id	sid	tid	token	lemma	pos
ejpam-6347	1	1	european	european	PROPN
ejpam-6347	1	2	journal	journal	PROPN
ejpam-6347	1	3	of	of	ADP
ejpam-6347	1	4	pure	pure	ADJ
ejpam-6347	1	5	and	and	CCONJ
ejpam-6347	1	6	applied	applied	ADJ
ejpam-6347	1	7	mathematics	mathematic	NOUN
ejpam-6347	1	8	2025	2025	NUM
ejpam-6347	1	9	,	,	PUNCT
ejpam-6347	1	10	vol	vol	NOUN
ejpam-6347	1	11	.	.	PROPN
ejpam-6347	1	12	18	18	NUM
ejpam-6347	1	13	,	,	PUNCT
ejpam-6347	1	14	issue	issue	NOUN
ejpam-6347	1	15	3	3	NUM
ejpam-6347	1	16	,	,	PUNCT
ejpam-6347	1	17	article	article	NOUN
ejpam-6347	1	18	number	number	NOUN
ejpam-6347	1	19	6347	6347	NUM
ejpam-6347	1	20	issn	issn	PROPN
ejpam-6347	1	21	1307	1307	NUM
ejpam-6347	1	22	-	-	SYM
ejpam-6347	1	23	5543	5543	NUM
ejpam-6347	1	24	–	–	PUNCT
ejpam-6347	1	25	ejpam.com	ejpam.com	X
ejpam-6347	1	26	published	publish	VERB
ejpam-6347	1	27	by	by	ADP
ejpam-6347	1	28	new	new	PROPN
ejpam-6347	1	29	york	york	PROPN
ejpam-6347	1	30	business	business	PROPN
ejpam-6347	1	31	global	global	PROPN
ejpam-6347	1	32	mathematical	mathematical	ADJ
ejpam-6347	1	33	modeling	modeling	NOUN
ejpam-6347	1	34	of	of	ADP
ejpam-6347	1	35	sars	sar	NOUN
ejpam-6347	1	36	-	-	PUNCT
ejpam-6347	1	37	cov-2	cov-2	PART
ejpam-6347	1	38	epidemics	epidemic	NOUN
ejpam-6347	1	39	using	use	VERB
ejpam-6347	1	40	fractional	fractional	ADJ
ejpam-6347	1	41	calculus	calculus	NOUN
ejpam-6347	1	42	and	and	CCONJ
ejpam-6347	1	43	optimal	optimal	ADJ
ejpam-6347	1	44	interventions	intervention	NOUN
ejpam-6347	1	45	nadeem	nadeem	PROPN
ejpam-6347	1	46	abbas1	abbas1	PROPN
ejpam-6347	1	47	,	,	PUNCT
ejpam-6347	1	48	wasfi	wasfi	ADV
ejpam-6347	1	49	shatanawi1,2,∗	shatanawi1,2,∗	PROPN
ejpam-6347	1	50	,	,	PUNCT
ejpam-6347	1	51	syeda	syeda	PROPN
ejpam-6347	1	52	alishwa	alishwa	PROPN
ejpam-6347	1	53	zanib3	zanib3	PROPN
ejpam-6347	1	54	1	1	NUM
ejpam-6347	1	55	department	department	NOUN
ejpam-6347	1	56	of	of	ADP
ejpam-6347	1	57	mathematics	mathematic	NOUN
ejpam-6347	1	58	and	and	CCONJ
ejpam-6347	1	59	sciences	science	NOUN
ejpam-6347	1	60	,	,	PUNCT
ejpam-6347	1	61	college	college	NOUN
ejpam-6347	1	62	of	of	ADP
ejpam-6347	1	63	humanities	humanity	NOUN
ejpam-6347	1	64	and	and	CCONJ
ejpam-6347	1	65	sciences	science	NOUN
ejpam-6347	1	66	,	,	PUNCT
ejpam-6347	1	67	prince	prince	PROPN
ejpam-6347	1	68	sultan	sultan	PROPN
ejpam-6347	1	69	university	university	PROPN
ejpam-6347	1	70	,	,	PUNCT
ejpam-6347	1	71	riyadh	riyadh	NOUN
ejpam-6347	1	72	,	,	PUNCT
ejpam-6347	1	73	11586	11586	NUM
ejpam-6347	1	74	,	,	PUNCT
ejpam-6347	1	75	saudi	saudi	PROPN
ejpam-6347	1	76	arabia	arabia	PROPN
ejpam-6347	1	77	2	2	NUM
ejpam-6347	1	78	department	department	NOUN
ejpam-6347	1	79	of	of	ADP
ejpam-6347	1	80	mathematics	mathematic	NOUN
ejpam-6347	1	81	,	,	PUNCT
ejpam-6347	1	82	faculty	faculty	NOUN
ejpam-6347	1	83	of	of	ADP
ejpam-6347	1	84	science	science	NOUN
ejpam-6347	1	85	,	,	PUNCT
ejpam-6347	1	86	the	the	DET
ejpam-6347	1	87	hashemite	hashemite	PROPN
ejpam-6347	1	88	university	university	PROPN
ejpam-6347	1	89	,	,	PUNCT
ejpam-6347	1	90	p.o	p.o	PROPN
ejpam-6347	1	91	box	box	PROPN
ejpam-6347	1	92	330127	330127	NUM
ejpam-6347	1	93	,	,	PUNCT
ejpam-6347	1	94	zarqa	zarqa	NOUN
ejpam-6347	1	95	13133	13133	NUM
ejpam-6347	1	96	,	,	PUNCT
ejpam-6347	1	97	jordan	jordan	PROPN
ejpam-6347	1	98	3department	3department	PROPN
ejpam-6347	1	99	of	of	ADP
ejpam-6347	1	100	mathematics	mathematic	NOUN
ejpam-6347	1	101	,	,	PUNCT
ejpam-6347	1	102	riphah	riphah	PROPN
ejpam-6347	1	103	international	international	PROPN
ejpam-6347	1	104	university	university	PROPN
ejpam-6347	1	105	,	,	PUNCT
ejpam-6347	1	106	main	main	ADJ
ejpam-6347	1	107	satyana	satyana	ADJ
ejpam-6347	1	108	road	road	NOUN
ejpam-6347	1	109	,	,	PUNCT
ejpam-6347	1	110	faisalabad	faisalabad	PROPN
ejpam-6347	1	111	44000	44000	NUM
ejpam-6347	1	112	,	,	PUNCT
ejpam-6347	1	113	pakistan	pakistan	PROPN
ejpam-6347	1	114	abstract	abstract	NOUN
ejpam-6347	1	115	.	.	PUNCT
ejpam-6347	2	1	in	in	ADP
ejpam-6347	2	2	december	december	PROPN
ejpam-6347	2	3	2019	2019	NUM
ejpam-6347	2	4	,	,	PUNCT
ejpam-6347	2	5	the	the	DET
ejpam-6347	2	6	sars	sar	NOUN
ejpam-6347	2	7	-	-	PUNCT
ejpam-6347	2	8	cov-2	cov-2	PART
ejpam-6347	2	9	(	(	PUNCT
ejpam-6347	2	10	covid-19	covid-19	PROPN
ejpam-6347	2	11	)	)	PUNCT
ejpam-6347	2	12	virus	virus	NOUN
ejpam-6347	2	13	was	be	AUX
ejpam-6347	2	14	identified	identify	VERB
ejpam-6347	2	15	and	and	CCONJ
ejpam-6347	2	16	quickly	quickly	ADV
ejpam-6347	2	17	spread	spread	VERB
ejpam-6347	2	18	worldwide	worldwide	ADV
ejpam-6347	2	19	,	,	PUNCT
ejpam-6347	2	20	causing	cause	VERB
ejpam-6347	2	21	a	a	DET
ejpam-6347	2	22	major	major	ADJ
ejpam-6347	2	23	global	global	ADJ
ejpam-6347	2	24	health	health	NOUN
ejpam-6347	2	25	crisis	crisis	NOUN
ejpam-6347	2	26	.	.	PUNCT
ejpam-6347	3	1	to	to	PART
ejpam-6347	3	2	investigate	investigate	VERB
ejpam-6347	3	3	its	its	PRON
ejpam-6347	3	4	transmission	transmission	NOUN
ejpam-6347	3	5	dynamics	dynamic	NOUN
ejpam-6347	3	6	,	,	PUNCT
ejpam-6347	3	7	we	we	PRON
ejpam-6347	3	8	developed	develop	VERB
ejpam-6347	3	9	a	a	DET
ejpam-6347	3	10	ten	ten	NUM
ejpam-6347	3	11	-	-	PUNCT
ejpam-6347	3	12	compartment	compartment	NOUN
ejpam-6347	3	13	mathematical	mathematical	ADJ
ejpam-6347	3	14	model	model	NOUN
ejpam-6347	3	15	,	,	PUNCT
ejpam-6347	3	16	named	name	VERB
ejpam-6347	3	17	covcom10	covcom10	NOUN
ejpam-6347	3	18	,	,	PUNCT
ejpam-6347	3	19	which	which	PRON
ejpam-6347	3	20	includes	include	VERB
ejpam-6347	3	21	key	key	ADJ
ejpam-6347	3	22	stages	stage	NOUN
ejpam-6347	3	23	such	such	ADJ
ejpam-6347	3	24	as	as	ADP
ejpam-6347	3	25	asymptomatic	asymptomatic	ADJ
ejpam-6347	3	26	(	(	PUNCT
ejpam-6347	3	27	f	f	PROPN
ejpam-6347	3	28	)	)	PUNCT
ejpam-6347	3	29	,	,	PUNCT
ejpam-6347	3	30	pre	pre	ADJ
ejpam-6347	3	31	-	-	ADJ
ejpam-6347	3	32	symptomatic	symptomatic	ADJ
ejpam-6347	3	33	(	(	PUNCT
ejpam-6347	3	34	e	e	NOUN
ejpam-6347	3	35	)	)	PUNCT
ejpam-6347	3	36	,	,	PUNCT
ejpam-6347	3	37	and	and	CCONJ
ejpam-6347	3	38	vaccinated	vaccinated	ADJ
ejpam-6347	3	39	(	(	PUNCT
ejpam-6347	3	40	v	v	NOUN
ejpam-6347	3	41	)	)	PUNCT
ejpam-6347	3	42	individuals	individual	NOUN
ejpam-6347	3	43	.	.	PUNCT
ejpam-6347	4	1	the	the	DET
ejpam-6347	4	2	basic	basic	ADJ
ejpam-6347	4	3	reproduction	reproduction	NOUN
ejpam-6347	4	4	number	number	NOUN
ejpam-6347	4	5	(	(	PUNCT
ejpam-6347	4	6	r0	r0	NOUN
ejpam-6347	4	7	)	)	PUNCT
ejpam-6347	4	8	has	have	AUX
ejpam-6347	4	9	been	be	AUX
ejpam-6347	4	10	calculated	calculate	VERB
ejpam-6347	4	11	to	to	PART
ejpam-6347	4	12	evaluate	evaluate	VERB
ejpam-6347	4	13	how	how	SCONJ
ejpam-6347	4	14	easily	easily	ADV
ejpam-6347	4	15	the	the	DET
ejpam-6347	4	16	virus	virus	NOUN
ejpam-6347	4	17	can	can	AUX
ejpam-6347	4	18	spread	spread	VERB
ejpam-6347	4	19	.	.	PUNCT
ejpam-6347	5	1	we	we	PRON
ejpam-6347	5	2	analyzed	analyze	VERB
ejpam-6347	5	3	the	the	DET
ejpam-6347	5	4	local	local	ADJ
ejpam-6347	5	5	and	and	CCONJ
ejpam-6347	5	6	global	global	ADJ
ejpam-6347	5	7	stability	stability	NOUN
ejpam-6347	5	8	of	of	ADP
ejpam-6347	5	9	the	the	DET
ejpam-6347	5	10	disease	disease	NOUN
ejpam-6347	5	11	-	-	PUNCT
ejpam-6347	5	12	free	free	ADJ
ejpam-6347	5	13	equilibrium	equilibrium	NOUN
ejpam-6347	5	14	and	and	CCONJ
ejpam-6347	5	15	prove	prove	VERB
ejpam-6347	5	16	that	that	SCONJ
ejpam-6347	5	17	the	the	DET
ejpam-6347	5	18	disease	disease	NOUN
ejpam-6347	5	19	under	under	ADP
ejpam-6347	5	20	control	control	NOUN
ejpam-6347	5	21	after	after	ADP
ejpam-6347	5	22	vaccination	vaccination	NOUN
ejpam-6347	5	23	when	when	SCONJ
ejpam-6347	5	24	r0	r0	NOUN
ejpam-6347	5	25	<	<	X
ejpam-6347	5	26	1	1	NUM
ejpam-6347	5	27	.	.	PUNCT
ejpam-6347	6	1	a	a	DET
ejpam-6347	6	2	sensitivity	sensitivity	NOUN
ejpam-6347	6	3	analysis	analysis	NOUN
ejpam-6347	6	4	was	be	AUX
ejpam-6347	6	5	conducted	conduct	VERB
ejpam-6347	6	6	to	to	PART
ejpam-6347	6	7	assess	assess	VERB
ejpam-6347	6	8	the	the	DET
ejpam-6347	6	9	impact	impact	NOUN
ejpam-6347	6	10	of	of	ADP
ejpam-6347	6	11	key	key	ADJ
ejpam-6347	6	12	parameters	parameter	NOUN
ejpam-6347	6	13	,	,	PUNCT
ejpam-6347	6	14	including	include	VERB
ejpam-6347	6	15	the	the	DET
ejpam-6347	6	16	vaccination	vaccination	NOUN
ejpam-6347	6	17	rate	rate	NOUN
ejpam-6347	6	18	from	from	ADP
ejpam-6347	6	19	susceptible	susceptible	ADJ
ejpam-6347	6	20	individuals	individual	NOUN
ejpam-6347	6	21	(	(	PUNCT
ejpam-6347	6	22	β	β	NOUN
ejpam-6347	6	23	)	)	PUNCT
ejpam-6347	6	24	,	,	PUNCT
ejpam-6347	6	25	transmission	transmission	NOUN
ejpam-6347	6	26	from	from	ADP
ejpam-6347	6	27	susceptible	susceptible	ADJ
ejpam-6347	6	28	to	to	ADP
ejpam-6347	6	29	pre	pre	ADJ
ejpam-6347	6	30	-	-	ADJ
ejpam-6347	6	31	symptomatic	symptomatic	ADJ
ejpam-6347	6	32	individuals	individual	NOUN
ejpam-6347	6	33	(	(	PUNCT
ejpam-6347	6	34	ϕ	ϕ	NOUN
ejpam-6347	6	35	)	)	PUNCT
ejpam-6347	6	36	,	,	PUNCT
ejpam-6347	6	37	and	and	CCONJ
ejpam-6347	6	38	the	the	DET
ejpam-6347	6	39	rate	rate	NOUN
ejpam-6347	6	40	of	of	ADP
ejpam-6347	6	41	vaccination	vaccination	NOUN
ejpam-6347	6	42	from	from	ADP
ejpam-6347	6	43	pre	pre	ADJ
ejpam-6347	6	44	-	-	ADJ
ejpam-6347	6	45	symptomatic	symptomatic	ADJ
ejpam-6347	6	46	individuals	individual	NOUN
ejpam-6347	6	47	(	(	PUNCT
ejpam-6347	6	48	γ	γ	NOUN
ejpam-6347	6	49	)	)	PUNCT
ejpam-6347	6	50	.	.	PUNCT
ejpam-6347	7	1	to	to	PART
ejpam-6347	7	2	evaluate	evaluate	VERB
ejpam-6347	7	3	intervention	intervention	NOUN
ejpam-6347	7	4	strategies	strategy	NOUN
ejpam-6347	7	5	,	,	PUNCT
ejpam-6347	7	6	we	we	PRON
ejpam-6347	7	7	extended	extend	VERB
ejpam-6347	7	8	the	the	DET
ejpam-6347	7	9	model	model	NOUN
ejpam-6347	7	10	by	by	ADP
ejpam-6347	7	11	incorporating	incorporate	VERB
ejpam-6347	7	12	time	time	NOUN
ejpam-6347	7	13	-	-	PUNCT
ejpam-6347	7	14	dependent	dependent	ADJ
ejpam-6347	7	15	control	control	NOUN
ejpam-6347	7	16	variables	variable	NOUN
ejpam-6347	7	17	representing	represent	VERB
ejpam-6347	7	18	vaccination	vaccination	NOUN
ejpam-6347	7	19	(	(	PUNCT
ejpam-6347	7	20	a1	a1	NOUN
ejpam-6347	7	21	)	)	PUNCT
ejpam-6347	7	22	,	,	PUNCT
ejpam-6347	7	23	hospitalization	hospitalization	NOUN
ejpam-6347	7	24	(	(	PUNCT
ejpam-6347	7	25	a2	a2	PROPN
ejpam-6347	7	26	)	)	PUNCT
ejpam-6347	7	27	,	,	PUNCT
ejpam-6347	7	28	and	and	CCONJ
ejpam-6347	7	29	isolation	isolation	NOUN
ejpam-6347	7	30	of	of	ADP
ejpam-6347	7	31	asymptomatic	asymptomatic	ADJ
ejpam-6347	7	32	individuals	individual	NOUN
ejpam-6347	7	33	(	(	PUNCT
ejpam-6347	7	34	a3	a3	NOUN
ejpam-6347	7	35	)	)	PUNCT
ejpam-6347	7	36	.	.	PUNCT
ejpam-6347	8	1	the	the	DET
ejpam-6347	8	2	pontryagin	pontryagin	NOUN
ejpam-6347	8	3	maximum	maximum	ADJ
ejpam-6347	8	4	principle	principle	NOUN
ejpam-6347	8	5	was	be	AUX
ejpam-6347	8	6	applied	apply	VERB
ejpam-6347	8	7	to	to	PART
ejpam-6347	8	8	identify	identify	VERB
ejpam-6347	8	9	optimal	optimal	ADJ
ejpam-6347	8	10	control	control	NOUN
ejpam-6347	8	11	strategies	strategy	NOUN
ejpam-6347	8	12	.	.	PUNCT
ejpam-6347	9	1	numerical	numerical	ADJ
ejpam-6347	9	2	simulations	simulation	NOUN
ejpam-6347	9	3	reveal	reveal	VERB
ejpam-6347	9	4	that	that	SCONJ
ejpam-6347	9	5	these	these	DET
ejpam-6347	9	6	interventions	intervention	NOUN
ejpam-6347	9	7	significantly	significantly	ADV
ejpam-6347	9	8	reduce	reduce	VERB
ejpam-6347	9	9	virus	virus	NOUN
ejpam-6347	9	10	transmission	transmission	NOUN
ejpam-6347	9	11	,	,	PUNCT
ejpam-6347	9	12	particularly	particularly	ADV
ejpam-6347	9	13	as	as	ADP
ejpam-6347	9	14	the	the	DET
ejpam-6347	9	15	fractional	fractional	ADJ
ejpam-6347	9	16	-	-	PUNCT
ejpam-6347	9	17	order	order	NOUN
ejpam-6347	9	18	parameter	parameter	NOUN
ejpam-6347	9	19	(	(	PUNCT
ejpam-6347	9	20	ς	ς	NOUN
ejpam-6347	9	21	)	)	PUNCT
ejpam-6347	9	22	approaches	approach	VERB
ejpam-6347	9	23	1	1	NUM
ejpam-6347	9	24	,	,	PUNCT
ejpam-6347	9	25	which	which	PRON
ejpam-6347	9	26	aligns	align	VERB
ejpam-6347	9	27	with	with	ADP
ejpam-6347	9	28	observed	observe	VERB
ejpam-6347	9	29	real	real	ADJ
ejpam-6347	9	30	-	-	PUNCT
ejpam-6347	9	31	world	world	NOUN
ejpam-6347	9	32	disease	disease	NOUN
ejpam-6347	9	33	dynamics	dynamic	NOUN
ejpam-6347	9	34	.	.	PUNCT
ejpam-6347	10	1	the	the	DET
ejpam-6347	10	2	study	study	NOUN
ejpam-6347	10	3	emphasizes	emphasize	VERB
ejpam-6347	10	4	the	the	DET
ejpam-6347	10	5	effectiveness	effectiveness	NOUN
ejpam-6347	10	6	of	of	ADP
ejpam-6347	10	7	integrated	integrate	VERB
ejpam-6347	10	8	vaccination	vaccination	NOUN
ejpam-6347	10	9	and	and	CCONJ
ejpam-6347	10	10	treatment	treatment	NOUN
ejpam-6347	10	11	strategies	strategy	NOUN
ejpam-6347	10	12	in	in	ADP
ejpam-6347	10	13	controlling	control	VERB
ejpam-6347	10	14	the	the	DET
ejpam-6347	10	15	spread	spread	NOUN
ejpam-6347	10	16	of	of	ADP
ejpam-6347	10	17	covid-19	covid-19	PROPN
ejpam-6347	10	18	.	.	PROPN
ejpam-6347	10	19	2020	2020	NUM
ejpam-6347	10	20	mathematics	mathematics	PROPN
ejpam-6347	10	21	subject	subject	NOUN
ejpam-6347	10	22	classifications	classification	NOUN
ejpam-6347	10	23	:	:	PUNCT
ejpam-6347	10	24	26a33	26a33	NUM
ejpam-6347	10	25	,	,	PUNCT
ejpam-6347	10	26	34a08	34a08	NUM
ejpam-6347	10	27	,	,	PUNCT
ejpam-6347	10	28	03c65	03c65	X
ejpam-6347	10	29	key	key	ADJ
ejpam-6347	10	30	words	word	NOUN
ejpam-6347	10	31	and	and	CCONJ
ejpam-6347	10	32	phrases	phrase	NOUN
ejpam-6347	10	33	:	:	PUNCT
ejpam-6347	10	34	sars	sar	NOUN
ejpam-6347	10	35	-	-	PUNCT
ejpam-6347	10	36	cov-2	cov-2	NOUN
ejpam-6347	10	37	,	,	PUNCT
ejpam-6347	10	38	fractional	fractional	ADJ
ejpam-6347	10	39	-	-	PUNCT
ejpam-6347	10	40	order	order	NOUN
ejpam-6347	10	41	model	model	NOUN
ejpam-6347	10	42	,	,	PUNCT
ejpam-6347	10	43	compartmental	compartmental	ADJ
ejpam-6347	10	44	model	model	NOUN
ejpam-6347	10	45	,	,	PUNCT
ejpam-6347	10	46	basic	basic	ADJ
ejpam-6347	10	47	reproduction	reproduction	NOUN
ejpam-6347	10	48	number	number	NOUN
ejpam-6347	10	49	,	,	PUNCT
ejpam-6347	10	50	stability	stability	NOUN
ejpam-6347	10	51	analysis	analysis	NOUN
ejpam-6347	10	52	,	,	PUNCT
ejpam-6347	10	53	pontryagin	pontryagin	NOUN
ejpam-6347	10	54	’s	’s	PART
ejpam-6347	10	55	maximum	maximum	ADJ
ejpam-6347	10	56	principle	principle	NOUN
ejpam-6347	10	57	∗corresponding	∗corresponde	VERB
ejpam-6347	10	58	author	author	NOUN
ejpam-6347	10	59	.	.	PUNCT
ejpam-6347	11	1	doi	doi	NOUN
ejpam-6347	11	2	:	:	PUNCT
ejpam-6347	11	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6347	https://doi.org/10.29020/nybg.ejpam.v18i3.6347	ADJ
ejpam-6347	11	4	email	email	NOUN
ejpam-6347	11	5	addresses	address	NOUN
ejpam-6347	11	6	:	:	PUNCT
ejpam-6347	11	7	nabbas@psu.edu.sa	nabbas@psu.edu.sa	PROPN
ejpam-6347	11	8	(	(	PUNCT
ejpam-6347	11	9	n.	n.	NOUN
ejpam-6347	11	10	abbas	abbas	PROPN
ejpam-6347	11	11	)	)	PUNCT
ejpam-6347	11	12	,	,	PUNCT
ejpam-6347	11	13	wshatanawi@psu.edu.sa	wshatanawi@psu.edu.sa	PROPN
ejpam-6347	11	14	(	(	PUNCT
ejpam-6347	11	15	w.	w.	PROPN
ejpam-6347	11	16	shatanawi	shatanawi	PROPN
ejpam-6347	11	17	)	)	PUNCT
ejpam-6347	11	18	,	,	PUNCT
ejpam-6347	11	19	19907@riphahfsd.edu.pk	19907@riphahfsd.edu.pk	NUM
ejpam-6347	11	20	(	(	PUNCT
ejpam-6347	11	21	s.	s.	PROPN
ejpam-6347	11	22	a.	a.	NOUN
ejpam-6347	11	23	zanib	zanib	PROPN
ejpam-6347	11	24	)	)	PUNCT
ejpam-6347	11	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6347	12	1	1	1	NUM
ejpam-6347	12	2	copyright	copyright	NOUN
ejpam-6347	12	3	:	:	PUNCT
ejpam-6347	12	4	©	©	PROPN
ejpam-6347	12	5	2025	2025	NUM
ejpam-6347	12	6	the	the	DET
ejpam-6347	12	7	author(s	author(s	NOUN
ejpam-6347	12	8	)	)	PUNCT
ejpam-6347	12	9	.	.	PUNCT
ejpam-6347	13	1	(	(	PUNCT
ejpam-6347	13	2	cc	cc	NOUN
ejpam-6347	13	3	by	by	ADP
ejpam-6347	13	4	-	-	PUNCT
ejpam-6347	13	5	nc	nc	PROPN
ejpam-6347	13	6	4.0	4.0	NUM
ejpam-6347	13	7	)	)	PUNCT
ejpam-6347	13	8	n.	n.	NOUN
ejpam-6347	13	9	abbas	abbas	PROPN
ejpam-6347	13	10	,	,	PUNCT
ejpam-6347	13	11	w.	w.	PROPN
ejpam-6347	13	12	shatanawi	shatanawi	PROPN
ejpam-6347	13	13	,	,	PUNCT
ejpam-6347	13	14	s.	s.	PROPN
ejpam-6347	13	15	a.	a.	NOUN
ejpam-6347	13	16	zanib	zanib	PROPN
ejpam-6347	13	17	/	/	SYM
ejpam-6347	13	18	eur	eur	PROPN
ejpam-6347	13	19	.	.	PUNCT
ejpam-6347	14	1	j.	j.	PROPN
ejpam-6347	14	2	pure	pure	PROPN
ejpam-6347	14	3	appl	appl	PROPN
ejpam-6347	14	4	.	.	PROPN
ejpam-6347	14	5	math	math	PROPN
ejpam-6347	14	6	,	,	PUNCT
ejpam-6347	14	7	18	18	NUM
ejpam-6347	14	8	(	(	PUNCT
ejpam-6347	14	9	3	3	NUM
ejpam-6347	14	10	)	)	PUNCT
ejpam-6347	14	11	(	(	PUNCT
ejpam-6347	14	12	2025	2025	NUM
ejpam-6347	14	13	)	)	PUNCT
ejpam-6347	14	14	,	,	PUNCT
ejpam-6347	14	15	6347	6347	NUM
ejpam-6347	14	16	2	2	NUM
ejpam-6347	14	17	of	of	ADP
ejpam-6347	14	18	34	34	NUM
ejpam-6347	14	19	1	1	NUM
ejpam-6347	14	20	.	.	PUNCT
ejpam-6347	15	1	introduction	introduction	NOUN
ejpam-6347	15	2	in	in	ADP
ejpam-6347	15	3	the	the	DET
ejpam-6347	15	4	middle	middle	NOUN
ejpam-6347	15	5	of	of	ADP
ejpam-6347	15	6	the	the	DET
ejpam-6347	15	7	1960s	1960	NOUN
ejpam-6347	15	8	,	,	PUNCT
ejpam-6347	15	9	human	human	ADJ
ejpam-6347	15	10	coronaviruses	coronaviruse	NOUN
ejpam-6347	15	11	were	be	AUX
ejpam-6347	15	12	first	first	ADV
ejpam-6347	15	13	discovered	discover	VERB
ejpam-6347	15	14	.	.	PUNCT
ejpam-6347	16	1	the	the	DET
ejpam-6347	16	2	well	well	ADV
ejpam-6347	16	3	-	-	PUNCT
ejpam-6347	16	4	known	know	VERB
ejpam-6347	16	5	coronaviruses	coronaviruse	NOUN
ejpam-6347	16	6	that	that	PRON
ejpam-6347	16	7	may	may	AUX
ejpam-6347	16	8	infect	infect	VERB
ejpam-6347	16	9	individuals	individual	NOUN
ejpam-6347	16	10	include	include	VERB
ejpam-6347	16	11	sars	sar	NOUN
ejpam-6347	16	12	-	-	PUNCT
ejpam-6347	16	13	cov	cov	PROPN
ejpam-6347	16	14	(	(	PUNCT
ejpam-6347	16	15	severe	severe	ADJ
ejpam-6347	16	16	acute	acute	ADJ
ejpam-6347	16	17	respiratory	respiratory	ADJ
ejpam-6347	16	18	syndrome	syndrome	NOUN
ejpam-6347	16	19	)	)	PUNCT
ejpam-6347	16	20	,	,	PUNCT
ejpam-6347	16	21	mers	mer	NOUN
ejpam-6347	16	22	-	-	PUNCT
ejpam-6347	16	23	cov	cov	NOUN
ejpam-6347	16	24	(	(	PUNCT
ejpam-6347	16	25	middle	middle	PROPN
ejpam-6347	16	26	east	east	PROPN
ejpam-6347	16	27	respiratory	respiratory	ADJ
ejpam-6347	16	28	syndrome	syndrome	NOUN
ejpam-6347	16	29	)	)	PUNCT
ejpam-6347	16	30	,	,	PUNCT
ejpam-6347	16	31	and	and	CCONJ
ejpam-6347	16	32	sars	sar	NOUN
ejpam-6347	16	33	-	-	PUNCT
ejpam-6347	16	34	cov-2	cov-2	PUNCT
ejpam-6347	16	35	(	(	PUNCT
ejpam-6347	16	36	the	the	DET
ejpam-6347	16	37	new	new	ADJ
ejpam-6347	16	38	coronavirus	coronavirus	NOUN
ejpam-6347	16	39	that	that	PRON
ejpam-6347	16	40	causes	cause	VERB
ejpam-6347	16	41	coronavirus	coronavirus	NOUN
ejpam-6347	16	42	disease	disease	NOUN
ejpam-6347	16	43	2019	2019	NUM
ejpam-6347	16	44	,	,	PUNCT
ejpam-6347	16	45	or	or	CCONJ
ejpam-6347	16	46	covid-19	covid-19	PROPN
ejpam-6347	16	47	)	)	PUNCT
ejpam-6347	16	48	,	,	PUNCT
ejpam-6347	16	49	which	which	PRON
ejpam-6347	16	50	is	be	AUX
ejpam-6347	16	51	the	the	DET
ejpam-6347	16	52	subject	subject	NOUN
ejpam-6347	16	53	of	of	ADP
ejpam-6347	16	54	this	this	DET
ejpam-6347	16	55	research	research	NOUN
ejpam-6347	16	56	.	.	PUNCT
ejpam-6347	17	1	corona	corona	PROPN
ejpam-6347	17	2	,	,	PUNCT
ejpam-6347	17	3	virus	virus	NOUN
ejpam-6347	17	4	,	,	PUNCT
ejpam-6347	17	5	and	and	CCONJ
ejpam-6347	17	6	disease	disease	NOUN
ejpam-6347	17	7	are	be	AUX
ejpam-6347	17	8	represented	represent	VERB
ejpam-6347	17	9	,	,	PUNCT
ejpam-6347	17	10	respectively	respectively	ADV
ejpam-6347	17	11	,	,	PUNCT
ejpam-6347	17	12	by	by	ADP
ejpam-6347	17	13	the	the	DET
ejpam-6347	17	14	letters	letter	NOUN
ejpam-6347	17	15	co	co	NOUN
ejpam-6347	17	16	,	,	PUNCT
ejpam-6347	17	17	vi	vi	PROPN
ejpam-6347	17	18	,	,	PUNCT
ejpam-6347	17	19	and	and	CCONJ
ejpam-6347	17	20	d	d	X
ejpam-6347	17	21	in	in	ADP
ejpam-6347	17	22	covid-19	covid-19	PROPN
ejpam-6347	17	23	.	.	PUNCT
ejpam-6347	18	1	in	in	ADP
ejpam-6347	18	2	december	december	PROPN
ejpam-6347	18	3	2019	2019	NUM
ejpam-6347	18	4	,	,	PUNCT
ejpam-6347	18	5	a	a	DET
ejpam-6347	18	6	novel	novel	ADJ
ejpam-6347	18	7	virus	virus	NOUN
ejpam-6347	18	8	was	be	AUX
ejpam-6347	18	9	discovered	discover	VERB
ejpam-6347	18	10	during	during	ADP
ejpam-6347	18	11	an	an	DET
ejpam-6347	18	12	outbreak	outbreak	NOUN
ejpam-6347	18	13	in	in	ADP
ejpam-6347	18	14	wuhan	wuhan	PROPN
ejpam-6347	18	15	,	,	PUNCT
ejpam-6347	18	16	china	china	PROPN
ejpam-6347	19	1	[	[	X
ejpam-6347	19	2	1–4	1–4	X
ejpam-6347	19	3	]	]	PUNCT
ejpam-6347	19	4	shown	show	VERB
ejpam-6347	19	5	in	in	ADP
ejpam-6347	19	6	figure	figure	NOUN
ejpam-6347	19	7	1	1	NUM
ejpam-6347	19	8	.	.	PUNCT
ejpam-6347	20	1	there	there	PRON
ejpam-6347	20	2	were	be	VERB
ejpam-6347	20	3	attempts	attempt	NOUN
ejpam-6347	20	4	to	to	PART
ejpam-6347	20	5	control	control	VERB
ejpam-6347	20	6	it	it	PRON
ejpam-6347	20	7	,	,	PUNCT
ejpam-6347	20	8	but	but	CCONJ
ejpam-6347	20	9	they	they	PRON
ejpam-6347	20	10	did	do	AUX
ejpam-6347	20	11	not	not	PART
ejpam-6347	20	12	succeed	succeed	VERB
ejpam-6347	20	13	,	,	PUNCT
ejpam-6347	20	14	allowing	allow	VERB
ejpam-6347	20	15	the	the	DET
ejpam-6347	20	16	virus	virus	NOUN
ejpam-6347	20	17	to	to	PART
ejpam-6347	20	18	spread	spread	VERB
ejpam-6347	20	19	to	to	ADP
ejpam-6347	20	20	other	other	ADJ
ejpam-6347	20	21	regions	region	NOUN
ejpam-6347	20	22	of	of	ADP
ejpam-6347	20	23	china	china	PROPN
ejpam-6347	20	24	and	and	CCONJ
ejpam-6347	20	25	,	,	PUNCT
ejpam-6347	20	26	subsequently	subsequently	ADV
ejpam-6347	20	27	the	the	DET
ejpam-6347	20	28	propagation	propagation	NOUN
ejpam-6347	20	29	of	of	ADP
ejpam-6347	20	30	the	the	DET
ejpam-6347	20	31	world	world	NOUN
ejpam-6347	20	32	.	.	PUNCT
ejpam-6347	21	1	according	accord	VERB
ejpam-6347	21	2	to	to	ADP
ejpam-6347	21	3	a	a	DET
ejpam-6347	21	4	survey	survey	NOUN
ejpam-6347	21	5	of	of	ADP
ejpam-6347	21	6	individuals	individual	NOUN
ejpam-6347	21	7	who	who	PRON
ejpam-6347	21	8	passed	pass	VERB
ejpam-6347	21	9	away	away	ADP
ejpam-6347	21	10	,	,	PUNCT
ejpam-6347	21	11	the	the	DET
ejpam-6347	21	12	majority	majority	NOUN
ejpam-6347	21	13	of	of	ADP
ejpam-6347	21	14	them	they	PRON
ejpam-6347	21	15	were	be	AUX
ejpam-6347	21	16	elderly	elderly	ADJ
ejpam-6347	21	17	or	or	CCONJ
ejpam-6347	21	18	had	have	VERB
ejpam-6347	21	19	serious	serious	ADJ
ejpam-6347	21	20	diseases	disease	NOUN
ejpam-6347	21	21	like	like	ADP
ejpam-6347	21	22	parkinson	parkinson	NOUN
ejpam-6347	21	23	’s	’s	PART
ejpam-6347	21	24	,	,	PUNCT
ejpam-6347	21	25	lung	lung	NOUN
ejpam-6347	21	26	,	,	PUNCT
ejpam-6347	21	27	diabetes	diabetes	NOUN
ejpam-6347	21	28	,	,	PUNCT
ejpam-6347	21	29	chronic	chronic	ADJ
ejpam-6347	21	30	heart	heart	NOUN
ejpam-6347	21	31	,	,	PUNCT
ejpam-6347	21	32	or	or	CCONJ
ejpam-6347	21	33	kidney	kidney	NOUN
ejpam-6347	21	34	disease	disease	NOUN
ejpam-6347	21	35	.	.	PUNCT
ejpam-6347	22	1	flu	flu	NOUN
ejpam-6347	22	2	and	and	CCONJ
ejpam-6347	22	3	other	other	ADJ
ejpam-6347	22	4	viruses	virus	NOUN
ejpam-6347	22	5	that	that	PRON
ejpam-6347	22	6	can	can	AUX
ejpam-6347	22	7	propagate	propagate	VERB
ejpam-6347	22	8	contact	contact	NOUN
ejpam-6347	22	9	with	with	ADP
ejpam-6347	22	10	the	the	DET
ejpam-6347	22	11	mouth	mouth	NOUN
ejpam-6347	22	12	and	and	CCONJ
ejpam-6347	22	13	touch	touch	VERB
ejpam-6347	22	14	with	with	ADP
ejpam-6347	22	15	the	the	DET
ejpam-6347	22	16	nose	nose	NOUN
ejpam-6347	22	17	can	can	AUX
ejpam-6347	22	18	spread	spread	VERB
ejpam-6347	22	19	quickly	quickly	ADV
ejpam-6347	22	20	.	.	PUNCT
ejpam-6347	23	1	coronaviruses	coronaviruse	NOUN
ejpam-6347	23	2	are	be	AUX
ejpam-6347	23	3	very	very	ADV
ejpam-6347	23	4	dangerous	dangerous	ADJ
ejpam-6347	23	5	and	and	CCONJ
ejpam-6347	23	6	spread	spread	VERB
ejpam-6347	23	7	readily	readily	ADV
ejpam-6347	23	8	from	from	ADP
ejpam-6347	23	9	person	person	NOUN
ejpam-6347	23	10	to	to	ADP
ejpam-6347	23	11	person	person	NOUN
ejpam-6347	23	12	[	[	X
ejpam-6347	23	13	5	5	NUM
ejpam-6347	23	14	]	]	PUNCT
ejpam-6347	23	15	.	.	PUNCT
ejpam-6347	24	1	figure	figure	NOUN
ejpam-6347	24	2	1	1	NUM
ejpam-6347	24	3	:	:	PUNCT
ejpam-6347	24	4	sars	sar	NOUN
ejpam-6347	24	5	-	-	PUNCT
ejpam-6347	24	6	cov-2	cov-2	NOUN
ejpam-6347	24	7	structure	structure	NOUN
ejpam-6347	24	8	many	many	ADJ
ejpam-6347	24	9	mathematicians	mathematician	NOUN
ejpam-6347	24	10	are	be	AUX
ejpam-6347	24	11	constantly	constantly	ADV
ejpam-6347	24	12	working	work	VERB
ejpam-6347	24	13	to	to	PART
ejpam-6347	24	14	construct	construct	VERB
ejpam-6347	24	15	new	new	ADJ
ejpam-6347	24	16	,	,	PUNCT
ejpam-6347	24	17	more	more	ADV
ejpam-6347	24	18	effective	effective	ADJ
ejpam-6347	24	19	models	model	NOUN
ejpam-6347	24	20	that	that	PRON
ejpam-6347	24	21	may	may	AUX
ejpam-6347	24	22	be	be	AUX
ejpam-6347	24	23	used	use	VERB
ejpam-6347	24	24	for	for	ADP
ejpam-6347	24	25	modeling	modeling	NOUN
ejpam-6347	24	26	to	to	PART
ejpam-6347	24	27	evaluate	evaluate	VERB
ejpam-6347	24	28	the	the	DET
ejpam-6347	24	29	relationship	relationship	NOUN
ejpam-6347	24	30	between	between	ADP
ejpam-6347	24	31	death	death	NOUN
ejpam-6347	24	32	and	and	CCONJ
ejpam-6347	24	33	infection	infection	NOUN
ejpam-6347	24	34	,	,	PUNCT
ejpam-6347	24	35	fluid	fluid	ADJ
ejpam-6347	24	36	dynamic	dynamic	NOUN
ejpam-6347	24	37	and	and	CCONJ
ejpam-6347	24	38	predict	predict	VERB
ejpam-6347	24	39	how	how	SCONJ
ejpam-6347	24	40	it	it	PRON
ejpam-6347	24	41	will	will	AUX
ejpam-6347	24	42	spread	spread	VERB
ejpam-6347	24	43	in	in	ADP
ejpam-6347	24	44	the	the	DET
ejpam-6347	24	45	future	future	NOUN
ejpam-6347	25	1	[	[	X
ejpam-6347	25	2	6–9	6–9	NOUN
ejpam-6347	25	3	]	]	PUNCT
ejpam-6347	25	4	.	.	PUNCT
ejpam-6347	26	1	fractional	fractional	ADJ
ejpam-6347	26	2	calculus	calculus	NOUN
ejpam-6347	26	3	plays	play	VERB
ejpam-6347	26	4	a	a	DET
ejpam-6347	26	5	vital	vital	ADJ
ejpam-6347	26	6	role	role	NOUN
ejpam-6347	26	7	in	in	ADP
ejpam-6347	26	8	biological	biological	ADJ
ejpam-6347	26	9	modeling	modeling	NOUN
ejpam-6347	26	10	,	,	PUNCT
ejpam-6347	26	11	offering	offer	VERB
ejpam-6347	26	12	a	a	DET
ejpam-6347	26	13	more	more	ADV
ejpam-6347	26	14	accurate	accurate	ADJ
ejpam-6347	26	15	and	and	CCONJ
ejpam-6347	26	16	flexible	flexible	ADJ
ejpam-6347	26	17	framework	framework	NOUN
ejpam-6347	26	18	for	for	ADP
ejpam-6347	26	19	capturing	capture	VERB
ejpam-6347	26	20	the	the	DET
ejpam-6347	26	21	memory	memory	NOUN
ejpam-6347	26	22	and	and	CCONJ
ejpam-6347	26	23	hereditary	hereditary	ADJ
ejpam-6347	26	24	characteristics	characteristic	NOUN
ejpam-6347	26	25	inherent	inherent	ADJ
ejpam-6347	26	26	in	in	ADP
ejpam-6347	26	27	biological	biological	ADJ
ejpam-6347	26	28	systems	system	NOUN
ejpam-6347	26	29	.	.	PUNCT
ejpam-6347	27	1	numerous	numerous	ADJ
ejpam-6347	27	2	researchers	researcher	NOUN
ejpam-6347	27	3	have	have	AUX
ejpam-6347	27	4	developed	develop	VERB
ejpam-6347	27	5	mathematical	mathematical	ADJ
ejpam-6347	27	6	models	model	NOUN
ejpam-6347	27	7	using	use	VERB
ejpam-6347	27	8	fractional	fractional	ADJ
ejpam-6347	27	9	calculus	calculus	NOUN
ejpam-6347	27	10	to	to	PART
ejpam-6347	27	11	enhance	enhance	VERB
ejpam-6347	27	12	the	the	DET
ejpam-6347	27	13	precision	precision	NOUN
ejpam-6347	27	14	of	of	ADP
ejpam-6347	27	15	numerical	numerical	ADJ
ejpam-6347	27	16	simulations	simulation	NOUN
ejpam-6347	27	17	and	and	CCONJ
ejpam-6347	27	18	better	well	ADV
ejpam-6347	27	19	reflect	reflect	VERB
ejpam-6347	27	20	real	real	ADJ
ejpam-6347	27	21	-	-	PUNCT
ejpam-6347	27	22	world	world	NOUN
ejpam-6347	27	23	disease	disease	NOUN
ejpam-6347	27	24	dynamics	dynamic	NOUN
ejpam-6347	27	25	[	[	X
ejpam-6347	27	26	10	10	NUM
ejpam-6347	27	27	]	]	PUNCT
ejpam-6347	27	28	.	.	PUNCT
ejpam-6347	28	1	in	in	ADP
ejpam-6347	28	2	a	a	DET
ejpam-6347	28	3	short	short	ADJ
ejpam-6347	28	4	period	period	NOUN
ejpam-6347	28	5	,	,	PUNCT
ejpam-6347	28	6	various	various	ADJ
ejpam-6347	28	7	types	type	NOUN
ejpam-6347	28	8	of	of	ADP
ejpam-6347	28	9	research	research	NOUN
ejpam-6347	28	10	on	on	ADP
ejpam-6347	28	11	covid-19	covid-19	PROPN
ejpam-6347	28	12	model	model	NOUN
ejpam-6347	28	13	,	,	PUNCT
ejpam-6347	28	14	pandemic	pandemic	ADJ
ejpam-6347	28	15	have	have	AUX
ejpam-6347	28	16	been	be	AUX
ejpam-6347	28	17	conducted	conduct	VERB
ejpam-6347	28	18	in	in	ADP
ejpam-6347	28	19	the	the	DET
ejpam-6347	28	20	literature	literature	NOUN
ejpam-6347	28	21	.	.	PUNCT
ejpam-6347	29	1	diagne	diagne	VERB
ejpam-6347	29	2	et	et	PROPN
ejpam-6347	29	3	al	al	PROPN
ejpam-6347	29	4	.	.	PROPN
ejpam-6347	29	5	,	,	PUNCT
ejpam-6347	29	6	(	(	PUNCT
ejpam-6347	29	7	2021	2021	NUM
ejpam-6347	29	8	)	)	PUNCT
ejpam-6347	30	1	[	[	X
ejpam-6347	30	2	11	11	NUM
ejpam-6347	30	3	]	]	PUNCT
ejpam-6347	30	4	studied	study	VERB
ejpam-6347	30	5	formulation	formulation	NOUN
ejpam-6347	30	6	of	of	ADP
ejpam-6347	30	7	covid-19	covid-19	PROPN
ejpam-6347	30	8	model	model	NOUN
ejpam-6347	30	9	with	with	ADP
ejpam-6347	30	10	vaccination	vaccination	NOUN
ejpam-6347	30	11	.	.	PUNCT
ejpam-6347	31	1	in	in	ADP
ejpam-6347	31	2	their	their	PRON
ejpam-6347	31	3	model	model	NOUN
ejpam-6347	31	4	,	,	PUNCT
ejpam-6347	31	5	various	various	ADJ
ejpam-6347	31	6	epidemiological	epidemiological	ADJ
ejpam-6347	31	7	stages	stage	NOUN
ejpam-6347	31	8	were	be	AUX
ejpam-6347	31	9	created	create	VERB
ejpam-6347	31	10	for	for	ADP
ejpam-6347	31	11	the	the	DET
ejpam-6347	31	12	entire	entire	ADJ
ejpam-6347	31	13	population	population	NOUN
ejpam-6347	31	14	n	n	CCONJ
ejpam-6347	31	15	based	base	VERB
ejpam-6347	31	16	on	on	ADP
ejpam-6347	31	17	each	each	DET
ejpam-6347	31	18	person	person	NOUN
ejpam-6347	31	19	’s	’s	PART
ejpam-6347	31	20	health	health	NOUN
ejpam-6347	31	21	at	at	ADP
ejpam-6347	31	22	any	any	DET
ejpam-6347	31	23	given	give	VERB
ejpam-6347	31	24	moment	moment	NOUN
ejpam-6347	31	25	t.	t.	NOUN
ejpam-6347	31	26	they	they	PRON
ejpam-6347	31	27	was	be	AUX
ejpam-6347	31	28	shown	show	VERB
ejpam-6347	31	29	how	how	SCONJ
ejpam-6347	31	30	to	to	PART
ejpam-6347	31	31	regulate	regulate	VERB
ejpam-6347	31	32	the	the	DET
ejpam-6347	31	33	model	model	NOUN
ejpam-6347	31	34	to	to	PART
ejpam-6347	31	35	minimize	minimize	VERB
ejpam-6347	31	36	the	the	DET
ejpam-6347	31	37	spread	spread	NOUN
ejpam-6347	31	38	of	of	ADP
ejpam-6347	31	39	covid-19	covid-19	PROPN
ejpam-6347	31	40	by	by	ADP
ejpam-6347	31	41	employing	employ	VERB
ejpam-6347	31	42	pontryagin	pontryagin	NOUN
ejpam-6347	31	43	’s	’s	PART
ejpam-6347	31	44	maximal	maximal	ADJ
ejpam-6347	31	45	principle	principle	NOUN
ejpam-6347	31	46	.	.	PUNCT
ejpam-6347	32	1	acheampong	acheampong	PROPN
ejpam-6347	32	2	et	et	PROPN
ejpam-6347	32	3	al	al	PROPN
ejpam-6347	32	4	.	.	PROPN
ejpam-6347	32	5	,	,	PUNCT
ejpam-6347	32	6	(	(	PUNCT
ejpam-6347	32	7	2022	2022	NUM
ejpam-6347	32	8	)	)	PUNCT
ejpam-6347	33	1	[	[	X
ejpam-6347	33	2	12	12	NUM
ejpam-6347	33	3	]	]	PUNCT
ejpam-6347	33	4	developed	develop	VERB
ejpam-6347	33	5	a	a	DET
ejpam-6347	33	6	model	model	NOUN
ejpam-6347	33	7	where	where	SCONJ
ejpam-6347	33	8	n.	n.	NOUN
ejpam-6347	33	9	abbas	abbas	PROPN
ejpam-6347	33	10	,	,	PUNCT
ejpam-6347	33	11	w.	w.	PROPN
ejpam-6347	33	12	shatanawi	shatanawi	PROPN
ejpam-6347	33	13	,	,	PUNCT
ejpam-6347	33	14	s.	s.	PROPN
ejpam-6347	33	15	a.	a.	NOUN
ejpam-6347	33	16	zanib	zanib	PROPN
ejpam-6347	33	17	/	/	SYM
ejpam-6347	33	18	eur	eur	PROPN
ejpam-6347	33	19	.	.	PUNCT
ejpam-6347	34	1	j.	j.	PROPN
ejpam-6347	34	2	pure	pure	PROPN
ejpam-6347	34	3	appl	appl	PROPN
ejpam-6347	34	4	.	.	PROPN
ejpam-6347	34	5	math	math	PROPN
ejpam-6347	34	6	,	,	PUNCT
ejpam-6347	34	7	18	18	NUM
ejpam-6347	34	8	(	(	PUNCT
ejpam-6347	34	9	3	3	NUM
ejpam-6347	34	10	)	)	PUNCT
ejpam-6347	34	11	(	(	PUNCT
ejpam-6347	34	12	2025	2025	NUM
ejpam-6347	34	13	)	)	PUNCT
ejpam-6347	34	14	,	,	PUNCT
ejpam-6347	34	15	6347	6347	NUM
ejpam-6347	34	16	3	3	NUM
ejpam-6347	34	17	of	of	ADP
ejpam-6347	34	18	34	34	NUM
ejpam-6347	34	19	pre	pre	ADJ
ejpam-6347	34	20	-	-	ADJ
ejpam-6347	34	21	symptomatic	symptomatic	ADJ
ejpam-6347	34	22	and	and	CCONJ
ejpam-6347	34	23	infectious	infectious	ADJ
ejpam-6347	34	24	epidemiological	epidemiological	ADJ
ejpam-6347	34	25	classes	class	NOUN
ejpam-6347	34	26	generate	generate	VERB
ejpam-6347	34	27	infectious	infectious	ADJ
ejpam-6347	34	28	disease	disease	NOUN
ejpam-6347	34	29	models	model	NOUN
ejpam-6347	34	30	,	,	PUNCT
ejpam-6347	34	31	leaving	leave	VERB
ejpam-6347	34	32	them	they	PRON
ejpam-6347	34	33	as	as	ADP
ejpam-6347	34	34	abstract	abstract	ADJ
ejpam-6347	34	35	ideas	idea	NOUN
ejpam-6347	34	36	.	.	PUNCT
ejpam-6347	35	1	because	because	SCONJ
ejpam-6347	35	2	of	of	ADP
ejpam-6347	35	3	the	the	DET
ejpam-6347	35	4	prevalence	prevalence	NOUN
ejpam-6347	35	5	of	of	ADP
ejpam-6347	35	6	asymptomatic	asymptomatic	ADJ
ejpam-6347	35	7	carriers	carrier	NOUN
ejpam-6347	35	8	,	,	PUNCT
ejpam-6347	35	9	it	it	PRON
ejpam-6347	35	10	was	be	AUX
ejpam-6347	35	11	difficult	difficult	ADJ
ejpam-6347	35	12	to	to	PART
ejpam-6347	35	13	identify	identify	VERB
ejpam-6347	35	14	those	those	PRON
ejpam-6347	35	15	who	who	PRON
ejpam-6347	35	16	have	have	AUX
ejpam-6347	35	17	been	be	AUX
ejpam-6347	35	18	pre	pre	ADJ
ejpam-6347	35	19	-	-	ADJ
ejpam-6347	35	20	symptomatic	symptomatic	ADJ
ejpam-6347	35	21	(	(	PUNCT
ejpam-6347	35	22	represented	represent	VERB
ejpam-6347	35	23	by	by	ADP
ejpam-6347	35	24	e	e	NOUN
ejpam-6347	35	25	)	)	PUNCT
ejpam-6347	35	26	to	to	ADP
ejpam-6347	35	27	or	or	CCONJ
ejpam-6347	35	28	infected	infect	VERB
ejpam-6347	35	29	(	(	PUNCT
ejpam-6347	35	30	represented	represent	VERB
ejpam-6347	35	31	by	by	ADP
ejpam-6347	35	32	i	i	PROPN
ejpam-6347	35	33	)	)	PUNCT
ejpam-6347	35	34	with	with	ADP
ejpam-6347	35	35	sars	sar	NOUN
ejpam-6347	35	36	-	-	PUNCT
ejpam-6347	35	37	cov-2	cov-2	NOUN
ejpam-6347	35	38	.	.	PUNCT
ejpam-6347	36	1	they	they	PRON
ejpam-6347	36	2	had	have	AUX
ejpam-6347	36	3	produced	produce	VERB
ejpam-6347	36	4	two	two	NUM
ejpam-6347	36	5	epidemiological	epidemiological	ADJ
ejpam-6347	36	6	classes	class	NOUN
ejpam-6347	36	7	:	:	PUNCT
ejpam-6347	36	8	(	(	PUNCT
ejpam-6347	36	9	1	1	X
ejpam-6347	36	10	)	)	PUNCT
ejpam-6347	36	11	a	a	DET
ejpam-6347	36	12	known	know	VERB
ejpam-6347	36	13	group	group	NOUN
ejpam-6347	36	14	of	of	ADP
ejpam-6347	36	15	pre	pre	ADJ
ejpam-6347	36	16	-	-	ADJ
ejpam-6347	36	17	symptomatic	symptomatic	ADJ
ejpam-6347	36	18	individuals	individual	NOUN
ejpam-6347	36	19	thought	think	VERB
ejpam-6347	36	20	to	to	PART
ejpam-6347	36	21	be	be	AUX
ejpam-6347	36	22	sars	sar	NOUN
ejpam-6347	36	23	-	-	PUNCT
ejpam-6347	36	24	cov-2	cov-2	PUNCT
ejpam-6347	36	25	(	(	PUNCT
ejpam-6347	36	26	represented	represent	VERB
ejpam-6347	36	27	by	by	ADP
ejpam-6347	36	28	q	q	NOUN
ejpam-6347	36	29	)	)	PUNCT
ejpam-6347	36	30	,	,	PUNCT
ejpam-6347	36	31	and	and	CCONJ
ejpam-6347	36	32	(	(	PUNCT
ejpam-6347	36	33	2	2	X
ejpam-6347	36	34	)	)	PUNCT
ejpam-6347	36	35	those	those	PRON
ejpam-6347	36	36	whose	whose	DET
ejpam-6347	36	37	sars	sar	NOUN
ejpam-6347	36	38	-	-	PUNCT
ejpam-6347	36	39	cov-2	cov-2	PART
ejpam-6347	36	40	status	status	NOUN
ejpam-6347	36	41	has	have	AUX
ejpam-6347	36	42	been	be	AUX
ejpam-6347	36	43	clinically	clinically	ADV
ejpam-6347	36	44	verified	verify	VERB
ejpam-6347	36	45	(	(	PUNCT
ejpam-6347	36	46	represented	represent	VERB
ejpam-6347	36	47	by	by	ADP
ejpam-6347	36	48	p	p	PROPN
ejpam-6347	36	49	)	)	PUNCT
ejpam-6347	36	50	.	.	PUNCT
ejpam-6347	37	1	those	those	PRON
ejpam-6347	37	2	who	who	PRON
ejpam-6347	37	3	have	have	AUX
ejpam-6347	37	4	been	be	AUX
ejpam-6347	37	5	recognized	recognize	VERB
ejpam-6347	37	6	as	as	ADP
ejpam-6347	37	7	vulnerable	vulnerable	ADJ
ejpam-6347	37	8	were	be	AUX
ejpam-6347	37	9	marked	mark	VERB
ejpam-6347	37	10	with	with	ADP
ejpam-6347	37	11	the	the	DET
ejpam-6347	37	12	letter	letter	NOUN
ejpam-6347	37	13	q	q	PROPN
ejpam-6347	37	14	as	as	SCONJ
ejpam-6347	37	15	they	they	PRON
ejpam-6347	37	16	were	be	AUX
ejpam-6347	37	17	required	require	VERB
ejpam-6347	37	18	to	to	PART
ejpam-6347	37	19	quarantine	quarantine	VERB
ejpam-6347	37	20	under	under	ADP
ejpam-6347	37	21	ghana	ghana	PROPN
ejpam-6347	37	22	’s	’s	PART
ejpam-6347	37	23	covid-19	covid-19	PROPN
ejpam-6347	37	24	principles	principle	NOUN
ejpam-6347	37	25	.	.	PUNCT
ejpam-6347	38	1	the	the	DET
ejpam-6347	38	2	same	same	ADJ
ejpam-6347	38	3	was	be	AUX
ejpam-6347	38	4	applied	apply	VERB
ejpam-6347	38	5	to	to	PART
ejpam-6347	38	6	confirm	confirm	VERB
ejpam-6347	38	7	positive	positive	ADJ
ejpam-6347	38	8	(	(	PUNCT
ejpam-6347	38	9	p	p	NOUN
ejpam-6347	38	10	)	)	PUNCT
ejpam-6347	38	11	where	where	SCONJ
ejpam-6347	38	12	clinical	clinical	ADJ
ejpam-6347	38	13	tests	test	NOUN
ejpam-6347	38	14	have	have	AUX
ejpam-6347	38	15	shown	show	VERB
ejpam-6347	38	16	that	that	SCONJ
ejpam-6347	38	17	they	they	PRON
ejpam-6347	38	18	had	have	VERB
ejpam-6347	38	19	sars	sar	NOUN
ejpam-6347	38	20	-	-	PUNCT
ejpam-6347	38	21	cov-2	cov-2	NOUN
ejpam-6347	38	22	.	.	PUNCT
ejpam-6347	39	1	they	they	PRON
ejpam-6347	39	2	named	name	VERB
ejpam-6347	39	3	their	their	PRON
ejpam-6347	39	4	model	model	NOUN
ejpam-6347	39	5	covcom-9	covcom-9	NOUN
ejpam-6347	39	6	.	.	PUNCT
ejpam-6347	40	1	butt	butt	PROPN
ejpam-6347	40	2	et	et	PROPN
ejpam-6347	40	3	al	al	PROPN
ejpam-6347	40	4	.	.	PROPN
ejpam-6347	41	1	(	(	PUNCT
ejpam-6347	41	2	2023	2023	NUM
ejpam-6347	41	3	)	)	PUNCT
ejpam-6347	42	1	[	[	X
ejpam-6347	42	2	13	13	NUM
ejpam-6347	42	3	]	]	PUNCT
ejpam-6347	42	4	developed	develop	VERB
ejpam-6347	42	5	a	a	DET
ejpam-6347	42	6	nonlinear	nonlinear	ADJ
ejpam-6347	42	7	seiqhr	seiqhr	NOUN
ejpam-6347	42	8	fractional	fractional	ADJ
ejpam-6347	42	9	model	model	NOUN
ejpam-6347	42	10	for	for	ADP
ejpam-6347	42	11	covid-19	covid-19	PROPN
ejpam-6347	42	12	using	use	VERB
ejpam-6347	42	13	the	the	DET
ejpam-6347	42	14	atangana	atangana	PROPN
ejpam-6347	42	15	–	–	PUNCT
ejpam-6347	42	16	baleanu	baleanu	PROPN
ejpam-6347	42	17	(	(	PUNCT
ejpam-6347	42	18	abc	abc	PROPN
ejpam-6347	42	19	)	)	PUNCT
ejpam-6347	42	20	derivative	derivative	NOUN
ejpam-6347	42	21	to	to	PART
ejpam-6347	42	22	capture	capture	VERB
ejpam-6347	42	23	the	the	DET
ejpam-6347	42	24	complex	complex	ADJ
ejpam-6347	42	25	dynamics	dynamic	NOUN
ejpam-6347	42	26	of	of	ADP
ejpam-6347	42	27	disease	disease	NOUN
ejpam-6347	42	28	transmission	transmission	NOUN
ejpam-6347	42	29	.	.	PUNCT
ejpam-6347	43	1	they	they	PRON
ejpam-6347	43	2	analyzed	analyze	VERB
ejpam-6347	43	3	equilibrium	equilibrium	NOUN
ejpam-6347	43	4	points	point	NOUN
ejpam-6347	43	5	,	,	PUNCT
ejpam-6347	43	6	performed	perform	VERB
ejpam-6347	43	7	sensitivity	sensitivity	NOUN
ejpam-6347	43	8	and	and	CCONJ
ejpam-6347	43	9	bifurcation	bifurcation	NOUN
ejpam-6347	43	10	analyses	analysis	NOUN
ejpam-6347	43	11	,	,	PUNCT
ejpam-6347	43	12	and	and	CCONJ
ejpam-6347	43	13	applied	apply	VERB
ejpam-6347	43	14	an	an	DET
ejpam-6347	43	15	optimal	optimal	ADJ
ejpam-6347	43	16	control	control	NOUN
ejpam-6347	43	17	framework	framework	NOUN
ejpam-6347	43	18	with	with	ADP
ejpam-6347	43	19	the	the	DET
ejpam-6347	43	20	toufik	toufik	ADJ
ejpam-6347	43	21	–	–	PUNCT
ejpam-6347	43	22	atangana	atangana	PROPN
ejpam-6347	43	23	numerical	numerical	PROPN
ejpam-6347	43	24	method	method	PROPN
ejpam-6347	43	25	to	to	PART
ejpam-6347	43	26	assess	assess	VERB
ejpam-6347	43	27	control	control	NOUN
ejpam-6347	43	28	strategies	strategy	NOUN
ejpam-6347	43	29	.	.	PUNCT
ejpam-6347	44	1	zanib	zanib	VERB
ejpam-6347	44	2	et	et	PROPN
ejpam-6347	45	1	al	al	PROPN
ejpam-6347	45	2	.	.	PROPN
ejpam-6347	45	3	,	,	PUNCT
ejpam-6347	45	4	(	(	PUNCT
ejpam-6347	45	5	2024	2024	NUM
ejpam-6347	45	6	)	)	PUNCT
ejpam-6347	46	1	[	[	X
ejpam-6347	46	2	14	14	NUM
ejpam-6347	46	3	]	]	PUNCT
ejpam-6347	46	4	developed	develop	VERB
ejpam-6347	46	5	a	a	DET
ejpam-6347	46	6	modified	modify	VERB
ejpam-6347	46	7	compartmental	compartmental	NOUN
ejpam-6347	46	8	covid-19	covid-19	PROPN
ejpam-6347	46	9	model	model	NOUN
ejpam-6347	46	10	incorporating	incorporate	VERB
ejpam-6347	46	11	vaccination	vaccination	NOUN
ejpam-6347	46	12	strategies	strategy	NOUN
ejpam-6347	46	13	using	use	VERB
ejpam-6347	46	14	conformable	conformable	ADJ
ejpam-6347	46	15	fractional	fractional	ADJ
ejpam-6347	46	16	derivatives	derivative	NOUN
ejpam-6347	46	17	to	to	PART
ejpam-6347	46	18	capture	capture	VERB
ejpam-6347	46	19	complex	complex	ADJ
ejpam-6347	46	20	transmission	transmission	NOUN
ejpam-6347	46	21	dynamics	dynamic	NOUN
ejpam-6347	46	22	.	.	PUNCT
ejpam-6347	47	1	the	the	DET
ejpam-6347	47	2	basic	basic	ADJ
ejpam-6347	47	3	reproduction	reproduction	NOUN
ejpam-6347	47	4	number	number	NOUN
ejpam-6347	47	5	r0	r0	NOUN
ejpam-6347	47	6	,	,	PUNCT
ejpam-6347	47	7	its	its	PRON
ejpam-6347	47	8	sensitivity	sensitivity	NOUN
ejpam-6347	47	9	indices	index	NOUN
ejpam-6347	47	10	,	,	PUNCT
ejpam-6347	47	11	and	and	CCONJ
ejpam-6347	47	12	the	the	DET
ejpam-6347	47	13	model	model	NOUN
ejpam-6347	47	14	’s	’s	PART
ejpam-6347	47	15	stability	stability	NOUN
ejpam-6347	47	16	were	be	AUX
ejpam-6347	47	17	analyzed	analyze	VERB
ejpam-6347	47	18	,	,	PUNCT
ejpam-6347	47	19	with	with	ADP
ejpam-6347	47	20	a	a	DET
ejpam-6347	47	21	finite	finite	ADJ
ejpam-6347	47	22	difference	difference	NOUN
ejpam-6347	47	23	method	method	NOUN
ejpam-6347	47	24	providing	provide	VERB
ejpam-6347	47	25	accurate	accurate	ADJ
ejpam-6347	47	26	numerical	numerical	ADJ
ejpam-6347	47	27	solutions	solution	NOUN
ejpam-6347	47	28	and	and	CCONJ
ejpam-6347	47	29	highlighting	highlight	VERB
ejpam-6347	47	30	the	the	DET
ejpam-6347	47	31	role	role	NOUN
ejpam-6347	47	32	of	of	ADP
ejpam-6347	47	33	vaccination	vaccination	NOUN
ejpam-6347	47	34	in	in	ADP
ejpam-6347	47	35	disease	disease	NOUN
ejpam-6347	47	36	control	control	NOUN
ejpam-6347	47	37	.	.	PUNCT
ejpam-6347	48	1	butt	butt	PROPN
ejpam-6347	48	2	et	et	PROPN
ejpam-6347	48	3	al	al	PROPN
ejpam-6347	48	4	.	.	PROPN
ejpam-6347	48	5	,	,	PUNCT
ejpam-6347	48	6	(	(	PUNCT
ejpam-6347	48	7	2024	2024	NUM
ejpam-6347	48	8	)	)	PUNCT
ejpam-6347	49	1	[	[	X
ejpam-6347	49	2	15	15	NUM
ejpam-6347	49	3	]	]	PUNCT
ejpam-6347	49	4	developed	develop	VERB
ejpam-6347	49	5	a	a	DET
ejpam-6347	49	6	nonlinear	nonlinear	ADJ
ejpam-6347	49	7	fractional	fractional	ADJ
ejpam-6347	49	8	bi	bi	ADJ
ejpam-6347	49	9	-	-	ADJ
ejpam-6347	49	10	susceptible	susceptible	ADJ
ejpam-6347	49	11	s1s2v1v2ihr	s1s2v1v2ihr	PROPN
ejpam-6347	49	12	model	model	NOUN
ejpam-6347	49	13	using	use	VERB
ejpam-6347	49	14	the	the	DET
ejpam-6347	49	15	atangana	atangana	PROPN
ejpam-6347	49	16	–	–	PUNCT
ejpam-6347	49	17	baleanu	baleanu	PROPN
ejpam-6347	49	18	caputo	caputo	PROPN
ejpam-6347	49	19	derivative	derivative	PROPN
ejpam-6347	49	20	to	to	PART
ejpam-6347	49	21	investigate	investigate	VERB
ejpam-6347	49	22	the	the	DET
ejpam-6347	49	23	dynamics	dynamic	NOUN
ejpam-6347	49	24	and	and	CCONJ
ejpam-6347	49	25	control	control	NOUN
ejpam-6347	49	26	of	of	ADP
ejpam-6347	49	27	covid-19	covid-19	PROPN
ejpam-6347	49	28	.	.	PUNCT
ejpam-6347	50	1	they	they	PRON
ejpam-6347	50	2	analyzed	analyze	VERB
ejpam-6347	50	3	the	the	DET
ejpam-6347	50	4	model	model	NOUN
ejpam-6347	50	5	’s	’s	PART
ejpam-6347	50	6	stability	stability	NOUN
ejpam-6347	50	7	,	,	PUNCT
ejpam-6347	50	8	validated	validate	VERB
ejpam-6347	50	9	results	result	NOUN
ejpam-6347	50	10	using	use	VERB
ejpam-6347	50	11	the	the	DET
ejpam-6347	50	12	toufik	toufik	ADJ
ejpam-6347	50	13	–	–	PUNCT
ejpam-6347	50	14	atangana	atangana	PROPN
ejpam-6347	50	15	numerical	numerical	PROPN
ejpam-6347	50	16	method	method	PROPN
ejpam-6347	50	17	,	,	PUNCT
ejpam-6347	50	18	and	and	CCONJ
ejpam-6347	50	19	demonstrated	demonstrate	VERB
ejpam-6347	50	20	the	the	DET
ejpam-6347	50	21	effectiveness	effectiveness	NOUN
ejpam-6347	50	22	of	of	ADP
ejpam-6347	50	23	optimized	optimize	VERB
ejpam-6347	50	24	control	control	NOUN
ejpam-6347	50	25	strategies	strategy	NOUN
ejpam-6347	50	26	through	through	ADP
ejpam-6347	50	27	simulations	simulation	NOUN
ejpam-6347	50	28	.	.	PUNCT
ejpam-6347	51	1	abboubakar	abboubakar	NOUN
ejpam-6347	51	2	and	and	CCONJ
ejpam-6347	51	3	racke	racke	ADJ
ejpam-6347	51	4	(	(	PUNCT
ejpam-6347	51	5	2025	2025	NUM
ejpam-6347	51	6	)	)	PUNCT
ejpam-6347	52	1	[	[	X
ejpam-6347	52	2	16	16	NUM
ejpam-6347	52	3	]	]	PUNCT
ejpam-6347	52	4	developed	develop	VERB
ejpam-6347	52	5	a	a	DET
ejpam-6347	52	6	covid-19	covid-19	PROPN
ejpam-6347	52	7	model	model	NOUN
ejpam-6347	52	8	using	use	VERB
ejpam-6347	52	9	integer	integer	NOUN
ejpam-6347	52	10	and	and	CCONJ
ejpam-6347	52	11	caputo	caputo	PROPN
ejpam-6347	52	12	fractional	fractional	ADJ
ejpam-6347	52	13	-	-	PUNCT
ejpam-6347	52	14	order	order	NOUN
ejpam-6347	52	15	derivatives	derivative	NOUN
ejpam-6347	52	16	,	,	PUNCT
ejpam-6347	52	17	incorporating	incorporate	VERB
ejpam-6347	52	18	vaccination	vaccination	NOUN
ejpam-6347	52	19	,	,	PUNCT
ejpam-6347	52	20	confinement	confinement	NOUN
ejpam-6347	52	21	,	,	PUNCT
ejpam-6347	52	22	and	and	CCONJ
ejpam-6347	52	23	treatment	treatment	NOUN
ejpam-6347	52	24	with	with	ADP
ejpam-6347	52	25	limited	limited	ADJ
ejpam-6347	52	26	resources	resource	NOUN
ejpam-6347	52	27	.	.	PUNCT
ejpam-6347	53	1	using	use	VERB
ejpam-6347	53	2	german	german	ADJ
ejpam-6347	53	3	data	datum	NOUN
ejpam-6347	53	4	,	,	PUNCT
ejpam-6347	53	5	it	it	PRON
ejpam-6347	53	6	was	be	AUX
ejpam-6347	53	7	shown	show	VERB
ejpam-6347	53	8	that	that	SCONJ
ejpam-6347	53	9	the	the	DET
ejpam-6347	53	10	fractional	fractional	ADJ
ejpam-6347	53	11	model	model	NOUN
ejpam-6347	53	12	provided	provide	VERB
ejpam-6347	53	13	more	more	ADV
ejpam-6347	53	14	accurate	accurate	ADJ
ejpam-6347	53	15	long	long	ADJ
ejpam-6347	53	16	-	-	PUNCT
ejpam-6347	53	17	term	term	NOUN
ejpam-6347	53	18	forecasts	forecast	NOUN
ejpam-6347	53	19	,	,	PUNCT
ejpam-6347	53	20	with	with	ADP
ejpam-6347	53	21	a	a	DET
ejpam-6347	53	22	reproduction	reproduction	NOUN
ejpam-6347	53	23	number	number	NOUN
ejpam-6347	53	24	around	around	ADP
ejpam-6347	53	25	1.90	1.90	NUM
ejpam-6347	53	26	,	,	PUNCT
ejpam-6347	53	27	indicating	indicate	VERB
ejpam-6347	53	28	endemic	endemic	ADJ
ejpam-6347	53	29	persistence	persistence	NOUN
ejpam-6347	53	30	.	.	PUNCT
ejpam-6347	54	1	kumar	kumar	PROPN
ejpam-6347	54	2	et	et	PROPN
ejpam-6347	54	3	al	al	PROPN
ejpam-6347	54	4	.	.	PROPN
ejpam-6347	54	5	,	,	PUNCT
ejpam-6347	54	6	(	(	PUNCT
ejpam-6347	54	7	2025)[17	2025)[17	NUM
ejpam-6347	54	8	]	]	PUNCT
ejpam-6347	54	9	developed	develop	VERB
ejpam-6347	54	10	an	an	DET
ejpam-6347	54	11	age	age	NOUN
ejpam-6347	54	12	-	-	PUNCT
ejpam-6347	54	13	structured	structure	VERB
ejpam-6347	54	14	seir	seir	NOUN
ejpam-6347	54	15	model	model	NOUN
ejpam-6347	54	16	to	to	PART
ejpam-6347	54	17	analyze	analyze	VERB
ejpam-6347	54	18	the	the	DET
ejpam-6347	54	19	spread	spread	NOUN
ejpam-6347	54	20	of	of	ADP
ejpam-6347	54	21	covid-19	covid-19	PROPN
ejpam-6347	54	22	and	and	CCONJ
ejpam-6347	54	23	estimate	estimate	VERB
ejpam-6347	54	24	key	key	ADJ
ejpam-6347	54	25	parameters	parameter	NOUN
ejpam-6347	54	26	such	such	ADJ
ejpam-6347	54	27	as	as	ADP
ejpam-6347	54	28	the	the	DET
ejpam-6347	54	29	basic	basic	ADJ
ejpam-6347	54	30	reproduction	reproduction	NOUN
ejpam-6347	54	31	number	number	NOUN
ejpam-6347	54	32	r0	r0	NOUN
ejpam-6347	54	33	and	and	CCONJ
ejpam-6347	54	34	case	case	NOUN
ejpam-6347	54	35	fatality	fatality	NOUN
ejpam-6347	54	36	ratio	ratio	NOUN
ejpam-6347	54	37	(	(	PUNCT
ejpam-6347	54	38	cfr	cfr	NOUN
ejpam-6347	54	39	)	)	PUNCT
ejpam-6347	54	40	.	.	PUNCT
ejpam-6347	55	1	the	the	DET
ejpam-6347	55	2	model	model	NOUN
ejpam-6347	55	3	,	,	PUNCT
ejpam-6347	55	4	validated	validate	VERB
ejpam-6347	55	5	using	use	VERB
ejpam-6347	55	6	epidemiological	epidemiological	ADJ
ejpam-6347	55	7	data	datum	NOUN
ejpam-6347	55	8	and	and	CCONJ
ejpam-6347	55	9	uncertainty	uncertainty	NOUN
ejpam-6347	55	10	analysis	analysis	NOUN
ejpam-6347	55	11	,	,	PUNCT
ejpam-6347	55	12	provided	provide	VERB
ejpam-6347	55	13	insights	insight	NOUN
ejpam-6347	55	14	for	for	ADP
ejpam-6347	55	15	public	public	ADJ
ejpam-6347	55	16	health	health	NOUN
ejpam-6347	55	17	interventions	intervention	NOUN
ejpam-6347	55	18	and	and	CCONJ
ejpam-6347	55	19	was	be	AUX
ejpam-6347	55	20	suggested	suggest	VERB
ejpam-6347	55	21	to	to	PART
ejpam-6347	55	22	be	be	AUX
ejpam-6347	55	23	extended	extend	VERB
ejpam-6347	55	24	using	use	VERB
ejpam-6347	55	25	agent	agent	NOUN
ejpam-6347	55	26	-	-	PUNCT
ejpam-6347	55	27	based	base	VERB
ejpam-6347	55	28	modeling	modeling	NOUN
ejpam-6347	55	29	.	.	PUNCT
ejpam-6347	56	1	while	while	SCONJ
ejpam-6347	56	2	reviewing	review	VERB
ejpam-6347	56	3	the	the	DET
ejpam-6347	56	4	literature	literature	NOUN
ejpam-6347	56	5	,	,	PUNCT
ejpam-6347	56	6	we	we	PRON
ejpam-6347	56	7	observed	observe	VERB
ejpam-6347	56	8	that	that	SCONJ
ejpam-6347	56	9	many	many	ADJ
ejpam-6347	56	10	existing	exist	VERB
ejpam-6347	56	11	covid-19	covid-19	PROPN
ejpam-6347	56	12	models	model	NOUN
ejpam-6347	56	13	skip	skip	VERB
ejpam-6347	56	14	critical	critical	ADJ
ejpam-6347	56	15	components	component	NOUN
ejpam-6347	56	16	,	,	PUNCT
ejpam-6347	56	17	particularly	particularly	ADV
ejpam-6347	56	18	the	the	DET
ejpam-6347	56	19	inclusion	inclusion	NOUN
ejpam-6347	56	20	of	of	ADP
ejpam-6347	56	21	a	a	DET
ejpam-6347	56	22	vaccinated	vaccinated	ADJ
ejpam-6347	56	23	compartment	compartment	NOUN
ejpam-6347	56	24	.	.	PUNCT
ejpam-6347	57	1	this	this	DET
ejpam-6347	57	2	limitation	limitation	NOUN
ejpam-6347	57	3	reduces	reduce	VERB
ejpam-6347	57	4	their	their	PRON
ejpam-6347	57	5	capacity	capacity	NOUN
ejpam-6347	57	6	to	to	PART
ejpam-6347	57	7	realistically	realistically	ADV
ejpam-6347	57	8	capture	capture	VERB
ejpam-6347	57	9	disease	disease	NOUN
ejpam-6347	57	10	dynamics	dynamic	NOUN
ejpam-6347	57	11	in	in	ADP
ejpam-6347	57	12	the	the	DET
ejpam-6347	57	13	post	post	ADJ
ejpam-6347	57	14	-	-	ADJ
ejpam-6347	57	15	vaccine	vaccine	ADJ
ejpam-6347	57	16	era	era	NOUN
ejpam-6347	57	17	.	.	PUNCT
ejpam-6347	58	1	to	to	PART
ejpam-6347	58	2	address	address	VERB
ejpam-6347	58	3	this	this	DET
ejpam-6347	58	4	gap	gap	NOUN
ejpam-6347	58	5	,	,	PUNCT
ejpam-6347	58	6	we	we	PRON
ejpam-6347	58	7	developed	develop	VERB
ejpam-6347	58	8	a	a	DET
ejpam-6347	58	9	comprehensive	comprehensive	ADJ
ejpam-6347	58	10	model	model	NOUN
ejpam-6347	58	11	that	that	PRON
ejpam-6347	58	12	consist	consist	VERB
ejpam-6347	58	13	for	for	ADP
ejpam-6347	58	14	all	all	DET
ejpam-6347	58	15	possible	possible	ADJ
ejpam-6347	58	16	stages	stage	NOUN
ejpam-6347	58	17	of	of	ADP
ejpam-6347	58	18	covid-19	covid-19	PROPN
ejpam-6347	58	19	progression	progression	NOUN
ejpam-6347	58	20	.	.	PUNCT
ejpam-6347	59	1	specifically	specifically	ADV
ejpam-6347	59	2	,	,	PUNCT
ejpam-6347	59	3	we	we	PRON
ejpam-6347	59	4	propose	propose	VERB
ejpam-6347	59	5	a	a	DET
ejpam-6347	59	6	ten	ten	NUM
ejpam-6347	59	7	-	-	PUNCT
ejpam-6347	59	8	compartment	compartment	NOUN
ejpam-6347	59	9	mathematical	mathematical	ADJ
ejpam-6347	59	10	model	model	NOUN
ejpam-6347	59	11	,	,	PUNCT
ejpam-6347	59	12	termed	term	VERB
ejpam-6347	59	13	covcom10	covcom10	NOUN
ejpam-6347	59	14	,	,	PUNCT
ejpam-6347	59	15	which	which	PRON
ejpam-6347	59	16	incorporates	incorporate	VERB
ejpam-6347	59	17	key	key	ADJ
ejpam-6347	59	18	categories	category	NOUN
ejpam-6347	59	19	such	such	ADJ
ejpam-6347	59	20	as	as	ADP
ejpam-6347	59	21	asymptomatic	asymptomatic	ADJ
ejpam-6347	59	22	(	(	PUNCT
ejpam-6347	59	23	f	f	PROPN
ejpam-6347	59	24	)	)	PUNCT
ejpam-6347	59	25	,	,	PUNCT
ejpam-6347	59	26	presymptomatic	presymptomatic	ADJ
ejpam-6347	59	27	(	(	PUNCT
ejpam-6347	59	28	e	e	NOUN
ejpam-6347	59	29	)	)	PUNCT
ejpam-6347	59	30	,	,	PUNCT
ejpam-6347	59	31	and	and	CCONJ
ejpam-6347	59	32	vaccinated	vaccinated	ADJ
ejpam-6347	59	33	(	(	PUNCT
ejpam-6347	59	34	v	v	NOUN
ejpam-6347	59	35	)	)	PUNCT
ejpam-6347	59	36	individuals	individual	NOUN
ejpam-6347	59	37	.	.	PUNCT
ejpam-6347	60	1	covcom10	covcom10	NOUN
ejpam-6347	60	2	builds	build	VERB
ejpam-6347	60	3	upon	upon	SCONJ
ejpam-6347	60	4	the	the	DET
ejpam-6347	60	5	previous	previous	ADJ
ejpam-6347	60	6	covcom9	covcom9	NOUN
ejpam-6347	60	7	framework	framework	NOUN
ejpam-6347	60	8	by	by	ADP
ejpam-6347	60	9	incorporating	incorporate	VERB
ejpam-6347	60	10	the	the	DET
ejpam-6347	60	11	vaccination	vaccination	NOUN
ejpam-6347	60	12	compartment	compartment	NOUN
ejpam-6347	60	13	,	,	PUNCT
ejpam-6347	60	14	enabling	enable	VERB
ejpam-6347	60	15	a	a	DET
ejpam-6347	60	16	more	more	ADV
ejpam-6347	60	17	accurate	accurate	ADJ
ejpam-6347	60	18	simulation	simulation	NOUN
ejpam-6347	60	19	of	of	ADP
ejpam-6347	60	20	immunization	immunization	NOUN
ejpam-6347	60	21	effects	effect	NOUN
ejpam-6347	60	22	on	on	ADP
ejpam-6347	60	23	sars	sar	NOUN
ejpam-6347	60	24	-	-	PUNCT
ejpam-6347	60	25	cov-2	cov-2	NOUN
ejpam-6347	60	26	transmission	transmission	NOUN
ejpam-6347	60	27	.	.	PUNCT
ejpam-6347	61	1	the	the	DET
ejpam-6347	61	2	addition	addition	NOUN
ejpam-6347	61	3	of	of	ADP
ejpam-6347	61	4	asymptomatic	asymptomatic	ADJ
ejpam-6347	61	5	and	and	CCONJ
ejpam-6347	61	6	pre	pre	ADJ
ejpam-6347	61	7	-	-	ADJ
ejpam-6347	61	8	symptomatic	symptomatic	ADJ
ejpam-6347	61	9	compartments	compartment	NOUN
ejpam-6347	61	10	is	be	AUX
ejpam-6347	61	11	essential	essential	ADJ
ejpam-6347	61	12	for	for	ADP
ejpam-6347	61	13	capturing	capture	VERB
ejpam-6347	61	14	hidden	hide	VERB
ejpam-6347	61	15	transmission	transmission	NOUN
ejpam-6347	61	16	routes	route	NOUN
ejpam-6347	61	17	and	and	CCONJ
ejpam-6347	61	18	reflecting	reflect	VERB
ejpam-6347	61	19	the	the	DET
ejpam-6347	61	20	full	full	ADJ
ejpam-6347	61	21	spectrum	spectrum	NOUN
ejpam-6347	61	22	of	of	ADP
ejpam-6347	61	23	covid-19	covid-19	PROPN
ejpam-6347	61	24	progression	progression	NOUN
ejpam-6347	61	25	.	.	PUNCT
ejpam-6347	62	1	these	these	DET
ejpam-6347	62	2	n.	n.	PROPN
ejpam-6347	62	3	abbas	abbas	PROPN
ejpam-6347	62	4	,	,	PUNCT
ejpam-6347	62	5	w.	w.	PROPN
ejpam-6347	62	6	shatanawi	shatanawi	PROPN
ejpam-6347	62	7	,	,	PUNCT
ejpam-6347	62	8	s.	s.	PROPN
ejpam-6347	62	9	a.	a.	NOUN
ejpam-6347	62	10	zanib	zanib	PROPN
ejpam-6347	62	11	/	/	SYM
ejpam-6347	62	12	eur	eur	PROPN
ejpam-6347	62	13	.	.	PUNCT
ejpam-6347	63	1	j.	j.	PROPN
ejpam-6347	63	2	pure	pure	PROPN
ejpam-6347	63	3	appl	appl	PROPN
ejpam-6347	63	4	.	.	PROPN
ejpam-6347	63	5	math	math	PROPN
ejpam-6347	63	6	,	,	PUNCT
ejpam-6347	63	7	18	18	NUM
ejpam-6347	63	8	(	(	PUNCT
ejpam-6347	63	9	3	3	NUM
ejpam-6347	63	10	)	)	PUNCT
ejpam-6347	63	11	(	(	PUNCT
ejpam-6347	63	12	2025	2025	NUM
ejpam-6347	63	13	)	)	PUNCT
ejpam-6347	63	14	,	,	PUNCT
ejpam-6347	63	15	6347	6347	NUM
ejpam-6347	63	16	4	4	NUM
ejpam-6347	63	17	of	of	ADP
ejpam-6347	63	18	34	34	NUM
ejpam-6347	63	19	improvements	improvement	NOUN
ejpam-6347	63	20	enhance	enhance	VERB
ejpam-6347	63	21	the	the	DET
ejpam-6347	63	22	epidemiological	epidemiological	ADJ
ejpam-6347	63	23	relevance	relevance	NOUN
ejpam-6347	63	24	of	of	ADP
ejpam-6347	63	25	the	the	DET
ejpam-6347	63	26	model	model	NOUN
ejpam-6347	63	27	and	and	CCONJ
ejpam-6347	63	28	support	support	VERB
ejpam-6347	63	29	the	the	DET
ejpam-6347	63	30	evaluation	evaluation	NOUN
ejpam-6347	63	31	of	of	ADP
ejpam-6347	63	32	various	various	ADJ
ejpam-6347	63	33	intervention	intervention	NOUN
ejpam-6347	63	34	strategies	strategy	NOUN
ejpam-6347	63	35	.	.	PUNCT
ejpam-6347	64	1	to	to	PART
ejpam-6347	64	2	further	far	ADV
ejpam-6347	64	3	improve	improve	VERB
ejpam-6347	64	4	the	the	DET
ejpam-6347	64	5	model	model	NOUN
ejpam-6347	64	6	’s	’s	PART
ejpam-6347	64	7	realism	realism	NOUN
ejpam-6347	64	8	,	,	PUNCT
ejpam-6347	64	9	we	we	PRON
ejpam-6347	64	10	employ	employ	VERB
ejpam-6347	64	11	the	the	DET
ejpam-6347	64	12	conformable	conformable	ADJ
ejpam-6347	64	13	fractional	fractional	ADJ
ejpam-6347	64	14	derivative	derivative	NOUN
ejpam-6347	64	15	,	,	PUNCT
ejpam-6347	64	16	which	which	PRON
ejpam-6347	64	17	accounts	account	VERB
ejpam-6347	64	18	for	for	ADP
ejpam-6347	64	19	memory	memory	NOUN
ejpam-6347	64	20	and	and	CCONJ
ejpam-6347	64	21	hereditary	hereditary	ADJ
ejpam-6347	64	22	effects	effect	NOUN
ejpam-6347	64	23	.	.	PUNCT
ejpam-6347	65	1	this	this	DET
ejpam-6347	65	2	approach	approach	NOUN
ejpam-6347	65	3	enables	enable	VERB
ejpam-6347	65	4	the	the	DET
ejpam-6347	65	5	model	model	NOUN
ejpam-6347	65	6	to	to	PART
ejpam-6347	65	7	incorporate	incorporate	VERB
ejpam-6347	65	8	the	the	DET
ejpam-6347	65	9	influence	influence	NOUN
ejpam-6347	65	10	of	of	ADP
ejpam-6347	65	11	past	past	ADJ
ejpam-6347	65	12	states	state	NOUN
ejpam-6347	65	13	on	on	ADP
ejpam-6347	65	14	current	current	ADJ
ejpam-6347	65	15	dynamics	dynamic	NOUN
ejpam-6347	65	16	,	,	PUNCT
ejpam-6347	65	17	thereby	thereby	ADV
ejpam-6347	65	18	capturing	capture	VERB
ejpam-6347	65	19	complex	complex	ADJ
ejpam-6347	65	20	behaviors	behavior	NOUN
ejpam-6347	65	21	such	such	ADJ
ejpam-6347	65	22	as	as	ADP
ejpam-6347	65	23	delayed	delay	VERB
ejpam-6347	65	24	responses	response	NOUN
ejpam-6347	65	25	and	and	CCONJ
ejpam-6347	65	26	long	long	ADJ
ejpam-6347	65	27	-	-	PUNCT
ejpam-6347	65	28	term	term	NOUN
ejpam-6347	65	29	persistence	persistence	NOUN
ejpam-6347	65	30	of	of	ADP
ejpam-6347	65	31	infections	infection	NOUN
ejpam-6347	65	32	.	.	PUNCT
ejpam-6347	66	1	the	the	DET
ejpam-6347	66	2	conformable	conformable	ADJ
ejpam-6347	66	3	fractional	fractional	ADJ
ejpam-6347	66	4	framework	framework	NOUN
ejpam-6347	66	5	preserves	preserve	VERB
ejpam-6347	66	6	key	key	ADJ
ejpam-6347	66	7	properties	property	NOUN
ejpam-6347	66	8	of	of	ADP
ejpam-6347	66	9	classical	classical	ADJ
ejpam-6347	66	10	calculus	calculus	NOUN
ejpam-6347	66	11	while	while	SCONJ
ejpam-6347	66	12	offering	offer	VERB
ejpam-6347	66	13	improved	improve	VERB
ejpam-6347	66	14	computational	computational	ADJ
ejpam-6347	66	15	tractability	tractability	NOUN
ejpam-6347	66	16	compared	compare	VERB
ejpam-6347	66	17	to	to	ADP
ejpam-6347	66	18	other	other	ADJ
ejpam-6347	66	19	fractional	fractional	ADJ
ejpam-6347	66	20	definitions	definition	NOUN
ejpam-6347	66	21	.	.	PUNCT
ejpam-6347	67	1	notably	notably	ADV
ejpam-6347	67	2	,	,	PUNCT
ejpam-6347	67	3	it	it	PRON
ejpam-6347	67	4	reduces	reduce	VERB
ejpam-6347	67	5	to	to	ADP
ejpam-6347	67	6	the	the	DET
ejpam-6347	67	7	classical	classical	ADJ
ejpam-6347	67	8	model	model	NOUN
ejpam-6347	67	9	when	when	SCONJ
ejpam-6347	67	10	the	the	DET
ejpam-6347	67	11	fractional	fractional	ADJ
ejpam-6347	67	12	order	order	NOUN
ejpam-6347	67	13	approaches	approach	VERB
ejpam-6347	67	14	one	one	NUM
ejpam-6347	67	15	,	,	PUNCT
ejpam-6347	67	16	ensuring	ensure	VERB
ejpam-6347	67	17	consistency	consistency	NOUN
ejpam-6347	67	18	with	with	ADP
ejpam-6347	67	19	traditional	traditional	ADJ
ejpam-6347	67	20	differential	differential	ADJ
ejpam-6347	67	21	models	model	NOUN
ejpam-6347	67	22	.	.	PUNCT
ejpam-6347	68	1	to	to	PART
ejpam-6347	68	2	validate	validate	VERB
ejpam-6347	68	3	the	the	DET
ejpam-6347	68	4	model	model	NOUN
ejpam-6347	68	5	’s	’s	PART
ejpam-6347	68	6	applicability	applicability	NOUN
ejpam-6347	68	7	,	,	PUNCT
ejpam-6347	68	8	we	we	PRON
ejpam-6347	68	9	compared	compare	VERB
ejpam-6347	68	10	its	its	PRON
ejpam-6347	68	11	simulation	simulation	NOUN
ejpam-6347	68	12	results	result	NOUN
ejpam-6347	68	13	with	with	ADP
ejpam-6347	68	14	real	real	ADJ
ejpam-6347	68	15	-	-	PUNCT
ejpam-6347	68	16	world	world	NOUN
ejpam-6347	68	17	covid-19	covid-19	PROPN
ejpam-6347	68	18	data	datum	NOUN
ejpam-6347	68	19	[	[	X
ejpam-6347	68	20	18	18	NUM
ejpam-6347	68	21	]	]	PUNCT
ejpam-6347	68	22	.	.	PUNCT
ejpam-6347	69	1	this	this	DET
ejpam-6347	69	2	comparison	comparison	NOUN
ejpam-6347	69	3	confirms	confirm	VERB
ejpam-6347	69	4	the	the	DET
ejpam-6347	69	5	model	model	NOUN
ejpam-6347	69	6	’s	’s	PART
ejpam-6347	69	7	capability	capability	NOUN
ejpam-6347	69	8	to	to	PART
ejpam-6347	69	9	realistically	realistically	ADV
ejpam-6347	69	10	represent	represent	VERB
ejpam-6347	69	11	the	the	DET
ejpam-6347	69	12	pandemic	pandemic	ADJ
ejpam-6347	69	13	’s	’s	PART
ejpam-6347	69	14	progression	progression	NOUN
ejpam-6347	69	15	and	and	CCONJ
ejpam-6347	69	16	evaluate	evaluate	VERB
ejpam-6347	69	17	the	the	DET
ejpam-6347	69	18	effectiveness	effectiveness	NOUN
ejpam-6347	69	19	of	of	ADP
ejpam-6347	69	20	various	various	ADJ
ejpam-6347	69	21	public	public	ADJ
ejpam-6347	69	22	health	health	NOUN
ejpam-6347	69	23	measures	measure	NOUN
ejpam-6347	69	24	.	.	PUNCT
ejpam-6347	70	1	despite	despite	SCONJ
ejpam-6347	70	2	the	the	DET
ejpam-6347	70	3	computational	computational	ADJ
ejpam-6347	70	4	challenges	challenge	NOUN
ejpam-6347	70	5	associated	associate	VERB
ejpam-6347	70	6	with	with	ADP
ejpam-6347	70	7	solving	solve	VERB
ejpam-6347	70	8	fractional	fractional	ADJ
ejpam-6347	70	9	differential	differential	ADJ
ejpam-6347	70	10	equations	equation	NOUN
ejpam-6347	70	11	,	,	PUNCT
ejpam-6347	70	12	the	the	DET
ejpam-6347	70	13	proposed	propose	VERB
ejpam-6347	70	14	model	model	NOUN
ejpam-6347	70	15	offers	offer	VERB
ejpam-6347	70	16	a	a	DET
ejpam-6347	70	17	valuable	valuable	ADJ
ejpam-6347	70	18	and	and	CCONJ
ejpam-6347	70	19	flexible	flexible	ADJ
ejpam-6347	70	20	framework	framework	NOUN
ejpam-6347	70	21	for	for	ADP
ejpam-6347	70	22	analyzing	analyze	VERB
ejpam-6347	70	23	the	the	DET
ejpam-6347	70	24	roles	role	NOUN
ejpam-6347	70	25	of	of	ADP
ejpam-6347	70	26	vaccination	vaccination	NOUN
ejpam-6347	70	27	,	,	PUNCT
ejpam-6347	70	28	asymptomatic	asymptomatic	ADJ
ejpam-6347	70	29	carriers	carrier	NOUN
ejpam-6347	70	30	,	,	PUNCT
ejpam-6347	70	31	and	and	CCONJ
ejpam-6347	70	32	control	control	NOUN
ejpam-6347	70	33	strategies	strategy	NOUN
ejpam-6347	70	34	in	in	ADP
ejpam-6347	70	35	managing	manage	VERB
ejpam-6347	70	36	covid-19	covid-19	PROPN
ejpam-6347	70	37	outbreaks	outbreak	NOUN
ejpam-6347	70	38	.	.	PUNCT
ejpam-6347	71	1	n.	n.	NOUN
ejpam-6347	71	2	abbas	abbas	PROPN
ejpam-6347	71	3	,	,	PUNCT
ejpam-6347	71	4	w.	w.	PROPN
ejpam-6347	71	5	shatanawi	shatanawi	PROPN
ejpam-6347	71	6	,	,	PUNCT
ejpam-6347	71	7	s.	s.	PROPN
ejpam-6347	71	8	a.	a.	NOUN
ejpam-6347	71	9	zanib	zanib	PROPN
ejpam-6347	71	10	/	/	SYM
ejpam-6347	71	11	eur	eur	PROPN
ejpam-6347	71	12	.	.	PUNCT
ejpam-6347	72	1	j.	j.	PROPN
ejpam-6347	72	2	pure	pure	PROPN
ejpam-6347	72	3	appl	appl	PROPN
ejpam-6347	72	4	.	.	PROPN
ejpam-6347	72	5	math	math	PROPN
ejpam-6347	72	6	,	,	PUNCT
ejpam-6347	72	7	18	18	NUM
ejpam-6347	72	8	(	(	PUNCT
ejpam-6347	72	9	3	3	NUM
ejpam-6347	72	10	)	)	PUNCT
ejpam-6347	72	11	(	(	PUNCT
ejpam-6347	72	12	2025	2025	NUM
ejpam-6347	72	13	)	)	PUNCT
ejpam-6347	72	14	,	,	PUNCT
ejpam-6347	72	15	6347	6347	NUM
ejpam-6347	72	16	5	5	NUM
ejpam-6347	72	17	of	of	ADP
ejpam-6347	72	18	34	34	NUM
ejpam-6347	72	19	2	2	NUM
ejpam-6347	72	20	.	.	PUNCT
ejpam-6347	72	21	model	model	NOUN
ejpam-6347	72	22	description	description	NOUN
ejpam-6347	72	23	and	and	CCONJ
ejpam-6347	72	24	formulation	formulation	NOUN
ejpam-6347	72	25	table	table	NOUN
ejpam-6347	72	26	1	1	NUM
ejpam-6347	72	27	:	:	PUNCT
ejpam-6347	72	28	list	list	NOUN
ejpam-6347	72	29	of	of	ADP
ejpam-6347	72	30	symbols	symbol	NOUN
ejpam-6347	72	31	,	,	PUNCT
ejpam-6347	72	32	parameters	parameter	NOUN
ejpam-6347	72	33	,	,	PUNCT
ejpam-6347	72	34	and	and	CCONJ
ejpam-6347	72	35	abbreviations	abbreviation	NOUN
ejpam-6347	72	36	state	state	NOUN
ejpam-6347	72	37	variables	variable	NOUN
ejpam-6347	72	38	s(t	s(t	PROPN
ejpam-6347	72	39	)	)	PUNCT
ejpam-6347	72	40	number	number	NOUN
ejpam-6347	72	41	of	of	ADP
ejpam-6347	72	42	susceptible	susceptible	ADJ
ejpam-6347	72	43	individuals	individual	NOUN
ejpam-6347	72	44	at	at	ADP
ejpam-6347	72	45	time	time	NOUN
ejpam-6347	72	46	t	t	PROPN
ejpam-6347	72	47	e(t	e(t	NOUN
ejpam-6347	72	48	)	)	PUNCT
ejpam-6347	72	49	number	number	NOUN
ejpam-6347	72	50	of	of	ADP
ejpam-6347	72	51	pre	pre	ADJ
ejpam-6347	72	52	-	-	ADJ
ejpam-6347	72	53	symptomatic	symptomatic	ADJ
ejpam-6347	72	54	individuals	individual	NOUN
ejpam-6347	72	55	at	at	ADP
ejpam-6347	72	56	time	time	NOUN
ejpam-6347	72	57	t	t	PROPN
ejpam-6347	72	58	u(t	u(t	PROPN
ejpam-6347	72	59	)	)	PUNCT
ejpam-6347	72	60	number	number	NOUN
ejpam-6347	72	61	of	of	ADP
ejpam-6347	72	62	infected	infected	ADJ
ejpam-6347	72	63	individuals	individual	NOUN
ejpam-6347	72	64	at	at	ADP
ejpam-6347	72	65	time	time	NOUN
ejpam-6347	72	66	t	t	PROPN
ejpam-6347	72	67	q(t	q(t	PROPN
ejpam-6347	72	68	)	)	PUNCT
ejpam-6347	72	69	number	number	NOUN
ejpam-6347	72	70	of	of	ADP
ejpam-6347	72	71	quarantined	quarantine	VERB
ejpam-6347	72	72	individuals	individual	NOUN
ejpam-6347	72	73	at	at	ADP
ejpam-6347	72	74	time	time	NOUN
ejpam-6347	72	75	t	t	PROPN
ejpam-6347	72	76	p	p	X
ejpam-6347	72	77	(	(	PUNCT
ejpam-6347	72	78	t	t	NOUN
ejpam-6347	72	79	)	)	PUNCT
ejpam-6347	72	80	number	number	NOUN
ejpam-6347	72	81	of	of	ADP
ejpam-6347	72	82	confirmed	confirm	VERB
ejpam-6347	72	83	positive	positive	ADJ
ejpam-6347	72	84	individuals	individual	NOUN
ejpam-6347	72	85	at	at	ADP
ejpam-6347	72	86	time	time	NOUN
ejpam-6347	72	87	t	t	PROPN
ejpam-6347	72	88	h(t	h(t	PROPN
ejpam-6347	72	89	)	)	PUNCT
ejpam-6347	72	90	number	number	NOUN
ejpam-6347	72	91	of	of	ADP
ejpam-6347	72	92	hospitalized	hospitalize	VERB
ejpam-6347	72	93	individuals	individual	NOUN
ejpam-6347	72	94	in	in	ADP
ejpam-6347	72	95	ordinary	ordinary	ADJ
ejpam-6347	72	96	wards	ward	NOUN
ejpam-6347	72	97	at	at	ADP
ejpam-6347	72	98	time	time	NOUN
ejpam-6347	72	99	t	t	PROPN
ejpam-6347	72	100	c(t	c(t	PROPN
ejpam-6347	72	101	)	)	PUNCT
ejpam-6347	72	102	number	number	NOUN
ejpam-6347	72	103	of	of	ADP
ejpam-6347	72	104	individuals	individual	NOUN
ejpam-6347	72	105	in	in	ADP
ejpam-6347	72	106	intensive	intensive	ADJ
ejpam-6347	72	107	care	care	NOUN
ejpam-6347	72	108	unit	unit	NOUN
ejpam-6347	72	109	at	at	ADP
ejpam-6347	72	110	time	time	NOUN
ejpam-6347	72	111	t	t	PROPN
ejpam-6347	72	112	f	f	PROPN
ejpam-6347	72	113	(	(	PUNCT
ejpam-6347	72	114	t	t	NOUN
ejpam-6347	72	115	)	)	PUNCT
ejpam-6347	72	116	number	number	NOUN
ejpam-6347	72	117	of	of	ADP
ejpam-6347	72	118	asymptomatic	asymptomatic	ADJ
ejpam-6347	72	119	individuals	individual	NOUN
ejpam-6347	72	120	at	at	ADP
ejpam-6347	72	121	time	time	NOUN
ejpam-6347	72	122	t	t	PROPN
ejpam-6347	72	123	v	v	PROPN
ejpam-6347	72	124	(	(	PUNCT
ejpam-6347	72	125	t	t	NOUN
ejpam-6347	72	126	)	)	PUNCT
ejpam-6347	72	127	number	number	NOUN
ejpam-6347	72	128	of	of	ADP
ejpam-6347	72	129	vaccinated	vaccinated	ADJ
ejpam-6347	72	130	individuals	individual	NOUN
ejpam-6347	72	131	at	at	ADP
ejpam-6347	72	132	time	time	NOUN
ejpam-6347	72	133	t	t	NOUN
ejpam-6347	72	134	r(t	r(t	NOUN
ejpam-6347	72	135	)	)	PUNCT
ejpam-6347	72	136	number	number	NOUN
ejpam-6347	72	137	of	of	ADP
ejpam-6347	72	138	recovered	recover	VERB
ejpam-6347	72	139	individuals	individual	NOUN
ejpam-6347	72	140	at	at	ADP
ejpam-6347	72	141	time	time	NOUN
ejpam-6347	72	142	t	t	PROPN
ejpam-6347	72	143	model	model	PROPN
ejpam-6347	72	144	parameters	parameters	PROPN
ejpam-6347	72	145	ϕ	ϕ	PROPN
ejpam-6347	72	146	transmission	transmission	NOUN
ejpam-6347	72	147	rate	rate	NOUN
ejpam-6347	72	148	from	from	ADP
ejpam-6347	72	149	s	s	PRON
ejpam-6347	72	150	to	to	ADP
ejpam-6347	72	151	e	e	PROPN
ejpam-6347	72	152	λ1	λ1	PROPN
ejpam-6347	72	153	transition	transition	NOUN
ejpam-6347	72	154	rate	rate	NOUN
ejpam-6347	72	155	from	from	ADP
ejpam-6347	72	156	e	e	NOUN
ejpam-6347	72	157	to	to	ADP
ejpam-6347	72	158	u	u	NOUN
ejpam-6347	72	159	λ2	λ2	NOUN
ejpam-6347	72	160	transition	transition	NOUN
ejpam-6347	72	161	rate	rate	NOUN
ejpam-6347	72	162	from	from	ADP
ejpam-6347	72	163	e	e	NOUN
ejpam-6347	72	164	to	to	ADP
ejpam-6347	72	165	q	q	PROPN
ejpam-6347	72	166	γ	γ	PROPN
ejpam-6347	72	167	transition	transition	NOUN
ejpam-6347	72	168	rate	rate	NOUN
ejpam-6347	72	169	from	from	ADP
ejpam-6347	72	170	e	e	PROPN
ejpam-6347	72	171	to	to	ADP
ejpam-6347	72	172	v	v	NUM
ejpam-6347	72	173	α1	α1	PROPN
ejpam-6347	72	174	recovery	recovery	NOUN
ejpam-6347	72	175	rate	rate	NOUN
ejpam-6347	72	176	of	of	ADP
ejpam-6347	72	177	u	u	PROPN
ejpam-6347	72	178	α2	α2	ADJ
ejpam-6347	72	179	transition	transition	NOUN
ejpam-6347	72	180	rate	rate	NOUN
ejpam-6347	72	181	from	from	ADP
ejpam-6347	72	182	u	u	PRON
ejpam-6347	72	183	to	to	ADP
ejpam-6347	72	184	p	p	NOUN
ejpam-6347	72	185	b1	b1	NOUN
ejpam-6347	72	186	transition	transition	NOUN
ejpam-6347	72	187	rate	rate	NOUN
ejpam-6347	72	188	from	from	ADP
ejpam-6347	72	189	q	q	NOUN
ejpam-6347	72	190	to	to	ADP
ejpam-6347	72	191	s	s	NOUN
ejpam-6347	72	192	b2	b2	NOUN
ejpam-6347	72	193	transition	transition	NOUN
ejpam-6347	72	194	rate	rate	NOUN
ejpam-6347	72	195	from	from	ADP
ejpam-6347	72	196	q	q	NOUN
ejpam-6347	72	197	to	to	ADP
ejpam-6347	72	198	v	v	NOUN
ejpam-6347	72	199	b3	b3	NOUN
ejpam-6347	72	200	transition	transition	NOUN
ejpam-6347	72	201	rate	rate	NOUN
ejpam-6347	72	202	from	from	ADP
ejpam-6347	72	203	q	q	NOUN
ejpam-6347	72	204	to	to	ADP
ejpam-6347	72	205	p	p	PROPN
ejpam-6347	72	206	φ1	φ1	PROPN
ejpam-6347	72	207	transition	transition	NOUN
ejpam-6347	72	208	rate	rate	NOUN
ejpam-6347	72	209	from	from	ADP
ejpam-6347	72	210	p	p	NOUN
ejpam-6347	72	211	to	to	ADP
ejpam-6347	72	212	h	h	PROPN
ejpam-6347	72	213	φ2	φ2	PROPN
ejpam-6347	72	214	transition	transition	NOUN
ejpam-6347	72	215	rate	rate	NOUN
ejpam-6347	72	216	from	from	ADP
ejpam-6347	72	217	p	p	NOUN
ejpam-6347	72	218	to	to	ADP
ejpam-6347	72	219	c	c	PROPN
ejpam-6347	72	220	φ3	φ3	NOUN
ejpam-6347	72	221	transition	transition	NOUN
ejpam-6347	72	222	rate	rate	NOUN
ejpam-6347	72	223	from	from	ADP
ejpam-6347	72	224	p	p	NOUN
ejpam-6347	72	225	to	to	ADP
ejpam-6347	72	226	f	f	PROPN
ejpam-6347	72	227	m1	m1	PROPN
ejpam-6347	72	228	recovery	recovery	NOUN
ejpam-6347	72	229	rate	rate	NOUN
ejpam-6347	72	230	from	from	ADP
ejpam-6347	72	231	h	h	NOUN
ejpam-6347	72	232	m2	m2	PROPN
ejpam-6347	72	233	transition	transition	NOUN
ejpam-6347	72	234	rate	rate	NOUN
ejpam-6347	72	235	from	from	ADP
ejpam-6347	72	236	h	h	NOUN
ejpam-6347	72	237	to	to	ADP
ejpam-6347	72	238	c	c	PROPN
ejpam-6347	72	239	m3	m3	PROPN
ejpam-6347	72	240	transition	transition	NOUN
ejpam-6347	72	241	rate	rate	NOUN
ejpam-6347	72	242	from	from	ADP
ejpam-6347	72	243	h	h	NOUN
ejpam-6347	72	244	to	to	ADP
ejpam-6347	72	245	f	f	PROPN
ejpam-6347	72	246	σ1	σ1	PROPN
ejpam-6347	72	247	self	self	NOUN
ejpam-6347	72	248	-	-	PUNCT
ejpam-6347	72	249	isolation	isolation	NOUN
ejpam-6347	72	250	rate	rate	NOUN
ejpam-6347	72	251	of	of	ADP
ejpam-6347	72	252	f	f	PROPN
ejpam-6347	72	253	σ2	σ2	PROPN
ejpam-6347	72	254	transition	transition	NOUN
ejpam-6347	72	255	rate	rate	NOUN
ejpam-6347	72	256	from	from	ADP
ejpam-6347	72	257	f	f	PROPN
ejpam-6347	72	258	to	to	ADP
ejpam-6347	72	259	h	h	PROPN
ejpam-6347	72	260	η	η	PROPN
ejpam-6347	72	261	recovery	recovery	NOUN
ejpam-6347	72	262	rate	rate	NOUN
ejpam-6347	72	263	from	from	ADP
ejpam-6347	72	264	c	c	PROPN
ejpam-6347	72	265	to	to	ADP
ejpam-6347	72	266	h	h	PROPN
ejpam-6347	72	267	β	β	NOUN
ejpam-6347	72	268	vaccination	vaccination	NOUN
ejpam-6347	72	269	rate	rate	NOUN
ejpam-6347	72	270	of	of	ADP
ejpam-6347	72	271	s	s	NOUN
ejpam-6347	72	272	λ	λ	NOUN
ejpam-6347	72	273	recruitment	recruitment	NOUN
ejpam-6347	72	274	/	/	SYM
ejpam-6347	72	275	birth	birth	NOUN
ejpam-6347	72	276	rate	rate	NOUN
ejpam-6347	72	277	into	into	ADP
ejpam-6347	72	278	s	s	PRON
ejpam-6347	72	279	µ	µ	PRON
ejpam-6347	72	280	natural	natural	ADJ
ejpam-6347	72	281	death	death	NOUN
ejpam-6347	72	282	rate	rate	NOUN
ejpam-6347	72	283	d1	d1	PROPN
ejpam-6347	72	284	–	–	PUNCT
ejpam-6347	72	285	d7	d7	PROPN
ejpam-6347	72	286	disease	disease	NOUN
ejpam-6347	72	287	-	-	PUNCT
ejpam-6347	72	288	induced	induce	VERB
ejpam-6347	72	289	death	death	NOUN
ejpam-6347	72	290	rates	rate	NOUN
ejpam-6347	72	291	in	in	ADP
ejpam-6347	72	292	e	e	NOUN
ejpam-6347	72	293	,	,	PUNCT
ejpam-6347	72	294	u	u	NOUN
ejpam-6347	72	295	,	,	PUNCT
ejpam-6347	72	296	q	q	X
ejpam-6347	72	297	,	,	PUNCT
ejpam-6347	72	298	p	p	X
ejpam-6347	72	299	,	,	PUNCT
ejpam-6347	72	300	h	h	NOUN
ejpam-6347	72	301	,	,	PUNCT
ejpam-6347	72	302	c	c	NOUN
ejpam-6347	72	303	,	,	PUNCT
ejpam-6347	72	304	and	and	CCONJ
ejpam-6347	72	305	f	f	PROPN
ejpam-6347	72	306	τ	τ	PROPN
ejpam-6347	72	307	loss	loss	NOUN
ejpam-6347	72	308	of	of	ADP
ejpam-6347	72	309	immunity	immunity	NOUN
ejpam-6347	72	310	rate	rate	NOUN
ejpam-6347	72	311	from	from	ADP
ejpam-6347	72	312	r	r	NOUN
ejpam-6347	72	313	to	to	ADP
ejpam-6347	72	314	s	s	NOUN
ejpam-6347	72	315	abbreviations	abbreviation	NOUN
ejpam-6347	72	316	dfep	dfep	NOUN
ejpam-6347	72	317	disease	disease	NOUN
ejpam-6347	72	318	-	-	PUNCT
ejpam-6347	72	319	free	free	ADJ
ejpam-6347	72	320	equilibrium	equilibrium	NOUN
ejpam-6347	72	321	point	point	NOUN
ejpam-6347	72	322	sars	sar	NOUN
ejpam-6347	72	323	-	-	PUNCT
ejpam-6347	72	324	cov-2	cov-2	NOUN
ejpam-6347	72	325	severe	severe	ADJ
ejpam-6347	72	326	acute	acute	ADJ
ejpam-6347	72	327	respiratory	respiratory	ADJ
ejpam-6347	72	328	syndrome	syndrome	NOUN
ejpam-6347	72	329	coronavirus	coronavirus	NOUN
ejpam-6347	72	330	2	2	NUM
ejpam-6347	72	331	covid-19	covid-19	PROPN
ejpam-6347	72	332	coronavirus	coronavirus	NOUN
ejpam-6347	72	333	disease	disease	NOUN
ejpam-6347	72	334	2019	2019	NUM
ejpam-6347	72	335	covcom10	covcom10	NOUN
ejpam-6347	72	336	coronavirus	coronavirus	NOUN
ejpam-6347	72	337	compartment	compartment	NOUN
ejpam-6347	72	338	model	model	NOUN
ejpam-6347	72	339	with	with	ADP
ejpam-6347	72	340	10	10	NUM
ejpam-6347	72	341	compartments	compartment	NOUN
ejpam-6347	72	342	cfd	cfd	NOUN
ejpam-6347	72	343	conformable	conformable	ADJ
ejpam-6347	72	344	fractional	fractional	ADJ
ejpam-6347	72	345	derivative	derivative	ADJ
ejpam-6347	72	346	n.	n.	NOUN
ejpam-6347	72	347	abbas	abbas	PROPN
ejpam-6347	72	348	,	,	PUNCT
ejpam-6347	72	349	w.	w.	PROPN
ejpam-6347	72	350	shatanawi	shatanawi	PROPN
ejpam-6347	72	351	,	,	PUNCT
ejpam-6347	72	352	s.	s.	PROPN
ejpam-6347	72	353	a.	a.	NOUN
ejpam-6347	72	354	zanib	zanib	PROPN
ejpam-6347	72	355	/	/	SYM
ejpam-6347	72	356	eur	eur	PROPN
ejpam-6347	72	357	.	.	PUNCT
ejpam-6347	73	1	j.	j.	PROPN
ejpam-6347	73	2	pure	pure	PROPN
ejpam-6347	73	3	appl	appl	PROPN
ejpam-6347	73	4	.	.	PROPN
ejpam-6347	73	5	math	math	PROPN
ejpam-6347	73	6	,	,	PUNCT
ejpam-6347	73	7	18	18	NUM
ejpam-6347	73	8	(	(	PUNCT
ejpam-6347	73	9	3	3	NUM
ejpam-6347	73	10	)	)	PUNCT
ejpam-6347	73	11	(	(	PUNCT
ejpam-6347	73	12	2025	2025	NUM
ejpam-6347	73	13	)	)	PUNCT
ejpam-6347	73	14	,	,	PUNCT
ejpam-6347	73	15	6347	6347	NUM
ejpam-6347	73	16	6	6	NUM
ejpam-6347	73	17	of	of	ADP
ejpam-6347	73	18	34	34	NUM
ejpam-6347	73	19	the	the	DET
ejpam-6347	73	20	total	total	ADJ
ejpam-6347	73	21	population	population	NOUN
ejpam-6347	73	22	n(t	n(t	NOUN
ejpam-6347	73	23	)	)	PUNCT
ejpam-6347	73	24	is	be	AUX
ejpam-6347	73	25	stratified	stratify	VERB
ejpam-6347	73	26	into	into	ADP
ejpam-6347	73	27	ten	ten	NUM
ejpam-6347	73	28	distinct	distinct	ADJ
ejpam-6347	73	29	epidemiological	epidemiological	ADJ
ejpam-6347	73	30	compartments	compartment	NOUN
ejpam-6347	73	31	to	to	PART
ejpam-6347	73	32	comprehensively	comprehensively	ADV
ejpam-6347	73	33	capture	capture	VERB
ejpam-6347	73	34	the	the	DET
ejpam-6347	73	35	transmission	transmission	NOUN
ejpam-6347	73	36	dynamics	dynamic	NOUN
ejpam-6347	73	37	of	of	ADP
ejpam-6347	73	38	covid-19	covid-19	PROPN
ejpam-6347	73	39	,	,	PUNCT
ejpam-6347	73	40	as	as	SCONJ
ejpam-6347	73	41	illustrated	illustrate	VERB
ejpam-6347	73	42	in	in	ADP
ejpam-6347	73	43	the	the	DET
ejpam-6347	73	44	flowchart	flowchart	NOUN
ejpam-6347	73	45	in	in	ADP
ejpam-6347	73	46	figure	figure	NOUN
ejpam-6347	73	47	2	2	NUM
ejpam-6347	73	48	.	.	PUNCT
ejpam-6347	74	1	the	the	DET
ejpam-6347	74	2	transitions	transition	NOUN
ejpam-6347	74	3	between	between	ADP
ejpam-6347	74	4	these	these	DET
ejpam-6347	74	5	compartments	compartment	NOUN
ejpam-6347	74	6	occur	occur	VERB
ejpam-6347	74	7	in	in	ADP
ejpam-6347	74	8	continuous	continuous	ADJ
ejpam-6347	74	9	time	time	NOUN
ejpam-6347	74	10	and	and	CCONJ
ejpam-6347	74	11	are	be	AUX
ejpam-6347	74	12	governed	govern	VERB
ejpam-6347	74	13	by	by	ADP
ejpam-6347	74	14	a	a	DET
ejpam-6347	74	15	system	system	NOUN
ejpam-6347	74	16	of	of	ADP
ejpam-6347	74	17	nonlinear	nonlinear	ADJ
ejpam-6347	74	18	ordinary	ordinary	ADJ
ejpam-6347	74	19	differential	differential	ADJ
ejpam-6347	74	20	equations	equation	NOUN
ejpam-6347	74	21	.	.	PUNCT
ejpam-6347	75	1	figure	figure	VERB
ejpam-6347	75	2	2	2	NUM
ejpam-6347	75	3	:	:	PUNCT
ejpam-6347	75	4	schematic	schematic	ADJ
ejpam-6347	75	5	diagram	diagram	NOUN
ejpam-6347	75	6	of	of	ADP
ejpam-6347	75	7	the	the	DET
ejpam-6347	75	8	covcom10	covcom10	NOUN
ejpam-6347	75	9	compartmental	compartmental	ADJ
ejpam-6347	75	10	model	model	NOUN
ejpam-6347	75	11	.	.	PUNCT
ejpam-6347	76	1	the	the	DET
ejpam-6347	76	2	governing	govern	VERB
ejpam-6347	76	3	system	system	NOUN
ejpam-6347	76	4	for	for	ADP
ejpam-6347	76	5	the	the	DET
ejpam-6347	76	6	model	model	NOUN
ejpam-6347	76	7	is	be	AUX
ejpam-6347	76	8	system	system	NOUN
ejpam-6347	76	9	of	of	ADP
ejpam-6347	76	10	differential	differential	ADJ
ejpam-6347	76	11	equations	equation	NOUN
ejpam-6347	76	12	shown	show	VERB
ejpam-6347	76	13	below	below	ADV
ejpam-6347	76	14	:	:	PUNCT
ejpam-6347	76	15	ds	ds	ADP
ejpam-6347	76	16	dt	dt	NOUN
ejpam-6347	76	17	=	=	PUNCT
ejpam-6347	76	18	λ+	λ+	PUNCT
ejpam-6347	76	19	τr+	τr+	PROPN
ejpam-6347	76	20	b2q−	b2q−	PROPN
ejpam-6347	76	21	(	(	PUNCT
ejpam-6347	76	22	ϕe	ϕe	X
ejpam-6347	76	23	+	+	X
ejpam-6347	76	24	β	β	X
ejpam-6347	76	25	+	+	SYM
ejpam-6347	76	26	µ)s	µ)s	NOUN
ejpam-6347	76	27	,	,	PUNCT
ejpam-6347	76	28	de	de	X
ejpam-6347	76	29	dt	dt	X
ejpam-6347	76	30	=	=	PUNCT
ejpam-6347	76	31	ϕes	ϕes	PROPN
ejpam-6347	76	32	+	+	CCONJ
ejpam-6347	76	33	γ	γ	X
ejpam-6347	76	34	v	v	X
ejpam-6347	76	35	e	e	X
ejpam-6347	76	36	−	−	PROPN
ejpam-6347	76	37	(	(	PUNCT
ejpam-6347	76	38	λ1u	λ1u	PROPN
ejpam-6347	76	39	+	+	NUM
ejpam-6347	76	40	λ2q+	λ2q+	PROPN
ejpam-6347	76	41	µ+	µ+	X
ejpam-6347	76	42	d1)e	d1)e	NOUN
ejpam-6347	76	43	,	,	PUNCT
ejpam-6347	76	44	du	du	PROPN
ejpam-6347	76	45	dt	dt	NOUN
ejpam-6347	77	1	=	=	PUNCT
ejpam-6347	77	2	λ1eu	λ1eu	PUNCT
ejpam-6347	77	3	−	−	PROPN
ejpam-6347	77	4	(	(	PUNCT
ejpam-6347	77	5	α1	α1	PROPN
ejpam-6347	77	6	+	+	CCONJ
ejpam-6347	77	7	α2	α2	ADJ
ejpam-6347	77	8	+	+	CCONJ
ejpam-6347	77	9	µ+	µ+	PUNCT
ejpam-6347	77	10	d2)u	d2)u	NOUN
ejpam-6347	77	11	,	,	PUNCT
ejpam-6347	77	12	dq	dq	NOUN
ejpam-6347	77	13	dt	dt	NOUN
ejpam-6347	78	1	=	=	SYM
ejpam-6347	78	2	λ2eq−	λ2eq−	PROPN
ejpam-6347	78	3	(	(	PUNCT
ejpam-6347	78	4	b1	b1	NOUN
ejpam-6347	78	5	+	+	CCONJ
ejpam-6347	78	6	b2	b2	NOUN
ejpam-6347	78	7	+	+	CCONJ
ejpam-6347	78	8	b3	b3	PROPN
ejpam-6347	78	9	+	+	CCONJ
ejpam-6347	78	10	µ+	µ+	X
ejpam-6347	78	11	d3)q	d3)q	NOUN
ejpam-6347	78	12	,	,	PUNCT
ejpam-6347	78	13	dp	dp	NOUN
ejpam-6347	78	14	dt	dt	NOUN
ejpam-6347	78	15	=	=	PUNCT
ejpam-6347	78	16	α2u	α2u	PROPN
ejpam-6347	78	17	+	+	CCONJ
ejpam-6347	78	18	b1q−	b1q−	X
ejpam-6347	78	19	(	(	PUNCT
ejpam-6347	78	20	φ1	φ1	NOUN
ejpam-6347	78	21	+	+	CCONJ
ejpam-6347	78	22	φ2	φ2	NOUN
ejpam-6347	78	23	+	+	NUM
ejpam-6347	78	24	φ3	φ3	NOUN
ejpam-6347	78	25	+	+	CCONJ
ejpam-6347	78	26	µ+	µ+	PUNCT
ejpam-6347	78	27	d4)p	d4)p	NOUN
ejpam-6347	78	28	,	,	PUNCT
ejpam-6347	78	29	dh	dh	NOUN
ejpam-6347	78	30	dt	dt	NOUN
ejpam-6347	78	31	=	=	PUNCT
ejpam-6347	79	1	φ1p	φ1p	VERB
ejpam-6347	79	2	+	+	NUM
ejpam-6347	79	3	η	η	PROPN
ejpam-6347	79	4	c	c	PROPN
ejpam-6347	79	5	+	+	PROPN
ejpam-6347	79	6	σ2f	σ2f	PROPN
ejpam-6347	79	7	−	−	PROPN
ejpam-6347	79	8	(	(	PUNCT
ejpam-6347	79	9	m1	m1	PROPN
ejpam-6347	79	10	+	+	PROPN
ejpam-6347	79	11	m2	m2	PROPN
ejpam-6347	79	12	+	+	PROPN
ejpam-6347	79	13	m3	m3	PROPN
ejpam-6347	79	14	+	+	CCONJ
ejpam-6347	79	15	µ+	µ+	PUNCT
ejpam-6347	79	16	d5)h	d5)h	NOUN
ejpam-6347	79	17	,	,	PUNCT
ejpam-6347	79	18	dc	dc	PROPN
ejpam-6347	79	19	dt	dt	NOUN
ejpam-6347	79	20	=	=	PUNCT
ejpam-6347	79	21	φ2p	φ2p	VERB
ejpam-6347	79	22	+	+	PROPN
ejpam-6347	79	23	m2h	m2h	ADJ
ejpam-6347	79	24	−	−	PROPN
ejpam-6347	79	25	(	(	PUNCT
ejpam-6347	79	26	η	η	PROPN
ejpam-6347	79	27	+	+	PROPN
ejpam-6347	79	28	µ+	µ+	PROPN
ejpam-6347	79	29	d6)c	d6)c	NOUN
ejpam-6347	79	30	,	,	PUNCT
ejpam-6347	79	31	df	df	NOUN
ejpam-6347	79	32	dt	dt	NOUN
ejpam-6347	80	1	=	=	PUNCT
ejpam-6347	80	2	φ3p	φ3p	NUM
ejpam-6347	80	3	+	+	NOUN
ejpam-6347	80	4	m3h	m3h	NOUN
ejpam-6347	80	5	−	−	PROPN
ejpam-6347	80	6	(	(	PUNCT
ejpam-6347	80	7	σ1	σ1	PROPN
ejpam-6347	80	8	+	+	CCONJ
ejpam-6347	80	9	σ2	σ2	PROPN
ejpam-6347	80	10	+	+	CCONJ
ejpam-6347	80	11	µ+	µ+	PROPN
ejpam-6347	80	12	d7)f	d7)f	PROPN
ejpam-6347	80	13	,	,	PUNCT
ejpam-6347	80	14	dv	dv	PROPN
ejpam-6347	80	15	dt	dt	X
ejpam-6347	81	1	=	=	PUNCT
ejpam-6347	81	2	β	β	X
ejpam-6347	81	3	s	s	X
ejpam-6347	81	4	+	+	CCONJ
ejpam-6347	81	5	b3q−	b3q−	PROPN
ejpam-6347	81	6	(	(	PUNCT
ejpam-6347	81	7	γ	γ	X
ejpam-6347	81	8	e	e	PROPN
ejpam-6347	81	9	+	+	X
ejpam-6347	81	10	µ)v	µ)v	ADJ
ejpam-6347	81	11	,	,	PUNCT
ejpam-6347	81	12	dr	dr	PROPN
ejpam-6347	81	13	dt	dt	NOUN
ejpam-6347	81	14	=	=	PUNCT
ejpam-6347	81	15	σ1f	σ1f	PROPN
ejpam-6347	81	16	+	+	CCONJ
ejpam-6347	81	17	α1u	α1u	PROPN
ejpam-6347	82	1	+	+	NOUN
ejpam-6347	82	2	m1h	m1h	X
ejpam-6347	82	3	−	−	PROPN
ejpam-6347	82	4	(	(	PUNCT
ejpam-6347	82	5	τ	τ	X
ejpam-6347	82	6	+	+	NOUN
ejpam-6347	82	7	µ)r	µ)r	NOUN
ejpam-6347	82	8	.	.	PUNCT
ejpam-6347	83	1	(	(	PUNCT
ejpam-6347	83	2	2.1	2.1	NUM
ejpam-6347	83	3	)	)	PUNCT
ejpam-6347	83	4	n.	n.	NOUN
ejpam-6347	83	5	abbas	abbas	PROPN
ejpam-6347	83	6	,	,	PUNCT
ejpam-6347	83	7	w.	w.	PROPN
ejpam-6347	83	8	shatanawi	shatanawi	PROPN
ejpam-6347	83	9	,	,	PUNCT
ejpam-6347	83	10	s.	s.	PROPN
ejpam-6347	83	11	a.	a.	NOUN
ejpam-6347	83	12	zanib	zanib	PROPN
ejpam-6347	83	13	/	/	SYM
ejpam-6347	83	14	eur	eur	PROPN
ejpam-6347	83	15	.	.	PUNCT
ejpam-6347	84	1	j.	j.	PROPN
ejpam-6347	84	2	pure	pure	PROPN
ejpam-6347	84	3	appl	appl	PROPN
ejpam-6347	84	4	.	.	PROPN
ejpam-6347	84	5	math	math	PROPN
ejpam-6347	84	6	,	,	PUNCT
ejpam-6347	84	7	18	18	NUM
ejpam-6347	84	8	(	(	PUNCT
ejpam-6347	84	9	3	3	NUM
ejpam-6347	84	10	)	)	PUNCT
ejpam-6347	84	11	(	(	PUNCT
ejpam-6347	84	12	2025	2025	NUM
ejpam-6347	84	13	)	)	PUNCT
ejpam-6347	84	14	,	,	PUNCT
ejpam-6347	84	15	6347	6347	NUM
ejpam-6347	84	16	7	7	NUM
ejpam-6347	84	17	of	of	ADP
ejpam-6347	84	18	34	34	NUM
ejpam-6347	84	19	therefore	therefore	ADV
ejpam-6347	84	20	,	,	PUNCT
ejpam-6347	84	21	n(t	n(t	PROPN
ejpam-6347	84	22	)	)	PUNCT
ejpam-6347	84	23	=	=	PUNCT
ejpam-6347	84	24	s(t	s(t	PROPN
ejpam-6347	84	25	)	)	PUNCT
ejpam-6347	84	26	+	+	SYM
ejpam-6347	84	27	e(t	e(t	NOUN
ejpam-6347	84	28	)	)	PUNCT
ejpam-6347	85	1	+	+	CCONJ
ejpam-6347	85	2	u(t	u(t	NOUN
ejpam-6347	85	3	)	)	PUNCT
ejpam-6347	86	1	+	+	NOUN
ejpam-6347	86	2	q(t	q(t	NOUN
ejpam-6347	86	3	)	)	PUNCT
ejpam-6347	86	4	+	+	NOUN
ejpam-6347	86	5	p	p	X
ejpam-6347	86	6	(	(	PUNCT
ejpam-6347	86	7	t	t	PROPN
ejpam-6347	86	8	)	)	PUNCT
ejpam-6347	86	9	+	+	NOUN
ejpam-6347	86	10	h(t	h(t	X
ejpam-6347	86	11	)	)	PUNCT
ejpam-6347	86	12	+	+	CCONJ
ejpam-6347	86	13	c(t	c(t	PROPN
ejpam-6347	86	14	)	)	PUNCT
ejpam-6347	86	15	+	+	NUM
ejpam-6347	86	16	f	f	X
ejpam-6347	86	17	(	(	PUNCT
ejpam-6347	86	18	t	t	PROPN
ejpam-6347	86	19	)	)	PUNCT
ejpam-6347	87	1	+	+	X
ejpam-6347	87	2	v	v	X
ejpam-6347	87	3	(	(	PUNCT
ejpam-6347	87	4	t	t	NOUN
ejpam-6347	87	5	)	)	PUNCT
ejpam-6347	87	6	+	+	NOUN
ejpam-6347	87	7	r(t	r(t	NOUN
ejpam-6347	87	8	)	)	PUNCT
ejpam-6347	87	9	.	.	PUNCT
ejpam-6347	88	1	each	each	DET
ejpam-6347	88	2	compartment	compartment	NOUN
ejpam-6347	88	3	,	,	PUNCT
ejpam-6347	88	4	along	along	ADP
ejpam-6347	88	5	with	with	ADP
ejpam-6347	88	6	its	its	PRON
ejpam-6347	88	7	associated	associated	ADJ
ejpam-6347	88	8	abbreviation	abbreviation	NOUN
ejpam-6347	88	9	and	and	CCONJ
ejpam-6347	88	10	biological	biological	ADJ
ejpam-6347	88	11	interpretation	interpretation	NOUN
ejpam-6347	88	12	,	,	PUNCT
ejpam-6347	88	13	is	be	AUX
ejpam-6347	88	14	detailed	detail	VERB
ejpam-6347	88	15	in	in	ADP
ejpam-6347	88	16	table	table	NOUN
ejpam-6347	88	17	1	1	NUM
ejpam-6347	88	18	,	,	PUNCT
ejpam-6347	88	19	which	which	PRON
ejpam-6347	88	20	also	also	ADV
ejpam-6347	88	21	includes	include	VERB
ejpam-6347	88	22	a	a	DET
ejpam-6347	88	23	complete	complete	ADJ
ejpam-6347	88	24	list	list	NOUN
ejpam-6347	88	25	of	of	ADP
ejpam-6347	88	26	model	model	NOUN
ejpam-6347	88	27	parameters	parameter	NOUN
ejpam-6347	88	28	and	and	CCONJ
ejpam-6347	88	29	their	their	PRON
ejpam-6347	88	30	descriptions	description	NOUN
ejpam-6347	88	31	.	.	PUNCT
ejpam-6347	89	1	fractional	fractional	ADJ
ejpam-6347	89	2	-	-	PUNCT
ejpam-6347	89	3	order	order	NOUN
ejpam-6347	89	4	model	model	NOUN
ejpam-6347	89	5	formulation	formulation	PROPN
ejpam-6347	89	6	khalil	khalil	PROPN
ejpam-6347	89	7	et	et	PROPN
ejpam-6347	89	8	al	al	PROPN
ejpam-6347	89	9	.	.	PUNCT
ejpam-6347	90	1	[	[	X
ejpam-6347	90	2	19	19	NUM
ejpam-6347	90	3	]	]	PUNCT
ejpam-6347	90	4	introduced	introduce	VERB
ejpam-6347	90	5	the	the	DET
ejpam-6347	90	6	conformable	conformable	ADJ
ejpam-6347	90	7	fractional	fractional	ADJ
ejpam-6347	90	8	derivative	derivative	NOUN
ejpam-6347	90	9	(	(	PUNCT
ejpam-6347	90	10	cfd	cfd	NOUN
ejpam-6347	90	11	)	)	PUNCT
ejpam-6347	90	12	,	,	PUNCT
ejpam-6347	90	13	a	a	DET
ejpam-6347	90	14	mathematical	mathematical	ADJ
ejpam-6347	90	15	operator	operator	NOUN
ejpam-6347	90	16	that	that	PRON
ejpam-6347	90	17	generalizes	generalize	VERB
ejpam-6347	90	18	classical	classical	ADJ
ejpam-6347	90	19	calculus	calculus	NOUN
ejpam-6347	90	20	while	while	SCONJ
ejpam-6347	90	21	maintaining	maintain	VERB
ejpam-6347	90	22	key	key	ADJ
ejpam-6347	90	23	differential	differential	ADJ
ejpam-6347	90	24	properties	property	NOUN
ejpam-6347	90	25	.	.	PUNCT
ejpam-6347	91	1	the	the	DET
ejpam-6347	91	2	cfd	cfd	NOUN
ejpam-6347	91	3	of	of	ADP
ejpam-6347	91	4	order	order	NOUN
ejpam-6347	91	5	ζ	ζ	X
ejpam-6347	91	6	∈	∈	NOUN
ejpam-6347	91	7	(	(	PUNCT
ejpam-6347	91	8	0	0	NUM
ejpam-6347	91	9	,	,	PUNCT
ejpam-6347	91	10	1	1	NUM
ejpam-6347	91	11	]	]	PUNCT
ejpam-6347	91	12	is	be	AUX
ejpam-6347	91	13	defined	define	VERB
ejpam-6347	91	14	as	as	ADP
ejpam-6347	91	15	:	:	PUNCT
ejpam-6347	91	16	dζ	dζ	NOUN
ejpam-6347	91	17	tm(t	tm(t	NOUN
ejpam-6347	91	18	)	)	PUNCT
ejpam-6347	92	1	=	=	VERB
ejpam-6347	92	2	lim	lim	PROPN
ejpam-6347	92	3	ϵ→0	ϵ→0	X
ejpam-6347	92	4	m(t+	m(t+	PROPN
ejpam-6347	92	5	ϵt1−ζ)−m(t	ϵt1−ζ)−m(t	NOUN
ejpam-6347	92	6	)	)	PUNCT
ejpam-6347	92	7	ϵ	ϵ	NOUN
ejpam-6347	92	8	,	,	PUNCT
ejpam-6347	92	9	(	(	PUNCT
ejpam-6347	92	10	2.2	2.2	NUM
ejpam-6347	92	11	)	)	PUNCT
ejpam-6347	92	12	which	which	PRON
ejpam-6347	92	13	simplifies	simplify	VERB
ejpam-6347	92	14	to	to	ADP
ejpam-6347	92	15	the	the	DET
ejpam-6347	92	16	classical	classical	ADJ
ejpam-6347	92	17	derivative	derivative	NOUN
ejpam-6347	92	18	when	when	SCONJ
ejpam-6347	92	19	ζ	ζ	NOUN
ejpam-6347	92	20	=	=	SYM
ejpam-6347	92	21	1	1	X
ejpam-6347	92	22	.	.	PUNCT
ejpam-6347	93	1	this	this	DET
ejpam-6347	93	2	operator	operator	NOUN
ejpam-6347	93	3	satisfies	satisfy	VERB
ejpam-6347	93	4	the	the	DET
ejpam-6347	93	5	composition	composition	NOUN
ejpam-6347	93	6	rule	rule	NOUN
ejpam-6347	93	7	:	:	PUNCT
ejpam-6347	93	8	dζ	dζ	NOUN
ejpam-6347	93	9	tm(t	tm(t	NOUN
ejpam-6347	93	10	)	)	PUNCT
ejpam-6347	94	1	=	=	SYM
ejpam-6347	94	2	t1−ζ	t1−ζ	PROPN
ejpam-6347	95	1	dm	dm	NOUN
ejpam-6347	95	2	dt	dt	INTJ
ejpam-6347	95	3	.	.	PUNCT
ejpam-6347	96	1	(	(	PUNCT
ejpam-6347	96	2	2.3	2.3	NUM
ejpam-6347	96	3	)	)	PUNCT
ejpam-6347	96	4	to	to	PART
ejpam-6347	96	5	capture	capture	VERB
ejpam-6347	96	6	memory	memory	NOUN
ejpam-6347	96	7	effects	effect	NOUN
ejpam-6347	96	8	in	in	ADP
ejpam-6347	96	9	covid-19	covid-19	PROPN
ejpam-6347	96	10	transmission	transmission	NOUN
ejpam-6347	96	11	,	,	PUNCT
ejpam-6347	96	12	we	we	PRON
ejpam-6347	96	13	reformulate	reformulate	VERB
ejpam-6347	96	14	the	the	DET
ejpam-6347	96	15	covcom10	covcom10	NOUN
ejpam-6347	96	16	model	model	NOUN
ejpam-6347	96	17	(	(	PUNCT
ejpam-6347	96	18	2.1	2.1	NUM
ejpam-6347	96	19	)	)	PUNCT
ejpam-6347	96	20	using	use	VERB
ejpam-6347	96	21	the	the	DET
ejpam-6347	96	22	cfd	cfd	NOUN
ejpam-6347	96	23	framework	framework	NOUN
ejpam-6347	96	24	[	[	X
ejpam-6347	96	25	19	19	NUM
ejpam-6347	96	26	]	]	X
ejpam-6347	96	27	:	:	PUNCT
ejpam-6347	96	28	dζ	dζ	PROPN
ejpam-6347	96	29	t	t	PROPN
ejpam-6347	96	30	s	s	PART
ejpam-6347	96	31	=	=	PUNCT
ejpam-6347	96	32	λ+	λ+	PUNCT
ejpam-6347	96	33	τr+	τr+	PROPN
ejpam-6347	96	34	b2q−	b2q−	PROPN
ejpam-6347	96	35	(	(	PUNCT
ejpam-6347	96	36	ϕe	ϕe	X
ejpam-6347	96	37	+	+	X
ejpam-6347	96	38	β	β	X
ejpam-6347	96	39	+	+	SYM
ejpam-6347	96	40	µ)s	µ)s	NOUN
ejpam-6347	96	41	,	,	PUNCT
ejpam-6347	96	42	dζ	dζ	PROPN
ejpam-6347	96	43	te	te	PROPN
ejpam-6347	96	44	=	=	PUNCT
ejpam-6347	96	45	ϕes	ϕes	PROPN
ejpam-6347	96	46	+	+	CCONJ
ejpam-6347	96	47	γv	γv	NOUN
ejpam-6347	96	48	e	e	X
ejpam-6347	96	49	−	−	PROPN
ejpam-6347	96	50	(	(	PUNCT
ejpam-6347	96	51	λ1u	λ1u	PROPN
ejpam-6347	96	52	+	+	NUM
ejpam-6347	96	53	λ2q+	λ2q+	PROPN
ejpam-6347	96	54	µ+	µ+	X
ejpam-6347	96	55	d1)e	d1)e	NOUN
ejpam-6347	96	56	,	,	PUNCT
ejpam-6347	96	57	dζ	dζ	PROPN
ejpam-6347	96	58	tu	tu	PROPN
ejpam-6347	96	59	=	=	PUNCT
ejpam-6347	96	60	λ1eu	λ1eu	PUNCT
ejpam-6347	96	61	−	−	PROPN
ejpam-6347	96	62	(	(	PUNCT
ejpam-6347	96	63	α1	α1	PROPN
ejpam-6347	96	64	+	+	CCONJ
ejpam-6347	96	65	α2	α2	ADJ
ejpam-6347	96	66	+	+	CCONJ
ejpam-6347	96	67	µ+	µ+	PUNCT
ejpam-6347	96	68	d2)u	d2)u	NOUN
ejpam-6347	96	69	,	,	PUNCT
ejpam-6347	96	70	dζ	dζ	VERB
ejpam-6347	96	71	tq	tq	ADP
ejpam-6347	96	72	=	=	SYM
ejpam-6347	96	73	λ2eq−	λ2eq−	PROPN
ejpam-6347	96	74	(	(	PUNCT
ejpam-6347	96	75	b1	b1	NOUN
ejpam-6347	96	76	+	+	CCONJ
ejpam-6347	96	77	b2	b2	NOUN
ejpam-6347	96	78	+	+	CCONJ
ejpam-6347	96	79	b3	b3	PROPN
ejpam-6347	96	80	+	+	CCONJ
ejpam-6347	96	81	µ+	µ+	X
ejpam-6347	96	82	d3)q	d3)q	NOUN
ejpam-6347	96	83	,	,	PUNCT
ejpam-6347	96	84	dζ	dζ	PROPN
ejpam-6347	96	85	tp	tp	ADP
ejpam-6347	96	86	=	=	PUNCT
ejpam-6347	96	87	α2u	α2u	PROPN
ejpam-6347	96	88	+	+	CCONJ
ejpam-6347	96	89	b1q−	b1q−	X
ejpam-6347	96	90	(	(	PUNCT
ejpam-6347	96	91	φ1	φ1	NOUN
ejpam-6347	96	92	+	+	CCONJ
ejpam-6347	96	93	φ2	φ2	NOUN
ejpam-6347	96	94	+	+	NUM
ejpam-6347	96	95	φ3	φ3	NOUN
ejpam-6347	96	96	+	+	CCONJ
ejpam-6347	96	97	µ+	µ+	PUNCT
ejpam-6347	96	98	d4)p	d4)p	NOUN
ejpam-6347	96	99	,	,	PUNCT
ejpam-6347	96	100	dζ	dζ	PROPN
ejpam-6347	96	101	th	th	X
ejpam-6347	96	102	=	=	PUNCT
ejpam-6347	96	103	φ1p	φ1p	PUNCT
ejpam-6347	96	104	+	+	CCONJ
ejpam-6347	96	105	ηc	ηc	PRON
ejpam-6347	96	106	+	+	NOUN
ejpam-6347	96	107	σ2f	σ2f	NOUN
ejpam-6347	96	108	−	−	PROPN
ejpam-6347	96	109	(	(	PUNCT
ejpam-6347	96	110	m1	m1	PROPN
ejpam-6347	96	111	+	+	PROPN
ejpam-6347	96	112	m2	m2	PROPN
ejpam-6347	96	113	+	+	PROPN
ejpam-6347	96	114	m3	m3	PROPN
ejpam-6347	96	115	+	+	CCONJ
ejpam-6347	96	116	µ+	µ+	PUNCT
ejpam-6347	96	117	d5)h	d5)h	NOUN
ejpam-6347	96	118	,	,	PUNCT
ejpam-6347	96	119	dζ	dζ	PROPN
ejpam-6347	96	120	tc	tc	NOUN
ejpam-6347	96	121	=	=	PUNCT
ejpam-6347	96	122	φ2p	φ2p	VERB
ejpam-6347	96	123	+	+	PROPN
ejpam-6347	96	124	m2h	m2h	ADJ
ejpam-6347	96	125	−	−	PROPN
ejpam-6347	96	126	(	(	PUNCT
ejpam-6347	96	127	η	η	PROPN
ejpam-6347	96	128	+	+	PROPN
ejpam-6347	96	129	µ+	µ+	PROPN
ejpam-6347	96	130	d6)c	d6)c	NOUN
ejpam-6347	96	131	,	,	PUNCT
ejpam-6347	96	132	dζ	dζ	PROPN
ejpam-6347	96	133	tf	tf	PROPN
ejpam-6347	96	134	=	=	PUNCT
ejpam-6347	96	135	φ3p	φ3p	PROPN
ejpam-6347	96	136	+	+	PROPN
ejpam-6347	96	137	m3h	m3h	NOUN
ejpam-6347	96	138	−	−	PROPN
ejpam-6347	97	1	(	(	PUNCT
ejpam-6347	97	2	σ1	σ1	PROPN
ejpam-6347	97	3	+	+	CCONJ
ejpam-6347	97	4	σ2	σ2	PROPN
ejpam-6347	97	5	+	+	CCONJ
ejpam-6347	97	6	µ+	µ+	PROPN
ejpam-6347	97	7	d7)f	d7)f	PROPN
ejpam-6347	97	8	,	,	PUNCT
ejpam-6347	97	9	dζ	dζ	PROPN
ejpam-6347	97	10	t	t	PROPN
ejpam-6347	97	11	v	v	NOUN
ejpam-6347	97	12	=	=	SYM
ejpam-6347	97	13	βs	β	NOUN
ejpam-6347	98	1	+	+	NUM
ejpam-6347	98	2	b3q−	b3q−	X
ejpam-6347	98	3	(	(	PUNCT
ejpam-6347	98	4	γe	γe	X
ejpam-6347	98	5	+	+	CCONJ
ejpam-6347	98	6	µ)v	µ)v	ADJ
ejpam-6347	98	7	,	,	PUNCT
ejpam-6347	98	8	dζ	dζ	PROPN
ejpam-6347	98	9	tr	tr	VERB
ejpam-6347	98	10	=	=	SYM
ejpam-6347	98	11	σ1f	σ1f	NOUN
ejpam-6347	98	12	+	+	CCONJ
ejpam-6347	98	13	α1u	α1u	PROPN
ejpam-6347	99	1	+	+	NOUN
ejpam-6347	99	2	m1h	m1h	X
ejpam-6347	99	3	−	−	PROPN
ejpam-6347	99	4	(	(	PUNCT
ejpam-6347	99	5	τ	τ	X
ejpam-6347	99	6	+	+	NOUN
ejpam-6347	99	7	µ)r	µ)r	NOUN
ejpam-6347	99	8	.	.	PUNCT
ejpam-6347	100	1	(	(	PUNCT
ejpam-6347	100	2	2.4	2.4	NUM
ejpam-6347	100	3	)	)	PUNCT
ejpam-6347	100	4	the	the	DET
ejpam-6347	100	5	system	system	NOUN
ejpam-6347	100	6	is	be	AUX
ejpam-6347	100	7	solved	solve	VERB
ejpam-6347	100	8	under	under	ADP
ejpam-6347	100	9	non	non	ADJ
ejpam-6347	100	10	-	-	ADJ
ejpam-6347	100	11	negative	negative	ADJ
ejpam-6347	100	12	initial	initial	ADJ
ejpam-6347	100	13	conditions	condition	NOUN
ejpam-6347	100	14	:	:	PUNCT
ejpam-6347	100	15	s(0	s(0	PROPN
ejpam-6347	100	16	)	)	PUNCT
ejpam-6347	100	17	=	=	PROPN
ejpam-6347	100	18	s0	s0	PROPN
ejpam-6347	100	19	≥	≥	NUM
ejpam-6347	100	20	0	0	NUM
ejpam-6347	100	21	,	,	PUNCT
ejpam-6347	100	22	e(0	e(0	NOUN
ejpam-6347	100	23	)	)	PUNCT
ejpam-6347	100	24	=	=	SYM
ejpam-6347	100	25	e0	e0	PROPN
ejpam-6347	100	26	≥	≥	NUM
ejpam-6347	100	27	0	0	NUM
ejpam-6347	100	28	,	,	PUNCT
ejpam-6347	100	29	u(0	u(0	NOUN
ejpam-6347	100	30	)	)	PUNCT
ejpam-6347	100	31	=	=	PUNCT
ejpam-6347	100	32	u0	u0	ADJ
ejpam-6347	100	33	≥	≥	NOUN
ejpam-6347	100	34	0	0	NUM
ejpam-6347	100	35	,	,	PUNCT
ejpam-6347	100	36	q(0	q(0	PROPN
ejpam-6347	100	37	)	)	PUNCT
ejpam-6347	101	1	=	=	VERB
ejpam-6347	101	2	q0	q0	VERB
ejpam-6347	101	3	≥	≥	NOUN
ejpam-6347	101	4	0	0	NUM
ejpam-6347	101	5	,	,	PUNCT
ejpam-6347	101	6	p	p	X
ejpam-6347	101	7	(	(	PUNCT
ejpam-6347	101	8	0	0	NUM
ejpam-6347	101	9	)	)	PUNCT
ejpam-6347	101	10	=	=	NOUN
ejpam-6347	101	11	p0	p0	NOUN
ejpam-6347	101	12	≥	≥	NUM
ejpam-6347	101	13	0	0	NUM
ejpam-6347	101	14	,	,	PUNCT
ejpam-6347	101	15	h(0	h(0	PROPN
ejpam-6347	101	16	)	)	PUNCT
ejpam-6347	101	17	=	=	SYM
ejpam-6347	101	18	h0	h0	NOUN
ejpam-6347	101	19	≥	≥	NOUN
ejpam-6347	101	20	0	0	NUM
ejpam-6347	101	21	,	,	PUNCT
ejpam-6347	101	22	c(0	c(0	NOUN
ejpam-6347	101	23	)	)	PUNCT
ejpam-6347	102	1	=	=	SYM
ejpam-6347	102	2	c0	c0	X
ejpam-6347	102	3	≥	≥	NUM
ejpam-6347	102	4	0	0	NUM
ejpam-6347	102	5	,	,	PUNCT
ejpam-6347	102	6	f	f	PROPN
ejpam-6347	102	7	(	(	PUNCT
ejpam-6347	102	8	0	0	NUM
ejpam-6347	102	9	)	)	PUNCT
ejpam-6347	102	10	=	=	SYM
ejpam-6347	102	11	f0	f0	X
ejpam-6347	102	12	≥	≥	NOUN
ejpam-6347	102	13	0	0	NUM
ejpam-6347	102	14	,	,	PUNCT
ejpam-6347	102	15	v	v	NOUN
ejpam-6347	102	16	(	(	PUNCT
ejpam-6347	102	17	0	0	NUM
ejpam-6347	102	18	)	)	PUNCT
ejpam-6347	102	19	=	=	SYM
ejpam-6347	102	20	v0	v0	NOUN
ejpam-6347	102	21	≥	≥	NOUN
ejpam-6347	102	22	0	0	NUM
ejpam-6347	102	23	,	,	PUNCT
ejpam-6347	102	24	r(0	r(0	PROPN
ejpam-6347	102	25	)	)	PUNCT
ejpam-6347	102	26	=	=	PUNCT
ejpam-6347	102	27	r0	r0	NOUN
ejpam-6347	102	28	≥	≥	NOUN
ejpam-6347	102	29	0	0	NUM
ejpam-6347	102	30	.	.	PUNCT
ejpam-6347	103	1	(	(	PUNCT
ejpam-6347	103	2	2.5	2.5	NUM
ejpam-6347	103	3	)	)	PUNCT
ejpam-6347	103	4	n.	n.	NOUN
ejpam-6347	103	5	abbas	abbas	PROPN
ejpam-6347	103	6	,	,	PUNCT
ejpam-6347	103	7	w.	w.	PROPN
ejpam-6347	103	8	shatanawi	shatanawi	PROPN
ejpam-6347	103	9	,	,	PUNCT
ejpam-6347	103	10	s.	s.	PROPN
ejpam-6347	103	11	a.	a.	NOUN
ejpam-6347	103	12	zanib	zanib	PROPN
ejpam-6347	103	13	/	/	SYM
ejpam-6347	103	14	eur	eur	PROPN
ejpam-6347	103	15	.	.	PUNCT
ejpam-6347	104	1	j.	j.	PROPN
ejpam-6347	104	2	pure	pure	PROPN
ejpam-6347	104	3	appl	appl	PROPN
ejpam-6347	104	4	.	.	PROPN
ejpam-6347	104	5	math	math	PROPN
ejpam-6347	104	6	,	,	PUNCT
ejpam-6347	104	7	18	18	NUM
ejpam-6347	104	8	(	(	PUNCT
ejpam-6347	104	9	3	3	NUM
ejpam-6347	104	10	)	)	PUNCT
ejpam-6347	104	11	(	(	PUNCT
ejpam-6347	104	12	2025	2025	NUM
ejpam-6347	104	13	)	)	PUNCT
ejpam-6347	104	14	,	,	PUNCT
ejpam-6347	104	15	6347	6347	NUM
ejpam-6347	104	16	8	8	NUM
ejpam-6347	104	17	of	of	ADP
ejpam-6347	104	18	34	34	NUM
ejpam-6347	104	19	mathematical	mathematical	ADJ
ejpam-6347	104	20	analysis	analysis	NOUN
ejpam-6347	104	21	the	the	DET
ejpam-6347	104	22	biologically	biologically	ADV
ejpam-6347	104	23	feasible	feasible	ADJ
ejpam-6347	104	24	region	region	NOUN
ejpam-6347	104	25	for	for	ADP
ejpam-6347	104	26	the	the	DET
ejpam-6347	104	27	fractional	fractional	ADJ
ejpam-6347	104	28	-	-	PUNCT
ejpam-6347	104	29	order	order	NOUN
ejpam-6347	104	30	model	model	NOUN
ejpam-6347	104	31	(	(	PUNCT
ejpam-6347	104	32	2.4	2.4	NUM
ejpam-6347	104	33	)	)	PUNCT
ejpam-6347	104	34	is	be	AUX
ejpam-6347	104	35	defined	define	VERB
ejpam-6347	104	36	as	as	ADP
ejpam-6347	104	37	:	:	PUNCT
ejpam-6347	104	38	d	d	X
ejpam-6347	104	39	=	=	SYM
ejpam-6347	104	40	{	{	PUNCT
ejpam-6347	104	41	(	(	PUNCT
ejpam-6347	104	42	s(t	s(t	PROPN
ejpam-6347	104	43	)	)	PUNCT
ejpam-6347	104	44	,	,	PUNCT
ejpam-6347	104	45	e(t	e(t	NOUN
ejpam-6347	104	46	)	)	PUNCT
ejpam-6347	104	47	,	,	PUNCT
ejpam-6347	104	48	u(t	u(t	PROPN
ejpam-6347	104	49	)	)	PUNCT
ejpam-6347	104	50	,	,	PUNCT
ejpam-6347	104	51	q(t	q(t	PROPN
ejpam-6347	104	52	)	)	PUNCT
ejpam-6347	104	53	,	,	PUNCT
ejpam-6347	104	54	p	p	X
ejpam-6347	104	55	(	(	PUNCT
ejpam-6347	104	56	t	t	PROPN
ejpam-6347	104	57	)	)	PUNCT
ejpam-6347	104	58	,	,	PUNCT
ejpam-6347	104	59	h(t	h(t	PROPN
ejpam-6347	104	60	)	)	PUNCT
ejpam-6347	104	61	,	,	PUNCT
ejpam-6347	104	62	c(t	c(t	PROPN
ejpam-6347	104	63	)	)	PUNCT
ejpam-6347	104	64	,	,	PUNCT
ejpam-6347	104	65	f	f	PROPN
ejpam-6347	104	66	(	(	PUNCT
ejpam-6347	104	67	t	t	PROPN
ejpam-6347	104	68	)	)	PUNCT
ejpam-6347	104	69	,	,	PUNCT
ejpam-6347	104	70	v	v	X
ejpam-6347	104	71	(	(	PUNCT
ejpam-6347	104	72	t	t	NOUN
ejpam-6347	104	73	)	)	PUNCT
ejpam-6347	104	74	,	,	PUNCT
ejpam-6347	104	75	r(t	r(t	NOUN
ejpam-6347	104	76	)	)	PUNCT
ejpam-6347	104	77	)	)	PUNCT
ejpam-6347	105	1	∈	∈	PROPN
ejpam-6347	105	2	r10	r10	NOUN
ejpam-6347	105	3	+	+	CCONJ
ejpam-6347	105	4	:	:	PUNCT
ejpam-6347	105	5	s	s	X
ejpam-6347	106	1	+	+	NUM
ejpam-6347	106	2	e	e	NOUN
ejpam-6347	106	3	+	+	NOUN
ejpam-6347	106	4	u	u	X
ejpam-6347	106	5	+	+	PROPN
ejpam-6347	106	6	q+	q+	ADP
ejpam-6347	106	7	p	p	NOUN
ejpam-6347	106	8	+	+	NOUN
ejpam-6347	106	9	h	h	NOUN
ejpam-6347	106	10	+	+	X
ejpam-6347	106	11	c	c	NOUN
ejpam-6347	107	1	+	+	NOUN
ejpam-6347	107	2	f	f	PROPN
ejpam-6347	108	1	+	+	CCONJ
ejpam-6347	108	2	v	v	ADP
ejpam-6347	108	3	+	+	NOUN
ejpam-6347	108	4	r	r	NOUN
ejpam-6347	108	5	≤	≤	NUM
ejpam-6347	108	6	λ	λ	PROPN
ejpam-6347	108	7	µ	µ	X
ejpam-6347	108	8	}	}	PUNCT
ejpam-6347	108	9	,	,	PUNCT
ejpam-6347	108	10	(	(	PUNCT
ejpam-6347	108	11	2.6	2.6	NUM
ejpam-6347	108	12	)	)	PUNCT
ejpam-6347	108	13	where	where	SCONJ
ejpam-6347	108	14	d	d	PROPN
ejpam-6347	108	15	forms	form	VERB
ejpam-6347	108	16	a	a	DET
ejpam-6347	108	17	positive	positive	ADJ
ejpam-6347	108	18	invariant	invariant	ADJ
ejpam-6347	108	19	set	set	NOUN
ejpam-6347	108	20	that	that	PRON
ejpam-6347	108	21	captures	capture	VERB
ejpam-6347	108	22	all	all	DET
ejpam-6347	108	23	epidemiologically	epidemiologically	ADV
ejpam-6347	108	24	meaningful	meaningful	ADJ
ejpam-6347	108	25	states	state	NOUN
ejpam-6347	108	26	of	of	ADP
ejpam-6347	108	27	the	the	DET
ejpam-6347	108	28	system	system	NOUN
ejpam-6347	108	29	.	.	PUNCT
ejpam-6347	109	1	the	the	DET
ejpam-6347	109	2	mathematical	mathematical	ADJ
ejpam-6347	109	3	analysis	analysis	NOUN
ejpam-6347	109	4	of	of	ADP
ejpam-6347	109	5	the	the	DET
ejpam-6347	109	6	model	model	NOUN
ejpam-6347	109	7	demonstrate	demonstrate	VERB
ejpam-6347	109	8	the	the	DET
ejpam-6347	109	9	the	the	DET
ejpam-6347	109	10	feasible	feasible	ADJ
ejpam-6347	109	11	region	region	NOUN
ejpam-6347	109	12	d	d	NOUN
ejpam-6347	109	13	in	in	ADP
ejpam-6347	109	14	terms	term	NOUN
ejpam-6347	109	15	of	of	ADP
ejpam-6347	109	16	bounded	bounded	ADJ
ejpam-6347	109	17	and	and	CCONJ
ejpam-6347	109	18	non	non	ADJ
ejpam-6347	109	19	-	-	ADJ
ejpam-6347	109	20	negative	negative	ADJ
ejpam-6347	109	21	,	,	PUNCT
ejpam-6347	109	22	stability	stability	NOUN
ejpam-6347	109	23	results	result	NOUN
ejpam-6347	109	24	,	,	PUNCT
ejpam-6347	109	25	and	and	CCONJ
ejpam-6347	109	26	epidemiological	epidemiological	ADJ
ejpam-6347	109	27	thresholds	threshold	NOUN
ejpam-6347	109	28	.	.	PUNCT
ejpam-6347	110	1	solutions	solution	NOUN
ejpam-6347	110	2	of	of	ADP
ejpam-6347	110	3	equations	equation	NOUN
ejpam-6347	110	4	(	(	PUNCT
ejpam-6347	110	5	2.4	2.4	NUM
ejpam-6347	110	6	)	)	PUNCT
ejpam-6347	110	7	with	with	ADP
ejpam-6347	110	8	initial	initial	ADJ
ejpam-6347	110	9	conditions	condition	NOUN
ejpam-6347	110	10	(	(	PUNCT
ejpam-6347	110	11	2.5	2.5	NUM
ejpam-6347	110	12	)	)	PUNCT
ejpam-6347	110	13	keep	keep	VERB
ejpam-6347	110	14	in	in	ADP
ejpam-6347	110	15	d	d	PRON
ejpam-6347	110	16	discuss	discuss	NOUN
ejpam-6347	110	17	in	in	ADP
ejpam-6347	110	18	the	the	DET
ejpam-6347	110	19	below	below	NOUN
ejpam-6347	110	20	theorem	theorem	PROPN
ejpam-6347	110	21	.	.	PUNCT
ejpam-6347	110	22	theorem	theorem	NOUN
ejpam-6347	110	23	1	1	NUM
ejpam-6347	110	24	.	.	PUNCT
ejpam-6347	111	1	(	(	PUNCT
ejpam-6347	111	2	positive	positive	ADJ
ejpam-6347	111	3	invariance	invariance	NOUN
ejpam-6347	111	4	of	of	ADP
ejpam-6347	111	5	feasible	feasible	ADJ
ejpam-6347	111	6	region	region	NOUN
ejpam-6347	111	7	)	)	PUNCT
ejpam-6347	111	8	for	for	ADP
ejpam-6347	111	9	the	the	DET
ejpam-6347	111	10	fractional	fractional	ADJ
ejpam-6347	111	11	-	-	PUNCT
ejpam-6347	111	12	order	order	NOUN
ejpam-6347	111	13	system	system	NOUN
ejpam-6347	111	14	(	(	PUNCT
ejpam-6347	111	15	2.4	2.4	NUM
ejpam-6347	111	16	)	)	PUNCT
ejpam-6347	111	17	with	with	ADP
ejpam-6347	111	18	non	non	ADJ
ejpam-6347	111	19	-	-	ADJ
ejpam-6347	111	20	negative	negative	ADJ
ejpam-6347	111	21	initial	initial	ADJ
ejpam-6347	111	22	conditions	condition	NOUN
ejpam-6347	111	23	(	(	PUNCT
ejpam-6347	111	24	2.5	2.5	NUM
ejpam-6347	111	25	)	)	PUNCT
ejpam-6347	111	26	,	,	PUNCT
ejpam-6347	111	27	the	the	DET
ejpam-6347	111	28	closed	closed	ADJ
ejpam-6347	111	29	set	set	NOUN
ejpam-6347	111	30	d	d	ADP
ejpam-6347	111	31	defined	define	VERB
ejpam-6347	111	32	in	in	ADP
ejpam-6347	111	33	(	(	PUNCT
ejpam-6347	111	34	2.6	2.6	NUM
ejpam-6347	111	35	)	)	PUNCT
ejpam-6347	111	36	forms	form	VERB
ejpam-6347	111	37	a	a	DET
ejpam-6347	111	38	positively	positively	ADV
ejpam-6347	111	39	invariant	invariant	ADJ
ejpam-6347	111	40	region	region	NOUN
ejpam-6347	111	41	under	under	ADP
ejpam-6347	111	42	conformable	conformable	ADJ
ejpam-6347	111	43	fractional	fractional	ADJ
ejpam-6347	111	44	dynamics	dynamic	NOUN
ejpam-6347	111	45	when	when	SCONJ
ejpam-6347	111	46	all	all	DET
ejpam-6347	111	47	parameters	parameter	NOUN
ejpam-6347	111	48	satisfy	satisfy	VERB
ejpam-6347	111	49	{	{	PUNCT
ejpam-6347	111	50	ϕ	ϕ	NOUN
ejpam-6347	111	51	,	,	PUNCT
ejpam-6347	111	52	β	β	X
ejpam-6347	111	53	,	,	PUNCT
ejpam-6347	111	54	µ	µ	NOUN
ejpam-6347	111	55	,	,	PUNCT
ejpam-6347	111	56	.	.	PUNCT
ejpam-6347	111	57	.	.	PUNCT
ejpam-6347	111	58	.	.	PUNCT
ejpam-6347	111	59	}	}	PUNCT
ejpam-6347	112	1	∈	∈	PROPN
ejpam-6347	112	2	r+	r+	NOUN
ejpam-6347	112	3	.	.	PUNCT
ejpam-6347	113	1	proof	proof	NOUN
ejpam-6347	113	2	.	.	PUNCT
ejpam-6347	114	1	let	let	VERB
ejpam-6347	114	2	n(t	n(t	PRON
ejpam-6347	114	3	)	)	PUNCT
ejpam-6347	114	4	=	=	SYM
ejpam-6347	115	1	∑10	∑10	NOUN
ejpam-6347	115	2	i=1xi(t	i=1xi(t	NOUN
ejpam-6347	115	3	)	)	PUNCT
ejpam-6347	115	4	represent	represent	VERB
ejpam-6347	115	5	the	the	DET
ejpam-6347	115	6	total	total	ADJ
ejpam-6347	115	7	population	population	NOUN
ejpam-6347	115	8	,	,	PUNCT
ejpam-6347	115	9	where	where	SCONJ
ejpam-6347	115	10	xi	xi	PROPN
ejpam-6347	115	11	denotes	denote	VERB
ejpam-6347	115	12	each	each	DET
ejpam-6347	115	13	compartment	compartment	NOUN
ejpam-6347	115	14	.	.	PUNCT
ejpam-6347	116	1	applying	apply	VERB
ejpam-6347	116	2	the	the	DET
ejpam-6347	116	3	conformable	conformable	ADJ
ejpam-6347	116	4	fractional	fractional	ADJ
ejpam-6347	116	5	derivative	derivative	ADJ
ejpam-6347	116	6	operator	operator	NOUN
ejpam-6347	116	7	:	:	PUNCT
ejpam-6347	116	8	dζ	dζ	PROPN
ejpam-6347	116	9	tn(t	tn(t	PRON
ejpam-6347	116	10	)	)	PUNCT
ejpam-6347	117	1	=	=	SYM
ejpam-6347	117	2	λ−	λ−	PROPN
ejpam-6347	117	3	µn(t)−	µn(t)−	PROPN
ejpam-6347	117	4	7∑	7∑	NUM
ejpam-6347	117	5	i=1	i=1	ADP
ejpam-6347	117	6	dixi(t	dixi(t	PROPN
ejpam-6347	117	7	)	)	PUNCT
ejpam-6347	117	8	.	.	PUNCT
ejpam-6347	118	1	(	(	PUNCT
ejpam-6347	118	2	2.7	2.7	NUM
ejpam-6347	118	3	)	)	PUNCT
ejpam-6347	118	4	using	use	VERB
ejpam-6347	118	5	the	the	DET
ejpam-6347	118	6	conformable	conformable	ADJ
ejpam-6347	118	7	derivative	derivative	ADJ
ejpam-6347	118	8	property	property	NOUN
ejpam-6347	118	9	dζ	dζ	PROPN
ejpam-6347	118	10	tn	tn	PROPN
ejpam-6347	118	11	=	=	SYM
ejpam-6347	118	12	t1−ζ	t1−ζ	PROPN
ejpam-6347	118	13	dn	dn	NOUN
ejpam-6347	118	14	dt	dt	PROPN
ejpam-6347	118	15	,	,	PUNCT
ejpam-6347	118	16	we	we	PRON
ejpam-6347	118	17	rewrite	rewrite	VERB
ejpam-6347	118	18	:	:	PUNCT
ejpam-6347	118	19	t1−ζ	t1−ζ	PROPN
ejpam-6347	118	20	dn	dn	ADP
ejpam-6347	118	21	dt	dt	NOUN
ejpam-6347	119	1	=	=	PUNCT
ejpam-6347	119	2	λ−	λ−	PROPN
ejpam-6347	119	3	µn−	µn−	NUM
ejpam-6347	119	4	7∑	7∑	NUM
ejpam-6347	119	5	i=1	i=1	PROPN
ejpam-6347	119	6	dixi(t)︸	dixi(t)︸	PROPN
ejpam-6347	119	7	︷︷	︷︷	PROPN
ejpam-6347	119	8	︸	︸	X
ejpam-6347	120	1	≥0	≥0	X
ejpam-6347	120	2	.	.	PUNCT
ejpam-6347	121	1	(	(	PUNCT
ejpam-6347	121	2	2.8	2.8	NUM
ejpam-6347	121	3	)	)	PUNCT
ejpam-6347	121	4	this	this	PRON
ejpam-6347	121	5	establishes	establish	VERB
ejpam-6347	121	6	the	the	DET
ejpam-6347	121	7	inequality	inequality	NOUN
ejpam-6347	121	8	:	:	PUNCT
ejpam-6347	121	9	dn	dn	PROPN
ejpam-6347	121	10	dt	dt	PUNCT
ejpam-6347	121	11	≤	≤	PROPN
ejpam-6347	121	12	tζ−1(λ−	tζ−1(λ−	PROPN
ejpam-6347	121	13	µn	µn	PROPN
ejpam-6347	121	14	)	)	PUNCT
ejpam-6347	121	15	.	.	PUNCT
ejpam-6347	122	1	(	(	PUNCT
ejpam-6347	122	2	2.9	2.9	NUM
ejpam-6347	122	3	)	)	PUNCT
ejpam-6347	122	4	solving	solve	VERB
ejpam-6347	122	5	this	this	DET
ejpam-6347	122	6	fractional	fractional	ADJ
ejpam-6347	122	7	differential	differential	NOUN
ejpam-6347	122	8	inequality	inequality	NOUN
ejpam-6347	122	9	through	through	ADP
ejpam-6347	122	10	separation	separation	NOUN
ejpam-6347	122	11	of	of	ADP
ejpam-6347	122	12	variables:∫	variables:∫	ADJ
ejpam-6347	122	13	n(t	n(t	PROPN
ejpam-6347	122	14	)	)	PUNCT
ejpam-6347	122	15	n(0	n(0	PROPN
ejpam-6347	122	16	)	)	PUNCT
ejpam-6347	122	17	dn	dn	NOUN
ejpam-6347	122	18	λ−	λ−	PROPN
ejpam-6347	122	19	µn	µn	PROPN
ejpam-6347	122	20	≤	≤	NUM
ejpam-6347	122	21	∫	∫	PROPN
ejpam-6347	122	22	t	t	PROPN
ejpam-6347	122	23	0	0	NUM
ejpam-6347	122	24	τ	τ	PROPN
ejpam-6347	122	25	ζ−1dτ	ζ−1dτ	VERB
ejpam-6347	122	26	,	,	PUNCT
ejpam-6347	122	27	(	(	PUNCT
ejpam-6347	122	28	2.10	2.10	NUM
ejpam-6347	122	29	)	)	PUNCT
ejpam-6347	122	30	taking	take	VERB
ejpam-6347	122	31	integrated	integrate	VERB
ejpam-6347	122	32	factor	factor	NOUN
ejpam-6347	122	33	and	and	CCONJ
ejpam-6347	122	34	after	after	ADP
ejpam-6347	122	35	simplify	simplify	NOUN
ejpam-6347	122	36	:	:	PUNCT
ejpam-6347	122	37	n(t	n(t	X
ejpam-6347	122	38	)	)	PUNCT
ejpam-6347	122	39	≤	≤	NUM
ejpam-6347	122	40	λ	λ	PROPN
ejpam-6347	122	41	µ	µ	X
ejpam-6347	122	42	−	−	PROPN
ejpam-6347	122	43	(	(	PUNCT
ejpam-6347	122	44	λ	λ	X
ejpam-6347	122	45	µ	µ	X
ejpam-6347	122	46	−	−	PROPN
ejpam-6347	122	47	n(0	n(0	PROPN
ejpam-6347	122	48	)	)	PUNCT
ejpam-6347	122	49	)	)	PUNCT
ejpam-6347	122	50	exp	exp	NOUN
ejpam-6347	122	51	(	(	PUNCT
ejpam-6347	122	52	−µ	−µ	ADV
ejpam-6347	122	53	ζ	ζ	NOUN
ejpam-6347	122	54	tζ	tζ	PROPN
ejpam-6347	122	55	)	)	PUNCT
ejpam-6347	122	56	.	.	PUNCT
ejpam-6347	123	1	(	(	PUNCT
ejpam-6347	123	2	2.11	2.11	NUM
ejpam-6347	123	3	)	)	PUNCT
ejpam-6347	123	4	for	for	ADP
ejpam-6347	123	5	n(0	n(0	PROPN
ejpam-6347	123	6	)	)	PUNCT
ejpam-6347	123	7	≤	≤	NUM
ejpam-6347	123	8	λ	λ	PROPN
ejpam-6347	123	9	µ	µ	X
ejpam-6347	123	10	,	,	PUNCT
ejpam-6347	123	11	the	the	DET
ejpam-6347	123	12	exponential	exponential	ADJ
ejpam-6347	123	13	term	term	NOUN
ejpam-6347	123	14	ensures	ensure	VERB
ejpam-6347	123	15	n(t	n(t	NOUN
ejpam-6347	123	16	)	)	PUNCT
ejpam-6347	123	17	≤	≤	PUNCT
ejpam-6347	123	18	λ	λ	PROPN
ejpam-6347	123	19	µ	µ	X
ejpam-6347	123	20	∀t	∀t	PROPN
ejpam-6347	123	21	≥	≥	NOUN
ejpam-6347	123	22	0	0	NUM
ejpam-6347	123	23	.	.	PUNCT
ejpam-6347	124	1	thus	thus	ADV
ejpam-6347	124	2	,	,	PUNCT
ejpam-6347	124	3	all	all	DET
ejpam-6347	124	4	solutions	solution	NOUN
ejpam-6347	124	5	remain	remain	VERB
ejpam-6347	124	6	bounded	bounded	ADJ
ejpam-6347	124	7	within	within	ADP
ejpam-6347	124	8	d	d	PROPN
ejpam-6347	124	9	,	,	PUNCT
ejpam-6347	124	10	making	make	VERB
ejpam-6347	124	11	it	it	PRON
ejpam-6347	124	12	positively	positively	ADV
ejpam-6347	124	13	invariant	invariant	ADJ
ejpam-6347	124	14	under	under	ADP
ejpam-6347	124	15	the	the	DET
ejpam-6347	124	16	fractional	fractional	ADJ
ejpam-6347	124	17	-	-	PUNCT
ejpam-6347	124	18	order	order	NOUN
ejpam-6347	124	19	dynamics	dynamic	NOUN
ejpam-6347	124	20	.	.	PUNCT
ejpam-6347	125	1	n.	n.	PROPN
ejpam-6347	125	2	abbas	abbas	PROPN
ejpam-6347	125	3	,	,	PUNCT
ejpam-6347	125	4	w.	w.	PROPN
ejpam-6347	125	5	shatanawi	shatanawi	PROPN
ejpam-6347	125	6	,	,	PUNCT
ejpam-6347	125	7	s.	s.	PROPN
ejpam-6347	125	8	a.	a.	NOUN
ejpam-6347	125	9	zanib	zanib	PROPN
ejpam-6347	125	10	/	/	SYM
ejpam-6347	125	11	eur	eur	PROPN
ejpam-6347	125	12	.	.	PUNCT
ejpam-6347	126	1	j.	j.	PROPN
ejpam-6347	126	2	pure	pure	PROPN
ejpam-6347	126	3	appl	appl	PROPN
ejpam-6347	126	4	.	.	PROPN
ejpam-6347	126	5	math	math	PROPN
ejpam-6347	126	6	,	,	PUNCT
ejpam-6347	126	7	18	18	NUM
ejpam-6347	126	8	(	(	PUNCT
ejpam-6347	126	9	3	3	NUM
ejpam-6347	126	10	)	)	PUNCT
ejpam-6347	126	11	(	(	PUNCT
ejpam-6347	126	12	2025	2025	NUM
ejpam-6347	126	13	)	)	PUNCT
ejpam-6347	126	14	,	,	PUNCT
ejpam-6347	126	15	6347	6347	NUM
ejpam-6347	126	16	9	9	NUM
ejpam-6347	126	17	of	of	ADP
ejpam-6347	126	18	34	34	NUM
ejpam-6347	126	19	positivity	positivity	NOUN
ejpam-6347	126	20	and	and	CCONJ
ejpam-6347	126	21	boundedness	boundedness	NOUN
ejpam-6347	126	22	of	of	ADP
ejpam-6347	126	23	solutions	solution	NOUN
ejpam-6347	126	24	theorem	theorem	VERB
ejpam-6347	126	25	2	2	NUM
ejpam-6347	126	26	.	.	X
ejpam-6347	126	27	for	for	ADP
ejpam-6347	126	28	the	the	DET
ejpam-6347	126	29	fractional	fractional	ADJ
ejpam-6347	126	30	-	-	PUNCT
ejpam-6347	126	31	order	order	NOUN
ejpam-6347	126	32	system	system	NOUN
ejpam-6347	126	33	(	(	PUNCT
ejpam-6347	126	34	2.4	2.4	NUM
ejpam-6347	126	35	)	)	PUNCT
ejpam-6347	126	36	with	with	ADP
ejpam-6347	126	37	non	non	ADJ
ejpam-6347	126	38	-	-	ADJ
ejpam-6347	126	39	negative	negative	ADJ
ejpam-6347	126	40	initial	initial	ADJ
ejpam-6347	126	41	conditions	condition	NOUN
ejpam-6347	126	42	(	(	PUNCT
ejpam-6347	126	43	2.5	2.5	NUM
ejpam-6347	126	44	)	)	PUNCT
ejpam-6347	126	45	and	and	CCONJ
ejpam-6347	126	46	non	non	ADJ
ejpam-6347	126	47	-	-	ADJ
ejpam-6347	126	48	negative	negative	ADJ
ejpam-6347	126	49	parameters	parameter	NOUN
ejpam-6347	126	50	,	,	PUNCT
ejpam-6347	126	51	the	the	DET
ejpam-6347	126	52	following	follow	VERB
ejpam-6347	126	53	holds	hold	VERB
ejpam-6347	126	54	:	:	PUNCT
ejpam-6347	126	55	•	•	ADP
ejpam-6347	126	56	all	all	DET
ejpam-6347	126	57	solutions	solution	NOUN
ejpam-6347	126	58	{	{	PUNCT
ejpam-6347	126	59	s(t	s(t	PROPN
ejpam-6347	126	60	)	)	PUNCT
ejpam-6347	126	61	,	,	PUNCT
ejpam-6347	126	62	e(t	e(t	NOUN
ejpam-6347	126	63	)	)	PUNCT
ejpam-6347	126	64	,	,	PUNCT
ejpam-6347	126	65	u(t	u(t	PROPN
ejpam-6347	126	66	)	)	PUNCT
ejpam-6347	126	67	,	,	PUNCT
ejpam-6347	126	68	q(t	q(t	PROPN
ejpam-6347	126	69	)	)	PUNCT
ejpam-6347	126	70	,	,	PUNCT
ejpam-6347	126	71	p	p	X
ejpam-6347	126	72	(	(	PUNCT
ejpam-6347	126	73	t	t	PROPN
ejpam-6347	126	74	)	)	PUNCT
ejpam-6347	126	75	,	,	PUNCT
ejpam-6347	126	76	h(t	h(t	PROPN
ejpam-6347	126	77	)	)	PUNCT
ejpam-6347	126	78	,	,	PUNCT
ejpam-6347	126	79	c(t	c(t	PROPN
ejpam-6347	126	80	)	)	PUNCT
ejpam-6347	126	81	,	,	PUNCT
ejpam-6347	126	82	f	f	PROPN
ejpam-6347	126	83	(	(	PUNCT
ejpam-6347	126	84	t	t	PROPN
ejpam-6347	126	85	)	)	PUNCT
ejpam-6347	126	86	,	,	PUNCT
ejpam-6347	126	87	v	v	X
ejpam-6347	126	88	(	(	PUNCT
ejpam-6347	126	89	t	t	NOUN
ejpam-6347	126	90	)	)	PUNCT
ejpam-6347	126	91	,	,	PUNCT
ejpam-6347	126	92	r(t	r(t	NOUN
ejpam-6347	126	93	)	)	PUNCT
ejpam-6347	126	94	}	}	PUNCT
ejpam-6347	126	95	remain	remain	VERB
ejpam-6347	126	96	nonnegative	nonnegative	ADJ
ejpam-6347	126	97	for	for	ADP
ejpam-6347	126	98	all	all	DET
ejpam-6347	126	99	t	t	PROPN
ejpam-6347	126	100	≥	≥	NOUN
ejpam-6347	126	101	0	0	NUM
ejpam-6347	126	102	.	.	NOUN
ejpam-6347	127	1	•	•	NUM
ejpam-6347	128	1	the	the	DET
ejpam-6347	128	2	total	total	ADJ
ejpam-6347	128	3	population	population	NOUN
ejpam-6347	128	4	satisfies	satisfy	VERB
ejpam-6347	128	5	lim	lim	PROPN
ejpam-6347	128	6	sup	sup	PROPN
ejpam-6347	128	7	t→∞	t→∞	ADP
ejpam-6347	128	8	n(t	n(t	NOUN
ejpam-6347	128	9	)	)	PUNCT
ejpam-6347	128	10	≤	≤	NUM
ejpam-6347	129	1	λ	λ	PROPN
ejpam-6347	129	2	µ	µ	X
ejpam-6347	129	3	.	.	PUNCT
ejpam-6347	130	1	proof	proof	NOUN
ejpam-6347	130	2	.	.	PUNCT
ejpam-6347	131	1	positivity	positivity	NOUN
ejpam-6347	131	2	consider	consider	VERB
ejpam-6347	131	3	the	the	DET
ejpam-6347	131	4	conformable	conformable	ADJ
ejpam-6347	131	5	fractional	fractional	ADJ
ejpam-6347	131	6	derivative	derivative	ADJ
ejpam-6347	131	7	formulation	formulation	NOUN
ejpam-6347	131	8	dζ	dζ	PROPN
ejpam-6347	131	9	tx	tx	PROPN
ejpam-6347	131	10	=	=	PUNCT
ejpam-6347	131	11	t1−ζx	t1−ζx	NUM
ejpam-6347	131	12	′.	′.	NOUN
ejpam-6347	131	13	for	for	ADP
ejpam-6347	131	14	each	each	DET
ejpam-6347	131	15	compartment	compartment	NOUN
ejpam-6347	131	16	x	x	SYM
ejpam-6347	131	17	∈	∈	NOUN
ejpam-6347	131	18	{	{	PUNCT
ejpam-6347	131	19	s	s	PROPN
ejpam-6347	131	20	,	,	PUNCT
ejpam-6347	131	21	e	e	NOUN
ejpam-6347	131	22	,	,	PUNCT
ejpam-6347	131	23	u	u	NOUN
ejpam-6347	131	24	,	,	PUNCT
ejpam-6347	131	25	q	q	INTJ
ejpam-6347	131	26	,	,	PUNCT
ejpam-6347	131	27	p	p	X
ejpam-6347	131	28	,	,	PUNCT
ejpam-6347	131	29	h	h	NOUN
ejpam-6347	131	30	,	,	PUNCT
ejpam-6347	131	31	c	c	X
ejpam-6347	131	32	,	,	PUNCT
ejpam-6347	131	33	f	f	PROPN
ejpam-6347	131	34	,	,	PUNCT
ejpam-6347	131	35	v	v	NOUN
ejpam-6347	131	36	,	,	PUNCT
ejpam-6347	131	37	r	r	NOUN
ejpam-6347	131	38	}	}	PUNCT
ejpam-6347	131	39	:	:	PUNCT
ejpam-6347	131	40	lemma	lemma	PROPN
ejpam-6347	131	41	1	1	X
ejpam-6347	131	42	.	.	PUNCT
ejpam-6347	132	1	let	let	VERB
ejpam-6347	132	2	dζ	dζ	PROPN
ejpam-6347	132	3	tx	tx	PROPN
ejpam-6347	132	4	≥	≥	PROPN
ejpam-6347	132	5	−ψx	−ψx	PROPN
ejpam-6347	132	6	with	with	ADP
ejpam-6347	132	7	ψ	ψ	X
ejpam-6347	132	8	≥	≥	NOUN
ejpam-6347	132	9	0	0	NUM
ejpam-6347	132	10	and	and	CCONJ
ejpam-6347	132	11	x(0	x(0	PROPN
ejpam-6347	132	12	)	)	PUNCT
ejpam-6347	132	13	≥	≥	NOUN
ejpam-6347	132	14	0	0	NUM
ejpam-6347	132	15	.	.	PUNCT
ejpam-6347	133	1	then	then	ADV
ejpam-6347	133	2	x(t	x(t	PROPN
ejpam-6347	133	3	)	)	PUNCT
ejpam-6347	133	4	≥	≥	NOUN
ejpam-6347	133	5	0	0	NUM
ejpam-6347	133	6	∀t	∀t	PROPN
ejpam-6347	133	7	≥	≥	NOUN
ejpam-6347	133	8	0	0	NUM
ejpam-6347	133	9	.	.	PUNCT
ejpam-6347	134	1	for	for	ADP
ejpam-6347	134	2	the	the	DET
ejpam-6347	134	3	susceptible	susceptible	ADJ
ejpam-6347	134	4	population	population	NOUN
ejpam-6347	134	5	:	:	PUNCT
ejpam-6347	134	6	dζ	dζ	PROPN
ejpam-6347	134	7	t	t	PROPN
ejpam-6347	134	8	s	s	PART
ejpam-6347	134	9	=	=	PUNCT
ejpam-6347	134	10	λ+	λ+	PUNCT
ejpam-6347	134	11	τr+	τr+	PROPN
ejpam-6347	134	12	b2q−	b2q−	PROPN
ejpam-6347	134	13	(	(	PUNCT
ejpam-6347	134	14	ϕe	ϕe	X
ejpam-6347	134	15	+	+	X
ejpam-6347	134	16	β	β	X
ejpam-6347	134	17	+	+	X
ejpam-6347	134	18	µ)s	µ)s	NOUN
ejpam-6347	134	19	≥	≥	NOUN
ejpam-6347	134	20	−(ϕe	−(ϕe	X
ejpam-6347	134	21	+	+	NUM
ejpam-6347	134	22	β	β	X
ejpam-6347	134	23	+	+	SYM
ejpam-6347	134	24	µ)s	µ)s	NOUN
ejpam-6347	134	25	,	,	PUNCT
ejpam-6347	134	26	(	(	PUNCT
ejpam-6347	134	27	2.12	2.12	NUM
ejpam-6347	134	28	)	)	PUNCT
ejpam-6347	134	29	applying	apply	VERB
ejpam-6347	134	30	the	the	DET
ejpam-6347	134	31	comparison	comparison	NOUN
ejpam-6347	134	32	principle	principle	NOUN
ejpam-6347	134	33	for	for	ADP
ejpam-6347	134	34	fractional	fractional	ADJ
ejpam-6347	134	35	differential	differential	ADJ
ejpam-6347	134	36	equations	equation	NOUN
ejpam-6347	134	37	:	:	PUNCT
ejpam-6347	134	38	s(t	s(t	PROPN
ejpam-6347	134	39	)	)	PUNCT
ejpam-6347	134	40	≥	≥	NOUN
ejpam-6347	134	41	s(0	s(0	PROPN
ejpam-6347	134	42	)	)	PUNCT
ejpam-6347	134	43	exp	exp	NOUN
ejpam-6347	134	44	(	(	PUNCT
ejpam-6347	134	45	−1	−1	NOUN
ejpam-6347	134	46	ζ	ζ	NOUN
ejpam-6347	134	47	(	(	PUNCT
ejpam-6347	134	48	ϕe	ϕe	X
ejpam-6347	134	49	+	+	X
ejpam-6347	134	50	β	β	X
ejpam-6347	134	51	+	+	X
ejpam-6347	134	52	µ)tζ	µ)tζ	PROPN
ejpam-6347	134	53	)	)	PUNCT
ejpam-6347	134	54	≥	≥	NOUN
ejpam-6347	134	55	0	0	NUM
ejpam-6347	134	56	.	.	PUNCT
ejpam-6347	135	1	(	(	PUNCT
ejpam-6347	135	2	2.13	2.13	NUM
ejpam-6347	135	3	)	)	PUNCT
ejpam-6347	135	4	similar	similar	ADJ
ejpam-6347	135	5	analysis	analysis	NOUN
ejpam-6347	135	6	for	for	ADP
ejpam-6347	135	7	other	other	ADJ
ejpam-6347	135	8	compartments	compartment	NOUN
ejpam-6347	135	9	yields	yield	NOUN
ejpam-6347	135	10	:	:	PUNCT
ejpam-6347	135	11	dζ	dζ	PROPN
ejpam-6347	135	12	te	te	PROPN
ejpam-6347	135	13	≥	≥	PROPN
ejpam-6347	135	14	−(λ1u	−(λ1u	PROPN
ejpam-6347	135	15	+	+	NOUN
ejpam-6347	135	16	λ2q+	λ2q+	PROPN
ejpam-6347	135	17	µ+	µ+	X
ejpam-6347	135	18	d1)e	d1)e	NOUN
ejpam-6347	135	19	,	,	PUNCT
ejpam-6347	135	20	dζ	dζ	PROPN
ejpam-6347	135	21	tu	tu	PROPN
ejpam-6347	135	22	≥	≥	PRON
ejpam-6347	135	23	−(α1	−(α1	NOUN
ejpam-6347	135	24	+	+	CCONJ
ejpam-6347	135	25	α2	α2	ADJ
ejpam-6347	135	26	+	+	CCONJ
ejpam-6347	135	27	µ+	µ+	PUNCT
ejpam-6347	135	28	d2)u	d2)u	NOUN
ejpam-6347	135	29	,	,	PUNCT
ejpam-6347	135	30	...	...	PUNCT
ejpam-6347	135	31	(	(	PUNCT
ejpam-6347	135	32	2.14	2.14	NUM
ejpam-6347	135	33	)	)	PUNCT
ejpam-6347	135	34	by	by	ADP
ejpam-6347	135	35	sequential	sequential	ADJ
ejpam-6347	135	36	application	application	NOUN
ejpam-6347	135	37	of	of	ADP
ejpam-6347	135	38	the	the	DET
ejpam-6347	135	39	comparison	comparison	NOUN
ejpam-6347	135	40	lemma	lemma	PROPN
ejpam-6347	135	41	,	,	PUNCT
ejpam-6347	135	42	all	all	DET
ejpam-6347	135	43	compartments	compartment	NOUN
ejpam-6347	135	44	maintain	maintain	VERB
ejpam-6347	135	45	nonnegativity	nonnegativity	NOUN
ejpam-6347	135	46	.	.	PUNCT
ejpam-6347	136	1	boundedness	boundedness	PROPN
ejpam-6347	136	2	from	from	ADP
ejpam-6347	136	3	theorem	theorem	ADJ
ejpam-6347	136	4	1	1	NUM
ejpam-6347	136	5	(	(	PUNCT
ejpam-6347	136	6	positive	positive	ADJ
ejpam-6347	136	7	invariance	invariance	NOUN
ejpam-6347	136	8	of	of	ADP
ejpam-6347	136	9	feasible	feasible	ADJ
ejpam-6347	136	10	region	region	NOUN
ejpam-6347	136	11	)	)	PUNCT
ejpam-6347	136	12	,	,	PUNCT
ejpam-6347	136	13	the	the	DET
ejpam-6347	136	14	total	total	ADJ
ejpam-6347	136	15	population	population	NOUN
ejpam-6347	136	16	dynamics	dynamic	NOUN
ejpam-6347	136	17	satisfy	satisfy	VERB
ejpam-6347	136	18	:	:	PUNCT
ejpam-6347	136	19	dζ	dζ	PROPN
ejpam-6347	136	20	tn	tn	PROPN
ejpam-6347	137	1	=	=	PUNCT
ejpam-6347	138	1	λ−	λ−	PROPN
ejpam-6347	139	1	µn−	µn−	NUM
ejpam-6347	139	2	7∑	7∑	NUM
ejpam-6347	139	3	i=1	i=1	PROPN
ejpam-6347	139	4	dixi	dixi	NOUN
ejpam-6347	139	5	≤	≤	PUNCT
ejpam-6347	139	6	λ−	λ−	PROPN
ejpam-6347	139	7	µn	µn	PROPN
ejpam-6347	139	8	.	.	PUNCT
ejpam-6347	140	1	(	(	PUNCT
ejpam-6347	140	2	2.15	2.15	NUM
ejpam-6347	140	3	)	)	PUNCT
ejpam-6347	140	4	solving	solve	VERB
ejpam-6347	140	5	the	the	DET
ejpam-6347	140	6	fractional	fractional	ADJ
ejpam-6347	140	7	inequality	inequality	NOUN
ejpam-6347	140	8	:	:	PUNCT
ejpam-6347	140	9	n(t	n(t	X
ejpam-6347	140	10	)	)	PUNCT
ejpam-6347	141	1	≤	≤	NUM
ejpam-6347	141	2	λ	λ	PROPN
ejpam-6347	141	3	µ	µ	X
ejpam-6347	141	4	−	−	PROPN
ejpam-6347	141	5	(	(	PUNCT
ejpam-6347	141	6	λ	λ	X
ejpam-6347	141	7	µ	µ	X
ejpam-6347	141	8	−	−	PROPN
ejpam-6347	141	9	n(0	n(0	PROPN
ejpam-6347	141	10	)	)	PUNCT
ejpam-6347	141	11	)	)	PUNCT
ejpam-6347	141	12	exp	exp	NOUN
ejpam-6347	141	13	(	(	PUNCT
ejpam-6347	141	14	−µ	−µ	ADV
ejpam-6347	141	15	ζ	ζ	NOUN
ejpam-6347	141	16	tζ	tζ	PROPN
ejpam-6347	141	17	)	)	PUNCT
ejpam-6347	141	18	.	.	PUNCT
ejpam-6347	142	1	(	(	PUNCT
ejpam-6347	142	2	2.16	2.16	NUM
ejpam-6347	142	3	)	)	PUNCT
ejpam-6347	142	4	as	as	ADP
ejpam-6347	142	5	t→	t→	X
ejpam-6347	142	6	∞	∞	PROPN
ejpam-6347	142	7	,	,	PUNCT
ejpam-6347	142	8	the	the	DET
ejpam-6347	142	9	exponential	exponential	ADJ
ejpam-6347	142	10	term	term	NOUN
ejpam-6347	142	11	vanishes	vanish	VERB
ejpam-6347	142	12	,	,	PUNCT
ejpam-6347	142	13	yielding	yield	VERB
ejpam-6347	142	14	:	:	PUNCT
ejpam-6347	142	15	lim	lim	PROPN
ejpam-6347	142	16	sup	sup	NOUN
ejpam-6347	142	17	t→∞	t→∞	NUM
ejpam-6347	142	18	n(t	n(t	NOUN
ejpam-6347	142	19	)	)	PUNCT
ejpam-6347	142	20	≤	≤	NUM
ejpam-6347	142	21	λ	λ	PROPN
ejpam-6347	142	22	µ	µ	X
ejpam-6347	142	23	.	.	PUNCT
ejpam-6347	143	1	(	(	PUNCT
ejpam-6347	143	2	2.17	2.17	NUM
ejpam-6347	143	3	)	)	PUNCT
ejpam-6347	143	4	n.	n.	NOUN
ejpam-6347	143	5	abbas	abbas	PROPN
ejpam-6347	143	6	,	,	PUNCT
ejpam-6347	143	7	w.	w.	PROPN
ejpam-6347	143	8	shatanawi	shatanawi	PROPN
ejpam-6347	143	9	,	,	PUNCT
ejpam-6347	143	10	s.	s.	PROPN
ejpam-6347	143	11	a.	a.	NOUN
ejpam-6347	143	12	zanib	zanib	PROPN
ejpam-6347	143	13	/	/	SYM
ejpam-6347	143	14	eur	eur	PROPN
ejpam-6347	143	15	.	.	PUNCT
ejpam-6347	144	1	j.	j.	PROPN
ejpam-6347	144	2	pure	pure	PROPN
ejpam-6347	144	3	appl	appl	PROPN
ejpam-6347	144	4	.	.	PROPN
ejpam-6347	144	5	math	math	PROPN
ejpam-6347	144	6	,	,	PUNCT
ejpam-6347	144	7	18	18	NUM
ejpam-6347	144	8	(	(	PUNCT
ejpam-6347	144	9	3	3	NUM
ejpam-6347	144	10	)	)	PUNCT
ejpam-6347	144	11	(	(	PUNCT
ejpam-6347	144	12	2025	2025	NUM
ejpam-6347	144	13	)	)	PUNCT
ejpam-6347	144	14	,	,	PUNCT
ejpam-6347	144	15	6347	6347	NUM
ejpam-6347	144	16	10	10	NUM
ejpam-6347	144	17	of	of	ADP
ejpam-6347	144	18	34	34	NUM
ejpam-6347	144	19	2.1	2.1	NUM
ejpam-6347	144	20	.	.	PUNCT
ejpam-6347	145	1	disease	disease	NOUN
ejpam-6347	145	2	-	-	PUNCT
ejpam-6347	145	3	free	free	ADJ
ejpam-6347	145	4	equilibrium	equilibrium	NOUN
ejpam-6347	145	5	point	point	NOUN
ejpam-6347	145	6	the	the	DET
ejpam-6347	145	7	disease	disease	NOUN
ejpam-6347	145	8	-	-	PUNCT
ejpam-6347	145	9	free	free	ADJ
ejpam-6347	145	10	equilibrium	equilibrium	NOUN
ejpam-6347	145	11	point	point	NOUN
ejpam-6347	145	12	(	(	PUNCT
ejpam-6347	145	13	dfe	dfe	PROPN
ejpam-6347	145	14	)	)	PUNCT
ejpam-6347	146	1	[	[	X
ejpam-6347	146	2	20	20	NUM
ejpam-6347	146	3	]	]	PUNCT
ejpam-6347	146	4	of	of	ADP
ejpam-6347	146	5	the	the	DET
ejpam-6347	146	6	model	model	NOUN
ejpam-6347	146	7	is	be	AUX
ejpam-6347	146	8	determined	determine	VERB
ejpam-6347	146	9	by	by	ADP
ejpam-6347	146	10	setting	set	VERB
ejpam-6347	146	11	all	all	DET
ejpam-6347	146	12	compartments	compartment	NOUN
ejpam-6347	146	13	associated	associate	VERB
ejpam-6347	146	14	with	with	ADP
ejpam-6347	146	15	infection	infection	NOUN
ejpam-6347	146	16	to	to	ADP
ejpam-6347	146	17	zero	zero	NUM
ejpam-6347	146	18	,	,	PUNCT
ejpam-6347	146	19	reflecting	reflect	VERB
ejpam-6347	146	20	the	the	DET
ejpam-6347	146	21	absence	absence	NOUN
ejpam-6347	146	22	of	of	ADP
ejpam-6347	146	23	disease	disease	NOUN
ejpam-6347	146	24	in	in	ADP
ejpam-6347	146	25	the	the	DET
ejpam-6347	146	26	population	population	NOUN
ejpam-6347	146	27	.	.	PUNCT
ejpam-6347	147	1	specifically	specifically	ADV
ejpam-6347	147	2	,	,	PUNCT
ejpam-6347	147	3	we	we	PRON
ejpam-6347	147	4	set	set	VERB
ejpam-6347	147	5	e	e	NOUN
ejpam-6347	147	6	=	=	SYM
ejpam-6347	147	7	u	u	NOUN
ejpam-6347	147	8	=	=	NOUN
ejpam-6347	147	9	q	q	PROPN
ejpam-6347	147	10	=	=	PUNCT
ejpam-6347	147	11	p	p	X
ejpam-6347	147	12	=	=	NOUN
ejpam-6347	148	1	h	h	NOUN
ejpam-6347	148	2	=	=	PUNCT
ejpam-6347	148	3	c	c	NOUN
ejpam-6347	148	4	=	=	SYM
ejpam-6347	149	1	f	f	PROPN
ejpam-6347	149	2	=	=	SYM
ejpam-6347	149	3	r	r	NOUN
ejpam-6347	149	4	=	=	SYM
ejpam-6347	149	5	0	0	NUM
ejpam-6347	149	6	.	.	PUNCT
ejpam-6347	150	1	at	at	ADP
ejpam-6347	150	2	equilibrium	equilibrium	NOUN
ejpam-6347	150	3	,	,	PUNCT
ejpam-6347	150	4	the	the	DET
ejpam-6347	150	5	rates	rate	NOUN
ejpam-6347	150	6	of	of	ADP
ejpam-6347	150	7	change	change	NOUN
ejpam-6347	150	8	for	for	ADP
ejpam-6347	150	9	the	the	DET
ejpam-6347	150	10	susceptible	susceptible	ADJ
ejpam-6347	150	11	(	(	PUNCT
ejpam-6347	150	12	s	s	NOUN
ejpam-6347	150	13	)	)	PUNCT
ejpam-6347	150	14	and	and	CCONJ
ejpam-6347	150	15	vaccinated	vaccinate	VERB
ejpam-6347	150	16	(	(	PUNCT
ejpam-6347	150	17	v	v	NOUN
ejpam-6347	150	18	)	)	PUNCT
ejpam-6347	150	19	compartments	compartment	NOUN
ejpam-6347	150	20	are	be	AUX
ejpam-6347	150	21	given	give	VERB
ejpam-6347	150	22	by	by	ADP
ejpam-6347	150	23	the	the	DET
ejpam-6347	150	24	following	follow	VERB
ejpam-6347	150	25	steady	steady	ADJ
ejpam-6347	150	26	-	-	PUNCT
ejpam-6347	150	27	state	state	NOUN
ejpam-6347	150	28	equations	equation	NOUN
ejpam-6347	150	29	:	:	PUNCT
ejpam-6347	150	30	ds	ds	ADJ
ejpam-6347	150	31	dt	dt	NOUN
ejpam-6347	150	32	=	=	SYM
ejpam-6347	150	33	λ−	λ−	PROPN
ejpam-6347	150	34	(	(	PUNCT
ejpam-6347	150	35	β	β	X
ejpam-6347	150	36	+	+	NOUN
ejpam-6347	150	37	µ)s	µ)s	NOUN
ejpam-6347	150	38	=	=	SYM
ejpam-6347	150	39	0	0	NUM
ejpam-6347	150	40	,	,	PUNCT
ejpam-6347	150	41	dv	dv	PROPN
ejpam-6347	150	42	dt	dt	PROPN
ejpam-6347	150	43	=	=	PUNCT
ejpam-6347	150	44	βs	βs	PROPN
ejpam-6347	150	45	−	−	PROPN
ejpam-6347	150	46	µv	µv	NOUN
ejpam-6347	150	47	=	=	SYM
ejpam-6347	150	48	0	0	X
ejpam-6347	150	49	.	.	PUNCT
ejpam-6347	151	1	solving	solve	VERB
ejpam-6347	151	2	these	these	DET
ejpam-6347	151	3	equations	equation	NOUN
ejpam-6347	151	4	yields	yield	VERB
ejpam-6347	151	5	the	the	DET
ejpam-6347	151	6	equilibrium	equilibrium	NOUN
ejpam-6347	151	7	values	value	NOUN
ejpam-6347	151	8	:	:	PUNCT
ejpam-6347	151	9	s∗	s∗	PROPN
ejpam-6347	151	10	=	=	SYM
ejpam-6347	151	11	λ	λ	X
ejpam-6347	151	12	β	β	X
ejpam-6347	151	13	+	+	X
ejpam-6347	151	14	µ	µ	X
ejpam-6347	151	15	,	,	PUNCT
ejpam-6347	151	16	v	v	NOUN
ejpam-6347	151	17	∗	∗	NOUN
ejpam-6347	151	18	=	=	SYM
ejpam-6347	151	19	λβ	λβ	X
ejpam-6347	151	20	(	(	PUNCT
ejpam-6347	151	21	β	β	NOUN
ejpam-6347	151	22	+	+	NOUN
ejpam-6347	151	23	µ)µ	µ)µ	X
ejpam-6347	151	24	.	.	PUNCT
ejpam-6347	152	1	(	(	PUNCT
ejpam-6347	152	2	2.18	2.18	NUM
ejpam-6347	152	3	)	)	PUNCT
ejpam-6347	152	4	therefore	therefore	ADV
ejpam-6347	152	5	,	,	PUNCT
ejpam-6347	152	6	the	the	DET
ejpam-6347	152	7	disease	disease	NOUN
ejpam-6347	152	8	-	-	PUNCT
ejpam-6347	152	9	free	free	ADJ
ejpam-6347	152	10	equilibrium	equilibrium	NOUN
ejpam-6347	152	11	point	point	NOUN
ejpam-6347	152	12	is	be	AUX
ejpam-6347	152	13	e0	e0	PROPN
ejpam-6347	152	14	=	=	PUNCT
ejpam-6347	152	15	(	(	PUNCT
ejpam-6347	152	16	s	s	X
ejpam-6347	152	17	,	,	PUNCT
ejpam-6347	152	18	e	e	NOUN
ejpam-6347	152	19	,	,	PUNCT
ejpam-6347	152	20	u	u	NOUN
ejpam-6347	152	21	,	,	PUNCT
ejpam-6347	152	22	q	q	INTJ
ejpam-6347	152	23	,	,	PUNCT
ejpam-6347	152	24	p	p	X
ejpam-6347	152	25	,	,	PUNCT
ejpam-6347	152	26	h	h	NOUN
ejpam-6347	152	27	,	,	PUNCT
ejpam-6347	152	28	c	c	X
ejpam-6347	152	29	,	,	PUNCT
ejpam-6347	152	30	f	f	PROPN
ejpam-6347	152	31	,	,	PUNCT
ejpam-6347	152	32	v	v	NOUN
ejpam-6347	152	33	,	,	PUNCT
ejpam-6347	152	34	r	r	NOUN
ejpam-6347	152	35	)	)	PUNCT
ejpam-6347	152	36	=	=	SYM
ejpam-6347	152	37	(	(	PUNCT
ejpam-6347	152	38	λ	λ	X
ejpam-6347	152	39	β	β	X
ejpam-6347	152	40	+	+	X
ejpam-6347	152	41	µ	µ	X
ejpam-6347	152	42	,	,	PUNCT
ejpam-6347	152	43	0	0	NUM
ejpam-6347	152	44	,	,	PUNCT
ejpam-6347	152	45	0	0	NUM
ejpam-6347	152	46	,	,	PUNCT
ejpam-6347	152	47	0	0	NUM
ejpam-6347	152	48	,	,	PUNCT
ejpam-6347	152	49	0	0	NUM
ejpam-6347	152	50	,	,	PUNCT
ejpam-6347	152	51	0	0	NUM
ejpam-6347	152	52	,	,	PUNCT
ejpam-6347	152	53	0	0	NUM
ejpam-6347	152	54	,	,	PUNCT
ejpam-6347	152	55	0	0	NUM
ejpam-6347	152	56	,	,	PUNCT
ejpam-6347	152	57	λβ	λβ	X
ejpam-6347	152	58	(	(	PUNCT
ejpam-6347	152	59	β	β	NOUN
ejpam-6347	152	60	+	+	CCONJ
ejpam-6347	152	61	µ)µ	µ)µ	X
ejpam-6347	152	62	,	,	PUNCT
ejpam-6347	152	63	0	0	NUM
ejpam-6347	152	64	)	)	PUNCT
ejpam-6347	152	65	.	.	PUNCT
ejpam-6347	153	1	3	3	X
ejpam-6347	153	2	.	.	X
ejpam-6347	153	3	basic	basic	ADJ
ejpam-6347	153	4	reproduction	reproduction	NOUN
ejpam-6347	153	5	number	number	NOUN
ejpam-6347	153	6	to	to	PART
ejpam-6347	153	7	analyze	analyze	VERB
ejpam-6347	153	8	the	the	DET
ejpam-6347	153	9	transmission	transmission	NOUN
ejpam-6347	153	10	potential	potential	NOUN
ejpam-6347	153	11	of	of	ADP
ejpam-6347	153	12	the	the	DET
ejpam-6347	153	13	covcom10	covcom10	NOUN
ejpam-6347	153	14	model	model	NOUN
ejpam-6347	153	15	(	(	PUNCT
ejpam-6347	153	16	2.4	2.4	NUM
ejpam-6347	153	17	)	)	PUNCT
ejpam-6347	153	18	,	,	PUNCT
ejpam-6347	153	19	we	we	PRON
ejpam-6347	153	20	employ	employ	VERB
ejpam-6347	153	21	the	the	DET
ejpam-6347	153	22	next	next	ADJ
ejpam-6347	153	23	-	-	PUNCT
ejpam-6347	153	24	generation	generation	NOUN
ejpam-6347	153	25	matrix	matrix	NOUN
ejpam-6347	153	26	approach	approach	NOUN
ejpam-6347	153	27	developed	develop	VERB
ejpam-6347	153	28	by	by	ADP
ejpam-6347	153	29	van	van	PROPN
ejpam-6347	153	30	den	den	PROPN
ejpam-6347	153	31	driessche	driessche	NOUN
ejpam-6347	153	32	and	and	CCONJ
ejpam-6347	153	33	watmough	watmough	NOUN
ejpam-6347	153	34	[	[	X
ejpam-6347	153	35	21	21	NUM
ejpam-6347	153	36	]	]	PUNCT
ejpam-6347	153	37	.	.	PUNCT
ejpam-6347	154	1	this	this	DET
ejpam-6347	154	2	method	method	NOUN
ejpam-6347	154	3	involves	involve	VERB
ejpam-6347	154	4	decomposing	decompose	VERB
ejpam-6347	154	5	the	the	DET
ejpam-6347	154	6	system	system	NOUN
ejpam-6347	154	7	into	into	ADP
ejpam-6347	154	8	two	two	NUM
ejpam-6347	154	9	main	main	ADJ
ejpam-6347	154	10	components	component	NOUN
ejpam-6347	154	11	:	:	PUNCT
ejpam-6347	154	12	the	the	DET
ejpam-6347	154	13	transmission	transmission	NOUN
ejpam-6347	154	14	matrix	matrix	NOUN
ejpam-6347	154	15	,	,	PUNCT
ejpam-6347	154	16	which	which	PRON
ejpam-6347	154	17	describes	describe	VERB
ejpam-6347	154	18	the	the	DET
ejpam-6347	154	19	generation	generation	NOUN
ejpam-6347	154	20	of	of	ADP
ejpam-6347	154	21	new	new	ADJ
ejpam-6347	154	22	infections	infection	NOUN
ejpam-6347	154	23	,	,	PUNCT
ejpam-6347	154	24	and	and	CCONJ
ejpam-6347	154	25	the	the	DET
ejpam-6347	154	26	transition	transition	NOUN
ejpam-6347	154	27	matrix	matrix	NOUN
ejpam-6347	154	28	,	,	PUNCT
ejpam-6347	154	29	which	which	PRON
ejpam-6347	154	30	captures	capture	VERB
ejpam-6347	154	31	the	the	DET
ejpam-6347	154	32	movement	movement	NOUN
ejpam-6347	154	33	of	of	ADP
ejpam-6347	154	34	individuals	individual	NOUN
ejpam-6347	154	35	between	between	ADP
ejpam-6347	154	36	different	different	ADJ
ejpam-6347	154	37	epidemiological	epidemiological	ADJ
ejpam-6347	154	38	states	state	NOUN
ejpam-6347	154	39	.	.	PUNCT
ejpam-6347	155	1	the	the	DET
ejpam-6347	155	2	transmission	transmission	NOUN
ejpam-6347	155	3	matrix	matrix	NOUN
ejpam-6347	155	4	a(x∗	a(x∗	NOUN
ejpam-6347	155	5	)	)	PUNCT
ejpam-6347	155	6	and	and	CCONJ
ejpam-6347	155	7	the	the	DET
ejpam-6347	155	8	transition	transition	NOUN
ejpam-6347	155	9	matrix	matrix	NOUN
ejpam-6347	155	10	b(x∗	b(x∗	NOUN
ejpam-6347	155	11	)	)	PUNCT
ejpam-6347	155	12	are	be	AUX
ejpam-6347	155	13	constructed	construct	VERB
ejpam-6347	155	14	as	as	SCONJ
ejpam-6347	155	15	follows	follow	VERB
ejpam-6347	155	16	:	:	PUNCT
ejpam-6347	155	17	a(x∗	a(x∗	ADV
ejpam-6347	155	18	)	)	PUNCT
ejpam-6347	156	1	=	=	SYM
ejpam-6347	156	2			NOUN
ejpam-6347	156	3	γ	γ	X
ejpam-6347	156	4	v	v	ADP
ejpam-6347	156	5	e	e	PROPN
ejpam-6347	156	6	+	+	CCONJ
ejpam-6347	156	7	ϕes	ϕe	VERB
ejpam-6347	156	8	λ1eu	λ1eu	PUNCT
ejpam-6347	156	9	λ2eq	λ2eq	SYM
ejpam-6347	156	10	0	0	NUM
ejpam-6347	156	11	0	0	NUM
ejpam-6347	156	12	0	0	NUM
ejpam-6347	156	13	0	0	NUM
ejpam-6347	156	14			NOUN
ejpam-6347	156	15	,	,	PUNCT
ejpam-6347	156	16	(	(	PUNCT
ejpam-6347	156	17	3.19	3.19	NUM
ejpam-6347	156	18	)	)	PUNCT
ejpam-6347	156	19	n.	n.	NOUN
ejpam-6347	156	20	abbas	abbas	PROPN
ejpam-6347	156	21	,	,	PUNCT
ejpam-6347	156	22	w.	w.	PROPN
ejpam-6347	156	23	shatanawi	shatanawi	PROPN
ejpam-6347	156	24	,	,	PUNCT
ejpam-6347	156	25	s.	s.	PROPN
ejpam-6347	156	26	a.	a.	NOUN
ejpam-6347	156	27	zanib	zanib	PROPN
ejpam-6347	156	28	/	/	SYM
ejpam-6347	156	29	eur	eur	PROPN
ejpam-6347	156	30	.	.	PUNCT
ejpam-6347	157	1	j.	j.	PROPN
ejpam-6347	157	2	pure	pure	PROPN
ejpam-6347	157	3	appl	appl	PROPN
ejpam-6347	157	4	.	.	PROPN
ejpam-6347	157	5	math	math	PROPN
ejpam-6347	157	6	,	,	PUNCT
ejpam-6347	157	7	18	18	NUM
ejpam-6347	157	8	(	(	PUNCT
ejpam-6347	157	9	3	3	NUM
ejpam-6347	157	10	)	)	PUNCT
ejpam-6347	157	11	(	(	PUNCT
ejpam-6347	157	12	2025	2025	NUM
ejpam-6347	157	13	)	)	PUNCT
ejpam-6347	157	14	,	,	PUNCT
ejpam-6347	157	15	6347	6347	NUM
ejpam-6347	157	16	11	11	NUM
ejpam-6347	157	17	of	of	ADP
ejpam-6347	157	18	34	34	NUM
ejpam-6347	157	19	b(x∗	b(x∗	NUM
ejpam-6347	157	20	)	)	PUNCT
ejpam-6347	157	21	=	=	SYM
ejpam-6347	157	22			NOUN
ejpam-6347	157	23	−π1e	−π1e	NUM
ejpam-6347	157	24	−π2u	−π2u	NUM
ejpam-6347	157	25	−π3q	−π3q	NUM
ejpam-6347	158	1	α2u	α2u	NOUN
ejpam-6347	159	1	+	+	CCONJ
ejpam-6347	160	1	b1q−π4p	b1q−π4p	PROPN
ejpam-6347	160	2	η	η	PROPN
ejpam-6347	160	3	c	c	PROPN
ejpam-6347	160	4	+	+	CCONJ
ejpam-6347	160	5	σ2f	σ2f	X
ejpam-6347	160	6	−π5h	−π5h	PROPN
ejpam-6347	160	7	+	+	CCONJ
ejpam-6347	160	8	φ1p	φ1p	PROPN
ejpam-6347	160	9	−π6c	−π6c	NUM
ejpam-6347	160	10	+	+	ADJ
ejpam-6347	160	11	m2h	m2h	ADJ
ejpam-6347	160	12	+	+	CCONJ
ejpam-6347	160	13	φ2p	φ2p	NOUN
ejpam-6347	160	14	−π7f	−π7f	NUM
ejpam-6347	160	15	+	+	ADJ
ejpam-6347	160	16	m3h	m3h	NOUN
ejpam-6347	160	17	+	+	CCONJ
ejpam-6347	160	18	φ3p	φ3p	PROPN
ejpam-6347	160	19			NOUN
ejpam-6347	160	20	.	.	PUNCT
ejpam-6347	161	1	(	(	PUNCT
ejpam-6347	161	2	3.20	3.20	NUM
ejpam-6347	161	3	)	)	PUNCT
ejpam-6347	161	4	the	the	DET
ejpam-6347	161	5	next	next	ADJ
ejpam-6347	161	6	-	-	PUNCT
ejpam-6347	161	7	generation	generation	NOUN
ejpam-6347	161	8	matrix	matrix	NOUN
ejpam-6347	161	9	ab−1	ab−1	NOUN
ejpam-6347	161	10	evaluated	evaluate	VERB
ejpam-6347	161	11	at	at	ADP
ejpam-6347	161	12	the	the	DET
ejpam-6347	161	13	disease	disease	NOUN
ejpam-6347	161	14	-	-	PUNCT
ejpam-6347	161	15	free	free	ADJ
ejpam-6347	161	16	equilibrium	equilibrium	NOUN
ejpam-6347	161	17	yields	yield	NOUN
ejpam-6347	161	18	,	,	PUNCT
ejpam-6347	161	19	ab−1	ab−1	NOUN
ejpam-6347	161	20	=	=	SYM
ejpam-6347	161	21			NOUN
ejpam-6347	161	22	1	1	NUM
ejpam-6347	161	23	π1	π1	NOUN
ejpam-6347	161	24	(	(	PUNCT
ejpam-6347	161	25	ϕλ	ϕλ	X
ejpam-6347	161	26	β+µ	β+µ	PUNCT
ejpam-6347	161	27	+	+	CCONJ
ejpam-6347	161	28	β	β	X
ejpam-6347	161	29	λ	λ	X
ejpam-6347	161	30	γ	γ	X
ejpam-6347	161	31	(	(	PUNCT
ejpam-6347	161	32	β+µ)µ	β+µ)µ	SYM
ejpam-6347	161	33	)	)	PUNCT
ejpam-6347	161	34	0	0	NUM
ejpam-6347	161	35	0	0	NUM
ejpam-6347	161	36	0	0	NUM
ejpam-6347	161	37	0	0	NUM
ejpam-6347	161	38	0	0	NUM
ejpam-6347	161	39	0	0	NUM
ejpam-6347	161	40	0	0	NUM
ejpam-6347	161	41	0	0	NUM
ejpam-6347	161	42	0	0	NUM
ejpam-6347	161	43	0	0	NUM
ejpam-6347	161	44	0	0	NUM
ejpam-6347	161	45	0	0	NUM
ejpam-6347	161	46	0	0	NUM
ejpam-6347	161	47	0	0	NUM
ejpam-6347	161	48	0	0	NUM
ejpam-6347	161	49	0	0	NUM
ejpam-6347	161	50	0	0	NUM
ejpam-6347	161	51	0	0	NUM
ejpam-6347	161	52	0	0	NUM
ejpam-6347	161	53	0	0	NUM
ejpam-6347	161	54	0	0	NUM
ejpam-6347	161	55	0	0	NUM
ejpam-6347	161	56	0	0	NUM
ejpam-6347	161	57	0	0	NUM
ejpam-6347	161	58	0	0	NUM
ejpam-6347	161	59	0	0	NUM
ejpam-6347	161	60	0	0	NUM
ejpam-6347	161	61	0	0	NUM
ejpam-6347	161	62	0	0	NUM
ejpam-6347	161	63	0	0	NUM
ejpam-6347	161	64	0	0	NUM
ejpam-6347	161	65	0	0	NUM
ejpam-6347	161	66	0	0	NUM
ejpam-6347	161	67	0	0	NUM
ejpam-6347	161	68	0	0	NUM
ejpam-6347	161	69	0	0	NUM
ejpam-6347	161	70	0	0	NUM
ejpam-6347	161	71	0	0	NUM
ejpam-6347	161	72	0	0	NUM
ejpam-6347	161	73	0	0	NUM
ejpam-6347	161	74	0	0	NUM
ejpam-6347	161	75	0	0	NUM
ejpam-6347	161	76	0	0	NUM
ejpam-6347	161	77	0	0	NUM
ejpam-6347	161	78	0	0	NUM
ejpam-6347	161	79	0	0	NUM
ejpam-6347	161	80	0	0	NUM
ejpam-6347	161	81	0	0	NUM
ejpam-6347	161	82			NUM
ejpam-6347	161	83	.	.	PUNCT
ejpam-6347	162	1	(	(	PUNCT
ejpam-6347	162	2	3.21	3.21	NUM
ejpam-6347	162	3	)	)	PUNCT
ejpam-6347	162	4	here	here	ADV
ejpam-6347	162	5	,	,	PUNCT
ejpam-6347	162	6	the	the	DET
ejpam-6347	162	7	composite	composite	ADJ
ejpam-6347	162	8	parameters	parameter	NOUN
ejpam-6347	162	9	πi	πi	ADV
ejpam-6347	162	10	are	be	AUX
ejpam-6347	162	11	defined	define	VERB
ejpam-6347	162	12	to	to	PART
ejpam-6347	162	13	combine	combine	VERB
ejpam-6347	162	14	various	various	ADJ
ejpam-6347	162	15	transition	transition	NOUN
ejpam-6347	162	16	rates	rate	NOUN
ejpam-6347	162	17	:	:	PUNCT
ejpam-6347	162	18	π1	π1	NOUN
ejpam-6347	162	19	=	=	PUNCT
ejpam-6347	162	20	λ1u	λ1u	PROPN
ejpam-6347	162	21	+	+	NUM
ejpam-6347	162	22	λ2q+	λ2q+	NOUN
ejpam-6347	162	23	µ+	µ+	VERB
ejpam-6347	162	24	d1	d1	NOUN
ejpam-6347	162	25	,	,	PUNCT
ejpam-6347	162	26	π2	π2	NOUN
ejpam-6347	162	27	=	=	SYM
ejpam-6347	162	28	α1	α1	PROPN
ejpam-6347	162	29	+	+	CCONJ
ejpam-6347	162	30	α2	α2	ADJ
ejpam-6347	162	31	+	+	CCONJ
ejpam-6347	162	32	µ+	µ+	PROPN
ejpam-6347	162	33	d2	d2	PROPN
ejpam-6347	162	34	,	,	PUNCT
ejpam-6347	163	1	π3	π3	NOUN
ejpam-6347	163	2	=	=	SYM
ejpam-6347	163	3	b1	b1	PROPN
ejpam-6347	163	4	+	+	CCONJ
ejpam-6347	163	5	b2	b2	NOUN
ejpam-6347	163	6	+	+	CCONJ
ejpam-6347	163	7	b3	b3	PROPN
ejpam-6347	163	8	+	+	CCONJ
ejpam-6347	163	9	µ+	µ+	PUNCT
ejpam-6347	163	10	d3	d3	PROPN
ejpam-6347	163	11	,	,	PUNCT
ejpam-6347	163	12	π4	π4	NOUN
ejpam-6347	163	13	=	=	SYM
ejpam-6347	163	14	φ1	φ1	PROPN
ejpam-6347	163	15	+	+	CCONJ
ejpam-6347	163	16	φ2	φ2	NOUN
ejpam-6347	163	17	+	+	CCONJ
ejpam-6347	163	18	φ3	φ3	NOUN
ejpam-6347	163	19	+	+	CCONJ
ejpam-6347	163	20	µ+	µ+	PROPN
ejpam-6347	163	21	d4	d4	PROPN
ejpam-6347	163	22	,	,	PUNCT
ejpam-6347	163	23	π5	π5	PROPN
ejpam-6347	163	24	=	=	SYM
ejpam-6347	163	25	m1	m1	PROPN
ejpam-6347	164	1	+	+	PROPN
ejpam-6347	164	2	m2	m2	PROPN
ejpam-6347	164	3	+	+	PROPN
ejpam-6347	164	4	m3	m3	PROPN
ejpam-6347	164	5	+	+	CCONJ
ejpam-6347	164	6	µ+	µ+	PROPN
ejpam-6347	164	7	d5	d5	NOUN
ejpam-6347	164	8	,	,	PUNCT
ejpam-6347	164	9	π6	π6	NOUN
ejpam-6347	164	10	=	=	SYM
ejpam-6347	164	11	η	η	PROPN
ejpam-6347	164	12	+	+	PROPN
ejpam-6347	164	13	µ+	µ+	PROPN
ejpam-6347	164	14	d6	d6	NOUN
ejpam-6347	164	15	,	,	PUNCT
ejpam-6347	164	16	π7	π7	NOUN
ejpam-6347	164	17	=	=	SYM
ejpam-6347	164	18	σ1	σ1	PROPN
ejpam-6347	164	19	+	+	CCONJ
ejpam-6347	164	20	σ2	σ2	PROPN
ejpam-6347	164	21	+	+	CCONJ
ejpam-6347	164	22	µ+	µ+	X
ejpam-6347	164	23	d7	d7	PROPN
ejpam-6347	164	24	.	.	PUNCT
ejpam-6347	165	1	(	(	PUNCT
ejpam-6347	165	2	3.22	3.22	NUM
ejpam-6347	165	3	)	)	PUNCT
ejpam-6347	165	4	by	by	ADP
ejpam-6347	165	5	evaluating	evaluate	VERB
ejpam-6347	165	6	the	the	DET
ejpam-6347	165	7	jacobians	jacobian	NOUN
ejpam-6347	165	8	of	of	ADP
ejpam-6347	165	9	a(x∗	a(x∗	PROPN
ejpam-6347	165	10	)	)	PUNCT
ejpam-6347	165	11	and	and	CCONJ
ejpam-6347	165	12	b(x∗	b(x∗	NUM
ejpam-6347	165	13	)	)	PUNCT
ejpam-6347	165	14	at	at	ADP
ejpam-6347	165	15	the	the	DET
ejpam-6347	165	16	disease	disease	NOUN
ejpam-6347	165	17	-	-	PUNCT
ejpam-6347	165	18	free	free	ADJ
ejpam-6347	165	19	equilibrium	equilibrium	NOUN
ejpam-6347	165	20	(	(	PUNCT
ejpam-6347	165	21	dfe	dfe	PROPN
ejpam-6347	165	22	)	)	PUNCT
ejpam-6347	165	23	and	and	CCONJ
ejpam-6347	165	24	computing	compute	VERB
ejpam-6347	165	25	the	the	DET
ejpam-6347	165	26	spectral	spectral	ADJ
ejpam-6347	165	27	radius	radius	NOUN
ejpam-6347	165	28	of	of	ADP
ejpam-6347	165	29	ab−1	ab−1	PROPN
ejpam-6347	165	30	,	,	PUNCT
ejpam-6347	165	31	we	we	PRON
ejpam-6347	165	32	obtain	obtain	VERB
ejpam-6347	165	33	the	the	DET
ejpam-6347	165	34	basic	basic	ADJ
ejpam-6347	165	35	reproduction	reproduction	NOUN
ejpam-6347	165	36	number	number	NOUN
ejpam-6347	165	37	:	:	PUNCT
ejpam-6347	165	38	r0	r0	NOUN
ejpam-6347	165	39	=	=	SYM
ejpam-6347	165	40	λ	λ	PROPN
ejpam-6347	165	41	(	(	PUNCT
ejpam-6347	165	42	γ	γ	X
ejpam-6347	165	43	β	β	X
ejpam-6347	165	44	+	+	CCONJ
ejpam-6347	165	45	µϕ	µϕ	X
ejpam-6347	165	46	)	)	PUNCT
ejpam-6347	165	47	µ	µ	X
ejpam-6347	165	48	(	(	PUNCT
ejpam-6347	165	49	β	β	X
ejpam-6347	165	50	+	+	X
ejpam-6347	165	51	µ	µ	X
ejpam-6347	165	52	)	)	PUNCT
ejpam-6347	165	53	(	(	PUNCT
ejpam-6347	165	54	µ+	µ+	X
ejpam-6347	165	55	d1	d1	NOUN
ejpam-6347	165	56	)	)	PUNCT
ejpam-6347	165	57	.	.	PUNCT
ejpam-6347	166	1	(	(	PUNCT
ejpam-6347	166	2	3.23	3.23	NUM
ejpam-6347	166	3	)	)	PUNCT
ejpam-6347	166	4	3.1	3.1	NUM
ejpam-6347	166	5	.	.	PUNCT
ejpam-6347	167	1	sensitivity	sensitivity	NOUN
ejpam-6347	167	2	analysis	analysis	NOUN
ejpam-6347	167	3	sensitivity	sensitivity	NOUN
ejpam-6347	167	4	analysis	analysis	NOUN
ejpam-6347	167	5	quantifies	quantifie	NOUN
ejpam-6347	167	6	how	how	SCONJ
ejpam-6347	167	7	variations	variation	NOUN
ejpam-6347	167	8	in	in	ADP
ejpam-6347	167	9	model	model	NOUN
ejpam-6347	167	10	parameters	parameter	NOUN
ejpam-6347	167	11	affect	affect	VERB
ejpam-6347	167	12	the	the	DET
ejpam-6347	167	13	basic	basic	ADJ
ejpam-6347	167	14	reproduction	reproduction	NOUN
ejpam-6347	167	15	number	number	NOUN
ejpam-6347	167	16	r0	r0	NOUN
ejpam-6347	168	1	[	[	X
ejpam-6347	168	2	22	22	NUM
ejpam-6347	168	3	]	]	PUNCT
ejpam-6347	168	4	.	.	PUNCT
ejpam-6347	169	1	the	the	DET
ejpam-6347	169	2	normalized	normalize	VERB
ejpam-6347	169	3	sensitivity	sensitivity	NOUN
ejpam-6347	169	4	index	index	NOUN
ejpam-6347	169	5	,	,	PUNCT
ejpam-6347	169	6	defined	define	VERB
ejpam-6347	169	7	as	as	ADP
ejpam-6347	169	8	υr0	υr0	PROPN
ejpam-6347	169	9	ξ	ξ	PROPN
ejpam-6347	169	10	,	,	PUNCT
ejpam-6347	169	11	represents	represent	VERB
ejpam-6347	169	12	n.	n.	NOUN
ejpam-6347	169	13	abbas	abbas	PROPN
ejpam-6347	169	14	,	,	PUNCT
ejpam-6347	169	15	w.	w.	PROPN
ejpam-6347	169	16	shatanawi	shatanawi	PROPN
ejpam-6347	169	17	,	,	PUNCT
ejpam-6347	169	18	s.	s.	PROPN
ejpam-6347	169	19	a.	a.	NOUN
ejpam-6347	169	20	zanib	zanib	PROPN
ejpam-6347	169	21	/	/	SYM
ejpam-6347	169	22	eur	eur	PROPN
ejpam-6347	169	23	.	.	PUNCT
ejpam-6347	170	1	j.	j.	PROPN
ejpam-6347	170	2	pure	pure	PROPN
ejpam-6347	170	3	appl	appl	PROPN
ejpam-6347	170	4	.	.	PROPN
ejpam-6347	170	5	math	math	PROPN
ejpam-6347	170	6	,	,	PUNCT
ejpam-6347	170	7	18	18	NUM
ejpam-6347	170	8	(	(	PUNCT
ejpam-6347	170	9	3	3	NUM
ejpam-6347	170	10	)	)	PUNCT
ejpam-6347	170	11	(	(	PUNCT
ejpam-6347	170	12	2025	2025	NUM
ejpam-6347	170	13	)	)	PUNCT
ejpam-6347	170	14	,	,	PUNCT
ejpam-6347	170	15	6347	6347	NUM
ejpam-6347	170	16	12	12	NUM
ejpam-6347	170	17	of	of	ADP
ejpam-6347	170	18	34	34	NUM
ejpam-6347	170	19	the	the	DET
ejpam-6347	170	20	relative	relative	ADJ
ejpam-6347	170	21	change	change	NOUN
ejpam-6347	170	22	in	in	ADP
ejpam-6347	170	23	r0	r0	NOUN
ejpam-6347	170	24	resulting	result	VERB
ejpam-6347	170	25	from	from	ADP
ejpam-6347	170	26	a	a	DET
ejpam-6347	170	27	relative	relative	ADJ
ejpam-6347	170	28	change	change	NOUN
ejpam-6347	170	29	in	in	ADP
ejpam-6347	170	30	a	a	DET
ejpam-6347	170	31	parameter	parameter	NOUN
ejpam-6347	170	32	ξ	ξ	NOUN
ejpam-6347	170	33	,	,	PUNCT
ejpam-6347	170	34	mathematically	mathematically	ADV
ejpam-6347	170	35	given	give	VERB
ejpam-6347	170	36	by	by	ADP
ejpam-6347	170	37	:	:	PUNCT
ejpam-6347	170	38	υr0	υr0	PROPN
ejpam-6347	170	39	ξ	ξ	X
ejpam-6347	170	40	=	=	PUNCT
ejpam-6347	171	1	∂r0	∂r0	ADP
ejpam-6347	171	2	∂ξ	∂ξ	NUM
ejpam-6347	171	3	×	×	NOUN
ejpam-6347	171	4	ξ	ξ	X
ejpam-6347	171	5	r0	r0	NOUN
ejpam-6347	171	6	.	.	PUNCT
ejpam-6347	172	1	(	(	PUNCT
ejpam-6347	172	2	3.24	3.24	NUM
ejpam-6347	172	3	)	)	PUNCT
ejpam-6347	172	4	applying	apply	VERB
ejpam-6347	172	5	this	this	DET
ejpam-6347	172	6	definition	definition	NOUN
ejpam-6347	172	7	to	to	PART
ejpam-6347	172	8	model	model	VERB
ejpam-6347	172	9	reproduction	reproduction	NOUN
ejpam-6347	172	10	number	number	NOUN
ejpam-6347	172	11	:	:	PUNCT
ejpam-6347	172	12	r0	r0	NOUN
ejpam-6347	172	13	=	=	SYM
ejpam-6347	172	14	λ	λ	PROPN
ejpam-6347	172	15	(	(	PUNCT
ejpam-6347	172	16	γ	γ	X
ejpam-6347	172	17	β	β	X
ejpam-6347	172	18	+	+	CCONJ
ejpam-6347	172	19	µϕ	µϕ	X
ejpam-6347	172	20	)	)	PUNCT
ejpam-6347	172	21	µ	µ	X
ejpam-6347	172	22	(	(	PUNCT
ejpam-6347	172	23	β	β	X
ejpam-6347	172	24	+	+	X
ejpam-6347	172	25	µ	µ	X
ejpam-6347	172	26	)	)	PUNCT
ejpam-6347	172	27	(	(	PUNCT
ejpam-6347	172	28	µ+	µ+	X
ejpam-6347	172	29	d1	d1	NOUN
ejpam-6347	172	30	)	)	PUNCT
ejpam-6347	172	31	,	,	PUNCT
ejpam-6347	172	32	(	(	PUNCT
ejpam-6347	172	33	3.25	3.25	NUM
ejpam-6347	172	34	)	)	PUNCT
ejpam-6347	172	35	we	we	PRON
ejpam-6347	172	36	compute	compute	VERB
ejpam-6347	172	37	sensitivity	sensitivity	NOUN
ejpam-6347	172	38	indices	indice	VERB
ejpam-6347	172	39	for	for	ADP
ejpam-6347	172	40	key	key	ADJ
ejpam-6347	172	41	parameters	parameter	NOUN
ejpam-6347	172	42	:	:	PUNCT
ejpam-6347	172	43	•	•	NUM
ejpam-6347	172	44	sensitivity	sensitivity	NOUN
ejpam-6347	172	45	with	with	ADP
ejpam-6347	172	46	respect	respect	NOUN
ejpam-6347	172	47	to	to	ADP
ejpam-6347	172	48	β	β	NOUN
ejpam-6347	172	49	:	:	PUNCT
ejpam-6347	172	50	υr0	υr0	PROPN
ejpam-6347	172	51	β	β	X
ejpam-6347	172	52	=	=	PUNCT
ejpam-6347	172	53	γ	γ	X
ejpam-6347	172	54	β	β	X
ejpam-6347	172	55	γ	γ	X
ejpam-6347	172	56	β	β	X
ejpam-6347	172	57	+	+	CCONJ
ejpam-6347	172	58	µϕ	µϕ	ADP
ejpam-6347	172	59	−	−	PROPN
ejpam-6347	172	60	β	β	X
ejpam-6347	172	61	β	β	X
ejpam-6347	172	62	+	+	X
ejpam-6347	172	63	µ	µ	X
ejpam-6347	172	64	.	.	PUNCT
ejpam-6347	173	1	(	(	PUNCT
ejpam-6347	173	2	3.26	3.26	NUM
ejpam-6347	173	3	)	)	PUNCT
ejpam-6347	173	4	an	an	DET
ejpam-6347	173	5	increase	increase	NOUN
ejpam-6347	173	6	in	in	ADP
ejpam-6347	173	7	β	β	X
ejpam-6347	173	8	will	will	AUX
ejpam-6347	173	9	increase	increase	VERB
ejpam-6347	173	10	r0	r0	NOUN
ejpam-6347	173	11	,	,	PUNCT
ejpam-6347	173	12	indicating	indicate	VERB
ejpam-6347	173	13	a	a	DET
ejpam-6347	173	14	higher	high	ADJ
ejpam-6347	173	15	transmission	transmission	NOUN
ejpam-6347	173	16	potential	potential	NOUN
ejpam-6347	173	17	.	.	PUNCT
ejpam-6347	174	1	•	•	NUM
ejpam-6347	174	2	sensitivity	sensitivity	NOUN
ejpam-6347	174	3	with	with	ADP
ejpam-6347	174	4	respect	respect	NOUN
ejpam-6347	174	5	to	to	ADP
ejpam-6347	174	6	γ	γ	PROPN
ejpam-6347	174	7	:	:	PUNCT
ejpam-6347	174	8	υr0	υr0	PROPN
ejpam-6347	174	9	γ	γ	X
ejpam-6347	174	10	=	=	SYM
ejpam-6347	174	11	γ	γ	X
ejpam-6347	174	12	β	β	X
ejpam-6347	174	13	γ	γ	X
ejpam-6347	174	14	β	β	X
ejpam-6347	174	15	+	+	X
ejpam-6347	174	16	µϕ	µϕ	ADV
ejpam-6347	174	17	.	.	PUNCT
ejpam-6347	175	1	(	(	PUNCT
ejpam-6347	175	2	3.27	3.27	NUM
ejpam-6347	175	3	)	)	PUNCT
ejpam-6347	175	4	a	a	DET
ejpam-6347	175	5	higher	high	ADJ
ejpam-6347	175	6	γ	γ	NOUN
ejpam-6347	175	7	elevates	elevate	VERB
ejpam-6347	175	8	r0	r0	NOUN
ejpam-6347	175	9	,	,	PUNCT
ejpam-6347	175	10	highlighting	highlight	VERB
ejpam-6347	175	11	increased	increase	VERB
ejpam-6347	175	12	transmission	transmission	NOUN
ejpam-6347	175	13	from	from	ADP
ejpam-6347	175	14	asymptomatic	asymptomatic	ADJ
ejpam-6347	175	15	or	or	CCONJ
ejpam-6347	175	16	pre	pre	ADJ
ejpam-6347	175	17	-	-	ADJ
ejpam-6347	175	18	symptomatic	symptomatic	ADJ
ejpam-6347	175	19	individuals	individual	NOUN
ejpam-6347	175	20	.	.	PUNCT
ejpam-6347	176	1	•	•	NUM
ejpam-6347	176	2	sensitivity	sensitivity	NOUN
ejpam-6347	176	3	with	with	ADP
ejpam-6347	176	4	respect	respect	NOUN
ejpam-6347	176	5	to	to	ADP
ejpam-6347	176	6	ϕ	ϕ	NOUN
ejpam-6347	176	7	:	:	PUNCT
ejpam-6347	176	8	υr0	υr0	PROPN
ejpam-6347	176	9	ϕ	ϕ	NOUN
ejpam-6347	177	1	=	=	X
ejpam-6347	177	2	µϕ	µϕ	ADP
ejpam-6347	177	3	γ	γ	X
ejpam-6347	177	4	β	β	X
ejpam-6347	178	1	+	+	X
ejpam-6347	178	2	µϕ	µϕ	ADV
ejpam-6347	178	3	.	.	PUNCT
ejpam-6347	179	1	(	(	PUNCT
ejpam-6347	179	2	3.28	3.28	NUM
ejpam-6347	179	3	)	)	PUNCT
ejpam-6347	179	4	an	an	DET
ejpam-6347	179	5	increase	increase	NOUN
ejpam-6347	179	6	in	in	ADP
ejpam-6347	179	7	exposure	exposure	NOUN
ejpam-6347	179	8	rate	rate	NOUN
ejpam-6347	179	9	ϕ	ϕ	PROPN
ejpam-6347	179	10	raises	raise	VERB
ejpam-6347	179	11	r0	r0	NOUN
ejpam-6347	179	12	,	,	PUNCT
ejpam-6347	179	13	demonstrating	demonstrate	VERB
ejpam-6347	179	14	greater	great	ADJ
ejpam-6347	179	15	susceptibility	susceptibility	NOUN
ejpam-6347	179	16	within	within	ADP
ejpam-6347	179	17	the	the	DET
ejpam-6347	179	18	population	population	NOUN
ejpam-6347	179	19	.	.	PUNCT
ejpam-6347	180	1	•	•	NUM
ejpam-6347	180	2	sensitivity	sensitivity	NOUN
ejpam-6347	180	3	with	with	ADP
ejpam-6347	180	4	respect	respect	NOUN
ejpam-6347	180	5	to	to	ADP
ejpam-6347	180	6	µ	µ	NUM
ejpam-6347	180	7	:	:	PUNCT
ejpam-6347	180	8	υr0	υr0	PROPN
ejpam-6347	180	9	µ	µ	X
ejpam-6347	180	10	=	=	X
ejpam-6347	180	11	µϕ	µϕ	ADP
ejpam-6347	180	12	γ	γ	X
ejpam-6347	180	13	β	β	X
ejpam-6347	180	14	+	+	CCONJ
ejpam-6347	180	15	µϕ	µϕ	ADP
ejpam-6347	180	16	−	−	PROPN
ejpam-6347	180	17	µ	µ	X
ejpam-6347	180	18	β	β	X
ejpam-6347	180	19	+	+	X
ejpam-6347	180	20	µ	µ	X
ejpam-6347	180	21	−	−	PROPN
ejpam-6347	180	22	µ	µ	PROPN
ejpam-6347	180	23	µ+	µ+	X
ejpam-6347	180	24	d1	d1	NOUN
ejpam-6347	180	25	−	−	PROPN
ejpam-6347	180	26	1	1	X
ejpam-6347	180	27	.	.	PUNCT
ejpam-6347	181	1	(	(	PUNCT
ejpam-6347	181	2	3.29	3.29	NUM
ejpam-6347	181	3	)	)	PUNCT
ejpam-6347	181	4	increasing	increase	VERB
ejpam-6347	181	5	the	the	DET
ejpam-6347	181	6	natural	natural	ADJ
ejpam-6347	181	7	death	death	NOUN
ejpam-6347	181	8	rate	rate	NOUN
ejpam-6347	181	9	µ	µ	PROPN
ejpam-6347	181	10	generally	generally	ADV
ejpam-6347	181	11	reduces	reduce	VERB
ejpam-6347	181	12	r0	r0	NOUN
ejpam-6347	181	13	,	,	PUNCT
ejpam-6347	181	14	as	as	SCONJ
ejpam-6347	181	15	fewer	few	ADJ
ejpam-6347	181	16	individuals	individual	NOUN
ejpam-6347	181	17	remain	remain	VERB
ejpam-6347	181	18	susceptible	susceptible	ADJ
ejpam-6347	181	19	to	to	ADP
ejpam-6347	181	20	infection	infection	NOUN
ejpam-6347	181	21	.	.	PUNCT
ejpam-6347	182	1	•	•	NUM
ejpam-6347	182	2	sensitivity	sensitivity	NOUN
ejpam-6347	182	3	with	with	ADP
ejpam-6347	182	4	respect	respect	NOUN
ejpam-6347	182	5	to	to	ADP
ejpam-6347	182	6	d1	d1	NOUN
ejpam-6347	182	7	:	:	PUNCT
ejpam-6347	182	8	υr0	υr0	NOUN
ejpam-6347	182	9	d1	d1	NOUN
ejpam-6347	182	10	=	=	PUNCT
ejpam-6347	182	11	−	−	ADP
ejpam-6347	182	12	d1	d1	PROPN
ejpam-6347	182	13	µ+	µ+	PRON
ejpam-6347	182	14	d1	d1	PROPN
ejpam-6347	182	15	.	.	PUNCT
ejpam-6347	183	1	(	(	PUNCT
ejpam-6347	183	2	3.30	3.30	X
ejpam-6347	183	3	)	)	PUNCT
ejpam-6347	183	4	increasing	increase	VERB
ejpam-6347	183	5	disease	disease	NOUN
ejpam-6347	183	6	-	-	PUNCT
ejpam-6347	183	7	induced	induce	VERB
ejpam-6347	183	8	death	death	NOUN
ejpam-6347	183	9	rate	rate	NOUN
ejpam-6347	183	10	d1	d1	PROPN
ejpam-6347	183	11	lowers	lower	VERB
ejpam-6347	183	12	r0	r0	NOUN
ejpam-6347	183	13	,	,	PUNCT
ejpam-6347	183	14	due	due	ADP
ejpam-6347	183	15	to	to	ADP
ejpam-6347	183	16	a	a	DET
ejpam-6347	183	17	reduction	reduction	NOUN
ejpam-6347	183	18	in	in	ADP
ejpam-6347	183	19	the	the	DET
ejpam-6347	183	20	number	number	NOUN
ejpam-6347	183	21	of	of	ADP
ejpam-6347	183	22	infectious	infectious	ADJ
ejpam-6347	183	23	contacts	contact	NOUN
ejpam-6347	183	24	.	.	PUNCT
ejpam-6347	184	1	n.	n.	PROPN
ejpam-6347	184	2	abbas	abbas	PROPN
ejpam-6347	184	3	,	,	PUNCT
ejpam-6347	184	4	w.	w.	PROPN
ejpam-6347	184	5	shatanawi	shatanawi	PROPN
ejpam-6347	184	6	,	,	PUNCT
ejpam-6347	184	7	s.	s.	PROPN
ejpam-6347	184	8	a.	a.	NOUN
ejpam-6347	184	9	zanib	zanib	PROPN
ejpam-6347	184	10	/	/	SYM
ejpam-6347	184	11	eur	eur	PROPN
ejpam-6347	184	12	.	.	PUNCT
ejpam-6347	185	1	j.	j.	PROPN
ejpam-6347	185	2	pure	pure	PROPN
ejpam-6347	185	3	appl	appl	PROPN
ejpam-6347	185	4	.	.	PROPN
ejpam-6347	185	5	math	math	PROPN
ejpam-6347	185	6	,	,	PUNCT
ejpam-6347	185	7	18	18	NUM
ejpam-6347	185	8	(	(	PUNCT
ejpam-6347	185	9	3	3	NUM
ejpam-6347	185	10	)	)	PUNCT
ejpam-6347	185	11	(	(	PUNCT
ejpam-6347	185	12	2025	2025	NUM
ejpam-6347	185	13	)	)	PUNCT
ejpam-6347	185	14	,	,	PUNCT
ejpam-6347	185	15	6347	6347	NUM
ejpam-6347	185	16	13	13	NUM
ejpam-6347	185	17	of	of	ADP
ejpam-6347	185	18	34	34	NUM
ejpam-6347	185	19	•	•	NOUN
ejpam-6347	185	20	sensitivity	sensitivity	NOUN
ejpam-6347	185	21	with	with	ADP
ejpam-6347	185	22	respect	respect	NOUN
ejpam-6347	185	23	to	to	ADP
ejpam-6347	185	24	λ	λ	NOUN
ejpam-6347	185	25	:	:	PUNCT
ejpam-6347	185	26	υr0	υr0	PROPN
ejpam-6347	185	27	λ	λ	NOUN
ejpam-6347	185	28	=	=	NOUN
ejpam-6347	185	29	1	1	X
ejpam-6347	185	30	.	.	PUNCT
ejpam-6347	185	31	(	(	PUNCT
ejpam-6347	185	32	3.31	3.31	NUM
ejpam-6347	185	33	)	)	PUNCT
ejpam-6347	185	34	an	an	DET
ejpam-6347	185	35	increase	increase	NOUN
ejpam-6347	185	36	in	in	ADP
ejpam-6347	185	37	λ	λ	PROPN
ejpam-6347	185	38	which	which	PRON
ejpam-6347	185	39	is	be	AUX
ejpam-6347	185	40	birth	birth	NOUN
ejpam-6347	185	41	rate	rate	NOUN
ejpam-6347	185	42	will	will	AUX
ejpam-6347	185	43	increase	increase	VERB
ejpam-6347	185	44	r0	r0	NOUN
ejpam-6347	185	45	,	,	PUNCT
ejpam-6347	185	46	indicating	indicate	VERB
ejpam-6347	185	47	a	a	DET
ejpam-6347	185	48	higher	high	ADJ
ejpam-6347	185	49	transmission	transmission	NOUN
ejpam-6347	185	50	potential	potential	NOUN
ejpam-6347	185	51	.	.	PUNCT
ejpam-6347	186	1	this	this	DET
ejpam-6347	186	2	sensitivity	sensitivity	NOUN
ejpam-6347	186	3	analysis	analysis	NOUN
ejpam-6347	186	4	identifies	identify	VERB
ejpam-6347	186	5	critical	critical	ADJ
ejpam-6347	186	6	parameters	parameter	NOUN
ejpam-6347	186	7	influencing	influence	VERB
ejpam-6347	186	8	disease	disease	NOUN
ejpam-6347	186	9	dynamics	dynamic	NOUN
ejpam-6347	186	10	,	,	PUNCT
ejpam-6347	186	11	guiding	guide	VERB
ejpam-6347	186	12	effective	effective	ADJ
ejpam-6347	186	13	strategies	strategy	NOUN
ejpam-6347	186	14	for	for	ADP
ejpam-6347	186	15	controlling	control	VERB
ejpam-6347	186	16	the	the	DET
ejpam-6347	186	17	epidemic	epidemic	NOUN
ejpam-6347	186	18	shown	show	VERB
ejpam-6347	186	19	in	in	ADP
ejpam-6347	186	20	figure	figure	NOUN
ejpam-6347	186	21	3	3	NUM
ejpam-6347	186	22	.	.	X
ejpam-6347	187	1	d1	d1	PROPN
ejpam-6347	187	2	sensitive	sensitive	ADJ
ejpam-6347	187	3	parameters	parameter	NOUN
ejpam-6347	187	4	1.00	1.00	NUM
ejpam-6347	187	5	0.75	0.75	NUM
ejpam-6347	187	6	0.50	0.50	NUM
ejpam-6347	187	7	0.25	0.25	NUM
ejpam-6347	187	8	0.00	0.00	NUM
ejpam-6347	187	9	0.25	0.25	NUM
ejpam-6347	187	10	0.50	0.50	NUM
ejpam-6347	187	11	0.75	0.75	NUM
ejpam-6347	187	12	1.00	1.00	NUM
ejpam-6347	187	13	se	se	X
ejpam-6347	187	14	ns	ns	PROPN
ejpam-6347	188	1	iti	iti	PROPN
ejpam-6347	188	2	vi	vi	NOUN
ejpam-6347	188	3	ty	ty	INTJ
ejpam-6347	188	4	in	in	ADP
ejpam-6347	188	5	di	di	X
ejpam-6347	188	6	ce	ce	PROPN
ejpam-6347	188	7	s	s	PROPN
ejpam-6347	188	8	0.013	0.013	NUM
ejpam-6347	188	9	0.996	0.996	NUM
ejpam-6347	188	10	0.004	0.004	NUM
ejpam-6347	188	11	-1.036	-1.036	NOUN
ejpam-6347	188	12	-0.957	-0.957	PUNCT
ejpam-6347	188	13	1.000	1.000	NUM
ejpam-6347	188	14	figure	figure	NOUN
ejpam-6347	188	15	3	3	NUM
ejpam-6347	188	16	:	:	PUNCT
ejpam-6347	188	17	sensitivity	sensitivity	NOUN
ejpam-6347	188	18	analysis	analysis	NOUN
ejpam-6347	188	19	3.2	3.2	NUM
ejpam-6347	188	20	.	.	PUNCT
ejpam-6347	189	1	stability	stability	NOUN
ejpam-6347	189	2	analysis	analysis	NOUN
ejpam-6347	189	3	local	local	ADJ
ejpam-6347	189	4	stability	stability	NOUN
ejpam-6347	189	5	of	of	ADP
ejpam-6347	189	6	disease	disease	NOUN
ejpam-6347	189	7	-	-	PUNCT
ejpam-6347	189	8	free	free	ADJ
ejpam-6347	189	9	equilibrium	equilibrium	NOUN
ejpam-6347	189	10	point	point	NOUN
ejpam-6347	189	11	to	to	PART
ejpam-6347	189	12	assess	assess	VERB
ejpam-6347	189	13	the	the	DET
ejpam-6347	189	14	behavior	behavior	NOUN
ejpam-6347	189	15	of	of	ADP
ejpam-6347	189	16	the	the	DET
ejpam-6347	189	17	covcom10	covcom10	NOUN
ejpam-6347	189	18	model	model	NOUN
ejpam-6347	189	19	(	(	PUNCT
ejpam-6347	189	20	2.4	2.4	NUM
ejpam-6347	189	21	)	)	PUNCT
ejpam-6347	189	22	near	near	ADP
ejpam-6347	189	23	the	the	DET
ejpam-6347	189	24	disease	disease	NOUN
ejpam-6347	189	25	-	-	PUNCT
ejpam-6347	189	26	free	free	ADJ
ejpam-6347	189	27	equilibrium	equilibrium	NOUN
ejpam-6347	190	1	,	,	PUNCT
ejpam-6347	190	2	it	it	PRON
ejpam-6347	190	3	is	be	AUX
ejpam-6347	190	4	essential	essential	ADJ
ejpam-6347	190	5	to	to	PART
ejpam-6347	190	6	analyze	analyze	VERB
ejpam-6347	190	7	its	its	PRON
ejpam-6347	190	8	local	local	ADJ
ejpam-6347	190	9	stability	stability	NOUN
ejpam-6347	190	10	.	.	PUNCT
ejpam-6347	191	1	this	this	DET
ejpam-6347	191	2	analysis	analysis	NOUN
ejpam-6347	191	3	determines	determine	VERB
ejpam-6347	191	4	whether	whether	SCONJ
ejpam-6347	191	5	small	small	ADJ
ejpam-6347	191	6	disturbances	disturbance	NOUN
ejpam-6347	191	7	from	from	ADP
ejpam-6347	191	8	the	the	DET
ejpam-6347	191	9	disease	disease	NOUN
ejpam-6347	191	10	-	-	PUNCT
ejpam-6347	191	11	free	free	ADJ
ejpam-6347	191	12	state	state	NOUN
ejpam-6347	191	13	will	will	AUX
ejpam-6347	191	14	decay	decay	VERB
ejpam-6347	191	15	or	or	CCONJ
ejpam-6347	191	16	grow	grow	VERB
ejpam-6347	191	17	,	,	PUNCT
ejpam-6347	191	18	which	which	PRON
ejpam-6347	191	19	is	be	AUX
ejpam-6347	191	20	crucial	crucial	ADJ
ejpam-6347	191	21	for	for	ADP
ejpam-6347	191	22	understanding	understand	VERB
ejpam-6347	191	23	epidemic	epidemic	NOUN
ejpam-6347	191	24	control	control	NOUN
ejpam-6347	191	25	strategies	strategy	NOUN
ejpam-6347	191	26	.	.	PUNCT
ejpam-6347	192	1	the	the	DET
ejpam-6347	192	2	following	follow	VERB
ejpam-6347	192	3	theorem	theorem	NOUN
ejpam-6347	192	4	and	and	CCONJ
ejpam-6347	192	5	proof	proof	NOUN
ejpam-6347	192	6	outline	outline	VERB
ejpam-6347	192	7	the	the	DET
ejpam-6347	192	8	conditions	condition	NOUN
ejpam-6347	192	9	under	under	ADP
ejpam-6347	192	10	which	which	PRON
ejpam-6347	192	11	the	the	DET
ejpam-6347	192	12	disease	disease	NOUN
ejpam-6347	192	13	-	-	PUNCT
ejpam-6347	192	14	free	free	ADJ
ejpam-6347	192	15	equilibrium	equilibrium	NOUN
ejpam-6347	192	16	point	point	NOUN
ejpam-6347	192	17	(	(	PUNCT
ejpam-6347	192	18	dfep	dfep	NOUN
ejpam-6347	192	19	)	)	PUNCT
ejpam-6347	192	20	is	be	AUX
ejpam-6347	192	21	locally	locally	ADV
ejpam-6347	192	22	asymptotically	asymptotically	ADV
ejpam-6347	192	23	stable	stable	ADJ
ejpam-6347	192	24	.	.	PUNCT
ejpam-6347	193	1	theorem	theorem	NOUN
ejpam-6347	193	2	3	3	NUM
ejpam-6347	193	3	.	.	PUNCT
ejpam-6347	194	1	the	the	DET
ejpam-6347	194	2	disease	disease	NOUN
ejpam-6347	194	3	-	-	PUNCT
ejpam-6347	194	4	free	free	ADJ
ejpam-6347	194	5	equilibrium	equilibrium	NOUN
ejpam-6347	194	6	point	point	NOUN
ejpam-6347	194	7	e0	e0	PROPN
ejpam-6347	194	8	of	of	ADP
ejpam-6347	194	9	the	the	DET
ejpam-6347	194	10	covcom10	covcom10	NOUN
ejpam-6347	194	11	model	model	NOUN
ejpam-6347	194	12	(	(	PUNCT
ejpam-6347	194	13	2.4	2.4	NUM
ejpam-6347	194	14	)	)	PUNCT
ejpam-6347	194	15	is	be	AUX
ejpam-6347	194	16	locally	locally	ADV
ejpam-6347	194	17	asymptotically	asymptotically	ADV
ejpam-6347	194	18	stable	stable	ADJ
ejpam-6347	194	19	if	if	SCONJ
ejpam-6347	194	20	the	the	DET
ejpam-6347	194	21	basic	basic	ADJ
ejpam-6347	194	22	reproduction	reproduction	NOUN
ejpam-6347	194	23	number	number	NOUN
ejpam-6347	194	24	r0	r0	NOUN
ejpam-6347	194	25	<	<	X
ejpam-6347	194	26	1	1	NUM
ejpam-6347	194	27	and	and	CCONJ
ejpam-6347	194	28	unstable	unstable	ADJ
ejpam-6347	194	29	if	if	SCONJ
ejpam-6347	194	30	r0	r0	NOUN
ejpam-6347	194	31	>	>	X
ejpam-6347	194	32	1	1	NUM
ejpam-6347	195	1	[	[	X
ejpam-6347	195	2	23	23	NUM
ejpam-6347	195	3	]	]	PUNCT
ejpam-6347	195	4	.	.	PUNCT
ejpam-6347	196	1	proof	proof	NOUN
ejpam-6347	196	2	.	.	PUNCT
ejpam-6347	197	1	to	to	PART
ejpam-6347	197	2	establish	establish	VERB
ejpam-6347	197	3	the	the	DET
ejpam-6347	197	4	local	local	ADJ
ejpam-6347	197	5	stability	stability	NOUN
ejpam-6347	197	6	of	of	ADP
ejpam-6347	197	7	the	the	DET
ejpam-6347	197	8	dfep	dfep	NOUN
ejpam-6347	197	9	,	,	PUNCT
ejpam-6347	197	10	we	we	PRON
ejpam-6347	197	11	compute	compute	VERB
ejpam-6347	197	12	the	the	DET
ejpam-6347	197	13	jacobian	jacobian	ADJ
ejpam-6347	197	14	matrix	matrix	NOUN
ejpam-6347	197	15	of	of	ADP
ejpam-6347	197	16	the	the	DET
ejpam-6347	197	17	system	system	NOUN
ejpam-6347	197	18	at	at	ADP
ejpam-6347	197	19	e0	e0	PROPN
ejpam-6347	197	20	.	.	PUNCT
ejpam-6347	198	1	the	the	DET
ejpam-6347	198	2	jacobian	jacobian	ADJ
ejpam-6347	198	3	matrix	matrix	NOUN
ejpam-6347	198	4	j0	j0	PROPN
ejpam-6347	198	5	is	be	AUX
ejpam-6347	198	6	given	give	VERB
ejpam-6347	198	7	by	by	ADP
ejpam-6347	198	8	:	:	PUNCT
ejpam-6347	198	9	n.	n.	NOUN
ejpam-6347	198	10	abbas	abbas	PROPN
ejpam-6347	198	11	,	,	PUNCT
ejpam-6347	198	12	w.	w.	PROPN
ejpam-6347	198	13	shatanawi	shatanawi	PROPN
ejpam-6347	198	14	,	,	PUNCT
ejpam-6347	198	15	s.	s.	PROPN
ejpam-6347	198	16	a.	a.	NOUN
ejpam-6347	198	17	zanib	zanib	PROPN
ejpam-6347	198	18	/	/	SYM
ejpam-6347	198	19	eur	eur	PROPN
ejpam-6347	198	20	.	.	PUNCT
ejpam-6347	199	1	j.	j.	PROPN
ejpam-6347	199	2	pure	pure	PROPN
ejpam-6347	199	3	appl	appl	PROPN
ejpam-6347	199	4	.	.	PROPN
ejpam-6347	199	5	math	math	PROPN
ejpam-6347	199	6	,	,	PUNCT
ejpam-6347	199	7	18	18	NUM
ejpam-6347	199	8	(	(	PUNCT
ejpam-6347	199	9	3	3	NUM
ejpam-6347	199	10	)	)	PUNCT
ejpam-6347	199	11	(	(	PUNCT
ejpam-6347	199	12	2025	2025	NUM
ejpam-6347	199	13	)	)	PUNCT
ejpam-6347	199	14	,	,	PUNCT
ejpam-6347	199	15	6347	6347	NUM
ejpam-6347	199	16	14	14	NUM
ejpam-6347	199	17	of	of	ADP
ejpam-6347	199	18	34	34	NUM
ejpam-6347	199	19	j0	j0	NOUN
ejpam-6347	199	20	=	=	PUNCT
ejpam-6347	199	21			NOUN
ejpam-6347	199	22	−β	−β	NOUN
ejpam-6347	199	23	−	−	PROPN
ejpam-6347	199	24	µ	µ	ADV
ejpam-6347	199	25	−	−	NOUN
ejpam-6347	200	1	ϕλ	ϕλ	X
ejpam-6347	200	2	β+µ	β+µ	SYM
ejpam-6347	200	3	0	0	NUM
ejpam-6347	200	4	b2	b2	NOUN
ejpam-6347	200	5	0	0	NUM
ejpam-6347	200	6	0	0	NUM
ejpam-6347	200	7	0	0	NUM
ejpam-6347	200	8	0	0	NUM
ejpam-6347	200	9	0	0	NUM
ejpam-6347	200	10	τ	τ	PROPN
ejpam-6347	200	11	0	0	NUM
ejpam-6347	200	12	γβλ	γβλ	NOUN
ejpam-6347	200	13	(	(	PUNCT
ejpam-6347	200	14	β+µ)µ	β+µ)µ	PUNCT
ejpam-6347	201	1	+	+	NUM
ejpam-6347	201	2	ϕλ	ϕλ	X
ejpam-6347	201	3	β+µ	β+µ	PUNCT
ejpam-6347	201	4	−π1	−π1	NOUN
ejpam-6347	201	5	0	0	NUM
ejpam-6347	201	6	0	0	NUM
ejpam-6347	201	7	0	0	NUM
ejpam-6347	201	8	0	0	NUM
ejpam-6347	201	9	0	0	NUM
ejpam-6347	201	10	0	0	NUM
ejpam-6347	201	11	0	0	NUM
ejpam-6347	201	12	0	0	NUM
ejpam-6347	201	13	0	0	NUM
ejpam-6347	201	14	0	0	NUM
ejpam-6347	201	15	−π2	−π2	NOUN
ejpam-6347	201	16	0	0	NUM
ejpam-6347	201	17	0	0	NUM
ejpam-6347	201	18	0	0	NUM
ejpam-6347	201	19	0	0	NUM
ejpam-6347	201	20	0	0	NUM
ejpam-6347	201	21	0	0	NUM
ejpam-6347	201	22	0	0	NUM
ejpam-6347	201	23	0	0	NUM
ejpam-6347	201	24	0	0	NUM
ejpam-6347	201	25	0	0	NUM
ejpam-6347	202	1	−π3	−π3	NOUN
ejpam-6347	202	2	0	0	NUM
ejpam-6347	202	3	0	0	NUM
ejpam-6347	202	4	0	0	NUM
ejpam-6347	202	5	0	0	NUM
ejpam-6347	202	6	0	0	NUM
ejpam-6347	202	7	0	0	NUM
ejpam-6347	202	8	0	0	SYM
ejpam-6347	202	9	0	0	NUM
ejpam-6347	202	10	α2	α2	ADJ
ejpam-6347	202	11	b1	b1	NOUN
ejpam-6347	202	12	−π4	−π4	PROPN
ejpam-6347	202	13	0	0	NUM
ejpam-6347	202	14	0	0	NUM
ejpam-6347	202	15	0	0	NUM
ejpam-6347	202	16	0	0	NUM
ejpam-6347	202	17	0	0	NUM
ejpam-6347	202	18	0	0	NUM
ejpam-6347	202	19	0	0	NUM
ejpam-6347	202	20	0	0	NUM
ejpam-6347	202	21	0	0	NUM
ejpam-6347	202	22	φ1	φ1	PROPN
ejpam-6347	202	23	−π5	−π5	PROPN
ejpam-6347	202	24	η	η	PROPN
ejpam-6347	202	25	σ2	σ2	PROPN
ejpam-6347	202	26	0	0	NUM
ejpam-6347	202	27	0	0	NUM
ejpam-6347	202	28	0	0	NUM
ejpam-6347	202	29	0	0	NUM
ejpam-6347	202	30	0	0	NUM
ejpam-6347	202	31	0	0	NUM
ejpam-6347	202	32	φ2	φ2	PROPN
ejpam-6347	202	33	m2	m2	PROPN
ejpam-6347	202	34	−π6	−π6	PROPN
ejpam-6347	202	35	0	0	NUM
ejpam-6347	202	36	0	0	NUM
ejpam-6347	202	37	0	0	NUM
ejpam-6347	202	38	0	0	NUM
ejpam-6347	202	39	0	0	NUM
ejpam-6347	202	40	0	0	NUM
ejpam-6347	202	41	0	0	NUM
ejpam-6347	202	42	φ3	φ3	NOUN
ejpam-6347	202	43	m3	m3	PROPN
ejpam-6347	202	44	0	0	PUNCT
ejpam-6347	203	1	−π7	−π7	PROPN
ejpam-6347	203	2	0	0	NUM
ejpam-6347	203	3	0	0	NUM
ejpam-6347	203	4	β	β	NOUN
ejpam-6347	203	5	−	−	PROPN
ejpam-6347	203	6	γβλ	γβλ	NOUN
ejpam-6347	203	7	(	(	PUNCT
ejpam-6347	203	8	β+µ)µ	β+µ)µ	SYM
ejpam-6347	203	9	0	0	NUM
ejpam-6347	203	10	b3	b3	PROPN
ejpam-6347	203	11	0	0	NUM
ejpam-6347	203	12	0	0	NUM
ejpam-6347	203	13	0	0	NUM
ejpam-6347	203	14	0	0	NUM
ejpam-6347	204	1	−µ	−µ	NOUN
ejpam-6347	204	2	0	0	NUM
ejpam-6347	204	3	0	0	NUM
ejpam-6347	204	4	0	0	NUM
ejpam-6347	204	5	α1	α1	PROPN
ejpam-6347	204	6	0	0	NUM
ejpam-6347	204	7	0	0	NUM
ejpam-6347	204	8	m1	m1	NOUN
ejpam-6347	204	9	0	0	NUM
ejpam-6347	205	1	σ1	σ1	PROPN
ejpam-6347	205	2	0	0	NUM
ejpam-6347	205	3	−τ	−τ	PROPN
ejpam-6347	205	4	−	−	PROPN
ejpam-6347	205	5	µ	µ	X
ejpam-6347	205	6			NUM
ejpam-6347	205	7	(	(	PUNCT
ejpam-6347	205	8	3.32	3.32	NUM
ejpam-6347	205	9	)	)	PUNCT
ejpam-6347	205	10	the	the	DET
ejpam-6347	205	11	characteristic	characteristic	ADJ
ejpam-6347	205	12	equation	equation	NOUN
ejpam-6347	205	13	of	of	ADP
ejpam-6347	205	14	j0	j0	PROPN
ejpam-6347	205	15	is	be	AUX
ejpam-6347	205	16	obtained	obtain	VERB
ejpam-6347	205	17	from	from	ADP
ejpam-6347	205	18	det(j0−∆i	det(j0−∆i	PROPN
ejpam-6347	205	19	)	)	PUNCT
ejpam-6347	205	20	=	=	SYM
ejpam-6347	206	1	0	0	NUM
ejpam-6347	206	2	,	,	PUNCT
ejpam-6347	206	3	where	where	SCONJ
ejpam-6347	206	4	i	i	PRON
ejpam-6347	206	5	is	be	AUX
ejpam-6347	206	6	the	the	DET
ejpam-6347	206	7	identity	identity	NOUN
ejpam-6347	206	8	matrix	matrix	NOUN
ejpam-6347	206	9	.	.	PUNCT
ejpam-6347	207	1	the	the	DET
ejpam-6347	207	2	coefficients	coefficient	NOUN
ejpam-6347	207	3	of	of	ADP
ejpam-6347	207	4	the	the	DET
ejpam-6347	207	5	characteristic	characteristic	ADJ
ejpam-6347	207	6	polynomial	polynomial	NOUN
ejpam-6347	207	7	are	be	AUX
ejpam-6347	207	8	:	:	PUNCT
ejpam-6347	207	9	c1	c1	PROPN
ejpam-6347	207	10	=	=	PROPN
ejpam-6347	207	11	1	1	NUM
ejpam-6347	207	12	,	,	PUNCT
ejpam-6347	207	13	c2	c2	PROPN
ejpam-6347	207	14	=	=	SYM
ejpam-6347	207	15	π5	π5	PROPN
ejpam-6347	207	16	+	+	CCONJ
ejpam-6347	207	17	π6	π6	NOUN
ejpam-6347	207	18	+	+	NOUN
ejpam-6347	207	19	π7	π7	NOUN
ejpam-6347	207	20	,	,	PUNCT
ejpam-6347	207	21	c3	c3	PROPN
ejpam-6347	207	22	=	=	PUNCT
ejpam-6347	207	23	(	(	PUNCT
ejpam-6347	207	24	π5	π5	PROPN
ejpam-6347	207	25	+	+	NOUN
ejpam-6347	207	26	π7)π6	π7)π6	PROPN
ejpam-6347	207	27	−	−	NOUN
ejpam-6347	207	28	ηm2	ηm2	PROPN
ejpam-6347	207	29	−m3σ2	−m3σ2	PROPN
ejpam-6347	207	30	+	+	ADJ
ejpam-6347	207	31	π5π7	π5π7	ADJ
ejpam-6347	207	32	,	,	PUNCT
ejpam-6347	207	33	c4	c4	NOUN
ejpam-6347	207	34	=	=	SYM
ejpam-6347	207	35	(	(	PUNCT
ejpam-6347	207	36	π5π7	π5π7	X
ejpam-6347	207	37	−m3σ2)π6	−m3σ2)π6	NOUN
ejpam-6347	207	38	−	−	X
ejpam-6347	207	39	ηπ7m2	ηπ7m2	X
ejpam-6347	207	40	.	.	PUNCT
ejpam-6347	208	1	(	(	PUNCT
ejpam-6347	208	2	3.33	3.33	NUM
ejpam-6347	208	3	)	)	PUNCT
ejpam-6347	208	4	the	the	DET
ejpam-6347	208	5	characteristic	characteristic	ADJ
ejpam-6347	208	6	polynomial	polynomial	NOUN
ejpam-6347	208	7	can	can	AUX
ejpam-6347	208	8	be	be	AUX
ejpam-6347	208	9	written	write	VERB
ejpam-6347	208	10	as	as	ADP
ejpam-6347	208	11	:	:	PUNCT
ejpam-6347	208	12	1	1	NUM
ejpam-6347	208	13	µ(β	µ(β	NOUN
ejpam-6347	208	14	+	+	CCONJ
ejpam-6347	208	15	µ	µ	X
ejpam-6347	208	16	)	)	PUNCT
ejpam-6347	208	17	[	[	PUNCT
ejpam-6347	208	18	(	(	PUNCT
ejpam-6347	208	19	β	β	X
ejpam-6347	208	20	+	+	X
ejpam-6347	208	21	µ+∆)(∆µβ	µ+∆)(∆µβ	PROPN
ejpam-6347	208	22	+	+	NOUN
ejpam-6347	208	23	∆µ2	∆µ2	NOUN
ejpam-6347	208	24	−	−	PROPN
ejpam-6347	208	25	λβγ	λβγ	NOUN
ejpam-6347	208	26	−	−	PROPN
ejpam-6347	208	27	λµϕ+	λµϕ+	PROPN
ejpam-6347	208	28	βµπ1	βµπ1	PROPN
ejpam-6347	208	29	+	+	CCONJ
ejpam-6347	208	30	µ2π1	µ2π1	X
ejpam-6347	208	31	)	)	PUNCT
ejpam-6347	208	32	×	×	NOUN
ejpam-6347	208	33	(	(	PUNCT
ejpam-6347	208	34	π2	π2	X
ejpam-6347	208	35	+	+	PROPN
ejpam-6347	208	36	∆)(π3	∆)(π3	PROPN
ejpam-6347	208	37	+	+	NOUN
ejpam-6347	208	38	∆)2(π4	∆)2(π4	ADJ
ejpam-6347	208	39	+	+	NOUN
ejpam-6347	208	40	∆)(µ+∆)(τ	∆)(µ+∆)(τ	NOUN
ejpam-6347	208	41	+	+	CCONJ
ejpam-6347	208	42	µ+∆)2	µ+∆)2	NOUN
ejpam-6347	208	43	×(β	×(β	NOUN
ejpam-6347	208	44	+	+	CCONJ
ejpam-6347	208	45	µ+∆)(c1∆	µ+∆)(c1∆	PROPN
ejpam-6347	208	46	3	3	NUM
ejpam-6347	208	47	+	+	NOUN
ejpam-6347	208	48	c2∆	c2∆	PROPN
ejpam-6347	208	49	2	2	NUM
ejpam-6347	208	50	+	+	CCONJ
ejpam-6347	208	51	c3∆+	c3∆+	PROPN
ejpam-6347	208	52	c4	c4	NOUN
ejpam-6347	208	53	)	)	PUNCT
ejpam-6347	208	54	]	]	PUNCT
ejpam-6347	209	1	=	=	PUNCT
ejpam-6347	209	2	0	0	PUNCT
ejpam-6347	209	3	(	(	PUNCT
ejpam-6347	209	4	3.34	3.34	NUM
ejpam-6347	209	5	)	)	PUNCT
ejpam-6347	209	6	the	the	DET
ejpam-6347	209	7	first	first	ADJ
ejpam-6347	209	8	seven	seven	NUM
ejpam-6347	209	9	roots	root	NOUN
ejpam-6347	209	10	of	of	ADP
ejpam-6347	209	11	the	the	DET
ejpam-6347	209	12	characteristic	characteristic	ADJ
ejpam-6347	209	13	equation	equation	NOUN
ejpam-6347	209	14	are	be	AUX
ejpam-6347	209	15	:	:	PUNCT
ejpam-6347	209	16	∆1	∆1	PUNCT
ejpam-6347	209	17	=	=	SYM
ejpam-6347	209	18	−(β	−(β	PROPN
ejpam-6347	209	19	+	+	CCONJ
ejpam-6347	209	20	µ	µ	X
ejpam-6347	209	21	)	)	PUNCT
ejpam-6347	209	22	,	,	PUNCT
ejpam-6347	209	23	∆2	∆2	X
ejpam-6347	209	24	=	=	PRON
ejpam-6347	209	25	(	(	PUNCT
ejpam-6347	209	26	r0	r0	NOUN
ejpam-6347	209	27	−	−	PROPN
ejpam-6347	209	28	1	1	NUM
ejpam-6347	209	29	)	)	PUNCT
ejpam-6347	209	30	(	(	PUNCT
ejpam-6347	209	31	1	1	NUM
ejpam-6347	209	32	µ(β	µ(β	NOUN
ejpam-6347	209	33	+	+	CCONJ
ejpam-6347	209	34	µ	µ	NOUN
ejpam-6347	209	35	)	)	PUNCT
ejpam-6347	209	36	)	)	PUNCT
ejpam-6347	209	37	,	,	PUNCT
ejpam-6347	209	38	∆3	∆3	NOUN
ejpam-6347	209	39	=	=	SYM
ejpam-6347	209	40	−π4	−π4	PROPN
ejpam-6347	209	41	,	,	PUNCT
ejpam-6347	209	42	∆4	∆4	NOUN
ejpam-6347	209	43	=	=	SYM
ejpam-6347	209	44	−µ	−µ	PROPN
ejpam-6347	209	45	,	,	PUNCT
ejpam-6347	209	46	∆5	∆5	PROPN
ejpam-6347	210	1	=	=	SYM
ejpam-6347	210	2	−(τ	−(τ	PROPN
ejpam-6347	210	3	+	+	NOUN
ejpam-6347	210	4	µ	µ	NOUN
ejpam-6347	210	5	)	)	PUNCT
ejpam-6347	210	6	,	,	PUNCT
ejpam-6347	210	7	∆6	∆6	X
ejpam-6347	210	8	=	=	SYM
ejpam-6347	210	9	−π3	−π3	PROPN
ejpam-6347	210	10	,	,	PUNCT
ejpam-6347	210	11	∆7	∆7	PROPN
ejpam-6347	210	12	=	=	SYM
ejpam-6347	210	13	−(τ	−(τ	PROPN
ejpam-6347	210	14	+	+	NOUN
ejpam-6347	210	15	µ	µ	NOUN
ejpam-6347	210	16	)	)	PUNCT
ejpam-6347	210	17	.	.	PUNCT
ejpam-6347	211	1	(	(	PUNCT
ejpam-6347	211	2	3.35	3.35	NUM
ejpam-6347	211	3	)	)	PUNCT
ejpam-6347	211	4	all	all	DET
ejpam-6347	211	5	explicit	explicit	ADJ
ejpam-6347	211	6	eigenvalues	eigenvalue	NOUN
ejpam-6347	211	7	have	have	VERB
ejpam-6347	211	8	negative	negative	ADJ
ejpam-6347	211	9	real	real	ADJ
ejpam-6347	211	10	parts	part	NOUN
ejpam-6347	211	11	when	when	SCONJ
ejpam-6347	211	12	r0	r0	VERB
ejpam-6347	211	13	<	<	X
ejpam-6347	211	14	1	1	NUM
ejpam-6347	211	15	.	.	PUNCT
ejpam-6347	212	1	for	for	ADP
ejpam-6347	212	2	the	the	DET
ejpam-6347	212	3	cubic	cubic	ADJ
ejpam-6347	212	4	polynomial	polynomial	ADJ
ejpam-6347	212	5	c1∆	c1∆	NOUN
ejpam-6347	212	6	3	3	NUM
ejpam-6347	212	7	+	+	CCONJ
ejpam-6347	212	8	c2∆	c2∆	PROPN
ejpam-6347	212	9	2	2	NUM
ejpam-6347	212	10	+	+	CCONJ
ejpam-6347	212	11	c3∆+	c3∆+	NOUN
ejpam-6347	212	12	c4	c4	NOUN
ejpam-6347	212	13	=	=	SYM
ejpam-6347	212	14	0	0	PROPN
ejpam-6347	212	15	,	,	PUNCT
ejpam-6347	212	16	the	the	DET
ejpam-6347	212	17	routh	routh	PROPN
ejpam-6347	212	18	-	-	PUNCT
ejpam-6347	212	19	hurwitz	hurwitz	PROPN
ejpam-6347	212	20	stability	stability	NOUN
ejpam-6347	212	21	conditions	condition	NOUN
ejpam-6347	212	22	are	be	AUX
ejpam-6347	212	23	:	:	PUNCT
ejpam-6347	212	24	c1	c1	PROPN
ejpam-6347	212	25	>	>	X
ejpam-6347	212	26	0	0	PROPN
ejpam-6347	212	27	,	,	PUNCT
ejpam-6347	212	28	c2	c2	PROPN
ejpam-6347	212	29	>	>	X
ejpam-6347	212	30	0	0	PROPN
ejpam-6347	212	31	,	,	PUNCT
ejpam-6347	212	32	c1c2c3	c1c2c3	PROPN
ejpam-6347	212	33	>	>	X
ejpam-6347	212	34	c23	c23	PROPN
ejpam-6347	212	35	+	+	PROPN
ejpam-6347	212	36	c21c4	c21c4	PROPN
ejpam-6347	212	37	.	.	PUNCT
ejpam-6347	213	1	(	(	PUNCT
ejpam-6347	213	2	3.36	3.36	NUM
ejpam-6347	213	3	)	)	PUNCT
ejpam-6347	213	4	n.	n.	NOUN
ejpam-6347	213	5	abbas	abbas	PROPN
ejpam-6347	213	6	,	,	PUNCT
ejpam-6347	213	7	w.	w.	PROPN
ejpam-6347	213	8	shatanawi	shatanawi	PROPN
ejpam-6347	213	9	,	,	PUNCT
ejpam-6347	213	10	s.	s.	PROPN
ejpam-6347	213	11	a.	a.	NOUN
ejpam-6347	213	12	zanib	zanib	PROPN
ejpam-6347	213	13	/	/	SYM
ejpam-6347	213	14	eur	eur	PROPN
ejpam-6347	213	15	.	.	PUNCT
ejpam-6347	214	1	j.	j.	PROPN
ejpam-6347	214	2	pure	pure	PROPN
ejpam-6347	214	3	appl	appl	PROPN
ejpam-6347	214	4	.	.	PROPN
ejpam-6347	214	5	math	math	PROPN
ejpam-6347	214	6	,	,	PUNCT
ejpam-6347	214	7	18	18	NUM
ejpam-6347	214	8	(	(	PUNCT
ejpam-6347	214	9	3	3	NUM
ejpam-6347	214	10	)	)	PUNCT
ejpam-6347	214	11	(	(	PUNCT
ejpam-6347	214	12	2025	2025	NUM
ejpam-6347	214	13	)	)	PUNCT
ejpam-6347	214	14	,	,	PUNCT
ejpam-6347	214	15	6347	6347	NUM
ejpam-6347	214	16	15	15	NUM
ejpam-6347	214	17	of	of	ADP
ejpam-6347	214	18	34	34	NUM
ejpam-6347	214	19	these	these	DET
ejpam-6347	214	20	conditions	condition	NOUN
ejpam-6347	214	21	are	be	AUX
ejpam-6347	214	22	satisfied	satisfied	ADJ
ejpam-6347	214	23	when	when	SCONJ
ejpam-6347	214	24	r0	r0	NOUN
ejpam-6347	214	25	<	<	X
ejpam-6347	214	26	1	1	NUM
ejpam-6347	214	27	,	,	PUNCT
ejpam-6347	214	28	as	as	SCONJ
ejpam-6347	214	29	confirmed	confirm	VERB
ejpam-6347	214	30	by	by	ADP
ejpam-6347	214	31	the	the	DET
ejpam-6347	214	32	structure	structure	NOUN
ejpam-6347	214	33	of	of	ADP
ejpam-6347	214	34	the	the	DET
ejpam-6347	214	35	composite	composite	ADJ
ejpam-6347	214	36	parameters	parameter	NOUN
ejpam-6347	214	37	πi	πi	ADV
ejpam-6347	214	38	.	.	PUNCT
ejpam-6347	215	1	therefore	therefore	ADV
ejpam-6347	215	2	,	,	PUNCT
ejpam-6347	215	3	all	all	PRON
ejpam-6347	215	4	eigenvalues	eigenvalue	VERB
ejpam-6347	215	5	of	of	ADP
ejpam-6347	215	6	the	the	DET
ejpam-6347	215	7	jacobian	jacobian	ADJ
ejpam-6347	215	8	matrix	matrix	NOUN
ejpam-6347	215	9	j0	j0	PROPN
ejpam-6347	215	10	have	have	VERB
ejpam-6347	215	11	negative	negative	ADJ
ejpam-6347	215	12	real	real	ADJ
ejpam-6347	215	13	parts	part	NOUN
ejpam-6347	215	14	if	if	SCONJ
ejpam-6347	216	1	and	and	CCONJ
ejpam-6347	216	2	only	only	ADV
ejpam-6347	216	3	if	if	SCONJ
ejpam-6347	216	4	r0	r0	NOUN
ejpam-6347	216	5	<	<	X
ejpam-6347	216	6	1	1	NUM
ejpam-6347	216	7	,	,	PUNCT
ejpam-6347	216	8	ensuring	ensure	VERB
ejpam-6347	216	9	local	local	ADJ
ejpam-6347	216	10	asymptotic	asymptotic	ADJ
ejpam-6347	216	11	stability	stability	NOUN
ejpam-6347	216	12	of	of	ADP
ejpam-6347	216	13	the	the	DET
ejpam-6347	216	14	dfep	dfep	NOUN
ejpam-6347	216	15	.	.	PUNCT
ejpam-6347	217	1	conversely	conversely	ADV
ejpam-6347	217	2	,	,	PUNCT
ejpam-6347	217	3	if	if	SCONJ
ejpam-6347	217	4	r0	r0	NOUN
ejpam-6347	217	5	>	>	X
ejpam-6347	217	6	1	1	NUM
ejpam-6347	217	7	,	,	PUNCT
ejpam-6347	217	8	the	the	DET
ejpam-6347	217	9	dfep	dfep	NOUN
ejpam-6347	217	10	becomes	become	VERB
ejpam-6347	217	11	unstable	unstable	ADJ
ejpam-6347	217	12	,	,	PUNCT
ejpam-6347	217	13	indicating	indicate	VERB
ejpam-6347	217	14	the	the	DET
ejpam-6347	217	15	potential	potential	NOUN
ejpam-6347	217	16	for	for	ADP
ejpam-6347	217	17	an	an	DET
ejpam-6347	217	18	epidemic	epidemic	NOUN
ejpam-6347	217	19	outbreak	outbreak	NOUN
ejpam-6347	217	20	.	.	PUNCT
ejpam-6347	218	1	global	global	ADJ
ejpam-6347	218	2	stability	stability	NOUN
ejpam-6347	218	3	of	of	ADP
ejpam-6347	218	4	disease	disease	NOUN
ejpam-6347	218	5	-	-	PUNCT
ejpam-6347	218	6	free	free	ADJ
ejpam-6347	218	7	equilibrium	equilibrium	NOUN
ejpam-6347	218	8	point	point	NOUN
ejpam-6347	218	9	lemma	lemma	PROPN
ejpam-6347	218	10	2	2	X
ejpam-6347	218	11	.	.	PUNCT
ejpam-6347	219	1	(	(	PUNCT
ejpam-6347	219	2	castillo	castillo	PROPN
ejpam-6347	219	3	-	-	PUNCT
ejpam-6347	219	4	chavez	chavez	PROPN
ejpam-6347	219	5	method	method	NOUN
ejpam-6347	219	6	[	[	X
ejpam-6347	219	7	24	24	NUM
ejpam-6347	219	8	]	]	PUNCT
ejpam-6347	219	9	)	)	PUNCT
ejpam-6347	219	10	the	the	DET
ejpam-6347	219	11	dfep	dfep	NOUN
ejpam-6347	219	12	e0	e0	PROPN
ejpam-6347	219	13	=	=	PUNCT
ejpam-6347	219	14	(	(	PUNCT
ejpam-6347	219	15	x0,0	x0,0	NOUN
ejpam-6347	219	16	)	)	PUNCT
ejpam-6347	219	17	of	of	ADP
ejpam-6347	219	18	system	system	NOUN
ejpam-6347	219	19	(	(	PUNCT
ejpam-6347	219	20	2.4	2.4	NUM
ejpam-6347	219	21	)	)	PUNCT
ejpam-6347	219	22	is	be	AUX
ejpam-6347	219	23	globally	globally	ADV
ejpam-6347	219	24	asymptotically	asymptotically	ADV
ejpam-6347	219	25	stable	stable	ADJ
ejpam-6347	219	26	if	if	SCONJ
ejpam-6347	219	27	:	:	PUNCT
ejpam-6347	219	28	(	(	PUNCT
ejpam-6347	219	29	z1	z1	NOUN
ejpam-6347	219	30	)	)	PUNCT
ejpam-6347	219	31	for	for	ADP
ejpam-6347	219	32	dx	dx	PROPN
ejpam-6347	219	33	dt	dt	PROPN
ejpam-6347	220	1	=	=	SYM
ejpam-6347	220	2	f	f	PROPN
ejpam-6347	220	3	(	(	PUNCT
ejpam-6347	220	4	x	x	X
ejpam-6347	220	5	,	,	PUNCT
ejpam-6347	220	6	0	0	NUM
ejpam-6347	220	7	)	)	PUNCT
ejpam-6347	220	8	,	,	PUNCT
ejpam-6347	220	9	x0	x0	PROPN
ejpam-6347	220	10	is	be	AUX
ejpam-6347	220	11	globally	globally	ADV
ejpam-6347	220	12	asymptotically	asymptotically	ADV
ejpam-6347	220	13	stable	stable	ADJ
ejpam-6347	220	14	(	(	PUNCT
ejpam-6347	220	15	z2	z2	NUM
ejpam-6347	220	16	)	)	PUNCT
ejpam-6347	220	17	h(x	h(x	PROPN
ejpam-6347	220	18	,	,	PUNCT
ejpam-6347	220	19	y	y	PROPN
ejpam-6347	220	20	)	)	PUNCT
ejpam-6347	220	21	=	=	PUNCT
ejpam-6347	221	1	py−	py−	PROPN
ejpam-6347	221	2	ĥ(x	ĥ(x	NOUN
ejpam-6347	221	3	,	,	PUNCT
ejpam-6347	221	4	y	y	PROPN
ejpam-6347	221	5	)	)	PUNCT
ejpam-6347	221	6	satisfies	satisfie	NOUN
ejpam-6347	221	7	ĥ(x	ĥ(x	NUM
ejpam-6347	221	8	,	,	PUNCT
ejpam-6347	221	9	y	y	PROPN
ejpam-6347	221	10	)	)	PUNCT
ejpam-6347	221	11	≥	≥	NOUN
ejpam-6347	221	12	0	0	NUM
ejpam-6347	221	13	in	in	ADP
ejpam-6347	221	14	ω	ω	PROPN
ejpam-6347	221	15	,	,	PUNCT
ejpam-6347	221	16	where	where	SCONJ
ejpam-6347	221	17	:	:	PUNCT
ejpam-6347	221	18	–	–	PUNCT
ejpam-6347	221	19	1	1	X
ejpam-6347	221	20	.	.	X
ejpam-6347	222	1	p	p	NOUN
ejpam-6347	222	2	=	=	PUNCT
ejpam-6347	222	3	dyh(x0	dyh(x0	PROPN
ejpam-6347	222	4	,	,	PUNCT
ejpam-6347	222	5	0	0	NUM
ejpam-6347	222	6	)	)	PUNCT
ejpam-6347	222	7	is	be	AUX
ejpam-6347	222	8	metzler	metzler	NOUN
ejpam-6347	222	9	(	(	PUNCT
ejpam-6347	222	10	non	non	ADJ
ejpam-6347	222	11	-	-	ADJ
ejpam-6347	222	12	negative	negative	ADJ
ejpam-6347	222	13	off	off	ADP
ejpam-6347	222	14	-	-	PUNCT
ejpam-6347	222	15	diagonal	diagonal	ADJ
ejpam-6347	222	16	elements	element	NOUN
ejpam-6347	222	17	)	)	PUNCT
ejpam-6347	222	18	–	–	PUNCT
ejpam-6347	222	19	2	2	X
ejpam-6347	222	20	.	.	X
ejpam-6347	222	21	ω	ω	PROPN
ejpam-6347	222	22	is	be	AUX
ejpam-6347	222	23	the	the	DET
ejpam-6347	222	24	biologically	biologically	ADV
ejpam-6347	222	25	feasible	feasible	ADJ
ejpam-6347	222	26	region	region	NOUN
ejpam-6347	222	27	theorem	theorem	VERB
ejpam-6347	222	28	4	4	NUM
ejpam-6347	222	29	.	.	PUNCT
ejpam-6347	223	1	the	the	DET
ejpam-6347	223	2	covcom10	covcom10	PROPN
ejpam-6347	223	3	model	model	NOUN
ejpam-6347	223	4	(	(	PUNCT
ejpam-6347	223	5	2.4	2.4	NUM
ejpam-6347	223	6	)	)	PUNCT
ejpam-6347	223	7	is	be	AUX
ejpam-6347	223	8	globally	globally	ADV
ejpam-6347	223	9	asymptotically	asymptotically	ADV
ejpam-6347	223	10	stable	stable	ADJ
ejpam-6347	223	11	at	at	ADP
ejpam-6347	223	12	dfep	dfep	NOUN
ejpam-6347	223	13	e0	e0	PROPN
ejpam-6347	223	14	when	when	SCONJ
ejpam-6347	223	15	r0	r0	VERB
ejpam-6347	223	16	<	<	X
ejpam-6347	223	17	1	1	NUM
ejpam-6347	223	18	,	,	PUNCT
ejpam-6347	223	19	satisfying	satisfy	VERB
ejpam-6347	223	20	both	both	DET
ejpam-6347	223	21	castillo	castillo	PROPN
ejpam-6347	223	22	-	-	PUNCT
ejpam-6347	223	23	chavez	chavez	PROPN
ejpam-6347	223	24	conditions	condition	NOUN
ejpam-6347	223	25	[	[	X
ejpam-6347	223	26	24	24	NUM
ejpam-6347	223	27	]	]	PUNCT
ejpam-6347	223	28	.	.	PUNCT
ejpam-6347	224	1	proof	proof	NOUN
ejpam-6347	224	2	.	.	PUNCT
ejpam-6347	225	1	firstly	firstly	ADV
ejpam-6347	225	2	,	,	PUNCT
ejpam-6347	225	3	to	to	PART
ejpam-6347	225	4	satisfy	satisfy	VERB
ejpam-6347	225	5	condition	condition	NOUN
ejpam-6347	225	6	(	(	PUNCT
ejpam-6347	225	7	z1	z1	NOUN
ejpam-6347	225	8	)	)	PUNCT
ejpam-6347	225	9	,	,	PUNCT
ejpam-6347	225	10	the	the	DET
ejpam-6347	225	11	model	model	NOUN
ejpam-6347	225	12	(	(	PUNCT
ejpam-6347	225	13	2.4	2.4	NUM
ejpam-6347	225	14	)	)	PUNCT
ejpam-6347	225	15	are	be	AUX
ejpam-6347	225	16	rewrite	rewrite	VERB
ejpam-6347	225	17	by	by	ADP
ejpam-6347	225	18	setting	set	VERB
ejpam-6347	225	19	,	,	PUNCT
ejpam-6347	225	20	th	th	X
ejpam-6347	225	21	=	=	SYM
ejpam-6347	225	22	(	(	PUNCT
ejpam-6347	225	23	s	s	PROPN
ejpam-6347	225	24	,	,	PUNCT
ejpam-6347	225	25	v	v	NOUN
ejpam-6347	225	26	)	)	PUNCT
ejpam-6347	225	27	and	and	CCONJ
ejpam-6347	225	28	,	,	PUNCT
ejpam-6347	225	29	gh	gh	PROPN
ejpam-6347	225	30	=	=	PUNCT
ejpam-6347	225	31	(	(	PUNCT
ejpam-6347	225	32	e	e	NOUN
ejpam-6347	225	33	,	,	PUNCT
ejpam-6347	225	34	u	u	NOUN
ejpam-6347	225	35	,	,	PUNCT
ejpam-6347	225	36	q	q	INTJ
ejpam-6347	225	37	,	,	PUNCT
ejpam-6347	225	38	p	p	X
ejpam-6347	225	39	,	,	PUNCT
ejpam-6347	225	40	h	h	NOUN
ejpam-6347	225	41	,	,	PUNCT
ejpam-6347	225	42	c	c	X
ejpam-6347	225	43	,	,	PUNCT
ejpam-6347	225	44	f	f	X
ejpam-6347	225	45	,	,	PUNCT
ejpam-6347	225	46	r	r	NOUN
ejpam-6347	225	47	)	)	PUNCT
ejpam-6347	225	48	.	.	PUNCT
ejpam-6347	226	1	then	then	ADV
ejpam-6347	226	2	,	,	PUNCT
ejpam-6347	226	3	disease	disease	NOUN
ejpam-6347	226	4	-	-	PUNCT
ejpam-6347	226	5	free	free	ADJ
ejpam-6347	226	6	equilibrium	equilibrium	NOUN
ejpam-6347	226	7	point	point	NOUN
ejpam-6347	226	8	is	be	AUX
ejpam-6347	226	9	given	give	VERB
ejpam-6347	226	10	by	by	ADP
ejpam-6347	226	11	the	the	DET
ejpam-6347	226	12	fixed	fix	VERB
ejpam-6347	226	13	point	point	NOUN
ejpam-6347	226	14	,	,	PUNCT
ejpam-6347	226	15	e0	e0	PROPN
ejpam-6347	226	16	=	=	PUNCT
ejpam-6347	226	17	(	(	PUNCT
ejpam-6347	226	18	x0	x0	PROPN
ejpam-6347	226	19	,	,	PUNCT
ejpam-6347	226	20	0	0	NUM
ejpam-6347	226	21	)	)	PUNCT
ejpam-6347	226	22	=	=	SYM
ejpam-6347	226	23	(	(	PUNCT
ejpam-6347	226	24	λ	λ	X
ejpam-6347	226	25	β	β	X
ejpam-6347	226	26	+	+	X
ejpam-6347	226	27	µ	µ	X
ejpam-6347	226	28	,	,	PUNCT
ejpam-6347	226	29	β	β	X
ejpam-6347	226	30	λ	λ	X
ejpam-6347	226	31	µ	µ	X
ejpam-6347	226	32	(	(	PUNCT
ejpam-6347	226	33	β	β	X
ejpam-6347	226	34	+	+	X
ejpam-6347	226	35	µ	µ	X
ejpam-6347	226	36	)	)	PUNCT
ejpam-6347	226	37	)	)	PUNCT
ejpam-6347	226	38	,	,	PUNCT
ejpam-6347	226	39	the	the	DET
ejpam-6347	226	40	system	system	NOUN
ejpam-6347	226	41	dth	dth	VERB
ejpam-6347	226	42	dt	dt	NOUN
ejpam-6347	226	43	=	=	SYM
ejpam-6347	226	44	f	f	PROPN
ejpam-6347	226	45	(	(	PUNCT
ejpam-6347	226	46	th	th	INTJ
ejpam-6347	226	47	,	,	PUNCT
ejpam-6347	226	48	0	0	NUM
ejpam-6347	226	49	)	)	PUNCT
ejpam-6347	226	50	becomes	become	VERB
ejpam-6347	226	51	,	,	PUNCT
ejpam-6347	226	52	ds∗	ds∗	NOUN
ejpam-6347	226	53	dt	dt	NOUN
ejpam-6347	227	1	=	=	SYM
ejpam-6347	227	2	λ−	λ−	PROPN
ejpam-6347	227	3	(	(	PUNCT
ejpam-6347	227	4	β	β	X
ejpam-6347	227	5	+	+	SYM
ejpam-6347	227	6	µ)s	µ)s	NOUN
ejpam-6347	227	7	,	,	PUNCT
ejpam-6347	227	8	dv	dv	PROPN
ejpam-6347	227	9	∗	∗	X
ejpam-6347	227	10	dt	dt	PUNCT
ejpam-6347	228	1	=	=	X
ejpam-6347	228	2	β	β	X
ejpam-6347	228	3	s	s	NUM
ejpam-6347	228	4	−	−	X
ejpam-6347	228	5	(	(	PUNCT
ejpam-6347	228	6	µ)v	µ)v	NOUN
ejpam-6347	228	7	.	.	PUNCT
ejpam-6347	229	1	(	(	PUNCT
ejpam-6347	229	2	3.37	3.37	NUM
ejpam-6347	229	3	)	)	PUNCT
ejpam-6347	229	4	by	by	ADP
ejpam-6347	229	5	solving	solve	VERB
ejpam-6347	229	6	eq	eq	ADJ
ejpam-6347	229	7	.	.	PUNCT
ejpam-6347	230	1	(	(	PUNCT
ejpam-6347	230	2	3.37	3.37	NUM
ejpam-6347	230	3	)	)	PUNCT
ejpam-6347	230	4	,	,	PUNCT
ejpam-6347	230	5	the	the	DET
ejpam-6347	230	6	equation	equation	NOUN
ejpam-6347	230	7	has	have	VERB
ejpam-6347	230	8	a	a	DET
ejpam-6347	230	9	unique	unique	ADJ
ejpam-6347	230	10	equilibrium	equilibrium	NOUN
ejpam-6347	230	11	point	point	NOUN
ejpam-6347	230	12	,	,	PUNCT
ejpam-6347	230	13	(	(	PUNCT
ejpam-6347	230	14	s∗	s∗	PROPN
ejpam-6347	230	15	,	,	PUNCT
ejpam-6347	230	16	v	v	NOUN
ejpam-6347	230	17	∗	∗	NOUN
ejpam-6347	230	18	)	)	PUNCT
ejpam-6347	231	1	=	=	SYM
ejpam-6347	231	2	(	(	PUNCT
ejpam-6347	231	3	λ	λ	X
ejpam-6347	231	4	β	β	X
ejpam-6347	231	5	+	+	X
ejpam-6347	231	6	µ	µ	X
ejpam-6347	231	7	,	,	PUNCT
ejpam-6347	231	8	β	β	X
ejpam-6347	231	9	λ	λ	X
ejpam-6347	231	10	µ	µ	X
ejpam-6347	231	11	(	(	PUNCT
ejpam-6347	231	12	β	β	X
ejpam-6347	231	13	+	+	X
ejpam-6347	231	14	µ	µ	X
ejpam-6347	231	15	)	)	PUNCT
ejpam-6347	231	16	)	)	PUNCT
ejpam-6347	231	17	,	,	PUNCT
ejpam-6347	231	18	(	(	PUNCT
ejpam-6347	231	19	3.38	3.38	NUM
ejpam-6347	231	20	)	)	PUNCT
ejpam-6347	231	21	hence	hence	ADV
ejpam-6347	231	22	x0	x0	PROPN
ejpam-6347	231	23	is	be	AUX
ejpam-6347	231	24	globally	globally	ADV
ejpam-6347	231	25	asymptotically	asymptotically	ADV
ejpam-6347	231	26	stable	stable	ADJ
ejpam-6347	231	27	.	.	PUNCT
ejpam-6347	232	1	so	so	ADV
ejpam-6347	232	2	we	we	PRON
ejpam-6347	232	3	can	can	AUX
ejpam-6347	232	4	say	say	VERB
ejpam-6347	232	5	the	the	DET
ejpam-6347	232	6	condition	condition	NOUN
ejpam-6347	232	7	(	(	PUNCT
ejpam-6347	232	8	z1	z1	NOUN
ejpam-6347	232	9	)	)	PUNCT
ejpam-6347	232	10	is	be	AUX
ejpam-6347	232	11	fulfilled	fulfil	VERB
ejpam-6347	232	12	.	.	PUNCT
ejpam-6347	233	1	now	now	ADV
ejpam-6347	233	2	,	,	PUNCT
ejpam-6347	233	3	to	to	PART
ejpam-6347	233	4	satisfy	satisfy	VERB
ejpam-6347	233	5	the	the	DET
ejpam-6347	233	6	second	second	ADJ
ejpam-6347	233	7	condition	condition	NOUN
ejpam-6347	233	8	(	(	PUNCT
ejpam-6347	233	9	z2	z2	NOUN
ejpam-6347	233	10	)	)	PUNCT
ejpam-6347	233	11	,	,	PUNCT
ejpam-6347	233	12	h(th	h(th	NUM
ejpam-6347	233	13	,	,	PUNCT
ejpam-6347	233	14	gh	gh	PROPN
ejpam-6347	233	15	)	)	PUNCT
ejpam-6347	233	16	=	=	SYM
ejpam-6347	233	17	phgn	phgn	NOUN
ejpam-6347	233	18	−	−	PROPN
ejpam-6347	234	1	ĥ(th	ĥ(th	PROPN
ejpam-6347	234	2	,	,	PUNCT
ejpam-6347	234	3	gh	gh	PROPN
ejpam-6347	234	4	)	)	PUNCT
ejpam-6347	234	5	,	,	PUNCT
ejpam-6347	234	6	and	and	CCONJ
ejpam-6347	234	7	n.	n.	PROPN
ejpam-6347	234	8	abbas	abbas	PROPN
ejpam-6347	234	9	,	,	PUNCT
ejpam-6347	234	10	w.	w.	PROPN
ejpam-6347	234	11	shatanawi	shatanawi	PROPN
ejpam-6347	234	12	,	,	PUNCT
ejpam-6347	234	13	s.	s.	PROPN
ejpam-6347	234	14	a.	a.	NOUN
ejpam-6347	234	15	zanib	zanib	PROPN
ejpam-6347	234	16	/	/	SYM
ejpam-6347	234	17	eur	eur	PROPN
ejpam-6347	234	18	.	.	PUNCT
ejpam-6347	235	1	j.	j.	PROPN
ejpam-6347	235	2	pure	pure	PROPN
ejpam-6347	235	3	appl	appl	PROPN
ejpam-6347	235	4	.	.	PROPN
ejpam-6347	235	5	math	math	PROPN
ejpam-6347	235	6	,	,	PUNCT
ejpam-6347	235	7	18	18	NUM
ejpam-6347	235	8	(	(	PUNCT
ejpam-6347	235	9	3	3	NUM
ejpam-6347	235	10	)	)	PUNCT
ejpam-6347	235	11	(	(	PUNCT
ejpam-6347	235	12	2025	2025	NUM
ejpam-6347	235	13	)	)	PUNCT
ejpam-6347	235	14	,	,	PUNCT
ejpam-6347	235	15	6347	6347	NUM
ejpam-6347	235	16	16	16	NUM
ejpam-6347	235	17	of	of	ADP
ejpam-6347	235	18	34	34	NUM
ejpam-6347	235	19	ĥ(th	ĥ(th	PROPN
ejpam-6347	235	20	,	,	PUNCT
ejpam-6347	235	21	gh	gh	PROPN
ejpam-6347	235	22	)	)	PUNCT
ejpam-6347	235	23	≥	≥	NOUN
ejpam-6347	235	24	0	0	NUM
ejpam-6347	235	25	,	,	PUNCT
ejpam-6347	235	26	for	for	ADP
ejpam-6347	235	27	that	that	PRON
ejpam-6347	235	28	,	,	PUNCT
ejpam-6347	235	29	system	system	NOUN
ejpam-6347	235	30	of	of	ADP
ejpam-6347	235	31	equations	equation	NOUN
ejpam-6347	235	32	(	(	PUNCT
ejpam-6347	235	33	2.4	2.4	NUM
ejpam-6347	235	34	)	)	PUNCT
ejpam-6347	235	35	.	.	PUNCT
ejpam-6347	236	1	we	we	PRON
ejpam-6347	236	2	have	have	VERB
ejpam-6347	236	3	,	,	PUNCT
ejpam-6347	236	4	h(th	h(th	NUM
ejpam-6347	236	5	,	,	PUNCT
ejpam-6347	236	6	gh	gh	PROPN
ejpam-6347	236	7	)	)	PUNCT
ejpam-6347	237	1	=	=	SYM
ejpam-6347	237	2			ADJ
ejpam-6347	237	3	eϕs	eϕs	NOUN
ejpam-6347	237	4	+	+	CCONJ
ejpam-6347	237	5	γ	γ	X
ejpam-6347	237	6	v	v	ADP
ejpam-6347	237	7	e	e	X
ejpam-6347	237	8	−	−	PROPN
ejpam-6347	237	9	(	(	PUNCT
ejpam-6347	237	10	λ1u	λ1u	PROPN
ejpam-6347	237	11	+	+	NUM
ejpam-6347	237	12	λ2q+	λ2q+	PROPN
ejpam-6347	237	13	µ+	µ+	X
ejpam-6347	237	14	d1)e	d1)e	NOUN
ejpam-6347	237	15	λ1eu	λ1eu	X
ejpam-6347	237	16	−	−	PROPN
ejpam-6347	238	1	(	(	PUNCT
ejpam-6347	238	2	α1	α1	PROPN
ejpam-6347	238	3	+	+	CCONJ
ejpam-6347	238	4	α2	α2	ADJ
ejpam-6347	238	5	+	+	CCONJ
ejpam-6347	238	6	µ+	µ+	X
ejpam-6347	238	7	d2)u	d2)u	ADJ
ejpam-6347	238	8	λ2eq−	λ2eq−	PROPN
ejpam-6347	238	9	(	(	PUNCT
ejpam-6347	238	10	b1	b1	NOUN
ejpam-6347	238	11	+	+	CCONJ
ejpam-6347	238	12	b2	b2	NOUN
ejpam-6347	238	13	+	+	CCONJ
ejpam-6347	238	14	b3	b3	PROPN
ejpam-6347	238	15	+	+	CCONJ
ejpam-6347	238	16	µ+	µ+	X
ejpam-6347	238	17	d3)q	d3)q	NOUN
ejpam-6347	238	18	α2u	α2u	PROPN
ejpam-6347	238	19	+	+	CCONJ
ejpam-6347	238	20	b1q−	b1q−	X
ejpam-6347	238	21	(	(	PUNCT
ejpam-6347	238	22	φ1	φ1	NOUN
ejpam-6347	238	23	+	+	CCONJ
ejpam-6347	238	24	φ2	φ2	NOUN
ejpam-6347	238	25	+	+	NUM
ejpam-6347	238	26	φ3	φ3	NOUN
ejpam-6347	238	27	+	+	CCONJ
ejpam-6347	238	28	µ+	µ+	PUNCT
ejpam-6347	238	29	d4)p	d4)p	PROPN
ejpam-6347	238	30	η	η	PROPN
ejpam-6347	238	31	c	c	PROPN
ejpam-6347	238	32	+	+	PROPN
ejpam-6347	238	33	σ2f	σ2f	NOUN
ejpam-6347	238	34	+	+	PUNCT
ejpam-6347	239	1	φ1p	φ1p	ADJ
ejpam-6347	239	2	−	−	PROPN
ejpam-6347	239	3	(	(	PUNCT
ejpam-6347	239	4	m1	m1	PROPN
ejpam-6347	239	5	+	+	PROPN
ejpam-6347	239	6	m2	m2	PROPN
ejpam-6347	239	7	+	+	PROPN
ejpam-6347	239	8	m3	m3	PROPN
ejpam-6347	239	9	+	+	CCONJ
ejpam-6347	239	10	µ+	µ+	PRON
ejpam-6347	239	11	d5)h	d5)h	ADJ
ejpam-6347	239	12	m2h	m2h	PROPN
ejpam-6347	239	13	+	+	CCONJ
ejpam-6347	239	14	φ2p	φ2p	PROPN
ejpam-6347	239	15	−	−	PROPN
ejpam-6347	239	16	(	(	PUNCT
ejpam-6347	239	17	η	η	PROPN
ejpam-6347	239	18	+	+	PROPN
ejpam-6347	239	19	µ+	µ+	PUNCT
ejpam-6347	239	20	d6)c	d6)c	NOUN
ejpam-6347	239	21	φ3f	φ3f	ADP
ejpam-6347	239	22	+	+	PROPN
ejpam-6347	239	23	m3h	m3h	NOUN
ejpam-6347	239	24	−	−	PROPN
ejpam-6347	239	25	(	(	PUNCT
ejpam-6347	239	26	σ1	σ1	PROPN
ejpam-6347	239	27	+	+	CCONJ
ejpam-6347	239	28	σ2	σ2	PROPN
ejpam-6347	239	29	+	+	CCONJ
ejpam-6347	239	30	µ+	µ+	DET
ejpam-6347	239	31	d7)f	d7)f	PROPN
ejpam-6347	239	32	σ1f	σ1f	PROPN
ejpam-6347	239	33	+	+	PROPN
ejpam-6347	239	34	m1h	m1h	NOUN
ejpam-6347	239	35	+	+	CCONJ
ejpam-6347	239	36	α1u	α1u	PROPN
ejpam-6347	239	37	−	−	PROPN
ejpam-6347	239	38	(	(	PUNCT
ejpam-6347	239	39	τ	τ	X
ejpam-6347	239	40	+	+	NUM
ejpam-6347	239	41	µ)r	µ)r	NOUN
ejpam-6347	239	42			NUM
ejpam-6347	239	43	,	,	PUNCT
ejpam-6347	239	44	(	(	PUNCT
ejpam-6347	239	45	3.39	3.39	NUM
ejpam-6347	239	46	)	)	PUNCT
ejpam-6347	239	47	ĥ(th	ĥ(th	PROPN
ejpam-6347	239	48	,	,	PUNCT
ejpam-6347	239	49	gh	gh	PROPN
ejpam-6347	239	50	)	)	PUNCT
ejpam-6347	239	51	=	=	SYM
ejpam-6347	240	1	phgn	phgn	PROPN
ejpam-6347	240	2	−h(th	−h(th	NOUN
ejpam-6347	240	3	,	,	PUNCT
ejpam-6347	240	4	gh	gh	PROPN
ejpam-6347	240	5	)	)	PUNCT
ejpam-6347	241	1	=	=	SYM
ejpam-6347	241	2			NOUN
ejpam-6347	241	3	(	(	PUNCT
ejpam-6347	241	4	(	(	PUNCT
ejpam-6347	241	5	ϕ(s∗	ϕ(s∗	NUM
ejpam-6347	241	6	−	−	PROPN
ejpam-6347	241	7	s	s	PART
ejpam-6347	241	8	)	)	PUNCT
ejpam-6347	241	9	+	+	CCONJ
ejpam-6347	241	10	γ(v	γ(v	ADJ
ejpam-6347	241	11	∗	∗	NOUN
ejpam-6347	241	12	−	−	PROPN
ejpam-6347	241	13	v	v	NOUN
ejpam-6347	241	14	)	)	PUNCT
ejpam-6347	241	15	−	−	PROPN
ejpam-6347	242	1	λ1u	λ1u	NOUN
ejpam-6347	242	2	−	−	PROPN
ejpam-6347	242	3	λ2q)e	λ2q)e	X
ejpam-6347	242	4	λ1eu	λ1eu	PUNCT
ejpam-6347	242	5	λ2eq	λ2eq	SYM
ejpam-6347	242	6	0	0	NUM
ejpam-6347	242	7	0	0	NUM
ejpam-6347	242	8	0	0	NUM
ejpam-6347	242	9	0	0	NUM
ejpam-6347	242	10	0	0	NUM
ejpam-6347	242	11			NUM
ejpam-6347	242	12	,	,	PUNCT
ejpam-6347	242	13	(	(	PUNCT
ejpam-6347	242	14	3.40	3.40	NUM
ejpam-6347	242	15	)	)	PUNCT
ejpam-6347	242	16	this	this	PRON
ejpam-6347	242	17	shows	show	VERB
ejpam-6347	242	18	that	that	SCONJ
ejpam-6347	242	19	,	,	PUNCT
ejpam-6347	242	20	ĥ(th	ĥ(th	PROPN
ejpam-6347	242	21	,	,	PUNCT
ejpam-6347	242	22	gh	gh	PROPN
ejpam-6347	242	23	)	)	PUNCT
ejpam-6347	242	24	≥	≥	NOUN
ejpam-6347	242	25	0	0	NUM
ejpam-6347	242	26	,	,	PUNCT
ejpam-6347	242	27	where	where	SCONJ
ejpam-6347	242	28	gn	gn	PROPN
ejpam-6347	242	29	represent	represent	VERB
ejpam-6347	242	30	an	an	DET
ejpam-6347	242	31	m	m	NOUN
ejpam-6347	242	32	matrix	matrix	NOUN
ejpam-6347	242	33	,	,	PUNCT
ejpam-6347	242	34	it	it	PRON
ejpam-6347	242	35	contains	contain	VERB
ejpam-6347	242	36	a	a	DET
ejpam-6347	242	37	nonnegative	nonnegative	ADJ
ejpam-6347	242	38	off	off	ADP
ejpam-6347	242	39	-	-	PUNCT
ejpam-6347	242	40	diagonal	diagonal	ADJ
ejpam-6347	242	41	element	element	NOUN
ejpam-6347	242	42	.	.	PUNCT
ejpam-6347	243	1	therefore	therefore	ADV
ejpam-6347	243	2	,	,	PUNCT
ejpam-6347	243	3	both	both	DET
ejpam-6347	243	4	conditions	condition	NOUN
ejpam-6347	243	5	(	(	PUNCT
ejpam-6347	243	6	z1	z1	NOUN
ejpam-6347	243	7	)	)	PUNCT
ejpam-6347	243	8	and	and	CCONJ
ejpam-6347	243	9	(	(	PUNCT
ejpam-6347	243	10	z2	z2	NOUN
ejpam-6347	243	11	)	)	PUNCT
ejpam-6347	243	12	are	be	AUX
ejpam-6347	243	13	satisfied	satisfied	ADJ
ejpam-6347	243	14	when	when	SCONJ
ejpam-6347	243	15	r0	r0	NOUN
ejpam-6347	243	16	<	<	X
ejpam-6347	243	17	1	1	NUM
ejpam-6347	243	18	,	,	PUNCT
ejpam-6347	243	19	proving	prove	VERB
ejpam-6347	243	20	global	global	ADJ
ejpam-6347	243	21	asymptotic	asymptotic	ADJ
ejpam-6347	243	22	stability	stability	NOUN
ejpam-6347	243	23	of	of	ADP
ejpam-6347	243	24	dfep	dfep	NOUN
ejpam-6347	243	25	e0	e0	PROPN
ejpam-6347	243	26	by	by	ADP
ejpam-6347	243	27	lemma	lemma	PROPN
ejpam-6347	243	28	2	2	NUM
ejpam-6347	243	29	.	.	PROPN
ejpam-6347	243	30	3.3	3.3	NUM
ejpam-6347	243	31	.	.	PUNCT
ejpam-6347	244	1	existence	existence	NOUN
ejpam-6347	244	2	and	and	CCONJ
ejpam-6347	244	3	uniqueness	uniqueness	NOUN
ejpam-6347	244	4	of	of	ADP
ejpam-6347	244	5	solution	solution	NOUN
ejpam-6347	244	6	the	the	DET
ejpam-6347	244	7	mathematical	mathematical	ADJ
ejpam-6347	244	8	results	result	NOUN
ejpam-6347	244	9	presented	present	VERB
ejpam-6347	244	10	in	in	ADP
ejpam-6347	244	11	this	this	DET
ejpam-6347	244	12	section	section	NOUN
ejpam-6347	244	13	that	that	DET
ejpam-6347	244	14	model	model	NOUN
ejpam-6347	244	15	(	(	PUNCT
ejpam-6347	244	16	2.4	2.4	NUM
ejpam-6347	244	17	)	)	PUNCT
ejpam-6347	244	18	and	and	CCONJ
ejpam-6347	244	19	(	(	PUNCT
ejpam-6347	244	20	2.5	2.5	NUM
ejpam-6347	244	21	)	)	PUNCT
ejpam-6347	244	22	(	(	PUNCT
ejpam-6347	244	23	covcom10	covcom10	NOUN
ejpam-6347	244	24	)	)	PUNCT
ejpam-6347	244	25	have	have	VERB
ejpam-6347	244	26	a	a	DET
ejpam-6347	244	27	unique	unique	ADJ
ejpam-6347	244	28	solution	solution	NOUN
ejpam-6347	244	29	under	under	ADP
ejpam-6347	244	30	certain	certain	ADJ
ejpam-6347	244	31	reasonable	reasonable	ADJ
ejpam-6347	244	32	assumptions	assumption	NOUN
ejpam-6347	244	33	.	.	PUNCT
ejpam-6347	245	1	from	from	ADP
ejpam-6347	245	2	an	an	DET
ejpam-6347	245	3	epidemiological	epidemiological	ADJ
ejpam-6347	245	4	viewpoint	viewpoint	NOUN
ejpam-6347	245	5	,	,	PUNCT
ejpam-6347	245	6	the	the	DET
ejpam-6347	245	7	existence	existence	NOUN
ejpam-6347	245	8	of	of	ADP
ejpam-6347	245	9	solutions	solution	NOUN
ejpam-6347	245	10	implies	imply	VERB
ejpam-6347	245	11	that	that	SCONJ
ejpam-6347	245	12	the	the	DET
ejpam-6347	245	13	model	model	NOUN
ejpam-6347	245	14	reliably	reliably	ADV
ejpam-6347	245	15	predicts	predict	VERB
ejpam-6347	245	16	disease	disease	NOUN
ejpam-6347	245	17	dynamics	dynamic	NOUN
ejpam-6347	245	18	,	,	PUNCT
ejpam-6347	245	19	confirming	confirm	VERB
ejpam-6347	245	20	that	that	SCONJ
ejpam-6347	245	21	realistic	realistic	ADJ
ejpam-6347	245	22	initial	initial	ADJ
ejpam-6347	245	23	conditions	condition	NOUN
ejpam-6347	245	24	and	and	CCONJ
ejpam-6347	245	25	parameters	parameter	NOUN
ejpam-6347	245	26	will	will	AUX
ejpam-6347	245	27	always	always	ADV
ejpam-6347	245	28	yield	yield	VERB
ejpam-6347	245	29	a	a	DET
ejpam-6347	245	30	meaningful	meaningful	ADJ
ejpam-6347	245	31	trajectory	trajectory	NOUN
ejpam-6347	245	32	of	of	ADP
ejpam-6347	245	33	the	the	DET
ejpam-6347	245	34	disease	disease	NOUN
ejpam-6347	245	35	.	.	PUNCT
ejpam-6347	246	1	uniqueness	uniqueness	NOUN
ejpam-6347	246	2	assures	assure	VERB
ejpam-6347	246	3	that	that	SCONJ
ejpam-6347	246	4	the	the	DET
ejpam-6347	246	5	models	model	NOUN
ejpam-6347	246	6	predictions	prediction	NOUN
ejpam-6347	246	7	are	be	AUX
ejpam-6347	246	8	consistent	consistent	ADJ
ejpam-6347	246	9	and	and	CCONJ
ejpam-6347	246	10	reproducible	reproducible	ADJ
ejpam-6347	246	11	,	,	PUNCT
ejpam-6347	246	12	crucial	crucial	ADJ
ejpam-6347	246	13	for	for	ADP
ejpam-6347	246	14	decision	decision	NOUN
ejpam-6347	246	15	-	-	PUNCT
ejpam-6347	246	16	making	making	NOUN
ejpam-6347	246	17	in	in	ADP
ejpam-6347	246	18	public	public	ADJ
ejpam-6347	246	19	health	health	NOUN
ejpam-6347	246	20	.	.	PUNCT
ejpam-6347	247	1	the	the	DET
ejpam-6347	247	2	covcom10	covcom10	PROPN
ejpam-6347	247	3	model	model	PROPN
ejpam-6347	247	4	’s	’s	PART
ejpam-6347	247	5	solutions	solution	NOUN
ejpam-6347	247	6	,	,	PUNCT
ejpam-6347	247	7	which	which	PRON
ejpam-6347	247	8	are	be	AUX
ejpam-6347	247	9	provided	provide	VERB
ejpam-6347	247	10	in	in	ADP
ejpam-6347	247	11	system	system	NOUN
ejpam-6347	247	12	of	of	ADP
ejpam-6347	247	13	equation	equation	NOUN
ejpam-6347	247	14	(	(	PUNCT
ejpam-6347	247	15	2.4	2.4	NUM
ejpam-6347	247	16	)	)	PUNCT
ejpam-6347	247	17	and	and	CCONJ
ejpam-6347	247	18	(	(	PUNCT
ejpam-6347	247	19	2.5	2.5	NUM
ejpam-6347	247	20	)	)	PUNCT
ejpam-6347	247	21	are	be	AUX
ejpam-6347	247	22	described	describe	VERB
ejpam-6347	247	23	in	in	ADP
ejpam-6347	247	24	this	this	DET
ejpam-6347	247	25	section	section	NOUN
ejpam-6347	247	26	by	by	ADP
ejpam-6347	247	27	their	their	PRON
ejpam-6347	247	28	qualitative	qualitative	ADJ
ejpam-6347	247	29	qualities	quality	NOUN
ejpam-6347	247	30	.	.	PUNCT
ejpam-6347	248	1	the	the	DET
ejpam-6347	248	2	following	follow	VERB
ejpam-6347	248	3	volterra	volterra	NOUN
ejpam-6347	248	4	-	-	PUNCT
ejpam-6347	248	5	type	type	NOUN
ejpam-6347	248	6	integral	integral	ADJ
ejpam-6347	248	7	equation	equation	NOUN
ejpam-6347	248	8	results	result	NOUN
ejpam-6347	248	9	from	from	ADP
ejpam-6347	248	10	first	first	ADV
ejpam-6347	248	11	taking	take	VERB
ejpam-6347	248	12	the	the	DET
ejpam-6347	248	13	both	both	DET
ejpam-6347	248	14	sides	side	NOUN
ejpam-6347	248	15	integral	integral	ADJ
ejpam-6347	248	16	,	,	PUNCT
ejpam-6347	248	17	where	where	SCONJ
ejpam-6347	248	18	∫	∫	PROPN
ejpam-6347	248	19	ζ	ζ	PROPN
ejpam-6347	248	20	t	t	PROPN
ejpam-6347	248	21	is	be	AUX
ejpam-6347	248	22	the	the	DET
ejpam-6347	248	23	integration	integration	NOUN
ejpam-6347	248	24	function	function	NOUN
ejpam-6347	248	25	having	have	VERB
ejpam-6347	248	26	n.	n.	NOUN
ejpam-6347	248	27	abbas	abbas	PROPN
ejpam-6347	248	28	,	,	PUNCT
ejpam-6347	248	29	w.	w.	PROPN
ejpam-6347	248	30	shatanawi	shatanawi	PROPN
ejpam-6347	248	31	,	,	PUNCT
ejpam-6347	248	32	s.	s.	PROPN
ejpam-6347	248	33	a.	a.	NOUN
ejpam-6347	248	34	zanib	zanib	PROPN
ejpam-6347	248	35	/	/	SYM
ejpam-6347	248	36	eur	eur	PROPN
ejpam-6347	248	37	.	.	PUNCT
ejpam-6347	249	1	j.	j.	PROPN
ejpam-6347	249	2	pure	pure	PROPN
ejpam-6347	249	3	appl	appl	PROPN
ejpam-6347	249	4	.	.	PROPN
ejpam-6347	249	5	math	math	PROPN
ejpam-6347	249	6	,	,	PUNCT
ejpam-6347	249	7	18	18	NUM
ejpam-6347	249	8	(	(	PUNCT
ejpam-6347	249	9	3	3	NUM
ejpam-6347	249	10	)	)	PUNCT
ejpam-6347	249	11	(	(	PUNCT
ejpam-6347	249	12	2025	2025	NUM
ejpam-6347	249	13	)	)	PUNCT
ejpam-6347	249	14	,	,	PUNCT
ejpam-6347	249	15	6347	6347	NUM
ejpam-6347	249	16	17	17	NUM
ejpam-6347	249	17	of	of	ADP
ejpam-6347	249	18	34	34	NUM
ejpam-6347	249	19	the	the	DET
ejpam-6347	249	20	order	order	NOUN
ejpam-6347	249	21	ζ	ζ	NOUN
ejpam-6347	249	22	with	with	ADP
ejpam-6347	249	23	respect	respect	NOUN
ejpam-6347	249	24	to	to	ADP
ejpam-6347	249	25	t	t	PROPN
ejpam-6347	249	26	now	now	ADV
ejpam-6347	249	27	by	by	ADP
ejpam-6347	249	28	using	use	VERB
ejpam-6347	249	29	the	the	DET
ejpam-6347	249	30	definition	definition	NOUN
ejpam-6347	249	31	of	of	ADP
ejpam-6347	249	32	khalilzadeh	khalilzadeh	PROPN
ejpam-6347	250	1	[	[	X
ejpam-6347	250	2	19	19	NUM
ejpam-6347	250	3	,	,	PUNCT
ejpam-6347	250	4	20	20	NUM
ejpam-6347	250	5	]	]	PUNCT
ejpam-6347	250	6	,	,	PUNCT
ejpam-6347	250	7	we	we	PRON
ejpam-6347	250	8	get	get	VERB
ejpam-6347	250	9	,	,	PUNCT
ejpam-6347	250	10	s(t)−	s(t)−	PROPN
ejpam-6347	250	11	s(0	s(0	PROPN
ejpam-6347	250	12	)	)	PUNCT
ejpam-6347	250	13	=	=	SYM
ejpam-6347	251	1	∫	∫	PROPN
ejpam-6347	251	2	t	t	NOUN
ejpam-6347	251	3	0	0	NUM
ejpam-6347	252	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	253	1	[	[	X
ejpam-6347	253	2	λ	λ	X
ejpam-6347	253	3	+	+	NOUN
ejpam-6347	253	4	τr(ρ	τr(ρ	PUNCT
ejpam-6347	253	5	)	)	PUNCT
ejpam-6347	254	1	+	+	CCONJ
ejpam-6347	254	2	b2q(ρ)−	b2q(ρ)−	PROPN
ejpam-6347	254	3	(	(	PUNCT
ejpam-6347	254	4	ϕe(ρ	ϕe(ρ	NUM
ejpam-6347	254	5	)	)	PUNCT
ejpam-6347	254	6	+	+	CCONJ
ejpam-6347	254	7	β	β	X
ejpam-6347	254	8	+	+	CCONJ
ejpam-6347	254	9	µ)s(ρ	µ)s(ρ	NOUN
ejpam-6347	254	10	)	)	PUNCT
ejpam-6347	254	11	]	]	X
ejpam-6347	254	12	dρ	dρ	PROPN
ejpam-6347	254	13	,	,	PUNCT
ejpam-6347	254	14	e(t)−	e(t)−	PROPN
ejpam-6347	254	15	e(0	e(0	PROPN
ejpam-6347	254	16	)	)	PUNCT
ejpam-6347	254	17	=	=	SYM
ejpam-6347	255	1	∫	∫	PROPN
ejpam-6347	255	2	t	t	NOUN
ejpam-6347	255	3	0	0	NUM
ejpam-6347	256	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	257	1	[	[	X
ejpam-6347	257	2	ϕe(ρ)s(ρ	ϕe(ρ)s(ρ	NOUN
ejpam-6347	257	3	)	)	PUNCT
ejpam-6347	258	1	+	+	CCONJ
ejpam-6347	258	2	γ	γ	X
ejpam-6347	258	3	v	v	NOUN
ejpam-6347	258	4	(	(	PUNCT
ejpam-6347	258	5	ρ)e(ρ)−	ρ)e(ρ)−	PROPN
ejpam-6347	258	6	(	(	PUNCT
ejpam-6347	258	7	λ1u(ρ	λ1u(ρ	PROPN
ejpam-6347	258	8	)	)	PUNCT
ejpam-6347	258	9	+	+	NUM
ejpam-6347	258	10	λ2q(ρ	λ2q(ρ	NOUN
ejpam-6347	258	11	)	)	PUNCT
ejpam-6347	259	1	+	+	CCONJ
ejpam-6347	259	2	µ+	µ+	DET
ejpam-6347	259	3	d1)e(ρ	d1)e(ρ	NUM
ejpam-6347	259	4	)	)	PUNCT
ejpam-6347	259	5	]	]	X
ejpam-6347	260	1	dρ	dρ	PROPN
ejpam-6347	260	2	,	,	PUNCT
ejpam-6347	260	3	u(t)−	u(t)−	PROPN
ejpam-6347	260	4	u(0	u(0	PROPN
ejpam-6347	260	5	)	)	PUNCT
ejpam-6347	260	6	=	=	SYM
ejpam-6347	261	1	∫	∫	PROPN
ejpam-6347	261	2	t	t	NOUN
ejpam-6347	261	3	0	0	NUM
ejpam-6347	262	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	263	1	[	[	X
ejpam-6347	263	2	λ1e(ρ)u(ρ)−	λ1e(ρ)u(ρ)−	PROPN
ejpam-6347	263	3	(	(	PUNCT
ejpam-6347	263	4	α1	α1	PROPN
ejpam-6347	263	5	+	+	CCONJ
ejpam-6347	263	6	α2	α2	ADJ
ejpam-6347	263	7	+	+	CCONJ
ejpam-6347	263	8	µ+	µ+	ADJ
ejpam-6347	263	9	d2)u(ρ	d2)u(ρ	PROPN
ejpam-6347	263	10	)	)	PUNCT
ejpam-6347	263	11	]	]	PUNCT
ejpam-6347	264	1	dρ	dρ	PROPN
ejpam-6347	264	2	,	,	PUNCT
ejpam-6347	264	3	q(t)−q(0	q(t)−q(0	X
ejpam-6347	264	4	)	)	PUNCT
ejpam-6347	265	1	=	=	SYM
ejpam-6347	266	1	∫	∫	PROPN
ejpam-6347	266	2	t	t	NOUN
ejpam-6347	266	3	0	0	NUM
ejpam-6347	267	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	268	1	[	[	X
ejpam-6347	268	2	λ2e(ρ)q(ρ)−	λ2e(ρ)q(ρ)−	PROPN
ejpam-6347	268	3	(	(	PUNCT
ejpam-6347	268	4	b1	b1	NOUN
ejpam-6347	268	5	+	+	CCONJ
ejpam-6347	268	6	b2	b2	NOUN
ejpam-6347	268	7	+	+	CCONJ
ejpam-6347	268	8	b3	b3	PROPN
ejpam-6347	268	9	+	+	CCONJ
ejpam-6347	268	10	µ+	µ+	DET
ejpam-6347	268	11	d3)q(ρ	d3)q(ρ	PROPN
ejpam-6347	268	12	)	)	PUNCT
ejpam-6347	268	13	]	]	PUNCT
ejpam-6347	269	1	dρ	dρ	PROPN
ejpam-6347	269	2	,	,	PUNCT
ejpam-6347	269	3	p	p	X
ejpam-6347	269	4	(	(	PUNCT
ejpam-6347	269	5	t)−	t)−	PROPN
ejpam-6347	269	6	p	p	X
ejpam-6347	269	7	(	(	PUNCT
ejpam-6347	269	8	0	0	NUM
ejpam-6347	269	9	)	)	PUNCT
ejpam-6347	269	10	=	=	SYM
ejpam-6347	270	1	∫	∫	PROPN
ejpam-6347	270	2	t	t	NOUN
ejpam-6347	270	3	0	0	NUM
ejpam-6347	271	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	272	1	[	[	X
ejpam-6347	272	2	α2i(ρ	α2i(ρ	NOUN
ejpam-6347	272	3	)	)	PUNCT
ejpam-6347	273	1	+	+	CCONJ
ejpam-6347	273	2	b1q(ρ)−	b1q(ρ)−	PRON
ejpam-6347	273	3	(	(	PUNCT
ejpam-6347	273	4	φ1	φ1	NOUN
ejpam-6347	273	5	+	+	CCONJ
ejpam-6347	273	6	φ2	φ2	NOUN
ejpam-6347	273	7	+	+	NUM
ejpam-6347	273	8	φ3	φ3	NOUN
ejpam-6347	273	9	+	+	CCONJ
ejpam-6347	273	10	µ+	µ+	PUNCT
ejpam-6347	273	11	d4)p	d4)p	VERB
ejpam-6347	273	12	(	(	PUNCT
ejpam-6347	273	13	ρ	ρ	PROPN
ejpam-6347	273	14	)	)	PUNCT
ejpam-6347	273	15	]	]	X
ejpam-6347	273	16	dρ	dρ	PROPN
ejpam-6347	273	17	,	,	PUNCT
ejpam-6347	273	18	h(t)−h(0	h(t)−h(0	NOUN
ejpam-6347	273	19	)	)	PUNCT
ejpam-6347	273	20	=	=	SYM
ejpam-6347	274	1	∫	∫	PROPN
ejpam-6347	274	2	t	t	NOUN
ejpam-6347	274	3	0	0	NUM
ejpam-6347	275	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	275	2	[	[	X
ejpam-6347	275	3	φ1p	φ1p	X
ejpam-6347	275	4	(	(	PUNCT
ejpam-6347	275	5	ρ	ρ	NOUN
ejpam-6347	275	6	)	)	PUNCT
ejpam-6347	275	7	+	+	NUM
ejpam-6347	275	8	η	η	PROPN
ejpam-6347	275	9	c(ρ	c(ρ	PROPN
ejpam-6347	275	10	)	)	PUNCT
ejpam-6347	276	1	+	+	CCONJ
ejpam-6347	276	2	σ2f	σ2f	X
ejpam-6347	276	3	(	(	PUNCT
ejpam-6347	276	4	ρ)−	ρ)−	PROPN
ejpam-6347	276	5	(	(	PUNCT
ejpam-6347	276	6	m1	m1	PROPN
ejpam-6347	276	7	+	+	PROPN
ejpam-6347	276	8	m2	m2	PROPN
ejpam-6347	276	9	+	+	PROPN
ejpam-6347	276	10	m3	m3	PROPN
ejpam-6347	276	11	+	+	CCONJ
ejpam-6347	276	12	µ+	µ+	X
ejpam-6347	276	13	d5)h(ρ	d5)h(ρ	NOUN
ejpam-6347	276	14	)	)	PUNCT
ejpam-6347	276	15	]	]	PUNCT
ejpam-6347	277	1	dρ	dρ	PROPN
ejpam-6347	277	2	,	,	PUNCT
ejpam-6347	277	3	c(t)−	c(t)−	PROPN
ejpam-6347	277	4	c(0	c(0	PROPN
ejpam-6347	277	5	)	)	PUNCT
ejpam-6347	277	6	=	=	SYM
ejpam-6347	278	1	∫	∫	PROPN
ejpam-6347	278	2	t	t	NOUN
ejpam-6347	278	3	0	0	NUM
ejpam-6347	279	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	280	1	[	[	X
ejpam-6347	280	2	φ2p	φ2p	X
ejpam-6347	280	3	(	(	PUNCT
ejpam-6347	280	4	ρ	ρ	NOUN
ejpam-6347	280	5	)	)	PUNCT
ejpam-6347	281	1	+	+	PROPN
ejpam-6347	281	2	m2h(ρ)−	m2h(ρ)−	PROPN
ejpam-6347	281	3	(	(	PUNCT
ejpam-6347	281	4	η	η	PROPN
ejpam-6347	281	5	+	+	PROPN
ejpam-6347	281	6	µ+	µ+	PROPN
ejpam-6347	281	7	d6)c(ρ	d6)c(ρ	PROPN
ejpam-6347	281	8	)	)	PUNCT
ejpam-6347	281	9	]	]	PUNCT
ejpam-6347	281	10	dρ	dρ	PROPN
ejpam-6347	281	11	,	,	PUNCT
ejpam-6347	281	12	f	f	PROPN
ejpam-6347	281	13	(	(	PUNCT
ejpam-6347	281	14	t)−	t)−	PROPN
ejpam-6347	281	15	f	f	X
ejpam-6347	281	16	(	(	PUNCT
ejpam-6347	281	17	0	0	NUM
ejpam-6347	281	18	)	)	PUNCT
ejpam-6347	281	19	=	=	SYM
ejpam-6347	282	1	∫	∫	PROPN
ejpam-6347	282	2	t	t	NOUN
ejpam-6347	282	3	0	0	NUM
ejpam-6347	283	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	283	2	[	[	X
ejpam-6347	283	3	φ3p	φ3p	X
ejpam-6347	283	4	(	(	PUNCT
ejpam-6347	283	5	ρ	ρ	NOUN
ejpam-6347	283	6	)	)	PUNCT
ejpam-6347	284	1	+	+	NOUN
ejpam-6347	284	2	m3h(ρ)−	m3h(ρ)−	PROPN
ejpam-6347	284	3	(	(	PUNCT
ejpam-6347	284	4	σ1	σ1	PROPN
ejpam-6347	284	5	+	+	CCONJ
ejpam-6347	284	6	σ2	σ2	PROPN
ejpam-6347	284	7	+	+	CCONJ
ejpam-6347	284	8	µ+	µ+	PROPN
ejpam-6347	284	9	d7)f	d7)f	PROPN
ejpam-6347	284	10	(	(	PUNCT
ejpam-6347	284	11	ρ	ρ	PROPN
ejpam-6347	284	12	)	)	PUNCT
ejpam-6347	284	13	]	]	X
ejpam-6347	284	14	dρ	dρ	PROPN
ejpam-6347	284	15	,	,	PUNCT
ejpam-6347	284	16	v	v	PROPN
ejpam-6347	284	17	(	(	PUNCT
ejpam-6347	284	18	t)−	t)−	PROPN
ejpam-6347	284	19	v	v	NOUN
ejpam-6347	284	20	(	(	PUNCT
ejpam-6347	284	21	0	0	NUM
ejpam-6347	284	22	)	)	PUNCT
ejpam-6347	284	23	=	=	SYM
ejpam-6347	285	1	∫	∫	PROPN
ejpam-6347	285	2	t	t	NOUN
ejpam-6347	285	3	0	0	NUM
ejpam-6347	286	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	286	2	[	[	X
ejpam-6347	286	3	β	β	X
ejpam-6347	286	4	s(ρ	s(ρ	PROPN
ejpam-6347	286	5	)	)	PUNCT
ejpam-6347	287	1	+	+	CCONJ
ejpam-6347	287	2	b3q(ρ)−	b3q(ρ)−	PROPN
ejpam-6347	287	3	(	(	PUNCT
ejpam-6347	287	4	γ	γ	X
ejpam-6347	287	5	e(ρ	e(ρ	PROPN
ejpam-6347	287	6	)	)	PUNCT
ejpam-6347	288	1	+	+	NUM
ejpam-6347	288	2	µ)v	µ)v	ADJ
ejpam-6347	288	3	(	(	PUNCT
ejpam-6347	288	4	ρ	ρ	NOUN
ejpam-6347	288	5	)	)	PUNCT
ejpam-6347	288	6	]	]	X
ejpam-6347	288	7	dρ	dρ	PROPN
ejpam-6347	288	8	,	,	PUNCT
ejpam-6347	288	9	r(t)−r(0	r(t)−r(0	PROPN
ejpam-6347	288	10	)	)	PUNCT
ejpam-6347	289	1	=	=	SYM
ejpam-6347	290	1	∫	∫	PROPN
ejpam-6347	290	2	t	t	NOUN
ejpam-6347	290	3	0	0	NUM
ejpam-6347	291	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	291	2	[	[	X
ejpam-6347	291	3	σ1f	σ1f	X
ejpam-6347	291	4	(	(	PUNCT
ejpam-6347	291	5	ρ	ρ	NOUN
ejpam-6347	291	6	)	)	PUNCT
ejpam-6347	291	7	+	+	CCONJ
ejpam-6347	291	8	α1i(ρ	α1i(ρ	NOUN
ejpam-6347	291	9	)	)	PUNCT
ejpam-6347	291	10	+	+	PROPN
ejpam-6347	291	11	m1h(ρ)−	m1h(ρ)−	PROPN
ejpam-6347	291	12	(	(	PUNCT
ejpam-6347	291	13	τ	τ	PROPN
ejpam-6347	291	14	+	+	PROPN
ejpam-6347	291	15	µ)r(ρ	µ)r(ρ	NOUN
ejpam-6347	291	16	)	)	PUNCT
ejpam-6347	291	17	]	]	X
ejpam-6347	292	1	dρ	dρ	PROPN
ejpam-6347	292	2	,	,	PUNCT
ejpam-6347	292	3	(	(	PUNCT
ejpam-6347	292	4	3.41	3.41	NUM
ejpam-6347	292	5	)	)	PUNCT
ejpam-6347	292	6	define	define	VERB
ejpam-6347	292	7	the	the	DET
ejpam-6347	292	8	kernels	kernel	NOUN
ejpam-6347	292	9	in	in	ADP
ejpam-6347	292	10	following	follow	VERB
ejpam-6347	292	11	,	,	PUNCT
ejpam-6347	292	12	φ1(t	φ1(t	PROPN
ejpam-6347	292	13	,	,	PUNCT
ejpam-6347	292	14	s	s	PART
ejpam-6347	292	15	)	)	PUNCT
ejpam-6347	292	16	=	=	SYM
ejpam-6347	292	17	λ	λ	NOUN
ejpam-6347	292	18	+	+	NOUN
ejpam-6347	292	19	τr(t	τr(t	PUNCT
ejpam-6347	292	20	)	)	PUNCT
ejpam-6347	293	1	+	+	SYM
ejpam-6347	293	2	b2q(t)−	b2q(t)−	PROPN
ejpam-6347	293	3	(	(	PUNCT
ejpam-6347	293	4	ϕe(t	ϕe(t	PUNCT
ejpam-6347	293	5	)	)	PUNCT
ejpam-6347	293	6	+	+	CCONJ
ejpam-6347	293	7	β	β	X
ejpam-6347	293	8	+	+	CCONJ
ejpam-6347	293	9	µ)s(t	µ)s(t	NOUN
ejpam-6347	293	10	)	)	PUNCT
ejpam-6347	293	11	,	,	PUNCT
ejpam-6347	293	12	φ2(t	φ2(t	PROPN
ejpam-6347	293	13	,	,	PUNCT
ejpam-6347	293	14	e	e	NOUN
ejpam-6347	293	15	)	)	PUNCT
ejpam-6347	293	16	=	=	SYM
ejpam-6347	293	17	ϕe(t)s(t	ϕe(t)s(t	PROPN
ejpam-6347	293	18	)	)	PUNCT
ejpam-6347	293	19	+	+	CCONJ
ejpam-6347	293	20	γ	γ	X
ejpam-6347	293	21	v	v	NOUN
ejpam-6347	293	22	(	(	PUNCT
ejpam-6347	293	23	t)e(t)−	t)e(t)−	PROPN
ejpam-6347	293	24	(	(	PUNCT
ejpam-6347	293	25	λ1u(t	λ1u(t	PROPN
ejpam-6347	293	26	)	)	PUNCT
ejpam-6347	293	27	+	+	CCONJ
ejpam-6347	293	28	λ2q(t	λ2q(t	X
ejpam-6347	293	29	)	)	PUNCT
ejpam-6347	293	30	+	+	CCONJ
ejpam-6347	293	31	µ+	µ+	X
ejpam-6347	293	32	d1)e(t	d1)e(t	PROPN
ejpam-6347	293	33	)	)	PUNCT
ejpam-6347	293	34	,	,	PUNCT
ejpam-6347	293	35	φ3(t	φ3(t	PROPN
ejpam-6347	293	36	,	,	PUNCT
ejpam-6347	293	37	u	u	NOUN
ejpam-6347	293	38	)	)	PUNCT
ejpam-6347	293	39	=	=	SYM
ejpam-6347	293	40	λ1e(t)u(t)−	λ1e(t)u(t)−	PROPN
ejpam-6347	293	41	(	(	PUNCT
ejpam-6347	293	42	α1	α1	PROPN
ejpam-6347	293	43	+	+	CCONJ
ejpam-6347	293	44	α2	α2	ADJ
ejpam-6347	293	45	+	+	CCONJ
ejpam-6347	293	46	µ+	µ+	DET
ejpam-6347	293	47	d2)u(t	d2)u(t	NOUN
ejpam-6347	293	48	)	)	PUNCT
ejpam-6347	293	49	,	,	PUNCT
ejpam-6347	293	50	φ4(t	φ4(t	PROPN
ejpam-6347	293	51	,	,	PUNCT
ejpam-6347	293	52	q	q	NOUN
ejpam-6347	293	53	)	)	PUNCT
ejpam-6347	293	54	=	=	SYM
ejpam-6347	293	55	λ2e(t)q(t)−	λ2e(t)q(t)−	PROPN
ejpam-6347	293	56	(	(	PUNCT
ejpam-6347	293	57	b1	b1	NOUN
ejpam-6347	293	58	+	+	CCONJ
ejpam-6347	293	59	b2	b2	NOUN
ejpam-6347	293	60	+	+	CCONJ
ejpam-6347	293	61	b3	b3	PROPN
ejpam-6347	293	62	+	+	CCONJ
ejpam-6347	293	63	µ+	µ+	X
ejpam-6347	293	64	d3)q(t	d3)q(t	PROPN
ejpam-6347	293	65	)	)	PUNCT
ejpam-6347	293	66	,	,	PUNCT
ejpam-6347	293	67	φ5(t	φ5(t	PROPN
ejpam-6347	293	68	,	,	PUNCT
ejpam-6347	293	69	p	p	NOUN
ejpam-6347	293	70	)	)	PUNCT
ejpam-6347	293	71	=	=	SYM
ejpam-6347	293	72	α2u(t	α2u(t	PROPN
ejpam-6347	293	73	)	)	PUNCT
ejpam-6347	294	1	+	+	NUM
ejpam-6347	294	2	b1q(t)−	b1q(t)−	X
ejpam-6347	294	3	(	(	PUNCT
ejpam-6347	294	4	φ1	φ1	NOUN
ejpam-6347	294	5	+	+	CCONJ
ejpam-6347	294	6	φ2	φ2	NOUN
ejpam-6347	294	7	+	+	NUM
ejpam-6347	294	8	φ3	φ3	NOUN
ejpam-6347	294	9	+	+	CCONJ
ejpam-6347	294	10	µ+	µ+	PUNCT
ejpam-6347	294	11	d4)p	d4)p	PROPN
ejpam-6347	294	12	(	(	PUNCT
ejpam-6347	294	13	t	t	PROPN
ejpam-6347	294	14	)	)	PUNCT
ejpam-6347	294	15	,	,	PUNCT
ejpam-6347	294	16	φ6(t	φ6(t	NOUN
ejpam-6347	294	17	,	,	PUNCT
ejpam-6347	294	18	h	h	NOUN
ejpam-6347	294	19	)	)	PUNCT
ejpam-6347	294	20	=	=	PUNCT
ejpam-6347	294	21	φ1p	φ1p	X
ejpam-6347	294	22	(	(	PUNCT
ejpam-6347	294	23	t	t	NOUN
ejpam-6347	294	24	)	)	PUNCT
ejpam-6347	294	25	+	+	CCONJ
ejpam-6347	294	26	η	η	PROPN
ejpam-6347	294	27	c(t	c(t	PROPN
ejpam-6347	294	28	)	)	PUNCT
ejpam-6347	294	29	+	+	NUM
ejpam-6347	294	30	σ2f	σ2f	NOUN
ejpam-6347	294	31	(	(	PUNCT
ejpam-6347	294	32	t)−	t)−	PROPN
ejpam-6347	294	33	(	(	PUNCT
ejpam-6347	294	34	m1	m1	PROPN
ejpam-6347	294	35	+	+	PROPN
ejpam-6347	294	36	m2	m2	PROPN
ejpam-6347	294	37	+	+	PROPN
ejpam-6347	294	38	m3	m3	PROPN
ejpam-6347	294	39	+	+	CCONJ
ejpam-6347	294	40	µ+	µ+	X
ejpam-6347	294	41	d5)h(t	d5)h(t	NUM
ejpam-6347	294	42	)	)	PUNCT
ejpam-6347	294	43	,	,	PUNCT
ejpam-6347	294	44	φ7(t	φ7(t	NOUN
ejpam-6347	294	45	,	,	PUNCT
ejpam-6347	294	46	c	c	NOUN
ejpam-6347	294	47	)	)	PUNCT
ejpam-6347	294	48	=	=	PUNCT
ejpam-6347	294	49	φ2p	φ2p	X
ejpam-6347	294	50	(	(	PUNCT
ejpam-6347	294	51	t	t	NOUN
ejpam-6347	294	52	)	)	PUNCT
ejpam-6347	294	53	+	+	NOUN
ejpam-6347	294	54	m2h(t)−	m2h(t)−	PROPN
ejpam-6347	294	55	(	(	PUNCT
ejpam-6347	294	56	η	η	PROPN
ejpam-6347	294	57	+	+	PROPN
ejpam-6347	294	58	µ+	µ+	X
ejpam-6347	294	59	d6)c(t	d6)c(t	NOUN
ejpam-6347	294	60	)	)	PUNCT
ejpam-6347	294	61	,	,	PUNCT
ejpam-6347	294	62	φ8(t	φ8(t	PROPN
ejpam-6347	294	63	,	,	PUNCT
ejpam-6347	294	64	f	f	X
ejpam-6347	294	65	)	)	PUNCT
ejpam-6347	295	1	=	=	SYM
ejpam-6347	295	2	φ3p	φ3p	PROPN
ejpam-6347	295	3	(	(	PUNCT
ejpam-6347	295	4	t	t	NOUN
ejpam-6347	295	5	)	)	PUNCT
ejpam-6347	295	6	+	+	PROPN
ejpam-6347	295	7	m3h(t)−	m3h(t)−	PROPN
ejpam-6347	295	8	(	(	PUNCT
ejpam-6347	295	9	σ1	σ1	PROPN
ejpam-6347	295	10	+	+	CCONJ
ejpam-6347	295	11	σ2	σ2	PROPN
ejpam-6347	295	12	+	+	CCONJ
ejpam-6347	295	13	µ+	µ+	PROPN
ejpam-6347	295	14	d7)f	d7)f	PROPN
ejpam-6347	295	15	(	(	PUNCT
ejpam-6347	295	16	t	t	PROPN
ejpam-6347	295	17	)	)	PUNCT
ejpam-6347	295	18	,	,	PUNCT
ejpam-6347	295	19	φ9(t	φ9(t	NOUN
ejpam-6347	295	20	,	,	PUNCT
ejpam-6347	295	21	v	v	NOUN
ejpam-6347	295	22	)	)	PUNCT
ejpam-6347	295	23	=	=	SYM
ejpam-6347	295	24	β	β	X
ejpam-6347	295	25	s(t	s(t	PROPN
ejpam-6347	295	26	)	)	PUNCT
ejpam-6347	296	1	+	+	CCONJ
ejpam-6347	296	2	b3q(t)−	b3q(t)−	PROPN
ejpam-6347	296	3	(	(	PUNCT
ejpam-6347	296	4	γ	γ	NOUN
ejpam-6347	296	5	e(t	e(t	PROPN
ejpam-6347	296	6	)	)	PUNCT
ejpam-6347	296	7	+	+	NUM
ejpam-6347	296	8	µ)v	µ)v	ADJ
ejpam-6347	296	9	(	(	PUNCT
ejpam-6347	296	10	t	t	NOUN
ejpam-6347	296	11	)	)	PUNCT
ejpam-6347	296	12	,	,	PUNCT
ejpam-6347	296	13	φ10(t	φ10(t	ADJ
ejpam-6347	296	14	,	,	PUNCT
ejpam-6347	296	15	r	r	NOUN
ejpam-6347	296	16	)	)	PUNCT
ejpam-6347	296	17	=	=	SYM
ejpam-6347	296	18	σ1f	σ1f	X
ejpam-6347	296	19	(	(	PUNCT
ejpam-6347	296	20	t	t	PROPN
ejpam-6347	296	21	)	)	PUNCT
ejpam-6347	296	22	+	+	CCONJ
ejpam-6347	296	23	α1u(t	α1u(t	PROPN
ejpam-6347	296	24	)	)	PUNCT
ejpam-6347	297	1	+	+	NOUN
ejpam-6347	297	2	m1h(t)−	m1h(t)−	PROPN
ejpam-6347	297	3	(	(	PUNCT
ejpam-6347	297	4	τ	τ	PROPN
ejpam-6347	297	5	+	+	PROPN
ejpam-6347	297	6	µ)r(t).,m	µ)r(t).,m	PROPN
ejpam-6347	297	7	(	(	PUNCT
ejpam-6347	297	8	3.42	3.42	NUM
ejpam-6347	297	9	)	)	PUNCT
ejpam-6347	297	10	theorem	theorem	NOUN
ejpam-6347	297	11	5	5	NUM
ejpam-6347	297	12	.	.	PUNCT
ejpam-6347	297	13	(	(	PUNCT
ejpam-6347	297	14	lipschitz	lipschitz	VERB
ejpam-6347	297	15	continuity	continuity	NOUN
ejpam-6347	297	16	and	and	CCONJ
ejpam-6347	297	17	contraction	contraction	NOUN
ejpam-6347	297	18	mapping	mapping	NOUN
ejpam-6347	297	19	of	of	ADP
ejpam-6347	297	20	kernel	kernel	PROPN
ejpam-6347	297	21	operators	operator	NOUN
ejpam-6347	297	22	)	)	PUNCT
ejpam-6347	297	23	let	let	VERB
ejpam-6347	297	24	φi	φi	ADV
ejpam-6347	297	25	:	:	PUNCT
ejpam-6347	297	26	r+	r+	NOUN
ejpam-6347	297	27	×	×	NOUN
ejpam-6347	297	28	x	x	INTJ
ejpam-6347	297	29	→	→	SYM
ejpam-6347	297	30	x	x	X
ejpam-6347	297	31	(	(	PUNCT
ejpam-6347	297	32	i	i	NOUN
ejpam-6347	297	33	=	=	NOUN
ejpam-6347	297	34	1	1	NUM
ejpam-6347	297	35	,	,	PUNCT
ejpam-6347	297	36	.	.	PUNCT
ejpam-6347	297	37	.	.	PUNCT
ejpam-6347	298	1	.	.	PUNCT
ejpam-6347	299	1	,	,	PUNCT
ejpam-6347	299	2	10	10	X
ejpam-6347	299	3	)	)	PUNCT
ejpam-6347	299	4	be	be	AUX
ejpam-6347	299	5	kernel	kernel	PROPN
ejpam-6347	299	6	operators	operator	NOUN
ejpam-6347	299	7	defined	define	VERB
ejpam-6347	299	8	on	on	ADP
ejpam-6347	299	9	a	a	DET
ejpam-6347	299	10	banach	banach	NOUN
ejpam-6347	299	11	space	space	NOUN
ejpam-6347	299	12	x	x	PUNCT
ejpam-6347	299	13	with	with	ADP
ejpam-6347	299	14	norm	norm	NOUN
ejpam-6347	299	15	∥	∥	X
ejpam-6347	299	16	·	·	PUNCT
ejpam-6347	299	17	∥.	∥.	PRON
ejpam-6347	300	1	assume	assume	VERB
ejpam-6347	300	2	:	:	PUNCT
ejpam-6347	300	3	n.	n.	NOUN
ejpam-6347	300	4	abbas	abbas	PROPN
ejpam-6347	300	5	,	,	PUNCT
ejpam-6347	300	6	w.	w.	PROPN
ejpam-6347	300	7	shatanawi	shatanawi	PROPN
ejpam-6347	300	8	,	,	PUNCT
ejpam-6347	300	9	s.	s.	PROPN
ejpam-6347	300	10	a.	a.	NOUN
ejpam-6347	300	11	zanib	zanib	PROPN
ejpam-6347	300	12	/	/	SYM
ejpam-6347	300	13	eur	eur	PROPN
ejpam-6347	300	14	.	.	PUNCT
ejpam-6347	301	1	j.	j.	PROPN
ejpam-6347	301	2	pure	pure	PROPN
ejpam-6347	301	3	appl	appl	PROPN
ejpam-6347	301	4	.	.	PROPN
ejpam-6347	301	5	math	math	PROPN
ejpam-6347	301	6	,	,	PUNCT
ejpam-6347	301	7	18	18	NUM
ejpam-6347	301	8	(	(	PUNCT
ejpam-6347	301	9	3	3	NUM
ejpam-6347	301	10	)	)	PUNCT
ejpam-6347	301	11	(	(	PUNCT
ejpam-6347	301	12	2025	2025	NUM
ejpam-6347	301	13	)	)	PUNCT
ejpam-6347	301	14	,	,	PUNCT
ejpam-6347	301	15	6347	6347	NUM
ejpam-6347	301	16	18	18	NUM
ejpam-6347	301	17	of	of	ADP
ejpam-6347	301	18	34	34	NUM
ejpam-6347	301	19	•	•	NOUN
ejpam-6347	301	20	population	population	NOUN
ejpam-6347	301	21	compartments	compartment	NOUN
ejpam-6347	301	22	are	be	AUX
ejpam-6347	301	23	bounded	bound	VERB
ejpam-6347	301	24	:	:	PUNCT
ejpam-6347	301	25	∥	∥	X
ejpam-6347	301	26	s	s	PART
ejpam-6347	301	27	∥≤	∥≤	PROPN
ejpam-6347	301	28	r1	r1	PROPN
ejpam-6347	301	29	,	,	PUNCT
ejpam-6347	301	30	∥	∥	PUNCT
ejpam-6347	301	31	e	e	X
ejpam-6347	301	32	∥≤	∥≤	PROPN
ejpam-6347	301	33	r2	r2	NOUN
ejpam-6347	301	34	,	,	PUNCT
ejpam-6347	301	35	∥	∥	PROPN
ejpam-6347	301	36	u	u	PROPN
ejpam-6347	301	37	∥≤	∥≤	PROPN
ejpam-6347	301	38	r3	r3	PROPN
ejpam-6347	301	39	,	,	PUNCT
ejpam-6347	301	40	∥	∥	PROPN
ejpam-6347	301	41	q	q	X
ejpam-6347	301	42	∥≤	∥≤	PROPN
ejpam-6347	301	43	r4	r4	NOUN
ejpam-6347	301	44	,	,	PUNCT
ejpam-6347	301	45	∥	∥	PROPN
ejpam-6347	301	46	p	p	PROPN
ejpam-6347	301	47	∥≤	∥≤	PROPN
ejpam-6347	301	48	r5	r5	PROPN
ejpam-6347	301	49	,	,	PUNCT
ejpam-6347	301	50	∥	∥	PROPN
ejpam-6347	301	51	h	h	NOUN
ejpam-6347	301	52	∥≤	∥≤	PROPN
ejpam-6347	301	53	r6	r6	NOUN
ejpam-6347	301	54	,	,	PUNCT
ejpam-6347	301	55	∥	∥	PROPN
ejpam-6347	301	56	c	c	X
ejpam-6347	301	57	∥≤	∥≤	PROPN
ejpam-6347	301	58	r7	r7	PROPN
ejpam-6347	301	59	,	,	PUNCT
ejpam-6347	301	60	∥	∥	PROPN
ejpam-6347	301	61	f	f	PROPN
ejpam-6347	301	62	∥≤	∥≤	PROPN
ejpam-6347	301	63	r8	r8	PROPN
ejpam-6347	301	64	,	,	PUNCT
ejpam-6347	301	65	∥	∥	PROPN
ejpam-6347	301	66	v	v	ADP
ejpam-6347	301	67	∥≤	∥≤	PROPN
ejpam-6347	301	68	r9	r9	NOUN
ejpam-6347	301	69	,	,	PUNCT
ejpam-6347	301	70	∥	∥	NUM
ejpam-6347	301	71	r	r	NOUN
ejpam-6347	301	72	∥≤	∥≤	PROPN
ejpam-6347	301	73	r10	r10	NOUN
ejpam-6347	301	74	•	•	NOUN
ejpam-6347	301	75	lipschitz	lipschitz	NOUN
ejpam-6347	301	76	coefficients	coefficient	NOUN
ejpam-6347	301	77	satisfy	satisfy	VERB
ejpam-6347	301	78	:	:	PUNCT
ejpam-6347	301	79	s∗1	s∗1	NOUN
ejpam-6347	301	80	=	=	PUNCT
ejpam-6347	301	81	ϕr2	ϕr2	NOUN
ejpam-6347	302	1	+	+	PUNCT
ejpam-6347	302	2	β	β	X
ejpam-6347	302	3	+	+	X
ejpam-6347	302	4	µ	µ	X
ejpam-6347	302	5	s∗2	s∗2	NOUN
ejpam-6347	302	6	=	=	PUNCT
ejpam-6347	302	7	ϕr1	ϕr1	ADJ
ejpam-6347	302	8	+	+	CCONJ
ejpam-6347	302	9	γr9	γr9	ADJ
ejpam-6347	302	10	+	+	ADJ
ejpam-6347	302	11	π1	π1	ADJ
ejpam-6347	302	12	s∗3	s∗3	NOUN
ejpam-6347	302	13	=	=	SYM
ejpam-6347	302	14	λ1r2	λ1r2	X
ejpam-6347	302	15	+	+	ADJ
ejpam-6347	302	16	π2	π2	ADJ
ejpam-6347	302	17	s∗4	s∗4	NOUN
ejpam-6347	302	18	=	=	PUNCT
ejpam-6347	303	1	λ2r2	λ2r2	PROPN
ejpam-6347	303	2	+	+	ADJ
ejpam-6347	303	3	π3	π3	NOUN
ejpam-6347	303	4	s∗5	s∗5	NOUN
ejpam-6347	303	5	=	=	SYM
ejpam-6347	303	6	π4	π4	PROPN
ejpam-6347	303	7	,	,	PUNCT
ejpam-6347	303	8	s	s	NOUN
ejpam-6347	303	9	∗	∗	NOUN
ejpam-6347	303	10	6	6	NUM
ejpam-6347	303	11	=	=	SYM
ejpam-6347	303	12	π5	π5	X
ejpam-6347	303	13	,	,	PUNCT
ejpam-6347	303	14	s	s	NOUN
ejpam-6347	303	15	∗	∗	NOUN
ejpam-6347	303	16	7	7	NUM
ejpam-6347	303	17	=	=	SYM
ejpam-6347	303	18	π6	π6	NOUN
ejpam-6347	303	19	,	,	PUNCT
ejpam-6347	303	20	s	s	NOUN
ejpam-6347	303	21	∗	∗	NOUN
ejpam-6347	303	22	8	8	NUM
ejpam-6347	303	23	=	=	SYM
ejpam-6347	303	24	π7	π7	NOUN
ejpam-6347	303	25	s∗9	s∗9	ADJ
ejpam-6347	304	1	=	=	PUNCT
ejpam-6347	305	1	γr2	γr2	NOUN
ejpam-6347	305	2	+	+	X
ejpam-6347	305	3	µ	µ	X
ejpam-6347	305	4	s∗10	s∗10	NOUN
ejpam-6347	306	1	=	=	PUNCT
ejpam-6347	306	2	τ	τ	PROPN
ejpam-6347	306	3	+	+	NUM
ejpam-6347	306	4	µ	µ	NUM
ejpam-6347	306	5	•	•	NOUN
ejpam-6347	306	6	parameter	parameter	NOUN
ejpam-6347	306	7	constraint	constraint	NOUN
ejpam-6347	306	8	:	:	PUNCT
ejpam-6347	306	9	0	0	NUM
ejpam-6347	306	10	≤	≤	NUM
ejpam-6347	306	11	s∗i	s∗i	PUNCT
ejpam-6347	306	12	<	<	X
ejpam-6347	306	13	1	1	NUM
ejpam-6347	306	14	∀i	∀i	NOUN
ejpam-6347	306	15	∈	∈	NOUN
ejpam-6347	306	16	{	{	PUNCT
ejpam-6347	306	17	1	1	NUM
ejpam-6347	306	18	,	,	PUNCT
ejpam-6347	306	19	.	.	PUNCT
ejpam-6347	306	20	.	.	PUNCT
ejpam-6347	306	21	.	.	PUNCT
ejpam-6347	307	1	,	,	PUNCT
ejpam-6347	307	2	10	10	NUM
ejpam-6347	307	3	}	}	PUNCT
ejpam-6347	307	4	then	then	ADV
ejpam-6347	307	5	each	each	PRON
ejpam-6347	307	6	φi	φi	ADP
ejpam-6347	307	7	satisfies	satisfy	VERB
ejpam-6347	307	8	the	the	DET
ejpam-6347	307	9	lipschitz	lipschitz	NOUN
ejpam-6347	307	10	condition	condition	NOUN
ejpam-6347	307	11	and	and	CCONJ
ejpam-6347	307	12	constitutes	constitute	VERB
ejpam-6347	307	13	a	a	DET
ejpam-6347	307	14	contraction	contraction	NOUN
ejpam-6347	307	15	mapping	mapping	NOUN
ejpam-6347	307	16	.	.	PUNCT
ejpam-6347	308	1	proof	proof	NOUN
ejpam-6347	308	2	.	.	PUNCT
ejpam-6347	309	1	we	we	PRON
ejpam-6347	309	2	demonstrate	demonstrate	VERB
ejpam-6347	309	3	the	the	DET
ejpam-6347	309	4	result	result	NOUN
ejpam-6347	309	5	for	for	ADP
ejpam-6347	309	6	φ1	φ1	PROPN
ejpam-6347	309	7	;	;	PUNCT
ejpam-6347	309	8	analogous	analogous	ADJ
ejpam-6347	309	9	arguments	argument	NOUN
ejpam-6347	309	10	apply	apply	VERB
ejpam-6347	309	11	to	to	ADP
ejpam-6347	309	12	φ2	φ2	PROPN
ejpam-6347	309	13	,	,	PUNCT
ejpam-6347	309	14	.	.	PUNCT
ejpam-6347	309	15	.	.	PUNCT
ejpam-6347	310	1	.	.	PUNCT
ejpam-6347	311	1	,	,	PUNCT
ejpam-6347	311	2	φ10	φ10	PROPN
ejpam-6347	311	3	.	.	PUNCT
ejpam-6347	312	1	let	let	VERB
ejpam-6347	312	2	s1	s1	NOUN
ejpam-6347	312	3	,	,	PUNCT
ejpam-6347	312	4	s2	s2	NOUN
ejpam-6347	312	5	∈	∈	PROPN
ejpam-6347	312	6	x	x	PUNCT
ejpam-6347	312	7	be	be	AUX
ejpam-6347	312	8	arbitrary	arbitrary	ADJ
ejpam-6347	312	9	functions	function	NOUN
ejpam-6347	312	10	.	.	PUNCT
ejpam-6347	313	1	then	then	ADV
ejpam-6347	313	2	:	:	PUNCT
ejpam-6347	313	3	∥	∥	PROPN
ejpam-6347	313	4	φ1(t	φ1(t	PROPN
ejpam-6347	313	5	,	,	PUNCT
ejpam-6347	313	6	s1)−	s1)−	PROPN
ejpam-6347	313	7	φ1(t	φ1(t	PROPN
ejpam-6347	313	8	,	,	PUNCT
ejpam-6347	313	9	s2	s2	PROPN
ejpam-6347	313	10	)	)	PUNCT
ejpam-6347	313	11	∥	∥	X
ejpam-6347	314	1	=	=	PUNCT
ejpam-6347	314	2	∥	∥	PRON
ejpam-6347	314	3	[	[	PUNCT
ejpam-6347	314	4	λ	λ	X
ejpam-6347	314	5	+	+	NOUN
ejpam-6347	314	6	τr(t	τr(t	PUNCT
ejpam-6347	314	7	)	)	PUNCT
ejpam-6347	315	1	+	+	SYM
ejpam-6347	315	2	b2q(t)−	b2q(t)−	PROPN
ejpam-6347	315	3	(	(	PUNCT
ejpam-6347	315	4	ϕe(t	ϕe(t	PUNCT
ejpam-6347	315	5	)	)	PUNCT
ejpam-6347	315	6	+	+	CCONJ
ejpam-6347	315	7	β	β	X
ejpam-6347	315	8	+	+	ADJ
ejpam-6347	315	9	µ)s1(t	µ)s1(t	NUM
ejpam-6347	315	10	)	)	PUNCT
ejpam-6347	315	11	]	]	PUNCT
ejpam-6347	316	1	−	−	PROPN
ejpam-6347	316	2	[	[	PUNCT
ejpam-6347	316	3	λ	λ	X
ejpam-6347	316	4	+	+	NOUN
ejpam-6347	316	5	τr(t	τr(t	PUNCT
ejpam-6347	316	6	)	)	PUNCT
ejpam-6347	317	1	+	+	SYM
ejpam-6347	317	2	b2q(t)−	b2q(t)−	PROPN
ejpam-6347	317	3	(	(	PUNCT
ejpam-6347	317	4	ϕe(t	ϕe(t	PUNCT
ejpam-6347	317	5	)	)	PUNCT
ejpam-6347	317	6	+	+	CCONJ
ejpam-6347	317	7	β	β	X
ejpam-6347	317	8	+	+	CCONJ
ejpam-6347	317	9	µ)s2(t	µ)s2(t	PROPN
ejpam-6347	317	10	)	)	PUNCT
ejpam-6347	317	11	]	]	PUNCT
ejpam-6347	317	12	∥	∥	PUNCT
ejpam-6347	317	13	=	=	SYM
ejpam-6347	317	14	∥	∥	SYM
ejpam-6347	317	15	−(ϕe(t	−(ϕe(t	NUM
ejpam-6347	317	16	)	)	PUNCT
ejpam-6347	318	1	+	+	NUM
ejpam-6347	318	2	β	β	X
ejpam-6347	318	3	+	+	NUM
ejpam-6347	318	4	µ)(s1(t)−	µ)(s1(t)−	PROPN
ejpam-6347	318	5	s2(t	s2(t	NUM
ejpam-6347	318	6	)	)	PUNCT
ejpam-6347	318	7	)	)	PUNCT
ejpam-6347	319	1	∥	∥	PUNCT
ejpam-6347	319	2	≤	≤	NOUN
ejpam-6347	319	3	(	(	PUNCT
ejpam-6347	319	4	ϕ	ϕ	X
ejpam-6347	319	5	∥	∥	X
ejpam-6347	319	6	e	e	NOUN
ejpam-6347	319	7	∥	∥	X
ejpam-6347	319	8	+	+	NUM
ejpam-6347	319	9	β	β	X
ejpam-6347	319	10	+	+	X
ejpam-6347	319	11	µ	µ	X
ejpam-6347	319	12	)	)	PUNCT
ejpam-6347	319	13	∥	∥	NUM
ejpam-6347	319	14	s1	s1	NOUN
ejpam-6347	319	15	−	−	PROPN
ejpam-6347	319	16	s2	s2	NOUN
ejpam-6347	319	17	∥	∥	X
ejpam-6347	319	18	(	(	PUNCT
ejpam-6347	319	19	by	by	ADP
ejpam-6347	319	20	triangle	triangle	NOUN
ejpam-6347	319	21	inequality	inequality	NOUN
ejpam-6347	319	22	)	)	PUNCT
ejpam-6347	319	23	≤	≤	PUNCT
ejpam-6347	319	24	s∗1	s∗1	NOUN
ejpam-6347	319	25	∥	∥	PUNCT
ejpam-6347	319	26	s1	s1	NOUN
ejpam-6347	319	27	−	−	PROPN
ejpam-6347	319	28	s2	s2	NOUN
ejpam-6347	319	29	∥	∥	NUM
ejpam-6347	319	30	,	,	PUNCT
ejpam-6347	319	31	(	(	PUNCT
ejpam-6347	319	32	3.43	3.43	NUM
ejpam-6347	319	33	)	)	PUNCT
ejpam-6347	319	34	where	where	SCONJ
ejpam-6347	319	35	s∗1	s∗1	NOUN
ejpam-6347	319	36	=	=	PUNCT
ejpam-6347	319	37	ϕr2	ϕr2	NOUN
ejpam-6347	320	1	+	+	PUNCT
ejpam-6347	320	2	β	β	X
ejpam-6347	320	3	+	+	X
ejpam-6347	320	4	µ	µ	X
ejpam-6347	320	5	by	by	ADP
ejpam-6347	320	6	the	the	DET
ejpam-6347	320	7	boundedness	boundedness	NOUN
ejpam-6347	320	8	assumption	assumption	NOUN
ejpam-6347	320	9	∥	∥	PUNCT
ejpam-6347	320	10	e	e	X
ejpam-6347	320	11	∥≤	∥≤	PROPN
ejpam-6347	320	12	r2	r2	NOUN
ejpam-6347	320	13	.	.	PUNCT
ejpam-6347	321	1	the	the	DET
ejpam-6347	321	2	contraction	contraction	NOUN
ejpam-6347	321	3	property	property	NOUN
ejpam-6347	321	4	follows	follow	VERB
ejpam-6347	321	5	from	from	ADP
ejpam-6347	321	6	0	0	NUM
ejpam-6347	321	7	≤	≤	NUM
ejpam-6347	321	8	s∗1	s∗1	NOUN
ejpam-6347	321	9	<	<	X
ejpam-6347	321	10	1	1	NUM
ejpam-6347	321	11	.	.	PUNCT
ejpam-6347	321	12	similar	similar	ADJ
ejpam-6347	321	13	calculations	calculation	NOUN
ejpam-6347	321	14	for	for	ADP
ejpam-6347	321	15	φ2	φ2	NOUN
ejpam-6347	321	16	,	,	PUNCT
ejpam-6347	321	17	.	.	PUNCT
ejpam-6347	321	18	.	.	PUNCT
ejpam-6347	322	1	.	.	PUNCT
ejpam-6347	323	1	,	,	PUNCT
ejpam-6347	323	2	φ10	φ10	NOUN
ejpam-6347	323	3	yield	yield	NOUN
ejpam-6347	323	4	corresponding	corresponding	ADJ
ejpam-6347	323	5	lipschitz	lipschitz	PROPN
ejpam-6347	323	6	constants	constant	NOUN
ejpam-6347	323	7	s∗2	s∗2	PROPN
ejpam-6347	323	8	,	,	PUNCT
ejpam-6347	323	9	.	.	PUNCT
ejpam-6347	323	10	.	.	PUNCT
ejpam-6347	323	11	.	.	PUNCT
ejpam-6347	324	1	,	,	PUNCT
ejpam-6347	324	2	s	s	NOUN
ejpam-6347	324	3	∗	∗	NOUN
ejpam-6347	324	4	10	10	NUM
ejpam-6347	324	5	with	with	ADP
ejpam-6347	324	6	contraction	contraction	NOUN
ejpam-6347	324	7	properties	property	NOUN
ejpam-6347	324	8	under	under	ADP
ejpam-6347	324	9	the	the	DET
ejpam-6347	324	10	stated	state	VERB
ejpam-6347	324	11	parameter	parameter	NOUN
ejpam-6347	324	12	constraints	constraint	NOUN
ejpam-6347	324	13	.	.	PUNCT
ejpam-6347	325	1	therefore	therefore	ADV
ejpam-6347	325	2	,	,	PUNCT
ejpam-6347	325	3	all	all	DET
ejpam-6347	325	4	kernel	kernel	PROPN
ejpam-6347	325	5	operators	operator	NOUN
ejpam-6347	325	6	satisfy	satisfy	VERB
ejpam-6347	325	7	both	both	PRON
ejpam-6347	325	8	lipschitz	lipschitz	VERB
ejpam-6347	325	9	continuity	continuity	NOUN
ejpam-6347	325	10	and	and	CCONJ
ejpam-6347	325	11	contraction	contraction	NOUN
ejpam-6347	325	12	mapping	mapping	NOUN
ejpam-6347	325	13	requirements	requirement	NOUN
ejpam-6347	325	14	.	.	PUNCT
ejpam-6347	326	1	by	by	ADP
ejpam-6347	326	2	considering	consider	VERB
ejpam-6347	326	3	the	the	DET
ejpam-6347	326	4	kernels	kernel	NOUN
ejpam-6347	326	5	φi	φi	ADV
ejpam-6347	326	6	,	,	PUNCT
ejpam-6347	326	7	i	i	PRON
ejpam-6347	326	8	=	=	NOUN
ejpam-6347	326	9	1	1	NUM
ejpam-6347	326	10	,	,	PUNCT
ejpam-6347	326	11	2	2	NUM
ejpam-6347	326	12	,	,	PUNCT
ejpam-6347	326	13	3	3	NUM
ejpam-6347	326	14	,	,	PUNCT
ejpam-6347	326	15	.	.	PUNCT
ejpam-6347	326	16	.	.	PUNCT
ejpam-6347	326	17	.	.	PUNCT
ejpam-6347	327	1	,	,	PUNCT
ejpam-6347	327	2	10	10	NUM
ejpam-6347	327	3	.	.	PUNCT
ejpam-6347	328	1	now	now	ADV
ejpam-6347	328	2	the	the	DET
ejpam-6347	328	3	system	system	NOUN
ejpam-6347	328	4	of	of	ADP
ejpam-6347	328	5	equation	equation	NOUN
ejpam-6347	328	6	have	have	VERB
ejpam-6347	328	7	(	(	PUNCT
ejpam-6347	328	8	3.41	3.41	NUM
ejpam-6347	328	9	)	)	PUNCT
ejpam-6347	328	10	then	then	ADV
ejpam-6347	328	11	,	,	PUNCT
ejpam-6347	328	12	recursive	recursive	ADJ
ejpam-6347	328	13	formula	formula	NOUN
ejpam-6347	328	14	can	can	AUX
ejpam-6347	328	15	be	be	AUX
ejpam-6347	328	16	proceed	procee	VERB
ejpam-6347	328	17	in	in	ADP
ejpam-6347	328	18	the	the	DET
ejpam-6347	328	19	following	following	NOUN
ejpam-6347	328	20	,	,	PUNCT
ejpam-6347	328	21	01v	01v	NOUN
ejpam-6347	328	22	=	=	SYM
ejpam-6347	328	23	s(t)−	s(t)−	PROPN
ejpam-6347	328	24	s(0	s(0	PROPN
ejpam-6347	328	25	)	)	PUNCT
ejpam-6347	328	26	=	=	SYM
ejpam-6347	329	1	∫	∫	PROPN
ejpam-6347	329	2	t	t	NOUN
ejpam-6347	329	3	0	0	NUM
ejpam-6347	330	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	330	2	(	(	PUNCT
ejpam-6347	330	3	φ1(ρ	φ1(ρ	PROPN
ejpam-6347	330	4	,	,	PUNCT
ejpam-6347	330	5	sv−1)−	sv−1)−	PROPN
ejpam-6347	330	6	φ1(ρ	φ1(ρ	PROPN
ejpam-6347	330	7	,	,	PUNCT
ejpam-6347	330	8	sv−2	sv−2	PROPN
ejpam-6347	330	9	)	)	PUNCT
ejpam-6347	330	10	)	)	PUNCT
ejpam-6347	330	11	dρ	dρ	PROPN
ejpam-6347	330	12	,	,	PUNCT
ejpam-6347	330	13	(	(	PUNCT
ejpam-6347	330	14	3.44	3.44	NUM
ejpam-6347	330	15	)	)	PUNCT
ejpam-6347	330	16	triangle	triangle	NOUN
ejpam-6347	330	17	inequality	inequality	NOUN
ejpam-6347	330	18	law	law	NOUN
ejpam-6347	330	19	will	will	AUX
ejpam-6347	330	20	be	be	AUX
ejpam-6347	330	21	apply	apply	VERB
ejpam-6347	330	22	on	on	ADP
ejpam-6347	330	23	eq	eq	ADP
ejpam-6347	330	24	.	.	PUNCT
ejpam-6347	331	1	(	(	PUNCT
ejpam-6347	331	2	3.44	3.44	NUM
ejpam-6347	331	3	)	)	PUNCT
ejpam-6347	331	4	,	,	PUNCT
ejpam-6347	331	5	∥	∥	PROPN
ejpam-6347	331	6	01v	01v	NUM
ejpam-6347	331	7	∥=∥	∥=∥	PROPN
ejpam-6347	331	8	sv(t)−	sv(t)−	PROPN
ejpam-6347	331	9	sv−1(t	sv−1(t	PROPN
ejpam-6347	331	10	)	)	PUNCT
ejpam-6347	331	11	∥≤	∥≤	VERB
ejpam-6347	331	12	s∗1	s∗1	ADJ
ejpam-6347	331	13	∫	∫	PROPN
ejpam-6347	332	1	t	t	NOUN
ejpam-6347	332	2	0	0	NUM
ejpam-6347	333	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	333	2	∥	∥	NOUN
ejpam-6347	333	3	(	(	PUNCT
ejpam-6347	333	4	sv−1	sv−1	PROPN
ejpam-6347	333	5	−	−	PROPN
ejpam-6347	333	6	sv−2	sv−2	PROPN
ejpam-6347	333	7	)	)	PUNCT
ejpam-6347	333	8	)	)	PUNCT
ejpam-6347	333	9	∥	∥	NUM
ejpam-6347	333	10	dρ	dρ	PROPN
ejpam-6347	333	11	,	,	PUNCT
ejpam-6347	333	12	(	(	PUNCT
ejpam-6347	333	13	3.45	3.45	NUM
ejpam-6347	333	14	)	)	PUNCT
ejpam-6347	333	15	n.	n.	NOUN
ejpam-6347	333	16	abbas	abbas	PROPN
ejpam-6347	333	17	,	,	PUNCT
ejpam-6347	333	18	w.	w.	PROPN
ejpam-6347	333	19	shatanawi	shatanawi	PROPN
ejpam-6347	333	20	,	,	PUNCT
ejpam-6347	333	21	s.	s.	PROPN
ejpam-6347	333	22	a.	a.	NOUN
ejpam-6347	333	23	zanib	zanib	PROPN
ejpam-6347	333	24	/	/	SYM
ejpam-6347	333	25	eur	eur	PROPN
ejpam-6347	333	26	.	.	PUNCT
ejpam-6347	334	1	j.	j.	PROPN
ejpam-6347	334	2	pure	pure	PROPN
ejpam-6347	334	3	appl	appl	PROPN
ejpam-6347	334	4	.	.	PROPN
ejpam-6347	334	5	math	math	PROPN
ejpam-6347	334	6	,	,	PUNCT
ejpam-6347	334	7	18	18	NUM
ejpam-6347	334	8	(	(	PUNCT
ejpam-6347	334	9	3	3	NUM
ejpam-6347	334	10	)	)	PUNCT
ejpam-6347	334	11	(	(	PUNCT
ejpam-6347	334	12	2025	2025	NUM
ejpam-6347	334	13	)	)	PUNCT
ejpam-6347	334	14	,	,	PUNCT
ejpam-6347	334	15	6347	6347	NUM
ejpam-6347	334	16	19	19	NUM
ejpam-6347	334	17	of	of	ADP
ejpam-6347	334	18	34	34	NUM
ejpam-6347	334	19	by	by	ADP
ejpam-6347	334	20	applying	apply	VERB
ejpam-6347	334	21	lipschitz	lipschitz	NOUN
ejpam-6347	334	22	conditions	condition	NOUN
ejpam-6347	334	23	(	(	PUNCT
ejpam-6347	334	24	5	5	NUM
ejpam-6347	334	25	)	)	PUNCT
ejpam-6347	334	26	,	,	PUNCT
ejpam-6347	334	27	∥	∥	X
ejpam-6347	334	28	01v	01v	NOUN
ejpam-6347	334	29	∥≤	∥≤	VERB
ejpam-6347	334	30	s∗1	s∗1	ADJ
ejpam-6347	334	31	∫	∫	PROPN
ejpam-6347	334	32	t	t	NOUN
ejpam-6347	334	33	0	0	NUM
ejpam-6347	335	1	∥	∥	NOUN
ejpam-6347	335	2	01v−1	01v−1	X
ejpam-6347	335	3	∥	∥	NOUN
ejpam-6347	335	4	dρ	dρ	PROPN
ejpam-6347	335	5	,	,	PUNCT
ejpam-6347	335	6	(	(	PUNCT
ejpam-6347	335	7	3.46	3.46	NUM
ejpam-6347	335	8	)	)	PUNCT
ejpam-6347	335	9	it	it	PRON
ejpam-6347	335	10	can	can	AUX
ejpam-6347	335	11	write	write	VERB
ejpam-6347	335	12	,	,	PUNCT
ejpam-6347	335	13	sv(t	sv(t	NOUN
ejpam-6347	335	14	)	)	PUNCT
ejpam-6347	336	1	=	=	SYM
ejpam-6347	337	1	v∑	v∑	X
ejpam-6347	337	2	i=1	i=1	PROPN
ejpam-6347	337	3	01v(t	01v(t	NOUN
ejpam-6347	337	4	)	)	PUNCT
ejpam-6347	337	5	.	.	PUNCT
ejpam-6347	338	1	(	(	PUNCT
ejpam-6347	338	2	3.47	3.47	NUM
ejpam-6347	338	3	)	)	PUNCT
ejpam-6347	338	4	similarly	similarly	ADV
ejpam-6347	338	5	for	for	ADP
ejpam-6347	338	6	others	other	NOUN
ejpam-6347	338	7	.	.	PUNCT
ejpam-6347	339	1	thus	thus	ADV
ejpam-6347	339	2	the	the	DET
ejpam-6347	339	3	following	follow	VERB
ejpam-6347	339	4	theorem	theorem	NOUN
ejpam-6347	339	5	may	may	AUX
ejpam-6347	339	6	be	be	AUX
ejpam-6347	339	7	derived	derive	VERB
ejpam-6347	339	8	from	from	ADP
ejpam-6347	339	9	these	these	DET
ejpam-6347	339	10	findings	finding	NOUN
ejpam-6347	339	11	.	.	PUNCT
ejpam-6347	340	1	theorem	theorem	VERB
ejpam-6347	340	2	6	6	NUM
ejpam-6347	340	3	.	.	PUNCT
ejpam-6347	341	1	(	(	PUNCT
ejpam-6347	341	2	existence	existence	NOUN
ejpam-6347	341	3	of	of	ADP
ejpam-6347	341	4	covcom10	covcom10	NOUN
ejpam-6347	341	5	model	model	NOUN
ejpam-6347	341	6	solutions	solution	NOUN
ejpam-6347	341	7	)	)	PUNCT
ejpam-6347	341	8	let	let	VERB
ejpam-6347	341	9	x	x	SYM
ejpam-6347	341	10	=	=	SYM
ejpam-6347	341	11	c([0	c([0	PROPN
ejpam-6347	341	12	,	,	PUNCT
ejpam-6347	341	13	tmax],r+	tmax],r+	PROPN
ejpam-6347	341	14	)	)	PUNCT
ejpam-6347	341	15	be	be	AUX
ejpam-6347	341	16	the	the	DET
ejpam-6347	341	17	banach	banach	NOUN
ejpam-6347	341	18	space	space	NOUN
ejpam-6347	341	19	of	of	ADP
ejpam-6347	341	20	continuous	continuous	ADJ
ejpam-6347	341	21	functions	function	NOUN
ejpam-6347	341	22	with	with	ADP
ejpam-6347	341	23	norm	norm	NOUN
ejpam-6347	341	24	∥	∥	X
ejpam-6347	341	25	·	·	PUNCT
ejpam-6347	341	26	∥.	∥.	NOUN
ejpam-6347	341	27	the	the	DET
ejpam-6347	341	28	covcom10	covcom10	PROPN
ejpam-6347	341	29	model	model	NOUN
ejpam-6347	341	30	admits	admit	VERB
ejpam-6347	341	31	a	a	DET
ejpam-6347	341	32	unique	unique	ADJ
ejpam-6347	341	33	solution	solution	NOUN
ejpam-6347	341	34	(	(	PUNCT
ejpam-6347	341	35	s	s	X
ejpam-6347	341	36	,	,	PUNCT
ejpam-6347	341	37	e	e	NOUN
ejpam-6347	341	38	,	,	PUNCT
ejpam-6347	341	39	u	u	NOUN
ejpam-6347	341	40	,	,	PUNCT
ejpam-6347	341	41	q	q	INTJ
ejpam-6347	341	42	,	,	PUNCT
ejpam-6347	341	43	p	p	X
ejpam-6347	341	44	,	,	PUNCT
ejpam-6347	341	45	h	h	NOUN
ejpam-6347	341	46	,	,	PUNCT
ejpam-6347	341	47	c	c	X
ejpam-6347	341	48	,	,	PUNCT
ejpam-6347	341	49	f	f	PROPN
ejpam-6347	341	50	,	,	PUNCT
ejpam-6347	341	51	v	v	NOUN
ejpam-6347	341	52	,	,	PUNCT
ejpam-6347	341	53	r	r	NOUN
ejpam-6347	341	54	)	)	PUNCT
ejpam-6347	341	55	∈	∈	NOUN
ejpam-6347	342	1	x	x	SYM
ejpam-6347	342	2	10	10	NUM
ejpam-6347	342	3	if	if	SCONJ
ejpam-6347	342	4	:	:	PUNCT
ejpam-6347	342	5	•	•	ADJ
ejpam-6347	342	6	lipschitz	lipschitz	NOUN
ejpam-6347	342	7	constants	constant	NOUN
ejpam-6347	342	8	s∗i	s∗i	NUM
ejpam-6347	342	9	from	from	ADP
ejpam-6347	342	10	theorem	theorem	ADJ
ejpam-6347	342	11	1	1	NUM
ejpam-6347	342	12	satisfy	satisfy	NOUN
ejpam-6347	342	13	:	:	PUNCT
ejpam-6347	342	14	sitmax	sitmax	VERB
ejpam-6347	342	15	≤	≤	ADV
ejpam-6347	342	16	1	1	NUM
ejpam-6347	342	17	.	.	PUNCT
ejpam-6347	343	1	∀i	∀i	X
ejpam-6347	343	2	∈	∈	NOUN
ejpam-6347	343	3	{	{	PUNCT
ejpam-6347	343	4	1	1	NUM
ejpam-6347	343	5	,	,	PUNCT
ejpam-6347	343	6	.	.	PUNCT
ejpam-6347	343	7	.	.	PUNCT
ejpam-6347	343	8	.	.	PUNCT
ejpam-6347	344	1	,	,	PUNCT
ejpam-6347	344	2	10	10	NUM
ejpam-6347	344	3	}	}	PUNCT
ejpam-6347	344	4	where	where	SCONJ
ejpam-6347	344	5	tmax	tmax	ADV
ejpam-6347	344	6	>	>	X
ejpam-6347	344	7	0	0	NUM
ejpam-6347	344	8	is	be	AUX
ejpam-6347	344	9	the	the	DET
ejpam-6347	344	10	maximal	maximal	ADJ
ejpam-6347	344	11	existence	existence	NOUN
ejpam-6347	344	12	time	time	NOUN
ejpam-6347	344	13	•	•	ADP
ejpam-6347	344	14	initial	initial	ADJ
ejpam-6347	344	15	conditions	condition	NOUN
ejpam-6347	344	16	(	(	PUNCT
ejpam-6347	344	17	s0	s0	NOUN
ejpam-6347	344	18	,	,	PUNCT
ejpam-6347	344	19	.	.	PUNCT
ejpam-6347	344	20	.	.	PUNCT
ejpam-6347	345	1	.	.	PUNCT
ejpam-6347	346	1	,	,	PUNCT
ejpam-6347	346	2	r0	r0	NOUN
ejpam-6347	346	3	)	)	PUNCT
ejpam-6347	346	4	are	be	AUX
ejpam-6347	346	5	bounded	bound	VERB
ejpam-6347	346	6	in	in	ADP
ejpam-6347	346	7	x	x	SYM
ejpam-6347	346	8	proof	proof	NOUN
ejpam-6347	346	9	.	.	PUNCT
ejpam-6347	347	1	using	use	VERB
ejpam-6347	347	2	the	the	DET
ejpam-6347	347	3	picard	picard	NOUN
ejpam-6347	347	4	iteration	iteration	NOUN
ejpam-6347	347	5	scheme	scheme	NOUN
ejpam-6347	347	6	for	for	ADP
ejpam-6347	347	7	the	the	DET
ejpam-6347	347	8	integral	integral	ADJ
ejpam-6347	347	9	equations	equation	NOUN
ejpam-6347	347	10	,	,	PUNCT
ejpam-6347	347	11	define	define	VERB
ejpam-6347	347	12	successive	successive	ADJ
ejpam-6347	347	13	approximations	approximation	NOUN
ejpam-6347	347	14	:	:	PUNCT
ejpam-6347	347	15	sv+1(t	sv+1(t	NUM
ejpam-6347	347	16	)	)	PUNCT
ejpam-6347	348	1	=	=	SYM
ejpam-6347	348	2	s0	s0	PROPN
ejpam-6347	348	3	+	+	CCONJ
ejpam-6347	348	4	∫	∫	PROPN
ejpam-6347	348	5	t	t	PROPN
ejpam-6347	348	6	0	0	NUM
ejpam-6347	349	1	φ1(ρ	φ1(ρ	PROPN
ejpam-6347	349	2	,	,	PUNCT
ejpam-6347	349	3	sv(ρ))dρ	sv(ρ))dρ	PROPN
ejpam-6347	349	4	,	,	PUNCT
ejpam-6347	349	5	with	with	ADP
ejpam-6347	349	6	analogous	analogous	ADJ
ejpam-6347	349	7	definitions	definition	NOUN
ejpam-6347	349	8	for	for	ADP
ejpam-6347	349	9	other	other	ADJ
ejpam-6347	349	10	compartments	compartment	NOUN
ejpam-6347	349	11	.	.	PUNCT
ejpam-6347	350	1	from	from	ADP
ejpam-6347	350	2	theorem	theorem	ADJ
ejpam-6347	350	3	1	1	NUM
ejpam-6347	350	4	’s	’s	PART
ejpam-6347	350	5	lipschitz	lipschitz	NOUN
ejpam-6347	350	6	conditions	condition	NOUN
ejpam-6347	350	7	:	:	PUNCT
ejpam-6347	350	8	∥	∥	NOUN
ejpam-6347	350	9	01v	01v	NOUN
ejpam-6347	350	10	∥	∥	NOUN
ejpam-6347	350	11	≤∥	≤∥	PUNCT
ejpam-6347	350	12	s0	s0	NOUN
ejpam-6347	350	13	∥	∥	PROPN
ejpam-6347	350	14	(	(	PUNCT
ejpam-6347	350	15	s∗1tmax	s∗1tmax	ADJ
ejpam-6347	350	16	)	)	PUNCT
ejpam-6347	350	17	v	v	NOUN
ejpam-6347	350	18	,	,	PUNCT
ejpam-6347	350	19	≤∥	≤∥	X
ejpam-6347	350	20	s0	s0	PROPN
ejpam-6347	350	21	∥	∥	PUNCT
ejpam-6347	350	22	.(s∗1tmax	.(s∗1tmax	PUNCT
ejpam-6347	350	23	)	)	PUNCT
ejpam-6347	351	1	v.	v.	CCONJ
ejpam-6347	351	2	(	(	PUNCT
ejpam-6347	351	3	by	by	ADP
ejpam-6347	351	4	induction	induction	NOUN
ejpam-6347	351	5	hypothesis	hypothesis	NOUN
ejpam-6347	351	6	)	)	PUNCT
ejpam-6347	351	7	(	(	PUNCT
ejpam-6347	351	8	3.48	3.48	NUM
ejpam-6347	351	9	)	)	PUNCT
ejpam-6347	351	10	for	for	ADP
ejpam-6347	351	11	residual	residual	ADJ
ejpam-6347	351	12	terms	term	NOUN
ejpam-6347	351	13	ℶ1v(t	ℶ1v(t	PROPN
ejpam-6347	351	14	)	)	PUNCT
ejpam-6347	351	15	:	:	PUNCT
ejpam-6347	351	16	=	=	PROPN
ejpam-6347	351	17	s(t)−	s(t)−	PROPN
ejpam-6347	351	18	sv(t	sv(t	NUM
ejpam-6347	351	19	):	):	PUNCT
ejpam-6347	351	20	∥	∥	PUNCT
ejpam-6347	351	21	ℶ1v(t	ℶ1v(t	PROPN
ejpam-6347	351	22	)	)	PUNCT
ejpam-6347	352	1	∥	∥	PUNCT
ejpam-6347	352	2	≤	≤	NUM
ejpam-6347	353	1	∫	∫	PROPN
ejpam-6347	353	2	t	t	NOUN
ejpam-6347	353	3	0	0	NUM
ejpam-6347	353	4	∥	∥	SYM
ejpam-6347	353	5	φ1(ρ	φ1(ρ	PROPN
ejpam-6347	353	6	,	,	PUNCT
ejpam-6347	353	7	s)−	s)−	PROPN
ejpam-6347	353	8	φ1(ρ	φ1(ρ	PROPN
ejpam-6347	353	9	,	,	PUNCT
ejpam-6347	353	10	sv−1	sv−1	PROPN
ejpam-6347	353	11	)	)	PUNCT
ejpam-6347	353	12	∥	∥	NUM
ejpam-6347	353	13	dρ	dρ	NOUN
ejpam-6347	353	14	,	,	PUNCT
ejpam-6347	353	15	≤	≤	X
ejpam-6347	353	16	s∗1	s∗1	ADJ
ejpam-6347	353	17	∫	∫	PROPN
ejpam-6347	353	18	t	t	PROPN
ejpam-6347	353	19	0	0	NUM
ejpam-6347	353	20	∥	∥	PROPN
ejpam-6347	353	21	s	s	PART
ejpam-6347	353	22	−	−	PROPN
ejpam-6347	353	23	sv−1	sv−1	PROPN
ejpam-6347	353	24	∥	∥	PUNCT
ejpam-6347	353	25	dρ	dρ	PROPN
ejpam-6347	353	26	,	,	PUNCT
ejpam-6347	353	27	≤	≤	NUM
ejpam-6347	353	28	(	(	PUNCT
ejpam-6347	353	29	s∗1tmax	s∗1tmax	ADV
ejpam-6347	353	30	)	)	PUNCT
ejpam-6347	353	31	v	v	NOUN
ejpam-6347	353	32	∥	∥	NOUN
ejpam-6347	353	33	s0	s0	X
ejpam-6347	353	34	∥	∥	PUNCT
ejpam-6347	353	35	.	.	PUNCT
ejpam-6347	354	1	(	(	PUNCT
ejpam-6347	354	2	via	via	ADP
ejpam-6347	354	3	recursive	recursive	ADJ
ejpam-6347	354	4	estimation	estimation	NOUN
ejpam-6347	354	5	)	)	PUNCT
ejpam-6347	354	6	under	under	ADP
ejpam-6347	354	7	condition	condition	NOUN
ejpam-6347	354	8	s∗i	s∗i	X
ejpam-6347	354	9	tmax	tmax	ADP
ejpam-6347	354	10	<	<	X
ejpam-6347	354	11	1	1	NUM
ejpam-6347	354	12	,	,	PUNCT
ejpam-6347	354	13	we	we	PRON
ejpam-6347	354	14	get	get	VERB
ejpam-6347	354	15	:	:	PUNCT
ejpam-6347	355	1	lim	lim	NOUN
ejpam-6347	355	2	v→∞	v→∞	NUM
ejpam-6347	355	3	∥	∥	PUNCT
ejpam-6347	355	4	ℶ1v(t	ℶ1v(t	PROPN
ejpam-6347	355	5	)	)	PUNCT
ejpam-6347	355	6	∥≤	∥≤	PROPN
ejpam-6347	355	7	lim	lim	PROPN
ejpam-6347	355	8	v→∞	v→∞	NUM
ejpam-6347	355	9	(	(	PUNCT
ejpam-6347	355	10	s∗1tmax	s∗1tmax	NOUN
ejpam-6347	355	11	)	)	PUNCT
ejpam-6347	355	12	v	v	NOUN
ejpam-6347	355	13	∥	∥	NUM
ejpam-6347	355	14	s0	s0	X
ejpam-6347	355	15	∥=	∥=	NOUN
ejpam-6347	355	16	0	0	NUM
ejpam-6347	355	17	.	.	PUNCT
ejpam-6347	356	1	similar	similar	ADJ
ejpam-6347	356	2	convergence	convergence	NOUN
ejpam-6347	356	3	holds	hold	VERB
ejpam-6347	356	4	for	for	ADP
ejpam-6347	356	5	other	other	ADJ
ejpam-6347	356	6	compartments	compartment	NOUN
ejpam-6347	356	7	by	by	ADP
ejpam-6347	356	8	identical	identical	ADJ
ejpam-6347	356	9	reasoning	reasoning	NOUN
ejpam-6347	356	10	.	.	PUNCT
ejpam-6347	357	1	by	by	ADP
ejpam-6347	357	2	banach	banach	ADV
ejpam-6347	357	3	fixed	fix	VERB
ejpam-6347	357	4	-	-	PUNCT
ejpam-6347	357	5	point	point	NOUN
ejpam-6347	357	6	theorem	theorem	NOUN
ejpam-6347	357	7	,	,	PUNCT
ejpam-6347	357	8	this	this	PRON
ejpam-6347	357	9	establishes	establish	VERB
ejpam-6347	357	10	existence	existence	NOUN
ejpam-6347	357	11	and	and	CCONJ
ejpam-6347	357	12	uniqueness	uniqueness	NOUN
ejpam-6347	357	13	of	of	ADP
ejpam-6347	357	14	solutions	solution	NOUN
ejpam-6347	357	15	in	in	ADP
ejpam-6347	357	16	x	x	PROPN
ejpam-6347	357	17	10	10	NUM
ejpam-6347	357	18	.	.	PUNCT
ejpam-6347	358	1	n.	n.	PROPN
ejpam-6347	358	2	abbas	abbas	PROPN
ejpam-6347	358	3	,	,	PUNCT
ejpam-6347	358	4	w.	w.	PROPN
ejpam-6347	358	5	shatanawi	shatanawi	PROPN
ejpam-6347	358	6	,	,	PUNCT
ejpam-6347	358	7	s.	s.	PROPN
ejpam-6347	358	8	a.	a.	NOUN
ejpam-6347	358	9	zanib	zanib	PROPN
ejpam-6347	358	10	/	/	SYM
ejpam-6347	358	11	eur	eur	PROPN
ejpam-6347	358	12	.	.	PUNCT
ejpam-6347	359	1	j.	j.	PROPN
ejpam-6347	359	2	pure	pure	PROPN
ejpam-6347	359	3	appl	appl	PROPN
ejpam-6347	359	4	.	.	PROPN
ejpam-6347	359	5	math	math	PROPN
ejpam-6347	359	6	,	,	PUNCT
ejpam-6347	359	7	18	18	NUM
ejpam-6347	359	8	(	(	PUNCT
ejpam-6347	359	9	3	3	NUM
ejpam-6347	359	10	)	)	PUNCT
ejpam-6347	359	11	(	(	PUNCT
ejpam-6347	359	12	2025	2025	NUM
ejpam-6347	359	13	)	)	PUNCT
ejpam-6347	359	14	,	,	PUNCT
ejpam-6347	359	15	6347	6347	NUM
ejpam-6347	359	16	20	20	NUM
ejpam-6347	359	17	of	of	ADP
ejpam-6347	359	18	34	34	NUM
ejpam-6347	359	19	theorem	theorem	NOUN
ejpam-6347	359	20	7	7	NUM
ejpam-6347	359	21	.	.	PUNCT
ejpam-6347	359	22	(	(	PUNCT
ejpam-6347	359	23	uniqueness	uniqueness	NOUN
ejpam-6347	359	24	of	of	ADP
ejpam-6347	359	25	solutions	solution	NOUN
ejpam-6347	359	26	for	for	ADP
ejpam-6347	359	27	fractional	fractional	ADJ
ejpam-6347	359	28	covcom10	covcom10	NOUN
ejpam-6347	359	29	model	model	NOUN
ejpam-6347	359	30	)	)	PUNCT
ejpam-6347	359	31	let	let	VERB
ejpam-6347	359	32	ζ	ζ	NOUN
ejpam-6347	359	33	∈	∈	NOUN
ejpam-6347	359	34	(	(	PUNCT
ejpam-6347	359	35	0	0	NUM
ejpam-6347	359	36	,	,	PUNCT
ejpam-6347	359	37	1	1	NUM
ejpam-6347	359	38	]	]	PUNCT
ejpam-6347	359	39	be	be	AUX
ejpam-6347	359	40	the	the	DET
ejpam-6347	359	41	fractional	fractional	ADJ
ejpam-6347	359	42	order	order	NOUN
ejpam-6347	359	43	and	and	CCONJ
ejpam-6347	359	44	t	t	NOUN
ejpam-6347	359	45	∈	∈	PROPN
ejpam-6347	360	1	[	[	X
ejpam-6347	360	2	0	0	NUM
ejpam-6347	360	3	,	,	PUNCT
ejpam-6347	360	4	t	t	X
ejpam-6347	360	5	]	]	PUNCT
ejpam-6347	360	6	with	with	ADP
ejpam-6347	360	7	t	t	PROPN
ejpam-6347	360	8	<	<	X
ejpam-6347	360	9	min{1	min{1	PROPN
ejpam-6347	360	10	/	/	SYM
ejpam-6347	360	11	s∗i	s∗i	PROPN
ejpam-6347	360	12	}	}	PUNCT
ejpam-6347	360	13	10i=1	10i=1	NUM
ejpam-6347	360	14	.	.	PUNCT
ejpam-6347	361	1	if	if	SCONJ
ejpam-6347	361	2	the	the	DET
ejpam-6347	361	3	kernels	kernel	NOUN
ejpam-6347	361	4	φi	φi	ADP
ejpam-6347	361	5	satisfy	satisfy	VERB
ejpam-6347	361	6	:	:	PUNCT
ejpam-6347	361	7	•	•	ADP
ejpam-6347	361	8	lipschitz	lipschitz	NOUN
ejpam-6347	361	9	continuity	continuity	NOUN
ejpam-6347	361	10	:	:	PUNCT
ejpam-6347	361	11	∃s∗i	∃s∗i	NOUN
ejpam-6347	361	12	>	>	X
ejpam-6347	361	13	0	0	NUM
ejpam-6347	362	1	such	such	ADJ
ejpam-6347	362	2	that	that	SCONJ
ejpam-6347	362	3	∥	∥	NOUN
ejpam-6347	362	4	φi(t	φi(t	NOUN
ejpam-6347	362	5	,	,	PUNCT
ejpam-6347	362	6	x)−	x)−	PROPN
ejpam-6347	362	7	φi(t	φi(t	PROPN
ejpam-6347	362	8	,	,	PUNCT
ejpam-6347	362	9	y	y	NOUN
ejpam-6347	362	10	)	)	PUNCT
ejpam-6347	362	11	∥≤	∥≤	VERB
ejpam-6347	362	12	s∗i	s∗i	NUM
ejpam-6347	362	13	∥	∥	NUM
ejpam-6347	362	14	x−	x−	NOUN
ejpam-6347	362	15	y	y	PROPN
ejpam-6347	362	16	∥	∥	PROPN
ejpam-6347	362	17	.	.	PUNCT
ejpam-6347	363	1	∀x	∀x	X
ejpam-6347	363	2	,	,	PUNCT
ejpam-6347	363	3	y	y	PROPN
ejpam-6347	363	4	∈	∈	PROPN
ejpam-6347	363	5	l1([0	l1([0	PROPN
ejpam-6347	363	6	,	,	PUNCT
ejpam-6347	363	7	t	t	X
ejpam-6347	363	8	]	]	PUNCT
ejpam-6347	363	9	)	)	PUNCT
ejpam-6347	363	10	•	•	PRON
ejpam-6347	363	11	time	time	NOUN
ejpam-6347	363	12	-	-	PUNCT
ejpam-6347	363	13	domain	domain	NOUN
ejpam-6347	363	14	constraint	constraint	NOUN
ejpam-6347	363	15	:	:	PUNCT
ejpam-6347	363	16	1−	1−	NUM
ejpam-6347	363	17	s∗i	s∗i	NUM
ejpam-6347	363	18	t	t	NOUN
ejpam-6347	363	19	ζ	ζ	NOUN
ejpam-6347	363	20	≥	≥	NUM
ejpam-6347	363	21	0	0	NUM
ejpam-6347	363	22	.	.	PUNCT
ejpam-6347	364	1	∀i	∀i	X
ejpam-6347	364	2	∈	∈	NOUN
ejpam-6347	364	3	{	{	PUNCT
ejpam-6347	364	4	1	1	NUM
ejpam-6347	364	5	,	,	PUNCT
ejpam-6347	364	6	.	.	PUNCT
ejpam-6347	364	7	.	.	PUNCT
ejpam-6347	364	8	.	.	PUNCT
ejpam-6347	365	1	,	,	PUNCT
ejpam-6347	365	2	10	10	NUM
ejpam-6347	365	3	}	}	PUNCT
ejpam-6347	365	4	,	,	PUNCT
ejpam-6347	365	5	t	t	PROPN
ejpam-6347	365	6	∈	∈	PROPN
ejpam-6347	366	1	[	[	X
ejpam-6347	366	2	0	0	NUM
ejpam-6347	366	3	,	,	PUNCT
ejpam-6347	366	4	t	t	NOUN
ejpam-6347	366	5	]	]	PUNCT
ejpam-6347	366	6	then	then	ADV
ejpam-6347	366	7	the	the	DET
ejpam-6347	366	8	fractional	fractional	ADJ
ejpam-6347	366	9	covcom10	covcom10	NOUN
ejpam-6347	366	10	system	system	NOUN
ejpam-6347	366	11	admits	admit	VERB
ejpam-6347	366	12	a	a	DET
ejpam-6347	366	13	unique	unique	ADJ
ejpam-6347	366	14	solution	solution	NOUN
ejpam-6347	366	15	(	(	PUNCT
ejpam-6347	366	16	s	s	X
ejpam-6347	366	17	,	,	PUNCT
ejpam-6347	366	18	e	e	NOUN
ejpam-6347	366	19	,	,	PUNCT
ejpam-6347	366	20	u	u	NOUN
ejpam-6347	366	21	,	,	PUNCT
ejpam-6347	366	22	q	q	INTJ
ejpam-6347	366	23	,	,	PUNCT
ejpam-6347	366	24	p	p	X
ejpam-6347	366	25	,	,	PUNCT
ejpam-6347	366	26	h	h	NOUN
ejpam-6347	366	27	,	,	PUNCT
ejpam-6347	366	28	c	c	X
ejpam-6347	366	29	,	,	PUNCT
ejpam-6347	366	30	f	f	PROPN
ejpam-6347	366	31	,	,	PUNCT
ejpam-6347	366	32	v	v	NOUN
ejpam-6347	366	33	,	,	PUNCT
ejpam-6347	366	34	r	r	NOUN
ejpam-6347	366	35	)	)	PUNCT
ejpam-6347	366	36	∈	∈	PROPN
ejpam-6347	366	37	(	(	PUNCT
ejpam-6347	366	38	c[0	c[0	PROPN
ejpam-6347	366	39	,	,	PUNCT
ejpam-6347	366	40	t	t	NOUN
ejpam-6347	366	41	]	]	PUNCT
ejpam-6347	366	42	)	)	PUNCT
ejpam-6347	366	43	10	10	NUM
ejpam-6347	366	44	.	.	PUNCT
ejpam-6347	367	1	proof	proof	NOUN
ejpam-6347	367	2	.	.	PUNCT
ejpam-6347	368	1	assume	assume	VERB
ejpam-6347	368	2	two	two	NUM
ejpam-6347	368	3	distinct	distinct	ADJ
ejpam-6347	368	4	solutions	solution	NOUN
ejpam-6347	368	5	x	x	PUNCT
ejpam-6347	368	6	=	=	SYM
ejpam-6347	368	7	(	(	PUNCT
ejpam-6347	368	8	s	s	X
ejpam-6347	368	9	,	,	PUNCT
ejpam-6347	368	10	.	.	PUNCT
ejpam-6347	368	11	.	.	PUNCT
ejpam-6347	369	1	.	.	PUNCT
ejpam-6347	370	1	,	,	PUNCT
ejpam-6347	370	2	r	r	X
ejpam-6347	370	3	)	)	PUNCT
ejpam-6347	370	4	and	and	CCONJ
ejpam-6347	370	5	x∗	x∗	PROPN
ejpam-6347	371	1	=	=	SYM
ejpam-6347	371	2	(	(	PUNCT
ejpam-6347	371	3	s∗	s∗	PROPN
ejpam-6347	371	4	,	,	PUNCT
ejpam-6347	371	5	.	.	PUNCT
ejpam-6347	371	6	.	.	PUNCT
ejpam-6347	372	1	.	.	PUNCT
ejpam-6347	373	1	,	,	PUNCT
ejpam-6347	373	2	r∗	r∗	PROPN
ejpam-6347	373	3	)	)	PUNCT
ejpam-6347	373	4	exist	exist	VERB
ejpam-6347	373	5	.	.	PUNCT
ejpam-6347	374	1	for	for	ADP
ejpam-6347	374	2	the	the	DET
ejpam-6347	374	3	s	s	NOUN
ejpam-6347	374	4	-	-	NOUN
ejpam-6347	374	5	compartment	compartment	NOUN
ejpam-6347	374	6	:	:	PUNCT
ejpam-6347	374	7	∥	∥	PROPN
ejpam-6347	374	8	s(t)−	s(t)−	PROPN
ejpam-6347	374	9	s∗(t	s∗(t	NOUN
ejpam-6347	374	10	)	)	PUNCT
ejpam-6347	374	11	∥	∥	PUNCT
ejpam-6347	374	12	≤	≤	NUM
ejpam-6347	374	13	∫	∫	PROPN
ejpam-6347	374	14	t	t	NOUN
ejpam-6347	374	15	0	0	NUM
ejpam-6347	374	16	ρζ−1	ρζ−1	PROPN
ejpam-6347	374	17	∥	∥	PUNCT
ejpam-6347	374	18	φ1(ρ	φ1(ρ	PROPN
ejpam-6347	374	19	,	,	PUNCT
ejpam-6347	374	20	s)−	s)−	PROPN
ejpam-6347	374	21	φ1(ρ	φ1(ρ	PROPN
ejpam-6347	374	22	,	,	PUNCT
ejpam-6347	374	23	s	s	NOUN
ejpam-6347	374	24	∗	∗	NOUN
ejpam-6347	374	25	)	)	PUNCT
ejpam-6347	374	26	∥	∥	NUM
ejpam-6347	374	27	dρ	dρ	NOUN
ejpam-6347	374	28	,	,	PUNCT
ejpam-6347	374	29	≤	≤	X
ejpam-6347	375	1	s∗1	s∗1	ADJ
ejpam-6347	375	2	∫	∫	PROPN
ejpam-6347	375	3	t	t	NOUN
ejpam-6347	375	4	0	0	NUM
ejpam-6347	376	1	ρζ−1	ρζ−1	PROPN
ejpam-6347	376	2	∥	∥	PUNCT
ejpam-6347	376	3	s(ρ)−	s(ρ)−	PROPN
ejpam-6347	376	4	s∗(ρ	s∗(ρ	NOUN
ejpam-6347	376	5	)	)	PUNCT
ejpam-6347	376	6	∥	∥	PUNCT
ejpam-6347	376	7	dρ	dρ	NOUN
ejpam-6347	376	8	.	.	PUNCT
ejpam-6347	377	1	(	(	PUNCT
ejpam-6347	377	2	by	by	ADP
ejpam-6347	377	3	lipschitz	lipschitz	VERB
ejpam-6347	377	4	condition	condition	NOUN
ejpam-6347	377	5	)	)	PUNCT
ejpam-6347	377	6	(	(	PUNCT
ejpam-6347	377	7	3.49	3.49	NUM
ejpam-6347	377	8	)	)	PUNCT
ejpam-6347	377	9	applying	apply	VERB
ejpam-6347	377	10	the	the	DET
ejpam-6347	377	11	generalized	generalized	ADJ
ejpam-6347	377	12	gronwall	gronwall	ADJ
ejpam-6347	377	13	inequality	inequality	NOUN
ejpam-6347	377	14	for	for	ADP
ejpam-6347	377	15	fractional	fractional	ADJ
ejpam-6347	377	16	integrals	integral	NOUN
ejpam-6347	377	17	:	:	PUNCT
ejpam-6347	377	18	∥	∥	PROPN
ejpam-6347	377	19	s(t)−	s(t)−	PROPN
ejpam-6347	377	20	s∗(t	s∗(t	NOUN
ejpam-6347	377	21	)	)	PUNCT
ejpam-6347	377	22	∥≤∥	∥≤∥	PROPN
ejpam-6347	377	23	s0	s0	PROPN
ejpam-6347	377	24	−	−	PROPN
ejpam-6347	377	25	s∗	s∗	PROPN
ejpam-6347	377	26	0	0	NUM
ejpam-6347	377	27	∥	∥	X
ejpam-6347	377	28	eζ(s	eζ(s	X
ejpam-6347	377	29	∗	∗	NOUN
ejpam-6347	377	30	1γ(ζ)t	1γ(ζ)t	NUM
ejpam-6347	377	31	ζ	ζ	NOUN
ejpam-6347	377	32	)	)	PUNCT
ejpam-6347	377	33	,	,	PUNCT
ejpam-6347	377	34	where	where	SCONJ
ejpam-6347	377	35	eζ	eζ	PROPN
ejpam-6347	377	36	is	be	AUX
ejpam-6347	377	37	the	the	DET
ejpam-6347	377	38	mittag	mittag	ADJ
ejpam-6347	377	39	-	-	PUNCT
ejpam-6347	377	40	leffler	leffler	NOUN
ejpam-6347	377	41	function	function	NOUN
ejpam-6347	377	42	.	.	PUNCT
ejpam-6347	378	1	given	give	VERB
ejpam-6347	378	2	identical	identical	ADJ
ejpam-6347	378	3	initial	initial	ADJ
ejpam-6347	378	4	conditions	condition	NOUN
ejpam-6347	378	5	s0	s0	NOUN
ejpam-6347	378	6	=	=	PUNCT
ejpam-6347	378	7	s∗	s∗	PROPN
ejpam-6347	378	8	0	0	PUNCT
ejpam-6347	379	1	and	and	CCONJ
ejpam-6347	379	2	t	t	X
ejpam-6347	379	3	<	<	X
ejpam-6347	379	4	(	(	PUNCT
ejpam-6347	379	5	s∗1	s∗1	NOUN
ejpam-6347	379	6	)	)	PUNCT
ejpam-6347	379	7	−1	−1	NOUN
ejpam-6347	379	8	/	/	SYM
ejpam-6347	379	9	ζ	ζ	NOUN
ejpam-6347	379	10	,	,	PUNCT
ejpam-6347	379	11	the	the	DET
ejpam-6347	379	12	growth	growth	NOUN
ejpam-6347	379	13	estimate	estimate	NOUN
ejpam-6347	379	14	implies	imply	VERB
ejpam-6347	379	15	:	:	PUNCT
ejpam-6347	379	16	∥	∥	PROPN
ejpam-6347	379	17	s(t)−	s(t)−	PROPN
ejpam-6347	379	18	s∗(t	s∗(t	NOUN
ejpam-6347	379	19	)	)	PUNCT
ejpam-6347	379	20	∥≤	∥≤	PROPN
ejpam-6347	379	21	0	0	PUNCT
ejpam-6347	379	22	·	·	PUNCT
ejpam-6347	380	1	eζ	eζ	PROPN
ejpam-6347	380	2	(	(	PUNCT
ejpam-6347	380	3	·	·	PUNCT
ejpam-6347	380	4	·	·	PUNCT
ejpam-6347	380	5	·	·	PUNCT
ejpam-6347	380	6	)	)	PUNCT
ejpam-6347	381	1	=	=	PUNCT
ejpam-6347	381	2	0	0	X
ejpam-6347	381	3	.	.	PUNCT
ejpam-6347	382	1	∀t	∀t	PROPN
ejpam-6347	382	2	∈	∈	PROPN
ejpam-6347	383	1	[	[	X
ejpam-6347	383	2	0	0	NUM
ejpam-6347	383	3	,	,	PUNCT
ejpam-6347	383	4	t	t	X
ejpam-6347	383	5	]	]	PUNCT
ejpam-6347	383	6	thus	thus	ADV
ejpam-6347	383	7	s(t	s(t	PROPN
ejpam-6347	383	8	)	)	PUNCT
ejpam-6347	383	9	≡	≡	PROPN
ejpam-6347	383	10	s∗(t	s∗(t	NOUN
ejpam-6347	383	11	)	)	PUNCT
ejpam-6347	383	12	.	.	PUNCT
ejpam-6347	384	1	repeating	repeat	VERB
ejpam-6347	384	2	this	this	DET
ejpam-6347	384	3	steps	step	NOUN
ejpam-6347	384	4	for	for	ADP
ejpam-6347	384	5	e(t	e(t	NOUN
ejpam-6347	384	6	)	)	PUNCT
ejpam-6347	384	7	,	,	PUNCT
ejpam-6347	384	8	.	.	PUNCT
ejpam-6347	384	9	.	.	PUNCT
ejpam-6347	385	1	.	.	PUNCT
ejpam-6347	386	1	,	,	PUNCT
ejpam-6347	386	2	r(t	r(t	NOUN
ejpam-6347	386	3	)	)	PUNCT
ejpam-6347	386	4	using	use	VERB
ejpam-6347	386	5	their	their	PRON
ejpam-6347	386	6	respective	respective	ADJ
ejpam-6347	386	7	lipschitz	lipschitz	NOUN
ejpam-6347	386	8	constants	constant	NOUN
ejpam-6347	386	9	s∗2	s∗2	PROPN
ejpam-6347	386	10	,	,	PUNCT
ejpam-6347	386	11	.	.	PUNCT
ejpam-6347	386	12	.	.	PUNCT
ejpam-6347	387	1	.	.	PUNCT
ejpam-6347	388	1	,	,	PUNCT
ejpam-6347	388	2	s	s	NOUN
ejpam-6347	388	3	∗	∗	NOUN
ejpam-6347	388	4	10	10	NUM
ejpam-6347	388	5	completes	complete	VERB
ejpam-6347	388	6	the	the	DET
ejpam-6347	388	7	proof	proof	NOUN
ejpam-6347	388	8	.	.	PUNCT
ejpam-6347	389	1	3.4	3.4	NUM
ejpam-6347	389	2	.	.	PUNCT
ejpam-6347	389	3	optimal	optimal	ADJ
ejpam-6347	389	4	control	control	NOUN
ejpam-6347	389	5	to	to	PART
ejpam-6347	389	6	stop	stop	VERB
ejpam-6347	389	7	covid-19	covid-19	PROPN
ejpam-6347	389	8	from	from	ADP
ejpam-6347	389	9	spreading	spread	VERB
ejpam-6347	389	10	,	,	PUNCT
ejpam-6347	389	11	the	the	DET
ejpam-6347	389	12	effects	effect	NOUN
ejpam-6347	389	13	will	will	AUX
ejpam-6347	389	14	be	be	AUX
ejpam-6347	389	15	examined	examine	VERB
ejpam-6347	389	16	by	by	ADP
ejpam-6347	389	17	using	use	VERB
ejpam-6347	389	18	medicinal	medicinal	ADJ
ejpam-6347	389	19	treatments	treatment	NOUN
ejpam-6347	389	20	.	.	PUNCT
ejpam-6347	390	1	to	to	PART
ejpam-6347	390	2	do	do	VERB
ejpam-6347	390	3	this	this	PRON
ejpam-6347	390	4	,	,	PUNCT
ejpam-6347	390	5	a	a	DET
ejpam-6347	390	6	set	set	NOUN
ejpam-6347	390	7	of	of	ADP
ejpam-6347	390	8	time	time	NOUN
ejpam-6347	390	9	-	-	PUNCT
ejpam-6347	390	10	dependent	dependent	ADJ
ejpam-6347	390	11	control	control	NOUN
ejpam-6347	390	12	variables	variable	NOUN
ejpam-6347	390	13	,	,	PUNCT
ejpam-6347	390	14	a1	a1	NOUN
ejpam-6347	390	15	,	,	PUNCT
ejpam-6347	390	16	a2	a2	PROPN
ejpam-6347	390	17	,	,	PUNCT
ejpam-6347	390	18	and	and	CCONJ
ejpam-6347	390	19	a3	a3	NOUN
ejpam-6347	390	20	have	have	AUX
ejpam-6347	390	21	been	be	AUX
ejpam-6347	390	22	introduced	introduce	VERB
ejpam-6347	390	23	,	,	PUNCT
ejpam-6347	390	24	•	•	SCONJ
ejpam-6347	390	25	the	the	DET
ejpam-6347	390	26	implementation	implementation	NOUN
ejpam-6347	390	27	of	of	ADP
ejpam-6347	390	28	continuous	continuous	ADJ
ejpam-6347	390	29	vaccination	vaccination	NOUN
ejpam-6347	390	30	is	be	AUX
ejpam-6347	390	31	represented	represent	VERB
ejpam-6347	390	32	by	by	ADP
ejpam-6347	390	33	a1	a1	NOUN
ejpam-6347	390	34	,	,	PUNCT
ejpam-6347	390	35	•	•	CCONJ
ejpam-6347	390	36	the	the	DET
ejpam-6347	390	37	social	social	ADJ
ejpam-6347	390	38	distancing	distancing	NOUN
ejpam-6347	390	39	and	and	CCONJ
ejpam-6347	390	40	lockdown	lockdown	NOUN
ejpam-6347	390	41	measures	measure	NOUN
ejpam-6347	390	42	is	be	AUX
ejpam-6347	390	43	represented	represent	VERB
ejpam-6347	390	44	by	by	ADP
ejpam-6347	390	45	a2	a2	PROPN
ejpam-6347	390	46	,	,	PUNCT
ejpam-6347	390	47	•	•	NUM
ejpam-6347	390	48	testing	testing	NOUN
ejpam-6347	390	49	and	and	CCONJ
ejpam-6347	390	50	quarantine	quarantine	NOUN
ejpam-6347	390	51	strategy	strategy	NOUN
ejpam-6347	390	52	is	be	AUX
ejpam-6347	390	53	represented	represent	VERB
ejpam-6347	390	54	by	by	ADP
ejpam-6347	390	55	a3	a3	NOUN
ejpam-6347	390	56	.	.	PUNCT
ejpam-6347	391	1	n.	n.	PROPN
ejpam-6347	391	2	abbas	abbas	PROPN
ejpam-6347	391	3	,	,	PUNCT
ejpam-6347	391	4	w.	w.	PROPN
ejpam-6347	391	5	shatanawi	shatanawi	PROPN
ejpam-6347	391	6	,	,	PUNCT
ejpam-6347	391	7	s.	s.	PROPN
ejpam-6347	391	8	a.	a.	NOUN
ejpam-6347	391	9	zanib	zanib	PROPN
ejpam-6347	391	10	/	/	SYM
ejpam-6347	391	11	eur	eur	PROPN
ejpam-6347	391	12	.	.	PUNCT
ejpam-6347	392	1	j.	j.	PROPN
ejpam-6347	392	2	pure	pure	PROPN
ejpam-6347	392	3	appl	appl	PROPN
ejpam-6347	392	4	.	.	PROPN
ejpam-6347	392	5	math	math	PROPN
ejpam-6347	392	6	,	,	PUNCT
ejpam-6347	392	7	18	18	NUM
ejpam-6347	392	8	(	(	PUNCT
ejpam-6347	392	9	3	3	NUM
ejpam-6347	392	10	)	)	PUNCT
ejpam-6347	392	11	(	(	PUNCT
ejpam-6347	392	12	2025	2025	NUM
ejpam-6347	392	13	)	)	PUNCT
ejpam-6347	392	14	,	,	PUNCT
ejpam-6347	392	15	6347	6347	NUM
ejpam-6347	392	16	21	21	NUM
ejpam-6347	392	17	of	of	ADP
ejpam-6347	392	18	34	34	NUM
ejpam-6347	392	19	the	the	DET
ejpam-6347	392	20	covid-19	covid-19	PROPN
ejpam-6347	392	21	model	model	NOUN
ejpam-6347	392	22	with	with	ADP
ejpam-6347	392	23	proposed	propose	VERB
ejpam-6347	392	24	optimal	optimal	ADJ
ejpam-6347	392	25	control	control	NOUN
ejpam-6347	392	26	a1	a1	PROPN
ejpam-6347	392	27	,	,	PUNCT
ejpam-6347	392	28	a2	a2	PROPN
ejpam-6347	392	29	,	,	PUNCT
ejpam-6347	392	30	and	and	CCONJ
ejpam-6347	392	31	a3	a3	NOUN
ejpam-6347	392	32	are	be	AUX
ejpam-6347	392	33	part	part	NOUN
ejpam-6347	392	34	of	of	ADP
ejpam-6347	392	35	the	the	DET
ejpam-6347	392	36	following	follow	VERB
ejpam-6347	392	37	nonautonomous	nonautonomous	ADJ
ejpam-6347	392	38	system	system	NOUN
ejpam-6347	392	39	of	of	ADP
ejpam-6347	392	40	nonlinear	nonlinear	ADJ
ejpam-6347	392	41	ordinary	ordinary	ADJ
ejpam-6347	392	42	differential	differential	ADJ
ejpam-6347	392	43	equations	equation	NOUN
ejpam-6347	392	44	.	.	PUNCT
ejpam-6347	393	1	s′	s′	VERB
ejpam-6347	393	2	=	=	PUNCT
ejpam-6347	393	3	λ+	λ+	PUNCT
ejpam-6347	393	4	τr+	τr+	ADJ
ejpam-6347	393	5	b2q−	b2q−	PROPN
ejpam-6347	393	6	(	(	PUNCT
ejpam-6347	393	7	ϕe	ϕe	X
ejpam-6347	393	8	+	+	CCONJ
ejpam-6347	393	9	a1	a1	NOUN
ejpam-6347	393	10	+	+	CCONJ
ejpam-6347	393	11	µ)s	µ)s	NOUN
ejpam-6347	393	12	,	,	PUNCT
ejpam-6347	393	13	(	(	PUNCT
ejpam-6347	393	14	3.50	3.50	NUM
ejpam-6347	393	15	)	)	PUNCT
ejpam-6347	393	16	e′	e′	X
ejpam-6347	394	1	=	=	SYM
ejpam-6347	394	2	ϕes	ϕes	PROPN
ejpam-6347	394	3	+	+	CCONJ
ejpam-6347	394	4	γ	γ	X
ejpam-6347	394	5	v	v	X
ejpam-6347	394	6	e	e	X
ejpam-6347	394	7	−	−	PROPN
ejpam-6347	394	8	(	(	PUNCT
ejpam-6347	394	9	λ1u	λ1u	PROPN
ejpam-6347	394	10	+	+	NUM
ejpam-6347	394	11	λ2q+	λ2q+	PROPN
ejpam-6347	394	12	µ+	µ+	X
ejpam-6347	394	13	d1)e	d1)e	NOUN
ejpam-6347	394	14	,	,	PUNCT
ejpam-6347	394	15	(	(	PUNCT
ejpam-6347	394	16	3.51	3.51	NUM
ejpam-6347	394	17	)	)	PUNCT
ejpam-6347	394	18	u	u	NOUN
ejpam-6347	394	19	′	′	NOUN
ejpam-6347	394	20	=	=	SYM
ejpam-6347	394	21	λ1eu	λ1eu	PUNCT
ejpam-6347	394	22	−	−	PROPN
ejpam-6347	394	23	(	(	PUNCT
ejpam-6347	394	24	α1	α1	PROPN
ejpam-6347	394	25	+	+	CCONJ
ejpam-6347	394	26	α2	α2	ADJ
ejpam-6347	394	27	+	+	CCONJ
ejpam-6347	394	28	µ+	µ+	PUNCT
ejpam-6347	394	29	d2)u	d2)u	NOUN
ejpam-6347	394	30	,	,	PUNCT
ejpam-6347	394	31	(	(	PUNCT
ejpam-6347	394	32	3.52	3.52	NUM
ejpam-6347	394	33	)	)	PUNCT
ejpam-6347	394	34	q′	q′	NOUN
ejpam-6347	395	1	=	=	SYM
ejpam-6347	395	2	λ2eq−	λ2eq−	PROPN
ejpam-6347	395	3	(	(	PUNCT
ejpam-6347	395	4	b1	b1	NOUN
ejpam-6347	395	5	+	+	CCONJ
ejpam-6347	395	6	b2	b2	NOUN
ejpam-6347	395	7	+	+	CCONJ
ejpam-6347	395	8	b3	b3	PROPN
ejpam-6347	395	9	+	+	CCONJ
ejpam-6347	395	10	µ+	µ+	X
ejpam-6347	395	11	d3)q	d3)q	NOUN
ejpam-6347	395	12	,	,	PUNCT
ejpam-6347	395	13	(	(	PUNCT
ejpam-6347	395	14	3.53	3.53	NUM
ejpam-6347	395	15	)	)	PUNCT
ejpam-6347	395	16	p	p	NOUN
ejpam-6347	395	17	′	′	NOUN
ejpam-6347	395	18	=	=	PUNCT
ejpam-6347	395	19	α2u	α2u	PROPN
ejpam-6347	395	20	+	+	CCONJ
ejpam-6347	395	21	b1q−	b1q−	X
ejpam-6347	395	22	(	(	PUNCT
ejpam-6347	395	23	φ1	φ1	NOUN
ejpam-6347	395	24	+	+	CCONJ
ejpam-6347	395	25	φ2	φ2	NOUN
ejpam-6347	395	26	+	+	NUM
ejpam-6347	395	27	φ3	φ3	NOUN
ejpam-6347	395	28	+	+	CCONJ
ejpam-6347	395	29	µ+	µ+	PUNCT
ejpam-6347	395	30	d4)p	d4)p	VERB
ejpam-6347	395	31	,	,	PUNCT
ejpam-6347	395	32	(	(	PUNCT
ejpam-6347	395	33	3.54	3.54	NUM
ejpam-6347	395	34	)	)	PUNCT
ejpam-6347	395	35	h	h	NOUN
ejpam-6347	395	36	′	′	NOUN
ejpam-6347	396	1	=	=	PUNCT
ejpam-6347	397	1	φ1p	φ1p	VERB
ejpam-6347	397	2	+	+	NUM
ejpam-6347	397	3	η	η	PROPN
ejpam-6347	397	4	c	c	PROPN
ejpam-6347	397	5	+	+	PROPN
ejpam-6347	397	6	σ2f	σ2f	PROPN
ejpam-6347	397	7	−	−	PROPN
ejpam-6347	397	8	(	(	PUNCT
ejpam-6347	397	9	a2	a2	PROPN
ejpam-6347	397	10	+	+	PROPN
ejpam-6347	397	11	m2	m2	PROPN
ejpam-6347	397	12	+	+	PROPN
ejpam-6347	397	13	m3	m3	PROPN
ejpam-6347	397	14	+	+	CCONJ
ejpam-6347	397	15	µ+	µ+	PUNCT
ejpam-6347	397	16	d5)h	d5)h	ADJ
ejpam-6347	397	17	,	,	PUNCT
ejpam-6347	397	18	(	(	PUNCT
ejpam-6347	397	19	3.55	3.55	NUM
ejpam-6347	397	20	)	)	PUNCT
ejpam-6347	397	21	c	c	NOUN
ejpam-6347	397	22	′	′	NOUN
ejpam-6347	397	23	=	=	PUNCT
ejpam-6347	397	24	φ2p	φ2p	VERB
ejpam-6347	397	25	+	+	PROPN
ejpam-6347	397	26	m2h	m2h	ADJ
ejpam-6347	397	27	−	−	PROPN
ejpam-6347	397	28	(	(	PUNCT
ejpam-6347	397	29	η	η	PROPN
ejpam-6347	397	30	+	+	PROPN
ejpam-6347	397	31	µ+	µ+	PROPN
ejpam-6347	397	32	d6)c	d6)c	NOUN
ejpam-6347	397	33	,	,	PUNCT
ejpam-6347	397	34	(	(	PUNCT
ejpam-6347	397	35	3.56	3.56	NUM
ejpam-6347	397	36	)	)	PUNCT
ejpam-6347	397	37	f	f	NOUN
ejpam-6347	397	38	′	′	NUM
ejpam-6347	398	1	=	=	PUNCT
ejpam-6347	398	2	φ3p	φ3p	NUM
ejpam-6347	398	3	+	+	NOUN
ejpam-6347	398	4	m3h	m3h	NOUN
ejpam-6347	398	5	−	−	PROPN
ejpam-6347	398	6	(	(	PUNCT
ejpam-6347	398	7	a3	a3	NOUN
ejpam-6347	398	8	+	+	CCONJ
ejpam-6347	398	9	σ2	σ2	PROPN
ejpam-6347	398	10	+	+	CCONJ
ejpam-6347	398	11	µ+	µ+	PROPN
ejpam-6347	398	12	d7)f	d7)f	PROPN
ejpam-6347	398	13	,	,	PUNCT
ejpam-6347	398	14	(	(	PUNCT
ejpam-6347	398	15	3.57	3.57	NUM
ejpam-6347	398	16	)	)	PUNCT
ejpam-6347	398	17	v	v	NOUN
ejpam-6347	398	18	′	′	NOUN
ejpam-6347	398	19	=	=	PUNCT
ejpam-6347	398	20	a1	a1	PROPN
ejpam-6347	398	21	s	s	PART
ejpam-6347	398	22	+	+	NUM
ejpam-6347	398	23	b3q−	b3q−	PROPN
ejpam-6347	398	24	(	(	PUNCT
ejpam-6347	398	25	γ	γ	X
ejpam-6347	398	26	e	e	PROPN
ejpam-6347	398	27	+	+	PROPN
ejpam-6347	398	28	µ+	µ+	X
ejpam-6347	398	29	a)v	a)v	X
ejpam-6347	398	30	,	,	PUNCT
ejpam-6347	398	31	(	(	PUNCT
ejpam-6347	398	32	3.58	3.58	NUM
ejpam-6347	398	33	)	)	PUNCT
ejpam-6347	398	34	r′	r′	PROPN
ejpam-6347	398	35	=	=	SYM
ejpam-6347	398	36	a3f	a3f	PROPN
ejpam-6347	398	37	+	+	CCONJ
ejpam-6347	398	38	α1u	α1u	PROPN
ejpam-6347	399	1	+	+	CCONJ
ejpam-6347	399	2	a2h	a2h	ADV
ejpam-6347	399	3	−	−	PROPN
ejpam-6347	399	4	(	(	PUNCT
ejpam-6347	399	5	τ	τ	X
ejpam-6347	399	6	+	+	NOUN
ejpam-6347	399	7	µ)r	µ)r	NOUN
ejpam-6347	399	8	.	.	PUNCT
ejpam-6347	400	1	(	(	PUNCT
ejpam-6347	400	2	3.59	3.59	NUM
ejpam-6347	400	3	)	)	PUNCT
ejpam-6347	400	4	the	the	DET
ejpam-6347	400	5	discussion	discussion	NOUN
ejpam-6347	400	6	of	of	ADP
ejpam-6347	400	7	optimal	optimal	ADJ
ejpam-6347	400	8	control	control	NOUN
ejpam-6347	400	9	in	in	ADP
ejpam-6347	400	10	the	the	DET
ejpam-6347	400	11	model	model	NOUN
ejpam-6347	400	12	is	be	AUX
ejpam-6347	400	13	done	do	VERB
ejpam-6347	400	14	to	to	PART
ejpam-6347	400	15	order	order	VERB
ejpam-6347	400	16	to	to	PART
ejpam-6347	400	17	determine	determine	VERB
ejpam-6347	400	18	the	the	DET
ejpam-6347	400	19	optimum	optimum	ADJ
ejpam-6347	400	20	values	value	NOUN
ejpam-6347	400	21	of	of	ADP
ejpam-6347	400	22	a1,a2	a1,a2	PROPN
ejpam-6347	400	23	,	,	PUNCT
ejpam-6347	400	24	and	and	CCONJ
ejpam-6347	400	25	a3	a3	VERB
ejpam-6347	400	26	that	that	PRON
ejpam-6347	400	27	minimise	minimise	VERB
ejpam-6347	400	28	the	the	DET
ejpam-6347	400	29	objective	objective	ADJ
ejpam-6347	400	30	function	function	NOUN
ejpam-6347	400	31	j(a1(t	j(a1(t	PROPN
ejpam-6347	400	32	)	)	PUNCT
ejpam-6347	400	33	,	,	PUNCT
ejpam-6347	400	34	a2(t	a2(t	PROPN
ejpam-6347	400	35	)	)	PUNCT
ejpam-6347	400	36	,	,	PUNCT
ejpam-6347	400	37	a3(t	a3(t	PROPN
ejpam-6347	400	38	)	)	PUNCT
ejpam-6347	400	39	)	)	PUNCT
ejpam-6347	400	40	affected	affect	VERB
ejpam-6347	400	41	by	by	ADP
ejpam-6347	400	42	the	the	DET
ejpam-6347	400	43	differential	differential	ADJ
ejpam-6347	400	44	equations	equation	NOUN
ejpam-6347	400	45	(	(	PUNCT
ejpam-6347	400	46	3.50	3.50	NUM
ejpam-6347	400	47	-	-	SYM
ejpam-6347	400	48	3.59	3.59	NUM
ejpam-6347	400	49	)	)	PUNCT
ejpam-6347	400	50	.	.	PUNCT
ejpam-6347	401	1	the	the	DET
ejpam-6347	401	2	provided	provide	VERB
ejpam-6347	401	3	objective	objective	ADJ
ejpam-6347	401	4	function	function	NOUN
ejpam-6347	401	5	is	be	AUX
ejpam-6347	401	6	,	,	PUNCT
ejpam-6347	401	7	j(a1	j(a1	NOUN
ejpam-6347	401	8	,	,	PUNCT
ejpam-6347	401	9	a2	a2	PROPN
ejpam-6347	401	10	,	,	PUNCT
ejpam-6347	401	11	a3	a3	NOUN
ejpam-6347	401	12	)	)	PUNCT
ejpam-6347	402	1	=	=	SYM
ejpam-6347	402	2	min	min	NOUN
ejpam-6347	402	3	a1,a2,a3	a1,a2,a3	ADP
ejpam-6347	402	4	∫	∫	PROPN
ejpam-6347	403	1	t	t	PROPN
ejpam-6347	403	2	0	0	NUM
ejpam-6347	404	1	[	[	X
ejpam-6347	404	2	x1e	x1e	PROPN
ejpam-6347	405	1	+	+	PROPN
ejpam-6347	405	2	x2u	x2u	PROPN
ejpam-6347	406	1	+	+	PROPN
ejpam-6347	406	2	x3q+x4p	x3q+x4p	PROPN
ejpam-6347	406	3	+	+	PROPN
ejpam-6347	406	4	x5f	x5f	PROPN
ejpam-6347	406	5	+	+	ADJ
ejpam-6347	406	6	x6c	x6c	PROPN
ejpam-6347	406	7	+	+	PROPN
ejpam-6347	406	8	x7h	x7h	PROPN
ejpam-6347	406	9	+	+	NOUN
ejpam-6347	406	10	y1	y1	PROPN
ejpam-6347	406	11	(	(	PUNCT
ejpam-6347	406	12	a1	a1	NOUN
ejpam-6347	406	13	(	(	PUNCT
ejpam-6347	406	14	t	t	NOUN
ejpam-6347	406	15	)	)	PUNCT
ejpam-6347	406	16	)	)	PUNCT
ejpam-6347	406	17	2	2	NUM
ejpam-6347	406	18	+	+	CCONJ
ejpam-6347	406	19	y2	y2	PROPN
ejpam-6347	406	20	(	(	PUNCT
ejpam-6347	406	21	a2	a2	PROPN
ejpam-6347	406	22	(	(	PUNCT
ejpam-6347	406	23	t	t	PROPN
ejpam-6347	406	24	)	)	PUNCT
ejpam-6347	406	25	)	)	PUNCT
ejpam-6347	406	26	2	2	NUM
ejpam-6347	407	1	+	+	X
ejpam-6347	407	2	y3	y3	NOUN
ejpam-6347	407	3	(	(	PUNCT
ejpam-6347	407	4	a3	a3	PROPN
ejpam-6347	407	5	(	(	PUNCT
ejpam-6347	407	6	t	t	NOUN
ejpam-6347	407	7	)	)	PUNCT
ejpam-6347	407	8	)	)	PUNCT
ejpam-6347	407	9	2]dt	2]dt	NUM
ejpam-6347	407	10	.	.	PUNCT
ejpam-6347	408	1	(	(	PUNCT
ejpam-6347	408	2	3.60	3.60	NUM
ejpam-6347	408	3	)	)	PUNCT
ejpam-6347	408	4	where	where	SCONJ
ejpam-6347	408	5	t	t	PROPN
ejpam-6347	408	6	is	be	AUX
ejpam-6347	408	7	final	final	ADJ
ejpam-6347	408	8	time	time	NOUN
ejpam-6347	408	9	,	,	PUNCT
ejpam-6347	408	10	x1	x1	PROPN
ejpam-6347	408	11	,	,	PUNCT
ejpam-6347	408	12	x2	x2	PROPN
ejpam-6347	408	13	,	,	PUNCT
ejpam-6347	408	14	x3	x3	PROPN
ejpam-6347	408	15	,	,	PUNCT
ejpam-6347	408	16	x4	x4	PROPN
ejpam-6347	408	17	,	,	PUNCT
ejpam-6347	408	18	x5	x5	PROPN
ejpam-6347	408	19	,	,	PUNCT
ejpam-6347	408	20	x6	x6	PROPN
ejpam-6347	408	21	,	,	PUNCT
ejpam-6347	408	22	andx7	andx7	NOUN
ejpam-6347	408	23	are	be	AUX
ejpam-6347	408	24	the	the	DET
ejpam-6347	408	25	weight	weight	NOUN
ejpam-6347	408	26	cost	cost	NOUN
ejpam-6347	408	27	of	of	ADP
ejpam-6347	408	28	pre	pre	ADJ
ejpam-6347	408	29	-	-	ADJ
ejpam-6347	408	30	symptomatic	symptomatic	ADJ
ejpam-6347	408	31	,	,	PUNCT
ejpam-6347	408	32	infected	infect	VERB
ejpam-6347	408	33	,	,	PUNCT
ejpam-6347	408	34	quarantine	quarantine	NOUN
ejpam-6347	408	35	,	,	PUNCT
ejpam-6347	408	36	confirm	confirm	VERB
ejpam-6347	408	37	-	-	PUNCT
ejpam-6347	408	38	positive	positive	ADJ
ejpam-6347	408	39	,	,	PUNCT
ejpam-6347	408	40	asymptomatic	asymptomatic	ADJ
ejpam-6347	408	41	,	,	PUNCT
ejpam-6347	408	42	hospitalized	hospitalize	VERB
ejpam-6347	408	43	at	at	ADP
ejpam-6347	408	44	intensive	intensive	ADJ
ejpam-6347	408	45	care	care	NOUN
ejpam-6347	408	46	unit	unit	NOUN
ejpam-6347	408	47	and	and	CCONJ
ejpam-6347	408	48	hospitalized	hospitalize	VERB
ejpam-6347	408	49	at	at	ADP
ejpam-6347	408	50	ordinary	ordinary	ADJ
ejpam-6347	408	51	ward	ward	NOUN
ejpam-6347	408	52	individuals	individual	NOUN
ejpam-6347	408	53	respectively	respectively	ADV
ejpam-6347	408	54	.	.	PUNCT
ejpam-6347	409	1	where	where	SCONJ
ejpam-6347	409	2	y1	y1	NOUN
ejpam-6347	409	3	,	,	PUNCT
ejpam-6347	409	4	y2	y2	PROPN
ejpam-6347	409	5	and	and	CCONJ
ejpam-6347	409	6	y3	y3	NOUN
ejpam-6347	409	7	are	be	AUX
ejpam-6347	409	8	weight	weight	NOUN
ejpam-6347	409	9	costs	cost	NOUN
ejpam-6347	409	10	for	for	ADP
ejpam-6347	409	11	each	each	DET
ejpam-6347	409	12	control	control	NOUN
ejpam-6347	409	13	measurable	measurable	ADJ
ejpam-6347	409	14	individuals	individual	NOUN
ejpam-6347	409	15	.	.	PUNCT
ejpam-6347	410	1	in	in	ADP
ejpam-6347	410	2	this	this	DET
ejpam-6347	410	3	paper	paper	NOUN
ejpam-6347	410	4	,	,	PUNCT
ejpam-6347	410	5	the	the	DET
ejpam-6347	410	6	weight	weight	NOUN
ejpam-6347	410	7	cost	cost	NOUN
ejpam-6347	410	8	of	of	ADP
ejpam-6347	410	9	the	the	DET
ejpam-6347	410	10	optimal	optimal	ADJ
ejpam-6347	410	11	control	control	NOUN
ejpam-6347	410	12	as	as	SCONJ
ejpam-6347	410	13	applied	apply	VERB
ejpam-6347	410	14	by	by	ADP
ejpam-6347	410	15	[	[	X
ejpam-6347	410	16	25	25	NUM
ejpam-6347	410	17	,	,	PUNCT
ejpam-6347	410	18	26	26	NUM
ejpam-6347	410	19	]	]	PUNCT
ejpam-6347	410	20	is	be	AUX
ejpam-6347	410	21	measured	measure	VERB
ejpam-6347	410	22	using	use	VERB
ejpam-6347	410	23	a	a	DET
ejpam-6347	410	24	quadratic	quadratic	ADJ
ejpam-6347	410	25	function	function	NOUN
ejpam-6347	410	26	that	that	PRON
ejpam-6347	410	27	fulfills	fulfill	VERB
ejpam-6347	410	28	the	the	DET
ejpam-6347	410	29	optimality	optimality	NOUN
ejpam-6347	410	30	criteria	criterion	NOUN
ejpam-6347	410	31	.	.	PUNCT
ejpam-6347	411	1	the	the	DET
ejpam-6347	411	2	objective	objective	NOUN
ejpam-6347	411	3	is	be	AUX
ejpam-6347	411	4	to	to	PART
ejpam-6347	411	5	identify	identify	VERB
ejpam-6347	411	6	the	the	DET
ejpam-6347	411	7	optimal	optimal	ADJ
ejpam-6347	411	8	control	control	NOUN
ejpam-6347	411	9	(	(	PUNCT
ejpam-6347	411	10	a∗1	a∗1	PROPN
ejpam-6347	411	11	,	,	PUNCT
ejpam-6347	411	12	a	a	DET
ejpam-6347	411	13	∗	∗	NOUN
ejpam-6347	411	14	2	2	NUM
ejpam-6347	411	15	,	,	PUNCT
ejpam-6347	411	16	a	a	DET
ejpam-6347	411	17	∗	∗	NOUN
ejpam-6347	411	18	3	3	NUM
ejpam-6347	411	19	)	)	PUNCT
ejpam-6347	411	20	.	.	PUNCT
ejpam-6347	412	1	j(a∗1	j(a∗1	PROPN
ejpam-6347	412	2	,	,	PUNCT
ejpam-6347	412	3	a	a	DET
ejpam-6347	412	4	∗	∗	NOUN
ejpam-6347	412	5	2	2	NUM
ejpam-6347	412	6	,	,	PUNCT
ejpam-6347	412	7	a	a	DET
ejpam-6347	412	8	∗	∗	NOUN
ejpam-6347	412	9	3	3	NUM
ejpam-6347	412	10	)	)	PUNCT
ejpam-6347	412	11	=	=	PUNCT
ejpam-6347	412	12	min(a1	min(a1	PROPN
ejpam-6347	412	13	,	,	PUNCT
ejpam-6347	412	14	a2	a2	PROPN
ejpam-6347	412	15	,	,	PUNCT
ejpam-6347	412	16	a3	a3	NOUN
ejpam-6347	412	17	)	)	PUNCT
ejpam-6347	412	18	.	.	PUNCT
ejpam-6347	413	1	where	where	SCONJ
ejpam-6347	413	2	,	,	PUNCT
ejpam-6347	413	3	(	(	PUNCT
ejpam-6347	413	4	a1	a1	PROPN
ejpam-6347	413	5	,	,	PUNCT
ejpam-6347	413	6	a2	a2	PROPN
ejpam-6347	413	7	,	,	PUNCT
ejpam-6347	413	8	a3	a3	NOUN
ejpam-6347	413	9	)	)	PUNCT
ejpam-6347	413	10	∈	∈	PROPN
ejpam-6347	413	11	u	u	NOUN
ejpam-6347	413	12	,	,	PUNCT
ejpam-6347	413	13	ai(t	ai(t	NOUN
ejpam-6347	413	14	)	)	PUNCT
ejpam-6347	413	15	is	be	AUX
ejpam-6347	413	16	measurable	measurable	ADJ
ejpam-6347	413	17	lebesgue	lebesgue	NOUN
ejpam-6347	413	18	on	on	ADP
ejpam-6347	413	19	[	[	X
ejpam-6347	413	20	0	0	NUM
ejpam-6347	413	21	,	,	PUNCT
ejpam-6347	413	22	t	t	X
ejpam-6347	413	23	]	]	PUNCT
ejpam-6347	413	24	,	,	PUNCT
ejpam-6347	413	25	0	0	NUM
ejpam-6347	413	26	≤	≤	NUM
ejpam-6347	413	27	ai(t	ai(t	NOUN
ejpam-6347	413	28	)	)	PUNCT
ejpam-6347	413	29	≤	≤	NUM
ejpam-6347	414	1	1	1	NUM
ejpam-6347	414	2	,	,	PUNCT
ejpam-6347	414	3	i	i	PRON
ejpam-6347	414	4	=	=	NOUN
ejpam-6347	414	5	1	1	NUM
ejpam-6347	414	6	,	,	PUNCT
ejpam-6347	414	7	2	2	NUM
ejpam-6347	414	8	,	,	PUNCT
ejpam-6347	414	9	3	3	NUM
ejpam-6347	414	10	.	.	NOUN
ejpam-6347	414	11	hamiltonian	hamiltonian	ADJ
ejpam-6347	414	12	and	and	CCONJ
ejpam-6347	414	13	optimality	optimality	NOUN
ejpam-6347	414	14	equation	equation	NOUN
ejpam-6347	414	15	pontryangin	pontryangin	NOUN
ejpam-6347	414	16	’s	’s	PART
ejpam-6347	414	17	maximum	maximum	ADJ
ejpam-6347	414	18	principle	principle	NOUN
ejpam-6347	414	19	[	[	X
ejpam-6347	414	20	27	27	NUM
ejpam-6347	414	21	]	]	PUNCT
ejpam-6347	414	22	is	be	AUX
ejpam-6347	414	23	used	use	VERB
ejpam-6347	414	24	to	to	PART
ejpam-6347	414	25	determine	determine	VERB
ejpam-6347	414	26	the	the	DET
ejpam-6347	414	27	requirements	requirement	NOUN
ejpam-6347	414	28	that	that	SCONJ
ejpam-6347	414	29	an	an	DET
ejpam-6347	414	30	optimal	optimal	ADJ
ejpam-6347	414	31	control	control	NOUN
ejpam-6347	414	32	must	must	AUX
ejpam-6347	414	33	satisfy	satisfy	VERB
ejpam-6347	414	34	.	.	PUNCT
ejpam-6347	415	1	equations	equation	NOUN
ejpam-6347	415	2	(	(	PUNCT
ejpam-6347	415	3	3.50	3.50	NUM
ejpam-6347	415	4	)	)	PUNCT
ejpam-6347	415	5	and	and	CCONJ
ejpam-6347	415	6	(	(	PUNCT
ejpam-6347	415	7	3.60	3.60	NUM
ejpam-6347	415	8	)	)	PUNCT
ejpam-6347	415	9	are	be	AUX
ejpam-6347	415	10	transformed	transform	VERB
ejpam-6347	415	11	into	into	ADP
ejpam-6347	415	12	a	a	DET
ejpam-6347	415	13	problem	problem	NOUN
ejpam-6347	415	14	n.	n.	PROPN
ejpam-6347	415	15	abbas	abbas	PROPN
ejpam-6347	415	16	,	,	PUNCT
ejpam-6347	415	17	w.	w.	PROPN
ejpam-6347	415	18	shatanawi	shatanawi	PROPN
ejpam-6347	415	19	,	,	PUNCT
ejpam-6347	415	20	s.	s.	PROPN
ejpam-6347	415	21	a.	a.	NOUN
ejpam-6347	415	22	zanib	zanib	PROPN
ejpam-6347	415	23	/	/	SYM
ejpam-6347	415	24	eur	eur	PROPN
ejpam-6347	415	25	.	.	PUNCT
ejpam-6347	416	1	j.	j.	PROPN
ejpam-6347	416	2	pure	pure	PROPN
ejpam-6347	416	3	appl	appl	PROPN
ejpam-6347	416	4	.	.	PROPN
ejpam-6347	416	5	math	math	PROPN
ejpam-6347	416	6	,	,	PUNCT
ejpam-6347	416	7	18	18	NUM
ejpam-6347	416	8	(	(	PUNCT
ejpam-6347	416	9	3	3	NUM
ejpam-6347	416	10	)	)	PUNCT
ejpam-6347	416	11	(	(	PUNCT
ejpam-6347	416	12	2025	2025	NUM
ejpam-6347	416	13	)	)	PUNCT
ejpam-6347	416	14	,	,	PUNCT
ejpam-6347	416	15	6347	6347	NUM
ejpam-6347	416	16	22	22	NUM
ejpam-6347	416	17	of	of	ADP
ejpam-6347	416	18	34	34	NUM
ejpam-6347	416	19	of	of	ADP
ejpam-6347	416	20	minimising	minimise	VERB
ejpam-6347	416	21	the	the	DET
ejpam-6347	416	22	point	point	NOUN
ejpam-6347	416	23	-	-	PUNCT
ejpam-6347	416	24	wise	wise	ADJ
ejpam-6347	416	25	hamiltonian	hamiltonian	NOUN
ejpam-6347	416	26	(	(	PUNCT
ejpam-6347	416	27	h	h	NOUN
ejpam-6347	416	28	)	)	PUNCT
ejpam-6347	416	29	with	with	ADP
ejpam-6347	416	30	respect	respect	NOUN
ejpam-6347	416	31	to	to	ADP
ejpam-6347	416	32	a1(t	a1(t	PROPN
ejpam-6347	416	33	)	)	PUNCT
ejpam-6347	416	34	,	,	PUNCT
ejpam-6347	416	35	a2(t	a2(t	NOUN
ejpam-6347	416	36	)	)	PUNCT
ejpam-6347	416	37	,	,	PUNCT
ejpam-6347	416	38	and	and	CCONJ
ejpam-6347	416	39	a3(t	a3(t	NOUN
ejpam-6347	416	40	)	)	PUNCT
ejpam-6347	416	41	as	as	ADP
ejpam-6347	416	42	a	a	DET
ejpam-6347	416	43	result	result	NOUN
ejpam-6347	416	44	of	of	ADP
ejpam-6347	416	45	his	his	PRON
ejpam-6347	416	46	principle	principle	NOUN
ejpam-6347	416	47	.	.	PUNCT
ejpam-6347	417	1	h	h	NOUN
ejpam-6347	418	1	=	=	PUNCT
ejpam-6347	418	2	x1e	x1e	PROPN
ejpam-6347	419	1	+	+	PROPN
ejpam-6347	419	2	x2u	x2u	PROPN
ejpam-6347	420	1	+	+	PROPN
ejpam-6347	420	2	x3q+x4p	x3q+x4p	PROPN
ejpam-6347	420	3	+	+	SYM
ejpam-6347	420	4	x5h	x5h	PROPN
ejpam-6347	420	5	+	+	ADJ
ejpam-6347	420	6	x6c	x6c	PROPN
ejpam-6347	420	7	+	+	ADJ
ejpam-6347	420	8	x7f	x7f	PROPN
ejpam-6347	420	9	+	+	CCONJ
ejpam-6347	420	10	y1	y1	INTJ
ejpam-6347	420	11	(	(	PUNCT
ejpam-6347	420	12	a1	a1	NOUN
ejpam-6347	420	13	(	(	PUNCT
ejpam-6347	420	14	t	t	NOUN
ejpam-6347	420	15	)	)	PUNCT
ejpam-6347	420	16	)	)	PUNCT
ejpam-6347	420	17	2	2	NUM
ejpam-6347	420	18	+	+	CCONJ
ejpam-6347	420	19	y2	y2	PROPN
ejpam-6347	420	20	(	(	PUNCT
ejpam-6347	420	21	a2	a2	PROPN
ejpam-6347	420	22	(	(	PUNCT
ejpam-6347	420	23	t	t	PROPN
ejpam-6347	420	24	)	)	PUNCT
ejpam-6347	420	25	)	)	PUNCT
ejpam-6347	420	26	2	2	NUM
ejpam-6347	421	1	+	+	X
ejpam-6347	421	2	y3	y3	NOUN
ejpam-6347	421	3	(	(	PUNCT
ejpam-6347	421	4	a3	a3	PROPN
ejpam-6347	421	5	(	(	PUNCT
ejpam-6347	421	6	t	t	NOUN
ejpam-6347	421	7	)	)	PUNCT
ejpam-6347	421	8	)	)	PUNCT
ejpam-6347	421	9	2	2	NUM
ejpam-6347	422	1	+	+	CCONJ
ejpam-6347	422	2	ξ1[λ	ξ1[λ	ADJ
ejpam-6347	422	3	+	+	CCONJ
ejpam-6347	422	4	τr+	τr+	ADJ
ejpam-6347	422	5	b2q−	b2q−	PROPN
ejpam-6347	422	6	(	(	PUNCT
ejpam-6347	422	7	ϕe	ϕe	X
ejpam-6347	422	8	+	+	CCONJ
ejpam-6347	422	9	a1	a1	NOUN
ejpam-6347	422	10	+	+	CCONJ
ejpam-6347	422	11	µ)s	µ)s	NOUN
ejpam-6347	422	12	]	]	X
ejpam-6347	422	13	+	+	CCONJ
ejpam-6347	422	14	ξ2[ϕes	ξ2[ϕes	PROPN
ejpam-6347	422	15	+	+	CCONJ
ejpam-6347	422	16	γ	γ	X
ejpam-6347	422	17	v	v	ADP
ejpam-6347	422	18	e	e	X
ejpam-6347	422	19	−	−	PROPN
ejpam-6347	422	20	(	(	PUNCT
ejpam-6347	422	21	λ1u	λ1u	PROPN
ejpam-6347	422	22	+	+	NUM
ejpam-6347	422	23	λ2q+	λ2q+	PROPN
ejpam-6347	422	24	µ+	µ+	X
ejpam-6347	422	25	d1)e	d1)e	NOUN
ejpam-6347	422	26	]	]	X
ejpam-6347	423	1	+	+	NUM
ejpam-6347	423	2	ξ3[λ1eu	ξ3[λ1eu	NOUN
ejpam-6347	423	3	−	−	PROPN
ejpam-6347	423	4	(	(	PUNCT
ejpam-6347	423	5	α1	α1	PROPN
ejpam-6347	423	6	+	+	CCONJ
ejpam-6347	423	7	α2	α2	ADJ
ejpam-6347	423	8	+	+	CCONJ
ejpam-6347	423	9	µ+	µ+	X
ejpam-6347	423	10	d2)u	d2)u	NOUN
ejpam-6347	423	11	]	]	PUNCT
ejpam-6347	424	1	+	+	PUNCT
ejpam-6347	424	2	ξ4[λ2eq−	ξ4[λ2eq−	NUM
ejpam-6347	424	3	(	(	PUNCT
ejpam-6347	424	4	b1	b1	NOUN
ejpam-6347	424	5	+	+	CCONJ
ejpam-6347	424	6	b2	b2	NOUN
ejpam-6347	424	7	+	+	CCONJ
ejpam-6347	424	8	b3	b3	PROPN
ejpam-6347	424	9	+	+	CCONJ
ejpam-6347	424	10	µ+	µ+	X
ejpam-6347	424	11	d3)q	d3)q	NOUN
ejpam-6347	424	12	]	]	X
ejpam-6347	424	13	+	+	CCONJ
ejpam-6347	424	14	ξ5[α2u	ξ5[α2u	NOUN
ejpam-6347	424	15	+	+	CCONJ
ejpam-6347	424	16	b1q−	b1q−	X
ejpam-6347	424	17	(	(	PUNCT
ejpam-6347	424	18	φ1	φ1	NOUN
ejpam-6347	424	19	+	+	CCONJ
ejpam-6347	424	20	φ2	φ2	NOUN
ejpam-6347	424	21	+	+	NUM
ejpam-6347	424	22	φ3	φ3	NOUN
ejpam-6347	424	23	+	+	CCONJ
ejpam-6347	424	24	µ+	µ+	PUNCT
ejpam-6347	424	25	d4)p	d4)p	NOUN
ejpam-6347	424	26	]	]	PUNCT
ejpam-6347	425	1	+	+	CCONJ
ejpam-6347	425	2	ξ6[φ1p	ξ6[φ1p	ADJ
ejpam-6347	425	3	+	+	CCONJ
ejpam-6347	425	4	η	η	PROPN
ejpam-6347	425	5	c	c	PROPN
ejpam-6347	425	6	+	+	PROPN
ejpam-6347	425	7	σ2f	σ2f	PROPN
ejpam-6347	425	8	−	−	PROPN
ejpam-6347	425	9	(	(	PUNCT
ejpam-6347	425	10	a2	a2	PROPN
ejpam-6347	425	11	+	+	PROPN
ejpam-6347	425	12	m2	m2	PROPN
ejpam-6347	425	13	+	+	PROPN
ejpam-6347	425	14	m3	m3	PROPN
ejpam-6347	425	15	+	+	CCONJ
ejpam-6347	425	16	µ+	µ+	X
ejpam-6347	425	17	d5)h	d5)h	NOUN
ejpam-6347	425	18	]	]	X
ejpam-6347	425	19	+	+	CCONJ
ejpam-6347	425	20	ξ7[φ2p	ξ7[φ2p	PROPN
ejpam-6347	425	21	+	+	ADJ
ejpam-6347	425	22	m2h	m2h	ADJ
ejpam-6347	425	23	−	−	PROPN
ejpam-6347	425	24	(	(	PUNCT
ejpam-6347	425	25	η	η	PROPN
ejpam-6347	425	26	+	+	PROPN
ejpam-6347	425	27	µ+	µ+	X
ejpam-6347	425	28	d6)c	d6)c	NOUN
ejpam-6347	425	29	]	]	X
ejpam-6347	425	30	+	+	CCONJ
ejpam-6347	425	31	ξ8[φ3p	ξ8[φ3p	NOUN
ejpam-6347	425	32	+	+	NOUN
ejpam-6347	425	33	m3h	m3h	NOUN
ejpam-6347	425	34	−	−	PROPN
ejpam-6347	425	35	(	(	PUNCT
ejpam-6347	425	36	a3	a3	NOUN
ejpam-6347	425	37	+	+	CCONJ
ejpam-6347	425	38	σ2	σ2	PROPN
ejpam-6347	425	39	+	+	CCONJ
ejpam-6347	425	40	µ+	µ+	PROPN
ejpam-6347	425	41	d7)f	d7)f	PROPN
ejpam-6347	425	42	]	]	PUNCT
ejpam-6347	425	43	+	+	CCONJ
ejpam-6347	425	44	ξ9[a1	ξ9[a1	PROPN
ejpam-6347	425	45	s	s	PART
ejpam-6347	425	46	+	+	CCONJ
ejpam-6347	425	47	b3q−	b3q−	PROPN
ejpam-6347	425	48	(	(	PUNCT
ejpam-6347	425	49	γ	γ	X
ejpam-6347	425	50	e	e	PROPN
ejpam-6347	425	51	+	+	PROPN
ejpam-6347	425	52	µ+	µ+	X
ejpam-6347	425	53	a)v	a)v	X
ejpam-6347	425	54	]	]	X
ejpam-6347	426	1	+	+	CCONJ
ejpam-6347	426	2	ξ10[a3f	ξ10[a3f	PROPN
ejpam-6347	426	3	+	+	CCONJ
ejpam-6347	426	4	α1u	α1u	NOUN
ejpam-6347	427	1	+	+	CCONJ
ejpam-6347	427	2	a2h	a2h	ADV
ejpam-6347	427	3	−	−	PROPN
ejpam-6347	427	4	(	(	PUNCT
ejpam-6347	427	5	τ	τ	X
ejpam-6347	427	6	+	+	SYM
ejpam-6347	427	7	µ)r	µ)r	NOUN
ejpam-6347	427	8	]	]	X
ejpam-6347	427	9	,	,	PUNCT
ejpam-6347	427	10	(	(	PUNCT
ejpam-6347	427	11	3.61	3.61	NUM
ejpam-6347	427	12	)	)	PUNCT
ejpam-6347	428	1	where	where	SCONJ
ejpam-6347	428	2	(	(	PUNCT
ejpam-6347	428	3	ξi	ξi	NOUN
ejpam-6347	428	4	)	)	PUNCT
ejpam-6347	428	5	,	,	PUNCT
ejpam-6347	429	1	i	i	PRON
ejpam-6347	429	2	=	=	NOUN
ejpam-6347	429	3	1	1	NUM
ejpam-6347	429	4	,	,	PUNCT
ejpam-6347	429	5	2	2	NUM
ejpam-6347	429	6	,	,	PUNCT
ejpam-6347	429	7	....	....	PUNCT
ejpam-6347	429	8	,	,	PUNCT
ejpam-6347	429	9	10	10	NUM
ejpam-6347	429	10	are	be	AUX
ejpam-6347	429	11	adjoint	adjoint	NOUN
ejpam-6347	429	12	variables	variable	NOUN
ejpam-6347	429	13	associate	associate	VERB
ejpam-6347	429	14	with	with	ADP
ejpam-6347	429	15	s	s	PROPN
ejpam-6347	429	16	,	,	PUNCT
ejpam-6347	429	17	e	e	NOUN
ejpam-6347	429	18	,	,	PUNCT
ejpam-6347	429	19	u	u	NOUN
ejpam-6347	429	20	,	,	PUNCT
ejpam-6347	429	21	q	q	INTJ
ejpam-6347	429	22	,	,	PUNCT
ejpam-6347	429	23	p	p	X
ejpam-6347	429	24	,	,	PUNCT
ejpam-6347	429	25	h	h	NOUN
ejpam-6347	429	26	,	,	PUNCT
ejpam-6347	429	27	c	c	X
ejpam-6347	429	28	,	,	PUNCT
ejpam-6347	429	29	f	f	PROPN
ejpam-6347	429	30	,	,	PUNCT
ejpam-6347	429	31	v	v	NOUN
ejpam-6347	429	32	and	and	CCONJ
ejpam-6347	429	33	,	,	PUNCT
ejpam-6347	429	34	r.	r.	PROPN
ejpam-6347	429	35	theorem	theorem	VERB
ejpam-6347	429	36	8	8	NUM
ejpam-6347	429	37	.	.	PUNCT
ejpam-6347	430	1	for	for	ADP
ejpam-6347	430	2	the	the	DET
ejpam-6347	430	3	optimal	optimal	ADJ
ejpam-6347	430	4	control	control	NOUN
ejpam-6347	430	5	(	(	PUNCT
ejpam-6347	430	6	a∗2	a∗2	PROPN
ejpam-6347	430	7	,	,	PUNCT
ejpam-6347	430	8	a	a	DET
ejpam-6347	430	9	∗	∗	NOUN
ejpam-6347	430	10	2	2	NUM
ejpam-6347	430	11	,	,	PUNCT
ejpam-6347	430	12	a	a	DET
ejpam-6347	430	13	∗	∗	NOUN
ejpam-6347	430	14	3	3	NUM
ejpam-6347	430	15	)	)	PUNCT
ejpam-6347	430	16	and	and	CCONJ
ejpam-6347	430	17	corresponding	correspond	VERB
ejpam-6347	430	18	state	state	NOUN
ejpam-6347	430	19	solution	solution	NOUN
ejpam-6347	430	20	(	(	PUNCT
ejpam-6347	430	21	s	s	X
ejpam-6347	430	22	,	,	PUNCT
ejpam-6347	430	23	e	e	NOUN
ejpam-6347	430	24	,	,	PUNCT
ejpam-6347	430	25	u	u	NOUN
ejpam-6347	430	26	,	,	PUNCT
ejpam-6347	430	27	q	q	INTJ
ejpam-6347	430	28	,	,	PUNCT
ejpam-6347	430	29	p	p	X
ejpam-6347	430	30	,	,	PUNCT
ejpam-6347	430	31	h	h	NOUN
ejpam-6347	430	32	,	,	PUNCT
ejpam-6347	430	33	c	c	X
ejpam-6347	430	34	,	,	PUNCT
ejpam-6347	430	35	f	f	PROPN
ejpam-6347	430	36	,	,	PUNCT
ejpam-6347	430	37	v	v	NOUN
ejpam-6347	430	38	,	,	PUNCT
ejpam-6347	430	39	r	r	NOUN
ejpam-6347	430	40	)	)	PUNCT
ejpam-6347	430	41	that	that	PRON
ejpam-6347	430	42	minimize	minimize	VERB
ejpam-6347	430	43	j	j	PROPN
ejpam-6347	430	44	over	over	ADP
ejpam-6347	430	45	u	u	NOUN
ejpam-6347	430	46	of	of	ADP
ejpam-6347	430	47	the	the	DET
ejpam-6347	430	48	corresponding	corresponding	ADJ
ejpam-6347	430	49	system	system	NOUN
ejpam-6347	430	50	of	of	ADP
ejpam-6347	430	51	equation	equation	NOUN
ejpam-6347	430	52	(	(	PUNCT
ejpam-6347	430	53	2.4	2.4	NUM
ejpam-6347	430	54	)	)	PUNCT
ejpam-6347	430	55	having	have	VERB
ejpam-6347	430	56	the	the	DET
ejpam-6347	430	57	adjoint	adjoint	PROPN
ejpam-6347	430	58	variable	variable	ADJ
ejpam-6347	430	59	ξ1	ξ1	PROPN
ejpam-6347	430	60	,	,	PUNCT
ejpam-6347	430	61	....	....	PUNCT
ejpam-6347	430	62	,	,	PUNCT
ejpam-6347	430	63	ξ10	ξ10	ADJ
ejpam-6347	430	64	such	such	ADJ
ejpam-6347	430	65	that	that	PRON
ejpam-6347	430	66	,	,	PUNCT
ejpam-6347	430	67	dξ1	dξ1	NOUN
ejpam-6347	430	68	dt	dt	X
ejpam-6347	431	1	=	=	PUNCT
ejpam-6347	431	2	(	(	PUNCT
ejpam-6347	431	3	ξ1	ξ1	PROPN
ejpam-6347	431	4	−	−	PROPN
ejpam-6347	431	5	ξ2)ϕe	ξ2)ϕe	NOUN
ejpam-6347	431	6	+	+	CCONJ
ejpam-6347	431	7	(	(	PUNCT
ejpam-6347	431	8	ξ1	ξ1	PROPN
ejpam-6347	431	9	−	−	PROPN
ejpam-6347	431	10	ξ9)a1	ξ9)a1	PROPN
ejpam-6347	431	11	−	−	PROPN
ejpam-6347	431	12	aξ1	aξ1	PROPN
ejpam-6347	431	13	,	,	PUNCT
ejpam-6347	431	14	(	(	PUNCT
ejpam-6347	431	15	3.62	3.62	NUM
ejpam-6347	431	16	)	)	PUNCT
ejpam-6347	431	17	dξ2	dξ2	NOUN
ejpam-6347	431	18	dt	dt	NOUN
ejpam-6347	432	1	=	=	PUNCT
ejpam-6347	432	2	(	(	PUNCT
ejpam-6347	432	3	ξ1	ξ1	PROPN
ejpam-6347	432	4	−	−	PROPN
ejpam-6347	432	5	ξ2)ϕs	ξ2)ϕs	PROPN
ejpam-6347	432	6	+	+	CCONJ
ejpam-6347	432	7	(	(	PUNCT
ejpam-6347	432	8	ξ9	ξ9	NOUN
ejpam-6347	432	9	−	−	PROPN
ejpam-6347	432	10	ξ2)γv	ξ2)γv	VERB
ejpam-6347	432	11	+	+	CCONJ
ejpam-6347	432	12	(	(	PUNCT
ejpam-6347	432	13	ξ2	ξ2	NOUN
ejpam-6347	432	14	−	−	PROPN
ejpam-6347	432	15	ξ3)λ1u	ξ3)λ1u	NOUN
ejpam-6347	433	1	−	−	PROPN
ejpam-6347	434	1	(	(	PUNCT
ejpam-6347	434	2	ξ2	ξ2	NOUN
ejpam-6347	434	3	−	−	NOUN
ejpam-6347	434	4	ξ4)λ2q+	ξ4)λ2q+	NOUN
ejpam-6347	434	5	ξ2(µ+	ξ2(µ+	PROPN
ejpam-6347	434	6	d1)−x1	d1)−x1	PROPN
ejpam-6347	434	7	,	,	PUNCT
ejpam-6347	434	8	(	(	PUNCT
ejpam-6347	434	9	3.63	3.63	NUM
ejpam-6347	434	10	)	)	PUNCT
ejpam-6347	434	11	dξ3	dξ3	NOUN
ejpam-6347	434	12	dt	dt	NOUN
ejpam-6347	435	1	=	=	PUNCT
ejpam-6347	436	1	(	(	PUNCT
ejpam-6347	436	2	ξ2	ξ2	NOUN
ejpam-6347	436	3	−	−	NOUN
ejpam-6347	436	4	ξ3)λ1e	ξ3)λ1e	NOUN
ejpam-6347	437	1	+	+	CCONJ
ejpam-6347	437	2	(	(	PUNCT
ejpam-6347	437	3	ξ3	ξ3	NOUN
ejpam-6347	437	4	−	−	PROPN
ejpam-6347	437	5	ξ10)α1	ξ10)α1	PROPN
ejpam-6347	437	6	+	+	CCONJ
ejpam-6347	437	7	(	(	PUNCT
ejpam-6347	437	8	ξ3	ξ3	PROPN
ejpam-6347	437	9	−	−	PROPN
ejpam-6347	437	10	ξ5)α2	ξ5)α2	PROPN
ejpam-6347	437	11	+	+	PROPN
ejpam-6347	437	12	ξ3(µ+	ξ3(µ+	PROPN
ejpam-6347	437	13	d2)−x2	d2)−x2	PROPN
ejpam-6347	437	14	,	,	PUNCT
ejpam-6347	437	15	(	(	PUNCT
ejpam-6347	437	16	3.64	3.64	NUM
ejpam-6347	437	17	)	)	PUNCT
ejpam-6347	437	18	dξ4	dξ4	NOUN
ejpam-6347	437	19	dt	dt	NOUN
ejpam-6347	437	20	=	=	PUNCT
ejpam-6347	437	21	(	(	PUNCT
ejpam-6347	437	22	ξ2	ξ2	NOUN
ejpam-6347	437	23	−	−	PROPN
ejpam-6347	437	24	ξ4)λ2e	ξ4)λ2e	PROPN
ejpam-6347	438	1	+	+	CCONJ
ejpam-6347	438	2	(	(	PUNCT
ejpam-6347	438	3	ξ4	ξ4	NOUN
ejpam-6347	438	4	−	−	PROPN
ejpam-6347	438	5	ξ5)b1	ξ5)b1	NOUN
ejpam-6347	438	6	+	+	CCONJ
ejpam-6347	438	7	(	(	PUNCT
ejpam-6347	438	8	ξ4	ξ4	PROPN
ejpam-6347	438	9	−	−	PROPN
ejpam-6347	438	10	ξ1)b2	ξ1)b2	PROPN
ejpam-6347	438	11	+	+	CCONJ
ejpam-6347	438	12	(	(	PUNCT
ejpam-6347	438	13	ξ4	ξ4	PROPN
ejpam-6347	438	14	−	−	PROPN
ejpam-6347	438	15	ξ9)b3	ξ9)b3	PROPN
ejpam-6347	438	16	+	+	CCONJ
ejpam-6347	438	17	ξ4(µ+	ξ4(µ+	PROPN
ejpam-6347	438	18	d3)−x3	d3)−x3	PROPN
ejpam-6347	438	19	,	,	PUNCT
ejpam-6347	438	20	(	(	PUNCT
ejpam-6347	438	21	3.65	3.65	NUM
ejpam-6347	438	22	)	)	PUNCT
ejpam-6347	438	23	dξ5	dξ5	NOUN
ejpam-6347	438	24	dt	dt	NOUN
ejpam-6347	439	1	=	=	PUNCT
ejpam-6347	439	2	(	(	PUNCT
ejpam-6347	439	3	ξ5	ξ5	NOUN
ejpam-6347	439	4	−	−	NOUN
ejpam-6347	439	5	ξ6)φ1	ξ6)φ1	NOUN
ejpam-6347	439	6	+	+	CCONJ
ejpam-6347	439	7	(	(	PUNCT
ejpam-6347	439	8	ξ5	ξ5	NOUN
ejpam-6347	439	9	−	−	PROPN
ejpam-6347	439	10	ξ7)φ2	ξ7)φ2	NOUN
ejpam-6347	439	11	+	+	CCONJ
ejpam-6347	439	12	(	(	PUNCT
ejpam-6347	439	13	ξ5	ξ5	NOUN
ejpam-6347	439	14	−	−	NOUN
ejpam-6347	439	15	ξ8)φ3	ξ8)φ3	X
ejpam-6347	440	1	+	+	CCONJ
ejpam-6347	440	2	ξ5(µ+	ξ5(µ+	PROPN
ejpam-6347	440	3	d4)−x4	d4)−x4	NOUN
ejpam-6347	440	4	,	,	PUNCT
ejpam-6347	440	5	(	(	PUNCT
ejpam-6347	440	6	3.66	3.66	NUM
ejpam-6347	440	7	)	)	PUNCT
ejpam-6347	440	8	dξ6	dξ6	NOUN
ejpam-6347	440	9	dt	dt	NOUN
ejpam-6347	441	1	=	=	PUNCT
ejpam-6347	441	2	(	(	PUNCT
ejpam-6347	441	3	ξ6	ξ6	NOUN
ejpam-6347	441	4	−	−	NOUN
ejpam-6347	441	5	ξ10)a2	ξ10)a2	ADP
ejpam-6347	441	6	+	+	CCONJ
ejpam-6347	441	7	(	(	PUNCT
ejpam-6347	441	8	ξ6	ξ6	NOUN
ejpam-6347	441	9	−	−	NOUN
ejpam-6347	441	10	ξ7)m2	ξ7)m2	NOUN
ejpam-6347	441	11	+	+	CCONJ
ejpam-6347	441	12	(	(	PUNCT
ejpam-6347	441	13	ξ6	ξ6	NOUN
ejpam-6347	441	14	−	−	NOUN
ejpam-6347	441	15	ξ8)m3	ξ8)m3	PROPN
ejpam-6347	441	16	+	+	PROPN
ejpam-6347	441	17	ξ6(µ+	ξ6(µ+	PROPN
ejpam-6347	441	18	d5)−x5	d5)−x5	PROPN
ejpam-6347	441	19	,	,	PUNCT
ejpam-6347	441	20	(	(	PUNCT
ejpam-6347	441	21	3.67	3.67	NUM
ejpam-6347	441	22	)	)	PUNCT
ejpam-6347	441	23	dξ7	dξ7	NOUN
ejpam-6347	441	24	dt	dt	NOUN
ejpam-6347	442	1	=	=	PUNCT
ejpam-6347	442	2	(	(	PUNCT
ejpam-6347	442	3	ξ7	ξ7	PROPN
ejpam-6347	442	4	−	−	NOUN
ejpam-6347	442	5	ξ6)η	ξ6)η	NOUN
ejpam-6347	442	6	+	+	CCONJ
ejpam-6347	442	7	ξ7(µ+	ξ7(µ+	PROPN
ejpam-6347	442	8	d6)−x6	d6)−x6	PROPN
ejpam-6347	442	9	,	,	PUNCT
ejpam-6347	442	10	(	(	PUNCT
ejpam-6347	442	11	3.68	3.68	NUM
ejpam-6347	442	12	)	)	PUNCT
ejpam-6347	442	13	dξ8	dξ8	NOUN
ejpam-6347	442	14	dt	dt	NOUN
ejpam-6347	442	15	=	=	SYM
ejpam-6347	442	16	(	(	PUNCT
ejpam-6347	442	17	ξ8	ξ8	NOUN
ejpam-6347	442	18	−	−	PROPN
ejpam-6347	442	19	ξ10)a3	ξ10)a3	PROPN
ejpam-6347	442	20	+	+	CCONJ
ejpam-6347	442	21	(	(	PUNCT
ejpam-6347	442	22	ξ8	ξ8	NOUN
ejpam-6347	442	23	−	−	NOUN
ejpam-6347	442	24	ξ6)σ2	ξ6)σ2	ADP
ejpam-6347	442	25	+	+	CCONJ
ejpam-6347	442	26	ξ8(µ+	ξ8(µ+	PROPN
ejpam-6347	442	27	d7)−x7	d7)−x7	NOUN
ejpam-6347	442	28	,	,	PUNCT
ejpam-6347	442	29	(	(	PUNCT
ejpam-6347	442	30	3.69	3.69	NUM
ejpam-6347	442	31	)	)	PUNCT
ejpam-6347	442	32	dξ9	dξ9	NOUN
ejpam-6347	442	33	dt	dt	NOUN
ejpam-6347	442	34	=	=	SYM
ejpam-6347	442	35	(	(	PUNCT
ejpam-6347	442	36	ξ9	ξ9	NOUN
ejpam-6347	442	37	−	−	PROPN
ejpam-6347	442	38	ξ2)γe	ξ2)γe	VERB
ejpam-6347	442	39	+	+	CCONJ
ejpam-6347	442	40	ξ9(µ)−	ξ9(µ)−	NUM
ejpam-6347	442	41	ξ9a	ξ9a	ADJ
ejpam-6347	442	42	,	,	PUNCT
ejpam-6347	442	43	(	(	PUNCT
ejpam-6347	442	44	3.70	3.70	NUM
ejpam-6347	442	45	)	)	PUNCT
ejpam-6347	443	1	dξ10	dξ10	NOUN
ejpam-6347	443	2	dt	dt	PUNCT
ejpam-6347	443	3	=	=	PUNCT
ejpam-6347	443	4	ξ10	ξ10	ADJ
ejpam-6347	443	5	(	(	PUNCT
ejpam-6347	443	6	µ+	µ+	PROPN
ejpam-6347	443	7	τ)−	τ)−	PROPN
ejpam-6347	443	8	ξ1τ	ξ1τ	PROPN
ejpam-6347	443	9	.	.	PUNCT
ejpam-6347	443	10	(	(	PUNCT
ejpam-6347	443	11	3.71	3.71	NUM
ejpam-6347	443	12	)	)	PUNCT
ejpam-6347	443	13	ξi(t	ξi(t	NUM
ejpam-6347	443	14	)	)	PUNCT
ejpam-6347	444	1	=	=	SYM
ejpam-6347	444	2	0	0	NUM
ejpam-6347	444	3	,	,	PUNCT
ejpam-6347	444	4	for	for	ADP
ejpam-6347	444	5	i	i	PROPN
ejpam-6347	444	6	=	=	SYM
ejpam-6347	444	7	1	1	NUM
ejpam-6347	444	8	,	,	PUNCT
ejpam-6347	444	9	2	2	NUM
ejpam-6347	444	10	,	,	PUNCT
ejpam-6347	444	11	3	3	NUM
ejpam-6347	444	12	....	....	SYM
ejpam-6347	444	13	10	10	NUM
ejpam-6347	444	14	having	have	VERB
ejpam-6347	444	15	conditions	condition	NOUN
ejpam-6347	444	16	,	,	PUNCT
ejpam-6347	444	17	a∗1	a∗1	NOUN
ejpam-6347	444	18	=	=	PUNCT
ejpam-6347	445	1	max{0,min(1,(ξ1	max{0,min(1,(ξ1	NOUN
ejpam-6347	445	2	−	−	PROPN
ejpam-6347	445	3	ξ9)s	ξ9)s	NOUN
ejpam-6347	445	4	2y1	2y1	NUM
ejpam-6347	445	5	)	)	PUNCT
ejpam-6347	445	6	}	}	PUNCT
ejpam-6347	445	7	,	,	PUNCT
ejpam-6347	445	8	a∗2	a∗2	ADJ
ejpam-6347	445	9	=	=	SYM
ejpam-6347	445	10	max{0,min(1	max{0,min(1	PROPN
ejpam-6347	445	11	,	,	PUNCT
ejpam-6347	445	12	(	(	PUNCT
ejpam-6347	445	13	ξ6	ξ6	NOUN
ejpam-6347	445	14	−	−	PROPN
ejpam-6347	445	15	ξ10)h	ξ10)h	PROPN
ejpam-6347	445	16	2y2	2y2	NUM
ejpam-6347	445	17	)	)	PUNCT
ejpam-6347	445	18	}	}	PUNCT
ejpam-6347	445	19	,	,	PUNCT
ejpam-6347	445	20	a∗3	a∗3	NOUN
ejpam-6347	445	21	=	=	SYM
ejpam-6347	445	22	max{0,min(1	max{0,min(1	PROPN
ejpam-6347	445	23	,	,	PUNCT
ejpam-6347	445	24	(	(	PUNCT
ejpam-6347	445	25	ξ8	ξ8	NOUN
ejpam-6347	445	26	−	−	PROPN
ejpam-6347	445	27	ξ10)f	ξ10)f	PROPN
ejpam-6347	445	28	2y3	2y3	NUM
ejpam-6347	445	29	)	)	PUNCT
ejpam-6347	445	30	}	}	PUNCT
ejpam-6347	445	31	,	,	PUNCT
ejpam-6347	445	32	(	(	PUNCT
ejpam-6347	445	33	3.72	3.72	NUM
ejpam-6347	445	34	)	)	PUNCT
ejpam-6347	445	35	n.	n.	NOUN
ejpam-6347	445	36	abbas	abbas	PROPN
ejpam-6347	445	37	,	,	PUNCT
ejpam-6347	445	38	w.	w.	PROPN
ejpam-6347	445	39	shatanawi	shatanawi	PROPN
ejpam-6347	445	40	,	,	PUNCT
ejpam-6347	445	41	s.	s.	PROPN
ejpam-6347	445	42	a.	a.	NOUN
ejpam-6347	445	43	zanib	zanib	PROPN
ejpam-6347	445	44	/	/	SYM
ejpam-6347	445	45	eur	eur	PROPN
ejpam-6347	445	46	.	.	PUNCT
ejpam-6347	446	1	j.	j.	PROPN
ejpam-6347	446	2	pure	pure	PROPN
ejpam-6347	446	3	appl	appl	PROPN
ejpam-6347	446	4	.	.	PROPN
ejpam-6347	446	5	math	math	PROPN
ejpam-6347	446	6	,	,	PUNCT
ejpam-6347	446	7	18	18	NUM
ejpam-6347	446	8	(	(	PUNCT
ejpam-6347	446	9	3	3	NUM
ejpam-6347	446	10	)	)	PUNCT
ejpam-6347	446	11	(	(	PUNCT
ejpam-6347	446	12	2025	2025	NUM
ejpam-6347	446	13	)	)	PUNCT
ejpam-6347	446	14	,	,	PUNCT
ejpam-6347	446	15	6347	6347	NUM
ejpam-6347	446	16	23	23	NUM
ejpam-6347	446	17	of	of	ADP
ejpam-6347	446	18	34	34	NUM
ejpam-6347	446	19	proof	proof	NOUN
ejpam-6347	446	20	.	.	PUNCT
ejpam-6347	447	1	using	use	VERB
ejpam-6347	447	2	pontryagin	pontryagin	NOUN
ejpam-6347	447	3	’s	’s	PART
ejpam-6347	447	4	maximal	maximal	ADJ
ejpam-6347	447	5	principle	principle	NOUN
ejpam-6347	447	6	[	[	X
ejpam-6347	447	7	28	28	NUM
ejpam-6347	447	8	]	]	X
ejpam-6347	447	9	,	,	PUNCT
ejpam-6347	447	10	adjoint	adjoint	NOUN
ejpam-6347	447	11	system	system	NOUN
ejpam-6347	447	12	is	be	AUX
ejpam-6347	447	13	written	write	VERB
ejpam-6347	447	14	as	as	ADP
ejpam-6347	447	15	a	a	DET
ejpam-6347	447	16	result	result	NOUN
ejpam-6347	447	17	of	of	ADP
ejpam-6347	447	18	our	our	PRON
ejpam-6347	447	19	differentiation	differentiation	NOUN
ejpam-6347	447	20	of	of	ADP
ejpam-6347	447	21	the	the	DET
ejpam-6347	447	22	hamiltonian	hamiltonian	NOUN
ejpam-6347	447	23	with	with	ADP
ejpam-6347	447	24	repect	repect	NOUN
ejpam-6347	447	25	to	to	ADP
ejpam-6347	447	26	the	the	DET
ejpam-6347	447	27	various	various	ADJ
ejpam-6347	447	28	states	state	NOUN
ejpam-6347	447	29	s	s	PART
ejpam-6347	447	30	,	,	PUNCT
ejpam-6347	447	31	e	e	NOUN
ejpam-6347	447	32	,	,	PUNCT
ejpam-6347	447	33	u	u	NOUN
ejpam-6347	447	34	,	,	PUNCT
ejpam-6347	447	35	q	q	INTJ
ejpam-6347	447	36	,	,	PUNCT
ejpam-6347	447	37	p	p	X
ejpam-6347	447	38	,	,	PUNCT
ejpam-6347	447	39	h	h	NOUN
ejpam-6347	447	40	,	,	PUNCT
ejpam-6347	447	41	c	c	X
ejpam-6347	447	42	,	,	PUNCT
ejpam-6347	447	43	f	f	PROPN
ejpam-6347	447	44	,	,	PUNCT
ejpam-6347	447	45	v	v	NOUN
ejpam-6347	447	46	and	and	CCONJ
ejpam-6347	447	47	r.	r.	PROPN
ejpam-6347	447	48	dξ1	dξ1	PROPN
ejpam-6347	447	49	dt	dt	PROPN
ejpam-6347	448	1	=	=	SYM
ejpam-6347	448	2	−dh	−dh	ADP
ejpam-6347	448	3	ds	ds	ADJ
ejpam-6347	448	4	,	,	PUNCT
ejpam-6347	448	5	dξ2	dξ2	NOUN
ejpam-6347	448	6	dt	dt	NOUN
ejpam-6347	448	7	=	=	SYM
ejpam-6347	448	8	−dh	−dh	PROPN
ejpam-6347	448	9	de	de	X
ejpam-6347	448	10	,	,	PUNCT
ejpam-6347	448	11	dξ3	dξ3	ADP
ejpam-6347	448	12	dt	dt	NOUN
ejpam-6347	448	13	=	=	SYM
ejpam-6347	448	14	−dh	−dh	PROPN
ejpam-6347	448	15	di	di	NOUN
ejpam-6347	448	16	,	,	PUNCT
ejpam-6347	448	17	dξ4	dξ4	NOUN
ejpam-6347	448	18	dt	dt	NOUN
ejpam-6347	448	19	=	=	SYM
ejpam-6347	448	20	−dh	−dh	PROPN
ejpam-6347	448	21	dq	dq	PROPN
ejpam-6347	448	22	,	,	PUNCT
ejpam-6347	448	23	dξ5	dξ5	INTJ
ejpam-6347	448	24	dt	dt	NOUN
ejpam-6347	448	25	=	=	SYM
ejpam-6347	448	26	−dh	−dh	NUM
ejpam-6347	448	27	dp	dp	NOUN
ejpam-6347	448	28	,	,	PUNCT
ejpam-6347	448	29	dξ6	dξ6	VERB
ejpam-6347	448	30	dt	dt	NOUN
ejpam-6347	449	1	=	=	PUNCT
ejpam-6347	449	2	−	−	PROPN
ejpam-6347	450	1	dh	dh	INTJ
ejpam-6347	450	2	dh	dh	NOUN
ejpam-6347	450	3	,	,	PUNCT
ejpam-6347	450	4	dξ7	dξ7	PROPN
ejpam-6347	450	5	dt	dt	NOUN
ejpam-6347	451	1	=	=	SYM
ejpam-6347	451	2	−dh	−dh	PROPN
ejpam-6347	451	3	dc	dc	PROPN
ejpam-6347	451	4	,	,	PUNCT
ejpam-6347	451	5	dξ8	dξ8	X
ejpam-6347	451	6	dt	dt	NOUN
ejpam-6347	451	7	=	=	SYM
ejpam-6347	452	1	−dh	−dh	PROPN
ejpam-6347	452	2	df	df	NOUN
ejpam-6347	452	3	,	,	PUNCT
ejpam-6347	452	4	dξ9	dξ9	INTJ
ejpam-6347	452	5	dt	dt	X
ejpam-6347	452	6	=	=	SYM
ejpam-6347	452	7	−dh	−dh	PROPN
ejpam-6347	452	8	dv	dv	PROPN
ejpam-6347	452	9	,	,	PUNCT
ejpam-6347	452	10	dξ10	dξ10	PROPN
ejpam-6347	452	11	dt	dt	PUNCT
ejpam-6347	452	12	=	=	SYM
ejpam-6347	452	13	−dh	−dh	PROPN
ejpam-6347	452	14	dr	dr	PROPN
ejpam-6347	452	15	.	.	PUNCT
ejpam-6347	453	1	(	(	PUNCT
ejpam-6347	453	2	3.73	3.73	NUM
ejpam-6347	453	3	)	)	PUNCT
ejpam-6347	453	4	with	with	ADP
ejpam-6347	453	5	conditions	condition	NOUN
ejpam-6347	453	6	,	,	PUNCT
ejpam-6347	453	7	ξi(t	ξi(t	NUM
ejpam-6347	453	8	)	)	PUNCT
ejpam-6347	453	9	=	=	SYM
ejpam-6347	453	10	0	0	NUM
ejpam-6347	453	11	,	,	PUNCT
ejpam-6347	453	12	for	for	ADP
ejpam-6347	453	13	i	i	PROPN
ejpam-6347	453	14	=	=	SYM
ejpam-6347	453	15	1	1	NUM
ejpam-6347	453	16	,	,	PUNCT
ejpam-6347	453	17	2	2	NUM
ejpam-6347	453	18	,	,	PUNCT
ejpam-6347	453	19	3	3	NUM
ejpam-6347	453	20	....	....	SYM
ejpam-6347	453	21	10	10	NUM
ejpam-6347	453	22	.	.	PUNCT
ejpam-6347	454	1	the	the	DET
ejpam-6347	454	2	optimal	optimal	ADJ
ejpam-6347	454	3	controls	control	NOUN
ejpam-6347	454	4	(	(	PUNCT
ejpam-6347	454	5	a∗1	a∗1	NOUN
ejpam-6347	454	6	,	,	PUNCT
ejpam-6347	454	7	a	a	DET
ejpam-6347	454	8	∗	∗	NOUN
ejpam-6347	454	9	2	2	NUM
ejpam-6347	454	10	,	,	PUNCT
ejpam-6347	454	11	a	a	DET
ejpam-6347	454	12	∗	∗	NOUN
ejpam-6347	454	13	3	3	NUM
ejpam-6347	454	14	)	)	PUNCT
ejpam-6347	454	15	are	be	AUX
ejpam-6347	454	16	characterized	characterize	VERB
ejpam-6347	454	17	by	by	ADP
ejpam-6347	454	18	adopting	adopt	VERB
ejpam-6347	454	19	the	the	DET
ejpam-6347	454	20	strategy	strategy	NOUN
ejpam-6347	454	21	used	use	VERB
ejpam-6347	454	22	by	by	ADP
ejpam-6347	454	23	pontryagin	pontryagin	NOUN
ejpam-6347	454	24	et	et	PROPN
ejpam-6347	454	25	al	al	PROPN
ejpam-6347	454	26	.	.	PROPN
ejpam-6347	454	27	,	,	PUNCT
ejpam-6347	455	1	[	[	X
ejpam-6347	455	2	27	27	NUM
ejpam-6347	455	3	]	]	PUNCT
ejpam-6347	455	4	,	,	PUNCT
ejpam-6347	455	5	based	base	VERB
ejpam-6347	455	6	on	on	ADP
ejpam-6347	455	7	the	the	DET
ejpam-6347	455	8	following	follow	VERB
ejpam-6347	455	9	conditions	condition	NOUN
ejpam-6347	455	10	,	,	PUNCT
ejpam-6347	455	11	∂h	∂h	PROPN
ejpam-6347	455	12	∂ai	∂ai	PROPN
ejpam-6347	455	13	,	,	PUNCT
ejpam-6347	455	14	for	for	ADP
ejpam-6347	455	15	i=1,2,3	i=1,2,3	NUM
ejpam-6347	455	16	....	....	SYM
ejpam-6347	455	17	10	10	NUM
ejpam-6347	455	18	.	.	PUNCT
ejpam-6347	456	1	for	for	ADP
ejpam-6347	456	2	a∗i	a∗i	NUM
ejpam-6347	456	3	,	,	PUNCT
ejpam-6347	456	4	the	the	DET
ejpam-6347	456	5	result	result	NOUN
ejpam-6347	456	6	are	be	AUX
ejpam-6347	456	7	,	,	PUNCT
ejpam-6347	456	8	a∗1	a∗1	NOUN
ejpam-6347	456	9	=	=	SYM
ejpam-6347	456	10	(	(	PUNCT
ejpam-6347	456	11	ξ1	ξ1	PROPN
ejpam-6347	456	12	−	−	PROPN
ejpam-6347	456	13	ξ9)s	ξ9)s	NOUN
ejpam-6347	456	14	2y1	2y1	NUM
ejpam-6347	456	15	,	,	PUNCT
ejpam-6347	456	16	a∗2	a∗2	ADJ
ejpam-6347	456	17	=	=	SYM
ejpam-6347	456	18	(	(	PUNCT
ejpam-6347	456	19	ξ6	ξ6	NOUN
ejpam-6347	456	20	−	−	PROPN
ejpam-6347	456	21	ξ10)h	ξ10)h	PROPN
ejpam-6347	456	22	2y2	2y2	NUM
ejpam-6347	456	23	,	,	PUNCT
ejpam-6347	456	24	a∗3	a∗3	NOUN
ejpam-6347	456	25	=	=	SYM
ejpam-6347	456	26	(	(	PUNCT
ejpam-6347	456	27	ξ8	ξ8	NOUN
ejpam-6347	456	28	−	−	PROPN
ejpam-6347	456	29	ξ10)f	ξ10)f	PROPN
ejpam-6347	456	30	2y3	2y3	NUM
ejpam-6347	456	31	,	,	PUNCT
ejpam-6347	456	32	(	(	PUNCT
ejpam-6347	456	33	3.74	3.74	NUM
ejpam-6347	456	34	)	)	PUNCT
ejpam-6347	456	35	by	by	ADP
ejpam-6347	456	36	including	include	VERB
ejpam-6347	456	37	the	the	DET
ejpam-6347	456	38	described	describe	VERB
ejpam-6347	456	39	control	control	NOUN
ejpam-6347	456	40	set	set	PROPN
ejpam-6347	456	41	,	,	PUNCT
ejpam-6347	456	42	initial	initial	ADJ
ejpam-6347	456	43	,	,	PUNCT
ejpam-6347	456	44	and	and	CCONJ
ejpam-6347	456	45	transversal	transversal	ADJ
ejpam-6347	456	46	conditions	condition	NOUN
ejpam-6347	456	47	,	,	PUNCT
ejpam-6347	456	48	the	the	DET
ejpam-6347	456	49	optimal	optimal	ADJ
ejpam-6347	456	50	control	control	NOUN
ejpam-6347	456	51	system	system	NOUN
ejpam-6347	456	52	is	be	AUX
ejpam-6347	456	53	generated	generate	VERB
ejpam-6347	456	54	from	from	ADP
ejpam-6347	456	55	the	the	DET
ejpam-6347	456	56	adjoint	adjoint	NOUN
ejpam-6347	456	57	variable	variable	ADJ
ejpam-6347	456	58	system	system	NOUN
ejpam-6347	456	59	and	and	CCONJ
ejpam-6347	456	60	the	the	DET
ejpam-6347	456	61	optimal	optimal	ADJ
ejpam-6347	456	62	control	control	NOUN
ejpam-6347	456	63	system	system	NOUN
ejpam-6347	456	64	.	.	PUNCT
ejpam-6347	457	1	4	4	X
ejpam-6347	457	2	.	.	X
ejpam-6347	457	3	numerical	numerical	ADJ
ejpam-6347	457	4	results	result	NOUN
ejpam-6347	457	5	and	and	CCONJ
ejpam-6347	457	6	discussion	discussion	NOUN
ejpam-6347	457	7	figure	figure	VERB
ejpam-6347	457	8	4	4	NUM
ejpam-6347	457	9	presents	present	VERB
ejpam-6347	457	10	a	a	DET
ejpam-6347	457	11	comparison	comparison	NOUN
ejpam-6347	457	12	between	between	ADP
ejpam-6347	457	13	the	the	DET
ejpam-6347	457	14	model	model	NOUN
ejpam-6347	457	15	-	-	PUNCT
ejpam-6347	457	16	predicted	predict	VERB
ejpam-6347	457	17	number	number	NOUN
ejpam-6347	457	18	of	of	ADP
ejpam-6347	457	19	infected	infect	VERB
ejpam-6347	457	20	individuals	individual	NOUN
ejpam-6347	457	21	(	(	PUNCT
ejpam-6347	457	22	u	u	NOUN
ejpam-6347	457	23	)	)	PUNCT
ejpam-6347	457	24	and	and	CCONJ
ejpam-6347	457	25	the	the	DET
ejpam-6347	457	26	smoothed	smooth	VERB
ejpam-6347	457	27	daily	daily	ADJ
ejpam-6347	457	28	new	new	ADJ
ejpam-6347	457	29	covid-19	covid-19	PROPN
ejpam-6347	457	30	cases	case	NOUN
ejpam-6347	457	31	per	per	ADP
ejpam-6347	457	32	100,000	100,000	NUM
ejpam-6347	457	33	people	people	NOUN
ejpam-6347	457	34	reported	report	VERB
ejpam-6347	457	35	in	in	ADP
ejpam-6347	457	36	the	the	DET
ejpam-6347	457	37	united	united	PROPN
ejpam-6347	457	38	states	states	PROPN
ejpam-6347	457	39	from	from	ADP
ejpam-6347	457	40	january	january	PROPN
ejpam-6347	457	41	2022	2022	NUM
ejpam-6347	457	42	onward	onward	ADV
ejpam-6347	457	43	.	.	PUNCT
ejpam-6347	458	1	the	the	DET
ejpam-6347	458	2	model	model	NOUN
ejpam-6347	458	3	output	output	NOUN
ejpam-6347	458	4	is	be	AUX
ejpam-6347	458	5	shown	show	VERB
ejpam-6347	458	6	in	in	ADP
ejpam-6347	458	7	red	red	ADJ
ejpam-6347	458	8	,	,	PUNCT
ejpam-6347	458	9	while	while	SCONJ
ejpam-6347	458	10	the	the	DET
ejpam-6347	458	11	real	real	ADJ
ejpam-6347	458	12	-	-	PUNCT
ejpam-6347	458	13	world	world	NOUN
ejpam-6347	458	14	data	datum	NOUN
ejpam-6347	458	15	is	be	AUX
ejpam-6347	458	16	plotted	plot	VERB
ejpam-6347	458	17	in	in	ADP
ejpam-6347	458	18	green	green	NOUN
ejpam-6347	458	19	.	.	PUNCT
ejpam-6347	459	1	the	the	DET
ejpam-6347	459	2	results	result	NOUN
ejpam-6347	459	3	demonstrate	demonstrate	VERB
ejpam-6347	459	4	the	the	DET
ejpam-6347	459	5	alignment	alignment	NOUN
ejpam-6347	459	6	of	of	ADP
ejpam-6347	459	7	model	model	NOUN
ejpam-6347	459	8	dynamics	dynamic	NOUN
ejpam-6347	459	9	with	with	ADP
ejpam-6347	459	10	observed	observed	ADJ
ejpam-6347	459	11	trends	trend	NOUN
ejpam-6347	459	12	in	in	ADP
ejpam-6347	459	13	case	case	NOUN
ejpam-6347	459	14	data	datum	NOUN
ejpam-6347	459	15	,	,	PUNCT
ejpam-6347	459	16	highlighting	highlight	VERB
ejpam-6347	459	17	the	the	DET
ejpam-6347	459	18	utility	utility	NOUN
ejpam-6347	459	19	of	of	ADP
ejpam-6347	459	20	the	the	DET
ejpam-6347	459	21	proposed	propose	VERB
ejpam-6347	459	22	compartmental	compartmental	ADJ
ejpam-6347	459	23	framework	framework	NOUN
ejpam-6347	459	24	for	for	ADP
ejpam-6347	459	25	capturing	capture	VERB
ejpam-6347	459	26	the	the	DET
ejpam-6347	459	27	progression	progression	NOUN
ejpam-6347	459	28	of	of	ADP
ejpam-6347	459	29	covid-19	covid-19	PROPN
ejpam-6347	459	30	infections	infection	NOUN
ejpam-6347	459	31	a	a	DET
ejpam-6347	459	32	numerical	numerical	ADJ
ejpam-6347	459	33	simulation	simulation	NOUN
ejpam-6347	459	34	of	of	ADP
ejpam-6347	459	35	the	the	DET
ejpam-6347	459	36	non	non	ADJ
ejpam-6347	459	37	-	-	ADJ
ejpam-6347	459	38	linear	linear	ADJ
ejpam-6347	459	39	integer	integer	NOUN
ejpam-6347	459	40	-	-	PUNCT
ejpam-6347	459	41	order	order	NOUN
ejpam-6347	459	42	system	system	NOUN
ejpam-6347	459	43	(	(	PUNCT
ejpam-6347	459	44	2.4	2.4	NUM
ejpam-6347	459	45	)	)	PUNCT
ejpam-6347	459	46	has	have	AUX
ejpam-6347	459	47	been	be	AUX
ejpam-6347	459	48	performed	perform	VERB
ejpam-6347	459	49	using	use	VERB
ejpam-6347	459	50	the	the	DET
ejpam-6347	459	51	classical	classical	ADJ
ejpam-6347	459	52	fourth	fourth	ADJ
ejpam-6347	459	53	-	-	PUNCT
ejpam-6347	459	54	order	order	NOUN
ejpam-6347	459	55	runge	runge	NOUN
ejpam-6347	459	56	-	-	PUNCT
ejpam-6347	459	57	kutta	kutta	NOUN
ejpam-6347	459	58	(	(	PUNCT
ejpam-6347	459	59	rk4	rk4	NOUN
ejpam-6347	459	60	)	)	PUNCT
ejpam-6347	459	61	method	method	NOUN
ejpam-6347	459	62	.	.	PUNCT
ejpam-6347	460	1	the	the	DET
ejpam-6347	460	2	initial	initial	ADJ
ejpam-6347	460	3	conditions	condition	NOUN
ejpam-6347	460	4	for	for	ADP
ejpam-6347	460	5	all	all	DET
ejpam-6347	460	6	compartments	compartment	NOUN
ejpam-6347	460	7	are	be	AUX
ejpam-6347	460	8	given	give	VERB
ejpam-6347	460	9	by	by	ADP
ejpam-6347	460	10	:	:	PUNCT
ejpam-6347	460	11	s(0	s(0	PROPN
ejpam-6347	460	12	)	)	PUNCT
ejpam-6347	460	13	=	=	SYM
ejpam-6347	460	14	500	500	NUM
ejpam-6347	460	15	,	,	PUNCT
ejpam-6347	460	16	e(0	e(0	NOUN
ejpam-6347	460	17	)	)	PUNCT
ejpam-6347	460	18	=	=	SYM
ejpam-6347	460	19	20	20	NUM
ejpam-6347	460	20	,	,	PUNCT
ejpam-6347	460	21	u(0	u(0	NOUN
ejpam-6347	460	22	)	)	PUNCT
ejpam-6347	460	23	=	=	SYM
ejpam-6347	460	24	10	10	NUM
ejpam-6347	460	25	,	,	PUNCT
ejpam-6347	460	26	q(0	q(0	PROPN
ejpam-6347	460	27	)	)	PUNCT
ejpam-6347	460	28	=	=	SYM
ejpam-6347	460	29	8	8	NUM
ejpam-6347	460	30	,	,	PUNCT
ejpam-6347	460	31	p	p	X
ejpam-6347	460	32	(	(	PUNCT
ejpam-6347	460	33	0	0	NUM
ejpam-6347	460	34	)	)	PUNCT
ejpam-6347	460	35	=	=	SYM
ejpam-6347	460	36	6	6	NUM
ejpam-6347	460	37	,	,	PUNCT
ejpam-6347	460	38	h(0	h(0	PROPN
ejpam-6347	460	39	)	)	PUNCT
ejpam-6347	460	40	=	=	SYM
ejpam-6347	460	41	4	4	NUM
ejpam-6347	460	42	,	,	PUNCT
ejpam-6347	460	43	f	f	PROPN
ejpam-6347	460	44	(	(	PUNCT
ejpam-6347	460	45	0	0	NUM
ejpam-6347	460	46	)	)	PUNCT
ejpam-6347	460	47	=	=	SYM
ejpam-6347	460	48	2	2	NUM
ejpam-6347	460	49	,	,	PUNCT
ejpam-6347	460	50	c(0	c(0	NOUN
ejpam-6347	460	51	)	)	PUNCT
ejpam-6347	460	52	=	=	SYM
ejpam-6347	461	1	1	1	NUM
ejpam-6347	461	2	,	,	PUNCT
ejpam-6347	461	3	v	v	NOUN
ejpam-6347	461	4	(	(	PUNCT
ejpam-6347	461	5	0	0	NUM
ejpam-6347	461	6	)	)	PUNCT
ejpam-6347	461	7	=	=	SYM
ejpam-6347	461	8	0	0	NUM
ejpam-6347	461	9	,	,	PUNCT
ejpam-6347	461	10	r(0	r(0	PROPN
ejpam-6347	461	11	)	)	PUNCT
ejpam-6347	461	12	=	=	SYM
ejpam-6347	462	1	0	0	X
ejpam-6347	462	2	.	.	PUNCT
ejpam-6347	463	1	the	the	DET
ejpam-6347	463	2	system	system	NOUN
ejpam-6347	463	3	of	of	ADP
ejpam-6347	463	4	ordinary	ordinary	ADJ
ejpam-6347	463	5	differential	differential	ADJ
ejpam-6347	463	6	equations	equation	NOUN
ejpam-6347	463	7	governing	govern	VERB
ejpam-6347	463	8	the	the	DET
ejpam-6347	463	9	covcom10	covcom10	NOUN
ejpam-6347	463	10	model	model	NOUN
ejpam-6347	463	11	was	be	AUX
ejpam-6347	463	12	solved	solve	VERB
ejpam-6347	463	13	using	use	VERB
ejpam-6347	463	14	the	the	DET
ejpam-6347	463	15	fourth	fourth	ADJ
ejpam-6347	463	16	-	-	PUNCT
ejpam-6347	463	17	order	order	NOUN
ejpam-6347	463	18	runge	runge	NOUN
ejpam-6347	463	19	-	-	PUNCT
ejpam-6347	463	20	kutta	kutta	NOUN
ejpam-6347	463	21	(	(	PUNCT
ejpam-6347	463	22	rk4	rk4	NOUN
ejpam-6347	463	23	)	)	PUNCT
ejpam-6347	463	24	method	method	NOUN
ejpam-6347	463	25	,	,	PUNCT
ejpam-6347	463	26	which	which	PRON
ejpam-6347	463	27	provides	provide	VERB
ejpam-6347	463	28	improved	improved	ADJ
ejpam-6347	463	29	accuracy	accuracy	NOUN
ejpam-6347	463	30	over	over	ADP
ejpam-6347	463	31	basic	basic	ADJ
ejpam-6347	463	32	euler	euler	NOUN
ejpam-6347	463	33	methods	method	NOUN
ejpam-6347	463	34	through	through	ADP
ejpam-6347	463	35	its	its	PRON
ejpam-6347	463	36	multi	multi	ADJ
ejpam-6347	463	37	-	-	ADJ
ejpam-6347	463	38	stage	stage	ADJ
ejpam-6347	463	39	slope	slope	NOUN
ejpam-6347	463	40	calculations	calculation	NOUN
ejpam-6347	463	41	.	.	PUNCT
ejpam-6347	464	1	for	for	ADP
ejpam-6347	464	2	a	a	DET
ejpam-6347	464	3	general	general	ADJ
ejpam-6347	464	4	ode	ode	ADJ
ejpam-6347	464	5	system	system	NOUN
ejpam-6347	464	6	:	:	PUNCT
ejpam-6347	464	7	dy	dy	NOUN
ejpam-6347	464	8	dt	dt	NOUN
ejpam-6347	464	9	=	=	PUNCT
ejpam-6347	464	10	f(t	f(t	PROPN
ejpam-6347	464	11	,	,	PUNCT
ejpam-6347	464	12	y	y	NOUN
ejpam-6347	464	13	)	)	PUNCT
ejpam-6347	464	14	,	,	PUNCT
ejpam-6347	464	15	y(t0	y(t0	PROPN
ejpam-6347	464	16	)	)	PUNCT
ejpam-6347	465	1	=	=	PUNCT
ejpam-6347	465	2	y0	y0	NOUN
ejpam-6347	465	3	where	where	SCONJ
ejpam-6347	465	4	y	y	NOUN
ejpam-6347	465	5	=	=	PUNCT
ejpam-6347	466	1	[	[	X
ejpam-6347	466	2	s	s	X
ejpam-6347	466	3	,	,	PUNCT
ejpam-6347	466	4	e	e	NOUN
ejpam-6347	466	5	,	,	PUNCT
ejpam-6347	466	6	u	u	NOUN
ejpam-6347	466	7	,	,	PUNCT
ejpam-6347	466	8	q	q	INTJ
ejpam-6347	466	9	,	,	PUNCT
ejpam-6347	466	10	p	p	X
ejpam-6347	466	11	,	,	PUNCT
ejpam-6347	466	12	h	h	NOUN
ejpam-6347	466	13	,	,	PUNCT
ejpam-6347	466	14	f	f	X
ejpam-6347	466	15	,	,	PUNCT
ejpam-6347	466	16	c	c	PROPN
ejpam-6347	466	17	,	,	PUNCT
ejpam-6347	466	18	v	v	NOUN
ejpam-6347	466	19	,	,	PUNCT
ejpam-6347	466	20	r]t	r]t	NOUN
ejpam-6347	466	21	,	,	PUNCT
ejpam-6347	466	22	the	the	DET
ejpam-6347	466	23	rk4	rk4	NOUN
ejpam-6347	466	24	method	method	NOUN
ejpam-6347	466	25	computes	compute	VERB
ejpam-6347	466	26	each	each	DET
ejpam-6347	466	27	time	time	NOUN
ejpam-6347	466	28	step	step	NOUN
ejpam-6347	466	29	as	as	ADP
ejpam-6347	466	30	:	:	PUNCT
ejpam-6347	466	31	k1	k1	NOUN
ejpam-6347	466	32	=	=	SYM
ejpam-6347	466	33	f(tn	f(tn	PROPN
ejpam-6347	466	34	,	,	PUNCT
ejpam-6347	466	35	yn	yn	NOUN
ejpam-6347	466	36	)	)	PUNCT
ejpam-6347	466	37	n.	n.	NOUN
ejpam-6347	466	38	abbas	abbas	PROPN
ejpam-6347	466	39	,	,	PUNCT
ejpam-6347	466	40	w.	w.	PROPN
ejpam-6347	466	41	shatanawi	shatanawi	PROPN
ejpam-6347	466	42	,	,	PUNCT
ejpam-6347	466	43	s.	s.	PROPN
ejpam-6347	466	44	a.	a.	NOUN
ejpam-6347	466	45	zanib	zanib	PROPN
ejpam-6347	466	46	/	/	SYM
ejpam-6347	466	47	eur	eur	PROPN
ejpam-6347	466	48	.	.	PUNCT
ejpam-6347	467	1	j.	j.	PROPN
ejpam-6347	467	2	pure	pure	PROPN
ejpam-6347	467	3	appl	appl	PROPN
ejpam-6347	467	4	.	.	PROPN
ejpam-6347	467	5	math	math	PROPN
ejpam-6347	467	6	,	,	PUNCT
ejpam-6347	467	7	18	18	NUM
ejpam-6347	467	8	(	(	PUNCT
ejpam-6347	467	9	3	3	NUM
ejpam-6347	467	10	)	)	PUNCT
ejpam-6347	467	11	(	(	PUNCT
ejpam-6347	467	12	2025	2025	NUM
ejpam-6347	467	13	)	)	PUNCT
ejpam-6347	467	14	,	,	PUNCT
ejpam-6347	467	15	6347	6347	NUM
ejpam-6347	467	16	24	24	NUM
ejpam-6347	467	17	of	of	ADP
ejpam-6347	467	18	34	34	NUM
ejpam-6347	467	19	2022	2022	NUM
ejpam-6347	467	20	-	-	SYM
ejpam-6347	467	21	01	01	NUM
ejpam-6347	467	22	2022	2022	NUM
ejpam-6347	467	23	-	-	SYM
ejpam-6347	467	24	02	02	NUM
ejpam-6347	467	25	2022	2022	NUM
ejpam-6347	467	26	-	-	SYM
ejpam-6347	467	27	03	03	NUM
ejpam-6347	467	28	2022	2022	NUM
ejpam-6347	467	29	-	-	SYM
ejpam-6347	467	30	04	04	NUM
ejpam-6347	467	31	2022	2022	NUM
ejpam-6347	467	32	-	-	SYM
ejpam-6347	467	33	05	05	NUM
ejpam-6347	467	34	2022	2022	NUM
ejpam-6347	467	35	-	-	SYM
ejpam-6347	467	36	06	06	NUM
ejpam-6347	467	37	2022	2022	NUM
ejpam-6347	467	38	-	-	SYM
ejpam-6347	467	39	07	07	NUM
ejpam-6347	467	40	2022	2022	NUM
ejpam-6347	467	41	-	-	SYM
ejpam-6347	467	42	08	08	NUM
ejpam-6347	467	43	2022	2022	NUM
ejpam-6347	467	44	-	-	SYM
ejpam-6347	467	45	09	09	NUM
ejpam-6347	467	46	2022	2022	NUM
ejpam-6347	467	47	-	-	SYM
ejpam-6347	467	48	10	10	NUM
ejpam-6347	467	49	2022	2022	NUM
ejpam-6347	467	50	-	-	SYM
ejpam-6347	467	51	11	11	NUM
ejpam-6347	467	52	2022	2022	NUM
ejpam-6347	467	53	-	-	SYM
ejpam-6347	467	54	12	12	NUM
ejpam-6347	467	55	2023	2023	NUM
ejpam-6347	467	56	-	-	SYM
ejpam-6347	467	57	01	01	NUM
ejpam-6347	467	58	2023	2023	NUM
ejpam-6347	467	59	-	-	SYM
ejpam-6347	467	60	02	02	NUM
ejpam-6347	467	61	2023	2023	NUM
ejpam-6347	467	62	-	-	SYM
ejpam-6347	467	63	03	03	NUM
ejpam-6347	467	64	2023	2023	NUM
ejpam-6347	467	65	-	-	SYM
ejpam-6347	467	66	04	04	NUM
ejpam-6347	467	67	2023	2023	NUM
ejpam-6347	467	68	-	-	SYM
ejpam-6347	467	69	05	05	NUM
ejpam-6347	467	70	2023	2023	NUM
ejpam-6347	467	71	-	-	SYM
ejpam-6347	467	72	06	06	NUM
ejpam-6347	467	73	date	date	NOUN
ejpam-6347	467	74	0	0	NUM
ejpam-6347	467	75	2	2	NUM
ejpam-6347	467	76	4	4	NUM
ejpam-6347	467	77	6	6	NUM
ejpam-6347	467	78	8	8	NUM
ejpam-6347	467	79	10	10	NUM
ejpam-6347	467	80	m	m	NOUN
ejpam-6347	467	81	od	od	PROPN
ejpam-6347	467	82	el	el	PROPN
ejpam-6347	467	83	:	:	PUNCT
ejpam-6347	468	1	i	i	PRON
ejpam-6347	468	2	nf	nf	VERB
ejpam-6347	468	3	ec	ec	PROPN
ejpam-6347	468	4	te	te	PROPN
ejpam-6347	468	5	d	d	NOUN
ejpam-6347	468	6	0	0	NUM
ejpam-6347	468	7	50	50	NUM
ejpam-6347	468	8	100	100	NUM
ejpam-6347	468	9	150	150	NUM
ejpam-6347	468	10	200	200	NUM
ejpam-6347	468	11	re	re	NOUN
ejpam-6347	468	12	al	al	PROPN
ejpam-6347	468	13	c	c	PROPN
ejpam-6347	468	14	as	as	ADP
ejpam-6347	468	15	es	es	X
ejpam-6347	468	16	(	(	PUNCT
ejpam-6347	468	17	p	p	X
ejpam-6347	468	18	er	er	INTJ
ejpam-6347	468	19	1	1	NUM
ejpam-6347	468	20	00	00	NUM
ejpam-6347	468	21	k	k	X
ejpam-6347	468	22	)	)	PUNCT
ejpam-6347	468	23	covid-19	covid-19	PROPN
ejpam-6347	468	24	model	model	NOUN
ejpam-6347	468	25	vs	vs	ADP
ejpam-6347	468	26	real	real	ADJ
ejpam-6347	468	27	cases	case	NOUN
ejpam-6347	468	28	(	(	PUNCT
ejpam-6347	468	29	usa	usa	NOUN
ejpam-6347	468	30	)	)	PUNCT
ejpam-6347	468	31	model	model	NOUN
ejpam-6347	468	32	infected	infect	VERB
ejpam-6347	468	33	(	(	PUNCT
ejpam-6347	468	34	u	u	NOUN
ejpam-6347	468	35	)	)	PUNCT
ejpam-6347	468	36	real	real	ADJ
ejpam-6347	468	37	cases	case	NOUN
ejpam-6347	468	38	(	(	PUNCT
ejpam-6347	468	39	per	per	ADP
ejpam-6347	468	40	100k	100k	NUM
ejpam-6347	468	41	)	)	PUNCT
ejpam-6347	468	42	figure	figure	NOUN
ejpam-6347	468	43	4	4	NUM
ejpam-6347	468	44	:	:	PUNCT
ejpam-6347	468	45	comparison	comparison	NOUN
ejpam-6347	468	46	of	of	ADP
ejpam-6347	468	47	model	model	NOUN
ejpam-6347	468	48	-	-	PUNCT
ejpam-6347	468	49	predicted	predict	VERB
ejpam-6347	468	50	infected	infected	ADJ
ejpam-6347	468	51	population	population	NOUN
ejpam-6347	468	52	(	(	PUNCT
ejpam-6347	468	53	u	u	NOUN
ejpam-6347	468	54	)	)	PUNCT
ejpam-6347	468	55	with	with	ADP
ejpam-6347	468	56	real	real	ADJ
ejpam-6347	468	57	-	-	PUNCT
ejpam-6347	468	58	world	world	NOUN
ejpam-6347	468	59	covid-19	covid-19	PROPN
ejpam-6347	468	60	cases	case	NOUN
ejpam-6347	468	61	per	per	ADP
ejpam-6347	468	62	100,000	100,000	NUM
ejpam-6347	468	63	people	people	NOUN
ejpam-6347	468	64	in	in	ADP
ejpam-6347	468	65	the	the	DET
ejpam-6347	468	66	united	united	PROPN
ejpam-6347	468	67	states	states	PROPN
ejpam-6347	468	68	.	.	PUNCT
ejpam-6347	469	1	the	the	DET
ejpam-6347	469	2	model	model	NOUN
ejpam-6347	469	3	output	output	NOUN
ejpam-6347	469	4	is	be	AUX
ejpam-6347	469	5	shown	show	VERB
ejpam-6347	469	6	in	in	ADP
ejpam-6347	469	7	red	red	ADJ
ejpam-6347	469	8	,	,	PUNCT
ejpam-6347	469	9	and	and	CCONJ
ejpam-6347	469	10	the	the	DET
ejpam-6347	469	11	real	real	ADJ
ejpam-6347	469	12	-	-	PUNCT
ejpam-6347	469	13	world	world	NOUN
ejpam-6347	469	14	data	datum	NOUN
ejpam-6347	469	15	is	be	AUX
ejpam-6347	469	16	plotted	plot	VERB
ejpam-6347	469	17	in	in	ADP
ejpam-6347	469	18	green	green	ADJ
ejpam-6347	469	19	.	.	PUNCT
ejpam-6347	470	1	k2	k2	PROPN
ejpam-6347	470	2	=	=	SYM
ejpam-6347	470	3	f	f	PROPN
ejpam-6347	470	4	(	(	PUNCT
ejpam-6347	470	5	tn	tn	PROPN
ejpam-6347	470	6	+	+	CCONJ
ejpam-6347	470	7	h	h	NOUN
ejpam-6347	470	8	2	2	NUM
ejpam-6347	470	9	,	,	PUNCT
ejpam-6347	470	10	yn	yn	PROPN
ejpam-6347	470	11	+	+	CCONJ
ejpam-6347	470	12	h	h	NOUN
ejpam-6347	470	13	2	2	NUM
ejpam-6347	470	14	k1	k1	NOUN
ejpam-6347	470	15	)	)	PUNCT
ejpam-6347	470	16	k3	k3	PROPN
ejpam-6347	470	17	=	=	SYM
ejpam-6347	470	18	f	f	PROPN
ejpam-6347	470	19	(	(	PUNCT
ejpam-6347	470	20	tn	tn	PROPN
ejpam-6347	471	1	+	+	CCONJ
ejpam-6347	471	2	h	h	NOUN
ejpam-6347	471	3	2	2	NUM
ejpam-6347	471	4	,	,	PUNCT
ejpam-6347	471	5	yn	yn	PROPN
ejpam-6347	471	6	+	+	CCONJ
ejpam-6347	471	7	h	h	PROPN
ejpam-6347	471	8	2	2	NUM
ejpam-6347	471	9	k2	k2	NOUN
ejpam-6347	471	10	)	)	PUNCT
ejpam-6347	471	11	k4	k4	NOUN
ejpam-6347	471	12	=	=	SYM
ejpam-6347	471	13	f	f	PROPN
ejpam-6347	471	14	(	(	PUNCT
ejpam-6347	471	15	tn	tn	PROPN
ejpam-6347	472	1	+	+	CCONJ
ejpam-6347	472	2	h	h	NOUN
ejpam-6347	472	3	,	,	PUNCT
ejpam-6347	472	4	yn	yn	PROPN
ejpam-6347	472	5	+	+	CCONJ
ejpam-6347	472	6	hk3	hk3	NOUN
ejpam-6347	472	7	)	)	PUNCT
ejpam-6347	472	8	with	with	ADP
ejpam-6347	472	9	the	the	DET
ejpam-6347	472	10	state	state	NOUN
ejpam-6347	472	11	update	update	NOUN
ejpam-6347	472	12	given	give	VERB
ejpam-6347	472	13	by	by	ADP
ejpam-6347	472	14	:	:	PUNCT
ejpam-6347	472	15	yn+1	yn+1	PROPN
ejpam-6347	472	16	=	=	SYM
ejpam-6347	472	17	yn	yn	PROPN
ejpam-6347	472	18	+	+	CCONJ
ejpam-6347	472	19	h	h	PROPN
ejpam-6347	472	20	6	6	NUM
ejpam-6347	472	21	(	(	PUNCT
ejpam-6347	472	22	k1	k1	X
ejpam-6347	472	23	+	+	CCONJ
ejpam-6347	472	24	2k2	2k2	NUM
ejpam-6347	472	25	+	+	CCONJ
ejpam-6347	472	26	2k3	2k3	NUM
ejpam-6347	472	27	+	+	CCONJ
ejpam-6347	472	28	k4	k4	NOUN
ejpam-6347	472	29	)	)	PUNCT
ejpam-6347	472	30	where	where	SCONJ
ejpam-6347	472	31	h	h	NOUN
ejpam-6347	472	32	represents	represent	VERB
ejpam-6347	472	33	the	the	DET
ejpam-6347	472	34	step	step	NOUN
ejpam-6347	472	35	size	size	NOUN
ejpam-6347	472	36	controlling	control	VERB
ejpam-6347	472	37	temporal	temporal	ADJ
ejpam-6347	472	38	resolution	resolution	NOUN
ejpam-6347	472	39	.	.	PUNCT
ejpam-6347	473	1	the	the	DET
ejpam-6347	473	2	method	method	NOUN
ejpam-6347	473	3	’s	’s	PART
ejpam-6347	473	4	fourthorder	fourthorder	NOUN
ejpam-6347	473	5	accuracy	accuracy	NOUN
ejpam-6347	473	6	makes	make	VERB
ejpam-6347	473	7	it	it	PRON
ejpam-6347	473	8	particularly	particularly	ADV
ejpam-6347	473	9	suitable	suitable	ADJ
ejpam-6347	473	10	for	for	ADP
ejpam-6347	473	11	capturing	capture	VERB
ejpam-6347	473	12	non	non	ADJ
ejpam-6347	473	13	-	-	ADJ
ejpam-6347	473	14	linear	linear	ADJ
ejpam-6347	473	15	epidemiological	epidemiological	ADJ
ejpam-6347	473	16	dynamics	dynamic	NOUN
ejpam-6347	473	17	while	while	SCONJ
ejpam-6347	473	18	maintaining	maintain	VERB
ejpam-6347	473	19	numerical	numerical	ADJ
ejpam-6347	473	20	stability	stability	NOUN
ejpam-6347	473	21	.	.	PUNCT
ejpam-6347	474	1	n.	n.	PROPN
ejpam-6347	474	2	abbas	abbas	PROPN
ejpam-6347	474	3	,	,	PUNCT
ejpam-6347	474	4	w.	w.	PROPN
ejpam-6347	474	5	shatanawi	shatanawi	PROPN
ejpam-6347	474	6	,	,	PUNCT
ejpam-6347	474	7	s.	s.	PROPN
ejpam-6347	474	8	a.	a.	NOUN
ejpam-6347	474	9	zanib	zanib	PROPN
ejpam-6347	474	10	/	/	SYM
ejpam-6347	474	11	eur	eur	PROPN
ejpam-6347	474	12	.	.	PUNCT
ejpam-6347	475	1	j.	j.	PROPN
ejpam-6347	475	2	pure	pure	PROPN
ejpam-6347	475	3	appl	appl	PROPN
ejpam-6347	475	4	.	.	PROPN
ejpam-6347	475	5	math	math	PROPN
ejpam-6347	475	6	,	,	PUNCT
ejpam-6347	475	7	18	18	NUM
ejpam-6347	475	8	(	(	PUNCT
ejpam-6347	475	9	3	3	NUM
ejpam-6347	475	10	)	)	PUNCT
ejpam-6347	475	11	(	(	PUNCT
ejpam-6347	475	12	2025	2025	NUM
ejpam-6347	475	13	)	)	PUNCT
ejpam-6347	475	14	,	,	PUNCT
ejpam-6347	475	15	6347	6347	NUM
ejpam-6347	475	16	25	25	NUM
ejpam-6347	475	17	of	of	ADP
ejpam-6347	475	18	34	34	NUM
ejpam-6347	475	19	0	0	NUM
ejpam-6347	475	20	20	20	NUM
ejpam-6347	475	21	40	40	NUM
ejpam-6347	475	22	60	60	NUM
ejpam-6347	475	23	80	80	NUM
ejpam-6347	475	24	100	100	NUM
ejpam-6347	475	25	days	day	NOUN
ejpam-6347	475	26	(	(	PUNCT
ejpam-6347	475	27	time	time	NOUN
ejpam-6347	475	28	)	)	PUNCT
ejpam-6347	475	29	500	500	NUM
ejpam-6347	475	30	1000	1000	NUM
ejpam-6347	475	31	1500	1500	NUM
ejpam-6347	475	32	2000	2000	NUM
ejpam-6347	475	33	2500	2500	NUM
ejpam-6347	475	34	3000	3000	NUM
ejpam-6347	475	35	in	in	ADP
ejpam-6347	475	36	di	di	X
ejpam-6347	475	37	vi	vi	PROPN
ejpam-6347	475	38	du	du	PROPN
ejpam-6347	475	39	al	al	PROPN
ejpam-6347	475	40	s	s	PROPN
ejpam-6347	475	41	susceptible	susceptible	ADJ
ejpam-6347	475	42	(	(	PUNCT
ejpam-6347	475	43	s	s	NOUN
ejpam-6347	475	44	)	)	PUNCT
ejpam-6347	475	45	0	0	NUM
ejpam-6347	475	46	20	20	NUM
ejpam-6347	475	47	40	40	NUM
ejpam-6347	475	48	60	60	NUM
ejpam-6347	475	49	80	80	NUM
ejpam-6347	475	50	100	100	NUM
ejpam-6347	475	51	days	day	NOUN
ejpam-6347	475	52	(	(	PUNCT
ejpam-6347	475	53	time	time	NOUN
ejpam-6347	475	54	)	)	PUNCT
ejpam-6347	475	55	0.0	0.0	NUM
ejpam-6347	475	56	2.5	2.5	NUM
ejpam-6347	475	57	5.0	5.0	NUM
ejpam-6347	475	58	7.5	7.5	NUM
ejpam-6347	475	59	10.0	10.0	NUM
ejpam-6347	475	60	12.5	12.5	NUM
ejpam-6347	475	61	15.0	15.0	NUM
ejpam-6347	475	62	17.5	17.5	NUM
ejpam-6347	475	63	20.0	20.0	NUM
ejpam-6347	475	64	in	in	ADP
ejpam-6347	475	65	di	di	X
ejpam-6347	475	66	vi	vi	PROPN
ejpam-6347	475	67	du	du	PROPN
ejpam-6347	475	68	al	al	PROPN
ejpam-6347	475	69	s	s	PART
ejpam-6347	475	70	pre	pre	ADJ
ejpam-6347	475	71	-	-	ADJ
ejpam-6347	475	72	symptomatic	symptomatic	ADJ
ejpam-6347	475	73	(	(	PUNCT
ejpam-6347	475	74	e	e	NOUN
ejpam-6347	475	75	)	)	PUNCT
ejpam-6347	475	76	0	0	NUM
ejpam-6347	475	77	20	20	NUM
ejpam-6347	475	78	40	40	NUM
ejpam-6347	475	79	60	60	NUM
ejpam-6347	475	80	80	80	NUM
ejpam-6347	475	81	100	100	NUM
ejpam-6347	475	82	days	day	NOUN
ejpam-6347	475	83	(	(	PUNCT
ejpam-6347	475	84	time	time	NOUN
ejpam-6347	475	85	)	)	PUNCT
ejpam-6347	475	86	4	4	NUM
ejpam-6347	475	87	5	5	NUM
ejpam-6347	475	88	6	6	NUM
ejpam-6347	475	89	7	7	NUM
ejpam-6347	475	90	8	8	NUM
ejpam-6347	475	91	9	9	NUM
ejpam-6347	475	92	10	10	NUM
ejpam-6347	475	93	in	in	ADP
ejpam-6347	475	94	di	di	X
ejpam-6347	475	95	vi	vi	PROPN
ejpam-6347	475	96	du	du	PROPN
ejpam-6347	475	97	al	al	PROPN
ejpam-6347	475	98	s	s	PROPN
ejpam-6347	476	1	infected	infected	ADJ
ejpam-6347	476	2	(	(	PUNCT
ejpam-6347	476	3	u	u	NOUN
ejpam-6347	476	4	)	)	PUNCT
ejpam-6347	476	5	0	0	NUM
ejpam-6347	476	6	20	20	NUM
ejpam-6347	476	7	40	40	NUM
ejpam-6347	476	8	60	60	NUM
ejpam-6347	476	9	80	80	NUM
ejpam-6347	476	10	100	100	NUM
ejpam-6347	476	11	days	day	NOUN
ejpam-6347	476	12	(	(	PUNCT
ejpam-6347	476	13	time	time	NOUN
ejpam-6347	476	14	)	)	PUNCT
ejpam-6347	476	15	10	10	NUM
ejpam-6347	476	16	15	15	NUM
ejpam-6347	476	17	20	20	NUM
ejpam-6347	476	18	25	25	NUM
ejpam-6347	476	19	30	30	NUM
ejpam-6347	476	20	in	in	ADP
ejpam-6347	476	21	di	di	X
ejpam-6347	476	22	vi	vi	PROPN
ejpam-6347	476	23	du	du	PROPN
ejpam-6347	476	24	al	al	PROPN
ejpam-6347	476	25	s	s	PROPN
ejpam-6347	476	26	quarantined	quarantined	ADJ
ejpam-6347	476	27	(	(	PUNCT
ejpam-6347	476	28	q	q	NOUN
ejpam-6347	476	29	)	)	PUNCT
ejpam-6347	476	30	0	0	NUM
ejpam-6347	476	31	20	20	NUM
ejpam-6347	476	32	40	40	NUM
ejpam-6347	476	33	60	60	NUM
ejpam-6347	476	34	80	80	NUM
ejpam-6347	476	35	100	100	NUM
ejpam-6347	476	36	days	day	NOUN
ejpam-6347	476	37	(	(	PUNCT
ejpam-6347	476	38	time	time	NOUN
ejpam-6347	476	39	)	)	PUNCT
ejpam-6347	476	40	2	2	NUM
ejpam-6347	476	41	3	3	NUM
ejpam-6347	476	42	4	4	NUM
ejpam-6347	476	43	5	5	NUM
ejpam-6347	476	44	6	6	NUM
ejpam-6347	476	45	in	in	ADP
ejpam-6347	476	46	di	di	X
ejpam-6347	476	47	vi	vi	PROPN
ejpam-6347	476	48	du	du	PROPN
ejpam-6347	476	49	al	al	PROPN
ejpam-6347	476	50	s	s	PROPN
ejpam-6347	476	51	clinically	clinically	ADV
ejpam-6347	476	52	positive	positive	ADJ
ejpam-6347	476	53	(	(	PUNCT
ejpam-6347	476	54	p	p	NOUN
ejpam-6347	476	55	)	)	PUNCT
ejpam-6347	476	56	0	0	NUM
ejpam-6347	476	57	20	20	NUM
ejpam-6347	476	58	40	40	NUM
ejpam-6347	476	59	60	60	NUM
ejpam-6347	476	60	80	80	NUM
ejpam-6347	476	61	100	100	NUM
ejpam-6347	476	62	days	day	NOUN
ejpam-6347	476	63	(	(	PUNCT
ejpam-6347	476	64	time	time	NOUN
ejpam-6347	476	65	)	)	PUNCT
ejpam-6347	476	66	0.0	0.0	NUM
ejpam-6347	476	67	0.5	0.5	NUM
ejpam-6347	476	68	1.0	1.0	NUM
ejpam-6347	476	69	1.5	1.5	NUM
ejpam-6347	476	70	2.0	2.0	NUM
ejpam-6347	476	71	2.5	2.5	NUM
ejpam-6347	476	72	3.0	3.0	NUM
ejpam-6347	476	73	3.5	3.5	NUM
ejpam-6347	476	74	4.0	4.0	NUM
ejpam-6347	476	75	in	in	ADP
ejpam-6347	476	76	di	di	X
ejpam-6347	476	77	vi	vi	PROPN
ejpam-6347	476	78	du	du	PROPN
ejpam-6347	476	79	al	al	PROPN
ejpam-6347	476	80	s	s	PROPN
ejpam-6347	476	81	hospitalized	hospitalize	VERB
ejpam-6347	476	82	(	(	PUNCT
ejpam-6347	476	83	h	h	NOUN
ejpam-6347	476	84	)	)	PUNCT
ejpam-6347	476	85	0	0	NUM
ejpam-6347	476	86	20	20	NUM
ejpam-6347	476	87	40	40	NUM
ejpam-6347	476	88	60	60	NUM
ejpam-6347	476	89	80	80	NUM
ejpam-6347	476	90	100	100	NUM
ejpam-6347	476	91	days	day	NOUN
ejpam-6347	476	92	(	(	PUNCT
ejpam-6347	476	93	time	time	NOUN
ejpam-6347	476	94	)	)	PUNCT
ejpam-6347	476	95	1.3	1.3	NUM
ejpam-6347	476	96	1.4	1.4	NUM
ejpam-6347	476	97	1.5	1.5	NUM
ejpam-6347	476	98	1.6	1.6	NUM
ejpam-6347	476	99	1.7	1.7	NUM
ejpam-6347	476	100	1.8	1.8	NUM
ejpam-6347	476	101	1.9	1.9	NUM
ejpam-6347	476	102	2.0	2.0	NUM
ejpam-6347	476	103	in	in	ADP
ejpam-6347	476	104	di	di	X
ejpam-6347	476	105	vi	vi	PROPN
ejpam-6347	476	106	du	du	PROPN
ejpam-6347	476	107	al	al	PROPN
ejpam-6347	476	108	s	s	PROPN
ejpam-6347	476	109	asymptomatic	asymptomatic	ADJ
ejpam-6347	476	110	(	(	PUNCT
ejpam-6347	476	111	f	f	X
ejpam-6347	476	112	)	)	PUNCT
ejpam-6347	476	113	0	0	NUM
ejpam-6347	476	114	20	20	NUM
ejpam-6347	476	115	40	40	NUM
ejpam-6347	476	116	60	60	NUM
ejpam-6347	476	117	80	80	NUM
ejpam-6347	476	118	100	100	NUM
ejpam-6347	476	119	days	day	NOUN
ejpam-6347	476	120	(	(	PUNCT
ejpam-6347	476	121	time	time	NOUN
ejpam-6347	476	122	)	)	PUNCT
ejpam-6347	476	123	0.5	0.5	NUM
ejpam-6347	476	124	0.6	0.6	NUM
ejpam-6347	476	125	0.7	0.7	NUM
ejpam-6347	476	126	0.8	0.8	NUM
ejpam-6347	476	127	0.9	0.9	NUM
ejpam-6347	476	128	1.0	1.0	NUM
ejpam-6347	476	129	in	in	ADP
ejpam-6347	476	130	di	di	X
ejpam-6347	476	131	vi	vi	PROPN
ejpam-6347	476	132	du	du	PROPN
ejpam-6347	476	133	al	al	PROPN
ejpam-6347	476	134	s	s	PROPN
ejpam-6347	476	135	icu	icu	PROPN
ejpam-6347	476	136	(	(	PUNCT
ejpam-6347	476	137	c	c	NOUN
ejpam-6347	476	138	)	)	PUNCT
ejpam-6347	476	139	0	0	NUM
ejpam-6347	476	140	20	20	NUM
ejpam-6347	476	141	40	40	NUM
ejpam-6347	476	142	60	60	NUM
ejpam-6347	476	143	80	80	NUM
ejpam-6347	476	144	100	100	NUM
ejpam-6347	476	145	days	day	NOUN
ejpam-6347	476	146	(	(	PUNCT
ejpam-6347	476	147	time	time	NOUN
ejpam-6347	476	148	)	)	PUNCT
ejpam-6347	476	149	0	0	NUM
ejpam-6347	476	150	5	5	NUM
ejpam-6347	476	151	10	10	NUM
ejpam-6347	476	152	15	15	NUM
ejpam-6347	476	153	20	20	NUM
ejpam-6347	476	154	25	25	NUM
ejpam-6347	476	155	30	30	NUM
ejpam-6347	476	156	in	in	ADP
ejpam-6347	476	157	di	di	X
ejpam-6347	476	158	vi	vi	PROPN
ejpam-6347	476	159	du	du	PROPN
ejpam-6347	476	160	al	al	PROPN
ejpam-6347	476	161	s	s	PROPN
ejpam-6347	476	162	vaccinated	vaccinated	ADJ
ejpam-6347	476	163	(	(	PUNCT
ejpam-6347	476	164	v	v	NOUN
ejpam-6347	476	165	)	)	PUNCT
ejpam-6347	476	166	0	0	NUM
ejpam-6347	476	167	20	20	NUM
ejpam-6347	476	168	40	40	NUM
ejpam-6347	476	169	60	60	NUM
ejpam-6347	476	170	80	80	NUM
ejpam-6347	476	171	100	100	NUM
ejpam-6347	476	172	days	day	NOUN
ejpam-6347	476	173	(	(	PUNCT
ejpam-6347	476	174	time	time	NOUN
ejpam-6347	476	175	)	)	PUNCT
ejpam-6347	476	176	0.0	0.0	NUM
ejpam-6347	476	177	0.5	0.5	NUM
ejpam-6347	476	178	1.0	1.0	NUM
ejpam-6347	476	179	1.5	1.5	NUM
ejpam-6347	476	180	2.0	2.0	NUM
ejpam-6347	476	181	2.5	2.5	NUM
ejpam-6347	476	182	3.0	3.0	NUM
ejpam-6347	476	183	in	in	ADP
ejpam-6347	476	184	di	di	X
ejpam-6347	476	185	vi	vi	PROPN
ejpam-6347	476	186	du	du	PROPN
ejpam-6347	476	187	al	al	PROPN
ejpam-6347	476	188	s	s	PROPN
ejpam-6347	476	189	recovered	recover	VERB
ejpam-6347	476	190	(	(	PUNCT
ejpam-6347	476	191	r	r	NOUN
ejpam-6347	476	192	)	)	PUNCT
ejpam-6347	476	193	figure	figure	NOUN
ejpam-6347	476	194	5	5	NUM
ejpam-6347	476	195	:	:	PUNCT
ejpam-6347	476	196	time	time	NOUN
ejpam-6347	476	197	series	series	PROPN
ejpam-6347	476	198	behavior	behavior	NOUN
ejpam-6347	476	199	of	of	ADP
ejpam-6347	476	200	covid-19	covid-19	PROPN
ejpam-6347	476	201	model	model	NOUN
ejpam-6347	476	202	using	use	VERB
ejpam-6347	476	203	rk4	rk4	NOUN
ejpam-6347	476	204	method	method	NOUN
ejpam-6347	476	205	the	the	DET
ejpam-6347	476	206	figure	figure	NOUN
ejpam-6347	476	207	5	5	NUM
ejpam-6347	476	208	highlight	highlight	VERB
ejpam-6347	476	209	the	the	DET
ejpam-6347	476	210	dynamic	dynamic	ADJ
ejpam-6347	476	211	evolution	evolution	NOUN
ejpam-6347	476	212	of	of	ADP
ejpam-6347	476	213	the	the	DET
ejpam-6347	476	214	different	different	ADJ
ejpam-6347	476	215	compartments	compartment	NOUN
ejpam-6347	476	216	in	in	ADP
ejpam-6347	476	217	the	the	DET
ejpam-6347	476	218	covcom10	covcom10	NOUN
ejpam-6347	476	219	model	model	NOUN
ejpam-6347	476	220	.	.	PUNCT
ejpam-6347	477	1	the	the	DET
ejpam-6347	477	2	susceptible	susceptible	ADJ
ejpam-6347	477	3	population	population	NOUN
ejpam-6347	477	4	increases	increase	VERB
ejpam-6347	477	5	over	over	ADP
ejpam-6347	477	6	time	time	NOUN
ejpam-6347	477	7	,	,	PUNCT
ejpam-6347	477	8	possibly	possibly	ADV
ejpam-6347	477	9	due	due	ADP
ejpam-6347	477	10	to	to	ADP
ejpam-6347	477	11	natural	natural	ADJ
ejpam-6347	477	12	recruitment	recruitment	NOUN
ejpam-6347	477	13	or	or	CCONJ
ejpam-6347	477	14	effective	effective	ADJ
ejpam-6347	477	15	preventive	preventive	ADJ
ejpam-6347	477	16	measures	measure	NOUN
ejpam-6347	477	17	reducing	reduce	VERB
ejpam-6347	477	18	disease	disease	NOUN
ejpam-6347	477	19	transmission	transmission	NOUN
ejpam-6347	477	20	.	.	PUNCT
ejpam-6347	478	1	the	the	DET
ejpam-6347	478	2	exposed	expose	VERB
ejpam-6347	478	3	and	and	CCONJ
ejpam-6347	478	4	pre	pre	ADJ
ejpam-6347	478	5	-	-	ADJ
ejpam-6347	478	6	symptomatic	symptomatic	ADJ
ejpam-6347	478	7	populations	population	NOUN
ejpam-6347	478	8	decrease	decrease	NOUN
ejpam-6347	478	9	,	,	PUNCT
ejpam-6347	478	10	indicating	indicate	VERB
ejpam-6347	478	11	early	early	ADJ
ejpam-6347	478	12	identification	identification	NOUN
ejpam-6347	478	13	and	and	CCONJ
ejpam-6347	478	14	isolation	isolation	NOUN
ejpam-6347	478	15	of	of	ADP
ejpam-6347	478	16	cases	case	NOUN
ejpam-6347	478	17	,	,	PUNCT
ejpam-6347	478	18	which	which	PRON
ejpam-6347	478	19	helps	help	VERB
ejpam-6347	478	20	prevent	prevent	VERB
ejpam-6347	478	21	further	further	ADJ
ejpam-6347	478	22	spread	spread	NOUN
ejpam-6347	478	23	.	.	PUNCT
ejpam-6347	479	1	the	the	DET
ejpam-6347	479	2	infected	infected	ADJ
ejpam-6347	479	3	and	and	CCONJ
ejpam-6347	479	4	clinically	clinically	ADV
ejpam-6347	479	5	positive	positive	ADJ
ejpam-6347	479	6	individuals	individual	NOUN
ejpam-6347	479	7	show	show	VERB
ejpam-6347	479	8	a	a	DET
ejpam-6347	479	9	gradual	gradual	ADJ
ejpam-6347	479	10	decline	decline	NOUN
ejpam-6347	479	11	,	,	PUNCT
ejpam-6347	479	12	suggesting	suggest	VERB
ejpam-6347	479	13	that	that	SCONJ
ejpam-6347	479	14	the	the	DET
ejpam-6347	479	15	disease	disease	NOUN
ejpam-6347	479	16	is	be	AUX
ejpam-6347	479	17	being	be	AUX
ejpam-6347	479	18	controlled	control	VERB
ejpam-6347	479	19	through	through	ADP
ejpam-6347	479	20	diagnosis	diagnosis	NOUN
ejpam-6347	479	21	,	,	PUNCT
ejpam-6347	479	22	treatment	treatment	NOUN
ejpam-6347	479	23	,	,	PUNCT
ejpam-6347	479	24	and	and	CCONJ
ejpam-6347	479	25	isolation	isolation	NOUN
ejpam-6347	479	26	.	.	PUNCT
ejpam-6347	480	1	the	the	DET
ejpam-6347	480	2	quarantined	quarantined	ADJ
ejpam-6347	480	3	population	population	NOUN
ejpam-6347	480	4	initially	initially	ADV
ejpam-6347	480	5	rises	rise	VERB
ejpam-6347	480	6	and	and	CCONJ
ejpam-6347	480	7	then	then	ADV
ejpam-6347	480	8	falls	fall	VERB
ejpam-6347	480	9	,	,	PUNCT
ejpam-6347	480	10	reflecting	reflect	VERB
ejpam-6347	480	11	efficient	efficient	ADJ
ejpam-6347	480	12	identification	identification	NOUN
ejpam-6347	480	13	and	and	CCONJ
ejpam-6347	480	14	management	management	NOUN
ejpam-6347	480	15	of	of	ADP
ejpam-6347	480	16	at	at	ADP
ejpam-6347	480	17	-	-	PUNCT
ejpam-6347	480	18	risk	risk	NOUN
ejpam-6347	480	19	individuals	individual	NOUN
ejpam-6347	480	20	.	.	PUNCT
ejpam-6347	481	1	a	a	DET
ejpam-6347	481	2	continuous	continuous	ADJ
ejpam-6347	481	3	decrease	decrease	NOUN
ejpam-6347	481	4	in	in	ADP
ejpam-6347	481	5	hospitalized	hospitalize	VERB
ejpam-6347	481	6	and	and	CCONJ
ejpam-6347	481	7	icu	icu	PROPN
ejpam-6347	481	8	cases	case	NOUN
ejpam-6347	481	9	demonstrates	demonstrate	VERB
ejpam-6347	481	10	effective	effective	ADJ
ejpam-6347	481	11	healthcare	healthcare	NOUN
ejpam-6347	481	12	response	response	NOUN
ejpam-6347	481	13	,	,	PUNCT
ejpam-6347	481	14	while	while	SCONJ
ejpam-6347	481	15	the	the	DET
ejpam-6347	481	16	asymptomatic	asymptomatic	ADJ
ejpam-6347	481	17	population	population	NOUN
ejpam-6347	481	18	also	also	ADV
ejpam-6347	481	19	declines	decline	VERB
ejpam-6347	481	20	,	,	PUNCT
ejpam-6347	481	21	possibly	possibly	ADV
ejpam-6347	481	22	due	due	ADP
ejpam-6347	481	23	to	to	ADP
ejpam-6347	481	24	detection	detection	NOUN
ejpam-6347	481	25	and	and	CCONJ
ejpam-6347	481	26	reclassification	reclassification	NOUN
ejpam-6347	481	27	into	into	ADP
ejpam-6347	481	28	other	other	ADJ
ejpam-6347	481	29	compartments	compartment	NOUN
ejpam-6347	481	30	.	.	PUNCT
ejpam-6347	482	1	the	the	DET
ejpam-6347	482	2	vaccinated	vaccinated	ADJ
ejpam-6347	482	3	population	population	NOUN
ejpam-6347	482	4	shows	show	VERB
ejpam-6347	482	5	a	a	DET
ejpam-6347	482	6	consistent	consistent	ADJ
ejpam-6347	482	7	increase	increase	NOUN
ejpam-6347	482	8	,	,	PUNCT
ejpam-6347	482	9	playing	play	VERB
ejpam-6347	482	10	a	a	DET
ejpam-6347	482	11	critical	critical	ADJ
ejpam-6347	482	12	role	role	NOUN
ejpam-6347	482	13	in	in	ADP
ejpam-6347	482	14	protecting	protect	VERB
ejpam-6347	482	15	susceptible	susceptible	ADJ
ejpam-6347	482	16	individuals	individual	NOUN
ejpam-6347	482	17	and	and	CCONJ
ejpam-6347	482	18	limiting	limit	VERB
ejpam-6347	482	19	transmission	transmission	NOUN
ejpam-6347	482	20	.	.	PUNCT
ejpam-6347	483	1	the	the	DET
ejpam-6347	483	2	recovered	recovered	ADJ
ejpam-6347	483	3	population	population	NOUN
ejpam-6347	483	4	increases	increase	NOUN
ejpam-6347	483	5	initially	initially	ADV
ejpam-6347	483	6	and	and	CCONJ
ejpam-6347	483	7	then	then	ADV
ejpam-6347	483	8	stabilizes	stabilize	VERB
ejpam-6347	483	9	,	,	PUNCT
ejpam-6347	483	10	indicating	indicate	VERB
ejpam-6347	483	11	successful	successful	ADJ
ejpam-6347	483	12	treatment	treatment	NOUN
ejpam-6347	483	13	and	and	CCONJ
ejpam-6347	483	14	acquired	acquire	VERB
ejpam-6347	483	15	immunity	immunity	NOUN
ejpam-6347	483	16	among	among	ADP
ejpam-6347	483	17	the	the	DET
ejpam-6347	483	18	affected	affected	ADJ
ejpam-6347	483	19	individuals	individual	NOUN
ejpam-6347	483	20	.	.	PUNCT
ejpam-6347	484	1	overall	overall	ADV
ejpam-6347	484	2	,	,	PUNCT
ejpam-6347	484	3	these	these	DET
ejpam-6347	484	4	results	result	NOUN
ejpam-6347	484	5	emphasize	emphasize	VERB
ejpam-6347	484	6	the	the	DET
ejpam-6347	484	7	imporn	imporn	PROPN
ejpam-6347	484	8	.	.	PUNCT
ejpam-6347	484	9	abbas	abbas	PROPN
ejpam-6347	484	10	,	,	PUNCT
ejpam-6347	484	11	w.	w.	PROPN
ejpam-6347	484	12	shatanawi	shatanawi	PROPN
ejpam-6347	484	13	,	,	PUNCT
ejpam-6347	484	14	s.	s.	PROPN
ejpam-6347	484	15	a.	a.	NOUN
ejpam-6347	484	16	zanib	zanib	PROPN
ejpam-6347	484	17	/	/	SYM
ejpam-6347	484	18	eur	eur	PROPN
ejpam-6347	484	19	.	.	PUNCT
ejpam-6347	485	1	j.	j.	PROPN
ejpam-6347	485	2	pure	pure	PROPN
ejpam-6347	485	3	appl	appl	PROPN
ejpam-6347	485	4	.	.	PROPN
ejpam-6347	485	5	math	math	PROPN
ejpam-6347	485	6	,	,	PUNCT
ejpam-6347	485	7	18	18	NUM
ejpam-6347	485	8	(	(	PUNCT
ejpam-6347	485	9	3	3	NUM
ejpam-6347	485	10	)	)	PUNCT
ejpam-6347	485	11	(	(	PUNCT
ejpam-6347	485	12	2025	2025	NUM
ejpam-6347	485	13	)	)	PUNCT
ejpam-6347	485	14	,	,	PUNCT
ejpam-6347	485	15	6347	6347	NUM
ejpam-6347	485	16	26	26	NUM
ejpam-6347	485	17	of	of	ADP
ejpam-6347	485	18	34	34	NUM
ejpam-6347	485	19	tance	tance	NOUN
ejpam-6347	485	20	of	of	ADP
ejpam-6347	485	21	timely	timely	ADJ
ejpam-6347	485	22	public	public	ADJ
ejpam-6347	485	23	health	health	NOUN
ejpam-6347	485	24	interventions	intervention	NOUN
ejpam-6347	485	25	—	—	PUNCT
ejpam-6347	485	26	such	such	ADJ
ejpam-6347	485	27	as	as	ADP
ejpam-6347	485	28	vaccination	vaccination	NOUN
ejpam-6347	485	29	,	,	PUNCT
ejpam-6347	485	30	quarantine	quarantine	NOUN
ejpam-6347	485	31	,	,	PUNCT
ejpam-6347	485	32	treatment	treatment	NOUN
ejpam-6347	485	33	,	,	PUNCT
ejpam-6347	485	34	and	and	CCONJ
ejpam-6347	485	35	healthcare	healthcare	NOUN
ejpam-6347	485	36	support	support	NOUN
ejpam-6347	485	37	—	—	PUNCT
ejpam-6347	485	38	in	in	ADP
ejpam-6347	485	39	curbing	curb	VERB
ejpam-6347	485	40	the	the	DET
ejpam-6347	485	41	spread	spread	NOUN
ejpam-6347	485	42	of	of	ADP
ejpam-6347	485	43	infection	infection	NOUN
ejpam-6347	485	44	and	and	CCONJ
ejpam-6347	485	45	improving	improve	VERB
ejpam-6347	485	46	population	population	NOUN
ejpam-6347	485	47	-	-	PUNCT
ejpam-6347	485	48	level	level	NOUN
ejpam-6347	485	49	health	health	NOUN
ejpam-6347	485	50	outcomes	outcome	NOUN
ejpam-6347	485	51	.	.	PUNCT
ejpam-6347	486	1	0	0	NUM
ejpam-6347	486	2	20	20	NUM
ejpam-6347	486	3	40	40	NUM
ejpam-6347	486	4	60	60	NUM
ejpam-6347	486	5	80	80	NUM
ejpam-6347	486	6	100	100	NUM
ejpam-6347	486	7	days	day	NOUN
ejpam-6347	486	8	500	500	NUM
ejpam-6347	486	9	1000	1000	NUM
ejpam-6347	486	10	1500	1500	NUM
ejpam-6347	486	11	2000	2000	NUM
ejpam-6347	486	12	2500	2500	NUM
ejpam-6347	486	13	3000	3000	NUM
ejpam-6347	486	14	3500	3500	NUM
ejpam-6347	486	15	in	in	ADP
ejpam-6347	486	16	di	di	X
ejpam-6347	486	17	vi	vi	PROPN
ejpam-6347	486	18	du	du	PROPN
ejpam-6347	486	19	al	al	PROPN
ejpam-6347	486	20	s	s	PROPN
ejpam-6347	486	21	susceptible	susceptible	ADJ
ejpam-6347	486	22	(	(	PUNCT
ejpam-6347	486	23	s	s	NOUN
ejpam-6347	486	24	)	)	PUNCT
ejpam-6347	486	25	small	small	ADJ
ejpam-6347	486	26	scale	scale	NOUN
ejpam-6347	486	27	large	large	ADJ
ejpam-6347	486	28	scale	scale	NOUN
ejpam-6347	486	29	0	0	NUM
ejpam-6347	486	30	20	20	NUM
ejpam-6347	486	31	40	40	NUM
ejpam-6347	486	32	60	60	NUM
ejpam-6347	486	33	80	80	NUM
ejpam-6347	486	34	100	100	NUM
ejpam-6347	486	35	days	day	NOUN
ejpam-6347	486	36	0	0	NUM
ejpam-6347	486	37	10	10	NUM
ejpam-6347	486	38	20	20	NUM
ejpam-6347	486	39	30	30	NUM
ejpam-6347	486	40	40	40	NUM
ejpam-6347	486	41	50	50	NUM
ejpam-6347	486	42	60	60	NUM
ejpam-6347	486	43	70	70	NUM
ejpam-6347	486	44	80	80	NUM
ejpam-6347	486	45	in	in	ADP
ejpam-6347	486	46	di	di	X
ejpam-6347	486	47	vi	vi	PROPN
ejpam-6347	486	48	du	du	PROPN
ejpam-6347	486	49	al	al	PROPN
ejpam-6347	486	50	s	s	PART
ejpam-6347	486	51	pre	pre	ADJ
ejpam-6347	486	52	-	-	ADJ
ejpam-6347	486	53	symptomatic	symptomatic	ADJ
ejpam-6347	486	54	(	(	PUNCT
ejpam-6347	486	55	e	e	NOUN
ejpam-6347	486	56	)	)	PUNCT
ejpam-6347	486	57	small	small	ADJ
ejpam-6347	486	58	scale	scale	NOUN
ejpam-6347	486	59	large	large	ADJ
ejpam-6347	486	60	scale	scale	NOUN
ejpam-6347	486	61	0	0	NUM
ejpam-6347	486	62	20	20	NUM
ejpam-6347	486	63	40	40	NUM
ejpam-6347	486	64	60	60	NUM
ejpam-6347	486	65	80	80	NUM
ejpam-6347	486	66	100	100	NUM
ejpam-6347	486	67	days	day	NOUN
ejpam-6347	486	68	10	10	NUM
ejpam-6347	486	69	20	20	NUM
ejpam-6347	486	70	30	30	NUM
ejpam-6347	486	71	40	40	NUM
ejpam-6347	486	72	50	50	NUM
ejpam-6347	486	73	60	60	NUM
ejpam-6347	486	74	in	in	ADP
ejpam-6347	486	75	di	di	X
ejpam-6347	486	76	vi	vi	PROPN
ejpam-6347	486	77	du	du	PROPN
ejpam-6347	486	78	al	al	PROPN
ejpam-6347	486	79	s	s	PROPN
ejpam-6347	486	80	infected	infected	ADJ
ejpam-6347	486	81	(	(	PUNCT
ejpam-6347	486	82	u	u	NOUN
ejpam-6347	486	83	)	)	PUNCT
ejpam-6347	486	84	small	small	ADJ
ejpam-6347	486	85	scale	scale	NOUN
ejpam-6347	486	86	large	large	ADJ
ejpam-6347	486	87	scale	scale	NOUN
ejpam-6347	486	88	0	0	NUM
ejpam-6347	486	89	20	20	NUM
ejpam-6347	486	90	40	40	NUM
ejpam-6347	486	91	60	60	NUM
ejpam-6347	486	92	80	80	NUM
ejpam-6347	486	93	100	100	NUM
ejpam-6347	486	94	days	day	NOUN
ejpam-6347	486	95	20	20	NUM
ejpam-6347	486	96	40	40	NUM
ejpam-6347	486	97	60	60	NUM
ejpam-6347	486	98	80	80	NUM
ejpam-6347	486	99	100	100	NUM
ejpam-6347	486	100	120	120	NUM
ejpam-6347	486	101	in	in	ADP
ejpam-6347	486	102	di	di	X
ejpam-6347	486	103	vi	vi	PROPN
ejpam-6347	486	104	du	du	PROPN
ejpam-6347	486	105	al	al	PROPN
ejpam-6347	486	106	s	s	PROPN
ejpam-6347	486	107	quarantined	quarantined	X
ejpam-6347	486	108	(	(	PUNCT
ejpam-6347	486	109	q	q	NOUN
ejpam-6347	486	110	)	)	PUNCT
ejpam-6347	486	111	small	small	ADJ
ejpam-6347	486	112	scale	scale	NOUN
ejpam-6347	486	113	large	large	ADJ
ejpam-6347	486	114	scale	scale	NOUN
ejpam-6347	486	115	0	0	NUM
ejpam-6347	486	116	20	20	NUM
ejpam-6347	486	117	40	40	NUM
ejpam-6347	486	118	60	60	NUM
ejpam-6347	486	119	80	80	NUM
ejpam-6347	486	120	100	100	NUM
ejpam-6347	486	121	days	day	NOUN
ejpam-6347	486	122	0	0	NUM
ejpam-6347	486	123	5	5	NUM
ejpam-6347	486	124	10	10	NUM
ejpam-6347	486	125	15	15	NUM
ejpam-6347	486	126	20	20	NUM
ejpam-6347	486	127	25	25	NUM
ejpam-6347	486	128	30	30	NUM
ejpam-6347	486	129	in	in	ADP
ejpam-6347	486	130	di	di	X
ejpam-6347	486	131	vi	vi	PROPN
ejpam-6347	486	132	du	du	PROPN
ejpam-6347	486	133	al	al	PROPN
ejpam-6347	486	134	s	s	PROPN
ejpam-6347	486	135	clinically	clinically	ADV
ejpam-6347	486	136	positive	positive	ADJ
ejpam-6347	486	137	(	(	PUNCT
ejpam-6347	486	138	p	p	NOUN
ejpam-6347	486	139	)	)	PUNCT
ejpam-6347	486	140	small	small	ADJ
ejpam-6347	486	141	scale	scale	NOUN
ejpam-6347	486	142	large	large	ADJ
ejpam-6347	486	143	scale	scale	NOUN
ejpam-6347	486	144	0	0	NUM
ejpam-6347	486	145	20	20	NUM
ejpam-6347	486	146	40	40	NUM
ejpam-6347	486	147	60	60	NUM
ejpam-6347	486	148	80	80	NUM
ejpam-6347	486	149	100	100	NUM
ejpam-6347	486	150	days	day	NOUN
ejpam-6347	486	151	0.0	0.0	NUM
ejpam-6347	486	152	2.5	2.5	NUM
ejpam-6347	486	153	5.0	5.0	NUM
ejpam-6347	486	154	7.5	7.5	NUM
ejpam-6347	486	155	10.0	10.0	NUM
ejpam-6347	486	156	12.5	12.5	NUM
ejpam-6347	486	157	15.0	15.0	NUM
ejpam-6347	486	158	17.5	17.5	NUM
ejpam-6347	486	159	20.0	20.0	NUM
ejpam-6347	486	160	in	in	ADP
ejpam-6347	486	161	di	di	X
ejpam-6347	486	162	vi	vi	PROPN
ejpam-6347	486	163	du	du	PROPN
ejpam-6347	486	164	al	al	PROPN
ejpam-6347	486	165	s	s	PROPN
ejpam-6347	486	166	hospitalized	hospitalize	VERB
ejpam-6347	486	167	(	(	PUNCT
ejpam-6347	486	168	h	h	NOUN
ejpam-6347	486	169	)	)	PUNCT
ejpam-6347	486	170	small	small	ADJ
ejpam-6347	486	171	scale	scale	NOUN
ejpam-6347	486	172	large	large	ADJ
ejpam-6347	486	173	scale	scale	NOUN
ejpam-6347	486	174	0	0	NUM
ejpam-6347	486	175	20	20	NUM
ejpam-6347	486	176	40	40	NUM
ejpam-6347	486	177	60	60	NUM
ejpam-6347	486	178	80	80	NUM
ejpam-6347	486	179	100	100	NUM
ejpam-6347	486	180	days	day	NOUN
ejpam-6347	486	181	0	0	NUM
ejpam-6347	486	182	2	2	NUM
ejpam-6347	486	183	4	4	NUM
ejpam-6347	486	184	6	6	NUM
ejpam-6347	486	185	8	8	NUM
ejpam-6347	486	186	10	10	NUM
ejpam-6347	486	187	in	in	ADP
ejpam-6347	486	188	di	di	X
ejpam-6347	486	189	vi	vi	PROPN
ejpam-6347	486	190	du	du	PROPN
ejpam-6347	486	191	al	al	PROPN
ejpam-6347	486	192	s	s	PROPN
ejpam-6347	486	193	icu	icu	PROPN
ejpam-6347	486	194	(	(	PUNCT
ejpam-6347	486	195	c	c	NOUN
ejpam-6347	486	196	)	)	PUNCT
ejpam-6347	486	197	small	small	ADJ
ejpam-6347	486	198	scale	scale	NOUN
ejpam-6347	486	199	large	large	ADJ
ejpam-6347	486	200	scale	scale	NOUN
ejpam-6347	486	201	0	0	NUM
ejpam-6347	486	202	20	20	NUM
ejpam-6347	486	203	40	40	NUM
ejpam-6347	486	204	60	60	NUM
ejpam-6347	486	205	80	80	NUM
ejpam-6347	486	206	100	100	NUM
ejpam-6347	486	207	days	day	NOUN
ejpam-6347	486	208	0	0	NUM
ejpam-6347	486	209	2	2	NUM
ejpam-6347	486	210	4	4	NUM
ejpam-6347	486	211	6	6	NUM
ejpam-6347	486	212	8	8	NUM
ejpam-6347	486	213	10	10	NUM
ejpam-6347	486	214	in	in	ADP
ejpam-6347	486	215	di	di	X
ejpam-6347	486	216	vi	vi	PROPN
ejpam-6347	486	217	du	du	PROPN
ejpam-6347	486	218	al	al	PROPN
ejpam-6347	486	219	s	s	PROPN
ejpam-6347	486	220	asymptomatic	asymptomatic	ADJ
ejpam-6347	486	221	(	(	PUNCT
ejpam-6347	486	222	f	f	X
ejpam-6347	486	223	)	)	PUNCT
ejpam-6347	486	224	small	small	ADJ
ejpam-6347	486	225	scale	scale	NOUN
ejpam-6347	486	226	large	large	ADJ
ejpam-6347	486	227	scale	scale	NOUN
ejpam-6347	486	228	0	0	NUM
ejpam-6347	486	229	20	20	NUM
ejpam-6347	486	230	40	40	NUM
ejpam-6347	486	231	60	60	NUM
ejpam-6347	486	232	80	80	NUM
ejpam-6347	486	233	100	100	NUM
ejpam-6347	486	234	days	day	NOUN
ejpam-6347	486	235	0	0	NUM
ejpam-6347	486	236	5	5	NUM
ejpam-6347	486	237	10	10	NUM
ejpam-6347	486	238	15	15	NUM
ejpam-6347	486	239	20	20	NUM
ejpam-6347	486	240	25	25	NUM
ejpam-6347	486	241	30	30	NUM
ejpam-6347	486	242	35	35	NUM
ejpam-6347	486	243	in	in	ADP
ejpam-6347	486	244	di	di	X
ejpam-6347	486	245	vi	vi	PROPN
ejpam-6347	486	246	du	du	PROPN
ejpam-6347	486	247	al	al	PROPN
ejpam-6347	486	248	s	s	PROPN
ejpam-6347	486	249	vaccinated	vaccinated	ADJ
ejpam-6347	486	250	(	(	PUNCT
ejpam-6347	486	251	v	v	NOUN
ejpam-6347	486	252	)	)	PUNCT
ejpam-6347	486	253	small	small	ADJ
ejpam-6347	486	254	scale	scale	NOUN
ejpam-6347	486	255	large	large	ADJ
ejpam-6347	486	256	scale	scale	NOUN
ejpam-6347	486	257	0	0	NUM
ejpam-6347	486	258	20	20	NUM
ejpam-6347	486	259	40	40	NUM
ejpam-6347	486	260	60	60	NUM
ejpam-6347	486	261	80	80	NUM
ejpam-6347	486	262	100	100	NUM
ejpam-6347	486	263	days	day	NOUN
ejpam-6347	486	264	0	0	NUM
ejpam-6347	486	265	2	2	NUM
ejpam-6347	486	266	4	4	NUM
ejpam-6347	486	267	6	6	NUM
ejpam-6347	486	268	8	8	NUM
ejpam-6347	486	269	10	10	NUM
ejpam-6347	486	270	12	12	NUM
ejpam-6347	486	271	14	14	NUM
ejpam-6347	486	272	in	in	ADP
ejpam-6347	486	273	di	di	X
ejpam-6347	486	274	vi	vi	PROPN
ejpam-6347	486	275	du	du	PROPN
ejpam-6347	486	276	al	al	PROPN
ejpam-6347	486	277	s	s	PROPN
ejpam-6347	486	278	recovered	recover	VERB
ejpam-6347	486	279	(	(	PUNCT
ejpam-6347	486	280	r	r	NOUN
ejpam-6347	486	281	)	)	PUNCT
ejpam-6347	486	282	small	small	ADJ
ejpam-6347	486	283	scale	scale	NOUN
ejpam-6347	486	284	large	large	ADJ
ejpam-6347	486	285	scale	scale	NOUN
ejpam-6347	486	286	figure	figure	NOUN
ejpam-6347	486	287	6	6	NUM
ejpam-6347	486	288	:	:	PUNCT
ejpam-6347	486	289	comparison	comparison	NOUN
ejpam-6347	486	290	of	of	ADP
ejpam-6347	486	291	model	model	NOUN
ejpam-6347	486	292	dynamics	dynamic	NOUN
ejpam-6347	486	293	under	under	ADP
ejpam-6347	486	294	smalland	smalland	NOUN
ejpam-6347	486	295	large	large	ADJ
ejpam-6347	486	296	-	-	PUNCT
ejpam-6347	486	297	scale	scale	NOUN
ejpam-6347	486	298	population	population	NOUN
ejpam-6347	486	299	settings	setting	NOUN
ejpam-6347	486	300	.	.	PUNCT
ejpam-6347	487	1	to	to	PART
ejpam-6347	487	2	evaluate	evaluate	VERB
ejpam-6347	487	3	the	the	DET
ejpam-6347	487	4	robustness	robustness	NOUN
ejpam-6347	487	5	and	and	CCONJ
ejpam-6347	487	6	reliability	reliability	NOUN
ejpam-6347	487	7	of	of	ADP
ejpam-6347	487	8	the	the	DET
ejpam-6347	487	9	proposed	propose	VERB
ejpam-6347	487	10	covcom10	covcom10	NOUN
ejpam-6347	487	11	model	model	NOUN
ejpam-6347	487	12	,	,	PUNCT
ejpam-6347	487	13	we	we	PRON
ejpam-6347	487	14	conducted	conduct	VERB
ejpam-6347	487	15	simulations	simulation	NOUN
ejpam-6347	487	16	using	use	VERB
ejpam-6347	487	17	two	two	NUM
ejpam-6347	487	18	distinct	distinct	ADJ
ejpam-6347	487	19	sets	set	NOUN
ejpam-6347	487	20	of	of	ADP
ejpam-6347	487	21	initial	initial	ADJ
ejpam-6347	487	22	population	population	NOUN
ejpam-6347	487	23	values	value	NOUN
ejpam-6347	487	24	.	.	PUNCT
ejpam-6347	488	1	in	in	ADP
ejpam-6347	488	2	the	the	DET
ejpam-6347	488	3	small	small	ADJ
ejpam-6347	488	4	-	-	PUNCT
ejpam-6347	488	5	scale	scale	NOUN
ejpam-6347	488	6	scenario	scenario	NOUN
ejpam-6347	488	7	,	,	PUNCT
ejpam-6347	488	8	the	the	DET
ejpam-6347	488	9	initial	initial	ADJ
ejpam-6347	488	10	conditions	condition	NOUN
ejpam-6347	488	11	were	be	AUX
ejpam-6347	488	12	:	:	PUNCT
ejpam-6347	488	13	s(0	s(0	PROPN
ejpam-6347	488	14	)	)	PUNCT
ejpam-6347	488	15	=	=	SYM
ejpam-6347	488	16	500	500	NUM
ejpam-6347	488	17	,	,	PUNCT
ejpam-6347	488	18	e(0	e(0	NOUN
ejpam-6347	488	19	)	)	PUNCT
ejpam-6347	488	20	=	=	SYM
ejpam-6347	488	21	20	20	NUM
ejpam-6347	488	22	,	,	PUNCT
ejpam-6347	488	23	u(0	u(0	NOUN
ejpam-6347	488	24	)	)	PUNCT
ejpam-6347	488	25	=	=	SYM
ejpam-6347	488	26	10	10	NUM
ejpam-6347	488	27	,	,	PUNCT
ejpam-6347	488	28	q(0	q(0	PROPN
ejpam-6347	488	29	)	)	PUNCT
ejpam-6347	488	30	=	=	SYM
ejpam-6347	488	31	8	8	NUM
ejpam-6347	488	32	,	,	PUNCT
ejpam-6347	488	33	p	p	X
ejpam-6347	488	34	(	(	PUNCT
ejpam-6347	488	35	0	0	NUM
ejpam-6347	488	36	)	)	PUNCT
ejpam-6347	488	37	=	=	SYM
ejpam-6347	488	38	6	6	NUM
ejpam-6347	488	39	,	,	PUNCT
ejpam-6347	488	40	h(0	h(0	PROPN
ejpam-6347	488	41	)	)	PUNCT
ejpam-6347	488	42	=	=	SYM
ejpam-6347	488	43	4	4	NUM
ejpam-6347	488	44	,	,	PUNCT
ejpam-6347	488	45	f	f	PROPN
ejpam-6347	488	46	(	(	PUNCT
ejpam-6347	488	47	0	0	NUM
ejpam-6347	488	48	)	)	PUNCT
ejpam-6347	488	49	=	=	SYM
ejpam-6347	488	50	2	2	NUM
ejpam-6347	488	51	,	,	PUNCT
ejpam-6347	488	52	c(0	c(0	NOUN
ejpam-6347	488	53	)	)	PUNCT
ejpam-6347	488	54	=	=	SYM
ejpam-6347	489	1	1	1	NUM
ejpam-6347	489	2	,	,	PUNCT
ejpam-6347	489	3	v	v	NOUN
ejpam-6347	489	4	(	(	PUNCT
ejpam-6347	489	5	0	0	NUM
ejpam-6347	489	6	)	)	PUNCT
ejpam-6347	489	7	=	=	SYM
ejpam-6347	489	8	0	0	NUM
ejpam-6347	489	9	,	,	PUNCT
ejpam-6347	489	10	r(0	r(0	PROPN
ejpam-6347	489	11	)	)	PUNCT
ejpam-6347	489	12	=	=	NOUN
ejpam-6347	490	1	0	0	X
ejpam-6347	490	2	.	.	PUNCT
ejpam-6347	491	1	in	in	ADP
ejpam-6347	491	2	contrast	contrast	NOUN
ejpam-6347	491	3	,	,	PUNCT
ejpam-6347	491	4	the	the	DET
ejpam-6347	491	5	large	large	ADJ
ejpam-6347	491	6	-	-	PUNCT
ejpam-6347	491	7	scale	scale	NOUN
ejpam-6347	491	8	scenario	scenario	NOUN
ejpam-6347	491	9	used	use	VERB
ejpam-6347	491	10	proportionally	proportionally	ADV
ejpam-6347	491	11	higher	high	ADJ
ejpam-6347	491	12	values	value	NOUN
ejpam-6347	491	13	:	:	PUNCT
ejpam-6347	491	14	s(0	s(0	PROPN
ejpam-6347	491	15	)	)	PUNCT
ejpam-6347	491	16	=	=	SYM
ejpam-6347	491	17	1000	1000	NUM
ejpam-6347	491	18	,	,	PUNCT
ejpam-6347	491	19	e(0	e(0	NOUN
ejpam-6347	491	20	)	)	PUNCT
ejpam-6347	491	21	=	=	SYM
ejpam-6347	491	22	80	80	NUM
ejpam-6347	491	23	,	,	PUNCT
ejpam-6347	491	24	u(0	u(0	NOUN
ejpam-6347	491	25	)	)	PUNCT
ejpam-6347	491	26	=	=	SYM
ejpam-6347	491	27	60	60	NUM
ejpam-6347	491	28	,	,	PUNCT
ejpam-6347	491	29	q(0	q(0	PROPN
ejpam-6347	491	30	)	)	PUNCT
ejpam-6347	492	1	=	=	NOUN
ejpam-6347	492	2	50	50	NUM
ejpam-6347	492	3	,	,	PUNCT
ejpam-6347	492	4	p	p	X
ejpam-6347	492	5	(	(	PUNCT
ejpam-6347	492	6	0	0	NUM
ejpam-6347	492	7	)	)	PUNCT
ejpam-6347	492	8	=	=	SYM
ejpam-6347	492	9	30	30	NUM
ejpam-6347	492	10	,	,	PUNCT
ejpam-6347	492	11	h(0	h(0	PROPN
ejpam-6347	492	12	)	)	PUNCT
ejpam-6347	492	13	=	=	SYM
ejpam-6347	492	14	20	20	NUM
ejpam-6347	492	15	,	,	PUNCT
ejpam-6347	492	16	f	f	PROPN
ejpam-6347	492	17	(	(	PUNCT
ejpam-6347	492	18	0	0	NUM
ejpam-6347	492	19	)	)	PUNCT
ejpam-6347	492	20	=	=	SYM
ejpam-6347	492	21	10	10	NUM
ejpam-6347	492	22	,	,	PUNCT
ejpam-6347	492	23	c(0	c(0	NOUN
ejpam-6347	492	24	)	)	PUNCT
ejpam-6347	492	25	=	=	SYM
ejpam-6347	493	1	10	10	NUM
ejpam-6347	493	2	,	,	PUNCT
ejpam-6347	493	3	v	v	NOUN
ejpam-6347	493	4	(	(	PUNCT
ejpam-6347	493	5	0	0	NUM
ejpam-6347	493	6	)	)	PUNCT
ejpam-6347	493	7	=	=	SYM
ejpam-6347	493	8	0	0	NUM
ejpam-6347	493	9	,	,	PUNCT
ejpam-6347	493	10	r(0	r(0	PROPN
ejpam-6347	493	11	)	)	PUNCT
ejpam-6347	493	12	=	=	SYM
ejpam-6347	494	1	0	0	X
ejpam-6347	494	2	.	.	PUNCT
ejpam-6347	495	1	the	the	DET
ejpam-6347	495	2	comparative	comparative	ADJ
ejpam-6347	495	3	outcomes	outcome	NOUN
ejpam-6347	495	4	,	,	PUNCT
ejpam-6347	495	5	illustrated	illustrate	VERB
ejpam-6347	495	6	in	in	ADP
ejpam-6347	495	7	figure	figure	NOUN
ejpam-6347	495	8	6	6	NUM
ejpam-6347	495	9	,	,	PUNCT
ejpam-6347	495	10	demonstrate	demonstrate	VERB
ejpam-6347	495	11	that	that	SCONJ
ejpam-6347	495	12	the	the	DET
ejpam-6347	495	13	qualitative	qualitative	ADJ
ejpam-6347	495	14	behavior	behavior	NOUN
ejpam-6347	495	15	of	of	ADP
ejpam-6347	495	16	all	all	DET
ejpam-6347	495	17	compartments	compartment	NOUN
ejpam-6347	495	18	is	be	AUX
ejpam-6347	495	19	consistent	consistent	ADJ
ejpam-6347	495	20	across	across	ADP
ejpam-6347	495	21	both	both	DET
ejpam-6347	495	22	population	population	NOUN
ejpam-6347	495	23	scales	scale	NOUN
ejpam-6347	495	24	.	.	PUNCT
ejpam-6347	496	1	while	while	SCONJ
ejpam-6347	496	2	the	the	DET
ejpam-6347	496	3	absolute	absolute	ADJ
ejpam-6347	496	4	values	value	NOUN
ejpam-6347	496	5	increase	increase	VERB
ejpam-6347	496	6	in	in	ADP
ejpam-6347	496	7	line	line	NOUN
ejpam-6347	496	8	with	with	ADP
ejpam-6347	496	9	population	population	NOUN
ejpam-6347	496	10	size	size	NOUN
ejpam-6347	496	11	,	,	PUNCT
ejpam-6347	496	12	the	the	DET
ejpam-6347	496	13	temporal	temporal	ADJ
ejpam-6347	496	14	progression	progression	NOUN
ejpam-6347	496	15	,	,	PUNCT
ejpam-6347	496	16	peak	peak	NOUN
ejpam-6347	496	17	values	value	NOUN
ejpam-6347	496	18	,	,	PUNCT
ejpam-6347	496	19	and	and	CCONJ
ejpam-6347	496	20	recovery	recovery	NOUN
ejpam-6347	496	21	dynamics	dynamic	NOUN
ejpam-6347	496	22	remain	remain	VERB
ejpam-6347	496	23	n.	n.	NOUN
ejpam-6347	496	24	abbas	abbas	PROPN
ejpam-6347	496	25	,	,	PUNCT
ejpam-6347	496	26	w.	w.	PROPN
ejpam-6347	496	27	shatanawi	shatanawi	PROPN
ejpam-6347	496	28	,	,	PUNCT
ejpam-6347	496	29	s.	s.	PROPN
ejpam-6347	496	30	a.	a.	NOUN
ejpam-6347	496	31	zanib	zanib	PROPN
ejpam-6347	496	32	/	/	SYM
ejpam-6347	496	33	eur	eur	PROPN
ejpam-6347	496	34	.	.	PUNCT
ejpam-6347	497	1	j.	j.	PROPN
ejpam-6347	497	2	pure	pure	PROPN
ejpam-6347	497	3	appl	appl	PROPN
ejpam-6347	497	4	.	.	PROPN
ejpam-6347	497	5	math	math	PROPN
ejpam-6347	497	6	,	,	PUNCT
ejpam-6347	497	7	18	18	NUM
ejpam-6347	497	8	(	(	PUNCT
ejpam-6347	497	9	3	3	NUM
ejpam-6347	497	10	)	)	PUNCT
ejpam-6347	497	11	(	(	PUNCT
ejpam-6347	497	12	2025	2025	NUM
ejpam-6347	497	13	)	)	PUNCT
ejpam-6347	497	14	,	,	PUNCT
ejpam-6347	497	15	6347	6347	NUM
ejpam-6347	497	16	27	27	NUM
ejpam-6347	497	17	of	of	ADP
ejpam-6347	497	18	34	34	NUM
ejpam-6347	497	19	largely	largely	ADV
ejpam-6347	497	20	unchanged	unchanged	ADJ
ejpam-6347	497	21	.	.	PUNCT
ejpam-6347	498	1	this	this	DET
ejpam-6347	498	2	consistency	consistency	NOUN
ejpam-6347	498	3	confirms	confirm	VERB
ejpam-6347	498	4	that	that	SCONJ
ejpam-6347	498	5	the	the	DET
ejpam-6347	498	6	model	model	NOUN
ejpam-6347	498	7	robustly	robustly	ADV
ejpam-6347	498	8	captures	capture	VERB
ejpam-6347	498	9	the	the	DET
ejpam-6347	498	10	intrinsic	intrinsic	ADJ
ejpam-6347	498	11	transmission	transmission	NOUN
ejpam-6347	498	12	dynamics	dynamic	NOUN
ejpam-6347	498	13	and	and	CCONJ
ejpam-6347	498	14	is	be	AUX
ejpam-6347	498	15	not	not	PART
ejpam-6347	498	16	overly	overly	ADV
ejpam-6347	498	17	sensitive	sensitive	ADJ
ejpam-6347	498	18	to	to	ADP
ejpam-6347	498	19	variations	variation	NOUN
ejpam-6347	498	20	in	in	ADP
ejpam-6347	498	21	initial	initial	ADJ
ejpam-6347	498	22	population	population	NOUN
ejpam-6347	498	23	sizes	size	NOUN
ejpam-6347	498	24	.	.	PUNCT
ejpam-6347	499	1	peak	peak	NOUN
ejpam-6347	499	2	e	e	NOUN
ejpam-6347	499	3	final	final	ADJ
ejpam-6347	499	4	r	r	NOUN
ejpam-6347	499	5	time	time	NOUN
ejpam-6347	499	6	to	to	PART
ejpam-6347	499	7	peak	peak	VERB
ejpam-6347	499	8	e	e	PROPN
ejpam-6347	499	9	0.2	0.2	NUM
ejpam-6347	499	10	0.4	0.4	NUM
ejpam-6347	499	11	0.6	0.6	NUM
ejpam-6347	499	12	0.8	0.8	NUM
ejpam-6347	499	13	1.0	1.0	NUM
ejpam-6347	499	14	0.00.00.0	0.00.00.0	ADJ
ejpam-6347	499	15	effect	effect	NOUN
ejpam-6347	499	16	of	of	ADP
ejpam-6347	499	17	varying	vary	VERB
ejpam-6347	499	18	=	=	SYM
ejpam-6347	499	19	5.0e-05	5.0e-05	NUM
ejpam-6347	499	20	=	=	SYM
ejpam-6347	499	21	1.0e-04	1.0e-04	NUM
ejpam-6347	499	22	=	=	SYM
ejpam-6347	499	23	2.0e-04	2.0e-04	NUM
ejpam-6347	499	24	peak	peak	NOUN
ejpam-6347	499	25	e	e	NOUN
ejpam-6347	499	26	final	final	ADJ
ejpam-6347	499	27	r	r	NOUN
ejpam-6347	499	28	time	time	NOUN
ejpam-6347	499	29	to	to	PART
ejpam-6347	499	30	peak	peak	VERB
ejpam-6347	499	31	e	e	PROPN
ejpam-6347	499	32	0.2	0.2	NUM
ejpam-6347	499	33	0.4	0.4	NUM
ejpam-6347	499	34	0.6	0.6	NUM
ejpam-6347	499	35	0.8	0.8	NUM
ejpam-6347	499	36	1.0	1.0	NUM
ejpam-6347	499	37	0.00.00.0	0.00.00.0	ADJ
ejpam-6347	499	38	effect	effect	NOUN
ejpam-6347	499	39	of	of	ADP
ejpam-6347	499	40	varying	vary	VERB
ejpam-6347	499	41	=	=	SYM
ejpam-6347	499	42	1.0e-04	1.0e-04	NUM
ejpam-6347	499	43	=	=	SYM
ejpam-6347	499	44	2.0e-04	2.0e-04	NUM
ejpam-6347	499	45	=	=	SYM
ejpam-6347	499	46	4.0e-04	4.0e-04	NUM
ejpam-6347	499	47	peak	peak	NOUN
ejpam-6347	499	48	e	e	X
ejpam-6347	499	49	final	final	ADJ
ejpam-6347	499	50	r	r	NOUN
ejpam-6347	499	51	time	time	NOUN
ejpam-6347	499	52	to	to	PART
ejpam-6347	499	53	peak	peak	VERB
ejpam-6347	499	54	e	e	PROPN
ejpam-6347	499	55	0.2	0.2	NUM
ejpam-6347	499	56	0.4	0.4	NUM
ejpam-6347	499	57	0.6	0.6	NUM
ejpam-6347	499	58	0.8	0.8	NUM
ejpam-6347	499	59	1.0	1.0	NUM
ejpam-6347	499	60	0.00.00.0	0.00.00.0	ADJ
ejpam-6347	499	61	effect	effect	NOUN
ejpam-6347	499	62	of	of	ADP
ejpam-6347	499	63	varying	vary	VERB
ejpam-6347	499	64	=	=	SYM
ejpam-6347	499	65	5.0e-05	5.0e-05	NUM
ejpam-6347	499	66	=	=	SYM
ejpam-6347	499	67	1.0e-04	1.0e-04	NUM
ejpam-6347	499	68	=	=	SYM
ejpam-6347	499	69	2.0e-04	2.0e-04	NUM
ejpam-6347	499	70	peak	peak	NOUN
ejpam-6347	499	71	e	e	NOUN
ejpam-6347	499	72	final	final	ADJ
ejpam-6347	499	73	r	r	NOUN
ejpam-6347	499	74	time	time	NOUN
ejpam-6347	499	75	to	to	PART
ejpam-6347	499	76	peak	peak	VERB
ejpam-6347	499	77	e	e	PROPN
ejpam-6347	499	78	0.2	0.2	NUM
ejpam-6347	499	79	0.4	0.4	NUM
ejpam-6347	499	80	0.6	0.6	NUM
ejpam-6347	499	81	0.8	0.8	NUM
ejpam-6347	499	82	1.0	1.0	NUM
ejpam-6347	499	83	0.00.00.0	0.00.00.0	ADJ
ejpam-6347	499	84	effect	effect	NOUN
ejpam-6347	499	85	of	of	ADP
ejpam-6347	499	86	varying	vary	VERB
ejpam-6347	499	87	=	=	SYM
ejpam-6347	499	88	3.0e-04	3.0e-04	NUM
ejpam-6347	499	89	=	=	SYM
ejpam-6347	500	1	5.0e-04	5.0e-04	NUM
ejpam-6347	500	2	=	=	SYM
ejpam-6347	500	3	7.0e-04	7.0e-04	NUM
ejpam-6347	500	4	figure	figure	NOUN
ejpam-6347	500	5	7	7	NUM
ejpam-6347	500	6	:	:	PUNCT
ejpam-6347	500	7	radar	radar	NOUN
ejpam-6347	500	8	plots	plot	NOUN
ejpam-6347	500	9	showing	show	VERB
ejpam-6347	500	10	the	the	DET
ejpam-6347	500	11	impact	impact	NOUN
ejpam-6347	500	12	of	of	ADP
ejpam-6347	500	13	varying	vary	VERB
ejpam-6347	500	14	ϕ	ϕ	PROPN
ejpam-6347	500	15	,	,	PUNCT
ejpam-6347	500	16	β	β	X
ejpam-6347	500	17	,	,	PUNCT
ejpam-6347	500	18	γ	γ	X
ejpam-6347	500	19	,	,	PUNCT
ejpam-6347	500	20	and	and	CCONJ
ejpam-6347	500	21	τ	τ	PROPN
ejpam-6347	500	22	on	on	ADP
ejpam-6347	500	23	peak	peak	NOUN
ejpam-6347	500	24	exposed	expose	VERB
ejpam-6347	500	25	,	,	PUNCT
ejpam-6347	500	26	final	final	ADJ
ejpam-6347	500	27	recovered	recover	VERB
ejpam-6347	500	28	,	,	PUNCT
ejpam-6347	500	29	and	and	CCONJ
ejpam-6347	500	30	time	time	NOUN
ejpam-6347	500	31	to	to	PART
ejpam-6347	500	32	peak	peak	VERB
ejpam-6347	500	33	exposure	exposure	NOUN
ejpam-6347	500	34	.	.	PUNCT
ejpam-6347	501	1	figure	figure	VERB
ejpam-6347	501	2	7	7	NUM
ejpam-6347	501	3	presents	present	NOUN
ejpam-6347	501	4	radar	radar	NOUN
ejpam-6347	501	5	plots	plot	NOUN
ejpam-6347	501	6	illustrating	illustrate	VERB
ejpam-6347	501	7	the	the	DET
ejpam-6347	501	8	impact	impact	NOUN
ejpam-6347	501	9	of	of	ADP
ejpam-6347	501	10	four	four	NUM
ejpam-6347	501	11	parameters	parameter	NOUN
ejpam-6347	501	12	ϕ	ϕ	NOUN
ejpam-6347	501	13	,	,	PUNCT
ejpam-6347	501	14	β	β	X
ejpam-6347	501	15	,	,	PUNCT
ejpam-6347	501	16	γ	γ	X
ejpam-6347	501	17	,	,	PUNCT
ejpam-6347	501	18	and	and	CCONJ
ejpam-6347	501	19	τ	τ	PROPN
ejpam-6347	501	20	on	on	ADP
ejpam-6347	501	21	key	key	ADJ
ejpam-6347	501	22	epidemic	epidemic	NOUN
ejpam-6347	501	23	outcomes	outcome	NOUN
ejpam-6347	501	24	.	.	PUNCT
ejpam-6347	502	1	each	each	DET
ejpam-6347	502	2	subplot	subplot	NOUN
ejpam-6347	502	3	compares	compare	VERB
ejpam-6347	502	4	peak	peak	NOUN
ejpam-6347	502	5	exposed	expose	VERB
ejpam-6347	502	6	(	(	PUNCT
ejpam-6347	502	7	e	e	NOUN
ejpam-6347	502	8	)	)	PUNCT
ejpam-6347	502	9	,	,	PUNCT
ejpam-6347	502	10	final	final	ADJ
ejpam-6347	502	11	recovered	recover	VERB
ejpam-6347	502	12	(	(	PUNCT
ejpam-6347	502	13	r	r	NOUN
ejpam-6347	502	14	)	)	PUNCT
ejpam-6347	502	15	,	,	PUNCT
ejpam-6347	502	16	and	and	CCONJ
ejpam-6347	502	17	time	time	NOUN
ejpam-6347	502	18	to	to	PART
ejpam-6347	502	19	peak	peak	VERB
ejpam-6347	502	20	e	e	NOUN
ejpam-6347	502	21	across	across	ADP
ejpam-6347	502	22	three	three	NUM
ejpam-6347	502	23	values	value	NOUN
ejpam-6347	502	24	of	of	ADP
ejpam-6347	502	25	the	the	DET
ejpam-6347	502	26	selected	select	VERB
ejpam-6347	502	27	parameter	parameter	NOUN
ejpam-6347	502	28	.	.	PUNCT
ejpam-6347	503	1	higher	high	ADJ
ejpam-6347	503	2	ϕ	ϕ	PROPN
ejpam-6347	503	3	and	and	CCONJ
ejpam-6347	503	4	τ	τ	PROPN
ejpam-6347	503	5	intensify	intensify	VERB
ejpam-6347	503	6	the	the	DET
ejpam-6347	503	7	outbreak	outbreak	NOUN
ejpam-6347	503	8	by	by	ADP
ejpam-6347	503	9	increasing	increase	VERB
ejpam-6347	503	10	peak	peak	NOUN
ejpam-6347	503	11	e	e	NOUN
ejpam-6347	503	12	and	and	CCONJ
ejpam-6347	503	13	reducing	reduce	VERB
ejpam-6347	503	14	final	final	ADJ
ejpam-6347	503	15	r.	r.	NOUN
ejpam-6347	503	16	conversely	conversely	ADV
ejpam-6347	503	17	,	,	PUNCT
ejpam-6347	503	18	increasing	increase	VERB
ejpam-6347	503	19	β	β	NOUN
ejpam-6347	503	20	and	and	CCONJ
ejpam-6347	503	21	γ	γ	PROPN
ejpam-6347	503	22	improves	improve	VERB
ejpam-6347	503	23	recovery	recovery	NOUN
ejpam-6347	503	24	and	and	CCONJ
ejpam-6347	503	25	reduces	reduce	VERB
ejpam-6347	503	26	the	the	DET
ejpam-6347	503	27	epidemic	epidemic	NOUN
ejpam-6347	503	28	size	size	NOUN
ejpam-6347	503	29	.	.	PUNCT
ejpam-6347	504	1	time	time	NOUN
ejpam-6347	504	2	to	to	PART
ejpam-6347	504	3	peak	peak	NOUN
ejpam-6347	504	4	remains	remain	VERB
ejpam-6347	504	5	relatively	relatively	ADV
ejpam-6347	504	6	stable	stable	ADJ
ejpam-6347	504	7	under	under	ADP
ejpam-6347	504	8	most	most	ADJ
ejpam-6347	504	9	changes	change	NOUN
ejpam-6347	504	10	.	.	PUNCT
ejpam-6347	505	1	these	these	DET
ejpam-6347	505	2	results	result	NOUN
ejpam-6347	505	3	emphasize	emphasize	VERB
ejpam-6347	505	4	the	the	DET
ejpam-6347	505	5	role	role	NOUN
ejpam-6347	505	6	of	of	ADP
ejpam-6347	505	7	transmission	transmission	NOUN
ejpam-6347	505	8	control	control	NOUN
ejpam-6347	505	9	and	and	CCONJ
ejpam-6347	505	10	immunity	immunity	NOUN
ejpam-6347	505	11	in	in	ADP
ejpam-6347	505	12	outbreak	outbreak	NOUN
ejpam-6347	505	13	management	management	NOUN
ejpam-6347	505	14	.	.	PUNCT
ejpam-6347	506	1	4.1	4.1	NUM
ejpam-6347	506	2	.	.	PUNCT
ejpam-6347	506	3	impact	impact	NOUN
ejpam-6347	506	4	of	of	ADP
ejpam-6347	506	5	optimal	optimal	ADJ
ejpam-6347	506	6	control	control	NOUN
ejpam-6347	506	7	strategies	strategy	NOUN
ejpam-6347	506	8	on	on	ADP
ejpam-6347	506	9	epidemic	epidemic	NOUN
ejpam-6347	506	10	disease	disease	NOUN
ejpam-6347	506	11	dynamics	dynamic	NOUN
ejpam-6347	506	12	this	this	DET
ejpam-6347	506	13	section	section	NOUN
ejpam-6347	506	14	presents	present	VERB
ejpam-6347	506	15	a	a	DET
ejpam-6347	506	16	detailed	detailed	ADJ
ejpam-6347	506	17	analysis	analysis	NOUN
ejpam-6347	506	18	of	of	ADP
ejpam-6347	506	19	the	the	DET
ejpam-6347	506	20	impact	impact	NOUN
ejpam-6347	506	21	of	of	ADP
ejpam-6347	506	22	various	various	ADJ
ejpam-6347	506	23	optimal	optimal	ADJ
ejpam-6347	506	24	control	control	NOUN
ejpam-6347	506	25	strategies	strategy	NOUN
ejpam-6347	506	26	on	on	ADP
ejpam-6347	506	27	covid-19	covid-19	PROPN
ejpam-6347	506	28	transmission	transmission	NOUN
ejpam-6347	506	29	dynamics	dynamic	NOUN
ejpam-6347	506	30	using	use	VERB
ejpam-6347	506	31	the	the	DET
ejpam-6347	506	32	covcom10	covcom10	NOUN
ejpam-6347	506	33	model	model	NOUN
ejpam-6347	506	34	.	.	PUNCT
ejpam-6347	507	1	we	we	PRON
ejpam-6347	507	2	systematically	systematically	ADV
ejpam-6347	507	3	evaluate	evaluate	VERB
ejpam-6347	507	4	the	the	DET
ejpam-6347	507	5	effectiveness	effectiveness	NOUN
ejpam-6347	507	6	of	of	ADP
ejpam-6347	507	7	different	different	ADJ
ejpam-6347	507	8	combinations	combination	NOUN
ejpam-6347	507	9	of	of	ADP
ejpam-6347	507	10	interventions	intervention	NOUN
ejpam-6347	507	11	,	,	PUNCT
ejpam-6347	507	12	such	such	ADJ
ejpam-6347	507	13	as	as	ADP
ejpam-6347	507	14	vaccination	vaccination	NOUN
ejpam-6347	507	15	,	,	PUNCT
ejpam-6347	507	16	hospitalization	hospitalization	NOUN
ejpam-6347	507	17	,	,	PUNCT
ejpam-6347	507	18	and	and	CCONJ
ejpam-6347	507	19	management	management	NOUN
ejpam-6347	507	20	of	of	ADP
ejpam-6347	507	21	asymptomatic	asymptomatic	ADJ
ejpam-6347	507	22	cases	case	NOUN
ejpam-6347	507	23	—	—	PUNCT
ejpam-6347	507	24	by	by	ADP
ejpam-6347	507	25	applying	apply	VERB
ejpam-6347	507	26	pontryagin	pontryagin	NOUN
ejpam-6347	507	27	’s	’s	PART
ejpam-6347	507	28	maximum	maximum	ADJ
ejpam-6347	507	29	principle	principle	NOUN
ejpam-6347	507	30	to	to	PART
ejpam-6347	507	31	determine	determine	VERB
ejpam-6347	507	32	the	the	DET
ejpam-6347	507	33	optimal	optimal	ADJ
ejpam-6347	507	34	allocation	allocation	NOUN
ejpam-6347	507	35	and	and	CCONJ
ejpam-6347	507	36	timing	timing	NOUN
ejpam-6347	507	37	of	of	ADP
ejpam-6347	507	38	these	these	DET
ejpam-6347	507	39	controls	control	NOUN
ejpam-6347	507	40	.	.	PUNCT
ejpam-6347	508	1	figure	figure	NOUN
ejpam-6347	508	2	8	8	NUM
ejpam-6347	508	3	illustrates	illustrate	VERB
ejpam-6347	508	4	the	the	DET
ejpam-6347	508	5	temporal	temporal	ADJ
ejpam-6347	508	6	evolution	evolution	NOUN
ejpam-6347	508	7	of	of	ADP
ejpam-6347	508	8	all	all	DET
ejpam-6347	508	9	compartments	compartment	NOUN
ejpam-6347	508	10	under	under	ADP
ejpam-6347	508	11	scenarios	scenario	NOUN
ejpam-6347	508	12	with	with	ADP
ejpam-6347	508	13	and	and	CCONJ
ejpam-6347	508	14	without	without	ADP
ejpam-6347	508	15	optimal	optimal	ADJ
ejpam-6347	508	16	interventions	intervention	NOUN
ejpam-6347	508	17	.	.	PUNCT
ejpam-6347	509	1	the	the	DET
ejpam-6347	509	2	simulation	simulation	NOUN
ejpam-6347	509	3	results	result	VERB
ejpam-6347	509	4	clearly	clearly	ADV
ejpam-6347	509	5	demonstrate	demonstrate	VERB
ejpam-6347	509	6	that	that	SCONJ
ejpam-6347	509	7	the	the	DET
ejpam-6347	509	8	coordinated	coordinated	ADJ
ejpam-6347	509	9	implementation	implementation	NOUN
ejpam-6347	509	10	of	of	ADP
ejpam-6347	509	11	vaccination	vaccination	NOUN
ejpam-6347	509	12	,	,	PUNCT
ejpam-6347	509	13	enhanced	enhance	VERB
ejpam-6347	509	14	hospitalization	hospitalization	NOUN
ejpam-6347	509	15	capacity	capacity	NOUN
ejpam-6347	509	16	,	,	PUNCT
ejpam-6347	509	17	and	and	CCONJ
ejpam-6347	509	18	targeted	target	VERB
ejpam-6347	509	19	management	management	NOUN
ejpam-6347	509	20	n.	n.	NOUN
ejpam-6347	509	21	abbas	abbas	PROPN
ejpam-6347	509	22	,	,	PUNCT
ejpam-6347	509	23	w.	w.	PROPN
ejpam-6347	509	24	shatanawi	shatanawi	PROPN
ejpam-6347	509	25	,	,	PUNCT
ejpam-6347	509	26	s.	s.	PROPN
ejpam-6347	509	27	a.	a.	NOUN
ejpam-6347	509	28	zanib	zanib	PROPN
ejpam-6347	509	29	/	/	SYM
ejpam-6347	509	30	eur	eur	PROPN
ejpam-6347	509	31	.	.	PUNCT
ejpam-6347	510	1	j.	j.	PROPN
ejpam-6347	510	2	pure	pure	PROPN
ejpam-6347	510	3	appl	appl	PROPN
ejpam-6347	510	4	.	.	PROPN
ejpam-6347	510	5	math	math	PROPN
ejpam-6347	510	6	,	,	PUNCT
ejpam-6347	510	7	18	18	NUM
ejpam-6347	510	8	(	(	PUNCT
ejpam-6347	510	9	3	3	NUM
ejpam-6347	510	10	)	)	PUNCT
ejpam-6347	510	11	(	(	PUNCT
ejpam-6347	510	12	2025	2025	NUM
ejpam-6347	510	13	)	)	PUNCT
ejpam-6347	510	14	,	,	PUNCT
ejpam-6347	510	15	6347	6347	NUM
ejpam-6347	510	16	28	28	NUM
ejpam-6347	510	17	of	of	ADP
ejpam-6347	510	18	34	34	NUM
ejpam-6347	510	19	of	of	ADP
ejpam-6347	510	20	asymptomatic	asymptomatic	ADJ
ejpam-6347	510	21	individuals	individual	NOUN
ejpam-6347	510	22	leads	lead	VERB
ejpam-6347	510	23	to	to	ADP
ejpam-6347	510	24	a	a	DET
ejpam-6347	510	25	substantial	substantial	ADJ
ejpam-6347	510	26	reduction	reduction	NOUN
ejpam-6347	510	27	in	in	ADP
ejpam-6347	510	28	the	the	DET
ejpam-6347	510	29	number	number	NOUN
ejpam-6347	510	30	of	of	ADP
ejpam-6347	510	31	infections	infection	NOUN
ejpam-6347	510	32	and	and	CCONJ
ejpam-6347	510	33	severe	severe	ADJ
ejpam-6347	510	34	cases	case	NOUN
ejpam-6347	510	35	over	over	ADP
ejpam-6347	510	36	time	time	NOUN
ejpam-6347	510	37	.	.	PUNCT
ejpam-6347	511	1	notably	notably	ADV
ejpam-6347	511	2	,	,	PUNCT
ejpam-6347	511	3	the	the	DET
ejpam-6347	511	4	model	model	NOUN
ejpam-6347	511	5	quantifies	quantify	VERB
ejpam-6347	511	6	the	the	DET
ejpam-6347	511	7	optimal	optimal	ADJ
ejpam-6347	511	8	intensity	intensity	NOUN
ejpam-6347	511	9	and	and	CCONJ
ejpam-6347	511	10	timing	timing	NOUN
ejpam-6347	511	11	for	for	ADP
ejpam-6347	511	12	each	each	DET
ejpam-6347	511	13	control	control	NOUN
ejpam-6347	511	14	measure	measure	NOUN
ejpam-6347	511	15	,	,	PUNCT
ejpam-6347	511	16	providing	provide	VERB
ejpam-6347	511	17	actionable	actionable	ADJ
ejpam-6347	511	18	guidance	guidance	NOUN
ejpam-6347	511	19	for	for	ADP
ejpam-6347	511	20	public	public	ADJ
ejpam-6347	511	21	health	health	NOUN
ejpam-6347	511	22	authorities	authority	NOUN
ejpam-6347	511	23	to	to	PART
ejpam-6347	511	24	maximize	maximize	VERB
ejpam-6347	511	25	resource	resource	NOUN
ejpam-6347	511	26	efficiency	efficiency	NOUN
ejpam-6347	511	27	and	and	CCONJ
ejpam-6347	511	28	intervention	intervention	NOUN
ejpam-6347	511	29	impact	impact	NOUN
ejpam-6347	511	30	.	.	PUNCT
ejpam-6347	512	1	these	these	DET
ejpam-6347	512	2	findings	finding	NOUN
ejpam-6347	512	3	underscore	underscore	VERB
ejpam-6347	512	4	the	the	DET
ejpam-6347	512	5	critical	critical	ADJ
ejpam-6347	512	6	importance	importance	NOUN
ejpam-6347	512	7	of	of	ADP
ejpam-6347	512	8	integrated	integrate	VERB
ejpam-6347	512	9	and	and	CCONJ
ejpam-6347	512	10	sustained	sustain	VERB
ejpam-6347	512	11	public	public	ADJ
ejpam-6347	512	12	health	health	NOUN
ejpam-6347	512	13	strategies	strategy	NOUN
ejpam-6347	512	14	.	.	PUNCT
ejpam-6347	513	1	by	by	ADP
ejpam-6347	513	2	combining	combine	VERB
ejpam-6347	513	3	multiple	multiple	ADJ
ejpam-6347	513	4	interventions	intervention	NOUN
ejpam-6347	513	5	,	,	PUNCT
ejpam-6347	513	6	the	the	DET
ejpam-6347	513	7	spread	spread	NOUN
ejpam-6347	513	8	of	of	ADP
ejpam-6347	513	9	sars	sar	NOUN
ejpam-6347	513	10	-	-	PUNCT
ejpam-6347	513	11	cov-2	cov-2	NUM
ejpam-6347	513	12	can	can	AUX
ejpam-6347	513	13	be	be	AUX
ejpam-6347	513	14	curbed	curb	VERB
ejpam-6347	513	15	more	more	ADV
ejpam-6347	513	16	effectively	effectively	ADV
ejpam-6347	513	17	and	and	CCONJ
ejpam-6347	513	18	sustainably	sustainably	ADV
ejpam-6347	513	19	than	than	ADP
ejpam-6347	513	20	by	by	ADP
ejpam-6347	513	21	relying	rely	VERB
ejpam-6347	513	22	on	on	ADP
ejpam-6347	513	23	any	any	DET
ejpam-6347	513	24	single	single	ADJ
ejpam-6347	513	25	measure	measure	NOUN
ejpam-6347	513	26	alone	alone	ADV
ejpam-6347	513	27	.	.	PUNCT
ejpam-6347	514	1	the	the	DET
ejpam-6347	514	2	numerical	numerical	ADJ
ejpam-6347	514	3	results	result	NOUN
ejpam-6347	514	4	offer	offer	VERB
ejpam-6347	514	5	practical	practical	ADJ
ejpam-6347	514	6	insights	insight	NOUN
ejpam-6347	514	7	for	for	ADP
ejpam-6347	514	8	policymakers	policymaker	NOUN
ejpam-6347	514	9	,	,	PUNCT
ejpam-6347	514	10	highlighting	highlight	VERB
ejpam-6347	514	11	the	the	DET
ejpam-6347	514	12	value	value	NOUN
ejpam-6347	514	13	of	of	ADP
ejpam-6347	514	14	adaptive	adaptive	ADJ
ejpam-6347	514	15	,	,	PUNCT
ejpam-6347	514	16	data	data	NOUN
ejpam-6347	514	17	-	-	PUNCT
ejpam-6347	514	18	driven	drive	VERB
ejpam-6347	514	19	approaches	approach	NOUN
ejpam-6347	514	20	to	to	ADP
ejpam-6347	514	21	epidemic	epidemic	NOUN
ejpam-6347	514	22	control	control	NOUN
ejpam-6347	514	23	.	.	PUNCT
ejpam-6347	515	1	0	0	NUM
ejpam-6347	515	2	20	20	NUM
ejpam-6347	515	3	40	40	NUM
ejpam-6347	515	4	60	60	NUM
ejpam-6347	515	5	80	80	NUM
ejpam-6347	515	6	100	100	NUM
ejpam-6347	515	7	days	day	NOUN
ejpam-6347	515	8	500	500	NUM
ejpam-6347	515	9	1000	1000	NUM
ejpam-6347	515	10	1500	1500	NUM
ejpam-6347	515	11	2000	2000	NUM
ejpam-6347	515	12	2500	2500	NUM
ejpam-6347	515	13	3000	3000	NUM
ejpam-6347	515	14	3500	3500	NUM
ejpam-6347	515	15	nu	nu	NOUN
ejpam-6347	515	16	m	m	VERB
ejpam-6347	515	17	be	be	VERB
ejpam-6347	516	1	r	r	NOUN
ejpam-6347	516	2	o	o	NOUN
ejpam-6347	517	1	f	f	X
ejpam-6347	518	1	s	s	VERB
ejpam-6347	519	1	us	us	PROPN
ejpam-6347	520	1	ce	ce	PROPN
ejpam-6347	520	2	pt	pt	PROPN
ejpam-6347	520	3	ib	ib	PROPN
ejpam-6347	520	4	le	le	X
ejpam-6347	520	5	(	(	PUNCT
ejpam-6347	520	6	s	s	NOUN
ejpam-6347	520	7	)	)	PUNCT
ejpam-6347	520	8	susceptible	susceptible	ADJ
ejpam-6347	520	9	(	(	PUNCT
ejpam-6347	520	10	s	s	NOUN
ejpam-6347	520	11	)	)	PUNCT
ejpam-6347	520	12	dynamics	dynamic	NOUN
ejpam-6347	520	13	without	without	ADP
ejpam-6347	520	14	control	control	NOUN
ejpam-6347	520	15	with	with	ADP
ejpam-6347	520	16	control	control	NOUN
ejpam-6347	520	17	0	0	NUM
ejpam-6347	520	18	20	20	NUM
ejpam-6347	520	19	40	40	NUM
ejpam-6347	520	20	60	60	NUM
ejpam-6347	520	21	80	80	NUM
ejpam-6347	520	22	100	100	NUM
ejpam-6347	520	23	days	day	NOUN
ejpam-6347	520	24	0.0	0.0	NUM
ejpam-6347	520	25	2.5	2.5	NUM
ejpam-6347	520	26	5.0	5.0	NUM
ejpam-6347	520	27	7.5	7.5	NUM
ejpam-6347	520	28	10.0	10.0	NUM
ejpam-6347	520	29	12.5	12.5	NUM
ejpam-6347	520	30	15.0	15.0	NUM
ejpam-6347	520	31	17.5	17.5	NUM
ejpam-6347	520	32	20.0	20.0	NUM
ejpam-6347	520	33	nu	nu	NOUN
ejpam-6347	520	34	m	m	VERB
ejpam-6347	520	35	be	be	VERB
ejpam-6347	520	36	r	r	NOUN
ejpam-6347	520	37	o	o	NOUN
ejpam-6347	521	1	f	f	X
ejpam-6347	522	1	p	p	X
ejpam-6347	522	2	re	re	ADP
ejpam-6347	522	3	-s	-s	PROPN
ejpam-6347	522	4	ym	ym	INTJ
ejpam-6347	522	5	pt	pt	INTJ
ejpam-6347	522	6	om	om	PROPN
ejpam-6347	522	7	at	at	ADP
ejpam-6347	522	8	ic	ic	PROPN
ejpam-6347	522	9	(	(	PUNCT
ejpam-6347	522	10	e	e	NOUN
ejpam-6347	522	11	)	)	PUNCT
ejpam-6347	522	12	pre	pre	ADJ
ejpam-6347	522	13	-	-	ADJ
ejpam-6347	522	14	symptomatic	symptomatic	ADJ
ejpam-6347	522	15	(	(	PUNCT
ejpam-6347	522	16	e	e	NOUN
ejpam-6347	522	17	)	)	PUNCT
ejpam-6347	522	18	dynamics	dynamic	NOUN
ejpam-6347	522	19	without	without	ADP
ejpam-6347	522	20	control	control	NOUN
ejpam-6347	522	21	with	with	ADP
ejpam-6347	522	22	control	control	NOUN
ejpam-6347	522	23	0	0	NUM
ejpam-6347	522	24	20	20	NUM
ejpam-6347	522	25	40	40	NUM
ejpam-6347	522	26	60	60	NUM
ejpam-6347	522	27	80	80	NUM
ejpam-6347	522	28	100	100	NUM
ejpam-6347	522	29	days	day	NOUN
ejpam-6347	522	30	2	2	NUM
ejpam-6347	522	31	4	4	NUM
ejpam-6347	522	32	6	6	NUM
ejpam-6347	522	33	8	8	NUM
ejpam-6347	522	34	10	10	NUM
ejpam-6347	522	35	nu	nu	NOUN
ejpam-6347	522	36	m	m	VERB
ejpam-6347	522	37	be	be	VERB
ejpam-6347	523	1	r	r	NOUN
ejpam-6347	523	2	o	o	NOUN
ejpam-6347	523	3	f	f	X
ejpam-6347	524	1	i	i	PRON
ejpam-6347	524	2	nf	nf	VERB
ejpam-6347	524	3	ec	ec	PROPN
ejpam-6347	524	4	te	te	PROPN
ejpam-6347	524	5	d	d	X
ejpam-6347	524	6	(	(	PUNCT
ejpam-6347	524	7	u	u	NOUN
ejpam-6347	524	8	)	)	PUNCT
ejpam-6347	524	9	infected	infected	ADJ
ejpam-6347	524	10	(	(	PUNCT
ejpam-6347	524	11	u	u	NOUN
ejpam-6347	524	12	)	)	PUNCT
ejpam-6347	524	13	dynamics	dynamic	NOUN
ejpam-6347	524	14	without	without	ADP
ejpam-6347	524	15	control	control	NOUN
ejpam-6347	524	16	with	with	ADP
ejpam-6347	524	17	control	control	NOUN
ejpam-6347	524	18	0	0	NUM
ejpam-6347	524	19	20	20	NUM
ejpam-6347	524	20	40	40	NUM
ejpam-6347	524	21	60	60	NUM
ejpam-6347	524	22	80	80	NUM
ejpam-6347	524	23	100	100	NUM
ejpam-6347	524	24	days	day	NOUN
ejpam-6347	524	25	10	10	NUM
ejpam-6347	524	26	15	15	NUM
ejpam-6347	524	27	20	20	NUM
ejpam-6347	524	28	25	25	NUM
ejpam-6347	524	29	30	30	NUM
ejpam-6347	524	30	nu	nu	NOUN
ejpam-6347	524	31	m	m	VERB
ejpam-6347	524	32	be	be	VERB
ejpam-6347	525	1	r	r	NOUN
ejpam-6347	525	2	o	o	NOUN
ejpam-6347	525	3	f	f	X
ejpam-6347	525	4	q	q	PROPN
ejpam-6347	525	5	ua	ua	PROPN
ejpam-6347	525	6	ra	ra	PROPN
ejpam-6347	525	7	nt	not	PART
ejpam-6347	525	8	in	in	ADP
ejpam-6347	525	9	ed	ed	PROPN
ejpam-6347	525	10	(	(	PUNCT
ejpam-6347	525	11	q	q	NOUN
ejpam-6347	525	12	)	)	PUNCT
ejpam-6347	525	13	quarantined	quarantined	ADJ
ejpam-6347	525	14	(	(	PUNCT
ejpam-6347	525	15	q	q	NOUN
ejpam-6347	525	16	)	)	PUNCT
ejpam-6347	525	17	dynamics	dynamic	NOUN
ejpam-6347	525	18	without	without	ADP
ejpam-6347	525	19	control	control	NOUN
ejpam-6347	525	20	with	with	ADP
ejpam-6347	525	21	control	control	NOUN
ejpam-6347	525	22	0	0	NUM
ejpam-6347	525	23	20	20	NUM
ejpam-6347	525	24	40	40	NUM
ejpam-6347	525	25	60	60	NUM
ejpam-6347	525	26	80	80	NUM
ejpam-6347	525	27	100	100	NUM
ejpam-6347	525	28	days	day	NOUN
ejpam-6347	525	29	2	2	NUM
ejpam-6347	525	30	3	3	NUM
ejpam-6347	525	31	4	4	NUM
ejpam-6347	525	32	5	5	NUM
ejpam-6347	525	33	6	6	NUM
ejpam-6347	525	34	nu	nu	NOUN
ejpam-6347	525	35	m	m	VERB
ejpam-6347	525	36	be	be	VERB
ejpam-6347	525	37	r	r	NOUN
ejpam-6347	525	38	o	o	NOUN
ejpam-6347	526	1	f	f	X
ejpam-6347	526	2	c	c	PROPN
ejpam-6347	526	3	lin	lin	PROPN
ejpam-6347	526	4	ica	ica	PROPN
ejpam-6347	526	5	lly	lly	ADV
ejpam-6347	526	6	p	p	X
ejpam-6347	526	7	os	os	PROPN
ejpam-6347	526	8	iti	iti	PROPN
ejpam-6347	526	9	ve	ve	VERB
ejpam-6347	526	10	(	(	PUNCT
ejpam-6347	526	11	p	p	NOUN
ejpam-6347	526	12	)	)	PUNCT
ejpam-6347	526	13	clinically	clinically	ADV
ejpam-6347	526	14	positive	positive	ADJ
ejpam-6347	526	15	(	(	PUNCT
ejpam-6347	526	16	p	p	NOUN
ejpam-6347	526	17	)	)	PUNCT
ejpam-6347	526	18	dynamics	dynamic	NOUN
ejpam-6347	526	19	without	without	ADP
ejpam-6347	526	20	control	control	NOUN
ejpam-6347	526	21	with	with	ADP
ejpam-6347	526	22	control	control	NOUN
ejpam-6347	526	23	0	0	NUM
ejpam-6347	526	24	20	20	NUM
ejpam-6347	526	25	40	40	NUM
ejpam-6347	526	26	60	60	NUM
ejpam-6347	526	27	80	80	NUM
ejpam-6347	526	28	100	100	NUM
ejpam-6347	526	29	days	day	NOUN
ejpam-6347	526	30	0.0	0.0	NUM
ejpam-6347	526	31	0.5	0.5	NUM
ejpam-6347	526	32	1.0	1.0	NUM
ejpam-6347	526	33	1.5	1.5	NUM
ejpam-6347	526	34	2.0	2.0	NUM
ejpam-6347	526	35	2.5	2.5	NUM
ejpam-6347	526	36	3.0	3.0	NUM
ejpam-6347	526	37	3.5	3.5	NUM
ejpam-6347	526	38	4.0	4.0	NUM
ejpam-6347	526	39	nu	nu	NOUN
ejpam-6347	526	40	m	m	VERB
ejpam-6347	526	41	be	be	VERB
ejpam-6347	527	1	r	r	NOUN
ejpam-6347	527	2	o	o	NOUN
ejpam-6347	528	1	f	f	NOUN
ejpam-6347	529	1	h	h	NOUN
ejpam-6347	530	1	os	os	NOUN
ejpam-6347	531	1	pi	pi	NOUN
ejpam-6347	531	2	ta	ta	X
ejpam-6347	532	1	liz	liz	PROPN
ejpam-6347	532	2	ed	ed	PROPN
ejpam-6347	532	3	(	(	PUNCT
ejpam-6347	532	4	h	h	PROPN
ejpam-6347	532	5	)	)	PUNCT
ejpam-6347	532	6	hospitalized	hospitalize	VERB
ejpam-6347	532	7	(	(	PUNCT
ejpam-6347	532	8	h	h	NOUN
ejpam-6347	532	9	)	)	PUNCT
ejpam-6347	532	10	dynamics	dynamic	NOUN
ejpam-6347	532	11	without	without	ADP
ejpam-6347	532	12	control	control	NOUN
ejpam-6347	532	13	with	with	ADP
ejpam-6347	532	14	control	control	NOUN
ejpam-6347	532	15	0	0	NUM
ejpam-6347	532	16	20	20	NUM
ejpam-6347	532	17	40	40	NUM
ejpam-6347	532	18	60	60	NUM
ejpam-6347	532	19	80	80	NUM
ejpam-6347	532	20	100	100	NUM
ejpam-6347	532	21	days	day	NOUN
ejpam-6347	532	22	1.3	1.3	NUM
ejpam-6347	532	23	1.4	1.4	NUM
ejpam-6347	532	24	1.5	1.5	NUM
ejpam-6347	532	25	1.6	1.6	NUM
ejpam-6347	532	26	1.7	1.7	NUM
ejpam-6347	532	27	1.8	1.8	NUM
ejpam-6347	532	28	1.9	1.9	NUM
ejpam-6347	532	29	2.0	2.0	NUM
ejpam-6347	532	30	nu	nu	INTJ
ejpam-6347	532	31	m	m	VERB
ejpam-6347	532	32	be	be	VERB
ejpam-6347	533	1	r	r	NOUN
ejpam-6347	533	2	o	o	NOUN
ejpam-6347	533	3	f	f	NOUN
ejpam-6347	533	4	a	a	DET
ejpam-6347	533	5	sy	sy	PROPN
ejpam-6347	533	6	m	m	ADJ
ejpam-6347	533	7	pt	pt	NOUN
ejpam-6347	533	8	om	om	PROPN
ejpam-6347	533	9	at	at	ADP
ejpam-6347	533	10	ic	ic	PROPN
ejpam-6347	533	11	(	(	PUNCT
ejpam-6347	533	12	f	f	PROPN
ejpam-6347	533	13	)	)	PUNCT
ejpam-6347	533	14	asymptomatic	asymptomatic	NOUN
ejpam-6347	533	15	(	(	PUNCT
ejpam-6347	533	16	f	f	X
ejpam-6347	533	17	)	)	PUNCT
ejpam-6347	533	18	dynamics	dynamic	NOUN
ejpam-6347	533	19	without	without	ADP
ejpam-6347	533	20	control	control	NOUN
ejpam-6347	533	21	with	with	ADP
ejpam-6347	533	22	control	control	NOUN
ejpam-6347	533	23	0	0	NUM
ejpam-6347	533	24	20	20	NUM
ejpam-6347	533	25	40	40	NUM
ejpam-6347	533	26	60	60	NUM
ejpam-6347	533	27	80	80	NUM
ejpam-6347	533	28	100	100	NUM
ejpam-6347	533	29	days	day	NOUN
ejpam-6347	533	30	0.4	0.4	NUM
ejpam-6347	533	31	0.2	0.2	NUM
ejpam-6347	533	32	0.0	0.0	NUM
ejpam-6347	533	33	0.2	0.2	NUM
ejpam-6347	533	34	0.4	0.4	NUM
ejpam-6347	533	35	0.6	0.6	NUM
ejpam-6347	533	36	0.8	0.8	NUM
ejpam-6347	533	37	1.0	1.0	NUM
ejpam-6347	533	38	nu	nu	INTJ
ejpam-6347	533	39	m	m	VERB
ejpam-6347	533	40	be	be	VERB
ejpam-6347	534	1	r	r	NOUN
ejpam-6347	534	2	o	o	NOUN
ejpam-6347	535	1	f	f	X
ejpam-6347	536	1	i	i	PRON
ejpam-6347	536	2	cu	cu	PROPN
ejpam-6347	536	3	(	(	PUNCT
ejpam-6347	536	4	c	c	PROPN
ejpam-6347	536	5	)	)	PUNCT
ejpam-6347	536	6	icu	icu	PROPN
ejpam-6347	536	7	(	(	PUNCT
ejpam-6347	536	8	c	c	NOUN
ejpam-6347	536	9	)	)	PUNCT
ejpam-6347	536	10	dynamics	dynamic	NOUN
ejpam-6347	536	11	without	without	ADP
ejpam-6347	536	12	control	control	NOUN
ejpam-6347	536	13	with	with	ADP
ejpam-6347	536	14	control	control	NOUN
ejpam-6347	536	15	0	0	NUM
ejpam-6347	536	16	20	20	NUM
ejpam-6347	536	17	40	40	NUM
ejpam-6347	536	18	60	60	NUM
ejpam-6347	536	19	80	80	NUM
ejpam-6347	536	20	100	100	NUM
ejpam-6347	536	21	days	day	NOUN
ejpam-6347	536	22	0	0	NUM
ejpam-6347	536	23	100	100	NUM
ejpam-6347	536	24	200	200	NUM
ejpam-6347	536	25	300	300	NUM
ejpam-6347	536	26	400	400	NUM
ejpam-6347	536	27	500	500	NUM
ejpam-6347	536	28	600	600	NUM
ejpam-6347	536	29	nu	nu	NOUN
ejpam-6347	536	30	m	m	VERB
ejpam-6347	536	31	be	be	NOUN
ejpam-6347	536	32	r	r	NOUN
ejpam-6347	536	33	o	o	NOUN
ejpam-6347	536	34	f	f	X
ejpam-6347	536	35	v	v	INTJ
ejpam-6347	536	36	ac	ac	PROPN
ejpam-6347	536	37	cin	cin	PROPN
ejpam-6347	536	38	at	at	ADP
ejpam-6347	536	39	ed	ed	PROPN
ejpam-6347	536	40	(	(	PUNCT
ejpam-6347	536	41	v	v	NOUN
ejpam-6347	536	42	)	)	PUNCT
ejpam-6347	536	43	vaccinated	vaccinate	VERB
ejpam-6347	536	44	(	(	PUNCT
ejpam-6347	536	45	v	v	NOUN
ejpam-6347	536	46	)	)	PUNCT
ejpam-6347	536	47	dynamics	dynamic	NOUN
ejpam-6347	536	48	without	without	ADP
ejpam-6347	536	49	control	control	NOUN
ejpam-6347	536	50	with	with	ADP
ejpam-6347	536	51	control	control	NOUN
ejpam-6347	536	52	0	0	NUM
ejpam-6347	536	53	20	20	NUM
ejpam-6347	536	54	40	40	NUM
ejpam-6347	536	55	60	60	NUM
ejpam-6347	536	56	80	80	NUM
ejpam-6347	536	57	100	100	NUM
ejpam-6347	536	58	days	day	NOUN
ejpam-6347	536	59	0	0	NUM
ejpam-6347	536	60	1	1	NUM
ejpam-6347	536	61	2	2	NUM
ejpam-6347	536	62	3	3	NUM
ejpam-6347	536	63	4	4	NUM
ejpam-6347	536	64	5	5	NUM
ejpam-6347	536	65	6	6	NUM
ejpam-6347	536	66	7	7	NUM
ejpam-6347	536	67	nu	nu	NOUN
ejpam-6347	536	68	m	m	VERB
ejpam-6347	536	69	be	be	VERB
ejpam-6347	537	1	r	r	NOUN
ejpam-6347	537	2	o	o	NOUN
ejpam-6347	537	3	f	f	X
ejpam-6347	537	4	r	r	NOUN
ejpam-6347	537	5	ec	ec	PROPN
ejpam-6347	537	6	ov	ov	INTJ
ejpam-6347	537	7	er	er	INTJ
ejpam-6347	537	8	ed	ed	NOUN
ejpam-6347	537	9	(	(	PUNCT
ejpam-6347	537	10	r	r	NOUN
ejpam-6347	537	11	)	)	PUNCT
ejpam-6347	537	12	recovered	recover	VERB
ejpam-6347	537	13	(	(	PUNCT
ejpam-6347	537	14	r	r	NOUN
ejpam-6347	537	15	)	)	PUNCT
ejpam-6347	537	16	dynamics	dynamic	NOUN
ejpam-6347	537	17	without	without	ADP
ejpam-6347	537	18	control	control	NOUN
ejpam-6347	537	19	with	with	ADP
ejpam-6347	537	20	control	control	NOUN
ejpam-6347	537	21	figure	figure	NOUN
ejpam-6347	537	22	8	8	NUM
ejpam-6347	537	23	:	:	PUNCT
ejpam-6347	537	24	temporal	temporal	ADJ
ejpam-6347	537	25	dynamics	dynamic	NOUN
ejpam-6347	537	26	of	of	ADP
ejpam-6347	537	27	covid-19	covid-19	PROPN
ejpam-6347	537	28	compartments	compartment	NOUN
ejpam-6347	537	29	with	with	ADP
ejpam-6347	537	30	and	and	CCONJ
ejpam-6347	537	31	without	without	ADP
ejpam-6347	537	32	optimal	optimal	ADJ
ejpam-6347	537	33	control	control	NOUN
ejpam-6347	537	34	interventions	intervention	NOUN
ejpam-6347	537	35	.	.	PUNCT
ejpam-6347	538	1	4.2	4.2	X
ejpam-6347	538	2	.	.	PUNCT
ejpam-6347	539	1	convergence	convergence	NOUN
ejpam-6347	539	2	analysis	analysis	NOUN
ejpam-6347	539	3	of	of	ADP
ejpam-6347	539	4	conformable	conformable	ADJ
ejpam-6347	539	5	fractional	fractional	ADJ
ejpam-6347	539	6	derivative	derivative	ADJ
ejpam-6347	539	7	model	model	NOUN
ejpam-6347	539	8	the	the	DET
ejpam-6347	539	9	structural	structural	ADJ
ejpam-6347	539	10	convergence	convergence	NOUN
ejpam-6347	539	11	of	of	ADP
ejpam-6347	539	12	the	the	DET
ejpam-6347	539	13	conformable	conformable	ADJ
ejpam-6347	539	14	fractional	fractional	ADJ
ejpam-6347	539	15	system	system	NOUN
ejpam-6347	539	16	(	(	PUNCT
ejpam-6347	539	17	2.4	2.4	NUM
ejpam-6347	539	18	)	)	PUNCT
ejpam-6347	539	19	was	be	AUX
ejpam-6347	539	20	rigorously	rigorously	ADV
ejpam-6347	539	21	analyzed	analyze	VERB
ejpam-6347	539	22	through	through	ADP
ejpam-6347	539	23	numerical	numerical	ADJ
ejpam-6347	539	24	simulations	simulation	NOUN
ejpam-6347	539	25	and	and	CCONJ
ejpam-6347	539	26	quantitative	quantitative	ADJ
ejpam-6347	539	27	error	error	NOUN
ejpam-6347	539	28	metrics	metric	NOUN
ejpam-6347	539	29	.	.	PUNCT
ejpam-6347	540	1	as	as	SCONJ
ejpam-6347	540	2	demonstrated	demonstrate	VERB
ejpam-6347	540	3	n.	n.	NOUN
ejpam-6347	540	4	abbas	abbas	PROPN
ejpam-6347	540	5	,	,	PUNCT
ejpam-6347	540	6	w.	w.	PROPN
ejpam-6347	540	7	shatanawi	shatanawi	PROPN
ejpam-6347	540	8	,	,	PUNCT
ejpam-6347	540	9	s.	s.	PROPN
ejpam-6347	540	10	a.	a.	NOUN
ejpam-6347	540	11	zanib	zanib	PROPN
ejpam-6347	540	12	/	/	SYM
ejpam-6347	540	13	eur	eur	PROPN
ejpam-6347	540	14	.	.	PUNCT
ejpam-6347	541	1	j.	j.	PROPN
ejpam-6347	541	2	pure	pure	PROPN
ejpam-6347	541	3	appl	appl	PROPN
ejpam-6347	541	4	.	.	PROPN
ejpam-6347	541	5	math	math	PROPN
ejpam-6347	541	6	,	,	PUNCT
ejpam-6347	541	7	18	18	NUM
ejpam-6347	541	8	(	(	PUNCT
ejpam-6347	541	9	3	3	NUM
ejpam-6347	541	10	)	)	PUNCT
ejpam-6347	541	11	(	(	PUNCT
ejpam-6347	541	12	2025	2025	NUM
ejpam-6347	541	13	)	)	PUNCT
ejpam-6347	541	14	,	,	PUNCT
ejpam-6347	541	15	6347	6347	NUM
ejpam-6347	541	16	29	29	NUM
ejpam-6347	541	17	of	of	ADP
ejpam-6347	541	18	34	34	NUM
ejpam-6347	541	19	in	in	ADP
ejpam-6347	541	20	figure	figure	NOUN
ejpam-6347	541	21	9	9	NUM
ejpam-6347	541	22	,	,	PUNCT
ejpam-6347	541	23	solution	solution	NOUN
ejpam-6347	541	24	trajectories	trajectory	NOUN
ejpam-6347	541	25	exhibit	exhibit	VERB
ejpam-6347	541	26	continuous	continuous	ADJ
ejpam-6347	541	27	dependence	dependence	NOUN
ejpam-6347	541	28	on	on	ADP
ejpam-6347	541	29	the	the	DET
ejpam-6347	541	30	fractional	fractional	ADJ
ejpam-6347	541	31	order	order	NOUN
ejpam-6347	541	32	parameter	parameter	NOUN
ejpam-6347	541	33	ς	ς	PROPN
ejpam-6347	541	34	,	,	PUNCT
ejpam-6347	541	35	asymptotically	asymptotically	ADV
ejpam-6347	541	36	approaching	approach	VERB
ejpam-6347	541	37	the	the	DET
ejpam-6347	541	38	classical	classical	ADJ
ejpam-6347	541	39	integer	integer	NOUN
ejpam-6347	541	40	-	-	PUNCT
ejpam-6347	541	41	order	order	NOUN
ejpam-6347	541	42	model	model	NOUN
ejpam-6347	541	43	(	(	PUNCT
ejpam-6347	541	44	2.1	2.1	NUM
ejpam-6347	541	45	)	)	PUNCT
ejpam-6347	541	46	as	as	ADP
ejpam-6347	541	47	ς	ς	PROPN
ejpam-6347	541	48	→	→	SYM
ejpam-6347	541	49	1	1	NUM
ejpam-6347	541	50	.	.	PUNCT
ejpam-6347	542	1	the	the	DET
ejpam-6347	542	2	convergence	convergence	NOUN
ejpam-6347	542	3	was	be	AUX
ejpam-6347	542	4	quantified	quantify	VERB
ejpam-6347	542	5	using	use	VERB
ejpam-6347	542	6	the	the	DET
ejpam-6347	542	7	l2	l2	NOUN
ejpam-6347	542	8	-	-	PUNCT
ejpam-6347	542	9	norm	norm	NOUN
ejpam-6347	542	10	difference	difference	NOUN
ejpam-6347	542	11	:	:	PUNCT
ejpam-6347	542	12	∥yς(t)−	∥yς(t)−	PROPN
ejpam-6347	542	13	y1(t)∥2	y1(t)∥2	PUNCT
ejpam-6347	543	1	=	=	PUNCT
ejpam-6347	543	2	√√√√	√√√√	DET
ejpam-6347	543	3	10∑	10∑	NUM
ejpam-6347	543	4	i=1	i=1	PROPN
ejpam-6347	543	5	∫	∫	PROPN
ejpam-6347	544	1	tf	tf	PROPN
ejpam-6347	544	2	t0	t0	PROPN
ejpam-6347	544	3	(	(	PUNCT
ejpam-6347	544	4	yς	yς	PROPN
ejpam-6347	544	5	,	,	PUNCT
ejpam-6347	544	6	i(t)−	i(t)−	PROPN
ejpam-6347	544	7	y1,i(t))2dt	y1,i(t))2dt	PROPN
ejpam-6347	544	8	where	where	SCONJ
ejpam-6347	544	9	yς(t	yς(t	PRON
ejpam-6347	544	10	)	)	PUNCT
ejpam-6347	544	11	=	=	PUNCT
ejpam-6347	545	1	[	[	X
ejpam-6347	545	2	sς	sς	X
ejpam-6347	545	3	,	,	PUNCT
ejpam-6347	545	4	eς	eς	PROPN
ejpam-6347	545	5	,	,	PUNCT
ejpam-6347	545	6	.	.	PUNCT
ejpam-6347	545	7	.	.	PUNCT
ejpam-6347	545	8	.	.	PUNCT
ejpam-6347	546	1	,	,	PUNCT
ejpam-6347	546	2	rς	rς	VERB
ejpam-6347	546	3	]	]	PUNCT
ejpam-6347	546	4	t	t	PROPN
ejpam-6347	546	5	and	and	CCONJ
ejpam-6347	546	6	y1(t	y1(t	X
ejpam-6347	546	7	)	)	PUNCT
ejpam-6347	546	8	represent	represent	VERB
ejpam-6347	546	9	the	the	DET
ejpam-6347	546	10	fractional	fractional	ADJ
ejpam-6347	546	11	and	and	CCONJ
ejpam-6347	546	12	integer	integer	NOUN
ejpam-6347	546	13	-	-	PUNCT
ejpam-6347	546	14	order	order	NOUN
ejpam-6347	546	15	solutions	solution	NOUN
ejpam-6347	546	16	respectively	respectively	ADV
ejpam-6347	546	17	.	.	PUNCT
ejpam-6347	547	1	numerical	numerical	ADJ
ejpam-6347	547	2	solutions	solution	NOUN
ejpam-6347	547	3	were	be	AUX
ejpam-6347	547	4	computed	compute	VERB
ejpam-6347	547	5	using	use	VERB
ejpam-6347	547	6	an	an	DET
ejpam-6347	547	7	implicit	implicit	ADJ
ejpam-6347	547	8	runge	runge	NOUN
ejpam-6347	547	9	-	-	PUNCT
ejpam-6347	547	10	kutta	kutta	NOUN
ejpam-6347	547	11	method	method	NOUN
ejpam-6347	547	12	with	with	ADP
ejpam-6347	547	13	adaptive	adaptive	ADJ
ejpam-6347	547	14	step	step	NOUN
ejpam-6347	547	15	size	size	NOUN
ejpam-6347	547	16	control	control	NOUN
ejpam-6347	547	17	h	h	NOUN
ejpam-6347	547	18	∈	∈	PROPN
ejpam-6347	548	1	[	[	X
ejpam-6347	548	2	0.01	0.01	NUM
ejpam-6347	548	3	,	,	PUNCT
ejpam-6347	548	4	0.1	0.1	NUM
ejpam-6347	548	5	]	]	PUNCT
ejpam-6347	548	6	to	to	PART
ejpam-6347	548	7	maintain	maintain	VERB
ejpam-6347	548	8	relative	relative	ADJ
ejpam-6347	548	9	error	error	NOUN
ejpam-6347	548	10	tolerance	tolerance	NOUN
ejpam-6347	548	11	below	below	ADP
ejpam-6347	548	12	10−5	10−5	NUM
ejpam-6347	548	13	.	.	PUNCT
ejpam-6347	549	1	0	0	NUM
ejpam-6347	549	2	20	20	NUM
ejpam-6347	549	3	40	40	NUM
ejpam-6347	549	4	60	60	NUM
ejpam-6347	549	5	80	80	NUM
ejpam-6347	549	6	100	100	NUM
ejpam-6347	549	7	days	day	NOUN
ejpam-6347	549	8	(	(	PUNCT
ejpam-6347	549	9	time	time	NOUN
ejpam-6347	549	10	)	)	PUNCT
ejpam-6347	549	11	500	500	NUM
ejpam-6347	549	12	1000	1000	NUM
ejpam-6347	549	13	1500	1500	NUM
ejpam-6347	549	14	2000	2000	NUM
ejpam-6347	549	15	2500	2500	NUM
ejpam-6347	549	16	su	su	PROPN
ejpam-6347	549	17	sc	sc	PROPN
ejpam-6347	549	18	ep	ep	PROPN
ejpam-6347	549	19	tib	tib	X
ejpam-6347	549	20	le	le	X
ejpam-6347	549	21	(	(	PUNCT
ejpam-6347	549	22	s	s	X
ejpam-6347	549	23	)	)	PUNCT
ejpam-6347	549	24	=	=	NOUN
ejpam-6347	549	25	0.1	0.1	NUM
ejpam-6347	549	26	=	=	SYM
ejpam-6347	549	27	0.3	0.3	NUM
ejpam-6347	549	28	=	=	SYM
ejpam-6347	549	29	0.5	0.5	NUM
ejpam-6347	549	30	=	=	NUM
ejpam-6347	549	31	0.7	0.7	NUM
ejpam-6347	549	32	=	=	NUM
ejpam-6347	549	33	0.9	0.9	NUM
ejpam-6347	549	34	0	0	NUM
ejpam-6347	549	35	20	20	NUM
ejpam-6347	549	36	40	40	NUM
ejpam-6347	549	37	60	60	NUM
ejpam-6347	549	38	80	80	NUM
ejpam-6347	549	39	100	100	NUM
ejpam-6347	549	40	days	day	NOUN
ejpam-6347	549	41	(	(	PUNCT
ejpam-6347	549	42	time	time	NOUN
ejpam-6347	549	43	)	)	PUNCT
ejpam-6347	549	44	0.0	0.0	NUM
ejpam-6347	549	45	2.5	2.5	NUM
ejpam-6347	549	46	5.0	5.0	NUM
ejpam-6347	549	47	7.5	7.5	NUM
ejpam-6347	549	48	10.0	10.0	NUM
ejpam-6347	549	49	12.5	12.5	NUM
ejpam-6347	549	50	15.0	15.0	NUM
ejpam-6347	549	51	17.5	17.5	NUM
ejpam-6347	549	52	20.0	20.0	NUM
ejpam-6347	549	53	pr	pr	NOUN
ejpam-6347	549	54	esy	esy	NOUN
ejpam-6347	549	55	m	m	INTJ
ejpam-6347	549	56	pt	pt	INTJ
ejpam-6347	549	57	om	om	NOUN
ejpam-6347	549	58	at	at	ADP
ejpam-6347	549	59	ic	ic	PROPN
ejpam-6347	549	60	(	(	PUNCT
ejpam-6347	549	61	e	e	NOUN
ejpam-6347	549	62	)	)	PUNCT
ejpam-6347	550	1	=	=	NOUN
ejpam-6347	550	2	0.1	0.1	NUM
ejpam-6347	550	3	=	=	SYM
ejpam-6347	550	4	0.3	0.3	NUM
ejpam-6347	550	5	=	=	SYM
ejpam-6347	550	6	0.5	0.5	NUM
ejpam-6347	550	7	=	=	NUM
ejpam-6347	550	8	0.7	0.7	NUM
ejpam-6347	550	9	=	=	NUM
ejpam-6347	550	10	0.9	0.9	NUM
ejpam-6347	550	11	0	0	NUM
ejpam-6347	550	12	20	20	NUM
ejpam-6347	550	13	40	40	NUM
ejpam-6347	550	14	60	60	NUM
ejpam-6347	550	15	80	80	NUM
ejpam-6347	550	16	100	100	NUM
ejpam-6347	550	17	days	day	NOUN
ejpam-6347	550	18	(	(	PUNCT
ejpam-6347	550	19	time	time	NOUN
ejpam-6347	550	20	)	)	PUNCT
ejpam-6347	550	21	6	6	NUM
ejpam-6347	550	22	7	7	NUM
ejpam-6347	550	23	8	8	NUM
ejpam-6347	550	24	9	9	NUM
ejpam-6347	550	25	10	10	NUM
ejpam-6347	550	26	in	in	ADP
ejpam-6347	550	27	fe	fe	X
ejpam-6347	550	28	ct	ct	PROPN
ejpam-6347	550	29	ed	ed	PROPN
ejpam-6347	550	30	(	(	PUNCT
ejpam-6347	550	31	u	u	NOUN
ejpam-6347	550	32	)	)	PUNCT
ejpam-6347	550	33	=	=	NOUN
ejpam-6347	550	34	0.1	0.1	NUM
ejpam-6347	550	35	=	=	SYM
ejpam-6347	550	36	0.3	0.3	NUM
ejpam-6347	550	37	=	=	SYM
ejpam-6347	550	38	0.5	0.5	NUM
ejpam-6347	550	39	=	=	NUM
ejpam-6347	550	40	0.7	0.7	NUM
ejpam-6347	550	41	=	=	NUM
ejpam-6347	550	42	0.9	0.9	NUM
ejpam-6347	550	43	0	0	NUM
ejpam-6347	550	44	20	20	NUM
ejpam-6347	550	45	40	40	NUM
ejpam-6347	550	46	60	60	NUM
ejpam-6347	550	47	80	80	NUM
ejpam-6347	550	48	100	100	NUM
ejpam-6347	550	49	days	day	NOUN
ejpam-6347	550	50	(	(	PUNCT
ejpam-6347	550	51	time	time	NOUN
ejpam-6347	550	52	)	)	PUNCT
ejpam-6347	550	53	10	10	NUM
ejpam-6347	550	54	15	15	NUM
ejpam-6347	550	55	20	20	NUM
ejpam-6347	550	56	25	25	NUM
ejpam-6347	550	57	30	30	NUM
ejpam-6347	550	58	qu	qu	PROPN
ejpam-6347	550	59	ar	ar	NOUN
ejpam-6347	550	60	an	an	DET
ejpam-6347	550	61	tin	tin	NOUN
ejpam-6347	550	62	ed	ed	NOUN
ejpam-6347	550	63	(	(	PUNCT
ejpam-6347	550	64	q	q	NOUN
ejpam-6347	550	65	)	)	PUNCT
ejpam-6347	551	1	=	=	SYM
ejpam-6347	551	2	0.1	0.1	NUM
ejpam-6347	551	3	=	=	SYM
ejpam-6347	551	4	0.3	0.3	NUM
ejpam-6347	551	5	=	=	SYM
ejpam-6347	551	6	0.5	0.5	NUM
ejpam-6347	551	7	=	=	NUM
ejpam-6347	551	8	0.7	0.7	NUM
ejpam-6347	551	9	=	=	NUM
ejpam-6347	551	10	0.9	0.9	NUM
ejpam-6347	551	11	0	0	NUM
ejpam-6347	551	12	20	20	NUM
ejpam-6347	551	13	40	40	NUM
ejpam-6347	551	14	60	60	NUM
ejpam-6347	551	15	80	80	NUM
ejpam-6347	551	16	100	100	NUM
ejpam-6347	551	17	days	day	NOUN
ejpam-6347	551	18	(	(	PUNCT
ejpam-6347	551	19	time	time	NOUN
ejpam-6347	551	20	)	)	PUNCT
ejpam-6347	551	21	2.0	2.0	NUM
ejpam-6347	551	22	2.5	2.5	NUM
ejpam-6347	551	23	3.0	3.0	NUM
ejpam-6347	551	24	3.5	3.5	NUM
ejpam-6347	551	25	4.0	4.0	NUM
ejpam-6347	551	26	4.5	4.5	NUM
ejpam-6347	551	27	5.0	5.0	NUM
ejpam-6347	551	28	5.5	5.5	NUM
ejpam-6347	551	29	6.0	6.0	NUM
ejpam-6347	551	30	cl	cl	NOUN
ejpam-6347	551	31	in	in	ADP
ejpam-6347	551	32	ica	ica	PROPN
ejpam-6347	551	33	lly	lly	ADV
ejpam-6347	551	34	p	p	X
ejpam-6347	551	35	os	os	PROPN
ejpam-6347	551	36	iti	iti	PROPN
ejpam-6347	551	37	ve	ve	VERB
ejpam-6347	551	38	(	(	PUNCT
ejpam-6347	551	39	p	p	NOUN
ejpam-6347	551	40	)	)	PUNCT
ejpam-6347	552	1	=	=	SYM
ejpam-6347	552	2	0.1	0.1	NUM
ejpam-6347	552	3	=	=	SYM
ejpam-6347	552	4	0.3	0.3	NUM
ejpam-6347	552	5	=	=	SYM
ejpam-6347	552	6	0.5	0.5	NUM
ejpam-6347	552	7	=	=	NUM
ejpam-6347	552	8	0.7	0.7	NUM
ejpam-6347	552	9	=	=	NUM
ejpam-6347	552	10	0.9	0.9	NUM
ejpam-6347	552	11	0	0	NUM
ejpam-6347	552	12	20	20	NUM
ejpam-6347	552	13	40	40	NUM
ejpam-6347	552	14	60	60	NUM
ejpam-6347	552	15	80	80	NUM
ejpam-6347	552	16	100	100	NUM
ejpam-6347	552	17	days	day	NOUN
ejpam-6347	552	18	(	(	PUNCT
ejpam-6347	552	19	time	time	NOUN
ejpam-6347	552	20	)	)	PUNCT
ejpam-6347	552	21	0.0	0.0	NUM
ejpam-6347	552	22	0.5	0.5	NUM
ejpam-6347	552	23	1.0	1.0	NUM
ejpam-6347	552	24	1.5	1.5	NUM
ejpam-6347	552	25	2.0	2.0	NUM
ejpam-6347	552	26	2.5	2.5	NUM
ejpam-6347	552	27	3.0	3.0	NUM
ejpam-6347	552	28	3.5	3.5	NUM
ejpam-6347	552	29	4.0	4.0	NUM
ejpam-6347	552	30	ho	ho	NOUN
ejpam-6347	552	31	sp	sp	ADP
ejpam-6347	552	32	ita	ita	PROPN
ejpam-6347	552	33	liz	liz	PROPN
ejpam-6347	552	34	ed	ed	PROPN
ejpam-6347	552	35	(	(	PUNCT
ejpam-6347	552	36	h	h	NOUN
ejpam-6347	552	37	)	)	PUNCT
ejpam-6347	553	1	=	=	SYM
ejpam-6347	553	2	0.1	0.1	NUM
ejpam-6347	553	3	=	=	SYM
ejpam-6347	553	4	0.3	0.3	NUM
ejpam-6347	553	5	=	=	SYM
ejpam-6347	553	6	0.5	0.5	NUM
ejpam-6347	553	7	=	=	NUM
ejpam-6347	553	8	0.7	0.7	NUM
ejpam-6347	553	9	=	=	NUM
ejpam-6347	553	10	0.9	0.9	NUM
ejpam-6347	553	11	0	0	NUM
ejpam-6347	553	12	20	20	NUM
ejpam-6347	553	13	40	40	NUM
ejpam-6347	553	14	60	60	NUM
ejpam-6347	553	15	80	80	NUM
ejpam-6347	553	16	100	100	NUM
ejpam-6347	553	17	days	day	NOUN
ejpam-6347	553	18	(	(	PUNCT
ejpam-6347	553	19	time	time	NOUN
ejpam-6347	553	20	)	)	PUNCT
ejpam-6347	553	21	1.5	1.5	NUM
ejpam-6347	553	22	1.6	1.6	NUM
ejpam-6347	553	23	1.7	1.7	NUM
ejpam-6347	553	24	1.8	1.8	NUM
ejpam-6347	553	25	1.9	1.9	NUM
ejpam-6347	553	26	2.0	2.0	NUM
ejpam-6347	553	27	as	as	ADP
ejpam-6347	553	28	ym	ym	PROPN
ejpam-6347	553	29	pt	pt	INTJ
ejpam-6347	553	30	om	om	PROPN
ejpam-6347	553	31	at	at	ADP
ejpam-6347	553	32	ic	ic	PROPN
ejpam-6347	553	33	(	(	PUNCT
ejpam-6347	553	34	f	f	PROPN
ejpam-6347	553	35	)	)	PUNCT
ejpam-6347	554	1	=	=	NOUN
ejpam-6347	554	2	0.1	0.1	NUM
ejpam-6347	554	3	=	=	SYM
ejpam-6347	554	4	0.3	0.3	NUM
ejpam-6347	554	5	=	=	SYM
ejpam-6347	554	6	0.5	0.5	NUM
ejpam-6347	554	7	=	=	NUM
ejpam-6347	554	8	0.7	0.7	NUM
ejpam-6347	554	9	=	=	NUM
ejpam-6347	554	10	0.9	0.9	NUM
ejpam-6347	554	11	0	0	NUM
ejpam-6347	554	12	20	20	NUM
ejpam-6347	554	13	40	40	NUM
ejpam-6347	554	14	60	60	NUM
ejpam-6347	554	15	80	80	NUM
ejpam-6347	554	16	100	100	NUM
ejpam-6347	554	17	days	day	NOUN
ejpam-6347	554	18	(	(	PUNCT
ejpam-6347	554	19	time	time	NOUN
ejpam-6347	554	20	)	)	PUNCT
ejpam-6347	554	21	0.70	0.70	NUM
ejpam-6347	554	22	0.75	0.75	NUM
ejpam-6347	554	23	0.80	0.80	NUM
ejpam-6347	554	24	0.85	0.85	NUM
ejpam-6347	554	25	0.90	0.90	NUM
ejpam-6347	554	26	0.95	0.95	NUM
ejpam-6347	554	27	1.00	1.00	NUM
ejpam-6347	554	28	ic	ic	PROPN
ejpam-6347	554	29	u	u	PROPN
ejpam-6347	554	30	(	(	PUNCT
ejpam-6347	554	31	c	c	NOUN
ejpam-6347	554	32	)	)	PUNCT
ejpam-6347	555	1	=	=	NOUN
ejpam-6347	555	2	0.1	0.1	NUM
ejpam-6347	555	3	=	=	SYM
ejpam-6347	555	4	0.3	0.3	NUM
ejpam-6347	555	5	=	=	SYM
ejpam-6347	555	6	0.5	0.5	NUM
ejpam-6347	555	7	=	=	NUM
ejpam-6347	555	8	0.7	0.7	NUM
ejpam-6347	555	9	=	=	NUM
ejpam-6347	555	10	0.9	0.9	NUM
ejpam-6347	555	11	0	0	NUM
ejpam-6347	555	12	20	20	NUM
ejpam-6347	555	13	40	40	NUM
ejpam-6347	555	14	60	60	NUM
ejpam-6347	555	15	80	80	NUM
ejpam-6347	555	16	100	100	NUM
ejpam-6347	555	17	days	day	NOUN
ejpam-6347	555	18	(	(	PUNCT
ejpam-6347	555	19	time	time	NOUN
ejpam-6347	555	20	)	)	PUNCT
ejpam-6347	555	21	0.0	0.0	NUM
ejpam-6347	555	22	2.5	2.5	NUM
ejpam-6347	555	23	5.0	5.0	NUM
ejpam-6347	555	24	7.5	7.5	NUM
ejpam-6347	555	25	10.0	10.0	NUM
ejpam-6347	555	26	12.5	12.5	NUM
ejpam-6347	555	27	15.0	15.0	NUM
ejpam-6347	555	28	17.5	17.5	NUM
ejpam-6347	555	29	va	va	NOUN
ejpam-6347	555	30	cc	cc	NOUN
ejpam-6347	555	31	in	in	ADV
ejpam-6347	555	32	at	at	ADP
ejpam-6347	555	33	ed	ed	PROPN
ejpam-6347	555	34	(	(	PUNCT
ejpam-6347	555	35	v	v	NOUN
ejpam-6347	555	36	)	)	PUNCT
ejpam-6347	555	37	=	=	NOUN
ejpam-6347	555	38	0.1	0.1	NUM
ejpam-6347	555	39	=	=	SYM
ejpam-6347	555	40	0.3	0.3	NUM
ejpam-6347	555	41	=	=	SYM
ejpam-6347	555	42	0.5	0.5	NUM
ejpam-6347	555	43	=	=	NUM
ejpam-6347	555	44	0.7	0.7	NUM
ejpam-6347	555	45	=	=	NUM
ejpam-6347	555	46	0.9	0.9	NUM
ejpam-6347	555	47	0	0	NUM
ejpam-6347	555	48	20	20	NUM
ejpam-6347	555	49	40	40	NUM
ejpam-6347	555	50	60	60	NUM
ejpam-6347	555	51	80	80	NUM
ejpam-6347	555	52	100	100	NUM
ejpam-6347	555	53	days	day	NOUN
ejpam-6347	555	54	(	(	PUNCT
ejpam-6347	555	55	time	time	NOUN
ejpam-6347	555	56	)	)	PUNCT
ejpam-6347	555	57	0.0	0.0	NUM
ejpam-6347	555	58	0.5	0.5	NUM
ejpam-6347	555	59	1.0	1.0	NUM
ejpam-6347	555	60	1.5	1.5	NUM
ejpam-6347	555	61	2.0	2.0	NUM
ejpam-6347	555	62	2.5	2.5	NUM
ejpam-6347	555	63	3.0	3.0	NUM
ejpam-6347	555	64	re	re	VERB
ejpam-6347	555	65	co	co	VERB
ejpam-6347	555	66	ve	ve	AUX
ejpam-6347	555	67	re	re	VERB
ejpam-6347	555	68	d	d	X
ejpam-6347	555	69	(	(	PUNCT
ejpam-6347	555	70	r	r	NOUN
ejpam-6347	555	71	)	)	PUNCT
ejpam-6347	555	72	=	=	NOUN
ejpam-6347	555	73	0.1	0.1	NUM
ejpam-6347	555	74	=	=	SYM
ejpam-6347	555	75	0.3	0.3	NUM
ejpam-6347	555	76	=	=	SYM
ejpam-6347	555	77	0.5	0.5	NUM
ejpam-6347	555	78	=	=	NUM
ejpam-6347	555	79	0.7	0.7	NUM
ejpam-6347	555	80	=	=	SYM
ejpam-6347	555	81	0.9	0.9	NUM
ejpam-6347	555	82	figure	figure	NOUN
ejpam-6347	555	83	9	9	NUM
ejpam-6347	555	84	:	:	PUNCT
ejpam-6347	555	85	dynamic	dynamic	ADJ
ejpam-6347	555	86	convergence	convergence	NOUN
ejpam-6347	555	87	of	of	ADP
ejpam-6347	555	88	conformable	conformable	ADJ
ejpam-6347	555	89	fractional	fractional	ADJ
ejpam-6347	555	90	model	model	NOUN
ejpam-6347	555	91	solutions	solution	NOUN
ejpam-6347	555	92	to	to	ADP
ejpam-6347	555	93	classical	classical	ADJ
ejpam-6347	555	94	solutions	solution	NOUN
ejpam-6347	555	95	as	as	ADP
ejpam-6347	555	96	ς	ς	PROPN
ejpam-6347	555	97	→	→	SYM
ejpam-6347	555	98	1	1	X
ejpam-6347	555	99	.	.	X
ejpam-6347	555	100	shading	shading	NOUN
ejpam-6347	555	101	represents	represent	VERB
ejpam-6347	555	102	solution	solution	NOUN
ejpam-6347	555	103	variance	variance	NOUN
ejpam-6347	555	104	across	across	ADP
ejpam-6347	555	105	ς	ς	PROPN
ejpam-6347	555	106	∈	∈	PROPN
ejpam-6347	556	1	[	[	X
ejpam-6347	556	2	0.1	0.1	NUM
ejpam-6347	556	3	,	,	PUNCT
ejpam-6347	556	4	0.9	0.9	NUM
ejpam-6347	556	5	]	]	PUNCT
ejpam-6347	556	6	.	.	PUNCT
ejpam-6347	557	1	n.	n.	PROPN
ejpam-6347	557	2	abbas	abbas	PROPN
ejpam-6347	557	3	,	,	PUNCT
ejpam-6347	557	4	w.	w.	PROPN
ejpam-6347	557	5	shatanawi	shatanawi	PROPN
ejpam-6347	557	6	,	,	PUNCT
ejpam-6347	557	7	s.	s.	PROPN
ejpam-6347	557	8	a.	a.	NOUN
ejpam-6347	557	9	zanib	zanib	PROPN
ejpam-6347	557	10	/	/	SYM
ejpam-6347	557	11	eur	eur	PROPN
ejpam-6347	557	12	.	.	PUNCT
ejpam-6347	558	1	j.	j.	PROPN
ejpam-6347	558	2	pure	pure	PROPN
ejpam-6347	558	3	appl	appl	PROPN
ejpam-6347	558	4	.	.	PROPN
ejpam-6347	558	5	math	math	PROPN
ejpam-6347	558	6	,	,	PUNCT
ejpam-6347	558	7	18	18	NUM
ejpam-6347	558	8	(	(	PUNCT
ejpam-6347	558	9	3	3	NUM
ejpam-6347	558	10	)	)	PUNCT
ejpam-6347	558	11	(	(	PUNCT
ejpam-6347	558	12	2025	2025	NUM
ejpam-6347	558	13	)	)	PUNCT
ejpam-6347	558	14	,	,	PUNCT
ejpam-6347	558	15	6347	6347	NUM
ejpam-6347	558	16	30	30	NUM
ejpam-6347	558	17	of	of	ADP
ejpam-6347	558	18	34	34	NUM
ejpam-6347	558	19	the	the	DET
ejpam-6347	558	20	conformable	conformable	ADJ
ejpam-6347	558	21	fractional	fractional	ADJ
ejpam-6347	558	22	derivative	derivative	ADJ
ejpam-6347	558	23	introduces	introduce	NOUN
ejpam-6347	558	24	time	time	NOUN
ejpam-6347	558	25	-	-	PUNCT
ejpam-6347	558	26	dependent	dependent	ADJ
ejpam-6347	558	27	memory	memory	NOUN
ejpam-6347	558	28	effects	effect	NOUN
ejpam-6347	558	29	into	into	ADP
ejpam-6347	558	30	epidemiological	epidemiological	ADJ
ejpam-6347	558	31	modeling	modeling	NOUN
ejpam-6347	558	32	,	,	PUNCT
ejpam-6347	558	33	capturing	capture	VERB
ejpam-6347	558	34	how	how	SCONJ
ejpam-6347	558	35	historical	historical	ADJ
ejpam-6347	558	36	transmission	transmission	NOUN
ejpam-6347	558	37	dynamics	dynamic	NOUN
ejpam-6347	558	38	,	,	PUNCT
ejpam-6347	558	39	immune	immune	ADJ
ejpam-6347	558	40	responses	response	NOUN
ejpam-6347	558	41	,	,	PUNCT
ejpam-6347	558	42	and	and	CCONJ
ejpam-6347	558	43	behavioral	behavioral	ADJ
ejpam-6347	558	44	adaptations	adaptation	NOUN
ejpam-6347	558	45	continuously	continuously	ADV
ejpam-6347	558	46	influence	influence	VERB
ejpam-6347	558	47	disease	disease	NOUN
ejpam-6347	558	48	spread	spread	VERB
ejpam-6347	558	49	.	.	PUNCT
ejpam-6347	559	1	unlike	unlike	ADP
ejpam-6347	559	2	classical	classical	ADJ
ejpam-6347	559	3	integer	integer	NOUN
ejpam-6347	559	4	-	-	PUNCT
ejpam-6347	559	5	order	order	NOUN
ejpam-6347	559	6	models	model	NOUN
ejpam-6347	559	7	that	that	PRON
ejpam-6347	559	8	assume	assume	VERB
ejpam-6347	559	9	instantaneous	instantaneous	ADJ
ejpam-6347	559	10	state	state	NOUN
ejpam-6347	559	11	transitions	transition	NOUN
ejpam-6347	559	12	,	,	PUNCT
ejpam-6347	559	13	the	the	DET
ejpam-6347	559	14	conformable	conformable	ADJ
ejpam-6347	559	15	operator	operator	NOUN
ejpam-6347	559	16	dς	dς	VERB
ejpam-6347	559	17	ty	ty	NOUN
ejpam-6347	559	18	=	=	SYM
ejpam-6347	559	19	t1−ς	t1−ς	PROPN
ejpam-6347	559	20	dy	dy	NOUN
ejpam-6347	559	21	dt	dt	NOUN
ejpam-6347	559	22	incorporates	incorporate	VERB
ejpam-6347	559	23	a	a	DET
ejpam-6347	559	24	temporal	temporal	ADJ
ejpam-6347	559	25	scaling	scale	VERB
ejpam-6347	559	26	factor	factor	NOUN
ejpam-6347	559	27	t1−ς	t1−ς	PROPN
ejpam-6347	559	28	,	,	PUNCT
ejpam-6347	559	29	modulating	modulate	VERB
ejpam-6347	559	30	transmission	transmission	NOUN
ejpam-6347	559	31	rates	rate	NOUN
ejpam-6347	559	32	through	through	ADP
ejpam-6347	559	33	the	the	DET
ejpam-6347	559	34	fractional	fractional	ADJ
ejpam-6347	559	35	order	order	NOUN
ejpam-6347	559	36	ς	ς	PROPN
ejpam-6347	559	37	.	.	PROPN
ejpam-6347	559	38	for	for	ADP
ejpam-6347	559	39	ς	ς	PROPN
ejpam-6347	559	40	<	<	X
ejpam-6347	559	41	1	1	NUM
ejpam-6347	559	42	,	,	PUNCT
ejpam-6347	559	43	slower	slow	ADJ
ejpam-6347	559	44	infection	infection	NOUN
ejpam-6347	559	45	progression	progression	NOUN
ejpam-6347	559	46	emerges	emerge	VERB
ejpam-6347	559	47	,	,	PUNCT
ejpam-6347	559	48	mimicking	mimic	VERB
ejpam-6347	559	49	real	real	ADJ
ejpam-6347	559	50	-	-	PUNCT
ejpam-6347	559	51	world	world	NOUN
ejpam-6347	559	52	delays	delay	NOUN
ejpam-6347	559	53	in	in	ADP
ejpam-6347	559	54	interventions	intervention	NOUN
ejpam-6347	559	55	such	such	ADJ
ejpam-6347	559	56	as	as	ADP
ejpam-6347	559	57	lockdowns	lockdown	NOUN
ejpam-6347	559	58	or	or	CCONJ
ejpam-6347	559	59	vaccine	vaccine	NOUN
ejpam-6347	559	60	rollouts	rollout	NOUN
ejpam-6347	559	61	.	.	PUNCT
ejpam-6347	560	1	this	this	DET
ejpam-6347	560	2	formulation	formulation	NOUN
ejpam-6347	560	3	avoids	avoid	VERB
ejpam-6347	560	4	non	non	ADJ
ejpam-6347	560	5	-	-	ADJ
ejpam-6347	560	6	physical	physical	ADJ
ejpam-6347	560	7	infinite	infinite	ADJ
ejpam-6347	560	8	memory	memory	NOUN
ejpam-6347	560	9	artifacts	artifact	NOUN
ejpam-6347	560	10	while	while	SCONJ
ejpam-6347	560	11	preserving	preserve	VERB
ejpam-6347	560	12	short	short	ADJ
ejpam-6347	560	13	-	-	PUNCT
ejpam-6347	560	14	term	term	NOUN
ejpam-6347	560	15	memory	memory	NOUN
ejpam-6347	560	16	effects	effect	NOUN
ejpam-6347	560	17	,	,	PUNCT
ejpam-6347	560	18	such	such	ADJ
ejpam-6347	560	19	as	as	ADP
ejpam-6347	560	20	waning	wane	VERB
ejpam-6347	560	21	immunity	immunity	NOUN
ejpam-6347	560	22	.	.	PUNCT
ejpam-6347	561	1	by	by	ADP
ejpam-6347	561	2	varying	vary	VERB
ejpam-6347	561	3	ς	ς	PROPN
ejpam-6347	561	4	∈	∈	PROPN
ejpam-6347	561	5	(	(	PUNCT
ejpam-6347	561	6	0	0	NUM
ejpam-6347	561	7	,	,	PUNCT
ejpam-6347	561	8	1	1	NUM
ejpam-6347	561	9	]	]	PUNCT
ejpam-6347	561	10	,	,	PUNCT
ejpam-6347	561	11	the	the	DET
ejpam-6347	561	12	model	model	NOUN
ejpam-6347	561	13	spans	span	VERB
ejpam-6347	561	14	rapid	rapid	ADJ
ejpam-6347	561	15	containment	containment	NOUN
ejpam-6347	561	16	(	(	PUNCT
ejpam-6347	561	17	ς	ς	PROPN
ejpam-6347	561	18	→	→	SYM
ejpam-6347	561	19	1	1	NUM
ejpam-6347	561	20	)	)	PUNCT
ejpam-6347	561	21	to	to	ADP
ejpam-6347	561	22	prolonged	prolong	VERB
ejpam-6347	561	23	transmission	transmission	NOUN
ejpam-6347	561	24	(	(	PUNCT
ejpam-6347	561	25	ς	ς	NOUN
ejpam-6347	561	26	≪	≪	ADJ
ejpam-6347	561	27	1	1	NUM
ejpam-6347	561	28	)	)	PUNCT
ejpam-6347	561	29	,	,	PUNCT
ejpam-6347	561	30	reflecting	reflect	VERB
ejpam-6347	561	31	heterogeneous	heterogeneous	ADJ
ejpam-6347	561	32	public	public	ADJ
ejpam-6347	561	33	health	health	NOUN
ejpam-6347	561	34	scenarios	scenario	NOUN
ejpam-6347	561	35	.	.	PUNCT
ejpam-6347	562	1	this	this	DET
ejpam-6347	562	2	approach	approach	NOUN
ejpam-6347	562	3	bridges	bridge	NOUN
ejpam-6347	562	4	idealized	idealize	VERB
ejpam-6347	562	5	compartmental	compartmental	ADJ
ejpam-6347	562	6	frameworks	framework	NOUN
ejpam-6347	562	7	with	with	ADP
ejpam-6347	562	8	empirical	empirical	ADJ
ejpam-6347	562	9	outbreak	outbreak	NOUN
ejpam-6347	562	10	patterns	pattern	NOUN
ejpam-6347	562	11	,	,	PUNCT
ejpam-6347	562	12	where	where	SCONJ
ejpam-6347	562	13	cumulative	cumulative	ADJ
ejpam-6347	562	14	interactions	interaction	NOUN
ejpam-6347	562	15	dictate	dictate	VERB
ejpam-6347	562	16	epidemic	epidemic	NOUN
ejpam-6347	562	17	trajectories	trajectory	NOUN
ejpam-6347	562	18	.	.	PUNCT
ejpam-6347	563	1	table	table	NOUN
ejpam-6347	563	2	2	2	NUM
ejpam-6347	563	3	:	:	PUNCT
ejpam-6347	563	4	quantitative	quantitative	ADJ
ejpam-6347	563	5	convergence	convergence	NOUN
ejpam-6347	563	6	analysis	analysis	NOUN
ejpam-6347	563	7	of	of	ADP
ejpam-6347	563	8	fractional	fractional	ADJ
ejpam-6347	563	9	-	-	PUNCT
ejpam-6347	563	10	order	order	NOUN
ejpam-6347	563	11	solutions	solution	NOUN
ejpam-6347	563	12	ς	ς	PROPN
ejpam-6347	563	13	l2	l2	NOUN
ejpam-6347	563	14	-	-	PUNCT
ejpam-6347	563	15	norm	norm	NOUN
ejpam-6347	563	16	difference	difference	NOUN
ejpam-6347	563	17	normalized	normalize	VERB
ejpam-6347	563	18	l2	l2	NOUN
ejpam-6347	563	19	-	-	PUNCT
ejpam-6347	563	20	norm	norm	NOUN
ejpam-6347	563	21	0.1	0.1	NUM
ejpam-6347	563	22	14986.57	14986.57	NUM
ejpam-6347	563	23	1.0000	1.0000	NUM
ejpam-6347	563	24	0.3	0.3	NUM
ejpam-6347	563	25	14317.17	14317.17	NUM
ejpam-6347	563	26	0.9553	0.9553	NUM
ejpam-6347	563	27	0.5	0.5	NUM
ejpam-6347	563	28	12602.19	12602.19	NUM
ejpam-6347	563	29	0.8409	0.8409	NUM
ejpam-6347	563	30	0.7	0.7	NUM
ejpam-6347	563	31	9295.42	9295.42	NUM
ejpam-6347	563	32	0.6202	0.6202	NUM
ejpam-6347	563	33	0.9	0.9	NUM
ejpam-6347	563	34	3712.78	3712.78	NUM
ejpam-6347	563	35	0.2477	0.2477	NUM
ejpam-6347	563	36	1.0	1.0	NUM
ejpam-6347	563	37	0.00	0.00	NUM
ejpam-6347	563	38	0.0000	0.0000	NUM
ejpam-6347	563	39	table	table	NOUN
ejpam-6347	563	40	3	3	NUM
ejpam-6347	563	41	:	:	PUNCT
ejpam-6347	563	42	parameters	parameter	NOUN
ejpam-6347	563	43	used	use	VERB
ejpam-6347	563	44	for	for	ADP
ejpam-6347	563	45	the	the	DET
ejpam-6347	563	46	covcom10	covcom10	NOUN
ejpam-6347	563	47	model	model	NOUN
ejpam-6347	563	48	parameters	parameter	NOUN
ejpam-6347	563	49	value	value	NOUN
ejpam-6347	563	50	source	source	NOUN
ejpam-6347	563	51	parameters	parameter	NOUN
ejpam-6347	563	52	value	value	VERB
ejpam-6347	563	53	source	source	NOUN
ejpam-6347	563	54	λ	λ	PROPN
ejpam-6347	563	55	50	50	NUM
ejpam-6347	564	1	[	[	X
ejpam-6347	564	2	12	12	NUM
ejpam-6347	564	3	]	]	PUNCT
ejpam-6347	564	4	λ1	λ1	PROPN
ejpam-6347	564	5	0.008	0.008	NUM
ejpam-6347	564	6	[	[	X
ejpam-6347	564	7	12	12	NUM
ejpam-6347	564	8	]	]	PUNCT
ejpam-6347	564	9	µ	µ	X
ejpam-6347	564	10	0.009	0.009	NUM
ejpam-6347	564	11	[	[	X
ejpam-6347	564	12	12	12	NUM
ejpam-6347	564	13	]	]	X
ejpam-6347	564	14	λ2	λ2	NOUN
ejpam-6347	564	15	0.0011	0.0011	NUM
ejpam-6347	564	16	estimated	estimate	VERB
ejpam-6347	564	17	γ	γ	X
ejpam-6347	564	18	0.08	0.08	NUM
ejpam-6347	564	19	estimated	estimate	VERB
ejpam-6347	564	20	α1	α1	PROPN
ejpam-6347	564	21	0.01004	0.01004	NUM
ejpam-6347	564	22	estimated	estimate	VERB
ejpam-6347	564	23	b1	b1	NOUN
ejpam-6347	564	24	0.002	0.002	NUM
ejpam-6347	564	25	[	[	X
ejpam-6347	564	26	12	12	NUM
ejpam-6347	564	27	]	]	X
ejpam-6347	564	28	α2	α2	PROPN
ejpam-6347	564	29	0.0083	0.0083	NUM
ejpam-6347	564	30	estimated	estimate	VERB
ejpam-6347	564	31	b2	b2	NOUN
ejpam-6347	564	32	0.0013	0.0013	NUM
ejpam-6347	564	33	estimated	estimate	VERB
ejpam-6347	564	34	b3	b3	PROPN
ejpam-6347	564	35	0.00379	0.00379	NUM
ejpam-6347	564	36	estimated	estimate	VERB
ejpam-6347	564	37	φ1	φ1	NOUN
ejpam-6347	564	38	0.001971	0.001971	NUM
ejpam-6347	564	39	[	[	X
ejpam-6347	564	40	12	12	NUM
ejpam-6347	564	41	]	]	PUNCT
ejpam-6347	564	42	m1	m1	NOUN
ejpam-6347	564	43	0.008619	0.008619	NUM
ejpam-6347	564	44	estimated	estimate	VERB
ejpam-6347	564	45	φ2	φ2	PROPN
ejpam-6347	564	46	0.0018	0.0018	NUM
ejpam-6347	564	47	estimated	estimate	VERB
ejpam-6347	564	48	m2	m2	PROPN
ejpam-6347	564	49	0.0012	0.0012	NUM
ejpam-6347	564	50	estimated	estimate	VERB
ejpam-6347	564	51	φ3	φ3	NOUN
ejpam-6347	564	52	0.004711	0.004711	NUM
ejpam-6347	564	53	[	[	X
ejpam-6347	564	54	12	12	NUM
ejpam-6347	564	55	]	]	PUNCT
ejpam-6347	564	56	m3	m3	PROPN
ejpam-6347	564	57	0.0003	0.0003	NUM
ejpam-6347	564	58	estimated	estimate	VERB
ejpam-6347	564	59	σ1	σ1	PROPN
ejpam-6347	564	60	0.0018	0.0018	NUM
ejpam-6347	564	61	estimated	estimate	VERB
ejpam-6347	564	62	η	η	PROPN
ejpam-6347	564	63	0.0009	0.0009	NUM
ejpam-6347	564	64	estimated	estimate	VERB
ejpam-6347	564	65	σ2	σ2	PROPN
ejpam-6347	564	66	0.0021	0.0021	NUM
ejpam-6347	564	67	estimated	estimate	VERB
ejpam-6347	564	68	β	β	X
ejpam-6347	564	69	0.5	0.5	NUM
ejpam-6347	564	70	estimated	estimate	VERB
ejpam-6347	564	71	β	β	X
ejpam-6347	564	72	0.5	0.5	NUM
ejpam-6347	565	1	[	[	X
ejpam-6347	565	2	11	11	NUM
ejpam-6347	565	3	]	]	PUNCT
ejpam-6347	565	4	τ	τ	X
ejpam-6347	565	5	0.05	0.05	NUM
ejpam-6347	565	6	[	[	X
ejpam-6347	565	7	11	11	NUM
ejpam-6347	565	8	]	]	SYM
ejpam-6347	565	9	ϕ	ϕ	X
ejpam-6347	565	10	0.02	0.02	NUM
ejpam-6347	565	11	estimated	estimate	VERB
ejpam-6347	565	12	d1	d1	PROPN
ejpam-6347	565	13	0.26	0.26	NUM
ejpam-6347	565	14	[	[	X
ejpam-6347	565	15	11	11	NUM
ejpam-6347	565	16	]	]	PUNCT
ejpam-6347	565	17	d2	d2	NOUN
ejpam-6347	565	18	0.25	0.25	NUM
ejpam-6347	565	19	estimated	estimate	VERB
ejpam-6347	565	20	d5	d5	NOUN
ejpam-6347	565	21	0.22	0.22	NUM
ejpam-6347	565	22	estimated	estimate	VERB
ejpam-6347	565	23	d3	d3	PROPN
ejpam-6347	565	24	0.24	0.24	NUM
ejpam-6347	565	25	estimated	estimate	VERB
ejpam-6347	565	26	d6	d6	NOUN
ejpam-6347	565	27	0.21	0.21	NUM
ejpam-6347	565	28	estimated	estimated	ADJ
ejpam-6347	565	29	d4	d4	PROPN
ejpam-6347	565	30	0.23	0.23	NUM
ejpam-6347	565	31	estimated	estimate	VERB
ejpam-6347	565	32	d7	d7	PROPN
ejpam-6347	565	33	0.20	0.20	NUM
ejpam-6347	565	34	estimated	estimate	VERB
ejpam-6347	565	35	n.	n.	NOUN
ejpam-6347	565	36	abbas	abbas	PROPN
ejpam-6347	565	37	,	,	PUNCT
ejpam-6347	565	38	w.	w.	PROPN
ejpam-6347	565	39	shatanawi	shatanawi	PROPN
ejpam-6347	565	40	,	,	PUNCT
ejpam-6347	565	41	s.	s.	PROPN
ejpam-6347	565	42	a.	a.	NOUN
ejpam-6347	565	43	zanib	zanib	PROPN
ejpam-6347	565	44	/	/	SYM
ejpam-6347	565	45	eur	eur	PROPN
ejpam-6347	565	46	.	.	PUNCT
ejpam-6347	566	1	j.	j.	PROPN
ejpam-6347	566	2	pure	pure	PROPN
ejpam-6347	566	3	appl	appl	PROPN
ejpam-6347	566	4	.	.	PROPN
ejpam-6347	566	5	math	math	PROPN
ejpam-6347	566	6	,	,	PUNCT
ejpam-6347	566	7	18	18	NUM
ejpam-6347	566	8	(	(	PUNCT
ejpam-6347	566	9	3	3	NUM
ejpam-6347	566	10	)	)	PUNCT
ejpam-6347	566	11	(	(	PUNCT
ejpam-6347	566	12	2025	2025	NUM
ejpam-6347	566	13	)	)	PUNCT
ejpam-6347	566	14	,	,	PUNCT
ejpam-6347	566	15	6347	6347	NUM
ejpam-6347	566	16	31	31	NUM
ejpam-6347	566	17	of	of	ADP
ejpam-6347	566	18	34	34	NUM
ejpam-6347	566	19	5	5	NUM
ejpam-6347	566	20	.	.	PUNCT
ejpam-6347	567	1	conclusion	conclusion	NOUN
ejpam-6347	567	2	this	this	DET
ejpam-6347	567	3	study	study	NOUN
ejpam-6347	567	4	investigated	investigate	VERB
ejpam-6347	567	5	the	the	DET
ejpam-6347	567	6	impact	impact	NOUN
ejpam-6347	567	7	of	of	ADP
ejpam-6347	567	8	vaccination	vaccination	NOUN
ejpam-6347	567	9	on	on	ADP
ejpam-6347	567	10	virus	virus	NOUN
ejpam-6347	567	11	transmission	transmission	NOUN
ejpam-6347	567	12	and	and	CCONJ
ejpam-6347	567	13	proposed	propose	VERB
ejpam-6347	567	14	effective	effective	ADJ
ejpam-6347	567	15	control	control	NOUN
ejpam-6347	567	16	strategies	strategy	NOUN
ejpam-6347	567	17	using	use	VERB
ejpam-6347	567	18	a	a	DET
ejpam-6347	567	19	ten	ten	NUM
ejpam-6347	567	20	-	-	PUNCT
ejpam-6347	567	21	compartment	compartment	NOUN
ejpam-6347	567	22	mathematical	mathematical	ADJ
ejpam-6347	567	23	model	model	NOUN
ejpam-6347	567	24	named	name	VERB
ejpam-6347	567	25	covcom10	covcom10	NOUN
ejpam-6347	567	26	,	,	PUNCT
ejpam-6347	567	27	formulated	formulate	VERB
ejpam-6347	567	28	as	as	ADP
ejpam-6347	567	29	a	a	DET
ejpam-6347	567	30	system	system	NOUN
ejpam-6347	567	31	of	of	ADP
ejpam-6347	567	32	nonlinear	nonlinear	ADJ
ejpam-6347	567	33	differential	differential	ADJ
ejpam-6347	567	34	equations	equation	NOUN
ejpam-6347	567	35	.	.	PUNCT
ejpam-6347	568	1	the	the	DET
ejpam-6347	568	2	model	model	NOUN
ejpam-6347	568	3	explicitly	explicitly	ADV
ejpam-6347	568	4	includes	include	VERB
ejpam-6347	568	5	vaccination	vaccination	NOUN
ejpam-6347	568	6	,	,	PUNCT
ejpam-6347	568	7	asymptomatic	asymptomatic	ADJ
ejpam-6347	568	8	,	,	PUNCT
ejpam-6347	568	9	and	and	CCONJ
ejpam-6347	568	10	pre	pre	ADJ
ejpam-6347	568	11	-	-	ADJ
ejpam-6347	568	12	symptomatic	symptomatic	ADJ
ejpam-6347	568	13	carriers	carrier	NOUN
ejpam-6347	568	14	to	to	PART
ejpam-6347	568	15	better	well	ADV
ejpam-6347	568	16	capture	capture	VERB
ejpam-6347	568	17	the	the	DET
ejpam-6347	568	18	real	real	ADJ
ejpam-6347	568	19	-	-	PUNCT
ejpam-6347	568	20	world	world	NOUN
ejpam-6347	568	21	transmission	transmission	NOUN
ejpam-6347	568	22	dynamics	dynamic	NOUN
ejpam-6347	568	23	.	.	PUNCT
ejpam-6347	569	1	our	our	PRON
ejpam-6347	569	2	results	result	NOUN
ejpam-6347	569	3	highlight	highlight	VERB
ejpam-6347	569	4	the	the	DET
ejpam-6347	569	5	critical	critical	ADJ
ejpam-6347	569	6	role	role	NOUN
ejpam-6347	569	7	of	of	ADP
ejpam-6347	569	8	vaccination	vaccination	NOUN
ejpam-6347	569	9	in	in	ADP
ejpam-6347	569	10	mitigating	mitigate	VERB
ejpam-6347	569	11	sars	sar	NOUN
ejpam-6347	569	12	-	-	PUNCT
ejpam-6347	569	13	cov-2	cov-2	NOUN
ejpam-6347	569	14	spread	spread	NOUN
ejpam-6347	569	15	.	.	PUNCT
ejpam-6347	570	1	the	the	DET
ejpam-6347	570	2	model	model	NOUN
ejpam-6347	570	3	alters	alter	VERB
ejpam-6347	570	4	the	the	DET
ejpam-6347	570	5	classical	classical	ADJ
ejpam-6347	570	6	susceptible	susceptible	ADJ
ejpam-6347	570	7	population	population	NOUN
ejpam-6347	570	8	expression	expression	NOUN
ejpam-6347	570	9	from	from	ADP
ejpam-6347	570	10	s0	s0	PROPN
ejpam-6347	570	11	=	=	PUNCT
ejpam-6347	570	12	λ	λ	X
ejpam-6347	570	13	µ	µ	X
ejpam-6347	570	14	(	(	PUNCT
ejpam-6347	570	15	as	as	SCONJ
ejpam-6347	570	16	seen	see	VERB
ejpam-6347	570	17	in	in	ADP
ejpam-6347	570	18	seir	seir	ADJ
ejpam-6347	570	19	models	model	NOUN
ejpam-6347	570	20	)	)	PUNCT
ejpam-6347	570	21	to	to	ADP
ejpam-6347	570	22	s0	s0	PROPN
ejpam-6347	570	23	=	=	PUNCT
ejpam-6347	570	24	λ	λ	PROPN
ejpam-6347	570	25	β+µ	β+µ	PUNCT
ejpam-6347	570	26	in	in	ADP
ejpam-6347	570	27	covcom10	covcom10	NOUN
ejpam-6347	570	28	,	,	PUNCT
ejpam-6347	570	29	reflecting	reflect	VERB
ejpam-6347	570	30	immunization	immunization	NOUN
ejpam-6347	570	31	’s	’s	PART
ejpam-6347	570	32	role	role	NOUN
ejpam-6347	570	33	in	in	ADP
ejpam-6347	570	34	reducing	reduce	VERB
ejpam-6347	570	35	susceptibility	susceptibility	NOUN
ejpam-6347	570	36	.	.	PUNCT
ejpam-6347	571	1	the	the	DET
ejpam-6347	571	2	basic	basic	ADJ
ejpam-6347	571	3	reproduction	reproduction	NOUN
ejpam-6347	571	4	number	number	NOUN
ejpam-6347	571	5	r0	r0	NOUN
ejpam-6347	571	6	was	be	AUX
ejpam-6347	571	7	computed	compute	VERB
ejpam-6347	571	8	to	to	PART
ejpam-6347	571	9	quantify	quantify	VERB
ejpam-6347	571	10	disease	disease	NOUN
ejpam-6347	571	11	potential	potential	NOUN
ejpam-6347	571	12	.	.	PUNCT
ejpam-6347	572	1	stability	stability	NOUN
ejpam-6347	572	2	analysis	analysis	NOUN
ejpam-6347	572	3	confirms	confirm	VERB
ejpam-6347	572	4	that	that	SCONJ
ejpam-6347	572	5	the	the	DET
ejpam-6347	572	6	disease	disease	NOUN
ejpam-6347	572	7	-	-	PUNCT
ejpam-6347	572	8	free	free	ADJ
ejpam-6347	572	9	equilibrium	equilibrium	NOUN
ejpam-6347	572	10	is	be	AUX
ejpam-6347	572	11	locally	locally	ADV
ejpam-6347	572	12	and	and	CCONJ
ejpam-6347	572	13	globally	globally	ADV
ejpam-6347	572	14	asymptotically	asymptotically	ADV
ejpam-6347	572	15	stable	stable	ADJ
ejpam-6347	572	16	when	when	SCONJ
ejpam-6347	572	17	r0	r0	NOUN
ejpam-6347	572	18	<	<	X
ejpam-6347	572	19	1	1	NUM
ejpam-6347	572	20	,	,	PUNCT
ejpam-6347	572	21	and	and	CCONJ
ejpam-6347	572	22	the	the	DET
ejpam-6347	572	23	endemic	endemic	ADJ
ejpam-6347	572	24	equilibrium	equilibrium	NOUN
ejpam-6347	572	25	is	be	AUX
ejpam-6347	572	26	stable	stable	ADJ
ejpam-6347	572	27	when	when	SCONJ
ejpam-6347	572	28	r0	r0	NOUN
ejpam-6347	572	29	>	>	X
ejpam-6347	572	30	1	1	NUM
ejpam-6347	572	31	.	.	PUNCT
ejpam-6347	572	32	time	time	NOUN
ejpam-6347	572	33	-	-	PUNCT
ejpam-6347	572	34	dependent	dependent	ADJ
ejpam-6347	572	35	control	control	NOUN
ejpam-6347	572	36	variables	variable	NOUN
ejpam-6347	572	37	for	for	ADP
ejpam-6347	572	38	vaccination	vaccination	NOUN
ejpam-6347	572	39	(	(	PUNCT
ejpam-6347	572	40	a1	a1	NOUN
ejpam-6347	572	41	)	)	PUNCT
ejpam-6347	572	42	,	,	PUNCT
ejpam-6347	572	43	hospitalization	hospitalization	NOUN
ejpam-6347	572	44	(	(	PUNCT
ejpam-6347	572	45	a2	a2	PROPN
ejpam-6347	572	46	)	)	PUNCT
ejpam-6347	572	47	,	,	PUNCT
ejpam-6347	572	48	and	and	CCONJ
ejpam-6347	572	49	asymptomatic	asymptomatic	ADJ
ejpam-6347	572	50	isolation	isolation	NOUN
ejpam-6347	572	51	(	(	PUNCT
ejpam-6347	572	52	a3	a3	NOUN
ejpam-6347	572	53	)	)	PUNCT
ejpam-6347	572	54	were	be	AUX
ejpam-6347	572	55	introduced	introduce	VERB
ejpam-6347	572	56	via	via	ADP
ejpam-6347	572	57	the	the	DET
ejpam-6347	572	58	pontryagin	pontryagin	NOUN
ejpam-6347	572	59	maximum	maximum	PROPN
ejpam-6347	572	60	principle	principle	NOUN
ejpam-6347	572	61	.	.	PUNCT
ejpam-6347	573	1	simulations	simulation	NOUN
ejpam-6347	573	2	demonstrated	demonstrate	VERB
ejpam-6347	573	3	that	that	SCONJ
ejpam-6347	573	4	optimizing	optimize	VERB
ejpam-6347	573	5	these	these	DET
ejpam-6347	573	6	controls	control	NOUN
ejpam-6347	573	7	significantly	significantly	ADV
ejpam-6347	573	8	reduces	reduce	VERB
ejpam-6347	573	9	transmission	transmission	NOUN
ejpam-6347	573	10	.	.	PUNCT
ejpam-6347	574	1	model	model	NOUN
ejpam-6347	574	2	parameters	parameter	NOUN
ejpam-6347	574	3	such	such	ADJ
ejpam-6347	574	4	as	as	ADP
ejpam-6347	574	5	ϕ	ϕ	PROPN
ejpam-6347	574	6	,	,	PUNCT
ejpam-6347	574	7	β	β	NOUN
ejpam-6347	574	8	,	,	PUNCT
ejpam-6347	574	9	and	and	CCONJ
ejpam-6347	574	10	γ	γ	NOUN
ejpam-6347	574	11	reflect	reflect	VERB
ejpam-6347	574	12	real	real	ADJ
ejpam-6347	574	13	-	-	PUNCT
ejpam-6347	574	14	world	world	NOUN
ejpam-6347	574	15	biological	biological	ADJ
ejpam-6347	574	16	mechanisms	mechanism	NOUN
ejpam-6347	574	17	of	of	ADP
ejpam-6347	574	18	infection	infection	NOUN
ejpam-6347	574	19	,	,	PUNCT
ejpam-6347	574	20	recovery	recovery	NOUN
ejpam-6347	574	21	,	,	PUNCT
ejpam-6347	574	22	and	and	CCONJ
ejpam-6347	574	23	exposure	exposure	NOUN
ejpam-6347	574	24	.	.	PUNCT
ejpam-6347	575	1	the	the	DET
ejpam-6347	575	2	success	success	NOUN
ejpam-6347	575	3	of	of	ADP
ejpam-6347	575	4	these	these	DET
ejpam-6347	575	5	strategies	strategy	NOUN
ejpam-6347	575	6	depends	depend	VERB
ejpam-6347	575	7	on	on	ADP
ejpam-6347	575	8	coordinated	coordinate	VERB
ejpam-6347	575	9	policy	policy	NOUN
ejpam-6347	575	10	implementation	implementation	NOUN
ejpam-6347	575	11	and	and	CCONJ
ejpam-6347	575	12	community	community	NOUN
ejpam-6347	575	13	behavior	behavior	NOUN
ejpam-6347	575	14	.	.	PUNCT
ejpam-6347	576	1	moreover	moreover	ADV
ejpam-6347	576	2	,	,	PUNCT
ejpam-6347	576	3	the	the	DET
ejpam-6347	576	4	modularity	modularity	NOUN
ejpam-6347	576	5	of	of	ADP
ejpam-6347	576	6	covcom10	covcom10	NOUN
ejpam-6347	576	7	makes	make	VERB
ejpam-6347	576	8	it	it	PRON
ejpam-6347	576	9	adaptable	adaptable	ADJ
ejpam-6347	576	10	to	to	ADP
ejpam-6347	576	11	other	other	ADJ
ejpam-6347	576	12	infectious	infectious	ADJ
ejpam-6347	576	13	diseases	disease	NOUN
ejpam-6347	576	14	like	like	ADP
ejpam-6347	576	15	influenza	influenza	NOUN
ejpam-6347	576	16	or	or	CCONJ
ejpam-6347	576	17	monkeypox	monkeypox	NOUN
ejpam-6347	576	18	,	,	PUNCT
ejpam-6347	576	19	or	or	CCONJ
ejpam-6347	576	20	emerging	emerge	VERB
ejpam-6347	576	21	sars	sar	NOUN
ejpam-6347	576	22	-	-	PUNCT
ejpam-6347	576	23	cov-2	cov-2	NOUN
ejpam-6347	576	24	variants	variant	NOUN
ejpam-6347	576	25	.	.	PUNCT
ejpam-6347	577	1	adjusting	adjust	VERB
ejpam-6347	577	2	compartments	compartment	NOUN
ejpam-6347	577	3	and	and	CCONJ
ejpam-6347	577	4	parameters	parameter	NOUN
ejpam-6347	577	5	allows	allow	VERB
ejpam-6347	577	6	the	the	DET
ejpam-6347	577	7	model	model	NOUN
ejpam-6347	577	8	to	to	PART
ejpam-6347	577	9	simulate	simulate	VERB
ejpam-6347	577	10	various	various	ADJ
ejpam-6347	577	11	epidemiological	epidemiological	ADJ
ejpam-6347	577	12	scenarios	scenario	NOUN
ejpam-6347	577	13	.	.	PUNCT
ejpam-6347	578	1	the	the	DET
ejpam-6347	578	2	use	use	NOUN
ejpam-6347	578	3	of	of	ADP
ejpam-6347	578	4	the	the	DET
ejpam-6347	578	5	conformable	conformable	ADJ
ejpam-6347	578	6	fractional	fractional	ADJ
ejpam-6347	578	7	derivative	derivative	ADJ
ejpam-6347	578	8	enhances	enhance	NOUN
ejpam-6347	578	9	the	the	DET
ejpam-6347	578	10	model	model	NOUN
ejpam-6347	578	11	’s	’s	PART
ejpam-6347	578	12	ability	ability	NOUN
ejpam-6347	578	13	to	to	PART
ejpam-6347	578	14	capture	capture	VERB
ejpam-6347	578	15	memory	memory	NOUN
ejpam-6347	578	16	effects	effect	NOUN
ejpam-6347	578	17	and	and	CCONJ
ejpam-6347	578	18	persistent	persistent	ADJ
ejpam-6347	578	19	behavior	behavior	NOUN
ejpam-6347	578	20	.	.	PUNCT
ejpam-6347	579	1	we	we	PRON
ejpam-6347	579	2	recommend	recommend	VERB
ejpam-6347	579	3	that	that	SCONJ
ejpam-6347	579	4	vaccination	vaccination	NOUN
ejpam-6347	579	5	campaigns	campaign	NOUN
ejpam-6347	579	6	be	be	AUX
ejpam-6347	579	7	complemented	complement	VERB
ejpam-6347	579	8	by	by	ADP
ejpam-6347	579	9	personal	personal	ADJ
ejpam-6347	579	10	preventive	preventive	ADJ
ejpam-6347	579	11	practices	practice	NOUN
ejpam-6347	579	12	such	such	ADJ
ejpam-6347	579	13	as	as	ADP
ejpam-6347	579	14	mask	mask	NOUN
ejpam-6347	579	15	-	-	PUNCT
ejpam-6347	579	16	wearing	wear	VERB
ejpam-6347	579	17	,	,	PUNCT
ejpam-6347	579	18	hand	hand	NOUN
ejpam-6347	579	19	hygiene	hygiene	NOUN
ejpam-6347	579	20	,	,	PUNCT
ejpam-6347	579	21	and	and	CCONJ
ejpam-6347	579	22	social	social	ADJ
ejpam-6347	579	23	distancing	distancing	NOUN
ejpam-6347	579	24	.	.	PUNCT
ejpam-6347	580	1	these	these	DET
ejpam-6347	580	2	combined	combine	VERB
ejpam-6347	580	3	interventions	intervention	NOUN
ejpam-6347	580	4	are	be	AUX
ejpam-6347	580	5	essential	essential	ADJ
ejpam-6347	580	6	for	for	ADP
ejpam-6347	580	7	managing	manage	VERB
ejpam-6347	580	8	current	current	ADJ
ejpam-6347	580	9	and	and	CCONJ
ejpam-6347	580	10	future	future	ADJ
ejpam-6347	580	11	infectious	infectious	ADJ
ejpam-6347	580	12	disease	disease	NOUN
ejpam-6347	580	13	outbreaks	outbreak	NOUN
ejpam-6347	580	14	.	.	PUNCT
ejpam-6347	581	1	as	as	ADP
ejpam-6347	581	2	a	a	DET
ejpam-6347	581	3	limitation	limitation	NOUN
ejpam-6347	581	4	of	of	ADP
ejpam-6347	581	5	the	the	DET
ejpam-6347	581	6	model	model	NOUN
ejpam-6347	581	7	,	,	PUNCT
ejpam-6347	581	8	despite	despite	SCONJ
ejpam-6347	581	9	its	its	PRON
ejpam-6347	581	10	validation	validation	NOUN
ejpam-6347	581	11	against	against	ADP
ejpam-6347	581	12	real	real	ADJ
ejpam-6347	581	13	epidemiological	epidemiological	ADJ
ejpam-6347	581	14	data	datum	NOUN
ejpam-6347	581	15	,	,	PUNCT
ejpam-6347	581	16	it	it	PRON
ejpam-6347	581	17	assumes	assume	VERB
ejpam-6347	581	18	homogeneous	homogeneous	ADJ
ejpam-6347	581	19	mixing	mixing	NOUN
ejpam-6347	581	20	and	and	CCONJ
ejpam-6347	581	21	does	do	AUX
ejpam-6347	581	22	not	not	PART
ejpam-6347	581	23	account	account	VERB
ejpam-6347	581	24	for	for	ADP
ejpam-6347	581	25	spatial	spatial	ADJ
ejpam-6347	581	26	heterogeneity	heterogeneity	NOUN
ejpam-6347	581	27	or	or	CCONJ
ejpam-6347	581	28	stochastic	stochastic	ADJ
ejpam-6347	581	29	variations	variation	NOUN
ejpam-6347	581	30	.	.	PUNCT
ejpam-6347	582	1	additionally	additionally	ADV
ejpam-6347	582	2	,	,	PUNCT
ejpam-6347	582	3	due	due	ADP
ejpam-6347	582	4	to	to	ADP
ejpam-6347	582	5	limited	limited	ADJ
ejpam-6347	582	6	data	data	NOUN
ejpam-6347	582	7	availability	availability	NOUN
ejpam-6347	582	8	,	,	PUNCT
ejpam-6347	582	9	some	some	DET
ejpam-6347	582	10	parameters	parameter	NOUN
ejpam-6347	582	11	were	be	AUX
ejpam-6347	582	12	estimated	estimate	VERB
ejpam-6347	582	13	,	,	PUNCT
ejpam-6347	582	14	which	which	PRON
ejpam-6347	582	15	may	may	AUX
ejpam-6347	582	16	affect	affect	VERB
ejpam-6347	582	17	the	the	DET
ejpam-6347	582	18	model	model	NOUN
ejpam-6347	582	19	’s	’s	PART
ejpam-6347	582	20	precision	precision	NOUN
ejpam-6347	582	21	.	.	PUNCT
ejpam-6347	583	1	future	future	ADJ
ejpam-6347	583	2	work	work	NOUN
ejpam-6347	583	3	could	could	AUX
ejpam-6347	583	4	enhance	enhance	VERB
ejpam-6347	583	5	this	this	DET
ejpam-6347	583	6	model	model	NOUN
ejpam-6347	583	7	by	by	ADP
ejpam-6347	583	8	incorporating	incorporate	VERB
ejpam-6347	583	9	stochastic	stochastic	ADJ
ejpam-6347	583	10	processes	process	NOUN
ejpam-6347	583	11	,	,	PUNCT
ejpam-6347	583	12	spatial	spatial	ADJ
ejpam-6347	583	13	heterogeneity	heterogeneity	NOUN
ejpam-6347	583	14	,	,	PUNCT
ejpam-6347	583	15	with	with	ADP
ejpam-6347	583	16	co	co	NOUN
ejpam-6347	583	17	-	-	NOUN
ejpam-6347	583	18	infection	infection	NOUN
ejpam-6347	583	19	or	or	CCONJ
ejpam-6347	583	20	network	network	NOUN
ejpam-6347	583	21	-	-	PUNCT
ejpam-6347	583	22	based	base	VERB
ejpam-6347	583	23	transmission	transmission	NOUN
ejpam-6347	583	24	to	to	PART
ejpam-6347	583	25	provide	provide	VERB
ejpam-6347	583	26	more	more	ADV
ejpam-6347	583	27	realistic	realistic	ADJ
ejpam-6347	583	28	and	and	CCONJ
ejpam-6347	583	29	robust	robust	ADJ
ejpam-6347	583	30	policy	policy	NOUN
ejpam-6347	583	31	guidance	guidance	NOUN
ejpam-6347	583	32	.	.	PUNCT
ejpam-6347	584	1	acknowledgements	acknowledgement	NOUN
ejpam-6347	584	2	authors	author	NOUN
ejpam-6347	584	3	(	(	PUNCT
ejpam-6347	584	4	dr	dr	PROPN
ejpam-6347	584	5	.	.	PROPN
ejpam-6347	584	6	nadeem	nadeem	PROPN
ejpam-6347	584	7	abbas	abbas	PROPN
ejpam-6347	584	8	and	and	CCONJ
ejpam-6347	584	9	prof	prof	PROPN
ejpam-6347	584	10	.	.	PUNCT
ejpam-6347	585	1	dr	dr	PROPN
ejpam-6347	585	2	.	.	PROPN
ejpam-6347	585	3	wasfi	wasfi	PROPN
ejpam-6347	585	4	shatanawi	shatanawi	PROPN
ejpam-6347	585	5	)	)	PUNCT
ejpam-6347	585	6	would	would	AUX
ejpam-6347	585	7	like	like	VERB
ejpam-6347	585	8	to	to	PART
ejpam-6347	585	9	thank	thank	VERB
ejpam-6347	585	10	prince	prince	PROPN
ejpam-6347	585	11	sultan	sultan	PROPN
ejpam-6347	585	12	university	university	PROPN
ejpam-6347	585	13	for	for	ADP
ejpam-6347	585	14	their	their	PRON
ejpam-6347	585	15	support	support	NOUN
ejpam-6347	585	16	through	through	ADP
ejpam-6347	585	17	the	the	DET
ejpam-6347	585	18	tas	tas	PROPN
ejpam-6347	585	19	research	research	NOUN
ejpam-6347	585	20	lab	lab	PROPN
ejpam-6347	585	21	.	.	PUNCT
ejpam-6347	586	1	data	datum	NOUN
ejpam-6347	586	2	availability	availability	NOUN
ejpam-6347	586	3	no	no	DET
ejpam-6347	586	4	data	datum	NOUN
ejpam-6347	586	5	availability	availability	NOUN
ejpam-6347	586	6	conflict	conflict	NOUN
ejpam-6347	586	7	of	of	ADP
ejpam-6347	586	8	interest	interest	NOUN
ejpam-6347	586	9	the	the	DET
ejpam-6347	586	10	authors	author	NOUN
ejpam-6347	586	11	declare	declare	VERB
ejpam-6347	586	12	that	that	SCONJ
ejpam-6347	586	13	there	there	PRON
ejpam-6347	586	14	is	be	VERB
ejpam-6347	586	15	no	no	DET
ejpam-6347	586	16	conflict	conflict	NOUN
ejpam-6347	586	17	of	of	ADP
ejpam-6347	586	18	interest	interest	NOUN
ejpam-6347	586	19	.	.	PUNCT
ejpam-6347	587	1	n.	n.	PROPN
ejpam-6347	587	2	abbas	abbas	PROPN
ejpam-6347	587	3	,	,	PUNCT
ejpam-6347	587	4	w.	w.	PROPN
ejpam-6347	587	5	shatanawi	shatanawi	PROPN
ejpam-6347	587	6	,	,	PUNCT
ejpam-6347	587	7	s.	s.	PROPN
ejpam-6347	587	8	a.	a.	NOUN
ejpam-6347	587	9	zanib	zanib	PROPN
ejpam-6347	587	10	/	/	SYM
ejpam-6347	587	11	eur	eur	PROPN
ejpam-6347	587	12	.	.	PUNCT
ejpam-6347	588	1	j.	j.	PROPN
ejpam-6347	588	2	pure	pure	PROPN
ejpam-6347	588	3	appl	appl	PROPN
ejpam-6347	588	4	.	.	PROPN
ejpam-6347	588	5	math	math	PROPN
ejpam-6347	588	6	,	,	PUNCT
ejpam-6347	588	7	18	18	NUM
ejpam-6347	588	8	(	(	PUNCT
ejpam-6347	588	9	3	3	NUM
ejpam-6347	588	10	)	)	PUNCT
ejpam-6347	588	11	(	(	PUNCT
ejpam-6347	588	12	2025	2025	NUM
ejpam-6347	588	13	)	)	PUNCT
ejpam-6347	588	14	,	,	PUNCT
ejpam-6347	588	15	6347	6347	NUM
ejpam-6347	588	16	32	32	NUM
ejpam-6347	588	17	of	of	ADP
ejpam-6347	588	18	34	34	NUM
ejpam-6347	588	19	references	reference	NOUN
ejpam-6347	588	20	[	[	X
ejpam-6347	588	21	1	1	NUM
ejpam-6347	588	22	]	]	PUNCT
ejpam-6347	588	23	qun	qun	PROPN
ejpam-6347	588	24	li	li	PROPN
ejpam-6347	588	25	,	,	PUNCT
ejpam-6347	588	26	xuhua	xuhua	PROPN
ejpam-6347	588	27	guan	guan	PROPN
ejpam-6347	588	28	,	,	PUNCT
ejpam-6347	588	29	peng	peng	PROPN
ejpam-6347	588	30	wu	wu	PROPN
ejpam-6347	588	31	,	,	PUNCT
ejpam-6347	588	32	xiaoye	xiaoye	PROPN
ejpam-6347	588	33	wang	wang	PROPN
ejpam-6347	588	34	,	,	PUNCT
ejpam-6347	588	35	lei	lei	PROPN
ejpam-6347	588	36	zhou	zhou	PROPN
ejpam-6347	588	37	,	,	PUNCT
ejpam-6347	588	38	yeqing	yeqe	VERB
ejpam-6347	588	39	tong	tong	PROPN
ejpam-6347	588	40	,	,	PUNCT
ejpam-6347	588	41	ruiqi	ruiqi	PROPN
ejpam-6347	588	42	ren	ren	PROPN
ejpam-6347	588	43	,	,	PUNCT
ejpam-6347	588	44	kathy	kathy	PROPN
ejpam-6347	588	45	sm	sm	PROPN
ejpam-6347	588	46	leung	leung	PROPN
ejpam-6347	588	47	,	,	PUNCT
ejpam-6347	588	48	eric	eric	PROPN
ejpam-6347	588	49	hy	hy	PROPN
ejpam-6347	588	50	lau	lau	PROPN
ejpam-6347	588	51	,	,	PUNCT
ejpam-6347	588	52	jessica	jessica	PROPN
ejpam-6347	588	53	y	y	PROPN
ejpam-6347	588	54	wong	wong	PROPN
ejpam-6347	588	55	,	,	PUNCT
ejpam-6347	588	56	et	et	PROPN
ejpam-6347	588	57	al	al	PROPN
ejpam-6347	588	58	.	.	PROPN
ejpam-6347	589	1	early	early	ADJ
ejpam-6347	589	2	transmission	transmission	NOUN
ejpam-6347	589	3	dynamics	dynamic	NOUN
ejpam-6347	589	4	in	in	ADP
ejpam-6347	589	5	wuhan	wuhan	PROPN
ejpam-6347	589	6	,	,	PUNCT
ejpam-6347	589	7	china	china	PROPN
ejpam-6347	589	8	,	,	PUNCT
ejpam-6347	589	9	of	of	ADP
ejpam-6347	589	10	novel	novel	ADJ
ejpam-6347	589	11	coronavirus	coronavirus	NOUN
ejpam-6347	589	12	–	–	PUNCT
ejpam-6347	589	13	infected	infected	ADJ
ejpam-6347	589	14	pneumonia	pneumonia	NOUN
ejpam-6347	589	15	.	.	PUNCT
ejpam-6347	590	1	new	new	PROPN
ejpam-6347	590	2	england	england	PROPN
ejpam-6347	590	3	journal	journal	PROPN
ejpam-6347	590	4	of	of	ADP
ejpam-6347	590	5	medicine	medicine	NOUN
ejpam-6347	590	6	,	,	PUNCT
ejpam-6347	590	7	382(13):1199–1207	382(13):1199–1207	NUM
ejpam-6347	590	8	,	,	PUNCT
ejpam-6347	590	9	2020	2020	NUM
ejpam-6347	590	10	.	.	PUNCT
ejpam-6347	591	1	[	[	X
ejpam-6347	591	2	2	2	X
ejpam-6347	591	3	]	]	PUNCT
ejpam-6347	591	4	sk	sk	ADP
ejpam-6347	591	5	shahid	shahid	PROPN
ejpam-6347	591	6	nadim	nadim	PROPN
ejpam-6347	591	7	and	and	CCONJ
ejpam-6347	591	8	joydev	joydev	PROPN
ejpam-6347	591	9	chattopadhyay	chattopadhyay	PROPN
ejpam-6347	591	10	.	.	PUNCT
ejpam-6347	592	1	occurrence	occurrence	NOUN
ejpam-6347	592	2	of	of	ADP
ejpam-6347	592	3	backward	backward	ADJ
ejpam-6347	592	4	bifurcation	bifurcation	NOUN
ejpam-6347	592	5	and	and	CCONJ
ejpam-6347	592	6	prediction	prediction	NOUN
ejpam-6347	592	7	of	of	ADP
ejpam-6347	592	8	disease	disease	NOUN
ejpam-6347	592	9	transmission	transmission	NOUN
ejpam-6347	592	10	with	with	ADP
ejpam-6347	592	11	imperfect	imperfect	ADJ
ejpam-6347	592	12	lockdown	lockdown	NOUN
ejpam-6347	592	13	:	:	PUNCT
ejpam-6347	592	14	a	a	DET
ejpam-6347	592	15	case	case	NOUN
ejpam-6347	592	16	study	study	NOUN
ejpam-6347	592	17	on	on	ADP
ejpam-6347	592	18	covid-19	covid-19	PROPN
ejpam-6347	592	19	.	.	PUNCT
ejpam-6347	592	20	chaos	chaos	PROPN
ejpam-6347	592	21	,	,	PUNCT
ejpam-6347	592	22	solitons	soliton	NOUN
ejpam-6347	592	23	&	&	CCONJ
ejpam-6347	592	24	fractals	fractal	NOUN
ejpam-6347	592	25	,	,	PUNCT
ejpam-6347	592	26	140:110163	140:110163	NUM
ejpam-6347	592	27	,	,	PUNCT
ejpam-6347	592	28	2020	2020	NUM
ejpam-6347	592	29	.	.	PUNCT
ejpam-6347	593	1	[	[	X
ejpam-6347	593	2	3	3	X
ejpam-6347	593	3	]	]	X
ejpam-6347	593	4	joseph	joseph	PROPN
ejpam-6347	593	5	t	t	PROPN
ejpam-6347	593	6	wu	wu	PROPN
ejpam-6347	593	7	,	,	PUNCT
ejpam-6347	593	8	kathy	kathy	PROPN
ejpam-6347	593	9	leung	leung	PROPN
ejpam-6347	593	10	,	,	PUNCT
ejpam-6347	593	11	and	and	CCONJ
ejpam-6347	593	12	gabriel	gabriel	PROPN
ejpam-6347	593	13	m	m	PROPN
ejpam-6347	593	14	leung	leung	PROPN
ejpam-6347	593	15	.	.	PUNCT
ejpam-6347	594	1	nowcasting	nowcasting	NOUN
ejpam-6347	594	2	and	and	CCONJ
ejpam-6347	594	3	forecasting	forecast	VERB
ejpam-6347	594	4	the	the	DET
ejpam-6347	594	5	potential	potential	ADJ
ejpam-6347	594	6	domestic	domestic	ADJ
ejpam-6347	594	7	and	and	CCONJ
ejpam-6347	594	8	international	international	ADJ
ejpam-6347	594	9	spread	spread	NOUN
ejpam-6347	594	10	of	of	ADP
ejpam-6347	594	11	the	the	DET
ejpam-6347	594	12	2019	2019	NUM
ejpam-6347	594	13	-	-	PUNCT
ejpam-6347	594	14	ncov	ncov	NOUN
ejpam-6347	594	15	outbreak	outbreak	NOUN
ejpam-6347	594	16	originating	originate	VERB
ejpam-6347	594	17	in	in	ADP
ejpam-6347	594	18	wuhan	wuhan	PROPN
ejpam-6347	594	19	,	,	PUNCT
ejpam-6347	594	20	china	china	PROPN
ejpam-6347	594	21	:	:	PUNCT
ejpam-6347	594	22	a	a	DET
ejpam-6347	594	23	modelling	model	VERB
ejpam-6347	594	24	study	study	NOUN
ejpam-6347	594	25	.	.	PUNCT
ejpam-6347	595	1	the	the	DET
ejpam-6347	595	2	lancet	lancet	NOUN
ejpam-6347	595	3	,	,	PUNCT
ejpam-6347	595	4	395(10225):689–697	395(10225):689–697	NUM
ejpam-6347	595	5	,	,	PUNCT
ejpam-6347	595	6	2020	2020	NUM
ejpam-6347	595	7	.	.	PUNCT
ejpam-6347	596	1	[	[	X
ejpam-6347	596	2	4	4	X
ejpam-6347	596	3	]	]	PUNCT
ejpam-6347	596	4	sansao	sansao	NOUN
ejpam-6347	596	5	a	a	DET
ejpam-6347	596	6	pedro	pedro	NOUN
ejpam-6347	596	7	,	,	PUNCT
ejpam-6347	596	8	frank	frank	PROPN
ejpam-6347	596	9	t	t	PROPN
ejpam-6347	596	10	ndjomatchoua	ndjomatchoua	PROPN
ejpam-6347	596	11	,	,	PUNCT
ejpam-6347	596	12	peter	peter	PROPN
ejpam-6347	596	13	jentsch	jentsch	PROPN
ejpam-6347	596	14	,	,	PUNCT
ejpam-6347	596	15	jean	jean	PROPN
ejpam-6347	596	16	m	m	PROPN
ejpam-6347	596	17	tchuenche	tchuenche	PROPN
ejpam-6347	596	18	,	,	PUNCT
ejpam-6347	596	19	madhur	madhur	PROPN
ejpam-6347	596	20	anand	anand	PROPN
ejpam-6347	596	21	,	,	PUNCT
ejpam-6347	596	22	and	and	CCONJ
ejpam-6347	596	23	chris	chris	PROPN
ejpam-6347	596	24	t	t	PROPN
ejpam-6347	596	25	bauch	bauch	PROPN
ejpam-6347	596	26	.	.	PUNCT
ejpam-6347	597	1	conditions	condition	NOUN
ejpam-6347	597	2	for	for	ADP
ejpam-6347	597	3	a	a	DET
ejpam-6347	597	4	second	second	ADJ
ejpam-6347	597	5	wave	wave	NOUN
ejpam-6347	597	6	of	of	ADP
ejpam-6347	597	7	covid-19	covid-19	PROPN
ejpam-6347	597	8	due	due	ADP
ejpam-6347	597	9	to	to	ADP
ejpam-6347	597	10	interactions	interaction	NOUN
ejpam-6347	597	11	between	between	ADP
ejpam-6347	597	12	disease	disease	NOUN
ejpam-6347	597	13	dynamics	dynamic	NOUN
ejpam-6347	597	14	and	and	CCONJ
ejpam-6347	597	15	social	social	ADJ
ejpam-6347	597	16	processes	process	NOUN
ejpam-6347	597	17	.	.	PUNCT
ejpam-6347	598	1	frontiers	frontier	NOUN
ejpam-6347	598	2	in	in	ADP
ejpam-6347	598	3	physics	physics	PROPN
ejpam-6347	598	4	,	,	PUNCT
ejpam-6347	598	5	8:574514	8:574514	NUM
ejpam-6347	598	6	,	,	PUNCT
ejpam-6347	598	7	2020	2020	NUM
ejpam-6347	598	8	.	.	PUNCT
ejpam-6347	599	1	[	[	X
ejpam-6347	599	2	5	5	NUM
ejpam-6347	599	3	]	]	X
ejpam-6347	599	4	li	li	PROPN
ejpam-6347	599	5	-	-	PROPN
ejpam-6347	599	6	xiang	xiang	PROPN
ejpam-6347	599	7	feng	feng	PROPN
ejpam-6347	599	8	,	,	PUNCT
ejpam-6347	599	9	shuang	shuang	PROPN
ejpam-6347	599	10	-	-	PROPN
ejpam-6347	599	11	lin	lin	PROPN
ejpam-6347	599	12	jing	jing	PROPN
ejpam-6347	599	13	,	,	PUNCT
ejpam-6347	599	14	shi	shi	PROPN
ejpam-6347	599	15	-	-	PUNCT
ejpam-6347	599	16	ke	ke	PROPN
ejpam-6347	599	17	hu	hu	PROPN
ejpam-6347	599	18	,	,	PUNCT
ejpam-6347	599	19	de	de	PROPN
ejpam-6347	599	20	-	-	ADJ
ejpam-6347	599	21	fen	fen	PROPN
ejpam-6347	599	22	wang	wang	PROPN
ejpam-6347	599	23	,	,	PUNCT
ejpam-6347	599	24	hai	hai	PROPN
ejpam-6347	599	25	-	-	PUNCT
ejpam-6347	599	26	feng	feng	PROPN
ejpam-6347	599	27	huo	huo	PROPN
ejpam-6347	599	28	,	,	PUNCT
ejpam-6347	599	29	et	et	PROPN
ejpam-6347	599	30	al	al	PROPN
ejpam-6347	599	31	.	.	PROPN
ejpam-6347	599	32	modelling	model	VERB
ejpam-6347	599	33	the	the	DET
ejpam-6347	599	34	effects	effect	NOUN
ejpam-6347	599	35	of	of	ADP
ejpam-6347	599	36	media	medium	NOUN
ejpam-6347	599	37	coverage	coverage	NOUN
ejpam-6347	599	38	and	and	CCONJ
ejpam-6347	599	39	quarantine	quarantine	NOUN
ejpam-6347	599	40	on	on	ADP
ejpam-6347	599	41	the	the	DET
ejpam-6347	599	42	covid-19	covid-19	PROPN
ejpam-6347	599	43	infections	infection	NOUN
ejpam-6347	599	44	in	in	ADP
ejpam-6347	599	45	the	the	DET
ejpam-6347	599	46	uk	uk	PROPN
ejpam-6347	599	47	.	.	PROPN
ejpam-6347	599	48	math	math	PROPN
ejpam-6347	599	49	.	.	PUNCT
ejpam-6347	600	1	biosci	biosci	PROPN
ejpam-6347	600	2	.	.	PUNCT
ejpam-6347	601	1	eng	eng	PROPN
ejpam-6347	601	2	,	,	PUNCT
ejpam-6347	601	3	17(4):3618–3636	17(4):3618–3636	NUM
ejpam-6347	601	4	,	,	PUNCT
ejpam-6347	601	5	2020	2020	NUM
ejpam-6347	601	6	.	.	PUNCT
ejpam-6347	602	1	[	[	X
ejpam-6347	602	2	6	6	X
ejpam-6347	602	3	]	]	PUNCT
ejpam-6347	602	4	muhammad	muhammad	PROPN
ejpam-6347	602	5	riaz	riaz	PROPN
ejpam-6347	602	6	,	,	PUNCT
ejpam-6347	602	7	kamal	kamal	PROPN
ejpam-6347	602	8	shah	shah	PROPN
ejpam-6347	602	9	,	,	PUNCT
ejpam-6347	602	10	thabet	thabet	ADJ
ejpam-6347	602	11	abdeljawad	abdeljawad	NOUN
ejpam-6347	602	12	,	,	PUNCT
ejpam-6347	602	13	inas	inas	PROPN
ejpam-6347	602	14	amacha	amacha	PROPN
ejpam-6347	602	15	,	,	PUNCT
ejpam-6347	602	16	asma	asma	PROPN
ejpam-6347	602	17	al	al	PROPN
ejpam-6347	602	18	-	-	PUNCT
ejpam-6347	602	19	jaser	jaser	NOUN
ejpam-6347	602	20	,	,	PUNCT
ejpam-6347	602	21	and	and	CCONJ
ejpam-6347	602	22	manar	manar	PROPN
ejpam-6347	602	23	alqudah	alqudah	PROPN
ejpam-6347	602	24	.	.	PUNCT
ejpam-6347	603	1	a	a	DET
ejpam-6347	603	2	comprehensive	comprehensive	ADJ
ejpam-6347	603	3	analysis	analysis	NOUN
ejpam-6347	603	4	of	of	ADP
ejpam-6347	603	5	covid-19	covid-19	PROPN
ejpam-6347	603	6	nonlinear	nonlinear	ADJ
ejpam-6347	603	7	mathematical	mathematical	ADJ
ejpam-6347	603	8	model	model	NOUN
ejpam-6347	603	9	by	by	ADP
ejpam-6347	603	10	incorporating	incorporate	VERB
ejpam-6347	603	11	the	the	DET
ejpam-6347	603	12	environment	environment	NOUN
ejpam-6347	603	13	and	and	CCONJ
ejpam-6347	603	14	social	social	ADJ
ejpam-6347	603	15	distancing	distancing	NOUN
ejpam-6347	603	16	.	.	PUNCT
ejpam-6347	604	1	scientific	scientific	ADJ
ejpam-6347	604	2	reports	report	NOUN
ejpam-6347	604	3	,	,	PUNCT
ejpam-6347	604	4	14(1):12238	14(1):12238	NUM
ejpam-6347	604	5	,	,	PUNCT
ejpam-6347	604	6	2024	2024	NUM
ejpam-6347	604	7	.	.	PUNCT
ejpam-6347	605	1	[	[	X
ejpam-6347	605	2	7	7	X
ejpam-6347	605	3	]	]	PUNCT
ejpam-6347	605	4	eyup	eyup	NOUN
ejpam-6347	605	5	cetin	cetin	PROPN
ejpam-6347	605	6	,	,	PUNCT
ejpam-6347	605	7	serap	serap	NOUN
ejpam-6347	605	8	kiremitci	kiremitci	NOUN
ejpam-6347	605	9	,	,	PUNCT
ejpam-6347	605	10	and	and	CCONJ
ejpam-6347	605	11	baris	baris	PROPN
ejpam-6347	605	12	kiremitci	kiremitci	NOUN
ejpam-6347	605	13	.	.	PUNCT
ejpam-6347	606	1	developing	develop	VERB
ejpam-6347	606	2	optimal	optimal	ADJ
ejpam-6347	606	3	policies	policy	NOUN
ejpam-6347	606	4	to	to	PART
ejpam-6347	606	5	fight	fight	VERB
ejpam-6347	606	6	pandemics	pandemic	NOUN
ejpam-6347	606	7	and	and	CCONJ
ejpam-6347	606	8	covid-19	covid-19	PROPN
ejpam-6347	606	9	combat	combat	NOUN
ejpam-6347	606	10	in	in	ADP
ejpam-6347	606	11	the	the	DET
ejpam-6347	606	12	united	united	PROPN
ejpam-6347	606	13	states	states	PROPN
ejpam-6347	606	14	.	.	PUNCT
ejpam-6347	607	1	european	european	PROPN
ejpam-6347	607	2	journal	journal	PROPN
ejpam-6347	607	3	of	of	ADP
ejpam-6347	607	4	pure	pure	ADJ
ejpam-6347	607	5	and	and	CCONJ
ejpam-6347	607	6	applied	applied	ADJ
ejpam-6347	607	7	mathematics	mathematic	NOUN
ejpam-6347	607	8	,	,	PUNCT
ejpam-6347	607	9	13(2):369–389	13(2):369–389	NUM
ejpam-6347	607	10	,	,	PUNCT
ejpam-6347	607	11	2020	2020	NUM
ejpam-6347	607	12	.	.	PUNCT
ejpam-6347	608	1	[	[	X
ejpam-6347	608	2	8	8	NUM
ejpam-6347	608	3	]	]	X
ejpam-6347	608	4	yasir	yasir	PROPN
ejpam-6347	608	5	nawaz	nawaz	PROPN
ejpam-6347	608	6	,	,	PUNCT
ejpam-6347	608	7	muhammad	muhammad	PROPN
ejpam-6347	608	8	shoaib	shoaib	PROPN
ejpam-6347	608	9	arif	arif	PROPN
ejpam-6347	608	10	,	,	PUNCT
ejpam-6347	608	11	and	and	CCONJ
ejpam-6347	608	12	kamaleldin	kamaleldin	NOUN
ejpam-6347	608	13	abodayeh	abodayeh	NOUN
ejpam-6347	608	14	.	.	PUNCT
ejpam-6347	609	1	predictor	predictor	NOUN
ejpam-6347	609	2	–	–	PUNCT
ejpam-6347	609	3	corrector	corrector	NOUN
ejpam-6347	609	4	scheme	scheme	NOUN
ejpam-6347	609	5	for	for	ADP
ejpam-6347	609	6	electrical	electrical	ADJ
ejpam-6347	609	7	magnetohydrodynamic	magnetohydrodynamic	ADJ
ejpam-6347	609	8	(	(	PUNCT
ejpam-6347	609	9	mhd	mhd	NOUN
ejpam-6347	609	10	)	)	PUNCT
ejpam-6347	609	11	casson	casson	PROPN
ejpam-6347	609	12	nanofluid	nanofluid	PROPN
ejpam-6347	609	13	flow	flow	NOUN
ejpam-6347	609	14	:	:	PUNCT
ejpam-6347	609	15	a	a	DET
ejpam-6347	609	16	computational	computational	ADJ
ejpam-6347	609	17	study	study	NOUN
ejpam-6347	609	18	.	.	PUNCT
ejpam-6347	610	1	applied	apply	VERB
ejpam-6347	610	2	sciences	science	NOUN
ejpam-6347	610	3	,	,	PUNCT
ejpam-6347	610	4	13(2):1209	13(2):1209	NUM
ejpam-6347	610	5	,	,	PUNCT
ejpam-6347	610	6	2023	2023	NUM
ejpam-6347	610	7	.	.	PUNCT
ejpam-6347	611	1	[	[	X
ejpam-6347	611	2	9	9	NUM
ejpam-6347	611	3	]	]	PUNCT
ejpam-6347	611	4	yasir	yasir	PROPN
ejpam-6347	611	5	nawaz	nawaz	PROPN
ejpam-6347	611	6	,	,	PUNCT
ejpam-6347	611	7	muhammad	muhammad	PROPN
ejpam-6347	611	8	shoaib	shoaib	PROPN
ejpam-6347	611	9	arif	arif	PROPN
ejpam-6347	611	10	,	,	PUNCT
ejpam-6347	611	11	kamaleldin	kamaleldin	NOUN
ejpam-6347	611	12	abodayeh	abodayeh	NOUN
ejpam-6347	611	13	,	,	PUNCT
ejpam-6347	611	14	muhammad	muhammad	PROPN
ejpam-6347	611	15	usman	usman	PROPN
ejpam-6347	611	16	ashraf	ashraf	PROPN
ejpam-6347	611	17	,	,	PUNCT
ejpam-6347	611	18	and	and	CCONJ
ejpam-6347	611	19	mehvish	mehvish	VERB
ejpam-6347	611	20	naz	naz	PROPN
ejpam-6347	611	21	.	.	PUNCT
ejpam-6347	612	1	a	a	DET
ejpam-6347	612	2	new	new	ADJ
ejpam-6347	612	3	explicit	explicit	ADJ
ejpam-6347	612	4	numerical	numerical	ADJ
ejpam-6347	612	5	scheme	scheme	NOUN
ejpam-6347	612	6	for	for	ADP
ejpam-6347	612	7	enhancement	enhancement	NOUN
ejpam-6347	612	8	of	of	ADP
ejpam-6347	612	9	heat	heat	NOUN
ejpam-6347	612	10	transfer	transfer	NOUN
ejpam-6347	612	11	in	in	ADP
ejpam-6347	612	12	sakiadis	sakiadis	ADJ
ejpam-6347	612	13	flow	flow	NOUN
ejpam-6347	612	14	of	of	ADP
ejpam-6347	612	15	micro	micro	ADJ
ejpam-6347	612	16	polar	polar	ADJ
ejpam-6347	612	17	fluid	fluid	NOUN
ejpam-6347	612	18	using	use	VERB
ejpam-6347	612	19	electric	electric	ADJ
ejpam-6347	612	20	field	field	NOUN
ejpam-6347	612	21	.	.	PUNCT
ejpam-6347	613	1	heliyon	heliyon	NOUN
ejpam-6347	613	2	,	,	PUNCT
ejpam-6347	613	3	9(10	9(10	NUM
ejpam-6347	613	4	)	)	PUNCT
ejpam-6347	613	5	,	,	PUNCT
ejpam-6347	613	6	2023	2023	NUM
ejpam-6347	613	7	.	.	PUNCT
ejpam-6347	614	1	[	[	X
ejpam-6347	614	2	10	10	NUM
ejpam-6347	614	3	]	]	X
ejpam-6347	614	4	muhammad	muhammad	PROPN
ejpam-6347	614	5	farhan	farhan	PROPN
ejpam-6347	614	6	,	,	PUNCT
ejpam-6347	614	7	zahir	zahir	ADJ
ejpam-6347	614	8	shah	shah	NOUN
ejpam-6347	614	9	,	,	PUNCT
ejpam-6347	614	10	rashid	rashid	PROPN
ejpam-6347	614	11	jan	jan	PROPN
ejpam-6347	614	12	,	,	PUNCT
ejpam-6347	614	13	and	and	CCONJ
ejpam-6347	614	14	saeed	saeed	PROPN
ejpam-6347	614	15	islam	islam	PROPN
ejpam-6347	614	16	.	.	PUNCT
ejpam-6347	615	1	a	a	DET
ejpam-6347	615	2	fractional	fractional	ADJ
ejpam-6347	615	3	modeling	modeling	NOUN
ejpam-6347	615	4	approach	approach	NOUN
ejpam-6347	615	5	of	of	ADP
ejpam-6347	615	6	buruli	buruli	ADJ
ejpam-6347	615	7	ulcer	ulcer	NOUN
ejpam-6347	615	8	in	in	ADP
ejpam-6347	615	9	possum	possum	NOUN
ejpam-6347	615	10	mammals	mammal	NOUN
ejpam-6347	615	11	.	.	PUNCT
ejpam-6347	616	1	physica	physica	PROPN
ejpam-6347	616	2	scripta	scripta	PROPN
ejpam-6347	616	3	,	,	PUNCT
ejpam-6347	616	4	98(6):065219	98(6):065219	NUM
ejpam-6347	616	5	,	,	PUNCT
ejpam-6347	616	6	2023	2023	NUM
ejpam-6347	616	7	.	.	PUNCT
ejpam-6347	617	1	[	[	X
ejpam-6347	617	2	11	11	NUM
ejpam-6347	617	3	]	]	PUNCT
ejpam-6347	617	4	ml	ml	X
ejpam-6347	617	5	diagne	diagne	NOUN
ejpam-6347	617	6	,	,	PUNCT
ejpam-6347	617	7	h	h	PROPN
ejpam-6347	617	8	rwezaura	rwezaura	ADJ
ejpam-6347	617	9	,	,	PUNCT
ejpam-6347	617	10	sy	sy	ADV
ejpam-6347	617	11	tchoumi	tchoumi	NOUN
ejpam-6347	617	12	,	,	PUNCT
ejpam-6347	617	13	and	and	CCONJ
ejpam-6347	617	14	jm	jm	PROPN
ejpam-6347	617	15	tchuenche	tchuenche	PROPN
ejpam-6347	617	16	.	.	PUNCT
ejpam-6347	618	1	a	a	DET
ejpam-6347	618	2	mathematical	mathematical	ADJ
ejpam-6347	618	3	model	model	NOUN
ejpam-6347	618	4	of	of	ADP
ejpam-6347	618	5	covid-19	covid-19	PROPN
ejpam-6347	618	6	with	with	ADP
ejpam-6347	618	7	vaccination	vaccination	NOUN
ejpam-6347	618	8	and	and	CCONJ
ejpam-6347	618	9	treatment	treatment	NOUN
ejpam-6347	618	10	.	.	PUNCT
ejpam-6347	619	1	computational	computational	ADJ
ejpam-6347	619	2	and	and	CCONJ
ejpam-6347	619	3	mathematical	mathematical	ADJ
ejpam-6347	619	4	methods	method	NOUN
ejpam-6347	619	5	in	in	ADP
ejpam-6347	619	6	medicine	medicine	NOUN
ejpam-6347	619	7	,	,	PUNCT
ejpam-6347	619	8	2021(1):1250129	2021(1):1250129	NUM
ejpam-6347	619	9	,	,	PUNCT
ejpam-6347	619	10	2021	2021	NUM
ejpam-6347	619	11	.	.	PUNCT
ejpam-6347	620	1	[	[	X
ejpam-6347	620	2	12	12	NUM
ejpam-6347	620	3	]	]	PUNCT
ejpam-6347	620	4	edward	edward	PROPN
ejpam-6347	620	5	acheampong	acheampong	PROPN
ejpam-6347	620	6	,	,	PUNCT
ejpam-6347	620	7	eric	eric	PROPN
ejpam-6347	620	8	okyere	okyere	PROPN
ejpam-6347	620	9	,	,	PUNCT
ejpam-6347	620	10	samuel	samuel	PROPN
ejpam-6347	620	11	iddi	iddi	PROPN
ejpam-6347	620	12	,	,	PUNCT
ejpam-6347	620	13	joseph	joseph	PROPN
ejpam-6347	620	14	hk	hk	PROPN
ejpam-6347	620	15	bonney	bonney	PROPN
ejpam-6347	620	16	,	,	PUNCT
ejpam-6347	620	17	joshua	joshua	PROPN
ejpam-6347	620	18	kiddy	kiddy	PROPN
ejpam-6347	620	19	k	k	PROPN
ejpam-6347	620	20	asamoah	asamoah	PROPN
ejpam-6347	620	21	,	,	PUNCT
ejpam-6347	620	22	jonathan	jonathan	PROPN
ejpam-6347	620	23	adwattis	adwattis	PROPN
ejpam-6347	620	24	,	,	PUNCT
ejpam-6347	620	25	and	and	CCONJ
ejpam-6347	620	26	rachel	rachel	PROPN
ejpam-6347	620	27	l	l	PROPN
ejpam-6347	620	28	gomes	gome	NOUN
ejpam-6347	620	29	.	.	PUNCT
ejpam-6347	621	1	mathematical	mathematical	ADJ
ejpam-6347	621	2	modelling	modelling	NOUN
ejpam-6347	621	3	of	of	ADP
ejpam-6347	621	4	earlier	early	ADJ
ejpam-6347	621	5	stages	stage	NOUN
ejpam-6347	621	6	of	of	ADP
ejpam-6347	621	7	covid-19	covid-19	PROPN
ejpam-6347	621	8	transmission	transmission	NOUN
ejpam-6347	621	9	dynamics	dynamic	NOUN
ejpam-6347	621	10	in	in	ADP
ejpam-6347	621	11	ghana	ghana	PROPN
ejpam-6347	621	12	.	.	PUNCT
ejpam-6347	622	1	results	result	NOUN
ejpam-6347	622	2	in	in	ADP
ejpam-6347	622	3	physics	physics	NOUN
ejpam-6347	622	4	,	,	PUNCT
ejpam-6347	622	5	34:105193	34:105193	NUM
ejpam-6347	622	6	,	,	PUNCT
ejpam-6347	622	7	2022	2022	NUM
ejpam-6347	622	8	.	.	PUNCT
ejpam-6347	623	1	[	[	X
ejpam-6347	623	2	13	13	NUM
ejpam-6347	623	3	]	]	X
ejpam-6347	623	4	aik	aik	NOUN
ejpam-6347	623	5	butt	butt	PROPN
ejpam-6347	623	6	,	,	PUNCT
ejpam-6347	623	7	w	w	PROPN
ejpam-6347	623	8	ahmad	ahmad	PROPN
ejpam-6347	623	9	,	,	PUNCT
ejpam-6347	623	10	m	m	PROPN
ejpam-6347	623	11	rafiq	rafiq	PROPN
ejpam-6347	623	12	,	,	PUNCT
ejpam-6347	623	13	n	n	CCONJ
ejpam-6347	623	14	ahmad	ahmad	NOUN
ejpam-6347	623	15	,	,	PUNCT
ejpam-6347	623	16	and	and	CCONJ
ejpam-6347	623	17	m	m	AUX
ejpam-6347	623	18	imran	imran	ADJ
ejpam-6347	623	19	.	.	PUNCT
ejpam-6347	624	1	optimally	optimally	ADV
ejpam-6347	624	2	analyzed	analyze	VERB
ejpam-6347	624	3	fractional	fractional	ADJ
ejpam-6347	624	4	coronavirus	coronavirus	NOUN
ejpam-6347	624	5	model	model	NOUN
ejpam-6347	624	6	with	with	ADP
ejpam-6347	624	7	atangana	atangana	PROPN
ejpam-6347	624	8	–	–	PUNCT
ejpam-6347	624	9	baleanu	baleanu	ADJ
ejpam-6347	624	10	derivative	derivative	NOUN
ejpam-6347	624	11	.	.	PUNCT
ejpam-6347	625	1	results	result	NOUN
ejpam-6347	625	2	in	in	ADP
ejpam-6347	625	3	physics	physics	NOUN
ejpam-6347	625	4	,	,	PUNCT
ejpam-6347	625	5	n.	n.	NOUN
ejpam-6347	625	6	abbas	abbas	PROPN
ejpam-6347	625	7	,	,	PUNCT
ejpam-6347	625	8	w.	w.	PROPN
ejpam-6347	625	9	shatanawi	shatanawi	PROPN
ejpam-6347	625	10	,	,	PUNCT
ejpam-6347	625	11	s.	s.	PROPN
ejpam-6347	625	12	a.	a.	NOUN
ejpam-6347	625	13	zanib	zanib	PROPN
ejpam-6347	625	14	/	/	SYM
ejpam-6347	625	15	eur	eur	PROPN
ejpam-6347	625	16	.	.	PUNCT
ejpam-6347	626	1	j.	j.	PROPN
ejpam-6347	626	2	pure	pure	PROPN
ejpam-6347	626	3	appl	appl	PROPN
ejpam-6347	626	4	.	.	PROPN
ejpam-6347	626	5	math	math	PROPN
ejpam-6347	626	6	,	,	PUNCT
ejpam-6347	626	7	18	18	NUM
ejpam-6347	626	8	(	(	PUNCT
ejpam-6347	626	9	3	3	NUM
ejpam-6347	626	10	)	)	PUNCT
ejpam-6347	626	11	(	(	PUNCT
ejpam-6347	626	12	2025	2025	NUM
ejpam-6347	626	13	)	)	PUNCT
ejpam-6347	626	14	,	,	PUNCT
ejpam-6347	626	15	6347	6347	NUM
ejpam-6347	626	16	33	33	NUM
ejpam-6347	626	17	of	of	ADP
ejpam-6347	626	18	34	34	NUM
ejpam-6347	626	19	53:106929	53:106929	NOUN
ejpam-6347	626	20	,	,	PUNCT
ejpam-6347	626	21	2023	2023	NUM
ejpam-6347	626	22	.	.	PUNCT
ejpam-6347	627	1	[	[	X
ejpam-6347	627	2	14	14	NUM
ejpam-6347	627	3	]	]	X
ejpam-6347	627	4	syeda	syeda	PROPN
ejpam-6347	627	5	alishwa	alishwa	PROPN
ejpam-6347	627	6	zanib	zanib	NOUN
ejpam-6347	627	7	,	,	PUNCT
ejpam-6347	627	8	tamour	tamour	PROPN
ejpam-6347	627	9	zubair	zubair	PROPN
ejpam-6347	627	10	,	,	PUNCT
ejpam-6347	627	11	sehrish	sehrish	PROPN
ejpam-6347	627	12	ramzan	ramzan	PROPN
ejpam-6347	627	13	,	,	PUNCT
ejpam-6347	627	14	muhammad	muhammad	PROPN
ejpam-6347	627	15	bilal	bilal	PROPN
ejpam-6347	627	16	riaz	riaz	PROPN
ejpam-6347	627	17	,	,	PUNCT
ejpam-6347	627	18	muhammad	muhammad	PROPN
ejpam-6347	627	19	imran	imran	PROPN
ejpam-6347	627	20	asjad	asjad	PROPN
ejpam-6347	627	21	,	,	PUNCT
ejpam-6347	627	22	and	and	CCONJ
ejpam-6347	627	23	taseer	taseer	PROPN
ejpam-6347	627	24	muhammad	muhammad	PROPN
ejpam-6347	627	25	.	.	PUNCT
ejpam-6347	628	1	a	a	DET
ejpam-6347	628	2	conformable	conformable	ADJ
ejpam-6347	628	3	fractional	fractional	ADJ
ejpam-6347	628	4	finite	finite	ADJ
ejpam-6347	628	5	difference	difference	NOUN
ejpam-6347	628	6	method	method	NOUN
ejpam-6347	628	7	for	for	ADP
ejpam-6347	628	8	modified	modify	VERB
ejpam-6347	628	9	mathematical	mathematical	ADJ
ejpam-6347	628	10	modeling	modeling	NOUN
ejpam-6347	628	11	of	of	ADP
ejpam-6347	628	12	sar	sar	NOUN
ejpam-6347	628	13	-	-	PUNCT
ejpam-6347	628	14	cov-2	cov-2	PART
ejpam-6347	628	15	(	(	PUNCT
ejpam-6347	628	16	covid-19	covid-19	PROPN
ejpam-6347	628	17	)	)	PUNCT
ejpam-6347	628	18	disease	disease	NOUN
ejpam-6347	628	19	.	.	PUNCT
ejpam-6347	629	1	plos	plos	PROPN
ejpam-6347	629	2	one	one	NUM
ejpam-6347	629	3	,	,	PUNCT
ejpam-6347	629	4	19(10):e0307707	19(10):e0307707	NUM
ejpam-6347	629	5	,	,	PUNCT
ejpam-6347	629	6	2024	2024	NUM
ejpam-6347	629	7	.	.	PUNCT
ejpam-6347	630	1	[	[	X
ejpam-6347	630	2	15	15	NUM
ejpam-6347	630	3	]	]	X
ejpam-6347	630	4	azhar	azhar	PROPN
ejpam-6347	630	5	iqbal	iqbal	PROPN
ejpam-6347	630	6	kashif	kashif	PROPN
ejpam-6347	630	7	butt	butt	PROPN
ejpam-6347	630	8	,	,	PUNCT
ejpam-6347	630	9	waheed	waheed	PROPN
ejpam-6347	630	10	ahmad	ahmad	PROPN
ejpam-6347	630	11	,	,	PUNCT
ejpam-6347	630	12	hafiz	hafiz	PROPN
ejpam-6347	630	13	ghulam	ghulam	PROPN
ejpam-6347	630	14	rabbani	rabbani	PROPN
ejpam-6347	630	15	,	,	PUNCT
ejpam-6347	630	16	muhammad	muhammad	PROPN
ejpam-6347	630	17	rafiq	rafiq	PROPN
ejpam-6347	630	18	,	,	PUNCT
ejpam-6347	630	19	shehbaz	shehbaz	PROPN
ejpam-6347	630	20	ahmad	ahmad	PROPN
ejpam-6347	630	21	,	,	PUNCT
ejpam-6347	630	22	naeed	naeed	NOUN
ejpam-6347	630	23	ahmad	ahmad	PROPN
ejpam-6347	630	24	,	,	PUNCT
ejpam-6347	630	25	and	and	CCONJ
ejpam-6347	630	26	saira	saira	PROPN
ejpam-6347	630	27	malik	malik	PROPN
ejpam-6347	630	28	.	.	PUNCT
ejpam-6347	631	1	exploring	explore	VERB
ejpam-6347	631	2	optimal	optimal	ADJ
ejpam-6347	631	3	control	control	NOUN
ejpam-6347	631	4	strategies	strategy	NOUN
ejpam-6347	631	5	in	in	ADP
ejpam-6347	631	6	a	a	DET
ejpam-6347	631	7	nonlinear	nonlinear	ADJ
ejpam-6347	631	8	fractional	fractional	ADJ
ejpam-6347	631	9	bi	bi	ADJ
ejpam-6347	631	10	-	-	ADJ
ejpam-6347	631	11	susceptible	susceptible	ADJ
ejpam-6347	631	12	model	model	NOUN
ejpam-6347	631	13	for	for	ADP
ejpam-6347	631	14	covid-19	covid-19	PROPN
ejpam-6347	631	15	dynamics	dynamic	NOUN
ejpam-6347	631	16	using	use	VERB
ejpam-6347	631	17	atanganabaleanu	atanganabaleanu	NOUN
ejpam-6347	631	18	derivative	derivative	NOUN
ejpam-6347	631	19	.	.	PUNCT
ejpam-6347	632	1	scientific	scientific	ADJ
ejpam-6347	632	2	reports	report	NOUN
ejpam-6347	632	3	,	,	PUNCT
ejpam-6347	632	4	14(1):31617	14(1):31617	NUM
ejpam-6347	632	5	,	,	PUNCT
ejpam-6347	632	6	2024	2024	NUM
ejpam-6347	632	7	.	.	PUNCT
ejpam-6347	633	1	[	[	X
ejpam-6347	633	2	16	16	NUM
ejpam-6347	633	3	]	]	X
ejpam-6347	633	4	hamadjam	hamadjam	NOUN
ejpam-6347	633	5	abboubakar	abboubakar	NOUN
ejpam-6347	633	6	and	and	CCONJ
ejpam-6347	633	7	reinhard	reinhard	PROPN
ejpam-6347	633	8	racke	racke	PROPN
ejpam-6347	633	9	.	.	PUNCT
ejpam-6347	634	1	mathematical	mathematical	ADJ
ejpam-6347	634	2	modeling	modeling	NOUN
ejpam-6347	634	3	of	of	ADP
ejpam-6347	634	4	the	the	DET
ejpam-6347	634	5	coronavirus	coronavirus	NOUN
ejpam-6347	634	6	(	(	PUNCT
ejpam-6347	634	7	covid-19	covid-19	PROPN
ejpam-6347	634	8	)	)	PUNCT
ejpam-6347	634	9	transmission	transmission	NOUN
ejpam-6347	634	10	dynamics	dynamic	NOUN
ejpam-6347	634	11	using	use	VERB
ejpam-6347	634	12	classical	classical	ADJ
ejpam-6347	634	13	and	and	CCONJ
ejpam-6347	634	14	fractional	fractional	ADJ
ejpam-6347	634	15	derivatives	derivative	NOUN
ejpam-6347	634	16	.	.	PUNCT
ejpam-6347	635	1	2022	2022	NUM
ejpam-6347	635	2	.	.	PUNCT
ejpam-6347	636	1	[	[	X
ejpam-6347	636	2	17	17	NUM
ejpam-6347	636	3	]	]	PUNCT
ejpam-6347	636	4	komal	komal	PROPN
ejpam-6347	636	5	sharma	sharma	PROPN
ejpam-6347	636	6	,	,	PUNCT
ejpam-6347	636	7	vivek	vivek	PROPN
ejpam-6347	636	8	srivastava	srivastava	PROPN
ejpam-6347	636	9	,	,	PUNCT
ejpam-6347	636	10	and	and	CCONJ
ejpam-6347	636	11	ravi	ravi	PROPN
ejpam-6347	636	12	kant	kant	PROPN
ejpam-6347	636	13	singh	singh	PROPN
ejpam-6347	636	14	.	.	PUNCT
ejpam-6347	637	1	from	from	ADP
ejpam-6347	637	2	data	datum	NOUN
ejpam-6347	637	3	to	to	ADP
ejpam-6347	637	4	cures	cure	NOUN
ejpam-6347	637	5	:	:	PUNCT
ejpam-6347	637	6	leveraging	leverage	VERB
ejpam-6347	637	7	machine	machine	NOUN
ejpam-6347	637	8	learning	learning	NOUN
ejpam-6347	637	9	,	,	PUNCT
ejpam-6347	637	10	deep	deep	ADJ
ejpam-6347	637	11	learning	learning	NOUN
ejpam-6347	637	12	and	and	CCONJ
ejpam-6347	637	13	pharmacore	pharmacore	NOUN
ejpam-6347	637	14	modelling	modelling	NOUN
ejpam-6347	637	15	for	for	ADP
ejpam-6347	637	16	targeted	target	VERB
ejpam-6347	637	17	therapies	therapy	NOUN
ejpam-6347	637	18	.	.	PUNCT
ejpam-6347	638	1	in	in	ADP
ejpam-6347	638	2	aip	aip	PROPN
ejpam-6347	638	3	conference	conference	NOUN
ejpam-6347	638	4	proceedings	proceeding	NOUN
ejpam-6347	638	5	,	,	PUNCT
ejpam-6347	638	6	volume	volume	NOUN
ejpam-6347	638	7	3254	3254	NUM
ejpam-6347	638	8	,	,	PUNCT
ejpam-6347	638	9	page	page	NOUN
ejpam-6347	638	10	020008	020008	NUM
ejpam-6347	638	11	.	.	PUNCT
ejpam-6347	639	1	aip	aip	PROPN
ejpam-6347	639	2	publishing	publishing	PROPN
ejpam-6347	639	3	llc	llc	PROPN
ejpam-6347	639	4	,	,	PUNCT
ejpam-6347	639	5	2025	2025	NUM
ejpam-6347	639	6	.	.	PUNCT
ejpam-6347	640	1	[	[	X
ejpam-6347	640	2	18	18	NUM
ejpam-6347	640	3	]	]	PUNCT
ejpam-6347	640	4	our	our	PRON
ejpam-6347	640	5	world	world	NOUN
ejpam-6347	640	6	in	in	ADP
ejpam-6347	640	7	data	datum	NOUN
ejpam-6347	640	8	.	.	PUNCT
ejpam-6347	641	1	covid-19	covid-19	PROPN
ejpam-6347	641	2	dataset	dataset	NOUN
ejpam-6347	641	3	.	.	PUNCT
ejpam-6347	642	1	https://covid.ourworldindata.org/data/owidcovid-data.csv	https://covid.ourworldindata.org/data/owidcovid-data.csv	VERB
ejpam-6347	642	2	.	.	PUNCT
ejpam-6347	643	1	[	[	X
ejpam-6347	643	2	19	19	NUM
ejpam-6347	643	3	]	]	PUNCT
ejpam-6347	643	4	roshdi	roshdi	NOUN
ejpam-6347	643	5	khalil	khalil	PROPN
ejpam-6347	643	6	,	,	PUNCT
ejpam-6347	643	7	mohammed	mohammed	PROPN
ejpam-6347	643	8	al	al	PROPN
ejpam-6347	643	9	horani	horani	PROPN
ejpam-6347	643	10	,	,	PUNCT
ejpam-6347	643	11	abdelrahman	abdelrahman	NOUN
ejpam-6347	643	12	yousef	yousef	PROPN
ejpam-6347	643	13	,	,	PUNCT
ejpam-6347	643	14	and	and	CCONJ
ejpam-6347	643	15	mohammad	mohammad	PROPN
ejpam-6347	643	16	sababheh	sababheh	PROPN
ejpam-6347	643	17	.	.	PUNCT
ejpam-6347	644	1	a	a	DET
ejpam-6347	644	2	new	new	ADJ
ejpam-6347	644	3	definition	definition	NOUN
ejpam-6347	644	4	of	of	ADP
ejpam-6347	644	5	fractional	fractional	ADJ
ejpam-6347	644	6	derivative	derivative	NOUN
ejpam-6347	644	7	.	.	PUNCT
ejpam-6347	645	1	journal	journal	PROPN
ejpam-6347	645	2	of	of	ADP
ejpam-6347	645	3	computational	computational	ADJ
ejpam-6347	645	4	and	and	CCONJ
ejpam-6347	645	5	applied	applied	ADJ
ejpam-6347	645	6	mathematics	mathematic	NOUN
ejpam-6347	645	7	,	,	PUNCT
ejpam-6347	645	8	264:65–70	264:65–70	NUM
ejpam-6347	645	9	,	,	PUNCT
ejpam-6347	645	10	2014	2014	NUM
ejpam-6347	645	11	.	.	PUNCT
ejpam-6347	646	1	[	[	X
ejpam-6347	646	2	20	20	NUM
ejpam-6347	646	3	]	]	X
ejpam-6347	646	4	nadeem	nadeem	ADJ
ejpam-6347	646	5	abbas	abbas	PROPN
ejpam-6347	646	6	,	,	PUNCT
ejpam-6347	646	7	syeda	syeda	PROPN
ejpam-6347	646	8	alishwa	alishwa	PROPN
ejpam-6347	646	9	zanib	zanib	NOUN
ejpam-6347	646	10	,	,	PUNCT
ejpam-6347	646	11	sehrish	sehrish	PROPN
ejpam-6347	646	12	ramzan	ramzan	PROPN
ejpam-6347	646	13	,	,	PUNCT
ejpam-6347	646	14	aqsa	aqsa	PROPN
ejpam-6347	646	15	nazir	nazir	PROPN
ejpam-6347	646	16	,	,	PUNCT
ejpam-6347	646	17	and	and	CCONJ
ejpam-6347	646	18	wasfi	wasfi	ADV
ejpam-6347	646	19	shatanawi	shatanawi	ADJ
ejpam-6347	646	20	.	.	PUNCT
ejpam-6347	647	1	a	a	DET
ejpam-6347	647	2	conformable	conformable	ADJ
ejpam-6347	647	3	mathematical	mathematical	ADJ
ejpam-6347	647	4	model	model	NOUN
ejpam-6347	647	5	of	of	ADP
ejpam-6347	647	6	ebola	ebola	PROPN
ejpam-6347	647	7	virus	virus	NOUN
ejpam-6347	647	8	disease	disease	NOUN
ejpam-6347	647	9	and	and	CCONJ
ejpam-6347	647	10	its	its	PRON
ejpam-6347	647	11	stability	stability	NOUN
ejpam-6347	647	12	analysis	analysis	NOUN
ejpam-6347	647	13	.	.	PUNCT
ejpam-6347	648	1	heliyon	heliyon	NOUN
ejpam-6347	648	2	,	,	PUNCT
ejpam-6347	648	3	10(16	10(16	NUM
ejpam-6347	648	4	)	)	PUNCT
ejpam-6347	648	5	,	,	PUNCT
ejpam-6347	648	6	2024	2024	NUM
ejpam-6347	648	7	.	.	PUNCT
ejpam-6347	649	1	[	[	X
ejpam-6347	649	2	21	21	NUM
ejpam-6347	649	3	]	]	X
ejpam-6347	649	4	pauline	pauline	PROPN
ejpam-6347	649	5	van	van	PROPN
ejpam-6347	649	6	den	den	PROPN
ejpam-6347	649	7	driessche	driessche	NOUN
ejpam-6347	649	8	and	and	CCONJ
ejpam-6347	649	9	james	james	PROPN
ejpam-6347	649	10	watmough	watmough	PROPN
ejpam-6347	649	11	.	.	PUNCT
ejpam-6347	650	1	reproduction	reproduction	NOUN
ejpam-6347	650	2	numbers	number	NOUN
ejpam-6347	650	3	and	and	CCONJ
ejpam-6347	650	4	subthreshold	subthreshold	ADJ
ejpam-6347	650	5	endemic	endemic	ADJ
ejpam-6347	650	6	equilibria	equilibrium	NOUN
ejpam-6347	650	7	for	for	ADP
ejpam-6347	650	8	compartmental	compartmental	ADJ
ejpam-6347	650	9	models	model	NOUN
ejpam-6347	650	10	of	of	ADP
ejpam-6347	650	11	disease	disease	NOUN
ejpam-6347	650	12	transmission	transmission	NOUN
ejpam-6347	650	13	.	.	PUNCT
ejpam-6347	651	1	mathematical	mathematical	ADJ
ejpam-6347	651	2	biosciences	bioscience	NOUN
ejpam-6347	651	3	,	,	PUNCT
ejpam-6347	651	4	180(1	180(1	NUM
ejpam-6347	651	5	-	-	SYM
ejpam-6347	651	6	2):29–48	2):29–48	NUM
ejpam-6347	651	7	,	,	PUNCT
ejpam-6347	651	8	2002	2002	NUM
ejpam-6347	651	9	.	.	PUNCT
ejpam-6347	652	1	[	[	X
ejpam-6347	652	2	22	22	NUM
ejpam-6347	652	3	]	]	X
ejpam-6347	652	4	helena	helena	PROPN
ejpam-6347	652	5	sofia	sofia	PROPN
ejpam-6347	652	6	rodrigues	rodrigues	PROPN
ejpam-6347	652	7	,	,	PUNCT
ejpam-6347	652	8	m	m	VERB
ejpam-6347	652	9	teresa	teresa	PROPN
ejpam-6347	652	10	t	t	PROPN
ejpam-6347	652	11	monteiro	monteiro	PROPN
ejpam-6347	652	12	,	,	PUNCT
ejpam-6347	652	13	and	and	CCONJ
ejpam-6347	652	14	delfim	delfim	PROPN
ejpam-6347	652	15	fm	fm	PROPN
ejpam-6347	652	16	torres	torre	NOUN
ejpam-6347	652	17	.	.	PUNCT
ejpam-6347	653	1	seasonality	seasonality	NOUN
ejpam-6347	653	2	effects	effect	NOUN
ejpam-6347	653	3	on	on	ADP
ejpam-6347	653	4	dengue	dengue	NOUN
ejpam-6347	653	5	:	:	PUNCT
ejpam-6347	653	6	basic	basic	ADJ
ejpam-6347	653	7	reproduction	reproduction	NOUN
ejpam-6347	653	8	number	number	NOUN
ejpam-6347	653	9	,	,	PUNCT
ejpam-6347	653	10	sensitivity	sensitivity	NOUN
ejpam-6347	653	11	analysis	analysis	NOUN
ejpam-6347	653	12	and	and	CCONJ
ejpam-6347	653	13	optimal	optimal	ADJ
ejpam-6347	653	14	control	control	NOUN
ejpam-6347	653	15	.	.	PUNCT
ejpam-6347	654	1	mathematical	mathematical	ADJ
ejpam-6347	654	2	methods	method	NOUN
ejpam-6347	654	3	in	in	ADP
ejpam-6347	654	4	the	the	DET
ejpam-6347	654	5	applied	apply	VERB
ejpam-6347	654	6	sciences	science	NOUN
ejpam-6347	654	7	,	,	PUNCT
ejpam-6347	654	8	39(16):4671–4679	39(16):4671–4679	NUM
ejpam-6347	654	9	,	,	PUNCT
ejpam-6347	654	10	2016	2016	NUM
ejpam-6347	654	11	.	.	PUNCT
ejpam-6347	655	1	[	[	X
ejpam-6347	655	2	23	23	NUM
ejpam-6347	655	3	]	]	X
ejpam-6347	655	4	sm	sm	PROPN
ejpam-6347	655	5	ashrafur	ashrafur	NOUN
ejpam-6347	655	6	rahman	rahman	PROPN
ejpam-6347	655	7	.	.	PUNCT
ejpam-6347	656	1	study	study	NOUN
ejpam-6347	656	2	of	of	ADP
ejpam-6347	656	3	infectious	infectious	ADJ
ejpam-6347	656	4	diseases	disease	NOUN
ejpam-6347	656	5	by	by	ADP
ejpam-6347	656	6	mathematical	mathematical	ADJ
ejpam-6347	656	7	models	model	NOUN
ejpam-6347	656	8	:	:	PUNCT
ejpam-6347	656	9	predictions	prediction	NOUN
ejpam-6347	656	10	and	and	CCONJ
ejpam-6347	656	11	controls	control	NOUN
ejpam-6347	656	12	.	.	PUNCT
ejpam-6347	657	1	2016	2016	NUM
ejpam-6347	657	2	.	.	PUNCT
ejpam-6347	658	1	[	[	X
ejpam-6347	658	2	24	24	NUM
ejpam-6347	658	3	]	]	X
ejpam-6347	658	4	carlos	carlos	PROPN
ejpam-6347	658	5	castillo	castillo	PROPN
ejpam-6347	658	6	-	-	PUNCT
ejpam-6347	658	7	chavez	chavez	PROPN
ejpam-6347	658	8	,	,	PUNCT
ejpam-6347	658	9	sally	sally	NOUN
ejpam-6347	658	10	blower	blower	NOUN
ejpam-6347	658	11	,	,	PUNCT
ejpam-6347	658	12	pauline	pauline	PROPN
ejpam-6347	658	13	van	van	PROPN
ejpam-6347	658	14	den	den	PROPN
ejpam-6347	658	15	driessche	driessche	PROPN
ejpam-6347	658	16	,	,	PUNCT
ejpam-6347	658	17	denise	denise	PROPN
ejpam-6347	658	18	kirschner	kirschner	PROPN
ejpam-6347	658	19	,	,	PUNCT
ejpam-6347	658	20	and	and	CCONJ
ejpam-6347	658	21	abdul	abdul	PROPN
ejpam-6347	658	22	-	-	PUNCT
ejpam-6347	658	23	aziz	aziz	PROPN
ejpam-6347	658	24	yakubu	yakubu	PROPN
ejpam-6347	658	25	.	.	PROPN
ejpam-6347	659	1	mathematical	mathematical	PROPN
ejpam-6347	659	2	approaches	approach	NOUN
ejpam-6347	659	3	for	for	ADP
ejpam-6347	659	4	emerging	emerge	VERB
ejpam-6347	659	5	and	and	CCONJ
ejpam-6347	659	6	reemerging	reemerging	ADJ
ejpam-6347	659	7	infectious	infectious	ADJ
ejpam-6347	659	8	diseases	disease	NOUN
ejpam-6347	659	9	:	:	PUNCT
ejpam-6347	659	10	models	model	NOUN
ejpam-6347	659	11	,	,	PUNCT
ejpam-6347	659	12	methods	method	NOUN
ejpam-6347	659	13	,	,	PUNCT
ejpam-6347	659	14	and	and	CCONJ
ejpam-6347	659	15	theory	theory	NOUN
ejpam-6347	659	16	,	,	PUNCT
ejpam-6347	659	17	volume	volume	NOUN
ejpam-6347	659	18	126	126	NUM
ejpam-6347	659	19	.	.	PUNCT
ejpam-6347	660	1	springer	springer	NOUN
ejpam-6347	660	2	science	science	PROPN
ejpam-6347	660	3	&	&	CCONJ
ejpam-6347	660	4	business	business	NOUN
ejpam-6347	660	5	media	medium	NOUN
ejpam-6347	660	6	,	,	PUNCT
ejpam-6347	660	7	2002	2002	NUM
ejpam-6347	660	8	.	.	PUNCT
ejpam-6347	661	1	[	[	X
ejpam-6347	661	2	25	25	NUM
ejpam-6347	661	3	]	]	PUNCT
ejpam-6347	661	4	getachew	getachew	VERB
ejpam-6347	661	5	teshome	teshome	VERB
ejpam-6347	661	6	tilahun	tilahun	NOUN
ejpam-6347	661	7	,	,	PUNCT
ejpam-6347	661	8	oluwole	oluwole	PROPN
ejpam-6347	661	9	daniel	daniel	PROPN
ejpam-6347	661	10	makinde	makinde	PROPN
ejpam-6347	661	11	,	,	PUNCT
ejpam-6347	661	12	and	and	CCONJ
ejpam-6347	661	13	david	david	PROPN
ejpam-6347	661	14	malonza	malonza	PROPN
ejpam-6347	661	15	.	.	PUNCT
ejpam-6347	662	1	modelling	modelling	NOUN
ejpam-6347	662	2	and	and	CCONJ
ejpam-6347	662	3	optimal	optimal	ADJ
ejpam-6347	662	4	control	control	NOUN
ejpam-6347	662	5	of	of	ADP
ejpam-6347	662	6	typhoid	typhoid	NOUN
ejpam-6347	662	7	fever	fever	NOUN
ejpam-6347	662	8	disease	disease	NOUN
ejpam-6347	662	9	with	with	ADP
ejpam-6347	662	10	cost	cost	NOUN
ejpam-6347	662	11	-	-	PUNCT
ejpam-6347	662	12	effective	effective	ADJ
ejpam-6347	662	13	strategies	strategy	NOUN
ejpam-6347	662	14	.	.	PUNCT
ejpam-6347	663	1	computational	computational	ADJ
ejpam-6347	663	2	and	and	CCONJ
ejpam-6347	663	3	mathematical	mathematical	ADJ
ejpam-6347	663	4	methods	method	NOUN
ejpam-6347	663	5	in	in	ADP
ejpam-6347	663	6	medicine	medicine	NOUN
ejpam-6347	663	7	,	,	PUNCT
ejpam-6347	663	8	2017(1):2324518	2017(1):2324518	PROPN
ejpam-6347	663	9	,	,	PUNCT
ejpam-6347	663	10	2017	2017	NUM
ejpam-6347	663	11	.	.	PUNCT
ejpam-6347	664	1	[	[	X
ejpam-6347	664	2	26	26	NUM
ejpam-6347	664	3	]	]	PUNCT
ejpam-6347	664	4	getachew	getachew	VERB
ejpam-6347	664	5	teshome	teshome	VERB
ejpam-6347	664	6	tilahun	tilahun	NOUN
ejpam-6347	664	7	,	,	PUNCT
ejpam-6347	664	8	oluwole	oluwole	PROPN
ejpam-6347	664	9	daniel	daniel	PROPN
ejpam-6347	664	10	makinde	makinde	PROPN
ejpam-6347	664	11	,	,	PUNCT
ejpam-6347	664	12	and	and	CCONJ
ejpam-6347	664	13	david	david	PROPN
ejpam-6347	664	14	malonza	malonza	PROPN
ejpam-6347	664	15	.	.	PUNCT
ejpam-6347	665	1	codynamics	codynamic	NOUN
ejpam-6347	665	2	of	of	ADP
ejpam-6347	665	3	pneumonia	pneumonia	NOUN
ejpam-6347	665	4	and	and	CCONJ
ejpam-6347	665	5	typhoid	typhoid	NOUN
ejpam-6347	665	6	fever	fever	NOUN
ejpam-6347	665	7	diseases	disease	NOUN
ejpam-6347	665	8	with	with	ADP
ejpam-6347	665	9	cost	cost	NOUN
ejpam-6347	665	10	effective	effective	ADJ
ejpam-6347	665	11	optimal	optimal	ADJ
ejpam-6347	665	12	control	control	NOUN
ejpam-6347	665	13	analysis	analysis	NOUN
ejpam-6347	665	14	.	.	PUNCT
ejpam-6347	666	1	applied	apply	VERB
ejpam-6347	666	2	mathematics	mathematic	NOUN
ejpam-6347	666	3	and	and	CCONJ
ejpam-6347	666	4	computation	computation	NOUN
ejpam-6347	666	5	,	,	PUNCT
ejpam-6347	666	6	316:438–459	316:438–459	NUM
ejpam-6347	666	7	,	,	PUNCT
ejpam-6347	666	8	2018	2018	NUM
ejpam-6347	666	9	.	.	PUNCT
ejpam-6347	667	1	[	[	X
ejpam-6347	667	2	27	27	NUM
ejpam-6347	667	3	]	]	SYM
ejpam-6347	667	4	lev	lev	NOUN
ejpam-6347	667	5	semenovich	semenovich	PROPN
ejpam-6347	667	6	pontryagin	pontryagin	NOUN
ejpam-6347	667	7	.	.	PUNCT
ejpam-6347	668	1	mathematical	mathematical	ADJ
ejpam-6347	668	2	theory	theory	NOUN
ejpam-6347	668	3	of	of	ADP
ejpam-6347	668	4	optimal	optimal	ADJ
ejpam-6347	668	5	processes	process	NOUN
ejpam-6347	668	6	.	.	PUNCT
ejpam-6347	669	1	routledge	routledge	PROPN
ejpam-6347	669	2	,	,	PUNCT
ejpam-6347	669	3	n.	n.	NOUN
ejpam-6347	669	4	abbas	abbas	PROPN
ejpam-6347	669	5	,	,	PUNCT
ejpam-6347	669	6	w.	w.	PROPN
ejpam-6347	669	7	shatanawi	shatanawi	PROPN
ejpam-6347	669	8	,	,	PUNCT
ejpam-6347	669	9	s.	s.	PROPN
ejpam-6347	669	10	a.	a.	NOUN
ejpam-6347	669	11	zanib	zanib	PROPN
ejpam-6347	669	12	/	/	SYM
ejpam-6347	669	13	eur	eur	PROPN
ejpam-6347	669	14	.	.	PUNCT
ejpam-6347	670	1	j.	j.	PROPN
ejpam-6347	670	2	pure	pure	PROPN
ejpam-6347	670	3	appl	appl	PROPN
ejpam-6347	670	4	.	.	PROPN
ejpam-6347	670	5	math	math	PROPN
ejpam-6347	670	6	,	,	PUNCT
ejpam-6347	670	7	18	18	NUM
ejpam-6347	670	8	(	(	PUNCT
ejpam-6347	670	9	3	3	NUM
ejpam-6347	670	10	)	)	PUNCT
ejpam-6347	670	11	(	(	PUNCT
ejpam-6347	670	12	2025	2025	NUM
ejpam-6347	670	13	)	)	PUNCT
ejpam-6347	670	14	,	,	PUNCT
ejpam-6347	670	15	6347	6347	NUM
ejpam-6347	670	16	34	34	NUM
ejpam-6347	670	17	of	of	ADP
ejpam-6347	670	18	34	34	NUM
ejpam-6347	670	19	2018	2018	NUM
ejpam-6347	670	20	.	.	PUNCT
ejpam-6347	671	1	[	[	X
ejpam-6347	671	2	28	28	NUM
ejpam-6347	671	3	]	]	X
ejpam-6347	671	4	k	k	PROPN
ejpam-6347	671	5	renee	renee	PROPN
ejpam-6347	671	6	fister	fister	PROPN
ejpam-6347	671	7	,	,	PUNCT
ejpam-6347	671	8	suzanne	suzanne	PROPN
ejpam-6347	671	9	lenhart	lenhart	PROPN
ejpam-6347	671	10	,	,	PUNCT
ejpam-6347	671	11	and	and	CCONJ
ejpam-6347	671	12	joseph	joseph	PROPN
ejpam-6347	671	13	scott	scott	PROPN
ejpam-6347	671	14	mcnally	mcnally	PROPN
ejpam-6347	671	15	.	.	PUNCT
ejpam-6347	672	1	optimizing	optimize	VERB
ejpam-6347	672	2	chemotherapy	chemotherapy	NOUN
ejpam-6347	672	3	in	in	ADP
ejpam-6347	672	4	an	an	DET
ejpam-6347	672	5	hiv	hiv	PROPN
ejpam-6347	672	6	model	model	NOUN
ejpam-6347	672	7	.	.	PUNCT
ejpam-6347	673	1	1998	1998	NUM
ejpam-6347	673	2	.	.	PUNCT