-6682	235	55	varying	vary	VERB
ejpam-6682	235	56	(	(	PUNCT
ejpam-6682	235	57	α	α	NOUN
ejpam-6682	235	58	)	)	PUNCT
ejpam-6682	235	59	.	.	PUNCT
ejpam-6682	236	1	the	the	DET
ejpam-6682	236	2	figure	figure	NOUN
ejpam-6682	236	3	illustrates	illustrate	VERB
ejpam-6682	236	4	the	the	DET
ejpam-6682	236	5	fractional	fractional	ADJ
ejpam-6682	236	6	-	-	PUNCT
ejpam-6682	236	7	order	order	NOUN
ejpam-6682	236	8	dynamics	dynamic	NOUN
ejpam-6682	236	9	of	of	ADP
ejpam-6682	236	10	model	model	NOUN
ejpam-6682	236	11	(	(	PUNCT
ejpam-6682	236	12	)	)	PUNCT
ejpam-6682	236	13	compartments	compartment	NOUN
ejpam-6682	236	14	under	under	ADP
ejpam-6682	236	15	varying	vary	VERB
ejpam-6682	236	16	fractional	fractional	ADJ
ejpam-6682	236	17	-	-	PUNCT
ejpam-6682	236	18	order	order	NOUN
ejpam-6682	236	19	parameters	parameter	NOUN
ejpam-6682	236	20	(	(	PUNCT
ejpam-6682	236	21	α	α	X
ejpam-6682	236	22	=	=	NOUN
ejpam-6682	236	23	0.90	0.90	NUM
ejpam-6682	236	24	,	,	PUNCT
ejpam-6682	236	25	0.91	0.91	NUM
ejpam-6682	236	26	,	,	PUNCT
ejpam-6682	236	27	0.92	0.92	NUM
ejpam-6682	236	28	,	,	PUNCT
ejpam-6682	236	29	0.94	0.94	NUM
ejpam-6682	236	30	)	)	PUNCT
ejpam-6682	236	31	.	.	PUNCT
ejpam-6682	237	1	fractional	fractional	ADJ
ejpam-6682	237	2	-	-	PUNCT
ejpam-6682	237	3	order	order	NOUN
ejpam-6682	237	4	models	model	NOUN
ejpam-6682	237	5	effectively	effectively	ADV
ejpam-6682	237	6	capture	capture	VERB
ejpam-6682	237	7	memory	memory	NOUN
ejpam-6682	237	8	effects	effect	NOUN
ejpam-6682	237	9	and	and	CCONJ
ejpam-6682	237	10	the	the	DET
ejpam-6682	237	11	long	long	ADJ
ejpam-6682	237	12	-	-	PUNCT
ejpam-6682	237	13	term	term	NOUN
ejpam-6682	237	14	dependence	dependence	NOUN
ejpam-6682	237	15	of	of	ADP
ejpam-6682	237	16	disease	disease	NOUN
ejpam-6682	237	17	progression	progression	NOUN
ejpam-6682	237	18	,	,	PUNCT
ejpam-6682	237	19	making	make	VERB
ejpam-6682	237	20	them	they	PRON
ejpam-6682	237	21	superior	superior	ADJ
ejpam-6682	237	22	to	to	ADP
ejpam-6682	237	23	classical	classical	ADJ
ejpam-6682	237	24	integer	integer	NOUN
ejpam-6682	237	25	-	-	PUNCT
ejpam-6682	237	26	order	order	NOUN
ejpam-6682	237	27	models	model	NOUN
ejpam-6682	237	28	in	in	ADP
ejpam-6682	237	29	representing	represent	VERB
ejpam-6682	237	30	dengue	dengue	NOUN
ejpam-6682	237	31	transmission	transmission	NOUN
ejpam-6682	237	32	dynamics	dynamic	NOUN
ejpam-6682	237	33	.	.	PUNCT
ejpam-6682	238	1	the	the	DET
ejpam-6682	238	2	(	(	PUNCT
ejpam-6682	238	3	s1	s1	NOUN
ejpam-6682	238	4	)	)	PUNCT
ejpam-6682	238	5	progressively	progressively	ADV
ejpam-6682	238	6	diminishes	diminish	VERB
ejpam-6682	238	7	over	over	ADP
ejpam-6682	238	8	time	time	NOUN
ejpam-6682	238	9	as	as	ADP
ejpam-6682	238	10	a	a	DET
ejpam-6682	238	11	result	result	NOUN
ejpam-6682	238	12	of	of	ADP
ejpam-6682	238	13	infection	infection	NOUN
ejpam-6682	238	14	transmission	transmission	NOUN
ejpam-6682	238	15	.	.	PUNCT
ejpam-6682	239	1	lower	low	ADJ
ejpam-6682	239	2	values	value	NOUN
ejpam-6682	239	3	of	of	ADP
ejpam-6682	239	4	α	α	NUM
ejpam-6682	239	5	lead	lead	NOUN
ejpam-6682	239	6	to	to	ADP
ejpam-6682	239	7	an	an	DET
ejpam-6682	239	8	accelerated	accelerated	ADJ
ejpam-6682	239	9	decline	decline	NOUN
ejpam-6682	239	10	,	,	PUNCT
ejpam-6682	239	11	indicating	indicate	VERB
ejpam-6682	239	12	that	that	SCONJ
ejpam-6682	239	13	fractional	fractional	ADJ
ejpam-6682	239	14	derivatives	derivative	NOUN
ejpam-6682	239	15	affect	affect	VERB
ejpam-6682	239	16	the	the	DET
ejpam-6682	239	17	rate	rate	NOUN
ejpam-6682	239	18	of	of	ADP
ejpam-6682	239	19	disease	disease	NOUN
ejpam-6682	239	20	transmission	transmission	NOUN
ejpam-6682	239	21	by	by	ADP
ejpam-6682	239	22	integrating	integrate	VERB
ejpam-6682	239	23	memory	memory	NOUN
ejpam-6682	239	24	effects	effect	NOUN
ejpam-6682	239	25	.	.	PUNCT
ejpam-6682	240	1	the	the	DET
ejpam-6682	240	2	(	(	PUNCT
ejpam-6682	240	3	i1	i1	NOUN
ejpam-6682	240	4	)	)	PUNCT
ejpam-6682	240	5	demonstrates	demonstrate	VERB
ejpam-6682	240	6	an	an	DET
ejpam-6682	240	7	exponential	exponential	ADJ
ejpam-6682	240	8	-	-	PUNCT
ejpam-6682	240	9	like	like	ADJ
ejpam-6682	240	10	growth	growth	NOUN
ejpam-6682	240	11	,	,	PUNCT
ejpam-6682	240	12	where	where	SCONJ
ejpam-6682	240	13	lower	low	ADJ
ejpam-6682	240	14	α	α	PROPN
ejpam-6682	240	15	values	value	NOUN
ejpam-6682	240	16	result	result	VERB
ejpam-6682	240	17	in	in	ADP
ejpam-6682	240	18	a	a	DET
ejpam-6682	240	19	greater	great	ADJ
ejpam-6682	240	20	peak	peak	NOUN
ejpam-6682	240	21	and	and	CCONJ
ejpam-6682	240	22	a	a	DET
ejpam-6682	240	23	more	more	ADV
ejpam-6682	240	24	gradual	gradual	ADJ
ejpam-6682	240	25	decay	decay	NOUN
ejpam-6682	240	26	.	.	PUNCT
ejpam-6682	241	1	this	this	DET
ejpam-6682	241	2	behaviour	behaviour	NOUN
ejpam-6682	241	3	illustrates	illustrate	VERB
ejpam-6682	241	4	the	the	DET
ejpam-6682	241	5	non	non	ADJ
ejpam-6682	241	6	-	-	ADJ
ejpam-6682	241	7	local	local	ADJ
ejpam-6682	241	8	effects	effect	NOUN
ejpam-6682	241	9	and	and	CCONJ
ejpam-6682	241	10	varied	varied	ADJ
ejpam-6682	241	11	characteristics	characteristic	NOUN
ejpam-6682	241	12	of	of	ADP
ejpam-6682	241	13	dengue	dengue	NOUN
ejpam-6682	241	14	transmission	transmission	NOUN
ejpam-6682	241	15	,	,	PUNCT
ejpam-6682	241	16	as	as	SCONJ
ejpam-6682	241	17	fractional	fractional	ADJ
ejpam-6682	241	18	models	model	NOUN
ejpam-6682	241	19	consider	consider	VERB
ejpam-6682	241	20	changes	change	NOUN
ejpam-6682	241	21	in	in	ADP
ejpam-6682	241	22	infection	infection	NOUN
ejpam-6682	241	23	duration	duration	NOUN
ejpam-6682	241	24	.	.	PUNCT
ejpam-6682	242	1	the	the	DET
ejpam-6682	242	2	(	(	PUNCT
ejpam-6682	242	3	a1	a1	NOUN
ejpam-6682	242	4	)	)	PUNCT
ejpam-6682	242	5	exhibits	exhibit	VERB
ejpam-6682	242	6	a	a	DET
ejpam-6682	242	7	comparable	comparable	ADJ
ejpam-6682	242	8	growth	growth	NOUN
ejpam-6682	242	9	trajectory	trajectory	NOUN
ejpam-6682	242	10	to	to	ADP
ejpam-6682	242	11	i1	i1	PROPN
ejpam-6682	242	12	,	,	PUNCT
ejpam-6682	242	13	albeit	albeit	SCONJ
ejpam-6682	242	14	with	with	ADP
ejpam-6682	242	15	diminished	diminished	ADJ
ejpam-6682	242	16	intensity	intensity	NOUN
ejpam-6682	242	17	.	.	PUNCT
ejpam-6682	243	1	the	the	DET
ejpam-6682	243	2	varying	vary	VERB
ejpam-6682	243	3	α	α	PROPN
ejpam-6682	243	4	values	value	NOUN
ejpam-6682	243	5	affect	affect	VERB
ejpam-6682	243	6	the	the	DET
ejpam-6682	243	7	trajectory	trajectory	NOUN
ejpam-6682	243	8	,	,	PUNCT
ejpam-6682	243	9	suggesting	suggest	VERB
ejpam-6682	243	10	that	that	SCONJ
ejpam-6682	243	11	fractional	fractional	ADJ
ejpam-6682	243	12	-	-	PUNCT
ejpam-6682	243	13	order	order	NOUN
ejpam-6682	243	14	models	model	NOUN
ejpam-6682	243	15	more	more	ADV
ejpam-6682	243	16	effectively	effectively	ADV
ejpam-6682	243	17	represent	represent	VERB
ejpam-6682	243	18	the	the	DET
ejpam-6682	243	19	delay	delay	NOUN
ejpam-6682	243	20	in	in	ADP
ejpam-6682	243	21	disease	disease	NOUN
ejpam-6682	243	22	progression	progression	NOUN
ejpam-6682	243	23	and	and	CCONJ
ejpam-6682	243	24	concealed	conceal	VERB
ejpam-6682	243	25	carriers	carrier	NOUN
ejpam-6682	243	26	.	.	PUNCT
ejpam-6682	244	1	r.	r.	PROPN
ejpam-6682	244	2	saadeh	saadeh	PROPN
ejpam-6682	244	3	et	et	PROPN
ejpam-6682	244	4	al	al	PROPN
ejpam-6682	244	5	.	.	PUNCT
ejpam-6682	244	6	/	/	SYM
ejpam-6682	244	7	eur	eur	PROPN
ejpam-6682	244	8	.	.	PUNCT
ejpam-6682	245	1	j.	j.	PROPN
ejpam-6682	245	2	pure	pure	PROPN
ejpam-6682	245	3	appl	appl	PROPN
ejpam-6682	245	4	.	.	PROPN
ejpam-6682	245	5	math	math	PROPN
ejpam-6682	245	6	,	,	PUNCT
ejpam-6682	245	7	18	18	NUM
ejpam-6682	245	8	(	(	PUNCT
ejpam-6682	245	9	4	4	NUM
ejpam-6682	245	10	)	)	PUNCT
ejpam-6682	245	11	(	(	PUNCT
ejpam-6682	245	12	2025	2025	NUM
ejpam-6682	245	13	)	)	PUNCT
ejpam-6682	245	14	,	,	PUNCT
ejpam-6682	245	15	6682	6682	NUM
ejpam-6682	245	16	12	12	NUM
ejpam-6682	245	17	of	of	ADP
ejpam-6682	245	18	21	21	NUM
ejpam-6682	245	19	4.2	4.2	NUM
ejpam-6682	245	20	.	.	PUNCT
ejpam-6682	246	1	fractal	fractal	ADJ
ejpam-6682	246	2	operator	operator	NOUN
ejpam-6682	246	3	in	in	ADP
ejpam-6682	246	4	this	this	DET
ejpam-6682	246	5	section	section	NOUN
ejpam-6682	246	6	,	,	PUNCT
ejpam-6682	246	7	we	we	PRON
ejpam-6682	246	8	present	present	VERB
ejpam-6682	246	9	the	the	DET
ejpam-6682	246	10	concept	concept	NOUN
ejpam-6682	246	11	of	of	ADP
ejpam-6682	246	12	fractal	fractal	ADJ
ejpam-6682	246	13	derivatives	derivative	NOUN
ejpam-6682	246	14	and	and	CCONJ
ejpam-6682	246	15	their	their	PRON
ejpam-6682	246	16	significance	significance	NOUN
ejpam-6682	246	17	in	in	ADP
ejpam-6682	246	18	dengue	dengue	NOUN
ejpam-6682	246	19	fever	fever	NOUN
ejpam-6682	246	20	spread	spread	VERB
ejpam-6682	246	21	modeling	modeling	NOUN
ejpam-6682	246	22	.	.	PUNCT
ejpam-6682	247	1	traditional	traditional	ADJ
ejpam-6682	247	2	differential	differential	ADJ
ejpam-6682	247	3	operators	operator	NOUN
ejpam-6682	247	4	fail	fail	VERB
ejpam-6682	247	5	to	to	PART
ejpam-6682	247	6	capture	capture	VERB
ejpam-6682	247	7	the	the	DET
ejpam-6682	247	8	complexities	complexity	NOUN
ejpam-6682	247	9	in	in	ADP
ejpam-6682	247	10	disease	disease	NOUN
ejpam-6682	247	11	dynamics	dynamic	NOUN
ejpam-6682	247	12	in	in	ADP
ejpam-6682	247	13	heterogeneous	heterogeneous	ADJ
ejpam-6682	247	14	environments	environment	NOUN
ejpam-6682	247	15	.	.	PUNCT
ejpam-6682	248	1	unlike	unlike	ADP
ejpam-6682	248	2	fractional	fractional	ADJ
ejpam-6682	248	3	derivatives	derivative	NOUN
ejpam-6682	248	4	,	,	PUNCT
ejpam-6682	248	5	which	which	PRON
ejpam-6682	248	6	are	be	AUX
ejpam-6682	248	7	typically	typically	ADV
ejpam-6682	248	8	defined	define	VERB
ejpam-6682	248	9	in	in	ADP
ejpam-6682	248	10	terms	term	NOUN
ejpam-6682	248	11	of	of	ADP
ejpam-6682	248	12	convolution	convolution	NOUN
ejpam-6682	248	13	integrals	integral	NOUN
ejpam-6682	248	14	,	,	PUNCT
ejpam-6682	248	15	the	the	DET
ejpam-6682	248	16	fractal	fractal	ADJ
ejpam-6682	248	17	derivative	derivative	NOUN
ejpam-6682	248	18	is	be	AUX
ejpam-6682	248	19	local	local	ADJ
ejpam-6682	248	20	,	,	PUNCT
ejpam-6682	248	21	thus	thus	ADV
ejpam-6682	248	22	being	be	AUX
ejpam-6682	248	23	computationally	computationally	ADV
ejpam-6682	248	24	efficient	efficient	ADJ
ejpam-6682	248	25	and	and	CCONJ
ejpam-6682	248	26	structurally	structurally	ADV
ejpam-6682	248	27	distinct	distinct	ADJ
ejpam-6682	248	28	[	[	X
ejpam-6682	248	29	42–44	42–44	NUM
ejpam-6682	248	30	]	]	X
ejpam-6682	248	31	.	.	PUNCT
ejpam-6682	249	1	it	it	PRON
ejpam-6682	249	2	is	be	AUX
ejpam-6682	249	3	formulated	formulate	VERB
ejpam-6682	249	4	in	in	ADP
ejpam-6682	249	5	a	a	DET
ejpam-6682	249	6	non	non	ADJ
ejpam-6682	249	7	-	-	ADJ
ejpam-6682	249	8	euclidean	euclidean	ADJ
ejpam-6682	249	9	fractal	fractal	ADJ
ejpam-6682	249	10	metric	metric	ADJ
ejpam-6682	249	11	space	space	NOUN
ejpam-6682	249	12	[	[	X
ejpam-6682	249	13	45	45	NUM
ejpam-6682	249	14	,	,	PUNCT
ejpam-6682	249	15	46	46	NUM
ejpam-6682	249	16	]	]	PUNCT
ejpam-6682	249	17	,	,	PUNCT
ejpam-6682	249	18	making	make	VERB
ejpam-6682	249	19	it	it	PRON
ejpam-6682	249	20	possible	possible	ADJ
ejpam-6682	249	21	to	to	PART
ejpam-6682	249	22	describe	describe	VERB
ejpam-6682	249	23	the	the	DET
ejpam-6682	249	24	irregularity	irregularity	NOUN
ejpam-6682	249	25	and	and	CCONJ
ejpam-6682	249	26	self	self	NOUN
ejpam-6682	249	27	-	-	PUNCT
ejpam-6682	249	28	similarity	similarity	NOUN
ejpam-6682	249	29	of	of	ADP
ejpam-6682	249	30	real	real	ADJ
ejpam-6682	249	31	phenomena	phenomenon	NOUN
ejpam-6682	249	32	.	.	PUNCT
ejpam-6682	250	1	the	the	DET
ejpam-6682	250	2	novelty	novelty	NOUN
ejpam-6682	250	3	of	of	ADP
ejpam-6682	250	4	this	this	DET
ejpam-6682	250	5	mathematical	mathematical	ADJ
ejpam-6682	250	6	strategy	strategy	NOUN
ejpam-6682	250	7	provides	provide	VERB
ejpam-6682	250	8	an	an	DET
ejpam-6682	250	9	improved	improved	ADJ
ejpam-6682	250	10	description	description	NOUN
ejpam-6682	250	11	of	of	ADP
ejpam-6682	250	12	dengue	dengue	NOUN
ejpam-6682	250	13	fever	fever	NOUN
ejpam-6682	250	14	transmission	transmission	NOUN
ejpam-6682	250	15	,	,	PUNCT
ejpam-6682	250	16	particularly	particularly	ADV
ejpam-6682	250	17	in	in	ADP
ejpam-6682	250	18	situations	situation	NOUN
ejpam-6682	250	19	where	where	SCONJ
ejpam-6682	250	20	spatial	spatial	ADJ
ejpam-6682	250	21	heterogeneity	heterogeneity	NOUN
ejpam-6682	250	22	is	be	AUX
ejpam-6682	250	23	of	of	ADP
ejpam-6682	250	24	the	the	DET
ejpam-6682	250	25	utmost	utmost	ADJ
ejpam-6682	250	26	importance	importance	NOUN
ejpam-6682	250	27	.	.	PUNCT
ejpam-6682	251	1	the	the	DET
ejpam-6682	251	2	application	application	NOUN
ejpam-6682	251	3	of	of	ADP
ejpam-6682	251	4	fractal	fractal	ADJ
ejpam-6682	251	5	derivatives	derivative	NOUN
ejpam-6682	251	6	to	to	ADP
ejpam-6682	251	7	epidemiological	epidemiological	ADJ
ejpam-6682	251	8	modeling	modeling	NOUN
ejpam-6682	251	9	provides	provide	VERB
ejpam-6682	251	10	an	an	DET
ejpam-6682	251	11	improved	improved	ADJ
ejpam-6682	251	12	understanding	understanding	NOUN
ejpam-6682	251	13	of	of	ADP
ejpam-6682	251	14	the	the	DET
ejpam-6682	251	15	transmission	transmission	NOUN
ejpam-6682	251	16	of	of	ADP
ejpam-6682	251	17	the	the	DET
ejpam-6682	251	18	disease	disease	NOUN
ejpam-6682	251	19	and	and	CCONJ
ejpam-6682	251	20	increases	increase	VERB
ejpam-6682	251	21	predictive	predictive	ADJ
ejpam-6682	251	22	capacity	capacity	NOUN
ejpam-6682	251	23	.	.	PUNCT
ejpam-6682	252	1	we	we	PRON
ejpam-6682	252	2	present	present	VERB
ejpam-6682	252	3	system	system	NOUN
ejpam-6682	252	4	1	1	NUM
ejpam-6682	252	5	with	with	ADP
ejpam-6682	252	6	a	a	DET
ejpam-6682	252	7	fractal	fractal	ADJ
ejpam-6682	252	8	operator	operator	NOUN
ejpam-6682	252	9	:	:	PUNCT
ejpam-6682	253	1	ds1	ds1	PROPN
ejpam-6682	253	2	dt	dt	PROPN
ejpam-6682	254	1	=	=	SYM
ejpam-6682	254	2	αtα−1µ1n1	αtα−1µ1n1	PROPN
ejpam-6682	254	3	−	−	PROPN
ejpam-6682	254	4	β1	β1	PROPN
ejpam-6682	254	5	s1i2	s1i2	INTJ
ejpam-6682	254	6	n1	n1	PROPN
ejpam-6682	254	7	−	−	PROPN
ejpam-6682	254	8	µ1s1	µ1s1	NOUN
ejpam-6682	254	9	,	,	PUNCT
ejpam-6682	254	10	di1	di1	INTJ
ejpam-6682	254	11	dt	dt	NOUN
ejpam-6682	254	12	=	=	SYM
ejpam-6682	254	13	αtα−1β1i2	αtα−1β1i2	NUM
ejpam-6682	254	14	n1	n1	NOUN
ejpam-6682	254	15	s1	s1	NOUN
ejpam-6682	254	16	+	+	CCONJ
ejpam-6682	254	17	δ1a1	δ1a1	NOUN
ejpam-6682	254	18	−	−	PROPN
ejpam-6682	254	19	(	(	PUNCT
ejpam-6682	254	20	µ1	µ1	PROPN
ejpam-6682	254	21	+	+	CCONJ
ejpam-6682	254	22	γ)i1	γ)i1	PROPN
ejpam-6682	254	23	,	,	PUNCT
ejpam-6682	254	24	da1	da1	PROPN
ejpam-6682	254	25	dt	dt	NOUN
ejpam-6682	255	1	=	=	SYM
ejpam-6682	255	2	αtα−1pγi1	αtα−1pγi1	ADJ
ejpam-6682	255	3	−	−	PROPN
ejpam-6682	255	4	(	(	PUNCT
ejpam-6682	255	5	µ1	µ1	PROPN
ejpam-6682	255	6	+	+	X
ejpam-6682	255	7	δ1)a1	δ1)a1	PROPN
ejpam-6682	255	8	,	,	PUNCT
ejpam-6682	255	9	dr1	dr1	PROPN
ejpam-6682	255	10	dt	dt	NOUN
ejpam-6682	255	11	=	=	SYM
ejpam-6682	255	12	αtα−1(1−	αtα−1(1−	NOUN
ejpam-6682	255	13	p)γi1	p)γi1	NOUN
ejpam-6682	255	14	−	−	NOUN
ejpam-6682	255	15	µ1r1	µ1r1	NOUN
ejpam-6682	255	16	.	.	PUNCT
ejpam-6682	256	1	ds2	ds2	PROPN
ejpam-6682	256	2	dt	dt	X
ejpam-6682	256	3	=	=	PUNCT
ejpam-6682	256	4	αtα−1µ2n2	αtα−1µ2n2	NOUN
ejpam-6682	256	5	−	−	NOUN
ejpam-6682	256	6	β2	β2	NOUN
ejpam-6682	256	7	s2i1	s2i1	CCONJ
ejpam-6682	256	8	n1	n1	NOUN
ejpam-6682	256	9	−	−	PROPN
ejpam-6682	256	10	µ2s2	µ2s2	PROPN
ejpam-6682	256	11	,	,	PUNCT
ejpam-6682	256	12	di2	di2	PROPN
ejpam-6682	256	13	dt	dt	X
ejpam-6682	257	1	=	=	SYM
ejpam-6682	257	2	αtα−1β2	αtα−1β2	NUM
ejpam-6682	257	3	s2i1	s2i1	ADV
ejpam-6682	257	4	n1	n1	NOUN
ejpam-6682	257	5	−	−	NUM
ejpam-6682	257	6	µ2i2	µ2i2	X
ejpam-6682	257	7	.	.	PUNCT
ejpam-6682	258	1	(	(	PUNCT
ejpam-6682	258	2	10	10	NUM
ejpam-6682	258	3	)	)	PUNCT
ejpam-6682	258	4	now	now	ADV
ejpam-6682	258	5	,	,	PUNCT
ejpam-6682	258	6	we	we	PRON
ejpam-6682	258	7	apply	apply	VERB
ejpam-6682	258	8	the	the	DET
ejpam-6682	258	9	4th	4th	ADJ
ejpam-6682	258	10	-	-	PUNCT
ejpam-6682	258	11	order	order	NOUN
ejpam-6682	258	12	runge	runge	NOUN
ejpam-6682	258	13	-	-	PUNCT
ejpam-6682	258	14	kutta	kutta	NOUN
ejpam-6682	258	15	method	method	NOUN
ejpam-6682	258	16	to	to	PART
ejpam-6682	258	17	solve	solve	VERB
ejpam-6682	258	18	the	the	DET
ejpam-6682	258	19	fractal	fractal	ADJ
ejpam-6682	258	20	system	system	NOUN
ejpam-6682	258	21	and	and	CCONJ
ejpam-6682	258	22	perform	perform	VERB
ejpam-6682	258	23	simulations	simulation	NOUN
ejpam-6682	258	24	using	use	VERB
ejpam-6682	258	25	rk4	rk4	NOUN
ejpam-6682	258	26	.	.	PUNCT
ejpam-6682	259	1	r.	r.	PROPN
ejpam-6682	259	2	saadeh	saadeh	PROPN
ejpam-6682	259	3	et	et	PROPN
ejpam-6682	259	4	al	al	PROPN
ejpam-6682	259	5	.	.	PUNCT
ejpam-6682	259	6	/	/	SYM
ejpam-6682	259	7	eur	eur	PROPN
ejpam-6682	259	8	.	.	PUNCT
ejpam-6682	260	1	j.	j.	PROPN
ejpam-6682	260	2	pure	pure	PROPN
ejpam-6682	260	3	appl	appl	PROPN
ejpam-6682	260	4	.	.	PROPN
ejpam-6682	260	5	math	math	PROPN
ejpam-6682	260	6	,	,	PUNCT
ejpam-6682	260	7	18	18	NUM
ejpam-6682	260	8	(	(	PUNCT
ejpam-6682	260	9	4	4	NUM
ejpam-6682	260	10	)	)	PUNCT
ejpam-6682	260	11	(	(	PUNCT
ejpam-6682	260	12	2025	2025	NUM
ejpam-6682	260	13	)	)	PUNCT
ejpam-6682	260	14	,	,	PUNCT
ejpam-6682	260	15	6682	6682	NUM
ejpam-6682	260	16	13	13	NUM
ejpam-6682	260	17	of	of	ADP
ejpam-6682	260	18	21	21	NUM
ejpam-6682	260	19	(	(	PUNCT
ejpam-6682	260	20	a	a	NOUN
ejpam-6682	260	21	)	)	PUNCT
ejpam-6682	260	22	s1	s1	NOUN
ejpam-6682	260	23	(	(	PUNCT
ejpam-6682	260	24	b	b	NOUN
ejpam-6682	260	25	)	)	PUNCT
ejpam-6682	260	26	i1	i1	NOUN
ejpam-6682	260	27	(	(	PUNCT
ejpam-6682	260	28	c	c	NOUN
ejpam-6682	260	29	)	)	PUNCT
ejpam-6682	260	30	a1	a1	NOUN
ejpam-6682	260	31	(	(	PUNCT
ejpam-6682	260	32	d	d	NOUN
ejpam-6682	260	33	)	)	PUNCT
ejpam-6682	260	34	r1	r1	NOUN
ejpam-6682	260	35	(	(	PUNCT
ejpam-6682	260	36	e	e	NOUN
ejpam-6682	260	37	)	)	PUNCT
ejpam-6682	260	38	s2	s2	NOUN
ejpam-6682	260	39	(	(	PUNCT
ejpam-6682	260	40	f	f	X
ejpam-6682	260	41	)	)	PUNCT
ejpam-6682	260	42	i2	i2	NOUN
ejpam-6682	260	43	figure	figure	NOUN
ejpam-6682	260	44	3	3	NUM
ejpam-6682	260	45	:	:	PUNCT
ejpam-6682	260	46	fractal	fractal	ADJ
ejpam-6682	260	47	dynamics	dynamic	NOUN
ejpam-6682	260	48	of	of	ADP
ejpam-6682	260	49	the	the	DET
ejpam-6682	260	50	compartmental	compartmental	ADJ
ejpam-6682	260	51	variables	variable	NOUN
ejpam-6682	260	52	s1(t	s1(t	PART
ejpam-6682	260	53	)	)	PUNCT
ejpam-6682	260	54	,	,	PUNCT
ejpam-6682	260	55	i1(t	i1(t	PROPN
ejpam-6682	260	56	)	)	PUNCT
ejpam-6682	260	57	,	,	PUNCT
ejpam-6682	260	58	a1(t	a1(t	PROPN
ejpam-6682	260	59	)	)	PUNCT
ejpam-6682	260	60	,	,	PUNCT
ejpam-6682	260	61	r1(t	r1(t	PROPN
ejpam-6682	260	62	)	)	PUNCT
ejpam-6682	260	63	,	,	PUNCT
ejpam-6682	260	64	s2(t	s2(t	PROPN
ejpam-6682	260	65	)	)	PUNCT
ejpam-6682	260	66	,	,	PUNCT
ejpam-6682	260	67	and	and	CCONJ
ejpam-6682	260	68	i2(t	i2(t	PROPN
ejpam-6682	260	69	)	)	PUNCT
ejpam-6682	260	70	under	under	ADP
ejpam-6682	260	71	varying	vary	VERB
ejpam-6682	260	72	fractal	fractal	ADJ
ejpam-6682	260	73	dimensions	dimension	NOUN
ejpam-6682	260	74	(	(	PUNCT
ejpam-6682	260	75	τ	τ	PROPN
ejpam-6682	260	76	)	)	PUNCT
ejpam-6682	260	77	.	.	PUNCT
ejpam-6682	261	1	figure	figure	NOUN
ejpam-6682	261	2	2	2	NUM
ejpam-6682	261	3	shows	show	VERB
ejpam-6682	261	4	how	how	SCONJ
ejpam-6682	261	5	the	the	DET
ejpam-6682	261	6	model	model	NOUN
ejpam-6682	261	7	compartments	compartment	NOUN
ejpam-6682	261	8	(	(	PUNCT
ejpam-6682	261	9	system	system	NOUN
ejpam-6682	261	10	1	1	NUM
ejpam-6682	261	11	)	)	PUNCT
ejpam-6682	261	12	changed	change	VERB
ejpam-6682	261	13	over	over	ADP
ejpam-6682	261	14	time	time	NOUN
ejpam-6682	261	15	when	when	SCONJ
ejpam-6682	261	16	the	the	DET
ejpam-6682	261	17	fractal	fractal	ADJ
ejpam-6682	261	18	values	value	NOUN
ejpam-6682	261	19	changed	change	VERB
ejpam-6682	261	20	(	(	PUNCT
ejpam-6682	261	21	α	α	NOUN
ejpam-6682	261	22	=	=	NOUN
ejpam-6682	261	23	0.90	0.90	NUM
ejpam-6682	261	24	,	,	PUNCT
ejpam-6682	261	25	0.91	0.91	NUM
ejpam-6682	261	26	,	,	PUNCT
ejpam-6682	261	27	0.92	0.92	NUM
ejpam-6682	261	28	,	,	PUNCT
ejpam-6682	261	29	0.94	0.94	NUM
ejpam-6682	261	30	)	)	PUNCT
ejpam-6682	261	31	.	.	PUNCT
ejpam-6682	262	1	the	the	DET
ejpam-6682	262	2	human	human	ADJ
ejpam-6682	262	3	susceptible	susceptible	ADJ
ejpam-6682	262	4	population	population	NOUN
ejpam-6682	262	5	(	(	PUNCT
ejpam-6682	262	6	s1	s1	NOUN
ejpam-6682	262	7	)	)	PUNCT
ejpam-6682	262	8	slowly	slowly	ADV
ejpam-6682	262	9	decreases	decrease	VERB
ejpam-6682	262	10	over	over	ADP
ejpam-6682	262	11	time	time	NOUN
ejpam-6682	262	12	as	as	SCONJ
ejpam-6682	262	13	more	more	ADJ
ejpam-6682	262	14	people	people	NOUN
ejpam-6682	262	15	become	become	VERB
ejpam-6682	262	16	infected	infect	VERB
ejpam-6682	262	17	.	.	PUNCT
ejpam-6682	263	1	the	the	DET
ejpam-6682	263	2	rate	rate	NOUN
ejpam-6682	263	3	of	of	ADP
ejpam-6682	263	4	decline	decline	NOUN
ejpam-6682	263	5	changes	change	NOUN
ejpam-6682	263	6	with	with	ADP
ejpam-6682	263	7	lower	low	ADJ
ejpam-6682	263	8	values	value	NOUN
ejpam-6682	263	9	of	of	ADP
ejpam-6682	263	10	alpha	alpha	NOUN
ejpam-6682	263	11	,	,	PUNCT
ejpam-6682	263	12	where	where	SCONJ
ejpam-6682	263	13	lower	low	ADJ
ejpam-6682	263	14	values	value	NOUN
ejpam-6682	263	15	of	of	ADP
ejpam-6682	263	16	fractal	fractal	ADJ
ejpam-6682	263	17	order	order	NOUN
ejpam-6682	263	18	accelerate	accelerate	VERB
ejpam-6682	263	19	the	the	DET
ejpam-6682	263	20	rate	rate	NOUN
ejpam-6682	263	21	of	of	ADP
ejpam-6682	263	22	decline	decline	NOUN
ejpam-6682	263	23	.	.	PUNCT
ejpam-6682	264	1	the	the	DET
ejpam-6682	264	2	asymmetric	asymmetric	ADJ
ejpam-6682	264	3	pattern	pattern	NOUN
ejpam-6682	264	4	shows	show	VERB
ejpam-6682	264	5	the	the	DET
ejpam-6682	264	6	importance	importance	NOUN
ejpam-6682	264	7	of	of	ADP
ejpam-6682	264	8	fractal	fractal	ADJ
ejpam-6682	264	9	derivatives	derivative	NOUN
ejpam-6682	264	10	in	in	ADP
ejpam-6682	264	11	modeling	model	VERB
ejpam-6682	264	12	complex	complex	ADJ
ejpam-6682	264	13	disease	disease	NOUN
ejpam-6682	264	14	spread	spread	VERB
ejpam-6682	264	15	patterns	pattern	NOUN
ejpam-6682	264	16	in	in	ADP
ejpam-6682	264	17	the	the	DET
ejpam-6682	264	18	real	real	ADJ
ejpam-6682	264	19	world	world	NOUN
ejpam-6682	264	20	.	.	PUNCT
ejpam-6682	265	1	the	the	DET
ejpam-6682	265	2	number	number	NOUN
ejpam-6682	265	3	of	of	ADP
ejpam-6682	265	4	infected	infected	ADJ
ejpam-6682	265	5	people	people	NOUN
ejpam-6682	265	6	(	(	PUNCT
ejpam-6682	265	7	i1	i1	PROPN
ejpam-6682	265	8	)	)	PUNCT
ejpam-6682	265	9	grows	grow	VERB
ejpam-6682	265	10	at	at	ADP
ejpam-6682	265	11	an	an	DET
ejpam-6682	265	12	exponential	exponential	ADJ
ejpam-6682	265	13	rate	rate	NOUN
ejpam-6682	265	14	over	over	ADP
ejpam-6682	265	15	time	time	NOUN
ejpam-6682	265	16	,	,	PUNCT
ejpam-6682	265	17	reaching	reach	VERB
ejpam-6682	265	18	a	a	DET
ejpam-6682	265	19	peak	peak	NOUN
ejpam-6682	265	20	before	before	ADP
ejpam-6682	265	21	starting	start	VERB
ejpam-6682	265	22	to	to	PART
ejpam-6682	265	23	fall	fall	VERB
ejpam-6682	265	24	.	.	PUNCT
ejpam-6682	266	1	the	the	DET
ejpam-6682	266	2	quantity	quantity	NOUN
ejpam-6682	266	3	i1	i1	PROPN
ejpam-6682	266	4	increases	increase	VERB
ejpam-6682	266	5	exponentially	exponentially	ADV
ejpam-6682	266	6	over	over	ADP
ejpam-6682	266	7	time	time	NOUN
ejpam-6682	266	8	,	,	PUNCT
ejpam-6682	266	9	attaining	attain	VERB
ejpam-6682	266	10	a	a	DET
ejpam-6682	266	11	maximum	maximum	ADJ
ejpam-6682	266	12	before	before	ADP
ejpam-6682	266	13	declining	decline	VERB
ejpam-6682	266	14	thereafter	thereafter	ADV
ejpam-6682	266	15	.	.	PUNCT
ejpam-6682	267	1	lower	low	ADJ
ejpam-6682	267	2	α	α	PROPN
ejpam-6682	267	3	values	value	NOUN
ejpam-6682	267	4	result	result	VERB
ejpam-6682	267	5	in	in	ADP
ejpam-6682	267	6	a	a	DET
ejpam-6682	267	7	higher	high	ADJ
ejpam-6682	267	8	peak	peak	NOUN
ejpam-6682	267	9	and	and	CCONJ
ejpam-6682	267	10	a	a	DET
ejpam-6682	267	11	slower	slow	ADJ
ejpam-6682	267	12	decay	decay	NOUN
ejpam-6682	267	13	,	,	PUNCT
ejpam-6682	267	14	suggesting	suggest	VERB
ejpam-6682	267	15	that	that	SCONJ
ejpam-6682	267	16	fractal	fractal	ADJ
ejpam-6682	267	17	dynamics	dynamic	NOUN
ejpam-6682	267	18	contribute	contribute	VERB
ejpam-6682	267	19	to	to	ADP
ejpam-6682	267	20	disease	disease	NOUN
ejpam-6682	267	21	persistence	persistence	NOUN
ejpam-6682	267	22	by	by	ADP
ejpam-6682	267	23	capturing	capture	VERB
ejpam-6682	267	24	delayed	delay	VERB
ejpam-6682	267	25	recovery	recovery	NOUN
ejpam-6682	267	26	and	and	CCONJ
ejpam-6682	267	27	spatially	spatially	ADV
ejpam-6682	267	28	heterogeneous	heterogeneous	ADJ
ejpam-6682	267	29	transmission	transmission	NOUN
ejpam-6682	267	30	.	.	PUNCT
ejpam-6682	268	1	over	over	ADP
ejpam-6682	268	2	time	time	NOUN
ejpam-6682	268	3	,	,	PUNCT
ejpam-6682	268	4	the	the	DET
ejpam-6682	268	5	asymptomatic	asymptomatic	ADJ
ejpam-6682	268	6	human	human	ADJ
ejpam-6682	268	7	population	population	NOUN
ejpam-6682	268	8	(	(	PUNCT
ejpam-6682	268	9	a1	a1	PROPN
ejpam-6682	268	10	)	)	PUNCT
ejpam-6682	268	11	follows	follow	VERB
ejpam-6682	268	12	a	a	DET
ejpam-6682	268	13	growth	growth	NOUN
ejpam-6682	268	14	trend	trend	NOUN
ejpam-6682	268	15	similar	similar	ADJ
ejpam-6682	268	16	to	to	ADP
ejpam-6682	268	17	i1	i1	PROPN
ejpam-6682	268	18	but	but	CCONJ
ejpam-6682	268	19	at	at	ADP
ejpam-6682	268	20	a	a	DET
ejpam-6682	268	21	lower	low	ADJ
ejpam-6682	268	22	intensity	intensity	NOUN
ejpam-6682	268	23	.	.	PUNCT
ejpam-6682	269	1	with	with	ADP
ejpam-6682	269	2	time	time	NOUN
ejpam-6682	269	3	,	,	PUNCT
ejpam-6682	269	4	the	the	DET
ejpam-6682	269	5	recovered	recovered	ADJ
ejpam-6682	269	6	population	population	NOUN
ejpam-6682	269	7	(	(	PUNCT
ejpam-6682	269	8	r1	r1	PROPN
ejpam-6682	269	9	)	)	PUNCT
ejpam-6682	269	10	gradually	gradually	ADV
ejpam-6682	269	11	increases	increase	VERB
ejpam-6682	269	12	.	.	PUNCT
ejpam-6682	270	1	the	the	DET
ejpam-6682	270	2	recovery	recovery	NOUN
ejpam-6682	270	3	trajectory	trajectory	NOUN
ejpam-6682	270	4	depends	depend	VERB
ejpam-6682	270	5	on	on	ADP
ejpam-6682	270	6	α	α	NOUN
ejpam-6682	270	7	,	,	PUNCT
ejpam-6682	270	8	where	where	SCONJ
ejpam-6682	270	9	lower	low	ADJ
ejpam-6682	270	10	values	value	NOUN
ejpam-6682	270	11	correspond	correspond	VERB
ejpam-6682	270	12	to	to	ADP
ejpam-6682	270	13	faster	fast	ADJ
ejpam-6682	270	14	accumulation	accumulation	NOUN
ejpam-6682	270	15	of	of	ADP
ejpam-6682	270	16	immunity	immunity	NOUN
ejpam-6682	270	17	,	,	PUNCT
ejpam-6682	270	18	likely	likely	ADJ
ejpam-6682	270	19	due	due	ADJ
ejpam-6682	270	20	to	to	ADP
ejpam-6682	270	21	shorter	short	ADJ
ejpam-6682	270	22	infectious	infectious	ADJ
ejpam-6682	270	23	periods	period	NOUN
ejpam-6682	270	24	and	and	CCONJ
ejpam-6682	270	25	delayed	delay	VERB
ejpam-6682	270	26	waning	wane	VERB
ejpam-6682	270	27	immunity	immunity	NOUN
ejpam-6682	270	28	,	,	PUNCT
ejpam-6682	270	29	as	as	SCONJ
ejpam-6682	270	30	captured	capture	VERB
ejpam-6682	270	31	by	by	ADP
ejpam-6682	270	32	fractal	fractal	ADJ
ejpam-6682	270	33	operators	operator	NOUN
ejpam-6682	270	34	.	.	PUNCT
ejpam-6682	271	1	based	base	VERB
ejpam-6682	271	2	on	on	ADP
ejpam-6682	271	3	this	this	DET
ejpam-6682	271	4	behavior	behavior	NOUN
ejpam-6682	271	5	,	,	PUNCT
ejpam-6682	271	6	it	it	PRON
ejpam-6682	271	7	seems	seem	VERB
ejpam-6682	271	8	that	that	SCONJ
ejpam-6682	271	9	fractal	fractal	ADJ
ejpam-6682	271	10	models	model	NOUN
ejpam-6682	271	11	are	be	AUX
ejpam-6682	271	12	a	a	DET
ejpam-6682	271	13	better	well	ADJ
ejpam-6682	271	14	way	way	NOUN
ejpam-6682	271	15	to	to	PART
ejpam-6682	271	16	show	show	VERB
ejpam-6682	271	17	immune	immune	ADJ
ejpam-6682	271	18	responses	response	NOUN
ejpam-6682	271	19	,	,	PUNCT
ejpam-6682	271	20	especially	especially	ADV
ejpam-6682	271	21	when	when	SCONJ
ejpam-6682	271	22	there	there	PRON
ejpam-6682	271	23	is	be	VERB
ejpam-6682	271	24	partial	partial	ADJ
ejpam-6682	271	25	immunity	immunity	NOUN
ejpam-6682	271	26	and	and	CCONJ
ejpam-6682	271	27	infections	infection	NOUN
ejpam-6682	271	28	keep	keep	VERB
ejpam-6682	271	29	happening	happen	VERB
ejpam-6682	271	30	.	.	PUNCT
ejpam-6682	272	1	the	the	DET
ejpam-6682	272	2	susceptible	susceptible	ADJ
ejpam-6682	272	3	vector	vector	NOUN
ejpam-6682	272	4	population	population	NOUN
ejpam-6682	272	5	(	(	PUNCT
ejpam-6682	272	6	s2	s2	PROPN
ejpam-6682	272	7	)	)	PUNCT
ejpam-6682	272	8	declines	decline	VERB
ejpam-6682	272	9	over	over	ADP
ejpam-6682	272	10	time	time	NOUN
ejpam-6682	272	11	,	,	PUNCT
ejpam-6682	272	12	similar	similar	ADJ
ejpam-6682	272	13	to	to	ADP
ejpam-6682	272	14	s1	s1	PROPN
ejpam-6682	272	15	.	.	PUNCT
ejpam-6682	273	1	however	however	ADV
ejpam-6682	273	2	,	,	PUNCT
ejpam-6682	273	3	its	its	PRON
ejpam-6682	273	4	trajectory	trajectory	NOUN
ejpam-6682	273	5	changes	change	NOUN
ejpam-6682	273	6	,	,	PUNCT
ejpam-6682	273	7	suggesting	suggest	VERB
ejpam-6682	273	8	that	that	SCONJ
ejpam-6682	273	9	reduced	reduce	VERB
ejpam-6682	273	10	sensitivity	sensitivity	NOUN
ejpam-6682	273	11	or	or	CCONJ
ejpam-6682	273	12	resistance	resistance	NOUN
ejpam-6682	273	13	to	to	ADP
ejpam-6682	273	14	reinfection	reinfection	NOUN
ejpam-6682	273	15	influences	influence	VERB
ejpam-6682	273	16	secondary	secondary	ADJ
ejpam-6682	273	17	exposure	exposure	NOUN
ejpam-6682	273	18	risks	risk	NOUN
ejpam-6682	273	19	.	.	PUNCT
ejpam-6682	274	1	the	the	DET
ejpam-6682	274	2	infected	infected	ADJ
ejpam-6682	274	3	vector	vector	NOUN
ejpam-6682	274	4	population	population	NOUN
ejpam-6682	274	5	(	(	PUNCT
ejpam-6682	274	6	i2	i2	PROPN
ejpam-6682	274	7	)	)	PUNCT
ejpam-6682	274	8	exhibits	exhibit	VERB
ejpam-6682	274	9	a	a	DET
ejpam-6682	274	10	multiwave	multiwave	NOUN
ejpam-6682	274	11	pattern	pattern	NOUN
ejpam-6682	274	12	,	,	PUNCT
ejpam-6682	274	13	suggesting	suggest	VERB
ejpam-6682	274	14	delayed	delay	VERB
ejpam-6682	274	15	r.	r.	PROPN
ejpam-6682	274	16	saadeh	saadeh	PROPN
ejpam-6682	275	1	et	et	PROPN
ejpam-6682	275	2	al	al	PROPN
ejpam-6682	275	3	.	.	PUNCT
ejpam-6682	275	4	/	/	SYM
ejpam-6682	275	5	eur	eur	PROPN
ejpam-6682	275	6	.	.	PUNCT
ejpam-6682	276	1	j.	j.	PROPN
ejpam-6682	276	2	pure	pure	PROPN
ejpam-6682	276	3	appl	appl	PROPN
ejpam-6682	276	4	.	.	PROPN
ejpam-6682	276	5	math	math	PROPN
ejpam-6682	276	6	,	,	PUNCT
ejpam-6682	276	7	18	18	NUM
ejpam-6682	276	8	(	(	PUNCT
ejpam-6682	276	9	4	4	NUM
ejpam-6682	276	10	)	)	PUNCT
ejpam-6682	276	11	(	(	PUNCT
ejpam-6682	276	12	2025	2025	NUM
ejpam-6682	276	13	)	)	PUNCT
ejpam-6682	276	14	,	,	PUNCT
ejpam-6682	276	15	6682	6682	NUM
ejpam-6682	276	16	14	14	NUM
ejpam-6682	276	17	of	of	ADP
ejpam-6682	276	18	21	21	NUM
ejpam-6682	276	19	secondary	secondary	ADJ
ejpam-6682	276	20	infections	infection	NOUN
ejpam-6682	276	21	or	or	CCONJ
ejpam-6682	276	22	reinfections	reinfection	NOUN
ejpam-6682	276	23	.	.	PUNCT
ejpam-6682	277	1	the	the	DET
ejpam-6682	277	2	fractal	fractal	ADJ
ejpam-6682	277	3	-	-	PUNCT
ejpam-6682	277	4	order	order	NOUN
ejpam-6682	277	5	operator	operator	NOUN
ejpam-6682	277	6	modifies	modify	VERB
ejpam-6682	277	7	the	the	DET
ejpam-6682	277	8	transmission	transmission	NOUN
ejpam-6682	277	9	dynamics	dynamic	NOUN
ejpam-6682	277	10	,	,	PUNCT
ejpam-6682	277	11	incorporating	incorporate	VERB
ejpam-6682	277	12	erratic	erratic	ADJ
ejpam-6682	277	13	disease	disease	NOUN
ejpam-6682	277	14	spread	spread	VERB
ejpam-6682	277	15	and	and	CCONJ
ejpam-6682	277	16	persistent	persistent	ADJ
ejpam-6682	277	17	outbreaks	outbreak	NOUN
ejpam-6682	277	18	.	.	PUNCT
ejpam-6682	278	1	this	this	PRON
ejpam-6682	278	2	means	mean	VERB
ejpam-6682	278	3	that	that	SCONJ
ejpam-6682	278	4	fractal	fractal	ADJ
ejpam-6682	278	5	models	model	NOUN
ejpam-6682	278	6	are	be	AUX
ejpam-6682	278	7	a	a	DET
ejpam-6682	278	8	better	well	ADJ
ejpam-6682	278	9	way	way	NOUN
ejpam-6682	278	10	to	to	PART
ejpam-6682	278	11	show	show	VERB
ejpam-6682	278	12	the	the	DET
ejpam-6682	278	13	chances	chance	NOUN
ejpam-6682	278	14	of	of	ADP
ejpam-6682	278	15	getting	get	VERB
ejpam-6682	278	16	dengue	dengue	NOUN
ejpam-6682	278	17	again	again	ADV
ejpam-6682	278	18	and	and	CCONJ
ejpam-6682	278	19	secondary	secondary	ADJ
ejpam-6682	278	20	waves	wave	NOUN
ejpam-6682	278	21	of	of	ADP
ejpam-6682	278	22	the	the	DET
ejpam-6682	278	23	disease	disease	NOUN
ejpam-6682	278	24	,	,	PUNCT
ejpam-6682	278	25	which	which	PRON
ejpam-6682	278	26	are	be	AUX
ejpam-6682	278	27	very	very	ADV
ejpam-6682	278	28	important	important	ADJ
ejpam-6682	278	29	for	for	ADP
ejpam-6682	278	30	understanding	understand	VERB
ejpam-6682	278	31	how	how	SCONJ
ejpam-6682	278	32	long	long	ADJ
ejpam-6682	278	33	-	-	PUNCT
ejpam-6682	278	34	term	term	NOUN
ejpam-6682	278	35	epidemics	epidemic	NOUN
ejpam-6682	278	36	work	work	NOUN
ejpam-6682	278	37	.	.	PUNCT
ejpam-6682	279	1	5	5	X
ejpam-6682	279	2	.	.	X
ejpam-6682	279	3	discussion	discussion	NOUN
ejpam-6682	279	4	in	in	ADP
ejpam-6682	279	5	this	this	DET
ejpam-6682	279	6	section	section	NOUN
ejpam-6682	279	7	,	,	PUNCT
ejpam-6682	279	8	we	we	PRON
ejpam-6682	279	9	conduct	conduct	VERB
ejpam-6682	279	10	a	a	DET
ejpam-6682	279	11	comparative	comparative	ADJ
ejpam-6682	279	12	analysis	analysis	NOUN
ejpam-6682	279	13	of	of	ADP
ejpam-6682	279	14	three	three	NUM
ejpam-6682	279	15	different	different	ADJ
ejpam-6682	279	16	dengue	dengue	NOUN
ejpam-6682	279	17	models	model	NOUN
ejpam-6682	279	18	:	:	PUNCT
ejpam-6682	279	19	classical	classical	ADJ
ejpam-6682	279	20	,	,	PUNCT
ejpam-6682	279	21	fractal	fractal	ADJ
ejpam-6682	279	22	,	,	PUNCT
ejpam-6682	279	23	and	and	CCONJ
ejpam-6682	279	24	fractional	fractional	ADJ
ejpam-6682	279	25	models	model	NOUN
ejpam-6682	279	26	.	.	PUNCT
ejpam-6682	280	1	the	the	DET
ejpam-6682	280	2	predictions	prediction	NOUN
ejpam-6682	280	3	obtained	obtain	VERB
ejpam-6682	280	4	from	from	ADP
ejpam-6682	280	5	these	these	DET
ejpam-6682	280	6	models	model	NOUN
ejpam-6682	280	7	are	be	AUX
ejpam-6682	280	8	compared	compare	VERB
ejpam-6682	280	9	with	with	ADP
ejpam-6682	280	10	accurate	accurate	ADJ
ejpam-6682	280	11	data	datum	NOUN
ejpam-6682	280	12	for	for	ADP
ejpam-6682	280	13	the	the	DET
ejpam-6682	280	14	2023	2023	NUM
ejpam-6682	280	15	dengue	dengue	NOUN
ejpam-6682	280	16	epidemic	epidemic	NOUN
ejpam-6682	280	17	in	in	ADP
ejpam-6682	280	18	gedaref	gedaref	NOUN
ejpam-6682	280	19	state	state	NOUN
ejpam-6682	280	20	,	,	PUNCT
ejpam-6682	280	21	eastern	eastern	PROPN
ejpam-6682	280	22	sudan	sudan	PROPN
ejpam-6682	280	23	.	.	PUNCT
ejpam-6682	281	1	the	the	DET
ejpam-6682	281	2	classical	classical	ADJ
ejpam-6682	281	3	model	model	NOUN
ejpam-6682	281	4	is	be	AUX
ejpam-6682	281	5	used	use	VERB
ejpam-6682	281	6	as	as	ADP
ejpam-6682	281	7	a	a	DET
ejpam-6682	281	8	baseline	baseline	NOUN
ejpam-6682	281	9	,	,	PUNCT
ejpam-6682	281	10	whereas	whereas	SCONJ
ejpam-6682	281	11	the	the	DET
ejpam-6682	281	12	fractal	fractal	ADJ
ejpam-6682	281	13	and	and	CCONJ
ejpam-6682	281	14	fractional	fractional	ADJ
ejpam-6682	281	15	models	model	NOUN
ejpam-6682	281	16	offer	offer	VERB
ejpam-6682	281	17	more	more	ADV
ejpam-6682	281	18	complex	complex	ADJ
ejpam-6682	281	19	and	and	CCONJ
ejpam-6682	281	20	general	general	ADJ
ejpam-6682	281	21	frameworks	framework	NOUN
ejpam-6682	281	22	that	that	PRON
ejpam-6682	281	23	take	take	VERB
ejpam-6682	281	24	into	into	ADP
ejpam-6682	281	25	account	account	NOUN
ejpam-6682	281	26	memory	memory	NOUN
ejpam-6682	281	27	effects	effect	NOUN
ejpam-6682	281	28	in	in	ADP
ejpam-6682	281	29	the	the	DET
ejpam-6682	281	30	spread	spread	NOUN
ejpam-6682	281	31	of	of	ADP
ejpam-6682	281	32	epidemics	epidemic	NOUN
ejpam-6682	281	33	.	.	PUNCT
ejpam-6682	282	1	compared	compare	VERB
ejpam-6682	282	2	to	to	ADP
ejpam-6682	282	3	the	the	DET
ejpam-6682	282	4	classical	classical	ADJ
ejpam-6682	282	5	model	model	NOUN
ejpam-6682	282	6	,	,	PUNCT
ejpam-6682	282	7	the	the	DET
ejpam-6682	282	8	fractal	fractal	ADJ
ejpam-6682	282	9	and	and	CCONJ
ejpam-6682	282	10	fractional	fractional	ADJ
ejpam-6682	282	11	models	model	NOUN
ejpam-6682	282	12	generally	generally	ADV
ejpam-6682	282	13	exhibit	exhibit	VERB
ejpam-6682	282	14	superior	superior	ADJ
ejpam-6682	282	15	predictive	predictive	ADJ
ejpam-6682	282	16	abilities	ability	NOUN
ejpam-6682	282	17	,	,	PUNCT
ejpam-6682	282	18	with	with	ADP
ejpam-6682	282	19	the	the	DET
ejpam-6682	282	20	fractional	fractional	ADJ
ejpam-6682	282	21	model	model	NOUN
ejpam-6682	282	22	offering	offer	VERB
ejpam-6682	282	23	the	the	DET
ejpam-6682	282	24	best	good	ADJ
ejpam-6682	282	25	fit	fit	ADJ
ejpam-6682	282	26	to	to	ADP
ejpam-6682	282	27	actual	actual	ADJ
ejpam-6682	282	28	data	datum	NOUN
ejpam-6682	282	29	.	.	PUNCT
ejpam-6682	283	1	figures	figure	NOUN
ejpam-6682	283	2	4	4	NUM
ejpam-6682	283	3	,	,	PUNCT
ejpam-6682	283	4	5	5	NUM
ejpam-6682	283	5	,	,	PUNCT
ejpam-6682	283	6	and	and	CCONJ
ejpam-6682	283	7	6	6	NUM
ejpam-6682	283	8	provide	provide	VERB
ejpam-6682	283	9	more	more	ADV
ejpam-6682	283	10	detailed	detailed	ADJ
ejpam-6682	283	11	insights	insight	NOUN
ejpam-6682	283	12	into	into	ADP
ejpam-6682	283	13	the	the	DET
ejpam-6682	283	14	evolution	evolution	NOUN
ejpam-6682	283	15	of	of	ADP
ejpam-6682	283	16	the	the	DET
ejpam-6682	283	17	susceptible	susceptible	ADJ
ejpam-6682	283	18	(	(	PUNCT
ejpam-6682	283	19	s1	s1	NOUN
ejpam-6682	283	20	,	,	PUNCT
ejpam-6682	283	21	s2	s2	PROPN
ejpam-6682	283	22	)	)	PUNCT
ejpam-6682	283	23	and	and	CCONJ
ejpam-6682	283	24	infected	infect	VERB
ejpam-6682	283	25	(	(	PUNCT
ejpam-6682	283	26	i1	i1	PROPN
ejpam-6682	283	27	,	,	PUNCT
ejpam-6682	283	28	i2	i2	PROPN
ejpam-6682	283	29	)	)	PUNCT
ejpam-6682	283	30	populations	population	NOUN
ejpam-6682	283	31	(	(	PUNCT
ejpam-6682	283	32	humans	human	NOUN
ejpam-6682	283	33	and	and	CCONJ
ejpam-6682	283	34	mosquitoes	mosquito	NOUN
ejpam-6682	283	35	)	)	PUNCT
ejpam-6682	283	36	over	over	ADP
ejpam-6682	283	37	a	a	DET
ejpam-6682	283	38	period	period	NOUN
ejpam-6682	283	39	of	of	ADP
ejpam-6682	283	40	200	200	NUM
ejpam-6682	283	41	days	day	NOUN
ejpam-6682	283	42	.	.	PUNCT
ejpam-6682	284	1	figure	figure	NOUN
ejpam-6682	284	2	4	4	NUM
ejpam-6682	284	3	,	,	PUNCT
ejpam-6682	284	4	the	the	DET
ejpam-6682	284	5	left	left	ADJ
ejpam-6682	284	6	panel	panel	NOUN
ejpam-6682	284	7	(	(	PUNCT
ejpam-6682	284	8	a	a	PRON
ejpam-6682	284	9	)	)	PUNCT
ejpam-6682	284	10	illustrates	illustrate	VERB
ejpam-6682	284	11	the	the	DET
ejpam-6682	284	12	decline	decline	NOUN
ejpam-6682	284	13	in	in	ADP
ejpam-6682	284	14	the	the	DET
ejpam-6682	284	15	susceptible	susceptible	ADJ
ejpam-6682	284	16	human	human	ADJ
ejpam-6682	284	17	population	population	NOUN
ejpam-6682	284	18	(	(	PUNCT
ejpam-6682	284	19	s1	s1	PROPN
ejpam-6682	284	20	)	)	PUNCT
ejpam-6682	284	21	,	,	PUNCT
ejpam-6682	284	22	while	while	SCONJ
ejpam-6682	284	23	the	the	DET
ejpam-6682	284	24	right	right	ADJ
ejpam-6682	284	25	panel	panel	NOUN
ejpam-6682	284	26	(	(	PUNCT
ejpam-6682	284	27	b	b	NOUN
ejpam-6682	284	28	)	)	PUNCT
ejpam-6682	284	29	depicts	depict	VERB
ejpam-6682	284	30	the	the	DET
ejpam-6682	284	31	corresponding	corresponding	ADJ
ejpam-6682	284	32	increase	increase	NOUN
ejpam-6682	284	33	in	in	ADP
ejpam-6682	284	34	the	the	DET
ejpam-6682	284	35	infected	infected	ADJ
ejpam-6682	284	36	population	population	NOUN
ejpam-6682	284	37	(	(	PUNCT
ejpam-6682	284	38	i1	i1	PROPN
ejpam-6682	284	39	)	)	PUNCT
ejpam-6682	284	40	.	.	PUNCT
ejpam-6682	285	1	the	the	DET
ejpam-6682	285	2	results	result	NOUN
ejpam-6682	285	3	indicate	indicate	VERB
ejpam-6682	285	4	that	that	SCONJ
ejpam-6682	285	5	individuals	individual	NOUN
ejpam-6682	285	6	become	become	AUX
ejpam-6682	285	7	infected	infect	VERB
ejpam-6682	285	8	more	more	ADV
ejpam-6682	285	9	rapidly	rapidly	ADV
ejpam-6682	285	10	in	in	ADP
ejpam-6682	285	11	the	the	DET
ejpam-6682	285	12	fractional	fractional	ADJ
ejpam-6682	285	13	and	and	CCONJ
ejpam-6682	285	14	fractal	fractal	ADJ
ejpam-6682	285	15	models	model	NOUN
ejpam-6682	285	16	compared	compare	VERB
ejpam-6682	285	17	to	to	ADP
ejpam-6682	285	18	the	the	DET
ejpam-6682	285	19	classical	classical	ADJ
ejpam-6682	285	20	model	model	NOUN
ejpam-6682	285	21	.	.	PUNCT
ejpam-6682	286	1	after	after	ADP
ejpam-6682	286	2	day	day	NOUN
ejpam-6682	286	3	100	100	NUM
ejpam-6682	286	4	,	,	PUNCT
ejpam-6682	286	5	we	we	PRON
ejpam-6682	286	6	observe	observe	VERB
ejpam-6682	286	7	a	a	DET
ejpam-6682	286	8	notable	notable	ADJ
ejpam-6682	286	9	reduction	reduction	NOUN
ejpam-6682	286	10	in	in	ADP
ejpam-6682	286	11	susceptibility	susceptibility	NOUN
ejpam-6682	286	12	,	,	PUNCT
ejpam-6682	286	13	followed	follow	VERB
ejpam-6682	286	14	by	by	ADP
ejpam-6682	286	15	a	a	DET
ejpam-6682	286	16	slow	slow	ADJ
ejpam-6682	286	17	decline	decline	NOUN
ejpam-6682	286	18	in	in	ADP
ejpam-6682	286	19	infection	infection	NOUN
ejpam-6682	286	20	due	due	ADP
ejpam-6682	286	21	to	to	ADP
ejpam-6682	286	22	recovery	recovery	NOUN
ejpam-6682	286	23	.	.	PUNCT
ejpam-6682	287	1	figure	figure	VERB
ejpam-6682	287	2	5,this	5,this	NUM
ejpam-6682	287	3	figure	figure	NOUN
ejpam-6682	287	4	illustrates	illustrate	VERB
ejpam-6682	287	5	the	the	DET
ejpam-6682	287	6	dynamics	dynamic	NOUN
ejpam-6682	287	7	of	of	ADP
ejpam-6682	287	8	the	the	DET
ejpam-6682	287	9	susceptible	susceptible	ADJ
ejpam-6682	287	10	(	(	PUNCT
ejpam-6682	287	11	s2	s2	PROPN
ejpam-6682	287	12	)	)	PUNCT
ejpam-6682	287	13	and	and	CCONJ
ejpam-6682	287	14	infected	infect	VERB
ejpam-6682	287	15	(	(	PUNCT
ejpam-6682	287	16	i2	i2	PROPN
ejpam-6682	287	17	)	)	PUNCT
ejpam-6682	287	18	mosquito	mosquito	ADJ
ejpam-6682	287	19	populations	population	NOUN
ejpam-6682	287	20	.	.	PUNCT
ejpam-6682	288	1	the	the	DET
ejpam-6682	288	2	fractional	fractional	ADJ
ejpam-6682	288	3	and	and	CCONJ
ejpam-6682	288	4	fractal	fractal	ADJ
ejpam-6682	288	5	models	model	NOUN
ejpam-6682	288	6	predict	predict	VERB
ejpam-6682	288	7	a	a	DET
ejpam-6682	288	8	more	more	ADV
ejpam-6682	288	9	significant	significant	ADJ
ejpam-6682	288	10	reduction	reduction	NOUN
ejpam-6682	288	11	in	in	ADP
ejpam-6682	288	12	the	the	DET
ejpam-6682	288	13	susceptible	susceptible	ADJ
ejpam-6682	288	14	mosquito	mosquito	ADJ
ejpam-6682	288	15	population	population	NOUN
ejpam-6682	288	16	and	and	CCONJ
ejpam-6682	288	17	a	a	DET
ejpam-6682	288	18	rapid	rapid	ADJ
ejpam-6682	288	19	increase	increase	NOUN
ejpam-6682	288	20	in	in	ADP
ejpam-6682	288	21	the	the	DET
ejpam-6682	288	22	infected	infected	ADJ
ejpam-6682	288	23	population	population	NOUN
ejpam-6682	288	24	.	.	PUNCT
ejpam-6682	289	1	this	this	DET
ejpam-6682	289	2	finding	finding	NOUN
ejpam-6682	289	3	confirms	confirm	VERB
ejpam-6682	289	4	the	the	DET
ejpam-6682	289	5	ability	ability	NOUN
ejpam-6682	289	6	of	of	ADP
ejpam-6682	289	7	these	these	DET
ejpam-6682	289	8	models	model	NOUN
ejpam-6682	289	9	to	to	PART
ejpam-6682	289	10	capture	capture	VERB
ejpam-6682	289	11	realistic	realistic	ADJ
ejpam-6682	289	12	disease	disease	NOUN
ejpam-6682	289	13	progression	progression	NOUN
ejpam-6682	289	14	patterns	pattern	NOUN
ejpam-6682	289	15	.	.	PUNCT
ejpam-6682	290	1	figure	figure	VERB
ejpam-6682	290	2	6,this	6,this	NUM
ejpam-6682	290	3	figure	figure	NOUN
ejpam-6682	290	4	compares	compare	VERB
ejpam-6682	290	5	a1	a1	NOUN
ejpam-6682	290	6	and	and	CCONJ
ejpam-6682	290	7	r1	r1	PROPN
ejpam-6682	290	8	,	,	PUNCT
ejpam-6682	290	9	which	which	PRON
ejpam-6682	290	10	represent	represent	VERB
ejpam-6682	290	11	asymptomatic	asymptomatic	ADJ
ejpam-6682	290	12	infections	infection	NOUN
ejpam-6682	290	13	and	and	CCONJ
ejpam-6682	290	14	recovered	recover	VERB
ejpam-6682	290	15	individuals	individual	NOUN
ejpam-6682	290	16	.	.	PUNCT
ejpam-6682	291	1	both	both	DET
ejpam-6682	291	2	quantities	quantity	NOUN
ejpam-6682	291	3	increase	increase	VERB
ejpam-6682	291	4	over	over	ADP
ejpam-6682	291	5	time	time	NOUN
ejpam-6682	291	6	,	,	PUNCT
ejpam-6682	291	7	with	with	ADP
ejpam-6682	291	8	the	the	DET
ejpam-6682	291	9	fractional	fractional	ADJ
ejpam-6682	291	10	model	model	NOUN
ejpam-6682	291	11	predicting	predict	VERB
ejpam-6682	291	12	a	a	DET
ejpam-6682	291	13	slightly	slightly	ADV
ejpam-6682	291	14	faster	fast	ADJ
ejpam-6682	291	15	growth	growth	NOUN
ejpam-6682	291	16	rate	rate	NOUN
ejpam-6682	291	17	.	.	PUNCT
ejpam-6682	292	1	the	the	DET
ejpam-6682	292	2	results	result	NOUN
ejpam-6682	292	3	show	show	VERB
ejpam-6682	292	4	that	that	SCONJ
ejpam-6682	292	5	the	the	DET
ejpam-6682	292	6	fractal	fractal	ADJ
ejpam-6682	292	7	and	and	CCONJ
ejpam-6682	292	8	fractional	fractional	ADJ
ejpam-6682	292	9	models	model	NOUN
ejpam-6682	292	10	better	well	ADV
ejpam-6682	292	11	show	show	VERB
ejpam-6682	292	12	how	how	SCONJ
ejpam-6682	292	13	complicated	complicated	ADJ
ejpam-6682	292	14	and	and	CCONJ
ejpam-6682	292	15	nonlinear	nonlinear	ADJ
ejpam-6682	292	16	dengue	dengue	NOUN
ejpam-6682	292	17	transmission	transmission	NOUN
ejpam-6682	292	18	is	be	AUX
ejpam-6682	292	19	.	.	PUNCT
ejpam-6682	293	1	these	these	DET
ejpam-6682	293	2	models	model	NOUN
ejpam-6682	293	3	are	be	AUX
ejpam-6682	293	4	better	well	ADJ
ejpam-6682	293	5	than	than	ADP
ejpam-6682	293	6	the	the	DET
ejpam-6682	293	7	classical	classical	ADJ
ejpam-6682	293	8	model	model	NOUN
ejpam-6682	293	9	because	because	SCONJ
ejpam-6682	293	10	they	they	PRON
ejpam-6682	293	11	give	give	VERB
ejpam-6682	293	12	a	a	DET
ejpam-6682	293	13	more	more	ADV
ejpam-6682	293	14	accurate	accurate	ADJ
ejpam-6682	293	15	picture	picture	NOUN
ejpam-6682	293	16	of	of	ADP
ejpam-6682	293	17	how	how	SCONJ
ejpam-6682	293	18	the	the	DET
ejpam-6682	293	19	disease	disease	NOUN
ejpam-6682	293	20	spreads	spread	VERB
ejpam-6682	293	21	between	between	ADP
ejpam-6682	293	22	susceptible	susceptible	ADJ
ejpam-6682	293	23	and	and	CCONJ
ejpam-6682	293	24	infected	infected	ADJ
ejpam-6682	293	25	groups	group	NOUN
ejpam-6682	293	26	and	and	CCONJ
ejpam-6682	293	27	make	make	VERB
ejpam-6682	293	28	predicting	predict	VERB
ejpam-6682	293	29	long	long	ADJ
ejpam-6682	293	30	-	-	PUNCT
ejpam-6682	293	31	term	term	NOUN
ejpam-6682	293	32	epidemics	epidemic	NOUN
ejpam-6682	293	33	easier	easy	ADJ
ejpam-6682	293	34	.	.	PUNCT
ejpam-6682	294	1	r.	r.	PROPN
ejpam-6682	294	2	saadeh	saadeh	PROPN
ejpam-6682	294	3	et	et	PROPN
ejpam-6682	294	4	al	al	PROPN
ejpam-6682	294	5	.	.	PUNCT
ejpam-6682	294	6	/	/	SYM
ejpam-6682	294	7	eur	eur	PROPN
ejpam-6682	294	8	.	.	PUNCT
ejpam-6682	295	1	j.	j.	PROPN
ejpam-6682	295	2	pure	pure	PROPN
ejpam-6682	295	3	appl	appl	PROPN
ejpam-6682	295	4	.	.	PROPN
ejpam-6682	295	5	math	math	PROPN
ejpam-6682	295	6	,	,	PUNCT
ejpam-6682	295	7	18	18	NUM
ejpam-6682	295	8	(	(	PUNCT
ejpam-6682	295	9	4	4	NUM
ejpam-6682	295	10	)	)	PUNCT
ejpam-6682	295	11	(	(	PUNCT
ejpam-6682	295	12	2025	2025	NUM
ejpam-6682	295	13	)	)	PUNCT
ejpam-6682	295	14	,	,	PUNCT
ejpam-6682	295	15	6682	6682	NUM
ejpam-6682	295	16	15	15	NUM
ejpam-6682	295	17	of	of	ADP
ejpam-6682	295	18	21	21	NUM
ejpam-6682	295	19	(	(	PUNCT
ejpam-6682	295	20	a	a	NOUN
ejpam-6682	295	21	)	)	PUNCT
ejpam-6682	295	22	s1	s1	NOUN
ejpam-6682	295	23	(	(	PUNCT
ejpam-6682	295	24	b	b	NOUN
ejpam-6682	295	25	)	)	PUNCT
ejpam-6682	295	26	i1	i1	PROPN
ejpam-6682	295	27	figure	figure	VERB
ejpam-6682	295	28	4	4	NUM
ejpam-6682	295	29	:	:	PUNCT
ejpam-6682	295	30	comparison	comparison	NOUN
ejpam-6682	295	31	of	of	ADP
ejpam-6682	295	32	fractal	fractal	ADJ
ejpam-6682	295	33	and	and	CCONJ
ejpam-6682	295	34	fractional	fractional	ADJ
ejpam-6682	295	35	dynamics	dynamic	NOUN
ejpam-6682	295	36	for	for	ADP
ejpam-6682	295	37	s1(t	s1(t	NOUN
ejpam-6682	295	38	)	)	PUNCT
ejpam-6682	295	39	and	and	CCONJ
ejpam-6682	295	40	i1(t	i1(t	PROPN
ejpam-6682	295	41	)	)	PUNCT
ejpam-6682	295	42	over	over	ADP
ejpam-6682	295	43	time	time	NOUN
ejpam-6682	295	44	.	.	PUNCT
ejpam-6682	296	1	(	(	PUNCT
ejpam-6682	296	2	a	a	X
ejpam-6682	296	3	)	)	PUNCT
ejpam-6682	296	4	s2	s2	NOUN
ejpam-6682	296	5	(	(	PUNCT
ejpam-6682	296	6	b	b	NOUN
ejpam-6682	296	7	)	)	PUNCT
ejpam-6682	296	8	i2	i2	NOUN
ejpam-6682	296	9	figure	figure	NOUN
ejpam-6682	296	10	5	5	NUM
ejpam-6682	296	11	:	:	PUNCT
ejpam-6682	296	12	comparison	comparison	NOUN
ejpam-6682	296	13	of	of	ADP
ejpam-6682	296	14	fractal	fractal	ADJ
ejpam-6682	296	15	and	and	CCONJ
ejpam-6682	296	16	fractional	fractional	ADJ
ejpam-6682	296	17	dynamics	dynamic	NOUN
ejpam-6682	296	18	for	for	ADP
ejpam-6682	296	19	s2(t	s2(t	PRON
ejpam-6682	296	20	)	)	PUNCT
ejpam-6682	296	21	and	and	CCONJ
ejpam-6682	296	22	i2(t	i2(t	PROPN
ejpam-6682	296	23	)	)	PUNCT
ejpam-6682	296	24	over	over	ADP
ejpam-6682	296	25	time	time	NOUN
ejpam-6682	296	26	..	..	PUNCT
ejpam-6682	296	27	(	(	PUNCT
ejpam-6682	296	28	a	a	X
ejpam-6682	296	29	)	)	PUNCT
ejpam-6682	296	30	a1	a1	NOUN
ejpam-6682	296	31	(	(	PUNCT
ejpam-6682	296	32	b	b	NOUN
ejpam-6682	296	33	)	)	PUNCT
ejpam-6682	296	34	r1	r1	NOUN
ejpam-6682	296	35	figure	figure	NOUN
ejpam-6682	296	36	6	6	NUM
ejpam-6682	296	37	:	:	PUNCT
ejpam-6682	296	38	comparison	comparison	NOUN
ejpam-6682	296	39	of	of	ADP
ejpam-6682	296	40	fractal	fractal	ADJ
ejpam-6682	296	41	and	and	CCONJ
ejpam-6682	296	42	fractional	fractional	ADJ
ejpam-6682	296	43	dynamics	dynamic	NOUN
ejpam-6682	296	44	for	for	ADP
ejpam-6682	296	45	a1(t	a1(t	NOUN
ejpam-6682	296	46	)	)	PUNCT
ejpam-6682	296	47	and	and	CCONJ
ejpam-6682	296	48	r1(t	r1(t	NOUN
ejpam-6682	296	49	)	)	PUNCT
ejpam-6682	296	50	over	over	ADP
ejpam-6682	296	51	time	time	NOUN
ejpam-6682	296	52	figure	figure	NOUN
ejpam-6682	296	53	7	7	NUM
ejpam-6682	296	54	illustrates	illustrate	VERB
ejpam-6682	296	55	the	the	DET
ejpam-6682	296	56	temporal	temporal	ADJ
ejpam-6682	296	57	evolution	evolution	NOUN
ejpam-6682	296	58	of	of	ADP
ejpam-6682	296	59	the	the	DET
ejpam-6682	296	60	infected	infected	ADJ
ejpam-6682	296	61	human	human	ADJ
ejpam-6682	296	62	population	population	NOUN
ejpam-6682	296	63	as	as	SCONJ
ejpam-6682	296	64	predicted	predict	VERB
ejpam-6682	296	65	by	by	ADP
ejpam-6682	296	66	the	the	DET
ejpam-6682	296	67	three	three	NUM
ejpam-6682	296	68	models	model	NOUN
ejpam-6682	296	69	,	,	PUNCT
ejpam-6682	296	70	using	use	VERB
ejpam-6682	296	71	precise	precise	ADJ
ejpam-6682	296	72	dengue	dengue	NOUN
ejpam-6682	296	73	data	datum	NOUN
ejpam-6682	296	74	.	.	PUNCT
ejpam-6682	297	1	the	the	DET
ejpam-6682	297	2	curves	curve	NOUN
ejpam-6682	297	3	reveal	reveal	VERB
ejpam-6682	297	4	marked	mark	VERB
ejpam-6682	297	5	discrepancies	discrepancy	NOUN
ejpam-6682	297	6	in	in	ADP
ejpam-6682	297	7	each	each	DET
ejpam-6682	297	8	model	model	NOUN
ejpam-6682	297	9	’s	’s	PART
ejpam-6682	297	10	ability	ability	NOUN
ejpam-6682	297	11	to	to	PART
ejpam-6682	297	12	accurately	accurately	ADV
ejpam-6682	297	13	depict	depict	VERB
ejpam-6682	297	14	the	the	DET
ejpam-6682	297	15	epidemic	epidemic	NOUN
ejpam-6682	297	16	’s	’s	PART
ejpam-6682	297	17	trajectory	trajectory	NOUN
ejpam-6682	297	18	.	.	PUNCT
ejpam-6682	298	1	the	the	DET
ejpam-6682	298	2	fractional	fractional	ADJ
ejpam-6682	298	3	model	model	NOUN
ejpam-6682	298	4	(	(	PUNCT
ejpam-6682	298	5	blue	blue	ADJ
ejpam-6682	298	6	line	line	NOUN
ejpam-6682	298	7	)	)	PUNCT
ejpam-6682	298	8	captures	capture	VERB
ejpam-6682	298	9	non	non	ADJ
ejpam-6682	298	10	-	-	ADJ
ejpam-6682	298	11	linear	linear	ADJ
ejpam-6682	298	12	and	and	CCONJ
ejpam-6682	298	13	varied	varied	ADJ
ejpam-6682	298	14	patterns	pattern	NOUN
ejpam-6682	298	15	of	of	ADP
ejpam-6682	298	16	disease	disease	PROPN
ejpam-6682	298	17	r.	r.	PROPN
ejpam-6682	298	18	saadeh	saadeh	PROPN
ejpam-6682	298	19	et	et	PROPN
ejpam-6682	298	20	al	al	PROPN
ejpam-6682	298	21	.	.	PUNCT
ejpam-6682	298	22	/	/	SYM
ejpam-6682	298	23	eur	eur	PROPN
ejpam-6682	298	24	.	.	PUNCT
ejpam-6682	299	1	j.	j.	PROPN
ejpam-6682	299	2	pure	pure	PROPN
ejpam-6682	299	3	appl	appl	PROPN
ejpam-6682	299	4	.	.	PROPN
ejpam-6682	299	5	math	math	PROPN
ejpam-6682	299	6	,	,	PUNCT
ejpam-6682	299	7	18	18	NUM
ejpam-6682	299	8	(	(	PUNCT
ejpam-6682	299	9	4	4	NUM
ejpam-6682	299	10	)	)	PUNCT
ejpam-6682	299	11	(	(	PUNCT
ejpam-6682	299	12	2025	2025	NUM
ejpam-6682	299	13	)	)	PUNCT
ejpam-6682	299	14	,	,	PUNCT
ejpam-6682	299	15	6682	6682	NUM
ejpam-6682	299	16	16	16	NUM
ejpam-6682	299	17	of	of	ADP
ejpam-6682	299	18	21	21	NUM
ejpam-6682	299	19	transmission	transmission	NOUN
ejpam-6682	299	20	.	.	PUNCT
ejpam-6682	300	1	it	it	PRON
ejpam-6682	300	2	closely	closely	ADV
ejpam-6682	300	3	matches	match	VERB
ejpam-6682	300	4	the	the	DET
ejpam-6682	300	5	data	datum	NOUN
ejpam-6682	300	6	in	in	ADP
ejpam-6682	300	7	later	later	ADJ
ejpam-6682	300	8	epidemic	epidemic	NOUN
ejpam-6682	300	9	stages	stage	NOUN
ejpam-6682	300	10	,	,	PUNCT
ejpam-6682	300	11	indicating	indicate	VERB
ejpam-6682	300	12	that	that	SCONJ
ejpam-6682	300	13	fractional	fractional	ADJ
ejpam-6682	300	14	derivatives	derivative	NOUN
ejpam-6682	300	15	effectively	effectively	ADV
ejpam-6682	300	16	capture	capture	VERB
ejpam-6682	300	17	long	long	ADJ
ejpam-6682	300	18	-	-	PUNCT
ejpam-6682	300	19	memory	memory	NOUN
ejpam-6682	300	20	effects	effect	NOUN
ejpam-6682	300	21	and	and	CCONJ
ejpam-6682	300	22	fluctuations	fluctuation	NOUN
ejpam-6682	300	23	in	in	ADP
ejpam-6682	300	24	disease	disease	NOUN
ejpam-6682	300	25	transmission	transmission	NOUN
ejpam-6682	300	26	.	.	PUNCT
ejpam-6682	301	1	the	the	DET
ejpam-6682	301	2	fractal	fractal	ADJ
ejpam-6682	301	3	model	model	NOUN
ejpam-6682	301	4	(	(	PUNCT
ejpam-6682	301	5	red	red	ADJ
ejpam-6682	301	6	line	line	NOUN
ejpam-6682	301	7	)	)	PUNCT
ejpam-6682	301	8	captures	capture	VERB
ejpam-6682	301	9	disease	disease	NOUN
ejpam-6682	301	10	dynamics	dynamic	NOUN
ejpam-6682	301	11	moderately	moderately	ADV
ejpam-6682	301	12	and	and	CCONJ
ejpam-6682	301	13	lies	lie	VERB
ejpam-6682	301	14	between	between	ADP
ejpam-6682	301	15	the	the	DET
ejpam-6682	301	16	classical	classical	ADJ
ejpam-6682	301	17	and	and	CCONJ
ejpam-6682	301	18	fractional	fractional	ADJ
ejpam-6682	301	19	models	model	NOUN
ejpam-6682	301	20	.	.	PUNCT
ejpam-6682	302	1	by	by	ADP
ejpam-6682	302	2	incorporating	incorporate	VERB
ejpam-6682	302	3	memory	memory	NOUN
ejpam-6682	302	4	-	-	PUNCT
ejpam-6682	302	5	dependent	dependent	ADJ
ejpam-6682	302	6	transmission	transmission	NOUN
ejpam-6682	302	7	effects	effect	NOUN
ejpam-6682	302	8	,	,	PUNCT
ejpam-6682	302	9	this	this	DET
ejpam-6682	302	10	model	model	NOUN
ejpam-6682	302	11	leads	lead	VERB
ejpam-6682	302	12	to	to	ADP
ejpam-6682	302	13	smoother	smooth	ADJ
ejpam-6682	302	14	and	and	CCONJ
ejpam-6682	302	15	more	more	ADV
ejpam-6682	302	16	gradual	gradual	ADJ
ejpam-6682	302	17	disease	disease	NOUN
ejpam-6682	302	18	progression	progression	NOUN
ejpam-6682	302	19	compared	compare	VERB
ejpam-6682	302	20	to	to	ADP
ejpam-6682	302	21	the	the	DET
ejpam-6682	302	22	classical	classical	ADJ
ejpam-6682	302	23	model	model	NOUN
ejpam-6682	302	24	.	.	PUNCT
ejpam-6682	303	1	the	the	DET
ejpam-6682	303	2	classical	classical	ADJ
ejpam-6682	303	3	model	model	NOUN
ejpam-6682	303	4	(	(	PUNCT
ejpam-6682	303	5	black	black	ADJ
ejpam-6682	303	6	line	line	NOUN
ejpam-6682	303	7	)	)	PUNCT
ejpam-6682	303	8	significantly	significantly	ADV
ejpam-6682	303	9	underestimates	underestimate	VERB
ejpam-6682	303	10	the	the	DET
ejpam-6682	303	11	actual	actual	ADJ
ejpam-6682	303	12	cases	case	NOUN
ejpam-6682	303	13	and	and	CCONJ
ejpam-6682	303	14	exhibits	exhibit	VERB
ejpam-6682	303	15	slower	slow	ADJ
ejpam-6682	303	16	infection	infection	NOUN
ejpam-6682	303	17	progression	progression	NOUN
ejpam-6682	303	18	.	.	PUNCT
ejpam-6682	304	1	the	the	DET
ejpam-6682	304	2	results	result	NOUN
ejpam-6682	304	3	indicate	indicate	VERB
ejpam-6682	304	4	that	that	SCONJ
ejpam-6682	304	5	this	this	DET
ejpam-6682	304	6	model	model	NOUN
ejpam-6682	304	7	fails	fail	VERB
ejpam-6682	304	8	to	to	PART
ejpam-6682	304	9	capture	capture	VERB
ejpam-6682	304	10	the	the	DET
ejpam-6682	304	11	long	long	ADJ
ejpam-6682	304	12	-	-	PUNCT
ejpam-6682	304	13	term	term	NOUN
ejpam-6682	304	14	dynamics	dynamic	NOUN
ejpam-6682	304	15	of	of	ADP
ejpam-6682	304	16	the	the	DET
ejpam-6682	304	17	epidemic	epidemic	NOUN
ejpam-6682	304	18	,	,	PUNCT
ejpam-6682	304	19	especially	especially	ADV
ejpam-6682	304	20	when	when	SCONJ
ejpam-6682	304	21	secondary	secondary	ADJ
ejpam-6682	304	22	waves	wave	NOUN
ejpam-6682	304	23	and	and	CCONJ
ejpam-6682	304	24	delayed	delay	VERB
ejpam-6682	304	25	transmission	transmission	NOUN
ejpam-6682	304	26	effects	effect	NOUN
ejpam-6682	304	27	are	be	AUX
ejpam-6682	304	28	considered	consider	VERB
ejpam-6682	304	29	.	.	PUNCT
ejpam-6682	305	1	the	the	DET
ejpam-6682	305	2	comparative	comparative	ADJ
ejpam-6682	305	3	study	study	NOUN
ejpam-6682	305	4	emphasizes	emphasize	VERB
ejpam-6682	305	5	the	the	DET
ejpam-6682	305	6	inadequacy	inadequacy	NOUN
ejpam-6682	305	7	of	of	ADP
ejpam-6682	305	8	the	the	DET
ejpam-6682	305	9	classical	classical	ADJ
ejpam-6682	305	10	model	model	NOUN
ejpam-6682	305	11	in	in	ADP
ejpam-6682	305	12	the	the	DET
ejpam-6682	305	13	correct	correct	ADJ
ejpam-6682	305	14	forecasting	forecasting	NOUN
ejpam-6682	305	15	of	of	ADP
ejpam-6682	305	16	dengue	dengue	NOUN
ejpam-6682	305	17	fever	fever	NOUN
ejpam-6682	305	18	outbreaks	outbreak	NOUN
ejpam-6682	305	19	since	since	SCONJ
ejpam-6682	305	20	it	it	PRON
ejpam-6682	305	21	does	do	AUX
ejpam-6682	305	22	not	not	PART
ejpam-6682	305	23	take	take	VERB
ejpam-6682	305	24	into	into	ADP
ejpam-6682	305	25	account	account	NOUN
ejpam-6682	305	26	the	the	DET
ejpam-6682	305	27	memory	memory	NOUN
ejpam-6682	305	28	effects	effect	NOUN
ejpam-6682	305	29	,	,	PUNCT
ejpam-6682	305	30	spatial	spatial	ADJ
ejpam-6682	305	31	heterogeneity	heterogeneity	NOUN
ejpam-6682	305	32	,	,	PUNCT
ejpam-6682	305	33	and	and	CCONJ
ejpam-6682	305	34	time	time	NOUN
ejpam-6682	305	35	-	-	PUNCT
ejpam-6682	305	36	delay	delay	NOUN
ejpam-6682	305	37	transmission	transmission	NOUN
ejpam-6682	305	38	dynamics	dynamic	NOUN
ejpam-6682	305	39	.	.	PUNCT
ejpam-6682	306	1	however	however	ADV
ejpam-6682	306	2	,	,	PUNCT
ejpam-6682	306	3	the	the	DET
ejpam-6682	306	4	fractal	fractal	ADJ
ejpam-6682	306	5	and	and	CCONJ
ejpam-6682	306	6	fractional	fractional	ADJ
ejpam-6682	306	7	models	model	NOUN
ejpam-6682	306	8	accurately	accurately	ADV
ejpam-6682	306	9	outline	outline	VERB
ejpam-6682	306	10	the	the	DET
ejpam-6682	306	11	disease	disease	NOUN
ejpam-6682	306	12	transmission	transmission	NOUN
ejpam-6682	306	13	process	process	NOUN
ejpam-6682	306	14	,	,	PUNCT
ejpam-6682	306	15	the	the	DET
ejpam-6682	306	16	best	good	ADJ
ejpam-6682	306	17	among	among	ADP
ejpam-6682	306	18	them	they	PRON
ejpam-6682	306	19	being	be	AUX
ejpam-6682	306	20	the	the	DET
ejpam-6682	306	21	fractional	fractional	ADJ
ejpam-6682	306	22	model	model	NOUN
ejpam-6682	306	23	,	,	PUNCT
ejpam-6682	306	24	to	to	ADP
ejpam-6682	306	25	actual	actual	ADJ
ejpam-6682	306	26	epidemiological	epidemiological	ADJ
ejpam-6682	306	27	data	datum	NOUN
ejpam-6682	306	28	.	.	PUNCT
ejpam-6682	307	1	with	with	ADP
ejpam-6682	307	2	the	the	DET
ejpam-6682	307	3	inclusion	inclusion	NOUN
ejpam-6682	307	4	of	of	ADP
ejpam-6682	307	5	long	long	ADJ
ejpam-6682	307	6	-	-	PUNCT
ejpam-6682	307	7	memory	memory	NOUN
ejpam-6682	307	8	effects	effect	NOUN
ejpam-6682	307	9	and	and	CCONJ
ejpam-6682	307	10	nonlinear	nonlinear	ADJ
ejpam-6682	307	11	transmission	transmission	NOUN
ejpam-6682	307	12	patterns	pattern	NOUN
ejpam-6682	307	13	,	,	PUNCT
ejpam-6682	307	14	predictive	predictive	ADJ
ejpam-6682	307	15	power	power	NOUN
ejpam-6682	307	16	is	be	AUX
ejpam-6682	307	17	introduced	introduce	VERB
ejpam-6682	307	18	by	by	ADP
ejpam-6682	307	19	the	the	DET
ejpam-6682	307	20	fractional	fractional	ADJ
ejpam-6682	307	21	model	model	NOUN
ejpam-6682	307	22	,	,	PUNCT
ejpam-6682	307	23	and	and	CCONJ
ejpam-6682	307	24	thus	thus	ADV
ejpam-6682	307	25	it	it	PRON
ejpam-6682	307	26	can	can	AUX
ejpam-6682	307	27	be	be	AUX
ejpam-6682	307	28	a	a	DET
ejpam-6682	307	29	useful	useful	ADJ
ejpam-6682	307	30	tool	tool	NOUN
ejpam-6682	307	31	for	for	ADP
ejpam-6682	307	32	epidemic	epidemic	NOUN
ejpam-6682	307	33	prediction	prediction	NOUN
ejpam-6682	307	34	as	as	ADV
ejpam-6682	307	35	well	well	ADV
ejpam-6682	307	36	as	as	ADP
ejpam-6682	307	37	public	public	ADJ
ejpam-6682	307	38	health	health	NOUN
ejpam-6682	307	39	intervention	intervention	NOUN
ejpam-6682	307	40	planning	planning	NOUN
ejpam-6682	307	41	.	.	PUNCT
ejpam-6682	308	1	the	the	DET
ejpam-6682	308	2	fractal	fractal	ADJ
ejpam-6682	308	3	model	model	NOUN
ejpam-6682	308	4	also	also	ADV
ejpam-6682	308	5	introduces	introduce	VERB
ejpam-6682	308	6	robustness	robustness	NOUN
ejpam-6682	308	7	to	to	ADP
ejpam-6682	308	8	disease	disease	NOUN
ejpam-6682	308	9	modeling	modeling	NOUN
ejpam-6682	308	10	by	by	ADP
ejpam-6682	308	11	the	the	DET
ejpam-6682	308	12	inclusion	inclusion	NOUN
ejpam-6682	308	13	of	of	ADP
ejpam-6682	308	14	spatial	spatial	ADJ
ejpam-6682	308	15	heterogeneity	heterogeneity	NOUN
ejpam-6682	308	16	,	,	PUNCT
ejpam-6682	308	17	which	which	PRON
ejpam-6682	308	18	is	be	AUX
ejpam-6682	308	19	applicable	applicable	ADJ
ejpam-6682	308	20	in	in	ADP
ejpam-6682	308	21	describing	describe	VERB
ejpam-6682	308	22	heterogeneous	heterogeneous	ADJ
ejpam-6682	308	23	transmission	transmission	NOUN
ejpam-6682	308	24	patterns	pattern	NOUN
ejpam-6682	308	25	.	.	PUNCT
ejpam-6682	309	1	such	such	ADJ
ejpam-6682	309	2	sophisticated	sophisticated	ADJ
ejpam-6682	309	3	models	model	NOUN
ejpam-6682	309	4	provide	provide	VERB
ejpam-6682	309	5	more	more	ADJ
ejpam-6682	309	6	flexibility	flexibility	NOUN
ejpam-6682	309	7	and	and	CCONJ
ejpam-6682	309	8	reliability	reliability	NOUN
ejpam-6682	309	9	for	for	ADP
ejpam-6682	309	10	improved	improved	ADJ
ejpam-6682	309	11	epidemic	epidemic	NOUN
ejpam-6682	309	12	control	control	NOUN
ejpam-6682	309	13	interventions	intervention	NOUN
ejpam-6682	309	14	and	and	CCONJ
ejpam-6682	309	15	policy	policy	NOUN
ejpam-6682	309	16	planning	planning	NOUN
ejpam-6682	309	17	effectiveness	effectiveness	NOUN
ejpam-6682	309	18	in	in	ADP
ejpam-6682	309	19	provinces	province	NOUN
ejpam-6682	309	20	such	such	ADJ
ejpam-6682	309	21	as	as	ADP
ejpam-6682	309	22	gedaref	gedaref	NOUN
ejpam-6682	309	23	.	.	PUNCT
ejpam-6682	310	1	figure	figure	VERB
ejpam-6682	310	2	7	7	NUM
ejpam-6682	310	3	:	:	PUNCT
ejpam-6682	310	4	comparison	comparison	NOUN
ejpam-6682	310	5	between	between	ADP
ejpam-6682	310	6	fractal	fractal	ADJ
ejpam-6682	310	7	,	,	PUNCT
ejpam-6682	310	8	fractional	fractional	ADJ
ejpam-6682	310	9	,	,	PUNCT
ejpam-6682	310	10	and	and	CCONJ
ejpam-6682	310	11	classical	classical	ADJ
ejpam-6682	310	12	models	model	NOUN
ejpam-6682	310	13	against	against	ADP
ejpam-6682	310	14	actual	actual	ADJ
ejpam-6682	310	15	data	datum	NOUN
ejpam-6682	310	16	for	for	ADP
ejpam-6682	310	17	i1(t	i1(t	PROPN
ejpam-6682	310	18	)	)	PUNCT
ejpam-6682	310	19	over	over	ADP
ejpam-6682	310	20	time	time	NOUN
ejpam-6682	310	21	.	.	PUNCT
ejpam-6682	311	1	r.	r.	PROPN
ejpam-6682	311	2	saadeh	saadeh	PROPN
ejpam-6682	311	3	et	et	PROPN
ejpam-6682	311	4	al	al	PROPN
ejpam-6682	311	5	.	.	PUNCT
ejpam-6682	311	6	/	/	SYM
ejpam-6682	311	7	eur	eur	PROPN
ejpam-6682	311	8	.	.	PUNCT
ejpam-6682	312	1	j.	j.	PROPN
ejpam-6682	312	2	pure	pure	PROPN
ejpam-6682	312	3	appl	appl	PROPN
ejpam-6682	312	4	.	.	PROPN
ejpam-6682	312	5	math	math	PROPN
ejpam-6682	312	6	,	,	PUNCT
ejpam-6682	312	7	18	18	NUM
ejpam-6682	312	8	(	(	PUNCT
ejpam-6682	312	9	4	4	NUM
ejpam-6682	312	10	)	)	PUNCT
ejpam-6682	312	11	(	(	PUNCT
ejpam-6682	312	12	2025	2025	NUM
ejpam-6682	312	13	)	)	PUNCT
ejpam-6682	312	14	,	,	PUNCT
ejpam-6682	312	15	6682	6682	NUM
ejpam-6682	312	16	17	17	NUM
ejpam-6682	312	17	of	of	ADP
ejpam-6682	312	18	21	21	NUM
ejpam-6682	312	19	6	6	NUM
ejpam-6682	312	20	.	.	PUNCT
ejpam-6682	313	1	conclusion	conclusion	NOUN
ejpam-6682	313	2	in	in	ADP
ejpam-6682	313	3	this	this	DET
ejpam-6682	313	4	article	article	NOUN
ejpam-6682	313	5	,	,	PUNCT
ejpam-6682	313	6	we	we	PRON
ejpam-6682	313	7	have	have	AUX
ejpam-6682	313	8	modeled	model	VERB
ejpam-6682	313	9	the	the	DET
ejpam-6682	313	10	spread	spread	NOUN
ejpam-6682	313	11	of	of	ADP
ejpam-6682	313	12	dengue	dengue	NOUN
ejpam-6682	313	13	by	by	ADP
ejpam-6682	313	14	three	three	NUM
ejpam-6682	313	15	different	different	ADJ
ejpam-6682	313	16	siar	siar	ADJ
ejpam-6682	313	17	-	-	PUNCT
ejpam-6682	313	18	si	si	PROPN
ejpam-6682	313	19	epidemic	epidemic	NOUN
ejpam-6682	313	20	models	model	NOUN
ejpam-6682	313	21	based	base	VERB
ejpam-6682	313	22	on	on	ADP
ejpam-6682	313	23	classical	classical	ADJ
ejpam-6682	313	24	,	,	PUNCT
ejpam-6682	313	25	fractional	fractional	ADJ
ejpam-6682	313	26	(	(	PUNCT
ejpam-6682	313	27	caputo	caputo	PROPN
ejpam-6682	313	28	)	)	PUNCT
ejpam-6682	313	29	,	,	PUNCT
ejpam-6682	313	30	and	and	CCONJ
ejpam-6682	313	31	fractal	fractal	ADJ
ejpam-6682	313	32	(	(	PUNCT
ejpam-6682	313	33	hausdorff	hausdorff	NOUN
ejpam-6682	313	34	)	)	PUNCT
ejpam-6682	313	35	derivatives	derivative	NOUN
ejpam-6682	313	36	.	.	PUNCT
ejpam-6682	314	1	to	to	PART
ejpam-6682	314	2	solve	solve	VERB
ejpam-6682	314	3	these	these	DET
ejpam-6682	314	4	models	model	NOUN
ejpam-6682	314	5	numerically	numerically	ADV
ejpam-6682	314	6	,	,	PUNCT
ejpam-6682	314	7	we	we	PRON
ejpam-6682	314	8	employed	employ	VERB
ejpam-6682	314	9	the	the	DET
ejpam-6682	314	10	classical	classical	ADJ
ejpam-6682	314	11	euler	euler	NOUN
ejpam-6682	314	12	method	method	NOUN
ejpam-6682	314	13	to	to	PART
ejpam-6682	314	14	solve	solve	VERB
ejpam-6682	314	15	the	the	DET
ejpam-6682	314	16	standard	standard	ADJ
ejpam-6682	314	17	model	model	NOUN
ejpam-6682	314	18	,	,	PUNCT
ejpam-6682	314	19	the	the	DET
ejpam-6682	314	20	fractional	fractional	PROPN
ejpam-6682	314	21	euler	euler	NOUN
ejpam-6682	314	22	method	method	NOUN
ejpam-6682	314	23	to	to	PART
ejpam-6682	314	24	solve	solve	VERB
ejpam-6682	314	25	the	the	DET
ejpam-6682	314	26	fractional	fractional	ADJ
ejpam-6682	314	27	model	model	NOUN
ejpam-6682	314	28	,	,	PUNCT
ejpam-6682	314	29	and	and	CCONJ
ejpam-6682	314	30	the	the	DET
ejpam-6682	314	31	fourthorder	fourthorder	NOUN
ejpam-6682	314	32	runge	runge	NOUN
ejpam-6682	314	33	-	-	PUNCT
ejpam-6682	314	34	kutta	kutta	NOUN
ejpam-6682	314	35	method	method	NOUN
ejpam-6682	314	36	to	to	PART
ejpam-6682	314	37	solve	solve	VERB
ejpam-6682	314	38	the	the	DET
ejpam-6682	314	39	fractal	fractal	ADJ
ejpam-6682	314	40	model	model	NOUN
ejpam-6682	314	41	.	.	PUNCT
ejpam-6682	315	1	we	we	PRON
ejpam-6682	315	2	also	also	ADV
ejpam-6682	315	3	examined	examine	VERB
ejpam-6682	315	4	the	the	DET
ejpam-6682	315	5	stability	stability	NOUN
ejpam-6682	315	6	of	of	ADP
ejpam-6682	315	7	both	both	CCONJ
ejpam-6682	315	8	the	the	DET
ejpam-6682	315	9	disease	disease	NOUN
ejpam-6682	315	10	-	-	PUNCT
ejpam-6682	315	11	free	free	ADJ
ejpam-6682	315	12	and	and	CCONJ
ejpam-6682	315	13	endemic	endemic	ADJ
ejpam-6682	315	14	equilibrium	equilibrium	NOUN
ejpam-6682	315	15	states	state	NOUN
ejpam-6682	315	16	,	,	PUNCT
ejpam-6682	315	17	which	which	PRON
ejpam-6682	315	18	reveals	reveal	VERB
ejpam-6682	315	19	the	the	DET
ejpam-6682	315	20	conditions	condition	NOUN
ejpam-6682	315	21	under	under	ADP
ejpam-6682	315	22	which	which	PRON
ejpam-6682	315	23	the	the	DET
ejpam-6682	315	24	disease	disease	NOUN
ejpam-6682	315	25	will	will	AUX
ejpam-6682	315	26	become	become	VERB
ejpam-6682	315	27	extinct	extinct	ADJ
ejpam-6682	315	28	or	or	CCONJ
ejpam-6682	315	29	persistent	persistent	ADJ
ejpam-6682	315	30	.	.	PUNCT
ejpam-6682	316	1	the	the	DET
ejpam-6682	316	2	model	model	NOUN
ejpam-6682	316	3	was	be	AUX
ejpam-6682	316	4	calibrated	calibrate	VERB
ejpam-6682	316	5	using	use	VERB
ejpam-6682	316	6	real	real	ADJ
ejpam-6682	316	7	data	datum	NOUN
ejpam-6682	316	8	from	from	ADP
ejpam-6682	316	9	gedaref	gedaref	NOUN
ejpam-6682	316	10	,	,	PUNCT
ejpam-6682	316	11	sudan	sudan	PROPN
ejpam-6682	316	12	,	,	PUNCT
ejpam-6682	316	13	and	and	CCONJ
ejpam-6682	316	14	parameters	parameter	NOUN
ejpam-6682	316	15	were	be	AUX
ejpam-6682	316	16	estimated	estimate	VERB
ejpam-6682	316	17	using	use	VERB
ejpam-6682	316	18	the	the	DET
ejpam-6682	316	19	markov	markov	NOUN
ejpam-6682	316	20	chain	chain	NOUN
ejpam-6682	316	21	monte	monte	PROPN
ejpam-6682	316	22	carlo	carlo	PROPN
ejpam-6682	316	23	method	method	NOUN
ejpam-6682	316	24	.	.	PUNCT
ejpam-6682	317	1	the	the	DET
ejpam-6682	317	2	basic	basic	ADJ
ejpam-6682	317	3	reproduction	reproduction	NOUN
ejpam-6682	317	4	number	number	NOUN
ejpam-6682	317	5	for	for	ADP
ejpam-6682	317	6	2023	2023	NUM
ejpam-6682	317	7	was	be	AUX
ejpam-6682	317	8	estimated	estimate	VERB
ejpam-6682	317	9	as	as	ADP
ejpam-6682	317	10	mathcalr0	mathcalr0	NOUN
ejpam-6682	317	11	=	=	SYM
ejpam-6682	317	12	3.27	3.27	NUM
ejpam-6682	317	13	,	,	PUNCT
ejpam-6682	317	14	confirming	confirm	VERB
ejpam-6682	317	15	the	the	DET
ejpam-6682	317	16	endemicity	endemicity	NOUN
ejpam-6682	317	17	of	of	ADP
ejpam-6682	317	18	the	the	DET
ejpam-6682	317	19	disease	disease	NOUN
ejpam-6682	317	20	.	.	PUNCT
ejpam-6682	318	1	among	among	ADP
ejpam-6682	318	2	the	the	DET
ejpam-6682	318	3	three	three	NUM
ejpam-6682	318	4	models	model	NOUN
ejpam-6682	318	5	,	,	PUNCT
ejpam-6682	318	6	the	the	DET
ejpam-6682	318	7	classical	classical	ADJ
ejpam-6682	318	8	model	model	NOUN
ejpam-6682	318	9	best	well	ADV
ejpam-6682	318	10	fits	fit	VERB
ejpam-6682	318	11	real	real	ADJ
ejpam-6682	318	12	data	datum	NOUN
ejpam-6682	318	13	.	.	PUNCT
ejpam-6682	319	1	the	the	DET
ejpam-6682	319	2	fractional	fractional	ADJ
ejpam-6682	319	3	model	model	NOUN
ejpam-6682	319	4	,	,	PUNCT
ejpam-6682	319	5	in	in	ADP
ejpam-6682	319	6	the	the	DET
ejpam-6682	319	7	form	form	NOUN
ejpam-6682	319	8	of	of	ADP
ejpam-6682	319	9	caputo	caputo	PROPN
ejpam-6682	319	10	derivatives	derivative	NOUN
ejpam-6682	319	11	,	,	PUNCT
ejpam-6682	319	12	could	could	AUX
ejpam-6682	319	13	include	include	VERB
ejpam-6682	319	14	memory	memory	NOUN
ejpam-6682	319	15	effects	effect	NOUN
ejpam-6682	319	16	and	and	CCONJ
ejpam-6682	319	17	hence	hence	ADV
ejpam-6682	319	18	give	give	VERB
ejpam-6682	319	19	a	a	DET
ejpam-6682	319	20	more	more	ADV
ejpam-6682	319	21	realistic	realistic	ADJ
ejpam-6682	319	22	representation	representation	NOUN
ejpam-6682	319	23	of	of	ADP
ejpam-6682	319	24	disease	disease	NOUN
ejpam-6682	319	25	spread	spread	VERB
ejpam-6682	319	26	.	.	PUNCT
ejpam-6682	320	1	the	the	DET
ejpam-6682	320	2	fractal	fractal	ADJ
ejpam-6682	320	3	model	model	NOUN
ejpam-6682	320	4	,	,	PUNCT
ejpam-6682	320	5	in	in	ADP
ejpam-6682	320	6	the	the	DET
ejpam-6682	320	7	form	form	NOUN
ejpam-6682	320	8	of	of	ADP
ejpam-6682	320	9	hausdorff	hausdorff	NOUN
ejpam-6682	320	10	derivatives	derivative	NOUN
ejpam-6682	320	11	,	,	PUNCT
ejpam-6682	320	12	offered	offer	VERB
ejpam-6682	320	13	a	a	DET
ejpam-6682	320	14	new	new	ADJ
ejpam-6682	320	15	insight	insight	NOUN
ejpam-6682	320	16	into	into	ADP
ejpam-6682	320	17	complex	complex	ADJ
ejpam-6682	320	18	transmission	transmission	NOUN
ejpam-6682	320	19	dynamics	dynamic	NOUN
ejpam-6682	320	20	.	.	PUNCT
ejpam-6682	321	1	for	for	ADP
ejpam-6682	321	2	further	further	ADJ
ejpam-6682	321	3	research	research	NOUN
ejpam-6682	321	4	,	,	PUNCT
ejpam-6682	321	5	some	some	DET
ejpam-6682	321	6	directions	direction	NOUN
ejpam-6682	321	7	of	of	ADP
ejpam-6682	321	8	extension	extension	NOUN
ejpam-6682	321	9	are	be	AUX
ejpam-6682	321	10	available	available	ADJ
ejpam-6682	321	11	.	.	PUNCT
ejpam-6682	322	1	the	the	DET
ejpam-6682	322	2	extension	extension	NOUN
ejpam-6682	322	3	of	of	ADP
ejpam-6682	322	4	the	the	DET
ejpam-6682	322	5	fractal	fractal	ADJ
ejpam-6682	322	6	model	model	NOUN
ejpam-6682	322	7	into	into	ADP
ejpam-6682	322	8	time	time	NOUN
ejpam-6682	322	9	-	-	PUNCT
ejpam-6682	322	10	evolving	evolve	VERB
ejpam-6682	322	11	parameters	parameter	NOUN
ejpam-6682	322	12	will	will	AUX
ejpam-6682	322	13	make	make	VERB
ejpam-6682	322	14	it	it	PRON
ejpam-6682	322	15	even	even	ADV
ejpam-6682	322	16	more	more	ADV
ejpam-6682	322	17	realistic	realistic	ADJ
ejpam-6682	322	18	in	in	ADP
ejpam-6682	322	19	its	its	PRON
ejpam-6682	322	20	ability	ability	NOUN
ejpam-6682	322	21	to	to	PART
ejpam-6682	322	22	cope	cope	VERB
ejpam-6682	322	23	with	with	ADP
ejpam-6682	322	24	real	real	ADJ
ejpam-6682	322	25	situations	situation	NOUN
ejpam-6682	322	26	.	.	PUNCT
ejpam-6682	323	1	the	the	DET
ejpam-6682	323	2	integration	integration	NOUN
ejpam-6682	323	3	of	of	ADP
ejpam-6682	323	4	stochastic	stochastic	ADJ
ejpam-6682	323	5	influence	influence	NOUN
ejpam-6682	323	6	into	into	ADP
ejpam-6682	323	7	fractional	fractional	ADJ
ejpam-6682	323	8	and	and	CCONJ
ejpam-6682	323	9	fractal	fractal	ADJ
ejpam-6682	323	10	models	model	NOUN
ejpam-6682	323	11	will	will	AUX
ejpam-6682	323	12	provide	provide	VERB
ejpam-6682	323	13	a	a	DET
ejpam-6682	323	14	better	well	ADJ
ejpam-6682	323	15	representation	representation	NOUN
ejpam-6682	323	16	of	of	ADP
ejpam-6682	323	17	the	the	DET
ejpam-6682	323	18	diffusion	diffusion	NOUN
ejpam-6682	323	19	of	of	ADP
ejpam-6682	323	20	uncertainty	uncertainty	NOUN
ejpam-6682	323	21	-	-	PUNCT
ejpam-6682	323	22	causing	cause	VERB
ejpam-6682	323	23	diseases	disease	NOUN
ejpam-6682	323	24	.	.	PUNCT
ejpam-6682	324	1	in	in	ADP
ejpam-6682	324	2	future	future	ADJ
ejpam-6682	324	3	work	work	NOUN
ejpam-6682	324	4	,	,	PUNCT
ejpam-6682	324	5	we	we	PRON
ejpam-6682	324	6	aim	aim	VERB
ejpam-6682	324	7	to	to	PART
ejpam-6682	324	8	solve	solve	VERB
ejpam-6682	324	9	new	new	ADJ
ejpam-6682	324	10	fractional	fractional	ADJ
ejpam-6682	324	11	models	model	NOUN
ejpam-6682	324	12	[	[	X
ejpam-6682	324	13	47–49	47–49	X
ejpam-6682	324	14	]	]	PUNCT
ejpam-6682	324	15	and	and	CCONJ
ejpam-6682	324	16	compare	compare	VERB
ejpam-6682	324	17	with	with	ADP
ejpam-6682	324	18	other	other	ADJ
ejpam-6682	324	19	numerical	numerical	ADJ
ejpam-6682	324	20	methods	method	NOUN
ejpam-6682	324	21	[	[	X
ejpam-6682	324	22	50–56	50–56	NUM
ejpam-6682	324	23	]	]	PUNCT
ejpam-6682	324	24	.	.	PUNCT
ejpam-6682	325	1	conflicts	conflict	NOUN
ejpam-6682	325	2	of	of	ADP
ejpam-6682	325	3	interest	interest	NOUN
ejpam-6682	325	4	:	:	PUNCT
ejpam-6682	325	5	the	the	DET
ejpam-6682	325	6	authors	author	NOUN
ejpam-6682	325	7	declare	declare	VERB
ejpam-6682	325	8	that	that	SCONJ
ejpam-6682	325	9	they	they	PRON
ejpam-6682	325	10	have	have	VERB
ejpam-6682	325	11	no	no	DET
ejpam-6682	325	12	conflict	conflict	NOUN
ejpam-6682	325	13	of	of	ADP
ejpam-6682	325	14	interest	interest	NOUN
ejpam-6682	325	15	.	.	PUNCT
ejpam-6682	326	1	references	reference	NOUN
ejpam-6682	326	2	[	[	X
ejpam-6682	326	3	1	1	NUM
ejpam-6682	326	4	]	]	X
ejpam-6682	326	5	victor	victor	PROPN
ejpam-6682	326	6	henrique	henrique	PROPN
ejpam-6682	326	7	ferreira	ferreira	PROPN
ejpam-6682	326	8	-	-	PUNCT
ejpam-6682	326	9	de	de	X
ejpam-6682	326	10	lima	lima	PROPN
ejpam-6682	326	11	and	and	CCONJ
ejpam-6682	326	12	tamara	tamara	PROPN
ejpam-6682	326	13	nunes	nunes	PROPN
ejpam-6682	326	14	lima	lima	PROPN
ejpam-6682	326	15	-	-	PUNCT
ejpam-6682	326	16	camara	camara	PROPN
ejpam-6682	326	17	.	.	PUNCT
ejpam-6682	326	18	natural	natural	ADJ
ejpam-6682	326	19	vertical	vertical	ADJ
ejpam-6682	326	20	transmission	transmission	NOUN
ejpam-6682	326	21	of	of	ADP
ejpam-6682	326	22	dengue	dengue	NOUN
ejpam-6682	326	23	virus	virus	NOUN
ejpam-6682	326	24	in	in	ADP
ejpam-6682	326	25	aedes	aedes	PROPN
ejpam-6682	326	26	aegypti	aegypti	PROPN
ejpam-6682	326	27	and	and	CCONJ
ejpam-6682	326	28	aedes	aedes	PROPN
ejpam-6682	326	29	albopictus	albopictus	PROPN
ejpam-6682	326	30	:	:	PUNCT
ejpam-6682	326	31	a	a	DET
ejpam-6682	326	32	systematic	systematic	ADJ
ejpam-6682	326	33	review	review	NOUN
ejpam-6682	326	34	.	.	PUNCT
ejpam-6682	327	1	parasites	parasite	NOUN
ejpam-6682	327	2	&	&	CCONJ
ejpam-6682	327	3	vectors	vector	NOUN
ejpam-6682	327	4	,	,	PUNCT
ejpam-6682	327	5	11:1–8	11:1–8	NUM
ejpam-6682	327	6	,	,	PUNCT
ejpam-6682	327	7	2018	2018	NUM
ejpam-6682	327	8	.	.	PUNCT
ejpam-6682	328	1	[	[	X
ejpam-6682	328	2	2	2	NUM
ejpam-6682	328	3	]	]	PUNCT
ejpam-6682	328	4	sudipta	sudipta	PROPN
ejpam-6682	328	5	kumar	kumar	PROPN
ejpam-6682	328	6	roy	roy	PROPN
ejpam-6682	328	7	and	and	CCONJ
ejpam-6682	328	8	soumen	soumen	PROPN
ejpam-6682	328	9	bhattacharjee	bhattacharjee	PROPN
ejpam-6682	328	10	.	.	PUNCT
ejpam-6682	328	11	dengue	dengue	PROPN
ejpam-6682	328	12	virus	virus	PROPN
ejpam-6682	328	13	:	:	PUNCT
ejpam-6682	328	14	epidemiology	epidemiology	NOUN
ejpam-6682	328	15	,	,	PUNCT
ejpam-6682	328	16	biology	biology	NOUN
ejpam-6682	328	17	,	,	PUNCT
ejpam-6682	328	18	and	and	CCONJ
ejpam-6682	328	19	disease	disease	NOUN
ejpam-6682	328	20	aetiology	aetiology	NOUN
ejpam-6682	328	21	.	.	PUNCT
ejpam-6682	329	1	canadian	canadian	ADJ
ejpam-6682	329	2	journal	journal	PROPN
ejpam-6682	329	3	of	of	ADP
ejpam-6682	329	4	microbiology	microbiology	NOUN
ejpam-6682	329	5	,	,	PUNCT
ejpam-6682	329	6	67(10):687–702	67(10):687–702	NUM
ejpam-6682	329	7	,	,	PUNCT
ejpam-6682	329	8	2021	2021	NUM
ejpam-6682	329	9	.	.	PUNCT
ejpam-6682	330	1	[	[	X
ejpam-6682	330	2	3	3	NUM
ejpam-6682	330	3	]	]	X
ejpam-6682	330	4	sweety	sweety	NOUN
ejpam-6682	330	5	trivedi	trivedi	PROPN
ejpam-6682	330	6	and	and	CCONJ
ejpam-6682	330	7	ambar	ambar	PROPN
ejpam-6682	330	8	chakravarty	chakravarty	PROPN
ejpam-6682	330	9	.	.	PUNCT
ejpam-6682	331	1	neurological	neurological	ADJ
ejpam-6682	331	2	complications	complication	NOUN
ejpam-6682	331	3	of	of	ADP
ejpam-6682	331	4	dengue	dengue	NOUN
ejpam-6682	331	5	fever	fever	NOUN
ejpam-6682	331	6	.	.	PUNCT
ejpam-6682	332	1	current	current	ADJ
ejpam-6682	332	2	neurology	neurology	NOUN
ejpam-6682	332	3	and	and	CCONJ
ejpam-6682	332	4	neuroscience	neuroscience	NOUN
ejpam-6682	332	5	reports	report	NOUN
ejpam-6682	332	6	,	,	PUNCT
ejpam-6682	332	7	22(8):515–529	22(8):515–529	NUM
ejpam-6682	332	8	,	,	PUNCT
ejpam-6682	332	9	2022	2022	NUM
ejpam-6682	332	10	.	.	PUNCT
ejpam-6682	333	1	[	[	X
ejpam-6682	333	2	4	4	X
ejpam-6682	333	3	]	]	PUNCT
ejpam-6682	333	4	viroj	viroj	VERB
ejpam-6682	333	5	wiwanitkit	wiwanitkit	PROPN
ejpam-6682	333	6	.	.	PUNCT
ejpam-6682	334	1	dengue	dengue	NOUN
ejpam-6682	334	2	fever	fever	NOUN
ejpam-6682	334	3	:	:	PUNCT
ejpam-6682	334	4	diagnosis	diagnosis	NOUN
ejpam-6682	334	5	and	and	CCONJ
ejpam-6682	334	6	treatment	treatment	NOUN
ejpam-6682	334	7	.	.	PUNCT
ejpam-6682	335	1	expert	expert	NOUN
ejpam-6682	335	2	review	review	PROPN
ejpam-6682	335	3	of	of	ADP
ejpam-6682	335	4	antiinfective	antiinfective	ADJ
ejpam-6682	335	5	therapy	therapy	NOUN
ejpam-6682	335	6	,	,	PUNCT
ejpam-6682	335	7	8(7):841–845	8(7):841–845	NUM
ejpam-6682	335	8	,	,	PUNCT
ejpam-6682	335	9	2010	2010	NUM
ejpam-6682	335	10	.	.	PUNCT
ejpam-6682	336	1	[	[	X
ejpam-6682	336	2	5	5	X
ejpam-6682	336	3	]	]	X
ejpam-6682	336	4	fridous	fridous	ADJ
ejpam-6682	336	5	jahan	jahan	PROPN
ejpam-6682	336	6	.	.	PUNCT
ejpam-6682	337	1	dengue	dengue	NOUN
ejpam-6682	337	2	fever	fever	PROPN
ejpam-6682	337	3	(	(	PUNCT
ejpam-6682	337	4	df	df	NOUN
ejpam-6682	337	5	)	)	PUNCT
ejpam-6682	337	6	in	in	ADP
ejpam-6682	337	7	pakistan	pakistan	PROPN
ejpam-6682	337	8	.	.	PUNCT
ejpam-6682	338	1	asia	asia	PROPN
ejpam-6682	338	2	pacific	pacific	PROPN
ejpam-6682	338	3	family	family	PROPN
ejpam-6682	338	4	medicine	medicine	NOUN
ejpam-6682	338	5	,	,	PUNCT
ejpam-6682	338	6	10:1–4	10:1–4	NUM
ejpam-6682	338	7	,	,	PUNCT
ejpam-6682	338	8	2011	2011	NUM
ejpam-6682	338	9	.	.	PUNCT
ejpam-6682	339	1	[	[	X
ejpam-6682	339	2	6	6	NUM
ejpam-6682	339	3	]	]	X
ejpam-6682	339	4	carlos	carlos	PROPN
ejpam-6682	339	5	letacio	letacio	PROPN
ejpam-6682	339	6	silveira	silveira	PROPN
ejpam-6682	339	7	lessa	lessa	PROPN
ejpam-6682	339	8	,	,	PUNCT
ejpam-6682	339	9	katharine	katharine	PROPN
ejpam-6682	339	10	valéria	valéria	PROPN
ejpam-6682	339	11	saraiva	saraiva	PROPN
ejpam-6682	339	12	hodel	hodel	PROPN
ejpam-6682	339	13	,	,	PUNCT
ejpam-6682	339	14	marilda	marilda	PROPN
ejpam-6682	339	15	de	de	PROPN
ejpam-6682	339	16	souza	souza	PROPN
ejpam-6682	339	17	gonçalves	gonçalves	PROPN
ejpam-6682	339	18	,	,	PUNCT
ejpam-6682	339	19	and	and	CCONJ
ejpam-6682	339	20	bruna	bruna	PROPN
ejpam-6682	339	21	aparecida	aparecida	PROPN
ejpam-6682	339	22	souza	souza	PROPN
ejpam-6682	339	23	machado	machado	PROPN
ejpam-6682	339	24	.	.	PUNCT
ejpam-6682	340	1	dengue	dengue	NOUN
ejpam-6682	340	2	as	as	ADP
ejpam-6682	340	3	a	a	DET
ejpam-6682	340	4	disease	disease	NOUN
ejpam-6682	340	5	threatening	threaten	VERB
ejpam-6682	340	6	global	global	ADJ
ejpam-6682	340	7	health	health	NOUN
ejpam-6682	340	8	:	:	PUNCT
ejpam-6682	340	9	a	a	DET
ejpam-6682	340	10	narrative	narrative	NOUN
ejpam-6682	340	11	review	review	NOUN
ejpam-6682	340	12	focusing	focus	VERB
ejpam-6682	340	13	on	on	ADP
ejpam-6682	340	14	latin	latin	PROPN
ejpam-6682	340	15	america	america	PROPN
ejpam-6682	340	16	and	and	CCONJ
ejpam-6682	340	17	brazil	brazil	PROPN
ejpam-6682	340	18	.	.	PUNCT
ejpam-6682	341	1	tropical	tropical	ADJ
ejpam-6682	341	2	medicine	medicine	NOUN
ejpam-6682	341	3	and	and	CCONJ
ejpam-6682	341	4	infectious	infectious	ADJ
ejpam-6682	341	5	disease	disease	NOUN
ejpam-6682	341	6	,	,	PUNCT
ejpam-6682	341	7	8(5):241	8(5):241	NUM
ejpam-6682	341	8	,	,	PUNCT
ejpam-6682	341	9	2023	2023	NUM
ejpam-6682	341	10	.	.	PUNCT
ejpam-6682	342	1	[	[	X
ejpam-6682	342	2	7	7	X
ejpam-6682	342	3	]	]	X
ejpam-6682	342	4	ayman	ayman	PROPN
ejpam-6682	342	5	ahmed	ahmed	PROPN
ejpam-6682	342	6	,	,	PUNCT
ejpam-6682	342	7	adel	adel	PROPN
ejpam-6682	342	8	elduma	elduma	PROPN
ejpam-6682	342	9	,	,	PUNCT
ejpam-6682	342	10	babiker	babiker	PROPN
ejpam-6682	342	11	magboul	magboul	PROPN
ejpam-6682	342	12	,	,	PUNCT
ejpam-6682	342	13	tarig	tarig	NOUN
ejpam-6682	342	14	higazi	higazi	NOUN
ejpam-6682	342	15	,	,	PUNCT
ejpam-6682	342	16	and	and	CCONJ
ejpam-6682	342	17	yousif	yousif	PROPN
ejpam-6682	342	18	ali	ali	PROPN
ejpam-6682	342	19	.	.	PUNCT
ejpam-6682	343	1	the	the	DET
ejpam-6682	343	2	r.	r.	PROPN
ejpam-6682	343	3	saadeh	saadeh	PROPN
ejpam-6682	343	4	et	et	PROPN
ejpam-6682	343	5	al	al	PROPN
ejpam-6682	343	6	.	.	PUNCT
ejpam-6682	343	7	/	/	SYM
ejpam-6682	343	8	eur	eur	PROPN
ejpam-6682	343	9	.	.	PUNCT
ejpam-6682	344	1	j.	j.	PROPN
ejpam-6682	344	2	pure	pure	PROPN
ejpam-6682	344	3	appl	appl	PROPN
ejpam-6682	344	4	.	.	PROPN
ejpam-6682	344	5	math	math	PROPN
ejpam-6682	344	6	,	,	PUNCT
ejpam-6682	344	7	18	18	NUM
ejpam-6682	344	8	(	(	PUNCT
ejpam-6682	344	9	4	4	NUM
ejpam-6682	344	10	)	)	PUNCT
ejpam-6682	344	11	(	(	PUNCT
ejpam-6682	344	12	2025	2025	NUM
ejpam-6682	344	13	)	)	PUNCT
ejpam-6682	344	14	,	,	PUNCT
ejpam-6682	344	15	6682	6682	NUM
ejpam-6682	344	16	18	18	NUM
ejpam-6682	344	17	of	of	ADP
ejpam-6682	344	18	21	21	NUM
ejpam-6682	344	19	first	first	ADJ
ejpam-6682	344	20	outbreak	outbreak	NOUN
ejpam-6682	344	21	of	of	ADP
ejpam-6682	344	22	dengue	dengue	NOUN
ejpam-6682	344	23	fever	fever	NOUN
ejpam-6682	344	24	in	in	ADP
ejpam-6682	344	25	greater	great	ADJ
ejpam-6682	344	26	darfur	darfur	NOUN
ejpam-6682	344	27	,	,	PUNCT
ejpam-6682	344	28	western	western	ADJ
ejpam-6682	344	29	sudan	sudan	PROPN
ejpam-6682	344	30	.	.	PUNCT
ejpam-6682	345	1	tropical	tropical	ADJ
ejpam-6682	345	2	medicine	medicine	NOUN
ejpam-6682	345	3	and	and	CCONJ
ejpam-6682	345	4	infectious	infectious	ADJ
ejpam-6682	345	5	disease	disease	NOUN
ejpam-6682	345	6	,	,	PUNCT
ejpam-6682	345	7	4(1):43	4(1):43	PROPN
ejpam-6682	345	8	,	,	PUNCT
ejpam-6682	345	9	2019	2019	NUM
ejpam-6682	345	10	.	.	PUNCT
ejpam-6682	346	1	[	[	X
ejpam-6682	346	2	8	8	NUM
ejpam-6682	346	3	]	]	X
ejpam-6682	346	4	duane	duane	PROPN
ejpam-6682	346	5	j.	j.	PROPN
ejpam-6682	346	6	gubler	gubler	PROPN
ejpam-6682	346	7	.	.	PUNCT
ejpam-6682	346	8	epidemic	epidemic	NOUN
ejpam-6682	346	9	dengue	dengue	PROPN
ejpam-6682	346	10	and	and	CCONJ
ejpam-6682	346	11	dengue	dengue	NOUN
ejpam-6682	346	12	hemorrhagic	hemorrhagic	PROPN
ejpam-6682	346	13	fever	fever	NOUN
ejpam-6682	346	14	:	:	PUNCT
ejpam-6682	346	15	a	a	DET
ejpam-6682	346	16	global	global	ADJ
ejpam-6682	346	17	public	public	ADJ
ejpam-6682	346	18	health	health	NOUN
ejpam-6682	346	19	problem	problem	NOUN
ejpam-6682	346	20	in	in	ADP
ejpam-6682	346	21	the	the	DET
ejpam-6682	346	22	21st	21st	ADJ
ejpam-6682	346	23	century	century	NOUN
ejpam-6682	346	24	.	.	PUNCT
ejpam-6682	347	1	emerging	emerge	VERB
ejpam-6682	347	2	infections	infection	NOUN
ejpam-6682	347	3	1	1	NUM
ejpam-6682	347	4	,	,	PUNCT
ejpam-6682	347	5	pages	page	NOUN
ejpam-6682	347	6	1–14	1–14	PROPN
ejpam-6682	347	7	,	,	PUNCT
ejpam-6682	347	8	1997	1997	NUM
ejpam-6682	347	9	.	.	PUNCT
ejpam-6682	348	1	[	[	X
ejpam-6682	348	2	9	9	NUM
ejpam-6682	348	3	]	]	SYM
ejpam-6682	348	4	xiaorong	xiaorong	PROPN
ejpam-6682	348	5	yang	yang	PROPN
ejpam-6682	348	6	,	,	PUNCT
ejpam-6682	348	7	mikkel	mikkel	PROPN
ejpam-6682	348	8	b.	b.	PROPN
ejpam-6682	348	9	m.	m.	PROPN
ejpam-6682	348	10	quam	quam	PROPN
ejpam-6682	348	11	,	,	PUNCT
ejpam-6682	348	12	tongchao	tongchao	PROPN
ejpam-6682	348	13	zhang	zhang	PROPN
ejpam-6682	348	14	,	,	PUNCT
ejpam-6682	348	15	and	and	CCONJ
ejpam-6682	348	16	shaowei	shaowei	NOUN
ejpam-6682	348	17	sang	sing	VERB
ejpam-6682	348	18	.	.	PUNCT
ejpam-6682	349	1	global	global	ADJ
ejpam-6682	349	2	burden	burden	NOUN
ejpam-6682	349	3	for	for	ADP
ejpam-6682	349	4	dengue	dengue	NOUN
ejpam-6682	349	5	and	and	CCONJ
ejpam-6682	349	6	the	the	DET
ejpam-6682	349	7	evolving	evolve	VERB
ejpam-6682	349	8	pattern	pattern	NOUN
ejpam-6682	349	9	in	in	ADP
ejpam-6682	349	10	the	the	DET
ejpam-6682	349	11	past	past	ADJ
ejpam-6682	349	12	30	30	NUM
ejpam-6682	349	13	years	year	NOUN
ejpam-6682	349	14	.	.	PUNCT
ejpam-6682	350	1	journal	journal	PROPN
ejpam-6682	350	2	of	of	ADP
ejpam-6682	350	3	travel	travel	NOUN
ejpam-6682	350	4	medicine	medicine	NOUN
ejpam-6682	350	5	,	,	PUNCT
ejpam-6682	350	6	28(8):taab146	28(8):taab146	NUM
ejpam-6682	350	7	,	,	PUNCT
ejpam-6682	350	8	2021	2021	NUM
ejpam-6682	350	9	.	.	PUNCT
ejpam-6682	351	1	[	[	X
ejpam-6682	351	2	10	10	NUM
ejpam-6682	351	3	]	]	X
ejpam-6682	351	4	fathelrhman	fathelrhman	NOUN
ejpam-6682	351	5	e.	e.	PROPN
ejpam-6682	351	6	l.	l.	PROPN
ejpam-6682	351	7	guma	guma	PROPN
ejpam-6682	351	8	,	,	PUNCT
ejpam-6682	351	9	ossama	ossama	NOUN
ejpam-6682	351	10	m.	m.	NOUN
ejpam-6682	351	11	badawy	badawy	PROPN
ejpam-6682	351	12	,	,	PUNCT
ejpam-6682	351	13	mohammed	mohammed	PROPN
ejpam-6682	351	14	berir	berir	PROPN
ejpam-6682	351	15	,	,	PUNCT
ejpam-6682	351	16	and	and	CCONJ
ejpam-6682	351	17	mohamed	mohamed	PROPN
ejpam-6682	351	18	a.	a.	PROPN
ejpam-6682	351	19	abdoon	abdoon	PROPN
ejpam-6682	351	20	.	.	PUNCT
ejpam-6682	352	1	numerical	numerical	ADJ
ejpam-6682	352	2	analysis	analysis	NOUN
ejpam-6682	352	3	of	of	ADP
ejpam-6682	352	4	fractional	fractional	ADJ
ejpam-6682	352	5	-	-	PUNCT
ejpam-6682	352	6	order	order	NOUN
ejpam-6682	352	7	dynamic	dynamic	ADJ
ejpam-6682	352	8	dengue	dengue	NOUN
ejpam-6682	352	9	disease	disease	NOUN
ejpam-6682	352	10	epidemic	epidemic	NOUN
ejpam-6682	352	11	in	in	ADP
ejpam-6682	352	12	sudan	sudan	PROPN
ejpam-6682	352	13	.	.	PUNCT
ejpam-6682	353	1	journal	journal	PROPN
ejpam-6682	353	2	of	of	ADP
ejpam-6682	353	3	the	the	DET
ejpam-6682	353	4	nigerian	nigerian	ADJ
ejpam-6682	353	5	society	society	NOUN
ejpam-6682	353	6	of	of	ADP
ejpam-6682	353	7	physical	physical	ADJ
ejpam-6682	353	8	sciences	science	NOUN
ejpam-6682	353	9	,	,	PUNCT
ejpam-6682	353	10	page	page	NOUN
ejpam-6682	353	11	1464	1464	NUM
ejpam-6682	353	12	,	,	PUNCT
ejpam-6682	353	13	2023	2023	NUM
ejpam-6682	353	14	.	.	PUNCT
ejpam-6682	354	1	[	[	X
ejpam-6682	354	2	11	11	NUM
ejpam-6682	354	3	]	]	X
ejpam-6682	354	4	arwa	arwa	PROPN
ejpam-6682	354	5	elaagip	elaagip	PROPN
ejpam-6682	354	6	,	,	PUNCT
ejpam-6682	354	7	khider	khider	PROPN
ejpam-6682	354	8	alsedig	alsedig	PROPN
ejpam-6682	354	9	,	,	PUNCT
ejpam-6682	354	10	omnia	omnia	PROPN
ejpam-6682	354	11	altahir	altahir	PROPN
ejpam-6682	354	12	,	,	PUNCT
ejpam-6682	354	13	tellal	tellal	PROPN
ejpam-6682	354	14	ageep	ageep	PROPN
ejpam-6682	354	15	,	,	PUNCT
ejpam-6682	354	16	ayman	ayman	PROPN
ejpam-6682	354	17	ahmed	ahmed	PROPN
ejpam-6682	354	18	,	,	PUNCT
ejpam-6682	354	19	hanaa	hanaa	PROPN
ejpam-6682	354	20	adli	adli	PROPN
ejpam-6682	354	21	siam	siam	PROPN
ejpam-6682	354	22	,	,	PUNCT
ejpam-6682	354	23	abdallah	abdallah	PROPN
ejpam-6682	354	24	m.	m.	PROPN
ejpam-6682	354	25	samy	samy	PROPN
ejpam-6682	354	26	,	,	PUNCT
ejpam-6682	354	27	waleed	waleed	PROPN
ejpam-6682	354	28	mohamed	mohamed	PROPN
ejpam-6682	354	29	,	,	PUNCT
ejpam-6682	354	30	fatima	fatima	PROPN
ejpam-6682	354	31	khalid	khalid	PROPN
ejpam-6682	354	32	,	,	PUNCT
ejpam-6682	354	33	suhaib	suhaib	PROPN
ejpam-6682	354	34	gumaa	gumaa	PROPN
ejpam-6682	354	35	,	,	PUNCT
ejpam-6682	354	36	et	et	PROPN
ejpam-6682	354	37	al	al	PROPN
ejpam-6682	354	38	.	.	PROPN
ejpam-6682	354	39	seroprevalence	seroprevalence	NOUN
ejpam-6682	354	40	and	and	CCONJ
ejpam-6682	354	41	associated	associate	VERB
ejpam-6682	354	42	risk	risk	NOUN
ejpam-6682	354	43	factors	factor	NOUN
ejpam-6682	354	44	of	of	ADP
ejpam-6682	354	45	dengue	dengue	NOUN
ejpam-6682	354	46	fever	fever	NOUN
ejpam-6682	354	47	in	in	ADP
ejpam-6682	354	48	kassala	kassala	PROPN
ejpam-6682	354	49	state	state	PROPN
ejpam-6682	354	50	,	,	PUNCT
ejpam-6682	354	51	eastern	eastern	PROPN
ejpam-6682	354	52	sudan	sudan	PROPN
ejpam-6682	354	53	.	.	PUNCT
ejpam-6682	355	1	plos	plos	PROPN
ejpam-6682	355	2	neglected	neglect	VERB
ejpam-6682	355	3	tropical	tropical	ADJ
ejpam-6682	355	4	diseases	disease	NOUN
ejpam-6682	355	5	,	,	PUNCT
ejpam-6682	355	6	14(12):e0008918	14(12):e0008918	NUM
ejpam-6682	355	7	,	,	PUNCT
ejpam-6682	355	8	2020	2020	NUM
ejpam-6682	355	9	.	.	PUNCT
ejpam-6682	356	1	[	[	X
ejpam-6682	356	2	12	12	NUM
ejpam-6682	356	3	]	]	X
ejpam-6682	356	4	máıra	máıra	NOUN
ejpam-6682	356	5	aguiar	aguiar	NOUN
ejpam-6682	356	6	,	,	PUNCT
ejpam-6682	356	7	vizda	vizda	VERB
ejpam-6682	356	8	anam	anam	PROPN
ejpam-6682	356	9	,	,	PUNCT
ejpam-6682	356	10	konstantin	konstantin	PROPN
ejpam-6682	356	11	b.	b.	PROPN
ejpam-6682	356	12	blyuss	blyuss	PROPN
ejpam-6682	356	13	,	,	PUNCT
ejpam-6682	356	14	carlo	carlo	PROPN
ejpam-6682	356	15	delfin	delfin	PROPN
ejpam-6682	356	16	s.	s.	PROPN
ejpam-6682	356	17	estadilla	estadilla	PROPN
ejpam-6682	356	18	,	,	PUNCT
ejpam-6682	356	19	bruno	bruno	PROPN
ejpam-6682	356	20	v.	v.	PROPN
ejpam-6682	356	21	guerrero	guerrero	PROPN
ejpam-6682	356	22	,	,	PUNCT
ejpam-6682	356	23	damián	damián	PROPN
ejpam-6682	356	24	knopoff	knopoff	PROPN
ejpam-6682	356	25	,	,	PUNCT
ejpam-6682	356	26	bob	bob	PROPN
ejpam-6682	356	27	w.	w.	PROPN
ejpam-6682	356	28	kooi	kooi	PROPN
ejpam-6682	356	29	,	,	PUNCT
ejpam-6682	356	30	akhil	akhil	PROPN
ejpam-6682	356	31	kumar	kumar	PROPN
ejpam-6682	356	32	srivastav	srivastav	PROPN
ejpam-6682	356	33	,	,	PUNCT
ejpam-6682	356	34	vanessa	vanessa	NOUN
ejpam-6682	356	35	steindorf	steindorf	PROPN
ejpam-6682	356	36	,	,	PUNCT
ejpam-6682	356	37	and	and	CCONJ
ejpam-6682	356	38	nico	nico	PROPN
ejpam-6682	356	39	stollenwerk	stollenwerk	PROPN
ejpam-6682	356	40	.	.	PUNCT
ejpam-6682	357	1	mathematical	mathematical	ADJ
ejpam-6682	357	2	models	model	NOUN
ejpam-6682	357	3	for	for	ADP
ejpam-6682	357	4	dengue	dengue	NOUN
ejpam-6682	357	5	fever	fever	NOUN
ejpam-6682	357	6	epidemiology	epidemiology	NOUN
ejpam-6682	357	7	:	:	PUNCT
ejpam-6682	357	8	a	a	DET
ejpam-6682	357	9	10	10	NUM
ejpam-6682	357	10	-	-	PUNCT
ejpam-6682	357	11	year	year	NOUN
ejpam-6682	357	12	systematic	systematic	ADJ
ejpam-6682	357	13	review	review	NOUN
ejpam-6682	357	14	.	.	PUNCT
ejpam-6682	358	1	physics	physics	PROPN
ejpam-6682	358	2	of	of	ADP
ejpam-6682	358	3	life	life	NOUN
ejpam-6682	358	4	reviews	review	NOUN
ejpam-6682	358	5	,	,	PUNCT
ejpam-6682	358	6	40:65–92	40:65–92	NUM
ejpam-6682	358	7	,	,	PUNCT
ejpam-6682	358	8	2022	2022	NUM
ejpam-6682	358	9	.	.	PUNCT
ejpam-6682	359	1	[	[	X
ejpam-6682	359	2	13	13	NUM
ejpam-6682	359	3	]	]	X
ejpam-6682	359	4	priyanka	priyanka	PROPN
ejpam-6682	359	5	harjule	harjule	PROPN
ejpam-6682	359	6	et	et	PROPN
ejpam-6682	359	7	al	al	PROPN
ejpam-6682	359	8	.	.	PROPN
ejpam-6682	359	9	mathematical	mathematical	ADJ
ejpam-6682	359	10	modelling	modelling	NOUN
ejpam-6682	359	11	and	and	CCONJ
ejpam-6682	359	12	analysis	analysis	NOUN
ejpam-6682	359	13	of	of	ADP
ejpam-6682	359	14	dengue	dengue	NOUN
ejpam-6682	359	15	transmission	transmission	NOUN
ejpam-6682	359	16	dynamics	dynamic	NOUN
ejpam-6682	359	17	.	.	PUNCT
ejpam-6682	360	1	procedia	procedia	PROPN
ejpam-6682	360	2	computer	computer	NOUN
ejpam-6682	360	3	science	science	NOUN
ejpam-6682	360	4	,	,	PUNCT
ejpam-6682	360	5	235:539–548	235:539–548	NUM
ejpam-6682	360	6	,	,	PUNCT
ejpam-6682	360	7	2024	2024	NUM
ejpam-6682	360	8	.	.	PUNCT
ejpam-6682	361	1	[	[	X
ejpam-6682	361	2	14	14	NUM
ejpam-6682	361	3	]	]	PUNCT
ejpam-6682	361	4	m.	m.	NOUN
ejpam-6682	361	5	a.	a.	PROPN
ejpam-6682	361	6	abdoon	abdoon	PROPN
ejpam-6682	361	7	.	.	PUNCT
ejpam-6682	362	1	fractional	fractional	ADJ
ejpam-6682	362	2	derivative	derivative	ADJ
ejpam-6682	362	3	approach	approach	NOUN
ejpam-6682	362	4	for	for	ADP
ejpam-6682	362	5	modeling	model	VERB
ejpam-6682	362	6	chaotic	chaotic	ADJ
ejpam-6682	362	7	dynamics	dynamic	NOUN
ejpam-6682	362	8	:	:	PUNCT
ejpam-6682	362	9	applications	application	NOUN
ejpam-6682	362	10	in	in	ADP
ejpam-6682	362	11	communication	communication	NOUN
ejpam-6682	362	12	and	and	CCONJ
ejpam-6682	362	13	engineering	engineering	NOUN
ejpam-6682	362	14	systems	system	NOUN
ejpam-6682	362	15	.	.	PUNCT
ejpam-6682	363	1	in	in	ADP
ejpam-6682	363	2	proceedings	proceeding	NOUN
ejpam-6682	363	3	of	of	ADP
ejpam-6682	363	4	the	the	DET
ejpam-6682	363	5	international	international	ADJ
ejpam-6682	363	6	conference	conference	NOUN
ejpam-6682	363	7	on	on	ADP
ejpam-6682	363	8	mathematical	mathematical	ADJ
ejpam-6682	363	9	modelling	modelling	NOUN
ejpam-6682	363	10	,	,	PUNCT
ejpam-6682	363	11	applied	apply	VERB
ejpam-6682	363	12	analysis	analysis	NOUN
ejpam-6682	363	13	and	and	CCONJ
ejpam-6682	363	14	computation	computation	NOUN
ejpam-6682	363	15	,	,	PUNCT
ejpam-6682	363	16	pages	page	NOUN
ejpam-6682	363	17	82–95	82–95	NUM
ejpam-6682	363	18	.	.	PUNCT
ejpam-6682	364	1	springer	springer	NOUN
ejpam-6682	364	2	,	,	PUNCT
ejpam-6682	364	3	2024	2024	NUM
ejpam-6682	364	4	.	.	PUNCT
ejpam-6682	365	1	[	[	X
ejpam-6682	365	2	15	15	NUM
ejpam-6682	365	3	]	]	X
ejpam-6682	365	4	md	md	PROPN
ejpam-6682	365	5	rafiul	rafiul	PROPN
ejpam-6682	365	6	islam	islam	PROPN
ejpam-6682	365	7	,	,	PUNCT
ejpam-6682	365	8	angela	angela	PROPN
ejpam-6682	365	9	peace	peace	PROPN
ejpam-6682	365	10	,	,	PUNCT
ejpam-6682	365	11	daniel	daniel	PROPN
ejpam-6682	365	12	medina	medina	PROPN
ejpam-6682	365	13	,	,	PUNCT
ejpam-6682	365	14	and	and	CCONJ
ejpam-6682	365	15	tamer	tame	ADJ
ejpam-6682	365	16	oraby	oraby	NOUN
ejpam-6682	365	17	.	.	PUNCT
ejpam-6682	366	1	integer	integer	NOUN
ejpam-6682	366	2	versus	versus	ADP
ejpam-6682	366	3	fractional	fractional	ADJ
ejpam-6682	366	4	order	order	NOUN
ejpam-6682	366	5	seir	seir	NOUN
ejpam-6682	366	6	deterministic	deterministic	ADJ
ejpam-6682	366	7	and	and	CCONJ
ejpam-6682	366	8	stochastic	stochastic	ADJ
ejpam-6682	366	9	models	model	NOUN
ejpam-6682	366	10	of	of	ADP
ejpam-6682	366	11	measles	measle	NOUN
ejpam-6682	366	12	.	.	PUNCT
ejpam-6682	367	1	international	international	ADJ
ejpam-6682	367	2	journal	journal	PROPN
ejpam-6682	367	3	of	of	ADP
ejpam-6682	367	4	environmental	environmental	ADJ
ejpam-6682	367	5	research	research	NOUN
ejpam-6682	367	6	and	and	CCONJ
ejpam-6682	367	7	public	public	ADJ
ejpam-6682	367	8	health	health	NOUN
ejpam-6682	367	9	,	,	PUNCT
ejpam-6682	367	10	17(6):2014	17(6):2014	NUM
ejpam-6682	367	11	,	,	PUNCT
ejpam-6682	367	12	2020	2020	NUM
ejpam-6682	367	13	.	.	PUNCT
ejpam-6682	368	1	[	[	X
ejpam-6682	368	2	16	16	NUM
ejpam-6682	368	3	]	]	X
ejpam-6682	368	4	nekmat	nekmat	NOUN
ejpam-6682	368	5	ullah	ullah	PROPN
ejpam-6682	368	6	,	,	PUNCT
ejpam-6682	368	7	zahir	zahir	ADJ
ejpam-6682	368	8	shah	shah	NOUN
ejpam-6682	368	9	,	,	PUNCT
ejpam-6682	368	10	rashid	rashid	PROPN
ejpam-6682	368	11	jan	jan	PROPN
ejpam-6682	368	12	,	,	PUNCT
ejpam-6682	368	13	narcisa	narcisa	ADJ
ejpam-6682	368	14	vrinceanu	vrinceanu	PROPN
ejpam-6682	368	15	,	,	PUNCT
ejpam-6682	368	16	muhammad	muhammad	PROPN
ejpam-6682	368	17	farhan	farhan	PROPN
ejpam-6682	368	18	,	,	PUNCT
ejpam-6682	368	19	and	and	CCONJ
ejpam-6682	368	20	elisabeta	elisabeta	PROPN
ejpam-6682	368	21	antonescu	antonescu	PROPN
ejpam-6682	368	22	.	.	PUNCT
ejpam-6682	369	1	modeling	model	VERB
ejpam-6682	369	2	the	the	DET
ejpam-6682	369	3	non	non	ADJ
ejpam-6682	369	4	-	-	ADJ
ejpam-6682	369	5	integer	integer	ADJ
ejpam-6682	369	6	dynamics	dynamic	NOUN
ejpam-6682	369	7	of	of	ADP
ejpam-6682	369	8	a	a	DET
ejpam-6682	369	9	vector	vector	NOUN
ejpam-6682	369	10	-	-	PUNCT
ejpam-6682	369	11	borne	bear	VERB
ejpam-6682	369	12	infection	infection	NOUN
ejpam-6682	369	13	with	with	ADP
ejpam-6682	369	14	nonlocal	nonlocal	ADJ
ejpam-6682	369	15	and	and	CCONJ
ejpam-6682	369	16	nonsingular	nonsingular	ADJ
ejpam-6682	369	17	kernel	kernel	PROPN
ejpam-6682	369	18	.	.	PUNCT
ejpam-6682	370	1	scientific	scientific	ADJ
ejpam-6682	370	2	reports	report	NOUN
ejpam-6682	370	3	,	,	PUNCT
ejpam-6682	370	4	15(1):6262	15(1):6262	NUM
ejpam-6682	370	5	,	,	PUNCT
ejpam-6682	370	6	2025	2025	NUM
ejpam-6682	370	7	.	.	PUNCT
ejpam-6682	371	1	[	[	X
ejpam-6682	371	2	17	17	NUM
ejpam-6682	371	3	]	]	X
ejpam-6682	371	4	tao	tao	PROPN
ejpam-6682	371	5	-	-	PUNCT
ejpam-6682	371	6	qian	qian	PROPN
ejpam-6682	371	7	tang	tang	PROPN
ejpam-6682	371	8	,	,	PUNCT
ejpam-6682	371	9	rashid	rashid	PROPN
ejpam-6682	371	10	jan	jan	PROPN
ejpam-6682	371	11	,	,	PUNCT
ejpam-6682	371	12	adil	adil	PROPN
ejpam-6682	371	13	khurshaid	khurshaid	PROPN
ejpam-6682	371	14	,	,	PUNCT
ejpam-6682	371	15	zahir	zahir	ADJ
ejpam-6682	371	16	shah	shah	NOUN
ejpam-6682	371	17	,	,	PUNCT
ejpam-6682	371	18	narcisa	narcisa	NOUN
ejpam-6682	371	19	vrinceanu	vrinceanu	NOUN
ejpam-6682	371	20	,	,	PUNCT
ejpam-6682	371	21	and	and	CCONJ
ejpam-6682	371	22	mihaela	mihaela	PROPN
ejpam-6682	371	23	racheriu	racheriu	PROPN
ejpam-6682	371	24	.	.	PUNCT
ejpam-6682	372	1	analysis	analysis	NOUN
ejpam-6682	372	2	of	of	ADP
ejpam-6682	372	3	the	the	DET
ejpam-6682	372	4	dynamics	dynamic	NOUN
ejpam-6682	372	5	of	of	ADP
ejpam-6682	372	6	a	a	DET
ejpam-6682	372	7	vector	vector	NOUN
ejpam-6682	372	8	-	-	PUNCT
ejpam-6682	372	9	borne	bear	VERB
ejpam-6682	372	10	infection	infection	NOUN
ejpam-6682	372	11	with	with	ADP
ejpam-6682	372	12	the	the	DET
ejpam-6682	372	13	effect	effect	NOUN
ejpam-6682	372	14	of	of	ADP
ejpam-6682	372	15	imperfect	imperfect	ADJ
ejpam-6682	372	16	vaccination	vaccination	NOUN
ejpam-6682	372	17	from	from	ADP
ejpam-6682	372	18	a	a	DET
ejpam-6682	372	19	fractional	fractional	ADJ
ejpam-6682	372	20	perspective	perspective	NOUN
ejpam-6682	372	21	.	.	PUNCT
ejpam-6682	373	1	scientific	scientific	ADJ
ejpam-6682	373	2	reports	report	NOUN
ejpam-6682	373	3	,	,	PUNCT
ejpam-6682	373	4	13(1):14398	13(1):14398	NUM
ejpam-6682	373	5	,	,	PUNCT
ejpam-6682	373	6	2023	2023	NUM
ejpam-6682	373	7	.	.	PUNCT
ejpam-6682	374	1	[	[	X
ejpam-6682	374	2	18	18	NUM
ejpam-6682	374	3	]	]	SYM
ejpam-6682	374	4	parvaiz	parvaiz	PROPN
ejpam-6682	374	5	ahmad	ahmad	PROPN
ejpam-6682	374	6	naik	naik	PROPN
ejpam-6682	374	7	,	,	PUNCT
ejpam-6682	374	8	mehmet	mehmet	PROPN
ejpam-6682	374	9	yavuz	yavuz	PROPN
ejpam-6682	374	10	,	,	PUNCT
ejpam-6682	374	11	sania	sania	PROPN
ejpam-6682	374	12	qureshi	qureshi	PROPN
ejpam-6682	374	13	,	,	PUNCT
ejpam-6682	374	14	kolade	kolade	ADJ
ejpam-6682	374	15	m.	m.	NOUN
ejpam-6682	374	16	owolabi	owolabi	NOUN
ejpam-6682	374	17	,	,	PUNCT
ejpam-6682	374	18	amanullah	amanullah	PROPN
ejpam-6682	374	19	soomro	soomro	PROPN
ejpam-6682	374	20	,	,	PUNCT
ejpam-6682	374	21	abdul	abdul	PROPN
ejpam-6682	374	22	hamid	hamid	PROPN
ejpam-6682	374	23	ganie	ganie	PROPN
ejpam-6682	374	24	,	,	PUNCT
ejpam-6682	374	25	et	et	PROPN
ejpam-6682	374	26	al	al	PROPN
ejpam-6682	374	27	.	.	PROPN
ejpam-6682	374	28	memory	memory	NOUN
ejpam-6682	374	29	impacts	impact	NOUN
ejpam-6682	374	30	in	in	ADP
ejpam-6682	374	31	hepatitis	hepatitis	PROPN
ejpam-6682	374	32	c	c	NOUN
ejpam-6682	374	33	:	:	PUNCT
ejpam-6682	374	34	a	a	DET
ejpam-6682	374	35	global	global	ADJ
ejpam-6682	374	36	analysis	analysis	NOUN
ejpam-6682	374	37	of	of	ADP
ejpam-6682	374	38	a	a	DET
ejpam-6682	374	39	fractional	fractional	ADJ
ejpam-6682	374	40	-	-	PUNCT
ejpam-6682	374	41	order	order	NOUN
ejpam-6682	374	42	model	model	NOUN
ejpam-6682	374	43	with	with	ADP
ejpam-6682	374	44	an	an	DET
ejpam-6682	374	45	effective	effective	ADJ
ejpam-6682	374	46	treatment	treatment	NOUN
ejpam-6682	374	47	.	.	PUNCT
ejpam-6682	375	1	computer	computer	NOUN
ejpam-6682	375	2	methods	method	NOUN
ejpam-6682	375	3	and	and	CCONJ
ejpam-6682	375	4	programs	program	NOUN
ejpam-6682	375	5	in	in	ADP
ejpam-6682	375	6	biomedicine	biomedicine	NOUN
ejpam-6682	375	7	,	,	PUNCT
ejpam-6682	375	8	254:108306	254:108306	NOUN
ejpam-6682	375	9	,	,	PUNCT
ejpam-6682	375	10	2024	2024	NUM
ejpam-6682	375	11	.	.	PUNCT
ejpam-6682	376	1	[	[	X
ejpam-6682	376	2	19	19	NUM
ejpam-6682	376	3	]	]	X
ejpam-6682	376	4	n.	n.	PROPN
ejpam-6682	376	5	e.	e.	PROPN
ejpam-6682	376	6	alsubaie	alsubaie	PROPN
ejpam-6682	376	7	,	,	PUNCT
ejpam-6682	376	8	fathelrhman	fathelrhman	PROPN
ejpam-6682	376	9	el	el	PROPN
ejpam-6682	376	10	guma	guma	PROPN
ejpam-6682	376	11	,	,	PUNCT
ejpam-6682	376	12	kaouther	kaouther	PROPN
ejpam-6682	376	13	boulehmi	boulehmi	PROPN
ejpam-6682	376	14	,	,	PUNCT
ejpam-6682	376	15	naseam	naseam	PROPN
ejpam-6682	376	16	al	al	PROPN
ejpam-6682	376	17	-	-	PUNCT
ejpam-6682	376	18	kuleab	kuleab	PROPN
ejpam-6682	376	19	,	,	PUNCT
ejpam-6682	376	20	and	and	CCONJ
ejpam-6682	376	21	mohamed	mohamed	PROPN
ejpam-6682	376	22	a.	a.	PROPN
ejpam-6682	376	23	abdoon	abdoon	PROPN
ejpam-6682	376	24	.	.	PUNCT
ejpam-6682	377	1	improving	improve	VERB
ejpam-6682	377	2	influenza	influenza	ADJ
ejpam-6682	377	3	epidemiological	epidemiological	ADJ
ejpam-6682	377	4	models	model	NOUN
ejpam-6682	377	5	under	under	ADP
ejpam-6682	377	6	caputo	caputo	PROPN
ejpam-6682	377	7	fractional	fractional	ADJ
ejpam-6682	377	8	-	-	PUNCT
ejpam-6682	377	9	order	order	NOUN
ejpam-6682	377	10	calculus	calculus	NOUN
ejpam-6682	377	11	.	.	PUNCT
ejpam-6682	377	12	symmetry	symmetry	NOUN
ejpam-6682	377	13	,	,	PUNCT
ejpam-6682	377	14	16(7):929	16(7):929	NOUN
ejpam-6682	377	15	,	,	PUNCT
ejpam-6682	377	16	2024	2024	NUM
ejpam-6682	377	17	.	.	PUNCT
ejpam-6682	378	1	[	[	X
ejpam-6682	378	2	20	20	NUM
ejpam-6682	378	3	]	]	PUNCT
ejpam-6682	378	4	mutum	mutum	PROPN
ejpam-6682	378	5	zico	zico	PROPN
ejpam-6682	378	6	meetei	meetei	PROPN
ejpam-6682	378	7	,	,	PUNCT
ejpam-6682	378	8	shahbaz	shahbaz	PROPN
ejpam-6682	378	9	zafar	zafar	PROPN
ejpam-6682	378	10	,	,	PUNCT
ejpam-6682	378	11	abdullah	abdullah	PROPN
ejpam-6682	378	12	a.	a.	NOUN
ejpam-6682	378	13	zaagan	zaagan	PROPN
ejpam-6682	378	14	,	,	PUNCT
ejpam-6682	378	15	ali	ali	PROPN
ejpam-6682	378	16	m.	m.	PROPN
ejpam-6682	378	17	mahnashi	mahnashi	PROPN
ejpam-6682	378	18	,	,	PUNCT
ejpam-6682	378	19	and	and	CCONJ
ejpam-6682	378	20	muhammad	muhammad	PROPN
ejpam-6682	378	21	idrees	idree	NOUN
ejpam-6682	378	22	.	.	PUNCT
ejpam-6682	379	1	dengue	dengue	NOUN
ejpam-6682	379	2	transmission	transmission	NOUN
ejpam-6682	379	3	dynamics	dynamic	NOUN
ejpam-6682	379	4	:	:	PUNCT
ejpam-6682	379	5	a	a	DET
ejpam-6682	379	6	fractional	fractional	ADJ
ejpam-6682	379	7	-	-	PUNCT
ejpam-6682	379	8	order	order	NOUN
ejpam-6682	379	9	approach	approach	NOUN
ejpam-6682	379	10	with	with	ADP
ejpam-6682	379	11	r.	r.	PROPN
ejpam-6682	379	12	saadeh	saadeh	PROPN
ejpam-6682	379	13	et	et	PROPN
ejpam-6682	379	14	al	al	PROPN
ejpam-6682	379	15	.	.	PUNCT
ejpam-6682	379	16	/	/	SYM
ejpam-6682	379	17	eur	eur	PROPN
ejpam-6682	379	18	.	.	PUNCT
ejpam-6682	380	1	j.	j.	PROPN
ejpam-6682	380	2	pure	pure	PROPN
ejpam-6682	380	3	appl	appl	PROPN
ejpam-6682	380	4	.	.	PROPN
ejpam-6682	380	5	math	math	PROPN
ejpam-6682	380	6	,	,	PUNCT
ejpam-6682	380	7	18	18	NUM
ejpam-6682	380	8	(	(	PUNCT
ejpam-6682	380	9	4	4	NUM
ejpam-6682	380	10	)	)	PUNCT
ejpam-6682	380	11	(	(	PUNCT
ejpam-6682	380	12	2025	2025	NUM
ejpam-6682	380	13	)	)	PUNCT
ejpam-6682	380	14	,	,	PUNCT
ejpam-6682	380	15	6682	6682	NUM
ejpam-6682	380	16	19	19	NUM
ejpam-6682	380	17	of	of	ADP
ejpam-6682	380	18	21	21	NUM
ejpam-6682	380	19	compartmental	compartmental	ADJ
ejpam-6682	380	20	modeling	modeling	NOUN
ejpam-6682	380	21	.	.	PUNCT
ejpam-6682	381	1	fractal	fractal	ADJ
ejpam-6682	381	2	and	and	CCONJ
ejpam-6682	381	3	fractional	fractional	ADJ
ejpam-6682	381	4	,	,	PUNCT
ejpam-6682	381	5	8(4):207	8(4):207	NUM
ejpam-6682	381	6	,	,	PUNCT
ejpam-6682	381	7	2024	2024	NUM
ejpam-6682	381	8	.	.	PUNCT
ejpam-6682	382	1	[	[	X
ejpam-6682	382	2	21	21	NUM
ejpam-6682	382	3	]	]	X
ejpam-6682	382	4	nausheen	nausheen	PROPN
ejpam-6682	382	5	razi	razi	PROPN
ejpam-6682	382	6	,	,	PUNCT
ejpam-6682	382	7	ambreen	ambreen	ADJ
ejpam-6682	382	8	bano	bano	PROPN
ejpam-6682	382	9	,	,	PUNCT
ejpam-6682	382	10	umar	umar	PROPN
ejpam-6682	382	11	ishtiaq	ishtiaq	PROPN
ejpam-6682	382	12	,	,	PUNCT
ejpam-6682	382	13	tayyab	tayyab	PROPN
ejpam-6682	382	14	kamran	kamran	PROPN
ejpam-6682	382	15	,	,	PUNCT
ejpam-6682	382	16	mubariz	mubariz	PROPN
ejpam-6682	382	17	garayev	garayev	NOUN
ejpam-6682	382	18	,	,	PUNCT
ejpam-6682	382	19	and	and	CCONJ
ejpam-6682	382	20	ioan	ioan	NOUN
ejpam-6682	382	21	-	-	PUNCT
ejpam-6682	382	22	lucian	lucian	PROPN
ejpam-6682	382	23	popa	popa	NOUN
ejpam-6682	382	24	.	.	PUNCT
ejpam-6682	383	1	probing	probe	VERB
ejpam-6682	383	2	malware	malware	NOUN
ejpam-6682	383	3	propagation	propagation	NOUN
ejpam-6682	383	4	model	model	NOUN
ejpam-6682	383	5	with	with	ADP
ejpam-6682	383	6	variable	variable	ADJ
ejpam-6682	383	7	infection	infection	NOUN
ejpam-6682	383	8	rates	rate	NOUN
ejpam-6682	383	9	under	under	ADP
ejpam-6682	383	10	integer	integer	NOUN
ejpam-6682	383	11	,	,	PUNCT
ejpam-6682	383	12	fractional	fractional	ADJ
ejpam-6682	383	13	,	,	PUNCT
ejpam-6682	383	14	and	and	CCONJ
ejpam-6682	383	15	fractal	fractal	ADJ
ejpam-6682	383	16	–	–	PUNCT
ejpam-6682	383	17	fractional	fractional	ADJ
ejpam-6682	383	18	orders	order	NOUN
ejpam-6682	383	19	.	.	PUNCT
ejpam-6682	384	1	fractal	fractal	ADJ
ejpam-6682	384	2	and	and	CCONJ
ejpam-6682	384	3	fractional	fractional	ADJ
ejpam-6682	384	4	,	,	PUNCT
ejpam-6682	384	5	9(2):90	9(2):90	NOUN
ejpam-6682	384	6	,	,	PUNCT
ejpam-6682	384	7	2025	2025	NUM
ejpam-6682	384	8	.	.	PUNCT
ejpam-6682	385	1	[	[	X
ejpam-6682	385	2	22	22	NUM
ejpam-6682	385	3	]	]	X
ejpam-6682	385	4	enrique	enrique	PROPN
ejpam-6682	385	5	c.	c.	PROPN
ejpam-6682	385	6	gabrick	gabrick	PROPN
ejpam-6682	385	7	,	,	PUNCT
ejpam-6682	385	8	ervin	ervin	PROPN
ejpam-6682	385	9	k.	k.	PROPN
ejpam-6682	385	10	lenzi	lenzi	PROPN
ejpam-6682	385	11	,	,	PUNCT
ejpam-6682	385	12	and	and	CCONJ
ejpam-6682	385	13	antonio	antonio	PROPN
ejpam-6682	385	14	m.	m.	PROPN
ejpam-6682	385	15	batista	batista	PROPN
ejpam-6682	385	16	.	.	PUNCT
ejpam-6682	386	1	fractional	fractional	ADJ
ejpam-6682	386	2	and	and	CCONJ
ejpam-6682	386	3	fractal	fractal	ADJ
ejpam-6682	386	4	extensions	extension	NOUN
ejpam-6682	386	5	of	of	ADP
ejpam-6682	386	6	epidemiological	epidemiological	ADJ
ejpam-6682	386	7	models	model	NOUN
ejpam-6682	386	8	.	.	PUNCT
ejpam-6682	387	1	in	in	ADP
ejpam-6682	387	2	mathematical	mathematical	ADJ
ejpam-6682	387	3	methods	method	NOUN
ejpam-6682	387	4	in	in	ADP
ejpam-6682	387	5	medical	medical	ADJ
ejpam-6682	387	6	and	and	CCONJ
ejpam-6682	387	7	biological	biological	ADJ
ejpam-6682	387	8	sciences	science	NOUN
ejpam-6682	387	9	,	,	PUNCT
ejpam-6682	387	10	pages	page	NOUN
ejpam-6682	387	11	39–62	39–62	NUM
ejpam-6682	387	12	.	.	PUNCT
ejpam-6682	388	1	elsevier	elsevier	NOUN
ejpam-6682	388	2	,	,	PUNCT
ejpam-6682	388	3	2025	2025	NUM
ejpam-6682	388	4	.	.	PUNCT
ejpam-6682	389	1	[	[	X
ejpam-6682	389	2	23	23	NUM
ejpam-6682	389	3	]	]	X
ejpam-6682	389	4	enrique	enrique	PROPN
ejpam-6682	389	5	c.	c.	PROPN
ejpam-6682	389	6	gabrick	gabrick	PROPN
ejpam-6682	389	7	,	,	PUNCT
ejpam-6682	389	8	elaheh	elaheh	PROPN
ejpam-6682	389	9	sayari	sayari	ADJ
ejpam-6682	389	10	,	,	PUNCT
ejpam-6682	389	11	diogo	diogo	PROPN
ejpam-6682	389	12	l.	l.	PROPN
ejpam-6682	389	13	m.	m.	PROPN
ejpam-6682	389	14	souza	souza	PROPN
ejpam-6682	389	15	,	,	PUNCT
ejpam-6682	389	16	fernando	fernando	PROPN
ejpam-6682	389	17	s.	s.	PROPN
ejpam-6682	389	18	borges	borges	PROPN
ejpam-6682	389	19	,	,	PUNCT
ejpam-6682	389	20	josé	josé	PROPN
ejpam-6682	389	21	trobia	trobia	PROPN
ejpam-6682	389	22	,	,	PUNCT
ejpam-6682	389	23	ervin	ervin	PROPN
ejpam-6682	389	24	k.	k.	PROPN
ejpam-6682	389	25	lenzi	lenzi	PROPN
ejpam-6682	389	26	,	,	PUNCT
ejpam-6682	389	27	and	and	CCONJ
ejpam-6682	389	28	antonio	antonio	PROPN
ejpam-6682	389	29	m.	m.	PROPN
ejpam-6682	389	30	batista	batista	PROPN
ejpam-6682	389	31	.	.	PUNCT
ejpam-6682	390	1	fractal	fractal	PROPN
ejpam-6682	390	2	and	and	CCONJ
ejpam-6682	390	3	fractional	fractional	ADJ
ejpam-6682	390	4	sis	sis	NOUN
ejpam-6682	390	5	model	model	NOUN
ejpam-6682	390	6	for	for	ADP
ejpam-6682	390	7	syphilis	syphilis	PROPN
ejpam-6682	390	8	data	datum	NOUN
ejpam-6682	390	9	.	.	PUNCT
ejpam-6682	391	1	chaos	chaos	NOUN
ejpam-6682	391	2	:	:	PUNCT
ejpam-6682	391	3	an	an	DET
ejpam-6682	391	4	interdisciplinary	interdisciplinary	ADJ
ejpam-6682	391	5	journal	journal	NOUN
ejpam-6682	391	6	of	of	ADP
ejpam-6682	391	7	nonlinear	nonlinear	ADJ
ejpam-6682	391	8	science	science	NOUN
ejpam-6682	391	9	,	,	PUNCT
ejpam-6682	391	10	33(9	33(9	NUM
ejpam-6682	391	11	)	)	PUNCT
ejpam-6682	391	12	,	,	PUNCT
ejpam-6682	391	13	2023	2023	NUM
ejpam-6682	391	14	.	.	PUNCT
ejpam-6682	392	1	[	[	X
ejpam-6682	392	2	24	24	NUM
ejpam-6682	392	3	]	]	X
ejpam-6682	392	4	rami	rami	PROPN
ejpam-6682	392	5	ahmad	ahmad	PROPN
ejpam-6682	392	6	el	el	PROPN
ejpam-6682	392	7	-	-	PUNCT
ejpam-6682	392	8	nabulsi	nabulsi	NOUN
ejpam-6682	392	9	.	.	PUNCT
ejpam-6682	393	1	qualitative	qualitative	ADJ
ejpam-6682	393	2	financial	financial	ADJ
ejpam-6682	393	3	modelling	modelling	NOUN
ejpam-6682	393	4	in	in	ADP
ejpam-6682	393	5	fractal	fractal	ADJ
ejpam-6682	393	6	dimensions	dimension	NOUN
ejpam-6682	393	7	.	.	PUNCT
ejpam-6682	394	1	financial	financial	ADJ
ejpam-6682	394	2	innovation	innovation	NOUN
ejpam-6682	394	3	,	,	PUNCT
ejpam-6682	394	4	11(1):42	11(1):42	NUM
ejpam-6682	394	5	,	,	PUNCT
ejpam-6682	394	6	2025	2025	NUM
ejpam-6682	394	7	.	.	PUNCT
ejpam-6682	395	1	[	[	X
ejpam-6682	395	2	25	25	NUM
ejpam-6682	395	3	]	]	PUNCT
ejpam-6682	395	4	zilong	zilong	ADP
ejpam-6682	395	5	hu	hu	PROPN
ejpam-6682	395	6	,	,	PUNCT
ejpam-6682	395	7	yanzhao	yanzhao	PROPN
ejpam-6682	395	8	wu	wu	PROPN
ejpam-6682	395	9	,	,	PUNCT
ejpam-6682	395	10	puxi	puxi	PROPN
ejpam-6682	395	11	li	li	PROPN
ejpam-6682	395	12	,	,	PUNCT
ejpam-6682	395	13	ruofu	ruofu	PROPN
ejpam-6682	395	14	xiao	xiao	PROPN
ejpam-6682	395	15	,	,	PUNCT
ejpam-6682	395	16	and	and	CCONJ
ejpam-6682	395	17	ran	run	VERB
ejpam-6682	395	18	tao	tao	PROPN
ejpam-6682	395	19	.	.	PUNCT
ejpam-6682	396	1	comparative	comparative	ADJ
ejpam-6682	396	2	study	study	NOUN
ejpam-6682	396	3	on	on	ADP
ejpam-6682	396	4	the	the	DET
ejpam-6682	396	5	fractal	fractal	ADJ
ejpam-6682	396	6	and	and	CCONJ
ejpam-6682	396	7	fractal	fractal	ADJ
ejpam-6682	396	8	dimension	dimension	NOUN
ejpam-6682	396	9	of	of	ADP
ejpam-6682	396	10	the	the	DET
ejpam-6682	396	11	vortex	vortex	NOUN
ejpam-6682	396	12	structure	structure	NOUN
ejpam-6682	396	13	of	of	ADP
ejpam-6682	396	14	hydrofoil	hydrofoil	PROPN
ejpam-6682	396	15	’s	’s	PART
ejpam-6682	396	16	tip	tip	PROPN
ejpam-6682	396	17	leakage	leakage	NOUN
ejpam-6682	396	18	flow	flow	NOUN
ejpam-6682	396	19	.	.	PUNCT
ejpam-6682	397	1	fractal	fractal	ADJ
ejpam-6682	397	2	and	and	CCONJ
ejpam-6682	397	3	fractional	fractional	ADJ
ejpam-6682	397	4	,	,	PUNCT
ejpam-6682	397	5	7(2):123	7(2):123	NUM
ejpam-6682	397	6	,	,	PUNCT
ejpam-6682	397	7	2023	2023	NUM
ejpam-6682	397	8	.	.	PUNCT
ejpam-6682	398	1	[	[	X
ejpam-6682	398	2	26	26	NUM
ejpam-6682	398	3	]	]	X
ejpam-6682	398	4	enrique	enrique	PROPN
ejpam-6682	398	5	c.	c.	PROPN
ejpam-6682	398	6	gabrick	gabrick	PROPN
ejpam-6682	398	7	,	,	PUNCT
ejpam-6682	398	8	ervin	ervin	PROPN
ejpam-6682	398	9	k.	k.	PROPN
ejpam-6682	398	10	lenzi	lenzi	PROPN
ejpam-6682	398	11	,	,	PUNCT
ejpam-6682	398	12	and	and	CCONJ
ejpam-6682	398	13	antonio	antonio	PROPN
ejpam-6682	398	14	m.	m.	PROPN
ejpam-6682	398	15	batista	batista	PROPN
ejpam-6682	398	16	.	.	PUNCT
ejpam-6682	399	1	fractional	fractional	ADJ
ejpam-6682	399	2	and	and	CCONJ
ejpam-6682	399	3	fractal	fractal	ADJ
ejpam-6682	399	4	extensions	extension	NOUN
ejpam-6682	399	5	of	of	ADP
ejpam-6682	399	6	epidemiological	epidemiological	ADJ
ejpam-6682	399	7	models	model	NOUN
ejpam-6682	399	8	.	.	PUNCT
ejpam-6682	400	1	in	in	ADP
ejpam-6682	400	2	mathematical	mathematical	ADJ
ejpam-6682	400	3	methods	method	NOUN
ejpam-6682	400	4	in	in	ADP
ejpam-6682	400	5	medical	medical	ADJ
ejpam-6682	400	6	and	and	CCONJ
ejpam-6682	400	7	biological	biological	ADJ
ejpam-6682	400	8	sciences	science	NOUN
ejpam-6682	400	9	,	,	PUNCT
ejpam-6682	400	10	pages	page	NOUN
ejpam-6682	400	11	39–62	39–62	NUM
ejpam-6682	400	12	.	.	PUNCT
ejpam-6682	401	1	elsevier	elsevier	NOUN
ejpam-6682	401	2	,	,	PUNCT
ejpam-6682	401	3	2025	2025	NUM
ejpam-6682	401	4	.	.	PUNCT
ejpam-6682	402	1	[	[	X
ejpam-6682	402	2	27	27	NUM
ejpam-6682	402	3	]	]	X
ejpam-6682	402	4	chien	chien	PROPN
ejpam-6682	402	5	-	-	PUNCT
ejpam-6682	402	6	hung	hung	PROPN
ejpam-6682	402	7	lee	lee	PROPN
ejpam-6682	402	8	,	,	PUNCT
ejpam-6682	402	9	ko	ko	PROPN
ejpam-6682	402	10	chang	chang	PROPN
ejpam-6682	402	11	,	,	PUNCT
ejpam-6682	402	12	yao	yao	PROPN
ejpam-6682	402	13	-	-	PUNCT
ejpam-6682	402	14	mei	mei	PROPN
ejpam-6682	402	15	chen	chen	PROPN
ejpam-6682	402	16	,	,	PUNCT
ejpam-6682	402	17	jinn	jinn	PROPN
ejpam-6682	402	18	-	-	PUNCT
ejpam-6682	402	19	tsong	tsong	ADP
ejpam-6682	402	20	tsai	tsai	PROPN
ejpam-6682	402	21	,	,	PUNCT
ejpam-6682	402	22	yenming	yenme	VERB
ejpam-6682	402	23	j.	j.	PROPN
ejpam-6682	402	24	chen	chen	PROPN
ejpam-6682	402	25	,	,	PUNCT
ejpam-6682	402	26	and	and	CCONJ
ejpam-6682	402	27	wen	wen	PROPN
ejpam-6682	402	28	-	-	PROPN
ejpam-6682	402	29	hsien	hsien	PROPN
ejpam-6682	402	30	ho	ho	PROPN
ejpam-6682	402	31	.	.	PROPN
ejpam-6682	402	32	epidemic	epidemic	NOUN
ejpam-6682	402	33	prediction	prediction	NOUN
ejpam-6682	402	34	of	of	ADP
ejpam-6682	402	35	dengue	dengue	NOUN
ejpam-6682	402	36	fever	fever	NOUN
ejpam-6682	402	37	based	base	VERB
ejpam-6682	402	38	on	on	ADP
ejpam-6682	402	39	vector	vector	NOUN
ejpam-6682	402	40	compartment	compartment	NOUN
ejpam-6682	402	41	model	model	NOUN
ejpam-6682	402	42	and	and	CCONJ
ejpam-6682	402	43	markov	markov	NOUN
ejpam-6682	402	44	chain	chain	NOUN
ejpam-6682	402	45	monte	monte	PROPN
ejpam-6682	402	46	carlo	carlo	PROPN
ejpam-6682	402	47	method	method	PROPN
ejpam-6682	402	48	.	.	PUNCT
ejpam-6682	403	1	bmc	bmc	ADJ
ejpam-6682	403	2	bioinformatics	bioinformatics	PROPN
ejpam-6682	403	3	,	,	PUNCT
ejpam-6682	403	4	22:1–11	22:1–11	NUM
ejpam-6682	403	5	,	,	PUNCT
ejpam-6682	403	6	2021	2021	NUM
ejpam-6682	403	7	.	.	PUNCT
ejpam-6682	404	1	[	[	X
ejpam-6682	404	2	28	28	NUM
ejpam-6682	404	3	]	]	X
ejpam-6682	404	4	muhammad	muhammad	PROPN
ejpam-6682	404	5	fahmi	fahmi	PROPN
ejpam-6682	404	6	,	,	PUNCT
ejpam-6682	404	7	norhayati	norhayati	NOUN
ejpam-6682	404	8	rosli	rosli	NOUN
ejpam-6682	404	9	,	,	PUNCT
ejpam-6682	404	10	and	and	CCONJ
ejpam-6682	404	11	noryanti	noryanti	PROPN
ejpam-6682	404	12	muhammad	muhammad	PROPN
ejpam-6682	404	13	.	.	PUNCT
ejpam-6682	404	14	estimation	estimation	NOUN
ejpam-6682	404	15	of	of	ADP
ejpam-6682	404	16	epidemiological	epidemiological	ADJ
ejpam-6682	404	17	parameter	parameter	NOUN
ejpam-6682	404	18	of	of	ADP
ejpam-6682	404	19	covid-19	covid-19	PROPN
ejpam-6682	404	20	using	use	VERB
ejpam-6682	404	21	the	the	DET
ejpam-6682	404	22	markov	markov	NOUN
ejpam-6682	404	23	chain	chain	NOUN
ejpam-6682	404	24	monte	monte	PROPN
ejpam-6682	404	25	carlo	carlo	PROPN
ejpam-6682	404	26	method	method	NOUN
ejpam-6682	404	27	.	.	PUNCT
ejpam-6682	405	1	in	in	ADP
ejpam-6682	405	2	aip	aip	PROPN
ejpam-6682	405	3	conference	conference	NOUN
ejpam-6682	405	4	proceedings	proceeding	NOUN
ejpam-6682	405	5	,	,	PUNCT
ejpam-6682	405	6	volume	volume	NOUN
ejpam-6682	405	7	3150	3150	NUM
ejpam-6682	405	8	.	.	PUNCT
ejpam-6682	406	1	aip	aip	PROPN
ejpam-6682	406	2	publishing	publishing	PROPN
ejpam-6682	406	3	,	,	PUNCT
ejpam-6682	406	4	2024	2024	NUM
ejpam-6682	406	5	.	.	PUNCT
ejpam-6682	407	1	[	[	X
ejpam-6682	407	2	29	29	NUM
ejpam-6682	407	3	]	]	PUNCT
ejpam-6682	407	4	luiz	luiz	PROPN
ejpam-6682	407	5	roberto	roberto	PROPN
ejpam-6682	407	6	evangelista	evangelista	PROPN
ejpam-6682	407	7	and	and	CCONJ
ejpam-6682	407	8	ervin	ervin	PROPN
ejpam-6682	407	9	kaminski	kaminski	PROPN
ejpam-6682	407	10	lenzi	lenzi	PROPN
ejpam-6682	407	11	.	.	PUNCT
ejpam-6682	408	1	fractional	fractional	ADJ
ejpam-6682	408	2	diffusion	diffusion	NOUN
ejpam-6682	408	3	equations	equation	NOUN
ejpam-6682	408	4	and	and	CCONJ
ejpam-6682	408	5	anomalous	anomalous	ADJ
ejpam-6682	408	6	diffusion	diffusion	NOUN
ejpam-6682	408	7	.	.	PUNCT
ejpam-6682	409	1	cambridge	cambridge	PROPN
ejpam-6682	409	2	university	university	PROPN
ejpam-6682	409	3	press	press	NOUN
ejpam-6682	409	4	,	,	PUNCT
ejpam-6682	409	5	2018	2018	NUM
ejpam-6682	409	6	.	.	PUNCT
ejpam-6682	410	1	[	[	X
ejpam-6682	410	2	30	30	NUM
ejpam-6682	410	3	]	]	X
ejpam-6682	410	4	richard	richard	PROPN
ejpam-6682	410	5	herrmann	herrmann	PROPN
ejpam-6682	410	6	.	.	PUNCT
ejpam-6682	410	7	fractional	fractional	ADJ
ejpam-6682	410	8	calculus	calculus	NOUN
ejpam-6682	410	9	:	:	PUNCT
ejpam-6682	410	10	an	an	DET
ejpam-6682	410	11	introduction	introduction	NOUN
ejpam-6682	410	12	for	for	ADP
ejpam-6682	410	13	physicists	physicist	NOUN
ejpam-6682	410	14	.	.	PUNCT
ejpam-6682	411	1	world	world	NOUN
ejpam-6682	411	2	scientific	scientific	PROPN
ejpam-6682	411	3	,	,	PUNCT
ejpam-6682	411	4	2011	2011	NUM
ejpam-6682	411	5	.	.	PUNCT
ejpam-6682	412	1	[	[	X
ejpam-6682	412	2	31	31	NUM
ejpam-6682	412	3	]	]	PUNCT
ejpam-6682	412	4	wei	wei	PROPN
ejpam-6682	412	5	cai	cai	PROPN
ejpam-6682	412	6	,	,	PUNCT
ejpam-6682	412	7	wen	wen	PROPN
ejpam-6682	412	8	chen	chen	PROPN
ejpam-6682	412	9	,	,	PUNCT
ejpam-6682	412	10	jun	jun	PROPN
ejpam-6682	412	11	fang	fang	X
ejpam-6682	412	12	,	,	PUNCT
ejpam-6682	412	13	and	and	CCONJ
ejpam-6682	412	14	sverre	sverre	PROPN
ejpam-6682	412	15	holm	holm	PROPN
ejpam-6682	412	16	.	.	PUNCT
ejpam-6682	413	1	a	a	DET
ejpam-6682	413	2	survey	survey	NOUN
ejpam-6682	413	3	on	on	ADP
ejpam-6682	413	4	fractional	fractional	ADJ
ejpam-6682	413	5	derivative	derivative	ADJ
ejpam-6682	413	6	modeling	modeling	NOUN
ejpam-6682	413	7	of	of	ADP
ejpam-6682	413	8	power	power	NOUN
ejpam-6682	413	9	-	-	PUNCT
ejpam-6682	413	10	law	law	NOUN
ejpam-6682	413	11	frequency	frequency	NOUN
ejpam-6682	413	12	-	-	PUNCT
ejpam-6682	413	13	dependent	dependent	ADJ
ejpam-6682	413	14	viscous	viscous	ADJ
ejpam-6682	413	15	dissipative	dissipative	NOUN
ejpam-6682	413	16	and	and	CCONJ
ejpam-6682	413	17	scattering	scatter	VERB
ejpam-6682	413	18	attenuation	attenuation	NOUN
ejpam-6682	413	19	in	in	ADP
ejpam-6682	413	20	acoustic	acoustic	ADJ
ejpam-6682	413	21	wave	wave	NOUN
ejpam-6682	413	22	propagation	propagation	NOUN
ejpam-6682	413	23	.	.	PUNCT
ejpam-6682	414	1	applied	apply	VERB
ejpam-6682	414	2	mechanics	mechanic	NOUN
ejpam-6682	414	3	reviews	review	NOUN
ejpam-6682	414	4	,	,	PUNCT
ejpam-6682	414	5	70(3):030802	70(3):030802	NUM
ejpam-6682	414	6	,	,	PUNCT
ejpam-6682	414	7	2018	2018	NUM
ejpam-6682	414	8	.	.	PUNCT
ejpam-6682	415	1	[	[	X
ejpam-6682	415	2	32	32	NUM
ejpam-6682	415	3	]	]	X
ejpam-6682	415	4	hongguang	hongguang	PROPN
ejpam-6682	415	5	sun	sun	PROPN
ejpam-6682	415	6	,	,	PUNCT
ejpam-6682	415	7	mark	mark	PROPN
ejpam-6682	415	8	m.	m.	PROPN
ejpam-6682	415	9	meerschaert	meerschaert	PROPN
ejpam-6682	415	10	,	,	PUNCT
ejpam-6682	415	11	yong	yong	PROPN
ejpam-6682	415	12	zhang	zhang	PROPN
ejpam-6682	415	13	,	,	PUNCT
ejpam-6682	415	14	jianting	jiante	VERB
ejpam-6682	415	15	zhu	zhu	PROPN
ejpam-6682	415	16	,	,	PUNCT
ejpam-6682	415	17	and	and	CCONJ
ejpam-6682	415	18	wen	wen	PROPN
ejpam-6682	415	19	chen	chen	PROPN
ejpam-6682	415	20	.	.	PUNCT
ejpam-6682	416	1	a	a	DET
ejpam-6682	416	2	fractal	fractal	ADJ
ejpam-6682	416	3	richards	richard	NOUN
ejpam-6682	416	4	’	'	PUNCT
ejpam-6682	416	5	equation	equation	NOUN
ejpam-6682	416	6	to	to	PART
ejpam-6682	416	7	capture	capture	VERB
ejpam-6682	416	8	the	the	DET
ejpam-6682	416	9	non	non	ADJ
ejpam-6682	416	10	-	-	ADJ
ejpam-6682	416	11	boltzmann	boltzmann	ADJ
ejpam-6682	416	12	scaling	scaling	NOUN
ejpam-6682	416	13	of	of	ADP
ejpam-6682	416	14	water	water	NOUN
ejpam-6682	416	15	transport	transport	NOUN
ejpam-6682	416	16	in	in	ADP
ejpam-6682	416	17	unsaturated	unsaturated	ADJ
ejpam-6682	416	18	media	medium	NOUN
ejpam-6682	416	19	.	.	PUNCT
ejpam-6682	417	1	advances	advance	NOUN
ejpam-6682	417	2	in	in	ADP
ejpam-6682	417	3	water	water	NOUN
ejpam-6682	417	4	resources	resource	NOUN
ejpam-6682	417	5	,	,	PUNCT
ejpam-6682	417	6	52:292–295	52:292–295	PROPN
ejpam-6682	417	7	,	,	PUNCT
ejpam-6682	417	8	2013	2013	NUM
ejpam-6682	417	9	.	.	PUNCT
ejpam-6682	418	1	[	[	X
ejpam-6682	418	2	33	33	NUM
ejpam-6682	418	3	]	]	X
ejpam-6682	418	4	yuli	yuli	PROPN
ejpam-6682	418	5	chen	chen	PROPN
ejpam-6682	418	6	,	,	PUNCT
ejpam-6682	418	7	fawang	fawang	PROPN
ejpam-6682	418	8	liu	liu	PROPN
ejpam-6682	418	9	,	,	PUNCT
ejpam-6682	418	10	qiang	qiang	PROPN
ejpam-6682	418	11	yu	yu	PROPN
ejpam-6682	418	12	,	,	PUNCT
ejpam-6682	418	13	and	and	CCONJ
ejpam-6682	418	14	tianzeng	tianzeng	PROPN
ejpam-6682	418	15	li	li	PROPN
ejpam-6682	418	16	.	.	PROPN
ejpam-6682	418	17	review	review	PROPN
ejpam-6682	418	18	of	of	ADP
ejpam-6682	418	19	fractional	fractional	ADJ
ejpam-6682	418	20	epidemic	epidemic	NOUN
ejpam-6682	418	21	models	model	NOUN
ejpam-6682	418	22	.	.	PUNCT
ejpam-6682	419	1	applied	apply	VERB
ejpam-6682	419	2	mathematical	mathematical	ADJ
ejpam-6682	419	3	modelling	modelling	NOUN
ejpam-6682	419	4	,	,	PUNCT
ejpam-6682	419	5	97:281–307	97:281–307	NUM
ejpam-6682	419	6	,	,	PUNCT
ejpam-6682	419	7	2021	2021	NUM
ejpam-6682	419	8	.	.	PUNCT
ejpam-6682	420	1	[	[	X
ejpam-6682	420	2	34	34	NUM
ejpam-6682	420	3	]	]	X
ejpam-6682	420	4	vladimir	vladimir	PROPN
ejpam-6682	420	5	v.	v.	ADP
ejpam-6682	420	6	kulish	kulish	PROPN
ejpam-6682	420	7	and	and	CCONJ
ejpam-6682	420	8	josé	josé	ADJ
ejpam-6682	420	9	l.	l.	PROPN
ejpam-6682	420	10	lage	lage	PROPN
ejpam-6682	420	11	.	.	PUNCT
ejpam-6682	421	1	application	application	NOUN
ejpam-6682	421	2	of	of	ADP
ejpam-6682	421	3	fractional	fractional	ADJ
ejpam-6682	421	4	calculus	calculus	NOUN
ejpam-6682	421	5	to	to	ADP
ejpam-6682	421	6	fluid	fluid	ADJ
ejpam-6682	421	7	mechanics	mechanic	NOUN
ejpam-6682	421	8	.	.	PUNCT
ejpam-6682	422	1	journal	journal	PROPN
ejpam-6682	422	2	of	of	ADP
ejpam-6682	422	3	fluids	fluid	NOUN
ejpam-6682	422	4	engineering	engineering	NOUN
ejpam-6682	422	5	,	,	PUNCT
ejpam-6682	422	6	124(3):803–806	124(3):803–806	NUM
ejpam-6682	422	7	,	,	PUNCT
ejpam-6682	422	8	2002	2002	NUM
ejpam-6682	422	9	.	.	PUNCT
ejpam-6682	423	1	[	[	X
ejpam-6682	423	2	35	35	NUM
ejpam-6682	423	3	]	]	PUNCT
ejpam-6682	423	4	abdon	abdon	PROPN
ejpam-6682	423	5	atangana	atangana	PROPN
ejpam-6682	423	6	.	.	PUNCT
ejpam-6682	424	1	fractal	fractal	ADJ
ejpam-6682	424	2	-	-	PUNCT
ejpam-6682	424	3	fractional	fractional	ADJ
ejpam-6682	424	4	differentiation	differentiation	NOUN
ejpam-6682	424	5	and	and	CCONJ
ejpam-6682	424	6	integration	integration	NOUN
ejpam-6682	424	7	:	:	PUNCT
ejpam-6682	424	8	connecting	connect	VERB
ejpam-6682	424	9	fractal	fractal	ADJ
ejpam-6682	424	10	calculus	calculus	NOUN
ejpam-6682	424	11	and	and	CCONJ
ejpam-6682	424	12	fractional	fractional	ADJ
ejpam-6682	424	13	calculus	calculus	NOUN
ejpam-6682	424	14	to	to	PART
ejpam-6682	424	15	predict	predict	VERB
ejpam-6682	424	16	complex	complex	ADJ
ejpam-6682	424	17	system	system	NOUN
ejpam-6682	424	18	.	.	PUNCT
ejpam-6682	425	1	chaos	chaos	NOUN
ejpam-6682	425	2	,	,	PUNCT
ejpam-6682	425	3	solitons	soliton	NOUN
ejpam-6682	425	4	&	&	CCONJ
ejpam-6682	425	5	fractals	fractal	NOUN
ejpam-6682	425	6	,	,	PUNCT
ejpam-6682	425	7	102:396–406	102:396–406	NUM
ejpam-6682	425	8	,	,	PUNCT
ejpam-6682	425	9	2017	2017	NUM
ejpam-6682	425	10	.	.	PUNCT
ejpam-6682	426	1	r.	r.	PROPN
ejpam-6682	426	2	saadeh	saadeh	PROPN
ejpam-6682	426	3	et	et	PROPN
ejpam-6682	426	4	al	al	PROPN
ejpam-6682	426	5	.	.	PUNCT
ejpam-6682	426	6	/	/	SYM
ejpam-6682	426	7	eur	eur	PROPN
ejpam-6682	426	8	.	.	PUNCT
ejpam-6682	427	1	j.	j.	PROPN
ejpam-6682	427	2	pure	pure	PROPN
ejpam-6682	427	3	appl	appl	PROPN
ejpam-6682	427	4	.	.	PROPN
ejpam-6682	427	5	math	math	PROPN
ejpam-6682	427	6	,	,	PUNCT
ejpam-6682	427	7	18	18	NUM
ejpam-6682	427	8	(	(	PUNCT
ejpam-6682	427	9	4	4	NUM
ejpam-6682	427	10	)	)	PUNCT
ejpam-6682	427	11	(	(	PUNCT
ejpam-6682	427	12	2025	2025	NUM
ejpam-6682	427	13	)	)	PUNCT
ejpam-6682	427	14	,	,	PUNCT
ejpam-6682	427	15	6682	6682	NUM
ejpam-6682	427	16	20	20	NUM
ejpam-6682	427	17	of	of	ADP
ejpam-6682	427	18	21	21	NUM
ejpam-6682	427	19	[	[	SYM
ejpam-6682	427	20	36	36	NUM
ejpam-6682	427	21	]	]	X
ejpam-6682	427	22	zeeshan	zeeshan	PROPN
ejpam-6682	427	23	ali	ali	PROPN
ejpam-6682	427	24	,	,	PUNCT
ejpam-6682	427	25	faranak	faranak	PROPN
ejpam-6682	427	26	rabiei	rabiei	PROPN
ejpam-6682	427	27	,	,	PUNCT
ejpam-6682	427	28	kamal	kamal	PROPN
ejpam-6682	427	29	shah	shah	NOUN
ejpam-6682	427	30	,	,	PUNCT
ejpam-6682	427	31	and	and	CCONJ
ejpam-6682	427	32	touraj	touraj	ADJ
ejpam-6682	427	33	khodadadi	khodadadi	PROPN
ejpam-6682	427	34	.	.	PUNCT
ejpam-6682	428	1	modeling	modeling	NOUN
ejpam-6682	428	2	and	and	CCONJ
ejpam-6682	428	3	analysis	analysis	NOUN
ejpam-6682	428	4	of	of	ADP
ejpam-6682	428	5	novel	novel	NOUN
ejpam-6682	428	6	covid-19	covid-19	PROPN
ejpam-6682	428	7	under	under	ADP
ejpam-6682	428	8	fractal	fractal	ADJ
ejpam-6682	428	9	-	-	PUNCT
ejpam-6682	428	10	fractional	fractional	ADJ
ejpam-6682	428	11	derivative	derivative	NOUN
ejpam-6682	428	12	with	with	ADP
ejpam-6682	428	13	case	case	NOUN
ejpam-6682	428	14	study	study	NOUN
ejpam-6682	428	15	of	of	ADP
ejpam-6682	428	16	malaysia	malaysia	PROPN
ejpam-6682	428	17	.	.	PUNCT
ejpam-6682	429	1	fractals	fractal	NOUN
ejpam-6682	429	2	,	,	PUNCT
ejpam-6682	429	3	29(01):2150020	29(01):2150020	NUM
ejpam-6682	429	4	,	,	PUNCT
ejpam-6682	429	5	2021	2021	NUM
ejpam-6682	429	6	.	.	PUNCT
ejpam-6682	430	1	[	[	X
ejpam-6682	430	2	37	37	NUM
ejpam-6682	430	3	]	]	X
ejpam-6682	430	4	ji	ji	PROPN
ejpam-6682	430	5	-	-	PROPN
ejpam-6682	430	6	huan	huan	PROPN
ejpam-6682	430	7	he	he	PROPN
ejpam-6682	430	8	.	.	PUNCT
ejpam-6682	431	1	a	a	DET
ejpam-6682	431	2	tutorial	tutorial	ADJ
ejpam-6682	431	3	review	review	NOUN
ejpam-6682	431	4	on	on	ADP
ejpam-6682	431	5	fractal	fractal	ADJ
ejpam-6682	431	6	spacetime	spacetime	NOUN
ejpam-6682	431	7	and	and	CCONJ
ejpam-6682	431	8	fractional	fractional	ADJ
ejpam-6682	431	9	calculus	calculus	NOUN
ejpam-6682	431	10	.	.	PUNCT
ejpam-6682	432	1	international	international	ADJ
ejpam-6682	432	2	journal	journal	PROPN
ejpam-6682	432	3	of	of	ADP
ejpam-6682	432	4	theoretical	theoretical	ADJ
ejpam-6682	432	5	physics	physics	NOUN
ejpam-6682	432	6	,	,	PUNCT
ejpam-6682	432	7	53:3698–3718	53:3698–3718	NUM
ejpam-6682	432	8	,	,	PUNCT
ejpam-6682	432	9	2014	2014	NUM
ejpam-6682	432	10	.	.	PUNCT
ejpam-6682	433	1	[	[	X
ejpam-6682	433	2	38	38	NUM
ejpam-6682	433	3	]	]	X
ejpam-6682	433	4	jatin	jatin	PROPN
ejpam-6682	433	5	bansal	bansal	PROPN
ejpam-6682	433	6	,	,	PUNCT
ejpam-6682	433	7	amit	amit	PROPN
ejpam-6682	433	8	kumar	kumar	PROPN
ejpam-6682	433	9	,	,	PUNCT
ejpam-6682	433	10	anoop	anoop	PROPN
ejpam-6682	433	11	kumar	kumar	PROPN
ejpam-6682	433	12	,	,	PUNCT
ejpam-6682	433	13	aziz	aziz	PROPN
ejpam-6682	433	14	khan	khan	PROPN
ejpam-6682	433	15	,	,	PUNCT
ejpam-6682	433	16	and	and	CCONJ
ejpam-6682	433	17	thabet	thabet	ADJ
ejpam-6682	433	18	abdeljawad	abdeljawad	NOUN
ejpam-6682	433	19	.	.	PUNCT
ejpam-6682	434	1	investigation	investigation	NOUN
ejpam-6682	434	2	of	of	ADP
ejpam-6682	434	3	monkeypox	monkeypox	NOUN
ejpam-6682	434	4	disease	disease	NOUN
ejpam-6682	434	5	transmission	transmission	NOUN
ejpam-6682	434	6	with	with	ADP
ejpam-6682	434	7	vaccination	vaccination	NOUN
ejpam-6682	434	8	effects	effect	NOUN
ejpam-6682	434	9	using	use	VERB
ejpam-6682	434	10	fractional	fractional	ADJ
ejpam-6682	434	11	order	order	NOUN
ejpam-6682	434	12	mathematical	mathematical	ADJ
ejpam-6682	434	13	model	model	NOUN
ejpam-6682	434	14	under	under	ADP
ejpam-6682	434	15	atangana	atangana	PROPN
ejpam-6682	434	16	-	-	PUNCT
ejpam-6682	434	17	baleanu	baleanu	PROPN
ejpam-6682	434	18	caputo	caputo	PROPN
ejpam-6682	434	19	derivative	derivative	PROPN
ejpam-6682	434	20	.	.	PUNCT
ejpam-6682	435	1	modeling	model	VERB
ejpam-6682	435	2	earth	earth	NOUN
ejpam-6682	435	3	systems	system	NOUN
ejpam-6682	435	4	and	and	CCONJ
ejpam-6682	435	5	environment	environment	NOUN
ejpam-6682	435	6	,	,	PUNCT
ejpam-6682	435	7	11(1):40	11(1):40	NUM
ejpam-6682	435	8	,	,	PUNCT
ejpam-6682	435	9	2025	2025	NUM
ejpam-6682	435	10	.	.	PUNCT
ejpam-6682	436	1	[	[	X
ejpam-6682	436	2	39	39	NUM
ejpam-6682	436	3	]	]	X
ejpam-6682	436	4	kang	kang	PROPN
ejpam-6682	436	5	-	-	PUNCT
ejpam-6682	436	6	jia	jia	PROPN
ejpam-6682	436	7	wang	wang	PROPN
ejpam-6682	436	8	.	.	PUNCT
ejpam-6682	437	1	an	an	DET
ejpam-6682	437	2	effective	effective	ADJ
ejpam-6682	437	3	computational	computational	ADJ
ejpam-6682	437	4	approach	approach	NOUN
ejpam-6682	437	5	to	to	ADP
ejpam-6682	437	6	the	the	DET
ejpam-6682	437	7	local	local	ADJ
ejpam-6682	437	8	fractional	fractional	ADJ
ejpam-6682	437	9	low	low	ADJ
ejpam-6682	437	10	-	-	PUNCT
ejpam-6682	437	11	pass	pass	NOUN
ejpam-6682	437	12	electrical	electrical	ADJ
ejpam-6682	437	13	transmission	transmission	NOUN
ejpam-6682	437	14	lines	line	NOUN
ejpam-6682	437	15	model	model	NOUN
ejpam-6682	437	16	.	.	PUNCT
ejpam-6682	438	1	alexandria	alexandria	PROPN
ejpam-6682	438	2	engineering	engineering	PROPN
ejpam-6682	438	3	journal	journal	PROPN
ejpam-6682	438	4	,	,	PUNCT
ejpam-6682	438	5	110:629–635	110:629–635	NUM
ejpam-6682	438	6	,	,	PUNCT
ejpam-6682	438	7	2025	2025	NUM
ejpam-6682	438	8	.	.	PUNCT
ejpam-6682	439	1	[	[	X
ejpam-6682	439	2	40	40	NUM
ejpam-6682	439	3	]	]	PUNCT
ejpam-6682	439	4	hasib	hasib	PROPN
ejpam-6682	439	5	khan	khan	PROPN
ejpam-6682	439	6	,	,	PUNCT
ejpam-6682	439	7	jehad	jehad	PROPN
ejpam-6682	439	8	alzabut	alzabut	PROPN
ejpam-6682	439	9	,	,	PUNCT
ejpam-6682	439	10	and	and	CCONJ
ejpam-6682	439	11	dk	dk	PROPN
ejpam-6682	439	12	almutairi	almutairi	NOUN
ejpam-6682	439	13	.	.	PUNCT
ejpam-6682	440	1	applications	application	NOUN
ejpam-6682	440	2	of	of	ADP
ejpam-6682	440	3	artificial	artificial	ADJ
ejpam-6682	440	4	intelligence	intelligence	NOUN
ejpam-6682	440	5	for	for	ADP
ejpam-6682	440	6	clusters	cluster	NOUN
ejpam-6682	440	7	analysis	analysis	NOUN
ejpam-6682	440	8	of	of	ADP
ejpam-6682	440	9	uranium	uranium	NOUN
ejpam-6682	440	10	decay	decay	NOUN
ejpam-6682	440	11	via	via	ADP
ejpam-6682	440	12	a	a	DET
ejpam-6682	440	13	fractional	fractional	ADJ
ejpam-6682	440	14	order	order	NOUN
ejpam-6682	440	15	discrete	discrete	ADJ
ejpam-6682	440	16	model	model	NOUN
ejpam-6682	440	17	.	.	PUNCT
ejpam-6682	441	1	partial	partial	ADJ
ejpam-6682	441	2	differential	differential	ADJ
ejpam-6682	441	3	equations	equation	NOUN
ejpam-6682	441	4	in	in	ADP
ejpam-6682	441	5	applied	applied	ADJ
ejpam-6682	441	6	mathematics	mathematic	NOUN
ejpam-6682	441	7	,	,	PUNCT
ejpam-6682	441	8	13:101056	13:101056	NUM
ejpam-6682	441	9	,	,	PUNCT
ejpam-6682	441	10	2025	2025	NUM
ejpam-6682	441	11	.	.	PUNCT
ejpam-6682	442	1	[	[	X
ejpam-6682	442	2	41	41	NUM
ejpam-6682	442	3	]	]	PUNCT
ejpam-6682	442	4	mohamed	mohamed	PROPN
ejpam-6682	442	5	a.	a.	PROPN
ejpam-6682	442	6	abdoon	abdoon	PROPN
ejpam-6682	442	7	and	and	CCONJ
ejpam-6682	442	8	abdulrahman	abdulrahman	PROPN
ejpam-6682	442	9	bm	bm	PROPN
ejpam-6682	442	10	alzahrani	alzahrani	PROPN
ejpam-6682	442	11	.	.	PUNCT
ejpam-6682	443	1	comparative	comparative	ADJ
ejpam-6682	443	2	analysis	analysis	NOUN
ejpam-6682	443	3	of	of	ADP
ejpam-6682	443	4	influenza	influenza	NOUN
ejpam-6682	443	5	modeling	modeling	NOUN
ejpam-6682	443	6	using	use	VERB
ejpam-6682	443	7	novel	novel	ADJ
ejpam-6682	443	8	fractional	fractional	ADJ
ejpam-6682	443	9	operators	operator	NOUN
ejpam-6682	443	10	with	with	ADP
ejpam-6682	443	11	real	real	ADJ
ejpam-6682	443	12	data	datum	NOUN
ejpam-6682	443	13	.	.	PUNCT
ejpam-6682	444	1	symmetry	symmetry	NOUN
ejpam-6682	444	2	,	,	PUNCT
ejpam-6682	444	3	16(9):1126	16(9):1126	NUM
ejpam-6682	444	4	,	,	PUNCT
ejpam-6682	444	5	2024	2024	NUM
ejpam-6682	444	6	.	.	PUNCT
ejpam-6682	445	1	[	[	X
ejpam-6682	445	2	42	42	NUM
ejpam-6682	445	3	]	]	X
ejpam-6682	445	4	hongguang	hongguang	PROPN
ejpam-6682	445	5	sun	sun	PROPN
ejpam-6682	445	6	,	,	PUNCT
ejpam-6682	445	7	mark	mark	PROPN
ejpam-6682	445	8	m.	m.	PROPN
ejpam-6682	445	9	meerschaert	meerschaert	PROPN
ejpam-6682	445	10	,	,	PUNCT
ejpam-6682	445	11	yong	yong	PROPN
ejpam-6682	445	12	zhang	zhang	PROPN
ejpam-6682	445	13	,	,	PUNCT
ejpam-6682	445	14	jianting	jiante	VERB
ejpam-6682	445	15	zhu	zhu	PROPN
ejpam-6682	445	16	,	,	PUNCT
ejpam-6682	445	17	and	and	CCONJ
ejpam-6682	445	18	wen	wen	PROPN
ejpam-6682	445	19	chen	chen	PROPN
ejpam-6682	445	20	.	.	PUNCT
ejpam-6682	446	1	a	a	DET
ejpam-6682	446	2	fractal	fractal	ADJ
ejpam-6682	446	3	richards	richard	NOUN
ejpam-6682	446	4	’	'	PUNCT
ejpam-6682	446	5	equation	equation	NOUN
ejpam-6682	446	6	to	to	PART
ejpam-6682	446	7	capture	capture	VERB
ejpam-6682	446	8	the	the	DET
ejpam-6682	446	9	non	non	ADJ
ejpam-6682	446	10	-	-	ADJ
ejpam-6682	446	11	boltzmann	boltzmann	ADJ
ejpam-6682	446	12	scaling	scaling	NOUN
ejpam-6682	446	13	of	of	ADP
ejpam-6682	446	14	water	water	NOUN
ejpam-6682	446	15	transport	transport	NOUN
ejpam-6682	446	16	in	in	ADP
ejpam-6682	446	17	unsaturated	unsaturated	ADJ
ejpam-6682	446	18	media	medium	NOUN
ejpam-6682	446	19	.	.	PUNCT
ejpam-6682	447	1	advances	advance	NOUN
ejpam-6682	447	2	in	in	ADP
ejpam-6682	447	3	water	water	NOUN
ejpam-6682	447	4	resources	resource	NOUN
ejpam-6682	447	5	,	,	PUNCT
ejpam-6682	447	6	52:292–295	52:292–295	PROPN
ejpam-6682	447	7	,	,	PUNCT
ejpam-6682	447	8	2013	2013	NUM
ejpam-6682	447	9	.	.	PUNCT
ejpam-6682	448	1	[	[	X
ejpam-6682	448	2	43	43	NUM
ejpam-6682	448	3	]	]	X
ejpam-6682	448	4	yong	yong	PROPN
ejpam-6682	448	5	zhang	zhang	PROPN
ejpam-6682	448	6	and	and	CCONJ
ejpam-6682	448	7	charalambos	charalambo	NOUN
ejpam-6682	448	8	papelis	papeli	NOUN
ejpam-6682	448	9	.	.	PUNCT
ejpam-6682	449	1	particle	particle	NOUN
ejpam-6682	449	2	-	-	PUNCT
ejpam-6682	449	3	tracking	track	VERB
ejpam-6682	449	4	simulation	simulation	NOUN
ejpam-6682	449	5	of	of	ADP
ejpam-6682	449	6	fractional	fractional	ADJ
ejpam-6682	449	7	diffusion	diffusion	NOUN
ejpam-6682	449	8	-	-	PUNCT
ejpam-6682	449	9	reaction	reaction	NOUN
ejpam-6682	449	10	processes	process	NOUN
ejpam-6682	449	11	.	.	PUNCT
ejpam-6682	450	1	physical	physical	ADJ
ejpam-6682	450	2	review	review	NOUN
ejpam-6682	450	3	e	e	NOUN
ejpam-6682	450	4	—	—	PUNCT
ejpam-6682	450	5	statistical	statistical	ADJ
ejpam-6682	450	6	,	,	PUNCT
ejpam-6682	450	7	nonlinear	nonlinear	ADJ
ejpam-6682	450	8	,	,	PUNCT
ejpam-6682	450	9	and	and	CCONJ
ejpam-6682	450	10	soft	soft	ADJ
ejpam-6682	450	11	matter	matter	NOUN
ejpam-6682	450	12	physics	physics	NOUN
ejpam-6682	450	13	,	,	PUNCT
ejpam-6682	450	14	84(6):066704	84(6):066704	NUM
ejpam-6682	450	15	,	,	PUNCT
ejpam-6682	450	16	2011	2011	NUM
ejpam-6682	450	17	.	.	PUNCT
ejpam-6682	451	1	[	[	X
ejpam-6682	451	2	44	44	NUM
ejpam-6682	451	3	]	]	SYM
ejpam-6682	451	4	yingjie	yingjie	PROPN
ejpam-6682	451	5	liang	liang	PROPN
ejpam-6682	451	6	,	,	PUNCT
ejpam-6682	451	7	wen	wen	PROPN
ejpam-6682	451	8	chen	chen	PROPN
ejpam-6682	451	9	,	,	PUNCT
ejpam-6682	451	10	wei	wei	PROPN
ejpam-6682	451	11	xu	xu	PROPN
ejpam-6682	451	12	,	,	PUNCT
ejpam-6682	451	13	and	and	CCONJ
ejpam-6682	451	14	hongguang	hongguang	PROPN
ejpam-6682	451	15	sun	sun	PROPN
ejpam-6682	451	16	.	.	PUNCT
ejpam-6682	452	1	distributed	distribute	VERB
ejpam-6682	452	2	order	order	NOUN
ejpam-6682	452	3	hausdorff	hausdorff	VERB
ejpam-6682	452	4	derivative	derivative	ADJ
ejpam-6682	452	5	diffusion	diffusion	NOUN
ejpam-6682	452	6	model	model	NOUN
ejpam-6682	452	7	to	to	PART
ejpam-6682	452	8	characterize	characterize	VERB
ejpam-6682	452	9	non	non	ADJ
ejpam-6682	452	10	-	-	ADJ
ejpam-6682	452	11	fickian	fickian	ADJ
ejpam-6682	452	12	diffusion	diffusion	NOUN
ejpam-6682	452	13	in	in	ADP
ejpam-6682	452	14	porous	porous	ADJ
ejpam-6682	452	15	media	medium	NOUN
ejpam-6682	452	16	.	.	PUNCT
ejpam-6682	453	1	communications	communication	NOUN
ejpam-6682	453	2	in	in	ADP
ejpam-6682	453	3	nonlinear	nonlinear	ADJ
ejpam-6682	453	4	science	science	NOUN
ejpam-6682	453	5	and	and	CCONJ
ejpam-6682	453	6	numerical	numerical	PROPN
ejpam-6682	453	7	simulation	simulation	PROPN
ejpam-6682	453	8	,	,	PUNCT
ejpam-6682	453	9	70:384–393	70:384–393	PROPN
ejpam-6682	453	10	,	,	PUNCT
ejpam-6682	453	11	2019	2019	NUM
ejpam-6682	453	12	.	.	PUNCT
ejpam-6682	454	1	[	[	X
ejpam-6682	454	2	45	45	NUM
ejpam-6682	454	3	]	]	X
ejpam-6682	454	4	wen	wen	PROPN
ejpam-6682	454	5	chen	chen	PROPN
ejpam-6682	454	6	.	.	PUNCT
ejpam-6682	455	1	time	time	NOUN
ejpam-6682	455	2	–	–	PUNCT
ejpam-6682	455	3	space	space	NOUN
ejpam-6682	455	4	fabric	fabric	NOUN
ejpam-6682	455	5	underlying	underlie	VERB
ejpam-6682	455	6	anomalous	anomalous	ADJ
ejpam-6682	455	7	diffusion	diffusion	NOUN
ejpam-6682	455	8	.	.	PUNCT
ejpam-6682	456	1	chaos	chaos	NOUN
ejpam-6682	456	2	,	,	PUNCT
ejpam-6682	456	3	solitons	soliton	NOUN
ejpam-6682	456	4	&	&	CCONJ
ejpam-6682	456	5	fractals	fractal	NOUN
ejpam-6682	456	6	,	,	PUNCT
ejpam-6682	456	7	28(4):923–929	28(4):923–929	NOUN
ejpam-6682	456	8	,	,	PUNCT
ejpam-6682	456	9	2006	2006	NUM
ejpam-6682	456	10	.	.	PUNCT
ejpam-6682	457	1	[	[	X
ejpam-6682	457	2	46	46	NUM
ejpam-6682	457	3	]	]	X
ejpam-6682	457	4	wen	wen	PROPN
ejpam-6682	457	5	chen	chen	PROPN
ejpam-6682	457	6	,	,	PUNCT
ejpam-6682	457	7	fajie	fajie	PROPN
ejpam-6682	457	8	wang	wang	PROPN
ejpam-6682	457	9	,	,	PUNCT
ejpam-6682	457	10	bin	bin	PROPN
ejpam-6682	457	11	zheng	zheng	PROPN
ejpam-6682	457	12	,	,	PUNCT
ejpam-6682	457	13	and	and	CCONJ
ejpam-6682	457	14	wei	wei	PROPN
ejpam-6682	457	15	cai	cai	PROPN
ejpam-6682	457	16	.	.	PUNCT
ejpam-6682	457	17	non	non	ADJ
ejpam-6682	457	18	-	-	ADJ
ejpam-6682	457	19	euclidean	euclidean	ADJ
ejpam-6682	457	20	distance	distance	NOUN
ejpam-6682	457	21	fundamental	fundamental	ADJ
ejpam-6682	457	22	solution	solution	NOUN
ejpam-6682	457	23	of	of	ADP
ejpam-6682	457	24	hausdorff	hausdorff	PROPN
ejpam-6682	457	25	derivative	derivative	ADJ
ejpam-6682	457	26	partial	partial	ADJ
ejpam-6682	457	27	differential	differential	NOUN
ejpam-6682	457	28	equations	equation	NOUN
ejpam-6682	457	29	.	.	PUNCT
ejpam-6682	458	1	engineering	engineer	VERB
ejpam-6682	458	2	analysis	analysis	NOUN
ejpam-6682	458	3	with	with	ADP
ejpam-6682	458	4	boundary	boundary	ADJ
ejpam-6682	458	5	elements	element	NOUN
ejpam-6682	458	6	,	,	PUNCT
ejpam-6682	458	7	84:213–219	84:213–219	NUM
ejpam-6682	458	8	,	,	PUNCT
ejpam-6682	458	9	2017	2017	NUM
ejpam-6682	458	10	.	.	PUNCT
ejpam-6682	459	1	[	[	X
ejpam-6682	459	2	47	47	NUM
ejpam-6682	459	3	]	]	X
ejpam-6682	459	4	f.	f.	PROPN
ejpam-6682	459	5	hasan	hasan	PROPN
ejpam-6682	459	6	,	,	PUNCT
ejpam-6682	459	7	m.	m.	NOUN
ejpam-6682	459	8	a.	a.	PROPN
ejpam-6682	459	9	abdoon	abdoon	PROPN
ejpam-6682	459	10	,	,	PUNCT
ejpam-6682	459	11	r.	r.	PROPN
ejpam-6682	459	12	saadeh	saadeh	PROPN
ejpam-6682	459	13	,	,	PUNCT
ejpam-6682	459	14	m.	m.	NOUN
ejpam-6682	459	15	berir	berir	NOUN
ejpam-6682	459	16	,	,	PUNCT
ejpam-6682	459	17	and	and	CCONJ
ejpam-6682	459	18	a.	a.	NOUN
ejpam-6682	459	19	qazza	qazza	PROPN
ejpam-6682	459	20	.	.	PUNCT
ejpam-6682	460	1	a	a	DET
ejpam-6682	460	2	new	new	ADJ
ejpam-6682	460	3	perspective	perspective	NOUN
ejpam-6682	460	4	on	on	ADP
ejpam-6682	460	5	the	the	DET
ejpam-6682	460	6	stochastic	stochastic	ADJ
ejpam-6682	460	7	fractional	fractional	ADJ
ejpam-6682	460	8	order	order	NOUN
ejpam-6682	460	9	materialized	materialize	VERB
ejpam-6682	460	10	by	by	ADP
ejpam-6682	460	11	the	the	DET
ejpam-6682	460	12	exact	exact	ADJ
ejpam-6682	460	13	solutions	solution	NOUN
ejpam-6682	460	14	of	of	ADP
ejpam-6682	460	15	allen	allen	ADJ
ejpam-6682	460	16	-	-	PUNCT
ejpam-6682	460	17	cahn	cahn	NOUN
ejpam-6682	460	18	equation	equation	NOUN
ejpam-6682	460	19	.	.	PUNCT
ejpam-6682	461	1	international	international	ADJ
ejpam-6682	461	2	journal	journal	PROPN
ejpam-6682	461	3	of	of	ADP
ejpam-6682	461	4	mathematical	mathematical	ADJ
ejpam-6682	461	5	,	,	PUNCT
ejpam-6682	461	6	engineering	engineering	NOUN
ejpam-6682	461	7	and	and	CCONJ
ejpam-6682	461	8	management	management	NOUN
ejpam-6682	461	9	sciences	science	NOUN
ejpam-6682	461	10	,	,	PUNCT
ejpam-6682	461	11	8(5):912	8(5):912	NUM
ejpam-6682	461	12	,	,	PUNCT
ejpam-6682	461	13	2023	2023	NUM
ejpam-6682	461	14	.	.	PUNCT
ejpam-6682	462	1	[	[	X
ejpam-6682	462	2	48	48	NUM
ejpam-6682	462	3	]	]	PUNCT
ejpam-6682	462	4	m.	m.	PROPN
ejpam-6682	462	5	ali	ali	PROPN
ejpam-6682	462	6	,	,	PUNCT
ejpam-6682	462	7	s.	s.	PROPN
ejpam-6682	462	8	m.	m.	PROPN
ejpam-6682	462	9	alzahrani	alzahrani	PROPN
ejpam-6682	462	10	,	,	PUNCT
ejpam-6682	462	11	r.	r.	PROPN
ejpam-6682	462	12	saadeh	saadeh	PROPN
ejpam-6682	462	13	,	,	PUNCT
ejpam-6682	462	14	m.	m.	NOUN
ejpam-6682	462	15	a.	a.	PROPN
ejpam-6682	462	16	abdoon	abdoon	PROPN
ejpam-6682	462	17	,	,	PUNCT
ejpam-6682	462	18	a.	a.	NOUN
ejpam-6682	462	19	qazza	qazza	PROPN
ejpam-6682	462	20	,	,	PUNCT
ejpam-6682	462	21	n.	n.	PROPN
ejpam-6682	462	22	al	al	PROPN
ejpam-6682	462	23	-	-	PUNCT
ejpam-6682	462	24	kuleab	kuleab	PROPN
ejpam-6682	462	25	,	,	PUNCT
ejpam-6682	462	26	and	and	CCONJ
ejpam-6682	462	27	f.	f.	PROPN
ejpam-6682	462	28	e.	e.	PROPN
ejpam-6682	462	29	guma	guma	PROPN
ejpam-6682	462	30	.	.	PUNCT
ejpam-6682	463	1	modeling	model	VERB
ejpam-6682	463	2	covid-19	covid-19	PROPN
ejpam-6682	463	3	spread	spread	VERB
ejpam-6682	463	4	and	and	CCONJ
ejpam-6682	463	5	non	non	ADJ
ejpam-6682	463	6	-	-	ADJ
ejpam-6682	463	7	pharmaceutical	pharmaceutical	ADJ
ejpam-6682	463	8	interventions	intervention	NOUN
ejpam-6682	463	9	in	in	ADP
ejpam-6682	463	10	south	south	PROPN
ejpam-6682	463	11	africa	africa	PROPN
ejpam-6682	463	12	:	:	PUNCT
ejpam-6682	463	13	a	a	DET
ejpam-6682	463	14	stochastic	stochastic	ADJ
ejpam-6682	463	15	approach	approach	NOUN
ejpam-6682	463	16	.	.	PUNCT
ejpam-6682	464	1	scientific	scientific	ADJ
ejpam-6682	464	2	african	african	PROPN
ejpam-6682	464	3	,	,	PUNCT
ejpam-6682	464	4	24	24	NUM
ejpam-6682	464	5	:	:	PUNCT
ejpam-6682	464	6	e02155	e02155	NOUN
ejpam-6682	464	7	,	,	PUNCT
ejpam-6682	464	8	2024	2024	NUM
ejpam-6682	464	9	.	.	PUNCT
ejpam-6682	465	1	[	[	X
ejpam-6682	465	2	49	49	NUM
ejpam-6682	465	3	]	]	PUNCT
ejpam-6682	465	4	r.	r.	PROPN
ejpam-6682	465	5	saadeh	saadeh	PROPN
ejpam-6682	465	6	,	,	PUNCT
ejpam-6682	465	7	m.	m.	NOUN
ejpam-6682	465	8	a.	a.	PROPN
ejpam-6682	465	9	abdoon	abdoon	PROPN
ejpam-6682	465	10	,	,	PUNCT
ejpam-6682	465	11	a.	a.	NOUN
ejpam-6682	465	12	qazza	qazza	PROPN
ejpam-6682	465	13	,	,	PUNCT
ejpam-6682	465	14	m.	m.	NOUN
ejpam-6682	465	15	berir	berir	NOUN
ejpam-6682	465	16	,	,	PUNCT
ejpam-6682	465	17	f.	f.	PROPN
ejpam-6682	465	18	e.	e.	PROPN
ejpam-6682	465	19	guma	guma	PROPN
ejpam-6682	465	20	,	,	PUNCT
ejpam-6682	465	21	n.	n.	PROPN
ejpam-6682	465	22	al	al	PROPN
ejpam-6682	465	23	-	-	PUNCT
ejpam-6682	465	24	kuleab	kuleab	PROPN
ejpam-6682	465	25	,	,	PUNCT
ejpam-6682	465	26	and	and	CCONJ
ejpam-6682	465	27	a.	a.	NOUN
ejpam-6682	465	28	m.	m.	NOUN
ejpam-6682	465	29	degoot	degoot	PROPN
ejpam-6682	465	30	.	.	PUNCT
ejpam-6682	466	1	mathematical	mathematical	ADJ
ejpam-6682	466	2	modeling	modeling	NOUN
ejpam-6682	466	3	and	and	CCONJ
ejpam-6682	466	4	stability	stability	NOUN
ejpam-6682	466	5	analysis	analysis	NOUN
ejpam-6682	466	6	of	of	ADP
ejpam-6682	466	7	the	the	DET
ejpam-6682	466	8	novel	novel	ADJ
ejpam-6682	466	9	fractional	fractional	ADJ
ejpam-6682	466	10	model	model	NOUN
ejpam-6682	466	11	in	in	ADP
ejpam-6682	466	12	the	the	DET
ejpam-6682	466	13	caputo	caputo	PROPN
ejpam-6682	466	14	derivative	derivative	ADJ
ejpam-6682	466	15	operator	operator	NOUN
ejpam-6682	466	16	:	:	PUNCT
ejpam-6682	466	17	a	a	DET
ejpam-6682	466	18	case	case	NOUN
ejpam-6682	466	19	study	study	NOUN
ejpam-6682	466	20	.	.	PUNCT
ejpam-6682	467	1	heliyon	heliyon	NOUN
ejpam-6682	467	2	,	,	PUNCT
ejpam-6682	467	3	10(5	10(5	NUM
ejpam-6682	467	4	)	)	PUNCT
ejpam-6682	467	5	,	,	PUNCT
ejpam-6682	467	6	2024	2024	NUM
ejpam-6682	467	7	.	.	PUNCT
ejpam-6682	468	1	[	[	X
ejpam-6682	468	2	50	50	NUM
ejpam-6682	468	3	]	]	PUNCT
ejpam-6682	468	4	a.	a.	PROPN
ejpam-6682	468	5	b.	b.	PROPN
ejpam-6682	468	6	m.	m.	PROPN
ejpam-6682	468	7	alzahrani	alzahrani	PROPN
ejpam-6682	468	8	,	,	PUNCT
ejpam-6682	468	9	r.	r.	PROPN
ejpam-6682	468	10	saadeh	saadeh	PROPN
ejpam-6682	468	11	,	,	PUNCT
ejpam-6682	468	12	m.	m.	NOUN
ejpam-6682	468	13	a.	a.	PROPN
ejpam-6682	468	14	abdoon	abdoon	PROPN
ejpam-6682	468	15	,	,	PUNCT
ejpam-6682	468	16	m.	m.	NOUN
ejpam-6682	468	17	elbadri	elbadri	PROPN
ejpam-6682	468	18	,	,	PUNCT
ejpam-6682	468	19	m.	m.	NOUN
ejpam-6682	468	20	berir	berir	NOUN
ejpam-6682	468	21	,	,	PUNCT
ejpam-6682	468	22	and	and	CCONJ
ejpam-6682	468	23	a.	a.	NOUN
ejpam-6682	468	24	qazza	qazza	PROPN
ejpam-6682	468	25	.	.	PUNCT
ejpam-6682	469	1	r.	r.	PROPN
ejpam-6682	469	2	saadeh	saadeh	PROPN
ejpam-6682	469	3	et	et	PROPN
ejpam-6682	469	4	al	al	PROPN
ejpam-6682	469	5	.	.	PUNCT
ejpam-6682	469	6	/	/	SYM
ejpam-6682	469	7	eur	eur	PROPN
ejpam-6682	469	8	.	.	PUNCT
ejpam-6682	470	1	j.	j.	PROPN
ejpam-6682	470	2	pure	pure	PROPN
ejpam-6682	470	3	appl	appl	PROPN
ejpam-6682	470	4	.	.	PROPN
ejpam-6682	470	5	math	math	PROPN
ejpam-6682	470	6	,	,	PUNCT
ejpam-6682	470	7	18	18	NUM
ejpam-6682	470	8	(	(	PUNCT
ejpam-6682	470	9	4	4	NUM
ejpam-6682	470	10	)	)	PUNCT
ejpam-6682	470	11	(	(	PUNCT
ejpam-6682	470	12	2025	2025	NUM
ejpam-6682	470	13	)	)	PUNCT
ejpam-6682	470	14	,	,	PUNCT
ejpam-6682	470	15	6682	6682	NUM
ejpam-6682	470	16	21	21	NUM
ejpam-6682	470	17	of	of	ADP
ejpam-6682	470	18	21	21	NUM
ejpam-6682	470	19	effective	effective	ADJ
ejpam-6682	470	20	methods	method	NOUN
ejpam-6682	470	21	for	for	ADP
ejpam-6682	470	22	numerical	numerical	ADJ
ejpam-6682	470	23	analysis	analysis	NOUN
ejpam-6682	470	24	of	of	ADP
ejpam-6682	470	25	the	the	DET
ejpam-6682	470	26	simplest	simple	ADJ
ejpam-6682	470	27	chaotic	chaotic	ADJ
ejpam-6682	470	28	circuit	circuit	NOUN
ejpam-6682	470	29	model	model	NOUN
ejpam-6682	470	30	with	with	ADP
ejpam-6682	470	31	atangana	atangana	PROPN
ejpam-6682	470	32	–	–	PUNCT
ejpam-6682	470	33	baleanu	baleanu	PROPN
ejpam-6682	470	34	caputo	caputo	PROPN
ejpam-6682	470	35	fractional	fractional	PROPN
ejpam-6682	470	36	derivative	derivative	PROPN
ejpam-6682	470	37	.	.	PUNCT
ejpam-6682	471	1	journal	journal	PROPN
ejpam-6682	471	2	of	of	ADP
ejpam-6682	471	3	engineering	engineering	NOUN
ejpam-6682	471	4	mathematics	mathematic	NOUN
ejpam-6682	471	5	,	,	PUNCT
ejpam-6682	471	6	144(1):9	144(1):9	NUM
ejpam-6682	471	7	,	,	PUNCT
ejpam-6682	471	8	2024	2024	NUM
ejpam-6682	471	9	.	.	PUNCT
ejpam-6682	472	1	[	[	X
ejpam-6682	472	2	51	51	NUM
ejpam-6682	472	3	]	]	X
ejpam-6682	472	4	e.	e.	PROPN
ejpam-6682	472	5	salah	salah	PROPN
ejpam-6682	472	6	,	,	PUNCT
ejpam-6682	472	7	a.	a.	NOUN
ejpam-6682	472	8	qazza	qazza	PROPN
ejpam-6682	472	9	,	,	PUNCT
ejpam-6682	472	10	r.	r.	PROPN
ejpam-6682	472	11	saadeh	saadeh	PROPN
ejpam-6682	472	12	,	,	PUNCT
ejpam-6682	472	13	and	and	CCONJ
ejpam-6682	472	14	a.	a.	PROPN
ejpam-6682	472	15	el	el	PROPN
ejpam-6682	472	16	-	-	PUNCT
ejpam-6682	472	17	ajou	ajou	ADJ
ejpam-6682	472	18	.	.	PUNCT
ejpam-6682	473	1	a	a	DET
ejpam-6682	473	2	hybrid	hybrid	ADJ
ejpam-6682	473	3	analytical	analytical	ADJ
ejpam-6682	473	4	technique	technique	NOUN
ejpam-6682	473	5	for	for	ADP
ejpam-6682	473	6	solving	solve	VERB
ejpam-6682	473	7	multi	multi	ADJ
ejpam-6682	473	8	-	-	ADJ
ejpam-6682	473	9	dimensional	dimensional	ADJ
ejpam-6682	473	10	time	time	NOUN
ejpam-6682	473	11	-	-	PUNCT
ejpam-6682	473	12	fractional	fractional	ADJ
ejpam-6682	473	13	navier	navier	NOUN
ejpam-6682	473	14	-	-	PUNCT
ejpam-6682	473	15	stokes	stoke	NOUN
ejpam-6682	473	16	system	system	NOUN
ejpam-6682	473	17	.	.	PUNCT
ejpam-6682	474	1	aims	aim	VERB
ejpam-6682	474	2	mathematics	mathematic	NOUN
ejpam-6682	474	3	,	,	PUNCT
ejpam-6682	474	4	8(1):1713–1736	8(1):1713–1736	PROPN
ejpam-6682	474	5	,	,	PUNCT
ejpam-6682	474	6	2023	2023	NUM
ejpam-6682	474	7	.	.	PUNCT
ejpam-6682	475	1	[	[	X
ejpam-6682	475	2	52	52	NUM
ejpam-6682	475	3	]	]	PUNCT
ejpam-6682	475	4	m.	m.	NOUN
ejpam-6682	475	5	abu	abu	PROPN
ejpam-6682	475	6	-	-	PUNCT
ejpam-6682	475	7	ghuwaleh	ghuwaleh	PROPN
ejpam-6682	475	8	,	,	PUNCT
ejpam-6682	475	9	r.	r.	PROPN
ejpam-6682	475	10	saadeh	saadeh	PROPN
ejpam-6682	475	11	,	,	PUNCT
ejpam-6682	475	12	and	and	CCONJ
ejpam-6682	475	13	a.	a.	NOUN
ejpam-6682	475	14	qazza	qazza	PROPN
ejpam-6682	475	15	.	.	PUNCT
ejpam-6682	476	1	general	general	ADJ
ejpam-6682	476	2	master	master	NOUN
ejpam-6682	476	3	theorems	theorem	NOUN
ejpam-6682	476	4	of	of	ADP
ejpam-6682	476	5	integrals	integral	NOUN
ejpam-6682	476	6	with	with	ADP
ejpam-6682	476	7	applications	application	NOUN
ejpam-6682	476	8	.	.	PUNCT
ejpam-6682	477	1	mathematics	mathematic	NOUN
ejpam-6682	477	2	,	,	PUNCT
ejpam-6682	477	3	10(19):3547	10(19):3547	NUM
ejpam-6682	477	4	,	,	PUNCT
ejpam-6682	477	5	2022	2022	NUM
ejpam-6682	477	6	.	.	PUNCT
ejpam-6682	478	1	[	[	X
ejpam-6682	478	2	53	53	NUM
ejpam-6682	478	3	]	]	X
ejpam-6682	478	4	r.	r.	PROPN
ejpam-6682	478	5	allogmany	allogmany	PROPN
ejpam-6682	478	6	,	,	PUNCT
ejpam-6682	478	7	a.	a.	PROPN
ejpam-6682	478	8	sarrah	sarrah	PROPN
ejpam-6682	478	9	,	,	PUNCT
ejpam-6682	478	10	m.	m.	NOUN
ejpam-6682	478	11	a.	a.	PROPN
ejpam-6682	478	12	abdoon	abdoon	PROPN
ejpam-6682	478	13	,	,	PUNCT
ejpam-6682	478	14	f.	f.	PROPN
ejpam-6682	478	15	j.	j.	PROPN
ejpam-6682	478	16	alanazi	alanazi	PROPN
ejpam-6682	478	17	,	,	PUNCT
ejpam-6682	478	18	m.	m.	NOUN
ejpam-6682	478	19	berir	berir	NOUN
ejpam-6682	478	20	,	,	PUNCT
ejpam-6682	478	21	and	and	CCONJ
ejpam-6682	478	22	s.	s.	PROPN
ejpam-6682	478	23	a.	a.	PROPN
ejpam-6682	478	24	alharbi	alharbi	PROPN
ejpam-6682	478	25	.	.	PUNCT
ejpam-6682	479	1	a	a	DET
ejpam-6682	479	2	comprehensive	comprehensive	ADJ
ejpam-6682	479	3	analysis	analysis	NOUN
ejpam-6682	479	4	of	of	ADP
ejpam-6682	479	5	complex	complex	ADJ
ejpam-6682	479	6	dynamics	dynamic	NOUN
ejpam-6682	479	7	in	in	ADP
ejpam-6682	479	8	the	the	DET
ejpam-6682	479	9	fractional	fractional	ADJ
ejpam-6682	479	10	-	-	PUNCT
ejpam-6682	479	11	order	order	NOUN
ejpam-6682	479	12	rössler	rössler	NOUN
ejpam-6682	479	13	system	system	NOUN
ejpam-6682	479	14	.	.	PUNCT
ejpam-6682	480	1	mathematics	mathematic	NOUN
ejpam-6682	480	2	,	,	PUNCT
ejpam-6682	480	3	13(19):3089	13(19):3089	NUM
ejpam-6682	480	4	,	,	PUNCT
ejpam-6682	480	5	2025	2025	NUM
ejpam-6682	480	6	.	.	PUNCT
ejpam-6682	481	1	[	[	X
ejpam-6682	481	2	54	54	NUM
ejpam-6682	481	3	]	]	PUNCT
ejpam-6682	481	4	i.	i.	PROPN
ejpam-6682	481	5	kadri	kadri	PROPN
ejpam-6682	481	6	,	,	PUNCT
ejpam-6682	481	7	r.	r.	PROPN
ejpam-6682	481	8	saadeh	saadeh	PROPN
ejpam-6682	481	9	,	,	PUNCT
ejpam-6682	481	10	d.	d.	PROPN
ejpam-6682	481	11	m.	m.	PROPN
ejpam-6682	481	12	almutairi	almutairi	PROPN
ejpam-6682	481	13	,	,	PUNCT
ejpam-6682	481	14	m.	m.	PROPN
ejpam-6682	481	15	e.	e.	PROPN
ejpam-6682	481	16	dafaalla	dafaalla	PROPN
ejpam-6682	481	17	,	,	PUNCT
ejpam-6682	481	18	m.	m.	NOUN
ejpam-6682	481	19	berir	berir	NOUN
ejpam-6682	481	20	,	,	PUNCT
ejpam-6682	481	21	and	and	CCONJ
ejpam-6682	481	22	m.	m.	PROPN
ejpam-6682	481	23	a.	a.	PROPN
ejpam-6682	481	24	abdoon	abdoon	PROPN
ejpam-6682	481	25	.	.	PUNCT
ejpam-6682	482	1	analytical	analytical	ADJ
ejpam-6682	482	2	and	and	CCONJ
ejpam-6682	482	3	numerical	numerical	ADJ
ejpam-6682	482	4	investigation	investigation	NOUN
ejpam-6682	482	5	of	of	ADP
ejpam-6682	482	6	a	a	DET
ejpam-6682	482	7	fractional	fractional	ADJ
ejpam-6682	482	8	order	order	NOUN
ejpam-6682	482	9	4d	4d	NUM
ejpam-6682	482	10	chaotic	chaotic	ADJ
ejpam-6682	482	11	system	system	NOUN
ejpam-6682	482	12	via	via	ADP
ejpam-6682	482	13	caputo	caputo	PROPN
ejpam-6682	482	14	fractional	fractional	PROPN
ejpam-6682	482	15	derivative	derivative	PROPN
ejpam-6682	482	16	.	.	PUNCT
ejpam-6682	483	1	european	european	PROPN
ejpam-6682	483	2	journal	journal	PROPN
ejpam-6682	483	3	of	of	ADP
ejpam-6682	483	4	pure	pure	ADJ
ejpam-6682	483	5	and	and	CCONJ
ejpam-6682	483	6	applied	applied	ADJ
ejpam-6682	483	7	mathematics	mathematic	NOUN
ejpam-6682	483	8	,	,	PUNCT
ejpam-6682	483	9	18(3):6381–6381	18(3):6381–6381	NUM
ejpam-6682	483	10	,	,	PUNCT
ejpam-6682	483	11	2025	2025	NUM
ejpam-6682	483	12	.	.	PUNCT
ejpam-6682	484	1	[	[	X
ejpam-6682	484	2	55	55	NUM
ejpam-6682	484	3	]	]	PUNCT
ejpam-6682	484	4	m.	m.	NOUN
ejpam-6682	484	5	berir	berir	NOUN
ejpam-6682	484	6	.	.	PUNCT
ejpam-6682	485	1	the	the	DET
ejpam-6682	485	2	impact	impact	NOUN
ejpam-6682	485	3	of	of	ADP
ejpam-6682	485	4	white	white	ADJ
ejpam-6682	485	5	noise	noise	NOUN
ejpam-6682	485	6	on	on	ADP
ejpam-6682	485	7	chaotic	chaotic	ADJ
ejpam-6682	485	8	behavior	behavior	NOUN
ejpam-6682	485	9	in	in	ADP
ejpam-6682	485	10	a	a	DET
ejpam-6682	485	11	financial	financial	ADJ
ejpam-6682	485	12	fractional	fractional	ADJ
ejpam-6682	485	13	system	system	NOUN
ejpam-6682	485	14	with	with	ADP
ejpam-6682	485	15	constant	constant	ADJ
ejpam-6682	485	16	and	and	CCONJ
ejpam-6682	485	17	variable	variable	ADJ
ejpam-6682	485	18	order	order	NOUN
ejpam-6682	485	19	:	:	PUNCT
ejpam-6682	485	20	a	a	DET
ejpam-6682	485	21	comparative	comparative	ADJ
ejpam-6682	485	22	study	study	NOUN
ejpam-6682	485	23	.	.	PUNCT
ejpam-6682	486	1	european	european	PROPN
ejpam-6682	486	2	journal	journal	PROPN
ejpam-6682	486	3	of	of	ADP
ejpam-6682	486	4	pure	pure	ADJ
ejpam-6682	486	5	and	and	CCONJ
ejpam-6682	486	6	applied	applied	ADJ
ejpam-6682	486	7	mathematics	mathematic	NOUN
ejpam-6682	486	8	,	,	PUNCT
ejpam-6682	486	9	17(4):3915–3931	17(4):3915–3931	NUM
ejpam-6682	486	10	,	,	PUNCT
ejpam-6682	486	11	2024	2024	NUM
ejpam-6682	486	12	.	.	PUNCT
ejpam-6682	487	1	[	[	X
ejpam-6682	487	2	56	56	NUM
ejpam-6682	487	3	]	]	PUNCT
ejpam-6682	487	4	m.	m.	NOUN
ejpam-6682	487	5	berir	berir	NOUN
ejpam-6682	487	6	.	.	PUNCT
ejpam-6682	488	1	a	a	DET
ejpam-6682	488	2	fractional	fractional	ADJ
ejpam-6682	488	3	study	study	NOUN
ejpam-6682	488	4	for	for	ADP
ejpam-6682	488	5	solving	solve	VERB
ejpam-6682	488	6	the	the	DET
ejpam-6682	488	7	smoking	smoking	NOUN
ejpam-6682	488	8	model	model	NOUN
ejpam-6682	488	9	and	and	CCONJ
ejpam-6682	488	10	the	the	DET
ejpam-6682	488	11	chaotic	chaotic	ADJ
ejpam-6682	488	12	engineering	engineering	NOUN
ejpam-6682	488	13	model	model	NOUN
ejpam-6682	488	14	.	.	PUNCT
ejpam-6682	489	1	in	in	ADP
ejpam-6682	489	2	proceedings	proceeding	NOUN
ejpam-6682	489	3	of	of	ADP
ejpam-6682	489	4	the	the	DET
ejpam-6682	489	5	2023	2023	NUM
ejpam-6682	489	6	2nd	2nd	ADJ
ejpam-6682	489	7	international	international	ADJ
ejpam-6682	489	8	engineering	engineering	NOUN
ejpam-6682	489	9	conference	conference	NOUN
ejpam-6682	489	10	on	on	ADP
ejpam-6682	489	11	electrical	electrical	ADJ
ejpam-6682	489	12	,	,	PUNCT
ejpam-6682	489	13	energy	energy	NOUN
ejpam-6682	489	14	,	,	PUNCT
ejpam-6682	489	15	and	and	CCONJ
ejpam-6682	489	16	artificial	artificial	ADJ
ejpam-6682	489	17	intelligence	intelligence	NOUN
ejpam-6682	489	18	(	(	PUNCT
ejpam-6682	489	19	eiceeai	eiceeai	PROPN
ejpam-6682	489	20	)	)	PUNCT
ejpam-6682	489	21	,	,	PUNCT
ejpam-6682	489	22	pages	page	NOUN
ejpam-6682	489	23	1–6	1–6	NUM
ejpam-6682	489	24	.	.	PUNCT
ejpam-6682	489	25	ieee	ieee	NOUN
ejpam-6682	489	26	,	,	PUNCT
ejpam-6682	489	27	2023	2023	NUM
ejpam-6682	489	28	.	.	PUNCT