id	sid	tid	token	lemma	pos
iajs-1810	1	1	microsoft	microsoft	PROPN
iajs-1810	1	2	word	word	NOUN
iajs-1810	1	3	510	510	NUM
iajs-1810	1	4	-	-	SYM
iajs-1810	1	5	522	522	NUM
iajs-1810	1	6	ihsciconf	ihsciconf	NOUN
iajs-1810	1	7	2017	2017	NUM
iajs-1810	1	8	special	special	ADJ
iajs-1810	1	9	issue	issue	NOUN
iajs-1810	1	10	ibn	ibn	PROPN
iajs-1810	1	11	al	al	PROPN
iajs-1810	1	12	-	-	PUNCT
iajs-1810	1	13	haitham	haitham	PROPN
iajs-1810	1	14	journal	journal	PROPN
iajs-1810	1	15	for	for	ADP
iajs-1810	1	16	pure	pure	ADJ
iajs-1810	1	17	and	and	CCONJ
iajs-1810	1	18	applied	apply	VERB
iajs-1810	1	19	science	science	NOUN
iajs-1810	1	20	https://doi.org/	https://doi.org/	VERB
iajs-1810	1	21	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	1	22	for	for	ADP
iajs-1810	1	23	more	more	ADJ
iajs-1810	1	24	information	information	NOUN
iajs-1810	1	25	about	about	ADP
iajs-1810	1	26	the	the	DET
iajs-1810	1	27	conference	conference	NOUN
iajs-1810	1	28	please	please	INTJ
iajs-1810	1	29	visit	visit	VERB
iajs-1810	1	30	the	the	DET
iajs-1810	1	31	websites	website	NOUN
iajs-1810	1	32	:	:	PUNCT
iajs-1810	1	33	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	1	34	  	  	SPACE
iajs-1810	1	35	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	1	36	   	   	SPACE
iajs-1810	1	37	mathematics|510	mathematics|510	PROPN
iajs-1810	1	38	    	    	SPACE
iajs-1810	1	39	dynamical	dynamical	ADJ
iajs-1810	1	40	study	study	NOUN
iajs-1810	1	41	of	of	ADP
iajs-1810	1	42	an	an	DET
iajs-1810	1	43	sir	sir	NOUN
iajs-1810	1	44	epidemic	epidemic	NOUN
iajs-1810	1	45	model	model	NOUN
iajs-1810	1	46	with	with	ADP
iajs-1810	1	47	nonlinear	nonlinear	ADJ
iajs-1810	1	48	incidence	incidence	NOUN
iajs-1810	1	49	rate	rate	NOUN
iajs-1810	1	50	and	and	CCONJ
iajs-1810	1	51	regress	regress	NOUN
iajs-1810	1	52	of	of	ADP
iajs-1810	1	53	treatment	treatment	NOUN
iajs-1810	1	54	saba	saba	PROPN
iajs-1810	1	55	noori	noori	PROPN
iajs-1810	1	56	majeed	majeed	PROPN
iajs-1810	1	57	snoori39@yahoo.com	snoori39@yahoo.com	PROPN
iajs-1810	1	58	dept	dept	PROPN
iajs-1810	1	59	.	.	PROPN
iajs-1810	2	1	of	of	ADP
iajs-1810	2	2	computer/	computer/	PROPN
iajs-1810	2	3	college	college	NOUN
iajs-1810	2	4	of	of	ADP
iajs-1810	2	5	education	education	NOUN
iajs-1810	2	6	for	for	ADP
iajs-1810	2	7	women/	women/	NUM
iajs-1810	2	8	university	university	NOUN
iajs-1810	2	9	of	of	ADP
iajs-1810	2	10	baghdad	baghdad	PROPN
iajs-1810	2	11	abstract	abstract	ADV
iajs-1810	2	12	in	in	ADP
iajs-1810	2	13	this	this	DET
iajs-1810	2	14	research	research	NOUN
iajs-1810	2	15	,	,	PUNCT
iajs-1810	2	16	dynamical	dynamical	ADJ
iajs-1810	2	17	study	study	NOUN
iajs-1810	2	18	of	of	ADP
iajs-1810	2	19	an	an	DET
iajs-1810	2	20	sir	sir	NOUN
iajs-1810	2	21	epidemical	epidemical	ADJ
iajs-1810	2	22	model	model	NOUN
iajs-1810	2	23	with	with	ADP
iajs-1810	2	24	nonlinear	nonlinear	ADJ
iajs-1810	2	25	direct	direct	ADJ
iajs-1810	2	26	incidence	incidence	NOUN
iajs-1810	2	27	rate	rate	NOUN
iajs-1810	2	28	(	(	PUNCT
iajs-1810	2	29	beddington	beddington	PROPN
iajs-1810	2	30	-	-	PUNCT
iajs-1810	2	31	de	de	X
iajs-1810	2	32	angelis	angelis	PROPN
iajs-1810	2	33	)	)	PUNCT
iajs-1810	2	34	type	type	NOUN
iajs-1810	2	35	,	,	PUNCT
iajs-1810	2	36	and	and	CCONJ
iajs-1810	2	37	regress	regress	NOUN
iajs-1810	2	38	of	of	ADP
iajs-1810	2	39	treatment	treatment	NOUN
iajs-1810	2	40	investigated	investigate	VERB
iajs-1810	2	41	.	.	PUNCT
iajs-1810	3	1	an	an	DET
iajs-1810	3	2	analytical	analytical	ADJ
iajs-1810	3	3	study	study	NOUN
iajs-1810	3	4	to	to	ADP
iajs-1810	3	5	the	the	DET
iajs-1810	3	6	model	model	NOUN
iajs-1810	3	7	shows	show	VERB
iajs-1810	3	8	that	that	SCONJ
iajs-1810	3	9	there	there	PRON
iajs-1810	3	10	are	be	VERB
iajs-1810	3	11	two	two	NUM
iajs-1810	3	12	equilibrium	equilibrium	NOUN
iajs-1810	3	13	points	point	NOUN
iajs-1810	3	14	appear	appear	VERB
iajs-1810	3	15	,	,	PUNCT
iajs-1810	3	16	the	the	DET
iajs-1810	3	17	discussed	discuss	VERB
iajs-1810	3	18	successfully	successfully	ADV
iajs-1810	3	19	with	with	ADP
iajs-1810	3	20	sufficient	sufficient	ADJ
iajs-1810	3	21	condition	condition	NOUN
iajs-1810	3	22	,	,	PUNCT
iajs-1810	3	23	the	the	DET
iajs-1810	3	24	existence	existence	NOUN
iajs-1810	3	25	of	of	ADP
iajs-1810	3	26	local	local	ADJ
iajs-1810	3	27	bifurcation	bifurcation	NOUN
iajs-1810	3	28	and	and	CCONJ
iajs-1810	3	29	hopf	hopf	ADJ
iajs-1810	3	30	bifurcation	bifurcation	NOUN
iajs-1810	3	31	was	be	AUX
iajs-1810	3	32	analyzed	analyze	VERB
iajs-1810	3	33	,	,	PUNCT
iajs-1810	3	34	finally	finally	ADV
iajs-1810	3	35	numerical	numerical	ADJ
iajs-1810	3	36	simulations	simulation	NOUN
iajs-1810	3	37	are	be	AUX
iajs-1810	3	38	done	do	VERB
iajs-1810	3	39	to	to	PART
iajs-1810	3	40	explain	explain	VERB
iajs-1810	3	41	the	the	DET
iajs-1810	3	42	analytic	analytic	ADJ
iajs-1810	3	43	studies	study	NOUN
iajs-1810	3	44	.	.	PUNCT
iajs-1810	4	1	keywords	keyword	NOUN
iajs-1810	4	2	:	:	PUNCT
iajs-1810	4	3	sir	sir	PROPN
iajs-1810	4	4	epidemic	epidemic	NOUN
iajs-1810	4	5	model	model	NOUN
iajs-1810	4	6	,	,	PUNCT
iajs-1810	4	7	nonlinear	nonlinear	ADJ
iajs-1810	4	8	incidence	incidence	NOUN
iajs-1810	4	9	rate	rate	NOUN
iajs-1810	4	10	,	,	PUNCT
iajs-1810	4	11	regress	regress	ADJ
iajs-1810	4	12	treatment	treatment	NOUN
iajs-1810	4	13	ihsciconf	ihsciconf	NOUN
iajs-1810	4	14	2017	2017	NUM
iajs-1810	4	15	special	special	ADJ
iajs-1810	4	16	issue	issue	NOUN
iajs-1810	4	17	ibn	ibn	PROPN
iajs-1810	4	18	al	al	PROPN
iajs-1810	4	19	-	-	PUNCT
iajs-1810	4	20	haitham	haitham	PROPN
iajs-1810	4	21	journal	journal	PROPN
iajs-1810	4	22	for	for	ADP
iajs-1810	4	23	pure	pure	ADJ
iajs-1810	4	24	and	and	CCONJ
iajs-1810	4	25	applied	apply	VERB
iajs-1810	4	26	science	science	NOUN
iajs-1810	4	27	https://doi.org/	https://doi.org/	VERB
iajs-1810	4	28	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	4	29	for	for	ADP
iajs-1810	4	30	more	more	ADJ
iajs-1810	4	31	information	information	NOUN
iajs-1810	4	32	about	about	ADP
iajs-1810	4	33	the	the	DET
iajs-1810	4	34	conference	conference	NOUN
iajs-1810	4	35	please	please	INTJ
iajs-1810	4	36	visit	visit	VERB
iajs-1810	4	37	the	the	DET
iajs-1810	4	38	websites	website	NOUN
iajs-1810	4	39	:	:	PUNCT
iajs-1810	4	40	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	4	41	  	  	SPACE
iajs-1810	4	42	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	4	43	   	   	SPACE
iajs-1810	4	44	mathematics|511	mathematics|511	NOUN
iajs-1810	4	45	    	    	SPACE
iajs-1810	4	46	1	1	NUM
iajs-1810	4	47	.	.	PUNCT
iajs-1810	5	1	introduction	introduction	NOUN
iajs-1810	5	2	many	many	ADJ
iajs-1810	5	3	theoretical	theoretical	ADJ
iajs-1810	5	4	mathematical	mathematical	ADJ
iajs-1810	5	5	study	study	NOUN
iajs-1810	5	6	focused	focus	VERB
iajs-1810	5	7	on	on	ADP
iajs-1810	5	8	sir	sir	PROPN
iajs-1810	5	9	epidemical	epidemical	ADJ
iajs-1810	5	10	model	model	NOUN
iajs-1810	5	11	,	,	PUNCT
iajs-1810	5	12	the	the	DET
iajs-1810	5	13	classical	classical	ADJ
iajs-1810	5	14	model	model	NOUN
iajs-1810	5	15	(	(	PUNCT
iajs-1810	5	16	sir	sir	NOUN
iajs-1810	5	17	)	)	PUNCT
iajs-1810	5	18	usually	usually	ADV
iajs-1810	5	19	has	have	VERB
iajs-1810	5	20	two	two	NUM
iajs-1810	5	21	equilibrium	equilibrium	NOUN
iajs-1810	5	22	points	point	NOUN
iajs-1810	5	23	,	,	PUNCT
iajs-1810	5	24	disease	disease	NOUN
iajs-1810	5	25	free	free	ADJ
iajs-1810	5	26	equilibrium	equilibrium	NOUN
iajs-1810	5	27	point	point	NOUN
iajs-1810	5	28	dfe	dfe	PROPN
iajs-1810	5	29	and	and	CCONJ
iajs-1810	5	30	at	at	ADP
iajs-1810	5	31	most	most	ADJ
iajs-1810	5	32	one	one	NUM
iajs-1810	5	33	endemic	endemic	ADJ
iajs-1810	5	34	equilibrium	equilibrium	NOUN
iajs-1810	5	35	point	point	NOUN
iajs-1810	5	36	eep	eep	PROPN
iajs-1810	5	37	,	,	PUNCT
iajs-1810	5	38	see	see	VERB
iajs-1810	5	39	[	[	X
iajs-1810	5	40	1	1	NUM
iajs-1810	5	41	]	]	PUNCT
iajs-1810	5	42	.	.	PUNCT
iajs-1810	6	1	the	the	DET
iajs-1810	6	2	basic	basic	ADJ
iajs-1810	6	3	reproduction	reproduction	NOUN
iajs-1810	6	4	number	number	NOUN
iajs-1810	6	5	(	(	PUNCT
iajs-1810	6	6	threshold	threshold	NOUN
iajs-1810	6	7	value	value	NOUN
iajs-1810	6	8	)	)	PUNCT
iajs-1810	6	9	r0	r0	NOUN
iajs-1810	6	10	is	be	AUX
iajs-1810	6	11	a	a	DET
iajs-1810	6	12	very	very	ADV
iajs-1810	6	13	important	important	ADJ
iajs-1810	6	14	tool	tool	NOUN
iajs-1810	6	15	to	to	PART
iajs-1810	6	16	discuss	discuss	VERB
iajs-1810	6	17	stability	stability	NOUN
iajs-1810	6	18	of	of	ADP
iajs-1810	6	19	the	the	DET
iajs-1810	6	20	equilibrium	equilibrium	NOUN
iajs-1810	6	21	points	point	NOUN
iajs-1810	7	1	[	[	X
iajs-1810	7	2	2	2	NUM
iajs-1810	7	3	]	]	PUNCT
iajs-1810	7	4	:	:	PUNCT
iajs-1810	7	5	when	when	SCONJ
iajs-1810	7	6	r0	r0	NOUN
iajs-1810	7	7	<	<	X
iajs-1810	7	8	1	1	NUM
iajs-1810	7	9	then	then	ADV
iajs-1810	7	10	dfe	dfe	PROPN
iajs-1810	7	11	exists	exist	VERB
iajs-1810	7	12	and	and	CCONJ
iajs-1810	7	13	stable	stable	ADJ
iajs-1810	7	14	,	,	PUNCT
iajs-1810	7	15	while	while	SCONJ
iajs-1810	7	16	if	if	SCONJ
iajs-1810	7	17	r0	r0	NOUN
iajs-1810	7	18	>	>	X
iajs-1810	7	19	1	1	NUM
iajs-1810	7	20	the	the	DET
iajs-1810	7	21	dfe	dfe	PROPN
iajs-1810	7	22	become	become	VERB
iajs-1810	7	23	unstable	unstable	ADJ
iajs-1810	7	24	and	and	CCONJ
iajs-1810	7	25	the	the	DET
iajs-1810	7	26	eep	eep	NOUN
iajs-1810	7	27	exists	exist	VERB
iajs-1810	7	28	and	and	CCONJ
iajs-1810	7	29	stable	stable	ADJ
iajs-1810	7	30	.	.	PUNCT
iajs-1810	8	1	the	the	DET
iajs-1810	8	2	bifurcation	bifurcation	NOUN
iajs-1810	8	3	happened	happen	VERB
iajs-1810	8	4	when	when	SCONJ
iajs-1810	8	5	the	the	DET
iajs-1810	8	6	dfe	dfe	PROPN
iajs-1810	8	7	stability	stability	NOUN
iajs-1810	8	8	turns	turn	VERB
iajs-1810	8	9	over	over	ADP
iajs-1810	8	10	from	from	ADP
iajs-1810	8	11	stable	stable	ADJ
iajs-1810	8	12	to	to	ADP
iajs-1810	8	13	unstable	unstable	ADJ
iajs-1810	8	14	,	,	PUNCT
iajs-1810	8	15	and	and	CCONJ
iajs-1810	8	16	eep	eep	NOUN
iajs-1810	8	17	occurs	occur	VERB
iajs-1810	8	18	and	and	CCONJ
iajs-1810	8	19	stable	stable	ADJ
iajs-1810	8	20	,	,	PUNCT
iajs-1810	8	21	and	and	CCONJ
iajs-1810	8	22	this	this	PRON
iajs-1810	8	23	is	be	AUX
iajs-1810	8	24	called	call	VERB
iajs-1810	8	25	trans	trans	PROPN
iajs-1810	8	26	critical	critical	ADJ
iajs-1810	8	27	bifurcation	bifurcation	NOUN
iajs-1810	8	28	.	.	PUNCT
iajs-1810	9	1	newly	newly	ADV
iajs-1810	9	2	many	many	ADJ
iajs-1810	9	3	researchers	researcher	NOUN
iajs-1810	9	4	have	have	AUX
iajs-1810	9	5	been	be	AUX
iajs-1810	9	6	very	very	ADV
iajs-1810	9	7	interested	interested	ADJ
iajs-1810	9	8	in	in	ADP
iajs-1810	9	9	nonlinear	nonlinear	ADJ
iajs-1810	9	10	epidemical	epidemical	ADJ
iajs-1810	9	11	dynamic	dynamic	NOUN
iajs-1810	9	12	(	(	PUNCT
iajs-1810	9	13	such	such	ADJ
iajs-1810	9	14	as	as	ADP
iajs-1810	9	15	saddlenode	saddlenode	NOUN
iajs-1810	9	16	bifurcation	bifurcation	NOUN
iajs-1810	9	17	and	and	CCONJ
iajs-1810	9	18	hopf	hopf	ADJ
iajs-1810	9	19	bifurcation	bifurcation	NOUN
iajs-1810	9	20	)	)	PUNCT
iajs-1810	9	21	,	,	PUNCT
iajs-1810	9	22	see	see	VERB
iajs-1810	9	23	[	[	X
iajs-1810	9	24	3,4,5,6	3,4,5,6	NUM
iajs-1810	9	25	]	]	X
iajs-1810	9	26	.	.	PUNCT
iajs-1810	10	1	for	for	ADP
iajs-1810	10	2	instance	instance	NOUN
iajs-1810	10	3	in	in	ADP
iajs-1810	10	4	[	[	X
iajs-1810	10	5	7	7	NUM
iajs-1810	10	6	]	]	X
iajs-1810	10	7	dubey	dubey	PROPN
iajs-1810	10	8	studied	study	VERB
iajs-1810	10	9	an	an	DET
iajs-1810	10	10	sir	sir	NOUN
iajs-1810	10	11	model	model	NOUN
iajs-1810	10	12	with	with	ADP
iajs-1810	10	13	both	both	CCONJ
iajs-1810	10	14	nonlinear	nonlinear	ADJ
iajs-1810	10	15	incidence	incidence	NOUN
iajs-1810	10	16	and	and	CCONJ
iajs-1810	10	17	treatment	treatment	NOUN
iajs-1810	10	18	rate	rate	NOUN
iajs-1810	10	19	,	,	PUNCT
iajs-1810	10	20	in	in	ADP
iajs-1810	10	21	[	[	X
iajs-1810	10	22	8	8	NUM
iajs-1810	10	23	]	]	SYM
iajs-1810	10	24	li	li	PROPN
iajs-1810	10	25	and	and	CCONJ
iajs-1810	10	26	gosh	gosh	PROPN
iajs-1810	10	27	proposed	propose	VERB
iajs-1810	10	28	an	an	DET
iajs-1810	10	29	sir	sir	NOUN
iajs-1810	10	30	model	model	NOUN
iajs-1810	10	31	with	with	ADP
iajs-1810	10	32	nonlinear	nonlinear	ADJ
iajs-1810	10	33	incidence	incidence	NOUN
iajs-1810	10	34	rate	rate	NOUN
iajs-1810	10	35	given	give	VERB
iajs-1810	10	36	by	by	ADP
iajs-1810	10	37	this	this	DET
iajs-1810	10	38	incidence	incidence	NOUN
iajs-1810	10	39	rate	rate	NOUN
iajs-1810	10	40	assumess	assumess	NOUN
iajs-1810	10	41	that	that	SCONJ
iajs-1810	10	42	crowding	crowd	VERB
iajs-1810	10	43	of	of	ADP
iajs-1810	10	44	infective	infective	ADJ
iajs-1810	10	45	individuals	individual	NOUN
iajs-1810	10	46	caused	cause	VERB
iajs-1810	10	47	effective	effective	ADJ
iajs-1810	10	48	contact	contact	NOUN
iajs-1810	10	49	between	between	ADP
iajs-1810	10	50	infective	infective	ADJ
iajs-1810	10	51	and	and	CCONJ
iajs-1810	10	52	susceptible	susceptible	ADJ
iajs-1810	10	53	.	.	PUNCT
iajs-1810	11	1	beddington	beddington	NOUN
iajs-1810	11	2	and	and	CCONJ
iajs-1810	11	3	de	de	X
iajs-1810	11	4	angelis	angeli	NOUN
iajs-1810	11	5	in	in	ADP
iajs-1810	11	6	[	[	X
iajs-1810	11	7	9	9	NUM
iajs-1810	11	8	]	]	PUNCT
iajs-1810	11	9	and	and	CCONJ
iajs-1810	11	10	[	[	X
iajs-1810	11	11	10	10	NUM
iajs-1810	11	12	]	]	PUNCT
iajs-1810	11	13	respectively	respectively	ADV
iajs-1810	11	14	,	,	PUNCT
iajs-1810	11	15	independently	independently	ADV
iajs-1810	11	16	introduced	introduce	VERB
iajs-1810	11	17	nonlinear	nonlinear	ADJ
iajs-1810	11	18	incidence	incidence	NOUN
iajs-1810	11	19	rate	rate	NOUN
iajs-1810	11	20	known	know	VERB
iajs-1810	11	21	as	as	ADP
iajs-1810	11	22	beddingtondeangelis	beddingtondeangeli	NOUN
iajs-1810	11	23	type	type	NOUN
iajs-1810	11	24	incidence	incidence	NOUN
iajs-1810	11	25	rate	rate	NOUN
iajs-1810	11	26	which	which	PRON
iajs-1810	11	27	is	be	AUX
iajs-1810	11	28	investigated	investigate	VERB
iajs-1810	11	29	in	in	ADP
iajs-1810	11	30	our	our	PRON
iajs-1810	11	31	research	research	NOUN
iajs-1810	11	32	.	.	PUNCT
iajs-1810	12	1	the	the	DET
iajs-1810	12	2	above	above	ADJ
iajs-1810	12	3	researchers	researcher	NOUN
iajs-1810	12	4	prove	prove	VERB
iajs-1810	12	5	that	that	SCONJ
iajs-1810	12	6	the	the	DET
iajs-1810	12	7	nonlinear	nonlinear	ADJ
iajs-1810	12	8	dynamics	dynamic	NOUN
iajs-1810	12	9	of	of	ADP
iajs-1810	12	10	these	these	DET
iajs-1810	12	11	epidemic	epidemic	NOUN
iajs-1810	12	12	models	model	NOUN
iajs-1810	12	13	are	be	AUX
iajs-1810	12	14	very	very	ADV
iajs-1810	12	15	sensitive	sensitive	ADJ
iajs-1810	12	16	to	to	ADP
iajs-1810	12	17	the	the	DET
iajs-1810	12	18	parameters	parameter	NOUN
iajs-1810	12	19	included	include	VERB
iajs-1810	12	20	in	in	ADP
iajs-1810	12	21	the	the	DET
iajs-1810	12	22	model	model	NOUN
iajs-1810	12	23	and	and	CCONJ
iajs-1810	12	24	the	the	DET
iajs-1810	12	25	outcomes	outcome	NOUN
iajs-1810	12	26	may	may	AUX
iajs-1810	12	27	be	be	AUX
iajs-1810	12	28	highly	highly	ADV
iajs-1810	12	29	affected	affect	VERB
iajs-1810	12	30	depending	depend	VERB
iajs-1810	12	31	on	on	ADP
iajs-1810	12	32	the	the	DET
iajs-1810	12	33	population	population	NOUN
iajs-1810	12	34	size	size	NOUN
iajs-1810	12	35	,	,	PUNCT
iajs-1810	12	36	direct	direct	ADJ
iajs-1810	12	37	and	and	CCONJ
iajs-1810	12	38	indirect	indirect	ADJ
iajs-1810	12	39	incidence	incidence	NOUN
iajs-1810	12	40	rate	rate	NOUN
iajs-1810	12	41	and	and	CCONJ
iajs-1810	12	42	treatment	treatment	NOUN
iajs-1810	12	43	rate	rate	NOUN
iajs-1810	12	44	.	.	PUNCT
iajs-1810	13	1	in	in	ADP
iajs-1810	13	2	view	view	NOUN
iajs-1810	13	3	of	of	ADP
iajs-1810	13	4	the	the	DET
iajs-1810	13	5	previous	previous	ADJ
iajs-1810	13	6	studies	study	NOUN
iajs-1810	13	7	we	we	PRON
iajs-1810	13	8	study	study	VERB
iajs-1810	13	9	the	the	DET
iajs-1810	13	10	dynamic	dynamic	NOUN
iajs-1810	13	11	of	of	ADP
iajs-1810	13	12	an	an	DET
iajs-1810	13	13	sir	sir	NOUN
iajs-1810	13	14	nonlinear	nonlinear	ADJ
iajs-1810	13	15	model	model	NOUN
iajs-1810	13	16	with	with	ADP
iajs-1810	13	17	nonlinear	nonlinear	ADJ
iajs-1810	13	18	direct	direct	ADJ
iajs-1810	13	19	incidence	incidence	NOUN
iajs-1810	13	20	rate	rate	NOUN
iajs-1810	13	21	as	as	ADP
iajs-1810	13	22	(	(	PUNCT
iajs-1810	13	23	beddington	beddington	PROPN
iajs-1810	13	24	-	-	PUNCT
iajs-1810	13	25	deangelis	deangelis	PROPN
iajs-1810	13	26	type	type	NOUN
iajs-1810	13	27	)	)	PUNCT
iajs-1810	13	28	incidence	incidence	NOUN
iajs-1810	13	29	rate	rate	NOUN
iajs-1810	13	30	,	,	PUNCT
iajs-1810	13	31	and	and	CCONJ
iajs-1810	13	32	regress	regress	NOUN
iajs-1810	13	33	of	of	ADP
iajs-1810	13	34	treatment	treatment	NOUN
iajs-1810	13	35	.	.	PUNCT
iajs-1810	14	1	the	the	DET
iajs-1810	14	2	research	research	NOUN
iajs-1810	14	3	is	be	AUX
iajs-1810	14	4	arranged	arrange	VERB
iajs-1810	14	5	into	into	ADP
iajs-1810	14	6	five	five	NUM
iajs-1810	14	7	sections	section	NOUN
iajs-1810	14	8	;	;	PUNCT
iajs-1810	14	9	section	section	NOUN
iajs-1810	14	10	2	2	NUM
iajs-1810	14	11	introduced	introduce	VERB
iajs-1810	14	12	the	the	DET
iajs-1810	14	13	improvement	improvement	NOUN
iajs-1810	14	14	of	of	ADP
iajs-1810	14	15	epidemic	epidemic	NOUN
iajs-1810	14	16	model	model	NOUN
iajs-1810	14	17	study	study	NOUN
iajs-1810	14	18	,	,	PUNCT
iajs-1810	14	19	section	section	NOUN
iajs-1810	14	20	3	3	NUM
iajs-1810	14	21	demonstrates	demonstrate	VERB
iajs-1810	14	22	the	the	DET
iajs-1810	14	23	existence	existence	NOUN
iajs-1810	14	24	of	of	ADP
iajs-1810	14	25	the	the	DET
iajs-1810	14	26	equilibrium	equilibrium	NOUN
iajs-1810	14	27	points	point	NOUN
iajs-1810	14	28	and	and	CCONJ
iajs-1810	14	29	prove	prove	VERB
iajs-1810	14	30	its	its	PRON
iajs-1810	14	31	local	local	ADJ
iajs-1810	14	32	and	and	CCONJ
iajs-1810	14	33	global	global	ADJ
iajs-1810	14	34	stabilities	stability	NOUN
iajs-1810	14	35	,	,	PUNCT
iajs-1810	14	36	in	in	ADP
iajs-1810	14	37	section	section	NOUN
iajs-1810	14	38	4	4	NUM
iajs-1810	14	39	we	we	PRON
iajs-1810	14	40	investigate	investigate	VERB
iajs-1810	14	41	the	the	DET
iajs-1810	14	42	sotomayor	sotomayor	NOUN
iajs-1810	14	43	theorem	theorem	ADJ
iajs-1810	14	44	[	[	X
iajs-1810	14	45	11	11	NUM
iajs-1810	14	46	]	]	PUNCT
iajs-1810	14	47	to	to	PART
iajs-1810	14	48	analyze	analyze	VERB
iajs-1810	14	49	the	the	DET
iajs-1810	14	50	local	local	ADJ
iajs-1810	14	51	bifurcation	bifurcation	NOUN
iajs-1810	14	52	,	,	PUNCT
iajs-1810	14	53	to	to	PART
iajs-1810	14	54	show	show	VERB
iajs-1810	14	55	the	the	DET
iajs-1810	14	56	occurance	occurance	NOUN
iajs-1810	14	57	of	of	ADP
iajs-1810	14	58	transcritical	transcritical	ADJ
iajs-1810	14	59	bifurcation	bifurcation	NOUN
iajs-1810	14	60	however	however	ADV
iajs-1810	14	61	there	there	ADV
iajs-1810	14	62	in	in	ADP
iajs-1810	14	63	no	no	DET
iajs-1810	14	64	saddle	saddle	NOUN
iajs-1810	14	65	node	node	NOUN
iajs-1810	14	66	and	and	CCONJ
iajs-1810	14	67	no	no	DET
iajs-1810	14	68	pitch	pitch	NOUN
iajs-1810	14	69	fork	fork	NOUN
iajs-1810	14	70	bifurcation	bifurcation	NOUN
iajs-1810	14	71	,	,	PUNCT
iajs-1810	14	72	as	as	ADV
iajs-1810	14	73	well	well	ADV
iajs-1810	14	74	no	no	DET
iajs-1810	14	75	occurance	occurance	NOUN
iajs-1810	14	76	of	of	ADP
iajs-1810	14	77	hopf	hopf	ADJ
iajs-1810	14	78	bifurcation	bifurcation	NOUN
iajs-1810	14	79	.	.	PUNCT
iajs-1810	15	1	finally	finally	ADV
iajs-1810	15	2	,	,	PUNCT
iajs-1810	15	3	in	in	ADP
iajs-1810	15	4	section	section	NOUN
iajs-1810	15	5	5	5	NUM
iajs-1810	15	6	a	a	DET
iajs-1810	15	7	numerical	numerical	ADJ
iajs-1810	15	8	simulation	simulation	NOUN
iajs-1810	15	9	is	be	AUX
iajs-1810	15	10	used	use	VERB
iajs-1810	15	11	to	to	PART
iajs-1810	15	12	confirm	confirm	VERB
iajs-1810	15	13	our	our	PRON
iajs-1810	15	14	obtained	obtain	VERB
iajs-1810	15	15	analytical	analytical	ADJ
iajs-1810	15	16	results	result	NOUN
iajs-1810	15	17	and	and	CCONJ
iajs-1810	15	18	specify	specify	VERB
iajs-1810	15	19	the	the	DET
iajs-1810	15	20	control	control	NOUN
iajs-1810	15	21	set	set	NOUN
iajs-1810	15	22	of	of	ADP
iajs-1810	15	23	parameters	parameter	NOUN
iajs-1810	15	24	.	.	PUNCT
iajs-1810	16	1	2	2	X
iajs-1810	16	2	.	.	X
iajs-1810	16	3	mathematical	mathematical	ADJ
iajs-1810	16	4	model	model	NOUN
iajs-1810	16	5	consider	consider	VERB
iajs-1810	16	6	a	a	DET
iajs-1810	16	7	community	community	NOUN
iajs-1810	16	8	of	of	ADP
iajs-1810	16	9	people	people	NOUN
iajs-1810	16	10	n(t	n(t	PROPN
iajs-1810	16	11	)	)	PUNCT
iajs-1810	16	12	at	at	ADP
iajs-1810	16	13	time	time	NOUN
iajs-1810	16	14	t	t	PROPN
iajs-1810	16	15	,	,	PUNCT
iajs-1810	16	16	whose	whose	DET
iajs-1810	16	17	population	population	NOUN
iajs-1810	16	18	is	be	AUX
iajs-1810	16	19	distinguished	distinguish	VERB
iajs-1810	16	20	into	into	ADP
iajs-1810	16	21	three	three	NUM
iajs-1810	16	22	compartments	compartment	NOUN
iajs-1810	16	23	,	,	PUNCT
iajs-1810	16	24	s(t	s(t	PROPN
iajs-1810	16	25	)	)	PUNCT
iajs-1810	16	26	represents	represent	VERB
iajs-1810	16	27	susceptible	susceptible	ADJ
iajs-1810	16	28	people	people	NOUN
iajs-1810	16	29	,	,	PUNCT
iajs-1810	16	30	i(t	i(t	PROPN
iajs-1810	16	31	)	)	PUNCT
iajs-1810	16	32	represents	represent	VERB
iajs-1810	16	33	infected	infected	ADJ
iajs-1810	16	34	people	people	NOUN
iajs-1810	16	35	and	and	CCONJ
iajs-1810	16	36	r(t)is	r(t)i	VERB
iajs-1810	16	37	the	the	DET
iajs-1810	16	38	recovered	recovered	ADJ
iajs-1810	16	39	people	people	NOUN
iajs-1810	16	40	at	at	ADP
iajs-1810	16	41	time	time	NOUN
iajs-1810	16	42	t.	t.	PROPN
iajs-1810	16	43	susceptible	susceptible	ADJ
iajs-1810	16	44	people	people	NOUN
iajs-1810	16	45	s	s	PART
iajs-1810	16	46	can	can	AUX
iajs-1810	16	47	become	become	VERB
iajs-1810	16	48	infected	infected	ADJ
iajs-1810	16	49	i	i	PRON
iajs-1810	16	50	with	with	ADP
iajs-1810	16	51	the	the	DET
iajs-1810	16	52	disease	disease	NOUN
iajs-1810	16	53	only	only	ADV
iajs-1810	16	54	in	in	ADP
iajs-1810	16	55	case	case	NOUN
iajs-1810	16	56	of	of	ADP
iajs-1810	16	57	direct	direct	ADJ
iajs-1810	16	58	contact	contact	NOUN
iajs-1810	16	59	with	with	ADP
iajs-1810	16	60	infected	infect	VERB
iajs-1810	16	61	individuals	individual	NOUN
iajs-1810	16	62	and	and	CCONJ
iajs-1810	16	63	their	their	PRON
iajs-1810	16	64	chances	chance	NOUN
iajs-1810	16	65	of	of	ADP
iajs-1810	16	66	recovery	recovery	NOUN
iajs-1810	16	67	are	be	AUX
iajs-1810	16	68	weak	weak	ADJ
iajs-1810	16	69	.	.	PUNCT
iajs-1810	17	1	the	the	DET
iajs-1810	17	2	recovery	recovery	NOUN
iajs-1810	17	3	r	r	NOUN
iajs-1810	17	4	regression	regression	NOUN
iajs-1810	17	5	happened	happen	VERB
iajs-1810	17	6	in	in	ADP
iajs-1810	17	7	many	many	ADJ
iajs-1810	17	8	different	different	ADJ
iajs-1810	17	9	ways	way	NOUN
iajs-1810	17	10	such	such	ADJ
iajs-1810	17	11	as	as	ADP
iajs-1810	17	12	the	the	DET
iajs-1810	17	13	treatment	treatment	NOUN
iajs-1810	17	14	is	be	AUX
iajs-1810	17	15	not	not	PART
iajs-1810	17	16	available	available	ADJ
iajs-1810	17	17	enough	enough	ADV
iajs-1810	17	18	,	,	PUNCT
iajs-1810	17	19	or	or	CCONJ
iajs-1810	17	20	because	because	SCONJ
iajs-1810	17	21	lack	lack	NOUN
iajs-1810	17	22	of	of	ADP
iajs-1810	17	23	efficacy	efficacy	NOUN
iajs-1810	17	24	of	of	ADP
iajs-1810	17	25	treatment	treatment	NOUN
iajs-1810	17	26	,	,	PUNCT
iajs-1810	17	27	or	or	CCONJ
iajs-1810	17	28	there	there	PRON
iajs-1810	17	29	is	be	VERB
iajs-1810	17	30	no	no	DET
iajs-1810	17	31	actual	actual	ADJ
iajs-1810	17	32	treatment	treatment	NOUN
iajs-1810	17	33	to	to	PART
iajs-1810	17	34	cure	cure	VERB
iajs-1810	17	35	the	the	DET
iajs-1810	17	36	injury	injury	NOUN
iajs-1810	17	37	,	,	PUNCT
iajs-1810	17	38	leaving	leave	VERB
iajs-1810	17	39	the	the	DET
iajs-1810	17	40	infected	infected	ADJ
iajs-1810	17	41	person	person	NOUN
iajs-1810	17	42	with	with	ADP
iajs-1810	17	43	the	the	DET
iajs-1810	17	44	disease	disease	NOUN
iajs-1810	17	45	and	and	CCONJ
iajs-1810	17	46	the	the	DET
iajs-1810	17	47	cause	cause	NOUN
iajs-1810	17	48	of	of	ADP
iajs-1810	17	49	transmission	transmission	NOUN
iajs-1810	17	50	of	of	ADP
iajs-1810	17	51	the	the	DET
iajs-1810	17	52	infection	infection	NOUN
iajs-1810	17	53	directly	directly	ADV
iajs-1810	17	54	,	,	PUNCT
iajs-1810	17	55	and	and	CCONJ
iajs-1810	17	56	the	the	DET
iajs-1810	17	57	effectiveness	effectiveness	NOUN
iajs-1810	17	58	of	of	ADP
iajs-1810	17	59	treatment	treatment	NOUN
iajs-1810	17	60	is	be	AUX
iajs-1810	17	61	limited	limit	VERB
iajs-1810	17	62	to	to	ADP
iajs-1810	17	63	temporary	temporary	ADJ
iajs-1810	17	64	suppression	suppression	NOUN
iajs-1810	17	65	of	of	ADP
iajs-1810	17	66	symptoms	symptom	NOUN
iajs-1810	17	67	of	of	ADP
iajs-1810	17	68	the	the	DET
iajs-1810	17	69	disease	disease	NOUN
iajs-1810	17	70	ends	end	VERB
iajs-1810	17	71	if	if	SCONJ
iajs-1810	17	72	the	the	DET
iajs-1810	17	73	patient	patient	NOUN
iajs-1810	17	74	stops	stop	VERB
iajs-1810	17	75	taking	take	VERB
iajs-1810	17	76	medication	medication	NOUN
iajs-1810	17	77	,	,	PUNCT
iajs-1810	17	78	for	for	ADP
iajs-1810	17	79	instance	instance	NOUN
iajs-1810	17	80	hepatitis	hepatitis	PROPN
iajs-1810	17	81	c	c	PROPN
iajs-1810	17	82	,	,	PUNCT
iajs-1810	17	83	hepatitis	hepatitis	PROPN
iajs-1810	17	84	b	b	PROPN
iajs-1810	17	85	and	and	CCONJ
iajs-1810	17	86	aids	aid	NOUN
iajs-1810	17	87	…	…	SYM
iajs-1810	17	88	etc	etc	X
iajs-1810	17	89	..	..	X
iajs-1810	17	90	according	accord	VERB
iajs-1810	17	91	to	to	ADP
iajs-1810	17	92	the	the	DET
iajs-1810	17	93	previous	previous	ADJ
iajs-1810	17	94	description	description	NOUN
iajs-1810	17	95	we	we	PRON
iajs-1810	17	96	assume	assume	VERB
iajs-1810	17	97	the	the	DET
iajs-1810	17	98	sir	sir	PROPN
iajs-1810	17	99	epidemic	epidemic	NOUN
iajs-1810	17	100	model	model	NOUN
iajs-1810	17	101	in	in	ADP
iajs-1810	17	102	our	our	PRON
iajs-1810	17	103	article	article	NOUN
iajs-1810	17	104	development	development	NOUN
iajs-1810	17	105	is	be	AUX
iajs-1810	17	106	based	base	VERB
iajs-1810	17	107	on	on	ADP
iajs-1810	17	108	model	model	NOUN
iajs-1810	17	109	(	(	PUNCT
iajs-1810	17	110	1	1	X
iajs-1810	17	111	)	)	PUNCT
iajs-1810	17	112	𝐴	𝐴	PROPN
iajs-1810	17	113	𝑎𝑆𝐼	𝑎𝑆𝐼	VERB
iajs-1810	17	114	𝛼𝑆	𝛼𝑆	NOUN
iajs-1810	17	115	𝑎𝑆𝐼	𝑎𝑆𝐼	NOUN
iajs-1810	17	116	𝛽𝑅	𝛽𝑅	PROPN
iajs-1810	17	117	𝛾	𝛾	PROPN
iajs-1810	17	118	1	1	NUM
iajs-1810	17	119	𝛿	𝛿	PROPN
iajs-1810	17	120	𝐼	𝐼	PROPN
iajs-1810	17	121	𝛼	𝛼	NOUN
iajs-1810	17	122	𝑘	𝑘	NOUN
iajs-1810	17	123	𝐼	𝐼	PROPN
iajs-1810	17	124	…	…	PUNCT
iajs-1810	17	125	…	…	PUNCT
iajs-1810	17	126	..	..	PUNCT
iajs-1810	17	127	(	(	PUNCT
iajs-1810	17	128	1	1	X
iajs-1810	17	129	)	)	PUNCT
iajs-1810	17	130	ihsciconf	ihsciconf	NOUN
iajs-1810	17	131	2017	2017	NUM
iajs-1810	17	132	special	special	ADJ
iajs-1810	17	133	issue	issue	NOUN
iajs-1810	17	134	ibn	ibn	PROPN
iajs-1810	17	135	al	al	PROPN
iajs-1810	17	136	-	-	PUNCT
iajs-1810	17	137	haitham	haitham	PROPN
iajs-1810	17	138	journal	journal	PROPN
iajs-1810	17	139	for	for	ADP
iajs-1810	17	140	pure	pure	ADJ
iajs-1810	17	141	and	and	CCONJ
iajs-1810	17	142	applied	apply	VERB
iajs-1810	17	143	science	science	NOUN
iajs-1810	17	144	https://doi.org/	https://doi.org/	VERB
iajs-1810	17	145	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	17	146	for	for	ADP
iajs-1810	17	147	more	more	ADJ
iajs-1810	17	148	information	information	NOUN
iajs-1810	17	149	about	about	ADP
iajs-1810	17	150	the	the	DET
iajs-1810	17	151	conference	conference	NOUN
iajs-1810	17	152	please	please	INTJ
iajs-1810	17	153	visit	visit	VERB
iajs-1810	17	154	the	the	DET
iajs-1810	17	155	websites	website	NOUN
iajs-1810	17	156	:	:	PUNCT
iajs-1810	17	157	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	17	158	  	  	SPACE
iajs-1810	17	159	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	17	160	   	   	SPACE
iajs-1810	17	161	mathematics|512	mathematics|512	NOUN
iajs-1810	17	162	    	    	SPACE
iajs-1810	17	163	𝛾	𝛾	PROPN
iajs-1810	17	164	1	1	NUM
iajs-1810	17	165	𝛿	𝛿	PROPN
iajs-1810	17	166	𝐼	𝐼	PROPN
iajs-1810	17	167	𝛼	𝛼	ADP
iajs-1810	17	168	𝛽	𝛽	PROPN
iajs-1810	17	169	𝑅	𝑅	PROPN
iajs-1810	17	170	model	model	NOUN
iajs-1810	17	171	(	(	PUNCT
iajs-1810	17	172	1	1	NUM
iajs-1810	17	173	)	)	PUNCT
iajs-1810	17	174	represents	represent	VERB
iajs-1810	17	175	an	an	DET
iajs-1810	17	176	sir	sir	NOUN
iajs-1810	17	177	nonlinear	nonlinear	PROPN
iajs-1810	17	178	epidemic	epidemic	NOUN
iajs-1810	17	179	model	model	NOUN
iajs-1810	17	180	with	with	ADP
iajs-1810	17	181	linear	linear	ADJ
iajs-1810	17	182	incidence	incidence	NOUN
iajs-1810	17	183	rate	rate	NOUN
iajs-1810	17	184	a	a	DET
iajs-1810	17	185	and	and	CCONJ
iajs-1810	17	186	failure	failure	NOUN
iajs-1810	17	187	treatment	treatment	NOUN
iajs-1810	17	188	rate	rate	NOUN
iajs-1810	17	189	𝛿.	𝛿.	NOUN
iajs-1810	17	190	in	in	ADP
iajs-1810	17	191	this	this	DET
iajs-1810	17	192	research	research	NOUN
iajs-1810	17	193	we	we	PRON
iajs-1810	17	194	adopt	adopt	VERB
iajs-1810	17	195	the	the	DET
iajs-1810	17	196	beddington	beddington	PROPN
iajs-1810	17	197	-	-	PUNCT
iajs-1810	17	198	deangelis	deangelis	PROPN
iajs-1810	17	199	incidence	incidence	NOUN
iajs-1810	17	200	rate	rate	NOUN
iajs-1810	17	201	see	see	VERB
iajs-1810	17	202	[	[	X
iajs-1810	17	203	7	7	NUM
iajs-1810	17	204	]	]	PUNCT
iajs-1810	17	205	,	,	PUNCT
iajs-1810	17	206	this	this	DET
iajs-1810	17	207	incidence	incidence	NOUN
iajs-1810	17	208	rate	rate	NOUN
iajs-1810	17	209	indicates	indicate	VERB
iajs-1810	17	210	direct	direct	ADJ
iajs-1810	17	211	contact	contact	NOUN
iajs-1810	17	212	between	between	ADP
iajs-1810	17	213	the	the	DET
iajs-1810	17	214	effective	effective	ADJ
iajs-1810	17	215	and	and	CCONJ
iajs-1810	17	216	susceptible	susceptible	ADJ
iajs-1810	17	217	individuals	individual	NOUN
iajs-1810	17	218	under	under	ADP
iajs-1810	17	219	crowded	crowded	ADJ
iajs-1810	17	220	number	number	NOUN
iajs-1810	17	221	of	of	ADP
iajs-1810	17	222	effective	effective	ADJ
iajs-1810	17	223	individuals	individual	NOUN
iajs-1810	17	224	,	,	PUNCT
iajs-1810	17	225	to	to	PART
iajs-1810	17	226	get	get	VERB
iajs-1810	17	227	model	model	NOUN
iajs-1810	17	228	(	(	PUNCT
iajs-1810	17	229	2	2	NUM
iajs-1810	17	230	)	)	PUNCT
iajs-1810	17	231	as	as	SCONJ
iajs-1810	17	232	follows	follow	VERB
iajs-1810	17	233	:	:	PUNCT
iajs-1810	17	234	𝐴	𝐴	PROPN
iajs-1810	17	235	𝛼𝑆	𝛼𝑆	PROPN
iajs-1810	17	236	𝛽𝑅	𝛽𝑅	PROPN
iajs-1810	17	237	𝛾	𝛾	PROPN
iajs-1810	17	238	1	1	NUM
iajs-1810	17	239	𝛿	𝛿	PROPN
iajs-1810	17	240	𝐼	𝐼	PROPN
iajs-1810	17	241	𝛼	𝛼	NOUN
iajs-1810	17	242	𝑘	𝑘	NOUN
iajs-1810	17	243	𝐼	𝐼	PROPN
iajs-1810	17	244	…	…	PUNCT
iajs-1810	17	245	…	…	PUNCT
iajs-1810	17	246	..	..	PUNCT
iajs-1810	17	247	(	(	PUNCT
iajs-1810	17	248	2	2	X
iajs-1810	17	249	)	)	PUNCT
iajs-1810	17	250	𝛾	𝛾	NOUN
iajs-1810	17	251	1	1	NUM
iajs-1810	17	252	𝛿	𝛿	PROPN
iajs-1810	17	253	𝐼	𝐼	PROPN
iajs-1810	17	254	𝛼	𝛼	ADP
iajs-1810	17	255	𝛽	𝛽	PROPN
iajs-1810	17	256	𝑅	𝑅	PROPN
iajs-1810	17	257	model	model	NOUN
iajs-1810	17	258	(	(	PUNCT
iajs-1810	17	259	2	2	NUM
iajs-1810	17	260	)	)	PUNCT
iajs-1810	17	261	is	be	AUX
iajs-1810	17	262	formulated	formulate	VERB
iajs-1810	17	263	with	with	ADP
iajs-1810	17	264	following	follow	VERB
iajs-1810	17	265	hypotheses	hypothesis	NOUN
iajs-1810	17	266	:	:	PUNCT
iajs-1810	17	267	a	a	DET
iajs-1810	17	268	>	>	X
iajs-1810	17	269	0	0	NUM
iajs-1810	17	270	,	,	PUNCT
iajs-1810	17	271	represents	represent	VERB
iajs-1810	17	272	the	the	DET
iajs-1810	17	273	natural	natural	ADJ
iajs-1810	17	274	birth	birth	NOUN
iajs-1810	17	275	rate	rate	NOUN
iajs-1810	17	276	of	of	ADP
iajs-1810	17	277	the	the	DET
iajs-1810	17	278	population	population	NOUN
iajs-1810	17	279	,	,	PUNCT
iajs-1810	17	280	b>0	b>0	VERB
iajs-1810	17	281	is	be	AUX
iajs-1810	17	282	the	the	DET
iajs-1810	17	283	measure	measure	NOUN
iajs-1810	17	284	rate	rate	NOUN
iajs-1810	17	285	of	of	ADP
iajs-1810	17	286	inhabitation	inhabitation	NOUN
iajs-1810	17	287	effect	effect	NOUN
iajs-1810	17	288	such	such	ADJ
iajs-1810	17	289	as	as	ADP
iajs-1810	17	290	preventive	preventive	ADJ
iajs-1810	17	291	measure	measure	NOUN
iajs-1810	17	292	taken	take	VERB
iajs-1810	17	293	by	by	ADP
iajs-1810	17	294	susceptible	susceptible	ADJ
iajs-1810	17	295	,	,	PUNCT
iajs-1810	17	296	c>0	c>0	NOUN
iajs-1810	17	297	is	be	AUX
iajs-1810	17	298	the	the	DET
iajs-1810	17	299	measure	measure	NOUN
iajs-1810	17	300	rate	rate	NOUN
iajs-1810	17	301	of	of	ADP
iajs-1810	17	302	inhabitation	inhabitation	NOUN
iajs-1810	17	303	effect	effect	NOUN
iajs-1810	17	304	such	such	ADJ
iajs-1810	17	305	as	as	ADP
iajs-1810	17	306	treatment	treatment	NOUN
iajs-1810	17	307	with	with	ADP
iajs-1810	17	308	respect	respect	NOUN
iajs-1810	17	309	to	to	ADP
iajs-1810	17	310	infective	infective	VERB
iajs-1810	17	311	,	,	PUNCT
iajs-1810	17	312	𝛼	𝛼	PROPN
iajs-1810	17	313	0	0	NUM
iajs-1810	17	314	,	,	PUNCT
iajs-1810	17	315	represents	represent	VERB
iajs-1810	17	316	natural	natural	ADJ
iajs-1810	17	317	death	death	NOUN
iajs-1810	17	318	rate	rate	NOUN
iajs-1810	17	319	,	,	PUNCT
iajs-1810	17	320	𝛽	𝛽	PROPN
iajs-1810	17	321	0	0	NUM
iajs-1810	17	322	retreat	retreat	NOUN
iajs-1810	17	323	rate	rate	NOUN
iajs-1810	17	324	with	with	ADP
iajs-1810	17	325	medication	medication	NOUN
iajs-1810	17	326	for	for	ADP
iajs-1810	17	327	individuals	individual	NOUN
iajs-1810	17	328	undergoing	undergo	VERB
iajs-1810	17	329	treatment	treatment	NOUN
iajs-1810	17	330	,	,	PUNCT
iajs-1810	17	331	k	k	PROPN
iajs-1810	17	332	>	>	X
iajs-1810	17	333	0	0	NUM
iajs-1810	17	334	disease	disease	NOUN
iajs-1810	17	335	related	relate	VERB
iajs-1810	17	336	death	death	NOUN
iajs-1810	17	337	rate	rate	NOUN
iajs-1810	17	338	.	.	PUNCT
iajs-1810	18	1	𝛾	𝛾	ADP
iajs-1810	18	2	0	0	NUM
iajs-1810	18	3	is	be	AUX
iajs-1810	18	4	the	the	DET
iajs-1810	18	5	recovery	recovery	NOUN
iajs-1810	18	6	rate	rate	NOUN
iajs-1810	18	7	due	due	ADP
iajs-1810	18	8	to	to	ADP
iajs-1810	18	9	success	success	NOUN
iajs-1810	18	10	of	of	ADP
iajs-1810	18	11	treatment	treatment	NOUN
iajs-1810	18	12	in	in	ADP
iajs-1810	18	13	some	some	DET
iajs-1810	18	14	cases	case	NOUN
iajs-1810	18	15	of	of	ADP
iajs-1810	18	16	infected	infected	ADJ
iajs-1810	18	17	individuals	individual	NOUN
iajs-1810	18	18	,	,	PUNCT
iajs-1810	18	19	finally	finally	ADV
iajs-1810	18	20	0	0	NUM
iajs-1810	18	21	𝛿	𝛿	PRON
iajs-1810	18	22	1	1	NUM
iajs-1810	18	23	,	,	PUNCT
iajs-1810	18	24	is	be	AUX
iajs-1810	18	25	the	the	DET
iajs-1810	18	26	failure	failure	NOUN
iajs-1810	18	27	treatment	treatment	NOUN
iajs-1810	18	28	rate	rate	NOUN
iajs-1810	18	29	of	of	ADP
iajs-1810	18	30	infected	infected	ADJ
iajs-1810	18	31	individuals	individual	NOUN
iajs-1810	18	32	,	,	PUNCT
iajs-1810	18	33	when	when	SCONJ
iajs-1810	18	34	𝛿	𝛿	ADJ
iajs-1810	18	35	0	0	NUM
iajs-1810	18	36	this	this	PRON
iajs-1810	18	37	means	mean	VERB
iajs-1810	18	38	the	the	DET
iajs-1810	18	39	treatment	treatment	NOUN
iajs-1810	18	40	is	be	AUX
iajs-1810	18	41	very	very	ADV
iajs-1810	18	42	effective	effective	ADJ
iajs-1810	18	43	to	to	PART
iajs-1810	18	44	treat	treat	VERB
iajs-1810	18	45	the	the	DET
iajs-1810	18	46	disease	disease	NOUN
iajs-1810	18	47	,	,	PUNCT
iajs-1810	18	48	however	however	ADV
iajs-1810	18	49	if	if	SCONJ
iajs-1810	18	50	𝛿	𝛿	ADJ
iajs-1810	18	51	1	1	NUM
iajs-1810	18	52	then	then	ADV
iajs-1810	18	53	the	the	DET
iajs-1810	18	54	treatment	treatment	NOUN
iajs-1810	18	55	used	use	VERB
iajs-1810	18	56	is	be	AUX
iajs-1810	18	57	ineffective	ineffective	ADJ
iajs-1810	18	58	at	at	ADV
iajs-1810	18	59	all	all	ADV
iajs-1810	18	60	.	.	PUNCT
iajs-1810	19	1	therefore	therefore	ADV
iajs-1810	19	2	the	the	DET
iajs-1810	19	3	dynamics	dynamic	NOUN
iajs-1810	19	4	of	of	ADP
iajs-1810	19	5	above	above	ADP
iajs-1810	19	6	described	describe	VERB
iajs-1810	19	7	epidemic	epidemic	NOUN
iajs-1810	19	8	system	system	NOUN
iajs-1810	19	9	can	can	AUX
iajs-1810	19	10	be	be	AUX
iajs-1810	19	11	described	describe	VERB
iajs-1810	19	12	by	by	ADP
iajs-1810	19	13	the	the	DET
iajs-1810	19	14	set	set	NOUN
iajs-1810	19	15	of	of	ADP
iajs-1810	19	16	differential	differential	ADJ
iajs-1810	19	17	equations	equation	NOUN
iajs-1810	19	18	in	in	ADP
iajs-1810	19	19	model	model	NOUN
iajs-1810	19	20	(	(	PUNCT
iajs-1810	19	21	2	2	NUM
iajs-1810	19	22	)	)	PUNCT
iajs-1810	19	23	,	,	PUNCT
iajs-1810	19	24	with	with	ADP
iajs-1810	19	25	an	an	DET
iajs-1810	19	26	initial	initial	ADJ
iajs-1810	19	27	condition	condition	NOUN
iajs-1810	19	28	in	in	ADP
iajs-1810	19	29	the	the	DET
iajs-1810	19	30	region	region	NOUN
iajs-1810	19	31	ℝ𝟑	ℝ𝟑	PROPN
iajs-1810	19	32	𝑆	𝑆	PROPN
iajs-1810	19	33	,	,	PUNCT
iajs-1810	19	34	𝐼	𝐼	PROPN
iajs-1810	19	35	,	,	PUNCT
iajs-1810	19	36	𝑅	𝑅	PROPN
iajs-1810	19	37	∈	∈	PROPN
iajs-1810	19	38	ℝ𝟑	ℝ𝟑	PRON
iajs-1810	19	39	;	;	PUNCT
iajs-1810	19	40	𝑆	𝑆	PROPN
iajs-1810	19	41	0	0	NUM
iajs-1810	19	42	,	,	PUNCT
iajs-1810	19	43	𝐼	𝐼	PROPN
iajs-1810	19	44	0	0	NUM
iajs-1810	19	45	,	,	PUNCT
iajs-1810	19	46	𝑅	𝑅	PROPN
iajs-1810	19	47	0	0	NUM
iajs-1810	19	48	;	;	PUNCT
iajs-1810	19	49	clearly	clearly	ADV
iajs-1810	19	50	the	the	DET
iajs-1810	19	51	interaction	interaction	NOUN
iajs-1810	19	52	functions	function	NOUN
iajs-1810	19	53	given	give	VERB
iajs-1810	19	54	on	on	ADP
iajs-1810	19	55	the	the	DET
iajs-1810	19	56	right	right	ADJ
iajs-1810	19	57	hand	hand	NOUN
iajs-1810	19	58	side	side	NOUN
iajs-1810	19	59	of	of	ADP
iajs-1810	19	60	model	model	NOUN
iajs-1810	19	61	(	(	PUNCT
iajs-1810	19	62	2	2	X
iajs-1810	19	63	)	)	PUNCT
iajs-1810	19	64	are	be	AUX
iajs-1810	19	65	continuously	continuously	ADV
iajs-1810	19	66	differentiable	differentiable	ADJ
iajs-1810	19	67	.	.	PUNCT
iajs-1810	20	1	therefore	therefore	ADV
iajs-1810	20	2	,	,	PUNCT
iajs-1810	20	3	the	the	DET
iajs-1810	20	4	solution	solution	NOUN
iajs-1810	20	5	of	of	ADP
iajs-1810	20	6	model	model	NOUN
iajs-1810	20	7	(	(	PUNCT
iajs-1810	20	8	2	2	NUM
iajs-1810	20	9	)	)	PUNCT
iajs-1810	20	10	with	with	ADP
iajs-1810	20	11	non	non	ADJ
iajs-1810	20	12	-	-	ADJ
iajs-1810	20	13	negative	negative	ADJ
iajs-1810	20	14	initial	initial	ADJ
iajs-1810	20	15	condition	condition	NOUN
iajs-1810	20	16	exists	exist	VERB
iajs-1810	20	17	and	and	CCONJ
iajs-1810	20	18	is	be	AUX
iajs-1810	20	19	unique	unique	ADJ
iajs-1810	20	20	.	.	PUNCT
iajs-1810	21	1	moreover	moreover	ADV
iajs-1810	21	2	,	,	PUNCT
iajs-1810	21	3	the	the	DET
iajs-1810	21	4	solution	solution	NOUN
iajs-1810	21	5	is	be	AUX
iajs-1810	21	6	uniformly	uniformly	ADV
iajs-1810	21	7	bounded	bound	VERB
iajs-1810	21	8	as	as	SCONJ
iajs-1810	21	9	shown	show	VERB
iajs-1810	21	10	in	in	ADP
iajs-1810	21	11	the	the	DET
iajs-1810	21	12	following	follow	VERB
iajs-1810	21	13	theorem	theorem	PROPN
iajs-1810	21	14	.	.	PUNCT
iajs-1810	21	15	theorem	theorem	VERB
iajs-1810	21	16	1	1	NUM
iajs-1810	21	17	all	all	DET
iajs-1810	21	18	the	the	DET
iajs-1810	21	19	solutions	solution	NOUN
iajs-1810	21	20	of	of	ADP
iajs-1810	21	21	model	model	NOUN
iajs-1810	21	22	(	(	PUNCT
iajs-1810	21	23	2	2	NUM
iajs-1810	21	24	)	)	PUNCT
iajs-1810	21	25	,	,	PUNCT
iajs-1810	21	26	which	which	PRON
iajs-1810	21	27	initiate	initiate	VERB
iajs-1810	21	28	in	in	ADP
iajs-1810	21	29	the	the	DET
iajs-1810	21	30	region	region	NOUN
iajs-1810	21	31	ℝ	ℝ	NOUN
iajs-1810	21	32	𝟑	𝟑	NOUN
iajs-1810	21	33	are	be	AUX
iajs-1810	21	34	uniformly	uniformly	ADV
iajs-1810	21	35	bounded	bound	VERB
iajs-1810	21	36	at	at	ADP
iajs-1810	21	37	the	the	DET
iajs-1810	21	38	set	set	PROPN
iajs-1810	21	39	ω	ω	PROPN
iajs-1810	21	40	𝑆	𝑆	PROPN
iajs-1810	21	41	,	,	PUNCT
iajs-1810	21	42	𝐼	𝐼	PROPN
iajs-1810	21	43	,	,	PUNCT
iajs-1810	21	44	𝑅	𝑅	PROPN
iajs-1810	21	45	∈	∈	PROPN
iajs-1810	21	46	ℝ	ℝ	NOUN
iajs-1810	21	47	:	:	PUNCT
iajs-1810	21	48	𝑅	𝑅	PROPN
iajs-1810	21	49	0	0	PROPN
iajs-1810	21	50	,	,	PUNCT
iajs-1810	21	51	𝐼	𝐼	PROPN
iajs-1810	21	52	0	0	NUM
iajs-1810	21	53	,	,	PUNCT
iajs-1810	21	54	𝑆	𝑆	PROPN
iajs-1810	21	55	0	0	NUM
iajs-1810	22	1	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-1810	22	2	0	0	PUNCT
iajs-1810	23	1	𝑁	𝑁	PROPN
iajs-1810	23	2	𝑡	𝑡	PROPN
iajs-1810	23	3	.	.	PUNCT
iajs-1810	24	1	proof	proof	NOUN
iajs-1810	24	2	let	let	VERB
iajs-1810	24	3	n(t	n(t	PRON
iajs-1810	24	4	)	)	PUNCT
iajs-1810	24	5	=	=	SYM
iajs-1810	24	6	s(t	s(t	PROPN
iajs-1810	24	7	)	)	PUNCT
iajs-1810	25	1	+	+	NUM
iajs-1810	25	2	i(t	i(t	NOUN
iajs-1810	25	3	)	)	PUNCT
iajs-1810	26	1	+	+	NUM
iajs-1810	26	2	r(t	r(t	NOUN
iajs-1810	26	3	)	)	PUNCT
iajs-1810	26	4	represents	represent	VERB
iajs-1810	26	5	the	the	DET
iajs-1810	26	6	population	population	NOUN
iajs-1810	26	7	size	size	NOUN
iajs-1810	26	8	,	,	PUNCT
iajs-1810	26	9	then	then	ADV
iajs-1810	26	10	𝐴	𝐴	PROPN
iajs-1810	26	11	𝛼𝑁	𝛼𝑁	PROPN
iajs-1810	26	12	𝑘𝐼	𝑘𝐼	NOUN
iajs-1810	26	13	,	,	PUNCT
iajs-1810	26	14	then	then	ADV
iajs-1810	26	15	we	we	PRON
iajs-1810	26	16	get	get	VERB
iajs-1810	26	17	𝑁	𝑁	PROPN
iajs-1810	26	18	𝑡	𝑡	PRON
iajs-1810	26	19	𝑁	𝑁	NOUN
iajs-1810	26	20	0	0	NUM
iajs-1810	26	21	𝑒	𝑒	PROPN
iajs-1810	26	22	1	1	NUM
iajs-1810	26	23	𝑒	𝑒	NOUN
iajs-1810	26	24	,	,	PUNCT
iajs-1810	26	25	and	and	CCONJ
iajs-1810	26	26	lim	lim	PROPN
iajs-1810	26	27	→	→	PUNCT
iajs-1810	26	28	𝑁	𝑁	PROPN
iajs-1810	26	29	𝑡	𝑡	PROPN
iajs-1810	26	30	,	,	PUNCT
iajs-1810	26	31	so	so	ADV
iajs-1810	26	32	0	0	PUNCT
iajs-1810	27	1	if	if	SCONJ
iajs-1810	27	2	𝑁	𝑁	PROPN
iajs-1810	27	3	𝑡	𝑡	PROPN
iajs-1810	27	4	,	,	PUNCT
iajs-1810	27	5	and	and	CCONJ
iajs-1810	27	6	the	the	DET
iajs-1810	27	7	solution	solution	NOUN
iajs-1810	27	8	of	of	ADP
iajs-1810	27	9	system	system	NOUN
iajs-1810	27	10	(	(	PUNCT
iajs-1810	27	11	2	2	X
iajs-1810	27	12	)	)	PUNCT
iajs-1810	27	13	is	be	AUX
iajs-1810	27	14	uniformly	uniformly	ADV
iajs-1810	27	15	bounded	bound	VERB
iajs-1810	27	16	and	and	CCONJ
iajs-1810	27	17	defined	define	VERB
iajs-1810	27	18	at	at	ADP
iajs-1810	27	19	the	the	DET
iajs-1810	27	20	set	set	PROPN
iajs-1810	27	21	ω	ω	PROPN
iajs-1810	27	22	,	,	PUNCT
iajs-1810	27	23	prove	prove	VERB
iajs-1810	27	24	complete	complete	ADJ
iajs-1810	27	25	.	.	PUNCT
iajs-1810	28	1	∎	∎	PROPN
iajs-1810	28	2	3	3	X
iajs-1810	28	3	.	.	NOUN
iajs-1810	28	4	existence	existence	NOUN
iajs-1810	28	5	and	and	CCONJ
iajs-1810	28	6	stability	stability	NOUN
iajs-1810	28	7	of	of	ADP
iajs-1810	28	8	equilibrium	equilibrium	NOUN
iajs-1810	28	9	points	point	NOUN
iajs-1810	28	10	.	.	PUNCT
iajs-1810	29	1	in	in	ADP
iajs-1810	29	2	this	this	DET
iajs-1810	29	3	section	section	NOUN
iajs-1810	29	4	,	,	PUNCT
iajs-1810	29	5	we	we	PRON
iajs-1810	29	6	study	study	VERB
iajs-1810	29	7	the	the	DET
iajs-1810	29	8	existence	existence	NOUN
iajs-1810	29	9	of	of	ADP
iajs-1810	29	10	equilibrium	equilibrium	NOUN
iajs-1810	29	11	points	point	NOUN
iajs-1810	29	12	of	of	ADP
iajs-1810	29	13	model	model	NOUN
iajs-1810	29	14	(	(	PUNCT
iajs-1810	29	15	2	2	NUM
iajs-1810	29	16	)	)	PUNCT
iajs-1810	29	17	,	,	PUNCT
iajs-1810	29	18	and	and	CCONJ
iajs-1810	29	19	their	their	PRON
iajs-1810	29	20	stability	stability	NOUN
iajs-1810	29	21	(	(	PUNCT
iajs-1810	29	22	local	local	ADJ
iajs-1810	29	23	and	and	CCONJ
iajs-1810	29	24	global	global	ADJ
iajs-1810	29	25	)	)	PUNCT
iajs-1810	29	26	.	.	PUNCT
iajs-1810	30	1	it	it	PRON
iajs-1810	30	2	is	be	AUX
iajs-1810	30	3	clear	clear	ADJ
iajs-1810	30	4	model	model	NOUN
iajs-1810	30	5	(	(	PUNCT
iajs-1810	30	6	2	2	NUM
iajs-1810	30	7	)	)	PUNCT
iajs-1810	30	8	has	have	VERB
iajs-1810	30	9	two	two	NUM
iajs-1810	30	10	equilibrium	equilibrium	NOUN
iajs-1810	30	11	points	point	NOUN
iajs-1810	30	12	,	,	PUNCT
iajs-1810	30	13	namely	namely	ADV
iajs-1810	30	14	e0	e0	PROPN
iajs-1810	30	15	and	and	CCONJ
iajs-1810	30	16	e1	e1	NOUN
iajs-1810	30	17	,	,	PUNCT
iajs-1810	30	18	disease	disease	NOUN
iajs-1810	30	19	free	free	ADJ
iajs-1810	30	20	equilibrium	equilibrium	NOUN
iajs-1810	30	21	point	point	NOUN
iajs-1810	30	22	dfe	dfe	PROPN
iajs-1810	30	23	and	and	CCONJ
iajs-1810	30	24	endemic	endemic	ADJ
iajs-1810	30	25	equilibrium	equilibrium	NOUN
iajs-1810	30	26	point	point	NOUN
iajs-1810	30	27	eep	eep	NOUN
iajs-1810	30	28	respectively	respectively	ADV
iajs-1810	30	29	.	.	PUNCT
iajs-1810	31	1	e0	e0	PROPN
iajs-1810	31	2	occurs	occur	VERB
iajs-1810	31	3	when	when	SCONJ
iajs-1810	31	4	the	the	DET
iajs-1810	31	5	population	population	NOUN
iajs-1810	31	6	consists	consist	VERB
iajs-1810	31	7	only	only	ADV
iajs-1810	31	8	of	of	ADP
iajs-1810	31	9	susceptible	susceptible	ADJ
iajs-1810	31	10	individuals	individual	NOUN
iajs-1810	31	11	,	,	PUNCT
iajs-1810	31	12	this	this	PRON
iajs-1810	31	13	means	mean	VERB
iajs-1810	31	14	there	there	PRON
iajs-1810	31	15	are	be	VERB
iajs-1810	31	16	no	no	DET
iajs-1810	31	17	ihsciconf	ihsciconf	ADJ
iajs-1810	31	18	2017	2017	NUM
iajs-1810	31	19	special	special	ADJ
iajs-1810	31	20	issue	issue	NOUN
iajs-1810	31	21	ibn	ibn	PROPN
iajs-1810	31	22	al	al	PROPN
iajs-1810	31	23	-	-	PUNCT
iajs-1810	31	24	haitham	haitham	PROPN
iajs-1810	31	25	journal	journal	PROPN
iajs-1810	31	26	for	for	ADP
iajs-1810	31	27	pure	pure	ADJ
iajs-1810	31	28	and	and	CCONJ
iajs-1810	31	29	applied	apply	VERB
iajs-1810	31	30	science	science	NOUN
iajs-1810	31	31	https://doi.org/	https://doi.org/	VERB
iajs-1810	31	32	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	31	33	for	for	ADP
iajs-1810	31	34	more	more	ADJ
iajs-1810	31	35	information	information	NOUN
iajs-1810	31	36	about	about	ADP
iajs-1810	31	37	the	the	DET
iajs-1810	31	38	conference	conference	NOUN
iajs-1810	31	39	please	please	INTJ
iajs-1810	31	40	visit	visit	VERB
iajs-1810	31	41	the	the	DET
iajs-1810	31	42	websites	website	NOUN
iajs-1810	31	43	:	:	PUNCT
iajs-1810	31	44	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	31	45	  	  	SPACE
iajs-1810	31	46	www.ihsciconf.org	www.ihsciconf.org	NOUN
iajs-1810	31	47	   	   	SPACE
iajs-1810	31	48	mathematics|513	mathematics|513	NOUN
iajs-1810	31	49	    	    	SPACE
iajs-1810	31	50	infected	infect	VERB
iajs-1810	31	51	individuals	individual	NOUN
iajs-1810	31	52	and	and	CCONJ
iajs-1810	31	53	no	no	DET
iajs-1810	31	54	recovered	recovered	ADJ
iajs-1810	31	55	individuals	individual	NOUN
iajs-1810	31	56	(	(	PUNCT
iajs-1810	31	57	i.e.	i.e.	X
iajs-1810	31	58	disease	disease	NOUN
iajs-1810	31	59	does	do	AUX
iajs-1810	31	60	not	not	PART
iajs-1810	31	61	exist	exist	VERB
iajs-1810	31	62	)	)	PUNCT
iajs-1810	31	63	,	,	PUNCT
iajs-1810	31	64	so	so	ADV
iajs-1810	31	65	i=0	i=0	PROPN
iajs-1810	31	66	,	,	PUNCT
iajs-1810	31	67	r=0	r=0	VERB
iajs-1810	31	68	from	from	ADP
iajs-1810	31	69	model(2	model(2	PROPN
iajs-1810	31	70	)	)	PUNCT
iajs-1810	31	71	we	we	PRON
iajs-1810	31	72	get	get	VERB
iajs-1810	31	73	e0	e0	PROPN
iajs-1810	31	74	=	=	SYM
iajs-1810	31	75	(	(	PUNCT
iajs-1810	31	76	s0,0,0	s0,0,0	NOUN
iajs-1810	31	77	)	)	PUNCT
iajs-1810	31	78	=	=	NOUN
iajs-1810	31	79	,	,	PUNCT
iajs-1810	31	80	0,0	0,0	NUM
iajs-1810	31	81	.	.	PUNCT
iajs-1810	32	1	however	however	ADV
iajs-1810	32	2	if	if	SCONJ
iajs-1810	32	3	the	the	DET
iajs-1810	32	4	disease	disease	NOUN
iajs-1810	32	5	is	be	AUX
iajs-1810	32	6	present	present	ADJ
iajs-1810	32	7	then	then	ADV
iajs-1810	32	8	infected	infect	VERB
iajs-1810	32	9	and	and	CCONJ
iajs-1810	32	10	recovered	recover	VERB
iajs-1810	32	11	individuals	individual	NOUN
iajs-1810	32	12	are	be	AUX
iajs-1810	32	13	present	present	ADJ
iajs-1810	32	14	and	and	CCONJ
iajs-1810	32	15	the	the	DET
iajs-1810	32	16	endemic	endemic	ADJ
iajs-1810	32	17	equilibrium	equilibrium	NOUN
iajs-1810	32	18	point	point	NOUN
iajs-1810	32	19	eep	eep	PROPN
iajs-1810	32	20	,	,	PUNCT
iajs-1810	32	21	e1=(s1,i1,r1	e1=(s1,i1,r1	PROPN
iajs-1810	32	22	)	)	PUNCT
iajs-1810	32	23	arises	arise	VERB
iajs-1810	32	24	,	,	PUNCT
iajs-1810	32	25	where	where	SCONJ
iajs-1810	32	26	i1≠0	i1≠0	NOUN
iajs-1810	32	27	,	,	PUNCT
iajs-1810	32	28	r1≠0	r1≠0	NOUN
iajs-1810	32	29	,	,	PUNCT
iajs-1810	32	30	note	note	VERB
iajs-1810	32	31	that	that	SCONJ
iajs-1810	32	32	s1	s1	NOUN
iajs-1810	32	33	,	,	PUNCT
iajs-1810	32	34	i1	i1	NOUN
iajs-1810	32	35	,	,	PUNCT
iajs-1810	32	36	and	and	CCONJ
iajs-1810	32	37	r1	r1	PROPN
iajs-1810	32	38	represent	represent	VERB
iajs-1810	32	39	the	the	DET
iajs-1810	32	40	positive	positive	ADJ
iajs-1810	32	41	solution	solution	NOUN
iajs-1810	32	42	of	of	ADP
iajs-1810	32	43	system	system	NOUN
iajs-1810	32	44	(	(	PUNCT
iajs-1810	32	45	3	3	NUM
iajs-1810	32	46	):	):	PUNCT
iajs-1810	32	47	𝐴	𝐴	PROPN
iajs-1810	32	48	𝛼𝑆	𝛼𝑆	NOUN
iajs-1810	32	49	0	0	NUM
iajs-1810	32	50	𝛽𝑅	𝛽𝑅	PROPN
iajs-1810	32	51	𝛾	𝛾	PROPN
iajs-1810	32	52	1	1	NUM
iajs-1810	32	53	𝛿	𝛿	PROPN
iajs-1810	32	54	𝐼	𝐼	PROPN
iajs-1810	32	55	𝛼	𝛼	NOUN
iajs-1810	32	56	𝑘	𝑘	NOUN
iajs-1810	32	57	𝐼	𝐼	ADP
iajs-1810	32	58	0	0	NUM
iajs-1810	32	59	…	…	PUNCT
iajs-1810	32	60	…	…	PUNCT
iajs-1810	32	61	…	…	PUNCT
iajs-1810	32	62	.	.	PUNCT
iajs-1810	33	1	3	3	NUM
iajs-1810	33	2	𝛾	𝛾	NOUN
iajs-1810	33	3	1	1	NUM
iajs-1810	33	4	𝛿	𝛿	PROPN
iajs-1810	33	5	𝐼	𝐼	PROPN
iajs-1810	33	6	𝛼	𝛼	ADP
iajs-1810	33	7	𝛽	𝛽	PROPN
iajs-1810	33	8	𝑅	𝑅	PROPN
iajs-1810	33	9	0	0	PUNCT
iajs-1810	33	10	now	now	ADV
iajs-1810	33	11	from	from	ADP
iajs-1810	33	12	the	the	DET
iajs-1810	33	13	third	third	ADJ
iajs-1810	33	14	equation	equation	NOUN
iajs-1810	33	15	of	of	ADP
iajs-1810	33	16	system	system	NOUN
iajs-1810	33	17	(	(	PUNCT
iajs-1810	33	18	3	3	X
iajs-1810	33	19	)	)	PUNCT
iajs-1810	33	20	we	we	PRON
iajs-1810	33	21	get	get	VERB
iajs-1810	33	22	𝑅	𝑅	PROPN
iajs-1810	33	23	𝐼	𝐼	PROPN
iajs-1810	33	24	..	..	PUNCT
iajs-1810	33	25	(	(	PUNCT
iajs-1810	33	26	4	4	X
iajs-1810	33	27	)	)	PUNCT
iajs-1810	33	28	substituting	substitute	VERB
iajs-1810	33	29	(	(	PUNCT
iajs-1810	33	30	4	4	NUM
iajs-1810	33	31	)	)	PUNCT
iajs-1810	33	32	in	in	ADP
iajs-1810	33	33	the	the	DET
iajs-1810	33	34	second	second	ADJ
iajs-1810	33	35	equation	equation	NOUN
iajs-1810	33	36	of	of	ADP
iajs-1810	33	37	system	system	NOUN
iajs-1810	33	38	(	(	PUNCT
iajs-1810	33	39	3	3	X
iajs-1810	33	40	)	)	PUNCT
iajs-1810	33	41	we	we	PRON
iajs-1810	33	42	get	get	VERB
iajs-1810	33	43	𝑆	𝑆	PROPN
iajs-1810	33	44	…	…	PUNCT
iajs-1810	33	45	(	(	PUNCT
iajs-1810	33	46	5	5	NUM
iajs-1810	33	47	)	)	PUNCT
iajs-1810	33	48	,	,	PUNCT
iajs-1810	33	49	while	while	SCONJ
iajs-1810	33	50	𝐼	𝐼	PROPN
iajs-1810	33	51	is	be	AUX
iajs-1810	33	52	a	a	DET
iajs-1810	33	53	positive	positive	ADJ
iajs-1810	33	54	root	root	NOUN
iajs-1810	33	55	of	of	ADP
iajs-1810	33	56	the	the	DET
iajs-1810	33	57	following	follow	VERB
iajs-1810	33	58	equation	equation	NOUN
iajs-1810	33	59	𝐵	𝐵	NOUN
iajs-1810	33	60	𝐼	𝐼	ADP
iajs-1810	33	61	𝐵	𝐵	NOUN
iajs-1810	33	62	𝐼	𝐼	ADP
iajs-1810	33	63	𝐵	𝐵	PROPN
iajs-1810	33	64	0	0	NUM
iajs-1810	33	65	..	..	PUNCT
iajs-1810	33	66	(	(	PUNCT
iajs-1810	33	67	6	6	NUM
iajs-1810	33	68	)	)	PUNCT
iajs-1810	33	69	here	here	ADV
iajs-1810	33	70	:	:	PUNCT
iajs-1810	33	71	𝐵	𝐵	NOUN
iajs-1810	33	72	𝑎𝑐	𝑎𝑐	VERB
iajs-1810	33	73	𝛾	𝛾	PROPN
iajs-1810	33	74	1	1	NUM
iajs-1810	33	75	𝛿	𝛿	NOUN
iajs-1810	33	76	𝛼	𝛼	NOUN
iajs-1810	33	77	𝑘	𝑘	NOUN
iajs-1810	33	78	𝑎	𝑎	NOUN
iajs-1810	33	79	𝑏	𝑏	NOUN
iajs-1810	33	80	𝛾	𝛾	PROPN
iajs-1810	33	81	1	1	NUM
iajs-1810	33	82	𝛿	𝛿	NOUN
iajs-1810	33	83	𝛼	𝛼	NOUN
iajs-1810	33	84	𝑘	𝑘	PRON
iajs-1810	33	85	𝑏	𝑏	DET
iajs-1810	33	86	𝛼𝑏𝑐	𝛼𝑏𝑐	NOUN
iajs-1810	33	87	𝛾	𝛾	PROPN
iajs-1810	33	88	1	1	NUM
iajs-1810	33	89	𝛿	𝛿	NOUN
iajs-1810	33	90	𝛼	𝛼	NOUN
iajs-1810	33	91	𝑘	𝑘	PRON
iajs-1810	33	92	𝛼𝑐	𝛼𝑐	NOUN
iajs-1810	33	93	𝑎	𝑎	PROPN
iajs-1810	33	94	𝑏	𝑏	NOUN
iajs-1810	33	95	𝛾	𝛾	PROPN
iajs-1810	33	96	1	1	NUM
iajs-1810	33	97	𝛿	𝛿	NOUN
iajs-1810	33	98	𝛼	𝛼	NOUN
iajs-1810	33	99	𝑘	𝑘	PRON
iajs-1810	33	100	𝑏	𝑏	NOUN
iajs-1810	33	101	…	…	PUNCT
iajs-1810	33	102	…	…	PUNCT
iajs-1810	33	103	…	…	PUNCT
iajs-1810	33	104	…	…	PUNCT
iajs-1810	33	105	…	…	PUNCT
iajs-1810	33	106	..	..	PUNCT
iajs-1810	33	107	(	(	PUNCT
iajs-1810	33	108	6a	6a	NOUN
iajs-1810	33	109	)	)	PUNCT
iajs-1810	33	110	𝐵	𝐵	NOUN
iajs-1810	33	111	𝑐𝑏𝐴	𝑐𝑏𝐴	NOUN
iajs-1810	33	112	𝛾	𝛾	PROPN
iajs-1810	33	113	1	1	NUM
iajs-1810	33	114	𝛿	𝛿	NOUN
iajs-1810	33	115	𝛼	𝛼	NOUN
iajs-1810	33	116	𝑘	𝑘	NOUN
iajs-1810	33	117	𝑎	𝑎	NOUN
iajs-1810	33	118	𝑏	𝑏	NOUN
iajs-1810	33	119	𝛾	𝛾	PROPN
iajs-1810	33	120	1	1	NUM
iajs-1810	33	121	𝛿	𝛿	NOUN
iajs-1810	33	122	𝛼	𝛼	NOUN
iajs-1810	33	123	𝑘	𝑘	PRON
iajs-1810	33	124	𝑏	𝑏	DET
iajs-1810	33	125	𝐴𝑐	𝐴𝑐	PROPN
iajs-1810	33	126	𝑎	𝑎	PROPN
iajs-1810	33	127	𝑏	𝑏	NOUN
iajs-1810	33	128	𝛾	𝛾	PROPN
iajs-1810	33	129	1	1	NUM
iajs-1810	33	130	𝛿	𝛿	NOUN
iajs-1810	33	131	𝛼	𝛼	NOUN
iajs-1810	33	132	𝑘	𝑘	ADP
iajs-1810	33	133	𝑏	𝑏	DET
iajs-1810	33	134	𝑎	𝑎	NOUN
iajs-1810	33	135	𝛾	𝛾	NOUN
iajs-1810	33	136	1	1	NUM
iajs-1810	33	137	𝛿	𝛿	NOUN
iajs-1810	33	138	𝛼	𝛼	NOUN
iajs-1810	33	139	𝑘	𝑘	NOUN
iajs-1810	33	140	𝑎	𝑎	NOUN
iajs-1810	33	141	𝑏	𝑏	NOUN
iajs-1810	33	142	𝛾	𝛾	PROPN
iajs-1810	33	143	1	1	NUM
iajs-1810	33	144	𝛿	𝛿	NOUN
iajs-1810	33	145	𝛼	𝛼	NOUN
iajs-1810	33	146	𝑘	𝑘	PRON
iajs-1810	33	147	𝑏	𝑏	DET
iajs-1810	33	148	𝛼𝑐	𝛼𝑐	NOUN
iajs-1810	33	149	𝛾	𝛾	PROPN
iajs-1810	33	150	1	1	NUM
iajs-1810	33	151	𝛿	𝛿	NOUN
iajs-1810	33	152	𝛼	𝛼	NOUN
iajs-1810	33	153	𝑘	𝑘	NOUN
iajs-1810	33	154	𝑎	𝑎	NOUN
iajs-1810	33	155	𝑏	𝑏	NOUN
iajs-1810	33	156	𝛾	𝛾	PROPN
iajs-1810	33	157	1	1	NUM
iajs-1810	33	158	𝛿	𝛿	NOUN
iajs-1810	33	159	𝛼	𝛼	NOUN
iajs-1810	33	160	𝑘	𝑘	ADP
iajs-1810	33	161	𝑏	𝑏	PRON
iajs-1810	33	162	2𝛼𝑐𝑏	2𝛼𝑐𝑏	PROPN
iajs-1810	33	163	𝛾	𝛾	PROPN
iajs-1810	33	164	1	1	NUM
iajs-1810	33	165	𝛿	𝛿	NOUN
iajs-1810	33	166	𝛼	𝛼	NOUN
iajs-1810	33	167	𝑘	𝑘	PRON
iajs-1810	33	168	𝛼𝑐	𝛼𝑐	NOUN
iajs-1810	33	169	𝛾	𝛾	PROPN
iajs-1810	33	170	1	1	NUM
iajs-1810	33	171	𝛿	𝛿	NOUN
iajs-1810	33	172	𝛼	𝛼	NOUN
iajs-1810	33	173	𝑘	𝑘	PRON
iajs-1810	33	174	…	…	PUNCT
iajs-1810	33	175	…	…	PUNCT
iajs-1810	33	176	…	…	PUNCT
iajs-1810	33	177	(	(	PUNCT
iajs-1810	33	178	b	b	NOUN
iajs-1810	33	179	)	)	PUNCT
iajs-1810	33	180	ihsciconf	ihsciconf	NOUN
iajs-1810	33	181	2017	2017	NUM
iajs-1810	33	182	special	special	ADJ
iajs-1810	33	183	issue	issue	NOUN
iajs-1810	33	184	ibn	ibn	PROPN
iajs-1810	33	185	al	al	PROPN
iajs-1810	33	186	-	-	PUNCT
iajs-1810	33	187	haitham	haitham	PROPN
iajs-1810	33	188	journal	journal	PROPN
iajs-1810	33	189	for	for	ADP
iajs-1810	33	190	pure	pure	ADJ
iajs-1810	33	191	and	and	CCONJ
iajs-1810	33	192	applied	apply	VERB
iajs-1810	33	193	science	science	NOUN
iajs-1810	33	194	https://doi.org/	https://doi.org/	VERB
iajs-1810	33	195	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	33	196	for	for	ADP
iajs-1810	33	197	more	more	ADJ
iajs-1810	33	198	information	information	NOUN
iajs-1810	33	199	about	about	ADP
iajs-1810	33	200	the	the	DET
iajs-1810	33	201	conference	conference	NOUN
iajs-1810	33	202	please	please	INTJ
iajs-1810	33	203	visit	visit	VERB
iajs-1810	33	204	the	the	DET
iajs-1810	33	205	websites	website	NOUN
iajs-1810	33	206	:	:	PUNCT
iajs-1810	33	207	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	33	208	  	  	SPACE
iajs-1810	33	209	www.ihsciconf.org	www.ihsciconf.org	NOUN
iajs-1810	33	210	   	   	SPACE
iajs-1810	33	211	mathematics|514	mathematics|514	NOUN
iajs-1810	33	212	    	    	SPACE
iajs-1810	33	213	𝐵	𝐵	NOUN
iajs-1810	33	214	𝐴𝑏	𝐴𝑏	PROPN
iajs-1810	33	215	𝛾	𝛾	NOUN
iajs-1810	33	216	1	1	NUM
iajs-1810	33	217	𝛿	𝛿	NOUN
iajs-1810	33	218	𝛼	𝛼	NOUN
iajs-1810	33	219	𝑘	𝑘	NOUN
iajs-1810	33	220	𝑎	𝑎	NOUN
iajs-1810	33	221	𝑏	𝑏	NOUN
iajs-1810	33	222	𝛾	𝛾	PROPN
iajs-1810	33	223	1	1	NUM
iajs-1810	33	224	𝛿	𝛿	NOUN
iajs-1810	33	225	𝛼	𝛼	NOUN
iajs-1810	33	226	𝑘	𝑘	PRON
iajs-1810	33	227	𝑏	𝑏	PRON
iajs-1810	33	228	𝛼	𝛼	NOUN
iajs-1810	33	229	𝛾	𝛾	PROPN
iajs-1810	33	230	1	1	NUM
iajs-1810	33	231	𝛿	𝛿	NOUN
iajs-1810	33	232	𝛼	𝛼	NOUN
iajs-1810	33	233	𝑘	𝑘	NOUN
iajs-1810	33	234	𝑎	𝑎	NOUN
iajs-1810	33	235	𝑏	𝑏	NOUN
iajs-1810	33	236	𝛾	𝛾	PROPN
iajs-1810	33	237	1	1	NUM
iajs-1810	33	238	𝛿	𝛿	NOUN
iajs-1810	33	239	𝛼	𝛼	NOUN
iajs-1810	33	240	𝑘	𝑘	PRON
iajs-1810	33	241	𝑏	𝑏	DET
iajs-1810	33	242	𝛼𝑏	𝛼𝑏	NOUN
iajs-1810	33	243	𝛾	𝛾	PROPN
iajs-1810	33	244	1	1	NUM
iajs-1810	33	245	𝛿	𝛿	PRON
iajs-1810	33	246	𝛼	𝛼	NOUN
iajs-1810	33	247	𝑘	𝑘	PRON
iajs-1810	33	248	…	…	PUNCT
iajs-1810	33	249	…	…	PUNCT
iajs-1810	33	250	…	…	PUNCT
iajs-1810	33	251	…	…	PUNCT
iajs-1810	33	252	.(6c	.(6c	PUNCT
iajs-1810	33	253	)	)	PUNCT
iajs-1810	33	254	clearly	clearly	ADV
iajs-1810	33	255	,	,	PUNCT
iajs-1810	33	256	by	by	ADP
iajs-1810	33	257	using	use	VERB
iajs-1810	33	258	descarte	descarte	NOUN
iajs-1810	33	259	’s	’s	PART
iajs-1810	33	260	rule	rule	NOUN
iajs-1810	33	261	[	[	X
iajs-1810	33	262	12	12	NUM
iajs-1810	33	263	]	]	PUNCT
iajs-1810	33	264	of	of	ADP
iajs-1810	33	265	signs	sign	NOUN
iajs-1810	33	266	then	then	ADV
iajs-1810	33	267	equation	equation	NOUN
iajs-1810	33	268	(	(	PUNCT
iajs-1810	33	269	6	6	NUM
iajs-1810	33	270	)	)	PUNCT
iajs-1810	33	271	has	have	VERB
iajs-1810	33	272	a	a	DET
iajs-1810	33	273	unique	unique	ADJ
iajs-1810	33	274	positive	positive	ADJ
iajs-1810	33	275	root	root	NOUN
iajs-1810	33	276	given	give	VERB
iajs-1810	33	277	by	by	ADP
iajs-1810	33	278	i1	i1	PROPN
iajs-1810	34	1	if	if	SCONJ
iajs-1810	34	2	and	and	CCONJ
iajs-1810	34	3	only	only	ADV
iajs-1810	34	4	if	if	SCONJ
iajs-1810	34	5	one	one	NUM
iajs-1810	34	6	of	of	ADP
iajs-1810	34	7	the	the	DET
iajs-1810	34	8	following	follow	VERB
iajs-1810	34	9	conditions	condition	NOUN
iajs-1810	34	10	hold	hold	VERB
iajs-1810	34	11	:	:	PUNCT
iajs-1810	34	12	b2	b2	NOUN
iajs-1810	34	13	<	<	X
iajs-1810	34	14	0	0	NUM
iajs-1810	34	15	or	or	CCONJ
iajs-1810	34	16	b3	b3	PROPN
iajs-1810	34	17	>	>	X
iajs-1810	34	18	0	0	X
iajs-1810	34	19	.	.	PUNCT
iajs-1810	35	1	in	in	ADP
iajs-1810	35	2	order	order	NOUN
iajs-1810	35	3	to	to	PART
iajs-1810	35	4	discuss	discuss	VERB
iajs-1810	35	5	stability	stability	NOUN
iajs-1810	35	6	of	of	ADP
iajs-1810	35	7	the	the	DET
iajs-1810	35	8	above	above	ADJ
iajs-1810	35	9	equilibrium	equilibrium	NOUN
iajs-1810	35	10	points	point	VERB
iajs-1810	35	11	the	the	DET
iajs-1810	35	12	basic	basic	ADJ
iajs-1810	35	13	reproduction	reproduction	NOUN
iajs-1810	35	14	number	number	NOUN
iajs-1810	35	15	𝑅	𝑅	PROPN
iajs-1810	36	1	[	[	NOUN
iajs-1810	36	2	2	2	NUM
iajs-1810	36	3	]	]	PUNCT
iajs-1810	36	4	,	,	PUNCT
iajs-1810	36	5	which	which	PRON
iajs-1810	36	6	represents	represent	VERB
iajs-1810	36	7	the	the	DET
iajs-1810	36	8	number	number	NOUN
iajs-1810	36	9	of	of	ADP
iajs-1810	36	10	new	new	ADJ
iajs-1810	36	11	infected	infected	ADJ
iajs-1810	36	12	people	people	NOUN
iajs-1810	36	13	caused	cause	VERB
iajs-1810	36	14	by	by	ADP
iajs-1810	36	15	a	a	DET
iajs-1810	36	16	single	single	ADJ
iajs-1810	36	17	infected	infected	ADJ
iajs-1810	36	18	patient	patient	NOUN
iajs-1810	36	19	when	when	SCONJ
iajs-1810	36	20	introduced	introduce	VERB
iajs-1810	36	21	into	into	ADP
iajs-1810	36	22	a	a	DET
iajs-1810	36	23	completely	completely	ADV
iajs-1810	36	24	susceptible	susceptible	ADJ
iajs-1810	36	25	population	population	NOUN
iajs-1810	36	26	,	,	PUNCT
iajs-1810	36	27	is	be	AUX
iajs-1810	36	28	computed	compute	VERB
iajs-1810	36	29	.	.	PUNCT
iajs-1810	37	1	it	it	PRON
iajs-1810	37	2	is	be	AUX
iajs-1810	37	3	well	well	ADV
iajs-1810	37	4	known	know	VERB
iajs-1810	37	5	that	that	SCONJ
iajs-1810	37	6	the	the	DET
iajs-1810	37	7	value	value	NOUN
iajs-1810	37	8	of	of	ADP
iajs-1810	37	9	this	this	DET
iajs-1810	37	10	number	number	NOUN
iajs-1810	37	11	plays	play	VERB
iajs-1810	37	12	a	a	DET
iajs-1810	37	13	necessary	necessary	ADJ
iajs-1810	37	14	role	role	NOUN
iajs-1810	37	15	in	in	ADP
iajs-1810	37	16	the	the	DET
iajs-1810	37	17	stability	stability	NOUN
iajs-1810	37	18	of	of	ADP
iajs-1810	37	19	the	the	DET
iajs-1810	37	20	model	model	NOUN
iajs-1810	37	21	(	(	PUNCT
iajs-1810	37	22	2	2	NUM
iajs-1810	37	23	)	)	PUNCT
iajs-1810	37	24	.	.	PUNCT
iajs-1810	38	1	according	accord	VERB
iajs-1810	38	2	to	to	ADP
iajs-1810	38	3	definition	definition	NOUN
iajs-1810	38	4	of	of	ADP
iajs-1810	38	5	basic	basic	ADJ
iajs-1810	38	6	reproduction	reproduction	NOUN
iajs-1810	38	7	number	number	NOUN
iajs-1810	38	8	that	that	PRON
iajs-1810	38	9	given	give	VERB
iajs-1810	38	10	in	in	ADP
iajs-1810	38	11	[	[	X
iajs-1810	38	12	2	2	NUM
iajs-1810	38	13	]	]	PUNCT
iajs-1810	38	14	,	,	PUNCT
iajs-1810	38	15	rewrite	rewrite	VERB
iajs-1810	38	16	model	model	NOUN
iajs-1810	38	17	(	(	PUNCT
iajs-1810	38	18	2	2	NUM
iajs-1810	38	19	)	)	PUNCT
iajs-1810	38	20	in	in	ADP
iajs-1810	38	21	the	the	DET
iajs-1810	38	22	form	form	NOUN
iajs-1810	38	23	𝑥	𝑥	X
iajs-1810	38	24	ℋ	ℋ	NOUN
iajs-1810	38	25	𝑥	𝑥	X
iajs-1810	38	26	ℳ	ℳ	PROPN
iajs-1810	38	27	𝑥	𝑥	NOUN
iajs-1810	38	28	…	…	PUNCT
iajs-1810	38	29	…	…	PUNCT
iajs-1810	38	30	…	…	PUNCT
iajs-1810	38	31	…	…	PUNCT
iajs-1810	38	32	(	(	PUNCT
iajs-1810	38	33	7	7	NUM
iajs-1810	38	34	)	)	PUNCT
iajs-1810	38	35	where	where	SCONJ
iajs-1810	38	36	𝑥	𝑥	X
iajs-1810	38	37	𝐼	𝐼	PROPN
iajs-1810	38	38	,	,	PUNCT
iajs-1810	38	39	𝑆	𝑆	PROPN
iajs-1810	38	40	,	,	PUNCT
iajs-1810	38	41	𝑅	𝑅	PROPN
iajs-1810	38	42	,	,	PUNCT
iajs-1810	38	43	ℋ	ℋ	PROPN
iajs-1810	38	44	𝑥	𝑥	PROPN
iajs-1810	38	45	is	be	AUX
iajs-1810	38	46	the	the	DET
iajs-1810	38	47	matrix	matrix	NOUN
iajs-1810	38	48	of	of	ADP
iajs-1810	38	49	new	new	ADJ
iajs-1810	38	50	infection	infection	NOUN
iajs-1810	38	51	individuals	individual	NOUN
iajs-1810	38	52	and	and	CCONJ
iajs-1810	38	53	ℳ	ℳ	PROPN
iajs-1810	38	54	𝑥	𝑥	PROPN
iajs-1810	38	55	is	be	AUX
iajs-1810	38	56	the	the	DET
iajs-1810	38	57	matrix	matrix	NOUN
iajs-1810	38	58	of	of	ADP
iajs-1810	38	59	transferred	transfer	VERB
iajs-1810	38	60	individuals	individual	NOUN
iajs-1810	38	61	between	between	ADP
iajs-1810	38	62	the	the	DET
iajs-1810	38	63	infected	infected	ADJ
iajs-1810	38	64	compartments	compartment	NOUN
iajs-1810	38	65	and	and	CCONJ
iajs-1810	38	66	out	out	ADP
iajs-1810	38	67	of	of	ADP
iajs-1810	38	68	the	the	DET
iajs-1810	38	69	infected	infected	ADJ
iajs-1810	38	70	compartments	compartment	NOUN
iajs-1810	38	71	.	.	PUNCT
iajs-1810	39	1	therefore	therefore	ADV
iajs-1810	39	2	ℋ	ℋ	VERB
iajs-1810	39	3	𝑥	𝑥	NOUN
iajs-1810	39	4	0	0	NUM
iajs-1810	39	5	0	0	NUM
iajs-1810	39	6	;	;	PUNCT
iajs-1810	39	7	ℳ	ℳ	PROPN
iajs-1810	39	8	𝑥	𝑥	PROPN
iajs-1810	39	9	𝛽𝑅	𝛽𝑅	PROPN
iajs-1810	39	10	𝛾	𝛾	PROPN
iajs-1810	39	11	1	1	NUM
iajs-1810	39	12	𝛿	𝛿	PROPN
iajs-1810	39	13	𝐼	𝐼	PROPN
iajs-1810	39	14	𝛼	𝛼	NOUN
iajs-1810	39	15	𝑘	𝑘	NOUN
iajs-1810	39	16	𝐼	𝐼	PROPN
iajs-1810	39	17	𝛼𝑆	𝛼𝑆	PROPN
iajs-1810	39	18	𝐴	𝐴	PROPN
iajs-1810	39	19	𝛼	𝛼	VERB
iajs-1810	39	20	𝛽	𝛽	PROPN
iajs-1810	39	21	𝑅	𝑅	PROPN
iajs-1810	39	22	𝛾	𝛾	PROPN
iajs-1810	39	23	1	1	NUM
iajs-1810	39	24	𝛿	𝛿	PROPN
iajs-1810	39	25	𝐼	𝐼	NOUN
iajs-1810	39	26	so	so	ADV
iajs-1810	39	27	the	the	DET
iajs-1810	39	28	derivative	derivative	NOUN
iajs-1810	39	29	of	of	ADP
iajs-1810	39	30	ℋ	ℋ	PROPN
iajs-1810	39	31	𝑥	𝑥	PROPN
iajs-1810	39	32	and	and	CCONJ
iajs-1810	39	33	ℳ	ℳ	PROPN
iajs-1810	39	34	𝑥	𝑥	PROPN
iajs-1810	39	35	,	,	PUNCT
iajs-1810	39	36	with	with	ADP
iajs-1810	39	37	respect	respect	NOUN
iajs-1810	39	38	to	to	ADP
iajs-1810	39	39	vector	vector	NOUN
iajs-1810	39	40	𝑥	𝑥	PROPN
iajs-1810	39	41	,	,	PUNCT
iajs-1810	39	42	at	at	ADP
iajs-1810	39	43	the	the	DET
iajs-1810	39	44	disease	disease	NOUN
iajs-1810	39	45	free	free	ADJ
iajs-1810	39	46	equilibrium	equilibrium	NOUN
iajs-1810	39	47	point	point	NOUN
iajs-1810	39	48	𝐸	𝐸	PROPN
iajs-1810	39	49	are	be	AUX
iajs-1810	39	50	computed	compute	VERB
iajs-1810	39	51	as	as	SCONJ
iajs-1810	39	52	follows	follow	VERB
iajs-1810	39	53	:	:	PUNCT
iajs-1810	39	54	𝐷ℋ	𝐷ℋ	NOUN
iajs-1810	39	55	x	x	SYM
iajs-1810	39	56	0	0	NUM
iajs-1810	39	57	0	0	NUM
iajs-1810	39	58	0	0	NUM
iajs-1810	39	59	0	0	NUM
iajs-1810	39	60	0	0	NUM
iajs-1810	39	61	0	0	NUM
iajs-1810	39	62	0	0	NUM
iajs-1810	39	63	0	0	X
iajs-1810	40	1	𝐻	𝐻	NOUN
iajs-1810	40	2	𝟎	𝟎	PROPN
iajs-1810	40	3	𝟎	𝟎	NUM
iajs-1810	40	4	𝟎	𝟎	NUM
iajs-1810	40	5	;	;	PUNCT
iajs-1810	40	6	ℳ	ℳ	PROPN
iajs-1810	40	7	𝑥	𝑥	NOUN
iajs-1810	40	8	𝛾	𝛾	PROPN
iajs-1810	40	9	1	1	NUM
iajs-1810	40	10	𝛿	𝛿	NOUN
iajs-1810	40	11	𝛼	𝛼	NOUN
iajs-1810	40	12	𝑘	𝑘	PRON
iajs-1810	40	13	0	0	NUM
iajs-1810	40	14	𝛽	𝛽	NOUN
iajs-1810	40	15	0	0	NUM
iajs-1810	40	16	0	0	NUM
iajs-1810	40	17	𝛾	𝛾	NOUN
iajs-1810	40	18	1	1	NUM
iajs-1810	40	19	𝛿	𝛿	NOUN
iajs-1810	40	20	0	0	NUM
iajs-1810	40	21	𝛼	𝛼	NOUN
iajs-1810	40	22	𝛽	𝛽	NOUN
iajs-1810	40	23	𝑀	𝑀	PROPN
iajs-1810	40	24	𝒋𝟏	𝒋𝟏	PROPN
iajs-1810	40	25	𝒋𝟐	𝒋𝟐	PROPN
iajs-1810	40	26	𝒋𝟑	𝒋𝟑	NOUN
iajs-1810	40	27	,	,	PUNCT
iajs-1810	40	28	where	where	SCONJ
iajs-1810	40	29	𝐻	𝐻	PROPN
iajs-1810	40	30	;	;	PUNCT
iajs-1810	40	31	and	and	CCONJ
iajs-1810	40	32	𝑀	𝑀	PROPN
iajs-1810	40	33	𝛾	𝛾	VERB
iajs-1810	40	34	1	1	NUM
iajs-1810	40	35	𝛿	𝛿	NOUN
iajs-1810	40	36	𝛼	𝛼	NOUN
iajs-1810	40	37	𝑘	𝑘	NOUN
iajs-1810	40	38	.	.	PUNCT
iajs-1810	41	1	consequently	consequently	ADV
iajs-1810	41	2	,	,	PUNCT
iajs-1810	41	3	according	accord	VERB
iajs-1810	41	4	to	to	ADP
iajs-1810	41	5	definition	definition	NOUN
iajs-1810	41	6	of	of	ADP
iajs-1810	41	7	𝑅	𝑅	PROPN
iajs-1810	41	8	that	that	PRON
iajs-1810	41	9	given	give	VERB
iajs-1810	41	10	in	in	ADP
iajs-1810	41	11	[	[	X
iajs-1810	41	12	2	2	NUM
iajs-1810	41	13	]	]	PUNCT
iajs-1810	41	14	,	,	PUNCT
iajs-1810	41	15	𝑅	𝑅	PROPN
iajs-1810	41	16	is	be	AUX
iajs-1810	41	17	equal	equal	ADJ
iajs-1810	41	18	to	to	ADP
iajs-1810	41	19	spectral	spectral	ADJ
iajs-1810	41	20	radius	radius	NOUN
iajs-1810	41	21	of	of	ADP
iajs-1810	41	22	new	new	ADJ
iajs-1810	41	23	generation	generation	NOUN
iajs-1810	41	24	matrix	matrix	NOUN
iajs-1810	41	25	ℋℳ	ℋℳ	NOUN
iajs-1810	41	26	.	.	PUNCT
iajs-1810	42	1	therefore	therefore	ADV
iajs-1810	42	2	,	,	PUNCT
iajs-1810	42	3	the	the	DET
iajs-1810	42	4	reproduction	reproduction	NOUN
iajs-1810	42	5	number	number	NOUN
iajs-1810	42	6	of	of	ADP
iajs-1810	42	7	model	model	NOUN
iajs-1810	42	8	(	(	PUNCT
iajs-1810	42	9	2	2	NUM
iajs-1810	42	10	)	)	PUNCT
iajs-1810	42	11	is	be	AUX
iajs-1810	42	12	given	give	VERB
iajs-1810	42	13	by	by	ADP
iajs-1810	42	14	𝑹𝟎	𝑹𝟎	PROPN
iajs-1810	42	15	𝝆	𝝆	PROPN
iajs-1810	42	16	𝓗𝓜	𝓗𝓜	PROPN
iajs-1810	42	17	𝟏	𝟏	PROPN
iajs-1810	42	18	𝒂𝑨	𝒂𝑨	NOUN
iajs-1810	42	19	𝜶	𝜶	NOUN
iajs-1810	42	20	𝒃𝑨	𝒃𝑨	NOUN
iajs-1810	42	21	𝜸	𝜸	X
iajs-1810	42	22	𝟏	𝟏	NUM
iajs-1810	42	23	𝜹	𝜹	NOUN
iajs-1810	42	24	𝜶	𝜶	X
iajs-1810	42	25	𝒌	𝒌	PROPN
iajs-1810	42	26	…	…	PUNCT
iajs-1810	42	27	…	…	PUNCT
iajs-1810	42	28	…	…	PUNCT
iajs-1810	42	29	(	(	PUNCT
iajs-1810	42	30	8)	8)	NUM
iajs-1810	42	31	theorem	theorem	NOUN
iajs-1810	42	32	2	2	NUM
iajs-1810	42	33	:	:	PUNCT
iajs-1810	42	34	the	the	DET
iajs-1810	42	35	disease	disease	NOUN
iajs-1810	42	36	free	free	ADJ
iajs-1810	42	37	equilibrium	equilibrium	NOUN
iajs-1810	42	38	point	point	NOUN
iajs-1810	42	39	dfe	dfe	PROPN
iajs-1810	42	40	of	of	ADP
iajs-1810	42	41	model	model	NOUN
iajs-1810	42	42	(	(	PUNCT
iajs-1810	42	43	2	2	NUM
iajs-1810	42	44	)	)	PUNCT
iajs-1810	42	45	is	be	AUX
iajs-1810	42	46	locally	locally	ADV
iajs-1810	42	47	asymptotically	asymptotically	ADV
iajs-1810	42	48	stable	stable	ADJ
iajs-1810	42	49	provided	provide	VERB
iajs-1810	42	50	that	that	SCONJ
iajs-1810	42	51	𝑅	𝑅	PROPN
iajs-1810	42	52	1	1	NUM
iajs-1810	42	53	…	…	PUNCT
iajs-1810	42	54	(	(	PUNCT
iajs-1810	42	55	9a	9a	NOUN
iajs-1810	42	56	)	)	PUNCT
iajs-1810	42	57	.	.	PUNCT
iajs-1810	43	1	while	while	SCONJ
iajs-1810	43	2	its	its	PRON
iajs-1810	43	3	unstable	unstable	ADJ
iajs-1810	43	4	for	for	ADP
iajs-1810	43	5	𝑅	𝑅	PROPN
iajs-1810	43	6	1	1	NUM
iajs-1810	43	7	...	...	PUNCT
iajs-1810	43	8	(	(	PUNCT
iajs-1810	43	9	9b	9b	NOUN
iajs-1810	43	10	)	)	PUNCT
iajs-1810	43	11	proof	proof	NOUN
iajs-1810	43	12	the	the	DET
iajs-1810	43	13	jacobian	jacobian	ADJ
iajs-1810	43	14	matrix	matrix	NOUN
iajs-1810	43	15	of	of	ADP
iajs-1810	43	16	model	model	NOUN
iajs-1810	43	17	(	(	PUNCT
iajs-1810	43	18	2	2	NUM
iajs-1810	43	19	)	)	PUNCT
iajs-1810	43	20	at	at	ADP
iajs-1810	43	21	𝐸	𝐸	PROPN
iajs-1810	43	22	can	can	AUX
iajs-1810	43	23	be	be	AUX
iajs-1810	43	24	written	write	VERB
iajs-1810	43	25	as	as	ADP
iajs-1810	43	26	:	:	PUNCT
iajs-1810	43	27	ihsciconf	ihsciconf	NOUN
iajs-1810	43	28	2017	2017	NUM
iajs-1810	43	29	special	special	ADJ
iajs-1810	43	30	issue	issue	NOUN
iajs-1810	43	31	ibn	ibn	PROPN
iajs-1810	43	32	al	al	PROPN
iajs-1810	43	33	-	-	PUNCT
iajs-1810	43	34	haitham	haitham	PROPN
iajs-1810	43	35	journal	journal	PROPN
iajs-1810	43	36	for	for	ADP
iajs-1810	43	37	pure	pure	ADJ
iajs-1810	43	38	and	and	CCONJ
iajs-1810	43	39	applied	apply	VERB
iajs-1810	43	40	science	science	NOUN
iajs-1810	43	41	https://doi.org/	https://doi.org/	VERB
iajs-1810	43	42	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	43	43	for	for	ADP
iajs-1810	43	44	more	more	ADJ
iajs-1810	43	45	information	information	NOUN
iajs-1810	43	46	about	about	ADP
iajs-1810	43	47	the	the	DET
iajs-1810	43	48	conference	conference	NOUN
iajs-1810	43	49	please	please	INTJ
iajs-1810	43	50	visit	visit	VERB
iajs-1810	43	51	the	the	DET
iajs-1810	43	52	websites	website	NOUN
iajs-1810	43	53	:	:	PUNCT
iajs-1810	43	54	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	43	55	  	  	SPACE
iajs-1810	43	56	www.ihsciconf.org	www.ihsciconf.org	NOUN
iajs-1810	43	57	   	   	SPACE
iajs-1810	43	58	mathematics|515	mathematics|515	PROPN
iajs-1810	43	59	    	    	SPACE
iajs-1810	44	1	𝐽	𝐽	PROPN
iajs-1810	44	2	𝐸	𝐸	NOUN
iajs-1810	44	3	𝑏	𝑏	NOUN
iajs-1810	44	4	⎣	⎣	ADJ
iajs-1810	44	5	⎢	⎢	NOUN
iajs-1810	44	6	⎢	⎢	NOUN
iajs-1810	44	7	⎡	⎡	VERB
iajs-1810	44	8	𝛼	𝛼	NOUN
iajs-1810	44	9	0	0	NUM
iajs-1810	44	10	0	0	NUM
iajs-1810	44	11	𝛾	𝛾	ADP
iajs-1810	44	12	1	1	NUM
iajs-1810	44	13	𝛿	𝛿	NOUN
iajs-1810	44	14	𝛼	𝛼	NOUN
iajs-1810	44	15	𝑘	𝑘	PRON
iajs-1810	44	16	𝛽	𝛽	NOUN
iajs-1810	44	17	0	0	NUM
iajs-1810	44	18	𝛾	𝛾	PROPN
iajs-1810	44	19	1	1	NUM
iajs-1810	44	20	𝛿	𝛿	NOUN
iajs-1810	44	21	𝛼	𝛼	PROPN
iajs-1810	44	22	𝛽	𝛽	PROPN
iajs-1810	44	23	⎦	⎦	NOUN
iajs-1810	44	24	⎥	⎥	PROPN
iajs-1810	44	25	⎥	⎥	PROPN
iajs-1810	44	26	⎤	⎤	PROPN
iajs-1810	44	27	…	…	PUNCT
iajs-1810	44	28	..	..	PUNCT
iajs-1810	44	29	(	(	PUNCT
iajs-1810	44	30	10a	10a	NOUN
iajs-1810	44	31	)	)	PUNCT
iajs-1810	44	32	then	then	ADV
iajs-1810	44	33	the	the	DET
iajs-1810	44	34	characteristic	characteristic	ADJ
iajs-1810	44	35	equation	equation	NOUN
iajs-1810	44	36	of	of	ADP
iajs-1810	44	37	𝐽	𝐽	PROPN
iajs-1810	44	38	𝐸	𝐸	PROPN
iajs-1810	44	39	is	be	AUX
iajs-1810	44	40	given	give	VERB
iajs-1810	44	41	by	by	ADP
iajs-1810	44	42	𝜆	𝜆	PROPN
iajs-1810	44	43	ω	ω	PROPN
iajs-1810	44	44	𝜆	𝜆	PROPN
iajs-1810	44	45	ω	ω	PROPN
iajs-1810	44	46	𝜆	𝜆	PROPN
iajs-1810	44	47	ω	ω	PROPN
iajs-1810	44	48	0	0	NUM
iajs-1810	44	49	…	…	PUNCT
iajs-1810	44	50	…	…	PUNCT
iajs-1810	44	51	…	…	PUNCT
iajs-1810	44	52	(	(	PUNCT
iajs-1810	44	53	10b	10b	NOUN
iajs-1810	44	54	)	)	PUNCT
iajs-1810	44	55	where	where	SCONJ
iajs-1810	44	56	:	:	PUNCT
iajs-1810	44	57	ω	ω	NUM
iajs-1810	44	58	𝑏	𝑏	NOUN
iajs-1810	44	59	𝑏	𝑏	NOUN
iajs-1810	45	1	𝑏	𝑏	PROPN
iajs-1810	45	2	ω	ω	NUM
iajs-1810	45	3	𝑏	𝑏	NOUN
iajs-1810	45	4	𝑏	𝑏	PROPN
iajs-1810	45	5	𝑏	𝑏	PROPN
iajs-1810	45	6	𝑏	𝑏	PROPN
iajs-1810	45	7	𝑏	𝑏	PROPN
iajs-1810	45	8	𝑏	𝑏	PROPN
iajs-1810	45	9	𝑏	𝑏	PROPN
iajs-1810	45	10	𝑏	𝑏	PROPN
iajs-1810	45	11	𝑏	𝑏	PROPN
iajs-1810	45	12	𝑏	𝑏	PROPN
iajs-1810	45	13	𝑏	𝑏	PROPN
iajs-1810	45	14	𝑏	𝑏	PROPN
iajs-1810	45	15	ω	ω	NUM
iajs-1810	45	16	𝑏	𝑏	NOUN
iajs-1810	45	17	𝑏	𝑏	PROPN
iajs-1810	45	18	𝑏	𝑏	PROPN
iajs-1810	45	19	𝑏	𝑏	PROPN
iajs-1810	45	20	𝑏	𝑏	PROPN
iajs-1810	45	21	𝑏	𝑏	NOUN
iajs-1810	45	22	further	far	ADV
iajs-1810	45	23	:	:	PUNCT
iajs-1810	45	24	δ	δ	PROPN
iajs-1810	45	25	ω	ω	PROPN
iajs-1810	45	26	ω	ω	PROPN
iajs-1810	45	27	ω	ω	PROPN
iajs-1810	45	28	now	now	ADV
iajs-1810	45	29	according	accord	VERB
iajs-1810	45	30	to	to	ADP
iajs-1810	45	31	(	(	PUNCT
iajs-1810	45	32	routh	routh	PROPN
iajs-1810	45	33	-	-	PUNCT
iajs-1810	45	34	hurwitz	hurwitz	PROPN
iajs-1810	45	35	)	)	PUNCT
iajs-1810	45	36	criterion	criterion	NOUN
iajs-1810	45	37	[	[	X
iajs-1810	45	38	13	13	NUM
iajs-1810	45	39	]	]	PUNCT
iajs-1810	45	40	,	,	PUNCT
iajs-1810	45	41	e0	e0	PROPN
iajs-1810	45	42	is	be	AUX
iajs-1810	45	43	locally	locally	ADV
iajs-1810	45	44	asymptotically	asymptotically	ADV
iajs-1810	45	45	stable	stable	ADJ
iajs-1810	45	46	provided	provide	VERB
iajs-1810	45	47	that	that	SCONJ
iajs-1810	45	48	ω	ω	NOUN
iajs-1810	45	49	0	0	PUNCT
iajs-1810	45	50	if	if	SCONJ
iajs-1810	45	51	𝑏	𝑏	PROPN
iajs-1810	45	52	0	0	NUM
iajs-1810	45	53	,	,	PUNCT
iajs-1810	45	54	ω	ω	NOUN
iajs-1810	45	55	0	0	PUNCT
iajs-1810	45	56	if	if	SCONJ
iajs-1810	45	57	𝑏	𝑏	PROPN
iajs-1810	45	58	0	0	NUM
iajs-1810	45	59	,	,	PUNCT
iajs-1810	45	60	and	and	CCONJ
iajs-1810	45	61	δ	δ	PROPN
iajs-1810	45	62	0	0	PUNCT
iajs-1810	46	1	if	if	SCONJ
iajs-1810	46	2	𝑏	𝑏	PROPN
iajs-1810	46	3	0	0	NUM
iajs-1810	46	4	,	,	PUNCT
iajs-1810	46	5	i.e.	i.e.	X
iajs-1810	46	6	𝑅	𝑅	PROPN
iajs-1810	46	7	1	1	PROPN
iajs-1810	46	8	.	.	PUNCT
iajs-1810	47	1	clearly	clearly	ADV
iajs-1810	47	2	ω	ω	PROPN
iajs-1810	47	3	0	0	NUM
iajs-1810	47	4	,	,	PUNCT
iajs-1810	47	5	ω	ω	NOUN
iajs-1810	47	6	0	0	NUM
iajs-1810	47	7	,	,	PUNCT
iajs-1810	47	8	and	and	CCONJ
iajs-1810	47	9	δ	δ	PROPN
iajs-1810	47	10	0	0	NUM
iajs-1810	47	11	holds	hold	VERB
iajs-1810	47	12	in	in	ADP
iajs-1810	47	13	case	case	NOUN
iajs-1810	47	14	condition	condition	NOUN
iajs-1810	47	15	(	(	PUNCT
iajs-1810	47	16	9a	9a	NOUN
iajs-1810	47	17	)	)	PUNCT
iajs-1810	47	18	satisfied	satisfied	ADJ
iajs-1810	47	19	.	.	PUNCT
iajs-1810	48	1	however	however	ADV
iajs-1810	48	2	if	if	SCONJ
iajs-1810	48	3	condition	condition	NOUN
iajs-1810	48	4	(	(	PUNCT
iajs-1810	48	5	10a	10a	NOUN
iajs-1810	48	6	)	)	PUNCT
iajs-1810	48	7	happened	happen	VERB
iajs-1810	48	8	then	then	ADV
iajs-1810	48	9	ω	ω	PROPN
iajs-1810	48	10	0	0	NUM
iajs-1810	48	11	,	,	PUNCT
iajs-1810	48	12	and	and	CCONJ
iajs-1810	48	13	e0	e0	PROPN
iajs-1810	48	14	in	in	ADP
iajs-1810	48	15	this	this	DET
iajs-1810	48	16	case	case	NOUN
iajs-1810	48	17	is	be	AUX
iajs-1810	48	18	unstable	unstable	ADJ
iajs-1810	48	19	equilibrium	equilibrium	NOUN
iajs-1810	48	20	point	point	NOUN
iajs-1810	48	21	.	.	PUNCT
iajs-1810	49	1	prove	prove	VERB
iajs-1810	49	2	complete	complete	ADJ
iajs-1810	49	3	∎	∎	PROPN
iajs-1810	49	4	theorem	theorem	VERB
iajs-1810	49	5	3	3	NUM
iajs-1810	49	6	:	:	PUNCT
iajs-1810	49	7	the	the	DET
iajs-1810	49	8	endemic	endemic	ADJ
iajs-1810	49	9	equilibrium	equilibrium	NOUN
iajs-1810	49	10	point	point	NOUN
iajs-1810	49	11	𝐸	𝐸	PROPN
iajs-1810	49	12	𝑆	𝑆	PROPN
iajs-1810	49	13	,	,	PUNCT
iajs-1810	49	14	𝐼	𝐼	PROPN
iajs-1810	49	15	,	,	PUNCT
iajs-1810	49	16	𝑅	𝑅	PROPN
iajs-1810	49	17	of	of	ADP
iajs-1810	49	18	model	model	NOUN
iajs-1810	49	19	(	(	PUNCT
iajs-1810	49	20	2	2	NUM
iajs-1810	49	21	)	)	PUNCT
iajs-1810	49	22	is	be	AUX
iajs-1810	49	23	locally	locally	ADV
iajs-1810	49	24	asymptotically	asymptotically	ADV
iajs-1810	49	25	stable	stable	ADJ
iajs-1810	49	26	,	,	PUNCT
iajs-1810	49	27	provided	provide	VERB
iajs-1810	49	28	that	that	SCONJ
iajs-1810	49	29	1	1	NUM
iajs-1810	49	30	𝑅	𝑅	PROPN
iajs-1810	49	31	…	…	PUNCT
iajs-1810	49	32	…	…	PUNCT
iajs-1810	49	33	..	..	PUNCT
iajs-1810	49	34	(	(	PUNCT
iajs-1810	49	35	11	11	X
iajs-1810	49	36	)	)	PUNCT
iajs-1810	49	37	proof	proof	NOUN
iajs-1810	49	38	the	the	DET
iajs-1810	49	39	jacobian	jacobian	ADJ
iajs-1810	49	40	matrix	matrix	NOUN
iajs-1810	49	41	of	of	ADP
iajs-1810	49	42	model	model	NOUN
iajs-1810	49	43	(	(	PUNCT
iajs-1810	49	44	2	2	NUM
iajs-1810	49	45	)	)	PUNCT
iajs-1810	49	46	at	at	ADP
iajs-1810	49	47	the	the	DET
iajs-1810	49	48	endemic	endemic	ADJ
iajs-1810	49	49	equilibrium	equilibrium	NOUN
iajs-1810	49	50	point	point	NOUN
iajs-1810	49	51	e1	e1	NOUN
iajs-1810	49	52	can	can	AUX
iajs-1810	49	53	be	be	AUX
iajs-1810	49	54	written	write	VERB
iajs-1810	49	55	as	as	ADP
iajs-1810	49	56	:	:	PUNCT
iajs-1810	49	57	𝐽	𝐽	PROPN
iajs-1810	49	58	𝐸	𝐸	PROPN
iajs-1810	49	59	𝑐	𝑐	PROPN
iajs-1810	49	60	⎣	⎣	ADJ
iajs-1810	49	61	⎢	⎢	NOUN
iajs-1810	49	62	⎢	⎢	NOUN
iajs-1810	49	63	⎢	⎢	NOUN
iajs-1810	49	64	⎡	⎡	VERB
iajs-1810	49	65	𝛼	𝛼	NOUN
iajs-1810	49	66	0	0	NUM
iajs-1810	49	67	𝛾	𝛾	PROPN
iajs-1810	49	68	1	1	NUM
iajs-1810	49	69	𝛿	𝛿	NOUN
iajs-1810	49	70	𝛼	𝛼	NOUN
iajs-1810	49	71	𝑘	𝑘	PRON
iajs-1810	49	72	𝛽	𝛽	NOUN
iajs-1810	49	73	0	0	NUM
iajs-1810	49	74	𝛾	𝛾	PROPN
iajs-1810	49	75	1	1	NUM
iajs-1810	49	76	𝛿	𝛿	NOUN
iajs-1810	49	77	𝛼	𝛼	PROPN
iajs-1810	49	78	𝛽	𝛽	PROPN
iajs-1810	49	79	⎦	⎦	NOUN
iajs-1810	49	80	⎥	⎥	PROPN
iajs-1810	49	81	⎥	⎥	PROPN
iajs-1810	49	82	⎥	⎥	PROPN
iajs-1810	49	83	⎤	⎤	PROPN
iajs-1810	49	84	then	then	ADV
iajs-1810	49	85	the	the	DET
iajs-1810	49	86	characteristic	characteristic	ADJ
iajs-1810	49	87	equation	equation	NOUN
iajs-1810	49	88	of	of	ADP
iajs-1810	49	89	𝐽	𝐽	PROPN
iajs-1810	49	90	𝐸	𝐸	PROPN
iajs-1810	49	91	is	be	AUX
iajs-1810	49	92	given	give	VERB
iajs-1810	49	93	by	by	ADP
iajs-1810	49	94	𝜆	𝜆	PROPN
iajs-1810	49	95	ω	ω	PROPN
iajs-1810	49	96	𝜆	𝜆	PROPN
iajs-1810	49	97	ω	ω	PROPN
iajs-1810	49	98	𝜆	𝜆	PROPN
iajs-1810	49	99	ω	ω	PROPN
iajs-1810	49	100	0	0	NUM
iajs-1810	49	101	..	..	PUNCT
iajs-1810	49	102	(	(	PUNCT
iajs-1810	49	103	10b	10b	NOUN
iajs-1810	49	104	)	)	PUNCT
iajs-1810	49	105	,	,	PUNCT
iajs-1810	49	106	where	where	SCONJ
iajs-1810	49	107	:	:	PUNCT
iajs-1810	49	108	ihsciconf	ihsciconf	NOUN
iajs-1810	49	109	2017	2017	NUM
iajs-1810	49	110	special	special	ADJ
iajs-1810	49	111	issue	issue	NOUN
iajs-1810	49	112	ibn	ibn	PROPN
iajs-1810	49	113	al	al	PROPN
iajs-1810	49	114	-	-	PUNCT
iajs-1810	49	115	haitham	haitham	PROPN
iajs-1810	49	116	journal	journal	PROPN
iajs-1810	49	117	for	for	ADP
iajs-1810	49	118	pure	pure	ADJ
iajs-1810	49	119	and	and	CCONJ
iajs-1810	49	120	applied	apply	VERB
iajs-1810	49	121	science	science	NOUN
iajs-1810	49	122	https://doi.org/	https://doi.org/	VERB
iajs-1810	49	123	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	49	124	for	for	ADP
iajs-1810	49	125	more	more	ADJ
iajs-1810	49	126	information	information	NOUN
iajs-1810	49	127	about	about	ADP
iajs-1810	49	128	the	the	DET
iajs-1810	49	129	conference	conference	NOUN
iajs-1810	49	130	please	please	INTJ
iajs-1810	49	131	visit	visit	VERB
iajs-1810	49	132	the	the	DET
iajs-1810	49	133	websites	website	NOUN
iajs-1810	49	134	:	:	PUNCT
iajs-1810	49	135	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	49	136	  	  	SPACE
iajs-1810	49	137	www.ihsciconf.org	www.ihsciconf.org	NOUN
iajs-1810	49	138	   	   	SPACE
iajs-1810	49	139	mathematics|516	mathematics|516	NOUN
iajs-1810	49	140	    	    	SPACE
iajs-1810	49	141	ω	ω	PROPN
iajs-1810	49	142	𝑐	𝑐	PROPN
iajs-1810	49	143	𝑐	𝑐	PROPN
iajs-1810	49	144	𝑐	𝑐	PROPN
iajs-1810	49	145	ω	ω	PROPN
iajs-1810	49	146	𝑐	𝑐	PROPN
iajs-1810	49	147	𝑐	𝑐	X
iajs-1810	49	148	𝑐	𝑐	X
iajs-1810	49	149	𝑐	𝑐	VERB
iajs-1810	49	150	𝑐	𝑐	VERB
iajs-1810	49	151	𝑐	𝑐	VERB
iajs-1810	49	152	𝑐	𝑐	VERB
iajs-1810	49	153	𝑐	𝑐	VERB
iajs-1810	49	154	𝑐	𝑐	VERB
iajs-1810	49	155	𝑐	𝑐	VERB
iajs-1810	49	156	𝑐	𝑐	VERB
iajs-1810	49	157	𝑐	𝑐	PROPN
iajs-1810	49	158	ω	ω	PROPN
iajs-1810	49	159	𝑐	𝑐	PROPN
iajs-1810	49	160	𝑐	𝑐	X
iajs-1810	49	161	𝑐	𝑐	X
iajs-1810	49	162	𝑐	𝑐	VERB
iajs-1810	49	163	𝑐	𝑐	VERB
iajs-1810	49	164	𝑐	𝑐	VERB
iajs-1810	49	165	𝑐	𝑐	VERB
iajs-1810	49	166	𝑐	𝑐	NOUN
iajs-1810	49	167	𝑐	𝑐	NOUN
iajs-1810	49	168	further	far	ADV
iajs-1810	49	169	:	:	PUNCT
iajs-1810	49	170	δ	δ	PROPN
iajs-1810	49	171	ω	ω	PROPN
iajs-1810	49	172	ω	ω	PROPN
iajs-1810	49	173	ω	ω	PROPN
iajs-1810	49	174	now	now	ADV
iajs-1810	49	175	according	accord	VERB
iajs-1810	49	176	to	to	ADP
iajs-1810	49	177	(	(	PUNCT
iajs-1810	49	178	routh	routh	PROPN
iajs-1810	49	179	-	-	PUNCT
iajs-1810	49	180	hurwitz	hurwitz	PROPN
iajs-1810	49	181	)	)	PUNCT
iajs-1810	49	182	criterion	criterion	NOUN
iajs-1810	50	1	[	[	X
iajs-1810	50	2	13	13	NUM
iajs-1810	50	3	]	]	PUNCT
iajs-1810	50	4	,	,	PUNCT
iajs-1810	50	5	e1	e1	PROPN
iajs-1810	50	6	is	be	AUX
iajs-1810	50	7	locally	locally	ADV
iajs-1810	50	8	asymptotically	asymptotically	ADV
iajs-1810	50	9	stable	stable	ADJ
iajs-1810	50	10	provided	provide	VERB
iajs-1810	50	11	that	that	SCONJ
iajs-1810	50	12	ω	ω	PROPN
iajs-1810	50	13	0	0	NUM
iajs-1810	50	14	,	,	PUNCT
iajs-1810	50	15	ω	ω	NOUN
iajs-1810	50	16	0	0	NUM
iajs-1810	50	17	,	,	PUNCT
iajs-1810	50	18	and	and	CCONJ
iajs-1810	50	19	δ	δ	PROPN
iajs-1810	50	20	0	0	NUM
iajs-1810	50	21	.	.	PUNCT
iajs-1810	51	1	it	it	PRON
iajs-1810	51	2	is	be	AUX
iajs-1810	51	3	easy	easy	ADJ
iajs-1810	51	4	to	to	PART
iajs-1810	51	5	verify	verify	VERB
iajs-1810	51	6	that	that	SCONJ
iajs-1810	51	7	ω	ω	PROPN
iajs-1810	51	8	0	0	PROPN
iajs-1810	51	9	,	,	PUNCT
iajs-1810	51	10	ω	ω	NOUN
iajs-1810	51	11	0	0	NUM
iajs-1810	51	12	,	,	PUNCT
iajs-1810	51	13	and	and	CCONJ
iajs-1810	51	14	δ	δ	PROPN
iajs-1810	51	15	0	0	NUM
iajs-1810	51	16	holds	hold	VERB
iajs-1810	51	17	in	in	ADP
iajs-1810	51	18	case	case	NOUN
iajs-1810	51	19	condition	condition	NOUN
iajs-1810	51	20	(	(	PUNCT
iajs-1810	51	21	11	11	NUM
iajs-1810	51	22	)	)	PUNCT
iajs-1810	51	23	come	come	VERB
iajs-1810	51	24	true	true	ADJ
iajs-1810	51	25	.	.	PUNCT
iajs-1810	52	1	prove	prove	VERB
iajs-1810	52	2	complete	complete	ADJ
iajs-1810	52	3	∎	∎	PROPN
iajs-1810	52	4	theorem	theorem	VERB
iajs-1810	52	5	4	4	NUM
iajs-1810	52	6	:	:	PUNCT
iajs-1810	52	7	assume	assume	VERB
iajs-1810	52	8	that	that	SCONJ
iajs-1810	52	9	the	the	DET
iajs-1810	52	10	disease	disease	NOUN
iajs-1810	52	11	free	free	ADJ
iajs-1810	52	12	equilibrium	equilibrium	NOUN
iajs-1810	52	13	point	point	NOUN
iajs-1810	52	14	of	of	ADP
iajs-1810	52	15	model	model	NOUN
iajs-1810	52	16	(	(	PUNCT
iajs-1810	52	17	2	2	NUM
iajs-1810	52	18	)	)	PUNCT
iajs-1810	52	19	is	be	AUX
iajs-1810	52	20	locally	locally	ADV
iajs-1810	52	21	asymptotically	asymptotically	ADV
iajs-1810	52	22	stable	stable	ADJ
iajs-1810	52	23	then	then	ADV
iajs-1810	52	24	it	it	PRON
iajs-1810	52	25	’s	’	VERB
iajs-1810	52	26	globally	globally	ADV
iajs-1810	52	27	asymptotically	asymptotically	ADV
iajs-1810	52	28	stable	stable	ADJ
iajs-1810	52	29	for	for	ADP
iajs-1810	52	30	all	all	PRON
iajs-1810	52	31	:	:	PUNCT
iajs-1810	52	32	s	s	X
iajs-1810	52	33	>	>	X
iajs-1810	52	34	0	0	NUM
iajs-1810	52	35	,	,	PUNCT
iajs-1810	53	1	i	i	PRON
iajs-1810	53	2	⩾	⩾	VERB
iajs-1810	53	3	0	0	PUNCT
iajs-1810	53	4	and	and	CCONJ
iajs-1810	53	5	r	r	NOUN
iajs-1810	53	6	⩾	⩾	NOUN
iajs-1810	53	7	0	0	NUM
iajs-1810	53	8	…	…	PUNCT
iajs-1810	53	9	…	…	PUNCT
iajs-1810	53	10	.(12	.(12	NUM
iajs-1810	53	11	)	)	PUNCT
iajs-1810	53	12	proof	proof	NOUN
iajs-1810	53	13	let	let	VERB
iajs-1810	53	14	𝒲	𝒲	NOUN
iajs-1810	53	15	s	s	NOUN
iajs-1810	53	16	s	s	NOUN
iajs-1810	53	17	s	s	X
iajs-1810	53	18	ln	ln	NOUN
iajs-1810	54	1	i	i	NOUN
iajs-1810	54	2	r	r	NOUN
iajs-1810	54	3	,	,	PUNCT
iajs-1810	54	4	clearly	clearly	ADV
iajs-1810	54	5	𝒲	𝒲	NOUN
iajs-1810	54	6	:	:	PUNCT
iajs-1810	54	7	ℝ	ℝ	PROPN
iajs-1810	54	8	→	→	SYM
iajs-1810	54	9	ℝ	ℝ	PROPN
iajs-1810	54	10	is	be	AUX
iajs-1810	54	11	continuously	continuously	ADV
iajs-1810	54	12	differential	differential	ADJ
iajs-1810	54	13	function	function	NOUN
iajs-1810	54	14	such	such	ADJ
iajs-1810	54	15	that	that	SCONJ
iajs-1810	54	16	𝒲	𝒲	PROPN
iajs-1810	54	17	s	s	PART
iajs-1810	54	18	,	,	PUNCT
iajs-1810	54	19	0,0	0,0	NUM
iajs-1810	54	20	0	0	NUM
iajs-1810	54	21	,	,	PUNCT
iajs-1810	54	22	and	and	CCONJ
iajs-1810	54	23	𝒲	𝒲	NOUN
iajs-1810	54	24	s	s	PROPN
iajs-1810	54	25	,	,	PUNCT
iajs-1810	54	26	i	i	PRON
iajs-1810	54	27	,	,	PUNCT
iajs-1810	54	28	r	r	NOUN
iajs-1810	54	29	0	0	NUM
iajs-1810	54	30	;	;	PUNCT
iajs-1810	54	31	∀	∀	X
iajs-1810	54	32	s	s	X
iajs-1810	54	33	,	,	PUNCT
iajs-1810	54	34	i	i	PRON
iajs-1810	54	35	,	,	PUNCT
iajs-1810	54	36	r	r	PROPN
iajs-1810	54	37	s	s	PROPN
iajs-1810	54	38	,	,	PUNCT
iajs-1810	54	39	0,0	0,0	NUM
iajs-1810	54	40	.	.	PUNCT
iajs-1810	55	1	differentiating	differentiate	VERB
iajs-1810	55	2	𝒲	𝒲	NOUN
iajs-1810	55	3	with	with	ADP
iajs-1810	55	4	respect	respect	NOUN
iajs-1810	55	5	to	to	ADP
iajs-1810	55	6	time	time	NOUN
iajs-1810	55	7	and	and	CCONJ
iajs-1810	55	8	then	then	ADV
iajs-1810	55	9	after	after	ADP
iajs-1810	55	10	doing	do	VERB
iajs-1810	55	11	some	some	DET
iajs-1810	55	12	algebraic	algebraic	ADJ
iajs-1810	55	13	computation	computation	NOUN
iajs-1810	55	14	,	,	PUNCT
iajs-1810	55	15	we	we	PRON
iajs-1810	55	16	have	have	VERB
iajs-1810	55	17	:	:	PUNCT
iajs-1810	55	18	𝒲	𝒲	NOUN
iajs-1810	56	1	α	α	NOUN
iajs-1810	56	2	α	α	NOUN
iajs-1810	56	3	r	r	NOUN
iajs-1810	56	4	i	i	PRON
iajs-1810	56	5	ki	ki	INTJ
iajs-1810	56	6	clearly	clearly	ADV
iajs-1810	56	7	condition	condition	NOUN
iajs-1810	56	8	(	(	PUNCT
iajs-1810	56	9	12	12	NUM
iajs-1810	56	10	)	)	PUNCT
iajs-1810	56	11	guarantee	guarantee	VERB
iajs-1810	56	12	that	that	SCONJ
iajs-1810	56	13	𝒲	𝒲	NOUN
iajs-1810	56	14	0	0	NUM
iajs-1810	56	15	.	.	PUNCT
iajs-1810	57	1	hence	hence	ADV
iajs-1810	57	2	according	accord	VERB
iajs-1810	57	3	to	to	ADP
iajs-1810	57	4	lyapunov	lyapunov	PROPN
iajs-1810	57	5	second	second	ADJ
iajs-1810	57	6	theorem	theorem	NOUN
iajs-1810	57	7	[	[	X
iajs-1810	57	8	14	14	NUM
iajs-1810	57	9	]	]	PUNCT
iajs-1810	57	10	,	,	PUNCT
iajs-1810	57	11	of	of	ADP
iajs-1810	57	12	stability	stability	NOUN
iajs-1810	57	13	the	the	DET
iajs-1810	57	14	free	free	ADJ
iajs-1810	57	15	disease	disease	NOUN
iajs-1810	57	16	equilibrium	equilibrium	NOUN
iajs-1810	57	17	point	point	NOUN
iajs-1810	57	18	𝐸	𝐸	PROPN
iajs-1810	57	19	is	be	AUX
iajs-1810	57	20	locally	locally	ADV
iajs-1810	57	21	asymptotically	asymptotically	ADV
iajs-1810	57	22	stable	stable	ADJ
iajs-1810	57	23	and	and	CCONJ
iajs-1810	57	24	the	the	DET
iajs-1810	57	25	proof	proof	NOUN
iajs-1810	57	26	is	be	AUX
iajs-1810	57	27	complete	complete	ADJ
iajs-1810	57	28	.	.	PUNCT
iajs-1810	58	1	■	■	PUNCT
iajs-1810	58	2	next	next	ADJ
iajs-1810	58	3	theorem	theorem	NOUN
iajs-1810	58	4	establishes	establish	VERB
iajs-1810	58	5	the	the	DET
iajs-1810	58	6	global	global	ADJ
iajs-1810	58	7	stability	stability	NOUN
iajs-1810	58	8	conditions	condition	NOUN
iajs-1810	58	9	for	for	ADP
iajs-1810	58	10	the	the	DET
iajs-1810	58	11	endemic	endemic	ADJ
iajs-1810	58	12	equilibrium	equilibrium	NOUN
iajs-1810	58	13	point	point	NOUN
iajs-1810	58	14	of	of	ADP
iajs-1810	58	15	model	model	NOUN
iajs-1810	58	16	(	(	PUNCT
iajs-1810	58	17	2	2	NUM
iajs-1810	58	18	)	)	PUNCT
iajs-1810	58	19	.	.	PUNCT
iajs-1810	59	1	theorem	theorem	ADJ
iajs-1810	59	2	5	5	NUM
iajs-1810	59	3	assume	assume	VERB
iajs-1810	59	4	that	that	SCONJ
iajs-1810	59	5	the	the	DET
iajs-1810	59	6	endemic	endemic	ADJ
iajs-1810	59	7	equilibrium	equilibrium	NOUN
iajs-1810	59	8	point	point	NOUN
iajs-1810	59	9	𝐸	𝐸	PROPN
iajs-1810	59	10	,	,	PUNCT
iajs-1810	59	11	of	of	ADP
iajs-1810	59	12	model	model	NOUN
iajs-1810	59	13	(	(	PUNCT
iajs-1810	59	14	2	2	NUM
iajs-1810	59	15	)	)	PUNCT
iajs-1810	59	16	is	be	AUX
iajs-1810	59	17	locally	locally	ADV
iajs-1810	59	18	asymptotically	asymptotically	ADV
iajs-1810	59	19	stable	stable	ADJ
iajs-1810	59	20	,	,	PUNCT
iajs-1810	59	21	then	then	ADV
iajs-1810	59	22	its	its	PRON
iajs-1810	59	23	globally	globally	ADV
iajs-1810	59	24	asymptotically	asymptotically	ADV
iajs-1810	59	25	stable	stable	ADJ
iajs-1810	59	26	for	for	ADP
iajs-1810	59	27	all	all	PRON
iajs-1810	59	28	:	:	PUNCT
iajs-1810	59	29	s	s	X
iajs-1810	59	30	>	>	X
iajs-1810	59	31	0	0	NUM
iajs-1810	59	32	,	,	PUNCT
iajs-1810	59	33	i	i	PRON
iajs-1810	59	34	⩾	⩾	VERB
iajs-1810	59	35	0	0	PUNCT
iajs-1810	59	36	and	and	CCONJ
iajs-1810	59	37	r	r	NOUN
iajs-1810	59	38	⩾	⩾	NOUN
iajs-1810	59	39	0	0	NUM
iajs-1810	59	40	…	…	PUNCT
iajs-1810	59	41	…	…	SYM
iajs-1810	59	42	.(13	.(13	SYM
iajs-1810	59	43	)	)	PUNCT
iajs-1810	59	44	proof	proof	NOUN
iajs-1810	59	45	consider	consider	VERB
iajs-1810	59	46	the	the	DET
iajs-1810	59	47	following	follow	VERB
iajs-1810	59	48	function	function	NOUN
iajs-1810	59	49	:	:	PUNCT
iajs-1810	59	50	𝒲	𝒲	NOUN
iajs-1810	59	51	,	,	PUNCT
iajs-1810	59	52	clearly	clearly	ADV
iajs-1810	59	53	𝒲	𝒲	PROPN
iajs-1810	59	54	ℝ	ℝ	PROPN
iajs-1810	59	55	→	→	SYM
iajs-1810	59	56	ℝ	ℝ	PROPN
iajs-1810	59	57	is	be	AUX
iajs-1810	59	58	continuously	continuously	ADV
iajs-1810	59	59	differential	differential	ADJ
iajs-1810	59	60	function	function	NOUN
iajs-1810	59	61	with	with	ADP
iajs-1810	59	62	𝒲	𝒲	PROPN
iajs-1810	59	63	𝑆	𝑆	PROPN
iajs-1810	59	64	,	,	PUNCT
iajs-1810	59	65	𝐼	𝐼	PROPN
iajs-1810	59	66	,	,	PUNCT
iajs-1810	59	67	𝑅	𝑅	PROPN
iajs-1810	59	68	0	0	PROPN
iajs-1810	59	69	,	,	PUNCT
iajs-1810	59	70	while	while	SCONJ
iajs-1810	59	71	𝒲	𝒲	PROPN
iajs-1810	59	72	𝑆	𝑆	PROPN
iajs-1810	59	73	,	,	PUNCT
iajs-1810	59	74	𝐼	𝐼	PROPN
iajs-1810	59	75	,	,	PUNCT
iajs-1810	59	76	𝑅	𝑅	PROPN
iajs-1810	59	77	0	0	NUM
iajs-1810	59	78	;	;	PUNCT
iajs-1810	59	79	∀	∀	X
iajs-1810	59	80	𝑆	𝑆	PROPN
iajs-1810	59	81	,	,	PUNCT
iajs-1810	59	82	𝐼	𝐼	PROPN
iajs-1810	59	83	,	,	PUNCT
iajs-1810	59	84	𝑅	𝑅	PROPN
iajs-1810	59	85	𝑆	𝑆	PROPN
iajs-1810	59	86	,	,	PUNCT
iajs-1810	59	87	𝐼	𝐼	PROPN
iajs-1810	59	88	,	,	PUNCT
iajs-1810	59	89	𝑅	𝑅	PROPN
iajs-1810	59	90	.	.	PUNCT
iajs-1810	60	1	moreover	moreover	ADV
iajs-1810	60	2	,	,	PUNCT
iajs-1810	60	3	straightforward	straightforward	ADJ
iajs-1810	60	4	computation	computation	NOUN
iajs-1810	60	5	gives	give	VERB
iajs-1810	60	6	that	that	PRON
iajs-1810	60	7	:	:	PUNCT
iajs-1810	60	8	𝑆	𝑆	PROPN
iajs-1810	60	9	𝑆	𝑆	PROPN
iajs-1810	60	10	𝑞	𝑞	PROPN
iajs-1810	60	11	𝐼	𝐼	PROPN
iajs-1810	60	12	𝐼	𝐼	PROPN
iajs-1810	60	13	𝑞	𝑞	PROPN
iajs-1810	60	14	𝑅	𝑅	PROPN
iajs-1810	60	15	𝑅	𝑅	PROPN
iajs-1810	60	16	𝑞	𝑞	PROPN
iajs-1810	60	17	.	.	PUNCT
iajs-1810	61	1	where	where	SCONJ
iajs-1810	61	2	:	:	PUNCT
iajs-1810	61	3	𝑞	𝑞	X
iajs-1810	61	4	,	,	PUNCT
iajs-1810	61	5	𝑞	𝑞	X
iajs-1810	61	6	and	and	CCONJ
iajs-1810	61	7	ihsciconf	ihsciconf	PROPN
iajs-1810	61	8	2017	2017	NUM
iajs-1810	61	9	special	special	ADJ
iajs-1810	61	10	issue	issue	NOUN
iajs-1810	61	11	ibn	ibn	PROPN
iajs-1810	61	12	al	al	PROPN
iajs-1810	61	13	-	-	PUNCT
iajs-1810	61	14	haitham	haitham	PROPN
iajs-1810	61	15	journal	journal	PROPN
iajs-1810	61	16	for	for	ADP
iajs-1810	61	17	pure	pure	ADJ
iajs-1810	61	18	and	and	CCONJ
iajs-1810	61	19	applied	apply	VERB
iajs-1810	61	20	science	science	NOUN
iajs-1810	61	21	https://doi.org/	https://doi.org/	VERB
iajs-1810	61	22	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	61	23	for	for	ADP
iajs-1810	61	24	more	more	ADJ
iajs-1810	61	25	information	information	NOUN
iajs-1810	61	26	about	about	ADP
iajs-1810	61	27	the	the	DET
iajs-1810	61	28	conference	conference	NOUN
iajs-1810	61	29	please	please	INTJ
iajs-1810	61	30	visit	visit	VERB
iajs-1810	61	31	the	the	DET
iajs-1810	61	32	websites	website	NOUN
iajs-1810	61	33	:	:	PUNCT
iajs-1810	61	34	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	61	35	  	  	SPACE
iajs-1810	61	36	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	61	37	   	   	SPACE
iajs-1810	61	38	mathematics|517	mathematics|517	PROPN
iajs-1810	61	39	    	    	SPACE
iajs-1810	61	40	𝑞	𝑞	PROPN
iajs-1810	61	41	𝛽	𝛽	PROPN
iajs-1810	61	42	𝛾	𝛾	AUX
iajs-1810	61	43	thus	thus	ADV
iajs-1810	61	44	according	accord	VERB
iajs-1810	61	45	to	to	ADP
iajs-1810	61	46	the	the	DET
iajs-1810	61	47	given	give	VERB
iajs-1810	61	48	conditions	condition	NOUN
iajs-1810	61	49	it	it	PRON
iajs-1810	61	50	’s	’	VERB
iajs-1810	61	51	easy	easy	ADJ
iajs-1810	61	52	to	to	PART
iajs-1810	61	53	verify	verify	VERB
iajs-1810	61	54	that	that	SCONJ
iajs-1810	61	55	clearly	clearly	ADV
iajs-1810	61	56	condition	condition	NOUN
iajs-1810	61	57	(	(	PUNCT
iajs-1810	61	58	13	13	NUM
iajs-1810	61	59	)	)	PUNCT
iajs-1810	61	60	come	come	VERB
iajs-1810	61	61	true	true	ADJ
iajs-1810	61	62	and	and	CCONJ
iajs-1810	61	63	𝒲	𝒲	NOUN
iajs-1810	61	64	0	0	NUM
iajs-1810	61	65	,	,	PUNCT
iajs-1810	61	66	hence	hence	ADV
iajs-1810	61	67	due	due	ADP
iajs-1810	61	68	to	to	ADP
iajs-1810	61	69	the	the	DET
iajs-1810	61	70	second	second	ADJ
iajs-1810	61	71	lyapunov	lyapunov	NOUN
iajs-1810	61	72	theorem	theorem	VERB
iajs-1810	61	73	[	[	X
iajs-1810	61	74	14	14	NUM
iajs-1810	61	75	]	]	PUNCT
iajs-1810	61	76	,	,	PUNCT
iajs-1810	61	77	the	the	DET
iajs-1810	61	78	endemic	endemic	ADJ
iajs-1810	61	79	equilibrium	equilibrium	NOUN
iajs-1810	61	80	point	point	NOUN
iajs-1810	61	81	of	of	ADP
iajs-1810	61	82	model	model	NOUN
iajs-1810	61	83	(	(	PUNCT
iajs-1810	61	84	2	2	NUM
iajs-1810	61	85	)	)	PUNCT
iajs-1810	61	86	,	,	PUNCT
iajs-1810	61	87	is	be	AUX
iajs-1810	61	88	globally	globally	ADV
iajs-1810	61	89	asymptotically	asymptotically	ADV
iajs-1810	61	90	stable	stable	ADJ
iajs-1810	61	91	.	.	PUNCT
iajs-1810	62	1	■	■	PUNCT
iajs-1810	62	2	4	4	X
iajs-1810	62	3	.	.	X
iajs-1810	62	4	local	local	ADJ
iajs-1810	62	5	bifurcation	bifurcation	NOUN
iajs-1810	62	6	analysis	analysis	NOUN
iajs-1810	62	7	in	in	ADP
iajs-1810	62	8	this	this	DET
iajs-1810	62	9	section	section	NOUN
iajs-1810	62	10	,	,	PUNCT
iajs-1810	62	11	the	the	DET
iajs-1810	62	12	local	local	ADJ
iajs-1810	62	13	bifurcation	bifurcation	NOUN
iajs-1810	62	14	(	(	PUNCT
iajs-1810	62	15	such	such	ADJ
iajs-1810	62	16	as	as	ADP
iajs-1810	62	17	saddle	saddle	NOUN
iajs-1810	62	18	-	-	PUNCT
iajs-1810	62	19	node	node	NOUN
iajs-1810	62	20	,	,	PUNCT
iajs-1810	62	21	transcritical	transcritical	ADJ
iajs-1810	62	22	and	and	CCONJ
iajs-1810	62	23	pitchfork	pitchfork	NOUN
iajs-1810	62	24	)	)	PUNCT
iajs-1810	62	25	is	be	AUX
iajs-1810	62	26	studied	study	VERB
iajs-1810	62	27	to	to	PART
iajs-1810	62	28	find	find	VERB
iajs-1810	62	29	out	out	ADP
iajs-1810	62	30	the	the	DET
iajs-1810	62	31	influence	influence	NOUN
iajs-1810	62	32	of	of	ADP
iajs-1810	62	33	changing	change	VERB
iajs-1810	62	34	one	one	NUM
iajs-1810	62	35	of	of	ADP
iajs-1810	62	36	the	the	DET
iajs-1810	62	37	parameters	parameter	NOUN
iajs-1810	62	38	value	value	NOUN
iajs-1810	62	39	,	,	PUNCT
iajs-1810	62	40	on	on	ADP
iajs-1810	62	41	the	the	DET
iajs-1810	62	42	dynamical	dynamical	ADJ
iajs-1810	62	43	behavior	behavior	NOUN
iajs-1810	62	44	of	of	ADP
iajs-1810	62	45	system	system	NOUN
iajs-1810	62	46	(	(	PUNCT
iajs-1810	62	47	1	1	NUM
iajs-1810	62	48	)	)	PUNCT
iajs-1810	62	49	around	around	ADP
iajs-1810	62	50	the	the	DET
iajs-1810	62	51	disease	disease	NOUN
iajs-1810	62	52	free	free	ADJ
iajs-1810	62	53	equilibrium	equilibrium	NOUN
iajs-1810	62	54	point	point	NOUN
iajs-1810	62	55	𝐸	𝐸	PROPN
iajs-1810	62	56	.	.	PUNCT
iajs-1810	63	1	an	an	DET
iajs-1810	63	2	application	application	NOUN
iajs-1810	63	3	of	of	ADP
iajs-1810	63	4	the	the	DET
iajs-1810	63	5	sotomayor	sotomayor	PROPN
iajs-1810	63	6	’s	’s	PART
iajs-1810	63	7	theorem	theorem	PROPN
iajs-1810	63	8	,	,	PUNCT
iajs-1810	63	9	which	which	PRON
iajs-1810	63	10	presented	present	VERB
iajs-1810	63	11	in	in	ADP
iajs-1810	63	12	[	[	X
iajs-1810	63	13	10	10	NUM
iajs-1810	63	14	]	]	PUNCT
iajs-1810	63	15	,	,	PUNCT
iajs-1810	63	16	for	for	SCONJ
iajs-1810	63	17	the	the	DET
iajs-1810	63	18	local	local	ADJ
iajs-1810	63	19	bifurcation	bifurcation	NOUN
iajs-1810	63	20	is	be	AUX
iajs-1810	63	21	carried	carry	VERB
iajs-1810	63	22	out	out	ADP
iajs-1810	63	23	in	in	ADP
iajs-1810	63	24	order	order	NOUN
iajs-1810	63	25	to	to	PART
iajs-1810	63	26	specify	specify	VERB
iajs-1810	63	27	the	the	DET
iajs-1810	63	28	type	type	NOUN
iajs-1810	63	29	of	of	ADP
iajs-1810	63	30	bifurcation	bifurcation	NOUN
iajs-1810	63	31	near	near	ADP
iajs-1810	63	32	the	the	DET
iajs-1810	63	33	equilibrium	equilibrium	NOUN
iajs-1810	63	34	point	point	NOUN
iajs-1810	63	35	as	as	SCONJ
iajs-1810	63	36	shown	show	VERB
iajs-1810	63	37	in	in	ADP
iajs-1810	63	38	the	the	DET
iajs-1810	63	39	following	follow	VERB
iajs-1810	63	40	theorem	theorem	PROPN
iajs-1810	63	41	.	.	PUNCT
iajs-1810	64	1	theorem	theorem	ADJ
iajs-1810	64	2	6	6	NUM
iajs-1810	64	3	assume	assume	VERB
iajs-1810	64	4	that	that	SCONJ
iajs-1810	64	5	𝛿	𝛿	ADJ
iajs-1810	64	6	1	1	NUM
iajs-1810	64	7	,	,	PUNCT
iajs-1810	64	8	then	then	ADV
iajs-1810	64	9	model	model	NOUN
iajs-1810	64	10	(	(	PUNCT
iajs-1810	64	11	2	2	X
iajs-1810	64	12	)	)	PUNCT
iajs-1810	64	13	undergoes	undergo	VERB
iajs-1810	64	14	a	a	DET
iajs-1810	64	15	transcritical	transcritical	ADJ
iajs-1810	64	16	bifurcation	bifurcation	NOUN
iajs-1810	64	17	near	near	ADP
iajs-1810	64	18	the	the	DET
iajs-1810	64	19	disease	disease	NOUN
iajs-1810	64	20	free	free	ADJ
iajs-1810	64	21	equilibrium	equilibrium	NOUN
iajs-1810	64	22	point	point	NOUN
iajs-1810	64	23	𝐸	𝐸	PROPN
iajs-1810	64	24	,	,	PUNCT
iajs-1810	64	25	but	but	CCONJ
iajs-1810	64	26	neither	neither	CCONJ
iajs-1810	64	27	saddle	saddle	NOUN
iajs-1810	64	28	-	-	PUNCT
iajs-1810	64	29	node	node	NOUN
iajs-1810	64	30	bifurcation	bifurcation	NOUN
iajs-1810	64	31	nor	nor	CCONJ
iajs-1810	64	32	pitchfork	pitchfork	NOUN
iajs-1810	64	33	bifurcation	bifurcation	NOUN
iajs-1810	64	34	can	can	AUX
iajs-1810	64	35	occur	occur	VERB
iajs-1810	64	36	,	,	PUNCT
iajs-1810	64	37	provided	provide	VERB
iajs-1810	64	38	that	that	PRON
iajs-1810	64	39	0	0	NUM
iajs-1810	64	40	..	..	PUNCT
iajs-1810	64	41	(	(	PUNCT
iajs-1810	64	42	14	14	NUM
iajs-1810	64	43	)	)	PUNCT
iajs-1810	64	44	,	,	PUNCT
iajs-1810	64	45	where	where	SCONJ
iajs-1810	64	46	q	q	NOUN
iajs-1810	64	47	is	be	AUX
iajs-1810	64	48	given	give	VERB
iajs-1810	64	49	in	in	ADP
iajs-1810	64	50	the	the	DET
iajs-1810	64	51	proof	proof	NOUN
iajs-1810	64	52	.	.	PUNCT
iajs-1810	65	1	proof	proof	NOUN
iajs-1810	65	2	it	it	PRON
iajs-1810	65	3	is	be	AUX
iajs-1810	65	4	easy	easy	ADJ
iajs-1810	65	5	to	to	PART
iajs-1810	65	6	verify	verify	VERB
iajs-1810	65	7	that	that	SCONJ
iajs-1810	65	8	when	when	SCONJ
iajs-1810	65	9	𝛿	𝛿	ADJ
iajs-1810	65	10	1	1	NUM
iajs-1810	65	11	then	then	ADV
iajs-1810	65	12	the	the	DET
iajs-1810	65	13	jacobian	jacobian	ADJ
iajs-1810	65	14	matrix	matrix	NOUN
iajs-1810	65	15	given	give	VERB
iajs-1810	65	16	by	by	ADP
iajs-1810	65	17	(	(	PUNCT
iajs-1810	65	18	8a	8a	NUM
iajs-1810	65	19	)	)	PUNCT
iajs-1810	65	20	would	would	AUX
iajs-1810	65	21	be	be	AUX
iajs-1810	65	22	:	:	PUNCT
iajs-1810	65	23	𝐽	𝐽	PROPN
iajs-1810	65	24	𝐷𝑓	𝐷𝑓	PROPN
iajs-1810	65	25	𝐸	𝐸	PROPN
iajs-1810	65	26	.	.	PUNCT
iajs-1810	66	1	𝛼∗	𝛼∗	PROPN
iajs-1810	67	1	𝛼	𝛼	X
iajs-1810	67	2	∗	∗	NOUN
iajs-1810	67	3	0	0	NUM
iajs-1810	67	4	0	0	NUM
iajs-1810	67	5	0	0	NUM
iajs-1810	68	1	𝛽	𝛽	NOUN
iajs-1810	68	2	0	0	NUM
iajs-1810	68	3	0	0	NUM
iajs-1810	68	4	𝛽	𝛽	NOUN
iajs-1810	68	5	𝛼	𝛼	NOUN
iajs-1810	68	6	;	;	PUNCT
iajs-1810	68	7	clearly	clearly	ADV
iajs-1810	68	8	the	the	DET
iajs-1810	68	9	second	second	ADJ
iajs-1810	68	10	eigenvalue	eigenvalue	NOUN
iajs-1810	68	11	of	of	ADP
iajs-1810	68	12	j	j	PROPN
iajs-1810	68	13	𝜆	𝜆	PROPN
iajs-1810	68	14	in	in	ADP
iajs-1810	68	15	the	the	DET
iajs-1810	68	16	i	i	NOUN
iajs-1810	68	17	-	-	PUNCT
iajs-1810	68	18	direction	direction	NOUN
iajs-1810	68	19	is	be	AUX
iajs-1810	68	20	zero	zero	NUM
iajs-1810	68	21	(	(	PUNCT
iajs-1810	68	22	𝜆	𝜆	NOUN
iajs-1810	68	23	0	0	NUM
iajs-1810	68	24	)	)	PUNCT
iajs-1810	68	25	,	,	PUNCT
iajs-1810	68	26	while	while	SCONJ
iajs-1810	68	27	𝜆	𝜆	ADP
iajs-1810	68	28	𝛼	𝛼	NOUN
iajs-1810	68	29	and	and	CCONJ
iajs-1810	68	30	𝜆	𝜆	ADP
iajs-1810	68	31	𝛽	𝛽	NOUN
iajs-1810	68	32	𝛼	𝛼	NOUN
iajs-1810	68	33	.	.	PUNCT
iajs-1810	69	1	hence	hence	ADV
iajs-1810	69	2	the	the	DET
iajs-1810	69	3	disease	disease	NOUN
iajs-1810	69	4	free	free	ADJ
iajs-1810	69	5	equilibrium	equilibrium	NOUN
iajs-1810	69	6	point	point	NOUN
iajs-1810	69	7	is	be	AUX
iajs-1810	69	8	a	a	DET
iajs-1810	69	9	non	non	ADJ
iajs-1810	69	10	-	-	ADJ
iajs-1810	69	11	hyperbolic	hyperbolic	ADJ
iajs-1810	69	12	point	point	NOUN
iajs-1810	69	13	for	for	ADP
iajs-1810	69	14	𝑅	𝑅	PROPN
iajs-1810	69	15	1	1	PROPN
iajs-1810	69	16	.	.	PUNCT
iajs-1810	70	1	further	far	ADV
iajs-1810	70	2	the	the	DET
iajs-1810	70	3	eigenvector	eigenvector	NOUN
iajs-1810	70	4	,	,	PUNCT
iajs-1810	70	5	say	say	VERB
iajs-1810	70	6	𝐾	𝐾	PROPN
iajs-1810	70	7	𝑘	𝑘	PROPN
iajs-1810	70	8	,	,	PUNCT
iajs-1810	70	9	𝑘	𝑘	INTJ
iajs-1810	70	10	,	,	PUNCT
iajs-1810	70	11	𝑘	𝑘	INTJ
iajs-1810	70	12	,	,	PUNCT
iajs-1810	70	13	that	that	PRON
iajs-1810	70	14	corresponds	correspond	VERB
iajs-1810	70	15	𝜆	𝜆	ADP
iajs-1810	70	16	0	0	NUM
iajs-1810	70	17	is	be	AUX
iajs-1810	70	18	determined	determine	VERB
iajs-1810	70	19	as	as	ADP
iajs-1810	70	20	:	:	PUNCT
iajs-1810	70	21	𝐾	𝐾	PROPN
iajs-1810	70	22	𝑞𝑘	𝑞𝑘	ADV
iajs-1810	70	23	,	,	PUNCT
iajs-1810	70	24	𝑘	𝑘	X
iajs-1810	70	25	,	,	PUNCT
iajs-1810	70	26	0	0	NUM
iajs-1810	70	27	(	(	PUNCT
iajs-1810	70	28	14a	14a	NOUN
iajs-1810	70	29	)	)	PUNCT
iajs-1810	70	30	,	,	PUNCT
iajs-1810	70	31	where	where	SCONJ
iajs-1810	70	32	𝑞	𝑞	PROPN
iajs-1810	70	33	∗	∗	NOUN
iajs-1810	70	34	and	and	CCONJ
iajs-1810	70	35	𝑘	𝑘	PRON
iajs-1810	70	36	is	be	AUX
iajs-1810	70	37	a	a	DET
iajs-1810	70	38	non	non	ADJ
iajs-1810	70	39	-	-	ADJ
iajs-1810	70	40	zero	zero	ADJ
iajs-1810	70	41	real	real	ADJ
iajs-1810	70	42	number	number	NOUN
iajs-1810	70	43	.	.	PUNCT
iajs-1810	71	1	similarly	similarly	ADV
iajs-1810	71	2	the	the	DET
iajs-1810	71	3	eigenvector	eigenvector	NOUN
iajs-1810	71	4	𝑊	𝑊	VERB
iajs-1810	71	5	𝑤	𝑤	NOUN
iajs-1810	71	6	𝑤	𝑤	PRON
iajs-1810	71	7	𝑤	𝑤	NOUN
iajs-1810	71	8	that	that	PRON
iajs-1810	71	9	corresponds	correspond	VERB
iajs-1810	71	10	𝜆	𝜆	ADP
iajs-1810	71	11	0	0	NUM
iajs-1810	71	12	of	of	ADP
iajs-1810	71	13	𝐽	𝐽	PROPN
iajs-1810	71	14	is	be	AUX
iajs-1810	71	15	determined	determine	VERB
iajs-1810	71	16	as	as	ADP
iajs-1810	71	17	:	:	PUNCT
iajs-1810	71	18	𝑊	𝑊	NOUN
iajs-1810	71	19	0	0	NUM
iajs-1810	71	20	,	,	PUNCT
iajs-1810	71	21	𝑝𝑤	𝑝𝑤	NOUN
iajs-1810	71	22	,	,	PUNCT
iajs-1810	71	23	𝑤	𝑤	X
iajs-1810	71	24	(	(	PUNCT
iajs-1810	71	25	14b	14b	NUM
iajs-1810	71	26	)	)	PUNCT
iajs-1810	71	27	,	,	PUNCT
iajs-1810	71	28	where	where	SCONJ
iajs-1810	71	29	𝑤	𝑤	PART
iajs-1810	71	30	is	be	AUX
iajs-1810	71	31	a	a	DET
iajs-1810	71	32	non	non	ADJ
iajs-1810	71	33	-	-	ADJ
iajs-1810	71	34	zero	zero	ADJ
iajs-1810	71	35	real	real	ADJ
iajs-1810	71	36	number	number	NOUN
iajs-1810	71	37	.	.	PUNCT
iajs-1810	72	1	now	now	ADV
iajs-1810	72	2	rewrite	rewrite	VERB
iajs-1810	72	3	model	model	NOUN
iajs-1810	72	4	(	(	PUNCT
iajs-1810	72	5	2	2	NUM
iajs-1810	72	6	)	)	PUNCT
iajs-1810	72	7	as	as	ADP
iajs-1810	72	8	vector	vector	NOUN
iajs-1810	72	9	form	form	NOUN
iajs-1810	72	10	𝑓	𝑓	ADV
iajs-1810	72	11	𝑥	𝑥	NOUN
iajs-1810	72	12	,	,	PUNCT
iajs-1810	72	13	where	where	SCONJ
iajs-1810	72	14	𝑋	𝑋	PROPN
iajs-1810	72	15	𝑆	𝑆	PROPN
iajs-1810	72	16	,	,	PUNCT
iajs-1810	72	17	𝐼	𝐼	PROPN
iajs-1810	72	18	,	,	PUNCT
iajs-1810	72	19	𝑅	𝑅	PROPN
iajs-1810	72	20	and	and	CCONJ
iajs-1810	72	21	𝑓	𝑓	PRON
iajs-1810	72	22	𝑓	𝑓	PRON
iajs-1810	72	23	,	,	PUNCT
iajs-1810	72	24	𝑓	𝑓	X
iajs-1810	72	25	,	,	PUNCT
iajs-1810	72	26	𝑓	𝑓	PRON
iajs-1810	72	27	be	be	AUX
iajs-1810	72	28	the	the	DET
iajs-1810	72	29	interaction	interaction	NOUN
iajs-1810	72	30	functions	function	NOUN
iajs-1810	72	31	vector	vector	NOUN
iajs-1810	72	32	given	give	VERB
iajs-1810	72	33	in	in	ADP
iajs-1810	72	34	model	model	NOUN
iajs-1810	72	35	(	(	PUNCT
iajs-1810	72	36	2	2	NUM
iajs-1810	72	37	)	)	PUNCT
iajs-1810	72	38	.	.	PUNCT
iajs-1810	73	1	then	then	ADV
iajs-1810	73	2	by	by	ADP
iajs-1810	73	3	determining	determine	VERB
iajs-1810	73	4	𝑓	𝑓	PRON
iajs-1810	73	5	,	,	PUNCT
iajs-1810	73	6	we	we	PRON
iajs-1810	73	7	get	get	VERB
iajs-1810	73	8	that	that	PRON
iajs-1810	73	9	:	:	PUNCT
iajs-1810	73	10	𝑓	𝑓	X
iajs-1810	73	11	0	0	NUM
iajs-1810	73	12	then	then	ADV
iajs-1810	73	13	𝑓	𝑓	DET
iajs-1810	73	14	𝐸	𝐸	PROPN
iajs-1810	73	15	,	,	PUNCT
iajs-1810	73	16	𝑎∗	𝑎∗	PROPN
iajs-1810	73	17	0	0	NUM
iajs-1810	73	18	0	0	NUM
iajs-1810	73	19	0	0	NUM
iajs-1810	73	20	therefore	therefore	ADV
iajs-1810	73	21	:	:	PUNCT
iajs-1810	73	22	𝑤	𝑤	X
iajs-1810	73	23	.	.	PUNCT
iajs-1810	74	1	𝑓	𝑓	DET
iajs-1810	74	2	𝐸	𝐸	PROPN
iajs-1810	74	3	,	,	PUNCT
iajs-1810	74	4	𝑎∗	𝑎∗	PROPN
iajs-1810	74	5	0	0	NUM
iajs-1810	74	6	,	,	PUNCT
iajs-1810	74	7	cosequently	cosequently	ADV
iajs-1810	74	8	,	,	PUNCT
iajs-1810	74	9	according	accord	VERB
iajs-1810	74	10	to	to	ADP
iajs-1810	74	11	sotomayor	sotomayor	PROPN
iajs-1810	74	12	theorem	theorem	PROPN
iajs-1810	74	13	,	,	PUNCT
iajs-1810	74	14	model	model	NOUN
iajs-1810	74	15	(	(	PUNCT
iajs-1810	74	16	2	2	NUM
iajs-1810	74	17	)	)	PUNCT
iajs-1810	74	18	has	have	VERB
iajs-1810	74	19	no	no	DET
iajs-1810	74	20	saddle	saddle	NOUN
iajs-1810	74	21	-	-	PUNCT
iajs-1810	74	22	node	node	NOUN
iajs-1810	74	23	bifurcation	bifurcation	NOUN
iajs-1810	74	24	near	near	ADP
iajs-1810	74	25	𝐸	𝐸	PROPN
iajs-1810	74	26	at	at	ADP
iajs-1810	74	27	𝑎	𝑎	PROPN
iajs-1810	74	28	𝑎∗.	𝑎∗.	PROPN
iajs-1810	74	29	now	now	ADV
iajs-1810	74	30	in	in	ADP
iajs-1810	74	31	order	order	NOUN
iajs-1810	74	32	to	to	PART
iajs-1810	74	33	investigate	investigate	VERB
iajs-1810	74	34	the	the	DET
iajs-1810	74	35	other	other	ADJ
iajs-1810	74	36	types	type	NOUN
iajs-1810	74	37	of	of	ADP
iajs-1810	74	38	bifurcation	bifurcation	NOUN
iajs-1810	74	39	,	,	PUNCT
iajs-1810	74	40	the	the	DET
iajs-1810	74	41	derivative	derivative	NOUN
iajs-1810	74	42	of	of	ADP
iajs-1810	74	43	𝑓	𝑓	PRON
iajs-1810	74	44	with	with	ADP
iajs-1810	74	45	respect	respect	NOUN
iajs-1810	74	46	to	to	ADP
iajs-1810	74	47	vector	vector	NOUN
iajs-1810	74	48	x	x	NOUN
iajs-1810	74	49	say	say	VERB
iajs-1810	74	50	𝐷𝑓	𝐷𝑓	PROPN
iajs-1810	74	51	𝐸	𝐸	PROPN
iajs-1810	74	52	,	,	PUNCT
iajs-1810	74	53	𝑎∗	𝑎∗	PROPN
iajs-1810	74	54	is	be	AUX
iajs-1810	74	55	computed	compute	VERB
iajs-1810	74	56	:	:	PUNCT
iajs-1810	74	57	ihsciconf	ihsciconf	PROPN
iajs-1810	74	58	2017	2017	NUM
iajs-1810	74	59	special	special	ADJ
iajs-1810	74	60	issue	issue	NOUN
iajs-1810	74	61	ibn	ibn	PROPN
iajs-1810	74	62	al	al	PROPN
iajs-1810	74	63	-	-	PUNCT
iajs-1810	74	64	haitham	haitham	PROPN
iajs-1810	74	65	journal	journal	PROPN
iajs-1810	74	66	for	for	ADP
iajs-1810	74	67	pure	pure	ADJ
iajs-1810	74	68	and	and	CCONJ
iajs-1810	74	69	applied	apply	VERB
iajs-1810	74	70	science	science	NOUN
iajs-1810	74	71	https://doi.org/	https://doi.org/	VERB
iajs-1810	74	72	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	74	73	for	for	ADP
iajs-1810	74	74	more	more	ADJ
iajs-1810	74	75	information	information	NOUN
iajs-1810	74	76	about	about	ADP
iajs-1810	74	77	the	the	DET
iajs-1810	74	78	conference	conference	NOUN
iajs-1810	74	79	please	please	INTJ
iajs-1810	74	80	visit	visit	VERB
iajs-1810	74	81	the	the	DET
iajs-1810	74	82	websites	website	NOUN
iajs-1810	74	83	:	:	PUNCT
iajs-1810	74	84	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	74	85	  	  	SPACE
iajs-1810	74	86	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	74	87	   	   	SPACE
iajs-1810	74	88	mathematics|518	mathematics|518	ADJ
iajs-1810	74	89	    	    	SPACE
iajs-1810	74	90	𝐷𝑓	𝐷𝑓	PROPN
iajs-1810	74	91	𝐸	𝐸	PROPN
iajs-1810	74	92	,	,	PUNCT
iajs-1810	74	93	𝛼∗	𝛼∗	PROPN
iajs-1810	75	1	⎣	⎣	ADV
iajs-1810	75	2	⎢	⎢	NOUN
iajs-1810	75	3	⎢	⎢	NOUN
iajs-1810	75	4	⎡0	⎡0	NOUN
iajs-1810	75	5	0	0	NUM
iajs-1810	75	6	0	0	NUM
iajs-1810	75	7	0	0	NUM
iajs-1810	75	8	0	0	NUM
iajs-1810	75	9	0	0	NUM
iajs-1810	76	1	0⎦	0⎦	NOUN
iajs-1810	76	2	⎥	⎥	PROPN
iajs-1810	76	3	⎥	⎥	PROPN
iajs-1810	76	4	⎤	⎤	PROPN
iajs-1810	76	5	,	,	PUNCT
iajs-1810	76	6	and	and	CCONJ
iajs-1810	76	7	𝑊	𝑊	X
iajs-1810	76	8	𝐷𝑓	𝐷𝑓	PROPN
iajs-1810	76	9	𝐸	𝐸	PROPN
iajs-1810	76	10	,	,	PUNCT
iajs-1810	76	11	𝑎∗	𝑎∗	PROPN
iajs-1810	76	12	,	,	PUNCT
iajs-1810	76	13	𝐾	𝐾	PROPN
iajs-1810	76	14	𝑤	𝑤	X
iajs-1810	76	15	𝑝𝑘	𝑝𝑘	ADP
iajs-1810	76	16	0	0	NUM
iajs-1810	76	17	.	.	PUNCT
iajs-1810	76	18	again	again	ADV
iajs-1810	76	19	,	,	PUNCT
iajs-1810	76	20	in	in	ADP
iajs-1810	76	21	view	view	NOUN
iajs-1810	76	22	of	of	ADP
iajs-1810	76	23	sotomayor	sotomayor	PROPN
iajs-1810	76	24	theorem	theorem	PROPN
iajs-1810	76	25	,	,	PUNCT
iajs-1810	76	26	if	if	SCONJ
iajs-1810	76	27	in	in	ADP
iajs-1810	76	28	addition	addition	NOUN
iajs-1810	76	29	to	to	ADP
iajs-1810	76	30	the	the	DET
iajs-1810	76	31	above	above	ADP
iajs-1810	76	32	the	the	DET
iajs-1810	76	33	following	follow	VERB
iajs-1810	76	34	holds	hold	VERB
iajs-1810	76	35	𝑊	𝑊	PROPN
iajs-1810	76	36	𝐷	𝐷	PROPN
iajs-1810	76	37	𝑓	𝑓	DET
iajs-1810	76	38	𝐸	𝐸	PROPN
iajs-1810	76	39	,	,	PUNCT
iajs-1810	76	40	𝑎∗	𝑎∗	PROPN
iajs-1810	76	41	,	,	PUNCT
iajs-1810	76	42	𝐾	𝐾	PROPN
iajs-1810	76	43	,	,	PUNCT
iajs-1810	76	44	𝐾	𝐾	PROPN
iajs-1810	76	45	0	0	NUM
iajs-1810	76	46	,	,	PUNCT
iajs-1810	76	47	then	then	ADV
iajs-1810	76	48	model	model	NOUN
iajs-1810	76	49	(	(	PUNCT
iajs-1810	76	50	2	2	X
iajs-1810	76	51	)	)	PUNCT
iajs-1810	76	52	possesses	possess	VERB
iajs-1810	76	53	a	a	DET
iajs-1810	76	54	transcritical	transcritical	ADJ
iajs-1810	76	55	bifurcation	bifurcation	NOUN
iajs-1810	76	56	but	but	CCONJ
iajs-1810	76	57	no	no	DET
iajs-1810	76	58	pitchfork	pitchfork	NOUN
iajs-1810	76	59	bifurcation	bifurcation	NOUN
iajs-1810	76	60	appear	appear	VERB
iajs-1810	76	61	.	.	PUNCT
iajs-1810	77	1	now	now	ADV
iajs-1810	77	2	since	since	SCONJ
iajs-1810	77	3	we	we	PRON
iajs-1810	77	4	get	get	VERB
iajs-1810	77	5	that	that	PRON
iajs-1810	78	1	:	:	PUNCT
iajs-1810	78	2	𝐷	𝐷	PROPN
iajs-1810	78	3	𝑓	𝑓	PRON
iajs-1810	78	4	𝐸	𝐸	PROPN
iajs-1810	78	5	,	,	PUNCT
iajs-1810	78	6	𝛼∗	𝛼∗	NOUN
iajs-1810	78	7	,	,	PUNCT
iajs-1810	78	8	𝐾	𝐾	PROPN
iajs-1810	78	9	,	,	PUNCT
iajs-1810	78	10	𝐾	𝐾	PROPN
iajs-1810	78	11	⎣	⎣	ADV
iajs-1810	78	12	⎢	⎢	NOUN
iajs-1810	78	13	⎢	⎢	NOUN
iajs-1810	78	14	⎢	⎢	NOUN
iajs-1810	78	15	⎡	⎡	VERB
iajs-1810	78	16	𝑞	𝑞	X
iajs-1810	78	17	𝑘	𝑘	X
iajs-1810	78	18	𝑞𝑘	𝑞𝑘	ADP
iajs-1810	78	19	𝑘	𝑘	X
iajs-1810	78	20	𝑞	𝑞	X
iajs-1810	78	21	𝑘	𝑘	X
iajs-1810	78	22	𝑞𝑘	𝑞𝑘	ADP
iajs-1810	78	23	𝑘	𝑘	PROPN
iajs-1810	78	24	0	0	NUM
iajs-1810	78	25	⎦	⎦	NOUN
iajs-1810	78	26	⎥	⎥	PROPN
iajs-1810	78	27	⎥	⎥	PROPN
iajs-1810	78	28	⎥	⎥	PROPN
iajs-1810	78	29	⎤	⎤	PROPN
iajs-1810	78	30	;	;	PUNCT
iajs-1810	78	31	thus	thus	ADV
iajs-1810	78	32	it	it	PRON
iajs-1810	78	33	follows	follow	VERB
iajs-1810	78	34	that	that	SCONJ
iajs-1810	78	35	:	:	PUNCT
iajs-1810	78	36	𝑊	𝑊	VERB
iajs-1810	78	37	𝐷	𝐷	PROPN
iajs-1810	78	38	𝑓	𝑓	DET
iajs-1810	78	39	𝐸	𝐸	PROPN
iajs-1810	78	40	,	,	PUNCT
iajs-1810	78	41	𝛼∗	𝛼∗	NOUN
iajs-1810	78	42	,	,	PUNCT
iajs-1810	78	43	𝐾	𝐾	PROPN
iajs-1810	78	44	,	,	PUNCT
iajs-1810	78	45	𝐾	𝐾	PROPN
iajs-1810	78	46	0	0	PROPN
iajs-1810	78	47	.	.	PUNCT
iajs-1810	79	1	therefore	therefore	ADV
iajs-1810	79	2	model	model	NOUN
iajs-1810	79	3	(	(	PUNCT
iajs-1810	79	4	2	2	NUM
iajs-1810	79	5	)	)	PUNCT
iajs-1810	79	6	has	have	VERB
iajs-1810	79	7	a	a	DET
iajs-1810	79	8	trans	tran	NOUN
iajs-1810	79	9	critical	critical	ADJ
iajs-1810	79	10	bifurcation	bifurcation	NOUN
iajs-1810	79	11	at	at	ADP
iajs-1810	79	12	𝐸	𝐸	PROPN
iajs-1810	79	13	with	with	ADP
iajs-1810	79	14	𝛼	𝛼	PROPN
iajs-1810	79	15	𝛼∗	𝛼∗	PROPN
iajs-1810	79	16	provided	provide	VERB
iajs-1810	79	17	that	that	DET
iajs-1810	79	18	condition	condition	NOUN
iajs-1810	79	19	(	(	PUNCT
iajs-1810	79	20	14	14	NUM
iajs-1810	79	21	)	)	PUNCT
iajs-1810	79	22	holds	hold	VERB
iajs-1810	79	23	.	.	PUNCT
iajs-1810	79	24	prove	prove	VERB
iajs-1810	79	25	complete	complete	ADJ
iajs-1810	79	26	∎	∎	PROPN
iajs-1810	80	1	now	now	ADV
iajs-1810	80	2	it	it	PRON
iajs-1810	80	3	is	be	AUX
iajs-1810	80	4	well	well	ADV
iajs-1810	80	5	known	know	VERB
iajs-1810	80	6	that	that	SCONJ
iajs-1810	80	7	,	,	PUNCT
iajs-1810	80	8	the	the	DET
iajs-1810	80	9	three	three	NUM
iajs-1810	80	10	dimensional	dimensional	ADJ
iajs-1810	80	11	dynamical	dynamical	ADJ
iajs-1810	80	12	system	system	NOUN
iajs-1810	80	13	undergoes	undergo	VERB
iajs-1810	80	14	a	a	DET
iajs-1810	80	15	hopf	hopf	ADJ
iajs-1810	80	16	bifurcation	bifurcation	NOUN
iajs-1810	80	17	if	if	SCONJ
iajs-1810	80	18	and	and	CCONJ
iajs-1810	80	19	only	only	ADV
iajs-1810	80	20	if	if	SCONJ
iajs-1810	80	21	there	there	PRON
iajs-1810	80	22	is	be	VERB
iajs-1810	80	23	a	a	DET
iajs-1810	80	24	complex	complex	ADJ
iajs-1810	80	25	conjugate	conjugate	ADJ
iajs-1810	80	26	eigenvalue	eigenvalue	NOUN
iajs-1810	80	27	,	,	PUNCT
iajs-1810	80	28	say	say	VERB
iajs-1810	80	29	𝜆	𝜆	ADP
iajs-1810	80	30	𝜌	𝜌	ADP
iajs-1810	80	31	∓	∓	PROPN
iajs-1810	80	32	𝑖𝜌	𝑖𝜌	INTJ
iajs-1810	80	33	,	,	PUNCT
iajs-1810	80	34	with	with	ADP
iajs-1810	80	35	third	third	ADJ
iajs-1810	80	36	eigenvalue	eigenvalue	NOUN
iajs-1810	80	37	is	be	AUX
iajs-1810	80	38	real	real	ADJ
iajs-1810	80	39	and	and	CCONJ
iajs-1810	80	40	negative	negative	ADJ
iajs-1810	80	41	,	,	PUNCT
iajs-1810	80	42	so	so	SCONJ
iajs-1810	80	43	that	that	SCONJ
iajs-1810	81	1	[	[	X
iajs-1810	81	2	14	14	NUM
iajs-1810	81	3	]	]	PUNCT
iajs-1810	81	4	𝜌	𝜌	ADP
iajs-1810	81	5	ℓ∗	ℓ∗	PROPN
iajs-1810	81	6	0	0	NUM
iajs-1810	81	7	(	(	PUNCT
iajs-1810	81	8	15a	15a	NOUN
iajs-1810	81	9	)	)	PUNCT
iajs-1810	81	10	,	,	PUNCT
iajs-1810	81	11	and	and	CCONJ
iajs-1810	81	12	ℓ	ℓ	PROPN
iajs-1810	81	13	|ℓ	|ℓ	VERB
iajs-1810	81	14	ℓ∗	ℓ∗	PROPN
iajs-1810	81	15	0	0	NUM
iajs-1810	81	16	(	(	PUNCT
iajs-1810	81	17	15b	15b	NOUN
iajs-1810	81	18	)	)	PUNCT
iajs-1810	81	19	where	where	SCONJ
iajs-1810	81	20	ℓ	ℓ	PROPN
iajs-1810	81	21	ℓ∗	ℓ∗	PROPN
iajs-1810	81	22	be	be	VERB
iajs-1810	81	23	a	a	DET
iajs-1810	81	24	specific	specific	ADJ
iajs-1810	81	25	general	general	ADJ
iajs-1810	81	26	parameter	parameter	NOUN
iajs-1810	81	27	.	.	PUNCT
iajs-1810	82	1	this	this	PRON
iajs-1810	82	2	is	be	AUX
iajs-1810	82	3	equivalent	equivalent	ADJ
iajs-1810	82	4	,	,	PUNCT
iajs-1810	82	5	according	accord	VERB
iajs-1810	82	6	to	to	ADP
iajs-1810	82	7	[	[	X
iajs-1810	82	8	14	14	NUM
iajs-1810	82	9	]	]	PUNCT
iajs-1810	82	10	,	,	PUNCT
iajs-1810	82	11	to	to	ADP
iajs-1810	82	12	that	that	DET
iajs-1810	82	13	model	model	NOUN
iajs-1810	82	14	(	(	PUNCT
iajs-1810	82	15	2	2	X
iajs-1810	82	16	)	)	PUNCT
iajs-1810	82	17	undergoes	undergo	VERB
iajs-1810	82	18	a	a	DET
iajs-1810	82	19	hopf	hopf	ADJ
iajs-1810	82	20	bifurcation	bifurcation	NOUN
iajs-1810	82	21	around	around	ADP
iajs-1810	82	22	the	the	DET
iajs-1810	82	23	endemic	endemic	ADJ
iajs-1810	82	24	equilibrium	equilibrium	NOUN
iajs-1810	82	25	point	point	NOUN
iajs-1810	82	26	if	if	SCONJ
iajs-1810	82	27	and	and	CCONJ
iajs-1810	82	28	only	only	ADV
iajs-1810	82	29	if	if	SCONJ
iajs-1810	82	30	the	the	DET
iajs-1810	82	31	coefficient	coefficient	NOUN
iajs-1810	82	32	’s	’s	NOUN
iajs-1810	82	33	of	of	ADP
iajs-1810	82	34	the	the	DET
iajs-1810	82	35	characteristic	characteristic	ADJ
iajs-1810	82	36	polynomial	polynomial	NOUN
iajs-1810	82	37	given	give	VERB
iajs-1810	82	38	by	by	ADP
iajs-1810	82	39	(	(	PUNCT
iajs-1810	82	40	10b	10b	NOUN
iajs-1810	82	41	)	)	PUNCT
iajs-1810	82	42	satisfy	satisfy	NOUN
iajs-1810	82	43	that	that	SCONJ
iajs-1810	83	1	ω	ω	PROPN
iajs-1810	83	2	0	0	NUM
iajs-1810	83	3	;	;	PUNCT
iajs-1810	83	4	∀𝑖	∀𝑖	PROPN
iajs-1810	83	5	1,2,3	1,2,3	NUM
iajs-1810	83	6	with	with	ADP
iajs-1810	83	7	ω	ω	PROPN
iajs-1810	83	8	ℓ∗	ℓ∗	PROPN
iajs-1810	83	9	ω	ω	PROPN
iajs-1810	83	10	ℓ∗	ℓ∗	PROPN
iajs-1810	83	11	ω	ω	NUM
iajs-1810	83	12	ℓ∗	ℓ∗	PROPN
iajs-1810	83	13	(	(	PUNCT
iajs-1810	83	14	i.e.	i.e.	X
iajs-1810	83	15	∆	∆	X
iajs-1810	83	16	ℓ∗	ℓ∗	NOUN
iajs-1810	83	17	0	0	NUM
iajs-1810	83	18	)	)	PUNCT
iajs-1810	83	19	such	such	ADJ
iajs-1810	83	20	that	that	SCONJ
iajs-1810	83	21	∆	∆	PROPN
iajs-1810	83	22	ℓ	ℓ	NOUN
iajs-1810	83	23	|ℓ	|ℓ	VERB
iajs-1810	83	24	ℓ∗	ℓ∗	PROPN
iajs-1810	83	25	0	0	NUM
iajs-1810	83	26	.	.	PUNCT
iajs-1810	84	1	since	since	SCONJ
iajs-1810	84	2	the	the	DET
iajs-1810	84	3	condition	condition	NOUN
iajs-1810	84	4	(	(	PUNCT
iajs-1810	84	5	11	11	NUM
iajs-1810	84	6	)	)	PUNCT
iajs-1810	84	7	that	that	PRON
iajs-1810	84	8	guarantees	guarantee	VERB
iajs-1810	84	9	ω	ω	NOUN
iajs-1810	84	10	0	0	NUM
iajs-1810	84	11	;	;	PUNCT
iajs-1810	84	12	∀𝑖	∀𝑖	PROPN
iajs-1810	84	13	1,2,3	1,2,3	NUM
iajs-1810	84	14	is	be	AUX
iajs-1810	84	15	the	the	DET
iajs-1810	84	16	same	same	ADJ
iajs-1810	84	17	condition	condition	NOUN
iajs-1810	84	18	which	which	PRON
iajs-1810	84	19	guarantees	guarantee	VERB
iajs-1810	84	20	∆	∆	PROPN
iajs-1810	84	21	0	0	NUM
iajs-1810	84	22	,	,	PUNCT
iajs-1810	84	23	therefore	therefore	ADV
iajs-1810	84	24	there	there	PRON
iajs-1810	84	25	is	be	VERB
iajs-1810	84	26	no	no	DET
iajs-1810	84	27	possibility	possibility	NOUN
iajs-1810	84	28	to	to	PART
iajs-1810	84	29	have	have	AUX
iajs-1810	84	30	a	a	DET
iajs-1810	84	31	hopf	hopf	ADJ
iajs-1810	84	32	bifurcation	bifurcation	NOUN
iajs-1810	84	33	for	for	ADP
iajs-1810	84	34	model	model	NOUN
iajs-1810	84	35	(	(	PUNCT
iajs-1810	84	36	2	2	NUM
iajs-1810	84	37	)	)	PUNCT
iajs-1810	84	38	.	.	PUNCT
iajs-1810	85	1	5	5	X
iajs-1810	85	2	.	.	NOUN
iajs-1810	85	3	results	result	NOUN
iajs-1810	85	4	and	and	CCONJ
iajs-1810	85	5	numerical	numerical	PROPN
iajs-1810	85	6	simulation	simulation	NOUN
iajs-1810	85	7	.	.	PUNCT
iajs-1810	86	1	in	in	ADP
iajs-1810	86	2	this	this	DET
iajs-1810	86	3	section	section	NOUN
iajs-1810	86	4	,	,	PUNCT
iajs-1810	86	5	we	we	PRON
iajs-1810	86	6	will	will	AUX
iajs-1810	86	7	emphasize	emphasize	VERB
iajs-1810	86	8	two	two	NUM
iajs-1810	86	9	main	main	ADJ
iajs-1810	86	10	analytic	analytic	ADJ
iajs-1810	86	11	results	result	NOUN
iajs-1810	86	12	numerically	numerically	ADV
iajs-1810	86	13	according	accord	VERB
iajs-1810	86	14	to	to	ADP
iajs-1810	86	15	the	the	DET
iajs-1810	86	16	parameters	parameter	NOUN
iajs-1810	86	17	hypotheses	hypothesis	NOUN
iajs-1810	86	18	in	in	ADP
iajs-1810	86	19	table	table	NOUN
iajs-1810	86	20	1	1	NUM
iajs-1810	86	21	,	,	PUNCT
iajs-1810	86	22	we	we	PRON
iajs-1810	86	23	get	get	VERB
iajs-1810	86	24	:	:	PUNCT
iajs-1810	86	25	1	1	X
iajs-1810	86	26	.	.	X
iajs-1810	86	27	stability	stability	NOUN
iajs-1810	86	28	of	of	ADP
iajs-1810	86	29	equilibrium	equilibrium	NOUN
iajs-1810	86	30	point	point	NOUN
iajs-1810	86	31	e0	e0	PROPN
iajs-1810	86	32	and	and	CCONJ
iajs-1810	86	33	e1	e1	PROPN
iajs-1810	86	34	based	base	VERB
iajs-1810	86	35	on	on	ADP
iajs-1810	86	36	(	(	PUNCT
iajs-1810	86	37	basic	basic	ADJ
iajs-1810	86	38	reproduction	reproduction	NOUN
iajs-1810	86	39	number	number	NOUN
iajs-1810	86	40	r0	r0	NOUN
iajs-1810	86	41	)	)	PUNCT
iajs-1810	86	42	.	.	PUNCT
iajs-1810	87	1	i.	i.	PROPN
iajs-1810	87	2	according	accord	VERB
iajs-1810	87	3	to	to	ADP
iajs-1810	87	4	data	datum	NOUN
iajs-1810	87	5	in	in	ADP
iajs-1810	87	6	table1	table1	PROPN
iajs-1810	87	7	,	,	PUNCT
iajs-1810	87	8	r0	r0	VERB
iajs-1810	87	9	<	<	X
iajs-1810	87	10	1=	1=	X
iajs-1810	87	11	0.0769	0.0769	NUM
iajs-1810	87	12	and	and	CCONJ
iajs-1810	87	13	the	the	DET
iajs-1810	87	14	disease	disease	NOUN
iajs-1810	87	15	free	free	ADJ
iajs-1810	87	16	equilibrium	equilibrium	NOUN
iajs-1810	87	17	point	point	NOUN
iajs-1810	87	18	of	of	ADP
iajs-1810	87	19	model	model	NOUN
iajs-1810	87	20	(	(	PUNCT
iajs-1810	87	21	2	2	NUM
iajs-1810	87	22	)	)	PUNCT
iajs-1810	87	23	,	,	PUNCT
iajs-1810	87	24	e0	e0	PROPN
iajs-1810	87	25	=	=	PUNCT
iajs-1810	87	26	(	(	PUNCT
iajs-1810	87	27	125,0,0	125,0,0	NUM
iajs-1810	87	28	)	)	PUNCT
iajs-1810	87	29	is	be	AUX
iajs-1810	87	30	locally	locally	ADV
iajs-1810	87	31	asymptotically	asymptotically	ADV
iajs-1810	87	32	stable	stable	ADJ
iajs-1810	87	33	.	.	PUNCT
iajs-1810	88	1	we	we	PRON
iajs-1810	88	2	find	find	VERB
iajs-1810	88	3	that	that	SCONJ
iajs-1810	88	4	all	all	DET
iajs-1810	88	5	trajectories	trajectory	NOUN
iajs-1810	88	6	p1,p2,and	p1,p2,and	PROPN
iajs-1810	88	7	p3	p3	PROPN
iajs-1810	88	8	are	be	AUX
iajs-1810	88	9	tends	tend	VERB
iajs-1810	88	10	to	to	ADP
iajs-1810	88	11	e0	e0	PROPN
iajs-1810	88	12	,	,	PUNCT
iajs-1810	88	13	which	which	PRON
iajs-1810	88	14	started	start	VERB
iajs-1810	88	15	from	from	ADP
iajs-1810	88	16	three	three	NUM
iajs-1810	88	17	different	different	ADJ
iajs-1810	88	18	initial	initial	ADJ
iajs-1810	88	19	points	point	NOUN
iajs-1810	88	20	:	:	PUNCT
iajs-1810	88	21	p1=	p1=	NOUN
iajs-1810	88	22	(	(	PUNCT
iajs-1810	88	23	25,15,20	25,15,20	NOUN
iajs-1810	88	24	)	)	PUNCT
iajs-1810	88	25	,	,	PUNCT
iajs-1810	88	26	p2=(35,25,40	p2=(35,25,40	NOUN
iajs-1810	88	27	)	)	PUNCT
iajs-1810	88	28	,	,	PUNCT
iajs-1810	88	29	p3=(75,35,50	p3=(75,35,50	NOUN
iajs-1810	88	30	)	)	PUNCT
iajs-1810	88	31	,	,	PUNCT
iajs-1810	88	32	as	as	SCONJ
iajs-1810	88	33	shown	show	VERB
iajs-1810	88	34	in	in	ADP
iajs-1810	88	35	(	(	PUNCT
iajs-1810	88	36	figure1	figure1	X
iajs-1810	88	37	)	)	PUNCT
iajs-1810	88	38	achieve	achieve	VERB
iajs-1810	88	39	the	the	DET
iajs-1810	88	40	result	result	NOUN
iajs-1810	88	41	we	we	PRON
iajs-1810	88	42	get	get	VERB
iajs-1810	88	43	in	in	ADP
iajs-1810	88	44	theorem	theorem	NOUN
iajs-1810	88	45	(	(	PUNCT
iajs-1810	88	46	2	2	NUM
iajs-1810	88	47	)	)	PUNCT
iajs-1810	88	48	at	at	ADP
iajs-1810	88	49	section	section	NOUN
iajs-1810	88	50	3	3	NUM
iajs-1810	88	51	.	.	PUNCT
iajs-1810	88	52	,	,	PUNCT
iajs-1810	88	53	however	however	ADV
iajs-1810	88	54	when	when	SCONJ
iajs-1810	88	55	the	the	DET
iajs-1810	88	56	incident	incident	NOUN
iajs-1810	88	57	rate	rate	NOUN
iajs-1810	88	58	a=0.1	a=0.1	NOUN
iajs-1810	88	59	preserving	preserve	VERB
iajs-1810	88	60	the	the	DET
iajs-1810	88	61	rest	rest	NOUN
iajs-1810	88	62	data	datum	NOUN
iajs-1810	88	63	in	in	ADP
iajs-1810	88	64	table	table	NOUN
iajs-1810	88	65	1	1	NUM
iajs-1810	88	66	,	,	PUNCT
iajs-1810	88	67	and	and	CCONJ
iajs-1810	88	68	r0	r0	NOUN
iajs-1810	88	69	=	=	NOUN
iajs-1810	88	70	0.769	0.769	NUM
iajs-1810	88	71	<	<	X
iajs-1810	88	72	1	1	NUM
iajs-1810	88	73	,	,	PUNCT
iajs-1810	88	74	the	the	DET
iajs-1810	88	75	disease	disease	NOUN
iajs-1810	88	76	free	free	ADJ
iajs-1810	88	77	equilibrium	equilibrium	NOUN
iajs-1810	88	78	point	point	NOUN
iajs-1810	88	79	disappears	disappear	VERB
iajs-1810	88	80	and	and	CCONJ
iajs-1810	88	81	the	the	DET
iajs-1810	88	82	endemic	endemic	ADJ
iajs-1810	88	83	equilibrium	equilibrium	NOUN
iajs-1810	88	84	point	point	NOUN
iajs-1810	88	85	e1=(78,27,5	e1=(78,27,5	PROPN
iajs-1810	88	86	)	)	PUNCT
iajs-1810	88	87	shows	show	VERB
iajs-1810	88	88	up	up	ADP
iajs-1810	88	89	as	as	ADP
iajs-1810	88	90	asymptotically	asymptotically	ADV
iajs-1810	88	91	stable	stable	ADJ
iajs-1810	88	92	point	point	NOUN
iajs-1810	88	93	as	as	SCONJ
iajs-1810	88	94	shown	show	VERB
iajs-1810	88	95	in	in	ADP
iajs-1810	88	96	(	(	PUNCT
iajs-1810	88	97	figure2	figure2	ADJ
iajs-1810	88	98	)	)	PUNCT
iajs-1810	88	99	.	.	PUNCT
iajs-1810	89	1	ii	ii	PROPN
iajs-1810	89	2	.	.	PUNCT
iajs-1810	90	1	according	accord	VERB
iajs-1810	90	2	to	to	ADP
iajs-1810	90	3	data	datum	NOUN
iajs-1810	90	4	in	in	ADP
iajs-1810	90	5	table	table	NOUN
iajs-1810	90	6	1	1	NUM
iajs-1810	90	7	when	when	SCONJ
iajs-1810	90	8	a	a	DET
iajs-1810	90	9	=	=	NOUN
iajs-1810	90	10	0.2	0.2	NUM
iajs-1810	90	11	we	we	PRON
iajs-1810	90	12	have	have	VERB
iajs-1810	90	13	r0	r0	NOUN
iajs-1810	90	14	=	=	NOUN
iajs-1810	90	15	1.587	1.587	NUM
iajs-1810	91	1	>	>	SYM
iajs-1810	91	2	1	1	NUM
iajs-1810	91	3	the	the	DET
iajs-1810	91	4	endemic	endemic	ADJ
iajs-1810	91	5	equilibrium	equilibrium	NOUN
iajs-1810	91	6	point	point	NOUN
iajs-1810	91	7	of	of	ADP
iajs-1810	91	8	model	model	NOUN
iajs-1810	91	9	(	(	PUNCT
iajs-1810	91	10	2	2	NUM
iajs-1810	91	11	)	)	PUNCT
iajs-1810	91	12	e1=(33,54,10	e1=(33,54,10	NOUN
iajs-1810	91	13	)	)	PUNCT
iajs-1810	91	14	is	be	AUX
iajs-1810	91	15	locally	locally	ADV
iajs-1810	91	16	asymptotically	asymptotically	ADV
iajs-1810	91	17	stable	stable	ADJ
iajs-1810	91	18	and	and	CCONJ
iajs-1810	91	19	all	all	DET
iajs-1810	91	20	ihsciconf	ihsciconf	ADJ
iajs-1810	91	21	2017	2017	NUM
iajs-1810	91	22	special	special	ADJ
iajs-1810	91	23	issue	issue	NOUN
iajs-1810	91	24	ibn	ibn	PROPN
iajs-1810	91	25	al	al	PROPN
iajs-1810	91	26	-	-	PUNCT
iajs-1810	91	27	haitham	haitham	PROPN
iajs-1810	91	28	journal	journal	PROPN
iajs-1810	91	29	for	for	ADP
iajs-1810	91	30	pure	pure	ADJ
iajs-1810	91	31	and	and	CCONJ
iajs-1810	91	32	applied	apply	VERB
iajs-1810	91	33	science	science	NOUN
iajs-1810	91	34	https://doi.org/	https://doi.org/	VERB
iajs-1810	91	35	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	91	36	for	for	ADP
iajs-1810	91	37	more	more	ADJ
iajs-1810	91	38	information	information	NOUN
iajs-1810	91	39	about	about	ADP
iajs-1810	91	40	the	the	DET
iajs-1810	91	41	conference	conference	NOUN
iajs-1810	91	42	please	please	INTJ
iajs-1810	91	43	visit	visit	VERB
iajs-1810	91	44	the	the	DET
iajs-1810	91	45	websites	website	NOUN
iajs-1810	91	46	:	:	PUNCT
iajs-1810	91	47	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	91	48	  	  	SPACE
iajs-1810	91	49	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	91	50	   	   	SPACE
iajs-1810	91	51	mathematics|519	mathematics|519	ADJ
iajs-1810	91	52	    	    	SPACE
iajs-1810	91	53	solution	solution	NOUN
iajs-1810	91	54	tends	tend	VERB
iajs-1810	91	55	to	to	SCONJ
iajs-1810	91	56	it	it	PRON
iajs-1810	91	57	started	start	VERB
iajs-1810	91	58	from	from	ADP
iajs-1810	91	59	three	three	NUM
iajs-1810	91	60	different	different	ADJ
iajs-1810	91	61	initial	initial	ADJ
iajs-1810	91	62	points	point	NOUN
iajs-1810	91	63	p1=	p1=	NOUN
iajs-1810	91	64	(	(	PUNCT
iajs-1810	91	65	25,15,20	25,15,20	NOUN
iajs-1810	91	66	)	)	PUNCT
iajs-1810	91	67	,	,	PUNCT
iajs-1810	91	68	p2=(35,25,40	p2=(35,25,40	NOUN
iajs-1810	91	69	)	)	PUNCT
iajs-1810	91	70	,	,	PUNCT
iajs-1810	91	71	p3=(75,35,50	p3=(75,35,50	NOUN
iajs-1810	91	72	)	)	PUNCT
iajs-1810	91	73	as	as	SCONJ
iajs-1810	91	74	shown	show	VERB
iajs-1810	91	75	in	in	ADP
iajs-1810	91	76	(	(	PUNCT
iajs-1810	91	77	fig.5	fig.5	NOUN
iajs-1810	91	78	)	)	PUNCT
iajs-1810	91	79	,	,	PUNCT
iajs-1810	91	80	achieve	achieve	VERB
iajs-1810	91	81	the	the	DET
iajs-1810	91	82	result	result	NOUN
iajs-1810	91	83	we	we	PRON
iajs-1810	91	84	get	get	VERB
iajs-1810	91	85	in	in	ADP
iajs-1810	91	86	theorem(3	theorem(3	NOUN
iajs-1810	91	87	)	)	PUNCT
iajs-1810	91	88	at	at	ADP
iajs-1810	91	89	section	section	NOUN
iajs-1810	91	90	3	3	NUM
iajs-1810	91	91	.	.	NOUN
iajs-1810	91	92	2	2	NUM
iajs-1810	91	93	.	.	X
iajs-1810	92	1	the	the	DET
iajs-1810	92	2	effect	effect	NOUN
iajs-1810	92	3	of	of	ADP
iajs-1810	92	4	the	the	DET
iajs-1810	92	5	parameter	parameter	NOUN
iajs-1810	92	6	𝛿	𝛿	PROPN
iajs-1810	92	7	that	that	ADV
iajs-1810	92	8	responsible	responsible	ADJ
iajs-1810	92	9	on	on	ADP
iajs-1810	92	10	failure	failure	NOUN
iajs-1810	92	11	of	of	ADP
iajs-1810	92	12	treatment	treatment	NOUN
iajs-1810	92	13	on	on	ADP
iajs-1810	92	14	model	model	NOUN
iajs-1810	92	15	(	(	PUNCT
iajs-1810	92	16	2	2	NUM
iajs-1810	92	17	)	)	PUNCT
iajs-1810	92	18	shown	show	VERB
iajs-1810	92	19	as	as	SCONJ
iajs-1810	92	20	follows	follow	VERB
iajs-1810	92	21	:	:	PUNCT
iajs-1810	92	22	i.	i.	PROPN
iajs-1810	92	23	according	accord	VERB
iajs-1810	92	24	to	to	ADP
iajs-1810	92	25	data	datum	NOUN
iajs-1810	92	26	in	in	ADP
iajs-1810	92	27	table	table	NOUN
iajs-1810	92	28	1	1	NUM
iajs-1810	92	29	,	,	PUNCT
iajs-1810	92	30	the	the	DET
iajs-1810	92	31	time	time	NOUN
iajs-1810	92	32	series	series	PROPN
iajs-1810	92	33	trajectories	trajectorie	VERB
iajs-1810	92	34	in	in	ADP
iajs-1810	92	35	(	(	PUNCT
iajs-1810	92	36	figure3	figure3	NOUN
iajs-1810	92	37	)	)	PUNCT
iajs-1810	92	38	shows	show	VERB
iajs-1810	92	39	that	that	SCONJ
iajs-1810	92	40	when	when	SCONJ
iajs-1810	92	41	𝛿	𝛿	ADJ
iajs-1810	92	42	0	0	NUM
iajs-1810	92	43	the	the	DET
iajs-1810	92	44	susceptible	susceptible	ADJ
iajs-1810	92	45	individuals	individual	NOUN
iajs-1810	92	46	trajectory	trajectory	NOUN
iajs-1810	92	47	increase	increase	VERB
iajs-1810	92	48	more	more	ADJ
iajs-1810	92	49	than	than	ADP
iajs-1810	92	50	50	50	NUM
iajs-1810	92	51	,	,	PUNCT
iajs-1810	92	52	while	while	SCONJ
iajs-1810	92	53	the	the	DET
iajs-1810	92	54	infected	infected	ADJ
iajs-1810	92	55	decrease	decrease	NOUN
iajs-1810	92	56	to	to	ADP
iajs-1810	92	57	20	20	NUM
iajs-1810	92	58	and	and	CCONJ
iajs-1810	92	59	recovered	recover	VERB
iajs-1810	92	60	individuals	individual	NOUN
iajs-1810	92	61	is	be	AUX
iajs-1810	92	62	less	less	ADV
iajs-1810	92	63	than10	than10	ADJ
iajs-1810	92	64	,	,	PUNCT
iajs-1810	92	65	this	this	DET
iajs-1810	92	66	support	support	NOUN
iajs-1810	92	67	model	model	NOUN
iajs-1810	92	68	(	(	PUNCT
iajs-1810	92	69	2	2	NUM
iajs-1810	92	70	)	)	PUNCT
iajs-1810	92	71	,	,	PUNCT
iajs-1810	92	72	when	when	SCONJ
iajs-1810	92	73	there	there	PRON
iajs-1810	92	74	is	be	VERB
iajs-1810	92	75	no	no	DET
iajs-1810	92	76	failure	failure	NOUN
iajs-1810	92	77	of	of	ADP
iajs-1810	92	78	treatment(i.e	treatment(i.e	NOUN
iajs-1810	92	79	.	.	PUNCT
iajs-1810	93	1	𝛿	𝛿	ADJ
iajs-1810	93	2	0	0	NUM
iajs-1810	93	3	)	)	PUNCT
iajs-1810	93	4	,	,	PUNCT
iajs-1810	93	5	the	the	DET
iajs-1810	93	6	population	population	NOUN
iajs-1810	93	7	follows	follow	VERB
iajs-1810	93	8	natural	natural	ADJ
iajs-1810	93	9	approach	approach	NOUN
iajs-1810	93	10	against	against	ADP
iajs-1810	93	11	the	the	DET
iajs-1810	93	12	epidemic	epidemic	NOUN
iajs-1810	93	13	disease	disease	NOUN
iajs-1810	93	14	.	.	PUNCT
iajs-1810	94	1	ii	ii	PROPN
iajs-1810	94	2	.	.	PUNCT
iajs-1810	95	1	while	while	SCONJ
iajs-1810	95	2	relatively	relatively	ADV
iajs-1810	95	3	to	to	AUX
iajs-1810	95	4	data	datum	NOUN
iajs-1810	95	5	in	in	ADP
iajs-1810	95	6	table	table	NOUN
iajs-1810	95	7	1	1	NUM
iajs-1810	95	8	,	,	PUNCT
iajs-1810	95	9	with	with	ADP
iajs-1810	95	10	𝑎	𝑎	PRON
iajs-1810	95	11	0.2	0.2	NUM
iajs-1810	95	12	(	(	PUNCT
iajs-1810	95	13	figure4	figure4	NOUN
iajs-1810	95	14	)	)	PUNCT
iajs-1810	95	15	shows	show	VERB
iajs-1810	95	16	that	that	SCONJ
iajs-1810	95	17	the	the	DET
iajs-1810	95	18	susceptible	susceptible	ADJ
iajs-1810	95	19	individuals	individual	NOUN
iajs-1810	95	20	trajectories	trajectory	NOUN
iajs-1810	95	21	decrease	decrease	VERB
iajs-1810	95	22	less	less	ADJ
iajs-1810	95	23	than	than	ADP
iajs-1810	95	24	40	40	NUM
iajs-1810	95	25	,	,	PUNCT
iajs-1810	95	26	however	however	ADV
iajs-1810	95	27	the	the	DET
iajs-1810	95	28	infected	infected	ADJ
iajs-1810	95	29	individuals	individual	NOUN
iajs-1810	95	30	increase	increase	VERB
iajs-1810	95	31	to	to	ADP
iajs-1810	95	32	70	70	NUM
iajs-1810	95	33	and	and	CCONJ
iajs-1810	95	34	recovered	recover	VERB
iajs-1810	95	35	individuals	individual	NOUN
iajs-1810	95	36	are	be	AUX
iajs-1810	95	37	exactly	exactly	ADV
iajs-1810	95	38	=	=	SYM
iajs-1810	95	39	0	0	NUM
iajs-1810	95	40	,	,	PUNCT
iajs-1810	95	41	again	again	ADV
iajs-1810	95	42	this	this	DET
iajs-1810	95	43	result	result	NOUN
iajs-1810	95	44	support	support	NOUN
iajs-1810	95	45	model	model	NOUN
iajs-1810	95	46	(	(	PUNCT
iajs-1810	95	47	2	2	NUM
iajs-1810	95	48	)	)	PUNCT
iajs-1810	95	49	,	,	PUNCT
iajs-1810	95	50	when	when	SCONJ
iajs-1810	95	51	the	the	DET
iajs-1810	95	52	failure	failure	NOUN
iajs-1810	95	53	of	of	ADP
iajs-1810	95	54	treatment	treatment	NOUN
iajs-1810	95	55	is	be	AUX
iajs-1810	95	56	full	full	ADJ
iajs-1810	95	57	(	(	PUNCT
iajs-1810	95	58	i.e.	i.e.	X
iajs-1810	95	59	𝛿	𝛿	DET
iajs-1810	95	60	1	1	NUM
iajs-1810	95	61	)	)	PUNCT
iajs-1810	95	62	,	,	PUNCT
iajs-1810	95	63	the	the	DET
iajs-1810	95	64	population	population	NOUN
iajs-1810	95	65	is	be	AUX
iajs-1810	95	66	in	in	ADP
iajs-1810	95	67	complete	complete	ADJ
iajs-1810	95	68	decline	decline	NOUN
iajs-1810	95	69	with	with	ADP
iajs-1810	95	70	treatment	treatment	NOUN
iajs-1810	95	71	.	.	PUNCT
iajs-1810	96	1	in	in	ADP
iajs-1810	96	2	addition	addition	NOUN
iajs-1810	96	3	a	a	DET
iajs-1810	96	4	transcritical	transcritical	ADJ
iajs-1810	96	5	bifurcation	bifurcation	NOUN
iajs-1810	96	6	happened	happen	VERB
iajs-1810	96	7	(	(	PUNCT
iajs-1810	96	8	when	when	SCONJ
iajs-1810	96	9	𝛿	𝛿	ADJ
iajs-1810	96	10	1	1	NUM
iajs-1810	96	11	)	)	PUNCT
iajs-1810	96	12	for	for	ADP
iajs-1810	96	13	the	the	DET
iajs-1810	96	14	disease	disease	NOUN
iajs-1810	96	15	free	free	ADJ
iajs-1810	96	16	equilibrium	equilibrium	NOUN
iajs-1810	96	17	point	point	NOUN
iajs-1810	96	18	e0	e0	PROPN
iajs-1810	96	19	and	and	CCONJ
iajs-1810	96	20	this	this	PRON
iajs-1810	96	21	demonstrates	demonstrate	VERB
iajs-1810	96	22	theorem	theorem	VERB
iajs-1810	96	23	6	6	NUM
iajs-1810	96	24	.	.	NOUN
iajs-1810	96	25	table	table	NOUN
iajs-1810	96	26	(	(	PUNCT
iajs-1810	96	27	1	1	NUM
iajs-1810	96	28	)	)	PUNCT
iajs-1810	97	1	a	a	DET
iajs-1810	97	2	a	a	DET
iajs-1810	97	3	b	b	NOUN
iajs-1810	97	4	c	c	NOUN
iajs-1810	97	5	k	k	PROPN
iajs-1810	97	6	𝛼	𝛼	PROPN
iajs-1810	97	7	𝛽	𝛽	NOUN
iajs-1810	97	8	𝛾	𝛾	ADP
iajs-1810	97	9	𝛿	𝛿	PRON
iajs-1810	97	10	e0	e0	NOUN
iajs-1810	97	11	e1	e1	NOUN
iajs-1810	97	12	r0	r0	NOUN
iajs-1810	97	13	50	50	NUM
iajs-1810	97	14	0.01	0.01	NUM
iajs-1810	97	15	0.1	0.1	NUM
iajs-1810	97	16	0.1	0.1	NUM
iajs-1810	97	17	0.2	0.2	NUM
iajs-1810	97	18	0.4	0.4	NUM
iajs-1810	97	19	0.2	0.2	NUM
iajs-1810	97	20	0.5	0.5	NUM
iajs-1810	97	21	0.4	0.4	NUM
iajs-1810	97	22	stable	stable	ADJ
iajs-1810	97	23	unstable	unstable	ADJ
iajs-1810	97	24	<	<	NOUN
iajs-1810	97	25	1	1	NUM
iajs-1810	97	26	0	0	NUM
iajs-1810	97	27	stable	stable	ADJ
iajs-1810	97	28	unstable	unstable	ADJ
iajs-1810	97	29	<	<	NOUN
iajs-1810	97	30	1	1	NUM
iajs-1810	97	31	1	1	NUM
iajs-1810	97	32	unstable	unstable	ADJ
iajs-1810	97	33	stable	stable	ADJ
iajs-1810	97	34	>	>	ADP
iajs-1810	97	35	1	1	NUM
iajs-1810	97	36	50	50	NUM
iajs-1810	97	37	0.1	0.1	NUM
iajs-1810	97	38	0.1	0.1	NUM
iajs-1810	97	39	0.1	0.1	NUM
iajs-1810	97	40	0.2	0.2	NUM
iajs-1810	97	41	0.4	0.4	NUM
iajs-1810	97	42	0.2	0.2	NUM
iajs-1810	97	43	0.5	0.5	NUM
iajs-1810	97	44	0.4	0.4	NUM
iajs-1810	97	45	unstable	unstable	ADJ
iajs-1810	97	46	stable	stable	ADJ
iajs-1810	97	47	≃1	≃1	NOUN
iajs-1810	97	48	50	50	NUM
iajs-1810	97	49	0.2	0.2	NUM
iajs-1810	97	50	0.1	0.1	NUM
iajs-1810	97	51	0.1	0.1	NUM
iajs-1810	97	52	0.2	0.2	NUM
iajs-1810	97	53	0.4	0.4	NUM
iajs-1810	97	54	0.2	0.2	NUM
iajs-1810	97	55	0.5	0.5	NUM
iajs-1810	97	56	1	1	NUM
iajs-1810	97	57	unstable	unstable	ADJ
iajs-1810	97	58	stable	stable	ADJ
iajs-1810	97	59	=	=	SYM
iajs-1810	97	60	1	1	NUM
iajs-1810	97	61	figure	figure	NOUN
iajs-1810	97	62	(	(	PUNCT
iajs-1810	97	63	1	1	NUM
iajs-1810	97	64	):	):	PUNCT
iajs-1810	97	65	stability	stability	NOUN
iajs-1810	97	66	of	of	ADP
iajs-1810	97	67	(	(	PUNCT
iajs-1810	97	68	e0	e0	PROPN
iajs-1810	97	69	)	)	PUNCT
iajs-1810	97	70	the	the	DET
iajs-1810	97	71	trajectories	trajectories	PROPN
iajs-1810	97	72	p1	p1	PROPN
iajs-1810	97	73	,	,	PUNCT
iajs-1810	97	74	p2	p2	PROPN
iajs-1810	97	75	and	and	CCONJ
iajs-1810	97	76	p3	p3	PROPN
iajs-1810	97	77	are	be	AUX
iajs-1810	97	78	started	start	VERB
iajs-1810	97	79	from	from	ADP
iajs-1810	97	80	three	three	NUM
iajs-1810	97	81	different	different	ADJ
iajs-1810	97	82	initial	initial	ADJ
iajs-1810	97	83	points	point	NOUN
iajs-1810	97	84	with	with	ADP
iajs-1810	97	85	r0	r0	NOUN
iajs-1810	97	86	<	<	X
iajs-1810	97	87	1	1	NUM
iajs-1810	97	88	and	and	CCONJ
iajs-1810	97	89	a=0.01	a=0.01	NOUN
iajs-1810	97	90	ihsciconf	ihsciconf	NOUN
iajs-1810	97	91	2017	2017	NUM
iajs-1810	97	92	special	special	ADJ
iajs-1810	97	93	issue	issue	NOUN
iajs-1810	97	94	ibn	ibn	PROPN
iajs-1810	97	95	al	al	PROPN
iajs-1810	97	96	-	-	PUNCT
iajs-1810	97	97	haitham	haitham	PROPN
iajs-1810	97	98	journal	journal	PROPN
iajs-1810	97	99	for	for	ADP
iajs-1810	97	100	pure	pure	ADJ
iajs-1810	97	101	and	and	CCONJ
iajs-1810	97	102	applied	apply	VERB
iajs-1810	97	103	science	science	NOUN
iajs-1810	97	104	https://doi.org/	https://doi.org/	VERB
iajs-1810	97	105	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	97	106	for	for	ADP
iajs-1810	97	107	more	more	ADJ
iajs-1810	97	108	information	information	NOUN
iajs-1810	97	109	about	about	ADP
iajs-1810	97	110	the	the	DET
iajs-1810	97	111	conference	conference	NOUN
iajs-1810	97	112	please	please	INTJ
iajs-1810	97	113	visit	visit	VERB
iajs-1810	97	114	the	the	DET
iajs-1810	97	115	websites	website	NOUN
iajs-1810	97	116	:	:	PUNCT
iajs-1810	97	117	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	97	118	  	  	SPACE
iajs-1810	97	119	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	97	120	   	   	SPACE
iajs-1810	97	121	mathematics|520	mathematics|520	NOUN
iajs-1810	97	122	    	    	SPACE
iajs-1810	97	123	figure	figure	NOUN
iajs-1810	97	124	(	(	PUNCT
iajs-1810	97	125	2	2	NUM
iajs-1810	97	126	):	):	PUNCT
iajs-1810	97	127	stability	stability	NOUN
iajs-1810	97	128	of	of	ADP
iajs-1810	97	129	(	(	PUNCT
iajs-1810	97	130	e1	e1	PROPN
iajs-1810	97	131	)	)	PUNCT
iajs-1810	97	132	the	the	DET
iajs-1810	97	133	trajectories	trajectory	NOUN
iajs-1810	97	134	started	start	VERB
iajs-1810	97	135	from	from	ADP
iajs-1810	97	136	three	three	NUM
iajs-1810	97	137	different	different	ADJ
iajs-1810	97	138	initial	initial	ADJ
iajs-1810	97	139	points	point	NOUN
iajs-1810	97	140	p1,p2	p1,p2	PROPN
iajs-1810	97	141	and	and	CCONJ
iajs-1810	97	142	p3	p3	PROPN
iajs-1810	97	143	and	and	CCONJ
iajs-1810	97	144	data	datum	NOUN
iajs-1810	97	145	in	in	ADP
iajs-1810	97	146	table	table	NOUN
iajs-1810	97	147	1	1	NUM
iajs-1810	97	148	,	,	PUNCT
iajs-1810	97	149	for	for	ADP
iajs-1810	97	150	r0	r0	NOUN
iajs-1810	97	151	<	<	X
iajs-1810	97	152	1and	1and	NUM
iajs-1810	97	153	a=0.1	a=0.1	ADJ
iajs-1810	97	154	figure	figure	NOUN
iajs-1810	97	155	(	(	PUNCT
iajs-1810	97	156	3	3	NUM
iajs-1810	97	157	):	):	PUNCT
iajs-1810	97	158	time	time	NOUN
iajs-1810	97	159	series	series	NOUN
iajs-1810	97	160	of	of	ADP
iajs-1810	97	161	model	model	NOUN
iajs-1810	97	162	(	(	PUNCT
iajs-1810	97	163	2	2	NUM
iajs-1810	97	164	)	)	PUNCT
iajs-1810	97	165	with	with	ADP
iajs-1810	97	166	respect	respect	NOUN
iajs-1810	97	167	to	to	ADP
iajs-1810	97	168	data	datum	NOUN
iajs-1810	97	169	in	in	ADP
iajs-1810	97	170	table	table	NOUN
iajs-1810	98	1	1,when	1,when	ADP
iajs-1810	98	2	𝛿	𝛿	ADJ
iajs-1810	98	3	0	0	NUM
iajs-1810	98	4	and	and	CCONJ
iajs-1810	98	5	a=0.01	a=0.01	NOUN
iajs-1810	98	6	.	.	PUNCT
iajs-1810	99	1	figure	figure	NOUN
iajs-1810	99	2	(	(	PUNCT
iajs-1810	99	3	4	4	NUM
iajs-1810	99	4	):	):	PUNCT
iajs-1810	99	5	time	time	NOUN
iajs-1810	99	6	series	series	NOUN
iajs-1810	99	7	of	of	ADP
iajs-1810	99	8	model	model	NOUN
iajs-1810	99	9	(	(	PUNCT
iajs-1810	99	10	2	2	NUM
iajs-1810	99	11	)	)	PUNCT
iajs-1810	99	12	with	with	ADP
iajs-1810	99	13	respect	respect	NOUN
iajs-1810	99	14	to	to	ADP
iajs-1810	99	15	data	datum	NOUN
iajs-1810	99	16	in	in	ADP
iajs-1810	99	17	table	table	NOUN
iajs-1810	99	18	1	1	NUM
iajs-1810	99	19	,	,	PUNCT
iajs-1810	99	20	when	when	SCONJ
iajs-1810	99	21	𝑎	𝑎	DET
iajs-1810	99	22	0.2	0.2	NUM
iajs-1810	99	23	.	.	PUNCT
iajs-1810	100	1	ihsciconf	ihsciconf	PROPN
iajs-1810	100	2	2017	2017	NUM
iajs-1810	100	3	special	special	ADJ
iajs-1810	100	4	issue	issue	NOUN
iajs-1810	100	5	ibn	ibn	PROPN
iajs-1810	100	6	al	al	PROPN
iajs-1810	100	7	-	-	PUNCT
iajs-1810	100	8	haitham	haitham	PROPN
iajs-1810	100	9	journal	journal	PROPN
iajs-1810	100	10	for	for	ADP
iajs-1810	100	11	pure	pure	ADJ
iajs-1810	100	12	and	and	CCONJ
iajs-1810	100	13	applied	apply	VERB
iajs-1810	100	14	science	science	NOUN
iajs-1810	100	15	https://doi.org/	https://doi.org/	VERB
iajs-1810	100	16	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	100	17	for	for	ADP
iajs-1810	100	18	more	more	ADJ
iajs-1810	100	19	information	information	NOUN
iajs-1810	100	20	about	about	ADP
iajs-1810	100	21	the	the	DET
iajs-1810	100	22	conference	conference	NOUN
iajs-1810	100	23	please	please	INTJ
iajs-1810	100	24	visit	visit	VERB
iajs-1810	100	25	the	the	DET
iajs-1810	100	26	websites	website	NOUN
iajs-1810	100	27	:	:	PUNCT
iajs-1810	100	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	100	29	  	  	SPACE
iajs-1810	100	30	www.ihsciconf.org	www.ihsciconf.org	NOUN
iajs-1810	100	31	   	   	SPACE
iajs-1810	100	32	mathematics|521	mathematics|521	NOUN
iajs-1810	100	33	    	    	SPACE
iajs-1810	100	34	figure	figure	NOUN
iajs-1810	100	35	(	(	PUNCT
iajs-1810	100	36	5	5	NUM
iajs-1810	100	37	):	):	PUNCT
iajs-1810	100	38	stability	stability	NOUN
iajs-1810	100	39	of	of	ADP
iajs-1810	100	40	(	(	PUNCT
iajs-1810	100	41	e1	e1	PROPN
iajs-1810	100	42	)	)	PUNCT
iajs-1810	100	43	the	the	DET
iajs-1810	100	44	trajectories	trajectory	NOUN
iajs-1810	100	45	started	start	VERB
iajs-1810	100	46	from	from	ADP
iajs-1810	100	47	three	three	NUM
iajs-1810	100	48	different	different	ADJ
iajs-1810	100	49	initial	initial	ADJ
iajs-1810	100	50	points	point	NOUN
iajs-1810	100	51	p1	p1	NOUN
iajs-1810	100	52	,	,	PUNCT
iajs-1810	100	53	p2	p2	PROPN
iajs-1810	100	54	and	and	CCONJ
iajs-1810	100	55	p3	p3	PROPN
iajs-1810	100	56	,	,	PUNCT
iajs-1810	100	57	for	for	ADP
iajs-1810	100	58	data	datum	NOUN
iajs-1810	100	59	in	in	ADP
iajs-1810	100	60	table	table	NOUN
iajs-1810	100	61	1	1	NUM
iajs-1810	100	62	when	when	SCONJ
iajs-1810	100	63	r0	r0	NOUN
iajs-1810	100	64	>	>	X
iajs-1810	100	65	1and	1and	NUM
iajs-1810	100	66	a=	a=	NOUN
iajs-1810	100	67	0.2	0.2	NUM
iajs-1810	100	68	.	.	PUNCT
iajs-1810	101	1	references	reference	NOUN
iajs-1810	101	2	[	[	X
iajs-1810	101	3	1	1	NUM
iajs-1810	101	4	]	]	PUNCT
iajs-1810	101	5	.	.	PUNCT
iajs-1810	102	1	v.	v.	ADP
iajs-1810	102	2	capasso	capasso	PROPN
iajs-1810	102	3	;	;	PUNCT
iajs-1810	102	4	g.	g.	PROPN
iajs-1810	102	5	serio	serio	PROPN
iajs-1810	102	6	,	,	PUNCT
iajs-1810	102	7	a	a	DET
iajs-1810	102	8	generalization	generalization	NOUN
iajs-1810	102	9	of	of	ADP
iajs-1810	102	10	the	the	DET
iajs-1810	102	11	kermack	kermack	NOUN
iajs-1810	102	12	–	–	PUNCT
iajs-1810	102	13	mckendrick	mckendrick	NOUN
iajs-1810	102	14	deterministic	deterministic	ADJ
iajs-1810	102	15	epidemic	epidemic	NOUN
iajs-1810	102	16	model	model	NOUN
iajs-1810	102	17	,	,	PUNCT
iajs-1810	102	18	math	math	NOUN
iajs-1810	102	19	.	.	PUNCT
iajs-1810	103	1	biosci	biosci	PROPN
iajs-1810	103	2	.	.	PUNCT
iajs-1810	103	3	,	,	PUNCT
iajs-1810	103	4	.	.	PUNCT
iajs-1810	104	1	41	41	NUM
iajs-1810	104	2	-	-	SYM
iajs-1810	104	3	42	42	NUM
iajs-1810	104	4	.	.	PUNCT
iajs-1810	105	1	1978	1978	NUM
iajs-1810	105	2	.	.	PUNCT
iajs-1810	106	1	[	[	X
iajs-1810	106	2	2	2	NUM
iajs-1810	106	3	]	]	PUNCT
iajs-1810	106	4	,	,	PUNCT
iajs-1810	106	5	p.	p.	PROPN
iajs-1810	106	6	van	van	PROPN
iajs-1810	106	7	den	den	PROPN
iajs-1810	106	8	driessche	driessche	NOUN
iajs-1810	106	9	;	;	PUNCT
iajs-1810	106	10	james	james	PROPN
iajs-1810	106	11	watmough	watmough	PROPN
iajs-1810	106	12	,	,	PUNCT
iajs-1810	106	13	reproduction	reproduction	NOUN
iajs-1810	106	14	numbers	number	NOUN
iajs-1810	106	15	and	and	CCONJ
iajs-1810	106	16	sub	sub	ADJ
iajs-1810	106	17	-	-	ADJ
iajs-1810	106	18	threshold	threshold	ADJ
iajs-1810	106	19	endemic	endemic	ADJ
iajs-1810	106	20	equilibria	equilibrium	NOUN
iajs-1810	106	21	for	for	ADP
iajs-1810	106	22	compartmental	compartmental	ADJ
iajs-1810	106	23	models	model	NOUN
iajs-1810	106	24	of	of	ADP
iajs-1810	106	25	disease	disease	NOUN
iajs-1810	106	26	transmission	transmission	NOUN
iajs-1810	106	27	,	,	PUNCT
iajs-1810	106	28	mathematical	mathematical	ADJ
iajs-1810	106	29	biosciences	bioscience	NOUN
iajs-1810	106	30	,	,	PUNCT
iajs-1810	106	31	elsevier	elsevier	NOUN
iajs-1810	106	32	,	,	PUNCT
iajs-1810	106	33	180	180	NUM
iajs-1810	106	34	(	(	PUNCT
iajs-1810	106	35	2002	2002	NUM
iajs-1810	106	36	)	)	PUNCT
iajs-1810	106	37	,	,	PUNCT
iajs-1810	106	38	pp	pp	ADP
iajs-1810	106	39	.	.	PUNCT
iajs-1810	107	1	29–48	29–48	NUM
iajs-1810	107	2	.	.	PUNCT
iajs-1810	108	1	[	[	X
iajs-1810	108	2	3	3	NUM
iajs-1810	108	3	]	]	PUNCT
iajs-1810	108	4	,	,	PUNCT
iajs-1810	108	5	hu	hu	PROPN
iajs-1810	108	6	.	.	PUNCT
iajs-1810	108	7	zhixing	zhixing	PROPN
iajs-1810	108	8	;	;	PUNCT
iajs-1810	108	9	ma	ma	PROPN
iajs-1810	108	10	,	,	PUNCT
iajs-1810	108	11	wanbiao	wanbiao	NOUN
iajs-1810	108	12	and	and	CCONJ
iajs-1810	108	13	shigui	shigui	NOUN
iajs-1810	108	14	ruan	ruan	NOUN
iajs-1810	108	15	,	,	PUNCT
iajs-1810	108	16	analysis	analysis	NOUN
iajs-1810	108	17	of	of	ADP
iajs-1810	108	18	sir	sir	NOUN
iajs-1810	108	19	epidemic	epidemic	NOUN
iajs-1810	108	20	models	model	NOUN
iajs-1810	108	21	with	with	ADP
iajs-1810	108	22	nonlinear	nonlinear	ADJ
iajs-1810	108	23	incidence	incidence	NOUN
iajs-1810	108	24	rate	rate	NOUN
iajs-1810	108	25	and	and	CCONJ
iajs-1810	108	26	treatment	treatment	NOUN
iajs-1810	108	27	,	,	PUNCT
iajs-1810	108	28	mathematical	mathematical	ADJ
iajs-1810	108	29	biosciences	bioscience	NOUN
iajs-1810	108	30	,	,	PUNCT
iajs-1810	108	31	elsevier	elsevier	NOUN
iajs-1810	108	32	,	,	PUNCT
iajs-1810	108	33	238	238	NUM
iajs-1810	108	34	12–20	12–20	NUM
iajs-1810	108	35	2012	2012	NUM
iajs-1810	108	36	.	.	PUNCT
iajs-1810	109	1	[	[	X
iajs-1810	109	2	4	4	NUM
iajs-1810	109	3	]	]	PUNCT
iajs-1810	109	4	.	.	PUNCT
iajs-1810	110	1	xue	xue	PROPN
iajs-1810	110	2	.	.	PUNCT
iajs-1810	111	1	yakui	yakui	PROPN
iajs-1810	111	2	and	and	CCONJ
iajs-1810	111	3	xlafeng	xlafeng	PROPN
iajs-1810	111	4	duan	duan	PROPN
iajs-1810	111	5	,	,	PUNCT
iajs-1810	111	6	dynamic	dynamic	ADJ
iajs-1810	111	7	analysis	analysis	NOUN
iajs-1810	111	8	of	of	ADP
iajs-1810	111	9	an	an	DET
iajs-1810	111	10	sir	sir	NOUN
iajs-1810	111	11	model	model	NOUN
iajs-1810	111	12	with	with	ADP
iajs-1810	111	13	nonlinear	nonlinear	ADJ
iajs-1810	111	14	incidence	incidence	NOUN
iajs-1810	111	15	rate	rate	NOUN
iajs-1810	111	16	and	and	CCONJ
iajs-1810	111	17	double	double	ADJ
iajs-1810	111	18	delays	delay	NOUN
iajs-1810	111	19	,	,	PUNCT
iajs-1810	111	20	international	international	ADJ
iajs-1810	111	21	journal	journal	NOUN
iajs-1810	111	22	of	of	ADP
iajs-1810	111	23	information	information	NOUN
iajs-1810	111	24	and	and	CCONJ
iajs-1810	111	25	systems	system	NOUN
iajs-1810	111	26	sciences	science	NOUN
iajs-1810	111	27	,	,	PUNCT
iajs-1810	111	28	7	7	NUM
iajs-1810	111	29	,	,	PUNCT
iajs-1810	111	30	1	1	NUM
iajs-1810	111	31	.	.	X
iajs-1810	111	32	92–10	92–10	NUM
iajs-1810	111	33	-	-	SYM
iajs-1810	111	34	2	2	NUM
iajs-1810	111	35	2011	2011	NUM
iajs-1810	111	36	.	.	PUNCT
iajs-1810	112	1	[	[	X
iajs-1810	112	2	5	5	NUM
iajs-1810	112	3	]	]	PUNCT
iajs-1810	112	4	.	.	PUNCT
iajs-1810	113	1	n.	n.	PROPN
iajs-1810	113	2	saba	saba	PROPN
iajs-1810	113	3	majeed	majeed	PROPN
iajs-1810	113	4	,	,	PUNCT
iajs-1810	113	5	stability	stability	NOUN
iajs-1810	113	6	analysis	analysis	NOUN
iajs-1810	113	7	of	of	ADP
iajs-1810	113	8	sir	sir	NOUN
iajs-1810	113	9	holing	hole	VERB
iajs-1810	113	10	type	type	NOUN
iajs-1810	113	11	ii	ii	PROPN
iajs-1810	113	12	infectious	infectious	ADJ
iajs-1810	113	13	epidemic	epidemic	NOUN
iajs-1810	113	14	model	model	NOUN
iajs-1810	113	15	with	with	ADP
iajs-1810	113	16	treatment	treatment	NOUN
iajs-1810	113	17	failure	failure	NOUN
iajs-1810	113	18	rate	rate	NOUN
iajs-1810	113	19	,	,	PUNCT
iajs-1810	113	20	mathematical	mathematical	ADJ
iajs-1810	113	21	theory	theory	NOUN
iajs-1810	113	22	and	and	CCONJ
iajs-1810	113	23	modeling.6,.2	modeling.6,.2	PROPN
iajs-1810	113	24	,	,	PUNCT
iajs-1810	113	25	.	.	PUNCT
iajs-1810	114	1	50	50	NUM
iajs-1810	114	2	-	-	SYM
iajs-1810	114	3	60	60	NUM
iajs-1810	114	4	.	.	PUNCT
iajs-1810	114	5	2016	2016	NUM
iajs-1810	115	1	[	[	X
iajs-1810	115	2	6	6	NUM
iajs-1810	115	3	]	]	PUNCT
iajs-1810	115	4	.	.	PUNCT
iajs-1810	116	1	n.	n.	PROPN
iajs-1810	116	2	saba	saba	PROPN
iajs-1810	116	3	majeed	majeed	PROPN
iajs-1810	116	4	,	,	PUNCT
iajs-1810	116	5	local	local	ADJ
iajs-1810	116	6	bifurcation	bifurcation	NOUN
iajs-1810	116	7	analysis	analysis	NOUN
iajs-1810	116	8	for	for	ADP
iajs-1810	116	9	a	a	DET
iajs-1810	116	10	special	special	ADJ
iajs-1810	116	11	type	type	NOUN
iajs-1810	116	12	of	of	ADP
iajs-1810	116	13	sir	sir	NOUN
iajs-1810	116	14	epidemic	epidemic	NOUN
iajs-1810	116	15	model	model	NOUN
iajs-1810	116	16	,	,	PUNCT
iajs-1810	116	17	international	international	ADJ
iajs-1810	116	18	journal	journal	NOUN
iajs-1810	116	19	of	of	ADP
iajs-1810	116	20	science	science	NOUN
iajs-1810	116	21	and	and	CCONJ
iajs-1810	116	22	research	research	NOUN
iajs-1810	116	23	ijsr	ijsr	NOUN
iajs-1810	116	24	,	,	PUNCT
iajs-1810	116	25	.	.	PUNCT
iajs-1810	117	1	6	6	NUM
iajs-1810	117	2	,	,	PUNCT
iajs-1810	117	3	2	2	NUM
iajs-1810	117	4	,	,	PUNCT
iajs-1810	117	5	.	.	PUNCT
iajs-1810	118	1	1143	1143	NUM
iajs-1810	118	2	-1146	-1146	NOUN
iajs-1810	118	3	.	.	PUNCT
iajs-1810	119	1	2017	2017	NUM
iajs-1810	119	2	.	.	PUNCT
iajs-1810	120	1	[	[	X
iajs-1810	120	2	7	7	NUM
iajs-1810	120	3	]	]	PUNCT
iajs-1810	120	4	.	.	PUNCT
iajs-1810	121	1	balram	balram	PROPN
iajs-1810	121	2	dubey	dubey	PROPN
iajs-1810	121	3	,	,	PUNCT
iajs-1810	121	4	preeti	preeti	PROPN
iajs-1810	121	5	dubey	dubey	PROPN
iajs-1810	121	6	,	,	PUNCT
iajs-1810	121	7	and	and	CCONJ
iajs-1810	121	8	s.	s.	PROPN
iajs-1810	121	9	uma	uma	PROPN
iajs-1810	121	10	dubey	dubey	PROPN
iajs-1810	121	11	,	,	PUNCT
iajs-1810	121	12	dynamics	dynamic	NOUN
iajs-1810	121	13	of	of	ADP
iajs-1810	121	14	an	an	DET
iajs-1810	121	15	sir	sir	NOUN
iajs-1810	121	16	model	model	NOUN
iajs-1810	121	17	with	with	ADP
iajs-1810	121	18	nonlinear	nonlinear	ADJ
iajs-1810	121	19	incidence	incidence	NOUN
iajs-1810	121	20	and	and	CCONJ
iajs-1810	121	21	treatment	treatment	NOUN
iajs-1810	121	22	rate	rate	NOUN
iajs-1810	121	23	,	,	PUNCT
iajs-1810	121	24	applications	application	NOUN
iajs-1810	121	25	and	and	CCONJ
iajs-1810	121	26	applied	apply	VERB
iajs-1810	121	27	mathematics	mathematic	NOUN
iajs-1810	121	28	:	:	PUNCT
iajs-1810	121	29	an	an	DET
iajs-1810	121	30	international	international	ADJ
iajs-1810	121	31	journal	journal	NOUN
iajs-1810	121	32	(	(	PUNCT
iajs-1810	121	33	aam	aam	PROPN
iajs-1810	121	34	)	)	PUNCT
iajs-1810	121	35	,	,	PUNCT
iajs-1810	121	36	.	.	PUNCT
iajs-1810	122	1	10	10	NUM
iajs-1810	122	2	,	,	PUNCT
iajs-1810	122	3	2	2	NUM
iajs-1810	122	4	,	,	PUNCT
iajs-1810	122	5	,	,	PUNCT
iajs-1810	122	6	.	.	PUNCT
iajs-1810	123	1	718	718	NUM
iajs-1810	123	2	–	–	PUNCT
iajs-1810	123	3	737	737	NUM
iajs-1810	123	4	.	.	NOUN
iajs-1810	123	5	2015	2015	NUM
iajs-1810	123	6	.	.	PUNCT
iajs-1810	124	1	[	[	X
iajs-1810	124	2	8	8	NUM
iajs-1810	124	3	]	]	PUNCT
iajs-1810	124	4	.	.	PUNCT
iajs-1810	125	1	x.	x.	PROPN
iajs-1810	125	2	li	li	PROPN
iajs-1810	125	3	;	;	PUNCT
iajs-1810	125	4	w.li	w.li	PROPN
iajs-1810	125	5	,	,	PUNCT
iajs-1810	125	6	and	and	CCONJ
iajs-1810	125	7	ghosh	ghosh	PROPN
iajs-1810	125	8	,	,	PUNCT
iajs-1810	125	9	m	m	PROPN
iajs-1810	125	10	..	..	PUNCT
iajs-1810	125	11	stability	stability	NOUN
iajs-1810	125	12	and	and	CCONJ
iajs-1810	125	13	bifurcation	bifurcation	NOUN
iajs-1810	125	14	of	of	ADP
iajs-1810	125	15	an	an	DET
iajs-1810	125	16	sir	sir	NOUN
iajs-1810	125	17	epidemic	epidemic	NOUN
iajs-1810	125	18	model	model	NOUN
iajs-1810	125	19	with	with	ADP
iajs-1810	125	20	nonlinear	nonlinear	ADJ
iajs-1810	125	21	incidence	incidence	NOUN
iajs-1810	125	22	and	and	CCONJ
iajs-1810	125	23	treatment	treatment	NOUN
iajs-1810	125	24	.	.	PUNCT
iajs-1810	126	1	applied	apply	VERB
iajs-1810	126	2	mathematics	mathematic	NOUN
iajs-1810	126	3	and	and	CCONJ
iajs-1810	126	4	computation	computation	NOUN
iajs-1810	126	5	.	.	PUNCT
iajs-1810	127	1	210	210	NUM
iajs-1810	127	2	,	,	PUNCT
iajs-1810	127	3	.	.	PUNCT
iajs-1810	128	1	141150	141150	NUM
iajs-1810	128	2	.	.	PUNCT
iajs-1810	129	1	(	(	PUNCT
iajs-1810	129	2	2009	2009	NUM
iajs-1810	129	3	)	)	PUNCT
iajs-1810	129	4	.	.	PUNCT
iajs-1810	130	1	[	[	X
iajs-1810	130	2	9	9	NUM
iajs-1810	130	3	]	]	PUNCT
iajs-1810	130	4	.	.	PUNCT
iajs-1810	131	1	j.	j.	PROPN
iajs-1810	131	2	beddington	beddington	PROPN
iajs-1810	131	3	;	;	PUNCT
iajs-1810	131	4	r.	r.	PROPN
iajs-1810	131	5	mutual	mutual	ADJ
iajs-1810	131	6	interference	interference	NOUN
iajs-1810	131	7	between	between	ADP
iajs-1810	131	8	parasites	parasite	NOUN
iajs-1810	131	9	or	or	CCONJ
iajs-1810	131	10	predators	predator	NOUN
iajs-1810	131	11	and	and	CCONJ
iajs-1810	131	12	its	its	PRON
iajs-1810	131	13	effect	effect	NOUN
iajs-1810	131	14	on	on	ADP
iajs-1810	131	15	searching	search	VERB
iajs-1810	131	16	efficiency	efficiency	NOUN
iajs-1810	131	17	.	.	PUNCT
iajs-1810	132	1	journal	journal	NOUN
iajs-1810	132	2	of	of	ADP
iajs-1810	132	3	animal	animal	NOUN
iajs-1810	132	4	ecology	ecology	NOUN
iajs-1810	132	5	,	,	PUNCT
iajs-1810	132	6	.	.	PUNCT
iajs-1810	133	1	44	44	NUM
iajs-1810	133	2	,	,	PUNCT
iajs-1810	133	3	.	.	PUNCT
iajs-1810	134	1	331	331	NUM
iajs-1810	134	2	-	-	SYM
iajs-1810	134	3	340	340	NUM
iajs-1810	134	4	.	.	PUNCT
iajs-1810	135	1	1975	1975	NUM
iajs-1810	135	2	.	.	PUNCT
iajs-1810	136	1	[	[	X
iajs-1810	136	2	10	10	NUM
iajs-1810	136	3	]	]	PUNCT
iajs-1810	136	4	.	.	PUNCT
iajs-1810	137	1	d.l	d.l	PROPN
iajs-1810	137	2	.	.	PROPN
iajs-1810	137	3	deangelis;r.a	deangelis;r.a	PROPN
iajs-1810	137	4	.	.	PUNCT
iajs-1810	137	5	goldstein	goldstein	PROPN
iajs-1810	137	6	,	,	PUNCT
iajs-1810	137	7	and	and	CCONJ
iajs-1810	137	8	o’neill	o’neill	PROPN
iajs-1810	137	9	,	,	PUNCT
iajs-1810	137	10	r.v	r.v	PROPN
iajs-1810	137	11	.	.	PUNCT
iajs-1810	137	12	a	a	DET
iajs-1810	137	13	model	model	NOUN
iajs-1810	137	14	for	for	ADP
iajs-1810	137	15	tropic	tropic	NOUN
iajs-1810	137	16	interaction	interaction	NOUN
iajs-1810	137	17	,	,	PUNCT
iajs-1810	137	18	ecology	ecology	NOUN
iajs-1810	137	19	,	,	PUNCT
iajs-1810	137	20	.	.	PUNCT
iajs-1810	138	1	56	56	NUM
iajs-1810	138	2	(	(	PUNCT
iajs-1810	138	3	1975	1975	NUM
iajs-1810	138	4	)	)	PUNCT
iajs-1810	138	5	.	.	PUNCT
iajs-1810	139	1	881	881	NUM
iajs-1810	139	2	-	-	SYM
iajs-1810	139	3	892	892	NUM
iajs-1810	139	4	.	.	PUNCT
iajs-1810	140	1	ihsciconf	ihsciconf	PROPN
iajs-1810	140	2	2017	2017	NUM
iajs-1810	140	3	special	special	ADJ
iajs-1810	140	4	issue	issue	NOUN
iajs-1810	140	5	ibn	ibn	PROPN
iajs-1810	140	6	al	al	PROPN
iajs-1810	140	7	-	-	PUNCT
iajs-1810	140	8	haitham	haitham	PROPN
iajs-1810	140	9	journal	journal	PROPN
iajs-1810	140	10	for	for	ADP
iajs-1810	140	11	pure	pure	ADJ
iajs-1810	140	12	and	and	CCONJ
iajs-1810	140	13	applied	apply	VERB
iajs-1810	140	14	science	science	NOUN
iajs-1810	140	15	https://doi.org/	https://doi.org/	VERB
iajs-1810	140	16	10.30526/2017.ihsciconf.1810	10.30526/2017.ihsciconf.1810	NUM
iajs-1810	140	17	for	for	ADP
iajs-1810	140	18	more	more	ADJ
iajs-1810	140	19	information	information	NOUN
iajs-1810	140	20	about	about	ADP
iajs-1810	140	21	the	the	DET
iajs-1810	140	22	conference	conference	NOUN
iajs-1810	140	23	please	please	INTJ
iajs-1810	140	24	visit	visit	VERB
iajs-1810	140	25	the	the	DET
iajs-1810	140	26	websites	website	NOUN
iajs-1810	140	27	:	:	PUNCT
iajs-1810	140	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1810	140	29	  	  	SPACE
iajs-1810	140	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1810	140	31	   	   	SPACE
iajs-1810	140	32	mathematics|522	mathematics|522	NOUN
iajs-1810	140	33	    	    	SPACE
iajs-1810	141	1	[	[	X
iajs-1810	141	2	11	11	NUM
iajs-1810	141	3	]	]	PUNCT
iajs-1810	141	4	.	.	PUNCT
iajs-1810	142	1	lawrence	lawrence	PROPN
iajs-1810	142	2	perko	perko	PROPN
iajs-1810	142	3	,	,	PUNCT
iajs-1810	142	4	differential	differential	ADJ
iajs-1810	142	5	equations	equation	NOUN
iajs-1810	142	6	and	and	CCONJ
iajs-1810	142	7	dynamical	dynamical	ADJ
iajs-1810	142	8	systems	system	NOUN
iajs-1810	142	9	,	,	PUNCT
iajs-1810	142	10	third	third	ADJ
iajs-1810	142	11	edition	edition	NOUN
iajs-1810	142	12	,	,	PUNCT
iajs-1810	142	13	springer	springer	NOUN
iajs-1810	142	14	,	,	PUNCT
iajs-1810	142	15	new	new	PROPN
iajs-1810	142	16	york	york	PROPN
iajs-1810	142	17	.	.	PUNCT
iajs-1810	142	18	,.349	,.349	PROPN
iajs-1810	142	19	-	-	PUNCT
iajs-1810	142	20	362	362	NUM
iajs-1810	142	21	.	.	PUNCT
iajs-1810	143	1	2001	2001	NUM
iajs-1810	143	2	online	online	ADV
iajs-1810	143	3	available	available	ADJ
iajs-1810	143	4	:	:	PUNCT
iajs-1810	144	1	http://journal.sapub.org/ajb	http://journal.sapub.org/ajb	PROPN
iajs-1810	144	2	.	.	PUNCT
iajs-1810	145	1	[	[	X
iajs-1810	145	2	12	12	NUM
iajs-1810	145	3	]	]	PUNCT
iajs-1810	145	4	.bruce	.bruce	NUM
iajs-1810	145	5	anderson	anderson	PROPN
iajs-1810	145	6	,	,	PUNCT
iajs-1810	145	7	jeffry	jeffry	PROPN
iajs-1810	145	8	jackson	jackson	PROPN
iajs-1810	145	9	and	and	CCONJ
iajs-1810	145	10	meera	meera	PROPN
iajs-1810	145	11	sitharam	sitharam	PROPN
iajs-1810	145	12	,	,	PUNCT
iajs-1810	145	13	descartes	descartes	PROPN
iajs-1810	145	14	'	'	PART
iajs-1810	145	15	rule	rule	NOUN
iajs-1810	145	16	of	of	ADP
iajs-1810	145	17	signs	sign	NOUN
iajs-1810	145	18	revisited	revisit	VERB
iajs-1810	145	19	,	,	PUNCT
iajs-1810	145	20	the	the	DET
iajs-1810	145	21	american	american	PROPN
iajs-1810	145	22	mathematical	mathematical	PROPN
iajs-1810	145	23	monthly	monthly	ADV
iajs-1810	145	24	,	,	PUNCT
iajs-1810	145	25	.	.	PUNCT
iajs-1810	146	1	105	105	NUM
iajs-1810	146	2	,	,	PUNCT
iajs-1810	146	3	no	no	INTJ
iajs-1810	146	4	.	.	NOUN
iajs-1810	146	5	5	5	NUM
iajs-1810	146	6	.	.	X
iajs-1810	146	7	447	447	NUM
iajs-1810	146	8	-	-	SYM
iajs-1810	146	9	451	451	NUM
iajs-1810	146	10	.	.	PUNCT
iajs-1810	147	1	1998	1998	NUM
iajs-1810	148	1	[	[	X
iajs-1810	148	2	13	13	NUM
iajs-1810	148	3	]	]	PUNCT
iajs-1810	148	4	.	.	PUNCT
iajs-1810	149	1	r.m	r.m	PROPN
iajs-1810	149	2	.	.	PROPN
iajs-1810	150	1	may	may	AUX
iajs-1810	150	2	,	,	PUNCT
iajs-1810	150	3	stability	stability	NOUN
iajs-1810	150	4	and	and	CCONJ
iajs-1810	150	5	complexity	complexity	NOUN
iajs-1810	150	6	in	in	ADP
iajs-1810	150	7	model	model	NOUN
iajs-1810	150	8	ecosystem	ecosystem	NOUN
iajs-1810	150	9	,	,	PUNCT
iajs-1810	150	10	ecology	ecology	NOUN
iajs-1810	150	11	,	,	PUNCT
iajs-1810	150	12	.	.	PUNCT
iajs-1810	151	1	54	54	NUM
iajs-1810	151	2	,	,	PUNCT
iajs-1810	151	3	.	.	PUNCT
iajs-1810	152	1	3	3	NUM
iajs-1810	152	2	,	,	PUNCT
iajs-1810	152	3	1973	1973	NUM
iajs-1810	152	4	.	.	PUNCT
iajs-1810	153	1	638641	638641	NUM
iajs-1810	153	2	.	.	PUNCT
iajs-1810	154	1	[	[	X
iajs-1810	154	2	14	14	NUM
iajs-1810	154	3	]	]	PUNCT
iajs-1810	154	4	.	.	PUNCT
iajs-1810	155	1	a.	a.	PROPN
iajs-1810	155	2	m.	m.	PROPN
iajs-1810	155	3	lyapunov	lyapunov	PROPN
iajs-1810	155	4	’s	’s	PART
iajs-1810	155	5	,	,	PUNCT
iajs-1810	155	6	the	the	DET
iajs-1810	155	7	general	general	ADJ
iajs-1810	155	8	problem	problem	NOUN
iajs-1810	155	9	of	of	ADP
iajs-1810	155	10	the	the	DET
iajs-1810	155	11	stability	stability	NOUN
iajs-1810	155	12	of	of	ADP
iajs-1810	155	13	motion	motion	NOUN
iajs-1810	155	14	,	,	PUNCT
iajs-1810	155	15	int	int	NOUN
iajs-1810	155	16	.	.	PUNCT
iajs-1810	156	1	j.	j.	PROPN
iajs-1810	156	2	control,55	control,55	PROPN
iajs-1810	156	3	,	,	PUNCT
iajs-1810	156	4	.	.	PUNCT
iajs-1810	157	1	3	3	NUM
iajs-1810	157	2	,	,	PUNCT
iajs-1810	157	3	531	531	NUM
iajs-1810	157	4	-	-	SYM
iajs-1810	157	5	773	773	NUM
iajs-1810	157	6	.	.	PUNCT
iajs-1810	157	7	1992	1992	NUM
iajs-1810	157	8	.	.	PUNCT