id	sid	tid	token	lemma	pos
cord-013977-xb0r2axf	1	1	key	key	JJ
cord-013977-xb0r2axf	1	2	:	:	:
cord-013977-xb0r2axf	1	3	cord-013977-xb0r2axf	cord-013977-xb0r2axf	NNP
cord-013977-xb0r2axf	1	4	authors	author	NNS
cord-013977-xb0r2axf	1	5	:	:	:
cord-013977-xb0r2axf	1	6	Heng	Heng	NNP
cord-013977-xb0r2axf	1	7	,	,	,
cord-013977-xb0r2axf	1	8	Kevin	Kevin	NNP
cord-013977-xb0r2axf	1	9	;	;	:
cord-013977-xb0r2axf	1	10	Althaus	Althaus	NNP
cord-013977-xb0r2axf	1	11	,	,	,
cord-013977-xb0r2axf	1	12	Christian	Christian	NNP
cord-013977-xb0r2axf	1	13	L.	L.	NNP
cord-013977-xb0r2axf	1	14	title	title	NN
cord-013977-xb0r2axf	1	15	:	:	:
cord-013977-xb0r2axf	2	1	The	the	DT
cord-013977-xb0r2axf	2	2	approximately	approximately	RB
cord-013977-xb0r2axf	2	3	universal	universal	JJ
cord-013977-xb0r2axf	2	4	shapes	shape	NNS
cord-013977-xb0r2axf	2	5	of	of	IN
cord-013977-xb0r2axf	2	6	epidemic	epidemic	NN
cord-013977-xb0r2axf	2	7	curves	curve	NNS
cord-013977-xb0r2axf	2	8	in	in	IN
cord-013977-xb0r2axf	2	9	the	the	DT
cord-013977-xb0r2axf	2	10	Susceptible	susceptible	JJ
cord-013977-xb0r2axf	2	11	-	-	HYPH
cord-013977-xb0r2axf	2	12	Exposed	exposed	JJ
cord-013977-xb0r2axf	2	13	-	-	HYPH
cord-013977-xb0r2axf	2	14	Infectious	Infectious	NNP
cord-013977-xb0r2axf	2	15	-	-	HYPH
cord-013977-xb0r2axf	2	16	Recovered	recovered	JJ
cord-013977-xb0r2axf	2	17	(	(	-LRB-
cord-013977-xb0r2axf	2	18	SEIR	SEIR	NNP
cord-013977-xb0r2axf	2	19	)	)	-RRB-
cord-013977-xb0r2axf	2	20	model	model	NN
cord-013977-xb0r2axf	2	21	date	date	NN
cord-013977-xb0r2axf	2	22	:	:	:
cord-013977-xb0r2axf	2	23	2020	2020	CD
cord-013977-xb0r2axf	2	24	-	-	HYPH
cord-013977-xb0r2axf	2	25	11	11	CD
cord-013977-xb0r2axf	2	26	-	-	HYPH
cord-013977-xb0r2axf	2	27	09	09	CD
cord-013977-xb0r2axf	2	28	journal	journal	NN
cord-013977-xb0r2axf	2	29	:	:	:
cord-013977-xb0r2axf	3	1	Sci	Sci	NNP
cord-013977-xb0r2axf	3	2	Rep	Rep	NNP
cord-013977-xb0r2axf	3	3	DOI	DOI	NNP
cord-013977-xb0r2axf	3	4	:	:	:
cord-013977-xb0r2axf	4	1	10.1038	10.1038	CD
cord-013977-xb0r2axf	4	2	/	/	SYM
cord-013977-xb0r2axf	4	3	s41598	s41598	CD
cord-013977-xb0r2axf	4	4	-	-	HYPH
cord-013977-xb0r2axf	4	5	020	020	CD
cord-013977-xb0r2axf	4	6	-	-	HYPH
cord-013977-xb0r2axf	4	7	76563	76563	CD
cord-013977-xb0r2axf	4	8	-	-	SYM
cord-013977-xb0r2axf	4	9	8	8	CD
cord-013977-xb0r2axf	4	10	sha	sha	NN
cord-013977-xb0r2axf	4	11	:	:	:
cord-013977-xb0r2axf	4	12	e72a7452c7bca0963f650715c96c293704bffee5	e72a7452c7bca0963f650715c96c293704bffee5	NNP
cord-013977-xb0r2axf	4	13	doc_id	doc_id	CD
cord-013977-xb0r2axf	4	14	:	:	:
cord-013977-xb0r2axf	4	15	13977	13977	CD
cord-013977-xb0r2axf	4	16	cord_uid	cord_uid	NNS
cord-013977-xb0r2axf	4	17	:	:	:
cord-013977-xb0r2axf	5	1	xb0r2axf	xb0r2axf	JJ
cord-013977-xb0r2axf	5	2	Compartmental	compartmental	JJ
cord-013977-xb0r2axf	5	3	transmission	transmission	NN
cord-013977-xb0r2axf	5	4	models	model	NNS
cord-013977-xb0r2axf	5	5	have	have	VBP
cord-013977-xb0r2axf	5	6	become	become	VBN
cord-013977-xb0r2axf	5	7	an	an	DT
cord-013977-xb0r2axf	5	8	invaluable	invaluable	JJ
cord-013977-xb0r2axf	5	9	tool	tool	NN
cord-013977-xb0r2axf	5	10	to	to	TO
cord-013977-xb0r2axf	5	11	study	study	VB
cord-013977-xb0r2axf	5	12	the	the	DT
cord-013977-xb0r2axf	5	13	dynamics	dynamic	NNS
cord-013977-xb0r2axf	5	14	of	of	IN
cord-013977-xb0r2axf	5	15	infectious	infectious	JJ
cord-013977-xb0r2axf	5	16	diseases	disease	NNS
cord-013977-xb0r2axf	5	17	.	.	.
cord-013977-xb0r2axf	6	1	The	the	DT
cord-013977-xb0r2axf	6	2	Susceptible	susceptible	JJ
cord-013977-xb0r2axf	6	3	-	-	HYPH
cord-013977-xb0r2axf	6	4	Infectious	Infectious	NNP
cord-013977-xb0r2axf	6	5	-	-	HYPH
cord-013977-xb0r2axf	6	6	Recovered	recovered	JJ
cord-013977-xb0r2axf	6	7	(	(	-LRB-
cord-013977-xb0r2axf	6	8	SIR	SIR	NNP
cord-013977-xb0r2axf	6	9	)	)	-RRB-
cord-013977-xb0r2axf	6	10	model	model	NN
cord-013977-xb0r2axf	6	11	is	be	VBZ
cord-013977-xb0r2axf	6	12	known	know	VBN
cord-013977-xb0r2axf	6	13	to	to	TO
cord-013977-xb0r2axf	6	14	have	have	VB
cord-013977-xb0r2axf	6	15	an	an	DT
cord-013977-xb0r2axf	6	16	exact	exact	JJ
cord-013977-xb0r2axf	6	17	semi	semi	JJ
cord-013977-xb0r2axf	6	18	-	-	JJ
cord-013977-xb0r2axf	6	19	analytical	analytical	JJ
cord-013977-xb0r2axf	6	20	solution	solution	NN
cord-013977-xb0r2axf	6	21	.	.	.
cord-013977-xb0r2axf	7	1	In	in	IN
cord-013977-xb0r2axf	7	2	the	the	DT
cord-013977-xb0r2axf	7	3	current	current	JJ
cord-013977-xb0r2axf	7	4	study	study	NN
cord-013977-xb0r2axf	7	5	,	,	,
cord-013977-xb0r2axf	7	6	the	the	DT
cord-013977-xb0r2axf	7	7	approach	approach	NN
cord-013977-xb0r2axf	7	8	of	of	IN
cord-013977-xb0r2axf	7	9	Harko	Harko	NNP
cord-013977-xb0r2axf	7	10	et	et	NNP
cord-013977-xb0r2axf	7	11	al	al	NNP
cord-013977-xb0r2axf	7	12	.	.	.
cord-013977-xb0r2axf	8	1	(	(	-LRB-
cord-013977-xb0r2axf	8	2	Appl	Appl	NNP
cord-013977-xb0r2axf	8	3	.	.	.
cord-013977-xb0r2axf	9	1	Math	math	NN
cord-013977-xb0r2axf	9	2	.	.	.
cord-013977-xb0r2axf	10	1	Comput	Comput	NNP
cord-013977-xb0r2axf	10	2	.	.	.
cord-013977-xb0r2axf	11	1	236:184–194	236:184–194	CD
cord-013977-xb0r2axf	11	2	,	,	,
cord-013977-xb0r2axf	11	3	2014	2014	CD
cord-013977-xb0r2axf	11	4	)	)	-RRB-
cord-013977-xb0r2axf	11	5	is	be	VBZ
cord-013977-xb0r2axf	11	6	generalised	generalise	VBN
cord-013977-xb0r2axf	11	7	to	to	TO
cord-013977-xb0r2axf	11	8	obtain	obtain	VB
cord-013977-xb0r2axf	11	9	an	an	DT
cord-013977-xb0r2axf	11	10	approximate	approximate	JJ
cord-013977-xb0r2axf	11	11	semi	semi	JJ
cord-013977-xb0r2axf	11	12	-	-	JJ
cord-013977-xb0r2axf	11	13	analytical	analytical	JJ
cord-013977-xb0r2axf	11	14	solution	solution	NN
cord-013977-xb0r2axf	11	15	of	of	IN
cord-013977-xb0r2axf	11	16	the	the	DT
cord-013977-xb0r2axf	11	17	Susceptible	susceptible	JJ
cord-013977-xb0r2axf	11	18	-	-	HYPH
cord-013977-xb0r2axf	11	19	Exposed	exposed	JJ
cord-013977-xb0r2axf	11	20	-	-	HYPH
cord-013977-xb0r2axf	11	21	Infectious	Infectious	NNP
cord-013977-xb0r2axf	11	22	-	-	HYPH
cord-013977-xb0r2axf	11	23	Recovered	recovered	JJ
cord-013977-xb0r2axf	11	24	(	(	-LRB-
cord-013977-xb0r2axf	11	25	SEIR	SEIR	NNP
cord-013977-xb0r2axf	11	26	)	)	-RRB-
cord-013977-xb0r2axf	11	27	model	model	NN
cord-013977-xb0r2axf	11	28	.	.	.
cord-013977-xb0r2axf	12	1	The	the	DT
cord-013977-xb0r2axf	12	2	SEIR	SEIR	NNP
cord-013977-xb0r2axf	12	3	model	model	NN
cord-013977-xb0r2axf	12	4	curves	curve	NNS
cord-013977-xb0r2axf	12	5	have	have	VBP
cord-013977-xb0r2axf	12	6	nearly	nearly	RB
cord-013977-xb0r2axf	12	7	the	the	DT
cord-013977-xb0r2axf	12	8	same	same	JJ
cord-013977-xb0r2axf	12	9	shapes	shape	NNS
cord-013977-xb0r2axf	12	10	as	as	IN
cord-013977-xb0r2axf	12	11	the	the	DT
cord-013977-xb0r2axf	12	12	SIR	SIR	NNP
cord-013977-xb0r2axf	12	13	ones	one	NNS
cord-013977-xb0r2axf	12	14	,	,	,
cord-013977-xb0r2axf	12	15	but	but	CC
cord-013977-xb0r2axf	12	16	with	with	IN
cord-013977-xb0r2axf	12	17	a	a	DT
cord-013977-xb0r2axf	12	18	stretch	stretch	NN
cord-013977-xb0r2axf	12	19	factor	factor	NN
cord-013977-xb0r2axf	12	20	applied	apply	VBN
cord-013977-xb0r2axf	12	21	to	to	IN
cord-013977-xb0r2axf	12	22	them	-PRON-	PRP
cord-013977-xb0r2axf	12	23	across	across	IN
cord-013977-xb0r2axf	12	24	time	time	NN
cord-013977-xb0r2axf	12	25	that	that	WDT
cord-013977-xb0r2axf	12	26	is	be	VBZ
cord-013977-xb0r2axf	12	27	related	relate	VBN
cord-013977-xb0r2axf	12	28	to	to	IN
cord-013977-xb0r2axf	12	29	the	the	DT
cord-013977-xb0r2axf	12	30	ratio	ratio	NN
cord-013977-xb0r2axf	12	31	of	of	IN
cord-013977-xb0r2axf	12	32	the	the	DT
cord-013977-xb0r2axf	12	33	incubation	incubation	NN
cord-013977-xb0r2axf	12	34	to	to	IN
cord-013977-xb0r2axf	12	35	infectious	infectious	JJ
cord-013977-xb0r2axf	12	36	periods	period	NNS
cord-013977-xb0r2axf	12	37	.	.	.
cord-013977-xb0r2axf	13	1	This	this	DT
cord-013977-xb0r2axf	13	2	finding	finding	NN
cord-013977-xb0r2axf	13	3	implies	imply	VBZ
cord-013977-xb0r2axf	13	4	an	an	DT
cord-013977-xb0r2axf	13	5	approximate	approximate	JJ
cord-013977-xb0r2axf	13	6	characteristic	characteristic	JJ
cord-013977-xb0r2axf	13	7	timescale	timescale	NN
cord-013977-xb0r2axf	13	8	,	,	,
cord-013977-xb0r2axf	13	9	scaled	scale	VBN
cord-013977-xb0r2axf	13	10	by	by	IN
cord-013977-xb0r2axf	13	11	this	this	DT
cord-013977-xb0r2axf	13	12	stretch	stretch	NN
cord-013977-xb0r2axf	13	13	factor	factor	NN
cord-013977-xb0r2axf	13	14	,	,	,
cord-013977-xb0r2axf	13	15	that	that	WDT
cord-013977-xb0r2axf	13	16	is	be	VBZ
cord-013977-xb0r2axf	13	17	universal	universal	JJ
cord-013977-xb0r2axf	13	18	to	to	IN
cord-013977-xb0r2axf	13	19	all	all	DT
cord-013977-xb0r2axf	13	20	SEIR	SEIR	NNP
cord-013977-xb0r2axf	13	21	models	model	NNS
cord-013977-xb0r2axf	13	22	,	,	,
cord-013977-xb0r2axf	13	23	which	which	WDT
cord-013977-xb0r2axf	13	24	only	only	RB
cord-013977-xb0r2axf	13	25	depends	depend	VBZ
cord-013977-xb0r2axf	13	26	on	on	IN
cord-013977-xb0r2axf	13	27	the	the	DT
cord-013977-xb0r2axf	13	28	basic	basic	JJ
cord-013977-xb0r2axf	13	29	reproduction	reproduction	NN
cord-013977-xb0r2axf	13	30	number	number	NN
cord-013977-xb0r2axf	13	31	and	and	CC
cord-013977-xb0r2axf	13	32	initial	initial	JJ
cord-013977-xb0r2axf	13	33	fraction	fraction	NN
cord-013977-xb0r2axf	13	34	of	of	IN
cord-013977-xb0r2axf	13	35	the	the	DT
cord-013977-xb0r2axf	13	36	population	population	NN
cord-013977-xb0r2axf	13	37	that	that	WDT
cord-013977-xb0r2axf	13	38	is	be	VBZ
cord-013977-xb0r2axf	13	39	infectious	infectious	JJ
cord-013977-xb0r2axf	13	40	.	.	.
cord-013977-xb0r2axf	14	1	Compartmental	Compartmental	NNP
cord-013977-xb0r2axf	14	2	models	model	NNS
cord-013977-xb0r2axf	14	3	provide	provide	VBP
cord-013977-xb0r2axf	14	4	a	a	DT
cord-013977-xb0r2axf	14	5	key	key	JJ
cord-013977-xb0r2axf	14	6	tool	tool	NN
cord-013977-xb0r2axf	14	7	in	in	IN
cord-013977-xb0r2axf	14	8	infectious	infectious	JJ
cord-013977-xb0r2axf	14	9	disease	disease	NN
cord-013977-xb0r2axf	14	10	epidemiology	epidemiology	NN
cord-013977-xb0r2axf	14	11	for	for	IN
cord-013977-xb0r2axf	14	12	studying	study	VBG
cord-013977-xb0r2axf	14	13	the	the	DT
cord-013977-xb0r2axf	14	14	transmission	transmission	NN
cord-013977-xb0r2axf	14	15	dynamics	dynamic	NNS
cord-013977-xb0r2axf	14	16	of	of	IN
cord-013977-xb0r2axf	14	17	various	various	JJ
cord-013977-xb0r2axf	14	18	pathogens	pathogen	NNS
cord-013977-xb0r2axf	14	19	[	[	-LRB-
cord-013977-xb0r2axf	14	20	1	1	CD
cord-013977-xb0r2axf	14	21	]	]	-RRB-
cord-013977-xb0r2axf	14	22	[	[	-LRB-
cord-013977-xb0r2axf	14	23	2	2	CD
cord-013977-xb0r2axf	14	24	]	]	-RRB-
cord-013977-xb0r2axf	14	25	[	[	-LRB-
cord-013977-xb0r2axf	14	26	3	3	CD
cord-013977-xb0r2axf	14	27	]	]	-RRB-
cord-013977-xb0r2axf	14	28	.	.	.
cord-013977-xb0r2axf	15	1	The	the	DT
cord-013977-xb0r2axf	15	2	Susceptible	susceptible	JJ
cord-013977-xb0r2axf	15	3	-	-	HYPH
cord-013977-xb0r2axf	15	4	Infectious	Infectious	NNP
cord-013977-xb0r2axf	15	5	-	-	HYPH
cord-013977-xb0r2axf	15	6	Recovered	recovered	JJ
cord-013977-xb0r2axf	15	7	(	(	-LRB-
cord-013977-xb0r2axf	15	8	SIR	SIR	NNP
cord-013977-xb0r2axf	15	9	)	)	-RRB-
cord-013977-xb0r2axf	15	10	model	model	NN
cord-013977-xb0r2axf	15	11	is	be	VBZ
cord-013977-xb0r2axf	15	12	known	know	VBN
cord-013977-xb0r2axf	15	13	to	to	TO
cord-013977-xb0r2axf	15	14	have	have	VB
cord-013977-xb0r2axf	15	15	an	an	DT
cord-013977-xb0r2axf	15	16	exact	exact	JJ
cord-013977-xb0r2axf	15	17	semi	semi	JJ
cord-013977-xb0r2axf	15	18	-	-	JJ
cord-013977-xb0r2axf	15	19	analytical	analytical	JJ
cord-013977-xb0r2axf	15	20	solution	solution	NN
cord-013977-xb0r2axf	15	21	[	[	-LRB-
cord-013977-xb0r2axf	15	22	4	4	CD
cord-013977-xb0r2axf	15	23	]	]	-RRB-
cord-013977-xb0r2axf	15	24	[	[	-LRB-
cord-013977-xb0r2axf	15	25	5	5	CD
cord-013977-xb0r2axf	15	26	]	]	-RRB-
cord-013977-xb0r2axf	15	27	[	[	-LRB-
cord-013977-xb0r2axf	15	28	6	6	CD
cord-013977-xb0r2axf	15	29	]	]	-RRB-
cord-013977-xb0r2axf	15	30	.	.	.
cord-013977-xb0r2axf	16	1	No	no	DT
cord-013977-xb0r2axf	16	2	such	such	JJ
cord-013977-xb0r2axf	16	3	solution	solution	NN
cord-013977-xb0r2axf	16	4	exists	exist	VBZ
cord-013977-xb0r2axf	16	5	for	for	IN
cord-013977-xb0r2axf	16	6	the	the	DT
cord-013977-xb0r2axf	16	7	Susceptible	susceptible	JJ
cord-013977-xb0r2axf	16	8	-	-	HYPH
cord-013977-xb0r2axf	16	9	Exposed	exposed	JJ
cord-013977-xb0r2axf	16	10	-	-	HYPH
cord-013977-xb0r2axf	16	11	Infectious	Infectious	NNP
cord-013977-xb0r2axf	16	12	-	-	HYPH
cord-013977-xb0r2axf	16	13	Recovered	recovered	JJ
cord-013977-xb0r2axf	16	14	(	(	-LRB-
cord-013977-xb0r2axf	16	15	SEIR	SEIR	NNP
cord-013977-xb0r2axf	16	16	)	)	-RRB-
cord-013977-xb0r2axf	16	17	model	model	NN
cord-013977-xb0r2axf	16	18	,	,	,
cord-013977-xb0r2axf	16	19	although	although	IN
cord-013977-xb0r2axf	16	20	some	some	DT
cord-013977-xb0r2axf	16	21	of	of	IN
cord-013977-xb0r2axf	16	22	its	-PRON-	PRP$
cord-013977-xb0r2axf	16	23	properties	property	NNS
cord-013977-xb0r2axf	16	24	have	have	VBP
cord-013977-xb0r2axf	16	25	been	be	VBN
cord-013977-xb0r2axf	16	26	examined	examine	VBN
cord-013977-xb0r2axf	16	27	using	use	VBG
cord-013977-xb0r2axf	16	28	an	an	DT
cord-013977-xb0r2axf	16	29	approximate	approximate	JJ
cord-013977-xb0r2axf	16	30	analytical	analytical	JJ
cord-013977-xb0r2axf	16	31	approach	approach	NN
cord-013977-xb0r2axf	16	32	7	7	CD
cord-013977-xb0r2axf	16	33	.	.	.
cord-013977-xb0r2axf	17	1	In	in	IN
cord-013977-xb0r2axf	17	2	the	the	DT
cord-013977-xb0r2axf	17	3	current	current	JJ
cord-013977-xb0r2axf	17	4	study	study	NN
cord-013977-xb0r2axf	17	5	,	,	,
cord-013977-xb0r2axf	17	6	the	the	DT
cord-013977-xb0r2axf	17	7	approach	approach	NN
cord-013977-xb0r2axf	17	8	of	of	IN
cord-013977-xb0r2axf	17	9	5	5	CD
cord-013977-xb0r2axf	17	10	is	be	VBZ
cord-013977-xb0r2axf	17	11	generalised	generalise	VBN
cord-013977-xb0r2axf	17	12	to	to	TO
cord-013977-xb0r2axf	17	13	demonstrate	demonstrate	VB
cord-013977-xb0r2axf	17	14	that	that	IN
cord-013977-xb0r2axf	17	15	,	,	,
cord-013977-xb0r2axf	17	16	while	while	IN
cord-013977-xb0r2axf	17	17	no	no	DT
cord-013977-xb0r2axf	17	18	exact	exact	JJ
cord-013977-xb0r2axf	17	19	semi	semi	JJ
cord-013977-xb0r2axf	17	20	-	-	JJ
cord-013977-xb0r2axf	17	21	analytical	analytical	JJ
cord-013977-xb0r2axf	17	22	solution	solution	NN
cord-013977-xb0r2axf	17	23	is	be	VBZ
cord-013977-xb0r2axf	17	24	possible	possible	JJ
cord-013977-xb0r2axf	17	25	,	,	,
cord-013977-xb0r2axf	17	26	an	an	DT
cord-013977-xb0r2axf	17	27	approximate	approximate	JJ
cord-013977-xb0r2axf	17	28	one	one	NN
cord-013977-xb0r2axf	17	29	does	do	VBZ
cord-013977-xb0r2axf	17	30	exist	exist	VB
cord-013977-xb0r2axf	17	31	.	.	.
cord-013977-xb0r2axf	18	1	It	-PRON-	PRP
cord-013977-xb0r2axf	18	2	will	will	MD
cord-013977-xb0r2axf	18	3	be	be	VB
cord-013977-xb0r2axf	18	4	demonstrated	demonstrate	VBN
cord-013977-xb0r2axf	18	5	that	that	IN
cord-013977-xb0r2axf	18	6	this	this	DT
cord-013977-xb0r2axf	18	7	approximate	approximate	JJ
cord-013977-xb0r2axf	18	8	solution	solution	NN
cord-013977-xb0r2axf	18	9	of	of	IN
cord-013977-xb0r2axf	18	10	the	the	DT
cord-013977-xb0r2axf	18	11	SEIR	SEIR	NNP
cord-013977-xb0r2axf	18	12	model	model	NN
cord-013977-xb0r2axf	18	13	implies	imply	VBZ
cord-013977-xb0r2axf	18	14	the	the	DT
cord-013977-xb0r2axf	18	15	curves	curve	NNS
cord-013977-xb0r2axf	18	16	of	of	IN
cord-013977-xb0r2axf	18	17	all	all	DT
cord-013977-xb0r2axf	18	18	SEIR	SEIR	NNP
cord-013977-xb0r2axf	18	19	models	model	NNS
cord-013977-xb0r2axf	18	20	are	be	VBP
cord-013977-xb0r2axf	18	21	simply	simply	RB
cord-013977-xb0r2axf	18	22	stretched	stretch	VBN
cord-013977-xb0r2axf	18	23	or	or	CC
cord-013977-xb0r2axf	18	24	compressed	compress	VBN
cord-013977-xb0r2axf	18	25	relative	relative	NN
cord-013977-xb0r2axf	18	26	to	to	IN
cord-013977-xb0r2axf	18	27	one	one	CD
cord-013977-xb0r2axf	18	28	another	another	DT
cord-013977-xb0r2axf	18	29	by	by	IN
cord-013977-xb0r2axf	18	30	the	the	DT
cord-013977-xb0r2axf	18	31	factor	factor	NN
cord-013977-xb0r2axf	18	32	,	,	,
cord-013977-xb0r2axf	18	33	where	where	WRB
cord-013977-xb0r2axf	18	34	the	the	DT
cord-013977-xb0r2axf	18	35	incubation	incubation	NN
cord-013977-xb0r2axf	18	36	period	period	NN
cord-013977-xb0r2axf	18	37	is	be	VBZ
cord-013977-xb0r2axf	19	1	1	1	LS
cord-013977-xb0r2axf	19	2	/	/	SYM
cord-013977-xb0r2axf	19	3	σ	σ	NNP
cord-013977-xb0r2axf	19	4	,	,	,
cord-013977-xb0r2axf	19	5	the	the	DT
cord-013977-xb0r2axf	19	6	infectious	infectious	JJ
cord-013977-xb0r2axf	19	7	period	period	NN
cord-013977-xb0r2axf	19	8	is	be	VBZ
cord-013977-xb0r2axf	19	9	1	1	CD
cord-013977-xb0r2axf	19	10	/	/	SYM
cord-013977-xb0r2axf	19	11	γ	γ	NN
cord-013977-xb0r2axf	19	12	and	and	CC
cord-013977-xb0r2axf	19	13	the	the	DT
cord-013977-xb0r2axf	19	14	generation	generation	NN
cord-013977-xb0r2axf	19	15	time	time	NN
cord-013977-xb0r2axf	19	16	is	be	VBZ
cord-013977-xb0r2axf	19	17	1	1	CD
cord-013977-xb0r2axf	19	18	/	/	SYM
cord-013977-xb0r2axf	19	19	σ	σ	NN
cord-013977-xb0r2axf	19	20	+	+	SYM
cord-013977-xb0r2axf	19	21	1	1	CD
cord-013977-xb0r2axf	19	22	/	/	SYM
cord-013977-xb0r2axf	19	23	γ	γ	NN
cord-013977-xb0r2axf	19	24	.	.	.
cord-013977-xb0r2axf	20	1	The	the	DT
cord-013977-xb0r2axf	20	2	SIR	SIR	NNP
cord-013977-xb0r2axf	20	3	model	model	NN
cord-013977-xb0r2axf	20	4	is	be	VBZ
cord-013977-xb0r2axf	20	5	a	a	DT
cord-013977-xb0r2axf	20	6	special	special	JJ
cord-013977-xb0r2axf	20	7	case	case	NN
cord-013977-xb0r2axf	20	8	with	with	IN
cord-013977-xb0r2axf	20	9	α	α	NN
cord-013977-xb0r2axf	20	10	=	=	SYM
cord-013977-xb0r2axf	20	11	1	1	CD
cord-013977-xb0r2axf	20	12	.	.	.
cord-013977-xb0r2axf	21	1	This	this	DT
cord-013977-xb0r2axf	21	2	property	property	NN
cord-013977-xb0r2axf	21	3	implies	imply	VBZ
cord-013977-xb0r2axf	21	4	the	the	DT
cord-013977-xb0r2axf	21	5	time	time	NN
cord-013977-xb0r2axf	21	6	taken	take	VBN
cord-013977-xb0r2axf	21	7	for	for	IN
cord-013977-xb0r2axf	21	8	the	the	DT
cord-013977-xb0r2axf	21	9	infectious	infectious	JJ
cord-013977-xb0r2axf	21	10	curve	curve	NN
cord-013977-xb0r2axf	21	11	to	to	IN
cord-013977-xb0r2axf	21	12	peak	peak	VB
cord-013977-xb0r2axf	21	13	is	be	VBZ
cord-013977-xb0r2axf	21	14	approximately	approximately	RB
cord-013977-xb0r2axf	21	15	universal	universal	JJ
cord-013977-xb0r2axf	21	16	for	for	IN
cord-013977-xb0r2axf	21	17	the	the	DT
cord-013977-xb0r2axf	21	18	SEIR	SEIR	NNP
cord-013977-xb0r2axf	21	19	model	model	NN
cord-013977-xb0r2axf	21	20	when	when	WRB
cord-013977-xb0r2axf	21	21	scaled	scale	VBN
cord-013977-xb0r2axf	21	22	by	by	IN
cord-013977-xb0r2axf	21	23	α	α	NN
cord-013977-xb0r2axf	21	24	.	.	.
cord-013977-xb0r2axf	22	1	In	in	IN
cord-013977-xb0r2axf	22	2	"	"	``
cord-013977-xb0r2axf	22	3	The	the	DT
cord-013977-xb0r2axf	22	4	SIR	SIR	NNP
cord-013977-xb0r2axf	22	5	model	model	NN
cord-013977-xb0r2axf	22	6	"	"	''
cord-013977-xb0r2axf	22	7	section	section	NN
cord-013977-xb0r2axf	22	8	,	,	,
cord-013977-xb0r2axf	22	9	the	the	DT
cord-013977-xb0r2axf	22	10	SIR	SIR	NNP
cord-013977-xb0r2axf	22	11	model	model	NN
cord-013977-xb0r2axf	22	12	is	be	VBZ
cord-013977-xb0r2axf	22	13	concisely	concisely	RB
cord-013977-xb0r2axf	22	14	reviewed	review	VBN
cord-013977-xb0r2axf	22	15	and	and	CC
cord-013977-xb0r2axf	22	16	extended	extend	VBN
cord-013977-xb0r2axf	22	17	.	.	.
cord-013977-xb0r2axf	23	1	In	in	IN
cord-013977-xb0r2axf	23	2	"	"	``
cord-013977-xb0r2axf	23	3	The	the	DT
cord-013977-xb0r2axf	23	4	SEIR	seir	NN
cord-013977-xb0r2axf	23	5	model	model	NN
cord-013977-xb0r2axf	23	6	"	"	''
cord-013977-xb0r2axf	23	7	section	section	NN
cord-013977-xb0r2axf	23	8	,	,	,
cord-013977-xb0r2axf	23	9	approximate	approximate	JJ
cord-013977-xb0r2axf	23	10	solutions	solution	NNS
cord-013977-xb0r2axf	23	11	of	of	IN
cord-013977-xb0r2axf	23	12	the	the	DT
cord-013977-xb0r2axf	23	13	SEIR	SEIR	NNP
cord-013977-xb0r2axf	23	14	model	model	NN
cord-013977-xb0r2axf	23	15	and	and	CC
cord-013977-xb0r2axf	23	16	their	-PRON-	PRP$
cord-013977-xb0r2axf	23	17	implications	implication	NNS
cord-013977-xb0r2axf	23	18	are	be	VBP
cord-013977-xb0r2axf	23	19	elucidated	elucidate	VBN
cord-013977-xb0r2axf	23	20	.	.	.
cord-013977-xb0r2axf	24	1	A	a	DT
cord-013977-xb0r2axf	24	2	concise	concise	JJ
cord-013977-xb0r2axf	24	3	summary	summary	NN
cord-013977-xb0r2axf	24	4	is	be	VBZ
cord-013977-xb0r2axf	24	5	provided	provide	VBN
cord-013977-xb0r2axf	24	6	in	in	IN
cord-013977-xb0r2axf	24	7	"	"	``
cord-013977-xb0r2axf	24	8	Summary	Summary	NNP
cord-013977-xb0r2axf	24	9	"	"	''
cord-013977-xb0r2axf	24	10	section	section	NN
cord-013977-xb0r2axf	24	11	.	.	.
cord-013977-xb0r2axf	25	1	In	in	IN
cord-013977-xb0r2axf	25	2	the	the	DT
cord-013977-xb0r2axf	25	3	SIR	SIR	NNP
cord-013977-xb0r2axf	25	4	model	model	NN
cord-013977-xb0r2axf	25	5	,	,	,
cord-013977-xb0r2axf	25	6	the	the	DT
cord-013977-xb0r2axf	25	7	fraction	fraction	NN
cord-013977-xb0r2axf	25	8	of	of	IN
cord-013977-xb0r2axf	25	9	the	the	DT
cord-013977-xb0r2axf	25	10	population	population	NN
cord-013977-xb0r2axf	25	11	that	that	WDT
cord-013977-xb0r2axf	25	12	is	be	VBZ
cord-013977-xb0r2axf	25	13	susceptible	susceptible	JJ
cord-013977-xb0r2axf	25	14	(	(	-LRB-
cord-013977-xb0r2axf	25	15	S	s	NN
cord-013977-xb0r2axf	25	16	)	)	-RRB-
cord-013977-xb0r2axf	25	17	becomes	become	VBZ
cord-013977-xb0r2axf	25	18	infected	infect	VBN
cord-013977-xb0r2axf	25	19	at	at	IN
cord-013977-xb0r2axf	25	20	a	a	DT
cord-013977-xb0r2axf	25	21	rate	rate	NN
cord-013977-xb0r2axf	25	22	β	β	NN
cord-013977-xb0r2axf	25	23	=	=	SYM
cord-013977-xb0r2axf	25	24	R	r	NN
cord-013977-xb0r2axf	25	25	0	0	CD
cord-013977-xb0r2axf	25	26	γ	γ	NN
cord-013977-xb0r2axf	25	27	,	,	,
cord-013977-xb0r2axf	25	28	where	where	WRB
cord-013977-xb0r2axf	25	29	R	r	NN
cord-013977-xb0r2axf	25	30	0	0	CD
cord-013977-xb0r2axf	25	31	is	be	VBZ
cord-013977-xb0r2axf	25	32	the	the	DT
cord-013977-xb0r2axf	25	33	basic	basic	JJ
cord-013977-xb0r2axf	25	34	reproduction	reproduction	NN
cord-013977-xb0r2axf	25	35	number	number	NN
cord-013977-xb0r2axf	25	36	.	.	.
cord-013977-xb0r2axf	26	1	There	there	EX
cord-013977-xb0r2axf	26	2	is	be	VBZ
cord-013977-xb0r2axf	26	3	no	no	DT
cord-013977-xb0r2axf	26	4	incubation	incubation	NN
cord-013977-xb0r2axf	26	5	period	period	NN
cord-013977-xb0r2axf	26	6	.	.	.
cord-013977-xb0r2axf	27	1	The	the	DT
cord-013977-xb0r2axf	27	2	fraction	fraction	NN
cord-013977-xb0r2axf	27	3	of	of	IN
cord-013977-xb0r2axf	27	4	the	the	DT
cord-013977-xb0r2axf	27	5	population	population	NN
cord-013977-xb0r2axf	27	6	that	that	WDT
cord-013977-xb0r2axf	27	7	is	be	VBZ
cord-013977-xb0r2axf	27	8	infected	infect	VBN
cord-013977-xb0r2axf	27	9	is	be	VBZ
cord-013977-xb0r2axf	27	10	immediately	immediately	RB
cord-013977-xb0r2axf	27	11	infectious	infectious	JJ
cord-013977-xb0r2axf	27	12	(	(	-LRB-
cord-013977-xb0r2axf	27	13	I	i	NN
cord-013977-xb0r2axf	27	14	)	)	-RRB-
cord-013977-xb0r2axf	27	15	for	for	IN
cord-013977-xb0r2axf	27	16	a	a	DT
cord-013977-xb0r2axf	27	17	period	period	NN
cord-013977-xb0r2axf	27	18	of	of	IN
cord-013977-xb0r2axf	27	19	1	1	CD
cord-013977-xb0r2axf	27	20	/	/	SYM
cord-013977-xb0r2axf	27	21	γ	γ	NN
cord-013977-xb0r2axf	27	22	,	,	,
cord-013977-xb0r2axf	27	23	after	after	IN
cord-013977-xb0r2axf	27	24	which	which	WDT
cord-013977-xb0r2axf	27	25	a	a	DT
cord-013977-xb0r2axf	27	26	fraction	fraction	NN
cord-013977-xb0r2axf	27	27	of	of	IN
cord-013977-xb0r2axf	27	28	the	the	DT
cord-013977-xb0r2axf	27	29	population	population	NN
cord-013977-xb0r2axf	27	30	recovers	recover	VBZ
cord-013977-xb0r2axf	27	31	(	(	-LRB-
cord-013977-xb0r2axf	27	32	R	r	NN
cord-013977-xb0r2axf	27	33	)	)	-RRB-
cord-013977-xb0r2axf	27	34	.	.	.
cord-013977-xb0r2axf	28	1	The	the	DT
cord-013977-xb0r2axf	28	2	SIR	SIR	NNP
cord-013977-xb0r2axf	28	3	model	model	NN
cord-013977-xb0r2axf	28	4	is	be	VBZ
cord-013977-xb0r2axf	28	5	described	describe	VBN
cord-013977-xb0r2axf	28	6	by	by	IN
cord-013977-xb0r2axf	28	7	the	the	DT
cord-013977-xb0r2axf	28	8	following	following	JJ
cord-013977-xb0r2axf	28	9	set	set	NN
cord-013977-xb0r2axf	28	10	of	of	IN
cord-013977-xb0r2axf	28	11	coupled	coupled	JJ
cord-013977-xb0r2axf	28	12	ordinary	ordinary	JJ
cord-013977-xb0r2axf	28	13	differential	differential	JJ
cord-013977-xb0r2axf	28	14	equations	equation	NNS
cord-013977-xb0r2axf	28	15	1,5	1,5	CD
cord-013977-xb0r2axf	28	16	,	,	,
cord-013977-xb0r2axf	28	17	Review	Review	NNP
cord-013977-xb0r2axf	28	18	of	of	IN
cord-013977-xb0r2axf	28	19	Harko	Harko	NNP
cord-013977-xb0r2axf	28	20	et	et	NNP
cord-013977-xb0r2axf	28	21	al	al	NNP
cord-013977-xb0r2axf	28	22	.	.	.
cord-013977-xb0r2axf	29	1	5	5	LS
cord-013977-xb0r2axf	29	2	.	.	.
cord-013977-xb0r2axf	30	1	As	as	IN
cord-013977-xb0r2axf	30	2	a	a	DT
cord-013977-xb0r2axf	30	3	starting	starting	NN
cord-013977-xb0r2axf	30	4	point	point	NN
cord-013977-xb0r2axf	30	5	,	,	,
cord-013977-xb0r2axf	30	6	the	the	DT
cord-013977-xb0r2axf	30	7	derivation	derivation	NN
cord-013977-xb0r2axf	30	8	of	of	IN
cord-013977-xb0r2axf	30	9	5	5	CD
cord-013977-xb0r2axf	30	10	is	be	VBZ
cord-013977-xb0r2axf	30	11	made	make	VBN
cord-013977-xb0r2axf	30	12	more	more	RBR
cord-013977-xb0r2axf	30	13	compact	compact	JJ
cord-013977-xb0r2axf	30	14	and	and	CC
cord-013977-xb0r2axf	30	15	cast	cast	VBN
cord-013977-xb0r2axf	30	16	in	in	IN
cord-013977-xb0r2axf	30	17	the	the	DT
cord-013977-xb0r2axf	30	18	mathematical	mathematical	JJ
cord-013977-xb0r2axf	30	19	notation	notation	NN
cord-013977-xb0r2axf	30	20	of	of	IN
cord-013977-xb0r2axf	30	21	the	the	DT
cord-013977-xb0r2axf	30	22	current	current	JJ
cord-013977-xb0r2axf	30	23	study	study	NN
cord-013977-xb0r2axf	30	24	.	.	.
cord-013977-xb0r2axf	31	1	By	by	IN
cord-013977-xb0r2axf	31	2	taking	take	VBG
cord-013977-xb0r2axf	31	3	the	the	DT
cord-013977-xb0r2axf	31	4	derivative	derivative	NN
cord-013977-xb0r2axf	31	5	of	of	IN
cord-013977-xb0r2axf	31	6	the	the	DT
cord-013977-xb0r2axf	31	7	first	first	JJ
cord-013977-xb0r2axf	31	8	equation	equation	NN
cord-013977-xb0r2axf	31	9	of	of	IN
cord-013977-xb0r2axf	31	10	(	(	-LRB-
cord-013977-xb0r2axf	31	11	2	2	CD
cord-013977-xb0r2axf	31	12	)	)	-RRB-
cord-013977-xb0r2axf	31	13	with	with	IN
cord-013977-xb0r2axf	31	14	respect	respect	NN
cord-013977-xb0r2axf	31	15	to	to	IN
cord-013977-xb0r2axf	31	16	time	time	NN
cord-013977-xb0r2axf	31	17	,	,	,
cord-013977-xb0r2axf	31	18	one	one	NN
cord-013977-xb0r2axf	31	19	obtains	obtain	VBZ
cord-013977-xb0r2axf	31	20	equation	equation	NN
cord-013977-xb0r2axf	31	21	(	(	-LRB-
cord-013977-xb0r2axf	31	22	12	12	CD
cord-013977-xb0r2axf	31	23	)	)	-RRB-
cord-013977-xb0r2axf	31	24	of	of	IN
cord-013977-xb0r2axf	31	25	5	5	CD
cord-013977-xb0r2axf	31	26	,	,	,
cord-013977-xb0r2axf	31	27	where	where	WRB
cord-013977-xb0r2axf	31	28	for	for	IN
cord-013977-xb0r2axf	31	29	convenience	convenience	NN
cord-013977-xb0r2axf	31	30	one	one	CD
cord-013977-xb0r2axf	31	31	uses	use	VBZ
cord-013977-xb0r2axf	31	32	shorthand	shorthand	NN
cord-013977-xb0r2axf	31	33	notation	notation	NN
cord-013977-xb0r2axf	31	34	for	for	IN
cord-013977-xb0r2axf	31	35	the	the	DT
cord-013977-xb0r2axf	31	36	derivatives	derivative	NNS
cord-013977-xb0r2axf	31	37	with	with	IN
cord-013977-xb0r2axf	31	38	respect	respect	NN
cord-013977-xb0r2axf	31	39	to	to	IN
cord-013977-xb0r2axf	31	40	time	time	NN
cord-013977-xb0r2axf	31	41	,	,	,
cord-013977-xb0r2axf	31	42	one	one	PRP
cord-013977-xb0r2axf	31	43	obtains	obtain	VBZ
cord-013977-xb0r2axf	31	44	from	from	IN
cord-013977-xb0r2axf	31	45	Eq	Eq	NNP
cord-013977-xb0r2axf	31	46	.	.	.
cord-013977-xb0r2axf	32	1	(	(	-LRB-
cord-013977-xb0r2axf	32	2	5	5	LS
cord-013977-xb0r2axf	32	3	)	)	-RRB-
cord-013977-xb0r2axf	32	4	an	an	DT
cord-013977-xb0r2axf	32	5	expression	expression	NN
cord-013977-xb0r2axf	32	6	that	that	WDT
cord-013977-xb0r2axf	32	7	is	be	VBZ
cord-013977-xb0r2axf	32	8	equivalent	equivalent	JJ
cord-013977-xb0r2axf	32	9	,	,	,
cord-013977-xb0r2axf	32	10	but	but	CC
cord-013977-xb0r2axf	32	11	not	not	RB
cord-013977-xb0r2axf	32	12	identical	identical	JJ
cord-013977-xb0r2axf	32	13	,	,	,
cord-013977-xb0r2axf	32	14	to	to	IN
cord-013977-xb0r2axf	32	15	equation	equation	NN
cord-013977-xb0r2axf	32	16	(	(	-LRB-
cord-013977-xb0r2axf	32	17	24	24	CD
cord-013977-xb0r2axf	32	18	)	)	-RRB-
cord-013977-xb0r2axf	32	19	of	of	IN
cord-013977-xb0r2axf	32	20	5	5	CD
cord-013977-xb0r2axf	32	21	,	,	,
cord-013977-xb0r2axf	32	22	because	because	IN
cord-013977-xb0r2axf	32	23	one	one	PRP
cord-013977-xb0r2axf	32	24	has	have	VBZ
cord-013977-xb0r2axf	32	25	chosen	choose	VBN
cord-013977-xb0r2axf	32	26	to	to	TO
cord-013977-xb0r2axf	32	27	work	work	VB
cord-013977-xb0r2axf	32	28	directly	directly	RB
cord-013977-xb0r2axf	32	29	with	with	IN
cord-013977-xb0r2axf	32	30	S	S	NNP
cord-013977-xb0r2axf	32	31	(	(	-LRB-
cord-013977-xb0r2axf	32	32	and	and	CC
cord-013977-xb0r2axf	32	33	not	not	RB
cord-013977-xb0r2axf	32	34	S	S	NNP
cord-013977-xb0r2axf	32	35	/	/	SYM
cord-013977-xb0r2axf	32	36	S	S	NNP
cord-013977-xb0r2axf	32	37	0	0	CD
cord-013977-xb0r2axf	32	38	)	)	-RRB-
cord-013977-xb0r2axf	32	39	as	as	IN
cord-013977-xb0r2axf	32	40	the	the	DT
cord-013977-xb0r2axf	32	41	independent	independent	JJ
cord-013977-xb0r2axf	32	42	variable	variable	NN
cord-013977-xb0r2axf	32	43	.	.	.
cord-013977-xb0r2axf	33	1	The	the	DT
cord-013977-xb0r2axf	33	2	preceding	precede	VBG
cord-013977-xb0r2axf	33	3	expression	expression	NN
cord-013977-xb0r2axf	33	4	is	be	VBZ
cord-013977-xb0r2axf	33	5	recognised	recognise	VBN
cord-013977-xb0r2axf	33	6	as	as	IN
cord-013977-xb0r2axf	33	7	a	a	DT
cord-013977-xb0r2axf	33	8	Bernoulli	Bernoulli	NNP
cord-013977-xb0r2axf	33	9	differential	differential	JJ
cord-013977-xb0r2axf	33	10	equation	equation	NN
cord-013977-xb0r2axf	33	11	,	,	,
cord-013977-xb0r2axf	33	12	which	which	WDT
cord-013977-xb0r2axf	33	13	may	may	MD
cord-013977-xb0r2axf	33	14	be	be	VB
cord-013977-xb0r2axf	33	15	solved	solve	VBN
cord-013977-xb0r2axf	33	16	to	to	TO
cord-013977-xb0r2axf	33	17	obtain	obtain	VB
cord-013977-xb0r2axf	33	18	an	an	DT
cord-013977-xb0r2axf	33	19	expression	expression	NN
cord-013977-xb0r2axf	33	20	that	that	WDT
cord-013977-xb0r2axf	33	21	is	be	VBZ
cord-013977-xb0r2axf	33	22	equivalent	equivalent	JJ
cord-013977-xb0r2axf	33	23	,	,	,
cord-013977-xb0r2axf	33	24	but	but	CC
cord-013977-xb0r2axf	33	25	not	not	RB
cord-013977-xb0r2axf	33	26	identical	identical	JJ
cord-013977-xb0r2axf	33	27	,	,	,
cord-013977-xb0r2axf	33	28	to	to	IN
cord-013977-xb0r2axf	33	29	equation	equation	NN
cord-013977-xb0r2axf	33	30	(	(	-LRB-
cord-013977-xb0r2axf	33	31	25	25	CD
cord-013977-xb0r2axf	33	32	)	)	-RRB-
cord-013977-xb0r2axf	33	33	of	of	IN
cord-013977-xb0r2axf	33	34	5	5	CD
cord-013977-xb0r2axf	33	35	,	,	,
cord-013977-xb0r2axf	33	36	where	where	WRB
cord-013977-xb0r2axf	33	37	the	the	DT
cord-013977-xb0r2axf	33	38	initial	initial	JJ
cord-013977-xb0r2axf	33	39	value	value	NN
cord-013977-xb0r2axf	33	40	of	of	IN
cord-013977-xb0r2axf	33	41	S	S	NNP
cord-013977-xb0r2axf	33	42	is	be	VBZ
cord-013977-xb0r2axf	33	43	denoted	denote	VBN
cord-013977-xb0r2axf	33	44	as	as	IN
cord-013977-xb0r2axf	33	45	S	S	NNP
cord-013977-xb0r2axf	33	46	0	0	CD
cord-013977-xb0r2axf	33	47	.	.	.
cord-013977-xb0r2axf	34	1	The	the	DT
cord-013977-xb0r2axf	34	2	constant	constant	NN
cord-013977-xb0r2axf	34	3	of	of	IN
cord-013977-xb0r2axf	34	4	integration	integration	NN
cord-013977-xb0r2axf	34	5	is	be	VBZ
cord-013977-xb0r2axf	34	6	set	set	VBN
cord-013977-xb0r2axf	34	7	by	by	IN
cord-013977-xb0r2axf	34	8	demanding	demand	VBG
cord-013977-xb0r2axf	34	9	that	that	DT
cord-013977-xb0r2axf	34	10	S	s	NN
cord-013977-xb0r2axf	35	1	+	+	CC
cord-013977-xb0r2axf	36	1	I	-PRON-	PRP
cord-013977-xb0r2axf	36	2	+	+	CC
cord-013977-xb0r2axf	36	3	R	r	NN
cord-013977-xb0r2axf	36	4	=	=	SYM
cord-013977-xb0r2axf	36	5	1	1	CD
cord-013977-xb0r2axf	36	6	.	.	.
cord-013977-xb0r2axf	37	1	Recalling	recall	VBG
cord-013977-xb0r2axf	37	2	the	the	DT
cord-013977-xb0r2axf	37	3	definition	definition	NN
cord-013977-xb0r2axf	37	4	of	of	IN
cord-013977-xb0r2axf	37	5	φ	φ	NN
cord-013977-xb0r2axf	37	6	,	,	,
cord-013977-xb0r2axf	37	7	an	an	DT
cord-013977-xb0r2axf	37	8	expression	expression	NN
cord-013977-xb0r2axf	37	9	that	that	WDT
cord-013977-xb0r2axf	37	10	is	be	VBZ
cord-013977-xb0r2axf	37	11	equivalent	equivalent	JJ
cord-013977-xb0r2axf	37	12	to	to	IN
cord-013977-xb0r2axf	37	13	equation	equation	NN
cord-013977-xb0r2axf	37	14	(	(	-LRB-
cord-013977-xb0r2axf	37	15	26	26	CD
cord-013977-xb0r2axf	37	16	)	)	-RRB-
cord-013977-xb0r2axf	37	17	of	of	IN
cord-013977-xb0r2axf	37	18	5	5	CD
cord-013977-xb0r2axf	37	19	 	 	_SP
cord-013977-xb0r2axf	37	20	where	where	WRB
cord-013977-xb0r2axf	37	21	t	t	NN
cord-013977-xb0r2axf	37	22	0	0	CD
cord-013977-xb0r2axf	37	23	is	be	VBZ
cord-013977-xb0r2axf	37	24	the	the	DT
cord-013977-xb0r2axf	37	25	initial	initial	JJ
cord-013977-xb0r2axf	37	26	time	time	NN
cord-013977-xb0r2axf	37	27	.	.	.
cord-013977-xb0r2axf	38	1	The	the	DT
cord-013977-xb0r2axf	38	2	preceding	precede	VBG
cord-013977-xb0r2axf	38	3	integral	integral	NN
cord-013977-xb0r2axf	38	4	has	have	VBZ
cord-013977-xb0r2axf	38	5	no	no	DT
cord-013977-xb0r2axf	38	6	exact	exact	JJ
cord-013977-xb0r2axf	38	7	analytical	analytical	JJ
cord-013977-xb0r2axf	38	8	(	(	-LRB-
cord-013977-xb0r2axf	38	9	closed	closed	JJ
cord-013977-xb0r2axf	38	10	-	-	HYPH
cord-013977-xb0r2axf	38	11	form	form	NN
cord-013977-xb0r2axf	38	12	)	)	-RRB-
cord-013977-xb0r2axf	38	13	solution	solution	NN
cord-013977-xb0r2axf	38	14	and	and	CC
cord-013977-xb0r2axf	38	15	needs	need	VBZ
cord-013977-xb0r2axf	38	16	to	to	TO
cord-013977-xb0r2axf	38	17	be	be	VB
cord-013977-xb0r2axf	38	18	evaluated	evaluate	VBN
cord-013977-xb0r2axf	38	19	numerically	numerically	RB
cord-013977-xb0r2axf	38	20	,	,	,
cord-013977-xb0r2axf	38	21	which	which	WDT
cord-013977-xb0r2axf	38	22	is	be	VBZ
cord-013977-xb0r2axf	38	23	why	why	WRB
cord-013977-xb0r2axf	38	24	it	-PRON-	PRP
cord-013977-xb0r2axf	38	25	is	be	VBZ
cord-013977-xb0r2axf	38	26	strictly	strictly	RB
cord-013977-xb0r2axf	38	27	speaking	speak	VBG
cord-013977-xb0r2axf	38	28	an	an	DT
cord-013977-xb0r2axf	38	29	exact	exact	JJ
cord-013977-xb0r2axf	38	30	semi	semi	JJ
cord-013977-xb0r2axf	38	31	-	-	JJ
cord-013977-xb0r2axf	38	32	analytical	analytical	JJ
cord-013977-xb0r2axf	38	33	solution	solution	NN
cord-013977-xb0r2axf	38	34	of	of	IN
cord-013977-xb0r2axf	38	35	the	the	DT
cord-013977-xb0r2axf	38	36	SIR	SIR	NNP
cord-013977-xb0r2axf	38	37	model	model	NN
cord-013977-xb0r2axf	38	38	.	.	.
cord-013977-xb0r2axf	39	1	The	the	DT
cord-013977-xb0r2axf	39	2	first	first	JJ
cord-013977-xb0r2axf	39	3	and	and	CC
cord-013977-xb0r2axf	39	4	third	third	JJ
cord-013977-xb0r2axf	39	5	equation	equation	NN
cord-013977-xb0r2axf	39	6	of	of	IN
cord-013977-xb0r2axf	39	7	(	(	-LRB-
cord-013977-xb0r2axf	39	8	2	2	CD
cord-013977-xb0r2axf	39	9	)	)	-RRB-
cord-013977-xb0r2axf	39	10	may	may	MD
cord-013977-xb0r2axf	39	11	be	be	VB
cord-013977-xb0r2axf	39	12	combined	combine	VBN
cord-013977-xb0r2axf	39	13	to	to	TO
cord-013977-xb0r2axf	39	14	obtain	obtain	VB
cord-013977-xb0r2axf	39	15	where	where	WRB
cord-013977-xb0r2axf	39	16	the	the	DT
cord-013977-xb0r2axf	39	17	initial	initial	JJ
cord-013977-xb0r2axf	39	18	fraction	fraction	NN
cord-013977-xb0r2axf	39	19	of	of	IN
cord-013977-xb0r2axf	39	20	the	the	DT
cord-013977-xb0r2axf	39	21	population	population	NN
cord-013977-xb0r2axf	39	22	that	that	WDT
cord-013977-xb0r2axf	39	23	has	have	VBZ
cord-013977-xb0r2axf	39	24	recovered	recover	VBN
cord-013977-xb0r2axf	39	25	is	be	VBZ
cord-013977-xb0r2axf	39	26	chosen	choose	VBN
cord-013977-xb0r2axf	39	27	to	to	TO
cord-013977-xb0r2axf	39	28	be	be	VB
cord-013977-xb0r2axf	39	29	R	r	NN
cord-013977-xb0r2axf	39	30	0	0	CD
cord-013977-xb0r2axf	39	31	=	=	SYM
cord-013977-xb0r2axf	39	32	0	0	CD
cord-013977-xb0r2axf	39	33	,	,	,
cord-013977-xb0r2axf	39	34	which	which	WDT
cord-013977-xb0r2axf	39	35	in	in	IN
cord-013977-xb0r2axf	39	36	turn	turn	NN
cord-013977-xb0r2axf	39	37	implies	imply	VBZ
cord-013977-xb0r2axf	39	38	that	that	IN
cord-013977-xb0r2axf	39	39	the	the	DT
cord-013977-xb0r2axf	39	40	initial	initial	JJ
cord-013977-xb0r2axf	39	41	fraction	fraction	NN
cord-013977-xb0r2axf	39	42	of	of	IN
cord-013977-xb0r2axf	39	43	the	the	DT
cord-013977-xb0r2axf	39	44	population	population	NN
cord-013977-xb0r2axf	39	45	that	that	WDT
cord-013977-xb0r2axf	39	46	is	be	VBZ
cord-013977-xb0r2axf	39	47	infectious	infectious	JJ
cord-013977-xb0r2axf	39	48	is	be	VBZ
cord-013977-xb0r2axf	39	49	Extension	Extension	NNP
cord-013977-xb0r2axf	39	50	of	of	IN
cord-013977-xb0r2axf	39	51	Harko	Harko	NNP
cord-013977-xb0r2axf	39	52	et	et	NNP
cord-013977-xb0r2axf	39	53	al	al	NNP
cord-013977-xb0r2axf	39	54	.	.	.
cord-013977-xb0r2axf	40	1	5	5	LS
cord-013977-xb0r2axf	40	2	.	.	.
cord-013977-xb0r2axf	41	1	By	by	IN
cord-013977-xb0r2axf	41	2	setting	set	VBG
cord-013977-xb0r2axf	41	3	I	-PRON-	PRP
cord-013977-xb0r2axf	41	4	′	′	CD
cord-013977-xb0r2axf	41	5	=	=	SYM
cord-013977-xb0r2axf	41	6	0	0	CD
cord-013977-xb0r2axf	42	1	in	in	IN
cord-013977-xb0r2axf	42	2	Eq	Eq	NNP
cord-013977-xb0r2axf	42	3	.	.	.
cord-013977-xb0r2axf	43	1	(	(	-LRB-
cord-013977-xb0r2axf	43	2	2	2	LS
cord-013977-xb0r2axf	43	3	)	)	-RRB-
cord-013977-xb0r2axf	43	4	,	,	,
cord-013977-xb0r2axf	43	5	one	one	PRP
cord-013977-xb0r2axf	43	6	realizes	realize	VBZ
cord-013977-xb0r2axf	43	7	that	that	IN
cord-013977-xb0r2axf	43	8	the	the	DT
cord-013977-xb0r2axf	43	9	infectious	infectious	JJ
cord-013977-xb0r2axf	43	10	curve	curve	NN
cord-013977-xb0r2axf	43	11	I	-PRON-	PRP
cord-013977-xb0r2axf	43	12	peaks	peak	NNS
cord-013977-xb0r2axf	43	13	at	at	IN
cord-013977-xb0r2axf	43	14	S	s	NN
cord-013977-xb0r2axf	43	15	=	=	SYM
cord-013977-xb0r2axf	43	16	γ	γ	NN
cord-013977-xb0r2axf	43	17	/β	/β	NNP
cord-013977-xb0r2axf	43	18	=	=	SYM
cord-013977-xb0r2axf	43	19	1	1	CD
cord-013977-xb0r2axf	43	20	/	/	SYM
cord-013977-xb0r2axf	43	21	R	r	NN
cord-013977-xb0r2axf	43	22	0	0	CD
cord-013977-xb0r2axf	43	23	.	.	.
cord-013977-xb0r2axf	44	1	Thus	thus	RB
cord-013977-xb0r2axf	44	2	,	,	,
cord-013977-xb0r2axf	44	3	Eq	Eq	NNP
cord-013977-xb0r2axf	44	4	.	.	.
cord-013977-xb0r2axf	45	1	(	(	-LRB-
cord-013977-xb0r2axf	45	2	9	9	LS
cord-013977-xb0r2axf	45	3	)	)	-RRB-
cord-013977-xb0r2axf	45	4	may	may	MD
cord-013977-xb0r2axf	45	5	be	be	VB
cord-013977-xb0r2axf	45	6	used	use	VBN
cord-013977-xb0r2axf	45	7	to	to	TO
cord-013977-xb0r2axf	45	8	express	express	VB
cord-013977-xb0r2axf	45	9	the	the	DT
cord-013977-xb0r2axf	45	10	time	time	NN
cord-013977-xb0r2axf	45	11	taken	take	VBN
cord-013977-xb0r2axf	45	12	for	for	IN
cord-013977-xb0r2axf	45	13	I	-PRON-	PRP
cord-013977-xb0r2axf	45	14	to	to	TO
cord-013977-xb0r2axf	45	15	peak	peak	VB
cord-013977-xb0r2axf	45	16	,	,	,
cord-013977-xb0r2axf	45	17	where	where	WRB
cord-013977-xb0r2axf	45	18	one	one	NN
cord-013977-xb0r2axf	45	19	assumes	assume	VBZ
cord-013977-xb0r2axf	45	20	I	-PRON-	PRP
cord-013977-xb0r2axf	45	21	0	0	CD
cord-013977-xb0r2axf	45	22	≪	≪	CD
cord-013977-xb0r2axf	45	23	1	1	CD
cord-013977-xb0r2axf	45	24	.	.	.
cord-013977-xb0r2axf	46	1	The	the	DT
cord-013977-xb0r2axf	46	2	quantity	quantity	NN
cord-013977-xb0r2axf	46	3	γ	γ	NN
cord-013977-xb0r2axf	46	4	�	�	NNP
cord-013977-xb0r2axf	46	5	t	t	NN
cord-013977-xb0r2axf	46	6	is	be	VBZ
cord-013977-xb0r2axf	46	7	the	the	DT
cord-013977-xb0r2axf	46	8	time	time	NN
cord-013977-xb0r2axf	46	9	interval	interval	NN
cord-013977-xb0r2axf	46	10	expressed	express	VBN
cord-013977-xb0r2axf	46	11	in	in	IN
cord-013977-xb0r2axf	46	12	terms	term	NNS
cord-013977-xb0r2axf	46	13	of	of	IN
cord-013977-xb0r2axf	46	14	the	the	DT
cord-013977-xb0r2axf	46	15	infectious	infectious	JJ
cord-013977-xb0r2axf	46	16	period	period	NN
cord-013977-xb0r2axf	46	17	and	and	CC
cord-013977-xb0r2axf	46	18	depends	depend	VBZ
cord-013977-xb0r2axf	46	19	only	only	RB
cord-013977-xb0r2axf	46	20	on	on	IN
cord-013977-xb0r2axf	46	21	two	two	CD
cord-013977-xb0r2axf	46	22	parameters	parameter	NNS
cord-013977-xb0r2axf	46	23	:	:	:
cord-013977-xb0r2axf	46	24	R	r	NN
cord-013977-xb0r2axf	46	25	0	0	CD
cord-013977-xb0r2axf	46	26	and	and	CC
cord-013977-xb0r2axf	46	27	I	-PRON-	PRP
cord-013977-xb0r2axf	46	28	0	0	CD
cord-013977-xb0r2axf	46	29	.	.	.
cord-013977-xb0r2axf	47	1	Variations	variation	NNS
cord-013977-xb0r2axf	47	2	in	in	IN
cord-013977-xb0r2axf	47	3	I	I	NNP
cord-013977-xb0r2axf	47	4	0	0	CD
cord-013977-xb0r2axf	47	5	shift	shift	NN
cord-013977-xb0r2axf	48	1	the	the	DT
cord-013977-xb0r2axf	48	2	S	S	NNP
cord-013977-xb0r2axf	48	3	,	,	,
cord-013977-xb0r2axf	48	4	I	-PRON-	PRP
cord-013977-xb0r2axf	48	5	and	and	CC
cord-013977-xb0r2axf	48	6	R	r	NN
cord-013977-xb0r2axf	48	7	curves	curve	NNS
cord-013977-xb0r2axf	48	8	back	back	RB
cord-013977-xb0r2axf	48	9	and	and	CC
cord-013977-xb0r2axf	48	10	forth	forth	RB
cord-013977-xb0r2axf	48	11	in	in	IN
cord-013977-xb0r2axf	48	12	time	time	NN
cord-013977-xb0r2axf	48	13	without	without	IN
cord-013977-xb0r2axf	48	14	changing	change	VBG
cord-013977-xb0r2axf	48	15	their	-PRON-	PRP$
cord-013977-xb0r2axf	48	16	shapes	shape	NNS
cord-013977-xb0r2axf	48	17	.	.	.
cord-013977-xb0r2axf	49	1	We	-PRON-	PRP
cord-013977-xb0r2axf	49	2	emphasize	emphasize	VBP
cord-013977-xb0r2axf	49	3	a	a	DT
cord-013977-xb0r2axf	49	4	subtle	subtle	JJ
cord-013977-xb0r2axf	49	5	choice	choice	NN
cord-013977-xb0r2axf	49	6	of	of	IN
cord-013977-xb0r2axf	49	7	notation	notation	NN
cord-013977-xb0r2axf	49	8	:	:	:
cord-013977-xb0r2axf	49	9	R	r	NN
cord-013977-xb0r2axf	49	10	0	0	CD
cord-013977-xb0r2axf	49	11	is	be	VBZ
cord-013977-xb0r2axf	49	12	the	the	DT
cord-013977-xb0r2axf	49	13	initial	initial	JJ
cord-013977-xb0r2axf	49	14	fraction	fraction	NN
cord-013977-xb0r2axf	49	15	of	of	IN
cord-013977-xb0r2axf	49	16	the	the	DT
cord-013977-xb0r2axf	49	17	www.nature.com/scientificreports/	www.nature.com/scientificreports/	NNP
cord-013977-xb0r2axf	49	18	population	population	NN
cord-013977-xb0r2axf	49	19	that	that	WDT
cord-013977-xb0r2axf	49	20	has	have	VBZ
cord-013977-xb0r2axf	49	21	recovered	recover	VBN
cord-013977-xb0r2axf	49	22	(	(	-LRB-
cord-013977-xb0r2axf	49	23	and	and	CC
cord-013977-xb0r2axf	49	24	is	be	VBZ
cord-013977-xb0r2axf	49	25	always	always	RB
cord-013977-xb0r2axf	49	26	set	set	VBN
cord-013977-xb0r2axf	49	27	to	to	IN
cord-013977-xb0r2axf	49	28	zero	zero	CD
cord-013977-xb0r2axf	49	29	in	in	IN
cord-013977-xb0r2axf	49	30	the	the	DT
cord-013977-xb0r2axf	49	31	current	current	JJ
cord-013977-xb0r2axf	49	32	study	study	NN
cord-013977-xb0r2axf	49	33	)	)	-RRB-
cord-013977-xb0r2axf	49	34	,	,	,
cord-013977-xb0r2axf	49	35	whereas	whereas	IN
cord-013977-xb0r2axf	49	36	R	r	NN
cord-013977-xb0r2axf	49	37	0	0	CD
cord-013977-xb0r2axf	49	38	is	be	VBZ
cord-013977-xb0r2axf	49	39	the	the	DT
cord-013977-xb0r2axf	49	40	basic	basic	JJ
cord-013977-xb0r2axf	49	41	reproduction	reproduction	NN
cord-013977-xb0r2axf	49	42	number	number	NN
cord-013977-xb0r2axf	49	43	.	.	.
cord-013977-xb0r2axf	50	1	When	when	WRB
cord-013977-xb0r2axf	50	2	the	the	DT
cord-013977-xb0r2axf	50	3	infectious	infectious	JJ
cord-013977-xb0r2axf	50	4	curve	curve	NN
cord-013977-xb0r2axf	50	5	I	-PRON-	PRP
cord-013977-xb0r2axf	50	6	first	first	RB
cord-013977-xb0r2axf	50	7	starts	start	VBZ
cord-013977-xb0r2axf	50	8	to	to	TO
cord-013977-xb0r2axf	50	9	rise	rise	VB
cord-013977-xb0r2axf	50	10	from	from	IN
cord-013977-xb0r2axf	50	11	its	-PRON-	PRP$
cord-013977-xb0r2axf	50	12	initial	initial	JJ
cord-013977-xb0r2axf	50	13	value	value	NN
cord-013977-xb0r2axf	50	14	,	,	,
cord-013977-xb0r2axf	50	15	the	the	DT
cord-013977-xb0r2axf	50	16	logarithm	logarithm	NN
cord-013977-xb0r2axf	50	17	term	term	NN
cord-013977-xb0r2axf	50	18	in	in	IN
cord-013977-xb0r2axf	50	19	the	the	DT
cord-013977-xb0r2axf	50	20	integral	integral	NN
cord-013977-xb0r2axf	50	21	of	of	IN
cord-013977-xb0r2axf	50	22	Eq	Eq	NNP
cord-013977-xb0r2axf	50	23	.	.	.
cord-013977-xb0r2axf	51	1	(	(	-LRB-
cord-013977-xb0r2axf	51	2	9	9	LS
cord-013977-xb0r2axf	51	3	)	)	-RRB-
cord-013977-xb0r2axf	51	4	may	may	MD
cord-013977-xb0r2axf	51	5	be	be	VB
cord-013977-xb0r2axf	51	6	approximated	approximate	VBN
cord-013977-xb0r2axf	51	7	as	as	IN
cord-013977-xb0r2axf	51	8	ln	ln	NNP
cord-013977-xb0r2axf	51	9	(	(	-LRB-
cord-013977-xb0r2axf	51	10	S	S	NNP
cord-013977-xb0r2axf	51	11	/	/	SYM
cord-013977-xb0r2axf	51	12	S	S	NNP
cord-013977-xb0r2axf	51	13	0	0	CD
cord-013977-xb0r2axf	51	14	)	)	-RRB-
cord-013977-xb0r2axf	52	1	≈	≈	NNP
cord-013977-xb0r2axf	52	2	S	S	NNP
cord-013977-xb0r2axf	52	3	/	/	SYM
cord-013977-xb0r2axf	52	4	S	S	NNP
cord-013977-xb0r2axf	52	5	0	0	CD
cord-013977-xb0r2axf	52	6	−	−	NNP
cord-013977-xb0r2axf	52	7	1	1	CD
cord-013977-xb0r2axf	52	8	,	,	,
cord-013977-xb0r2axf	52	9	which	which	WDT
cord-013977-xb0r2axf	52	10	allows	allow	VBZ
cord-013977-xb0r2axf	52	11	the	the	DT
cord-013977-xb0r2axf	52	12	integral	integral	NN
cord-013977-xb0r2axf	52	13	to	to	TO
cord-013977-xb0r2axf	52	14	be	be	VB
cord-013977-xb0r2axf	52	15	evaluated	evaluate	VBN
cord-013977-xb0r2axf	52	16	analytically	analytically	RB
cord-013977-xb0r2axf	52	17	.	.	.
cord-013977-xb0r2axf	53	1	It	-PRON-	PRP
cord-013977-xb0r2axf	53	2	follows	follow	VBZ
cord-013977-xb0r2axf	53	3	that	that	IN
cord-013977-xb0r2axf	53	4	where	where	WRB
cord-013977-xb0r2axf	53	5	we	-PRON-	PRP
cord-013977-xb0r2axf	53	6	have	have	VBP
cord-013977-xb0r2axf	53	7	defined	define	VBN
cord-013977-xb0r2axf	53	8	the	the	DT
cord-013977-xb0r2axf	53	9	epidemic	epidemic	NN
cord-013977-xb0r2axf	53	10	growth	growth	NN
cord-013977-xb0r2axf	53	11	rate	rate	NN
cord-013977-xb0r2axf	53	12	as	as	IN
cord-013977-xb0r2axf	53	13	from	from	IN
cord-013977-xb0r2axf	53	14	which	which	WDT
cord-013977-xb0r2axf	53	15	one	one	PRP
cord-013977-xb0r2axf	53	16	obtains	obtain	VBZ
cord-013977-xb0r2axf	53	17	the	the	DT
cord-013977-xb0r2axf	53	18	known	know	VBN
cord-013977-xb0r2axf	53	19	relationship	relationship	NN
cord-013977-xb0r2axf	53	20	between	between	IN
cord-013977-xb0r2axf	53	21	the	the	DT
cord-013977-xb0r2axf	53	22	basic	basic	JJ
cord-013977-xb0r2axf	53	23	reproduction	reproduction	NN
cord-013977-xb0r2axf	53	24	number	number	NN
cord-013977-xb0r2axf	53	25	and	and	CC
cord-013977-xb0r2axf	53	26	the	the	DT
cord-013977-xb0r2axf	53	27	growth	growth	NN
cord-013977-xb0r2axf	53	28	rate	rate	NN
cord-013977-xb0r2axf	53	29	1,8	1,8	CD
cord-013977-xb0r2axf	53	30	,	,	,
cord-013977-xb0r2axf	53	31	where	where	WRB
cord-013977-xb0r2axf	53	32	D	D	NNP
cord-013977-xb0r2axf	53	33	≡	≡	NNP
cord-013977-xb0r2axf	53	34	1	1	CD
cord-013977-xb0r2axf	53	35	/	/	SYM
cord-013977-xb0r2axf	53	36	γ	γ	NN
cord-013977-xb0r2axf	53	37	is	be	VBZ
cord-013977-xb0r2axf	53	38	the	the	DT
cord-013977-xb0r2axf	53	39	infectious	infectious	JJ
cord-013977-xb0r2axf	53	40	period	period	NN
cord-013977-xb0r2axf	53	41	.	.	.
cord-013977-xb0r2axf	54	1	Seeking	seek	VBG
cord-013977-xb0r2axf	54	2	an	an	DT
cord-013977-xb0r2axf	54	3	approximate	approximate	JJ
cord-013977-xb0r2axf	54	4	semi	semi	JJ
cord-013977-xb0r2axf	54	5	-	-	JJ
cord-013977-xb0r2axf	54	6	analytical	analytical	JJ
cord-013977-xb0r2axf	54	7	solution	solution	NN
cord-013977-xb0r2axf	54	8	.	.	.
cord-013977-xb0r2axf	55	1	The	the	DT
cord-013977-xb0r2axf	55	2	SEIR	seir	NN
cord-013977-xb0r2axf	55	3	model	model	NN
cord-013977-xb0r2axf	55	4	builds	build	VBZ
cord-013977-xb0r2axf	55	5	on	on	IN
cord-013977-xb0r2axf	55	6	the	the	DT
cord-013977-xb0r2axf	55	7	SIR	SIR	NNP
cord-013977-xb0r2axf	55	8	model	model	NN
cord-013977-xb0r2axf	55	9	by	by	IN
cord-013977-xb0r2axf	55	10	considering	consider	VBG
cord-013977-xb0r2axf	55	11	an	an	DT
cord-013977-xb0r2axf	55	12	additional	additional	JJ
cord-013977-xb0r2axf	55	13	compartment	compartment	NN
cord-013977-xb0r2axf	55	14	for	for	IN
cord-013977-xb0r2axf	55	15	the	the	DT
cord-013977-xb0r2axf	55	16	fraction	fraction	NN
cord-013977-xb0r2axf	55	17	of	of	IN
cord-013977-xb0r2axf	55	18	the	the	DT
cord-013977-xb0r2axf	55	19	population	population	NN
cord-013977-xb0r2axf	55	20	that	that	WDT
cord-013977-xb0r2axf	55	21	is	be	VBZ
cord-013977-xb0r2axf	55	22	exposed	expose	VBN
cord-013977-xb0r2axf	55	23	(	(	-LRB-
cord-013977-xb0r2axf	55	24	E	e	NN
cord-013977-xb0r2axf	55	25	)	)	-RRB-
cord-013977-xb0r2axf	56	1	:	:	:
cord-013977-xb0r2axf	56	2	infected	infect	VBN
cord-013977-xb0r2axf	56	3	but	but	CC
cord-013977-xb0r2axf	56	4	not	not	RB
cord-013977-xb0r2axf	56	5	yet	yet	RB
cord-013977-xb0r2axf	56	6	infectious	infectious	JJ
cord-013977-xb0r2axf	56	7	.	.	.
cord-013977-xb0r2axf	57	1	The	the	DT
cord-013977-xb0r2axf	57	2	incubation	incubation	NN
cord-013977-xb0r2axf	57	3	period	period	NN
cord-013977-xb0r2axf	57	4	is	be	VBZ
cord-013977-xb0r2axf	57	5	1	1	CD
cord-013977-xb0r2axf	57	6	/	/	SYM
cord-013977-xb0r2axf	57	7	σ	σ	NN
cord-013977-xb0r2axf	57	8	.	.	.
cord-013977-xb0r2axf	58	1	The	the	DT
cord-013977-xb0r2axf	58	2	SEIR	SEIR	NNP
cord-013977-xb0r2axf	58	3	model	model	NN
cord-013977-xb0r2axf	58	4	is	be	VBZ
cord-013977-xb0r2axf	58	5	described	describe	VBN
cord-013977-xb0r2axf	58	6	by	by	IN
cord-013977-xb0r2axf	58	7	the	the	DT
cord-013977-xb0r2axf	58	8	following	following	JJ
cord-013977-xb0r2axf	58	9	set	set	NN
cord-013977-xb0r2axf	58	10	of	of	IN
cord-013977-xb0r2axf	58	11	coupled	coupled	JJ
cord-013977-xb0r2axf	58	12	ordinary	ordinary	JJ
cord-013977-xb0r2axf	58	13	differential	differential	JJ
cord-013977-xb0r2axf	58	14	equations	equation	NNS
cord-013977-xb0r2axf	58	15	1	1	CD
cord-013977-xb0r2axf	58	16	,	,	,
cord-013977-xb0r2axf	58	17	Since	since	IN
cord-013977-xb0r2axf	58	18	this	this	DT
cord-013977-xb0r2axf	58	19	set	set	NN
cord-013977-xb0r2axf	58	20	of	of	IN
cord-013977-xb0r2axf	58	21	equations	equation	NNS
cord-013977-xb0r2axf	58	22	does	do	VBZ
cord-013977-xb0r2axf	58	23	not	not	RB
cord-013977-xb0r2axf	58	24	consider	consider	VB
cord-013977-xb0r2axf	58	25	births	birth	NNS
cord-013977-xb0r2axf	58	26	or	or	CC
cord-013977-xb0r2axf	58	27	deaths	death	NNS
cord-013977-xb0r2axf	58	28	,	,	,
cord-013977-xb0r2axf	58	29	we	-PRON-	PRP
cord-013977-xb0r2axf	58	30	have	have	VBP
cord-013977-xb0r2axf	58	31	S	s	NN
cord-013977-xb0r2axf	58	32	+	+	CC
cord-013977-xb0r2axf	58	33	E	e	NN
cord-013977-xb0r2axf	59	1	+	+	CC
cord-013977-xb0r2axf	60	1	I	-PRON-	PRP
cord-013977-xb0r2axf	60	2	+	+	CC
cord-013977-xb0r2axf	60	3	R	r	NN
cord-013977-xb0r2axf	60	4	=	=	SYM
cord-013977-xb0r2axf	60	5	1	1	CD
cord-013977-xb0r2axf	60	6	.	.	.
cord-013977-xb0r2axf	61	1	The	the	DT
cord-013977-xb0r2axf	61	2	first	first	JJ
cord-013977-xb0r2axf	61	3	and	and	CC
cord-013977-xb0r2axf	61	4	fourth	fourth	JJ
cord-013977-xb0r2axf	61	5	equations	equation	NNS
cord-013977-xb0r2axf	61	6	may	may	MD
cord-013977-xb0r2axf	61	7	be	be	VB
cord-013977-xb0r2axf	61	8	combined	combine	VBN
cord-013977-xb0r2axf	61	9	to	to	TO
cord-013977-xb0r2axf	61	10	obtain	obtain	VB
cord-013977-xb0r2axf	61	11	which	which	WDT
cord-013977-xb0r2axf	61	12	is	be	VBZ
cord-013977-xb0r2axf	61	13	identical	identical	JJ
cord-013977-xb0r2axf	61	14	to	to	IN
cord-013977-xb0r2axf	61	15	the	the	DT
cord-013977-xb0r2axf	61	16	SIR	SIR	NNP
cord-013977-xb0r2axf	61	17	model	model	NN
cord-013977-xb0r2axf	61	18	.	.	.
cord-013977-xb0r2axf	62	1	Again	again	RB
cord-013977-xb0r2axf	62	2	,	,	,
cord-013977-xb0r2axf	62	3	the	the	DT
cord-013977-xb0r2axf	62	4	choice	choice	NN
cord-013977-xb0r2axf	62	5	of	of	IN
cord-013977-xb0r2axf	62	6	R	r	NN
cord-013977-xb0r2axf	62	7	0	0	CD
cord-013977-xb0r2axf	62	8	=	=	SYM
cord-013977-xb0r2axf	62	9	0	0	NFP
cord-013977-xb0r2axf	62	10	is	be	VBZ
cord-013977-xb0r2axf	62	11	made	make	VBN
cord-013977-xb0r2axf	62	12	with	with	IN
cord-013977-xb0r2axf	62	13	no	no	DT
cord-013977-xb0r2axf	62	14	loss	loss	NN
cord-013977-xb0r2axf	62	15	of	of	IN
cord-013977-xb0r2axf	62	16	generality	generality	NN
cord-013977-xb0r2axf	62	17	.	.	.
cord-013977-xb0r2axf	63	1	By	by	IN
cord-013977-xb0r2axf	63	2	combining	combine	VBG
cord-013977-xb0r2axf	63	3	all	all	DT
cord-013977-xb0r2axf	63	4	four	four	CD
cord-013977-xb0r2axf	63	5	equations	equation	NNS
cord-013977-xb0r2axf	63	6	,	,	,
cord-013977-xb0r2axf	63	7	one	one	PRP
cord-013977-xb0r2axf	63	8	obtains	obtain	VBZ
cord-013977-xb0r2axf	63	9	The	the	DT
cord-013977-xb0r2axf	63	10	approximation	approximation	NN
cord-013977-xb0r2axf	63	11	is	be	VBZ
cord-013977-xb0r2axf	63	12	taken	take	VBN
cord-013977-xb0r2axf	63	13	that	that	IN
cord-013977-xb0r2axf	63	14	the	the	DT
cord-013977-xb0r2axf	63	15	rate	rate	NN
cord-013977-xb0r2axf	63	16	of	of	IN
cord-013977-xb0r2axf	63	17	change	change	NN
cord-013977-xb0r2axf	63	18	of	of	IN
cord-013977-xb0r2axf	63	19	the	the	DT
cord-013977-xb0r2axf	63	20	acceleration	acceleration	NN
cord-013977-xb0r2axf	63	21	of	of	IN
cord-013977-xb0r2axf	63	22	R	r	NN
cord-013977-xb0r2axf	63	23	is	be	VBZ
cord-013977-xb0r2axf	63	24	vanishingly	vanishingly	RB
cord-013977-xb0r2axf	63	25	small	small	JJ
cord-013977-xb0r2axf	63	26	,	,	,
cord-013977-xb0r2axf	63	27	Retaining	retain	VBG
cord-013977-xb0r2axf	63	28	the	the	DT
cord-013977-xb0r2axf	63	29	R	r	NN
cord-013977-xb0r2axf	63	30	′′′	′′′	CD
cord-013977-xb0r2axf	63	31	term	term	NN
cord-013977-xb0r2axf	63	32	in	in	IN
cord-013977-xb0r2axf	63	33	Eq	Eq	NNP
cord-013977-xb0r2axf	63	34	.	.	.
cord-013977-xb0r2axf	64	1	(	(	-LRB-
cord-013977-xb0r2axf	64	2	17	17	CD
cord-013977-xb0r2axf	64	3	)	)	-RRB-
cord-013977-xb0r2axf	64	4	would	would	MD
cord-013977-xb0r2axf	64	5	lead	lead	VB
cord-013977-xb0r2axf	64	6	to	to	IN
cord-013977-xb0r2axf	64	7	a	a	DT
cord-013977-xb0r2axf	64	8	second	second	JJ
cord-013977-xb0r2axf	64	9	-	-	HYPH
cord-013977-xb0r2axf	64	10	order	order	NN
cord-013977-xb0r2axf	64	11	,	,	,
cord-013977-xb0r2axf	64	12	non	non	JJ
cord-013977-xb0r2axf	64	13	-	-	JJ
cord-013977-xb0r2axf	64	14	linear	linear	JJ
cord-013977-xb0r2axf	64	15	ordinary	ordinary	JJ
cord-013977-xb0r2axf	64	16	differential	differential	JJ
cord-013977-xb0r2axf	64	17	equation	equation	NN
cord-013977-xb0r2axf	64	18	of	of	IN
cord-013977-xb0r2axf	64	19	φ(S	φ(S	NNP
cord-013977-xb0r2axf	64	20	)	)	-RRB-
cord-013977-xb0r2axf	64	21	with	with	IN
cord-013977-xb0r2axf	64	22	no	no	DT
cord-013977-xb0r2axf	64	23	known	know	VBN
cord-013977-xb0r2axf	64	24	analytical	analytical	JJ
cord-013977-xb0r2axf	64	25	solution	solution	NN
cord-013977-xb0r2axf	64	26	.	.	.
cord-013977-xb0r2axf	65	1	(	(	-LRB-
cord-013977-xb0r2axf	65	2	12	12	CD
cord-013977-xb0r2axf	65	3	)	)	-RRB-
cord-013977-xb0r2axf	66	1	www.nature.com/scientificreports/	www.nature.com/scientificreports/	IN
cord-013977-xb0r2axf	66	2	Solving	solve	VBG
cord-013977-xb0r2axf	66	3	for	for	IN
cord-013977-xb0r2axf	66	4	φ	φ	NN
cord-013977-xb0r2axf	66	5	as	as	IN
cord-013977-xb0r2axf	66	6	in	in	IN
cord-013977-xb0r2axf	66	7	"	"	``
cord-013977-xb0r2axf	66	8	Review	Review	NNP
cord-013977-xb0r2axf	66	9	of	of	IN
cord-013977-xb0r2axf	66	10	Harko	Harko	NNP
cord-013977-xb0r2axf	66	11	et	et	NNP
cord-013977-xb0r2axf	66	12	al	al	NNP
cord-013977-xb0r2axf	66	13	.	.	.
cord-013977-xb0r2axf	67	1	5	5	LS
cord-013977-xb0r2axf	67	2	"	"	``
cord-013977-xb0r2axf	67	3	section	section	NN
cord-013977-xb0r2axf	67	4	yields	yield	NNS
cord-013977-xb0r2axf	67	5	where	where	WRB
cord-013977-xb0r2axf	67	6	φ	φ	NN
cord-013977-xb0r2axf	67	7	0	0	NFP
cord-013977-xb0r2axf	67	8	is	be	VBZ
cord-013977-xb0r2axf	67	9	the	the	DT
cord-013977-xb0r2axf	67	10	initial	initial	JJ
cord-013977-xb0r2axf	67	11	value	value	NN
cord-013977-xb0r2axf	67	12	of	of	IN
cord-013977-xb0r2axf	67	13	φ	φ	NN
cord-013977-xb0r2axf	67	14	.	.	.
cord-013977-xb0r2axf	68	1	The	the	DT
cord-013977-xb0r2axf	68	2	preceding	precede	VBG
cord-013977-xb0r2axf	68	3	expression	expression	NN
cord-013977-xb0r2axf	68	4	leads	lead	VBZ
cord-013977-xb0r2axf	68	5	to	to	IN
cord-013977-xb0r2axf	68	6	an	an	DT
cord-013977-xb0r2axf	68	7	expression	expression	NN
cord-013977-xb0r2axf	68	8	for	for	IN
cord-013977-xb0r2axf	68	9	I	-PRON-	PRP
cord-013977-xb0r2axf	68	10	,	,	,
cord-013977-xb0r2axf	68	11	in	in	IN
cord-013977-xb0r2axf	68	12	terms	term	NNS
cord-013977-xb0r2axf	68	13	of	of	IN
cord-013977-xb0r2axf	68	14	S	S	NNP
cord-013977-xb0r2axf	68	15	,	,	,
cord-013977-xb0r2axf	68	16	with	with	IN
cord-013977-xb0r2axf	68	17	a	a	DT
cord-013977-xb0r2axf	68	18	yet	yet	RB
cord-013977-xb0r2axf	68	19	unspecified	unspecified	JJ
cord-013977-xb0r2axf	68	20	constant	constant	NN
cord-013977-xb0r2axf	68	21	of	of	IN
cord-013977-xb0r2axf	68	22	integration	integration	NN
cord-013977-xb0r2axf	68	23	(	(	-LRB-
cord-013977-xb0r2axf	68	24	φ	φ	NNP
cord-013977-xb0r2axf	68	25	0	0	CD
cord-013977-xb0r2axf	68	26	)	)	-RRB-
cord-013977-xb0r2axf	69	1	,	,	,
cord-013977-xb0r2axf	69	2	Let	let	VB
cord-013977-xb0r2axf	69	3	the	the	DT
cord-013977-xb0r2axf	69	4	initial	initial	JJ
cord-013977-xb0r2axf	69	5	fraction	fraction	NN
cord-013977-xb0r2axf	69	6	of	of	IN
cord-013977-xb0r2axf	69	7	the	the	DT
cord-013977-xb0r2axf	69	8	population	population	NN
cord-013977-xb0r2axf	69	9	that	that	WDT
cord-013977-xb0r2axf	69	10	is	be	VBZ
cord-013977-xb0r2axf	69	11	exposed	expose	VBN
cord-013977-xb0r2axf	69	12	be	be	NN
cord-013977-xb0r2axf	69	13	E	e	NN
cord-013977-xb0r2axf	69	14	0	0	CD
cord-013977-xb0r2axf	69	15	.	.	.
cord-013977-xb0r2axf	70	1	Demanding	demand	VBG
cord-013977-xb0r2axf	70	2	that	that	IN
cord-013977-xb0r2axf	70	3	S	s	NN
cord-013977-xb0r2axf	70	4	0	0	CD
cord-013977-xb0r2axf	71	1	+	+	CC
cord-013977-xb0r2axf	72	1	E	e	NN
cord-013977-xb0r2axf	72	2	0	0	CD
cord-013977-xb0r2axf	72	3	+	+	CC
cord-013977-xb0r2axf	72	4	I	i	NN
cord-013977-xb0r2axf	72	5	0	0	CD
cord-013977-xb0r2axf	72	6	+	+	CC
cord-013977-xb0r2axf	72	7	R	r	NN
cord-013977-xb0r2axf	72	8	0	0	CD
cord-013977-xb0r2axf	73	1	=	=	SYM
cord-013977-xb0r2axf	73	2	1	1	CD
cord-013977-xb0r2axf	73	3	yields	yield	NNS
cord-013977-xb0r2axf	73	4	Expressions	expression	NNS
cord-013977-xb0r2axf	73	5	for	for	IN
cord-013977-xb0r2axf	73	6	E	e	NN
cord-013977-xb0r2axf	73	7	and	and	CC
cord-013977-xb0r2axf	73	8	I	-PRON-	PRP
cord-013977-xb0r2axf	73	9	,	,	,
cord-013977-xb0r2axf	73	10	in	in	IN
cord-013977-xb0r2axf	73	11	terms	term	NNS
cord-013977-xb0r2axf	73	12	of	of	IN
cord-013977-xb0r2axf	73	13	S	S	NNP
cord-013977-xb0r2axf	73	14	,	,	,
cord-013977-xb0r2axf	73	15	are	be	VBP
cord-013977-xb0r2axf	73	16	obtained	obtain	VBN
cord-013977-xb0r2axf	73	17	Finally	finally	RB
cord-013977-xb0r2axf	73	18	,	,	,
cord-013977-xb0r2axf	73	19	S	S	NNP
cord-013977-xb0r2axf	73	20	can	can	MD
cord-013977-xb0r2axf	73	21	be	be	VB
cord-013977-xb0r2axf	73	22	expressed	express	VBN
cord-013977-xb0r2axf	73	23	in	in	IN
cord-013977-xb0r2axf	73	24	terms	term	NNS
cord-013977-xb0r2axf	73	25	of	of	IN
cord-013977-xb0r2axf	73	26	t	t	NN
cord-013977-xb0r2axf	73	27	via	via	IN
cord-013977-xb0r2axf	73	28	the	the	DT
cord-013977-xb0r2axf	73	29	following	follow	VBG
cord-013977-xb0r2axf	73	30	integral	integral	NN
cord-013977-xb0r2axf	73	31	,	,	,
cord-013977-xb0r2axf	73	32	Since	since	IN
cord-013977-xb0r2axf	73	33	I	-PRON-	PRP
cord-013977-xb0r2axf	73	34	0	0	CD
cord-013977-xb0r2axf	73	35	≪	≪	CD
cord-013977-xb0r2axf	73	36	1	1	CD
cord-013977-xb0r2axf	73	37	,	,	,
cord-013977-xb0r2axf	73	38	the	the	DT
cord-013977-xb0r2axf	73	39	time	time	NN
cord-013977-xb0r2axf	73	40	taken	take	VBN
cord-013977-xb0r2axf	73	41	for	for	IN
cord-013977-xb0r2axf	73	42	I	-PRON-	PRP
cord-013977-xb0r2axf	73	43	to	to	TO
cord-013977-xb0r2axf	73	44	peak	peak	VB
cord-013977-xb0r2axf	73	45	is	be	VBZ
cord-013977-xb0r2axf	73	46	The	the	DT
cord-013977-xb0r2axf	73	47	preceding	precede	VBG
cord-013977-xb0r2axf	73	48	expression	expression	NN
cord-013977-xb0r2axf	73	49	is	be	VBZ
cord-013977-xb0r2axf	73	50	identical	identical	JJ
cord-013977-xb0r2axf	73	51	to	to	IN
cord-013977-xb0r2axf	73	52	Eq	Eq	NNP
cord-013977-xb0r2axf	73	53	.	.	.
cord-013977-xb0r2axf	74	1	(	(	-LRB-
cord-013977-xb0r2axf	74	2	11	11	CD
cord-013977-xb0r2axf	74	3	)	)	-RRB-
cord-013977-xb0r2axf	74	4	of	of	IN
cord-013977-xb0r2axf	74	5	the	the	DT
cord-013977-xb0r2axf	74	6	SIR	SIR	NNP
cord-013977-xb0r2axf	74	7	model	model	NN
cord-013977-xb0r2axf	74	8	,	,	,
cord-013977-xb0r2axf	74	9	except	except	IN
cord-013977-xb0r2axf	74	10	for	for	IN
cord-013977-xb0r2axf	74	11	the	the	DT
cord-013977-xb0r2axf	74	12	extra	extra	JJ
cord-013977-xb0r2axf	74	13	factor	factor	NN
cord-013977-xb0r2axf	74	14	of	of	IN
cord-013977-xb0r2axf	74	15	α	α	NN
cord-013977-xb0r2axf	74	16	.	.	.
cord-013977-xb0r2axf	75	1	It	-PRON-	PRP
cord-013977-xb0r2axf	75	2	should	should	MD
cord-013977-xb0r2axf	75	3	be	be	VB
cord-013977-xb0r2axf	75	4	noted	note	VBN
cord-013977-xb0r2axf	75	5	that	that	IN
cord-013977-xb0r2axf	75	6	the	the	DT
cord-013977-xb0r2axf	75	7	upper	upper	JJ
cord-013977-xb0r2axf	75	8	limit	limit	NN
cord-013977-xb0r2axf	75	9	of	of	IN
cord-013977-xb0r2axf	75	10	the	the	DT
cord-013977-xb0r2axf	75	11	integral	integral	JJ
cord-013977-xb0r2axf	75	12	(	(	-LRB-
cord-013977-xb0r2axf	75	13	1	1	CD
cord-013977-xb0r2axf	75	14	/	/	SYM
cord-013977-xb0r2axf	75	15	R	r	NN
cord-013977-xb0r2axf	75	16	0	0	CD
cord-013977-xb0r2axf	75	17	)	)	-RRB-
cord-013977-xb0r2axf	75	18	assumes	assume	VBZ
cord-013977-xb0r2axf	75	19	the	the	DT
cord-013977-xb0r2axf	75	20	approximation	approximation	NN
cord-013977-xb0r2axf	76	1	I	-PRON-	PRP
cord-013977-xb0r2axf	76	2	′	′	CD
cord-013977-xb0r2axf	77	1	=	=	NFP
cord-013977-xb0r2axf	78	1	E	e	NN
cord-013977-xb0r2axf	78	2	′	′	CD
cord-013977-xb0r2axf	79	1	=	=	SYM
cord-013977-xb0r2axf	79	2	0	0	NFP
cord-013977-xb0r2axf	79	3	.	.	.
cord-013977-xb0r2axf	80	1	However	however	RB
cord-013977-xb0r2axf	80	2	,	,	,
cord-013977-xb0r2axf	80	3	Eq	Eq	NNP
cord-013977-xb0r2axf	80	4	.	.	.
cord-013977-xb0r2axf	81	1	(	(	-LRB-
cord-013977-xb0r2axf	81	2	27	27	CD
cord-013977-xb0r2axf	81	3	)	)	-RRB-
cord-013977-xb0r2axf	81	4	is	be	VBZ
cord-013977-xb0r2axf	81	5	not	not	RB
cord-013977-xb0r2axf	81	6	used	use	VBN
cord-013977-xb0r2axf	81	7	to	to	TO
cord-013977-xb0r2axf	81	8	compute	compute	VB
cord-013977-xb0r2axf	81	9	the	the	DT
cord-013977-xb0r2axf	81	10	peak	peak	NN
cord-013977-xb0r2axf	81	11	times	time	NNS
cord-013977-xb0r2axf	81	12	in	in	IN
cord-013977-xb0r2axf	81	13	Fig	Fig	NNP
cord-013977-xb0r2axf	81	14	.	.	.
cord-013977-xb0r2axf	82	1	2	2	LS
cord-013977-xb0r2axf	82	2	.	.	.
cord-013977-xb0r2axf	83	1	Its	-PRON-	PRP$
cord-013977-xb0r2axf	83	2	only	only	JJ
cord-013977-xb0r2axf	83	3	purpose	purpose	NN
cord-013977-xb0r2axf	83	4	is	be	VBZ
cord-013977-xb0r2axf	83	5	to	to	TO
cord-013977-xb0r2axf	83	6	demonstrate	demonstrate	VB
cord-013977-xb0r2axf	83	7	that	that	IN
cord-013977-xb0r2axf	83	8	one	one	PRP
cord-013977-xb0r2axf	83	9	may	may	MD
cord-013977-xb0r2axf	83	10	factor	factor	VB
cord-013977-xb0r2axf	83	11	out	out	RP
cord-013977-xb0r2axf	83	12	αγ	αγ	XX
cord-013977-xb0r2axf	83	13	from	from	IN
cord-013977-xb0r2axf	83	14	the	the	DT
cord-013977-xb0r2axf	83	15	integral	integral	NN
cord-013977-xb0r2axf	83	16	.	.	.
cord-013977-xb0r2axf	84	1	Stating	state	VBG
cord-013977-xb0r2axf	84	2	the	the	DT
cord-013977-xb0r2axf	84	3	upper	upper	JJ
cord-013977-xb0r2axf	84	4	limit	limit	NN
cord-013977-xb0r2axf	84	5	of	of	IN
cord-013977-xb0r2axf	84	6	the	the	DT
cord-013977-xb0r2axf	84	7	integral	integral	JJ
cord-013977-xb0r2axf	84	8	in	in	IN
cord-013977-xb0r2axf	84	9	Eq	Eq	NNP
cord-013977-xb0r2axf	84	10	.	.	.
cord-013977-xb0r2axf	85	1	(	(	-LRB-
cord-013977-xb0r2axf	85	2	27	27	CD
cord-013977-xb0r2axf	85	3	)	)	-RRB-
cord-013977-xb0r2axf	85	4	more	more	RBR
cord-013977-xb0r2axf	85	5	accurately	accurately	RB
cord-013977-xb0r2axf	85	6	does	do	VBZ
cord-013977-xb0r2axf	85	7	not	not	RB
cord-013977-xb0r2axf	85	8	alter	alter	VB
cord-013977-xb0r2axf	85	9	the	the	DT
cord-013977-xb0r2axf	85	10	main	main	JJ
cord-013977-xb0r2axf	85	11	conclusion	conclusion	NN
cord-013977-xb0r2axf	85	12	of	of	IN
cord-013977-xb0r2axf	85	13	the	the	DT
cord-013977-xb0r2axf	85	14	current	current	JJ
cord-013977-xb0r2axf	85	15	study	study	NN
cord-013977-xb0r2axf	85	16	.	.	.
cord-013977-xb0r2axf	86	1	The	the	DT
cord-013977-xb0r2axf	86	2	relationship	relationship	NN
cord-013977-xb0r2axf	86	3	between	between	IN
cord-013977-xb0r2axf	86	4	the	the	DT
cord-013977-xb0r2axf	86	5	growth	growth	NN
cord-013977-xb0r2axf	86	6	rate	rate	NN
cord-013977-xb0r2axf	86	7	and	and	CC
cord-013977-xb0r2axf	86	8	the	the	DT
cord-013977-xb0r2axf	86	9	basic	basic	JJ
cord-013977-xb0r2axf	86	10	reproduction	reproduction	NN
cord-013977-xb0r2axf	86	11	number	number	NN
cord-013977-xb0r2axf	86	12	can	can	MD
cord-013977-xb0r2axf	86	13	again	again	RB
cord-013977-xb0r2axf	86	14	be	be	VB
cord-013977-xb0r2axf	86	15	derived	derive	VBN
cord-013977-xb0r2axf	86	16	.	.	.
cord-013977-xb0r2axf	87	1	Using	use	VBG
cord-013977-xb0r2axf	87	2	the	the	DT
cord-013977-xb0r2axf	87	3	same	same	JJ
cord-013977-xb0r2axf	87	4	series	series	NN
cord-013977-xb0r2axf	87	5	expansion	expansion	NN
cord-013977-xb0r2axf	87	6	of	of	IN
cord-013977-xb0r2axf	87	7	the	the	DT
cord-013977-xb0r2axf	87	8	logarithm	logarithm	NN
cord-013977-xb0r2axf	87	9	term	term	NN
cord-013977-xb0r2axf	87	10	in	in	IN
cord-013977-xb0r2axf	87	11	the	the	DT
cord-013977-xb0r2axf	87	12	integral	integral	NN
cord-013977-xb0r2axf	87	13	of	of	IN
cord-013977-xb0r2axf	87	14	Eq	Eq	NNP
cord-013977-xb0r2axf	87	15	.	.	.
cord-013977-xb0r2axf	88	1	(	(	-LRB-
cord-013977-xb0r2axf	88	2	26	26	CD
cord-013977-xb0r2axf	88	3	)	)	-RRB-
cord-013977-xb0r2axf	88	4	,	,	,
cord-013977-xb0r2axf	88	5	one	one	NN
cord-013977-xb0r2axf	88	6	obtains	obtain	VBZ
cord-013977-xb0r2axf	88	7	albeit	albeit	IN
cord-013977-xb0r2axf	88	8	with	with	IN
cord-013977-xb0r2axf	88	9	a	a	DT
cord-013977-xb0r2axf	88	10	different	different	JJ
cord-013977-xb0r2axf	88	11	definition	definition	NN
cord-013977-xb0r2axf	88	12	of	of	IN
cord-013977-xb0r2axf	88	13	the	the	DT
cord-013977-xb0r2axf	88	14	growth	growth	NN
cord-013977-xb0r2axf	88	15	rate	rate	NN
cord-013977-xb0r2axf	88	16	,	,	,
cord-013977-xb0r2axf	88	17	It	-PRON-	PRP
cord-013977-xb0r2axf	88	18	follows	follow	VBZ
cord-013977-xb0r2axf	88	19	that	that	IN
cord-013977-xb0r2axf	88	20	where	where	WRB
cord-013977-xb0r2axf	88	21	D	D	NNP
cord-013977-xb0r2axf	88	22	′	′	CD
cord-013977-xb0r2axf	88	23	≡	≡	NNP
cord-013977-xb0r2axf	88	24	1	1	CD
cord-013977-xb0r2axf	88	25	/	/	SYM
cord-013977-xb0r2axf	88	26	σ	σ	NN
cord-013977-xb0r2axf	88	27	is	be	VBZ
cord-013977-xb0r2axf	88	28	the	the	DT
cord-013977-xb0r2axf	88	29	incubation	incubation	NN
cord-013977-xb0r2axf	88	30	period	period	NN
cord-013977-xb0r2axf	88	31	.	.	.
cord-013977-xb0r2axf	89	1	When	when	WRB
cord-013977-xb0r2axf	89	2	α	α	NN
cord-013977-xb0r2axf	89	3	=	=	SYM
cord-013977-xb0r2axf	89	4	1	1	CD
cord-013977-xb0r2axf	89	5	,	,	,
cord-013977-xb0r2axf	89	6	the	the	DT
cord-013977-xb0r2axf	89	7	expression	expression	NN
cord-013977-xb0r2axf	89	8	for	for	IN
cord-013977-xb0r2axf	89	9	the	the	DT
cord-013977-xb0r2axf	89	10	SIR	SIR	NNP
cord-013977-xb0r2axf	89	11	model	model	NN
cord-013977-xb0r2axf	89	12	in	in	IN
cord-013977-xb0r2axf	89	13	Eq	Eq	NNP
cord-013977-xb0r2axf	89	14	.	.	.
cord-013977-xb0r2axf	90	1	(	(	-LRB-
cord-013977-xb0r2axf	90	2	14	14	CD
cord-013977-xb0r2axf	90	3	)	)	-RRB-
cord-013977-xb0r2axf	90	4	is	be	VBZ
cord-013977-xb0r2axf	90	5	recovered	recover	VBN
cord-013977-xb0r2axf	90	6	.	.	.
cord-013977-xb0r2axf	91	1	If	if	IN
cord-013977-xb0r2axf	91	2	S	s	NN
cord-013977-xb0r2axf	91	3	0	0	CD
cord-013977-xb0r2axf	91	4	≈	≈	NNP
cord-013977-xb0r2axf	91	5	1	1	CD
cord-013977-xb0r2axf	92	1	and	and	CC
cord-013977-xb0r2axf	92	2	I	i	NN
cord-013977-xb0r2axf	92	3	0	0	CD
cord-013977-xb0r2axf	92	4	≪	≪	CD
cord-013977-xb0r2axf	92	5	1	1	CD
cord-013977-xb0r2axf	93	1	,	,	,
cord-013977-xb0r2axf	93	2	then	then	RB
cord-013977-xb0r2axf	93	3	one	one	NN
cord-013977-xb0r2axf	93	4	obtains	obtain	VBZ
cord-013977-xb0r2axf	93	5	R	r	NN
cord-013977-xb0r2axf	93	6	0	0	CD
cord-013977-xb0r2axf	93	7	≈	≈	NNP
cord-013977-xb0r2axf	93	8	1	1	CD
cord-013977-xb0r2axf	94	1	+	+	CC
cord-013977-xb0r2axf	94	2	�	�	JJ
cord-013977-xb0r2axf	94	3	(	(	-LRB-
cord-013977-xb0r2axf	94	4	D	d	NN
cord-013977-xb0r2axf	94	5	+	+	CC
cord-013977-xb0r2axf	94	6	D	d	NN
cord-013977-xb0r2axf	94	7	′	′	CD
cord-013977-xb0r2axf	94	8	)	)	-RRB-
cord-013977-xb0r2axf	94	9	.	.	.
cord-013977-xb0r2axf	95	1	The	the	DT
cord-013977-xb0r2axf	95	2	exact	exact	JJ
cord-013977-xb0r2axf	95	3	relationship	relationship	NN
cord-013977-xb0r2axf	95	4	between	between	IN
cord-013977-xb0r2axf	95	5	the	the	DT
cord-013977-xb0r2axf	95	6	growth	growth	NN
cord-013977-xb0r2axf	95	7	rate	rate	NN
cord-013977-xb0r2axf	95	8	and	and	CC
cord-013977-xb0r2axf	95	9	R	r	NN
cord-013977-xb0r2axf	95	10	0	0	CD
cord-013977-xb0r2axf	95	11	has	have	VBZ
cord-013977-xb0r2axf	95	12	been	be	VBN
cord-013977-xb0r2axf	95	13	derived	derive	VBN
cord-013977-xb0r2axf	95	14	in	in	IN
cord-013977-xb0r2axf	95	15	various	various	JJ
cord-013977-xb0r2axf	95	16	ways	way	NNS
cord-013977-xb0r2axf	95	17	8	8	CD
cord-013977-xb0r2axf	95	18	(	(	-LRB-
cord-013977-xb0r2axf	95	19	and	and	CC
cord-013977-xb0r2axf	95	20	references	reference	NNS
cord-013977-xb0r2axf	95	21	therein	therein	RB
cord-013977-xb0r2axf	95	22	)	)	-RRB-
cord-013977-xb0r2axf	95	23	and	and	CC
cord-013977-xb0r2axf	95	24	is	be	VBZ
cord-013977-xb0r2axf	95	25	given	give	VBN
cord-013977-xb0r2axf	95	26	by	by	IN
cord-013977-xb0r2axf	95	27	R	r	NN
cord-013977-xb0r2axf	95	28	0	0	CD
cord-013977-xb0r2axf	95	29	=	=	NFP
cord-013977-xb0r2axf	96	1	(	(	-LRB-
cord-013977-xb0r2axf	96	2	1	1	CD
cord-013977-xb0r2axf	96	3	+	+	SYM
cord-013977-xb0r2axf	96	4	�	�	NN
cord-013977-xb0r2axf	96	5	D	d	NN
cord-013977-xb0r2axf	96	6	′	′	CD
cord-013977-xb0r2axf	96	7	)	)	-RRB-
cord-013977-xb0r2axf	97	1	(	(	-LRB-
cord-013977-xb0r2axf	97	2	1	1	CD
cord-013977-xb0r2axf	97	3	+	+	SYM
cord-013977-xb0r2axf	97	4	�	�	NN
cord-013977-xb0r2axf	97	5	D	d	NN
cord-013977-xb0r2axf	97	6	)	)	-RRB-
cord-013977-xb0r2axf	97	7	.	.	.
cord-013977-xb0r2axf	98	1	This	this	DT
cord-013977-xb0r2axf	98	2	equation	equation	NN
cord-013977-xb0r2axf	98	3	accounts	account	VBZ
cord-013977-xb0r2axf	98	4	for	for	IN
cord-013977-xb0r2axf	98	5	the	the	DT
cord-013977-xb0r2axf	98	6	characteristic	characteristic	JJ
cord-013977-xb0r2axf	98	7	generation	generation	NN
cord-013977-xb0r2axf	98	8	time	time	NN
cord-013977-xb0r2axf	98	9	distribution	distribution	NN
cord-013977-xb0r2axf	98	10	of	of	IN
cord-013977-xb0r2axf	98	11	SEIR	SEIR	NNP
cord-013977-xb0r2axf	98	12	models	model	NNS
cord-013977-xb0r2axf	98	13	,	,	,
cord-013977-xb0r2axf	98	14	which	which	WDT
cord-013977-xb0r2axf	98	15	is	be	VBZ
cord-013977-xb0r2axf	98	16	a	a	DT
cord-013977-xb0r2axf	98	17	convolution	convolution	NN
cord-013977-xb0r2axf	98	18	of	of	IN
cord-013977-xb0r2axf	98	19	the	the	DT
cord-013977-xb0r2axf	98	20	exponentially	exponentially	RB
cord-013977-xb0r2axf	98	21	distributed	distribute	VBN
cord-013977-xb0r2axf	98	22	incubation	incubation	NN
cord-013977-xb0r2axf	98	23	and	and	CC
cord-013977-xb0r2axf	98	24	infectious	infectious	JJ
cord-013977-xb0r2axf	98	25	periods	period	NNS
cord-013977-xb0r2axf	98	26	with	with	IN
cord-013977-xb0r2axf	98	27	mean	mean	JJ
cord-013977-xb0r2axf	98	28	durations	duration	NNS
cord-013977-xb0r2axf	98	29	of	of	IN
cord-013977-xb0r2axf	98	30	D	d	NN
cord-013977-xb0r2axf	98	31	′	′	CD
cord-013977-xb0r2axf	98	32	and	and	CC
cord-013977-xb0r2axf	98	33	D	d	NN
cord-013977-xb0r2axf	98	34	,	,	,
cord-013977-xb0r2axf	98	35	respectively	respectively	RB
cord-013977-xb0r2axf	98	36	.	.	.
cord-013977-xb0r2axf	99	1	The	the	DT
cord-013977-xb0r2axf	99	2	approximate	approximate	JJ
cord-013977-xb0r2axf	99	3	solution	solution	NN
cord-013977-xb0r2axf	99	4	of	of	IN
cord-013977-xb0r2axf	99	5	Eq	Eq	NNP
cord-013977-xb0r2axf	99	6	.	.	.
cord-013977-xb0r2axf	100	1	(	(	-LRB-
cord-013977-xb0r2axf	100	2	30	30	CD
cord-013977-xb0r2axf	100	3	)	)	-RRB-
cord-013977-xb0r2axf	100	4	lacks	lack	VBZ
cord-013977-xb0r2axf	100	5	the	the	DT
cord-013977-xb0r2axf	100	6	term	term	NN
cord-013977-xb0r2axf	100	7	2	2	CD
cord-013977-xb0r2axf	100	8	D	d	NN
cord-013977-xb0r2axf	100	9	′	′	CD
cord-013977-xb0r2axf	100	10	D	d	NN
cord-013977-xb0r2axf	100	11	.	.	.
cord-013977-xb0r2axf	101	1	Hence	hence	RB
cord-013977-xb0r2axf	101	2	,	,	,
cord-013977-xb0r2axf	101	3	it	-PRON-	PRP
cord-013977-xb0r2axf	101	4	corresponds	correspond	VBZ
cord-013977-xb0r2axf	101	5	to	to	IN
cord-013977-xb0r2axf	101	6	the	the	DT
cord-013977-xb0r2axf	101	7	case	case	NN
cord-013977-xb0r2axf	101	8	of	of	IN
cord-013977-xb0r2axf	101	9	an	an	DT
cord-013977-xb0r2axf	101	10	exponentially	exponentially	RB
cord-013977-xb0r2axf	101	11	distributed	distribute	VBN
cord-013977-xb0r2axf	101	12	generation	generation	NN
cord-013977-xb0r2axf	101	13	time	time	NN
cord-013977-xb0r2axf	101	14	with	with	IN
cord-013977-xb0r2axf	101	15	mean	mean	JJ
cord-013977-xb0r2axf	101	16	duration	duration	NN
cord-013977-xb0r2axf	101	17	D	d	NN
cord-013977-xb0r2axf	101	18	′	′	CD
cord-013977-xb0r2axf	101	19	+	+	CC
cord-013977-xb0r2axf	101	20	D	d	NN
cord-013977-xb0r2axf	101	21	,	,	,
cord-013977-xb0r2axf	101	22	which	which	WDT
cord-013977-xb0r2axf	101	23	is	be	VBZ
cord-013977-xb0r2axf	101	24	the	the	DT
cord-013977-xb0r2axf	101	25	same	same	JJ
cord-013977-xb0r2axf	101	26	as	as	IN
cord-013977-xb0r2axf	101	27	the	the	DT
cord-013977-xb0r2axf	101	28	solution	solution	NN
cord-013977-xb0r2axf	101	29	for	for	IN
cord-013977-xb0r2axf	101	30	the	the	DT
cord-013977-xb0r2axf	101	31	SIR	SIR	NNP
cord-013977-xb0r2axf	101	32	model	model	NN
cord-013977-xb0r2axf	101	33	assuming	assume	VBG
cord-013977-xb0r2axf	101	34	an	an	DT
cord-013977-xb0r2axf	101	35	infectious	infectious	JJ
cord-013977-xb0r2axf	101	36	period	period	NN
cord-013977-xb0r2axf	101	37	of	of	IN
cord-013977-xb0r2axf	101	38	D	d	NN
cord-013977-xb0r2axf	101	39	′	′	CD
cord-013977-xb0r2axf	101	40	+	+	CC
cord-013977-xb0r2axf	101	41	D.	D.	NNP
cord-013977-xb0r2axf	101	42	(	(	-LRB-
cord-013977-xb0r2axf	101	43	27	27	CD
cord-013977-xb0r2axf	101	44	)	)	-RRB-
cord-013977-xb0r2axf	101	45	has	have	VBZ
cord-013977-xb0r2axf	101	46	non	non	JJ
cord-013977-xb0r2axf	101	47	-	-	JJ
cord-013977-xb0r2axf	101	48	trivial	trivial	JJ
cord-013977-xb0r2axf	101	49	implications	implication	NNS
cord-013977-xb0r2axf	101	50	.	.	.
cord-013977-xb0r2axf	102	1	It	-PRON-	PRP
cord-013977-xb0r2axf	102	2	suggests	suggest	VBZ
cord-013977-xb0r2axf	102	3	that	that	IN
cord-013977-xb0r2axf	102	4	the	the	DT
cord-013977-xb0r2axf	102	5	susceptible	susceptible	JJ
cord-013977-xb0r2axf	102	6	,	,	,
cord-013977-xb0r2axf	102	7	exposed	expose	VBN
cord-013977-xb0r2axf	102	8	,	,	,
cord-013977-xb0r2axf	102	9	infectious	infectious	JJ
cord-013977-xb0r2axf	102	10	and	and	CC
cord-013977-xb0r2axf	102	11	recovered	recover	VBD
cord-013977-xb0r2axf	102	12	curves	curve	NNS
cord-013977-xb0r2axf	102	13	of	of	IN
cord-013977-xb0r2axf	102	14	SEIR	SEIR	NNP
cord-013977-xb0r2axf	102	15	models	model	NNS
cord-013977-xb0r2axf	102	16	,	,	,
cord-013977-xb0r2axf	102	17	with	with	IN
cord-013977-xb0r2axf	102	18	different	different	JJ
cord-013977-xb0r2axf	102	19	values	value	NNS
cord-013977-xb0r2axf	102	20	of	of	IN
cord-013977-xb0r2axf	102	21	D	d	NN
cord-013977-xb0r2axf	102	22	′	′	CD
cord-013977-xb0r2axf	102	23	and	and	CC
cord-013977-xb0r2axf	102	24	D	D	NNP
cord-013977-xb0r2axf	102	25	,	,	,
cord-013977-xb0r2axf	102	26	follow	follow	VB
cord-013977-xb0r2axf	102	27	approximately	approximately	RB
cord-013977-xb0r2axf	102	28	universal	universal	JJ
cord-013977-xb0r2axf	102	29	shapes	shape	NNS
cord-013977-xb0r2axf	102	30	that	that	WDT
cord-013977-xb0r2axf	102	31	are	be	VBP
cord-013977-xb0r2axf	102	32	stretched	stretch	VBN
cord-013977-xb0r2axf	102	33	by	by	IN
cord-013977-xb0r2axf	102	34	a	a	DT
cord-013977-xb0r2axf	102	35	factor	factor	NN
cord-013977-xb0r2axf	102	36	of	of	IN
cord-013977-xb0r2axf	102	37	1	1	CD
cord-013977-xb0r2axf	102	38	/	/	SYM
cord-013977-xb0r2axf	102	39	α	α	NN
cord-013977-xb0r2axf	102	40	=	=	SYM
cord-013977-xb0r2axf	102	41	1	1	CD
cord-013977-xb0r2axf	102	42	+	+	CC
cord-013977-xb0r2axf	102	43	D	d	NN
cord-013977-xb0r2axf	102	44	′	′	CD
cord-013977-xb0r2axf	102	45	/D	/d	NN
cord-013977-xb0r2axf	102	46	relative	relative	JJ
cord-013977-xb0r2axf	102	47	to	to	IN
cord-013977-xb0r2axf	102	48	one	one	CD
cord-013977-xb0r2axf	102	49	another	another	DT
cord-013977-xb0r2axf	102	50	.	.	.
cord-013977-xb0r2axf	103	1	To	to	TO
cord-013977-xb0r2axf	103	2	demonstrate	demonstrate	VB
cord-013977-xb0r2axf	103	3	this	this	DT
cord-013977-xb0r2axf	103	4	property	property	NN
cord-013977-xb0r2axf	103	5	,	,	,
cord-013977-xb0r2axf	103	6	the	the	DT
cord-013977-xb0r2axf	103	7	full	full	JJ
cord-013977-xb0r2axf	103	8	set	set	NN
cord-013977-xb0r2axf	103	9	of	of	IN
cord-013977-xb0r2axf	103	10	coupled	coupled	JJ
cord-013977-xb0r2axf	103	11	equations	equation	NNS
cord-013977-xb0r2axf	103	12	in	in	IN
cord-013977-xb0r2axf	103	13	(	(	-LRB-
cord-013977-xb0r2axf	103	14	15	15	CD
cord-013977-xb0r2axf	103	15	)	)	-RRB-
cord-013977-xb0r2axf	103	16	is	be	VBZ
cord-013977-xb0r2axf	103	17	solved	solve	VBN
cord-013977-xb0r2axf	103	18	numerically	numerically	RB
cord-013977-xb0r2axf	103	19	using	use	VBG
cord-013977-xb0r2axf	103	20	the	the	DT
cord-013977-xb0r2axf	103	21	solve_ivp	solve_ivp	JJ
cord-013977-xb0r2axf	103	22	routine	routine	NN
cord-013977-xb0r2axf	103	23	of	of	IN
cord-013977-xb0r2axf	103	24	the	the	DT
cord-013977-xb0r2axf	103	25	Python	Python	NNP
cord-013977-xb0r2axf	103	26	programming	programming	NN
cord-013977-xb0r2axf	103	27	(	(	-LRB-
cord-013977-xb0r2axf	103	28	24	24	CD
cord-013977-xb0r2axf	103	29	)	)	-RRB-
cord-013977-xb0r2axf	104	1	www.nature.com/scientificreports/	www.nature.com/scientificreports/	NNP
cord-013977-xb0r2axf	104	2	language	language	NN
cord-013977-xb0r2axf	104	3	suite	suite	NN
cord-013977-xb0r2axf	104	4	9	9	CD
cord-013977-xb0r2axf	104	5	.	.	.
cord-013977-xb0r2axf	105	1	For	for	IN
cord-013977-xb0r2axf	105	2	illustration	illustration	NN
cord-013977-xb0r2axf	105	3	,	,	,
cord-013977-xb0r2axf	105	4	one	one	PRP
cord-013977-xb0r2axf	105	5	assumes	assume	VBZ
cord-013977-xb0r2axf	105	6	R	r	NN
cord-013977-xb0r2axf	105	7	0	0	CD
cord-013977-xb0r2axf	105	8	=	=	SYM
cord-013977-xb0r2axf	105	9	2	2	CD
cord-013977-xb0r2axf	106	1	and	and	CC
cord-013977-xb0r2axf	106	2	I	i	NN
cord-013977-xb0r2axf	106	3	0	0	CD
cord-013977-xb0r2axf	106	4	=	=	SYM
cord-013977-xb0r2axf	106	5	10	10	CD
cord-013977-xb0r2axf	106	6	−4	−4	CD
cord-013977-xb0r2axf	106	7	.	.	.
cord-013977-xb0r2axf	107	1	Figure	figure	NN
cord-013977-xb0r2axf	107	2	1	1	CD
cord-013977-xb0r2axf	107	3	shows	show	VBZ
cord-013977-xb0r2axf	107	4	the	the	DT
cord-013977-xb0r2axf	107	5	solution	solution	NN
cord-013977-xb0r2axf	107	6	curves	curve	NNS
cord-013977-xb0r2axf	107	7	of	of	IN
cord-013977-xb0r2axf	107	8	100	100	CD
cord-013977-xb0r2axf	107	9	SEIR	SEIR	NNP
cord-013977-xb0r2axf	107	10	models	model	NNS
cord-013977-xb0r2axf	107	11	,	,	,
cord-013977-xb0r2axf	107	12	where	where	WRB
cord-013977-xb0r2axf	107	13	the	the	DT
cord-013977-xb0r2axf	107	14	values	value	NNS
cord-013977-xb0r2axf	107	15	of	of	IN
cord-013977-xb0r2axf	107	16	the	the	DT
cord-013977-xb0r2axf	107	17	incubation	incubation	NN
cord-013977-xb0r2axf	107	18	(	(	-LRB-
cord-013977-xb0r2axf	107	19	D	D	NNP
cord-013977-xb0r2axf	107	20	′	′	CD
cord-013977-xb0r2axf	107	21	≡	≡	NNP
cord-013977-xb0r2axf	107	22	1	1	CD
cord-013977-xb0r2axf	107	23	/	/	SYM
cord-013977-xb0r2axf	107	24	σ	σ	NNP
cord-013977-xb0r2axf	107	25	)	)	-RRB-
cord-013977-xb0r2axf	107	26	and	and	CC
cord-013977-xb0r2axf	107	27	infectious	infectious	JJ
cord-013977-xb0r2axf	107	28	(	(	-LRB-
cord-013977-xb0r2axf	107	29	D	D	NNP
cord-013977-xb0r2axf	107	30	≡	≡	NNP
cord-013977-xb0r2axf	107	31	1	1	CD
cord-013977-xb0r2axf	107	32	/	/	SYM
cord-013977-xb0r2axf	107	33	γ	γ	NN
cord-013977-xb0r2axf	107	34	)	)	-RRB-
cord-013977-xb0r2axf	107	35	periods	period	NNS
cord-013977-xb0r2axf	107	36	are	be	VBP
cord-013977-xb0r2axf	107	37	randomly	randomly	RB
cord-013977-xb0r2axf	107	38	drawn	draw	VBN
cord-013977-xb0r2axf	107	39	from	from	IN
cord-013977-xb0r2axf	107	40	an	an	DT
cord-013977-xb0r2axf	107	41	interval	interval	NN
cord-013977-xb0r2axf	107	42	between	between	IN
cord-013977-xb0r2axf	107	43	2	2	CD
cord-013977-xb0r2axf	107	44	and	and	CC
cord-013977-xb0r2axf	107	45	5	5	CD
cord-013977-xb0r2axf	107	46	days	day	NNS
cord-013977-xb0r2axf	107	47	.	.	.
cord-013977-xb0r2axf	108	1	When	when	WRB
cord-013977-xb0r2axf	108	2	time	time	NN
cord-013977-xb0r2axf	108	3	is	be	VBZ
cord-013977-xb0r2axf	108	4	scaled	scale	VBN
cord-013977-xb0r2axf	108	5	by	by	IN
cord-013977-xb0r2axf	108	6	the	the	DT
cord-013977-xb0r2axf	108	7	factor	factor	NN
cord-013977-xb0r2axf	108	8	αγ	αγ	XX
cord-013977-xb0r2axf	108	9	,	,	,
cord-013977-xb0r2axf	108	10	the	the	DT
cord-013977-xb0r2axf	108	11	100	100	CD
cord-013977-xb0r2axf	108	12	susceptible	susceptible	JJ
cord-013977-xb0r2axf	108	13	,	,	,
cord-013977-xb0r2axf	108	14	exposed	expose	VBN
cord-013977-xb0r2axf	108	15	,	,	,
cord-013977-xb0r2axf	108	16	infectious	infectious	JJ
cord-013977-xb0r2axf	108	17	and	and	CC
cord-013977-xb0r2axf	108	18	recovered	recover	VBD
cord-013977-xb0r2axf	108	19	curves	curve	NNS
cord-013977-xb0r2axf	108	20	lie	lie	VBP
cord-013977-xb0r2axf	108	21	approximately	approximately	RB
cord-013977-xb0r2axf	108	22	on	on	IN
cord-013977-xb0r2axf	108	23	top	top	NN
cord-013977-xb0r2axf	108	24	of	of	IN
cord-013977-xb0r2axf	108	25	one	one	CD
cord-013977-xb0r2axf	108	26	another	another	DT
cord-013977-xb0r2axf	108	27	.	.	.
cord-013977-xb0r2axf	109	1	The	the	DT
cord-013977-xb0r2axf	109	2	second	second	JJ
cord-013977-xb0r2axf	109	3	implication	implication	NN
cord-013977-xb0r2axf	109	4	is	be	VBZ
cord-013977-xb0r2axf	109	5	that	that	IN
cord-013977-xb0r2axf	109	6	the	the	DT
cord-013977-xb0r2axf	109	7	time	time	NN
cord-013977-xb0r2axf	109	8	taken	take	VBN
cord-013977-xb0r2axf	109	9	for	for	IN
cord-013977-xb0r2axf	109	10	the	the	DT
cord-013977-xb0r2axf	109	11	infectious	infectious	JJ
cord-013977-xb0r2axf	109	12	curve	curve	NN
cord-013977-xb0r2axf	109	13	to	to	IN
cord-013977-xb0r2axf	109	14	peak	peak	VB
cord-013977-xb0r2axf	109	15	is	be	VBZ
cord-013977-xb0r2axf	109	16	approximately	approximately	RB
cord-013977-xb0r2axf	109	17	universal	universal	JJ
cord-013977-xb0r2axf	109	18	for	for	IN
cord-013977-xb0r2axf	109	19	all	all	DT
cord-013977-xb0r2axf	109	20	SEIR	SEIR	NNP
cord-013977-xb0r2axf	109	21	models	model	NNS
cord-013977-xb0r2axf	109	22	when	when	WRB
cord-013977-xb0r2axf	109	23	scaled	scale	VBN
cord-013977-xb0r2axf	109	24	by	by	IN
cord-013977-xb0r2axf	109	25	α	α	NN
cord-013977-xb0r2axf	109	26	and	and	CC
cord-013977-xb0r2axf	109	27	expressed	express	VBN
cord-013977-xb0r2axf	109	28	in	in	IN
cord-013977-xb0r2axf	109	29	terms	term	NNS
cord-013977-xb0r2axf	109	30	of	of	IN
cord-013977-xb0r2axf	109	31	the	the	DT
cord-013977-xb0r2axf	109	32	infectious	infectious	JJ
cord-013977-xb0r2axf	109	33	period	period	NN
cord-013977-xb0r2axf	109	34	.	.	.
cord-013977-xb0r2axf	110	1	In	in	IN
cord-013977-xb0r2axf	110	2	other	other	JJ
cord-013977-xb0r2axf	110	3	words	word	NNS
cord-013977-xb0r2axf	110	4	,	,	,
cord-013977-xb0r2axf	110	5	αγ	αγ	NNP
cord-013977-xb0r2axf	110	6	�	�	NNP
cord-013977-xb0r2axf	110	7	t	t	NNP
cord-013977-xb0r2axf	110	8	should	should	MD
cord-013977-xb0r2axf	110	9	only	only	RB
cord-013977-xb0r2axf	110	10	depend	depend	VB
cord-013977-xb0r2axf	110	11	on	on	IN
cord-013977-xb0r2axf	110	12	R	r	NN
cord-013977-xb0r2axf	110	13	0	0	CD
cord-013977-xb0r2axf	110	14	and	and	CC
cord-013977-xb0r2axf	110	15	I	-PRON-	PRP
cord-013977-xb0r2axf	110	16	0	0	CD
cord-013977-xb0r2axf	110	17	.	.	.
cord-013977-xb0r2axf	111	1	To	to	TO
cord-013977-xb0r2axf	111	2	demonstrate	demonstrate	VB
cord-013977-xb0r2axf	111	3	this	this	DT
cord-013977-xb0r2axf	111	4	property	property	NN
cord-013977-xb0r2axf	111	5	,	,	,
cord-013977-xb0r2axf	111	6	the	the	DT
cord-013977-xb0r2axf	111	7	full	full	JJ
cord-013977-xb0r2axf	111	8	set	set	NN
cord-013977-xb0r2axf	111	9	of	of	IN
cord-013977-xb0r2axf	111	10	equations	equation	NNS
cord-013977-xb0r2axf	111	11	in	in	IN
cord-013977-xb0r2axf	111	12	(	(	-LRB-
cord-013977-xb0r2axf	111	13	15	15	CD
cord-013977-xb0r2axf	111	14	)	)	-RRB-
cord-013977-xb0r2axf	111	15	is	be	VBZ
cord-013977-xb0r2axf	111	16	again	again	RB
cord-013977-xb0r2axf	111	17	solved	solve	VBN
cord-013977-xb0r2axf	111	18	numerically	numerically	RB
cord-013977-xb0r2axf	111	19	for	for	IN
cord-013977-xb0r2axf	111	20	10,000	10,000	CD
cord-013977-xb0r2axf	111	21	random	random	JJ
cord-013977-xb0r2axf	111	22	draws	draw	NNS
cord-013977-xb0r2axf	111	23	of	of	IN
cord-013977-xb0r2axf	111	24	1	1	CD
cord-013977-xb0r2axf	111	25	/	/	SYM
cord-013977-xb0r2axf	111	26	σ	σ	NN
cord-013977-xb0r2axf	111	27	and	and	CC
cord-013977-xb0r2axf	111	28	1	1	CD
cord-013977-xb0r2axf	111	29	/	/	SYM
cord-013977-xb0r2axf	111	30	γ	γ	NN
cord-013977-xb0r2axf	111	31	and	and	CC
cord-013977-xb0r2axf	111	32	for	for	IN
cord-013977-xb0r2axf	111	33	R	r	NN
cord-013977-xb0r2axf	111	34	0	0	CD
cord-013977-xb0r2axf	111	35	=	=	SYM
cord-013977-xb0r2axf	111	36	2	2	CD
cord-013977-xb0r2axf	111	37	to	to	IN
cord-013977-xb0r2axf	111	38	7	7	CD
cord-013977-xb0r2axf	111	39	.	.	.
cord-013977-xb0r2axf	112	1	For	for	IN
cord-013977-xb0r2axf	112	2	each	each	DT
cord-013977-xb0r2axf	112	3	SEIR	SEIR	NNP
cord-013977-xb0r2axf	112	4	model	model	NN
cord-013977-xb0r2axf	112	5	,	,	,
cord-013977-xb0r2axf	112	6	the	the	DT
cord-013977-xb0r2axf	112	7	time	time	NN
cord-013977-xb0r2axf	112	8	taken	take	VBN
cord-013977-xb0r2axf	112	9	for	for	IN
cord-013977-xb0r2axf	112	10	the	the	DT
cord-013977-xb0r2axf	112	11	infectious	infectious	JJ
cord-013977-xb0r2axf	112	12	curve	curve	NN
cord-013977-xb0r2axf	112	13	to	to	TO
cord-013977-xb0r2axf	112	14	peak	peak	VB
cord-013977-xb0r2axf	112	15	(	(	-LRB-
cord-013977-xb0r2axf	112	16	t	t	NN
cord-013977-xb0r2axf	112	17	)	)	-RRB-
cord-013977-xb0r2axf	112	18	is	be	VBZ
cord-013977-xb0r2axf	112	19	calculated	calculate	VBN
cord-013977-xb0r2axf	112	20	numerically	numerically	RB
cord-013977-xb0r2axf	112	21	.	.	.
cord-013977-xb0r2axf	113	1	All	all	DT
cord-013977-xb0r2axf	113	2	10,000	10,000	CD
cord-013977-xb0r2axf	113	3	values	value	NNS
cord-013977-xb0r2axf	113	4	of	of	IN
cord-013977-xb0r2axf	113	5	t	t	NN
cord-013977-xb0r2axf	113	6	are	be	VBP
cord-013977-xb0r2axf	113	7	multiplied	multiply	VBN
cord-013977-xb0r2axf	113	8	by	by	IN
cord-013977-xb0r2axf	113	9	αγ	αγ	XX
cord-013977-xb0r2axf	113	10	;	;	:
cord-013977-xb0r2axf	113	11	two	two	CD
cord-013977-xb0r2axf	113	12	sets	set	NNS
cord-013977-xb0r2axf	113	13	of	of	IN
cord-013977-xb0r2axf	113	14	curves	curve	NNS
cord-013977-xb0r2axf	113	15	with	with	IN
cord-013977-xb0r2axf	113	16	different	different	JJ
cord-013977-xb0r2axf	113	17	I	-PRON-	PRP
cord-013977-xb0r2axf	113	18	0	0	CD
cord-013977-xb0r2axf	113	19	values	value	NNS
cord-013977-xb0r2axf	113	20	are	be	VBP
cord-013977-xb0r2axf	113	21	shown	show	VBN
cord-013977-xb0r2axf	113	22	in	in	IN
cord-013977-xb0r2axf	113	23	Fig	Fig	NNP
cord-013977-xb0r2axf	113	24	.	.	NNP
cord-013977-xb0r2axf	113	25	2	2	CD
cord-013977-xb0r2axf	113	26	for	for	IN
cord-013977-xb0r2axf	113	27	illustration	illustration	NN
cord-013977-xb0r2axf	113	28	.	.	.
cord-013977-xb0r2axf	114	1	For	for	IN
cord-013977-xb0r2axf	114	2	all	all	DT
cord-013977-xb0r2axf	114	3	10,000	10,000	CD
cord-013977-xb0r2axf	114	4	SEIR	SEIR	NNP
cord-013977-xb0r2axf	114	5	models	model	NNS
cord-013977-xb0r2axf	114	6	,	,	,
cord-013977-xb0r2axf	114	7	the	the	DT
cord-013977-xb0r2axf	114	8	αγ	αγ	XX
cord-013977-xb0r2axf	114	9	�	�	NNP
cord-013977-xb0r2axf	114	10	t	t	NNP
cord-013977-xb0r2axf	114	11	values	value	NNS
cord-013977-xb0r2axf	114	12	lie	lie	VBP
cord-013977-xb0r2axf	114	13	approximately	approximately	RB
cord-013977-xb0r2axf	114	14	on	on	IN
cord-013977-xb0r2axf	114	15	the	the	DT
cord-013977-xb0r2axf	114	16	same	same	JJ
cord-013977-xb0r2axf	114	17	curve	curve	NN
cord-013977-xb0r2axf	114	18	across	across	IN
cord-013977-xb0r2axf	114	19	R	r	NN
cord-013977-xb0r2axf	114	20	0	0	CD
cord-013977-xb0r2axf	114	21	for	for	IN
cord-013977-xb0r2axf	114	22	a	a	DT
cord-013977-xb0r2axf	114	23	given	give	VBN
cord-013977-xb0r2axf	114	24	value	value	NN
cord-013977-xb0r2axf	114	25	of	of	IN
cord-013977-xb0r2axf	114	26	I	i	NN
cord-013977-xb0r2axf	114	27	0	0	CD
cord-013977-xb0r2axf	114	28	,	,	,
cord-013977-xb0r2axf	114	29	demonstrating	demonstrate	VBG
cord-013977-xb0r2axf	114	30	that	that	IN
cord-013977-xb0r2axf	114	31	αγ	αγ	XX
cord-013977-xb0r2axf	114	32	�	�	NNP
cord-013977-xb0r2axf	114	33	t	t	NNP
cord-013977-xb0r2axf	114	34	is	be	VBZ
cord-013977-xb0r2axf	114	35	a	a	DT
cord-013977-xb0r2axf	114	36	dimensionless	dimensionless	NN
cord-013977-xb0r2axf	114	37	(	(	-LRB-
cord-013977-xb0r2axf	114	38	with	with	IN
cord-013977-xb0r2axf	114	39	no	no	DT
cord-013977-xb0r2axf	114	40	physical	physical	JJ
cord-013977-xb0r2axf	114	41	units	unit	NNS
cord-013977-xb0r2axf	114	42	)	)	-RRB-
cord-013977-xb0r2axf	114	43	,	,	,
cord-013977-xb0r2axf	114	44	approximately	approximately	RB
cord-013977-xb0r2axf	114	45	universal	universal	JJ
cord-013977-xb0r2axf	114	46	timescale	timescale	NN
cord-013977-xb0r2axf	114	47	of	of	IN
cord-013977-xb0r2axf	114	48	the	the	DT
cord-013977-xb0r2axf	114	49	SEIR	SEIR	NNP
cord-013977-xb0r2axf	114	50	model	model	NN
cord-013977-xb0r2axf	114	51	.	.	.
cord-013977-xb0r2axf	115	1	In	in	IN
cord-013977-xb0r2axf	115	2	the	the	DT
cord-013977-xb0r2axf	115	3	current	current	JJ
cord-013977-xb0r2axf	115	4	study	study	NN
cord-013977-xb0r2axf	115	5	,	,	,
cord-013977-xb0r2axf	115	6	approximate	approximate	JJ
cord-013977-xb0r2axf	115	7	semi	semi	JJ
cord-013977-xb0r2axf	115	8	-	-	JJ
cord-013977-xb0r2axf	115	9	analytical	analytical	JJ
cord-013977-xb0r2axf	115	10	solutions	solution	NNS
cord-013977-xb0r2axf	115	11	of	of	IN
cord-013977-xb0r2axf	115	12	the	the	DT
cord-013977-xb0r2axf	115	13	SEIR	SEIR	NNP
cord-013977-xb0r2axf	115	14	model	model	NN
cord-013977-xb0r2axf	115	15	are	be	VBP
cord-013977-xb0r2axf	115	16	found	find	VBN
cord-013977-xb0r2axf	115	17	by	by	IN
cord-013977-xb0r2axf	115	18	generalising	generalise	VBG
cord-013977-xb0r2axf	115	19	a	a	DT
cord-013977-xb0r2axf	115	20	previous	previous	JJ
cord-013977-xb0r2axf	115	21	approach	approach	NN
cord-013977-xb0r2axf	115	22	for	for	IN
cord-013977-xb0r2axf	115	23	deriving	derive	VBG
cord-013977-xb0r2axf	115	24	an	an	DT
cord-013977-xb0r2axf	115	25	exact	exact	JJ
cord-013977-xb0r2axf	115	26	solution	solution	NN
cord-013977-xb0r2axf	115	27	of	of	IN
cord-013977-xb0r2axf	115	28	the	the	DT
cord-013977-xb0r2axf	115	29	SIR	SIR	NNP
cord-013977-xb0r2axf	115	30	model	model	NN
cord-013977-xb0r2axf	115	31	.	.	.
cord-013977-xb0r2axf	116	1	This	this	DT
cord-013977-xb0r2axf	116	2	finding	finding	NN
cord-013977-xb0r2axf	116	3	implies	imply	VBZ
cord-013977-xb0r2axf	116	4	that	that	IN
cord-013977-xb0r2axf	116	5	the	the	DT
cord-013977-xb0r2axf	116	6	entire	entire	JJ
cord-013977-xb0r2axf	116	7	family	family	NN
cord-013977-xb0r2axf	116	8	of	of	IN
cord-013977-xb0r2axf	116	9	susceptible	susceptible	JJ
cord-013977-xb0r2axf	116	10	,	,	,
cord-013977-xb0r2axf	116	11	exposed	expose	VBN
cord-013977-xb0r2axf	116	12	,	,	,
cord-013977-xb0r2axf	116	13	infectious	infectious	JJ
cord-013977-xb0r2axf	116	14	and	and	CC
cord-013977-xb0r2axf	116	15	recovered	recovered	JJ
cord-013977-xb0r2axf	116	16	curves	curve	NNS
cord-013977-xb0r2axf	116	17	of	of	IN
cord-013977-xb0r2axf	116	18	the	the	DT
cord-013977-xb0r2axf	116	19	SEIR	SEIR	NNP
cord-013977-xb0r2axf	116	20	model	model	NN
cord-013977-xb0r2axf	116	21	follow	follow	VB
cord-013977-xb0r2axf	116	22	approximately	approximately	RB
cord-013977-xb0r2axf	116	23	universal	universal	JJ
cord-013977-xb0r2axf	116	24	shapes	shape	NNS
cord-013977-xb0r2axf	116	25	that	that	WDT
cord-013977-xb0r2axf	116	26	are	be	VBP
cord-013977-xb0r2axf	116	27	stretched	stretch	VBN
cord-013977-xb0r2axf	116	28	or	or	CC
cord-013977-xb0r2axf	116	29	compressed	compress	VBN
cord-013977-xb0r2axf	116	30	,	,	,
cord-013977-xb0r2axf	116	31	relative	relative	JJ
cord-013977-xb0r2axf	116	32	to	to	IN
cord-013977-xb0r2axf	116	33	one	one	CD
cord-013977-xb0r2axf	116	34	another	another	DT
cord-013977-xb0r2axf	116	35	,	,	,
cord-013977-xb0r2axf	116	36	by	by	IN
cord-013977-xb0r2axf	116	37	a	a	DT
cord-013977-xb0r2axf	116	38	factor	factor	NN
cord-013977-xb0r2axf	116	39	consisting	consist	VBG
cord-013977-xb0r2axf	116	40	of	of	IN
cord-013977-xb0r2axf	116	41	the	the	DT
cord-013977-xb0r2axf	116	42	incubation	incubation	NN
cord-013977-xb0r2axf	116	43	and	and	CC
cord-013977-xb0r2axf	116	44	infectious	infectious	JJ
cord-013977-xb0r2axf	116	45	periods	period	NNS
cord-013977-xb0r2axf	116	46	.	.	.
cord-013977-xb0r2axf	117	1	The	the	DT
cord-013977-xb0r2axf	117	2	time	time	NN
cord-013977-xb0r2axf	117	3	taken	take	VBN
cord-013977-xb0r2axf	117	4	for	for	IN
cord-013977-xb0r2axf	117	5	the	the	DT
cord-013977-xb0r2axf	117	6	infectious	infectious	JJ
cord-013977-xb0r2axf	117	7	curve	curve	NN
cord-013977-xb0r2axf	117	8	to	to	IN
cord-013977-xb0r2axf	117	9	peak	peak	NN
cord-013977-xb0r2axf	117	10	is	be	VBZ
cord-013977-xb0r2axf	117	11	the	the	DT
cord-013977-xb0r2axf	117	12	characteristic	characteristic	JJ
cord-013977-xb0r2axf	117	13	timescale	timescale	NN
cord-013977-xb0r2axf	117	14	of	of	IN
cord-013977-xb0r2axf	117	15	the	the	DT
cord-013977-xb0r2axf	117	16	system	system	NN
cord-013977-xb0r2axf	117	17	and	and	CC
cord-013977-xb0r2axf	117	18	depends	depend	VBZ
cord-013977-xb0r2axf	117	19	only	only	RB
cord-013977-xb0r2axf	117	20	on	on	IN
cord-013977-xb0r2axf	117	21	the	the	DT
cord-013977-xb0r2axf	117	22	basic	basic	JJ
cord-013977-xb0r2axf	117	23	reproduction	reproduction	NN
cord-013977-xb0r2axf	117	24	number	number	NN
cord-013977-xb0r2axf	117	25	and	and	CC
cord-013977-xb0r2axf	117	26	the	the	DT
cord-013977-xb0r2axf	117	27	initial	initial	JJ
cord-013977-xb0r2axf	117	28	fraction	fraction	NN
cord-013977-xb0r2axf	117	29	of	of	IN
cord-013977-xb0r2axf	117	30	the	the	DT
cord-013977-xb0r2axf	117	31	population	population	NN
cord-013977-xb0r2axf	117	32	that	that	WDT
cord-013977-xb0r2axf	117	33	is	be	VBZ
cord-013977-xb0r2axf	117	34	infectious	infectious	JJ
cord-013977-xb0r2axf	117	35	when	when	WRB
cord-013977-xb0r2axf	117	36	scaled	scale	VBN
cord-013977-xb0r2axf	117	37	by	by	IN
cord-013977-xb0r2axf	117	38	the	the	DT
cord-013977-xb0r2axf	117	39	infectious	infectious	JJ
cord-013977-xb0r2axf	117	40	period	period	NN
cord-013977-xb0r2axf	117	41	and	and	CC
cord-013977-xb0r2axf	117	42	this	this	DT
cord-013977-xb0r2axf	117	43	stretch	stretch	NN
cord-013977-xb0r2axf	117	44	factor	factor	NN
cord-013977-xb0r2axf	117	45	.	.	.
cord-013977-xb0r2axf	118	1	For	for	IN
cord-013977-xb0r2axf	118	2	illustration	illustration	NN
cord-013977-xb0r2axf	118	3	,	,	,
cord-013977-xb0r2axf	118	4	the	the	DT
cord-013977-xb0r2axf	118	5	basic	basic	JJ
cord-013977-xb0r2axf	118	6	reproduction	reproduction	NN
cord-013977-xb0r2axf	118	7	number	number	NN
cord-013977-xb0r2axf	118	8	has	have	VBZ
cord-013977-xb0r2axf	118	9	been	be	VBN
cord-013977-xb0r2axf	118	10	set	set	VBN
cord-013977-xb0r2axf	118	11	to	to	IN
cord-013977-xb0r2axf	118	12	R	r	NN
cord-013977-xb0r2axf	118	13	0	0	CD
cord-013977-xb0r2axf	118	14	=	=	SYM
cord-013977-xb0r2axf	118	15	2	2	CD
cord-013977-xb0r2axf	118	16	and	and	CC
cord-013977-xb0r2axf	118	17	the	the	DT
cord-013977-xb0r2axf	118	18	initial	initial	JJ
cord-013977-xb0r2axf	118	19	fraction	fraction	NN
cord-013977-xb0r2axf	118	20	of	of	IN
cord-013977-xb0r2axf	118	21	the	the	DT
cord-013977-xb0r2axf	118	22	population	population	NN
cord-013977-xb0r2axf	118	23	that	that	WDT
cord-013977-xb0r2axf	118	24	is	be	VBZ
cord-013977-xb0r2axf	118	25	infectious	infectious	JJ
cord-013977-xb0r2axf	118	26	has	have	VBZ
cord-013977-xb0r2axf	118	27	been	be	VBN
cord-013977-xb0r2axf	118	28	set	set	VBN
cord-013977-xb0r2axf	118	29	to	to	IN
cord-013977-xb0r2axf	118	30	I	i	NN
cord-013977-xb0r2axf	118	31	0	0	CD
cord-013977-xb0r2axf	118	32	=	=	SYM
cord-013977-xb0r2axf	118	33	10	10	CD
cord-013977-xb0r2axf	118	34	−4	−4	CD
cord-013977-xb0r2axf	118	35	.	.	.
cord-013977-xb0r2axf	119	1	Each	each	DT
cord-013977-xb0r2axf	119	2	set	set	NN
cord-013977-xb0r2axf	119	3	of	of	IN
cord-013977-xb0r2axf	119	4	curves	curve	NNS
cord-013977-xb0r2axf	119	5	is	be	VBZ
cord-013977-xb0r2axf	119	6	generated	generate	VBN
cord-013977-xb0r2axf	119	7	using	use	VBG
cord-013977-xb0r2axf	119	8	100	100	CD
cord-013977-xb0r2axf	119	9	random	random	JJ
cord-013977-xb0r2axf	119	10	realisations	realisation	NNS
cord-013977-xb0r2axf	119	11	of	of	IN
cord-013977-xb0r2axf	119	12	the	the	DT
cord-013977-xb0r2axf	119	13	incubation	incubation	NN
cord-013977-xb0r2axf	119	14	and	and	CC
cord-013977-xb0r2axf	119	15	infectious	infectious	JJ
cord-013977-xb0r2axf	119	16	periods	period	NNS
cord-013977-xb0r2axf	119	17	,	,	,
cord-013977-xb0r2axf	119	18	each	each	DT
cord-013977-xb0r2axf	119	19	drawn	draw	VBN
cord-013977-xb0r2axf	119	20	from	from	IN
cord-013977-xb0r2axf	119	21	an	an	DT
cord-013977-xb0r2axf	119	22	interval	interval	NN
cord-013977-xb0r2axf	119	23	between	between	IN
cord-013977-xb0r2axf	119	24	2	2	CD
cord-013977-xb0r2axf	119	25	and	and	CC
cord-013977-xb0r2axf	119	26	5	5	CD
cord-013977-xb0r2axf	119	27	days	day	NNS
cord-013977-xb0r2axf	119	28	for	for	IN
cord-013977-xb0r2axf	119	29	illustration	illustration	NN
cord-013977-xb0r2axf	119	30	.	.	.
cord-013977-xb0r2axf	120	1	Figure	figure	NN
cord-013977-xb0r2axf	120	2	2	2	CD
cord-013977-xb0r2axf	120	3	.	.	.
cord-013977-xb0r2axf	121	1	Time	time	NN
cord-013977-xb0r2axf	121	2	until	until	IN
cord-013977-xb0r2axf	121	3	the	the	DT
cord-013977-xb0r2axf	121	4	infectious	infectious	JJ
cord-013977-xb0r2axf	121	5	curve	curve	NN
cord-013977-xb0r2axf	121	6	(	(	-LRB-
cord-013977-xb0r2axf	121	7	I	i	NN
cord-013977-xb0r2axf	121	8	)	)	-RRB-
cord-013977-xb0r2axf	121	9	peaks	peak	VBZ
cord-013977-xb0r2axf	121	10	as	as	IN
cord-013977-xb0r2axf	121	11	a	a	DT
cord-013977-xb0r2axf	121	12	function	function	NN
cord-013977-xb0r2axf	121	13	of	of	IN
cord-013977-xb0r2axf	121	14	the	the	DT
cord-013977-xb0r2axf	121	15	basic	basic	JJ
cord-013977-xb0r2axf	121	16	reproduction	reproduction	NN
cord-013977-xb0r2axf	121	17	number	number	NN
cord-013977-xb0r2axf	121	18	R	r	NN
cord-013977-xb0r2axf	121	19	0	0	CD
cord-013977-xb0r2axf	121	20	.	.	.
cord-013977-xb0r2axf	122	1	In	in	IN
cord-013977-xb0r2axf	122	2	the	the	DT
cord-013977-xb0r2axf	122	3	SEIR	SEIR	NNP
cord-013977-xb0r2axf	122	4	model	model	NN
cord-013977-xb0r2axf	122	5	,	,	,
cord-013977-xb0r2axf	122	6	the	the	DT
cord-013977-xb0r2axf	122	7	time	time	NN
cord-013977-xb0r2axf	122	8	to	to	IN
cord-013977-xb0r2axf	122	9	the	the	DT
cord-013977-xb0r2axf	122	10	epidemic	epidemic	NN
cord-013977-xb0r2axf	122	11	peak	peak	NN
cord-013977-xb0r2axf	122	12	(	(	-LRB-
cord-013977-xb0r2axf	122	13	t	t	NN
cord-013977-xb0r2axf	122	14	)	)	-RRB-
cord-013977-xb0r2axf	122	15	scales	scale	VBZ
cord-013977-xb0r2axf	122	16	approximately	approximately	RB
cord-013977-xb0r2axf	122	17	with	with	IN
cord-013977-xb0r2axf	122	18	α	α	NN
cord-013977-xb0r2axf	122	19	and	and	CC
cord-013977-xb0r2axf	122	20	γ	γ	NN
cord-013977-xb0r2axf	122	21	.	.	.
cord-013977-xb0r2axf	123	1	For	for	IN
cord-013977-xb0r2axf	123	2	illustration	illustration	NN
cord-013977-xb0r2axf	123	3	,	,	,
cord-013977-xb0r2axf	123	4	two	two	CD
cord-013977-xb0r2axf	123	5	values	value	NNS
cord-013977-xb0r2axf	123	6	of	of	IN
cord-013977-xb0r2axf	123	7	the	the	DT
cord-013977-xb0r2axf	123	8	initial	initial	JJ
cord-013977-xb0r2axf	123	9	fraction	fraction	NN
cord-013977-xb0r2axf	123	10	of	of	IN
cord-013977-xb0r2axf	123	11	population	population	NN
cord-013977-xb0r2axf	123	12	that	that	WDT
cord-013977-xb0r2axf	123	13	is	be	VBZ
cord-013977-xb0r2axf	123	14	infectious	infectious	JJ
cord-013977-xb0r2axf	123	15	(	(	-LRB-
cord-013977-xb0r2axf	123	16	I	i	NN
cord-013977-xb0r2axf	123	17	0	0	CD
cord-013977-xb0r2axf	123	18	)	)	-RRB-
cord-013977-xb0r2axf	123	19	are	be	VBP
cord-013977-xb0r2axf	123	20	considered	consider	VBN
cord-013977-xb0r2axf	123	21	.	.	.
cord-013977-xb0r2axf	124	1	Each	each	DT
cord-013977-xb0r2axf	124	2	set	set	NN
cord-013977-xb0r2axf	124	3	of	of	IN
cord-013977-xb0r2axf	124	4	curves	curve	NNS
cord-013977-xb0r2axf	124	5	is	be	VBZ
cord-013977-xb0r2axf	124	6	generated	generate	VBN
cord-013977-xb0r2axf	124	7	using	use	VBG
cord-013977-xb0r2axf	124	8	10,000	10,000	CD
cord-013977-xb0r2axf	124	9	random	random	JJ
cord-013977-xb0r2axf	124	10	draws	draw	NNS
cord-013977-xb0r2axf	124	11	of	of	IN
cord-013977-xb0r2axf	124	12	the	the	DT
cord-013977-xb0r2axf	124	13	incubation	incubation	NN
cord-013977-xb0r2axf	124	14	and	and	CC
cord-013977-xb0r2axf	124	15	infectious	infectious	JJ
cord-013977-xb0r2axf	124	16	periods	period	NNS
cord-013977-xb0r2axf	124	17	from	from	IN
cord-013977-xb0r2axf	124	18	an	an	DT
cord-013977-xb0r2axf	124	19	interval	interval	NN
cord-013977-xb0r2axf	124	20	between	between	IN
cord-013977-xb0r2axf	124	21	2	2	CD
cord-013977-xb0r2axf	124	22	and	and	CC
cord-013977-xb0r2axf	124	23	5	5	CD
cord-013977-xb0r2axf	124	24	days	day	NNS
cord-013977-xb0r2axf	124	25	.	.	.
cord-013977-xb0r2axf	125	1	An	an	DT
cord-013977-xb0r2axf	125	2	Introduction	introduction	NN
cord-013977-xb0r2axf	125	3	to	to	IN
cord-013977-xb0r2axf	125	4	Infectious	Infectious	NNP
cord-013977-xb0r2axf	125	5	Disease	Disease	NNP
cord-013977-xb0r2axf	125	6	Modelling	Modelling	NNP
cord-013977-xb0r2axf	125	7	Message	message	NN
cord-013977-xb0r2axf	125	8	passing	pass	VBG
cord-013977-xb0r2axf	125	9	approach	approach	NN
cord-013977-xb0r2axf	125	10	for	for	IN
cord-013977-xb0r2axf	125	11	general	general	JJ
cord-013977-xb0r2axf	125	12	epidemic	epidemic	NN
cord-013977-xb0r2axf	125	13	models	model	NNS
cord-013977-xb0r2axf	126	1	Impact	impact	NN
cord-013977-xb0r2axf	126	2	of	of	IN
cord-013977-xb0r2axf	126	3	the	the	DT
cord-013977-xb0r2axf	126	4	infectious	infectious	JJ
cord-013977-xb0r2axf	126	5	period	period	NN
cord-013977-xb0r2axf	126	6	on	on	IN
cord-013977-xb0r2axf	126	7	epidemics	epidemic	NNS
cord-013977-xb0r2axf	127	1	A	a	DT
cord-013977-xb0r2axf	127	2	contribution	contribution	NN
cord-013977-xb0r2axf	127	3	to	to	IN
cord-013977-xb0r2axf	127	4	the	the	DT
cord-013977-xb0r2axf	127	5	mathematical	mathematical	JJ
cord-013977-xb0r2axf	127	6	theory	theory	NN
cord-013977-xb0r2axf	127	7	of	of	IN
cord-013977-xb0r2axf	127	8	epidemics	epidemic	NNS
cord-013977-xb0r2axf	128	1	Exact	exact	JJ
cord-013977-xb0r2axf	128	2	analytical	analytical	JJ
cord-013977-xb0r2axf	128	3	solutions	solution	NNS
cord-013977-xb0r2axf	128	4	of	of	IN
cord-013977-xb0r2axf	128	5	the	the	DT
cord-013977-xb0r2axf	128	6	Susceptible	susceptible	JJ
cord-013977-xb0r2axf	128	7	-	-	HYPH
cord-013977-xb0r2axf	128	8	Infected	Infected	NNP
cord-013977-xb0r2axf	128	9	-	-	HYPH
cord-013977-xb0r2axf	128	10	Recovered	recovered	JJ
cord-013977-xb0r2axf	128	11	(	(	-LRB-
cord-013977-xb0r2axf	128	12	SIR	SIR	NNP
cord-013977-xb0r2axf	128	13	)	)	-RRB-
cord-013977-xb0r2axf	128	14	epidemic	epidemic	NN
cord-013977-xb0r2axf	128	15	model	model	NN
cord-013977-xb0r2axf	128	16	and	and	CC
cord-013977-xb0r2axf	128	17	of	of	IN
cord-013977-xb0r2axf	128	18	the	the	DT
cord-013977-xb0r2axf	128	19	SIR	SIR	NNP
cord-013977-xb0r2axf	128	20	model	model	NN
cord-013977-xb0r2axf	128	21	with	with	IN
cord-013977-xb0r2axf	128	22	equal	equal	JJ
cord-013977-xb0r2axf	128	23	death	death	NN
cord-013977-xb0r2axf	128	24	and	and	CC
cord-013977-xb0r2axf	128	25	birth	birth	NN
cord-013977-xb0r2axf	128	26	rates	rate	NNS
cord-013977-xb0r2axf	129	1	Mathematical	mathematical	JJ
cord-013977-xb0r2axf	129	2	models	model	NNS
cord-013977-xb0r2axf	129	3	of	of	IN
cord-013977-xb0r2axf	129	4	SIR	SIR	NNP
cord-013977-xb0r2axf	129	5	disease	disease	NN
cord-013977-xb0r2axf	129	6	spread	spread	VBD
cord-013977-xb0r2axf	129	7	with	with	IN
cord-013977-xb0r2axf	129	8	combined	combine	VBN
cord-013977-xb0r2axf	129	9	non	non	JJ
cord-013977-xb0r2axf	129	10	-	-	JJ
cord-013977-xb0r2axf	129	11	sexual	sexual	JJ
cord-013977-xb0r2axf	129	12	and	and	CC
cord-013977-xb0r2axf	129	13	sexual	sexual	JJ
cord-013977-xb0r2axf	129	14	transmission	transmission	NN
cord-013977-xb0r2axf	129	15	route	route	NN
cord-013977-xb0r2axf	129	16	Analytical	analytical	JJ
cord-013977-xb0r2axf	129	17	solution	solution	NN
cord-013977-xb0r2axf	129	18	of	of	IN
cord-013977-xb0r2axf	129	19	SEIR	SEIR	NNP
cord-013977-xb0r2axf	129	20	model	model	NN
cord-013977-xb0r2axf	129	21	describing	describe	VBG
cord-013977-xb0r2axf	129	22	the	the	DT
cord-013977-xb0r2axf	129	23	free	free	JJ
cord-013977-xb0r2axf	129	24	spread	spread	NN
cord-013977-xb0r2axf	129	25	of	of	IN
cord-013977-xb0r2axf	129	26	the	the	DT
cord-013977-xb0r2axf	129	27	COVID-19	covid-19	JJ
cord-013977-xb0r2axf	129	28	pandemic	pandemic	NN
cord-013977-xb0r2axf	129	29	How	how	WRB
cord-013977-xb0r2axf	129	30	generation	generation	NN
cord-013977-xb0r2axf	129	31	intervals	interval	NNS
cord-013977-xb0r2axf	129	32	shape	shape	VBP
cord-013977-xb0r2axf	129	33	the	the	DT
cord-013977-xb0r2axf	129	34	relationship	relationship	NN
cord-013977-xb0r2axf	129	35	between	between	IN
cord-013977-xb0r2axf	129	36	growth	growth	NN
cord-013977-xb0r2axf	129	37	rates	rate	NNS
cord-013977-xb0r2axf	129	38	and	and	CC
cord-013977-xb0r2axf	129	39	reproductive	reproductive	JJ
cord-013977-xb0r2axf	129	40	numbers	number	NNS
cord-013977-xb0r2axf	130	1	SciPy	SciPy	NNP
cord-013977-xb0r2axf	130	2	1.0	1.0	CD
cord-013977-xb0r2axf	130	3	:	:	:
cord-013977-xb0r2axf	131	1	fundamental	fundamental	JJ
cord-013977-xb0r2axf	131	2	algorithms	algorithm	NNS
cord-013977-xb0r2axf	131	3	for	for	IN
cord-013977-xb0r2axf	131	4	scientific	scientific	JJ
cord-013977-xb0r2axf	131	5	computing	computing	NN
cord-013977-xb0r2axf	131	6	in	in	IN
cord-013977-xb0r2axf	131	7	Python	Python	NNP
cord-013977-xb0r2axf	131	8	K.H.	K.H.	NNP
cord-013977-xb0r2axf	131	9	formulated	formulate	VBD
cord-013977-xb0r2axf	131	10	the	the	DT
cord-013977-xb0r2axf	131	11	problem	problem	NN
cord-013977-xb0r2axf	131	12	,	,	,
cord-013977-xb0r2axf	131	13	derived	derive	VBD
cord-013977-xb0r2axf	131	14	the	the	DT
cord-013977-xb0r2axf	131	15	equations	equation	NNS
cord-013977-xb0r2axf	131	16	,	,	,
cord-013977-xb0r2axf	131	17	performed	perform	VBD
cord-013977-xb0r2axf	131	18	the	the	DT
cord-013977-xb0r2axf	131	19	numerical	numerical	JJ
cord-013977-xb0r2axf	131	20	calculations	calculation	NNS
cord-013977-xb0r2axf	131	21	and	and	CC
cord-013977-xb0r2axf	131	22	wrote	write	VBD
cord-013977-xb0r2axf	131	23	the	the	DT
cord-013977-xb0r2axf	131	24	manuscript	manuscript	NN
cord-013977-xb0r2axf	131	25	.	.	.
cord-013977-xb0r2axf	132	1	C.L.A.	C.L.A.	NNP
cord-013977-xb0r2axf	132	2	made	make	VBD
cord-013977-xb0r2axf	132	3	the	the	DT
cord-013977-xb0r2axf	132	4	link	link	NN
cord-013977-xb0r2axf	132	5	between	between	IN
cord-013977-xb0r2axf	132	6	the	the	DT
cord-013977-xb0r2axf	132	7	reproduction	reproduction	NN
cord-013977-xb0r2axf	132	8	number	number	NN
cord-013977-xb0r2axf	132	9	and	and	CC
cord-013977-xb0r2axf	132	10	growth	growth	NN
cord-013977-xb0r2axf	132	11	rate	rate	NN
cord-013977-xb0r2axf	132	12	,	,	,
cord-013977-xb0r2axf	132	13	checked	check	VBD
cord-013977-xb0r2axf	132	14	the	the	DT
cord-013977-xb0r2axf	132	15	equations	equation	NNS
cord-013977-xb0r2axf	132	16	and	and	CC
cord-013977-xb0r2axf	132	17	edited	edit	VBD
cord-013977-xb0r2axf	132	18	the	the	DT
cord-013977-xb0r2axf	132	19	manuscript	manuscript	NN
cord-013977-xb0r2axf	132	20	.	.	.
cord-013977-xb0r2axf	133	1	The	the	DT
cord-013977-xb0r2axf	133	2	authors	author	NNS
cord-013977-xb0r2axf	133	3	declare	declare	VBP
cord-013977-xb0r2axf	133	4	no	no	DT
cord-013977-xb0r2axf	133	5	competing	compete	VBG
cord-013977-xb0r2axf	133	6	interests	interest	NNS
cord-013977-xb0r2axf	133	7	.	.	.
cord-013977-xb0r2axf	134	1	Correspondence	correspondence	NN
cord-013977-xb0r2axf	134	2	and	and	CC
cord-013977-xb0r2axf	134	3	requests	request	NNS
cord-013977-xb0r2axf	134	4	for	for	IN
cord-013977-xb0r2axf	134	5	materials	material	NNS
cord-013977-xb0r2axf	134	6	should	should	MD
cord-013977-xb0r2axf	134	7	be	be	VB
cord-013977-xb0r2axf	134	8	addressed	address	VBN
cord-013977-xb0r2axf	134	9	to	to	IN
cord-013977-xb0r2axf	134	10	K.H.	K.H.	NNP
cord-013977-xb0r2axf	134	11	Publisher	Publisher	NNP
cord-013977-xb0r2axf	134	12	's	's	POS
cord-013977-xb0r2axf	134	13	note	note	NN
cord-013977-xb0r2axf	134	14	Springer	Springer	NNP
cord-013977-xb0r2axf	134	15	Nature	Nature	NNP
cord-013977-xb0r2axf	134	16	remains	remain	VBZ
cord-013977-xb0r2axf	134	17	neutral	neutral	JJ
cord-013977-xb0r2axf	134	18	with	with	IN
cord-013977-xb0r2axf	134	19	regard	regard	NN
cord-013977-xb0r2axf	134	20	to	to	IN
cord-013977-xb0r2axf	134	21	jurisdictional	jurisdictional	JJ
cord-013977-xb0r2axf	134	22	claims	claim	NNS
cord-013977-xb0r2axf	134	23	in	in	IN
cord-013977-xb0r2axf	134	24	published	publish	VBN
cord-013977-xb0r2axf	134	25	maps	map	NNS
cord-013977-xb0r2axf	134	26	and	and	CC
cord-013977-xb0r2axf	134	27	institutional	institutional	JJ
cord-013977-xb0r2axf	134	28	affiliations	affiliation	NNS
cord-013977-xb0r2axf	134	29	.	.	.
cord-013977-xb0r2axf	135	1	Open	open	VB
cord-013977-xb0r2axf	135	2	Access	Access	NNP
cord-013977-xb0r2axf	136	1	This	this	DT
cord-013977-xb0r2axf	136	2	article	article	NN
cord-013977-xb0r2axf	136	3	is	be	VBZ
cord-013977-xb0r2axf	136	4	licensed	license	VBN
cord-013977-xb0r2axf	136	5	under	under	IN
cord-013977-xb0r2axf	136	6	a	a	DT
cord-013977-xb0r2axf	136	7	Creative	Creative	NNP
cord-013977-xb0r2axf	136	8	Commons	Commons	NNP
cord-013977-xb0r2axf	136	9	Attribution	Attribution	NNP
cord-013977-xb0r2axf	136	10	4.0	4.0	CD
cord-013977-xb0r2axf	136	11	International	International	NNP
cord-013977-xb0r2axf	136	12	License	License	NNP
cord-013977-xb0r2axf	136	13	,	,	,
cord-013977-xb0r2axf	136	14	which	which	WDT
cord-013977-xb0r2axf	136	15	permits	permit	VBZ
cord-013977-xb0r2axf	136	16	use	use	NN
cord-013977-xb0r2axf	136	17	,	,	,
cord-013977-xb0r2axf	136	18	sharing	sharing	NN
cord-013977-xb0r2axf	136	19	,	,	,
cord-013977-xb0r2axf	136	20	adaptation	adaptation	NN
cord-013977-xb0r2axf	136	21	,	,	,
cord-013977-xb0r2axf	136	22	distribution	distribution	NN
cord-013977-xb0r2axf	136	23	and	and	CC
cord-013977-xb0r2axf	136	24	reproduction	reproduction	NN
cord-013977-xb0r2axf	136	25	in	in	IN
cord-013977-xb0r2axf	136	26	any	any	DT
cord-013977-xb0r2axf	136	27	medium	medium	NN
cord-013977-xb0r2axf	136	28	or	or	CC
cord-013977-xb0r2axf	136	29	format	format	NN
cord-013977-xb0r2axf	136	30	,	,	,
cord-013977-xb0r2axf	136	31	as	as	RB
cord-013977-xb0r2axf	136	32	long	long	RB
cord-013977-xb0r2axf	136	33	as	as	IN
cord-013977-xb0r2axf	136	34	you	-PRON-	PRP
cord-013977-xb0r2axf	136	35	give	give	VBP
cord-013977-xb0r2axf	136	36	appropriate	appropriate	JJ
cord-013977-xb0r2axf	136	37	credit	credit	NN
cord-013977-xb0r2axf	136	38	to	to	IN
cord-013977-xb0r2axf	136	39	the	the	DT
cord-013977-xb0r2axf	136	40	original	original	JJ
cord-013977-xb0r2axf	136	41	author(s	author(s	NNP
cord-013977-xb0r2axf	136	42	)	)	-RRB-
cord-013977-xb0r2axf	136	43	and	and	CC
cord-013977-xb0r2axf	136	44	the	the	DT
cord-013977-xb0r2axf	136	45	source	source	NN
cord-013977-xb0r2axf	136	46	,	,	,
cord-013977-xb0r2axf	136	47	provide	provide	VB
cord-013977-xb0r2axf	136	48	a	a	DT
cord-013977-xb0r2axf	136	49	link	link	NN
cord-013977-xb0r2axf	136	50	to	to	IN
cord-013977-xb0r2axf	136	51	the	the	DT
cord-013977-xb0r2axf	136	52	Creative	Creative	NNP
cord-013977-xb0r2axf	136	53	Commons	Commons	NNP
cord-013977-xb0r2axf	136	54	licence	licence	NN
cord-013977-xb0r2axf	136	55	,	,	,
cord-013977-xb0r2axf	136	56	and	and	CC
cord-013977-xb0r2axf	136	57	indicate	indicate	VBP
cord-013977-xb0r2axf	136	58	if	if	IN
cord-013977-xb0r2axf	136	59	changes	change	NNS
cord-013977-xb0r2axf	136	60	were	be	VBD
cord-013977-xb0r2axf	136	61	made	make	VBN
cord-013977-xb0r2axf	136	62	.	.	.
cord-013977-xb0r2axf	137	1	The	the	DT
cord-013977-xb0r2axf	137	2	images	image	NNS
cord-013977-xb0r2axf	137	3	or	or	CC
cord-013977-xb0r2axf	137	4	other	other	JJ
cord-013977-xb0r2axf	137	5	third	third	JJ
cord-013977-xb0r2axf	137	6	party	party	NN
cord-013977-xb0r2axf	137	7	material	material	NN
cord-013977-xb0r2axf	137	8	in	in	IN
cord-013977-xb0r2axf	137	9	this	this	DT
cord-013977-xb0r2axf	137	10	article	article	NN
cord-013977-xb0r2axf	137	11	are	be	VBP
cord-013977-xb0r2axf	137	12	included	include	VBN
cord-013977-xb0r2axf	137	13	in	in	IN
cord-013977-xb0r2axf	137	14	the	the	DT
cord-013977-xb0r2axf	137	15	article	article	NN
cord-013977-xb0r2axf	137	16	's	's	POS
cord-013977-xb0r2axf	137	17	Creative	Creative	NNP
cord-013977-xb0r2axf	137	18	Commons	Commons	NNP
cord-013977-xb0r2axf	137	19	licence	licence	NN
cord-013977-xb0r2axf	137	20	,	,	,
cord-013977-xb0r2axf	137	21	unless	unless	IN
cord-013977-xb0r2axf	137	22	indicated	indicate	VBN
cord-013977-xb0r2axf	137	23	otherwise	otherwise	RB
cord-013977-xb0r2axf	137	24	in	in	IN
cord-013977-xb0r2axf	137	25	a	a	DT
cord-013977-xb0r2axf	137	26	credit	credit	NN
cord-013977-xb0r2axf	137	27	line	line	NN
cord-013977-xb0r2axf	137	28	to	to	IN
cord-013977-xb0r2axf	137	29	the	the	DT
cord-013977-xb0r2axf	137	30	material	material	NN
cord-013977-xb0r2axf	137	31	.	.	.
cord-013977-xb0r2axf	138	1	If	if	IN
cord-013977-xb0r2axf	138	2	material	material	NN
cord-013977-xb0r2axf	138	3	is	be	VBZ
cord-013977-xb0r2axf	138	4	not	not	RB
cord-013977-xb0r2axf	138	5	included	include	VBN
cord-013977-xb0r2axf	138	6	in	in	IN
cord-013977-xb0r2axf	138	7	the	the	DT
cord-013977-xb0r2axf	138	8	article	article	NN
cord-013977-xb0r2axf	138	9	's	's	POS
cord-013977-xb0r2axf	138	10	Creative	Creative	NNP
cord-013977-xb0r2axf	138	11	Commons	Commons	NNP
cord-013977-xb0r2axf	138	12	licence	licence	NN
cord-013977-xb0r2axf	138	13	and	and	CC
cord-013977-xb0r2axf	138	14	your	-PRON-	PRP$
cord-013977-xb0r2axf	138	15	intended	intend	VBN
cord-013977-xb0r2axf	138	16	use	use	NN
cord-013977-xb0r2axf	138	17	is	be	VBZ
cord-013977-xb0r2axf	138	18	not	not	RB
cord-013977-xb0r2axf	138	19	permitted	permit	VBN
cord-013977-xb0r2axf	138	20	by	by	IN
cord-013977-xb0r2axf	138	21	statutory	statutory	JJ
cord-013977-xb0r2axf	138	22	regulation	regulation	NN
cord-013977-xb0r2axf	138	23	or	or	CC
cord-013977-xb0r2axf	138	24	exceeds	exceed	VBZ
cord-013977-xb0r2axf	138	25	the	the	DT
cord-013977-xb0r2axf	138	26	permitted	permit	VBN
cord-013977-xb0r2axf	138	27	use	use	NN
cord-013977-xb0r2axf	138	28	,	,	,
cord-013977-xb0r2axf	138	29	you	-PRON-	PRP
cord-013977-xb0r2axf	138	30	will	will	MD
cord-013977-xb0r2axf	138	31	need	need	VB
cord-013977-xb0r2axf	138	32	to	to	TO
cord-013977-xb0r2axf	138	33	obtain	obtain	VB
cord-013977-xb0r2axf	138	34	permission	permission	NN
cord-013977-xb0r2axf	138	35	directly	directly	RB
cord-013977-xb0r2axf	138	36	from	from	IN
cord-013977-xb0r2axf	138	37	the	the	DT
cord-013977-xb0r2axf	138	38	copyright	copyright	NN
cord-013977-xb0r2axf	138	39	holder	holder	NN
cord-013977-xb0r2axf	138	40	.	.	.
cord-013977-xb0r2axf	139	1	To	to	TO
cord-013977-xb0r2axf	139	2	view	view	VB
cord-013977-xb0r2axf	139	3	a	a	DT
cord-013977-xb0r2axf	139	4	copy	copy	NN
cord-013977-xb0r2axf	139	5	of	of	IN
cord-013977-xb0r2axf	139	6	this	this	DT
cord-013977-xb0r2axf	139	7	licence	licence	NN
cord-013977-xb0r2axf	139	8	,	,	,
cord-013977-xb0r2axf	139	9	visit	visit	VB
cord-013977-xb0r2axf	139	10	http://creat	http://creat	NNP
cord-013977-xb0r2axf	139	11	iveco	iveco	NNP
cord-013977-xb0r2axf	139	12	mmons	mmons	NNP
cord-013977-xb0r2axf	139	13	.org	.org	.
cord-013977-xb0r2axf	140	1	/	/	NFP
cord-013977-xb0r2axf	141	1	licen	licen	NNP
cord-013977-xb0r2axf	141	2	ses	ses	NNP
cord-013977-xb0r2axf	141	3	/	/	SYM
cord-013977-xb0r2axf	141	4	by/4.0/.	by/4.0/.	NNP