id	sid	tid	token	lemma	pos
ejpam-4805	1	1	european	european	PROPN
ejpam-4805	1	2	journal	journal	PROPN
ejpam-4805	1	3	of	of	ADP
ejpam-4805	1	4	pure	pure	ADJ
ejpam-4805	1	5	and	and	CCONJ
ejpam-4805	1	6	applied	apply	VERB
ejpam-4805	1	7	mathematics	mathematic	NOUN
ejpam-4805	1	8	vol	vol	NOUN
ejpam-4805	1	9	.	.	PUNCT
ejpam-4805	2	1	16	16	NUM
ejpam-4805	2	2	,	,	PUNCT
ejpam-4805	2	3	no	no	INTJ
ejpam-4805	2	4	.	.	NOUN
ejpam-4805	2	5	4	4	NUM
ejpam-4805	2	6	,	,	PUNCT
ejpam-4805	2	7	2023	2023	NUM
ejpam-4805	2	8	,	,	PUNCT
ejpam-4805	2	9	2450	2450	NUM
ejpam-4805	2	10	-	-	SYM
ejpam-4805	2	11	2460	2460	NUM
ejpam-4805	2	12	issn	issn	PROPN
ejpam-4805	2	13	1307	1307	NUM
ejpam-4805	2	14	-	-	SYM
ejpam-4805	2	15	5543	5543	NUM
ejpam-4805	2	16	–	–	PUNCT
ejpam-4805	2	17	ejpam.com	ejpam.com	X
ejpam-4805	2	18	published	publish	VERB
ejpam-4805	2	19	by	by	ADP
ejpam-4805	2	20	new	new	PROPN
ejpam-4805	2	21	york	york	PROPN
ejpam-4805	2	22	business	business	PROPN
ejpam-4805	2	23	global	global	PROPN
ejpam-4805	3	1	a	a	DET
ejpam-4805	3	2	model	model	NOUN
ejpam-4805	3	3	of	of	ADP
ejpam-4805	3	4	covid-19	covid-19	PROPN
ejpam-4805	3	5	epidemic	epidemic	NOUN
ejpam-4805	3	6	based	base	VERB
ejpam-4805	3	7	on	on	ADP
ejpam-4805	3	8	vaccination	vaccination	NOUN
ejpam-4805	3	9	and	and	CCONJ
ejpam-4805	3	10	treatment	treatment	NOUN
ejpam-4805	3	11	fahdah	fahdah	NOUN
ejpam-4805	3	12	alshammari1	alshammari1	PROPN
ejpam-4805	3	13	,	,	PUNCT
ejpam-4805	3	14	alaa	alaa	PROPN
ejpam-4805	3	15	mustafa1,∗	mustafa1,∗	NOUN
ejpam-4805	3	16	,	,	PUNCT
ejpam-4805	3	17	ehssan	ehssan	ADJ
ejpam-4805	3	18	omer2	omer2	PROPN
ejpam-4805	3	19	,	,	PUNCT
ejpam-4805	3	20	fatima	fatima	PROPN
ejpam-4805	3	21	alnoor3	alnoor3	PROPN
ejpam-4805	3	22	1	1	NUM
ejpam-4805	3	23	department	department	NOUN
ejpam-4805	3	24	of	of	ADP
ejpam-4805	3	25	biology	biology	NOUN
ejpam-4805	3	26	,	,	PUNCT
ejpam-4805	3	27	faculty	faculty	NOUN
ejpam-4805	3	28	of	of	ADP
ejpam-4805	3	29	science	science	NOUN
ejpam-4805	3	30	and	and	CCONJ
ejpam-4805	3	31	arts	art	NOUN
ejpam-4805	3	32	-	-	PUNCT
ejpam-4805	3	33	rafha	rafha	NOUN
ejpam-4805	3	34	,	,	PUNCT
ejpam-4805	3	35	northrn	northrn	NOUN
ejpam-4805	3	36	border	border	NOUN
ejpam-4805	3	37	university	university	NOUN
ejpam-4805	3	38	,	,	PUNCT
ejpam-4805	3	39	arar	arar	NOUN
ejpam-4805	3	40	73213	73213	NUM
ejpam-4805	3	41	kingdom	kingdom	NOUN
ejpam-4805	3	42	of	of	ADP
ejpam-4805	3	43	saudi	saudi	PROPN
ejpam-4805	3	44	arabia	arabia	PROPN
ejpam-4805	3	45	2	2	NUM
ejpam-4805	3	46	department	department	NOUN
ejpam-4805	3	47	of	of	ADP
ejpam-4805	3	48	mathematics	mathematic	NOUN
ejpam-4805	3	49	,	,	PUNCT
ejpam-4805	3	50	faculty	faculty	NOUN
ejpam-4805	3	51	of	of	ADP
ejpam-4805	3	52	science	science	NOUN
ejpam-4805	3	53	-arar	-arar	PROPN
ejpam-4805	3	54	,	,	PUNCT
ejpam-4805	3	55	northrn	northrn	NOUN
ejpam-4805	3	56	border	border	NOUN
ejpam-4805	3	57	university	university	NOUN
ejpam-4805	3	58	,	,	PUNCT
ejpam-4805	3	59	arar	arar	NOUN
ejpam-4805	3	60	75211	75211	NUM
ejpam-4805	3	61	kingdom	kingdom	NOUN
ejpam-4805	3	62	of	of	ADP
ejpam-4805	3	63	saudi	saudi	PROPN
ejpam-4805	3	64	arabia	arabia	PROPN
ejpam-4805	3	65	3	3	NUM
ejpam-4805	3	66	department	department	NOUN
ejpam-4805	3	67	of	of	ADP
ejpam-4805	3	68	mathematics	mathematic	NOUN
ejpam-4805	3	69	,	,	PUNCT
ejpam-4805	3	70	faculty	faculty	NOUN
ejpam-4805	3	71	of	of	ADP
ejpam-4805	3	72	science	science	NOUN
ejpam-4805	3	73	and	and	CCONJ
ejpam-4805	3	74	arts	art	NOUN
ejpam-4805	3	75	-	-	PUNCT
ejpam-4805	3	76	turiaf	turiaf	NOUN
ejpam-4805	3	77	,	,	PUNCT
ejpam-4805	3	78	northrn	northrn	NOUN
ejpam-4805	3	79	border	border	NOUN
ejpam-4805	3	80	university	university	NOUN
ejpam-4805	3	81	,	,	PUNCT
ejpam-4805	3	82	arar	arar	NOUN
ejpam-4805	3	83	75211	75211	NUM
ejpam-4805	3	84	kingdom	kingdom	NOUN
ejpam-4805	3	85	of	of	ADP
ejpam-4805	3	86	saudi	saudi	PROPN
ejpam-4805	3	87	arabia	arabia	PROPN
ejpam-4805	3	88	abstract	abstract	NOUN
ejpam-4805	3	89	.	.	PUNCT
ejpam-4805	4	1	this	this	DET
ejpam-4805	4	2	article	article	NOUN
ejpam-4805	4	3	presents	present	VERB
ejpam-4805	4	4	a	a	DET
ejpam-4805	4	5	mathematical	mathematical	ADJ
ejpam-4805	4	6	model	model	NOUN
ejpam-4805	4	7	of	of	ADP
ejpam-4805	4	8	the	the	DET
ejpam-4805	4	9	covid-19	covid-19	PROPN
ejpam-4805	4	10	transmission	transmission	NOUN
ejpam-4805	4	11	mechanism	mechanism	NOUN
ejpam-4805	4	12	,	,	PUNCT
ejpam-4805	4	13	considering	consider	VERB
ejpam-4805	4	14	therapeutic	therapeutic	ADJ
ejpam-4805	4	15	interventions	intervention	NOUN
ejpam-4805	4	16	like	like	ADP
ejpam-4805	4	17	immunization	immunization	NOUN
ejpam-4805	4	18	and	and	CCONJ
ejpam-4805	4	19	recovery	recovery	NOUN
ejpam-4805	4	20	or	or	CCONJ
ejpam-4805	4	21	treatment	treatment	NOUN
ejpam-4805	4	22	.	.	PUNCT
ejpam-4805	5	1	the	the	DET
ejpam-4805	5	2	model	model	NOUN
ejpam-4805	5	3	shows	show	VERB
ejpam-4805	5	4	that	that	SCONJ
ejpam-4805	5	5	the	the	DET
ejpam-4805	5	6	disease	disease	NOUN
ejpam-4805	5	7	-	-	PUNCT
ejpam-4805	5	8	free	free	ADJ
ejpam-4805	5	9	and	and	CCONJ
ejpam-4805	5	10	endemic	endemic	ADJ
ejpam-4805	5	11	equilibriums	equilibrium	NOUN
ejpam-4805	5	12	are	be	AUX
ejpam-4805	5	13	globally	globally	ADV
ejpam-4805	5	14	asymptotically	asymptotically	ADV
ejpam-4805	5	15	stable	stable	ADJ
ejpam-4805	5	16	when	when	SCONJ
ejpam-4805	5	17	effective	effective	ADJ
ejpam-4805	5	18	reproduction	reproduction	NOUN
ejpam-4805	5	19	numbers	number	NOUN
ejpam-4805	5	20	are	be	AUX
ejpam-4805	5	21	less	less	ADJ
ejpam-4805	5	22	than	than	ADP
ejpam-4805	5	23	or	or	CCONJ
ejpam-4805	5	24	larger	large	ADJ
ejpam-4805	5	25	than	than	ADP
ejpam-4805	5	26	unity	unity	NOUN
ejpam-4805	5	27	.	.	PUNCT
ejpam-4805	6	1	the	the	DET
ejpam-4805	6	2	critical	critical	ADJ
ejpam-4805	6	3	vaccination	vaccination	NOUN
ejpam-4805	6	4	threshold	threshold	NOUN
ejpam-4805	6	5	depends	depend	VERB
ejpam-4805	6	6	on	on	ADP
ejpam-4805	6	7	the	the	DET
ejpam-4805	6	8	vaccine	vaccine	NOUN
ejpam-4805	6	9	’s	’s	PART
ejpam-4805	6	10	ability	ability	NOUN
ejpam-4805	6	11	to	to	PART
ejpam-4805	6	12	prevent	prevent	VERB
ejpam-4805	6	13	or	or	CCONJ
ejpam-4805	6	14	cure	cure	VERB
ejpam-4805	6	15	the	the	DET
ejpam-4805	6	16	illness	illness	NOUN
ejpam-4805	6	17	.	.	PUNCT
ejpam-4805	7	1	the	the	DET
ejpam-4805	7	2	model	model	NOUN
ejpam-4805	7	3	predicts	predict	VERB
ejpam-4805	7	4	the	the	DET
ejpam-4805	7	5	effectiveness	effectiveness	NOUN
ejpam-4805	7	6	of	of	ADP
ejpam-4805	7	7	vaccination	vaccination	NOUN
ejpam-4805	7	8	based	base	VERB
ejpam-4805	7	9	on	on	ADP
ejpam-4805	7	10	factors	factor	NOUN
ejpam-4805	7	11	like	like	ADP
ejpam-4805	7	12	vaccination	vaccination	NOUN
ejpam-4805	7	13	efficiency	efficiency	NOUN
ejpam-4805	7	14	,	,	PUNCT
ejpam-4805	7	15	scheduling	scheduling	NOUN
ejpam-4805	7	16	,	,	PUNCT
ejpam-4805	7	17	and	and	CCONJ
ejpam-4805	7	18	relaxation	relaxation	NOUN
ejpam-4805	7	19	of	of	ADP
ejpam-4805	7	20	social	social	ADJ
ejpam-4805	7	21	measures	measure	NOUN
ejpam-4805	7	22	.	.	PUNCT
ejpam-4805	8	1	the	the	DET
ejpam-4805	8	2	subsiding	subsiding	NOUN
ejpam-4805	8	3	of	of	ADP
ejpam-4805	8	4	the	the	DET
ejpam-4805	8	5	epidemic	epidemic	NOUN
ejpam-4805	8	6	as	as	ADP
ejpam-4805	8	7	vaccination	vaccination	NOUN
ejpam-4805	8	8	is	be	AUX
ejpam-4805	8	9	implemented	implement	VERB
ejpam-4805	8	10	depends	depend	VERB
ejpam-4805	8	11	on	on	ADP
ejpam-4805	8	12	the	the	DET
ejpam-4805	8	13	scale	scale	NOUN
ejpam-4805	8	14	of	of	ADP
ejpam-4805	8	15	relaxation	relaxation	NOUN
ejpam-4805	8	16	of	of	ADP
ejpam-4805	8	17	social	social	ADJ
ejpam-4805	8	18	measures	measure	NOUN
ejpam-4805	8	19	.	.	PUNCT
ejpam-4805	9	1	2020	2020	NUM
ejpam-4805	9	2	mathematics	mathematic	NOUN
ejpam-4805	9	3	subject	subject	NOUN
ejpam-4805	9	4	classifications	classification	NOUN
ejpam-4805	9	5	:	:	PUNCT
ejpam-4805	9	6	37n25	37n25	NUM
ejpam-4805	9	7	key	key	ADJ
ejpam-4805	9	8	words	word	NOUN
ejpam-4805	9	9	and	and	CCONJ
ejpam-4805	9	10	phrases	phrase	NOUN
ejpam-4805	9	11	:	:	PUNCT
ejpam-4805	9	12	covid-19	covid-19	PROPN
ejpam-4805	9	13	epidemic	epidemic	NOUN
ejpam-4805	9	14	,	,	PUNCT
ejpam-4805	9	15	mathematical	mathematical	ADJ
ejpam-4805	9	16	modeling	modeling	NOUN
ejpam-4805	9	17	,	,	PUNCT
ejpam-4805	9	18	vaccination	vaccination	NOUN
ejpam-4805	9	19	,	,	PUNCT
ejpam-4805	9	20	social	social	ADJ
ejpam-4805	9	21	measures	measure	NOUN
ejpam-4805	9	22	,	,	PUNCT
ejpam-4805	9	23	transmission	transmission	NOUN
ejpam-4805	9	24	1	1	NUM
ejpam-4805	9	25	.	.	PUNCT
ejpam-4805	9	26	introduction	introduction	NOUN
ejpam-4805	9	27	years	year	NOUN
ejpam-4805	9	28	of	of	ADP
ejpam-4805	9	29	study	study	NOUN
ejpam-4805	9	30	and	and	CCONJ
ejpam-4805	9	31	testing	testing	NOUN
ejpam-4805	9	32	are	be	AUX
ejpam-4805	9	33	frequently	frequently	ADV
ejpam-4805	9	34	needed	need	VERB
ejpam-4805	9	35	to	to	PART
ejpam-4805	9	36	create	create	VERB
ejpam-4805	9	37	vaccinations	vaccination	NOUN
ejpam-4805	9	38	that	that	PRON
ejpam-4805	9	39	are	be	AUX
ejpam-4805	9	40	safe	safe	ADJ
ejpam-4805	9	41	and	and	CCONJ
ejpam-4805	9	42	effective	effective	ADJ
ejpam-4805	9	43	against	against	ADP
ejpam-4805	9	44	infectious	infectious	ADJ
ejpam-4805	9	45	agents	agent	NOUN
ejpam-4805	9	46	.	.	PUNCT
ejpam-4805	10	1	in	in	ADP
ejpam-4805	10	2	comparison	comparison	NOUN
ejpam-4805	10	3	,	,	PUNCT
ejpam-4805	10	4	covid-19	covid-19	PROPN
ejpam-4805	10	5	vaccine	vaccine	NOUN
ejpam-4805	10	6	development	development	NOUN
ejpam-4805	10	7	and	and	CCONJ
ejpam-4805	10	8	distribution	distribution	NOUN
ejpam-4805	10	9	took	take	VERB
ejpam-4805	10	10	less	less	ADJ
ejpam-4805	10	11	than	than	ADP
ejpam-4805	10	12	a	a	PRON
ejpam-4805	10	13	year	year	NOUN
ejpam-4805	10	14	[	[	X
ejpam-4805	10	15	18	18	NUM
ejpam-4805	10	16	]	]	PUNCT
ejpam-4805	10	17	.	.	PUNCT
ejpam-4805	11	1	the	the	DET
ejpam-4805	11	2	effectiveness	effectiveness	NOUN
ejpam-4805	11	3	of	of	ADP
ejpam-4805	11	4	the	the	DET
ejpam-4805	11	5	epidemiological	epidemiological	ADJ
ejpam-4805	11	6	models	model	NOUN
ejpam-4805	11	7	suggested	suggest	VERB
ejpam-4805	11	8	for	for	SCONJ
ejpam-4805	11	9	the	the	DET
ejpam-4805	11	10	covid-19	covid-19	PROPN
ejpam-4805	11	11	outbreak	outbreak	NOUN
ejpam-4805	11	12	may	may	AUX
ejpam-4805	11	13	be	be	AUX
ejpam-4805	11	14	impacted	impact	VERB
ejpam-4805	11	15	by	by	ADP
ejpam-4805	11	16	the	the	DET
ejpam-4805	11	17	answers	answer	NOUN
ejpam-4805	11	18	to	to	ADP
ejpam-4805	11	19	the	the	DET
ejpam-4805	11	20	many	many	ADJ
ejpam-4805	11	21	unanswered	unanswered	ADJ
ejpam-4805	11	22	issues	issue	NOUN
ejpam-4805	11	23	created	create	VERB
ejpam-4805	11	24	by	by	ADP
ejpam-4805	11	25	this	this	DET
ejpam-4805	11	26	rapid	rapid	ADJ
ejpam-4805	11	27	development	development	NOUN
ejpam-4805	11	28	.	.	PUNCT
ejpam-4805	12	1	for	for	ADP
ejpam-4805	12	2	instance	instance	NOUN
ejpam-4805	12	3	,	,	PUNCT
ejpam-4805	12	4	vaccine	vaccine	NOUN
ejpam-4805	12	5	efficiency	efficiency	NOUN
ejpam-4805	12	6	rates	rate	NOUN
ejpam-4805	12	7	vary	vary	VERB
ejpam-4805	12	8	depending	depend	VERB
ejpam-4805	12	9	on	on	ADP
ejpam-4805	12	10	the	the	DET
ejpam-4805	12	11	level	level	NOUN
ejpam-4805	12	12	and	and	CCONJ
ejpam-4805	12	13	length	length	NOUN
ejpam-4805	12	14	of	of	ADP
ejpam-4805	12	15	immunization	immunization	NOUN
ejpam-4805	12	16	for	for	ADP
ejpam-4805	12	17	various	various	ADJ
ejpam-4805	12	18	groups	group	NOUN
ejpam-4805	12	19	[	[	X
ejpam-4805	12	20	23	23	NUM
ejpam-4805	12	21	]	]	PUNCT
ejpam-4805	12	22	,	,	PUNCT
ejpam-4805	12	23	[	[	X
ejpam-4805	12	24	24	24	NUM
ejpam-4805	12	25	]	]	PUNCT
ejpam-4805	12	26	,	,	PUNCT
ejpam-4805	12	27	[	[	X
ejpam-4805	12	28	13	13	NUM
ejpam-4805	12	29	]	]	PUNCT
ejpam-4805	12	30	,	,	PUNCT
ejpam-4805	12	31	[	[	X
ejpam-4805	12	32	17	17	NUM
ejpam-4805	12	33	]	]	PUNCT
ejpam-4805	12	34	.	.	PUNCT
ejpam-4805	13	1	according	accord	VERB
ejpam-4805	13	2	to	to	ADP
ejpam-4805	13	3	the	the	DET
ejpam-4805	13	4	epidemic	epidemic	NOUN
ejpam-4805	13	5	status	status	NOUN
ejpam-4805	13	6	of	of	ADP
ejpam-4805	13	7	the	the	DET
ejpam-4805	13	8	vaccinated	vaccinated	ADJ
ejpam-4805	13	9	individuals	individual	NOUN
ejpam-4805	13	10	—	—	PUNCT
ejpam-4805	13	11	vulnerable	vulnerable	ADJ
ejpam-4805	13	12	,	,	PUNCT
ejpam-4805	13	13	∗corresponding	∗corresponde	VERB
ejpam-4805	13	14	author	author	NOUN
ejpam-4805	13	15	.	.	PUNCT
ejpam-4805	14	1	doi	doi	PROPN
ejpam-4805	14	2	:	:	PUNCT
ejpam-4805	14	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4805	https://doi.org/10.29020/nybg.ejpam.v16i4.4805	PROPN
ejpam-4805	14	4	email	email	NOUN
ejpam-4805	14	5	addresses	address	NOUN
ejpam-4805	14	6	:	:	PUNCT
ejpam-4805	14	7	bfahdah1402@hotmail.com	bfahdah1402@hotmail.com	X
ejpam-4805	14	8	(	(	PUNCT
ejpam-4805	14	9	f.	f.	PROPN
ejpam-4805	14	10	alshammari	alshammari	PROPN
ejpam-4805	14	11	)	)	PUNCT
ejpam-4805	14	12	,	,	PUNCT
ejpam-4805	14	13	alal200949@yahoo.com	alal200949@yahoo.com	X
ejpam-4805	14	14	(	(	PUNCT
ejpam-4805	14	15	a.mustafa	a.mustafa	PROPN
ejpam-4805	14	16	)	)	PUNCT
ejpam-4805	14	17	,	,	PUNCT
ejpam-4805	14	18	ehssanomerphdd@gmail.com	ehssanomerphdd@gmail.com	X
ejpam-4805	14	19	(	(	PUNCT
ejpam-4805	14	20	e.omer	e.omer	NOUN
ejpam-4805	14	21	)	)	PUNCT
ejpam-4805	14	22	,	,	PUNCT
ejpam-4805	14	23	fattoshaa1988@gmail.com	fattoshaa1988@gmail.com	X
ejpam-4805	15	1	(	(	PUNCT
ejpam-4805	15	2	f.	f.	PROPN
ejpam-4805	15	3	alnoor	alnoor	PROPN
ejpam-4805	15	4	)	)	PUNCT
ejpam-4805	15	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4805	15	6	2450	2450	NUM
ejpam-4805	16	1	©	©	ADP
ejpam-4805	16	2	2023	2023	NUM
ejpam-4805	16	3	ejpam	ejpam	NOUN
ejpam-4805	16	4	all	all	DET
ejpam-4805	16	5	rights	right	NOUN
ejpam-4805	16	6	reserved	reserve	VERB
ejpam-4805	16	7	.	.	PUNCT
ejpam-4805	17	1	a.	a.	PROPN
ejpam-4805	17	2	mustafa	mustafa	PROPN
ejpam-4805	17	3	et	et	PROPN
ejpam-4805	17	4	al	al	PROPN
ejpam-4805	17	5	.	.	PUNCT
ejpam-4805	17	6	/	/	SYM
ejpam-4805	17	7	eur	eur	PROPN
ejpam-4805	17	8	.	.	PUNCT
ejpam-4805	18	1	j.	j.	PROPN
ejpam-4805	18	2	pure	pure	PROPN
ejpam-4805	18	3	appl	appl	PROPN
ejpam-4805	18	4	.	.	PROPN
ejpam-4805	18	5	math	math	PROPN
ejpam-4805	18	6	,	,	PUNCT
ejpam-4805	18	7	16	16	NUM
ejpam-4805	18	8	(	(	PUNCT
ejpam-4805	18	9	4	4	NUM
ejpam-4805	18	10	)	)	PUNCT
ejpam-4805	18	11	(	(	PUNCT
ejpam-4805	18	12	2023	2023	NUM
ejpam-4805	18	13	)	)	PUNCT
ejpam-4805	18	14	,	,	PUNCT
ejpam-4805	18	15	2450	2450	NUM
ejpam-4805	18	16	-	-	SYM
ejpam-4805	18	17	2460	2460	NUM
ejpam-4805	18	18	2451	2451	NUM
ejpam-4805	18	19	infected	infect	VERB
ejpam-4805	18	20	,	,	PUNCT
ejpam-4805	18	21	or	or	CCONJ
ejpam-4805	18	22	having	having	AUX
ejpam-4805	18	23	received	receive	VERB
ejpam-4805	18	24	vaccine	vaccine	NOUN
ejpam-4805	18	25	doses	dose	NOUN
ejpam-4805	18	26	—	—	PUNCT
ejpam-4805	18	27	we	we	PRON
ejpam-4805	18	28	will	will	AUX
ejpam-4805	18	29	examine	examine	VERB
ejpam-4805	18	30	the	the	DET
ejpam-4805	18	31	efficacy	efficacy	NOUN
ejpam-4805	18	32	of	of	ADP
ejpam-4805	18	33	vaccination	vaccination	NOUN
ejpam-4805	18	34	[	[	X
ejpam-4805	18	35	22	22	NUM
ejpam-4805	18	36	]	]	PUNCT
ejpam-4805	18	37	.	.	PUNCT
ejpam-4805	19	1	since	since	SCONJ
ejpam-4805	19	2	the	the	DET
ejpam-4805	19	3	start	start	NOUN
ejpam-4805	19	4	of	of	ADP
ejpam-4805	19	5	the	the	DET
ejpam-4805	19	6	covid-19	covid-19	PROPN
ejpam-4805	19	7	pandemic	pandemic	NOUN
ejpam-4805	19	8	[	[	X
ejpam-4805	19	9	[	[	X
ejpam-4805	19	10	11	11	NUM
ejpam-4805	19	11	]	]	PUNCT
ejpam-4805	19	12	,	,	PUNCT
ejpam-4805	19	13	[	[	X
ejpam-4805	19	14	14	14	NUM
ejpam-4805	19	15	]	]	PUNCT
ejpam-4805	19	16	,	,	PUNCT
ejpam-4805	19	17	[	[	X
ejpam-4805	19	18	12	12	NUM
ejpam-4805	19	19	]	]	PUNCT
ejpam-4805	19	20	,	,	PUNCT
ejpam-4805	19	21	[	[	X
ejpam-4805	19	22	5	5	NUM
ejpam-4805	19	23	]	]	PUNCT
ejpam-4805	19	24	,	,	PUNCT
ejpam-4805	19	25	[	[	X
ejpam-4805	19	26	21	21	NUM
ejpam-4805	19	27	]	]	PUNCT
ejpam-4805	19	28	,	,	PUNCT
ejpam-4805	19	29	[	[	X
ejpam-4805	19	30	4][19	4][19	NOUN
ejpam-4805	19	31	]	]	X
ejpam-4805	19	32	]	]	PUNCT
ejpam-4805	19	33	,	,	PUNCT
ejpam-4805	19	34	mathematical	mathematical	ADJ
ejpam-4805	19	35	modeling	modeling	NOUN
ejpam-4805	19	36	has	have	AUX
ejpam-4805	19	37	been	be	AUX
ejpam-4805	19	38	utilized	utilize	VERB
ejpam-4805	19	39	to	to	PART
ejpam-4805	19	40	examine	examine	VERB
ejpam-4805	19	41	the	the	DET
ejpam-4805	19	42	reliability	reliability	NOUN
ejpam-4805	19	43	of	of	ADP
ejpam-4805	19	44	parameters	parameter	NOUN
ejpam-4805	19	45	,	,	PUNCT
ejpam-4805	19	46	forecast	forecast	VERB
ejpam-4805	19	47	its	its	PRON
ejpam-4805	19	48	progression	progression	NOUN
ejpam-4805	19	49	,	,	PUNCT
ejpam-4805	19	50	and	and	CCONJ
ejpam-4805	19	51	contrast	contrast	VERB
ejpam-4805	19	52	various	various	ADJ
ejpam-4805	19	53	.	.	PUNCT
ejpam-4805	20	1	despite	despite	SCONJ
ejpam-4805	20	2	these	these	DET
ejpam-4805	20	3	limitations	limitation	NOUN
ejpam-4805	20	4	,	,	PUNCT
ejpam-4805	20	5	a	a	DET
ejpam-4805	20	6	first	first	ADJ
ejpam-4805	20	7	simplified	simplified	ADJ
ejpam-4805	20	8	approach	approach	NOUN
ejpam-4805	20	9	can	can	AUX
ejpam-4805	20	10	lead	lead	VERB
ejpam-4805	20	11	to	to	ADP
ejpam-4805	20	12	a	a	DET
ejpam-4805	20	13	model	model	NOUN
ejpam-4805	20	14	,	,	PUNCT
ejpam-4805	20	15	making	make	VERB
ejpam-4805	20	16	it	it	PRON
ejpam-4805	20	17	possible	possible	ADJ
ejpam-4805	20	18	to	to	PART
ejpam-4805	20	19	predict	predict	VERB
ejpam-4805	20	20	effective	effective	ADJ
ejpam-4805	20	21	vaccination	vaccination	NOUN
ejpam-4805	20	22	coverage	coverage	NOUN
ejpam-4805	20	23	at	at	ADP
ejpam-4805	20	24	the	the	DET
ejpam-4805	20	25	population	population	NOUN
ejpam-4805	20	26	level	level	NOUN
ejpam-4805	20	27	that	that	PRON
ejpam-4805	20	28	will	will	AUX
ejpam-4805	20	29	prevent	prevent	VERB
ejpam-4805	20	30	the	the	DET
ejpam-4805	20	31	appearance	appearance	NOUN
ejpam-4805	20	32	of	of	ADP
ejpam-4805	20	33	successive	successive	ADJ
ejpam-4805	20	34	epidemic	epidemic	NOUN
ejpam-4805	20	35	waves	wave	NOUN
ejpam-4805	20	36	.	.	PUNCT
ejpam-4805	21	1	[	[	X
ejpam-4805	21	2	15	15	NUM
ejpam-4805	21	3	]	]	X
ejpam-4805	21	4	daily	daily	ADJ
ejpam-4805	21	5	vaccination	vaccination	NOUN
ejpam-4805	21	6	data	datum	NOUN
ejpam-4805	21	7	,	,	PUNCT
ejpam-4805	21	8	even	even	ADV
ejpam-4805	21	9	if	if	SCONJ
ejpam-4805	21	10	they	they	PRON
ejpam-4805	21	11	are	be	AUX
ejpam-4805	21	12	global	global	ADJ
ejpam-4805	21	13	and	and	CCONJ
ejpam-4805	21	14	unrefined	unrefined	ADJ
ejpam-4805	21	15	(	(	PUNCT
ejpam-4805	21	16	for	for	ADP
ejpam-4805	21	17	example	example	NOUN
ejpam-4805	21	18	,	,	PUNCT
ejpam-4805	21	19	[	[	X
ejpam-4805	21	20	14	14	NUM
ejpam-4805	21	21	]	]	PUNCT
ejpam-4805	21	22	by	by	ADP
ejpam-4805	21	23	age	age	NOUN
ejpam-4805	21	24	group	group	NOUN
ejpam-4805	21	25	or	or	CCONJ
ejpam-4805	21	26	social	social	ADJ
ejpam-4805	21	27	classification	classification	NOUN
ejpam-4805	21	28	)	)	PUNCT
ejpam-4805	21	29	,	,	PUNCT
ejpam-4805	21	30	make	make	VERB
ejpam-4805	21	31	it	it	PRON
ejpam-4805	21	32	possible	possible	ADJ
ejpam-4805	21	33	to	to	PART
ejpam-4805	21	34	better	well	ADV
ejpam-4805	21	35	understand	understand	VERB
ejpam-4805	21	36	the	the	DET
ejpam-4805	21	37	effect	effect	NOUN
ejpam-4805	21	38	of	of	ADP
ejpam-4805	21	39	vaccination	vaccination	NOUN
ejpam-4805	21	40	policy	policy	NOUN
ejpam-4805	21	41	and	and	CCONJ
ejpam-4805	21	42	test	test	VERB
ejpam-4805	21	43	the	the	DET
ejpam-4805	21	44	consequences	consequence	NOUN
ejpam-4805	21	45	of	of	ADP
ejpam-4805	21	46	changes	change	NOUN
ejpam-4805	21	47	in	in	ADP
ejpam-4805	21	48	this	this	DET
ejpam-4805	21	49	policy	policy	NOUN
ejpam-4805	21	50	to	to	PART
ejpam-4805	21	51	improve	improve	VERB
ejpam-4805	21	52	its	its	PRON
ejpam-4805	21	53	effectiveness[19	effectiveness[19	NOUN
ejpam-4805	21	54	]	]	X
ejpam-4805	21	55	.	.	PUNCT
ejpam-4805	22	1	we	we	PRON
ejpam-4805	22	2	use	use	VERB
ejpam-4805	22	3	an	an	DET
ejpam-4805	22	4	epidemic	epidemic	NOUN
ejpam-4805	22	5	model	model	NOUN
ejpam-4805	22	6	to	to	PART
ejpam-4805	22	7	understand	understand	VERB
ejpam-4805	22	8	the	the	DET
ejpam-4805	22	9	complex	complex	ADJ
ejpam-4805	22	10	interactions	interaction	NOUN
ejpam-4805	22	11	between	between	ADP
ejpam-4805	22	12	epidemic	epidemic	NOUN
ejpam-4805	22	13	control	control	NOUN
ejpam-4805	22	14	and	and	CCONJ
ejpam-4805	22	15	epidemic	epidemic	NOUN
ejpam-4805	22	16	data	datum	NOUN
ejpam-4805	22	17	.	.	PUNCT
ejpam-4805	23	1	[	[	X
ejpam-4805	23	2	[	[	X
ejpam-4805	23	3	18	18	NUM
ejpam-4805	23	4	]	]	PUNCT
ejpam-4805	23	5	,	,	PUNCT
ejpam-4805	23	6	[	[	X
ejpam-4805	23	7	9	9	NUM
ejpam-4805	23	8	]	]	X
ejpam-4805	23	9	]	]	X
ejpam-4805	23	10	our	our	PRON
ejpam-4805	23	11	model	model	NOUN
ejpam-4805	23	12	considers	consider	VERB
ejpam-4805	23	13	the	the	DET
ejpam-4805	23	14	changes	change	NOUN
ejpam-4805	23	15	in	in	ADP
ejpam-4805	23	16	public	public	ADJ
ejpam-4805	23	17	health	health	NOUN
ejpam-4805	23	18	policy	policy	NOUN
ejpam-4805	24	1	[	[	X
ejpam-4805	24	2	[	[	X
ejpam-4805	24	3	1	1	NUM
ejpam-4805	24	4	]	]	PUNCT
ejpam-4805	24	5	,	,	PUNCT
ejpam-4805	24	6	[	[	X
ejpam-4805	24	7	20	20	NUM
ejpam-4805	24	8	]	]	PUNCT
ejpam-4805	24	9	,	,	PUNCT
ejpam-4805	25	1	[	[	X
ejpam-4805	25	2	12	12	NUM
ejpam-4805	25	3	]	]	X
ejpam-4805	25	4	]	]	X
ejpam-4805	25	5	,	,	PUNCT
ejpam-4805	25	6	such	such	ADJ
ejpam-4805	25	7	as	as	ADP
ejpam-4805	25	8	confinement	confinement	ADJ
ejpam-4805	25	9	,	,	PUNCT
ejpam-4805	25	10	social	social	ADJ
ejpam-4805	25	11	distancing	distancing	NOUN
ejpam-4805	25	12	measures	measure	NOUN
ejpam-4805	25	13	,	,	PUNCT
ejpam-4805	25	14	etc	etc	X
ejpam-4805	25	15	.	.	X
ejpam-4805	25	16	,	,	PUNCT
ejpam-4805	25	17	through	through	ADP
ejpam-4805	25	18	the	the	DET
ejpam-4805	25	19	time	time	NOUN
ejpam-4805	25	20	-	-	PUNCT
ejpam-4805	25	21	dependent	dependent	ADJ
ejpam-4805	25	22	transmission	transmission	NOUN
ejpam-4805	25	23	rate	rate	NOUN
ejpam-4805	25	24	in	in	ADP
ejpam-4805	25	25	the	the	DET
ejpam-4805	25	26	model	model	NOUN
ejpam-4805	25	27	.	.	PUNCT
ejpam-4805	26	1	the	the	DET
ejpam-4805	26	2	data	data	NOUN
ejpam-4805	26	3	consists	consist	VERB
ejpam-4805	26	4	of	of	ADP
ejpam-4805	26	5	the	the	DET
ejpam-4805	26	6	daily	daily	ADJ
ejpam-4805	26	7	number	number	NOUN
ejpam-4805	26	8	of	of	ADP
ejpam-4805	26	9	reported	report	VERB
ejpam-4805	26	10	cases	case	NOUN
ejpam-4805	26	11	and	and	CCONJ
ejpam-4805	26	12	the	the	DET
ejpam-4805	26	13	daily	daily	ADJ
ejpam-4805	26	14	number	number	NOUN
ejpam-4805	26	15	of	of	ADP
ejpam-4805	26	16	second	second	ADJ
ejpam-4805	26	17	doses	dose	NOUN
ejpam-4805	26	18	of	of	ADP
ejpam-4805	26	19	vaccine	vaccine	NOUN
ejpam-4805	26	20	.	.	PUNCT
ejpam-4805	27	1	we	we	PRON
ejpam-4805	27	2	refer	refer	VERB
ejpam-4805	27	3	to	to	ADP
ejpam-4805	27	4	[	[	X
ejpam-4805	27	5	[	[	X
ejpam-4805	27	6	13	13	NUM
ejpam-4805	27	7	]	]	PUNCT
ejpam-4805	27	8	,	,	PUNCT
ejpam-4805	27	9	[	[	X
ejpam-4805	27	10	17	17	NUM
ejpam-4805	27	11	]	]	PUNCT
ejpam-4805	27	12	,	,	PUNCT
ejpam-4805	27	13	[	[	X
ejpam-4805	27	14	9	9	NUM
ejpam-4805	27	15	]	]	PUNCT
ejpam-4805	27	16	,	,	PUNCT
ejpam-4805	28	1	[	[	X
ejpam-4805	28	2	5	5	X
ejpam-4805	28	3	]	]	X
ejpam-4805	28	4	[	[	X
ejpam-4805	28	5	15	15	NUM
ejpam-4805	28	6	]	]	X
ejpam-4805	28	7	]	]	PUNCT
ejpam-4805	28	8	for	for	ADP
ejpam-4805	28	9	more	more	ADJ
ejpam-4805	28	10	results	result	NOUN
ejpam-4805	28	11	on	on	ADP
ejpam-4805	28	12	the	the	DET
ejpam-4805	28	13	subject	subject	NOUN
ejpam-4805	28	14	.	.	PUNCT
ejpam-4805	29	1	in	in	ADP
ejpam-4805	29	2	the	the	DET
ejpam-4805	29	3	study	study	NOUN
ejpam-4805	29	4	,	,	PUNCT
ejpam-4805	29	5	we	we	PRON
ejpam-4805	29	6	propose	propose	VERB
ejpam-4805	29	7	a	a	DET
ejpam-4805	29	8	new	new	ADJ
ejpam-4805	29	9	model	model	NOUN
ejpam-4805	29	10	for	for	ADP
ejpam-4805	29	11	vaccination	vaccination	NOUN
ejpam-4805	29	12	implementation	implementation	NOUN
ejpam-4805	29	13	.	.	PUNCT
ejpam-4805	30	1	we	we	PRON
ejpam-4805	30	2	can	can	AUX
ejpam-4805	30	3	connect	connect	VERB
ejpam-4805	30	4	the	the	DET
ejpam-4805	30	5	model	model	NOUN
ejpam-4805	30	6	with	with	ADP
ejpam-4805	30	7	vaccination	vaccination	NOUN
ejpam-4805	30	8	to	to	ADP
ejpam-4805	30	9	a	a	DET
ejpam-4805	30	10	model	model	NOUN
ejpam-4805	30	11	without	without	ADP
ejpam-4805	30	12	vaccination	vaccination	NOUN
ejpam-4805	30	13	.	.	PUNCT
ejpam-4805	31	1	we	we	PRON
ejpam-4805	31	2	will	will	AUX
ejpam-4805	31	3	find	find	VERB
ejpam-4805	31	4	a	a	DET
ejpam-4805	31	5	simple	simple	ADJ
ejpam-4805	31	6	transformation	transformation	NOUN
ejpam-4805	31	7	for	for	ADP
ejpam-4805	31	8	the	the	DET
ejpam-4805	31	9	epidemic	epidemic	NOUN
ejpam-4805	31	10	data	datum	NOUN
ejpam-4805	31	11	to	to	PART
ejpam-4805	31	12	combine	combine	VERB
ejpam-4805	31	13	the	the	DET
ejpam-4805	31	14	daily	daily	ADJ
ejpam-4805	31	15	reported	report	VERB
ejpam-4805	31	16	case	case	NOUN
ejpam-4805	31	17	data	datum	NOUN
ejpam-4805	31	18	and	and	CCONJ
ejpam-4805	31	19	the	the	DET
ejpam-4805	31	20	cumulative	cumulative	ADJ
ejpam-4805	31	21	number	number	NOUN
ejpam-4805	31	22	of	of	ADP
ejpam-4805	31	23	vaccinated	vaccinated	ADJ
ejpam-4805	31	24	individuals[12	individuals[12	NOUN
ejpam-4805	31	25	]	]	PUNCT
ejpam-4805	31	26	.	.	PUNCT
ejpam-4805	32	1	we	we	PRON
ejpam-4805	32	2	can	can	AUX
ejpam-4805	32	3	use	use	VERB
ejpam-4805	32	4	the	the	DET
ejpam-4805	32	5	model	model	NOUN
ejpam-4805	32	6	to	to	PART
ejpam-4805	32	7	explore	explore	VERB
ejpam-4805	32	8	controlling	control	VERB
ejpam-4805	32	9	the	the	DET
ejpam-4805	32	10	dynamics	dynamic	NOUN
ejpam-4805	32	11	of	of	ADP
ejpam-4805	32	12	virus	virus	NOUN
ejpam-4805	32	13	propagation	propagation	NOUN
ejpam-4805	32	14	,	,	PUNCT
ejpam-4805	32	15	for	for	ADP
ejpam-4805	32	16	example	example	NOUN
ejpam-4805	32	17	,	,	PUNCT
ejpam-4805	32	18	by	by	ADP
ejpam-4805	32	19	rapidly	rapidly	ADV
ejpam-4805	32	20	slowing	slow	VERB
ejpam-4805	32	21	down	down	ADP
ejpam-4805	32	22	an	an	DET
ejpam-4805	32	23	epidemic	epidemic	NOUN
ejpam-4805	32	24	wave	wave	NOUN
ejpam-4805	32	25	.	.	PUNCT
ejpam-4805	33	1	in	in	ADP
ejpam-4805	33	2	this	this	DET
ejpam-4805	33	3	new	new	ADJ
ejpam-4805	33	4	model	model	NOUN
ejpam-4805	33	5	,	,	PUNCT
ejpam-4805	33	6	we	we	PRON
ejpam-4805	33	7	will	will	AUX
ejpam-4805	33	8	explicitly	explicitly	ADV
ejpam-4805	33	9	take	take	VERB
ejpam-4805	33	10	into	into	ADP
ejpam-4805	33	11	account	account	NOUN
ejpam-4805	33	12	the	the	DET
ejpam-4805	33	13	variable	variable	NOUN
ejpam-4805	33	14	corresponding	correspond	VERB
ejpam-4805	33	15	to	to	ADP
ejpam-4805	33	16	the	the	DET
ejpam-4805	33	17	size	size	NOUN
ejpam-4805	33	18	of	of	ADP
ejpam-4805	33	19	the	the	DET
ejpam-4805	33	20	vaccinated	vaccinated	ADJ
ejpam-4805	33	21	population	population	NOUN
ejpam-4805	33	22	,	,	PUNCT
ejpam-4805	33	23	and	and	CCONJ
ejpam-4805	33	24	we	we	PRON
ejpam-4805	33	25	will	will	AUX
ejpam-4805	33	26	simulate	simulate	VERB
ejpam-4805	33	27	the	the	DET
ejpam-4805	33	28	increasing	increase	VERB
ejpam-4805	33	29	efficacy	efficacy	NOUN
ejpam-4805	33	30	of	of	ADP
ejpam-4805	33	31	several	several	ADJ
ejpam-4805	33	32	vaccination	vaccination	NOUN
ejpam-4805	33	33	scenarios	scenario	NOUN
ejpam-4805	33	34	.	.	PUNCT
ejpam-4805	34	1	then	then	ADV
ejpam-4805	34	2	,	,	PUNCT
ejpam-4805	34	3	we	we	PRON
ejpam-4805	34	4	will	will	AUX
ejpam-4805	34	5	apply	apply	VERB
ejpam-4805	34	6	our	our	PRON
ejpam-4805	34	7	model	model	NOUN
ejpam-4805	34	8	to	to	ADP
ejpam-4805	34	9	the	the	DET
ejpam-4805	34	10	covid-19	covid-19	PROPN
ejpam-4805	34	11	epidemic	epidemic	NOUN
ejpam-4805	34	12	.	.	PUNCT
ejpam-4805	35	1	by	by	ADP
ejpam-4805	35	2	applying	apply	VERB
ejpam-4805	35	3	the	the	DET
ejpam-4805	35	4	maximum	maximum	ADJ
ejpam-4805	35	5	principle	principle	ADJ
ejpam-4805	35	6	,	,	PUNCT
ejpam-4805	35	7	optimal	optimal	ADJ
ejpam-4805	35	8	control	control	NOUN
ejpam-4805	35	9	of	of	ADP
ejpam-4805	35	10	the	the	DET
ejpam-4805	35	11	model	model	NOUN
ejpam-4805	35	12	can	can	AUX
ejpam-4805	35	13	mitigate	mitigate	VERB
ejpam-4805	35	14	the	the	DET
ejpam-4805	35	15	spread	spread	NOUN
ejpam-4805	35	16	of	of	ADP
ejpam-4805	35	17	covid-19[7	covid-19[7	NOUN
ejpam-4805	35	18	]	]	X
ejpam-4805	35	19	.	.	PUNCT
ejpam-4805	36	1	2	2	X
ejpam-4805	36	2	.	.	X
ejpam-4805	36	3	mathematical	mathematical	ADJ
ejpam-4805	36	4	covid-19	covid-19	PROPN
ejpam-4805	36	5	epidemic	epidemic	NOUN
ejpam-4805	36	6	models	model	NOUN
ejpam-4805	36	7	.	.	PUNCT
ejpam-4805	37	1	s.(t	s.(t	NUM
ejpam-4805	37	2	)	)	PUNCT
ejpam-4805	37	3	=	=	SYM
ejpam-4805	37	4	−ρ(t)[i(t	−ρ(t)[i(t	NOUN
ejpam-4805	37	5	)	)	PUNCT
ejpam-4805	38	1	+	+	CCONJ
ejpam-4805	38	2	ωn(t)]s(t)−	ωn(t)]s(t)−	X
ejpam-4805	38	3	εv	εv	NOUN
ejpam-4805	38	4	adata(t	adata(t	PROPN
ejpam-4805	38	5	)	)	PUNCT
ejpam-4805	38	6	s(t	s(t	PROPN
ejpam-4805	38	7	)	)	PUNCT
ejpam-4805	38	8	uv(t	uv(t	NUM
ejpam-4805	38	9	)	)	PUNCT
ejpam-4805	38	10	e.(t	e.(t	NUM
ejpam-4805	38	11	)	)	PUNCT
ejpam-4805	38	12	=	=	SYM
ejpam-4805	39	1	−ρ(t)[i(t	−ρ(t)[i(t	NOUN
ejpam-4805	39	2	)	)	PUNCT
ejpam-4805	40	1	+	+	CCONJ
ejpam-4805	40	2	ωn(t)]s(t)−	ωn(t)]s(t)−	PROPN
ejpam-4805	41	1	βe(t)−	βe(t)−	PROPN
ejpam-4805	41	2	εv	εv	PROPN
ejpam-4805	41	3	adata(t	adata(t	NOUN
ejpam-4805	41	4	)	)	PUNCT
ejpam-4805	41	5	e(t	e(t	NOUN
ejpam-4805	41	6	)	)	PUNCT
ejpam-4805	41	7	uv(t	uv(t	NUM
ejpam-4805	41	8	)	)	PUNCT
ejpam-4805	41	9	i	i	PRON
ejpam-4805	41	10	.(t	.(t	PUNCT
ejpam-4805	41	11	)	)	PUNCT
ejpam-4805	41	12	=	=	PUNCT
ejpam-4805	42	1	βe(t)−	βe(t)−	PROPN
ejpam-4805	42	2	σi(t)−	σi(t)−	PROPN
ejpam-4805	42	3	εv	εv	PRON
ejpam-4805	42	4	adata(t	adata(t	PROPN
ejpam-4805	42	5	)	)	PUNCT
ejpam-4805	42	6	e(t	e(t	NOUN
ejpam-4805	42	7	)	)	PUNCT
ejpam-4805	42	8	uv(t	uv(t	NUM
ejpam-4805	42	9	)	)	PUNCT
ejpam-4805	42	10	(	(	PUNCT
ejpam-4805	42	11	1	1	X
ejpam-4805	42	12	)	)	PUNCT
ejpam-4805	42	13	n	n	NOUN
ejpam-4805	42	14	.(t	.(t	NUM
ejpam-4805	42	15	)	)	PUNCT
ejpam-4805	43	1	=	=	PUNCT
ejpam-4805	43	2	σ(1−	σ(1−	PROPN
ejpam-4805	43	3	r)i(t)−	r)i(t)−	PROPN
ejpam-4805	43	4	γn(t)−	γn(t)−	PROPN
ejpam-4805	43	5	εv	εv	PROPN
ejpam-4805	43	6	adata(t	adata(t	NOUN
ejpam-4805	43	7	)	)	PUNCT
ejpam-4805	43	8	e(t	e(t	NOUN
ejpam-4805	43	9	)	)	PUNCT
ejpam-4805	43	10	uv(t	uv(t	NUM
ejpam-4805	43	11	)	)	PUNCT
ejpam-4805	43	12	r.(t	r.(t	PROPN
ejpam-4805	43	13	)	)	PUNCT
ejpam-4805	43	14	=	=	SYM
ejpam-4805	43	15	σri(t)−	σri(t)−	PROPN
ejpam-4805	43	16	γr(t	γr(t	NUM
ejpam-4805	43	17	)	)	PUNCT
ejpam-4805	43	18	)	)	PUNCT
ejpam-4805	44	1	where	where	SCONJ
ejpam-4805	44	2	,	,	PUNCT
ejpam-4805	44	3	when	when	SCONJ
ejpam-4805	44	4	t	t	PROPN
ejpam-4805	44	5	,	,	PUNCT
ejpam-4805	44	6	s(t	s(t	PROPN
ejpam-4805	44	7	)	)	PUNCT
ejpam-4805	44	8	is	be	AUX
ejpam-4805	44	9	the	the	DET
ejpam-4805	44	10	proportion	proportion	NOUN
ejpam-4805	44	11	of	of	ADP
ejpam-4805	44	12	susceptible	susceptible	ADJ
ejpam-4805	44	13	,	,	PUNCT
ejpam-4805	44	14	individual	individual	ADJ
ejpam-4805	44	15	health	health	NOUN
ejpam-4805	44	16	,	,	PUNCT
ejpam-4805	44	17	e(t	e(t	PROPN
ejpam-4805	44	18	)	)	PUNCT
ejpam-4805	44	19	is	be	AUX
ejpam-4805	44	20	the	the	DET
ejpam-4805	44	21	proportion	proportion	NOUN
ejpam-4805	44	22	of	of	ADP
ejpam-4805	44	23	those	those	PRON
ejpam-4805	44	24	who	who	PRON
ejpam-4805	44	25	were	be	AUX
ejpam-4805	44	26	exposed	expose	VERB
ejpam-4805	44	27	,	,	PUNCT
ejpam-4805	44	28	i(t	i(t	PROPN
ejpam-4805	44	29	)	)	PUNCT
ejpam-4805	44	30	is	be	AUX
ejpam-4805	44	31	the	the	DET
ejpam-4805	44	32	proportion	proportion	NOUN
ejpam-4805	44	33	of	of	ADP
ejpam-4805	44	34	infected	infected	ADJ
ejpam-4805	44	35	yet	yet	CCONJ
ejpam-4805	44	36	asymptomatic	asymptomatic	ADJ
ejpam-4805	44	37	a.	a.	NOUN
ejpam-4805	44	38	mustafa	mustafa	PROPN
ejpam-4805	44	39	et	et	PROPN
ejpam-4805	44	40	al	al	PROPN
ejpam-4805	44	41	.	.	PUNCT
ejpam-4805	44	42	/	/	SYM
ejpam-4805	44	43	eur	eur	PROPN
ejpam-4805	44	44	.	.	PUNCT
ejpam-4805	45	1	j.	j.	PROPN
ejpam-4805	45	2	pure	pure	PROPN
ejpam-4805	45	3	appl	appl	PROPN
ejpam-4805	45	4	.	.	PROPN
ejpam-4805	45	5	math	math	PROPN
ejpam-4805	45	6	,	,	PUNCT
ejpam-4805	45	7	16	16	NUM
ejpam-4805	45	8	(	(	PUNCT
ejpam-4805	45	9	4	4	NUM
ejpam-4805	45	10	)	)	PUNCT
ejpam-4805	45	11	(	(	PUNCT
ejpam-4805	45	12	2023	2023	NUM
ejpam-4805	45	13	)	)	PUNCT
ejpam-4805	45	14	,	,	PUNCT
ejpam-4805	45	15	2450	2450	NUM
ejpam-4805	45	16	-	-	SYM
ejpam-4805	45	17	2460	2460	NUM
ejpam-4805	45	18	2452	2452	NUM
ejpam-4805	45	19	persons	person	NOUN
ejpam-4805	45	20	,	,	PUNCT
ejpam-4805	45	21	n(t	n(t	PROPN
ejpam-4805	45	22	)	)	PUNCT
ejpam-4805	45	23	is	be	AUX
ejpam-4805	45	24	the	the	DET
ejpam-4805	45	25	proportion	proportion	NOUN
ejpam-4805	45	26	of	of	ADP
ejpam-4805	45	27	symptomatic	symptomatic	ADJ
ejpam-4805	45	28	infected	infected	ADJ
ejpam-4805	45	29	people	people	NOUN
ejpam-4805	45	30	who	who	PRON
ejpam-4805	45	31	go	go	VERB
ejpam-4805	45	32	undetected	undetected	ADJ
ejpam-4805	45	33	,	,	PUNCT
ejpam-4805	45	34	and	and	CCONJ
ejpam-4805	45	35	r(t	r(t	NOUN
ejpam-4805	45	36	)	)	PUNCT
ejpam-4805	45	37	is	be	AUX
ejpam-4805	45	38	the	the	DET
ejpam-4805	45	39	proportion	proportion	NOUN
ejpam-4805	45	40	of	of	ADP
ejpam-4805	45	41	symptomatic	symptomatic	ADJ
ejpam-4805	45	42	infected	infected	ADJ
ejpam-4805	45	43	people	people	NOUN
ejpam-4805	45	44	who	who	PRON
ejpam-4805	45	45	have	have	AUX
ejpam-4805	45	46	been	be	AUX
ejpam-4805	45	47	reported[10].uv(t	reported[10].uv(t	PRON
ejpam-4805	45	48	)	)	PUNCT
ejpam-4805	45	49	is	be	AUX
ejpam-4805	45	50	the	the	DET
ejpam-4805	45	51	proportion	proportion	NOUN
ejpam-4805	45	52	of	of	ADP
ejpam-4805	45	53	unvaccinated	unvaccinated	ADJ
ejpam-4805	45	54	people	people	NOUN
ejpam-4805	45	55	.	.	PUNCT
ejpam-4805	46	1	the	the	DET
ejpam-4805	46	2	biological	biological	ADJ
ejpam-4805	46	3	interpretations	interpretation	NOUN
ejpam-4805	46	4	of	of	ADP
ejpam-4805	46	5	all	all	DET
ejpam-4805	46	6	parameters	parameter	NOUN
ejpam-4805	46	7	are	be	AUX
ejpam-4805	46	8	provided	provide	VERB
ejpam-4805	46	9	in	in	ADP
ejpam-4805	46	10	table	table	NOUN
ejpam-4805	46	11	1	1	NUM
ejpam-4805	46	12	.	.	PUNCT
ejpam-4805	47	1	the	the	DET
ejpam-4805	47	2	primary	primary	ADJ
ejpam-4805	47	3	information	information	NOUN
ejpam-4805	47	4	is	be	AUX
ejpam-4805	47	5	added	add	VERB
ejpam-4805	47	6	to	to	ADP
ejpam-4805	47	7	the	the	DET
ejpam-4805	47	8	system	system	NOUN
ejpam-4805	47	9	(	(	PUNCT
ejpam-4805	47	10	1	1	NUM
ejpam-4805	47	11	)	)	PUNCT
ejpam-4805	47	12	.	.	PUNCT
ejpam-4805	48	1	s(t1	s(t1	VERB
ejpam-4805	48	2	)	)	PUNCT
ejpam-4805	48	3	=	=	SYM
ejpam-4805	48	4	s1	s1	PROPN
ejpam-4805	48	5	,	,	PUNCT
ejpam-4805	48	6	e(t1	e(t1	NOUN
ejpam-4805	48	7	)	)	PUNCT
ejpam-4805	49	1	=	=	SYM
ejpam-4805	49	2	e1	e1	PROPN
ejpam-4805	49	3	,	,	PUNCT
ejpam-4805	49	4	i(t1	i(t1	NOUN
ejpam-4805	49	5	)	)	PUNCT
ejpam-4805	49	6	=	=	SYM
ejpam-4805	49	7	i1	i1	PROPN
ejpam-4805	49	8	,	,	PUNCT
ejpam-4805	49	9	n(t1	n(t1	NOUN
ejpam-4805	49	10	)	)	PUNCT
ejpam-4805	49	11	=	=	SYM
ejpam-4805	49	12	n1	n1	NOUN
ejpam-4805	49	13	,	,	PUNCT
ejpam-4805	49	14	r(t1	r(t1	NOUN
ejpam-4805	49	15	)	)	PUNCT
ejpam-4805	50	1	=	=	SYM
ejpam-4805	50	2	r1	r1	NOUN
ejpam-4805	50	3	(	(	PUNCT
ejpam-4805	50	4	2	2	NUM
ejpam-4805	50	5	)	)	PUNCT
ejpam-4805	50	6	the	the	DET
ejpam-4805	50	7	model	model	NOUN
ejpam-4805	50	8	features	feature	VERB
ejpam-4805	50	9	,	,	PUNCT
ejpam-4805	50	10	∅(t	∅(t	PROPN
ejpam-4805	50	11	)	)	PUNCT
ejpam-4805	50	12	is	be	AUX
ejpam-4805	50	13	the	the	DET
ejpam-4805	50	14	transmission	transmission	NOUN
ejpam-4805	50	15	rate	rate	NOUN
ejpam-4805	50	16	that	that	PRON
ejpam-4805	50	17	varies	vary	VERB
ejpam-4805	50	18	with	with	ADP
ejpam-4805	50	19	time	time	NOUN
ejpam-4805	50	20	,	,	PUNCT
ejpam-4805	50	21	1	1	NUM
ejpam-4805	50	22	/	/	SYM
ejpam-4805	50	23	β	β	X
ejpam-4805	50	24	is	be	AUX
ejpam-4805	50	25	the	the	DET
ejpam-4805	50	26	median	median	ADJ
ejpam-4805	50	27	amount	amount	NOUN
ejpam-4805	50	28	of	of	ADP
ejpam-4805	50	29	the	the	DET
ejpam-4805	50	30	exposure	exposure	NOUN
ejpam-4805	50	31	time	time	NOUN
ejpam-4805	50	32	,	,	PUNCT
ejpam-4805	50	33	1	1	NUM
ejpam-4805	50	34	/	/	SYM
ejpam-4805	50	35	σ	σ	PROPN
ejpam-4805	50	36	is	be	AUX
ejpam-4805	50	37	the	the	DET
ejpam-4805	50	38	maximum	maximum	ADJ
ejpam-4805	50	39	range	range	NOUN
ejpam-4805	50	40	of	of	ADP
ejpam-4805	50	41	the	the	DET
ejpam-4805	50	42	infectious	infectious	ADJ
ejpam-4805	50	43	period	period	NOUN
ejpam-4805	50	44	without	without	ADP
ejpam-4805	50	45	symptoms	symptom	NOUN
ejpam-4805	50	46	,	,	PUNCT
ejpam-4805	50	47	and	and	CCONJ
ejpam-4805	50	48	for	for	ADP
ejpam-4805	50	49	the	the	DET
ejpam-4805	50	50	sake	sake	NOUN
ejpam-4805	50	51	of	of	ADP
ejpam-4805	50	52	simplicity	simplicity	NOUN
ejpam-4805	50	53	,	,	PUNCT
ejpam-4805	50	54	we	we	PRON
ejpam-4805	50	55	divide	divide	VERB
ejpam-4805	50	56	the	the	DET
ejpam-4805	50	57	group	group	NOUN
ejpam-4805	50	58	of	of	ADP
ejpam-4805	50	59	symptomatic	symptomatic	ADJ
ejpam-4805	50	60	infectious	infectious	ADJ
ejpam-4805	50	61	persons	person	NOUN
ejpam-4805	50	62	into	into	ADP
ejpam-4805	50	63	two	two	NUM
ejpam-4805	50	64	fractions	fraction	NOUN
ejpam-4805	50	65	:	:	PUNCT
ejpam-4805	50	66	the	the	DET
ejpam-4805	50	67	fraction	fraction	NOUN
ejpam-4805	50	68	0	0	NUM
ejpam-4805	50	69	≤	≤	NUM
ejpam-4805	50	70	r	r	NOUN
ejpam-4805	50	71	≤	≤	NUM
ejpam-4805	50	72	1	1	NUM
ejpam-4805	50	73	showing	show	VERB
ejpam-4805	50	74	severe	severe	ADJ
ejpam-4805	50	75	symptoms	symptom	NOUN
ejpam-4805	50	76	and	and	CCONJ
ejpam-4805	50	77	the	the	DET
ejpam-4805	50	78	fraction	fraction	NOUN
ejpam-4805	50	79	1−r	1−r	NUM
ejpam-4805	50	80	showing	show	VERB
ejpam-4805	50	81	moderate	moderate	ADJ
ejpam-4805	50	82	symptoms	symptom	NOUN
ejpam-4805	50	83	,	,	PUNCT
ejpam-4805	50	84	which	which	PRON
ejpam-4805	50	85	is	be	AUX
ejpam-4805	50	86	considered	consider	VERB
ejpam-4805	50	87	to	to	PART
ejpam-4805	50	88	be	be	AUX
ejpam-4805	50	89	undiagnosed	undiagnosed	ADJ
ejpam-4805	50	90	.	.	PUNCT
ejpam-4805	51	1	for	for	ADP
ejpam-4805	51	2	both	both	CCONJ
ejpam-4805	51	3	unreported	unreported	ADJ
ejpam-4805	51	4	and	and	CCONJ
ejpam-4805	51	5	reported	report	VERB
ejpam-4805	51	6	symptomatic	symptomatic	ADJ
ejpam-4805	51	7	individuals	individual	NOUN
ejpam-4805	51	8	,	,	PUNCT
ejpam-4805	51	9	the	the	DET
ejpam-4805	51	10	amount	amount	NOUN
ejpam-4805	51	11	1	1	NUM
ejpam-4805	51	12	/	/	SYM
ejpam-4805	51	13	γ	γ	NOUN
ejpam-4805	51	14	represents	represent	VERB
ejpam-4805	51	15	the	the	DET
ejpam-4805	51	16	average	average	ADJ
ejpam-4805	51	17	length	length	NOUN
ejpam-4805	51	18	of	of	ADP
ejpam-4805	51	19	the	the	DET
ejpam-4805	51	20	symptomatic	symptomatic	ADJ
ejpam-4805	51	21	infectious	infectious	ADJ
ejpam-4805	51	22	period	period	NOUN
ejpam-4805	51	23	.	.	PUNCT
ejpam-4805	52	1	[	[	X
ejpam-4805	52	2	23	23	NUM
ejpam-4805	52	3	]	]	PUNCT
ejpam-4805	52	4	the	the	DET
ejpam-4805	52	5	factor	factor	NOUN
ejpam-4805	52	6	(	(	PUNCT
ejpam-4805	52	7	0	0	NUM
ejpam-4805	52	8	≤	≤	NUM
ejpam-4805	52	9	ω	ω	NUM
ejpam-4805	52	10	≤	≤	NUM
ejpam-4805	52	11	1	1	NUM
ejpam-4805	52	12	)	)	PUNCT
ejpam-4805	52	13	represents	represent	VERB
ejpam-4805	52	14	the	the	DET
ejpam-4805	52	15	relative	relative	ADJ
ejpam-4805	52	16	contributions	contribution	NOUN
ejpam-4805	52	17	of	of	ADP
ejpam-4805	52	18	undetected	undetected	ADJ
ejpam-4805	52	19	and	and	CCONJ
ejpam-4805	52	20	unreported	unreported	ADJ
ejpam-4805	52	21	clinical	clinical	ADJ
ejpam-4805	52	22	infectious	infectious	ADJ
ejpam-4805	52	23	persons	person	NOUN
ejpam-4805	52	24	to	to	ADP
ejpam-4805	52	25	the	the	DET
ejpam-4805	52	26	infection	infection	NOUN
ejpam-4805	52	27	of	of	ADP
ejpam-4805	52	28	susceptible	susceptible	ADJ
ejpam-4805	52	29	individuals	individual	NOUN
ejpam-4805	52	30	.	.	PUNCT
ejpam-4805	53	1	the	the	DET
ejpam-4805	53	2	potency	potency	NOUN
ejpam-4805	53	3	of	of	ADP
ejpam-4805	53	4	the	the	DET
ejpam-4805	53	5	vaccine	vaccine	NOUN
ejpam-4805	53	6	is	be	AUX
ejpam-4805	53	7	the	the	DET
ejpam-4805	53	8	parameter	parameter	NOUN
ejpam-4805	53	9	0	0	NUM
ejpam-4805	53	10	≤	≤	NUM
ejpam-4805	53	11	ε	ε	PROPN
ejpam-4805	53	12	≤	≤	ADJ
ejpam-4805	53	13	1	1	NUM
ejpam-4805	53	14	.	.	PUNCT
ejpam-4805	54	1	this	this	PRON
ejpam-4805	54	2	implies	imply	VERB
ejpam-4805	54	3	that	that	SCONJ
ejpam-4805	54	4	the	the	DET
ejpam-4805	54	5	vaccination	vaccination	NOUN
ejpam-4805	54	6	is	be	AUX
ejpam-4805	54	7	totally	totally	ADV
ejpam-4805	54	8	effective	effective	ADJ
ejpam-4805	54	9	at	at	ADP
ejpam-4805	54	10	ε	ε	PROPN
ejpam-4805	54	11	=	=	SYM
ejpam-4805	54	12	1	1	NUM
ejpam-4805	54	13	and	and	CCONJ
ejpam-4805	54	14	completely	completely	ADV
ejpam-4805	54	15	ineffective	ineffective	ADJ
ejpam-4805	54	16	at	at	ADP
ejpam-4805	54	17	ε	ε	PROPN
ejpam-4805	54	18	=	=	SYM
ejpam-4805	54	19	0	0	NUM
ejpam-4805	54	20	,	,	PUNCT
ejpam-4805	54	21	respectively	respectively	ADV
ejpam-4805	54	22	.	.	PUNCT
ejpam-4805	55	1	the	the	DET
ejpam-4805	55	2	equation	equation	NOUN
ejpam-4805	55	3	is	be	AUX
ejpam-4805	55	4	satisfied	satisfied	ADJ
ejpam-4805	55	5	by	by	ADP
ejpam-4805	55	6	the	the	DET
ejpam-4805	55	7	total	total	ADJ
ejpam-4805	55	8	number	number	NOUN
ejpam-4805	55	9	of	of	ADP
ejpam-4805	55	10	removed	remove	VERB
ejpam-4805	55	11	persons	person	NOUN
ejpam-4805	55	12	t	t	NOUN
ejpam-4805	55	13	→	→	SYM
ejpam-4805	55	14	m(t	m(t	PROPN
ejpam-4805	55	15	)	)	PUNCT
ejpam-4805	55	16	,	,	PUNCT
ejpam-4805	55	17	immunized	immunize	VERB
ejpam-4805	55	18	(	(	PUNCT
ejpam-4805	55	19	recovered	recovered	ADJ
ejpam-4805	55	20	or	or	CCONJ
ejpam-4805	55	21	vaccinated	vaccinate	VERB
ejpam-4805	55	22	)	)	PUNCT
ejpam-4805	55	23	,	,	PUNCT
ejpam-4805	55	24	and/or	and/or	CCONJ
ejpam-4805	55	25	dead[6	dead[6	PROPN
ejpam-4805	55	26	]	]	PUNCT
ejpam-4805	55	27	.	.	PUNCT
ejpam-4805	56	1	m	m	VERB
ejpam-4805	56	2	′	′	NUM
ejpam-4805	56	3	(	(	PUNCT
ejpam-4805	56	4	t	t	NOUN
ejpam-4805	56	5	)	)	PUNCT
ejpam-4805	56	6	=	=	SYM
ejpam-4805	56	7	γ[r(t	γ[r(t	NOUN
ejpam-4805	56	8	)	)	PUNCT
ejpam-4805	57	1	+	+	NOUN
ejpam-4805	57	2	n(t	n(t	X
ejpam-4805	57	3	)	)	PUNCT
ejpam-4805	57	4	]	]	PUNCT
ejpam-4805	58	1	+	+	CCONJ
ejpam-4805	58	2	eva(t	eva(t	NOUN
ejpam-4805	58	3	)	)	PUNCT
ejpam-4805	58	4	[	[	PUNCT
ejpam-4805	58	5	s(t	s(t	PROPN
ejpam-4805	58	6	)	)	PUNCT
ejpam-4805	58	7	+	+	SYM
ejpam-4805	58	8	e(t	e(t	NOUN
ejpam-4805	58	9	)	)	PUNCT
ejpam-4805	58	10	+	+	CCONJ
ejpam-4805	58	11	i(t	i(t	NOUN
ejpam-4805	58	12	)	)	PUNCT
ejpam-4805	58	13	+	+	NOUN
ejpam-4805	58	14	n(t	n(t	X
ejpam-4805	58	15	)	)	PUNCT
ejpam-4805	58	16	uv(t	uv(t	NUM
ejpam-4805	58	17	)	)	PUNCT
ejpam-4805	58	18	]	]	PUNCT
ejpam-4805	58	19	(	(	PUNCT
ejpam-4805	58	20	3	3	X
ejpam-4805	58	21	)	)	PUNCT
ejpam-4805	58	22	in	in	ADP
ejpam-4805	58	23	this	this	DET
ejpam-4805	58	24	instance	instance	NOUN
ejpam-4805	58	25	,	,	PUNCT
ejpam-4805	58	26	va(t	va(t	NUM
ejpam-4805	58	27	)	)	PUNCT
ejpam-4805	58	28	there	there	PRON
ejpam-4805	58	29	is	be	VERB
ejpam-4805	58	30	steady	steady	ADJ
ejpam-4805	58	31	stream	stream	NOUN
ejpam-4805	58	32	of	of	ADP
ejpam-4805	58	33	properly	properly	ADV
ejpam-4805	58	34	vaccinated	vaccinated	ADJ
ejpam-4805	58	35	people	people	NOUN
ejpam-4805	58	36	.	.	PUNCT
ejpam-4805	59	1	it	it	PRON
ejpam-4805	59	2	implies	imply	VERB
ejpam-4805	59	3	that	that	SCONJ
ejpam-4805	59	4	∫	∫	PROPN
ejpam-4805	59	5	t	t	PROPN
ejpam-4805	59	6	t1	t1	PROPN
ejpam-4805	59	7	va(α).dα	va(α).dα	PROPN
ejpam-4805	59	8	is	be	AUX
ejpam-4805	59	9	the	the	DET
ejpam-4805	59	10	overall	overall	ADJ
ejpam-4805	59	11	vaccination	vaccination	NOUN
ejpam-4805	59	12	rate	rate	NOUN
ejpam-4805	59	13	between	between	ADP
ejpam-4805	59	14	time	time	NOUN
ejpam-4805	59	15	points	point	NOUN
ejpam-4805	59	16	a	a	PRON
ejpam-4805	59	17	and	and	CCONJ
ejpam-4805	59	18	b[2	b[2	PROPN
ejpam-4805	59	19	]	]	X
ejpam-4805	59	20	.	.	PUNCT
ejpam-4805	60	1	since	since	SCONJ
ejpam-4805	60	2	no	no	DET
ejpam-4805	60	3	people	people	NOUN
ejpam-4805	60	4	received	receive	VERB
ejpam-4805	60	5	vaccinations	vaccination	NOUN
ejpam-4805	60	6	at	at	ADP
ejpam-4805	60	7	the	the	DET
ejpam-4805	60	8	beginning	beginning	NOUN
ejpam-4805	60	9	of	of	ADP
ejpam-4805	60	10	the	the	DET
ejpam-4805	60	11	disease	disease	NOUN
ejpam-4805	60	12	(	(	PUNCT
ejpam-4805	60	13	i.e.	i.e.	X
ejpam-4805	60	14	,	,	PUNCT
ejpam-4805	60	15	for	for	ADP
ejpam-4805	60	16	t	t	PROPN
ejpam-4805	60	17	=	=	SYM
ejpam-4805	60	18	t1	t1	PROPN
ejpam-4805	60	19	)	)	PUNCT
ejpam-4805	60	20	,	,	PUNCT
ejpam-4805	60	21	we	we	PRON
ejpam-4805	60	22	can	can	AUX
ejpam-4805	60	23	assume	assume	VERB
ejpam-4805	60	24	that	that	SCONJ
ejpam-4805	60	25	the	the	DET
ejpam-4805	60	26	total	total	ADJ
ejpam-4805	60	27	population	population	NOUN
ejpam-4805	60	28	p	p	NOUN
ejpam-4805	60	29	at	at	ADP
ejpam-4805	60	30	time	time	NOUN
ejpam-4805	60	31	t1	t1	PROPN
ejpam-4805	60	32	is	be	AUX
ejpam-4805	60	33	p	p	NOUN
ejpam-4805	60	34	=	=	PROPN
ejpam-4805	60	35	s1	s1	PROPN
ejpam-4805	60	36	+	+	CCONJ
ejpam-4805	60	37	e1	e1	PROPN
ejpam-4805	60	38	+	+	CCONJ
ejpam-4805	60	39	i1	i1	PROPN
ejpam-4805	61	1	+	+	CCONJ
ejpam-4805	61	2	r1	r1	PROPN
ejpam-4805	61	3	+	+	CCONJ
ejpam-4805	61	4	n1	n1	ADJ
ejpam-4805	61	5	the	the	DET
ejpam-4805	61	6	total	total	ADJ
ejpam-4805	61	7	number	number	NOUN
ejpam-4805	61	8	of	of	ADP
ejpam-4805	61	9	people	people	NOUN
ejpam-4805	61	10	who	who	PRON
ejpam-4805	61	11	have	have	AUX
ejpam-4805	61	12	received	receive	VERB
ejpam-4805	61	13	vaccinations	vaccination	NOUN
ejpam-4805	61	14	is	be	AUX
ejpam-4805	61	15	provided	provide	VERB
ejpam-4805	61	16	by	by	ADP
ejpam-4805	61	17	lva(t1	lva(t1	NOUN
ejpam-4805	61	18	)	)	PUNCT
ejpam-4805	61	19	=	=	SYM
ejpam-4805	61	20	0	0	NUM
ejpam-4805	61	21	and	and	CCONJ
ejpam-4805	61	22	lv	lv	PROPN
ejpam-4805	61	23	′	′	NUM
ejpam-4805	61	24	a(t	a(t	NOUN
ejpam-4805	61	25	)	)	PUNCT
ejpam-4805	61	26	=	=	PUNCT
ejpam-4805	62	1	va(t	va(t	NUM
ejpam-4805	62	2	)	)	PUNCT
ejpam-4805	62	3	,	,	PUNCT
ejpam-4805	62	4	it	it	PRON
ejpam-4805	62	5	is	be	AUX
ejpam-4805	62	6	comparable	comparable	ADJ
ejpam-4805	62	7	to	to	ADP
ejpam-4805	62	8	lva(t	lva(t	PROPN
ejpam-4805	62	9	)	)	PUNCT
ejpam-4805	63	1	=	=	SYM
ejpam-4805	63	2	∫	∫	PROPN
ejpam-4805	63	3	t	t	PROPN
ejpam-4805	63	4	t1	t1	NOUN
ejpam-4805	63	5	va(α).dα	va(α).dα	PROPN
ejpam-4805	63	6	the	the	DET
ejpam-4805	63	7	number	number	NOUN
ejpam-4805	63	8	of	of	ADP
ejpam-4805	63	9	people	people	NOUN
ejpam-4805	63	10	that	that	PRON
ejpam-4805	63	11	are	be	AUX
ejpam-4805	63	12	n’t	n’t	ADJ
ejpam-4805	63	13	vaccinations	vaccination	NOUN
ejpam-4805	63	14	is	be	AUX
ejpam-4805	63	15	uv(t	uv(t	VERB
ejpam-4805	63	16	)	)	PUNCT
ejpam-4805	63	17	=	=	SYM
ejpam-4805	64	1	p	p	NOUN
ejpam-4805	64	2	−	−	PROPN
ejpam-4805	64	3	lva(t	lva(t	PROPN
ejpam-4805	64	4	)	)	PUNCT
ejpam-4805	64	5	a.	a.	NOUN
ejpam-4805	64	6	mustafa	mustafa	PROPN
ejpam-4805	64	7	et	et	PROPN
ejpam-4805	64	8	al	al	PROPN
ejpam-4805	64	9	.	.	PUNCT
ejpam-4805	64	10	/	/	SYM
ejpam-4805	64	11	eur	eur	PROPN
ejpam-4805	64	12	.	.	PUNCT
ejpam-4805	65	1	j.	j.	PROPN
ejpam-4805	65	2	pure	pure	PROPN
ejpam-4805	65	3	appl	appl	PROPN
ejpam-4805	65	4	.	.	PROPN
ejpam-4805	65	5	math	math	PROPN
ejpam-4805	65	6	,	,	PUNCT
ejpam-4805	65	7	16	16	NUM
ejpam-4805	65	8	(	(	PUNCT
ejpam-4805	65	9	4	4	NUM
ejpam-4805	65	10	)	)	PUNCT
ejpam-4805	65	11	(	(	PUNCT
ejpam-4805	65	12	2023	2023	NUM
ejpam-4805	65	13	)	)	PUNCT
ejpam-4805	65	14	,	,	PUNCT
ejpam-4805	65	15	2450	2450	NUM
ejpam-4805	65	16	-	-	SYM
ejpam-4805	65	17	2460	2460	NUM
ejpam-4805	65	18	2453	2453	NUM
ejpam-4805	65	19	it	it	PRON
ejpam-4805	65	20	’s	’s	AUX
ejpam-4805	65	21	expected	expect	VERB
ejpam-4805	65	22	that	that	SCONJ
ejpam-4805	65	23	a	a	DET
ejpam-4805	65	24	fraction	fraction	NOUN
ejpam-4805	65	25	0	0	PUNCT
ejpam-4805	65	26	<	<	X
ejpam-4805	65	27	r	r	NOUN
ejpam-4805	65	28	≤	≤	NUM
ejpam-4805	65	29	1	1	NUM
ejpam-4805	65	30	of	of	ADP
ejpam-4805	65	31	infectious	infectious	ADJ
ejpam-4805	65	32	persons	person	NOUN
ejpam-4805	65	33	is	be	AUX
ejpam-4805	65	34	reported	report	VERB
ejpam-4805	65	35	at	at	ADP
ejpam-4805	65	36	the	the	DET
ejpam-4805	65	37	end	end	NOUN
ejpam-4805	65	38	of	of	ADP
ejpam-4805	65	39	the	the	DET
ejpam-4805	65	40	asymptomatic	asymptomatic	ADJ
ejpam-4805	65	41	infectious	infectious	ADJ
ejpam-4805	65	42	period	period	NOUN
ejpam-4805	65	43	.	.	PUNCT
ejpam-4805	66	1	therefore	therefore	ADV
ejpam-4805	66	2	,	,	PUNCT
ejpam-4805	66	3	the	the	DET
ejpam-4805	66	4	following	follow	VERB
ejpam-4805	66	5	connection	connection	NOUN
ejpam-4805	66	6	links	link	VERB
ejpam-4805	66	7	the	the	DET
ejpam-4805	66	8	epidemic	epidemic	NOUN
ejpam-4805	66	9	model	model	NOUN
ejpam-4805	66	10	to	to	ADP
ejpam-4805	66	11	the	the	DET
ejpam-4805	66	12	total	total	ADJ
ejpam-4805	66	13	number	number	NOUN
ejpam-4805	66	14	of	of	ADP
ejpam-4805	66	15	reported	report	VERB
ejpam-4805	66	16	cases	case	NOUN
ejpam-4805	66	17	lr(t	lr(t	NOUN
ejpam-4805	66	18	)	)	PUNCT
ejpam-4805	66	19	.	.	PUNCT
ejpam-4805	67	1	,	,	PUNCT
ejpam-4805	67	2	for	for	ADP
ejpam-4805	67	3	t	t	PROPN
ejpam-4805	67	4	≥	≥	NOUN
ejpam-4805	67	5	t1	t1	NOUN
ejpam-4805	67	6	,	,	PUNCT
ejpam-4805	67	7	and	and	CCONJ
ejpam-4805	67	8	lr0(t1	lr0(t1	NOUN
ejpam-4805	67	9	)	)	PUNCT
ejpam-4805	67	10	=	=	SYM
ejpam-4805	67	11	lr0	lr0	NOUN
ejpam-4805	67	12	.	.	PUNCT
ejpam-4805	68	1	lr	lr	INTJ
ejpam-4805	68	2	′	′	NUM
ejpam-4805	68	3	a(t	a(t	NOUN
ejpam-4805	68	4	)	)	PUNCT
ejpam-4805	68	5	=	=	PUNCT
ejpam-4805	68	6	σri(t	σri(t	PROPN
ejpam-4805	68	7	)	)	PUNCT
ejpam-4805	68	8	,	,	PUNCT
ejpam-4805	68	9	(	(	PUNCT
ejpam-4805	68	10	4	4	X
ejpam-4805	68	11	)	)	PUNCT
ejpam-4805	68	12	beginning	begin	VERB
ejpam-4805	68	13	at	at	ADP
ejpam-4805	68	14	time	time	NOUN
ejpam-4805	68	15	t1	t1	PROPN
ejpam-4805	68	16	,	,	PUNCT
ejpam-4805	68	17	we	we	PRON
ejpam-4805	68	18	define	define	VERB
ejpam-4805	68	19	the	the	DET
ejpam-4805	68	20	fraction	fraction	NOUN
ejpam-4805	68	21	of	of	ADP
ejpam-4805	68	22	people	people	NOUN
ejpam-4805	68	23	who	who	PRON
ejpam-4805	68	24	are	be	AUX
ejpam-4805	68	25	not	not	PART
ejpam-4805	68	26	fully	fully	ADV
ejpam-4805	68	27	immunized	immunize	VERB
ejpam-4805	68	28	at	at	ADP
ejpam-4805	68	29	time	time	NOUN
ejpam-4805	68	30	t	t	PROPN
ejpam-4805	68	31	as	as	ADP
ejpam-4805	68	32	g(t	g(t	PROPN
ejpam-4805	68	33	)	)	PUNCT
ejpam-4805	68	34	=	=	SYM
ejpam-4805	68	35	exp	exp	NOUN
ejpam-4805	68	36	(	(	PUNCT
ejpam-4805	68	37	ε	ε	PROPN
ejpam-4805	68	38	∫	∫	PROPN
ejpam-4805	68	39	t	t	PROPN
ejpam-4805	68	40	t1	t1	NOUN
ejpam-4805	68	41	p	p	NOUN
ejpam-4805	68	42	−	−	NOUN
ejpam-4805	68	43	va(α	va(α	PUNCT
ejpam-4805	68	44	)	)	PUNCT
ejpam-4805	68	45	p	p	PRON
ejpam-4805	68	46	−	−	NOUN
ejpam-4805	68	47	va(α	va(α	PUNCT
ejpam-4805	68	48	)	)	PUNCT
ejpam-4805	68	49	dα	dα	NOUN
ejpam-4805	68	50	)	)	PUNCT
ejpam-4805	68	51	.	.	PUNCT
ejpam-4805	69	1	then	then	ADV
ejpam-4805	69	2	,	,	PUNCT
ejpam-4805	69	3	g(t	g(t	PROPN
ejpam-4805	69	4	)	)	PUNCT
ejpam-4805	69	5	=	=	SYM
ejpam-4805	69	6	exp	exp	NOUN
ejpam-4805	69	7	(	(	PUNCT
ejpam-4805	69	8	ε(ln	ε(ln	X
ejpam-4805	69	9	[	[	X
ejpam-4805	69	10	p	p	X
ejpam-4805	69	11	−	−	PROPN
ejpam-4805	69	12	va(t)]−	va(t)]−	PROPN
ejpam-4805	69	13	ln	ln	NOUN
ejpam-4805	70	1	[	[	X
ejpam-4805	70	2	p	p	X
ejpam-4805	70	3	−	−	PROPN
ejpam-4805	70	4	va(t1	va(t1	NOUN
ejpam-4805	70	5	]	]	PUNCT
ejpam-4805	70	6	)	)	PUNCT
ejpam-4805	70	7	)	)	PUNCT
ejpam-4805	71	1	therefore	therefore	ADV
ejpam-4805	71	2	,	,	PUNCT
ejpam-4805	71	3	g(t	g(t	PROPN
ejpam-4805	71	4	)	)	PUNCT
ejpam-4805	71	5	=	=	PRON
ejpam-4805	71	6	(	(	PUNCT
ejpam-4805	71	7	(	(	PUNCT
ejpam-4805	71	8	p	p	NOUN
ejpam-4805	71	9	−	−	PROPN
ejpam-4805	71	10	lva(t	lva(t	PROPN
ejpam-4805	71	11	)	)	PUNCT
ejpam-4805	71	12	)	)	PUNCT
ejpam-4805	72	1	(	(	PUNCT
ejpam-4805	72	2	p	p	NOUN
ejpam-4805	72	3	−	−	PROPN
ejpam-4805	72	4	lva(t1	lva(t1	NOUN
ejpam-4805	72	5	)	)	PUNCT
ejpam-4805	72	6	)	)	PUNCT
ejpam-4805	72	7	)	)	PUNCT
ejpam-4805	72	8	ε	ε	PROPN
ejpam-4805	72	9	(	(	PUNCT
ejpam-4805	72	10	5	5	NUM
ejpam-4805	72	11	)	)	PUNCT
ejpam-4805	72	12	if	if	SCONJ
ejpam-4805	72	13	lva(t	lva(t	PROPN
ejpam-4805	72	14	)	)	PUNCT
ejpam-4805	72	15	is	be	AUX
ejpam-4805	72	16	the	the	DET
ejpam-4805	72	17	total	total	ADJ
ejpam-4805	72	18	number	number	NOUN
ejpam-4805	72	19	of	of	ADP
ejpam-4805	72	20	recipients	recipient	NOUN
ejpam-4805	72	21	of	of	ADP
ejpam-4805	72	22	the	the	DET
ejpam-4805	72	23	second	second	ADJ
ejpam-4805	72	24	dose	dose	NOUN
ejpam-4805	72	25	vaccination	vaccination	NOUN
ejpam-4805	72	26	.	.	PUNCT
ejpam-4805	73	1	when	when	SCONJ
ejpam-4805	73	2	g(0	g(0	NOUN
ejpam-4805	73	3	)	)	PUNCT
ejpam-4805	73	4	=	=	SYM
ejpam-4805	73	5	1	1	NUM
ejpam-4805	73	6	,	,	PUNCT
ejpam-4805	73	7	the	the	DET
ejpam-4805	73	8	function	function	NOUN
ejpam-4805	73	9	t	t	PROPN
ejpam-4805	73	10	,	,	PUNCT
ejpam-4805	73	11	w	w	PROPN
ejpam-4805	73	12	(	(	PUNCT
ejpam-4805	73	13	t	t	PROPN
ejpam-4805	73	14	)	)	PUNCT
ejpam-4805	73	15	is	be	AUX
ejpam-4805	73	16	non	non	ADJ
ejpam-4805	73	17	-	-	ADJ
ejpam-4805	73	18	increasing	increase	VERB
ejpam-4805	73	19	.	.	PUNCT
ejpam-4805	74	1	define	define	VERB
ejpam-4805	74	2	lra(t	lra(t	PROPN
ejpam-4805	74	3	)	)	PUNCT
ejpam-4805	74	4	=	=	SYM
ejpam-4805	75	1	∫	∫	PROPN
ejpam-4805	75	2	t	t	PROPN
ejpam-4805	75	3	t1	t1	NOUN
ejpam-4805	75	4	lr	lr	PROPN
ejpam-4805	75	5	′	′	NUM
ejpam-4805	75	6	a(α	a(α	NOUN
ejpam-4805	75	7	)	)	PUNCT
ejpam-4805	75	8	g(α	g(α	PROPN
ejpam-4805	75	9	)	)	PUNCT
ejpam-4805	75	10	dα	dα	NOUN
ejpam-4805	75	11	)	)	PUNCT
ejpam-4805	75	12	(	(	PUNCT
ejpam-4805	75	13	6	6	NUM
ejpam-4805	75	14	)	)	PUNCT
ejpam-4805	75	15	2.1	2.1	NUM
ejpam-4805	75	16	.	.	PUNCT
ejpam-4805	76	1	measuring	measure	VERB
ejpam-4805	76	2	the	the	DET
ejpam-4805	76	3	data	data	NOUN
ejpam-4805	76	4	transmission	transmission	NOUN
ejpam-4805	76	5	.	.	PUNCT
ejpam-4805	77	1	the	the	DET
ejpam-4805	77	2	parameters	parameter	NOUN
ejpam-4805	77	3	ω	ω	PROPN
ejpam-4805	77	4	,	,	PUNCT
ejpam-4805	77	5	β	β	X
ejpam-4805	77	6	,	,	PUNCT
ejpam-4805	77	7	σ	σ	PROPN
ejpam-4805	77	8	,	,	PUNCT
ejpam-4805	77	9	γ	γ	X
ejpam-4805	77	10	,	,	PUNCT
ejpam-4805	77	11	r	r	NOUN
ejpam-4805	77	12	,	,	PUNCT
ejpam-4805	77	13	s1	s1	NOUN
ejpam-4805	77	14	,	,	PUNCT
ejpam-4805	77	15	e1	e1	PROPN
ejpam-4805	77	16	,	,	PUNCT
ejpam-4805	77	17	i1	i1	PROPN
ejpam-4805	77	18	,	,	PUNCT
ejpam-4805	77	19	n1	n1	NOUN
ejpam-4805	77	20	,	,	PUNCT
ejpam-4805	77	21	and	and	CCONJ
ejpam-4805	77	22	the	the	DET
ejpam-4805	77	23	five	five	NUM
ejpam-4805	77	24	subsequent	subsequent	ADJ
ejpam-4805	77	25	equations	equation	NOUN
ejpam-4805	77	26	t	t	PROPN
ejpam-4805	77	27	≥	≥	PROPN
ejpam-4805	77	28	t1	t1	PROPN
ejpam-4805	77	29	fully	fully	ADV
ejpam-4805	77	30	indicate	indicate	VERB
ejpam-4805	77	31	the	the	DET
ejpam-4805	77	32	data	data	NOUN
ejpam-4805	77	33	transmission	transmission	NOUN
ejpam-4805	77	34	.	.	PUNCT
ejpam-4805	78	1	∅(t	∅(t	NOUN
ejpam-4805	78	2	)	)	PUNCT
ejpam-4805	78	3	=	=	SYM
ejpam-4805	78	4	∅̂(t	∅̂(t	PROPN
ejpam-4805	78	5	)	)	PUNCT
ejpam-4805	78	6	g(t	g(t	PROPN
ejpam-4805	78	7	)	)	PUNCT
ejpam-4805	78	8	(	(	PUNCT
ejpam-4805	78	9	7	7	NUM
ejpam-4805	78	10	)	)	PUNCT
ejpam-4805	78	11	therefore	therefore	ADV
ejpam-4805	78	12	,	,	PUNCT
ejpam-4805	78	13	at	at	ADP
ejpam-4805	78	14	t	t	PROPN
ejpam-4805	78	15	≥	≥	PROPN
ejpam-4805	78	16	t1	t1	PROPN
ejpam-4805	78	17	î(t	î(t	NOUN
ejpam-4805	78	18	)	)	PUNCT
ejpam-4805	78	19	=	=	SYM
ejpam-4805	78	20	(	(	PUNCT
ejpam-4805	78	21	i(t	i(t	PROPN
ejpam-4805	78	22	)	)	PUNCT
ejpam-4805	78	23	g(t	g(t	PROPN
ejpam-4805	78	24	)	)	PUNCT
ejpam-4805	78	25	,	,	PUNCT
ejpam-4805	78	26	n̂(t	n̂(t	NOUN
ejpam-4805	78	27	)	)	PUNCT
ejpam-4805	78	28	=	=	SYM
ejpam-4805	78	29	n(t	n(t	PROPN
ejpam-4805	78	30	)	)	PUNCT
ejpam-4805	78	31	g(t	g(t	PROPN
ejpam-4805	78	32	)	)	PUNCT
ejpam-4805	78	33	,	,	PUNCT
ejpam-4805	78	34	and	and	CCONJ
ejpam-4805	78	35	∅̂(t	∅̂(t	PROPN
ejpam-4805	78	36	)	)	PUNCT
ejpam-4805	78	37	=	=	PUNCT
ejpam-4805	79	1	∅(t)g(t	∅(t)g(t	ADJ
ejpam-4805	79	2	)	)	PUNCT
ejpam-4805	79	3	.	.	PUNCT
ejpam-4805	80	1	∅̂(t	∅̂(t	PROPN
ejpam-4805	80	2	)	)	PUNCT
ejpam-4805	80	3	=	=	SYM
ejpam-4805	80	4	1	1	NUM
ejpam-4805	80	5	∅̂(t)ωn̂(t	∅̂(t)ωn̂(t	NOUN
ejpam-4805	80	6	)	)	PUNCT
ejpam-4805	80	7	×	×	NOUN
ejpam-4805	80	8	l̂e(t	l̂e(t	ADV
ejpam-4805	80	9	)	)	PUNCT
ejpam-4805	80	10	+	+	CCONJ
ejpam-4805	80	11	β	β	NOUN
ejpam-4805	80	12	ˆle′(t	ˆle′(t	NOUN
ejpam-4805	80	13	)	)	PUNCT
ejpam-4805	80	14	e1	e1	NOUN
ejpam-4805	80	15	+	+	CCONJ
ejpam-4805	80	16	s1	s1	NOUN
ejpam-4805	80	17	−	−	NOUN
ejpam-4805	80	18	ˆle′(t	ˆle′(t	NOUN
ejpam-4805	80	19	)	)	PUNCT
ejpam-4805	81	1	+	+	CCONJ
ejpam-4805	81	2	β	β	NOUN
ejpam-4805	81	3	ˆle′(t	ˆle′(t	NOUN
ejpam-4805	81	4	)	)	PUNCT
ejpam-4805	81	5	and	and	CCONJ
ejpam-4805	81	6	∅̂(t	∅̂(t	NOUN
ejpam-4805	81	7	)	)	PUNCT
ejpam-4805	81	8	=	=	SYM
ejpam-4805	81	9	lr	lr	NOUN
ejpam-4805	81	10	′	′	NUM
ejpam-4805	81	11	a(t	a(t	PROPN
ejpam-4805	81	12	(	(	PUNCT
ejpam-4805	81	13	σr	σr	PROPN
ejpam-4805	81	14	,	,	PUNCT
ejpam-4805	81	15	l̂e(t	l̂e(t	PROPN
ejpam-4805	81	16	)	)	PUNCT
ejpam-4805	81	17	=	=	SYM
ejpam-4805	81	18	1	1	NUM
ejpam-4805	81	19	βσr	βσr	NUM
ejpam-4805	81	20	(	(	PUNCT
ejpam-4805	81	21	l̂r′	l̂r′	ADJ
ejpam-4805	81	22	a(t)−	a(t)−	PROPN
ejpam-4805	81	23	σri1	σri1	NOUN
ejpam-4805	81	24	+	+	CCONJ
ejpam-4805	81	25	σ(lr	σ(lr	NOUN
ejpam-4805	81	26	)	)	PUNCT
ejpam-4805	81	27	′	′	NUM
ejpam-4805	81	28	a(t	a(t	NOUN
ejpam-4805	81	29	)	)	PUNCT
ejpam-4805	81	30	)	)	PUNCT
ejpam-4805	81	31	n̂(t	n̂(t	NOUN
ejpam-4805	81	32	)	)	PUNCT
ejpam-4805	81	33	=	=	NOUN
ejpam-4805	81	34	e−γ(t−t1)n1	e−γ(t−t1)n1	PROPN
ejpam-4805	81	35	+	+	CCONJ
ejpam-4805	81	36	∫	∫	PROPN
ejpam-4805	81	37	t	t	PROPN
ejpam-4805	81	38	t1	t1	PROPN
ejpam-4805	81	39	e−γ(t−s0	e−γ(t−s0	PROPN
ejpam-4805	82	1	1−	1−	NUM
ejpam-4805	82	2	r	r	NOUN
ejpam-4805	82	3	r	r	NOUN
ejpam-4805	82	4	l̂r	l̂r	NOUN
ejpam-4805	82	5	′	′	NUM
ejpam-4805	82	6	a(s1).ds1	a(s1).ds1	ADJ
ejpam-4805	82	7	a.	a.	NOUN
ejpam-4805	82	8	mustafa	mustafa	PROPN
ejpam-4805	82	9	et	et	PROPN
ejpam-4805	82	10	al	al	PROPN
ejpam-4805	82	11	.	.	PUNCT
ejpam-4805	82	12	/	/	SYM
ejpam-4805	82	13	eur	eur	PROPN
ejpam-4805	82	14	.	.	PUNCT
ejpam-4805	83	1	j.	j.	PROPN
ejpam-4805	83	2	pure	pure	PROPN
ejpam-4805	83	3	appl	appl	PROPN
ejpam-4805	83	4	.	.	PROPN
ejpam-4805	83	5	math	math	PROPN
ejpam-4805	83	6	,	,	PUNCT
ejpam-4805	83	7	16	16	NUM
ejpam-4805	83	8	(	(	PUNCT
ejpam-4805	83	9	4	4	NUM
ejpam-4805	83	10	)	)	PUNCT
ejpam-4805	83	11	(	(	PUNCT
ejpam-4805	83	12	2023	2023	NUM
ejpam-4805	83	13	)	)	PUNCT
ejpam-4805	83	14	,	,	PUNCT
ejpam-4805	83	15	2450	2450	NUM
ejpam-4805	83	16	-	-	SYM
ejpam-4805	83	17	2460	2460	NUM
ejpam-4805	83	18	2454	2454	NUM
ejpam-4805	83	19	the	the	DET
ejpam-4805	83	20	data	datum	NOUN
ejpam-4805	83	21	used	use	VERB
ejpam-4805	83	22	in	in	ADP
ejpam-4805	83	23	formula	formula	NOUN
ejpam-4805	83	24	(	(	PUNCT
ejpam-4805	83	25	6	6	NUM
ejpam-4805	83	26	)	)	PUNCT
ejpam-4805	83	27	to	to	ADP
ejpam-4805	83	28	define(lra)(t	define(lra)(t	NOUN
ejpam-4805	83	29	)	)	PUNCT
ejpam-4805	83	30	are	be	AUX
ejpam-4805	83	31	those	those	PRON
ejpam-4805	83	32	represented	represent	VERB
ejpam-4805	83	33	by	by	ADP
ejpam-4805	83	34	functions	function	NOUN
ejpam-4805	83	35	t	t	PROPN
ejpam-4805	83	36	→	→	SYM
ejpam-4805	83	37	lra(t	lra(t	PROPN
ejpam-4805	83	38	)	)	PUNCT
ejpam-4805	83	39	the	the	DET
ejpam-4805	83	40	cumulative	cumulative	ADJ
ejpam-4805	83	41	number	number	NOUN
ejpam-4805	83	42	of	of	ADP
ejpam-4805	83	43	reported	report	VERB
ejpam-4805	83	44	cases	case	NOUN
ejpam-4805	83	45	and	and	CCONJ
ejpam-4805	83	46	t	t	NOUN
ejpam-4805	83	47	→	→	PUNCT
ejpam-4805	83	48	va(t	va(t	NOUN
ejpam-4805	83	49	)	)	PUNCT
ejpam-4805	83	50	resources	resource	NOUN
ejpam-4805	83	51	spent	spend	VERB
ejpam-4805	83	52	on	on	ADP
ejpam-4805	83	53	second	second	ADJ
ejpam-4805	83	54	doses	dose	NOUN
ejpam-4805	83	55	of	of	ADP
ejpam-4805	83	56	vaccination	vaccination	NOUN
ejpam-4805	83	57	(	(	PUNCT
ejpam-4805	83	58	t	t	NOUN
ejpam-4805	83	59	)	)	PUNCT
ejpam-4805	84	1	[	[	X
ejpam-4805	84	2	12	12	NUM
ejpam-4805	84	3	]	]	PUNCT
ejpam-4805	84	4	.	.	PUNCT
ejpam-4805	85	1	we	we	PRON
ejpam-4805	85	2	arrive	arrive	VERB
ejpam-4805	85	3	at	at	ADP
ejpam-4805	85	4	the	the	DET
ejpam-4805	85	5	following	follow	VERB
ejpam-4805	85	6	equation	equation	NOUN
ejpam-4805	85	7	to	to	PART
ejpam-4805	85	8	define	define	VERB
ejpam-4805	85	9	the	the	DET
ejpam-4805	85	10	rate	rate	NOUN
ejpam-4805	85	11	of	of	ADP
ejpam-4805	85	12	transmission	transmission	NOUN
ejpam-4805	85	13	as	as	ADP
ejpam-4805	85	14	a	a	DET
ejpam-4805	85	15	function	function	NOUN
ejpam-4805	85	16	of	of	ADP
ejpam-4805	85	17	the	the	DET
ejpam-4805	85	18	total	total	ADJ
ejpam-4805	85	19	number	number	NOUN
ejpam-4805	85	20	of	of	ADP
ejpam-4805	85	21	reported	report	VERB
ejpam-4805	85	22	cases	case	NOUN
ejpam-4805	85	23	t	t	NOUN
ejpam-4805	85	24	→	→	SYM
ejpam-4805	85	25	lra(t	lra(t	PROPN
ejpam-4805	85	26	)	)	PUNCT
ejpam-4805	85	27	and	and	CCONJ
ejpam-4805	85	28	the	the	DET
ejpam-4805	85	29	total	total	ADJ
ejpam-4805	85	30	number	number	NOUN
ejpam-4805	85	31	of	of	ADP
ejpam-4805	85	32	immunized	immunize	VERB
ejpam-4805	85	33	people	people	NOUN
ejpam-4805	85	34	t	t	PROPN
ejpam-4805	85	35	→	→	PUNCT
ejpam-4805	85	36	lva(t)[11	lva(t)[11	PROPN
ejpam-4805	85	37	]	]	PUNCT
ejpam-4805	85	38	.	.	PUNCT
ejpam-4805	86	1	2.2	2.2	NUM
ejpam-4805	86	2	.	.	PUNCT
ejpam-4805	86	3	statistics	statistic	NOUN
ejpam-4805	86	4	homogenized	homogenize	VERB
ejpam-4805	86	5	by	by	ADP
ejpam-4805	86	6	g(t	g(t	PROPN
ejpam-4805	86	7	)	)	PUNCT
ejpam-4805	86	8	the	the	DET
ejpam-4805	86	9	everyday	everyday	ADJ
ejpam-4805	86	10	number	number	NOUN
ejpam-4805	86	11	of	of	ADP
ejpam-4805	86	12	identified	identify	VERB
ejpam-4805	86	13	cases	case	NOUN
ejpam-4805	86	14	normalized	normalize	VERB
ejpam-4805	86	15	by	by	ADP
ejpam-4805	86	16	g(t	g(t	PROPN
ejpam-4805	86	17	)	)	PUNCT
ejpam-4805	86	18	,	,	PUNCT
ejpam-4805	86	19	or	or	CCONJ
ejpam-4805	86	20	the	the	DET
ejpam-4805	86	21	percentage	percentage	NOUN
ejpam-4805	86	22	of	of	ADP
ejpam-4805	86	23	those	those	PRON
ejpam-4805	86	24	who	who	PRON
ejpam-4805	86	25	were	be	AUX
ejpam-4805	86	26	n’t	not	PART
ejpam-4805	86	27	effectively	effectively	ADV
ejpam-4805	86	28	immunized	immunize	VERB
ejpam-4805	86	29	at	at	ADP
ejpam-4805	86	30	time	time	NOUN
ejpam-4805	86	31	t	t	PROPN
ejpam-4805	86	32	,	,	PUNCT
ejpam-4805	86	33	l̂ra(t	l̂ra(t	PROPN
ejpam-4805	86	34	)	)	PUNCT
ejpam-4805	86	35	′	′	NUM
ejpam-4805	87	1	=	=	PUNCT
ejpam-4805	87	2	lra(t	lra(t	PROPN
ejpam-4805	87	3	)	)	PUNCT
ejpam-4805	87	4	′	′	NUM
ejpam-4805	88	1	g(t	g(t	PROPN
ejpam-4805	88	2	)	)	PUNCT
ejpam-4805	89	1	=	=	SYM
ejpam-4805	89	2	lra(t	lra(t	PROPN
ejpam-4805	89	3	)	)	PUNCT
ejpam-4805	89	4	′	′	NUM
ejpam-4805	90	1	(	(	PUNCT
ejpam-4805	90	2	p	p	X
ejpam-4805	90	3	p	p	X
ejpam-4805	90	4	−	−	PROPN
ejpam-4805	90	5	lva(t	lva(t	PROPN
ejpam-4805	90	6	)	)	PUNCT
ejpam-4805	90	7	)	)	PUNCT
ejpam-4805	91	1	ε	ε	PROPN
ejpam-4805	91	2	case	case	NOUN
ejpam-4805	91	3	frequency	frequency	NOUN
ejpam-4805	91	4	on	on	ADP
ejpam-4805	91	5	a	a	DET
ejpam-4805	91	6	regular	regular	ADJ
ejpam-4805	91	7	schedule	schedule	NOUN
ejpam-4805	91	8	standardized	standardize	VERB
ejpam-4805	91	9	by	by	ADP
ejpam-4805	91	10	w(t	w(t	PROPN
ejpam-4805	91	11	)	)	PUNCT
ejpam-4805	91	12	is	be	AUX
ejpam-4805	91	13	l̂ra(t	l̂ra(t	PROPN
ejpam-4805	91	14	)	)	PUNCT
ejpam-4805	92	1	=	=	SYM
ejpam-4805	92	2	∫	∫	PROPN
ejpam-4805	92	3	t	t	PROPN
ejpam-4805	92	4	t1	t1	NOUN
ejpam-4805	92	5	lr	lr	PROPN
ejpam-4805	92	6	′	′	NUM
ejpam-4805	92	7	a(α	a(α	NOUN
ejpam-4805	92	8	)	)	PUNCT
ejpam-4805	92	9	g(α	g(α	PROPN
ejpam-4805	92	10	)	)	PUNCT
ejpam-4805	92	11	dα	dα	NOUN
ejpam-4805	92	12	)	)	PUNCT
ejpam-4805	92	13	(	(	PUNCT
ejpam-4805	92	14	p	p	X
ejpam-4805	92	15	p	p	X
ejpam-4805	92	16	−	−	PROPN
ejpam-4805	92	17	lva(t	lva(t	PROPN
ejpam-4805	92	18	)	)	PUNCT
ejpam-4805	92	19	)	)	PUNCT
ejpam-4805	92	20	ε	ε	PROPN
ejpam-4805	92	21	2.3	2.3	NUM
ejpam-4805	92	22	.	.	PUNCT
ejpam-4805	93	1	reproduction	reproduction	NOUN
ejpam-4805	93	2	numbers	number	NOUN
ejpam-4805	93	3	utilizing	utilize	VERB
ejpam-4805	93	4	the	the	DET
ejpam-4805	93	5	formula	formula	NOUN
ejpam-4805	93	6	,	,	PUNCT
ejpam-4805	93	7	we	we	PRON
ejpam-4805	93	8	can	can	AUX
ejpam-4805	93	9	get	get	VERB
ejpam-4805	93	10	the	the	DET
ejpam-4805	93	11	daily	daily	ADJ
ejpam-4805	93	12	transmission	transmission	NOUN
ejpam-4805	93	13	rate	rate	NOUN
ejpam-4805	93	14	t	t	PROPN
ejpam-4805	93	15	→	→	SYM
ejpam-4805	93	16	ρ(t).[16	ρ(t).[16	NUM
ejpam-4805	93	17	]	]	X
ejpam-4805	94	1	the	the	DET
ejpam-4805	94	2	issue	issue	NOUN
ejpam-4805	94	3	of	of	ADP
ejpam-4805	94	4	the	the	DET
ejpam-4805	94	5	immediate	immediate	ADJ
ejpam-4805	94	6	reproduction	reproduction	NOUN
ejpam-4805	94	7	numbers	number	NOUN
ejpam-4805	94	8	may	may	AUX
ejpam-4805	94	9	then	then	ADV
ejpam-4805	94	10	be	be	AUX
ejpam-4805	94	11	considered	consider	VERB
ejpam-4805	94	12	by	by	ADP
ejpam-4805	94	13	utilizing	utilize	VERB
ejpam-4805	94	14	model	model	NOUN
ejpam-4805	94	15	(	(	PUNCT
ejpam-4805	94	16	6	6	NUM
ejpam-4805	94	17	)	)	PUNCT
ejpam-4805	94	18	(	(	PUNCT
ejpam-4805	94	19	see	see	VERB
ejpam-4805	94	20	[	[	X
ejpam-4805	94	21	24	24	NUM
ejpam-4805	94	22	]	]	PUNCT
ejpam-4805	94	23	for	for	ADP
ejpam-4805	94	24	more	more	ADJ
ejpam-4805	94	25	information	information	NOUN
ejpam-4805	94	26	)	)	PUNCT
ejpam-4805	94	27	.	.	PUNCT
ejpam-4805	95	1	we	we	PRON
ejpam-4805	95	2	apply	apply	VERB
ejpam-4805	95	3	our	our	PRON
ejpam-4805	95	4	approach	approach	NOUN
ejpam-4805	95	5	to	to	PART
ejpam-4805	95	6	calculate	calculate	VERB
ejpam-4805	95	7	the	the	DET
ejpam-4805	95	8	transmission	transmission	NOUN
ejpam-4805	95	9	rate	rate	NOUN
ejpam-4805	95	10	and	and	CCONJ
ejpam-4805	95	11	take	take	VERB
ejpam-4805	95	12	into	into	ADP
ejpam-4805	95	13	account	account	NOUN
ejpam-4805	95	14	the	the	DET
ejpam-4805	95	15	immediate	immediate	ADJ
ejpam-4805	95	16	reproduction	reproduction	NOUN
ejpam-4805	95	17	number	number	NOUN
ejpam-4805	95	18	with	with	ADP
ejpam-4805	95	19	vaccination	vaccination	NOUN
ejpam-4805	95	20	to	to	PART
ejpam-4805	95	21	explore	explore	VERB
ejpam-4805	95	22	the	the	DET
ejpam-4805	95	23	role	role	NOUN
ejpam-4805	95	24	of	of	ADP
ejpam-4805	95	25	vaccination	vaccination	NOUN
ejpam-4805	95	26	in	in	ADP
ejpam-4805	95	27	the	the	DET
ejpam-4805	95	28	covid-19	covid-19	PROPN
ejpam-4805	95	29	data[13	data[13	PROPN
ejpam-4805	95	30	]	]	PUNCT
ejpam-4805	95	31	.	.	PUNCT
ejpam-4805	96	1	rv	rv	PROPN
ejpam-4805	96	2	(	(	PUNCT
ejpam-4805	96	3	t	t	PROPN
ejpam-4805	96	4	)	)	PUNCT
ejpam-4805	96	5	=	=	PUNCT
ejpam-4805	96	6	ρ(t)s(t	ρ(t)s(t	NUM
ejpam-4805	96	7	)	)	PUNCT
ejpam-4805	96	8	γσ	γσ	ADP
ejpam-4805	96	9	×	×	NOUN
ejpam-4805	96	10	γ	γ	X
ejpam-4805	96	11	+	+	CCONJ
ejpam-4805	96	12	ωσ(1−	ωσ(1−	PROPN
ejpam-4805	96	13	r	r	NOUN
ejpam-4805	96	14	)	)	PUNCT
ejpam-4805	96	15	(	(	PUNCT
ejpam-4805	96	16	8)	8)	NUM
ejpam-4805	96	17	the	the	DET
ejpam-4805	96	18	reproduction	reproduction	NOUN
ejpam-4805	96	19	rate	rate	NOUN
ejpam-4805	96	20	with	with	ADP
ejpam-4805	96	21	vaccination	vaccination	NOUN
ejpam-4805	96	22	r1	r1	NOUN
ejpam-4805	96	23	v	v	ADP
ejpam-4805	96	24	(	(	PUNCT
ejpam-4805	96	25	t	t	PROPN
ejpam-4805	96	26	)	)	PUNCT
ejpam-4805	96	27	=	=	SYM
ejpam-4805	97	1	ρ(t)g(t)s1	ρ(t)g(t)s1	NUM
ejpam-4805	97	2	γσ	γσ	INTJ
ejpam-4805	97	3	×	×	NOUN
ejpam-4805	97	4	γ	γ	X
ejpam-4805	97	5	+	+	CCONJ
ejpam-4805	97	6	ωσ(1−	ωσ(1−	PROPN
ejpam-4805	97	7	r	r	NOUN
ejpam-4805	97	8	)	)	PUNCT
ejpam-4805	97	9	(	(	PUNCT
ejpam-4805	97	10	9	9	X
ejpam-4805	97	11	)	)	PUNCT
ejpam-4805	97	12	the	the	DET
ejpam-4805	97	13	reproduction	reproduction	NOUN
ejpam-4805	97	14	rate	rate	NOUN
ejpam-4805	97	15	without	without	ADP
ejpam-4805	97	16	vaccination	vaccination	NOUN
ejpam-4805	97	17	r1(t	r1(t	NOUN
ejpam-4805	97	18	)	)	PUNCT
ejpam-4805	97	19	=	=	PUNCT
ejpam-4805	97	20	ρ(t)s1	ρ(t)s1	NOUN
ejpam-4805	97	21	γσ	γσ	ADP
ejpam-4805	97	22	×	×	NOUN
ejpam-4805	97	23	(	(	PUNCT
ejpam-4805	97	24	γ	γ	X
ejpam-4805	97	25	+	+	CCONJ
ejpam-4805	97	26	ωσ(1−	ωσ(1−	PROPN
ejpam-4805	97	27	r	r	NOUN
ejpam-4805	97	28	)	)	PUNCT
ejpam-4805	97	29	,	,	PUNCT
ejpam-4805	97	30	(	(	PUNCT
ejpam-4805	97	31	10	10	NUM
ejpam-4805	97	32	)	)	PUNCT
ejpam-4805	97	33	3	3	NUM
ejpam-4805	97	34	.	.	X
ejpam-4805	97	35	mathematical	mathematical	ADJ
ejpam-4805	97	36	analysis	analysis	NOUN
ejpam-4805	97	37	of	of	ADP
ejpam-4805	97	38	the	the	DET
ejpam-4805	97	39	epidemic	epidemic	NOUN
ejpam-4805	97	40	model	model	NOUN
ejpam-4805	97	41	in	in	ADP
ejpam-4805	97	42	this	this	DET
ejpam-4805	97	43	section	section	NOUN
ejpam-4805	97	44	,	,	PUNCT
ejpam-4805	97	45	we	we	PRON
ejpam-4805	97	46	explain	explain	VERB
ejpam-4805	97	47	the	the	DET
ejpam-4805	97	48	covid-19	covid-19	PROPN
ejpam-4805	97	49	model	model	NOUN
ejpam-4805	97	50	’s	’s	PART
ejpam-4805	97	51	boundedness	boundedness	NOUN
ejpam-4805	97	52	,	,	PUNCT
ejpam-4805	97	53	positiveness	positiveness	NOUN
ejpam-4805	97	54	,	,	PUNCT
ejpam-4805	97	55	epidemic	epidemic	NOUN
ejpam-4805	97	56	and	and	CCONJ
ejpam-4805	97	57	endemic	endemic	ADJ
ejpam-4805	97	58	stability	stability	NOUN
ejpam-4805	97	59	,	,	PUNCT
ejpam-4805	97	60	and	and	CCONJ
ejpam-4805	97	61	fundamental	fundamental	ADJ
ejpam-4805	97	62	reproduction	reproduction	NOUN
ejpam-4805	97	63	frequency[4	frequency[4	PROPN
ejpam-4805	97	64	]	]	PUNCT
ejpam-4805	97	65	.	.	PUNCT
ejpam-4805	98	1	a.	a.	PROPN
ejpam-4805	98	2	mustafa	mustafa	PROPN
ejpam-4805	98	3	et	et	PROPN
ejpam-4805	98	4	al	al	PROPN
ejpam-4805	98	5	.	.	PUNCT
ejpam-4805	98	6	/	/	SYM
ejpam-4805	98	7	eur	eur	PROPN
ejpam-4805	98	8	.	.	PUNCT
ejpam-4805	99	1	j.	j.	PROPN
ejpam-4805	99	2	pure	pure	PROPN
ejpam-4805	99	3	appl	appl	PROPN
ejpam-4805	99	4	.	.	PROPN
ejpam-4805	99	5	math	math	PROPN
ejpam-4805	99	6	,	,	PUNCT
ejpam-4805	99	7	16	16	NUM
ejpam-4805	99	8	(	(	PUNCT
ejpam-4805	99	9	4	4	NUM
ejpam-4805	99	10	)	)	PUNCT
ejpam-4805	99	11	(	(	PUNCT
ejpam-4805	99	12	2023	2023	NUM
ejpam-4805	99	13	)	)	PUNCT
ejpam-4805	99	14	,	,	PUNCT
ejpam-4805	99	15	2450	2450	NUM
ejpam-4805	99	16	-	-	SYM
ejpam-4805	99	17	2460	2460	NUM
ejpam-4805	99	18	2455	2455	NUM
ejpam-4805	99	19	theorem	theorem	VERB
ejpam-4805	99	20	1	1	NUM
ejpam-4805	99	21	.	.	PUNCT
ejpam-4805	100	1	if	if	SCONJ
ejpam-4805	100	2	s1	s1	PROPN
ejpam-4805	100	3	≥	≥	NOUN
ejpam-4805	100	4	0	0	NUM
ejpam-4805	100	5	,	,	PUNCT
ejpam-4805	100	6	e1	e1	VERB
ejpam-4805	100	7	≥	≥	NOUN
ejpam-4805	100	8	0	0	NUM
ejpam-4805	100	9	,	,	PUNCT
ejpam-4805	100	10	i1	i1	PROPN
ejpam-4805	100	11	≥	≥	PROPN
ejpam-4805	100	12	0	0	NUM
ejpam-4805	100	13	,	,	PUNCT
ejpam-4805	100	14	n1	n1	ADJ
ejpam-4805	100	15	≥	≥	NOUN
ejpam-4805	100	16	0	0	NUM
ejpam-4805	100	17	,	,	PUNCT
ejpam-4805	100	18	r1	r1	PROPN
ejpam-4805	100	19	≥	≥	NUM
ejpam-4805	100	20	0,then	0,then	PUNCT
ejpam-4805	100	21	the	the	DET
ejpam-4805	100	22	solutions	solution	NOUN
ejpam-4805	100	23	of	of	ADP
ejpam-4805	100	24	system	system	NOUN
ejpam-4805	100	25	(	(	PUNCT
ejpam-4805	100	26	1	1	X
ejpam-4805	100	27	)	)	PUNCT
ejpam-4805	100	28	remain	remain	VERB
ejpam-4805	100	29	positiveness	positiveness	NOUN
ejpam-4805	100	30	for	for	ADP
ejpam-4805	100	31	all	all	DET
ejpam-4805	100	32	t	t	PROPN
ejpam-4805	100	33	>	>	X
ejpam-4805	100	34	0	0	X
ejpam-4805	100	35	.	.	PUNCT
ejpam-4805	101	1	proof	proof	NOUN
ejpam-4805	101	2	.	.	PUNCT
ejpam-4805	102	1	proof	proof	NOUN
ejpam-4805	102	2	.	.	PUNCT
ejpam-4805	103	1	we	we	PRON
ejpam-4805	103	2	obtain	obtain	VERB
ejpam-4805	103	3	the	the	DET
ejpam-4805	103	4	following	following	NOUN
ejpam-4805	103	5	from	from	ADP
ejpam-4805	103	6	system	system	NOUN
ejpam-4805	103	7	(	(	PUNCT
ejpam-4805	103	8	1.1	1.1	NUM
ejpam-4805	103	9	)	)	PUNCT
ejpam-4805	103	10	’s	’s	PART
ejpam-4805	103	11	first	first	ADJ
ejpam-4805	103	12	equation	equation	NOUN
ejpam-4805	103	13	:	:	PUNCT
ejpam-4805	103	14	ds	ds	ADJ
ejpam-4805	103	15	dt	dt	X
ejpam-4805	103	16	≥	≥	PROPN
ejpam-4805	103	17	−ωs	−ωs	PROPN
ejpam-4805	103	18	(	(	PUNCT
ejpam-4805	103	19	11)∫	11)∫	NUM
ejpam-4805	103	20	ds	ds	ADJ
ejpam-4805	103	21	≥	≥	NOUN
ejpam-4805	103	22	−ωs.dt	−ωs.dt	NOUN
ejpam-4805	103	23	s(t	s(t	PROPN
ejpam-4805	103	24	)	)	PUNCT
ejpam-4805	103	25	≥	≥	NOUN
ejpam-4805	103	26	s1e	s1e	NOUN
ejpam-4805	103	27	−ωt	−ωt	NOUN
ejpam-4805	103	28	(	(	PUNCT
ejpam-4805	103	29	12	12	NUM
ejpam-4805	103	30	)	)	PUNCT
ejpam-4805	103	31	therefore	therefore	ADV
ejpam-4805	103	32	,	,	PUNCT
ejpam-4805	103	33	for	for	ADP
ejpam-4805	103	34	any	any	DET
ejpam-4805	103	35	t	t	NOUN
ejpam-4805	103	36	>	>	X
ejpam-4805	103	37	0	0	NUM
ejpam-4805	103	38	,	,	PUNCT
ejpam-4805	103	39	s(t	s(t	PROPN
ejpam-4805	103	40	)	)	PUNCT
ejpam-4805	103	41	stays	stay	VERB
ejpam-4805	103	42	positive	positive	ADJ
ejpam-4805	103	43	.	.	PUNCT
ejpam-4805	104	1	we	we	PRON
ejpam-4805	104	2	also	also	ADV
ejpam-4805	104	3	get	get	VERB
ejpam-4805	104	4	e(t	e(t	NOUN
ejpam-4805	104	5	)	)	PUNCT
ejpam-4805	104	6	≥	≥	NOUN
ejpam-4805	104	7	0	0	NUM
ejpam-4805	104	8	,	,	PUNCT
ejpam-4805	104	9	i(t	i(t	PROPN
ejpam-4805	104	10	)	)	PUNCT
ejpam-4805	104	11	≥	≥	NOUN
ejpam-4805	104	12	0	0	NUM
ejpam-4805	104	13	,	,	PUNCT
ejpam-4805	104	14	n(t	n(t	PROPN
ejpam-4805	104	15	)	)	PUNCT
ejpam-4805	104	16	≥	≥	NOUN
ejpam-4805	104	17	0	0	NUM
ejpam-4805	104	18	,	,	PUNCT
ejpam-4805	104	19	andr(t	andr(t	NOUN
ejpam-4805	104	20	)	)	PUNCT
ejpam-4805	104	21	≥	≥	NOUN
ejpam-4805	104	22	0	0	NUM
ejpam-4805	104	23	,	,	PUNCT
ejpam-4805	104	24	using	use	VERB
ejpam-4805	104	25	the	the	DET
ejpam-4805	104	26	remaining	remain	VERB
ejpam-4805	104	27	equations	equation	NOUN
ejpam-4805	104	28	of	of	ADP
ejpam-4805	104	29	system	system	NOUN
ejpam-4805	104	30	(	(	PUNCT
ejpam-4805	104	31	1	1	NUM
ejpam-4805	104	32	)	)	PUNCT
ejpam-4805	104	33	.	.	PUNCT
ejpam-4805	105	1	theorem	theorem	NOUN
ejpam-4805	105	2	1	1	NUM
ejpam-4805	105	3	is	be	AUX
ejpam-4805	105	4	verified	verify	VERB
ejpam-4805	105	5	.	.	PUNCT
ejpam-4805	106	1	theorem	theorem	NOUN
ejpam-4805	106	2	2	2	NUM
ejpam-4805	106	3	.	.	PUNCT
ejpam-4805	107	1	all	all	DET
ejpam-4805	107	2	solutions	solution	NOUN
ejpam-4805	107	3	of	of	ADP
ejpam-4805	107	4	the	the	DET
ejpam-4805	107	5	proposed	propose	VERB
ejpam-4805	107	6	model	model	NOUN
ejpam-4805	107	7	with	with	ADP
ejpam-4805	107	8	positiveness	positiveness	NOUN
ejpam-4805	107	9	initial	initial	ADJ
ejpam-4805	107	10	conditions	condition	NOUN
ejpam-4805	107	11	are	be	AUX
ejpam-4805	107	12	bounded	bound	VERB
ejpam-4805	107	13	and	and	CCONJ
ejpam-4805	107	14	p	p	PROPN
ejpam-4805	107	15	(	(	PUNCT
ejpam-4805	107	16	t	t	PROPN
ejpam-4805	107	17	)	)	PUNCT
ejpam-4805	107	18	≤	≤	NOUN
ejpam-4805	107	19	ρ	ρ	PROPN
ejpam-4805	107	20	ω	ω	PROPN
ejpam-4805	107	21	for	for	ADP
ejpam-4805	107	22	all	all	DET
ejpam-4805	107	23	t	t	PROPN
ejpam-4805	107	24	>	>	X
ejpam-4805	107	25	0	0	X
ejpam-4805	107	26	.	.	PUNCT
ejpam-4805	108	1	proof	proof	NOUN
ejpam-4805	108	2	.	.	PUNCT
ejpam-4805	109	1	the	the	DET
ejpam-4805	109	2	overall	overall	ADJ
ejpam-4805	109	3	population	population	NOUN
ejpam-4805	109	4	’s	’s	PART
ejpam-4805	109	5	growth	growth	NOUN
ejpam-4805	109	6	rate	rate	NOUN
ejpam-4805	109	7	may	may	AUX
ejpam-4805	109	8	be	be	AUX
ejpam-4805	109	9	expressed	express	VERB
ejpam-4805	109	10	as	as	ADP
ejpam-4805	109	11	the	the	DET
ejpam-4805	109	12	sum	sum	NOUN
ejpam-4805	109	13	of	of	ADP
ejpam-4805	109	14	all	all	DET
ejpam-4805	109	15	the	the	DET
ejpam-4805	109	16	equations	equation	NOUN
ejpam-4805	109	17	in	in	ADP
ejpam-4805	109	18	the	the	DET
ejpam-4805	109	19	system	system	NOUN
ejpam-4805	109	20	(	(	PUNCT
ejpam-4805	109	21	1	1	NUM
ejpam-4805	109	22	)	)	PUNCT
ejpam-4805	109	23	.	.	PUNCT
ejpam-4805	110	1	dp	dp	NOUN
ejpam-4805	111	1	dt	dt	NOUN
ejpam-4805	111	2	=	=	NOUN
ejpam-4805	111	3	ds	ds	ADJ
ejpam-4805	112	1	dt	dt	X
ejpam-4805	112	2	+	+	CCONJ
ejpam-4805	112	3	de	de	X
ejpam-4805	112	4	dt	dt	X
ejpam-4805	112	5	+	+	CCONJ
ejpam-4805	112	6	di	di	X
ejpam-4805	112	7	dt	dt	NOUN
ejpam-4805	112	8	+	+	CCONJ
ejpam-4805	112	9	dn	dn	PROPN
ejpam-4805	112	10	dt	dt	PROPN
ejpam-4805	112	11	+	+	CCONJ
ejpam-4805	112	12	dr	dr	PROPN
ejpam-4805	112	13	dt	dt	PROPN
ejpam-4805	112	14	(	(	PUNCT
ejpam-4805	112	15	13	13	NUM
ejpam-4805	112	16	)	)	PUNCT
ejpam-4805	112	17	equation	equation	NOUN
ejpam-4805	112	18	(	(	PUNCT
ejpam-4805	112	19	3	3	X
ejpam-4805	112	20	)	)	PUNCT
ejpam-4805	112	21	gives	give	VERB
ejpam-4805	112	22	the	the	DET
ejpam-4805	112	23	following	follow	VERB
ejpam-4805	112	24	formula	formula	NOUN
ejpam-4805	112	25	:	:	PUNCT
ejpam-4805	113	1	dp	dp	NOUN
ejpam-4805	113	2	dt	dt	NOUN
ejpam-4805	113	3	=	=	PUNCT
ejpam-4805	114	1	ρ−	ρ−	NOUN
ejpam-4805	114	2	ωp	ωp	NUM
ejpam-4805	114	3	(	(	PUNCT
ejpam-4805	114	4	14	14	NUM
ejpam-4805	114	5	)	)	PUNCT
ejpam-4805	114	6	the	the	DET
ejpam-4805	114	7	solution	solution	NOUN
ejpam-4805	114	8	is	be	AUX
ejpam-4805	114	9	obtained	obtain	VERB
ejpam-4805	114	10	by	by	ADP
ejpam-4805	114	11	integrating	integrate	VERB
ejpam-4805	114	12	two	two	NUM
ejpam-4805	114	13	sides	side	NOUN
ejpam-4805	114	14	of	of	ADP
ejpam-4805	114	15	equation	equation	NOUN
ejpam-4805	114	16	(	(	PUNCT
ejpam-4805	114	17	14	14	NUM
ejpam-4805	114	18	)	)	PUNCT
ejpam-4805	114	19	as	as	SCONJ
ejpam-4805	114	20	follows	follow	VERB
ejpam-4805	114	21	:	:	PUNCT
ejpam-4805	114	22	p	p	X
ejpam-4805	114	23	(	(	PUNCT
ejpam-4805	114	24	t	t	NOUN
ejpam-4805	114	25	)	)	PUNCT
ejpam-4805	114	26	=	=	SYM
ejpam-4805	114	27	ρ	ρ	PROPN
ejpam-4805	114	28	ω	ω	PROPN
ejpam-4805	114	29	+	+	CCONJ
ejpam-4805	114	30	(	(	PUNCT
ejpam-4805	114	31	p1	p1	PROPN
ejpam-4805	114	32	−	−	PROPN
ejpam-4805	114	33	ρ	ρ	PROPN
ejpam-4805	114	34	ω	ω	PROPN
ejpam-4805	114	35	)	)	PUNCT
ejpam-4805	114	36	e−ωt	e−ωt	PROPN
ejpam-4805	114	37	.	.	PUNCT
ejpam-4805	115	1	(	(	PUNCT
ejpam-4805	115	2	15	15	NUM
ejpam-4805	115	3	)	)	PUNCT
ejpam-4805	115	4	therefore	therefore	ADV
ejpam-4805	115	5	,	,	PUNCT
ejpam-4805	115	6	for	for	ADP
ejpam-4805	115	7	t	t	PROPN
ejpam-4805	115	8	→	→	SYM
ejpam-4805	115	9	∞	∞	PROPN
ejpam-4805	115	10	,	,	PUNCT
ejpam-4805	115	11	we	we	PRON
ejpam-4805	115	12	have	have	VERB
ejpam-4805	115	13	that	that	DET
ejpam-4805	115	14	p	p	X
ejpam-4805	115	15	(	(	PUNCT
ejpam-4805	115	16	t	t	NOUN
ejpam-4805	115	17	)	)	PUNCT
ejpam-4805	115	18	≤	≤	NOUN
ejpam-4805	115	19	ρ	ρ	PROPN
ejpam-4805	115	20	ω	ω	PROPN
ejpam-4805	115	21	(	(	PUNCT
ejpam-4805	115	22	16	16	NUM
ejpam-4805	115	23	)	)	PUNCT
ejpam-4805	115	24	thus	thus	ADV
ejpam-4805	115	25	,	,	PUNCT
ejpam-4805	115	26	theorem	theorem	VERB
ejpam-4805	115	27	1	1	NUM
ejpam-4805	115	28	as	as	ADV
ejpam-4805	115	29	well	well	ADV
ejpam-4805	115	30	as	as	ADP
ejpam-4805	115	31	equation	equation	NOUN
ejpam-4805	115	32	(	(	PUNCT
ejpam-4805	115	33	16	16	NUM
ejpam-4805	115	34	)	)	PUNCT
ejpam-4805	115	35	conclude	conclude	VERB
ejpam-4805	115	36	in	in	ADP
ejpam-4805	115	37	0	0	NUM
ejpam-4805	115	38	≤	≤	NOUN
ejpam-4805	115	39	p	p	NOUN
ejpam-4805	115	40	(	(	PUNCT
ejpam-4805	115	41	t	t	PROPN
ejpam-4805	115	42	)	)	PUNCT
ejpam-4805	115	43	≤	≤	NOUN
ejpam-4805	115	44	ρ	ρ	PROPN
ejpam-4805	115	45	ω	ω	PROPN
ejpam-4805	115	46	therefore	therefore	ADV
ejpam-4805	115	47	,	,	PUNCT
ejpam-4805	115	48	s(t	s(t	PROPN
ejpam-4805	115	49	)	)	PUNCT
ejpam-4805	115	50	,	,	PUNCT
ejpam-4805	115	51	e(t	e(t	NOUN
ejpam-4805	115	52	)	)	PUNCT
ejpam-4805	115	53	,	,	PUNCT
ejpam-4805	115	54	i(t	i(t	PROPN
ejpam-4805	115	55	)	)	PUNCT
ejpam-4805	115	56	,	,	PUNCT
ejpam-4805	115	57	n(t	n(t	PROPN
ejpam-4805	115	58	)	)	PUNCT
ejpam-4805	115	59	,	,	PUNCT
ejpam-4805	115	60	and	and	CCONJ
ejpam-4805	115	61	r(t	r(t	NOUN
ejpam-4805	115	62	)	)	PUNCT
ejpam-4805	115	63	are	be	AUX
ejpam-4805	115	64	bounded.theorem	bounded.theorem	VERB
ejpam-4805	115	65	2	2	NUM
ejpam-4805	115	66	is	be	AUX
ejpam-4805	115	67	so	so	ADV
ejpam-4805	115	68	verified	verified	ADJ
ejpam-4805	115	69	a.	a.	NOUN
ejpam-4805	115	70	mustafa	mustafa	PROPN
ejpam-4805	115	71	et	et	PROPN
ejpam-4805	115	72	al	al	PROPN
ejpam-4805	115	73	.	.	PUNCT
ejpam-4805	115	74	/	/	SYM
ejpam-4805	115	75	eur	eur	PROPN
ejpam-4805	115	76	.	.	PUNCT
ejpam-4805	116	1	j.	j.	PROPN
ejpam-4805	116	2	pure	pure	PROPN
ejpam-4805	116	3	appl	appl	PROPN
ejpam-4805	116	4	.	.	PROPN
ejpam-4805	116	5	math	math	PROPN
ejpam-4805	116	6	,	,	PUNCT
ejpam-4805	116	7	16	16	NUM
ejpam-4805	116	8	(	(	PUNCT
ejpam-4805	116	9	4	4	NUM
ejpam-4805	116	10	)	)	PUNCT
ejpam-4805	116	11	(	(	PUNCT
ejpam-4805	116	12	2023	2023	NUM
ejpam-4805	116	13	)	)	PUNCT
ejpam-4805	116	14	,	,	PUNCT
ejpam-4805	116	15	2450	2450	NUM
ejpam-4805	116	16	-	-	SYM
ejpam-4805	116	17	2460	2460	NUM
ejpam-4805	116	18	2456	2456	NUM
ejpam-4805	116	19	3.1	3.1	NUM
ejpam-4805	116	20	.	.	PUNCT
ejpam-4805	117	1	epidemic	epidemic	NOUN
ejpam-4805	117	2	equilibrium	equilibrium	NOUN
ejpam-4805	117	3	and	and	CCONJ
ejpam-4805	117	4	the	the	DET
ejpam-4805	117	5	model	model	NOUN
ejpam-4805	117	6	’s	’s	PART
ejpam-4805	117	7	essential	essential	ADJ
ejpam-4805	117	8	reproduction	reproduction	NOUN
ejpam-4805	117	9	number	number	NOUN
ejpam-4805	117	10	when	when	SCONJ
ejpam-4805	117	11	all	all	DET
ejpam-4805	117	12	derivatives	derivative	NOUN
ejpam-4805	117	13	are	be	AUX
ejpam-4805	117	14	set	set	VERB
ejpam-4805	117	15	to	to	ADP
ejpam-4805	117	16	zero	zero	NUM
ejpam-4805	117	17	with	with	ADP
ejpam-4805	117	18	i	i	PROPN
ejpam-4805	117	19	=	=	SYM
ejpam-4805	117	20	0	0	PROPN
ejpam-4805	117	21	,	,	PUNCT
ejpam-4805	117	22	the	the	DET
ejpam-4805	117	23	epidemic	epidemic	NOUN
ejpam-4805	117	24	equilibrium	equilibrium	NOUN
ejpam-4805	117	25	y	y	PROPN
ejpam-4805	117	26	0	0	PROPN
ejpam-4805	117	27	a	a	DET
ejpam-4805	117	28	system	system	NOUN
ejpam-4805	117	29	(	(	PUNCT
ejpam-4805	117	30	1	1	X
ejpam-4805	117	31	)	)	PUNCT
ejpam-4805	117	32	is	be	AUX
ejpam-4805	117	33	attained	attain	VERB
ejpam-4805	117	34	,	,	PUNCT
ejpam-4805	117	35	which	which	PRON
ejpam-4805	117	36	results	result	VERB
ejpam-4805	117	37	in	in	ADP
ejpam-4805	117	38	:	:	PUNCT
ejpam-4805	117	39	y	y	NOUN
ejpam-4805	117	40	0	0	PUNCT
ejpam-4805	118	1	=	=	SYM
ejpam-4805	118	2	ρ	ρ	PROPN
ejpam-4805	118	3	ω	ω	PROPN
ejpam-4805	118	4	+	+	NUM
ejpam-4805	118	5	w′	w′	PROPN
ejpam-4805	118	6	,	,	PUNCT
ejpam-4805	118	7	0	0	NUM
ejpam-4805	118	8	,	,	PUNCT
ejpam-4805	118	9	0	0	NUM
ejpam-4805	118	10	,	,	PUNCT
ejpam-4805	118	11	0	0	NUM
ejpam-4805	118	12	,	,	PUNCT
ejpam-4805	118	13	wρ	wρ	ADP
ejpam-4805	118	14	ω(ω	ω(ω	PROPN
ejpam-4805	118	15	+	+	NOUN
ejpam-4805	118	16	w	w	NOUN
ejpam-4805	118	17	)	)	PUNCT
ejpam-4805	118	18	(	(	PUNCT
ejpam-4805	118	19	17	17	NUM
ejpam-4805	118	20	)	)	PUNCT
ejpam-4805	118	21	the	the	DET
ejpam-4805	118	22	disease	disease	NOUN
ejpam-4805	118	23	-	-	PUNCT
ejpam-4805	118	24	free	free	ADJ
ejpam-4805	118	25	equilibrium	equilibrium	NOUN
ejpam-4805	118	26	y	y	PROPN
ejpam-4805	118	27	0	0	NUM
ejpam-4805	118	28	is	be	AUX
ejpam-4805	118	29	locally	locally	ADV
ejpam-4805	118	30	asymptotically	asymptotically	ADV
ejpam-4805	118	31	stable	stable	ADJ
ejpam-4805	118	32	if	if	SCONJ
ejpam-4805	118	33	r1	r1	PROPN
ejpam-4805	118	34	<	<	X
ejpam-4805	118	35	1	1	NUM
ejpam-4805	118	36	,	,	PUNCT
ejpam-4805	118	37	and	and	CCONJ
ejpam-4805	118	38	unstable	unstable	ADJ
ejpam-4805	118	39	if	if	SCONJ
ejpam-4805	118	40	r1	r1	PROPN
ejpam-4805	118	41	>	>	X
ejpam-4805	118	42	1	1	NUM
ejpam-4805	119	1	[	[	X
ejpam-4805	119	2	1	1	NUM
ejpam-4805	119	3	]	]	PUNCT
ejpam-4805	119	4	.	.	PUNCT
ejpam-4805	120	1	3.2	3.2	NUM
ejpam-4805	120	2	.	.	PUNCT
ejpam-4805	121	1	transmission	transmission	NOUN
ejpam-4805	121	2	rate	rate	NOUN
ejpam-4805	121	3	the	the	DET
ejpam-4805	121	4	model	model	NOUN
ejpam-4805	121	5	calculates	calculate	VERB
ejpam-4805	121	6	the	the	DET
ejpam-4805	121	7	time	time	NOUN
ejpam-4805	121	8	-	-	PUNCT
ejpam-4805	121	9	dependent	dependent	ADJ
ejpam-4805	121	10	transmission	transmission	NOUN
ejpam-4805	121	11	rate	rate	NOUN
ejpam-4805	121	12	before	before	ADP
ejpam-4805	121	13	the	the	DET
ejpam-4805	121	14	last	last	ADJ
ejpam-4805	121	15	date	date	NOUN
ejpam-4805	121	16	of	of	ADP
ejpam-4805	121	17	daily	daily	ADJ
ejpam-4805	121	18	reported	report	VERB
ejpam-4805	121	19	cases	case	NOUN
ejpam-4805	121	20	using	use	VERB
ejpam-4805	121	21	daily	daily	ADV
ejpam-4805	121	22	reported	report	VERB
ejpam-4805	121	23	cases	case	NOUN
ejpam-4805	121	24	data	datum	NOUN
ejpam-4805	121	25	.	.	PUNCT
ejpam-4805	122	1	a	a	DET
ejpam-4805	122	2	rolling	rolling	ADJ
ejpam-4805	122	3	weekly	weekly	ADJ
ejpam-4805	122	4	average	average	NOUN
ejpam-4805	122	5	is	be	AUX
ejpam-4805	122	6	used	use	VERB
ejpam-4805	122	7	to	to	PART
ejpam-4805	122	8	smooth	smooth	VERB
ejpam-4805	122	9	the	the	DET
ejpam-4805	122	10	data[17	data[17	NOUN
ejpam-4805	122	11	]	]	X
ejpam-4805	122	12	.	.	PUNCT
ejpam-4805	123	1	3.3	3.3	NUM
ejpam-4805	123	2	.	.	PUNCT
ejpam-4805	124	1	vaccination	vaccination	NOUN
ejpam-4805	124	2	rate	rate	NOUN
ejpam-4805	124	3	the	the	DET
ejpam-4805	124	4	study	study	NOUN
ejpam-4805	124	5	aims	aim	VERB
ejpam-4805	124	6	to	to	PART
ejpam-4805	124	7	determine	determine	VERB
ejpam-4805	124	8	the	the	DET
ejpam-4805	124	9	effectiveness	effectiveness	NOUN
ejpam-4805	124	10	of	of	ADP
ejpam-4805	124	11	vaccination	vaccination	NOUN
ejpam-4805	124	12	in	in	ADP
ejpam-4805	124	13	removing	remove	VERB
ejpam-4805	124	14	susceptible	susceptible	ADJ
ejpam-4805	124	15	individuals	individual	NOUN
ejpam-4805	124	16	from	from	ADP
ejpam-4805	124	17	infection	infection	NOUN
ejpam-4805	124	18	risk	risk	NOUN
ejpam-4805	124	19	.	.	PUNCT
ejpam-4805	125	1	the	the	DET
ejpam-4805	125	2	daily	daily	ADJ
ejpam-4805	125	3	number	number	NOUN
ejpam-4805	125	4	of	of	ADP
ejpam-4805	125	5	vaccinated	vaccinated	ADJ
ejpam-4805	125	6	individuals	individual	NOUN
ejpam-4805	125	7	and	and	CCONJ
ejpam-4805	125	8	cumulative	cumulative	ADJ
ejpam-4805	125	9	vaccination	vaccination	NOUN
ejpam-4805	125	10	rate	rate	NOUN
ejpam-4805	125	11	are	be	AUX
ejpam-4805	125	12	graphed	graph	VERB
ejpam-4805	125	13	from	from	ADP
ejpam-4805	125	14	december	december	PROPN
ejpam-4805	125	15	2020	2020	NUM
ejpam-4805	125	16	to	to	ADP
ejpam-4805	125	17	june	june	PROPN
ejpam-4805	125	18	2021	2021	NUM
ejpam-4805	125	19	.	.	PUNCT
ejpam-4805	126	1	the	the	DET
ejpam-4805	126	2	efficiency	efficiency	NOUN
ejpam-4805	126	3	of	of	ADP
ejpam-4805	126	4	vaccination	vaccination	NOUN
ejpam-4805	126	5	is	be	AUX
ejpam-4805	126	6	assumed	assume	VERB
ejpam-4805	126	7	to	to	PART
ejpam-4805	126	8	be	be	AUX
ejpam-4805	126	9	98	98	NUM
ejpam-4805	126	10	%	%	NOUN
ejpam-4805	126	11	,	,	PUNCT
ejpam-4805	126	12	in	in	ADP
ejpam-4805	126	13	table	table	NOUN
ejpam-4805	126	14	2	2	NUM
ejpam-4805	126	15	and	and	CCONJ
ejpam-4805	126	16	the	the	DET
ejpam-4805	126	17	removal	removal	NOUN
ejpam-4805	126	18	of	of	ADP
ejpam-4805	126	19	susceptible	susceptible	ADJ
ejpam-4805	126	20	is	be	AUX
ejpam-4805	126	21	the	the	DET
ejpam-4805	126	22	fraction	fraction	NOUN
ejpam-4805	126	23	of	of	ADP
ejpam-4805	126	24	the	the	DET
ejpam-4805	126	25	number	number	NOUN
ejpam-4805	126	26	vaccinated	vaccinate	VERB
ejpam-4805	126	27	,	,	PUNCT
ejpam-4805	126	28	excluding	exclude	VERB
ejpam-4805	126	29	previously	previously	ADV
ejpam-4805	126	30	infected	infect	VERB
ejpam-4805	126	31	individuals	individual	NOUN
ejpam-4805	126	32	.	.	PUNCT
ejpam-4805	127	1	future	future	ADJ
ejpam-4805	127	2	daily	daily	ADJ
ejpam-4805	127	3	vaccination	vaccination	NOUN
ejpam-4805	127	4	rates	rate	NOUN
ejpam-4805	127	5	are	be	AUX
ejpam-4805	127	6	chosen	choose	VERB
ejpam-4805	127	7	for	for	ADP
ejpam-4805	127	8	illustration	illustration	NOUN
ejpam-4805	127	9	due	due	ADP
ejpam-4805	127	10	to	to	ADP
ejpam-4805	127	11	their	their	PRON
ejpam-4805	127	12	uncertain	uncertain	ADJ
ejpam-4805	127	13	values[3	values[3	PROPN
ejpam-4805	127	14	]	]	NOUN
ejpam-4805	127	15	.	.	PUNCT
ejpam-4805	128	1	4	4	X
ejpam-4805	128	2	.	.	NOUN
ejpam-4805	128	3	result	result	NOUN
ejpam-4805	128	4	and	and	CCONJ
ejpam-4805	128	5	discussion	discussion	NOUN
ejpam-4805	128	6	the	the	DET
ejpam-4805	128	7	covid-19	covid-19	PROPN
ejpam-4805	128	8	pandemic	pandemic	NOUN
ejpam-4805	128	9	was	be	AUX
ejpam-4805	128	10	predicted	predict	VERB
ejpam-4805	128	11	using	use	VERB
ejpam-4805	128	12	the	the	DET
ejpam-4805	128	13	suggested	suggest	VERB
ejpam-4805	128	14	modeling	modeling	NOUN
ejpam-4805	128	15	technique	technique	NOUN
ejpam-4805	128	16	.	.	PUNCT
ejpam-4805	129	1	the	the	DET
ejpam-4805	129	2	centers	center	NOUN
ejpam-4805	129	3	for	for	ADP
ejpam-4805	129	4	disease	disease	NOUN
ejpam-4805	129	5	prevention	prevention	NOUN
ejpam-4805	129	6	and	and	CCONJ
ejpam-4805	129	7	control	control	NOUN
ejpam-4805	129	8	have	have	VERB
ejpam-4805	129	9	data	datum	NOUN
ejpam-4805	129	10	accessible	accessible	ADJ
ejpam-4805	129	11	[	[	X
ejpam-4805	129	12	8	8	NUM
ejpam-4805	129	13	]	]	PUNCT
ejpam-4805	129	14	.	.	PUNCT
ejpam-4805	130	1	the	the	DET
ejpam-4805	130	2	number	number	NOUN
ejpam-4805	130	3	of	of	ADP
ejpam-4805	130	4	fatalities	fatality	NOUN
ejpam-4805	130	5	as	as	ADV
ejpam-4805	130	6	well	well	ADV
ejpam-4805	130	7	as	as	ADP
ejpam-4805	130	8	those	those	PRON
ejpam-4805	130	9	retrieved	retrieve	VERB
ejpam-4805	130	10	and	and	CCONJ
ejpam-4805	130	11	verified	verify	VERB
ejpam-4805	130	12	are	be	AUX
ejpam-4805	130	13	among	among	ADP
ejpam-4805	130	14	them	they	PRON
ejpam-4805	130	15	.	.	PUNCT
ejpam-4805	131	1	daily	daily	ADJ
ejpam-4805	131	2	assimilation	assimilation	NOUN
ejpam-4805	131	3	of	of	ADP
ejpam-4805	131	4	the	the	DET
ejpam-4805	131	5	overall	overall	ADJ
ejpam-4805	131	6	mortality	mortality	NOUN
ejpam-4805	131	7	toll	toll	NOUN
ejpam-4805	131	8	,	,	PUNCT
ejpam-4805	131	9	active	active	ADJ
ejpam-4805	131	10	cases	case	NOUN
ejpam-4805	131	11	,	,	PUNCT
ejpam-4805	131	12	and	and	CCONJ
ejpam-4805	131	13	recovered	recovered	ADJ
ejpam-4805	131	14	cases	case	NOUN
ejpam-4805	131	15	took	take	VERB
ejpam-4805	131	16	place	place	NOUN
ejpam-4805	131	17	.	.	PUNCT
ejpam-4805	132	1	4.1	4.1	NUM
ejpam-4805	132	2	.	.	PUNCT
ejpam-4805	133	1	the	the	DET
ejpam-4805	133	2	number	number	NOUN
ejpam-4805	133	3	of	of	ADP
ejpam-4805	133	4	instantaneous	instantaneous	ADJ
ejpam-4805	133	5	reproduction	reproduction	NOUN
ejpam-4805	133	6	on	on	ADP
ejpam-4805	133	7	the	the	DET
ejpam-4805	133	8	fundamental	fundamental	ADJ
ejpam-4805	133	9	reproduction	reproduction	NOUN
ejpam-4805	133	10	number	number	NOUN
ejpam-4805	133	11	,	,	PUNCT
ejpam-4805	133	12	we	we	PRON
ejpam-4805	133	13	see	see	VERB
ejpam-4805	133	14	essentially	essentially	ADV
ejpam-4805	133	15	little	little	ADJ
ejpam-4805	133	16	effect	effect	NOUN
ejpam-4805	133	17	on	on	ADP
ejpam-4805	133	18	the	the	DET
ejpam-4805	133	19	vaccine	vaccine	NOUN
ejpam-4805	133	20	’s	’s	PART
ejpam-4805	133	21	effectiveness	effectiveness	NOUN
ejpam-4805	133	22	.	.	PUNCT
ejpam-4805	134	1	this	this	PRON
ejpam-4805	134	2	results	result	VERB
ejpam-4805	134	3	from	from	ADP
ejpam-4805	134	4	compensating	compensate	VERB
ejpam-4805	134	5	effects	effect	NOUN
ejpam-4805	134	6	between	between	ADP
ejpam-4805	134	7	r(t	r(t	NOUN
ejpam-4805	134	8	)	)	PUNCT
ejpam-4805	134	9	and	and	CCONJ
ejpam-4805	134	10	s(t	s(t	NUM
ejpam-4805	134	11	)	)	PUNCT
ejpam-4805	134	12	,	,	PUNCT
ejpam-4805	134	13	which	which	PRON
ejpam-4805	134	14	are	be	AUX
ejpam-4805	134	15	assessed	assess	VERB
ejpam-4805	134	16	to	to	PART
ejpam-4805	134	17	change	change	VERB
ejpam-4805	134	18	the	the	DET
ejpam-4805	134	19	fixed	fix	VERB
ejpam-4805	134	20	number	number	NOUN
ejpam-4805	134	21	of	of	ADP
ejpam-4805	134	22	cumulative	cumulative	ADJ
ejpam-4805	134	23	reported	report	VERB
ejpam-4805	134	24	cases	case	NOUN
ejpam-4805	134	25	.	.	PUNCT
ejpam-4805	135	1	we	we	PRON
ejpam-4805	135	2	hardly	hardly	ADV
ejpam-4805	135	3	notice	notice	VERB
ejpam-4805	135	4	any	any	DET
ejpam-4805	135	5	change	change	NOUN
ejpam-4805	135	6	.	.	PUNCT
ejpam-4805	136	1	it	it	PRON
ejpam-4805	136	2	indicates	indicate	VERB
ejpam-4805	136	3	that	that	SCONJ
ejpam-4805	136	4	the	the	DET
ejpam-4805	136	5	cumulative	cumulative	ADJ
ejpam-4805	136	6	infection	infection	NOUN
ejpam-4805	136	7	rate	rate	NOUN
ejpam-4805	136	8	is	be	AUX
ejpam-4805	136	9	so	so	ADV
ejpam-4805	136	10	low	low	ADJ
ejpam-4805	136	11	relative	relative	ADJ
ejpam-4805	136	12	to	to	ADP
ejpam-4805	136	13	the	the	DET
ejpam-4805	136	14	size	size	NOUN
ejpam-4805	136	15	of	of	ADP
ejpam-4805	136	16	the	the	DET
ejpam-4805	136	17	whole	whole	ADJ
ejpam-4805	136	18	population	population	NOUN
ejpam-4805	136	19	that	that	PRON
ejpam-4805	136	20	the	the	DET
ejpam-4805	136	21	r(t	r(t	NOUN
ejpam-4805	136	22	)	)	PUNCT
ejpam-4805	136	23	remains	remain	VERB
ejpam-4805	136	24	essentially	essentially	ADV
ejpam-4805	136	25	unchanged	unchanged	ADJ
ejpam-4805	136	26	from	from	ADP
ejpam-4805	136	27	r1(t)[22	r1(t)[22	PROPN
ejpam-4805	136	28	]	]	X
ejpam-4805	136	29	.this	.this	PRON
ejpam-4805	136	30	indicates	indicate	VERB
ejpam-4805	136	31	that	that	SCONJ
ejpam-4805	136	32	the	the	DET
ejpam-4805	136	33	total	total	ADJ
ejpam-4805	136	34	number	number	NOUN
ejpam-4805	136	35	of	of	ADP
ejpam-4805	136	36	infected	infected	ADJ
ejpam-4805	136	37	people	people	NOUN
ejpam-4805	136	38	is	be	AUX
ejpam-4805	136	39	insufficient	insufficient	ADJ
ejpam-4805	136	40	to	to	PART
ejpam-4805	136	41	significantly	significantly	ADV
ejpam-4805	136	42	affect	affect	VERB
ejpam-4805	136	43	the	the	DET
ejpam-4805	136	44	rate	rate	NOUN
ejpam-4805	136	45	of	of	ADP
ejpam-4805	136	46	basic	basic	ADJ
ejpam-4805	136	47	reproduction	reproduction	NOUN
ejpam-4805	136	48	.	.	PUNCT
ejpam-4805	137	1	to	to	PART
ejpam-4805	137	2	put	put	VERB
ejpam-4805	137	3	it	it	PRON
ejpam-4805	137	4	another	another	DET
ejpam-4805	137	5	way	way	NOUN
ejpam-4805	137	6	,	,	PUNCT
ejpam-4805	137	7	the	the	DET
ejpam-4805	137	8	changes	change	NOUN
ejpam-4805	137	9	in	in	ADP
ejpam-4805	137	10	the	the	DET
ejpam-4805	137	11	population	population	NOUN
ejpam-4805	137	12	of	of	ADP
ejpam-4805	137	13	vulnerable	vulnerable	ADJ
ejpam-4805	137	14	individuals	individual	NOUN
ejpam-4805	137	15	are	be	AUX
ejpam-4805	137	16	not	not	PART
ejpam-4805	137	17	big	big	ADJ
ejpam-4805	137	18	enough	enough	ADV
ejpam-4805	137	19	to	to	PART
ejpam-4805	137	20	be	be	AUX
ejpam-4805	137	21	seen	see	VERB
ejpam-4805	137	22	immediately	immediately	ADV
ejpam-4805	137	23	.	.	PUNCT
ejpam-4805	138	1	the	the	DET
ejpam-4805	138	2	r1	r1	PROPN
ejpam-4805	138	3	is	be	AUX
ejpam-4805	138	4	shown	show	VERB
ejpam-4805	138	5	by	by	ADP
ejpam-4805	138	6	the	the	DET
ejpam-4805	138	7	blue	blue	ADJ
ejpam-4805	138	8	curve	curve	NOUN
ejpam-4805	138	9	r(t	r(t	NOUN
ejpam-4805	138	10	)	)	PUNCT
ejpam-4805	138	11	.	.	PUNCT
ejpam-4805	139	1	given	give	VERB
ejpam-4805	139	2	that	that	SCONJ
ejpam-4805	139	3	the	the	DET
ejpam-4805	139	4	vaccine	vaccine	NOUN
ejpam-4805	139	5	is	be	AUX
ejpam-4805	139	6	entirely	entirely	ADV
ejpam-4805	139	7	effective	effective	ADJ
ejpam-4805	139	8	,	,	PUNCT
ejpam-4805	139	9	a.	a.	PROPN
ejpam-4805	139	10	mustafa	mustafa	PROPN
ejpam-4805	139	11	et	et	PROPN
ejpam-4805	139	12	al	al	PROPN
ejpam-4805	139	13	.	.	PUNCT
ejpam-4805	139	14	/	/	SYM
ejpam-4805	139	15	eur	eur	PROPN
ejpam-4805	139	16	.	.	PUNCT
ejpam-4805	140	1	j.	j.	PROPN
ejpam-4805	140	2	pure	pure	PROPN
ejpam-4805	140	3	appl	appl	PROPN
ejpam-4805	140	4	.	.	PROPN
ejpam-4805	140	5	math	math	PROPN
ejpam-4805	140	6	,	,	PUNCT
ejpam-4805	140	7	16	16	NUM
ejpam-4805	140	8	(	(	PUNCT
ejpam-4805	140	9	4	4	NUM
ejpam-4805	140	10	)	)	PUNCT
ejpam-4805	140	11	(	(	PUNCT
ejpam-4805	140	12	2023	2023	NUM
ejpam-4805	140	13	)	)	PUNCT
ejpam-4805	140	14	,	,	PUNCT
ejpam-4805	140	15	2450	2450	NUM
ejpam-4805	140	16	-	-	SYM
ejpam-4805	140	17	2460	2460	NUM
ejpam-4805	140	18	2457	2457	NUM
ejpam-4805	140	19	the	the	DET
ejpam-4805	140	20	instantaneous	instantaneous	ADJ
ejpam-4805	140	21	reproduction	reproduction	NOUN
ejpam-4805	140	22	number	number	NOUN
ejpam-4805	140	23	should	should	AUX
ejpam-4805	140	24	be	be	AUX
ejpam-4805	140	25	understood	understand	VERB
ejpam-4805	140	26	as	as	ADP
ejpam-4805	140	27	the	the	DET
ejpam-4805	140	28	instantaneous	instantaneous	ADJ
ejpam-4805	140	29	reproduction	reproduction	NOUN
ejpam-4805	140	30	number	number	NOUN
ejpam-4805	140	31	in	in	ADP
ejpam-4805	140	32	the	the	DET
ejpam-4805	140	33	absence	absence	NOUN
ejpam-4805	140	34	of	of	ADP
ejpam-4805	140	35	immunization	immunization	NOUN
ejpam-4805	140	36	.	.	PUNCT
ejpam-4805	141	1	[	[	X
ejpam-4805	141	2	2	2	X
ejpam-4805	141	3	]	]	PUNCT
ejpam-4805	141	4	the	the	DET
ejpam-4805	141	5	same	same	ADJ
ejpam-4805	141	6	explanation	explanation	NOUN
ejpam-4805	141	7	applies	apply	VERB
ejpam-4805	141	8	to	to	ADP
ejpam-4805	141	9	ε	ε	PROPN
ejpam-4805	141	10	=	=	SYM
ejpam-4805	141	11	0.75	0.75	NUM
ejpam-4805	141	12	,	,	PUNCT
ejpam-4805	141	13	0.5	0.5	NUM
ejpam-4805	141	14	,	,	PUNCT
ejpam-4805	141	15	0.25	0.25	NUM
ejpam-4805	141	16	,	,	PUNCT
ejpam-4805	141	17	and	and	CCONJ
ejpam-4805	141	18	0	0	X
ejpam-4805	141	19	.	.	PUNCT
ejpam-4805	142	1	this	this	PRON
ejpam-4805	142	2	indicates	indicate	VERB
ejpam-4805	142	3	that	that	SCONJ
ejpam-4805	142	4	vaccination	vaccination	NOUN
ejpam-4805	142	5	significantly	significantly	ADV
ejpam-4805	142	6	affects	affect	VERB
ejpam-4805	142	7	the	the	DET
ejpam-4805	142	8	dynamics	dynamic	NOUN
ejpam-4805	142	9	of	of	ADP
ejpam-4805	142	10	the	the	DET
ejpam-4805	142	11	epidemic	epidemic	NOUN
ejpam-4805	142	12	.	.	PUNCT
ejpam-4805	143	1	the	the	DET
ejpam-4805	143	2	effectiveness	effectiveness	NOUN
ejpam-4805	143	3	of	of	ADP
ejpam-4805	143	4	the	the	DET
ejpam-4805	143	5	vaccination	vaccination	NOUN
ejpam-4805	143	6	is	be	AUX
ejpam-4805	143	7	a	a	DET
ejpam-4805	143	8	key	key	ADJ
ejpam-4805	143	9	factor	factor	NOUN
ejpam-4805	143	10	in	in	ADP
ejpam-4805	143	11	this	this	DET
ejpam-4805	143	12	influence	influence	NOUN
ejpam-4805	143	13	.	.	PUNCT
ejpam-4805	144	1	we	we	PRON
ejpam-4805	144	2	can	can	AUX
ejpam-4805	144	3	see	see	VERB
ejpam-4805	144	4	that	that	SCONJ
ejpam-4805	144	5	without	without	ADP
ejpam-4805	144	6	vaccination	vaccination	NOUN
ejpam-4805	144	7	.	.	PUNCT
ejpam-4805	145	1	the	the	DET
ejpam-4805	145	2	final	final	ADJ
ejpam-4805	145	3	peak	peak	NOUN
ejpam-4805	145	4	of	of	ADP
ejpam-4805	145	5	the	the	DET
ejpam-4805	145	6	red	red	ADJ
ejpam-4805	145	7	curve	curve	NOUN
ejpam-4805	145	8	,	,	PUNCT
ejpam-4805	145	9	which	which	PRON
ejpam-4805	145	10	represents	represent	VERB
ejpam-4805	145	11	r1(t	r1(t	NOUN
ejpam-4805	145	12	)	)	PUNCT
ejpam-4805	145	13	about	about	ADP
ejpam-4805	145	14	theorem	theorem	ADJ
ejpam-4805	145	15	2	2	NUM
ejpam-4805	145	16	,	,	PUNCT
ejpam-4805	145	17	is	be	AUX
ejpam-4805	145	18	present	present	ADJ
ejpam-4805	145	19	for	for	ADP
ejpam-4805	145	20	ε	ε	PROPN
ejpam-4805	145	21	=	=	SYM
ejpam-4805	145	22	0.75	0.75	NUM
ejpam-4805	146	1	[	[	X
ejpam-4805	146	2	9	9	NUM
ejpam-4805	146	3	]	]	SYM
ejpam-4805	146	4	.	.	PUNCT
ejpam-4805	147	1	4.2	4.2	NUM
ejpam-4805	147	2	.	.	PUNCT
ejpam-4805	147	3	impact	impact	NOUN
ejpam-4805	147	4	of	of	ADP
ejpam-4805	147	5	vaccination	vaccination	NOUN
ejpam-4805	147	6	began	begin	VERB
ejpam-4805	147	7	a	a	DET
ejpam-4805	147	8	three	three	NUM
ejpam-4805	147	9	-	-	PUNCT
ejpam-4805	147	10	phase	phase	NOUN
ejpam-4805	147	11	covid-19	covid-19	PROPN
ejpam-4805	147	12	immunization	immunization	NOUN
ejpam-4805	147	13	campaign	campaign	NOUN
ejpam-4805	147	14	on	on	ADP
ejpam-4805	147	15	july	july	PROPN
ejpam-4805	147	16	17	17	NUM
ejpam-4805	147	17	,	,	PUNCT
ejpam-4805	147	18	2022	2022	NUM
ejpam-4805	147	19	,	,	PUNCT
ejpam-4805	147	20	to	to	ADP
ejpam-4805	147	21	december	december	PROPN
ejpam-4805	147	22	20	20	NUM
ejpam-4805	147	23	,	,	PUNCT
ejpam-4805	147	24	2022	2022	NUM
ejpam-4805	147	25	,	,	PUNCT
ejpam-4805	147	26	making	make	VERB
ejpam-4805	147	27	it	it	PRON
ejpam-4805	147	28	the	the	DET
ejpam-4805	147	29	first	first	ADJ
ejpam-4805	147	30	arab	arab	ADJ
ejpam-4805	147	31	nation	nation	NOUN
ejpam-4805	147	32	to	to	PART
ejpam-4805	147	33	introduce	introduce	VERB
ejpam-4805	147	34	the	the	DET
ejpam-4805	147	35	pfizer	pfizer	NOUN
ejpam-4805	147	36	-	-	PUNCT
ejpam-4805	147	37	biontech	biontech	NOUN
ejpam-4805	147	38	vaccine	vaccine	NOUN
ejpam-4805	147	39	.	.	PUNCT
ejpam-4805	148	1	[	[	X
ejpam-4805	148	2	23	23	NUM
ejpam-4805	148	3	]	]	PUNCT
ejpam-4805	148	4	the	the	DET
ejpam-4805	148	5	first	first	ADJ
ejpam-4805	148	6	phase	phase	NOUN
ejpam-4805	148	7	focuses	focus	VERB
ejpam-4805	148	8	on	on	ADP
ejpam-4805	148	9	those	those	DET
ejpam-4805	148	10	over	over	ADP
ejpam-4805	148	11	65	65	NUM
ejpam-4805	148	12	and	and	CCONJ
ejpam-4805	148	13	those	those	PRON
ejpam-4805	148	14	who	who	PRON
ejpam-4805	148	15	are	be	AUX
ejpam-4805	148	16	most	most	ADV
ejpam-4805	148	17	at	at	ADP
ejpam-4805	148	18	risk	risk	NOUN
ejpam-4805	148	19	for	for	ADP
ejpam-4805	148	20	the	the	DET
ejpam-4805	148	21	disease	disease	NOUN
ejpam-4805	148	22	.	.	PUNCT
ejpam-4805	149	1	people	people	NOUN
ejpam-4805	149	2	over	over	ADP
ejpam-4805	149	3	50	50	NUM
ejpam-4805	149	4	and	and	CCONJ
ejpam-4805	149	5	those	those	PRON
ejpam-4805	149	6	with	with	ADP
ejpam-4805	149	7	particular	particular	ADJ
ejpam-4805	149	8	chronic	chronic	ADJ
ejpam-4805	149	9	conditions	condition	NOUN
ejpam-4805	149	10	,	,	PUNCT
ejpam-4805	149	11	such	such	ADJ
ejpam-4805	149	12	as	as	ADP
ejpam-4805	149	13	diabetes	diabetes	NOUN
ejpam-4805	149	14	and	and	CCONJ
ejpam-4805	149	15	asthma	asthma	NOUN
ejpam-4805	149	16	,	,	PUNCT
ejpam-4805	149	17	will	will	AUX
ejpam-4805	149	18	be	be	AUX
ejpam-4805	149	19	included	include	VERB
ejpam-4805	149	20	in	in	ADP
ejpam-4805	149	21	the	the	DET
ejpam-4805	149	22	second	second	ADJ
ejpam-4805	149	23	phase	phase	NOUN
ejpam-4805	149	24	.	.	PUNCT
ejpam-4805	150	1	in	in	ADP
ejpam-4805	150	2	the	the	DET
ejpam-4805	150	3	third	third	ADJ
ejpam-4805	150	4	step	step	NOUN
ejpam-4805	150	5	,	,	PUNCT
ejpam-4805	150	6	the	the	DET
ejpam-4805	150	7	vaccine	vaccine	NOUN
ejpam-4805	150	8	will	will	AUX
ejpam-4805	150	9	be	be	AUX
ejpam-4805	150	10	administered	administer	VERB
ejpam-4805	150	11	to	to	ADP
ejpam-4805	150	12	the	the	DET
ejpam-4805	150	13	remaining	remain	VERB
ejpam-4805	150	14	population	population	NOUN
ejpam-4805	150	15	.	.	PUNCT
ejpam-4805	151	1	the	the	DET
ejpam-4805	151	2	ministry	ministry	NOUN
ejpam-4805	151	3	has	have	AUX
ejpam-4805	151	4	,	,	PUNCT
ejpam-4805	151	5	however	however	ADV
ejpam-4805	151	6	,	,	PUNCT
ejpam-4805	151	7	identified	identify	VERB
ejpam-4805	151	8	people	people	NOUN
ejpam-4805	151	9	who	who	PRON
ejpam-4805	151	10	should	should	AUX
ejpam-4805	151	11	n’t	not	PART
ejpam-4805	151	12	receive	receive	VERB
ejpam-4805	151	13	the	the	DET
ejpam-4805	151	14	vaccination	vaccination	NOUN
ejpam-4805	151	15	.	.	PUNCT
ejpam-4805	152	1	women	woman	NOUN
ejpam-4805	152	2	who	who	PRON
ejpam-4805	152	3	are	be	AUX
ejpam-4805	152	4	pregnant	pregnant	ADJ
ejpam-4805	152	5	or	or	CCONJ
ejpam-4805	152	6	nursing	nursing	NOUN
ejpam-4805	152	7	,	,	PUNCT
ejpam-4805	152	8	those	those	PRON
ejpam-4805	152	9	who	who	PRON
ejpam-4805	152	10	want	want	VERB
ejpam-4805	152	11	to	to	PART
ejpam-4805	152	12	get	get	VERB
ejpam-4805	152	13	pregnant	pregnant	ADJ
ejpam-4805	152	14	within	within	ADP
ejpam-4805	152	15	the	the	DET
ejpam-4805	152	16	next	next	ADJ
ejpam-4805	152	17	two	two	NUM
ejpam-4805	152	18	months	month	NOUN
ejpam-4805	152	19	,	,	PUNCT
ejpam-4805	152	20	those	those	PRON
ejpam-4805	152	21	who	who	PRON
ejpam-4805	152	22	experience	experience	VERB
ejpam-4805	152	23	severe	severe	ADJ
ejpam-4805	152	24	allergic	allergic	ADJ
ejpam-4805	152	25	reactions	reaction	NOUN
ejpam-4805	152	26	,	,	PUNCT
ejpam-4805	152	27	and	and	CCONJ
ejpam-4805	152	28	those	those	PRON
ejpam-4805	152	29	who	who	PRON
ejpam-4805	152	30	have	have	AUX
ejpam-4805	152	31	been	be	AUX
ejpam-4805	152	32	exposed	expose	VERB
ejpam-4805	152	33	to	to	ADP
ejpam-4805	152	34	the	the	DET
ejpam-4805	152	35	virus	virus	NOUN
ejpam-4805	152	36	within	within	ADP
ejpam-4805	152	37	the	the	DET
ejpam-4805	152	38	last	last	ADJ
ejpam-4805	152	39	90	90	NUM
ejpam-4805	152	40	days	day	NOUN
ejpam-4805	152	41	are	be	AUX
ejpam-4805	152	42	among	among	ADP
ejpam-4805	152	43	them[19	them[19	NOUN
ejpam-4805	152	44	]	]	X
ejpam-4805	152	45	.	.	PUNCT
ejpam-4805	153	1	4.3	4.3	NUM
ejpam-4805	153	2	.	.	PUNCT
ejpam-4805	154	1	future	future	ADJ
ejpam-4805	154	2	work	work	NOUN
ejpam-4805	154	3	and	and	CCONJ
ejpam-4805	154	4	modeling	model	VERB
ejpam-4805	154	5	expansions	expansion	NOUN
ejpam-4805	154	6	.	.	PUNCT
ejpam-4805	154	7	.	.	PUNCT
ejpam-4805	155	1	despite	despite	SCONJ
ejpam-4805	155	2	these	these	DET
ejpam-4805	155	3	flaws	flaw	NOUN
ejpam-4805	155	4	,	,	PUNCT
ejpam-4805	155	5	the	the	DET
ejpam-4805	155	6	model	model	NOUN
ejpam-4805	155	7	effectively	effectively	ADV
ejpam-4805	155	8	illustrates	illustrate	VERB
ejpam-4805	155	9	how	how	SCONJ
ejpam-4805	155	10	vaccination	vaccination	NOUN
ejpam-4805	155	11	policies	policy	NOUN
ejpam-4805	155	12	affect	affect	VERB
ejpam-4805	155	13	epidemic	epidemic	NOUN
ejpam-4805	155	14	dynamics	dynamic	NOUN
ejpam-4805	155	15	,	,	PUNCT
ejpam-4805	155	16	in	in	ADP
ejpam-4805	155	17	part	part	NOUN
ejpam-4805	155	18	because	because	SCONJ
ejpam-4805	155	19	precise	precise	ADJ
ejpam-4805	155	20	formulas	formula	NOUN
ejpam-4805	155	21	allow	allow	VERB
ejpam-4805	155	22	for	for	ADP
ejpam-4805	155	23	the	the	DET
ejpam-4805	155	24	computation	computation	NOUN
ejpam-4805	155	25	of	of	ADP
ejpam-4805	155	26	crucial	crucial	ADJ
ejpam-4805	155	27	variables	variable	NOUN
ejpam-4805	155	28	like	like	ADP
ejpam-4805	155	29	transmission	transmission	NOUN
ejpam-4805	155	30	rate	rate	NOUN
ejpam-4805	155	31	.	.	PUNCT
ejpam-4805	156	1	in	in	ADP
ejpam-4805	156	2	addition	addition	NOUN
ejpam-4805	156	3	,	,	PUNCT
ejpam-4805	156	4	the	the	DET
ejpam-4805	156	5	model	model	NOUN
ejpam-4805	156	6	permits	permit	VERB
ejpam-4805	156	7	the	the	DET
ejpam-4805	156	8	incorporation	incorporation	NOUN
ejpam-4805	156	9	of	of	ADP
ejpam-4805	156	10	other	other	ADJ
ejpam-4805	156	11	components	component	NOUN
ejpam-4805	156	12	,	,	PUNCT
ejpam-4805	156	13	including	include	VERB
ejpam-4805	156	14	age	age	NOUN
ejpam-4805	156	15	,	,	PUNCT
ejpam-4805	156	16	immunization	immunization	NOUN
ejpam-4805	156	17	loss	loss	NOUN
ejpam-4805	156	18	,	,	PUNCT
ejpam-4805	156	19	and	and	CCONJ
ejpam-4805	156	20	cross	cross	NOUN
ejpam-4805	156	21	-	-	NOUN
ejpam-4805	156	22	immunization	immunization	NOUN
ejpam-4805	156	23	,	,	PUNCT
ejpam-4805	156	24	when	when	SCONJ
ejpam-4805	156	25	supported	support	VERB
ejpam-4805	156	26	by	by	ADP
ejpam-4805	156	27	actual	actual	ADJ
ejpam-4805	156	28	data	datum	NOUN
ejpam-4805	156	29	.	.	PUNCT
ejpam-4805	157	1	the	the	DET
ejpam-4805	157	2	efficiency	efficiency	NOUN
ejpam-4805	157	3	of	of	ADP
ejpam-4805	157	4	the	the	DET
ejpam-4805	157	5	immunization	immunization	NOUN
ejpam-4805	157	6	strategy	strategy	NOUN
ejpam-4805	157	7	is	be	AUX
ejpam-4805	157	8	weighed	weigh	VERB
ejpam-4805	157	9	down	down	ADP
ejpam-4805	157	10	by	by	ADP
ejpam-4805	157	11	this	this	DET
ejpam-4805	157	12	most	most	ADV
ejpam-4805	157	13	recent	recent	ADJ
ejpam-4805	157	14	phenomenon	phenomenon	NOUN
ejpam-4805	157	15	,	,	PUNCT
ejpam-4805	157	16	which	which	PRON
ejpam-4805	157	17	merits	merit	VERB
ejpam-4805	157	18	more	more	ADJ
ejpam-4805	157	19	study	study	NOUN
ejpam-4805	157	20	.	.	PUNCT
ejpam-4805	158	1	the	the	DET
ejpam-4805	158	2	vaccination	vaccination	NOUN
ejpam-4805	158	3	policy	policy	NOUN
ejpam-4805	158	4	may	may	AUX
ejpam-4805	158	5	be	be	AUX
ejpam-4805	158	6	changed	change	VERB
ejpam-4805	158	7	in	in	ADP
ejpam-4805	158	8	light	light	NOUN
ejpam-4805	158	9	of	of	ADP
ejpam-4805	158	10	the	the	DET
ejpam-4805	158	11	response	response	NOUN
ejpam-4805	158	12	via	via	ADP
ejpam-4805	158	13	cross	cross	NOUN
ejpam-4805	158	14	-	-	NOUN
ejpam-4805	158	15	immunity	immunity	NOUN
ejpam-4805	158	16	against	against	ADP
ejpam-4805	158	17	epitopes	epitope	NOUN
ejpam-4805	158	18	shared	share	VERB
ejpam-4805	158	19	by	by	ADP
ejpam-4805	158	20	several	several	ADJ
ejpam-4805	158	21	corona	corona	NOUN
ejpam-4805	158	22	viruses	virus	NOUN
ejpam-4805	158	23	.	.	PUNCT
ejpam-4805	159	1	vaccination	vaccination	NOUN
ejpam-4805	159	2	provides	provide	VERB
ejpam-4805	159	3	new	new	ADJ
ejpam-4805	159	4	immunity	immunity	NOUN
ejpam-4805	159	5	in	in	ADP
ejpam-4805	159	6	addition	addition	NOUN
ejpam-4805	159	7	to	to	ADP
ejpam-4805	159	8	any	any	DET
ejpam-4805	159	9	potential	potential	ADJ
ejpam-4805	159	10	pre	pre	ADJ
ejpam-4805	159	11	-	-	ADJ
ejpam-4805	159	12	existing	exist	VERB
ejpam-4805	159	13	cross	cross	NOUN
ejpam-4805	159	14	-	-	NOUN
ejpam-4805	159	15	immunity	immunity	NOUN
ejpam-4805	159	16	[	[	X
ejpam-4805	159	17	19	19	NUM
ejpam-4805	159	18	]	]	PUNCT
ejpam-4805	159	19	.	.	PUNCT
ejpam-4805	160	1	for	for	ADP
ejpam-4805	160	2	instance	instance	NOUN
ejpam-4805	160	3	,	,	PUNCT
ejpam-4805	160	4	when	when	SCONJ
ejpam-4805	160	5	age	age	NOUN
ejpam-4805	160	6	groups	group	NOUN
ejpam-4805	160	7	are	be	AUX
ejpam-4805	160	8	taken	take	VERB
ejpam-4805	160	9	into	into	ADP
ejpam-4805	160	10	account	account	NOUN
ejpam-4805	160	11	,	,	PUNCT
ejpam-4805	160	12	young	young	ADJ
ejpam-4805	160	13	people	people	NOUN
ejpam-4805	160	14	are	be	AUX
ejpam-4805	160	15	those	those	PRON
ejpam-4805	160	16	whose	whose	DET
ejpam-4805	160	17	cross	cross	NOUN
ejpam-4805	160	18	-	-	NOUN
ejpam-4805	160	19	immunity	immunity	NOUN
ejpam-4805	160	20	is	be	AUX
ejpam-4805	160	21	still	still	ADV
ejpam-4805	160	22	active	active	ADJ
ejpam-4805	160	23	.	.	PUNCT
ejpam-4805	161	1	5	5	X
ejpam-4805	161	2	.	.	X
ejpam-4805	161	3	conclusions	conclusion	NOUN
ejpam-4805	161	4	the	the	DET
ejpam-4805	161	5	study	study	NOUN
ejpam-4805	161	6	presents	present	VERB
ejpam-4805	161	7	an	an	DET
ejpam-4805	161	8	enhanced	enhanced	ADJ
ejpam-4805	161	9	seir	seir	NOUN
ejpam-4805	161	10	model	model	NOUN
ejpam-4805	161	11	for	for	ADP
ejpam-4805	161	12	including	include	VERB
ejpam-4805	161	13	vaccines	vaccine	NOUN
ejpam-4805	161	14	in	in	ADP
ejpam-4805	161	15	epidemic	epidemic	NOUN
ejpam-4805	161	16	models	model	NOUN
ejpam-4805	161	17	,	,	PUNCT
ejpam-4805	161	18	considering	consider	VERB
ejpam-4805	161	19	seven	seven	NUM
ejpam-4805	161	20	infection	infection	NOUN
ejpam-4805	161	21	phases	phase	NOUN
ejpam-4805	161	22	and	and	CCONJ
ejpam-4805	161	23	vaccination	vaccination	NOUN
ejpam-4805	161	24	.	.	PUNCT
ejpam-4805	162	1	the	the	DET
ejpam-4805	162	2	model	model	NOUN
ejpam-4805	162	3	demonstrates	demonstrate	VERB
ejpam-4805	162	4	nonnegativity	nonnegativity	NOUN
ejpam-4805	162	5	,	,	PUNCT
ejpam-4805	162	6	boundedness	boundedness	NOUN
ejpam-4805	162	7	,	,	PUNCT
ejpam-4805	162	8	epidemic	epidemic	NOUN
ejpam-4805	162	9	equilibrium	equilibrium	NOUN
ejpam-4805	162	10	,	,	PUNCT
ejpam-4805	162	11	existence	existence	NOUN
ejpam-4805	162	12	,	,	PUNCT
ejpam-4805	162	13	distinctiveness	distinctiveness	NOUN
ejpam-4805	162	14	of	of	ADP
ejpam-4805	162	15	endemic	endemic	ADJ
ejpam-4805	162	16	equilibrium	equilibrium	NOUN
ejpam-4805	162	17	,	,	PUNCT
ejpam-4805	162	18	and	and	CCONJ
ejpam-4805	162	19	fundamental	fundamental	ADJ
ejpam-4805	162	20	reproduction	reproduction	NOUN
ejpam-4805	162	21	number	number	NOUN
ejpam-4805	162	22	.	.	PUNCT
ejpam-4805	163	1	it	it	PRON
ejpam-4805	163	2	incorporates	incorporate	VERB
ejpam-4805	163	3	covid-19	covid-19	PROPN
ejpam-4805	163	4	dynamics	dynamic	NOUN
ejpam-4805	163	5	,	,	PUNCT
ejpam-4805	163	6	transmission	transmission	NOUN
ejpam-4805	163	7	,	,	PUNCT
ejpam-4805	163	8	reported	report	VERB
ejpam-4805	163	9	and	and	CCONJ
ejpam-4805	163	10	unreported	unreported	ADJ
ejpam-4805	163	11	cases	case	NOUN
ejpam-4805	163	12	,	,	PUNCT
ejpam-4805	163	13	and	and	CCONJ
ejpam-4805	163	14	social	social	ADJ
ejpam-4805	163	15	distancing	distancing	NOUN
ejpam-4805	163	16	measures	measure	NOUN
ejpam-4805	163	17	.	.	PUNCT
ejpam-4805	164	1	the	the	DET
ejpam-4805	164	2	model	model	NOUN
ejpam-4805	164	3	predicts	predict	VERB
ejpam-4805	164	4	vaccination	vaccination	NOUN
ejpam-4805	164	5	effectiveness	effectiveness	NOUN
ejpam-4805	164	6	in	in	ADP
ejpam-4805	164	7	the	the	DET
ejpam-4805	164	8	us	us	PROPN
ejpam-4805	164	9	,	,	PUNCT
ejpam-4805	164	10	with	with	ADP
ejpam-4805	164	11	varying	vary	VERB
ejpam-4805	164	12	vaccination	vaccination	NOUN
ejpam-4805	164	13	rates	rate	NOUN
ejpam-4805	164	14	due	due	ADJ
ejpam-4805	164	15	to	to	ADP
ejpam-4805	164	16	hesitancy	hesitancy	NOUN
ejpam-4805	164	17	and	and	CCONJ
ejpam-4805	164	18	opposition	opposition	NOUN
ejpam-4805	164	19	.	.	PUNCT
ejpam-4805	165	1	future	future	ADJ
ejpam-4805	165	2	research	research	NOUN
ejpam-4805	165	3	will	will	AUX
ejpam-4805	165	4	explore	explore	VERB
ejpam-4805	165	5	other	other	ADJ
ejpam-4805	165	6	countries	country	NOUN
ejpam-4805	165	7	and	and	CCONJ
ejpam-4805	165	8	locations	location	NOUN
ejpam-4805	165	9	.	.	PUNCT
ejpam-4805	166	1	references	reference	NOUN
ejpam-4805	166	2	2458	2458	NUM
ejpam-4805	166	3	table	table	NOUN
ejpam-4805	166	4	1	1	NUM
ejpam-4805	166	5	:	:	PUNCT
ejpam-4805	166	6	descriptions	description	NOUN
ejpam-4805	166	7	of	of	ADP
ejpam-4805	166	8	parameters	parameter	NOUN
ejpam-4805	166	9	in	in	ADP
ejpam-4805	166	10	system(1	system(1	NOUN
ejpam-4805	166	11	)	)	PUNCT
ejpam-4805	166	12	.	.	PUNCT
ejpam-4805	167	1	parameter	parameter	NOUN
ejpam-4805	167	2	description	description	NOUN
ejpam-4805	167	3	value	value	NOUN
ejpam-4805	167	4	ω	ω	NUM
ejpam-4805	167	5	unreported	unreported	ADJ
ejpam-4805	167	6	symptomatic	symptomatic	ADJ
ejpam-4805	167	7	infectious	infectious	ADJ
ejpam-4805	167	8	cases	case	NOUN
ejpam-4805	167	9	that	that	PRON
ejpam-4805	167	10	can	can	AUX
ejpam-4805	167	11	spread	spread	VERB
ejpam-4805	167	12	the	the	DET
ejpam-4805	167	13	disease	disease	NOUN
ejpam-4805	167	14	[	[	X
ejpam-4805	167	15	25	25	NUM
ejpam-4805	167	16	]	]	SYM
ejpam-4805	167	17	1	1	NUM
ejpam-4805	167	18	β	β	NOUN
ejpam-4805	167	19	average	average	ADJ
ejpam-4805	167	20	time	time	NOUN
ejpam-4805	167	21	expended	expend	VERB
ejpam-4805	167	22	having	having	AUX
ejpam-4805	167	23	exposed	expose	VERB
ejpam-4805	167	24	estimated	estimate	VERB
ejpam-4805	167	25	1	1	NUM
ejpam-4805	167	26	σ	σ	NOUN
ejpam-4805	167	27	the	the	DET
ejpam-4805	167	28	average	average	ADJ
ejpam-4805	167	29	duration	duration	NOUN
ejpam-4805	167	30	of	of	ADP
ejpam-4805	167	31	the	the	DET
ejpam-4805	167	32	infectious	infectious	ADJ
ejpam-4805	167	33	period	period	NOUN
ejpam-4805	167	34	without	without	ADP
ejpam-4805	167	35	indications	indication	NOUN
ejpam-4805	167	36	estimated	estimate	VERB
ejpam-4805	167	37	1	1	NUM
ejpam-4805	167	38	γ	γ	NOUN
ejpam-4805	167	39	frequency	frequency	NOUN
ejpam-4805	167	40	of	of	ADP
ejpam-4805	167	41	the	the	DET
ejpam-4805	167	42	symptomatic	symptomatic	ADJ
ejpam-4805	167	43	infectious	infectious	ADJ
ejpam-4805	167	44	phase	phase	NOUN
ejpam-4805	167	45	,	,	PUNCT
ejpam-4805	167	46	on	on	ADP
ejpam-4805	167	47	average	average	ADJ
ejpam-4805	167	48	estimated	estimate	VERB
ejpam-4805	167	49	r	r	NOUN
ejpam-4805	167	50	proportion	proportion	NOUN
ejpam-4805	167	51	of	of	ADP
ejpam-4805	167	52	symptomatic	symptomatic	ADJ
ejpam-4805	167	53	infectious	infectious	ADJ
ejpam-4805	167	54	disease	disease	NOUN
ejpam-4805	167	55	estimated	estimate	VERB
ejpam-4805	167	56	s1	s1	NOUN
ejpam-4805	167	57	number	number	NOUN
ejpam-4805	167	58	of	of	ADP
ejpam-4805	167	59	people	people	NOUN
ejpam-4805	167	60	who	who	PRON
ejpam-4805	167	61	are	be	AUX
ejpam-4805	167	62	at	at	ADP
ejpam-4805	167	63	risk	risk	NOUN
ejpam-4805	167	64	at	at	ADP
ejpam-4805	167	65	time	time	NOUN
ejpam-4805	167	66	t1	t1	NUM
ejpam-4805	167	67	estimated	estimate	VERB
ejpam-4805	167	68	e1	e1	NOUN
ejpam-4805	167	69	quantity	quantity	NOUN
ejpam-4805	167	70	of	of	ADP
ejpam-4805	167	71	individuals	individual	NOUN
ejpam-4805	167	72	who	who	PRON
ejpam-4805	167	73	were	be	AUX
ejpam-4805	167	74	exposed	expose	VERB
ejpam-4805	167	75	at	at	ADP
ejpam-4805	167	76	time	time	NOUN
ejpam-4805	167	77	t1	t1	PROPN
ejpam-4805	167	78	estimated	estimate	VERB
ejpam-4805	167	79	i1	i1	PROPN
ejpam-4805	167	80	number	number	NOUN
ejpam-4805	167	81	of	of	ADP
ejpam-4805	167	82	infected	infected	ADJ
ejpam-4805	167	83	people	people	NOUN
ejpam-4805	167	84	that	that	PRON
ejpam-4805	167	85	are	be	AUX
ejpam-4805	167	86	asymptomatic	asymptomatic	ADJ
ejpam-4805	167	87	at	at	ADP
ejpam-4805	167	88	time	time	NOUN
ejpam-4805	167	89	t1	t1	PROPN
ejpam-4805	167	90	estimated	estimate	VERB
ejpam-4805	167	91	n1	n1	PROPN
ejpam-4805	167	92	indicative	indicative	ADJ
ejpam-4805	167	93	infectious	infectious	ADJ
ejpam-4805	167	94	cases	case	NOUN
ejpam-4805	167	95	that	that	PRON
ejpam-4805	167	96	were	be	AUX
ejpam-4805	167	97	not	not	PART
ejpam-4805	167	98	identified	identify	VERB
ejpam-4805	167	99	at	at	ADP
ejpam-4805	167	100	time	time	NOUN
ejpam-4805	167	101	t1	t1	PROPN
ejpam-4805	167	102	estimated	estimate	VERB
ejpam-4805	167	103	ε	ε	PROPN
ejpam-4805	167	104	vaccine	vaccine	NOUN
ejpam-4805	167	105	impact	impact	VERB
ejpam-4805	167	106	0.03	0.03	NUM
ejpam-4805	167	107	table	table	NOUN
ejpam-4805	167	108	2	2	NUM
ejpam-4805	167	109	:	:	PUNCT
ejpam-4805	167	110	simulations	simulation	NOUN
ejpam-4805	167	111	of	of	ADP
ejpam-4805	167	112	daily	daily	ADJ
ejpam-4805	167	113	reported	report	VERB
ejpam-4805	167	114	incidents	incident	NOUN
ejpam-4805	167	115	using	use	VERB
ejpam-4805	167	116	models	model	NOUN
ejpam-4805	167	117	ar.(t	ar.(t	NOUN
ejpam-4805	167	118	)	)	PUNCT
ejpam-4805	167	119	,	,	PUNCT
ejpam-4805	167	120	susceptibles	susceptible	NOUN
ejpam-4805	167	121	s.(t	s.(t	NUM
ejpam-4805	167	122	)	)	PUNCT
ejpam-4805	167	123	,	,	PUNCT
ejpam-4805	167	124	and	and	CCONJ
ejpam-4805	167	125	cumulative	cumulative	ADJ
ejpam-4805	167	126	reported	report	VERB
ejpam-4805	167	127	cases	case	NOUN
ejpam-4805	167	128	mr.(t),mr.(t	mr.(t),mr.(t	PROPN
ejpam-4805	167	129	)	)	PUNCT
ejpam-4805	167	130	since	since	SCONJ
ejpam-4805	167	131	the	the	DET
ejpam-4805	167	132	last	last	ADJ
ejpam-4805	167	133	data	data	NOUN
ejpam-4805	167	134	point	point	NOUN
ejpam-4805	167	135	were	be	AUX
ejpam-4805	167	136	calculated	calculate	VERB
ejpam-4805	167	137	using	use	VERB
ejpam-4805	167	138	t	t	NOUN
ejpam-4805	167	139	=	=	SYM
ejpam-4805	167	140	1	1	NUM
ejpam-4805	167	141	july	july	PROPN
ejpam-4805	167	142	2022	2022	NUM
ejpam-4805	167	143	for	for	ADP
ejpam-4805	167	144	entirely	entirely	ADV
ejpam-4805	167	145	vaccinated	vaccinate	VERB
ejpam-4805	167	146	=	=	NUM
ejpam-4805	167	147	98	98	NUM
ejpam-4805	167	148	%	%	NOUN
ejpam-4805	167	149	,	,	PUNCT
ejpam-4805	167	150	88	88	NUM
ejpam-4805	167	151	%	%	NOUN
ejpam-4805	167	152	,	,	PUNCT
ejpam-4805	167	153	78	78	NUM
ejpam-4805	167	154	%	%	NOUN
ejpam-4805	167	155	,	,	PUNCT
ejpam-4805	167	156	and	and	CCONJ
ejpam-4805	167	157	social	social	ADJ
ejpam-4805	167	158	behaviour	behaviour	NOUN
ejpam-4805	167	159	scaling	scale	VERB
ejpam-4805	167	160	factor=	factor=	NUM
ejpam-4805	167	161	0.03	0.03	NUM
ejpam-4805	167	162	,	,	PUNCT
ejpam-4805	167	163	0.023	0.023	NUM
ejpam-4805	167	164	,	,	PUNCT
ejpam-4805	167	165	0.016	0.016	NUM
ejpam-4805	167	166	,	,	PUNCT
ejpam-4805	167	167	0.010	0.010	NUM
ejpam-4805	167	168	..	..	PUNCT
ejpam-4805	167	169	vaccinated	vaccinate	VERB
ejpam-4805	167	170	ε	ε	PROPN
ejpam-4805	167	171	ε	ε	PROPN
ejpam-4805	167	172	=	=	SYM
ejpam-4805	167	173	0.03	0.03	NUM
ejpam-4805	167	174	ε	ε	X
ejpam-4805	167	175	=	=	SYM
ejpam-4805	167	176	0.023	0.023	NUM
ejpam-4805	167	177	ε	ε	X
ejpam-4805	167	178	=	=	SYM
ejpam-4805	167	179	0.016	0.016	NUM
ejpam-4805	167	180	ε	ε	PROPN
ejpam-4805	167	181	=	=	NOUN
ejpam-4805	167	182	0.01	0.01	NUM
ejpam-4805	167	183	98	98	NUM
ejpam-4805	167	184	%	%	NOUN
ejpam-4805	167	185	ar.(t	ar.(t	NOUN
ejpam-4805	167	186	)	)	PUNCT
ejpam-4805	167	187	=	=	SYM
ejpam-4805	167	188	829	829	NUM
ejpam-4805	167	189	ar.(t	ar.(t	NOUN
ejpam-4805	167	190	)	)	PUNCT
ejpam-4805	167	191	=	=	SYM
ejpam-4805	167	192	461	461	NUM
ejpam-4805	167	193	ar.(t	ar.(t	NOUN
ejpam-4805	167	194	)	)	PUNCT
ejpam-4805	168	1	=	=	SYM
ejpam-4805	168	2	124	124	NUM
ejpam-4805	168	3	ar.(t	ar.(t	NOUN
ejpam-4805	168	4	)	)	PUNCT
ejpam-4805	168	5	=	=	NOUN
ejpam-4805	168	6	25	25	NUM
ejpam-4805	168	7	s.(t	s.(t	NUM
ejpam-4805	168	8	)	)	PUNCT
ejpam-4805	168	9	=	=	SYM
ejpam-4805	168	10	15513000	15513000	NUM
ejpam-4805	168	11	s.(t	s.(t	NUM
ejpam-4805	168	12	)	)	PUNCT
ejpam-4805	168	13	=	=	SYM
ejpam-4805	168	14	18684000	18684000	NUM
ejpam-4805	168	15	s.(t	s.(t	NUM
ejpam-4805	168	16	)	)	PUNCT
ejpam-4805	168	17	=	=	SYM
ejpam-4805	168	18	20992000	20992000	NUM
ejpam-4805	168	19	s.(t	s.(t	NUM
ejpam-4805	168	20	)	)	PUNCT
ejpam-4805	168	21	=	=	SYM
ejpam-4805	168	22	22561000	22561000	NUM
ejpam-4805	168	23	mr.(t	mr.(t	NOUN
ejpam-4805	168	24	)	)	PUNCT
ejpam-4805	168	25	−	−	NOUN
ejpam-4805	168	26	mr.(t0	mr.(t0	NOUN
ejpam-4805	168	27	)	)	PUNCT
ejpam-4805	168	28	=	=	SYM
ejpam-4805	168	29	4513000	4513000	NUM
ejpam-4805	168	30	mr.(t	mr.(t	NOUN
ejpam-4805	168	31	)	)	PUNCT
ejpam-4805	168	32	−	−	NOUN
ejpam-4805	168	33	mr.(t0	mr.(t0	NOUN
ejpam-4805	168	34	)	)	PUNCT
ejpam-4805	168	35	=	=	SYM
ejpam-4805	168	36	3074000	3074000	NUM
ejpam-4805	168	37	s.(t	s.(t	NUM
ejpam-4805	168	38	)	)	PUNCT
ejpam-4805	168	39	=	=	SYM
ejpam-4805	168	40	20992000	20992000	NUM
ejpam-4805	168	41	s.(t	s.(t	NUM
ejpam-4805	168	42	)	)	PUNCT
ejpam-4805	168	43	=	=	SYM
ejpam-4805	169	1	22561000	22561000	NUM
ejpam-4805	169	2	88	88	NUM
ejpam-4805	169	3	%	%	NOUN
ejpam-4805	169	4	ar.(t	ar.(t	NOUN
ejpam-4805	169	5	)	)	PUNCT
ejpam-4805	169	6	=	=	SYM
ejpam-4805	169	7	3742	3742	NUM
ejpam-4805	169	8	ar.(t	ar.(t	NOUN
ejpam-4805	169	9	)	)	PUNCT
ejpam-4805	169	10	=	=	SYM
ejpam-4805	169	11	1867	1867	NUM
ejpam-4805	169	12	ar.(t	ar.(t	NOUN
ejpam-4805	169	13	)	)	PUNCT
ejpam-4805	170	1	=	=	SYM
ejpam-4805	170	2	589	589	NUM
ejpam-4805	170	3	ar.(t	ar.(t	NOUN
ejpam-4805	170	4	)	)	PUNCT
ejpam-4805	171	1	=	=	SYM
ejpam-4805	171	2	81	81	NUM
ejpam-4805	171	3	s.(t	s.(t	NUM
ejpam-4805	171	4	)	)	PUNCT
ejpam-4805	171	5	=	=	SYM
ejpam-4805	171	6	21891000	21891000	NUM
ejpam-4805	171	7	s.(t	s.(t	NUM
ejpam-4805	171	8	)	)	PUNCT
ejpam-4805	171	9	=	=	SYM
ejpam-4805	171	10	27054000	27054000	NUM
ejpam-4805	171	11	s.(t	s.(t	NUM
ejpam-4805	171	12	)	)	PUNCT
ejpam-4805	171	13	=	=	SYM
ejpam-4805	171	14	29723000	29723000	NUM
ejpam-4805	171	15	s.(t	s.(t	NUM
ejpam-4805	171	16	)	)	PUNCT
ejpam-4805	171	17	=	=	SYM
ejpam-4805	171	18	31641000	31641000	NUM
ejpam-4805	171	19	mr.(t	mr.(t	NOUN
ejpam-4805	171	20	)	)	PUNCT
ejpam-4805	171	21	−	−	NOUN
ejpam-4805	171	22	mr.(t0	mr.(t0	NOUN
ejpam-4805	171	23	)	)	PUNCT
ejpam-4805	171	24	=	=	SYM
ejpam-4805	171	25	4786000	4786000	NUM
ejpam-4805	171	26	mr.(t	mr.(t	NOUN
ejpam-4805	171	27	)	)	PUNCT
ejpam-4805	171	28	−	−	NOUN
ejpam-4805	171	29	mr.(t0	mr.(t0	NOUN
ejpam-4805	171	30	)	)	PUNCT
ejpam-4805	171	31	=	=	SYM
ejpam-4805	171	32	3074000	3074000	NUM
ejpam-4805	171	33	s.(t	s.(t	NUM
ejpam-4805	171	34	)	)	PUNCT
ejpam-4805	171	35	=	=	SYM
ejpam-4805	171	36	1356000	1356000	NUM
ejpam-4805	171	37	s.(t	s.(t	NUM
ejpam-4805	171	38	)	)	PUNCT
ejpam-4805	171	39	=	=	SYM
ejpam-4805	171	40	1565000	1565000	NUM
ejpam-4805	171	41	78	78	NUM
ejpam-4805	171	42	%	%	NOUN
ejpam-4805	171	43	ar.(t	ar.(t	NOUN
ejpam-4805	171	44	)	)	PUNCT
ejpam-4805	171	45	=	=	SYM
ejpam-4805	171	46	11246	11246	NUM
ejpam-4805	171	47	ar.(t	ar.(t	NOUN
ejpam-4805	171	48	)	)	PUNCT
ejpam-4805	171	49	=	=	SYM
ejpam-4805	171	50	8379	8379	NUM
ejpam-4805	171	51	ar.(t	ar.(t	NOUN
ejpam-4805	171	52	)	)	PUNCT
ejpam-4805	171	53	=	=	SYM
ejpam-4805	171	54	2170	2170	NUM
ejpam-4805	171	55	ar.(t	ar.(t	NOUN
ejpam-4805	171	56	)	)	PUNCT
ejpam-4805	171	57	=	=	NOUN
ejpam-4805	172	1	378	378	NUM
ejpam-4805	172	2	s.(t	s.(t	NUM
ejpam-4805	172	3	)	)	PUNCT
ejpam-4805	172	4	=	=	SYM
ejpam-4805	172	5	26847000	26847000	NUM
ejpam-4805	172	6	s.(t	s.(t	NUM
ejpam-4805	172	7	)	)	PUNCT
ejpam-4805	172	8	=	=	SYM
ejpam-4805	172	9	37241000	37241000	NUM
ejpam-4805	172	10	s.(t	s.(t	NUM
ejpam-4805	172	11	)	)	PUNCT
ejpam-4805	172	12	=	=	SYM
ejpam-4805	172	13	41592000	41592000	NUM
ejpam-4805	172	14	s.(t	s.(t	NUM
ejpam-4805	172	15	)	)	PUNCT
ejpam-4805	172	16	=	=	SYM
ejpam-4805	172	17	38683000	38683000	NUM
ejpam-4805	172	18	mr.(t	mr.(t	NOUN
ejpam-4805	172	19	)	)	PUNCT
ejpam-4805	172	20	−	−	NOUN
ejpam-4805	172	21	mr.(t0	mr.(t0	NOUN
ejpam-4805	172	22	)	)	PUNCT
ejpam-4805	172	23	=	=	SYM
ejpam-4805	172	24	5893000	5893000	NUM
ejpam-4805	172	25	mr.(t	mr.(t	NOUN
ejpam-4805	172	26	)	)	PUNCT
ejpam-4805	172	27	−	−	NOUN
ejpam-4805	172	28	mr.(t0	mr.(t0	NOUN
ejpam-4805	172	29	)	)	PUNCT
ejpam-4805	172	30	=	=	SYM
ejpam-4805	172	31	3936000	3936000	NUM
ejpam-4805	172	32	s.(t	s.(t	NUM
ejpam-4805	172	33	)	)	PUNCT
ejpam-4805	172	34	=	=	SYM
ejpam-4805	172	35	21320000	21320000	NUM
ejpam-4805	172	36	s.(t	s.(t	NUM
ejpam-4805	172	37	)	)	PUNCT
ejpam-4805	172	38	=	=	SYM
ejpam-4805	172	39	885000	885000	NUM
ejpam-4805	172	40	acknowledgements	acknowledgement	VERB
ejpam-4805	172	41	the	the	DET
ejpam-4805	172	42	authors	author	NOUN
ejpam-4805	172	43	gratefully	gratefully	ADV
ejpam-4805	172	44	acknowledge	acknowledge	VERB
ejpam-4805	172	45	the	the	DET
ejpam-4805	172	46	approval	approval	NOUN
ejpam-4805	172	47	and	and	CCONJ
ejpam-4805	172	48	the	the	DET
ejpam-4805	172	49	support	support	NOUN
ejpam-4805	172	50	of	of	ADP
ejpam-4805	172	51	this	this	DET
ejpam-4805	172	52	research	research	NOUN
ejpam-4805	172	53	study	study	NOUN
ejpam-4805	172	54	by	by	ADP
ejpam-4805	172	55	the	the	DET
ejpam-4805	172	56	grand	grand	ADJ
ejpam-4805	172	57	no	no	NOUN
ejpam-4805	172	58	:	:	PUNCT
ejpam-4805	172	59	scar-2022	scar-2022	NOUN
ejpam-4805	172	60	-	-	PUNCT
ejpam-4805	172	61	11	11	NUM
ejpam-4805	172	62	-	-	SYM
ejpam-4805	172	63	1743	1743	NUM
ejpam-4805	172	64	from	from	ADP
ejpam-4805	172	65	the	the	DET
ejpam-4805	172	66	deanship	deanship	NOUN
ejpam-4805	172	67	of	of	ADP
ejpam-4805	172	68	scientific	scientific	ADJ
ejpam-4805	172	69	research	research	NOUN
ejpam-4805	172	70	at	at	ADP
ejpam-4805	172	71	northern	northern	ADJ
ejpam-4805	172	72	border	border	PROPN
ejpam-4805	172	73	university	university	PROPN
ejpam-4805	172	74	arar	arar	NOUN
ejpam-4805	172	75	,	,	PUNCT
ejpam-4805	172	76	k.s.a	k.s.a	PROPN
ejpam-4805	172	77	.	.	PUNCT
ejpam-4805	173	1	references	reference	NOUN
ejpam-4805	173	2	[	[	X
ejpam-4805	173	3	1	1	X
ejpam-4805	173	4	]	]	PUNCT
ejpam-4805	173	5	eid	eid	NOUN
ejpam-4805	173	6	alhmadi	alhmadi	NOUN
ejpam-4805	173	7	.	.	PUNCT
ejpam-4805	174	1	mathematical	mathematical	ADJ
ejpam-4805	174	2	analysis	analysis	NOUN
ejpam-4805	174	3	of	of	ADP
ejpam-4805	174	4	a	a	DET
ejpam-4805	174	5	seir	seir	ADJ
ejpam-4805	174	6	model	model	NOUN
ejpam-4805	174	7	with	with	ADP
ejpam-4805	174	8	nonlinear	nonlinear	ADJ
ejpam-4805	174	9	incidence	incidence	NOUN
ejpam-4805	174	10	rate	rate	NOUN
ejpam-4805	174	11	for	for	ADP
ejpam-4805	174	12	covid-19	covid-19	PROPN
ejpam-4805	174	13	dynamics	dynamic	NOUN
ejpam-4805	174	14	.	.	PUNCT
ejpam-4805	175	1	asian	asian	ADJ
ejpam-4805	175	2	research	research	PROPN
ejpam-4805	175	3	journal	journal	NOUN
ejpam-4805	175	4	of	of	ADP
ejpam-4805	175	5	mathematics	mathematic	NOUN
ejpam-4805	175	6	,	,	PUNCT
ejpam-4805	175	7	pages	page	NOUN
ejpam-4805	175	8	56–68	56–68	NUM
ejpam-4805	175	9	,	,	PUNCT
ejpam-4805	175	10	2022	2022	NUM
ejpam-4805	175	11	.	.	PUNCT
ejpam-4805	176	1	[	[	X
ejpam-4805	176	2	2	2	NUM
ejpam-4805	176	3	]	]	X
ejpam-4805	176	4	rubayyi	rubayyi	PROPN
ejpam-4805	176	5	t	t	PROPN
ejpam-4805	176	6	alqahtani	alqahtani	PROPN
ejpam-4805	176	7	.	.	PUNCT
ejpam-4805	177	1	mathematical	mathematical	ADJ
ejpam-4805	177	2	model	model	NOUN
ejpam-4805	177	3	of	of	ADP
ejpam-4805	177	4	sir	sir	NOUN
ejpam-4805	177	5	epidemic	epidemic	NOUN
ejpam-4805	177	6	system	system	NOUN
ejpam-4805	177	7	(	(	PUNCT
ejpam-4805	177	8	covid-19	covid-19	PROPN
ejpam-4805	177	9	)	)	PUNCT
ejpam-4805	177	10	with	with	ADP
ejpam-4805	177	11	references	reference	NOUN
ejpam-4805	177	12	2459	2459	NUM
ejpam-4805	177	13	fractional	fractional	ADJ
ejpam-4805	177	14	derivative	derivative	NOUN
ejpam-4805	177	15	:	:	PUNCT
ejpam-4805	177	16	stability	stability	NOUN
ejpam-4805	177	17	and	and	CCONJ
ejpam-4805	177	18	numerical	numerical	ADJ
ejpam-4805	177	19	analysis	analysis	NOUN
ejpam-4805	177	20	.	.	PUNCT
ejpam-4805	178	1	advances	advance	NOUN
ejpam-4805	178	2	in	in	ADP
ejpam-4805	178	3	difference	difference	NOUN
ejpam-4805	178	4	equations	equation	NOUN
ejpam-4805	178	5	,	,	PUNCT
ejpam-4805	178	6	2021(1):1–16	2021(1):1–16	NOUN
ejpam-4805	178	7	,	,	PUNCT
ejpam-4805	178	8	2021	2021	NUM
ejpam-4805	178	9	.	.	PUNCT
ejpam-4805	179	1	[	[	X
ejpam-4805	179	2	3	3	NUM
ejpam-4805	179	3	]	]	X
ejpam-4805	179	4	eitan	eitan	PROPN
ejpam-4805	179	5	altman	altman	PROPN
ejpam-4805	179	6	,	,	PUNCT
ejpam-4805	179	7	konstantin	konstantin	PROPN
ejpam-4805	179	8	avrachenkov	avrachenkov	PROPN
ejpam-4805	179	9	,	,	PUNCT
ejpam-4805	179	10	francesco	francesco	PROPN
ejpam-4805	179	11	de	de	PROPN
ejpam-4805	179	12	pellegrini	pellegrini	PROPN
ejpam-4805	179	13	,	,	PUNCT
ejpam-4805	179	14	rachid	rachid	PROPN
ejpam-4805	179	15	el	el	PROPN
ejpam-4805	179	16	-	-	PROPN
ejpam-4805	179	17	azouzi	azouzi	PROPN
ejpam-4805	179	18	,	,	PUNCT
ejpam-4805	179	19	and	and	CCONJ
ejpam-4805	179	20	huijuanwang	huijuanwang	PROPN
ejpam-4805	179	21	.	.	PUNCT
ejpam-4805	180	1	multilevel	multilevel	PROPN
ejpam-4805	180	2	strategic	strategic	ADJ
ejpam-4805	180	3	interaction	interaction	NOUN
ejpam-4805	180	4	game	game	NOUN
ejpam-4805	180	5	models	model	NOUN
ejpam-4805	180	6	for	for	ADP
ejpam-4805	180	7	complex	complex	ADJ
ejpam-4805	180	8	networks	network	NOUN
ejpam-4805	180	9	.	.	PUNCT
ejpam-4805	181	1	springer	springer	NOUN
ejpam-4805	181	2	,	,	PUNCT
ejpam-4805	181	3	2019	2019	NUM
ejpam-4805	181	4	.	.	PUNCT
ejpam-4805	182	1	[	[	X
ejpam-4805	182	2	4	4	NUM
ejpam-4805	182	3	]	]	X
ejpam-4805	182	4	fred	fred	PROPN
ejpam-4805	182	5	brauer	brauer	PROPN
ejpam-4805	182	6	,	,	PUNCT
ejpam-4805	182	7	carlos	carlos	PROPN
ejpam-4805	182	8	castillo	castillo	PROPN
ejpam-4805	182	9	-	-	PUNCT
ejpam-4805	182	10	chavez	chavez	PROPN
ejpam-4805	182	11	,	,	PUNCT
ejpam-4805	182	12	zhilan	zhilan	PROPN
ejpam-4805	182	13	feng	feng	PROPN
ejpam-4805	182	14	,	,	PUNCT
ejpam-4805	182	15	fred	fred	PROPN
ejpam-4805	182	16	brauer	brauer	PROPN
ejpam-4805	182	17	,	,	PUNCT
ejpam-4805	182	18	carlos	carlos	PROPN
ejpam-4805	182	19	castillochavez	castillochavez	PROPN
ejpam-4805	182	20	,	,	PUNCT
ejpam-4805	182	21	and	and	CCONJ
ejpam-4805	182	22	zhilan	zhilan	PROPN
ejpam-4805	182	23	feng	feng	PROPN
ejpam-4805	182	24	.	.	PUNCT
ejpam-4805	183	1	introduction	introduction	NOUN
ejpam-4805	183	2	:	:	PUNCT
ejpam-4805	183	3	a	a	DET
ejpam-4805	183	4	prelude	prelude	NOUN
ejpam-4805	183	5	to	to	ADP
ejpam-4805	183	6	mathematical	mathematical	ADJ
ejpam-4805	183	7	epidemiology	epidemiology	NOUN
ejpam-4805	183	8	.	.	PUNCT
ejpam-4805	184	1	mathematical	mathematical	ADJ
ejpam-4805	184	2	models	model	NOUN
ejpam-4805	184	3	in	in	ADP
ejpam-4805	184	4	epidemiology	epidemiology	NOUN
ejpam-4805	184	5	,	,	PUNCT
ejpam-4805	184	6	pages	page	NOUN
ejpam-4805	184	7	3–19	3–19	PROPN
ejpam-4805	184	8	,	,	PUNCT
ejpam-4805	184	9	2019	2019	NUM
ejpam-4805	184	10	.	.	PUNCT
ejpam-4805	185	1	[	[	X
ejpam-4805	185	2	5	5	NUM
ejpam-4805	185	3	]	]	PUNCT
ejpam-4805	185	4	bruno	bruno	PROPN
ejpam-4805	185	5	buonomo	buonomo	NOUN
ejpam-4805	185	6	.	.	PUNCT
ejpam-4805	186	1	analysis	analysis	NOUN
ejpam-4805	186	2	of	of	ADP
ejpam-4805	186	3	a	a	DET
ejpam-4805	186	4	malaria	malaria	NOUN
ejpam-4805	186	5	model	model	NOUN
ejpam-4805	186	6	with	with	ADP
ejpam-4805	186	7	mosquito	mosquito	ADJ
ejpam-4805	186	8	host	host	NOUN
ejpam-4805	186	9	choice	choice	NOUN
ejpam-4805	186	10	and	and	CCONJ
ejpam-4805	186	11	bed	bed	NOUN
ejpam-4805	186	12	-	-	PUNCT
ejpam-4805	186	13	net	net	NOUN
ejpam-4805	186	14	control	control	NOUN
ejpam-4805	186	15	.	.	PUNCT
ejpam-4805	187	1	international	international	ADJ
ejpam-4805	187	2	journal	journal	NOUN
ejpam-4805	187	3	of	of	ADP
ejpam-4805	187	4	biomathematics	biomathematic	NOUN
ejpam-4805	187	5	,	,	PUNCT
ejpam-4805	187	6	8(06):1550077	8(06):1550077	NUM
ejpam-4805	187	7	,	,	PUNCT
ejpam-4805	187	8	2015	2015	NUM
ejpam-4805	187	9	.	.	PUNCT
ejpam-4805	188	1	[	[	X
ejpam-4805	188	2	6	6	NUM
ejpam-4805	188	3	]	]	PUNCT
ejpam-4805	188	4	atsegine	atsegine	NOUN
ejpam-4805	188	5	canga	canga	NOUN
ejpam-4805	188	6	garcés	garcés	PROPN
ejpam-4805	188	7	et	et	NOUN
ejpam-4805	188	8	al	al	PROPN
ejpam-4805	188	9	.	.	PROPN
ejpam-4805	189	1	modelling	model	VERB
ejpam-4805	189	2	the	the	DET
ejpam-4805	189	3	effect	effect	NOUN
ejpam-4805	189	4	of	of	ADP
ejpam-4805	189	5	the	the	DET
ejpam-4805	189	6	interaction	interaction	NOUN
ejpam-4805	189	7	between	between	ADP
ejpam-4805	189	8	vaccination	vaccination	NOUN
ejpam-4805	189	9	and	and	CCONJ
ejpam-4805	189	10	nonpharmaceutical	nonpharmaceutical	ADJ
ejpam-4805	189	11	measures	measure	NOUN
ejpam-4805	189	12	on	on	ADP
ejpam-4805	189	13	covid-19	covid-19	PROPN
ejpam-4805	189	14	incidence	incidence	NOUN
ejpam-4805	189	15	.	.	PUNCT
ejpam-4805	190	1	2022	2022	NUM
ejpam-4805	190	2	.	.	PUNCT
ejpam-4805	191	1	[	[	X
ejpam-4805	191	2	7	7	NUM
ejpam-4805	191	3	]	]	X
ejpam-4805	191	4	leonardo	leonardo	PROPN
ejpam-4805	191	5	da	da	PROPN
ejpam-4805	191	6	vinci	vinci	PROPN
ejpam-4805	191	7	.	.	PUNCT
ejpam-4805	191	8	leonardo	leonardo	PROPN
ejpam-4805	191	9	’s	’s	PART
ejpam-4805	191	10	manuscripts	manuscript	NOUN
ejpam-4805	191	11	.	.	PUNCT
ejpam-4805	192	1	in	in	ADP
ejpam-4805	192	2	handbook	handbook	NOUN
ejpam-4805	192	3	of	of	ADP
ejpam-4805	192	4	geophysical	geophysical	ADJ
ejpam-4805	192	5	exploration	exploration	NOUN
ejpam-4805	192	6	:	:	PUNCT
ejpam-4805	192	7	seismic	seismic	ADJ
ejpam-4805	192	8	exploration	exploration	NOUN
ejpam-4805	192	9	,	,	PUNCT
ejpam-4805	192	10	volume	volume	NOUN
ejpam-4805	192	11	38	38	NUM
ejpam-4805	192	12	,	,	PUNCT
ejpam-4805	192	13	pages	page	NOUN
ejpam-4805	192	14	443–446	443–446	NUM
ejpam-4805	192	15	.	.	PUNCT
ejpam-4805	192	16	elsevier	elsevier	NOUN
ejpam-4805	192	17	,	,	PUNCT
ejpam-4805	192	18	2007	2007	NUM
ejpam-4805	192	19	.	.	PUNCT
ejpam-4805	193	1	[	[	X
ejpam-4805	193	2	8	8	NUM
ejpam-4805	193	3	]	]	PUNCT
ejpam-4805	193	4	luke	luke	PROPN
ejpam-4805	193	5	ekundayo	ekundayo	PROPN
ejpam-4805	193	6	edungbola	edungbola	PROPN
ejpam-4805	193	7	.	.	PUNCT
ejpam-4805	194	1	the	the	DET
ejpam-4805	194	2	eradication	eradication	NOUN
ejpam-4805	194	3	of	of	ADP
ejpam-4805	194	4	dracunculiasis	dracunculiasis	NOUN
ejpam-4805	194	5	(	(	PUNCT
ejpam-4805	194	6	guinea	guinea	NOUN
ejpam-4805	194	7	worm	worm	NOUN
ejpam-4805	194	8	disease	disease	NOUN
ejpam-4805	194	9	)	)	PUNCT
ejpam-4805	194	10	in	in	ADP
ejpam-4805	194	11	nigeria	nigeria	PROPN
ejpam-4805	194	12	:	:	PUNCT
ejpam-4805	194	13	an	an	DET
ejpam-4805	194	14	eyewitness	eyewitness	NOUN
ejpam-4805	194	15	account	account	NOUN
ejpam-4805	194	16	.	.	PUNCT
ejpam-4805	195	1	academic	academic	ADJ
ejpam-4805	195	2	press	press	NOUN
ejpam-4805	195	3	,	,	PUNCT
ejpam-4805	195	4	2018	2018	NUM
ejpam-4805	195	5	.	.	PUNCT
ejpam-4805	196	1	[	[	X
ejpam-4805	196	2	9	9	NUM
ejpam-4805	196	3	]	]	SYM
ejpam-4805	196	4	scott	scott	PROPN
ejpam-4805	196	5	greenhalgh	greenhalgh	PROPN
ejpam-4805	196	6	and	and	CCONJ
ejpam-4805	196	7	carly	carly	PROPN
ejpam-4805	196	8	rozins	rozin	VERB
ejpam-4805	196	9	.	.	PUNCT
ejpam-4805	197	1	a	a	DET
ejpam-4805	197	2	generalized	generalize	VERB
ejpam-4805	197	3	differential	differential	NOUN
ejpam-4805	197	4	equation	equation	NOUN
ejpam-4805	197	5	compartmental	compartmental	NOUN
ejpam-4805	197	6	model	model	NOUN
ejpam-4805	197	7	of	of	ADP
ejpam-4805	197	8	infectious	infectious	ADJ
ejpam-4805	197	9	disease	disease	NOUN
ejpam-4805	197	10	transmission	transmission	NOUN
ejpam-4805	197	11	.	.	PUNCT
ejpam-4805	198	1	infectious	infectious	ADJ
ejpam-4805	198	2	disease	disease	NOUN
ejpam-4805	198	3	modelling	modelling	NOUN
ejpam-4805	198	4	,	,	PUNCT
ejpam-4805	198	5	6:1073	6:1073	NUM
ejpam-4805	198	6	–	–	PUNCT
ejpam-4805	198	7	1091	1091	NUM
ejpam-4805	198	8	,	,	PUNCT
ejpam-4805	198	9	2021	2021	NUM
ejpam-4805	198	10	.	.	PUNCT
ejpam-4805	199	1	[	[	X
ejpam-4805	199	2	10	10	NUM
ejpam-4805	199	3	]	]	X
ejpam-4805	199	4	mj	mj	PROPN
ejpam-4805	199	5	keeling	keeling	PROPN
ejpam-4805	199	6	and	and	CCONJ
ejpam-4805	199	7	p	p	PROPN
ejpam-4805	199	8	rohani	rohani	PROPN
ejpam-4805	199	9	.	.	PUNCT
ejpam-4805	200	1	modeling	model	VERB
ejpam-4805	200	2	infectious	infectious	ADJ
ejpam-4805	200	3	diseases	disease	NOUN
ejpam-4805	200	4	in	in	ADP
ejpam-4805	200	5	humans	human	NOUN
ejpam-4805	200	6	and	and	CCONJ
ejpam-4805	200	7	animals	animal	NOUN
ejpam-4805	200	8	princeton	princeton	PROPN
ejpam-4805	200	9	univ	univ	PROPN
ejpam-4805	200	10	.	.	PUNCT
ejpam-4805	201	1	princeton	princeton	PROPN
ejpam-4805	201	2	,	,	PUNCT
ejpam-4805	201	3	nj	nj	PROPN
ejpam-4805	201	4	,	,	PUNCT
ejpam-4805	201	5	2008	2008	NUM
ejpam-4805	201	6	.	.	PUNCT
ejpam-4805	202	1	[	[	X
ejpam-4805	202	2	11	11	NUM
ejpam-4805	202	3	]	]	PUNCT
ejpam-4805	202	4	eugenio	eugenio	PROPN
ejpam-4805	202	5	lippiello	lippiello	PROPN
ejpam-4805	202	6	,	,	PUNCT
ejpam-4805	202	7	giuseppe	giuseppe	PROPN
ejpam-4805	202	8	petrillo	petrillo	PROPN
ejpam-4805	202	9	,	,	PUNCT
ejpam-4805	202	10	and	and	CCONJ
ejpam-4805	202	11	lucilla	lucilla	PROPN
ejpam-4805	202	12	de	de	PROPN
ejpam-4805	202	13	arcangelis	arcangelis	PROPN
ejpam-4805	202	14	.	.	PUNCT
ejpam-4805	203	1	estimating	estimate	VERB
ejpam-4805	203	2	the	the	DET
ejpam-4805	203	3	generation	generation	NOUN
ejpam-4805	203	4	interval	interval	NOUN
ejpam-4805	203	5	from	from	ADP
ejpam-4805	203	6	the	the	DET
ejpam-4805	203	7	incidence	incidence	NOUN
ejpam-4805	203	8	rate	rate	NOUN
ejpam-4805	203	9	,	,	PUNCT
ejpam-4805	203	10	the	the	DET
ejpam-4805	203	11	optimal	optimal	ADJ
ejpam-4805	203	12	quarantine	quarantine	NOUN
ejpam-4805	203	13	duration	duration	NOUN
ejpam-4805	203	14	and	and	CCONJ
ejpam-4805	203	15	the	the	DET
ejpam-4805	203	16	efficiency	efficiency	NOUN
ejpam-4805	203	17	of	of	ADP
ejpam-4805	203	18	fast	fast	ADJ
ejpam-4805	203	19	switching	switch	VERB
ejpam-4805	203	20	periodic	periodic	ADJ
ejpam-4805	203	21	protocols	protocol	NOUN
ejpam-4805	203	22	for	for	ADP
ejpam-4805	203	23	covid-19	covid-19	PROPN
ejpam-4805	203	24	.	.	PUNCT
ejpam-4805	204	1	scientific	scientific	ADJ
ejpam-4805	204	2	reports	report	NOUN
ejpam-4805	204	3	,	,	PUNCT
ejpam-4805	204	4	12(1):4623	12(1):4623	NUM
ejpam-4805	204	5	,	,	PUNCT
ejpam-4805	204	6	2022	2022	NUM
ejpam-4805	204	7	.	.	PUNCT
ejpam-4805	205	1	[	[	X
ejpam-4805	205	2	12	12	NUM
ejpam-4805	205	3	]	]	PUNCT
ejpam-4805	205	4	banan	banan	NOUN
ejpam-4805	205	5	maayah	maayah	PROPN
ejpam-4805	205	6	,	,	PUNCT
ejpam-4805	205	7	asma	asma	PROPN
ejpam-4805	205	8	moussaoui	moussaoui	PROPN
ejpam-4805	205	9	,	,	PUNCT
ejpam-4805	205	10	samia	samia	PROPN
ejpam-4805	205	11	bushnaq	bushnaq	PROPN
ejpam-4805	205	12	,	,	PUNCT
ejpam-4805	205	13	and	and	CCONJ
ejpam-4805	205	14	omar	omar	PROPN
ejpam-4805	205	15	abu	abu	PROPN
ejpam-4805	205	16	arqub	arqub	PROPN
ejpam-4805	205	17	.	.	PUNCT
ejpam-4805	206	1	the	the	DET
ejpam-4805	206	2	multistep	multistep	ADJ
ejpam-4805	206	3	laplace	laplace	NOUN
ejpam-4805	206	4	optimized	optimize	VERB
ejpam-4805	206	5	decomposition	decomposition	NOUN
ejpam-4805	206	6	method	method	NOUN
ejpam-4805	206	7	for	for	ADP
ejpam-4805	206	8	solving	solve	VERB
ejpam-4805	206	9	fractional	fractional	ADJ
ejpam-4805	206	10	-	-	PUNCT
ejpam-4805	206	11	order	order	NOUN
ejpam-4805	206	12	coronavirus	coronavirus	NOUN
ejpam-4805	206	13	disease	disease	NOUN
ejpam-4805	206	14	model	model	NOUN
ejpam-4805	206	15	(	(	PUNCT
ejpam-4805	206	16	covid-19	covid-19	PROPN
ejpam-4805	206	17	)	)	PUNCT
ejpam-4805	206	18	via	via	ADP
ejpam-4805	206	19	the	the	DET
ejpam-4805	206	20	caputo	caputo	PROPN
ejpam-4805	206	21	fractional	fractional	PROPN
ejpam-4805	206	22	approach	approach	NOUN
ejpam-4805	206	23	.	.	PUNCT
ejpam-4805	207	1	demonstratio	demonstratio	PROPN
ejpam-4805	207	2	mathematica	mathematica	PROPN
ejpam-4805	207	3	,	,	PUNCT
ejpam-4805	207	4	55(1):963–977	55(1):963–977	PROPN
ejpam-4805	207	5	,	,	PUNCT
ejpam-4805	207	6	2022	2022	NUM
ejpam-4805	207	7	.	.	PUNCT
ejpam-4805	208	1	[	[	X
ejpam-4805	208	2	13	13	NUM
ejpam-4805	208	3	]	]	X
ejpam-4805	208	4	maia	maia	PROPN
ejpam-4805	208	5	martcheva	martcheva	PROPN
ejpam-4805	208	6	.	.	PUNCT
ejpam-4805	209	1	an	an	DET
ejpam-4805	209	2	introduction	introduction	NOUN
ejpam-4805	209	3	to	to	ADP
ejpam-4805	209	4	mathematical	mathematical	ADJ
ejpam-4805	209	5	epidemiology	epidemiology	NOUN
ejpam-4805	209	6	,	,	PUNCT
ejpam-4805	209	7	volume	volume	NOUN
ejpam-4805	209	8	61	61	NUM
ejpam-4805	209	9	.	.	PUNCT
ejpam-4805	209	10	springer	springer	NOUN
ejpam-4805	209	11	,	,	PUNCT
ejpam-4805	209	12	2015	2015	NUM
ejpam-4805	209	13	.	.	PUNCT
ejpam-4805	210	1	[	[	X
ejpam-4805	210	2	14	14	NUM
ejpam-4805	210	3	]	]	X
ejpam-4805	210	4	edouard	edouard	PROPN
ejpam-4805	210	5	mathieu	mathieu	PROPN
ejpam-4805	210	6	,	,	PUNCT
ejpam-4805	210	7	hannah	hannah	PROPN
ejpam-4805	210	8	ritchie	ritchie	PROPN
ejpam-4805	210	9	,	,	PUNCT
ejpam-4805	210	10	esteban	esteban	PROPN
ejpam-4805	210	11	ortiz	ortiz	PROPN
ejpam-4805	210	12	-	-	PUNCT
ejpam-4805	210	13	ospina	ospina	PROPN
ejpam-4805	210	14	,	,	PUNCT
ejpam-4805	210	15	max	max	PROPN
ejpam-4805	210	16	roser	roser	PROPN
ejpam-4805	210	17	,	,	PUNCT
ejpam-4805	210	18	joe	joe	PROPN
ejpam-4805	210	19	hasell	hasell	PROPN
ejpam-4805	210	20	,	,	PUNCT
ejpam-4805	210	21	cameron	cameron	PROPN
ejpam-4805	210	22	appel	appel	PROPN
ejpam-4805	210	23	,	,	PUNCT
ejpam-4805	210	24	charlie	charlie	PROPN
ejpam-4805	210	25	giattino	giattino	PROPN
ejpam-4805	210	26	,	,	PUNCT
ejpam-4805	210	27	and	and	CCONJ
ejpam-4805	210	28	lucas	lucas	PROPN
ejpam-4805	210	29	rodés	rodés	PROPN
ejpam-4805	210	30	-	-	PUNCT
ejpam-4805	210	31	guirao	guirao	NOUN
ejpam-4805	210	32	.	.	PUNCT
ejpam-4805	211	1	a	a	DET
ejpam-4805	211	2	global	global	ADJ
ejpam-4805	211	3	database	database	NOUN
ejpam-4805	211	4	of	of	ADP
ejpam-4805	211	5	covid-19	covid-19	PROPN
ejpam-4805	211	6	vaccinations	vaccination	NOUN
ejpam-4805	211	7	.	.	PUNCT
ejpam-4805	212	1	nature	nature	NOUN
ejpam-4805	212	2	human	human	ADJ
ejpam-4805	212	3	behaviour	behaviour	NOUN
ejpam-4805	212	4	,	,	PUNCT
ejpam-4805	212	5	5(7):947–953	5(7):947–953	NUM
ejpam-4805	212	6	,	,	PUNCT
ejpam-4805	212	7	2021	2021	NUM
ejpam-4805	212	8	.	.	PUNCT
ejpam-4805	213	1	references	reference	NOUN
ejpam-4805	213	2	2460	2460	NUM
ejpam-4805	214	1	[	[	X
ejpam-4805	214	2	15	15	NUM
ejpam-4805	214	3	]	]	X
ejpam-4805	214	4	sam	sam	PROPN
ejpam-4805	214	5	moore	moore	PROPN
ejpam-4805	214	6	,	,	PUNCT
ejpam-4805	214	7	edward	edward	PROPN
ejpam-4805	214	8	m	m	PROPN
ejpam-4805	214	9	hill	hill	PROPN
ejpam-4805	214	10	,	,	PUNCT
ejpam-4805	214	11	louise	louise	PROPN
ejpam-4805	214	12	dyson	dyson	PROPN
ejpam-4805	214	13	,	,	PUNCT
ejpam-4805	214	14	michael	michael	PROPN
ejpam-4805	214	15	j	j	PROPN
ejpam-4805	214	16	tildesley	tildesley	PROPN
ejpam-4805	214	17	,	,	PUNCT
ejpam-4805	214	18	and	and	CCONJ
ejpam-4805	214	19	matt	matt	PROPN
ejpam-4805	214	20	j	j	PROPN
ejpam-4805	214	21	keeling	keeling	PROPN
ejpam-4805	214	22	.	.	PUNCT
ejpam-4805	215	1	modelling	model	VERB
ejpam-4805	215	2	optimal	optimal	ADJ
ejpam-4805	215	3	vaccination	vaccination	NOUN
ejpam-4805	215	4	strategy	strategy	NOUN
ejpam-4805	215	5	for	for	ADP
ejpam-4805	215	6	sars	sar	NOUN
ejpam-4805	215	7	-	-	PUNCT
ejpam-4805	215	8	cov-2	cov-2	NOUN
ejpam-4805	215	9	in	in	ADP
ejpam-4805	215	10	the	the	DET
ejpam-4805	215	11	uk	uk	PROPN
ejpam-4805	215	12	.	.	PROPN
ejpam-4805	216	1	plos	plos	PROPN
ejpam-4805	216	2	computational	computational	ADJ
ejpam-4805	216	3	biology	biology	NOUN
ejpam-4805	216	4	,	,	PUNCT
ejpam-4805	216	5	17(5):e1008849	17(5):e1008849	NUM
ejpam-4805	216	6	,	,	PUNCT
ejpam-4805	216	7	2021	2021	NUM
ejpam-4805	216	8	.	.	PUNCT
ejpam-4805	217	1	[	[	X
ejpam-4805	217	2	16	16	NUM
ejpam-4805	217	3	]	]	X
ejpam-4805	217	4	james	james	PROPN
ejpam-4805	217	5	dickson	dickson	PROPN
ejpam-4805	217	6	murray	murray	PROPN
ejpam-4805	217	7	and	and	CCONJ
ejpam-4805	217	8	james	james	PROPN
ejpam-4805	217	9	dickson	dickson	PROPN
ejpam-4805	217	10	murray	murray	PROPN
ejpam-4805	217	11	.	.	PUNCT
ejpam-4805	218	1	mathematical	mathematical	ADJ
ejpam-4805	218	2	biology	biology	NOUN
ejpam-4805	218	3	:	:	PUNCT
ejpam-4805	218	4	ii	ii	NOUN
ejpam-4805	218	5	:	:	PUNCT
ejpam-4805	218	6	spatial	spatial	ADJ
ejpam-4805	218	7	models	model	NOUN
ejpam-4805	218	8	and	and	CCONJ
ejpam-4805	218	9	biomedical	biomedical	ADJ
ejpam-4805	218	10	applications	application	NOUN
ejpam-4805	218	11	,	,	PUNCT
ejpam-4805	218	12	volume	volume	NOUN
ejpam-4805	218	13	3	3	NUM
ejpam-4805	218	14	.	.	PUNCT
ejpam-4805	218	15	springer	springer	NOUN
ejpam-4805	218	16	,	,	PUNCT
ejpam-4805	218	17	2003	2003	NUM
ejpam-4805	218	18	.	.	PUNCT
ejpam-4805	219	1	[	[	X
ejpam-4805	219	2	17	17	NUM
ejpam-4805	219	3	]	]	X
ejpam-4805	219	4	zaid	zaid	PROPN
ejpam-4805	219	5	odibat	odibat	NOUN
ejpam-4805	219	6	.	.	PUNCT
ejpam-4805	220	1	a	a	DET
ejpam-4805	220	2	universal	universal	ADJ
ejpam-4805	220	3	predictor	predictor	NOUN
ejpam-4805	220	4	–	–	PUNCT
ejpam-4805	220	5	corrector	corrector	NOUN
ejpam-4805	220	6	algorithm	algorithm	NOUN
ejpam-4805	220	7	for	for	ADP
ejpam-4805	220	8	numerical	numerical	ADJ
ejpam-4805	220	9	simulation	simulation	NOUN
ejpam-4805	220	10	of	of	ADP
ejpam-4805	220	11	generalized	generalized	ADJ
ejpam-4805	220	12	fractional	fractional	ADJ
ejpam-4805	220	13	differential	differential	ADJ
ejpam-4805	220	14	equations	equation	NOUN
ejpam-4805	220	15	.	.	PUNCT
ejpam-4805	221	1	nonlinear	nonlinear	ADJ
ejpam-4805	221	2	dynamics	dynamic	NOUN
ejpam-4805	221	3	,	,	PUNCT
ejpam-4805	221	4	105(3):2363–2374	105(3):2363–2374	NUM
ejpam-4805	221	5	,	,	PUNCT
ejpam-4805	221	6	2021	2021	NUM
ejpam-4805	221	7	.	.	PUNCT
ejpam-4805	222	1	[	[	X
ejpam-4805	222	2	18	18	NUM
ejpam-4805	222	3	]	]	X
ejpam-4805	222	4	jørn	jørn	X
ejpam-4805	222	5	olsen	olsen	PROPN
ejpam-4805	222	6	,	,	PUNCT
ejpam-4805	222	7	kaare	kaare	PROPN
ejpam-4805	222	8	christensen	christensen	PROPN
ejpam-4805	222	9	,	,	PUNCT
ejpam-4805	222	10	jeff	jeff	PROPN
ejpam-4805	222	11	murray	murray	PROPN
ejpam-4805	222	12	,	,	PUNCT
ejpam-4805	222	13	anders	anders	PROPN
ejpam-4805	222	14	ekbom	ekbom	NOUN
ejpam-4805	222	15	,	,	PUNCT
ejpam-4805	222	16	jørn	jørn	PROPN
ejpam-4805	222	17	olsen	olsen	NOUN
ejpam-4805	222	18	,	,	PUNCT
ejpam-4805	222	19	kaare	kaare	PROPN
ejpam-4805	222	20	christensen	christensen	PROPN
ejpam-4805	222	21	,	,	PUNCT
ejpam-4805	222	22	jeff	jeff	PROPN
ejpam-4805	222	23	murray	murray	PROPN
ejpam-4805	222	24	,	,	PUNCT
ejpam-4805	222	25	and	and	CCONJ
ejpam-4805	222	26	anders	anders	PROPN
ejpam-4805	222	27	ekbom	ekbom	PROPN
ejpam-4805	222	28	.	.	PUNCT
ejpam-4805	223	1	descriptive	descriptive	ADJ
ejpam-4805	223	2	epidemiology	epidemiology	NOUN
ejpam-4805	223	3	in	in	ADP
ejpam-4805	223	4	clinical	clinical	ADJ
ejpam-4805	223	5	epidemiology	epidemiology	NOUN
ejpam-4805	223	6	.	.	PUNCT
ejpam-4805	224	1	an	an	DET
ejpam-4805	224	2	introduction	introduction	NOUN
ejpam-4805	224	3	to	to	ADP
ejpam-4805	224	4	epidemiology	epidemiology	NOUN
ejpam-4805	224	5	for	for	ADP
ejpam-4805	224	6	health	health	NOUN
ejpam-4805	224	7	professionals	professional	NOUN
ejpam-4805	224	8	,	,	PUNCT
ejpam-4805	224	9	pages	page	NOUN
ejpam-4805	224	10	43–47	43–47	NUM
ejpam-4805	224	11	,	,	PUNCT
ejpam-4805	224	12	2010	2010	NUM
ejpam-4805	224	13	.	.	PUNCT
ejpam-4805	225	1	[	[	X
ejpam-4805	225	2	19	19	NUM
ejpam-4805	225	3	]	]	X
ejpam-4805	225	4	arjun	arjun	PROPN
ejpam-4805	225	5	puranik	puranik	NOUN
ejpam-4805	225	6	,	,	PUNCT
ejpam-4805	225	7	patrick	patrick	PROPN
ejpam-4805	225	8	j	j	PROPN
ejpam-4805	225	9	lenehan	lenehan	PROPN
ejpam-4805	225	10	,	,	PUNCT
ejpam-4805	225	11	eli	eli	PROPN
ejpam-4805	225	12	silvert	silvert	PROPN
ejpam-4805	225	13	,	,	PUNCT
ejpam-4805	225	14	michiel	michiel	PROPN
ejpam-4805	225	15	jm	jm	PROPN
ejpam-4805	225	16	niesen	niesen	PROPN
ejpam-4805	225	17	,	,	PUNCT
ejpam-4805	225	18	juan	juan	PROPN
ejpam-4805	225	19	corchadogarcia	corchadogarcia	PROPN
ejpam-4805	225	20	,	,	PUNCT
ejpam-4805	225	21	john	john	PROPN
ejpam-4805	225	22	c	c	PROPN
ejpam-4805	225	23	o’horo	o’horo	PROPN
ejpam-4805	225	24	,	,	PUNCT
ejpam-4805	225	25	abinash	abinash	PROPN
ejpam-4805	225	26	virk	virk	PROPN
ejpam-4805	225	27	,	,	PUNCT
ejpam-4805	225	28	melanie	melanie	PROPN
ejpam-4805	225	29	d	d	PROPN
ejpam-4805	225	30	swift	swift	PROPN
ejpam-4805	225	31	,	,	PUNCT
ejpam-4805	225	32	john	john	PROPN
ejpam-4805	225	33	halamka	halamka	PROPN
ejpam-4805	225	34	,	,	PUNCT
ejpam-4805	225	35	andrew	andrew	PROPN
ejpam-4805	225	36	d	d	PROPN
ejpam-4805	225	37	badley	badley	PROPN
ejpam-4805	225	38	,	,	PUNCT
ejpam-4805	225	39	et	et	PROPN
ejpam-4805	225	40	al	al	PROPN
ejpam-4805	225	41	.	.	PROPN
ejpam-4805	225	42	comparison	comparison	NOUN
ejpam-4805	225	43	of	of	ADP
ejpam-4805	225	44	two	two	NUM
ejpam-4805	225	45	highly	highly	ADV
ejpam-4805	225	46	-	-	PUNCT
ejpam-4805	225	47	effective	effective	ADJ
ejpam-4805	225	48	mrna	mrna	NOUN
ejpam-4805	225	49	vaccines	vaccine	NOUN
ejpam-4805	225	50	for	for	ADP
ejpam-4805	225	51	covid-19	covid-19	PROPN
ejpam-4805	225	52	during	during	ADP
ejpam-4805	225	53	periods	period	NOUN
ejpam-4805	225	54	of	of	ADP
ejpam-4805	225	55	alpha	alpha	NOUN
ejpam-4805	225	56	and	and	CCONJ
ejpam-4805	225	57	delta	delta	NOUN
ejpam-4805	225	58	variant	variant	ADJ
ejpam-4805	225	59	prevalence	prevalence	NOUN
ejpam-4805	225	60	.	.	PUNCT
ejpam-4805	226	1	medrxiv	medrxiv	PROPN
ejpam-4805	226	2	,	,	PUNCT
ejpam-4805	226	3	2021	2021	NUM
ejpam-4805	226	4	.	.	PUNCT
ejpam-4805	227	1	[	[	X
ejpam-4805	227	2	20	20	NUM
ejpam-4805	227	3	]	]	X
ejpam-4805	227	4	negar	negar	PROPN
ejpam-4805	227	5	bakhshi	bakhshi	PROPN
ejpam-4805	227	6	sadabadi	sadabadi	PROPN
ejpam-4805	227	7	and	and	CCONJ
ejpam-4805	227	8	fariba	fariba	PROPN
ejpam-4805	227	9	maheri	maheri	PROPN
ejpam-4805	227	10	.	.	PUNCT
ejpam-4805	228	1	sies	sies	PROPN
ejpam-4805	228	2	epidemic	epidemic	NOUN
ejpam-4805	228	3	model	model	NOUN
ejpam-4805	228	4	for	for	ADP
ejpam-4805	228	5	novel	novel	NOUN
ejpam-4805	228	6	covid-19	covid-19	PROPN
ejpam-4805	228	7	by	by	ADP
ejpam-4805	228	8	conformable	conformable	ADJ
ejpam-4805	228	9	fractional	fractional	ADJ
ejpam-4805	228	10	derivative	derivative	NOUN
ejpam-4805	228	11	.	.	PUNCT
ejpam-4805	229	1	2022	2022	NUM
ejpam-4805	229	2	.	.	PUNCT
ejpam-4805	230	1	[	[	X
ejpam-4805	230	2	21	21	NUM
ejpam-4805	230	3	]	]	X
ejpam-4805	230	4	debashis	debashis	PROPN
ejpam-4805	230	5	saikia	saikia	PROPN
ejpam-4805	230	6	,	,	PUNCT
ejpam-4805	230	7	kalpana	kalpana	PROPN
ejpam-4805	230	8	bora	bora	PROPN
ejpam-4805	230	9	,	,	PUNCT
ejpam-4805	230	10	and	and	CCONJ
ejpam-4805	230	11	madhurjya	madhurjya	PROPN
ejpam-4805	230	12	p	p	PROPN
ejpam-4805	230	13	bora	bora	PROPN
ejpam-4805	230	14	.	.	PUNCT
ejpam-4805	231	1	covid-19	covid-19	PROPN
ejpam-4805	231	2	outbreak	outbreak	NOUN
ejpam-4805	231	3	in	in	ADP
ejpam-4805	231	4	india	india	PROPN
ejpam-4805	231	5	:	:	PUNCT
ejpam-4805	231	6	an	an	DET
ejpam-4805	231	7	seir	seir	ADJ
ejpam-4805	231	8	model	model	NOUN
ejpam-4805	231	9	-	-	PUNCT
ejpam-4805	231	10	based	base	VERB
ejpam-4805	231	11	analysis	analysis	NOUN
ejpam-4805	231	12	.	.	PUNCT
ejpam-4805	232	1	nonlinear	nonlinear	ADJ
ejpam-4805	232	2	dynamics	dynamic	NOUN
ejpam-4805	232	3	,	,	PUNCT
ejpam-4805	232	4	104(4):4727–4751	104(4):4727–4751	NUM
ejpam-4805	232	5	,	,	PUNCT
ejpam-4805	232	6	2021	2021	NUM
ejpam-4805	232	7	.	.	PUNCT
ejpam-4805	233	1	[	[	X
ejpam-4805	233	2	22	22	NUM
ejpam-4805	233	3	]	]	X
ejpam-4805	233	4	hal	hal	PROPN
ejpam-4805	233	5	l	l	PROPN
ejpam-4805	233	6	smith	smith	PROPN
ejpam-4805	233	7	.	.	PUNCT
ejpam-4805	234	1	monotone	monotone	ADJ
ejpam-4805	234	2	dynamical	dynamical	ADJ
ejpam-4805	234	3	systems	system	NOUN
ejpam-4805	234	4	:	:	PUNCT
ejpam-4805	234	5	an	an	DET
ejpam-4805	234	6	introduction	introduction	NOUN
ejpam-4805	234	7	to	to	ADP
ejpam-4805	234	8	the	the	DET
ejpam-4805	234	9	theory	theory	NOUN
ejpam-4805	234	10	of	of	ADP
ejpam-4805	234	11	competitive	competitive	ADJ
ejpam-4805	234	12	and	and	CCONJ
ejpam-4805	234	13	cooperative	cooperative	ADJ
ejpam-4805	234	14	systems	system	NOUN
ejpam-4805	234	15	:	:	PUNCT
ejpam-4805	234	16	an	an	DET
ejpam-4805	234	17	introduction	introduction	NOUN
ejpam-4805	234	18	to	to	ADP
ejpam-4805	234	19	the	the	DET
ejpam-4805	234	20	theory	theory	NOUN
ejpam-4805	234	21	of	of	ADP
ejpam-4805	234	22	competitive	competitive	ADJ
ejpam-4805	234	23	and	and	CCONJ
ejpam-4805	234	24	cooperative	cooperative	ADJ
ejpam-4805	234	25	systems	system	NOUN
ejpam-4805	234	26	.	.	PUNCT
ejpam-4805	235	1	number	number	NOUN
ejpam-4805	235	2	41	41	NUM
ejpam-4805	235	3	.	.	PUNCT
ejpam-4805	236	1	american	american	PROPN
ejpam-4805	236	2	mathematical	mathematical	PROPN
ejpam-4805	236	3	soc	soc	PROPN
ejpam-4805	236	4	.	.	PUNCT
ejpam-4805	236	5	,	,	PUNCT
ejpam-4805	236	6	1995	1995	NUM
ejpam-4805	236	7	.	.	PUNCT
ejpam-4805	237	1	[	[	X
ejpam-4805	237	2	23	23	NUM
ejpam-4805	237	3	]	]	X
ejpam-4805	237	4	glenn	glenn	PROPN
ejpam-4805	237	5	webb	webb	PROPN
ejpam-4805	237	6	.	.	PUNCT
ejpam-4805	238	1	a	a	DET
ejpam-4805	238	2	covid-19	covid-19	PROPN
ejpam-4805	238	3	epidemic	epidemic	NOUN
ejpam-4805	238	4	model	model	NOUN
ejpam-4805	238	5	predicting	predict	VERB
ejpam-4805	238	6	the	the	DET
ejpam-4805	238	7	effectiveness	effectiveness	NOUN
ejpam-4805	238	8	of	of	ADP
ejpam-4805	238	9	vaccination	vaccination	NOUN
ejpam-4805	238	10	in	in	ADP
ejpam-4805	238	11	the	the	DET
ejpam-4805	238	12	us	us	PROPN
ejpam-4805	238	13	.	.	PUNCT
ejpam-4805	239	1	infectious	infectious	ADJ
ejpam-4805	239	2	disease	disease	NOUN
ejpam-4805	239	3	reports	report	VERB
ejpam-4805	239	4	,	,	PUNCT
ejpam-4805	239	5	13(3):654–667	13(3):654–667	PROPN
ejpam-4805	239	6	,	,	PUNCT
ejpam-4805	239	7	2021	2021	NUM
ejpam-4805	239	8	.	.	PUNCT
ejpam-4805	240	1	[	[	X
ejpam-4805	240	2	24	24	NUM
ejpam-4805	240	3	]	]	PUNCT
ejpam-4805	240	4	liuqian	liuqian	PROPN
ejpam-4805	240	5	yu	yu	PROPN
ejpam-4805	240	6	,	,	PUNCT
ejpam-4805	240	7	katja	katja	PROPN
ejpam-4805	240	8	fennel	fennel	NOUN
ejpam-4805	240	9	,	,	PUNCT
ejpam-4805	240	10	laurent	laurent	PROPN
ejpam-4805	240	11	bertino	bertino	PROPN
ejpam-4805	240	12	,	,	PUNCT
ejpam-4805	240	13	mohamad	mohamad	PROPN
ejpam-4805	240	14	el	el	PROPN
ejpam-4805	240	15	gharamti	gharamti	PROPN
ejpam-4805	240	16	,	,	PUNCT
ejpam-4805	240	17	and	and	CCONJ
ejpam-4805	240	18	keith	keith	PROPN
ejpam-4805	240	19	r	r	PROPN
ejpam-4805	240	20	thompson	thompson	PROPN
ejpam-4805	240	21	.	.	PUNCT
ejpam-4805	241	1	insights	insight	NOUN
ejpam-4805	241	2	on	on	ADP
ejpam-4805	241	3	multivariate	multivariate	NOUN
ejpam-4805	241	4	updates	update	NOUN
ejpam-4805	241	5	of	of	ADP
ejpam-4805	241	6	physical	physical	ADJ
ejpam-4805	241	7	and	and	CCONJ
ejpam-4805	241	8	biogeochemical	biogeochemical	ADJ
ejpam-4805	241	9	ocean	ocean	NOUN
ejpam-4805	241	10	variables	variable	NOUN
ejpam-4805	241	11	using	use	VERB
ejpam-4805	241	12	an	an	DET
ejpam-4805	241	13	ensemble	ensemble	ADJ
ejpam-4805	241	14	kalman	kalman	NOUN
ejpam-4805	241	15	filter	filter	NOUN
ejpam-4805	241	16	and	and	CCONJ
ejpam-4805	241	17	an	an	DET
ejpam-4805	241	18	idealized	idealized	ADJ
ejpam-4805	241	19	model	model	NOUN
ejpam-4805	241	20	of	of	ADP
ejpam-4805	241	21	upwelling	upwelle	VERB
ejpam-4805	241	22	.	.	PUNCT
ejpam-4805	242	1	ocean	ocean	NOUN
ejpam-4805	242	2	modelling	modelling	NOUN
ejpam-4805	242	3	,	,	PUNCT
ejpam-4805	242	4	126:13–28	126:13–28	NUM
ejpam-4805	242	5	,	,	PUNCT
ejpam-4805	242	6	2018	2018	NUM
ejpam-4805	242	7	.	.	PUNCT