id	sid	tid	token	lemma	pos
cord-191574-1g38scnj	1	1	key	key	JJ
cord-191574-1g38scnj	1	2	:	:	:
cord-191574-1g38scnj	1	3	cord-191574	cord-191574	NNP
cord-191574-1g38scnj	1	4	-	-	HYPH
cord-191574-1g38scnj	1	5	1g38scnj	1g38scnj	CD
cord-191574-1g38scnj	1	6	authors	author	NNS
cord-191574-1g38scnj	1	7	:	:	:
cord-191574-1g38scnj	1	8	Harko	Harko	NNP
cord-191574-1g38scnj	1	9	,	,	,
cord-191574-1g38scnj	1	10	Tiberiu	Tiberiu	NNP
cord-191574-1g38scnj	1	11	;	;	:
cord-191574-1g38scnj	1	12	Mak	Mak	NNP
cord-191574-1g38scnj	1	13	,	,	,
cord-191574-1g38scnj	1	14	Man	Man	NNP
cord-191574-1g38scnj	1	15	Kwong	Kwong	NNP
cord-191574-1g38scnj	2	1	title	title	NN
cord-191574-1g38scnj	2	2	:	:	:
cord-191574-1g38scnj	2	3	Series	series	NN
cord-191574-1g38scnj	2	4	solution	solution	NN
cord-191574-1g38scnj	2	5	of	of	IN
cord-191574-1g38scnj	2	6	the	the	DT
cord-191574-1g38scnj	2	7	Susceptible	susceptible	JJ
cord-191574-1g38scnj	2	8	-	-	HYPH
cord-191574-1g38scnj	2	9	Infected	Infected	NNP
cord-191574-1g38scnj	2	10	-	-	HYPH
cord-191574-1g38scnj	2	11	Recovered	recovered	JJ
cord-191574-1g38scnj	2	12	(	(	-LRB-
cord-191574-1g38scnj	2	13	SIR	SIR	NNP
cord-191574-1g38scnj	2	14	)	)	-RRB-
cord-191574-1g38scnj	2	15	epidemic	epidemic	NN
cord-191574-1g38scnj	2	16	model	model	NN
cord-191574-1g38scnj	2	17	with	with	IN
cord-191574-1g38scnj	2	18	vital	vital	JJ
cord-191574-1g38scnj	2	19	dynamics	dynamic	NNS
cord-191574-1g38scnj	2	20	via	via	IN
cord-191574-1g38scnj	2	21	the	the	DT
cord-191574-1g38scnj	2	22	Adomian	Adomian	NNP
cord-191574-1g38scnj	2	23	and	and	CC
cord-191574-1g38scnj	2	24	Laplace	Laplace	NNP
cord-191574-1g38scnj	2	25	-	-	HYPH
cord-191574-1g38scnj	2	26	Adomian	Adomian	NNP
cord-191574-1g38scnj	2	27	Decomposition	decomposition	NN
cord-191574-1g38scnj	2	28	Methods	Methods	NNPS
cord-191574-1g38scnj	2	29	date	date	NN
cord-191574-1g38scnj	2	30	:	:	:
cord-191574-1g38scnj	2	31	2020	2020	CD
cord-191574-1g38scnj	2	32	-	-	HYPH
cord-191574-1g38scnj	2	33	08	08	CD
cord-191574-1g38scnj	2	34	-	-	HYPH
cord-191574-1g38scnj	2	35	28	28	CD
cord-191574-1g38scnj	2	36	journal	journal	NN
cord-191574-1g38scnj	2	37	:	:	:
cord-191574-1g38scnj	2	38	nan	nan	NNP
cord-191574-1g38scnj	2	39	DOI	DOI	NNP
cord-191574-1g38scnj	2	40	:	:	:
cord-191574-1g38scnj	2	41	nan	nan	NNP
cord-191574-1g38scnj	2	42	sha	sha	NNP
cord-191574-1g38scnj	2	43	:	:	:
cord-191574-1g38scnj	3	1	26ad48f61f8d6fe11dc94400795cdb6178d3a55c	26ad48f61f8d6fe11dc94400795cdb6178d3a55c	CD
cord-191574-1g38scnj	3	2	doc_id	doc_id	CD
cord-191574-1g38scnj	3	3	:	:	:
cord-191574-1g38scnj	3	4	191574	191574	CD
cord-191574-1g38scnj	3	5	cord_uid	cord_uid	NNS
cord-191574-1g38scnj	3	6	:	:	:
cord-191574-1g38scnj	4	1	1g38scnj	1g38scnj	CD
cord-191574-1g38scnj	5	1	The	the	DT
cord-191574-1g38scnj	5	2	Susceptible	susceptible	JJ
cord-191574-1g38scnj	5	3	-	-	HYPH
cord-191574-1g38scnj	5	4	Infected	infected	JJ
cord-191574-1g38scnj	5	5	-	-	HYPH
cord-191574-1g38scnj	5	6	Recovered	recovered	JJ
cord-191574-1g38scnj	5	7	(	(	-LRB-
cord-191574-1g38scnj	5	8	SIR	SIR	NNP
cord-191574-1g38scnj	5	9	)	)	-RRB-
cord-191574-1g38scnj	5	10	epidemic	epidemic	NN
cord-191574-1g38scnj	5	11	model	model	NN
cord-191574-1g38scnj	5	12	as	as	RB
cord-191574-1g38scnj	5	13	well	well	RB
cord-191574-1g38scnj	5	14	as	as	IN
cord-191574-1g38scnj	5	15	its	-PRON-	PRP$
cord-191574-1g38scnj	5	16	generalizations	generalization	NNS
cord-191574-1g38scnj	5	17	are	be	VBP
cord-191574-1g38scnj	5	18	extensively	extensively	RB
cord-191574-1g38scnj	5	19	used	use	VBN
cord-191574-1g38scnj	5	20	for	for	IN
cord-191574-1g38scnj	5	21	the	the	DT
cord-191574-1g38scnj	5	22	study	study	NN
cord-191574-1g38scnj	5	23	of	of	IN
cord-191574-1g38scnj	5	24	the	the	DT
cord-191574-1g38scnj	5	25	spread	spread	NN
cord-191574-1g38scnj	5	26	of	of	IN
cord-191574-1g38scnj	5	27	infectious	infectious	JJ
cord-191574-1g38scnj	5	28	diseases	disease	NNS
cord-191574-1g38scnj	5	29	,	,	,
cord-191574-1g38scnj	5	30	and	and	CC
cord-191574-1g38scnj	5	31	for	for	IN
cord-191574-1g38scnj	5	32	the	the	DT
cord-191574-1g38scnj	5	33	understanding	understanding	NN
cord-191574-1g38scnj	5	34	of	of	IN
cord-191574-1g38scnj	5	35	the	the	DT
cord-191574-1g38scnj	5	36	dynamical	dynamical	JJ
cord-191574-1g38scnj	5	37	evolution	evolution	NN
cord-191574-1g38scnj	5	38	of	of	IN
cord-191574-1g38scnj	5	39	epidemics	epidemic	NNS
cord-191574-1g38scnj	5	40	.	.	.
cord-191574-1g38scnj	6	1	From	from	IN
cord-191574-1g38scnj	6	2	SIR	SIR	NNP
cord-191574-1g38scnj	6	3	type	type	NN
cord-191574-1g38scnj	6	4	models	model	NNS
cord-191574-1g38scnj	6	5	only	only	RB
cord-191574-1g38scnj	6	6	the	the	DT
cord-191574-1g38scnj	6	7	model	model	NN
cord-191574-1g38scnj	6	8	without	without	IN
cord-191574-1g38scnj	6	9	vital	vital	JJ
cord-191574-1g38scnj	6	10	dynamics	dynamic	NNS
cord-191574-1g38scnj	6	11	has	have	VBZ
cord-191574-1g38scnj	6	12	an	an	DT
cord-191574-1g38scnj	6	13	exact	exact	JJ
cord-191574-1g38scnj	6	14	analytic	analytic	JJ
cord-191574-1g38scnj	6	15	solution	solution	NN
cord-191574-1g38scnj	6	16	,	,	,
cord-191574-1g38scnj	6	17	which	which	WDT
cord-191574-1g38scnj	6	18	can	can	MD
cord-191574-1g38scnj	6	19	be	be	VB
cord-191574-1g38scnj	6	20	obtained	obtain	VBN
cord-191574-1g38scnj	6	21	in	in	IN
cord-191574-1g38scnj	6	22	an	an	DT
cord-191574-1g38scnj	6	23	exact	exact	JJ
cord-191574-1g38scnj	6	24	parametric	parametric	JJ
cord-191574-1g38scnj	6	25	form	form	NN
cord-191574-1g38scnj	6	26	.	.	.
cord-191574-1g38scnj	7	1	The	the	DT
cord-191574-1g38scnj	7	2	SIR	SIR	NNP
cord-191574-1g38scnj	7	3	model	model	NN
cord-191574-1g38scnj	7	4	with	with	IN
cord-191574-1g38scnj	7	5	vital	vital	JJ
cord-191574-1g38scnj	7	6	dynamics	dynamic	NNS
cord-191574-1g38scnj	7	7	,	,	,
cord-191574-1g38scnj	7	8	the	the	DT
cord-191574-1g38scnj	7	9	simplest	simple	JJS
cord-191574-1g38scnj	7	10	extension	extension	NN
cord-191574-1g38scnj	7	11	of	of	IN
cord-191574-1g38scnj	7	12	the	the	DT
cord-191574-1g38scnj	7	13	basic	basic	JJ
cord-191574-1g38scnj	7	14	SIR	SIR	NNP
cord-191574-1g38scnj	7	15	model	model	NN
cord-191574-1g38scnj	7	16	,	,	,
cord-191574-1g38scnj	7	17	does	do	VBZ
cord-191574-1g38scnj	7	18	not	not	RB
cord-191574-1g38scnj	7	19	admit	admit	VB
cord-191574-1g38scnj	7	20	a	a	DT
cord-191574-1g38scnj	7	21	closed	closed	JJ
cord-191574-1g38scnj	7	22	form	form	NN
cord-191574-1g38scnj	7	23	representation	representation	NN
cord-191574-1g38scnj	7	24	of	of	IN
cord-191574-1g38scnj	7	25	the	the	DT
cord-191574-1g38scnj	7	26	solution	solution	NN
cord-191574-1g38scnj	7	27	.	.	.
cord-191574-1g38scnj	8	1	However	however	RB
cord-191574-1g38scnj	8	2	,	,	,
cord-191574-1g38scnj	8	3	in	in	IN
cord-191574-1g38scnj	8	4	order	order	NN
cord-191574-1g38scnj	8	5	to	to	TO
cord-191574-1g38scnj	8	6	perform	perform	VB
cord-191574-1g38scnj	8	7	the	the	DT
cord-191574-1g38scnj	8	8	comparison	comparison	NN
cord-191574-1g38scnj	8	9	with	with	IN
cord-191574-1g38scnj	8	10	the	the	DT
cord-191574-1g38scnj	8	11	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	8	12	data	data	NN
cord-191574-1g38scnj	8	13	accurate	accurate	JJ
cord-191574-1g38scnj	8	14	representations	representation	NNS
cord-191574-1g38scnj	8	15	of	of	IN
cord-191574-1g38scnj	8	16	the	the	DT
cord-191574-1g38scnj	8	17	time	time	NN
cord-191574-1g38scnj	8	18	evolution	evolution	NN
cord-191574-1g38scnj	8	19	of	of	IN
cord-191574-1g38scnj	8	20	the	the	DT
cord-191574-1g38scnj	8	21	SIR	SIR	NNP
cord-191574-1g38scnj	8	22	model	model	NN
cord-191574-1g38scnj	8	23	with	with	IN
cord-191574-1g38scnj	8	24	vital	vital	JJ
cord-191574-1g38scnj	8	25	dynamics	dynamic	NNS
cord-191574-1g38scnj	8	26	would	would	MD
cord-191574-1g38scnj	8	27	be	be	VB
cord-191574-1g38scnj	8	28	very	very	RB
cord-191574-1g38scnj	8	29	useful	useful	JJ
cord-191574-1g38scnj	8	30	.	.	.
cord-191574-1g38scnj	9	1	In	in	IN
cord-191574-1g38scnj	9	2	the	the	DT
cord-191574-1g38scnj	9	3	present	present	JJ
cord-191574-1g38scnj	9	4	paper	paper	NN
cord-191574-1g38scnj	9	5	,	,	,
cord-191574-1g38scnj	9	6	we	-PRON-	PRP
cord-191574-1g38scnj	9	7	obtain	obtain	VBP
cord-191574-1g38scnj	9	8	first	first	RB
cord-191574-1g38scnj	9	9	the	the	DT
cord-191574-1g38scnj	9	10	basic	basic	JJ
cord-191574-1g38scnj	9	11	evolution	evolution	NN
cord-191574-1g38scnj	9	12	equation	equation	NN
cord-191574-1g38scnj	9	13	of	of	IN
cord-191574-1g38scnj	9	14	the	the	DT
cord-191574-1g38scnj	9	15	SIR	SIR	NNP
cord-191574-1g38scnj	9	16	model	model	NN
cord-191574-1g38scnj	9	17	with	with	IN
cord-191574-1g38scnj	9	18	vital	vital	JJ
cord-191574-1g38scnj	9	19	dynamics	dynamic	NNS
cord-191574-1g38scnj	9	20	,	,	,
cord-191574-1g38scnj	9	21	which	which	WDT
cord-191574-1g38scnj	9	22	is	be	VBZ
cord-191574-1g38scnj	9	23	given	give	VBN
cord-191574-1g38scnj	9	24	by	by	IN
cord-191574-1g38scnj	9	25	a	a	DT
cord-191574-1g38scnj	9	26	strongly	strongly	RB
cord-191574-1g38scnj	9	27	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	9	28	second	second	JJ
cord-191574-1g38scnj	9	29	order	order	NN
cord-191574-1g38scnj	9	30	differential	differential	NN
cord-191574-1g38scnj	9	31	equation	equation	NN
cord-191574-1g38scnj	9	32	.	.	.
cord-191574-1g38scnj	10	1	Then	then	RB
cord-191574-1g38scnj	10	2	we	-PRON-	PRP
cord-191574-1g38scnj	10	3	obtain	obtain	VBP
cord-191574-1g38scnj	10	4	a	a	DT
cord-191574-1g38scnj	10	5	series	series	NN
cord-191574-1g38scnj	10	6	representation	representation	NN
cord-191574-1g38scnj	10	7	of	of	IN
cord-191574-1g38scnj	10	8	the	the	DT
cord-191574-1g38scnj	10	9	solution	solution	NN
cord-191574-1g38scnj	10	10	of	of	IN
cord-191574-1g38scnj	10	11	the	the	DT
cord-191574-1g38scnj	10	12	model	model	NN
cord-191574-1g38scnj	10	13	,	,	,
cord-191574-1g38scnj	10	14	by	by	IN
cord-191574-1g38scnj	10	15	using	use	VBG
cord-191574-1g38scnj	10	16	the	the	DT
cord-191574-1g38scnj	10	17	Adomian	Adomian	NNP
cord-191574-1g38scnj	10	18	and	and	CC
cord-191574-1g38scnj	10	19	Laplace	Laplace	NNP
cord-191574-1g38scnj	10	20	-	-	HYPH
cord-191574-1g38scnj	10	21	Adomian	Adomian	NNP
cord-191574-1g38scnj	10	22	Decomposition	decomposition	NN
cord-191574-1g38scnj	10	23	Methods	Methods	NNPS
cord-191574-1g38scnj	10	24	to	to	TO
cord-191574-1g38scnj	10	25	solve	solve	VB
cord-191574-1g38scnj	10	26	the	the	DT
cord-191574-1g38scnj	10	27	dynamical	dynamical	JJ
cord-191574-1g38scnj	10	28	evolution	evolution	NN
cord-191574-1g38scnj	10	29	equation	equation	NN
cord-191574-1g38scnj	10	30	of	of	IN
cord-191574-1g38scnj	10	31	the	the	DT
cord-191574-1g38scnj	10	32	model	model	NN
cord-191574-1g38scnj	10	33	.	.	.
cord-191574-1g38scnj	11	1	The	the	DT
cord-191574-1g38scnj	11	2	solutions	solution	NNS
cord-191574-1g38scnj	11	3	are	be	VBP
cord-191574-1g38scnj	11	4	expressed	express	VBN
cord-191574-1g38scnj	11	5	in	in	IN
cord-191574-1g38scnj	11	6	the	the	DT
cord-191574-1g38scnj	11	7	form	form	NN
cord-191574-1g38scnj	11	8	of	of	IN
cord-191574-1g38scnj	11	9	infinite	infinite	JJ
cord-191574-1g38scnj	11	10	series	series	NN
cord-191574-1g38scnj	11	11	.	.	.
cord-191574-1g38scnj	12	1	The	the	DT
cord-191574-1g38scnj	12	2	series	series	NN
cord-191574-1g38scnj	12	3	representations	representation	NNS
cord-191574-1g38scnj	12	4	of	of	IN
cord-191574-1g38scnj	12	5	the	the	DT
cord-191574-1g38scnj	12	6	time	time	NN
cord-191574-1g38scnj	12	7	evolution	evolution	NN
cord-191574-1g38scnj	12	8	of	of	IN
cord-191574-1g38scnj	12	9	the	the	DT
cord-191574-1g38scnj	12	10	SIR	SIR	NNP
cord-191574-1g38scnj	12	11	model	model	NN
cord-191574-1g38scnj	12	12	with	with	IN
cord-191574-1g38scnj	12	13	vital	vital	JJ
cord-191574-1g38scnj	12	14	dynamics	dynamic	NNS
cord-191574-1g38scnj	12	15	are	be	VBP
cord-191574-1g38scnj	12	16	compared	compare	VBN
cord-191574-1g38scnj	12	17	with	with	IN
cord-191574-1g38scnj	12	18	the	the	DT
cord-191574-1g38scnj	12	19	exact	exact	JJ
cord-191574-1g38scnj	12	20	numerical	numerical	JJ
cord-191574-1g38scnj	12	21	solutions	solution	NNS
cord-191574-1g38scnj	12	22	of	of	IN
cord-191574-1g38scnj	12	23	the	the	DT
cord-191574-1g38scnj	12	24	model	model	NN
cord-191574-1g38scnj	12	25	,	,	,
cord-191574-1g38scnj	12	26	and	and	CC
cord-191574-1g38scnj	12	27	we	-PRON-	PRP
cord-191574-1g38scnj	12	28	find	find	VBP
cord-191574-1g38scnj	12	29	that	that	IN
cord-191574-1g38scnj	12	30	,	,	,
cord-191574-1g38scnj	12	31	at	at	IN
cord-191574-1g38scnj	12	32	least	least	JJS
cord-191574-1g38scnj	12	33	for	for	IN
cord-191574-1g38scnj	12	34	a	a	DT
cord-191574-1g38scnj	12	35	specific	specific	JJ
cord-191574-1g38scnj	12	36	range	range	NN
cord-191574-1g38scnj	12	37	of	of	IN
cord-191574-1g38scnj	12	38	parameters	parameter	NNS
cord-191574-1g38scnj	12	39	,	,	,
cord-191574-1g38scnj	12	40	there	there	EX
cord-191574-1g38scnj	12	41	is	be	VBZ
cord-191574-1g38scnj	12	42	a	a	DT
cord-191574-1g38scnj	12	43	good	good	JJ
cord-191574-1g38scnj	12	44	agreement	agreement	NN
cord-191574-1g38scnj	12	45	between	between	IN
cord-191574-1g38scnj	12	46	the	the	DT
cord-191574-1g38scnj	12	47	Adomian	Adomian	NNP
cord-191574-1g38scnj	12	48	and	and	CC
cord-191574-1g38scnj	12	49	Laplace	Laplace	NNP
cord-191574-1g38scnj	12	50	-	-	HYPH
cord-191574-1g38scnj	12	51	Adomian	adomian	JJ
cord-191574-1g38scnj	12	52	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	12	53	solutions	solution	NNS
cord-191574-1g38scnj	12	54	,	,	,
cord-191574-1g38scnj	12	55	containing	contain	VBG
cord-191574-1g38scnj	12	56	only	only	RB
cord-191574-1g38scnj	12	57	a	a	DT
cord-191574-1g38scnj	12	58	small	small	JJ
cord-191574-1g38scnj	12	59	number	number	NN
cord-191574-1g38scnj	12	60	of	of	IN
cord-191574-1g38scnj	12	61	terms	term	NNS
cord-191574-1g38scnj	12	62	,	,	,
cord-191574-1g38scnj	12	63	and	and	CC
cord-191574-1g38scnj	12	64	the	the	DT
cord-191574-1g38scnj	12	65	numerical	numerical	JJ
cord-191574-1g38scnj	12	66	results	result	NNS
cord-191574-1g38scnj	12	67	.	.	.
cord-191574-1g38scnj	13	1	The	the	DT
cord-191574-1g38scnj	13	2	study	study	NN
cord-191574-1g38scnj	13	3	of	of	IN
cord-191574-1g38scnj	13	4	the	the	DT
cord-191574-1g38scnj	13	5	epidemic	epidemic	NN
cord-191574-1g38scnj	13	6	mathematical	mathematical	JJ
cord-191574-1g38scnj	13	7	models	model	NNS
cord-191574-1g38scnj	13	8	in	in	IN
cord-191574-1g38scnj	13	9	different	different	JJ
cord-191574-1g38scnj	13	10	formal	formal	JJ
cord-191574-1g38scnj	13	11	formulation	formulation	NN
cord-191574-1g38scnj	13	12	has	have	VBZ
cord-191574-1g38scnj	13	13	been	be	VBN
cord-191574-1g38scnj	13	14	proved	prove	VBN
cord-191574-1g38scnj	13	15	to	to	TO
cord-191574-1g38scnj	13	16	be	be	VB
cord-191574-1g38scnj	13	17	of	of	IN
cord-191574-1g38scnj	13	18	crucial	crucial	JJ
cord-191574-1g38scnj	13	19	interest	interest	NN
cord-191574-1g38scnj	13	20	in	in	IN
cord-191574-1g38scnj	13	21	the	the	DT
cord-191574-1g38scnj	13	22	understanding	understanding	NN
cord-191574-1g38scnj	13	23	of	of	IN
cord-191574-1g38scnj	13	24	the	the	DT
cord-191574-1g38scnj	13	25	dynamics	dynamic	NNS
cord-191574-1g38scnj	13	26	,	,	,
cord-191574-1g38scnj	13	27	spread	spread	VB
cord-191574-1g38scnj	13	28	and	and	CC
cord-191574-1g38scnj	13	29	control	control	NN
cord-191574-1g38scnj	13	30	of	of	IN
cord-191574-1g38scnj	13	31	epidemic	epidemic	NN
cord-191574-1g38scnj	13	32	diseases	disease	NNS
cord-191574-1g38scnj	13	33	[	[	-LRB-
cord-191574-1g38scnj	13	34	1	1	CD
cord-191574-1g38scnj	13	35	]	]	-RRB-
cord-191574-1g38scnj	13	36	[	[	-LRB-
cord-191574-1g38scnj	13	37	2	2	CD
cord-191574-1g38scnj	13	38	]	]	-RRB-
cord-191574-1g38scnj	13	39	[	[	-LRB-
cord-191574-1g38scnj	13	40	3	3	CD
cord-191574-1g38scnj	13	41	]	]	-RRB-
cord-191574-1g38scnj	13	42	[	[	-LRB-
cord-191574-1g38scnj	13	43	4	4	CD
cord-191574-1g38scnj	13	44	]	]	-RRB-
cord-191574-1g38scnj	13	45	[	[	-LRB-
cord-191574-1g38scnj	13	46	5	5	CD
cord-191574-1g38scnj	13	47	]	]	-RRB-
cord-191574-1g38scnj	13	48	[	[	-LRB-
cord-191574-1g38scnj	13	49	6	6	CD
cord-191574-1g38scnj	13	50	]	]	-RRB-
cord-191574-1g38scnj	13	51	.	.	.
cord-191574-1g38scnj	14	1	The	the	DT
cord-191574-1g38scnj	14	2	simplest	simple	JJS
cord-191574-1g38scnj	14	3	of	of	IN
cord-191574-1g38scnj	14	4	the	the	DT
cord-191574-1g38scnj	14	5	epidemic	epidemic	NN
cord-191574-1g38scnj	14	6	models	model	NNS
cord-191574-1g38scnj	14	7	are	be	VBP
cord-191574-1g38scnj	14	8	the	the	DT
cord-191574-1g38scnj	14	9	so	so	RB
cord-191574-1g38scnj	14	10	-	-	HYPH
cord-191574-1g38scnj	14	11	called	call	VBN
cord-191574-1g38scnj	14	12	deterministic	deterministic	JJ
cord-191574-1g38scnj	14	13	compartmental	compartmental	JJ
cord-191574-1g38scnj	14	14	models	model	NNS
cord-191574-1g38scnj	14	15	,	,	,
cord-191574-1g38scnj	14	16	consisting	consist	VBG
cord-191574-1g38scnj	14	17	of	of	IN
cord-191574-1g38scnj	14	18	at	at	RB
cord-191574-1g38scnj	14	19	least	least	RBS
cord-191574-1g38scnj	14	20	three	three	CD
cord-191574-1g38scnj	14	21	compartments	compartment	NNS
cord-191574-1g38scnj	14	22	:	:	:
cord-191574-1g38scnj	14	23	given	give	VBN
cord-191574-1g38scnj	14	24	by	by	IN
cord-191574-1g38scnj	14	25	:	:	:
cord-191574-1g38scnj	14	26	the	the	DT
cord-191574-1g38scnj	14	27	number	number	NN
cord-191574-1g38scnj	14	28	of	of	IN
cord-191574-1g38scnj	14	29	susceptible	susceptible	JJ
cord-191574-1g38scnj	14	30	individuals	individual	NNS
cord-191574-1g38scnj	14	31	(	(	-LRB-
cord-191574-1g38scnj	14	32	S	S	NNP
cord-191574-1g38scnj	14	33	)	)	-RRB-
cord-191574-1g38scnj	14	34	,	,	,
cord-191574-1g38scnj	14	35	the	the	DT
cord-191574-1g38scnj	14	36	number	number	NN
cord-191574-1g38scnj	14	37	of	of	IN
cord-191574-1g38scnj	14	38	infectious	infectious	JJ
cord-191574-1g38scnj	14	39	individuals	individual	NNS
cord-191574-1g38scnj	14	40	(	(	-LRB-
cord-191574-1g38scnj	14	41	I	i	NN
cord-191574-1g38scnj	14	42	)	)	-RRB-
cord-191574-1g38scnj	14	43	,	,	,
cord-191574-1g38scnj	14	44	and	and	CC
cord-191574-1g38scnj	14	45	the	the	DT
cord-191574-1g38scnj	14	46	number	number	NN
cord-191574-1g38scnj	14	47	of	of	IN
cord-191574-1g38scnj	14	48	removed	remove	VBN
cord-191574-1g38scnj	14	49	(	(	-LRB-
cord-191574-1g38scnj	14	50	and	and	CC
cord-191574-1g38scnj	14	51	immune	immune	JJ
cord-191574-1g38scnj	14	52	)	)	-RRB-
cord-191574-1g38scnj	14	53	,	,	,
cord-191574-1g38scnj	14	54	or	or	CC
cord-191574-1g38scnj	14	55	deceased	decease	VBN
cord-191574-1g38scnj	14	56	individuals	individual	NNS
cord-191574-1g38scnj	14	57	(	(	-LRB-
cord-191574-1g38scnj	14	58	R	r	NN
cord-191574-1g38scnj	14	59	)	)	-RRB-
cord-191574-1g38scnj	14	60	,	,	,
cord-191574-1g38scnj	14	61	respectively	respectively	RB
cord-191574-1g38scnj	14	62	.	.	.
cord-191574-1g38scnj	15	1	The	the	DT
cord-191574-1g38scnj	15	2	first	first	JJ
cord-191574-1g38scnj	15	3	compartmental	compartmental	JJ
cord-191574-1g38scnj	15	4	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	15	5	models	model	NNS
cord-191574-1g38scnj	15	6	have	have	VBP
cord-191574-1g38scnj	15	7	been	be	VBN
cord-191574-1g38scnj	15	8	proposed	propose	VBN
cord-191574-1g38scnj	15	9	and	and	CC
cord-191574-1g38scnj	15	10	investigated	investigate	VBN
cord-191574-1g38scnj	15	11	in	in	IN
cord-191574-1g38scnj	15	12	[	[	-LRB-
cord-191574-1g38scnj	15	13	7	7	CD
cord-191574-1g38scnj	15	14	]	]	-RRB-
cord-191574-1g38scnj	15	15	.	.	.
cord-191574-1g38scnj	16	1	Despite	despite	IN
cord-191574-1g38scnj	16	2	their	-PRON-	PRP$
cord-191574-1g38scnj	16	3	apparent	apparent	JJ
cord-191574-1g38scnj	16	4	phenomenological	phenomenological	JJ
cord-191574-1g38scnj	16	5	simplicity	simplicity	NN
cord-191574-1g38scnj	16	6	,	,	,
cord-191574-1g38scnj	16	7	the	the	DT
cord-191574-1g38scnj	16	8	mathematical	mathematical	JJ
cord-191574-1g38scnj	16	9	equations	equation	NNS
cord-191574-1g38scnj	16	10	describing	describe	VBG
cord-191574-1g38scnj	16	11	the	the	DT
cord-191574-1g38scnj	16	12	SIR	SIR	NNP
cord-191574-1g38scnj	16	13	type	type	NN
cord-191574-1g38scnj	16	14	models	model	NNS
cord-191574-1g38scnj	16	15	are	be	VBP
cord-191574-1g38scnj	16	16	essentially	essentially	RB
cord-191574-1g38scnj	16	17	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	16	18	,	,	,
cord-191574-1g38scnj	16	19	with	with	IN
cord-191574-1g38scnj	16	20	this	this	DT
cord-191574-1g38scnj	16	21	nonlinearity	nonlinearity	NN
cord-191574-1g38scnj	16	22	raising	raise	VBG
cord-191574-1g38scnj	16	23	a	a	DT
cord-191574-1g38scnj	16	24	number	number	NN
cord-191574-1g38scnj	16	25	of	of	IN
cord-191574-1g38scnj	16	26	important	important	JJ
cord-191574-1g38scnj	16	27	and	and	CC
cord-191574-1g38scnj	16	28	interesting	interesting	JJ
cord-191574-1g38scnj	16	29	mathematical	mathematical	JJ
cord-191574-1g38scnj	16	30	problems	problem	NNS
cord-191574-1g38scnj	16	31	in	in	IN
cord-191574-1g38scnj	16	32	the	the	DT
cord-191574-1g38scnj	16	33	study	study	NN
cord-191574-1g38scnj	16	34	of	of	IN
cord-191574-1g38scnj	16	35	even	even	RB
cord-191574-1g38scnj	16	36	the	the	DT
cord-191574-1g38scnj	16	37	simplest	simple	JJS
cord-191574-1g38scnj	16	38	models	model	NNS
cord-191574-1g38scnj	16	39	of	of	IN
cord-191574-1g38scnj	16	40	epidemics	epidemic	NNS
cord-191574-1g38scnj	16	41	.	.	.
cord-191574-1g38scnj	17	1	On	on	IN
cord-191574-1g38scnj	17	2	the	the	DT
cord-191574-1g38scnj	17	3	other	other	JJ
cord-191574-1g38scnj	17	4	hand	hand	NN
cord-191574-1g38scnj	17	5	the	the	DT
cord-191574-1g38scnj	17	6	SIR	SIR	NNP
cord-191574-1g38scnj	17	7	type	type	NN
cord-191574-1g38scnj	17	8	models	model	NNS
cord-191574-1g38scnj	17	9	still	still	RB
cord-191574-1g38scnj	17	10	have	have	VBP
cord-191574-1g38scnj	17	11	a	a	DT
cord-191574-1g38scnj	17	12	powerful	powerful	JJ
cord-191574-1g38scnj	17	13	predictive	predictive	NN
cord-191574-1g38scnj	17	14	and	and	CC
cord-191574-1g38scnj	17	15	investigating	investigate	VBG
cord-191574-1g38scnj	17	16	power	power	NN
cord-191574-1g38scnj	17	17	,	,	,
cord-191574-1g38scnj	17	18	and	and	CC
cord-191574-1g38scnj	17	19	many	many	JJ
cord-191574-1g38scnj	17	20	of	of	IN
cord-191574-1g38scnj	17	21	them	-PRON-	PRP
cord-191574-1g38scnj	17	22	have	have	VBP
cord-191574-1g38scnj	17	23	been	be	VBN
cord-191574-1g38scnj	17	24	used	use	VBN
cord-191574-1g38scnj	17	25	to	to	TO
cord-191574-1g38scnj	17	26	investigate	investigate	VB
cord-191574-1g38scnj	17	27	the	the	DT
cord-191574-1g38scnj	17	28	recent	recent	JJ
cord-191574-1g38scnj	17	29	COVID-19	COVID-19	NNP
cord-191574-1g38scnj	17	30	pandemic	pandemic	NN
cord-191574-1g38scnj	17	31	[	[	-LRB-
cord-191574-1g38scnj	17	32	8	8	CD
cord-191574-1g38scnj	17	33	]	]	-RRB-
cord-191574-1g38scnj	17	34	,	,	,
cord-191574-1g38scnj	17	35	like	like	UH
cord-191574-1g38scnj	17	36	,	,	,
cord-191574-1g38scnj	17	37	for	for	IN
cord-191574-1g38scnj	17	38	example	example	NN
cord-191574-1g38scnj	17	39	,	,	,
cord-191574-1g38scnj	17	40	in	in	IN
cord-191574-1g38scnj	17	41	[	[	-LRB-
cord-191574-1g38scnj	17	42	9	9	CD
cord-191574-1g38scnj	17	43	]	]	-RRB-
cord-191574-1g38scnj	17	44	[	[	-LRB-
cord-191574-1g38scnj	17	45	10	10	CD
cord-191574-1g38scnj	17	46	]	]	-RRB-
cord-191574-1g38scnj	18	1	[	[	-LRB-
cord-191574-1g38scnj	18	2	11	11	CD
cord-191574-1g38scnj	18	3	]	]	-RRB-
cord-191574-1g38scnj	18	4	[	[	-LRB-
cord-191574-1g38scnj	18	5	12	12	CD
cord-191574-1g38scnj	18	6	]	]	-RRB-
cord-191574-1g38scnj	18	7	[	[	-LRB-
cord-191574-1g38scnj	18	8	13	13	CD
cord-191574-1g38scnj	18	9	]	]	-RRB-
cord-191574-1g38scnj	19	1	[	[	-LRB-
cord-191574-1g38scnj	19	2	14	14	CD
cord-191574-1g38scnj	19	3	]	]	-RRB-
cord-191574-1g38scnj	20	1	[	[	-LRB-
cord-191574-1g38scnj	20	2	15	15	CD
cord-191574-1g38scnj	20	3	]	]	-RRB-
cord-191574-1g38scnj	20	4	[	[	-LRB-
cord-191574-1g38scnj	20	5	16	16	CD
cord-191574-1g38scnj	20	6	]	]	-RRB-
cord-191574-1g38scnj	20	7	[	[	-LRB-
cord-191574-1g38scnj	20	8	17	17	CD
cord-191574-1g38scnj	20	9	]	]	-RRB-
cord-191574-1g38scnj	20	10	[	[	-LRB-
cord-191574-1g38scnj	20	11	18	18	CD
cord-191574-1g38scnj	20	12	]	]	-RRB-
cord-191574-1g38scnj	20	13	[	[	-LRB-
cord-191574-1g38scnj	20	14	19	19	CD
cord-191574-1g38scnj	20	15	]	]	-RRB-
cord-191574-1g38scnj	21	1	[	[	-LRB-
cord-191574-1g38scnj	21	2	20	20	CD
cord-191574-1g38scnj	21	3	]	]	-RRB-
cord-191574-1g38scnj	21	4	[	[	-LRB-
cord-191574-1g38scnj	21	5	21	21	CD
cord-191574-1g38scnj	21	6	]	]	-RRB-
cord-191574-1g38scnj	22	1	[	[	-LRB-
cord-191574-1g38scnj	22	2	22	22	CD
cord-191574-1g38scnj	22	3	]	]	-RRB-
cord-191574-1g38scnj	22	4	[	[	-LRB-
cord-191574-1g38scnj	22	5	23	23	CD
cord-191574-1g38scnj	22	6	]	]	-RRB-
cord-191574-1g38scnj	23	1	[	[	-LRB-
cord-191574-1g38scnj	23	2	24	24	CD
cord-191574-1g38scnj	23	3	]	]	-RRB-
cord-191574-1g38scnj	23	4	.	.	.
cord-191574-1g38scnj	24	1	The	the	DT
cord-191574-1g38scnj	24	2	basic	basic	JJ
cord-191574-1g38scnj	24	3	equations	equation	NNS
cord-191574-1g38scnj	24	4	of	of	IN
cord-191574-1g38scnj	24	5	the	the	DT
cord-191574-1g38scnj	24	6	SIR	SIR	NNP
cord-191574-1g38scnj	24	7	model	model	NN
cord-191574-1g38scnj	24	8	are	be	VBP
cord-191574-1g38scnj	24	9	given	give	VBN
cord-191574-1g38scnj	24	10	by	by	IN
cord-191574-1g38scnj	24	11	the	the	DT
cord-191574-1g38scnj	24	12	following	follow	VBG
cord-191574-1g38scnj	24	13	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	24	14	system	system	NN
cord-191574-1g38scnj	24	15	of	of	IN
cord-191574-1g38scnj	24	16	ordinary	ordinary	JJ
cord-191574-1g38scnj	24	17	differential	differential	JJ
cord-191574-1g38scnj	24	18	equations	equation	NNS
cord-191574-1g38scnj	24	19	[	[	-LRB-
cord-191574-1g38scnj	24	20	7	7	CD
cord-191574-1g38scnj	24	21	,	,	,
cord-191574-1g38scnj	24	22	25	25	CD
cord-191574-1g38scnj	24	23	]	]	-RRB-
cord-191574-1g38scnj	24	24	 	 	_SP
cord-191574-1g38scnj	24	25	respectively	respectively	RB
cord-191574-1g38scnj	24	26	,	,	,
cord-191574-1g38scnj	24	27	where	where	WRB
cord-191574-1g38scnj	24	28	x(t	x(t	NNP
cord-191574-1g38scnj	24	29	)	)	-RRB-
cord-191574-1g38scnj	24	30	>	>	XX
cord-191574-1g38scnj	24	31	0	0	NFP
cord-191574-1g38scnj	24	32	,	,	,
cord-191574-1g38scnj	24	33	y(t	y(t	NN
cord-191574-1g38scnj	24	34	)	)	-RRB-
cord-191574-1g38scnj	24	35	>	>	NFP
cord-191574-1g38scnj	24	36	0	0	NFP
cord-191574-1g38scnj	24	37	and	and	CC
cord-191574-1g38scnj	24	38	z(t	z(t	CD
cord-191574-1g38scnj	24	39	)	)	-RRB-
cord-191574-1g38scnj	24	40	>	>	XX
cord-191574-1g38scnj	24	41	0	0	NFP
cord-191574-1g38scnj	24	42	,	,	,
cord-191574-1g38scnj	24	43	∀t	∀t	NNP
cord-191574-1g38scnj	24	44	≥	≥	CD
cord-191574-1g38scnj	24	45	0	0	NNP
cord-191574-1g38scnj	24	46	.	.	.
cord-191574-1g38scnj	25	1	The	the	DT
cord-191574-1g38scnj	25	2	system	system	NN
cord-191574-1g38scnj	25	3	of	of	IN
cord-191574-1g38scnj	25	4	equations	equation	NNS
cord-191574-1g38scnj	25	5	(	(	-LRB-
cord-191574-1g38scnj	25	6	1	1	CD
cord-191574-1g38scnj	25	7	)	)	-RRB-
cord-191574-1g38scnj	25	8	must	must	MD
cord-191574-1g38scnj	25	9	be	be	VB
cord-191574-1g38scnj	25	10	integrated	integrate	VBN
cord-191574-1g38scnj	25	11	with	with	IN
cord-191574-1g38scnj	25	12	the	the	DT
cord-191574-1g38scnj	25	13	initial	initial	JJ
cord-191574-1g38scnj	25	14	conditions	condition	NNS
cord-191574-1g38scnj	25	15	x	x	,
cord-191574-1g38scnj	25	16	(	(	-LRB-
cord-191574-1g38scnj	25	17	0	0	NFP
cord-191574-1g38scnj	25	18	)	)	-RRB-
cord-191574-1g38scnj	26	1	=	=	NFP
cord-191574-1g38scnj	27	1	N	n	NN
cord-191574-1g38scnj	27	2	1	1	CD
cord-191574-1g38scnj	27	3	≥	≥	CD
cord-191574-1g38scnj	27	4	0	0	CD
cord-191574-1g38scnj	27	5	,	,	,
cord-191574-1g38scnj	27	6	y	y	NNP
cord-191574-1g38scnj	27	7	(	(	-LRB-
cord-191574-1g38scnj	27	8	0	0	NFP
cord-191574-1g38scnj	27	9	)	)	-RRB-
cord-191574-1g38scnj	27	10	=	=	NFP
cord-191574-1g38scnj	28	1	N	n	CD
cord-191574-1g38scnj	28	2	2	2	CD
cord-191574-1g38scnj	28	3	≥	≥	CD
cord-191574-1g38scnj	28	4	0	0	CD
cord-191574-1g38scnj	28	5	and	and	CC
cord-191574-1g38scnj	28	6	z	z	NNP
cord-191574-1g38scnj	28	7	(	(	-LRB-
cord-191574-1g38scnj	28	8	0	0	NFP
cord-191574-1g38scnj	28	9	)	)	-RRB-
cord-191574-1g38scnj	28	10	=	=	NFP
cord-191574-1g38scnj	29	1	N	n	NN
cord-191574-1g38scnj	29	2	3	3	CD
cord-191574-1g38scnj	29	3	≥	≥	CD
cord-191574-1g38scnj	29	4	0	0	CD
cord-191574-1g38scnj	29	5	,	,	,
cord-191574-1g38scnj	29	6	respectively	respectively	RB
cord-191574-1g38scnj	29	7	,	,	,
cord-191574-1g38scnj	29	8	where	where	WRB
cord-191574-1g38scnj	29	9	N	n	NN
cord-191574-1g38scnj	29	10	i	i	PRP
cord-191574-1g38scnj	29	11	∈	∈	VBP
cord-191574-1g38scnj	29	12	ℜ	ℜ	NNP
cord-191574-1g38scnj	29	13	,	,	,
cord-191574-1g38scnj	29	14	i	i	PRP
cord-191574-1g38scnj	29	15	=	=	SYM
cord-191574-1g38scnj	29	16	1	1	CD
cord-191574-1g38scnj	29	17	,	,	,
cord-191574-1g38scnj	29	18	2	2	CD
cord-191574-1g38scnj	29	19	,	,	,
cord-191574-1g38scnj	29	20	3	3	CD
cord-191574-1g38scnj	29	21	.	.	.
cord-191574-1g38scnj	30	1	The	the	DT
cord-191574-1g38scnj	30	2	time	time	NN
cord-191574-1g38scnj	30	3	evolution	evolution	NN
cord-191574-1g38scnj	30	4	of	of	IN
cord-191574-1g38scnj	30	5	the	the	DT
cord-191574-1g38scnj	30	6	SIR	SIR	NNP
cord-191574-1g38scnj	30	7	epidemic	epidemic	NN
cord-191574-1g38scnj	30	8	model	model	NN
cord-191574-1g38scnj	30	9	,	,	,
cord-191574-1g38scnj	30	10	as	as	RB
cord-191574-1g38scnj	30	11	well	well	RB
cord-191574-1g38scnj	30	12	as	as	IN
cord-191574-1g38scnj	30	13	its	-PRON-	PRP$
cord-191574-1g38scnj	30	14	intrinsic	intrinsic	JJ
cord-191574-1g38scnj	30	15	dynamics	dynamic	NNS
cord-191574-1g38scnj	30	16	is	be	VBZ
cord-191574-1g38scnj	30	17	determined	determine	VBN
cord-191574-1g38scnj	30	18	by	by	IN
cord-191574-1g38scnj	30	19	two	two	CD
cord-191574-1g38scnj	30	20	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	30	21	parameters	parameter	NNS
cord-191574-1g38scnj	30	22	only	only	RB
cord-191574-1g38scnj	30	23	,	,	,
cord-191574-1g38scnj	30	24	the	the	DT
cord-191574-1g38scnj	30	25	infection	infection	NN
cord-191574-1g38scnj	30	26	rate	rate	NN
cord-191574-1g38scnj	30	27	β	β	NN
cord-191574-1g38scnj	30	28	,	,	,
cord-191574-1g38scnj	30	29	and	and	CC
cord-191574-1g38scnj	30	30	the	the	DT
cord-191574-1g38scnj	30	31	mean	mean	JJ
cord-191574-1g38scnj	30	32	recovery	recovery	NN
cord-191574-1g38scnj	30	33	rate	rate	NN
cord-191574-1g38scnj	30	34	γ	γ	NN
cord-191574-1g38scnj	30	35	,	,	,
cord-191574-1g38scnj	30	36	respectively	respectively	RB
cord-191574-1g38scnj	30	37	,	,	,
cord-191574-1g38scnj	30	38	which	which	WDT
cord-191574-1g38scnj	30	39	are	be	VBP
cord-191574-1g38scnj	30	40	assumed	assume	VBN
cord-191574-1g38scnj	30	41	to	to	TO
cord-191574-1g38scnj	30	42	be	be	VB
cord-191574-1g38scnj	30	43	positive	positive	JJ
cord-191574-1g38scnj	30	44	constants	constant	NNS
cord-191574-1g38scnj	30	45	.	.	.
cord-191574-1g38scnj	31	1	The	the	DT
cord-191574-1g38scnj	31	2	exact	exact	JJ
cord-191574-1g38scnj	31	3	solution	solution	NN
cord-191574-1g38scnj	31	4	of	of	IN
cord-191574-1g38scnj	31	5	the	the	DT
cord-191574-1g38scnj	31	6	SIR	SIR	NNP
cord-191574-1g38scnj	31	7	model	model	NN
cord-191574-1g38scnj	31	8	(	(	-LRB-
cord-191574-1g38scnj	31	9	1	1	CD
cord-191574-1g38scnj	31	10	)	)	-RRB-
cord-191574-1g38scnj	31	11	can	can	MD
cord-191574-1g38scnj	31	12	be	be	VB
cord-191574-1g38scnj	31	13	obtained	obtain	VBN
cord-191574-1g38scnj	31	14	in	in	IN
cord-191574-1g38scnj	31	15	an	an	DT
cord-191574-1g38scnj	31	16	exact	exact	JJ
cord-191574-1g38scnj	31	17	parametric	parametric	JJ
cord-191574-1g38scnj	31	18	form	form	NN
cord-191574-1g38scnj	31	19	,	,	,
cord-191574-1g38scnj	31	20	and	and	CC
cord-191574-1g38scnj	31	21	it	-PRON-	PRP
cord-191574-1g38scnj	31	22	is	be	VBZ
cord-191574-1g38scnj	31	23	given	give	VBN
cord-191574-1g38scnj	31	24	by	by	IN
cord-191574-1g38scnj	31	25	[	[	-LRB-
cord-191574-1g38scnj	31	26	25	25	CD
cord-191574-1g38scnj	31	27	]	]	-RRB-
cord-191574-1g38scnj	32	1	x	x	LS
cord-191574-1g38scnj	32	2	=	=	NFP
cord-191574-1g38scnj	33	1	x	x	LS
cord-191574-1g38scnj	33	2	0	0	CD
cord-191574-1g38scnj	33	3	u	u	NN
cord-191574-1g38scnj	33	4	,	,	,
cord-191574-1g38scnj	34	1	where	where	WRB
cord-191574-1g38scnj	34	2	N	N	NNP
cord-191574-1g38scnj	34	3	=	=	SYM
cord-191574-1g38scnj	34	4	∑	∑	NNP
cord-191574-1g38scnj	34	5	3	3	CD
cord-191574-1g38scnj	34	6	i=1	i=1	JJ
cord-191574-1g38scnj	34	7	N	n	CD
cord-191574-1g38scnj	35	1	i	i	PRP
cord-191574-1g38scnj	35	2	,	,	,
cord-191574-1g38scnj	35	3	x	x	NN
cord-191574-1g38scnj	35	4	0	0	CD
cord-191574-1g38scnj	35	5	=	=	SYM
cord-191574-1g38scnj	35	6	N	n	NN
cord-191574-1g38scnj	35	7	1	1	CD
cord-191574-1g38scnj	35	8	e	e	NN
cord-191574-1g38scnj	35	9	(	(	-LRB-
cord-191574-1g38scnj	35	10	β	β	NN
cord-191574-1g38scnj	35	11	/γ	/γ	NNP
cord-191574-1g38scnj	35	12	)	)	-RRB-
cord-191574-1g38scnj	35	13	N	n	CD
cord-191574-1g38scnj	35	14	3	3	CD
cord-191574-1g38scnj	35	15	,	,	,
cord-191574-1g38scnj	36	1	and	and	CC
cord-191574-1g38scnj	36	2	u	u	NNP
cord-191574-1g38scnj	36	3	is	be	VBZ
cord-191574-1g38scnj	36	4	a	a	DT
cord-191574-1g38scnj	36	5	parameter	parameter	NN
cord-191574-1g38scnj	36	6	.	.	.
cord-191574-1g38scnj	37	1	In	in	IN
cord-191574-1g38scnj	37	2	these	these	DT
cord-191574-1g38scnj	37	3	equations	equation	NNS
cord-191574-1g38scnj	37	4	x(t	x(t	VBD
cord-191574-1g38scnj	37	5	)	)	-RRB-
cord-191574-1g38scnj	37	6	gives	give	VBZ
cord-191574-1g38scnj	37	7	the	the	DT
cord-191574-1g38scnj	37	8	number	number	NN
cord-191574-1g38scnj	37	9	of	of	IN
cord-191574-1g38scnj	37	10	individuals	individual	NNS
cord-191574-1g38scnj	37	11	not	not	RB
cord-191574-1g38scnj	37	12	yet	yet	RB
cord-191574-1g38scnj	37	13	infected	infect	VBN
cord-191574-1g38scnj	37	14	with	with	IN
cord-191574-1g38scnj	37	15	the	the	DT
cord-191574-1g38scnj	37	16	epidemics	epidemic	NNS
cord-191574-1g38scnj	37	17	at	at	IN
cord-191574-1g38scnj	37	18	time	time	NN
cord-191574-1g38scnj	37	19	t	t	NN
cord-191574-1g38scnj	37	20	,	,	,
cord-191574-1g38scnj	37	21	or	or	CC
cord-191574-1g38scnj	37	22	those	those	DT
cord-191574-1g38scnj	37	23	susceptible	susceptible	JJ
cord-191574-1g38scnj	37	24	to	to	IN
cord-191574-1g38scnj	37	25	the	the	DT
cord-191574-1g38scnj	37	26	infection	infection	NN
cord-191574-1g38scnj	37	27	,	,	,
cord-191574-1g38scnj	37	28	y(t	y(t	NN
cord-191574-1g38scnj	37	29	)	)	-RRB-
cord-191574-1g38scnj	38	1	represents	represent	VBZ
cord-191574-1g38scnj	38	2	the	the	DT
cord-191574-1g38scnj	38	3	number	number	NN
cord-191574-1g38scnj	38	4	of	of	IN
cord-191574-1g38scnj	38	5	individuals	individual	NNS
cord-191574-1g38scnj	38	6	who	who	WP
cord-191574-1g38scnj	38	7	have	have	VBP
cord-191574-1g38scnj	38	8	already	already	RB
cord-191574-1g38scnj	38	9	been	be	VBN
cord-191574-1g38scnj	38	10	infected	infect	VBN
cord-191574-1g38scnj	38	11	with	with	IN
cord-191574-1g38scnj	38	12	the	the	DT
cord-191574-1g38scnj	38	13	disease	disease	NN
cord-191574-1g38scnj	38	14	,	,	,
cord-191574-1g38scnj	38	15	and	and	CC
cord-191574-1g38scnj	38	16	hence	hence	RB
cord-191574-1g38scnj	38	17	are	be	VBP
cord-191574-1g38scnj	38	18	able	able	JJ
cord-191574-1g38scnj	38	19	to	to	TO
cord-191574-1g38scnj	38	20	spread	spread	VB
cord-191574-1g38scnj	38	21	the	the	DT
cord-191574-1g38scnj	38	22	disease	disease	NN
cord-191574-1g38scnj	38	23	to	to	IN
cord-191574-1g38scnj	38	24	the	the	DT
cord-191574-1g38scnj	38	25	persons	person	NNS
cord-191574-1g38scnj	38	26	in	in	IN
cord-191574-1g38scnj	38	27	the	the	DT
cord-191574-1g38scnj	38	28	susceptible	susceptible	JJ
cord-191574-1g38scnj	38	29	category	category	NN
cord-191574-1g38scnj	38	30	,	,	,
cord-191574-1g38scnj	38	31	while	while	IN
cord-191574-1g38scnj	38	32	z(t	z(t	CD
cord-191574-1g38scnj	38	33	)	)	-RRB-
cord-191574-1g38scnj	38	34	denotes	denote	VBZ
cord-191574-1g38scnj	38	35	the	the	DT
cord-191574-1g38scnj	38	36	individuals	individual	NNS
cord-191574-1g38scnj	38	37	who	who	WP
cord-191574-1g38scnj	38	38	have	have	VBP
cord-191574-1g38scnj	38	39	been	be	VBN
cord-191574-1g38scnj	38	40	infected	infect	VBN
cord-191574-1g38scnj	38	41	,	,	,
cord-191574-1g38scnj	38	42	but	but	CC
cord-191574-1g38scnj	38	43	did	do	VBD
cord-191574-1g38scnj	38	44	recover	recover	VB
cord-191574-1g38scnj	38	45	from	from	IN
cord-191574-1g38scnj	38	46	the	the	DT
cord-191574-1g38scnj	38	47	disease	disease	NN
cord-191574-1g38scnj	38	48	.	.	.
cord-191574-1g38scnj	39	1	For	for	IN
cord-191574-1g38scnj	39	2	a	a	DT
cord-191574-1g38scnj	39	3	pedagogical	pedagogical	JJ
cord-191574-1g38scnj	39	4	discussion	discussion	NN
cord-191574-1g38scnj	39	5	of	of	IN
cord-191574-1g38scnj	39	6	the	the	DT
cord-191574-1g38scnj	39	7	SIR	SIR	NNP
cord-191574-1g38scnj	39	8	model	model	NN
cord-191574-1g38scnj	39	9	and	and	CC
cord-191574-1g38scnj	39	10	of	of	IN
cord-191574-1g38scnj	39	11	its	-PRON-	PRP$
cord-191574-1g38scnj	39	12	exact	exact	JJ
cord-191574-1g38scnj	39	13	solution	solution	NN
cord-191574-1g38scnj	39	14	see	see	VBP
cord-191574-1g38scnj	39	15	[	[	-LRB-
cord-191574-1g38scnj	39	16	26	26	CD
cord-191574-1g38scnj	39	17	]	]	-RRB-
cord-191574-1g38scnj	39	18	.	.	.
cord-191574-1g38scnj	40	1	However	however	RB
cord-191574-1g38scnj	40	2	,	,	,
cord-191574-1g38scnj	40	3	due	due	IN
cord-191574-1g38scnj	40	4	to	to	IN
cord-191574-1g38scnj	40	5	the	the	DT
cord-191574-1g38scnj	40	6	integral	integral	JJ
cord-191574-1g38scnj	40	7	representation	representation	NN
cord-191574-1g38scnj	40	8	of	of	IN
cord-191574-1g38scnj	40	9	the	the	DT
cord-191574-1g38scnj	40	10	time	time	NN
cord-191574-1g38scnj	40	11	variable	variable	NN
cord-191574-1g38scnj	40	12	,	,	,
cord-191574-1g38scnj	40	13	some	some	DT
cord-191574-1g38scnj	40	14	alternative	alternative	JJ
cord-191574-1g38scnj	40	15	representations	representation	NNS
cord-191574-1g38scnj	40	16	and	and	CC
cord-191574-1g38scnj	40	17	methods	method	NNS
cord-191574-1g38scnj	40	18	have	have	VBP
cord-191574-1g38scnj	40	19	been	be	VBN
cord-191574-1g38scnj	40	20	used	use	VBN
cord-191574-1g38scnj	40	21	for	for	IN
cord-191574-1g38scnj	40	22	the	the	DT
cord-191574-1g38scnj	40	23	study	study	NN
cord-191574-1g38scnj	40	24	of	of	IN
cord-191574-1g38scnj	40	25	the	the	DT
cord-191574-1g38scnj	40	26	solution	solution	NN
cord-191574-1g38scnj	40	27	of	of	IN
cord-191574-1g38scnj	40	28	the	the	DT
cord-191574-1g38scnj	40	29	SIR	SIR	NNP
cord-191574-1g38scnj	40	30	model	model	NN
cord-191574-1g38scnj	40	31	[	[	-LRB-
cord-191574-1g38scnj	40	32	27	27	CD
cord-191574-1g38scnj	40	33	]	]	-RRB-
cord-191574-1g38scnj	40	34	[	[	-LRB-
cord-191574-1g38scnj	40	35	28	28	CD
cord-191574-1g38scnj	40	36	]	]	-RRB-
cord-191574-1g38scnj	40	37	[	[	-LRB-
cord-191574-1g38scnj	40	38	29	29	CD
cord-191574-1g38scnj	40	39	]	]	-RRB-
cord-191574-1g38scnj	40	40	,	,	,
cord-191574-1g38scnj	40	41	including	include	VBG
cord-191574-1g38scnj	40	42	the	the	DT
cord-191574-1g38scnj	40	43	variational	variational	JJ
cord-191574-1g38scnj	40	44	iteration	iteration	NN
cord-191574-1g38scnj	40	45	method	method	NN
cord-191574-1g38scnj	40	46	,	,	,
cord-191574-1g38scnj	40	47	and	and	CC
cord-191574-1g38scnj	40	48	the	the	DT
cord-191574-1g38scnj	40	49	homotopy	homotopy	JJ
cord-191574-1g38scnj	40	50	perturbation	perturbation	NN
cord-191574-1g38scnj	40	51	method	method	NN
cord-191574-1g38scnj	40	52	.	.	.
cord-191574-1g38scnj	41	1	A	a	DT
cord-191574-1g38scnj	41	2	powerful	powerful	JJ
cord-191574-1g38scnj	41	3	method	method	NN
cord-191574-1g38scnj	41	4	for	for	IN
cord-191574-1g38scnj	41	5	obtaining	obtain	VBG
cord-191574-1g38scnj	41	6	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	41	7	solutions	solution	NNS
cord-191574-1g38scnj	41	8	of	of	IN
cord-191574-1g38scnj	41	9	strongly	strongly	RB
cord-191574-1g38scnj	41	10	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	41	11	differential	differential	JJ
cord-191574-1g38scnj	41	12	equations	equation	NNS
cord-191574-1g38scnj	41	13	is	be	VBZ
cord-191574-1g38scnj	41	14	represented	represent	VBN
cord-191574-1g38scnj	41	15	by	by	IN
cord-191574-1g38scnj	41	16	the	the	DT
cord-191574-1g38scnj	41	17	Adomian	adomian	JJ
cord-191574-1g38scnj	41	18	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	41	19	Method	Method	NNP
cord-191574-1g38scnj	41	20	[	[	-LRB-
cord-191574-1g38scnj	41	21	30	30	CD
cord-191574-1g38scnj	41	22	]	]	-RRB-
cord-191574-1g38scnj	41	23	[	[	-LRB-
cord-191574-1g38scnj	41	24	31	31	CD
cord-191574-1g38scnj	41	25	]	]	-RRB-
cord-191574-1g38scnj	42	1	[	[	-LRB-
cord-191574-1g38scnj	42	2	32	32	CD
cord-191574-1g38scnj	42	3	]	]	-RRB-
cord-191574-1g38scnj	42	4	[	[	-LRB-
cord-191574-1g38scnj	42	5	33	33	CD
cord-191574-1g38scnj	42	6	]	]	-RRB-
cord-191574-1g38scnj	42	7	,	,	,
cord-191574-1g38scnj	42	8	whose	whose	WP$
cord-191574-1g38scnj	42	9	basic	basic	JJ
cord-191574-1g38scnj	42	10	idea	idea	NN
cord-191574-1g38scnj	42	11	is	be	VBZ
cord-191574-1g38scnj	42	12	to	to	TO
cord-191574-1g38scnj	42	13	decompose	decompose	VB
cord-191574-1g38scnj	42	14	the	the	DT
cord-191574-1g38scnj	42	15	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	42	16	terms	term	NNS
cord-191574-1g38scnj	42	17	appearing	appear	VBG
cord-191574-1g38scnj	42	18	in	in	IN
cord-191574-1g38scnj	42	19	a	a	DT
cord-191574-1g38scnj	42	20	differential	differential	JJ
cord-191574-1g38scnj	42	21	equation	equation	NN
cord-191574-1g38scnj	42	22	in	in	IN
cord-191574-1g38scnj	42	23	terms	term	NNS
cord-191574-1g38scnj	42	24	of	of	IN
cord-191574-1g38scnj	42	25	the	the	DT
cord-191574-1g38scnj	42	26	Adomian	adomian	JJ
cord-191574-1g38scnj	42	27	polynomials	polynomial	NNS
cord-191574-1g38scnj	42	28	,	,	,
cord-191574-1g38scnj	42	29	which	which	WDT
cord-191574-1g38scnj	42	30	are	be	VBP
cord-191574-1g38scnj	42	31	constructed	construct	VBN
cord-191574-1g38scnj	42	32	recursively	recursively	RB
cord-191574-1g38scnj	42	33	.	.	.
cord-191574-1g38scnj	43	1	The	the	DT
cord-191574-1g38scnj	43	2	Adomian	adomian	JJ
cord-191574-1g38scnj	43	3	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	43	4	Method	Method	NNP
cord-191574-1g38scnj	43	5	,	,	,
cord-191574-1g38scnj	43	6	as	as	RB
cord-191574-1g38scnj	43	7	well	well	RB
cord-191574-1g38scnj	43	8	as	as	IN
cord-191574-1g38scnj	43	9	its	-PRON-	PRP$
cord-191574-1g38scnj	43	10	very	very	RB
cord-191574-1g38scnj	43	11	effective	effective	JJ
cord-191574-1g38scnj	43	12	version	version	NN
cord-191574-1g38scnj	43	13	,	,	,
cord-191574-1g38scnj	43	14	the	the	DT
cord-191574-1g38scnj	43	15	Laplace	Laplace	NNP
cord-191574-1g38scnj	43	16	-	-	HYPH
cord-191574-1g38scnj	43	17	Adomian	Adomian	NNP
cord-191574-1g38scnj	43	18	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	43	19	Method	Method	NNP
cord-191574-1g38scnj	43	20	,	,	,
cord-191574-1g38scnj	43	21	has	have	VBZ
cord-191574-1g38scnj	43	22	been	be	VBN
cord-191574-1g38scnj	43	23	extensively	extensively	RB
cord-191574-1g38scnj	43	24	used	use	VBN
cord-191574-1g38scnj	43	25	to	to	TO
cord-191574-1g38scnj	43	26	study	study	VB
cord-191574-1g38scnj	43	27	the	the	DT
cord-191574-1g38scnj	43	28	approximate	approximate	JJ
cord-191574-1g38scnj	43	29	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	43	30	solutions	solution	NNS
cord-191574-1g38scnj	43	31	of	of	IN
cord-191574-1g38scnj	43	32	different	different	JJ
cord-191574-1g38scnj	43	33	types	type	NNS
cord-191574-1g38scnj	43	34	of	of	IN
cord-191574-1g38scnj	43	35	differential	differential	JJ
cord-191574-1g38scnj	43	36	equations	equation	NNS
cord-191574-1g38scnj	43	37	,	,	,
cord-191574-1g38scnj	43	38	and	and	CC
cord-191574-1g38scnj	43	39	physical	physical	JJ
cord-191574-1g38scnj	43	40	models	model	NNS
cord-191574-1g38scnj	43	41	[	[	-LRB-
cord-191574-1g38scnj	43	42	34	34	CD
cord-191574-1g38scnj	43	43	]	]	-RRB-
cord-191574-1g38scnj	43	44	[	[	-LRB-
cord-191574-1g38scnj	43	45	35	35	CD
cord-191574-1g38scnj	43	46	]	]	-RRB-
cord-191574-1g38scnj	43	47	[	[	-LRB-
cord-191574-1g38scnj	43	48	36	36	CD
cord-191574-1g38scnj	43	49	]	]	-RRB-
cord-191574-1g38scnj	43	50	[	[	-LRB-
cord-191574-1g38scnj	43	51	37	37	CD
cord-191574-1g38scnj	43	52	]	]	-RRB-
cord-191574-1g38scnj	43	53	[	[	-LRB-
cord-191574-1g38scnj	43	54	38	38	CD
cord-191574-1g38scnj	43	55	]	]	-RRB-
cord-191574-1g38scnj	43	56	[	[	-LRB-
cord-191574-1g38scnj	43	57	39	39	CD
cord-191574-1g38scnj	43	58	]	]	-RRB-
cord-191574-1g38scnj	43	59	.	.	.
cord-191574-1g38scnj	44	1	The	the	DT
cord-191574-1g38scnj	44	2	Adomian	adomian	JJ
cord-191574-1g38scnj	44	3	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	44	4	Method	Method	NNP
cord-191574-1g38scnj	44	5	was	be	VBD
cord-191574-1g38scnj	44	6	used	use	VBN
cord-191574-1g38scnj	44	7	for	for	IN
cord-191574-1g38scnj	44	8	the	the	DT
cord-191574-1g38scnj	44	9	study	study	NN
cord-191574-1g38scnj	44	10	of	of	IN
cord-191574-1g38scnj	44	11	the	the	DT
cord-191574-1g38scnj	44	12	SIR	SIR	NNP
cord-191574-1g38scnj	44	13	model	model	NN
cord-191574-1g38scnj	44	14	in	in	IN
cord-191574-1g38scnj	44	15	[	[	-LRB-
cord-191574-1g38scnj	44	16	40	40	CD
cord-191574-1g38scnj	44	17	]	]	-RRB-
cord-191574-1g38scnj	44	18	,	,	,
cord-191574-1g38scnj	44	19	while	while	IN
cord-191574-1g38scnj	44	20	a	a	DT
cord-191574-1g38scnj	44	21	series	series	NN
cord-191574-1g38scnj	44	22	solution	solution	NN
cord-191574-1g38scnj	44	23	of	of	IN
cord-191574-1g38scnj	44	24	the	the	DT
cord-191574-1g38scnj	44	25	SIR	SIR	NNP
cord-191574-1g38scnj	44	26	model	model	NN
cord-191574-1g38scnj	44	27	by	by	IN
cord-191574-1g38scnj	44	28	using	use	VBG
cord-191574-1g38scnj	44	29	the	the	DT
cord-191574-1g38scnj	44	30	Laplace	Laplace	NNP
cord-191574-1g38scnj	44	31	-	-	HYPH
cord-191574-1g38scnj	44	32	Adomian	Adomian	NNP
cord-191574-1g38scnj	44	33	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	44	34	Method	Method	NNP
cord-191574-1g38scnj	44	35	was	be	VBD
cord-191574-1g38scnj	44	36	obtained	obtain	VBN
cord-191574-1g38scnj	44	37	in	in	IN
cord-191574-1g38scnj	44	38	[	[	-LRB-
cord-191574-1g38scnj	44	39	41	41	CD
cord-191574-1g38scnj	44	40	]	]	-RRB-
cord-191574-1g38scnj	44	41	,	,	,
cord-191574-1g38scnj	44	42	where	where	WRB
cord-191574-1g38scnj	44	43	the	the	DT
cord-191574-1g38scnj	44	44	solutions	solution	NNS
cord-191574-1g38scnj	44	45	have	have	VBP
cord-191574-1g38scnj	44	46	been	be	VBN
cord-191574-1g38scnj	44	47	expressed	express	VBN
cord-191574-1g38scnj	44	48	in	in	IN
cord-191574-1g38scnj	44	49	the	the	DT
cord-191574-1g38scnj	44	50	form	form	NN
cord-191574-1g38scnj	44	51	of	of	IN
cord-191574-1g38scnj	44	52	infinite	infinite	JJ
cord-191574-1g38scnj	44	53	series	series	NN
cord-191574-1g38scnj	44	54	.	.	.
cord-191574-1g38scnj	45	1	The	the	DT
cord-191574-1g38scnj	45	2	series	series	NN
cord-191574-1g38scnj	45	3	representations	representation	NNS
cord-191574-1g38scnj	45	4	of	of	IN
cord-191574-1g38scnj	45	5	the	the	DT
cord-191574-1g38scnj	45	6	time	time	NN
cord-191574-1g38scnj	45	7	evolution	evolution	NN
cord-191574-1g38scnj	45	8	of	of	IN
cord-191574-1g38scnj	45	9	the	the	DT
cord-191574-1g38scnj	45	10	SIR	SIR	NNP
cord-191574-1g38scnj	45	11	compartments	compartment	NNS
cord-191574-1g38scnj	45	12	obtained	obtain	VBN
cord-191574-1g38scnj	45	13	in	in	IN
cord-191574-1g38scnj	45	14	[	[	-LRB-
cord-191574-1g38scnj	45	15	41	41	CD
cord-191574-1g38scnj	45	16	]	]	-RRB-
cord-191574-1g38scnj	45	17	have	have	VBP
cord-191574-1g38scnj	45	18	been	be	VBN
cord-191574-1g38scnj	45	19	compared	compare	VBN
cord-191574-1g38scnj	45	20	with	with	IN
cord-191574-1g38scnj	45	21	the	the	DT
cord-191574-1g38scnj	45	22	exact	exact	JJ
cord-191574-1g38scnj	45	23	numerical	numerical	JJ
cord-191574-1g38scnj	45	24	solutions	solution	NNS
cord-191574-1g38scnj	45	25	of	of	IN
cord-191574-1g38scnj	45	26	the	the	DT
cord-191574-1g38scnj	45	27	model	model	NN
cord-191574-1g38scnj	45	28	,	,	,
cord-191574-1g38scnj	45	29	and	and	CC
cord-191574-1g38scnj	45	30	,	,	,
cord-191574-1g38scnj	45	31	for	for	IN
cord-191574-1g38scnj	45	32	a	a	DT
cord-191574-1g38scnj	45	33	specific	specific	JJ
cord-191574-1g38scnj	45	34	range	range	NN
cord-191574-1g38scnj	45	35	of	of	IN
cord-191574-1g38scnj	45	36	the	the	DT
cord-191574-1g38scnj	45	37	model	model	NN
cord-191574-1g38scnj	45	38	parameters	parameter	NNS
cord-191574-1g38scnj	45	39	,	,	,
cord-191574-1g38scnj	45	40	a	a	DT
cord-191574-1g38scnj	45	41	good	good	JJ
cord-191574-1g38scnj	45	42	agreement	agreement	NN
cord-191574-1g38scnj	45	43	between	between	IN
cord-191574-1g38scnj	45	44	the	the	DT
cord-191574-1g38scnj	45	45	Laplace	Laplace	NNP
cord-191574-1g38scnj	45	46	-	-	HYPH
cord-191574-1g38scnj	45	47	Adomian	adomian	JJ
cord-191574-1g38scnj	45	48	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	45	49	solutions	solution	NNS
cord-191574-1g38scnj	45	50	,	,	,
cord-191574-1g38scnj	45	51	containing	contain	VBG
cord-191574-1g38scnj	45	52	only	only	RB
cord-191574-1g38scnj	45	53	three	three	CD
cord-191574-1g38scnj	45	54	terms	term	NNS
cord-191574-1g38scnj	45	55	,	,	,
cord-191574-1g38scnj	45	56	and	and	CC
cord-191574-1g38scnj	45	57	the	the	DT
cord-191574-1g38scnj	45	58	numerical	numerical	JJ
cord-191574-1g38scnj	45	59	results	result	NNS
cord-191574-1g38scnj	45	60	,	,	,
cord-191574-1g38scnj	45	61	was	be	VBD
cord-191574-1g38scnj	45	62	obtained	obtain	VBN
cord-191574-1g38scnj	45	63	.	.	.
cord-191574-1g38scnj	46	1	One	one	CD
cord-191574-1g38scnj	46	2	of	of	IN
cord-191574-1g38scnj	46	3	the	the	DT
cord-191574-1g38scnj	46	4	simplest	simple	JJS
cord-191574-1g38scnj	46	5	generalizations	generalization	NNS
cord-191574-1g38scnj	46	6	of	of	IN
cord-191574-1g38scnj	46	7	the	the	DT
cord-191574-1g38scnj	46	8	SIR	SIR	NNP
cord-191574-1g38scnj	46	9	model	model	NN
cord-191574-1g38scnj	46	10	is	be	VBZ
cord-191574-1g38scnj	46	11	given	give	VBN
cord-191574-1g38scnj	46	12	by	by	IN
cord-191574-1g38scnj	46	13	the	the	DT
cord-191574-1g38scnj	46	14	SIR	SIR	NNP
cord-191574-1g38scnj	46	15	model	model	NN
cord-191574-1g38scnj	46	16	with	with	IN
cord-191574-1g38scnj	46	17	vital	vital	JJ
cord-191574-1g38scnj	46	18	dynamics	dynamic	NNS
cord-191574-1g38scnj	46	19	[	[	-LRB-
cord-191574-1g38scnj	46	20	1	1	CD
cord-191574-1g38scnj	46	21	,	,	,
cord-191574-1g38scnj	46	22	2	2	CD
cord-191574-1g38scnj	46	23	,	,	,
cord-191574-1g38scnj	46	24	4	4	CD
cord-191574-1g38scnj	46	25	,	,	,
cord-191574-1g38scnj	46	26	6	6	CD
cord-191574-1g38scnj	46	27	]	]	-RRB-
cord-191574-1g38scnj	46	28	,	,	,
cord-191574-1g38scnj	46	29	in	in	IN
cord-191574-1g38scnj	46	30	which	which	WDT
cord-191574-1g38scnj	46	31	the	the	DT
cord-191574-1g38scnj	46	32	number	number	NN
cord-191574-1g38scnj	46	33	of	of	IN
cord-191574-1g38scnj	46	34	deaths	death	NNS
cord-191574-1g38scnj	46	35	and	and	CC
cord-191574-1g38scnj	46	36	births	birth	NNS
cord-191574-1g38scnj	46	37	is	be	VBZ
cord-191574-1g38scnj	46	38	included	include	VBN
cord-191574-1g38scnj	46	39	in	in	IN
cord-191574-1g38scnj	46	40	the	the	DT
cord-191574-1g38scnj	46	41	model	model	NN
cord-191574-1g38scnj	46	42	via	via	IN
cord-191574-1g38scnj	46	43	a	a	DT
cord-191574-1g38scnj	46	44	new	new	JJ
cord-191574-1g38scnj	46	45	constant	constant	JJ
cord-191574-1g38scnj	46	46	µ.	µ.	NN
cord-191574-1g38scnj	47	1	Usually	usually	RB
cord-191574-1g38scnj	47	2	it	-PRON-	PRP
cord-191574-1g38scnj	47	3	is	be	VBZ
cord-191574-1g38scnj	47	4	assumed	assume	VBN
cord-191574-1g38scnj	47	5	that	that	IN
cord-191574-1g38scnj	47	6	the	the	DT
cord-191574-1g38scnj	47	7	death	death	NN
cord-191574-1g38scnj	47	8	rate	rate	NN
cord-191574-1g38scnj	47	9	is	be	VBZ
cord-191574-1g38scnj	47	10	equal	equal	JJ
cord-191574-1g38scnj	47	11	to	to	IN
cord-191574-1g38scnj	47	12	the	the	DT
cord-191574-1g38scnj	47	13	birth	birth	NN
cord-191574-1g38scnj	47	14	rate	rate	NN
cord-191574-1g38scnj	47	15	.	.	.
cord-191574-1g38scnj	48	1	Even	even	RB
cord-191574-1g38scnj	48	2	if	if	IN
cord-191574-1g38scnj	48	3	the	the	DT
cord-191574-1g38scnj	48	4	mathematical	mathematical	JJ
cord-191574-1g38scnj	48	5	modifications	modification	NNS
cord-191574-1g38scnj	48	6	of	of	IN
cord-191574-1g38scnj	48	7	the	the	DT
cord-191574-1g38scnj	48	8	initial	initial	JJ
cord-191574-1g38scnj	48	9	SIR	SIR	NNP
cord-191574-1g38scnj	48	10	model	model	NN
cord-191574-1g38scnj	48	11	with	with	IN
cord-191574-1g38scnj	48	12	µ	µ	NN
cord-191574-1g38scnj	48	13	=	=	SYM
cord-191574-1g38scnj	48	14	0	0	CD
cord-191574-1g38scnj	48	15	look	look	VB
cord-191574-1g38scnj	48	16	,	,	,
cord-191574-1g38scnj	48	17	at	at	IN
cord-191574-1g38scnj	48	18	first	first	JJ
cord-191574-1g38scnj	48	19	sight	sight	NN
cord-191574-1g38scnj	48	20	,	,	,
cord-191574-1g38scnj	48	21	minimal	minimal	JJ
cord-191574-1g38scnj	48	22	,	,	,
cord-191574-1g38scnj	48	23	the	the	DT
cord-191574-1g38scnj	48	24	SIR	SIR	NNP
cord-191574-1g38scnj	48	25	model	model	NN
cord-191574-1g38scnj	48	26	with	with	IN
cord-191574-1g38scnj	48	27	vital	vital	JJ
cord-191574-1g38scnj	48	28	dynamics	dynamic	NNS
cord-191574-1g38scnj	48	29	has	have	VBZ
cord-191574-1g38scnj	48	30	very	very	RB
cord-191574-1g38scnj	48	31	important	important	JJ
cord-191574-1g38scnj	48	32	differences	difference	NNS
cord-191574-1g38scnj	48	33	as	as	IN
cord-191574-1g38scnj	48	34	compared	compare	VBN
cord-191574-1g38scnj	48	35	to	to	IN
cord-191574-1g38scnj	48	36	the	the	DT
cord-191574-1g38scnj	48	37	SIR	SIR	NNP
cord-191574-1g38scnj	48	38	model	model	NN
cord-191574-1g38scnj	48	39	(	(	-LRB-
cord-191574-1g38scnj	48	40	1	1	CD
cord-191574-1g38scnj	48	41	)	)	-RRB-
cord-191574-1g38scnj	48	42	.	.	.
cord-191574-1g38scnj	49	1	The	the	DT
cord-191574-1g38scnj	49	2	SIR	SIR	NNP
cord-191574-1g38scnj	49	3	model	model	NN
cord-191574-1g38scnj	49	4	without	without	IN
cord-191574-1g38scnj	49	5	vital	vital	JJ
cord-191574-1g38scnj	49	6	dynamics	dynamic	NNS
cord-191574-1g38scnj	49	7	with	with	IN
cord-191574-1g38scnj	49	8	µ	µ	NN
cord-191574-1g38scnj	49	9	=	=	SYM
cord-191574-1g38scnj	49	10	0	0	NFP
cord-191574-1g38scnj	49	11	,	,	,
cord-191574-1g38scnj	49	12	has	have	VBZ
cord-191574-1g38scnj	49	13	a	a	DT
cord-191574-1g38scnj	49	14	first	first	JJ
cord-191574-1g38scnj	49	15	integral	integral	JJ
cord-191574-1g38scnj	49	16	N	n	NN
cord-191574-1g38scnj	49	17	=	=	NN
cord-191574-1g38scnj	49	18	S	s	NN
cord-191574-1g38scnj	50	1	+	+	CC
cord-191574-1g38scnj	51	1	I	-PRON-	PRP
cord-191574-1g38scnj	51	2	+	+	CC
cord-191574-1g38scnj	51	3	R	r	NN
cord-191574-1g38scnj	51	4	,	,	,
cord-191574-1g38scnj	51	5	which	which	WDT
cord-191574-1g38scnj	51	6	is	be	VBZ
cord-191574-1g38scnj	51	7	the	the	DT
cord-191574-1g38scnj	51	8	total	total	JJ
cord-191574-1g38scnj	51	9	number	number	NN
cord-191574-1g38scnj	51	10	of	of	IN
cord-191574-1g38scnj	51	11	individuals	individual	NNS
cord-191574-1g38scnj	51	12	in	in	IN
cord-191574-1g38scnj	51	13	the	the	DT
cord-191574-1g38scnj	51	14	given	give	VBN
cord-191574-1g38scnj	51	15	population	population	NN
cord-191574-1g38scnj	51	16	.	.	.
cord-191574-1g38scnj	52	1	Moreover	moreover	RB
cord-191574-1g38scnj	52	2	,	,	,
cord-191574-1g38scnj	52	3	it	-PRON-	PRP
cord-191574-1g38scnj	52	4	also	also	RB
cord-191574-1g38scnj	52	5	has	have	VBZ
cord-191574-1g38scnj	52	6	a	a	DT
cord-191574-1g38scnj	52	7	second	second	JJ
cord-191574-1g38scnj	52	8	first	first	JJ
cord-191574-1g38scnj	52	9	integral	integral	JJ
cord-191574-1g38scnj	52	10	G(S	G(S	NNP
cord-191574-1g38scnj	52	11	,	,	,
cord-191574-1g38scnj	52	12	I	-PRON-	PRP
cord-191574-1g38scnj	52	13	,	,	,
cord-191574-1g38scnj	52	14	R	r	NN
cord-191574-1g38scnj	52	15	)	)	-RRB-
cord-191574-1g38scnj	52	16	=	=	NFP
cord-191574-1g38scnj	53	1	β	β	NNP
cord-191574-1g38scnj	53	2	R	r	NN
cord-191574-1g38scnj	53	3	+	+	CC
cord-191574-1g38scnj	53	4	γ	γ	NN
cord-191574-1g38scnj	53	5	ln	ln	NN
cord-191574-1g38scnj	53	6	S	S	NNP
cord-191574-1g38scnj	53	7	[	[	-LRB-
cord-191574-1g38scnj	53	8	42	42	CD
cord-191574-1g38scnj	53	9	]	]	-RRB-
cord-191574-1g38scnj	53	10	.	.	.
cord-191574-1g38scnj	54	1	Hence	hence	RB
cord-191574-1g38scnj	54	2	the	the	DT
cord-191574-1g38scnj	54	3	SIR	SIR	NNP
cord-191574-1g38scnj	54	4	system	system	NN
cord-191574-1g38scnj	54	5	with	with	IN
cord-191574-1g38scnj	54	6	µ	µ	NN
cord-191574-1g38scnj	54	7	=	=	SYM
cord-191574-1g38scnj	54	8	0	0	NFP
cord-191574-1g38scnj	54	9	is	be	VBZ
cord-191574-1g38scnj	54	10	a	a	DT
cord-191574-1g38scnj	54	11	completely	completely	RB
cord-191574-1g38scnj	54	12	integrable	integrable	JJ
cord-191574-1g38scnj	54	13	system	system	NN
cord-191574-1g38scnj	54	14	with	with	IN
cord-191574-1g38scnj	54	15	two	two	CD
cord-191574-1g38scnj	54	16	functionally	functionally	RB
cord-191574-1g38scnj	54	17	independent	independent	JJ
cord-191574-1g38scnj	54	18	first	first	JJ
cord-191574-1g38scnj	54	19	integrals	integral	NNS
cord-191574-1g38scnj	54	20	.	.	.
cord-191574-1g38scnj	55	1	On	on	IN
cord-191574-1g38scnj	55	2	the	the	DT
cord-191574-1g38scnj	55	3	other	other	JJ
cord-191574-1g38scnj	55	4	hand	hand	NN
cord-191574-1g38scnj	55	5	in	in	IN
cord-191574-1g38scnj	55	6	the	the	DT
cord-191574-1g38scnj	55	7	case	case	NN
cord-191574-1g38scnj	55	8	of	of	IN
cord-191574-1g38scnj	55	9	µ	µ	NN
cord-191574-1g38scnj	55	10	=	=	SYM
cord-191574-1g38scnj	55	11	0	0	CD
cord-191574-1g38scnj	55	12	,	,	,
cord-191574-1g38scnj	55	13	in	in	IN
cord-191574-1g38scnj	55	14	[	[	-LRB-
cord-191574-1g38scnj	55	15	42	42	CD
cord-191574-1g38scnj	55	16	]	]	-RRB-
cord-191574-1g38scnj	55	17	it	-PRON-	PRP
cord-191574-1g38scnj	55	18	was	be	VBD
cord-191574-1g38scnj	55	19	proved	prove	VBN
cord-191574-1g38scnj	55	20	that	that	IN
cord-191574-1g38scnj	55	21	the	the	DT
cord-191574-1g38scnj	55	22	SIR	SIR	NNP
cord-191574-1g38scnj	55	23	model	model	NN
cord-191574-1g38scnj	55	24	has	have	VBZ
cord-191574-1g38scnj	55	25	no	no	DT
cord-191574-1g38scnj	55	26	polynomial	polynomial	JJ
cord-191574-1g38scnj	55	27	or	or	CC
cord-191574-1g38scnj	55	28	proper	proper	JJ
cord-191574-1g38scnj	55	29	rational	rational	JJ
cord-191574-1g38scnj	55	30	first	first	JJ
cord-191574-1g38scnj	55	31	integrals	integral	NNS
cord-191574-1g38scnj	55	32	.	.	.
cord-191574-1g38scnj	56	1	This	this	DT
cord-191574-1g38scnj	56	2	result	result	NN
cord-191574-1g38scnj	56	3	is	be	VBZ
cord-191574-1g38scnj	56	4	obtained	obtain	VBN
cord-191574-1g38scnj	56	5	by	by	IN
cord-191574-1g38scnj	56	6	studying	study	VBG
cord-191574-1g38scnj	56	7	the	the	DT
cord-191574-1g38scnj	56	8	invariant	invariant	JJ
cord-191574-1g38scnj	56	9	algebraic	algebraic	JJ
cord-191574-1g38scnj	56	10	surfaces	surface	NNS
cord-191574-1g38scnj	56	11	.	.	.
cord-191574-1g38scnj	57	1	Moreover	moreover	RB
cord-191574-1g38scnj	57	2	,	,	,
cord-191574-1g38scnj	57	3	although	although	IN
cord-191574-1g38scnj	57	4	the	the	DT
cord-191574-1g38scnj	57	5	SIR	SIR	NNP
cord-191574-1g38scnj	57	6	model	model	NN
cord-191574-1g38scnj	57	7	with	with	IN
cord-191574-1g38scnj	57	8	µ	µ	NN
cord-191574-1g38scnj	57	9	=	=	SYM
cord-191574-1g38scnj	57	10	0	0	NFP
cord-191574-1g38scnj	57	11	is	be	VBZ
cord-191574-1g38scnj	57	12	not	not	RB
cord-191574-1g38scnj	57	13	integrable	integrable	JJ
cord-191574-1g38scnj	57	14	,	,	,
cord-191574-1g38scnj	57	15	and	and	CC
cord-191574-1g38scnj	57	16	hence	hence	RB
cord-191574-1g38scnj	57	17	it	-PRON-	PRP
cord-191574-1g38scnj	57	18	does	do	VBZ
cord-191574-1g38scnj	57	19	not	not	RB
cord-191574-1g38scnj	57	20	have	have	VB
cord-191574-1g38scnj	57	21	an	an	DT
cord-191574-1g38scnj	57	22	exact	exact	JJ
cord-191574-1g38scnj	57	23	solution	solution	NN
cord-191574-1g38scnj	57	24	,	,	,
cord-191574-1g38scnj	57	25	the	the	DT
cord-191574-1g38scnj	57	26	global	global	JJ
cord-191574-1g38scnj	57	27	dynamics	dynamic	NNS
cord-191574-1g38scnj	57	28	of	of	IN
cord-191574-1g38scnj	57	29	the	the	DT
cord-191574-1g38scnj	57	30	SIR	SIR	NNP
cord-191574-1g38scnj	57	31	model	model	NN
cord-191574-1g38scnj	57	32	with	with	IN
cord-191574-1g38scnj	57	33	vital	vital	JJ
cord-191574-1g38scnj	57	34	dynamics	dynamic	NNS
cord-191574-1g38scnj	57	35	can	can	MD
cord-191574-1g38scnj	57	36	be	be	VB
cord-191574-1g38scnj	57	37	studied	study	VBN
cord-191574-1g38scnj	57	38	based	base	VBN
cord-191574-1g38scnj	57	39	on	on	IN
cord-191574-1g38scnj	57	40	the	the	DT
cord-191574-1g38scnj	57	41	existence	existence	NN
cord-191574-1g38scnj	57	42	of	of	IN
cord-191574-1g38scnj	57	43	an	an	DT
cord-191574-1g38scnj	57	44	invariant	invariant	JJ
cord-191574-1g38scnj	57	45	algebraic	algebraic	JJ
cord-191574-1g38scnj	57	46	surface	surface	NN
cord-191574-1g38scnj	57	47	.	.	.
cord-191574-1g38scnj	58	1	In	in	IN
cord-191574-1g38scnj	58	2	[	[	-LRB-
cord-191574-1g38scnj	58	3	25	25	CD
cord-191574-1g38scnj	58	4	]	]	-RRB-
cord-191574-1g38scnj	58	5	it	-PRON-	PRP
cord-191574-1g38scnj	58	6	was	be	VBD
cord-191574-1g38scnj	58	7	shown	show	VBN
cord-191574-1g38scnj	58	8	that	that	IN
cord-191574-1g38scnj	58	9	the	the	DT
cord-191574-1g38scnj	58	10	generalization	generalization	NN
cord-191574-1g38scnj	58	11	of	of	IN
cord-191574-1g38scnj	58	12	the	the	DT
cord-191574-1g38scnj	58	13	SIR	SIR	NNP
cord-191574-1g38scnj	58	14	model	model	NN
cord-191574-1g38scnj	58	15	with	with	IN
cord-191574-1g38scnj	58	16	µ	µ	NN
cord-191574-1g38scnj	58	17	=	=	SYM
cord-191574-1g38scnj	58	18	0	0	CD
cord-191574-1g38scnj	58	19	,	,	,
cord-191574-1g38scnj	58	20	including	include	VBG
cord-191574-1g38scnj	58	21	births	birth	NNS
cord-191574-1g38scnj	58	22	and	and	CC
cord-191574-1g38scnj	58	23	deaths	death	NNS
cord-191574-1g38scnj	58	24	,	,	,
cord-191574-1g38scnj	58	25	and	and	CC
cord-191574-1g38scnj	58	26	described	describe	VBN
cord-191574-1g38scnj	58	27	by	by	IN
cord-191574-1g38scnj	58	28	a	a	DT
cord-191574-1g38scnj	58	29	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	58	30	system	system	NN
cord-191574-1g38scnj	58	31	of	of	IN
cord-191574-1g38scnj	58	32	differential	differential	JJ
cord-191574-1g38scnj	58	33	equations	equation	NNS
cord-191574-1g38scnj	58	34	,	,	,
cord-191574-1g38scnj	58	35	can	can	MD
cord-191574-1g38scnj	58	36	be	be	VB
cord-191574-1g38scnj	58	37	reduced	reduce	VBN
cord-191574-1g38scnj	58	38	to	to	IN
cord-191574-1g38scnj	58	39	an	an	DT
cord-191574-1g38scnj	58	40	Abel	Abel	NNP
cord-191574-1g38scnj	58	41	type	type	NN
cord-191574-1g38scnj	58	42	equation	equation	NN
cord-191574-1g38scnj	58	43	.	.	.
cord-191574-1g38scnj	59	1	The	the	DT
cord-191574-1g38scnj	59	2	reduction	reduction	NN
cord-191574-1g38scnj	59	3	of	of	IN
cord-191574-1g38scnj	59	4	the	the	DT
cord-191574-1g38scnj	59	5	SIR	SIR	NNP
cord-191574-1g38scnj	59	6	model	model	NN
cord-191574-1g38scnj	59	7	with	with	IN
cord-191574-1g38scnj	59	8	vital	vital	JJ
cord-191574-1g38scnj	59	9	dynamics	dynamic	NNS
cord-191574-1g38scnj	59	10	to	to	IN
cord-191574-1g38scnj	59	11	an	an	DT
cord-191574-1g38scnj	59	12	Abel	Abel	NNP
cord-191574-1g38scnj	59	13	type	type	NN
cord-191574-1g38scnj	59	14	first	first	JJ
cord-191574-1g38scnj	59	15	order	order	NN
cord-191574-1g38scnj	59	16	differential	differential	NN
cord-191574-1g38scnj	59	17	equation	equation	NN
cord-191574-1g38scnj	59	18	greatly	greatly	RB
cord-191574-1g38scnj	59	19	simplifies	simplify	VBZ
cord-191574-1g38scnj	59	20	the	the	DT
cord-191574-1g38scnj	59	21	analysis	analysis	NN
cord-191574-1g38scnj	59	22	of	of	IN
cord-191574-1g38scnj	59	23	its	-PRON-	PRP$
cord-191574-1g38scnj	59	24	properties	property	NNS
cord-191574-1g38scnj	59	25	.	.	.
cord-191574-1g38scnj	60	1	An	an	DT
cord-191574-1g38scnj	60	2	approximate	approximate	JJ
cord-191574-1g38scnj	60	3	solution	solution	NN
cord-191574-1g38scnj	60	4	of	of	IN
cord-191574-1g38scnj	60	5	the	the	DT
cord-191574-1g38scnj	60	6	Abel	Abel	NNP
cord-191574-1g38scnj	60	7	equation	equation	NN
cord-191574-1g38scnj	60	8	was	be	VBD
cord-191574-1g38scnj	60	9	obtained	obtain	VBN
cord-191574-1g38scnj	60	10	by	by	IN
cord-191574-1g38scnj	60	11	using	use	VBG
cord-191574-1g38scnj	60	12	a	a	DT
cord-191574-1g38scnj	60	13	perturbative	perturbative	JJ
cord-191574-1g38scnj	60	14	approach	approach	NN
cord-191574-1g38scnj	60	15	,	,	,
cord-191574-1g38scnj	60	16	in	in	IN
cord-191574-1g38scnj	60	17	a	a	DT
cord-191574-1g38scnj	60	18	power	power	NN
cord-191574-1g38scnj	60	19	series	series	NN
cord-191574-1g38scnj	60	20	form	form	NN
cord-191574-1g38scnj	60	21	.	.	.
cord-191574-1g38scnj	61	1	Moreover	moreover	RB
cord-191574-1g38scnj	61	2	,	,	,
cord-191574-1g38scnj	61	3	the	the	DT
cord-191574-1g38scnj	61	4	general	general	JJ
cord-191574-1g38scnj	61	5	solution	solution	NN
cord-191574-1g38scnj	61	6	of	of	IN
cord-191574-1g38scnj	61	7	the	the	DT
cord-191574-1g38scnj	61	8	SIR	SIR	NNP
cord-191574-1g38scnj	61	9	model	model	NN
cord-191574-1g38scnj	61	10	with	with	IN
cord-191574-1g38scnj	61	11	vital	vital	JJ
cord-191574-1g38scnj	61	12	dynamics	dynamic	NNS
cord-191574-1g38scnj	61	13	can	can	MD
cord-191574-1g38scnj	61	14	be	be	VB
cord-191574-1g38scnj	61	15	represented	represent	VBN
cord-191574-1g38scnj	61	16	in	in	IN
cord-191574-1g38scnj	61	17	an	an	DT
cord-191574-1g38scnj	61	18	exact	exact	JJ
cord-191574-1g38scnj	61	19	parametric	parametric	JJ
cord-191574-1g38scnj	61	20	form	form	NN
cord-191574-1g38scnj	61	21	.	.	.
cord-191574-1g38scnj	62	1	In	in	IN
cord-191574-1g38scnj	62	2	the	the	DT
cord-191574-1g38scnj	62	3	present	present	JJ
cord-191574-1g38scnj	62	4	work	work	NN
cord-191574-1g38scnj	62	5	we	-PRON-	PRP
cord-191574-1g38scnj	62	6	consider	consider	VBP
cord-191574-1g38scnj	62	7	the	the	DT
cord-191574-1g38scnj	62	8	possibility	possibility	NN
cord-191574-1g38scnj	62	9	of	of	IN
cord-191574-1g38scnj	62	10	obtaining	obtain	VBG
cord-191574-1g38scnj	62	11	some	some	DT
cord-191574-1g38scnj	62	12	accurate	accurate	JJ
cord-191574-1g38scnj	62	13	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	62	14	solutions	solution	NNS
cord-191574-1g38scnj	62	15	of	of	IN
cord-191574-1g38scnj	62	16	the	the	DT
cord-191574-1g38scnj	62	17	equations	equation	NNS
cord-191574-1g38scnj	62	18	of	of	IN
cord-191574-1g38scnj	62	19	the	the	DT
cord-191574-1g38scnj	62	20	SIR	SIR	NNP
cord-191574-1g38scnj	62	21	model	model	NN
cord-191574-1g38scnj	62	22	with	with	IN
cord-191574-1g38scnj	62	23	vital	vital	JJ
cord-191574-1g38scnj	62	24	dynamics	dynamic	NNS
cord-191574-1g38scnj	62	25	by	by	IN
cord-191574-1g38scnj	62	26	using	use	VBG
cord-191574-1g38scnj	62	27	the	the	DT
cord-191574-1g38scnj	62	28	Adomian	Adomian	NNP
cord-191574-1g38scnj	62	29	and	and	CC
cord-191574-1g38scnj	62	30	the	the	DT
cord-191574-1g38scnj	62	31	Laplace	Laplace	NNP
cord-191574-1g38scnj	62	32	-	-	HYPH
cord-191574-1g38scnj	62	33	Adomian	Adomian	NNP
cord-191574-1g38scnj	62	34	Decomposition	decomposition	NN
cord-191574-1g38scnj	62	35	Methods	Methods	NNPS
cord-191574-1g38scnj	62	36	,	,	,
cord-191574-1g38scnj	62	37	respectively	respectively	RB
cord-191574-1g38scnj	62	38	.	.	.
cord-191574-1g38scnj	63	1	As	as	IN
cord-191574-1g38scnj	63	2	a	a	DT
cord-191574-1g38scnj	63	3	first	first	JJ
cord-191574-1g38scnj	63	4	step	step	NN
cord-191574-1g38scnj	63	5	in	in	IN
cord-191574-1g38scnj	63	6	our	-PRON-	PRP$
cord-191574-1g38scnj	63	7	analysis	analysis	NN
cord-191574-1g38scnj	63	8	we	-PRON-	PRP
cord-191574-1g38scnj	63	9	reduce	reduce	VBP
cord-191574-1g38scnj	63	10	the	the	DT
cord-191574-1g38scnj	63	11	SIR	SIR	NNP
cord-191574-1g38scnj	63	12	model	model	NN
cord-191574-1g38scnj	63	13	with	with	IN
cord-191574-1g38scnj	63	14	µ	µ	NN
cord-191574-1g38scnj	63	15	=	=	SYM
cord-191574-1g38scnj	63	16	0	0	CD
cord-191574-1g38scnj	63	17	to	to	IN
cord-191574-1g38scnj	63	18	a	a	DT
cord-191574-1g38scnj	63	19	basic	basic	JJ
cord-191574-1g38scnj	63	20	second	second	JJ
cord-191574-1g38scnj	63	21	order	order	NN
cord-191574-1g38scnj	63	22	differential	differential	NN
cord-191574-1g38scnj	63	23	equation	equation	NN
cord-191574-1g38scnj	63	24	,	,	,
cord-191574-1g38scnj	63	25	describing	describe	VBG
cord-191574-1g38scnj	63	26	the	the	DT
cord-191574-1g38scnj	63	27	evolution	evolution	NN
cord-191574-1g38scnj	63	28	of	of	IN
cord-191574-1g38scnj	63	29	the	the	DT
cord-191574-1g38scnj	63	30	individuals	individual	NNS
cord-191574-1g38scnj	63	31	infected	infect	VBN
cord-191574-1g38scnj	63	32	with	with	IN
cord-191574-1g38scnj	63	33	the	the	DT
cord-191574-1g38scnj	63	34	disease	disease	NN
cord-191574-1g38scnj	63	35	.	.	.
cord-191574-1g38scnj	64	1	Then	then	RB
cord-191574-1g38scnj	64	2	,	,	,
cord-191574-1g38scnj	64	3	once	once	IN
cord-191574-1g38scnj	64	4	the	the	DT
cord-191574-1g38scnj	64	5	solution	solution	NN
cord-191574-1g38scnj	64	6	of	of	IN
cord-191574-1g38scnj	64	7	the	the	DT
cord-191574-1g38scnj	64	8	basic	basic	JJ
cord-191574-1g38scnj	64	9	equation	equation	NN
cord-191574-1g38scnj	64	10	is	be	VBZ
cord-191574-1g38scnj	64	11	known	know	VBN
cord-191574-1g38scnj	64	12	,	,	,
cord-191574-1g38scnj	64	13	the	the	DT
cord-191574-1g38scnj	64	14	general	general	JJ
cord-191574-1g38scnj	64	15	solution	solution	NN
cord-191574-1g38scnj	64	16	of	of	IN
cord-191574-1g38scnj	64	17	the	the	DT
cord-191574-1g38scnj	64	18	SIR	SIR	NNP
cord-191574-1g38scnj	64	19	model	model	NN
cord-191574-1g38scnj	64	20	with	with	IN
cord-191574-1g38scnj	64	21	vital	vital	JJ
cord-191574-1g38scnj	64	22	dynamics	dynamic	NNS
cord-191574-1g38scnj	64	23	can	can	MD
cord-191574-1g38scnj	64	24	be	be	VB
cord-191574-1g38scnj	64	25	obtained	obtain	VBN
cord-191574-1g38scnj	64	26	in	in	IN
cord-191574-1g38scnj	64	27	terms	term	NNS
cord-191574-1g38scnj	64	28	of	of	IN
cord-191574-1g38scnj	64	29	the	the	DT
cord-191574-1g38scnj	64	30	variable	variable	NN
cord-191574-1g38scnj	64	31	u	u	NN
cord-191574-1g38scnj	64	32	related	relate	VBD
cord-191574-1g38scnj	64	33	to	to	IN
cord-191574-1g38scnj	64	34	the	the	DT
cord-191574-1g38scnj	64	35	number	number	NN
cord-191574-1g38scnj	64	36	y	y	NN
cord-191574-1g38scnj	64	37	of	of	IN
cord-191574-1g38scnj	64	38	the	the	DT
cord-191574-1g38scnj	64	39	infected	infected	JJ
cord-191574-1g38scnj	64	40	individuals	individual	NNS
cord-191574-1g38scnj	64	41	.	.	.
cord-191574-1g38scnj	65	1	In	in	IN
cord-191574-1g38scnj	65	2	order	order	NN
cord-191574-1g38scnj	65	3	to	to	TO
cord-191574-1g38scnj	65	4	obtain	obtain	VB
cord-191574-1g38scnj	65	5	some	some	DT
cord-191574-1g38scnj	65	6	approximate	approximate	JJ
cord-191574-1g38scnj	65	7	solutions	solution	NNS
cord-191574-1g38scnj	65	8	of	of	IN
cord-191574-1g38scnj	65	9	the	the	DT
cord-191574-1g38scnj	65	10	basic	basic	JJ
cord-191574-1g38scnj	65	11	evolution	evolution	NN
cord-191574-1g38scnj	65	12	equation	equation	NN
cord-191574-1g38scnj	65	13	we	-PRON-	PRP
cord-191574-1g38scnj	65	14	will	will	MD
cord-191574-1g38scnj	65	15	apply	apply	VB
cord-191574-1g38scnj	65	16	to	to	IN
cord-191574-1g38scnj	65	17	it	-PRON-	PRP
cord-191574-1g38scnj	65	18	both	both	CC
cord-191574-1g38scnj	65	19	the	the	DT
cord-191574-1g38scnj	65	20	Adomian	Adomian	NNP
cord-191574-1g38scnj	65	21	and	and	CC
cord-191574-1g38scnj	65	22	the	the	DT
cord-191574-1g38scnj	65	23	Laplace	Laplace	NNP
cord-191574-1g38scnj	65	24	-	-	HYPH
cord-191574-1g38scnj	65	25	Adomian	Adomian	NNP
cord-191574-1g38scnj	65	26	Decomposition	decomposition	NN
cord-191574-1g38scnj	65	27	Methods	Methods	NNPS
cord-191574-1g38scnj	65	28	,	,	,
cord-191574-1g38scnj	65	29	We	-PRON-	PRP
cord-191574-1g38scnj	65	30	obtain	obtain	VBP
cord-191574-1g38scnj	65	31	in	in	IN
cord-191574-1g38scnj	65	32	each	each	DT
cord-191574-1g38scnj	65	33	case	case	NN
cord-191574-1g38scnj	65	34	the	the	DT
cord-191574-1g38scnj	65	35	recurrence	recurrence	NN
cord-191574-1g38scnj	65	36	relations	relation	NNS
cord-191574-1g38scnj	65	37	giving	give	VBG
cord-191574-1g38scnj	65	38	the	the	DT
cord-191574-1g38scnj	65	39	successive	successive	JJ
cord-191574-1g38scnj	65	40	terms	term	NNS
cord-191574-1g38scnj	65	41	in	in	IN
cord-191574-1g38scnj	65	42	the	the	DT
cord-191574-1g38scnj	65	43	Adomian	adomian	JJ
cord-191574-1g38scnj	65	44	series	series	NN
cord-191574-1g38scnj	65	45	representation	representation	NN
cord-191574-1g38scnj	65	46	as	as	IN
cord-191574-1g38scnj	65	47	a	a	DT
cord-191574-1g38scnj	65	48	function	function	NN
cord-191574-1g38scnj	65	49	of	of	IN
cord-191574-1g38scnj	65	50	the	the	DT
cord-191574-1g38scnj	65	51	Adomian	adomian	JJ
cord-191574-1g38scnj	65	52	polynomials	polynomial	NNS
cord-191574-1g38scnj	65	53	.	.	.
cord-191574-1g38scnj	66	1	In	in	IN
cord-191574-1g38scnj	66	2	the	the	DT
cord-191574-1g38scnj	66	3	case	case	NN
cord-191574-1g38scnj	66	4	of	of	IN
cord-191574-1g38scnj	66	5	the	the	DT
cord-191574-1g38scnj	66	6	Adomian	adomian	JJ
cord-191574-1g38scnj	66	7	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	66	8	Method	Method	NNP
cord-191574-1g38scnj	66	9	the	the	DT
cord-191574-1g38scnj	66	10	iterative	iterative	JJ
cord-191574-1g38scnj	66	11	solution	solution	NN
cord-191574-1g38scnj	66	12	can	can	MD
cord-191574-1g38scnj	66	13	be	be	VB
cord-191574-1g38scnj	66	14	evaluated	evaluate	VBN
cord-191574-1g38scnj	66	15	exactly	exactly	RB
cord-191574-1g38scnj	66	16	only	only	RB
cord-191574-1g38scnj	66	17	for	for	IN
cord-191574-1g38scnj	66	18	the	the	DT
cord-191574-1g38scnj	66	19	first	first	JJ
cord-191574-1g38scnj	66	20	two	two	CD
cord-191574-1g38scnj	66	21	terms	term	NNS
cord-191574-1g38scnj	66	22	of	of	IN
cord-191574-1g38scnj	66	23	the	the	DT
cord-191574-1g38scnj	66	24	series	series	NN
cord-191574-1g38scnj	66	25	expansion	expansion	NN
cord-191574-1g38scnj	66	26	,	,	,
cord-191574-1g38scnj	66	27	while	while	IN
cord-191574-1g38scnj	66	28	for	for	IN
cord-191574-1g38scnj	66	29	the	the	DT
cord-191574-1g38scnj	66	30	Laplace	Laplace	NNP
cord-191574-1g38scnj	66	31	-	-	HYPH
cord-191574-1g38scnj	66	32	Adomian	Adomian	NNP
cord-191574-1g38scnj	66	33	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	66	34	Method	Method	NNP
cord-191574-1g38scnj	66	35	all	all	PDT
cord-191574-1g38scnj	66	36	the	the	DT
cord-191574-1g38scnj	66	37	terms	term	NNS
cord-191574-1g38scnj	66	38	in	in	IN
cord-191574-1g38scnj	66	39	the	the	DT
cord-191574-1g38scnj	66	40	series	series	NN
cord-191574-1g38scnj	66	41	expansion	expansion	NN
cord-191574-1g38scnj	66	42	can	can	MD
cord-191574-1g38scnj	66	43	be	be	VB
cord-191574-1g38scnj	66	44	obtained	obtain	VBN
cord-191574-1g38scnj	66	45	exactly	exactly	RB
cord-191574-1g38scnj	66	46	.	.	.
cord-191574-1g38scnj	67	1	We	-PRON-	PRP
cord-191574-1g38scnj	67	2	also	also	RB
cord-191574-1g38scnj	67	3	perform	perform	VBP
cord-191574-1g38scnj	67	4	a	a	DT
cord-191574-1g38scnj	67	5	careful	careful	JJ
cord-191574-1g38scnj	67	6	comparison	comparison	NN
cord-191574-1g38scnj	67	7	of	of	IN
cord-191574-1g38scnj	67	8	the	the	DT
cord-191574-1g38scnj	67	9	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	67	10	results	result	NNS
cord-191574-1g38scnj	67	11	with	with	IN
cord-191574-1g38scnj	67	12	the	the	DT
cord-191574-1g38scnj	67	13	exact	exact	JJ
cord-191574-1g38scnj	67	14	numerical	numerical	JJ
cord-191574-1g38scnj	67	15	solutions	solution	NNS
cord-191574-1g38scnj	67	16	,	,	,
cord-191574-1g38scnj	67	17	and	and	CC
cord-191574-1g38scnj	67	18	it	-PRON-	PRP
cord-191574-1g38scnj	67	19	turns	turn	VBZ
cord-191574-1g38scnj	67	20	out	out	RP
cord-191574-1g38scnj	67	21	that	that	IN
cord-191574-1g38scnj	67	22	for	for	IN
cord-191574-1g38scnj	67	23	certain	certain	JJ
cord-191574-1g38scnj	67	24	ranges	range	NNS
cord-191574-1g38scnj	67	25	of	of	IN
cord-191574-1g38scnj	67	26	the	the	DT
cord-191574-1g38scnj	67	27	model	model	NN
cord-191574-1g38scnj	67	28	parameters	parameter	VBZ
cord-191574-1g38scnj	67	29	β	β	NNP
cord-191574-1g38scnj	67	30	,	,	,
cord-191574-1g38scnj	67	31	γ	γ	NN
cord-191574-1g38scnj	67	32	,	,	,
cord-191574-1g38scnj	67	33	µ	µ	LS
cord-191574-1g38scnj	67	34	)	)	-RRB-
cord-191574-1g38scnj	67	35	both	both	CC
cord-191574-1g38scnj	67	36	the	the	DT
cord-191574-1g38scnj	67	37	Adomian	Adomian	NNP
cord-191574-1g38scnj	67	38	and	and	CC
cord-191574-1g38scnj	67	39	the	the	DT
cord-191574-1g38scnj	67	40	Laplace	Laplace	NNP
cord-191574-1g38scnj	67	41	-	-	HYPH
cord-191574-1g38scnj	67	42	Adomian	Adomian	NNP
cord-191574-1g38scnj	67	43	Decomposition	decomposition	NN
cord-191574-1g38scnj	67	44	Methods	Methods	NNPS
cord-191574-1g38scnj	67	45	can	can	MD
cord-191574-1g38scnj	67	46	give	give	VB
cord-191574-1g38scnj	67	47	a	a	DT
cord-191574-1g38scnj	67	48	good	good	JJ
cord-191574-1g38scnj	67	49	description	description	NN
cord-191574-1g38scnj	67	50	of	of	IN
cord-191574-1g38scnj	67	51	the	the	DT
cord-191574-1g38scnj	67	52	numerical	numerical	JJ
cord-191574-1g38scnj	67	53	results	result	NNS
cord-191574-1g38scnj	67	54	.	.	.
cord-191574-1g38scnj	68	1	The	the	DT
cord-191574-1g38scnj	68	2	present	present	JJ
cord-191574-1g38scnj	68	3	paper	paper	NN
cord-191574-1g38scnj	68	4	is	be	VBZ
cord-191574-1g38scnj	68	5	organized	organize	VBN
cord-191574-1g38scnj	68	6	as	as	IN
cord-191574-1g38scnj	68	7	follows	follow	NNS
cord-191574-1g38scnj	68	8	.	.	.
cord-191574-1g38scnj	69	1	The	the	DT
cord-191574-1g38scnj	69	2	basic	basic	JJ
cord-191574-1g38scnj	69	3	equation	equation	NN
cord-191574-1g38scnj	69	4	describing	describe	VBG
cord-191574-1g38scnj	69	5	the	the	DT
cord-191574-1g38scnj	69	6	dynamical	dynamical	JJ
cord-191574-1g38scnj	69	7	evolution	evolution	NN
cord-191574-1g38scnj	69	8	of	of	IN
cord-191574-1g38scnj	69	9	the	the	DT
cord-191574-1g38scnj	69	10	SIR	SIR	NNP
cord-191574-1g38scnj	69	11	model	model	NN
cord-191574-1g38scnj	69	12	with	with	IN
cord-191574-1g38scnj	69	13	vital	vital	JJ
cord-191574-1g38scnj	69	14	dynamics	dynamic	NNS
cord-191574-1g38scnj	69	15	is	be	VBZ
cord-191574-1g38scnj	69	16	obtained	obtain	VBN
cord-191574-1g38scnj	69	17	in	in	IN
cord-191574-1g38scnj	69	18	Section	Section	NNP
cord-191574-1g38scnj	69	19	II	II	NNP
cord-191574-1g38scnj	69	20	.	.	.
cord-191574-1g38scnj	70	1	The	the	DT
cord-191574-1g38scnj	70	2	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	70	3	solutions	solution	NNS
cord-191574-1g38scnj	70	4	of	of	IN
cord-191574-1g38scnj	70	5	the	the	DT
cord-191574-1g38scnj	70	6	SIR	SIR	NNP
cord-191574-1g38scnj	70	7	system	system	NN
cord-191574-1g38scnj	70	8	for	for	IN
cord-191574-1g38scnj	70	9	µ	µ	NN
cord-191574-1g38scnj	70	10	=	=	SYM
cord-191574-1g38scnj	70	11	0	0	NFP
cord-191574-1g38scnj	70	12	are	be	VBP
cord-191574-1g38scnj	70	13	obtained	obtain	VBN
cord-191574-1g38scnj	70	14	,	,	,
cord-191574-1g38scnj	70	15	by	by	IN
cord-191574-1g38scnj	70	16	using	use	VBG
cord-191574-1g38scnj	70	17	the	the	DT
cord-191574-1g38scnj	70	18	Adomian	Adomian	NNP
cord-191574-1g38scnj	70	19	and	and	CC
cord-191574-1g38scnj	70	20	the	the	DT
cord-191574-1g38scnj	70	21	Laplace	Laplace	NNP
cord-191574-1g38scnj	70	22	-	-	HYPH
cord-191574-1g38scnj	70	23	Adomian	Adomian	NNP
cord-191574-1g38scnj	70	24	Decomposition	decomposition	NN
cord-191574-1g38scnj	70	25	Methods	Methods	NNPS
cord-191574-1g38scnj	70	26	in	in	IN
cord-191574-1g38scnj	70	27	Section	section	NN
cord-191574-1g38scnj	70	28	III	III	NNP
cord-191574-1g38scnj	70	29	.	.	.
cord-191574-1g38scnj	71	1	The	the	DT
cord-191574-1g38scnj	71	2	comparison	comparison	NN
cord-191574-1g38scnj	71	3	with	with	IN
cord-191574-1g38scnj	71	4	the	the	DT
cord-191574-1g38scnj	71	5	exact	exact	JJ
cord-191574-1g38scnj	71	6	numerical	numerical	JJ
cord-191574-1g38scnj	71	7	solutions	solution	NNS
cord-191574-1g38scnj	71	8	is	be	VBZ
cord-191574-1g38scnj	71	9	performed	perform	VBN
cord-191574-1g38scnj	71	10	in	in	IN
cord-191574-1g38scnj	71	11	Section	Section	NNP
cord-191574-1g38scnj	71	12	IV	IV	NNP
cord-191574-1g38scnj	71	13	.	.	.
cord-191574-1g38scnj	72	1	We	-PRON-	PRP
cord-191574-1g38scnj	72	2	discuss	discuss	VBP
cord-191574-1g38scnj	72	3	and	and	CC
cord-191574-1g38scnj	72	4	conclude	conclude	VBP
cord-191574-1g38scnj	72	5	our	-PRON-	PRP$
cord-191574-1g38scnj	72	6	results	result	NNS
cord-191574-1g38scnj	72	7	in	in	IN
cord-191574-1g38scnj	72	8	Section	section	NN
cord-191574-1g38scnj	72	9	V.	V.	NNP
cord-191574-1g38scnj	73	1	In	in	IN
cord-191574-1g38scnj	73	2	the	the	DT
cord-191574-1g38scnj	73	3	present	present	JJ
cord-191574-1g38scnj	73	4	Section	section	NN
cord-191574-1g38scnj	73	5	we	-PRON-	PRP
cord-191574-1g38scnj	73	6	will	will	MD
cord-191574-1g38scnj	73	7	obtain	obtain	VB
cord-191574-1g38scnj	73	8	the	the	DT
cord-191574-1g38scnj	73	9	basic	basic	JJ
cord-191574-1g38scnj	73	10	equation	equation	NN
cord-191574-1g38scnj	73	11	describing	describe	VBG
cord-191574-1g38scnj	73	12	the	the	DT
cord-191574-1g38scnj	73	13	dynamics	dynamic	NNS
cord-191574-1g38scnj	73	14	of	of	IN
cord-191574-1g38scnj	73	15	the	the	DT
cord-191574-1g38scnj	73	16	SIR	SIR	NNP
cord-191574-1g38scnj	73	17	model	model	NN
cord-191574-1g38scnj	73	18	with	with	IN
cord-191574-1g38scnj	73	19	vital	vital	JJ
cord-191574-1g38scnj	73	20	dynamics	dynamic	NNS
cord-191574-1g38scnj	73	21	.	.	.
cord-191574-1g38scnj	74	1	Then	then	RB
cord-191574-1g38scnj	74	2	,	,	,
cord-191574-1g38scnj	74	3	by	by	IN
cord-191574-1g38scnj	74	4	using	use	VBG
cord-191574-1g38scnj	74	5	this	this	DT
cord-191574-1g38scnj	74	6	equation	equation	NN
cord-191574-1g38scnj	74	7	,	,	,
cord-191574-1g38scnj	74	8	we	-PRON-	PRP
cord-191574-1g38scnj	74	9	will	will	MD
cord-191574-1g38scnj	74	10	obtain	obtain	VB
cord-191574-1g38scnj	74	11	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	74	12	,	,	,
cord-191574-1g38scnj	74	13	but	but	CC
cord-191574-1g38scnj	74	14	still	still	RB
cord-191574-1g38scnj	74	15	having	have	VBG
cord-191574-1g38scnj	74	16	a	a	DT
cord-191574-1g38scnj	74	17	high	high	JJ
cord-191574-1g38scnj	74	18	numerical	numerical	JJ
cord-191574-1g38scnj	74	19	precision	precision	NN
cord-191574-1g38scnj	74	20	,	,	,
cord-191574-1g38scnj	74	21	solutions	solution	NNS
cord-191574-1g38scnj	74	22	of	of	IN
cord-191574-1g38scnj	74	23	the	the	DT
cord-191574-1g38scnj	74	24	SIR	SIR	NNP
cord-191574-1g38scnj	74	25	model	model	NN
cord-191574-1g38scnj	74	26	with	with	IN
cord-191574-1g38scnj	74	27	vital	vital	JJ
cord-191574-1g38scnj	74	28	dynamics	dynamic	NNS
cord-191574-1g38scnj	74	29	,	,	,
cord-191574-1g38scnj	74	30	represented	represent	VBN
cord-191574-1g38scnj	74	31	in	in	IN
cord-191574-1g38scnj	74	32	the	the	DT
cord-191574-1g38scnj	74	33	forms	form	NNS
cord-191574-1g38scnj	74	34	of	of	IN
cord-191574-1g38scnj	74	35	Adomian	adomian	JJ
cord-191574-1g38scnj	74	36	type	type	NN
cord-191574-1g38scnj	74	37	series	series	NN
cord-191574-1g38scnj	74	38	,	,	,
cord-191574-1g38scnj	74	39	containing	contain	VBG
cord-191574-1g38scnj	74	40	exponential	exponential	JJ
cord-191574-1g38scnj	74	41	terms	term	NNS
cord-191574-1g38scnj	74	42	.	.	.
cord-191574-1g38scnj	75	1	The	the	DT
cord-191574-1g38scnj	75	2	strongly	strongly	RB
cord-191574-1g38scnj	75	3	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	75	4	system	system	NN
cord-191574-1g38scnj	75	5	of	of	IN
cord-191574-1g38scnj	75	6	equations	equation	NNS
cord-191574-1g38scnj	75	7	describing	describe	VBG
cord-191574-1g38scnj	75	8	the	the	DT
cord-191574-1g38scnj	75	9	SIR	SIR	NNP
cord-191574-1g38scnj	75	10	model	model	NN
cord-191574-1g38scnj	75	11	with	with	IN
cord-191574-1g38scnj	75	12	vital	vital	JJ
cord-191574-1g38scnj	75	13	dynamics	dynamic	NNS
cord-191574-1g38scnj	75	14	is	be	VBZ
cord-191574-1g38scnj	75	15	given	give	VBN
cord-191574-1g38scnj	75	16	by	by	IN
cord-191574-1g38scnj	75	17	[	[	-LRB-
cord-191574-1g38scnj	75	18	1	1	CD
cord-191574-1g38scnj	75	19	,	,	,
cord-191574-1g38scnj	75	20	2	2	CD
cord-191574-1g38scnj	75	21	,	,	,
cord-191574-1g38scnj	75	22	4	4	CD
cord-191574-1g38scnj	75	23	,	,	,
cord-191574-1g38scnj	75	24	6	6	CD
cord-191574-1g38scnj	75	25	]	]	-RRB-
cord-191574-1g38scnj	75	26	,	,	,
cord-191574-1g38scnj	75	27	where	where	WRB
cord-191574-1g38scnj	75	28	x(t	x(t	NNP
cord-191574-1g38scnj	75	29	)	)	-RRB-
cord-191574-1g38scnj	76	1	>	>	XX
cord-191574-1g38scnj	76	2	0	0	CD
cord-191574-1g38scnj	76	3	,	,	,
cord-191574-1g38scnj	76	4	y(t	y(t	NN
cord-191574-1g38scnj	76	5	)	)	-RRB-
cord-191574-1g38scnj	76	6	>	>	NFP
cord-191574-1g38scnj	76	7	0	0	NFP
cord-191574-1g38scnj	76	8	and	and	CC
cord-191574-1g38scnj	76	9	z(t	z(t	CD
cord-191574-1g38scnj	76	10	)	)	-RRB-
cord-191574-1g38scnj	77	1	>	>	XX
cord-191574-1g38scnj	77	2	0	0	CD
cord-191574-1g38scnj	77	3	,	,	,
cord-191574-1g38scnj	77	4	∀t	∀t	NNP
cord-191574-1g38scnj	77	5	≥	≥	CD
cord-191574-1g38scnj	77	6	0	0	NNP
cord-191574-1g38scnj	77	7	.	.	.
cord-191574-1g38scnj	78	1	The	the	DT
cord-191574-1g38scnj	78	2	system	system	NN
cord-191574-1g38scnj	78	3	of	of	IN
cord-191574-1g38scnj	78	4	strongly	strongly	RB
cord-191574-1g38scnj	78	5	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	78	6	differential	differential	JJ
cord-191574-1g38scnj	78	7	equations	equation	NNS
cord-191574-1g38scnj	78	8	(	(	-LRB-
cord-191574-1g38scnj	78	9	3)-(5	3)-(5	CD
cord-191574-1g38scnj	78	10	)	)	-RRB-
cord-191574-1g38scnj	78	11	must	must	MD
cord-191574-1g38scnj	78	12	be	be	VB
cord-191574-1g38scnj	78	13	integrated	integrate	VBN
cord-191574-1g38scnj	78	14	with	with	IN
cord-191574-1g38scnj	78	15	the	the	DT
cord-191574-1g38scnj	78	16	initial	initial	JJ
cord-191574-1g38scnj	78	17	conditions	condition	NNS
cord-191574-1g38scnj	78	18	The	the	DT
cord-191574-1g38scnj	78	19	time	time	NN
cord-191574-1g38scnj	78	20	evolution	evolution	NN
cord-191574-1g38scnj	78	21	of	of	IN
cord-191574-1g38scnj	78	22	the	the	DT
cord-191574-1g38scnj	78	23	model	model	NN
cord-191574-1g38scnj	78	24	is	be	VBZ
cord-191574-1g38scnj	78	25	determined	determine	VBN
cord-191574-1g38scnj	78	26	by	by	IN
cord-191574-1g38scnj	78	27	three	three	CD
cord-191574-1g38scnj	78	28	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	78	29	parameters	parameter	NNS
cord-191574-1g38scnj	78	30	,	,	,
cord-191574-1g38scnj	78	31	the	the	DT
cord-191574-1g38scnj	78	32	infection	infection	NN
cord-191574-1g38scnj	78	33	rate	rate	NN
cord-191574-1g38scnj	78	34	β	β	NN
cord-191574-1g38scnj	78	35	,	,	,
cord-191574-1g38scnj	78	36	the	the	DT
cord-191574-1g38scnj	78	37	mean	mean	JJ
cord-191574-1g38scnj	78	38	recovery	recovery	NN
cord-191574-1g38scnj	78	39	rate	rate	NN
cord-191574-1g38scnj	78	40	γ	γ	NN
cord-191574-1g38scnj	78	41	,	,	,
cord-191574-1g38scnj	78	42	and	and	CC
cord-191574-1g38scnj	78	43	µ	µ	NN
cord-191574-1g38scnj	78	44	,	,	,
cord-191574-1g38scnj	78	45	representing	represent	VBG
cord-191574-1g38scnj	78	46	the	the	DT
cord-191574-1g38scnj	78	47	natural	natural	JJ
cord-191574-1g38scnj	78	48	death	death	NN
cord-191574-1g38scnj	78	49	rate	rate	NN
cord-191574-1g38scnj	78	50	,	,	,
cord-191574-1g38scnj	78	51	which	which	WDT
cord-191574-1g38scnj	78	52	in	in	IN
cord-191574-1g38scnj	78	53	the	the	DT
cord-191574-1g38scnj	78	54	present	present	JJ
cord-191574-1g38scnj	78	55	investigation	investigation	NN
cord-191574-1g38scnj	78	56	is	be	VBZ
cord-191574-1g38scnj	78	57	assumed	assume	VBN
cord-191574-1g38scnj	78	58	to	to	TO
cord-191574-1g38scnj	78	59	be	be	VB
cord-191574-1g38scnj	78	60	equal	equal	JJ
cord-191574-1g38scnj	78	61	to	to	IN
cord-191574-1g38scnj	78	62	the	the	DT
cord-191574-1g38scnj	78	63	birth	birth	NN
cord-191574-1g38scnj	78	64	rate	rate	NN
cord-191574-1g38scnj	78	65	.	.	.
cord-191574-1g38scnj	79	1	In	in	IN
cord-191574-1g38scnj	79	2	the	the	DT
cord-191574-1g38scnj	79	3	following	follow	VBG
cord-191574-1g38scnj	79	4	β	β	NN
cord-191574-1g38scnj	79	5	,	,	,
cord-191574-1g38scnj	79	6	γ	γ	NN
cord-191574-1g38scnj	79	7	,	,	,
cord-191574-1g38scnj	79	8	and	and	CC
cord-191574-1g38scnj	79	9	µ	µ	NNS
cord-191574-1g38scnj	79	10	are	be	VBP
cord-191574-1g38scnj	79	11	assumed	assume	VBN
cord-191574-1g38scnj	79	12	to	to	TO
cord-191574-1g38scnj	79	13	be	be	VB
cord-191574-1g38scnj	79	14	positive	positive	JJ
cord-191574-1g38scnj	79	15	constants	constant	NNS
cord-191574-1g38scnj	79	16	.	.	.
cord-191574-1g38scnj	80	1	By	by	IN
cord-191574-1g38scnj	80	2	adding	add	VBG
cord-191574-1g38scnj	80	3	Eqs	Eqs	NNP
cord-191574-1g38scnj	80	4	.	.	.
cord-191574-1g38scnj	81	1	(	(	-LRB-
cord-191574-1g38scnj	81	2	3)-(5	3)-(5	CD
cord-191574-1g38scnj	81	3	)	)	-RRB-
cord-191574-1g38scnj	81	4	,	,	,
cord-191574-1g38scnj	81	5	and	and	CC
cord-191574-1g38scnj	81	6	integrating	integrate	VBG
cord-191574-1g38scnj	81	7	the	the	DT
cord-191574-1g38scnj	81	8	resulting	result	VBG
cord-191574-1g38scnj	81	9	equation	equation	NN
cord-191574-1g38scnj	81	10	we	-PRON-	PRP
cord-191574-1g38scnj	81	11	immediately	immediately	RB
cord-191574-1g38scnj	81	12	obtain	obtain	VBP
cord-191574-1g38scnj	81	13	where	where	WRB
cord-191574-1g38scnj	81	14	N	n	NN
cord-191574-1g38scnj	81	15	0	0	CD
cord-191574-1g38scnj	81	16	is	be	VBZ
cord-191574-1g38scnj	81	17	an	an	DT
cord-191574-1g38scnj	81	18	arbitrary	arbitrary	JJ
cord-191574-1g38scnj	81	19	integration	integration	NN
cord-191574-1g38scnj	81	20	constant	constant	NN
cord-191574-1g38scnj	81	21	.	.	.
cord-191574-1g38scnj	82	1	In	in	IN
cord-191574-1g38scnj	82	2	order	order	NN
cord-191574-1g38scnj	82	3	to	to	TO
cord-191574-1g38scnj	82	4	assure	assure	VB
cord-191574-1g38scnj	82	5	that	that	IN
cord-191574-1g38scnj	82	6	the	the	DT
cord-191574-1g38scnj	82	7	total	total	JJ
cord-191574-1g38scnj	82	8	number	number	NN
cord-191574-1g38scnj	82	9	of	of	IN
cord-191574-1g38scnj	82	10	individuals	individual	NNS
cord-191574-1g38scnj	82	11	in	in	IN
cord-191574-1g38scnj	82	12	the	the	DT
cord-191574-1g38scnj	82	13	group	group	NN
cord-191574-1g38scnj	82	14	is	be	VBZ
cord-191574-1g38scnj	82	15	a	a	DT
cord-191574-1g38scnj	82	16	constant	constant	NN
cord-191574-1g38scnj	82	17	,	,	,
cord-191574-1g38scnj	82	18	we	-PRON-	PRP
cord-191574-1g38scnj	82	19	must	must	MD
cord-191574-1g38scnj	82	20	fix	fix	VB
cord-191574-1g38scnj	82	21	the	the	DT
cord-191574-1g38scnj	82	22	integration	integration	NN
cord-191574-1g38scnj	82	23	constant	constant	JJ
cord-191574-1g38scnj	82	24	N	n	CD
cord-191574-1g38scnj	82	25	0	0	CD
cord-191574-1g38scnj	82	26	as	as	IN
cord-191574-1g38scnj	82	27	zero	zero	CD
cord-191574-1g38scnj	82	28	,	,	,
cord-191574-1g38scnj	82	29	N	n	CD
cord-191574-1g38scnj	82	30	0	0	CD
cord-191574-1g38scnj	82	31	=	=	SYM
cord-191574-1g38scnj	82	32	0	0	CD
cord-191574-1g38scnj	82	33	.	.	.
cord-191574-1g38scnj	83	1	In	in	IN
cord-191574-1g38scnj	83	2	the	the	DT
cord-191574-1g38scnj	83	3	following	following	NN
cord-191574-1g38scnj	83	4	,	,	,
cord-191574-1g38scnj	83	5	in	in	IN
cord-191574-1g38scnj	83	6	order	order	NN
cord-191574-1g38scnj	83	7	to	to	TO
cord-191574-1g38scnj	83	8	significantly	significantly	RB
cord-191574-1g38scnj	83	9	simplify	simplify	VB
cord-191574-1g38scnj	83	10	the	the	DT
cord-191574-1g38scnj	83	11	mathematical	mathematical	JJ
cord-191574-1g38scnj	83	12	formalism	formalism	NN
cord-191574-1g38scnj	83	13	we	-PRON-	PRP
cord-191574-1g38scnj	83	14	introduce	introduce	VBP
cord-191574-1g38scnj	83	15	first	first	RB
cord-191574-1g38scnj	83	16	a	a	DT
cord-191574-1g38scnj	83	17	new	new	JJ
cord-191574-1g38scnj	83	18	function	function	NN
cord-191574-1g38scnj	83	19	u(t	u(t	NNP
cord-191574-1g38scnj	83	20	)	)	-RRB-
cord-191574-1g38scnj	83	21	,	,	,
cord-191574-1g38scnj	83	22	related	relate	VBN
cord-191574-1g38scnj	83	23	to	to	IN
cord-191574-1g38scnj	83	24	y(t	y(t	NN
cord-191574-1g38scnj	83	25	)	)	-RRB-
cord-191574-1g38scnj	83	26	by	by	IN
cord-191574-1g38scnj	83	27	and	and	CC
cord-191574-1g38scnj	83	28	which	which	WDT
cord-191574-1g38scnj	83	29	satisfies	satisfy	VBZ
cord-191574-1g38scnj	83	30	the	the	DT
cord-191574-1g38scnj	83	31	initial	initial	JJ
cord-191574-1g38scnj	83	32	condition	condition	NN
cord-191574-1g38scnj	83	33	and	and	CC
cord-191574-1g38scnj	83	34	thus	thus	RB
cord-191574-1g38scnj	83	35	obviously	obviously	RB
cord-191574-1g38scnj	83	36	giving	give	VBG
cord-191574-1g38scnj	83	37	y(0	y(0	NNP
cord-191574-1g38scnj	83	38	)	)	-RRB-
cord-191574-1g38scnj	83	39	=	=	SYM
cord-191574-1g38scnj	83	40	N	n	CD
cord-191574-1g38scnj	83	41	2	2	CD
cord-191574-1g38scnj	83	42	.	.	.
cord-191574-1g38scnj	84	1	Then	then	RB
cord-191574-1g38scnj	84	2	from	from	IN
cord-191574-1g38scnj	84	3	Eq	Eq	NNP
cord-191574-1g38scnj	84	4	.	.	.
cord-191574-1g38scnj	85	1	(	(	-LRB-
cord-191574-1g38scnj	85	2	4	4	LS
cord-191574-1g38scnj	85	3	)	)	-RRB-
cord-191574-1g38scnj	85	4	we	-PRON-	PRP
cord-191574-1g38scnj	85	5	obtain	obtain	VBP
cord-191574-1g38scnj	85	6	for	for	IN
cord-191574-1g38scnj	85	7	x(t	x(t	NNP
cord-191574-1g38scnj	85	8	)	)	-RRB-
cord-191574-1g38scnj	86	1	the	the	DT
cord-191574-1g38scnj	86	2	simple	simple	JJ
cord-191574-1g38scnj	86	3	expression	expression	NN
cord-191574-1g38scnj	86	4	By	by	IN
cord-191574-1g38scnj	86	5	substituting	substitute	VBG
cord-191574-1g38scnj	86	6	Eqs	Eqs	NNP
cord-191574-1g38scnj	86	7	.	.	.
cord-191574-1g38scnj	87	1	(	(	-LRB-
cord-191574-1g38scnj	87	2	8)	8)	NNP
cord-191574-1g38scnj	87	3	and	and	CC
cord-191574-1g38scnj	87	4	(	(	-LRB-
cord-191574-1g38scnj	87	5	10	10	CD
cord-191574-1g38scnj	87	6	)	)	-RRB-
cord-191574-1g38scnj	87	7	into	into	IN
cord-191574-1g38scnj	87	8	Eq	Eq	NNP
cord-191574-1g38scnj	87	9	.	.	.
cord-191574-1g38scnj	88	1	(	(	-LRB-
cord-191574-1g38scnj	88	2	3	3	LS
cord-191574-1g38scnj	88	3	)	)	-RRB-
cord-191574-1g38scnj	88	4	,	,	,
cord-191574-1g38scnj	88	5	the	the	DT
cord-191574-1g38scnj	88	6	latter	latter	NN
cord-191574-1g38scnj	88	7	becomes	become	VBZ
cord-191574-1g38scnj	88	8	Eq	Eq	NNP
cord-191574-1g38scnj	88	9	.	.	.
cord-191574-1g38scnj	89	1	(	(	-LRB-
cord-191574-1g38scnj	89	2	11	11	CD
cord-191574-1g38scnj	89	3	)	)	-RRB-
cord-191574-1g38scnj	89	4	can	can	MD
cord-191574-1g38scnj	89	5	be	be	VB
cord-191574-1g38scnj	89	6	reformulated	reformulate	VBN
cord-191574-1g38scnj	89	7	as	as	IN
cord-191574-1g38scnj	89	8	Eq	Eq	NNP
cord-191574-1g38scnj	89	9	.	.	.
cord-191574-1g38scnj	90	1	(	(	-LRB-
cord-191574-1g38scnj	90	2	12	12	CD
cord-191574-1g38scnj	90	3	)	)	-RRB-
cord-191574-1g38scnj	90	4	represents	represent	VBZ
cord-191574-1g38scnj	90	5	the	the	DT
cord-191574-1g38scnj	90	6	basic	basic	JJ
cord-191574-1g38scnj	90	7	dynamical	dynamical	JJ
cord-191574-1g38scnj	90	8	evolution	evolution	NN
cord-191574-1g38scnj	90	9	equation	equation	NN
cord-191574-1g38scnj	90	10	of	of	IN
cord-191574-1g38scnj	90	11	the	the	DT
cord-191574-1g38scnj	90	12	SIR	SIR	NNP
cord-191574-1g38scnj	90	13	model	model	NN
cord-191574-1g38scnj	90	14	with	with	IN
cord-191574-1g38scnj	90	15	vital	vital	JJ
cord-191574-1g38scnj	90	16	dynamics	dynamic	NNS
cord-191574-1g38scnj	90	17	.	.	.
cord-191574-1g38scnj	91	1	It	-PRON-	PRP
cord-191574-1g38scnj	91	2	must	must	MD
cord-191574-1g38scnj	91	3	be	be	VB
cord-191574-1g38scnj	91	4	solved	solve	VBN
cord-191574-1g38scnj	91	5	with	with	IN
cord-191574-1g38scnj	91	6	the	the	DT
cord-191574-1g38scnj	91	7	initial	initial	JJ
cord-191574-1g38scnj	91	8	conditions	condition	NNS
cord-191574-1g38scnj	91	9	By	by	IN
cord-191574-1g38scnj	91	10	representing	represent	VBG
cord-191574-1g38scnj	91	11	z(t	z(t	CD
cord-191574-1g38scnj	91	12	)	)	-RRB-
cord-191574-1g38scnj	91	13	as	as	IN
cord-191574-1g38scnj	91	14	Eq	Eq	NNP
cord-191574-1g38scnj	91	15	.	.	.
cord-191574-1g38scnj	92	1	(	(	-LRB-
cord-191574-1g38scnj	92	2	5	5	LS
cord-191574-1g38scnj	92	3	)	)	-RRB-
cord-191574-1g38scnj	92	4	becomes	become	VBZ
cord-191574-1g38scnj	92	5	giving	giving	NN
cord-191574-1g38scnj	92	6	and	and	CC
cord-191574-1g38scnj	92	7	respectively	respectively	RB
cord-191574-1g38scnj	92	8	,	,	,
cord-191574-1g38scnj	92	9	where	where	WRB
cord-191574-1g38scnj	92	10	we	-PRON-	PRP
cord-191574-1g38scnj	92	11	have	have	VBP
cord-191574-1g38scnj	92	12	used	use	VBN
cord-191574-1g38scnj	92	13	the	the	DT
cord-191574-1g38scnj	92	14	condition	condition	NN
cord-191574-1g38scnj	92	15	w(0	w(0	VBN
cord-191574-1g38scnj	92	16	)	)	-RRB-
cord-191574-1g38scnj	92	17	=	=	NFP
cord-191574-1g38scnj	93	1	z(0	z(0	LS
cord-191574-1g38scnj	93	2	)	)	-RRB-
cord-191574-1g38scnj	94	1	=	=	SYM
cord-191574-1g38scnj	94	2	N	N	NNP
cord-191574-1g38scnj	94	3	3	3	CD
cord-191574-1g38scnj	94	4	.	.	.
cord-191574-1g38scnj	95	1	The	the	DT
cord-191574-1g38scnj	95	2	general	general	JJ
cord-191574-1g38scnj	95	3	solution	solution	NN
cord-191574-1g38scnj	95	4	of	of	IN
cord-191574-1g38scnj	95	5	Eq	Eq	NNP
cord-191574-1g38scnj	95	6	.	.	.
cord-191574-1g38scnj	96	1	(	(	-LRB-
cord-191574-1g38scnj	96	2	12	12	CD
cord-191574-1g38scnj	96	3	)	)	-RRB-
cord-191574-1g38scnj	96	4	can	can	MD
cord-191574-1g38scnj	96	5	not	not	RB
cord-191574-1g38scnj	96	6	be	be	VB
cord-191574-1g38scnj	96	7	obtained	obtain	VBN
cord-191574-1g38scnj	96	8	in	in	IN
cord-191574-1g38scnj	96	9	a	a	DT
cord-191574-1g38scnj	96	10	closed	closed	JJ
cord-191574-1g38scnj	96	11	(	(	-LRB-
cord-191574-1g38scnj	96	12	exact	exact	JJ
cord-191574-1g38scnj	96	13	)	)	-RRB-
cord-191574-1g38scnj	96	14	form	form	NN
cord-191574-1g38scnj	96	15	.	.	.
cord-191574-1g38scnj	97	1	In	in	IN
cord-191574-1g38scnj	97	2	the	the	DT
cord-191574-1g38scnj	97	3	present	present	JJ
cord-191574-1g38scnj	97	4	Section	section	NN
cord-191574-1g38scnj	97	5	we	-PRON-	PRP
cord-191574-1g38scnj	97	6	will	will	MD
cord-191574-1g38scnj	97	7	consider	consider	VB
cord-191574-1g38scnj	97	8	the	the	DT
cord-191574-1g38scnj	97	9	applications	application	NNS
cord-191574-1g38scnj	97	10	of	of	IN
cord-191574-1g38scnj	97	11	the	the	DT
cord-191574-1g38scnj	97	12	Adomian	adomian	JJ
cord-191574-1g38scnj	97	13	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	97	14	Method	Method	NNP
cord-191574-1g38scnj	97	15	for	for	IN
cord-191574-1g38scnj	97	16	the	the	DT
cord-191574-1g38scnj	97	17	study	study	NN
cord-191574-1g38scnj	97	18	of	of	IN
cord-191574-1g38scnj	97	19	the	the	DT
cord-191574-1g38scnj	97	20	SIR	SIR	NNP
cord-191574-1g38scnj	97	21	model	model	NN
cord-191574-1g38scnj	97	22	with	with	IN
cord-191574-1g38scnj	97	23	vital	vital	JJ
cord-191574-1g38scnj	97	24	dynamics	dynamic	NNS
cord-191574-1g38scnj	97	25	.	.	.
cord-191574-1g38scnj	98	1	In	in	IN
cord-191574-1g38scnj	98	2	order	order	NN
cord-191574-1g38scnj	98	3	to	to	TO
cord-191574-1g38scnj	98	4	obtain	obtain	VB
cord-191574-1g38scnj	98	5	a	a	DT
cord-191574-1g38scnj	98	6	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	98	7	solution	solution	NN
cord-191574-1g38scnj	98	8	of	of	IN
cord-191574-1g38scnj	98	9	the	the	DT
cord-191574-1g38scnj	98	10	model	model	NN
cord-191574-1g38scnj	98	11	we	-PRON-	PRP
cord-191574-1g38scnj	98	12	will	will	MD
cord-191574-1g38scnj	98	13	consider	consider	VB
cord-191574-1g38scnj	98	14	first	first	RB
cord-191574-1g38scnj	98	15	the	the	DT
cord-191574-1g38scnj	98	16	solution	solution	NN
cord-191574-1g38scnj	98	17	of	of	IN
cord-191574-1g38scnj	98	18	the	the	DT
cord-191574-1g38scnj	98	19	basic	basic	JJ
cord-191574-1g38scnj	98	20	evolution	evolution	NN
cord-191574-1g38scnj	98	21	equation	equation	NN
cord-191574-1g38scnj	98	22	(	(	-LRB-
cord-191574-1g38scnj	98	23	12	12	CD
cord-191574-1g38scnj	98	24	)	)	-RRB-
cord-191574-1g38scnj	98	25	by	by	IN
cord-191574-1g38scnj	98	26	obtaining	obtain	VBG
cord-191574-1g38scnj	98	27	the	the	DT
cord-191574-1g38scnj	98	28	Adomian	adomian	JJ
cord-191574-1g38scnj	98	29	type	type	NN
cord-191574-1g38scnj	98	30	recursive	recursive	JJ
cord-191574-1g38scnj	98	31	relations	relation	NNS
cord-191574-1g38scnj	98	32	for	for	IN
cord-191574-1g38scnj	98	33	solving	solve	VBG
cord-191574-1g38scnj	98	34	Eq	Eq	NNP
cord-191574-1g38scnj	98	35	.	.	.
cord-191574-1g38scnj	99	1	(	(	-LRB-
cord-191574-1g38scnj	99	2	12	12	CD
cord-191574-1g38scnj	99	3	)	)	-RRB-
cord-191574-1g38scnj	99	4	in	in	IN
cord-191574-1g38scnj	99	5	both	both	CC
cord-191574-1g38scnj	99	6	the	the	DT
cord-191574-1g38scnj	99	7	standard	standard	JJ
cord-191574-1g38scnj	99	8	Adomian	Adomian	NNP
cord-191574-1g38scnj	99	9	as	as	RB
cord-191574-1g38scnj	99	10	well	well	RB
cord-191574-1g38scnj	99	11	as	as	IN
cord-191574-1g38scnj	99	12	in	in	IN
cord-191574-1g38scnj	99	13	the	the	DT
cord-191574-1g38scnj	99	14	Laplace	Laplace	NNP
cord-191574-1g38scnj	99	15	-	-	HYPH
cord-191574-1g38scnj	99	16	Adomian	Adomian	NNP
cord-191574-1g38scnj	99	17	Decomposition	decomposition	NN
cord-191574-1g38scnj	99	18	methods	method	NNS
cord-191574-1g38scnj	99	19	.	.	.
cord-191574-1g38scnj	100	1	We	-PRON-	PRP
cord-191574-1g38scnj	100	2	will	will	MD
cord-191574-1g38scnj	100	3	begin	begin	VB
cord-191574-1g38scnj	100	4	our	-PRON-	PRP$
cord-191574-1g38scnj	100	5	investigations	investigation	NNS
cord-191574-1g38scnj	100	6	of	of	IN
cord-191574-1g38scnj	100	7	Eq	Eq	NNP
cord-191574-1g38scnj	100	8	.	.	.
cord-191574-1g38scnj	101	1	(	(	-LRB-
cord-191574-1g38scnj	101	2	12	12	CD
cord-191574-1g38scnj	101	3	)	)	-RRB-
cord-191574-1g38scnj	101	4	by	by	IN
cord-191574-1g38scnj	101	5	applying	apply	VBG
cord-191574-1g38scnj	101	6	first	first	RB
cord-191574-1g38scnj	101	7	the	the	DT
cord-191574-1g38scnj	101	8	standard	standard	JJ
cord-191574-1g38scnj	101	9	Adomian	adomian	JJ
cord-191574-1g38scnj	101	10	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	101	11	Method	Method	NNP
cord-191574-1g38scnj	101	12	.	.	.
cord-191574-1g38scnj	102	1	We	-PRON-	PRP
cord-191574-1g38scnj	102	2	integrate	integrate	VBP
cord-191574-1g38scnj	102	3	Eq	Eq	NNP
cord-191574-1g38scnj	102	4	.	.	.
cord-191574-1g38scnj	103	1	(	(	-LRB-
cord-191574-1g38scnj	103	2	12	12	CD
cord-191574-1g38scnj	103	3	)	)	-RRB-
cord-191574-1g38scnj	103	4	between	between	IN
cord-191574-1g38scnj	103	5	0	0	CD
cord-191574-1g38scnj	103	6	and	and	CC
cord-191574-1g38scnj	103	7	t.	t.	NN
cord-191574-1g38scnj	104	1	With	with	IN
cord-191574-1g38scnj	104	2	the	the	DT
cord-191574-1g38scnj	104	3	use	use	NN
cord-191574-1g38scnj	104	4	of	of	IN
cord-191574-1g38scnj	104	5	the	the	DT
cord-191574-1g38scnj	104	6	initial	initial	JJ
cord-191574-1g38scnj	104	7	conditions	condition	NNS
cord-191574-1g38scnj	104	8	we	-PRON-	PRP
cord-191574-1g38scnj	104	9	obtain	obtain	VBP
cord-191574-1g38scnj	104	10	Again	again	RB
cord-191574-1g38scnj	104	11	we	-PRON-	PRP
cord-191574-1g38scnj	104	12	integrate	integrate	VBP
cord-191574-1g38scnj	104	13	Eq	Eq	NNP
cord-191574-1g38scnj	104	14	.	.	.
cord-191574-1g38scnj	105	1	(	(	-LRB-
cord-191574-1g38scnj	105	2	18	18	CD
cord-191574-1g38scnj	105	3	)	)	-RRB-
cord-191574-1g38scnj	105	4	between	between	IN
cord-191574-1g38scnj	105	5	0	0	CD
cord-191574-1g38scnj	105	6	and	and	CC
cord-191574-1g38scnj	105	7	t	t	NN
cord-191574-1g38scnj	105	8	to	to	TO
cord-191574-1g38scnj	105	9	find	find	VB
cord-191574-1g38scnj	105	10	Now	now	RB
cord-191574-1g38scnj	105	11	we	-PRON-	PRP
cord-191574-1g38scnj	105	12	will	will	MD
cord-191574-1g38scnj	105	13	apply	apply	VB
cord-191574-1g38scnj	105	14	the	the	DT
cord-191574-1g38scnj	105	15	Adomian	adomian	JJ
cord-191574-1g38scnj	105	16	Decomposition	decomposition	NN
cord-191574-1g38scnj	105	17	method	method	NN
cord-191574-1g38scnj	105	18	to	to	IN
cord-191574-1g38scnj	105	19	Eq	Eq	NNP
cord-191574-1g38scnj	105	20	.	.	.
cord-191574-1g38scnj	106	1	(	(	-LRB-
cord-191574-1g38scnj	106	2	19	19	CD
cord-191574-1g38scnj	106	3	)	)	-RRB-
cord-191574-1g38scnj	106	4	.	.	.
cord-191574-1g38scnj	107	1	For	for	IN
cord-191574-1g38scnj	107	2	this	this	DT
cord-191574-1g38scnj	107	3	we	-PRON-	PRP
cord-191574-1g38scnj	107	4	assume	assume	VBP
cord-191574-1g38scnj	107	5	and	and	CC
cord-191574-1g38scnj	107	6	where	where	WRB
cord-191574-1g38scnj	107	7	A	a	DT
cord-191574-1g38scnj	107	8	n	n	NN
cord-191574-1g38scnj	107	9	(	(	-LRB-
cord-191574-1g38scnj	107	10	t	t	NN
cord-191574-1g38scnj	107	11	)	)	-RRB-
cord-191574-1g38scnj	107	12	are	be	VBP
cord-191574-1g38scnj	107	13	the	the	DT
cord-191574-1g38scnj	107	14	Adomian	adomian	JJ
cord-191574-1g38scnj	107	15	polynomials	polynomial	NNS
cord-191574-1g38scnj	107	16	,	,	,
cord-191574-1g38scnj	107	17	defined	define	VBN
cord-191574-1g38scnj	107	18	for	for	IN
cord-191574-1g38scnj	107	19	an	an	DT
cord-191574-1g38scnj	107	20	arbitrary	arbitrary	JJ
cord-191574-1g38scnj	107	21	function	function	NN
cord-191574-1g38scnj	107	22	f	f	NN
cord-191574-1g38scnj	107	23	(	(	-LRB-
cord-191574-1g38scnj	107	24	u(t	u(t	NNP
cord-191574-1g38scnj	107	25	)	)	-RRB-
cord-191574-1g38scnj	107	26	)	)	-RRB-
cord-191574-1g38scnj	107	27	according	accord	VBG
cord-191574-1g38scnj	107	28	to	to	IN
cord-191574-1g38scnj	107	29	the	the	DT
cord-191574-1g38scnj	107	30	general	general	JJ
cord-191574-1g38scnj	107	31	formula	formula	NN
cord-191574-1g38scnj	107	32	[	[	-LRB-
cord-191574-1g38scnj	107	33	32	32	CD
cord-191574-1g38scnj	107	34	]	]	-RRB-
cord-191574-1g38scnj	107	35	Substituting	substitute	VBG
cord-191574-1g38scnj	107	36	Eqs	Eqs	NNP
cord-191574-1g38scnj	107	37	.	.	.
cord-191574-1g38scnj	108	1	(	(	-LRB-
cord-191574-1g38scnj	108	2	20	20	CD
cord-191574-1g38scnj	108	3	)	)	-RRB-
cord-191574-1g38scnj	108	4	and	and	CC
cord-191574-1g38scnj	108	5	(	(	-LRB-
cord-191574-1g38scnj	108	6	21	21	CD
cord-191574-1g38scnj	108	7	)	)	-RRB-
cord-191574-1g38scnj	108	8	into	into	IN
cord-191574-1g38scnj	108	9	Eq	Eq	NNP
cord-191574-1g38scnj	108	10	.	.	.
cord-191574-1g38scnj	109	1	(	(	-LRB-
cord-191574-1g38scnj	109	2	19	19	CD
cord-191574-1g38scnj	109	3	)	)	-RRB-
cord-191574-1g38scnj	109	4	we	-PRON-	PRP
cord-191574-1g38scnj	109	5	obtain	obtain	VBP
cord-191574-1g38scnj	109	6	Explicitly	explicitly	RB
cord-191574-1g38scnj	109	7	,	,	,
cord-191574-1g38scnj	109	8	we	-PRON-	PRP
cord-191574-1g38scnj	109	9	can	can	MD
cord-191574-1g38scnj	109	10	write	write	VB
cord-191574-1g38scnj	109	11	the	the	DT
cord-191574-1g38scnj	109	12	above	above	JJ
cord-191574-1g38scnj	109	13	equation	equation	NN
cord-191574-1g38scnj	109	14	as	as	IN
cord-191574-1g38scnj	109	15	Now	now	RB
cord-191574-1g38scnj	109	16	we	-PRON-	PRP
cord-191574-1g38scnj	109	17	take	take	VBP
cord-191574-1g38scnj	109	18	...	...	.
cord-191574-1g38scnj	110	1	Therefore	therefore	RB
cord-191574-1g38scnj	110	2	we	-PRON-	PRP
cord-191574-1g38scnj	110	3	have	have	VBP
cord-191574-1g38scnj	110	4	obtained	obtain	VBN
cord-191574-1g38scnj	110	5	the	the	DT
cord-191574-1g38scnj	110	6	iteration	iteration	NN
cord-191574-1g38scnj	111	1	Now	now	RB
cord-191574-1g38scnj	111	2	we	-PRON-	PRP
cord-191574-1g38scnj	111	3	can	can	MD
cord-191574-1g38scnj	111	4	use	use	VB
cord-191574-1g38scnj	111	5	the	the	DT
cord-191574-1g38scnj	111	6	Cauchy	Cauchy	NNP
cord-191574-1g38scnj	111	7	formula	formula	NN
cord-191574-1g38scnj	111	8	for	for	IN
cord-191574-1g38scnj	111	9	repeated	repeat	VBN
cord-191574-1g38scnj	111	10	integration	integration	NN
cord-191574-1g38scnj	111	11	,	,	,
cord-191574-1g38scnj	111	12	which	which	WDT
cord-191574-1g38scnj	111	13	gives	give	VBZ
cord-191574-1g38scnj	111	14	Thus	thus	RB
cord-191574-1g38scnj	111	15	Eq	Eq	NNP
cord-191574-1g38scnj	111	16	.	.	.
cord-191574-1g38scnj	112	1	(	(	-LRB-
cord-191574-1g38scnj	112	2	30	30	CD
cord-191574-1g38scnj	112	3	)	)	-RRB-
cord-191574-1g38scnj	112	4	becomes	become	VBZ
cord-191574-1g38scnj	112	5	In	in	IN
cord-191574-1g38scnj	112	6	the	the	DT
cord-191574-1g38scnj	112	7	following	following	NN
cord-191574-1g38scnj	112	8	we	-PRON-	PRP
cord-191574-1g38scnj	112	9	denote	denote	VBP
cord-191574-1g38scnj	113	1	Hence	hence	RB
cord-191574-1g38scnj	113	2	The	the	DT
cord-191574-1g38scnj	113	3	first	first	JJ
cord-191574-1g38scnj	113	4	Adomian	adomian	JJ
cord-191574-1g38scnj	113	5	polynomial	polynomial	NN
cord-191574-1g38scnj	113	6	is	be	VBZ
cord-191574-1g38scnj	113	7	given	give	VBN
cord-191574-1g38scnj	113	8	by	by	IN
cord-191574-1g38scnj	114	1	For	for	IN
cord-191574-1g38scnj	114	2	u	u	NNP
cord-191574-1g38scnj	114	3	1	1	CD
cord-191574-1g38scnj	114	4	(	(	-LRB-
cord-191574-1g38scnj	114	5	t	t	NN
cord-191574-1g38scnj	114	6	)	)	-RRB-
cord-191574-1g38scnj	114	7	we	-PRON-	PRP
cord-191574-1g38scnj	114	8	obtain	obtain	VBP
cord-191574-1g38scnj	115	1	where	where	WRB
cord-191574-1g38scnj	115	2	erf(z	erf(z	NNP
cord-191574-1g38scnj	115	3	)	)	-RRB-
cord-191574-1g38scnj	115	4	=	=	SYM
cord-191574-1g38scnj	115	5	2/	2/	CD
cord-191574-1g38scnj	115	6	√	√	NNP
cord-191574-1g38scnj	116	1	π	π	LS
cord-191574-1g38scnj	117	1	z	z	LS
cord-191574-1g38scnj	117	2	0	0	CD
cord-191574-1g38scnj	117	3	e	e	NN
cord-191574-1g38scnj	117	4	−t	−t	NNP
cord-191574-1g38scnj	117	5	2	2	CD
cord-191574-1g38scnj	117	6	dt	dt	NN
cord-191574-1g38scnj	117	7	is	be	VBZ
cord-191574-1g38scnj	117	8	the	the	DT
cord-191574-1g38scnj	117	9	error	error	NN
cord-191574-1g38scnj	117	10	function	function	NN
cord-191574-1g38scnj	117	11	.	.	.
cord-191574-1g38scnj	118	1	The	the	DT
cord-191574-1g38scnj	118	2	next	next	JJ
cord-191574-1g38scnj	118	3	term	term	NN
cord-191574-1g38scnj	118	4	u	u	NN
cord-191574-1g38scnj	118	5	2	2	CD
cord-191574-1g38scnj	118	6	can	can	MD
cord-191574-1g38scnj	118	7	not	not	RB
cord-191574-1g38scnj	118	8	be	be	VB
cord-191574-1g38scnj	118	9	obtained	obtain	VBN
cord-191574-1g38scnj	118	10	in	in	IN
cord-191574-1g38scnj	118	11	an	an	DT
cord-191574-1g38scnj	118	12	exact	exact	JJ
cord-191574-1g38scnj	118	13	form	form	NN
cord-191574-1g38scnj	118	14	,	,	,
cord-191574-1g38scnj	118	15	and	and	CC
cord-191574-1g38scnj	118	16	hence	hence	RB
cord-191574-1g38scnj	118	17	we	-PRON-	PRP
cord-191574-1g38scnj	118	18	will	will	MD
cord-191574-1g38scnj	118	19	not	not	RB
cord-191574-1g38scnj	118	20	present	present	VB
cord-191574-1g38scnj	118	21	it	-PRON-	PRP
cord-191574-1g38scnj	118	22	.	.	.
cord-191574-1g38scnj	119	1	In	in	IN
cord-191574-1g38scnj	119	2	the	the	DT
cord-191574-1g38scnj	119	3	following	following	NN
cord-191574-1g38scnj	119	4	we	-PRON-	PRP
cord-191574-1g38scnj	119	5	will	will	MD
cord-191574-1g38scnj	119	6	look	look	VB
cord-191574-1g38scnj	119	7	for	for	IN
cord-191574-1g38scnj	119	8	a	a	DT
cord-191574-1g38scnj	119	9	series	series	NN
cord-191574-1g38scnj	119	10	solution	solution	NN
cord-191574-1g38scnj	119	11	of	of	IN
cord-191574-1g38scnj	119	12	Eq	Eq	NNP
cord-191574-1g38scnj	119	13	.	.	.
cord-191574-1g38scnj	120	1	(	(	-LRB-
cord-191574-1g38scnj	120	2	12	12	CD
cord-191574-1g38scnj	120	3	)	)	-RRB-
cord-191574-1g38scnj	120	4	,	,	,
cord-191574-1g38scnj	120	5	by	by	IN
cord-191574-1g38scnj	120	6	using	use	VBG
cord-191574-1g38scnj	120	7	the	the	DT
cord-191574-1g38scnj	120	8	Laplace	Laplace	NNP
cord-191574-1g38scnj	120	9	-	-	HYPH
cord-191574-1g38scnj	120	10	Adomian	Adomian	NNP
cord-191574-1g38scnj	120	11	Decomposition	decomposition	NN
cord-191574-1g38scnj	120	12	Method	Method	NNP
cord-191574-1g38scnj	120	13	.	.	.
cord-191574-1g38scnj	121	1	In	in	IN
cord-191574-1g38scnj	121	2	the	the	DT
cord-191574-1g38scnj	121	3	Laplace	Laplace	NNP
cord-191574-1g38scnj	121	4	-	-	HYPH
cord-191574-1g38scnj	121	5	Adomian	Adomian	NNP
cord-191574-1g38scnj	121	6	Decomposition	decomposition	NN
cord-191574-1g38scnj	121	7	Method	Method	NNP
cord-191574-1g38scnj	121	8	we	-PRON-	PRP
cord-191574-1g38scnj	121	9	first	first	RB
cord-191574-1g38scnj	121	10	apply	apply	VBP
cord-191574-1g38scnj	121	11	the	the	DT
cord-191574-1g38scnj	121	12	Laplace	Laplace	NNP
cord-191574-1g38scnj	121	13	transformation	transformation	NN
cord-191574-1g38scnj	121	14	operator	operator	NN
cord-191574-1g38scnj	121	15	L	L	NNP
cord-191574-1g38scnj	121	16	x	x	NNP
cord-191574-1g38scnj	121	17	,	,	,
cord-191574-1g38scnj	121	18	defined	define	VBN
cord-191574-1g38scnj	121	19	as	as	IN
cord-191574-1g38scnj	121	20	By	by	IN
cord-191574-1g38scnj	121	21	using	use	VBG
cord-191574-1g38scnj	121	22	the	the	DT
cord-191574-1g38scnj	121	23	properties	property	NNS
cord-191574-1g38scnj	121	24	of	of	IN
cord-191574-1g38scnj	121	25	the	the	DT
cord-191574-1g38scnj	121	26	Laplace	Laplace	NNP
cord-191574-1g38scnj	121	27	transform	transform	NN
cord-191574-1g38scnj	121	28	,	,	,
cord-191574-1g38scnj	121	29	giving	give	VBG
cord-191574-1g38scnj	121	30	for	for	IN
cord-191574-1g38scnj	121	31	the	the	DT
cord-191574-1g38scnj	121	32	Laplace	Laplace	NNP
cord-191574-1g38scnj	121	33	transform	transform	NN
cord-191574-1g38scnj	121	34	of	of	IN
cord-191574-1g38scnj	121	35	u(t	u(t	NN
cord-191574-1g38scnj	121	36	)	)	-RRB-
cord-191574-1g38scnj	122	1	the	the	DT
cord-191574-1g38scnj	122	2	equation	equation	NN
cord-191574-1g38scnj	122	3	We	-PRON-	PRP
cord-191574-1g38scnj	122	4	assume	assume	VBP
cord-191574-1g38scnj	122	5	now	now	RB
cord-191574-1g38scnj	122	6	that	that	IN
cord-191574-1g38scnj	122	7	the	the	DT
cord-191574-1g38scnj	122	8	function	function	NN
cord-191574-1g38scnj	122	9	u(t	u(t	NN
cord-191574-1g38scnj	122	10	)	)	-RRB-
cord-191574-1g38scnj	122	11	can	can	MD
cord-191574-1g38scnj	122	12	be	be	VB
cord-191574-1g38scnj	122	13	represented	represent	VBN
cord-191574-1g38scnj	122	14	in	in	IN
cord-191574-1g38scnj	122	15	the	the	DT
cord-191574-1g38scnj	122	16	form	form	NN
cord-191574-1g38scnj	122	17	of	of	IN
cord-191574-1g38scnj	122	18	an	an	DT
cord-191574-1g38scnj	122	19	infinite	infinite	JJ
cord-191574-1g38scnj	122	20	series	series	NN
cord-191574-1g38scnj	122	21	,	,	,
cord-191574-1g38scnj	122	22	where	where	WRB
cord-191574-1g38scnj	122	23	all	all	PDT
cord-191574-1g38scnj	122	24	the	the	DT
cord-191574-1g38scnj	122	25	terms	term	NNS
cord-191574-1g38scnj	122	26	v	v	NNP
cord-191574-1g38scnj	122	27	n	n	NN
cord-191574-1g38scnj	122	28	(	(	-LRB-
cord-191574-1g38scnj	122	29	t	t	NNP
cord-191574-1g38scnj	122	30	)	)	-RRB-
cord-191574-1g38scnj	122	31	,	,	,
cord-191574-1g38scnj	122	32	n	n	NN
cord-191574-1g38scnj	122	33	=	=	SYM
cord-191574-1g38scnj	122	34	0	0	CD
cord-191574-1g38scnj	122	35	,	,	,
cord-191574-1g38scnj	122	36	1	1	CD
cord-191574-1g38scnj	122	37	,	,	,
cord-191574-1g38scnj	122	38	2	2	CD
cord-191574-1g38scnj	122	39	,	,	,
cord-191574-1g38scnj	122	40	...	...	:
cord-191574-1g38scnj	122	41	can	can	MD
cord-191574-1g38scnj	122	42	be	be	VB
cord-191574-1g38scnj	122	43	computed	compute	VBN
cord-191574-1g38scnj	122	44	recursively	recursively	RB
cord-191574-1g38scnj	122	45	.	.	.
cord-191574-1g38scnj	123	1	As	as	IN
cord-191574-1g38scnj	123	2	for	for	IN
cord-191574-1g38scnj	123	3	the	the	DT
cord-191574-1g38scnj	123	4	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	123	5	operator	operator	NN
cord-191574-1g38scnj	123	6	f	f	NNP
cord-191574-1g38scnj	123	7	(	(	-LRB-
cord-191574-1g38scnj	123	8	u(t	u(t	NNP
cord-191574-1g38scnj	123	9	)	)	-RRB-
cord-191574-1g38scnj	123	10	)	)	-RRB-
cord-191574-1g38scnj	124	1	=	=	NFP
cord-191574-1g38scnj	125	1	e	e	LS
cord-191574-1g38scnj	125	2	u(t	u(t	NNP
cord-191574-1g38scnj	125	3	)	)	-RRB-
cord-191574-1g38scnj	126	1	,	,	,
cord-191574-1g38scnj	126	2	we	-PRON-	PRP
cord-191574-1g38scnj	126	3	assume	assume	VBP
cord-191574-1g38scnj	126	4	that	that	IN
cord-191574-1g38scnj	126	5	it	-PRON-	PRP
cord-191574-1g38scnj	126	6	can	can	MD
cord-191574-1g38scnj	126	7	be	be	VB
cord-191574-1g38scnj	126	8	decomposed	decompose	VBN
cord-191574-1g38scnj	126	9	as	as	IN
cord-191574-1g38scnj	126	10	where	where	WRB
cord-191574-1g38scnj	126	11	A	a	DT
cord-191574-1g38scnj	126	12	n	n	NN
cord-191574-1g38scnj	126	13	(	(	-LRB-
cord-191574-1g38scnj	126	14	t	t	NN
cord-191574-1g38scnj	126	15	)	)	-RRB-
cord-191574-1g38scnj	126	16	are	be	VBP
cord-191574-1g38scnj	126	17	the	the	DT
cord-191574-1g38scnj	126	18	Adomian	adomian	JJ
cord-191574-1g38scnj	126	19	polynomials	polynomial	NNS
cord-191574-1g38scnj	126	20	,	,	,
cord-191574-1g38scnj	126	21	defined	define	VBN
cord-191574-1g38scnj	126	22	according	accord	VBG
cord-191574-1g38scnj	126	23	to	to	IN
cord-191574-1g38scnj	126	24	Eq	Eq	NNP
cord-191574-1g38scnj	126	25	.	.	.
cord-191574-1g38scnj	127	1	(	(	-LRB-
cord-191574-1g38scnj	127	2	22	22	CD
cord-191574-1g38scnj	127	3	)	)	-RRB-
cord-191574-1g38scnj	127	4	.	.	.
cord-191574-1g38scnj	128	1	The	the	DT
cord-191574-1g38scnj	128	2	first	first	JJ
cord-191574-1g38scnj	128	3	five	five	CD
cord-191574-1g38scnj	128	4	Adomian	adomian	JJ
cord-191574-1g38scnj	128	5	polynomials	polynomial	NNS
cord-191574-1g38scnj	128	6	can	can	MD
cord-191574-1g38scnj	128	7	be	be	VB
cord-191574-1g38scnj	128	8	obtained	obtain	VBN
cord-191574-1g38scnj	128	9	in	in	IN
cord-191574-1g38scnj	128	10	the	the	DT
cord-191574-1g38scnj	128	11	following	follow	VBG
cord-191574-1g38scnj	128	12	form	form	NN
cord-191574-1g38scnj	128	13	,	,	,
cord-191574-1g38scnj	128	14	Substituting	substitute	VBG
cord-191574-1g38scnj	128	15	Eqs	Eqs	NNP
cord-191574-1g38scnj	128	16	.	.	.
cord-191574-1g38scnj	129	1	(	(	-LRB-
cord-191574-1g38scnj	129	2	40	40	CD
cord-191574-1g38scnj	129	3	)	)	-RRB-
cord-191574-1g38scnj	129	4	and	and	CC
cord-191574-1g38scnj	129	5	(	(	-LRB-
cord-191574-1g38scnj	129	6	41	41	CD
cord-191574-1g38scnj	129	7	)	)	-RRB-
cord-191574-1g38scnj	129	8	into	into	IN
cord-191574-1g38scnj	129	9	Eq	Eq	NNP
cord-191574-1g38scnj	129	10	.	.	.
cord-191574-1g38scnj	130	1	(	(	-LRB-
cord-191574-1g38scnj	130	2	39	39	CD
cord-191574-1g38scnj	130	3	)	)	-RRB-
cord-191574-1g38scnj	130	4	we	-PRON-	PRP
cord-191574-1g38scnj	130	5	obtain	obtain	VBP
cord-191574-1g38scnj	130	6	The	the	DT
cord-191574-1g38scnj	130	7	matching	matching	NN
cord-191574-1g38scnj	130	8	of	of	IN
cord-191574-1g38scnj	130	9	both	both	DT
cord-191574-1g38scnj	130	10	sides	side	NNS
cord-191574-1g38scnj	130	11	of	of	IN
cord-191574-1g38scnj	130	12	Eq	Eq	NNP
cord-191574-1g38scnj	130	13	.	.	.
cord-191574-1g38scnj	131	1	(	(	-LRB-
cord-191574-1g38scnj	131	2	47	47	CD
cord-191574-1g38scnj	131	3	)	)	-RRB-
cord-191574-1g38scnj	131	4	gives	give	VBZ
cord-191574-1g38scnj	131	5	the	the	DT
cord-191574-1g38scnj	131	6	following	follow	VBG
cord-191574-1g38scnj	131	7	iterative	iterative	JJ
cord-191574-1g38scnj	131	8	algorithm	algorithm	NN
cord-191574-1g38scnj	131	9	for	for	IN
cord-191574-1g38scnj	131	10	obtaining	obtain	VBG
cord-191574-1g38scnj	131	11	the	the	DT
cord-191574-1g38scnj	131	12	power	power	NNP
cord-191574-1g38scnj	131	13	series	series	NN
cord-191574-1g38scnj	131	14	solution	solution	NN
cord-191574-1g38scnj	131	15	of	of	IN
cord-191574-1g38scnj	131	16	the	the	DT
cord-191574-1g38scnj	131	17	basic	basic	JJ
cord-191574-1g38scnj	131	18	evolution	evolution	NN
cord-191574-1g38scnj	131	19	equation	equation	NN
cord-191574-1g38scnj	131	20	of	of	IN
cord-191574-1g38scnj	131	21	the	the	DT
cord-191574-1g38scnj	131	22	SIR	SIR	NNP
cord-191574-1g38scnj	131	23	model	model	NN
cord-191574-1g38scnj	131	24	with	with	IN
cord-191574-1g38scnj	131	25	vital	vital	JJ
cord-191574-1g38scnj	131	26	dynamics	dynamic	NNS
cord-191574-1g38scnj	131	27	,	,	,
cord-191574-1g38scnj	131	28	...	...	:
cord-191574-1g38scnj	132	1	By	by	IN
cord-191574-1g38scnj	132	2	applying	apply	VBG
cord-191574-1g38scnj	132	3	the	the	DT
cord-191574-1g38scnj	132	4	inverse	inverse	JJ
cord-191574-1g38scnj	132	5	Laplace	Laplace	NNP
cord-191574-1g38scnj	132	6	transformation	transformation	NN
cord-191574-1g38scnj	132	7	to	to	IN
cord-191574-1g38scnj	132	8	Eq	Eq	NNP
cord-191574-1g38scnj	132	9	.	.	.
cord-191574-1g38scnj	133	1	(	(	-LRB-
cord-191574-1g38scnj	133	2	48	48	CD
cord-191574-1g38scnj	133	3	)	)	-RRB-
cord-191574-1g38scnj	133	4	,	,	,
cord-191574-1g38scnj	133	5	we	-PRON-	PRP
cord-191574-1g38scnj	133	6	obtain	obtain	VBP
cord-191574-1g38scnj	133	7	the	the	DT
cord-191574-1g38scnj	133	8	expression	expression	NN
cord-191574-1g38scnj	133	9	of	of	IN
cord-191574-1g38scnj	133	10	u	u	NNP
cord-191574-1g38scnj	133	11	0	0	CD
cord-191574-1g38scnj	133	12	(	(	-LRB-
cord-191574-1g38scnj	133	13	t	t	NN
cord-191574-1g38scnj	133	14	)	)	-RRB-
cord-191574-1g38scnj	133	15	as	as	IN
cord-191574-1g38scnj	133	16	We	-PRON-	PRP
cord-191574-1g38scnj	133	17	expand	expand	VBP
cord-191574-1g38scnj	133	18	the	the	DT
cord-191574-1g38scnj	133	19	term	term	NN
cord-191574-1g38scnj	133	20	(	(	-LRB-
cord-191574-1g38scnj	134	1	β	β	NNP
cord-191574-1g38scnj	134	2	N	N	NNP
cord-191574-1g38scnj	134	3	3	3	CD
cord-191574-1g38scnj	134	4	/µN	/µN	.
cord-191574-1g38scnj	134	5	)	)	-RRB-
cord-191574-1g38scnj	135	1	e	e	LS
cord-191574-1g38scnj	135	2	−µt	−µt	NN
cord-191574-1g38scnj	135	3	in	in	IN
cord-191574-1g38scnj	135	4	power	power	NN
cord-191574-1g38scnj	135	5	series	series	NN
cord-191574-1g38scnj	135	6	,	,	,
cord-191574-1g38scnj	135	7	and	and	CC
cord-191574-1g38scnj	135	8	hence	hence	RB
cord-191574-1g38scnj	135	9	in	in	IN
cord-191574-1g38scnj	135	10	the	the	DT
cord-191574-1g38scnj	135	11	first	first	JJ
cord-191574-1g38scnj	135	12	order	order	NN
cord-191574-1g38scnj	135	13	approximation	approximation	NN
cord-191574-1g38scnj	135	14	we	-PRON-	PRP
cord-191574-1g38scnj	135	15	obtain	obtain	VBP
cord-191574-1g38scnj	136	1	The	the	DT
cord-191574-1g38scnj	136	2	first	first	JJ
cord-191574-1g38scnj	136	3	Adomian	adomian	JJ
cord-191574-1g38scnj	136	4	polynomial	polynomial	NN
cord-191574-1g38scnj	136	5	is	be	VBZ
cord-191574-1g38scnj	136	6	given	give	VBN
cord-191574-1g38scnj	136	7	by	by	IN
cord-191574-1g38scnj	136	8	Therefore	therefore	RB
cord-191574-1g38scnj	136	9	,	,	,
cord-191574-1g38scnj	136	10	within	within	IN
cord-191574-1g38scnj	136	11	the	the	DT
cord-191574-1g38scnj	136	12	adopted	adopt	VBN
cord-191574-1g38scnj	136	13	approximation	approximation	NN
cord-191574-1g38scnj	136	14	,	,	,
cord-191574-1g38scnj	136	15	we	-PRON-	PRP
cord-191574-1g38scnj	136	16	immediately	immediately	RB
cord-191574-1g38scnj	136	17	obtain	obtain	VBP
cord-191574-1g38scnj	136	18	The	the	DT
cord-191574-1g38scnj	136	19	second	second	JJ
cord-191574-1g38scnj	136	20	Adomian	adomian	JJ
cord-191574-1g38scnj	136	21	polynomial	polynomial	NN
cord-191574-1g38scnj	136	22	is	be	VBZ
cord-191574-1g38scnj	136	23	obtained	obtain	VBN
cord-191574-1g38scnj	136	24	as	as	IN
cord-191574-1g38scnj	136	25	and	and	CC
cord-191574-1g38scnj	136	26	thus	thus	RB
cord-191574-1g38scnj	136	27	we	-PRON-	PRP
cord-191574-1g38scnj	136	28	find	find	VBP
cord-191574-1g38scnj	136	29	Similarly	similarly	RB
cord-191574-1g38scnj	136	30	,	,	,
cord-191574-1g38scnj	136	31	after	after	IN
cord-191574-1g38scnj	136	32	computing	compute	VBG
cord-191574-1g38scnj	136	33	the	the	DT
cord-191574-1g38scnj	136	34	third	third	JJ
cord-191574-1g38scnj	136	35	Adomian	adomian	JJ
cord-191574-1g38scnj	136	36	polynomial	polynomial	NN
cord-191574-1g38scnj	136	37	,	,	,
cord-191574-1g38scnj	136	38	given	give	VBN
cord-191574-1g38scnj	136	39	by	by	IN
cord-191574-1g38scnj	136	40	we	-PRON-	PRP
cord-191574-1g38scnj	136	41	obtain	obtain	VBP
cord-191574-1g38scnj	136	42	u	u	NNP
cord-191574-1g38scnj	136	43	3	3	CD
cord-191574-1g38scnj	136	44	(	(	-LRB-
cord-191574-1g38scnj	136	45	t	t	NN
cord-191574-1g38scnj	136	46	)	)	-RRB-
cord-191574-1g38scnj	136	47	.	.	.
cord-191574-1g38scnj	137	1	The	the	DT
cord-191574-1g38scnj	137	2	higher	high	JJR
cord-191574-1g38scnj	137	3	order	order	NN
cord-191574-1g38scnj	137	4	terms	term	NNS
cord-191574-1g38scnj	137	5	in	in	IN
cord-191574-1g38scnj	137	6	the	the	DT
cord-191574-1g38scnj	137	7	Laplace	Laplace	NNP
cord-191574-1g38scnj	137	8	-	-	HYPH
cord-191574-1g38scnj	137	9	Adomian	adomian	JJ
cord-191574-1g38scnj	137	10	power	power	NN
cord-191574-1g38scnj	137	11	series	series	NN
cord-191574-1g38scnj	137	12	representation	representation	NN
cord-191574-1g38scnj	137	13	of	of	IN
cord-191574-1g38scnj	137	14	u(t	u(t	NNP
cord-191574-1g38scnj	137	15	)	)	-RRB-
cord-191574-1g38scnj	137	16	can	can	MD
cord-191574-1g38scnj	137	17	be	be	VB
cord-191574-1g38scnj	137	18	obtained	obtain	VBN
cord-191574-1g38scnj	137	19	by	by	IN
cord-191574-1g38scnj	137	20	following	follow	VBG
cord-191574-1g38scnj	137	21	the	the	DT
cord-191574-1g38scnj	137	22	same	same	JJ
cord-191574-1g38scnj	137	23	approach	approach	NN
cord-191574-1g38scnj	137	24	,	,	,
cord-191574-1g38scnj	137	25	but	but	CC
cord-191574-1g38scnj	137	26	due	due	IN
cord-191574-1g38scnj	137	27	to	to	IN
cord-191574-1g38scnj	137	28	their	-PRON-	PRP$
cord-191574-1g38scnj	137	29	length	length	NN
cord-191574-1g38scnj	137	30	we	-PRON-	PRP
cord-191574-1g38scnj	137	31	will	will	MD
cord-191574-1g38scnj	137	32	not	not	RB
cord-191574-1g38scnj	137	33	present	present	VB
cord-191574-1g38scnj	137	34	them	-PRON-	PRP
cord-191574-1g38scnj	137	35	here	here	RB
cord-191574-1g38scnj	137	36	.	.	.
cord-191574-1g38scnj	138	1	Hence	hence	RB
cord-191574-1g38scnj	138	2	,	,	,
cord-191574-1g38scnj	138	3	once	once	IN
cord-191574-1g38scnj	138	4	the	the	DT
cord-191574-1g38scnj	138	5	expressions	expression	NNS
cord-191574-1g38scnj	138	6	of	of	IN
cord-191574-1g38scnj	138	7	the	the	DT
cord-191574-1g38scnj	138	8	terms	term	NNS
cord-191574-1g38scnj	138	9	u	u	NNP
cord-191574-1g38scnj	138	10	n	n	NN
cord-191574-1g38scnj	138	11	(	(	-LRB-
cord-191574-1g38scnj	138	12	t	t	NNP
cord-191574-1g38scnj	138	13	)	)	-RRB-
cord-191574-1g38scnj	138	14	,	,	,
cord-191574-1g38scnj	138	15	n	n	NN
cord-191574-1g38scnj	138	16	=	=	SYM
cord-191574-1g38scnj	138	17	0	0	CD
cord-191574-1g38scnj	138	18	,	,	,
cord-191574-1g38scnj	138	19	1	1	CD
cord-191574-1g38scnj	138	20	,	,	,
cord-191574-1g38scnj	138	21	2	2	CD
cord-191574-1g38scnj	138	22	,	,	,
cord-191574-1g38scnj	138	23	..	..	NFP
cord-191574-1g38scnj	138	24	in	in	IN
cord-191574-1g38scnj	138	25	the	the	DT
cord-191574-1g38scnj	138	26	Adomian	adomian	JJ
cord-191574-1g38scnj	138	27	Decomposition	decomposition	NN
cord-191574-1g38scnj	138	28	are	be	VBP
cord-191574-1g38scnj	138	29	known	know	VBN
cord-191574-1g38scnj	138	30	,	,	,
cord-191574-1g38scnj	138	31	the	the	DT
cord-191574-1g38scnj	138	32	approximate	approximate	JJ
cord-191574-1g38scnj	138	33	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	138	34	solution	solution	NN
cord-191574-1g38scnj	138	35	of	of	IN
cord-191574-1g38scnj	138	36	the	the	DT
cord-191574-1g38scnj	138	37	SIR	SIR	NNP
cord-191574-1g38scnj	138	38	model	model	NN
cord-191574-1g38scnj	138	39	with	with	IN
cord-191574-1g38scnj	138	40	vital	vital	JJ
cord-191574-1g38scnj	138	41	dynamics	dynamic	NNS
cord-191574-1g38scnj	138	42	can	can	MD
cord-191574-1g38scnj	138	43	be	be	VB
cord-191574-1g38scnj	138	44	obtained	obtain	VBN
cord-191574-1g38scnj	138	45	as	as	IN
cord-191574-1g38scnj	138	46	The	the	DT
cord-191574-1g38scnj	138	47	present	present	JJ
cord-191574-1g38scnj	138	48	Laplace	Laplace	NNP
cord-191574-1g38scnj	138	49	-	-	HYPH
cord-191574-1g38scnj	138	50	Adomian	adomian	JJ
cord-191574-1g38scnj	138	51	series	series	NN
cord-191574-1g38scnj	138	52	solution	solution	NN
cord-191574-1g38scnj	138	53	is	be	VBZ
cord-191574-1g38scnj	138	54	valid	valid	JJ
cord-191574-1g38scnj	138	55	only	only	RB
cord-191574-1g38scnj	138	56	for	for	IN
cord-191574-1g38scnj	138	57	some	some	DT
cord-191574-1g38scnj	138	58	specific	specific	JJ
cord-191574-1g38scnj	138	59	ranges	range	NNS
cord-191574-1g38scnj	138	60	of	of	IN
cord-191574-1g38scnj	138	61	the	the	DT
cord-191574-1g38scnj	138	62	model	model	NN
cord-191574-1g38scnj	138	63	parameters	parameter	NNS
cord-191574-1g38scnj	138	64	(	(	-LRB-
cord-191574-1g38scnj	138	65	β	β	NN
cord-191574-1g38scnj	138	66	,	,	,
cord-191574-1g38scnj	138	67	γ	γ	NN
cord-191574-1g38scnj	138	68	,	,	,
cord-191574-1g38scnj	138	69	µ	µ	NNP
cord-191574-1g38scnj	138	70	)	)	-RRB-
cord-191574-1g38scnj	138	71	and	and	CC
cord-191574-1g38scnj	138	72	of	of	IN
cord-191574-1g38scnj	138	73	initial	initial	JJ
cord-191574-1g38scnj	138	74	conditions	condition	NNS
cord-191574-1g38scnj	138	75	(	(	-LRB-
cord-191574-1g38scnj	138	76	N	N	NNP
cord-191574-1g38scnj	138	77	1	1	CD
cord-191574-1g38scnj	138	78	,	,	,
cord-191574-1g38scnj	138	79	N	n	CD
cord-191574-1g38scnj	138	80	2	2	CD
cord-191574-1g38scnj	138	81	,	,	,
cord-191574-1g38scnj	138	82	N	n	CD
cord-191574-1g38scnj	138	83	3	3	CD
cord-191574-1g38scnj	138	84	)	)	-RRB-
cord-191574-1g38scnj	138	85	.	.	.
cord-191574-1g38scnj	139	1	If	if	IN
cord-191574-1g38scnj	139	2	(	(	-LRB-
cord-191574-1g38scnj	139	3	N	n	CD
cord-191574-1g38scnj	139	4	1	1	CD
cord-191574-1g38scnj	139	5	+	+	SYM
cord-191574-1g38scnj	139	6	N	n	CD
cord-191574-1g38scnj	139	7	2	2	CD
cord-191574-1g38scnj	139	8	)	)	-RRB-
cord-191574-1g38scnj	139	9	N	n	NN
cord-191574-1g38scnj	139	10	>	>	XX
cord-191574-1g38scnj	139	11	(	(	-LRB-
cord-191574-1g38scnj	139	12	γ	γ	NN
cord-191574-1g38scnj	139	13	+	+	CC
cord-191574-1g38scnj	139	14	µ	µ	NN
cord-191574-1g38scnj	139	15	)	)	-RRB-
cord-191574-1g38scnj	139	16	/β	/β	NNP
cord-191574-1g38scnj	139	17	,	,	,
cord-191574-1g38scnj	139	18	or	or	CC
cord-191574-1g38scnj	140	1	(	(	-LRB-
cord-191574-1g38scnj	140	2	N	n	NN
cord-191574-1g38scnj	140	3	1	1	CD
cord-191574-1g38scnj	140	4	+	+	SYM
cord-191574-1g38scnj	140	5	N	n	CD
cord-191574-1g38scnj	140	6	2	2	CD
cord-191574-1g38scnj	140	7	)	)	-RRB-
cord-191574-1g38scnj	140	8	N	n	NN
cord-191574-1g38scnj	140	9	>	>	XX
cord-191574-1g38scnj	140	10	(	(	-LRB-
cord-191574-1g38scnj	140	11	γ	γ	NN
cord-191574-1g38scnj	140	12	+	+	SYM
cord-191574-1g38scnj	140	13	2µ)/β	2µ)/β	CD
cord-191574-1g38scnj	140	14	,	,	,
cord-191574-1g38scnj	140	15	the	the	DT
cord-191574-1g38scnj	140	16	exponential	exponential	JJ
cord-191574-1g38scnj	140	17	functions	function	NNS
cord-191574-1g38scnj	140	18	in	in	IN
cord-191574-1g38scnj	140	19	Eq	Eq	NNP
cord-191574-1g38scnj	140	20	.	.	.
cord-191574-1g38scnj	141	1	(	(	-LRB-
cord-191574-1g38scnj	141	2	57	57	CD
cord-191574-1g38scnj	141	3	)	)	-RRB-
cord-191574-1g38scnj	141	4	do	do	VBP
cord-191574-1g38scnj	141	5	diverge	diverge	VB
cord-191574-1g38scnj	141	6	in	in	IN
cord-191574-1g38scnj	141	7	the	the	DT
cord-191574-1g38scnj	141	8	long	long	JJ
cord-191574-1g38scnj	141	9	time	time	NN
cord-191574-1g38scnj	141	10	limit	limit	NN
cord-191574-1g38scnj	141	11	.	.	.
cord-191574-1g38scnj	142	1	Similarly	similarly	RB
cord-191574-1g38scnj	142	2	,	,	,
cord-191574-1g38scnj	142	3	for	for	IN
cord-191574-1g38scnj	142	4	N	n	CD
cord-191574-1g38scnj	142	5	2	2	CD
cord-191574-1g38scnj	142	6	)	)	-RRB-
cord-191574-1g38scnj	142	7	,	,	,
cord-191574-1g38scnj	142	8	singularities	singularity	NNS
cord-191574-1g38scnj	142	9	develop	develop	VBP
cord-191574-1g38scnj	142	10	in	in	IN
cord-191574-1g38scnj	142	11	the	the	DT
cord-191574-1g38scnj	142	12	Adomian	adomian	JJ
cord-191574-1g38scnj	142	13	series	series	NN
cord-191574-1g38scnj	142	14	.	.	.
cord-191574-1g38scnj	143	1	In	in	IN
cord-191574-1g38scnj	143	2	the	the	DT
cord-191574-1g38scnj	143	3	present	present	JJ
cord-191574-1g38scnj	143	4	Section	section	NN
cord-191574-1g38scnj	143	5	we	-PRON-	PRP
cord-191574-1g38scnj	143	6	compare	compare	VBP
cord-191574-1g38scnj	143	7	the	the	DT
cord-191574-1g38scnj	143	8	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	143	9	predictions	prediction	NNS
cord-191574-1g38scnj	143	10	of	of	IN
cord-191574-1g38scnj	143	11	the	the	DT
cord-191574-1g38scnj	143	12	Adomian	adomian	JJ
cord-191574-1g38scnj	143	13	and	and	CC
cord-191574-1g38scnj	143	14	Laplace	Laplace	NNP
cord-191574-1g38scnj	143	15	Adomian	Adomian	NNP
cord-191574-1g38scnj	143	16	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	143	17	Methods	Methods	NNPS
cord-191574-1g38scnj	143	18	as	as	IN
cord-191574-1g38scnj	143	19	applied	apply	VBN
cord-191574-1g38scnj	143	20	to	to	IN
cord-191574-1g38scnj	143	21	the	the	DT
cord-191574-1g38scnj	143	22	SIR	SIR	NNP
cord-191574-1g38scnj	143	23	model	model	NN
cord-191574-1g38scnj	143	24	with	with	IN
cord-191574-1g38scnj	143	25	vital	vital	JJ
cord-191574-1g38scnj	143	26	dynamics	dynamic	NNS
cord-191574-1g38scnj	143	27	with	with	IN
cord-191574-1g38scnj	143	28	the	the	DT
cord-191574-1g38scnj	143	29	exact	exact	JJ
cord-191574-1g38scnj	143	30	numerical	numerical	JJ
cord-191574-1g38scnj	143	31	solutions	solution	NNS
cord-191574-1g38scnj	143	32	,	,	,
cord-191574-1g38scnj	143	33	obtained	obtain	VBN
cord-191574-1g38scnj	143	34	by	by	IN
cord-191574-1g38scnj	143	35	numerically	numerically	RB
cord-191574-1g38scnj	143	36	integrating	integrate	VBG
cord-191574-1g38scnj	143	37	the	the	DT
cord-191574-1g38scnj	143	38	system	system	NN
cord-191574-1g38scnj	143	39	of	of	IN
cord-191574-1g38scnj	143	40	equations	equation	NNS
cord-191574-1g38scnj	143	41	(	(	-LRB-
cord-191574-1g38scnj	143	42	3)-(5	3)-(5	CD
cord-191574-1g38scnj	143	43	)	)	-RRB-
cord-191574-1g38scnj	143	44	.	.	.
cord-191574-1g38scnj	144	1	In	in	IN
cord-191574-1g38scnj	144	2	the	the	DT
cord-191574-1g38scnj	144	3	case	case	NN
cord-191574-1g38scnj	144	4	of	of	IN
cord-191574-1g38scnj	144	5	the	the	DT
cord-191574-1g38scnj	144	6	Adomian	adomian	JJ
cord-191574-1g38scnj	144	7	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	144	8	Method	Method	NNP
cord-191574-1g38scnj	144	9	we	-PRON-	PRP
cord-191574-1g38scnj	144	10	will	will	MD
cord-191574-1g38scnj	144	11	approximate	approximate	VB
cord-191574-1g38scnj	144	12	the	the	DT
cord-191574-1g38scnj	144	13	solution	solution	NN
cord-191574-1g38scnj	144	14	by	by	IN
cord-191574-1g38scnj	144	15	using	use	VBG
cord-191574-1g38scnj	144	16	only	only	RB
cord-191574-1g38scnj	144	17	two	two	CD
cord-191574-1g38scnj	144	18	first	first	JJ
cord-191574-1g38scnj	144	19	two	two	CD
cord-191574-1g38scnj	144	20	terms	term	NNS
cord-191574-1g38scnj	144	21	in	in	IN
cord-191574-1g38scnj	144	22	the	the	DT
cord-191574-1g38scnj	144	23	Adomian	adomian	JJ
cord-191574-1g38scnj	144	24	iterative	iterative	JJ
cord-191574-1g38scnj	144	25	scheme	scheme	NN
cord-191574-1g38scnj	144	26	.	.	.
cord-191574-1g38scnj	145	1	However	however	RB
cord-191574-1g38scnj	145	2	,	,	,
cord-191574-1g38scnj	145	3	we	-PRON-	PRP
cord-191574-1g38scnj	145	4	will	will	MD
cord-191574-1g38scnj	145	5	also	also	RB
cord-191574-1g38scnj	145	6	add	add	VB
cord-191574-1g38scnj	145	7	to	to	IN
cord-191574-1g38scnj	145	8	the	the	DT
cord-191574-1g38scnj	145	9	series	series	NN
cord-191574-1g38scnj	145	10	solution	solution	NN
cord-191574-1g38scnj	145	11	a	a	DT
cord-191574-1g38scnj	145	12	truncation	truncation	NN
cord-191574-1g38scnj	145	13	of	of	IN
cord-191574-1g38scnj	145	14	the	the	DT
cord-191574-1g38scnj	145	15	term	term	NN
cord-191574-1g38scnj	145	16	u	u	NNP
cord-191574-1g38scnj	145	17	2	2	CD
cord-191574-1g38scnj	145	18	,	,	,
cord-191574-1g38scnj	145	19	approximated	approximate	VBN
cord-191574-1g38scnj	145	20	by	by	IN
cord-191574-1g38scnj	145	21	u	u	NNP
cord-191574-1g38scnj	145	22	2	2	CD
cord-191574-1g38scnj	146	1	(	(	-LRB-
cord-191574-1g38scnj	146	2	t	t	NN
cord-191574-1g38scnj	146	3	)	)	-RRB-
cord-191574-1g38scnj	146	4	≈	≈	NNP
cord-191574-1g38scnj	146	5	−µ	−µ	NNS
cord-191574-1g38scnj	147	1	t	t	NNP
cord-191574-1g38scnj	147	2	0	0	CD
cord-191574-1g38scnj	147	3	u	u	NNP
cord-191574-1g38scnj	147	4	1	1	CD
cord-191574-1g38scnj	147	5	(	(	-LRB-
cord-191574-1g38scnj	147	6	t)dt	t)dt	XX
cord-191574-1g38scnj	147	7	.	.	.
cord-191574-1g38scnj	148	1	Hence	hence	RB
cord-191574-1g38scnj	148	2	we	-PRON-	PRP
cord-191574-1g38scnj	148	3	approximate	approximate	VBP
cord-191574-1g38scnj	148	4	the	the	DT
cord-191574-1g38scnj	148	5	Adomian	adomian	JJ
cord-191574-1g38scnj	148	6	solution	solution	NN
cord-191574-1g38scnj	148	7	of	of	IN
cord-191574-1g38scnj	148	8	the	the	DT
cord-191574-1g38scnj	148	9	basic	basic	JJ
cord-191574-1g38scnj	148	10	evolution	evolution	NN
cord-191574-1g38scnj	148	11	equation	equation	NN
cord-191574-1g38scnj	148	12	of	of	IN
cord-191574-1g38scnj	148	13	the	the	DT
cord-191574-1g38scnj	148	14	SIR	SIR	NNP
cord-191574-1g38scnj	148	15	model	model	NN
cord-191574-1g38scnj	148	16	with	with	IN
cord-191574-1g38scnj	148	17	vital	vital	JJ
cord-191574-1g38scnj	148	18	dynamics	dynamic	NNS
cord-191574-1g38scnj	148	19	as	as	IN
cord-191574-1g38scnj	148	20	The	the	DT
cord-191574-1g38scnj	148	21	comparison	comparison	NN
cord-191574-1g38scnj	148	22	of	of	IN
cord-191574-1g38scnj	148	23	the	the	DT
cord-191574-1g38scnj	148	24	numerical	numerical	JJ
cord-191574-1g38scnj	148	25	and	and	CC
cord-191574-1g38scnj	148	26	of	of	IN
cord-191574-1g38scnj	148	27	the	the	DT
cord-191574-1g38scnj	148	28	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	148	29	Adomian	adomian	JJ
cord-191574-1g38scnj	148	30	approximate	approximate	JJ
cord-191574-1g38scnj	148	31	solution	solution	NN
cord-191574-1g38scnj	148	32	is	be	VBZ
cord-191574-1g38scnj	148	33	presented	present	VBN
cord-191574-1g38scnj	148	34	,	,	,
cord-191574-1g38scnj	148	35	for	for	IN
cord-191574-1g38scnj	148	36	different	different	JJ
cord-191574-1g38scnj	148	37	values	value	NNS
cord-191574-1g38scnj	148	38	of	of	IN
cord-191574-1g38scnj	148	39	the	the	DT
cord-191574-1g38scnj	148	40	model	model	NN
cord-191574-1g38scnj	148	41	parameters	parameter	VBZ
cord-191574-1g38scnj	148	42	β	β	NNP
cord-191574-1g38scnj	148	43	,	,	,
cord-191574-1g38scnj	148	44	γ	γ	NN
cord-191574-1g38scnj	148	45	and	and	CC
cord-191574-1g38scnj	148	46	µ	µ	NN
cord-191574-1g38scnj	148	47	in	in	IN
cord-191574-1g38scnj	148	48	Fig	Fig	NNP
cord-191574-1g38scnj	148	49	.	.	NNP
cord-191574-1g38scnj	148	50	1	1	CD
cord-191574-1g38scnj	148	51	.	.	.
cord-191574-1g38scnj	149	1	(	(	-LRB-
cord-191574-1g38scnj	149	2	or	or	CC
cord-191574-1g38scnj	149	3	a	a	DT
cord-191574-1g38scnj	149	4	vaccine	vaccine	NN
cord-191574-1g38scnj	149	5	)	)	-RRB-
cord-191574-1g38scnj	149	6	for	for	IN
cord-191574-1g38scnj	149	7	it	-PRON-	PRP
cord-191574-1g38scnj	149	8	is	be	VBZ
cord-191574-1g38scnj	149	9	mostly	mostly	RB
cord-191574-1g38scnj	149	10	a	a	DT
cord-191574-1g38scnj	149	11	medical	medical	JJ
cord-191574-1g38scnj	149	12	/	/	SYM
cord-191574-1g38scnj	149	13	biological	biological	JJ
cord-191574-1g38scnj	149	14	/	/	SYM
cord-191574-1g38scnj	149	15	virusological	virusological	NN
cord-191574-1g38scnj	149	16	problem	problem	NN
cord-191574-1g38scnj	149	17	,	,	,
cord-191574-1g38scnj	149	18	the	the	DT
cord-191574-1g38scnj	149	19	understanding	understanding	NN
cord-191574-1g38scnj	149	20	of	of	IN
cord-191574-1g38scnj	149	21	the	the	DT
cord-191574-1g38scnj	149	22	spread	spread	NN
cord-191574-1g38scnj	149	23	of	of	IN
cord-191574-1g38scnj	149	24	the	the	DT
cord-191574-1g38scnj	149	25	epidemics	epidemic	NNS
cord-191574-1g38scnj	149	26	may	may	MD
cord-191574-1g38scnj	149	27	lead	lead	VB
cord-191574-1g38scnj	149	28	to	to	IN
cord-191574-1g38scnj	149	29	the	the	DT
cord-191574-1g38scnj	149	30	adoption	adoption	NN
cord-191574-1g38scnj	149	31	/	/	SYM
cord-191574-1g38scnj	149	32	imposition	imposition	NN
cord-191574-1g38scnj	149	33	of	of	IN
cord-191574-1g38scnj	149	34	quarantine	quarantine	NN
cord-191574-1g38scnj	149	35	or	or	CC
cord-191574-1g38scnj	149	36	safety	safety	NN
cord-191574-1g38scnj	149	37	measures	measure	NNS
cord-191574-1g38scnj	149	38	that	that	WDT
cord-191574-1g38scnj	149	39	could	could	MD
cord-191574-1g38scnj	149	40	drastically	drastically	RB
cord-191574-1g38scnj	149	41	reduce	reduce	VB
cord-191574-1g38scnj	149	42	its	-PRON-	PRP$
cord-191574-1g38scnj	149	43	intensity	intensity	NN
cord-191574-1g38scnj	149	44	.	.	.
cord-191574-1g38scnj	150	1	In	in	IN
cord-191574-1g38scnj	150	2	this	this	DT
cord-191574-1g38scnj	150	3	context	context	NN
cord-191574-1g38scnj	150	4	the	the	DT
cord-191574-1g38scnj	150	5	mathematical	mathematical	JJ
cord-191574-1g38scnj	150	6	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	150	7	models	model	NNS
cord-191574-1g38scnj	150	8	could	could	MD
cord-191574-1g38scnj	150	9	play	play	VB
cord-191574-1g38scnj	150	10	an	an	DT
cord-191574-1g38scnj	150	11	important	important	JJ
cord-191574-1g38scnj	150	12	role	role	NN
cord-191574-1g38scnj	150	13	,	,	,
cord-191574-1g38scnj	150	14	since	since	IN
cord-191574-1g38scnj	150	15	a	a	DT
cord-191574-1g38scnj	150	16	successful	successful	JJ
cord-191574-1g38scnj	150	17	modeling	modeling	NN
cord-191574-1g38scnj	150	18	of	of	IN
cord-191574-1g38scnj	150	19	the	the	DT
cord-191574-1g38scnj	150	20	spread	spread	NN
cord-191574-1g38scnj	150	21	of	of	IN
cord-191574-1g38scnj	150	22	the	the	DT
cord-191574-1g38scnj	150	23	disease	disease	NN
cord-191574-1g38scnj	150	24	could	could	MD
cord-191574-1g38scnj	150	25	essentially	essentially	RB
cord-191574-1g38scnj	150	26	contribute	contribute	VB
cord-191574-1g38scnj	150	27	,	,	,
cord-191574-1g38scnj	150	28	on	on	IN
cord-191574-1g38scnj	150	29	the	the	DT
cord-191574-1g38scnj	150	30	level	level	NN
cord-191574-1g38scnj	150	31	of	of	IN
cord-191574-1g38scnj	150	32	the	the	DT
cord-191574-1g38scnj	150	33	society	society	NN
cord-191574-1g38scnj	150	34	,	,	,
cord-191574-1g38scnj	150	35	to	to	IN
cord-191574-1g38scnj	150	36	the	the	DT
cord-191574-1g38scnj	150	37	implementation	implementation	NN
cord-191574-1g38scnj	150	38	of	of	IN
cord-191574-1g38scnj	150	39	the	the	DT
cord-191574-1g38scnj	150	40	best	good	JJS
cord-191574-1g38scnj	150	41	policies	policy	NNS
cord-191574-1g38scnj	150	42	that	that	WDT
cord-191574-1g38scnj	150	43	could	could	MD
cord-191574-1g38scnj	150	44	guarantee	guarantee	VB
cord-191574-1g38scnj	150	45	the	the	DT
cord-191574-1g38scnj	150	46	maximal	maximal	JJ
cord-191574-1g38scnj	150	47	safety	safety	NN
cord-191574-1g38scnj	150	48	of	of	IN
cord-191574-1g38scnj	150	49	the	the	DT
cord-191574-1g38scnj	150	50	citizens	citizen	NNS
cord-191574-1g38scnj	150	51	.	.	.
cord-191574-1g38scnj	151	1	Despite	despite	IN
cord-191574-1g38scnj	151	2	their	-PRON-	PRP$
cord-191574-1g38scnj	151	3	(	(	-LRB-
cord-191574-1g38scnj	151	4	apparent	apparent	JJ
cord-191574-1g38scnj	151	5	)	)	-RRB-
cord-191574-1g38scnj	151	6	mathematical	mathematical	JJ
cord-191574-1g38scnj	151	7	simplicity	simplicity	NN
cord-191574-1g38scnj	151	8	,	,	,
cord-191574-1g38scnj	151	9	the	the	DT
cord-191574-1g38scnj	151	10	compartmental	compartmental	JJ
cord-191574-1g38scnj	151	11	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	151	12	models	model	NNS
cord-191574-1g38scnj	151	13	did	do	VBD
cord-191574-1g38scnj	151	14	play	play	VB
cord-191574-1g38scnj	151	15	an	an	DT
cord-191574-1g38scnj	151	16	important	important	JJ
cord-191574-1g38scnj	151	17	role	role	NN
cord-191574-1g38scnj	151	18	in	in	IN
cord-191574-1g38scnj	151	19	the	the	DT
cord-191574-1g38scnj	151	20	analysis	analysis	NN
cord-191574-1g38scnj	151	21	of	of	IN
cord-191574-1g38scnj	151	22	the	the	DT
cord-191574-1g38scnj	151	23	Covid	covid	JJ
cord-191574-1g38scnj	151	24	pandemic	pandemic	NN
cord-191574-1g38scnj	151	25	.	.	.
cord-191574-1g38scnj	152	1	These	these	DT
cord-191574-1g38scnj	152	2	models	model	NNS
cord-191574-1g38scnj	152	3	contain	contain	VBP
cord-191574-1g38scnj	152	4	the	the	DT
cord-191574-1g38scnj	152	5	basic	basic	JJ
cord-191574-1g38scnj	152	6	features	feature	NNS
cord-191574-1g38scnj	152	7	of	of	IN
cord-191574-1g38scnj	152	8	the	the	DT
cord-191574-1g38scnj	152	9	evolution	evolution	NN
cord-191574-1g38scnj	152	10	of	of	IN
cord-191574-1g38scnj	152	11	an	an	DT
cord-191574-1g38scnj	152	12	epidemics	epidemic	NNS
cord-191574-1g38scnj	152	13	,	,	,
cord-191574-1g38scnj	152	14	and	and	CC
cord-191574-1g38scnj	152	15	once	once	IN
cord-191574-1g38scnj	152	16	the	the	DT
cord-191574-1g38scnj	152	17	parameters	parameter	NNS
cord-191574-1g38scnj	152	18	of	of	IN
cord-191574-1g38scnj	152	19	the	the	DT
cord-191574-1g38scnj	152	20	model	model	NN
cord-191574-1g38scnj	152	21	are	be	VBP
cord-191574-1g38scnj	152	22	fixed	fix	VBN
cord-191574-1g38scnj	152	23	from	from	IN
cord-191574-1g38scnj	152	24	the	the	DT
cord-191574-1g38scnj	152	25	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	152	26	data	datum	NNS
cord-191574-1g38scnj	152	27	they	-PRON-	PRP
cord-191574-1g38scnj	152	28	can	can	MD
cord-191574-1g38scnj	152	29	provide	provide	VB
cord-191574-1g38scnj	152	30	some	some	DT
cord-191574-1g38scnj	152	31	accurate	accurate	JJ
cord-191574-1g38scnj	152	32	predictions	prediction	NNS
cord-191574-1g38scnj	152	33	for	for	IN
cord-191574-1g38scnj	152	34	the	the	DT
cord-191574-1g38scnj	152	35	evolution	evolution	NN
cord-191574-1g38scnj	152	36	of	of	IN
cord-191574-1g38scnj	152	37	the	the	DT
cord-191574-1g38scnj	152	38	infectious	infectious	JJ
cord-191574-1g38scnj	152	39	diseases	disease	NNS
cord-191574-1g38scnj	152	40	.	.	.
cord-191574-1g38scnj	153	1	From	from	IN
cord-191574-1g38scnj	153	2	a	a	DT
cord-191574-1g38scnj	153	3	mathematical	mathematical	JJ
cord-191574-1g38scnj	153	4	point	point	NN
cord-191574-1g38scnj	153	5	of	of	IN
cord-191574-1g38scnj	153	6	view	view	NN
cord-191574-1g38scnj	153	7	the	the	DT
cord-191574-1g38scnj	153	8	SIR	SIR	NNP
cord-191574-1g38scnj	153	9	model	model	NN
cord-191574-1g38scnj	153	10	is	be	VBZ
cord-191574-1g38scnj	153	11	exactly	exactly	RB
cord-191574-1g38scnj	153	12	integrable	integrable	JJ
cord-191574-1g38scnj	153	13	,	,	,
cord-191574-1g38scnj	153	14	which	which	WDT
cord-191574-1g38scnj	153	15	simplifies	simplify	VBZ
cord-191574-1g38scnj	153	16	its	-PRON-	PRP$
cord-191574-1g38scnj	153	17	analysis	analysis	NN
cord-191574-1g38scnj	153	18	,	,	,
cord-191574-1g38scnj	153	19	since	since	IN
cord-191574-1g38scnj	153	20	its	-PRON-	PRP$
cord-191574-1g38scnj	153	21	exact	exact	JJ
cord-191574-1g38scnj	153	22	solution	solution	NN
cord-191574-1g38scnj	153	23	is	be	VBZ
cord-191574-1g38scnj	153	24	known	know	VBN
cord-191574-1g38scnj	153	25	[	[	-LRB-
cord-191574-1g38scnj	153	26	25	25	CD
cord-191574-1g38scnj	153	27	]	]	-RRB-
cord-191574-1g38scnj	153	28	.	.	.
cord-191574-1g38scnj	154	1	On	on	IN
cord-191574-1g38scnj	154	2	the	the	DT
cord-191574-1g38scnj	154	3	other	other	JJ
cord-191574-1g38scnj	154	4	hand	hand	NN
cord-191574-1g38scnj	154	5	the	the	DT
cord-191574-1g38scnj	154	6	SIR	SIR	NNP
cord-191574-1g38scnj	154	7	model	model	NN
cord-191574-1g38scnj	154	8	with	with	IN
cord-191574-1g38scnj	154	9	vital	vital	JJ
cord-191574-1g38scnj	154	10	dynamics	dynamic	NNS
cord-191574-1g38scnj	154	11	is	be	VBZ
cord-191574-1g38scnj	154	12	non	non	JJ
cord-191574-1g38scnj	154	13	-	-	JJ
cord-191574-1g38scnj	154	14	integrable	integrable	JJ
cord-191574-1g38scnj	154	15	,	,	,
cord-191574-1g38scnj	154	16	and	and	CC
cord-191574-1g38scnj	154	17	therefore	therefore	RB
cord-191574-1g38scnj	154	18	it	-PRON-	PRP
cord-191574-1g38scnj	154	19	can	can	MD
cord-191574-1g38scnj	154	20	be	be	VB
cord-191574-1g38scnj	154	21	investigated	investigate	VBN
cord-191574-1g38scnj	154	22	only	only	RB
cord-191574-1g38scnj	154	23	by	by	IN
cord-191574-1g38scnj	154	24	using	use	VBG
cord-191574-1g38scnj	154	25	numerical	numerical	JJ
cord-191574-1g38scnj	154	26	or	or	CC
cord-191574-1g38scnj	154	27	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	154	28	methods	method	NNS
cord-191574-1g38scnj	154	29	.	.	.
cord-191574-1g38scnj	155	1	In	in	IN
cord-191574-1g38scnj	155	2	the	the	DT
cord-191574-1g38scnj	155	3	present	present	JJ
cord-191574-1g38scnj	155	4	paper	paper	NN
cord-191574-1g38scnj	155	5	we	-PRON-	PRP
cord-191574-1g38scnj	155	6	have	have	VBP
cord-191574-1g38scnj	155	7	introduced	introduce	VBN
cord-191574-1g38scnj	155	8	the	the	DT
cord-191574-1g38scnj	155	9	powerful	powerful	JJ
cord-191574-1g38scnj	155	10	Adomian	Adomian	NNP
cord-191574-1g38scnj	155	11	and	and	CC
cord-191574-1g38scnj	155	12	Laplace	Laplace	NNP
cord-191574-1g38scnj	155	13	-	-	HYPH
cord-191574-1g38scnj	155	14	Adomian	Adomian	NNP
cord-191574-1g38scnj	155	15	Decomposition	decomposition	NN
cord-191574-1g38scnj	155	16	Methods	Methods	NNPS
cord-191574-1g38scnj	155	17	for	for	IN
cord-191574-1g38scnj	155	18	the	the	DT
cord-191574-1g38scnj	155	19	study	study	NN
cord-191574-1g38scnj	155	20	of	of	IN
cord-191574-1g38scnj	155	21	this	this	DT
cord-191574-1g38scnj	155	22	model	model	NN
cord-191574-1g38scnj	155	23	.	.	.
cord-191574-1g38scnj	156	1	However	however	RB
cord-191574-1g38scnj	156	2	,	,	,
cord-191574-1g38scnj	156	3	in	in	IN
cord-191574-1g38scnj	156	4	obtaining	obtain	VBG
cord-191574-1g38scnj	156	5	the	the	DT
cord-191574-1g38scnj	156	6	explicit	explicit	JJ
cord-191574-1g38scnj	156	7	form	form	NN
cord-191574-1g38scnj	156	8	of	of	IN
cord-191574-1g38scnj	156	9	the	the	DT
cord-191574-1g38scnj	156	10	Adomian	adomian	JJ
cord-191574-1g38scnj	156	11	polynomials	polynomial	NNS
cord-191574-1g38scnj	156	12	one	one	PRP
cord-191574-1g38scnj	156	13	must	must	MD
cord-191574-1g38scnj	156	14	use	use	VB
cord-191574-1g38scnj	156	15	some	some	DT
cord-191574-1g38scnj	156	16	approximations	approximation	NNS
cord-191574-1g38scnj	156	17	for	for	IN
cord-191574-1g38scnj	156	18	their	-PRON-	PRP$
cord-191574-1g38scnj	156	19	estimation	estimation	NN
cord-191574-1g38scnj	156	20	.	.	.
cord-191574-1g38scnj	157	1	In	in	IN
cord-191574-1g38scnj	157	2	the	the	DT
cord-191574-1g38scnj	157	3	present	present	JJ
cord-191574-1g38scnj	157	4	approach	approach	NN
cord-191574-1g38scnj	157	5	we	-PRON-	PRP
cord-191574-1g38scnj	157	6	have	have	VBP
cord-191574-1g38scnj	157	7	approximated	approximate	VBN
cord-191574-1g38scnj	157	8	the	the	DT
cord-191574-1g38scnj	157	9	u	u	NNP
cord-191574-1g38scnj	157	10	0	0	CD
cord-191574-1g38scnj	157	11	(	(	-LRB-
cord-191574-1g38scnj	157	12	t	t	NN
cord-191574-1g38scnj	157	13	)	)	-RRB-
cord-191574-1g38scnj	157	14	term	term	NN
cord-191574-1g38scnj	157	15	by	by	IN
cord-191574-1g38scnj	157	16	its	-PRON-	PRP$
cord-191574-1g38scnj	157	17	first	first	JJ
cord-191574-1g38scnj	157	18	order	order	NN
cord-191574-1g38scnj	157	19	series	series	NN
cord-191574-1g38scnj	157	20	expansion	expansion	NN
cord-191574-1g38scnj	157	21	,	,	,
cord-191574-1g38scnj	157	22	leading	lead	VBG
cord-191574-1g38scnj	157	23	to	to	IN
cord-191574-1g38scnj	157	24	the	the	DT
cord-191574-1g38scnj	157	25	first	first	JJ
cord-191574-1g38scnj	157	26	Adomian	adomian	JJ
cord-191574-1g38scnj	157	27	polynomial	polynomial	NN
cord-191574-1g38scnj	157	28	as	as	IN
cord-191574-1g38scnj	157	29	given	give	VBN
cord-191574-1g38scnj	157	30	by	by	IN
cord-191574-1g38scnj	157	31	Eq	Eq	NNP
cord-191574-1g38scnj	157	32	.	.	.
cord-191574-1g38scnj	158	1	(	(	-LRB-
cord-191574-1g38scnj	158	2	54	54	CD
cord-191574-1g38scnj	158	3	)	)	-RRB-
cord-191574-1g38scnj	158	4	.	.	.
cord-191574-1g38scnj	159	1	In	in	IN
cord-191574-1g38scnj	159	2	the	the	DT
cord-191574-1g38scnj	159	3	large	large	JJ
cord-191574-1g38scnj	159	4	time	time	NN
cord-191574-1g38scnj	159	5	limit	limit	NN
cord-191574-1g38scnj	159	6	if	if	IN
cord-191574-1g38scnj	159	7	β	β	NNP
cord-191574-1g38scnj	159	8	(	(	-LRB-
cord-191574-1g38scnj	159	9	N	n	NN
cord-191574-1g38scnj	159	10	1	1	CD
cord-191574-1g38scnj	160	1	+	+	CC
cord-191574-1g38scnj	161	1	N	n	CD
cord-191574-1g38scnj	161	2	2	2	CD
cord-191574-1g38scnj	161	3	)	)	-RRB-
cord-191574-1g38scnj	161	4	/N	/N	.
cord-191574-1g38scnj	161	5	>	>	XX
cord-191574-1g38scnj	161	6	γ	γ	NN
cord-191574-1g38scnj	161	7	+	+	CC
cord-191574-1g38scnj	161	8	µ	µ	NN
cord-191574-1g38scnj	161	9	,	,	,
cord-191574-1g38scnj	161	10	A	a	DT
cord-191574-1g38scnj	161	11	0	0	CD
cord-191574-1g38scnj	161	12	diverges	diverge	VBZ
cord-191574-1g38scnj	161	13	.	.	.
cord-191574-1g38scnj	162	1	Hence	hence	RB
cord-191574-1g38scnj	162	2	the	the	DT
cord-191574-1g38scnj	162	3	Laplace	Laplace	NNP
cord-191574-1g38scnj	162	4	-	-	HYPH
cord-191574-1g38scnj	162	5	Adomian	Adomian	NNP
cord-191574-1g38scnj	162	6	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	162	7	Method	Method	NNP
cord-191574-1g38scnj	162	8	works	work	VBZ
cord-191574-1g38scnj	162	9	in	in	IN
cord-191574-1g38scnj	162	10	the	the	DT
cord-191574-1g38scnj	162	11	present	present	JJ
cord-191574-1g38scnj	162	12	case	case	NN
cord-191574-1g38scnj	162	13	optimally	optimally	RB
cord-191574-1g38scnj	162	14	if	if	IN
cord-191574-1g38scnj	162	15	the	the	DT
cord-191574-1g38scnj	162	16	condition	condition	NN
cord-191574-1g38scnj	162	17	(	(	-LRB-
cord-191574-1g38scnj	162	18	N	N	NNP
cord-191574-1g38scnj	162	19	1	1	CD
cord-191574-1g38scnj	162	20	+	+	SYM
cord-191574-1g38scnj	162	21	N	n	CD
cord-191574-1g38scnj	162	22	2	2	CD
cord-191574-1g38scnj	162	23	)	)	-RRB-
cord-191574-1g38scnj	162	24	/N	/N	.
cord-191574-1g38scnj	162	25	<	<	XX
cord-191574-1g38scnj	162	26	(	(	-LRB-
cord-191574-1g38scnj	162	27	γ	γ	NN
cord-191574-1g38scnj	162	28	+	+	CC
cord-191574-1g38scnj	162	29	µ)/β	µ)/β	NNS
cord-191574-1g38scnj	162	30	.	.	.
cord-191574-1g38scnj	163	1	In	in	IN
cord-191574-1g38scnj	163	2	the	the	DT
cord-191574-1g38scnj	163	3	present	present	JJ
cord-191574-1g38scnj	163	4	paper	paper	NN
cord-191574-1g38scnj	163	5	we	-PRON-	PRP
cord-191574-1g38scnj	163	6	have	have	VBP
cord-191574-1g38scnj	163	7	presented	present	VBN
cord-191574-1g38scnj	163	8	a	a	DT
cord-191574-1g38scnj	163	9	series	series	NN
cord-191574-1g38scnj	163	10	solution	solution	NN
cord-191574-1g38scnj	163	11	of	of	IN
cord-191574-1g38scnj	163	12	the	the	DT
cord-191574-1g38scnj	163	13	non	non	JJ
cord-191574-1g38scnj	163	14	-	-	JJ
cord-191574-1g38scnj	163	15	integrable	integrable	JJ
cord-191574-1g38scnj	163	16	SIR	SIR	NNP
cord-191574-1g38scnj	163	17	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	163	18	model	model	NN
cord-191574-1g38scnj	163	19	with	with	IN
cord-191574-1g38scnj	163	20	vital	vital	JJ
cord-191574-1g38scnj	163	21	dynamics	dynamic	NNS
cord-191574-1g38scnj	163	22	,	,	,
cord-191574-1g38scnj	163	23	by	by	IN
cord-191574-1g38scnj	163	24	using	use	VBG
cord-191574-1g38scnj	163	25	both	both	CC
cord-191574-1g38scnj	163	26	the	the	DT
cord-191574-1g38scnj	163	27	Adomian	adomian	JJ
cord-191574-1g38scnj	163	28	and	and	CC
cord-191574-1g38scnj	163	29	the	the	DT
cord-191574-1g38scnj	163	30	Laplace	Laplace	NNP
cord-191574-1g38scnj	163	31	-	-	HYPH
cord-191574-1g38scnj	163	32	Adomian	Adomian	NNP
cord-191574-1g38scnj	163	33	Decomposition	decomposition	NN
cord-191574-1g38scnj	163	34	Methods	Methods	NNPS
cord-191574-1g38scnj	163	35	.	.	.
cord-191574-1g38scnj	164	1	The	the	DT
cord-191574-1g38scnj	164	2	application	application	NN
cord-191574-1g38scnj	164	3	of	of	IN
cord-191574-1g38scnj	164	4	these	these	DT
cord-191574-1g38scnj	164	5	methods	method	NNS
cord-191574-1g38scnj	164	6	allows	allow	VBZ
cord-191574-1g38scnj	164	7	to	to	TO
cord-191574-1g38scnj	164	8	obtain	obtain	VB
cord-191574-1g38scnj	164	9	the	the	DT
cord-191574-1g38scnj	164	10	explicit	explicit	JJ
cord-191574-1g38scnj	164	11	time	time	NN
cord-191574-1g38scnj	164	12	dependencies	dependency	NNS
cord-191574-1g38scnj	164	13	of	of	IN
cord-191574-1g38scnj	164	14	x(t	x(t	NNP
cord-191574-1g38scnj	164	15	)	)	-RRB-
cord-191574-1g38scnj	164	16	,	,	,
cord-191574-1g38scnj	164	17	y(t	y(t	NN
cord-191574-1g38scnj	164	18	)	)	-RRB-
cord-191574-1g38scnj	164	19	and	and	CC
cord-191574-1g38scnj	164	20	z(t	z(t	CD
cord-191574-1g38scnj	164	21	)	)	-RRB-
cord-191574-1g38scnj	164	22	.	.	.
cord-191574-1g38scnj	165	1	The	the	DT
cord-191574-1g38scnj	165	2	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	165	3	solutions	solution	NNS
cord-191574-1g38scnj	165	4	have	have	VBP
cord-191574-1g38scnj	165	5	a	a	DT
cord-191574-1g38scnj	165	6	simple	simple	JJ
cord-191574-1g38scnj	165	7	mathematical	mathematical	JJ
cord-191574-1g38scnj	165	8	form	form	NN
cord-191574-1g38scnj	165	9	,	,	,
cord-191574-1g38scnj	165	10	and	and	CC
cord-191574-1g38scnj	165	11	they	-PRON-	PRP
cord-191574-1g38scnj	165	12	describes	describe	VBZ
cord-191574-1g38scnj	165	13	very	very	RB
cord-191574-1g38scnj	165	14	precisely	precisely	RB
cord-191574-1g38scnj	165	15	the	the	DT
cord-191574-1g38scnj	165	16	numerical	numerical	JJ
cord-191574-1g38scnj	165	17	behavior	behavior	NN
cord-191574-1g38scnj	165	18	of	of	IN
cord-191574-1g38scnj	165	19	the	the	DT
cord-191574-1g38scnj	165	20	model	model	NN
cord-191574-1g38scnj	165	21	for	for	IN
cord-191574-1g38scnj	165	22	a	a	DT
cord-191574-1g38scnj	165	23	large	large	JJ
cord-191574-1g38scnj	165	24	range	range	NN
cord-191574-1g38scnj	165	25	of	of	IN
cord-191574-1g38scnj	165	26	the	the	DT
cord-191574-1g38scnj	165	27	model	model	NN
cord-191574-1g38scnj	165	28	parameters	parameter	NNS
cord-191574-1g38scnj	165	29	(	(	-LRB-
cord-191574-1g38scnj	165	30	β	β	NN
cord-191574-1g38scnj	165	31	,	,	,
cord-191574-1g38scnj	165	32	γ	γ	NN
cord-191574-1g38scnj	165	33	,	,	,
cord-191574-1g38scnj	165	34	µ	µ	NNP
cord-191574-1g38scnj	165	35	)	)	-RRB-
cord-191574-1g38scnj	165	36	.	.	.
cord-191574-1g38scnj	166	1	The	the	DT
cord-191574-1g38scnj	166	2	time	time	NN
cord-191574-1g38scnj	166	3	dependence	dependence	NN
cord-191574-1g38scnj	166	4	of	of	IN
cord-191574-1g38scnj	166	5	the	the	DT
cord-191574-1g38scnj	166	6	three	three	CD
cord-191574-1g38scnj	166	7	compartments	compartment	NNS
cord-191574-1g38scnj	166	8	in	in	IN
cord-191574-1g38scnj	166	9	the	the	DT
cord-191574-1g38scnj	166	10	semianalytical	semianalytical	JJ
cord-191574-1g38scnj	166	11	solution	solution	NN
cord-191574-1g38scnj	166	12	obtained	obtain	VBN
cord-191574-1g38scnj	166	13	by	by	IN
cord-191574-1g38scnj	166	14	using	use	VBG
cord-191574-1g38scnj	166	15	the	the	DT
cord-191574-1g38scnj	166	16	Laplace	Laplace	NNP
cord-191574-1g38scnj	166	17	-	-	HYPH
cord-191574-1g38scnj	166	18	Adomian	Adomian	NNP
cord-191574-1g38scnj	166	19	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	166	20	Method	Method	NNP
cord-191574-1g38scnj	166	21	is	be	VBZ
cord-191574-1g38scnj	166	22	given	give	VBN
cord-191574-1g38scnj	166	23	by	by	IN
cord-191574-1g38scnj	166	24	a	a	DT
cord-191574-1g38scnj	166	25	sum	sum	NN
cord-191574-1g38scnj	166	26	containing	contain	VBG
cord-191574-1g38scnj	166	27	exponential	exponential	JJ
cord-191574-1g38scnj	166	28	terms	term	NNS
cord-191574-1g38scnj	166	29	.	.	.
cord-191574-1g38scnj	167	1	Such	such	PDT
cord-191574-1g38scnj	167	2	a	a	DT
cord-191574-1g38scnj	167	3	representation	representation	NN
cord-191574-1g38scnj	167	4	may	may	MD
cord-191574-1g38scnj	167	5	simplify	simplify	VB
cord-191574-1g38scnj	167	6	the	the	DT
cord-191574-1g38scnj	167	7	fitting	fitting	NN
cord-191574-1g38scnj	167	8	with	with	IN
cord-191574-1g38scnj	167	9	the	the	DT
cord-191574-1g38scnj	167	10	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	167	11	results	result	NNS
cord-191574-1g38scnj	167	12	.	.	.
cord-191574-1g38scnj	168	1	The	the	DT
cord-191574-1g38scnj	168	2	series	series	NN
cord-191574-1g38scnj	168	3	,	,	,
cord-191574-1g38scnj	168	4	truncated	truncate	VBN
cord-191574-1g38scnj	168	5	to	to	IN
cord-191574-1g38scnj	168	6	a	a	DT
cord-191574-1g38scnj	168	7	small	small	JJ
cord-191574-1g38scnj	168	8	number	number	NN
cord-191574-1g38scnj	168	9	of	of	IN
cord-191574-1g38scnj	168	10	terms	term	NNS
cord-191574-1g38scnj	168	11	,	,	,
cord-191574-1g38scnj	168	12	give	give	VB
cord-191574-1g38scnj	168	13	a	a	DT
cord-191574-1g38scnj	168	14	very	very	RB
cord-191574-1g38scnj	168	15	good	good	JJ
cord-191574-1g38scnj	168	16	description	description	NN
cord-191574-1g38scnj	168	17	of	of	IN
cord-191574-1g38scnj	168	18	the	the	DT
cord-191574-1g38scnj	168	19	numerical	numerical	JJ
cord-191574-1g38scnj	168	20	results	result	NNS
cord-191574-1g38scnj	168	21	for	for	IN
cord-191574-1g38scnj	168	22	a	a	DT
cord-191574-1g38scnj	168	23	large	large	JJ
cord-191574-1g38scnj	168	24	number	number	NN
cord-191574-1g38scnj	168	25	of	of	IN
cord-191574-1g38scnj	168	26	values	value	NNS
cord-191574-1g38scnj	168	27	of	of	IN
cord-191574-1g38scnj	168	28	the	the	DT
cord-191574-1g38scnj	168	29	model	model	NN
cord-191574-1g38scnj	168	30	parameters	parameter	NNS
cord-191574-1g38scnj	168	31	,	,	,
cord-191574-1g38scnj	168	32	and	and	CC
cord-191574-1g38scnj	168	33	of	of	IN
cord-191574-1g38scnj	168	34	the	the	DT
cord-191574-1g38scnj	168	35	initial	initial	JJ
cord-191574-1g38scnj	168	36	conditions	condition	NNS
cord-191574-1g38scnj	168	37	.	.	.
cord-191574-1g38scnj	169	1	In	in	IN
cord-191574-1g38scnj	169	2	fact	fact	NN
cord-191574-1g38scnj	169	3	,	,	,
cord-191574-1g38scnj	169	4	the	the	DT
cord-191574-1g38scnj	169	5	two	two	CD
cord-191574-1g38scnj	169	6	terms	term	NNS
cord-191574-1g38scnj	169	7	approximation	approximation	NN
cord-191574-1g38scnj	169	8	obtained	obtain	VBN
cord-191574-1g38scnj	169	9	with	with	IN
cord-191574-1g38scnj	169	10	the	the	DT
cord-191574-1g38scnj	169	11	use	use	NN
cord-191574-1g38scnj	169	12	of	of	IN
cord-191574-1g38scnj	169	13	the	the	DT
cord-191574-1g38scnj	169	14	Adomian	Adomian	NNP
cord-191574-1g38scnj	169	15	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	169	16	Method	Method	NNP
cord-191574-1g38scnj	169	17	also	also	RB
cord-191574-1g38scnj	169	18	gives	give	VBZ
cord-191574-1g38scnj	169	19	a	a	DT
cord-191574-1g38scnj	169	20	good	good	JJ
cord-191574-1g38scnj	169	21	approximation	approximation	NN
cord-191574-1g38scnj	169	22	of	of	IN
cord-191574-1g38scnj	169	23	the	the	DT
cord-191574-1g38scnj	169	24	results	result	NNS
cord-191574-1g38scnj	169	25	of	of	IN
cord-191574-1g38scnj	169	26	the	the	DT
cord-191574-1g38scnj	169	27	numerical	numerical	JJ
cord-191574-1g38scnj	169	28	integration	integration	NN
cord-191574-1g38scnj	169	29	of	of	IN
cord-191574-1g38scnj	169	30	the	the	DT
cord-191574-1g38scnj	169	31	SIR	SIR	NNP
cord-191574-1g38scnj	169	32	model	model	NN
cord-191574-1g38scnj	169	33	with	with	IN
cord-191574-1g38scnj	169	34	vital	vital	JJ
cord-191574-1g38scnj	169	35	dynamics	dynamic	NNS
cord-191574-1g38scnj	169	36	for	for	IN
cord-191574-1g38scnj	169	37	a	a	DT
cord-191574-1g38scnj	169	38	large	large	JJ
cord-191574-1g38scnj	169	39	range	range	NN
cord-191574-1g38scnj	169	40	of	of	IN
cord-191574-1g38scnj	169	41	parameter	parameter	NN
cord-191574-1g38scnj	169	42	values	value	NNS
cord-191574-1g38scnj	169	43	.	.	.
cord-191574-1g38scnj	170	1	Exact	exact	JJ
cord-191574-1g38scnj	170	2	solutions	solution	NNS
cord-191574-1g38scnj	170	3	of	of	IN
cord-191574-1g38scnj	170	4	the	the	DT
cord-191574-1g38scnj	170	5	epidemiological	epidemiological	JJ
cord-191574-1g38scnj	170	6	models	model	NNS
cord-191574-1g38scnj	170	7	are	be	VBP
cord-191574-1g38scnj	170	8	important	important	JJ
cord-191574-1g38scnj	170	9	for	for	IN
cord-191574-1g38scnj	170	10	epidemiologists	epidemiologist	NNS
cord-191574-1g38scnj	170	11	because	because	IN
cord-191574-1g38scnj	170	12	they	-PRON-	PRP
cord-191574-1g38scnj	170	13	allow	allow	VBP
cord-191574-1g38scnj	170	14	the	the	DT
cord-191574-1g38scnj	170	15	study	study	NN
cord-191574-1g38scnj	170	16	of	of	IN
cord-191574-1g38scnj	170	17	the	the	DT
cord-191574-1g38scnj	170	18	spreading	spreading	NN
cord-191574-1g38scnj	170	19	of	of	IN
cord-191574-1g38scnj	170	20	infectious	infectious	JJ
cord-191574-1g38scnj	170	21	diseases	disease	NNS
cord-191574-1g38scnj	170	22	in	in	IN
cord-191574-1g38scnj	170	23	different	different	JJ
cord-191574-1g38scnj	170	24	situations	situation	NNS
cord-191574-1g38scnj	170	25	.	.	.
cord-191574-1g38scnj	171	1	They	-PRON-	PRP
cord-191574-1g38scnj	171	2	are	be	VBP
cord-191574-1g38scnj	171	3	also	also	RB
cord-191574-1g38scnj	171	4	helpful	helpful	JJ
cord-191574-1g38scnj	171	5	in	in	IN
cord-191574-1g38scnj	171	6	the	the	DT
cord-191574-1g38scnj	171	7	design	design	NN
cord-191574-1g38scnj	171	8	of	of	IN
cord-191574-1g38scnj	171	9	the	the	DT
cord-191574-1g38scnj	171	10	best	good	JJS
cord-191574-1g38scnj	171	11	social	social	JJ
cord-191574-1g38scnj	171	12	strategies	strategy	NNS
cord-191574-1g38scnj	171	13	for	for	IN
cord-191574-1g38scnj	171	14	their	-PRON-	PRP$
cord-191574-1g38scnj	171	15	control	control	NN
cord-191574-1g38scnj	171	16	.	.	.
cord-191574-1g38scnj	172	1	Hopefully	hopefully	RB
cord-191574-1g38scnj	172	2	the	the	DT
cord-191574-1g38scnj	172	3	results	result	NNS
cord-191574-1g38scnj	172	4	obtained	obtain	VBN
cord-191574-1g38scnj	172	5	in	in	IN
cord-191574-1g38scnj	172	6	the	the	DT
cord-191574-1g38scnj	172	7	present	present	JJ
cord-191574-1g38scnj	172	8	paper	paper	NN
cord-191574-1g38scnj	172	9	may	may	MD
cord-191574-1g38scnj	172	10	also	also	RB
cord-191574-1g38scnj	172	11	contribute	contribute	VB
cord-191574-1g38scnj	172	12	to	to	IN
cord-191574-1g38scnj	172	13	the	the	DT
cord-191574-1g38scnj	172	14	investigations	investigation	NNS
cord-191574-1g38scnj	172	15	of	of	IN
cord-191574-1g38scnj	172	16	the	the	DT
cord-191574-1g38scnj	172	17	dynamics	dynamic	NNS
cord-191574-1g38scnj	172	18	,	,	,
cord-191574-1g38scnj	172	19	evolution	evolution	NN
cord-191574-1g38scnj	172	20	and	and	CC
cord-191574-1g38scnj	172	21	long	long	JJ
cord-191574-1g38scnj	172	22	term	term	NN
cord-191574-1g38scnj	172	23	impact	impact	NN
cord-191574-1g38scnj	172	24	of	of	IN
cord-191574-1g38scnj	172	25	the	the	DT
cord-191574-1g38scnj	172	26	present	present	JJ
cord-191574-1g38scnj	172	27	and	and	CC
cord-191574-1g38scnj	172	28	of	of	IN
cord-191574-1g38scnj	172	29	the	the	DT
cord-191574-1g38scnj	172	30	future	future	JJ
cord-191574-1g38scnj	172	31	epidemics	epidemic	NNS
cord-191574-1g38scnj	172	32	.	.	.
cord-191574-1g38scnj	173	1	Mathematical	mathematical	JJ
cord-191574-1g38scnj	173	2	Biology	biology	NN
cord-191574-1g38scnj	173	3	:	:	:
cord-191574-1g38scnj	173	4	I.	I.	NNP
cord-191574-1g38scnj	173	5	An	an	DT
cord-191574-1g38scnj	173	6	Introduction	introduction	NN
cord-191574-1g38scnj	173	7	Epidemic	epidemic	NN
cord-191574-1g38scnj	173	8	Modeling	modeling	NN
cord-191574-1g38scnj	173	9	:	:	:
cord-191574-1g38scnj	174	1	An	an	DT
cord-191574-1g38scnj	174	2	Introduction	introduction	NN
cord-191574-1g38scnj	174	3	Modeling	Modeling	NNP
cord-191574-1g38scnj	174	4	Infectious	Infectious	NNP
cord-191574-1g38scnj	174	5	Diseases	Diseases	NNPS
cord-191574-1g38scnj	174	6	Contribution	Contribution	NNP
cord-191574-1g38scnj	174	7	to	to	IN
cord-191574-1g38scnj	174	8	the	the	DT
cord-191574-1g38scnj	174	9	mathematical	mathematical	JJ
cord-191574-1g38scnj	174	10	theory	theory	NN
cord-191574-1g38scnj	174	11	of	of	IN
cord-191574-1g38scnj	174	12	epidemics	epidemic	NNS
cord-191574-1g38scnj	175	1	Clinical	clinical	JJ
cord-191574-1g38scnj	175	2	features	feature	NNS
cord-191574-1g38scnj	175	3	of	of	IN
cord-191574-1g38scnj	175	4	patients	patient	NNS
cord-191574-1g38scnj	175	5	infected	infect	VBN
cord-191574-1g38scnj	175	6	with	with	IN
cord-191574-1g38scnj	175	7	2019	2019	CD
cord-191574-1g38scnj	175	8	novel	novel	JJ
cord-191574-1g38scnj	175	9	coronavirus	coronavirus	NN
cord-191574-1g38scnj	175	10	in	in	IN
cord-191574-1g38scnj	175	11	Effective	effective	JJ
cord-191574-1g38scnj	175	12	containment	containment	NN
cord-191574-1g38scnj	175	13	explains	explain	VBZ
cord-191574-1g38scnj	175	14	subexponential	subexponential	JJ
cord-191574-1g38scnj	175	15	growth	growth	NN
cord-191574-1g38scnj	175	16	in	in	IN
cord-191574-1g38scnj	175	17	recent	recent	JJ
cord-191574-1g38scnj	175	18	confirmed	confirm	VBD
cord-191574-1g38scnj	175	19	COVID-19	covid-19	CD
cord-191574-1g38scnj	175	20	cases	case	NNS
cord-191574-1g38scnj	175	21	in	in	IN
cord-191574-1g38scnj	175	22	China	China	NNP
cord-191574-1g38scnj	175	23	Simulating	simulate	VBG
cord-191574-1g38scnj	175	24	the	the	DT
cord-191574-1g38scnj	175	25	spread	spread	NN
cord-191574-1g38scnj	175	26	of	of	IN
cord-191574-1g38scnj	175	27	COVID-19	covid-19	NN
cord-191574-1g38scnj	175	28	via	via	IN
cord-191574-1g38scnj	175	29	spatially	spatially	RB
cord-191574-1g38scnj	175	30	-	-	HYPH
cord-191574-1g38scnj	175	31	resolved	resolve	VBN
cord-191574-1g38scnj	175	32	susceptible	susceptible	JJ
cord-191574-1g38scnj	175	33	-	-	HYPH
cord-191574-1g38scnj	175	34	exposed	expose	VBN
cord-191574-1g38scnj	175	35	-	-	HYPH
cord-191574-1g38scnj	175	36	infected	infect	VBN
cord-191574-1g38scnj	175	37	-	-	HYPH
cord-191574-1g38scnj	175	38	recovered	recover	VBN
cord-191574-1g38scnj	175	39	deceased	deceased	JJ
cord-191574-1g38scnj	175	40	(	(	-LRB-
cord-191574-1g38scnj	175	41	SEIRD	SEIRD	NNP
cord-191574-1g38scnj	175	42	)	)	-RRB-
cord-191574-1g38scnj	175	43	model	model	NN
cord-191574-1g38scnj	175	44	with	with	IN
cord-191574-1g38scnj	175	45	heterogeneous	heterogeneous	JJ
cord-191574-1g38scnj	175	46	diffusion	diffusion	NN
cord-191574-1g38scnj	175	47	Size	size	NN
cord-191574-1g38scnj	175	48	and	and	CC
cord-191574-1g38scnj	175	49	timescale	timescale	NN
cord-191574-1g38scnj	175	50	of	of	IN
cord-191574-1g38scnj	175	51	epidemics	epidemic	NNS
cord-191574-1g38scnj	175	52	in	in	IN
cord-191574-1g38scnj	175	53	the	the	DT
cord-191574-1g38scnj	175	54	SIR	SIR	NNP
cord-191574-1g38scnj	175	55	framework	framework	NN
cord-191574-1g38scnj	175	56	,	,	,
cord-191574-1g38scnj	175	57	Phys	Phys	NNP
cord-191574-1g38scnj	175	58	.	.	.
cord-191574-1g38scnj	176	1	D	D	NNP
cord-191574-1g38scnj	176	2	Nonlinear	Nonlinear	NNP
cord-191574-1g38scnj	176	3	Phenom	Phenom	NNP
cord-191574-1g38scnj	176	4	Computing	compute	VBG
cord-191574-1g38scnj	176	5	the	the	DT
cord-191574-1g38scnj	176	6	density	density	NN
cord-191574-1g38scnj	176	7	function	function	NN
cord-191574-1g38scnj	176	8	of	of	IN
cord-191574-1g38scnj	176	9	complex	complex	JJ
cord-191574-1g38scnj	176	10	models	model	NNS
cord-191574-1g38scnj	176	11	with	with	IN
cord-191574-1g38scnj	176	12	randomness	randomness	NN
cord-191574-1g38scnj	176	13	by	by	IN
cord-191574-1g38scnj	176	14	using	use	VBG
cord-191574-1g38scnj	176	15	polynomial	polynomial	JJ
cord-191574-1g38scnj	176	16	expansions	expansion	NNS
cord-191574-1g38scnj	176	17	and	and	CC
cord-191574-1g38scnj	176	18	the	the	DT
cord-191574-1g38scnj	176	19	RVT	RVT	NNP
cord-191574-1g38scnj	176	20	technique	technique	NN
cord-191574-1g38scnj	176	21	.	.	.
cord-191574-1g38scnj	177	1	Application	application	NN
cord-191574-1g38scnj	177	2	to	to	IN
cord-191574-1g38scnj	177	3	the	the	DT
cord-191574-1g38scnj	177	4	SIR	SIR	NNP
cord-191574-1g38scnj	177	5	epidemic	epidemic	NN
cord-191574-1g38scnj	177	6	model	model	NN
cord-191574-1g38scnj	178	1	Susceptible	susceptible	JJ
cord-191574-1g38scnj	178	2	-	-	HYPH
cord-191574-1g38scnj	178	3	Infected	Infected	NNP
cord-191574-1g38scnj	178	4	-	-	HYPH
cord-191574-1g38scnj	178	5	Recovered	recovered	JJ
cord-191574-1g38scnj	178	6	(	(	-LRB-
cord-191574-1g38scnj	178	7	SIR	SIR	NNP
cord-191574-1g38scnj	178	8	)	)	-RRB-
cord-191574-1g38scnj	178	9	Dynamics	Dynamics	NNPS
cord-191574-1g38scnj	178	10	of	of	IN
cord-191574-1g38scnj	178	11	COVID-19	COVID-19	NNP
cord-191574-1g38scnj	178	12	and	and	CC
cord-191574-1g38scnj	178	13	Economic	Economic	NNP
cord-191574-1g38scnj	178	14	Impact	Impact	NNP
cord-191574-1g38scnj	179	1	Inferring	infer	VBG
cord-191574-1g38scnj	179	2	change	change	NN
cord-191574-1g38scnj	179	3	points	point	NNS
cord-191574-1g38scnj	179	4	in	in	IN
cord-191574-1g38scnj	179	5	the	the	DT
cord-191574-1g38scnj	179	6	COVID-19	covid-19	JJ
cord-191574-1g38scnj	179	7	spreading	spreading	NN
cord-191574-1g38scnj	179	8	reveals	reveal	VBZ
cord-191574-1g38scnj	179	9	the	the	DT
cord-191574-1g38scnj	179	10	effectiveness	effectiveness	NN
cord-191574-1g38scnj	179	11	of	of	IN
cord-191574-1g38scnj	179	12	interventions	intervention	NNS
cord-191574-1g38scnj	179	13	How	how	WRB
cord-191574-1g38scnj	179	14	to	to	TO
cord-191574-1g38scnj	179	15	reduce	reduce	VB
cord-191574-1g38scnj	179	16	epidemic	epidemic	NN
cord-191574-1g38scnj	179	17	peaks	peak	NNS
cord-191574-1g38scnj	179	18	keeping	keep	VBG
cord-191574-1g38scnj	179	19	under	under	IN
cord-191574-1g38scnj	179	20	control	control	NN
cord-191574-1g38scnj	179	21	the	the	DT
cord-191574-1g38scnj	179	22	time	time	NN
cord-191574-1g38scnj	179	23	-	-	HYPH
cord-191574-1g38scnj	179	24	span	span	NN
cord-191574-1g38scnj	179	25	of	of	IN
cord-191574-1g38scnj	179	26	the	the	DT
cord-191574-1g38scnj	179	27	epidemic	epidemic	NN
cord-191574-1g38scnj	180	1	Forecasting	forecasting	NN
cord-191574-1g38scnj	180	2	COVID	COVID	NNP
cord-191574-1g38scnj	180	3	19	19	CD
cord-191574-1g38scnj	180	4	growth	growth	NN
cord-191574-1g38scnj	180	5	in	in	IN
cord-191574-1g38scnj	180	6	India	India	NNP
cord-191574-1g38scnj	180	7	using	use	VBG
cord-191574-1g38scnj	180	8	Susceptible	susceptible	JJ
cord-191574-1g38scnj	180	9	-	-	HYPH
cord-191574-1g38scnj	180	10	Infected	Infected	NNP
cord-191574-1g38scnj	180	11	-	-	HYPH
cord-191574-1g38scnj	180	12	Recovered	recovered	JJ
cord-191574-1g38scnj	180	13	(	(	-LRB-
cord-191574-1g38scnj	180	14	SIR	SIR	NNP
cord-191574-1g38scnj	180	15	)	)	-RRB-
cord-191574-1g38scnj	180	16	model	model	NN
cord-191574-1g38scnj	181	1	The	the	DT
cord-191574-1g38scnj	181	2	challenges	challenge	NNS
cord-191574-1g38scnj	181	3	of	of	IN
cord-191574-1g38scnj	181	4	modeling	model	VBG
cord-191574-1g38scnj	181	5	and	and	CC
cord-191574-1g38scnj	181	6	forecasting	forecast	VBG
cord-191574-1g38scnj	181	7	the	the	DT
cord-191574-1g38scnj	181	8	spread	spread	NN
cord-191574-1g38scnj	181	9	of	of	IN
cord-191574-1g38scnj	181	10	COVID-19	COVID-19	NNP
cord-191574-1g38scnj	181	11	A	a	DT
cord-191574-1g38scnj	181	12	feedback	feedback	NN
cord-191574-1g38scnj	181	13	SIR	SIR	NNP
cord-191574-1g38scnj	181	14	(	(	-LRB-
cord-191574-1g38scnj	181	15	fSIR	fsir	JJ
cord-191574-1g38scnj	181	16	)	)	-RRB-
cord-191574-1g38scnj	181	17	model	model	NN
cord-191574-1g38scnj	181	18	highlights	highlight	VBZ
cord-191574-1g38scnj	181	19	advantages	advantage	NNS
cord-191574-1g38scnj	181	20	and	and	CC
cord-191574-1g38scnj	181	21	limitations	limitation	NNS
cord-191574-1g38scnj	181	22	of	of	IN
cord-191574-1g38scnj	181	23	infection	infection	NN
cord-191574-1g38scnj	181	24	-	-	HYPH
cord-191574-1g38scnj	181	25	based	base	VBN
cord-191574-1g38scnj	181	26	social	social	JJ
cord-191574-1g38scnj	181	27	distancing	distance	VBG
cord-191574-1g38scnj	181	28	Estimation	Estimation	NNP
cord-191574-1g38scnj	181	29	of	of	IN
cord-191574-1g38scnj	181	30	COVID-19	COVID-19	NNP
cord-191574-1g38scnj	181	31	spread	spread	NN
cord-191574-1g38scnj	181	32	curves	curve	NNS
cord-191574-1g38scnj	181	33	integrating	integrate	VBG
cord-191574-1g38scnj	181	34	global	global	JJ
cord-191574-1g38scnj	181	35	data	datum	NNS
cord-191574-1g38scnj	181	36	and	and	CC
cord-191574-1g38scnj	181	37	borrowing	borrow	VBG
cord-191574-1g38scnj	181	38	information	information	NN
cord-191574-1g38scnj	181	39	Phenomenological	phenomenological	JJ
cord-191574-1g38scnj	181	40	dynamics	dynamic	NNS
cord-191574-1g38scnj	181	41	of	of	IN
cord-191574-1g38scnj	181	42	COVID-19	COVID-19	NNP
cord-191574-1g38scnj	181	43	pandemic	pandemic	NN
cord-191574-1g38scnj	181	44	:	:	:
cord-191574-1g38scnj	181	45	meta	meta	NN
cord-191574-1g38scnj	181	46	-	-	HYPH
cord-191574-1g38scnj	181	47	analysis	analysis	NN
cord-191574-1g38scnj	181	48	for	for	IN
cord-191574-1g38scnj	181	49	adjustment	adjustment	NN
cord-191574-1g38scnj	181	50	parameters	parameter	NNS
cord-191574-1g38scnj	181	51	On	on	IN
cord-191574-1g38scnj	181	52	the	the	DT
cord-191574-1g38scnj	181	53	Emergence	emergence	NN
cord-191574-1g38scnj	181	54	of	of	IN
cord-191574-1g38scnj	181	55	a	a	DT
cord-191574-1g38scnj	181	56	Power	Power	NNP
cord-191574-1g38scnj	181	57	Law	Law	NNP
cord-191574-1g38scnj	181	58	in	in	IN
cord-191574-1g38scnj	181	59	the	the	DT
cord-191574-1g38scnj	181	60	Distribution	Distribution	NNP
cord-191574-1g38scnj	181	61	of	of	IN
cord-191574-1g38scnj	181	62	COVID-19	COVID-19	NNP
cord-191574-1g38scnj	181	63	Cases	Cases	NNPS
cord-191574-1g38scnj	181	64	Optimal	Optimal	NNP
cord-191574-1g38scnj	181	65	control	control	NN
cord-191574-1g38scnj	181	66	of	of	IN
cord-191574-1g38scnj	181	67	an	an	DT
cord-191574-1g38scnj	181	68	SIR	SIR	NNP
cord-191574-1g38scnj	181	69	epidemic	epidemic	NN
cord-191574-1g38scnj	181	70	through	through	IN
cord-191574-1g38scnj	181	71	finite	finite	JJ
cord-191574-1g38scnj	181	72	-	-	HYPH
cord-191574-1g38scnj	181	73	time	time	NN
cord-191574-1g38scnj	181	74	non	non	JJ
cord-191574-1g38scnj	181	75	-	-	JJ
cord-191574-1g38scnj	181	76	pharmaceutical	pharmaceutical	JJ
cord-191574-1g38scnj	181	77	intervention	intervention	NN
cord-191574-1g38scnj	181	78	Understanding	understand	VBG
cord-191574-1g38scnj	181	79	the	the	DT
cord-191574-1g38scnj	181	80	COVID19	COVID19	NNP
cord-191574-1g38scnj	181	81	infection	infection	NN
cord-191574-1g38scnj	182	1	curves	curve	NNS
cord-191574-1g38scnj	183	1	-finding	-finde	VBG
cord-191574-1g38scnj	184	1	the	the	DT
cord-191574-1g38scnj	184	2	right	right	JJ
cord-191574-1g38scnj	184	3	numbers	number	NNS
cord-191574-1g38scnj	184	4	Exact	exact	JJ
cord-191574-1g38scnj	184	5	analytical	analytical	JJ
cord-191574-1g38scnj	184	6	solutions	solution	NNS
cord-191574-1g38scnj	184	7	of	of	IN
cord-191574-1g38scnj	184	8	the	the	DT
cord-191574-1g38scnj	184	9	Susceptible	susceptible	JJ
cord-191574-1g38scnj	184	10	-	-	HYPH
cord-191574-1g38scnj	184	11	Infected	Infected	NNP
cord-191574-1g38scnj	184	12	-	-	HYPH
cord-191574-1g38scnj	184	13	Recovered	recovered	JJ
cord-191574-1g38scnj	184	14	(	(	-LRB-
cord-191574-1g38scnj	184	15	SIR	SIR	NNP
cord-191574-1g38scnj	184	16	)	)	-RRB-
cord-191574-1g38scnj	184	17	epidemic	epidemic	NN
cord-191574-1g38scnj	184	18	model	model	NN
cord-191574-1g38scnj	184	19	and	and	CC
cord-191574-1g38scnj	184	20	of	of	IN
cord-191574-1g38scnj	184	21	the	the	DT
cord-191574-1g38scnj	184	22	SIR	SIR	NNP
cord-191574-1g38scnj	184	23	model	model	NN
cord-191574-1g38scnj	184	24	with	with	IN
cord-191574-1g38scnj	184	25	equal	equal	JJ
cord-191574-1g38scnj	184	26	death	death	NN
cord-191574-1g38scnj	184	27	and	and	CC
cord-191574-1g38scnj	184	28	birth	birth	NN
cord-191574-1g38scnj	184	29	rates	rate	NNS
cord-191574-1g38scnj	184	30	A	a	DT
cord-191574-1g38scnj	184	31	Mathematical	Mathematical	NNP
cord-191574-1g38scnj	184	32	Model	Model	NNP
cord-191574-1g38scnj	184	33	of	of	IN
cord-191574-1g38scnj	184	34	Epidemics-	Epidemics-	NNP
cord-191574-1g38scnj	185	1	A	a	DT
cord-191574-1g38scnj	185	2	Tutorial	Tutorial	NNP
cord-191574-1g38scnj	185	3	for	for	IN
cord-191574-1g38scnj	185	4	Students	student	NNS
cord-191574-1g38scnj	185	5	,	,	,
cord-191574-1g38scnj	185	6	Mathematics	mathematic	NNS
cord-191574-1g38scnj	185	7	2020	2020	CD
cord-191574-1g38scnj	185	8	Variational	Variational	NNP
cord-191574-1g38scnj	185	9	iteration	iteration	NN
cord-191574-1g38scnj	185	10	method	method	NN
cord-191574-1g38scnj	185	11	for	for	IN
cord-191574-1g38scnj	185	12	solving	solve	VBG
cord-191574-1g38scnj	185	13	the	the	DT
cord-191574-1g38scnj	185	14	epidemic	epidemic	NN
cord-191574-1g38scnj	185	15	model	model	NN
cord-191574-1g38scnj	185	16	and	and	CC
cord-191574-1g38scnj	185	17	the	the	DT
cord-191574-1g38scnj	185	18	prey	prey	NN
cord-191574-1g38scnj	185	19	and	and	CC
cord-191574-1g38scnj	185	20	predator	predator	NN
cord-191574-1g38scnj	185	21	problem	problem	NN
cord-191574-1g38scnj	185	22	Solution	Solution	NNP
cord-191574-1g38scnj	185	23	of	of	IN
cord-191574-1g38scnj	185	24	the	the	DT
cord-191574-1g38scnj	185	25	epidemic	epidemic	NN
cord-191574-1g38scnj	185	26	model	model	NN
cord-191574-1g38scnj	185	27	by	by	IN
cord-191574-1g38scnj	185	28	homotopy	homotopy	JJ
cord-191574-1g38scnj	185	29	perturbation	perturbation	NN
cord-191574-1g38scnj	185	30	method	method	NN
cord-191574-1g38scnj	185	31	A	a	DT
cord-191574-1g38scnj	185	32	new	new	JJ
cord-191574-1g38scnj	185	33	method	method	NN
cord-191574-1g38scnj	185	34	for	for	IN
cord-191574-1g38scnj	185	35	solving	solve	VBG
cord-191574-1g38scnj	185	36	epidemic	epidemic	NN
cord-191574-1g38scnj	185	37	model	model	NN
cord-191574-1g38scnj	186	1	A	a	DT
cord-191574-1g38scnj	186	2	review	review	NN
cord-191574-1g38scnj	186	3	of	of	IN
cord-191574-1g38scnj	186	4	the	the	DT
cord-191574-1g38scnj	186	5	decomposition	decomposition	NN
cord-191574-1g38scnj	186	6	method	method	NN
cord-191574-1g38scnj	186	7	in	in	IN
cord-191574-1g38scnj	186	8	applied	apply	VBN
cord-191574-1g38scnj	186	9	mathematics	mathematic	NNS
cord-191574-1g38scnj	186	10	Solving	Solving	NNP
cord-191574-1g38scnj	186	11	Frontier	Frontier	NNP
cord-191574-1g38scnj	186	12	Problems	Problems	NNPS
cord-191574-1g38scnj	186	13	of	of	IN
cord-191574-1g38scnj	186	14	Physics	Physics	NNP
cord-191574-1g38scnj	186	15	:	:	:
cord-191574-1g38scnj	186	16	the	the	DT
cord-191574-1g38scnj	186	17	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	186	18	Method	Method	NNP
cord-191574-1g38scnj	186	19	A	a	DT
cord-191574-1g38scnj	186	20	comparison	comparison	NN
cord-191574-1g38scnj	186	21	between	between	IN
cord-191574-1g38scnj	186	22	the	the	DT
cord-191574-1g38scnj	186	23	variational	variational	JJ
cord-191574-1g38scnj	186	24	iteration	iteration	NN
cord-191574-1g38scnj	186	25	method	method	NN
cord-191574-1g38scnj	186	26	and	and	CC
cord-191574-1g38scnj	186	27	Adomian	adomian	JJ
cord-191574-1g38scnj	186	28	decomposition	decomposition	NN
cord-191574-1g38scnj	186	29	method	method	NN
cord-191574-1g38scnj	186	30	Solving	solve	VBG
cord-191574-1g38scnj	186	31	New	New	NNP
cord-191574-1g38scnj	186	32	Fourth	fourth	JJ
cord-191574-1g38scnj	186	33	-	-	HYPH
cord-191574-1g38scnj	186	34	Order	Order	NNP
cord-191574-1g38scnj	186	35	Emden	Emden	NNP
cord-191574-1g38scnj	186	36	-	-	HYPH
cord-191574-1g38scnj	186	37	Fowler	Fowler	NNP
cord-191574-1g38scnj	186	38	-	-	HYPH
cord-191574-1g38scnj	186	39	Type	Type	NNP
cord-191574-1g38scnj	186	40	Equations	Equations	NNPS
cord-191574-1g38scnj	186	41	by	by	IN
cord-191574-1g38scnj	187	1	the	the	DT
cord-191574-1g38scnj	187	2	Adomian	Adomian	NNP
cord-191574-1g38scnj	187	3	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	187	4	Method	Method	NNP
cord-191574-1g38scnj	187	5	A	a	DT
cord-191574-1g38scnj	187	6	reliable	reliable	JJ
cord-191574-1g38scnj	187	7	algorithm	algorithm	NN
cord-191574-1g38scnj	187	8	for	for	IN
cord-191574-1g38scnj	187	9	positive	positive	JJ
cord-191574-1g38scnj	187	10	solutions	solution	NNS
cord-191574-1g38scnj	187	11	of	of	IN
cord-191574-1g38scnj	187	12	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	187	13	boundary	boundary	JJ
cord-191574-1g38scnj	187	14	value	value	NN
cord-191574-1g38scnj	187	15	problems	problem	NNS
cord-191574-1g38scnj	187	16	by	by	IN
cord-191574-1g38scnj	187	17	the	the	DT
cord-191574-1g38scnj	187	18	multistage	multistage	JJ
cord-191574-1g38scnj	187	19	Adomian	adomian	JJ
cord-191574-1g38scnj	187	20	decomposition	decomposition	NN
cord-191574-1g38scnj	187	21	method	method	NN
cord-191574-1g38scnj	187	22	Computation	computation	NN
cord-191574-1g38scnj	187	23	of	of	IN
cord-191574-1g38scnj	187	24	the	the	DT
cord-191574-1g38scnj	187	25	general	general	JJ
cord-191574-1g38scnj	187	26	relativistic	relativistic	JJ
cord-191574-1g38scnj	187	27	perihelion	perihelion	NN
cord-191574-1g38scnj	187	28	precession	precession	NN
cord-191574-1g38scnj	187	29	and	and	CC
cord-191574-1g38scnj	187	30	of	of	IN
cord-191574-1g38scnj	187	31	light	light	JJ
cord-191574-1g38scnj	187	32	deflection	deflection	NN
cord-191574-1g38scnj	187	33	via	via	IN
cord-191574-1g38scnj	187	34	the	the	DT
cord-191574-1g38scnj	187	35	Laplace	Laplace	NNP
cord-191574-1g38scnj	187	36	-	-	HYPH
cord-191574-1g38scnj	187	37	Adomian	Adomian	NNP
cord-191574-1g38scnj	187	38	Decomposition	decomposition	NN
cord-191574-1g38scnj	187	39	Method	method	NN
cord-191574-1g38scnj	187	40	Analytical	analytical	JJ
cord-191574-1g38scnj	187	41	and	and	CC
cord-191574-1g38scnj	187	42	numerical	numerical	JJ
cord-191574-1g38scnj	187	43	treatment	treatment	NN
cord-191574-1g38scnj	187	44	of	of	IN
cord-191574-1g38scnj	187	45	Falkner	Falkner	NNP
cord-191574-1g38scnj	187	46	-	-	HYPH
cord-191574-1g38scnj	187	47	Skan	Skan	NNP
cord-191574-1g38scnj	187	48	equation	equation	NN
cord-191574-1g38scnj	187	49	via	via	IN
cord-191574-1g38scnj	187	50	a	a	DT
cord-191574-1g38scnj	187	51	transformation	transformation	NN
cord-191574-1g38scnj	187	52	and	and	CC
cord-191574-1g38scnj	187	53	Adomian	Adomian	NNP
cord-191574-1g38scnj	187	54	's	's	POS
cord-191574-1g38scnj	187	55	method	method	NN
cord-191574-1g38scnj	187	56	Solving	solve	VBG
cord-191574-1g38scnj	187	57	the	the	DT
cord-191574-1g38scnj	187	58	nonlinear	nonlinear	JJ
cord-191574-1g38scnj	187	59	biharmonic	biharmonic	JJ
cord-191574-1g38scnj	187	60	equation	equation	NN
cord-191574-1g38scnj	187	61	by	by	IN
cord-191574-1g38scnj	187	62	the	the	DT
cord-191574-1g38scnj	187	63	Laplace	Laplace	NNP
cord-191574-1g38scnj	187	64	-	-	HYPH
cord-191574-1g38scnj	187	65	Adomian	Adomian	NNP
cord-191574-1g38scnj	187	66	and	and	CC
cord-191574-1g38scnj	187	67	Adomian	adomian	JJ
cord-191574-1g38scnj	187	68	Decomposition	decomposition	NN
cord-191574-1g38scnj	187	69	Methods	Methods	NNPS
cord-191574-1g38scnj	187	70	,	,	,
cord-191574-1g38scnj	187	71	Surveys	Surveys	NNPS
cord-191574-1g38scnj	187	72	in	in	IN
cord-191574-1g38scnj	187	73	Mathematics	Mathematics	NNP
cord-191574-1g38scnj	187	74	and	and	CC
cord-191574-1g38scnj	187	75	its	-PRON-	PRP$
cord-191574-1g38scnj	187	76	Applications	application	NNS
cord-191574-1g38scnj	187	77	Vortex	Vortex	NNP
cord-191574-1g38scnj	187	78	solutions	solution	NNS
cord-191574-1g38scnj	187	79	in	in	IN
cord-191574-1g38scnj	187	80	atomic	atomic	JJ
cord-191574-1g38scnj	187	81	Bose	Bose	NNP
cord-191574-1g38scnj	187	82	-	-	HYPH
cord-191574-1g38scnj	187	83	Einstein	Einstein	NNP
cord-191574-1g38scnj	187	84	condensates	condensate	NNS
cord-191574-1g38scnj	187	85	via	via	IN
cord-191574-1g38scnj	187	86	the	the	DT
cord-191574-1g38scnj	187	87	Adomian	adomian	JJ
cord-191574-1g38scnj	187	88	Decomposition	Decomposition	NNP
cord-191574-1g38scnj	187	89	Method	Method	NNP
cord-191574-1g38scnj	187	90	Solution	Solution	NNP
cord-191574-1g38scnj	187	91	of	of	IN
cord-191574-1g38scnj	187	92	the	the	DT
cord-191574-1g38scnj	187	93	epidemic	epidemic	NN
cord-191574-1g38scnj	187	94	model	model	NN
cord-191574-1g38scnj	187	95	by	by	IN
cord-191574-1g38scnj	187	96	Adomian	adomian	JJ
cord-191574-1g38scnj	187	97	decomposition	decomposition	NN
cord-191574-1g38scnj	187	98	method	method	NN
cord-191574-1g38scnj	188	1	A	a	DT
cord-191574-1g38scnj	188	2	simple	simple	JJ
cord-191574-1g38scnj	188	3	computational	computational	JJ
cord-191574-1g38scnj	188	4	approach	approach	NN
cord-191574-1g38scnj	188	5	to	to	IN
cord-191574-1g38scnj	188	6	the	the	DT
cord-191574-1g38scnj	188	7	Susceptible	Susceptible	NNP
cord-191574-1g38scnj	188	8	-	-	HYPH
cord-191574-1g38scnj	188	9	Infected	Infected	NNP
cord-191574-1g38scnj	188	10	-	-	HYPH
cord-191574-1g38scnj	188	11	Recovered	recovered	JJ
cord-191574-1g38scnj	188	12	(	(	-LRB-
cord-191574-1g38scnj	188	13	SIR	SIR	NNP
cord-191574-1g38scnj	188	14	)	)	-RRB-
cord-191574-1g38scnj	188	15	epidemic	epidemic	NN
cord-191574-1g38scnj	188	16	model	model	NN
cord-191574-1g38scnj	188	17	via	via	IN
cord-191574-1g38scnj	188	18	the	the	DT
cord-191574-1g38scnj	188	19	Laplace	Laplace	NNP
cord-191574-1g38scnj	188	20	-	-	HYPH
cord-191574-1g38scnj	188	21	Adomian	Adomian	NNP
cord-191574-1g38scnj	188	22	Decomposition	decomposition	NN
cord-191574-1g38scnj	188	23	Method	Method	NNP
cord-191574-1g38scnj	188	24	On	on	IN
cord-191574-1g38scnj	188	25	the	the	DT
cord-191574-1g38scnj	188	26	Integrability	Integrability	NNP
cord-191574-1g38scnj	188	27	of	of	IN
cord-191574-1g38scnj	188	28	the	the	DT
cord-191574-1g38scnj	188	29	SIR	SIR	NNP
cord-191574-1g38scnj	188	30	Epidemic	Epidemic	NNP
cord-191574-1g38scnj	188	31	Model	Model	NNP
cord-191574-1g38scnj	188	32	with	with	IN
cord-191574-1g38scnj	188	33	Vital	vital	JJ
cord-191574-1g38scnj	188	34	Dynamics	dynamic	NNS