id	sid	tid	token	lemma	pos
ejpam-6176	1	1	european	european	PROPN
ejpam-6176	1	2	journal	journal	PROPN
ejpam-6176	1	3	of	of	ADP
ejpam-6176	1	4	pure	pure	ADJ
ejpam-6176	1	5	and	and	CCONJ
ejpam-6176	1	6	applied	applied	ADJ
ejpam-6176	1	7	mathematics	mathematic	NOUN
ejpam-6176	1	8	2025	2025	NUM
ejpam-6176	1	9	,	,	PUNCT
ejpam-6176	1	10	vol	vol	NOUN
ejpam-6176	1	11	.	.	PROPN
ejpam-6176	1	12	18	18	NUM
ejpam-6176	1	13	,	,	PUNCT
ejpam-6176	1	14	issue	issue	NOUN
ejpam-6176	1	15	3	3	NUM
ejpam-6176	1	16	,	,	PUNCT
ejpam-6176	1	17	article	article	NOUN
ejpam-6176	1	18	number	number	NOUN
ejpam-6176	1	19	6176	6176	NUM
ejpam-6176	1	20	issn	issn	PROPN
ejpam-6176	1	21	1307	1307	NUM
ejpam-6176	1	22	-	-	SYM
ejpam-6176	1	23	5543	5543	NUM
ejpam-6176	1	24	–	–	PUNCT
ejpam-6176	1	25	ejpam.com	ejpam.com	X
ejpam-6176	1	26	published	publish	VERB
ejpam-6176	1	27	by	by	ADP
ejpam-6176	1	28	new	new	PROPN
ejpam-6176	1	29	york	york	PROPN
ejpam-6176	1	30	business	business	PROPN
ejpam-6176	1	31	global	global	PROPN
ejpam-6176	1	32	a	a	DET
ejpam-6176	1	33	hybrid	hybrid	ADJ
ejpam-6176	1	34	exponential	exponential	ADJ
ejpam-6176	1	35	runge	runge	NOUN
ejpam-6176	1	36	-	-	PUNCT
ejpam-6176	1	37	kutta	kutta	NOUN
ejpam-6176	1	38	scheme	scheme	NOUN
ejpam-6176	1	39	for	for	ADP
ejpam-6176	1	40	stochastic	stochastic	ADJ
ejpam-6176	1	41	siqr	siqr	ADJ
ejpam-6176	1	42	disease	disease	NOUN
ejpam-6176	1	43	modeling	model	VERB
ejpam-6176	1	44	muhammad	muhammad	PROPN
ejpam-6176	1	45	shoaib	shoaib	PROPN
ejpam-6176	1	46	arif1,∗	arif1,∗	PROPN
ejpam-6176	1	47	,	,	PUNCT
ejpam-6176	1	48	kamaleldin	kamaleldin	NOUN
ejpam-6176	1	49	abodayeh1	abodayeh1	PROPN
ejpam-6176	1	50	,	,	PUNCT
ejpam-6176	1	51	yasir	yasir	PROPN
ejpam-6176	1	52	nawaz2	nawaz2	PROPN
ejpam-6176	1	53	1	1	NUM
ejpam-6176	1	54	department	department	NOUN
ejpam-6176	1	55	of	of	ADP
ejpam-6176	1	56	mathematics	mathematic	NOUN
ejpam-6176	1	57	and	and	CCONJ
ejpam-6176	1	58	sciences	science	NOUN
ejpam-6176	1	59	,	,	PUNCT
ejpam-6176	1	60	college	college	NOUN
ejpam-6176	1	61	of	of	ADP
ejpam-6176	1	62	humanities	humanity	NOUN
ejpam-6176	1	63	and	and	CCONJ
ejpam-6176	1	64	sciences	science	NOUN
ejpam-6176	1	65	,	,	PUNCT
ejpam-6176	1	66	prince	prince	PROPN
ejpam-6176	1	67	sultan	sultan	PROPN
ejpam-6176	1	68	university	university	PROPN
ejpam-6176	1	69	,	,	PUNCT
ejpam-6176	1	70	riyadh	riyadh	NOUN
ejpam-6176	1	71	,	,	PUNCT
ejpam-6176	1	72	11586	11586	NUM
ejpam-6176	1	73	,	,	PUNCT
ejpam-6176	1	74	saudi	saudi	PROPN
ejpam-6176	1	75	arabia	arabia	PROPN
ejpam-6176	1	76	2	2	NUM
ejpam-6176	1	77	department	department	NOUN
ejpam-6176	1	78	of	of	ADP
ejpam-6176	1	79	mathematics	mathematics	PROPN
ejpam-6176	1	80	,	,	PUNCT
ejpam-6176	1	81	air	air	PROPN
ejpam-6176	1	82	university	university	PROPN
ejpam-6176	1	83	,	,	PUNCT
ejpam-6176	1	84	paf	paf	PROPN
ejpam-6176	1	85	complex	complex	PROPN
ejpam-6176	1	86	e-9	e-9	PROPN
ejpam-6176	1	87	,	,	PUNCT
ejpam-6176	1	88	islamabad	islamabad	PROPN
ejpam-6176	1	89	,	,	PUNCT
ejpam-6176	1	90	44000	44000	NUM
ejpam-6176	1	91	,	,	PUNCT
ejpam-6176	1	92	pakistan	pakistan	PROPN
ejpam-6176	1	93	abstract	abstract	NOUN
ejpam-6176	1	94	.	.	PUNCT
ejpam-6176	2	1	understanding	understanding	NOUN
ejpam-6176	2	2	and	and	CCONJ
ejpam-6176	2	3	reducing	reduce	VERB
ejpam-6176	2	4	the	the	DET
ejpam-6176	2	5	spread	spread	NOUN
ejpam-6176	2	6	of	of	ADP
ejpam-6176	2	7	epidemics	epidemic	NOUN
ejpam-6176	2	8	depends	depend	VERB
ejpam-6176	2	9	much	much	ADV
ejpam-6176	2	10	on	on	ADP
ejpam-6176	2	11	the	the	DET
ejpam-6176	2	12	modelling	modelling	NOUN
ejpam-6176	2	13	and	and	CCONJ
ejpam-6176	2	14	study	study	NOUN
ejpam-6176	2	15	of	of	ADP
ejpam-6176	2	16	infectious	infectious	ADJ
ejpam-6176	2	17	disease	disease	NOUN
ejpam-6176	2	18	dynamics	dynamic	NOUN
ejpam-6176	2	19	.	.	PUNCT
ejpam-6176	3	1	among	among	ADP
ejpam-6176	3	2	several	several	ADJ
ejpam-6176	3	3	compartmental	compartmental	ADJ
ejpam-6176	3	4	models	model	NOUN
ejpam-6176	3	5	,	,	PUNCT
ejpam-6176	3	6	the	the	DET
ejpam-6176	3	7	susceptibleinfected	susceptibleinfecte	VERB
ejpam-6176	3	8	-	-	PUNCT
ejpam-6176	3	9	quarantined	quarantine	VERB
ejpam-6176	3	10	-	-	PUNCT
ejpam-6176	3	11	recovered	recover	VERB
ejpam-6176	3	12	siqr	siqr	ADJ
ejpam-6176	3	13	framework	framework	NOUN
ejpam-6176	3	14	has	have	AUX
ejpam-6176	3	15	become	become	VERB
ejpam-6176	3	16	more	more	ADV
ejpam-6176	3	17	popular	popular	ADJ
ejpam-6176	3	18	as	as	SCONJ
ejpam-6176	3	19	it	it	PRON
ejpam-6176	3	20	can	can	AUX
ejpam-6176	3	21	include	include	VERB
ejpam-6176	3	22	the	the	DET
ejpam-6176	3	23	influence	influence	NOUN
ejpam-6176	3	24	of	of	ADP
ejpam-6176	3	25	quarantine	quarantine	NOUN
ejpam-6176	3	26	,	,	PUNCT
ejpam-6176	3	27	a	a	DET
ejpam-6176	3	28	significant	significant	ADJ
ejpam-6176	3	29	intervention	intervention	NOUN
ejpam-6176	3	30	in	in	ADP
ejpam-6176	3	31	many	many	ADJ
ejpam-6176	3	32	actual	actual	ADJ
ejpam-6176	3	33	epidemics	epidemic	NOUN
ejpam-6176	3	34	.	.	PUNCT
ejpam-6176	4	1	fundamental	fundamental	ADJ
ejpam-6176	4	2	epidemic	epidemic	NOUN
ejpam-6176	4	3	processes	process	NOUN
ejpam-6176	4	4	are	be	AUX
ejpam-6176	4	5	naturally	naturally	ADV
ejpam-6176	4	6	vulnerable	vulnerable	ADJ
ejpam-6176	4	7	to	to	ADP
ejpam-6176	4	8	random	random	ADJ
ejpam-6176	4	9	variations	variation	NOUN
ejpam-6176	4	10	brought	bring	VERB
ejpam-6176	4	11	on	on	ADP
ejpam-6176	4	12	by	by	ADP
ejpam-6176	4	13	environmental	environmental	ADJ
ejpam-6176	4	14	variability	variability	NOUN
ejpam-6176	4	15	,	,	PUNCT
ejpam-6176	4	16	population	population	NOUN
ejpam-6176	4	17	stochasticity	stochasticity	NOUN
ejpam-6176	4	18	,	,	PUNCT
ejpam-6176	4	19	and	and	CCONJ
ejpam-6176	4	20	other	other	ADJ
ejpam-6176	4	21	unknown	unknown	ADJ
ejpam-6176	4	22	elements	element	NOUN
ejpam-6176	4	23	.	.	PUNCT
ejpam-6176	5	1	hence	hence	ADV
ejpam-6176	5	2	,	,	PUNCT
ejpam-6176	5	3	including	include	VERB
ejpam-6176	5	4	stochastic	stochastic	ADJ
ejpam-6176	5	5	influences	influence	NOUN
ejpam-6176	5	6	in	in	ADP
ejpam-6176	5	7	such	such	ADJ
ejpam-6176	5	8	models	model	NOUN
ejpam-6176	5	9	is	be	AUX
ejpam-6176	5	10	crucial	crucial	ADJ
ejpam-6176	5	11	.	.	PUNCT
ejpam-6176	6	1	furthermore	furthermore	ADV
ejpam-6176	6	2	,	,	PUNCT
ejpam-6176	6	3	spatial	spatial	ADJ
ejpam-6176	6	4	dispersion	dispersion	NOUN
ejpam-6176	6	5	and	and	CCONJ
ejpam-6176	6	6	diffusion	diffusion	NOUN
ejpam-6176	6	7	effects	effect	NOUN
ejpam-6176	6	8	are	be	AUX
ejpam-6176	6	9	essential	essential	ADJ
ejpam-6176	6	10	,	,	PUNCT
ejpam-6176	6	11	particularly	particularly	ADV
ejpam-6176	6	12	in	in	ADP
ejpam-6176	6	13	significant	significant	ADJ
ejpam-6176	6	14	populations	population	NOUN
ejpam-6176	6	15	and	and	CCONJ
ejpam-6176	6	16	varied	varied	ADJ
ejpam-6176	6	17	settings	setting	NOUN
ejpam-6176	6	18	,	,	PUNCT
ejpam-6176	6	19	which	which	PRON
ejpam-6176	6	20	call	call	VERB
ejpam-6176	6	21	for	for	ADP
ejpam-6176	6	22	stochastic	stochastic	ADJ
ejpam-6176	6	23	partial	partial	ADJ
ejpam-6176	6	24	differential	differential	NOUN
ejpam-6176	6	25	equations	equation	NOUN
ejpam-6176	6	26	(	(	PUNCT
ejpam-6176	6	27	spdes	spdes	PROPN
ejpam-6176	6	28	)	)	PUNCT
ejpam-6176	6	29	.	.	PUNCT
ejpam-6176	7	1	a	a	DET
ejpam-6176	7	2	two	two	NUM
ejpam-6176	7	3	-	-	PUNCT
ejpam-6176	7	4	stage	stage	NOUN
ejpam-6176	7	5	mixture	mixture	NOUN
ejpam-6176	7	6	of	of	ADP
ejpam-6176	7	7	exponential	exponential	ADJ
ejpam-6176	7	8	integrator	integrator	NOUN
ejpam-6176	7	9	and	and	CCONJ
ejpam-6176	7	10	runge	runge	NOUN
ejpam-6176	7	11	-	-	PUNCT
ejpam-6176	7	12	kutta	kutta	NOUN
ejpam-6176	7	13	scheme	scheme	NOUN
ejpam-6176	7	14	is	be	AUX
ejpam-6176	7	15	proposed	propose	VERB
ejpam-6176	7	16	for	for	ADP
ejpam-6176	7	17	solving	solve	VERB
ejpam-6176	7	18	stochastic	stochastic	ADJ
ejpam-6176	7	19	epidemic	epidemic	NOUN
ejpam-6176	7	20	disease	disease	NOUN
ejpam-6176	7	21	models	model	NOUN
ejpam-6176	7	22	.	.	PUNCT
ejpam-6176	8	1	the	the	DET
ejpam-6176	8	2	scheme	scheme	NOUN
ejpam-6176	8	3	is	be	AUX
ejpam-6176	8	4	more	more	ADV
ejpam-6176	8	5	accurate	accurate	ADJ
ejpam-6176	8	6	than	than	ADP
ejpam-6176	8	7	the	the	DET
ejpam-6176	8	8	existing	exist	VERB
ejpam-6176	8	9	euler	euler	NOUN
ejpam-6176	8	10	maruyama	maruyama	NOUN
ejpam-6176	8	11	method	method	NOUN
ejpam-6176	8	12	.	.	PUNCT
ejpam-6176	9	1	the	the	DET
ejpam-6176	9	2	stability	stability	NOUN
ejpam-6176	9	3	and	and	CCONJ
ejpam-6176	9	4	consistency	consistency	NOUN
ejpam-6176	9	5	of	of	ADP
ejpam-6176	9	6	the	the	DET
ejpam-6176	9	7	scheme	scheme	NOUN
ejpam-6176	9	8	in	in	ADP
ejpam-6176	9	9	the	the	DET
ejpam-6176	9	10	mean	mean	ADJ
ejpam-6176	9	11	square	square	ADJ
ejpam-6176	9	12	sense	sense	NOUN
ejpam-6176	9	13	are	be	AUX
ejpam-6176	9	14	provided	provide	VERB
ejpam-6176	9	15	.	.	PUNCT
ejpam-6176	10	1	the	the	DET
ejpam-6176	10	2	scheme	scheme	NOUN
ejpam-6176	10	3	only	only	ADV
ejpam-6176	10	4	discretizes	discretize	VERB
ejpam-6176	10	5	time	time	NOUN
ejpam-6176	10	6	-	-	PUNCT
ejpam-6176	10	7	dependent	dependent	ADJ
ejpam-6176	10	8	terms	term	NOUN
ejpam-6176	10	9	in	in	ADP
ejpam-6176	10	10	given	give	VERB
ejpam-6176	10	11	stochastic	stochastic	ADJ
ejpam-6176	10	12	partial	partial	ADJ
ejpam-6176	10	13	differential	differential	NOUN
ejpam-6176	10	14	equations	equation	NOUN
ejpam-6176	10	15	.	.	PUNCT
ejpam-6176	11	1	moreover	moreover	ADV
ejpam-6176	11	2	,	,	PUNCT
ejpam-6176	11	3	a	a	DET
ejpam-6176	11	4	stochastic	stochastic	ADJ
ejpam-6176	11	5	siqr	siqr	ADJ
ejpam-6176	11	6	diffusive	diffusive	ADJ
ejpam-6176	11	7	model	model	NOUN
ejpam-6176	11	8	is	be	AUX
ejpam-6176	11	9	presented	present	VERB
ejpam-6176	11	10	with	with	ADP
ejpam-6176	11	11	the	the	DET
ejpam-6176	11	12	effect	effect	NOUN
ejpam-6176	11	13	of	of	ADP
ejpam-6176	11	14	incidence	incidence	NOUN
ejpam-6176	11	15	rate	rate	NOUN
ejpam-6176	11	16	.	.	PUNCT
ejpam-6176	12	1	the	the	DET
ejpam-6176	12	2	deterministic	deterministic	ADJ
ejpam-6176	12	3	and	and	CCONJ
ejpam-6176	12	4	stochastic	stochastic	ADJ
ejpam-6176	12	5	models	model	NOUN
ejpam-6176	12	6	are	be	AUX
ejpam-6176	12	7	solved	solve	VERB
ejpam-6176	12	8	using	use	VERB
ejpam-6176	12	9	the	the	DET
ejpam-6176	12	10	euler	euler	NOUN
ejpam-6176	12	11	-	-	PUNCT
ejpam-6176	12	12	maruyama	maruyama	NOUN
ejpam-6176	12	13	method	method	NOUN
ejpam-6176	12	14	,	,	PUNCT
ejpam-6176	12	15	the	the	DET
ejpam-6176	12	16	proposed	propose	VERB
ejpam-6176	12	17	scheme	scheme	NOUN
ejpam-6176	12	18	,	,	PUNCT
ejpam-6176	12	19	and	and	CCONJ
ejpam-6176	12	20	the	the	DET
ejpam-6176	12	21	nonstandard	nonstandard	ADJ
ejpam-6176	12	22	finite	finite	ADJ
ejpam-6176	12	23	difference	difference	NOUN
ejpam-6176	12	24	method	method	NOUN
ejpam-6176	12	25	.	.	PUNCT
ejpam-6176	13	1	the	the	DET
ejpam-6176	13	2	comparison	comparison	NOUN
ejpam-6176	13	3	shows	show	VERB
ejpam-6176	13	4	that	that	SCONJ
ejpam-6176	13	5	the	the	DET
ejpam-6176	13	6	proposed	propose	VERB
ejpam-6176	13	7	scheme	scheme	NOUN
ejpam-6176	13	8	provides	provide	VERB
ejpam-6176	13	9	less	less	ADJ
ejpam-6176	13	10	error	error	NOUN
ejpam-6176	13	11	than	than	ADP
ejpam-6176	13	12	the	the	DET
ejpam-6176	13	13	existing	exist	VERB
ejpam-6176	13	14	nonstandard	nonstandard	ADJ
ejpam-6176	13	15	finite	finite	ADJ
ejpam-6176	13	16	difference	difference	NOUN
ejpam-6176	13	17	method	method	NOUN
ejpam-6176	13	18	.	.	PUNCT
ejpam-6176	14	1	the	the	DET
ejpam-6176	14	2	results	result	NOUN
ejpam-6176	14	3	indicate	indicate	VERB
ejpam-6176	14	4	that	that	SCONJ
ejpam-6176	14	5	the	the	DET
ejpam-6176	14	6	proposed	propose	VERB
ejpam-6176	14	7	scheme	scheme	NOUN
ejpam-6176	14	8	attains	attain	NOUN
ejpam-6176	14	9	superior	superior	ADJ
ejpam-6176	14	10	accuracy	accuracy	NOUN
ejpam-6176	14	11	and	and	CCONJ
ejpam-6176	14	12	diminished	diminish	VERB
ejpam-6176	14	13	errors	error	NOUN
ejpam-6176	14	14	relative	relative	ADJ
ejpam-6176	14	15	to	to	ADP
ejpam-6176	14	16	current	current	ADJ
ejpam-6176	14	17	methods	method	NOUN
ejpam-6176	14	18	.	.	PUNCT
ejpam-6176	15	1	this	this	PRON
ejpam-6176	15	2	underscores	underscore	VERB
ejpam-6176	15	3	its	its	PRON
ejpam-6176	15	4	capability	capability	NOUN
ejpam-6176	15	5	as	as	ADP
ejpam-6176	15	6	an	an	DET
ejpam-6176	15	7	effective	effective	ADJ
ejpam-6176	15	8	instrument	instrument	NOUN
ejpam-6176	15	9	for	for	ADP
ejpam-6176	15	10	simulating	simulate	VERB
ejpam-6176	15	11	complex	complex	ADJ
ejpam-6176	15	12	stochastic	stochastic	ADJ
ejpam-6176	15	13	epidemic	epidemic	NOUN
ejpam-6176	15	14	models	model	NOUN
ejpam-6176	15	15	incorporating	incorporate	VERB
ejpam-6176	15	16	spatial	spatial	ADJ
ejpam-6176	15	17	effects	effect	NOUN
ejpam-6176	15	18	and	and	CCONJ
ejpam-6176	15	19	non	non	ADJ
ejpam-6176	15	20	-	-	ADJ
ejpam-6176	15	21	linear	linear	ADJ
ejpam-6176	15	22	dynamics	dynamic	NOUN
ejpam-6176	15	23	.	.	PUNCT
ejpam-6176	16	1	2020	2020	NUM
ejpam-6176	16	2	mathematics	mathematic	NOUN
ejpam-6176	16	3	subject	subject	NOUN
ejpam-6176	16	4	classifications	classification	NOUN
ejpam-6176	16	5	:	:	PUNCT
ejpam-6176	16	6	65c30	65c30	NUM
ejpam-6176	16	7	,	,	PUNCT
ejpam-6176	16	8	35r60	35r60	NUM
ejpam-6176	16	9	,	,	PUNCT
ejpam-6176	16	10	92d30	92d30	NUM
ejpam-6176	16	11	key	key	ADJ
ejpam-6176	16	12	words	word	NOUN
ejpam-6176	16	13	and	and	CCONJ
ejpam-6176	16	14	phrases	phrase	NOUN
ejpam-6176	16	15	:	:	PUNCT
ejpam-6176	16	16	exponential	exponential	ADJ
ejpam-6176	16	17	integrator	integrator	NOUN
ejpam-6176	16	18	scheme	scheme	NOUN
ejpam-6176	16	19	,	,	PUNCT
ejpam-6176	16	20	runge	runge	NOUN
ejpam-6176	16	21	-	-	PUNCT
ejpam-6176	16	22	kutta	kutta	NOUN
ejpam-6176	16	23	scheme	scheme	NOUN
ejpam-6176	16	24	,	,	PUNCT
ejpam-6176	16	25	stability	stability	NOUN
ejpam-6176	16	26	,	,	PUNCT
ejpam-6176	16	27	mean	mean	ADJ
ejpam-6176	16	28	square	square	ADJ
ejpam-6176	16	29	consistency	consistency	NOUN
ejpam-6176	16	30	,	,	PUNCT
ejpam-6176	16	31	siqr	siqr	PROPN
ejpam-6176	16	32	model	model	NOUN
ejpam-6176	16	33	,	,	PUNCT
ejpam-6176	16	34	computational	computational	ADJ
ejpam-6176	16	35	epidemiology	epidemiology	NOUN
ejpam-6176	16	36	∗corresponding	∗corresponde	VERB
ejpam-6176	16	37	author	author	NOUN
ejpam-6176	16	38	.	.	PUNCT
ejpam-6176	17	1	doi	doi	NOUN
ejpam-6176	17	2	:	:	PUNCT
ejpam-6176	17	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6176	https://doi.org/10.29020/nybg.ejpam.v18i3.6176	PROPN
ejpam-6176	17	4	email	email	NOUN
ejpam-6176	17	5	address	address	NOUN
ejpam-6176	17	6	:	:	PUNCT
ejpam-6176	17	7	marif@psu.edu.sa	marif@psu.edu.sa	NOUN
ejpam-6176	17	8	(	(	PUNCT
ejpam-6176	17	9	m.	m.	PROPN
ejpam-6176	17	10	s.	s.	PROPN
ejpam-6176	17	11	arif	arif	PROPN
ejpam-6176	17	12	)	)	PUNCT
ejpam-6176	17	13	,	,	PUNCT
ejpam-6176	17	14	kamal@psu.edu.sa	kamal@psu.edu.sa	PROPN
ejpam-6176	17	15	(	(	PUNCT
ejpam-6176	17	16	k.	k.	PROPN
ejpam-6176	17	17	abodayeh	abodayeh	PROPN
ejpam-6176	17	18	)	)	PUNCT
ejpam-6176	17	19	,	,	PUNCT
ejpam-6176	17	20	yasir	yasir	PROPN
ejpam-6176	17	21	maths@yahoo.com	maths@yahoo.com	PROPN
ejpam-6176	17	22	(	(	PUNCT
ejpam-6176	17	23	y.	y.	NOUN
ejpam-6176	17	24	nawaz	nawaz	NOUN
ejpam-6176	17	25	)	)	PUNCT
ejpam-6176	17	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6176	17	27	1	1	NUM
ejpam-6176	17	28	copyright	copyright	NOUN
ejpam-6176	17	29	:	:	PUNCT
ejpam-6176	18	1	©	©	PROPN
ejpam-6176	18	2	2025	2025	NUM
ejpam-6176	18	3	the	the	DET
ejpam-6176	18	4	author(s	author(s	NOUN
ejpam-6176	18	5	)	)	PUNCT
ejpam-6176	18	6	.	.	PUNCT
ejpam-6176	19	1	(	(	PUNCT
ejpam-6176	19	2	cc	cc	NOUN
ejpam-6176	19	3	by	by	ADP
ejpam-6176	19	4	-	-	PUNCT
ejpam-6176	19	5	nc	nc	PROPN
ejpam-6176	19	6	4.0	4.0	NUM
ejpam-6176	19	7	)	)	PUNCT
ejpam-6176	19	8	m.	m.	NOUN
ejpam-6176	19	9	s.	s.	PROPN
ejpam-6176	19	10	arif	arif	PROPN
ejpam-6176	19	11	,	,	PUNCT
ejpam-6176	19	12	k.	k.	PROPN
ejpam-6176	19	13	abodayeh	abodayeh	PROPN
ejpam-6176	19	14	,	,	PUNCT
ejpam-6176	19	15	y.	y.	NOUN
ejpam-6176	19	16	nawaz	nawaz	PROPN
ejpam-6176	19	17	/	/	SYM
ejpam-6176	19	18	eur	eur	PROPN
ejpam-6176	19	19	.	.	PUNCT
ejpam-6176	20	1	j.	j.	PROPN
ejpam-6176	20	2	pure	pure	PROPN
ejpam-6176	20	3	appl	appl	PROPN
ejpam-6176	20	4	.	.	PROPN
ejpam-6176	20	5	math	math	PROPN
ejpam-6176	20	6	,	,	PUNCT
ejpam-6176	20	7	18	18	NUM
ejpam-6176	20	8	(	(	PUNCT
ejpam-6176	20	9	3	3	NUM
ejpam-6176	20	10	)	)	PUNCT
ejpam-6176	20	11	(	(	PUNCT
ejpam-6176	20	12	2025	2025	NUM
ejpam-6176	20	13	)	)	PUNCT
ejpam-6176	20	14	,	,	PUNCT
ejpam-6176	20	15	6176	6176	NUM
ejpam-6176	20	16	2	2	NUM
ejpam-6176	20	17	of	of	ADP
ejpam-6176	20	18	21	21	NUM
ejpam-6176	20	19	1	1	NUM
ejpam-6176	20	20	.	.	PUNCT
ejpam-6176	20	21	introduction	introduction	NOUN
ejpam-6176	20	22	in	in	ADP
ejpam-6176	20	23	recent	recent	ADJ
ejpam-6176	20	24	decades	decade	NOUN
ejpam-6176	20	25	,	,	PUNCT
ejpam-6176	20	26	the	the	DET
ejpam-6176	20	27	increasing	increase	VERB
ejpam-6176	20	28	number	number	NOUN
ejpam-6176	20	29	of	of	ADP
ejpam-6176	20	30	infectious	infectious	ADJ
ejpam-6176	20	31	diseases	disease	NOUN
ejpam-6176	20	32	has	have	AUX
ejpam-6176	20	33	created	create	VERB
ejpam-6176	20	34	significant	significant	ADJ
ejpam-6176	20	35	difficulties	difficulty	NOUN
ejpam-6176	20	36	for	for	ADP
ejpam-6176	20	37	public	public	ADJ
ejpam-6176	20	38	health	health	NOUN
ejpam-6176	20	39	systems	system	NOUN
ejpam-6176	20	40	.	.	PUNCT
ejpam-6176	21	1	mathematical	mathematical	ADJ
ejpam-6176	21	2	modelling	modelling	NOUN
ejpam-6176	21	3	has	have	AUX
ejpam-6176	21	4	greatly	greatly	ADV
ejpam-6176	21	5	aided	aid	VERB
ejpam-6176	21	6	in	in	ADP
ejpam-6176	21	7	understanding	understand	VERB
ejpam-6176	21	8	the	the	DET
ejpam-6176	21	9	dynamics	dynamic	NOUN
ejpam-6176	21	10	of	of	ADP
ejpam-6176	21	11	disease	disease	NOUN
ejpam-6176	21	12	transmission	transmission	NOUN
ejpam-6176	21	13	and	and	CCONJ
ejpam-6176	21	14	assessing	assess	VERB
ejpam-6176	21	15	control	control	NOUN
ejpam-6176	21	16	measures	measure	NOUN
ejpam-6176	21	17	.	.	PUNCT
ejpam-6176	22	1	among	among	ADP
ejpam-6176	22	2	many	many	ADJ
ejpam-6176	22	3	compartmental	compartmental	ADJ
ejpam-6176	22	4	models	model	NOUN
ejpam-6176	22	5	,	,	PUNCT
ejpam-6176	22	6	the	the	DET
ejpam-6176	22	7	siqr	siqr	PROPN
ejpam-6176	22	8	(	(	PUNCT
ejpam-6176	22	9	susceptible	susceptible	ADJ
ejpam-6176	22	10	-	-	PUNCT
ejpam-6176	22	11	infected	infect	VERB
ejpam-6176	22	12	-	-	PUNCT
ejpam-6176	22	13	quarantined	quarantine	VERB
ejpam-6176	22	14	-	-	PUNCT
ejpam-6176	22	15	recovered	recover	VERB
ejpam-6176	22	16	)	)	PUNCT
ejpam-6176	22	17	model	model	NOUN
ejpam-6176	22	18	has	have	AUX
ejpam-6176	22	19	attracted	attract	VERB
ejpam-6176	22	20	significant	significant	ADJ
ejpam-6176	22	21	interest	interest	NOUN
ejpam-6176	22	22	because	because	SCONJ
ejpam-6176	22	23	it	it	PRON
ejpam-6176	22	24	can	can	AUX
ejpam-6176	22	25	reflect	reflect	VERB
ejpam-6176	22	26	the	the	DET
ejpam-6176	22	27	consequences	consequence	NOUN
ejpam-6176	22	28	of	of	ADP
ejpam-6176	22	29	recovery	recovery	NOUN
ejpam-6176	22	30	processes	process	NOUN
ejpam-6176	22	31	and	and	CCONJ
ejpam-6176	22	32	quarantine	quarantine	NOUN
ejpam-6176	22	33	actions	action	NOUN
ejpam-6176	22	34	.	.	PUNCT
ejpam-6176	23	1	although	although	SCONJ
ejpam-6176	23	2	insightful	insightful	ADJ
ejpam-6176	23	3	,	,	PUNCT
ejpam-6176	23	4	conventional	conventional	ADJ
ejpam-6176	23	5	deterministic	deterministic	ADJ
ejpam-6176	23	6	models	model	NOUN
ejpam-6176	23	7	can	can	AUX
ejpam-6176	23	8	overlook	overlook	VERB
ejpam-6176	23	9	the	the	DET
ejpam-6176	23	10	natural	natural	ADJ
ejpam-6176	23	11	randomness	randomness	NOUN
ejpam-6176	23	12	in	in	ADP
ejpam-6176	23	13	actual	actual	ADJ
ejpam-6176	23	14	epidemic	epidemic	NOUN
ejpam-6176	23	15	data	datum	NOUN
ejpam-6176	23	16	.	.	PUNCT
ejpam-6176	24	1	this	this	DET
ejpam-6176	24	2	constraint	constraint	NOUN
ejpam-6176	24	3	emphasizes	emphasize	VERB
ejpam-6176	24	4	the	the	DET
ejpam-6176	24	5	need	need	NOUN
ejpam-6176	24	6	for	for	ADP
ejpam-6176	24	7	stochastic	stochastic	ADJ
ejpam-6176	24	8	modelling	modelling	NOUN
ejpam-6176	24	9	,	,	PUNCT
ejpam-6176	24	10	which	which	PRON
ejpam-6176	24	11	considers	consider	VERB
ejpam-6176	24	12	random	random	ADJ
ejpam-6176	24	13	variations	variation	NOUN
ejpam-6176	24	14	in	in	ADP
ejpam-6176	24	15	disease	disease	NOUN
ejpam-6176	24	16	transmission	transmission	NOUN
ejpam-6176	24	17	and	and	CCONJ
ejpam-6176	24	18	other	other	ADJ
ejpam-6176	24	19	epidemiological	epidemiological	ADJ
ejpam-6176	24	20	factors	factor	NOUN
ejpam-6176	24	21	and	and	CCONJ
ejpam-6176	24	22	offers	offer	VERB
ejpam-6176	24	23	a	a	DET
ejpam-6176	24	24	more	more	ADV
ejpam-6176	24	25	realistic	realistic	ADJ
ejpam-6176	24	26	picture	picture	NOUN
ejpam-6176	24	27	of	of	ADP
ejpam-6176	24	28	disease	disease	NOUN
ejpam-6176	24	29	dynamics	dynamic	NOUN
ejpam-6176	24	30	.	.	PUNCT
ejpam-6176	25	1	particularly	particularly	ADV
ejpam-6176	25	2	in	in	ADP
ejpam-6176	25	3	situations	situation	NOUN
ejpam-6176	25	4	with	with	ADP
ejpam-6176	25	5	small	small	ADJ
ejpam-6176	25	6	populations	population	NOUN
ejpam-6176	25	7	or	or	CCONJ
ejpam-6176	25	8	unknown	unknown	ADJ
ejpam-6176	25	9	settings	setting	NOUN
ejpam-6176	25	10	,	,	PUNCT
ejpam-6176	25	11	the	the	DET
ejpam-6176	25	12	standard	standard	ADJ
ejpam-6176	25	13	siqr	siqr	PROPN
ejpam-6176	25	14	model	model	PROPN
ejpam-6176	25	15	’s	’s	PART
ejpam-6176	25	16	incorporation	incorporation	NOUN
ejpam-6176	25	17	of	of	ADP
ejpam-6176	25	18	stochastic	stochastic	ADJ
ejpam-6176	25	19	components	component	NOUN
ejpam-6176	25	20	improves	improve	VERB
ejpam-6176	25	21	the	the	DET
ejpam-6176	25	22	prediction	prediction	NOUN
ejpam-6176	25	23	and	and	CCONJ
ejpam-6176	25	24	analysis	analysis	NOUN
ejpam-6176	25	25	of	of	ADP
ejpam-6176	25	26	epidemic	epidemic	ADJ
ejpam-6176	25	27	trends	trend	NOUN
ejpam-6176	25	28	.	.	PUNCT
ejpam-6176	26	1	furthermore	furthermore	ADV
ejpam-6176	26	2	,	,	PUNCT
ejpam-6176	26	3	the	the	DET
ejpam-6176	26	4	model	model	NOUN
ejpam-6176	26	5	’s	’s	PART
ejpam-6176	26	6	relevance	relevance	NOUN
ejpam-6176	26	7	is	be	AUX
ejpam-6176	26	8	increased	increase	VERB
ejpam-6176	26	9	by	by	ADP
ejpam-6176	26	10	considering	consider	VERB
ejpam-6176	26	11	a	a	DET
ejpam-6176	26	12	generalized	generalized	ADJ
ejpam-6176	26	13	incidence	incidence	NOUN
ejpam-6176	26	14	rate	rate	NOUN
ejpam-6176	26	15	instead	instead	ADV
ejpam-6176	26	16	of	of	ADP
ejpam-6176	26	17	the	the	DET
ejpam-6176	26	18	straightforward	straightforward	ADJ
ejpam-6176	26	19	bilinear	bilinear	NOUN
ejpam-6176	26	20	form	form	NOUN
ejpam-6176	26	21	,	,	PUNCT
ejpam-6176	26	22	capturing	capture	VERB
ejpam-6176	26	23	nonlinear	nonlinear	ADJ
ejpam-6176	26	24	infection	infection	NOUN
ejpam-6176	26	25	patterns	pattern	NOUN
ejpam-6176	26	26	seen	see	VERB
ejpam-6176	26	27	in	in	ADP
ejpam-6176	26	28	real	real	ADJ
ejpam-6176	26	29	epidemics	epidemic	NOUN
ejpam-6176	26	30	.	.	PUNCT
ejpam-6176	27	1	accurately	accurately	ADV
ejpam-6176	27	2	portraying	portray	VERB
ejpam-6176	27	3	situations	situation	NOUN
ejpam-6176	27	4	where	where	SCONJ
ejpam-6176	27	5	new	new	ADJ
ejpam-6176	27	6	infection	infection	NOUN
ejpam-6176	27	7	rates	rate	NOUN
ejpam-6176	27	8	are	be	AUX
ejpam-6176	27	9	affected	affect	VERB
ejpam-6176	27	10	by	by	ADP
ejpam-6176	27	11	variables	variable	NOUN
ejpam-6176	27	12	,	,	PUNCT
ejpam-6176	27	13	including	include	VERB
ejpam-6176	27	14	behavioural	behavioural	ADJ
ejpam-6176	27	15	changes	change	NOUN
ejpam-6176	27	16	,	,	PUNCT
ejpam-6176	27	17	demographic	demographic	ADJ
ejpam-6176	27	18	diversity	diversity	NOUN
ejpam-6176	27	19	,	,	PUNCT
ejpam-6176	27	20	or	or	CCONJ
ejpam-6176	27	21	public	public	ADJ
ejpam-6176	27	22	health	health	NOUN
ejpam-6176	27	23	measures	measure	NOUN
ejpam-6176	27	24	,	,	PUNCT
ejpam-6176	27	25	requires	require	VERB
ejpam-6176	27	26	this	this	DET
ejpam-6176	27	27	shift	shift	NOUN
ejpam-6176	27	28	.	.	PUNCT
ejpam-6176	28	1	the	the	DET
ejpam-6176	28	2	main	main	ADJ
ejpam-6176	28	3	objectives	objective	NOUN
ejpam-6176	28	4	of	of	ADP
ejpam-6176	28	5	this	this	DET
ejpam-6176	28	6	research	research	NOUN
ejpam-6176	28	7	are	be	AUX
ejpam-6176	28	8	as	as	SCONJ
ejpam-6176	28	9	follows	follow	VERB
ejpam-6176	28	10	:	:	PUNCT
ejpam-6176	28	11	•	•	ADP
ejpam-6176	28	12	we	we	PRON
ejpam-6176	28	13	present	present	VERB
ejpam-6176	28	14	a	a	DET
ejpam-6176	28	15	novel	novel	ADJ
ejpam-6176	28	16	two	two	NUM
ejpam-6176	28	17	-	-	PUNCT
ejpam-6176	28	18	stage	stage	NOUN
ejpam-6176	28	19	numerical	numerical	ADJ
ejpam-6176	28	20	approach	approach	NOUN
ejpam-6176	28	21	for	for	ADP
ejpam-6176	28	22	solving	solve	VERB
ejpam-6176	28	23	stochastic	stochastic	ADJ
ejpam-6176	28	24	epidemic	epidemic	NOUN
ejpam-6176	28	25	models	model	NOUN
ejpam-6176	28	26	,	,	PUNCT
ejpam-6176	28	27	especially	especially	ADV
ejpam-6176	28	28	spdes	spde	NOUN
ejpam-6176	28	29	,	,	PUNCT
ejpam-6176	28	30	that	that	PRON
ejpam-6176	28	31	integrates	integrate	VERB
ejpam-6176	28	32	runge	runge	NOUN
ejpam-6176	28	33	-	-	PUNCT
ejpam-6176	28	34	kutta	kutta	NOUN
ejpam-6176	28	35	schemes	scheme	NOUN
ejpam-6176	28	36	with	with	ADP
ejpam-6176	28	37	exponential	exponential	ADJ
ejpam-6176	28	38	integrators	integrator	NOUN
ejpam-6176	28	39	.	.	PUNCT
ejpam-6176	29	1	•	•	NOUN
ejpam-6176	29	2	we	we	PRON
ejpam-6176	29	3	develop	develop	VERB
ejpam-6176	29	4	a	a	DET
ejpam-6176	29	5	diffusive	diffusive	ADJ
ejpam-6176	29	6	siqr	siqr	ADJ
ejpam-6176	29	7	model	model	NOUN
ejpam-6176	29	8	with	with	ADP
ejpam-6176	29	9	a	a	DET
ejpam-6176	29	10	general	general	ADJ
ejpam-6176	29	11	incidence	incidence	NOUN
ejpam-6176	29	12	rate	rate	NOUN
ejpam-6176	29	13	and	and	CCONJ
ejpam-6176	29	14	stochastic	stochastic	ADJ
ejpam-6176	29	15	influences	influence	NOUN
ejpam-6176	29	16	to	to	PART
ejpam-6176	29	17	more	more	ADV
ejpam-6176	29	18	precisely	precisely	ADV
ejpam-6176	29	19	represent	represent	VERB
ejpam-6176	29	20	actual	actual	ADJ
ejpam-6176	29	21	epidemic	epidemic	NOUN
ejpam-6176	29	22	dynamics	dynamic	NOUN
ejpam-6176	29	23	.	.	PUNCT
ejpam-6176	30	1	•	•	INTJ
ejpam-6176	30	2	we	we	PRON
ejpam-6176	30	3	prove	prove	VERB
ejpam-6176	30	4	the	the	DET
ejpam-6176	30	5	mean	mean	ADJ
ejpam-6176	30	6	-	-	PUNCT
ejpam-6176	30	7	square	square	ADJ
ejpam-6176	30	8	stability	stability	NOUN
ejpam-6176	30	9	and	and	CCONJ
ejpam-6176	30	10	consistency	consistency	NOUN
ejpam-6176	30	11	of	of	ADP
ejpam-6176	30	12	the	the	DET
ejpam-6176	30	13	suggested	suggest	VERB
ejpam-6176	30	14	numerical	numerical	ADJ
ejpam-6176	30	15	scheme	scheme	NOUN
ejpam-6176	30	16	to	to	PART
ejpam-6176	30	17	guarantee	guarantee	VERB
ejpam-6176	30	18	its	its	PRON
ejpam-6176	30	19	dependability	dependability	NOUN
ejpam-6176	30	20	in	in	ADP
ejpam-6176	30	21	long	long	ADJ
ejpam-6176	30	22	-	-	PUNCT
ejpam-6176	30	23	term	term	NOUN
ejpam-6176	30	24	simulations	simulation	NOUN
ejpam-6176	30	25	.	.	PUNCT
ejpam-6176	31	1	•	•	INTJ
ejpam-6176	31	2	we	we	PRON
ejpam-6176	31	3	reduce	reduce	VERB
ejpam-6176	31	4	computational	computational	ADJ
ejpam-6176	31	5	complexity	complexity	NOUN
ejpam-6176	31	6	and	and	CCONJ
ejpam-6176	31	7	improve	improve	VERB
ejpam-6176	31	8	efficiency	efficiency	NOUN
ejpam-6176	31	9	by	by	ADP
ejpam-6176	31	10	developing	develop	VERB
ejpam-6176	31	11	a	a	DET
ejpam-6176	31	12	strategy	strategy	NOUN
ejpam-6176	31	13	focusing	focus	VERB
ejpam-6176	31	14	on	on	ADP
ejpam-6176	31	15	time	time	NOUN
ejpam-6176	31	16	-	-	PUNCT
ejpam-6176	31	17	dependent	dependent	ADJ
ejpam-6176	31	18	terms	term	NOUN
ejpam-6176	31	19	and	and	CCONJ
ejpam-6176	31	20	avoiding	avoid	VERB
ejpam-6176	31	21	spatial	spatial	ADJ
ejpam-6176	31	22	discretization	discretization	NOUN
ejpam-6176	31	23	.	.	PUNCT
ejpam-6176	32	1	•	•	INTJ
ejpam-6176	32	2	we	we	PRON
ejpam-6176	32	3	solve	solve	VERB
ejpam-6176	32	4	both	both	CCONJ
ejpam-6176	32	5	deterministic	deterministic	ADJ
ejpam-6176	32	6	and	and	CCONJ
ejpam-6176	32	7	stochastic	stochastic	ADJ
ejpam-6176	32	8	versions	version	NOUN
ejpam-6176	32	9	of	of	ADP
ejpam-6176	32	10	the	the	DET
ejpam-6176	32	11	siqr	siqr	PROPN
ejpam-6176	32	12	model	model	NOUN
ejpam-6176	32	13	by	by	ADP
ejpam-6176	32	14	the	the	DET
ejpam-6176	32	15	eulermaruyama	eulermaruyama	PROPN
ejpam-6176	32	16	method	method	NOUN
ejpam-6176	32	17	,	,	PUNCT
ejpam-6176	32	18	the	the	DET
ejpam-6176	32	19	nonstandard	nonstandard	ADJ
ejpam-6176	32	20	finite	finite	ADJ
ejpam-6176	32	21	difference	difference	NOUN
ejpam-6176	32	22	(	(	PUNCT
ejpam-6176	32	23	nsfd	nsfd	ADJ
ejpam-6176	32	24	)	)	PUNCT
ejpam-6176	32	25	method	method	NOUN
ejpam-6176	32	26	,	,	PUNCT
ejpam-6176	32	27	and	and	CCONJ
ejpam-6176	32	28	the	the	DET
ejpam-6176	32	29	proposed	propose	VERB
ejpam-6176	32	30	scheme	scheme	NOUN
ejpam-6176	32	31	,	,	PUNCT
ejpam-6176	32	32	and	and	CCONJ
ejpam-6176	32	33	demonstrate	demonstrate	VERB
ejpam-6176	32	34	that	that	SCONJ
ejpam-6176	32	35	the	the	DET
ejpam-6176	32	36	proposed	propose	VERB
ejpam-6176	32	37	method	method	NOUN
ejpam-6176	32	38	yields	yield	VERB
ejpam-6176	32	39	lower	low	ADJ
ejpam-6176	32	40	error	error	NOUN
ejpam-6176	32	41	and	and	CCONJ
ejpam-6176	32	42	higher	high	ADJ
ejpam-6176	32	43	accuracy	accuracy	NOUN
ejpam-6176	32	44	.	.	PUNCT
ejpam-6176	33	1	infectious	infectious	ADJ
ejpam-6176	33	2	diseases	disease	NOUN
ejpam-6176	33	3	have	have	AUX
ejpam-6176	33	4	seriously	seriously	ADV
ejpam-6176	33	5	threatened	threaten	VERB
ejpam-6176	33	6	humankind	humankind	NOUN
ejpam-6176	33	7	for	for	ADP
ejpam-6176	33	8	a	a	DET
ejpam-6176	33	9	long	long	ADJ
ejpam-6176	33	10	time	time	NOUN
ejpam-6176	33	11	,	,	PUNCT
ejpam-6176	33	12	and	and	CCONJ
ejpam-6176	33	13	they	they	PRON
ejpam-6176	33	14	continue	continue	VERB
ejpam-6176	33	15	to	to	PART
ejpam-6176	33	16	do	do	VERB
ejpam-6176	33	17	so	so	ADV
ejpam-6176	33	18	now	now	ADV
ejpam-6176	33	19	.	.	PUNCT
ejpam-6176	34	1	the	the	DET
ejpam-6176	34	2	world	world	PROPN
ejpam-6176	34	3	health	health	PROPN
ejpam-6176	34	4	organization	organization	NOUN
ejpam-6176	34	5	reports	report	VERB
ejpam-6176	34	6	that	that	SCONJ
ejpam-6176	34	7	between	between	ADP
ejpam-6176	34	8	1	1	NUM
ejpam-6176	34	9	january	january	NOUN
ejpam-6176	34	10	2020	2020	NUM
ejpam-6176	34	11	and	and	CCONJ
ejpam-6176	34	12	1	1	NUM
ejpam-6176	34	13	may	may	PROPN
ejpam-6176	34	14	2020	2020	NUM
ejpam-6176	34	15	,	,	PUNCT
ejpam-6176	34	16	infectious	infectious	ADJ
ejpam-6176	34	17	diseases	disease	NOUN
ejpam-6176	34	18	claimed	claim	VERB
ejpam-6176	34	19	the	the	DET
ejpam-6176	34	20	lives	life	NOUN
ejpam-6176	34	21	of	of	ADP
ejpam-6176	34	22	more	more	ADJ
ejpam-6176	34	23	than	than	ADP
ejpam-6176	34	24	4	4	NUM
ejpam-6176	34	25	million	million	NUM
ejpam-6176	34	26	people	people	NOUN
ejpam-6176	34	27	across	across	ADP
ejpam-6176	34	28	the	the	DET
ejpam-6176	34	29	globe	globe	NOUN
ejpam-6176	34	30	.	.	PUNCT
ejpam-6176	35	1	consequently	consequently	ADV
ejpam-6176	35	2	,	,	PUNCT
ejpam-6176	35	3	it	it	PRON
ejpam-6176	35	4	is	be	AUX
ejpam-6176	35	5	crucial	crucial	ADJ
ejpam-6176	35	6	to	to	PART
ejpam-6176	35	7	regulate	regulate	VERB
ejpam-6176	35	8	the	the	DET
ejpam-6176	35	9	spread	spread	NOUN
ejpam-6176	35	10	of	of	ADP
ejpam-6176	35	11	diseases	disease	NOUN
ejpam-6176	35	12	and	and	CCONJ
ejpam-6176	35	13	have	have	VERB
ejpam-6176	35	14	a	a	DET
ejpam-6176	35	15	firm	firm	ADJ
ejpam-6176	35	16	grasp	grasp	NOUN
ejpam-6176	35	17	of	of	ADP
ejpam-6176	35	18	epidemiological	epidemiological	ADJ
ejpam-6176	35	19	patterns	pattern	NOUN
ejpam-6176	35	20	.	.	PUNCT
ejpam-6176	36	1	in	in	ADP
ejpam-6176	36	2	recent	recent	ADJ
ejpam-6176	36	3	years	year	NOUN
ejpam-6176	36	4	,	,	PUNCT
ejpam-6176	36	5	mathematical	mathematical	ADJ
ejpam-6176	36	6	epidemic	epidemic	NOUN
ejpam-6176	36	7	modelling	modelling	NOUN
ejpam-6176	36	8	has	have	AUX
ejpam-6176	36	9	emerged	emerge	VERB
ejpam-6176	36	10	as	as	ADP
ejpam-6176	36	11	a	a	DET
ejpam-6176	36	12	powerful	powerful	ADJ
ejpam-6176	36	13	and	and	CCONJ
ejpam-6176	36	14	significant	significant	ADJ
ejpam-6176	36	15	tool	tool	NOUN
ejpam-6176	36	16	for	for	ADP
ejpam-6176	36	17	comprehending	comprehend	VERB
ejpam-6176	36	18	the	the	DET
ejpam-6176	36	19	spread	spread	NOUN
ejpam-6176	36	20	of	of	ADP
ejpam-6176	36	21	contagious	contagious	ADJ
ejpam-6176	36	22	illnesses	illness	NOUN
ejpam-6176	36	23	.	.	PUNCT
ejpam-6176	37	1	mathematical	mathematical	ADJ
ejpam-6176	37	2	models	model	NOUN
ejpam-6176	37	3	m.	m.	PROPN
ejpam-6176	37	4	s.	s.	PROPN
ejpam-6176	37	5	arif	arif	PROPN
ejpam-6176	37	6	,	,	PUNCT
ejpam-6176	37	7	k.	k.	PROPN
ejpam-6176	37	8	abodayeh	abodayeh	PROPN
ejpam-6176	37	9	,	,	PUNCT
ejpam-6176	37	10	y.	y.	NOUN
ejpam-6176	37	11	nawaz	nawaz	PROPN
ejpam-6176	37	12	/	/	SYM
ejpam-6176	37	13	eur	eur	PROPN
ejpam-6176	37	14	.	.	PUNCT
ejpam-6176	38	1	j.	j.	PROPN
ejpam-6176	38	2	pure	pure	PROPN
ejpam-6176	38	3	appl	appl	PROPN
ejpam-6176	38	4	.	.	PROPN
ejpam-6176	38	5	math	math	PROPN
ejpam-6176	38	6	,	,	PUNCT
ejpam-6176	38	7	18	18	NUM
ejpam-6176	38	8	(	(	PUNCT
ejpam-6176	38	9	3	3	NUM
ejpam-6176	38	10	)	)	PUNCT
ejpam-6176	38	11	(	(	PUNCT
ejpam-6176	38	12	2025	2025	NUM
ejpam-6176	38	13	)	)	PUNCT
ejpam-6176	38	14	,	,	PUNCT
ejpam-6176	38	15	6176	6176	NUM
ejpam-6176	38	16	3	3	NUM
ejpam-6176	38	17	of	of	ADP
ejpam-6176	38	18	21	21	NUM
ejpam-6176	38	19	of	of	ADP
ejpam-6176	38	20	epidemiology	epidemiology	NOUN
ejpam-6176	38	21	,	,	PUNCT
ejpam-6176	38	22	initially	initially	ADV
ejpam-6176	38	23	proposed	propose	VERB
ejpam-6176	38	24	by	by	ADP
ejpam-6176	38	25	kermack	kermack	NOUN
ejpam-6176	38	26	and	and	CCONJ
ejpam-6176	38	27	mckendrick	mckendrick	NOUN
ejpam-6176	38	28	,	,	PUNCT
ejpam-6176	38	29	describe	describe	VERB
ejpam-6176	38	30	the	the	DET
ejpam-6176	38	31	processes	process	NOUN
ejpam-6176	38	32	that	that	PRON
ejpam-6176	38	33	cause	cause	VERB
ejpam-6176	38	34	epidemics	epidemic	NOUN
ejpam-6176	38	35	to	to	PART
ejpam-6176	38	36	spread	spread	VERB
ejpam-6176	38	37	.	.	PUNCT
ejpam-6176	39	1	both	both	PRON
ejpam-6176	39	2	theoretically	theoretically	ADV
ejpam-6176	39	3	and	and	CCONJ
ejpam-6176	39	4	pragmatically	pragmatically	ADV
ejpam-6176	39	5	,	,	PUNCT
ejpam-6176	39	6	their	their	PRON
ejpam-6176	39	7	work	work	NOUN
ejpam-6176	39	8	serves	serve	VERB
ejpam-6176	39	9	as	as	ADP
ejpam-6176	39	10	a	a	DET
ejpam-6176	39	11	reference	reference	NOUN
ejpam-6176	39	12	for	for	ADP
ejpam-6176	39	13	future	future	ADJ
ejpam-6176	39	14	mathematical	mathematical	ADJ
ejpam-6176	39	15	modelling	modelling	NOUN
ejpam-6176	39	16	studies	study	NOUN
ejpam-6176	39	17	and	and	CCONJ
ejpam-6176	39	18	applications	application	NOUN
ejpam-6176	39	19	in	in	ADP
ejpam-6176	39	20	epidemiology	epidemiology	NOUN
ejpam-6176	39	21	.	.	PUNCT
ejpam-6176	40	1	a	a	DET
ejpam-6176	40	2	plethora	plethora	NOUN
ejpam-6176	40	3	of	of	ADP
ejpam-6176	40	4	subsequent	subsequent	ADJ
ejpam-6176	40	5	epidemic	epidemic	NOUN
ejpam-6176	40	6	models	model	NOUN
ejpam-6176	40	7	have	have	AUX
ejpam-6176	40	8	been	be	AUX
ejpam-6176	40	9	put	put	VERB
ejpam-6176	40	10	forth	forth	ADP
ejpam-6176	40	11	in	in	ADP
ejpam-6176	40	12	the	the	DET
ejpam-6176	40	13	literature	literature	NOUN
ejpam-6176	40	14	[	[	X
ejpam-6176	40	15	1–4	1–4	PROPN
ejpam-6176	40	16	]	]	PUNCT
ejpam-6176	40	17	.	.	PUNCT
ejpam-6176	41	1	vaccination	vaccination	NOUN
ejpam-6176	41	2	,	,	PUNCT
ejpam-6176	41	3	transient	transient	ADJ
ejpam-6176	41	4	immunity	immunity	NOUN
ejpam-6176	41	5	,	,	PUNCT
ejpam-6176	41	6	and	and	CCONJ
ejpam-6176	41	7	fluctuating	fluctuate	VERB
ejpam-6176	41	8	population	population	NOUN
ejpam-6176	41	9	sizes	size	NOUN
ejpam-6176	41	10	were	be	AUX
ejpam-6176	41	11	all	all	DET
ejpam-6176	41	12	factors	factor	NOUN
ejpam-6176	41	13	in	in	ADP
ejpam-6176	41	14	the	the	DET
ejpam-6176	41	15	sis	sis	NOUN
ejpam-6176	41	16	epidemic	epidemic	NOUN
ejpam-6176	41	17	model	model	NOUN
ejpam-6176	41	18	that	that	PRON
ejpam-6176	41	19	li	li	PROPN
ejpam-6176	41	20	and	and	CCONJ
ejpam-6176	41	21	ma	ma	PROPN
ejpam-6176	41	22	examined	examine	VERB
ejpam-6176	41	23	[	[	X
ejpam-6176	41	24	5	5	NUM
ejpam-6176	41	25	]	]	PUNCT
ejpam-6176	41	26	.	.	PUNCT
ejpam-6176	42	1	kilicman	kilicman	PROPN
ejpam-6176	42	2	and	and	CCONJ
ejpam-6176	42	3	hamdan	hamdan	PROPN
ejpam-6176	42	4	suggested	suggest	VERB
ejpam-6176	42	5	a	a	DET
ejpam-6176	42	6	fractional	fractional	ADJ
ejpam-6176	42	7	-	-	PUNCT
ejpam-6176	42	8	order	order	NOUN
ejpam-6176	42	9	sir	sir	NOUN
ejpam-6176	42	10	epidemic	epidemic	NOUN
ejpam-6176	42	11	dengue	dengue	PROPN
ejpam-6176	42	12	transmission	transmission	NOUN
ejpam-6176	42	13	model	model	NOUN
ejpam-6176	42	14	[	[	X
ejpam-6176	42	15	6	6	NUM
ejpam-6176	42	16	]	]	PUNCT
ejpam-6176	42	17	.	.	PUNCT
ejpam-6176	43	1	xiang	xiang	PROPN
ejpam-6176	43	2	et	et	PROPN
ejpam-6176	43	3	al	al	PROPN
ejpam-6176	43	4	.	.	PROPN
ejpam-6176	43	5	demonstrated	demonstrate	VERB
ejpam-6176	43	6	local	local	ADJ
ejpam-6176	43	7	stability	stability	NOUN
ejpam-6176	43	8	in	in	ADP
ejpam-6176	43	9	their	their	PRON
ejpam-6176	43	10	discrete	discrete	ADJ
ejpam-6176	43	11	sirs	sir	NOUN
ejpam-6176	43	12	epidemic	epidemic	NOUN
ejpam-6176	43	13	model	model	NOUN
ejpam-6176	43	14	with	with	ADP
ejpam-6176	43	15	vaccination	vaccination	NOUN
ejpam-6176	43	16	[	[	X
ejpam-6176	43	17	7	7	NUM
ejpam-6176	43	18	]	]	PUNCT
ejpam-6176	43	19	.	.	PUNCT
ejpam-6176	44	1	quarantine	quarantine	NOUN
ejpam-6176	44	2	was	be	AUX
ejpam-6176	44	3	thought	think	VERB
ejpam-6176	44	4	to	to	PART
ejpam-6176	44	5	be	be	AUX
ejpam-6176	44	6	the	the	DET
ejpam-6176	44	7	most	most	ADV
ejpam-6176	44	8	essential	essential	ADJ
ejpam-6176	44	9	way	way	NOUN
ejpam-6176	44	10	to	to	PART
ejpam-6176	44	11	prevent	prevent	VERB
ejpam-6176	44	12	the	the	DET
ejpam-6176	44	13	spread	spread	NOUN
ejpam-6176	44	14	of	of	ADP
ejpam-6176	44	15	contagious	contagious	ADJ
ejpam-6176	44	16	diseases	disease	NOUN
ejpam-6176	44	17	for	for	ADP
ejpam-6176	44	18	a	a	DET
ejpam-6176	44	19	long	long	ADJ
ejpam-6176	44	20	time	time	NOUN
ejpam-6176	44	21	.	.	PUNCT
ejpam-6176	45	1	coronavirus	coronavirus	NOUN
ejpam-6176	45	2	,	,	PUNCT
ejpam-6176	45	3	influenza	influenza	NOUN
ejpam-6176	45	4	,	,	PUNCT
ejpam-6176	45	5	rubella	rubella	NOUN
ejpam-6176	45	6	,	,	PUNCT
ejpam-6176	45	7	and	and	CCONJ
ejpam-6176	45	8	other	other	ADJ
ejpam-6176	45	9	epidemics	epidemic	NOUN
ejpam-6176	45	10	have	have	AUX
ejpam-6176	45	11	been	be	AUX
ejpam-6176	45	12	contained	contain	VERB
ejpam-6176	45	13	with	with	ADP
ejpam-6176	45	14	its	its	PRON
ejpam-6176	45	15	help	help	NOUN
ejpam-6176	45	16	.	.	PUNCT
ejpam-6176	46	1	quarantine	quarantine	NOUN
ejpam-6176	46	2	has	have	AUX
ejpam-6176	46	3	recently	recently	ADV
ejpam-6176	46	4	proven	prove	VERB
ejpam-6176	46	5	effective	effective	ADJ
ejpam-6176	46	6	in	in	ADP
ejpam-6176	46	7	limiting	limit	VERB
ejpam-6176	46	8	the	the	DET
ejpam-6176	46	9	spread	spread	NOUN
ejpam-6176	46	10	of	of	ADP
ejpam-6176	46	11	the	the	DET
ejpam-6176	46	12	deadly	deadly	ADJ
ejpam-6176	46	13	new	new	ADJ
ejpam-6176	46	14	coronavirus	coronavirus	NOUN
ejpam-6176	46	15	[	[	X
ejpam-6176	46	16	8	8	NUM
ejpam-6176	46	17	,	,	PUNCT
ejpam-6176	46	18	9	9	NUM
ejpam-6176	46	19	]	]	PUNCT
ejpam-6176	46	20	.	.	PUNCT
ejpam-6176	47	1	as	as	ADP
ejpam-6176	47	2	a	a	DET
ejpam-6176	47	3	result	result	NOUN
ejpam-6176	47	4	,	,	PUNCT
ejpam-6176	47	5	research	research	NOUN
ejpam-6176	47	6	into	into	ADP
ejpam-6176	47	7	how	how	SCONJ
ejpam-6176	47	8	quarantine	quarantine	NOUN
ejpam-6176	47	9	affects	affect	VERB
ejpam-6176	47	10	epidemic	epidemic	NOUN
ejpam-6176	47	11	behaviour	behaviour	NOUN
ejpam-6176	47	12	is	be	AUX
ejpam-6176	47	13	crucial	crucial	ADJ
ejpam-6176	47	14	.	.	PUNCT
ejpam-6176	48	1	to	to	PART
ejpam-6176	48	2	illustrate	illustrate	VERB
ejpam-6176	48	3	this	this	PRON
ejpam-6176	48	4	,	,	PUNCT
ejpam-6176	48	5	heathcote	heathcote	PROPN
ejpam-6176	48	6	et	et	PROPN
ejpam-6176	48	7	al	al	PROPN
ejpam-6176	48	8	.	.	PROPN
ejpam-6176	48	9	created	create	VERB
ejpam-6176	48	10	an	an	DET
ejpam-6176	48	11	siqr	siqr	ADJ
ejpam-6176	48	12	model	model	NOUN
ejpam-6176	48	13	[	[	X
ejpam-6176	48	14	10	10	NUM
ejpam-6176	48	15	]	]	PUNCT
ejpam-6176	48	16	.	.	PUNCT
ejpam-6176	49	1	the	the	DET
ejpam-6176	49	2	effects	effect	NOUN
ejpam-6176	49	3	of	of	ADP
ejpam-6176	49	4	quarantine	quarantine	NOUN
ejpam-6176	49	5	on	on	ADP
ejpam-6176	49	6	influenza	influenza	NOUN
ejpam-6176	49	7	transmission	transmission	NOUN
ejpam-6176	49	8	dynamics	dynamic	NOUN
ejpam-6176	49	9	were	be	AUX
ejpam-6176	49	10	investigated	investigate	VERB
ejpam-6176	49	11	by	by	ADP
ejpam-6176	49	12	erdem	erdem	PROPN
ejpam-6176	49	13	et	et	PROPN
ejpam-6176	49	14	al	al	PROPN
ejpam-6176	49	15	.	.	PUNCT
ejpam-6176	50	1	[	[	X
ejpam-6176	50	2	11	11	NUM
ejpam-6176	50	3	]	]	PUNCT
ejpam-6176	50	4	.	.	PUNCT
ejpam-6176	51	1	an	an	DET
ejpam-6176	51	2	siqr	siqr	ADJ
ejpam-6176	51	3	epidemic	epidemic	NOUN
ejpam-6176	51	4	model	model	NOUN
ejpam-6176	51	5	was	be	AUX
ejpam-6176	51	6	created	create	VERB
ejpam-6176	51	7	by	by	ADP
ejpam-6176	51	8	ma	ma	PROPN
ejpam-6176	51	9	et	et	PROPN
ejpam-6176	51	10	al	al	PROPN
ejpam-6176	51	11	.	.	PUNCT
ejpam-6176	52	1	[	[	X
ejpam-6176	52	2	12	12	NUM
ejpam-6176	52	3	]	]	PUNCT
ejpam-6176	52	4	that	that	SCONJ
ejpam-6176	52	5	integrated	integrate	VERB
ejpam-6176	52	6	hybrid	hybrid	ADJ
ejpam-6176	52	7	techniques	technique	NOUN
ejpam-6176	52	8	for	for	ADP
ejpam-6176	52	9	vaccination	vaccination	NOUN
ejpam-6176	52	10	and	and	CCONJ
ejpam-6176	52	11	elimination	elimination	NOUN
ejpam-6176	52	12	.	.	PUNCT
ejpam-6176	53	1	an	an	DET
ejpam-6176	53	2	infectious	infectious	ADJ
ejpam-6176	53	3	disease	disease	NOUN
ejpam-6176	53	4	’s	’s	PART
ejpam-6176	53	5	incidence	incidence	NOUN
ejpam-6176	53	6	rate	rate	NOUN
ejpam-6176	53	7	is	be	AUX
ejpam-6176	53	8	defined	define	VERB
ejpam-6176	53	9	as	as	ADP
ejpam-6176	53	10	the	the	DET
ejpam-6176	53	11	number	number	NOUN
ejpam-6176	53	12	of	of	ADP
ejpam-6176	53	13	newly	newly	ADV
ejpam-6176	53	14	reported	report	VERB
ejpam-6176	53	15	cases	case	NOUN
ejpam-6176	53	16	in	in	ADP
ejpam-6176	53	17	a	a	DET
ejpam-6176	53	18	population	population	NOUN
ejpam-6176	53	19	as	as	ADP
ejpam-6176	53	20	a	a	DET
ejpam-6176	53	21	function	function	NOUN
ejpam-6176	53	22	of	of	ADP
ejpam-6176	53	23	time	time	NOUN
ejpam-6176	53	24	.	.	PUNCT
ejpam-6176	54	1	it	it	PRON
ejpam-6176	54	2	is	be	AUX
ejpam-6176	54	3	crucial	crucial	ADJ
ejpam-6176	54	4	to	to	PART
ejpam-6176	54	5	model	model	VERB
ejpam-6176	54	6	the	the	DET
ejpam-6176	54	7	spread	spread	NOUN
ejpam-6176	54	8	of	of	ADP
ejpam-6176	54	9	infectious	infectious	ADJ
ejpam-6176	54	10	diseases	disease	NOUN
ejpam-6176	54	11	[	[	X
ejpam-6176	54	12	13–15	13–15	NUM
ejpam-6176	54	13	]	]	PUNCT
ejpam-6176	54	14	.	.	PUNCT
ejpam-6176	55	1	the	the	DET
ejpam-6176	55	2	standard	standard	ADJ
ejpam-6176	55	3	incidence	incidence	NOUN
ejpam-6176	55	4	rate	rate	NOUN
ejpam-6176	55	5	βsi	βsi	NOUN
ejpam-6176	55	6	and	and	CCONJ
ejpam-6176	55	7	bilinear	bilinear	ADJ
ejpam-6176	55	8	incidence	incidence	NOUN
ejpam-6176	55	9	rate	rate	NOUN
ejpam-6176	55	10	βsi	βsi	NOUN
ejpam-6176	55	11	are	be	AUX
ejpam-6176	55	12	commonly	commonly	ADV
ejpam-6176	55	13	used	use	VERB
ejpam-6176	55	14	in	in	ADP
ejpam-6176	55	15	epidemiological	epidemiological	ADJ
ejpam-6176	55	16	models	model	NOUN
ejpam-6176	55	17	.	.	PUNCT
ejpam-6176	56	1	however	however	ADV
ejpam-6176	56	2	,	,	PUNCT
ejpam-6176	56	3	these	these	PRON
ejpam-6176	56	4	may	may	AUX
ejpam-6176	56	5	be	be	AUX
ejpam-6176	56	6	inadequate	inadequate	ADJ
ejpam-6176	56	7	in	in	ADP
ejpam-6176	56	8	scenarios	scenario	NOUN
ejpam-6176	56	9	such	such	ADJ
ejpam-6176	56	10	as	as	ADP
ejpam-6176	56	11	population	population	NOUN
ejpam-6176	56	12	saturation	saturation	NOUN
ejpam-6176	56	13	[	[	X
ejpam-6176	56	14	16	16	NUM
ejpam-6176	56	15	,	,	PUNCT
ejpam-6176	56	16	17	17	NUM
ejpam-6176	56	17	]	]	PUNCT
ejpam-6176	56	18	.	.	PUNCT
ejpam-6176	57	1	non	non	ADJ
ejpam-6176	57	2	-	-	ADJ
ejpam-6176	57	3	linear	linear	ADJ
ejpam-6176	57	4	incidence	incidence	NOUN
ejpam-6176	57	5	models	model	NOUN
ejpam-6176	57	6	,	,	PUNCT
ejpam-6176	57	7	such	such	ADJ
ejpam-6176	57	8	as	as	ADP
ejpam-6176	57	9	βipsq	βipsq	NOUN
ejpam-6176	57	10	and	and	CCONJ
ejpam-6176	57	11	αi/(s	αi/(s	PRON
ejpam-6176	57	12	+	+	CCONJ
ejpam-6176	57	13	βi	βi	X
ejpam-6176	57	14	)	)	PUNCT
ejpam-6176	57	15	,	,	PUNCT
ejpam-6176	57	16	better	well	ADJ
ejpam-6176	57	17	capture	capture	VERB
ejpam-6176	57	18	realistic	realistic	ADJ
ejpam-6176	57	19	infection	infection	NOUN
ejpam-6176	57	20	patterns	pattern	NOUN
ejpam-6176	57	21	[	[	X
ejpam-6176	57	22	18–20	18–20	NUM
ejpam-6176	57	23	]	]	PUNCT
ejpam-6176	57	24	.	.	PUNCT
ejpam-6176	58	1	infectious	infectious	ADJ
ejpam-6176	58	2	diseases	disease	NOUN
ejpam-6176	58	3	inflict	inflict	VERB
ejpam-6176	58	4	not	not	PART
ejpam-6176	58	5	only	only	ADV
ejpam-6176	58	6	physical	physical	ADJ
ejpam-6176	58	7	suffering	suffering	NOUN
ejpam-6176	58	8	on	on	ADP
ejpam-6176	58	9	humans	human	NOUN
ejpam-6176	58	10	but	but	CCONJ
ejpam-6176	58	11	also	also	ADV
ejpam-6176	58	12	result	result	VERB
ejpam-6176	58	13	in	in	ADP
ejpam-6176	58	14	property	property	NOUN
ejpam-6176	58	15	loss	loss	NOUN
ejpam-6176	58	16	and	and	CCONJ
ejpam-6176	58	17	significant	significant	ADJ
ejpam-6176	58	18	environmental	environmental	ADJ
ejpam-6176	58	19	impact	impact	NOUN
ejpam-6176	58	20	.	.	PUNCT
ejpam-6176	59	1	with	with	ADP
ejpam-6176	59	2	globalization	globalization	NOUN
ejpam-6176	59	3	and	and	CCONJ
ejpam-6176	59	4	technological	technological	ADJ
ejpam-6176	59	5	advancement	advancement	NOUN
ejpam-6176	59	6	,	,	PUNCT
ejpam-6176	59	7	cross	cross	ADJ
ejpam-6176	59	8	-	-	ADJ
ejpam-6176	59	9	regional	regional	ADJ
ejpam-6176	59	10	disease	disease	NOUN
ejpam-6176	59	11	transmission	transmission	NOUN
ejpam-6176	59	12	is	be	AUX
ejpam-6176	59	13	accelerating	accelerate	VERB
ejpam-6176	59	14	.	.	PUNCT
ejpam-6176	60	1	though	though	SCONJ
ejpam-6176	60	2	many	many	ADJ
ejpam-6176	60	3	studies	study	NOUN
ejpam-6176	60	4	on	on	ADP
ejpam-6176	60	5	conventional	conventional	ADJ
ejpam-6176	60	6	compartment	compartment	NOUN
ejpam-6176	60	7	models	model	NOUN
ejpam-6176	60	8	assume	assume	VERB
ejpam-6176	60	9	homogeneous	homogeneous	ADJ
ejpam-6176	60	10	mixing	mixing	NOUN
ejpam-6176	60	11	[	[	X
ejpam-6176	60	12	21–25	21–25	NUM
ejpam-6176	60	13	]	]	PUNCT
ejpam-6176	60	14	,	,	PUNCT
ejpam-6176	60	15	these	these	DET
ejpam-6176	60	16	assumptions	assumption	NOUN
ejpam-6176	60	17	fail	fail	VERB
ejpam-6176	60	18	in	in	ADP
ejpam-6176	60	19	light	light	NOUN
ejpam-6176	60	20	of	of	ADP
ejpam-6176	60	21	heterogeneous	heterogeneous	ADJ
ejpam-6176	60	22	disease	disease	NOUN
ejpam-6176	60	23	patterns	pattern	NOUN
ejpam-6176	60	24	seen	see	VERB
ejpam-6176	60	25	in	in	ADP
ejpam-6176	60	26	sars	sar	NOUN
ejpam-6176	60	27	and	and	CCONJ
ejpam-6176	60	28	aids	aid	NOUN
ejpam-6176	60	29	[	[	X
ejpam-6176	60	30	26	26	NUM
ejpam-6176	60	31	,	,	PUNCT
ejpam-6176	60	32	27	27	NUM
ejpam-6176	60	33	]	]	PUNCT
ejpam-6176	60	34	.	.	PUNCT
ejpam-6176	61	1	many	many	ADJ
ejpam-6176	61	2	real	real	ADJ
ejpam-6176	61	3	-	-	PUNCT
ejpam-6176	61	4	world	world	NOUN
ejpam-6176	61	5	systems	system	NOUN
ejpam-6176	61	6	,	,	PUNCT
ejpam-6176	61	7	such	such	ADJ
ejpam-6176	61	8	as	as	ADP
ejpam-6176	61	9	the	the	DET
ejpam-6176	61	10	world	world	NOUN
ejpam-6176	61	11	wide	wide	ADJ
ejpam-6176	61	12	web	web	NOUN
ejpam-6176	61	13	[	[	X
ejpam-6176	61	14	28	28	NUM
ejpam-6176	61	15	,	,	PUNCT
ejpam-6176	61	16	29	29	NUM
ejpam-6176	61	17	]	]	PUNCT
ejpam-6176	61	18	and	and	CCONJ
ejpam-6176	61	19	human	human	ADJ
ejpam-6176	61	20	contact	contact	NOUN
ejpam-6176	61	21	networks	network	NOUN
ejpam-6176	61	22	,	,	PUNCT
ejpam-6176	61	23	are	be	AUX
ejpam-6176	61	24	scale	scale	NOUN
ejpam-6176	61	25	-	-	PUNCT
ejpam-6176	61	26	free	free	ADJ
ejpam-6176	61	27	,	,	PUNCT
ejpam-6176	61	28	as	as	SCONJ
ejpam-6176	61	29	described	describe	VERB
ejpam-6176	61	30	by	by	ADP
ejpam-6176	61	31	barabási	barabási	ADV
ejpam-6176	61	32	and	and	CCONJ
ejpam-6176	61	33	albert	albert	PROPN
ejpam-6176	62	1	[	[	X
ejpam-6176	62	2	30	30	NUM
ejpam-6176	62	3	]	]	PUNCT
ejpam-6176	62	4	.	.	PUNCT
ejpam-6176	63	1	the	the	DET
ejpam-6176	63	2	scale	scale	NOUN
ejpam-6176	63	3	-	-	PUNCT
ejpam-6176	63	4	free	free	ADJ
ejpam-6176	63	5	network	network	NOUN
ejpam-6176	63	6	model	model	NOUN
ejpam-6176	63	7	leads	lead	VERB
ejpam-6176	63	8	to	to	ADP
ejpam-6176	63	9	power	power	NOUN
ejpam-6176	63	10	-	-	PUNCT
ejpam-6176	63	11	law	law	NOUN
ejpam-6176	63	12	degree	degree	NOUN
ejpam-6176	63	13	distributions	distribution	NOUN
ejpam-6176	63	14	and	and	CCONJ
ejpam-6176	63	15	challenges	challenge	VERB
ejpam-6176	63	16	traditional	traditional	ADJ
ejpam-6176	63	17	threshold	threshold	NOUN
ejpam-6176	63	18	-	-	PUNCT
ejpam-6176	63	19	based	base	VERB
ejpam-6176	63	20	epidemic	epidemic	NOUN
ejpam-6176	63	21	predictions	prediction	NOUN
ejpam-6176	63	22	[	[	X
ejpam-6176	63	23	31	31	NUM
ejpam-6176	63	24	]	]	PUNCT
ejpam-6176	63	25	.	.	PUNCT
ejpam-6176	64	1	for	for	ADP
ejpam-6176	64	2	example	example	NOUN
ejpam-6176	64	3	,	,	PUNCT
ejpam-6176	64	4	pastor	pastor	NOUN
ejpam-6176	64	5	-	-	PUNCT
ejpam-6176	64	6	satorras	satorra	NOUN
ejpam-6176	64	7	and	and	CCONJ
ejpam-6176	64	8	vespignani	vespignani	PROPN
ejpam-6176	64	9	showed	show	VERB
ejpam-6176	64	10	that	that	SCONJ
ejpam-6176	64	11	epidemic	epidemic	NOUN
ejpam-6176	64	12	thresholds	threshold	NOUN
ejpam-6176	64	13	tend	tend	VERB
ejpam-6176	64	14	to	to	PART
ejpam-6176	64	15	zero	zero	NUM
ejpam-6176	64	16	in	in	ADP
ejpam-6176	64	17	large	large	ADJ
ejpam-6176	64	18	scale	scale	NOUN
ejpam-6176	64	19	-	-	PUNCT
ejpam-6176	64	20	free	free	ADJ
ejpam-6176	64	21	networks	network	NOUN
ejpam-6176	64	22	[	[	X
ejpam-6176	64	23	32	32	NUM
ejpam-6176	64	24	,	,	PUNCT
ejpam-6176	64	25	33	33	NUM
ejpam-6176	64	26	]	]	PUNCT
ejpam-6176	64	27	.	.	PUNCT
ejpam-6176	65	1	li	li	PROPN
ejpam-6176	65	2	et	et	PROPN
ejpam-6176	65	3	al	al	PROPN
ejpam-6176	65	4	.	.	PROPN
ejpam-6176	65	5	analyzed	analyze	VERB
ejpam-6176	65	6	a	a	DET
ejpam-6176	65	7	siqrs	siqrs	NOUN
ejpam-6176	65	8	model	model	NOUN
ejpam-6176	65	9	on	on	ADP
ejpam-6176	65	10	such	such	ADJ
ejpam-6176	65	11	networks	network	NOUN
ejpam-6176	65	12	and	and	CCONJ
ejpam-6176	65	13	highlighted	highlight	VERB
ejpam-6176	65	14	the	the	DET
ejpam-6176	65	15	combined	combined	ADJ
ejpam-6176	65	16	role	role	NOUN
ejpam-6176	65	17	of	of	ADP
ejpam-6176	65	18	quarantine	quarantine	NOUN
ejpam-6176	65	19	and	and	CCONJ
ejpam-6176	65	20	network	network	NOUN
ejpam-6176	65	21	topology	topology	NOUN
ejpam-6176	66	1	[	[	X
ejpam-6176	66	2	34	34	NUM
ejpam-6176	66	3	]	]	PUNCT
ejpam-6176	66	4	.	.	PUNCT
ejpam-6176	67	1	demographics	demographic	NOUN
ejpam-6176	67	2	and	and	CCONJ
ejpam-6176	67	3	vaccination	vaccination	NOUN
ejpam-6176	67	4	further	further	ADJ
ejpam-6176	67	5	influence	influence	NOUN
ejpam-6176	67	6	dynamics	dynamic	NOUN
ejpam-6176	67	7	,	,	PUNCT
ejpam-6176	67	8	as	as	SCONJ
ejpam-6176	67	9	shown	show	VERB
ejpam-6176	67	10	by	by	ADP
ejpam-6176	67	11	huang	huang	PROPN
ejpam-6176	67	12	et	et	PROPN
ejpam-6176	67	13	al	al	PROPN
ejpam-6176	67	14	.	.	PUNCT
ejpam-6176	68	1	[	[	X
ejpam-6176	68	2	35	35	NUM
ejpam-6176	68	3	]	]	PUNCT
ejpam-6176	68	4	.	.	PUNCT
ejpam-6176	69	1	a	a	DET
ejpam-6176	69	2	stochastic	stochastic	ADJ
ejpam-6176	69	3	diffusive	diffusive	ADJ
ejpam-6176	69	4	model	model	NOUN
ejpam-6176	69	5	is	be	AUX
ejpam-6176	69	6	created	create	VERB
ejpam-6176	69	7	in	in	ADP
ejpam-6176	69	8	this	this	DET
ejpam-6176	69	9	study	study	NOUN
ejpam-6176	69	10	[	[	X
ejpam-6176	69	11	36	36	NUM
ejpam-6176	69	12	]	]	PUNCT
ejpam-6176	69	13	to	to	PART
ejpam-6176	69	14	handle	handle	VERB
ejpam-6176	69	15	the	the	DET
ejpam-6176	69	16	intricate	intricate	ADJ
ejpam-6176	69	17	dynamics	dynamic	NOUN
ejpam-6176	69	18	of	of	ADP
ejpam-6176	69	19	co2	co2	NOUN
ejpam-6176	69	20	concentration	concentration	NOUN
ejpam-6176	69	21	,	,	PUNCT
ejpam-6176	69	22	population	population	NOUN
ejpam-6176	69	23	expansion	expansion	NOUN
ejpam-6176	69	24	,	,	PUNCT
ejpam-6176	69	25	and	and	CCONJ
ejpam-6176	69	26	energy	energy	NOUN
ejpam-6176	69	27	production	production	NOUN
ejpam-6176	69	28	.	.	PUNCT
ejpam-6176	70	1	the	the	DET
ejpam-6176	70	2	researcher	researcher	NOUN
ejpam-6176	70	3	offers	offer	VERB
ejpam-6176	70	4	a	a	DET
ejpam-6176	70	5	new	new	ADJ
ejpam-6176	70	6	computational	computational	ADJ
ejpam-6176	70	7	technique	technique	NOUN
ejpam-6176	70	8	for	for	ADP
ejpam-6176	70	9	solving	solve	VERB
ejpam-6176	70	10	deterministic	deterministic	ADJ
ejpam-6176	70	11	and	and	CCONJ
ejpam-6176	70	12	stochastic	stochastic	ADJ
ejpam-6176	70	13	pdes	pde	NOUN
ejpam-6176	70	14	in	in	ADP
ejpam-6176	70	15	the	the	DET
ejpam-6176	70	16	papers	paper	NOUN
ejpam-6176	70	17	[	[	X
ejpam-6176	70	18	37	37	NUM
ejpam-6176	70	19	,	,	PUNCT
ejpam-6176	70	20	38	38	NUM
ejpam-6176	70	21	]	]	PUNCT
ejpam-6176	70	22	.	.	PUNCT
ejpam-6176	71	1	to	to	PART
ejpam-6176	71	2	account	account	VERB
ejpam-6176	71	3	for	for	ADP
ejpam-6176	71	4	individual	individual	ADJ
ejpam-6176	71	5	behavior	behavior	NOUN
ejpam-6176	71	6	changes	change	NOUN
ejpam-6176	71	7	,	,	PUNCT
ejpam-6176	71	8	xiao	xiao	PROPN
ejpam-6176	71	9	and	and	CCONJ
ejpam-6176	71	10	ruan	ruan	PROPN
ejpam-6176	71	11	proposed	propose	VERB
ejpam-6176	71	12	a	a	DET
ejpam-6176	71	13	non	non	ADJ
ejpam-6176	71	14	-	-	ADJ
ejpam-6176	71	15	monotone	monotone	ADJ
ejpam-6176	71	16	incidence	incidence	NOUN
ejpam-6176	71	17	rate	rate	NOUN
ejpam-6176	71	18	g(i)s	g(i)s	PROPN
ejpam-6176	71	19	=	=	SYM
ejpam-6176	72	1	kis	kis	PROPN
ejpam-6176	72	2	1+αi2	1+αi2	NUM
ejpam-6176	72	3	,	,	PUNCT
ejpam-6176	72	4	further	far	ADV
ejpam-6176	72	5	studied	study	VERB
ejpam-6176	72	6	by	by	ADP
ejpam-6176	72	7	li	li	PROPN
ejpam-6176	73	1	[	[	X
ejpam-6176	73	2	39	39	NUM
ejpam-6176	73	3	]	]	PUNCT
ejpam-6176	73	4	.	.	PUNCT
ejpam-6176	74	1	random	random	ADJ
ejpam-6176	74	2	environmental	environmental	ADJ
ejpam-6176	74	3	effects	effect	NOUN
ejpam-6176	74	4	,	,	PUNCT
ejpam-6176	74	5	modeled	model	VERB
ejpam-6176	74	6	as	as	ADP
ejpam-6176	74	7	white	white	ADJ
ejpam-6176	74	8	noise	noise	NOUN
ejpam-6176	74	9	,	,	PUNCT
ejpam-6176	74	10	influence	influence	NOUN
ejpam-6176	74	11	disease	disease	NOUN
ejpam-6176	74	12	dynamics	dynamic	NOUN
ejpam-6176	74	13	,	,	PUNCT
ejpam-6176	74	14	prompting	prompt	VERB
ejpam-6176	74	15	the	the	DET
ejpam-6176	74	16	development	development	NOUN
ejpam-6176	74	17	of	of	ADP
ejpam-6176	74	18	stochastic	stochastic	ADJ
ejpam-6176	74	19	models	model	NOUN
ejpam-6176	74	20	.	.	PUNCT
ejpam-6176	75	1	these	these	DET
ejpam-6176	75	2	models	model	NOUN
ejpam-6176	75	3	explore	explore	VERB
ejpam-6176	75	4	extinction	extinction	NOUN
ejpam-6176	75	5	,	,	PUNCT
ejpam-6176	75	6	persistence	persistence	NOUN
ejpam-6176	75	7	,	,	PUNCT
ejpam-6176	75	8	and	and	CCONJ
ejpam-6176	75	9	ergodic	ergodic	ADJ
ejpam-6176	75	10	stationary	stationary	ADJ
ejpam-6176	75	11	distributions	distribution	NOUN
ejpam-6176	75	12	[	[	X
ejpam-6176	75	13	40–46	40–46	NUM
ejpam-6176	75	14	]	]	PUNCT
ejpam-6176	75	15	.	.	PUNCT
ejpam-6176	76	1	m.	m.	PROPN
ejpam-6176	76	2	s.	s.	PROPN
ejpam-6176	76	3	arif	arif	PROPN
ejpam-6176	76	4	,	,	PUNCT
ejpam-6176	76	5	k.	k.	PROPN
ejpam-6176	76	6	abodayeh	abodayeh	PROPN
ejpam-6176	76	7	,	,	PUNCT
ejpam-6176	76	8	y.	y.	NOUN
ejpam-6176	76	9	nawaz	nawaz	PROPN
ejpam-6176	76	10	/	/	SYM
ejpam-6176	76	11	eur	eur	PROPN
ejpam-6176	76	12	.	.	PUNCT
ejpam-6176	77	1	j.	j.	PROPN
ejpam-6176	77	2	pure	pure	PROPN
ejpam-6176	77	3	appl	appl	PROPN
ejpam-6176	77	4	.	.	PROPN
ejpam-6176	77	5	math	math	PROPN
ejpam-6176	77	6	,	,	PUNCT
ejpam-6176	77	7	18	18	NUM
ejpam-6176	77	8	(	(	PUNCT
ejpam-6176	77	9	3	3	NUM
ejpam-6176	77	10	)	)	PUNCT
ejpam-6176	77	11	(	(	PUNCT
ejpam-6176	77	12	2025	2025	NUM
ejpam-6176	77	13	)	)	PUNCT
ejpam-6176	77	14	,	,	PUNCT
ejpam-6176	77	15	6176	6176	NUM
ejpam-6176	77	16	4	4	NUM
ejpam-6176	77	17	of	of	ADP
ejpam-6176	77	18	21	21	NUM
ejpam-6176	77	19	this	this	DET
ejpam-6176	77	20	work	work	NOUN
ejpam-6176	77	21	offers	offer	VERB
ejpam-6176	77	22	a	a	DET
ejpam-6176	77	23	new	new	ADJ
ejpam-6176	77	24	computational	computational	ADJ
ejpam-6176	77	25	method	method	NOUN
ejpam-6176	77	26	tailored	tailor	VERB
ejpam-6176	77	27	for	for	ADP
ejpam-6176	77	28	the	the	DET
ejpam-6176	77	29	stochastic	stochastic	ADJ
ejpam-6176	77	30	siqr	siqr	ADJ
ejpam-6176	77	31	model	model	NOUN
ejpam-6176	77	32	with	with	ADP
ejpam-6176	77	33	generalized	generalized	ADJ
ejpam-6176	77	34	incidence	incidence	NOUN
ejpam-6176	77	35	rate	rate	NOUN
ejpam-6176	77	36	.	.	PUNCT
ejpam-6176	78	1	the	the	DET
ejpam-6176	78	2	proposed	propose	VERB
ejpam-6176	78	3	scheme	scheme	NOUN
ejpam-6176	78	4	preserves	preserve	VERB
ejpam-6176	78	5	positivity	positivity	NOUN
ejpam-6176	78	6	and	and	CCONJ
ejpam-6176	78	7	boundedness	boundedness	NOUN
ejpam-6176	78	8	—	—	PUNCT
ejpam-6176	78	9	key	key	NOUN
ejpam-6176	78	10	for	for	ADP
ejpam-6176	78	11	epidemiological	epidemiological	ADJ
ejpam-6176	78	12	validity	validity	NOUN
ejpam-6176	78	13	.	.	PUNCT
ejpam-6176	79	1	the	the	DET
ejpam-6176	79	2	main	main	ADJ
ejpam-6176	79	3	goals	goal	NOUN
ejpam-6176	79	4	of	of	ADP
ejpam-6176	79	5	this	this	DET
ejpam-6176	79	6	paper	paper	NOUN
ejpam-6176	79	7	are	be	AUX
ejpam-6176	79	8	:	:	PUNCT
ejpam-6176	79	9	•	•	ADP
ejpam-6176	79	10	to	to	PART
ejpam-6176	79	11	build	build	VERB
ejpam-6176	79	12	and	and	CCONJ
ejpam-6176	79	13	apply	apply	VERB
ejpam-6176	79	14	a	a	DET
ejpam-6176	79	15	robust	robust	ADJ
ejpam-6176	79	16	numerical	numerical	ADJ
ejpam-6176	79	17	method	method	NOUN
ejpam-6176	79	18	for	for	ADP
ejpam-6176	79	19	the	the	DET
ejpam-6176	79	20	stochastic	stochastic	ADJ
ejpam-6176	79	21	siqr	siqr	PROPN
ejpam-6176	79	22	model	model	NOUN
ejpam-6176	79	23	.	.	PUNCT
ejpam-6176	80	1	•	•	NUM
ejpam-6176	80	2	to	to	PART
ejpam-6176	80	3	study	study	VERB
ejpam-6176	80	4	how	how	SCONJ
ejpam-6176	80	5	stochasticity	stochasticity	NOUN
ejpam-6176	80	6	and	and	CCONJ
ejpam-6176	80	7	varying	vary	VERB
ejpam-6176	80	8	incidence	incidence	NOUN
ejpam-6176	80	9	rates	rate	NOUN
ejpam-6176	80	10	affect	affect	VERB
ejpam-6176	80	11	disease	disease	NOUN
ejpam-6176	80	12	dynamics	dynamic	NOUN
ejpam-6176	80	13	.	.	PUNCT
ejpam-6176	81	1	•	•	NUM
ejpam-6176	81	2	to	to	PART
ejpam-6176	81	3	validate	validate	VERB
ejpam-6176	81	4	theoretical	theoretical	ADJ
ejpam-6176	81	5	results	result	NOUN
ejpam-6176	81	6	with	with	ADP
ejpam-6176	81	7	numerical	numerical	ADJ
ejpam-6176	81	8	experiments	experiment	NOUN
ejpam-6176	81	9	.	.	PUNCT
ejpam-6176	82	1	we	we	PRON
ejpam-6176	82	2	solve	solve	VERB
ejpam-6176	82	3	the	the	DET
ejpam-6176	82	4	siqr	siqr	PROPN
ejpam-6176	82	5	model	model	NOUN
ejpam-6176	82	6	using	use	VERB
ejpam-6176	82	7	four	four	NUM
ejpam-6176	82	8	techniques	technique	NOUN
ejpam-6176	82	9	,	,	PUNCT
ejpam-6176	82	10	including	include	VERB
ejpam-6176	82	11	the	the	DET
ejpam-6176	82	12	pdepe	pdepe	NOUN
ejpam-6176	82	13	solver	solver	ADV
ejpam-6176	82	14	in	in	ADP
ejpam-6176	82	15	matlab	matlab	PROPN
ejpam-6176	82	16	,	,	PUNCT
ejpam-6176	82	17	suitable	suitable	ADJ
ejpam-6176	82	18	for	for	ADP
ejpam-6176	82	19	diffusive	diffusive	ADJ
ejpam-6176	82	20	and	and	CCONJ
ejpam-6176	82	21	reactive	reactive	ADJ
ejpam-6176	82	22	models	model	NOUN
ejpam-6176	82	23	.	.	PUNCT
ejpam-6176	83	1	as	as	SCONJ
ejpam-6176	83	2	no	no	DET
ejpam-6176	83	3	exact	exact	ADJ
ejpam-6176	83	4	solution	solution	NOUN
ejpam-6176	83	5	exists	exist	VERB
ejpam-6176	83	6	,	,	PUNCT
ejpam-6176	83	7	the	the	DET
ejpam-6176	83	8	pdepe	pdepe	ADJ
ejpam-6176	83	9	output	output	NOUN
ejpam-6176	83	10	serves	serve	VERB
ejpam-6176	83	11	as	as	ADP
ejpam-6176	83	12	the	the	DET
ejpam-6176	83	13	reference	reference	NOUN
ejpam-6176	83	14	.	.	PUNCT
ejpam-6176	84	1	the	the	DET
ejpam-6176	84	2	comparison	comparison	NOUN
ejpam-6176	84	3	indicates	indicate	VERB
ejpam-6176	84	4	that	that	SCONJ
ejpam-6176	84	5	our	our	PRON
ejpam-6176	84	6	proposed	propose	VERB
ejpam-6176	84	7	scheme	scheme	NOUN
ejpam-6176	84	8	achieves	achieve	VERB
ejpam-6176	84	9	higher	high	ADJ
ejpam-6176	84	10	accuracy	accuracy	NOUN
ejpam-6176	84	11	than	than	ADP
ejpam-6176	84	12	the	the	DET
ejpam-6176	84	13	nsfd	nsfd	ADJ
ejpam-6176	84	14	method	method	NOUN
ejpam-6176	84	15	.	.	PUNCT
ejpam-6176	85	1	the	the	DET
ejpam-6176	85	2	remainder	remainder	NOUN
ejpam-6176	85	3	of	of	ADP
ejpam-6176	85	4	the	the	DET
ejpam-6176	85	5	paper	paper	NOUN
ejpam-6176	85	6	is	be	AUX
ejpam-6176	85	7	organized	organize	VERB
ejpam-6176	85	8	as	as	SCONJ
ejpam-6176	85	9	follows	follow	VERB
ejpam-6176	85	10	:	:	PUNCT
ejpam-6176	85	11	section	section	NOUN
ejpam-6176	85	12	2	2	NUM
ejpam-6176	85	13	constructs	construct	VERB
ejpam-6176	85	14	the	the	DET
ejpam-6176	85	15	numerical	numerical	ADJ
ejpam-6176	85	16	scheme	scheme	NOUN
ejpam-6176	85	17	for	for	ADP
ejpam-6176	85	18	stochastic	stochastic	ADJ
ejpam-6176	85	19	differential	differential	ADJ
ejpam-6176	85	20	equations	equation	NOUN
ejpam-6176	85	21	.	.	PUNCT
ejpam-6176	86	1	section	section	NOUN
ejpam-6176	86	2	3	3	NUM
ejpam-6176	86	3	presents	present	VERB
ejpam-6176	86	4	a	a	DET
ejpam-6176	86	5	stability	stability	NOUN
ejpam-6176	86	6	analysis	analysis	NOUN
ejpam-6176	86	7	.	.	PUNCT
ejpam-6176	87	1	section	section	NOUN
ejpam-6176	87	2	4	4	NUM
ejpam-6176	87	3	discusses	discuss	VERB
ejpam-6176	87	4	the	the	DET
ejpam-6176	87	5	stochastic	stochastic	ADJ
ejpam-6176	87	6	siqr	siqr	ADJ
ejpam-6176	87	7	model	model	NOUN
ejpam-6176	87	8	and	and	CCONJ
ejpam-6176	87	9	its	its	PRON
ejpam-6176	87	10	local	local	ADJ
ejpam-6176	87	11	stability	stability	NOUN
ejpam-6176	87	12	.	.	PUNCT
ejpam-6176	88	1	section	section	NOUN
ejpam-6176	88	2	5	5	NUM
ejpam-6176	88	3	provides	provide	VERB
ejpam-6176	88	4	numerical	numerical	ADJ
ejpam-6176	88	5	results	result	NOUN
ejpam-6176	88	6	.	.	PUNCT
ejpam-6176	89	1	section	section	NOUN
ejpam-6176	89	2	6	6	NUM
ejpam-6176	89	3	concludes	conclude	VERB
ejpam-6176	89	4	the	the	DET
ejpam-6176	89	5	paper	paper	NOUN
ejpam-6176	89	6	.	.	PUNCT
ejpam-6176	90	1	2	2	X
ejpam-6176	90	2	.	.	NUM
ejpam-6176	90	3	proposed	propose	VERB
ejpam-6176	90	4	numerical	numerical	PROPN
ejpam-6176	90	5	scheme	scheme	PROPN
ejpam-6176	90	6	the	the	DET
ejpam-6176	90	7	proposed	propose	VERB
ejpam-6176	90	8	scheme	scheme	NOUN
ejpam-6176	90	9	is	be	AUX
ejpam-6176	90	10	explicit	explicit	ADJ
ejpam-6176	90	11	and	and	CCONJ
ejpam-6176	90	12	constructed	construct	VERB
ejpam-6176	90	13	on	on	ADP
ejpam-6176	90	14	two	two	NUM
ejpam-6176	90	15	time	time	NOUN
ejpam-6176	90	16	levels	level	NOUN
ejpam-6176	90	17	.	.	PUNCT
ejpam-6176	91	1	the	the	DET
ejpam-6176	91	2	solution	solution	NOUN
ejpam-6176	91	3	is	be	AUX
ejpam-6176	91	4	found	find	VERB
ejpam-6176	91	5	by	by	ADP
ejpam-6176	91	6	using	use	VERB
ejpam-6176	91	7	a	a	DET
ejpam-6176	91	8	predictor	predictor	NOUN
ejpam-6176	91	9	-	-	PUNCT
ejpam-6176	91	10	corrector	corrector	NOUN
ejpam-6176	91	11	strategy	strategy	NOUN
ejpam-6176	91	12	.	.	PUNCT
ejpam-6176	92	1	the	the	DET
ejpam-6176	92	2	predictor	predictor	NOUN
ejpam-6176	92	3	stage	stage	NOUN
ejpam-6176	92	4	finds	find	VERB
ejpam-6176	92	5	a	a	DET
ejpam-6176	92	6	solution	solution	NOUN
ejpam-6176	92	7	at	at	ADP
ejpam-6176	92	8	an	an	DET
ejpam-6176	92	9	arbitrary	arbitrary	ADJ
ejpam-6176	92	10	time	time	NOUN
ejpam-6176	92	11	level	level	NOUN
ejpam-6176	92	12	,	,	PUNCT
ejpam-6176	92	13	and	and	CCONJ
ejpam-6176	92	14	the	the	DET
ejpam-6176	92	15	solution	solution	NOUN
ejpam-6176	92	16	obtained	obtain	VERB
ejpam-6176	92	17	by	by	ADP
ejpam-6176	92	18	the	the	DET
ejpam-6176	92	19	predictor	predictor	NOUN
ejpam-6176	92	20	is	be	AUX
ejpam-6176	92	21	utilized	utilize	VERB
ejpam-6176	92	22	in	in	ADP
ejpam-6176	92	23	the	the	DET
ejpam-6176	92	24	corrector	corrector	NOUN
ejpam-6176	92	25	stage	stage	NOUN
ejpam-6176	92	26	to	to	PART
ejpam-6176	92	27	find	find	VERB
ejpam-6176	92	28	the	the	DET
ejpam-6176	92	29	solution	solution	NOUN
ejpam-6176	92	30	at	at	ADP
ejpam-6176	92	31	the	the	DET
ejpam-6176	92	32	next	next	ADJ
ejpam-6176	92	33	time	time	NOUN
ejpam-6176	92	34	level	level	NOUN
ejpam-6176	92	35	.	.	PUNCT
ejpam-6176	93	1	the	the	DET
ejpam-6176	93	2	scheme	scheme	NOUN
ejpam-6176	93	3	will	will	AUX
ejpam-6176	93	4	be	be	AUX
ejpam-6176	93	5	proposed	propose	VERB
ejpam-6176	93	6	for	for	ADP
ejpam-6176	93	7	stochastic	stochastic	ADJ
ejpam-6176	93	8	differential	differential	ADJ
ejpam-6176	93	9	equations	equation	NOUN
ejpam-6176	93	10	but	but	CCONJ
ejpam-6176	93	11	is	be	AUX
ejpam-6176	93	12	first	first	ADV
ejpam-6176	93	13	developed	develop	VERB
ejpam-6176	93	14	for	for	ADP
ejpam-6176	93	15	deterministic	deterministic	ADJ
ejpam-6176	93	16	models	model	NOUN
ejpam-6176	93	17	.	.	PUNCT
ejpam-6176	94	1	to	to	PART
ejpam-6176	94	2	propose	propose	VERB
ejpam-6176	94	3	the	the	DET
ejpam-6176	94	4	scheme	scheme	NOUN
ejpam-6176	94	5	,	,	PUNCT
ejpam-6176	94	6	consider	consider	VERB
ejpam-6176	94	7	the	the	DET
ejpam-6176	94	8	differential	differential	ADJ
ejpam-6176	94	9	equation	equation	NOUN
ejpam-6176	94	10	:	:	PUNCT
ejpam-6176	94	11	∂p	∂p	PROPN
ejpam-6176	94	12	∂t	∂t	PROPN
ejpam-6176	94	13	=	=	PUNCT
ejpam-6176	94	14	γ	γ	PROPN
ejpam-6176	94	15	∂2p	∂2p	PROPN
ejpam-6176	94	16	∂x2	∂x2	PROPN
ejpam-6176	94	17	+	+	CCONJ
ejpam-6176	94	18	f(p	f(p	NOUN
ejpam-6176	94	19	)	)	PUNCT
ejpam-6176	94	20	(	(	PUNCT
ejpam-6176	94	21	1	1	X
ejpam-6176	94	22	)	)	PUNCT
ejpam-6176	94	23	where	where	SCONJ
ejpam-6176	94	24	γ	γ	PROPN
ejpam-6176	94	25	is	be	AUX
ejpam-6176	94	26	a	a	DET
ejpam-6176	94	27	constant	constant	ADJ
ejpam-6176	94	28	diffusion	diffusion	NOUN
ejpam-6176	94	29	coefficient	coefficient	NOUN
ejpam-6176	94	30	and	and	CCONJ
ejpam-6176	94	31	f(p	f(p	NOUN
ejpam-6176	94	32	)	)	PUNCT
ejpam-6176	94	33	is	be	AUX
ejpam-6176	94	34	a	a	DET
ejpam-6176	94	35	non	non	ADJ
ejpam-6176	94	36	-	-	ADJ
ejpam-6176	94	37	linear	linear	ADJ
ejpam-6176	94	38	source	source	NOUN
ejpam-6176	94	39	term	term	NOUN
ejpam-6176	94	40	.	.	PUNCT
ejpam-6176	95	1	2.1	2.1	NUM
ejpam-6176	95	2	.	.	PUNCT
ejpam-6176	95	3	predictor	predictor	NOUN
ejpam-6176	95	4	-	-	PUNCT
ejpam-6176	95	5	corrector	corrector	NOUN
ejpam-6176	95	6	framework	framework	NOUN
ejpam-6176	95	7	we	we	PRON
ejpam-6176	95	8	propose	propose	VERB
ejpam-6176	95	9	a	a	DET
ejpam-6176	95	10	two	two	NUM
ejpam-6176	95	11	-	-	PUNCT
ejpam-6176	95	12	stage	stage	NOUN
ejpam-6176	95	13	predictor	predictor	NOUN
ejpam-6176	95	14	-	-	PUNCT
ejpam-6176	95	15	corrector	corrector	NOUN
ejpam-6176	95	16	method	method	NOUN
ejpam-6176	95	17	in	in	ADP
ejpam-6176	95	18	time	time	NOUN
ejpam-6176	95	19	:	:	PUNCT
ejpam-6176	95	20	predictor	predictor	NOUN
ejpam-6176	95	21	stage	stage	NOUN
ejpam-6176	95	22	:	:	PUNCT
ejpam-6176	96	1	p̄n+1	p̄n+1	NOUN
ejpam-6176	96	2	i	i	NOUN
ejpam-6176	96	3	=	=	NOUN
ejpam-6176	96	4	1	1	NUM
ejpam-6176	96	5	2	2	NUM
ejpam-6176	96	6	pn	pn	NOUN
ejpam-6176	96	7	i	i	NOUN
ejpam-6176	96	8	e	e	PROPN
ejpam-6176	96	9	∆t	∆t	PROPN
ejpam-6176	96	10	+	+	CCONJ
ejpam-6176	96	11	1	1	NUM
ejpam-6176	96	12	2	2	NUM
ejpam-6176	96	13	pn	pn	NOUN
ejpam-6176	96	14	i	i	NOUN
ejpam-6176	96	15	e	e	NOUN
ejpam-6176	96	16	5∆t	5∆t	PUNCT
ejpam-6176	97	1	+	+	CCONJ
ejpam-6176	97	2	(	(	PUNCT
ejpam-6176	97	3	e∆t	e∆t	AUX
ejpam-6176	97	4	+	+	CCONJ
ejpam-6176	97	5	e5∆t	e5∆t	VERB
ejpam-6176	97	6	−	−	PROPN
ejpam-6176	97	7	2	2	NUM
ejpam-6176	97	8	)	)	PUNCT
ejpam-6176	97	9	6	6	NUM
ejpam-6176	97	10	(	(	PUNCT
ejpam-6176	97	11	∂p	∂p	PROPN
ejpam-6176	97	12	∂t	∂t	PROPN
ejpam-6176	97	13	∣∣∣∣n	∣∣∣∣n	NOUN
ejpam-6176	98	1	i	i	PRON
ejpam-6176	99	1	−	−	PROPN
ejpam-6176	99	2	3pn	3pn	NOUN
ejpam-6176	100	1	i	i	NOUN
ejpam-6176	100	2	)	)	PUNCT
ejpam-6176	100	3	(	(	PUNCT
ejpam-6176	100	4	2	2	X
ejpam-6176	100	5	)	)	PUNCT
ejpam-6176	100	6	m.	m.	NOUN
ejpam-6176	100	7	s.	s.	PROPN
ejpam-6176	100	8	arif	arif	PROPN
ejpam-6176	100	9	,	,	PUNCT
ejpam-6176	100	10	k.	k.	PROPN
ejpam-6176	100	11	abodayeh	abodayeh	PROPN
ejpam-6176	100	12	,	,	PUNCT
ejpam-6176	100	13	y.	y.	NOUN
ejpam-6176	100	14	nawaz	nawaz	PROPN
ejpam-6176	100	15	/	/	SYM
ejpam-6176	100	16	eur	eur	PROPN
ejpam-6176	100	17	.	.	PUNCT
ejpam-6176	101	1	j.	j.	PROPN
ejpam-6176	101	2	pure	pure	PROPN
ejpam-6176	101	3	appl	appl	PROPN
ejpam-6176	101	4	.	.	PROPN
ejpam-6176	101	5	math	math	PROPN
ejpam-6176	101	6	,	,	PUNCT
ejpam-6176	101	7	18	18	NUM
ejpam-6176	101	8	(	(	PUNCT
ejpam-6176	101	9	3	3	NUM
ejpam-6176	101	10	)	)	PUNCT
ejpam-6176	101	11	(	(	PUNCT
ejpam-6176	101	12	2025	2025	NUM
ejpam-6176	101	13	)	)	PUNCT
ejpam-6176	101	14	,	,	PUNCT
ejpam-6176	101	15	6176	6176	NUM
ejpam-6176	101	16	5	5	NUM
ejpam-6176	101	17	of	of	ADP
ejpam-6176	101	18	21	21	NUM
ejpam-6176	101	19	corrector	corrector	NOUN
ejpam-6176	101	20	stage	stage	NOUN
ejpam-6176	101	21	:	:	PUNCT
ejpam-6176	101	22	pn+1	pn+1	NOUN
ejpam-6176	101	23	i	i	NOUN
ejpam-6176	101	24	=	=	PUNCT
ejpam-6176	101	25	apn	apn	PROPN
ejpam-6176	102	1	i	i	PRON
ejpam-6176	102	2	+	+	CCONJ
ejpam-6176	102	3	bp̄n+1	bp̄n+1	VERB
ejpam-6176	103	1	i	i	PRON
ejpam-6176	104	1	+	+	CCONJ
ejpam-6176	104	2	c(e∆t	c(e∆t	ADJ
ejpam-6176	104	3	−	−	PROPN
ejpam-6176	104	4	1	1	NUM
ejpam-6176	104	5	)	)	PUNCT
ejpam-6176	104	6	(	(	PUNCT
ejpam-6176	104	7	∂p̄	∂p̄	PROPN
ejpam-6176	104	8	∂t	∂t	PROPN
ejpam-6176	104	9	∣∣∣∣n+1	∣∣∣∣n+1	PROPN
ejpam-6176	104	10	i	i	PROPN
ejpam-6176	104	11	)	)	PUNCT
ejpam-6176	104	12	(	(	PUNCT
ejpam-6176	104	13	3	3	X
ejpam-6176	104	14	)	)	PUNCT
ejpam-6176	104	15	here	here	ADV
ejpam-6176	104	16	,	,	PUNCT
ejpam-6176	104	17	a	a	DET
ejpam-6176	104	18	,	,	PUNCT
ejpam-6176	104	19	b	b	NOUN
ejpam-6176	104	20	,	,	PUNCT
ejpam-6176	104	21	and	and	CCONJ
ejpam-6176	104	22	c	c	NOUN
ejpam-6176	104	23	are	be	AUX
ejpam-6176	104	24	parameters	parameter	NOUN
ejpam-6176	104	25	determined	determine	VERB
ejpam-6176	104	26	using	use	VERB
ejpam-6176	104	27	taylor	taylor	PROPN
ejpam-6176	104	28	expansion	expansion	NOUN
ejpam-6176	104	29	for	for	ADP
ejpam-6176	104	30	improved	improved	ADJ
ejpam-6176	104	31	accuracy	accuracy	NOUN
ejpam-6176	104	32	.	.	PUNCT
ejpam-6176	105	1	2.2	2.2	NUM
ejpam-6176	105	2	.	.	PUNCT
ejpam-6176	105	3	determine	determine	VERB
ejpam-6176	105	4	parameters	parameter	NOUN
ejpam-6176	105	5	via	via	ADP
ejpam-6176	105	6	taylor	taylor	PROPN
ejpam-6176	105	7	expansion	expansion	NOUN
ejpam-6176	105	8	we	we	PRON
ejpam-6176	105	9	use	use	VERB
ejpam-6176	105	10	the	the	DET
ejpam-6176	105	11	taylor	taylor	PROPN
ejpam-6176	105	12	series	series	PROPN
ejpam-6176	105	13	expansion	expansion	NOUN
ejpam-6176	105	14	:	:	PUNCT
ejpam-6176	106	1	pn+1	pn+1	NOUN
ejpam-6176	106	2	i	i	PRON
ejpam-6176	107	1	=	=	PUNCT
ejpam-6176	108	1	pn	pn	VERB
ejpam-6176	109	1	i	i	PRON
ejpam-6176	110	1	+	+	PROPN
ejpam-6176	110	2	∆t	∆t	PROPN
ejpam-6176	110	3	∂p	∂p	PROPN
ejpam-6176	110	4	∂t	∂t	PROPN
ejpam-6176	110	5	∣∣∣∣n	∣∣∣∣n	NOUN
ejpam-6176	111	1	i	i	PROPN
ejpam-6176	111	2	+	+	CCONJ
ejpam-6176	111	3	∆t2	∆t2	VERB
ejpam-6176	111	4	2	2	NUM
ejpam-6176	111	5	∂2p	∂2p	NOUN
ejpam-6176	111	6	∂t2	∂t2	NOUN
ejpam-6176	111	7	∣∣∣∣n	∣∣∣∣n	NOUN
ejpam-6176	111	8	i	i	PRON
ejpam-6176	111	9	+	+	NOUN
ejpam-6176	111	10	o(∆t3	o(∆t3	NOUN
ejpam-6176	111	11	)	)	PUNCT
ejpam-6176	111	12	(	(	PUNCT
ejpam-6176	111	13	4	4	X
ejpam-6176	111	14	)	)	PUNCT
ejpam-6176	111	15	substitute	substitute	PROPN
ejpam-6176	111	16	eqs	eqs	PROPN
ejpam-6176	111	17	.	.	PUNCT
ejpam-6176	112	1	(	(	PUNCT
ejpam-6176	112	2	2	2	NUM
ejpam-6176	112	3	)	)	PUNCT
ejpam-6176	112	4	and	and	CCONJ
ejpam-6176	112	5	(	(	PUNCT
ejpam-6176	112	6	4	4	NUM
ejpam-6176	112	7	)	)	PUNCT
ejpam-6176	112	8	into	into	ADP
ejpam-6176	112	9	(	(	PUNCT
ejpam-6176	112	10	3	3	X
ejpam-6176	112	11	)	)	PUNCT
ejpam-6176	112	12	to	to	PART
ejpam-6176	112	13	match	match	VERB
ejpam-6176	112	14	terms	term	NOUN
ejpam-6176	112	15	.	.	PUNCT
ejpam-6176	113	1	this	this	PRON
ejpam-6176	113	2	leads	lead	VERB
ejpam-6176	113	3	to	to	ADP
ejpam-6176	113	4	the	the	DET
ejpam-6176	113	5	following	follow	VERB
ejpam-6176	113	6	system	system	NOUN
ejpam-6176	113	7	of	of	ADP
ejpam-6176	113	8	equations:	equations:	PROPN
ejpam-6176	113	9	1	1	NUM
ejpam-6176	113	10	=	=	SYM
ejpam-6176	113	11	a+	a+	PUNCT
ejpam-6176	113	12	b	b	X
ejpam-6176	113	13	(	(	PUNCT
ejpam-6176	113	14	1	1	NUM
ejpam-6176	113	15	2	2	NUM
ejpam-6176	113	16	e∆t	e∆t	NOUN
ejpam-6176	113	17	+	+	CCONJ
ejpam-6176	113	18	1	1	NUM
ejpam-6176	113	19	2	2	NUM
ejpam-6176	113	20	e5∆t	e5∆t	NOUN
ejpam-6176	113	21	−	−	NOUN
ejpam-6176	113	22	(	(	PUNCT
ejpam-6176	113	23	e∆t	e∆t	NOUN
ejpam-6176	113	24	+	+	CCONJ
ejpam-6176	113	25	e5∆t	e5∆t	VERB
ejpam-6176	113	26	−	−	PROPN
ejpam-6176	113	27	2	2	NUM
ejpam-6176	113	28	)	)	SYM
ejpam-6176	113	29	2	2	NUM
ejpam-6176	113	30	)	)	PUNCT
ejpam-6176	113	31	∆t	∆t	PROPN
ejpam-6176	114	1	=	=	SYM
ejpam-6176	114	2	b	b	PROPN
ejpam-6176	114	3	·	·	PUNCT
ejpam-6176	114	4	(	(	PUNCT
ejpam-6176	114	5	e	e	NOUN
ejpam-6176	114	6	∆t	∆t	PROPN
ejpam-6176	114	7	+	+	CCONJ
ejpam-6176	114	8	e5∆t	e5∆t	VERB
ejpam-6176	114	9	−	−	PROPN
ejpam-6176	114	10	2	2	NUM
ejpam-6176	114	11	)	)	PUNCT
ejpam-6176	114	12	6	6	NUM
ejpam-6176	114	13	+	+	CCONJ
ejpam-6176	114	14	c(e∆t	c(e∆t	ADJ
ejpam-6176	114	15	−	−	NOUN
ejpam-6176	114	16	1	1	NUM
ejpam-6176	114	17	)	)	PUNCT
ejpam-6176	114	18	(	(	PUNCT
ejpam-6176	114	19	1	1	NUM
ejpam-6176	114	20	2	2	NUM
ejpam-6176	114	21	e∆t	e∆t	NOUN
ejpam-6176	114	22	+	+	CCONJ
ejpam-6176	114	23	1	1	NUM
ejpam-6176	114	24	2	2	NUM
ejpam-6176	114	25	e5∆t	e5∆t	NOUN
ejpam-6176	114	26	−	−	NOUN
ejpam-6176	114	27	(	(	PUNCT
ejpam-6176	114	28	e∆t	e∆t	NOUN
ejpam-6176	114	29	+	+	CCONJ
ejpam-6176	114	30	e5∆t	e5∆t	VERB
ejpam-6176	114	31	−	−	PROPN
ejpam-6176	114	32	2	2	NUM
ejpam-6176	114	33	)	)	PUNCT
ejpam-6176	114	34	2	2	NUM
ejpam-6176	114	35	)	)	PUNCT
ejpam-6176	114	36	∆t2	∆t2	VERB
ejpam-6176	114	37	2	2	NUM
ejpam-6176	114	38	=	=	SYM
ejpam-6176	114	39	c(e∆t	c(e∆t	NOUN
ejpam-6176	114	40	−	−	NOUN
ejpam-6176	114	41	1	1	NUM
ejpam-6176	114	42	)	)	PUNCT
ejpam-6176	114	43	·	·	PUNCT
ejpam-6176	115	1	(	(	PUNCT
ejpam-6176	115	2	e	e	X
ejpam-6176	115	3	∆t	∆t	PROPN
ejpam-6176	115	4	+	+	CCONJ
ejpam-6176	115	5	e5∆t	e5∆t	VERB
ejpam-6176	115	6	−	−	PROPN
ejpam-6176	115	7	2	2	NUM
ejpam-6176	115	8	)	)	PUNCT
ejpam-6176	115	9	6	6	NUM
ejpam-6176	115	10	solving	solve	VERB
ejpam-6176	115	11	the	the	DET
ejpam-6176	115	12	system	system	NOUN
ejpam-6176	115	13	yields	yield	VERB
ejpam-6176	115	14	the	the	DET
ejpam-6176	115	15	values	value	NOUN
ejpam-6176	115	16	of	of	ADP
ejpam-6176	115	17	a	a	DET
ejpam-6176	115	18	,	,	PUNCT
ejpam-6176	115	19	b	b	NOUN
ejpam-6176	115	20	,	,	PUNCT
ejpam-6176	115	21	and	and	CCONJ
ejpam-6176	115	22	c.	c.	PROPN
ejpam-6176	115	23	2.3	2.3	NUM
ejpam-6176	115	24	.	.	PUNCT
ejpam-6176	116	1	final	final	ADJ
ejpam-6176	116	2	deterministic	deterministic	ADJ
ejpam-6176	116	3	scheme	scheme	NOUN
ejpam-6176	116	4	after	after	ADP
ejpam-6176	116	5	computing	compute	VERB
ejpam-6176	116	6	a	a	DET
ejpam-6176	116	7	,	,	PUNCT
ejpam-6176	116	8	b	b	NOUN
ejpam-6176	116	9	,	,	PUNCT
ejpam-6176	116	10	and	and	CCONJ
ejpam-6176	116	11	c	c	X
ejpam-6176	116	12	,	,	PUNCT
ejpam-6176	116	13	the	the	DET
ejpam-6176	116	14	deterministic	deterministic	ADJ
ejpam-6176	116	15	scheme	scheme	NOUN
ejpam-6176	116	16	becomes	become	VERB
ejpam-6176	116	17	:	:	PUNCT
ejpam-6176	116	18	final	final	ADJ
ejpam-6176	116	19	predictor	predictor	NOUN
ejpam-6176	116	20	:	:	PUNCT
ejpam-6176	117	1	p̄n+1	p̄n+1	NOUN
ejpam-6176	117	2	i	i	NOUN
ejpam-6176	117	3	=	=	NOUN
ejpam-6176	117	4	1	1	NUM
ejpam-6176	117	5	2	2	NUM
ejpam-6176	117	6	pn	pn	NOUN
ejpam-6176	117	7	i	i	NOUN
ejpam-6176	117	8	e	e	PROPN
ejpam-6176	117	9	∆t	∆t	PROPN
ejpam-6176	117	10	+	+	CCONJ
ejpam-6176	117	11	1	1	NUM
ejpam-6176	117	12	2	2	NUM
ejpam-6176	117	13	pn	pn	NOUN
ejpam-6176	117	14	i	i	NOUN
ejpam-6176	117	15	e	e	NOUN
ejpam-6176	117	16	5∆t	5∆t	PUNCT
ejpam-6176	118	1	+	+	CCONJ
ejpam-6176	118	2	(	(	PUNCT
ejpam-6176	118	3	e∆t	e∆t	AUX
ejpam-6176	118	4	+	+	CCONJ
ejpam-6176	118	5	e5∆t	e5∆t	VERB
ejpam-6176	118	6	−	−	PROPN
ejpam-6176	118	7	2	2	NUM
ejpam-6176	118	8	)	)	PUNCT
ejpam-6176	118	9	6	6	NUM
ejpam-6176	118	10	(	(	PUNCT
ejpam-6176	118	11	γ	γ	PROPN
ejpam-6176	118	12	∂2p	∂2p	PROPN
ejpam-6176	118	13	∂x2	∂x2	NOUN
ejpam-6176	118	14	∣∣∣∣n	∣∣∣∣n	NOUN
ejpam-6176	119	1	i	i	PRON
ejpam-6176	119	2	+	+	CCONJ
ejpam-6176	119	3	f(pn	f(pn	PROPN
ejpam-6176	119	4	i	i	NOUN
ejpam-6176	119	5	)	)	PUNCT
ejpam-6176	119	6	−	−	PROPN
ejpam-6176	119	7	3pn	3pn	NOUN
ejpam-6176	120	1	i	i	NOUN
ejpam-6176	120	2	)	)	PUNCT
ejpam-6176	120	3	(	(	PUNCT
ejpam-6176	120	4	5	5	X
ejpam-6176	120	5	)	)	PUNCT
ejpam-6176	120	6	final	final	ADJ
ejpam-6176	120	7	corrector	corrector	NOUN
ejpam-6176	120	8	:	:	PUNCT
ejpam-6176	120	9	pn+1	pn+1	NOUN
ejpam-6176	120	10	i	i	NOUN
ejpam-6176	120	11	=	=	PUNCT
ejpam-6176	120	12	apn	apn	PROPN
ejpam-6176	121	1	i	i	PRON
ejpam-6176	121	2	+	+	CCONJ
ejpam-6176	121	3	bp̄n+1	bp̄n+1	VERB
ejpam-6176	122	1	i	i	PRON
ejpam-6176	123	1	+	+	CCONJ
ejpam-6176	123	2	c(e∆t	c(e∆t	ADJ
ejpam-6176	123	3	−	−	PROPN
ejpam-6176	123	4	1	1	NUM
ejpam-6176	123	5	)	)	PUNCT
ejpam-6176	123	6	(	(	PUNCT
ejpam-6176	123	7	γ	γ	X
ejpam-6176	123	8	∂2p̄	∂2p̄	ADJ
ejpam-6176	123	9	∂x2	∂x2	NOUN
ejpam-6176	123	10	∣∣∣∣n+1	∣∣∣∣n+1	NOUN
ejpam-6176	124	1	i	i	PRON
ejpam-6176	124	2	+	+	CCONJ
ejpam-6176	124	3	f(p̄n+1	f(p̄n+1	VERB
ejpam-6176	124	4	i	i	PROPN
ejpam-6176	124	5	)	)	PUNCT
ejpam-6176	124	6	)	)	PUNCT
ejpam-6176	125	1	(	(	PUNCT
ejpam-6176	125	2	6	6	NUM
ejpam-6176	125	3	)	)	PUNCT
ejpam-6176	125	4	2.4	2.4	NUM
ejpam-6176	125	5	.	.	PUNCT
ejpam-6176	126	1	space	space	NOUN
ejpam-6176	126	2	discretization	discretization	NOUN
ejpam-6176	126	3	using	use	VERB
ejpam-6176	126	4	compact	compact	ADJ
ejpam-6176	126	5	scheme	scheme	NOUN
ejpam-6176	126	6	the	the	DET
ejpam-6176	126	7	above	above	ADJ
ejpam-6176	126	8	scheme	scheme	NOUN
ejpam-6176	126	9	discretizes	discretize	NOUN
ejpam-6176	126	10	only	only	ADV
ejpam-6176	126	11	in	in	ADP
ejpam-6176	126	12	time	time	NOUN
ejpam-6176	126	13	.	.	PUNCT
ejpam-6176	127	1	for	for	ADP
ejpam-6176	127	2	spatial	spatial	ADJ
ejpam-6176	127	3	discretization	discretization	NOUN
ejpam-6176	127	4	,	,	PUNCT
ejpam-6176	127	5	we	we	PRON
ejpam-6176	127	6	apply	apply	VERB
ejpam-6176	127	7	a	a	DET
ejpam-6176	127	8	compact	compact	ADJ
ejpam-6176	127	9	finite	finite	ADJ
ejpam-6176	127	10	difference	difference	NOUN
ejpam-6176	127	11	scheme	scheme	NOUN
ejpam-6176	127	12	:	:	PUNCT
ejpam-6176	127	13	m.	m.	PROPN
ejpam-6176	127	14	s.	s.	PROPN
ejpam-6176	127	15	arif	arif	PROPN
ejpam-6176	127	16	,	,	PUNCT
ejpam-6176	127	17	k.	k.	PROPN
ejpam-6176	127	18	abodayeh	abodayeh	PROPN
ejpam-6176	127	19	,	,	PUNCT
ejpam-6176	127	20	y.	y.	NOUN
ejpam-6176	127	21	nawaz	nawaz	PROPN
ejpam-6176	127	22	/	/	SYM
ejpam-6176	127	23	eur	eur	PROPN
ejpam-6176	127	24	.	.	PUNCT
ejpam-6176	128	1	j.	j.	PROPN
ejpam-6176	128	2	pure	pure	PROPN
ejpam-6176	128	3	appl	appl	PROPN
ejpam-6176	128	4	.	.	PROPN
ejpam-6176	128	5	math	math	PROPN
ejpam-6176	128	6	,	,	PUNCT
ejpam-6176	128	7	18	18	NUM
ejpam-6176	128	8	(	(	PUNCT
ejpam-6176	128	9	3	3	NUM
ejpam-6176	128	10	)	)	PUNCT
ejpam-6176	128	11	(	(	PUNCT
ejpam-6176	128	12	2025	2025	NUM
ejpam-6176	128	13	)	)	PUNCT
ejpam-6176	128	14	,	,	PUNCT
ejpam-6176	128	15	6176	6176	NUM
ejpam-6176	128	16	6	6	NUM
ejpam-6176	128	17	of	of	ADP
ejpam-6176	128	18	21	21	NUM
ejpam-6176	128	19	predictor	predictor	NOUN
ejpam-6176	128	20	with	with	ADP
ejpam-6176	128	21	space	space	NOUN
ejpam-6176	128	22	discretization	discretization	NOUN
ejpam-6176	128	23	:	:	PUNCT
ejpam-6176	128	24	p̄n+1	p̄n+1	NOUN
ejpam-6176	129	1	i	i	NOUN
ejpam-6176	129	2	=	=	NOUN
ejpam-6176	129	3	1	1	NUM
ejpam-6176	129	4	2	2	NUM
ejpam-6176	129	5	pn	pn	NOUN
ejpam-6176	129	6	i	i	NOUN
ejpam-6176	129	7	e	e	PROPN
ejpam-6176	129	8	∆t	∆t	PROPN
ejpam-6176	130	1	+	+	CCONJ
ejpam-6176	130	2	1	1	NUM
ejpam-6176	130	3	2	2	NUM
ejpam-6176	130	4	pn	pn	NOUN
ejpam-6176	130	5	i	i	NOUN
ejpam-6176	130	6	e	e	NOUN
ejpam-6176	130	7	5∆t	5∆t	PUNCT
ejpam-6176	131	1	+	+	CCONJ
ejpam-6176	131	2	(	(	PUNCT
ejpam-6176	131	3	e∆t	e∆t	AUX
ejpam-6176	131	4	+	+	CCONJ
ejpam-6176	131	5	e5∆t	e5∆t	VERB
ejpam-6176	131	6	−	−	PROPN
ejpam-6176	131	7	2	2	NUM
ejpam-6176	131	8	)	)	PUNCT
ejpam-6176	131	9	6	6	NUM
ejpam-6176	131	10	(	(	PUNCT
ejpam-6176	131	11	γa−1bpn	γa−1bpn	VERB
ejpam-6176	131	12	i	i	PRON
ejpam-6176	131	13	+	+	CCONJ
ejpam-6176	131	14	f(pn	f(pn	PROPN
ejpam-6176	131	15	i	i	NOUN
ejpam-6176	131	16	)	)	PUNCT
ejpam-6176	131	17	−	−	PROPN
ejpam-6176	131	18	3pn	3pn	NOUN
ejpam-6176	132	1	i	i	NOUN
ejpam-6176	132	2	)	)	PUNCT
ejpam-6176	132	3	(	(	PUNCT
ejpam-6176	132	4	7	7	X
ejpam-6176	132	5	)	)	PUNCT
ejpam-6176	132	6	corrector	corrector	NOUN
ejpam-6176	132	7	with	with	ADP
ejpam-6176	132	8	space	space	NOUN
ejpam-6176	132	9	discretization	discretization	NOUN
ejpam-6176	132	10	:	:	PUNCT
ejpam-6176	132	11	pn+1	pn+1	NOUN
ejpam-6176	132	12	i	i	NOUN
ejpam-6176	132	13	=	=	PUNCT
ejpam-6176	132	14	apn	apn	PROPN
ejpam-6176	133	1	i	i	PRON
ejpam-6176	133	2	+	+	CCONJ
ejpam-6176	133	3	bp̄n+1	bp̄n+1	VERB
ejpam-6176	134	1	i	i	PRON
ejpam-6176	135	1	+	+	CCONJ
ejpam-6176	135	2	c(e∆t	c(e∆t	ADJ
ejpam-6176	135	3	−	−	PROPN
ejpam-6176	135	4	1	1	NUM
ejpam-6176	135	5	)	)	PUNCT
ejpam-6176	135	6	(	(	PUNCT
ejpam-6176	135	7	γa−1bp̄n	γa−1bp̄n	NOUN
ejpam-6176	136	1	i	i	PRON
ejpam-6176	136	2	+	+	NUM
ejpam-6176	136	3	f(p̄n+1	f(p̄n+1	VERB
ejpam-6176	136	4	i	i	PROPN
ejpam-6176	136	5	)	)	PUNCT
ejpam-6176	136	6	)	)	PUNCT
ejpam-6176	137	1	(	(	PUNCT
ejpam-6176	137	2	8)	8)	NUM
ejpam-6176	137	3	here	here	ADV
ejpam-6176	137	4	,	,	PUNCT
ejpam-6176	137	5	a	a	DET
ejpam-6176	137	6	and	and	CCONJ
ejpam-6176	137	7	b	b	NOUN
ejpam-6176	137	8	are	be	AUX
ejpam-6176	137	9	matrices	matrix	NOUN
ejpam-6176	137	10	defined	define	VERB
ejpam-6176	137	11	from	from	ADP
ejpam-6176	137	12	the	the	DET
ejpam-6176	137	13	following	follow	VERB
ejpam-6176	137	14	compact	compact	ADJ
ejpam-6176	137	15	scheme	scheme	NOUN
ejpam-6176	137	16	:	:	PUNCT
ejpam-6176	137	17	α1p	α1p	NOUN
ejpam-6176	137	18	′′	′′	PROPN
ejpam-6176	137	19	i−1	i−1	PROPN
ejpam-6176	137	20	+	+	CCONJ
ejpam-6176	137	21	p	p	PROPN
ejpam-6176	137	22	′′	′′	PROPN
ejpam-6176	138	1	i	i	PRON
ejpam-6176	138	2	+	+	CCONJ
ejpam-6176	138	3	α1p	α1p	PROPN
ejpam-6176	138	4	′′	′′	PROPN
ejpam-6176	138	5	i+1	i+1	NOUN
ejpam-6176	138	6	=	=	NOUN
ejpam-6176	138	7	b0	b0	VERB
ejpam-6176	138	8	pn	pn	PROPN
ejpam-6176	138	9	i+1	i+1	ADV
ejpam-6176	138	10	−	−	PROPN
ejpam-6176	138	11	2pn	2pn	NOUN
ejpam-6176	139	1	i	i	PRON
ejpam-6176	139	2	+	+	CCONJ
ejpam-6176	139	3	pn	pn	PROPN
ejpam-6176	139	4	i−1	i−1	PROPN
ejpam-6176	139	5	∆x2	∆x2	PROPN
ejpam-6176	139	6	+	+	CCONJ
ejpam-6176	139	7	b1	b1	PROPN
ejpam-6176	139	8	pn	pn	PROPN
ejpam-6176	139	9	i+2	i+2	INTJ
ejpam-6176	140	1	−	−	PROPN
ejpam-6176	140	2	2pn	2pn	NOUN
ejpam-6176	140	3	i	i	PRON
ejpam-6176	141	1	+	+	CCONJ
ejpam-6176	141	2	pn	pn	PROPN
ejpam-6176	141	3	i−2	i−2	VERB
ejpam-6176	141	4	4∆x2	4∆x2	NUM
ejpam-6176	141	5	(	(	PUNCT
ejpam-6176	141	6	9	9	NUM
ejpam-6176	141	7	)	)	PUNCT
ejpam-6176	141	8	with	with	ADP
ejpam-6176	141	9	b0	b0	NOUN
ejpam-6176	141	10	=	=	SYM
ejpam-6176	141	11	4	4	NUM
ejpam-6176	141	12	3	3	NUM
ejpam-6176	141	13	(	(	PUNCT
ejpam-6176	141	14	1−	1−	NUM
ejpam-6176	141	15	α1	α1	PROPN
ejpam-6176	141	16	)	)	PUNCT
ejpam-6176	141	17	,	,	PUNCT
ejpam-6176	141	18	b1	b1	NOUN
ejpam-6176	141	19	=	=	SYM
ejpam-6176	141	20	1	1	NUM
ejpam-6176	141	21	3	3	NUM
ejpam-6176	141	22	(	(	PUNCT
ejpam-6176	141	23	10α1	10α1	NUM
ejpam-6176	141	24	−	−	NOUN
ejpam-6176	141	25	1	1	NUM
ejpam-6176	141	26	)	)	PUNCT
ejpam-6176	141	27	2.5	2.5	NUM
ejpam-6176	141	28	.	.	PUNCT
ejpam-6176	142	1	extension	extension	NOUN
ejpam-6176	142	2	to	to	ADP
ejpam-6176	142	3	stochastic	stochastic	ADJ
ejpam-6176	142	4	model	model	NOUN
ejpam-6176	142	5	now	now	ADV
ejpam-6176	142	6	we	we	PRON
ejpam-6176	142	7	extend	extend	VERB
ejpam-6176	142	8	the	the	DET
ejpam-6176	142	9	scheme	scheme	NOUN
ejpam-6176	142	10	to	to	ADP
ejpam-6176	142	11	the	the	DET
ejpam-6176	142	12	stochastic	stochastic	ADJ
ejpam-6176	142	13	differential	differential	ADJ
ejpam-6176	142	14	equation	equation	NOUN
ejpam-6176	142	15	:	:	PUNCT
ejpam-6176	142	16	∂p	∂p	NOUN
ejpam-6176	142	17	=	=	PUNCT
ejpam-6176	142	18	(	(	PUNCT
ejpam-6176	142	19	γ	γ	X
ejpam-6176	142	20	∂2p	∂2p	PROPN
ejpam-6176	142	21	∂x2	∂x2	PROPN
ejpam-6176	142	22	+	+	CCONJ
ejpam-6176	142	23	f(p	f(p	NOUN
ejpam-6176	142	24	)	)	PUNCT
ejpam-6176	142	25	)	)	PUNCT
ejpam-6176	143	1	dt+	dt+	NOUN
ejpam-6176	143	2	σ1pdw	σ1pdw	VERB
ejpam-6176	143	3	(	(	PUNCT
ejpam-6176	143	4	10	10	NUM
ejpam-6176	143	5	)	)	PUNCT
ejpam-6176	143	6	where	where	SCONJ
ejpam-6176	143	7	w	w	NOUN
ejpam-6176	143	8	is	be	AUX
ejpam-6176	143	9	a	a	DET
ejpam-6176	143	10	wiener	wiener	NOUN
ejpam-6176	143	11	process	process	NOUN
ejpam-6176	143	12	and	and	CCONJ
ejpam-6176	143	13	σ1	σ1	PROPN
ejpam-6176	143	14	is	be	AUX
ejpam-6176	143	15	the	the	DET
ejpam-6176	143	16	noise	noise	NOUN
ejpam-6176	143	17	intensity	intensity	NOUN
ejpam-6176	143	18	.	.	PUNCT
ejpam-6176	144	1	the	the	DET
ejpam-6176	144	2	predictor	predictor	NOUN
ejpam-6176	144	3	stage	stage	NOUN
ejpam-6176	144	4	remains	remain	VERB
ejpam-6176	144	5	the	the	DET
ejpam-6176	144	6	same	same	ADJ
ejpam-6176	144	7	as	as	ADP
ejpam-6176	144	8	in	in	ADP
ejpam-6176	144	9	the	the	DET
ejpam-6176	144	10	deterministic	deterministic	ADJ
ejpam-6176	144	11	case	case	NOUN
ejpam-6176	144	12	.	.	PUNCT
ejpam-6176	145	1	the	the	DET
ejpam-6176	145	2	corrector	corrector	NOUN
ejpam-6176	145	3	stage	stage	NOUN
ejpam-6176	145	4	becomes	become	VERB
ejpam-6176	145	5	:	:	PUNCT
ejpam-6176	145	6	stochastic	stochastic	ADJ
ejpam-6176	145	7	corrector	corrector	NOUN
ejpam-6176	145	8	:	:	PUNCT
ejpam-6176	145	9	pn+1	pn+1	PROPN
ejpam-6176	145	10	i	i	NOUN
ejpam-6176	145	11	=	=	PUNCT
ejpam-6176	145	12	apn	apn	PROPN
ejpam-6176	146	1	i	i	PRON
ejpam-6176	146	2	+	+	CCONJ
ejpam-6176	146	3	bp̄n+1	bp̄n+1	VERB
ejpam-6176	147	1	i	i	PRON
ejpam-6176	148	1	+	+	CCONJ
ejpam-6176	148	2	c(e∆t	c(e∆t	ADJ
ejpam-6176	148	3	−	−	PROPN
ejpam-6176	148	4	1	1	NUM
ejpam-6176	148	5	)	)	PUNCT
ejpam-6176	148	6	(	(	PUNCT
ejpam-6176	148	7	γa−1bp̄n+1	γa−1bp̄n+1	VERB
ejpam-6176	148	8	i	i	PRON
ejpam-6176	148	9	+	+	CCONJ
ejpam-6176	148	10	f(p̄n+1	f(p̄n+1	VERB
ejpam-6176	148	11	i	i	PROPN
ejpam-6176	148	12	)	)	PUNCT
ejpam-6176	148	13	)	)	PUNCT
ejpam-6176	149	1	+	+	CCONJ
ejpam-6176	149	2	σ1p	σ1p	VERB
ejpam-6176	149	3	n	n	VERB
ejpam-6176	149	4	i	i	PRON
ejpam-6176	149	5	∆w	∆w	PROPN
ejpam-6176	149	6	(	(	PUNCT
ejpam-6176	149	7	11	11	NUM
ejpam-6176	149	8	)	)	PUNCT
ejpam-6176	149	9	where	where	SCONJ
ejpam-6176	149	10	∆w	∆w	PROPN
ejpam-6176	149	11	∼	∼	NOUN
ejpam-6176	149	12	n	n	CCONJ
ejpam-6176	149	13	(	(	PUNCT
ejpam-6176	149	14	0,∆t	0,∆t	NOUN
ejpam-6176	149	15	)	)	PUNCT
ejpam-6176	149	16	is	be	AUX
ejpam-6176	149	17	sampled	sample	VERB
ejpam-6176	149	18	from	from	ADP
ejpam-6176	149	19	a	a	DET
ejpam-6176	149	20	normal	normal	ADJ
ejpam-6176	149	21	distribution	distribution	NOUN
ejpam-6176	149	22	.	.	PUNCT
ejpam-6176	150	1	summary	summary	NOUN
ejpam-6176	150	2	:	:	PUNCT
ejpam-6176	150	3	our	our	PRON
ejpam-6176	150	4	scheme	scheme	NOUN
ejpam-6176	150	5	is	be	AUX
ejpam-6176	150	6	explicit	explicit	ADJ
ejpam-6176	150	7	and	and	CCONJ
ejpam-6176	150	8	predictor	predictor	NOUN
ejpam-6176	150	9	-	-	PUNCT
ejpam-6176	150	10	corrector	corrector	NOUN
ejpam-6176	150	11	-	-	PUNCT
ejpam-6176	150	12	based	base	VERB
ejpam-6176	150	13	.	.	PUNCT
ejpam-6176	151	1	it	it	PRON
ejpam-6176	151	2	handles	handle	VERB
ejpam-6176	151	3	nonlinearity	nonlinearity	NOUN
ejpam-6176	151	4	and	and	CCONJ
ejpam-6176	151	5	diffusion	diffusion	NOUN
ejpam-6176	151	6	using	use	VERB
ejpam-6176	151	7	exponential	exponential	ADJ
ejpam-6176	151	8	weights	weight	NOUN
ejpam-6176	151	9	and	and	CCONJ
ejpam-6176	151	10	accurate	accurate	ADJ
ejpam-6176	151	11	coefficient	coefficient	NOUN
ejpam-6176	151	12	matching	matching	NOUN
ejpam-6176	151	13	.	.	PUNCT
ejpam-6176	152	1	it	it	PRON
ejpam-6176	152	2	is	be	AUX
ejpam-6176	152	3	constructed	construct	VERB
ejpam-6176	152	4	first	first	ADV
ejpam-6176	152	5	for	for	ADP
ejpam-6176	152	6	the	the	DET
ejpam-6176	152	7	deterministic	deterministic	ADJ
ejpam-6176	152	8	model	model	NOUN
ejpam-6176	152	9	and	and	CCONJ
ejpam-6176	152	10	then	then	ADV
ejpam-6176	152	11	extended	extend	VERB
ejpam-6176	152	12	to	to	ADP
ejpam-6176	152	13	the	the	DET
ejpam-6176	152	14	stochastic	stochastic	ADJ
ejpam-6176	152	15	model	model	NOUN
ejpam-6176	152	16	by	by	ADP
ejpam-6176	152	17	adding	add	VERB
ejpam-6176	152	18	the	the	DET
ejpam-6176	152	19	noise	noise	NOUN
ejpam-6176	152	20	term	term	NOUN
ejpam-6176	152	21	in	in	ADP
ejpam-6176	152	22	the	the	DET
ejpam-6176	152	23	corrector	corrector	NOUN
ejpam-6176	152	24	stage	stage	NOUN
ejpam-6176	152	25	.	.	PUNCT
ejpam-6176	153	1	spatial	spatial	ADJ
ejpam-6176	153	2	terms	term	NOUN
ejpam-6176	153	3	are	be	AUX
ejpam-6176	153	4	discretized	discretize	VERB
ejpam-6176	153	5	using	use	VERB
ejpam-6176	153	6	a	a	DET
ejpam-6176	153	7	compact	compact	ADJ
ejpam-6176	153	8	finite	finite	ADJ
ejpam-6176	153	9	difference	difference	NOUN
ejpam-6176	153	10	scheme	scheme	NOUN
ejpam-6176	153	11	,	,	PUNCT
ejpam-6176	153	12	increasing	increase	VERB
ejpam-6176	153	13	accuracy	accuracy	NOUN
ejpam-6176	153	14	without	without	ADP
ejpam-6176	153	15	requiring	require	VERB
ejpam-6176	153	16	a	a	DET
ejpam-6176	153	17	fine	fine	ADJ
ejpam-6176	153	18	mesh	mesh	NOUN
ejpam-6176	153	19	and	and	CCONJ
ejpam-6176	153	20	thus	thus	ADV
ejpam-6176	153	21	improving	improve	VERB
ejpam-6176	153	22	computational	computational	ADJ
ejpam-6176	153	23	performance	performance	NOUN
ejpam-6176	153	24	.	.	PUNCT
ejpam-6176	154	1	m.	m.	PROPN
ejpam-6176	154	2	s.	s.	PROPN
ejpam-6176	154	3	arif	arif	PROPN
ejpam-6176	154	4	,	,	PUNCT
ejpam-6176	154	5	k.	k.	PROPN
ejpam-6176	154	6	abodayeh	abodayeh	PROPN
ejpam-6176	154	7	,	,	PUNCT
ejpam-6176	154	8	y.	y.	NOUN
ejpam-6176	154	9	nawaz	nawaz	PROPN
ejpam-6176	154	10	/	/	SYM
ejpam-6176	154	11	eur	eur	PROPN
ejpam-6176	154	12	.	.	PUNCT
ejpam-6176	155	1	j.	j.	PROPN
ejpam-6176	155	2	pure	pure	PROPN
ejpam-6176	155	3	appl	appl	PROPN
ejpam-6176	155	4	.	.	PROPN
ejpam-6176	155	5	math	math	PROPN
ejpam-6176	155	6	,	,	PUNCT
ejpam-6176	155	7	18	18	NUM
ejpam-6176	155	8	(	(	PUNCT
ejpam-6176	155	9	3	3	NUM
ejpam-6176	155	10	)	)	PUNCT
ejpam-6176	155	11	(	(	PUNCT
ejpam-6176	155	12	2025	2025	NUM
ejpam-6176	155	13	)	)	PUNCT
ejpam-6176	155	14	,	,	PUNCT
ejpam-6176	155	15	6176	6176	NUM
ejpam-6176	155	16	7	7	NUM
ejpam-6176	155	17	of	of	ADP
ejpam-6176	155	18	21	21	NUM
ejpam-6176	155	19	3	3	NUM
ejpam-6176	155	20	.	.	PUNCT
ejpam-6176	156	1	stability	stability	NOUN
ejpam-6176	156	2	analysis	analysis	NOUN
ejpam-6176	156	3	von	von	PROPN
ejpam-6176	156	4	neumann	neumann	PROPN
ejpam-6176	156	5	analysis	analysis	NOUN
ejpam-6176	156	6	is	be	AUX
ejpam-6176	156	7	one	one	NUM
ejpam-6176	156	8	of	of	ADP
ejpam-6176	156	9	the	the	DET
ejpam-6176	156	10	classical	classical	ADJ
ejpam-6176	156	11	techniques	technique	NOUN
ejpam-6176	156	12	for	for	ADP
ejpam-6176	156	13	determining	determine	VERB
ejpam-6176	156	14	the	the	DET
ejpam-6176	156	15	stability	stability	NOUN
ejpam-6176	156	16	conditions	condition	NOUN
ejpam-6176	156	17	of	of	ADP
ejpam-6176	156	18	finite	finite	ADJ
ejpam-6176	156	19	difference	difference	NOUN
ejpam-6176	156	20	schemes	scheme	NOUN
ejpam-6176	156	21	applied	apply	VERB
ejpam-6176	156	22	to	to	ADP
ejpam-6176	156	23	linear	linear	VERB
ejpam-6176	156	24	partial	partial	ADJ
ejpam-6176	156	25	differential	differential	NOUN
ejpam-6176	156	26	equations	equation	NOUN
ejpam-6176	156	27	.	.	PUNCT
ejpam-6176	157	1	this	this	DET
ejpam-6176	157	2	criterion	criterion	NOUN
ejpam-6176	157	3	,	,	PUNCT
ejpam-6176	157	4	based	base	VERB
ejpam-6176	157	5	on	on	ADP
ejpam-6176	157	6	fourier	fourier	ADJ
ejpam-6176	157	7	series	series	NOUN
ejpam-6176	157	8	,	,	PUNCT
ejpam-6176	157	9	transforms	transform	VERB
ejpam-6176	157	10	linear	linear	ADJ
ejpam-6176	157	11	difference	difference	NOUN
ejpam-6176	157	12	equations	equation	NOUN
ejpam-6176	157	13	into	into	ADP
ejpam-6176	157	14	trigonometric	trigonometric	ADJ
ejpam-6176	157	15	equations	equation	NOUN
ejpam-6176	157	16	,	,	PUNCT
ejpam-6176	157	17	from	from	ADP
ejpam-6176	157	18	which	which	PRON
ejpam-6176	157	19	stability	stability	NOUN
ejpam-6176	157	20	conditions	condition	NOUN
ejpam-6176	157	21	are	be	AUX
ejpam-6176	157	22	derived	derive	VERB
ejpam-6176	157	23	.	.	PUNCT
ejpam-6176	158	1	to	to	PART
ejpam-6176	158	2	apply	apply	VERB
ejpam-6176	158	3	this	this	DET
ejpam-6176	158	4	method	method	NOUN
ejpam-6176	158	5	,	,	PUNCT
ejpam-6176	158	6	we	we	PRON
ejpam-6176	158	7	use	use	VERB
ejpam-6176	158	8	the	the	DET
ejpam-6176	158	9	following	follow	VERB
ejpam-6176	158	10	transformations	transformation	NOUN
ejpam-6176	158	11	:	:	PUNCT
ejpam-6176	158	12	aeiiθ	aeiiθ	ADJ
ejpam-6176	158	13	=	=	SYM
ejpam-6176	158	14	α1e	α1e	PROPN
ejpam-6176	158	15	(	(	PUNCT
ejpam-6176	158	16	i−1)iθ	i−1)iθ	NOUN
ejpam-6176	158	17	+	+	CCONJ
ejpam-6176	158	18	eiiθ	eiiθ	NOUN
ejpam-6176	158	19	+	+	CCONJ
ejpam-6176	158	20	α1e	α1e	PROPN
ejpam-6176	158	21	(	(	PUNCT
ejpam-6176	158	22	i+1)iθ	i+1)iθ	NOUN
ejpam-6176	158	23	(	(	PUNCT
ejpam-6176	158	24	12	12	NUM
ejpam-6176	158	25	)	)	PUNCT
ejpam-6176	158	26	beiiθ	beiiθ	NOUN
ejpam-6176	158	27	=	=	SYM
ejpam-6176	158	28	b0	b0	PROPN
ejpam-6176	158	29	∆x2	∆x2	PRON
ejpam-6176	158	30	(	(	PUNCT
ejpam-6176	158	31	e(i+1)iθ	e(i+1)iθ	NOUN
ejpam-6176	158	32	−	−	NOUN
ejpam-6176	158	33	2eiiθ	2eiiθ	NUM
ejpam-6176	158	34	+	+	NUM
ejpam-6176	158	35	e(i−1)iθ	e(i−1)iθ	NOUN
ejpam-6176	158	36	)	)	PUNCT
ejpam-6176	158	37	+	+	CCONJ
ejpam-6176	158	38	b1	b1	NOUN
ejpam-6176	158	39	4∆x2	4∆x2	NUM
ejpam-6176	158	40	(	(	PUNCT
ejpam-6176	158	41	e(i+2)iθ	e(i+2)iθ	NOUN
ejpam-6176	158	42	−	−	PROPN
ejpam-6176	158	43	2eiiθ	2eiiθ	NUM
ejpam-6176	158	44	+	+	CCONJ
ejpam-6176	158	45	e(i−2)iθ	e(i−2)iθ	NOUN
ejpam-6176	158	46	)	)	PUNCT
ejpam-6176	158	47	(	(	PUNCT
ejpam-6176	158	48	13	13	NUM
ejpam-6176	158	49	)	)	PUNCT
ejpam-6176	158	50	substituting	substituting	NOUN
ejpam-6176	158	51	(	(	PUNCT
ejpam-6176	158	52	12	12	NUM
ejpam-6176	158	53	)	)	PUNCT
ejpam-6176	158	54	and	and	CCONJ
ejpam-6176	158	55	(	(	PUNCT
ejpam-6176	158	56	13	13	NUM
ejpam-6176	158	57	)	)	PUNCT
ejpam-6176	158	58	into	into	ADP
ejpam-6176	158	59	the	the	DET
ejpam-6176	158	60	predictor	predictor	NOUN
ejpam-6176	158	61	stage	stage	NOUN
ejpam-6176	158	62	of	of	ADP
ejpam-6176	158	63	the	the	DET
ejpam-6176	158	64	scheme	scheme	NOUN
ejpam-6176	158	65	(	(	PUNCT
ejpam-6176	158	66	2	2	NUM
ejpam-6176	158	67	)	)	PUNCT
ejpam-6176	158	68	with	with	ADP
ejpam-6176	158	69	f	f	PROPN
ejpam-6176	158	70	=	=	SYM
ejpam-6176	158	71	0	0	PROPN
ejpam-6176	158	72	,	,	PUNCT
ejpam-6176	158	73	we	we	PRON
ejpam-6176	158	74	obtain	obtain	VERB
ejpam-6176	158	75	:	:	PUNCT
ejpam-6176	158	76	p̄n+1	p̄n+1	NOUN
ejpam-6176	159	1	i	i	NOUN
ejpam-6176	159	2	=	=	NOUN
ejpam-6176	159	3	1	1	NUM
ejpam-6176	159	4	2	2	NUM
ejpam-6176	159	5	pn	pn	NOUN
ejpam-6176	159	6	i	i	PROPN
ejpam-6176	159	7	e	e	PROPN
ejpam-6176	159	8	∆t+	∆t+	PROPN
ejpam-6176	159	9	1	1	NUM
ejpam-6176	159	10	2	2	NUM
ejpam-6176	159	11	pn	pn	NOUN
ejpam-6176	159	12	i	i	PROPN
ejpam-6176	159	13	e	e	PROPN
ejpam-6176	159	14	5∆t+	5∆t+	PROPN
ejpam-6176	159	15	(	(	PUNCT
ejpam-6176	159	16	e∆t	e∆t	NOUN
ejpam-6176	159	17	+	+	CCONJ
ejpam-6176	159	18	e5∆t	e5∆t	VERB
ejpam-6176	159	19	−	−	PROPN
ejpam-6176	159	20	2	2	NUM
ejpam-6176	159	21	)	)	PUNCT
ejpam-6176	159	22	6	6	NUM
ejpam-6176	159	23	{	{	PUNCT
ejpam-6176	159	24	γ	γ	X
ejpam-6176	159	25	[	[	X
ejpam-6176	159	26	4b0(cos	4b0(cos	NUM
ejpam-6176	159	27	θ	θ	NOUN
ejpam-6176	159	28	−	−	NOUN
ejpam-6176	159	29	1	1	NUM
ejpam-6176	159	30	)	)	PUNCT
ejpam-6176	160	1	+	+	NUM
ejpam-6176	160	2	b1(cos	b1(co	NOUN
ejpam-6176	160	3	2θ	2θ	NUM
ejpam-6176	160	4	−	−	NOUN
ejpam-6176	160	5	1	1	NUM
ejpam-6176	160	6	)	)	PUNCT
ejpam-6176	160	7	]	]	PUNCT
ejpam-6176	161	1	2∆x2(2α1	2∆x2(2α1	NUM
ejpam-6176	161	2	cos	cos	ADP
ejpam-6176	161	3	θ	θ	PROPN
ejpam-6176	161	4	+	+	PROPN
ejpam-6176	161	5	1	1	X
ejpam-6176	161	6	)	)	PUNCT
ejpam-6176	161	7	−	−	NOUN
ejpam-6176	161	8	3	3	X
ejpam-6176	161	9	}	}	PUNCT
ejpam-6176	161	10	pn	pn	PROPN
ejpam-6176	161	11	i	i	PRON
ejpam-6176	161	12	(	(	PUNCT
ejpam-6176	161	13	14	14	NUM
ejpam-6176	161	14	)	)	PUNCT
ejpam-6176	161	15	let	let	VERB
ejpam-6176	161	16	β	β	PRON
ejpam-6176	161	17	denote	denote	VERB
ejpam-6176	161	18	the	the	DET
ejpam-6176	161	19	amplification	amplification	NOUN
ejpam-6176	161	20	factor	factor	NOUN
ejpam-6176	161	21	from	from	ADP
ejpam-6176	161	22	the	the	DET
ejpam-6176	161	23	predictor	predictor	NOUN
ejpam-6176	161	24	:	:	PUNCT
ejpam-6176	162	1	p̄n+1	p̄n+1	NOUN
ejpam-6176	162	2	i	i	PRON
ejpam-6176	163	1	=	=	VERB
ejpam-6176	164	1	βpn	βpn	NOUN
ejpam-6176	165	1	i	i	NOUN
ejpam-6176	165	2	(	(	PUNCT
ejpam-6176	165	3	15	15	NUM
ejpam-6176	165	4	)	)	PUNCT
ejpam-6176	165	5	then	then	ADV
ejpam-6176	165	6	,	,	PUNCT
ejpam-6176	165	7	β	β	X
ejpam-6176	165	8	=	=	NOUN
ejpam-6176	165	9	1	1	NUM
ejpam-6176	165	10	2	2	NUM
ejpam-6176	165	11	e∆t	e∆t	NOUN
ejpam-6176	166	1	+	+	CCONJ
ejpam-6176	166	2	1	1	NUM
ejpam-6176	166	3	2	2	NUM
ejpam-6176	166	4	e5∆t	e5∆t	NOUN
ejpam-6176	166	5	+	+	CCONJ
ejpam-6176	166	6	(	(	PUNCT
ejpam-6176	166	7	e∆t	e∆t	NOUN
ejpam-6176	166	8	+	+	CCONJ
ejpam-6176	166	9	e5∆t	e5∆t	VERB
ejpam-6176	166	10	−	−	PROPN
ejpam-6176	166	11	2	2	NUM
ejpam-6176	166	12	)	)	PUNCT
ejpam-6176	166	13	6	6	NUM
ejpam-6176	166	14	{	{	PUNCT
ejpam-6176	166	15	γ	γ	X
ejpam-6176	166	16	[	[	X
ejpam-6176	166	17	4b0(cos	4b0(cos	NUM
ejpam-6176	166	18	θ	θ	NOUN
ejpam-6176	166	19	−	−	NOUN
ejpam-6176	166	20	1	1	NUM
ejpam-6176	166	21	)	)	PUNCT
ejpam-6176	167	1	+	+	NUM
ejpam-6176	167	2	b1(cos	b1(co	NOUN
ejpam-6176	167	3	2θ	2θ	NUM
ejpam-6176	167	4	−	−	NOUN
ejpam-6176	167	5	1	1	NUM
ejpam-6176	167	6	)	)	PUNCT
ejpam-6176	167	7	]	]	PUNCT
ejpam-6176	168	1	2∆x2(2α1	2∆x2(2α1	NUM
ejpam-6176	168	2	cos	cos	ADP
ejpam-6176	168	3	θ	θ	PROPN
ejpam-6176	168	4	+	+	PROPN
ejpam-6176	168	5	1	1	X
ejpam-6176	168	6	)	)	PUNCT
ejpam-6176	168	7	−	−	NOUN
ejpam-6176	168	8	3	3	NUM
ejpam-6176	168	9	}	}	PUNCT
ejpam-6176	168	10	(	(	PUNCT
ejpam-6176	168	11	16	16	NUM
ejpam-6176	168	12	)	)	PUNCT
ejpam-6176	168	13	now	now	ADV
ejpam-6176	168	14	,	,	PUNCT
ejpam-6176	168	15	substituting	substitute	VERB
ejpam-6176	168	16	(	(	PUNCT
ejpam-6176	168	17	12	12	NUM
ejpam-6176	168	18	)	)	PUNCT
ejpam-6176	168	19	and	and	CCONJ
ejpam-6176	168	20	(	(	PUNCT
ejpam-6176	168	21	13	13	NUM
ejpam-6176	168	22	)	)	PUNCT
ejpam-6176	168	23	into	into	ADP
ejpam-6176	168	24	the	the	DET
ejpam-6176	168	25	corrector	corrector	NOUN
ejpam-6176	168	26	stage	stage	NOUN
ejpam-6176	168	27	of	of	ADP
ejpam-6176	168	28	the	the	DET
ejpam-6176	168	29	scheme	scheme	NOUN
ejpam-6176	168	30	(	(	PUNCT
ejpam-6176	168	31	with	with	ADP
ejpam-6176	168	32	f	f	PROPN
ejpam-6176	168	33	=	=	SYM
ejpam-6176	168	34	0	0	NUM
ejpam-6176	168	35	)	)	PUNCT
ejpam-6176	168	36	,	,	PUNCT
ejpam-6176	168	37	we	we	PRON
ejpam-6176	168	38	get	get	VERB
ejpam-6176	168	39	:	:	PUNCT
ejpam-6176	168	40	pn+1	pn+1	VERB
ejpam-6176	168	41	i	i	NOUN
ejpam-6176	168	42	=	=	PUNCT
ejpam-6176	168	43	apn	apn	PROPN
ejpam-6176	169	1	i	i	PRON
ejpam-6176	169	2	+	+	CCONJ
ejpam-6176	169	3	bp̄n+1	bp̄n+1	VERB
ejpam-6176	170	1	i	i	PRON
ejpam-6176	171	1	+	+	CCONJ
ejpam-6176	171	2	c(e∆t	c(e∆t	ADJ
ejpam-6176	171	3	−	−	NOUN
ejpam-6176	171	4	1	1	NUM
ejpam-6176	171	5	)	)	PUNCT
ejpam-6176	171	6	{	{	PUNCT
ejpam-6176	171	7	γ	γ	X
ejpam-6176	171	8	[	[	X
ejpam-6176	171	9	4b0(cos	4b0(cos	NUM
ejpam-6176	171	10	θ	θ	NOUN
ejpam-6176	171	11	−	−	NOUN
ejpam-6176	171	12	1	1	NUM
ejpam-6176	171	13	)	)	PUNCT
ejpam-6176	172	1	+	+	NUM
ejpam-6176	172	2	b1(cos	b1(co	NOUN
ejpam-6176	172	3	2θ	2θ	NUM
ejpam-6176	172	4	−	−	NOUN
ejpam-6176	172	5	1	1	NUM
ejpam-6176	172	6	)	)	PUNCT
ejpam-6176	172	7	]	]	PUNCT
ejpam-6176	173	1	2∆x2(2α1	2∆x2(2α1	NUM
ejpam-6176	173	2	cos	cos	ADP
ejpam-6176	173	3	θ	θ	PROPN
ejpam-6176	173	4	+	+	PROPN
ejpam-6176	173	5	1	1	NUM
ejpam-6176	173	6	)	)	PUNCT
ejpam-6176	173	7	}	}	PUNCT
ejpam-6176	173	8	p̄n+1	p̄n+1	NOUN
ejpam-6176	174	1	i	i	PRON
ejpam-6176	174	2	+	+	CCONJ
ejpam-6176	174	3	σ1p	σ1p	VERB
ejpam-6176	174	4	n	n	CCONJ
ejpam-6176	174	5	i	i	PRON
ejpam-6176	174	6	∆w	∆w	PROPN
ejpam-6176	174	7	(	(	PUNCT
ejpam-6176	174	8	17	17	NUM
ejpam-6176	174	9	)	)	PUNCT
ejpam-6176	174	10	using	use	VERB
ejpam-6176	174	11	(	(	PUNCT
ejpam-6176	174	12	15	15	NUM
ejpam-6176	174	13	)	)	PUNCT
ejpam-6176	174	14	,	,	PUNCT
ejpam-6176	174	15	we	we	PRON
ejpam-6176	174	16	rewrite	rewrite	VERB
ejpam-6176	174	17	the	the	DET
ejpam-6176	174	18	above	above	ADV
ejpam-6176	174	19	as	as	ADP
ejpam-6176	174	20	:	:	PUNCT
ejpam-6176	174	21	pn+1	pn+1	NOUN
ejpam-6176	174	22	i	i	NOUN
ejpam-6176	174	23	=	=	PRON
ejpam-6176	174	24	[	[	PUNCT
ejpam-6176	174	25	a+	a+	PUNCT
ejpam-6176	174	26	bβ	bβ	NOUN
ejpam-6176	174	27	+	+	CCONJ
ejpam-6176	174	28	c(e∆t	c(e∆t	NOUN
ejpam-6176	174	29	−	−	NOUN
ejpam-6176	174	30	1	1	NUM
ejpam-6176	174	31	)	)	PUNCT
ejpam-6176	174	32	{	{	PUNCT
ejpam-6176	174	33	γ	γ	X
ejpam-6176	174	34	[	[	X
ejpam-6176	174	35	4b0(cos	4b0(cos	NUM
ejpam-6176	174	36	θ	θ	NOUN
ejpam-6176	174	37	−	−	NOUN
ejpam-6176	174	38	1	1	NUM
ejpam-6176	174	39	)	)	PUNCT
ejpam-6176	175	1	+	+	NUM
ejpam-6176	175	2	b1(cos	b1(co	NOUN
ejpam-6176	175	3	2θ	2θ	NUM
ejpam-6176	175	4	−	−	NOUN
ejpam-6176	175	5	1	1	NUM
ejpam-6176	175	6	)	)	PUNCT
ejpam-6176	175	7	]	]	PUNCT
ejpam-6176	176	1	2∆x2(2α1	2∆x2(2α1	NUM
ejpam-6176	176	2	cos	cos	ADP
ejpam-6176	176	3	θ	θ	PROPN
ejpam-6176	176	4	+	+	PROPN
ejpam-6176	176	5	1	1	NUM
ejpam-6176	176	6	)	)	PUNCT
ejpam-6176	176	7	}	}	PUNCT
ejpam-6176	176	8	β	β	X
ejpam-6176	176	9	]	]	PUNCT
ejpam-6176	176	10	pn	pn	PROPN
ejpam-6176	176	11	i	i	PRON
ejpam-6176	177	1	+	+	CCONJ
ejpam-6176	177	2	σ1p	σ1p	VERB
ejpam-6176	177	3	n	n	CCONJ
ejpam-6176	177	4	i	i	PRON
ejpam-6176	177	5	∆w	∆w	PROPN
ejpam-6176	177	6	(	(	PUNCT
ejpam-6176	177	7	18	18	NUM
ejpam-6176	177	8	)	)	PUNCT
ejpam-6176	177	9	define	define	NOUN
ejpam-6176	177	10	:	:	PUNCT
ejpam-6176	177	11	β1	β1	PROPN
ejpam-6176	177	12	=	=	SYM
ejpam-6176	177	13	a+	a+	PUNCT
ejpam-6176	177	14	bβ	bβ	NOUN
ejpam-6176	178	1	+	+	CCONJ
ejpam-6176	178	2	c(e∆t	c(e∆t	NOUN
ejpam-6176	178	3	−	−	NOUN
ejpam-6176	178	4	1	1	NUM
ejpam-6176	178	5	)	)	PUNCT
ejpam-6176	178	6	{	{	PUNCT
ejpam-6176	178	7	γ	γ	X
ejpam-6176	178	8	[	[	X
ejpam-6176	178	9	4b0(cos	4b0(cos	NUM
ejpam-6176	178	10	θ	θ	NOUN
ejpam-6176	178	11	−	−	NOUN
ejpam-6176	178	12	1	1	NUM
ejpam-6176	178	13	)	)	PUNCT
ejpam-6176	179	1	+	+	NUM
ejpam-6176	179	2	b1(cos	b1(co	NOUN
ejpam-6176	179	3	2θ	2θ	NUM
ejpam-6176	179	4	−	−	NOUN
ejpam-6176	179	5	1	1	NUM
ejpam-6176	179	6	)	)	PUNCT
ejpam-6176	179	7	]	]	PUNCT
ejpam-6176	180	1	2∆x2(2α1	2∆x2(2α1	NUM
ejpam-6176	180	2	cos	cos	ADP
ejpam-6176	180	3	θ	θ	PROPN
ejpam-6176	180	4	+	+	PROPN
ejpam-6176	180	5	1	1	NUM
ejpam-6176	180	6	)	)	PUNCT
ejpam-6176	180	7	}	}	PUNCT
ejpam-6176	180	8	β	β	PROPN
ejpam-6176	180	9	(	(	PUNCT
ejpam-6176	180	10	19	19	NUM
ejpam-6176	180	11	)	)	PUNCT
ejpam-6176	180	12	then	then	ADV
ejpam-6176	180	13	,	,	PUNCT
ejpam-6176	180	14	the	the	DET
ejpam-6176	180	15	amplification	amplification	NOUN
ejpam-6176	180	16	factor	factor	NOUN
ejpam-6176	180	17	becomes	become	VERB
ejpam-6176	180	18	:	:	PUNCT
ejpam-6176	180	19	pn+1	pn+1	VERB
ejpam-6176	180	20	i	i	PRON
ejpam-6176	180	21	pn	pn	VERB
ejpam-6176	180	22	i	i	NOUN
ejpam-6176	181	1	=	=	PUNCT
ejpam-6176	181	2	β1	β1	PROPN
ejpam-6176	181	3	+	+	NUM
ejpam-6176	181	4	σ1∆w	σ1∆w	NOUN
ejpam-6176	181	5	(	(	PUNCT
ejpam-6176	181	6	20	20	NUM
ejpam-6176	181	7	)	)	PUNCT
ejpam-6176	181	8	m.	m.	NOUN
ejpam-6176	181	9	s.	s.	PROPN
ejpam-6176	181	10	arif	arif	PROPN
ejpam-6176	181	11	,	,	PUNCT
ejpam-6176	181	12	k.	k.	PROPN
ejpam-6176	181	13	abodayeh	abodayeh	PROPN
ejpam-6176	181	14	,	,	PUNCT
ejpam-6176	181	15	y.	y.	NOUN
ejpam-6176	181	16	nawaz	nawaz	PROPN
ejpam-6176	181	17	/	/	SYM
ejpam-6176	181	18	eur	eur	PROPN
ejpam-6176	181	19	.	.	PUNCT
ejpam-6176	182	1	j.	j.	PROPN
ejpam-6176	182	2	pure	pure	PROPN
ejpam-6176	182	3	appl	appl	PROPN
ejpam-6176	182	4	.	.	PROPN
ejpam-6176	182	5	math	math	PROPN
ejpam-6176	182	6	,	,	PUNCT
ejpam-6176	182	7	18	18	NUM
ejpam-6176	182	8	(	(	PUNCT
ejpam-6176	182	9	3	3	NUM
ejpam-6176	182	10	)	)	PUNCT
ejpam-6176	182	11	(	(	PUNCT
ejpam-6176	182	12	2025	2025	NUM
ejpam-6176	182	13	)	)	PUNCT
ejpam-6176	182	14	,	,	PUNCT
ejpam-6176	182	15	6176	6176	NUM
ejpam-6176	182	16	8	8	NUM
ejpam-6176	182	17	of	of	ADP
ejpam-6176	182	18	21	21	NUM
ejpam-6176	182	19	taking	take	VERB
ejpam-6176	182	20	expectations	expectation	NOUN
ejpam-6176	182	21	on	on	ADP
ejpam-6176	182	22	the	the	DET
ejpam-6176	182	23	squared	square	VERB
ejpam-6176	182	24	modulus	modulus	NOUN
ejpam-6176	182	25	yields	yield	NOUN
ejpam-6176	182	26	:	:	PUNCT
ejpam-6176	182	27	e	e	X
ejpam-6176	182	28	∣∣∣∣pn+1	∣∣∣∣pn+1	VERB
ejpam-6176	183	1	i	i	PRON
ejpam-6176	183	2	pn	pn	VERB
ejpam-6176	183	3	i	i	PRON
ejpam-6176	183	4	∣∣∣∣2	∣∣∣∣2	VERB
ejpam-6176	184	1	≤	≤	NOUN
ejpam-6176	185	1	2|β1|2	2|β1|2	NUM
ejpam-6176	186	1	+	+	CCONJ
ejpam-6176	186	2	2σ2	2σ2	NUM
ejpam-6176	186	3	1e|∆w	1e|∆w	NUM
ejpam-6176	186	4	|2	|2	NUM
ejpam-6176	186	5	(	(	PUNCT
ejpam-6176	186	6	21	21	NUM
ejpam-6176	186	7	)	)	PUNCT
ejpam-6176	186	8	if	if	SCONJ
ejpam-6176	186	9	|β1|2	|β1|2	PUNCT
ejpam-6176	186	10	<	<	X
ejpam-6176	186	11	1	1	NUM
ejpam-6176	186	12	2	2	NUM
ejpam-6176	186	13	and	and	CCONJ
ejpam-6176	186	14	2σ2	2σ2	NUM
ejpam-6176	186	15	1	1	NUM
ejpam-6176	186	16	=	=	SYM
ejpam-6176	186	17	λ	λ	NOUN
ejpam-6176	186	18	,	,	PUNCT
ejpam-6176	186	19	we	we	PRON
ejpam-6176	186	20	obtain	obtain	VERB
ejpam-6176	186	21	:	:	PUNCT
ejpam-6176	186	22	e	e	X
ejpam-6176	186	23	∣∣∣∣pn+1	∣∣∣∣pn+1	VERB
ejpam-6176	186	24	i	i	PRON
ejpam-6176	186	25	pn	pn	VERB
ejpam-6176	187	1	i	i	PRON
ejpam-6176	187	2	∣∣∣∣2	∣∣∣∣2	VERB
ejpam-6176	187	3	≤	≤	ADV
ejpam-6176	187	4	1	1	NUM
ejpam-6176	187	5	+	+	CCONJ
ejpam-6176	187	6	λ∆t	λ∆t	NOUN
ejpam-6176	187	7	(	(	PUNCT
ejpam-6176	187	8	22	22	NUM
ejpam-6176	187	9	)	)	PUNCT
ejpam-6176	187	10	hence	hence	ADV
ejpam-6176	187	11	,	,	PUNCT
ejpam-6176	187	12	the	the	DET
ejpam-6176	187	13	proposed	propose	VERB
ejpam-6176	187	14	scheme	scheme	NOUN
ejpam-6176	187	15	is	be	AUX
ejpam-6176	187	16	conditionally	conditionally	ADV
ejpam-6176	187	17	stable	stable	ADJ
ejpam-6176	187	18	in	in	ADP
ejpam-6176	187	19	the	the	DET
ejpam-6176	187	20	mean	mean	ADJ
ejpam-6176	187	21	-	-	PUNCT
ejpam-6176	187	22	square	square	ADJ
ejpam-6176	187	23	sense	sense	NOUN
ejpam-6176	187	24	.	.	PUNCT
ejpam-6176	188	1	theorem	theorem	NOUN
ejpam-6176	188	2	1	1	NUM
ejpam-6176	188	3	.	.	PUNCT
ejpam-6176	189	1	the	the	DET
ejpam-6176	189	2	proposed	propose	VERB
ejpam-6176	189	3	schemes	scheme	NOUN
ejpam-6176	189	4	(	(	PUNCT
ejpam-6176	189	5	2	2	NUM
ejpam-6176	189	6	)	)	PUNCT
ejpam-6176	189	7	and	and	CCONJ
ejpam-6176	189	8	(	(	PUNCT
ejpam-6176	189	9	3	3	X
ejpam-6176	189	10	)	)	PUNCT
ejpam-6176	189	11	with	with	ADP
ejpam-6176	189	12	compact	compact	ADJ
ejpam-6176	189	13	spatial	spatial	ADJ
ejpam-6176	189	14	discretization	discretization	NOUN
ejpam-6176	189	15	are	be	AUX
ejpam-6176	189	16	consistent	consistent	ADJ
ejpam-6176	189	17	in	in	ADP
ejpam-6176	189	18	the	the	DET
ejpam-6176	189	19	mean	mean	ADJ
ejpam-6176	189	20	-	-	PUNCT
ejpam-6176	189	21	square	square	ADJ
ejpam-6176	189	22	sense	sense	NOUN
ejpam-6176	189	23	.	.	PUNCT
ejpam-6176	190	1	proof	proof	NOUN
ejpam-6176	190	2	.	.	PUNCT
ejpam-6176	191	1	let	let	VERB
ejpam-6176	191	2	h	h	PRON
ejpam-6176	191	3	be	be	AUX
ejpam-6176	191	4	a	a	DET
ejpam-6176	191	5	smooth	smooth	ADJ
ejpam-6176	191	6	function	function	NOUN
ejpam-6176	191	7	.	.	PUNCT
ejpam-6176	192	1	define	define	VERB
ejpam-6176	192	2	:	:	PUNCT
ejpam-6176	192	3	l(h)ni	l(h)ni	ADV
ejpam-6176	192	4	=	=	PUNCT
ejpam-6176	192	5	h((n+	h((n+	X
ejpam-6176	192	6	1)∆t	1)∆t	NUM
ejpam-6176	192	7	,	,	PUNCT
ejpam-6176	192	8	i∆x)−h(n∆t	i∆x)−h(n∆t	PROPN
ejpam-6176	192	9	,	,	PUNCT
ejpam-6176	192	10	i∆x)−	i∆x)−	PROPN
ejpam-6176	192	11	γ	γ	X
ejpam-6176	192	12	∫	∫	PROPN
ejpam-6176	192	13	(	(	PUNCT
ejpam-6176	192	14	n+1)∆t	n+1)∆t	PROPN
ejpam-6176	192	15	n∆t	n∆t	PROPN
ejpam-6176	192	16	hxx(s	hxx(s	PROPN
ejpam-6176	192	17	,	,	PUNCT
ejpam-6176	192	18	i∆x)ds−	i∆x)ds−	VERB
ejpam-6176	192	19	σ1	σ1	PROPN
ejpam-6176	192	20	∫	∫	PROPN
ejpam-6176	192	21	(	(	PUNCT
ejpam-6176	192	22	n+1)∆t	n+1)∆t	PROPN
ejpam-6176	192	23	n∆t	n∆t	PROPN
ejpam-6176	192	24	h(s	h(s	PROPN
ejpam-6176	192	25	,	,	PUNCT
ejpam-6176	192	26	i∆x)dw	i∆x)dw	PROPN
ejpam-6176	192	27	(	(	PUNCT
ejpam-6176	192	28	s	s	NOUN
ejpam-6176	192	29	)	)	PUNCT
ejpam-6176	192	30	(	(	PUNCT
ejpam-6176	192	31	23	23	NUM
ejpam-6176	192	32	)	)	PUNCT
ejpam-6176	192	33	ln	ln	NOUN
ejpam-6176	193	1	i	i	PRON
ejpam-6176	193	2	h	h	NOUN
ejpam-6176	193	3	=	=	PUNCT
ejpam-6176	193	4	h((n+	h((n+	NOUN
ejpam-6176	193	5	1)∆t	1)∆t	NUM
ejpam-6176	193	6	,	,	PUNCT
ejpam-6176	193	7	i∆x)−h(n∆t	i∆x)−h(n∆t	PROPN
ejpam-6176	193	8	,	,	PUNCT
ejpam-6176	193	9	i∆x)−	i∆x)−	PROPN
ejpam-6176	193	10	γb	γb	NOUN
ejpam-6176	193	11	(	(	PUNCT
ejpam-6176	193	12	e∆t	e∆t	NOUN
ejpam-6176	193	13	+	+	CCONJ
ejpam-6176	193	14	e5∆t	e5∆t	VERB
ejpam-6176	193	15	−	−	PROPN
ejpam-6176	193	16	2	2	NUM
ejpam-6176	193	17	)	)	PUNCT
ejpam-6176	193	18	6	6	NUM
ejpam-6176	193	19	a−1bh(n∆t	a−1bh(n∆t	PROPN
ejpam-6176	193	20	,	,	PUNCT
ejpam-6176	193	21	i∆x	i∆x	X
ejpam-6176	193	22	)	)	PUNCT
ejpam-6176	193	23	−	−	PROPN
ejpam-6176	194	1	γc(e∆t	γc(e∆t	NOUN
ejpam-6176	195	1	−	−	PROPN
ejpam-6176	195	2	1)a−1bh̄((n+	1)a−1bh̄((n+	NUM
ejpam-6176	195	3	1)∆t	1)∆t	NUM
ejpam-6176	195	4	,	,	PUNCT
ejpam-6176	195	5	i∆x)−	i∆x)−	PROPN
ejpam-6176	195	6	σ1h(n∆t	σ1h(n∆t	NOUN
ejpam-6176	195	7	,	,	PUNCT
ejpam-6176	195	8	i∆x)(w	i∆x)(w	NOUN
ejpam-6176	195	9	(	(	PUNCT
ejpam-6176	195	10	(	(	PUNCT
ejpam-6176	195	11	n+	n+	NUM
ejpam-6176	195	12	1)∆t)−w	1)∆t)−w	NUM
ejpam-6176	195	13	(	(	PUNCT
ejpam-6176	195	14	n∆t	n∆t	NOUN
ejpam-6176	195	15	)	)	PUNCT
ejpam-6176	195	16	)	)	PUNCT
ejpam-6176	196	1	(	(	PUNCT
ejpam-6176	196	2	24	24	NUM
ejpam-6176	196	3	)	)	PUNCT
ejpam-6176	196	4	where	where	SCONJ
ejpam-6176	196	5	h̄((n+1)∆t	h̄((n+1)∆t	NUM
ejpam-6176	196	6	,	,	PUNCT
ejpam-6176	196	7	i∆x	i∆x	X
ejpam-6176	196	8	)	)	PUNCT
ejpam-6176	196	9	=	=	SYM
ejpam-6176	196	10	1	1	NUM
ejpam-6176	196	11	2	2	NUM
ejpam-6176	196	12	h((n+1)∆t	h((n+1)∆t	VERB
ejpam-6176	196	13	,	,	PUNCT
ejpam-6176	196	14	i∆x	i∆x	ADJ
ejpam-6176	196	15	)	)	PUNCT
ejpam-6176	196	16	e∆t	e∆t	NOUN
ejpam-6176	197	1	+	+	CCONJ
ejpam-6176	197	2	1	1	NUM
ejpam-6176	197	3	2	2	NUM
ejpam-6176	197	4	h(n∆t	h(n∆t	PROPN
ejpam-6176	197	5	,	,	PUNCT
ejpam-6176	197	6	i∆x	i∆x	X
ejpam-6176	197	7	)	)	PUNCT
ejpam-6176	197	8	e5∆t	e5∆t	VERB
ejpam-6176	197	9	+	+	PUNCT
ejpam-6176	197	10	e∆t	e∆t	NOUN
ejpam-6176	198	1	+	+	CCONJ
ejpam-6176	198	2	e5∆t	e5∆t	VERB
ejpam-6176	198	3	−	−	PROPN
ejpam-6176	198	4	2	2	NUM
ejpam-6176	198	5	6	6	NUM
ejpam-6176	198	6	{	{	PUNCT
ejpam-6176	198	7	a−1bh(n∆t	a−1bh(n∆t	PROPN
ejpam-6176	198	8	,	,	PUNCT
ejpam-6176	198	9	i∆x)−	i∆x)−	PROPN
ejpam-6176	198	10	1	1	NUM
ejpam-6176	198	11	2	2	NUM
ejpam-6176	198	12	h(n∆t	h(n∆t	PROPN
ejpam-6176	198	13	,	,	PUNCT
ejpam-6176	198	14	i∆x	i∆x	PROPN
ejpam-6176	198	15	)	)	PUNCT
ejpam-6176	198	16	}	}	PUNCT
ejpam-6176	198	17	(	(	PUNCT
ejpam-6176	198	18	25	25	NUM
ejpam-6176	198	19	)	)	PUNCT
ejpam-6176	198	20	then	then	ADV
ejpam-6176	198	21	the	the	DET
ejpam-6176	198	22	error	error	NOUN
ejpam-6176	198	23	between	between	ADP
ejpam-6176	198	24	exact	exact	ADJ
ejpam-6176	198	25	and	and	CCONJ
ejpam-6176	198	26	numerical	numerical	ADJ
ejpam-6176	198	27	evolution	evolution	NOUN
ejpam-6176	198	28	becomes	become	VERB
ejpam-6176	198	29	:	:	PUNCT
ejpam-6176	198	30	e|l(h)ni	e|l(h)ni	NOUN
ejpam-6176	198	31	−	−	PROPN
ejpam-6176	199	1	ln	ln	INTJ
ejpam-6176	199	2	i	i	PRON
ejpam-6176	199	3	h|2	h|2	VERB
ejpam-6176	199	4	≤	≤	NUM
ejpam-6176	199	5	2γ2e	2γ2e	NUM
ejpam-6176	199	6	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-6176	200	1	∫	∫	PROPN
ejpam-6176	200	2	(	(	PUNCT
ejpam-6176	200	3	n+1)∆t	n+1)∆t	PROPN
ejpam-6176	200	4	n∆t	n∆t	PROPN
ejpam-6176	200	5	hxx(s	hxx(s	PROPN
ejpam-6176	200	6	,	,	PUNCT
ejpam-6176	200	7	i∆x)ds−	i∆x)ds−	NOUN
ejpam-6176	200	8	b	b	X
ejpam-6176	200	9	(	(	PUNCT
ejpam-6176	200	10	e∆t	e∆t	NOUN
ejpam-6176	200	11	+	+	CCONJ
ejpam-6176	200	12	e5∆t	e5∆t	VERB
ejpam-6176	200	13	−	−	PROPN
ejpam-6176	200	14	2	2	NUM
ejpam-6176	200	15	)	)	PUNCT
ejpam-6176	200	16	6	6	NUM
ejpam-6176	200	17	a−1bh(n∆t	a−1bh(n∆t	PROPN
ejpam-6176	200	18	,	,	PUNCT
ejpam-6176	200	19	i∆x	i∆x	X
ejpam-6176	200	20	)	)	PUNCT
ejpam-6176	201	1	+	+	PROPN
ejpam-6176	201	2	c(e∆t	c(e∆t	NOUN
ejpam-6176	201	3	−	−	PROPN
ejpam-6176	201	4	1)a−1bh̄((n+	1)a−1bh̄((n+	NUM
ejpam-6176	201	5	1)∆t	1)∆t	NUM
ejpam-6176	201	6	,	,	PUNCT
ejpam-6176	201	7	i∆x	i∆x	PROPN
ejpam-6176	201	8	)	)	PUNCT
ejpam-6176	201	9	∣∣2	∣∣2	PROPN
ejpam-6176	201	10	+	+	CCONJ
ejpam-6176	201	11	2σ2	2σ2	NUM
ejpam-6176	201	12	1∆t	1∆t	NUM
ejpam-6176	201	13	∫	∫	PROPN
ejpam-6176	201	14	(	(	PUNCT
ejpam-6176	201	15	n+1)∆t	n+1)∆t	PROPN
ejpam-6176	201	16	n∆t	n∆t	PROPN
ejpam-6176	201	17	e	e	PROPN
ejpam-6176	201	18	[	[	PUNCT
ejpam-6176	201	19	|h(s	|h(s	PROPN
ejpam-6176	201	20	,	,	PUNCT
ejpam-6176	201	21	i∆x)−h(n∆t	i∆x)−h(n∆t	PROPN
ejpam-6176	201	22	,	,	PUNCT
ejpam-6176	201	23	i∆x)|2	i∆x)|2	X
ejpam-6176	201	24	]	]	PUNCT
ejpam-6176	201	25	ds	ds	PROPN
ejpam-6176	201	26	(	(	PUNCT
ejpam-6176	201	27	26	26	NUM
ejpam-6176	201	28	)	)	PUNCT
ejpam-6176	201	29	using	use	VERB
ejpam-6176	201	30	stochastic	stochastic	ADJ
ejpam-6176	201	31	integral	integral	ADJ
ejpam-6176	201	32	inequalities	inequality	NOUN
ejpam-6176	201	33	such	such	ADJ
ejpam-6176	201	34	as	as	ADP
ejpam-6176	201	35	:	:	PUNCT
ejpam-6176	201	36	e	e	X
ejpam-6176	201	37	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6176	201	38	t	t	PROPN
ejpam-6176	201	39	t0	t0	PROPN
ejpam-6176	201	40	u(s)dw	u(s)dw	PROPN
ejpam-6176	201	41	(	(	PUNCT
ejpam-6176	201	42	s	s	NOUN
ejpam-6176	201	43	)	)	PUNCT
ejpam-6176	201	44	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-6176	201	45	m	m	PROPN
ejpam-6176	201	46	≤	≤	NOUN
ejpam-6176	201	47	(	(	PUNCT
ejpam-6176	201	48	t−	t−	PROPN
ejpam-6176	201	49	t0	t0	PROPN
ejpam-6176	201	50	)	)	PUNCT
ejpam-6176	201	51	m−1[m(2m−	m−1[m(2m−	NOUN
ejpam-6176	201	52	1)]m	1)]m	NUM
ejpam-6176	201	53	∫	∫	PROPN
ejpam-6176	201	54	t	t	PROPN
ejpam-6176	201	55	t0	t0	PROPN
ejpam-6176	201	56	e|u(s)|2mds	e|u(s)|2mds	PROPN
ejpam-6176	201	57	(	(	PUNCT
ejpam-6176	201	58	27	27	NUM
ejpam-6176	201	59	)	)	PUNCT
ejpam-6176	201	60	taking	take	VERB
ejpam-6176	201	61	the	the	DET
ejpam-6176	201	62	limit	limit	NOUN
ejpam-6176	201	63	as	as	ADP
ejpam-6176	201	64	∆x	∆x	PROPN
ejpam-6176	201	65	→	→	SYM
ejpam-6176	201	66	0	0	NUM
ejpam-6176	201	67	,	,	PUNCT
ejpam-6176	201	68	∆t	∆t	PROPN
ejpam-6176	201	69	→	→	SYM
ejpam-6176	201	70	0	0	NUM
ejpam-6176	201	71	,	,	PUNCT
ejpam-6176	201	72	and	and	CCONJ
ejpam-6176	201	73	(	(	PUNCT
ejpam-6176	201	74	n∆t	n∆t	NOUN
ejpam-6176	201	75	,	,	PUNCT
ejpam-6176	201	76	i∆x	i∆x	PROPN
ejpam-6176	201	77	)	)	PUNCT
ejpam-6176	201	78	→	→	SYM
ejpam-6176	201	79	(	(	PUNCT
ejpam-6176	201	80	t	t	PROPN
ejpam-6176	201	81	,	,	PUNCT
ejpam-6176	201	82	x	x	NOUN
ejpam-6176	201	83	)	)	PUNCT
ejpam-6176	201	84	,	,	PUNCT
ejpam-6176	201	85	we	we	PRON
ejpam-6176	201	86	get	get	VERB
ejpam-6176	201	87	:	:	PUNCT
ejpam-6176	201	88	e|l(h)ni	e|l(h)ni	NOUN
ejpam-6176	201	89	−	−	PROPN
ejpam-6176	202	1	ln	ln	INTJ
ejpam-6176	202	2	i	i	PROPN
ejpam-6176	202	3	h|2	h|2	PROPN
ejpam-6176	202	4	→	→	SYM
ejpam-6176	202	5	0	0	NUM
ejpam-6176	202	6	(	(	PUNCT
ejpam-6176	202	7	28	28	NUM
ejpam-6176	202	8	)	)	PUNCT
ejpam-6176	202	9	thus	thus	ADV
ejpam-6176	202	10	,	,	PUNCT
ejpam-6176	202	11	the	the	DET
ejpam-6176	202	12	proposed	propose	VERB
ejpam-6176	202	13	scheme	scheme	NOUN
ejpam-6176	202	14	is	be	AUX
ejpam-6176	202	15	consistent	consistent	ADJ
ejpam-6176	202	16	in	in	ADP
ejpam-6176	202	17	the	the	DET
ejpam-6176	202	18	mean	mean	ADJ
ejpam-6176	202	19	-	-	PUNCT
ejpam-6176	202	20	square	square	ADJ
ejpam-6176	202	21	sense	sense	NOUN
ejpam-6176	202	22	.	.	PUNCT
ejpam-6176	203	1	m.	m.	PROPN
ejpam-6176	203	2	s.	s.	PROPN
ejpam-6176	203	3	arif	arif	PROPN
ejpam-6176	203	4	,	,	PUNCT
ejpam-6176	203	5	k.	k.	PROPN
ejpam-6176	203	6	abodayeh	abodayeh	PROPN
ejpam-6176	203	7	,	,	PUNCT
ejpam-6176	203	8	y.	y.	NOUN
ejpam-6176	203	9	nawaz	nawaz	PROPN
ejpam-6176	203	10	/	/	SYM
ejpam-6176	203	11	eur	eur	PROPN
ejpam-6176	203	12	.	.	PUNCT
ejpam-6176	204	1	j.	j.	PROPN
ejpam-6176	204	2	pure	pure	PROPN
ejpam-6176	204	3	appl	appl	PROPN
ejpam-6176	204	4	.	.	PROPN
ejpam-6176	204	5	math	math	PROPN
ejpam-6176	204	6	,	,	PUNCT
ejpam-6176	204	7	18	18	NUM
ejpam-6176	204	8	(	(	PUNCT
ejpam-6176	204	9	3	3	NUM
ejpam-6176	204	10	)	)	PUNCT
ejpam-6176	204	11	(	(	PUNCT
ejpam-6176	204	12	2025	2025	NUM
ejpam-6176	204	13	)	)	PUNCT
ejpam-6176	204	14	,	,	PUNCT
ejpam-6176	204	15	6176	6176	NUM
ejpam-6176	204	16	9	9	NUM
ejpam-6176	204	17	of	of	ADP
ejpam-6176	204	18	21	21	NUM
ejpam-6176	204	19	4	4	NUM
ejpam-6176	204	20	.	.	PUNCT
ejpam-6176	204	21	mathematical	mathematical	ADJ
ejpam-6176	204	22	model	model	NOUN
ejpam-6176	204	23	the	the	DET
ejpam-6176	204	24	population	population	NOUN
ejpam-6176	204	25	is	be	AUX
ejpam-6176	204	26	divided	divide	VERB
ejpam-6176	204	27	into	into	ADP
ejpam-6176	204	28	four	four	NUM
ejpam-6176	204	29	compartments	compartment	NOUN
ejpam-6176	204	30	:	:	PUNCT
ejpam-6176	204	31	susceptible	susceptible	ADJ
ejpam-6176	204	32	(	(	PUNCT
ejpam-6176	204	33	s(t	s(t	PROPN
ejpam-6176	204	34	,	,	PUNCT
ejpam-6176	204	35	x	x	NOUN
ejpam-6176	204	36	)	)	PUNCT
ejpam-6176	204	37	)	)	PUNCT
ejpam-6176	204	38	,	,	PUNCT
ejpam-6176	204	39	infected	infect	VERB
ejpam-6176	204	40	(	(	PUNCT
ejpam-6176	204	41	i(t	i(t	PROPN
ejpam-6176	204	42	,	,	PUNCT
ejpam-6176	204	43	x	x	NOUN
ejpam-6176	204	44	)	)	PUNCT
ejpam-6176	204	45	)	)	PUNCT
ejpam-6176	204	46	,	,	PUNCT
ejpam-6176	204	47	quarantined	quarantine	VERB
ejpam-6176	204	48	(	(	PUNCT
ejpam-6176	204	49	q(t	q(t	ADJ
ejpam-6176	204	50	,	,	PUNCT
ejpam-6176	204	51	x	x	NOUN
ejpam-6176	204	52	)	)	PUNCT
ejpam-6176	204	53	)	)	PUNCT
ejpam-6176	204	54	,	,	PUNCT
ejpam-6176	204	55	and	and	CCONJ
ejpam-6176	204	56	recovered	recover	VERB
ejpam-6176	204	57	(	(	PUNCT
ejpam-6176	204	58	r(t	r(t	NOUN
ejpam-6176	204	59	,	,	PUNCT
ejpam-6176	204	60	x	x	NOUN
ejpam-6176	204	61	)	)	PUNCT
ejpam-6176	204	62	)	)	PUNCT
ejpam-6176	204	63	,	,	PUNCT
ejpam-6176	204	64	where	where	SCONJ
ejpam-6176	204	65	t	t	NOUN
ejpam-6176	204	66	and	and	CCONJ
ejpam-6176	204	67	x	x	ADP
ejpam-6176	204	68	represent	represent	VERB
ejpam-6176	204	69	time	time	NOUN
ejpam-6176	204	70	and	and	CCONJ
ejpam-6176	204	71	space	space	NOUN
ejpam-6176	204	72	,	,	PUNCT
ejpam-6176	204	73	respectively	respectively	ADV
ejpam-6176	204	74	.	.	PUNCT
ejpam-6176	205	1	this	this	DET
ejpam-6176	205	2	formulation	formulation	NOUN
ejpam-6176	205	3	captures	capture	VERB
ejpam-6176	205	4	both	both	DET
ejpam-6176	205	5	temporal	temporal	ADJ
ejpam-6176	205	6	and	and	CCONJ
ejpam-6176	205	7	spatial	spatial	ADJ
ejpam-6176	205	8	dynamics	dynamic	NOUN
ejpam-6176	205	9	of	of	ADP
ejpam-6176	205	10	disease	disease	NOUN
ejpam-6176	205	11	transmission	transmission	NOUN
ejpam-6176	205	12	with	with	ADP
ejpam-6176	205	13	quarantine	quarantine	NOUN
ejpam-6176	205	14	and	and	CCONJ
ejpam-6176	205	15	recovery	recovery	NOUN
ejpam-6176	205	16	effects	effect	NOUN
ejpam-6176	205	17	.	.	PUNCT
ejpam-6176	206	1	4.1	4.1	NUM
ejpam-6176	206	2	.	.	PUNCT
ejpam-6176	206	3	deterministic	deterministic	ADJ
ejpam-6176	206	4	diffusive	diffusive	ADJ
ejpam-6176	206	5	model	model	NOUN
ejpam-6176	206	6	the	the	DET
ejpam-6176	206	7	deterministic	deterministic	ADJ
ejpam-6176	206	8	reaction	reaction	NOUN
ejpam-6176	206	9	-	-	PUNCT
ejpam-6176	206	10	diffusion	diffusion	NOUN
ejpam-6176	206	11	model	model	NOUN
ejpam-6176	206	12	is	be	AUX
ejpam-6176	206	13	given	give	VERB
ejpam-6176	206	14	by	by	ADP
ejpam-6176	206	15	:	:	PUNCT
ejpam-6176	206	16	∂s	∂s	PROPN
ejpam-6176	206	17	∂t	∂t	PROPN
ejpam-6176	206	18	=	=	SYM
ejpam-6176	206	19	d1	d1	PROPN
ejpam-6176	206	20	∂2s	∂2s	PROPN
ejpam-6176	206	21	∂x2	∂x2	NOUN
ejpam-6176	206	22	+	+	CCONJ
ejpam-6176	206	23	λ−	λ−	PROPN
ejpam-6176	206	24	β1si	β1si	ADJ
ejpam-6176	206	25	1	1	NUM
ejpam-6176	206	26	+	+	NUM
ejpam-6176	206	27	αi	αi	VERB
ejpam-6176	206	28	−	−	NOUN
ejpam-6176	206	29	ds	ds	NOUN
ejpam-6176	206	30	−	−	PROPN
ejpam-6176	207	1	ρs	ρs	CCONJ
ejpam-6176	207	2	(	(	PUNCT
ejpam-6176	207	3	29	29	NUM
ejpam-6176	207	4	)	)	PUNCT
ejpam-6176	207	5	∂i	∂i	PROPN
ejpam-6176	207	6	∂t	∂t	PROPN
ejpam-6176	207	7	=	=	SYM
ejpam-6176	207	8	d2	d2	PROPN
ejpam-6176	207	9	∂2i	∂2i	NOUN
ejpam-6176	207	10	∂x2	∂x2	NOUN
ejpam-6176	207	11	+	+	CCONJ
ejpam-6176	207	12	β1si	β1si	SYM
ejpam-6176	207	13	1	1	NUM
ejpam-6176	207	14	+	+	NUM
ejpam-6176	207	15	αi	αi	VERB
ejpam-6176	207	16	−	−	PROPN
ejpam-6176	207	17	(	(	PUNCT
ejpam-6176	207	18	γ1	γ1	PROPN
ejpam-6176	207	19	+	+	CCONJ
ejpam-6176	207	20	δ	δ	PROPN
ejpam-6176	207	21	+	+	CCONJ
ejpam-6176	207	22	d+	d+	X
ejpam-6176	207	23	α2	α2	ADJ
ejpam-6176	207	24	+	+	CCONJ
ejpam-6176	207	25	ζ)i	ζ)i	NOUN
ejpam-6176	207	26	(	(	PUNCT
ejpam-6176	207	27	30	30	NUM
ejpam-6176	207	28	)	)	PUNCT
ejpam-6176	207	29	∂q	∂q	PROPN
ejpam-6176	207	30	∂t	∂t	PROPN
ejpam-6176	207	31	=	=	PUNCT
ejpam-6176	207	32	d3	d3	PROPN
ejpam-6176	207	33	∂2q	∂2q	PROPN
ejpam-6176	207	34	∂x2	∂x2	PROPN
ejpam-6176	207	35	+	+	CCONJ
ejpam-6176	207	36	δi	δi	ADP
ejpam-6176	207	37	−	−	PROPN
ejpam-6176	207	38	(	(	PUNCT
ejpam-6176	207	39	d+	d+	PROPN
ejpam-6176	207	40	α3	α3	ADJ
ejpam-6176	207	41	+	+	NOUN
ejpam-6176	207	42	ϵ)q	ϵ)q	X
ejpam-6176	207	43	(	(	PUNCT
ejpam-6176	207	44	31	31	NUM
ejpam-6176	207	45	)	)	PUNCT
ejpam-6176	208	1	∂r	∂r	PROPN
ejpam-6176	208	2	∂t	∂t	PROPN
ejpam-6176	208	3	=	=	SYM
ejpam-6176	208	4	d4	d4	PROPN
ejpam-6176	208	5	∂2r	∂2r	NOUN
ejpam-6176	208	6	∂x2	∂x2	NOUN
ejpam-6176	208	7	+	+	X
ejpam-6176	208	8	ϵq+	ϵq+	PROPN
ejpam-6176	209	1	ρs	ρs	ADP
ejpam-6176	209	2	−	−	PROPN
ejpam-6176	210	1	dr	dr	PROPN
ejpam-6176	210	2	(	(	PUNCT
ejpam-6176	210	3	32	32	NUM
ejpam-6176	210	4	)	)	PUNCT
ejpam-6176	210	5	here	here	ADV
ejpam-6176	210	6	:	:	PUNCT
ejpam-6176	210	7	•	•	NUM
ejpam-6176	210	8	λ	λ	NOUN
ejpam-6176	210	9	is	be	AUX
ejpam-6176	210	10	the	the	DET
ejpam-6176	210	11	recruitment	recruitment	NOUN
ejpam-6176	210	12	rate	rate	NOUN
ejpam-6176	210	13	.	.	PUNCT
ejpam-6176	211	1	•	•	NUM
ejpam-6176	211	2	β1	β1	PROPN
ejpam-6176	211	3	is	be	AUX
ejpam-6176	211	4	the	the	DET
ejpam-6176	211	5	transmission	transmission	NOUN
ejpam-6176	211	6	rate	rate	NOUN
ejpam-6176	211	7	.	.	PUNCT
ejpam-6176	212	1	•	•	NUM
ejpam-6176	212	2	α	α	NOUN
ejpam-6176	212	3	,	,	PUNCT
ejpam-6176	212	4	α2	α2	ADJ
ejpam-6176	212	5	,	,	PUNCT
ejpam-6176	212	6	α3	α3	NOUN
ejpam-6176	212	7	denote	denote	VERB
ejpam-6176	212	8	saturation	saturation	NOUN
ejpam-6176	212	9	and	and	CCONJ
ejpam-6176	212	10	comorbidity	comorbidity	NOUN
ejpam-6176	212	11	-	-	PUNCT
ejpam-6176	212	12	induced	induce	VERB
ejpam-6176	212	13	death	death	NOUN
ejpam-6176	212	14	.	.	PUNCT
ejpam-6176	213	1	•	•	NUM
ejpam-6176	213	2	d	d	NOUN
ejpam-6176	213	3	is	be	AUX
ejpam-6176	213	4	the	the	DET
ejpam-6176	213	5	natural	natural	ADJ
ejpam-6176	213	6	death	death	NOUN
ejpam-6176	213	7	rate	rate	NOUN
ejpam-6176	213	8	.	.	PUNCT
ejpam-6176	214	1	•	•	NUM
ejpam-6176	214	2	δ	δ	PROPN
ejpam-6176	214	3	,	,	PUNCT
ejpam-6176	214	4	ϵ	ϵ	X
ejpam-6176	214	5	,	,	PUNCT
ejpam-6176	214	6	γ1	γ1	PROPN
ejpam-6176	214	7	,	,	PUNCT
ejpam-6176	214	8	ζ	ζ	NOUN
ejpam-6176	214	9	represent	represent	VERB
ejpam-6176	214	10	quarantine	quarantine	NOUN
ejpam-6176	214	11	,	,	PUNCT
ejpam-6176	214	12	recovery	recovery	NOUN
ejpam-6176	214	13	,	,	PUNCT
ejpam-6176	214	14	and	and	CCONJ
ejpam-6176	214	15	disease	disease	NOUN
ejpam-6176	214	16	-	-	PUNCT
ejpam-6176	214	17	induced	induce	VERB
ejpam-6176	214	18	death	death	NOUN
ejpam-6176	214	19	rates	rate	NOUN
ejpam-6176	214	20	.	.	PUNCT
ejpam-6176	215	1	•	•	NUM
ejpam-6176	215	2	ρ	ρ	PROPN
ejpam-6176	215	3	is	be	AUX
ejpam-6176	215	4	the	the	DET
ejpam-6176	215	5	vaccination	vaccination	NOUN
ejpam-6176	215	6	rate	rate	NOUN
ejpam-6176	215	7	.	.	PUNCT
ejpam-6176	216	1	•	•	NUM
ejpam-6176	216	2	di	di	X
ejpam-6176	216	3	(	(	PUNCT
ejpam-6176	216	4	i	i	NOUN
ejpam-6176	216	5	=	=	NOUN
ejpam-6176	216	6	1	1	NUM
ejpam-6176	216	7	,	,	PUNCT
ejpam-6176	216	8	2	2	NUM
ejpam-6176	216	9	,	,	PUNCT
ejpam-6176	216	10	3	3	NUM
ejpam-6176	216	11	,	,	PUNCT
ejpam-6176	216	12	4	4	NUM
ejpam-6176	216	13	)	)	PUNCT
ejpam-6176	216	14	are	be	AUX
ejpam-6176	216	15	diffusion	diffusion	NOUN
ejpam-6176	216	16	coefficients	coefficient	NOUN
ejpam-6176	216	17	.	.	PUNCT
ejpam-6176	217	1	the	the	DET
ejpam-6176	217	2	boundary	boundary	ADJ
ejpam-6176	217	3	conditions	condition	NOUN
ejpam-6176	217	4	are	be	AUX
ejpam-6176	217	5	:	:	PUNCT
ejpam-6176	217	6	∂s	∂s	PROPN
ejpam-6176	217	7	∂x	∂x	PROPN
ejpam-6176	217	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6176	217	9	x=0,l	x=0,l	PROPN
ejpam-6176	218	1	=	=	PUNCT
ejpam-6176	218	2	∂i	∂i	PROPN
ejpam-6176	218	3	∂x	∂x	PROPN
ejpam-6176	218	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6176	218	5	x=0,l	x=0,l	PROPN
ejpam-6176	218	6	=	=	PUNCT
ejpam-6176	218	7	∂q	∂q	PROPN
ejpam-6176	218	8	∂x	∂x	PROPN
ejpam-6176	218	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6176	218	10	x=0,l	x=0,l	PROPN
ejpam-6176	218	11	=	=	PUNCT
ejpam-6176	219	1	∂r	∂r	PROPN
ejpam-6176	219	2	∂x	∂x	PROPN
ejpam-6176	219	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6176	219	4	x=0,l	x=0,l	PROPN
ejpam-6176	219	5	=	=	SYM
ejpam-6176	219	6	0	0	NUM
ejpam-6176	219	7	(	(	PUNCT
ejpam-6176	219	8	33	33	NUM
ejpam-6176	219	9	)	)	PUNCT
ejpam-6176	219	10	these	these	DET
ejpam-6176	219	11	neumann	neumann	PROPN
ejpam-6176	219	12	(	(	PUNCT
ejpam-6176	219	13	no	no	DET
ejpam-6176	219	14	-	-	PUNCT
ejpam-6176	219	15	flux	flux	NOUN
ejpam-6176	219	16	)	)	PUNCT
ejpam-6176	219	17	conditions	condition	NOUN
ejpam-6176	219	18	assume	assume	VERB
ejpam-6176	219	19	no	no	DET
ejpam-6176	219	20	migration	migration	NOUN
ejpam-6176	219	21	at	at	ADP
ejpam-6176	219	22	the	the	DET
ejpam-6176	219	23	domain	domain	NOUN
ejpam-6176	219	24	boundaries	boundary	NOUN
ejpam-6176	219	25	.	.	PUNCT
ejpam-6176	220	1	m.	m.	PROPN
ejpam-6176	220	2	s.	s.	PROPN
ejpam-6176	220	3	arif	arif	PROPN
ejpam-6176	220	4	,	,	PUNCT
ejpam-6176	220	5	k.	k.	PROPN
ejpam-6176	220	6	abodayeh	abodayeh	PROPN
ejpam-6176	220	7	,	,	PUNCT
ejpam-6176	220	8	y.	y.	NOUN
ejpam-6176	220	9	nawaz	nawaz	PROPN
ejpam-6176	220	10	/	/	SYM
ejpam-6176	220	11	eur	eur	PROPN
ejpam-6176	220	12	.	.	PUNCT
ejpam-6176	221	1	j.	j.	PROPN
ejpam-6176	221	2	pure	pure	PROPN
ejpam-6176	221	3	appl	appl	PROPN
ejpam-6176	221	4	.	.	PROPN
ejpam-6176	221	5	math	math	PROPN
ejpam-6176	221	6	,	,	PUNCT
ejpam-6176	221	7	18	18	NUM
ejpam-6176	221	8	(	(	PUNCT
ejpam-6176	221	9	3	3	NUM
ejpam-6176	221	10	)	)	PUNCT
ejpam-6176	221	11	(	(	PUNCT
ejpam-6176	221	12	2025	2025	NUM
ejpam-6176	221	13	)	)	PUNCT
ejpam-6176	221	14	,	,	PUNCT
ejpam-6176	221	15	6176	6176	NUM
ejpam-6176	221	16	10	10	NUM
ejpam-6176	221	17	of	of	ADP
ejpam-6176	221	18	21	21	NUM
ejpam-6176	221	19	4.2	4.2	NUM
ejpam-6176	221	20	.	.	PUNCT
ejpam-6176	222	1	disease	disease	NOUN
ejpam-6176	222	2	-	-	PUNCT
ejpam-6176	222	3	free	free	ADJ
ejpam-6176	222	4	equilibrium	equilibrium	NOUN
ejpam-6176	222	5	(	(	PUNCT
ejpam-6176	222	6	dfe	dfe	PROPN
ejpam-6176	222	7	)	)	PUNCT
ejpam-6176	222	8	the	the	DET
ejpam-6176	222	9	disease	disease	NOUN
ejpam-6176	222	10	-	-	PUNCT
ejpam-6176	222	11	free	free	ADJ
ejpam-6176	222	12	equilibrium	equilibrium	NOUN
ejpam-6176	222	13	(	(	PUNCT
ejpam-6176	222	14	dfe	dfe	PROPN
ejpam-6176	222	15	)	)	PUNCT
ejpam-6176	222	16	is	be	AUX
ejpam-6176	222	17	obtained	obtain	VERB
ejpam-6176	222	18	by	by	ADP
ejpam-6176	222	19	setting	set	VERB
ejpam-6176	222	20	the	the	DET
ejpam-6176	222	21	right	right	ADJ
ejpam-6176	222	22	-	-	PUNCT
ejpam-6176	222	23	hand	hand	NOUN
ejpam-6176	222	24	sides	side	NOUN
ejpam-6176	222	25	of	of	ADP
ejpam-6176	222	26	eqs	eqs	PROPN
ejpam-6176	222	27	.	.	PUNCT
ejpam-6176	223	1	(	(	PUNCT
ejpam-6176	223	2	29)–(32	29)–(32	NUM
ejpam-6176	223	3	)	)	PUNCT
ejpam-6176	223	4	to	to	ADP
ejpam-6176	223	5	zero	zero	NUM
ejpam-6176	223	6	and	and	CCONJ
ejpam-6176	223	7	assuming	assume	VERB
ejpam-6176	223	8	i	i	PRON
ejpam-6176	223	9	=	=	PUNCT
ejpam-6176	223	10	q	q	NOUN
ejpam-6176	224	1	=	=	NOUN
ejpam-6176	224	2	0	0	NUM
ejpam-6176	224	3	:	:	PUNCT
ejpam-6176	224	4	λ−	λ−	PROPN
ejpam-6176	224	5	ds	ds	ADJ
ejpam-6176	224	6	−	−	PROPN
ejpam-6176	225	1	ρs	ρs	NOUN
ejpam-6176	225	2	=	=	NOUN
ejpam-6176	225	3	0	0	NUM
ejpam-6176	226	1	(	(	PUNCT
ejpam-6176	226	2	34	34	NUM
ejpam-6176	226	3	)	)	PUNCT
ejpam-6176	226	4	δi	δi	PROPN
ejpam-6176	226	5	=	=	SYM
ejpam-6176	226	6	0	0	NUM
ejpam-6176	227	1	(	(	PUNCT
ejpam-6176	227	2	35	35	NUM
ejpam-6176	227	3	)	)	PUNCT
ejpam-6176	227	4	(	(	PUNCT
ejpam-6176	227	5	d+	d+	X
ejpam-6176	227	6	α3	α3	ADJ
ejpam-6176	227	7	+	+	NOUN
ejpam-6176	227	8	ϵ)q	ϵ)q	X
ejpam-6176	227	9	=	=	SYM
ejpam-6176	227	10	0	0	NUM
ejpam-6176	227	11	(	(	PUNCT
ejpam-6176	227	12	36	36	NUM
ejpam-6176	227	13	)	)	PUNCT
ejpam-6176	227	14	ϵq+	ϵq+	NOUN
ejpam-6176	228	1	ρs	ρs	ADP
ejpam-6176	228	2	−	−	PROPN
ejpam-6176	229	1	dr	dr	PROPN
ejpam-6176	229	2	=	=	PROPN
ejpam-6176	229	3	0	0	PROPN
ejpam-6176	229	4	(	(	PUNCT
ejpam-6176	229	5	37	37	NUM
ejpam-6176	229	6	)	)	PUNCT
ejpam-6176	229	7	solving	solve	VERB
ejpam-6176	229	8	yields	yield	NOUN
ejpam-6176	229	9	the	the	DET
ejpam-6176	229	10	dfe	dfe	PROPN
ejpam-6176	229	11	point	point	NOUN
ejpam-6176	229	12	:	:	PUNCT
ejpam-6176	229	13	e	e	X
ejpam-6176	229	14	◦	◦	NOUN
ejpam-6176	229	15	=	=	SYM
ejpam-6176	229	16	(	(	PUNCT
ejpam-6176	229	17	s	s	NOUN
ejpam-6176	229	18	=	=	X
ejpam-6176	229	19	λ	λ	X
ejpam-6176	229	20	d+	d+	PUNCT
ejpam-6176	229	21	ρ	ρ	PROPN
ejpam-6176	229	22	,	,	PUNCT
ejpam-6176	229	23	i	i	PRON
ejpam-6176	229	24	=	=	NOUN
ejpam-6176	229	25	0	0	NUM
ejpam-6176	229	26	,	,	PUNCT
ejpam-6176	229	27	q	q	NOUN
ejpam-6176	229	28	=	=	SYM
ejpam-6176	229	29	0	0	NUM
ejpam-6176	229	30	,	,	PUNCT
ejpam-6176	229	31	r	r	NOUN
ejpam-6176	229	32	=	=	PUNCT
ejpam-6176	229	33	ρλ	ρλ	VERB
ejpam-6176	229	34	d(d+	d(d+	PROPN
ejpam-6176	229	35	ρ	ρ	NOUN
ejpam-6176	229	36	)	)	PUNCT
ejpam-6176	229	37	)	)	PUNCT
ejpam-6176	230	1	(	(	PUNCT
ejpam-6176	230	2	38	38	NUM
ejpam-6176	230	3	)	)	PUNCT
ejpam-6176	230	4	4.3	4.3	NUM
ejpam-6176	230	5	.	.	PUNCT
ejpam-6176	231	1	local	local	ADJ
ejpam-6176	231	2	stability	stability	NOUN
ejpam-6176	231	3	of	of	ADP
ejpam-6176	231	4	the	the	DET
ejpam-6176	231	5	dfe	dfe	PROPN
ejpam-6176	231	6	theorem	theorem	NOUN
ejpam-6176	231	7	2	2	NUM
ejpam-6176	231	8	.	.	PUNCT
ejpam-6176	232	1	the	the	DET
ejpam-6176	232	2	dfe	dfe	PROPN
ejpam-6176	232	3	is	be	AUX
ejpam-6176	232	4	locally	locally	ADV
ejpam-6176	232	5	asymptotically	asymptotically	ADV
ejpam-6176	232	6	stable	stable	ADJ
ejpam-6176	232	7	if	if	SCONJ
ejpam-6176	232	8	the	the	DET
ejpam-6176	232	9	following	follow	VERB
ejpam-6176	232	10	condition	condition	NOUN
ejpam-6176	232	11	is	be	AUX
ejpam-6176	232	12	satisfied	satisfied	ADJ
ejpam-6176	232	13	:	:	PUNCT
ejpam-6176	232	14	β1λ	β1λ	PUNCT
ejpam-6176	232	15	<	<	X
ejpam-6176	232	16	ζα2d+	ζα2d+	PROPN
ejpam-6176	232	17	d2	d2	NOUN
ejpam-6176	232	18	+	+	CCONJ
ejpam-6176	232	19	dδ	dδ	ADP
ejpam-6176	232	20	+	+	NUM
ejpam-6176	232	21	dγ1	dγ1	NOUN
ejpam-6176	232	22	−	−	NOUN
ejpam-6176	232	23	ζα2ρ+	ζα2ρ+	NOUN
ejpam-6176	232	24	dρ+	dρ+	NOUN
ejpam-6176	232	25	δρ+	δρ+	NOUN
ejpam-6176	232	26	γ1ρ	γ1ρ	PROPN
ejpam-6176	232	27	proof	proof	NOUN
ejpam-6176	232	28	.	.	PUNCT
ejpam-6176	233	1	with	with	ADP
ejpam-6176	233	2	di	di	NOUN
ejpam-6176	233	3	=	=	SYM
ejpam-6176	233	4	0	0	PROPN
ejpam-6176	233	5	,	,	PUNCT
ejpam-6176	233	6	the	the	DET
ejpam-6176	233	7	jacobian	jacobian	ADJ
ejpam-6176	233	8	matrix	matrix	NOUN
ejpam-6176	233	9	j	j	PROPN
ejpam-6176	233	10	of	of	ADP
ejpam-6176	233	11	the	the	DET
ejpam-6176	233	12	system	system	NOUN
ejpam-6176	233	13	(	(	PUNCT
ejpam-6176	233	14	29)–(32	29)–(32	NUM
ejpam-6176	233	15	)	)	PUNCT
ejpam-6176	233	16	is	be	AUX
ejpam-6176	233	17	:	:	PUNCT
ejpam-6176	233	18	j	j	PROPN
ejpam-6176	233	19	=	=	SYM
ejpam-6176	233	20			PROPN
ejpam-6176	233	21	−d−	−d−	PROPN
ejpam-6176	233	22	β1i	β1i	X
ejpam-6176	233	23	(	(	PUNCT
ejpam-6176	233	24	1+αi)2	1+αi)2	NUM
ejpam-6176	233	25	−	−	PROPN
ejpam-6176	233	26	ρ	ρ	NOUN
ejpam-6176	233	27	−	−	PROPN
ejpam-6176	233	28	β1s	β1s	PUNCT
ejpam-6176	233	29	(	(	PUNCT
ejpam-6176	233	30	1+αi)2	1+αi)2	NUM
ejpam-6176	233	31	+	+	CCONJ
ejpam-6176	233	32	2αβ1is	2αβ1is	NUM
ejpam-6176	233	33	(	(	PUNCT
ejpam-6176	233	34	1+αi)3	1+αi)3	NUM
ejpam-6176	233	35	0	0	NUM
ejpam-6176	233	36	0	0	NUM
ejpam-6176	233	37	β1i	β1i	PUNCT
ejpam-6176	233	38	(	(	PUNCT
ejpam-6176	233	39	1+αi)2	1+αi)2	NUM
ejpam-6176	233	40	−ζα2	−ζα2	NOUN
ejpam-6176	233	41	−	−	NUM
ejpam-6176	233	42	d−	d−	PROPN
ejpam-6176	233	43	δ	δ	PROPN
ejpam-6176	233	44	−	−	PROPN
ejpam-6176	233	45	γ1	γ1	NOUN
ejpam-6176	233	46	+	+	CCONJ
ejpam-6176	233	47	β1s	β1s	PUNCT
ejpam-6176	233	48	(	(	PUNCT
ejpam-6176	233	49	1+αi)2	1+αi)2	NUM
ejpam-6176	233	50	−	−	NOUN
ejpam-6176	233	51	2αβ1is	2αβ1is	NUM
ejpam-6176	233	52	(	(	PUNCT
ejpam-6176	233	53	1+αi)3	1+αi)3	NUM
ejpam-6176	233	54	0	0	NUM
ejpam-6176	233	55	0	0	NUM
ejpam-6176	233	56	0	0	NUM
ejpam-6176	233	57	δ	δ	PROPN
ejpam-6176	233	58	−α3	−α3	PROPN
ejpam-6176	233	59	−	−	ADP
ejpam-6176	233	60	d−	d−	PROPN
ejpam-6176	233	61	ϵ	ϵ	ADP
ejpam-6176	233	62	0	0	NUM
ejpam-6176	233	63	ρ	ρ	PROPN
ejpam-6176	233	64	γ1	γ1	PROPN
ejpam-6176	233	65	ϵ	ϵ	PROPN
ejpam-6176	233	66	−d	−d	PROPN
ejpam-6176	233	67			PROPN
ejpam-6176	233	68	evaluated	evaluate	VERB
ejpam-6176	233	69	at	at	ADP
ejpam-6176	233	70	e	e	NOUN
ejpam-6176	233	71	◦	◦	NOUN
ejpam-6176	233	72	:	:	PUNCT
ejpam-6176	233	73	j	j	PROPN
ejpam-6176	233	74	|e	|e	PROPN
ejpam-6176	233	75	◦	◦	NOUN
ejpam-6176	233	76	=	=	SYM
ejpam-6176	233	77			NOUN
ejpam-6176	233	78	−d−	−d−	NOUN
ejpam-6176	233	79	ρ	ρ	PROPN
ejpam-6176	233	80	−	−	PROPN
ejpam-6176	233	81	β1λ	β1λ	PUNCT
ejpam-6176	233	82	d+ρ	d+ρ	NOUN
ejpam-6176	233	83	0	0	NUM
ejpam-6176	233	84	0	0	NUM
ejpam-6176	233	85	0	0	NUM
ejpam-6176	234	1	−ζα2	−ζα2	PRON
ejpam-6176	234	2	−	−	PROPN
ejpam-6176	234	3	d−	d−	PROPN
ejpam-6176	234	4	δ	δ	PROPN
ejpam-6176	234	5	+	+	CCONJ
ejpam-6176	234	6	β1λ	β1λ	PUNCT
ejpam-6176	234	7	d+ρ	d+ρ	NOUN
ejpam-6176	234	8	0	0	NUM
ejpam-6176	234	9	0	0	NUM
ejpam-6176	234	10	0	0	NUM
ejpam-6176	234	11	δ	δ	PROPN
ejpam-6176	234	12	−α3	−α3	PROPN
ejpam-6176	234	13	−	−	ADP
ejpam-6176	234	14	d−	d−	PROPN
ejpam-6176	234	15	ϵ	ϵ	ADP
ejpam-6176	234	16	0	0	NUM
ejpam-6176	234	17	ρ	ρ	PROPN
ejpam-6176	234	18	γ1	γ1	PROPN
ejpam-6176	234	19	ϵ	ϵ	PROPN
ejpam-6176	234	20	−d	−d	PROPN
ejpam-6176	234	21			VERB
ejpam-6176	234	22	the	the	DET
ejpam-6176	234	23	eigenvalues	eigenvalues	PROPN
ejpam-6176	234	24	of	of	ADP
ejpam-6176	234	25	j	j	PROPN
ejpam-6176	234	26	|e	|e	PROPN
ejpam-6176	234	27	◦	◦	NOUN
ejpam-6176	234	28	are	be	AUX
ejpam-6176	234	29	:	:	PUNCT
ejpam-6176	234	30	λ1	λ1	ADJ
ejpam-6176	234	31	=	=	PUNCT
ejpam-6176	234	32	−d	−d	ADJ
ejpam-6176	234	33	,	,	PUNCT
ejpam-6176	234	34	λ2	λ2	NOUN
ejpam-6176	234	35	=	=	SYM
ejpam-6176	234	36	−α3	−α3	PROPN
ejpam-6176	234	37	−	−	NUM
ejpam-6176	234	38	d−	d−	PROPN
ejpam-6176	234	39	ϵ	ϵ	NOUN
ejpam-6176	234	40	,	,	PUNCT
ejpam-6176	234	41	λ3	λ3	PROPN
ejpam-6176	234	42	=	=	PROPN
ejpam-6176	234	43	−d−	−d−	PROPN
ejpam-6176	234	44	ρ	ρ	PROPN
ejpam-6176	234	45	,	,	PUNCT
ejpam-6176	234	46	λ4	λ4	PROPN
ejpam-6176	234	47	=	=	SYM
ejpam-6176	235	1	1	1	NUM
ejpam-6176	235	2	d+	d+	NOUN
ejpam-6176	235	3	ρ	ρ	NOUN
ejpam-6176	236	1	[	[	X
ejpam-6176	236	2	β1λ−	β1λ−	X
ejpam-6176	236	3	(	(	PUNCT
ejpam-6176	236	4	stability	stability	NOUN
ejpam-6176	236	5	threshold	threshold	NOUN
ejpam-6176	236	6	)	)	PUNCT
ejpam-6176	236	7	]	]	PUNCT
ejpam-6176	236	8	if	if	SCONJ
ejpam-6176	236	9	all	all	DET
ejpam-6176	236	10	eigenvalues	eigenvalue	NOUN
ejpam-6176	236	11	are	be	AUX
ejpam-6176	236	12	negative	negative	ADJ
ejpam-6176	236	13	,	,	PUNCT
ejpam-6176	236	14	the	the	DET
ejpam-6176	236	15	dfe	dfe	PROPN
ejpam-6176	236	16	is	be	AUX
ejpam-6176	236	17	locally	locally	ADV
ejpam-6176	236	18	asymptotically	asymptotically	ADV
ejpam-6176	236	19	stable	stable	ADJ
ejpam-6176	236	20	.	.	PUNCT
ejpam-6176	237	1	m.	m.	PROPN
ejpam-6176	237	2	s.	s.	PROPN
ejpam-6176	237	3	arif	arif	PROPN
ejpam-6176	237	4	,	,	PUNCT
ejpam-6176	237	5	k.	k.	PROPN
ejpam-6176	237	6	abodayeh	abodayeh	PROPN
ejpam-6176	237	7	,	,	PUNCT
ejpam-6176	237	8	y.	y.	NOUN
ejpam-6176	237	9	nawaz	nawaz	PROPN
ejpam-6176	237	10	/	/	SYM
ejpam-6176	237	11	eur	eur	PROPN
ejpam-6176	237	12	.	.	PUNCT
ejpam-6176	238	1	j.	j.	PROPN
ejpam-6176	238	2	pure	pure	PROPN
ejpam-6176	238	3	appl	appl	PROPN
ejpam-6176	238	4	.	.	PROPN
ejpam-6176	238	5	math	math	PROPN
ejpam-6176	238	6	,	,	PUNCT
ejpam-6176	238	7	18	18	NUM
ejpam-6176	238	8	(	(	PUNCT
ejpam-6176	238	9	3	3	NUM
ejpam-6176	238	10	)	)	PUNCT
ejpam-6176	238	11	(	(	PUNCT
ejpam-6176	238	12	2025	2025	NUM
ejpam-6176	238	13	)	)	PUNCT
ejpam-6176	238	14	,	,	PUNCT
ejpam-6176	238	15	6176	6176	NUM
ejpam-6176	238	16	11	11	NUM
ejpam-6176	238	17	of	of	ADP
ejpam-6176	238	18	21	21	NUM
ejpam-6176	238	19	4.4	4.4	NUM
ejpam-6176	238	20	.	.	PUNCT
ejpam-6176	239	1	stochastic	stochastic	ADJ
ejpam-6176	239	2	diffusive	diffusive	ADJ
ejpam-6176	239	3	model	model	NOUN
ejpam-6176	239	4	to	to	PART
ejpam-6176	239	5	capture	capture	VERB
ejpam-6176	239	6	random	random	ADJ
ejpam-6176	239	7	fluctuations	fluctuation	NOUN
ejpam-6176	239	8	,	,	PUNCT
ejpam-6176	239	9	we	we	PRON
ejpam-6176	239	10	introduce	introduce	VERB
ejpam-6176	239	11	stochasticity	stochasticity	NOUN
ejpam-6176	239	12	into	into	ADP
ejpam-6176	239	13	the	the	DET
ejpam-6176	239	14	model	model	NOUN
ejpam-6176	239	15	:	:	PUNCT
ejpam-6176	239	16	ds	ds	ADJ
ejpam-6176	239	17	=	=	SYM
ejpam-6176	239	18	(	(	PUNCT
ejpam-6176	239	19	d1	d1	PROPN
ejpam-6176	239	20	∂2s	∂2s	PROPN
ejpam-6176	239	21	∂x2	∂x2	NOUN
ejpam-6176	239	22	+	+	CCONJ
ejpam-6176	239	23	λ−	λ−	PROPN
ejpam-6176	239	24	β1si	β1si	ADJ
ejpam-6176	239	25	1	1	NUM
ejpam-6176	239	26	+	+	NUM
ejpam-6176	239	27	αi	αi	VERB
ejpam-6176	239	28	−	−	NOUN
ejpam-6176	239	29	ds	ds	NOUN
ejpam-6176	239	30	−	−	PROPN
ejpam-6176	239	31	ρs	ρs	NOUN
ejpam-6176	239	32	)	)	PUNCT
ejpam-6176	239	33	dt+	dt+	NOUN
ejpam-6176	239	34	σ1sdw	σ1sdw	NOUN
ejpam-6176	239	35	(	(	PUNCT
ejpam-6176	239	36	39	39	NUM
ejpam-6176	239	37	)	)	PUNCT
ejpam-6176	239	38	di	di	NOUN
ejpam-6176	239	39	=	=	PUNCT
ejpam-6176	239	40	(	(	PUNCT
ejpam-6176	239	41	d2	d2	PROPN
ejpam-6176	239	42	∂2i	∂2i	NOUN
ejpam-6176	239	43	∂x2	∂x2	NOUN
ejpam-6176	239	44	+	+	CCONJ
ejpam-6176	239	45	β1si	β1si	SYM
ejpam-6176	239	46	1	1	NUM
ejpam-6176	239	47	+	+	NUM
ejpam-6176	239	48	αi	αi	VERB
ejpam-6176	239	49	−	−	PROPN
ejpam-6176	239	50	(	(	PUNCT
ejpam-6176	239	51	γ1	γ1	PROPN
ejpam-6176	239	52	+	+	CCONJ
ejpam-6176	239	53	δ	δ	PROPN
ejpam-6176	239	54	+	+	CCONJ
ejpam-6176	239	55	d+	d+	X
ejpam-6176	239	56	α2	α2	ADJ
ejpam-6176	239	57	+	+	CCONJ
ejpam-6176	239	58	ζ)i	ζ)i	NOUN
ejpam-6176	239	59	)	)	PUNCT
ejpam-6176	240	1	dt+	dt+	NOUN
ejpam-6176	240	2	σ2idw	σ2idw	NOUN
ejpam-6176	240	3	(	(	PUNCT
ejpam-6176	240	4	40	40	NUM
ejpam-6176	240	5	)	)	PUNCT
ejpam-6176	240	6	dq	dq	NOUN
ejpam-6176	240	7	=	=	PUNCT
ejpam-6176	240	8	(	(	PUNCT
ejpam-6176	240	9	d3	d3	PROPN
ejpam-6176	240	10	∂2q	∂2q	PROPN
ejpam-6176	240	11	∂x2	∂x2	PROPN
ejpam-6176	240	12	+	+	CCONJ
ejpam-6176	240	13	δi	δi	ADP
ejpam-6176	240	14	−	−	PROPN
ejpam-6176	240	15	(	(	PUNCT
ejpam-6176	240	16	d+	d+	PROPN
ejpam-6176	240	17	α3	α3	ADJ
ejpam-6176	240	18	+	+	NOUN
ejpam-6176	240	19	ϵ)q	ϵ)q	X
ejpam-6176	240	20	)	)	PUNCT
ejpam-6176	241	1	dt+	dt+	NOUN
ejpam-6176	241	2	σ3qdw	σ3qdw	NUM
ejpam-6176	241	3	(	(	PUNCT
ejpam-6176	241	4	41	41	NUM
ejpam-6176	241	5	)	)	PUNCT
ejpam-6176	241	6	dr	dr	NOUN
ejpam-6176	241	7	=	=	PRON
ejpam-6176	241	8	(	(	PUNCT
ejpam-6176	241	9	d4	d4	PROPN
ejpam-6176	241	10	∂2r	∂2r	PROPN
ejpam-6176	241	11	∂x2	∂x2	NOUN
ejpam-6176	241	12	+	+	X
ejpam-6176	241	13	ϵq+	ϵq+	PROPN
ejpam-6176	242	1	ρs	ρs	ADP
ejpam-6176	242	2	−	−	PROPN
ejpam-6176	243	1	dr	dr	PROPN
ejpam-6176	243	2	)	)	PUNCT
ejpam-6176	243	3	dt+	dt+	NOUN
ejpam-6176	243	4	σ4rdw	σ4rdw	PROPN
ejpam-6176	243	5	(	(	PUNCT
ejpam-6176	243	6	42	42	NUM
ejpam-6176	243	7	)	)	PUNCT
ejpam-6176	243	8	here	here	ADV
ejpam-6176	243	9	,	,	PUNCT
ejpam-6176	243	10	σi	σi	X
ejpam-6176	243	11	(	(	PUNCT
ejpam-6176	243	12	i	i	NOUN
ejpam-6176	243	13	=	=	NOUN
ejpam-6176	243	14	1	1	NUM
ejpam-6176	243	15	,	,	PUNCT
ejpam-6176	243	16	2	2	NUM
ejpam-6176	243	17	,	,	PUNCT
ejpam-6176	243	18	3	3	NUM
ejpam-6176	243	19	,	,	PUNCT
ejpam-6176	243	20	4	4	NUM
ejpam-6176	243	21	)	)	PUNCT
ejpam-6176	243	22	are	be	AUX
ejpam-6176	243	23	noise	noise	NOUN
ejpam-6176	243	24	intensities	intensity	NOUN
ejpam-6176	243	25	,	,	PUNCT
ejpam-6176	243	26	and	and	CCONJ
ejpam-6176	243	27	w	w	PROPN
ejpam-6176	243	28	represents	represent	VERB
ejpam-6176	243	29	a	a	DET
ejpam-6176	243	30	wiener	wiener	NOUN
ejpam-6176	243	31	process	process	NOUN
ejpam-6176	243	32	(	(	PUNCT
ejpam-6176	243	33	brownian	brownian	ADJ
ejpam-6176	243	34	motion	motion	NOUN
ejpam-6176	243	35	)	)	PUNCT
ejpam-6176	243	36	.	.	PUNCT
ejpam-6176	244	1	4.5	4.5	NUM
ejpam-6176	244	2	.	.	PUNCT
ejpam-6176	245	1	model	model	NOUN
ejpam-6176	245	2	relevance	relevance	NOUN
ejpam-6176	245	3	to	to	ADP
ejpam-6176	245	4	real	real	ADJ
ejpam-6176	245	5	epidemics	epidemic	NOUN
ejpam-6176	245	6	this	this	DET
ejpam-6176	245	7	model	model	NOUN
ejpam-6176	245	8	integrates	integrate	VERB
ejpam-6176	245	9	several	several	ADJ
ejpam-6176	245	10	realistic	realistic	ADJ
ejpam-6176	245	11	epidemic	epidemic	NOUN
ejpam-6176	245	12	mechanisms	mechanism	NOUN
ejpam-6176	245	13	:	:	PUNCT
ejpam-6176	245	14	•	•	NUM
ejpam-6176	245	15	spatial	spatial	ADJ
ejpam-6176	245	16	diffusion	diffusion	NOUN
ejpam-6176	245	17	accounts	account	VERB
ejpam-6176	245	18	for	for	ADP
ejpam-6176	245	19	movement	movement	NOUN
ejpam-6176	245	20	/	/	SYM
ejpam-6176	245	21	contact	contact	NOUN
ejpam-6176	245	22	patterns	pattern	NOUN
ejpam-6176	245	23	,	,	PUNCT
ejpam-6176	245	24	critical	critical	ADJ
ejpam-6176	245	25	for	for	ADP
ejpam-6176	245	26	modeling	model	VERB
ejpam-6176	245	27	localized	localized	ADJ
ejpam-6176	245	28	outbreaks	outbreak	NOUN
ejpam-6176	245	29	.	.	PUNCT
ejpam-6176	246	1	•	•	NUM
ejpam-6176	246	2	nonlinear	nonlinear	ADJ
ejpam-6176	246	3	incidence	incidence	NOUN
ejpam-6176	246	4	rate	rate	NOUN
ejpam-6176	246	5	reflects	reflect	VERB
ejpam-6176	246	6	saturation	saturation	NOUN
ejpam-6176	246	7	effects	effect	NOUN
ejpam-6176	246	8	when	when	SCONJ
ejpam-6176	246	9	infection	infection	NOUN
ejpam-6176	246	10	levels	level	NOUN
ejpam-6176	246	11	are	be	AUX
ejpam-6176	246	12	high	high	ADJ
ejpam-6176	246	13	.	.	PUNCT
ejpam-6176	247	1	•	•	NOUN
ejpam-6176	247	2	stochastic	stochastic	ADJ
ejpam-6176	247	3	terms	term	NOUN
ejpam-6176	247	4	introduce	introduce	VERB
ejpam-6176	247	5	variability	variability	NOUN
ejpam-6176	247	6	and	and	CCONJ
ejpam-6176	247	7	environmental	environmental	ADJ
ejpam-6176	247	8	uncertainty	uncertainty	NOUN
ejpam-6176	247	9	into	into	ADP
ejpam-6176	247	10	epidemic	epidemic	NOUN
ejpam-6176	247	11	dynamics	dynamic	NOUN
ejpam-6176	247	12	.	.	PUNCT
ejpam-6176	248	1	•	•	NUM
ejpam-6176	248	2	quarantine	quarantine	NOUN
ejpam-6176	248	3	and	and	CCONJ
ejpam-6176	248	4	vaccination	vaccination	NOUN
ejpam-6176	248	5	model	model	NOUN
ejpam-6176	248	6	disease	disease	NOUN
ejpam-6176	248	7	control	control	NOUN
ejpam-6176	248	8	strategies	strategy	NOUN
ejpam-6176	248	9	.	.	PUNCT
ejpam-6176	249	1	•	•	NOUN
ejpam-6176	249	2	stability	stability	NOUN
ejpam-6176	249	3	analysis	analysis	NOUN
ejpam-6176	249	4	provides	provide	VERB
ejpam-6176	249	5	threshold	threshold	NOUN
ejpam-6176	249	6	criteria	criterion	NOUN
ejpam-6176	249	7	for	for	ADP
ejpam-6176	249	8	disease	disease	NOUN
ejpam-6176	249	9	eradication	eradication	NOUN
ejpam-6176	249	10	,	,	PUNCT
ejpam-6176	249	11	assisting	assist	VERB
ejpam-6176	249	12	in	in	ADP
ejpam-6176	249	13	public	public	ADJ
ejpam-6176	249	14	health	health	NOUN
ejpam-6176	249	15	decision	decision	NOUN
ejpam-6176	249	16	-	-	PUNCT
ejpam-6176	249	17	making	making	NOUN
ejpam-6176	249	18	.	.	PUNCT
ejpam-6176	250	1	5	5	X
ejpam-6176	250	2	.	.	NOUN
ejpam-6176	250	3	results	result	NOUN
ejpam-6176	250	4	and	and	CCONJ
ejpam-6176	250	5	discussions	discussion	NOUN
ejpam-6176	250	6	a	a	DET
ejpam-6176	250	7	computational	computational	ADJ
ejpam-6176	250	8	framework	framework	NOUN
ejpam-6176	250	9	is	be	AUX
ejpam-6176	250	10	presented	present	VERB
ejpam-6176	250	11	for	for	ADP
ejpam-6176	250	12	solving	solve	VERB
ejpam-6176	250	13	both	both	CCONJ
ejpam-6176	250	14	deterministic	deterministic	ADJ
ejpam-6176	250	15	and	and	CCONJ
ejpam-6176	250	16	stochastic	stochastic	ADJ
ejpam-6176	250	17	models	model	NOUN
ejpam-6176	250	18	.	.	PUNCT
ejpam-6176	251	1	the	the	DET
ejpam-6176	251	2	technique	technique	NOUN
ejpam-6176	251	3	is	be	AUX
ejpam-6176	251	4	comprised	comprise	VERB
ejpam-6176	251	5	of	of	ADP
ejpam-6176	251	6	two	two	NUM
ejpam-6176	251	7	distinct	distinct	ADJ
ejpam-6176	251	8	phases	phase	NOUN
ejpam-6176	251	9	,	,	PUNCT
ejpam-6176	251	10	referred	refer	VERB
ejpam-6176	251	11	to	to	ADP
ejpam-6176	251	12	as	as	ADP
ejpam-6176	251	13	the	the	DET
ejpam-6176	251	14	predictor	predictor	NOUN
ejpam-6176	251	15	and	and	CCONJ
ejpam-6176	251	16	corrector	corrector	NOUN
ejpam-6176	251	17	stages	stage	NOUN
ejpam-6176	251	18	.	.	PUNCT
ejpam-6176	252	1	the	the	DET
ejpam-6176	252	2	predictor	predictor	NOUN
ejpam-6176	252	3	stage	stage	NOUN
ejpam-6176	252	4	is	be	AUX
ejpam-6176	252	5	utilized	utilize	VERB
ejpam-6176	252	6	to	to	PART
ejpam-6176	252	7	ascertain	ascertain	VERB
ejpam-6176	252	8	solutions	solution	NOUN
ejpam-6176	252	9	at	at	ADP
ejpam-6176	252	10	any	any	DET
ejpam-6176	252	11	given	give	VERB
ejpam-6176	252	12	time	time	NOUN
ejpam-6176	252	13	level	level	NOUN
ejpam-6176	252	14	.	.	PUNCT
ejpam-6176	253	1	however	however	ADV
ejpam-6176	253	2	,	,	PUNCT
ejpam-6176	253	3	the	the	DET
ejpam-6176	253	4	corrector	corrector	NOUN
ejpam-6176	253	5	stage	stage	NOUN
ejpam-6176	253	6	determines	determine	VERB
ejpam-6176	253	7	solutions	solution	NOUN
ejpam-6176	253	8	at	at	ADP
ejpam-6176	253	9	the	the	DET
ejpam-6176	253	10	subsequent	subsequent	ADJ
ejpam-6176	253	11	time	time	NOUN
ejpam-6176	253	12	level	level	NOUN
ejpam-6176	253	13	.	.	PUNCT
ejpam-6176	254	1	the	the	DET
ejpam-6176	254	2	predictor	predictor	NOUN
ejpam-6176	254	3	step	step	NOUN
ejpam-6176	254	4	disregards	disregard	VERB
ejpam-6176	254	5	the	the	DET
ejpam-6176	254	6	stochastic	stochastic	ADJ
ejpam-6176	254	7	component	component	NOUN
ejpam-6176	254	8	of	of	ADP
ejpam-6176	254	9	stochastic	stochastic	ADJ
ejpam-6176	254	10	partial	partial	ADJ
ejpam-6176	254	11	differential	differential	NOUN
ejpam-6176	254	12	equations	equation	NOUN
ejpam-6176	254	13	,	,	PUNCT
ejpam-6176	254	14	whereas	whereas	SCONJ
ejpam-6176	254	15	the	the	DET
ejpam-6176	254	16	corrector	corrector	NOUN
ejpam-6176	254	17	stage	stage	NOUN
ejpam-6176	254	18	incorporates	incorporate	VERB
ejpam-6176	254	19	this	this	DET
ejpam-6176	254	20	stochastic	stochastic	ADJ
ejpam-6176	254	21	element	element	NOUN
ejpam-6176	254	22	.	.	PUNCT
ejpam-6176	255	1	the	the	DET
ejpam-6176	255	2	approach	approach	NOUN
ejpam-6176	255	3	provides	provide	VERB
ejpam-6176	255	4	a	a	DET
ejpam-6176	255	5	second	second	ADJ
ejpam-6176	255	6	-	-	PUNCT
ejpam-6176	255	7	order	order	NOUN
ejpam-6176	255	8	accurate	accurate	ADJ
ejpam-6176	255	9	solution	solution	NOUN
ejpam-6176	255	10	for	for	ADP
ejpam-6176	255	11	deterministic	deterministic	ADJ
ejpam-6176	255	12	models	model	NOUN
ejpam-6176	255	13	.	.	PUNCT
ejpam-6176	256	1	the	the	DET
ejpam-6176	256	2	initial	initial	ADJ
ejpam-6176	256	3	stage	stage	NOUN
ejpam-6176	256	4	of	of	ADP
ejpam-6176	256	5	the	the	DET
ejpam-6176	256	6	scheme	scheme	NOUN
ejpam-6176	256	7	diverges	diverge	VERB
ejpam-6176	256	8	from	from	ADP
ejpam-6176	256	9	the	the	DET
ejpam-6176	256	10	conventional	conventional	ADJ
ejpam-6176	256	11	runge	runge	NOUN
ejpam-6176	256	12	-	-	PUNCT
ejpam-6176	256	13	kutta	kutta	NOUN
ejpam-6176	256	14	method	method	NOUN
ejpam-6176	256	15	,	,	PUNCT
ejpam-6176	256	16	but	but	CCONJ
ejpam-6176	256	17	the	the	DET
ejpam-6176	256	18	subsequent	subsequent	ADJ
ejpam-6176	256	19	stage	stage	NOUN
ejpam-6176	256	20	aligns	align	VERB
ejpam-6176	256	21	with	with	ADP
ejpam-6176	256	22	the	the	DET
ejpam-6176	256	23	second	second	ADJ
ejpam-6176	256	24	stage	stage	NOUN
ejpam-6176	256	25	of	of	ADP
ejpam-6176	256	26	the	the	DET
ejpam-6176	256	27	runge	runge	NOUN
ejpam-6176	256	28	-	-	PUNCT
ejpam-6176	256	29	kutta	kutta	NOUN
ejpam-6176	256	30	scheme	scheme	NOUN
ejpam-6176	256	31	;	;	PUNCT
ejpam-6176	256	32	hence	hence	ADV
ejpam-6176	256	33	,	,	PUNCT
ejpam-6176	256	34	the	the	DET
ejpam-6176	256	35	entire	entire	ADJ
ejpam-6176	256	36	scheme	scheme	NOUN
ejpam-6176	256	37	represents	represent	VERB
ejpam-6176	256	38	a	a	DET
ejpam-6176	256	39	hybrid	hybrid	NOUN
ejpam-6176	256	40	of	of	ADP
ejpam-6176	256	41	a	a	DET
ejpam-6176	256	42	modified	modify	VERB
ejpam-6176	256	43	exponential	exponential	ADJ
ejpam-6176	256	44	integrator	integrator	NOUN
ejpam-6176	256	45	and	and	CCONJ
ejpam-6176	256	46	the	the	DET
ejpam-6176	256	47	runge	runge	NOUN
ejpam-6176	256	48	-	-	PUNCT
ejpam-6176	256	49	kutta	kutta	NOUN
ejpam-6176	256	50	method	method	NOUN
ejpam-6176	256	51	.	.	PUNCT
ejpam-6176	257	1	the	the	DET
ejpam-6176	257	2	m.	m.	NOUN
ejpam-6176	257	3	s.	s.	PROPN
ejpam-6176	257	4	arif	arif	PROPN
ejpam-6176	257	5	,	,	PUNCT
ejpam-6176	257	6	k.	k.	PROPN
ejpam-6176	257	7	abodayeh	abodayeh	PROPN
ejpam-6176	257	8	,	,	PUNCT
ejpam-6176	257	9	y.	y.	NOUN
ejpam-6176	257	10	nawaz	nawaz	PROPN
ejpam-6176	257	11	/	/	SYM
ejpam-6176	257	12	eur	eur	PROPN
ejpam-6176	257	13	.	.	PUNCT
ejpam-6176	258	1	j.	j.	PROPN
ejpam-6176	258	2	pure	pure	PROPN
ejpam-6176	258	3	appl	appl	PROPN
ejpam-6176	258	4	.	.	PROPN
ejpam-6176	258	5	math	math	PROPN
ejpam-6176	258	6	,	,	PUNCT
ejpam-6176	258	7	18	18	NUM
ejpam-6176	258	8	(	(	PUNCT
ejpam-6176	258	9	3	3	NUM
ejpam-6176	258	10	)	)	PUNCT
ejpam-6176	258	11	(	(	PUNCT
ejpam-6176	258	12	2025	2025	NUM
ejpam-6176	258	13	)	)	PUNCT
ejpam-6176	258	14	,	,	PUNCT
ejpam-6176	258	15	6176	6176	NUM
ejpam-6176	258	16	12	12	NUM
ejpam-6176	258	17	of	of	ADP
ejpam-6176	258	18	21	21	NUM
ejpam-6176	258	19	suggested	suggest	VERB
ejpam-6176	258	20	technique	technique	NOUN
ejpam-6176	258	21	is	be	AUX
ejpam-6176	258	22	preferable	preferable	ADJ
ejpam-6176	258	23	to	to	ADP
ejpam-6176	258	24	the	the	DET
ejpam-6176	258	25	existing	exist	VERB
ejpam-6176	258	26	euler	euler	NOUN
ejpam-6176	258	27	-	-	PUNCT
ejpam-6176	258	28	maruyama	maruyama	NOUN
ejpam-6176	258	29	method	method	NOUN
ejpam-6176	258	30	due	due	ADP
ejpam-6176	258	31	to	to	ADP
ejpam-6176	258	32	its	its	PRON
ejpam-6176	258	33	superior	superior	ADJ
ejpam-6176	258	34	accuracy	accuracy	NOUN
ejpam-6176	258	35	for	for	ADP
ejpam-6176	258	36	deterministic	deterministic	ADJ
ejpam-6176	258	37	models	model	NOUN
ejpam-6176	258	38	while	while	SCONJ
ejpam-6176	258	39	addressing	address	VERB
ejpam-6176	258	40	the	the	DET
ejpam-6176	258	41	stochastic	stochastic	ADJ
ejpam-6176	258	42	component	component	NOUN
ejpam-6176	258	43	,	,	PUNCT
ejpam-6176	258	44	similar	similar	ADJ
ejpam-6176	258	45	to	to	ADP
ejpam-6176	258	46	the	the	DET
ejpam-6176	258	47	current	current	ADJ
ejpam-6176	258	48	euler	euler	VERB
ejpam-6176	258	49	-	-	PUNCT
ejpam-6176	258	50	maruyama	maruyama	NOUN
ejpam-6176	258	51	method	method	NOUN
ejpam-6176	258	52	.	.	PUNCT
ejpam-6176	259	1	for	for	ADP
ejpam-6176	259	2	simulation	simulation	NOUN
ejpam-6176	259	3	,	,	PUNCT
ejpam-6176	259	4	we	we	PRON
ejpam-6176	259	5	take	take	VERB
ejpam-6176	259	6	the	the	DET
ejpam-6176	259	7	birth	birth	NOUN
ejpam-6176	259	8	/	/	SYM
ejpam-6176	259	9	death	death	NOUN
ejpam-6176	259	10	rate	rate	NOUN
ejpam-6176	259	11	d	d	NOUN
ejpam-6176	259	12	=	=	SYM
ejpam-6176	259	13	0.1	0.1	NUM
ejpam-6176	259	14	,	,	PUNCT
ejpam-6176	259	15	transmission	transmission	NOUN
ejpam-6176	259	16	rate	rate	NOUN
ejpam-6176	259	17	β1	β1	NOUN
ejpam-6176	259	18	=	=	NOUN
ejpam-6176	259	19	0.1	0.1	NUM
ejpam-6176	259	20	,	,	PUNCT
ejpam-6176	259	21	recruitment	recruitment	NOUN
ejpam-6176	259	22	rate	rate	NOUN
ejpam-6176	259	23	λ	λ	NOUN
ejpam-6176	259	24	=	=	NOUN
ejpam-6176	259	25	0.1	0.1	NUM
ejpam-6176	259	26	,	,	PUNCT
ejpam-6176	259	27	vaccination	vaccination	NOUN
ejpam-6176	259	28	rate	rate	NOUN
ejpam-6176	259	29	ρ	ρ	NOUN
ejpam-6176	259	30	=	=	SYM
ejpam-6176	259	31	0.1	0.1	NUM
ejpam-6176	259	32	,	,	PUNCT
ejpam-6176	259	33	quarantine	quarantine	NOUN
ejpam-6176	259	34	rate	rate	NOUN
ejpam-6176	259	35	δ	δ	PROPN
ejpam-6176	259	36	=	=	SYM
ejpam-6176	259	37	0.1	0.1	NUM
ejpam-6176	259	38	,	,	PUNCT
ejpam-6176	259	39	nonlinear	nonlinear	ADJ
ejpam-6176	259	40	incidence	incidence	NOUN
ejpam-6176	259	41	factor	factor	NOUN
ejpam-6176	259	42	α	α	NOUN
ejpam-6176	259	43	=	=	SYM
ejpam-6176	259	44	0.3	0.3	NUM
ejpam-6176	259	45	,	,	PUNCT
ejpam-6176	259	46	comorbidity	comorbidity	NOUN
ejpam-6176	259	47	death	death	NOUN
ejpam-6176	259	48	from	from	ADP
ejpam-6176	259	49	infection	infection	NOUN
ejpam-6176	259	50	α2	α2	NOUN
ejpam-6176	259	51	=	=	SYM
ejpam-6176	259	52	0.1	0.1	NUM
ejpam-6176	259	53	,	,	PUNCT
ejpam-6176	259	54	comorbidity	comorbidity	NOUN
ejpam-6176	259	55	death	death	NOUN
ejpam-6176	259	56	from	from	ADP
ejpam-6176	259	57	quarantine	quarantine	NOUN
ejpam-6176	259	58	α3	α3	NOUN
ejpam-6176	259	59	=	=	NOUN
ejpam-6176	259	60	0.1	0.1	NUM
ejpam-6176	259	61	,	,	PUNCT
ejpam-6176	259	62	total	total	ADJ
ejpam-6176	259	63	population	population	NOUN
ejpam-6176	259	64	size	size	NOUN
ejpam-6176	259	65	n	n	PROPN
ejpam-6176	259	66	=	=	SYM
ejpam-6176	259	67	15	15	NUM
ejpam-6176	259	68	obtained	obtain	VERB
ejpam-6176	259	69	using	use	VERB
ejpam-6176	259	70	the	the	DET
ejpam-6176	259	71	initial	initial	ADJ
ejpam-6176	259	72	distribution	distribution	NOUN
ejpam-6176	259	73	as	as	ADP
ejpam-6176	259	74	s0	s0	PROPN
ejpam-6176	259	75	+	+	CCONJ
ejpam-6176	259	76	i0	i0	PROPN
ejpam-6176	259	77	+	+	CCONJ
ejpam-6176	259	78	q0	q0	PROPN
ejpam-6176	259	79	+	+	CCONJ
ejpam-6176	259	80	r0	r0	NOUN
ejpam-6176	259	81	=	=	NOUN
ejpam-6176	259	82	3	3	NUM
ejpam-6176	260	1	+	+	NUM
ejpam-6176	260	2	4	4	NUM
ejpam-6176	260	3	+	+	SYM
ejpam-6176	260	4	3	3	NUM
ejpam-6176	260	5	+	+	SYM
ejpam-6176	260	6	5	5	NUM
ejpam-6176	260	7	,	,	PUNCT
ejpam-6176	260	8	disease	disease	NOUN
ejpam-6176	260	9	elimination	elimination	NOUN
ejpam-6176	260	10	from	from	ADP
ejpam-6176	260	11	infected	infected	ADJ
ejpam-6176	260	12	class	class	NOUN
ejpam-6176	260	13	ζ	ζ	NOUN
ejpam-6176	260	14	=	=	SYM
ejpam-6176	260	15	0.1	0.1	NUM
ejpam-6176	260	16	,	,	PUNCT
ejpam-6176	260	17	recovery	recovery	NOUN
ejpam-6176	260	18	rate	rate	NOUN
ejpam-6176	260	19	from	from	ADP
ejpam-6176	260	20	infection	infection	NOUN
ejpam-6176	260	21	γ1	γ1	NOUN
ejpam-6176	260	22	=	=	NOUN
ejpam-6176	260	23	0.3	0.3	NUM
ejpam-6176	260	24	,	,	PUNCT
ejpam-6176	260	25	and	and	CCONJ
ejpam-6176	260	26	removal	removal	NOUN
ejpam-6176	260	27	rate	rate	NOUN
ejpam-6176	260	28	from	from	ADP
ejpam-6176	260	29	quarantine	quarantine	NOUN
ejpam-6176	260	30	ϵ	ϵ	NOUN
ejpam-6176	260	31	=	=	SYM
ejpam-6176	260	32	0.1	0.1	NUM
ejpam-6176	260	33	.	.	PUNCT
ejpam-6176	261	1	furthermore	furthermore	ADV
ejpam-6176	261	2	,	,	PUNCT
ejpam-6176	261	3	σi	σi	NOUN
ejpam-6176	261	4	=	=	NOUN
ejpam-6176	261	5	0.1	0.1	NUM
ejpam-6176	261	6	,	,	PUNCT
ejpam-6176	261	7	di	di	NOUN
ejpam-6176	261	8	=	=	NOUN
ejpam-6176	261	9	0.1	0.1	NUM
ejpam-6176	261	10	for	for	ADP
ejpam-6176	261	11	i	i	PRON
ejpam-6176	261	12	=	=	NOUN
ejpam-6176	261	13	1	1	NUM
ejpam-6176	261	14	,	,	PUNCT
ejpam-6176	261	15	2	2	NUM
ejpam-6176	261	16	,	,	PUNCT
ejpam-6176	261	17	3	3	NUM
ejpam-6176	261	18	,	,	PUNCT
ejpam-6176	261	19	4	4	NUM
ejpam-6176	261	20	.	.	PUNCT
ejpam-6176	261	21	to	to	PART
ejpam-6176	261	22	determine	determine	VERB
ejpam-6176	261	23	the	the	DET
ejpam-6176	261	24	eigenvalues	eigenvalue	NOUN
ejpam-6176	261	25	of	of	ADP
ejpam-6176	261	26	the	the	DET
ejpam-6176	261	27	jacobian	jacobian	ADJ
ejpam-6176	261	28	matrix	matrix	NOUN
ejpam-6176	261	29	at	at	ADP
ejpam-6176	261	30	the	the	DET
ejpam-6176	261	31	disease	disease	NOUN
ejpam-6176	261	32	-	-	PUNCT
ejpam-6176	261	33	free	free	ADJ
ejpam-6176	261	34	equilibrium	equilibrium	NOUN
ejpam-6176	261	35	(	(	PUNCT
ejpam-6176	261	36	dfe	dfe	PROPN
ejpam-6176	261	37	)	)	PUNCT
ejpam-6176	262	1	e	e	X
ejpam-6176	262	2	◦	◦	NOUN
ejpam-6176	262	3	for	for	ADP
ejpam-6176	262	4	the	the	DET
ejpam-6176	262	5	given	give	VERB
ejpam-6176	262	6	parameter	parameter	NOUN
ejpam-6176	262	7	values	value	NOUN
ejpam-6176	262	8	,	,	PUNCT
ejpam-6176	262	9	note	note	VERB
ejpam-6176	262	10	that	that	SCONJ
ejpam-6176	262	11	at	at	ADP
ejpam-6176	262	12	the	the	DET
ejpam-6176	262	13	equilibrium	equilibrium	NOUN
ejpam-6176	262	14	state	state	NOUN
ejpam-6176	262	15	,	,	PUNCT
ejpam-6176	262	16	s	s	PART
ejpam-6176	262	17	=	=	ADJ
ejpam-6176	262	18	λ/(d+ρ	λ/(d+ρ	NUM
ejpam-6176	262	19	)	)	PUNCT
ejpam-6176	262	20	and	and	CCONJ
ejpam-6176	262	21	i	i	NOUN
ejpam-6176	262	22	=	=	NOUN
ejpam-6176	262	23	0	0	NUM
ejpam-6176	262	24	,	,	PUNCT
ejpam-6176	262	25	q	q	NOUN
ejpam-6176	263	1	=	=	SYM
ejpam-6176	263	2	0	0	NUM
ejpam-6176	263	3	,	,	PUNCT
ejpam-6176	263	4	r	r	NOUN
ejpam-6176	263	5	=	=	SYM
ejpam-6176	263	6	ρλ/(d(d+	ρλ/(d(d+	PROPN
ejpam-6176	263	7	ρ	ρ	PROPN
ejpam-6176	263	8	)	)	PUNCT
ejpam-6176	263	9	)	)	PUNCT
ejpam-6176	263	10	,	,	PUNCT
ejpam-6176	263	11	which	which	PRON
ejpam-6176	263	12	gives	give	VERB
ejpam-6176	263	13	:	:	PUNCT
ejpam-6176	263	14	j	j	PROPN
ejpam-6176	263	15	|e	|e	PROPN
ejpam-6176	263	16	◦	◦	NOUN
ejpam-6176	263	17	=	=	SYM
ejpam-6176	263	18			NOUN
ejpam-6176	264	1	−0.2	−0.2	NOUN
ejpam-6176	264	2	−0.05	−0.05	ADV
ejpam-6176	264	3	0	0	NUM
ejpam-6176	264	4	0	0	NUM
ejpam-6176	264	5	0	0	NUM
ejpam-6176	265	1	−0.16	−0.16	NOUN
ejpam-6176	265	2	0	0	NUM
ejpam-6176	265	3	0	0	NUM
ejpam-6176	265	4	0	0	NUM
ejpam-6176	265	5	0.1	0.1	NUM
ejpam-6176	265	6	−0.3	−0.3	PROPN
ejpam-6176	265	7	0	0	NUM
ejpam-6176	265	8	0.1	0.1	NUM
ejpam-6176	265	9	0.3	0.3	NUM
ejpam-6176	265	10	0.1	0.1	NUM
ejpam-6176	265	11	−0.1	−0.1	NOUN
ejpam-6176	265	12			NOUN
ejpam-6176	265	13	solving	solve	VERB
ejpam-6176	265	14	the	the	DET
ejpam-6176	265	15	characteristic	characteristic	ADJ
ejpam-6176	265	16	equation	equation	NOUN
ejpam-6176	265	17	|j	|j	NOUN
ejpam-6176	265	18	−	−	PUNCT
ejpam-6176	266	1	λi|	λi|	NOUN
ejpam-6176	266	2	=	=	SYM
ejpam-6176	266	3	0	0	NUM
ejpam-6176	266	4	,	,	PUNCT
ejpam-6176	266	5	i.e.	i.e.	X
ejpam-6176	266	6	,∣∣∣∣∣∣∣∣	,∣∣∣∣∣∣∣∣	PUNCT
ejpam-6176	266	7	−0.2−	−0.2−	PROPN
ejpam-6176	266	8	λ	λ	NOUN
ejpam-6176	266	9	−0.05	−0.05	NOUN
ejpam-6176	266	10	0	0	NUM
ejpam-6176	266	11	0	0	NUM
ejpam-6176	266	12	0	0	NUM
ejpam-6176	266	13	−0.16−	−0.16−	PROPN
ejpam-6176	266	14	λ	λ	NOUN
ejpam-6176	266	15	0	0	NUM
ejpam-6176	266	16	0	0	NUM
ejpam-6176	266	17	0	0	NUM
ejpam-6176	266	18	0.1	0.1	NUM
ejpam-6176	266	19	−0.3−	−0.3−	PROPN
ejpam-6176	266	20	λ	λ	X
ejpam-6176	266	21	0	0	NUM
ejpam-6176	266	22	0.1	0.1	NUM
ejpam-6176	266	23	0.3	0.3	NUM
ejpam-6176	266	24	0.1	0.1	NUM
ejpam-6176	266	25	−0.1−	−0.1−	NOUN
ejpam-6176	266	26	λ	λ	NOUN
ejpam-6176	266	27	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-6176	266	28	=	=	SYM
ejpam-6176	266	29	0	0	NUM
ejpam-6176	267	1	we	we	PRON
ejpam-6176	267	2	obtain	obtain	VERB
ejpam-6176	267	3	the	the	DET
ejpam-6176	267	4	eigenvalues	eigenvalue	NOUN
ejpam-6176	267	5	:	:	PUNCT
ejpam-6176	267	6	λ1	λ1	ADJ
ejpam-6176	267	7	=	=	SYM
ejpam-6176	267	8	−0.1	−0.1	PROPN
ejpam-6176	267	9	,	,	PUNCT
ejpam-6176	267	10	λ2	λ2	NOUN
ejpam-6176	267	11	=	=	SYM
ejpam-6176	267	12	−0.2	−0.2	PROPN
ejpam-6176	267	13	,	,	PUNCT
ejpam-6176	267	14	λ3	λ3	PROPN
ejpam-6176	267	15	=	=	SYM
ejpam-6176	267	16	−0.3	−0.3	PROPN
ejpam-6176	267	17	,	,	PUNCT
ejpam-6176	267	18	λ4	λ4	PROPN
ejpam-6176	267	19	=	=	PROPN
ejpam-6176	268	1	−0.16	−0.16	PROPN
ejpam-6176	268	2	since	since	SCONJ
ejpam-6176	268	3	all	all	DET
ejpam-6176	268	4	eigenvalues	eigenvalue	NOUN
ejpam-6176	268	5	are	be	AUX
ejpam-6176	268	6	real	real	ADJ
ejpam-6176	268	7	and	and	CCONJ
ejpam-6176	268	8	negative	negative	ADJ
ejpam-6176	268	9	,	,	PUNCT
ejpam-6176	268	10	the	the	DET
ejpam-6176	268	11	disease	disease	NOUN
ejpam-6176	268	12	-	-	PUNCT
ejpam-6176	268	13	free	free	ADJ
ejpam-6176	268	14	equilibrium	equilibrium	NOUN
ejpam-6176	268	15	is	be	AUX
ejpam-6176	268	16	locally	locally	ADV
ejpam-6176	268	17	asymptotically	asymptotically	ADV
ejpam-6176	268	18	stable	stable	ADJ
ejpam-6176	268	19	.	.	PUNCT
ejpam-6176	269	1	this	this	PRON
ejpam-6176	269	2	supports	support	VERB
ejpam-6176	269	3	the	the	DET
ejpam-6176	269	4	theoretical	theoretical	ADJ
ejpam-6176	269	5	result	result	NOUN
ejpam-6176	269	6	stated	state	VERB
ejpam-6176	269	7	in	in	ADP
ejpam-6176	269	8	theorem	theorem	NOUN
ejpam-6176	269	9	2	2	NUM
ejpam-6176	269	10	for	for	ADP
ejpam-6176	269	11	the	the	DET
ejpam-6176	269	12	given	give	VERB
ejpam-6176	269	13	parameter	parameter	NOUN
ejpam-6176	269	14	set	set	PROPN
ejpam-6176	269	15	.	.	PUNCT
ejpam-6176	270	1	comparison	comparison	NOUN
ejpam-6176	270	2	of	of	ADP
ejpam-6176	270	3	numerical	numerical	ADJ
ejpam-6176	270	4	schemes	scheme	NOUN
ejpam-6176	270	5	(	(	PUNCT
ejpam-6176	270	6	proposed	propose	VERB
ejpam-6176	270	7	vs	vs	ADP
ejpam-6176	270	8	euler	euler	NOUN
ejpam-6176	270	9	-	-	PUNCT
ejpam-6176	270	10	maruyama	maruyama	NOUN
ejpam-6176	270	11	)	)	PUNCT
ejpam-6176	270	12	to	to	PART
ejpam-6176	270	13	compare	compare	VERB
ejpam-6176	270	14	the	the	DET
ejpam-6176	270	15	performance	performance	NOUN
ejpam-6176	270	16	of	of	ADP
ejpam-6176	270	17	the	the	DET
ejpam-6176	270	18	proposed	propose	VERB
ejpam-6176	270	19	scheme	scheme	NOUN
ejpam-6176	270	20	for	for	ADP
ejpam-6176	270	21	the	the	DET
ejpam-6176	270	22	stochastic	stochastic	ADJ
ejpam-6176	270	23	siqr	siqr	PROPN
ejpam-6176	270	24	model	model	NOUN
ejpam-6176	270	25	,	,	PUNCT
ejpam-6176	270	26	figure	figure	NOUN
ejpam-6176	270	27	1	1	NUM
ejpam-6176	270	28	shows	show	VERB
ejpam-6176	270	29	the	the	DET
ejpam-6176	270	30	epidemic	epidemic	NOUN
ejpam-6176	270	31	dynamics	dynamic	NOUN
ejpam-6176	270	32	obtained	obtain	VERB
ejpam-6176	270	33	using	use	VERB
ejpam-6176	270	34	the	the	DET
ejpam-6176	270	35	euler	euler	NOUN
ejpam-6176	270	36	-	-	PUNCT
ejpam-6176	270	37	maruyama	maruyama	NOUN
ejpam-6176	270	38	method	method	NOUN
ejpam-6176	270	39	(	(	PUNCT
ejpam-6176	270	40	right	right	ADJ
ejpam-6176	270	41	)	)	PUNCT
ejpam-6176	270	42	and	and	CCONJ
ejpam-6176	270	43	the	the	DET
ejpam-6176	270	44	proposed	propose	VERB
ejpam-6176	270	45	numerical	numerical	ADJ
ejpam-6176	270	46	scheme	scheme	NOUN
ejpam-6176	270	47	(	(	PUNCT
ejpam-6176	270	48	left	leave	VERB
ejpam-6176	270	49	)	)	PUNCT
ejpam-6176	270	50	for	for	ADP
ejpam-6176	270	51	the	the	DET
ejpam-6176	270	52	given	give	VERB
ejpam-6176	270	53	parameter	parameter	NOUN
ejpam-6176	270	54	set	set	NOUN
ejpam-6176	270	55	:	:	PUNCT
ejpam-6176	270	56	d1	d1	PROPN
ejpam-6176	270	57	=	=	SYM
ejpam-6176	270	58	d2	d2	PROPN
ejpam-6176	270	59	=	=	PUNCT
ejpam-6176	270	60	d3	d3	PROPN
ejpam-6176	270	61	=	=	SYM
ejpam-6176	270	62	d4	d4	PROPN
ejpam-6176	270	63	=	=	SYM
ejpam-6176	270	64	0.1	0.1	NUM
ejpam-6176	270	65	,	,	PUNCT
ejpam-6176	270	66	β1	β1	PROPN
ejpam-6176	270	67	=	=	PUNCT
ejpam-6176	270	68	0.1	0.1	NUM
ejpam-6176	270	69	,	,	PUNCT
ejpam-6176	270	70	ρ	ρ	PROPN
ejpam-6176	270	71	=	=	SYM
ejpam-6176	270	72	0.5	0.5	NUM
ejpam-6176	270	73	,	,	PUNCT
ejpam-6176	270	74	δ	δ	X
ejpam-6176	270	75	=	=	SYM
ejpam-6176	270	76	0.1	0.1	NUM
ejpam-6176	270	77	,	,	PUNCT
ejpam-6176	270	78	γ1	γ1	NOUN
ejpam-6176	270	79	=	=	NOUN
ejpam-6176	270	80	0.1	0.1	NUM
ejpam-6176	270	81	,	,	PUNCT
ejpam-6176	270	82	d	d	NOUN
ejpam-6176	270	83	=	=	SYM
ejpam-6176	270	84	0.1	0.1	NUM
ejpam-6176	270	85	,	,	PUNCT
ejpam-6176	270	86	λ	λ	X
ejpam-6176	270	87	=	=	NOUN
ejpam-6176	270	88	0.1	0.1	NUM
ejpam-6176	270	89	,	,	PUNCT
ejpam-6176	270	90	α	α	NOUN
ejpam-6176	270	91	=	=	SYM
ejpam-6176	270	92	0.3	0.3	NUM
ejpam-6176	270	93	,	,	PUNCT
ejpam-6176	270	94	α2	α2	NOUN
ejpam-6176	270	95	=	=	SYM
ejpam-6176	270	96	0.1	0.1	NUM
ejpam-6176	270	97	,	,	PUNCT
ejpam-6176	270	98	α3	α3	NOUN
ejpam-6176	270	99	=	=	NOUN
ejpam-6176	270	100	0.1	0.1	NUM
ejpam-6176	270	101	,	,	PUNCT
ejpam-6176	270	102	ϵ	ϵ	X
ejpam-6176	270	103	=	=	SYM
ejpam-6176	270	104	0.1	0.1	NUM
ejpam-6176	270	105	,	,	PUNCT
ejpam-6176	270	106	ζ	ζ	NOUN
ejpam-6176	270	107	=	=	SYM
ejpam-6176	270	108	0.1	0.1	NUM
ejpam-6176	270	109	,	,	PUNCT
ejpam-6176	270	110	x	x	PUNCT
ejpam-6176	270	111	=	=	SYM
ejpam-6176	270	112	0.1429	0.1429	NUM
ejpam-6176	270	113	,	,	PUNCT
ejpam-6176	270	114	σ1	σ1	PROPN
ejpam-6176	270	115	=	=	PROPN
ejpam-6176	270	116	σ2	σ2	PROPN
ejpam-6176	270	117	=	=	PROPN
ejpam-6176	270	118	σ3	σ3	PROPN
ejpam-6176	270	119	=	=	PROPN
ejpam-6176	270	120	σ4	σ4	NOUN
ejpam-6176	270	121	=	=	NOUN
ejpam-6176	270	122	0.1	0.1	NUM
ejpam-6176	270	123	.	.	PUNCT
ejpam-6176	271	1	the	the	DET
ejpam-6176	271	2	difference	difference	NOUN
ejpam-6176	271	3	in	in	ADP
ejpam-6176	271	4	the	the	DET
ejpam-6176	271	5	solutions	solution	NOUN
ejpam-6176	271	6	obtained	obtain	VERB
ejpam-6176	271	7	using	use	VERB
ejpam-6176	271	8	the	the	DET
ejpam-6176	271	9	two	two	NUM
ejpam-6176	271	10	methods	method	NOUN
ejpam-6176	271	11	is	be	AUX
ejpam-6176	271	12	due	due	ADJ
ejpam-6176	271	13	to	to	ADP
ejpam-6176	271	14	their	their	PRON
ejpam-6176	271	15	differing	differ	VERB
ejpam-6176	271	16	order	order	NOUN
ejpam-6176	271	17	of	of	ADP
ejpam-6176	271	18	accuracy	accuracy	NOUN
ejpam-6176	271	19	for	for	ADP
ejpam-6176	271	20	solving	solve	VERB
ejpam-6176	271	21	the	the	DET
ejpam-6176	271	22	deterministic	deterministic	ADJ
ejpam-6176	271	23	part	part	NOUN
ejpam-6176	271	24	of	of	ADP
ejpam-6176	271	25	the	the	DET
ejpam-6176	271	26	model	model	NOUN
ejpam-6176	271	27	.	.	PUNCT
ejpam-6176	272	1	as	as	SCONJ
ejpam-6176	272	2	previously	previously	ADV
ejpam-6176	272	3	discussed	discuss	VERB
ejpam-6176	272	4	,	,	PUNCT
ejpam-6176	272	5	the	the	DET
ejpam-6176	272	6	euler	euler	NOUN
ejpam-6176	272	7	-	-	PUNCT
ejpam-6176	272	8	maruyama	maruyama	NOUN
ejpam-6176	272	9	method	method	NOUN
ejpam-6176	272	10	is	be	AUX
ejpam-6176	272	11	first	first	ADJ
ejpam-6176	272	12	-	-	PUNCT
ejpam-6176	272	13	order	order	NOUN
ejpam-6176	272	14	accurate	accurate	ADJ
ejpam-6176	272	15	,	,	PUNCT
ejpam-6176	272	16	while	while	SCONJ
ejpam-6176	272	17	the	the	DET
ejpam-6176	272	18	proposed	propose	VERB
ejpam-6176	272	19	scheme	scheme	NOUN
ejpam-6176	272	20	is	be	AUX
ejpam-6176	272	21	second	second	ADJ
ejpam-6176	272	22	-	-	PUNCT
ejpam-6176	272	23	order	order	NOUN
ejpam-6176	272	24	accurate	accurate	ADJ
ejpam-6176	272	25	in	in	ADP
ejpam-6176	272	26	time	time	NOUN
ejpam-6176	272	27	.	.	PUNCT
ejpam-6176	273	1	both	both	DET
ejpam-6176	273	2	methods	method	NOUN
ejpam-6176	273	3	employ	employ	VERB
ejpam-6176	273	4	the	the	DET
ejpam-6176	273	5	same	same	ADJ
ejpam-6176	273	6	approach	approach	NOUN
ejpam-6176	273	7	to	to	PART
ejpam-6176	273	8	incorporate	incorporate	VERB
ejpam-6176	273	9	m.	m.	NOUN
ejpam-6176	273	10	s.	s.	PROPN
ejpam-6176	273	11	arif	arif	PROPN
ejpam-6176	273	12	,	,	PUNCT
ejpam-6176	273	13	k.	k.	PROPN
ejpam-6176	273	14	abodayeh	abodayeh	PROPN
ejpam-6176	273	15	,	,	PUNCT
ejpam-6176	273	16	y.	y.	NOUN
ejpam-6176	273	17	nawaz	nawaz	PROPN
ejpam-6176	273	18	/	/	SYM
ejpam-6176	273	19	eur	eur	PROPN
ejpam-6176	273	20	.	.	PUNCT
ejpam-6176	274	1	j.	j.	PROPN
ejpam-6176	274	2	pure	pure	PROPN
ejpam-6176	274	3	appl	appl	PROPN
ejpam-6176	274	4	.	.	PROPN
ejpam-6176	274	5	math	math	PROPN
ejpam-6176	274	6	,	,	PUNCT
ejpam-6176	274	7	18	18	NUM
ejpam-6176	274	8	(	(	PUNCT
ejpam-6176	274	9	3	3	NUM
ejpam-6176	274	10	)	)	PUNCT
ejpam-6176	274	11	(	(	PUNCT
ejpam-6176	274	12	2025	2025	NUM
ejpam-6176	274	13	)	)	PUNCT
ejpam-6176	274	14	,	,	PUNCT
ejpam-6176	274	15	6176	6176	NUM
ejpam-6176	274	16	13	13	NUM
ejpam-6176	274	17	of	of	ADP
ejpam-6176	274	18	21	21	NUM
ejpam-6176	274	19	figure	figure	NOUN
ejpam-6176	274	20	1	1	NUM
ejpam-6176	274	21	:	:	PUNCT
ejpam-6176	274	22	comparison	comparison	NOUN
ejpam-6176	274	23	of	of	ADP
ejpam-6176	274	24	proposed	propose	VERB
ejpam-6176	274	25	and	and	CCONJ
ejpam-6176	274	26	euler	euler	NOUN
ejpam-6176	274	27	-	-	PUNCT
ejpam-6176	274	28	maruyama	maruyama	NOUN
ejpam-6176	274	29	method	method	NOUN
ejpam-6176	274	30	for	for	ADP
ejpam-6176	274	31	solving	solve	VERB
ejpam-6176	274	32	the	the	DET
ejpam-6176	274	33	stochastic	stochastic	ADJ
ejpam-6176	274	34	model	model	NOUN
ejpam-6176	274	35	using	use	VERB
ejpam-6176	274	36	d1	d1	PROPN
ejpam-6176	274	37	=	=	SYM
ejpam-6176	274	38	0.1	0.1	NUM
ejpam-6176	274	39	,	,	PUNCT
ejpam-6176	274	40	d2	d2	PROPN
ejpam-6176	274	41	=	=	SYM
ejpam-6176	274	42	0.1	0.1	NUM
ejpam-6176	274	43	,	,	PUNCT
ejpam-6176	274	44	d3	d3	PROPN
ejpam-6176	274	45	=	=	SYM
ejpam-6176	274	46	0.1	0.1	NUM
ejpam-6176	274	47	,	,	PUNCT
ejpam-6176	274	48	d4	d4	PROPN
ejpam-6176	274	49	=	=	SYM
ejpam-6176	274	50	0.1	0.1	NUM
ejpam-6176	274	51	,	,	PUNCT
ejpam-6176	274	52	β1	β1	PROPN
ejpam-6176	274	53	=	=	PUNCT
ejpam-6176	274	54	0.1	0.1	NUM
ejpam-6176	274	55	,	,	PUNCT
ejpam-6176	274	56	ρ	ρ	PROPN
ejpam-6176	274	57	=	=	SYM
ejpam-6176	274	58	0.5	0.5	NUM
ejpam-6176	274	59	,	,	PUNCT
ejpam-6176	274	60	δ	δ	X
ejpam-6176	274	61	=	=	SYM
ejpam-6176	274	62	0.1	0.1	NUM
ejpam-6176	274	63	,	,	PUNCT
ejpam-6176	274	64	γ1	γ1	NOUN
ejpam-6176	274	65	=	=	NOUN
ejpam-6176	274	66	0.1	0.1	NUM
ejpam-6176	274	67	,	,	PUNCT
ejpam-6176	274	68	d	d	NOUN
ejpam-6176	274	69	=	=	SYM
ejpam-6176	274	70	0.1	0.1	NUM
ejpam-6176	274	71	,	,	PUNCT
ejpam-6176	274	72	λ	λ	X
ejpam-6176	274	73	=	=	NOUN
ejpam-6176	274	74	0.1	0.1	NUM
ejpam-6176	274	75	,	,	PUNCT
ejpam-6176	274	76	α	α	NOUN
ejpam-6176	274	77	=	=	SYM
ejpam-6176	274	78	0.3	0.3	NUM
ejpam-6176	274	79	,	,	PUNCT
ejpam-6176	274	80	α2	α2	NOUN
ejpam-6176	274	81	=	=	SYM
ejpam-6176	274	82	0.1	0.1	NUM
ejpam-6176	274	83	,	,	PUNCT
ejpam-6176	274	84	α3	α3	NOUN
ejpam-6176	274	85	=	=	NOUN
ejpam-6176	274	86	0.1	0.1	NUM
ejpam-6176	274	87	,	,	PUNCT
ejpam-6176	274	88	ϵ	ϵ	X
ejpam-6176	274	89	=	=	SYM
ejpam-6176	274	90	0.1	0.1	NUM
ejpam-6176	274	91	,	,	PUNCT
ejpam-6176	274	92	ζ	ζ	NOUN
ejpam-6176	274	93	=	=	SYM
ejpam-6176	274	94	0.1	0.1	NUM
ejpam-6176	274	95	,	,	PUNCT
ejpam-6176	274	96	x	x	PUNCT
ejpam-6176	274	97	=	=	SYM
ejpam-6176	274	98	0.1429	0.1429	NUM
ejpam-6176	274	99	,	,	PUNCT
ejpam-6176	274	100	σ1	σ1	NOUN
ejpam-6176	274	101	=	=	SYM
ejpam-6176	274	102	0.1	0.1	NUM
ejpam-6176	274	103	,	,	PUNCT
ejpam-6176	274	104	σ2	σ2	NOUN
ejpam-6176	274	105	=	=	SYM
ejpam-6176	274	106	0.1	0.1	NUM
ejpam-6176	274	107	,	,	PUNCT
ejpam-6176	274	108	σ3	σ3	NOUN
ejpam-6176	274	109	=	=	PROPN
ejpam-6176	274	110	0.1	0.1	NUM
ejpam-6176	274	111	,	,	PUNCT
ejpam-6176	274	112	σ4	σ4	NOUN
ejpam-6176	274	113	=	=	NOUN
ejpam-6176	274	114	0.1	0.1	NUM
ejpam-6176	274	115	.	.	PUNCT
ejpam-6176	275	1	the	the	DET
ejpam-6176	275	2	stochastic	stochastic	ADJ
ejpam-6176	275	3	(	(	PUNCT
ejpam-6176	275	4	wiener	wiener	NOUN
ejpam-6176	275	5	)	)	PUNCT
ejpam-6176	275	6	terms	term	NOUN
ejpam-6176	275	7	.	.	PUNCT
ejpam-6176	276	1	the	the	DET
ejpam-6176	276	2	euler	euler	NOUN
ejpam-6176	276	3	-	-	PUNCT
ejpam-6176	276	4	maruyama	maruyama	NOUN
ejpam-6176	276	5	method	method	NOUN
ejpam-6176	276	6	results	result	NOUN
ejpam-6176	276	7	in	in	ADP
ejpam-6176	276	8	visibly	visibly	ADV
ejpam-6176	276	9	noisier	noisy	ADJ
ejpam-6176	276	10	trajectories	trajectory	NOUN
ejpam-6176	276	11	,	,	PUNCT
ejpam-6176	276	12	particularly	particularly	ADV
ejpam-6176	276	13	for	for	ADP
ejpam-6176	276	14	the	the	DET
ejpam-6176	276	15	susceptible	susceptible	ADJ
ejpam-6176	276	16	(	(	PUNCT
ejpam-6176	276	17	purple	purple	ADJ
ejpam-6176	276	18	)	)	PUNCT
ejpam-6176	276	19	and	and	CCONJ
ejpam-6176	276	20	recovered	recover	VERB
ejpam-6176	276	21	(	(	PUNCT
ejpam-6176	276	22	cyan	cyan	ADJ
ejpam-6176	276	23	)	)	PUNCT
ejpam-6176	276	24	subpopulations	subpopulation	NOUN
ejpam-6176	276	25	.	.	PUNCT
ejpam-6176	277	1	in	in	ADP
ejpam-6176	277	2	contrast	contrast	NOUN
ejpam-6176	277	3	,	,	PUNCT
ejpam-6176	277	4	the	the	DET
ejpam-6176	277	5	proposed	propose	VERB
ejpam-6176	277	6	scheme	scheme	NOUN
ejpam-6176	277	7	yields	yield	NOUN
ejpam-6176	277	8	smoother	smooth	ADJ
ejpam-6176	277	9	and	and	CCONJ
ejpam-6176	277	10	more	more	ADV
ejpam-6176	277	11	stable	stable	ADJ
ejpam-6176	277	12	dynamics	dynamic	NOUN
ejpam-6176	277	13	,	,	PUNCT
ejpam-6176	277	14	following	follow	VERB
ejpam-6176	277	15	expected	expect	VERB
ejpam-6176	277	16	epidemic	epidemic	NOUN
ejpam-6176	277	17	trends	trend	NOUN
ejpam-6176	277	18	closely	closely	ADV
ejpam-6176	277	19	.	.	PUNCT
ejpam-6176	278	1	this	this	DET
ejpam-6176	278	2	highlights	highlight	VERB
ejpam-6176	278	3	the	the	DET
ejpam-6176	278	4	superiority	superiority	NOUN
ejpam-6176	278	5	of	of	ADP
ejpam-6176	278	6	the	the	DET
ejpam-6176	278	7	proposed	propose	VERB
ejpam-6176	278	8	method	method	NOUN
ejpam-6176	278	9	for	for	ADP
ejpam-6176	278	10	accurately	accurately	ADV
ejpam-6176	278	11	and	and	CCONJ
ejpam-6176	278	12	efficiently	efficiently	ADV
ejpam-6176	278	13	solving	solve	VERB
ejpam-6176	278	14	complex	complex	ADJ
ejpam-6176	278	15	stochastic	stochastic	ADJ
ejpam-6176	278	16	partial	partial	ADJ
ejpam-6176	278	17	differential	differential	NOUN
ejpam-6176	278	18	equation	equation	NOUN
ejpam-6176	278	19	models	model	NOUN
ejpam-6176	278	20	in	in	ADP
ejpam-6176	278	21	disease	disease	NOUN
ejpam-6176	278	22	transmission	transmission	NOUN
ejpam-6176	278	23	analysis	analysis	NOUN
ejpam-6176	278	24	.	.	PUNCT
ejpam-6176	279	1	effect	effect	NOUN
ejpam-6176	279	2	of	of	ADP
ejpam-6176	279	3	transmission	transmission	NOUN
ejpam-6176	279	4	rate	rate	NOUN
ejpam-6176	279	5	β1	β1	PROPN
ejpam-6176	279	6	on	on	ADP
ejpam-6176	279	7	susceptible	susceptible	ADJ
ejpam-6176	279	8	and	and	CCONJ
ejpam-6176	279	9	infected	infected	ADJ
ejpam-6176	279	10	classes	class	NOUN
ejpam-6176	279	11	next	next	ADV
ejpam-6176	279	12	,	,	PUNCT
ejpam-6176	279	13	we	we	PRON
ejpam-6176	279	14	investigate	investigate	VERB
ejpam-6176	279	15	the	the	DET
ejpam-6176	279	16	effect	effect	NOUN
ejpam-6176	279	17	of	of	ADP
ejpam-6176	279	18	the	the	DET
ejpam-6176	279	19	transmission	transmission	NOUN
ejpam-6176	279	20	rate	rate	NOUN
ejpam-6176	279	21	β1	β1	PROPN
ejpam-6176	279	22	on	on	ADP
ejpam-6176	279	23	the	the	DET
ejpam-6176	279	24	susceptible	susceptible	ADJ
ejpam-6176	279	25	s	s	NOUN
ejpam-6176	279	26	and	and	CCONJ
ejpam-6176	279	27	infected	infected	ADJ
ejpam-6176	279	28	i	i	PRON
ejpam-6176	279	29	classes	class	NOUN
ejpam-6176	279	30	.	.	PUNCT
ejpam-6176	280	1	to	to	PART
ejpam-6176	280	2	see	see	VERB
ejpam-6176	280	3	the	the	DET
ejpam-6176	280	4	effect	effect	NOUN
ejpam-6176	280	5	more	more	ADV
ejpam-6176	280	6	clearly	clearly	ADV
ejpam-6176	280	7	,	,	PUNCT
ejpam-6176	280	8	we	we	PRON
ejpam-6176	280	9	demonstrate	demonstrate	VERB
ejpam-6176	280	10	using	use	VERB
ejpam-6176	280	11	the	the	DET
ejpam-6176	280	12	deterministic	deterministic	ADJ
ejpam-6176	280	13	model	model	NOUN
ejpam-6176	280	14	,	,	PUNCT
ejpam-6176	280	15	i.e.	i.e.	X
ejpam-6176	280	16	,	,	PUNCT
ejpam-6176	280	17	σi	σi	X
ejpam-6176	280	18	=	=	SYM
ejpam-6176	280	19	0	0	PROPN
ejpam-6176	280	20	,	,	PUNCT
ejpam-6176	280	21	(	(	PUNCT
ejpam-6176	280	22	i	i	NOUN
ejpam-6176	280	23	=	=	NOUN
ejpam-6176	280	24	1	1	NUM
ejpam-6176	280	25	,	,	PUNCT
ejpam-6176	280	26	2	2	NUM
ejpam-6176	280	27	,	,	PUNCT
ejpam-6176	280	28	3	3	NUM
ejpam-6176	280	29	,	,	PUNCT
ejpam-6176	280	30	4	4	NUM
ejpam-6176	280	31	)	)	PUNCT
ejpam-6176	280	32	.	.	PUNCT
ejpam-6176	281	1	the	the	DET
ejpam-6176	281	2	left	left	ADJ
ejpam-6176	281	3	subplot	subplot	NOUN
ejpam-6176	281	4	shows	show	VERB
ejpam-6176	281	5	the	the	DET
ejpam-6176	281	6	susceptible	susceptible	ADJ
ejpam-6176	281	7	s	s	PART
ejpam-6176	281	8	population	population	NOUN
ejpam-6176	281	9	over	over	ADP
ejpam-6176	281	10	time	time	NOUN
ejpam-6176	281	11	for	for	ADP
ejpam-6176	281	12	different	different	ADJ
ejpam-6176	281	13	values	value	NOUN
ejpam-6176	281	14	of	of	ADP
ejpam-6176	281	15	β1	β1	PROPN
ejpam-6176	281	16	.	.	PUNCT
ejpam-6176	282	1	the	the	DET
ejpam-6176	282	2	right	right	ADJ
ejpam-6176	282	3	subplot	subplot	NOUN
ejpam-6176	282	4	shows	show	VERB
ejpam-6176	282	5	the	the	DET
ejpam-6176	282	6	corresponding	corresponding	ADJ
ejpam-6176	282	7	infective	infective	ADJ
ejpam-6176	282	8	i	i	PROPN
ejpam-6176	282	9	population	population	NOUN
ejpam-6176	282	10	over	over	ADP
ejpam-6176	282	11	time	time	NOUN
ejpam-6176	282	12	.	.	PUNCT
ejpam-6176	283	1	three	three	NUM
ejpam-6176	283	2	values	value	NOUN
ejpam-6176	283	3	of	of	ADP
ejpam-6176	283	4	transmission	transmission	NOUN
ejpam-6176	283	5	rate	rate	NOUN
ejpam-6176	283	6	β1	β1	PROPN
ejpam-6176	283	7	are	be	AUX
ejpam-6176	283	8	tested	test	VERB
ejpam-6176	283	9	:	:	PUNCT
ejpam-6176	283	10	•	•	NUM
ejpam-6176	283	11	solid	solid	ADJ
ejpam-6176	283	12	lines	line	NOUN
ejpam-6176	283	13	:	:	PUNCT
ejpam-6176	283	14	β1	β1	NOUN
ejpam-6176	283	15	=	=	PUNCT
ejpam-6176	283	16	0.1	0.1	NUM
ejpam-6176	283	17	•	•	NUM
ejpam-6176	283	18	dashed	dash	VERB
ejpam-6176	283	19	lines	line	NOUN
ejpam-6176	283	20	:	:	PUNCT
ejpam-6176	283	21	β1	β1	PROPN
ejpam-6176	283	22	=	=	PUNCT
ejpam-6176	283	23	0.3	0.3	NUM
ejpam-6176	283	24	•	•	ADV
ejpam-6176	283	25	dotted	dotted	ADJ
ejpam-6176	283	26	lines	line	NOUN
ejpam-6176	283	27	:	:	PUNCT
ejpam-6176	283	28	β1	β1	PROPN
ejpam-6176	283	29	=	=	PUNCT
ejpam-6176	283	30	0.5	0.5	NUM
ejpam-6176	283	31	the	the	DET
ejpam-6176	283	32	parameter	parameter	NOUN
ejpam-6176	283	33	settings	setting	NOUN
ejpam-6176	283	34	are	be	AUX
ejpam-6176	283	35	d1	d1	PROPN
ejpam-6176	283	36	=	=	SYM
ejpam-6176	283	37	d2	d2	PROPN
ejpam-6176	283	38	=	=	PUNCT
ejpam-6176	283	39	d3	d3	PROPN
ejpam-6176	283	40	=	=	SYM
ejpam-6176	283	41	d4	d4	PROPN
ejpam-6176	283	42	=	=	SYM
ejpam-6176	283	43	0.1	0.1	NUM
ejpam-6176	283	44	,	,	PUNCT
ejpam-6176	283	45	ρ	ρ	PROPN
ejpam-6176	283	46	=	=	SYM
ejpam-6176	283	47	0.3	0.3	NUM
ejpam-6176	283	48	,	,	PUNCT
ejpam-6176	283	49	δ	δ	PROPN
ejpam-6176	283	50	=	=	SYM
ejpam-6176	283	51	0.1	0.1	NUM
ejpam-6176	283	52	,	,	PUNCT
ejpam-6176	283	53	γ1	γ1	NOUN
ejpam-6176	283	54	=	=	NOUN
ejpam-6176	283	55	0.1	0.1	NUM
ejpam-6176	283	56	,	,	PUNCT
ejpam-6176	283	57	d	d	NOUN
ejpam-6176	283	58	=	=	SYM
ejpam-6176	283	59	0.1	0.1	NUM
ejpam-6176	283	60	,	,	PUNCT
ejpam-6176	283	61	λ	λ	X
ejpam-6176	283	62	=	=	NOUN
ejpam-6176	283	63	0.1	0.1	NUM
ejpam-6176	283	64	,	,	PUNCT
ejpam-6176	283	65	α	α	NOUN
ejpam-6176	283	66	=	=	SYM
ejpam-6176	283	67	0.3	0.3	NUM
ejpam-6176	283	68	,	,	PUNCT
ejpam-6176	283	69	α2	α2	NOUN
ejpam-6176	283	70	=	=	SYM
ejpam-6176	283	71	0.1	0.1	NUM
ejpam-6176	283	72	,	,	PUNCT
ejpam-6176	283	73	α3	α3	NOUN
ejpam-6176	283	74	=	=	NOUN
ejpam-6176	283	75	0.1	0.1	NUM
ejpam-6176	283	76	,	,	PUNCT
ejpam-6176	283	77	ϵ	ϵ	X
ejpam-6176	283	78	=	=	SYM
ejpam-6176	283	79	0.1	0.1	NUM
ejpam-6176	283	80	,	,	PUNCT
ejpam-6176	283	81	ζ	ζ	NOUN
ejpam-6176	283	82	=	=	SYM
ejpam-6176	283	83	0.1	0.1	NUM
ejpam-6176	283	84	.	.	PUNCT
ejpam-6176	284	1	as	as	SCONJ
ejpam-6176	284	2	β1	β1	NOUN
ejpam-6176	284	3	increases	increase	NOUN
ejpam-6176	284	4	,	,	PUNCT
ejpam-6176	284	5	the	the	DET
ejpam-6176	284	6	susceptible	susceptible	ADJ
ejpam-6176	284	7	population	population	NOUN
ejpam-6176	284	8	declines	decline	VERB
ejpam-6176	284	9	more	more	ADV
ejpam-6176	284	10	rapidly	rapidly	ADV
ejpam-6176	284	11	.	.	PUNCT
ejpam-6176	285	1	higher	high	ADJ
ejpam-6176	285	2	transmission	transmission	NOUN
ejpam-6176	285	3	rates	rate	NOUN
ejpam-6176	285	4	cause	cause	VERB
ejpam-6176	285	5	faster	fast	ADJ
ejpam-6176	285	6	infection	infection	NOUN
ejpam-6176	285	7	to	to	PART
ejpam-6176	285	8	spread	spread	VERB
ejpam-6176	285	9	,	,	PUNCT
ejpam-6176	285	10	meaning	mean	VERB
ejpam-6176	285	11	more	more	ADJ
ejpam-6176	285	12	people	people	NOUN
ejpam-6176	285	13	move	move	VERB
ejpam-6176	285	14	from	from	ADP
ejpam-6176	285	15	susceptible	susceptible	ADJ
ejpam-6176	285	16	to	to	ADP
ejpam-6176	285	17	infective	infective	VERB
ejpam-6176	285	18	in	in	ADP
ejpam-6176	285	19	a	a	DET
ejpam-6176	285	20	shorter	short	ADJ
ejpam-6176	285	21	time	time	NOUN
ejpam-6176	285	22	.	.	PUNCT
ejpam-6176	286	1	as	as	SCONJ
ejpam-6176	286	2	β1	β1	NOUN
ejpam-6176	286	3	increases	increase	NOUN
ejpam-6176	286	4	,	,	PUNCT
ejpam-6176	286	5	the	the	DET
ejpam-6176	286	6	infective	infective	ADJ
ejpam-6176	286	7	population	population	NOUN
ejpam-6176	286	8	rises	rise	VERB
ejpam-6176	286	9	sharply	sharply	ADV
ejpam-6176	286	10	at	at	ADP
ejpam-6176	286	11	the	the	DET
ejpam-6176	286	12	beginning	beginning	NOUN
ejpam-6176	286	13	,	,	PUNCT
ejpam-6176	286	14	peaks	peak	NOUN
ejpam-6176	286	15	earlier	early	ADV
ejpam-6176	286	16	,	,	PUNCT
ejpam-6176	286	17	and	and	CCONJ
ejpam-6176	286	18	then	then	ADV
ejpam-6176	286	19	declines	decline	VERB
ejpam-6176	286	20	.	.	PUNCT
ejpam-6176	287	1	interestingly	interestingly	ADV
ejpam-6176	287	2	,	,	PUNCT
ejpam-6176	287	3	even	even	ADV
ejpam-6176	287	4	with	with	ADP
ejpam-6176	287	5	higher	high	ADJ
ejpam-6176	287	6	β1	β1	PROPN
ejpam-6176	287	7	,	,	PUNCT
ejpam-6176	287	8	the	the	DET
ejpam-6176	287	9	infective	infective	ADJ
ejpam-6176	287	10	population	population	NOUN
ejpam-6176	287	11	eventually	eventually	ADV
ejpam-6176	287	12	declines	decline	VERB
ejpam-6176	287	13	to	to	ADP
ejpam-6176	287	14	near	near	ADP
ejpam-6176	287	15	zero	zero	NUM
ejpam-6176	287	16	,	,	PUNCT
ejpam-6176	287	17	indicating	indicate	VERB
ejpam-6176	287	18	that	that	SCONJ
ejpam-6176	287	19	the	the	DET
ejpam-6176	287	20	model	model	NOUN
ejpam-6176	287	21	includes	include	VERB
ejpam-6176	287	22	effective	effective	ADJ
ejpam-6176	287	23	recovery	recovery	NOUN
ejpam-6176	287	24	or	or	CCONJ
ejpam-6176	287	25	control	control	NOUN
ejpam-6176	287	26	mechanisms	mechanism	NOUN
ejpam-6176	287	27	.	.	PUNCT
ejpam-6176	288	1	m.	m.	PROPN
ejpam-6176	288	2	s.	s.	PROPN
ejpam-6176	288	3	arif	arif	PROPN
ejpam-6176	288	4	,	,	PUNCT
ejpam-6176	288	5	k.	k.	PROPN
ejpam-6176	288	6	abodayeh	abodayeh	PROPN
ejpam-6176	288	7	,	,	PUNCT
ejpam-6176	288	8	y.	y.	NOUN
ejpam-6176	288	9	nawaz	nawaz	PROPN
ejpam-6176	288	10	/	/	SYM
ejpam-6176	288	11	eur	eur	PROPN
ejpam-6176	288	12	.	.	PUNCT
ejpam-6176	289	1	j.	j.	PROPN
ejpam-6176	289	2	pure	pure	PROPN
ejpam-6176	289	3	appl	appl	PROPN
ejpam-6176	289	4	.	.	PROPN
ejpam-6176	289	5	math	math	PROPN
ejpam-6176	289	6	,	,	PUNCT
ejpam-6176	289	7	18	18	NUM
ejpam-6176	289	8	(	(	PUNCT
ejpam-6176	289	9	3	3	NUM
ejpam-6176	289	10	)	)	PUNCT
ejpam-6176	289	11	(	(	PUNCT
ejpam-6176	289	12	2025	2025	NUM
ejpam-6176	289	13	)	)	PUNCT
ejpam-6176	289	14	,	,	PUNCT
ejpam-6176	289	15	6176	6176	NUM
ejpam-6176	289	16	14	14	NUM
ejpam-6176	289	17	of	of	ADP
ejpam-6176	289	18	21	21	NUM
ejpam-6176	289	19	figure	figure	NOUN
ejpam-6176	289	20	2	2	NUM
ejpam-6176	289	21	:	:	PUNCT
ejpam-6176	289	22	effect	effect	NOUN
ejpam-6176	289	23	of	of	ADP
ejpam-6176	289	24	transmission	transmission	NOUN
ejpam-6176	289	25	rate	rate	NOUN
ejpam-6176	289	26	(	(	PUNCT
ejpam-6176	289	27	from	from	ADP
ejpam-6176	289	28	susceptible	susceptible	ADJ
ejpam-6176	289	29	to	to	ADP
ejpam-6176	289	30	infective	infective	ADJ
ejpam-6176	289	31	)	)	PUNCT
ejpam-6176	289	32	on	on	ADP
ejpam-6176	289	33	susceptible	susceptible	ADJ
ejpam-6176	289	34	and	and	CCONJ
ejpam-6176	289	35	infective	infective	ADJ
ejpam-6176	289	36	using	use	VERB
ejpam-6176	289	37	d1	d1	PROPN
ejpam-6176	289	38	=	=	SYM
ejpam-6176	289	39	0.1	0.1	NUM
ejpam-6176	289	40	,	,	PUNCT
ejpam-6176	289	41	d2	d2	PROPN
ejpam-6176	289	42	=	=	SYM
ejpam-6176	289	43	0.1	0.1	NUM
ejpam-6176	289	44	,	,	PUNCT
ejpam-6176	289	45	d3	d3	PROPN
ejpam-6176	289	46	=	=	SYM
ejpam-6176	289	47	0.1	0.1	NUM
ejpam-6176	289	48	,	,	PUNCT
ejpam-6176	289	49	d4	d4	PROPN
ejpam-6176	289	50	=	=	SYM
ejpam-6176	289	51	0.1	0.1	NUM
ejpam-6176	289	52	,	,	PUNCT
ejpam-6176	289	53	ρ	ρ	PROPN
ejpam-6176	289	54	=	=	SYM
ejpam-6176	289	55	0.3	0.3	NUM
ejpam-6176	289	56	,	,	PUNCT
ejpam-6176	289	57	δ	δ	PROPN
ejpam-6176	289	58	=	=	SYM
ejpam-6176	289	59	0.1	0.1	NUM
ejpam-6176	289	60	,	,	PUNCT
ejpam-6176	289	61	γ1	γ1	NOUN
ejpam-6176	289	62	=	=	NOUN
ejpam-6176	289	63	0.1	0.1	NUM
ejpam-6176	289	64	,	,	PUNCT
ejpam-6176	289	65	d	d	NOUN
ejpam-6176	289	66	=	=	SYM
ejpam-6176	289	67	0.1	0.1	NUM
ejpam-6176	289	68	,	,	PUNCT
ejpam-6176	289	69	λ	λ	X
ejpam-6176	289	70	=	=	NOUN
ejpam-6176	289	71	0.1	0.1	NUM
ejpam-6176	289	72	,	,	PUNCT
ejpam-6176	289	73	α	α	NOUN
ejpam-6176	289	74	=	=	SYM
ejpam-6176	289	75	0.3	0.3	NUM
ejpam-6176	289	76	,	,	PUNCT
ejpam-6176	289	77	α2	α2	NOUN
ejpam-6176	289	78	=	=	SYM
ejpam-6176	289	79	0.1	0.1	NUM
ejpam-6176	289	80	,	,	PUNCT
ejpam-6176	289	81	α3	α3	NOUN
ejpam-6176	289	82	=	=	NOUN
ejpam-6176	289	83	0.1	0.1	NUM
ejpam-6176	289	84	,	,	PUNCT
ejpam-6176	289	85	ϵ	ϵ	X
ejpam-6176	289	86	=	=	SYM
ejpam-6176	289	87	0.1	0.1	NUM
ejpam-6176	289	88	,	,	PUNCT
ejpam-6176	289	89	ζ	ζ	NOUN
ejpam-6176	289	90	=	=	SYM
ejpam-6176	289	91	0.1	0.1	NUM
ejpam-6176	289	92	,	,	PUNCT
ejpam-6176	289	93	σ1	σ1	NOUN
ejpam-6176	289	94	=	=	SYM
ejpam-6176	289	95	0	0	PROPN
ejpam-6176	289	96	,	,	PUNCT
ejpam-6176	289	97	σ2	σ2	NOUN
ejpam-6176	289	98	=	=	SYM
ejpam-6176	289	99	0	0	NUM
ejpam-6176	289	100	,	,	PUNCT
ejpam-6176	289	101	σ3	σ3	NOUN
ejpam-6176	289	102	=	=	SYM
ejpam-6176	289	103	0	0	NUM
ejpam-6176	289	104	,	,	PUNCT
ejpam-6176	289	105	σ4	σ4	NOUN
ejpam-6176	289	106	=	=	SYM
ejpam-6176	289	107	0	0	PROPN
ejpam-6176	289	108	.	.	PUNCT
ejpam-6176	289	109	effect	effect	NOUN
ejpam-6176	289	110	of	of	ADP
ejpam-6176	289	111	quarantine	quarantine	NOUN
ejpam-6176	289	112	rate	rate	NOUN
ejpam-6176	289	113	δ	δ	PROPN
ejpam-6176	289	114	on	on	ADP
ejpam-6176	289	115	infective	infective	ADJ
ejpam-6176	289	116	and	and	CCONJ
ejpam-6176	289	117	quarantined	quarantined	ADJ
ejpam-6176	289	118	classes	class	NOUN
ejpam-6176	289	119	figure	figure	VERB
ejpam-6176	289	120	3	3	NUM
ejpam-6176	289	121	illustrates	illustrate	VERB
ejpam-6176	289	122	the	the	DET
ejpam-6176	289	123	effect	effect	NOUN
ejpam-6176	289	124	of	of	ADP
ejpam-6176	289	125	the	the	DET
ejpam-6176	289	126	quarantine	quarantine	NOUN
ejpam-6176	289	127	rate	rate	NOUN
ejpam-6176	289	128	of	of	ADP
ejpam-6176	289	129	infective	infective	ADJ
ejpam-6176	289	130	individuals	individual	NOUN
ejpam-6176	289	131	δ	δ	PROPN
ejpam-6176	289	132	on	on	ADP
ejpam-6176	289	133	the	the	DET
ejpam-6176	289	134	infective	infective	ADJ
ejpam-6176	289	135	and	and	CCONJ
ejpam-6176	289	136	quarantined	quarantined	ADJ
ejpam-6176	289	137	compartments	compartment	NOUN
ejpam-6176	289	138	in	in	ADP
ejpam-6176	289	139	the	the	DET
ejpam-6176	289	140	deterministic	deterministic	ADJ
ejpam-6176	289	141	siqr	siqr	PROPN
ejpam-6176	289	142	model	model	NOUN
ejpam-6176	289	143	.	.	PUNCT
ejpam-6176	290	1	the	the	DET
ejpam-6176	290	2	left	left	ADJ
ejpam-6176	290	3	plot	plot	NOUN
ejpam-6176	290	4	shows	show	VERB
ejpam-6176	290	5	the	the	DET
ejpam-6176	290	6	time	time	NOUN
ejpam-6176	290	7	evolution	evolution	NOUN
ejpam-6176	290	8	of	of	ADP
ejpam-6176	290	9	the	the	DET
ejpam-6176	290	10	infective	infective	ADJ
ejpam-6176	290	11	i	i	PROPN
ejpam-6176	290	12	population	population	NOUN
ejpam-6176	290	13	.	.	PUNCT
ejpam-6176	291	1	the	the	DET
ejpam-6176	291	2	right	right	ADJ
ejpam-6176	291	3	plot	plot	NOUN
ejpam-6176	291	4	shows	show	VERB
ejpam-6176	291	5	the	the	DET
ejpam-6176	291	6	time	time	NOUN
ejpam-6176	291	7	evolution	evolution	NOUN
ejpam-6176	291	8	of	of	ADP
ejpam-6176	291	9	the	the	DET
ejpam-6176	291	10	quarantined	quarantine	VERB
ejpam-6176	291	11	q	q	PROPN
ejpam-6176	291	12	population	population	NOUN
ejpam-6176	291	13	.	.	PUNCT
ejpam-6176	292	1	three	three	NUM
ejpam-6176	292	2	values	value	NOUN
ejpam-6176	292	3	of	of	ADP
ejpam-6176	292	4	δ	δ	PROPN
ejpam-6176	292	5	are	be	AUX
ejpam-6176	292	6	tested	test	VERB
ejpam-6176	292	7	:	:	PUNCT
ejpam-6176	292	8	•	•	NUM
ejpam-6176	292	9	solid	solid	ADJ
ejpam-6176	292	10	line	line	NOUN
ejpam-6176	292	11	:	:	PUNCT
ejpam-6176	292	12	δ	δ	X
ejpam-6176	292	13	=	=	NOUN
ejpam-6176	292	14	0.1	0.1	NUM
ejpam-6176	292	15	•	•	NUM
ejpam-6176	292	16	dashed	dash	VERB
ejpam-6176	292	17	line	line	NOUN
ejpam-6176	292	18	:	:	PUNCT
ejpam-6176	292	19	δ	δ	X
ejpam-6176	292	20	=	=	NOUN
ejpam-6176	292	21	0.3	0.3	NUM
ejpam-6176	292	22	•	•	ADV
ejpam-6176	292	23	dotted	dotted	ADJ
ejpam-6176	292	24	line	line	NOUN
ejpam-6176	292	25	:	:	PUNCT
ejpam-6176	292	26	δ	δ	X
ejpam-6176	292	27	=	=	PUNCT
ejpam-6176	292	28	0.5	0.5	NUM
ejpam-6176	292	29	the	the	DET
ejpam-6176	292	30	parameter	parameter	NOUN
ejpam-6176	292	31	settings	setting	NOUN
ejpam-6176	292	32	are	be	AUX
ejpam-6176	292	33	d1	d1	PROPN
ejpam-6176	292	34	=	=	SYM
ejpam-6176	292	35	d2	d2	PROPN
ejpam-6176	292	36	=	=	PUNCT
ejpam-6176	292	37	d3	d3	PROPN
ejpam-6176	292	38	=	=	SYM
ejpam-6176	292	39	d4	d4	PROPN
ejpam-6176	292	40	=	=	SYM
ejpam-6176	292	41	0.1	0.1	NUM
ejpam-6176	292	42	,	,	PUNCT
ejpam-6176	292	43	ρ	ρ	PROPN
ejpam-6176	292	44	=	=	SYM
ejpam-6176	292	45	0.3	0.3	NUM
ejpam-6176	292	46	,	,	PUNCT
ejpam-6176	292	47	β1	β1	PROPN
ejpam-6176	292	48	=	=	SYM
ejpam-6176	292	49	0.1	0.1	NUM
ejpam-6176	292	50	,	,	PUNCT
ejpam-6176	292	51	γ1	γ1	NOUN
ejpam-6176	292	52	=	=	NOUN
ejpam-6176	292	53	0.1	0.1	NUM
ejpam-6176	292	54	,	,	PUNCT
ejpam-6176	292	55	d	d	NOUN
ejpam-6176	292	56	=	=	SYM
ejpam-6176	292	57	0.1	0.1	NUM
ejpam-6176	292	58	,	,	PUNCT
ejpam-6176	292	59	λ	λ	X
ejpam-6176	292	60	=	=	NOUN
ejpam-6176	292	61	0.1	0.1	NUM
ejpam-6176	292	62	,	,	PUNCT
ejpam-6176	292	63	α	α	NOUN
ejpam-6176	292	64	=	=	SYM
ejpam-6176	292	65	0.3	0.3	NUM
ejpam-6176	292	66	,	,	PUNCT
ejpam-6176	292	67	α2	α2	NOUN
ejpam-6176	292	68	=	=	SYM
ejpam-6176	292	69	0.1	0.1	NUM
ejpam-6176	292	70	,	,	PUNCT
ejpam-6176	292	71	α3	α3	NOUN
ejpam-6176	292	72	=	=	NOUN
ejpam-6176	292	73	0.1	0.1	NUM
ejpam-6176	292	74	,	,	PUNCT
ejpam-6176	292	75	ϵ	ϵ	X
ejpam-6176	292	76	=	=	SYM
ejpam-6176	292	77	0.1	0.1	NUM
ejpam-6176	292	78	,	,	PUNCT
ejpam-6176	292	79	ζ	ζ	NOUN
ejpam-6176	292	80	=	=	SYM
ejpam-6176	292	81	0.1	0.1	NUM
ejpam-6176	292	82	.	.	PUNCT
ejpam-6176	293	1	figure	figure	VERB
ejpam-6176	293	2	3	3	NUM
ejpam-6176	293	3	:	:	PUNCT
ejpam-6176	293	4	effect	effect	NOUN
ejpam-6176	293	5	of	of	ADP
ejpam-6176	293	6	rate	rate	NOUN
ejpam-6176	293	7	of	of	ADP
ejpam-6176	293	8	quarantine	quarantine	NOUN
ejpam-6176	293	9	of	of	ADP
ejpam-6176	293	10	infective	infective	ADJ
ejpam-6176	293	11	on	on	ADP
ejpam-6176	293	12	infective	infective	ADJ
ejpam-6176	293	13	and	and	CCONJ
ejpam-6176	293	14	quarantined	quarantine	VERB
ejpam-6176	293	15	individuals	individual	NOUN
ejpam-6176	293	16	using	use	VERB
ejpam-6176	293	17	d1	d1	PROPN
ejpam-6176	293	18	=	=	SYM
ejpam-6176	293	19	0.1	0.1	NUM
ejpam-6176	293	20	,	,	PUNCT
ejpam-6176	293	21	d2	d2	PROPN
ejpam-6176	293	22	=	=	SYM
ejpam-6176	293	23	0.1	0.1	NUM
ejpam-6176	293	24	,	,	PUNCT
ejpam-6176	293	25	d3	d3	PROPN
ejpam-6176	293	26	=	=	SYM
ejpam-6176	293	27	0.1	0.1	NUM
ejpam-6176	293	28	,	,	PUNCT
ejpam-6176	293	29	d4	d4	PROPN
ejpam-6176	293	30	=	=	SYM
ejpam-6176	293	31	0.1	0.1	NUM
ejpam-6176	293	32	,	,	PUNCT
ejpam-6176	293	33	ρ	ρ	PROPN
ejpam-6176	293	34	=	=	SYM
ejpam-6176	293	35	0.3	0.3	NUM
ejpam-6176	293	36	,	,	PUNCT
ejpam-6176	293	37	β1	β1	PROPN
ejpam-6176	293	38	=	=	SYM
ejpam-6176	293	39	0.1	0.1	NUM
ejpam-6176	293	40	,	,	PUNCT
ejpam-6176	293	41	γ1	γ1	NOUN
ejpam-6176	293	42	=	=	NOUN
ejpam-6176	293	43	0.1	0.1	NUM
ejpam-6176	293	44	,	,	PUNCT
ejpam-6176	293	45	d	d	NOUN
ejpam-6176	293	46	=	=	SYM
ejpam-6176	293	47	0.1	0.1	NUM
ejpam-6176	293	48	,	,	PUNCT
ejpam-6176	293	49	λ	λ	X
ejpam-6176	293	50	=	=	NOUN
ejpam-6176	293	51	0.1	0.1	NUM
ejpam-6176	293	52	,	,	PUNCT
ejpam-6176	293	53	α	α	NOUN
ejpam-6176	293	54	=	=	SYM
ejpam-6176	293	55	0.3	0.3	NUM
ejpam-6176	293	56	,	,	PUNCT
ejpam-6176	293	57	α2	α2	NOUN
ejpam-6176	293	58	=	=	SYM
ejpam-6176	293	59	0.1	0.1	NUM
ejpam-6176	293	60	,	,	PUNCT
ejpam-6176	293	61	α3	α3	NOUN
ejpam-6176	293	62	=	=	NOUN
ejpam-6176	293	63	0.1	0.1	NUM
ejpam-6176	293	64	,	,	PUNCT
ejpam-6176	293	65	ϵ	ϵ	X
ejpam-6176	293	66	=	=	SYM
ejpam-6176	293	67	0.1	0.1	NUM
ejpam-6176	293	68	,	,	PUNCT
ejpam-6176	293	69	ζ	ζ	NOUN
ejpam-6176	293	70	=	=	SYM
ejpam-6176	293	71	0.1	0.1	NUM
ejpam-6176	293	72	,	,	PUNCT
ejpam-6176	293	73	σ1	σ1	NOUN
ejpam-6176	293	74	=	=	SYM
ejpam-6176	293	75	0	0	PROPN
ejpam-6176	293	76	,	,	PUNCT
ejpam-6176	293	77	σ2	σ2	NOUN
ejpam-6176	293	78	=	=	SYM
ejpam-6176	293	79	0	0	NUM
ejpam-6176	293	80	,	,	PUNCT
ejpam-6176	293	81	σ3	σ3	NOUN
ejpam-6176	293	82	=	=	SYM
ejpam-6176	293	83	0	0	NUM
ejpam-6176	293	84	,	,	PUNCT
ejpam-6176	293	85	σ4	σ4	NOUN
ejpam-6176	293	86	=	=	NOUN
ejpam-6176	293	87	0	0	NUM
ejpam-6176	293	88	.	.	PUNCT
ejpam-6176	294	1	as	as	SCONJ
ejpam-6176	294	2	δ	δ	PROPN
ejpam-6176	294	3	increases	increase	VERB
ejpam-6176	294	4	(	(	PUNCT
ejpam-6176	294	5	stronger	strong	ADJ
ejpam-6176	294	6	quarantine	quarantine	NOUN
ejpam-6176	294	7	enforcement	enforcement	NOUN
ejpam-6176	294	8	)	)	PUNCT
ejpam-6176	294	9	,	,	PUNCT
ejpam-6176	294	10	the	the	DET
ejpam-6176	294	11	infective	infective	ADJ
ejpam-6176	294	12	population	population	NOUN
ejpam-6176	294	13	declines	decline	VERB
ejpam-6176	294	14	more	more	ADV
ejpam-6176	294	15	rapidly	rapidly	ADV
ejpam-6176	294	16	.	.	PUNCT
ejpam-6176	295	1	higher	high	ADJ
ejpam-6176	295	2	quarantine	quarantine	NOUN
ejpam-6176	295	3	rates	rate	NOUN
ejpam-6176	295	4	move	move	VERB
ejpam-6176	295	5	individuals	individual	NOUN
ejpam-6176	295	6	more	more	ADV
ejpam-6176	295	7	quickly	quickly	ADV
ejpam-6176	295	8	out	out	ADP
ejpam-6176	295	9	of	of	ADP
ejpam-6176	295	10	the	the	DET
ejpam-6176	295	11	infective	infective	ADJ
ejpam-6176	295	12	m.	m.	NOUN
ejpam-6176	295	13	s.	s.	PROPN
ejpam-6176	295	14	arif	arif	PROPN
ejpam-6176	295	15	,	,	PUNCT
ejpam-6176	295	16	k.	k.	PROPN
ejpam-6176	295	17	abodayeh	abodayeh	PROPN
ejpam-6176	295	18	,	,	PUNCT
ejpam-6176	295	19	y.	y.	NOUN
ejpam-6176	295	20	nawaz	nawaz	PROPN
ejpam-6176	295	21	/	/	SYM
ejpam-6176	295	22	eur	eur	PROPN
ejpam-6176	295	23	.	.	PUNCT
ejpam-6176	296	1	j.	j.	PROPN
ejpam-6176	296	2	pure	pure	PROPN
ejpam-6176	296	3	appl	appl	PROPN
ejpam-6176	296	4	.	.	PROPN
ejpam-6176	296	5	math	math	PROPN
ejpam-6176	296	6	,	,	PUNCT
ejpam-6176	296	7	18	18	NUM
ejpam-6176	296	8	(	(	PUNCT
ejpam-6176	296	9	3	3	NUM
ejpam-6176	296	10	)	)	PUNCT
ejpam-6176	296	11	(	(	PUNCT
ejpam-6176	296	12	2025	2025	NUM
ejpam-6176	296	13	)	)	PUNCT
ejpam-6176	296	14	,	,	PUNCT
ejpam-6176	296	15	6176	6176	NUM
ejpam-6176	296	16	15	15	NUM
ejpam-6176	296	17	of	of	ADP
ejpam-6176	296	18	21	21	NUM
ejpam-6176	296	19	class	class	NOUN
ejpam-6176	296	20	into	into	ADP
ejpam-6176	296	21	the	the	DET
ejpam-6176	296	22	quarantine	quarantine	NOUN
ejpam-6176	296	23	class	class	NOUN
ejpam-6176	296	24	.	.	PUNCT
ejpam-6176	297	1	increasing	increase	VERB
ejpam-6176	297	2	δ	δ	PROPN
ejpam-6176	297	3	leads	lead	VERB
ejpam-6176	297	4	to	to	ADP
ejpam-6176	297	5	a	a	DET
ejpam-6176	297	6	higher	high	ADJ
ejpam-6176	297	7	and	and	CCONJ
ejpam-6176	297	8	earlier	early	ADJ
ejpam-6176	297	9	peak	peak	NOUN
ejpam-6176	297	10	in	in	ADP
ejpam-6176	297	11	the	the	DET
ejpam-6176	297	12	quarantined	quarantined	ADJ
ejpam-6176	297	13	population	population	NOUN
ejpam-6176	297	14	.	.	PUNCT
ejpam-6176	298	1	over	over	ADP
ejpam-6176	298	2	time	time	NOUN
ejpam-6176	298	3	,	,	PUNCT
ejpam-6176	298	4	the	the	DET
ejpam-6176	298	5	quarantined	quarantined	ADJ
ejpam-6176	298	6	population	population	NOUN
ejpam-6176	298	7	also	also	ADV
ejpam-6176	298	8	declines	decline	VERB
ejpam-6176	298	9	due	due	ADP
ejpam-6176	298	10	to	to	ADP
ejpam-6176	298	11	recovery	recovery	NOUN
ejpam-6176	298	12	ϵ	ϵ	NOUN
ejpam-6176	298	13	or	or	CCONJ
ejpam-6176	298	14	death	death	NOUN
ejpam-6176	298	15	(	(	PUNCT
ejpam-6176	298	16	α3	α3	NOUN
ejpam-6176	298	17	,	,	PUNCT
ejpam-6176	298	18	d	d	NOUN
ejpam-6176	298	19	)	)	PUNCT
ejpam-6176	298	20	.	.	PUNCT
ejpam-6176	299	1	influence	influence	NOUN
ejpam-6176	299	2	of	of	ADP
ejpam-6176	299	3	vaccination	vaccination	NOUN
ejpam-6176	299	4	rate	rate	NOUN
ejpam-6176	299	5	ρ	ρ	PROPN
ejpam-6176	299	6	on	on	ADP
ejpam-6176	299	7	susceptible	susceptible	ADJ
ejpam-6176	299	8	and	and	CCONJ
ejpam-6176	299	9	recovered	recovered	ADJ
ejpam-6176	299	10	classes	class	NOUN
ejpam-6176	299	11	figure	figure	VERB
ejpam-6176	299	12	4	4	NUM
ejpam-6176	299	13	illustrates	illustrate	VERB
ejpam-6176	299	14	the	the	DET
ejpam-6176	299	15	influence	influence	NOUN
ejpam-6176	299	16	of	of	ADP
ejpam-6176	299	17	the	the	DET
ejpam-6176	299	18	vaccination	vaccination	NOUN
ejpam-6176	299	19	rate	rate	NOUN
ejpam-6176	299	20	ρ	ρ	PROPN
ejpam-6176	299	21	on	on	ADP
ejpam-6176	299	22	the	the	DET
ejpam-6176	299	23	susceptible	susceptible	ADJ
ejpam-6176	299	24	s	s	NOUN
ejpam-6176	299	25	and	and	CCONJ
ejpam-6176	299	26	recovered	recover	VERB
ejpam-6176	299	27	r	r	NOUN
ejpam-6176	299	28	populations	population	NOUN
ejpam-6176	299	29	in	in	ADP
ejpam-6176	299	30	the	the	DET
ejpam-6176	299	31	deterministic	deterministic	ADJ
ejpam-6176	299	32	siqr	siqr	PROPN
ejpam-6176	299	33	model	model	NOUN
ejpam-6176	299	34	.	.	PUNCT
ejpam-6176	300	1	the	the	DET
ejpam-6176	300	2	left	left	ADJ
ejpam-6176	300	3	plot	plot	NOUN
ejpam-6176	300	4	shows	show	VERB
ejpam-6176	300	5	how	how	SCONJ
ejpam-6176	300	6	the	the	DET
ejpam-6176	300	7	susceptible	susceptible	ADJ
ejpam-6176	300	8	population	population	NOUN
ejpam-6176	300	9	s(t	s(t	PROPN
ejpam-6176	300	10	)	)	PUNCT
ejpam-6176	300	11	evolves	evolve	VERB
ejpam-6176	300	12	over	over	ADP
ejpam-6176	300	13	time	time	NOUN
ejpam-6176	300	14	.	.	PUNCT
ejpam-6176	301	1	the	the	DET
ejpam-6176	301	2	right	right	ADJ
ejpam-6176	301	3	plot	plot	NOUN
ejpam-6176	301	4	shows	show	VERB
ejpam-6176	301	5	how	how	SCONJ
ejpam-6176	301	6	the	the	DET
ejpam-6176	301	7	recovered	recovered	ADJ
ejpam-6176	301	8	population	population	NOUN
ejpam-6176	301	9	r(t	r(t	NOUN
ejpam-6176	301	10	)	)	PUNCT
ejpam-6176	301	11	evolves	evolve	VERB
ejpam-6176	301	12	over	over	ADP
ejpam-6176	301	13	time	time	NOUN
ejpam-6176	301	14	.	.	PUNCT
ejpam-6176	302	1	three	three	NUM
ejpam-6176	302	2	values	value	NOUN
ejpam-6176	302	3	of	of	ADP
ejpam-6176	302	4	ρ	ρ	PROPN
ejpam-6176	302	5	are	be	AUX
ejpam-6176	302	6	tested	test	VERB
ejpam-6176	302	7	:	:	PUNCT
ejpam-6176	302	8	•	•	NUM
ejpam-6176	302	9	solid	solid	ADJ
ejpam-6176	302	10	line	line	NOUN
ejpam-6176	302	11	:	:	PUNCT
ejpam-6176	302	12	ρ	ρ	PROPN
ejpam-6176	302	13	=	=	SYM
ejpam-6176	302	14	0.1	0.1	NUM
ejpam-6176	302	15	•	•	NOUN
ejpam-6176	302	16	dashed	dash	VERB
ejpam-6176	302	17	line	line	NOUN
ejpam-6176	302	18	:	:	PUNCT
ejpam-6176	302	19	ρ	ρ	PROPN
ejpam-6176	302	20	=	=	SYM
ejpam-6176	302	21	0.3	0.3	NUM
ejpam-6176	302	22	•	•	ADV
ejpam-6176	302	23	dotted	dotted	ADJ
ejpam-6176	302	24	line	line	NOUN
ejpam-6176	302	25	:	:	PUNCT
ejpam-6176	302	26	ρ	ρ	PROPN
ejpam-6176	302	27	=	=	SYM
ejpam-6176	302	28	0.5	0.5	NUM
ejpam-6176	302	29	the	the	DET
ejpam-6176	302	30	parameter	parameter	NOUN
ejpam-6176	302	31	settings	setting	NOUN
ejpam-6176	302	32	are	be	AUX
ejpam-6176	302	33	d1	d1	PROPN
ejpam-6176	302	34	=	=	SYM
ejpam-6176	302	35	d2	d2	PROPN
ejpam-6176	302	36	=	=	PUNCT
ejpam-6176	302	37	d3	d3	PROPN
ejpam-6176	302	38	=	=	SYM
ejpam-6176	302	39	d4	d4	PROPN
ejpam-6176	302	40	=	=	SYM
ejpam-6176	302	41	0.1	0.1	NUM
ejpam-6176	302	42	,	,	PUNCT
ejpam-6176	302	43	δ	δ	X
ejpam-6176	302	44	=	=	SYM
ejpam-6176	302	45	0.1	0.1	NUM
ejpam-6176	302	46	,	,	PUNCT
ejpam-6176	302	47	β1	β1	PROPN
ejpam-6176	302	48	=	=	SYM
ejpam-6176	302	49	0.1	0.1	NUM
ejpam-6176	302	50	,	,	PUNCT
ejpam-6176	302	51	γ1	γ1	NOUN
ejpam-6176	302	52	=	=	NOUN
ejpam-6176	302	53	0.1	0.1	NUM
ejpam-6176	302	54	,	,	PUNCT
ejpam-6176	302	55	d	d	NOUN
ejpam-6176	302	56	=	=	SYM
ejpam-6176	302	57	0.1	0.1	NUM
ejpam-6176	302	58	,	,	PUNCT
ejpam-6176	302	59	λ	λ	X
ejpam-6176	302	60	=	=	NOUN
ejpam-6176	302	61	0.1	0.1	NUM
ejpam-6176	302	62	,	,	PUNCT
ejpam-6176	302	63	α	α	NOUN
ejpam-6176	302	64	=	=	SYM
ejpam-6176	302	65	0.3	0.3	NUM
ejpam-6176	302	66	,	,	PUNCT
ejpam-6176	302	67	α2	α2	NOUN
ejpam-6176	302	68	=	=	SYM
ejpam-6176	302	69	0.1	0.1	NUM
ejpam-6176	302	70	,	,	PUNCT
ejpam-6176	302	71	α3	α3	NOUN
ejpam-6176	302	72	=	=	NOUN
ejpam-6176	302	73	0.1	0.1	NUM
ejpam-6176	302	74	,	,	PUNCT
ejpam-6176	302	75	ϵ	ϵ	X
ejpam-6176	302	76	=	=	SYM
ejpam-6176	302	77	0.1	0.1	NUM
ejpam-6176	302	78	,	,	PUNCT
ejpam-6176	302	79	ζ	ζ	NOUN
ejpam-6176	302	80	=	=	SYM
ejpam-6176	302	81	0.1	0.1	NUM
ejpam-6176	302	82	.	.	PUNCT
ejpam-6176	303	1	figure	figure	VERB
ejpam-6176	303	2	4	4	NUM
ejpam-6176	303	3	:	:	PUNCT
ejpam-6176	303	4	effect	effect	NOUN
ejpam-6176	303	5	of	of	ADP
ejpam-6176	303	6	vaccination	vaccination	NOUN
ejpam-6176	303	7	rate	rate	NOUN
ejpam-6176	303	8	on	on	ADP
ejpam-6176	303	9	susceptible	susceptible	ADJ
ejpam-6176	303	10	and	and	CCONJ
ejpam-6176	303	11	recovered	recover	VERB
ejpam-6176	303	12	individuals	individual	NOUN
ejpam-6176	303	13	using	use	VERB
ejpam-6176	303	14	d1	d1	PROPN
ejpam-6176	303	15	=	=	SYM
ejpam-6176	303	16	0.1	0.1	NUM
ejpam-6176	303	17	,	,	PUNCT
ejpam-6176	303	18	d2	d2	PROPN
ejpam-6176	303	19	=	=	SYM
ejpam-6176	303	20	0.1	0.1	NUM
ejpam-6176	303	21	,	,	PUNCT
ejpam-6176	303	22	d3	d3	PROPN
ejpam-6176	303	23	=	=	SYM
ejpam-6176	303	24	0.1	0.1	NUM
ejpam-6176	303	25	,	,	PUNCT
ejpam-6176	303	26	d4	d4	PROPN
ejpam-6176	303	27	=	=	SYM
ejpam-6176	303	28	0.1	0.1	NUM
ejpam-6176	303	29	,	,	PUNCT
ejpam-6176	303	30	δ	δ	X
ejpam-6176	303	31	=	=	SYM
ejpam-6176	303	32	0.1	0.1	NUM
ejpam-6176	303	33	,	,	PUNCT
ejpam-6176	303	34	β1	β1	PROPN
ejpam-6176	303	35	=	=	SYM
ejpam-6176	303	36	0.1	0.1	NUM
ejpam-6176	303	37	,	,	PUNCT
ejpam-6176	303	38	γ1	γ1	NOUN
ejpam-6176	303	39	=	=	NOUN
ejpam-6176	303	40	0.1	0.1	NUM
ejpam-6176	303	41	,	,	PUNCT
ejpam-6176	303	42	d	d	NOUN
ejpam-6176	303	43	=	=	SYM
ejpam-6176	303	44	0.1	0.1	NUM
ejpam-6176	303	45	,	,	PUNCT
ejpam-6176	303	46	λ	λ	X
ejpam-6176	303	47	=	=	NOUN
ejpam-6176	303	48	0.1	0.1	NUM
ejpam-6176	303	49	,	,	PUNCT
ejpam-6176	303	50	α	α	NOUN
ejpam-6176	303	51	=	=	SYM
ejpam-6176	303	52	0.3	0.3	NUM
ejpam-6176	303	53	,	,	PUNCT
ejpam-6176	303	54	α2	α2	NOUN
ejpam-6176	303	55	=	=	SYM
ejpam-6176	303	56	0.1	0.1	NUM
ejpam-6176	303	57	,	,	PUNCT
ejpam-6176	303	58	α3	α3	NOUN
ejpam-6176	303	59	=	=	NOUN
ejpam-6176	303	60	0.1	0.1	NUM
ejpam-6176	303	61	,	,	PUNCT
ejpam-6176	303	62	ϵ	ϵ	X
ejpam-6176	303	63	=	=	SYM
ejpam-6176	303	64	0.1	0.1	NUM
ejpam-6176	303	65	,	,	PUNCT
ejpam-6176	303	66	ζ	ζ	NOUN
ejpam-6176	303	67	=	=	SYM
ejpam-6176	303	68	0.1	0.1	NUM
ejpam-6176	303	69	,	,	PUNCT
ejpam-6176	303	70	σ1	σ1	NOUN
ejpam-6176	303	71	=	=	SYM
ejpam-6176	303	72	0	0	PROPN
ejpam-6176	303	73	,	,	PUNCT
ejpam-6176	303	74	σ2	σ2	NOUN
ejpam-6176	303	75	=	=	SYM
ejpam-6176	303	76	0	0	NUM
ejpam-6176	303	77	,	,	PUNCT
ejpam-6176	303	78	σ3	σ3	NOUN
ejpam-6176	303	79	=	=	SYM
ejpam-6176	303	80	0	0	NUM
ejpam-6176	303	81	,	,	PUNCT
ejpam-6176	303	82	σ4	σ4	NOUN
ejpam-6176	303	83	=	=	NOUN
ejpam-6176	303	84	0	0	NUM
ejpam-6176	303	85	.	.	PUNCT
ejpam-6176	304	1	as	as	ADP
ejpam-6176	304	2	ρ	ρ	PROPN
ejpam-6176	304	3	increases	increase	NOUN
ejpam-6176	304	4	,	,	PUNCT
ejpam-6176	304	5	the	the	DET
ejpam-6176	304	6	susceptible	susceptible	ADJ
ejpam-6176	304	7	population	population	NOUN
ejpam-6176	304	8	decreases	decrease	VERB
ejpam-6176	304	9	faster	fast	ADV
ejpam-6176	304	10	.	.	PUNCT
ejpam-6176	305	1	higher	high	ADJ
ejpam-6176	305	2	vaccination	vaccination	NOUN
ejpam-6176	305	3	rates	rate	NOUN
ejpam-6176	305	4	remove	remove	VERB
ejpam-6176	305	5	individuals	individual	NOUN
ejpam-6176	305	6	from	from	ADP
ejpam-6176	305	7	the	the	DET
ejpam-6176	305	8	susceptible	susceptible	ADJ
ejpam-6176	305	9	class	class	NOUN
ejpam-6176	305	10	and	and	CCONJ
ejpam-6176	305	11	transfer	transfer	VERB
ejpam-6176	305	12	them	they	PRON
ejpam-6176	305	13	to	to	ADP
ejpam-6176	305	14	the	the	DET
ejpam-6176	305	15	recovered	recovered	ADJ
ejpam-6176	305	16	class	class	NOUN
ejpam-6176	305	17	.	.	PUNCT
ejpam-6176	306	1	thus	thus	ADV
ejpam-6176	306	2	,	,	PUNCT
ejpam-6176	306	3	higher	high	ADJ
ejpam-6176	306	4	ρ	ρ	PROPN
ejpam-6176	306	5	leads	lead	VERB
ejpam-6176	306	6	to	to	ADP
ejpam-6176	306	7	a	a	DET
ejpam-6176	306	8	quicker	quick	ADJ
ejpam-6176	306	9	and	and	CCONJ
ejpam-6176	306	10	higher	high	ADJ
ejpam-6176	306	11	peak	peak	NOUN
ejpam-6176	306	12	in	in	ADP
ejpam-6176	306	13	the	the	DET
ejpam-6176	306	14	recovered	recovered	ADJ
ejpam-6176	306	15	population	population	NOUN
ejpam-6176	306	16	.	.	PUNCT
ejpam-6176	307	1	the	the	DET
ejpam-6176	307	2	recovered	recovered	ADJ
ejpam-6176	307	3	curve	curve	NOUN
ejpam-6176	307	4	rises	rise	VERB
ejpam-6176	307	5	steeply	steeply	ADV
ejpam-6176	307	6	and	and	CCONJ
ejpam-6176	307	7	reaches	reach	VERB
ejpam-6176	307	8	a	a	DET
ejpam-6176	307	9	higher	high	ADJ
ejpam-6176	307	10	maximum	maximum	NOUN
ejpam-6176	307	11	when	when	SCONJ
ejpam-6176	307	12	vaccination	vaccination	NOUN
ejpam-6176	307	13	is	be	AUX
ejpam-6176	307	14	more	more	ADV
ejpam-6176	307	15	aggressive	aggressive	ADJ
ejpam-6176	307	16	.	.	PUNCT
ejpam-6176	308	1	comparison	comparison	NOUN
ejpam-6176	308	2	with	with	ADP
ejpam-6176	308	3	the	the	DET
ejpam-6176	308	4	nonstandard	nonstandard	ADJ
ejpam-6176	308	5	finite	finite	ADJ
ejpam-6176	308	6	difference	difference	NOUN
ejpam-6176	308	7	(	(	PUNCT
ejpam-6176	308	8	nsfd	nsfd	ADJ
ejpam-6176	308	9	)	)	PUNCT
ejpam-6176	308	10	method	method	NOUN
ejpam-6176	308	11	finally	finally	ADV
ejpam-6176	308	12	,	,	PUNCT
ejpam-6176	308	13	we	we	PRON
ejpam-6176	308	14	compare	compare	VERB
ejpam-6176	308	15	the	the	DET
ejpam-6176	308	16	performance	performance	NOUN
ejpam-6176	308	17	of	of	ADP
ejpam-6176	308	18	the	the	DET
ejpam-6176	308	19	proposed	propose	VERB
ejpam-6176	308	20	numerical	numerical	ADJ
ejpam-6176	308	21	scheme	scheme	NOUN
ejpam-6176	308	22	with	with	ADP
ejpam-6176	308	23	the	the	DET
ejpam-6176	308	24	nonstandard	nonstandard	ADJ
ejpam-6176	308	25	finite	finite	ADJ
ejpam-6176	308	26	difference	difference	NOUN
ejpam-6176	308	27	(	(	PUNCT
ejpam-6176	308	28	nsfd	nsfd	ADJ
ejpam-6176	308	29	)	)	PUNCT
ejpam-6176	308	30	method	method	NOUN
ejpam-6176	308	31	.	.	PUNCT
ejpam-6176	309	1	for	for	ADP
ejpam-6176	309	2	clarity	clarity	NOUN
ejpam-6176	309	3	,	,	PUNCT
ejpam-6176	309	4	in	in	ADP
ejpam-6176	309	5	figures	figure	NOUN
ejpam-6176	309	6	5	5	NUM
ejpam-6176	309	7	to	to	PART
ejpam-6176	309	8	8	8	NUM
ejpam-6176	309	9	,	,	PUNCT
ejpam-6176	309	10	we	we	PRON
ejpam-6176	309	11	only	only	ADV
ejpam-6176	309	12	show	show	VERB
ejpam-6176	309	13	the	the	DET
ejpam-6176	309	14	results	result	NOUN
ejpam-6176	309	15	for	for	ADP
ejpam-6176	309	16	the	the	DET
ejpam-6176	309	17	deterministic	deterministic	ADJ
ejpam-6176	309	18	model	model	NOUN
ejpam-6176	309	19	.	.	PUNCT
ejpam-6176	310	1	the	the	DET
ejpam-6176	310	2	superiority	superiority	NOUN
ejpam-6176	310	3	of	of	ADP
ejpam-6176	310	4	the	the	DET
ejpam-6176	310	5	proposed	propose	VERB
ejpam-6176	310	6	scheme	scheme	NOUN
ejpam-6176	310	7	for	for	ADP
ejpam-6176	310	8	the	the	DET
ejpam-6176	310	9	sde	sde	PROPN
ejpam-6176	310	10	model	model	NOUN
ejpam-6176	310	11	is	be	AUX
ejpam-6176	310	12	demonstrated	demonstrate	VERB
ejpam-6176	310	13	in	in	ADP
ejpam-6176	310	14	figure	figure	NOUN
ejpam-6176	310	15	1	1	NUM
ejpam-6176	310	16	above	above	ADV
ejpam-6176	310	17	.	.	PUNCT
ejpam-6176	311	1	m.	m.	PROPN
ejpam-6176	311	2	s.	s.	PROPN
ejpam-6176	311	3	arif	arif	PROPN
ejpam-6176	311	4	,	,	PUNCT
ejpam-6176	311	5	k.	k.	PROPN
ejpam-6176	311	6	abodayeh	abodayeh	PROPN
ejpam-6176	311	7	,	,	PUNCT
ejpam-6176	311	8	y.	y.	NOUN
ejpam-6176	311	9	nawaz	nawaz	PROPN
ejpam-6176	311	10	/	/	SYM
ejpam-6176	311	11	eur	eur	PROPN
ejpam-6176	311	12	.	.	PUNCT
ejpam-6176	312	1	j.	j.	PROPN
ejpam-6176	312	2	pure	pure	PROPN
ejpam-6176	312	3	appl	appl	PROPN
ejpam-6176	312	4	.	.	PROPN
ejpam-6176	312	5	math	math	PROPN
ejpam-6176	312	6	,	,	PUNCT
ejpam-6176	312	7	18	18	NUM
ejpam-6176	312	8	(	(	PUNCT
ejpam-6176	312	9	3	3	NUM
ejpam-6176	312	10	)	)	PUNCT
ejpam-6176	312	11	(	(	PUNCT
ejpam-6176	312	12	2025	2025	NUM
ejpam-6176	312	13	)	)	PUNCT
ejpam-6176	312	14	,	,	PUNCT
ejpam-6176	312	15	6176	6176	NUM
ejpam-6176	312	16	16	16	NUM
ejpam-6176	312	17	of	of	ADP
ejpam-6176	312	18	21	21	NUM
ejpam-6176	312	19	figure	figure	NOUN
ejpam-6176	312	20	5	5	NUM
ejpam-6176	312	21	:	:	PUNCT
ejpam-6176	312	22	comparison	comparison	NOUN
ejpam-6176	312	23	of	of	ADP
ejpam-6176	312	24	proposed	propose	VERB
ejpam-6176	312	25	and	and	CCONJ
ejpam-6176	312	26	existing	exist	VERB
ejpam-6176	312	27	nsfd	nsfd	NOUN
ejpam-6176	312	28	method	method	NOUN
ejpam-6176	312	29	for	for	ADP
ejpam-6176	312	30	susceptible	susceptible	ADJ
ejpam-6176	312	31	using	use	VERB
ejpam-6176	312	32	d1	d1	PROPN
ejpam-6176	312	33	=	=	SYM
ejpam-6176	312	34	0.1	0.1	NUM
ejpam-6176	312	35	,	,	PUNCT
ejpam-6176	312	36	d2	d2	PROPN
ejpam-6176	312	37	=	=	SYM
ejpam-6176	312	38	0.1	0.1	NUM
ejpam-6176	312	39	,	,	PUNCT
ejpam-6176	312	40	d3	d3	PROPN
ejpam-6176	312	41	=	=	SYM
ejpam-6176	312	42	0.1	0.1	NUM
ejpam-6176	312	43	,	,	PUNCT
ejpam-6176	312	44	d4	d4	PROPN
ejpam-6176	312	45	=	=	SYM
ejpam-6176	312	46	0.1	0.1	NUM
ejpam-6176	312	47	,	,	PUNCT
ejpam-6176	312	48	δ	δ	X
ejpam-6176	312	49	=	=	SYM
ejpam-6176	312	50	0.1	0.1	NUM
ejpam-6176	312	51	,	,	PUNCT
ejpam-6176	312	52	ρ	ρ	PROPN
ejpam-6176	312	53	=	=	SYM
ejpam-6176	312	54	0.5	0.5	NUM
ejpam-6176	312	55	,	,	PUNCT
ejpam-6176	312	56	β1	β1	PROPN
ejpam-6176	312	57	=	=	SYM
ejpam-6176	312	58	0.1	0.1	NUM
ejpam-6176	312	59	,	,	PUNCT
ejpam-6176	312	60	γ1	γ1	NOUN
ejpam-6176	312	61	=	=	NOUN
ejpam-6176	312	62	0.1	0.1	NUM
ejpam-6176	312	63	,	,	PUNCT
ejpam-6176	312	64	d	d	NOUN
ejpam-6176	312	65	=	=	SYM
ejpam-6176	312	66	0.1	0.1	NUM
ejpam-6176	312	67	,	,	PUNCT
ejpam-6176	312	68	λ	λ	X
ejpam-6176	312	69	=	=	NOUN
ejpam-6176	312	70	0.1	0.1	NUM
ejpam-6176	312	71	,	,	PUNCT
ejpam-6176	312	72	α	α	NOUN
ejpam-6176	312	73	=	=	SYM
ejpam-6176	312	74	0.3	0.3	NUM
ejpam-6176	312	75	,	,	PUNCT
ejpam-6176	312	76	α2	α2	NOUN
ejpam-6176	312	77	=	=	SYM
ejpam-6176	312	78	0.1	0.1	NUM
ejpam-6176	312	79	,	,	PUNCT
ejpam-6176	312	80	α3	α3	NOUN
ejpam-6176	312	81	=	=	NOUN
ejpam-6176	312	82	0.1	0.1	NUM
ejpam-6176	312	83	,	,	PUNCT
ejpam-6176	312	84	ϵ	ϵ	X
ejpam-6176	312	85	=	=	SYM
ejpam-6176	312	86	0.1	0.1	NUM
ejpam-6176	312	87	,	,	PUNCT
ejpam-6176	312	88	ζ	ζ	NOUN
ejpam-6176	312	89	=	=	SYM
ejpam-6176	312	90	0.1	0.1	NUM
ejpam-6176	312	91	,	,	PUNCT
ejpam-6176	312	92	σ1	σ1	NOUN
ejpam-6176	312	93	=	=	SYM
ejpam-6176	312	94	0	0	PROPN
ejpam-6176	312	95	,	,	PUNCT
ejpam-6176	312	96	σ2	σ2	NOUN
ejpam-6176	312	97	=	=	SYM
ejpam-6176	312	98	0	0	NUM
ejpam-6176	312	99	,	,	PUNCT
ejpam-6176	312	100	σ3	σ3	NOUN
ejpam-6176	312	101	=	=	SYM
ejpam-6176	312	102	0	0	NUM
ejpam-6176	312	103	,	,	PUNCT
ejpam-6176	312	104	σ4	σ4	NOUN
ejpam-6176	312	105	=	=	NOUN
ejpam-6176	312	106	0	0	NUM
ejpam-6176	312	107	.	.	PUNCT
ejpam-6176	313	1	since	since	SCONJ
ejpam-6176	313	2	the	the	DET
ejpam-6176	313	3	exact	exact	ADJ
ejpam-6176	313	4	solution	solution	NOUN
ejpam-6176	313	5	is	be	AUX
ejpam-6176	313	6	not	not	PART
ejpam-6176	313	7	available	available	ADJ
ejpam-6176	313	8	,	,	PUNCT
ejpam-6176	313	9	we	we	PRON
ejpam-6176	313	10	use	use	VERB
ejpam-6176	313	11	the	the	DET
ejpam-6176	313	12	numerical	numerical	ADJ
ejpam-6176	313	13	solution	solution	NOUN
ejpam-6176	313	14	obtained	obtain	VERB
ejpam-6176	313	15	using	use	VERB
ejpam-6176	313	16	the	the	DET
ejpam-6176	313	17	matlab	matlab	PROPN
ejpam-6176	313	18	built	build	VERB
ejpam-6176	313	19	-	-	PUNCT
ejpam-6176	313	20	in	in	ADP
ejpam-6176	313	21	utility	utility	NOUN
ejpam-6176	313	22	(	(	PUNCT
ejpam-6176	313	23	which	which	PRON
ejpam-6176	313	24	can	can	AUX
ejpam-6176	313	25	solve	solve	VERB
ejpam-6176	313	26	parabolic	parabolic	ADJ
ejpam-6176	313	27	pdes	pde	NOUN
ejpam-6176	313	28	)	)	PUNCT
ejpam-6176	313	29	as	as	ADP
ejpam-6176	313	30	a	a	DET
ejpam-6176	313	31	surrogate	surrogate	NOUN
ejpam-6176	313	32	for	for	ADP
ejpam-6176	313	33	the	the	DET
ejpam-6176	313	34	exact	exact	ADJ
ejpam-6176	313	35	solution	solution	NOUN
ejpam-6176	313	36	.	.	PUNCT
ejpam-6176	314	1	using	use	VERB
ejpam-6176	314	2	d1	d1	PROPN
ejpam-6176	314	3	=	=	SYM
ejpam-6176	314	4	d2	d2	PROPN
ejpam-6176	314	5	=	=	PUNCT
ejpam-6176	314	6	d3	d3	PROPN
ejpam-6176	314	7	=	=	SYM
ejpam-6176	314	8	d4	d4	PROPN
ejpam-6176	314	9	=	=	SYM
ejpam-6176	314	10	0.1	0.1	NUM
ejpam-6176	314	11	,	,	PUNCT
ejpam-6176	314	12	δ	δ	X
ejpam-6176	314	13	=	=	SYM
ejpam-6176	314	14	0.1	0.1	NUM
ejpam-6176	314	15	,	,	PUNCT
ejpam-6176	314	16	ρ	ρ	PROPN
ejpam-6176	314	17	=	=	SYM
ejpam-6176	314	18	0.5	0.5	NUM
ejpam-6176	314	19	,	,	PUNCT
ejpam-6176	314	20	β1	β1	PROPN
ejpam-6176	314	21	=	=	SYM
ejpam-6176	314	22	0.1	0.1	NUM
ejpam-6176	314	23	,	,	PUNCT
ejpam-6176	314	24	γ1	γ1	NOUN
ejpam-6176	314	25	=	=	NOUN
ejpam-6176	314	26	0.1	0.1	NUM
ejpam-6176	314	27	,	,	PUNCT
ejpam-6176	314	28	d	d	NOUN
ejpam-6176	314	29	=	=	SYM
ejpam-6176	314	30	0.1	0.1	NUM
ejpam-6176	314	31	,	,	PUNCT
ejpam-6176	314	32	λ	λ	X
ejpam-6176	314	33	=	=	NOUN
ejpam-6176	314	34	0.1	0.1	NUM
ejpam-6176	314	35	,	,	PUNCT
ejpam-6176	314	36	α	α	NOUN
ejpam-6176	314	37	=	=	SYM
ejpam-6176	314	38	0.3	0.3	NUM
ejpam-6176	314	39	,	,	PUNCT
ejpam-6176	314	40	α2	α2	NOUN
ejpam-6176	314	41	=	=	SYM
ejpam-6176	314	42	0.1	0.1	NUM
ejpam-6176	314	43	,	,	PUNCT
ejpam-6176	314	44	α3	α3	NOUN
ejpam-6176	314	45	=	=	NOUN
ejpam-6176	314	46	0.1	0.1	NUM
ejpam-6176	314	47	,	,	PUNCT
ejpam-6176	314	48	ϵ	ϵ	X
ejpam-6176	314	49	=	=	SYM
ejpam-6176	314	50	0.1	0.1	NUM
ejpam-6176	314	51	,	,	PUNCT
ejpam-6176	314	52	ζ	ζ	NOUN
ejpam-6176	314	53	=	=	SYM
ejpam-6176	314	54	0.1	0.1	NUM
ejpam-6176	314	55	,	,	PUNCT
ejpam-6176	314	56	figures	figure	VERB
ejpam-6176	314	57	5–8	5–8	NOUN
ejpam-6176	314	58	show	show	VERB
ejpam-6176	314	59	the	the	DET
ejpam-6176	314	60	error	error	NOUN
ejpam-6176	314	61	incurred	incur	VERB
ejpam-6176	314	62	by	by	ADP
ejpam-6176	314	63	the	the	DET
ejpam-6176	314	64	proposed	propose	VERB
ejpam-6176	314	65	and	and	CCONJ
ejpam-6176	314	66	nsfd	nsfd	ADJ
ejpam-6176	314	67	schemes	scheme	NOUN
ejpam-6176	314	68	.	.	PUNCT
ejpam-6176	315	1	figure	figure	VERB
ejpam-6176	315	2	6	6	NUM
ejpam-6176	315	3	:	:	PUNCT
ejpam-6176	315	4	comparison	comparison	NOUN
ejpam-6176	315	5	of	of	ADP
ejpam-6176	315	6	proposed	propose	VERB
ejpam-6176	315	7	and	and	CCONJ
ejpam-6176	315	8	existing	exist	VERB
ejpam-6176	315	9	nsfd	nsfd	NOUN
ejpam-6176	315	10	method	method	NOUN
ejpam-6176	315	11	for	for	ADP
ejpam-6176	315	12	infective	infective	ADJ
ejpam-6176	315	13	using	use	VERB
ejpam-6176	315	14	d1	d1	PROPN
ejpam-6176	315	15	=	=	SYM
ejpam-6176	315	16	0.1	0.1	NUM
ejpam-6176	315	17	,	,	PUNCT
ejpam-6176	315	18	d2	d2	PROPN
ejpam-6176	315	19	=	=	SYM
ejpam-6176	315	20	0.1	0.1	NUM
ejpam-6176	315	21	,	,	PUNCT
ejpam-6176	315	22	d3	d3	PROPN
ejpam-6176	315	23	=	=	SYM
ejpam-6176	315	24	0.1	0.1	NUM
ejpam-6176	315	25	,	,	PUNCT
ejpam-6176	315	26	d4	d4	PROPN
ejpam-6176	315	27	=	=	SYM
ejpam-6176	315	28	0.1	0.1	NUM
ejpam-6176	315	29	,	,	PUNCT
ejpam-6176	315	30	δ	δ	X
ejpam-6176	315	31	=	=	SYM
ejpam-6176	315	32	0.1	0.1	NUM
ejpam-6176	315	33	,	,	PUNCT
ejpam-6176	315	34	ρ	ρ	PROPN
ejpam-6176	315	35	=	=	SYM
ejpam-6176	315	36	0.5	0.5	NUM
ejpam-6176	315	37	,	,	PUNCT
ejpam-6176	315	38	β1	β1	PROPN
ejpam-6176	315	39	=	=	SYM
ejpam-6176	315	40	0.1	0.1	NUM
ejpam-6176	315	41	,	,	PUNCT
ejpam-6176	315	42	γ1	γ1	NOUN
ejpam-6176	315	43	=	=	NOUN
ejpam-6176	315	44	0.1	0.1	NUM
ejpam-6176	315	45	,	,	PUNCT
ejpam-6176	315	46	d	d	NOUN
ejpam-6176	315	47	=	=	SYM
ejpam-6176	315	48	0.1	0.1	NUM
ejpam-6176	315	49	,	,	PUNCT
ejpam-6176	315	50	λ	λ	X
ejpam-6176	315	51	=	=	NOUN
ejpam-6176	315	52	0.1	0.1	NUM
ejpam-6176	315	53	,	,	PUNCT
ejpam-6176	315	54	α	α	NOUN
ejpam-6176	315	55	=	=	SYM
ejpam-6176	315	56	0.3	0.3	NUM
ejpam-6176	315	57	,	,	PUNCT
ejpam-6176	315	58	α2	α2	NOUN
ejpam-6176	315	59	=	=	SYM
ejpam-6176	315	60	0.1	0.1	NUM
ejpam-6176	315	61	,	,	PUNCT
ejpam-6176	315	62	α3	α3	NOUN
ejpam-6176	315	63	=	=	NOUN
ejpam-6176	315	64	0.1	0.1	NUM
ejpam-6176	315	65	,	,	PUNCT
ejpam-6176	315	66	ϵ	ϵ	X
ejpam-6176	315	67	=	=	SYM
ejpam-6176	315	68	0.1	0.1	NUM
ejpam-6176	315	69	,	,	PUNCT
ejpam-6176	315	70	ζ	ζ	NOUN
ejpam-6176	315	71	=	=	SYM
ejpam-6176	315	72	0.1	0.1	NUM
ejpam-6176	315	73	,	,	PUNCT
ejpam-6176	315	74	σ1	σ1	NOUN
ejpam-6176	315	75	=	=	SYM
ejpam-6176	315	76	0	0	PROPN
ejpam-6176	315	77	,	,	PUNCT
ejpam-6176	315	78	σ2	σ2	NOUN
ejpam-6176	315	79	=	=	SYM
ejpam-6176	315	80	0	0	NUM
ejpam-6176	315	81	,	,	PUNCT
ejpam-6176	315	82	σ3	σ3	NOUN
ejpam-6176	315	83	=	=	SYM
ejpam-6176	315	84	0	0	NUM
ejpam-6176	315	85	,	,	PUNCT
ejpam-6176	315	86	σ4	σ4	NOUN
ejpam-6176	315	87	=	=	NOUN
ejpam-6176	315	88	0	0	PROPN
ejpam-6176	315	89	.	.	PUNCT
ejpam-6176	316	1	the	the	DET
ejpam-6176	316	2	proposed	propose	VERB
ejpam-6176	316	3	scheme	scheme	NOUN
ejpam-6176	316	4	provides	provide	VERB
ejpam-6176	316	5	a	a	DET
ejpam-6176	316	6	considerably	considerably	ADV
ejpam-6176	316	7	better	well	ADJ
ejpam-6176	316	8	approximation	approximation	NOUN
ejpam-6176	316	9	than	than	ADP
ejpam-6176	316	10	the	the	DET
ejpam-6176	316	11	nsfd	nsfd	PROPN
ejpam-6176	316	12	method	method	NOUN
ejpam-6176	316	13	,	,	PUNCT
ejpam-6176	316	14	which	which	PRON
ejpam-6176	316	15	suffers	suffer	VERB
ejpam-6176	316	16	from	from	ADP
ejpam-6176	316	17	a	a	DET
ejpam-6176	316	18	consistency	consistency	NOUN
ejpam-6176	316	19	issue	issue	NOUN
ejpam-6176	316	20	,	,	PUNCT
ejpam-6176	316	21	as	as	SCONJ
ejpam-6176	316	22	discussed	discuss	VERB
ejpam-6176	316	23	in	in	ADP
ejpam-6176	316	24	[	[	X
ejpam-6176	316	25	47	47	NUM
ejpam-6176	316	26	]	]	PUNCT
ejpam-6176	316	27	.	.	PUNCT
ejpam-6176	317	1	moreover	moreover	ADV
ejpam-6176	317	2	,	,	PUNCT
ejpam-6176	317	3	the	the	DET
ejpam-6176	317	4	nsfd	nsfd	ADJ
ejpam-6176	317	5	method	method	NOUN
ejpam-6176	317	6	does	do	AUX
ejpam-6176	317	7	not	not	PART
ejpam-6176	317	8	allow	allow	VERB
ejpam-6176	317	9	a	a	DET
ejpam-6176	317	10	higher	high	ADJ
ejpam-6176	317	11	-	-	PUNCT
ejpam-6176	317	12	order	order	NOUN
ejpam-6176	317	13	scheme	scheme	NOUN
ejpam-6176	317	14	for	for	ADP
ejpam-6176	317	15	space	space	NOUN
ejpam-6176	317	16	discretization	discretization	NOUN
ejpam-6176	317	17	.	.	PUNCT
ejpam-6176	318	1	the	the	DET
ejpam-6176	318	2	proposed	propose	VERB
ejpam-6176	318	3	scheme	scheme	NOUN
ejpam-6176	318	4	is	be	AUX
ejpam-6176	318	5	not	not	PART
ejpam-6176	318	6	subject	subject	ADJ
ejpam-6176	318	7	to	to	ADP
ejpam-6176	318	8	the	the	DET
ejpam-6176	318	9	same	same	ADJ
ejpam-6176	318	10	limitation	limitation	NOUN
ejpam-6176	318	11	.	.	PUNCT
ejpam-6176	319	1	6	6	X
ejpam-6176	319	2	.	.	X
ejpam-6176	319	3	conclusion	conclusion	NOUN
ejpam-6176	319	4	in	in	ADP
ejpam-6176	319	5	this	this	DET
ejpam-6176	319	6	paper	paper	NOUN
ejpam-6176	319	7	,	,	PUNCT
ejpam-6176	319	8	we	we	PRON
ejpam-6176	319	9	suggested	suggest	VERB
ejpam-6176	319	10	a	a	DET
ejpam-6176	319	11	new	new	ADJ
ejpam-6176	319	12	two	two	NUM
ejpam-6176	319	13	-	-	PUNCT
ejpam-6176	319	14	stage	stage	NOUN
ejpam-6176	319	15	computing	computing	NOUN
ejpam-6176	319	16	methodology	methodology	NOUN
ejpam-6176	319	17	that	that	PRON
ejpam-6176	319	18	combines	combine	VERB
ejpam-6176	319	19	runge	runge	NOUN
ejpam-6176	319	20	-	-	PUNCT
ejpam-6176	319	21	kutta	kutta	NOUN
ejpam-6176	319	22	methods	method	NOUN
ejpam-6176	319	23	with	with	ADP
ejpam-6176	319	24	exponential	exponential	ADJ
ejpam-6176	319	25	integrator	integrator	NOUN
ejpam-6176	319	26	techniques	technique	NOUN
ejpam-6176	319	27	to	to	PART
ejpam-6176	319	28	solve	solve	VERB
ejpam-6176	319	29	stochastic	stochastic	ADJ
ejpam-6176	319	30	diffusive	diffusive	ADJ
ejpam-6176	319	31	siqr	siqr	ADJ
ejpam-6176	319	32	epidemic	epidemic	NOUN
ejpam-6176	319	33	models	model	NOUN
ejpam-6176	319	34	with	with	ADP
ejpam-6176	319	35	a	a	DET
ejpam-6176	319	36	broad	broad	ADJ
ejpam-6176	319	37	incidence	incidence	NOUN
ejpam-6176	319	38	rate	rate	NOUN
ejpam-6176	319	39	.	.	PUNCT
ejpam-6176	320	1	the	the	DET
ejpam-6176	320	2	fundamental	fundamental	ADJ
ejpam-6176	320	3	benefit	benefit	NOUN
ejpam-6176	320	4	of	of	ADP
ejpam-6176	320	5	the	the	DET
ejpam-6176	320	6	suggested	suggest	VERB
ejpam-6176	320	7	approach	approach	NOUN
ejpam-6176	320	8	is	be	AUX
ejpam-6176	320	9	its	its	PRON
ejpam-6176	320	10	capacity	capacity	NOUN
ejpam-6176	320	11	to	to	PART
ejpam-6176	320	12	discretize	discretize	VERB
ejpam-6176	320	13	just	just	ADV
ejpam-6176	320	14	the	the	DET
ejpam-6176	320	15	time	time	NOUN
ejpam-6176	320	16	-	-	PUNCT
ejpam-6176	320	17	dependent	dependent	ADJ
ejpam-6176	320	18	parts	part	NOUN
ejpam-6176	320	19	of	of	ADP
ejpam-6176	320	20	the	the	DET
ejpam-6176	320	21	underlying	underlie	VERB
ejpam-6176	320	22	stochastic	stochastic	ADJ
ejpam-6176	320	23	partial	partial	ADJ
ejpam-6176	320	24	differential	differential	NOUN
ejpam-6176	320	25	equations	equation	NOUN
ejpam-6176	320	26	,	,	PUNCT
ejpam-6176	320	27	lowering	lower	VERB
ejpam-6176	320	28	computational	computational	ADJ
ejpam-6176	320	29	complexity	complexity	NOUN
ejpam-6176	320	30	while	while	SCONJ
ejpam-6176	320	31	m.	m.	PROPN
ejpam-6176	320	32	s.	s.	PROPN
ejpam-6176	320	33	arif	arif	PROPN
ejpam-6176	320	34	,	,	PUNCT
ejpam-6176	320	35	k.	k.	PROPN
ejpam-6176	320	36	abodayeh	abodayeh	PROPN
ejpam-6176	320	37	,	,	PUNCT
ejpam-6176	320	38	y.	y.	NOUN
ejpam-6176	320	39	nawaz	nawaz	PROPN
ejpam-6176	320	40	/	/	SYM
ejpam-6176	320	41	eur	eur	PROPN
ejpam-6176	320	42	.	.	PUNCT
ejpam-6176	321	1	j.	j.	PROPN
ejpam-6176	321	2	pure	pure	PROPN
ejpam-6176	321	3	appl	appl	PROPN
ejpam-6176	321	4	.	.	PROPN
ejpam-6176	321	5	math	math	PROPN
ejpam-6176	321	6	,	,	PUNCT
ejpam-6176	321	7	18	18	NUM
ejpam-6176	321	8	(	(	PUNCT
ejpam-6176	321	9	3	3	NUM
ejpam-6176	321	10	)	)	PUNCT
ejpam-6176	321	11	(	(	PUNCT
ejpam-6176	321	12	2025	2025	NUM
ejpam-6176	321	13	)	)	PUNCT
ejpam-6176	321	14	,	,	PUNCT
ejpam-6176	321	15	6176	6176	NUM
ejpam-6176	321	16	17	17	NUM
ejpam-6176	321	17	of	of	ADP
ejpam-6176	321	18	21	21	NUM
ejpam-6176	321	19	figure	figure	NOUN
ejpam-6176	321	20	7	7	NUM
ejpam-6176	321	21	:	:	PUNCT
ejpam-6176	321	22	comparison	comparison	NOUN
ejpam-6176	321	23	of	of	ADP
ejpam-6176	321	24	proposed	propose	VERB
ejpam-6176	321	25	and	and	CCONJ
ejpam-6176	321	26	existing	exist	VERB
ejpam-6176	321	27	nsfd	nsfd	NOUN
ejpam-6176	321	28	method	method	NOUN
ejpam-6176	321	29	for	for	ADP
ejpam-6176	321	30	quarantined	quarantine	VERB
ejpam-6176	321	31	individuals	individual	NOUN
ejpam-6176	321	32	using	use	VERB
ejpam-6176	321	33	d1	d1	PROPN
ejpam-6176	321	34	=	=	SYM
ejpam-6176	321	35	0.1	0.1	NUM
ejpam-6176	321	36	,	,	PUNCT
ejpam-6176	321	37	d2	d2	PROPN
ejpam-6176	321	38	=	=	SYM
ejpam-6176	321	39	0.1	0.1	NUM
ejpam-6176	321	40	,	,	PUNCT
ejpam-6176	321	41	d3	d3	PROPN
ejpam-6176	321	42	=	=	SYM
ejpam-6176	321	43	0.1	0.1	NUM
ejpam-6176	321	44	,	,	PUNCT
ejpam-6176	321	45	d4	d4	PROPN
ejpam-6176	321	46	=	=	SYM
ejpam-6176	321	47	0.1	0.1	NUM
ejpam-6176	321	48	,	,	PUNCT
ejpam-6176	321	49	δ	δ	X
ejpam-6176	321	50	=	=	SYM
ejpam-6176	321	51	0.1	0.1	NUM
ejpam-6176	321	52	,	,	PUNCT
ejpam-6176	321	53	ρ	ρ	PROPN
ejpam-6176	321	54	=	=	SYM
ejpam-6176	321	55	0.5	0.5	NUM
ejpam-6176	321	56	,	,	PUNCT
ejpam-6176	321	57	β1	β1	PROPN
ejpam-6176	321	58	=	=	SYM
ejpam-6176	321	59	0.1	0.1	NUM
ejpam-6176	321	60	,	,	PUNCT
ejpam-6176	321	61	γ1	γ1	NOUN
ejpam-6176	321	62	=	=	NOUN
ejpam-6176	321	63	0.1	0.1	NUM
ejpam-6176	321	64	,	,	PUNCT
ejpam-6176	321	65	d	d	NOUN
ejpam-6176	321	66	=	=	SYM
ejpam-6176	321	67	0.1	0.1	NUM
ejpam-6176	321	68	,	,	PUNCT
ejpam-6176	321	69	λ	λ	X
ejpam-6176	321	70	=	=	NOUN
ejpam-6176	321	71	0.1	0.1	NUM
ejpam-6176	321	72	,	,	PUNCT
ejpam-6176	321	73	α	α	NOUN
ejpam-6176	321	74	=	=	SYM
ejpam-6176	321	75	0.3	0.3	NUM
ejpam-6176	321	76	,	,	PUNCT
ejpam-6176	321	77	α2	α2	NOUN
ejpam-6176	321	78	=	=	SYM
ejpam-6176	321	79	0.1	0.1	NUM
ejpam-6176	321	80	,	,	PUNCT
ejpam-6176	321	81	α3	α3	NOUN
ejpam-6176	321	82	=	=	NOUN
ejpam-6176	321	83	0.1	0.1	NUM
ejpam-6176	321	84	,	,	PUNCT
ejpam-6176	321	85	ϵ	ϵ	X
ejpam-6176	321	86	=	=	SYM
ejpam-6176	321	87	0.1	0.1	NUM
ejpam-6176	321	88	,	,	PUNCT
ejpam-6176	321	89	ζ	ζ	NOUN
ejpam-6176	321	90	=	=	SYM
ejpam-6176	321	91	0.1	0.1	NUM
ejpam-6176	321	92	,	,	PUNCT
ejpam-6176	321	93	σ1	σ1	NOUN
ejpam-6176	321	94	=	=	SYM
ejpam-6176	321	95	0	0	PROPN
ejpam-6176	321	96	,	,	PUNCT
ejpam-6176	321	97	σ2	σ2	NOUN
ejpam-6176	321	98	=	=	SYM
ejpam-6176	321	99	0	0	NUM
ejpam-6176	321	100	,	,	PUNCT
ejpam-6176	321	101	σ3	σ3	NOUN
ejpam-6176	321	102	=	=	SYM
ejpam-6176	321	103	0	0	NUM
ejpam-6176	321	104	,	,	PUNCT
ejpam-6176	321	105	σ4	σ4	NOUN
ejpam-6176	321	106	=	=	SYM
ejpam-6176	321	107	0	0	PROPN
ejpam-6176	321	108	.	.	PUNCT
ejpam-6176	321	109	figure	figure	NOUN
ejpam-6176	321	110	8	8	NUM
ejpam-6176	321	111	:	:	PUNCT
ejpam-6176	321	112	comparison	comparison	NOUN
ejpam-6176	321	113	of	of	ADP
ejpam-6176	321	114	proposed	propose	VERB
ejpam-6176	321	115	and	and	CCONJ
ejpam-6176	321	116	existing	exist	VERB
ejpam-6176	321	117	nsfd	nsfd	NOUN
ejpam-6176	321	118	method	method	NOUN
ejpam-6176	321	119	for	for	ADP
ejpam-6176	321	120	recovered	recovered	ADJ
ejpam-6176	321	121	using	use	VERB
ejpam-6176	321	122	d1	d1	PROPN
ejpam-6176	321	123	=	=	SYM
ejpam-6176	321	124	0.1	0.1	NUM
ejpam-6176	321	125	,	,	PUNCT
ejpam-6176	321	126	d2	d2	PROPN
ejpam-6176	321	127	=	=	SYM
ejpam-6176	321	128	0.1	0.1	NUM
ejpam-6176	321	129	,	,	PUNCT
ejpam-6176	321	130	d3	d3	PROPN
ejpam-6176	321	131	=	=	SYM
ejpam-6176	321	132	0.1	0.1	NUM
ejpam-6176	321	133	,	,	PUNCT
ejpam-6176	321	134	d4	d4	PROPN
ejpam-6176	321	135	=	=	SYM
ejpam-6176	321	136	0.1	0.1	NUM
ejpam-6176	321	137	,	,	PUNCT
ejpam-6176	321	138	δ	δ	X
ejpam-6176	321	139	=	=	SYM
ejpam-6176	321	140	0.1	0.1	NUM
ejpam-6176	321	141	,	,	PUNCT
ejpam-6176	321	142	ρ	ρ	PROPN
ejpam-6176	321	143	=	=	SYM
ejpam-6176	321	144	0.5	0.5	NUM
ejpam-6176	321	145	,	,	PUNCT
ejpam-6176	321	146	β1	β1	PROPN
ejpam-6176	321	147	=	=	SYM
ejpam-6176	321	148	0.1	0.1	NUM
ejpam-6176	321	149	,	,	PUNCT
ejpam-6176	321	150	γ1	γ1	NOUN
ejpam-6176	321	151	=	=	NOUN
ejpam-6176	321	152	0.1	0.1	NUM
ejpam-6176	321	153	,	,	PUNCT
ejpam-6176	321	154	d	d	NOUN
ejpam-6176	321	155	=	=	SYM
ejpam-6176	321	156	0.1	0.1	NUM
ejpam-6176	321	157	,	,	PUNCT
ejpam-6176	321	158	λ	λ	X
ejpam-6176	321	159	=	=	NOUN
ejpam-6176	321	160	0.1	0.1	NUM
ejpam-6176	321	161	,	,	PUNCT
ejpam-6176	321	162	α	α	NOUN
ejpam-6176	321	163	=	=	SYM
ejpam-6176	321	164	0.3	0.3	NUM
ejpam-6176	321	165	,	,	PUNCT
ejpam-6176	321	166	α2	α2	NOUN
ejpam-6176	321	167	=	=	SYM
ejpam-6176	321	168	0.1	0.1	NUM
ejpam-6176	321	169	,	,	PUNCT
ejpam-6176	321	170	α3	α3	NOUN
ejpam-6176	321	171	=	=	NOUN
ejpam-6176	321	172	0.1	0.1	NUM
ejpam-6176	321	173	,	,	PUNCT
ejpam-6176	321	174	ϵ	ϵ	X
ejpam-6176	321	175	=	=	SYM
ejpam-6176	321	176	0.1	0.1	NUM
ejpam-6176	321	177	,	,	PUNCT
ejpam-6176	321	178	ζ	ζ	NOUN
ejpam-6176	321	179	=	=	SYM
ejpam-6176	321	180	0.1	0.1	NUM
ejpam-6176	321	181	,	,	PUNCT
ejpam-6176	321	182	σ1	σ1	NOUN
ejpam-6176	321	183	=	=	SYM
ejpam-6176	321	184	0	0	PROPN
ejpam-6176	321	185	,	,	PUNCT
ejpam-6176	321	186	σ2	σ2	NOUN
ejpam-6176	321	187	=	=	SYM
ejpam-6176	321	188	0	0	NUM
ejpam-6176	321	189	,	,	PUNCT
ejpam-6176	321	190	σ3	σ3	NOUN
ejpam-6176	321	191	=	=	SYM
ejpam-6176	321	192	0	0	NUM
ejpam-6176	321	193	,	,	PUNCT
ejpam-6176	321	194	σ4	σ4	NOUN
ejpam-6176	321	195	=	=	SYM
ejpam-6176	321	196	0	0	NUM
ejpam-6176	321	197	.	.	PUNCT
ejpam-6176	321	198	preserving	preserve	VERB
ejpam-6176	321	199	great	great	ADJ
ejpam-6176	321	200	accuracy	accuracy	NOUN
ejpam-6176	321	201	.	.	PUNCT
ejpam-6176	322	1	a	a	DET
ejpam-6176	322	2	mixture	mixture	NOUN
ejpam-6176	322	3	of	of	ADP
ejpam-6176	322	4	two	two	NUM
ejpam-6176	322	5	schemes	scheme	NOUN
ejpam-6176	322	6	has	have	AUX
ejpam-6176	322	7	been	be	AUX
ejpam-6176	322	8	proposed	propose	VERB
ejpam-6176	322	9	to	to	PART
ejpam-6176	322	10	handle	handle	VERB
ejpam-6176	322	11	deterministic	deterministic	ADJ
ejpam-6176	322	12	and	and	CCONJ
ejpam-6176	322	13	stochastic	stochastic	ADJ
ejpam-6176	322	14	partial	partial	ADJ
ejpam-6176	322	15	differential	differential	NOUN
ejpam-6176	322	16	equations	equation	NOUN
ejpam-6176	322	17	.	.	PUNCT
ejpam-6176	323	1	the	the	DET
ejpam-6176	323	2	scheme	scheme	NOUN
ejpam-6176	323	3	was	be	AUX
ejpam-6176	323	4	comprised	comprise	VERB
ejpam-6176	323	5	of	of	ADP
ejpam-6176	323	6	two	two	NUM
ejpam-6176	323	7	stages	stage	NOUN
ejpam-6176	323	8	called	call	VERB
ejpam-6176	323	9	the	the	DET
ejpam-6176	323	10	predictor	predictor	NOUN
ejpam-6176	323	11	and	and	CCONJ
ejpam-6176	323	12	corrector	corrector	NOUN
ejpam-6176	323	13	stages	stage	NOUN
ejpam-6176	323	14	.	.	PUNCT
ejpam-6176	324	1	the	the	DET
ejpam-6176	324	2	predictor	predictor	NOUN
ejpam-6176	324	3	stage	stage	NOUN
ejpam-6176	324	4	found	find	VERB
ejpam-6176	324	5	the	the	DET
ejpam-6176	324	6	solution	solution	NOUN
ejpam-6176	324	7	at	at	ADP
ejpam-6176	324	8	an	an	DET
ejpam-6176	324	9	arbitrary	arbitrary	ADJ
ejpam-6176	324	10	time	time	NOUN
ejpam-6176	324	11	level	level	NOUN
ejpam-6176	324	12	,	,	PUNCT
ejpam-6176	324	13	and	and	CCONJ
ejpam-6176	324	14	the	the	DET
ejpam-6176	324	15	corrector	corrector	NOUN
ejpam-6176	324	16	stage	stage	NOUN
ejpam-6176	324	17	found	find	VERB
ejpam-6176	324	18	the	the	DET
ejpam-6176	324	19	solution	solution	NOUN
ejpam-6176	324	20	at	at	ADP
ejpam-6176	324	21	the	the	DET
ejpam-6176	324	22	next	next	ADJ
ejpam-6176	324	23	time	time	NOUN
ejpam-6176	324	24	level	level	NOUN
ejpam-6176	324	25	.	.	PUNCT
ejpam-6176	325	1	the	the	DET
ejpam-6176	325	2	scheme	scheme	NOUN
ejpam-6176	325	3	has	have	AUX
ejpam-6176	325	4	been	be	AUX
ejpam-6176	325	5	applied	apply	VERB
ejpam-6176	325	6	to	to	ADP
ejpam-6176	325	7	the	the	DET
ejpam-6176	325	8	deterministic	deterministic	ADJ
ejpam-6176	325	9	and	and	CCONJ
ejpam-6176	325	10	stochastic	stochastic	ADJ
ejpam-6176	325	11	siqr	siqr	PROPN
ejpam-6176	325	12	model	model	NOUN
ejpam-6176	325	13	.	.	PUNCT
ejpam-6176	326	1	in	in	ADP
ejpam-6176	326	2	addition	addition	NOUN
ejpam-6176	326	3	to	to	ADP
ejpam-6176	326	4	this	this	PRON
ejpam-6176	326	5	,	,	PUNCT
ejpam-6176	326	6	the	the	DET
ejpam-6176	326	7	deterministic	deterministic	ADJ
ejpam-6176	326	8	model	model	NOUN
ejpam-6176	326	9	was	be	AUX
ejpam-6176	326	10	solved	solve	VERB
ejpam-6176	326	11	using	use	VERB
ejpam-6176	326	12	the	the	DET
ejpam-6176	326	13	matlab	matlab	PROPN
ejpam-6176	326	14	solver	solver	NOUN
ejpam-6176	326	15	pdepe	pdepe	NOUN
ejpam-6176	326	16	.	.	PUNCT
ejpam-6176	327	1	the	the	DET
ejpam-6176	327	2	solver	solver	NOUN
ejpam-6176	327	3	can	can	AUX
ejpam-6176	327	4	be	be	AUX
ejpam-6176	327	5	used	use	VERB
ejpam-6176	327	6	to	to	PART
ejpam-6176	327	7	find	find	VERB
ejpam-6176	327	8	solutions	solution	NOUN
ejpam-6176	327	9	for	for	ADP
ejpam-6176	327	10	diffusive	diffusive	ADJ
ejpam-6176	327	11	epidemic	epidemic	NOUN
ejpam-6176	327	12	models	model	NOUN
ejpam-6176	327	13	using	use	VERB
ejpam-6176	327	14	built	build	VERB
ejpam-6176	327	15	-	-	PUNCT
ejpam-6176	327	16	in	in	ADP
ejpam-6176	327	17	code	code	NOUN
ejpam-6176	327	18	available	available	ADJ
ejpam-6176	327	19	in	in	ADP
ejpam-6176	327	20	matlab	matlab	PROPN
ejpam-6176	327	21	software	software	NOUN
ejpam-6176	327	22	.	.	PUNCT
ejpam-6176	328	1	we	we	PRON
ejpam-6176	328	2	established	establish	VERB
ejpam-6176	328	3	the	the	DET
ejpam-6176	328	4	stability	stability	NOUN
ejpam-6176	328	5	and	and	CCONJ
ejpam-6176	328	6	consistency	consistency	NOUN
ejpam-6176	328	7	of	of	ADP
ejpam-6176	328	8	the	the	DET
ejpam-6176	328	9	proposed	propose	VERB
ejpam-6176	328	10	scheme	scheme	NOUN
ejpam-6176	328	11	in	in	ADP
ejpam-6176	328	12	the	the	DET
ejpam-6176	328	13	mean	mean	ADJ
ejpam-6176	328	14	-	-	PUNCT
ejpam-6176	328	15	square	square	ADJ
ejpam-6176	328	16	sense	sense	NOUN
ejpam-6176	328	17	,	,	PUNCT
ejpam-6176	328	18	confirming	confirm	VERB
ejpam-6176	328	19	its	its	PRON
ejpam-6176	328	20	theoretical	theoretical	ADJ
ejpam-6176	328	21	soundness	soundness	NOUN
ejpam-6176	328	22	.	.	PUNCT
ejpam-6176	329	1	numerical	numerical	ADJ
ejpam-6176	329	2	experiments	experiment	NOUN
ejpam-6176	329	3	were	be	AUX
ejpam-6176	329	4	conducted	conduct	VERB
ejpam-6176	329	5	to	to	PART
ejpam-6176	329	6	compare	compare	VERB
ejpam-6176	329	7	the	the	DET
ejpam-6176	329	8	performance	performance	NOUN
ejpam-6176	329	9	of	of	ADP
ejpam-6176	329	10	the	the	DET
ejpam-6176	329	11	proposed	propose	VERB
ejpam-6176	329	12	method	method	NOUN
ejpam-6176	329	13	with	with	ADP
ejpam-6176	329	14	the	the	DET
ejpam-6176	329	15	widely	widely	ADV
ejpam-6176	329	16	used	use	VERB
ejpam-6176	329	17	euler	euler	NOUN
ejpam-6176	329	18	-	-	PUNCT
ejpam-6176	329	19	maruyama	maruyama	NOUN
ejpam-6176	329	20	method	method	NOUN
ejpam-6176	329	21	and	and	CCONJ
ejpam-6176	329	22	the	the	DET
ejpam-6176	329	23	nonstandard	nonstandard	ADJ
ejpam-6176	329	24	finite	finite	ADJ
ejpam-6176	329	25	difference	difference	NOUN
ejpam-6176	329	26	(	(	PUNCT
ejpam-6176	329	27	nsfd	nsfd	ADJ
ejpam-6176	329	28	)	)	PUNCT
ejpam-6176	329	29	scheme	scheme	NOUN
ejpam-6176	329	30	.	.	PUNCT
ejpam-6176	330	1	the	the	DET
ejpam-6176	330	2	results	result	NOUN
ejpam-6176	330	3	demonstrated	demonstrate	VERB
ejpam-6176	330	4	that	that	SCONJ
ejpam-6176	330	5	the	the	DET
ejpam-6176	330	6	proposed	propose	VERB
ejpam-6176	330	7	method	method	NOUN
ejpam-6176	330	8	outperforms	outperform	VERB
ejpam-6176	330	9	existing	exist	VERB
ejpam-6176	330	10	techniques	technique	NOUN
ejpam-6176	330	11	by	by	ADP
ejpam-6176	330	12	producing	produce	VERB
ejpam-6176	330	13	more	more	ADV
ejpam-6176	330	14	accurate	accurate	ADJ
ejpam-6176	330	15	solutions	solution	NOUN
ejpam-6176	330	16	with	with	ADP
ejpam-6176	330	17	lower	low	ADJ
ejpam-6176	330	18	numerical	numerical	ADJ
ejpam-6176	330	19	errors	error	NOUN
ejpam-6176	330	20	.	.	PUNCT
ejpam-6176	331	1	the	the	DET
ejpam-6176	331	2	following	follow	VERB
ejpam-6176	331	3	points	point	NOUN
ejpam-6176	331	4	can	can	AUX
ejpam-6176	331	5	be	be	AUX
ejpam-6176	331	6	concluded	conclude	VERB
ejpam-6176	331	7	:	:	PUNCT
ejpam-6176	331	8	•	•	SCONJ
ejpam-6176	331	9	the	the	DET
ejpam-6176	331	10	proposed	propose	VERB
ejpam-6176	331	11	scheme	scheme	NOUN
ejpam-6176	331	12	performed	perform	VERB
ejpam-6176	331	13	better	well	ADV
ejpam-6176	331	14	than	than	ADP
ejpam-6176	331	15	the	the	DET
ejpam-6176	331	16	existing	exist	VERB
ejpam-6176	331	17	nonstandard	nonstandard	ADJ
ejpam-6176	331	18	finite	finite	ADJ
ejpam-6176	331	19	difference	difference	NOUN
ejpam-6176	331	20	scheme	scheme	NOUN
ejpam-6176	331	21	in	in	ADP
ejpam-6176	331	22	accuracy	accuracy	NOUN
ejpam-6176	331	23	.	.	PUNCT
ejpam-6176	332	1	m.	m.	PROPN
ejpam-6176	332	2	s.	s.	PROPN
ejpam-6176	332	3	arif	arif	PROPN
ejpam-6176	332	4	,	,	PUNCT
ejpam-6176	332	5	k.	k.	PROPN
ejpam-6176	332	6	abodayeh	abodayeh	PROPN
ejpam-6176	332	7	,	,	PUNCT
ejpam-6176	332	8	y.	y.	NOUN
ejpam-6176	332	9	nawaz	nawaz	PROPN
ejpam-6176	332	10	/	/	SYM
ejpam-6176	332	11	eur	eur	PROPN
ejpam-6176	332	12	.	.	PUNCT
ejpam-6176	333	1	j.	j.	PROPN
ejpam-6176	333	2	pure	pure	PROPN
ejpam-6176	333	3	appl	appl	PROPN
ejpam-6176	333	4	.	.	PROPN
ejpam-6176	333	5	math	math	PROPN
ejpam-6176	333	6	,	,	PUNCT
ejpam-6176	333	7	18	18	NUM
ejpam-6176	333	8	(	(	PUNCT
ejpam-6176	333	9	3	3	NUM
ejpam-6176	333	10	)	)	PUNCT
ejpam-6176	333	11	(	(	PUNCT
ejpam-6176	333	12	2025	2025	NUM
ejpam-6176	333	13	)	)	PUNCT
ejpam-6176	333	14	,	,	PUNCT
ejpam-6176	333	15	6176	6176	NUM
ejpam-6176	333	16	18	18	NUM
ejpam-6176	333	17	of	of	ADP
ejpam-6176	333	18	21	21	NUM
ejpam-6176	333	19	•	•	NUM
ejpam-6176	333	20	the	the	DET
ejpam-6176	333	21	rise	rise	NOUN
ejpam-6176	333	22	in	in	ADP
ejpam-6176	333	23	transmission	transmission	NOUN
ejpam-6176	333	24	parameters	parameter	NOUN
ejpam-6176	333	25	from	from	ADP
ejpam-6176	333	26	susceptible	susceptible	ADJ
ejpam-6176	333	27	to	to	ADP
ejpam-6176	333	28	infective	infective	ADJ
ejpam-6176	333	29	produced	produce	VERB
ejpam-6176	333	30	a	a	DET
ejpam-6176	333	31	decline	decline	NOUN
ejpam-6176	333	32	in	in	ADP
ejpam-6176	333	33	susceptible	susceptible	ADJ
ejpam-6176	333	34	and	and	CCONJ
ejpam-6176	333	35	growth	growth	NOUN
ejpam-6176	333	36	in	in	ADP
ejpam-6176	333	37	infective	infective	ADJ
ejpam-6176	333	38	.	.	PUNCT
ejpam-6176	334	1	•	•	NUM
ejpam-6176	334	2	the	the	DET
ejpam-6176	334	3	vaccination	vaccination	NOUN
ejpam-6176	334	4	rate	rate	NOUN
ejpam-6176	334	5	yields	yield	VERB
ejpam-6176	334	6	a	a	DET
ejpam-6176	334	7	decline	decline	NOUN
ejpam-6176	334	8	in	in	ADP
ejpam-6176	334	9	susceptible	susceptible	ADJ
ejpam-6176	334	10	and	and	CCONJ
ejpam-6176	334	11	growth	growth	NOUN
ejpam-6176	334	12	in	in	ADP
ejpam-6176	334	13	recovered	recovered	ADJ
ejpam-6176	334	14	individuals	individual	NOUN
ejpam-6176	334	15	.	.	PUNCT
ejpam-6176	335	1	this	this	DET
ejpam-6176	335	2	study	study	NOUN
ejpam-6176	335	3	offers	offer	VERB
ejpam-6176	335	4	a	a	DET
ejpam-6176	335	5	powerful	powerful	ADJ
ejpam-6176	335	6	and	and	CCONJ
ejpam-6176	335	7	effective	effective	ADJ
ejpam-6176	335	8	computational	computational	ADJ
ejpam-6176	335	9	instrument	instrument	NOUN
ejpam-6176	335	10	for	for	ADP
ejpam-6176	335	11	stochastic	stochastic	ADJ
ejpam-6176	335	12	epidemic	epidemic	NOUN
ejpam-6176	335	13	models	model	NOUN
ejpam-6176	335	14	characterized	characterize	VERB
ejpam-6176	335	15	by	by	ADP
ejpam-6176	335	16	spatial	spatial	ADJ
ejpam-6176	335	17	diffusion	diffusion	NOUN
ejpam-6176	335	18	and	and	CCONJ
ejpam-6176	335	19	non	non	ADJ
ejpam-6176	335	20	-	-	ADJ
ejpam-6176	335	21	linear	linear	ADJ
ejpam-6176	335	22	dynamics	dynamic	NOUN
ejpam-6176	335	23	.	.	PUNCT
ejpam-6176	336	1	the	the	DET
ejpam-6176	336	2	suggested	suggest	VERB
ejpam-6176	336	3	framework	framework	NOUN
ejpam-6176	336	4	can	can	AUX
ejpam-6176	336	5	be	be	AUX
ejpam-6176	336	6	adapted	adapt	VERB
ejpam-6176	336	7	to	to	ADP
ejpam-6176	336	8	many	many	ADJ
ejpam-6176	336	9	stochastic	stochastic	ADJ
ejpam-6176	336	10	models	model	NOUN
ejpam-6176	336	11	in	in	ADP
ejpam-6176	336	12	epidemiology	epidemiology	NOUN
ejpam-6176	336	13	and	and	CCONJ
ejpam-6176	336	14	related	relate	VERB
ejpam-6176	336	15	disciplines	discipline	NOUN
ejpam-6176	336	16	,	,	PUNCT
ejpam-6176	336	17	presenting	present	VERB
ejpam-6176	336	18	a	a	DET
ejpam-6176	336	19	viable	viable	ADJ
ejpam-6176	336	20	avenue	avenue	NOUN
ejpam-6176	336	21	for	for	ADP
ejpam-6176	336	22	future	future	ADJ
ejpam-6176	336	23	study	study	NOUN
ejpam-6176	336	24	in	in	ADP
ejpam-6176	336	25	computational	computational	ADJ
ejpam-6176	336	26	disease	disease	NOUN
ejpam-6176	336	27	modelling	modelling	NOUN
ejpam-6176	336	28	.	.	PUNCT
ejpam-6176	337	1	acknowledgements	acknowledgement	NOUN
ejpam-6176	337	2	the	the	DET
ejpam-6176	337	3	authors	author	NOUN
ejpam-6176	337	4	would	would	AUX
ejpam-6176	337	5	like	like	VERB
ejpam-6176	337	6	to	to	PART
ejpam-6176	337	7	acknowledge	acknowledge	VERB
ejpam-6176	337	8	the	the	DET
ejpam-6176	337	9	support	support	NOUN
ejpam-6176	337	10	of	of	ADP
ejpam-6176	337	11	prince	prince	PROPN
ejpam-6176	337	12	sultan	sultan	PROPN
ejpam-6176	337	13	university	university	PROPN
ejpam-6176	337	14	for	for	ADP
ejpam-6176	337	15	paying	pay	VERB
ejpam-6176	337	16	the	the	DET
ejpam-6176	337	17	article	article	NOUN
ejpam-6176	337	18	processing	processing	NOUN
ejpam-6176	337	19	charges	charge	NOUN
ejpam-6176	337	20	(	(	PUNCT
ejpam-6176	337	21	apc	apc	PROPN
ejpam-6176	337	22	)	)	PUNCT
ejpam-6176	337	23	of	of	ADP
ejpam-6176	337	24	this	this	DET
ejpam-6176	337	25	publication	publication	NOUN
ejpam-6176	337	26	.	.	PUNCT
ejpam-6176	338	1	references	reference	NOUN
ejpam-6176	338	2	[	[	X
ejpam-6176	338	3	1	1	X
ejpam-6176	338	4	]	]	PUNCT
ejpam-6176	338	5	j.	j.	PROPN
ejpam-6176	338	6	mann	mann	PROPN
ejpam-6176	338	7	and	and	CCONJ
ejpam-6176	338	8	m.	m.	PROPN
ejpam-6176	338	9	roberts	roberts	PROPN
ejpam-6176	338	10	.	.	PUNCT
ejpam-6176	339	1	modelling	model	VERB
ejpam-6176	339	2	the	the	DET
ejpam-6176	339	3	epidemiology	epidemiology	NOUN
ejpam-6176	339	4	of	of	ADP
ejpam-6176	339	5	hepatitis	hepatitis	PROPN
ejpam-6176	339	6	b	b	PROPN
ejpam-6176	339	7	in	in	ADP
ejpam-6176	339	8	new	new	PROPN
ejpam-6176	339	9	zealand	zealand	PROPN
ejpam-6176	339	10	.	.	PUNCT
ejpam-6176	340	1	journal	journal	PROPN
ejpam-6176	340	2	of	of	ADP
ejpam-6176	340	3	theoretical	theoretical	ADJ
ejpam-6176	340	4	biology	biology	NOUN
ejpam-6176	340	5	,	,	PUNCT
ejpam-6176	340	6	269(1):266–272	269(1):266–272	NUM
ejpam-6176	340	7	,	,	PUNCT
ejpam-6176	340	8	2011	2011	NUM
ejpam-6176	340	9	.	.	PUNCT
ejpam-6176	341	1	[	[	X
ejpam-6176	341	2	2	2	NUM
ejpam-6176	341	3	]	]	PUNCT
ejpam-6176	341	4	c.	c.	PROPN
ejpam-6176	341	5	tian	tian	PROPN
ejpam-6176	341	6	,	,	PUNCT
ejpam-6176	341	7	q.	q.	PROPN
ejpam-6176	341	8	zhang	zhang	PROPN
ejpam-6176	341	9	,	,	PUNCT
ejpam-6176	341	10	and	and	CCONJ
ejpam-6176	341	11	l.	l.	PROPN
ejpam-6176	341	12	zhang	zhang	PROPN
ejpam-6176	341	13	.	.	PUNCT
ejpam-6176	342	1	global	global	ADJ
ejpam-6176	342	2	stability	stability	NOUN
ejpam-6176	342	3	in	in	ADP
ejpam-6176	342	4	a	a	DET
ejpam-6176	342	5	networked	networked	ADJ
ejpam-6176	342	6	sir	sir	NOUN
ejpam-6176	342	7	epidemic	epidemic	NOUN
ejpam-6176	342	8	model	model	NOUN
ejpam-6176	342	9	.	.	PUNCT
ejpam-6176	343	1	applied	apply	VERB
ejpam-6176	343	2	mathematics	mathematics	NOUN
ejpam-6176	343	3	letters	letter	NOUN
ejpam-6176	343	4	,	,	PUNCT
ejpam-6176	343	5	107:106444	107:106444	NUM
ejpam-6176	343	6	,	,	PUNCT
ejpam-6176	343	7	2020	2020	NUM
ejpam-6176	343	8	.	.	PUNCT
ejpam-6176	344	1	[	[	X
ejpam-6176	344	2	3	3	NUM
ejpam-6176	344	3	]	]	PUNCT
ejpam-6176	344	4	x.	x.	NOUN
ejpam-6176	344	5	meng	meng	PROPN
ejpam-6176	344	6	,	,	PUNCT
ejpam-6176	344	7	s.	s.	PROPN
ejpam-6176	344	8	zhao	zhao	PROPN
ejpam-6176	344	9	,	,	PUNCT
ejpam-6176	344	10	t.	t.	PROPN
ejpam-6176	344	11	feng	feng	PROPN
ejpam-6176	344	12	,	,	PUNCT
ejpam-6176	344	13	and	and	CCONJ
ejpam-6176	344	14	t.	t.	PROPN
ejpam-6176	344	15	zhang	zhang	PROPN
ejpam-6176	344	16	.	.	PUNCT
ejpam-6176	345	1	dynamics	dynamic	NOUN
ejpam-6176	345	2	of	of	ADP
ejpam-6176	345	3	a	a	DET
ejpam-6176	345	4	novel	novel	ADJ
ejpam-6176	345	5	non	non	ADJ
ejpam-6176	345	6	-	-	ADJ
ejpam-6176	345	7	linear	linear	ADJ
ejpam-6176	345	8	stochastic	stochastic	ADJ
ejpam-6176	345	9	sis	sis	NOUN
ejpam-6176	345	10	epidemic	epidemic	NOUN
ejpam-6176	345	11	model	model	NOUN
ejpam-6176	345	12	with	with	ADP
ejpam-6176	345	13	double	double	ADJ
ejpam-6176	345	14	epidemic	epidemic	NOUN
ejpam-6176	345	15	hypothesis	hypothesis	NOUN
ejpam-6176	345	16	.	.	PUNCT
ejpam-6176	346	1	journal	journal	PROPN
ejpam-6176	346	2	of	of	ADP
ejpam-6176	346	3	mathematical	mathematical	ADJ
ejpam-6176	346	4	analysis	analysis	NOUN
ejpam-6176	346	5	and	and	CCONJ
ejpam-6176	346	6	applications	application	NOUN
ejpam-6176	346	7	,	,	PUNCT
ejpam-6176	346	8	433(1):227–242	433(1):227–242	PROPN
ejpam-6176	346	9	,	,	PUNCT
ejpam-6176	346	10	2016	2016	NUM
ejpam-6176	346	11	.	.	PUNCT
ejpam-6176	347	1	[	[	X
ejpam-6176	347	2	4	4	NUM
ejpam-6176	347	3	]	]	PUNCT
ejpam-6176	347	4	a.	a.	NOUN
ejpam-6176	347	5	el	el	PROPN
ejpam-6176	347	6	koufi	koufi	PROPN
ejpam-6176	347	7	,	,	PUNCT
ejpam-6176	347	8	j.	j.	PROPN
ejpam-6176	347	9	adnani	adnani	PROPN
ejpam-6176	347	10	,	,	PUNCT
ejpam-6176	347	11	a.	a.	NOUN
ejpam-6176	347	12	bennar	bennar	NOUN
ejpam-6176	347	13	,	,	PUNCT
ejpam-6176	347	14	and	and	CCONJ
ejpam-6176	347	15	n.	n.	PROPN
ejpam-6176	347	16	yousfi	yousfi	PROPN
ejpam-6176	347	17	.	.	PUNCT
ejpam-6176	348	1	analysis	analysis	NOUN
ejpam-6176	348	2	of	of	ADP
ejpam-6176	348	3	a	a	DET
ejpam-6176	348	4	stochastic	stochastic	ADJ
ejpam-6176	348	5	sir	sir	NOUN
ejpam-6176	348	6	model	model	NOUN
ejpam-6176	348	7	with	with	ADP
ejpam-6176	348	8	vaccination	vaccination	NOUN
ejpam-6176	348	9	and	and	CCONJ
ejpam-6176	348	10	non	non	ADJ
ejpam-6176	348	11	-	-	ADJ
ejpam-6176	348	12	linear	linear	ADJ
ejpam-6176	348	13	incidence	incidence	NOUN
ejpam-6176	348	14	rate	rate	NOUN
ejpam-6176	348	15	.	.	PUNCT
ejpam-6176	349	1	international	international	ADJ
ejpam-6176	349	2	journal	journal	PROPN
ejpam-6176	349	3	of	of	ADP
ejpam-6176	349	4	differential	differential	ADJ
ejpam-6176	349	5	equations	equation	NOUN
ejpam-6176	349	6	,	,	PUNCT
ejpam-6176	349	7	2019	2019	NUM
ejpam-6176	349	8	,	,	PUNCT
ejpam-6176	349	9	2019	2019	NUM
ejpam-6176	349	10	.	.	PUNCT
ejpam-6176	350	1	[	[	X
ejpam-6176	350	2	5	5	X
ejpam-6176	350	3	]	]	PUNCT
ejpam-6176	350	4	j.	j.	PROPN
ejpam-6176	350	5	li	li	PROPN
ejpam-6176	350	6	and	and	CCONJ
ejpam-6176	350	7	z.	z.	PROPN
ejpam-6176	350	8	ma	ma	PROPN
ejpam-6176	350	9	.	.	PROPN
ejpam-6176	350	10	qualitative	qualitative	ADJ
ejpam-6176	350	11	analyses	analysis	NOUN
ejpam-6176	350	12	of	of	ADP
ejpam-6176	350	13	sis	sis	NOUN
ejpam-6176	350	14	epidemic	epidemic	NOUN
ejpam-6176	350	15	model	model	NOUN
ejpam-6176	350	16	with	with	ADP
ejpam-6176	350	17	vaccination	vaccination	NOUN
ejpam-6176	350	18	and	and	CCONJ
ejpam-6176	350	19	varying	vary	VERB
ejpam-6176	350	20	total	total	ADJ
ejpam-6176	350	21	population	population	NOUN
ejpam-6176	350	22	size	size	NOUN
ejpam-6176	350	23	.	.	PUNCT
ejpam-6176	351	1	mathematical	mathematical	ADJ
ejpam-6176	351	2	and	and	CCONJ
ejpam-6176	351	3	computer	computer	NOUN
ejpam-6176	351	4	modelling	modelling	NOUN
ejpam-6176	351	5	,	,	PUNCT
ejpam-6176	351	6	35(11–12):1235	35(11–12):1235	NUM
ejpam-6176	351	7	–	–	PUNCT
ejpam-6176	351	8	1243	1243	NUM
ejpam-6176	351	9	,	,	PUNCT
ejpam-6176	351	10	2002	2002	NUM
ejpam-6176	351	11	.	.	PUNCT
ejpam-6176	352	1	[	[	X
ejpam-6176	352	2	6	6	NUM
ejpam-6176	352	3	]	]	PUNCT
ejpam-6176	352	4	a.	a.	NOUN
ejpam-6176	352	5	kilicman	kilicman	NOUN
ejpam-6176	352	6	.	.	PUNCT
ejpam-6176	353	1	a	a	DET
ejpam-6176	353	2	fractional	fractional	ADJ
ejpam-6176	353	3	order	order	NOUN
ejpam-6176	353	4	sir	sir	NOUN
ejpam-6176	353	5	epidemic	epidemic	NOUN
ejpam-6176	353	6	model	model	NOUN
ejpam-6176	353	7	for	for	ADP
ejpam-6176	353	8	dengue	dengue	NOUN
ejpam-6176	353	9	transmission	transmission	NOUN
ejpam-6176	353	10	.	.	PUNCT
ejpam-6176	354	1	chaos	chaos	NOUN
ejpam-6176	354	2	,	,	PUNCT
ejpam-6176	354	3	solitons	soliton	NOUN
ejpam-6176	354	4	&	&	CCONJ
ejpam-6176	354	5	fractals	fractal	NOUN
ejpam-6176	354	6	,	,	PUNCT
ejpam-6176	354	7	114:55–62	114:55–62	NUM
ejpam-6176	354	8	,	,	PUNCT
ejpam-6176	354	9	2018	2018	NUM
ejpam-6176	354	10	.	.	PUNCT
ejpam-6176	355	1	[	[	X
ejpam-6176	355	2	7	7	X
ejpam-6176	355	3	]	]	X
ejpam-6176	355	4	l.	l.	PROPN
ejpam-6176	355	5	xiang	xiang	PROPN
ejpam-6176	355	6	,	,	PUNCT
ejpam-6176	355	7	y.	y.	PROPN
ejpam-6176	355	8	zhang	zhang	PROPN
ejpam-6176	355	9	,	,	PUNCT
ejpam-6176	355	10	and	and	CCONJ
ejpam-6176	355	11	j.	j.	PROPN
ejpam-6176	355	12	huang	huang	PROPN
ejpam-6176	355	13	.	.	PUNCT
ejpam-6176	355	14	stability	stability	NOUN
ejpam-6176	355	15	analysis	analysis	NOUN
ejpam-6176	355	16	of	of	ADP
ejpam-6176	355	17	a	a	DET
ejpam-6176	355	18	discrete	discrete	ADJ
ejpam-6176	355	19	sirs	sir	NOUN
ejpam-6176	355	20	epidemic	epidemic	NOUN
ejpam-6176	355	21	model	model	NOUN
ejpam-6176	355	22	with	with	ADP
ejpam-6176	355	23	vaccination	vaccination	NOUN
ejpam-6176	355	24	.	.	PUNCT
ejpam-6176	356	1	journal	journal	NOUN
ejpam-6176	356	2	of	of	ADP
ejpam-6176	356	3	difference	difference	NOUN
ejpam-6176	356	4	equations	equation	NOUN
ejpam-6176	356	5	and	and	CCONJ
ejpam-6176	356	6	applications	application	NOUN
ejpam-6176	356	7	,	,	PUNCT
ejpam-6176	356	8	26(3):309–327	26(3):309–327	PROPN
ejpam-6176	356	9	,	,	PUNCT
ejpam-6176	356	10	2020	2020	NUM
ejpam-6176	356	11	.	.	PUNCT
ejpam-6176	357	1	[	[	X
ejpam-6176	357	2	8	8	X
ejpam-6176	357	3	]	]	PUNCT
ejpam-6176	357	4	t.	t.	NOUN
ejpam-6176	357	5	odagaki	odagaki	ADJ
ejpam-6176	357	6	.	.	PUNCT
ejpam-6176	358	1	exact	exact	ADJ
ejpam-6176	358	2	properties	property	NOUN
ejpam-6176	358	3	of	of	ADP
ejpam-6176	358	4	siqr	siqr	PROPN
ejpam-6176	358	5	model	model	NOUN
ejpam-6176	358	6	for	for	ADP
ejpam-6176	358	7	covid-19	covid-19	PROPN
ejpam-6176	358	8	.	.	PUNCT
ejpam-6176	358	9	physica	physica	PROPN
ejpam-6176	358	10	a	a	DET
ejpam-6176	358	11	,	,	PUNCT
ejpam-6176	358	12	564:125564	564:125564	NUM
ejpam-6176	358	13	,	,	PUNCT
ejpam-6176	358	14	2021	2021	NUM
ejpam-6176	358	15	.	.	PUNCT
ejpam-6176	359	1	[	[	X
ejpam-6176	359	2	9	9	NUM
ejpam-6176	359	3	]	]	PUNCT
ejpam-6176	359	4	t.	t.	NOUN
ejpam-6176	359	5	odagaki	odagaki	NOUN
ejpam-6176	359	6	.	.	PUNCT
ejpam-6176	360	1	analysis	analysis	NOUN
ejpam-6176	360	2	of	of	ADP
ejpam-6176	360	3	the	the	DET
ejpam-6176	360	4	outbreak	outbreak	NOUN
ejpam-6176	360	5	of	of	ADP
ejpam-6176	360	6	covid-19	covid-19	PROPN
ejpam-6176	360	7	in	in	ADP
ejpam-6176	360	8	japan	japan	PROPN
ejpam-6176	360	9	by	by	ADP
ejpam-6176	360	10	siqr	siqr	PROPN
ejpam-6176	360	11	model	model	PROPN
ejpam-6176	360	12	.	.	PUNCT
ejpam-6176	361	1	infectious	infectious	ADJ
ejpam-6176	361	2	disease	disease	NOUN
ejpam-6176	361	3	modelling	modelling	NOUN
ejpam-6176	361	4	,	,	PUNCT
ejpam-6176	361	5	5:691–698	5:691–698	NUM
ejpam-6176	361	6	,	,	PUNCT
ejpam-6176	361	7	2020	2020	NUM
ejpam-6176	361	8	.	.	PUNCT
ejpam-6176	362	1	[	[	X
ejpam-6176	362	2	10	10	NUM
ejpam-6176	362	3	]	]	X
ejpam-6176	362	4	h.	h.	PROPN
ejpam-6176	362	5	hethcote	hethcote	PROPN
ejpam-6176	362	6	,	,	PUNCT
ejpam-6176	362	7	m.	m.	NOUN
ejpam-6176	362	8	zhien	zhien	PROPN
ejpam-6176	362	9	,	,	PUNCT
ejpam-6176	362	10	and	and	CCONJ
ejpam-6176	362	11	l.	l.	PROPN
ejpam-6176	362	12	shengbing	shengbing	PROPN
ejpam-6176	362	13	.	.	PUNCT
ejpam-6176	363	1	effects	effect	NOUN
ejpam-6176	363	2	of	of	ADP
ejpam-6176	363	3	quarantine	quarantine	NOUN
ejpam-6176	363	4	in	in	ADP
ejpam-6176	363	5	six	six	NUM
ejpam-6176	363	6	endemic	endemic	ADJ
ejpam-6176	363	7	models	model	NOUN
ejpam-6176	363	8	for	for	ADP
ejpam-6176	363	9	infectious	infectious	ADJ
ejpam-6176	363	10	diseases	disease	NOUN
ejpam-6176	363	11	.	.	PUNCT
ejpam-6176	364	1	mathematical	mathematical	ADJ
ejpam-6176	364	2	biosciences	bioscience	NOUN
ejpam-6176	364	3	,	,	PUNCT
ejpam-6176	364	4	180(1–2):141–160	180(1–2):141–160	NUM
ejpam-6176	364	5	,	,	PUNCT
ejpam-6176	364	6	2002	2002	NUM
ejpam-6176	364	7	.	.	PUNCT
ejpam-6176	365	1	[	[	X
ejpam-6176	365	2	11	11	NUM
ejpam-6176	365	3	]	]	PUNCT
ejpam-6176	365	4	m.	m.	NOUN
ejpam-6176	365	5	erdem	erdem	PROPN
ejpam-6176	365	6	,	,	PUNCT
ejpam-6176	365	7	m.	m.	NOUN
ejpam-6176	365	8	safan	safan	PROPN
ejpam-6176	365	9	,	,	PUNCT
ejpam-6176	365	10	and	and	CCONJ
ejpam-6176	365	11	c.	c.	PROPN
ejpam-6176	365	12	castillo	castillo	PROPN
ejpam-6176	365	13	-	-	PUNCT
ejpam-6176	365	14	chavez	chavez	PROPN
ejpam-6176	365	15	.	.	PUNCT
ejpam-6176	366	1	mathematical	mathematical	ADJ
ejpam-6176	366	2	analysis	analysis	NOUN
ejpam-6176	366	3	of	of	ADP
ejpam-6176	366	4	an	an	DET
ejpam-6176	366	5	siqr	siqr	ADJ
ejpam-6176	366	6	influenza	influenza	NOUN
ejpam-6176	366	7	model	model	NOUN
ejpam-6176	366	8	with	with	ADP
ejpam-6176	366	9	imperfect	imperfect	ADJ
ejpam-6176	366	10	quarantine	quarantine	NOUN
ejpam-6176	366	11	.	.	PUNCT
ejpam-6176	367	1	bulletin	bulletin	NOUN
ejpam-6176	367	2	of	of	ADP
ejpam-6176	367	3	mathematical	mathematical	ADJ
ejpam-6176	367	4	biology	biology	NOUN
ejpam-6176	367	5	,	,	PUNCT
ejpam-6176	367	6	79(7):1612–1636	79(7):1612–1636	NUM
ejpam-6176	367	7	,	,	PUNCT
ejpam-6176	367	8	2017	2017	NUM
ejpam-6176	367	9	.	.	PUNCT
ejpam-6176	368	1	m.	m.	PROPN
ejpam-6176	368	2	s.	s.	PROPN
ejpam-6176	368	3	arif	arif	PROPN
ejpam-6176	368	4	,	,	PUNCT
ejpam-6176	368	5	k.	k.	PROPN
ejpam-6176	368	6	abodayeh	abodayeh	PROPN
ejpam-6176	368	7	,	,	PUNCT
ejpam-6176	368	8	y.	y.	NOUN
ejpam-6176	368	9	nawaz	nawaz	PROPN
ejpam-6176	368	10	/	/	SYM
ejpam-6176	368	11	eur	eur	PROPN
ejpam-6176	368	12	.	.	PUNCT
ejpam-6176	369	1	j.	j.	PROPN
ejpam-6176	369	2	pure	pure	PROPN
ejpam-6176	369	3	appl	appl	PROPN
ejpam-6176	369	4	.	.	PROPN
ejpam-6176	369	5	math	math	PROPN
ejpam-6176	369	6	,	,	PUNCT
ejpam-6176	369	7	18	18	NUM
ejpam-6176	369	8	(	(	PUNCT
ejpam-6176	369	9	3	3	NUM
ejpam-6176	369	10	)	)	PUNCT
ejpam-6176	369	11	(	(	PUNCT
ejpam-6176	369	12	2025	2025	NUM
ejpam-6176	369	13	)	)	PUNCT
ejpam-6176	369	14	,	,	PUNCT
ejpam-6176	369	15	6176	6176	NUM
ejpam-6176	369	16	19	19	NUM
ejpam-6176	369	17	of	of	ADP
ejpam-6176	369	18	21	21	NUM
ejpam-6176	370	1	[	[	X
ejpam-6176	370	2	12	12	NUM
ejpam-6176	370	3	]	]	X
ejpam-6176	370	4	y.	y.	PROPN
ejpam-6176	370	5	ma	ma	PROPN
ejpam-6176	370	6	,	,	PUNCT
ejpam-6176	370	7	j.b	j.b	PROPN
ejpam-6176	370	8	.	.	PUNCT
ejpam-6176	370	9	liu	liu	PROPN
ejpam-6176	370	10	,	,	PUNCT
ejpam-6176	370	11	and	and	CCONJ
ejpam-6176	370	12	h.	h.	PROPN
ejpam-6176	370	13	li	li	PROPN
ejpam-6176	370	14	.	.	PROPN
ejpam-6176	371	1	global	global	ADJ
ejpam-6176	371	2	dynamics	dynamic	NOUN
ejpam-6176	371	3	of	of	ADP
ejpam-6176	371	4	an	an	DET
ejpam-6176	371	5	siqr	siqr	ADJ
ejpam-6176	371	6	model	model	NOUN
ejpam-6176	371	7	with	with	ADP
ejpam-6176	371	8	vaccination	vaccination	NOUN
ejpam-6176	371	9	and	and	CCONJ
ejpam-6176	371	10	elimination	elimination	NOUN
ejpam-6176	371	11	hybrid	hybrid	ADJ
ejpam-6176	371	12	strategies	strategy	NOUN
ejpam-6176	371	13	.	.	PUNCT
ejpam-6176	372	1	mathematics	mathematic	NOUN
ejpam-6176	372	2	,	,	PUNCT
ejpam-6176	372	3	6(12):328	6(12):328	NUM
ejpam-6176	372	4	,	,	PUNCT
ejpam-6176	372	5	2018	2018	NUM
ejpam-6176	372	6	.	.	PUNCT
ejpam-6176	373	1	[	[	X
ejpam-6176	373	2	13	13	NUM
ejpam-6176	373	3	]	]	X
ejpam-6176	373	4	h.	h.	PROPN
ejpam-6176	373	5	cheng	cheng	PROPN
ejpam-6176	373	6	,	,	PUNCT
ejpam-6176	373	7	f.	f.	PROPN
ejpam-6176	373	8	wang	wang	PROPN
ejpam-6176	373	9	,	,	PUNCT
ejpam-6176	373	10	and	and	CCONJ
ejpam-6176	373	11	t.	t.	PROPN
ejpam-6176	373	12	zhang	zhang	PROPN
ejpam-6176	373	13	.	.	PUNCT
ejpam-6176	374	1	multi	multi	ADJ
ejpam-6176	374	2	-	-	ADJ
ejpam-6176	374	3	state	state	ADJ
ejpam-6176	374	4	dependent	dependent	ADJ
ejpam-6176	374	5	impulsive	impulsive	ADJ
ejpam-6176	374	6	control	control	NOUN
ejpam-6176	374	7	for	for	ADP
ejpam-6176	374	8	holling	holle	VERB
ejpam-6176	374	9	i	i	PRON
ejpam-6176	374	10	predator	predator	NOUN
ejpam-6176	374	11	-	-	PUNCT
ejpam-6176	374	12	prey	prey	NOUN
ejpam-6176	374	13	model	model	NOUN
ejpam-6176	374	14	.	.	PUNCT
ejpam-6176	375	1	discrete	discrete	ADJ
ejpam-6176	375	2	dynamics	dynamic	NOUN
ejpam-6176	375	3	in	in	ADP
ejpam-6176	375	4	nature	nature	NOUN
ejpam-6176	375	5	and	and	CCONJ
ejpam-6176	375	6	society	society	NOUN
ejpam-6176	375	7	,	,	PUNCT
ejpam-6176	375	8	2012	2012	NUM
ejpam-6176	375	9	,	,	PUNCT
ejpam-6176	375	10	2012	2012	NUM
ejpam-6176	375	11	.	.	PUNCT
ejpam-6176	376	1	[	[	X
ejpam-6176	376	2	14	14	NUM
ejpam-6176	376	3	]	]	X
ejpam-6176	376	4	w.	w.	PROPN
ejpam-6176	376	5	zou	zou	PROPN
ejpam-6176	376	6	,	,	PUNCT
ejpam-6176	376	7	j.	j.	PROPN
ejpam-6176	376	8	xie	xie	PROPN
ejpam-6176	376	9	,	,	PUNCT
ejpam-6176	376	10	and	and	CCONJ
ejpam-6176	376	11	z.	z.	PROPN
ejpam-6176	376	12	xiong	xiong	PROPN
ejpam-6176	376	13	.	.	PUNCT
ejpam-6176	377	1	stability	stability	NOUN
ejpam-6176	377	2	and	and	CCONJ
ejpam-6176	377	3	hopf	hopf	ADJ
ejpam-6176	377	4	bifurcation	bifurcation	NOUN
ejpam-6176	377	5	for	for	ADP
ejpam-6176	377	6	an	an	DET
ejpam-6176	377	7	eco	eco	NOUN
ejpam-6176	377	8	-	-	PUNCT
ejpam-6176	377	9	epidemiology	epidemiology	NOUN
ejpam-6176	377	10	model	model	NOUN
ejpam-6176	377	11	with	with	ADP
ejpam-6176	377	12	holling	holle	VERB
ejpam-6176	377	13	-	-	PUNCT
ejpam-6176	377	14	iii	iii	NOUN
ejpam-6176	377	15	functional	functional	ADJ
ejpam-6176	377	16	response	response	NOUN
ejpam-6176	377	17	and	and	CCONJ
ejpam-6176	377	18	delays	delay	NOUN
ejpam-6176	377	19	.	.	PUNCT
ejpam-6176	378	1	international	international	ADJ
ejpam-6176	378	2	journal	journal	PROPN
ejpam-6176	378	3	of	of	ADP
ejpam-6176	378	4	biomathematics	biomathematic	NOUN
ejpam-6176	378	5	,	,	PUNCT
ejpam-6176	378	6	1(3):377–389	1(3):377–389	NUM
ejpam-6176	378	7	,	,	PUNCT
ejpam-6176	378	8	2008	2008	NUM
ejpam-6176	378	9	.	.	PUNCT
ejpam-6176	379	1	[	[	X
ejpam-6176	379	2	15	15	NUM
ejpam-6176	379	3	]	]	X
ejpam-6176	379	4	y.	y.	PROPN
ejpam-6176	379	5	jin	jin	PROPN
ejpam-6176	379	6	,	,	PUNCT
ejpam-6176	379	7	w.	w.	PROPN
ejpam-6176	379	8	wang	wang	PROPN
ejpam-6176	379	9	,	,	PUNCT
ejpam-6176	379	10	and	and	CCONJ
ejpam-6176	379	11	s.	s.	PROPN
ejpam-6176	379	12	xiao	xiao	PROPN
ejpam-6176	379	13	.	.	PUNCT
ejpam-6176	380	1	an	an	DET
ejpam-6176	380	2	sirs	sirs	PROPN
ejpam-6176	380	3	model	model	NOUN
ejpam-6176	380	4	with	with	ADP
ejpam-6176	380	5	a	a	DET
ejpam-6176	380	6	non	non	ADJ
ejpam-6176	380	7	-	-	ADJ
ejpam-6176	380	8	linear	linear	ADJ
ejpam-6176	380	9	incidence	incidence	NOUN
ejpam-6176	380	10	rate	rate	NOUN
ejpam-6176	380	11	.	.	PUNCT
ejpam-6176	381	1	chaos	chaos	NOUN
ejpam-6176	381	2	,	,	PUNCT
ejpam-6176	381	3	solitons	soliton	NOUN
ejpam-6176	381	4	&	&	CCONJ
ejpam-6176	381	5	fractals	fractal	NOUN
ejpam-6176	381	6	,	,	PUNCT
ejpam-6176	381	7	34(5):1482–1497	34(5):1482–1497	NUM
ejpam-6176	381	8	,	,	PUNCT
ejpam-6176	381	9	2007	2007	NUM
ejpam-6176	381	10	.	.	PUNCT
ejpam-6176	382	1	[	[	X
ejpam-6176	382	2	16	16	NUM
ejpam-6176	382	3	]	]	X
ejpam-6176	382	4	m.a	m.a	PROPN
ejpam-6176	382	5	.	.	PROPN
ejpam-6176	382	6	khan	khan	PROPN
ejpam-6176	382	7	,	,	PUNCT
ejpam-6176	382	8	y.	y.	PROPN
ejpam-6176	382	9	khan	khan	PROPN
ejpam-6176	382	10	,	,	PUNCT
ejpam-6176	382	11	and	and	CCONJ
ejpam-6176	382	12	s.	s.	PROPN
ejpam-6176	382	13	islam	islam	PROPN
ejpam-6176	382	14	.	.	PUNCT
ejpam-6176	383	1	complex	complex	ADJ
ejpam-6176	383	2	dynamics	dynamic	NOUN
ejpam-6176	383	3	of	of	ADP
ejpam-6176	383	4	an	an	DET
ejpam-6176	383	5	seir	seir	ADJ
ejpam-6176	383	6	epidemic	epidemic	NOUN
ejpam-6176	383	7	model	model	NOUN
ejpam-6176	383	8	with	with	ADP
ejpam-6176	383	9	saturated	saturate	VERB
ejpam-6176	383	10	incidence	incidence	NOUN
ejpam-6176	383	11	rate	rate	NOUN
ejpam-6176	383	12	and	and	CCONJ
ejpam-6176	383	13	treatment	treatment	NOUN
ejpam-6176	383	14	.	.	PUNCT
ejpam-6176	384	1	physica	physica	PROPN
ejpam-6176	384	2	a	a	DET
ejpam-6176	384	3	,	,	PUNCT
ejpam-6176	384	4	493:210–227	493:210–227	NUM
ejpam-6176	384	5	,	,	PUNCT
ejpam-6176	384	6	2018	2018	NUM
ejpam-6176	384	7	.	.	PUNCT
ejpam-6176	385	1	[	[	X
ejpam-6176	385	2	17	17	NUM
ejpam-6176	385	3	]	]	X
ejpam-6176	385	4	e.a	e.a	PROPN
ejpam-6176	385	5	.	.	PROPN
ejpam-6176	385	6	algehyne	algehyne	PROPN
ejpam-6176	385	7	and	and	CCONJ
ejpam-6176	385	8	r.	r.	PROPN
ejpam-6176	385	9	ud	ud	PROPN
ejpam-6176	385	10	din	din	PROPN
ejpam-6176	385	11	.	.	PROPN
ejpam-6176	386	1	on	on	ADP
ejpam-6176	386	2	global	global	ADJ
ejpam-6176	386	3	dynamics	dynamic	NOUN
ejpam-6176	386	4	of	of	ADP
ejpam-6176	386	5	covid-19	covid-19	PROPN
ejpam-6176	386	6	by	by	ADP
ejpam-6176	386	7	using	use	VERB
ejpam-6176	386	8	sqir	sqir	NOUN
ejpam-6176	386	9	type	type	NOUN
ejpam-6176	386	10	model	model	NOUN
ejpam-6176	386	11	under	under	ADP
ejpam-6176	386	12	non	non	ADJ
ejpam-6176	386	13	-	-	ADJ
ejpam-6176	386	14	linear	linear	ADJ
ejpam-6176	386	15	saturated	saturated	ADJ
ejpam-6176	386	16	incidence	incidence	NOUN
ejpam-6176	386	17	rate	rate	NOUN
ejpam-6176	386	18	.	.	PUNCT
ejpam-6176	387	1	alexandria	alexandria	PROPN
ejpam-6176	387	2	engineering	engineering	PROPN
ejpam-6176	387	3	journal	journal	PROPN
ejpam-6176	387	4	,	,	PUNCT
ejpam-6176	387	5	60(1):393–399	60(1):393–399	PROPN
ejpam-6176	387	6	,	,	PUNCT
ejpam-6176	387	7	2021	2021	NUM
ejpam-6176	387	8	.	.	PUNCT
ejpam-6176	388	1	[	[	X
ejpam-6176	388	2	18	18	NUM
ejpam-6176	388	3	]	]	X
ejpam-6176	388	4	s.	s.	PROPN
ejpam-6176	388	5	han	han	PROPN
ejpam-6176	388	6	and	and	CCONJ
ejpam-6176	388	7	c.	c.	PROPN
ejpam-6176	388	8	lei	lei	PROPN
ejpam-6176	388	9	.	.	PUNCT
ejpam-6176	388	10	global	global	ADJ
ejpam-6176	388	11	stability	stability	NOUN
ejpam-6176	388	12	of	of	ADP
ejpam-6176	388	13	equilibria	equilibrium	NOUN
ejpam-6176	388	14	of	of	ADP
ejpam-6176	388	15	a	a	DET
ejpam-6176	388	16	diffusive	diffusive	ADJ
ejpam-6176	388	17	seir	seir	ADJ
ejpam-6176	388	18	epidemic	epidemic	NOUN
ejpam-6176	388	19	model	model	NOUN
ejpam-6176	388	20	with	with	ADP
ejpam-6176	388	21	non	non	ADJ
ejpam-6176	388	22	-	-	ADJ
ejpam-6176	388	23	linear	linear	ADJ
ejpam-6176	388	24	incidence	incidence	NOUN
ejpam-6176	388	25	.	.	PUNCT
ejpam-6176	389	1	applied	apply	VERB
ejpam-6176	389	2	mathematics	mathematics	NOUN
ejpam-6176	389	3	letters	letter	NOUN
ejpam-6176	389	4	,	,	PUNCT
ejpam-6176	389	5	98:114–120	98:114–120	NUM
ejpam-6176	389	6	,	,	PUNCT
ejpam-6176	389	7	2019	2019	NUM
ejpam-6176	389	8	.	.	PUNCT
ejpam-6176	390	1	[	[	X
ejpam-6176	390	2	19	19	NUM
ejpam-6176	390	3	]	]	PUNCT
ejpam-6176	390	4	a.	a.	NOUN
ejpam-6176	390	5	kumar	kumar	PROPN
ejpam-6176	390	6	and	and	CCONJ
ejpam-6176	390	7	m.	m.	PROPN
ejpam-6176	390	8	kumar	kumar	PROPN
ejpam-6176	390	9	.	.	PUNCT
ejpam-6176	391	1	a	a	DET
ejpam-6176	391	2	study	study	NOUN
ejpam-6176	391	3	on	on	ADP
ejpam-6176	391	4	the	the	DET
ejpam-6176	391	5	stability	stability	NOUN
ejpam-6176	391	6	behavior	behavior	NOUN
ejpam-6176	391	7	of	of	ADP
ejpam-6176	391	8	an	an	DET
ejpam-6176	391	9	epidemic	epidemic	NOUN
ejpam-6176	391	10	model	model	NOUN
ejpam-6176	391	11	with	with	ADP
ejpam-6176	391	12	ratio	ratio	NOUN
ejpam-6176	391	13	-	-	PUNCT
ejpam-6176	391	14	dependent	dependent	ADJ
ejpam-6176	391	15	incidence	incidence	NOUN
ejpam-6176	391	16	and	and	CCONJ
ejpam-6176	391	17	saturated	saturated	ADJ
ejpam-6176	391	18	treatment	treatment	NOUN
ejpam-6176	391	19	.	.	PUNCT
ejpam-6176	392	1	theory	theory	NOUN
ejpam-6176	392	2	in	in	ADP
ejpam-6176	392	3	biosciences	bioscience	NOUN
ejpam-6176	392	4	,	,	PUNCT
ejpam-6176	392	5	139(2):225–234	139(2):225–234	NUM
ejpam-6176	392	6	,	,	PUNCT
ejpam-6176	392	7	2020	2020	NUM
ejpam-6176	392	8	.	.	PUNCT
ejpam-6176	393	1	[	[	X
ejpam-6176	393	2	20	20	NUM
ejpam-6176	393	3	]	]	X
ejpam-6176	393	4	y.	y.	PROPN
ejpam-6176	393	5	zhang	zhang	PROPN
ejpam-6176	393	6	,	,	PUNCT
ejpam-6176	393	7	k.	k.	PROPN
ejpam-6176	393	8	fan	fan	PROPN
ejpam-6176	393	9	,	,	PUNCT
ejpam-6176	393	10	s.	s.	PROPN
ejpam-6176	393	11	gao	gao	PROPN
ejpam-6176	393	12	,	,	PUNCT
ejpam-6176	393	13	y.	y.	PROPN
ejpam-6176	393	14	liu	liu	PROPN
ejpam-6176	393	15	,	,	PUNCT
ejpam-6176	393	16	and	and	CCONJ
ejpam-6176	393	17	s.	s.	PROPN
ejpam-6176	393	18	chen	chen	PROPN
ejpam-6176	393	19	.	.	PUNCT
ejpam-6176	394	1	ergodic	ergodic	ADJ
ejpam-6176	394	2	stationary	stationary	ADJ
ejpam-6176	394	3	distribution	distribution	NOUN
ejpam-6176	394	4	of	of	ADP
ejpam-6176	394	5	a	a	DET
ejpam-6176	394	6	stochastic	stochastic	ADJ
ejpam-6176	394	7	sirs	sir	NOUN
ejpam-6176	394	8	epidemic	epidemic	NOUN
ejpam-6176	394	9	model	model	NOUN
ejpam-6176	394	10	incorporating	incorporate	VERB
ejpam-6176	394	11	media	medium	NOUN
ejpam-6176	394	12	coverage	coverage	NOUN
ejpam-6176	394	13	and	and	CCONJ
ejpam-6176	394	14	saturated	saturated	ADJ
ejpam-6176	394	15	incidence	incidence	NOUN
ejpam-6176	394	16	rate	rate	NOUN
ejpam-6176	394	17	.	.	PUNCT
ejpam-6176	395	1	physica	physica	PROPN
ejpam-6176	395	2	a	a	PRON
ejpam-6176	395	3	,	,	PUNCT
ejpam-6176	395	4	514:671–685	514:671–685	NUM
ejpam-6176	395	5	,	,	PUNCT
ejpam-6176	395	6	2019	2019	NUM
ejpam-6176	395	7	.	.	PUNCT
ejpam-6176	396	1	[	[	X
ejpam-6176	396	2	21	21	NUM
ejpam-6176	396	3	]	]	X
ejpam-6176	396	4	h.	h.	PROPN
ejpam-6176	396	5	hethcote	hethcote	ADV
ejpam-6176	396	6	.	.	PUNCT
ejpam-6176	397	1	the	the	DET
ejpam-6176	397	2	mathematics	mathematic	NOUN
ejpam-6176	397	3	of	of	ADP
ejpam-6176	397	4	infectious	infectious	ADJ
ejpam-6176	397	5	diseases	disease	NOUN
ejpam-6176	397	6	.	.	PUNCT
ejpam-6176	398	1	siam	siam	PROPN
ejpam-6176	398	2	review	review	PROPN
ejpam-6176	398	3	,	,	PUNCT
ejpam-6176	398	4	42:599–653	42:599–653	PROPN
ejpam-6176	398	5	,	,	PUNCT
ejpam-6176	398	6	2000	2000	NUM
ejpam-6176	398	7	.	.	PUNCT
ejpam-6176	399	1	[	[	X
ejpam-6176	399	2	22	22	NUM
ejpam-6176	399	3	]	]	X
ejpam-6176	399	4	g.	g.	PROPN
ejpam-6176	399	5	zhu	zhu	PROPN
ejpam-6176	399	6	,	,	PUNCT
ejpam-6176	399	7	g.	g.	PROPN
ejpam-6176	399	8	chen	chen	PROPN
ejpam-6176	399	9	,	,	PUNCT
ejpam-6176	399	10	h.	h.	PROPN
ejpam-6176	399	11	zhang	zhang	PROPN
ejpam-6176	399	12	,	,	PUNCT
ejpam-6176	399	13	and	and	CCONJ
ejpam-6176	399	14	x.	x.	NOUN
ejpam-6176	399	15	fu	fu	PROPN
ejpam-6176	399	16	.	.	PUNCT
ejpam-6176	400	1	propagation	propagation	NOUN
ejpam-6176	400	2	dynamics	dynamic	NOUN
ejpam-6176	400	3	of	of	ADP
ejpam-6176	400	4	an	an	DET
ejpam-6176	400	5	epidemic	epidemic	NOUN
ejpam-6176	400	6	model	model	NOUN
ejpam-6176	400	7	with	with	ADP
ejpam-6176	400	8	infective	infective	ADJ
ejpam-6176	400	9	media	medium	NOUN
ejpam-6176	400	10	connecting	connect	VERB
ejpam-6176	400	11	two	two	NUM
ejpam-6176	400	12	separated	separate	VERB
ejpam-6176	400	13	networks	network	NOUN
ejpam-6176	400	14	of	of	ADP
ejpam-6176	400	15	populations	population	NOUN
ejpam-6176	400	16	.	.	PUNCT
ejpam-6176	401	1	communications	communication	NOUN
ejpam-6176	401	2	in	in	ADP
ejpam-6176	401	3	nonlinear	nonlinear	ADJ
ejpam-6176	401	4	science	science	NOUN
ejpam-6176	401	5	and	and	CCONJ
ejpam-6176	401	6	numerical	numerical	PROPN
ejpam-6176	401	7	simulation	simulation	PROPN
ejpam-6176	401	8	,	,	PUNCT
ejpam-6176	401	9	20:240–249	20:240–249	NUM
ejpam-6176	401	10	,	,	PUNCT
ejpam-6176	401	11	2015	2015	NUM
ejpam-6176	401	12	.	.	PUNCT
ejpam-6176	402	1	[	[	X
ejpam-6176	402	2	23	23	NUM
ejpam-6176	402	3	]	]	X
ejpam-6176	402	4	s.	s.	PROPN
ejpam-6176	402	5	djilali	djilali	PROPN
ejpam-6176	402	6	,	,	PUNCT
ejpam-6176	402	7	b.	b.	PROPN
ejpam-6176	402	8	ghanbari	ghanbari	PROPN
ejpam-6176	402	9	,	,	PUNCT
ejpam-6176	402	10	s.	s.	PROPN
ejpam-6176	402	11	bentout	bentout	PROPN
ejpam-6176	402	12	,	,	PUNCT
ejpam-6176	402	13	and	and	CCONJ
ejpam-6176	402	14	a.	a.	PROPN
ejpam-6176	402	15	mezouaghi	mezouaghi	PROPN
ejpam-6176	402	16	.	.	PUNCT
ejpam-6176	403	1	turing	ture	VERB
ejpam-6176	403	2	-	-	PUNCT
ejpam-6176	403	3	hopf	hopf	ADJ
ejpam-6176	403	4	bifurcation	bifurcation	NOUN
ejpam-6176	403	5	in	in	ADP
ejpam-6176	403	6	a	a	DET
ejpam-6176	403	7	diffusive	diffusive	ADJ
ejpam-6176	403	8	mussel	mussel	ADJ
ejpam-6176	403	9	-	-	PUNCT
ejpam-6176	403	10	algae	algae	NOUN
ejpam-6176	403	11	model	model	NOUN
ejpam-6176	403	12	with	with	ADP
ejpam-6176	403	13	time	time	NOUN
ejpam-6176	403	14	-	-	PUNCT
ejpam-6176	403	15	fractional	fractional	ADJ
ejpam-6176	403	16	-	-	PUNCT
ejpam-6176	403	17	order	order	NOUN
ejpam-6176	403	18	derivative	derivative	NOUN
ejpam-6176	403	19	.	.	PUNCT
ejpam-6176	404	1	chaos	chaos	NOUN
ejpam-6176	404	2	,	,	PUNCT
ejpam-6176	404	3	solitons	soliton	NOUN
ejpam-6176	404	4	&	&	CCONJ
ejpam-6176	404	5	fractals	fractal	NOUN
ejpam-6176	404	6	,	,	PUNCT
ejpam-6176	404	7	138:109954	138:109954	NUM
ejpam-6176	404	8	,	,	PUNCT
ejpam-6176	404	9	2020	2020	NUM
ejpam-6176	404	10	.	.	PUNCT
ejpam-6176	405	1	[	[	X
ejpam-6176	405	2	24	24	NUM
ejpam-6176	405	3	]	]	PUNCT
ejpam-6176	405	4	b.	b.	PROPN
ejpam-6176	405	5	pgda	pgda	PROPN
ejpam-6176	405	6	,	,	PUNCT
ejpam-6176	405	7	d.	d.	PROPN
ejpam-6176	405	8	cckc	cckc	PROPN
ejpam-6176	405	9	,	,	PUNCT
ejpam-6176	405	10	and	and	CCONJ
ejpam-6176	405	11	f.	f.	PROPN
ejpam-6176	405	12	rmse	rmse	PROPN
ejpam-6176	405	13	.	.	PUNCT
ejpam-6176	406	1	determining	determine	VERB
ejpam-6176	406	2	the	the	DET
ejpam-6176	406	3	optimal	optimal	ADJ
ejpam-6176	406	4	strategy	strategy	NOUN
ejpam-6176	406	5	for	for	ADP
ejpam-6176	406	6	reopening	reopen	VERB
ejpam-6176	406	7	schools	school	NOUN
ejpam-6176	406	8	,	,	PUNCT
ejpam-6176	406	9	the	the	DET
ejpam-6176	406	10	impact	impact	NOUN
ejpam-6176	406	11	of	of	ADP
ejpam-6176	406	12	test	test	NOUN
ejpam-6176	406	13	and	and	CCONJ
ejpam-6176	406	14	trace	trace	NOUN
ejpam-6176	406	15	interventions	intervention	NOUN
ejpam-6176	406	16	,	,	PUNCT
ejpam-6176	406	17	and	and	CCONJ
ejpam-6176	406	18	the	the	DET
ejpam-6176	406	19	risk	risk	NOUN
ejpam-6176	406	20	of	of	ADP
ejpam-6176	406	21	occurrence	occurrence	NOUN
ejpam-6176	406	22	of	of	ADP
ejpam-6176	406	23	a	a	DET
ejpam-6176	406	24	second	second	ADJ
ejpam-6176	406	25	covid-19	covid-19	PROPN
ejpam-6176	406	26	epidemic	epidemic	NOUN
ejpam-6176	406	27	wave	wave	NOUN
ejpam-6176	406	28	in	in	ADP
ejpam-6176	406	29	the	the	DET
ejpam-6176	406	30	uk	uk	PROPN
ejpam-6176	406	31	:	:	PUNCT
ejpam-6176	406	32	a	a	DET
ejpam-6176	406	33	modelling	model	VERB
ejpam-6176	406	34	study	study	NOUN
ejpam-6176	406	35	.	.	PUNCT
ejpam-6176	407	1	the	the	DET
ejpam-6176	407	2	lancet	lancet	PROPN
ejpam-6176	407	3	child	child	PROPN
ejpam-6176	407	4	&	&	CCONJ
ejpam-6176	407	5	adolescent	adolescent	ADJ
ejpam-6176	407	6	health	health	PROPN
ejpam-6176	407	7	,	,	PUNCT
ejpam-6176	407	8	4:817–827	4:817–827	PROPN
ejpam-6176	407	9	,	,	PUNCT
ejpam-6176	407	10	2020	2020	NUM
ejpam-6176	407	11	.	.	PUNCT
ejpam-6176	408	1	[	[	X
ejpam-6176	408	2	25	25	NUM
ejpam-6176	408	3	]	]	PUNCT
ejpam-6176	408	4	a.	a.	NOUN
ejpam-6176	408	5	alkhazzan	alkhazzan	PROPN
ejpam-6176	408	6	,	,	PUNCT
ejpam-6176	408	7	j.	j.	PROPN
ejpam-6176	408	8	wang	wang	PROPN
ejpam-6176	408	9	,	,	PUNCT
ejpam-6176	408	10	y.	y.	PROPN
ejpam-6176	408	11	nie	nie	PROPN
ejpam-6176	408	12	,	,	PUNCT
ejpam-6176	408	13	h.	h.	PROPN
ejpam-6176	408	14	khan	khan	PROPN
ejpam-6176	408	15	,	,	PUNCT
ejpam-6176	408	16	and	and	CCONJ
ejpam-6176	408	17	j.	j.	PROPN
ejpam-6176	408	18	alzabut	alzabut	PROPN
ejpam-6176	408	19	.	.	PUNCT
ejpam-6176	409	1	a	a	DET
ejpam-6176	409	2	stochastic	stochastic	ADJ
ejpam-6176	409	3	susceptible	susceptible	ADJ
ejpam-6176	409	4	vaccinees	vaccinee	NOUN
ejpam-6176	409	5	infected	infect	VERB
ejpam-6176	409	6	recovered	recover	VERB
ejpam-6176	409	7	epidemic	epidemic	NOUN
ejpam-6176	409	8	model	model	NOUN
ejpam-6176	409	9	with	with	ADP
ejpam-6176	409	10	three	three	NUM
ejpam-6176	409	11	types	type	NOUN
ejpam-6176	409	12	of	of	ADP
ejpam-6176	409	13	noises	noise	NOUN
ejpam-6176	409	14	.	.	PUNCT
ejpam-6176	410	1	mathematical	mathematical	ADJ
ejpam-6176	410	2	methods	method	NOUN
ejpam-6176	410	3	in	in	ADP
ejpam-6176	410	4	the	the	DET
ejpam-6176	410	5	applied	apply	VERB
ejpam-6176	410	6	sciences	science	NOUN
ejpam-6176	410	7	,	,	PUNCT
ejpam-6176	410	8	47(11):8748–8770	47(11):8748–8770	NOUN
ejpam-6176	410	9	,	,	PUNCT
ejpam-6176	410	10	2024	2024	NUM
ejpam-6176	410	11	.	.	PUNCT
ejpam-6176	411	1	[	[	X
ejpam-6176	411	2	26	26	NUM
ejpam-6176	411	3	]	]	X
ejpam-6176	411	4	f.	f.	PROPN
ejpam-6176	411	5	liljeros	liljeros	PROPN
ejpam-6176	411	6	,	,	PUNCT
ejpam-6176	411	7	c.r	c.r	PROPN
ejpam-6176	411	8	.	.	PROPN
ejpam-6176	411	9	edling	edling	PROPN
ejpam-6176	411	10	,	,	PUNCT
ejpam-6176	411	11	and	and	CCONJ
ejpam-6176	411	12	l.a.n	l.a.n	PROPN
ejpam-6176	411	13	.	.	PUNCT
ejpam-6176	411	14	amaral	amaral	PROPN
ejpam-6176	411	15	.	.	PUNCT
ejpam-6176	412	1	the	the	DET
ejpam-6176	412	2	web	web	NOUN
ejpam-6176	412	3	of	of	ADP
ejpam-6176	412	4	human	human	ADJ
ejpam-6176	412	5	sexual	sexual	ADJ
ejpam-6176	412	6	contacts	contact	NOUN
ejpam-6176	412	7	.	.	PUNCT
ejpam-6176	413	1	nature	nature	NOUN
ejpam-6176	413	2	,	,	PUNCT
ejpam-6176	413	3	411:907–908	411:907–908	NUM
ejpam-6176	413	4	,	,	PUNCT
ejpam-6176	413	5	2001	2001	NUM
ejpam-6176	413	6	.	.	PUNCT
ejpam-6176	414	1	[	[	X
ejpam-6176	414	2	27	27	NUM
ejpam-6176	414	3	]	]	PUNCT
ejpam-6176	414	4	z.	z.	PROPN
ejpam-6176	414	5	wang	wang	PROPN
ejpam-6176	414	6	,	,	PUNCT
ejpam-6176	414	7	m.	m.	PROPN
ejpam-6176	414	8	andrews	andrews	PROPN
ejpam-6176	414	9	,	,	PUNCT
ejpam-6176	414	10	z.	z.	PROPN
ejpam-6176	414	11	wu	wu	PROPN
ejpam-6176	414	12	,	,	PUNCT
ejpam-6176	414	13	l.	l.	PROPN
ejpam-6176	414	14	wang	wang	PROPN
ejpam-6176	414	15	,	,	PUNCT
ejpam-6176	414	16	and	and	CCONJ
ejpam-6176	414	17	c.	c.	PROPN
ejpam-6176	414	18	bauch	bauch	PROPN
ejpam-6176	414	19	.	.	PUNCT
ejpam-6176	414	20	coupled	couple	VERB
ejpam-6176	414	21	disease	disease	NOUN
ejpam-6176	414	22	–	–	PUNCT
ejpam-6176	414	23	behavior	behavior	NOUN
ejpam-6176	414	24	dynamics	dynamic	NOUN
ejpam-6176	414	25	on	on	ADP
ejpam-6176	414	26	complex	complex	ADJ
ejpam-6176	414	27	networks	network	NOUN
ejpam-6176	414	28	:	:	PUNCT
ejpam-6176	414	29	a	a	DET
ejpam-6176	414	30	review	review	NOUN
ejpam-6176	414	31	.	.	PUNCT
ejpam-6176	415	1	physics	physics	PROPN
ejpam-6176	415	2	of	of	ADP
ejpam-6176	415	3	life	life	NOUN
ejpam-6176	415	4	reviews	review	NOUN
ejpam-6176	415	5	,	,	PUNCT
ejpam-6176	415	6	15:1–29	15:1–29	NUM
ejpam-6176	415	7	,	,	PUNCT
ejpam-6176	415	8	2015	2015	NUM
ejpam-6176	415	9	.	.	PUNCT
ejpam-6176	416	1	[	[	X
ejpam-6176	416	2	28	28	NUM
ejpam-6176	416	3	]	]	X
ejpam-6176	416	4	r.	r.	PROPN
ejpam-6176	416	5	albert	albert	PROPN
ejpam-6176	416	6	,	,	PUNCT
ejpam-6176	416	7	h.	h.	PROPN
ejpam-6176	416	8	jeong	jeong	PROPN
ejpam-6176	416	9	,	,	PUNCT
ejpam-6176	416	10	and	and	CCONJ
ejpam-6176	416	11	a.l	a.l	PROPN
ejpam-6176	416	12	.	.	PROPN
ejpam-6176	416	13	barabási	barabási	PROPN
ejpam-6176	416	14	.	.	PUNCT
ejpam-6176	417	1	diameter	diameter	NOUN
ejpam-6176	417	2	of	of	ADP
ejpam-6176	417	3	the	the	DET
ejpam-6176	417	4	world	world	NOUN
ejpam-6176	417	5	wide	wide	ADJ
ejpam-6176	417	6	web	web	NOUN
ejpam-6176	417	7	.	.	PROPN
ejpam-6176	417	8	nature	nature	NOUN
ejpam-6176	417	9	,	,	PUNCT
ejpam-6176	417	10	401:130–131	401:130–131	NUM
ejpam-6176	417	11	,	,	PUNCT
ejpam-6176	417	12	1999	1999	NUM
ejpam-6176	417	13	.	.	PUNCT
ejpam-6176	418	1	m.	m.	PROPN
ejpam-6176	418	2	s.	s.	PROPN
ejpam-6176	418	3	arif	arif	PROPN
ejpam-6176	418	4	,	,	PUNCT
ejpam-6176	418	5	k.	k.	PROPN
ejpam-6176	418	6	abodayeh	abodayeh	PROPN
ejpam-6176	418	7	,	,	PUNCT
ejpam-6176	418	8	y.	y.	NOUN
ejpam-6176	418	9	nawaz	nawaz	PROPN
ejpam-6176	418	10	/	/	SYM
ejpam-6176	418	11	eur	eur	PROPN
ejpam-6176	418	12	.	.	PUNCT
ejpam-6176	419	1	j.	j.	PROPN
ejpam-6176	419	2	pure	pure	PROPN
ejpam-6176	419	3	appl	appl	PROPN
ejpam-6176	419	4	.	.	PROPN
ejpam-6176	419	5	math	math	PROPN
ejpam-6176	419	6	,	,	PUNCT
ejpam-6176	419	7	18	18	NUM
ejpam-6176	419	8	(	(	PUNCT
ejpam-6176	419	9	3	3	NUM
ejpam-6176	419	10	)	)	PUNCT
ejpam-6176	419	11	(	(	PUNCT
ejpam-6176	419	12	2025	2025	NUM
ejpam-6176	419	13	)	)	PUNCT
ejpam-6176	419	14	,	,	PUNCT
ejpam-6176	419	15	6176	6176	NUM
ejpam-6176	419	16	20	20	NUM
ejpam-6176	419	17	of	of	ADP
ejpam-6176	419	18	21	21	NUM
ejpam-6176	419	19	[	[	SYM
ejpam-6176	419	20	29	29	NUM
ejpam-6176	419	21	]	]	PUNCT
ejpam-6176	419	22	m.	m.	NOUN
ejpam-6176	419	23	faloutsos	faloutsos	PROPN
ejpam-6176	419	24	,	,	PUNCT
ejpam-6176	419	25	p.	p.	NOUN
ejpam-6176	419	26	faloutsos	faloutsos	PROPN
ejpam-6176	419	27	,	,	PUNCT
ejpam-6176	419	28	and	and	CCONJ
ejpam-6176	419	29	c.	c.	PROPN
ejpam-6176	419	30	faloutsos	faloutsos	PROPN
ejpam-6176	419	31	.	.	PUNCT
ejpam-6176	420	1	on	on	ADP
ejpam-6176	420	2	power	power	NOUN
ejpam-6176	420	3	-	-	PUNCT
ejpam-6176	420	4	law	law	NOUN
ejpam-6176	420	5	relationships	relationship	NOUN
ejpam-6176	420	6	of	of	ADP
ejpam-6176	420	7	the	the	DET
ejpam-6176	420	8	internet	internet	NOUN
ejpam-6176	420	9	topology	topology	NOUN
ejpam-6176	420	10	.	.	PUNCT
ejpam-6176	421	1	computer	computer	NOUN
ejpam-6176	421	2	communication	communication	NOUN
ejpam-6176	421	3	review	review	NOUN
ejpam-6176	421	4	,	,	PUNCT
ejpam-6176	421	5	29:251–262	29:251–262	PROPN
ejpam-6176	421	6	,	,	PUNCT
ejpam-6176	421	7	1999	1999	NUM
ejpam-6176	421	8	.	.	PUNCT
ejpam-6176	422	1	[	[	X
ejpam-6176	422	2	30	30	NUM
ejpam-6176	422	3	]	]	X
ejpam-6176	422	4	a.l	a.l	PROPN
ejpam-6176	422	5	.	.	PROPN
ejpam-6176	422	6	barabási	barabási	PROPN
ejpam-6176	422	7	and	and	CCONJ
ejpam-6176	422	8	r.	r.	PROPN
ejpam-6176	422	9	albert	albert	PROPN
ejpam-6176	422	10	.	.	PROPN
ejpam-6176	423	1	emergence	emergence	NOUN
ejpam-6176	423	2	of	of	ADP
ejpam-6176	423	3	scaling	scale	VERB
ejpam-6176	423	4	in	in	ADP
ejpam-6176	423	5	random	random	ADJ
ejpam-6176	423	6	networks	network	NOUN
ejpam-6176	423	7	.	.	PUNCT
ejpam-6176	424	1	science	science	NOUN
ejpam-6176	424	2	,	,	PUNCT
ejpam-6176	424	3	286:509–512	286:509–512	NUM
ejpam-6176	424	4	,	,	PUNCT
ejpam-6176	424	5	1999	1999	NUM
ejpam-6176	424	6	.	.	PUNCT
ejpam-6176	425	1	[	[	X
ejpam-6176	425	2	31	31	NUM
ejpam-6176	425	3	]	]	PUNCT
ejpam-6176	425	4	b.	b.	PROPN
ejpam-6176	425	5	geraldine	geraldine	PROPN
ejpam-6176	425	6	and	and	CCONJ
ejpam-6176	425	7	m.	m.	PROPN
ejpam-6176	425	8	antoine	antoine	PROPN
ejpam-6176	425	9	.	.	PUNCT
ejpam-6176	426	1	social	social	ADJ
ejpam-6176	426	2	interactions	interaction	NOUN
ejpam-6176	426	3	and	and	CCONJ
ejpam-6176	426	4	the	the	DET
ejpam-6176	426	5	prophylaxis	prophylaxis	NOUN
ejpam-6176	426	6	of	of	ADP
ejpam-6176	426	7	si	si	X
ejpam-6176	426	8	epidemics	epidemic	NOUN
ejpam-6176	426	9	on	on	ADP
ejpam-6176	426	10	networks	network	NOUN
ejpam-6176	426	11	.	.	PUNCT
ejpam-6176	427	1	journal	journal	PROPN
ejpam-6176	427	2	of	of	ADP
ejpam-6176	427	3	mathematical	mathematical	ADJ
ejpam-6176	427	4	economics	economic	NOUN
ejpam-6176	427	5	,	,	PUNCT
ejpam-6176	427	6	93:102486	93:102486	NUM
ejpam-6176	427	7	,	,	PUNCT
ejpam-6176	427	8	2021	2021	NUM
ejpam-6176	427	9	.	.	PUNCT
ejpam-6176	428	1	[	[	X
ejpam-6176	428	2	32	32	NUM
ejpam-6176	428	3	]	]	X
ejpam-6176	428	4	p.s	p.s	PROPN
ejpam-6176	428	5	.	.	PROPN
ejpam-6176	428	6	romualdo	romualdo	PROPN
ejpam-6176	428	7	and	and	CCONJ
ejpam-6176	428	8	v.	v.	ADP
ejpam-6176	428	9	alessandro	alessandro	NOUN
ejpam-6176	428	10	.	.	PUNCT
ejpam-6176	429	1	epidemic	epidemic	NOUN
ejpam-6176	429	2	spreading	spread	VERB
ejpam-6176	429	3	in	in	ADP
ejpam-6176	429	4	scale	scale	NOUN
ejpam-6176	429	5	-	-	PUNCT
ejpam-6176	429	6	free	free	ADJ
ejpam-6176	429	7	networks	network	NOUN
ejpam-6176	429	8	.	.	PUNCT
ejpam-6176	430	1	physical	physical	ADJ
ejpam-6176	430	2	review	review	NOUN
ejpam-6176	430	3	letters	letter	NOUN
ejpam-6176	430	4	,	,	PUNCT
ejpam-6176	430	5	86:3200–3203	86:3200–3203	NUM
ejpam-6176	430	6	,	,	PUNCT
ejpam-6176	430	7	2000	2000	NUM
ejpam-6176	430	8	.	.	PUNCT
ejpam-6176	431	1	[	[	X
ejpam-6176	431	2	33	33	NUM
ejpam-6176	431	3	]	]	PUNCT
ejpam-6176	431	4	x.	x.	PROPN
ejpam-6176	431	5	wei	wei	PROPN
ejpam-6176	431	6	,	,	PUNCT
ejpam-6176	431	7	g.	g.	PROPN
ejpam-6176	431	8	xu	xu	PROPN
ejpam-6176	431	9	,	,	PUNCT
ejpam-6176	431	10	and	and	CCONJ
ejpam-6176	431	11	l.	l.	PROPN
ejpam-6176	431	12	liu	liu	PROPN
ejpam-6176	431	13	.	.	PUNCT
ejpam-6176	432	1	global	global	ADJ
ejpam-6176	432	2	stability	stability	NOUN
ejpam-6176	432	3	of	of	ADP
ejpam-6176	432	4	endemic	endemic	ADJ
ejpam-6176	432	5	equilibrium	equilibrium	NOUN
ejpam-6176	432	6	of	of	ADP
ejpam-6176	432	7	an	an	DET
ejpam-6176	432	8	epidemic	epidemic	NOUN
ejpam-6176	432	9	model	model	NOUN
ejpam-6176	432	10	with	with	ADP
ejpam-6176	432	11	birth	birth	NOUN
ejpam-6176	432	12	and	and	CCONJ
ejpam-6176	432	13	death	death	NOUN
ejpam-6176	432	14	on	on	ADP
ejpam-6176	432	15	complex	complex	ADJ
ejpam-6176	432	16	networks	network	NOUN
ejpam-6176	432	17	.	.	PUNCT
ejpam-6176	433	1	physica	physica	PROPN
ejpam-6176	433	2	a	a	DET
ejpam-6176	433	3	,	,	PUNCT
ejpam-6176	433	4	477:8–84	477:8–84	PROPN
ejpam-6176	433	5	,	,	PUNCT
ejpam-6176	433	6	2017	2017	NUM
ejpam-6176	433	7	.	.	PUNCT
ejpam-6176	434	1	[	[	X
ejpam-6176	434	2	34	34	NUM
ejpam-6176	434	3	]	]	PUNCT
ejpam-6176	434	4	t.	t.	PROPN
ejpam-6176	434	5	li	li	PROPN
ejpam-6176	434	6	,	,	PUNCT
ejpam-6176	434	7	y.	y.	PROPN
ejpam-6176	434	8	wang	wang	PROPN
ejpam-6176	434	9	,	,	PUNCT
ejpam-6176	434	10	and	and	CCONJ
ejpam-6176	434	11	z.	z.	PROPN
ejpam-6176	434	12	guan	guan	PROPN
ejpam-6176	434	13	.	.	PUNCT
ejpam-6176	434	14	spreading	spread	VERB
ejpam-6176	434	15	dynamics	dynamic	NOUN
ejpam-6176	434	16	of	of	ADP
ejpam-6176	434	17	a	a	DET
ejpam-6176	434	18	siqrs	siqrs	ADJ
ejpam-6176	434	19	epidemic	epidemic	NOUN
ejpam-6176	434	20	model	model	NOUN
ejpam-6176	434	21	on	on	ADP
ejpam-6176	434	22	scale	scale	NOUN
ejpam-6176	434	23	-	-	PUNCT
ejpam-6176	434	24	free	free	ADJ
ejpam-6176	434	25	networks	network	NOUN
ejpam-6176	434	26	.	.	PUNCT
ejpam-6176	435	1	communications	communication	NOUN
ejpam-6176	435	2	in	in	ADP
ejpam-6176	435	3	nonlinear	nonlinear	ADJ
ejpam-6176	435	4	science	science	NOUN
ejpam-6176	435	5	and	and	CCONJ
ejpam-6176	435	6	numerical	numerical	PROPN
ejpam-6176	435	7	simulation	simulation	PROPN
ejpam-6176	435	8	,	,	PUNCT
ejpam-6176	435	9	19:686–692	19:686–692	NUM
ejpam-6176	435	10	,	,	PUNCT
ejpam-6176	435	11	2014	2014	NUM
ejpam-6176	435	12	.	.	PUNCT
ejpam-6176	436	1	[	[	X
ejpam-6176	436	2	35	35	NUM
ejpam-6176	436	3	]	]	X
ejpam-6176	436	4	s.	s.	PROPN
ejpam-6176	436	5	huang	huang	PROPN
ejpam-6176	436	6	,	,	PUNCT
ejpam-6176	436	7	f.	f.	PROPN
ejpam-6176	436	8	chen	chen	PROPN
ejpam-6176	436	9	,	,	PUNCT
ejpam-6176	436	10	and	and	CCONJ
ejpam-6176	436	11	l.	l.	PROPN
ejpam-6176	436	12	chen	chen	PROPN
ejpam-6176	436	13	.	.	PUNCT
ejpam-6176	437	1	global	global	ADJ
ejpam-6176	437	2	dynamics	dynamic	NOUN
ejpam-6176	437	3	of	of	ADP
ejpam-6176	437	4	a	a	DET
ejpam-6176	437	5	network	network	NOUN
ejpam-6176	437	6	-	-	PUNCT
ejpam-6176	437	7	based	base	VERB
ejpam-6176	437	8	siqrs	siqrs	NOUN
ejpam-6176	437	9	epidemic	epidemic	NOUN
ejpam-6176	437	10	model	model	NOUN
ejpam-6176	437	11	with	with	ADP
ejpam-6176	437	12	demographics	demographic	NOUN
ejpam-6176	437	13	and	and	CCONJ
ejpam-6176	437	14	vaccination	vaccination	NOUN
ejpam-6176	437	15	.	.	PUNCT
ejpam-6176	438	1	communications	communication	NOUN
ejpam-6176	438	2	in	in	ADP
ejpam-6176	438	3	nonlinear	nonlinear	ADJ
ejpam-6176	438	4	science	science	NOUN
ejpam-6176	438	5	and	and	CCONJ
ejpam-6176	438	6	numerical	numerical	PROPN
ejpam-6176	438	7	simulation	simulation	PROPN
ejpam-6176	438	8	,	,	PUNCT
ejpam-6176	438	9	43:296–310	43:296–310	PROPN
ejpam-6176	438	10	,	,	PUNCT
ejpam-6176	438	11	2017	2017	NUM
ejpam-6176	438	12	.	.	PUNCT
ejpam-6176	439	1	[	[	X
ejpam-6176	439	2	36	36	NUM
ejpam-6176	439	3	]	]	PUNCT
ejpam-6176	439	4	m.	m.	PROPN
ejpam-6176	439	5	s.	s.	PROPN
ejpam-6176	439	6	arif	arif	PROPN
ejpam-6176	439	7	,	,	PUNCT
ejpam-6176	439	8	k.	k.	PROPN
ejpam-6176	439	9	abodayeh	abodayeh	PROPN
ejpam-6176	439	10	,	,	PUNCT
ejpam-6176	439	11	h.	h.	PROPN
ejpam-6176	439	12	m.	m.	PROPN
ejpam-6176	439	13	al	al	PROPN
ejpam-6176	439	14	-	-	PUNCT
ejpam-6176	439	15	khawar	khawar	PROPN
ejpam-6176	439	16	,	,	PUNCT
ejpam-6176	439	17	and	and	CCONJ
ejpam-6176	439	18	y.	y.	NOUN
ejpam-6176	439	19	nawaz	nawaz	NOUN
ejpam-6176	439	20	.	.	PUNCT
ejpam-6176	440	1	stochastic	stochastic	ADJ
ejpam-6176	440	2	diffusive	diffusive	ADJ
ejpam-6176	440	3	modeling	modeling	NOUN
ejpam-6176	440	4	of	of	ADP
ejpam-6176	440	5	co2	co2	NOUN
ejpam-6176	440	6	emissions	emission	NOUN
ejpam-6176	440	7	with	with	ADP
ejpam-6176	440	8	population	population	NOUN
ejpam-6176	440	9	and	and	CCONJ
ejpam-6176	440	10	energy	energy	NOUN
ejpam-6176	440	11	dynamics	dynamic	NOUN
ejpam-6176	440	12	.	.	PUNCT
ejpam-6176	441	1	emerging	emerge	VERB
ejpam-6176	441	2	science	science	NOUN
ejpam-6176	441	3	journal	journal	NOUN
ejpam-6176	441	4	,	,	PUNCT
ejpam-6176	441	5	9(1):210–228	9(1):210–228	NUM
ejpam-6176	441	6	,	,	PUNCT
ejpam-6176	441	7	2025	2025	NUM
ejpam-6176	441	8	.	.	PUNCT
ejpam-6176	442	1	[	[	X
ejpam-6176	442	2	37	37	NUM
ejpam-6176	442	3	]	]	PUNCT
ejpam-6176	442	4	m.	m.	PROPN
ejpam-6176	442	5	s.	s.	PROPN
ejpam-6176	442	6	arif	arif	PROPN
ejpam-6176	442	7	.	.	PUNCT
ejpam-6176	443	1	a	a	DET
ejpam-6176	443	2	novel	novel	ADJ
ejpam-6176	443	3	explicit	explicit	ADJ
ejpam-6176	443	4	scheme	scheme	NOUN
ejpam-6176	443	5	for	for	ADP
ejpam-6176	443	6	stochastic	stochastic	ADJ
ejpam-6176	443	7	diffusive	diffusive	ADJ
ejpam-6176	443	8	sis	sis	NOUN
ejpam-6176	443	9	models	model	NOUN
ejpam-6176	443	10	with	with	ADP
ejpam-6176	443	11	treatment	treatment	NOUN
ejpam-6176	443	12	effects	effect	NOUN
ejpam-6176	443	13	.	.	PUNCT
ejpam-6176	444	1	partial	partial	ADJ
ejpam-6176	444	2	differential	differential	ADJ
ejpam-6176	444	3	equations	equation	NOUN
ejpam-6176	444	4	in	in	ADP
ejpam-6176	444	5	applied	applied	ADJ
ejpam-6176	444	6	mathematics	mathematic	NOUN
ejpam-6176	444	7	,	,	PUNCT
ejpam-6176	444	8	page	page	NOUN
ejpam-6176	444	9	101215	101215	NUM
ejpam-6176	444	10	,	,	PUNCT
ejpam-6176	444	11	2025	2025	NUM
ejpam-6176	444	12	.	.	PUNCT
ejpam-6176	445	1	[	[	X
ejpam-6176	445	2	38	38	NUM
ejpam-6176	445	3	]	]	PUNCT
ejpam-6176	445	4	m.	m.	NOUN
ejpam-6176	445	5	s.	s.	PROPN
ejpam-6176	445	6	arif	arif	PROPN
ejpam-6176	445	7	.	.	PUNCT
ejpam-6176	446	1	numerical	numerical	ADJ
ejpam-6176	446	2	analysis	analysis	NOUN
ejpam-6176	446	3	of	of	ADP
ejpam-6176	446	4	deterministic	deterministic	ADJ
ejpam-6176	446	5	and	and	CCONJ
ejpam-6176	446	6	stochastic	stochastic	ADJ
ejpam-6176	446	7	model	model	NOUN
ejpam-6176	446	8	of	of	ADP
ejpam-6176	446	9	covid-19	covid-19	PROPN
ejpam-6176	446	10	co	co	NOUN
ejpam-6176	446	11	-	-	NOUN
ejpam-6176	446	12	infection	infection	NOUN
ejpam-6176	446	13	with	with	ADP
ejpam-6176	446	14	influenza	influenza	NOUN
ejpam-6176	446	15	.	.	PUNCT
ejpam-6176	447	1	european	european	ADJ
ejpam-6176	447	2	journal	journal	PROPN
ejpam-6176	447	3	of	of	ADP
ejpam-6176	447	4	pure	pure	ADJ
ejpam-6176	447	5	and	and	CCONJ
ejpam-6176	447	6	applied	applied	ADJ
ejpam-6176	447	7	mathematics	mathematic	NOUN
ejpam-6176	447	8	,	,	PUNCT
ejpam-6176	447	9	18(2):6005–6005	18(2):6005–6005	NUM
ejpam-6176	447	10	,	,	PUNCT
ejpam-6176	447	11	2025	2025	NUM
ejpam-6176	447	12	.	.	PUNCT
ejpam-6176	448	1	[	[	X
ejpam-6176	448	2	39	39	NUM
ejpam-6176	448	3	]	]	PUNCT
ejpam-6176	448	4	h.	h.	PROPN
ejpam-6176	448	5	tahir	tahir	PROPN
ejpam-6176	448	6	,	,	PUNCT
ejpam-6176	448	7	a.	a.	PROPN
ejpam-6176	448	8	din	din	PROPN
ejpam-6176	448	9	,	,	PUNCT
ejpam-6176	448	10	k.	k.	PROPN
ejpam-6176	448	11	shah	shah	PROPN
ejpam-6176	448	12	,	,	PUNCT
ejpam-6176	448	13	b.	b.	PROPN
ejpam-6176	448	14	abdalla	abdalla	PROPN
ejpam-6176	448	15	,	,	PUNCT
ejpam-6176	448	16	and	and	CCONJ
ejpam-6176	448	17	t.	t.	PROPN
ejpam-6176	448	18	abdeljawad	abdeljawad	NOUN
ejpam-6176	448	19	.	.	PUNCT
ejpam-6176	449	1	advances	advance	NOUN
ejpam-6176	449	2	in	in	ADP
ejpam-6176	449	3	stochastic	stochastic	ADJ
ejpam-6176	449	4	epidemic	epidemic	NOUN
ejpam-6176	449	5	modeling	modeling	NOUN
ejpam-6176	449	6	:	:	PUNCT
ejpam-6176	449	7	tackling	tackle	VERB
ejpam-6176	449	8	worm	worm	NOUN
ejpam-6176	449	9	transmission	transmission	NOUN
ejpam-6176	449	10	in	in	ADP
ejpam-6176	449	11	wireless	wireless	ADJ
ejpam-6176	449	12	sensor	sensor	NOUN
ejpam-6176	449	13	networks	network	NOUN
ejpam-6176	449	14	.	.	PUNCT
ejpam-6176	450	1	mathematical	mathematical	ADJ
ejpam-6176	450	2	and	and	CCONJ
ejpam-6176	450	3	computer	computer	NOUN
ejpam-6176	450	4	modelling	modelling	NOUN
ejpam-6176	450	5	of	of	ADP
ejpam-6176	450	6	dynamical	dynamical	ADJ
ejpam-6176	450	7	systems	system	NOUN
ejpam-6176	450	8	,	,	PUNCT
ejpam-6176	450	9	30(1):658–682	30(1):658–682	ADV
ejpam-6176	450	10	,	,	PUNCT
ejpam-6176	450	11	2024	2024	NUM
ejpam-6176	450	12	.	.	PUNCT
ejpam-6176	451	1	[	[	X
ejpam-6176	451	2	40	40	NUM
ejpam-6176	451	3	]	]	PUNCT
ejpam-6176	451	4	m.	m.	NOUN
ejpam-6176	451	5	mediani	mediani	NOUN
ejpam-6176	451	6	,	,	PUNCT
ejpam-6176	451	7	a.	a.	NOUN
ejpam-6176	451	8	slama	slama	PROPN
ejpam-6176	451	9	,	,	PUNCT
ejpam-6176	451	10	a.	a.	PROPN
ejpam-6176	451	11	boudaoui	boudaoui	PROPN
ejpam-6176	451	12	,	,	PUNCT
ejpam-6176	451	13	and	and	CCONJ
ejpam-6176	451	14	t.	t.	PROPN
ejpam-6176	451	15	abdeljawad	abdeljawad	NOUN
ejpam-6176	451	16	.	.	PUNCT
ejpam-6176	452	1	analysis	analysis	NOUN
ejpam-6176	452	2	of	of	ADP
ejpam-6176	452	3	a	a	DET
ejpam-6176	452	4	stochastic	stochastic	ADJ
ejpam-6176	452	5	seiuirr	seiuirr	ADJ
ejpam-6176	452	6	epidemic	epidemic	NOUN
ejpam-6176	452	7	model	model	NOUN
ejpam-6176	452	8	incorporating	incorporate	VERB
ejpam-6176	452	9	the	the	DET
ejpam-6176	452	10	ornstein	ornstein	PROPN
ejpam-6176	452	11	-	-	PUNCT
ejpam-6176	452	12	uhlenbeck	uhlenbeck	PROPN
ejpam-6176	452	13	process	process	NOUN
ejpam-6176	452	14	.	.	PUNCT
ejpam-6176	453	1	heliyon	heliyon	NOUN
ejpam-6176	453	2	,	,	PUNCT
ejpam-6176	453	3	10(16	10(16	NUM
ejpam-6176	453	4	)	)	PUNCT
ejpam-6176	453	5	,	,	PUNCT
ejpam-6176	453	6	2024	2024	NUM
ejpam-6176	453	7	.	.	PUNCT
ejpam-6176	454	1	[	[	X
ejpam-6176	454	2	41	41	NUM
ejpam-6176	454	3	]	]	PUNCT
ejpam-6176	454	4	q.	q.	PROPN
ejpam-6176	454	5	liu	liu	PROPN
ejpam-6176	454	6	,	,	PUNCT
ejpam-6176	454	7	d.	d.	PROPN
ejpam-6176	454	8	jiang	jiang	PROPN
ejpam-6176	454	9	,	,	PUNCT
ejpam-6176	454	10	and	and	CCONJ
ejpam-6176	454	11	n.	n.	PROPN
ejpam-6176	454	12	shi	shi	PROPN
ejpam-6176	454	13	.	.	PUNCT
ejpam-6176	455	1	stationary	stationary	ADJ
ejpam-6176	455	2	distribution	distribution	NOUN
ejpam-6176	455	3	and	and	CCONJ
ejpam-6176	455	4	extinction	extinction	NOUN
ejpam-6176	455	5	of	of	ADP
ejpam-6176	455	6	a	a	DET
ejpam-6176	455	7	stochastic	stochastic	ADJ
ejpam-6176	455	8	seir	seir	ADJ
ejpam-6176	455	9	epidemic	epidemic	NOUN
ejpam-6176	455	10	model	model	NOUN
ejpam-6176	455	11	with	with	ADP
ejpam-6176	455	12	standard	standard	ADJ
ejpam-6176	455	13	incidence	incidence	NOUN
ejpam-6176	455	14	.	.	PUNCT
ejpam-6176	456	1	physica	physica	PROPN
ejpam-6176	456	2	a	a	DET
ejpam-6176	456	3	,	,	PUNCT
ejpam-6176	456	4	469:510–517	469:510–517	PROPN
ejpam-6176	456	5	,	,	PUNCT
ejpam-6176	456	6	2017	2017	NUM
ejpam-6176	456	7	.	.	PUNCT
ejpam-6176	457	1	[	[	X
ejpam-6176	457	2	42	42	NUM
ejpam-6176	457	3	]	]	X
ejpam-6176	457	4	y.	y.	PROPN
ejpam-6176	457	5	zhang	zhang	PROPN
ejpam-6176	457	6	and	and	CCONJ
ejpam-6176	457	7	y.	y.	PROPN
ejpam-6176	457	8	li	li	PROPN
ejpam-6176	457	9	.	.	PROPN
ejpam-6176	457	10	evolutionary	evolutionary	ADJ
ejpam-6176	457	11	dynamics	dynamic	NOUN
ejpam-6176	457	12	of	of	ADP
ejpam-6176	457	13	stochastic	stochastic	ADJ
ejpam-6176	457	14	seir	seir	NOUN
ejpam-6176	457	15	models	model	NOUN
ejpam-6176	457	16	with	with	ADP
ejpam-6176	457	17	migration	migration	NOUN
ejpam-6176	457	18	and	and	CCONJ
ejpam-6176	457	19	human	human	ADJ
ejpam-6176	457	20	awareness	awareness	NOUN
ejpam-6176	457	21	in	in	ADP
ejpam-6176	457	22	complex	complex	ADJ
ejpam-6176	457	23	networks	network	NOUN
ejpam-6176	457	24	.	.	PUNCT
ejpam-6176	458	1	complexity	complexity	NOUN
ejpam-6176	458	2	,	,	PUNCT
ejpam-6176	458	3	2020:3768083	2020:3768083	NUM
ejpam-6176	458	4	,	,	PUNCT
ejpam-6176	458	5	2020	2020	NUM
ejpam-6176	458	6	.	.	PUNCT
ejpam-6176	459	1	[	[	X
ejpam-6176	459	2	43	43	NUM
ejpam-6176	459	3	]	]	PUNCT
ejpam-6176	459	4	r.	r.	PROPN
ejpam-6176	459	5	zhao	zhao	PROPN
ejpam-6176	459	6	,	,	PUNCT
ejpam-6176	459	7	q.	q.	PROPN
ejpam-6176	459	8	liu	liu	PROPN
ejpam-6176	459	9	,	,	PUNCT
ejpam-6176	459	10	and	and	CCONJ
ejpam-6176	459	11	m.	m.	NOUN
ejpam-6176	459	12	sun	sun	PROPN
ejpam-6176	459	13	.	.	PUNCT
ejpam-6176	460	1	dynamical	dynamical	ADJ
ejpam-6176	460	2	behavior	behavior	NOUN
ejpam-6176	460	3	of	of	ADP
ejpam-6176	460	4	a	a	DET
ejpam-6176	460	5	stochastic	stochastic	ADJ
ejpam-6176	460	6	siqs	siqs	ADJ
ejpam-6176	460	7	epidemic	epidemic	NOUN
ejpam-6176	460	8	model	model	NOUN
ejpam-6176	460	9	on	on	ADP
ejpam-6176	460	10	scale	scale	NOUN
ejpam-6176	460	11	-	-	PUNCT
ejpam-6176	460	12	free	free	ADJ
ejpam-6176	460	13	networks	network	NOUN
ejpam-6176	460	14	.	.	PUNCT
ejpam-6176	461	1	journal	journal	NOUN
ejpam-6176	461	2	of	of	ADP
ejpam-6176	461	3	applied	apply	VERB
ejpam-6176	461	4	mathematics	mathematic	NOUN
ejpam-6176	461	5	and	and	CCONJ
ejpam-6176	461	6	computing	computing	NOUN
ejpam-6176	461	7	,	,	PUNCT
ejpam-6176	461	8	9:1–26	9:1–26	NUM
ejpam-6176	461	9	,	,	PUNCT
ejpam-6176	461	10	2021	2021	NUM
ejpam-6176	461	11	.	.	PUNCT
ejpam-6176	462	1	[	[	X
ejpam-6176	462	2	44	44	NUM
ejpam-6176	462	3	]	]	X
ejpam-6176	462	4	y.	y.	PROPN
ejpam-6176	462	5	chen	chen	PROPN
ejpam-6176	462	6	,	,	PUNCT
ejpam-6176	462	7	b.	b.	PROPN
ejpam-6176	462	8	wen	wen	PROPN
ejpam-6176	462	9	,	,	PUNCT
ejpam-6176	462	10	and	and	CCONJ
ejpam-6176	462	11	z.	z.	PROPN
ejpam-6176	462	12	teng	teng	PROPN
ejpam-6176	462	13	.	.	PUNCT
ejpam-6176	463	1	the	the	DET
ejpam-6176	463	2	global	global	ADJ
ejpam-6176	463	3	dynamics	dynamic	NOUN
ejpam-6176	463	4	for	for	ADP
ejpam-6176	463	5	a	a	DET
ejpam-6176	463	6	stochastic	stochastic	ADJ
ejpam-6176	463	7	sis	sis	NOUN
ejpam-6176	463	8	epidemic	epidemic	NOUN
ejpam-6176	463	9	model	model	NOUN
ejpam-6176	463	10	with	with	ADP
ejpam-6176	463	11	isolation	isolation	NOUN
ejpam-6176	463	12	.	.	PUNCT
ejpam-6176	464	1	physica	physica	PROPN
ejpam-6176	464	2	a	a	PRON
ejpam-6176	464	3	,	,	PUNCT
ejpam-6176	464	4	492:1604–1624	492:1604–1624	PRON
ejpam-6176	464	5	,	,	PUNCT
ejpam-6176	464	6	2018	2018	NUM
ejpam-6176	464	7	.	.	PUNCT
ejpam-6176	465	1	[	[	X
ejpam-6176	465	2	45	45	NUM
ejpam-6176	465	3	]	]	X
ejpam-6176	465	4	l.j	l.j	PROPN
ejpam-6176	465	5	.	.	PROPN
ejpam-6176	465	6	pan	pan	PROPN
ejpam-6176	465	7	,	,	PUNCT
ejpam-6176	465	8	j.d	j.d	PROPN
ejpam-6176	465	9	.	.	PROPN
ejpam-6176	465	10	cao	cao	PROPN
ejpam-6176	465	11	,	,	PUNCT
ejpam-6176	465	12	and	and	CCONJ
ejpam-6176	465	13	a.	a.	PROPN
ejpam-6176	465	14	ahmed	ahmed	PROPN
ejpam-6176	465	15	.	.	PUNCT
ejpam-6176	466	1	stability	stability	NOUN
ejpam-6176	466	2	of	of	ADP
ejpam-6176	466	3	reaction	reaction	NOUN
ejpam-6176	466	4	–	–	PUNCT
ejpam-6176	466	5	diffusion	diffusion	NOUN
ejpam-6176	466	6	systems	system	NOUN
ejpam-6176	466	7	with	with	ADP
ejpam-6176	466	8	stochastic	stochastic	ADJ
ejpam-6176	466	9	switching	switching	NOUN
ejpam-6176	466	10	.	.	PUNCT
ejpam-6176	467	1	nonlinear	nonlinear	ADJ
ejpam-6176	467	2	analysis	analysis	NOUN
ejpam-6176	467	3	:	:	PUNCT
ejpam-6176	467	4	modelling	modelling	NOUN
ejpam-6176	467	5	and	and	CCONJ
ejpam-6176	467	6	control	control	NOUN
ejpam-6176	467	7	,	,	PUNCT
ejpam-6176	467	8	24:315–331	24:315–331	NUM
ejpam-6176	467	9	,	,	PUNCT
ejpam-6176	467	10	2019	2019	NUM
ejpam-6176	467	11	.	.	PUNCT
ejpam-6176	468	1	[	[	X
ejpam-6176	468	2	46	46	NUM
ejpam-6176	468	3	]	]	X
ejpam-6176	468	4	m.e	m.e	PROPN
ejpam-6176	468	5	.	.	PROPN
ejpam-6176	468	6	fatini	fatini	PROPN
ejpam-6176	468	7	,	,	PUNCT
ejpam-6176	468	8	r.	r.	PROPN
ejpam-6176	468	9	pettersson	pettersson	PROPN
ejpam-6176	468	10	,	,	PUNCT
ejpam-6176	468	11	and	and	CCONJ
ejpam-6176	468	12	i.	i.	PROPN
ejpam-6176	468	13	sekkak	sekkak	PROPN
ejpam-6176	468	14	.	.	PUNCT
ejpam-6176	469	1	a	a	DET
ejpam-6176	469	2	stochastic	stochastic	ADJ
ejpam-6176	469	3	analysis	analysis	NOUN
ejpam-6176	469	4	for	for	ADP
ejpam-6176	469	5	a	a	DET
ejpam-6176	469	6	triple	triple	ADJ
ejpam-6176	469	7	delayed	delay	VERB
ejpam-6176	469	8	siqr	siqr	ADJ
ejpam-6176	469	9	epidemic	epidemic	NOUN
ejpam-6176	469	10	model	model	NOUN
ejpam-6176	469	11	with	with	ADP
ejpam-6176	469	12	vaccination	vaccination	NOUN
ejpam-6176	469	13	and	and	CCONJ
ejpam-6176	469	14	elimination	elimination	NOUN
ejpam-6176	469	15	strategies	strategy	NOUN
ejpam-6176	469	16	.	.	PUNCT
ejpam-6176	470	1	journal	journal	NOUN
ejpam-6176	470	2	of	of	ADP
ejpam-6176	470	3	applied	apply	VERB
ejpam-6176	470	4	mathematics	mathematic	NOUN
ejpam-6176	470	5	and	and	CCONJ
ejpam-6176	470	6	computing	computing	NOUN
ejpam-6176	470	7	,	,	PUNCT
ejpam-6176	470	8	64:781–805	64:781–805	PROPN
ejpam-6176	470	9	,	,	PUNCT
ejpam-6176	470	10	2020	2020	NUM
ejpam-6176	470	11	.	.	PUNCT
ejpam-6176	471	1	m.	m.	PROPN
ejpam-6176	471	2	s.	s.	PROPN
ejpam-6176	471	3	arif	arif	PROPN
ejpam-6176	471	4	,	,	PUNCT
ejpam-6176	471	5	k.	k.	PROPN
ejpam-6176	471	6	abodayeh	abodayeh	PROPN
ejpam-6176	471	7	,	,	PUNCT
ejpam-6176	471	8	y.	y.	NOUN
ejpam-6176	471	9	nawaz	nawaz	PROPN
ejpam-6176	471	10	/	/	SYM
ejpam-6176	471	11	eur	eur	PROPN
ejpam-6176	471	12	.	.	PUNCT
ejpam-6176	472	1	j.	j.	PROPN
ejpam-6176	472	2	pure	pure	PROPN
ejpam-6176	472	3	appl	appl	PROPN
ejpam-6176	472	4	.	.	PROPN
ejpam-6176	472	5	math	math	PROPN
ejpam-6176	472	6	,	,	PUNCT
ejpam-6176	472	7	18	18	NUM
ejpam-6176	472	8	(	(	PUNCT
ejpam-6176	472	9	3	3	NUM
ejpam-6176	472	10	)	)	PUNCT
ejpam-6176	472	11	(	(	PUNCT
ejpam-6176	472	12	2025	2025	NUM
ejpam-6176	472	13	)	)	PUNCT
ejpam-6176	472	14	,	,	PUNCT
ejpam-6176	472	15	6176	6176	NUM
ejpam-6176	472	16	21	21	NUM
ejpam-6176	472	17	of	of	ADP
ejpam-6176	472	18	21	21	NUM
ejpam-6176	472	19	[	[	SYM
ejpam-6176	472	20	47	47	NUM
ejpam-6176	472	21	]	]	PUNCT
ejpam-6176	472	22	syed	syed	PROPN
ejpam-6176	472	23	ahmed	ahmed	PROPN
ejpam-6176	472	24	pasha	pasha	PROPN
ejpam-6176	472	25	,	,	PUNCT
ejpam-6176	472	26	yasir	yasir	PROPN
ejpam-6176	472	27	nawaz	nawaz	NOUN
ejpam-6176	472	28	,	,	PUNCT
ejpam-6176	472	29	and	and	CCONJ
ejpam-6176	472	30	muhammad	muhammad	PROPN
ejpam-6176	472	31	shoaib	shoaib	PROPN
ejpam-6176	472	32	arif	arif	PROPN
ejpam-6176	472	33	.	.	PUNCT
ejpam-6176	473	1	on	on	ADP
ejpam-6176	473	2	the	the	DET
ejpam-6176	473	3	nonstandard	nonstandard	ADJ
ejpam-6176	473	4	finite	finite	ADJ
ejpam-6176	473	5	difference	difference	NOUN
ejpam-6176	473	6	method	method	NOUN
ejpam-6176	473	7	for	for	ADP
ejpam-6176	473	8	reaction	reaction	NOUN
ejpam-6176	473	9	–	–	PUNCT
ejpam-6176	473	10	diffusion	diffusion	NOUN
ejpam-6176	473	11	models	model	NOUN
ejpam-6176	473	12	.	.	PUNCT
ejpam-6176	474	1	chaos	chaos	NOUN
ejpam-6176	474	2	,	,	PUNCT
ejpam-6176	474	3	solitons	soliton	NOUN
ejpam-6176	474	4	&	&	CCONJ
ejpam-6176	474	5	fractals	fractal	NOUN
ejpam-6176	474	6	,	,	PUNCT
ejpam-6176	474	7	166:112929	166:112929	NOUN
ejpam-6176	474	8	,	,	PUNCT
ejpam-6176	474	9	2023	2023	NUM
ejpam-6176	474	10	.	.	PUNCT