id	sid	tid	token	lemma	pos
cana-5488	1	1	communications	communication	NOUN
cana-5488	1	2	on	on	ADP
cana-5488	1	3	applied	apply	VERB
cana-5488	1	4	nonlinear	nonlinear	ADJ
cana-5488	1	5	analysis	analysis	NOUN
cana-5488	1	6	issn	issn	NOUN
cana-5488	1	7	:	:	PUNCT
cana-5488	1	8	1074	1074	NUM
cana-5488	1	9	-	-	PUNCT
cana-5488	1	10	133x	133x	NUM
cana-5488	1	11	vol	vol	VERB
cana-5488	1	12	32	32	NUM
cana-5488	1	13	no	no	NOUN
cana-5488	1	14	.	.	PUNCT
cana-5488	2	1	10s	10	NOUN
cana-5488	2	2	(	(	PUNCT
cana-5488	2	3	2025	2025	NUM
cana-5488	2	4	)	)	PUNCT
cana-5488	2	5	2392	2392	NUM
cana-5488	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	2	7	numerical	numerical	ADJ
cana-5488	2	8	solution	solution	NOUN
cana-5488	2	9	of	of	ADP
cana-5488	2	10	stochastic	stochastic	ADJ
cana-5488	2	11	seiqr	seiqr	ADJ
cana-5488	2	12	epidemic	epidemic	NOUN
cana-5488	2	13	model	model	NOUN
cana-5488	2	14	with	with	ADP
cana-5488	2	15	differential	differential	ADJ
cana-5488	2	16	transformation	transformation	NOUN
cana-5488	2	17	method	method	NOUN
cana-5488	2	18	m.	m.	NOUN
cana-5488	2	19	priyadharshini1	priyadharshini1	PROPN
cana-5488	2	20	,	,	PUNCT
cana-5488	2	21	j.	j.	PROPN
cana-5488	2	22	senbagamalar2	senbagamalar2	PROPN
cana-5488	2	23	*	*	PROPN
cana-5488	2	24	,	,	PUNCT
cana-5488	2	25	and	and	CCONJ
cana-5488	2	26	g.	g.	PROPN
cana-5488	2	27	sathishkumar	sathishkumar	PROPN
cana-5488	2	28	1	1	NUM
cana-5488	2	29	1	1	NUM
cana-5488	2	30	department	department	NOUN
cana-5488	2	31	of	of	ADP
cana-5488	2	32	mathematics	mathematic	NOUN
cana-5488	2	33	,	,	PUNCT
cana-5488	2	34	faculty	faculty	NOUN
cana-5488	2	35	of	of	ADP
cana-5488	2	36	science	science	NOUN
cana-5488	2	37	and	and	CCONJ
cana-5488	2	38	humanities	humanity	NOUN
cana-5488	2	39	,	,	PUNCT
cana-5488	2	40	srm	srm	PROPN
cana-5488	2	41	institute	institute	PROPN
cana-5488	2	42	of	of	ADP
cana-5488	2	43	science	science	NOUN
cana-5488	2	44	and	and	CCONJ
cana-5488	2	45	technology	technology	NOUN
cana-5488	2	46	,	,	PUNCT
cana-5488	2	47	chennai	chennai	NOUN
cana-5488	2	48	ramapuram	ramapuram	PROPN
cana-5488	2	49	,	,	PUNCT
cana-5488	2	50	chennai-600	chennai-600	NOUN
cana-5488	2	51	089	089	NUM
cana-5488	2	52	,	,	PUNCT
cana-5488	2	53	india	india	PROPN
cana-5488	2	54	.	.	PUNCT
cana-5488	3	1	2*department	2*department	NUM
cana-5488	3	2	of	of	ADP
cana-5488	3	3	mathematics	mathematic	NOUN
cana-5488	3	4	,	,	PUNCT
cana-5488	3	5	vel	vel	PROPN
cana-5488	3	6	tech	tech	PROPN
cana-5488	3	7	rangarajan	rangarajan	PROPN
cana-5488	3	8	dr	dr	PROPN
cana-5488	3	9	.	.	PROPN
cana-5488	3	10	sagunthala	sagunthala	PROPN
cana-5488	3	11	r&d	r&d	PROPN
cana-5488	3	12	institute	institute	PROPN
cana-5488	3	13	of	of	ADP
cana-5488	3	14	science	science	NOUN
cana-5488	3	15	and	and	CCONJ
cana-5488	3	16	technology	technology	NOUN
cana-5488	3	17	,	,	PUNCT
cana-5488	3	18	chennai	chennai	VERB
cana-5488	3	19	600	600	NUM
cana-5488	3	20	062	062	NUM
cana-5488	3	21	,	,	PUNCT
cana-5488	3	22	india	india	PROPN
cana-5488	3	23	e	e	PROPN
cana-5488	3	24	-	-	NOUN
cana-5488	3	25	mail	mail	NOUN
cana-5488	3	26	:	:	PUNCT
cana-5488	3	27	priya88.mathra@gmail.com	priya88.mathra@gmail.com	X
cana-5488	3	28	*	*	PUNCT
cana-5488	4	1	e	e	X
cana-5488	4	2	-	-	NOUN
cana-5488	4	3	mail	mail	NOUN
cana-5488	4	4	:	:	PUNCT
cana-5488	4	5	senbagamalar2005@yahoo.com	senbagamalar2005@yahoo.com	X
cana-5488	5	1	e	e	X
cana-5488	5	2	-	-	NOUN
cana-5488	5	3	mail	mail	NOUN
cana-5488	5	4	:	:	PUNCT
cana-5488	5	5	gskmathspu@gmail.com	gskmathspu@gmail.com	X
cana-5488	5	6	article	article	NOUN
cana-5488	5	7	history	history	NOUN
cana-5488	5	8	:	:	PUNCT
cana-5488	5	9	received	receive	VERB
cana-5488	5	10	:	:	PUNCT
cana-5488	5	11	12	12	NUM
cana-5488	5	12	-	-	SYM
cana-5488	5	13	01	01	NUM
cana-5488	5	14	-	-	PUNCT
cana-5488	5	15	2025	2025	NUM
cana-5488	5	16	revised	revise	VERB
cana-5488	5	17	:	:	PUNCT
cana-5488	5	18	15	15	NUM
cana-5488	5	19	-	-	NUM
cana-5488	5	20	02	02	NUM
cana-5488	5	21	-	-	PUNCT
cana-5488	5	22	2025	2025	NUM
cana-5488	5	23	accepted	accept	VERB
cana-5488	5	24	:	:	PUNCT
cana-5488	5	25	01	01	NUM
cana-5488	5	26	-	-	SYM
cana-5488	5	27	03	03	NUM
cana-5488	5	28	-	-	PUNCT
cana-5488	5	29	2025	2025	NUM
cana-5488	5	30	abstract	abstract	NOUN
cana-5488	5	31	:	:	PUNCT
cana-5488	5	32	in	in	ADP
cana-5488	5	33	this	this	PRON
cana-5488	5	34	we	we	PRON
cana-5488	5	35	solve	solve	VERB
cana-5488	5	36	the	the	DET
cana-5488	5	37	policy	policy	NOUN
cana-5488	5	38	decision	decision	NOUN
cana-5488	5	39	-	-	PUNCT
cana-5488	5	40	making	making	NOUN
cana-5488	5	41	for	for	ADP
cana-5488	5	42	quarantine	quarantine	NOUN
cana-5488	5	43	policy	policy	NOUN
cana-5488	5	44	.	.	PUNCT
cana-5488	6	1	the	the	DET
cana-5488	6	2	quarantine	quarantine	NOUN
cana-5488	6	3	variable	variable	NOUN
cana-5488	6	4	in	in	ADP
cana-5488	6	5	the	the	DET
cana-5488	6	6	seiqr	seiqr	ADJ
cana-5488	6	7	model	model	NOUN
cana-5488	6	8	enables	enable	VERB
cana-5488	6	9	the	the	DET
cana-5488	6	10	policymakers	policymaker	NOUN
cana-5488	6	11	to	to	PART
cana-5488	6	12	examine	examine	VERB
cana-5488	6	13	the	the	DET
cana-5488	6	14	relative	relative	ADJ
cana-5488	6	15	impact	impact	NOUN
cana-5488	6	16	of	of	ADP
cana-5488	6	17	isolation	isolation	NOUN
cana-5488	6	18	measures	measure	NOUN
cana-5488	6	19	on	on	ADP
cana-5488	6	20	controlling	control	VERB
cana-5488	6	21	disease	disease	NOUN
cana-5488	6	22	transmission	transmission	NOUN
cana-5488	6	23	.	.	PUNCT
cana-5488	7	1	real	real	ADJ
cana-5488	7	2	-	-	PUNCT
cana-5488	7	3	world	world	NOUN
cana-5488	7	4	disease	disease	NOUN
cana-5488	7	5	modeling	modeling	NOUN
cana-5488	7	6	can	can	AUX
cana-5488	7	7	be	be	AUX
cana-5488	7	8	used	use	VERB
cana-5488	7	9	to	to	PART
cana-5488	7	10	model	model	VERB
cana-5488	7	11	different	different	ADJ
cana-5488	7	12	infectious	infectious	ADJ
cana-5488	7	13	diseases	disease	NOUN
cana-5488	7	14	like	like	ADP
cana-5488	7	15	covid-19	covid-19	PROPN
cana-5488	7	16	,	,	PUNCT
cana-5488	7	17	sars	sar	NOUN
cana-5488	7	18	,	,	PUNCT
cana-5488	7	19	mers	mer	NOUN
cana-5488	7	20	and	and	CCONJ
cana-5488	7	21	influenza	influenza	NOUN
cana-5488	7	22	,	,	PUNCT
cana-5488	7	23	where	where	SCONJ
cana-5488	7	24	quarantine	quarantine	NOUN
cana-5488	7	25	is	be	AUX
cana-5488	7	26	an	an	DET
cana-5488	7	27	important	important	ADJ
cana-5488	7	28	factor	factor	NOUN
cana-5488	7	29	.	.	PUNCT
cana-5488	8	1	the	the	DET
cana-5488	8	2	reproduction	reproduction	NOUN
cana-5488	8	3	number	number	NOUN
cana-5488	8	4	and	and	CCONJ
cana-5488	8	5	disease	disease	NOUN
cana-5488	8	6	dynamics	dynamic	NOUN
cana-5488	8	7	,	,	PUNCT
cana-5488	8	8	derivation	derivation	NOUN
cana-5488	8	9	of	of	ADP
cana-5488	8	10	equilibrium	equilibrium	NOUN
cana-5488	8	11	points	point	NOUN
cana-5488	8	12	under	under	ADP
cana-5488	8	13	which	which	PRON
cana-5488	8	14	a	a	DET
cana-5488	8	15	disease	disease	NOUN
cana-5488	8	16	dies	die	VERB
cana-5488	8	17	out	out	ADV
cana-5488	8	18	or	or	CCONJ
cana-5488	8	19	continues	continue	VERB
cana-5488	8	20	to	to	PART
cana-5488	8	21	multiple	multiple	NOUN
cana-5488	8	22	.	.	PUNCT
cana-5488	9	1	the	the	DET
cana-5488	9	2	research	research	NOUN
cana-5488	9	3	compares	compare	VERB
cana-5488	9	4	(	(	PUNCT
cana-5488	9	5	dtm	dtm	PROPN
cana-5488	9	6	)	)	PUNCT
cana-5488	9	7	with	with	ADP
cana-5488	9	8	the	the	DET
cana-5488	9	9	(	(	PUNCT
cana-5488	9	10	rk4	rk4	NOUN
cana-5488	9	11	)	)	PUNCT
cana-5488	9	12	method	method	NOUN
cana-5488	9	13	to	to	PART
cana-5488	9	14	determine	determine	VERB
cana-5488	9	15	its	its	PRON
cana-5488	9	16	accuracy	accuracy	NOUN
cana-5488	9	17	and	and	CCONJ
cana-5488	9	18	efficiency	efficiency	NOUN
cana-5488	9	19	.	.	PUNCT
cana-5488	10	1	the	the	DET
cana-5488	10	2	aim	aim	NOUN
cana-5488	10	3	of	of	ADP
cana-5488	10	4	this	this	DET
cana-5488	10	5	research	research	NOUN
cana-5488	10	6	is	be	AUX
cana-5488	10	7	to	to	PART
cana-5488	10	8	examine	examine	VERB
cana-5488	10	9	the	the	DET
cana-5488	10	10	application	application	NOUN
cana-5488	10	11	of	of	ADP
cana-5488	10	12	the	the	DET
cana-5488	10	13	differential	differential	ADJ
cana-5488	10	14	transformation	transformation	NOUN
cana-5488	10	15	to	to	PART
cana-5488	10	16	determine	determine	VERB
cana-5488	10	17	the	the	DET
cana-5488	10	18	approximate	approximate	ADJ
cana-5488	10	19	solutions	solution	NOUN
cana-5488	10	20	to	to	ADP
cana-5488	10	21	the	the	DET
cana-5488	10	22	seiqr	seiqr	ADJ
cana-5488	10	23	epidemiology	epidemiology	NOUN
cana-5488	10	24	model	model	NOUN
cana-5488	10	25	.	.	PUNCT
cana-5488	11	1	in	in	ADP
cana-5488	11	2	solving	solve	VERB
cana-5488	11	3	differential	differential	NOUN
cana-5488	11	4	and	and	CCONJ
cana-5488	11	5	integral	integral	ADJ
cana-5488	11	6	equations	equation	NOUN
cana-5488	11	7	,	,	PUNCT
cana-5488	11	8	numerical	numerical	ADJ
cana-5488	11	9	and	and	CCONJ
cana-5488	11	10	semianalytical	semianalytical	ADJ
cana-5488	11	11	techniques	technique	NOUN
cana-5488	11	12	are	be	AUX
cana-5488	11	13	employed	employ	VERB
cana-5488	11	14	respectively	respectively	ADV
cana-5488	11	15	through	through	ADP
cana-5488	11	16	this	this	DET
cana-5488	11	17	method	method	NOUN
cana-5488	11	18	.	.	PUNCT
cana-5488	12	1	through	through	ADP
cana-5488	12	2	the	the	DET
cana-5488	12	3	application	application	NOUN
cana-5488	12	4	of	of	ADP
cana-5488	12	5	the	the	DET
cana-5488	12	6	dtm	dtm	PROPN
cana-5488	12	7	(	(	PUNCT
cana-5488	12	8	differential	differential	ADJ
cana-5488	12	9	transformation	transformation	NOUN
cana-5488	12	10	method	method	NOUN
cana-5488	12	11	)	)	PUNCT
cana-5488	12	12	,	,	PUNCT
cana-5488	12	13	a	a	DET
cana-5488	12	14	seiqr	seiqr	ADJ
cana-5488	12	15	model	model	NOUN
cana-5488	12	16	was	be	AUX
cana-5488	12	17	solved	solve	VERB
cana-5488	12	18	and	and	CCONJ
cana-5488	12	19	two	two	NUM
cana-5488	12	20	cases	case	NOUN
cana-5488	12	21	were	be	AUX
cana-5488	12	22	discussed	discuss	VERB
cana-5488	12	23	,	,	PUNCT
cana-5488	12	24	one	one	NUM
cana-5488	12	25	of	of	ADP
cana-5488	12	26	which	which	PRON
cana-5488	12	27	is	be	AUX
cana-5488	12	28	endemic	endemic	ADJ
cana-5488	12	29	and	and	CCONJ
cana-5488	12	30	another	another	PRON
cana-5488	12	31	is	be	AUX
cana-5488	12	32	disease	disease	NOUN
cana-5488	12	33	-	-	PUNCT
cana-5488	12	34	free	free	ADJ
cana-5488	12	35	case	case	NOUN
cana-5488	12	36	.	.	PUNCT
cana-5488	13	1	in	in	ADP
cana-5488	13	2	addition	addition	NOUN
cana-5488	13	3	,	,	PUNCT
cana-5488	13	4	we	we	PRON
cana-5488	13	5	solve	solve	VERB
cana-5488	13	6	the	the	DET
cana-5488	13	7	solutions	solution	NOUN
cana-5488	13	8	using	use	VERB
cana-5488	13	9	runge	runge	NOUN
cana-5488	13	10	-	-	PUNCT
cana-5488	13	11	kutta	kutta	NOUN
cana-5488	13	12	method	method	NOUN
cana-5488	13	13	of	of	ADP
cana-5488	13	14	order	order	NOUN
cana-5488	13	15	four	four	NUM
cana-5488	13	16	.	.	PUNCT
cana-5488	14	1	at	at	ADP
cana-5488	14	2	last	last	ADV
cana-5488	14	3	,	,	PUNCT
cana-5488	14	4	we	we	PRON
cana-5488	14	5	compare	compare	VERB
cana-5488	14	6	both	both	CCONJ
cana-5488	14	7	the	the	DET
cana-5488	14	8	solutions	solution	NOUN
cana-5488	14	9	obtained	obtain	VERB
cana-5488	14	10	by	by	ADP
cana-5488	14	11	using	use	VERB
cana-5488	14	12	differential	differential	ADJ
cana-5488	14	13	transformation	transformation	NOUN
cana-5488	14	14	method	method	NOUN
cana-5488	14	15	(	(	PUNCT
cana-5488	14	16	dtm	dtm	PROPN
cana-5488	14	17	)	)	PUNCT
cana-5488	14	18	and	and	CCONJ
cana-5488	14	19	the	the	DET
cana-5488	14	20	(	(	PUNCT
cana-5488	14	21	rk4	rk4	NOUN
cana-5488	14	22	)	)	PUNCT
cana-5488	14	23	method	method	NOUN
cana-5488	14	24	.	.	PUNCT
cana-5488	15	1	the	the	DET
cana-5488	15	2	solution	solution	NOUN
cana-5488	15	3	,	,	PUNCT
cana-5488	15	4	so	so	ADV
cana-5488	15	5	obtained	obtain	VERB
cana-5488	15	6	is	be	AUX
cana-5488	15	7	more	more	ADV
cana-5488	15	8	precise	precise	ADJ
cana-5488	15	9	to	to	PART
cana-5488	15	10	use	use	VERB
cana-5488	15	11	than	than	ADP
cana-5488	15	12	dtm	dtm	PROPN
cana-5488	15	13	.	.	PUNCT
cana-5488	16	1	keywords	keyword	NOUN
cana-5488	16	2	:	:	PUNCT
cana-5488	16	3	differential	differential	ADJ
cana-5488	16	4	transformation	transformation	NOUN
cana-5488	16	5	method	method	NOUN
cana-5488	16	6	,	,	PUNCT
cana-5488	16	7	seiqr	seiqr	ADJ
cana-5488	16	8	epidemiology	epidemiology	NOUN
cana-5488	16	9	model	model	NOUN
cana-5488	16	10	,	,	PUNCT
cana-5488	16	11	rk4	rk4	NOUN
cana-5488	16	12	method	method	NOUN
cana-5488	16	13	,	,	PUNCT
cana-5488	16	14	transformed	transform	VERB
cana-5488	16	15	function	function	NOUN
cana-5488	16	16	,	,	PUNCT
cana-5488	16	17	numerical	numerical	ADJ
cana-5488	16	18	solutions	solution	NOUN
cana-5488	16	19	.	.	PUNCT
cana-5488	17	1	1	1	X
cana-5488	17	2	.	.	X
cana-5488	17	3	introduction	introduction	NOUN
cana-5488	17	4	the	the	DET
cana-5488	17	5	study	study	NOUN
cana-5488	17	6	of	of	ADP
cana-5488	17	7	mathematics	mathematics	PROPN
cana-5488	17	8	is	be	AUX
cana-5488	17	9	the	the	DET
cana-5488	17	10	science	science	NOUN
cana-5488	17	11	of	of	ADP
cana-5488	17	12	order	order	NOUN
cana-5488	17	13	,	,	PUNCT
cana-5488	17	14	relation	relation	NOUN
cana-5488	17	15	and	and	CCONJ
cana-5488	17	16	structure	structure	NOUN
cana-5488	17	17	which	which	PRON
cana-5488	17	18	is	be	AUX
cana-5488	17	19	used	use	VERB
cana-5488	17	20	across	across	ADP
cana-5488	17	21	a	a	DET
cana-5488	17	22	variety	variety	NOUN
cana-5488	17	23	of	of	ADP
cana-5488	17	24	disciplines	discipline	NOUN
cana-5488	17	25	.	.	PUNCT
cana-5488	18	1	it	it	PRON
cana-5488	18	2	is	be	AUX
cana-5488	18	3	possible	possible	ADJ
cana-5488	18	4	to	to	PART
cana-5488	18	5	solve	solve	VERB
cana-5488	18	6	many	many	ADJ
cana-5488	18	7	problems	problem	NOUN
cana-5488	18	8	mathematically	mathematically	ADV
cana-5488	18	9	.	.	PUNCT
cana-5488	19	1	solving	solve	VERB
cana-5488	19	2	and	and	CCONJ
cana-5488	19	3	analyzing	analyze	VERB
cana-5488	19	4	differential	differential	ADJ
cana-5488	19	5	equations	equation	NOUN
cana-5488	19	6	involves	involve	VERB
cana-5488	19	7	analytical	analytical	ADJ
cana-5488	19	8	and	and	CCONJ
cana-5488	19	9	numerical	numerical	ADJ
cana-5488	19	10	methods	method	NOUN
cana-5488	19	11	.	.	PUNCT
cana-5488	20	1	we	we	PRON
cana-5488	20	2	use	use	VERB
cana-5488	20	3	analytical	analytical	ADJ
cana-5488	20	4	taylor	taylor	PROPN
cana-5488	20	5	series	series	PROPN
cana-5488	20	6	method	method	PROPN
cana-5488	20	7	;	;	PUNCT
cana-5488	20	8	the	the	DET
cana-5488	20	9	differential	differential	ADJ
cana-5488	20	10	transform	transform	NOUN
cana-5488	20	11	method	method	NOUN
cana-5488	20	12	(	(	PUNCT
cana-5488	20	13	dtm	dtm	NOUN
cana-5488	20	14	)	)	PUNCT
cana-5488	20	15	solves	solve	VERB
cana-5488	20	16	integral	integral	ADJ
cana-5488	20	17	equations	equation	NOUN
cana-5488	20	18	as	as	ADV
cana-5488	20	19	well	well	ADV
cana-5488	20	20	as	as	ADP
cana-5488	20	21	differential	differential	ADJ
cana-5488	20	22	equations	equation	NOUN
cana-5488	20	23	.	.	PUNCT
cana-5488	21	1	as	as	ADP
cana-5488	21	2	a	a	DET
cana-5488	21	3	result	result	NOUN
cana-5488	21	4	of	of	ADP
cana-5488	21	5	all	all	DET
cana-5488	21	6	these	these	DET
cana-5488	21	7	activities	activity	NOUN
cana-5488	21	8	,	,	PUNCT
cana-5488	21	9	we	we	PRON
cana-5488	21	10	should	should	AUX
cana-5488	21	11	be	be	AUX
cana-5488	21	12	able	able	ADJ
cana-5488	21	13	to	to	PART
cana-5488	21	14	gain	gain	VERB
cana-5488	21	15	information	information	NOUN
cana-5488	21	16	about	about	ADP
cana-5488	21	17	how	how	SCONJ
cana-5488	21	18	the	the	DET
cana-5488	21	19	disease	disease	NOUN
cana-5488	21	20	is	be	AUX
cana-5488	21	21	spreading	spread	VERB
cana-5488	21	22	throughout	throughout	ADP
cana-5488	21	23	the	the	DET
cana-5488	21	24	population	population	NOUN
cana-5488	21	25	,	,	PUNCT
cana-5488	21	26	how	how	SCONJ
cana-5488	21	27	we	we	PRON
cana-5488	21	28	can	can	AUX
cana-5488	21	29	control	control	VERB
cana-5488	21	30	the	the	DET
cana-5488	21	31	spread	spread	NOUN
cana-5488	21	32	,	,	PUNCT
cana-5488	21	33	and	and	CCONJ
cana-5488	21	34	how	how	SCONJ
cana-5488	21	35	to	to	PART
cana-5488	21	36	eradicate	eradicate	VERB
cana-5488	21	37	the	the	DET
cana-5488	21	38	disease	disease	NOUN
cana-5488	21	39	completely	completely	ADV
cana-5488	21	40	[	[	X
cana-5488	21	41	1	1	NUM
cana-5488	21	42	]	]	PUNCT
cana-5488	21	43	.	.	PUNCT
cana-5488	22	1	it	it	PRON
cana-5488	22	2	is	be	AUX
cana-5488	22	3	most	most	ADV
cana-5488	22	4	often	often	ADV
cana-5488	22	5	infectious	infectious	ADJ
cana-5488	22	6	diseases	disease	NOUN
cana-5488	22	7	that	that	PRON
cana-5488	22	8	are	be	AUX
cana-5488	22	9	modeled	model	VERB
cana-5488	22	10	,	,	PUNCT
cana-5488	22	11	i.e.	i.e.	X
cana-5488	22	12	disease	disease	NOUN
cana-5488	22	13	that	that	PRON
cana-5488	22	14	can	can	AUX
cana-5488	22	15	communications	communication	NOUN
cana-5488	22	16	on	on	ADP
cana-5488	22	17	applied	apply	VERB
cana-5488	22	18	nonlinear	nonlinear	ADJ
cana-5488	22	19	analysis	analysis	NOUN
cana-5488	22	20	issn	issn	NOUN
cana-5488	22	21	:	:	PUNCT
cana-5488	22	22	1074	1074	NUM
cana-5488	22	23	-	-	PUNCT
cana-5488	22	24	133x	133x	NUM
cana-5488	22	25	vol	vol	VERB
cana-5488	22	26	32	32	NUM
cana-5488	22	27	no	no	NOUN
cana-5488	22	28	.	.	PUNCT
cana-5488	23	1	10s	10	NOUN
cana-5488	23	2	(	(	PUNCT
cana-5488	23	3	2025	2025	NUM
cana-5488	23	4	)	)	PUNCT
cana-5488	23	5	2393	2393	NUM
cana-5488	23	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	23	7	be	be	AUX
cana-5488	23	8	transmitted	transmit	VERB
cana-5488	23	9	from	from	ADP
cana-5488	23	10	one	one	NUM
cana-5488	23	11	person	person	NOUN
cana-5488	23	12	to	to	ADP
cana-5488	23	13	another	another	PRON
cana-5488	23	14	.	.	PUNCT
cana-5488	24	1	in	in	ADP
cana-5488	24	2	many	many	ADJ
cana-5488	24	3	diseases	disease	NOUN
cana-5488	24	4	affect	affect	VERB
cana-5488	24	5	children	child	NOUN
cana-5488	24	6	,	,	PUNCT
cana-5488	24	7	including	include	VERB
cana-5488	24	8	measles	measle	NOUN
cana-5488	24	9	,	,	PUNCT
cana-5488	24	10	rubella	rubella	NOUN
cana-5488	24	11	,	,	PUNCT
cana-5488	24	12	chicken	chicken	NOUN
cana-5488	24	13	pox	pox	NOUN
cana-5488	24	14	and	and	CCONJ
cana-5488	24	15	mumps	mump	NOUN
cana-5488	24	16	,	,	PUNCT
cana-5488	24	17	along	along	ADP
cana-5488	24	18	with	with	ADP
cana-5488	24	19	gonorrhea	gonorrhea	NOUN
cana-5488	24	20	,	,	PUNCT
cana-5488	24	21	syphilis	syphili	NOUN
cana-5488	24	22	and	and	CCONJ
cana-5488	24	23	hiv	hiv	PROPN
cana-5488	24	24	/	/	SYM
cana-5488	24	25	aids	aids	PROPN
cana-5488	24	26	,	,	PUNCT
cana-5488	24	27	as	as	ADV
cana-5488	24	28	well	well	ADV
cana-5488	24	29	as	as	ADP
cana-5488	24	30	sexually	sexually	ADV
cana-5488	24	31	transmitted	transmit	VERB
cana-5488	24	32	diseases	disease	NOUN
cana-5488	24	33	.	.	PUNCT
cana-5488	25	1	runge	runge	NOUN
cana-5488	25	2	-	-	PUNCT
cana-5488	25	3	kutta	kutta	NOUN
cana-5488	25	4	methods	method	NOUN
cana-5488	25	5	are	be	AUX
cana-5488	25	6	a	a	DET
cana-5488	25	7	class	class	NOUN
cana-5488	25	8	of	of	ADP
cana-5488	25	9	methods	method	NOUN
cana-5488	25	10	that	that	PRON
cana-5488	25	11	extrapolate	extrapolate	VERB
cana-5488	25	12	the	the	DET
cana-5488	25	13	solution	solution	NOUN
cana-5488	25	14	to	to	ADP
cana-5488	25	15	the	the	DET
cana-5488	25	16	next	next	ADJ
cana-5488	25	17	time	time	NOUN
cana-5488	25	18	step	step	NOUN
cana-5488	25	19	by	by	ADP
cana-5488	25	20	carefully	carefully	ADV
cana-5488	25	21	using	use	VERB
cana-5488	25	22	the	the	DET
cana-5488	25	23	information	information	NOUN
cana-5488	25	24	on	on	ADP
cana-5488	25	25	the	the	DET
cana-5488	25	26	"	"	PUNCT
cana-5488	25	27	slope	slope	NOUN
cana-5488	25	28	"	"	PUNCT
cana-5488	25	29	at	at	ADP
cana-5488	25	30	many	many	ADJ
cana-5488	25	31	points	point	NOUN
cana-5488	25	32	.	.	PUNCT
cana-5488	26	1	the	the	DET
cana-5488	26	2	fourth	fourth	ADJ
cana-5488	26	3	order	order	NOUN
cana-5488	26	4	runge	runge	VERB
cana-5488	26	5	kutta	kutta	NOUN
cana-5488	26	6	(	(	PUNCT
cana-5488	26	7	rk4	rk4	NOUN
cana-5488	26	8	)	)	PUNCT
cana-5488	26	9	method	method	NOUN
cana-5488	26	10	is	be	AUX
cana-5488	26	11	explicit	explicit	ADJ
cana-5488	26	12	and	and	CCONJ
cana-5488	26	13	one	one	NUM
cana-5488	26	14	of	of	ADP
cana-5488	26	15	the	the	DET
cana-5488	26	16	most	most	ADV
cana-5488	26	17	used	used	ADJ
cana-5488	26	18	approaches	approach	NOUN
cana-5488	26	19	for	for	ADP
cana-5488	26	20	solving	solve	VERB
cana-5488	26	21	ivps	ivps	PROPN
cana-5488	26	22	.	.	PUNCT
cana-5488	27	1	there	there	PRON
cana-5488	27	2	is	be	VERB
cana-5488	27	3	a	a	DET
cana-5488	27	4	need	need	NOUN
cana-5488	27	5	for	for	ADP
cana-5488	27	6	a	a	DET
cana-5488	27	7	method	method	NOUN
cana-5488	27	8	that	that	PRON
cana-5488	27	9	precisely	precisely	ADV
cana-5488	27	10	use	use	VERB
cana-5488	27	11	the	the	DET
cana-5488	27	12	nonlinear	nonlinear	ADJ
cana-5488	27	13	terms	term	NOUN
cana-5488	27	14	easily	easily	ADV
cana-5488	27	15	without	without	ADP
cana-5488	27	16	any	any	DET
cana-5488	27	17	restrictions	restriction	NOUN
cana-5488	27	18	and	and	CCONJ
cana-5488	27	19	with	with	ADP
cana-5488	27	20	less	less	ADJ
cana-5488	27	21	number	number	NOUN
cana-5488	27	22	of	of	ADP
cana-5488	27	23	computations	computation	NOUN
cana-5488	27	24	.	.	PUNCT
cana-5488	28	1	indeed	indeed	ADV
cana-5488	28	2	,	,	PUNCT
cana-5488	28	3	the	the	DET
cana-5488	28	4	so	so	ADV
cana-5488	28	5	called	call	VERB
cana-5488	28	6	differential	differential	ADJ
cana-5488	28	7	transform	transform	NOUN
cana-5488	28	8	method	method	NOUN
cana-5488	28	9	(	(	PUNCT
cana-5488	28	10	dtm	dtm	PROPN
cana-5488	28	11	)	)	PUNCT
cana-5488	28	12	which	which	PRON
cana-5488	28	13	gives	give	VERB
cana-5488	28	14	a	a	DET
cana-5488	28	15	series	series	NOUN
cana-5488	28	16	solutions	solution	NOUN
cana-5488	28	17	can	can	AUX
cana-5488	28	18	overcome	overcome	VERB
cana-5488	28	19	some	some	PRON
cana-5488	28	20	of	of	ADP
cana-5488	28	21	the	the	DET
cana-5488	28	22	above	above	ADJ
cana-5488	28	23	difficulties	difficulty	NOUN
cana-5488	28	24	.	.	PUNCT
cana-5488	29	1	the	the	DET
cana-5488	29	2	dtm	dtm	PROPN
cana-5488	29	3	is	be	AUX
cana-5488	29	4	very	very	ADV
cana-5488	29	5	effective	effective	ADJ
cana-5488	29	6	numerical	numerical	ADJ
cana-5488	29	7	and	and	CCONJ
cana-5488	29	8	analytical	analytical	ADJ
cana-5488	29	9	method	method	NOUN
cana-5488	29	10	for	for	ADP
cana-5488	29	11	solving	solve	VERB
cana-5488	29	12	different	different	ADJ
cana-5488	29	13	types	type	NOUN
cana-5488	29	14	of	of	ADP
cana-5488	29	15	differential	differential	ADJ
cana-5488	29	16	equations	equation	NOUN
cana-5488	29	17	as	as	ADV
cana-5488	29	18	well	well	ADV
cana-5488	29	19	as	as	ADP
cana-5488	29	20	integral	integral	ADJ
cana-5488	29	21	equations	equation	NOUN
cana-5488	29	22	.	.	PUNCT
cana-5488	30	1	this	this	DET
cana-5488	30	2	method	method	NOUN
cana-5488	30	3	converts	convert	VERB
cana-5488	30	4	the	the	DET
cana-5488	30	5	differential	differential	ADJ
cana-5488	30	6	equations	equation	NOUN
cana-5488	30	7	into	into	ADP
cana-5488	30	8	recurrence	recurrence	NOUN
cana-5488	30	9	relations	relation	NOUN
cana-5488	30	10	and	and	CCONJ
cana-5488	30	11	then	then	ADV
cana-5488	30	12	by	by	ADP
cana-5488	30	13	taylor	taylor	PROPN
cana-5488	30	14	series	series	PROPN
cana-5488	30	15	expansion	expansion	NOUN
cana-5488	30	16	will	will	AUX
cana-5488	30	17	give	give	VERB
cana-5488	30	18	a	a	DET
cana-5488	30	19	different	different	ADJ
cana-5488	30	20	approach	approach	NOUN
cana-5488	30	21	to	to	PART
cana-5488	30	22	obtain	obtain	VERB
cana-5488	30	23	the	the	DET
cana-5488	30	24	convergent	convergent	NOUN
cana-5488	30	25	series	series	NOUN
cana-5488	30	26	solutions	solution	NOUN
cana-5488	30	27	.	.	PUNCT
cana-5488	31	1	the	the	DET
cana-5488	31	2	differential	differential	ADJ
cana-5488	31	3	transformation	transformation	NOUN
cana-5488	31	4	method	method	NOUN
cana-5488	31	5	is	be	AUX
cana-5488	31	6	very	very	ADV
cana-5488	31	7	much	much	ADV
cana-5488	31	8	familiar	familiar	ADJ
cana-5488	31	9	technique	technique	NOUN
cana-5488	31	10	to	to	PART
cana-5488	31	11	solve	solve	VERB
cana-5488	31	12	all	all	DET
cana-5488	31	13	the	the	DET
cana-5488	31	14	kinds	kind	NOUN
cana-5488	31	15	of	of	ADP
cana-5488	31	16	differential	differential	ADJ
cana-5488	31	17	equations	equation	NOUN
cana-5488	31	18	.	.	PUNCT
cana-5488	32	1	the	the	DET
cana-5488	32	2	method	method	NOUN
cana-5488	32	3	was	be	AUX
cana-5488	32	4	originally	originally	ADV
cana-5488	32	5	developed	develop	VERB
cana-5488	32	6	by	by	ADP
cana-5488	32	7	zhou	zhou	PROPN
cana-5488	33	1	[	[	X
cana-5488	33	2	2	2	NUM
cana-5488	33	3	]	]	PUNCT
cana-5488	33	4	for	for	ADP
cana-5488	33	5	solving	solve	VERB
cana-5488	33	6	both	both	CCONJ
cana-5488	33	7	linear	linear	ADJ
cana-5488	33	8	and	and	CCONJ
cana-5488	33	9	non	non	ADJ
cana-5488	33	10	-	-	ADJ
cana-5488	33	11	linear	linear	ADJ
cana-5488	33	12	initial	initial	ADJ
cana-5488	33	13	value	value	NOUN
cana-5488	33	14	problems	problem	NOUN
cana-5488	33	15	in	in	ADP
cana-5488	33	16	electrical	electrical	ADJ
cana-5488	33	17	circuits	circuit	NOUN
cana-5488	33	18	.	.	PUNCT
cana-5488	34	1	later	later	ADV
cana-5488	34	2	,	,	PUNCT
cana-5488	34	3	several	several	ADJ
cana-5488	34	4	researches	research	NOUN
cana-5488	34	5	have	have	AUX
cana-5488	34	6	been	be	AUX
cana-5488	34	7	conducted	conduct	VERB
cana-5488	34	8	in	in	ADP
cana-5488	34	9	applying	apply	VERB
cana-5488	34	10	differential	differential	ADJ
cana-5488	34	11	transform	transform	NOUN
cana-5488	34	12	method	method	NOUN
cana-5488	34	13	to	to	ADP
cana-5488	34	14	different	different	ADJ
cana-5488	34	15	types	type	NOUN
cana-5488	34	16	of	of	ADP
cana-5488	34	17	equations	equation	NOUN
cana-5488	34	18	.	.	PUNCT
cana-5488	35	1	these	these	DET
cana-5488	35	2	researches	research	NOUN
cana-5488	35	3	confirm	confirm	VERB
cana-5488	35	4	the	the	DET
cana-5488	35	5	fact	fact	NOUN
cana-5488	35	6	that	that	SCONJ
cana-5488	35	7	this	this	DET
cana-5488	35	8	method	method	NOUN
cana-5488	35	9	is	be	AUX
cana-5488	35	10	reliable	reliable	ADJ
cana-5488	35	11	,	,	PUNCT
cana-5488	35	12	efficient	efficient	ADJ
cana-5488	35	13	as	as	ADV
cana-5488	35	14	well	well	ADV
cana-5488	35	15	as	as	ADP
cana-5488	35	16	having	have	VERB
cana-5488	35	17	a	a	DET
cana-5488	35	18	wider	wide	ADJ
cana-5488	35	19	applicability	applicability	NOUN
cana-5488	35	20	.	.	PUNCT
cana-5488	36	1	according	accord	VERB
cana-5488	36	2	to	to	ADP
cana-5488	36	3	hasan	hasan	PROPN
cana-5488	36	4	[	[	X
cana-5488	36	5	3	3	X
cana-5488	36	6	]	]	PUNCT
cana-5488	36	7	the	the	DET
cana-5488	36	8	differential	differential	ADJ
cana-5488	36	9	equation	equation	NOUN
cana-5488	36	10	system	system	NOUN
cana-5488	36	11	was	be	AUX
cana-5488	36	12	completed	complete	VERB
cana-5488	36	13	by	by	ADP
cana-5488	36	14	using	use	VERB
cana-5488	36	15	dtm	dtm	PROPN
cana-5488	36	16	and	and	CCONJ
cana-5488	36	17	compared	compare	VERB
cana-5488	36	18	with	with	ADP
cana-5488	36	19	rk	rk	NOUN
cana-5488	36	20	method	method	NOUN
cana-5488	36	21	in	in	ADP
cana-5488	36	22	2008	2008	NUM
cana-5488	36	23	.	.	PUNCT
cana-5488	37	1	in	in	ADP
cana-5488	37	2	his	his	PRON
cana-5488	37	3	opinion	opinion	NOUN
cana-5488	37	4	,	,	PUNCT
cana-5488	37	5	dtm	dtm	PROPN
cana-5488	37	6	is	be	AUX
cana-5488	37	7	one	one	NUM
cana-5488	37	8	of	of	ADP
cana-5488	37	9	the	the	DET
cana-5488	37	10	most	most	ADV
cana-5488	37	11	accurate	accurate	ADJ
cana-5488	37	12	and	and	CCONJ
cana-5488	37	13	easiest	easy	ADJ
cana-5488	37	14	to	to	PART
cana-5488	37	15	explore	explore	VERB
cana-5488	37	16	the	the	DET
cana-5488	37	17	technologies	technology	NOUN
cana-5488	37	18	.	.	PUNCT
cana-5488	38	1	despite	despite	SCONJ
cana-5488	38	2	its	its	PRON
cana-5488	38	3	advantages	advantage	NOUN
cana-5488	38	4	,	,	PUNCT
cana-5488	38	5	the	the	DET
cana-5488	38	6	only	only	ADJ
cana-5488	38	7	disadvantage	disadvantage	NOUN
cana-5488	38	8	of	of	ADP
cana-5488	38	9	the	the	DET
cana-5488	38	10	dtm	dtm	NOUN
cana-5488	38	11	is	be	AUX
cana-5488	38	12	that	that	SCONJ
cana-5488	38	13	it	it	PRON
cana-5488	38	14	produces	produce	VERB
cana-5488	38	15	an	an	DET
cana-5488	38	16	approximate	approximate	ADJ
cana-5488	38	17	solution	solution	NOUN
cana-5488	38	18	in	in	ADP
cana-5488	38	19	the	the	DET
cana-5488	38	20	truncated	truncated	ADJ
cana-5488	38	21	series	series	NOUN
cana-5488	38	22	form	form	NOUN
cana-5488	38	23	and	and	CCONJ
cana-5488	38	24	also	also	ADV
cana-5488	38	25	the	the	DET
cana-5488	38	26	convergence	convergence	NOUN
cana-5488	38	27	interval	interval	NOUN
cana-5488	38	28	is	be	AUX
cana-5488	38	29	pretty	pretty	ADV
cana-5488	38	30	limited	limited	ADJ
cana-5488	38	31	.	.	PUNCT
cana-5488	39	1	in	in	ADP
cana-5488	39	2	a	a	DET
cana-5488	39	3	tiny	tiny	ADJ
cana-5488	39	4	area	area	NOUN
cana-5488	39	5	,	,	PUNCT
cana-5488	39	6	dtm	dtm	PROPN
cana-5488	39	7	produces	produce	VERB
cana-5488	39	8	a	a	DET
cana-5488	39	9	series	series	NOUN
cana-5488	39	10	of	of	ADP
cana-5488	39	11	solution	solution	NOUN
cana-5488	39	12	which	which	PRON
cana-5488	39	13	is	be	AUX
cana-5488	39	14	not	not	PART
cana-5488	39	15	reflect	reflect	VERB
cana-5488	39	16	the	the	DET
cana-5488	39	17	real	real	ADJ
cana-5488	39	18	time	time	NOUN
cana-5488	39	19	behavior	behavior	NOUN
cana-5488	39	20	of	of	ADP
cana-5488	39	21	the	the	DET
cana-5488	39	22	given	give	VERB
cana-5488	39	23	problem	problem	NOUN
cana-5488	39	24	,	,	PUNCT
cana-5488	39	25	but	but	CCONJ
cana-5488	39	26	does	do	AUX
cana-5488	39	27	provide	provide	VERB
cana-5488	39	28	a	a	DET
cana-5488	39	29	good	good	ADJ
cana-5488	39	30	estimate	estimate	NOUN
cana-5488	39	31	to	to	ADP
cana-5488	39	32	the	the	DET
cana-5488	39	33	correct	correct	ADJ
cana-5488	39	34	solution	solution	NOUN
cana-5488	39	35	.	.	PUNCT
cana-5488	40	1	a	a	DET
cana-5488	40	2	number	number	NOUN
cana-5488	40	3	of	of	ADP
cana-5488	40	4	differential	differential	ADJ
cana-5488	40	5	algebraic	algebraic	ADJ
cana-5488	40	6	equations	equation	NOUN
cana-5488	40	7	have	have	AUX
cana-5488	40	8	been	be	AUX
cana-5488	40	9	solved	solve	VERB
cana-5488	40	10	by	by	ADP
cana-5488	40	11	using	use	VERB
cana-5488	40	12	this	this	DET
cana-5488	40	13	method	method	NOUN
cana-5488	40	14	,	,	PUNCT
cana-5488	40	15	as	as	ADV
cana-5488	40	16	well	well	ADV
cana-5488	40	17	as	as	ADP
cana-5488	40	18	schrödinger	schrödinger	ADJ
cana-5488	40	19	equations	equation	NOUN
cana-5488	40	20	[	[	X
cana-5488	40	21	4	4	NUM
cana-5488	40	22	]	]	PUNCT
cana-5488	40	23	,	,	PUNCT
cana-5488	40	24	fractional	fractional	ADJ
cana-5488	40	25	differential	differential	ADJ
cana-5488	40	26	equations	equation	NOUN
cana-5488	41	1	[	[	X
cana-5488	41	2	5,10	5,10	NUM
cana-5488	41	3	]	]	X
cana-5488	41	4	an	an	DET
cana-5488	41	5	equation	equation	NOUN
cana-5488	41	6	of	of	ADP
cana-5488	41	7	the	the	DET
cana-5488	41	8	type	type	NOUN
cana-5488	41	9	laneemden	laneemden	NOUN
cana-5488	41	10	and	and	CCONJ
cana-5488	41	11	equations	equation	NOUN
cana-5488	41	12	describing	describe	VERB
cana-5488	41	13	the	the	DET
cana-5488	41	14	unsteady	unsteady	ADJ
cana-5488	41	15	movements	movement	NOUN
cana-5488	41	16	of	of	ADP
cana-5488	41	17	rotating	rotate	VERB
cana-5488	41	18	spheres	sphere	NOUN
cana-5488	41	19	in	in	ADP
cana-5488	41	20	inclined	inclined	ADJ
cana-5488	41	21	tubes	tube	NOUN
cana-5488	41	22	.	.	PUNCT
cana-5488	42	1	there	there	PRON
cana-5488	42	2	are	be	VERB
cana-5488	42	3	many	many	ADJ
cana-5488	42	4	advantages	advantage	NOUN
cana-5488	42	5	in	in	ADP
cana-5488	42	6	this	this	DET
cana-5488	42	7	method	method	NOUN
cana-5488	42	8	,	,	PUNCT
cana-5488	42	9	including	include	VERB
cana-5488	42	10	the	the	DET
cana-5488	42	11	fact	fact	NOUN
cana-5488	42	12	that	that	SCONJ
cana-5488	42	13	it	it	PRON
cana-5488	42	14	can	can	AUX
cana-5488	42	15	be	be	AUX
cana-5488	42	16	used	use	VERB
cana-5488	42	17	directly	directly	ADV
cana-5488	42	18	with	with	ADP
cana-5488	42	19	all	all	DET
cana-5488	42	20	odes	ode	NOUN
cana-5488	42	21	without	without	ADP
cana-5488	42	22	the	the	DET
cana-5488	42	23	requirement	requirement	NOUN
cana-5488	42	24	of	of	ADP
cana-5488	42	25	perturbation	perturbation	NOUN
cana-5488	42	26	,	,	PUNCT
cana-5488	42	27	discretization	discretization	NOUN
cana-5488	42	28	or	or	CCONJ
cana-5488	42	29	linearization	linearization	NOUN
cana-5488	42	30	.	.	PUNCT
cana-5488	43	1	in	in	ADP
cana-5488	43	2	[	[	X
cana-5488	43	3	9	9	NUM
cana-5488	43	4	]	]	PUNCT
cana-5488	43	5	an	an	DET
cana-5488	43	6	artificial	artificial	ADJ
cana-5488	43	7	infectious	infectious	ADJ
cana-5488	43	8	disease	disease	NOUN
cana-5488	43	9	optimization	optimization	NOUN
cana-5488	43	10	algorithm	algorithm	NOUN
cana-5488	43	11	based	base	VERB
cana-5488	43	12	on	on	ADP
cana-5488	43	13	the	the	DET
cana-5488	43	14	seiqr	seiqr	ADJ
cana-5488	43	15	epidemic	epidemic	NOUN
cana-5488	43	16	model	model	NOUN
cana-5488	43	17	is	be	AUX
cana-5488	43	18	constructed	construct	VERB
cana-5488	43	19	.	.	PUNCT
cana-5488	44	1	this	this	DET
cana-5488	44	2	method	method	NOUN
cana-5488	44	3	have	have	VERB
cana-5488	44	4	an	an	DET
cana-5488	44	5	advantage	advantage	NOUN
cana-5488	44	6	in	in	ADP
cana-5488	44	7	the	the	DET
cana-5488	44	8	way	way	NOUN
cana-5488	44	9	it	it	PRON
cana-5488	44	10	is	be	AUX
cana-5488	44	11	able	able	ADJ
cana-5488	44	12	to	to	PART
cana-5488	44	13	reduce	reduce	VERB
cana-5488	44	14	the	the	DET
cana-5488	44	15	amount	amount	NOUN
cana-5488	44	16	of	of	ADP
cana-5488	44	17	computations	computation	NOUN
cana-5488	44	18	needed	need	VERB
cana-5488	44	19	to	to	PART
cana-5488	44	20	compute	compute	VERB
cana-5488	44	21	the	the	DET
cana-5488	44	22	series	series	NOUN
cana-5488	44	23	of	of	ADP
cana-5488	44	24	solution	solution	NOUN
cana-5488	44	25	while	while	SCONJ
cana-5488	44	26	even	even	ADV
cana-5488	44	27	maintaining	maintain	VERB
cana-5488	44	28	accuracy	accuracy	NOUN
cana-5488	44	29	and	and	CCONJ
cana-5488	44	30	providing	provide	VERB
cana-5488	44	31	the	the	DET
cana-5488	44	32	series	series	NOUN
cana-5488	44	33	solution	solution	NOUN
cana-5488	44	34	’s	’s	PART
cana-5488	44	35	fast	fast	ADJ
cana-5488	44	36	convergence	convergence	NOUN
cana-5488	44	37	as	as	ADV
cana-5488	44	38	well	well	ADV
cana-5488	44	39	.	.	PUNCT
cana-5488	45	1	the	the	DET
cana-5488	45	2	runge	runge	NOUN
cana-5488	45	3	-	-	PUNCT
cana-5488	45	4	kutta	kutta	NOUN
cana-5488	45	5	method	method	NOUN
cana-5488	45	6	has	have	AUX
cana-5488	45	7	been	be	AUX
cana-5488	45	8	used	use	VERB
cana-5488	45	9	by	by	ADP
cana-5488	45	10	many	many	ADJ
cana-5488	45	11	authors	author	NOUN
cana-5488	45	12	to	to	PART
cana-5488	45	13	solve	solve	VERB
cana-5488	45	14	nonlinear	nonlinear	ADJ
cana-5488	45	15	odes	ode	NOUN
cana-5488	45	16	[	[	X
cana-5488	45	17	6	6	NUM
cana-5488	45	18	,	,	PUNCT
cana-5488	45	19	7	7	NUM
cana-5488	45	20	,	,	PUNCT
cana-5488	45	21	8	8	NUM
cana-5488	45	22	]	]	PUNCT
cana-5488	45	23	.	.	PUNCT
cana-5488	46	1	in	in	ADP
cana-5488	46	2	this	this	DET
cana-5488	46	3	paper	paper	NOUN
cana-5488	46	4	,	,	PUNCT
cana-5488	46	5	we	we	PRON
cana-5488	46	6	apply	apply	VERB
cana-5488	46	7	the	the	DET
cana-5488	46	8	application	application	NOUN
cana-5488	46	9	of	of	ADP
cana-5488	46	10	the	the	DET
cana-5488	46	11	differential	differential	ADJ
cana-5488	46	12	transform	transform	NOUN
cana-5488	46	13	method	method	NOUN
cana-5488	46	14	to	to	ADP
cana-5488	46	15	the	the	DET
cana-5488	46	16	proposed	propose	VERB
cana-5488	46	17	model	model	NOUN
cana-5488	46	18	and	and	CCONJ
cana-5488	46	19	verify	verify	VERB
cana-5488	46	20	that	that	PRON
cana-5488	46	21	maple	maple	PROPN
cana-5488	46	22	18	18	NUM
cana-5488	46	23	and	and	CCONJ
cana-5488	46	24	matlab	matlab	PROPN
cana-5488	46	25	’s	’s	PART
cana-5488	46	26	classical	classical	ADJ
cana-5488	46	27	(	(	PUNCT
cana-5488	46	28	rk4	rk4	NOUN
cana-5488	46	29	)	)	PUNCT
cana-5488	46	30	method	method	NOUN
cana-5488	46	31	is	be	AUX
cana-5488	46	32	valid	valid	ADJ
cana-5488	46	33	for	for	ADP
cana-5488	46	34	solving	solve	VERB
cana-5488	46	35	the	the	DET
cana-5488	46	36	model	model	NOUN
cana-5488	46	37	.	.	PUNCT
cana-5488	47	1	throughout	throughout	ADP
cana-5488	47	2	this	this	DET
cana-5488	47	3	paper	paper	NOUN
cana-5488	47	4	,	,	PUNCT
cana-5488	47	5	the	the	DET
cana-5488	47	6	following	follow	VERB
cana-5488	47	7	topics	topic	NOUN
cana-5488	47	8	are	be	AUX
cana-5488	47	9	discussed	discuss	VERB
cana-5488	47	10	.	.	PUNCT
cana-5488	48	1	the	the	DET
cana-5488	48	2	approach	approach	NOUN
cana-5488	48	3	of	of	ADP
cana-5488	48	4	differential	differential	ADJ
cana-5488	48	5	transformation	transformation	NOUN
cana-5488	48	6	method	method	NOUN
cana-5488	48	7	is	be	AUX
cana-5488	48	8	covered	cover	VERB
cana-5488	48	9	in	in	ADP
cana-5488	48	10	section	section	NOUN
cana-5488	48	11	2	2	NUM
cana-5488	48	12	.	.	PUNCT
cana-5488	48	13	to	to	PART
cana-5488	48	14	construct	construct	VERB
cana-5488	48	15	the	the	DET
cana-5488	48	16	seiqr	seiqr	ADJ
cana-5488	48	17	model	model	NOUN
cana-5488	48	18	in	in	ADP
cana-5488	48	19	a	a	DET
cana-5488	48	20	dynamical	dynamical	ADJ
cana-5488	48	21	system	system	NOUN
cana-5488	48	22	is	be	AUX
cana-5488	48	23	discussed	discuss	VERB
cana-5488	48	24	in	in	ADP
cana-5488	48	25	section	section	NOUN
cana-5488	48	26	3	3	NUM
cana-5488	48	27	.	.	PUNCT
cana-5488	49	1	the	the	DET
cana-5488	49	2	equilibrium	equilibrium	NOUN
cana-5488	49	3	point	point	NOUN
cana-5488	49	4	of	of	ADP
cana-5488	49	5	the	the	DET
cana-5488	49	6	model	model	NOUN
cana-5488	49	7	is	be	AUX
cana-5488	49	8	analyzed	analyze	VERB
cana-5488	49	9	in	in	ADP
cana-5488	49	10	section	section	NOUN
cana-5488	49	11	4	4	NUM
cana-5488	49	12	.	.	PUNCT
cana-5488	50	1	in	in	ADP
cana-5488	50	2	section	section	NOUN
cana-5488	50	3	5	5	NUM
cana-5488	50	4	,	,	PUNCT
cana-5488	50	5	an	an	DET
cana-5488	50	6	application	application	NOUN
cana-5488	50	7	of	of	ADP
cana-5488	50	8	the	the	DET
cana-5488	50	9	differential	differential	ADJ
cana-5488	50	10	transformation	transformation	NOUN
cana-5488	50	11	method	method	NOUN
cana-5488	50	12	and	and	CCONJ
cana-5488	50	13	graphical	graphical	ADJ
cana-5488	50	14	representation	representation	NOUN
cana-5488	50	15	for	for	ADP
cana-5488	50	16	seiqr	seiqr	ADJ
cana-5488	50	17	https://www.sciencedirect.com/topics/computer-science/optimization-algorithm	https://www.sciencedirect.com/topics/computer-science/optimization-algorithm	PROPN
cana-5488	50	18	communications	communication	NOUN
cana-5488	50	19	on	on	ADP
cana-5488	50	20	applied	apply	VERB
cana-5488	50	21	nonlinear	nonlinear	ADJ
cana-5488	50	22	analysis	analysis	NOUN
cana-5488	50	23	issn	issn	NOUN
cana-5488	50	24	:	:	PUNCT
cana-5488	50	25	1074	1074	NUM
cana-5488	50	26	-	-	PUNCT
cana-5488	50	27	133x	133x	NUM
cana-5488	50	28	vol	vol	VERB
cana-5488	50	29	32	32	NUM
cana-5488	50	30	no	no	NOUN
cana-5488	50	31	.	.	PUNCT
cana-5488	51	1	10s	10	NOUN
cana-5488	51	2	(	(	PUNCT
cana-5488	51	3	2025	2025	NUM
cana-5488	51	4	)	)	PUNCT
cana-5488	51	5	2394	2394	NUM
cana-5488	51	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	51	7	model	model	NOUN
cana-5488	51	8	is	be	AUX
cana-5488	51	9	seen	see	VERB
cana-5488	51	10	.	.	PUNCT
cana-5488	52	1	in	in	ADP
cana-5488	52	2	section	section	NOUN
cana-5488	52	3	6	6	NUM
cana-5488	52	4	,	,	PUNCT
cana-5488	52	5	the	the	DET
cana-5488	52	6	comparison	comparison	NOUN
cana-5488	52	7	of	of	ADP
cana-5488	52	8	the	the	DET
cana-5488	52	9	values	value	NOUN
cana-5488	52	10	of	of	ADP
cana-5488	52	11	runge	runge	NOUN
cana-5488	52	12	-	-	PUNCT
cana-5488	52	13	kutta	kutta	NOUN
cana-5488	52	14	method	method	NOUN
cana-5488	52	15	of	of	ADP
cana-5488	52	16	fourth	fourth	ADJ
cana-5488	52	17	order	order	NOUN
cana-5488	52	18	and	and	CCONJ
cana-5488	52	19	dtm	dtm	PROPN
cana-5488	52	20	are	be	AUX
cana-5488	52	21	shown	show	VERB
cana-5488	52	22	in	in	ADP
cana-5488	52	23	the	the	DET
cana-5488	52	24	table	table	NOUN
cana-5488	52	25	.	.	PUNCT
cana-5488	53	1	2	2	X
cana-5488	53	2	.	.	X
cana-5488	53	3	methodology	methodology	NOUN
cana-5488	53	4	the	the	DET
cana-5488	53	5	purpose	purpose	NOUN
cana-5488	53	6	of	of	ADP
cana-5488	53	7	this	this	DET
cana-5488	53	8	section	section	NOUN
cana-5488	53	9	is	be	AUX
cana-5488	53	10	to	to	PART
cana-5488	53	11	provide	provide	VERB
cana-5488	53	12	insight	insight	NOUN
cana-5488	53	13	into	into	ADP
cana-5488	53	14	the	the	DET
cana-5488	53	15	methodology	methodology	NOUN
cana-5488	53	16	we	we	PRON
cana-5488	53	17	used	use	VERB
cana-5488	53	18	to	to	PART
cana-5488	53	19	solve	solve	VERB
cana-5488	53	20	our	our	PRON
cana-5488	53	21	problem	problem	NOUN
cana-5488	53	22	.	.	PUNCT
cana-5488	54	1	2.1	2.1	NUM
cana-5488	54	2	.	.	PUNCT
cana-5488	54	3	method	method	NOUN
cana-5488	54	4	of	of	ADP
cana-5488	54	5	differential	differential	ADJ
cana-5488	54	6	transformation	transformation	NOUN
cana-5488	54	7	if	if	SCONJ
cana-5488	54	8	a	a	DET
cana-5488	54	9	function	function	NOUN
cana-5488	54	10	h(x	h(x	PROPN
cana-5488	54	11	)	)	PUNCT
cana-5488	54	12	has	have	VERB
cana-5488	54	13	kth	kth	PROPN
cana-5488	54	14	derivatives	derivative	NOUN
cana-5488	54	15	,	,	PUNCT
cana-5488	54	16	then	then	ADV
cana-5488	54	17	it	it	PRON
cana-5488	54	18	can	can	AUX
cana-5488	54	19	be	be	AUX
cana-5488	54	20	written	write	VERB
cana-5488	54	21	in	in	ADP
cana-5488	54	22	taylor	taylor	PROPN
cana-5488	54	23	series	series	PROPN
cana-5488	54	24	expans	expans	PROPN
cana-5488	54	25	ion	ion	VERB
cana-5488	54	26	about	about	ADV
cana-5488	54	27	a	a	DET
cana-5488	54	28	point	point	NOUN
cana-5488	54	29	at	at	ADP
cana-5488	54	30	x	x	X
cana-5488	54	31	=	=	SYM
cana-5488	54	32	x0	x0	PROPN
cana-5488	54	33	as	as	ADP
cana-5488	54	34	ℎ(𝑥	ℎ(𝑥	NOUN
cana-5488	54	35	)	)	PUNCT
cana-5488	54	36	=	=	PUNCT
cana-5488	54	37	∑	∑	PUNCT
cana-5488	55	1	𝑥𝑘	𝑥𝑘	X
cana-5488	55	2	𝑘	𝑘	NOUN
cana-5488	55	3	!	!	PUNCT
cana-5488	56	1	[	[	PUNCT
cana-5488	56	2	𝑑𝑘ℎ(𝑥	𝑑𝑘ℎ(𝑥	PROPN
cana-5488	56	3	)	)	PUNCT
cana-5488	56	4	𝑑𝑥𝑘	𝑑𝑥𝑘	NOUN
cana-5488	56	5	]	]	PUNCT
cana-5488	56	6	𝑥=𝑥0	𝑥=𝑥0	X
cana-5488	56	7	∞	∞	NUM
cana-5488	56	8	𝑘=0	𝑘=0	PROPN
cana-5488	56	9	.	.	PUNCT
cana-5488	57	1	table	table	NOUN
cana-5488	57	2	1	1	NUM
cana-5488	57	3	:	:	PUNCT
cana-5488	57	4	a	a	DET
cana-5488	57	5	description	description	NOUN
cana-5488	57	6	of	of	ADP
cana-5488	57	7	the	the	DET
cana-5488	57	8	fundamental	fundamental	ADJ
cana-5488	57	9	operations	operation	NOUN
cana-5488	57	10	of	of	ADP
cana-5488	57	11	differential	differential	ADJ
cana-5488	57	12	transformation	transformation	NOUN
cana-5488	57	13	methods	method	NOUN
cana-5488	57	14	(	(	PUNCT
cana-5488	57	15	dtms	dtms	NOUN
cana-5488	57	16	)	)	PUNCT
cana-5488	57	17	s.no	s.no	VERB
cana-5488	57	18	original	original	ADJ
cana-5488	57	19	function	function	NOUN
cana-5488	57	20	transformed	transform	VERB
cana-5488	57	21	function	function	NOUN
cana-5488	57	22	1	1	NUM
cana-5488	57	23	h(x	h(x	PROPN
cana-5488	57	24	)	)	PUNCT
cana-5488	57	25	=	=	SYM
cana-5488	58	1	m(x	m(x	PROPN
cana-5488	58	2	)	)	PUNCT
cana-5488	58	3	±	±	NOUN
cana-5488	58	4	n(x	n(x	PROPN
cana-5488	58	5	)	)	PUNCT
cana-5488	58	6	h(k	h(k	PROPN
cana-5488	58	7	)	)	PUNCT
cana-5488	59	1	=	=	PUNCT
cana-5488	59	2	m	m	PROPN
cana-5488	59	3	(	(	PUNCT
cana-5488	59	4	k	k	NOUN
cana-5488	59	5	)	)	PUNCT
cana-5488	59	6	±	±	NUM
cana-5488	59	7	n	n	CCONJ
cana-5488	59	8	(	(	PUNCT
cana-5488	59	9	k	k	NOUN
cana-5488	59	10	)	)	PUNCT
cana-5488	59	11	2	2	NUM
cana-5488	59	12	h(x	h(x	PROPN
cana-5488	59	13	)	)	PUNCT
cana-5488	59	14	=	=	SYM
cana-5488	59	15	cm(x	cm(x	X
cana-5488	59	16	)	)	PUNCT
cana-5488	59	17	h(k	h(k	PROPN
cana-5488	59	18	)	)	PUNCT
cana-5488	60	1	=	=	SYM
cana-5488	60	2	cm	cm	NOUN
cana-5488	60	3	(	(	PUNCT
cana-5488	60	4	k	k	NOUN
cana-5488	60	5	)	)	PUNCT
cana-5488	60	6	,	,	PUNCT
cana-5488	60	7	where	where	SCONJ
cana-5488	60	8	c	c	NOUN
cana-5488	60	9	is	be	AUX
cana-5488	60	10	constant	constant	ADJ
cana-5488	60	11	.	.	PUNCT
cana-5488	61	1	3	3	NUM
cana-5488	61	2	ℎ(𝑥	ℎ(𝑥	NUM
cana-5488	61	3	)	)	PUNCT
cana-5488	61	4	=	=	SYM
cana-5488	61	5	𝑑𝑚(𝑥	𝑑𝑚(𝑥	NUM
cana-5488	61	6	)	)	PUNCT
cana-5488	61	7	𝑑𝑥	𝑑𝑥	ADP
cana-5488	61	8	h(k	h(k	PROPN
cana-5488	61	9	)	)	PUNCT
cana-5488	61	10	=	=	PUNCT
cana-5488	62	1	(	(	PUNCT
cana-5488	62	2	k	k	PROPN
cana-5488	62	3	+	+	NUM
cana-5488	62	4	1)m	1)m	NUM
cana-5488	62	5	(	(	PUNCT
cana-5488	62	6	k	k	NOUN
cana-5488	62	7	+	+	PROPN
cana-5488	62	8	1	1	X
cana-5488	62	9	)	)	PUNCT
cana-5488	62	10	4	4	NUM
cana-5488	62	11	ℎ(𝑥	ℎ(𝑥	NUM
cana-5488	62	12	)	)	PUNCT
cana-5488	62	13	=	=	SYM
cana-5488	62	14	𝑑2𝑚(𝑥	𝑑2𝑚(𝑥	NOUN
cana-5488	62	15	)	)	PUNCT
cana-5488	62	16	𝑑𝑥2	𝑑𝑥2	NOUN
cana-5488	62	17	h(k	h(k	PROPN
cana-5488	62	18	)	)	PUNCT
cana-5488	63	1	=	=	PRON
cana-5488	64	1	(	(	PUNCT
cana-5488	64	2	k	k	PROPN
cana-5488	64	3	+	+	NOUN
cana-5488	64	4	1)(k	1)(k	NUM
cana-5488	64	5	+	+	NUM
cana-5488	64	6	2)m	2)m	NUM
cana-5488	64	7	(	(	PUNCT
cana-5488	64	8	k	k	NOUN
cana-5488	64	9	+	+	PROPN
cana-5488	64	10	2	2	X
cana-5488	64	11	)	)	PUNCT
cana-5488	64	12	5	5	NUM
cana-5488	64	13	ℎ(𝑥	ℎ(𝑥	NUM
cana-5488	64	14	)	)	PUNCT
cana-5488	64	15	=	=	SYM
cana-5488	64	16	𝑑𝑟𝑚(𝑥	𝑑𝑟𝑚(𝑥	X
cana-5488	64	17	)	)	PUNCT
cana-5488	64	18	𝑑𝑥𝑟	𝑑𝑥𝑟	NOUN
cana-5488	64	19	h(k	h(k	PROPN
cana-5488	64	20	)	)	PUNCT
cana-5488	64	21	=	=	PRON
cana-5488	65	1	(	(	PUNCT
cana-5488	65	2	k	k	PROPN
cana-5488	65	3	+	+	NOUN
cana-5488	65	4	1)(k	1)(k	NUM
cana-5488	65	5	+	+	CCONJ
cana-5488	65	6	2	2	NUM
cana-5488	65	7	)	)	PUNCT
cana-5488	65	8	+	+	CCONJ
cana-5488	65	9	...	...	PUNCT
cana-5488	66	1	+	+	CCONJ
cana-5488	66	2	(	(	PUNCT
cana-5488	66	3	k	k	X
cana-5488	66	4	+	+	X
cana-5488	66	5	l)m	l)m	ADJ
cana-5488	66	6	(	(	PUNCT
cana-5488	66	7	k	k	PROPN
cana-5488	66	8	+	+	NUM
cana-5488	66	9	l	l	NOUN
cana-5488	66	10	)	)	PUNCT
cana-5488	66	11	6	6	NUM
cana-5488	66	12	h(x	h(x	PROPN
cana-5488	66	13	)	)	PUNCT
cana-5488	66	14	=	=	NOUN
cana-5488	66	15	1	1	NUM
cana-5488	66	16	h(k	h(k	PROPN
cana-5488	66	17	)	)	PUNCT
cana-5488	66	18	=	=	SYM
cana-5488	66	19	δ(k	δ(k	NOUN
cana-5488	66	20	)	)	PUNCT
cana-5488	66	21	7	7	NUM
cana-5488	66	22	h(x	h(x	PROPN
cana-5488	66	23	)	)	PUNCT
cana-5488	66	24	=	=	PUNCT
cana-5488	67	1	x	x	SYM
cana-5488	67	2	h(k	h(k	PROPN
cana-5488	67	3	)	)	PUNCT
cana-5488	68	1	=	=	NOUN
cana-5488	68	2	δ(k	δ(k	VERB
cana-5488	68	3	−	−	NOUN
cana-5488	68	4	1	1	NUM
cana-5488	68	5	)	)	PUNCT
cana-5488	68	6	,	,	PUNCT
cana-5488	68	7	where	where	SCONJ
cana-5488	68	8	δ	δ	PROPN
cana-5488	68	9	is	be	AUX
cana-5488	68	10	kronecker	kronecker	NOUN
cana-5488	68	11	delta	delta	NOUN
cana-5488	68	12	.	.	PUNCT
cana-5488	69	1	8	8	NUM
cana-5488	69	2	h(x	h(x	PROPN
cana-5488	69	3	)	)	PUNCT
cana-5488	70	1	=	=	PUNCT
cana-5488	70	2	eλx	eλx	NOUN
cana-5488	70	3	𝐻(𝑘	𝐻(𝑘	NOUN
cana-5488	70	4	)	)	PUNCT
cana-5488	70	5	=	=	PRON
cana-5488	70	6	𝜆𝑘	𝜆𝑘	NUM
cana-5488	70	7	𝑘	𝑘	NOUN
cana-5488	70	8	!	!	PROPN
cana-5488	70	9	9	9	NUM
cana-5488	70	10	h(x	h(x	PROPN
cana-5488	70	11	)	)	PUNCT
cana-5488	70	12	=	=	SYM
cana-5488	70	13	m(x)n(x	m(x)n(x	NOUN
cana-5488	70	14	)	)	PUNCT
cana-5488	70	15	𝐻(𝑘	𝐻(𝑘	NOUN
cana-5488	70	16	)	)	PUNCT
cana-5488	70	17	=	=	SYM
cana-5488	70	18	∑	∑	PROPN
cana-5488	70	19	𝑀(𝑙)𝑁(𝑘	𝑀(𝑙)𝑁(𝑘	PROPN
cana-5488	70	20	−	−	NUM
cana-5488	70	21	𝑙	𝑙	SYM
cana-5488	70	22	)	)	PUNCT
cana-5488	70	23	𝑘	𝑘	PRON
cana-5488	70	24	𝑙=0	𝑙=0	PROPN
cana-5488	70	25	10	10	NUM
cana-5488	70	26	h(x	h(x	PROPN
cana-5488	70	27	)	)	PUNCT
cana-5488	70	28	=	=	PUNCT
cana-5488	71	1	(	(	PUNCT
cana-5488	71	2	1	1	NUM
cana-5488	71	3	+	+	CCONJ
cana-5488	71	4	x)r	x)r	PUNCT
cana-5488	72	1	𝐻(𝑘	𝐻(𝑘	X
cana-5488	72	2	)	)	PUNCT
cana-5488	72	3	=	=	SYM
cana-5488	72	4	𝑟(𝑟	𝑟(𝑟	PROPN
cana-5488	72	5	−	−	PROPN
cana-5488	72	6	1)(𝑟	1)(𝑟	NUM
cana-5488	72	7	−	−	PROPN
cana-5488	72	8	2	2	NUM
cana-5488	72	9	)	)	PUNCT
cana-5488	72	10	.	.	PUNCT
cana-5488	72	11	.	.	PUNCT
cana-5488	72	12	.	.	PUNCT
cana-5488	73	1	(	(	PUNCT
cana-5488	73	2	𝑟	𝑟	X
cana-5488	73	3	−	−	X
cana-5488	73	4	𝑘	𝑘	X
cana-5488	73	5	+	+	NOUN
cana-5488	73	6	1	1	NUM
cana-5488	73	7	)	)	PUNCT
cana-5488	73	8	𝑘	𝑘	NOUN
cana-5488	73	9	!	!	PUNCT
cana-5488	74	1	if	if	SCONJ
cana-5488	74	2	h(x	h(x	PROPN
cana-5488	74	3	)	)	PUNCT
cana-5488	74	4	is	be	AUX
cana-5488	74	5	differentially	differentially	ADV
cana-5488	74	6	transformed	transform	VERB
cana-5488	74	7	,	,	PUNCT
cana-5488	74	8	it	it	PRON
cana-5488	74	9	has	have	VERB
cana-5488	74	10	the	the	DET
cana-5488	74	11	following	follow	VERB
cana-5488	74	12	definition	definition	NOUN
cana-5488	74	13	𝐻(𝑥	𝐻(𝑥	NUM
cana-5488	74	14	)	)	PUNCT
cana-5488	74	15	=	=	SYM
cana-5488	74	16	1	1	NUM
cana-5488	74	17	𝑘	𝑘	NOUN
cana-5488	74	18	!	!	PUNCT
cana-5488	75	1	[	[	PUNCT
cana-5488	75	2	𝑑𝑘ℎ(𝑥	𝑑𝑘ℎ(𝑥	PROPN
cana-5488	75	3	)	)	PUNCT
cana-5488	75	4	𝑑𝑥𝑘	𝑑𝑥𝑘	NOUN
cana-5488	75	5	]	]	PUNCT
cana-5488	75	6	𝑥=𝑥0	𝑥=𝑥0	PROPN
cana-5488	75	7	.	.	PUNCT
cana-5488	76	1	communications	communication	NOUN
cana-5488	76	2	on	on	ADP
cana-5488	76	3	applied	apply	VERB
cana-5488	76	4	nonlinear	nonlinear	ADJ
cana-5488	76	5	analysis	analysis	NOUN
cana-5488	76	6	issn	issn	NOUN
cana-5488	76	7	:	:	PUNCT
cana-5488	76	8	1074	1074	NUM
cana-5488	76	9	-	-	PUNCT
cana-5488	76	10	133x	133x	NUM
cana-5488	76	11	vol	vol	VERB
cana-5488	76	12	32	32	NUM
cana-5488	76	13	no	no	NOUN
cana-5488	76	14	.	.	PUNCT
cana-5488	77	1	10s	10	NOUN
cana-5488	77	2	(	(	PUNCT
cana-5488	77	3	2025	2025	NUM
cana-5488	77	4	)	)	PUNCT
cana-5488	77	5	2395	2395	NUM
cana-5488	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	78	1	the	the	DET
cana-5488	78	2	inverse	inverse	NOUN
cana-5488	78	3	of	of	ADP
cana-5488	78	4	differential	differential	ADJ
cana-5488	78	5	transformation	transformation	NOUN
cana-5488	78	6	method	method	NOUN
cana-5488	78	7	of	of	ADP
cana-5488	78	8	h(x	h(x	PROPN
cana-5488	78	9	)	)	PUNCT
cana-5488	78	10	is	be	AUX
cana-5488	78	11	ℎ(𝑥	ℎ(𝑥	NUM
cana-5488	78	12	)	)	PUNCT
cana-5488	78	13	=	=	SYM
cana-5488	78	14	∑	∑	PUNCT
cana-5488	78	15	𝑥𝑘𝐻(𝑘	𝑥𝑘𝐻(𝑘	PROPN
cana-5488	78	16	)	)	PUNCT
cana-5488	78	17	.	.	PUNCT
cana-5488	79	1	∞	∞	PROPN
cana-5488	79	2	𝑘=0	𝑘=0	VERB
cana-5488	79	3	table-1	table-1	PRON
cana-5488	79	4	will	will	AUX
cana-5488	79	5	provide	provide	VERB
cana-5488	79	6	a	a	DET
cana-5488	79	7	comprehensive	comprehensive	ADJ
cana-5488	79	8	overview	overview	NOUN
cana-5488	79	9	of	of	ADP
cana-5488	79	10	the	the	DET
cana-5488	79	11	st	st	PROPN
cana-5488	79	12	rong	rong	PROPN
cana-5488	79	13	fundamental	fundamental	PROPN
cana-5488	79	14	mathematical	mathematical	ADJ
cana-5488	79	15	operations	operation	NOUN
cana-5488	79	16	that	that	PRON
cana-5488	79	17	are	be	AUX
cana-5488	79	18	accomplished	accomplish	VERB
cana-5488	79	19	with	with	ADP
cana-5488	79	20	differential	differential	ADJ
cana-5488	79	21	transforms	transform	NOUN
cana-5488	79	22	.	.	PUNCT
cana-5488	80	1	3	3	X
cana-5488	80	2	.	.	X
cana-5488	80	3	stochastic	stochastic	ADJ
cana-5488	80	4	seiqr	seiqr	ADJ
cana-5488	80	5	model	model	NOUN
cana-5488	80	6	to	to	PART
cana-5488	80	7	understand	understand	VERB
cana-5488	80	8	the	the	DET
cana-5488	80	9	dynamics	dynamic	NOUN
cana-5488	80	10	of	of	ADP
cana-5488	80	11	epidemics	epidemic	NOUN
cana-5488	80	12	in	in	ADP
cana-5488	80	13	mathematical	mathematical	ADJ
cana-5488	80	14	terms	term	NOUN
cana-5488	80	15	,	,	PUNCT
cana-5488	80	16	several	several	ADJ
cana-5488	80	17	models	model	NOUN
cana-5488	80	18	incorporating	incorporate	VERB
cana-5488	80	19	quarantine	quarantine	NOUN
cana-5488	80	20	have	have	AUX
cana-5488	80	21	been	be	AUX
cana-5488	80	22	developed	develop	VERB
cana-5488	80	23	.	.	PUNCT
cana-5488	81	1	according	accord	VERB
cana-5488	81	2	to	to	ADP
cana-5488	81	3	this	this	DET
cana-5488	81	4	model	model	NOUN
cana-5488	81	5	,	,	PUNCT
cana-5488	81	6	the	the	DET
cana-5488	81	7	whole	whole	ADJ
cana-5488	81	8	population	population	NOUN
cana-5488	81	9	can	can	AUX
cana-5488	81	10	be	be	AUX
cana-5488	81	11	classified	classify	VERB
cana-5488	81	12	into	into	ADP
cana-5488	81	13	five	five	NUM
cana-5488	81	14	groups	group	NOUN
cana-5488	81	15	:	:	PUNCT
cana-5488	81	16	susceptible	susceptible	ADJ
cana-5488	81	17	,	,	PUNCT
cana-5488	81	18	exposed	expose	VERB
cana-5488	81	19	,	,	PUNCT
cana-5488	81	20	infectious	infectious	ADJ
cana-5488	81	21	,	,	PUNCT
cana-5488	81	22	quarantined	quarantined	ADJ
cana-5488	81	23	,	,	PUNCT
cana-5488	81	24	and	and	CCONJ
cana-5488	81	25	recovered	recover	VERB
cana-5488	81	26	.	.	PUNCT
cana-5488	82	1	table	table	NOUN
cana-5488	82	2	2	2	NUM
cana-5488	82	3	:	:	PUNCT
cana-5488	82	4	model	model	NOUN
cana-5488	82	5	variables	variable	NOUN
cana-5488	82	6	and	and	CCONJ
cana-5488	82	7	description	description	NOUN
cana-5488	82	8	[	[	X
cana-5488	82	9	11	11	NUM
cana-5488	82	10	]	]	SYM
cana-5488	82	11	variable	variable	ADJ
cana-5488	82	12	description	description	NOUN
cana-5488	82	13	s(t	s(t	PROPN
cana-5488	82	14	)	)	PUNCT
cana-5488	82	15	susceptible	susceptible	ADJ
cana-5488	82	16	population	population	NOUN
cana-5488	82	17	e(t	e(t	NOUN
cana-5488	82	18	)	)	PUNCT
cana-5488	82	19	exposed	expose	VERB
cana-5488	82	20	population	population	NOUN
cana-5488	82	21	i(t	i(t	PROPN
cana-5488	82	22	)	)	PUNCT
cana-5488	82	23	infected	infect	VERB
cana-5488	82	24	population	population	NOUN
cana-5488	82	25	q(t	q(t	PROPN
cana-5488	82	26	)	)	PUNCT
cana-5488	82	27	quarantined	quarantine	VERB
cana-5488	82	28	population	population	NOUN
cana-5488	82	29	r(t	r(t	NOUN
cana-5488	82	30	)	)	PUNCT
cana-5488	82	31	recovered	recover	VERB
cana-5488	82	32	population	population	NOUN
cana-5488	82	33	in	in	ADP
cana-5488	82	34	this	this	DET
cana-5488	82	35	study	study	NOUN
cana-5488	82	36	,	,	PUNCT
cana-5488	82	37	we	we	PRON
cana-5488	82	38	examine	examine	VERB
cana-5488	82	39	the	the	DET
cana-5488	82	40	seiqr	seiqr	ADJ
cana-5488	82	41	model	model	NOUN
cana-5488	82	42	as	as	SCONJ
cana-5488	82	43	described	describe	VERB
cana-5488	82	44	below	below	ADV
cana-5488	82	45	,	,	PUNCT
cana-5488	82	46	𝑑𝑠	𝑑𝑠	ADV
cana-5488	82	47	𝑑𝑡	𝑑𝑡	ADP
cana-5488	82	48	=	=	PROPN
cana-5488	82	49	𝑏	𝑏	PROPN
cana-5488	82	50	−	−	PROPN
cana-5488	82	51	𝜇	𝜇	ADP
cana-5488	82	52	𝑆	𝑆	PROPN
cana-5488	82	53	−	−	PROPN
cana-5488	82	54	𝛽	𝛽	NOUN
cana-5488	82	55	𝑆𝐼	𝑆𝐼	ADV
cana-5488	82	56	𝑁	𝑁	PROPN
cana-5488	82	57	𝑑𝐸	𝑑𝐸	ADJ
cana-5488	82	58	𝑑𝑡	𝑑𝑡	ADP
cana-5488	82	59	=	=	SYM
cana-5488	82	60	𝛽	𝛽	PROPN
cana-5488	82	61	𝑆𝐼	𝑆𝐼	NOUN
cana-5488	82	62	𝑁	𝑁	PROPN
cana-5488	82	63	−	−	PROPN
cana-5488	82	64	(	(	PUNCT
cana-5488	82	65	𝛾	𝛾	NOUN
cana-5488	83	1	+	+	PUNCT
cana-5488	83	2	𝜇)𝐸	𝜇)𝐸	ADV
cana-5488	83	3	𝑑𝐼	𝑑𝐼	ADJ
cana-5488	83	4	𝑑𝑡	𝑑𝑡	ADP
cana-5488	83	5	=	=	PROPN
cana-5488	83	6	𝛾𝐸	𝛾𝐸	NOUN
cana-5488	83	7	−	−	PROPN
cana-5488	83	8	(	(	PUNCT
cana-5488	83	9	𝜉	𝜉	PROPN
cana-5488	83	10	+	+	NOUN
cana-5488	83	11	𝜂	𝜂	NOUN
cana-5488	83	12	+	+	NUM
cana-5488	83	13	𝛼1	𝛼1	NOUN
cana-5488	83	14	+	+	CCONJ
cana-5488	83	15	𝜇)𝐼	𝜇)𝐼	ADJ
cana-5488	83	16	(	(	PUNCT
cana-5488	83	17	3.1	3.1	NUM
cana-5488	83	18	)	)	PUNCT
cana-5488	83	19	𝑑𝑄	𝑑𝑄	NOUN
cana-5488	83	20	𝑑𝑡	𝑑𝑡	ADP
cana-5488	83	21	=	=	PUNCT
cana-5488	83	22	𝜂𝐼	𝜂𝐼	NOUN
cana-5488	83	23	−	−	PROPN
cana-5488	83	24	(	(	PUNCT
cana-5488	83	25	𝛿	𝛿	PROPN
cana-5488	83	26	+	+	X
cana-5488	83	27	𝛼2	𝛼2	ADJ
cana-5488	83	28	+	+	CCONJ
cana-5488	83	29	𝜇)𝑄	𝜇)𝑄	VERB
cana-5488	83	30	𝑑𝑅	𝑑𝑅	NOUN
cana-5488	83	31	𝑑𝑡	𝑑𝑡	ADP
cana-5488	83	32	=	=	SYM
cana-5488	83	33	𝜉𝐼	𝜉𝐼	PROPN
cana-5488	83	34	+	+	CCONJ
cana-5488	83	35	𝛿𝑄	𝛿𝑄	VERB
cana-5488	83	36	−	−	NOUN
cana-5488	83	37	𝜇𝑅.	𝜇𝑅.	PROPN
cana-5488	83	38	in	in	ADP
cana-5488	83	39	total	total	NOUN
cana-5488	83	40	,	,	PUNCT
cana-5488	83	41	the	the	DET
cana-5488	83	42	size	size	NOUN
cana-5488	83	43	of	of	ADP
cana-5488	83	44	the	the	DET
cana-5488	83	45	population	population	NOUN
cana-5488	83	46	n(t	n(t	NOUN
cana-5488	83	47	)	)	PUNCT
cana-5488	83	48	=	=	PUNCT
cana-5488	83	49	s(t	s(t	PROPN
cana-5488	83	50	)	)	PUNCT
cana-5488	83	51	+	+	SYM
cana-5488	83	52	e(t	e(t	NOUN
cana-5488	83	53	)	)	PUNCT
cana-5488	83	54	+	+	CCONJ
cana-5488	83	55	i(t	i(t	NOUN
cana-5488	83	56	)	)	PUNCT
cana-5488	83	57	+	+	NUM
cana-5488	83	58	r(t	r(t	NOUN
cana-5488	83	59	)	)	PUNCT
cana-5488	83	60	.	.	PUNCT
cana-5488	84	1	obviously	obviously	ADV
cana-5488	84	2	the	the	DET
cana-5488	84	3	region	region	NOUN
cana-5488	85	1	d	d	NOUN
cana-5488	85	2	=	=	PRON
cana-5488	85	3	{	{	PUNCT
cana-5488	85	4	(	(	PUNCT
cana-5488	85	5	s	s	X
cana-5488	85	6	,	,	PUNCT
cana-5488	85	7	e	e	NOUN
cana-5488	85	8	,	,	PUNCT
cana-5488	85	9	i	i	PRON
cana-5488	85	10	,	,	PUNCT
cana-5488	85	11	q	q	INTJ
cana-5488	85	12	,	,	PUNCT
cana-5488	85	13	r)/s	r)/s	PROPN
cana-5488	85	14	≥	≥	NOUN
cana-5488	85	15	0	0	NUM
cana-5488	85	16	,	,	PUNCT
cana-5488	85	17	e	e	X
cana-5488	85	18	≥	≥	NOUN
cana-5488	85	19	0	0	NUM
cana-5488	85	20	,	,	PUNCT
cana-5488	85	21	i	i	PRON
cana-5488	85	22	≥	≥	VERB
cana-5488	85	23	0	0	NUM
cana-5488	85	24	,	,	PUNCT
cana-5488	85	25	q	q	X
cana-5488	85	26	≥	≥	NOUN
cana-5488	85	27	0	0	NUM
cana-5488	85	28	,	,	PUNCT
cana-5488	85	29	r	r	NOUN
cana-5488	85	30	≥	≥	NOUN
cana-5488	85	31	0	0	NUM
cana-5488	85	32	,	,	PUNCT
cana-5488	85	33	s	s	PART
cana-5488	85	34	+	+	NUM
cana-5488	85	35	e	e	NOUN
cana-5488	85	36	+	+	NOUN
cana-5488	85	37	i	i	PRON
cana-5488	85	38	+	+	NOUN
cana-5488	85	39	q	q	NOUN
cana-5488	86	1	+	+	CCONJ
cana-5488	86	2	r	r	NOUN
cana-5488	86	3	≤	≤	NUM
cana-5488	86	4	b/µ	b/µ	NOUN
cana-5488	86	5	}	}	PUNCT
cana-5488	86	6	communications	communication	NOUN
cana-5488	86	7	on	on	ADP
cana-5488	86	8	applied	apply	VERB
cana-5488	86	9	nonlinear	nonlinear	ADJ
cana-5488	86	10	analysis	analysis	NOUN
cana-5488	86	11	issn	issn	NOUN
cana-5488	86	12	:	:	PUNCT
cana-5488	86	13	1074	1074	NUM
cana-5488	86	14	-	-	PUNCT
cana-5488	86	15	133x	133x	NUM
cana-5488	86	16	vol	vol	VERB
cana-5488	86	17	32	32	NUM
cana-5488	86	18	no	no	NOUN
cana-5488	86	19	.	.	PUNCT
cana-5488	87	1	10s	10	NOUN
cana-5488	87	2	(	(	PUNCT
cana-5488	87	3	2025	2025	NUM
cana-5488	87	4	)	)	PUNCT
cana-5488	87	5	2396	2396	NUM
cana-5488	88	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	88	2	is	be	AUX
cana-5488	88	3	a	a	DET
cana-5488	88	4	collection	collection	NOUN
cana-5488	88	5	of	of	ADP
cana-5488	88	6	model	model	NOUN
cana-5488	88	7	(	(	PUNCT
cana-5488	88	8	3.1	3.1	NUM
cana-5488	88	9	)	)	PUNCT
cana-5488	88	10	that	that	PRON
cana-5488	88	11	is	be	AUX
cana-5488	88	12	positively	positively	ADV
cana-5488	88	13	invariant	invariant	ADJ
cana-5488	88	14	.	.	PUNCT
cana-5488	89	1	the	the	DET
cana-5488	89	2	reproduction	reproduction	NOUN
cana-5488	89	3	number	number	NOUN
cana-5488	89	4	of	of	ADP
cana-5488	89	5	the	the	DET
cana-5488	89	6	model	model	NOUN
cana-5488	89	7	is	be	AUX
cana-5488	89	8	𝐑𝟎	𝐑𝟎	NOUN
cana-5488	89	9	=	=	SYM
cana-5488	89	10	𝛃𝐛𝛄	𝛃𝐛𝛄	NOUN
cana-5488	89	11	𝛍(𝛄+𝛍)(𝛏+𝛍+𝛂𝟏+𝛈	𝛍(𝛄+𝛍)(𝛏+𝛍+𝛂𝟏+𝛈	NOUN
cana-5488	89	12	)	)	PUNCT
cana-5488	89	13	.	.	PUNCT
cana-5488	90	1	table	table	NOUN
cana-5488	90	2	3	3	NUM
cana-5488	90	3	:	:	PUNCT
cana-5488	90	4	model	model	NOUN
cana-5488	90	5	parameter	parameter	NOUN
cana-5488	90	6	and	and	CCONJ
cana-5488	90	7	units	unit	NOUN
cana-5488	90	8	parameter	parameter	NOUN
cana-5488	90	9	description	description	NOUN
cana-5488	90	10	units	unit	NOUN
cana-5488	90	11	b	b	PROPN
cana-5488	90	12	birth	birth	NOUN
cana-5488	90	13	rate	rate	NOUN
cana-5488	90	14	individual	individual	ADJ
cana-5488	90	15	/	/	SYM
cana-5488	90	16	day	day	NOUN
cana-5488	90	17	β	β	X
cana-5488	90	18	transmission	transmission	NOUN
cana-5488	90	19	co	co	NOUN
cana-5488	90	20	-	-	ADJ
cana-5488	90	21	efficient	efficient	ADJ
cana-5488	90	22	(	(	PUNCT
cana-5488	90	23	individual×	individual×	NOUN
cana-5488	90	24	day)−1	day)−1	VERB
cana-5488	90	25	µ	µ	PRON
cana-5488	90	26	natural	natural	ADJ
cana-5488	90	27	death	death	NOUN
cana-5488	90	28	rate	rate	NOUN
cana-5488	90	29	1	1	NUM
cana-5488	90	30	/	/	SYM
cana-5488	90	31	day	day	NOUN
cana-5488	90	32	γ	γ	NOUN
cana-5488	90	33	infective	infective	ADJ
cana-5488	90	34	individuals	individual	NOUN
cana-5488	90	35	of	of	ADP
cana-5488	90	36	exposed	expose	VERB
cana-5488	90	37	people	people	NOUN
cana-5488	90	38	1	1	NUM
cana-5488	90	39	/	/	SYM
cana-5488	90	40	day	day	NOUN
cana-5488	90	41	η	η	PROPN
cana-5488	90	42	infective	infective	ADJ
cana-5488	90	43	individuals	individual	NOUN
cana-5488	90	44	of	of	ADP
cana-5488	90	45	quarantined	quarantine	VERB
cana-5488	90	46	recovery	recovery	NOUN
cana-5488	90	47	rate	rate	NOUN
cana-5488	90	48	1	1	NUM
cana-5488	90	49	/	/	SYM
cana-5488	90	50	day	day	NOUN
cana-5488	90	51	ε	ε	PROPN
cana-5488	90	52	recovered	recover	VERB
cana-5488	90	53	rate	rate	NOUN
cana-5488	90	54	of	of	ADP
cana-5488	90	55	infective	infective	ADJ
cana-5488	90	56	people	people	NOUN
cana-5488	90	57	1	1	NUM
cana-5488	90	58	/	/	SYM
cana-5488	90	59	day	day	NOUN
cana-5488	90	60	α1	α1	PROPN
cana-5488	90	61	disease	disease	NOUN
cana-5488	90	62	induced	induce	VERB
cana-5488	90	63	death	death	NOUN
cana-5488	90	64	rate	rate	NOUN
cana-5488	90	65	of	of	ADP
cana-5488	90	66	infected	infected	ADJ
cana-5488	90	67	people	people	NOUN
cana-5488	90	68	1	1	NUM
cana-5488	90	69	/	/	SYM
cana-5488	90	70	day	day	NOUN
cana-5488	90	71	α2	α2	ADJ
cana-5488	90	72	disease	disease	NOUN
cana-5488	90	73	induced	induce	VERB
cana-5488	90	74	death	death	NOUN
cana-5488	90	75	rate	rate	NOUN
cana-5488	90	76	of	of	ADP
cana-5488	90	77	quarantined	quarantine	VERB
cana-5488	90	78	people	people	NOUN
cana-5488	90	79	1	1	NUM
cana-5488	90	80	/	/	SYM
cana-5488	90	81	day	day	NOUN
cana-5488	90	82	δ	δ	PROPN
cana-5488	90	83	recovered	recover	VERB
cana-5488	90	84	people	people	NOUN
cana-5488	90	85	quarantined	quarantine	VERB
cana-5488	90	86	people	people	NOUN
cana-5488	90	87	rate	rate	VERB
cana-5488	90	88	1	1	NUM
cana-5488	90	89	/	/	SYM
cana-5488	90	90	day	day	NOUN
cana-5488	90	91	4	4	NUM
cana-5488	90	92	.	.	PUNCT
cana-5488	90	93	equilibrium	equilibrium	NOUN
cana-5488	90	94	analysis	analysis	NOUN
cana-5488	90	95	the	the	DET
cana-5488	90	96	following	follow	VERB
cana-5488	90	97	section	section	NOUN
cana-5488	90	98	discusses	discuss	VERB
cana-5488	90	99	the	the	DET
cana-5488	90	100	endemic	endemic	ADJ
cana-5488	90	101	equilibrium	equilibrium	NOUN
cana-5488	90	102	as	as	ADV
cana-5488	90	103	well	well	ADV
cana-5488	90	104	as	as	ADP
cana-5488	90	105	the	the	DET
cana-5488	90	106	disease	disease	NOUN
cana-5488	90	107	-	-	PUNCT
cana-5488	90	108	free	free	ADJ
cana-5488	90	109	equilibrium	equilibrium	NOUN
cana-5488	90	110	that	that	PRON
cana-5488	90	111	will	will	AUX
cana-5488	90	112	prevail	prevail	VERB
cana-5488	90	113	in	in	ADP
cana-5488	90	114	the	the	DET
cana-5488	90	115	future	future	NOUN
cana-5488	90	116	.	.	PUNCT
cana-5488	91	1	there	there	PRON
cana-5488	91	2	are	be	VERB
cana-5488	91	3	two	two	NUM
cana-5488	91	4	ways	way	NOUN
cana-5488	91	5	to	to	PART
cana-5488	91	6	analyze	analyze	VERB
cana-5488	91	7	the	the	DET
cana-5488	91	8	qualitative	qualitative	ADJ
cana-5488	91	9	system	system	NOUN
cana-5488	91	10	:	:	PUNCT
cana-5488	91	11	1	1	X
cana-5488	91	12	.	.	X
cana-5488	91	13	disease	disease	NOUN
cana-5488	91	14	-	-	PUNCT
cana-5488	91	15	free	free	ADJ
cana-5488	91	16	equilibrium	equilibrium	NOUN
cana-5488	91	17	2	2	NUM
cana-5488	91	18	.	.	PUNCT
cana-5488	91	19	endemic	endemic	ADJ
cana-5488	91	20	equilibrium	equilibrium	NOUN
cana-5488	91	21	.	.	PUNCT
cana-5488	92	1	4.1	4.1	NUM
cana-5488	92	2	disease	disease	NOUN
cana-5488	92	3	free	free	ADJ
cana-5488	92	4	equilibrium	equilibrium	NOUN
cana-5488	92	5	in	in	ADP
cana-5488	92	6	the	the	DET
cana-5488	92	7	event	event	NOUN
cana-5488	92	8	of	of	ADP
cana-5488	92	9	disease	disease	NOUN
cana-5488	92	10	death	death	NOUN
cana-5488	92	11	naturally	naturally	ADV
cana-5488	92	12	,	,	PUNCT
cana-5488	92	13	an	an	DET
cana-5488	92	14	equilibrium	equilibrium	NOUN
cana-5488	92	15	resulting	result	VERB
cana-5488	92	16	from	from	ADP
cana-5488	92	17	the	the	DET
cana-5488	92	18	above	above	ADJ
cana-5488	92	19	system	system	NOUN
cana-5488	92	20	takes	take	VERB
cana-5488	92	21	the	the	DET
cana-5488	92	22	form	form	NOUN
cana-5488	92	23	of	of	ADP
cana-5488	92	24	a	a	DET
cana-5488	92	25	disease	disease	NOUN
cana-5488	92	26	-	-	PUNCT
cana-5488	92	27	free	free	ADJ
cana-5488	92	28	population	population	NOUN
cana-5488	92	29	or	or	CCONJ
cana-5488	92	30	a	a	DET
cana-5488	92	31	disease	disease	NOUN
cana-5488	92	32	-	-	PUNCT
cana-5488	92	33	free	free	ADJ
cana-5488	92	34	equilibrium	equilibrium	NOUN
cana-5488	92	35	,	,	PUNCT
cana-5488	92	36	s	s	PART
cana-5488	92	37	=	=	SYM
cana-5488	92	38	b/µ	b/µ	PROPN
cana-5488	92	39	,	,	PUNCT
cana-5488	92	40	e	e	X
cana-5488	92	41	=	=	SYM
cana-5488	92	42	0	0	NUM
cana-5488	92	43	,	,	PUNCT
cana-5488	92	44	i	i	PRON
cana-5488	92	45	=	=	NOUN
cana-5488	92	46	0	0	NUM
cana-5488	92	47	,	,	PUNCT
cana-5488	92	48	q	q	NOUN
cana-5488	92	49	=	=	SYM
cana-5488	92	50	0	0	NUM
cana-5488	92	51	,	,	PUNCT
cana-5488	92	52	r	r	NOUN
cana-5488	92	53	=	=	SYM
cana-5488	92	54	0	0	NUM
cana-5488	92	55	,	,	PUNCT
cana-5488	92	56	hence	hence	ADV
cana-5488	92	57	(	(	PUNCT
cana-5488	92	58	𝑆	𝑆	PROPN
cana-5488	92	59	,	,	PUNCT
cana-5488	92	60	𝐸	𝐸	PROPN
cana-5488	92	61	,	,	PUNCT
cana-5488	92	62	𝐼	𝐼	PROPN
cana-5488	92	63	,	,	PUNCT
cana-5488	92	64	𝑄	𝑄	PROPN
cana-5488	92	65	,	,	PUNCT
cana-5488	92	66	𝑅	𝑅	PROPN
cana-5488	92	67	)	)	PUNCT
cana-5488	92	68	=	=	PUNCT
cana-5488	92	69	(	(	PUNCT
cana-5488	92	70	b	b	X
cana-5488	92	71	𝜇	𝜇	X
cana-5488	92	72	,	,	PUNCT
cana-5488	92	73	0	0	NUM
cana-5488	92	74	,	,	PUNCT
cana-5488	92	75	0	0	NUM
cana-5488	92	76	,	,	PUNCT
cana-5488	92	77	0	0	NUM
cana-5488	92	78	,	,	PUNCT
cana-5488	92	79	0	0	NUM
cana-5488	92	80	)	)	PUNCT
cana-5488	92	81	.	.	PUNCT
cana-5488	93	1	the	the	DET
cana-5488	93	2	disease	disease	NOUN
cana-5488	93	3	-	-	PUNCT
cana-5488	93	4	free	free	ADJ
cana-5488	93	5	equilibrium	equilibrium	NOUN
cana-5488	93	6	is	be	AUX
cana-5488	93	7	locally	locally	ADV
cana-5488	93	8	stable	stable	ADJ
cana-5488	93	9	when	when	SCONJ
cana-5488	93	10	r0	r0	NOUN
cana-5488	93	11	<	<	X
cana-5488	93	12	1	1	NUM
cana-5488	93	13	,	,	PUNCT
cana-5488	93	14	but	but	CCONJ
cana-5488	93	15	it	it	PRON
cana-5488	93	16	is	be	AUX
cana-5488	93	17	unstable	unstable	ADJ
cana-5488	93	18	when	when	SCONJ
cana-5488	93	19	r0	r0	NOUN
cana-5488	93	20	>	>	X
cana-5488	93	21	1	1	NUM
cana-5488	93	22	.	.	X
cana-5488	93	23	4.2	4.2	NUM
cana-5488	93	24	endemic	endemic	ADJ
cana-5488	93	25	equilibrium	equilibrium	NOUN
cana-5488	93	26	in	in	ADP
cana-5488	93	27	the	the	DET
cana-5488	93	28	case	case	NOUN
cana-5488	93	29	of	of	ADP
cana-5488	93	30	r0	r0	PROPN
cana-5488	93	31	>	>	X
cana-5488	93	32	1	1	NUM
cana-5488	93	33	,	,	PUNCT
cana-5488	93	34	the	the	DET
cana-5488	93	35	endemic	endemic	ADJ
cana-5488	93	36	equilibrium	equilibrium	NOUN
cana-5488	93	37	is	be	AUX
cana-5488	93	38	always	always	ADV
cana-5488	93	39	stable	stable	ADJ
cana-5488	93	40	.	.	PUNCT
cana-5488	94	1	it	it	PRON
cana-5488	94	2	will	will	AUX
cana-5488	94	3	take	take	VERB
cana-5488	94	4	the	the	DET
cana-5488	94	5	form	form	NOUN
cana-5488	94	6	of	of	ADP
cana-5488	94	7	an	an	DET
cana-5488	94	8	endemic	endemic	ADJ
cana-5488	94	9	equilibrium	equilibrium	NOUN
cana-5488	94	10	if	if	SCONJ
cana-5488	94	11	there	there	PRON
cana-5488	94	12	is	be	VERB
cana-5488	94	13	a	a	DET
cana-5488	94	14	disease	disease	NOUN
cana-5488	94	15	-	-	PUNCT
cana-5488	94	16	free	free	ADJ
cana-5488	94	17	equilibrium	equilibrium	NOUN
cana-5488	94	18	by	by	ADP
cana-5488	94	19	the	the	DET
cana-5488	94	20	population	population	NOUN
cana-5488	94	21	and	and	CCONJ
cana-5488	94	22	diseases	disease	NOUN
cana-5488	94	23	remain	remain	VERB
cana-5488	94	24	communications	communication	NOUN
cana-5488	94	25	on	on	ADP
cana-5488	94	26	applied	apply	VERB
cana-5488	94	27	nonlinear	nonlinear	ADJ
cana-5488	94	28	analysis	analysis	NOUN
cana-5488	94	29	issn	issn	NOUN
cana-5488	94	30	:	:	PUNCT
cana-5488	94	31	1074	1074	NUM
cana-5488	94	32	-	-	PUNCT
cana-5488	94	33	133x	133x	NUM
cana-5488	94	34	vol	vol	VERB
cana-5488	94	35	32	32	NUM
cana-5488	94	36	no	no	NOUN
cana-5488	94	37	.	.	PUNCT
cana-5488	95	1	10s	10	NOUN
cana-5488	95	2	(	(	PUNCT
cana-5488	95	3	2025	2025	NUM
cana-5488	95	4	)	)	PUNCT
cana-5488	95	5	2397	2397	NUM
cana-5488	95	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	95	7	unstable	unstable	ADJ
cana-5488	95	8	.	.	PUNCT
cana-5488	96	1	we	we	PRON
cana-5488	96	2	set	set	VERB
cana-5488	96	3	the	the	DET
cana-5488	96	4	rhs	rhs	PROPN
cana-5488	96	5	of	of	ADP
cana-5488	96	6	equation	equation	NOUN
cana-5488	96	7	(	(	PUNCT
cana-5488	96	8	3.1	3.1	NUM
cana-5488	96	9	)	)	PUNCT
cana-5488	96	10	equal	equal	ADJ
cana-5488	96	11	to	to	ADP
cana-5488	96	12	zero	zero	NUM
cana-5488	96	13	.	.	PUNCT
cana-5488	97	1	the	the	DET
cana-5488	97	2	disease	disease	NOUN
cana-5488	97	3	endemic	endemic	ADJ
cana-5488	97	4	equilibrium	equilibrium	NOUN
cana-5488	97	5	(	(	PUNCT
cana-5488	97	6	s∗	s∗	PROPN
cana-5488	97	7	,	,	PUNCT
cana-5488	97	8	e∗	e∗	NOUN
cana-5488	97	9	,	,	PUNCT
cana-5488	97	10	i∗	i∗	NOUN
cana-5488	97	11	,	,	PUNCT
cana-5488	97	12	q∗	q∗	NOUN
cana-5488	97	13	,	,	PUNCT
cana-5488	97	14	r∗	r∗	PROPN
cana-5488	97	15	)	)	PUNCT
cana-5488	97	16	with	with	ADP
cana-5488	97	17	the	the	DET
cana-5488	97	18	positive	positive	ADJ
cana-5488	97	19	components	component	NOUN
cana-5488	97	20	,	,	PUNCT
cana-5488	97	21	where	where	SCONJ
cana-5488	97	22	𝑆∗	𝑆∗	PROPN
cana-5488	97	23	=	=	SYM
cana-5488	97	24	1	1	NUM
cana-5488	97	25	𝑅0	𝑅0	NOUN
cana-5488	97	26	,	,	PUNCT
cana-5488	97	27	𝐸∗	𝐸∗	NOUN
cana-5488	97	28	=	=	SYM
cana-5488	97	29	𝑏	𝑏	PROPN
cana-5488	97	30	𝜇	𝜇	ADP
cana-5488	97	31	−	−	PROPN
cana-5488	97	32	(	(	PUNCT
cana-5488	97	33	𝜖+𝜂+𝜇+𝛼1)𝜇	𝜖+𝜂+𝜇+𝛼1)𝜇	PROPN
cana-5488	97	34	𝛽𝛾	𝛽𝛾	PROPN
cana-5488	97	35	,	,	PUNCT
cana-5488	97	36	𝐼∗	𝐼∗	NOUN
cana-5488	97	37	=	=	SYM
cana-5488	97	38	𝑏𝛾	𝑏𝛾	PROPN
cana-5488	97	39	(	(	PUNCT
cana-5488	97	40	𝛾+𝜇)(𝜖+𝜂++𝛼1	𝛾+𝜇)(𝜖+𝜂++𝛼1	PROPN
cana-5488	97	41	)	)	PUNCT
cana-5488	97	42	−	−	PROPN
cana-5488	97	43	𝜇	𝜇	ADP
cana-5488	97	44	𝛽	𝛽	NOUN
cana-5488	97	45	,	,	PUNCT
cana-5488	97	46	𝑄∗	𝑄∗	PUNCT
cana-5488	97	47	=	=	PUNCT
cana-5488	97	48	𝜂𝐼∗	𝜂𝐼∗	X
cana-5488	97	49	(	(	PUNCT
cana-5488	97	50	𝛿	𝛿	ADJ
cana-5488	97	51	+	+	X
cana-5488	97	52	𝛼2	𝛼2	ADJ
cana-5488	97	53	+	+	CCONJ
cana-5488	97	54	𝜇	𝜇	X
cana-5488	97	55	)	)	PUNCT
cana-5488	97	56	&	&	CCONJ
cana-5488	97	57	𝑅∗	𝑅∗	PUNCT
cana-5488	97	58	=	=	SYM
cana-5488	97	59	𝐻	𝐻	NOUN
cana-5488	97	60	+	+	CCONJ
cana-5488	97	61	𝛿𝜂	𝛿𝜂	VERB
cana-5488	97	62	𝜇(𝛿	𝜇(𝛿	PROPN
cana-5488	97	63	+	+	CCONJ
cana-5488	97	64	𝛼2	𝛼2	ADJ
cana-5488	97	65	+	+	SYM
cana-5488	97	66	𝜇	𝜇	X
cana-5488	97	67	)	)	PUNCT
cana-5488	97	68	−	−	PROPN
cana-5488	97	69	𝜖	𝜖	PROPN
cana-5488	97	70	𝛽	𝛽	NOUN
cana-5488	97	71	where	where	SCONJ
cana-5488	97	72	h	h	NOUN
cana-5488	97	73	=	=	SYM
cana-5488	97	74	𝑏𝛾	𝑏𝛾	PROPN
cana-5488	97	75	(	(	PUNCT
cana-5488	97	76	𝛾+𝜇)(𝜖+𝜂++𝛼1	𝛾+𝜇)(𝜖+𝜂++𝛼1	PROPN
cana-5488	97	77	)	)	PUNCT
cana-5488	97	78	(	(	PUNCT
cana-5488	97	79	ϵ	ϵ	PART
cana-5488	97	80	−	−	PROPN
cana-5488	97	81	𝛿𝜂	𝛿𝜂	X
cana-5488	97	82	𝜇(𝛿+𝛼2+𝜇	𝜇(𝛿+𝛼2+𝜇	PROPN
cana-5488	97	83	)	)	PUNCT
cana-5488	97	84	)	)	PUNCT
cana-5488	97	85	.	.	PUNCT
cana-5488	98	1	5	5	X
cana-5488	98	2	.	.	X
cana-5488	98	3	an	an	DET
cana-5488	98	4	application	application	NOUN
cana-5488	98	5	of	of	ADP
cana-5488	98	6	the	the	DET
cana-5488	98	7	dtm	dtm	NOUN
cana-5488	98	8	based	base	VERB
cana-5488	98	9	on	on	ADP
cana-5488	98	10	the	the	DET
cana-5488	98	11	transformed	transform	VERB
cana-5488	98	12	function	function	NOUN
cana-5488	98	13	of	of	ADP
cana-5488	98	14	the	the	DET
cana-5488	98	15	given	give	VERB
cana-5488	98	16	function	function	NOUN
cana-5488	98	17	in	in	ADP
cana-5488	98	18	table	table	NOUN
cana-5488	98	19	1	1	NUM
cana-5488	98	20	,	,	PUNCT
cana-5488	98	21	equation	equation	NOUN
cana-5488	98	22	(	(	PUNCT
cana-5488	98	23	1	1	X
cana-5488	98	24	)	)	PUNCT
cana-5488	98	25	has	have	VERB
cana-5488	98	26	the	the	DET
cana-5488	98	27	following	follow	VERB
cana-5488	98	28	recurrence	recurrence	NOUN
cana-5488	98	29	relation	relation	PROPN
cana-5488	98	30	:	:	PUNCT
cana-5488	98	31	𝑆(1	𝑆(1	PROPN
cana-5488	99	1	+	+	CCONJ
cana-5488	99	2	𝑘	𝑘	X
cana-5488	99	3	)	)	PUNCT
cana-5488	99	4	=	=	SYM
cana-5488	100	1	1	1	NUM
cana-5488	100	2	𝑘+1	𝑘+1	NUM
cana-5488	101	1	[	[	X
cana-5488	101	2	𝑏	𝑏	X
cana-5488	101	3	−	−	PROPN
cana-5488	101	4	𝛽	𝛽	NOUN
cana-5488	101	5	𝑁	𝑁	PROPN
cana-5488	101	6	∑	∑	PUNCT
cana-5488	101	7	𝐼(𝑘	𝐼(𝑘	ADP
cana-5488	101	8	−	−	PROPN
cana-5488	101	9	𝑟	𝑟	NOUN
cana-5488	101	10	)	)	PUNCT
cana-5488	101	11	−	−	NOUN
cana-5488	101	12	𝜇	𝜇	ADP
cana-5488	101	13	𝑆(𝑘)𝑘	𝑆(𝑘)𝑘	NOUN
cana-5488	101	14	𝑟=0	𝑟=0	PRON
cana-5488	101	15	]	]	PUNCT
cana-5488	101	16	𝐸(1	𝐸(1	NUM
cana-5488	101	17	+	+	CCONJ
cana-5488	101	18	𝑘	𝑘	X
cana-5488	101	19	)	)	PUNCT
cana-5488	101	20	=	=	SYM
cana-5488	101	21	1	1	NUM
cana-5488	101	22	𝑘+1	𝑘+1	NUM
cana-5488	101	23	[	[	PUNCT
cana-5488	101	24	𝛽	𝛽	NOUN
cana-5488	101	25	𝑁	𝑁	PROPN
cana-5488	101	26	∑	∑	PUNCT
cana-5488	101	27	𝐼(𝑘	𝐼(𝑘	ADP
cana-5488	101	28	−	−	PROPN
cana-5488	101	29	𝑟	𝑟	NOUN
cana-5488	101	30	)	)	PUNCT
cana-5488	101	31	−	−	PROPN
cana-5488	101	32	𝛾𝐸(𝑘	𝛾𝐸(𝑘	NUM
cana-5488	101	33	)	)	PUNCT
cana-5488	101	34	−	−	NOUN
cana-5488	101	35	𝜇	𝜇	ADP
cana-5488	101	36	𝑆(𝑘)𝑘	𝑆(𝑘)𝑘	NOUN
cana-5488	101	37	𝑟=0	𝑟=0	PUNCT
cana-5488	101	38	]	]	PUNCT
cana-5488	102	1	𝐼(1	𝐼(1	NUM
cana-5488	103	1	+	+	CCONJ
cana-5488	103	2	𝑘	𝑘	X
cana-5488	103	3	)	)	PUNCT
cana-5488	103	4	=	=	SYM
cana-5488	104	1	1	1	NUM
cana-5488	104	2	𝑘+1	𝑘+1	NUM
cana-5488	104	3	[	[	X
cana-5488	104	4	𝛾𝐸(𝑘	𝛾𝐸(𝑘	NOUN
cana-5488	104	5	)	)	PUNCT
cana-5488	104	6	−	−	PROPN
cana-5488	105	1	𝜖𝐼(𝑘	𝜖𝐼(𝑘	PROPN
cana-5488	105	2	)	)	PUNCT
cana-5488	105	3	−	−	PROPN
cana-5488	106	1	𝜂𝐼(𝑘	𝜂𝐼(𝑘	NUM
cana-5488	106	2	)	)	PUNCT
cana-5488	106	3	−	−	PROPN
cana-5488	106	4	𝛼1𝐼(𝑘	𝛼1𝐼(𝑘	PROPN
cana-5488	106	5	)	)	PUNCT
cana-5488	106	6	−	−	PROPN
cana-5488	107	1	𝜇𝐼(𝑘	𝜇𝐼(𝑘	PROPN
cana-5488	107	2	)	)	PUNCT
cana-5488	107	3	]	]	X
cana-5488	107	4	(	(	PUNCT
cana-5488	107	5	5.1	5.1	NUM
cana-5488	107	6	)	)	PUNCT
cana-5488	107	7	𝑄(1	𝑄(1	X
cana-5488	108	1	+	+	CCONJ
cana-5488	108	2	𝑘	𝑘	X
cana-5488	108	3	)	)	PUNCT
cana-5488	108	4	=	=	SYM
cana-5488	109	1	1	1	NUM
cana-5488	109	2	𝑘+1	𝑘+1	NUM
cana-5488	109	3	[	[	X
cana-5488	109	4	𝜂𝐼(𝑘	𝜂𝐼(𝑘	NUM
cana-5488	109	5	)	)	PUNCT
cana-5488	109	6	−	−	PROPN
cana-5488	109	7	𝛿𝑄(𝑘	𝛿𝑄(𝑘	PROPN
cana-5488	109	8	)	)	PUNCT
cana-5488	109	9	−	−	PROPN
cana-5488	109	10	𝛼2𝑄(𝑘	𝛼2𝑄(𝑘	NOUN
cana-5488	109	11	)	)	PUNCT
cana-5488	109	12	−	−	NOUN
cana-5488	109	13	𝜇𝑄(𝑘	𝜇𝑄(𝑘	NOUN
cana-5488	109	14	)	)	PUNCT
cana-5488	109	15	]	]	PUNCT
cana-5488	109	16	𝑅(1	𝑅(1	PUNCT
cana-5488	110	1	+	+	CCONJ
cana-5488	110	2	𝑘	𝑘	X
cana-5488	110	3	)	)	PUNCT
cana-5488	110	4	=	=	SYM
cana-5488	111	1	1	1	NUM
cana-5488	111	2	𝑘+1	𝑘+1	NUM
cana-5488	111	3	[	[	X
cana-5488	111	4	𝜉𝐼(𝑘	𝜉𝐼(𝑘	NOUN
cana-5488	111	5	)	)	PUNCT
cana-5488	111	6	−	−	PROPN
cana-5488	111	7	𝛿𝑄(𝑘	𝛿𝑄(𝑘	PROPN
cana-5488	111	8	)	)	PUNCT
cana-5488	111	9	−	−	PROPN
cana-5488	112	1	𝜇𝑅(𝑘	𝜇𝑅(𝑘	NUM
cana-5488	112	2	)	)	PUNCT
cana-5488	112	3	]	]	PUNCT
cana-5488	112	4	with	with	ADP
cana-5488	112	5	the	the	DET
cana-5488	112	6	initial	initial	ADJ
cana-5488	112	7	points	point	NOUN
cana-5488	112	8	s(0	s(0	PROPN
cana-5488	112	9	)	)	PUNCT
cana-5488	112	10	=	=	SYM
cana-5488	112	11	500	500	NUM
cana-5488	112	12	,	,	PUNCT
cana-5488	112	13	e(0	e(0	NOUN
cana-5488	112	14	)	)	PUNCT
cana-5488	112	15	=	=	SYM
cana-5488	112	16	100	100	NUM
cana-5488	112	17	,	,	PUNCT
cana-5488	112	18	i(0	i(0	PROPN
cana-5488	112	19	)	)	PUNCT
cana-5488	113	1	=	=	SYM
cana-5488	113	2	100	100	NUM
cana-5488	113	3	,	,	PUNCT
cana-5488	113	4	q(0	q(0	PROPN
cana-5488	113	5	)	)	PUNCT
cana-5488	113	6	=	=	NOUN
cana-5488	113	7	200	200	NUM
cana-5488	113	8	,	,	PUNCT
cana-5488	113	9	r(0	r(0	PROPN
cana-5488	113	10	)	)	PUNCT
cana-5488	113	11	=	=	NOUN
cana-5488	113	12	100	100	NUM
cana-5488	113	13	and	and	CCONJ
cana-5488	113	14	the	the	DET
cana-5488	113	15	parameters	parameter	NOUN
cana-5488	113	16	n	n	X
cana-5488	113	17	=	=	SYM
cana-5488	113	18	1000	1000	NUM
cana-5488	113	19	,	,	PUNCT
cana-5488	113	20	b	b	NOUN
cana-5488	113	21	=	=	SYM
cana-5488	113	22	5	5	NUM
cana-5488	113	23	,	,	PUNCT
cana-5488	113	24	γ	γ	X
cana-5488	113	25	=	=	SYM
cana-5488	113	26	0.75	0.75	NUM
cana-5488	113	27	,	,	PUNCT
cana-5488	113	28	α1	α1	PROPN
cana-5488	113	29	=	=	SYM
cana-5488	113	30	0.01	0.01	NUM
cana-5488	113	31	,	,	PUNCT
cana-5488	113	32	α2	α2	NOUN
cana-5488	113	33	=	=	SYM
cana-5488	113	34	0.01	0.01	NUM
cana-5488	113	35	,	,	PUNCT
cana-5488	113	36	η	η	PROPN
cana-5488	113	37	=	=	PROPN
cana-5488	113	38	0.5	0.5	NUM
cana-5488	113	39	,	,	PUNCT
cana-5488	113	40	µ	µ	X
cana-5488	113	41	=	=	SYM
cana-5488	113	42	0.5	0.5	NUM
cana-5488	113	43	,	,	PUNCT
cana-5488	113	44	β	β	X
cana-5488	113	45	=	=	SYM
cana-5488	113	46	1.5	1.5	NUM
cana-5488	113	47	,	,	PUNCT
cana-5488	113	48	ϵ	ϵ	X
cana-5488	113	49	=	=	SYM
cana-5488	113	50	0.5	0.5	NUM
cana-5488	113	51	,	,	PUNCT
cana-5488	113	52	δ	δ	X
cana-5488	113	53	=	=	SYM
cana-5488	113	54	0.75	0.75	NUM
cana-5488	113	55	.	.	PUNCT
cana-5488	114	1	based	base	VERB
cana-5488	114	2	on	on	ADP
cana-5488	114	3	the	the	DET
cana-5488	114	4	equation	equation	NOUN
cana-5488	114	5	,	,	PUNCT
cana-5488	114	6	we	we	PRON
cana-5488	114	7	can	can	AUX
cana-5488	114	8	derive	derive	VERB
cana-5488	114	9	the	the	DET
cana-5488	114	10	dtm	dtm	PROPN
cana-5488	114	11	series	series	NOUN
cana-5488	114	12	solution	solution	NOUN
cana-5488	114	13	of	of	ADP
cana-5488	114	14	the	the	DET
cana-5488	114	15	seiqr	seiqr	ADJ
cana-5488	114	16	model	model	NOUN
cana-5488	114	17	as	as	SCONJ
cana-5488	114	18	follows	follow	VERB
cana-5488	114	19	:	:	PUNCT
cana-5488	114	20	𝑆(𝑡	𝑆(𝑡	ADJ
cana-5488	114	21	)	)	PUNCT
cana-5488	114	22	=	=	PUNCT
cana-5488	115	1	∑	∑	PUNCT
cana-5488	115	2	𝑆(𝑘)𝑡𝑘	𝑆(𝑘)𝑡𝑘	VERB
cana-5488	115	3	𝑘	𝑘	X
cana-5488	115	4	𝑙=0	𝑙=0	PUNCT
cana-5488	115	5	𝐸(𝑡	𝐸(𝑡	NUM
cana-5488	115	6	)	)	PUNCT
cana-5488	115	7	=	=	PUNCT
cana-5488	115	8	∑	∑	PUNCT
cana-5488	115	9	𝐸(𝑘)𝑡𝑘	𝐸(𝑘)𝑡𝑘	VERB
cana-5488	115	10	𝑘	𝑘	DET
cana-5488	115	11	𝑙=0	𝑙=0	PROPN
cana-5488	115	12	𝐼(𝑡	𝐼(𝑡	PROPN
cana-5488	115	13	)	)	PUNCT
cana-5488	115	14	=	=	PUNCT
cana-5488	116	1	∑	∑	PUNCT
cana-5488	116	2	𝐼(𝑘)𝑡𝑘	𝐼(𝑘)𝑡𝑘	NOUN
cana-5488	116	3	𝑘	𝑘	PROPN
cana-5488	116	4	𝑙=0	𝑙=0	PROPN
cana-5488	116	5	𝑄(𝑡	𝑄(𝑡	X
cana-5488	116	6	)	)	PUNCT
cana-5488	116	7	=	=	PUNCT
cana-5488	117	1	∑	∑	PUNCT
cana-5488	117	2	𝑆(𝑘)𝑡𝑘	𝑆(𝑘)𝑡𝑘	VERB
cana-5488	117	3	𝑘	𝑘	PRON
cana-5488	117	4	𝑙=0	𝑙=0	NOUN
cana-5488	117	5	communications	communication	NOUN
cana-5488	117	6	on	on	ADP
cana-5488	117	7	applied	apply	VERB
cana-5488	117	8	nonlinear	nonlinear	ADJ
cana-5488	117	9	analysis	analysis	NOUN
cana-5488	117	10	issn	issn	NOUN
cana-5488	117	11	:	:	PUNCT
cana-5488	117	12	1074	1074	NUM
cana-5488	117	13	-	-	PUNCT
cana-5488	117	14	133x	133x	NUM
cana-5488	117	15	vol	vol	VERB
cana-5488	117	16	32	32	NUM
cana-5488	117	17	no	no	NOUN
cana-5488	117	18	.	.	PUNCT
cana-5488	118	1	10s	10	NOUN
cana-5488	118	2	(	(	PUNCT
cana-5488	118	3	2025	2025	NUM
cana-5488	118	4	)	)	PUNCT
cana-5488	118	5	2398	2398	NUM
cana-5488	118	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	118	7	𝑅(𝑡	𝑅(𝑡	NOUN
cana-5488	118	8	)	)	PUNCT
cana-5488	118	9	=	=	PUNCT
cana-5488	118	10	∑	∑	PUNCT
cana-5488	118	11	𝑅(𝑘)𝑡𝑘	𝑅(𝑘)𝑡𝑘	VERB
cana-5488	118	12	𝑘	𝑘	ADP
cana-5488	118	13	𝑙=0	𝑙=0	PROPN
cana-5488	118	14	.	.	PUNCT
cana-5488	119	1	by	by	ADP
cana-5488	119	2	applying	apply	VERB
cana-5488	119	3	the	the	DET
cana-5488	119	4	condition	condition	NOUN
cana-5488	119	5	in	in	ADP
cana-5488	119	6	(	(	PUNCT
cana-5488	119	7	5.1	5.1	NUM
cana-5488	119	8	)	)	PUNCT
cana-5488	119	9	,	,	PUNCT
cana-5488	119	10	we	we	PRON
cana-5488	119	11	get	get	VERB
cana-5488	119	12	s(1	s(1	PROPN
cana-5488	119	13	)	)	PUNCT
cana-5488	119	14	=	=	SYM
cana-5488	120	1	−245	−245	PROPN
cana-5488	120	2	,	,	PUNCT
cana-5488	120	3	s(2	s(2	NOUN
cana-5488	120	4	)	)	PUNCT
cana-5488	120	5	=	=	SYM
cana-5488	120	6	129	129	NUM
cana-5488	120	7	,	,	PUNCT
cana-5488	120	8	s(3	s(3	NOUN
cana-5488	120	9	)	)	PUNCT
cana-5488	120	10	=	=	PUNCT
cana-5488	121	1	−60.52083	−60.52083	NOUN
cana-5488	121	2	,	,	PUNCT
cana-5488	121	3	s(4	s(4	NOUN
cana-5488	121	4	)	)	PUNCT
cana-5488	121	5	=	=	SYM
cana-5488	121	6	17.6802	17.6802	NUM
cana-5488	121	7	,	,	PUNCT
cana-5488	121	8	e(1	e(1	PROPN
cana-5488	121	9	)	)	PUNCT
cana-5488	121	10	=	=	SYM
cana-5488	121	11	−50	−50	NOUN
cana-5488	121	12	e(2	e(2	NOUN
cana-5488	121	13	)	)	PUNCT
cana-5488	121	14	=	=	SYM
cana-5488	122	1	−34	−34	NOUN
cana-5488	122	2	,	,	PUNCT
cana-5488	122	3	e(3	e(3	PROPN
cana-5488	122	4	)	)	PUNCT
cana-5488	122	5	=	=	NOUN
cana-5488	122	6	27.66875	27.66875	NUM
cana-5488	122	7	,	,	PUNCT
cana-5488	122	8	e(4	e(4	NOUN
cana-5488	122	9	)	)	PUNCT
cana-5488	122	10	=	=	SYM
cana-5488	123	1	−32.6418	−32.6418	PROPN
cana-5488	123	2	,	,	PUNCT
cana-5488	123	3	i(1	i(1	PROPN
cana-5488	123	4	)	)	PUNCT
cana-5488	123	5	=	=	SYM
cana-5488	123	6	−125	−125	VERB
cana-5488	123	7	i(2	i(2	PROPN
cana-5488	123	8	)	)	PUNCT
cana-5488	123	9	=	=	SYM
cana-5488	124	1	75.625	75.625	NUM
cana-5488	124	2	,	,	PUNCT
cana-5488	124	3	i(3	i(3	NOUN
cana-5488	124	4	)	)	PUNCT
cana-5488	124	5	=	=	PUNCT
cana-5488	124	6	−46.5646	−46.5646	PROPN
cana-5488	124	7	,	,	PUNCT
cana-5488	124	8	i(4	i(4	NOUN
cana-5488	124	9	)	)	PUNCT
cana-5488	124	10	=	=	SYM
cana-5488	124	11	22.7660	22.7660	NUM
cana-5488	124	12	,	,	PUNCT
cana-5488	124	13	q(1	q(1	NOUN
cana-5488	124	14	)	)	PUNCT
cana-5488	124	15	=	=	NOUN
cana-5488	124	16	−250	−250	PROPN
cana-5488	124	17	q(2	q(2	PROPN
cana-5488	124	18	)	)	PUNCT
cana-5488	124	19	=	=	PUNCT
cana-5488	125	1	126.25	126.25	NUM
cana-5488	125	2	,	,	PUNCT
cana-5488	125	3	q(3	q(3	PROPN
cana-5488	125	4	)	)	PUNCT
cana-5488	125	5	=	=	SYM
cana-5488	125	6	−40.4208	−40.4208	NOUN
cana-5488	125	7	,	,	PUNCT
cana-5488	125	8	q(4	q(4	PROPN
cana-5488	125	9	)	)	PUNCT
cana-5488	125	10	=	=	PUNCT
cana-5488	125	11	2.3646	2.3646	NUM
cana-5488	125	12	,	,	PUNCT
cana-5488	125	13	r(1	r(1	PROPN
cana-5488	125	14	)	)	PUNCT
cana-5488	125	15	=	=	NOUN
cana-5488	125	16	150	150	NUM
cana-5488	125	17	r(2	r(2	NOUN
cana-5488	125	18	)	)	PUNCT
cana-5488	125	19	=	=	SYM
cana-5488	125	20	−162.5	−162.5	NOUN
cana-5488	125	21	,	,	PUNCT
cana-5488	125	22	r(3	r(3	PROPN
cana-5488	125	23	)	)	PUNCT
cana-5488	125	24	=	=	SYM
cana-5488	125	25	71.25	71.25	NUM
cana-5488	125	26	,	,	PUNCT
cana-5488	125	27	r(4	r(4	PROPN
cana-5488	125	28	)	)	PUNCT
cana-5488	125	29	=	=	PUNCT
cana-5488	125	30	−22.3057	−22.3057	PROPN
cana-5488	125	31	.	.	PUNCT
cana-5488	126	1	communications	communication	NOUN
cana-5488	126	2	on	on	ADP
cana-5488	126	3	applied	apply	VERB
cana-5488	126	4	nonlinear	nonlinear	ADJ
cana-5488	126	5	analysis	analysis	NOUN
cana-5488	126	6	issn	issn	NOUN
cana-5488	126	7	:	:	PUNCT
cana-5488	126	8	1074	1074	NUM
cana-5488	126	9	-	-	PUNCT
cana-5488	126	10	133x	133x	NUM
cana-5488	126	11	vol	vol	VERB
cana-5488	126	12	32	32	NUM
cana-5488	126	13	no	no	NOUN
cana-5488	126	14	.	.	PUNCT
cana-5488	127	1	10s	10	NOUN
cana-5488	127	2	(	(	PUNCT
cana-5488	127	3	2025	2025	NUM
cana-5488	127	4	)	)	PUNCT
cana-5488	127	5	2399	2399	NUM
cana-5488	127	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	127	7	figure	figure	NOUN
cana-5488	127	8	1	1	NUM
cana-5488	127	9	:	:	PUNCT
cana-5488	127	10	a	a	DET
cana-5488	127	11	relationship	relationship	NOUN
cana-5488	127	12	between	between	ADP
cana-5488	127	13	s(t	s(t	PROPN
cana-5488	127	14	)	)	PUNCT
cana-5488	127	15	,	,	PUNCT
cana-5488	127	16	e(t	e(t	NOUN
cana-5488	127	17	)	)	PUNCT
cana-5488	127	18	,	,	PUNCT
cana-5488	127	19	i(t	i(t	PROPN
cana-5488	127	20	)	)	PUNCT
cana-5488	127	21	,	,	PUNCT
cana-5488	127	22	q(t	q(t	PROPN
cana-5488	127	23	)	)	PUNCT
cana-5488	127	24	and	and	CCONJ
cana-5488	127	25	r(t	r(t	NOUN
cana-5488	127	26	)	)	PUNCT
cana-5488	127	27	population	population	NOUN
cana-5488	127	28	and	and	CCONJ
cana-5488	127	29	time	time	NOUN
cana-5488	127	30	in	in	ADP
cana-5488	127	31	years	year	NOUN
cana-5488	127	32	.	.	PUNCT
cana-5488	128	1	hence	hence	ADV
cana-5488	128	2	the	the	DET
cana-5488	128	3	closed	closed	ADJ
cana-5488	128	4	form	form	NOUN
cana-5488	128	5	of	of	ADP
cana-5488	128	6	a	a	DET
cana-5488	128	7	solution	solution	NOUN
cana-5488	128	8	,	,	PUNCT
cana-5488	128	9	with	with	ADP
cana-5488	128	10	k	k	PROPN
cana-5488	128	11	=	=	SYM
cana-5488	128	12	4	4	NUM
cana-5488	128	13	,	,	PUNCT
cana-5488	128	14	is	be	AUX
cana-5488	128	15	as	as	SCONJ
cana-5488	128	16	follows	follow	VERB
cana-5488	128	17	:	:	PUNCT
cana-5488	128	18	𝑆(𝑡	𝑆(𝑡	ADJ
cana-5488	128	19	)	)	PUNCT
cana-5488	128	20	=	=	PUNCT
cana-5488	128	21	∑	∑	PUNCT
cana-5488	128	22	𝑆(𝑘)𝑡𝑘	𝑆(𝑘)𝑡𝑘	VERB
cana-5488	128	23	𝑘	𝑘	INTJ
cana-5488	128	24	𝑙=0	𝑙=0	PUNCT
cana-5488	128	25	=	=	SYM
cana-5488	129	1	500	500	NUM
cana-5488	129	2	−	−	NUM
cana-5488	129	3	245𝑡	245𝑡	PROPN
cana-5488	130	1	+	+	CCONJ
cana-5488	130	2	129𝑡2	129𝑡2	NUM
cana-5488	130	3	−	−	NOUN
cana-5488	130	4	60.52083𝑡3	60.52083𝑡3	NUM
cana-5488	131	1	+	+	CCONJ
cana-5488	131	2	17.6802𝑡4	17.6802𝑡4	NUM
cana-5488	132	1	+	+	CCONJ
cana-5488	132	2	.	.	PUNCT
cana-5488	133	1	..	..	PUNCT
cana-5488	133	2	𝐸(𝑡	𝐸(𝑡	NUM
cana-5488	133	3	)	)	PUNCT
cana-5488	133	4	=	=	SYM
cana-5488	133	5	∑	∑	PUNCT
cana-5488	133	6	𝐸(𝑘)𝑡𝑘	𝐸(𝑘)𝑡𝑘	NOUN
cana-5488	133	7	=	=	PUNCT
cana-5488	133	8	100	100	NUM
cana-5488	133	9	−	−	NUM
cana-5488	133	10	50𝑡	50𝑡	NOUN
cana-5488	133	11	–	–	PUNCT
cana-5488	134	1	34𝑡2	34𝑡2	NUM
cana-5488	134	2	+	+	CCONJ
cana-5488	134	3	27.66875𝑡3	27.66875𝑡3	NUM
cana-5488	134	4	–	–	PUNCT
cana-5488	134	5	32.6418𝑡4	32.6418𝑡4	PROPN
cana-5488	134	6	+	+	NUM
cana-5488	134	7	…	…	PUNCT
cana-5488	134	8	𝑘	𝑘	PRON
cana-5488	134	9	𝑙=0	𝑙=0	NOUN
cana-5488	134	10	𝐼(𝑡	𝐼(𝑡	NUM
cana-5488	134	11	)	)	PUNCT
cana-5488	134	12	=	=	PUNCT
cana-5488	134	13	∑	∑	PUNCT
cana-5488	134	14	𝐼(𝑘)𝑡𝑘	𝐼(𝑘)𝑡𝑘	NOUN
cana-5488	134	15	𝑘	𝑘	X
cana-5488	134	16	𝑙=0	𝑙=0	PUNCT
cana-5488	134	17	=	=	NUM
cana-5488	135	1	100	100	NUM
cana-5488	135	2	−	−	NUM
cana-5488	135	3	125𝑡	125𝑡	PROPN
cana-5488	135	4	+	+	CCONJ
cana-5488	135	5	75.625𝑡2	75.625𝑡2	NUM
cana-5488	135	6	−	−	NOUN
cana-5488	135	7	46.5646𝑡3	46.5646𝑡3	NOUN
cana-5488	135	8	+	+	NOUN
cana-5488	135	9	22.76660𝑡4	22.76660𝑡4	NUM
cana-5488	135	10	+	+	NUM
cana-5488	135	11	.	.	PUNCT
cana-5488	135	12	..	..	PUNCT
cana-5488	136	1	𝑄(𝑡	𝑄(𝑡	X
cana-5488	136	2	)	)	PUNCT
cana-5488	136	3	=	=	PUNCT
cana-5488	136	4	∑	∑	PUNCT
cana-5488	136	5	𝑆(𝑘)𝑡𝑘	𝑆(𝑘)𝑡𝑘	NOUN
cana-5488	136	6	=	=	NOUN
cana-5488	136	7	200	200	NUM
cana-5488	136	8	−	−	PROPN
cana-5488	136	9	250𝑡	250𝑡	PROPN
cana-5488	136	10	+	+	CCONJ
cana-5488	137	1	126.25𝑡2	126.25𝑡2	NUM
cana-5488	137	2	−	−	NOUN
cana-5488	137	3	40.4208𝑡3	40.4208𝑡3	PROPN
cana-5488	137	4	+	+	CCONJ
cana-5488	137	5	2.3646𝑡4	2.3646𝑡4	NUM
cana-5488	137	6	+	+	CCONJ
cana-5488	137	7	.	.	PUNCT
cana-5488	137	8	.	.	PUNCT
cana-5488	138	1	.𝑘	.𝑘	X
cana-5488	139	1	𝑙=0	𝑙=0	PUNCT
cana-5488	139	2	𝑅(𝑡	𝑅(𝑡	NUM
cana-5488	139	3	)	)	PUNCT
cana-5488	139	4	=	=	PUNCT
cana-5488	139	5	∑	∑	PUNCT
cana-5488	139	6	𝑅(𝑘)𝑡𝑘	𝑅(𝑘)𝑡𝑘	X
cana-5488	139	7	=	=	PUNCT
cana-5488	140	1	100	100	NUM
cana-5488	140	2	+	+	NUM
cana-5488	140	3	150𝑡	150𝑡	NUM
cana-5488	140	4	−	−	PROPN
cana-5488	140	5	162.5𝑡2	162.5𝑡2	NUM
cana-5488	141	1	+	+	CCONJ
cana-5488	141	2	71.25𝑡3	71.25𝑡3	NUM
cana-5488	141	3	−	−	ADP
cana-5488	141	4	22.3057𝑡4	22.3057𝑡4	PROPN
cana-5488	141	5	+	+	PROPN
cana-5488	141	6	.	.	PUNCT
cana-5488	141	7	.	.	PUNCT
cana-5488	142	1	.𝑘	.𝑘	X
cana-5488	143	1	𝑙=0	𝑙=0	PUNCT
cana-5488	144	1	6	6	X
cana-5488	144	2	.	.	PUNCT
cana-5488	145	1	the	the	DET
cana-5488	145	2	comparison	comparison	NOUN
cana-5488	145	3	between	between	ADP
cana-5488	145	4	rk4	rk4	NOUN
cana-5488	145	5	method	method	NOUN
cana-5488	145	6	and	and	CCONJ
cana-5488	145	7	dtm	dtm	PROPN
cana-5488	145	8	now	now	ADV
cana-5488	145	9	take	take	VERB
cana-5488	145	10	the	the	DET
cana-5488	145	11	solution	solution	NOUN
cana-5488	145	12	of	of	ADP
cana-5488	145	13	the	the	DET
cana-5488	145	14	seiqr	seiqr	ADJ
cana-5488	145	15	model	model	NOUN
cana-5488	145	16	and	and	CCONJ
cana-5488	145	17	compute	compute	VERB
cana-5488	145	18	it	it	PRON
cana-5488	145	19	by	by	ADP
cana-5488	145	20	the	the	DET
cana-5488	145	21	dtm	dtm	PROPN
cana-5488	145	22	and	and	CCONJ
cana-5488	145	23	rk4	rk4	PROPN
cana-5488	145	24	method	method	NOUN
cana-5488	145	25	.	.	PUNCT
cana-5488	146	1	the	the	DET
cana-5488	146	2	values	value	NOUN
cana-5488	146	3	are	be	AUX
cana-5488	146	4	discussed	discuss	VERB
cana-5488	146	5	in	in	ADP
cana-5488	146	6	the	the	DET
cana-5488	146	7	table	table	NOUN
cana-5488	146	8	4	4	NUM
cana-5488	146	9	.	.	PUNCT
cana-5488	146	10	table	table	NOUN
cana-5488	146	11	4	4	NUM
cana-5488	146	12	:	:	PUNCT
cana-5488	146	13	comparison	comparison	NOUN
cana-5488	146	14	between	between	ADP
cana-5488	146	15	rk4	rk4	PROPN
cana-5488	146	16	and	and	CCONJ
cana-5488	146	17	dtm	dtm	NOUN
cana-5488	146	18	ti	ti	NOUN
cana-5488	146	19	0	0	NUM
cana-5488	146	20	0.25	0.25	NUM
cana-5488	146	21	0.5	0.5	NUM
cana-5488	146	22	0.75	0.75	NUM
cana-5488	146	23	1	1	NUM
cana-5488	146	24	susceptible	susceptible	ADJ
cana-5488	146	25	rk4	rk4	NOUN
cana-5488	146	26	500	500	NUM
cana-5488	146	27	444.3097	444.3097	NUM
cana-5488	146	28	395.7261	395.7261	NUM
cana-5488	146	29	353.2100	353.2100	NUM
cana-5488	146	30	315.8906	315.8906	NUM
cana-5488	146	31	dtm	dtm	NOUN
cana-5488	146	32	500	500	NUM
cana-5488	146	33	445.9359	445.9359	NUM
cana-5488	146	34	403.2899	403.2899	NUM
cana-5488	146	35	368.8744	368.8744	NUM
cana-5488	146	36	341.1594	341.1594	NUM
cana-5488	146	37	exposed	expose	VERB
cana-5488	146	38	rk4	rk4	NOUN
cana-5488	146	39	100	100	NUM
cana-5488	146	40	86.8303	86.8303	NUM
cana-5488	146	41	75.0636	75.0636	NUM
cana-5488	146	42	64.6330	64.6330	NUM
cana-5488	146	43	55.4509	55.4509	NUM
cana-5488	146	44	dtm	dtm	NOUN
cana-5488	146	45	100	100	NUM
cana-5488	146	46	85.6798	85.6798	NUM
cana-5488	146	47	67.9184	67.9184	NUM
cana-5488	146	48	44.7196	44.7196	NUM
cana-5488	146	49	11.0269	11.0269	NUM
cana-5488	146	50	infected	infect	VERB
cana-5488	146	51	rk4	rk4	NOUN
cana-5488	146	52	100	100	NUM
cana-5488	146	53	87.9395	87.9395	NUM
cana-5488	146	54	76.9315	76.9315	NUM
cana-5488	146	55	66.9970	66.9970	NUM
cana-5488	146	56	58.1147	58.1147	NUM
cana-5488	146	57	dtm	dtm	NOUN
cana-5488	146	58	100	100	NUM
cana-5488	146	59	72.8379	72.8379	NUM
cana-5488	146	60	52.0085	52.0085	NUM
cana-5488	146	61	36.3481	36.3481	NUM
cana-5488	146	62	26.8270	26.8270	NUM
cana-5488	146	63	quarantined	quarantine	VERB
cana-5488	146	64	rk4	rk4	NOUN
cana-5488	146	65	200	200	NUM
cana-5488	146	66	191.1697	191.1697	NUM
cana-5488	146	67	183.4350	183.4350	NUM
cana-5488	146	68	176.6936	176.6936	NUM
cana-5488	146	69	170.8434	170.8434	NUM
cana-5488	146	70	dtm	dtm	NOUN
cana-5488	146	71	200	200	NUM
cana-5488	146	72	144.7683	144.7683	NUM
cana-5488	146	73	101.6576	101.6576	NUM
cana-5488	146	74	67.2112	67.2112	NUM
cana-5488	146	75	38.1938	38.1938	NUM
cana-5488	146	76	communications	communication	NOUN
cana-5488	146	77	on	on	ADP
cana-5488	146	78	applied	apply	VERB
cana-5488	146	79	nonlinear	nonlinear	ADJ
cana-5488	146	80	analysis	analysis	NOUN
cana-5488	146	81	issn	issn	NOUN
cana-5488	146	82	:	:	PUNCT
cana-5488	146	83	1074	1074	NUM
cana-5488	146	84	-	-	PUNCT
cana-5488	146	85	133x	133x	NUM
cana-5488	146	86	vol	vol	VERB
cana-5488	146	87	32	32	NUM
cana-5488	146	88	no	no	NOUN
cana-5488	146	89	.	.	PUNCT
cana-5488	147	1	10s	10	NOUN
cana-5488	147	2	(	(	PUNCT
cana-5488	147	3	2025	2025	NUM
cana-5488	147	4	)	)	PUNCT
cana-5488	147	5	2400	2400	NUM
cana-5488	148	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	148	2	recovered	recover	VERB
cana-5488	148	3	rk4	rk4	NOUN
cana-5488	148	4	100	100	NUM
cana-5488	148	5	82.9566	82.9566	NUM
cana-5488	148	6	66.7665	66.7665	NUM
cana-5488	148	7	51.4759	51.4759	NUM
cana-5488	148	8	37.1038	37.1038	NUM
cana-5488	148	9	dtm	dtm	NOUN
cana-5488	148	10	100	100	NUM
cana-5488	148	11	128.3698	128.3698	NUM
cana-5488	148	12	141.8871	141.8871	NUM
cana-5488	148	13	144.0946	144.0946	NUM
cana-5488	148	14	136.4443	136.4443	NUM
cana-5488	148	15	it	it	PRON
cana-5488	148	16	is	be	AUX
cana-5488	148	17	evident	evident	ADJ
cana-5488	148	18	from	from	ADP
cana-5488	148	19	table	table	NOUN
cana-5488	148	20	4	4	NUM
cana-5488	148	21	that	that	ADV
cana-5488	148	22	susceptible	susceptible	ADJ
cana-5488	148	23	and	and	CCONJ
cana-5488	148	24	recovered	recovered	ADJ
cana-5488	148	25	populations	population	NOUN
cana-5488	148	26	are	be	AUX
cana-5488	148	27	increasing	increase	VERB
cana-5488	148	28	in	in	ADP
cana-5488	148	29	our	our	PRON
cana-5488	148	30	cases	case	NOUN
cana-5488	148	31	.	.	PUNCT
cana-5488	149	1	it	it	PRON
cana-5488	149	2	is	be	AUX
cana-5488	149	3	noticeable	noticeable	ADJ
cana-5488	149	4	that	that	SCONJ
cana-5488	149	5	exposed	expose	VERB
cana-5488	149	6	,	,	PUNCT
cana-5488	149	7	infected	infected	ADJ
cana-5488	149	8	and	and	CCONJ
cana-5488	149	9	quarantined	quarantine	VERB
cana-5488	149	10	populations	population	NOUN
cana-5488	149	11	are	be	AUX
cana-5488	149	12	decreasing	decrease	VERB
cana-5488	149	13	.	.	PUNCT
cana-5488	150	1	7	7	X
cana-5488	150	2	.	.	X
cana-5488	150	3	conclusion	conclusion	NOUN
cana-5488	150	4	the	the	DET
cana-5488	150	5	seiqr	seiqr	ADJ
cana-5488	150	6	model	model	NOUN
cana-5488	150	7	with	with	ADP
cana-5488	150	8	starting	start	VERB
cana-5488	150	9	conditions	condition	NOUN
cana-5488	150	10	has	have	AUX
cana-5488	150	11	successfully	successfully	ADV
cana-5488	150	12	been	be	AUX
cana-5488	150	13	solved	solve	VERB
cana-5488	150	14	approximately	approximately	ADV
cana-5488	150	15	in	in	ADP
cana-5488	150	16	this	this	DET
cana-5488	150	17	study	study	NOUN
cana-5488	150	18	using	use	VERB
cana-5488	150	19	the	the	DET
cana-5488	150	20	differential	differential	ADJ
cana-5488	150	21	transformation	transformation	NOUN
cana-5488	150	22	method	method	NOUN
cana-5488	150	23	(	(	PUNCT
cana-5488	150	24	dtm	dtm	PROPN
cana-5488	150	25	)	)	PUNCT
cana-5488	150	26	.	.	PUNCT
cana-5488	151	1	we	we	PRON
cana-5488	151	2	have	have	AUX
cana-5488	151	3	applied	apply	VERB
cana-5488	151	4	the	the	DET
cana-5488	151	5	presented	present	VERB
cana-5488	151	6	methods	method	NOUN
cana-5488	151	7	directly	directly	ADV
cana-5488	151	8	,	,	PUNCT
cana-5488	151	9	without	without	ADP
cana-5488	151	10	linearizing	linearize	VERB
cana-5488	151	11	,	,	PUNCT
cana-5488	151	12	discretizing	discretizing	ADJ
cana-5488	151	13	,	,	PUNCT
cana-5488	151	14	or	or	CCONJ
cana-5488	151	15	perturbing	perturb	VERB
cana-5488	151	16	.	.	PUNCT
cana-5488	152	1	in	in	ADP
cana-5488	152	2	this	this	DET
cana-5488	152	3	method	method	NOUN
cana-5488	152	4	,	,	PUNCT
cana-5488	152	5	results	result	NOUN
cana-5488	152	6	show	show	VERB
cana-5488	152	7	excellent	excellent	ADJ
cana-5488	152	8	agreement	agreement	NOUN
cana-5488	152	9	,	,	PUNCT
cana-5488	152	10	indicating	indicate	VERB
cana-5488	152	11	reliability	reliability	NOUN
cana-5488	152	12	and	and	CCONJ
cana-5488	152	13	effectiveness	effectiveness	NOUN
cana-5488	152	14	.	.	PUNCT
cana-5488	153	1	this	this	DET
cana-5488	153	2	tool	tool	NOUN
cana-5488	153	3	can	can	AUX
cana-5488	153	4	be	be	AUX
cana-5488	153	5	used	use	VERB
cana-5488	153	6	in	in	ADP
cana-5488	153	7	a	a	DET
cana-5488	153	8	wide	wide	ADJ
cana-5488	153	9	range	range	NOUN
cana-5488	153	10	of	of	ADP
cana-5488	153	11	fields	field	NOUN
cana-5488	153	12	of	of	ADP
cana-5488	153	13	study	study	NOUN
cana-5488	153	14	to	to	PART
cana-5488	153	15	solve	solve	VERB
cana-5488	153	16	linear	linear	ADJ
cana-5488	153	17	problems	problem	NOUN
cana-5488	153	18	and	and	CCONJ
cana-5488	153	19	non	non	ADJ
cana-5488	153	20	-	-	ADJ
cana-5488	153	21	linear	linear	ADJ
cana-5488	153	22	too	too	ADV
cana-5488	153	23	.	.	PUNCT
cana-5488	154	1	we	we	PRON
cana-5488	154	2	used	use	VERB
cana-5488	154	3	the	the	DET
cana-5488	154	4	differential	differential	ADJ
cana-5488	154	5	transformation	transformation	NOUN
cana-5488	154	6	method	method	NOUN
cana-5488	154	7	(	(	PUNCT
cana-5488	154	8	dtm	dtm	PROPN
cana-5488	154	9	)	)	PUNCT
cana-5488	154	10	in	in	ADP
cana-5488	154	11	this	this	DET
cana-5488	154	12	work	work	NOUN
cana-5488	154	13	to	to	PART
cana-5488	154	14	analyze	analyze	VERB
cana-5488	154	15	the	the	DET
cana-5488	154	16	stochastic	stochastic	ADJ
cana-5488	154	17	seiqr	seiqr	ADJ
cana-5488	154	18	model	model	NOUN
cana-5488	154	19	that	that	PRON
cana-5488	154	20	explains	explain	VERB
cana-5488	154	21	infectious	infectious	ADJ
cana-5488	154	22	disease	disease	NOUN
cana-5488	154	23	transmission	transmission	NOUN
cana-5488	154	24	with	with	ADP
cana-5488	154	25	quarantine	quarantine	NOUN
cana-5488	154	26	strategies	strategy	NOUN
cana-5488	154	27	.	.	PUNCT
cana-5488	155	1	the	the	DET
cana-5488	155	2	method	method	NOUN
cana-5488	155	3	offered	offer	VERB
cana-5488	155	4	is	be	AUX
cana-5488	155	5	an	an	DET
cana-5488	155	6	efficient	efficient	ADJ
cana-5488	155	7	approximate	approximate	ADJ
cana-5488	155	8	solution	solution	NOUN
cana-5488	155	9	method	method	NOUN
cana-5488	155	10	that	that	PRON
cana-5488	155	11	does	do	AUX
cana-5488	155	12	not	not	PART
cana-5488	155	13	need	need	VERB
cana-5488	155	14	linearization	linearization	NOUN
cana-5488	155	15	,	,	PUNCT
cana-5488	155	16	discretization	discretization	NOUN
cana-5488	155	17	,	,	PUNCT
cana-5488	155	18	or	or	CCONJ
cana-5488	155	19	perturbation	perturbation	NOUN
cana-5488	155	20	.	.	PUNCT
cana-5488	156	1	comparison	comparison	NOUN
cana-5488	156	2	between	between	ADP
cana-5488	156	3	the	the	DET
cana-5488	156	4	(	(	PUNCT
cana-5488	156	5	dtm	dtm	PROPN
cana-5488	156	6	)	)	PUNCT
cana-5488	156	7	and	and	CCONJ
cana-5488	156	8	(	(	PUNCT
cana-5488	156	9	rk4	rk4	NOUN
cana-5488	156	10	)	)	PUNCT
cana-5488	156	11	methods	method	NOUN
cana-5488	156	12	confirms	confirm	VERB
cana-5488	156	13	the	the	DET
cana-5488	156	14	precision	precision	NOUN
cana-5488	156	15	and	and	CCONJ
cana-5488	156	16	efficacy	efficacy	NOUN
cana-5488	156	17	of	of	ADP
cana-5488	156	18	the	the	DET
cana-5488	156	19	dtm	dtm	PROPN
cana-5488	156	20	approach	approach	NOUN
cana-5488	156	21	to	to	ADP
cana-5488	156	22	nonlinear	nonlinear	ADJ
cana-5488	156	23	epidemiological	epidemiological	ADJ
cana-5488	156	24	models	model	NOUN
cana-5488	156	25	.	.	PUNCT
cana-5488	157	1	this	this	DET
cana-5488	157	2	paper	paper	NOUN
cana-5488	157	3	suggesting	suggest	VERB
cana-5488	157	4	that	that	DET
cana-5488	157	5	quarantine	quarantine	NOUN
cana-5488	157	6	playing	play	VERB
cana-5488	157	7	a	a	DET
cana-5488	157	8	vital	vital	ADJ
cana-5488	157	9	role	role	NOUN
cana-5488	157	10	in	in	ADP
cana-5488	157	11	the	the	DET
cana-5488	157	12	control	control	NOUN
cana-5488	157	13	of	of	ADP
cana-5488	157	14	the	the	DET
cana-5488	157	15	spread	spread	NOUN
cana-5488	157	16	of	of	ADP
cana-5488	157	17	infection	infection	NOUN
cana-5488	157	18	,	,	PUNCT
cana-5488	157	19	and	and	CCONJ
cana-5488	157	20	the	the	DET
cana-5488	157	21	model	model	NOUN
cana-5488	157	22	can	can	AUX
cana-5488	157	23	predict	predict	VERB
cana-5488	157	24	disease	disease	NOUN
cana-5488	157	25	development	development	NOUN
cana-5488	157	26	under	under	ADP
cana-5488	157	27	varying	vary	VERB
cana-5488	157	28	parameter	parameter	NOUN
cana-5488	157	29	conditions	condition	NOUN
cana-5488	157	30	.	.	PUNCT
cana-5488	158	1	moreover	moreover	ADV
cana-5488	158	2	,	,	PUNCT
cana-5488	158	3	the	the	DET
cana-5488	158	4	equilibrium	equilibrium	NOUN
cana-5488	158	5	analysis	analysis	NOUN
cana-5488	158	6	shows	show	VERB
cana-5488	158	7	that	that	SCONJ
cana-5488	158	8	the	the	DET
cana-5488	158	9	disease	disease	NOUN
cana-5488	158	10	-	-	PUNCT
cana-5488	158	11	free	free	ADJ
cana-5488	158	12	equilibrium	equilibrium	NOUN
cana-5488	158	13	is	be	AUX
cana-5488	158	14	stable	stable	ADJ
cana-5488	158	15	if	if	SCONJ
cana-5488	158	16	r0	r0	NOUN
cana-5488	158	17	<	<	X
cana-5488	158	18	1	1	NUM
cana-5488	158	19	and	and	CCONJ
cana-5488	158	20	an	an	DET
cana-5488	158	21	endemic	endemic	ADJ
cana-5488	158	22	equilibrium	equilibrium	NOUN
cana-5488	158	23	exists	exist	VERB
cana-5488	158	24	and	and	CCONJ
cana-5488	158	25	indicating	indicate	VERB
cana-5488	158	26	the	the	DET
cana-5488	158	27	threshold	threshold	NOUN
cana-5488	158	28	value	value	NOUN
cana-5488	158	29	for	for	ADP
cana-5488	158	30	disease	disease	NOUN
cana-5488	158	31	control	control	NOUN
cana-5488	158	32	if	if	SCONJ
cana-5488	158	33	r0	r0	NOUN
cana-5488	158	34	>	>	X
cana-5488	158	35	1	1	NUM
cana-5488	158	36	.	.	PUNCT
cana-5488	158	37	seiqr	seiqr	ADJ
cana-5488	158	38	model	model	NOUN
cana-5488	158	39	and	and	CCONJ
cana-5488	158	40	dtm	dtm	PROPN
cana-5488	158	41	framework	framework	NOUN
cana-5488	158	42	can	can	AUX
cana-5488	158	43	be	be	AUX
cana-5488	158	44	generalized	generalize	VERB
cana-5488	158	45	to	to	ADP
cana-5488	158	46	other	other	ADJ
cana-5488	158	47	contagious	contagious	ADJ
cana-5488	158	48	diseases	disease	NOUN
cana-5488	158	49	,	,	PUNCT
cana-5488	158	50	such	such	ADJ
cana-5488	158	51	as	as	ADP
cana-5488	158	52	covid-19	covid-19	PROPN
cana-5488	158	53	,	,	PUNCT
cana-5488	158	54	sars	sar	NOUN
cana-5488	158	55	,	,	PUNCT
cana-5488	158	56	and	and	CCONJ
cana-5488	158	57	influenza	influenza	NOUN
cana-5488	158	58	,	,	PUNCT
cana-5488	158	59	in	in	ADP
cana-5488	158	60	support	support	NOUN
cana-5488	158	61	of	of	ADP
cana-5488	158	62	public	public	ADJ
cana-5488	158	63	health	health	NOUN
cana-5488	158	64	decision	decision	NOUN
cana-5488	158	65	-	-	PUNCT
cana-5488	158	66	making	make	VERB
cana-5488	158	67	and	and	CCONJ
cana-5488	158	68	policy	policy	NOUN
cana-5488	158	69	design	design	NOUN
cana-5488	158	70	.	.	PUNCT
cana-5488	159	1	research	research	NOUN
cana-5488	159	2	should	should	AUX
cana-5488	159	3	be	be	AUX
cana-5488	159	4	done	do	VERB
cana-5488	159	5	on	on	ADP
cana-5488	159	6	fractional	fractional	ADJ
cana-5488	159	7	-	-	PUNCT
cana-5488	159	8	order	order	NOUN
cana-5488	159	9	models	model	NOUN
cana-5488	159	10	,	,	PUNCT
cana-5488	159	11	stochastic	stochastic	ADJ
cana-5488	159	12	phenomena	phenomenon	NOUN
cana-5488	159	13	,	,	PUNCT
cana-5488	159	14	and	and	CCONJ
cana-5488	159	15	vaccine	vaccine	NOUN
cana-5488	159	16	strategies	strategy	NOUN
cana-5488	159	17	inorder	inorder	VERB
cana-5488	159	18	to	to	PART
cana-5488	159	19	extend	extend	VERB
cana-5488	159	20	this	this	DET
cana-5488	159	21	approach	approach	NOUN
cana-5488	159	22	towards	towards	ADP
cana-5488	159	23	applications	application	NOUN
cana-5488	159	24	in	in	ADP
cana-5488	159	25	real	real	ADJ
cana-5488	159	26	epidemiology	epidemiology	NOUN
cana-5488	159	27	.	.	PUNCT
cana-5488	160	1	refrences	refrence	VERB
cana-5488	161	1	[	[	X
cana-5488	161	2	1	1	X
cana-5488	161	3	]	]	X
cana-5488	161	4	j.	j.	PROPN
cana-5488	161	5	biazar	biazar	PROPN
cana-5488	161	6	,	,	PUNCT
cana-5488	161	7	“	"	PUNCT
cana-5488	161	8	solution	solution	NOUN
cana-5488	161	9	of	of	ADP
cana-5488	161	10	the	the	DET
cana-5488	161	11	epidemic	epidemic	NOUN
cana-5488	161	12	model	model	NOUN
cana-5488	161	13	by	by	ADP
cana-5488	161	14	adomian	adomian	NOUN
cana-5488	161	15	decomposition	decomposition	NOUN
cana-5488	161	16	method	method	NOUN
cana-5488	161	17	”	"	PUNCT
cana-5488	161	18	,	,	PUNCT
cana-5488	161	19	[	[	X
cana-5488	161	20	2	2	NUM
cana-5488	161	21	]	]	PUNCT
cana-5488	161	22	applied	apply	VERB
cana-5488	161	23	mathematics	mathematic	NOUN
cana-5488	161	24	and	and	CCONJ
cana-5488	161	25	computation	computation	NOUN
cana-5488	161	26	,	,	PUNCT
cana-5488	161	27	173(2	173(2	NUM
cana-5488	161	28	)	)	PUNCT
cana-5488	161	29	(	(	PUNCT
cana-5488	161	30	2006	2006	NUM
cana-5488	161	31	)	)	PUNCT
cana-5488	161	32	,	,	PUNCT
cana-5488	161	33	1101	1101	NUM
cana-5488	161	34	-	-	SYM
cana-5488	161	35	1106	1106	NUM
cana-5488	161	36	.	.	PUNCT
cana-5488	162	1	http://dx.doi.org/10.1016/j.amc.2005.04.036	http://dx.doi.org/10.1016/j.amc.2005.04.036	NOUN
cana-5488	163	1	[	[	X
cana-5488	163	2	3	3	X
cana-5488	163	3	]	]	X
cana-5488	163	4	j.k	j.k	PROPN
cana-5488	163	5	.	.	PROPN
cana-5488	163	6	zhou	zhou	PROPN
cana-5488	163	7	,	,	PUNCT
cana-5488	163	8	“	"	PUNCT
cana-5488	163	9	differential	differential	ADJ
cana-5488	163	10	transformation	transformation	NOUN
cana-5488	163	11	and	and	CCONJ
cana-5488	163	12	its	its	PRON
cana-5488	163	13	applications	application	NOUN
cana-5488	163	14	for	for	ADP
cana-5488	163	15	electrical	electrical	ADJ
cana-5488	163	16	circuits	circuit	NOUN
cana-5488	163	17	”	"	PUNCT
cana-5488	163	18	,	,	PUNCT
cana-5488	163	19	huazhong	huazhong	PROPN
cana-5488	163	20	university	university	PROPN
cana-5488	163	21	press	press	NOUN
cana-5488	163	22	,	,	PUNCT
cana-5488	163	23	wuhan	wuhan	PROPN
cana-5488	163	24	,	,	PUNCT
cana-5488	163	25	china	china	PROPN
cana-5488	163	26	,	,	PUNCT
cana-5488	163	27	(	(	PUNCT
cana-5488	163	28	1986	1986	NUM
cana-5488	163	29	)	)	PUNCT
cana-5488	163	30	(	(	PUNCT
cana-5488	163	31	in	in	ADP
cana-5488	163	32	chinese	chinese	PROPN
cana-5488	163	33	)	)	PUNCT
cana-5488	163	34	.	.	PUNCT
cana-5488	164	1	[	[	X
cana-5488	164	2	4	4	X
cana-5488	164	3	]	]	X
cana-5488	164	4	i.h	i.h	PROPN
cana-5488	164	5	.	.	PUNCT
cana-5488	164	6	hassan	hassan	PROPN
cana-5488	164	7	,	,	PUNCT
cana-5488	164	8	“	"	PUNCT
cana-5488	164	9	comparison	comparison	NOUN
cana-5488	164	10	differential	differential	NOUN
cana-5488	164	11	transformation	transformation	NOUN
cana-5488	164	12	technique	technique	NOUN
cana-5488	164	13	with	with	ADP
cana-5488	164	14	adomian	adomian	NOUN
cana-5488	164	15	decomposition	decomposition	NOUN
cana-5488	164	16	method	method	NOUN
cana-5488	164	17	for	for	ADP
cana-5488	164	18	linear	linear	ADJ
cana-5488	164	19	and	and	CCONJ
cana-5488	164	20	nonlinear	nonlinear	ADJ
cana-5488	164	21	initial	initial	ADJ
cana-5488	164	22	value	value	NOUN
cana-5488	164	23	problems	problem	NOUN
cana-5488	164	24	”	"	PUNCT
cana-5488	164	25	,	,	PUNCT
cana-5488	164	26	chaos	chaos	NOUN
cana-5488	164	27	solitons	soliton	NOUN
cana-5488	164	28	fractals	fractal	NOUN
cana-5488	164	29	,	,	PUNCT
cana-5488	164	30	36	36	NUM
cana-5488	164	31	(	(	PUNCT
cana-5488	164	32	1	1	NUM
cana-5488	164	33	)	)	PUNCT
cana-5488	164	34	(	(	PUNCT
cana-5488	164	35	2008	2008	NUM
cana-5488	164	36	)	)	PUNCT
cana-5488	164	37	,	,	PUNCT
cana-5488	164	38	53–65	53–65	NUM
cana-5488	164	39	.	.	PUNCT
cana-5488	165	1	https://doi.org/10.1016/j.chaos.2006.06.040	https://doi.org/10.1016/j.chaos.2006.06.040	NOUN
cana-5488	165	2	[	[	SYM
cana-5488	165	3	5	5	NUM
cana-5488	165	4	]	]	X
cana-5488	165	5	s.v	s.v	PROPN
cana-5488	165	6	.	.	PROPN
cana-5488	165	7	kanth	kanth	PROPN
cana-5488	165	8	and	and	CCONJ
cana-5488	165	9	k.	k.	PROPN
cana-5488	165	10	aruna	aruna	PROPN
cana-5488	165	11	,	,	PUNCT
cana-5488	165	12	“	"	PUNCT
cana-5488	165	13	two	two	NUM
cana-5488	165	14	-	-	PUNCT
cana-5488	165	15	dimensional	dimensional	ADJ
cana-5488	165	16	differential	differential	ADJ
cana-5488	165	17	transform	transform	NOUN
cana-5488	165	18	method	method	NOUN
cana-5488	165	19	for	for	ADP
cana-5488	165	20	solving	solve	VERB
cana-5488	165	21	linear	linear	ADJ
cana-5488	165	22	and	and	CCONJ
cana-5488	165	23	non	non	ADJ
cana-5488	165	24	-	-	ADJ
cana-5488	165	25	linear	linear	ADJ
cana-5488	165	26	schrodinger	schrodinger	PROPN
cana-5488	165	27	equations	equation	NOUN
cana-5488	165	28	”	"	PUNCT
cana-5488	165	29	,	,	PUNCT
cana-5488	165	30	chaos	chaos	NOUN
cana-5488	165	31	solitons	soliton	NOUN
cana-5488	165	32	and	and	CCONJ
cana-5488	165	33	fractals	fractal	NOUN
cana-5488	165	34	,	,	PUNCT
cana-5488	165	35	41(5	41(5	NUM
cana-5488	165	36	)	)	PUNCT
cana-5488	165	37	(	(	PUNCT
cana-5488	165	38	2009	2009	NUM
cana-5488	165	39	)	)	PUNCT
cana-5488	165	40	,	,	PUNCT
cana-5488	165	41	22772281	22772281	NUM
cana-5488	165	42	.	.	PUNCT
cana-5488	166	1	http://dx.doi.org/10.1016/j.chaos.2008.08.037	http://dx.doi.org/10.1016/j.chaos.2008.08.037	NUM
cana-5488	166	2	http://dx.doi.org/10.1016/j.amc.2005.04.036	http://dx.doi.org/10.1016/j.amc.2005.04.036	NOUN
cana-5488	166	3	https://doi.org/10.1016/j.chaos.2006.06.040	https://doi.org/10.1016/j.chaos.2006.06.040	VERB
cana-5488	166	4	http://dx.doi.org/10.1016/j.chaos.2008.08.037	http://dx.doi.org/10.1016/j.chaos.2008.08.037	PROPN
cana-5488	166	5	communications	communication	NOUN
cana-5488	166	6	on	on	ADP
cana-5488	166	7	applied	apply	VERB
cana-5488	166	8	nonlinear	nonlinear	ADJ
cana-5488	166	9	analysis	analysis	NOUN
cana-5488	166	10	issn	issn	NOUN
cana-5488	166	11	:	:	PUNCT
cana-5488	166	12	1074	1074	NUM
cana-5488	166	13	-	-	PUNCT
cana-5488	166	14	133x	133x	NUM
cana-5488	166	15	vol	vol	VERB
cana-5488	166	16	32	32	NUM
cana-5488	166	17	no	no	NOUN
cana-5488	166	18	.	.	PUNCT
cana-5488	167	1	10s	10	NOUN
cana-5488	167	2	(	(	PUNCT
cana-5488	167	3	2025	2025	NUM
cana-5488	167	4	)	)	PUNCT
cana-5488	167	5	2401	2401	NUM
cana-5488	167	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5488	168	1	[	[	X
cana-5488	168	2	6	6	NUM
cana-5488	168	3	]	]	X
cana-5488	168	4	arikoglu	arikoglu	NOUN
cana-5488	168	5	and	and	CCONJ
cana-5488	168	6	i.	i.	NOUN
cana-5488	168	7	ozkol	ozkol	NOUN
cana-5488	168	8	,	,	PUNCT
cana-5488	168	9	“	"	PUNCT
cana-5488	168	10	solution	solution	NOUN
cana-5488	168	11	of	of	ADP
cana-5488	168	12	fractional	fractional	ADJ
cana-5488	168	13	differential	differential	ADJ
cana-5488	168	14	equations	equation	NOUN
cana-5488	168	15	by	by	ADP
cana-5488	168	16	using	use	VERB
cana-5488	168	17	differential	differential	ADJ
cana-5488	168	18	transform	transform	NOUN
cana-5488	168	19	method	method	NOUN
cana-5488	168	20	”	"	PUNCT
cana-5488	168	21	,	,	PUNCT
cana-5488	168	22	chaos	chaos	NOUN
cana-5488	168	23	solitons	soliton	NOUN
cana-5488	168	24	and	and	CCONJ
cana-5488	168	25	fractals	fractal	NOUN
cana-5488	168	26	,	,	PUNCT
cana-5488	168	27	34	34	NUM
cana-5488	168	28	(	(	PUNCT
cana-5488	168	29	2007	2007	NUM
cana-5488	168	30	)	)	PUNCT
cana-5488	168	31	,	,	PUNCT
cana-5488	168	32	1473	1473	NUM
cana-5488	168	33	-	-	SYM
cana-5488	168	34	1481	1481	NUM
cana-5488	168	35	.	.	PUNCT
cana-5488	169	1	https://doi.org/10.1016/j.chaos.2006.09.004	https://doi.org/10.1016/j.chaos.2006.09.004	NOUN
cana-5488	169	2	[	[	X
cana-5488	169	3	7	7	NUM
cana-5488	169	4	]	]	X
cana-5488	169	5	b.	b.	PROPN
cana-5488	169	6	s.	s.	PROPN
cana-5488	169	7	desale	desale	PROPN
cana-5488	169	8	and	and	CCONJ
cana-5488	169	9	n.	n.	PROPN
cana-5488	169	10	r.	r.	PROPN
cana-5488	169	11	dasre	dasre	PROPN
cana-5488	169	12	,	,	PUNCT
cana-5488	169	13	“	"	PUNCT
cana-5488	169	14	numerical	numerical	ADJ
cana-5488	169	15	solution	solution	NOUN
cana-5488	169	16	of	of	ADP
cana-5488	169	17	the	the	DET
cana-5488	169	18	system	system	NOUN
cana-5488	169	19	of	of	ADP
cana-5488	169	20	six	six	NUM
cana-5488	169	21	coupled	couple	VERB
cana-5488	169	22	nonlinear	nonlinear	ADJ
cana-5488	169	23	odes	ode	NOUN
cana-5488	169	24	by	by	ADP
cana-5488	169	25	runge	runge	NOUN
cana-5488	169	26	-	-	PUNCT
cana-5488	169	27	kutta	kutta	NOUN
cana-5488	169	28	fourth	fourth	ADJ
cana-5488	169	29	order	order	NOUN
cana-5488	169	30	method	method	NOUN
cana-5488	169	31	”	"	PUNCT
cana-5488	169	32	,	,	PUNCT
cana-5488	169	33	applied	apply	VERB
cana-5488	169	34	mathematical	mathematical	ADJ
cana-5488	169	35	sciences	science	NOUN
cana-5488	169	36	,	,	PUNCT
cana-5488	169	37	7	7	NUM
cana-5488	169	38	(	(	PUNCT
cana-5488	169	39	2013	2013	NUM
cana-5488	169	40	)	)	PUNCT
cana-5488	169	41	,	,	PUNCT
cana-5488	169	42	287	287	NUM
cana-5488	169	43	305	305	NUM
cana-5488	169	44	.	.	PUNCT
cana-5488	169	45	http://dx.doi.org/10.12988/ams.2013.13026	http://dx.doi.org/10.12988/ams.2013.13026	PUNCT
cana-5488	170	1	[	[	X
cana-5488	170	2	8	8	NUM
cana-5488	170	3	]	]	PUNCT
cana-5488	170	4	z.	z.	PROPN
cana-5488	170	5	kalogiratou	kalogiratou	PROPN
cana-5488	170	6	,	,	PUNCT
cana-5488	170	7	t.	t.	NOUN
cana-5488	170	8	monovasilis	monovasilis	PROPN
cana-5488	170	9	and	and	CCONJ
cana-5488	170	10	t.	t.	PROPN
cana-5488	170	11	e.	e.	PROPN
cana-5488	170	12	simos	simos	PROPN
cana-5488	170	13	,	,	PUNCT
cana-5488	170	14	“	"	PUNCT
cana-5488	170	15	simplistic	simplistic	ADJ
cana-5488	170	16	runge	runge	NOUN
cana-5488	170	17	-	-	PUNCT
cana-5488	170	18	kutta	kutta	PROPN
cana-5488	170	19	-	-	PUNCT
cana-5488	170	20	nystrom	nystrom	NOUN
cana-5488	170	21	methods	method	NOUN
cana-5488	170	22	with	with	ADP
cana-5488	170	23	phase	phase	NOUN
cana-5488	170	24	-	-	PUNCT
cana-5488	170	25	lag	lag	NOUN
cana-5488	170	26	oder	oder	NOUN
cana-5488	170	27	8	8	NUM
cana-5488	170	28	and	and	CCONJ
cana-5488	170	29	infinity	infinity	NOUN
cana-5488	170	30	”	"	PUNCT
cana-5488	170	31	,	,	PUNCT
cana-5488	170	32	applied	apply	VERB
cana-5488	170	33	mathematics	mathematics	PROPN
cana-5488	170	34	&	&	CCONJ
cana-5488	170	35	information	information	NOUN
cana-5488	170	36	sciences	sciences	PROPN
cana-5488	170	37	,	,	PUNCT
cana-5488	170	38	3	3	NUM
cana-5488	170	39	(	(	PUNCT
cana-5488	170	40	2015	2015	NUM
cana-5488	170	41	)	)	PUNCT
cana-5488	170	42	,	,	PUNCT
cana-5488	170	43	1105	1105	NUM
cana-5488	170	44	-	-	SYM
cana-5488	170	45	1112	1112	NUM
cana-5488	170	46	.	.	PUNCT
cana-5488	171	1	http://dx.doi.org/10.1063/1.3498573	http://dx.doi.org/10.1063/1.3498573	PROPN
cana-5488	172	1	[	[	X
cana-5488	172	2	9	9	NUM
cana-5488	172	3	]	]	PUNCT
cana-5488	172	4	v.	v.	CCONJ
cana-5488	172	5	s.	s.	PROPN
cana-5488	172	6	erturk	erturk	PROPN
cana-5488	172	7	and	and	CCONJ
cana-5488	172	8	s.	s.	PROPN
cana-5488	172	9	momani	momani	PROPN
cana-5488	172	10	,	,	PUNCT
cana-5488	172	11	“	"	PUNCT
cana-5488	172	12	solving	solve	VERB
cana-5488	172	13	systems	system	NOUN
cana-5488	172	14	of	of	ADP
cana-5488	172	15	fractional	fractional	ADJ
cana-5488	172	16	differential	differential	ADJ
cana-5488	172	17	equations	equation	NOUN
cana-5488	172	18	using	use	VERB
cana-5488	172	19	differential	differential	ADJ
cana-5488	172	20	transform	transform	NOUN
cana-5488	172	21	method	method	NOUN
cana-5488	172	22	”	"	PUNCT
cana-5488	172	23	,	,	PUNCT
cana-5488	172	24	j.	j.	PROPN
cana-5488	172	25	comput	comput	PROPN
cana-5488	172	26	.	.	PUNCT
cana-5488	173	1	appl	appl	PROPN
cana-5488	173	2	.	.	PROPN
cana-5488	173	3	math	math	NOUN
cana-5488	173	4	.	.	PUNCT
cana-5488	174	1	215	215	NUM
cana-5488	174	2	(	(	PUNCT
cana-5488	174	3	2008	2008	NUM
cana-5488	174	4	)	)	PUNCT
cana-5488	174	5	,	,	PUNCT
cana-5488	174	6	142	142	NUM
cana-5488	174	7	-	-	SYM
cana-5488	174	8	151	151	NUM
cana-5488	174	9	.	.	PUNCT
cana-5488	175	1	https://doi.org/10.1016/j.cam.2007.03.029	https://doi.org/10.1016/j.cam.2007.03.029	NOUN
cana-5488	176	1	[	[	X
cana-5488	176	2	10	10	NUM
cana-5488	176	3	]	]	X
cana-5488	176	4	guangqiu	guangqiu	PROPN
cana-5488	176	5	huang	huang	PROPN
cana-5488	176	6	,	,	PUNCT
cana-5488	176	7	“	"	PUNCT
cana-5488	176	8	artificial	artificial	ADJ
cana-5488	176	9	infectious	infectious	ADJ
cana-5488	176	10	disease	disease	NOUN
cana-5488	176	11	optimization	optimization	NOUN
cana-5488	176	12	:	:	PUNCT
cana-5488	176	13	a	a	DET
cana-5488	176	14	seiqr	seiqr	ADJ
cana-5488	176	15	epidemic	epidemic	NOUN
cana-5488	176	16	dynamic	dynamic	ADJ
cana-5488	176	17	model	model	NOUN
cana-5488	176	18	-	-	PUNCT
cana-5488	176	19	based	base	VERB
cana-5488	176	20	function	function	NOUN
cana-5488	176	21	optimization	optimization	NOUN
cana-5488	176	22	algorithm	algorithm	NOUN
cana-5488	176	23	”	"	PUNCT
cana-5488	176	24	,	,	PUNCT
cana-5488	176	25	swarm	swarm	NOUN
cana-5488	176	26	and	and	CCONJ
cana-5488	176	27	evolutionary	evolutionary	ADJ
cana-5488	176	28	computation	computation	NOUN
cana-5488	176	29	,	,	PUNCT
cana-5488	176	30	27	27	NUM
cana-5488	176	31	(	(	PUNCT
cana-5488	176	32	2016	2016	NUM
cana-5488	176	33	)	)	PUNCT
cana-5488	176	34	,	,	PUNCT
cana-5488	176	35	31	31	NUM
cana-5488	176	36	-	-	SYM
cana-5488	176	37	67	67	NUM
cana-5488	176	38	.	.	PUNCT
cana-5488	177	1	https://doi.org/10.1016/j.swevo.2015.09.007	https://doi.org/10.1016/j.swevo.2015.09.007	PRON
cana-5488	177	2	[	[	X
cana-5488	177	3	11	11	NUM
cana-5488	177	4	]	]	X
cana-5488	177	5	paul	paul	PROPN
cana-5488	177	6	s	s	PROPN
cana-5488	177	7	,	,	PUNCT
cana-5488	177	8	mahata	mahata	VERB
cana-5488	177	9	a	a	DET
cana-5488	177	10	,	,	PUNCT
cana-5488	177	11	mukherjee	mukherjee	PROPN
cana-5488	177	12	s	s	PROPN
cana-5488	177	13	,	,	PUNCT
cana-5488	177	14	mali	mali	ADJ
cana-5488	177	15	pc	pc	NOUN
cana-5488	177	16	and	and	CCONJ
cana-5488	177	17	roy	roy	PROPN
cana-5488	177	18	b	b	PROPN
cana-5488	177	19	,	,	PUNCT
cana-5488	177	20	“	"	PUNCT
cana-5488	177	21	fractional	fractional	ADJ
cana-5488	177	22	order	order	NOUN
cana-5488	177	23	seiqrd	seiqrd	PROPN
cana-5488	177	24	epidemic	epidemic	NOUN
cana-5488	177	25	model	model	NOUN
cana-5488	177	26	of	of	ADP
cana-5488	177	27	covid-19	covid-19	PROPN
cana-5488	177	28	:	:	PUNCT
cana-5488	177	29	a	a	DET
cana-5488	177	30	case	case	NOUN
cana-5488	177	31	study	study	NOUN
cana-5488	177	32	of	of	ADP
cana-5488	177	33	italy	italy	PROPN
cana-5488	177	34	”	"	PUNCT
cana-5488	177	35	,	,	PUNCT
cana-5488	177	36	plos	plos	PROPN
cana-5488	177	37	one	one	NUM
cana-5488	177	38	18(3	18(3	NUM
cana-5488	177	39	):	):	PUNCT
cana-5488	177	40	e0278880	e0278880	PROPN
cana-5488	177	41	.	.	PUNCT
cana-5488	178	1	https://doi.org/10.1371/journal.pone.0278880	https://doi.org/10.1371/journal.pone.0278880	VERB
cana-5488	178	2	[	[	X
cana-5488	178	3	12	12	NUM
cana-5488	178	4	]	]	PUNCT
cana-5488	178	5	m.	m.	NOUN
cana-5488	178	6	sinan	sinan	PROPN
cana-5488	178	7	,	,	PUNCT
cana-5488	178	8	a.	a.	PROPN
cana-5488	178	9	ali	ali	PROPN
cana-5488	178	10	,	,	PUNCT
cana-5488	178	11	k.	k.	PROPN
cana-5488	178	12	shah	shah	PROPN
cana-5488	178	13	,	,	PUNCT
cana-5488	178	14	t.	t.	PROPN
cana-5488	178	15	a.	a.	NOUN
cana-5488	178	16	assiri	assiri	PROPN
cana-5488	178	17	and	and	CCONJ
cana-5488	178	18	t.	t.	PROPN
cana-5488	178	19	a.	a.	PROPN
cana-5488	178	20	nofal	nofal	PROPN
cana-5488	178	21	,	,	PUNCT
cana-5488	178	22	“	"	PUNCT
cana-5488	178	23	stability	stability	NOUN
cana-5488	178	24	analysis	analysis	NOUN
cana-5488	178	25	and	and	CCONJ
cana-5488	178	26	optimal	optimal	ADJ
cana-5488	178	27	control	control	NOUN
cana-5488	178	28	of	of	ADP
cana-5488	178	29	covid-19	covid-19	PROPN
cana-5488	178	30	pandemic	pandemic	ADJ
cana-5488	178	31	seiqr	seiqr	ADJ
cana-5488	178	32	fractional	fractional	ADJ
cana-5488	178	33	mathematical	mathematical	ADJ
cana-5488	178	34	model	model	NOUN
cana-5488	178	35	with	with	ADP
cana-5488	178	36	harmonic	harmonic	ADJ
cana-5488	178	37	mean	mean	NOUN
cana-5488	178	38	type	type	NOUN
cana-5488	178	39	incidence	incidence	NOUN
cana-5488	178	40	rate	rate	NOUN
cana-5488	178	41	and	and	CCONJ
cana-5488	178	42	treatment	treatment	NOUN
cana-5488	178	43	”	"	PUNCT
cana-5488	178	44	,	,	PUNCT
cana-5488	178	45	results	result	NOUN
cana-5488	178	46	in	in	ADP
cana-5488	178	47	physics	physics	NOUN
cana-5488	178	48	,	,	PUNCT
cana-5488	178	49	22	22	NUM
cana-5488	178	50	(	(	PUNCT
cana-5488	178	51	2021	2021	NUM
cana-5488	178	52	)	)	PUNCT
cana-5488	178	53	,	,	PUNCT
cana-5488	178	54	103873	103873	NUM
cana-5488	178	55	.	.	PUNCT
cana-5488	179	1	https://doi.org/10.1016/j.rinp.2021.103873	https://doi.org/10.1016/j.rinp.2021.103873	ADJ
cana-5488	179	2	https://doi.org/10.1016/j.chaos.2006.09.004	https://doi.org/10.1016/j.chaos.2006.09.004	NOUN
cana-5488	179	3	.	.	PUNCT
cana-5488	180	1	http://dx.doi.org/10.12988/ams.2013.13026	http://dx.doi.org/10.12988/ams.2013.13026	PROPN
cana-5488	180	2	.	.	PUNCT
cana-5488	181	1	http://dx.doi.org/10.1063/1.3498573	http://dx.doi.org/10.1063/1.3498573	PROPN
cana-5488	181	2	https://doi.org/10.1016/j.cam.2007.03.029	https://doi.org/10.1016/j.cam.2007.03.029	VERB
cana-5488	181	3	https://www.sciencedirect.com/journal/swarm-and-evolutionary-computation	https://www.sciencedirect.com/journal/swarm-and-evolutionary-computation	PROPN
cana-5488	181	4	https://www.sciencedirect.com/journal/swarm-and-evolutionary-computation/vol/27/suppl/c	https://www.sciencedirect.com/journal/swarm-and-evolutionary-computation/vol/27/suppl/c	PROPN
cana-5488	181	5	https://doi.org/10.1016/j.swevo.2015.09.007	https://doi.org/10.1016/j.swevo.2015.09.007	ADJ
cana-5488	181	6	https://doi.org/10.1371/journal.pone.0278880	https://doi.org/10.1371/journal.pone.0278880	VERB
cana-5488	181	7	https://doi.org/10.1016/j.rinp.2021.103873	https://doi.org/10.1016/j.rinp.2021.103873	NOUN