id	sid	tid	token	lemma	pos
ijassa-1064	1	1	adv	adv	PROPN
ijassa-1064	1	2	syst	syst	PROPN
ijassa-1064	1	3	sci	sci	PROPN
ijassa-1064	1	4	appl	appl	PROPN
ijassa-1064	1	5	2021	2021	NUM
ijassa-1064	1	6	;	;	PUNCT
ijassa-1064	1	7	02:83–103	02:83–103	NUM
ijassa-1064	1	8	published	publish	VERB
ijassa-1064	1	9	online	online	ADV
ijassa-1064	1	10	at	at	ADP
ijassa-1064	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADJ
ijassa-1064	1	12	.	.	PUNCT
ijassa-1064	2	1	stability	stability	NOUN
ijassa-1064	2	2	analysis	analysis	NOUN
ijassa-1064	2	3	and	and	CCONJ
ijassa-1064	2	4	optimal	optimal	ADJ
ijassa-1064	2	5	measure	measure	NOUN
ijassa-1064	2	6	for	for	ADP
ijassa-1064	2	7	controlling	control	VERB
ijassa-1064	2	8	eco	eco	PROPN
ijassa-1064	2	9	-	-	PUNCT
ijassa-1064	2	10	epidemiological	epidemiological	ADJ
ijassa-1064	2	11	dynamics	dynamic	NOUN
ijassa-1064	2	12	of	of	ADP
ijassa-1064	2	13	prey	prey	NOUN
ijassa-1064	2	14	-	-	PUNCT
ijassa-1064	2	15	predator	predator	NOUN
ijassa-1064	2	16	model	model	NOUN
ijassa-1064	2	17	jamiu	jamiu	PROPN
ijassa-1064	2	18	a.	a.	PROPN
ijassa-1064	2	19	ademosu	ademosu	PROPN
ijassa-1064	2	20	,	,	PUNCT
ijassa-1064	2	21	samson	samson	PROPN
ijassa-1064	2	22	olaniyi	olaniyi	PROPN
ijassa-1064	2	23	*	*	PROPN
ijassa-1064	2	24	,	,	PUNCT
ijassa-1064	2	25	sunday	sunday	PROPN
ijassa-1064	2	26	o.	o.	PROPN
ijassa-1064	2	27	adewale	adewale	PROPN
ijassa-1064	2	28	department	department	PROPN
ijassa-1064	2	29	of	of	ADP
ijassa-1064	2	30	pure	pure	ADJ
ijassa-1064	2	31	and	and	CCONJ
ijassa-1064	2	32	applied	applied	ADJ
ijassa-1064	2	33	mathematics	mathematic	NOUN
ijassa-1064	2	34	,	,	PUNCT
ijassa-1064	2	35	ladoke	ladoke	ADJ
ijassa-1064	2	36	akintola	akintola	PROPN
ijassa-1064	2	37	university	university	PROPN
ijassa-1064	2	38	of	of	ADP
ijassa-1064	2	39	technology	technology	NOUN
ijassa-1064	2	40	,	,	PUNCT
ijassa-1064	2	41	ogbomoso	ogbomoso	ADJ
ijassa-1064	2	42	,	,	PUNCT
ijassa-1064	2	43	nigeria	nigeria	PROPN
ijassa-1064	2	44	abstract	abstract	NOUN
ijassa-1064	2	45	:	:	PUNCT
ijassa-1064	2	46	an	an	DET
ijassa-1064	2	47	eco	eco	NOUN
ijassa-1064	2	48	-	-	PUNCT
ijassa-1064	2	49	epidemiological	epidemiological	ADJ
ijassa-1064	2	50	model	model	NOUN
ijassa-1064	2	51	representing	represent	VERB
ijassa-1064	2	52	the	the	DET
ijassa-1064	2	53	interactions	interaction	NOUN
ijassa-1064	2	54	between	between	ADP
ijassa-1064	2	55	prey	prey	NOUN
ijassa-1064	2	56	and	and	CCONJ
ijassa-1064	2	57	predator	predator	NOUN
ijassa-1064	2	58	populations	population	NOUN
ijassa-1064	2	59	affected	affect	VERB
ijassa-1064	2	60	by	by	ADP
ijassa-1064	2	61	a	a	DET
ijassa-1064	2	62	disease	disease	NOUN
ijassa-1064	2	63	in	in	ADP
ijassa-1064	2	64	an	an	DET
ijassa-1064	2	65	ecosystem	ecosystem	NOUN
ijassa-1064	2	66	is	be	AUX
ijassa-1064	2	67	presented	present	VERB
ijassa-1064	2	68	.	.	PUNCT
ijassa-1064	3	1	the	the	DET
ijassa-1064	3	2	model	model	NOUN
ijassa-1064	3	3	is	be	AUX
ijassa-1064	3	4	governed	govern	VERB
ijassa-1064	3	5	by	by	ADP
ijassa-1064	3	6	a	a	DET
ijassa-1064	3	7	five	five	NUM
ijassa-1064	3	8	-	-	PUNCT
ijassa-1064	3	9	dimensional	dimensional	ADJ
ijassa-1064	3	10	nonlinear	nonlinear	ADJ
ijassa-1064	3	11	system	system	NOUN
ijassa-1064	3	12	of	of	ADP
ijassa-1064	3	13	ordinary	ordinary	ADJ
ijassa-1064	3	14	differential	differential	ADJ
ijassa-1064	3	15	equations	equation	NOUN
ijassa-1064	3	16	coupling	couple	VERB
ijassa-1064	3	17	both	both	CCONJ
ijassa-1064	3	18	ecological	ecological	ADJ
ijassa-1064	3	19	and	and	CCONJ
ijassa-1064	3	20	epidemiological	epidemiological	ADJ
ijassa-1064	3	21	features	feature	NOUN
ijassa-1064	3	22	of	of	ADP
ijassa-1064	3	23	interacting	interact	VERB
ijassa-1064	3	24	populations	population	NOUN
ijassa-1064	3	25	.	.	PUNCT
ijassa-1064	4	1	the	the	DET
ijassa-1064	4	2	well	well	ADV
ijassa-1064	4	3	-	-	PUNCT
ijassa-1064	4	4	posedness	posedness	NOUN
ijassa-1064	4	5	of	of	ADP
ijassa-1064	4	6	the	the	DET
ijassa-1064	4	7	model	model	NOUN
ijassa-1064	4	8	is	be	AUX
ijassa-1064	4	9	established	establish	VERB
ijassa-1064	4	10	with	with	ADP
ijassa-1064	4	11	respect	respect	NOUN
ijassa-1064	4	12	to	to	ADP
ijassa-1064	4	13	positivity	positivity	NOUN
ijassa-1064	4	14	and	and	CCONJ
ijassa-1064	4	15	boundedness	boundedness	NOUN
ijassa-1064	4	16	of	of	ADP
ijassa-1064	4	17	solutions	solution	NOUN
ijassa-1064	4	18	.	.	PUNCT
ijassa-1064	5	1	conditions	condition	NOUN
ijassa-1064	5	2	for	for	ADP
ijassa-1064	5	3	asymptotic	asymptotic	ADJ
ijassa-1064	5	4	stability	stability	NOUN
ijassa-1064	5	5	of	of	ADP
ijassa-1064	5	6	different	different	ADJ
ijassa-1064	5	7	equilibrium	equilibrium	NOUN
ijassa-1064	5	8	points	point	NOUN
ijassa-1064	5	9	are	be	AUX
ijassa-1064	5	10	extensively	extensively	ADV
ijassa-1064	5	11	investigated	investigate	VERB
ijassa-1064	5	12	to	to	PART
ijassa-1064	5	13	determine	determine	VERB
ijassa-1064	5	14	the	the	DET
ijassa-1064	5	15	existence	existence	NOUN
ijassa-1064	5	16	and	and	CCONJ
ijassa-1064	5	17	coexistence	coexistence	NOUN
ijassa-1064	5	18	of	of	ADP
ijassa-1064	5	19	prey	prey	NOUN
ijassa-1064	5	20	and	and	CCONJ
ijassa-1064	5	21	predator	predator	NOUN
ijassa-1064	5	22	species	specie	NOUN
ijassa-1064	5	23	using	use	VERB
ijassa-1064	5	24	local	local	ADJ
ijassa-1064	5	25	linearization	linearization	NOUN
ijassa-1064	5	26	and	and	CCONJ
ijassa-1064	5	27	lyapunov	lyapunov	NOUN
ijassa-1064	5	28	functions	function	NOUN
ijassa-1064	5	29	techniques	technique	NOUN
ijassa-1064	5	30	.	.	PUNCT
ijassa-1064	6	1	additionally	additionally	ADV
ijassa-1064	6	2	,	,	PUNCT
ijassa-1064	6	3	the	the	DET
ijassa-1064	6	4	analysis	analysis	NOUN
ijassa-1064	6	5	of	of	ADP
ijassa-1064	6	6	the	the	DET
ijassa-1064	6	7	model	model	NOUN
ijassa-1064	6	8	is	be	AUX
ijassa-1064	6	9	extended	extend	VERB
ijassa-1064	6	10	to	to	PART
ijassa-1064	6	11	assess	assess	VERB
ijassa-1064	6	12	the	the	DET
ijassa-1064	6	13	effects	effect	NOUN
ijassa-1064	6	14	of	of	ADP
ijassa-1064	6	15	three	three	NUM
ijassa-1064	6	16	timedependent	timedependent	NOUN
ijassa-1064	6	17	control	control	NOUN
ijassa-1064	6	18	functions	function	NOUN
ijassa-1064	6	19	,	,	PUNCT
ijassa-1064	6	20	such	such	ADJ
ijassa-1064	6	21	as	as	ADP
ijassa-1064	6	22	disease	disease	NOUN
ijassa-1064	6	23	prevention	prevention	NOUN
ijassa-1064	6	24	,	,	PUNCT
ijassa-1064	6	25	treatment	treatment	NOUN
ijassa-1064	6	26	and	and	CCONJ
ijassa-1064	6	27	alternative	alternative	ADJ
ijassa-1064	6	28	resource	resource	NOUN
ijassa-1064	6	29	for	for	ADP
ijassa-1064	6	30	predator	predator	NOUN
ijassa-1064	6	31	,	,	PUNCT
ijassa-1064	6	32	on	on	ADP
ijassa-1064	6	33	the	the	DET
ijassa-1064	6	34	population	population	NOUN
ijassa-1064	6	35	dynamics	dynamic	NOUN
ijassa-1064	6	36	of	of	ADP
ijassa-1064	6	37	the	the	DET
ijassa-1064	6	38	prey	prey	NOUN
ijassa-1064	6	39	-	-	PUNCT
ijassa-1064	6	40	predator	predator	NOUN
ijassa-1064	6	41	coexistence	coexistence	NOUN
ijassa-1064	6	42	in	in	ADP
ijassa-1064	6	43	the	the	DET
ijassa-1064	6	44	system	system	NOUN
ijassa-1064	6	45	.	.	PUNCT
ijassa-1064	7	1	keywords	keyword	NOUN
ijassa-1064	7	2	:	:	PUNCT
ijassa-1064	7	3	ecology	ecology	NOUN
ijassa-1064	7	4	,	,	PUNCT
ijassa-1064	7	5	epidemiology	epidemiology	NOUN
ijassa-1064	7	6	,	,	PUNCT
ijassa-1064	7	7	prey	prey	NOUN
ijassa-1064	7	8	-	-	PUNCT
ijassa-1064	7	9	predator	predator	NOUN
ijassa-1064	7	10	model	model	NOUN
ijassa-1064	7	11	,	,	PUNCT
ijassa-1064	7	12	stability	stability	NOUN
ijassa-1064	7	13	,	,	PUNCT
ijassa-1064	7	14	optimal	optimal	ADJ
ijassa-1064	7	15	control	control	NOUN
ijassa-1064	7	16	problem	problem	NOUN
ijassa-1064	7	17	,	,	PUNCT
ijassa-1064	7	18	simulations	simulation	NOUN
ijassa-1064	7	19	1	1	NUM
ijassa-1064	7	20	.	.	PUNCT
ijassa-1064	8	1	introduction	introduction	NOUN
ijassa-1064	8	2	interaction	interaction	NOUN
ijassa-1064	8	3	between	between	ADP
ijassa-1064	8	4	organisms	organism	NOUN
ijassa-1064	8	5	of	of	ADP
ijassa-1064	8	6	different	different	ADJ
ijassa-1064	8	7	species	specie	NOUN
ijassa-1064	8	8	is	be	AUX
ijassa-1064	8	9	a	a	DET
ijassa-1064	8	10	common	common	ADJ
ijassa-1064	8	11	phenomenon	phenomenon	NOUN
ijassa-1064	8	12	in	in	ADP
ijassa-1064	8	13	an	an	DET
ijassa-1064	8	14	ecosystem	ecosystem	NOUN
ijassa-1064	8	15	.	.	PUNCT
ijassa-1064	9	1	it	it	PRON
ijassa-1064	9	2	is	be	AUX
ijassa-1064	9	3	an	an	DET
ijassa-1064	9	4	intrinsic	intrinsic	ADJ
ijassa-1064	9	5	feature	feature	NOUN
ijassa-1064	9	6	which	which	PRON
ijassa-1064	9	7	can	can	AUX
ijassa-1064	9	8	not	not	PART
ijassa-1064	9	9	be	be	AUX
ijassa-1064	9	10	downplayed	downplay	VERB
ijassa-1064	9	11	in	in	ADP
ijassa-1064	9	12	the	the	DET
ijassa-1064	9	13	study	study	NOUN
ijassa-1064	9	14	of	of	ADP
ijassa-1064	9	15	ecological	ecological	ADJ
ijassa-1064	9	16	system	system	NOUN
ijassa-1064	9	17	.	.	PUNCT
ijassa-1064	10	1	this	this	DET
ijassa-1064	10	2	interaction	interaction	NOUN
ijassa-1064	10	3	,	,	PUNCT
ijassa-1064	10	4	especially	especially	ADV
ijassa-1064	10	5	between	between	ADP
ijassa-1064	10	6	prey	prey	NOUN
ijassa-1064	10	7	and	and	CCONJ
ijassa-1064	10	8	predator	predator	NOUN
ijassa-1064	10	9	species	specie	NOUN
ijassa-1064	10	10	,	,	PUNCT
ijassa-1064	10	11	often	often	ADV
ijassa-1064	10	12	affects	affect	VERB
ijassa-1064	10	13	or	or	CCONJ
ijassa-1064	10	14	changes	change	VERB
ijassa-1064	10	15	the	the	DET
ijassa-1064	10	16	population	population	NOUN
ijassa-1064	10	17	sizes	size	NOUN
ijassa-1064	10	18	of	of	ADP
ijassa-1064	10	19	organisms	organism	NOUN
ijassa-1064	10	20	in	in	ADP
ijassa-1064	10	21	the	the	DET
ijassa-1064	10	22	system	system	NOUN
ijassa-1064	10	23	[	[	X
ijassa-1064	10	24	11	11	NUM
ijassa-1064	10	25	]	]	PUNCT
ijassa-1064	10	26	.	.	PUNCT
ijassa-1064	11	1	since	since	SCONJ
ijassa-1064	11	2	the	the	DET
ijassa-1064	11	3	advent	advent	NOUN
ijassa-1064	11	4	of	of	ADP
ijassa-1064	11	5	the	the	DET
ijassa-1064	11	6	classical	classical	ADJ
ijassa-1064	11	7	lotka	lotka	PROPN
ijassa-1064	11	8	and	and	CCONJ
ijassa-1064	11	9	volterra	volterra	NOUN
ijassa-1064	11	10	prey	prey	PROPN
ijassa-1064	11	11	-	-	PUNCT
ijassa-1064	11	12	predator	predator	NOUN
ijassa-1064	11	13	models	model	NOUN
ijassa-1064	11	14	[	[	X
ijassa-1064	11	15	20	20	NUM
ijassa-1064	11	16	,	,	PUNCT
ijassa-1064	11	17	31	31	NUM
ijassa-1064	11	18	]	]	PUNCT
ijassa-1064	11	19	,	,	PUNCT
ijassa-1064	11	20	many	many	ADJ
ijassa-1064	11	21	ecosystem	ecosystem	NOUN
ijassa-1064	11	22	models	model	NOUN
ijassa-1064	11	23	,	,	PUNCT
ijassa-1064	11	24	which	which	PRON
ijassa-1064	11	25	can	can	AUX
ijassa-1064	11	26	be	be	AUX
ijassa-1064	11	27	defined	define	VERB
ijassa-1064	11	28	as	as	ADP
ijassa-1064	11	29	mathematical	mathematical	ADJ
ijassa-1064	11	30	representations	representation	NOUN
ijassa-1064	11	31	of	of	ADP
ijassa-1064	11	32	ecological	ecological	ADJ
ijassa-1064	11	33	system	system	NOUN
ijassa-1064	11	34	of	of	ADP
ijassa-1064	11	35	prey	prey	NOUN
ijassa-1064	11	36	and	and	CCONJ
ijassa-1064	11	37	predator	predator	NOUN
ijassa-1064	11	38	interactions	interaction	NOUN
ijassa-1064	11	39	,	,	PUNCT
ijassa-1064	11	40	have	have	AUX
ijassa-1064	11	41	been	be	AUX
ijassa-1064	11	42	studied	study	VERB
ijassa-1064	11	43	in	in	ADP
ijassa-1064	11	44	literature	literature	NOUN
ijassa-1064	11	45	to	to	PART
ijassa-1064	11	46	better	well	ADV
ijassa-1064	11	47	understand	understand	VERB
ijassa-1064	11	48	the	the	DET
ijassa-1064	11	49	real	real	ADJ
ijassa-1064	11	50	system	system	NOUN
ijassa-1064	11	51	(	(	PUNCT
ijassa-1064	11	52	see	see	VERB
ijassa-1064	11	53	,	,	PUNCT
ijassa-1064	11	54	e.g.	e.g.	ADV
ijassa-1064	11	55	[	[	X
ijassa-1064	11	56	5	5	NUM
ijassa-1064	11	57	,	,	PUNCT
ijassa-1064	11	58	11	11	NUM
ijassa-1064	11	59	,	,	PUNCT
ijassa-1064	11	60	13	13	NUM
ijassa-1064	11	61	,	,	PUNCT
ijassa-1064	11	62	17	17	NUM
ijassa-1064	11	63	,	,	PUNCT
ijassa-1064	11	64	27	27	NUM
ijassa-1064	11	65	]	]	PUNCT
ijassa-1064	11	66	)	)	PUNCT
ijassa-1064	11	67	.	.	PUNCT
ijassa-1064	12	1	in	in	ADP
ijassa-1064	12	2	[	[	X
ijassa-1064	12	3	11	11	NUM
ijassa-1064	12	4	]	]	PUNCT
ijassa-1064	12	5	,	,	PUNCT
ijassa-1064	12	6	analysis	analysis	NOUN
ijassa-1064	12	7	of	of	ADP
ijassa-1064	12	8	modified	modify	VERB
ijassa-1064	12	9	lotka	lotka	PROPN
ijassa-1064	12	10	-	-	PUNCT
ijassa-1064	12	11	volterra	volterra	PROPN
ijassa-1064	12	12	model	model	NOUN
ijassa-1064	12	13	was	be	AUX
ijassa-1064	12	14	carried	carry	VERB
ijassa-1064	12	15	out	out	ADP
ijassa-1064	12	16	by	by	ADP
ijassa-1064	12	17	taking	take	VERB
ijassa-1064	12	18	into	into	ADP
ijassa-1064	12	19	consideration	consideration	NOUN
ijassa-1064	12	20	an	an	DET
ijassa-1064	12	21	environmental	environmental	ADJ
ijassa-1064	12	22	case	case	NOUN
ijassa-1064	12	23	containing	contain	VERB
ijassa-1064	12	24	two	two	NUM
ijassa-1064	12	25	related	related	ADJ
ijassa-1064	12	26	populations	population	NOUN
ijassa-1064	12	27	of	of	ADP
ijassa-1064	12	28	prey	prey	NOUN
ijassa-1064	12	29	and	and	CCONJ
ijassa-1064	12	30	predator	predator	NOUN
ijassa-1064	12	31	species	specie	NOUN
ijassa-1064	12	32	having	have	VERB
ijassa-1064	12	33	influence	influence	NOUN
ijassa-1064	12	34	on	on	ADP
ijassa-1064	12	35	the	the	DET
ijassa-1064	12	36	size	size	NOUN
ijassa-1064	12	37	of	of	ADP
ijassa-1064	12	38	each	each	DET
ijassa-1064	12	39	other	other	ADJ
ijassa-1064	12	40	.	.	PUNCT
ijassa-1064	13	1	kumar	kumar	PROPN
ijassa-1064	13	2	and	and	CCONJ
ijassa-1064	13	3	kumari	kumari	PROPN
ijassa-1064	13	4	[	[	X
ijassa-1064	13	5	17	17	NUM
ijassa-1064	13	6	]	]	PUNCT
ijassa-1064	13	7	studied	study	VERB
ijassa-1064	13	8	the	the	DET
ijassa-1064	13	9	impact	impact	NOUN
ijassa-1064	13	10	of	of	ADP
ijassa-1064	13	11	fear	fear	NOUN
ijassa-1064	13	12	on	on	ADP
ijassa-1064	13	13	a	a	DET
ijassa-1064	13	14	chaotic	chaotic	ADJ
ijassa-1064	13	15	model	model	NOUN
ijassa-1064	13	16	describing	describe	VERB
ijassa-1064	13	17	the	the	DET
ijassa-1064	13	18	interactions	interaction	NOUN
ijassa-1064	13	19	of	of	ADP
ijassa-1064	13	20	the	the	DET
ijassa-1064	13	21	species	specie	NOUN
ijassa-1064	13	22	in	in	ADP
ijassa-1064	13	23	the	the	DET
ijassa-1064	13	24	food	food	NOUN
ijassa-1064	13	25	chain	chain	NOUN
ijassa-1064	13	26	of	of	ADP
ijassa-1064	13	27	one	one	NUM
ijassa-1064	13	28	prey	prey	NOUN
ijassa-1064	13	29	and	and	CCONJ
ijassa-1064	13	30	two	two	NUM
ijassa-1064	13	31	predators	predator	NOUN
ijassa-1064	13	32	.	.	PUNCT
ijassa-1064	14	1	prasad	prasad	PROPN
ijassa-1064	14	2	et	et	PROPN
ijassa-1064	14	3	al	al	PROPN
ijassa-1064	14	4	.	.	PUNCT
ijassa-1064	15	1	[	[	X
ijassa-1064	15	2	27	27	NUM
ijassa-1064	15	3	]	]	PUNCT
ijassa-1064	15	4	investigated	investigate	VERB
ijassa-1064	15	5	the	the	DET
ijassa-1064	15	6	role	role	NOUN
ijassa-1064	15	7	of	of	ADP
ijassa-1064	15	8	mutual	mutual	ADJ
ijassa-1064	15	9	interference	interference	NOUN
ijassa-1064	15	10	between	between	ADP
ijassa-1064	15	11	predators	predator	NOUN
ijassa-1064	15	12	on	on	ADP
ijassa-1064	15	13	the	the	DET
ijassa-1064	15	14	dynamics	dynamic	NOUN
ijassa-1064	15	15	of	of	ADP
ijassa-1064	15	16	additional	additional	ADJ
ijassa-1064	15	17	food	food	NOUN
ijassa-1064	15	18	provided	provide	VERB
ijassa-1064	15	19	predator	predator	NOUN
ijassa-1064	15	20	-	-	PUNCT
ijassa-1064	15	21	prey	prey	NOUN
ijassa-1064	15	22	system	system	NOUN
ijassa-1064	15	23	.	.	PUNCT
ijassa-1064	16	1	in	in	ADP
ijassa-1064	16	2	recent	recent	ADJ
ijassa-1064	16	3	decades	decade	NOUN
ijassa-1064	16	4	,	,	PUNCT
ijassa-1064	16	5	a	a	DET
ijassa-1064	16	6	number	number	NOUN
ijassa-1064	16	7	of	of	ADP
ijassa-1064	16	8	studies	study	NOUN
ijassa-1064	16	9	have	have	AUX
ijassa-1064	16	10	considered	consider	VERB
ijassa-1064	16	11	ecosystems	ecosystem	NOUN
ijassa-1064	16	12	of	of	ADP
ijassa-1064	16	13	interacting	interact	VERB
ijassa-1064	16	14	populations	population	NOUN
ijassa-1064	16	15	among	among	ADP
ijassa-1064	16	16	which	which	PRON
ijassa-1064	16	17	diseases	disease	NOUN
ijassa-1064	16	18	spread	spread	VERB
ijassa-1064	16	19	.	.	PUNCT
ijassa-1064	17	1	the	the	DET
ijassa-1064	17	2	resulting	result	VERB
ijassa-1064	17	3	ecological	ecological	ADJ
ijassa-1064	17	4	systems	system	NOUN
ijassa-1064	17	5	are	be	AUX
ijassa-1064	17	6	described	describe	VERB
ijassa-1064	17	7	by	by	ADP
ijassa-1064	17	8	eco	eco	PROPN
ijassa-1064	17	9	-	-	PUNCT
ijassa-1064	17	10	epidemiological	epidemiological	ADJ
ijassa-1064	17	11	models	model	NOUN
ijassa-1064	18	1	[	[	X
ijassa-1064	18	2	7–9	7–9	NUM
ijassa-1064	18	3	,	,	PUNCT
ijassa-1064	18	4	21	21	NUM
ijassa-1064	18	5	,	,	PUNCT
ijassa-1064	18	6	29	29	NUM
ijassa-1064	18	7	]	]	PUNCT
ijassa-1064	18	8	.	.	PUNCT
ijassa-1064	19	1	das	das	PROPN
ijassa-1064	20	1	[	[	X
ijassa-1064	20	2	9	9	NUM
ijassa-1064	20	3	]	]	PUNCT
ijassa-1064	20	4	studied	study	VERB
ijassa-1064	20	5	the	the	DET
ijassa-1064	20	6	predator	predator	NOUN
ijassa-1064	20	7	-	-	PUNCT
ijassa-1064	20	8	prey	prey	NOUN
ijassa-1064	20	9	model	model	NOUN
ijassa-1064	20	10	with	with	ADP
ijassa-1064	20	11	parasitic	parasitic	ADJ
ijassa-1064	20	12	infection	infection	NOUN
ijassa-1064	20	13	transmitting	transmit	VERB
ijassa-1064	20	14	among	among	ADP
ijassa-1064	20	15	the	the	DET
ijassa-1064	20	16	predator	predator	NOUN
ijassa-1064	20	17	population	population	NOUN
ijassa-1064	20	18	only	only	ADV
ijassa-1064	20	19	.	.	PUNCT
ijassa-1064	21	1	nandi	nandi	NOUN
ijassa-1064	21	2	et	et	PROPN
ijassa-1064	21	3	al	al	PROPN
ijassa-1064	21	4	.	.	PUNCT
ijassa-1064	22	1	[	[	X
ijassa-1064	22	2	21	21	NUM
ijassa-1064	22	3	]	]	PUNCT
ijassa-1064	22	4	developed	develop	VERB
ijassa-1064	22	5	a	a	DET
ijassa-1064	22	6	predator	predator	NOUN
ijassa-1064	22	7	-	-	PUNCT
ijassa-1064	22	8	prey	prey	NOUN
ijassa-1064	22	9	system	system	NOUN
ijassa-1064	22	10	where	where	SCONJ
ijassa-1064	22	11	prey	prey	PROPN
ijassa-1064	22	12	species	specie	NOUN
ijassa-1064	22	13	only	only	ADV
ijassa-1064	22	14	are	be	AUX
ijassa-1064	22	15	infected	infect	VERB
ijassa-1064	22	16	with	with	ADP
ijassa-1064	22	17	a	a	DET
ijassa-1064	22	18	viral	viral	ADJ
ijassa-1064	22	19	disease	disease	NOUN
ijassa-1064	22	20	resulting	result	VERB
ijassa-1064	22	21	into	into	ADP
ijassa-1064	22	22	susceptible	susceptible	ADJ
ijassa-1064	22	23	and	and	CCONJ
ijassa-1064	22	24	two	two	NUM
ijassa-1064	22	25	-	-	PUNCT
ijassa-1064	22	26	stage	stage	NOUN
ijassa-1064	22	27	infected	infected	ADJ
ijassa-1064	22	28	classes	class	NOUN
ijassa-1064	22	29	.	.	PUNCT
ijassa-1064	23	1	bera	bera	NOUN
ijassa-1064	23	2	et	et	PROPN
ijassa-1064	23	3	al	al	PROPN
ijassa-1064	23	4	.	.	PUNCT
ijassa-1064	24	1	[	[	X
ijassa-1064	24	2	8	8	NUM
ijassa-1064	24	3	]	]	PUNCT
ijassa-1064	24	4	presented	present	VERB
ijassa-1064	24	5	theoretical	theoretical	ADJ
ijassa-1064	24	6	analysis	analysis	NOUN
ijassa-1064	24	7	supported	support	VERB
ijassa-1064	24	8	by	by	ADP
ijassa-1064	24	9	simulation	simulation	NOUN
ijassa-1064	24	10	of	of	ADP
ijassa-1064	24	11	the	the	DET
ijassa-1064	24	12	dynamical	dynamical	ADJ
ijassa-1064	24	13	behaviors	behavior	NOUN
ijassa-1064	24	14	of	of	ADP
ijassa-1064	24	15	a	a	DET
ijassa-1064	24	16	prey	prey	NOUN
ijassa-1064	24	17	-	-	PUNCT
ijassa-1064	24	18	predator	predator	NOUN
ijassa-1064	24	19	system	system	NOUN
ijassa-1064	24	20	where	where	SCONJ
ijassa-1064	24	21	both	both	DET
ijassa-1064	24	22	populations	population	NOUN
ijassa-1064	24	23	are	be	AUX
ijassa-1064	24	24	affected	affect	VERB
ijassa-1064	24	25	by	by	ADP
ijassa-1064	24	26	diseases	disease	NOUN
ijassa-1064	24	27	.	.	PUNCT
ijassa-1064	25	1	∗corresponding	∗corresponde	VERB
ijassa-1064	25	2	author	author	NOUN
ijassa-1064	25	3	:	:	PUNCT
ijassa-1064	25	4	solaniyi@lautech.edu.ng	solaniyi@lautech.edu.ng	ADJ
ijassa-1064	25	5	84	84	NUM
ijassa-1064	25	6	j.a	j.a	PROPN
ijassa-1064	25	7	.	.	PROPN
ijassa-1064	25	8	ademosu	ademosu	PROPN
ijassa-1064	25	9	,	,	PUNCT
ijassa-1064	25	10	s.	s.	PROPN
ijassa-1064	25	11	olaniyi	olaniyi	PROPN
ijassa-1064	25	12	,	,	PUNCT
ijassa-1064	25	13	s.o	s.o	PROPN
ijassa-1064	25	14	.	.	PROPN
ijassa-1064	25	15	adewale	adewale	PROPN
ijassa-1064	25	16	interest	interest	PROPN
ijassa-1064	25	17	has	have	AUX
ijassa-1064	25	18	been	be	AUX
ijassa-1064	25	19	growing	grow	VERB
ijassa-1064	25	20	recently	recently	ADV
ijassa-1064	25	21	in	in	ADP
ijassa-1064	25	22	the	the	DET
ijassa-1064	25	23	application	application	NOUN
ijassa-1064	25	24	of	of	ADP
ijassa-1064	25	25	optimal	optimal	ADJ
ijassa-1064	25	26	control	control	NOUN
ijassa-1064	25	27	theory	theory	NOUN
ijassa-1064	25	28	to	to	ADP
ijassa-1064	25	29	the	the	DET
ijassa-1064	25	30	dynamics	dynamic	NOUN
ijassa-1064	25	31	of	of	ADP
ijassa-1064	25	32	eco	eco	PROPN
ijassa-1064	25	33	-	-	PUNCT
ijassa-1064	25	34	epidemiological	epidemiological	ADJ
ijassa-1064	25	35	models	model	NOUN
ijassa-1064	25	36	for	for	ADP
ijassa-1064	25	37	prey	prey	NOUN
ijassa-1064	25	38	-	-	PUNCT
ijassa-1064	25	39	predator	predator	NOUN
ijassa-1064	25	40	system	system	NOUN
ijassa-1064	25	41	.	.	PUNCT
ijassa-1064	26	1	al	al	PROPN
ijassa-1064	26	2	-	-	PUNCT
ijassa-1064	26	3	nassir	nassir	PROPN
ijassa-1064	26	4	[	[	X
ijassa-1064	26	5	6	6	NUM
ijassa-1064	26	6	]	]	PUNCT
ijassa-1064	26	7	studied	study	VERB
ijassa-1064	26	8	a	a	DET
ijassa-1064	26	9	two	two	NUM
ijassa-1064	26	10	-	-	PUNCT
ijassa-1064	26	11	dimensional	dimensional	ADJ
ijassa-1064	26	12	continuous	continuous	ADJ
ijassa-1064	26	13	prey	prey	NOUN
ijassa-1064	26	14	-	-	PUNCT
ijassa-1064	26	15	predator	predator	NOUN
ijassa-1064	26	16	system	system	NOUN
ijassa-1064	26	17	incorporating	incorporate	VERB
ijassa-1064	26	18	an	an	DET
ijassa-1064	26	19	optimal	optimal	ADJ
ijassa-1064	26	20	control	control	NOUN
ijassa-1064	26	21	variable	variable	NOUN
ijassa-1064	26	22	with	with	ADP
ijassa-1064	26	23	the	the	DET
ijassa-1064	26	24	aim	aim	NOUN
ijassa-1064	26	25	of	of	ADP
ijassa-1064	26	26	reducing	reduce	VERB
ijassa-1064	26	27	the	the	DET
ijassa-1064	26	28	number	number	NOUN
ijassa-1064	26	29	of	of	ADP
ijassa-1064	26	30	the	the	DET
ijassa-1064	26	31	predator	predator	NOUN
ijassa-1064	26	32	density	density	NOUN
ijassa-1064	26	33	in	in	ADP
ijassa-1064	26	34	the	the	DET
ijassa-1064	26	35	population	population	NOUN
ijassa-1064	26	36	.	.	PUNCT
ijassa-1064	27	1	in	in	ADP
ijassa-1064	27	2	[	[	X
ijassa-1064	27	3	10	10	NUM
ijassa-1064	27	4	]	]	PUNCT
ijassa-1064	27	5	,	,	PUNCT
ijassa-1064	27	6	the	the	DET
ijassa-1064	27	7	authors	author	NOUN
ijassa-1064	27	8	extended	extend	VERB
ijassa-1064	27	9	a	a	DET
ijassa-1064	27	10	prey	prey	NOUN
ijassa-1064	27	11	-	-	PUNCT
ijassa-1064	27	12	predator	predator	NOUN
ijassa-1064	27	13	mathematical	mathematical	ADJ
ijassa-1064	27	14	model	model	NOUN
ijassa-1064	27	15	with	with	ADP
ijassa-1064	27	16	infection	infection	NOUN
ijassa-1064	27	17	and	and	CCONJ
ijassa-1064	27	18	harvesting	harvesting	NOUN
ijassa-1064	27	19	on	on	ADP
ijassa-1064	27	20	prey	prey	NOUN
ijassa-1064	27	21	to	to	PART
ijassa-1064	27	22	include	include	VERB
ijassa-1064	27	23	one	one	NUM
ijassa-1064	27	24	time	time	NOUN
ijassa-1064	27	25	-	-	PUNCT
ijassa-1064	27	26	dependent	dependent	ADJ
ijassa-1064	27	27	control	control	NOUN
ijassa-1064	27	28	for	for	ADP
ijassa-1064	27	29	preventing	prevent	VERB
ijassa-1064	27	30	infection	infection	NOUN
ijassa-1064	27	31	in	in	ADP
ijassa-1064	27	32	the	the	DET
ijassa-1064	27	33	prey	prey	NOUN
ijassa-1064	27	34	population	population	NOUN
ijassa-1064	27	35	only	only	ADV
ijassa-1064	27	36	.	.	PUNCT
ijassa-1064	28	1	in	in	ADP
ijassa-1064	28	2	another	another	DET
ijassa-1064	28	3	development	development	NOUN
ijassa-1064	28	4	,	,	PUNCT
ijassa-1064	28	5	hugo	hugo	PROPN
ijassa-1064	28	6	et	et	PROPN
ijassa-1064	28	7	al	al	PROPN
ijassa-1064	28	8	.	.	PUNCT
ijassa-1064	29	1	[	[	X
ijassa-1064	29	2	16	16	NUM
ijassa-1064	29	3	]	]	PUNCT
ijassa-1064	29	4	applied	apply	VERB
ijassa-1064	29	5	optimal	optimal	ADJ
ijassa-1064	29	6	control	control	NOUN
ijassa-1064	29	7	theory	theory	NOUN
ijassa-1064	29	8	in	in	ADP
ijassa-1064	29	9	minimizing	minimize	VERB
ijassa-1064	29	10	the	the	DET
ijassa-1064	29	11	spread	spread	NOUN
ijassa-1064	29	12	of	of	ADP
ijassa-1064	29	13	newcastle	newcastle	PROPN
ijassa-1064	29	14	disease	disease	NOUN
ijassa-1064	29	15	among	among	ADP
ijassa-1064	29	16	chickens	chicken	NOUN
ijassa-1064	29	17	(	(	PUNCT
ijassa-1064	29	18	prey	prey	PROPN
ijassa-1064	29	19	)	)	PUNCT
ijassa-1064	29	20	and	and	CCONJ
ijassa-1064	29	21	humans	human	NOUN
ijassa-1064	29	22	(	(	PUNCT
ijassa-1064	29	23	predator	predator	NOUN
ijassa-1064	29	24	)	)	PUNCT
ijassa-1064	29	25	populations	population	NOUN
ijassa-1064	29	26	using	use	VERB
ijassa-1064	29	27	three	three	NUM
ijassa-1064	29	28	control	control	NOUN
ijassa-1064	29	29	variables	variable	NOUN
ijassa-1064	29	30	,	,	PUNCT
ijassa-1064	29	31	such	such	ADJ
ijassa-1064	29	32	as	as	ADP
ijassa-1064	29	33	vaccination	vaccination	NOUN
ijassa-1064	29	34	of	of	ADP
ijassa-1064	29	35	prey	prey	NOUN
ijassa-1064	29	36	,	,	PUNCT
ijassa-1064	29	37	education	education	NOUN
ijassa-1064	29	38	campaign	campaign	NOUN
ijassa-1064	29	39	and	and	CCONJ
ijassa-1064	29	40	treatment	treatment	NOUN
ijassa-1064	29	41	of	of	ADP
ijassa-1064	29	42	infected	infected	ADJ
ijassa-1064	29	43	humans	human	NOUN
ijassa-1064	29	44	.	.	PUNCT
ijassa-1064	30	1	in	in	ADP
ijassa-1064	30	2	this	this	DET
ijassa-1064	30	3	work	work	NOUN
ijassa-1064	30	4	,	,	PUNCT
ijassa-1064	30	5	a	a	DET
ijassa-1064	30	6	five	five	NUM
ijassa-1064	30	7	-	-	PUNCT
ijassa-1064	30	8	dimensional	dimensional	ADJ
ijassa-1064	30	9	nonlinear	nonlinear	ADJ
ijassa-1064	30	10	prey	prey	NOUN
ijassa-1064	30	11	-	-	PUNCT
ijassa-1064	30	12	predator	predator	NOUN
ijassa-1064	30	13	model	model	NOUN
ijassa-1064	30	14	is	be	AUX
ijassa-1064	30	15	studied	study	VERB
ijassa-1064	30	16	to	to	PART
ijassa-1064	30	17	gain	gain	VERB
ijassa-1064	30	18	further	further	ADJ
ijassa-1064	30	19	insights	insight	NOUN
ijassa-1064	30	20	into	into	ADP
ijassa-1064	30	21	the	the	DET
ijassa-1064	30	22	dynamics	dynamic	NOUN
ijassa-1064	30	23	of	of	ADP
ijassa-1064	30	24	eco	eco	PROPN
ijassa-1064	30	25	-	-	PUNCT
ijassa-1064	30	26	epidemiological	epidemiological	ADJ
ijassa-1064	30	27	interactions	interaction	NOUN
ijassa-1064	30	28	between	between	ADP
ijassa-1064	30	29	prey	prey	NOUN
ijassa-1064	30	30	and	and	CCONJ
ijassa-1064	30	31	predator	predator	NOUN
ijassa-1064	30	32	populations	population	NOUN
ijassa-1064	30	33	.	.	PUNCT
ijassa-1064	31	1	the	the	DET
ijassa-1064	31	2	analysis	analysis	NOUN
ijassa-1064	31	3	of	of	ADP
ijassa-1064	31	4	the	the	DET
ijassa-1064	31	5	model	model	NOUN
ijassa-1064	31	6	is	be	AUX
ijassa-1064	31	7	extended	extend	VERB
ijassa-1064	31	8	to	to	PART
ijassa-1064	31	9	investigate	investigate	VERB
ijassa-1064	31	10	the	the	DET
ijassa-1064	31	11	impact	impact	NOUN
ijassa-1064	31	12	of	of	ADP
ijassa-1064	31	13	three	three	NUM
ijassa-1064	31	14	optimal	optimal	ADJ
ijassa-1064	31	15	control	control	NOUN
ijassa-1064	31	16	variables	variable	NOUN
ijassa-1064	31	17	,	,	PUNCT
ijassa-1064	31	18	namely	namely	ADV
ijassa-1064	31	19	disease	disease	NOUN
ijassa-1064	31	20	prevention	prevention	NOUN
ijassa-1064	31	21	in	in	ADP
ijassa-1064	31	22	both	both	DET
ijassa-1064	31	23	prey	prey	NOUN
ijassa-1064	31	24	and	and	CCONJ
ijassa-1064	31	25	predator	predator	NOUN
ijassa-1064	31	26	populations	population	NOUN
ijassa-1064	31	27	,	,	PUNCT
ijassa-1064	31	28	treatment	treatment	NOUN
ijassa-1064	31	29	control	control	NOUN
ijassa-1064	31	30	for	for	ADP
ijassa-1064	31	31	prey	prey	NOUN
ijassa-1064	31	32	,	,	PUNCT
ijassa-1064	31	33	and	and	CCONJ
ijassa-1064	31	34	provision	provision	NOUN
ijassa-1064	31	35	of	of	ADP
ijassa-1064	31	36	alternative	alternative	ADJ
ijassa-1064	31	37	resources	resource	NOUN
ijassa-1064	31	38	control	control	NOUN
ijassa-1064	31	39	for	for	ADP
ijassa-1064	31	40	predator	predator	NOUN
ijassa-1064	31	41	population	population	NOUN
ijassa-1064	31	42	.	.	PUNCT
ijassa-1064	32	1	the	the	DET
ijassa-1064	32	2	rest	rest	NOUN
ijassa-1064	32	3	of	of	ADP
ijassa-1064	32	4	the	the	DET
ijassa-1064	32	5	work	work	NOUN
ijassa-1064	32	6	is	be	AUX
ijassa-1064	32	7	organized	organize	VERB
ijassa-1064	32	8	as	as	SCONJ
ijassa-1064	32	9	follows	follow	VERB
ijassa-1064	32	10	:	:	PUNCT
ijassa-1064	32	11	the	the	DET
ijassa-1064	32	12	model	model	NOUN
ijassa-1064	32	13	is	be	AUX
ijassa-1064	32	14	formulated	formulate	VERB
ijassa-1064	32	15	and	and	CCONJ
ijassa-1064	32	16	its	its	PRON
ijassa-1064	32	17	well	well	ADJ
ijassa-1064	32	18	-	-	PUNCT
ijassa-1064	32	19	posedness	posedness	NOUN
ijassa-1064	32	20	is	be	AUX
ijassa-1064	32	21	established	establish	VERB
ijassa-1064	32	22	in	in	ADP
ijassa-1064	32	23	section	section	NOUN
ijassa-1064	32	24	2	2	NUM
ijassa-1064	32	25	.	.	PUNCT
ijassa-1064	33	1	in	in	ADP
ijassa-1064	33	2	section	section	NOUN
ijassa-1064	33	3	3	3	NUM
ijassa-1064	33	4	,	,	PUNCT
ijassa-1064	33	5	existence	existence	NOUN
ijassa-1064	33	6	and	and	CCONJ
ijassa-1064	33	7	stability	stability	NOUN
ijassa-1064	33	8	of	of	ADP
ijassa-1064	33	9	possible	possible	ADJ
ijassa-1064	33	10	equilibrium	equilibrium	NOUN
ijassa-1064	33	11	points	point	NOUN
ijassa-1064	33	12	are	be	AUX
ijassa-1064	33	13	investigated	investigate	VERB
ijassa-1064	33	14	.	.	PUNCT
ijassa-1064	34	1	in	in	ADP
ijassa-1064	34	2	section	section	NOUN
ijassa-1064	34	3	4	4	NUM
ijassa-1064	34	4	,	,	PUNCT
ijassa-1064	34	5	the	the	DET
ijassa-1064	34	6	model	model	NOUN
ijassa-1064	34	7	is	be	AUX
ijassa-1064	34	8	extended	extend	VERB
ijassa-1064	34	9	to	to	PART
ijassa-1064	34	10	explore	explore	VERB
ijassa-1064	34	11	optimal	optimal	ADJ
ijassa-1064	34	12	control	control	NOUN
ijassa-1064	34	13	dynamics	dynamic	NOUN
ijassa-1064	34	14	with	with	ADP
ijassa-1064	34	15	numerical	numerical	ADJ
ijassa-1064	34	16	simulations	simulation	NOUN
ijassa-1064	34	17	.	.	PUNCT
ijassa-1064	35	1	section	section	NOUN
ijassa-1064	35	2	5	5	NUM
ijassa-1064	35	3	is	be	AUX
ijassa-1064	35	4	devoted	devote	VERB
ijassa-1064	35	5	to	to	ADP
ijassa-1064	35	6	concluding	conclude	VERB
ijassa-1064	35	7	remarks	remark	NOUN
ijassa-1064	35	8	.	.	PUNCT
ijassa-1064	36	1	2	2	X
ijassa-1064	36	2	.	.	X
ijassa-1064	36	3	model	model	NOUN
ijassa-1064	36	4	formulation	formulation	NOUN
ijassa-1064	36	5	the	the	DET
ijassa-1064	36	6	dynamic	dynamic	ADJ
ijassa-1064	36	7	eco	eco	NOUN
ijassa-1064	36	8	-	-	PUNCT
ijassa-1064	36	9	epidemiological	epidemiological	ADJ
ijassa-1064	36	10	prey	prey	NOUN
ijassa-1064	36	11	-	-	PUNCT
ijassa-1064	36	12	predator	predator	NOUN
ijassa-1064	36	13	system	system	NOUN
ijassa-1064	36	14	is	be	AUX
ijassa-1064	36	15	formulated	formulate	VERB
ijassa-1064	36	16	by	by	ADP
ijassa-1064	36	17	sub	sub	NOUN
ijassa-1064	36	18	-	-	ADJ
ijassa-1064	36	19	dividing	divide	VERB
ijassa-1064	36	20	the	the	DET
ijassa-1064	36	21	prey	prey	NOUN
ijassa-1064	36	22	population	population	NOUN
ijassa-1064	36	23	at	at	ADP
ijassa-1064	36	24	time	time	NOUN
ijassa-1064	36	25	,	,	PUNCT
ijassa-1064	36	26	t	t	PROPN
ijassa-1064	36	27	,	,	PUNCT
ijassa-1064	36	28	into	into	ADP
ijassa-1064	36	29	susceptible	susceptible	ADJ
ijassa-1064	36	30	xs(t	xs(t	NOUN
ijassa-1064	36	31	)	)	PUNCT
ijassa-1064	36	32	,	,	PUNCT
ijassa-1064	36	33	infected	infect	VERB
ijassa-1064	36	34	xi(t	xi(t	PUNCT
ijassa-1064	36	35	)	)	PUNCT
ijassa-1064	36	36	and	and	CCONJ
ijassa-1064	36	37	recovered	recover	VERB
ijassa-1064	36	38	xr(t	xr(t	NUM
ijassa-1064	36	39	)	)	PUNCT
ijassa-1064	36	40	.	.	PUNCT
ijassa-1064	37	1	on	on	ADP
ijassa-1064	37	2	the	the	DET
ijassa-1064	37	3	other	other	ADJ
ijassa-1064	37	4	hand	hand	NOUN
ijassa-1064	37	5	,	,	PUNCT
ijassa-1064	37	6	the	the	DET
ijassa-1064	37	7	predator	predator	NOUN
ijassa-1064	37	8	population	population	NOUN
ijassa-1064	37	9	is	be	AUX
ijassa-1064	37	10	sub	sub	ADJ
ijassa-1064	37	11	-	-	ADJ
ijassa-1064	37	12	divided	divide	VERB
ijassa-1064	37	13	into	into	ADP
ijassa-1064	37	14	two	two	NUM
ijassa-1064	37	15	,	,	PUNCT
ijassa-1064	37	16	namely	namely	ADV
ijassa-1064	37	17	susceptible	susceptible	ADJ
ijassa-1064	37	18	ys(t	ys(t	NOUN
ijassa-1064	37	19	)	)	PUNCT
ijassa-1064	37	20	and	and	CCONJ
ijassa-1064	37	21	infected	infect	VERB
ijassa-1064	37	22	yi(t	yi(t	NOUN
ijassa-1064	37	23	)	)	PUNCT
ijassa-1064	37	24	.	.	PUNCT
ijassa-1064	38	1	it	it	PRON
ijassa-1064	38	2	is	be	AUX
ijassa-1064	38	3	assumed	assume	VERB
ijassa-1064	38	4	that	that	SCONJ
ijassa-1064	38	5	the	the	DET
ijassa-1064	38	6	susceptible	susceptible	ADJ
ijassa-1064	38	7	prey	prey	NOUN
ijassa-1064	38	8	population	population	NOUN
ijassa-1064	38	9	increases	increase	VERB
ijassa-1064	38	10	logistically	logistically	ADV
ijassa-1064	38	11	with	with	ADP
ijassa-1064	38	12	intrinsic	intrinsic	ADJ
ijassa-1064	38	13	growth	growth	NOUN
ijassa-1064	38	14	rate	rate	NOUN
ijassa-1064	38	15	r	r	NOUN
ijassa-1064	38	16	and	and	CCONJ
ijassa-1064	38	17	carrying	carry	VERB
ijassa-1064	38	18	capacity	capacity	NOUN
ijassa-1064	38	19	k.	k.	NOUN
ijassa-1064	38	20	following	follow	VERB
ijassa-1064	38	21	effective	effective	ADJ
ijassa-1064	38	22	contact	contact	NOUN
ijassa-1064	38	23	with	with	ADP
ijassa-1064	38	24	the	the	DET
ijassa-1064	38	25	infected	infected	ADJ
ijassa-1064	38	26	prey	prey	NOUN
ijassa-1064	38	27	,	,	PUNCT
ijassa-1064	38	28	the	the	DET
ijassa-1064	38	29	susceptible	susceptible	ADJ
ijassa-1064	38	30	prey	prey	NOUN
ijassa-1064	38	31	becomes	becomes	AUX
ijassa-1064	38	32	infected	infect	VERB
ijassa-1064	38	33	at	at	ADP
ijassa-1064	38	34	rate	rate	NOUN
ijassa-1064	38	35	β1	β1	PROPN
ijassa-1064	38	36	.	.	PUNCT
ijassa-1064	39	1	to	to	PART
ijassa-1064	39	2	avoid	avoid	VERB
ijassa-1064	39	3	extinction	extinction	NOUN
ijassa-1064	39	4	of	of	ADP
ijassa-1064	39	5	the	the	DET
ijassa-1064	39	6	prey	prey	NOUN
ijassa-1064	39	7	population	population	NOUN
ijassa-1064	39	8	due	due	ADP
ijassa-1064	39	9	to	to	ADP
ijassa-1064	39	10	disease	disease	NOUN
ijassa-1064	39	11	,	,	PUNCT
ijassa-1064	39	12	the	the	DET
ijassa-1064	39	13	infected	infected	ADJ
ijassa-1064	39	14	prey	prey	NOUN
ijassa-1064	39	15	is	be	AUX
ijassa-1064	39	16	allowed	allow	VERB
ijassa-1064	39	17	to	to	PART
ijassa-1064	39	18	recover	recover	VERB
ijassa-1064	39	19	at	at	ADP
ijassa-1064	39	20	per	per	ADP
ijassa-1064	39	21	capita	capita	NOUN
ijassa-1064	39	22	rate	rate	NOUN
ijassa-1064	39	23	γ	γ	PROPN
ijassa-1064	39	24	.	.	PUNCT
ijassa-1064	40	1	the	the	DET
ijassa-1064	40	2	natural	natural	ADJ
ijassa-1064	40	3	mortality	mortality	NOUN
ijassa-1064	40	4	rate	rate	NOUN
ijassa-1064	40	5	for	for	ADP
ijassa-1064	40	6	the	the	DET
ijassa-1064	40	7	prey	prey	NOUN
ijassa-1064	40	8	population	population	NOUN
ijassa-1064	40	9	is	be	AUX
ijassa-1064	40	10	given	give	VERB
ijassa-1064	40	11	by	by	ADP
ijassa-1064	40	12	µ1	µ1	PROPN
ijassa-1064	40	13	.	.	PUNCT
ijassa-1064	41	1	further	far	ADV
ijassa-1064	41	2	,	,	PUNCT
ijassa-1064	41	3	it	it	PRON
ijassa-1064	41	4	is	be	AUX
ijassa-1064	41	5	assumed	assume	VERB
ijassa-1064	41	6	that	that	SCONJ
ijassa-1064	41	7	the	the	DET
ijassa-1064	41	8	susceptible	susceptible	ADJ
ijassa-1064	41	9	predator	predator	NOUN
ijassa-1064	41	10	,	,	PUNCT
ijassa-1064	41	11	being	be	AUX
ijassa-1064	41	12	healthy	healthy	ADJ
ijassa-1064	41	13	,	,	PUNCT
ijassa-1064	41	14	has	have	VERB
ijassa-1064	41	15	the	the	DET
ijassa-1064	41	16	capacity	capacity	NOUN
ijassa-1064	41	17	to	to	PART
ijassa-1064	41	18	attack	attack	VERB
ijassa-1064	41	19	and	and	CCONJ
ijassa-1064	41	20	consume	consume	VERB
ijassa-1064	41	21	both	both	CCONJ
ijassa-1064	41	22	susceptible	susceptible	ADJ
ijassa-1064	41	23	and	and	CCONJ
ijassa-1064	41	24	infected	infected	ADJ
ijassa-1064	41	25	prey	prey	NOUN
ijassa-1064	41	26	,	,	PUNCT
ijassa-1064	41	27	while	while	SCONJ
ijassa-1064	41	28	the	the	DET
ijassa-1064	41	29	recovered	recover	VERB
ijassa-1064	41	30	prey	prey	NOUN
ijassa-1064	41	31	is	be	AUX
ijassa-1064	41	32	assumed	assume	VERB
ijassa-1064	41	33	to	to	PART
ijassa-1064	41	34	be	be	AUX
ijassa-1064	41	35	under	under	ADP
ijassa-1064	41	36	cover	cover	NOUN
ijassa-1064	41	37	from	from	ADP
ijassa-1064	41	38	predation	predation	NOUN
ijassa-1064	41	39	.	.	PUNCT
ijassa-1064	42	1	it	it	PRON
ijassa-1064	42	2	is	be	AUX
ijassa-1064	42	3	also	also	ADV
ijassa-1064	42	4	assumed	assume	VERB
ijassa-1064	42	5	that	that	SCONJ
ijassa-1064	42	6	predators	predator	NOUN
ijassa-1064	42	7	depend	depend	VERB
ijassa-1064	42	8	on	on	ADP
ijassa-1064	42	9	prey	prey	NOUN
ijassa-1064	42	10	for	for	ADP
ijassa-1064	42	11	sustenance	sustenance	NOUN
ijassa-1064	42	12	.	.	PUNCT
ijassa-1064	43	1	the	the	DET
ijassa-1064	43	2	susceptible	susceptible	ADJ
ijassa-1064	43	3	predator	predator	NOUN
ijassa-1064	43	4	contracts	contract	NOUN
ijassa-1064	43	5	disease	disease	NOUN
ijassa-1064	43	6	from	from	ADP
ijassa-1064	43	7	infected	infected	ADJ
ijassa-1064	43	8	predator	predator	NOUN
ijassa-1064	43	9	at	at	ADP
ijassa-1064	43	10	rate	rate	NOUN
ijassa-1064	43	11	β2	β2	PROPN
ijassa-1064	43	12	,	,	PUNCT
ijassa-1064	43	13	while	while	SCONJ
ijassa-1064	43	14	the	the	DET
ijassa-1064	43	15	infected	infected	ADJ
ijassa-1064	43	16	predator	predator	NOUN
ijassa-1064	43	17	,	,	PUNCT
ijassa-1064	43	18	being	be	AUX
ijassa-1064	43	19	unhealthy	unhealthy	ADJ
ijassa-1064	43	20	,	,	PUNCT
ijassa-1064	43	21	has	have	VERB
ijassa-1064	43	22	the	the	DET
ijassa-1064	43	23	capacity	capacity	NOUN
ijassa-1064	43	24	to	to	PART
ijassa-1064	43	25	attack	attack	VERB
ijassa-1064	43	26	and	and	CCONJ
ijassa-1064	43	27	consume	consume	VERB
ijassa-1064	43	28	infected	infected	ADJ
ijassa-1064	43	29	prey	prey	NOUN
ijassa-1064	43	30	only	only	ADV
ijassa-1064	43	31	as	as	SCONJ
ijassa-1064	43	32	assumed	assume	VERB
ijassa-1064	43	33	in	in	ADP
ijassa-1064	43	34	[	[	X
ijassa-1064	43	35	8	8	NUM
ijassa-1064	43	36	]	]	PUNCT
ijassa-1064	43	37	.	.	PUNCT
ijassa-1064	44	1	it	it	PRON
ijassa-1064	44	2	has	have	AUX
ijassa-1064	44	3	been	be	AUX
ijassa-1064	44	4	assumed	assume	VERB
ijassa-1064	44	5	that	that	SCONJ
ijassa-1064	44	6	only	only	ADV
ijassa-1064	44	7	infected	infected	ADJ
ijassa-1064	44	8	prey	prey	NOUN
ijassa-1064	44	9	population	population	NOUN
ijassa-1064	44	10	recovers	recover	NOUN
ijassa-1064	44	11	due	due	ADP
ijassa-1064	44	12	to	to	ADP
ijassa-1064	44	13	their	their	PRON
ijassa-1064	44	14	accessibility	accessibility	NOUN
ijassa-1064	44	15	to	to	ADP
ijassa-1064	44	16	treatment	treatment	NOUN
ijassa-1064	44	17	.	.	PUNCT
ijassa-1064	45	1	hence	hence	ADV
ijassa-1064	45	2	,	,	PUNCT
ijassa-1064	45	3	recovered	recovered	ADJ
ijassa-1064	45	4	class	class	NOUN
ijassa-1064	45	5	for	for	ADP
ijassa-1064	45	6	predators	predator	NOUN
ijassa-1064	45	7	is	be	AUX
ijassa-1064	45	8	not	not	PART
ijassa-1064	45	9	considered	consider	VERB
ijassa-1064	45	10	.	.	PUNCT
ijassa-1064	46	1	this	this	DET
ijassa-1064	46	2	assumption	assumption	NOUN
ijassa-1064	46	3	is	be	AUX
ijassa-1064	46	4	based	base	VERB
ijassa-1064	46	5	on	on	ADP
ijassa-1064	46	6	some	some	DET
ijassa-1064	46	7	eco	eco	NOUN
ijassa-1064	46	8	-	-	PUNCT
ijassa-1064	46	9	epidemiological	epidemiological	ADJ
ijassa-1064	46	10	cases	case	NOUN
ijassa-1064	46	11	,	,	PUNCT
ijassa-1064	46	12	for	for	ADP
ijassa-1064	46	13	examples	example	NOUN
ijassa-1064	46	14	:	:	PUNCT
ijassa-1064	46	15	carnivorous	carnivorous	ADJ
ijassa-1064	46	16	animals	animal	NOUN
ijassa-1064	46	17	(	(	PUNCT
ijassa-1064	46	18	predator	predator	NOUN
ijassa-1064	46	19	)	)	PUNCT
ijassa-1064	46	20	and	and	CCONJ
ijassa-1064	46	21	humans	human	NOUN
ijassa-1064	46	22	(	(	PUNCT
ijassa-1064	46	23	prey	prey	PROPN
ijassa-1064	46	24	)	)	PUNCT
ijassa-1064	46	25	,	,	PUNCT
ijassa-1064	46	26	and	and	CCONJ
ijassa-1064	46	27	hawks	hawk	NOUN
ijassa-1064	46	28	(	(	PUNCT
ijassa-1064	46	29	predator	predator	NOUN
ijassa-1064	46	30	)	)	PUNCT
ijassa-1064	46	31	and	and	CCONJ
ijassa-1064	46	32	chicks	chick	NOUN
ijassa-1064	46	33	(	(	PUNCT
ijassa-1064	46	34	prey	prey	PROPN
ijassa-1064	46	35	)	)	PUNCT
ijassa-1064	46	36	.	.	PUNCT
ijassa-1064	47	1	the	the	DET
ijassa-1064	47	2	predation	predation	NOUN
ijassa-1064	47	3	and	and	CCONJ
ijassa-1064	47	4	conversion	conversion	NOUN
ijassa-1064	47	5	rates	rate	NOUN
ijassa-1064	47	6	for	for	ADP
ijassa-1064	47	7	the	the	DET
ijassa-1064	47	8	predator	predator	NOUN
ijassa-1064	47	9	population	population	NOUN
ijassa-1064	47	10	are	be	AUX
ijassa-1064	47	11	given	give	VERB
ijassa-1064	47	12	,	,	PUNCT
ijassa-1064	47	13	respectively	respectively	ADV
ijassa-1064	47	14	,	,	PUNCT
ijassa-1064	47	15	by	by	ADP
ijassa-1064	47	16	pi	pi	NOUN
ijassa-1064	47	17	and	and	CCONJ
ijassa-1064	47	18	ci	ci	NOUN
ijassa-1064	47	19	,	,	PUNCT
ijassa-1064	47	20	for	for	ADP
ijassa-1064	47	21	i	i	PROPN
ijassa-1064	47	22	=	=	SYM
ijassa-1064	47	23	1	1	NUM
ijassa-1064	47	24	,	,	PUNCT
ijassa-1064	47	25	2	2	NUM
ijassa-1064	47	26	,	,	PUNCT
ijassa-1064	47	27	3	3	NUM
ijassa-1064	47	28	.	.	PUNCT
ijassa-1064	48	1	the	the	DET
ijassa-1064	48	2	natural	natural	ADJ
ijassa-1064	48	3	mortality	mortality	NOUN
ijassa-1064	48	4	rate	rate	NOUN
ijassa-1064	48	5	for	for	ADP
ijassa-1064	48	6	predator	predator	NOUN
ijassa-1064	48	7	population	population	NOUN
ijassa-1064	48	8	is	be	AUX
ijassa-1064	48	9	given	give	VERB
ijassa-1064	48	10	by	by	ADP
ijassa-1064	48	11	µ2	µ2	PROPN
ijassa-1064	48	12	.	.	PUNCT
ijassa-1064	49	1	concise	concise	ADJ
ijassa-1064	49	2	description	description	NOUN
ijassa-1064	49	3	of	of	ADP
ijassa-1064	49	4	the	the	DET
ijassa-1064	49	5	variables	variable	NOUN
ijassa-1064	49	6	and	and	CCONJ
ijassa-1064	49	7	the	the	DET
ijassa-1064	49	8	parameters	parameter	NOUN
ijassa-1064	49	9	of	of	ADP
ijassa-1064	49	10	the	the	DET
ijassa-1064	49	11	prey	prey	NOUN
ijassa-1064	49	12	-	-	PUNCT
ijassa-1064	49	13	predator	predator	NOUN
ijassa-1064	49	14	system	system	NOUN
ijassa-1064	49	15	is	be	AUX
ijassa-1064	49	16	presented	present	VERB
ijassa-1064	49	17	in	in	ADP
ijassa-1064	49	18	table	table	NOUN
ijassa-1064	49	19	2.1	2.1	NUM
ijassa-1064	49	20	and	and	CCONJ
ijassa-1064	49	21	the	the	DET
ijassa-1064	49	22	nonlinear	nonlinear	ADJ
ijassa-1064	49	23	ordinary	ordinary	ADJ
ijassa-1064	49	24	differential	differential	ADJ
ijassa-1064	49	25	equations	equation	NOUN
ijassa-1064	49	26	describing	describe	VERB
ijassa-1064	49	27	the	the	DET
ijassa-1064	49	28	interacting	interact	VERB
ijassa-1064	49	29	prey	prey	NOUN
ijassa-1064	49	30	and	and	CCONJ
ijassa-1064	49	31	predator	predator	NOUN
ijassa-1064	49	32	populations	population	NOUN
ijassa-1064	49	33	is	be	AUX
ijassa-1064	49	34	given	give	VERB
ijassa-1064	49	35	by	by	ADP
ijassa-1064	49	36	copyright	copyright	NOUN
ijassa-1064	49	37	©	©	PROPN
ijassa-1064	49	38	2021	2021	NUM
ijassa-1064	49	39	assa	assa	NOUN
ijassa-1064	49	40	.	.	PUNCT
ijassa-1064	50	1	adv	adv	PROPN
ijassa-1064	50	2	syst	syst	PROPN
ijassa-1064	50	3	sci	sci	PROPN
ijassa-1064	50	4	appl	appl	PROPN
ijassa-1064	50	5	(	(	PUNCT
ijassa-1064	50	6	2021	2021	NUM
ijassa-1064	50	7	)	)	PUNCT
ijassa-1064	50	8	stability	stability	NOUN
ijassa-1064	50	9	analysis	analysis	NOUN
ijassa-1064	50	10	and	and	CCONJ
ijassa-1064	50	11	optimal	optimal	ADJ
ijassa-1064	50	12	measure	measure	NOUN
ijassa-1064	50	13	85	85	NUM
ijassa-1064	50	14	dxs	dxs	PROPN
ijassa-1064	50	15	dt	dt	NOUN
ijassa-1064	51	1	=	=	NOUN
ijassa-1064	51	2	rxs	rxs	X
ijassa-1064	51	3	(	(	PUNCT
ijassa-1064	51	4	1−	1−	NUM
ijassa-1064	51	5	xs	xs	PROPN
ijassa-1064	51	6	k	k	PROPN
ijassa-1064	51	7	)	)	PUNCT
ijassa-1064	51	8	−	−	PROPN
ijassa-1064	52	1	β1xsxi	β1xsxi	NUM
ijassa-1064	52	2	−	−	NUM
ijassa-1064	52	3	p1xsys	p1xsy	NOUN
ijassa-1064	52	4	−	−	NOUN
ijassa-1064	52	5	µ1xs	µ1xs	NOUN
ijassa-1064	52	6	dxi	dxi	NOUN
ijassa-1064	52	7	dt	dt	NOUN
ijassa-1064	53	1	=	=	NOUN
ijassa-1064	53	2	β1xsxi	β1xsxi	NOUN
ijassa-1064	53	3	−	−	PROPN
ijassa-1064	53	4	p2xiys	p2xiys	ADP
ijassa-1064	53	5	−	−	PROPN
ijassa-1064	53	6	p3xiyi	p3xiyi	NOUN
ijassa-1064	53	7	−	−	PROPN
ijassa-1064	53	8	(	(	PUNCT
ijassa-1064	53	9	µ1	µ1	PROPN
ijassa-1064	53	10	+	+	CCONJ
ijassa-1064	53	11	γ)xi	γ)xi	PROPN
ijassa-1064	53	12	dxr	dxr	ADJ
ijassa-1064	53	13	dt	dt	X
ijassa-1064	53	14	=	=	SYM
ijassa-1064	53	15	γxi	γxi	NOUN
ijassa-1064	53	16	−	−	PROPN
ijassa-1064	53	17	µ1xr	µ1xr	PUNCT
ijassa-1064	53	18	dys	dys	NOUN
ijassa-1064	53	19	dt	dt	NOUN
ijassa-1064	53	20	=	=	NOUN
ijassa-1064	53	21	c1p1xsys	c1p1xsys	X
ijassa-1064	53	22	+	+	CCONJ
ijassa-1064	53	23	c2p2xiys	c2p2xiy	VERB
ijassa-1064	53	24	−	−	PROPN
ijassa-1064	53	25	β2ysyi	β2ysyi	NOUN
ijassa-1064	53	26	−	−	PROPN
ijassa-1064	53	27	µ2ys	µ2ys	PUNCT
ijassa-1064	53	28	dyi	dyi	PROPN
ijassa-1064	53	29	dt	dt	NOUN
ijassa-1064	53	30	=	=	NOUN
ijassa-1064	53	31	β2ysyi	β2ysyi	X
ijassa-1064	53	32	+	+	CCONJ
ijassa-1064	53	33	c3p3xiyi	c3p3xiyi	NOUN
ijassa-1064	53	34	−	−	PRON
ijassa-1064	53	35	µ2yi	µ2yi	NOUN
ijassa-1064	53	36	.	.	PUNCT
ijassa-1064	54	1	(	(	PUNCT
ijassa-1064	54	2	2.1	2.1	NUM
ijassa-1064	54	3	)	)	PUNCT
ijassa-1064	54	4	table	table	NOUN
ijassa-1064	54	5	2.1	2.1	NUM
ijassa-1064	54	6	.	.	PUNCT
ijassa-1064	55	1	the	the	DET
ijassa-1064	55	2	variables	variable	NOUN
ijassa-1064	55	3	and	and	CCONJ
ijassa-1064	55	4	parameters	parameter	NOUN
ijassa-1064	55	5	of	of	ADP
ijassa-1064	55	6	the	the	DET
ijassa-1064	55	7	malaria	malaria	NOUN
ijassa-1064	55	8	model	model	NOUN
ijassa-1064	55	9	(	(	PUNCT
ijassa-1064	55	10	2.1	2.1	NUM
ijassa-1064	55	11	)	)	PUNCT
ijassa-1064	55	12	variable	variable	ADJ
ijassa-1064	55	13	description	description	NOUN
ijassa-1064	55	14	xs(t	xs(t	NOUN
ijassa-1064	55	15	)	)	PUNCT
ijassa-1064	55	16	susceptible	susceptible	ADJ
ijassa-1064	55	17	(	(	PUNCT
ijassa-1064	55	18	healthy	healthy	ADJ
ijassa-1064	55	19	)	)	PUNCT
ijassa-1064	55	20	prey	prey	NOUN
ijassa-1064	55	21	xi(t	xi(t	ADV
ijassa-1064	55	22	)	)	PUNCT
ijassa-1064	55	23	infected	infect	VERB
ijassa-1064	55	24	(	(	PUNCT
ijassa-1064	55	25	unhealthy	unhealthy	ADJ
ijassa-1064	55	26	)	)	PUNCT
ijassa-1064	55	27	prey	prey	NOUN
ijassa-1064	55	28	xr(t	xr(t	PUNCT
ijassa-1064	55	29	)	)	PUNCT
ijassa-1064	55	30	recovered	recover	VERB
ijassa-1064	55	31	prey	prey	NOUN
ijassa-1064	55	32	ys(t	ys(t	NOUN
ijassa-1064	55	33	)	)	PUNCT
ijassa-1064	55	34	susceptible	susceptible	ADJ
ijassa-1064	55	35	(	(	PUNCT
ijassa-1064	55	36	healthy	healthy	ADJ
ijassa-1064	55	37	)	)	PUNCT
ijassa-1064	55	38	predator	predator	NOUN
ijassa-1064	55	39	yi(t	yi(t	NOUN
ijassa-1064	55	40	)	)	PUNCT
ijassa-1064	55	41	infected	infect	VERB
ijassa-1064	55	42	(	(	PUNCT
ijassa-1064	55	43	unhealthy	unhealthy	ADJ
ijassa-1064	55	44	)	)	PUNCT
ijassa-1064	55	45	predator	predator	NOUN
ijassa-1064	55	46	parameter	parameter	NOUN
ijassa-1064	55	47	description	description	NOUN
ijassa-1064	55	48	r	r	NOUN
ijassa-1064	55	49	intrinsic	intrinsic	ADJ
ijassa-1064	55	50	growth	growth	NOUN
ijassa-1064	55	51	rate	rate	NOUN
ijassa-1064	55	52	k	k	NOUN
ijassa-1064	55	53	carrying	carry	VERB
ijassa-1064	55	54	capacity	capacity	NOUN
ijassa-1064	55	55	β1	β1	NOUN
ijassa-1064	55	56	disease	disease	NOUN
ijassa-1064	55	57	transmission	transmission	NOUN
ijassa-1064	55	58	rate	rate	NOUN
ijassa-1064	55	59	in	in	ADP
ijassa-1064	55	60	prey	prey	PROPN
ijassa-1064	55	61	β2	β2	PROPN
ijassa-1064	55	62	disease	disease	NOUN
ijassa-1064	55	63	transmission	transmission	NOUN
ijassa-1064	55	64	rate	rate	NOUN
ijassa-1064	55	65	in	in	ADP
ijassa-1064	55	66	predator	predator	NOUN
ijassa-1064	55	67	pi	pi	NOUN
ijassa-1064	55	68	,	,	PUNCT
ijassa-1064	55	69	i	i	PRON
ijassa-1064	55	70	=	=	NOUN
ijassa-1064	55	71	1	1	NUM
ijassa-1064	55	72	,	,	PUNCT
ijassa-1064	55	73	2	2	NUM
ijassa-1064	55	74	,	,	PUNCT
ijassa-1064	55	75	3	3	NUM
ijassa-1064	55	76	predation	predation	NOUN
ijassa-1064	55	77	coefficients	coefficient	VERB
ijassa-1064	55	78	ci	ci	PROPN
ijassa-1064	55	79	,	,	PUNCT
ijassa-1064	55	80	i	i	PRON
ijassa-1064	55	81	=	=	NOUN
ijassa-1064	55	82	1	1	NUM
ijassa-1064	55	83	,	,	PUNCT
ijassa-1064	55	84	2	2	NUM
ijassa-1064	55	85	,	,	PUNCT
ijassa-1064	55	86	3	3	NUM
ijassa-1064	55	87	conversion	conversion	NOUN
ijassa-1064	55	88	rates	rate	NOUN
ijassa-1064	55	89	γ	γ	PROPN
ijassa-1064	55	90	recovery	recovery	NOUN
ijassa-1064	55	91	rate	rate	NOUN
ijassa-1064	55	92	of	of	ADP
ijassa-1064	55	93	infected	infected	ADJ
ijassa-1064	55	94	prey	prey	NOUN
ijassa-1064	55	95	µ1	µ1	PROPN
ijassa-1064	55	96	natural	natural	ADJ
ijassa-1064	55	97	mortality	mortality	NOUN
ijassa-1064	55	98	rate	rate	NOUN
ijassa-1064	55	99	of	of	ADP
ijassa-1064	55	100	prey	prey	NOUN
ijassa-1064	55	101	µ2	µ2	PROPN
ijassa-1064	55	102	natural	natural	ADJ
ijassa-1064	55	103	mortality	mortality	NOUN
ijassa-1064	55	104	rate	rate	NOUN
ijassa-1064	55	105	of	of	ADP
ijassa-1064	55	106	predator	predator	NOUN
ijassa-1064	55	107	2.1	2.1	NUM
ijassa-1064	55	108	.	.	PUNCT
ijassa-1064	56	1	well	well	ADJ
ijassa-1064	56	2	-	-	PUNCT
ijassa-1064	56	3	posedness	posedness	NOUN
ijassa-1064	56	4	of	of	ADP
ijassa-1064	56	5	the	the	DET
ijassa-1064	56	6	model	model	NOUN
ijassa-1064	56	7	the	the	DET
ijassa-1064	56	8	mathematical	mathematical	ADJ
ijassa-1064	56	9	and	and	CCONJ
ijassa-1064	56	10	eco	eco	NOUN
ijassa-1064	56	11	-	-	PUNCT
ijassa-1064	56	12	epidemiological	epidemiological	ADJ
ijassa-1064	56	13	relevance	relevance	NOUN
ijassa-1064	56	14	of	of	ADP
ijassa-1064	56	15	the	the	DET
ijassa-1064	56	16	prey	prey	NOUN
ijassa-1064	56	17	-	-	PUNCT
ijassa-1064	56	18	predator	predator	NOUN
ijassa-1064	56	19	system	system	NOUN
ijassa-1064	56	20	(	(	PUNCT
ijassa-1064	56	21	2.1	2.1	NUM
ijassa-1064	56	22	)	)	PUNCT
ijassa-1064	56	23	depends	depend	VERB
ijassa-1064	56	24	on	on	ADP
ijassa-1064	56	25	the	the	DET
ijassa-1064	56	26	well	well	NOUN
ijassa-1064	56	27	-	-	PUNCT
ijassa-1064	56	28	posedness	posedness	NOUN
ijassa-1064	56	29	of	of	ADP
ijassa-1064	56	30	the	the	DET
ijassa-1064	56	31	model	model	NOUN
ijassa-1064	56	32	.	.	PUNCT
ijassa-1064	57	1	keeping	keep	VERB
ijassa-1064	57	2	in	in	ADP
ijassa-1064	57	3	mind	mind	NOUN
ijassa-1064	57	4	that	that	SCONJ
ijassa-1064	57	5	all	all	DET
ijassa-1064	57	6	the	the	DET
ijassa-1064	57	7	parameters	parameter	NOUN
ijassa-1064	57	8	of	of	ADP
ijassa-1064	57	9	the	the	DET
ijassa-1064	57	10	model	model	NOUN
ijassa-1064	57	11	are	be	AUX
ijassa-1064	57	12	non	non	ADJ
ijassa-1064	57	13	-	-	ADJ
ijassa-1064	57	14	negative	negative	ADJ
ijassa-1064	57	15	.	.	PUNCT
ijassa-1064	58	1	here	here	ADV
ijassa-1064	58	2	,	,	PUNCT
ijassa-1064	58	3	the	the	DET
ijassa-1064	58	4	boundedness	boundedness	NOUN
ijassa-1064	58	5	and	and	CCONJ
ijassa-1064	58	6	positivity	positivity	NOUN
ijassa-1064	58	7	of	of	ADP
ijassa-1064	58	8	solutions	solution	NOUN
ijassa-1064	58	9	of	of	ADP
ijassa-1064	58	10	the	the	DET
ijassa-1064	58	11	model	model	NOUN
ijassa-1064	58	12	are	be	AUX
ijassa-1064	58	13	investigated	investigate	VERB
ijassa-1064	58	14	to	to	PART
ijassa-1064	58	15	establish	establish	VERB
ijassa-1064	58	16	the	the	DET
ijassa-1064	58	17	well	well	NOUN
ijassa-1064	58	18	-	-	PUNCT
ijassa-1064	58	19	posedness	posedness	NOUN
ijassa-1064	58	20	of	of	ADP
ijassa-1064	58	21	the	the	DET
ijassa-1064	58	22	model	model	NOUN
ijassa-1064	58	23	.	.	PUNCT
ijassa-1064	59	1	2.1.1	2.1.1	X
ijassa-1064	59	2	.	.	PUNCT
ijassa-1064	59	3	boundedness	boundedness	NOUN
ijassa-1064	59	4	of	of	ADP
ijassa-1064	59	5	solutions	solution	NOUN
ijassa-1064	59	6	the	the	DET
ijassa-1064	59	7	following	following	ADJ
ijassa-1064	59	8	result	result	NOUN
ijassa-1064	59	9	is	be	AUX
ijassa-1064	59	10	required	require	VERB
ijassa-1064	59	11	to	to	PART
ijassa-1064	59	12	establish	establish	VERB
ijassa-1064	59	13	the	the	DET
ijassa-1064	59	14	boundedness	boundedness	NOUN
ijassa-1064	59	15	of	of	ADP
ijassa-1064	59	16	solutions	solution	NOUN
ijassa-1064	59	17	of	of	ADP
ijassa-1064	59	18	the	the	DET
ijassa-1064	59	19	model	model	NOUN
ijassa-1064	59	20	(	(	PUNCT
ijassa-1064	59	21	2.1	2.1	NUM
ijassa-1064	59	22	)	)	PUNCT
ijassa-1064	59	23	.	.	PUNCT
ijassa-1064	60	1	lemma	lemma	PROPN
ijassa-1064	60	2	2.1	2.1	NUM
ijassa-1064	60	3	:	:	PUNCT
ijassa-1064	60	4	the	the	DET
ijassa-1064	60	5	susceptible	susceptible	ADJ
ijassa-1064	60	6	prey	prey	NOUN
ijassa-1064	60	7	population	population	NOUN
ijassa-1064	60	8	xs(t	xs(t	PUNCT
ijassa-1064	60	9	)	)	PUNCT
ijassa-1064	60	10	is	be	AUX
ijassa-1064	60	11	bounded	bound	VERB
ijassa-1064	60	12	.	.	PUNCT
ijassa-1064	61	1	proof	proof	NOUN
ijassa-1064	61	2	it	it	PRON
ijassa-1064	61	3	is	be	AUX
ijassa-1064	61	4	clear	clear	ADJ
ijassa-1064	61	5	from	from	ADP
ijassa-1064	61	6	the	the	DET
ijassa-1064	61	7	first	first	ADJ
ijassa-1064	61	8	equation	equation	NOUN
ijassa-1064	61	9	of	of	ADP
ijassa-1064	61	10	the	the	DET
ijassa-1064	61	11	model	model	NOUN
ijassa-1064	61	12	(	(	PUNCT
ijassa-1064	61	13	2.1	2.1	NUM
ijassa-1064	61	14	)	)	PUNCT
ijassa-1064	61	15	that	that	PRON
ijassa-1064	61	16	dxs	dxs	PROPN
ijassa-1064	61	17	dt	dt	PROPN
ijassa-1064	61	18	≤	≤	PROPN
ijassa-1064	61	19	rxs	rxs	NOUN
ijassa-1064	61	20	−	−	PROPN
ijassa-1064	62	1	x2	x2	PROPN
ijassa-1064	62	2	s	s	PROPN
ijassa-1064	62	3	k	k	X
ijassa-1064	62	4	.	.	PUNCT
ijassa-1064	63	1	(	(	PUNCT
ijassa-1064	63	2	2.2	2.2	NUM
ijassa-1064	63	3	)	)	PUNCT
ijassa-1064	63	4	copyright	copyright	NOUN
ijassa-1064	63	5	©	©	PROPN
ijassa-1064	63	6	2021	2021	NUM
ijassa-1064	63	7	assa	assa	NOUN
ijassa-1064	63	8	.	.	PUNCT
ijassa-1064	64	1	adv	adv	PROPN
ijassa-1064	64	2	syst	syst	PROPN
ijassa-1064	64	3	sci	sci	PROPN
ijassa-1064	64	4	appl	appl	PROPN
ijassa-1064	64	5	(	(	PUNCT
ijassa-1064	64	6	2021	2021	NUM
ijassa-1064	64	7	)	)	PUNCT
ijassa-1064	64	8	86	86	NUM
ijassa-1064	64	9	j.a	j.a	PROPN
ijassa-1064	64	10	.	.	PROPN
ijassa-1064	64	11	ademosu	ademosu	PROPN
ijassa-1064	64	12	,	,	PUNCT
ijassa-1064	64	13	s.	s.	PROPN
ijassa-1064	64	14	olaniyi	olaniyi	PROPN
ijassa-1064	64	15	,	,	PUNCT
ijassa-1064	64	16	s.o	s.o	PROPN
ijassa-1064	64	17	.	.	PROPN
ijassa-1064	64	18	adewale	adewale	PROPN
ijassa-1064	64	19	solving	solve	VERB
ijassa-1064	64	20	the	the	DET
ijassa-1064	64	21	nonlinear	nonlinear	ADJ
ijassa-1064	64	22	first	first	ADJ
ijassa-1064	64	23	order	order	NOUN
ijassa-1064	64	24	differential	differential	ADJ
ijassa-1064	64	25	inequality	inequality	NOUN
ijassa-1064	64	26	of	of	ADP
ijassa-1064	64	27	bernoulli	bernoulli	PROPN
ijassa-1064	64	28	type	type	NOUN
ijassa-1064	64	29	(	(	PUNCT
ijassa-1064	64	30	2.2	2.2	NUM
ijassa-1064	64	31	)	)	PUNCT
ijassa-1064	64	32	yields	yield	NOUN
ijassa-1064	64	33	xs(t	xs(t	NOUN
ijassa-1064	64	34	)	)	PUNCT
ijassa-1064	64	35	≤	≤	NUM
ijassa-1064	64	36	kxs(0	kxs(0	NOUN
ijassa-1064	64	37	)	)	PUNCT
ijassa-1064	64	38	ke−rt	ke−rt	NOUN
ijassa-1064	65	1	+	+	PUNCT
ijassa-1064	65	2	xs(0)(1−	xs(0)(1−	PROPN
ijassa-1064	65	3	e−rt	e−rt	X
ijassa-1064	65	4	)	)	PUNCT
ijassa-1064	65	5	.	.	PUNCT
ijassa-1064	66	1	it	it	PRON
ijassa-1064	66	2	follows	follow	VERB
ijassa-1064	66	3	that	that	SCONJ
ijassa-1064	66	4	the	the	DET
ijassa-1064	66	5	lim	lim	PROPN
ijassa-1064	66	6	supxs(t	supxs(t	PROPN
ijassa-1064	66	7	)	)	PUNCT
ijassa-1064	66	8	<	<	X
ijassa-1064	66	9	k	k	PROPN
ijassa-1064	66	10	as	as	SCONJ
ijassa-1064	66	11	t→∞.	t→∞.	NUM
ijassa-1064	66	12	theorem	theorem	VERB
ijassa-1064	66	13	2.1	2.1	NUM
ijassa-1064	66	14	:	:	PUNCT
ijassa-1064	66	15	the	the	DET
ijassa-1064	66	16	solutions	solution	NOUN
ijassa-1064	66	17	of	of	ADP
ijassa-1064	66	18	the	the	DET
ijassa-1064	66	19	system	system	NOUN
ijassa-1064	66	20	(	(	PUNCT
ijassa-1064	66	21	2.1	2.1	NUM
ijassa-1064	66	22	)	)	PUNCT
ijassa-1064	66	23	are	be	AUX
ijassa-1064	66	24	uniformly	uniformly	ADV
ijassa-1064	66	25	bounded	bound	VERB
ijassa-1064	66	26	.	.	PUNCT
ijassa-1064	67	1	proof	proof	NOUN
ijassa-1064	67	2	let	let	VERB
ijassa-1064	67	3	the	the	DET
ijassa-1064	67	4	total	total	ADJ
ijassa-1064	67	5	prey	prey	NOUN
ijassa-1064	67	6	and	and	CCONJ
ijassa-1064	67	7	predator	predator	NOUN
ijassa-1064	67	8	populations	population	NOUN
ijassa-1064	67	9	be	be	AUX
ijassa-1064	67	10	represented	represent	VERB
ijassa-1064	67	11	,	,	PUNCT
ijassa-1064	67	12	respectively	respectively	ADV
ijassa-1064	67	13	,	,	PUNCT
ijassa-1064	67	14	by	by	ADP
ijassa-1064	67	15	x	x	PUNCT
ijassa-1064	67	16	and	and	CCONJ
ijassa-1064	67	17	y	y	PROPN
ijassa-1064	67	18	,	,	PUNCT
ijassa-1064	67	19	so	so	SCONJ
ijassa-1064	67	20	that	that	SCONJ
ijassa-1064	67	21	the	the	DET
ijassa-1064	67	22	total	total	ADJ
ijassa-1064	67	23	population	population	NOUN
ijassa-1064	67	24	of	of	ADP
ijassa-1064	67	25	both	both	DET
ijassa-1064	67	26	species	specie	NOUN
ijassa-1064	67	27	be	be	VERB
ijassa-1064	67	28	t	t	NOUN
ijassa-1064	67	29	=	=	PUNCT
ijassa-1064	67	30	x	x	PROPN
ijassa-1064	68	1	+	+	NUM
ijassa-1064	68	2	y	y	PROPN
ijassa-1064	68	3	.	.	PUNCT
ijassa-1064	69	1	then	then	ADV
ijassa-1064	69	2	it	it	PRON
ijassa-1064	69	3	follows	follow	VERB
ijassa-1064	69	4	that	that	SCONJ
ijassa-1064	69	5	dt	dt	PUNCT
ijassa-1064	69	6	dt	dt	X
ijassa-1064	69	7	≤	≤	X
ijassa-1064	69	8	rxs	rxs	NOUN
ijassa-1064	69	9	−	−	NOUN
ijassa-1064	69	10	µ1x	µ1x	NOUN
ijassa-1064	69	11	−	−	NOUN
ijassa-1064	69	12	µ2y	µ2y	X
ijassa-1064	69	13	.	.	PUNCT
ijassa-1064	70	1	(	(	PUNCT
ijassa-1064	70	2	2.3	2.3	NUM
ijassa-1064	70	3	)	)	PUNCT
ijassa-1064	70	4	using	use	VERB
ijassa-1064	70	5	lemma	lemma	PROPN
ijassa-1064	70	6	2.1	2.1	NUM
ijassa-1064	70	7	and	and	CCONJ
ijassa-1064	70	8	let	let	VERB
ijassa-1064	70	9	µ	µ	X
ijassa-1064	70	10	=	=	SYM
ijassa-1064	70	11	min{µ1	min{µ1	NUM
ijassa-1064	70	12	,	,	PUNCT
ijassa-1064	70	13	µ2	µ2	PROPN
ijassa-1064	70	14	}	}	PUNCT
ijassa-1064	70	15	,	,	PUNCT
ijassa-1064	70	16	then	then	ADV
ijassa-1064	70	17	(	(	PUNCT
ijassa-1064	70	18	2.3	2.3	NUM
ijassa-1064	70	19	)	)	PUNCT
ijassa-1064	70	20	becomes	become	VERB
ijassa-1064	70	21	dt	dt	NOUN
ijassa-1064	70	22	dt	dt	NOUN
ijassa-1064	71	1	+	+	CCONJ
ijassa-1064	71	2	µt	µt	ADJ
ijassa-1064	71	3	≤	≤	ADJ
ijassa-1064	71	4	rxs	rxs	ADJ
ijassa-1064	71	5	≤	≤	PROPN
ijassa-1064	71	6	rk	rk	NOUN
ijassa-1064	71	7	,	,	PUNCT
ijassa-1064	71	8	which	which	PRON
ijassa-1064	71	9	on	on	ADP
ijassa-1064	71	10	integration	integration	NOUN
ijassa-1064	71	11	gives	give	VERB
ijassa-1064	71	12	t	t	PROPN
ijassa-1064	71	13	(	(	PUNCT
ijassa-1064	71	14	t	t	PROPN
ijassa-1064	71	15	)	)	PUNCT
ijassa-1064	71	16	≤	≤	NUM
ijassa-1064	71	17	rk	rk	NOUN
ijassa-1064	71	18	µ	µ	X
ijassa-1064	71	19	(	(	PUNCT
ijassa-1064	71	20	1−	1−	NUM
ijassa-1064	71	21	e−µt	e−µt	PROPN
ijassa-1064	71	22	)	)	PUNCT
ijassa-1064	72	1	+	+	NUM
ijassa-1064	72	2	t	t	PROPN
ijassa-1064	72	3	(	(	PUNCT
ijassa-1064	72	4	0)e−µt	0)e−µt	X
ijassa-1064	72	5	.	.	PUNCT
ijassa-1064	73	1	consequently	consequently	ADV
ijassa-1064	73	2	,	,	PUNCT
ijassa-1064	73	3	lim	lim	PROPN
ijassa-1064	73	4	supt	supt	PROPN
ijassa-1064	73	5	(	(	PUNCT
ijassa-1064	73	6	t	t	PROPN
ijassa-1064	73	7	)	)	PUNCT
ijassa-1064	73	8	<	<	X
ijassa-1064	73	9	(	(	PUNCT
ijassa-1064	73	10	rk/µ	rk/µ	PROPN
ijassa-1064	73	11	)	)	PUNCT
ijassa-1064	74	1	+	+	CCONJ
ijassa-1064	74	2	ε	ε	PROPN
ijassa-1064	74	3	,	,	PUNCT
ijassa-1064	74	4	∀	∀	X
ijassa-1064	74	5	ε	ε	X
ijassa-1064	74	6	>	>	X
ijassa-1064	74	7	0	0	PUNCT
ijassa-1064	75	1	as	as	ADP
ijassa-1064	75	2	t→∞.	t→∞.	PROPN
ijassa-1064	75	3	this	this	PRON
ijassa-1064	75	4	ends	end	VERB
ijassa-1064	75	5	the	the	DET
ijassa-1064	75	6	proof	proof	NOUN
ijassa-1064	75	7	.	.	PUNCT
ijassa-1064	76	1	2.1.2	2.1.2	X
ijassa-1064	76	2	.	.	X
ijassa-1064	76	3	positivity	positivity	NOUN
ijassa-1064	76	4	of	of	ADP
ijassa-1064	76	5	solutions	solution	NOUN
ijassa-1064	76	6	theorem	theorem	VERB
ijassa-1064	76	7	2.2	2.2	NUM
ijassa-1064	76	8	:	:	PUNCT
ijassa-1064	76	9	the	the	DET
ijassa-1064	76	10	solution	solution	NOUN
ijassa-1064	76	11	set	set	NOUN
ijassa-1064	76	12	{	{	PUNCT
ijassa-1064	76	13	xs	xs	PROPN
ijassa-1064	76	14	,	,	PUNCT
ijassa-1064	76	15	xi	xi	PROPN
ijassa-1064	76	16	,	,	PUNCT
ijassa-1064	76	17	xr	xr	PROPN
ijassa-1064	76	18	,	,	PUNCT
ijassa-1064	76	19	ys	ys	NOUN
ijassa-1064	76	20	,	,	PUNCT
ijassa-1064	76	21	yi	yi	NOUN
ijassa-1064	76	22	}	}	PUNCT
ijassa-1064	76	23	of	of	ADP
ijassa-1064	76	24	the	the	DET
ijassa-1064	76	25	eco	eco	NOUN
ijassa-1064	76	26	-	-	PUNCT
ijassa-1064	76	27	epidemiological	epidemiological	ADJ
ijassa-1064	76	28	model	model	NOUN
ijassa-1064	76	29	(	(	PUNCT
ijassa-1064	76	30	2.1	2.1	NUM
ijassa-1064	76	31	)	)	PUNCT
ijassa-1064	76	32	with	with	ADP
ijassa-1064	76	33	nonnegative	nonnegative	ADJ
ijassa-1064	76	34	initial	initial	ADJ
ijassa-1064	76	35	conditions	condition	NOUN
ijassa-1064	76	36	,	,	PUNCT
ijassa-1064	76	37	xs(0	xs(0	PROPN
ijassa-1064	76	38	)	)	PUNCT
ijassa-1064	76	39	,	,	PUNCT
ijassa-1064	76	40	xi(0	xi(0	PROPN
ijassa-1064	76	41	)	)	PUNCT
ijassa-1064	76	42	,	,	PUNCT
ijassa-1064	76	43	xr(0	xr(0	PROPN
ijassa-1064	76	44	)	)	PUNCT
ijassa-1064	76	45	,	,	PUNCT
ijassa-1064	76	46	ys(0	ys(0	PROPN
ijassa-1064	76	47	)	)	PUNCT
ijassa-1064	76	48	,	,	PUNCT
ijassa-1064	76	49	yi(0	yi(0	PROPN
ijassa-1064	76	50	)	)	PUNCT
ijassa-1064	76	51	in	in	ADP
ijassa-1064	76	52	ω	ω	PROPN
ijassa-1064	76	53	,	,	PUNCT
ijassa-1064	76	54	remain	remain	VERB
ijassa-1064	76	55	non	non	ADJ
ijassa-1064	76	56	-	-	ADJ
ijassa-1064	76	57	negative	negative	ADJ
ijassa-1064	76	58	for	for	ADP
ijassa-1064	76	59	all	all	DET
ijassa-1064	76	60	time	time	NOUN
ijassa-1064	76	61	t	t	X
ijassa-1064	76	62	>	>	X
ijassa-1064	76	63	0	0	X
ijassa-1064	76	64	.	.	PUNCT
ijassa-1064	77	1	proof	proof	NOUN
ijassa-1064	77	2	sincexs(t	sincexs(t	PROPN
ijassa-1064	77	3	)	)	PUNCT
ijassa-1064	78	1	<	<	X
ijassa-1064	78	2	k	k	PROPN
ijassa-1064	78	3	as	as	SCONJ
ijassa-1064	78	4	shown	show	VERB
ijassa-1064	78	5	in	in	ADP
ijassa-1064	78	6	lemma	lemma	PROPN
ijassa-1064	78	7	2.1	2.1	NUM
ijassa-1064	78	8	,	,	PUNCT
ijassa-1064	78	9	then	then	ADV
ijassa-1064	78	10	(	(	PUNCT
ijassa-1064	78	11	1−xs	1−xs	NUM
ijassa-1064	78	12	/	/	SYM
ijassa-1064	78	13	k	k	NOUN
ijassa-1064	78	14	)	)	PUNCT
ijassa-1064	78	15	≥	≥	NOUN
ijassa-1064	78	16	0	0	NUM
ijassa-1064	78	17	with	with	ADP
ijassa-1064	78	18	equality	equality	NOUN
ijassa-1064	78	19	if	if	SCONJ
ijassa-1064	78	20	the	the	DET
ijassa-1064	78	21	size	size	NOUN
ijassa-1064	78	22	of	of	ADP
ijassa-1064	78	23	the	the	DET
ijassa-1064	78	24	susceptible	susceptible	ADJ
ijassa-1064	78	25	prey	prey	NOUN
ijassa-1064	78	26	is	be	AUX
ijassa-1064	78	27	exactly	exactly	ADV
ijassa-1064	78	28	its	its	PRON
ijassa-1064	78	29	carrying	carry	VERB
ijassa-1064	78	30	capacity	capacity	NOUN
ijassa-1064	78	31	.	.	PUNCT
ijassa-1064	79	1	hence	hence	ADV
ijassa-1064	79	2	,	,	PUNCT
ijassa-1064	79	3	the	the	DET
ijassa-1064	79	4	first	first	ADJ
ijassa-1064	79	5	equation	equation	NOUN
ijassa-1064	79	6	of	of	ADP
ijassa-1064	79	7	the	the	DET
ijassa-1064	79	8	model	model	NOUN
ijassa-1064	79	9	(	(	PUNCT
ijassa-1064	79	10	2.1	2.1	NUM
ijassa-1064	79	11	)	)	PUNCT
ijassa-1064	79	12	implies	imply	VERB
ijassa-1064	79	13	that	that	SCONJ
ijassa-1064	79	14	dxs(t	dxs(t	VERB
ijassa-1064	79	15	)	)	PUNCT
ijassa-1064	79	16	dt	dt	NOUN
ijassa-1064	80	1	+	+	CCONJ
ijassa-1064	80	2	(	(	PUNCT
ijassa-1064	80	3	β1xi	β1xi	PUNCT
ijassa-1064	80	4	+	+	NUM
ijassa-1064	80	5	p1ys	p1ys	X
ijassa-1064	80	6	+	+	SYM
ijassa-1064	80	7	µ1)xs(t	µ1)xs(t	PROPN
ijassa-1064	80	8	)	)	PUNCT
ijassa-1064	80	9	≥	≥	NOUN
ijassa-1064	80	10	0	0	NUM
ijassa-1064	80	11	,	,	PUNCT
ijassa-1064	80	12	(	(	PUNCT
ijassa-1064	80	13	2.4	2.4	NUM
ijassa-1064	80	14	)	)	PUNCT
ijassa-1064	80	15	which	which	PRON
ijassa-1064	80	16	on	on	ADP
ijassa-1064	80	17	using	use	VERB
ijassa-1064	80	18	integrating	integrate	VERB
ijassa-1064	80	19	factor	factor	NOUN
ijassa-1064	80	20	gives	give	VERB
ijassa-1064	80	21	d	d	PROPN
ijassa-1064	80	22	dt	dt	X
ijassa-1064	80	23	[	[	PUNCT
ijassa-1064	80	24	xs(t	xs(t	NOUN
ijassa-1064	80	25	)	)	PUNCT
ijassa-1064	80	26	exp	exp	NOUN
ijassa-1064	80	27	(	(	PUNCT
ijassa-1064	80	28	∫	∫	PROPN
ijassa-1064	80	29	t	t	PROPN
ijassa-1064	80	30	0	0	NUM
ijassa-1064	80	31	(	(	PUNCT
ijassa-1064	80	32	β1xi(φ	β1xi(φ	PROPN
ijassa-1064	80	33	)	)	PUNCT
ijassa-1064	81	1	+	+	CCONJ
ijassa-1064	81	2	p1ys(φ))dφ+	p1ys(φ))dφ+	NUM
ijassa-1064	81	3	µ1	µ1	PROPN
ijassa-1064	81	4	t	t	PROPN
ijassa-1064	81	5	)	)	PUNCT
ijassa-1064	81	6	]	]	PUNCT
ijassa-1064	81	7	≥	≥	NOUN
ijassa-1064	81	8	0	0	NUM
ijassa-1064	81	9	.	.	PUNCT
ijassa-1064	82	1	(	(	PUNCT
ijassa-1064	82	2	2.5	2.5	NUM
ijassa-1064	82	3	)	)	PUNCT
ijassa-1064	82	4	further	further	ADJ
ijassa-1064	82	5	integration	integration	NOUN
ijassa-1064	82	6	of	of	ADP
ijassa-1064	82	7	(	(	PUNCT
ijassa-1064	82	8	2.5	2.5	NUM
ijassa-1064	82	9	)	)	PUNCT
ijassa-1064	82	10	gives	give	VERB
ijassa-1064	82	11	xs(t	xs(t	NUM
ijassa-1064	82	12	)	)	PUNCT
ijassa-1064	82	13	≥	≥	NOUN
ijassa-1064	82	14	xs(0	xs(0	PROPN
ijassa-1064	82	15	)	)	PUNCT
ijassa-1064	82	16	exp	exp	NOUN
ijassa-1064	82	17	[	[	PUNCT
ijassa-1064	82	18	−	−	PROPN
ijassa-1064	82	19	(	(	PUNCT
ijassa-1064	82	20	∫	∫	PROPN
ijassa-1064	82	21	t	t	PROPN
ijassa-1064	82	22	0	0	NUM
ijassa-1064	82	23	(	(	PUNCT
ijassa-1064	82	24	β1xi(φ	β1xi(φ	PROPN
ijassa-1064	82	25	)	)	PUNCT
ijassa-1064	83	1	+	+	CCONJ
ijassa-1064	83	2	p1ys(φ))dφ+	p1ys(φ))dφ+	NUM
ijassa-1064	83	3	µ1	µ1	PROPN
ijassa-1064	83	4	t	t	PROPN
ijassa-1064	83	5	)	)	PUNCT
ijassa-1064	83	6	]	]	PUNCT
ijassa-1064	84	1	>	>	X
ijassa-1064	84	2	0	0	NUM
ijassa-1064	84	3	,	,	PUNCT
ijassa-1064	84	4	∀t	∀t	PROPN
ijassa-1064	84	5	>	>	X
ijassa-1064	84	6	0	0	NUM
ijassa-1064	84	7	.	.	PUNCT
ijassa-1064	85	1	(	(	PUNCT
ijassa-1064	85	2	2.6	2.6	NUM
ijassa-1064	85	3	)	)	PUNCT
ijassa-1064	85	4	all	all	DET
ijassa-1064	85	5	other	other	ADJ
ijassa-1064	85	6	variables	variable	NOUN
ijassa-1064	85	7	can	can	AUX
ijassa-1064	85	8	be	be	AUX
ijassa-1064	85	9	proved	prove	VERB
ijassa-1064	85	10	to	to	PART
ijassa-1064	85	11	be	be	AUX
ijassa-1064	85	12	positive	positive	ADJ
ijassa-1064	85	13	in	in	ADP
ijassa-1064	85	14	a	a	DET
ijassa-1064	85	15	similar	similar	ADJ
ijassa-1064	85	16	approach	approach	NOUN
ijassa-1064	85	17	.	.	PUNCT
ijassa-1064	86	1	copyright	copyright	NOUN
ijassa-1064	86	2	©	©	PROPN
ijassa-1064	86	3	2021	2021	NUM
ijassa-1064	86	4	assa	assa	NOUN
ijassa-1064	86	5	.	.	PUNCT
ijassa-1064	87	1	adv	adv	PROPN
ijassa-1064	87	2	syst	syst	PROPN
ijassa-1064	87	3	sci	sci	PROPN
ijassa-1064	87	4	appl	appl	PROPN
ijassa-1064	87	5	(	(	PUNCT
ijassa-1064	87	6	2021	2021	NUM
ijassa-1064	87	7	)	)	PUNCT
ijassa-1064	87	8	stability	stability	NOUN
ijassa-1064	87	9	analysis	analysis	NOUN
ijassa-1064	87	10	and	and	CCONJ
ijassa-1064	87	11	optimal	optimal	ADJ
ijassa-1064	87	12	measure	measure	NOUN
ijassa-1064	87	13	87	87	NUM
ijassa-1064	87	14	hence	hence	ADV
ijassa-1064	87	15	,	,	PUNCT
ijassa-1064	87	16	it	it	PRON
ijassa-1064	87	17	is	be	AUX
ijassa-1064	87	18	sufficient	sufficient	ADJ
ijassa-1064	87	19	to	to	PART
ijassa-1064	87	20	consider	consider	VERB
ijassa-1064	87	21	the	the	DET
ijassa-1064	87	22	dynamics	dynamic	NOUN
ijassa-1064	87	23	of	of	ADP
ijassa-1064	87	24	the	the	DET
ijassa-1064	87	25	flow	flow	NOUN
ijassa-1064	87	26	generated	generate	VERB
ijassa-1064	87	27	by	by	ADP
ijassa-1064	87	28	the	the	DET
ijassa-1064	87	29	system	system	NOUN
ijassa-1064	87	30	(	(	PUNCT
ijassa-1064	87	31	2.1	2.1	NUM
ijassa-1064	87	32	)	)	PUNCT
ijassa-1064	87	33	in	in	ADP
ijassa-1064	87	34	a	a	DET
ijassa-1064	87	35	feasible	feasible	ADJ
ijassa-1064	87	36	region	region	NOUN
ijassa-1064	87	37	defined	define	VERB
ijassa-1064	87	38	by	by	ADP
ijassa-1064	87	39	ω	ω	PROPN
ijassa-1064	87	40	=	=	SYM
ijassa-1064	87	41	{	{	PUNCT
ijassa-1064	87	42	(	(	PUNCT
ijassa-1064	87	43	xs	xs	PROPN
ijassa-1064	87	44	,	,	PUNCT
ijassa-1064	87	45	xi	xi	PROPN
ijassa-1064	87	46	,	,	PUNCT
ijassa-1064	87	47	xr	xr	PROPN
ijassa-1064	87	48	,	,	PUNCT
ijassa-1064	87	49	ys	ys	NOUN
ijassa-1064	87	50	,	,	PUNCT
ijassa-1064	87	51	yi	yi	PROPN
ijassa-1064	87	52	)	)	PUNCT
ijassa-1064	87	53	∈	∈	PROPN
ijassa-1064	87	54	r5	r5	PROPN
ijassa-1064	87	55	+	+	CCONJ
ijassa-1064	87	56	:	:	PUNCT
ijassa-1064	87	57	t	t	X
ijassa-1064	87	58	<	<	X
ijassa-1064	87	59	rk	rk	PROPN
ijassa-1064	87	60	µ	µ	PROPN
ijassa-1064	87	61	+	+	CCONJ
ijassa-1064	87	62	ε	ε	PROPN
ijassa-1064	87	63	}	}	PUNCT
ijassa-1064	87	64	.	.	PUNCT
ijassa-1064	88	1	in	in	ADP
ijassa-1064	88	2	the	the	DET
ijassa-1064	88	3	region	region	NOUN
ijassa-1064	88	4	ω	ω	PROPN
ijassa-1064	88	5	,	,	PUNCT
ijassa-1064	88	6	the	the	DET
ijassa-1064	88	7	prey	prey	NOUN
ijassa-1064	88	8	-	-	PUNCT
ijassa-1064	88	9	predator	predator	NOUN
ijassa-1064	88	10	model	model	NOUN
ijassa-1064	88	11	(	(	PUNCT
ijassa-1064	88	12	2.1	2.1	NUM
ijassa-1064	88	13	)	)	PUNCT
ijassa-1064	88	14	can	can	AUX
ijassa-1064	88	15	be	be	AUX
ijassa-1064	88	16	said	say	VERB
ijassa-1064	88	17	to	to	PART
ijassa-1064	88	18	be	be	AUX
ijassa-1064	88	19	eco	eco	NOUN
ijassa-1064	88	20	-	-	PUNCT
ijassa-1064	88	21	epidemiologically	epidemiologically	NOUN
ijassa-1064	88	22	wellposed	wellpose	VERB
ijassa-1064	88	23	.	.	PUNCT
ijassa-1064	89	1	3	3	X
ijassa-1064	89	2	.	.	X
ijassa-1064	89	3	analysis	analysis	NOUN
ijassa-1064	89	4	of	of	ADP
ijassa-1064	89	5	the	the	DET
ijassa-1064	89	6	model	model	NOUN
ijassa-1064	89	7	in	in	ADP
ijassa-1064	89	8	this	this	DET
ijassa-1064	89	9	section	section	NOUN
ijassa-1064	89	10	,	,	PUNCT
ijassa-1064	89	11	the	the	DET
ijassa-1064	89	12	prey	prey	NOUN
ijassa-1064	89	13	-	-	PUNCT
ijassa-1064	89	14	predator	predator	NOUN
ijassa-1064	89	15	model	model	NOUN
ijassa-1064	89	16	is	be	AUX
ijassa-1064	89	17	analysed	analyse	VERB
ijassa-1064	89	18	around	around	ADP
ijassa-1064	89	19	the	the	DET
ijassa-1064	89	20	possible	possible	ADJ
ijassa-1064	89	21	equilibrium	equilibrium	NOUN
ijassa-1064	89	22	points	point	NOUN
ijassa-1064	89	23	.	.	PUNCT
ijassa-1064	90	1	3.1	3.1	NUM
ijassa-1064	90	2	.	.	PUNCT
ijassa-1064	90	3	existence	existence	NOUN
ijassa-1064	90	4	of	of	ADP
ijassa-1064	90	5	equilibrium	equilibrium	NOUN
ijassa-1064	90	6	points	point	NOUN
ijassa-1064	90	7	the	the	DET
ijassa-1064	90	8	prey	prey	NOUN
ijassa-1064	90	9	-	-	PUNCT
ijassa-1064	90	10	predator	predator	NOUN
ijassa-1064	90	11	model	model	NOUN
ijassa-1064	90	12	(	(	PUNCT
ijassa-1064	90	13	2.1	2.1	NUM
ijassa-1064	90	14	)	)	PUNCT
ijassa-1064	90	15	has	have	VERB
ijassa-1064	90	16	the	the	DET
ijassa-1064	90	17	following	follow	VERB
ijassa-1064	90	18	possible	possible	ADJ
ijassa-1064	90	19	equilibrium	equilibrium	NOUN
ijassa-1064	90	20	points	point	NOUN
ijassa-1064	90	21	:	:	PUNCT
ijassa-1064	91	1	3.1.1	3.1.1	X
ijassa-1064	91	2	.	.	PUNCT
ijassa-1064	91	3	trivial	trivial	ADJ
ijassa-1064	91	4	equilibrium	equilibrium	NOUN
ijassa-1064	91	5	point	point	NOUN
ijassa-1064	91	6	(	(	PUNCT
ijassa-1064	91	7	e0	e0	PROPN
ijassa-1064	91	8	)	)	PUNCT
ijassa-1064	91	9	this	this	PRON
ijassa-1064	91	10	is	be	AUX
ijassa-1064	91	11	a	a	DET
ijassa-1064	91	12	steady	steady	ADJ
ijassa-1064	91	13	state	state	NOUN
ijassa-1064	91	14	in	in	ADP
ijassa-1064	91	15	the	the	DET
ijassa-1064	91	16	absence	absence	NOUN
ijassa-1064	91	17	of	of	ADP
ijassa-1064	91	18	prey	prey	NOUN
ijassa-1064	91	19	and	and	CCONJ
ijassa-1064	91	20	predator	predator	NOUN
ijassa-1064	91	21	populations	population	NOUN
ijassa-1064	91	22	.	.	PUNCT
ijassa-1064	92	1	hence	hence	ADV
ijassa-1064	92	2	,	,	PUNCT
ijassa-1064	92	3	no	no	DET
ijassa-1064	92	4	interactions	interaction	NOUN
ijassa-1064	92	5	exist	exist	VERB
ijassa-1064	92	6	.	.	PUNCT
ijassa-1064	93	1	the	the	DET
ijassa-1064	93	2	equilibrium	equilibrium	NOUN
ijassa-1064	93	3	point	point	NOUN
ijassa-1064	93	4	is	be	AUX
ijassa-1064	93	5	given	give	VERB
ijassa-1064	93	6	by	by	ADP
ijassa-1064	93	7	e0	e0	PROPN
ijassa-1064	93	8	=	=	PUNCT
ijassa-1064	93	9	(	(	PUNCT
ijassa-1064	93	10	0	0	NUM
ijassa-1064	93	11	,	,	PUNCT
ijassa-1064	93	12	0	0	NUM
ijassa-1064	93	13	,	,	PUNCT
ijassa-1064	93	14	0	0	NUM
ijassa-1064	93	15	,	,	PUNCT
ijassa-1064	93	16	0	0	NUM
ijassa-1064	93	17	,	,	PUNCT
ijassa-1064	93	18	0	0	NUM
ijassa-1064	93	19	)	)	PUNCT
ijassa-1064	93	20	.	.	PUNCT
ijassa-1064	94	1	(	(	PUNCT
ijassa-1064	94	2	3.7	3.7	NUM
ijassa-1064	94	3	)	)	PUNCT
ijassa-1064	94	4	3.1.2	3.1.2	NUM
ijassa-1064	94	5	.	.	PUNCT
ijassa-1064	94	6	axial	axial	ADJ
ijassa-1064	94	7	equilibrium	equilibrium	NOUN
ijassa-1064	94	8	point	point	NOUN
ijassa-1064	94	9	(	(	PUNCT
ijassa-1064	94	10	e1	e1	NOUN
ijassa-1064	94	11	)	)	PUNCT
ijassa-1064	94	12	this	this	PRON
ijassa-1064	94	13	is	be	AUX
ijassa-1064	94	14	a	a	DET
ijassa-1064	94	15	steady	steady	ADJ
ijassa-1064	94	16	state	state	NOUN
ijassa-1064	94	17	where	where	SCONJ
ijassa-1064	94	18	only	only	ADV
ijassa-1064	94	19	the	the	DET
ijassa-1064	94	20	susceptible	susceptible	ADJ
ijassa-1064	94	21	prey	prey	NOUN
ijassa-1064	94	22	is	be	AUX
ijassa-1064	94	23	present	present	ADJ
ijassa-1064	94	24	.	.	PUNCT
ijassa-1064	95	1	in	in	ADP
ijassa-1064	95	2	other	other	ADJ
ijassa-1064	95	3	words	word	NOUN
ijassa-1064	95	4	,	,	PUNCT
ijassa-1064	95	5	it	it	PRON
ijassa-1064	95	6	is	be	AUX
ijassa-1064	95	7	the	the	DET
ijassa-1064	95	8	disease	disease	NOUN
ijassa-1064	95	9	-	-	PUNCT
ijassa-1064	95	10	free	free	ADJ
ijassa-1064	95	11	cum	cum	NOUN
ijassa-1064	95	12	predator	predator	NOUN
ijassa-1064	95	13	-	-	PUNCT
ijassa-1064	95	14	free	free	ADJ
ijassa-1064	95	15	equilibrium	equilibrium	NOUN
ijassa-1064	95	16	point	point	NOUN
ijassa-1064	95	17	.	.	PUNCT
ijassa-1064	96	1	it	it	PRON
ijassa-1064	96	2	exists	exist	VERB
ijassa-1064	96	3	provided	provide	VERB
ijassa-1064	96	4	that	that	SCONJ
ijassa-1064	96	5	the	the	DET
ijassa-1064	96	6	intrinsic	intrinsic	ADJ
ijassa-1064	96	7	growth	growth	NOUN
ijassa-1064	96	8	rate	rate	NOUN
ijassa-1064	96	9	r	r	NOUN
ijassa-1064	96	10	exceeds	exceed	VERB
ijassa-1064	96	11	the	the	DET
ijassa-1064	96	12	natural	natural	ADJ
ijassa-1064	96	13	mortality	mortality	NOUN
ijassa-1064	96	14	rate	rate	NOUN
ijassa-1064	96	15	µ1	µ1	PROPN
ijassa-1064	96	16	.	.	PUNCT
ijassa-1064	97	1	the	the	DET
ijassa-1064	97	2	equilibrium	equilibrium	NOUN
ijassa-1064	97	3	point	point	NOUN
ijassa-1064	97	4	is	be	AUX
ijassa-1064	97	5	given	give	VERB
ijassa-1064	97	6	by	by	ADP
ijassa-1064	97	7	e1	e1	NOUN
ijassa-1064	97	8	=	=	SYM
ijassa-1064	97	9	(	(	PUNCT
ijassa-1064	97	10	k	k	X
ijassa-1064	97	11	[	[	PUNCT
ijassa-1064	97	12	1−	1−	NUM
ijassa-1064	97	13	µ1	µ1	NOUN
ijassa-1064	97	14	r	r	NOUN
ijassa-1064	97	15	]	]	PUNCT
ijassa-1064	97	16	,	,	PUNCT
ijassa-1064	97	17	0	0	NUM
ijassa-1064	97	18	,	,	PUNCT
ijassa-1064	97	19	0	0	NUM
ijassa-1064	97	20	,	,	PUNCT
ijassa-1064	97	21	0	0	NUM
ijassa-1064	97	22	,	,	PUNCT
ijassa-1064	97	23	0	0	NUM
ijassa-1064	97	24	)	)	PUNCT
ijassa-1064	97	25	.	.	PUNCT
ijassa-1064	98	1	(	(	PUNCT
ijassa-1064	98	2	3.8	3.8	NUM
ijassa-1064	98	3	)	)	PUNCT
ijassa-1064	98	4	3.1.3	3.1.3	NUM
ijassa-1064	98	5	.	.	PUNCT
ijassa-1064	98	6	disease	disease	NOUN
ijassa-1064	98	7	-	-	PUNCT
ijassa-1064	98	8	free	free	ADJ
ijassa-1064	98	9	equilibrium	equilibrium	NOUN
ijassa-1064	98	10	point	point	NOUN
ijassa-1064	98	11	(	(	PUNCT
ijassa-1064	98	12	e2	e2	PROPN
ijassa-1064	98	13	)	)	PUNCT
ijassa-1064	98	14	this	this	PRON
ijassa-1064	98	15	is	be	AUX
ijassa-1064	98	16	a	a	DET
ijassa-1064	98	17	steady	steady	ADJ
ijassa-1064	98	18	state	state	NOUN
ijassa-1064	98	19	where	where	SCONJ
ijassa-1064	98	20	there	there	PRON
ijassa-1064	98	21	is	be	VERB
ijassa-1064	98	22	no	no	DET
ijassa-1064	98	23	disease	disease	NOUN
ijassa-1064	98	24	in	in	ADP
ijassa-1064	98	25	both	both	PRON
ijassa-1064	98	26	prey	prey	NOUN
ijassa-1064	98	27	and	and	CCONJ
ijassa-1064	98	28	predator	predator	NOUN
ijassa-1064	98	29	populations	population	NOUN
ijassa-1064	98	30	.	.	PUNCT
ijassa-1064	99	1	it	it	PRON
ijassa-1064	99	2	exists	exist	VERB
ijassa-1064	99	3	provided	provide	VERB
ijassa-1064	99	4	the	the	DET
ijassa-1064	99	5	inequality	inequality	NOUN
ijassa-1064	99	6	r	r	NOUN
ijassa-1064	99	7	(	(	PUNCT
ijassa-1064	99	8	1−	1−	NUM
ijassa-1064	99	9	µ2	µ2	PROPN
ijassa-1064	99	10	kc1p1	kc1p1	PROPN
ijassa-1064	99	11	)	)	PUNCT
ijassa-1064	99	12	>	>	PUNCT
ijassa-1064	99	13	µ1	µ1	PROPN
ijassa-1064	99	14	holds	hold	VERB
ijassa-1064	99	15	.	.	PUNCT
ijassa-1064	100	1	hence	hence	ADV
ijassa-1064	100	2	,	,	PUNCT
ijassa-1064	100	3	it	it	PRON
ijassa-1064	100	4	is	be	AUX
ijassa-1064	100	5	obtained	obtain	VERB
ijassa-1064	100	6	as	as	ADP
ijassa-1064	100	7	e2	e2	PROPN
ijassa-1064	100	8	=	=	PUNCT
ijassa-1064	100	9	(	(	PUNCT
ijassa-1064	100	10	µ2	µ2	PROPN
ijassa-1064	100	11	c1p1	c1p1	PROPN
ijassa-1064	100	12	,	,	PUNCT
ijassa-1064	100	13	0	0	NUM
ijassa-1064	100	14	,	,	PUNCT
ijassa-1064	100	15	0	0	NUM
ijassa-1064	100	16	,	,	PUNCT
ijassa-1064	100	17	1	1	NUM
ijassa-1064	100	18	p1	p1	NOUN
ijassa-1064	100	19	[	[	PUNCT
ijassa-1064	100	20	r	r	NOUN
ijassa-1064	100	21	(	(	PUNCT
ijassa-1064	100	22	1−	1−	NUM
ijassa-1064	100	23	µ2	µ2	PROPN
ijassa-1064	100	24	kc1p1	kc1p1	PROPN
ijassa-1064	100	25	)	)	PUNCT
ijassa-1064	101	1	−	−	PROPN
ijassa-1064	102	1	µ1	µ1	PROPN
ijassa-1064	102	2	]	]	PUNCT
ijassa-1064	102	3	,	,	PUNCT
ijassa-1064	102	4	0	0	NUM
ijassa-1064	102	5	)	)	PUNCT
ijassa-1064	102	6	.	.	PUNCT
ijassa-1064	103	1	(	(	PUNCT
ijassa-1064	103	2	3.9	3.9	NUM
ijassa-1064	103	3	)	)	PUNCT
ijassa-1064	103	4	3.1.4	3.1.4	NUM
ijassa-1064	103	5	.	.	PUNCT
ijassa-1064	104	1	predator	predator	NOUN
ijassa-1064	104	2	-	-	PUNCT
ijassa-1064	104	3	free	free	ADJ
ijassa-1064	104	4	equilibrium	equilibrium	NOUN
ijassa-1064	104	5	point	point	NOUN
ijassa-1064	104	6	(	(	PUNCT
ijassa-1064	104	7	e3	e3	NOUN
ijassa-1064	104	8	)	)	PUNCT
ijassa-1064	104	9	this	this	PRON
ijassa-1064	104	10	is	be	AUX
ijassa-1064	104	11	a	a	DET
ijassa-1064	104	12	steady	steady	ADJ
ijassa-1064	104	13	state	state	NOUN
ijassa-1064	104	14	where	where	SCONJ
ijassa-1064	104	15	there	there	PRON
ijassa-1064	104	16	is	be	VERB
ijassa-1064	104	17	no	no	DET
ijassa-1064	104	18	predator	predator	NOUN
ijassa-1064	104	19	in	in	ADP
ijassa-1064	104	20	the	the	DET
ijassa-1064	104	21	system	system	NOUN
ijassa-1064	104	22	.	.	PUNCT
ijassa-1064	105	1	it	it	PRON
ijassa-1064	105	2	exists	exist	VERB
ijassa-1064	105	3	provided	provide	VERB
ijassa-1064	105	4	the	the	DET
ijassa-1064	105	5	inequality	inequality	NOUN
ijassa-1064	105	6	r	r	NOUN
ijassa-1064	105	7	(	(	PUNCT
ijassa-1064	105	8	1−	1−	NUM
ijassa-1064	105	9	(	(	PUNCT
ijassa-1064	105	10	µ1+γ	µ1+γ	PROPN
ijassa-1064	105	11	kβ1	kβ1	NOUN
ijassa-1064	105	12	)	)	PUNCT
ijassa-1064	105	13	)	)	PUNCT
ijassa-1064	105	14	>	>	PUNCT
ijassa-1064	106	1	µ1	µ1	PROPN
ijassa-1064	106	2	holds	hold	VERB
ijassa-1064	106	3	.	.	PUNCT
ijassa-1064	107	1	the	the	DET
ijassa-1064	107	2	equilibrium	equilibrium	NOUN
ijassa-1064	107	3	is	be	AUX
ijassa-1064	107	4	given	give	VERB
ijassa-1064	107	5	as	as	ADP
ijassa-1064	107	6	e3	e3	NOUN
ijassa-1064	107	7	=	=	SYM
ijassa-1064	107	8	(	(	PUNCT
ijassa-1064	107	9	µ1	µ1	PROPN
ijassa-1064	107	10	+	+	CCONJ
ijassa-1064	107	11	γ	γ	X
ijassa-1064	107	12	β1	β1	PROPN
ijassa-1064	107	13	,	,	PUNCT
ijassa-1064	107	14	1	1	NUM
ijassa-1064	107	15	β1	β1	PROPN
ijassa-1064	107	16	[	[	PUNCT
ijassa-1064	107	17	r	r	NOUN
ijassa-1064	107	18	(	(	PUNCT
ijassa-1064	107	19	1−	1−	NUM
ijassa-1064	107	20	(	(	PUNCT
ijassa-1064	107	21	µ1	µ1	PROPN
ijassa-1064	107	22	+	+	X
ijassa-1064	107	23	γ	γ	X
ijassa-1064	107	24	kβ1	kβ1	NOUN
ijassa-1064	107	25	)	)	PUNCT
ijassa-1064	107	26	)	)	PUNCT
ijassa-1064	107	27	−	−	PROPN
ijassa-1064	107	28	µ1	µ1	PROPN
ijassa-1064	107	29	]	]	PUNCT
ijassa-1064	107	30	,	,	PUNCT
ijassa-1064	107	31	γ	γ	X
ijassa-1064	107	32	β1µ1	β1µ1	X
ijassa-1064	107	33	[	[	PUNCT
ijassa-1064	107	34	r	r	X
ijassa-1064	107	35	(	(	PUNCT
ijassa-1064	107	36	1−	1−	NUM
ijassa-1064	107	37	(	(	PUNCT
ijassa-1064	107	38	µ1	µ1	PROPN
ijassa-1064	107	39	+	+	X
ijassa-1064	107	40	γ	γ	X
ijassa-1064	107	41	kβ1	kβ1	NOUN
ijassa-1064	107	42	)	)	PUNCT
ijassa-1064	107	43	)	)	PUNCT
ijassa-1064	108	1	−	−	PROPN
ijassa-1064	108	2	µ1	µ1	PROPN
ijassa-1064	108	3	]	]	PUNCT
ijassa-1064	108	4	,	,	PUNCT
ijassa-1064	108	5	0	0	NUM
ijassa-1064	108	6	,	,	PUNCT
ijassa-1064	108	7	0	0	NUM
ijassa-1064	108	8	)	)	PUNCT
ijassa-1064	108	9	.	.	PUNCT
ijassa-1064	109	1	(	(	PUNCT
ijassa-1064	109	2	3.10	3.10	NUM
ijassa-1064	109	3	)	)	PUNCT
ijassa-1064	109	4	3.1.5	3.1.5	PROPN
ijassa-1064	109	5	.	.	PUNCT
ijassa-1064	110	1	infected	infect	VERB
ijassa-1064	110	2	prey	prey	NOUN
ijassa-1064	110	3	-	-	PUNCT
ijassa-1064	110	4	free	free	ADJ
ijassa-1064	110	5	equilibrium	equilibrium	NOUN
ijassa-1064	110	6	(	(	PUNCT
ijassa-1064	110	7	e4	e4	PROPN
ijassa-1064	110	8	)	)	PUNCT
ijassa-1064	110	9	this	this	PRON
ijassa-1064	110	10	is	be	AUX
ijassa-1064	110	11	a	a	DET
ijassa-1064	110	12	steady	steady	ADJ
ijassa-1064	110	13	state	state	NOUN
ijassa-1064	110	14	where	where	SCONJ
ijassa-1064	110	15	the	the	DET
ijassa-1064	110	16	infected	infected	ADJ
ijassa-1064	110	17	prey	prey	NOUN
ijassa-1064	110	18	does	do	AUX
ijassa-1064	110	19	not	not	PART
ijassa-1064	110	20	exist	exist	VERB
ijassa-1064	110	21	.	.	PUNCT
ijassa-1064	111	1	the	the	DET
ijassa-1064	111	2	equilibrium	equilibrium	NOUN
ijassa-1064	111	3	will	will	AUX
ijassa-1064	111	4	exist	exist	VERB
ijassa-1064	111	5	if	if	SCONJ
ijassa-1064	111	6	k	k	PROPN
ijassa-1064	111	7	>	>	X
ijassa-1064	112	1	k	k	PROPN
ijassa-1064	113	1	r	r	NOUN
ijassa-1064	113	2	(	(	PUNCT
ijassa-1064	113	3	p1µ2	p1µ2	PUNCT
ijassa-1064	113	4	β2	β2	VERB
ijassa-1064	113	5	+	+	CCONJ
ijassa-1064	113	6	µ1	µ1	PROPN
ijassa-1064	113	7	)	)	PUNCT
ijassa-1064	113	8	and	and	CCONJ
ijassa-1064	113	9	c1p1	c1p1	ADV
ijassa-1064	113	10	β2	β2	VERB
ijassa-1064	113	11	[	[	PUNCT
ijassa-1064	113	12	k	k	PROPN
ijassa-1064	113	13	−	−	PROPN
ijassa-1064	113	14	k	k	NOUN
ijassa-1064	113	15	r	r	NOUN
ijassa-1064	113	16	(	(	PUNCT
ijassa-1064	113	17	p1µ2	p1µ2	PUNCT
ijassa-1064	113	18	β2	β2	VERB
ijassa-1064	113	19	+	+	CCONJ
ijassa-1064	113	20	µ1	µ1	PROPN
ijassa-1064	113	21	)	)	PUNCT
ijassa-1064	113	22	]	]	PUNCT
ijassa-1064	113	23	>	>	X
ijassa-1064	113	24	µ2	µ2	PROPN
ijassa-1064	113	25	.	.	PUNCT
ijassa-1064	114	1	thus	thus	ADV
ijassa-1064	114	2	,	,	PUNCT
ijassa-1064	114	3	it	it	PRON
ijassa-1064	114	4	is	be	AUX
ijassa-1064	114	5	given	give	VERB
ijassa-1064	114	6	by	by	ADP
ijassa-1064	114	7	e4	e4	PROPN
ijassa-1064	114	8	=	=	SYM
ijassa-1064	114	9	(	(	PUNCT
ijassa-1064	114	10	k	k	NOUN
ijassa-1064	114	11	−	−	PROPN
ijassa-1064	115	1	k	k	NOUN
ijassa-1064	115	2	r	r	NOUN
ijassa-1064	115	3	(	(	PUNCT
ijassa-1064	115	4	p1µ2	p1µ2	PUNCT
ijassa-1064	115	5	β2	β2	VERB
ijassa-1064	115	6	+	+	CCONJ
ijassa-1064	115	7	µ1	µ1	PROPN
ijassa-1064	115	8	)	)	PUNCT
ijassa-1064	115	9	,	,	PUNCT
ijassa-1064	115	10	0	0	NUM
ijassa-1064	115	11	,	,	PUNCT
ijassa-1064	115	12	0	0	NUM
ijassa-1064	115	13	,	,	PUNCT
ijassa-1064	115	14	µ2	µ2	PROPN
ijassa-1064	115	15	β2	β2	PROPN
ijassa-1064	115	16	,	,	PUNCT
ijassa-1064	115	17	c1p1	c1p1	X
ijassa-1064	115	18	β2	β2	NOUN
ijassa-1064	115	19	[	[	PUNCT
ijassa-1064	115	20	k	k	PROPN
ijassa-1064	115	21	−	−	PROPN
ijassa-1064	115	22	k	k	NOUN
ijassa-1064	115	23	r	r	NOUN
ijassa-1064	115	24	(	(	PUNCT
ijassa-1064	115	25	p1µ2	p1µ2	PUNCT
ijassa-1064	115	26	β2	β2	VERB
ijassa-1064	115	27	+	+	CCONJ
ijassa-1064	115	28	µ1	µ1	PROPN
ijassa-1064	115	29	)	)	PUNCT
ijassa-1064	115	30	]	]	PUNCT
ijassa-1064	116	1	−	−	PROPN
ijassa-1064	116	2	µ2	µ2	PROPN
ijassa-1064	116	3	)	)	PUNCT
ijassa-1064	116	4	.	.	PUNCT
ijassa-1064	117	1	(	(	PUNCT
ijassa-1064	117	2	3.11	3.11	NUM
ijassa-1064	117	3	)	)	PUNCT
ijassa-1064	117	4	copyright	copyright	NOUN
ijassa-1064	117	5	©	©	PROPN
ijassa-1064	117	6	2021	2021	NUM
ijassa-1064	117	7	assa	assa	NOUN
ijassa-1064	117	8	.	.	PUNCT
ijassa-1064	118	1	adv	adv	PROPN
ijassa-1064	118	2	syst	syst	PROPN
ijassa-1064	118	3	sci	sci	PROPN
ijassa-1064	118	4	appl	appl	PROPN
ijassa-1064	118	5	(	(	PUNCT
ijassa-1064	118	6	2021	2021	NUM
ijassa-1064	118	7	)	)	PUNCT
ijassa-1064	118	8	88	88	NUM
ijassa-1064	118	9	j.a	j.a	PROPN
ijassa-1064	118	10	.	.	PROPN
ijassa-1064	118	11	ademosu	ademosu	PROPN
ijassa-1064	118	12	,	,	PUNCT
ijassa-1064	118	13	s.	s.	PROPN
ijassa-1064	118	14	olaniyi	olaniyi	PROPN
ijassa-1064	118	15	,	,	PUNCT
ijassa-1064	118	16	s.o	s.o	PROPN
ijassa-1064	118	17	.	.	PROPN
ijassa-1064	118	18	adewale	adewale	PROPN
ijassa-1064	118	19	3.1.6	3.1.6	PROPN
ijassa-1064	118	20	.	.	PUNCT
ijassa-1064	118	21	infected	infect	VERB
ijassa-1064	118	22	predator	predator	NOUN
ijassa-1064	118	23	-	-	PUNCT
ijassa-1064	118	24	free	free	ADJ
ijassa-1064	118	25	equilibrium	equilibrium	NOUN
ijassa-1064	118	26	(	(	PUNCT
ijassa-1064	118	27	e5	e5	PROPN
ijassa-1064	118	28	)	)	PUNCT
ijassa-1064	118	29	this	this	PRON
ijassa-1064	118	30	is	be	AUX
ijassa-1064	118	31	a	a	DET
ijassa-1064	118	32	steady	steady	ADJ
ijassa-1064	118	33	state	state	NOUN
ijassa-1064	118	34	where	where	SCONJ
ijassa-1064	118	35	the	the	DET
ijassa-1064	118	36	infected	infected	ADJ
ijassa-1064	118	37	predator	predator	NOUN
ijassa-1064	118	38	is	be	AUX
ijassa-1064	118	39	absent	absent	ADJ
ijassa-1064	118	40	in	in	ADP
ijassa-1064	118	41	the	the	DET
ijassa-1064	118	42	ecosystem	ecosystem	NOUN
ijassa-1064	118	43	.	.	PUNCT
ijassa-1064	119	1	the	the	DET
ijassa-1064	119	2	equilibrium	equilibrium	NOUN
ijassa-1064	119	3	is	be	AUX
ijassa-1064	119	4	given	give	VERB
ijassa-1064	119	5	by	by	ADP
ijassa-1064	119	6	e5	e5	PROPN
ijassa-1064	119	7	=	=	PUNCT
ijassa-1064	119	8	(	(	PUNCT
ijassa-1064	119	9	x∗	x∗	PROPN
ijassa-1064	119	10	s	s	PART
ijassa-1064	119	11	,	,	PUNCT
ijassa-1064	119	12	x	x	PROPN
ijassa-1064	119	13	∗	∗	NOUN
ijassa-1064	119	14	i	i	PRON
ijassa-1064	119	15	,	,	PUNCT
ijassa-1064	119	16	x	x	X
ijassa-1064	119	17	∗	∗	NOUN
ijassa-1064	119	18	r	r	NOUN
ijassa-1064	119	19	,	,	PUNCT
ijassa-1064	119	20	y	y	PROPN
ijassa-1064	119	21	∗	∗	NOUN
ijassa-1064	119	22	s	s	NOUN
ijassa-1064	119	23	,	,	PUNCT
ijassa-1064	119	24	0	0	NUM
ijassa-1064	119	25	)	)	PUNCT
ijassa-1064	119	26	,	,	PUNCT
ijassa-1064	119	27	(	(	PUNCT
ijassa-1064	119	28	3.12	3.12	NUM
ijassa-1064	119	29	)	)	PUNCT
ijassa-1064	119	30	such	such	ADJ
ijassa-1064	119	31	that	that	SCONJ
ijassa-1064	119	32	x∗	x∗	PROPN
ijassa-1064	119	33	s	s	PART
ijassa-1064	119	34	>	>	X
ijassa-1064	119	35	0	0	PROPN
ijassa-1064	119	36	,	,	PUNCT
ijassa-1064	119	37	x∗	x∗	PROPN
ijassa-1064	119	38	i	i	PRON
ijassa-1064	119	39	>	>	X
ijassa-1064	119	40	0	0	PROPN
ijassa-1064	119	41	,	,	PUNCT
ijassa-1064	119	42	x∗	x∗	PROPN
ijassa-1064	119	43	r	r	NOUN
ijassa-1064	119	44	>	>	X
ijassa-1064	119	45	0	0	PROPN
ijassa-1064	119	46	,	,	PUNCT
ijassa-1064	119	47	y	y	PROPN
ijassa-1064	119	48	∗	∗	NOUN
ijassa-1064	119	49	s	s	PROPN
ijassa-1064	119	50	>	>	X
ijassa-1064	119	51	0	0	NUM
ijassa-1064	119	52	,	,	PUNCT
ijassa-1064	119	53	and	and	CCONJ
ijassa-1064	119	54	where	where	SCONJ
ijassa-1064	119	55	x∗	x∗	PROPN
ijassa-1064	119	56	s	s	PART
ijassa-1064	119	57	=	=	X
ijassa-1064	119	58	c2[p2(r	c2[p2(r	X
ijassa-1064	119	59	−	−	PROPN
ijassa-1064	119	60	µ1)−	µ1)−	PROPN
ijassa-1064	119	61	p1(µ1	p1(µ1	NOUN
ijassa-1064	119	62	+	+	CCONJ
ijassa-1064	119	63	γ)]−	γ)]−	X
ijassa-1064	119	64	β1µ2	β1µ2	ADP
ijassa-1064	119	65	c2p2	c2p2	PROPN
ijassa-1064	119	66	(	(	PUNCT
ijassa-1064	119	67	1	1	NUM
ijassa-1064	119	68	k	k	NOUN
ijassa-1064	119	69	+	+	NUM
ijassa-1064	119	70	p1β1	p1β1	X
ijassa-1064	119	71	p2	p2	PROPN
ijassa-1064	119	72	)	)	PUNCT
ijassa-1064	120	1	−	−	PROPN
ijassa-1064	120	2	c1p1β1	c1p1β1	NOUN
ijassa-1064	120	3	,	,	PUNCT
ijassa-1064	120	4	x∗	x∗	PROPN
ijassa-1064	121	1	i	i	PRON
ijassa-1064	121	2	=	=	VERB
ijassa-1064	122	1	µ2	µ2	PROPN
ijassa-1064	122	2	c2p2	c2p2	VERB
ijassa-1064	122	3	−	−	PROPN
ijassa-1064	122	4	c1p1	c1p1	ADV
ijassa-1064	122	5	c2p2	c2p2	ADV
ijassa-1064	122	6	c2[p2(r	c2[p2(r	ADJ
ijassa-1064	122	7	−	−	PUNCT
ijassa-1064	122	8	µ1)−	µ1)−	ADJ
ijassa-1064	122	9	p1(µ1	p1(µ1	NOUN
ijassa-1064	122	10	+	+	CCONJ
ijassa-1064	122	11	γ)]−	γ)]−	X
ijassa-1064	122	12	β1µ2	β1µ2	ADP
ijassa-1064	122	13	c2p2	c2p2	PROPN
ijassa-1064	122	14	(	(	PUNCT
ijassa-1064	122	15	1	1	NUM
ijassa-1064	122	16	k	k	NOUN
ijassa-1064	122	17	+	+	NUM
ijassa-1064	122	18	p1β1	p1β1	X
ijassa-1064	122	19	p2	p2	PROPN
ijassa-1064	122	20	)	)	PUNCT
ijassa-1064	122	21	−	−	ADP
ijassa-1064	122	22	c1p1β1	c1p1β1	NOUN
ijassa-1064	122	23			NOUN
ijassa-1064	122	24	,	,	PUNCT
ijassa-1064	122	25	x∗	x∗	PROPN
ijassa-1064	122	26	r	r	NOUN
ijassa-1064	122	27	=	=	PUNCT
ijassa-1064	122	28	γx∗	γx∗	NOUN
ijassa-1064	122	29	i	i	PRON
ijassa-1064	122	30	µ1	µ1	VERB
ijassa-1064	122	31	,	,	PUNCT
ijassa-1064	122	32	y	y	PROPN
ijassa-1064	122	33	∗	∗	NOUN
ijassa-1064	122	34	s	s	PART
ijassa-1064	122	35	=	=	SYM
ijassa-1064	122	36	β1x	β1x	NOUN
ijassa-1064	122	37	∗	∗	NOUN
ijassa-1064	122	38	s	s	PART
ijassa-1064	122	39	−	−	PROPN
ijassa-1064	122	40	(	(	PUNCT
ijassa-1064	122	41	µ1	µ1	PROPN
ijassa-1064	122	42	+	+	CCONJ
ijassa-1064	122	43	γ	γ	NOUN
ijassa-1064	122	44	)	)	PUNCT
ijassa-1064	122	45	p2	p2	NOUN
ijassa-1064	122	46	.	.	PUNCT
ijassa-1064	123	1	3.1.7	3.1.7	X
ijassa-1064	123	2	.	.	PUNCT
ijassa-1064	124	1	interior	interior	ADJ
ijassa-1064	124	2	equilibrium	equilibrium	NOUN
ijassa-1064	124	3	point	point	NOUN
ijassa-1064	124	4	(	(	PUNCT
ijassa-1064	124	5	e6	e6	PROPN
ijassa-1064	124	6	)	)	PUNCT
ijassa-1064	124	7	this	this	PRON
ijassa-1064	124	8	is	be	AUX
ijassa-1064	124	9	a	a	DET
ijassa-1064	124	10	steady	steady	ADJ
ijassa-1064	124	11	state	state	NOUN
ijassa-1064	124	12	where	where	SCONJ
ijassa-1064	124	13	all	all	DET
ijassa-1064	124	14	the	the	DET
ijassa-1064	124	15	populations	population	NOUN
ijassa-1064	124	16	for	for	ADP
ijassa-1064	124	17	prey	prey	NOUN
ijassa-1064	124	18	and	and	CCONJ
ijassa-1064	124	19	predator	predator	NOUN
ijassa-1064	124	20	species	specie	NOUN
ijassa-1064	124	21	are	be	AUX
ijassa-1064	124	22	present	present	ADJ
ijassa-1064	124	23	in	in	ADP
ijassa-1064	124	24	the	the	DET
ijassa-1064	124	25	system	system	NOUN
ijassa-1064	124	26	.	.	PUNCT
ijassa-1064	125	1	the	the	DET
ijassa-1064	125	2	equilibrium	equilibrium	NOUN
ijassa-1064	125	3	is	be	AUX
ijassa-1064	125	4	given	give	VERB
ijassa-1064	125	5	by	by	ADP
ijassa-1064	125	6	e6	e6	PROPN
ijassa-1064	125	7	=	=	SYM
ijassa-1064	125	8	(	(	PUNCT
ijassa-1064	125	9	x∗∗	x∗∗	PROPN
ijassa-1064	125	10	s	s	X
ijassa-1064	125	11	,	,	PUNCT
ijassa-1064	125	12	x	x	PUNCT
ijassa-1064	125	13	∗∗	∗∗	NOUN
ijassa-1064	126	1	i	i	PRON
ijassa-1064	126	2	,	,	PUNCT
ijassa-1064	126	3	x	x	PUNCT
ijassa-1064	126	4	∗∗	∗∗	NOUN
ijassa-1064	126	5	r	r	NOUN
ijassa-1064	126	6	,	,	PUNCT
ijassa-1064	126	7	y	y	PROPN
ijassa-1064	126	8	∗∗	∗∗	PROPN
ijassa-1064	126	9	s	s	X
ijassa-1064	126	10	,	,	PUNCT
ijassa-1064	126	11	y	y	PROPN
ijassa-1064	126	12	∗∗	∗∗	PROPN
ijassa-1064	126	13	i	i	INTJ
ijassa-1064	126	14	)	)	PUNCT
ijassa-1064	126	15	,	,	PUNCT
ijassa-1064	126	16	(	(	PUNCT
ijassa-1064	126	17	3.13	3.13	NUM
ijassa-1064	126	18	)	)	PUNCT
ijassa-1064	126	19	such	such	ADJ
ijassa-1064	126	20	that	that	SCONJ
ijassa-1064	126	21	x∗∗	x∗∗	PROPN
ijassa-1064	126	22	s	s	PROPN
ijassa-1064	126	23	>	>	X
ijassa-1064	126	24	0	0	PROPN
ijassa-1064	126	25	,	,	PUNCT
ijassa-1064	126	26	x∗∗	x∗∗	PROPN
ijassa-1064	127	1	i	i	PROPN
ijassa-1064	127	2	>	>	X
ijassa-1064	127	3	0	0	PROPN
ijassa-1064	127	4	,	,	PUNCT
ijassa-1064	127	5	x∗∗	x∗∗	PROPN
ijassa-1064	128	1	r	r	NOUN
ijassa-1064	128	2	>	>	X
ijassa-1064	128	3	0	0	PROPN
ijassa-1064	128	4	,	,	PUNCT
ijassa-1064	128	5	y	y	PROPN
ijassa-1064	128	6	∗∗	∗∗	PROPN
ijassa-1064	128	7	s	s	X
ijassa-1064	128	8	>	>	X
ijassa-1064	128	9	0	0	PROPN
ijassa-1064	128	10	,	,	PUNCT
ijassa-1064	128	11	y	y	PROPN
ijassa-1064	128	12	∗∗	∗∗	PROPN
ijassa-1064	128	13	i	i	X
ijassa-1064	128	14	>	>	X
ijassa-1064	128	15	0	0	NUM
ijassa-1064	128	16	,	,	PUNCT
ijassa-1064	128	17	and	and	CCONJ
ijassa-1064	128	18	where	where	SCONJ
ijassa-1064	128	19	x∗∗	x∗∗	PROPN
ijassa-1064	128	20	s	s	PART
ijassa-1064	128	21	=	=	SYM
ijassa-1064	128	22	1	1	NUM
ijassa-1064	128	23	k	k	NOUN
ijassa-1064	128	24	[	[	PUNCT
ijassa-1064	128	25	(	(	PUNCT
ijassa-1064	128	26	r	r	NOUN
ijassa-1064	128	27	−	−	NOUN
ijassa-1064	128	28	µ1)−x∗∗	µ1)−x∗∗	VERB
ijassa-1064	128	29	i	i	PRON
ijassa-1064	128	30	(	(	PUNCT
ijassa-1064	128	31	β1	β1	PROPN
ijassa-1064	128	32	−	−	PROPN
ijassa-1064	128	33	c3p1c3	c3p1c3	PROPN
ijassa-1064	128	34	β2	β2	PROPN
ijassa-1064	128	35	)	)	PUNCT
ijassa-1064	128	36	]	]	PUNCT
ijassa-1064	128	37	,	,	PUNCT
ijassa-1064	128	38	x∗∗	x∗∗	PROPN
ijassa-1064	129	1	i	i	PROPN
ijassa-1064	129	2	=	=	SYM
ijassa-1064	129	3	β2[(p2	β2[(p2	PROPN
ijassa-1064	129	4	−	−	PROPN
ijassa-1064	129	5	p3)µ2	p3)µ2	NOUN
ijassa-1064	130	1	+	+	CCONJ
ijassa-1064	130	2	β2(µ1	β2(µ1	NOUN
ijassa-1064	130	3	+	+	X
ijassa-1064	131	1	γ)−	γ)−	PROPN
ijassa-1064	132	1	(	(	PUNCT
ijassa-1064	132	2	r	r	NOUN
ijassa-1064	132	3	−	−	PROPN
ijassa-1064	132	4	µ1)(β1β2	µ1)(β1β2	PROPN
ijassa-1064	132	5	−	−	PROPN
ijassa-1064	132	6	c1p1p3	c1p1p3	PROPN
ijassa-1064	132	7	)	)	PUNCT
ijassa-1064	132	8	]	]	PUNCT
ijassa-1064	133	1	β2(p2p3c3	β2(p2p3c3	PROPN
ijassa-1064	133	2	+	+	CCONJ
ijassa-1064	133	3	c2p2p3	c2p2p3	PROPN
ijassa-1064	133	4	)	)	PUNCT
ijassa-1064	133	5	+	+	CCONJ
ijassa-1064	133	6	(	(	PUNCT
ijassa-1064	133	7	β1β2	β1β2	ADP
ijassa-1064	133	8	−	−	X
ijassa-1064	133	9	c1p1p3)(β1β2	c1p1p3)(β1β2	PUNCT
ijassa-1064	133	10	−	−	PROPN
ijassa-1064	133	11	c3p1p3	c3p1p3	NUM
ijassa-1064	133	12	)	)	PUNCT
ijassa-1064	133	13	,	,	PUNCT
ijassa-1064	133	14	x∗∗	x∗∗	PROPN
ijassa-1064	133	15	r	r	NOUN
ijassa-1064	133	16	=	=	PUNCT
ijassa-1064	133	17	γx∗∗	γx∗∗	NOUN
ijassa-1064	133	18	i	i	PRON
ijassa-1064	133	19	µ1	µ1	VERB
ijassa-1064	133	20	,	,	PUNCT
ijassa-1064	133	21	y	y	PROPN
ijassa-1064	133	22	∗∗	∗∗	PROPN
ijassa-1064	133	23	s	s	X
ijassa-1064	133	24	=	=	PUNCT
ijassa-1064	133	25	µ2	µ2	PROPN
ijassa-1064	133	26	−	−	NOUN
ijassa-1064	133	27	c3p3x	c3p3x	NOUN
ijassa-1064	133	28	∗∗	∗∗	X
ijassa-1064	134	1	i	i	PRON
ijassa-1064	134	2	β2	β2	VERB
ijassa-1064	134	3	,	,	PUNCT
ijassa-1064	134	4	y	y	PROPN
ijassa-1064	135	1	∗∗	∗∗	PROPN
ijassa-1064	136	1	i	i	PRON
ijassa-1064	136	2	=	=	PUNCT
ijassa-1064	136	3	β1x	β1x	NOUN
ijassa-1064	137	1	∗∗	∗∗	PROPN
ijassa-1064	137	2	s	s	PART
ijassa-1064	137	3	−	−	PROPN
ijassa-1064	137	4	p2y	p2y	NOUN
ijassa-1064	137	5	∗∗	∗∗	PROPN
ijassa-1064	137	6	s	s	PART
ijassa-1064	137	7	−	−	PROPN
ijassa-1064	137	8	(	(	PUNCT
ijassa-1064	137	9	µ1	µ1	PROPN
ijassa-1064	137	10	+	+	CCONJ
ijassa-1064	137	11	γ	γ	X
ijassa-1064	137	12	)	)	PUNCT
ijassa-1064	137	13	p3	p3	NOUN
ijassa-1064	137	14	.	.	PUNCT
ijassa-1064	138	1	3.2	3.2	NUM
ijassa-1064	138	2	.	.	PUNCT
ijassa-1064	139	1	stability	stability	NOUN
ijassa-1064	139	2	analysis	analysis	NOUN
ijassa-1064	139	3	the	the	DET
ijassa-1064	139	4	jacobian	jacobian	ADJ
ijassa-1064	139	5	matrix	matrix	NOUN
ijassa-1064	139	6	of	of	ADP
ijassa-1064	139	7	the	the	DET
ijassa-1064	139	8	prey	prey	NOUN
ijassa-1064	139	9	-	-	PUNCT
ijassa-1064	139	10	predator	predator	NOUN
ijassa-1064	139	11	system	system	NOUN
ijassa-1064	139	12	(	(	PUNCT
ijassa-1064	139	13	2.1	2.1	NUM
ijassa-1064	139	14	)	)	PUNCT
ijassa-1064	139	15	is	be	AUX
ijassa-1064	139	16	given	give	VERB
ijassa-1064	139	17	by	by	ADP
ijassa-1064	139	18	j	j	PROPN
ijassa-1064	139	19	=	=	SYM
ijassa-1064	139	20			NOUN
ijassa-1064	139	21	j1	j1	PROPN
ijassa-1064	139	22	−β1xs	−β1xs	NUM
ijassa-1064	139	23	0	0	NUM
ijassa-1064	139	24	−p1xs	−p1x	NOUN
ijassa-1064	139	25	0	0	PUNCT
ijassa-1064	139	26	β1xi	β1xi	PUNCT
ijassa-1064	139	27	j2	j2	PROPN
ijassa-1064	139	28	0	0	NUM
ijassa-1064	139	29	−p2xi	−p2xi	NUM
ijassa-1064	139	30	−p3xi	−p3xi	NUM
ijassa-1064	139	31	0	0	NUM
ijassa-1064	139	32	γ	γ	X
ijassa-1064	139	33	−µ1	−µ1	PROPN
ijassa-1064	139	34	0	0	NUM
ijassa-1064	139	35	0	0	NUM
ijassa-1064	139	36	c1p1ys	c1p1ys	X
ijassa-1064	139	37	c2p2ys	c2p2ys	X
ijassa-1064	139	38	0	0	PUNCT
ijassa-1064	140	1	j3	j3	PROPN
ijassa-1064	140	2	−β2ys	−β2ys	NUM
ijassa-1064	140	3	0	0	NUM
ijassa-1064	140	4	0	0	NUM
ijassa-1064	140	5	0	0	NUM
ijassa-1064	140	6	β2yi	β2yi	PUNCT
ijassa-1064	140	7	β2ys	β2ys	PUNCT
ijassa-1064	141	1	+	+	PUNCT
ijassa-1064	141	2	c3p3xi	c3p3xi	NOUN
ijassa-1064	141	3	−	−	PROPN
ijassa-1064	141	4	µ2	µ2	PROPN
ijassa-1064	141	5			PROPN
ijassa-1064	141	6	,	,	PUNCT
ijassa-1064	141	7	(	(	PUNCT
ijassa-1064	141	8	3.14	3.14	NUM
ijassa-1064	141	9	)	)	PUNCT
ijassa-1064	141	10	copyright	copyright	NOUN
ijassa-1064	141	11	©	©	PROPN
ijassa-1064	141	12	2021	2021	NUM
ijassa-1064	141	13	assa	assa	NOUN
ijassa-1064	141	14	.	.	PUNCT
ijassa-1064	142	1	adv	adv	PROPN
ijassa-1064	142	2	syst	syst	PROPN
ijassa-1064	142	3	sci	sci	PROPN
ijassa-1064	142	4	appl	appl	PROPN
ijassa-1064	142	5	(	(	PUNCT
ijassa-1064	142	6	2021	2021	NUM
ijassa-1064	142	7	)	)	PUNCT
ijassa-1064	142	8	stability	stability	NOUN
ijassa-1064	142	9	analysis	analysis	NOUN
ijassa-1064	142	10	and	and	CCONJ
ijassa-1064	142	11	optimal	optimal	ADJ
ijassa-1064	142	12	measure	measure	NOUN
ijassa-1064	142	13	89	89	NUM
ijassa-1064	142	14	where	where	SCONJ
ijassa-1064	142	15	j1	j1	NOUN
ijassa-1064	142	16	=	=	PUNCT
ijassa-1064	143	1	r	r	NOUN
ijassa-1064	143	2	−	−	NUM
ijassa-1064	143	3	2rxs	2rxs	NOUN
ijassa-1064	143	4	k	k	NOUN
ijassa-1064	144	1	−	−	PROPN
ijassa-1064	144	2	β1xi	β1xi	PUNCT
ijassa-1064	144	3	−	−	PROPN
ijassa-1064	144	4	p1ys	p1ys	PROPN
ijassa-1064	144	5	−	−	PROPN
ijassa-1064	144	6	µ1	µ1	PROPN
ijassa-1064	144	7	,	,	PUNCT
ijassa-1064	144	8	j2	j2	PROPN
ijassa-1064	144	9	=	=	SYM
ijassa-1064	144	10	β1xs	β1xs	PUNCT
ijassa-1064	144	11	−	−	PROPN
ijassa-1064	144	12	p2ys	p2ys	X
ijassa-1064	144	13	−	−	PROPN
ijassa-1064	144	14	p3yi	p3yi	X
ijassa-1064	144	15	−	−	PROPN
ijassa-1064	144	16	(	(	PUNCT
ijassa-1064	144	17	µ1	µ1	PROPN
ijassa-1064	144	18	+	+	X
ijassa-1064	144	19	γ	γ	X
ijassa-1064	144	20	)	)	PUNCT
ijassa-1064	144	21	,	,	PUNCT
ijassa-1064	144	22	j3	j3	PROPN
ijassa-1064	144	23	=	=	SYM
ijassa-1064	144	24	c1p1xs	c1p1xs	PROPN
ijassa-1064	144	25	+	+	NUM
ijassa-1064	144	26	c2p2xi	c2p2xi	NOUN
ijassa-1064	144	27	−	−	NOUN
ijassa-1064	144	28	β2yi	β2yi	PUNCT
ijassa-1064	145	1	−	−	PROPN
ijassa-1064	145	2	µ2	µ2	PROPN
ijassa-1064	145	3	.	.	PUNCT
ijassa-1064	146	1	the	the	DET
ijassa-1064	146	2	stability	stability	NOUN
ijassa-1064	146	3	of	of	ADP
ijassa-1064	146	4	each	each	PRON
ijassa-1064	146	5	of	of	ADP
ijassa-1064	146	6	the	the	DET
ijassa-1064	146	7	equilibrium	equilibrium	NOUN
ijassa-1064	146	8	points	point	NOUN
ijassa-1064	146	9	is	be	AUX
ijassa-1064	146	10	analysed	analyse	VERB
ijassa-1064	146	11	by	by	ADP
ijassa-1064	146	12	finding	find	VERB
ijassa-1064	146	13	the	the	DET
ijassa-1064	146	14	eigenvalues	eigenvalue	NOUN
ijassa-1064	146	15	of	of	ADP
ijassa-1064	146	16	the	the	DET
ijassa-1064	146	17	jacobian	jacobian	ADJ
ijassa-1064	146	18	matrix	matrix	NOUN
ijassa-1064	146	19	(	(	PUNCT
ijassa-1064	146	20	3.14	3.14	NUM
ijassa-1064	146	21	)	)	PUNCT
ijassa-1064	146	22	evaluated	evaluate	VERB
ijassa-1064	146	23	at	at	ADP
ijassa-1064	146	24	each	each	DET
ijassa-1064	146	25	point	point	NOUN
ijassa-1064	146	26	.	.	PUNCT
ijassa-1064	147	1	3.2.1	3.2.1	X
ijassa-1064	147	2	.	.	PUNCT
ijassa-1064	148	1	stability	stability	NOUN
ijassa-1064	148	2	of	of	ADP
ijassa-1064	148	3	e0	e0	PROPN
ijassa-1064	148	4	the	the	DET
ijassa-1064	148	5	jacobian	jacobian	ADJ
ijassa-1064	148	6	matrix	matrix	NOUN
ijassa-1064	148	7	(	(	PUNCT
ijassa-1064	148	8	3.14	3.14	NUM
ijassa-1064	148	9	)	)	PUNCT
ijassa-1064	148	10	is	be	AUX
ijassa-1064	148	11	evaluated	evaluate	VERB
ijassa-1064	148	12	at	at	ADP
ijassa-1064	148	13	the	the	DET
ijassa-1064	148	14	trivial	trivial	ADJ
ijassa-1064	148	15	equilibrium	equilibrium	NOUN
ijassa-1064	148	16	point	point	NOUN
ijassa-1064	148	17	(	(	PUNCT
ijassa-1064	148	18	3.7	3.7	NUM
ijassa-1064	148	19	)	)	PUNCT
ijassa-1064	148	20	.	.	PUNCT
ijassa-1064	149	1	hence	hence	ADV
ijassa-1064	149	2	,	,	PUNCT
ijassa-1064	149	3	solving	solve	VERB
ijassa-1064	149	4	the	the	DET
ijassa-1064	149	5	corresponding	corresponding	ADJ
ijassa-1064	149	6	characteristic	characteristic	ADJ
ijassa-1064	149	7	equation	equation	NOUN
ijassa-1064	149	8	|j(e0)−	|j(e0)−	NOUN
ijassa-1064	149	9	λi5)|	λi5)|	PROPN
ijassa-1064	149	10	=	=	SYM
ijassa-1064	149	11	0	0	NUM
ijassa-1064	149	12	,	,	PUNCT
ijassa-1064	149	13	where	where	SCONJ
ijassa-1064	149	14	λ	λ	PROPN
ijassa-1064	149	15	is	be	AUX
ijassa-1064	149	16	the	the	DET
ijassa-1064	149	17	eigenvalue	eigenvalue	PROPN
ijassa-1064	149	18	and	and	CCONJ
ijassa-1064	149	19	i5	i5	NOUN
ijassa-1064	149	20	is	be	AUX
ijassa-1064	149	21	the	the	DET
ijassa-1064	149	22	identity	identity	NOUN
ijassa-1064	149	23	matrix	matrix	NOUN
ijassa-1064	149	24	of	of	ADP
ijassa-1064	149	25	order	order	NOUN
ijassa-1064	149	26	five	five	NUM
ijassa-1064	149	27	,	,	PUNCT
ijassa-1064	149	28	the	the	DET
ijassa-1064	149	29	following	follow	VERB
ijassa-1064	149	30	eigenvalues	eigenvalue	NOUN
ijassa-1064	149	31	are	be	AUX
ijassa-1064	149	32	obtained	obtain	VERB
ijassa-1064	149	33	:	:	PUNCT
ijassa-1064	149	34	λ1	λ1	ADJ
ijassa-1064	149	35	=	=	SYM
ijassa-1064	149	36	r	r	NOUN
ijassa-1064	149	37	−	−	NOUN
ijassa-1064	149	38	µ1	µ1	PROPN
ijassa-1064	149	39	,	,	PUNCT
ijassa-1064	149	40	λ2	λ2	NOUN
ijassa-1064	149	41	=	=	SYM
ijassa-1064	149	42	−µ1	−µ1	PROPN
ijassa-1064	149	43	,	,	PUNCT
ijassa-1064	149	44	λ3	λ3	PROPN
ijassa-1064	149	45	=	=	PROPN
ijassa-1064	149	46	−µ2	−µ2	PROPN
ijassa-1064	149	47	,	,	PUNCT
ijassa-1064	149	48	λ4	λ4	PROPN
ijassa-1064	149	49	=	=	SYM
ijassa-1064	149	50	−(µ1	−(µ1	X
ijassa-1064	149	51	+	+	CCONJ
ijassa-1064	149	52	γ	γ	X
ijassa-1064	149	53	)	)	PUNCT
ijassa-1064	149	54	,	,	PUNCT
ijassa-1064	149	55	λ5	λ5	NOUN
ijassa-1064	149	56	=	=	SYM
ijassa-1064	149	57	−µ2	−µ2	NOUN
ijassa-1064	149	58	.	.	PUNCT
ijassa-1064	150	1	it	it	PRON
ijassa-1064	150	2	can	can	AUX
ijassa-1064	150	3	be	be	AUX
ijassa-1064	150	4	seen	see	VERB
ijassa-1064	150	5	that	that	SCONJ
ijassa-1064	150	6	all	all	DET
ijassa-1064	150	7	the	the	DET
ijassa-1064	150	8	eigenvalues	eigenvalue	NOUN
ijassa-1064	150	9	are	be	AUX
ijassa-1064	150	10	unconditionally	unconditionally	ADV
ijassa-1064	150	11	negative	negative	ADJ
ijassa-1064	150	12	except	except	SCONJ
ijassa-1064	150	13	λ1	λ1	PROPN
ijassa-1064	150	14	.	.	PUNCT
ijassa-1064	151	1	thus	thus	ADV
ijassa-1064	151	2	,	,	PUNCT
ijassa-1064	151	3	e0	e0	PROPN
ijassa-1064	151	4	will	will	AUX
ijassa-1064	151	5	be	be	AUX
ijassa-1064	151	6	stable	stable	ADJ
ijassa-1064	151	7	if	if	SCONJ
ijassa-1064	151	8	r	r	NOUN
ijassa-1064	151	9	<	<	X
ijassa-1064	151	10	µ1	µ1	NOUN
ijassa-1064	151	11	and	and	CCONJ
ijassa-1064	151	12	unstable	unstable	ADJ
ijassa-1064	151	13	if	if	SCONJ
ijassa-1064	151	14	r	r	NOUN
ijassa-1064	151	15	>	>	X
ijassa-1064	151	16	µ1	µ1	PROPN
ijassa-1064	151	17	.	.	PUNCT
ijassa-1064	152	1	this	this	DET
ijassa-1064	152	2	result	result	NOUN
ijassa-1064	152	3	is	be	AUX
ijassa-1064	152	4	theorized	theorize	VERB
ijassa-1064	152	5	as	as	ADP
ijassa-1064	152	6	follows	follow	NOUN
ijassa-1064	152	7	.	.	PUNCT
ijassa-1064	153	1	theorem	theorem	VERB
ijassa-1064	153	2	3.1	3.1	NUM
ijassa-1064	153	3	:	:	PUNCT
ijassa-1064	153	4	the	the	DET
ijassa-1064	153	5	trivial	trivial	ADJ
ijassa-1064	153	6	equilibrium	equilibrium	NOUN
ijassa-1064	153	7	point	point	NOUN
ijassa-1064	153	8	e0	e0	PROPN
ijassa-1064	153	9	of	of	ADP
ijassa-1064	153	10	the	the	DET
ijassa-1064	153	11	prey	prey	NOUN
ijassa-1064	153	12	-	-	PUNCT
ijassa-1064	153	13	predator	predator	NOUN
ijassa-1064	153	14	model	model	NOUN
ijassa-1064	153	15	(	(	PUNCT
ijassa-1064	153	16	2.1	2.1	NUM
ijassa-1064	153	17	)	)	PUNCT
ijassa-1064	153	18	,	,	PUNCT
ijassa-1064	153	19	given	give	VERB
ijassa-1064	153	20	by	by	ADP
ijassa-1064	153	21	(	(	PUNCT
ijassa-1064	153	22	3.7	3.7	NUM
ijassa-1064	153	23	)	)	PUNCT
ijassa-1064	153	24	,	,	PUNCT
ijassa-1064	153	25	is	be	AUX
ijassa-1064	153	26	stable	stable	ADJ
ijassa-1064	153	27	if	if	SCONJ
ijassa-1064	153	28	r	r	NOUN
ijassa-1064	153	29	<	<	X
ijassa-1064	153	30	µ1	µ1	NOUN
ijassa-1064	153	31	and	and	CCONJ
ijassa-1064	153	32	unstable	unstable	ADJ
ijassa-1064	153	33	if	if	SCONJ
ijassa-1064	153	34	r	r	NOUN
ijassa-1064	153	35	>	>	X
ijassa-1064	153	36	µ1	µ1	PROPN
ijassa-1064	153	37	.	.	PUNCT
ijassa-1064	154	1	the	the	DET
ijassa-1064	154	2	implication	implication	NOUN
ijassa-1064	154	3	of	of	ADP
ijassa-1064	154	4	theorem	theorem	ADJ
ijassa-1064	154	5	3.1	3.1	NUM
ijassa-1064	154	6	is	be	AUX
ijassa-1064	154	7	that	that	SCONJ
ijassa-1064	154	8	the	the	DET
ijassa-1064	154	9	coexistence	coexistence	NOUN
ijassa-1064	154	10	of	of	ADP
ijassa-1064	154	11	prey	prey	NOUN
ijassa-1064	154	12	-	-	PUNCT
ijassa-1064	154	13	predator	predator	NOUN
ijassa-1064	154	14	population	population	NOUN
ijassa-1064	154	15	will	will	AUX
ijassa-1064	154	16	not	not	PART
ijassa-1064	154	17	occur	occur	VERB
ijassa-1064	154	18	if	if	SCONJ
ijassa-1064	154	19	the	the	DET
ijassa-1064	154	20	intrinsic	intrinsic	ADJ
ijassa-1064	154	21	growth	growth	NOUN
ijassa-1064	154	22	rate	rate	NOUN
ijassa-1064	154	23	r	r	NOUN
ijassa-1064	154	24	does	do	AUX
ijassa-1064	154	25	not	not	PART
ijassa-1064	154	26	exceed	exceed	VERB
ijassa-1064	154	27	the	the	DET
ijassa-1064	154	28	natural	natural	ADJ
ijassa-1064	154	29	mortality	mortality	NOUN
ijassa-1064	154	30	rate	rate	NOUN
ijassa-1064	154	31	µ1	µ1	PROPN
ijassa-1064	154	32	.	.	PUNCT
ijassa-1064	155	1	in	in	ADP
ijassa-1064	155	2	other	other	ADJ
ijassa-1064	155	3	words	word	NOUN
ijassa-1064	155	4	,	,	PUNCT
ijassa-1064	155	5	stable	stable	ADJ
ijassa-1064	155	6	equilibrium	equilibrium	NOUN
ijassa-1064	155	7	point	point	NOUN
ijassa-1064	155	8	e0	e0	PROPN
ijassa-1064	155	9	will	will	AUX
ijassa-1064	155	10	result	result	VERB
ijassa-1064	155	11	into	into	ADP
ijassa-1064	155	12	extinction	extinction	NOUN
ijassa-1064	155	13	of	of	ADP
ijassa-1064	155	14	prey	prey	NOUN
ijassa-1064	155	15	and	and	CCONJ
ijassa-1064	155	16	predator	predator	NOUN
ijassa-1064	155	17	species	specie	NOUN
ijassa-1064	155	18	in	in	ADP
ijassa-1064	155	19	the	the	DET
ijassa-1064	155	20	ecosystem	ecosystem	NOUN
ijassa-1064	155	21	.	.	PUNCT
ijassa-1064	156	1	3.2.2	3.2.2	NUM
ijassa-1064	156	2	.	.	PUNCT
ijassa-1064	157	1	stability	stability	NOUN
ijassa-1064	157	2	of	of	ADP
ijassa-1064	157	3	e1	e1	VERB
ijassa-1064	157	4	the	the	DET
ijassa-1064	157	5	characteristic	characteristic	ADJ
ijassa-1064	157	6	equation	equation	NOUN
ijassa-1064	157	7	of	of	ADP
ijassa-1064	157	8	the	the	DET
ijassa-1064	157	9	matrix	matrix	NOUN
ijassa-1064	157	10	(	(	PUNCT
ijassa-1064	157	11	3.14	3.14	NUM
ijassa-1064	157	12	)	)	PUNCT
ijassa-1064	157	13	evaluated	evaluate	VERB
ijassa-1064	157	14	at	at	ADP
ijassa-1064	157	15	the	the	DET
ijassa-1064	157	16	axial	axial	ADJ
ijassa-1064	157	17	equilibrium	equilibrium	NOUN
ijassa-1064	157	18	point	point	NOUN
ijassa-1064	157	19	e1	e1	NOUN
ijassa-1064	157	20	is	be	AUX
ijassa-1064	157	21	given	give	VERB
ijassa-1064	157	22	by	by	ADP
ijassa-1064	157	23	|j(e1)−	|j(e1)−	PROPN
ijassa-1064	157	24	λi5)|	λi5)|	PROPN
ijassa-1064	157	25	=	=	SYM
ijassa-1064	157	26	0	0	NUM
ijassa-1064	157	27	,	,	PUNCT
ijassa-1064	157	28	which	which	PRON
ijassa-1064	157	29	gives	give	VERB
ijassa-1064	157	30	the	the	DET
ijassa-1064	157	31	following	follow	VERB
ijassa-1064	157	32	eigenvalues	eigenvalue	NOUN
ijassa-1064	157	33	:	:	PUNCT
ijassa-1064	157	34	λ1	λ1	ADJ
ijassa-1064	157	35	=	=	PUNCT
ijassa-1064	157	36	µ1	µ1	PROPN
ijassa-1064	157	37	−	−	NOUN
ijassa-1064	157	38	r	r	NOUN
ijassa-1064	157	39	,	,	PUNCT
ijassa-1064	157	40	λ2	λ2	NOUN
ijassa-1064	157	41	=	=	SYM
ijassa-1064	157	42	−µ1	−µ1	PROPN
ijassa-1064	157	43	,	,	PUNCT
ijassa-1064	157	44	λ3	λ3	PROPN
ijassa-1064	157	45	=	=	PROPN
ijassa-1064	157	46	β1k	β1k	PUNCT
ijassa-1064	157	47	(	(	PUNCT
ijassa-1064	157	48	1−	1−	NUM
ijassa-1064	157	49	µ1	µ1	NOUN
ijassa-1064	157	50	r	r	NOUN
ijassa-1064	157	51	)	)	PUNCT
ijassa-1064	157	52	−	−	PROPN
ijassa-1064	158	1	(	(	PUNCT
ijassa-1064	158	2	µ1	µ1	PROPN
ijassa-1064	158	3	+	+	X
ijassa-1064	158	4	γ	γ	X
ijassa-1064	158	5	)	)	PUNCT
ijassa-1064	158	6	,	,	PUNCT
ijassa-1064	158	7	λ4	λ4	PROPN
ijassa-1064	158	8	=	=	SYM
ijassa-1064	158	9	c1p1k	c1p1k	NUM
ijassa-1064	159	1	(	(	PUNCT
ijassa-1064	159	2	1−	1−	NUM
ijassa-1064	159	3	µ1	µ1	NOUN
ijassa-1064	159	4	r	r	NOUN
ijassa-1064	159	5	)	)	PUNCT
ijassa-1064	159	6	−	−	NOUN
ijassa-1064	160	1	µ2	µ2	PROPN
ijassa-1064	160	2	,	,	PUNCT
ijassa-1064	160	3	λ5	λ5	NOUN
ijassa-1064	160	4	=	=	SYM
ijassa-1064	160	5	−µ2	−µ2	PROPN
ijassa-1064	160	6	.	.	PUNCT
ijassa-1064	161	1	the	the	DET
ijassa-1064	161	2	stability	stability	NOUN
ijassa-1064	161	3	result	result	NOUN
ijassa-1064	161	4	is	be	AUX
ijassa-1064	161	5	theorized	theorize	VERB
ijassa-1064	161	6	as	as	ADP
ijassa-1064	161	7	follows	follow	NOUN
ijassa-1064	161	8	.	.	PUNCT
ijassa-1064	162	1	theorem	theorem	ADJ
ijassa-1064	162	2	3.2	3.2	NUM
ijassa-1064	162	3	:	:	PUNCT
ijassa-1064	162	4	the	the	DET
ijassa-1064	162	5	axial	axial	ADJ
ijassa-1064	162	6	equilibrium	equilibrium	NOUN
ijassa-1064	162	7	point	point	NOUN
ijassa-1064	162	8	e1	e1	NOUN
ijassa-1064	162	9	of	of	ADP
ijassa-1064	162	10	the	the	DET
ijassa-1064	162	11	prey	prey	NOUN
ijassa-1064	162	12	-	-	PUNCT
ijassa-1064	162	13	predator	predator	NOUN
ijassa-1064	162	14	model	model	NOUN
ijassa-1064	162	15	(	(	PUNCT
ijassa-1064	162	16	2.1	2.1	NUM
ijassa-1064	162	17	)	)	PUNCT
ijassa-1064	162	18	,	,	PUNCT
ijassa-1064	162	19	given	give	VERB
ijassa-1064	162	20	by	by	ADP
ijassa-1064	162	21	(	(	PUNCT
ijassa-1064	162	22	3.8	3.8	NUM
ijassa-1064	162	23	)	)	PUNCT
ijassa-1064	162	24	,	,	PUNCT
ijassa-1064	162	25	is	be	AUX
ijassa-1064	162	26	stable	stable	ADJ
ijassa-1064	162	27	if	if	SCONJ
ijassa-1064	162	28	the	the	DET
ijassa-1064	162	29	inequalities	inequality	NOUN
ijassa-1064	162	30	:	:	PUNCT
ijassa-1064	162	31	µ1	µ1	PROPN
ijassa-1064	162	32	<	<	X
ijassa-1064	162	33	r	r	NOUN
ijassa-1064	162	34	,	,	PUNCT
ijassa-1064	162	35	β1k	β1k	PUNCT
ijassa-1064	162	36	(	(	PUNCT
ijassa-1064	162	37	1−	1−	NUM
ijassa-1064	162	38	µ1	µ1	NOUN
ijassa-1064	162	39	r	r	NOUN
ijassa-1064	162	40	)	)	PUNCT
ijassa-1064	162	41	<	<	X
ijassa-1064	162	42	(	(	PUNCT
ijassa-1064	162	43	µ1	µ1	PROPN
ijassa-1064	162	44	+	+	X
ijassa-1064	162	45	γ	γ	X
ijassa-1064	162	46	)	)	PUNCT
ijassa-1064	162	47	and	and	CCONJ
ijassa-1064	162	48	c1p1k	c1p1k	NUM
ijassa-1064	162	49	(	(	PUNCT
ijassa-1064	162	50	1−	1−	NUM
ijassa-1064	162	51	µ1	µ1	NOUN
ijassa-1064	162	52	r	r	NOUN
ijassa-1064	162	53	)	)	PUNCT
ijassa-1064	163	1	<	<	X
ijassa-1064	163	2	µ2	µ2	PROPN
ijassa-1064	163	3	hold	hold	VERB
ijassa-1064	163	4	.	.	PUNCT
ijassa-1064	164	1	the	the	DET
ijassa-1064	164	2	implication	implication	NOUN
ijassa-1064	164	3	of	of	ADP
ijassa-1064	164	4	theorem	theorem	ADJ
ijassa-1064	164	5	3.2	3.2	NUM
ijassa-1064	164	6	is	be	AUX
ijassa-1064	164	7	that	that	SCONJ
ijassa-1064	164	8	the	the	DET
ijassa-1064	164	9	stable	stable	ADJ
ijassa-1064	164	10	e1	e1	PROPN
ijassa-1064	164	11	will	will	AUX
ijassa-1064	164	12	support	support	VERB
ijassa-1064	164	13	the	the	DET
ijassa-1064	164	14	existence	existence	NOUN
ijassa-1064	164	15	of	of	ADP
ijassa-1064	164	16	prey	prey	PROPN
ijassa-1064	164	17	population	population	NOUN
ijassa-1064	164	18	only	only	ADV
ijassa-1064	164	19	in	in	ADP
ijassa-1064	164	20	the	the	DET
ijassa-1064	164	21	ecosystem	ecosystem	NOUN
ijassa-1064	164	22	provided	provide	VERB
ijassa-1064	164	23	these	these	DET
ijassa-1064	164	24	threshold	threshold	NOUN
ijassa-1064	164	25	conditions	condition	NOUN
ijassa-1064	164	26	are	be	AUX
ijassa-1064	164	27	satisfied	satisfied	ADJ
ijassa-1064	164	28	:	:	PUNCT
ijassa-1064	164	29	r01	r01	PROPN
ijassa-1064	164	30	<	<	X
ijassa-1064	164	31	1,r02	1,r02	NUM
ijassa-1064	164	32	<	<	X
ijassa-1064	164	33	1	1	NUM
ijassa-1064	164	34	andr03	andr03	NOUN
ijassa-1064	164	35	<	<	X
ijassa-1064	164	36	1	1	NUM
ijassa-1064	164	37	,	,	PUNCT
ijassa-1064	164	38	where	where	SCONJ
ijassa-1064	164	39	r01	r01	PROPN
ijassa-1064	164	40	=	=	SYM
ijassa-1064	164	41	µ1	µ1	PROPN
ijassa-1064	164	42	r	r	NOUN
ijassa-1064	164	43	,	,	PUNCT
ijassa-1064	164	44	r02	r02	X
ijassa-1064	164	45	=	=	PUNCT
ijassa-1064	164	46	β1k	β1k	X
ijassa-1064	164	47	(	(	PUNCT
ijassa-1064	164	48	1−	1−	NUM
ijassa-1064	164	49	µ1	µ1	NOUN
ijassa-1064	164	50	r	r	NOUN
ijassa-1064	164	51	)	)	PUNCT
ijassa-1064	164	52	µ1	µ1	PROPN
ijassa-1064	164	53	+	+	X
ijassa-1064	164	54	γ	γ	NOUN
ijassa-1064	164	55	,	,	PUNCT
ijassa-1064	164	56	and	and	CCONJ
ijassa-1064	164	57	r03	r03	NUM
ijassa-1064	164	58	=	=	SYM
ijassa-1064	164	59	c1p1k	c1p1k	NUM
ijassa-1064	165	1	(	(	PUNCT
ijassa-1064	165	2	1−	1−	NUM
ijassa-1064	165	3	µ1	µ1	NOUN
ijassa-1064	165	4	r	r	NOUN
ijassa-1064	165	5	)	)	PUNCT
ijassa-1064	165	6	µ2	µ2	PROPN
ijassa-1064	165	7	.	.	PUNCT
ijassa-1064	166	1	now	now	ADV
ijassa-1064	166	2	,	,	PUNCT
ijassa-1064	166	3	suppose	suppose	VERB
ijassa-1064	166	4	r0	r0	NOUN
ijassa-1064	166	5	=	=	SYM
ijassa-1064	166	6	max{r01,r02,r03	max{r01,r02,r03	PROPN
ijassa-1064	166	7	}	}	PUNCT
ijassa-1064	166	8	,	,	PUNCT
ijassa-1064	166	9	and	and	CCONJ
ijassa-1064	166	10	considering	consider	VERB
ijassa-1064	166	11	the	the	DET
ijassa-1064	166	12	prey	prey	NOUN
ijassa-1064	166	13	sub	sub	NOUN
ijassa-1064	166	14	-	-	NOUN
ijassa-1064	166	15	model	model	NOUN
ijassa-1064	166	16	only	only	ADV
ijassa-1064	166	17	such	such	ADJ
ijassa-1064	166	18	that	that	SCONJ
ijassa-1064	166	19	the	the	DET
ijassa-1064	166	20	axial	axial	ADJ
ijassa-1064	166	21	equilibrium	equilibrium	NOUN
ijassa-1064	166	22	point	point	NOUN
ijassa-1064	166	23	e1	e1	NOUN
ijassa-1064	166	24	becomes	become	VERB
ijassa-1064	166	25	ẽ1	ẽ1	NOUN
ijassa-1064	166	26	=	=	PUNCT
ijassa-1064	166	27	(	(	PUNCT
ijassa-1064	166	28	x0	x0	PROPN
ijassa-1064	166	29	s	s	PART
ijassa-1064	166	30	,	,	PUNCT
ijassa-1064	166	31	0	0	NUM
ijassa-1064	166	32	,	,	PUNCT
ijassa-1064	166	33	0	0	NUM
ijassa-1064	166	34	)	)	PUNCT
ijassa-1064	166	35	,	,	PUNCT
ijassa-1064	166	36	where	where	SCONJ
ijassa-1064	166	37	x0	x0	PROPN
ijassa-1064	166	38	s	s	PART
ijassa-1064	166	39	=	=	SYM
ijassa-1064	166	40	k	k	X
ijassa-1064	166	41	[	[	PUNCT
ijassa-1064	166	42	1−	1−	NUM
ijassa-1064	166	43	µ1	µ1	NOUN
ijassa-1064	166	44	r	r	NOUN
ijassa-1064	166	45	]	]	PUNCT
ijassa-1064	166	46	.	.	PUNCT
ijassa-1064	167	1	the	the	DET
ijassa-1064	167	2	following	follow	VERB
ijassa-1064	167	3	global	global	ADJ
ijassa-1064	167	4	stability	stability	NOUN
ijassa-1064	167	5	result	result	NOUN
ijassa-1064	167	6	is	be	AUX
ijassa-1064	167	7	proved	prove	VERB
ijassa-1064	167	8	.	.	PUNCT
ijassa-1064	168	1	theorem	theorem	VERB
ijassa-1064	168	2	3.3	3.3	NUM
ijassa-1064	168	3	:	:	PUNCT
ijassa-1064	168	4	the	the	DET
ijassa-1064	168	5	equilibrium	equilibrium	NOUN
ijassa-1064	168	6	point	point	NOUN
ijassa-1064	168	7	ẽ1	ẽ1	NOUN
ijassa-1064	168	8	is	be	AUX
ijassa-1064	168	9	globally	globally	ADV
ijassa-1064	168	10	asymptotically	asymptotically	ADV
ijassa-1064	168	11	stable	stable	ADJ
ijassa-1064	168	12	ifr0	ifr0	NOUN
ijassa-1064	168	13	<	<	X
ijassa-1064	168	14	1	1	X
ijassa-1064	168	15	.	.	X
ijassa-1064	168	16	proof	proof	NOUN
ijassa-1064	168	17	since	since	SCONJ
ijassa-1064	168	18	p1	p1	PROPN
ijassa-1064	168	19	=	=	NOUN
ijassa-1064	168	20	0	0	NUM
ijassa-1064	168	21	in	in	ADP
ijassa-1064	168	22	the	the	DET
ijassa-1064	168	23	absence	absence	NOUN
ijassa-1064	168	24	of	of	ADP
ijassa-1064	168	25	predation	predation	NOUN
ijassa-1064	168	26	,	,	PUNCT
ijassa-1064	168	27	thenr0	thenr0	X
ijassa-1064	169	1	=	=	PUNCT
ijassa-1064	169	2	max{r01,r02	max{r01,r02	PROPN
ijassa-1064	169	3	}	}	PUNCT
ijassa-1064	169	4	.	.	PUNCT
ijassa-1064	170	1	consider	consider	VERB
ijassa-1064	170	2	the	the	DET
ijassa-1064	170	3	lyapunov	lyapunov	ADJ
ijassa-1064	170	4	copyright	copyright	NOUN
ijassa-1064	170	5	©	©	PROPN
ijassa-1064	170	6	2021	2021	NUM
ijassa-1064	170	7	assa	assa	NOUN
ijassa-1064	170	8	.	.	PUNCT
ijassa-1064	171	1	adv	adv	PROPN
ijassa-1064	171	2	syst	syst	PROPN
ijassa-1064	171	3	sci	sci	PROPN
ijassa-1064	171	4	appl	appl	PROPN
ijassa-1064	171	5	(	(	PUNCT
ijassa-1064	171	6	2021	2021	NUM
ijassa-1064	171	7	)	)	PUNCT
ijassa-1064	171	8	90	90	NUM
ijassa-1064	171	9	j.a	j.a	PROPN
ijassa-1064	171	10	.	.	PROPN
ijassa-1064	171	11	ademosu	ademosu	PROPN
ijassa-1064	171	12	,	,	PUNCT
ijassa-1064	171	13	s.	s.	PROPN
ijassa-1064	171	14	olaniyi	olaniyi	PROPN
ijassa-1064	171	15	,	,	PUNCT
ijassa-1064	171	16	s.o	s.o	PROPN
ijassa-1064	171	17	.	.	PROPN
ijassa-1064	171	18	adewale	adewale	PROPN
ijassa-1064	171	19	function	function	PROPN
ijassa-1064	171	20	(	(	PUNCT
ijassa-1064	171	21	combination	combination	NOUN
ijassa-1064	171	22	of	of	ADP
ijassa-1064	171	23	goh	goh	PROPN
ijassa-1064	171	24	-	-	PUNCT
ijassa-1064	171	25	volterra	volterra	PROPN
ijassa-1064	171	26	[	[	X
ijassa-1064	171	27	2	2	NUM
ijassa-1064	171	28	,	,	PUNCT
ijassa-1064	171	29	3	3	NUM
ijassa-1064	171	30	,	,	PUNCT
ijassa-1064	171	31	13	13	NUM
ijassa-1064	171	32	,	,	PUNCT
ijassa-1064	171	33	15	15	NUM
ijassa-1064	171	34	,	,	PUNCT
ijassa-1064	171	35	22	22	NUM
ijassa-1064	171	36	]	]	PUNCT
ijassa-1064	171	37	and	and	CCONJ
ijassa-1064	171	38	linear	linear	ADJ
ijassa-1064	171	39	types	type	NOUN
ijassa-1064	171	40	)	)	PUNCT
ijassa-1064	171	41	given	give	VERB
ijassa-1064	171	42	by	by	ADP
ijassa-1064	171	43	l	l	NOUN
ijassa-1064	171	44	=	=	SYM
ijassa-1064	171	45	xs	xs	PROPN
ijassa-1064	171	46	−x0	−x0	PROPN
ijassa-1064	171	47	s	s	PROPN
ijassa-1064	171	48	−x0	−x0	NOUN
ijassa-1064	171	49	s	s	PART
ijassa-1064	171	50	ln	ln	NOUN
ijassa-1064	171	51	xs	xs	PROPN
ijassa-1064	172	1	x0	x0	PROPN
ijassa-1064	172	2	s	s	PART
ijassa-1064	172	3	+	+	NOUN
ijassa-1064	172	4	xi	xi	PROPN
ijassa-1064	172	5	.	.	PUNCT
ijassa-1064	173	1	(	(	PUNCT
ijassa-1064	173	2	3.15	3.15	NUM
ijassa-1064	173	3	)	)	PUNCT
ijassa-1064	173	4	the	the	DET
ijassa-1064	173	5	time	time	NOUN
ijassa-1064	173	6	derivative	derivative	NOUN
ijassa-1064	173	7	of	of	ADP
ijassa-1064	173	8	lyapunov	lyapunov	ADJ
ijassa-1064	173	9	function	function	NOUN
ijassa-1064	173	10	(	(	PUNCT
ijassa-1064	173	11	3.15	3.15	NUM
ijassa-1064	173	12	)	)	PUNCT
ijassa-1064	173	13	along	along	ADP
ijassa-1064	173	14	the	the	DET
ijassa-1064	173	15	trajectory	trajectory	NOUN
ijassa-1064	173	16	of	of	ADP
ijassa-1064	173	17	the	the	DET
ijassa-1064	173	18	prey	prey	NOUN
ijassa-1064	173	19	only	only	ADV
ijassa-1064	173	20	submodel	submodel	PROPN
ijassa-1064	173	21	is	be	AUX
ijassa-1064	173	22	given	give	VERB
ijassa-1064	173	23	by	by	ADP
ijassa-1064	173	24	l̇	l̇	PROPN
ijassa-1064	173	25	=	=	PUNCT
ijassa-1064	173	26	(	(	PUNCT
ijassa-1064	173	27	1−	1−	NUM
ijassa-1064	173	28	x0	x0	PROPN
ijassa-1064	173	29	s	s	PART
ijassa-1064	173	30	xs	xs	PROPN
ijassa-1064	173	31	)	)	PUNCT
ijassa-1064	174	1	dxs	dxs	PROPN
ijassa-1064	174	2	dt	dt	PROPN
ijassa-1064	175	1	+	+	NUM
ijassa-1064	175	2	dxi	dxi	NOUN
ijassa-1064	175	3	dt	dt	NOUN
ijassa-1064	175	4	.	.	PUNCT
ijassa-1064	176	1	(	(	PUNCT
ijassa-1064	176	2	3.16	3.16	NUM
ijassa-1064	176	3	)	)	PUNCT
ijassa-1064	176	4	using	use	VERB
ijassa-1064	176	5	dxs	dxs	PROPN
ijassa-1064	176	6	dt	dt	NOUN
ijassa-1064	176	7	=	=	SYM
ijassa-1064	176	8	rxs	rxs	X
ijassa-1064	176	9	(	(	PUNCT
ijassa-1064	176	10	1−	1−	NUM
ijassa-1064	176	11	xs	xs	PROPN
ijassa-1064	176	12	k	k	PROPN
ijassa-1064	176	13	)	)	PUNCT
ijassa-1064	177	1	−	−	PROPN
ijassa-1064	178	1	β1xsxi	β1xsxi	NUM
ijassa-1064	178	2	−	−	PROPN
ijassa-1064	178	3	µ1xs	µ1xs	NOUN
ijassa-1064	178	4	and	and	CCONJ
ijassa-1064	178	5	dxi	dxi	NOUN
ijassa-1064	178	6	dt	dt	NOUN
ijassa-1064	178	7	=	=	SYM
ijassa-1064	179	1	β1xsxi	β1xsxi	NUM
ijassa-1064	179	2	−	−	PROPN
ijassa-1064	179	3	(	(	PUNCT
ijassa-1064	179	4	µ1	µ1	PROPN
ijassa-1064	179	5	+	+	X
ijassa-1064	179	6	γ)xi	γ)xi	PROPN
ijassa-1064	179	7	in	in	ADP
ijassa-1064	179	8	(	(	PUNCT
ijassa-1064	179	9	3.16	3.16	NUM
ijassa-1064	179	10	)	)	PUNCT
ijassa-1064	179	11	with	with	ADP
ijassa-1064	179	12	xs	xs	PROPN
ijassa-1064	179	13	≤	≤	NUM
ijassa-1064	179	14	x0	x0	PROPN
ijassa-1064	179	15	s	s	PART
ijassa-1064	179	16	,	,	PUNCT
ijassa-1064	179	17	it	it	PRON
ijassa-1064	179	18	follows	follow	VERB
ijassa-1064	179	19	that	that	SCONJ
ijassa-1064	179	20	l̇	l̇	PROPN
ijassa-1064	179	21	=	=	PRON
ijassa-1064	179	22	(	(	PUNCT
ijassa-1064	179	23	xs	xs	PROPN
ijassa-1064	179	24	−x0	−x0	PROPN
ijassa-1064	179	25	s	s	PART
ijassa-1064	179	26	)	)	PUNCT
ijassa-1064	179	27	(	(	PUNCT
ijassa-1064	179	28	r	r	X
ijassa-1064	179	29	[	[	PUNCT
ijassa-1064	179	30	1−	1−	NUM
ijassa-1064	179	31	xs	xs	PROPN
ijassa-1064	180	1	k	k	X
ijassa-1064	180	2	]	]	PUNCT
ijassa-1064	180	3	−	−	PROPN
ijassa-1064	180	4	β1xi	β1xi	PUNCT
ijassa-1064	180	5	−	−	PROPN
ijassa-1064	180	6	µ1	µ1	NOUN
ijassa-1064	180	7	)	)	PUNCT
ijassa-1064	181	1	+	+	CCONJ
ijassa-1064	182	1	β1xsxi	β1xsxi	NUM
ijassa-1064	182	2	−	−	PROPN
ijassa-1064	183	1	(	(	PUNCT
ijassa-1064	183	2	µ1	µ1	PROPN
ijassa-1064	183	3	+	+	CCONJ
ijassa-1064	183	4	γ)xi	γ)xi	PROPN
ijassa-1064	183	5	≤	≤	NOUN
ijassa-1064	183	6	r	r	NOUN
ijassa-1064	183	7	[	[	PUNCT
ijassa-1064	183	8	1−	1−	NUM
ijassa-1064	183	9	x0	x0	PROPN
ijassa-1064	183	10	s	s	PART
ijassa-1064	183	11	k	k	X
ijassa-1064	183	12	]	]	X
ijassa-1064	183	13	−	−	PROPN
ijassa-1064	183	14	β1xi	β1xi	PUNCT
ijassa-1064	184	1	−	−	PROPN
ijassa-1064	184	2	µ1	µ1	PROPN
ijassa-1064	184	3	+	+	PROPN
ijassa-1064	184	4	β1x	β1x	NOUN
ijassa-1064	184	5	0	0	NUM
ijassa-1064	184	6	sxi	sxi	PROPN
ijassa-1064	184	7	−	−	PROPN
ijassa-1064	184	8	(	(	PUNCT
ijassa-1064	184	9	µ1	µ1	PROPN
ijassa-1064	184	10	+	+	PROPN
ijassa-1064	184	11	γ)xi	γ)xi	PROPN
ijassa-1064	184	12	.	.	PUNCT
ijassa-1064	185	1	(	(	PUNCT
ijassa-1064	185	2	3.17	3.17	NUM
ijassa-1064	185	3	)	)	PUNCT
ijassa-1064	185	4	since	since	SCONJ
ijassa-1064	185	5	r	r	NOUN
ijassa-1064	185	6	[	[	PUNCT
ijassa-1064	185	7	1−	1−	NUM
ijassa-1064	185	8	x0	x0	PROPN
ijassa-1064	185	9	s	s	PART
ijassa-1064	186	1	k	k	X
ijassa-1064	186	2	]	]	X
ijassa-1064	186	3	=	=	PUNCT
ijassa-1064	186	4	µ1	µ1	PROPN
ijassa-1064	186	5	at	at	ADP
ijassa-1064	186	6	the	the	DET
ijassa-1064	186	7	disease	disease	NOUN
ijassa-1064	186	8	-	-	PUNCT
ijassa-1064	186	9	free	free	ADJ
ijassa-1064	186	10	steady	steady	ADJ
ijassa-1064	186	11	state	state	NOUN
ijassa-1064	186	12	of	of	ADP
ijassa-1064	186	13	the	the	DET
ijassa-1064	186	14	prey	prey	NOUN
ijassa-1064	186	15	only	only	ADV
ijassa-1064	186	16	sub	sub	NOUN
ijassa-1064	186	17	-	-	NOUN
ijassa-1064	186	18	model	model	NOUN
ijassa-1064	186	19	,	,	PUNCT
ijassa-1064	186	20	then	then	ADV
ijassa-1064	186	21	it	it	PRON
ijassa-1064	186	22	follows	follow	VERB
ijassa-1064	186	23	from	from	ADP
ijassa-1064	186	24	(	(	PUNCT
ijassa-1064	186	25	3.17	3.17	NUM
ijassa-1064	186	26	)	)	PUNCT
ijassa-1064	186	27	,	,	PUNCT
ijassa-1064	186	28	by	by	ADP
ijassa-1064	186	29	further	further	ADJ
ijassa-1064	186	30	simplifications	simplification	NOUN
ijassa-1064	186	31	,	,	PUNCT
ijassa-1064	186	32	that	that	SCONJ
ijassa-1064	186	33	l̇	l̇	PROPN
ijassa-1064	186	34	≤	≤	NOUN
ijassa-1064	186	35	−β1xi	−β1xi	NUM
ijassa-1064	186	36	−	−	PROPN
ijassa-1064	187	1	(	(	PUNCT
ijassa-1064	187	2	µ1	µ1	PROPN
ijassa-1064	187	3	+	+	X
ijassa-1064	187	4	γ	γ	X
ijassa-1064	187	5	)	)	PUNCT
ijassa-1064	187	6	(	(	PUNCT
ijassa-1064	187	7	1−	1−	NUM
ijassa-1064	187	8	β1x	β1x	NOUN
ijassa-1064	187	9	0	0	NUM
ijassa-1064	187	10	s	s	PART
ijassa-1064	187	11	µ1	µ1	NOUN
ijassa-1064	187	12	+	+	X
ijassa-1064	187	13	γ	γ	NOUN
ijassa-1064	187	14	)	)	PUNCT
ijassa-1064	187	15	xi	xi	PROPN
ijassa-1064	187	16	.	.	PUNCT
ijassa-1064	188	1	(	(	PUNCT
ijassa-1064	188	2	3.18	3.18	NUM
ijassa-1064	188	3	)	)	PUNCT
ijassa-1064	188	4	sincer02	sincer02	NOUN
ijassa-1064	188	5	=	=	PUNCT
ijassa-1064	189	1	β1x	β1x	NOUN
ijassa-1064	189	2	0	0	NUM
ijassa-1064	189	3	s	s	PART
ijassa-1064	189	4	µ1	µ1	NOUN
ijassa-1064	189	5	+	+	X
ijassa-1064	189	6	γ	γ	X
ijassa-1064	189	7	,	,	PUNCT
ijassa-1064	189	8	consequently	consequently	ADV
ijassa-1064	189	9	(	(	PUNCT
ijassa-1064	189	10	3.18	3.18	NUM
ijassa-1064	189	11	)	)	PUNCT
ijassa-1064	189	12	becomes	become	VERB
ijassa-1064	189	13	l̇	l̇	PROPN
ijassa-1064	189	14	≤	≤	NOUN
ijassa-1064	189	15	−β1xi	−β1xi	NUM
ijassa-1064	189	16	−	−	PROPN
ijassa-1064	190	1	(	(	PUNCT
ijassa-1064	190	2	µ1	µ1	PROPN
ijassa-1064	190	3	+	+	X
ijassa-1064	190	4	γ	γ	X
ijassa-1064	190	5	)	)	PUNCT
ijassa-1064	190	6	(	(	PUNCT
ijassa-1064	190	7	1−r02)xi	1−r02)xi	NOUN
ijassa-1064	190	8	.	.	PUNCT
ijassa-1064	191	1	therefore	therefore	ADV
ijassa-1064	191	2	,	,	PUNCT
ijassa-1064	191	3	l̇	l̇	PROPN
ijassa-1064	191	4	≤	≤	NOUN
ijassa-1064	191	5	0	0	PUNCT
ijassa-1064	191	6	when	when	SCONJ
ijassa-1064	191	7	r02	r02	VERB
ijassa-1064	191	8	<	<	X
ijassa-1064	191	9	1	1	NUM
ijassa-1064	191	10	with	with	ADP
ijassa-1064	191	11	equality	equality	NOUN
ijassa-1064	191	12	,	,	PUNCT
ijassa-1064	191	13	l̇	l̇	PROPN
ijassa-1064	191	14	=	=	NOUN
ijassa-1064	191	15	0	0	NUM
ijassa-1064	191	16	,	,	PUNCT
ijassa-1064	191	17	if	if	SCONJ
ijassa-1064	191	18	and	and	CCONJ
ijassa-1064	191	19	only	only	ADV
ijassa-1064	191	20	if	if	SCONJ
ijassa-1064	191	21	xi	xi	X
ijassa-1064	191	22	=	=	NOUN
ijassa-1064	191	23	0	0	PROPN
ijassa-1064	191	24	.	.	PUNCT
ijassa-1064	192	1	it	it	PRON
ijassa-1064	192	2	follows	follow	VERB
ijassa-1064	192	3	from	from	ADP
ijassa-1064	192	4	lasalle	lasalle	PROPN
ijassa-1064	192	5	’s	’s	PART
ijassa-1064	192	6	invariance	invariance	NOUN
ijassa-1064	192	7	principle	principle	NOUN
ijassa-1064	192	8	[	[	X
ijassa-1064	192	9	19	19	NUM
ijassa-1064	192	10	]	]	PUNCT
ijassa-1064	192	11	that	that	SCONJ
ijassa-1064	192	12	the	the	DET
ijassa-1064	192	13	largest	large	ADJ
ijassa-1064	192	14	invariant	invariant	ADJ
ijassa-1064	192	15	set	set	NOUN
ijassa-1064	192	16	contained	contain	VERB
ijassa-1064	192	17	in	in	ADP
ijassa-1064	192	18	{	{	PUNCT
ijassa-1064	192	19	(	(	PUNCT
ijassa-1064	192	20	xs	xs	PROPN
ijassa-1064	192	21	,	,	PUNCT
ijassa-1064	192	22	xi	xi	PROPN
ijassa-1064	192	23	,	,	PUNCT
ijassa-1064	192	24	xr	xr	PROPN
ijassa-1064	192	25	)	)	PUNCT
ijassa-1064	192	26	∈	∈	PROPN
ijassa-1064	192	27	r3	r3	PROPN
ijassa-1064	193	1	+	+	CCONJ
ijassa-1064	193	2	:	:	PUNCT
ijassa-1064	193	3	l̇	l̇	PROPN
ijassa-1064	193	4	=	=	PUNCT
ijassa-1064	193	5	0	0	NUM
ijassa-1064	193	6	}	}	PUNCT
ijassa-1064	193	7	is	be	AUX
ijassa-1064	193	8	the	the	DET
ijassa-1064	193	9	singleton	singleton	PROPN
ijassa-1064	193	10	set	set	NOUN
ijassa-1064	193	11	{	{	PUNCT
ijassa-1064	193	12	ẽ1	ẽ1	NOUN
ijassa-1064	193	13	}	}	PUNCT
ijassa-1064	193	14	.	.	PUNCT
ijassa-1064	194	1	hence	hence	ADV
ijassa-1064	194	2	,	,	PUNCT
ijassa-1064	194	3	the	the	DET
ijassa-1064	194	4	equilibrium	equilibrium	NOUN
ijassa-1064	194	5	point	point	NOUN
ijassa-1064	194	6	ẽ1	ẽ1	PROPN
ijassa-1064	194	7	=	=	SYM
ijassa-1064	194	8	(	(	PUNCT
ijassa-1064	194	9	k[1−	k[1−	PROPN
ijassa-1064	194	10	(	(	PUNCT
ijassa-1064	194	11	µ1	µ1	PROPN
ijassa-1064	194	12	/	/	SYM
ijassa-1064	194	13	r	r	NOUN
ijassa-1064	194	14	)	)	PUNCT
ijassa-1064	194	15	]	]	PUNCT
ijassa-1064	194	16	,	,	PUNCT
ijassa-1064	194	17	0	0	NUM
ijassa-1064	194	18	,	,	PUNCT
ijassa-1064	194	19	0	0	NUM
ijassa-1064	194	20	)	)	PUNCT
ijassa-1064	194	21	is	be	AUX
ijassa-1064	194	22	globally	globally	ADV
ijassa-1064	194	23	asymptotically	asymptotically	ADV
ijassa-1064	194	24	stable	stable	ADJ
ijassa-1064	194	25	.	.	PUNCT
ijassa-1064	195	1	the	the	DET
ijassa-1064	195	2	implication	implication	NOUN
ijassa-1064	195	3	of	of	ADP
ijassa-1064	195	4	theorem	theorem	ADJ
ijassa-1064	195	5	3.3	3.3	NUM
ijassa-1064	195	6	is	be	AUX
ijassa-1064	195	7	that	that	SCONJ
ijassa-1064	195	8	the	the	DET
ijassa-1064	195	9	presence	presence	NOUN
ijassa-1064	195	10	of	of	ADP
ijassa-1064	195	11	disease	disease	NOUN
ijassa-1064	195	12	in	in	ADP
ijassa-1064	195	13	the	the	DET
ijassa-1064	195	14	prey	prey	NOUN
ijassa-1064	195	15	population	population	NOUN
ijassa-1064	195	16	can	can	AUX
ijassa-1064	195	17	be	be	AUX
ijassa-1064	195	18	eliminated	eliminate	VERB
ijassa-1064	195	19	if	if	SCONJ
ijassa-1064	195	20	r02	r02	VERB
ijassa-1064	195	21	<	<	X
ijassa-1064	195	22	1	1	NUM
ijassa-1064	195	23	,	,	PUNCT
ijassa-1064	195	24	irrespective	irrespective	ADV
ijassa-1064	195	25	of	of	ADP
ijassa-1064	195	26	the	the	DET
ijassa-1064	195	27	initial	initial	ADJ
ijassa-1064	195	28	sizes	size	NOUN
ijassa-1064	195	29	of	of	ADP
ijassa-1064	195	30	the	the	DET
ijassa-1064	195	31	infected	infected	ADJ
ijassa-1064	195	32	prey	prey	NOUN
ijassa-1064	195	33	in	in	ADP
ijassa-1064	195	34	the	the	DET
ijassa-1064	195	35	ecosystem	ecosystem	NOUN
ijassa-1064	195	36	.	.	PUNCT
ijassa-1064	196	1	thus	thus	ADV
ijassa-1064	196	2	,	,	PUNCT
ijassa-1064	196	3	every	every	DET
ijassa-1064	196	4	solution	solution	NOUN
ijassa-1064	196	5	of	of	ADP
ijassa-1064	196	6	the	the	DET
ijassa-1064	196	7	prey	prey	NOUN
ijassa-1064	196	8	only	only	ADV
ijassa-1064	196	9	sub	sub	NOUN
ijassa-1064	196	10	-	-	NOUN
ijassa-1064	196	11	model	model	NOUN
ijassa-1064	196	12	will	will	AUX
ijassa-1064	196	13	always	always	ADV
ijassa-1064	196	14	converge	converge	VERB
ijassa-1064	196	15	to	to	ADP
ijassa-1064	196	16	the	the	DET
ijassa-1064	196	17	point	point	NOUN
ijassa-1064	196	18	ẽ1	ẽ1	NOUN
ijassa-1064	196	19	wheneverr02	wheneverr02	NOUN
ijassa-1064	196	20	is	be	AUX
ijassa-1064	196	21	less	less	ADJ
ijassa-1064	196	22	than	than	ADP
ijassa-1064	196	23	unity	unity	NOUN
ijassa-1064	196	24	.	.	PUNCT
ijassa-1064	197	1	this	this	DET
ijassa-1064	197	2	theoretical	theoretical	ADJ
ijassa-1064	197	3	result	result	NOUN
ijassa-1064	197	4	is	be	AUX
ijassa-1064	197	5	demonstrated	demonstrate	VERB
ijassa-1064	197	6	in	in	ADP
ijassa-1064	197	7	figure	figure	NOUN
ijassa-1064	197	8	3.1	3.1	NUM
ijassa-1064	197	9	.	.	PUNCT
ijassa-1064	198	1	3.2.3	3.2.3	X
ijassa-1064	198	2	.	.	PUNCT
ijassa-1064	199	1	stability	stability	NOUN
ijassa-1064	199	2	of	of	ADP
ijassa-1064	199	3	e2	e2	PROPN
ijassa-1064	199	4	considering	consider	VERB
ijassa-1064	199	5	that	that	SCONJ
ijassa-1064	199	6	there	there	PRON
ijassa-1064	199	7	are	be	VERB
ijassa-1064	199	8	only	only	ADV
ijassa-1064	199	9	two	two	NUM
ijassa-1064	199	10	disease	disease	NOUN
ijassa-1064	199	11	classes	class	NOUN
ijassa-1064	199	12	in	in	ADP
ijassa-1064	199	13	the	the	DET
ijassa-1064	199	14	prey	prey	NOUN
ijassa-1064	199	15	-	-	PUNCT
ijassa-1064	199	16	predator	predator	NOUN
ijassa-1064	199	17	system	system	NOUN
ijassa-1064	199	18	(	(	PUNCT
ijassa-1064	199	19	2.1	2.1	NUM
ijassa-1064	199	20	)	)	PUNCT
ijassa-1064	199	21	,	,	PUNCT
ijassa-1064	199	22	then	then	ADV
ijassa-1064	199	23	using	use	VERB
ijassa-1064	199	24	the	the	DET
ijassa-1064	199	25	notations	notation	NOUN
ijassa-1064	199	26	in	in	ADP
ijassa-1064	199	27	the	the	DET
ijassa-1064	199	28	next	next	ADJ
ijassa-1064	199	29	generation	generation	NOUN
ijassa-1064	199	30	operator	operator	NOUN
ijassa-1064	199	31	method	method	NOUN
ijassa-1064	199	32	[	[	X
ijassa-1064	199	33	30	30	NUM
ijassa-1064	199	34	]	]	PUNCT
ijassa-1064	200	1	,	,	PUNCT
ijassa-1064	200	2	it	it	PRON
ijassa-1064	200	3	follows	follow	VERB
ijassa-1064	200	4	that	that	SCONJ
ijassa-1064	200	5	f	f	PROPN
ijassa-1064	201	1	=	=	PRON
ijassa-1064	202	1	[	[	PUNCT
ijassa-1064	202	2	β1µ2	β1µ2	ADJ
ijassa-1064	202	3	c1p1	c1p1	X
ijassa-1064	202	4	0	0	NUM
ijassa-1064	202	5	0	0	NUM
ijassa-1064	202	6	β2	β2	NOUN
ijassa-1064	202	7	p1	p1	PROPN
ijassa-1064	202	8	m1	m1	PROPN
ijassa-1064	202	9	]	]	PUNCT
ijassa-1064	202	10	and	and	CCONJ
ijassa-1064	202	11	v	v	X
ijassa-1064	202	12	=	=	SYM
ijassa-1064	202	13	[	[	PUNCT
ijassa-1064	202	14	p2	p2	PROPN
ijassa-1064	202	15	p1	p1	PROPN
ijassa-1064	202	16	m1	m1	PROPN
ijassa-1064	202	17	+	+	CCONJ
ijassa-1064	202	18	µ1	µ1	PROPN
ijassa-1064	202	19	+	+	X
ijassa-1064	202	20	γ	γ	X
ijassa-1064	202	21	0	0	NUM
ijassa-1064	202	22	0	0	NUM
ijassa-1064	203	1	µ2	µ2	PROPN
ijassa-1064	203	2	]	]	PUNCT
ijassa-1064	203	3	,	,	PUNCT
ijassa-1064	204	1	where	where	SCONJ
ijassa-1064	204	2	m1	m1	PROPN
ijassa-1064	204	3	=	=	SYM
ijassa-1064	204	4	r	r	NOUN
ijassa-1064	204	5	(	(	PUNCT
ijassa-1064	204	6	1−	1−	NUM
ijassa-1064	204	7	µ2	µ2	PROPN
ijassa-1064	204	8	kc1p1	kc1p1	PROPN
ijassa-1064	204	9	)	)	PUNCT
ijassa-1064	204	10	−	−	PROPN
ijassa-1064	204	11	µ1	µ1	PROPN
ijassa-1064	204	12	.	.	PUNCT
ijassa-1064	205	1	hence	hence	ADV
ijassa-1064	205	2	,	,	PUNCT
ijassa-1064	205	3	the	the	DET
ijassa-1064	205	4	basic	basic	ADJ
ijassa-1064	205	5	reproduction	reproduction	NOUN
ijassa-1064	205	6	number	number	NOUN
ijassa-1064	205	7	of	of	ADP
ijassa-1064	205	8	the	the	DET
ijassa-1064	205	9	full	full	ADJ
ijassa-1064	205	10	system	system	NOUN
ijassa-1064	205	11	(	(	PUNCT
ijassa-1064	205	12	2.1	2.1	NUM
ijassa-1064	205	13	)	)	PUNCT
ijassa-1064	205	14	,	,	PUNCT
ijassa-1064	205	15	denoted	denote	VERB
ijassa-1064	205	16	by	by	ADP
ijassa-1064	205	17	r∗	r∗	PROPN
ijassa-1064	205	18	0	0	NUM
ijassa-1064	205	19	,	,	PUNCT
ijassa-1064	205	20	is	be	AUX
ijassa-1064	205	21	given	give	VERB
ijassa-1064	205	22	by	by	ADP
ijassa-1064	205	23	r∗	r∗	PROPN
ijassa-1064	205	24	0	0	NUM
ijassa-1064	206	1	=	=	SYM
ijassa-1064	206	2	ρ(fv	ρ(fv	NUM
ijassa-1064	206	3	−1	−1	NOUN
ijassa-1064	206	4	)	)	PUNCT
ijassa-1064	207	1	=	=	SYM
ijassa-1064	207	2	max	max	PROPN
ijassa-1064	207	3			PUNCT
ijassa-1064	207	4	β1µ2	β1µ2	PROPN
ijassa-1064	207	5	c1p1	c1p1	PUNCT
ijassa-1064	207	6	(	(	PUNCT
ijassa-1064	207	7	p2	p2	PROPN
ijassa-1064	207	8	p1	p1	PROPN
ijassa-1064	207	9	m1	m1	PROPN
ijassa-1064	207	10	+	+	CCONJ
ijassa-1064	207	11	µ1	µ1	PROPN
ijassa-1064	207	12	+	+	X
ijassa-1064	207	13	γ	γ	NOUN
ijassa-1064	207	14	)	)	PUNCT
ijassa-1064	207	15	,	,	PUNCT
ijassa-1064	207	16	β2m1	β2m1	X
ijassa-1064	207	17	p1µ2	p1µ2	ADP
ijassa-1064	207	18			NOUN
ijassa-1064	207	19	.	.	PUNCT
ijassa-1064	208	1	(	(	PUNCT
ijassa-1064	208	2	3.19	3.19	NUM
ijassa-1064	208	3	)	)	PUNCT
ijassa-1064	208	4	copyright	copyright	NOUN
ijassa-1064	208	5	©	©	PROPN
ijassa-1064	208	6	2021	2021	NUM
ijassa-1064	208	7	assa	assa	NOUN
ijassa-1064	208	8	.	.	PUNCT
ijassa-1064	209	1	adv	adv	PROPN
ijassa-1064	209	2	syst	syst	PROPN
ijassa-1064	209	3	sci	sci	PROPN
ijassa-1064	209	4	appl	appl	PROPN
ijassa-1064	209	5	(	(	PUNCT
ijassa-1064	209	6	2021	2021	NUM
ijassa-1064	209	7	)	)	PUNCT
ijassa-1064	209	8	stability	stability	NOUN
ijassa-1064	209	9	analysis	analysis	NOUN
ijassa-1064	209	10	and	and	CCONJ
ijassa-1064	209	11	optimal	optimal	ADJ
ijassa-1064	209	12	measure	measure	NOUN
ijassa-1064	209	13	91	91	NUM
ijassa-1064	209	14	0	0	NUM
ijassa-1064	209	15	5	5	NUM
ijassa-1064	209	16	10	10	NUM
ijassa-1064	209	17	15	15	NUM
ijassa-1064	209	18	0	0	NUM
ijassa-1064	209	19	10	10	NUM
ijassa-1064	209	20	20	20	NUM
ijassa-1064	209	21	30	30	NUM
ijassa-1064	209	22	40	40	NUM
ijassa-1064	209	23	50	50	NUM
ijassa-1064	209	24	60	60	NUM
ijassa-1064	209	25	70	70	NUM
ijassa-1064	209	26	time	time	NOUN
ijassa-1064	209	27	in	in	ADP
ijassa-1064	209	28	fe	fe	X
ijassa-1064	209	29	ct	ct	PROPN
ijassa-1064	209	30	ed	ed	PROPN
ijassa-1064	209	31	p	p	X
ijassa-1064	209	32	re	re	PROPN
ijassa-1064	209	33	y	y	PROPN
ijassa-1064	209	34	fig	fig	PROPN
ijassa-1064	209	35	.	.	PUNCT
ijassa-1064	210	1	3.1	3.1	NUM
ijassa-1064	210	2	.	.	PUNCT
ijassa-1064	210	3	convergence	convergence	NOUN
ijassa-1064	210	4	of	of	ADP
ijassa-1064	210	5	solution	solution	NOUN
ijassa-1064	210	6	trajectories	trajectory	NOUN
ijassa-1064	210	7	of	of	ADP
ijassa-1064	210	8	prey	prey	PROPN
ijassa-1064	210	9	sub	sub	NOUN
ijassa-1064	210	10	-	-	NOUN
ijassa-1064	210	11	model	model	NOUN
ijassa-1064	210	12	to	to	ADP
ijassa-1064	210	13	the	the	DET
ijassa-1064	210	14	equilibrium	equilibrium	NOUN
ijassa-1064	210	15	point	point	NOUN
ijassa-1064	211	1	ẽ1	ẽ1	NOUN
ijassa-1064	211	2	at	at	ADP
ijassa-1064	211	3	different	different	ADJ
ijassa-1064	211	4	initial	initial	ADJ
ijassa-1064	211	5	sizes	size	NOUN
ijassa-1064	211	6	.	.	PUNCT
ijassa-1064	212	1	the	the	DET
ijassa-1064	212	2	parameter	parameter	NOUN
ijassa-1064	212	3	values	value	NOUN
ijassa-1064	212	4	used	use	VERB
ijassa-1064	212	5	are	be	AUX
ijassa-1064	212	6	:	:	PUNCT
ijassa-1064	212	7	r	r	NOUN
ijassa-1064	212	8	=	=	SYM
ijassa-1064	212	9	11.2	11.2	NUM
ijassa-1064	212	10	,	,	PUNCT
ijassa-1064	212	11	β1	β1	PROPN
ijassa-1064	212	12	=	=	PUNCT
ijassa-1064	212	13	0.04	0.04	NUM
ijassa-1064	212	14	,	,	PUNCT
ijassa-1064	212	15	µ1	µ1	PROPN
ijassa-1064	212	16	=	=	SYM
ijassa-1064	212	17	0.85	0.85	NUM
ijassa-1064	212	18	,	,	PUNCT
ijassa-1064	212	19	γ	γ	X
ijassa-1064	212	20	=	=	SYM
ijassa-1064	212	21	0.75	0.75	NUM
ijassa-1064	212	22	,	,	PUNCT
ijassa-1064	212	23	k	k	PROPN
ijassa-1064	212	24	=	=	SYM
ijassa-1064	212	25	30	30	NUM
ijassa-1064	212	26	,	,	PUNCT
ijassa-1064	212	27	so	so	ADV
ijassa-1064	212	28	thatr01	thatr01	NOUN
ijassa-1064	213	1	=	=	NOUN
ijassa-1064	214	1	0.0759	0.0759	NUM
ijassa-1064	214	2	andr02	andr02	NOUN
ijassa-1064	214	3	=	=	SYM
ijassa-1064	214	4	0.6931	0.6931	NUM
ijassa-1064	214	5	,	,	PUNCT
ijassa-1064	214	6	implying	imply	VERB
ijassa-1064	214	7	thatr0	thatr0	PUNCT
ijassa-1064	215	1	=	=	PRON
ijassa-1064	215	2	r02	r02	VERB
ijassa-1064	215	3	<	<	X
ijassa-1064	215	4	1	1	NUM
ijassa-1064	215	5	.	.	PUNCT
ijassa-1064	215	6	therefore	therefore	ADV
ijassa-1064	215	7	,	,	PUNCT
ijassa-1064	215	8	by	by	ADP
ijassa-1064	215	9	theorem	theorem	NOUN
ijassa-1064	215	10	2	2	NUM
ijassa-1064	215	11	of	of	ADP
ijassa-1064	215	12	[	[	X
ijassa-1064	215	13	30	30	NUM
ijassa-1064	215	14	]	]	PUNCT
ijassa-1064	215	15	,	,	PUNCT
ijassa-1064	215	16	the	the	DET
ijassa-1064	215	17	following	follow	VERB
ijassa-1064	215	18	stability	stability	NOUN
ijassa-1064	215	19	result	result	NOUN
ijassa-1064	215	20	is	be	AUX
ijassa-1064	215	21	claimed	claim	VERB
ijassa-1064	215	22	.	.	PUNCT
ijassa-1064	216	1	theorem	theorem	VERB
ijassa-1064	216	2	3.4	3.4	NUM
ijassa-1064	216	3	:	:	PUNCT
ijassa-1064	216	4	the	the	DET
ijassa-1064	216	5	disease	disease	NOUN
ijassa-1064	216	6	-	-	PUNCT
ijassa-1064	216	7	free	free	ADJ
ijassa-1064	216	8	equilibrium	equilibrium	NOUN
ijassa-1064	216	9	point	point	NOUN
ijassa-1064	216	10	e2	e2	PROPN
ijassa-1064	216	11	of	of	ADP
ijassa-1064	216	12	the	the	DET
ijassa-1064	216	13	prey	prey	NOUN
ijassa-1064	216	14	-	-	PUNCT
ijassa-1064	216	15	predator	predator	NOUN
ijassa-1064	216	16	model	model	NOUN
ijassa-1064	216	17	(	(	PUNCT
ijassa-1064	216	18	2.1	2.1	NUM
ijassa-1064	216	19	)	)	PUNCT
ijassa-1064	216	20	,	,	PUNCT
ijassa-1064	216	21	given	give	VERB
ijassa-1064	216	22	by	by	ADP
ijassa-1064	216	23	(	(	PUNCT
ijassa-1064	216	24	3.9	3.9	NUM
ijassa-1064	216	25	)	)	PUNCT
ijassa-1064	216	26	,	,	PUNCT
ijassa-1064	216	27	is	be	AUX
ijassa-1064	216	28	stable	stable	ADJ
ijassa-1064	216	29	provided	provide	VERB
ijassa-1064	216	30	that	that	SCONJ
ijassa-1064	216	31	r∗	r∗	NOUN
ijassa-1064	216	32	0	0	PUNCT
ijassa-1064	216	33	<	<	X
ijassa-1064	216	34	1	1	NUM
ijassa-1064	216	35	.	.	PUNCT
ijassa-1064	217	1	the	the	DET
ijassa-1064	217	2	implication	implication	NOUN
ijassa-1064	217	3	of	of	ADP
ijassa-1064	217	4	theorem	theorem	NOUN
ijassa-1064	217	5	3.4	3.4	NUM
ijassa-1064	217	6	is	be	AUX
ijassa-1064	217	7	that	that	SCONJ
ijassa-1064	217	8	the	the	DET
ijassa-1064	217	9	presence	presence	NOUN
ijassa-1064	217	10	of	of	ADP
ijassa-1064	217	11	few	few	ADJ
ijassa-1064	217	12	species	specie	NOUN
ijassa-1064	217	13	around	around	ADP
ijassa-1064	217	14	the	the	DET
ijassa-1064	217	15	equilibrium	equilibrium	NOUN
ijassa-1064	217	16	point	point	NOUN
ijassa-1064	217	17	e2	e2	PROPN
ijassa-1064	217	18	will	will	AUX
ijassa-1064	217	19	support	support	VERB
ijassa-1064	217	20	the	the	DET
ijassa-1064	217	21	coexistence	coexistence	NOUN
ijassa-1064	217	22	of	of	ADP
ijassa-1064	217	23	both	both	DET
ijassa-1064	217	24	prey	prey	NOUN
ijassa-1064	217	25	and	and	CCONJ
ijassa-1064	217	26	predator	predator	NOUN
ijassa-1064	217	27	species	specie	NOUN
ijassa-1064	217	28	in	in	ADP
ijassa-1064	217	29	a	a	DET
ijassa-1064	217	30	disease	disease	NOUN
ijassa-1064	217	31	-	-	PUNCT
ijassa-1064	217	32	free	free	ADJ
ijassa-1064	217	33	ecosystem	ecosystem	NOUN
ijassa-1064	217	34	whenever	whenever	SCONJ
ijassa-1064	217	35	the	the	DET
ijassa-1064	217	36	basic	basic	ADJ
ijassa-1064	217	37	reproduction	reproduction	NOUN
ijassa-1064	217	38	number	number	NOUN
ijassa-1064	217	39	,	,	PUNCT
ijassa-1064	217	40	r∗	r∗	PROPN
ijassa-1064	217	41	0	0	NUM
ijassa-1064	217	42	,	,	PUNCT
ijassa-1064	217	43	is	be	AUX
ijassa-1064	217	44	less	less	ADJ
ijassa-1064	217	45	than	than	ADP
ijassa-1064	217	46	unity	unity	NOUN
ijassa-1064	217	47	.	.	PUNCT
ijassa-1064	218	1	the	the	DET
ijassa-1064	218	2	global	global	ADJ
ijassa-1064	218	3	dynamics	dynamic	NOUN
ijassa-1064	218	4	of	of	ADP
ijassa-1064	218	5	the	the	DET
ijassa-1064	218	6	prey	prey	NOUN
ijassa-1064	218	7	-	-	PUNCT
ijassa-1064	218	8	predator	predator	NOUN
ijassa-1064	218	9	around	around	ADP
ijassa-1064	218	10	the	the	DET
ijassa-1064	218	11	disease	disease	NOUN
ijassa-1064	218	12	-	-	PUNCT
ijassa-1064	218	13	free	free	ADJ
ijassa-1064	218	14	equilibrium	equilibrium	NOUN
ijassa-1064	218	15	point	point	NOUN
ijassa-1064	218	16	e2	e2	PROPN
ijassa-1064	218	17	is	be	AUX
ijassa-1064	218	18	explored	explore	VERB
ijassa-1064	218	19	next	next	ADV
ijassa-1064	218	20	.	.	PUNCT
ijassa-1064	219	1	theorem	theorem	VERB
ijassa-1064	219	2	3.5	3.5	NUM
ijassa-1064	219	3	:	:	PUNCT
ijassa-1064	219	4	the	the	DET
ijassa-1064	219	5	disease	disease	NOUN
ijassa-1064	219	6	-	-	PUNCT
ijassa-1064	219	7	free	free	ADJ
ijassa-1064	219	8	equilibrium	equilibrium	NOUN
ijassa-1064	219	9	point	point	NOUN
ijassa-1064	219	10	of	of	ADP
ijassa-1064	219	11	the	the	DET
ijassa-1064	219	12	prey	prey	NOUN
ijassa-1064	219	13	-	-	PUNCT
ijassa-1064	219	14	predator	predator	NOUN
ijassa-1064	219	15	model	model	NOUN
ijassa-1064	219	16	(	(	PUNCT
ijassa-1064	219	17	2.1	2.1	NUM
ijassa-1064	219	18	)	)	PUNCT
ijassa-1064	219	19	,	,	PUNCT
ijassa-1064	219	20	given	give	VERB
ijassa-1064	219	21	by	by	ADP
ijassa-1064	219	22	(	(	PUNCT
ijassa-1064	219	23	3.9	3.9	NUM
ijassa-1064	219	24	)	)	PUNCT
ijassa-1064	219	25	,	,	PUNCT
ijassa-1064	219	26	is	be	AUX
ijassa-1064	219	27	globally	globally	ADV
ijassa-1064	219	28	asymptotically	asymptotically	ADV
ijassa-1064	219	29	stable	stable	ADJ
ijassa-1064	219	30	if	if	SCONJ
ijassa-1064	219	31	r∗	r∗	PROPN
ijassa-1064	219	32	0	0	NUM
ijassa-1064	219	33	>	>	X
ijassa-1064	219	34	1	1	X
ijassa-1064	219	35	.	.	X
ijassa-1064	219	36	proof	proof	NOUN
ijassa-1064	219	37	the	the	DET
ijassa-1064	219	38	proof	proof	NOUN
ijassa-1064	219	39	is	be	AUX
ijassa-1064	219	40	based	base	VERB
ijassa-1064	219	41	on	on	ADP
ijassa-1064	219	42	using	use	VERB
ijassa-1064	219	43	the	the	DET
ijassa-1064	219	44	lyapunov	lyapunov	ADJ
ijassa-1064	219	45	function	function	NOUN
ijassa-1064	219	46	defined	define	VERB
ijassa-1064	219	47	by	by	ADP
ijassa-1064	219	48	f	f	PROPN
ijassa-1064	219	49	=	=	SYM
ijassa-1064	219	50	p1	p1	PROPN
ijassa-1064	219	51	p2m1	p2m1	X
ijassa-1064	219	52	+	+	CCONJ
ijassa-1064	219	53	p1(µ1	p1(µ1	NOUN
ijassa-1064	219	54	+	+	CCONJ
ijassa-1064	219	55	γ	γ	X
ijassa-1064	219	56	)	)	PUNCT
ijassa-1064	219	57	xi	xi	VERB
ijassa-1064	220	1	+	+	CCONJ
ijassa-1064	220	2	1	1	NUM
ijassa-1064	220	3	µ2	µ2	PROPN
ijassa-1064	220	4	yi	yi	NOUN
ijassa-1064	220	5	,	,	PUNCT
ijassa-1064	220	6	(	(	PUNCT
ijassa-1064	220	7	3.20	3.20	NUM
ijassa-1064	220	8	)	)	PUNCT
ijassa-1064	220	9	which	which	PRON
ijassa-1064	220	10	when	when	SCONJ
ijassa-1064	220	11	differentiated	differentiate	VERB
ijassa-1064	220	12	with	with	ADP
ijassa-1064	220	13	respect	respect	NOUN
ijassa-1064	220	14	to	to	ADP
ijassa-1064	220	15	time	time	NOUN
ijassa-1064	220	16	,	,	PUNCT
ijassa-1064	220	17	t	t	PROPN
ijassa-1064	220	18	,	,	PUNCT
ijassa-1064	220	19	gives	give	VERB
ijassa-1064	220	20	df	df	PRON
ijassa-1064	220	21	dt	dt	NOUN
ijassa-1064	220	22	=	=	SYM
ijassa-1064	220	23	p1	p1	PROPN
ijassa-1064	220	24	p2m1	p2m1	X
ijassa-1064	220	25	+	+	CCONJ
ijassa-1064	220	26	p1(µ1	p1(µ1	NOUN
ijassa-1064	220	27	+	+	CCONJ
ijassa-1064	220	28	γ	γ	X
ijassa-1064	220	29	)	)	PUNCT
ijassa-1064	221	1	[	[	X
ijassa-1064	221	2	β1xsxi	β1xsxi	NOUN
ijassa-1064	221	3	−	−	X
ijassa-1064	221	4	p2xiys	p2xiys	ADP
ijassa-1064	221	5	−	−	PROPN
ijassa-1064	221	6	p3xiyi	p3xiyi	NOUN
ijassa-1064	221	7	−	−	PROPN
ijassa-1064	221	8	(	(	PUNCT
ijassa-1064	221	9	µ1	µ1	PROPN
ijassa-1064	221	10	+	+	PROPN
ijassa-1064	221	11	γ)xi	γ)xi	PROPN
ijassa-1064	221	12	]	]	X
ijassa-1064	222	1	+	+	CCONJ
ijassa-1064	222	2	1	1	NUM
ijassa-1064	222	3	µ2	µ2	NOUN
ijassa-1064	222	4	(	(	PUNCT
ijassa-1064	222	5	β2ysyi	β2ysyi	X
ijassa-1064	222	6	+	+	CCONJ
ijassa-1064	222	7	c3p3xiyi	c3p3xiyi	NOUN
ijassa-1064	222	8	−	−	NOUN
ijassa-1064	222	9	µ2yi	µ2yi	NOUN
ijassa-1064	222	10	)	)	PUNCT
ijassa-1064	222	11	.	.	PUNCT
ijassa-1064	223	1	copyright	copyright	NOUN
ijassa-1064	223	2	©	©	PROPN
ijassa-1064	223	3	2021	2021	NUM
ijassa-1064	223	4	assa	assa	NOUN
ijassa-1064	223	5	.	.	PUNCT
ijassa-1064	224	1	adv	adv	PROPN
ijassa-1064	224	2	syst	syst	PROPN
ijassa-1064	224	3	sci	sci	PROPN
ijassa-1064	224	4	appl	appl	PROPN
ijassa-1064	224	5	(	(	PUNCT
ijassa-1064	224	6	2021	2021	NUM
ijassa-1064	224	7	)	)	PUNCT
ijassa-1064	224	8	92	92	NUM
ijassa-1064	224	9	j.a	j.a	PROPN
ijassa-1064	224	10	.	.	PROPN
ijassa-1064	224	11	ademosu	ademosu	PROPN
ijassa-1064	224	12	,	,	PUNCT
ijassa-1064	224	13	s.	s.	PROPN
ijassa-1064	224	14	olaniyi	olaniyi	PROPN
ijassa-1064	224	15	,	,	PUNCT
ijassa-1064	224	16	s.o	s.o	PROPN
ijassa-1064	224	17	.	.	PROPN
ijassa-1064	224	18	adewale	adewale	PROPN
ijassa-1064	224	19	since	since	SCONJ
ijassa-1064	224	20	xs	xs	PROPN
ijassa-1064	224	21	≤	≤	PROPN
ijassa-1064	224	22	β1µ2	β1µ2	PUNCT
ijassa-1064	224	23	c1p1	c1p1	VERB
ijassa-1064	224	24	and	and	CCONJ
ijassa-1064	224	25	ys	y	VERB
ijassa-1064	224	26	≤	≤	ADJ
ijassa-1064	224	27	1	1	NUM
ijassa-1064	224	28	p1	p1	NOUN
ijassa-1064	224	29	[	[	PUNCT
ijassa-1064	224	30	r	r	NOUN
ijassa-1064	224	31	(	(	PUNCT
ijassa-1064	224	32	1−	1−	NUM
ijassa-1064	224	33	µ2	µ2	PROPN
ijassa-1064	224	34	kc1p1	kc1p1	PROPN
ijassa-1064	224	35	)	)	PUNCT
ijassa-1064	225	1	−	−	PROPN
ijassa-1064	226	1	µ1	µ1	PROPN
ijassa-1064	226	2	]	]	PUNCT
ijassa-1064	226	3	,	,	PUNCT
ijassa-1064	226	4	noting	note	VERB
ijassa-1064	226	5	that	that	SCONJ
ijassa-1064	226	6	m1	m1	PROPN
ijassa-1064	226	7	=	=	PUNCT
ijassa-1064	226	8	r	r	NOUN
ijassa-1064	226	9	(	(	PUNCT
ijassa-1064	226	10	1−	1−	NUM
ijassa-1064	226	11	µ2	µ2	PROPN
ijassa-1064	226	12	kc1p1	kc1p1	PROPN
ijassa-1064	226	13	)	)	PUNCT
ijassa-1064	226	14	−	−	PROPN
ijassa-1064	226	15	µ1	µ1	PROPN
ijassa-1064	226	16	.	.	PUNCT
ijassa-1064	227	1	therefore	therefore	ADV
ijassa-1064	227	2	,	,	PUNCT
ijassa-1064	227	3	it	it	PRON
ijassa-1064	227	4	follows	follow	VERB
ijassa-1064	227	5	,	,	PUNCT
ijassa-1064	227	6	after	after	ADP
ijassa-1064	227	7	simplification	simplification	NOUN
ijassa-1064	227	8	,	,	PUNCT
ijassa-1064	227	9	that	that	SCONJ
ijassa-1064	227	10	df	df	PROPN
ijassa-1064	227	11	dt	dt	NOUN
ijassa-1064	227	12	≤	≤	PROPN
ijassa-1064	227	13			PROPN
ijassa-1064	227	14	β1µ2	β1µ2	PUNCT
ijassa-1064	227	15	c1p1	c1p1	PUNCT
ijassa-1064	227	16	(	(	PUNCT
ijassa-1064	227	17	p2	p2	PROPN
ijassa-1064	227	18	p1	p1	PROPN
ijassa-1064	227	19	m1	m1	PROPN
ijassa-1064	227	20	+	+	CCONJ
ijassa-1064	227	21	µ1	µ1	PROPN
ijassa-1064	227	22	+	+	X
ijassa-1064	227	23	γ	γ	X
ijassa-1064	227	24	)	)	PUNCT
ijassa-1064	227	25	−	−	PROPN
ijassa-1064	227	26	1	1	NUM
ijassa-1064	227	27	xi	xi	NOUN
ijassa-1064	227	28	−	−	NOUN
ijassa-1064	227	29	p1p3	p1p3	ADP
ijassa-1064	227	30	p2m1	p2m1	X
ijassa-1064	227	31	+	+	CCONJ
ijassa-1064	227	32	p1(µ1	p1(µ1	NOUN
ijassa-1064	227	33	+	+	CCONJ
ijassa-1064	227	34	γ	γ	X
ijassa-1064	227	35	)	)	PUNCT
ijassa-1064	227	36	xiyi	xiyi	PROPN
ijassa-1064	228	1	+	+	CCONJ
ijassa-1064	228	2	[	[	PUNCT
ijassa-1064	228	3	β2m1	β2m1	X
ijassa-1064	228	4	p1µ2	p1µ2	VERB
ijassa-1064	228	5	−	−	PROPN
ijassa-1064	228	6	1	1	X
ijassa-1064	228	7	]	]	PUNCT
ijassa-1064	228	8	yi	yi	NOUN
ijassa-1064	228	9	+	+	CCONJ
ijassa-1064	228	10	1	1	NUM
ijassa-1064	228	11	µ2	µ2	PROPN
ijassa-1064	228	12	(	(	PUNCT
ijassa-1064	228	13	c3p3xiyi	c3p3xiyi	PROPN
ijassa-1064	228	14	)	)	PUNCT
ijassa-1064	228	15	≤	≤	NOUN
ijassa-1064	228	16	max	max	NUM
ijassa-1064	228	17			PUNCT
ijassa-1064	228	18	β1µ2	β1µ2	VERB
ijassa-1064	228	19	c1p1	c1p1	PUNCT
ijassa-1064	228	20	(	(	PUNCT
ijassa-1064	228	21	p2	p2	PROPN
ijassa-1064	228	22	p1	p1	PROPN
ijassa-1064	228	23	m1	m1	PROPN
ijassa-1064	228	24	+	+	CCONJ
ijassa-1064	228	25	µ1	µ1	PROPN
ijassa-1064	228	26	+	+	X
ijassa-1064	228	27	γ	γ	NOUN
ijassa-1064	228	28	)	)	PUNCT
ijassa-1064	228	29	,	,	PUNCT
ijassa-1064	228	30	β2m1	β2m1	X
ijassa-1064	228	31	p1µ2	p1µ2	PUNCT
ijassa-1064	228	32	−	−	PROPN
ijassa-1064	228	33	1	1	NUM
ijassa-1064	228	34			NOUN
ijassa-1064	228	35	(	(	PUNCT
ijassa-1064	228	36	xi	xi	X
ijassa-1064	228	37	+	+	CCONJ
ijassa-1064	228	38	yi	yi	PROPN
ijassa-1064	228	39	)	)	PUNCT
ijassa-1064	228	40	−	−	PROPN
ijassa-1064	229	1	[	[	PUNCT
ijassa-1064	229	2	p1	p1	NOUN
ijassa-1064	229	3	p2m1	p2m1	X
ijassa-1064	229	4	+	+	CCONJ
ijassa-1064	229	5	p1(µ1	p1(µ1	NOUN
ijassa-1064	229	6	+	+	CCONJ
ijassa-1064	229	7	γ	γ	X
ijassa-1064	229	8	)	)	PUNCT
ijassa-1064	229	9	−	−	PROPN
ijassa-1064	229	10	c3	c3	PROPN
ijassa-1064	229	11	µ2	µ2	PROPN
ijassa-1064	229	12	]	]	PUNCT
ijassa-1064	229	13	p3xiyi	p3xiyi	X
ijassa-1064	229	14	=	=	PUNCT
ijassa-1064	230	1	[	[	X
ijassa-1064	230	2	r∗	r∗	NOUN
ijassa-1064	230	3	0	0	NUM
ijassa-1064	230	4	−	−	NUM
ijassa-1064	230	5	1](xi	1](xi	NUM
ijassa-1064	230	6	+	+	NUM
ijassa-1064	230	7	yi)−	yi)−	NOUN
ijassa-1064	230	8	[	[	PUNCT
ijassa-1064	230	9	p1	p1	NOUN
ijassa-1064	230	10	p2m1	p2m1	X
ijassa-1064	230	11	+	+	CCONJ
ijassa-1064	230	12	p1(µ1	p1(µ1	NOUN
ijassa-1064	230	13	+	+	CCONJ
ijassa-1064	230	14	γ	γ	X
ijassa-1064	230	15	)	)	PUNCT
ijassa-1064	230	16	−	−	PROPN
ijassa-1064	231	1	c3	c3	PROPN
ijassa-1064	231	2	µ2	µ2	PROPN
ijassa-1064	231	3	]	]	PUNCT
ijassa-1064	231	4	p3xiyi	p3xiyi	PROPN
ijassa-1064	231	5	.	.	PUNCT
ijassa-1064	232	1	consequently	consequently	ADV
ijassa-1064	232	2	,	,	PUNCT
ijassa-1064	232	3	df	df	PROPN
ijassa-1064	232	4	/	/	SYM
ijassa-1064	232	5	dt	dt	NOUN
ijassa-1064	232	6	≤	≤	NUM
ijassa-1064	232	7	0	0	PUNCT
ijassa-1064	233	1	if	if	SCONJ
ijassa-1064	233	2	r∗	r∗	PROPN
ijassa-1064	233	3	0	0	PUNCT
ijassa-1064	233	4	<	<	X
ijassa-1064	233	5	1	1	NUM
ijassa-1064	233	6	and	and	CCONJ
ijassa-1064	233	7	xi	xi	X
ijassa-1064	233	8	=	=	NOUN
ijassa-1064	233	9	0	0	NUM
ijassa-1064	233	10	or	or	CCONJ
ijassa-1064	233	11	yi	yi	ADJ
ijassa-1064	233	12	=	=	SYM
ijassa-1064	233	13	0	0	PROPN
ijassa-1064	233	14	.	.	PUNCT
ijassa-1064	234	1	thus	thus	ADV
ijassa-1064	234	2	,	,	PUNCT
ijassa-1064	234	3	xs	xs	PROPN
ijassa-1064	234	4	→	→	SYM
ijassa-1064	234	5	µ2/(c1p1	µ2/(c1p1	PROPN
ijassa-1064	234	6	)	)	PUNCT
ijassa-1064	234	7	,	,	PUNCT
ijassa-1064	234	8	xr	xr	PROPN
ijassa-1064	234	9	→	→	SYM
ijassa-1064	234	10	0	0	NUM
ijassa-1064	234	11	and	and	CCONJ
ijassa-1064	234	12	ys	ys	PROPN
ijassa-1064	234	13	→	→	SYM
ijassa-1064	234	14	m1	m1	PROPN
ijassa-1064	234	15	/	/	SYM
ijassa-1064	234	16	p1	p1	PROPN
ijassa-1064	234	17	as	as	ADV
ijassa-1064	234	18	both	both	PRON
ijassa-1064	234	19	xi	xi	ADP
ijassa-1064	234	20	→	→	SYM
ijassa-1064	234	21	0	0	NUM
ijassa-1064	234	22	and	and	CCONJ
ijassa-1064	234	23	yi	yi	NOUN
ijassa-1064	234	24	→	→	SYM
ijassa-1064	234	25	0	0	X
ijassa-1064	234	26	.	.	PUNCT
ijassa-1064	235	1	therefore	therefore	ADV
ijassa-1064	235	2	,	,	PUNCT
ijassa-1064	235	3	by	by	ADP
ijassa-1064	235	4	lasalle	lasalle	PROPN
ijassa-1064	235	5	’s	’s	PART
ijassa-1064	235	6	invariance	invariance	NOUN
ijassa-1064	235	7	principle	principle	NOUN
ijassa-1064	235	8	[	[	X
ijassa-1064	235	9	19	19	NUM
ijassa-1064	235	10	]	]	PUNCT
ijassa-1064	235	11	,	,	PUNCT
ijassa-1064	235	12	the	the	DET
ijassa-1064	235	13	disease	disease	NOUN
ijassa-1064	235	14	-	-	PUNCT
ijassa-1064	235	15	free	free	ADJ
ijassa-1064	235	16	equilibrium	equilibrium	NOUN
ijassa-1064	235	17	point	point	NOUN
ijassa-1064	235	18	e2	e2	PROPN
ijassa-1064	235	19	is	be	AUX
ijassa-1064	235	20	globally	globally	ADV
ijassa-1064	235	21	asymptotically	asymptotically	ADV
ijassa-1064	235	22	stable	stable	ADJ
ijassa-1064	235	23	.	.	PUNCT
ijassa-1064	236	1	the	the	DET
ijassa-1064	236	2	implication	implication	NOUN
ijassa-1064	236	3	of	of	ADP
ijassa-1064	236	4	theorem	theorem	ADJ
ijassa-1064	236	5	3.5	3.5	NUM
ijassa-1064	236	6	is	be	AUX
ijassa-1064	236	7	that	that	DET
ijassa-1064	236	8	elimination	elimination	NOUN
ijassa-1064	236	9	of	of	ADP
ijassa-1064	236	10	disease	disease	NOUN
ijassa-1064	236	11	in	in	ADP
ijassa-1064	236	12	the	the	DET
ijassa-1064	236	13	ecosystem	ecosystem	NOUN
ijassa-1064	236	14	is	be	AUX
ijassa-1064	236	15	independent	independent	ADJ
ijassa-1064	236	16	of	of	ADP
ijassa-1064	236	17	initial	initial	ADJ
ijassa-1064	236	18	sizes	size	NOUN
ijassa-1064	236	19	of	of	ADP
ijassa-1064	236	20	infected	infected	ADJ
ijassa-1064	236	21	prey	prey	NOUN
ijassa-1064	236	22	and	and	CCONJ
ijassa-1064	236	23	infected	infect	VERB
ijassa-1064	236	24	predator	predator	NOUN
ijassa-1064	236	25	whenever	whenever	SCONJ
ijassa-1064	236	26	r∗	r∗	PROPN
ijassa-1064	236	27	0	0	PUNCT
ijassa-1064	236	28	<	<	X
ijassa-1064	236	29	1	1	NUM
ijassa-1064	236	30	.	.	PUNCT
ijassa-1064	237	1	this	this	DET
ijassa-1064	237	2	result	result	NOUN
ijassa-1064	237	3	is	be	AUX
ijassa-1064	237	4	demonstrated	demonstrate	VERB
ijassa-1064	237	5	in	in	ADP
ijassa-1064	237	6	figure	figure	NOUN
ijassa-1064	237	7	3.2(a	3.2(a	NUM
ijassa-1064	237	8	)	)	PUNCT
ijassa-1064	237	9	for	for	ADP
ijassa-1064	237	10	infected	infected	ADJ
ijassa-1064	237	11	prey	prey	NOUN
ijassa-1064	237	12	and	and	CCONJ
ijassa-1064	237	13	figure	figure	VERB
ijassa-1064	237	14	3.2(b	3.2(b	NUM
ijassa-1064	237	15	)	)	PUNCT
ijassa-1064	237	16	for	for	ADP
ijassa-1064	237	17	infected	infect	VERB
ijassa-1064	237	18	predator	predator	NOUN
ijassa-1064	237	19	population	population	NOUN
ijassa-1064	237	20	,	,	PUNCT
ijassa-1064	237	21	where	where	SCONJ
ijassa-1064	237	22	every	every	DET
ijassa-1064	237	23	solution	solution	NOUN
ijassa-1064	237	24	trajectory	trajectory	NOUN
ijassa-1064	237	25	converges	converge	VERB
ijassa-1064	237	26	to	to	ADP
ijassa-1064	237	27	the	the	DET
ijassa-1064	237	28	disease	disease	NOUN
ijassa-1064	237	29	-	-	PUNCT
ijassa-1064	237	30	free	free	ADJ
ijassa-1064	237	31	equilibrium	equilibrium	NOUN
ijassa-1064	237	32	.	.	PUNCT
ijassa-1064	238	1	0	0	NUM
ijassa-1064	239	1	5	5	NUM
ijassa-1064	239	2	10	10	NUM
ijassa-1064	239	3	15	15	NUM
ijassa-1064	239	4	20	20	NUM
ijassa-1064	239	5	25	25	NUM
ijassa-1064	239	6	30	30	NUM
ijassa-1064	239	7	35	35	NUM
ijassa-1064	239	8	40	40	NUM
ijassa-1064	239	9	0	0	NUM
ijassa-1064	239	10	1	1	NUM
ijassa-1064	239	11	2	2	NUM
ijassa-1064	239	12	3	3	NUM
ijassa-1064	239	13	4	4	NUM
ijassa-1064	239	14	5	5	NUM
ijassa-1064	239	15	6	6	NUM
ijassa-1064	239	16	7	7	NUM
ijassa-1064	239	17	8	8	NUM
ijassa-1064	239	18	9	9	NUM
ijassa-1064	239	19	10	10	NUM
ijassa-1064	239	20	time	time	NOUN
ijassa-1064	239	21	in	in	ADP
ijassa-1064	239	22	fe	fe	X
ijassa-1064	239	23	c	c	X
ijassa-1064	239	24	te	te	PROPN
ijassa-1064	239	25	d	d	X
ijassa-1064	239	26	p	p	X
ijassa-1064	239	27	re	re	ADP
ijassa-1064	239	28	y	y	PROPN
ijassa-1064	239	29	(	(	PUNCT
ijassa-1064	239	30	a	a	PROPN
ijassa-1064	239	31	)	)	PUNCT
ijassa-1064	239	32	0	0	NUM
ijassa-1064	239	33	5	5	NUM
ijassa-1064	239	34	10	10	NUM
ijassa-1064	239	35	15	15	NUM
ijassa-1064	239	36	0	0	NUM
ijassa-1064	239	37	5	5	NUM
ijassa-1064	239	38	10	10	NUM
ijassa-1064	239	39	15	15	NUM
ijassa-1064	239	40	20	20	NUM
ijassa-1064	239	41	25	25	NUM
ijassa-1064	239	42	time	time	NOUN
ijassa-1064	239	43	in	in	ADP
ijassa-1064	239	44	fe	fe	X
ijassa-1064	239	45	c	c	X
ijassa-1064	239	46	te	te	PROPN
ijassa-1064	239	47	d	d	X
ijassa-1064	239	48	p	p	X
ijassa-1064	239	49	re	re	ADP
ijassa-1064	239	50	d	d	NOUN
ijassa-1064	239	51	a	a	PRON
ijassa-1064	239	52	to	to	ADP
ijassa-1064	239	53	r	r	NOUN
ijassa-1064	239	54	(	(	PUNCT
ijassa-1064	239	55	b	b	NOUN
ijassa-1064	239	56	)	)	PUNCT
ijassa-1064	239	57	fig	fig	NOUN
ijassa-1064	239	58	.	.	PUNCT
ijassa-1064	240	1	3.2	3.2	NUM
ijassa-1064	240	2	.	.	PUNCT
ijassa-1064	241	1	convergence	convergence	NOUN
ijassa-1064	241	2	of	of	ADP
ijassa-1064	241	3	solution	solution	NOUN
ijassa-1064	241	4	trajectories	trajectory	NOUN
ijassa-1064	241	5	of	of	ADP
ijassa-1064	241	6	prey	prey	NOUN
ijassa-1064	241	7	-	-	PUNCT
ijassa-1064	241	8	predator	predator	NOUN
ijassa-1064	241	9	model	model	NOUN
ijassa-1064	241	10	to	to	ADP
ijassa-1064	241	11	the	the	DET
ijassa-1064	241	12	disease	disease	NOUN
ijassa-1064	241	13	-	-	PUNCT
ijassa-1064	241	14	free	free	ADJ
ijassa-1064	241	15	equilibrium	equilibrium	NOUN
ijassa-1064	241	16	point	point	NOUN
ijassa-1064	241	17	e2	e2	PROPN
ijassa-1064	241	18	at	at	ADP
ijassa-1064	241	19	different	different	ADJ
ijassa-1064	241	20	initial	initial	ADJ
ijassa-1064	241	21	sizes	size	NOUN
ijassa-1064	241	22	.	.	PUNCT
ijassa-1064	242	1	the	the	DET
ijassa-1064	242	2	parameter	parameter	NOUN
ijassa-1064	242	3	values	value	NOUN
ijassa-1064	242	4	used	use	VERB
ijassa-1064	242	5	are	be	AUX
ijassa-1064	242	6	:	:	PUNCT
ijassa-1064	242	7	mu1	mu1	X
ijassa-1064	242	8	=	=	SYM
ijassa-1064	242	9	0.8	0.8	NUM
ijassa-1064	242	10	,	,	PUNCT
ijassa-1064	242	11	r	r	NOUN
ijassa-1064	242	12	=	=	SYM
ijassa-1064	242	13	3	3	NUM
ijassa-1064	242	14	,	,	PUNCT
ijassa-1064	242	15	β1	β1	PROPN
ijassa-1064	242	16	=	=	PUNCT
ijassa-1064	242	17	0.4	0.4	NUM
ijassa-1064	242	18	,	,	PUNCT
ijassa-1064	242	19	p1	p1	NOUN
ijassa-1064	242	20	=	=	SYM
ijassa-1064	242	21	1.0	1.0	NUM
ijassa-1064	242	22	,	,	PUNCT
ijassa-1064	242	23	γ	γ	X
ijassa-1064	242	24	=	=	SYM
ijassa-1064	242	25	0.35	0.35	NUM
ijassa-1064	242	26	,	,	PUNCT
ijassa-1064	242	27	p2	p2	X
ijassa-1064	242	28	=	=	SYM
ijassa-1064	242	29	0.2	0.2	NUM
ijassa-1064	242	30	,	,	PUNCT
ijassa-1064	242	31	p3	p3	PROPN
ijassa-1064	242	32	=	=	PUNCT
ijassa-1064	242	33	1.0	1.0	NUM
ijassa-1064	242	34	,	,	PUNCT
ijassa-1064	242	35	µ2	µ2	PROPN
ijassa-1064	242	36	=	=	PROPN
ijassa-1064	242	37	0.85	0.85	NUM
ijassa-1064	242	38	,	,	PUNCT
ijassa-1064	242	39	k	k	PROPN
ijassa-1064	242	40	=	=	SYM
ijassa-1064	242	41	30	30	NUM
ijassa-1064	242	42	,	,	PUNCT
ijassa-1064	242	43	β2	β2	NOUN
ijassa-1064	242	44	=	=	NOUN
ijassa-1064	242	45	0.3	0.3	NUM
ijassa-1064	242	46	,	,	PUNCT
ijassa-1064	242	47	c1	c1	NOUN
ijassa-1064	242	48	=	=	PROPN
ijassa-1064	242	49	0.25	0.25	NUM
ijassa-1064	242	50	,	,	PUNCT
ijassa-1064	242	51	c2	c2	PROPN
ijassa-1064	242	52	=	=	PUNCT
ijassa-1064	242	53	0.25	0.25	NUM
ijassa-1064	242	54	,	,	PUNCT
ijassa-1064	242	55	c3	c3	NOUN
ijassa-1064	242	56	=	=	PUNCT
ijassa-1064	242	57	0.15	0.15	NUM
ijassa-1064	242	58	,	,	PUNCT
ijassa-1064	242	59	so	so	SCONJ
ijassa-1064	242	60	that	that	PRON
ijassa-1064	242	61	r∗	r∗	VERB
ijassa-1064	242	62	0	0	NUM
ijassa-1064	243	1	=	=	SYM
ijassa-1064	243	2	0.6565	0.6565	NUM
ijassa-1064	243	3	<	<	X
ijassa-1064	243	4	1	1	NUM
ijassa-1064	243	5	.	.	PUNCT
ijassa-1064	243	6	copyright	copyright	NOUN
ijassa-1064	243	7	©	©	PROPN
ijassa-1064	243	8	2021	2021	NUM
ijassa-1064	243	9	assa	assa	NOUN
ijassa-1064	243	10	.	.	PUNCT
ijassa-1064	244	1	adv	adv	PROPN
ijassa-1064	244	2	syst	syst	PROPN
ijassa-1064	244	3	sci	sci	PROPN
ijassa-1064	244	4	appl	appl	PROPN
ijassa-1064	244	5	(	(	PUNCT
ijassa-1064	244	6	2021	2021	NUM
ijassa-1064	244	7	)	)	PUNCT
ijassa-1064	244	8	stability	stability	NOUN
ijassa-1064	244	9	analysis	analysis	NOUN
ijassa-1064	244	10	and	and	CCONJ
ijassa-1064	244	11	optimal	optimal	ADJ
ijassa-1064	244	12	measure	measure	NOUN
ijassa-1064	244	13	93	93	NUM
ijassa-1064	244	14	3.2.4	3.2.4	NUM
ijassa-1064	244	15	.	.	PUNCT
ijassa-1064	245	1	stability	stability	NOUN
ijassa-1064	245	2	of	of	ADP
ijassa-1064	245	3	e3	e3	NOUN
ijassa-1064	245	4	evaluating	evaluate	VERB
ijassa-1064	245	5	the	the	DET
ijassa-1064	245	6	jacobian	jacobian	ADJ
ijassa-1064	245	7	matrix	matrix	NOUN
ijassa-1064	245	8	(	(	PUNCT
ijassa-1064	245	9	2.1	2.1	NUM
ijassa-1064	245	10	)	)	PUNCT
ijassa-1064	245	11	at	at	ADP
ijassa-1064	245	12	predator	predator	NOUN
ijassa-1064	245	13	-	-	PUNCT
ijassa-1064	245	14	free	free	ADJ
ijassa-1064	245	15	equilibriume3	equilibriume3	NOUN
ijassa-1064	245	16	leads	lead	VERB
ijassa-1064	245	17	to	to	ADP
ijassa-1064	245	18	the	the	DET
ijassa-1064	245	19	characteristic	characteristic	ADJ
ijassa-1064	245	20	equation	equation	NOUN
ijassa-1064	245	21	|j(e3)−	|j(e3)−	NOUN
ijassa-1064	245	22	λi5|	λi5|	PUNCT
ijassa-1064	246	1	=	=	PUNCT
ijassa-1064	246	2	0	0	X
ijassa-1064	246	3	.	.	PUNCT
ijassa-1064	247	1	thus	thus	ADV
ijassa-1064	247	2	,	,	PUNCT
ijassa-1064	247	3	the	the	DET
ijassa-1064	247	4	following	follow	VERB
ijassa-1064	247	5	eigenvalues	eigenvalue	NOUN
ijassa-1064	247	6	are	be	AUX
ijassa-1064	247	7	obtained	obtain	VERB
ijassa-1064	247	8	:	:	PUNCT
ijassa-1064	247	9	λ1	λ1	ADJ
ijassa-1064	247	10	=	=	SYM
ijassa-1064	247	11	−µ1	−µ1	PROPN
ijassa-1064	247	12	λ2	λ2	NOUN
ijassa-1064	247	13	=	=	SYM
ijassa-1064	247	14	−µ2	−µ2	PROPN
ijassa-1064	247	15	,	,	PUNCT
ijassa-1064	247	16	λ3	λ3	PROPN
ijassa-1064	247	17	=	=	NOUN
ijassa-1064	247	18	c1p1	c1p1	PROPN
ijassa-1064	247	19	β1	β1	PROPN
ijassa-1064	247	20	(	(	PUNCT
ijassa-1064	247	21	µ1	µ1	PROPN
ijassa-1064	247	22	+	+	CCONJ
ijassa-1064	247	23	γ)−	γ)−	PROPN
ijassa-1064	247	24	c2p2	c2p2	VERB
ijassa-1064	247	25	β1	β1	PROPN
ijassa-1064	247	26	(	(	PUNCT
ijassa-1064	247	27	m2	m2	PROPN
ijassa-1064	247	28	+	+	PROPN
ijassa-1064	247	29	µ2	µ2	PROPN
ijassa-1064	247	30	)	)	PUNCT
ijassa-1064	247	31	,	,	PUNCT
ijassa-1064	247	32	λ4	λ4	PROPN
ijassa-1064	247	33	=	=	SYM
ijassa-1064	247	34	−r	−r	ADJ
ijassa-1064	247	35	2	2	NUM
ijassa-1064	247	36	(	(	PUNCT
ijassa-1064	247	37	µ1	µ1	PROPN
ijassa-1064	247	38	+	+	X
ijassa-1064	247	39	γ	γ	X
ijassa-1064	247	40	kβ1	kβ1	NOUN
ijassa-1064	247	41	)	)	PUNCT
ijassa-1064	248	1	+	+	CCONJ
ijassa-1064	248	2	1	1	NUM
ijassa-1064	248	3	2	2	NUM
ijassa-1064	248	4	√	√	NOUN
ijassa-1064	248	5	r2	r2	PROPN
ijassa-1064	248	6	(	(	PUNCT
ijassa-1064	248	7	µ1	µ1	PROPN
ijassa-1064	248	8	+	+	X
ijassa-1064	248	9	γ	γ	X
ijassa-1064	248	10	kβ1	kβ1	X
ijassa-1064	248	11	)	)	PUNCT
ijassa-1064	248	12	2	2	NUM
ijassa-1064	248	13	+	+	NUM
ijassa-1064	248	14	4m2(µ1	4m2(µ1	NUM
ijassa-1064	248	15	+	+	CCONJ
ijassa-1064	248	16	γ	γ	NOUN
ijassa-1064	248	17	)	)	PUNCT
ijassa-1064	248	18	,	,	PUNCT
ijassa-1064	248	19	λ5	λ5	NOUN
ijassa-1064	248	20	=	=	PUNCT
ijassa-1064	248	21	−r	−r	ADJ
ijassa-1064	248	22	2	2	NUM
ijassa-1064	248	23	(	(	PUNCT
ijassa-1064	248	24	µ1	µ1	PROPN
ijassa-1064	248	25	+	+	X
ijassa-1064	248	26	γ	γ	X
ijassa-1064	248	27	kβ1	kβ1	NOUN
ijassa-1064	248	28	)	)	PUNCT
ijassa-1064	248	29	−	−	PROPN
ijassa-1064	248	30	1	1	NUM
ijassa-1064	248	31	2	2	NUM
ijassa-1064	248	32	√	√	NOUN
ijassa-1064	248	33	r2	r2	PROPN
ijassa-1064	248	34	(	(	PUNCT
ijassa-1064	248	35	µ1	µ1	PROPN
ijassa-1064	248	36	+	+	X
ijassa-1064	248	37	γ	γ	X
ijassa-1064	248	38	kβ1	kβ1	X
ijassa-1064	248	39	)	)	PUNCT
ijassa-1064	248	40	2	2	NUM
ijassa-1064	248	41	+	+	NUM
ijassa-1064	248	42	4m2(µ1	4m2(µ1	NUM
ijassa-1064	248	43	+	+	CCONJ
ijassa-1064	248	44	γ	γ	NOUN
ijassa-1064	248	45	)	)	PUNCT
ijassa-1064	248	46	,	,	PUNCT
ijassa-1064	248	47	where	where	SCONJ
ijassa-1064	248	48	m2	m2	PROPN
ijassa-1064	248	49	=	=	PROPN
ijassa-1064	248	50	r	r	PROPN
ijassa-1064	248	51	(	(	PUNCT
ijassa-1064	248	52	1−	1−	NUM
ijassa-1064	248	53	µ1+γ	µ1+γ	PROPN
ijassa-1064	248	54	kβ1	kβ1	NOUN
ijassa-1064	248	55	)	)	PUNCT
ijassa-1064	248	56	−	−	PROPN
ijassa-1064	249	1	µ1	µ1	PROPN
ijassa-1064	249	2	.	.	PUNCT
ijassa-1064	250	1	the	the	DET
ijassa-1064	250	2	stability	stability	NOUN
ijassa-1064	250	3	of	of	ADP
ijassa-1064	250	4	e3	e3	NOUN
ijassa-1064	250	5	is	be	AUX
ijassa-1064	250	6	theorized	theorize	VERB
ijassa-1064	250	7	as	as	SCONJ
ijassa-1064	250	8	follows	follow	NOUN
ijassa-1064	250	9	theorem	theorem	VERB
ijassa-1064	250	10	3.6	3.6	NUM
ijassa-1064	250	11	:	:	PUNCT
ijassa-1064	250	12	the	the	DET
ijassa-1064	250	13	predator	predator	NOUN
ijassa-1064	250	14	-	-	PUNCT
ijassa-1064	250	15	free	free	ADJ
ijassa-1064	250	16	equilibrium	equilibrium	NOUN
ijassa-1064	250	17	point	point	NOUN
ijassa-1064	250	18	e3	e3	NOUN
ijassa-1064	250	19	of	of	ADP
ijassa-1064	250	20	the	the	DET
ijassa-1064	250	21	prey	prey	NOUN
ijassa-1064	250	22	-	-	PUNCT
ijassa-1064	250	23	predator	predator	NOUN
ijassa-1064	250	24	model	model	NOUN
ijassa-1064	250	25	(	(	PUNCT
ijassa-1064	250	26	2.1	2.1	NUM
ijassa-1064	250	27	)	)	PUNCT
ijassa-1064	250	28	,	,	PUNCT
ijassa-1064	250	29	given	give	VERB
ijassa-1064	250	30	by	by	ADP
ijassa-1064	250	31	(	(	PUNCT
ijassa-1064	250	32	3.10	3.10	NUM
ijassa-1064	250	33	)	)	PUNCT
ijassa-1064	250	34	,	,	PUNCT
ijassa-1064	250	35	is	be	AUX
ijassa-1064	250	36	stable	stable	ADJ
ijassa-1064	250	37	if	if	SCONJ
ijassa-1064	250	38	the	the	DET
ijassa-1064	250	39	following	follow	VERB
ijassa-1064	250	40	conditions	condition	NOUN
ijassa-1064	250	41	hold	hold	VERB
ijassa-1064	250	42	c1p1(µ1	c1p1(µ1	NOUN
ijassa-1064	251	1	+	+	CCONJ
ijassa-1064	251	2	γ	γ	X
ijassa-1064	251	3	)	)	PUNCT
ijassa-1064	251	4	<	<	X
ijassa-1064	251	5	c2p2(m2	c2p2(m2	X
ijassa-1064	251	6	+	+	X
ijassa-1064	251	7	µ2	µ2	ADJ
ijassa-1064	251	8	)	)	PUNCT
ijassa-1064	251	9	and	and	CCONJ
ijassa-1064	251	10	√	√	NUM
ijassa-1064	251	11	r2	r2	PROPN
ijassa-1064	251	12	(	(	PUNCT
ijassa-1064	251	13	µ1	µ1	PROPN
ijassa-1064	251	14	+	+	X
ijassa-1064	251	15	γ	γ	X
ijassa-1064	251	16	kβ1	kβ1	X
ijassa-1064	251	17	)	)	PUNCT
ijassa-1064	251	18	2	2	NUM
ijassa-1064	252	1	+	+	NUM
ijassa-1064	252	2	4m2(µ1	4m2(µ1	NUM
ijassa-1064	252	3	+	+	CCONJ
ijassa-1064	252	4	γ	γ	X
ijassa-1064	252	5	)	)	PUNCT
ijassa-1064	252	6	<	<	X
ijassa-1064	252	7	r	r	NOUN
ijassa-1064	252	8	(	(	PUNCT
ijassa-1064	252	9	µ1	µ1	PROPN
ijassa-1064	252	10	+	+	X
ijassa-1064	252	11	γ	γ	X
ijassa-1064	252	12	kβ1	kβ1	NOUN
ijassa-1064	252	13	)	)	PUNCT
ijassa-1064	252	14	.	.	PUNCT
ijassa-1064	253	1	this	this	DET
ijassa-1064	253	2	result	result	NOUN
ijassa-1064	253	3	implies	imply	VERB
ijassa-1064	253	4	that	that	SCONJ
ijassa-1064	253	5	stable	stable	ADJ
ijassa-1064	253	6	e3	e3	NOUN
ijassa-1064	253	7	will	will	AUX
ijassa-1064	253	8	not	not	PART
ijassa-1064	253	9	be	be	AUX
ijassa-1064	253	10	able	able	ADJ
ijassa-1064	253	11	to	to	PART
ijassa-1064	253	12	support	support	VERB
ijassa-1064	253	13	the	the	DET
ijassa-1064	253	14	coexistence	coexistence	NOUN
ijassa-1064	253	15	of	of	ADP
ijassa-1064	253	16	both	both	DET
ijassa-1064	253	17	prey	prey	NOUN
ijassa-1064	253	18	and	and	CCONJ
ijassa-1064	253	19	predator	predator	NOUN
ijassa-1064	253	20	populations	population	NOUN
ijassa-1064	253	21	.	.	PUNCT
ijassa-1064	254	1	the	the	DET
ijassa-1064	254	2	presence	presence	NOUN
ijassa-1064	254	3	of	of	ADP
ijassa-1064	254	4	few	few	ADJ
ijassa-1064	254	5	species	specie	NOUN
ijassa-1064	254	6	around	around	ADP
ijassa-1064	254	7	the	the	DET
ijassa-1064	254	8	predator	predator	NOUN
ijassa-1064	254	9	-	-	PUNCT
ijassa-1064	254	10	free	free	ADJ
ijassa-1064	254	11	equilibrium	equilibrium	NOUN
ijassa-1064	254	12	point	point	NOUN
ijassa-1064	254	13	e3	e3	NOUN
ijassa-1064	254	14	will	will	AUX
ijassa-1064	254	15	make	make	VERB
ijassa-1064	254	16	predator	predator	NOUN
ijassa-1064	254	17	population	population	NOUN
ijassa-1064	254	18	to	to	PART
ijassa-1064	254	19	go	go	VERB
ijassa-1064	254	20	extinct	extinct	ADJ
ijassa-1064	254	21	in	in	ADP
ijassa-1064	254	22	the	the	DET
ijassa-1064	254	23	ecosystem	ecosystem	NOUN
ijassa-1064	254	24	.	.	PUNCT
ijassa-1064	255	1	3.2.5	3.2.5	NUM
ijassa-1064	255	2	.	.	PUNCT
ijassa-1064	256	1	stability	stability	NOUN
ijassa-1064	256	2	of	of	ADP
ijassa-1064	256	3	e4	e4	PROPN
ijassa-1064	256	4	the	the	DET
ijassa-1064	256	5	jacobian	jacobian	ADJ
ijassa-1064	256	6	matrix	matrix	NOUN
ijassa-1064	256	7	(	(	PUNCT
ijassa-1064	256	8	3.14	3.14	NUM
ijassa-1064	256	9	)	)	PUNCT
ijassa-1064	256	10	is	be	AUX
ijassa-1064	256	11	evaluated	evaluate	VERB
ijassa-1064	256	12	at	at	ADP
ijassa-1064	256	13	the	the	DET
ijassa-1064	256	14	infected	infect	VERB
ijassa-1064	256	15	prey	prey	NOUN
ijassa-1064	256	16	-	-	PUNCT
ijassa-1064	256	17	free	free	ADJ
ijassa-1064	256	18	equilibrium	equilibrium	NOUN
ijassa-1064	256	19	point	point	NOUN
ijassa-1064	256	20	(	(	PUNCT
ijassa-1064	256	21	3.11	3.11	NUM
ijassa-1064	256	22	)	)	PUNCT
ijassa-1064	256	23	.	.	PUNCT
ijassa-1064	257	1	hence	hence	ADV
ijassa-1064	257	2	,	,	PUNCT
ijassa-1064	257	3	solving	solve	VERB
ijassa-1064	257	4	the	the	DET
ijassa-1064	257	5	corresponding	corresponding	ADJ
ijassa-1064	257	6	characteristic	characteristic	ADJ
ijassa-1064	257	7	equation	equation	NOUN
ijassa-1064	257	8	|j(e4)−	|j(e4)−	VERB
ijassa-1064	257	9	λi5)|	λi5)|	PROPN
ijassa-1064	257	10	=	=	SYM
ijassa-1064	257	11	0	0	NUM
ijassa-1064	257	12	gives	give	VERB
ijassa-1064	257	13	one	one	NUM
ijassa-1064	257	14	eigenvalue	eigenvalue	NOUN
ijassa-1064	257	15	,	,	PUNCT
ijassa-1064	257	16	λ1	λ1	ADJ
ijassa-1064	257	17	=	=	SYM
ijassa-1064	257	18	−µ1	−µ1	PROPN
ijassa-1064	257	19	,	,	PUNCT
ijassa-1064	257	20	and	and	CCONJ
ijassa-1064	257	21	the	the	DET
ijassa-1064	257	22	remaining	remain	VERB
ijassa-1064	257	23	four	four	NUM
ijassa-1064	257	24	eigenvalues	eigenvalue	NOUN
ijassa-1064	257	25	are	be	AUX
ijassa-1064	257	26	obtainable	obtainable	ADJ
ijassa-1064	257	27	from	from	ADP
ijassa-1064	257	28	λ4	λ4	PROPN
ijassa-1064	258	1	+	+	PROPN
ijassa-1064	258	2	w1λ	w1λ	ADJ
ijassa-1064	258	3	3	3	NUM
ijassa-1064	258	4	+	+	NOUN
ijassa-1064	258	5	w2λ	w2λ	PROPN
ijassa-1064	258	6	2	2	NUM
ijassa-1064	258	7	+	+	NOUN
ijassa-1064	258	8	w3λ+w4	w3λ+w4	NOUN
ijassa-1064	258	9	=	=	SYM
ijassa-1064	258	10	0	0	NUM
ijassa-1064	258	11	,	,	PUNCT
ijassa-1064	258	12	(	(	PUNCT
ijassa-1064	258	13	3.21	3.21	NUM
ijassa-1064	258	14	)	)	PUNCT
ijassa-1064	258	15	where	where	SCONJ
ijassa-1064	258	16	w1	w1	NOUN
ijassa-1064	258	17	=	=	NOUN
ijassa-1064	258	18	r	r	NOUN
ijassa-1064	258	19	−	−	PROPN
ijassa-1064	258	20	µ1	µ1	NOUN
ijassa-1064	258	21	−	−	PROPN
ijassa-1064	258	22	p1	p1	PROPN
ijassa-1064	258	23	µ2	µ2	PROPN
ijassa-1064	258	24	β2	β2	PROPN
ijassa-1064	258	25	,	,	PUNCT
ijassa-1064	258	26	w2	w2	NOUN
ijassa-1064	258	27	=	=	PUNCT
ijassa-1064	258	28	d1d2	d1d2	PUNCT
ijassa-1064	258	29	−	−	X
ijassa-1064	258	30	2µ2(d1	2µ2(d1	NUM
ijassa-1064	258	31	+	+	X
ijassa-1064	258	32	d2	d2	NOUN
ijassa-1064	258	33	)	)	PUNCT
ijassa-1064	259	1	+	+	CCONJ
ijassa-1064	259	2	µ2	µ2	PROPN
ijassa-1064	259	3	+	+	CCONJ
ijassa-1064	259	4	c1p1d3	c1p1d3	ADV
ijassa-1064	259	5	−	−	PROPN
ijassa-1064	259	6	c1p1	c1p1	PUNCT
ijassa-1064	259	7	µ2	µ2	NOUN
ijassa-1064	259	8	β2	β2	NOUN
ijassa-1064	259	9	with	with	ADP
ijassa-1064	259	10	d1	d1	PROPN
ijassa-1064	259	11	=	=	PUNCT
ijassa-1064	260	1	r	r	NOUN
ijassa-1064	260	2	−	−	PROPN
ijassa-1064	260	3	2r	2r	NUM
ijassa-1064	260	4	d3	d3	PROPN
ijassa-1064	260	5	k	k	PROPN
ijassa-1064	260	6	−	−	PROPN
ijassa-1064	260	7	p1	p1	PROPN
ijassa-1064	260	8	µ2	µ2	PROPN
ijassa-1064	260	9	β2	β2	PROPN
ijassa-1064	260	10	−	−	PROPN
ijassa-1064	260	11	µ1	µ1	PROPN
ijassa-1064	260	12	,	,	PUNCT
ijassa-1064	260	13	d2	d2	PROPN
ijassa-1064	260	14	=	=	SYM
ijassa-1064	260	15	β1d3	β1d3	PUNCT
ijassa-1064	260	16	−	−	PROPN
ijassa-1064	260	17	p2	p2	PROPN
ijassa-1064	260	18	µ2	µ2	PROPN
ijassa-1064	260	19	β2	β2	PROPN
ijassa-1064	260	20	−	−	PROPN
ijassa-1064	260	21	c1p1p3	c1p1p3	PROPN
ijassa-1064	260	22	d3	d3	PROPN
ijassa-1064	260	23	β2	β2	PROPN
ijassa-1064	260	24	−	−	PROPN
ijassa-1064	261	1	(	(	PUNCT
ijassa-1064	261	2	µ1	µ1	PROPN
ijassa-1064	261	3	+	+	X
ijassa-1064	261	4	µ2	µ2	PROPN
ijassa-1064	261	5	+	+	CCONJ
ijassa-1064	261	6	γ	γ	X
ijassa-1064	261	7	)	)	PUNCT
ijassa-1064	261	8	and	and	CCONJ
ijassa-1064	261	9	d3	d3	PROPN
ijassa-1064	262	1	=	=	SYM
ijassa-1064	262	2	k	k	PROPN
ijassa-1064	263	1	−	−	PROPN
ijassa-1064	264	1	k	k	NOUN
ijassa-1064	264	2	r	r	NOUN
ijassa-1064	264	3	(	(	PUNCT
ijassa-1064	264	4	p1µ2	p1µ2	PUNCT
ijassa-1064	264	5	β2	β2	NOUN
ijassa-1064	264	6	+	+	CCONJ
ijassa-1064	264	7	µ2	µ2	PROPN
ijassa-1064	264	8	)	)	PUNCT
ijassa-1064	264	9	.	.	PUNCT
ijassa-1064	265	1	w3	w3	PROPN
ijassa-1064	265	2	=	=	PUNCT
ijassa-1064	265	3	c1p1	c1p1	X
ijassa-1064	265	4	[	[	PUNCT
ijassa-1064	265	5	(	(	PUNCT
ijassa-1064	265	6	d2	d2	PROPN
ijassa-1064	265	7	−	−	PROPN
ijassa-1064	265	8	µ2	µ2	PROPN
ijassa-1064	265	9	)	)	PUNCT
ijassa-1064	265	10	µ2	µ2	PROPN
ijassa-1064	265	11	β2	β2	NOUN
ijassa-1064	265	12	−	−	PROPN
ijassa-1064	265	13	d3(d2µ2	d3(d2µ2	PROPN
ijassa-1064	265	14	+	+	CCONJ
ijassa-1064	265	15	d1	d1	NOUN
ijassa-1064	265	16	)	)	PUNCT
ijassa-1064	265	17	]	]	PUNCT
ijassa-1064	266	1	−	−	PROPN
ijassa-1064	267	1	d2µ2(2d1	d2µ2(2d1	PROPN
ijassa-1064	267	2	+	+	CCONJ
ijassa-1064	267	3	µ2	µ2	ADJ
ijassa-1064	267	4	)	)	PUNCT
ijassa-1064	267	5	and	and	CCONJ
ijassa-1064	267	6	w4	w4	NOUN
ijassa-1064	267	7	=	=	SYM
ijassa-1064	267	8	d2µ	d2µ	PUNCT
ijassa-1064	267	9	2	2	NUM
ijassa-1064	267	10	2	2	NUM
ijassa-1064	267	11	(	(	PUNCT
ijassa-1064	267	12	d1	d1	NOUN
ijassa-1064	267	13	+	+	CCONJ
ijassa-1064	267	14	p1	p1	PROPN
ijassa-1064	267	15	β2	β2	PROPN
ijassa-1064	267	16	)	)	PUNCT
ijassa-1064	267	17	.	.	PUNCT
ijassa-1064	268	1	copyright	copyright	NOUN
ijassa-1064	268	2	©	©	PROPN
ijassa-1064	268	3	2021	2021	NUM
ijassa-1064	268	4	assa	assa	NOUN
ijassa-1064	268	5	.	.	PUNCT
ijassa-1064	269	1	adv	adv	PROPN
ijassa-1064	269	2	syst	syst	PROPN
ijassa-1064	269	3	sci	sci	PROPN
ijassa-1064	269	4	appl	appl	PROPN
ijassa-1064	269	5	(	(	PUNCT
ijassa-1064	269	6	2021	2021	NUM
ijassa-1064	269	7	)	)	PUNCT
ijassa-1064	269	8	94	94	NUM
ijassa-1064	270	1	j.a	j.a	PROPN
ijassa-1064	270	2	.	.	PROPN
ijassa-1064	270	3	ademosu	ademosu	PROPN
ijassa-1064	270	4	,	,	PUNCT
ijassa-1064	270	5	s.	s.	PROPN
ijassa-1064	270	6	olaniyi	olaniyi	PROPN
ijassa-1064	270	7	,	,	PUNCT
ijassa-1064	270	8	s.o	s.o	PROPN
ijassa-1064	270	9	.	.	PROPN
ijassa-1064	270	10	adewale	adewale	PROPN
ijassa-1064	270	11	applying	apply	VERB
ijassa-1064	270	12	routh	routh	PROPN
ijassa-1064	270	13	-	-	PUNCT
ijassa-1064	270	14	hurwitz	hurwitz	PROPN
ijassa-1064	270	15	’s	’s	PART
ijassa-1064	270	16	criterion	criterion	NOUN
ijassa-1064	270	17	,	,	PUNCT
ijassa-1064	270	18	the	the	DET
ijassa-1064	270	19	roots	root	NOUN
ijassa-1064	270	20	of	of	ADP
ijassa-1064	270	21	(	(	PUNCT
ijassa-1064	270	22	3.21	3.21	NUM
ijassa-1064	270	23	)	)	PUNCT
ijassa-1064	270	24	will	will	AUX
ijassa-1064	270	25	have	have	VERB
ijassa-1064	270	26	negative	negative	ADJ
ijassa-1064	270	27	real	real	ADJ
ijassa-1064	270	28	parts	part	NOUN
ijassa-1064	270	29	if	if	SCONJ
ijassa-1064	270	30	w1	w1	PROPN
ijassa-1064	270	31	>	>	X
ijassa-1064	270	32	0	0	NUM
ijassa-1064	270	33	,	,	PUNCT
ijassa-1064	270	34	w1w2	w1w2	X
ijassa-1064	270	35	>	>	X
ijassa-1064	270	36	w3	w3	PROPN
ijassa-1064	270	37	,	,	PUNCT
ijassa-1064	270	38	w1w2w3	w1w2w3	PROPN
ijassa-1064	270	39	>	>	X
ijassa-1064	270	40	w	w	PROPN
ijassa-1064	270	41	2	2	NUM
ijassa-1064	270	42	1w4	1w4	NUM
ijassa-1064	270	43	+	+	NOUN
ijassa-1064	270	44	w	w	PROPN
ijassa-1064	270	45	2	2	NUM
ijassa-1064	270	46	3	3	NUM
ijassa-1064	270	47	.	.	PUNCT
ijassa-1064	271	1	the	the	DET
ijassa-1064	271	2	stability	stability	NOUN
ijassa-1064	271	3	result	result	NOUN
ijassa-1064	271	4	is	be	AUX
ijassa-1064	271	5	hereby	hereby	ADV
ijassa-1064	271	6	theorized	theorize	VERB
ijassa-1064	271	7	as	as	ADP
ijassa-1064	271	8	follows	follow	NOUN
ijassa-1064	271	9	.	.	PUNCT
ijassa-1064	272	1	theorem	theorem	VERB
ijassa-1064	272	2	3.7	3.7	NUM
ijassa-1064	272	3	:	:	PUNCT
ijassa-1064	272	4	the	the	DET
ijassa-1064	272	5	infected	infected	ADJ
ijassa-1064	272	6	prey	prey	NOUN
ijassa-1064	272	7	-	-	PUNCT
ijassa-1064	272	8	free	free	ADJ
ijassa-1064	272	9	equilibrium	equilibrium	NOUN
ijassa-1064	272	10	of	of	ADP
ijassa-1064	272	11	the	the	DET
ijassa-1064	272	12	prey	prey	NOUN
ijassa-1064	272	13	-	-	PUNCT
ijassa-1064	272	14	predator	predator	NOUN
ijassa-1064	272	15	model	model	NOUN
ijassa-1064	272	16	(	(	PUNCT
ijassa-1064	272	17	2.1	2.1	NUM
ijassa-1064	272	18	)	)	PUNCT
ijassa-1064	272	19	,	,	PUNCT
ijassa-1064	272	20	given	give	VERB
ijassa-1064	272	21	by	by	ADP
ijassa-1064	272	22	(	(	PUNCT
ijassa-1064	272	23	3.11	3.11	NUM
ijassa-1064	272	24	)	)	PUNCT
ijassa-1064	272	25	,	,	PUNCT
ijassa-1064	272	26	is	be	AUX
ijassa-1064	272	27	stable	stable	ADJ
ijassa-1064	272	28	if	if	SCONJ
ijassa-1064	272	29	w1	w1	PROPN
ijassa-1064	272	30	>	>	X
ijassa-1064	272	31	0	0	NUM
ijassa-1064	272	32	,	,	PUNCT
ijassa-1064	272	33	w1w2	w1w2	X
ijassa-1064	272	34	>	>	X
ijassa-1064	272	35	w3	w3	PROPN
ijassa-1064	272	36	and	and	CCONJ
ijassa-1064	272	37	w1w2w3	w1w2w3	PROPN
ijassa-1064	272	38	>	>	X
ijassa-1064	272	39	w	w	PROPN
ijassa-1064	272	40	2	2	NUM
ijassa-1064	272	41	1w4	1w4	NUM
ijassa-1064	272	42	+	+	NOUN
ijassa-1064	272	43	w	w	PROPN
ijassa-1064	272	44	2	2	NUM
ijassa-1064	272	45	3	3	NUM
ijassa-1064	272	46	.	.	PUNCT
ijassa-1064	273	1	the	the	DET
ijassa-1064	273	2	implication	implication	NOUN
ijassa-1064	273	3	of	of	ADP
ijassa-1064	273	4	theorem	theorem	ADJ
ijassa-1064	273	5	3.7	3.7	NUM
ijassa-1064	273	6	is	be	AUX
ijassa-1064	273	7	that	that	SCONJ
ijassa-1064	273	8	the	the	DET
ijassa-1064	273	9	presence	presence	NOUN
ijassa-1064	273	10	of	of	ADP
ijassa-1064	273	11	few	few	ADJ
ijassa-1064	273	12	species	specie	NOUN
ijassa-1064	273	13	around	around	ADP
ijassa-1064	273	14	the	the	DET
ijassa-1064	273	15	stable	stable	ADJ
ijassa-1064	273	16	infected	infected	ADJ
ijassa-1064	273	17	prey	prey	NOUN
ijassa-1064	273	18	-	-	PUNCT
ijassa-1064	273	19	free	free	ADJ
ijassa-1064	273	20	equilibrium	equilibrium	NOUN
ijassa-1064	273	21	e4	e4	PROPN
ijassa-1064	273	22	will	will	AUX
ijassa-1064	273	23	support	support	VERB
ijassa-1064	273	24	the	the	DET
ijassa-1064	273	25	coexistence	coexistence	NOUN
ijassa-1064	273	26	of	of	ADP
ijassa-1064	273	27	both	both	DET
ijassa-1064	273	28	prey	prey	NOUN
ijassa-1064	273	29	and	and	CCONJ
ijassa-1064	273	30	predator	predator	NOUN
ijassa-1064	273	31	populations	population	NOUN
ijassa-1064	273	32	in	in	ADP
ijassa-1064	273	33	the	the	DET
ijassa-1064	273	34	ecosystem	ecosystem	NOUN
ijassa-1064	273	35	.	.	PUNCT
ijassa-1064	274	1	3.2.6	3.2.6	NUM
ijassa-1064	274	2	.	.	PUNCT
ijassa-1064	274	3	stability	stability	NOUN
ijassa-1064	274	4	of	of	ADP
ijassa-1064	274	5	e5	e5	PROPN
ijassa-1064	274	6	two	two	NUM
ijassa-1064	274	7	of	of	ADP
ijassa-1064	274	8	the	the	DET
ijassa-1064	274	9	eigenvalues	eigenvalue	NOUN
ijassa-1064	274	10	of	of	ADP
ijassa-1064	274	11	the	the	DET
ijassa-1064	274	12	jacobian	jacobian	ADJ
ijassa-1064	274	13	matrix	matrix	NOUN
ijassa-1064	274	14	(	(	PUNCT
ijassa-1064	274	15	3.14	3.14	NUM
ijassa-1064	274	16	)	)	PUNCT
ijassa-1064	274	17	evaluated	evaluate	VERB
ijassa-1064	274	18	at	at	ADP
ijassa-1064	274	19	the	the	DET
ijassa-1064	274	20	infected	infect	VERB
ijassa-1064	274	21	predator	predator	NOUN
ijassa-1064	274	22	-	-	PUNCT
ijassa-1064	274	23	free	free	ADJ
ijassa-1064	274	24	equilibrium	equilibrium	NOUN
ijassa-1064	274	25	point	point	NOUN
ijassa-1064	274	26	e5	e5	PROPN
ijassa-1064	274	27	are	be	AUX
ijassa-1064	274	28	given	give	VERB
ijassa-1064	274	29	by	by	ADP
ijassa-1064	274	30	λ1	λ1	PROPN
ijassa-1064	274	31	=	=	SYM
ijassa-1064	274	32	−µ1	−µ1	PROPN
ijassa-1064	274	33	and	and	CCONJ
ijassa-1064	274	34	λ2	λ2	PROPN
ijassa-1064	274	35	=	=	SYM
ijassa-1064	274	36	−µ2	−µ2	PROPN
ijassa-1064	274	37	,	,	PUNCT
ijassa-1064	274	38	while	while	SCONJ
ijassa-1064	274	39	the	the	DET
ijassa-1064	274	40	remaining	remain	VERB
ijassa-1064	274	41	can	can	AUX
ijassa-1064	274	42	be	be	AUX
ijassa-1064	274	43	obtained	obtain	VERB
ijassa-1064	274	44	from	from	ADP
ijassa-1064	274	45	the	the	DET
ijassa-1064	274	46	characteristic	characteristic	ADJ
ijassa-1064	274	47	equation	equation	NOUN
ijassa-1064	275	1	λ3	λ3	PROPN
ijassa-1064	275	2	+	+	CCONJ
ijassa-1064	275	3	e1λ	e1λ	PROPN
ijassa-1064	275	4	2	2	NUM
ijassa-1064	275	5	+	+	CCONJ
ijassa-1064	275	6	e2λ+	e2λ+	NOUN
ijassa-1064	275	7	e3	e3	NOUN
ijassa-1064	275	8	=	=	SYM
ijassa-1064	275	9	0	0	NUM
ijassa-1064	275	10	,	,	PUNCT
ijassa-1064	275	11	(	(	PUNCT
ijassa-1064	275	12	3.22	3.22	NUM
ijassa-1064	275	13	)	)	PUNCT
ijassa-1064	275	14	where	where	SCONJ
ijassa-1064	275	15	e1	e1	NOUN
ijassa-1064	275	16	=	=	PUNCT
ijassa-1064	275	17	−(f1	−(f1	PUNCT
ijassa-1064	275	18	+	+	CCONJ
ijassa-1064	275	19	f2	f2	PROPN
ijassa-1064	275	20	+	+	CCONJ
ijassa-1064	275	21	f3	f3	ADJ
ijassa-1064	275	22	)	)	PUNCT
ijassa-1064	275	23	,	,	PUNCT
ijassa-1064	275	24	with	with	ADP
ijassa-1064	275	25	f1	f1	PROPN
ijassa-1064	275	26	=	=	SYM
ijassa-1064	275	27	2c1p1f̃1	2c1p1f̃1	NUM
ijassa-1064	275	28	−	−	PROPN
ijassa-1064	275	29	µ2(1	µ2(1	PROPN
ijassa-1064	275	30	+	+	CCONJ
ijassa-1064	275	31	c2p2	c2p2	X
ijassa-1064	275	32	)	)	PUNCT
ijassa-1064	275	33	such	such	ADJ
ijassa-1064	275	34	that	that	SCONJ
ijassa-1064	275	35	f̃1	f̃1	PROPN
ijassa-1064	275	36	=	=	PUNCT
ijassa-1064	275	37	c2p2(r	c2p2(r	PROPN
ijassa-1064	275	38	−	−	PROPN
ijassa-1064	275	39	µ1)−	µ1)−	INTJ
ijassa-1064	275	40	p1c2(µ1	p1c2(µ1	NOUN
ijassa-1064	275	41	+	+	CCONJ
ijassa-1064	275	42	γ)−	γ)−	PROPN
ijassa-1064	275	43	βµ2	βµ2	NOUN
ijassa-1064	275	44	c2p2	c2p2	PROPN
ijassa-1064	275	45	(	(	PUNCT
ijassa-1064	275	46	1	1	NUM
ijassa-1064	275	47	k	k	NOUN
ijassa-1064	275	48	+	+	NUM
ijassa-1064	275	49	p1β1	p1β1	X
ijassa-1064	275	50	p2	p2	PROPN
ijassa-1064	275	51	)	)	PUNCT
ijassa-1064	276	1	−	−	PROPN
ijassa-1064	276	2	c1p1β1	c1p1β1	NOUN
ijassa-1064	276	3	,	,	PUNCT
ijassa-1064	276	4	f2	f2	ADV
ijassa-1064	276	5	=	=	NOUN
ijassa-1064	276	6	r	r	NOUN
ijassa-1064	276	7	−	−	PROPN
ijassa-1064	276	8	µ2	µ2	NOUN
ijassa-1064	276	9	−	−	PROPN
ijassa-1064	277	1	[	[	PUNCT
ijassa-1064	277	2	2r	2r	NUM
ijassa-1064	277	3	k	k	PROPN
ijassa-1064	278	1	+	+	CCONJ
ijassa-1064	278	2	c2p2	c2p2	PROPN
ijassa-1064	278	3	+	+	CCONJ
ijassa-1064	278	4	kp1β1(c2	kp1β1(c2	ADJ
ijassa-1064	278	5	−	−	PROPN
ijassa-1064	278	6	c1	c1	PROPN
ijassa-1064	278	7	)	)	PUNCT
ijassa-1064	278	8	k(c2p2	k(c2p2	PROPN
ijassa-1064	278	9	+	+	CCONJ
ijassa-1064	278	10	kp1c2	kp1c2	PROPN
ijassa-1064	278	11	−	−	PROPN
ijassa-1064	278	12	c1p1β1	c1p1β1	PROPN
ijassa-1064	278	13	)	)	PUNCT
ijassa-1064	278	14	]	]	PUNCT
ijassa-1064	279	1	f̃1	f̃1	PROPN
ijassa-1064	279	2	−	−	PROPN
ijassa-1064	279	3	β1	β1	PROPN
ijassa-1064	279	4	(	(	PUNCT
ijassa-1064	279	5	µ2	µ2	PROPN
ijassa-1064	279	6	−	−	PROPN
ijassa-1064	279	7	c1p1	c1p1	ADV
ijassa-1064	279	8	c2p2	c2p2	X
ijassa-1064	279	9	f̃1	f̃1	PROPN
ijassa-1064	279	10	)	)	PUNCT
ijassa-1064	279	11	(	(	PUNCT
ijassa-1064	279	12	1−	1−	NUM
ijassa-1064	279	13	p1	p1	NOUN
ijassa-1064	279	14	)	)	PUNCT
ijassa-1064	279	15	f3	f3	NOUN
ijassa-1064	279	16	=	=	SYM
ijassa-1064	279	17	β1f̃1	β1f̃1	PUNCT
ijassa-1064	279	18	−	−	NOUN
ijassa-1064	279	19	p2	p2	PROPN
ijassa-1064	280	1	[	[	X
ijassa-1064	280	2	(	(	PUNCT
ijassa-1064	280	3	c2p2	c2p2	X
ijassa-1064	280	4	+	+	CCONJ
ijassa-1064	280	5	kp1β1(c2	kp1β1(c2	ADJ
ijassa-1064	280	6	−	−	PROPN
ijassa-1064	280	7	c1	c1	PROPN
ijassa-1064	280	8	)	)	PUNCT
ijassa-1064	280	9	k(c2p2	k(c2p2	PROPN
ijassa-1064	280	10	+	+	CCONJ
ijassa-1064	280	11	kp1c2	kp1c2	PROPN
ijassa-1064	280	12	−	−	PROPN
ijassa-1064	280	13	c1p1β1	c1p1β1	PROPN
ijassa-1064	280	14	)	)	PUNCT
ijassa-1064	280	15	)	)	PUNCT
ijassa-1064	281	1	f̃1	f̃1	PROPN
ijassa-1064	282	1	−	−	PROPN
ijassa-1064	282	2	β1	β1	PROPN
ijassa-1064	282	3	(	(	PUNCT
ijassa-1064	282	4	µ2	µ2	PROPN
ijassa-1064	282	5	−	−	PROPN
ijassa-1064	282	6	c1p1	c1p1	ADV
ijassa-1064	282	7	c2p2	c2p2	X
ijassa-1064	282	8	f̃1	f̃1	PROPN
ijassa-1064	282	9	)	)	PUNCT
ijassa-1064	282	10	]	]	PUNCT
ijassa-1064	283	1	−	−	PROPN
ijassa-1064	283	2	(	(	PUNCT
ijassa-1064	283	3	µ1	µ1	PROPN
ijassa-1064	283	4	+	+	X
ijassa-1064	283	5	γ	γ	NOUN
ijassa-1064	283	6	)	)	PUNCT
ijassa-1064	283	7	.	.	PUNCT
ijassa-1064	284	1	e2	e2	PROPN
ijassa-1064	284	2	=	=	PUNCT
ijassa-1064	284	3	f1f2	f1f2	X
ijassa-1064	284	4	+	+	CCONJ
ijassa-1064	285	1	f3(f1	f3(f1	ADJ
ijassa-1064	285	2	+	+	CCONJ
ijassa-1064	285	3	f2	f2	PROPN
ijassa-1064	285	4	)	)	PUNCT
ijassa-1064	286	1	+	+	CCONJ
ijassa-1064	286	2	β2	β2	NOUN
ijassa-1064	286	3	1	1	NUM
ijassa-1064	286	4	f̃1	f̃1	PROPN
ijassa-1064	286	5	(	(	PUNCT
ijassa-1064	286	6	µ2	µ2	PROPN
ijassa-1064	286	7	−	−	PROPN
ijassa-1064	286	8	c1p1	c1p1	ADV
ijassa-1064	286	9	c2p2	c2p2	X
ijassa-1064	286	10	f̃1	f̃1	PROPN
ijassa-1064	286	11	)	)	PUNCT
ijassa-1064	287	1	+	+	CCONJ
ijassa-1064	287	2	p	p	SYM
ijassa-1064	287	3	2	2	NUM
ijassa-1064	287	4	1	1	NUM
ijassa-1064	287	5	c1	c1	NOUN
ijassa-1064	287	6	p2	p2	PROPN
ijassa-1064	287	7	f̃1(f3	f̃1(f3	PROPN
ijassa-1064	287	8	+	+	CCONJ
ijassa-1064	287	9	(	(	PUNCT
ijassa-1064	287	10	µ1	µ1	PROPN
ijassa-1064	287	11	+	+	X
ijassa-1064	287	12	γ)−	γ)−	PROPN
ijassa-1064	287	13	β1f̃1	β1f̃1	NUM
ijassa-1064	287	14	)	)	PUNCT
ijassa-1064	287	15	,	,	PUNCT
ijassa-1064	287	16	e3	e3	NOUN
ijassa-1064	287	17	=	=	SYM
ijassa-1064	287	18	1	1	NUM
ijassa-1064	287	19	p2	p2	NOUN
ijassa-1064	287	20	(	(	PUNCT
ijassa-1064	287	21	f3	f3	PROPN
ijassa-1064	287	22	+	+	CCONJ
ijassa-1064	287	23	(	(	PUNCT
ijassa-1064	287	24	µ1	µ1	PROPN
ijassa-1064	287	25	+	+	X
ijassa-1064	287	26	γ)−	γ)−	PROPN
ijassa-1064	287	27	β1f̃1	β1f̃1	PUNCT
ijassa-1064	287	28	)	)	PUNCT
ijassa-1064	288	1	[	[	X
ijassa-1064	288	2	(	(	PUNCT
ijassa-1064	288	3	µ2	µ2	PROPN
ijassa-1064	288	4	−	−	PROPN
ijassa-1064	288	5	c1p1	c1p1	ADV
ijassa-1064	288	6	c2p2	c2p2	X
ijassa-1064	288	7	f̃1	f̃1	PROPN
ijassa-1064	288	8	)	)	PUNCT
ijassa-1064	288	9	(	(	PUNCT
ijassa-1064	288	10	p2(c2[p1f̃1	p2(c2[p1f̃1	NOUN
ijassa-1064	288	11	−	−	VERB
ijassa-1064	288	12	p2]−	p2]−	NOUN
ijassa-1064	288	13	c1p1))−	c1p1))−	NOUN
ijassa-1064	288	14	c1p	c1p	NOUN
ijassa-1064	288	15	2	2	NUM
ijassa-1064	288	16	1	1	NUM
ijassa-1064	288	17	f̃1(f3	f̃1(f3	NOUN
ijassa-1064	288	18	+	+	CCONJ
ijassa-1064	288	19	f1f2	f1f2	PROPN
ijassa-1064	288	20	)	)	PUNCT
ijassa-1064	288	21	]	]	PUNCT
ijassa-1064	288	22	.	.	PUNCT
ijassa-1064	289	1	by	by	ADP
ijassa-1064	289	2	routh	routh	PROPN
ijassa-1064	289	3	-	-	PUNCT
ijassa-1064	289	4	hurwitz	hurwitz	PROPN
ijassa-1064	289	5	’s	’s	PART
ijassa-1064	289	6	criterion	criterion	NOUN
ijassa-1064	289	7	,	,	PUNCT
ijassa-1064	289	8	the	the	DET
ijassa-1064	289	9	roots	root	NOUN
ijassa-1064	289	10	of	of	ADP
ijassa-1064	289	11	the	the	DET
ijassa-1064	289	12	characteristic	characteristic	ADJ
ijassa-1064	289	13	equation	equation	NOUN
ijassa-1064	289	14	(	(	PUNCT
ijassa-1064	289	15	3.22	3.22	NUM
ijassa-1064	289	16	)	)	PUNCT
ijassa-1064	289	17	will	will	AUX
ijassa-1064	289	18	have	have	VERB
ijassa-1064	289	19	negative	negative	ADJ
ijassa-1064	289	20	real	real	ADJ
ijassa-1064	289	21	parts	part	NOUN
ijassa-1064	289	22	if	if	SCONJ
ijassa-1064	289	23	e1	e1	VERB
ijassa-1064	289	24	>	>	X
ijassa-1064	289	25	0	0	PUNCT
ijassa-1064	289	26	and	and	CCONJ
ijassa-1064	289	27	e1e2	e1e2	X
ijassa-1064	289	28	>	>	PUNCT
ijassa-1064	289	29	e3	e3	NOUN
ijassa-1064	289	30	.	.	PUNCT
ijassa-1064	290	1	this	this	DET
ijassa-1064	290	2	result	result	NOUN
ijassa-1064	290	3	is	be	AUX
ijassa-1064	290	4	stated	state	VERB
ijassa-1064	290	5	as	as	SCONJ
ijassa-1064	290	6	follows	follow	VERB
ijassa-1064	290	7	.	.	PUNCT
ijassa-1064	291	1	theorem	theorem	VERB
ijassa-1064	291	2	3.8	3.8	NUM
ijassa-1064	291	3	:	:	PUNCT
ijassa-1064	291	4	the	the	DET
ijassa-1064	291	5	infected	infected	ADJ
ijassa-1064	291	6	predator	predator	NOUN
ijassa-1064	291	7	-	-	PUNCT
ijassa-1064	291	8	free	free	ADJ
ijassa-1064	291	9	equilibrium	equilibrium	NOUN
ijassa-1064	291	10	point	point	NOUN
ijassa-1064	291	11	of	of	ADP
ijassa-1064	291	12	the	the	DET
ijassa-1064	291	13	prey	prey	NOUN
ijassa-1064	291	14	-	-	PUNCT
ijassa-1064	291	15	predator	predator	NOUN
ijassa-1064	291	16	system	system	NOUN
ijassa-1064	291	17	(	(	PUNCT
ijassa-1064	291	18	2.1	2.1	NUM
ijassa-1064	291	19	)	)	PUNCT
ijassa-1064	291	20	,	,	PUNCT
ijassa-1064	291	21	given	give	VERB
ijassa-1064	291	22	by	by	ADP
ijassa-1064	291	23	(	(	PUNCT
ijassa-1064	291	24	3.12	3.12	NUM
ijassa-1064	291	25	)	)	PUNCT
ijassa-1064	291	26	,	,	PUNCT
ijassa-1064	291	27	is	be	AUX
ijassa-1064	291	28	stable	stable	ADJ
ijassa-1064	291	29	if	if	SCONJ
ijassa-1064	291	30	e1	e1	NOUN
ijassa-1064	291	31	>	>	X
ijassa-1064	291	32	0	0	PUNCT
ijassa-1064	291	33	and	and	CCONJ
ijassa-1064	291	34	e1e2	e1e2	X
ijassa-1064	291	35	>	>	PUNCT
ijassa-1064	291	36	e3	e3	NOUN
ijassa-1064	291	37	.	.	PUNCT
ijassa-1064	292	1	the	the	DET
ijassa-1064	292	2	result	result	NOUN
ijassa-1064	292	3	in	in	ADP
ijassa-1064	292	4	theorem	theorem	ADJ
ijassa-1064	292	5	3.8	3.8	NUM
ijassa-1064	292	6	implies	imply	VERB
ijassa-1064	292	7	that	that	SCONJ
ijassa-1064	292	8	coexistence	coexistence	NOUN
ijassa-1064	292	9	of	of	ADP
ijassa-1064	292	10	prey	prey	NOUN
ijassa-1064	292	11	and	and	CCONJ
ijassa-1064	292	12	predator	predator	NOUN
ijassa-1064	292	13	species	specie	NOUN
ijassa-1064	292	14	in	in	ADP
ijassa-1064	292	15	the	the	DET
ijassa-1064	292	16	ecosystem	ecosystem	NOUN
ijassa-1064	292	17	is	be	AUX
ijassa-1064	292	18	possible	possible	ADJ
ijassa-1064	292	19	in	in	ADP
ijassa-1064	292	20	the	the	DET
ijassa-1064	292	21	absence	absence	NOUN
ijassa-1064	292	22	of	of	ADP
ijassa-1064	292	23	infected	infected	ADJ
ijassa-1064	292	24	predator	predator	NOUN
ijassa-1064	292	25	,	,	PUNCT
ijassa-1064	292	26	provided	provide	VERB
ijassa-1064	292	27	that	that	SCONJ
ijassa-1064	292	28	the	the	DET
ijassa-1064	292	29	given	give	VERB
ijassa-1064	292	30	parametric	parametric	ADJ
ijassa-1064	292	31	conditions	condition	NOUN
ijassa-1064	292	32	are	be	AUX
ijassa-1064	292	33	valid	valid	ADJ
ijassa-1064	292	34	.	.	PUNCT
ijassa-1064	293	1	3.2.7	3.2.7	NUM
ijassa-1064	293	2	.	.	PUNCT
ijassa-1064	294	1	stability	stability	NOUN
ijassa-1064	294	2	of	of	ADP
ijassa-1064	294	3	e6	e6	PROPN
ijassa-1064	294	4	recall	recall	VERB
ijassa-1064	294	5	from	from	ADP
ijassa-1064	294	6	(	(	PUNCT
ijassa-1064	294	7	3.19	3.19	NUM
ijassa-1064	294	8	)	)	PUNCT
ijassa-1064	294	9	that	that	SCONJ
ijassa-1064	294	10	the	the	DET
ijassa-1064	294	11	basic	basic	ADJ
ijassa-1064	294	12	reproduction	reproduction	NOUN
ijassa-1064	294	13	number	number	NOUN
ijassa-1064	294	14	of	of	ADP
ijassa-1064	294	15	the	the	DET
ijassa-1064	294	16	full	full	ADJ
ijassa-1064	294	17	system	system	NOUN
ijassa-1064	294	18	(	(	PUNCT
ijassa-1064	294	19	2.1	2.1	NUM
ijassa-1064	294	20	)	)	PUNCT
ijassa-1064	294	21	is	be	AUX
ijassa-1064	294	22	given	give	VERB
ijassa-1064	294	23	by	by	ADP
ijassa-1064	294	24	r∗	r∗	PROPN
ijassa-1064	294	25	0	0	NUM
ijassa-1064	295	1	=	=	SYM
ijassa-1064	295	2	max	max	PROPN
ijassa-1064	295	3			PUNCT
ijassa-1064	295	4	β1µ2	β1µ2	PROPN
ijassa-1064	295	5	c1p1	c1p1	PUNCT
ijassa-1064	295	6	(	(	PUNCT
ijassa-1064	295	7	p2	p2	PROPN
ijassa-1064	295	8	p1	p1	PROPN
ijassa-1064	295	9	m1	m1	PROPN
ijassa-1064	295	10	+	+	CCONJ
ijassa-1064	295	11	µ1	µ1	PROPN
ijassa-1064	295	12	+	+	X
ijassa-1064	295	13	γ	γ	NOUN
ijassa-1064	295	14	)	)	PUNCT
ijassa-1064	295	15	,	,	PUNCT
ijassa-1064	295	16	β2m1	β2m1	X
ijassa-1064	295	17	p1µ2	p1µ2	ADP
ijassa-1064	295	18			NOUN
ijassa-1064	295	19	.	.	PUNCT
ijassa-1064	296	1	the	the	DET
ijassa-1064	296	2	following	follow	VERB
ijassa-1064	296	3	global	global	ADJ
ijassa-1064	296	4	stability	stability	NOUN
ijassa-1064	296	5	result	result	NOUN
ijassa-1064	296	6	is	be	AUX
ijassa-1064	296	7	explored	explore	VERB
ijassa-1064	296	8	.	.	PUNCT
ijassa-1064	297	1	copyright	copyright	NOUN
ijassa-1064	297	2	©	©	PROPN
ijassa-1064	297	3	2021	2021	NUM
ijassa-1064	297	4	assa	assa	NOUN
ijassa-1064	297	5	.	.	PUNCT
ijassa-1064	298	1	adv	adv	PROPN
ijassa-1064	298	2	syst	syst	PROPN
ijassa-1064	298	3	sci	sci	PROPN
ijassa-1064	298	4	appl	appl	PROPN
ijassa-1064	298	5	(	(	PUNCT
ijassa-1064	298	6	2021	2021	NUM
ijassa-1064	298	7	)	)	PUNCT
ijassa-1064	298	8	stability	stability	NOUN
ijassa-1064	298	9	analysis	analysis	NOUN
ijassa-1064	298	10	and	and	CCONJ
ijassa-1064	298	11	optimal	optimal	ADJ
ijassa-1064	298	12	measure	measure	NOUN
ijassa-1064	298	13	95	95	NUM
ijassa-1064	298	14	theorem	theorem	NOUN
ijassa-1064	298	15	3.9	3.9	NUM
ijassa-1064	298	16	:	:	PUNCT
ijassa-1064	298	17	the	the	DET
ijassa-1064	298	18	interior	interior	ADJ
ijassa-1064	298	19	equilibrium	equilibrium	NOUN
ijassa-1064	298	20	point	point	NOUN
ijassa-1064	298	21	e6	e6	NOUN
ijassa-1064	298	22	of	of	ADP
ijassa-1064	298	23	the	the	DET
ijassa-1064	298	24	prey	prey	NOUN
ijassa-1064	298	25	-	-	PUNCT
ijassa-1064	298	26	predator	predator	NOUN
ijassa-1064	298	27	model	model	NOUN
ijassa-1064	298	28	(	(	PUNCT
ijassa-1064	298	29	2.1	2.1	NUM
ijassa-1064	298	30	)	)	PUNCT
ijassa-1064	298	31	is	be	AUX
ijassa-1064	298	32	globally	globally	ADV
ijassa-1064	298	33	asymptotically	asymptotically	ADV
ijassa-1064	298	34	stable	stable	ADJ
ijassa-1064	298	35	if	if	SCONJ
ijassa-1064	298	36	r∗	r∗	PROPN
ijassa-1064	298	37	0	0	NUM
ijassa-1064	298	38	>	>	X
ijassa-1064	298	39	1	1	X
ijassa-1064	298	40	.	.	X
ijassa-1064	299	1	proof	proof	NOUN
ijassa-1064	299	2	let	let	AUX
ijassa-1064	299	3	r∗	r∗	VERB
ijassa-1064	299	4	0	0	PUNCT
ijassa-1064	299	5	>	>	X
ijassa-1064	299	6	1	1	NUM
ijassa-1064	299	7	,	,	PUNCT
ijassa-1064	299	8	such	such	ADJ
ijassa-1064	299	9	that	that	SCONJ
ijassa-1064	299	10	the	the	DET
ijassa-1064	299	11	interior	interior	ADJ
ijassa-1064	299	12	equilibrium	equilibrium	NOUN
ijassa-1064	299	13	point	point	NOUN
ijassa-1064	299	14	e6	e6	PROPN
ijassa-1064	299	15	exists	exist	VERB
ijassa-1064	299	16	.	.	PUNCT
ijassa-1064	300	1	noting	note	VERB
ijassa-1064	300	2	from	from	ADP
ijassa-1064	300	3	(	(	PUNCT
ijassa-1064	300	4	3.13	3.13	NUM
ijassa-1064	300	5	)	)	PUNCT
ijassa-1064	300	6	that	that	PRON
ijassa-1064	300	7	e6	e6	VERB
ijassa-1064	300	8	=	=	PUNCT
ijassa-1064	300	9	(	(	PUNCT
ijassa-1064	300	10	x∗∗	x∗∗	PROPN
ijassa-1064	300	11	s	s	X
ijassa-1064	300	12	,	,	PUNCT
ijassa-1064	300	13	x	x	PUNCT
ijassa-1064	300	14	∗∗	∗∗	NOUN
ijassa-1064	301	1	i	i	PRON
ijassa-1064	301	2	,	,	PUNCT
ijassa-1064	301	3	x	x	PUNCT
ijassa-1064	301	4	∗∗	∗∗	NOUN
ijassa-1064	301	5	r	r	NOUN
ijassa-1064	301	6	,	,	PUNCT
ijassa-1064	301	7	y	y	PROPN
ijassa-1064	301	8	∗∗	∗∗	PROPN
ijassa-1064	301	9	s	s	X
ijassa-1064	301	10	,	,	PUNCT
ijassa-1064	301	11	y	y	PROPN
ijassa-1064	301	12	∗∗	∗∗	PROPN
ijassa-1064	301	13	i	i	INTJ
ijassa-1064	301	14	)	)	PUNCT
ijassa-1064	301	15	,	,	PUNCT
ijassa-1064	301	16	then	then	ADV
ijassa-1064	301	17	the	the	DET
ijassa-1064	301	18	following	follow	VERB
ijassa-1064	301	19	lyapunov	lyapunov	ADJ
ijassa-1064	301	20	function	function	NOUN
ijassa-1064	301	21	of	of	ADP
ijassa-1064	301	22	quadratic	quadratic	ADJ
ijassa-1064	301	23	type	type	NOUN
ijassa-1064	301	24	[	[	X
ijassa-1064	301	25	28	28	NUM
ijassa-1064	301	26	]	]	PUNCT
ijassa-1064	301	27	is	be	AUX
ijassa-1064	301	28	defined	define	VERB
ijassa-1064	301	29	:	:	PUNCT
ijassa-1064	301	30	v	v	X
ijassa-1064	301	31	=	=	SYM
ijassa-1064	301	32	1	1	NUM
ijassa-1064	301	33	2	2	NUM
ijassa-1064	301	34	[	[	X
ijassa-1064	301	35	(	(	PUNCT
ijassa-1064	301	36	xs	xs	PROPN
ijassa-1064	301	37	−x∗∗	−x∗∗	NOUN
ijassa-1064	301	38	s	s	PART
ijassa-1064	301	39	)	)	PUNCT
ijassa-1064	302	1	+	+	CCONJ
ijassa-1064	302	2	(	(	PUNCT
ijassa-1064	302	3	xi	xi	ADP
ijassa-1064	302	4	−x∗∗	−x∗∗	PROPN
ijassa-1064	302	5	i	i	PRON
ijassa-1064	302	6	)	)	PUNCT
ijassa-1064	303	1	+	+	CCONJ
ijassa-1064	303	2	(	(	PUNCT
ijassa-1064	303	3	xr	xr	PROPN
ijassa-1064	303	4	−x∗∗	−x∗∗	ADP
ijassa-1064	303	5	r	r	NOUN
ijassa-1064	303	6	)	)	PUNCT
ijassa-1064	304	1	+	+	CCONJ
ijassa-1064	304	2	(	(	PUNCT
ijassa-1064	304	3	ys	ys	INTJ
ijassa-1064	304	4	−	−	PROPN
ijassa-1064	304	5	y	y	PROPN
ijassa-1064	304	6	∗∗	∗∗	PROPN
ijassa-1064	304	7	s	s	PART
ijassa-1064	304	8	)	)	PUNCT
ijassa-1064	305	1	+	+	CCONJ
ijassa-1064	305	2	(	(	PUNCT
ijassa-1064	305	3	yi	yi	INTJ
ijassa-1064	305	4	−	−	PROPN
ijassa-1064	305	5	y	y	PROPN
ijassa-1064	305	6	∗∗	∗∗	PROPN
ijassa-1064	305	7	i	i	INTJ
ijassa-1064	305	8	)	)	PUNCT
ijassa-1064	306	1	]	]	SYM
ijassa-1064	306	2	2	2	NUM
ijassa-1064	306	3	(	(	PUNCT
ijassa-1064	306	4	3.23	3.23	NUM
ijassa-1064	306	5	)	)	PUNCT
ijassa-1064	306	6	the	the	DET
ijassa-1064	306	7	time	time	NOUN
ijassa-1064	306	8	derivative	derivative	NOUN
ijassa-1064	306	9	of	of	ADP
ijassa-1064	306	10	v	v	NOUN
ijassa-1064	306	11	in	in	ADP
ijassa-1064	306	12	(	(	PUNCT
ijassa-1064	306	13	3.23	3.23	NUM
ijassa-1064	306	14	)	)	PUNCT
ijassa-1064	306	15	along	along	ADP
ijassa-1064	306	16	the	the	DET
ijassa-1064	306	17	solution	solution	NOUN
ijassa-1064	306	18	path	path	NOUN
ijassa-1064	306	19	of	of	ADP
ijassa-1064	306	20	the	the	DET
ijassa-1064	306	21	full	full	ADJ
ijassa-1064	306	22	system	system	NOUN
ijassa-1064	306	23	(	(	PUNCT
ijassa-1064	306	24	2.1	2.1	NUM
ijassa-1064	306	25	)	)	PUNCT
ijassa-1064	306	26	is	be	AUX
ijassa-1064	306	27	given	give	VERB
ijassa-1064	306	28	by	by	ADP
ijassa-1064	306	29	v̇	v̇	NOUN
ijassa-1064	306	30	=	=	PUNCT
ijassa-1064	307	1	[	[	X
ijassa-1064	307	2	(	(	PUNCT
ijassa-1064	307	3	xs	xs	PROPN
ijassa-1064	307	4	−x∗∗	−x∗∗	NOUN
ijassa-1064	307	5	s	s	PART
ijassa-1064	307	6	)	)	PUNCT
ijassa-1064	307	7	+	+	CCONJ
ijassa-1064	307	8	(	(	PUNCT
ijassa-1064	307	9	xi	xi	ADP
ijassa-1064	307	10	−x∗∗	−x∗∗	PROPN
ijassa-1064	307	11	i	i	PRON
ijassa-1064	307	12	)	)	PUNCT
ijassa-1064	308	1	+	+	CCONJ
ijassa-1064	308	2	(	(	PUNCT
ijassa-1064	308	3	xr	xr	PROPN
ijassa-1064	308	4	−x∗∗	−x∗∗	ADP
ijassa-1064	308	5	r	r	NOUN
ijassa-1064	308	6	)	)	PUNCT
ijassa-1064	309	1	+	+	CCONJ
ijassa-1064	309	2	(	(	PUNCT
ijassa-1064	309	3	ys	ys	INTJ
ijassa-1064	309	4	−	−	PROPN
ijassa-1064	309	5	y	y	PROPN
ijassa-1064	309	6	∗∗	∗∗	PROPN
ijassa-1064	309	7	s	s	PART
ijassa-1064	309	8	)	)	PUNCT
ijassa-1064	310	1	+	+	CCONJ
ijassa-1064	310	2	(	(	PUNCT
ijassa-1064	310	3	yi	yi	INTJ
ijassa-1064	310	4	−	−	PROPN
ijassa-1064	310	5	y	y	PROPN
ijassa-1064	310	6	∗∗	∗∗	PROPN
ijassa-1064	310	7	i	i	INTJ
ijassa-1064	310	8	)	)	PUNCT
ijassa-1064	310	9	]	]	PUNCT
ijassa-1064	311	1	dt	dt	PUNCT
ijassa-1064	311	2	dt	dt	X
ijassa-1064	311	3	,	,	PUNCT
ijassa-1064	311	4	(	(	PUNCT
ijassa-1064	311	5	3.24	3.24	NUM
ijassa-1064	311	6	)	)	PUNCT
ijassa-1064	311	7	where	where	SCONJ
ijassa-1064	311	8	t	t	PROPN
ijassa-1064	311	9	(	(	PUNCT
ijassa-1064	311	10	t	t	PROPN
ijassa-1064	311	11	)	)	PUNCT
ijassa-1064	311	12	=	=	PUNCT
ijassa-1064	311	13	xs	xs	PROPN
ijassa-1064	312	1	+	+	PROPN
ijassa-1064	312	2	xi	xi	PROPN
ijassa-1064	312	3	+	+	NOUN
ijassa-1064	312	4	xr	xr	PROPN
ijassa-1064	312	5	+	+	CCONJ
ijassa-1064	312	6	ys	ys	PROPN
ijassa-1064	312	7	+	+	CCONJ
ijassa-1064	312	8	yi	yi	PROPN
ijassa-1064	312	9	.	.	PUNCT
ijassa-1064	313	1	recall	recall	PROPN
ijassa-1064	313	2	from	from	ADP
ijassa-1064	313	3	(	(	PUNCT
ijassa-1064	313	4	2.3	2.3	NUM
ijassa-1064	313	5	)	)	PUNCT
ijassa-1064	313	6	of	of	ADP
ijassa-1064	313	7	the	the	DET
ijassa-1064	313	8	boundedness	boundedness	NOUN
ijassa-1064	313	9	result	result	NOUN
ijassa-1064	313	10	(	(	PUNCT
ijassa-1064	313	11	theorem	theorem	VERB
ijassa-1064	313	12	2.1	2.1	NUM
ijassa-1064	313	13	)	)	PUNCT
ijassa-1064	314	1	that	that	PRON
ijassa-1064	314	2	dt	dt	PUNCT
ijassa-1064	314	3	dt	dt	PUNCT
ijassa-1064	314	4	≤	≤	NUM
ijassa-1064	314	5	rk	rk	VERB
ijassa-1064	314	6	−	−	PROPN
ijassa-1064	314	7	µt	µt	ADP
ijassa-1064	314	8	,	,	PUNCT
ijassa-1064	314	9	and	and	CCONJ
ijassa-1064	314	10	since	since	SCONJ
ijassa-1064	314	11	x∗∗	x∗∗	PROPN
ijassa-1064	314	12	s	s	PART
ijassa-1064	314	13	+	+	NOUN
ijassa-1064	314	14	x∗∗	x∗∗	PROPN
ijassa-1064	314	15	i	i	PROPN
ijassa-1064	314	16	+	+	PROPN
ijassa-1064	314	17	x∗∗	x∗∗	PROPN
ijassa-1064	315	1	r	r	NOUN
ijassa-1064	316	1	+	+	PROPN
ijassa-1064	317	1	y	y	PROPN
ijassa-1064	318	1	∗∗	∗∗	PROPN
ijassa-1064	318	2	s	s	PART
ijassa-1064	318	3	+	+	NUM
ijassa-1064	318	4	y	y	PROPN
ijassa-1064	318	5	∗∗	∗∗	NOUN
ijassa-1064	319	1	i	i	PRON
ijassa-1064	319	2	=	=	VERB
ijassa-1064	319	3	rk	rk	PROPN
ijassa-1064	319	4	µ	µ	NOUN
ijassa-1064	319	5	.	.	PUNCT
ijassa-1064	320	1	it	it	PRON
ijassa-1064	320	2	follows	follow	VERB
ijassa-1064	320	3	from	from	ADP
ijassa-1064	320	4	(	(	PUNCT
ijassa-1064	320	5	3.24	3.24	NUM
ijassa-1064	320	6	)	)	PUNCT
ijassa-1064	320	7	that	that	PRON
ijassa-1064	320	8	v̇	v̇	VERB
ijassa-1064	320	9	≤	≤	X
ijassa-1064	320	10	[	[	PUNCT
ijassa-1064	320	11	t	t	NOUN
ijassa-1064	321	1	(	(	PUNCT
ijassa-1064	321	2	t)−	t)−	PROPN
ijassa-1064	321	3	rk	rk	NOUN
ijassa-1064	321	4	µ	µ	X
ijassa-1064	321	5	]	]	PUNCT
ijassa-1064	322	1	[	[	X
ijassa-1064	322	2	rk	rk	NOUN
ijassa-1064	322	3	−	−	X
ijassa-1064	322	4	µt	µt	INTJ
ijassa-1064	322	5	(	(	PUNCT
ijassa-1064	322	6	t	t	PROPN
ijassa-1064	322	7	)	)	PUNCT
ijassa-1064	322	8	]	]	PUNCT
ijassa-1064	322	9	=	=	SYM
ijassa-1064	322	10	µ	µ	X
ijassa-1064	322	11	[	[	PUNCT
ijassa-1064	322	12	t	t	X
ijassa-1064	322	13	(	(	PUNCT
ijassa-1064	322	14	t)−	t)−	PROPN
ijassa-1064	322	15	rk	rk	NOUN
ijassa-1064	322	16	µ	µ	X
ijassa-1064	322	17	]	]	PUNCT
ijassa-1064	322	18	[	[	PUNCT
ijassa-1064	322	19	rk	rk	NOUN
ijassa-1064	322	20	µ	µ	PROPN
ijassa-1064	322	21	−	−	PROPN
ijassa-1064	322	22	t	t	PROPN
ijassa-1064	322	23	(	(	PUNCT
ijassa-1064	322	24	t	t	PROPN
ijassa-1064	322	25	)	)	PUNCT
ijassa-1064	322	26	]	]	PUNCT
ijassa-1064	323	1	=	=	PUNCT
ijassa-1064	323	2	−µ	−µ	ADJ
ijassa-1064	323	3	[	[	PUNCT
ijassa-1064	323	4	t	t	X
ijassa-1064	323	5	(	(	PUNCT
ijassa-1064	323	6	t)−	t)−	PROPN
ijassa-1064	323	7	rk	rk	VERB
ijassa-1064	323	8	µ	µ	X
ijassa-1064	323	9	]	]	SYM
ijassa-1064	323	10	2	2	NUM
ijassa-1064	323	11	=	=	NOUN
ijassa-1064	323	12	−µ[(xs	−µ[(x	NOUN
ijassa-1064	323	13	−x∗∗	−x∗∗	NOUN
ijassa-1064	323	14	s	s	PART
ijassa-1064	323	15	)	)	PUNCT
ijassa-1064	323	16	+	+	CCONJ
ijassa-1064	323	17	(	(	PUNCT
ijassa-1064	323	18	xi	xi	ADP
ijassa-1064	323	19	−x∗∗	−x∗∗	PROPN
ijassa-1064	323	20	i	i	PRON
ijassa-1064	323	21	)	)	PUNCT
ijassa-1064	324	1	+	+	CCONJ
ijassa-1064	324	2	(	(	PUNCT
ijassa-1064	324	3	xr	xr	PROPN
ijassa-1064	324	4	−x∗∗	−x∗∗	ADP
ijassa-1064	324	5	r	r	NOUN
ijassa-1064	324	6	)	)	PUNCT
ijassa-1064	325	1	+	+	CCONJ
ijassa-1064	325	2	(	(	PUNCT
ijassa-1064	325	3	ys	ys	INTJ
ijassa-1064	325	4	−	−	PROPN
ijassa-1064	325	5	y	y	PROPN
ijassa-1064	325	6	∗∗	∗∗	PROPN
ijassa-1064	325	7	s	s	PART
ijassa-1064	325	8	)	)	PUNCT
ijassa-1064	326	1	+	+	CCONJ
ijassa-1064	326	2	(	(	PUNCT
ijassa-1064	326	3	yi	yi	INTJ
ijassa-1064	326	4	−	−	PROPN
ijassa-1064	326	5	y	y	PROPN
ijassa-1064	326	6	∗∗	∗∗	PROPN
ijassa-1064	326	7	i	i	INTJ
ijassa-1064	326	8	)	)	PUNCT
ijassa-1064	327	1	]	]	X
ijassa-1064	327	2	2	2	X
ijassa-1064	327	3	.	.	PUNCT
ijassa-1064	327	4	it	it	PRON
ijassa-1064	327	5	can	can	AUX
ijassa-1064	327	6	be	be	AUX
ijassa-1064	327	7	seen	see	VERB
ijassa-1064	327	8	that	that	SCONJ
ijassa-1064	327	9	v̇	v̇	VERB
ijassa-1064	327	10	≤	≤	NOUN
ijassa-1064	327	11	0	0	NUM
ijassa-1064	327	12	with	with	ADP
ijassa-1064	327	13	equality	equality	NOUN
ijassa-1064	327	14	if	if	SCONJ
ijassa-1064	327	15	and	and	CCONJ
ijassa-1064	327	16	only	only	ADV
ijassa-1064	327	17	if	if	SCONJ
ijassa-1064	327	18	xs	xs	PROPN
ijassa-1064	327	19	=	=	PUNCT
ijassa-1064	328	1	x∗∗	x∗∗	PROPN
ijassa-1064	328	2	s	s	X
ijassa-1064	328	3	,	,	PUNCT
ijassa-1064	328	4	xi	xi	PUNCT
ijassa-1064	329	1	=	=	PUNCT
ijassa-1064	329	2	x∗∗	x∗∗	PROPN
ijassa-1064	330	1	i	i	PRON
ijassa-1064	330	2	,	,	PUNCT
ijassa-1064	330	3	xr	xr	PROPN
ijassa-1064	330	4	=	=	PUNCT
ijassa-1064	331	1	x∗∗	x∗∗	PROPN
ijassa-1064	331	2	r	r	NOUN
ijassa-1064	331	3	,	,	PUNCT
ijassa-1064	331	4	ys	ys	NOUN
ijassa-1064	331	5	=	=	SYM
ijassa-1064	331	6	y	y	PROPN
ijassa-1064	331	7	∗∗	∗∗	PROPN
ijassa-1064	331	8	s	s	X
ijassa-1064	331	9	and	and	CCONJ
ijassa-1064	331	10	yi	yi	NOUN
ijassa-1064	331	11	=	=	SYM
ijassa-1064	332	1	y	y	PROPN
ijassa-1064	332	2	∗∗	∗∗	PROPN
ijassa-1064	333	1	i	i	INTJ
ijassa-1064	333	2	.	.	PUNCT
ijassa-1064	334	1	hence	hence	ADV
ijassa-1064	334	2	,	,	PUNCT
ijassa-1064	334	3	by	by	ADP
ijassa-1064	334	4	lasalle	lasalle	PROPN
ijassa-1064	334	5	’s	’s	PART
ijassa-1064	334	6	invariance	invariance	NOUN
ijassa-1064	334	7	principle	principle	NOUN
ijassa-1064	335	1	[	[	X
ijassa-1064	335	2	19	19	NUM
ijassa-1064	335	3	]	]	PUNCT
ijassa-1064	335	4	,	,	PUNCT
ijassa-1064	335	5	the	the	DET
ijassa-1064	335	6	largest	large	ADJ
ijassa-1064	335	7	invariant	invariant	ADJ
ijassa-1064	335	8	set	set	NOUN
ijassa-1064	335	9	in	in	ADP
ijassa-1064	335	10	{	{	PUNCT
ijassa-1064	335	11	(	(	PUNCT
ijassa-1064	335	12	xs	xs	PROPN
ijassa-1064	335	13	,	,	PUNCT
ijassa-1064	335	14	xi	xi	PROPN
ijassa-1064	335	15	,	,	PUNCT
ijassa-1064	335	16	xr	xr	PROPN
ijassa-1064	335	17	,	,	PUNCT
ijassa-1064	335	18	ys	ys	NOUN
ijassa-1064	335	19	,	,	PUNCT
ijassa-1064	335	20	yi	yi	PROPN
ijassa-1064	335	21	)	)	PUNCT
ijassa-1064	335	22	∈	∈	PROPN
ijassa-1064	335	23	r5	r5	PROPN
ijassa-1064	335	24	+	+	CCONJ
ijassa-1064	335	25	:	:	PUNCT
ijassa-1064	335	26	v̇	v̇	NOUN
ijassa-1064	335	27	=	=	SYM
ijassa-1064	335	28	0	0	NUM
ijassa-1064	335	29	}	}	PUNCT
ijassa-1064	335	30	is	be	AUX
ijassa-1064	335	31	the	the	DET
ijassa-1064	335	32	only	only	ADJ
ijassa-1064	335	33	set	set	NOUN
ijassa-1064	335	34	{	{	PUNCT
ijassa-1064	335	35	e6	e6	PROPN
ijassa-1064	335	36	}	}	PUNCT
ijassa-1064	335	37	.	.	PUNCT
ijassa-1064	336	1	thus	thus	ADV
ijassa-1064	336	2	,	,	PUNCT
ijassa-1064	336	3	the	the	DET
ijassa-1064	336	4	interior	interior	ADJ
ijassa-1064	336	5	equilibrium	equilibrium	NOUN
ijassa-1064	336	6	point	point	NOUN
ijassa-1064	336	7	e6	e6	PROPN
ijassa-1064	336	8	=	=	SYM
ijassa-1064	336	9	(	(	PUNCT
ijassa-1064	336	10	x∗∗	x∗∗	PROPN
ijassa-1064	336	11	s	s	X
ijassa-1064	336	12	,	,	PUNCT
ijassa-1064	336	13	x	x	PUNCT
ijassa-1064	336	14	∗∗	∗∗	NOUN
ijassa-1064	337	1	i	i	PRON
ijassa-1064	337	2	,	,	PUNCT
ijassa-1064	337	3	x	x	PUNCT
ijassa-1064	337	4	∗∗	∗∗	NOUN
ijassa-1064	337	5	r	r	NOUN
ijassa-1064	337	6	,	,	PUNCT
ijassa-1064	337	7	y	y	PROPN
ijassa-1064	337	8	∗∗	∗∗	PROPN
ijassa-1064	337	9	s	s	X
ijassa-1064	337	10	,	,	PUNCT
ijassa-1064	337	11	y	y	PROPN
ijassa-1064	337	12	∗∗	∗∗	PROPN
ijassa-1064	337	13	i	i	INTJ
ijassa-1064	337	14	)	)	PUNCT
ijassa-1064	337	15	is	be	AUX
ijassa-1064	337	16	globally	globally	ADV
ijassa-1064	337	17	asymptotically	asymptotically	ADV
ijassa-1064	337	18	stable	stable	ADJ
ijassa-1064	337	19	.	.	PUNCT
ijassa-1064	338	1	this	this	PRON
ijassa-1064	338	2	completes	complete	VERB
ijassa-1064	338	3	the	the	DET
ijassa-1064	338	4	proof	proof	NOUN
ijassa-1064	338	5	.	.	PUNCT
ijassa-1064	339	1	the	the	DET
ijassa-1064	339	2	implication	implication	NOUN
ijassa-1064	339	3	of	of	ADP
ijassa-1064	339	4	theorem	theorem	ADJ
ijassa-1064	339	5	3.9	3.9	NUM
ijassa-1064	339	6	is	be	AUX
ijassa-1064	339	7	that	that	DET
ijassa-1064	339	8	coexistence	coexistence	NOUN
ijassa-1064	339	9	of	of	ADP
ijassa-1064	339	10	prey	prey	NOUN
ijassa-1064	339	11	and	and	CCONJ
ijassa-1064	339	12	predator	predator	NOUN
ijassa-1064	339	13	species	specie	NOUN
ijassa-1064	339	14	in	in	ADP
ijassa-1064	339	15	the	the	DET
ijassa-1064	339	16	ecosystem	ecosystem	NOUN
ijassa-1064	339	17	is	be	AUX
ijassa-1064	339	18	possible	possible	ADJ
ijassa-1064	339	19	while	while	SCONJ
ijassa-1064	339	20	disease	disease	NOUN
ijassa-1064	339	21	persists	persist	VERB
ijassa-1064	339	22	in	in	ADP
ijassa-1064	339	23	the	the	DET
ijassa-1064	339	24	population	population	NOUN
ijassa-1064	339	25	.	.	PUNCT
ijassa-1064	340	1	the	the	DET
ijassa-1064	340	2	presence	presence	NOUN
ijassa-1064	340	3	of	of	ADP
ijassa-1064	340	4	disease	disease	NOUN
ijassa-1064	340	5	in	in	ADP
ijassa-1064	340	6	the	the	DET
ijassa-1064	340	7	ecosystem	ecosystem	NOUN
ijassa-1064	340	8	,	,	PUNCT
ijassa-1064	340	9	such	such	ADJ
ijassa-1064	340	10	that	that	DET
ijassa-1064	340	11	r∗	r∗	NOUN
ijassa-1064	340	12	0	0	PUNCT
ijassa-1064	340	13	>	>	X
ijassa-1064	340	14	1	1	NUM
ijassa-1064	340	15	,	,	PUNCT
ijassa-1064	340	16	is	be	AUX
ijassa-1064	340	17	independent	independent	ADJ
ijassa-1064	340	18	of	of	ADP
ijassa-1064	340	19	initial	initial	ADJ
ijassa-1064	340	20	population	population	NOUN
ijassa-1064	340	21	sizes	size	NOUN
ijassa-1064	340	22	of	of	ADP
ijassa-1064	340	23	both	both	DET
ijassa-1064	340	24	infected	infected	ADJ
ijassa-1064	340	25	prey	prey	NOUN
ijassa-1064	340	26	and	and	CCONJ
ijassa-1064	340	27	predator	predator	NOUN
ijassa-1064	340	28	species	specie	NOUN
ijassa-1064	340	29	.	.	PUNCT
ijassa-1064	341	1	this	this	DET
ijassa-1064	341	2	global	global	ADJ
ijassa-1064	341	3	stability	stability	NOUN
ijassa-1064	341	4	result	result	NOUN
ijassa-1064	341	5	is	be	AUX
ijassa-1064	341	6	depicted	depict	VERB
ijassa-1064	341	7	in	in	ADP
ijassa-1064	341	8	figure	figure	NOUN
ijassa-1064	341	9	3.3(a	3.3(a	NUM
ijassa-1064	341	10	)	)	PUNCT
ijassa-1064	341	11	for	for	ADP
ijassa-1064	341	12	infected	infected	ADJ
ijassa-1064	341	13	prey	prey	NOUN
ijassa-1064	341	14	population	population	NOUN
ijassa-1064	341	15	and	and	CCONJ
ijassa-1064	341	16	figure	figure	VERB
ijassa-1064	341	17	3.3(b	3.3(b	NUM
ijassa-1064	341	18	)	)	PUNCT
ijassa-1064	341	19	for	for	ADP
ijassa-1064	341	20	infected	infect	VERB
ijassa-1064	341	21	predator	predator	NOUN
ijassa-1064	341	22	population	population	NOUN
ijassa-1064	341	23	.	.	PUNCT
ijassa-1064	342	1	the	the	DET
ijassa-1064	342	2	phase	phase	NOUN
ijassa-1064	342	3	portrait	portrait	NOUN
ijassa-1064	342	4	which	which	PRON
ijassa-1064	342	5	illustrates	illustrate	VERB
ijassa-1064	342	6	the	the	DET
ijassa-1064	342	7	stable	stable	ADJ
ijassa-1064	342	8	coexistence	coexistence	NOUN
ijassa-1064	342	9	of	of	ADP
ijassa-1064	342	10	prey	prey	NOUN
ijassa-1064	342	11	and	and	CCONJ
ijassa-1064	342	12	predator	predator	NOUN
ijassa-1064	342	13	populations	population	NOUN
ijassa-1064	342	14	is	be	AUX
ijassa-1064	342	15	presented	present	VERB
ijassa-1064	342	16	in	in	ADP
ijassa-1064	342	17	figure	figure	NOUN
ijassa-1064	342	18	3.4	3.4	NUM
ijassa-1064	342	19	.	.	NOUN
ijassa-1064	343	1	4	4	NUM
ijassa-1064	343	2	.	.	X
ijassa-1064	343	3	optimal	optimal	ADJ
ijassa-1064	343	4	control	control	NOUN
ijassa-1064	343	5	model	model	NOUN
ijassa-1064	343	6	in	in	ADP
ijassa-1064	343	7	order	order	NOUN
ijassa-1064	343	8	to	to	PART
ijassa-1064	343	9	enhance	enhance	VERB
ijassa-1064	343	10	the	the	DET
ijassa-1064	343	11	coexistence	coexistence	NOUN
ijassa-1064	343	12	of	of	ADP
ijassa-1064	343	13	both	both	DET
ijassa-1064	343	14	prey	prey	NOUN
ijassa-1064	343	15	and	and	CCONJ
ijassa-1064	343	16	predator	predator	NOUN
ijassa-1064	343	17	species	specie	NOUN
ijassa-1064	343	18	in	in	ADP
ijassa-1064	343	19	the	the	DET
ijassa-1064	343	20	ecosystem	ecosystem	NOUN
ijassa-1064	343	21	,	,	PUNCT
ijassa-1064	343	22	the	the	DET
ijassa-1064	343	23	prey	prey	NOUN
ijassa-1064	343	24	-	-	PUNCT
ijassa-1064	343	25	predator	predator	NOUN
ijassa-1064	343	26	model	model	NOUN
ijassa-1064	343	27	(	(	PUNCT
ijassa-1064	343	28	2.1	2.1	NUM
ijassa-1064	343	29	)	)	PUNCT
ijassa-1064	343	30	is	be	AUX
ijassa-1064	343	31	extended	extend	VERB
ijassa-1064	343	32	by	by	ADP
ijassa-1064	343	33	incorporating	incorporate	VERB
ijassa-1064	343	34	the	the	DET
ijassa-1064	343	35	following	follow	VERB
ijassa-1064	343	36	three	three	NUM
ijassa-1064	343	37	time	time	NOUN
ijassa-1064	343	38	-	-	PUNCT
ijassa-1064	343	39	dependent	dependent	ADJ
ijassa-1064	343	40	optimal	optimal	ADJ
ijassa-1064	343	41	control	control	NOUN
ijassa-1064	343	42	functions	function	NOUN
ijassa-1064	343	43	:	:	PUNCT
ijassa-1064	343	44	copyright	copyright	NOUN
ijassa-1064	343	45	©	©	PROPN
ijassa-1064	343	46	2021	2021	NUM
ijassa-1064	343	47	assa	assa	NOUN
ijassa-1064	343	48	.	.	PUNCT
ijassa-1064	344	1	adv	adv	PROPN
ijassa-1064	344	2	syst	syst	PROPN
ijassa-1064	344	3	sci	sci	PROPN
ijassa-1064	344	4	appl	appl	PROPN
ijassa-1064	344	5	(	(	PUNCT
ijassa-1064	344	6	2021	2021	NUM
ijassa-1064	344	7	)	)	PUNCT
ijassa-1064	344	8	96	96	NUM
ijassa-1064	345	1	j.a	j.a	PROPN
ijassa-1064	345	2	.	.	PROPN
ijassa-1064	345	3	ademosu	ademosu	PROPN
ijassa-1064	345	4	,	,	PUNCT
ijassa-1064	345	5	s.	s.	PROPN
ijassa-1064	345	6	olaniyi	olaniyi	PROPN
ijassa-1064	345	7	,	,	PUNCT
ijassa-1064	345	8	s.o	s.o	PROPN
ijassa-1064	345	9	.	.	PROPN
ijassa-1064	345	10	adewale	adewale	PROPN
ijassa-1064	345	11	0	0	NUM
ijassa-1064	345	12	5	5	NUM
ijassa-1064	345	13	10	10	NUM
ijassa-1064	345	14	15	15	NUM
ijassa-1064	345	15	20	20	NUM
ijassa-1064	345	16	25	25	NUM
ijassa-1064	345	17	30	30	NUM
ijassa-1064	345	18	35	35	NUM
ijassa-1064	345	19	40	40	NUM
ijassa-1064	345	20	0	0	NUM
ijassa-1064	345	21	2	2	NUM
ijassa-1064	345	22	4	4	NUM
ijassa-1064	345	23	6	6	NUM
ijassa-1064	345	24	8	8	NUM
ijassa-1064	345	25	10	10	NUM
ijassa-1064	345	26	12	12	NUM
ijassa-1064	345	27	14	14	NUM
ijassa-1064	345	28	16	16	NUM
ijassa-1064	345	29	18	18	NUM
ijassa-1064	345	30	20	20	NUM
ijassa-1064	345	31	time	time	NOUN
ijassa-1064	345	32	in	in	ADP
ijassa-1064	345	33	fe	fe	X
ijassa-1064	345	34	c	c	X
ijassa-1064	345	35	te	te	PROPN
ijassa-1064	345	36	d	d	X
ijassa-1064	345	37	p	p	X
ijassa-1064	345	38	re	re	ADP
ijassa-1064	345	39	y	y	PROPN
ijassa-1064	345	40	(	(	PUNCT
ijassa-1064	345	41	a	a	PROPN
ijassa-1064	345	42	)	)	PUNCT
ijassa-1064	345	43	0	0	NUM
ijassa-1064	345	44	5	5	NUM
ijassa-1064	345	45	10	10	NUM
ijassa-1064	345	46	15	15	NUM
ijassa-1064	345	47	0	0	NUM
ijassa-1064	345	48	5	5	NUM
ijassa-1064	345	49	10	10	NUM
ijassa-1064	345	50	15	15	NUM
ijassa-1064	345	51	20	20	NUM
ijassa-1064	345	52	25	25	NUM
ijassa-1064	345	53	time	time	NOUN
ijassa-1064	345	54	in	in	ADP
ijassa-1064	345	55	fe	fe	X
ijassa-1064	345	56	c	c	X
ijassa-1064	345	57	te	te	PROPN
ijassa-1064	345	58	d	d	X
ijassa-1064	345	59	p	p	X
ijassa-1064	345	60	re	re	ADP
ijassa-1064	345	61	d	d	NOUN
ijassa-1064	345	62	a	a	PRON
ijassa-1064	345	63	to	to	ADP
ijassa-1064	345	64	r	r	NOUN
ijassa-1064	345	65	(	(	PUNCT
ijassa-1064	345	66	b	b	NOUN
ijassa-1064	345	67	)	)	PUNCT
ijassa-1064	345	68	fig	fig	NOUN
ijassa-1064	345	69	.	.	PUNCT
ijassa-1064	346	1	3.3	3.3	NUM
ijassa-1064	346	2	.	.	PUNCT
ijassa-1064	347	1	convergence	convergence	NOUN
ijassa-1064	347	2	of	of	ADP
ijassa-1064	347	3	solution	solution	NOUN
ijassa-1064	347	4	trajectories	trajectory	NOUN
ijassa-1064	347	5	of	of	ADP
ijassa-1064	347	6	prey	prey	NOUN
ijassa-1064	347	7	-	-	PUNCT
ijassa-1064	347	8	predator	predator	NOUN
ijassa-1064	347	9	model	model	NOUN
ijassa-1064	347	10	to	to	ADP
ijassa-1064	347	11	the	the	DET
ijassa-1064	347	12	interior	interior	ADJ
ijassa-1064	347	13	equilibrium	equilibrium	NOUN
ijassa-1064	347	14	point	point	NOUN
ijassa-1064	347	15	e6	e6	NOUN
ijassa-1064	347	16	at	at	ADP
ijassa-1064	347	17	different	different	ADJ
ijassa-1064	347	18	initial	initial	ADJ
ijassa-1064	347	19	sizes	size	NOUN
ijassa-1064	347	20	.	.	PUNCT
ijassa-1064	348	1	the	the	DET
ijassa-1064	348	2	parameter	parameter	NOUN
ijassa-1064	348	3	values	value	NOUN
ijassa-1064	348	4	used	use	VERB
ijassa-1064	348	5	are	be	AUX
ijassa-1064	348	6	:	:	PUNCT
ijassa-1064	348	7	mu1	mu1	X
ijassa-1064	348	8	=	=	SYM
ijassa-1064	348	9	0.5	0.5	NUM
ijassa-1064	348	10	,	,	PUNCT
ijassa-1064	348	11	r	r	NOUN
ijassa-1064	348	12	=	=	SYM
ijassa-1064	348	13	11.2	11.2	NUM
ijassa-1064	348	14	,	,	PUNCT
ijassa-1064	348	15	β1	β1	PROPN
ijassa-1064	348	16	=	=	PUNCT
ijassa-1064	348	17	0.4	0.4	NUM
ijassa-1064	348	18	,	,	PUNCT
ijassa-1064	348	19	p1	p1	NOUN
ijassa-1064	348	20	=	=	SYM
ijassa-1064	348	21	1.0	1.0	NUM
ijassa-1064	348	22	,	,	PUNCT
ijassa-1064	348	23	γ	γ	X
ijassa-1064	348	24	=	=	SYM
ijassa-1064	348	25	0.35	0.35	NUM
ijassa-1064	348	26	,	,	PUNCT
ijassa-1064	348	27	p2	p2	X
ijassa-1064	348	28	=	=	SYM
ijassa-1064	348	29	0.2	0.2	NUM
ijassa-1064	348	30	,	,	PUNCT
ijassa-1064	348	31	p3	p3	PROPN
ijassa-1064	348	32	=	=	PUNCT
ijassa-1064	348	33	1.0	1.0	NUM
ijassa-1064	348	34	,	,	PUNCT
ijassa-1064	348	35	µ2	µ2	PROPN
ijassa-1064	348	36	=	=	PROPN
ijassa-1064	348	37	0.65	0.65	NUM
ijassa-1064	348	38	,	,	PUNCT
ijassa-1064	348	39	k	k	PROPN
ijassa-1064	348	40	=	=	SYM
ijassa-1064	348	41	30	30	NUM
ijassa-1064	348	42	,	,	PUNCT
ijassa-1064	348	43	β2	β2	NOUN
ijassa-1064	348	44	=	=	NOUN
ijassa-1064	348	45	0.65	0.65	NUM
ijassa-1064	348	46	,	,	PUNCT
ijassa-1064	348	47	c1	c1	NOUN
ijassa-1064	348	48	=	=	PROPN
ijassa-1064	348	49	0.25	0.25	NUM
ijassa-1064	348	50	,	,	PUNCT
ijassa-1064	348	51	c2	c2	PROPN
ijassa-1064	348	52	=	=	PUNCT
ijassa-1064	348	53	0.25	0.25	NUM
ijassa-1064	348	54	,	,	PUNCT
ijassa-1064	348	55	c3	c3	NOUN
ijassa-1064	348	56	=	=	PUNCT
ijassa-1064	348	57	0.15	0.15	NUM
ijassa-1064	348	58	,	,	PUNCT
ijassa-1064	348	59	so	so	SCONJ
ijassa-1064	348	60	that	that	PRON
ijassa-1064	348	61	r∗	r∗	VERB
ijassa-1064	348	62	0	0	NUM
ijassa-1064	349	1	=	=	SYM
ijassa-1064	349	2	9.7293	9.7293	NUM
ijassa-1064	349	3	>	>	SYM
ijassa-1064	349	4	1	1	NUM
ijassa-1064	349	5	.	.	SYM
ijassa-1064	349	6	0	0	NUM
ijassa-1064	349	7	1	1	NUM
ijassa-1064	349	8	2	2	NUM
ijassa-1064	349	9	3	3	NUM
ijassa-1064	349	10	4	4	NUM
ijassa-1064	349	11	5	5	NUM
ijassa-1064	349	12	6	6	NUM
ijassa-1064	349	13	7	7	NUM
ijassa-1064	349	14	8	8	NUM
ijassa-1064	349	15	0	0	NUM
ijassa-1064	349	16	1	1	NUM
ijassa-1064	349	17	2	2	NUM
ijassa-1064	349	18	3	3	NUM
ijassa-1064	349	19	4	4	NUM
ijassa-1064	349	20	5	5	NUM
ijassa-1064	349	21	6	6	NUM
ijassa-1064	349	22	7	7	NUM
ijassa-1064	349	23	prey	prey	NOUN
ijassa-1064	349	24	p	p	PROPN
ijassa-1064	349	25	re	re	ADP
ijassa-1064	349	26	da	da	NOUN
ijassa-1064	349	27	to	to	ADP
ijassa-1064	349	28	r	r	PROPN
ijassa-1064	349	29	fig	fig	NOUN
ijassa-1064	349	30	.	.	PUNCT
ijassa-1064	350	1	3.4	3.4	NUM
ijassa-1064	350	2	.	.	PUNCT
ijassa-1064	350	3	phase	phase	NOUN
ijassa-1064	350	4	portrait	portrait	NOUN
ijassa-1064	350	5	of	of	ADP
ijassa-1064	350	6	predator	predator	NOUN
ijassa-1064	350	7	against	against	ADP
ijassa-1064	350	8	prey	prey	NOUN
ijassa-1064	350	9	showing	show	VERB
ijassa-1064	350	10	stable	stable	ADJ
ijassa-1064	350	11	coexistence	coexistence	NOUN
ijassa-1064	350	12	of	of	ADP
ijassa-1064	350	13	both	both	DET
ijassa-1064	350	14	populations	population	NOUN
ijassa-1064	350	15	around	around	ADP
ijassa-1064	350	16	the	the	DET
ijassa-1064	350	17	interior	interior	ADJ
ijassa-1064	350	18	(	(	PUNCT
ijassa-1064	350	19	positive	positive	ADJ
ijassa-1064	350	20	)	)	PUNCT
ijassa-1064	350	21	equilibrium	equilibrium	NOUN
ijassa-1064	350	22	point	point	NOUN
ijassa-1064	350	23	.	.	PUNCT
ijassa-1064	351	1	1	1	X
ijassa-1064	351	2	.	.	X
ijassa-1064	351	3	the	the	DET
ijassa-1064	351	4	control	control	NOUN
ijassa-1064	351	5	function	function	VERB
ijassa-1064	351	6	u1(t	u1(t	PRON
ijassa-1064	351	7	)	)	PUNCT
ijassa-1064	351	8	∈	∈	PROPN
ijassa-1064	352	1	[	[	X
ijassa-1064	352	2	0	0	NUM
ijassa-1064	352	3	,	,	PUNCT
ijassa-1064	352	4	1	1	NUM
ijassa-1064	352	5	]	]	PUNCT
ijassa-1064	352	6	,	,	PUNCT
ijassa-1064	352	7	which	which	PRON
ijassa-1064	352	8	represents	represent	VERB
ijassa-1064	352	9	disease	disease	NOUN
ijassa-1064	352	10	prevention	prevention	NOUN
ijassa-1064	352	11	measure	measure	NOUN
ijassa-1064	352	12	for	for	ADP
ijassa-1064	352	13	both	both	CCONJ
ijassa-1064	352	14	prey	prey	NOUN
ijassa-1064	352	15	and	and	CCONJ
ijassa-1064	352	16	predator	predator	NOUN
ijassa-1064	352	17	populations	population	NOUN
ijassa-1064	352	18	.	.	PUNCT
ijassa-1064	353	1	2	2	X
ijassa-1064	353	2	.	.	X
ijassa-1064	353	3	the	the	DET
ijassa-1064	353	4	function	function	NOUN
ijassa-1064	353	5	u2(t	u2(t	NOUN
ijassa-1064	353	6	)	)	PUNCT
ijassa-1064	353	7	∈	∈	NOUN
ijassa-1064	354	1	[	[	X
ijassa-1064	354	2	0	0	NUM
ijassa-1064	354	3	,	,	PUNCT
ijassa-1064	354	4	1	1	NUM
ijassa-1064	354	5	]	]	PUNCT
ijassa-1064	354	6	,	,	PUNCT
ijassa-1064	354	7	which	which	PRON
ijassa-1064	354	8	represents	represent	VERB
ijassa-1064	354	9	treatment	treatment	NOUN
ijassa-1064	354	10	control	control	NOUN
ijassa-1064	354	11	for	for	ADP
ijassa-1064	354	12	prey	prey	PROPN
ijassa-1064	354	13	population	population	NOUN
ijassa-1064	354	14	.	.	PUNCT
ijassa-1064	355	1	3	3	X
ijassa-1064	355	2	.	.	X
ijassa-1064	355	3	the	the	DET
ijassa-1064	355	4	control	control	NOUN
ijassa-1064	355	5	function	function	VERB
ijassa-1064	355	6	u3(t	u3(t	PRON
ijassa-1064	355	7	)	)	PUNCT
ijassa-1064	355	8	∈	∈	NOUN
ijassa-1064	356	1	[	[	X
ijassa-1064	356	2	0	0	NUM
ijassa-1064	356	3	,	,	PUNCT
ijassa-1064	356	4	1	1	NUM
ijassa-1064	356	5	]	]	PUNCT
ijassa-1064	356	6	representing	represent	VERB
ijassa-1064	356	7	alternative	alternative	ADJ
ijassa-1064	356	8	source	source	NOUN
ijassa-1064	356	9	of	of	ADP
ijassa-1064	356	10	food	food	NOUN
ijassa-1064	356	11	for	for	ADP
ijassa-1064	356	12	predator	predator	NOUN
ijassa-1064	356	13	survival	survival	NOUN
ijassa-1064	356	14	.	.	PUNCT
ijassa-1064	357	1	therefore	therefore	ADV
ijassa-1064	357	2	,	,	PUNCT
ijassa-1064	357	3	the	the	DET
ijassa-1064	357	4	prey	prey	NOUN
ijassa-1064	357	5	-	-	PUNCT
ijassa-1064	357	6	predator	predator	NOUN
ijassa-1064	357	7	model	model	NOUN
ijassa-1064	357	8	(	(	PUNCT
ijassa-1064	357	9	2.1	2.1	NUM
ijassa-1064	357	10	)	)	PUNCT
ijassa-1064	357	11	becomes	become	VERB
ijassa-1064	357	12	a	a	DET
ijassa-1064	357	13	non	non	ADJ
ijassa-1064	357	14	-	-	ADJ
ijassa-1064	357	15	autonomous	autonomous	ADJ
ijassa-1064	357	16	system	system	NOUN
ijassa-1064	357	17	of	of	ADP
ijassa-1064	357	18	ordinary	ordinary	ADJ
ijassa-1064	357	19	differential	differential	ADJ
ijassa-1064	357	20	equations	equation	NOUN
ijassa-1064	357	21	of	of	ADP
ijassa-1064	357	22	the	the	DET
ijassa-1064	357	23	form	form	NOUN
ijassa-1064	357	24	:	:	PUNCT
ijassa-1064	357	25	copyright	copyright	NOUN
ijassa-1064	357	26	©	©	PROPN
ijassa-1064	357	27	2021	2021	NUM
ijassa-1064	357	28	assa	assa	NOUN
ijassa-1064	357	29	.	.	PUNCT
ijassa-1064	358	1	adv	adv	PROPN
ijassa-1064	358	2	syst	syst	PROPN
ijassa-1064	358	3	sci	sci	PROPN
ijassa-1064	358	4	appl	appl	PROPN
ijassa-1064	358	5	(	(	PUNCT
ijassa-1064	358	6	2021	2021	NUM
ijassa-1064	358	7	)	)	PUNCT
ijassa-1064	358	8	stability	stability	NOUN
ijassa-1064	358	9	analysis	analysis	NOUN
ijassa-1064	358	10	and	and	CCONJ
ijassa-1064	358	11	optimal	optimal	ADJ
ijassa-1064	358	12	measure	measure	NOUN
ijassa-1064	358	13	97	97	NUM
ijassa-1064	358	14	dxs	dxs	PROPN
ijassa-1064	358	15	dt	dt	NOUN
ijassa-1064	358	16	=	=	SYM
ijassa-1064	358	17	rxs	rxs	X
ijassa-1064	358	18	(	(	PUNCT
ijassa-1064	358	19	1−	1−	NUM
ijassa-1064	358	20	xs	xs	PROPN
ijassa-1064	358	21	k	k	PROPN
ijassa-1064	358	22	)	)	PUNCT
ijassa-1064	358	23	−	−	PROPN
ijassa-1064	359	1	(	(	PUNCT
ijassa-1064	359	2	1−	1−	NUM
ijassa-1064	359	3	u1(t))β1xsxi	u1(t))β1xsxi	NOUN
ijassa-1064	359	4	−	−	PROPN
ijassa-1064	359	5	p1xsys	p1xsy	NOUN
ijassa-1064	359	6	−	−	PROPN
ijassa-1064	359	7	µ1xs	µ1xs	NOUN
ijassa-1064	359	8	dxi	dxi	NOUN
ijassa-1064	359	9	dt	dt	NOUN
ijassa-1064	360	1	=	=	SYM
ijassa-1064	360	2	β1xsxi	β1xsxi	NUM
ijassa-1064	360	3	−	−	PROPN
ijassa-1064	361	1	p2xiys	p2xiys	ADP
ijassa-1064	361	2	−	−	PROPN
ijassa-1064	361	3	p3xiyi	p3xiyi	NOUN
ijassa-1064	361	4	−	−	PROPN
ijassa-1064	361	5	(	(	PUNCT
ijassa-1064	361	6	µ1	µ1	PROPN
ijassa-1064	361	7	+	+	PROPN
ijassa-1064	362	1	γ)xi	γ)xi	PROPN
ijassa-1064	362	2	−	−	PROPN
ijassa-1064	362	3	u2(t)r0xi	u2(t)r0xi	PRON
ijassa-1064	362	4	dxr	dxr	ADJ
ijassa-1064	362	5	dt	dt	X
ijassa-1064	362	6	=	=	SYM
ijassa-1064	362	7	γxi	γxi	NOUN
ijassa-1064	362	8	+	+	CCONJ
ijassa-1064	362	9	u2(t)r0xi	u2(t)r0xi	PROPN
ijassa-1064	362	10	−	−	NOUN
ijassa-1064	362	11	µ1xr	µ1xr	PUNCT
ijassa-1064	362	12	dys	dys	NOUN
ijassa-1064	362	13	dt	dt	NOUN
ijassa-1064	362	14	=	=	PUNCT
ijassa-1064	362	15	c1p1xsys	c1p1xsys	X
ijassa-1064	362	16	+	+	CCONJ
ijassa-1064	362	17	c2p2xiys	c2p2xiy	VERB
ijassa-1064	362	18	−	−	X
ijassa-1064	362	19	(	(	PUNCT
ijassa-1064	362	20	1−	1−	NUM
ijassa-1064	362	21	u1(t))β2ysyi	u1(t))β2ysyi	ADJ
ijassa-1064	362	22	−	−	NOUN
ijassa-1064	362	23	µ2ys	µ2ys	PUNCT
ijassa-1064	363	1	+	+	CCONJ
ijassa-1064	363	2	u3(t)c0ys	u3(t)c0ys	PROPN
ijassa-1064	363	3	dyi	dyi	NOUN
ijassa-1064	363	4	dt	dt	NOUN
ijassa-1064	363	5	=	=	PUNCT
ijassa-1064	363	6	(	(	PUNCT
ijassa-1064	363	7	1−	1−	NUM
ijassa-1064	363	8	u1(t))β2ysyi	u1(t))β2ysyi	NOUN
ijassa-1064	363	9	+	+	NUM
ijassa-1064	363	10	c3p3xiyi	c3p3xiyi	NOUN
ijassa-1064	363	11	−	−	ADP
ijassa-1064	363	12	µ2yi	µ2yi	NOUN
ijassa-1064	363	13	,	,	PUNCT
ijassa-1064	363	14	(	(	PUNCT
ijassa-1064	363	15	4.25	4.25	NUM
ijassa-1064	363	16	)	)	PUNCT
ijassa-1064	363	17	where	where	SCONJ
ijassa-1064	363	18	r0	r0	NOUN
ijassa-1064	363	19	and	and	CCONJ
ijassa-1064	363	20	c0	c0	PROPN
ijassa-1064	363	21	are	be	AUX
ijassa-1064	363	22	the	the	DET
ijassa-1064	363	23	rate	rate	NOUN
ijassa-1064	363	24	constants	constant	NOUN
ijassa-1064	363	25	for	for	ADP
ijassa-1064	363	26	the	the	DET
ijassa-1064	363	27	optimal	optimal	ADJ
ijassa-1064	363	28	controls	control	NOUN
ijassa-1064	363	29	u2(t	u2(t	NOUN
ijassa-1064	363	30	)	)	PUNCT
ijassa-1064	363	31	and	and	CCONJ
ijassa-1064	363	32	u3(t	u3(t	NUM
ijassa-1064	363	33	)	)	PUNCT
ijassa-1064	363	34	,	,	PUNCT
ijassa-1064	363	35	respectively	respectively	ADV
ijassa-1064	363	36	.	.	PUNCT
ijassa-1064	364	1	since	since	SCONJ
ijassa-1064	364	2	the	the	DET
ijassa-1064	364	3	goal	goal	NOUN
ijassa-1064	364	4	is	be	AUX
ijassa-1064	364	5	to	to	PART
ijassa-1064	364	6	reduce	reduce	VERB
ijassa-1064	364	7	the	the	DET
ijassa-1064	364	8	risk	risk	NOUN
ijassa-1064	364	9	of	of	ADP
ijassa-1064	364	10	both	both	DET
ijassa-1064	364	11	prey	prey	NOUN
ijassa-1064	364	12	and	and	CCONJ
ijassa-1064	364	13	predator	predator	NOUN
ijassa-1064	364	14	species	specie	NOUN
ijassa-1064	364	15	going	go	VERB
ijassa-1064	364	16	extinct	extinct	ADJ
ijassa-1064	364	17	,	,	PUNCT
ijassa-1064	364	18	such	such	ADJ
ijassa-1064	364	19	that	that	SCONJ
ijassa-1064	364	20	the	the	DET
ijassa-1064	364	21	populations	population	NOUN
ijassa-1064	364	22	of	of	ADP
ijassa-1064	364	23	infected	infected	ADJ
ijassa-1064	364	24	prey	prey	NOUN
ijassa-1064	364	25	and	and	CCONJ
ijassa-1064	364	26	predator	predator	NOUN
ijassa-1064	364	27	are	be	AUX
ijassa-1064	364	28	minimized	minimize	VERB
ijassa-1064	364	29	at	at	ADP
ijassa-1064	364	30	minimum	minimum	ADJ
ijassa-1064	364	31	costs	cost	NOUN
ijassa-1064	364	32	possible	possible	ADJ
ijassa-1064	364	33	,	,	PUNCT
ijassa-1064	364	34	then	then	ADV
ijassa-1064	364	35	the	the	DET
ijassa-1064	364	36	following	follow	VERB
ijassa-1064	364	37	objective	objective	ADJ
ijassa-1064	364	38	functional	functional	NOUN
ijassa-1064	364	39	is	be	AUX
ijassa-1064	364	40	formed	form	VERB
ijassa-1064	365	1	j	j	PROPN
ijassa-1064	365	2	=	=	SYM
ijassa-1064	365	3	∫	∫	PROPN
ijassa-1064	366	1	tf	tf	INTJ
ijassa-1064	366	2	0	0	NUM
ijassa-1064	366	3	(	(	PUNCT
ijassa-1064	366	4	a1xi	a1xi	PUNCT
ijassa-1064	366	5	+	+	NUM
ijassa-1064	366	6	a2yi	a2yi	PUNCT
ijassa-1064	366	7	+	+	NOUN
ijassa-1064	366	8	1	1	NUM
ijassa-1064	366	9	2	2	NUM
ijassa-1064	367	1	[	[	X
ijassa-1064	367	2	b1u	b1u	ADP
ijassa-1064	367	3	2	2	NUM
ijassa-1064	367	4	1	1	NUM
ijassa-1064	367	5	+	+	NOUN
ijassa-1064	367	6	b2u	b2u	PROPN
ijassa-1064	367	7	2	2	NUM
ijassa-1064	367	8	2	2	NUM
ijassa-1064	367	9	+	+	NOUN
ijassa-1064	367	10	b3u	b3u	NOUN
ijassa-1064	367	11	2	2	NUM
ijassa-1064	367	12	3	3	NUM
ijassa-1064	367	13	]	]	PUNCT
ijassa-1064	367	14	)	)	PUNCT
ijassa-1064	368	1	dt	dt	X
ijassa-1064	368	2	,	,	PUNCT
ijassa-1064	368	3	(	(	PUNCT
ijassa-1064	368	4	4.26	4.26	NUM
ijassa-1064	368	5	)	)	PUNCT
ijassa-1064	368	6	where	where	SCONJ
ijassa-1064	368	7	a1	a1	NOUN
ijassa-1064	368	8	,	,	PUNCT
ijassa-1064	368	9	a2	a2	PROPN
ijassa-1064	368	10	,	,	PUNCT
ijassa-1064	368	11	b1	b1	NOUN
ijassa-1064	368	12	,	,	PUNCT
ijassa-1064	368	13	b2	b2	NOUN
ijassa-1064	368	14	and	and	CCONJ
ijassa-1064	368	15	b3	b3	PROPN
ijassa-1064	368	16	are	be	AUX
ijassa-1064	368	17	the	the	DET
ijassa-1064	368	18	positive	positive	ADJ
ijassa-1064	368	19	weight	weight	NOUN
ijassa-1064	368	20	constants	constant	NOUN
ijassa-1064	368	21	for	for	ADP
ijassa-1064	368	22	balancing	balance	VERB
ijassa-1064	368	23	the	the	DET
ijassa-1064	368	24	terms	term	NOUN
ijassa-1064	368	25	in	in	ADP
ijassa-1064	368	26	the	the	DET
ijassa-1064	368	27	objective	objective	ADJ
ijassa-1064	368	28	functional	functional	NOUN
ijassa-1064	368	29	over	over	ADP
ijassa-1064	368	30	the	the	DET
ijassa-1064	368	31	time	time	NOUN
ijassa-1064	368	32	interval	interval	NOUN
ijassa-1064	368	33	[	[	X
ijassa-1064	368	34	0	0	NUM
ijassa-1064	368	35	,	,	PUNCT
ijassa-1064	368	36	tf	tf	X
ijassa-1064	368	37	]	]	PUNCT
ijassa-1064	368	38	.	.	PUNCT
ijassa-1064	369	1	further	far	ADV
ijassa-1064	369	2	,	,	PUNCT
ijassa-1064	369	3	the	the	DET
ijassa-1064	369	4	cost	cost	NOUN
ijassa-1064	369	5	function	function	NOUN
ijassa-1064	369	6	associated	associate	VERB
ijassa-1064	369	7	with	with	ADP
ijassa-1064	369	8	the	the	DET
ijassa-1064	369	9	disease	disease	NOUN
ijassa-1064	369	10	prevention	prevention	NOUN
ijassa-1064	369	11	measure	measure	NOUN
ijassa-1064	369	12	for	for	ADP
ijassa-1064	369	13	prey	prey	NOUN
ijassa-1064	369	14	and	and	CCONJ
ijassa-1064	369	15	predator	predator	NOUN
ijassa-1064	369	16	populations	population	NOUN
ijassa-1064	369	17	is	be	AUX
ijassa-1064	369	18	represented	represent	VERB
ijassa-1064	369	19	by	by	ADP
ijassa-1064	369	20	the	the	DET
ijassa-1064	369	21	term	term	NOUN
ijassa-1064	369	22	1/2b1u	1/2b1u	NUM
ijassa-1064	369	23	2	2	NUM
ijassa-1064	369	24	1	1	NUM
ijassa-1064	369	25	,	,	PUNCT
ijassa-1064	369	26	while	while	SCONJ
ijassa-1064	369	27	the	the	DET
ijassa-1064	369	28	treatment	treatment	NOUN
ijassa-1064	369	29	measure	measure	NOUN
ijassa-1064	369	30	for	for	ADP
ijassa-1064	369	31	prey	prey	NOUN
ijassa-1064	369	32	population	population	NOUN
ijassa-1064	369	33	and	and	CCONJ
ijassa-1064	369	34	the	the	DET
ijassa-1064	369	35	provision	provision	NOUN
ijassa-1064	369	36	of	of	ADP
ijassa-1064	369	37	alternative	alternative	ADJ
ijassa-1064	369	38	food	food	NOUN
ijassa-1064	369	39	source	source	NOUN
ijassa-1064	369	40	for	for	ADP
ijassa-1064	369	41	predator	predator	NOUN
ijassa-1064	369	42	are	be	AUX
ijassa-1064	369	43	,	,	PUNCT
ijassa-1064	369	44	respectively	respectively	ADV
ijassa-1064	369	45	,	,	PUNCT
ijassa-1064	369	46	represented	represent	VERB
ijassa-1064	369	47	by	by	ADP
ijassa-1064	369	48	the	the	DET
ijassa-1064	369	49	terms	term	NOUN
ijassa-1064	369	50	1/2b2u	1/2b2u	NUM
ijassa-1064	369	51	2	2	NUM
ijassa-1064	369	52	2	2	NUM
ijassa-1064	369	53	and	and	CCONJ
ijassa-1064	369	54	1/2b3u	1/2b3u	NUM
ijassa-1064	369	55	2	2	NUM
ijassa-1064	369	56	3	3	NUM
ijassa-1064	369	57	.	.	PUNCT
ijassa-1064	370	1	the	the	DET
ijassa-1064	370	2	objective	objective	ADJ
ijassa-1064	370	3	functional	functional	NOUN
ijassa-1064	370	4	is	be	AUX
ijassa-1064	370	5	made	make	VERB
ijassa-1064	370	6	of	of	ADP
ijassa-1064	370	7	nonlinear	nonlinear	ADJ
ijassa-1064	370	8	cost	cost	NOUN
ijassa-1064	370	9	on	on	ADP
ijassa-1064	370	10	controls	control	NOUN
ijassa-1064	370	11	of	of	ADP
ijassa-1064	370	12	quadratic	quadratic	ADJ
ijassa-1064	370	13	type	type	NOUN
ijassa-1064	370	14	in	in	ADP
ijassa-1064	370	15	line	line	NOUN
ijassa-1064	370	16	with	with	ADP
ijassa-1064	370	17	the	the	DET
ijassa-1064	370	18	standards	standard	NOUN
ijassa-1064	370	19	for	for	ADP
ijassa-1064	370	20	optimal	optimal	ADJ
ijassa-1064	370	21	control	control	NOUN
ijassa-1064	370	22	problems	problem	NOUN
ijassa-1064	370	23	(	(	PUNCT
ijassa-1064	370	24	see	see	VERB
ijassa-1064	370	25	,	,	PUNCT
ijassa-1064	371	1	e.g.	e.g.	ADV
ijassa-1064	371	2	[	[	X
ijassa-1064	371	3	1	1	NUM
ijassa-1064	371	4	,	,	PUNCT
ijassa-1064	371	5	4	4	NUM
ijassa-1064	371	6	,	,	PUNCT
ijassa-1064	371	7	14	14	NUM
ijassa-1064	371	8	,	,	PUNCT
ijassa-1064	371	9	16	16	NUM
ijassa-1064	371	10	,	,	PUNCT
ijassa-1064	371	11	24	24	NUM
ijassa-1064	371	12	,	,	PUNCT
ijassa-1064	371	13	25	25	NUM
ijassa-1064	371	14	]	]	PUNCT
ijassa-1064	371	15	)	)	PUNCT
ijassa-1064	371	16	.	.	PUNCT
ijassa-1064	372	1	therefore	therefore	ADV
ijassa-1064	372	2	,	,	PUNCT
ijassa-1064	372	3	the	the	DET
ijassa-1064	372	4	optimal	optimal	ADJ
ijassa-1064	372	5	control	control	NOUN
ijassa-1064	372	6	problem	problem	NOUN
ijassa-1064	372	7	for	for	ADP
ijassa-1064	372	8	the	the	DET
ijassa-1064	372	9	prey	prey	NOUN
ijassa-1064	372	10	-	-	PUNCT
ijassa-1064	372	11	predator	predator	NOUN
ijassa-1064	372	12	system	system	NOUN
ijassa-1064	372	13	(	(	PUNCT
ijassa-1064	372	14	4.25	4.25	NUM
ijassa-1064	372	15	)	)	PUNCT
ijassa-1064	372	16	is	be	AUX
ijassa-1064	372	17	to	to	PART
ijassa-1064	372	18	seek	seek	VERB
ijassa-1064	372	19	a	a	DET
ijassa-1064	372	20	control	control	NOUN
ijassa-1064	372	21	triple	triple	NOUN
ijassa-1064	372	22	u∗	u∗	ADJ
ijassa-1064	372	23	=	=	PUNCT
ijassa-1064	372	24	(	(	PUNCT
ijassa-1064	372	25	u∗1	u∗1	PROPN
ijassa-1064	372	26	,	,	PUNCT
ijassa-1064	372	27	u	u	NOUN
ijassa-1064	372	28	∗	∗	NOUN
ijassa-1064	372	29	2	2	NUM
ijassa-1064	372	30	,	,	PUNCT
ijassa-1064	372	31	u	u	NOUN
ijassa-1064	372	32	∗	∗	NOUN
ijassa-1064	372	33	3	3	NUM
ijassa-1064	372	34	,	,	PUNCT
ijassa-1064	372	35	)	)	PUNCT
ijassa-1064	372	36	,	,	PUNCT
ijassa-1064	372	37	such	such	ADJ
ijassa-1064	372	38	that	that	PRON
ijassa-1064	372	39	j(u∗	j(u∗	NOUN
ijassa-1064	372	40	)	)	PUNCT
ijassa-1064	373	1	=	=	SYM
ijassa-1064	373	2	min	min	NOUN
ijassa-1064	373	3	{	{	PUNCT
ijassa-1064	373	4	j(u1	j(u1	NOUN
ijassa-1064	373	5	,	,	PUNCT
ijassa-1064	373	6	u2	u2	NOUN
ijassa-1064	373	7	,	,	PUNCT
ijassa-1064	373	8	u3	u3	NOUN
ijassa-1064	373	9	)	)	PUNCT
ijassa-1064	373	10	:	:	PUNCT
ijassa-1064	373	11	u1	u1	NOUN
ijassa-1064	373	12	,	,	PUNCT
ijassa-1064	373	13	u2	u2	NOUN
ijassa-1064	373	14	,	,	PUNCT
ijassa-1064	373	15	u3	u3	NOUN
ijassa-1064	373	16	∈	∈	PROPN
ijassa-1064	373	17	u	u	NOUN
ijassa-1064	373	18	}	}	PUNCT
ijassa-1064	373	19	,	,	PUNCT
ijassa-1064	373	20	(	(	PUNCT
ijassa-1064	373	21	4.27	4.27	NUM
ijassa-1064	373	22	)	)	PUNCT
ijassa-1064	373	23	where	where	SCONJ
ijassa-1064	373	24	u	u	NOUN
ijassa-1064	373	25	=	=	X
ijassa-1064	373	26	{	{	PUNCT
ijassa-1064	373	27	ui(t	ui(t	NOUN
ijassa-1064	373	28	)	)	PUNCT
ijassa-1064	373	29	:	:	PUNCT
ijassa-1064	373	30	0	0	NUM
ijassa-1064	373	31	≤	≤	NUM
ijassa-1064	373	32	ui(t	ui(t	NOUN
ijassa-1064	373	33	)	)	PUNCT
ijassa-1064	373	34	≤	≤	NUM
ijassa-1064	373	35	1,lebesgue	1,lebesgue	NUM
ijassa-1064	373	36	measurable	measurable	NOUN
ijassa-1064	373	37	,	,	PUNCT
ijassa-1064	373	38	t	t	PROPN
ijassa-1064	373	39	∈	∈	PROPN
ijassa-1064	374	1	[	[	X
ijassa-1064	374	2	0	0	NUM
ijassa-1064	374	3	,	,	PUNCT
ijassa-1064	374	4	tf	tf	X
ijassa-1064	374	5	]	]	X
ijassa-1064	374	6	,	,	PUNCT
ijassa-1064	374	7	for	for	ADP
ijassa-1064	374	8	i	i	PROPN
ijassa-1064	374	9	=	=	SYM
ijassa-1064	374	10	1	1	NUM
ijassa-1064	374	11	,	,	PUNCT
ijassa-1064	374	12	2	2	NUM
ijassa-1064	374	13	,	,	PUNCT
ijassa-1064	374	14	3	3	NUM
ijassa-1064	374	15	}	}	PUNCT
ijassa-1064	374	16	is	be	AUX
ijassa-1064	374	17	a	a	DET
ijassa-1064	374	18	nonempty	nonempty	ADJ
ijassa-1064	374	19	set	set	NOUN
ijassa-1064	374	20	of	of	ADP
ijassa-1064	374	21	all	all	DET
ijassa-1064	374	22	admissible	admissible	ADJ
ijassa-1064	374	23	controls	control	NOUN
ijassa-1064	374	24	.	.	PUNCT
ijassa-1064	375	1	4.1	4.1	NUM
ijassa-1064	375	2	.	.	PUNCT
ijassa-1064	375	3	analysis	analysis	NOUN
ijassa-1064	375	4	of	of	ADP
ijassa-1064	375	5	the	the	DET
ijassa-1064	375	6	control	control	NOUN
ijassa-1064	375	7	model	model	NOUN
ijassa-1064	375	8	the	the	DET
ijassa-1064	375	9	necessary	necessary	ADJ
ijassa-1064	375	10	conditions	condition	NOUN
ijassa-1064	375	11	that	that	PRON
ijassa-1064	375	12	must	must	AUX
ijassa-1064	375	13	be	be	AUX
ijassa-1064	375	14	satisfied	satisfied	ADJ
ijassa-1064	375	15	by	by	ADP
ijassa-1064	375	16	the	the	DET
ijassa-1064	375	17	optimal	optimal	ADJ
ijassa-1064	375	18	control	control	NOUN
ijassa-1064	375	19	triple	triple	ADJ
ijassa-1064	375	20	u∗	u∗	ADV
ijassa-1064	375	21	for	for	ADP
ijassa-1064	375	22	the	the	DET
ijassa-1064	375	23	minimization	minimization	NOUN
ijassa-1064	375	24	problem	problem	NOUN
ijassa-1064	375	25	are	be	AUX
ijassa-1064	375	26	derivable	derivable	ADJ
ijassa-1064	375	27	from	from	ADP
ijassa-1064	375	28	pontryagin	pontryagin	NOUN
ijassa-1064	375	29	’s	’s	PART
ijassa-1064	375	30	maximum	maximum	ADJ
ijassa-1064	375	31	principle	principle	NOUN
ijassa-1064	375	32	[	[	X
ijassa-1064	375	33	26	26	NUM
ijassa-1064	375	34	]	]	PUNCT
ijassa-1064	375	35	.	.	PUNCT
ijassa-1064	376	1	this	this	DET
ijassa-1064	376	2	principle	principle	NOUN
ijassa-1064	376	3	converts	convert	VERB
ijassa-1064	376	4	the	the	DET
ijassa-1064	376	5	problem	problem	NOUN
ijassa-1064	376	6	in	in	ADP
ijassa-1064	376	7	(	(	PUNCT
ijassa-1064	376	8	4.27	4.27	NUM
ijassa-1064	376	9	)	)	PUNCT
ijassa-1064	376	10	with	with	ADP
ijassa-1064	376	11	(	(	PUNCT
ijassa-1064	376	12	4.26	4.26	NUM
ijassa-1064	376	13	)	)	PUNCT
ijassa-1064	376	14	subject	subject	NOUN
ijassa-1064	376	15	to	to	ADP
ijassa-1064	376	16	the	the	DET
ijassa-1064	376	17	state	state	NOUN
ijassa-1064	376	18	system	system	NOUN
ijassa-1064	376	19	(	(	PUNCT
ijassa-1064	376	20	4.25	4.25	NUM
ijassa-1064	376	21	)	)	PUNCT
ijassa-1064	376	22	into	into	ADP
ijassa-1064	376	23	a	a	DET
ijassa-1064	376	24	problem	problem	NOUN
ijassa-1064	376	25	of	of	ADP
ijassa-1064	376	26	minimizing	minimize	VERB
ijassa-1064	376	27	pointwise	pointwise	NOUN
ijassa-1064	376	28	a	a	DET
ijassa-1064	376	29	hamiltonian	hamiltonian	ADJ
ijassa-1064	376	30	h	h	NOUN
ijassa-1064	376	31	,	,	PUNCT
ijassa-1064	376	32	with	with	ADP
ijassa-1064	376	33	respect	respect	NOUN
ijassa-1064	376	34	to	to	ADP
ijassa-1064	376	35	u1(t	u1(t	NOUN
ijassa-1064	376	36	)	)	PUNCT
ijassa-1064	376	37	,	,	PUNCT
ijassa-1064	376	38	u2(t	u2(t	PROPN
ijassa-1064	376	39	)	)	PUNCT
ijassa-1064	376	40	and	and	CCONJ
ijassa-1064	376	41	u3(t	u3(t	NUM
ijassa-1064	376	42	)	)	PUNCT
ijassa-1064	376	43	.	.	PUNCT
ijassa-1064	377	1	thus	thus	ADV
ijassa-1064	377	2	,	,	PUNCT
ijassa-1064	377	3	the	the	DET
ijassa-1064	377	4	hamiltonian	hamiltonian	NOUN
ijassa-1064	377	5	for	for	ADP
ijassa-1064	377	6	the	the	DET
ijassa-1064	377	7	control	control	NOUN
ijassa-1064	377	8	problem	problem	NOUN
ijassa-1064	377	9	is	be	AUX
ijassa-1064	377	10	given	give	VERB
ijassa-1064	377	11	by	by	ADP
ijassa-1064	377	12	copyright	copyright	NOUN
ijassa-1064	377	13	©	©	PROPN
ijassa-1064	377	14	2021	2021	NUM
ijassa-1064	377	15	assa	assa	NOUN
ijassa-1064	377	16	.	.	PUNCT
ijassa-1064	378	1	adv	adv	PROPN
ijassa-1064	378	2	syst	syst	PROPN
ijassa-1064	378	3	sci	sci	PROPN
ijassa-1064	378	4	appl	appl	PROPN
ijassa-1064	378	5	(	(	PUNCT
ijassa-1064	378	6	2021	2021	NUM
ijassa-1064	378	7	)	)	PUNCT
ijassa-1064	378	8	98	98	NUM
ijassa-1064	379	1	j.a	j.a	PROPN
ijassa-1064	379	2	.	.	PROPN
ijassa-1064	379	3	ademosu	ademosu	PROPN
ijassa-1064	379	4	,	,	PUNCT
ijassa-1064	379	5	s.	s.	PROPN
ijassa-1064	379	6	olaniyi	olaniyi	PROPN
ijassa-1064	379	7	,	,	PUNCT
ijassa-1064	379	8	s.o	s.o	PROPN
ijassa-1064	379	9	.	.	PROPN
ijassa-1064	379	10	adewale	adewale	PROPN
ijassa-1064	379	11	h	h	PROPN
ijassa-1064	379	12	=	=	PUNCT
ijassa-1064	379	13	a1xi	a1xi	PROPN
ijassa-1064	379	14	+	+	NUM
ijassa-1064	379	15	a2yi	a2yi	PUNCT
ijassa-1064	380	1	+	+	NOUN
ijassa-1064	380	2	1	1	NUM
ijassa-1064	380	3	2	2	NUM
ijassa-1064	380	4	[	[	X
ijassa-1064	380	5	b1u	b1u	ADP
ijassa-1064	380	6	2	2	NUM
ijassa-1064	380	7	1	1	NUM
ijassa-1064	380	8	+	+	NOUN
ijassa-1064	380	9	b2u	b2u	PROPN
ijassa-1064	380	10	2	2	NUM
ijassa-1064	380	11	2	2	NUM
ijassa-1064	380	12	+	+	NOUN
ijassa-1064	380	13	b3u	b3u	NOUN
ijassa-1064	380	14	2	2	NUM
ijassa-1064	380	15	3	3	NUM
ijassa-1064	380	16	]	]	PUNCT
ijassa-1064	380	17	+	+	NUM
ijassa-1064	380	18	η1	η1	NOUN
ijassa-1064	380	19	[	[	PUNCT
ijassa-1064	380	20	rxs	rxs	X
ijassa-1064	380	21	(	(	PUNCT
ijassa-1064	380	22	1−	1−	NUM
ijassa-1064	380	23	xs	xs	PROPN
ijassa-1064	380	24	k	k	PROPN
ijassa-1064	380	25	)	)	PUNCT
ijassa-1064	380	26	−	−	PROPN
ijassa-1064	381	1	(	(	PUNCT
ijassa-1064	381	2	1−	1−	NUM
ijassa-1064	381	3	u2(t))β1xsxi	u2(t))β1xsxi	NOUN
ijassa-1064	381	4	−	−	ADP
ijassa-1064	381	5	p1xsys	p1xsy	NOUN
ijassa-1064	381	6	−	−	NOUN
ijassa-1064	381	7	µ1xs	µ1x	NOUN
ijassa-1064	381	8	]	]	PUNCT
ijassa-1064	382	1	+	+	X
ijassa-1064	382	2	η2	η2	X
ijassa-1064	383	1	[	[	X
ijassa-1064	383	2	β1xsxi	β1xsxi	NOUN
ijassa-1064	383	3	−	−	X
ijassa-1064	383	4	p2xiys	p2xiys	ADP
ijassa-1064	383	5	−	−	PROPN
ijassa-1064	383	6	p3xiyi	p3xiyi	NOUN
ijassa-1064	383	7	−	−	PROPN
ijassa-1064	383	8	(	(	PUNCT
ijassa-1064	383	9	µ1	µ1	PROPN
ijassa-1064	383	10	+	+	PROPN
ijassa-1064	383	11	γ)xi	γ)xi	PROPN
ijassa-1064	383	12	−	−	X
ijassa-1064	384	1	u2(t)r0xi	u2(t)r0xi	PROPN
ijassa-1064	384	2	]	]	PUNCT
ijassa-1064	385	1	+	+	NOUN
ijassa-1064	385	2	η3[γxi	η3[γxi	PROPN
ijassa-1064	385	3	+	+	X
ijassa-1064	386	1	u2(t)r0xi	u2(t)r0xi	PROPN
ijassa-1064	386	2	−	−	PROPN
ijassa-1064	386	3	µ1xr	µ1xr	PUNCT
ijassa-1064	386	4	]	]	X
ijassa-1064	386	5	+	+	PUNCT
ijassa-1064	386	6	η4[c1p1xsys	η4[c1p1xsys	PROPN
ijassa-1064	386	7	+	+	CCONJ
ijassa-1064	386	8	c2p2xiys	c2p2xiy	VERB
ijassa-1064	386	9	−	−	X
ijassa-1064	386	10	(	(	PUNCT
ijassa-1064	386	11	1−	1−	NUM
ijassa-1064	386	12	u1(t))β2ysyi	u1(t))β2ysyi	ADJ
ijassa-1064	386	13	−	−	NOUN
ijassa-1064	386	14	µ2ys	µ2ys	PUNCT
ijassa-1064	387	1	+	+	CCONJ
ijassa-1064	387	2	u3(t)c0ys	u3(t)c0ys	PROPN
ijassa-1064	387	3	]	]	PUNCT
ijassa-1064	388	1	+	+	ADJ
ijassa-1064	388	2	η5[(1−	η5[(1−	PROPN
ijassa-1064	388	3	u1(t))β2ysyi	u1(t))β2ysyi	ADJ
ijassa-1064	388	4	+	+	NUM
ijassa-1064	388	5	c3p3xiyi	c3p3xiyi	NOUN
ijassa-1064	388	6	−	−	ADP
ijassa-1064	388	7	µ2yi	µ2yi	NOUN
ijassa-1064	388	8	]	]	PUNCT
ijassa-1064	388	9	,	,	PUNCT
ijassa-1064	388	10	(	(	PUNCT
ijassa-1064	388	11	4.28	4.28	NUM
ijassa-1064	388	12	)	)	PUNCT
ijassa-1064	388	13	where	where	SCONJ
ijassa-1064	388	14	η1	η1	NOUN
ijassa-1064	388	15	,	,	PUNCT
ijassa-1064	388	16	η2	η2	NOUN
ijassa-1064	388	17	,	,	PUNCT
ijassa-1064	388	18	η3	η3	NOUN
ijassa-1064	388	19	,	,	PUNCT
ijassa-1064	388	20	η4	η4	VERB
ijassa-1064	388	21	and	and	CCONJ
ijassa-1064	388	22	η5	η5	PROPN
ijassa-1064	388	23	are	be	AUX
ijassa-1064	388	24	the	the	DET
ijassa-1064	388	25	adjoint	adjoint	NOUN
ijassa-1064	388	26	or	or	CCONJ
ijassa-1064	388	27	co	co	NOUN
ijassa-1064	388	28	-	-	NOUN
ijassa-1064	388	29	state	state	ADJ
ijassa-1064	388	30	variables	variable	NOUN
ijassa-1064	388	31	corresponding	correspond	VERB
ijassa-1064	388	32	to	to	ADP
ijassa-1064	388	33	the	the	DET
ijassa-1064	388	34	state	state	NOUN
ijassa-1064	388	35	variables	variable	VERB
ijassa-1064	388	36	xs	xs	PROPN
ijassa-1064	388	37	,	,	PUNCT
ijassa-1064	388	38	xi	xi	PROPN
ijassa-1064	388	39	,	,	PUNCT
ijassa-1064	388	40	xr	xr	PROPN
ijassa-1064	388	41	,	,	PUNCT
ijassa-1064	388	42	ys	ys	PROPN
ijassa-1064	388	43	and	and	CCONJ
ijassa-1064	388	44	yi	yi	PROPN
ijassa-1064	388	45	,	,	PUNCT
ijassa-1064	388	46	respectively	respectively	ADV
ijassa-1064	388	47	.	.	PUNCT
ijassa-1064	389	1	applying	apply	VERB
ijassa-1064	389	2	the	the	DET
ijassa-1064	389	3	existence	existence	NOUN
ijassa-1064	389	4	results	result	NOUN
ijassa-1064	389	5	as	as	SCONJ
ijassa-1064	389	6	given	give	VERB
ijassa-1064	389	7	in	in	ADP
ijassa-1064	389	8	[	[	X
ijassa-1064	389	9	2	2	NUM
ijassa-1064	389	10	,	,	PUNCT
ijassa-1064	389	11	12	12	NUM
ijassa-1064	389	12	]	]	PUNCT
ijassa-1064	389	13	,	,	PUNCT
ijassa-1064	389	14	the	the	DET
ijassa-1064	389	15	following	following	ADJ
ijassa-1064	389	16	result	result	NOUN
ijassa-1064	389	17	is	be	AUX
ijassa-1064	389	18	obtained	obtain	VERB
ijassa-1064	389	19	.	.	PUNCT
ijassa-1064	390	1	theorem	theorem	VERB
ijassa-1064	390	2	4.1	4.1	NUM
ijassa-1064	390	3	:	:	PUNCT
ijassa-1064	390	4	for	for	ADP
ijassa-1064	390	5	the	the	DET
ijassa-1064	390	6	optimal	optimal	ADJ
ijassa-1064	390	7	control	control	NOUN
ijassa-1064	390	8	triple	triple	ADJ
ijassa-1064	390	9	u∗	u∗	ADJ
ijassa-1064	390	10	that	that	PRON
ijassa-1064	390	11	minimizes	minimize	VERB
ijassa-1064	390	12	the	the	DET
ijassa-1064	390	13	objective	objective	ADJ
ijassa-1064	390	14	functional	functional	ADJ
ijassa-1064	390	15	(	(	PUNCT
ijassa-1064	390	16	4.26	4.26	NUM
ijassa-1064	390	17	)	)	PUNCT
ijassa-1064	390	18	over	over	ADP
ijassa-1064	390	19	u	u	NOUN
ijassa-1064	390	20	subject	subject	ADJ
ijassa-1064	390	21	to	to	ADP
ijassa-1064	390	22	(	(	PUNCT
ijassa-1064	390	23	4.25	4.25	NUM
ijassa-1064	390	24	)	)	PUNCT
ijassa-1064	390	25	,	,	PUNCT
ijassa-1064	390	26	there	there	PRON
ijassa-1064	390	27	exist	exist	VERB
ijassa-1064	390	28	adjoint	adjoint	NOUN
ijassa-1064	390	29	variables	variable	NOUN
ijassa-1064	390	30	η1	η1	NOUN
ijassa-1064	390	31	,	,	PUNCT
ijassa-1064	390	32	η2	η2	NOUN
ijassa-1064	390	33	,	,	PUNCT
ijassa-1064	390	34	η3	η3	NOUN
ijassa-1064	390	35	,	,	PUNCT
ijassa-1064	390	36	η4	η4	VERB
ijassa-1064	390	37	and	and	CCONJ
ijassa-1064	390	38	η5	η5	NOUN
ijassa-1064	390	39	satisfying	satisfy	VERB
ijassa-1064	390	40	the	the	DET
ijassa-1064	390	41	system	system	NOUN
ijassa-1064	390	42	governing	govern	VERB
ijassa-1064	390	43	the	the	DET
ijassa-1064	390	44	adjoint	adjoint	NOUN
ijassa-1064	390	45	variables	variable	VERB
ijassa-1064	390	46	dη1	dη1	NOUN
ijassa-1064	390	47	dt	dt	PUNCT
ijassa-1064	390	48	=	=	SYM
ijassa-1064	390	49	2rxs	2rx	NOUN
ijassa-1064	390	50	k	k	NOUN
ijassa-1064	390	51	η1	η1	NOUN
ijassa-1064	390	52	+	+	CCONJ
ijassa-1064	390	53	(	(	PUNCT
ijassa-1064	390	54	1−	1−	NUM
ijassa-1064	390	55	u1)β1xi(η1	u1)β1xi(η1	NOUN
ijassa-1064	390	56	−	−	PROPN
ijassa-1064	390	57	η2	η2	X
ijassa-1064	390	58	)	)	PUNCT
ijassa-1064	391	1	+	+	CCONJ
ijassa-1064	392	1	p1ys(η1	p1ys(η1	NUM
ijassa-1064	392	2	−	−	NOUN
ijassa-1064	393	1	c1η4	c1η4	NOUN
ijassa-1064	393	2	)	)	PUNCT
ijassa-1064	393	3	+	+	CCONJ
ijassa-1064	393	4	(	(	PUNCT
ijassa-1064	393	5	µ1	µ1	PROPN
ijassa-1064	393	6	−	−	PROPN
ijassa-1064	393	7	r)η1	r)η1	PROPN
ijassa-1064	393	8	dη2	dη2	NOUN
ijassa-1064	393	9	dt	dt	NOUN
ijassa-1064	393	10	=	=	SYM
ijassa-1064	393	11	(	(	PUNCT
ijassa-1064	393	12	1−	1−	NUM
ijassa-1064	393	13	u1)β1xs(η1	u1)β1xs(η1	NUM
ijassa-1064	393	14	−	−	PROPN
ijassa-1064	393	15	η2	η2	PROPN
ijassa-1064	393	16	)	)	PUNCT
ijassa-1064	394	1	+	+	CCONJ
ijassa-1064	394	2	p2ys(η2	p2ys(η2	ADJ
ijassa-1064	394	3	−	−	NOUN
ijassa-1064	394	4	c2η4	c2η4	X
ijassa-1064	394	5	)	)	PUNCT
ijassa-1064	394	6	+	+	CCONJ
ijassa-1064	394	7	p3yi(η2	p3yi(η2	PROPN
ijassa-1064	394	8	−	−	PROPN
ijassa-1064	394	9	c3η5	c3η5	NOUN
ijassa-1064	394	10	)	)	PUNCT
ijassa-1064	394	11	+	+	PROPN
ijassa-1064	394	12	(	(	PUNCT
ijassa-1064	394	13	γ	γ	X
ijassa-1064	394	14	+	+	NUM
ijassa-1064	394	15	u2r0)(η2	u2r0)(η2	PROPN
ijassa-1064	394	16	−	−	PROPN
ijassa-1064	394	17	η3	η3	NOUN
ijassa-1064	394	18	)	)	PUNCT
ijassa-1064	395	1	+	+	CCONJ
ijassa-1064	395	2	µ1η2	µ1η2	PUNCT
ijassa-1064	395	3	−	−	NOUN
ijassa-1064	395	4	a1	a1	NOUN
ijassa-1064	395	5	dη3	dη3	NOUN
ijassa-1064	395	6	dt	dt	PUNCT
ijassa-1064	395	7	=	=	NOUN
ijassa-1064	396	1	µ1η3	µ1η3	VERB
ijassa-1064	396	2	dη4	dη4	NOUN
ijassa-1064	396	3	dt	dt	NOUN
ijassa-1064	396	4	=	=	SYM
ijassa-1064	396	5	p1xs(η1	p1xs(η1	PROPN
ijassa-1064	396	6	−	−	NOUN
ijassa-1064	396	7	c1η4	c1η4	NOUN
ijassa-1064	396	8	)	)	PUNCT
ijassa-1064	396	9	+	+	CCONJ
ijassa-1064	396	10	p2xi(η2	p2xi(η2	PROPN
ijassa-1064	396	11	−	−	PROPN
ijassa-1064	396	12	c2η4	c2η4	X
ijassa-1064	396	13	)	)	PUNCT
ijassa-1064	397	1	+	+	CCONJ
ijassa-1064	397	2	(	(	PUNCT
ijassa-1064	397	3	1−	1−	NUM
ijassa-1064	397	4	u1)β2yi(η4	u1)β2yi(η4	NOUN
ijassa-1064	397	5	−	−	PROPN
ijassa-1064	397	6	η5	η5	PROPN
ijassa-1064	397	7	)	)	PUNCT
ijassa-1064	398	1	+	+	PROPN
ijassa-1064	398	2	(	(	PUNCT
ijassa-1064	398	3	µ2	µ2	PROPN
ijassa-1064	398	4	−	−	PROPN
ijassa-1064	398	5	u3c0)η4	u3c0)η4	VERB
ijassa-1064	398	6	dη5	dη5	X
ijassa-1064	398	7	dt	dt	PROPN
ijassa-1064	399	1	=	=	SYM
ijassa-1064	399	2	p3xi(η2	p3xi(η2	PROPN
ijassa-1064	399	3	−	−	PROPN
ijassa-1064	399	4	c3η5	c3η5	NOUN
ijassa-1064	399	5	)	)	PUNCT
ijassa-1064	400	1	+	+	CCONJ
ijassa-1064	400	2	(	(	PUNCT
ijassa-1064	400	3	1−	1−	NUM
ijassa-1064	400	4	µ1)β2ys(η4	µ1)β2ys(η4	NOUN
ijassa-1064	400	5	−	−	PROPN
ijassa-1064	400	6	η5	η5	PROPN
ijassa-1064	400	7	)	)	PUNCT
ijassa-1064	400	8	+	+	CCONJ
ijassa-1064	400	9	µ2η5	µ2η5	PUNCT
ijassa-1064	400	10	−	−	PROPN
ijassa-1064	400	11	a2	a2	PROPN
ijassa-1064	400	12	(	(	PUNCT
ijassa-1064	400	13	4.29	4.29	NUM
ijassa-1064	400	14	)	)	PUNCT
ijassa-1064	400	15	and	and	CCONJ
ijassa-1064	400	16	with	with	ADP
ijassa-1064	400	17	the	the	DET
ijassa-1064	400	18	transversality	transversality	NOUN
ijassa-1064	400	19	conditions	condition	NOUN
ijassa-1064	400	20	η1(tf	η1(tf	PRON
ijassa-1064	400	21	)	)	PUNCT
ijassa-1064	401	1	=	=	SYM
ijassa-1064	401	2	η2(tf	η2(tf	X
ijassa-1064	401	3	)	)	PUNCT
ijassa-1064	402	1	=	=	SYM
ijassa-1064	402	2	η3(tf	η3(tf	PROPN
ijassa-1064	402	3	)	)	PUNCT
ijassa-1064	402	4	=	=	SYM
ijassa-1064	402	5	η4(tf	η4(tf	X
ijassa-1064	402	6	)	)	PUNCT
ijassa-1064	402	7	=	=	SYM
ijassa-1064	402	8	η5(tf	η5(tf	PROPN
ijassa-1064	402	9	)	)	PUNCT
ijassa-1064	403	1	=	=	PUNCT
ijassa-1064	403	2	0	0	X
ijassa-1064	403	3	.	.	PUNCT
ijassa-1064	404	1	(	(	PUNCT
ijassa-1064	404	2	4.30	4.30	NUM
ijassa-1064	404	3	)	)	PUNCT
ijassa-1064	404	4	moreover	moreover	ADV
ijassa-1064	404	5	,	,	PUNCT
ijassa-1064	404	6	the	the	DET
ijassa-1064	404	7	optimal	optimal	ADJ
ijassa-1064	404	8	control	control	NOUN
ijassa-1064	404	9	triple	triple	ADJ
ijassa-1064	404	10	(	(	PUNCT
ijassa-1064	404	11	u∗1	u∗1	NOUN
ijassa-1064	404	12	,	,	PUNCT
ijassa-1064	404	13	u	u	NOUN
ijassa-1064	404	14	∗	∗	NOUN
ijassa-1064	404	15	2	2	NUM
ijassa-1064	404	16	,	,	PUNCT
ijassa-1064	404	17	u	u	NOUN
ijassa-1064	404	18	∗	∗	NOUN
ijassa-1064	404	19	3	3	NUM
ijassa-1064	404	20	)	)	PUNCT
ijassa-1064	404	21	is	be	AUX
ijassa-1064	404	22	characterized	characterize	VERB
ijassa-1064	404	23	as	as	SCONJ
ijassa-1064	404	24	follows	follow	VERB
ijassa-1064	404	25	u∗1	u∗1	NOUN
ijassa-1064	404	26	=	=	SYM
ijassa-1064	404	27	max	max	PROPN
ijassa-1064	404	28	{	{	PUNCT
ijassa-1064	404	29	0,min	0,min	PROPN
ijassa-1064	404	30	{	{	PUNCT
ijassa-1064	404	31	1	1	NUM
ijassa-1064	404	32	,	,	PUNCT
ijassa-1064	404	33	1	1	NUM
ijassa-1064	404	34	b1	b1	NOUN
ijassa-1064	404	35	[	[	X
ijassa-1064	404	36	β1xsxi(η2	β1xsxi(η2	PROPN
ijassa-1064	404	37	−	−	PROPN
ijassa-1064	404	38	η1	η1	NOUN
ijassa-1064	404	39	)	)	PUNCT
ijassa-1064	405	1	+	+	CCONJ
ijassa-1064	406	1	β2ysyi(η5	β2ysyi(η5	VERB
ijassa-1064	406	2	−	−	NOUN
ijassa-1064	406	3	η4	η4	VERB
ijassa-1064	406	4	)	)	PUNCT
ijassa-1064	406	5	]	]	PUNCT
ijassa-1064	406	6	}	}	PUNCT
ijassa-1064	406	7	}	}	PUNCT
ijassa-1064	406	8	,	,	PUNCT
ijassa-1064	406	9	u∗2	u∗2	ADJ
ijassa-1064	406	10	=	=	SYM
ijassa-1064	406	11	max	max	PROPN
ijassa-1064	406	12	{	{	PUNCT
ijassa-1064	406	13	0,min	0,min	PROPN
ijassa-1064	406	14	{	{	PUNCT
ijassa-1064	406	15	1	1	NUM
ijassa-1064	406	16	,	,	PUNCT
ijassa-1064	406	17	1	1	NUM
ijassa-1064	406	18	b2	b2	NOUN
ijassa-1064	407	1	[	[	X
ijassa-1064	407	2	r0xi(η2	r0xi(η2	PROPN
ijassa-1064	407	3	−	−	PROPN
ijassa-1064	407	4	η3	η3	PROPN
ijassa-1064	407	5	)	)	PUNCT
ijassa-1064	407	6	]	]	PUNCT
ijassa-1064	407	7	}	}	PUNCT
ijassa-1064	407	8	}	}	PUNCT
ijassa-1064	407	9	,	,	PUNCT
ijassa-1064	407	10	u∗3	u∗3	NOUN
ijassa-1064	407	11	=	=	SYM
ijassa-1064	407	12	max	max	PROPN
ijassa-1064	407	13	{	{	PUNCT
ijassa-1064	407	14	0,min	0,min	PROPN
ijassa-1064	407	15	{	{	PUNCT
ijassa-1064	407	16	1	1	NUM
ijassa-1064	407	17	,	,	PUNCT
ijassa-1064	407	18	−c0ysη4	−c0ysη4	NOUN
ijassa-1064	407	19	b3	b3	NOUN
ijassa-1064	407	20	}	}	PUNCT
ijassa-1064	407	21	}	}	PUNCT
ijassa-1064	407	22	.	.	PUNCT
ijassa-1064	408	1	(	(	PUNCT
ijassa-1064	408	2	4.31	4.31	NUM
ijassa-1064	408	3	)	)	PUNCT
ijassa-1064	408	4	proof	proof	NOUN
ijassa-1064	408	5	the	the	DET
ijassa-1064	408	6	system	system	NOUN
ijassa-1064	408	7	(	(	PUNCT
ijassa-1064	408	8	4.29	4.29	NUM
ijassa-1064	408	9	)	)	PUNCT
ijassa-1064	408	10	governing	govern	VERB
ijassa-1064	408	11	the	the	DET
ijassa-1064	408	12	adjoint	adjoint	NOUN
ijassa-1064	408	13	variables	variable	NOUN
ijassa-1064	408	14	is	be	AUX
ijassa-1064	408	15	obtained	obtain	VERB
ijassa-1064	408	16	by	by	ADP
ijassa-1064	408	17	finding	find	VERB
ijassa-1064	408	18	the	the	DET
ijassa-1064	408	19	partial	partial	ADJ
ijassa-1064	408	20	derivative	derivative	NOUN
ijassa-1064	408	21	of	of	ADP
ijassa-1064	408	22	the	the	DET
ijassa-1064	408	23	hamiltonian	hamiltonian	ADJ
ijassa-1064	408	24	h	h	NOUN
ijassa-1064	408	25	(	(	PUNCT
ijassa-1064	408	26	4.28	4.28	NUM
ijassa-1064	408	27	)	)	PUNCT
ijassa-1064	408	28	as	as	SCONJ
ijassa-1064	408	29	follows	follow	VERB
ijassa-1064	408	30	:	:	PUNCT
ijassa-1064	408	31	dη1	dη1	NOUN
ijassa-1064	408	32	dt	dt	NOUN
ijassa-1064	408	33	=	=	PUNCT
ijassa-1064	408	34	−	−	PROPN
ijassa-1064	408	35	∂h	∂h	PROPN
ijassa-1064	408	36	∂xs	∂xs	PROPN
ijassa-1064	408	37	,	,	PUNCT
ijassa-1064	408	38	dη2	dη2	NOUN
ijassa-1064	408	39	dt	dt	NOUN
ijassa-1064	408	40	=	=	SYM
ijassa-1064	408	41	−	−	PROPN
ijassa-1064	408	42	∂h	∂h	PROPN
ijassa-1064	408	43	∂xi	∂xi	PROPN
ijassa-1064	408	44	,	,	PUNCT
ijassa-1064	408	45	dη3	dη3	NOUN
ijassa-1064	408	46	dt	dt	NOUN
ijassa-1064	409	1	=	=	PUNCT
ijassa-1064	410	1	−	−	PROPN
ijassa-1064	411	1	∂h	∂h	PROPN
ijassa-1064	411	2	∂xr	∂xr	PROPN
ijassa-1064	411	3	,	,	PUNCT
ijassa-1064	411	4	dη4	dη4	NOUN
ijassa-1064	411	5	dt	dt	NOUN
ijassa-1064	411	6	=	=	PUNCT
ijassa-1064	412	1	−	−	PROPN
ijassa-1064	412	2	∂h	∂h	PROPN
ijassa-1064	412	3	∂ys	∂ys	PROPN
ijassa-1064	412	4	,	,	PUNCT
ijassa-1064	412	5	dη5	dη5	PROPN
ijassa-1064	412	6	dt	dt	X
ijassa-1064	412	7	=	=	PUNCT
ijassa-1064	413	1	−	−	PROPN
ijassa-1064	413	2	∂h	∂h	PROPN
ijassa-1064	413	3	∂yi	∂yi	PROPN
ijassa-1064	413	4	copyright	copyright	NOUN
ijassa-1064	413	5	©	©	PROPN
ijassa-1064	413	6	2021	2021	NUM
ijassa-1064	413	7	assa	assa	NOUN
ijassa-1064	413	8	.	.	PUNCT
ijassa-1064	414	1	adv	adv	PROPN
ijassa-1064	414	2	syst	syst	PROPN
ijassa-1064	414	3	sci	sci	PROPN
ijassa-1064	414	4	appl	appl	PROPN
ijassa-1064	414	5	(	(	PUNCT
ijassa-1064	414	6	2021	2021	NUM
ijassa-1064	414	7	)	)	PUNCT
ijassa-1064	414	8	stability	stability	NOUN
ijassa-1064	414	9	analysis	analysis	NOUN
ijassa-1064	414	10	and	and	CCONJ
ijassa-1064	414	11	optimal	optimal	ADJ
ijassa-1064	414	12	measure	measure	NOUN
ijassa-1064	414	13	99	99	NUM
ijassa-1064	414	14	with	with	ADP
ijassa-1064	414	15	the	the	DET
ijassa-1064	414	16	transversality	transversality	NOUN
ijassa-1064	414	17	conditions	condition	NOUN
ijassa-1064	414	18	:	:	PUNCT
ijassa-1064	414	19	η1(tf	η1(tf	X
ijassa-1064	414	20	)	)	PUNCT
ijassa-1064	415	1	=	=	SYM
ijassa-1064	415	2	η2(tf	η2(tf	X
ijassa-1064	415	3	)	)	PUNCT
ijassa-1064	416	1	=	=	SYM
ijassa-1064	416	2	η3(tf	η3(tf	PROPN
ijassa-1064	416	3	)	)	PUNCT
ijassa-1064	416	4	=	=	SYM
ijassa-1064	416	5	η4(tf	η4(tf	X
ijassa-1064	416	6	)	)	PUNCT
ijassa-1064	416	7	=	=	SYM
ijassa-1064	416	8	η5(tf	η5(tf	PROPN
ijassa-1064	416	9	)	)	PUNCT
ijassa-1064	417	1	=	=	PUNCT
ijassa-1064	417	2	0	0	X
ijassa-1064	417	3	.	.	PUNCT
ijassa-1064	418	1	finally	finally	ADV
ijassa-1064	418	2	,	,	PUNCT
ijassa-1064	418	3	differentiating	differentiate	VERB
ijassa-1064	418	4	the	the	DET
ijassa-1064	418	5	hamiltonian	hamiltonian	ADJ
ijassa-1064	418	6	h	h	NOUN
ijassa-1064	418	7	partially	partially	ADV
ijassa-1064	418	8	with	with	ADP
ijassa-1064	418	9	respect	respect	NOUN
ijassa-1064	418	10	to	to	ADP
ijassa-1064	418	11	each	each	PRON
ijassa-1064	418	12	of	of	ADP
ijassa-1064	418	13	the	the	DET
ijassa-1064	418	14	three	three	NUM
ijassa-1064	418	15	controls	control	NOUN
ijassa-1064	418	16	u1	u1	NOUN
ijassa-1064	418	17	,	,	PUNCT
ijassa-1064	418	18	u2	u2	NOUN
ijassa-1064	418	19	and	and	CCONJ
ijassa-1064	418	20	u3	u3	NOUN
ijassa-1064	418	21	,	,	PUNCT
ijassa-1064	418	22	so	so	SCONJ
ijassa-1064	418	23	that	that	SCONJ
ijassa-1064	418	24	∂h	∂h	PROPN
ijassa-1064	418	25	∂u1	∂u1	PROPN
ijassa-1064	418	26	≡	≡	PROPN
ijassa-1064	418	27	b1u1	b1u1	PUNCT
ijassa-1064	418	28	+	+	CCONJ
ijassa-1064	418	29	β1xsxi(η1	β1xsxi(η1	PROPN
ijassa-1064	418	30	−	−	NOUN
ijassa-1064	418	31	η2	η2	ADJ
ijassa-1064	418	32	)	)	PUNCT
ijassa-1064	419	1	+	+	CCONJ
ijassa-1064	419	2	β2ysyi(η4	β2ysyi(η4	NOUN
ijassa-1064	419	3	−	−	NOUN
ijassa-1064	419	4	η5	η5	PROPN
ijassa-1064	419	5	)	)	PUNCT
ijassa-1064	419	6	=	=	SYM
ijassa-1064	419	7	0	0	NUM
ijassa-1064	419	8	,	,	PUNCT
ijassa-1064	419	9	∂h	∂h	PROPN
ijassa-1064	419	10	∂u2	∂u2	PROPN
ijassa-1064	419	11	≡	≡	PROPN
ijassa-1064	419	12	b2u2	b2u2	ADP
ijassa-1064	419	13	+	+	PUNCT
ijassa-1064	419	14	r0xi(η3	r0xi(η3	NUM
ijassa-1064	419	15	−	−	NOUN
ijassa-1064	419	16	η2	η2	ADJ
ijassa-1064	419	17	)	)	PUNCT
ijassa-1064	419	18	=	=	SYM
ijassa-1064	419	19	0	0	NUM
ijassa-1064	419	20	,	,	PUNCT
ijassa-1064	419	21	∂h	∂h	PUNCT
ijassa-1064	419	22	∂u3	∂u3	NOUN
ijassa-1064	419	23	≡	≡	ADJ
ijassa-1064	419	24	b3u3	b3u3	PROPN
ijassa-1064	419	25	+	+	NUM
ijassa-1064	419	26	c0ysη4	c0ysη4	NOUN
ijassa-1064	419	27	=	=	SYM
ijassa-1064	419	28	0	0	NUM
ijassa-1064	419	29	,	,	PUNCT
ijassa-1064	419	30	which	which	PRON
ijassa-1064	419	31	when	when	SCONJ
ijassa-1064	419	32	solved	solve	VERB
ijassa-1064	419	33	on	on	ADP
ijassa-1064	419	34	the	the	DET
ijassa-1064	419	35	interior	interior	NOUN
ijassa-1064	419	36	of	of	ADP
ijassa-1064	419	37	the	the	DET
ijassa-1064	419	38	control	control	NOUN
ijassa-1064	419	39	set	set	VERB
ijassa-1064	419	40	u	u	NOUN
ijassa-1064	419	41	gives	give	VERB
ijassa-1064	419	42	the	the	DET
ijassa-1064	419	43	required	require	VERB
ijassa-1064	419	44	characterization	characterization	NOUN
ijassa-1064	419	45	(	(	PUNCT
ijassa-1064	419	46	4.31	4.31	NUM
ijassa-1064	419	47	)	)	PUNCT
ijassa-1064	419	48	.	.	PUNCT
ijassa-1064	420	1	hence	hence	ADV
ijassa-1064	420	2	,	,	PUNCT
ijassa-1064	420	3	the	the	DET
ijassa-1064	420	4	proof	proof	NOUN
ijassa-1064	420	5	.	.	PUNCT
ijassa-1064	421	1	4.2	4.2	NUM
ijassa-1064	421	2	.	.	PUNCT
ijassa-1064	421	3	simulations	simulation	NOUN
ijassa-1064	421	4	of	of	ADP
ijassa-1064	421	5	the	the	DET
ijassa-1064	421	6	control	control	NOUN
ijassa-1064	421	7	model	model	NOUN
ijassa-1064	421	8	here	here	ADV
ijassa-1064	421	9	,	,	PUNCT
ijassa-1064	421	10	the	the	DET
ijassa-1064	421	11	numerical	numerical	ADJ
ijassa-1064	421	12	simulations	simulation	NOUN
ijassa-1064	421	13	of	of	ADP
ijassa-1064	421	14	the	the	DET
ijassa-1064	421	15	coupled	couple	VERB
ijassa-1064	421	16	system	system	NOUN
ijassa-1064	421	17	of	of	ADP
ijassa-1064	421	18	state	state	NOUN
ijassa-1064	421	19	equations	equation	NOUN
ijassa-1064	421	20	(	(	PUNCT
ijassa-1064	421	21	4.25	4.25	NUM
ijassa-1064	421	22	)	)	PUNCT
ijassa-1064	421	23	with	with	ADP
ijassa-1064	421	24	adjoint	adjoint	NOUN
ijassa-1064	421	25	equations	equation	NOUN
ijassa-1064	421	26	(	(	PUNCT
ijassa-1064	421	27	4.29	4.29	NUM
ijassa-1064	421	28	)	)	PUNCT
ijassa-1064	421	29	are	be	AUX
ijassa-1064	421	30	conducted	conduct	VERB
ijassa-1064	421	31	.	.	PUNCT
ijassa-1064	422	1	the	the	DET
ijassa-1064	422	2	standard	standard	ADJ
ijassa-1064	422	3	iterative	iterative	ADJ
ijassa-1064	422	4	fourth	fourth	ADJ
ijassa-1064	422	5	order	order	NOUN
ijassa-1064	422	6	forward	forward	ADV
ijassa-1064	422	7	-	-	PUNCT
ijassa-1064	422	8	backward	backward	ADJ
ijassa-1064	422	9	rungekutta	rungekutta	NOUN
ijassa-1064	422	10	method	method	NOUN
ijassa-1064	422	11	is	be	AUX
ijassa-1064	422	12	used	use	VERB
ijassa-1064	422	13	to	to	PART
ijassa-1064	422	14	solve	solve	VERB
ijassa-1064	422	15	the	the	DET
ijassa-1064	422	16	optimality	optimality	NOUN
ijassa-1064	422	17	system	system	NOUN
ijassa-1064	422	18	due	due	ADP
ijassa-1064	422	19	to	to	ADP
ijassa-1064	422	20	difference	difference	NOUN
ijassa-1064	422	21	in	in	ADP
ijassa-1064	422	22	time	time	NOUN
ijassa-1064	422	23	orientations	orientation	NOUN
ijassa-1064	422	24	of	of	ADP
ijassa-1064	422	25	the	the	DET
ijassa-1064	422	26	state	state	NOUN
ijassa-1064	422	27	and	and	CCONJ
ijassa-1064	422	28	adjoint	adjoint	PROPN
ijassa-1064	422	29	equations	equation	NOUN
ijassa-1064	422	30	[	[	X
ijassa-1064	422	31	18	18	NUM
ijassa-1064	422	32	,	,	PUNCT
ijassa-1064	422	33	23	23	NUM
ijassa-1064	422	34	]	]	PUNCT
ijassa-1064	422	35	.	.	PUNCT
ijassa-1064	423	1	the	the	DET
ijassa-1064	423	2	optimal	optimal	ADJ
ijassa-1064	423	3	control	control	NOUN
ijassa-1064	423	4	problem	problem	NOUN
ijassa-1064	423	5	is	be	AUX
ijassa-1064	423	6	simulated	simulate	VERB
ijassa-1064	423	7	over	over	ADP
ijassa-1064	423	8	the	the	DET
ijassa-1064	423	9	time	time	NOUN
ijassa-1064	423	10	interval	interval	NOUN
ijassa-1064	423	11	[	[	X
ijassa-1064	423	12	0	0	NUM
ijassa-1064	423	13	,	,	PUNCT
ijassa-1064	423	14	15	15	NUM
ijassa-1064	423	15	]	]	PUNCT
ijassa-1064	423	16	in	in	ADP
ijassa-1064	423	17	years	year	NOUN
ijassa-1064	423	18	using	use	VERB
ijassa-1064	423	19	these	these	DET
ijassa-1064	423	20	parameter	parameter	NOUN
ijassa-1064	423	21	values	value	NOUN
ijassa-1064	423	22	:	:	PUNCT
ijassa-1064	423	23	µ1	µ1	PROPN
ijassa-1064	423	24	=	=	SYM
ijassa-1064	423	25	0.5	0.5	NUM
ijassa-1064	423	26	,	,	PUNCT
ijassa-1064	423	27	r	r	NOUN
ijassa-1064	423	28	=	=	SYM
ijassa-1064	423	29	11.2	11.2	NUM
ijassa-1064	423	30	,	,	PUNCT
ijassa-1064	423	31	β1	β1	PROPN
ijassa-1064	423	32	=	=	PUNCT
ijassa-1064	423	33	0.4	0.4	NUM
ijassa-1064	423	34	,	,	PUNCT
ijassa-1064	423	35	p1	p1	NOUN
ijassa-1064	423	36	=	=	SYM
ijassa-1064	423	37	1.0	1.0	NUM
ijassa-1064	423	38	,	,	PUNCT
ijassa-1064	423	39	γ	γ	X
ijassa-1064	423	40	=	=	SYM
ijassa-1064	423	41	0.35	0.35	NUM
ijassa-1064	423	42	,	,	PUNCT
ijassa-1064	423	43	p2	p2	X
ijassa-1064	423	44	=	=	SYM
ijassa-1064	423	45	0.2	0.2	NUM
ijassa-1064	423	46	,	,	PUNCT
ijassa-1064	423	47	p3	p3	PROPN
ijassa-1064	423	48	=	=	PUNCT
ijassa-1064	423	49	1.0	1.0	NUM
ijassa-1064	423	50	,	,	PUNCT
ijassa-1064	423	51	µ2	µ2	PROPN
ijassa-1064	423	52	=	=	PROPN
ijassa-1064	423	53	0.65	0.65	NUM
ijassa-1064	423	54	,	,	PUNCT
ijassa-1064	423	55	k	k	PROPN
ijassa-1064	423	56	=	=	SYM
ijassa-1064	423	57	30	30	NUM
ijassa-1064	423	58	,	,	PUNCT
ijassa-1064	423	59	β2	β2	NOUN
ijassa-1064	423	60	=	=	NOUN
ijassa-1064	423	61	0.65	0.65	NUM
ijassa-1064	423	62	,	,	PUNCT
ijassa-1064	423	63	c1	c1	NOUN
ijassa-1064	423	64	=	=	PROPN
ijassa-1064	423	65	0.25	0.25	NUM
ijassa-1064	423	66	,	,	PUNCT
ijassa-1064	423	67	c2	c2	PROPN
ijassa-1064	423	68	=	=	PUNCT
ijassa-1064	423	69	0.25	0.25	NUM
ijassa-1064	423	70	,	,	PUNCT
ijassa-1064	423	71	c3	c3	NOUN
ijassa-1064	423	72	=	=	PUNCT
ijassa-1064	424	1	0.15	0.15	NUM
ijassa-1064	424	2	.	.	PUNCT
ijassa-1064	425	1	in	in	ADP
ijassa-1064	425	2	addition	addition	NOUN
ijassa-1064	425	3	,	,	PUNCT
ijassa-1064	425	4	the	the	DET
ijassa-1064	425	5	balancing	balance	VERB
ijassa-1064	425	6	weight	weight	NOUN
ijassa-1064	425	7	constants	constant	NOUN
ijassa-1064	425	8	are	be	AUX
ijassa-1064	425	9	given	give	VERB
ijassa-1064	425	10	as	as	ADP
ijassa-1064	425	11	a1	a1	NOUN
ijassa-1064	425	12	=	=	SYM
ijassa-1064	425	13	1	1	NUM
ijassa-1064	425	14	,	,	PUNCT
ijassa-1064	425	15	a2	a2	NOUN
ijassa-1064	425	16	=	=	SYM
ijassa-1064	425	17	0.1	0.1	NUM
ijassa-1064	425	18	,	,	PUNCT
ijassa-1064	425	19	b1	b1	NOUN
ijassa-1064	425	20	=	=	NOUN
ijassa-1064	425	21	0.01	0.01	NUM
ijassa-1064	425	22	,	,	PUNCT
ijassa-1064	425	23	b2	b2	NOUN
ijassa-1064	425	24	=	=	SYM
ijassa-1064	425	25	0.0001	0.0001	NUM
ijassa-1064	425	26	and	and	CCONJ
ijassa-1064	425	27	b3	b3	PROPN
ijassa-1064	425	28	=	=	SYM
ijassa-1064	425	29	0.008	0.008	NUM
ijassa-1064	425	30	.	.	PUNCT
ijassa-1064	426	1	the	the	DET
ijassa-1064	426	2	rate	rate	NOUN
ijassa-1064	426	3	constants	constant	NOUN
ijassa-1064	426	4	for	for	ADP
ijassa-1064	426	5	the	the	DET
ijassa-1064	426	6	controls	control	NOUN
ijassa-1064	426	7	are	be	AUX
ijassa-1064	426	8	chosen	choose	VERB
ijassa-1064	426	9	as	as	ADP
ijassa-1064	426	10	r0	r0	NOUN
ijassa-1064	426	11	=	=	PROPN
ijassa-1064	426	12	0.4	0.4	NUM
ijassa-1064	426	13	and	and	CCONJ
ijassa-1064	426	14	c0	c0	PROPN
ijassa-1064	426	15	=	=	PROPN
ijassa-1064	427	1	0.15	0.15	NUM
ijassa-1064	427	2	.	.	PUNCT
ijassa-1064	428	1	thus	thus	ADV
ijassa-1064	428	2	,	,	PUNCT
ijassa-1064	428	3	to	to	PART
ijassa-1064	428	4	minimize	minimize	VERB
ijassa-1064	428	5	the	the	DET
ijassa-1064	428	6	objective	objective	ADJ
ijassa-1064	428	7	functional	functional	ADJ
ijassa-1064	428	8	(	(	PUNCT
ijassa-1064	428	9	4.26	4.26	NUM
ijassa-1064	428	10	)	)	PUNCT
ijassa-1064	428	11	with	with	ADP
ijassa-1064	428	12	disease	disease	NOUN
ijassa-1064	428	13	prevention	prevention	NOUN
ijassa-1064	428	14	control	control	NOUN
ijassa-1064	428	15	only	only	ADV
ijassa-1064	428	16	at	at	ADP
ijassa-1064	428	17	low	low	ADJ
ijassa-1064	428	18	cost	cost	NOUN
ijassa-1064	428	19	of	of	ADP
ijassa-1064	428	20	implementation	implementation	NOUN
ijassa-1064	428	21	,	,	PUNCT
ijassa-1064	428	22	the	the	DET
ijassa-1064	428	23	control	control	NOUN
ijassa-1064	428	24	u1	u1	NOUN
ijassa-1064	428	25	should	should	AUX
ijassa-1064	428	26	be	be	AUX
ijassa-1064	428	27	maintained	maintain	VERB
ijassa-1064	428	28	at	at	ADP
ijassa-1064	428	29	maximum	maximum	ADJ
ijassa-1064	428	30	(	(	PUNCT
ijassa-1064	428	31	100	100	NUM
ijassa-1064	428	32	%	%	NOUN
ijassa-1064	428	33	)	)	PUNCT
ijassa-1064	428	34	effort	effort	NOUN
ijassa-1064	428	35	for	for	ADP
ijassa-1064	428	36	8	8	NUM
ijassa-1064	428	37	years	year	NOUN
ijassa-1064	428	38	before	before	ADP
ijassa-1064	428	39	being	be	AUX
ijassa-1064	428	40	dropped	drop	VERB
ijassa-1064	428	41	to	to	ADP
ijassa-1064	428	42	zero	zero	NUM
ijassa-1064	428	43	in	in	ADP
ijassa-1064	428	44	final	final	ADJ
ijassa-1064	428	45	time	time	NOUN
ijassa-1064	428	46	as	as	SCONJ
ijassa-1064	428	47	shown	show	VERB
ijassa-1064	428	48	in	in	ADP
ijassa-1064	428	49	the	the	DET
ijassa-1064	428	50	figure	figure	NOUN
ijassa-1064	428	51	4.5(a	4.5(a	NUM
ijassa-1064	428	52	)	)	PUNCT
ijassa-1064	428	53	.	.	PUNCT
ijassa-1064	429	1	the	the	DET
ijassa-1064	429	2	control	control	NOUN
ijassa-1064	429	3	profile	profile	NOUN
ijassa-1064	429	4	shown	show	VERB
ijassa-1064	429	5	in	in	ADP
ijassa-1064	429	6	figure	figure	NOUN
ijassa-1064	429	7	4.5(b	4.5(b	NUM
ijassa-1064	429	8	)	)	PUNCT
ijassa-1064	429	9	indicates	indicate	VERB
ijassa-1064	429	10	that	that	SCONJ
ijassa-1064	429	11	single	single	ADJ
ijassa-1064	429	12	implementation	implementation	NOUN
ijassa-1064	429	13	of	of	ADP
ijassa-1064	429	14	treatment	treatment	NOUN
ijassa-1064	429	15	control	control	NOUN
ijassa-1064	429	16	u2	u2	PROPN
ijassa-1064	429	17	requires	require	VERB
ijassa-1064	429	18	maximum	maximum	ADJ
ijassa-1064	429	19	(	(	PUNCT
ijassa-1064	429	20	100	100	NUM
ijassa-1064	429	21	%	%	NOUN
ijassa-1064	429	22	)	)	PUNCT
ijassa-1064	429	23	effort	effort	NOUN
ijassa-1064	429	24	throughout	throughout	ADP
ijassa-1064	429	25	the	the	DET
ijassa-1064	429	26	period	period	NOUN
ijassa-1064	429	27	of	of	ADP
ijassa-1064	429	28	the	the	DET
ijassa-1064	429	29	control	control	NOUN
ijassa-1064	429	30	intervention	intervention	NOUN
ijassa-1064	429	31	.	.	PUNCT
ijassa-1064	430	1	it	it	PRON
ijassa-1064	430	2	is	be	AUX
ijassa-1064	430	3	observed	observe	VERB
ijassa-1064	430	4	in	in	ADP
ijassa-1064	430	5	figure	figure	NOUN
ijassa-1064	430	6	4.5(c	4.5(c	NUM
ijassa-1064	430	7	)	)	PUNCT
ijassa-1064	430	8	that	that	PRON
ijassa-1064	430	9	alternative	alternative	ADJ
ijassa-1064	430	10	food	food	NOUN
ijassa-1064	430	11	source	source	NOUN
ijassa-1064	430	12	control	control	NOUN
ijassa-1064	430	13	u3	u3	NOUN
ijassa-1064	430	14	should	should	AUX
ijassa-1064	430	15	be	be	AUX
ijassa-1064	430	16	at	at	ADP
ijassa-1064	430	17	the	the	DET
ijassa-1064	430	18	upper	upper	ADJ
ijassa-1064	430	19	bound	bind	VERB
ijassa-1064	430	20	for	for	ADP
ijassa-1064	430	21	14	14	NUM
ijassa-1064	430	22	years	year	NOUN
ijassa-1064	430	23	before	before	ADP
ijassa-1064	430	24	coming	come	VERB
ijassa-1064	430	25	to	to	ADP
ijassa-1064	430	26	the	the	DET
ijassa-1064	430	27	lower	lower	ADV
ijassa-1064	430	28	bound	bind	VERB
ijassa-1064	430	29	.	.	PUNCT
ijassa-1064	431	1	the	the	DET
ijassa-1064	431	2	combined	combined	ADJ
ijassa-1064	431	3	implementation	implementation	NOUN
ijassa-1064	431	4	of	of	ADP
ijassa-1064	431	5	the	the	DET
ijassa-1064	431	6	three	three	NUM
ijassa-1064	431	7	controls	control	NOUN
ijassa-1064	431	8	for	for	ADP
ijassa-1064	431	9	minimizing	minimize	VERB
ijassa-1064	431	10	the	the	DET
ijassa-1064	431	11	objective	objective	ADJ
ijassa-1064	431	12	functional	functional	NOUN
ijassa-1064	431	13	is	be	AUX
ijassa-1064	431	14	depicted	depict	VERB
ijassa-1064	431	15	in	in	ADP
ijassa-1064	431	16	figure	figure	NOUN
ijassa-1064	431	17	4.5(d	4.5(d	NUM
ijassa-1064	431	18	)	)	PUNCT
ijassa-1064	431	19	,	,	PUNCT
ijassa-1064	431	20	where	where	SCONJ
ijassa-1064	431	21	it	it	PRON
ijassa-1064	431	22	is	be	AUX
ijassa-1064	431	23	can	can	AUX
ijassa-1064	431	24	be	be	AUX
ijassa-1064	431	25	observed	observe	VERB
ijassa-1064	431	26	that	that	SCONJ
ijassa-1064	431	27	prevention	prevention	NOUN
ijassa-1064	431	28	control	control	NOUN
ijassa-1064	431	29	u1	u1	NOUN
ijassa-1064	431	30	should	should	AUX
ijassa-1064	431	31	be	be	AUX
ijassa-1064	431	32	maintained	maintain	VERB
ijassa-1064	431	33	at	at	ADP
ijassa-1064	431	34	the	the	DET
ijassa-1064	431	35	upper	upper	ADJ
ijassa-1064	431	36	bound	bind	VERB
ijassa-1064	431	37	for	for	ADP
ijassa-1064	431	38	8	8	NUM
ijassa-1064	431	39	years	year	NOUN
ijassa-1064	431	40	before	before	ADP
ijassa-1064	431	41	declining	decline	VERB
ijassa-1064	431	42	to	to	ADP
ijassa-1064	431	43	the	the	DET
ijassa-1064	431	44	lower	lower	ADV
ijassa-1064	431	45	bound	bind	VERB
ijassa-1064	431	46	,	,	PUNCT
ijassa-1064	431	47	treatment	treatment	NOUN
ijassa-1064	431	48	control	control	NOUN
ijassa-1064	431	49	u2	u2	NOUN
ijassa-1064	431	50	and	and	CCONJ
ijassa-1064	431	51	provision	provision	NOUN
ijassa-1064	431	52	of	of	ADP
ijassa-1064	431	53	alternative	alternative	ADJ
ijassa-1064	431	54	food	food	NOUN
ijassa-1064	431	55	source	source	NOUN
ijassa-1064	431	56	u3	u3	NOUN
ijassa-1064	431	57	should	should	AUX
ijassa-1064	431	58	be	be	AUX
ijassa-1064	431	59	maintained	maintain	VERB
ijassa-1064	431	60	at	at	ADP
ijassa-1064	431	61	maximum	maximum	ADJ
ijassa-1064	431	62	(	(	PUNCT
ijassa-1064	431	63	100	100	NUM
ijassa-1064	431	64	%	%	NOUN
ijassa-1064	431	65	)	)	PUNCT
ijassa-1064	431	66	for	for	ADP
ijassa-1064	431	67	about	about	ADV
ijassa-1064	431	68	2	2	NUM
ijassa-1064	431	69	years	year	NOUN
ijassa-1064	431	70	and	and	CCONJ
ijassa-1064	431	71	almost	almost	ADV
ijassa-1064	431	72	1	1	NUM
ijassa-1064	431	73	year	year	NOUN
ijassa-1064	431	74	,	,	PUNCT
ijassa-1064	431	75	respectively	respectively	ADV
ijassa-1064	431	76	.	.	PUNCT
ijassa-1064	432	1	the	the	DET
ijassa-1064	432	2	effects	effect	NOUN
ijassa-1064	432	3	of	of	ADP
ijassa-1064	432	4	combining	combine	VERB
ijassa-1064	432	5	all	all	DET
ijassa-1064	432	6	the	the	DET
ijassa-1064	432	7	three	three	NUM
ijassa-1064	432	8	optimal	optimal	ADJ
ijassa-1064	432	9	controls	control	NOUN
ijassa-1064	432	10	on	on	ADP
ijassa-1064	432	11	the	the	DET
ijassa-1064	432	12	dynamical	dynamical	ADJ
ijassa-1064	432	13	behaviors	behavior	NOUN
ijassa-1064	432	14	of	of	ADP
ijassa-1064	432	15	prey	prey	NOUN
ijassa-1064	432	16	and	and	CCONJ
ijassa-1064	432	17	predator	predator	NOUN
ijassa-1064	432	18	populations	population	NOUN
ijassa-1064	432	19	are	be	AUX
ijassa-1064	432	20	illustrated	illustrate	VERB
ijassa-1064	432	21	in	in	ADP
ijassa-1064	432	22	figure	figure	NOUN
ijassa-1064	432	23	4.6	4.6	NUM
ijassa-1064	432	24	.	.	PUNCT
ijassa-1064	433	1	the	the	DET
ijassa-1064	433	2	size	size	NOUN
ijassa-1064	433	3	of	of	ADP
ijassa-1064	433	4	susceptible	susceptible	ADJ
ijassa-1064	433	5	prey	prey	NOUN
ijassa-1064	433	6	population	population	NOUN
ijassa-1064	433	7	with	with	ADP
ijassa-1064	433	8	control	control	NOUN
ijassa-1064	433	9	reduces	reduce	VERB
ijassa-1064	433	10	due	due	ADJ
ijassa-1064	433	11	to	to	ADP
ijassa-1064	433	12	predation	predation	NOUN
ijassa-1064	433	13	when	when	SCONJ
ijassa-1064	433	14	compared	compare	VERB
ijassa-1064	433	15	with	with	ADP
ijassa-1064	433	16	the	the	DET
ijassa-1064	433	17	size	size	NOUN
ijassa-1064	433	18	without	without	ADP
ijassa-1064	433	19	control	control	NOUN
ijassa-1064	433	20	,	,	PUNCT
ijassa-1064	433	21	but	but	CCONJ
ijassa-1064	433	22	the	the	DET
ijassa-1064	433	23	population	population	NOUN
ijassa-1064	433	24	does	do	AUX
ijassa-1064	433	25	not	not	PART
ijassa-1064	433	26	go	go	VERB
ijassa-1064	433	27	extinct	extinct	ADJ
ijassa-1064	433	28	due	due	ADP
ijassa-1064	433	29	to	to	ADP
ijassa-1064	433	30	the	the	DET
ijassa-1064	433	31	presence	presence	NOUN
ijassa-1064	433	32	of	of	ADP
ijassa-1064	433	33	the	the	DET
ijassa-1064	433	34	combined	combine	VERB
ijassa-1064	433	35	optimal	optimal	ADJ
ijassa-1064	433	36	control	control	NOUN
ijassa-1064	433	37	as	as	SCONJ
ijassa-1064	433	38	shown	show	VERB
ijassa-1064	433	39	in	in	ADP
ijassa-1064	433	40	figure	figure	NOUN
ijassa-1064	433	41	4.6(a	4.6(a	NUM
ijassa-1064	433	42	)	)	PUNCT
ijassa-1064	433	43	.	.	PUNCT
ijassa-1064	434	1	this	this	PRON
ijassa-1064	434	2	suggests	suggest	VERB
ijassa-1064	434	3	the	the	DET
ijassa-1064	434	4	possibility	possibility	NOUN
ijassa-1064	434	5	of	of	ADP
ijassa-1064	434	6	stable	stable	ADJ
ijassa-1064	434	7	coexistence	coexistence	NOUN
ijassa-1064	434	8	of	of	ADP
ijassa-1064	434	9	predators	predator	NOUN
ijassa-1064	434	10	with	with	ADP
ijassa-1064	434	11	low	low	ADJ
ijassa-1064	434	12	density	density	NOUN
ijassa-1064	434	13	of	of	ADP
ijassa-1064	434	14	prey	prey	ADJ
ijassa-1064	434	15	population	population	NOUN
ijassa-1064	434	16	as	as	SCONJ
ijassa-1064	434	17	indicated	indicate	VERB
ijassa-1064	434	18	in	in	ADP
ijassa-1064	434	19	[	[	X
ijassa-1064	434	20	27	27	NUM
ijassa-1064	434	21	]	]	PUNCT
ijassa-1064	434	22	.	.	PUNCT
ijassa-1064	435	1	the	the	DET
ijassa-1064	435	2	infected	infected	ADJ
ijassa-1064	435	3	prey	prey	NOUN
ijassa-1064	435	4	population	population	NOUN
ijassa-1064	435	5	with	with	ADP
ijassa-1064	435	6	optimal	optimal	ADJ
ijassa-1064	435	7	control	control	NOUN
ijassa-1064	435	8	(	(	PUNCT
ijassa-1064	435	9	figure	figure	NOUN
ijassa-1064	435	10	4.6(b	4.6(b	NUM
ijassa-1064	435	11	)	)	PUNCT
ijassa-1064	435	12	)	)	PUNCT
ijassa-1064	435	13	decreases	decrease	VERB
ijassa-1064	435	14	sharply	sharply	ADV
ijassa-1064	435	15	when	when	SCONJ
ijassa-1064	435	16	compared	compare	VERB
ijassa-1064	435	17	with	with	ADP
ijassa-1064	435	18	the	the	DET
ijassa-1064	435	19	case	case	NOUN
ijassa-1064	435	20	without	without	ADP
ijassa-1064	435	21	control	control	NOUN
ijassa-1064	435	22	.	.	PUNCT
ijassa-1064	436	1	further	far	ADV
ijassa-1064	436	2	,	,	PUNCT
ijassa-1064	436	3	in	in	ADP
ijassa-1064	436	4	figure	figure	NOUN
ijassa-1064	436	5	4.6(c	4.6(c	NUM
ijassa-1064	436	6	)	)	PUNCT
ijassa-1064	436	7	,	,	PUNCT
ijassa-1064	436	8	it	it	PRON
ijassa-1064	436	9	can	can	AUX
ijassa-1064	436	10	be	be	AUX
ijassa-1064	436	11	seen	see	VERB
ijassa-1064	436	12	that	that	SCONJ
ijassa-1064	436	13	the	the	DET
ijassa-1064	436	14	size	size	NOUN
ijassa-1064	436	15	of	of	ADP
ijassa-1064	436	16	susceptible	susceptible	ADJ
ijassa-1064	436	17	predator	predator	NOUN
ijassa-1064	436	18	population	population	NOUN
ijassa-1064	436	19	with	with	ADP
ijassa-1064	436	20	combined	combine	VERB
ijassa-1064	436	21	optimal	optimal	ADJ
ijassa-1064	436	22	control	control	NOUN
ijassa-1064	436	23	is	be	AUX
ijassa-1064	436	24	higher	high	ADJ
ijassa-1064	436	25	than	than	ADP
ijassa-1064	436	26	the	the	DET
ijassa-1064	436	27	size	size	NOUN
ijassa-1064	436	28	without	without	ADP
ijassa-1064	436	29	control	control	NOUN
ijassa-1064	436	30	.	.	PUNCT
ijassa-1064	437	1	whereas	whereas	SCONJ
ijassa-1064	437	2	,	,	PUNCT
ijassa-1064	437	3	the	the	DET
ijassa-1064	437	4	presence	presence	NOUN
ijassa-1064	437	5	of	of	ADP
ijassa-1064	437	6	the	the	DET
ijassa-1064	437	7	combined	combine	VERB
ijassa-1064	437	8	optimal	optimal	ADJ
ijassa-1064	437	9	control	control	NOUN
ijassa-1064	437	10	reduces	reduce	VERB
ijassa-1064	437	11	the	the	DET
ijassa-1064	437	12	population	population	NOUN
ijassa-1064	437	13	size	size	NOUN
ijassa-1064	437	14	of	of	ADP
ijassa-1064	437	15	the	the	DET
ijassa-1064	437	16	infected	infected	ADJ
ijassa-1064	437	17	predator	predator	NOUN
ijassa-1064	437	18	in	in	ADP
ijassa-1064	437	19	the	the	DET
ijassa-1064	437	20	ecosystem	ecosystem	NOUN
ijassa-1064	437	21	.	.	PUNCT
ijassa-1064	438	1	copyright	copyright	NOUN
ijassa-1064	438	2	©	©	PROPN
ijassa-1064	438	3	2021	2021	NUM
ijassa-1064	438	4	assa	assa	NOUN
ijassa-1064	438	5	.	.	PUNCT
ijassa-1064	439	1	adv	adv	PROPN
ijassa-1064	439	2	syst	syst	PROPN
ijassa-1064	439	3	sci	sci	PROPN
ijassa-1064	439	4	appl	appl	PROPN
ijassa-1064	439	5	(	(	PUNCT
ijassa-1064	439	6	2021	2021	NUM
ijassa-1064	439	7	)	)	PUNCT
ijassa-1064	439	8	100	100	NUM
ijassa-1064	439	9	j.a	j.a	PROPN
ijassa-1064	439	10	.	.	PROPN
ijassa-1064	439	11	ademosu	ademosu	PROPN
ijassa-1064	439	12	,	,	PUNCT
ijassa-1064	439	13	s.	s.	PROPN
ijassa-1064	439	14	olaniyi	olaniyi	PROPN
ijassa-1064	439	15	,	,	PUNCT
ijassa-1064	439	16	s.o	s.o	PROPN
ijassa-1064	439	17	.	.	PROPN
ijassa-1064	439	18	adewale	adewale	PROPN
ijassa-1064	439	19	0	0	NUM
ijassa-1064	439	20	5	5	NUM
ijassa-1064	439	21	10	10	NUM
ijassa-1064	439	22	15	15	NUM
ijassa-1064	439	23	0	0	NUM
ijassa-1064	439	24	0.1	0.1	NUM
ijassa-1064	439	25	0.2	0.2	NUM
ijassa-1064	439	26	0.3	0.3	NUM
ijassa-1064	439	27	0.4	0.4	NUM
ijassa-1064	439	28	0.5	0.5	NUM
ijassa-1064	439	29	0.6	0.6	NUM
ijassa-1064	439	30	0.7	0.7	NUM
ijassa-1064	439	31	0.8	0.8	NUM
ijassa-1064	439	32	0.9	0.9	NUM
ijassa-1064	439	33	1	1	NUM
ijassa-1064	439	34	o	o	NOUN
ijassa-1064	439	35	p	p	X
ijassa-1064	439	36	tim	tim	PROPN
ijassa-1064	439	37	a	a	PRON
ijassa-1064	439	38	l	l	NOUN
ijassa-1064	439	39	c	c	NOUN
ijassa-1064	439	40	o	o	NOUN
ijassa-1064	439	41	n	n	PRON
ijassa-1064	439	42	tr	tr	NOUN
ijassa-1064	439	43	o	o	NOUN
ijassa-1064	439	44	l	l	NOUN
ijassa-1064	439	45	u	u	NOUN
ijassa-1064	439	46	1	1	NUM
ijassa-1064	439	47	time	time	NOUN
ijassa-1064	439	48	(	(	PUNCT
ijassa-1064	439	49	a	a	X
ijassa-1064	439	50	)	)	PUNCT
ijassa-1064	439	51	0	0	NUM
ijassa-1064	439	52	5	5	NUM
ijassa-1064	439	53	10	10	NUM
ijassa-1064	439	54	15	15	NUM
ijassa-1064	439	55	0	0	NUM
ijassa-1064	439	56	0.1	0.1	NUM
ijassa-1064	439	57	0.2	0.2	NUM
ijassa-1064	439	58	0.3	0.3	NUM
ijassa-1064	439	59	0.4	0.4	NUM
ijassa-1064	439	60	0.5	0.5	NUM
ijassa-1064	439	61	0.6	0.6	NUM
ijassa-1064	439	62	0.7	0.7	NUM
ijassa-1064	439	63	0.8	0.8	NUM
ijassa-1064	439	64	0.9	0.9	NUM
ijassa-1064	439	65	1	1	NUM
ijassa-1064	439	66	o	o	NOUN
ijassa-1064	439	67	p	p	X
ijassa-1064	439	68	tim	tim	PROPN
ijassa-1064	439	69	a	a	PRON
ijassa-1064	439	70	l	l	NOUN
ijassa-1064	439	71	c	c	NOUN
ijassa-1064	439	72	o	o	NOUN
ijassa-1064	439	73	n	n	PRON
ijassa-1064	439	74	tr	tr	NOUN
ijassa-1064	439	75	o	o	NOUN
ijassa-1064	439	76	l	l	NOUN
ijassa-1064	439	77	u	u	NOUN
ijassa-1064	439	78	2	2	NUM
ijassa-1064	439	79	time	time	NOUN
ijassa-1064	439	80	(	(	PUNCT
ijassa-1064	439	81	b	b	NOUN
ijassa-1064	439	82	)	)	PUNCT
ijassa-1064	439	83	0	0	NUM
ijassa-1064	439	84	5	5	NUM
ijassa-1064	439	85	10	10	NUM
ijassa-1064	439	86	15	15	NUM
ijassa-1064	439	87	0	0	NUM
ijassa-1064	439	88	0.1	0.1	NUM
ijassa-1064	439	89	0.2	0.2	NUM
ijassa-1064	439	90	0.3	0.3	NUM
ijassa-1064	439	91	0.4	0.4	NUM
ijassa-1064	439	92	0.5	0.5	NUM
ijassa-1064	439	93	0.6	0.6	NUM
ijassa-1064	439	94	0.7	0.7	NUM
ijassa-1064	439	95	0.8	0.8	NUM
ijassa-1064	439	96	0.9	0.9	NUM
ijassa-1064	439	97	1	1	NUM
ijassa-1064	439	98	o	o	NOUN
ijassa-1064	439	99	p	p	X
ijassa-1064	439	100	tim	tim	PROPN
ijassa-1064	439	101	a	a	PRON
ijassa-1064	439	102	l	l	NOUN
ijassa-1064	439	103	c	c	NOUN
ijassa-1064	439	104	o	o	NOUN
ijassa-1064	439	105	n	n	PRON
ijassa-1064	439	106	tr	tr	NOUN
ijassa-1064	439	107	o	o	NOUN
ijassa-1064	439	108	l	l	NOUN
ijassa-1064	439	109	u	u	NOUN
ijassa-1064	439	110	3	3	NUM
ijassa-1064	439	111	time	time	NOUN
ijassa-1064	439	112	(	(	PUNCT
ijassa-1064	439	113	c	c	NOUN
ijassa-1064	439	114	)	)	PUNCT
ijassa-1064	439	115	0	0	NUM
ijassa-1064	439	116	5	5	NUM
ijassa-1064	439	117	10	10	NUM
ijassa-1064	439	118	15	15	NUM
ijassa-1064	439	119	0	0	NUM
ijassa-1064	439	120	0.1	0.1	NUM
ijassa-1064	439	121	0.2	0.2	NUM
ijassa-1064	439	122	0.3	0.3	NUM
ijassa-1064	439	123	0.4	0.4	NUM
ijassa-1064	439	124	0.5	0.5	NUM
ijassa-1064	439	125	0.6	0.6	NUM
ijassa-1064	439	126	0.7	0.7	NUM
ijassa-1064	439	127	0.8	0.8	NUM
ijassa-1064	439	128	0.9	0.9	NUM
ijassa-1064	439	129	1	1	NUM
ijassa-1064	439	130	time	time	NOUN
ijassa-1064	440	1	o	o	NOUN
ijassa-1064	441	1	p	p	X
ijassa-1064	442	1	ti	ti	NOUN
ijassa-1064	442	2	m	m	NOUN
ijassa-1064	442	3	a	a	DET
ijassa-1064	442	4	l	l	NOUN
ijassa-1064	442	5	c	c	NOUN
ijassa-1064	442	6	o	o	NOUN
ijassa-1064	442	7	n	n	PRON
ijassa-1064	442	8	tr	tr	NOUN
ijassa-1064	442	9	o	o	NOUN
ijassa-1064	442	10	l	l	NOUN
ijassa-1064	442	11	p	p	X
ijassa-1064	442	12	ro	ro	INTJ
ijassa-1064	442	13	fi	fi	NOUN
ijassa-1064	442	14	le	le	X
ijassa-1064	442	15	s	s	PROPN
ijassa-1064	442	16	u	u	NOUN
ijassa-1064	442	17	1	1	NUM
ijassa-1064	442	18	u	u	NOUN
ijassa-1064	442	19	2	2	NUM
ijassa-1064	442	20	u	u	NOUN
ijassa-1064	442	21	3	3	NUM
ijassa-1064	442	22	(	(	PUNCT
ijassa-1064	442	23	d	d	NOUN
ijassa-1064	442	24	)	)	PUNCT
ijassa-1064	442	25	fig	fig	NOUN
ijassa-1064	442	26	.	.	PUNCT
ijassa-1064	443	1	4.5	4.5	NUM
ijassa-1064	443	2	.	.	PUNCT
ijassa-1064	444	1	control	control	NOUN
ijassa-1064	444	2	profiles	profile	NOUN
ijassa-1064	444	3	for	for	ADP
ijassa-1064	444	4	single	single	ADJ
ijassa-1064	444	5	and	and	CCONJ
ijassa-1064	444	6	combined	combined	ADJ
ijassa-1064	444	7	implementations	implementation	NOUN
ijassa-1064	444	8	of	of	ADP
ijassa-1064	444	9	u1	u1	NOUN
ijassa-1064	444	10	,	,	PUNCT
ijassa-1064	444	11	u2	u2	NOUN
ijassa-1064	444	12	and	and	CCONJ
ijassa-1064	444	13	u3	u3	NOUN
ijassa-1064	444	14	.	.	PROPN
ijassa-1064	445	1	5	5	NUM
ijassa-1064	445	2	.	.	X
ijassa-1064	445	3	conclusion	conclusion	NOUN
ijassa-1064	445	4	a	a	DET
ijassa-1064	445	5	nonlinear	nonlinear	ADJ
ijassa-1064	445	6	mathematical	mathematical	ADJ
ijassa-1064	445	7	model	model	NOUN
ijassa-1064	445	8	of	of	ADP
ijassa-1064	445	9	prey	prey	NOUN
ijassa-1064	445	10	-	-	PUNCT
ijassa-1064	445	11	predator	predator	NOUN
ijassa-1064	445	12	interacting	interact	VERB
ijassa-1064	445	13	populations	population	NOUN
ijassa-1064	445	14	in	in	ADP
ijassa-1064	445	15	an	an	DET
ijassa-1064	445	16	ecological	ecological	ADJ
ijassa-1064	445	17	system	system	NOUN
ijassa-1064	445	18	with	with	ADP
ijassa-1064	445	19	disease	disease	NOUN
ijassa-1064	445	20	spread	spread	NOUN
ijassa-1064	445	21	is	be	AUX
ijassa-1064	445	22	studied	study	VERB
ijassa-1064	445	23	.	.	PUNCT
ijassa-1064	446	1	the	the	DET
ijassa-1064	446	2	five	five	NUM
ijassa-1064	446	3	-	-	PUNCT
ijassa-1064	446	4	dimensional	dimensional	ADJ
ijassa-1064	446	5	eco	eco	NOUN
ijassa-1064	446	6	-	-	PUNCT
ijassa-1064	446	7	epidemiological	epidemiological	ADJ
ijassa-1064	446	8	model	model	NOUN
ijassa-1064	446	9	is	be	AUX
ijassa-1064	446	10	analyzed	analyze	VERB
ijassa-1064	446	11	with	with	ADP
ijassa-1064	446	12	a	a	DET
ijassa-1064	446	13	view	view	NOUN
ijassa-1064	446	14	to	to	ADP
ijassa-1064	446	15	providing	provide	VERB
ijassa-1064	446	16	insights	insight	NOUN
ijassa-1064	446	17	into	into	ADP
ijassa-1064	446	18	the	the	DET
ijassa-1064	446	19	behavior	behavior	NOUN
ijassa-1064	446	20	of	of	ADP
ijassa-1064	446	21	ecosystem	ecosystem	NOUN
ijassa-1064	446	22	in	in	ADP
ijassa-1064	446	23	the	the	DET
ijassa-1064	446	24	presence	presence	NOUN
ijassa-1064	446	25	of	of	ADP
ijassa-1064	446	26	disease	disease	NOUN
ijassa-1064	446	27	.	.	PUNCT
ijassa-1064	447	1	seven	seven	NUM
ijassa-1064	447	2	possible	possible	ADJ
ijassa-1064	447	3	equilibrium	equilibrium	NOUN
ijassa-1064	447	4	points	point	NOUN
ijassa-1064	447	5	,	,	PUNCT
ijassa-1064	447	6	namely	namely	ADV
ijassa-1064	447	7	trivial	trivial	ADJ
ijassa-1064	447	8	,	,	PUNCT
ijassa-1064	447	9	axial	axial	ADJ
ijassa-1064	447	10	,	,	PUNCT
ijassa-1064	447	11	disease	disease	NOUN
ijassa-1064	447	12	-	-	PUNCT
ijassa-1064	447	13	free	free	ADJ
ijassa-1064	447	14	,	,	PUNCT
ijassa-1064	447	15	predatorfree	predatorfree	NOUN
ijassa-1064	447	16	,	,	PUNCT
ijassa-1064	447	17	infected	infected	ADJ
ijassa-1064	447	18	prey	prey	NOUN
ijassa-1064	447	19	-	-	PUNCT
ijassa-1064	447	20	free	free	ADJ
ijassa-1064	447	21	,	,	PUNCT
ijassa-1064	447	22	infected	infected	ADJ
ijassa-1064	447	23	predator	predator	NOUN
ijassa-1064	447	24	-	-	PUNCT
ijassa-1064	447	25	free	free	ADJ
ijassa-1064	447	26	and	and	CCONJ
ijassa-1064	447	27	interior	interior	ADJ
ijassa-1064	447	28	equilibrium	equilibrium	NOUN
ijassa-1064	447	29	points	point	NOUN
ijassa-1064	447	30	are	be	AUX
ijassa-1064	447	31	analytically	analytically	ADV
ijassa-1064	447	32	determined	determine	VERB
ijassa-1064	447	33	.	.	PUNCT
ijassa-1064	448	1	asymptotic	asymptotic	ADJ
ijassa-1064	448	2	stability	stability	NOUN
ijassa-1064	448	3	of	of	ADP
ijassa-1064	448	4	the	the	DET
ijassa-1064	448	5	eco	eco	NOUN
ijassa-1064	448	6	-	-	PUNCT
ijassa-1064	448	7	epidemiological	epidemiological	ADJ
ijassa-1064	448	8	system	system	NOUN
ijassa-1064	448	9	is	be	AUX
ijassa-1064	448	10	analyzed	analyze	VERB
ijassa-1064	448	11	to	to	PART
ijassa-1064	448	12	investigate	investigate	VERB
ijassa-1064	448	13	the	the	DET
ijassa-1064	448	14	behavior	behavior	NOUN
ijassa-1064	448	15	of	of	ADP
ijassa-1064	448	16	the	the	DET
ijassa-1064	448	17	system	system	NOUN
ijassa-1064	448	18	around	around	ADP
ijassa-1064	448	19	each	each	PRON
ijassa-1064	448	20	of	of	ADP
ijassa-1064	448	21	the	the	DET
ijassa-1064	448	22	obtained	obtain	VERB
ijassa-1064	448	23	equilibrium	equilibrium	NOUN
ijassa-1064	448	24	points	point	NOUN
ijassa-1064	448	25	.	.	PUNCT
ijassa-1064	449	1	some	some	DET
ijassa-1064	449	2	conditions	condition	NOUN
ijassa-1064	449	3	that	that	PRON
ijassa-1064	449	4	guarantee	guarantee	VERB
ijassa-1064	449	5	the	the	DET
ijassa-1064	449	6	existence	existence	NOUN
ijassa-1064	449	7	of	of	ADP
ijassa-1064	449	8	each	each	DET
ijassa-1064	449	9	prey	prey	NOUN
ijassa-1064	449	10	and	and	CCONJ
ijassa-1064	449	11	predator	predator	NOUN
ijassa-1064	449	12	species	specie	NOUN
ijassa-1064	449	13	,	,	PUNCT
ijassa-1064	449	14	as	as	ADV
ijassa-1064	449	15	well	well	ADV
ijassa-1064	449	16	as	as	ADP
ijassa-1064	449	17	coexistence	coexistence	NOUN
ijassa-1064	449	18	of	of	ADP
ijassa-1064	449	19	both	both	DET
ijassa-1064	449	20	prey	prey	NOUN
ijassa-1064	449	21	and	and	CCONJ
ijassa-1064	449	22	predator	predator	NOUN
ijassa-1064	449	23	populations	population	NOUN
ijassa-1064	449	24	are	be	AUX
ijassa-1064	449	25	given	give	VERB
ijassa-1064	449	26	using	use	VERB
ijassa-1064	449	27	local	local	ADJ
ijassa-1064	449	28	linearization	linearization	NOUN
ijassa-1064	449	29	and	and	CCONJ
ijassa-1064	449	30	lyapunov	lyapunov	NOUN
ijassa-1064	449	31	functions	function	NOUN
ijassa-1064	449	32	techniques	technique	NOUN
ijassa-1064	449	33	.	.	PUNCT
ijassa-1064	450	1	in	in	ADP
ijassa-1064	450	2	addition	addition	NOUN
ijassa-1064	450	3	,	,	PUNCT
ijassa-1064	450	4	the	the	DET
ijassa-1064	450	5	eco	eco	PROPN
ijassa-1064	450	6	-	-	PUNCT
ijassa-1064	450	7	epidemiological	epidemiological	ADJ
ijassa-1064	450	8	model	model	NOUN
ijassa-1064	450	9	is	be	AUX
ijassa-1064	450	10	extended	extend	VERB
ijassa-1064	450	11	to	to	PART
ijassa-1064	450	12	include	include	VERB
ijassa-1064	450	13	three	three	NUM
ijassa-1064	450	14	time	time	NOUN
ijassa-1064	450	15	-	-	PUNCT
ijassa-1064	450	16	dependent	dependent	ADJ
ijassa-1064	450	17	optimal	optimal	ADJ
ijassa-1064	450	18	controls	control	NOUN
ijassa-1064	450	19	,	,	PUNCT
ijassa-1064	450	20	such	such	ADJ
ijassa-1064	450	21	as	as	ADP
ijassa-1064	450	22	disease	disease	NOUN
ijassa-1064	450	23	prevention	prevention	NOUN
ijassa-1064	450	24	in	in	ADP
ijassa-1064	450	25	both	both	DET
ijassa-1064	450	26	species	specie	NOUN
ijassa-1064	450	27	,	,	PUNCT
ijassa-1064	450	28	treatment	treatment	NOUN
ijassa-1064	450	29	strategy	strategy	NOUN
ijassa-1064	450	30	for	for	ADP
ijassa-1064	450	31	prey	prey	NOUN
ijassa-1064	450	32	and	and	CCONJ
ijassa-1064	450	33	provision	provision	NOUN
ijassa-1064	450	34	of	of	ADP
ijassa-1064	450	35	alternative	alternative	ADJ
ijassa-1064	450	36	food	food	NOUN
ijassa-1064	450	37	source	source	NOUN
ijassa-1064	450	38	for	for	ADP
ijassa-1064	450	39	predator	predator	NOUN
ijassa-1064	450	40	survival	survival	NOUN
ijassa-1064	450	41	.	.	PUNCT
ijassa-1064	451	1	hence	hence	ADV
ijassa-1064	451	2	,	,	PUNCT
ijassa-1064	451	3	the	the	DET
ijassa-1064	451	4	optimal	optimal	ADJ
ijassa-1064	451	5	control	control	NOUN
ijassa-1064	451	6	preypredator	preypredator	NOUN
ijassa-1064	451	7	model	model	NOUN
ijassa-1064	451	8	is	be	AUX
ijassa-1064	451	9	analyzed	analyze	VERB
ijassa-1064	451	10	using	use	VERB
ijassa-1064	451	11	pontryagin	pontryagin	NOUN
ijassa-1064	451	12	’s	’s	PART
ijassa-1064	451	13	maximum	maximum	ADJ
ijassa-1064	451	14	principle	principle	NOUN
ijassa-1064	451	15	in	in	ADP
ijassa-1064	451	16	order	order	NOUN
ijassa-1064	451	17	to	to	PART
ijassa-1064	451	18	enhance	enhance	VERB
ijassa-1064	451	19	the	the	DET
ijassa-1064	451	20	coexistence	coexistence	NOUN
ijassa-1064	451	21	of	of	ADP
ijassa-1064	451	22	both	both	DET
ijassa-1064	451	23	prey	prey	NOUN
ijassa-1064	451	24	and	and	CCONJ
ijassa-1064	451	25	predator	predator	NOUN
ijassa-1064	451	26	species	specie	NOUN
ijassa-1064	451	27	by	by	ADP
ijassa-1064	451	28	reducing	reduce	VERB
ijassa-1064	451	29	the	the	DET
ijassa-1064	451	30	risks	risk	NOUN
ijassa-1064	451	31	of	of	ADP
ijassa-1064	451	32	their	their	PRON
ijassa-1064	451	33	extinction	extinction	NOUN
ijassa-1064	451	34	in	in	ADP
ijassa-1064	451	35	the	the	DET
ijassa-1064	451	36	ecosystem	ecosystem	NOUN
ijassa-1064	451	37	,	,	PUNCT
ijassa-1064	451	38	such	such	ADJ
ijassa-1064	451	39	that	that	SCONJ
ijassa-1064	451	40	the	the	DET
ijassa-1064	451	41	populations	population	NOUN
ijassa-1064	451	42	of	of	ADP
ijassa-1064	451	43	infected	infected	ADJ
ijassa-1064	451	44	prey	prey	NOUN
ijassa-1064	451	45	and	and	CCONJ
ijassa-1064	451	46	predator	predator	NOUN
ijassa-1064	451	47	species	specie	NOUN
ijassa-1064	451	48	are	be	AUX
ijassa-1064	451	49	minimized	minimize	VERB
ijassa-1064	451	50	at	at	ADP
ijassa-1064	451	51	minimum	minimum	ADJ
ijassa-1064	451	52	costs	cost	NOUN
ijassa-1064	451	53	possible	possible	ADJ
ijassa-1064	451	54	.	.	PUNCT
ijassa-1064	452	1	copyright	copyright	NOUN
ijassa-1064	452	2	©	©	PROPN
ijassa-1064	452	3	2021	2021	NUM
ijassa-1064	452	4	assa	assa	NOUN
ijassa-1064	452	5	.	.	PUNCT
ijassa-1064	453	1	adv	adv	PROPN
ijassa-1064	453	2	syst	syst	PROPN
ijassa-1064	453	3	sci	sci	PROPN
ijassa-1064	453	4	appl	appl	PROPN
ijassa-1064	453	5	(	(	PUNCT
ijassa-1064	453	6	2021	2021	NUM
ijassa-1064	453	7	)	)	PUNCT
ijassa-1064	453	8	stability	stability	NOUN
ijassa-1064	453	9	analysis	analysis	NOUN
ijassa-1064	453	10	and	and	CCONJ
ijassa-1064	453	11	optimal	optimal	ADJ
ijassa-1064	453	12	measure	measure	NOUN
ijassa-1064	453	13	101	101	NUM
ijassa-1064	453	14	0	0	NUM
ijassa-1064	453	15	5	5	NUM
ijassa-1064	453	16	10	10	NUM
ijassa-1064	453	17	15	15	NUM
ijassa-1064	453	18	0	0	NUM
ijassa-1064	453	19	5	5	NUM
ijassa-1064	453	20	10	10	NUM
ijassa-1064	453	21	15	15	NUM
ijassa-1064	453	22	20	20	NUM
ijassa-1064	453	23	25	25	NUM
ijassa-1064	453	24	30	30	NUM
ijassa-1064	453	25	time	time	NOUN
ijassa-1064	453	26	s	s	PART
ijassa-1064	453	27	u	u	NOUN
ijassa-1064	453	28	s	s	PRON
ijassa-1064	453	29	c	c	NOUN
ijassa-1064	453	30	e	e	NOUN
ijassa-1064	453	31	p	p	X
ijassa-1064	453	32	ti	ti	PROPN
ijassa-1064	453	33	b	b	PROPN
ijassa-1064	453	34	le	le	ADP
ijassa-1064	453	35	p	p	X
ijassa-1064	453	36	re	re	ADP
ijassa-1064	453	37	y	y	PROPN
ijassa-1064	453	38	u	u	PROPN
ijassa-1064	453	39	1	1	NUM
ijassa-1064	453	40	≠	≠	PROPN
ijassa-1064	453	41	0	0	NUM
ijassa-1064	453	42	,	,	PUNCT
ijassa-1064	453	43	u	u	NOUN
ijassa-1064	453	44	2	2	PROPN
ijassa-1064	453	45	≠	≠	PROPN
ijassa-1064	453	46	0	0	NUM
ijassa-1064	453	47	,	,	PUNCT
ijassa-1064	453	48	u	u	NOUN
ijassa-1064	453	49	3	3	NUM
ijassa-1064	453	50	≠	≠	PROPN
ijassa-1064	453	51	0	0	NUM
ijassa-1064	453	52	u	u	NOUN
ijassa-1064	453	53	1	1	NUM
ijassa-1064	453	54	=	=	NOUN
ijassa-1064	453	55	u	u	NOUN
ijassa-1064	453	56	2	2	NUM
ijassa-1064	453	57	=	=	SYM
ijassa-1064	453	58	u	u	NOUN
ijassa-1064	453	59	3	3	NUM
ijassa-1064	453	60	=	=	SYM
ijassa-1064	453	61	0	0	NUM
ijassa-1064	453	62	(	(	PUNCT
ijassa-1064	453	63	a	a	NOUN
ijassa-1064	453	64	)	)	PUNCT
ijassa-1064	453	65	0	0	NUM
ijassa-1064	453	66	5	5	NUM
ijassa-1064	453	67	10	10	NUM
ijassa-1064	453	68	15	15	NUM
ijassa-1064	453	69	0	0	NUM
ijassa-1064	453	70	0.5	0.5	NUM
ijassa-1064	453	71	1	1	NUM
ijassa-1064	453	72	1.5	1.5	NUM
ijassa-1064	453	73	2	2	NUM
ijassa-1064	453	74	2.5	2.5	NUM
ijassa-1064	453	75	time	time	NOUN
ijassa-1064	453	76	in	in	ADP
ijassa-1064	453	77	fe	fe	X
ijassa-1064	453	78	c	c	X
ijassa-1064	453	79	te	te	PROPN
ijassa-1064	453	80	d	d	X
ijassa-1064	453	81	p	p	X
ijassa-1064	453	82	re	re	ADP
ijassa-1064	453	83	y	y	PROPN
ijassa-1064	453	84	u	u	PROPN
ijassa-1064	453	85	1	1	NUM
ijassa-1064	453	86	≠	≠	PROPN
ijassa-1064	453	87	0	0	NUM
ijassa-1064	453	88	,	,	PUNCT
ijassa-1064	453	89	u	u	NOUN
ijassa-1064	453	90	2	2	PROPN
ijassa-1064	453	91	≠	≠	PROPN
ijassa-1064	453	92	0	0	NUM
ijassa-1064	453	93	,	,	PUNCT
ijassa-1064	453	94	u	u	NOUN
ijassa-1064	453	95	3	3	NUM
ijassa-1064	453	96	≠	≠	PROPN
ijassa-1064	453	97	0	0	NUM
ijassa-1064	453	98	u	u	NOUN
ijassa-1064	453	99	1	1	NUM
ijassa-1064	453	100	=	=	NOUN
ijassa-1064	453	101	u	u	NOUN
ijassa-1064	453	102	2	2	NUM
ijassa-1064	453	103	=	=	SYM
ijassa-1064	453	104	u	u	NOUN
ijassa-1064	453	105	3	3	NUM
ijassa-1064	453	106	=	=	SYM
ijassa-1064	453	107	0	0	NUM
ijassa-1064	453	108	(	(	PUNCT
ijassa-1064	453	109	b	b	NOUN
ijassa-1064	453	110	)	)	PUNCT
ijassa-1064	453	111	0	0	NUM
ijassa-1064	453	112	5	5	NUM
ijassa-1064	453	113	10	10	NUM
ijassa-1064	453	114	15	15	NUM
ijassa-1064	453	115	0	0	NUM
ijassa-1064	453	116	2	2	NUM
ijassa-1064	453	117	4	4	NUM
ijassa-1064	453	118	6	6	NUM
ijassa-1064	453	119	8	8	NUM
ijassa-1064	453	120	10	10	NUM
ijassa-1064	453	121	12	12	NUM
ijassa-1064	453	122	14	14	NUM
ijassa-1064	453	123	time	time	NOUN
ijassa-1064	453	124	s	s	PART
ijassa-1064	453	125	u	u	NOUN
ijassa-1064	453	126	s	s	PRON
ijassa-1064	453	127	c	c	NOUN
ijassa-1064	453	128	e	e	NOUN
ijassa-1064	453	129	p	p	X
ijassa-1064	453	130	ti	ti	PROPN
ijassa-1064	453	131	b	b	PROPN
ijassa-1064	453	132	le	le	X
ijassa-1064	453	133	p	p	X
ijassa-1064	453	134	re	re	PROPN
ijassa-1064	453	135	d	d	X
ijassa-1064	453	136	a	a	PRON
ijassa-1064	453	137	to	to	ADP
ijassa-1064	453	138	r	r	NOUN
ijassa-1064	453	139	u	u	NOUN
ijassa-1064	453	140	1	1	NUM
ijassa-1064	453	141	≠	≠	PROPN
ijassa-1064	453	142	0	0	NUM
ijassa-1064	453	143	,	,	PUNCT
ijassa-1064	453	144	u	u	NOUN
ijassa-1064	453	145	2	2	PROPN
ijassa-1064	453	146	≠	≠	PROPN
ijassa-1064	453	147	0	0	NUM
ijassa-1064	453	148	,	,	PUNCT
ijassa-1064	453	149	u	u	NOUN
ijassa-1064	453	150	3	3	NUM
ijassa-1064	453	151	≠0	≠0	VERB
ijassa-1064	453	152	u	u	NOUN
ijassa-1064	453	153	1	1	NUM
ijassa-1064	453	154	=	=	PROPN
ijassa-1064	453	155	u	u	NOUN
ijassa-1064	453	156	2	2	NUM
ijassa-1064	453	157	=	=	SYM
ijassa-1064	453	158	u	u	NOUN
ijassa-1064	453	159	3	3	NUM
ijassa-1064	453	160	=	=	SYM
ijassa-1064	453	161	0	0	NUM
ijassa-1064	453	162	(	(	PUNCT
ijassa-1064	453	163	c	c	NOUN
ijassa-1064	453	164	)	)	PUNCT
ijassa-1064	453	165	0	0	NUM
ijassa-1064	453	166	5	5	NUM
ijassa-1064	453	167	10	10	NUM
ijassa-1064	453	168	15	15	NUM
ijassa-1064	453	169	0	0	NUM
ijassa-1064	453	170	2	2	NUM
ijassa-1064	453	171	4	4	NUM
ijassa-1064	453	172	6	6	NUM
ijassa-1064	453	173	8	8	NUM
ijassa-1064	453	174	10	10	NUM
ijassa-1064	453	175	12	12	NUM
ijassa-1064	453	176	time	time	NOUN
ijassa-1064	453	177	in	in	ADP
ijassa-1064	453	178	fe	fe	X
ijassa-1064	453	179	c	c	X
ijassa-1064	453	180	te	te	PROPN
ijassa-1064	453	181	d	d	X
ijassa-1064	453	182	p	p	X
ijassa-1064	453	183	re	re	ADP
ijassa-1064	453	184	d	d	NOUN
ijassa-1064	453	185	a	a	PRON
ijassa-1064	453	186	to	to	ADP
ijassa-1064	453	187	r	r	NOUN
ijassa-1064	453	188	u	u	NOUN
ijassa-1064	453	189	1	1	NUM
ijassa-1064	453	190	≠	≠	PROPN
ijassa-1064	453	191	0	0	NUM
ijassa-1064	453	192	,	,	PUNCT
ijassa-1064	453	193	u	u	NOUN
ijassa-1064	453	194	2	2	PROPN
ijassa-1064	453	195	≠	≠	PROPN
ijassa-1064	453	196	0	0	NUM
ijassa-1064	453	197	,	,	PUNCT
ijassa-1064	453	198	u	u	NOUN
ijassa-1064	453	199	3	3	NUM
ijassa-1064	453	200	≠0	≠0	VERB
ijassa-1064	453	201	u	u	NOUN
ijassa-1064	453	202	1	1	NUM
ijassa-1064	453	203	=	=	PROPN
ijassa-1064	453	204	u	u	NOUN
ijassa-1064	453	205	2	2	NUM
ijassa-1064	453	206	=	=	SYM
ijassa-1064	453	207	u	u	NOUN
ijassa-1064	453	208	3	3	NUM
ijassa-1064	453	209	=	=	SYM
ijassa-1064	453	210	0	0	NUM
ijassa-1064	453	211	(	(	PUNCT
ijassa-1064	453	212	d	d	NOUN
ijassa-1064	453	213	)	)	PUNCT
ijassa-1064	453	214	fig	fig	NOUN
ijassa-1064	453	215	.	.	PUNCT
ijassa-1064	454	1	4.6	4.6	NUM
ijassa-1064	454	2	.	.	PUNCT
ijassa-1064	454	3	combined	combine	VERB
ijassa-1064	454	4	effects	effect	NOUN
ijassa-1064	454	5	of	of	ADP
ijassa-1064	454	6	optimal	optimal	ADJ
ijassa-1064	454	7	controls	control	NOUN
ijassa-1064	454	8	u1	u1	NOUN
ijassa-1064	454	9	,	,	PUNCT
ijassa-1064	454	10	u2	u2	NOUN
ijassa-1064	454	11	and	and	CCONJ
ijassa-1064	454	12	u3	u3	NOUN
ijassa-1064	454	13	on	on	ADP
ijassa-1064	454	14	the	the	DET
ijassa-1064	454	15	dynamics	dynamic	NOUN
ijassa-1064	454	16	of	of	ADP
ijassa-1064	454	17	the	the	DET
ijassa-1064	454	18	prey	prey	NOUN
ijassa-1064	454	19	-	-	PUNCT
ijassa-1064	454	20	predator	predator	NOUN
ijassa-1064	454	21	model	model	NOUN
ijassa-1064	454	22	.	.	PUNCT
ijassa-1064	455	1	the	the	DET
ijassa-1064	455	2	analysis	analysis	NOUN
ijassa-1064	455	3	of	of	ADP
ijassa-1064	455	4	the	the	DET
ijassa-1064	455	5	eco	eco	NOUN
ijassa-1064	455	6	-	-	PUNCT
ijassa-1064	455	7	epidemiological	epidemiological	ADJ
ijassa-1064	455	8	model	model	NOUN
ijassa-1064	455	9	presented	present	VERB
ijassa-1064	455	10	in	in	ADP
ijassa-1064	455	11	this	this	DET
ijassa-1064	455	12	study	study	NOUN
ijassa-1064	455	13	can	can	AUX
ijassa-1064	455	14	be	be	AUX
ijassa-1064	455	15	applied	apply	VERB
ijassa-1064	455	16	to	to	ADP
ijassa-1064	455	17	a	a	DET
ijassa-1064	455	18	wide	wide	ADJ
ijassa-1064	455	19	spectrum	spectrum	NOUN
ijassa-1064	455	20	of	of	ADP
ijassa-1064	455	21	interactions	interaction	NOUN
ijassa-1064	455	22	between	between	ADP
ijassa-1064	455	23	different	different	ADJ
ijassa-1064	455	24	kinds	kind	NOUN
ijassa-1064	455	25	of	of	ADP
ijassa-1064	455	26	living	live	VERB
ijassa-1064	455	27	beings	being	NOUN
ijassa-1064	455	28	in	in	ADP
ijassa-1064	455	29	the	the	DET
ijassa-1064	455	30	environment	environment	NOUN
ijassa-1064	455	31	.	.	PUNCT
ijassa-1064	456	1	acknowledgement	acknowledgement	NOUN
ijassa-1064	456	2	the	the	DET
ijassa-1064	456	3	authors	author	NOUN
ijassa-1064	456	4	are	be	AUX
ijassa-1064	456	5	thankful	thankful	ADJ
ijassa-1064	456	6	for	for	ADP
ijassa-1064	456	7	the	the	DET
ijassa-1064	456	8	constructive	constructive	ADJ
ijassa-1064	456	9	comments	comment	NOUN
ijassa-1064	456	10	and	and	CCONJ
ijassa-1064	456	11	suggestions	suggestion	NOUN
ijassa-1064	456	12	of	of	ADP
ijassa-1064	456	13	the	the	DET
ijassa-1064	456	14	editor	editor	NOUN
ijassa-1064	456	15	and	and	CCONJ
ijassa-1064	456	16	the	the	DET
ijassa-1064	456	17	anonymous	anonymous	ADJ
ijassa-1064	456	18	reviewers	reviewer	NOUN
ijassa-1064	456	19	.	.	PUNCT
ijassa-1064	457	1	initial	initial	ADJ
ijassa-1064	457	2	discussion	discussion	NOUN
ijassa-1064	457	3	on	on	ADP
ijassa-1064	457	4	the	the	DET
ijassa-1064	457	5	original	original	ADJ
ijassa-1064	457	6	manuscript	manuscript	NOUN
ijassa-1064	457	7	with	with	ADP
ijassa-1064	457	8	professor	professor	PROPN
ijassa-1064	457	9	mini	mini	PROPN
ijassa-1064	457	10	ghosh	ghosh	PROPN
ijassa-1064	457	11	of	of	ADP
ijassa-1064	457	12	vellore	vellore	PROPN
ijassa-1064	457	13	institute	institute	PROPN
ijassa-1064	457	14	of	of	ADP
ijassa-1064	457	15	technology	technology	PROPN
ijassa-1064	457	16	,	,	PUNCT
ijassa-1064	457	17	chennai	chennai	PROPN
ijassa-1064	457	18	,	,	PUNCT
ijassa-1064	457	19	india	india	PROPN
ijassa-1064	457	20	is	be	AUX
ijassa-1064	457	21	also	also	ADV
ijassa-1064	457	22	acknowledged	acknowledge	VERB
ijassa-1064	457	23	with	with	ADP
ijassa-1064	457	24	thanks	thank	NOUN
ijassa-1064	457	25	.	.	PUNCT
ijassa-1064	458	1	references	reference	NOUN
ijassa-1064	458	2	1	1	NUM
ijassa-1064	458	3	.	.	PUNCT
ijassa-1064	458	4	abidemi	abidemi	PROPN
ijassa-1064	458	5	,	,	PUNCT
ijassa-1064	458	6	a.	a.	NOUN
ijassa-1064	458	7	and	and	CCONJ
ijassa-1064	458	8	aziz	aziz	PROPN
ijassa-1064	458	9	,	,	PUNCT
ijassa-1064	458	10	n.a.b	n.a.b	NOUN
ijassa-1064	458	11	.	.	PUNCT
ijassa-1064	458	12	(	(	PUNCT
ijassa-1064	458	13	2020	2020	NUM
ijassa-1064	458	14	)	)	PUNCT
ijassa-1064	458	15	.	.	PUNCT
ijassa-1064	459	1	optimal	optimal	ADJ
ijassa-1064	459	2	control	control	NOUN
ijassa-1064	459	3	strategies	strategy	NOUN
ijassa-1064	459	4	for	for	ADP
ijassa-1064	459	5	dengue	dengue	NOUN
ijassa-1064	459	6	fever	fever	NOUN
ijassa-1064	459	7	spread	spread	VERB
ijassa-1064	459	8	in	in	ADP
ijassa-1064	459	9	johor	johor	PROPN
ijassa-1064	459	10	,	,	PUNCT
ijassa-1064	459	11	malaysia	malaysia	PROPN
ijassa-1064	459	12	,	,	PUNCT
ijassa-1064	459	13	comput	comput	NOUN
ijassa-1064	459	14	.	.	PUNCT
ijassa-1064	460	1	meth	meth	NOUN
ijassa-1064	460	2	.	.	PUNCT
ijassa-1064	461	1	prog	prog	PROPN
ijassa-1064	461	2	.	.	PUNCT
ijassa-1064	462	1	bio	bio	PROPN
ijassa-1064	462	2	.	.	PROPN
ijassa-1064	462	3	,	,	PUNCT
ijassa-1064	462	4	196	196	NUM
ijassa-1064	462	5	,	,	PUNCT
ijassa-1064	462	6	105585	105585	NUM
ijassa-1064	462	7	.	.	PUNCT
ijassa-1064	463	1	https://doi.org/10.1016/j.cmpb.2020.105585	https://doi.org/10.1016/j.cmpb.2020.105585	NOUN
ijassa-1064	463	2	2	2	NUM
ijassa-1064	463	3	.	.	PUNCT
ijassa-1064	463	4	abimbade	abimbade	PROPN
ijassa-1064	463	5	,	,	PUNCT
ijassa-1064	463	6	s.f	s.f	PROPN
ijassa-1064	463	7	.	.	PROPN
ijassa-1064	463	8	,	,	PUNCT
ijassa-1064	463	9	olaniyi	olaniyi	PROPN
ijassa-1064	463	10	,	,	PUNCT
ijassa-1064	463	11	s.	s.	PROPN
ijassa-1064	463	12	,	,	PUNCT
ijassa-1064	463	13	ajala	ajala	NOUN
ijassa-1064	463	14	,	,	PUNCT
ijassa-1064	463	15	o.a	o.a	PROPN
ijassa-1064	463	16	.	.	PROPN
ijassa-1064	463	17	and	and	CCONJ
ijassa-1064	463	18	ibrahim	ibrahim	PROPN
ijassa-1064	463	19	,	,	PUNCT
ijassa-1064	463	20	m.o	m.o	PROPN
ijassa-1064	463	21	.	.	PROPN
ijassa-1064	463	22	(	(	PUNCT
ijassa-1064	463	23	2020	2020	NUM
ijassa-1064	463	24	)	)	PUNCT
ijassa-1064	463	25	.	.	PUNCT
ijassa-1064	464	1	optimal	optimal	ADJ
ijassa-1064	464	2	control	control	NOUN
ijassa-1064	464	3	analysis	analysis	NOUN
ijassa-1064	464	4	of	of	ADP
ijassa-1064	464	5	a	a	DET
ijassa-1064	464	6	tuberculosis	tuberculosis	NOUN
ijassa-1064	464	7	model	model	NOUN
ijassa-1064	464	8	with	with	ADP
ijassa-1064	464	9	exogenous	exogenous	ADJ
ijassa-1064	464	10	re	re	NOUN
ijassa-1064	464	11	-	-	NOUN
ijassa-1064	464	12	infection	infection	NOUN
ijassa-1064	464	13	and	and	CCONJ
ijassa-1064	464	14	incomplete	incomplete	ADJ
ijassa-1064	464	15	treatment	treatment	NOUN
ijassa-1064	464	16	,	,	PUNCT
ijassa-1064	464	17	optim	optim	ADJ
ijassa-1064	464	18	.	.	PUNCT
ijassa-1064	465	1	control	control	PROPN
ijassa-1064	465	2	appl	appl	PROPN
ijassa-1064	465	3	.	.	PUNCT
ijassa-1064	466	1	meth	meth	PROPN
ijassa-1064	466	2	.	.	PUNCT
ijassa-1064	467	1	,	,	PUNCT
ijassa-1064	467	2	(	(	PUNCT
ijassa-1064	467	3	41	41	NUM
ijassa-1064	467	4	)	)	PUNCT
ijassa-1064	467	5	,	,	PUNCT
ijassa-1064	467	6	2349–2368	2349–2368	NUM
ijassa-1064	467	7	.	.	PUNCT
ijassa-1064	468	1	https://doi.org/10.1002/oca.2658	https://doi.org/10.1002/oca.2658	NOUN
ijassa-1064	468	2	copyright	copyright	NOUN
ijassa-1064	468	3	©	©	PROPN
ijassa-1064	468	4	2021	2021	NUM
ijassa-1064	468	5	assa	assa	NOUN
ijassa-1064	468	6	.	.	PUNCT
ijassa-1064	469	1	adv	adv	PROPN
ijassa-1064	469	2	syst	syst	PROPN
ijassa-1064	469	3	sci	sci	PROPN
ijassa-1064	469	4	appl	appl	PROPN
ijassa-1064	469	5	(	(	PUNCT
ijassa-1064	469	6	2021	2021	NUM
ijassa-1064	469	7	)	)	PUNCT
ijassa-1064	469	8	102	102	NUM
ijassa-1064	469	9	j.a	j.a	PROPN
ijassa-1064	469	10	.	.	PROPN
ijassa-1064	469	11	ademosu	ademosu	PROPN
ijassa-1064	469	12	,	,	PUNCT
ijassa-1064	469	13	s.	s.	PROPN
ijassa-1064	469	14	olaniyi	olaniyi	PROPN
ijassa-1064	469	15	,	,	PUNCT
ijassa-1064	469	16	s.o	s.o	PROPN
ijassa-1064	469	17	.	.	PROPN
ijassa-1064	469	18	adewale	adewale	PROPN
ijassa-1064	469	19	3	3	PROPN
ijassa-1064	469	20	.	.	PUNCT
ijassa-1064	470	1	adewale	adewale	PROPN
ijassa-1064	470	2	,	,	PUNCT
ijassa-1064	470	3	s.o	s.o	PROPN
ijassa-1064	470	4	.	.	PROPN
ijassa-1064	470	5	,	,	PUNCT
ijassa-1064	470	6	podder	podder	NOUN
ijassa-1064	470	7	,	,	PUNCT
ijassa-1064	470	8	c.n	c.n	PROPN
ijassa-1064	470	9	.	.	PROPN
ijassa-1064	470	10	and	and	CCONJ
ijassa-1064	470	11	gumel	gumel	PROPN
ijassa-1064	470	12	,	,	PUNCT
ijassa-1064	470	13	a.b	a.b	PROPN
ijassa-1064	470	14	.	.	PROPN
ijassa-1064	470	15	(	(	PUNCT
ijassa-1064	470	16	2009	2009	NUM
ijassa-1064	470	17	)	)	PUNCT
ijassa-1064	470	18	.	.	PUNCT
ijassa-1064	471	1	mathematical	mathematical	ADJ
ijassa-1064	471	2	analysis	analysis	NOUN
ijassa-1064	471	3	of	of	ADP
ijassa-1064	471	4	a	a	DET
ijassa-1064	471	5	tb	tb	NOUN
ijassa-1064	471	6	transmission	transmission	NOUN
ijassa-1064	471	7	model	model	NOUN
ijassa-1064	471	8	with	with	ADP
ijassa-1064	471	9	dots	dot	NOUN
ijassa-1064	471	10	,	,	PUNCT
ijassa-1064	471	11	can	can	AUX
ijassa-1064	471	12	.	.	PUNCT
ijassa-1064	472	1	appl	appl	PROPN
ijassa-1064	472	2	.	.	PROPN
ijassa-1064	472	3	math	math	PROPN
ijassa-1064	472	4	.	.	PUNCT
ijassa-1064	473	1	q.	q.	PROPN
ijassa-1064	473	2	,	,	PUNCT
ijassa-1064	473	3	17	17	NUM
ijassa-1064	473	4	,	,	PUNCT
ijassa-1064	473	5	1–36	1–36	PROPN
ijassa-1064	473	6	.	.	PUNCT
ijassa-1064	474	1	4	4	X
ijassa-1064	474	2	.	.	X
ijassa-1064	474	3	akanni	akanni	PROPN
ijassa-1064	474	4	,	,	PUNCT
ijassa-1064	474	5	j.o	j.o	PROPN
ijassa-1064	474	6	.	.	PROPN
ijassa-1064	474	7	,	,	PUNCT
ijassa-1064	474	8	akinpelu	akinpelu	PROPN
ijassa-1064	474	9	,	,	PUNCT
ijassa-1064	474	10	f.o	f.o	PROPN
ijassa-1064	474	11	.	.	PROPN
ijassa-1064	474	12	,	,	PUNCT
ijassa-1064	474	13	olaniyi	olaniyi	PROPN
ijassa-1064	474	14	,	,	PUNCT
ijassa-1064	474	15	s.	s.	PROPN
ijassa-1064	474	16	,	,	PUNCT
ijassa-1064	474	17	oladipo	oladipo	PROPN
ijassa-1064	474	18	,	,	PUNCT
ijassa-1064	474	19	a.t	a.t	PROPN
ijassa-1064	474	20	.	.	PROPN
ijassa-1064	474	21	,	,	PUNCT
ijassa-1064	474	22	and	and	CCONJ
ijassa-1064	474	23	ogunsola	ogunsola	PROPN
ijassa-1064	474	24	,	,	PUNCT
ijassa-1064	474	25	a.w	a.w	PROPN
ijassa-1064	474	26	.	.	PROPN
ijassa-1064	474	27	(	(	PUNCT
ijassa-1064	474	28	2020	2020	NUM
ijassa-1064	474	29	)	)	PUNCT
ijassa-1064	474	30	.	.	PUNCT
ijassa-1064	475	1	modelling	model	VERB
ijassa-1064	475	2	financial	financial	ADJ
ijassa-1064	475	3	crime	crime	NOUN
ijassa-1064	475	4	population	population	NOUN
ijassa-1064	475	5	dynamics	dynamic	NOUN
ijassa-1064	475	6	:	:	PUNCT
ijassa-1064	475	7	optimal	optimal	ADJ
ijassa-1064	475	8	control	control	NOUN
ijassa-1064	475	9	and	and	CCONJ
ijassa-1064	475	10	cost	cost	NOUN
ijassa-1064	475	11	-	-	PUNCT
ijassa-1064	475	12	effectiveness	effectiveness	NOUN
ijassa-1064	475	13	analysis	analysis	NOUN
ijassa-1064	475	14	,	,	PUNCT
ijassa-1064	475	15	int	int	NOUN
ijassa-1064	475	16	.	.	PUNCT
ijassa-1064	476	1	j.	j.	PROPN
ijassa-1064	476	2	dynam	dynam	PROPN
ijassa-1064	476	3	.	.	PUNCT
ijassa-1064	477	1	control	control	NOUN
ijassa-1064	477	2	,	,	PUNCT
ijassa-1064	477	3	8	8	NUM
ijassa-1064	477	4	,	,	PUNCT
ijassa-1064	477	5	531–544	531–544	NUM
ijassa-1064	477	6	.	.	NOUN
ijassa-1064	477	7	5	5	NUM
ijassa-1064	477	8	.	.	X
ijassa-1064	478	1	al	al	PROPN
ijassa-1064	478	2	-	-	PUNCT
ijassa-1064	478	3	darabsah	darabsah	PROPN
ijassa-1064	478	4	,	,	PUNCT
ijassa-1064	478	5	i.	i.	PROPN
ijassa-1064	478	6	,	,	PUNCT
ijassa-1064	478	7	tang	tang	PROPN
ijassa-1064	478	8	,	,	PUNCT
ijassa-1064	478	9	x.	x.	NOUN
ijassa-1064	478	10	and	and	CCONJ
ijassa-1064	478	11	yaun	yaun	PROPN
ijassa-1064	478	12	,	,	PUNCT
ijassa-1064	478	13	y.	y.	PROPN
ijassa-1064	478	14	(	(	PUNCT
ijassa-1064	478	15	2016	2016	NUM
ijassa-1064	478	16	)	)	PUNCT
ijassa-1064	478	17	.	.	PUNCT
ijassa-1064	479	1	a	a	DET
ijassa-1064	479	2	prey	prey	NOUN
ijassa-1064	479	3	-	-	PUNCT
ijassa-1064	479	4	predator	predator	NOUN
ijassa-1064	479	5	model	model	NOUN
ijassa-1064	479	6	with	with	ADP
ijassa-1064	479	7	migrations	migration	NOUN
ijassa-1064	479	8	and	and	CCONJ
ijassa-1064	479	9	delays	delay	NOUN
ijassa-1064	479	10	,	,	PUNCT
ijassa-1064	479	11	discrete	discrete	ADJ
ijassa-1064	479	12	contin	contin	NOUN
ijassa-1064	479	13	dyn	dyn	PROPN
ijassa-1064	479	14	syst	syst	PROPN
ijassa-1064	479	15	ser	ser	PROPN
ijassa-1064	479	16	b.	b.	PROPN
ijassa-1064	479	17	,	,	PUNCT
ijassa-1064	479	18	21(3	21(3	NUM
ijassa-1064	479	19	)	)	PUNCT
ijassa-1064	479	20	,	,	PUNCT
ijassa-1064	479	21	737–761	737–761	NUM
ijassa-1064	479	22	.	.	PUNCT
ijassa-1064	480	1	6	6	NUM
ijassa-1064	480	2	.	.	X
ijassa-1064	480	3	al	al	PROPN
ijassa-1064	480	4	-	-	PUNCT
ijassa-1064	480	5	nassir	nassir	PROPN
ijassa-1064	480	6	,	,	PUNCT
ijassa-1064	480	7	s.	s.	PROPN
ijassa-1064	480	8	(	(	PUNCT
ijassa-1064	480	9	2017	2017	NUM
ijassa-1064	480	10	)	)	PUNCT
ijassa-1064	480	11	.	.	PUNCT
ijassa-1064	481	1	the	the	DET
ijassa-1064	481	2	dynamics	dynamic	NOUN
ijassa-1064	481	3	and	and	CCONJ
ijassa-1064	481	4	optimal	optimal	ADJ
ijassa-1064	481	5	control	control	NOUN
ijassa-1064	481	6	of	of	ADP
ijassa-1064	481	7	a	a	DET
ijassa-1064	481	8	prey	prey	NOUN
ijassa-1064	481	9	-	-	PUNCT
ijassa-1064	481	10	predator	predator	NOUN
ijassa-1064	481	11	system	system	NOUN
ijassa-1064	481	12	,	,	PUNCT
ijassa-1064	481	13	global	global	ADJ
ijassa-1064	481	14	j.	j.	PROPN
ijassa-1064	481	15	pure	pure	PROPN
ijassa-1064	481	16	appl	appl	PROPN
ijassa-1064	481	17	.	.	PUNCT
ijassa-1064	481	18	math	math	PROPN
ijassa-1064	481	19	.	.	PUNCT
ijassa-1064	481	20	,	,	PUNCT
ijassa-1064	481	21	13	13	NUM
ijassa-1064	481	22	,	,	PUNCT
ijassa-1064	481	23	5287–5298	5287–5298	NUM
ijassa-1064	481	24	.	.	PUNCT
ijassa-1064	482	1	7	7	X
ijassa-1064	482	2	.	.	X
ijassa-1064	482	3	bakare	bakare	PROPN
ijassa-1064	482	4	,	,	PUNCT
ijassa-1064	482	5	e.a	e.a	PROPN
ijassa-1064	482	6	.	.	PROPN
ijassa-1064	482	7	,	,	PUNCT
ijassa-1064	482	8	adekunle	adekunle	PROPN
ijassa-1064	482	9	,	,	PUNCT
ijassa-1064	482	10	y.a	y.a	PROPN
ijassa-1064	482	11	.	.	PROPN
ijassa-1064	482	12	and	and	CCONJ
ijassa-1064	482	13	nwagwo	nwagwo	PROPN
ijassa-1064	482	14	,	,	PUNCT
ijassa-1064	482	15	a.	a.	NOUN
ijassa-1064	482	16	(	(	PUNCT
ijassa-1064	482	17	2012	2012	NUM
ijassa-1064	482	18	)	)	PUNCT
ijassa-1064	482	19	.	.	PUNCT
ijassa-1064	483	1	mathematical	mathematical	ADJ
ijassa-1064	483	2	analysis	analysis	NOUN
ijassa-1064	483	3	of	of	ADP
ijassa-1064	483	4	the	the	DET
ijassa-1064	483	5	control	control	NOUN
ijassa-1064	483	6	of	of	ADP
ijassa-1064	483	7	the	the	DET
ijassa-1064	483	8	spread	spread	NOUN
ijassa-1064	483	9	of	of	ADP
ijassa-1064	483	10	infectious	infectious	ADJ
ijassa-1064	483	11	disease	disease	NOUN
ijassa-1064	483	12	in	in	ADP
ijassa-1064	483	13	a	a	DET
ijassa-1064	483	14	prey	prey	NOUN
ijassa-1064	483	15	-	-	PUNCT
ijassa-1064	483	16	predator	predator	NOUN
ijassa-1064	483	17	ecosystem	ecosystem	NOUN
ijassa-1064	483	18	,	,	PUNCT
ijassa-1064	483	19	int	int	NOUN
ijassa-1064	483	20	.	.	PUNCT
ijassa-1064	484	1	j.	j.	PROPN
ijassa-1064	484	2	comp	comp	PROPN
ijassa-1064	484	3	.	.	PUNCT
ijassa-1064	485	1	organ	organ	PROPN
ijassa-1064	485	2	.	.	PUNCT
ijassa-1064	486	1	trends	trend	NOUN
ijassa-1064	486	2	,	,	PUNCT
ijassa-1064	486	3	2(1	2(1	NUM
ijassa-1064	486	4	)	)	PUNCT
ijassa-1064	486	5	,	,	PUNCT
ijassa-1064	486	6	27–32	27–32	NUM
ijassa-1064	486	7	.	.	NOUN
ijassa-1064	486	8	8	8	NUM
ijassa-1064	486	9	.	.	X
ijassa-1064	486	10	bera	bera	NOUN
ijassa-1064	486	11	,	,	PUNCT
ijassa-1064	486	12	s.p	s.p	PROPN
ijassa-1064	486	13	.	.	PROPN
ijassa-1064	486	14	,	,	PUNCT
ijassa-1064	486	15	maiti	maiti	PROPN
ijassa-1064	486	16	,	,	PUNCT
ijassa-1064	486	17	a.	a.	NOUN
ijassa-1064	486	18	and	and	CCONJ
ijassa-1064	486	19	samanta	samanta	PROPN
ijassa-1064	486	20	,	,	PUNCT
ijassa-1064	486	21	g.p	g.p	PROPN
ijassa-1064	486	22	.	.	PROPN
ijassa-1064	486	23	(	(	PUNCT
ijassa-1064	486	24	2015	2015	NUM
ijassa-1064	486	25	)	)	PUNCT
ijassa-1064	486	26	.	.	PUNCT
ijassa-1064	487	1	a	a	DET
ijassa-1064	487	2	prey	prey	NOUN
ijassa-1064	487	3	-	-	PUNCT
ijassa-1064	487	4	predator	predator	NOUN
ijassa-1064	487	5	model	model	NOUN
ijassa-1064	487	6	with	with	ADP
ijassa-1064	487	7	infection	infection	NOUN
ijassa-1064	487	8	in	in	ADP
ijassa-1064	487	9	both	both	DET
ijassa-1064	487	10	prey	prey	NOUN
ijassa-1064	487	11	and	and	CCONJ
ijassa-1064	487	12	predator	predator	NOUN
ijassa-1064	487	13	,	,	PUNCT
ijassa-1064	487	14	filomat	filomat	NOUN
ijassa-1064	487	15	,	,	PUNCT
ijassa-1064	487	16	29(8	29(8	NOUN
ijassa-1064	487	17	)	)	PUNCT
ijassa-1064	487	18	,	,	PUNCT
ijassa-1064	487	19	1753–1767	1753–1767	NUM
ijassa-1064	487	20	.	.	NOUN
ijassa-1064	487	21	9	9	NUM
ijassa-1064	487	22	.	.	X
ijassa-1064	487	23	das	das	PROPN
ijassa-1064	487	24	,	,	PUNCT
ijassa-1064	487	25	k.p	k.p	PROPN
ijassa-1064	487	26	.	.	PROPN
ijassa-1064	488	1	(	(	PUNCT
ijassa-1064	488	2	2011	2011	NUM
ijassa-1064	488	3	)	)	PUNCT
ijassa-1064	488	4	.	.	PUNCT
ijassa-1064	489	1	a	a	DET
ijassa-1064	489	2	mathematical	mathematical	ADJ
ijassa-1064	489	3	study	study	NOUN
ijassa-1064	489	4	of	of	ADP
ijassa-1064	489	5	a	a	DET
ijassa-1064	489	6	predator	predator	NOUN
ijassa-1064	489	7	-	-	PUNCT
ijassa-1064	489	8	prey	prey	NOUN
ijassa-1064	489	9	dynamics	dynamic	NOUN
ijassa-1064	489	10	with	with	ADP
ijassa-1064	489	11	disease	disease	NOUN
ijassa-1064	489	12	in	in	ADP
ijassa-1064	489	13	predator	predator	NOUN
ijassa-1064	489	14	,	,	PUNCT
ijassa-1064	489	15	isrn	isrn	PROPN
ijassa-1064	489	16	appl	appl	PROPN
ijassa-1064	489	17	.	.	PUNCT
ijassa-1064	489	18	math	math	PROPN
ijassa-1064	489	19	.	.	PUNCT
ijassa-1064	489	20	,	,	PUNCT
ijassa-1064	489	21	article	article	NOUN
ijassa-1064	489	22	i	i	PROPN
ijassa-1064	489	23	d	d	PROPN
ijassa-1064	489	24	807486	807486	NUM
ijassa-1064	489	25	,	,	PUNCT
ijassa-1064	489	26	1–16	1–16	PROPN
ijassa-1064	489	27	.	.	PUNCT
ijassa-1064	490	1	10	10	NUM
ijassa-1064	490	2	.	.	X
ijassa-1064	491	1	diva	diva	PROPN
ijassa-1064	491	2	,	,	PUNCT
ijassa-1064	491	3	a.r	a.r	PROPN
ijassa-1064	491	4	.	.	PROPN
ijassa-1064	491	5	,	,	PUNCT
ijassa-1064	491	6	fatmawati	fatmawati	PROPN
ijassa-1064	491	7	,	,	PUNCT
ijassa-1064	491	8	windarto	windarto	NOUN
ijassa-1064	491	9	and	and	CCONJ
ijassa-1064	491	10	didik	didik	NOUN
ijassa-1064	491	11	,	,	PUNCT
ijassa-1064	491	12	k.a	k.a	PROPN
ijassa-1064	491	13	.	.	PROPN
ijassa-1064	491	14	(	(	PUNCT
ijassa-1064	491	15	2018	2018	NUM
ijassa-1064	491	16	)	)	PUNCT
ijassa-1064	491	17	.	.	PUNCT
ijassa-1064	492	1	optimal	optimal	ADJ
ijassa-1064	492	2	control	control	NOUN
ijassa-1064	492	3	of	of	ADP
ijassa-1064	492	4	predatorprey	predatorprey	PROPN
ijassa-1064	492	5	mathematical	mathematical	ADJ
ijassa-1064	492	6	model	model	NOUN
ijassa-1064	492	7	with	with	ADP
ijassa-1064	492	8	infection	infection	NOUN
ijassa-1064	492	9	and	and	CCONJ
ijassa-1064	492	10	harvesting	harvesting	NOUN
ijassa-1064	492	11	on	on	ADP
ijassa-1064	492	12	prey	prey	NOUN
ijassa-1064	492	13	,	,	PUNCT
ijassa-1064	492	14	journal	journal	NOUN
ijassa-1064	492	15	of	of	ADP
ijassa-1064	492	16	physics	physics	PROPN
ijassa-1064	492	17	:	:	PUNCT
ijassa-1064	492	18	conf	conf	PROPN
ijassa-1064	492	19	.	.	PUNCT
ijassa-1064	493	1	series	series	PROPN
ijassa-1064	493	2	,	,	PUNCT
ijassa-1064	493	3	974	974	NUM
ijassa-1064	493	4	,	,	PUNCT
ijassa-1064	493	5	012050	012050	NUM
ijassa-1064	493	6	.	.	PUNCT
ijassa-1064	494	1	11	11	NUM
ijassa-1064	494	2	.	.	X
ijassa-1064	495	1	doust	doust	ADJ
ijassa-1064	495	2	,	,	PUNCT
ijassa-1064	495	3	m.h.r	m.h.r	NOUN
ijassa-1064	495	4	.	.	PUNCT
ijassa-1064	495	5	and	and	CCONJ
ijassa-1064	495	6	gholizade	gholizade	VERB
ijassa-1064	495	7	,	,	PUNCT
ijassa-1064	495	8	s.	s.	PROPN
ijassa-1064	495	9	(	(	PUNCT
ijassa-1064	495	10	2014	2014	NUM
ijassa-1064	495	11	)	)	PUNCT
ijassa-1064	495	12	.	.	PUNCT
ijassa-1064	496	1	an	an	DET
ijassa-1064	496	2	analysis	analysis	NOUN
ijassa-1064	496	3	of	of	ADP
ijassa-1064	496	4	the	the	DET
ijassa-1064	496	5	modified	modify	VERB
ijassa-1064	496	6	lotka	lotka	PROPN
ijassa-1064	496	7	-	-	PUNCT
ijassa-1064	496	8	volterra	volterra	NOUN
ijassa-1064	496	9	predator	predator	NOUN
ijassa-1064	496	10	-	-	PUNCT
ijassa-1064	496	11	prey	prey	NOUN
ijassa-1064	496	12	model	model	NOUN
ijassa-1064	496	13	,	,	PUNCT
ijassa-1064	496	14	gen	gen	PROPN
ijassa-1064	496	15	.	.	PROPN
ijassa-1064	496	16	math	math	PROPN
ijassa-1064	496	17	.	.	PUNCT
ijassa-1064	497	1	notes	note	NOUN
ijassa-1064	497	2	,	,	PUNCT
ijassa-1064	497	3	25(2	25(2	NUM
ijassa-1064	497	4	)	)	PUNCT
ijassa-1064	497	5	,	,	PUNCT
ijassa-1064	497	6	1–5	1–5	PROPN
ijassa-1064	497	7	.	.	NOUN
ijassa-1064	497	8	12	12	NUM
ijassa-1064	497	9	.	.	PUNCT
ijassa-1064	498	1	fleming	fleming	PROPN
ijassa-1064	498	2	,	,	PUNCT
ijassa-1064	498	3	w.h	w.h	PROPN
ijassa-1064	498	4	.	.	PROPN
ijassa-1064	498	5	and	and	CCONJ
ijassa-1064	498	6	richel	richel	PROPN
ijassa-1064	498	7	,	,	PUNCT
ijassa-1064	498	8	r.w	r.w	PROPN
ijassa-1064	498	9	.	.	PROPN
ijassa-1064	498	10	(	(	PUNCT
ijassa-1064	498	11	1975	1975	NUM
ijassa-1064	498	12	)	)	PUNCT
ijassa-1064	498	13	.	.	PUNCT
ijassa-1064	499	1	deterministic	deterministic	ADJ
ijassa-1064	499	2	and	and	CCONJ
ijassa-1064	499	3	stochastic	stochastic	ADJ
ijassa-1064	499	4	optimal	optimal	ADJ
ijassa-1064	499	5	control	control	NOUN
ijassa-1064	499	6	.	.	PUNCT
ijassa-1064	500	1	new	new	PROPN
ijassa-1064	500	2	york	york	PROPN
ijassa-1064	500	3	:	:	PUNCT
ijassa-1064	500	4	springer	springer	NOUN
ijassa-1064	500	5	.	.	PUNCT
ijassa-1064	501	1	13	13	NUM
ijassa-1064	501	2	.	.	X
ijassa-1064	502	1	ghosh	ghosh	PROPN
ijassa-1064	502	2	,	,	PUNCT
ijassa-1064	502	3	m.	m.	NOUN
ijassa-1064	502	4	(	(	PUNCT
ijassa-1064	502	5	2010	2010	NUM
ijassa-1064	502	6	)	)	PUNCT
ijassa-1064	502	7	.	.	PUNCT
ijassa-1064	503	1	modeling	model	VERB
ijassa-1064	503	2	prey	prey	NOUN
ijassa-1064	503	3	-	-	PUNCT
ijassa-1064	503	4	predator	predator	NOUN
ijassa-1064	503	5	type	type	NOUN
ijassa-1064	503	6	fishery	fishery	NOUN
ijassa-1064	503	7	with	with	ADP
ijassa-1064	503	8	reserve	reserve	PROPN
ijassa-1064	503	9	area	area	NOUN
ijassa-1064	503	10	,	,	PUNCT
ijassa-1064	503	11	int	int	NOUN
ijassa-1064	503	12	.	.	PUNCT
ijassa-1064	504	1	j.	j.	PROPN
ijassa-1064	504	2	biomath	biomath	PROPN
ijassa-1064	504	3	.	.	PUNCT
ijassa-1064	504	4	,	,	PUNCT
ijassa-1064	504	5	3	3	NUM
ijassa-1064	504	6	,	,	PUNCT
ijassa-1064	504	7	351–365	351–365	NUM
ijassa-1064	504	8	.	.	PUNCT
ijassa-1064	505	1	14	14	NUM
ijassa-1064	505	2	.	.	PUNCT
ijassa-1064	506	1	ghosh	ghosh	PROPN
ijassa-1064	506	2	,	,	PUNCT
ijassa-1064	506	3	m.	m.	NOUN
ijassa-1064	506	4	,	,	PUNCT
ijassa-1064	506	5	olaniyi	olaniyi	PROPN
ijassa-1064	506	6	,	,	PUNCT
ijassa-1064	506	7	s.	s.	PROPN
ijassa-1064	506	8	and	and	CCONJ
ijassa-1064	506	9	obabiyi	obabiyi	PROPN
ijassa-1064	506	10	,	,	PUNCT
ijassa-1064	506	11	o.s	o.s	PROPN
ijassa-1064	506	12	.	.	PROPN
ijassa-1064	506	13	(	(	PUNCT
ijassa-1064	506	14	2020	2020	NUM
ijassa-1064	506	15	)	)	PUNCT
ijassa-1064	506	16	.	.	PUNCT
ijassa-1064	507	1	mathematical	mathematical	ADJ
ijassa-1064	507	2	analysis	analysis	NOUN
ijassa-1064	507	3	of	of	ADP
ijassa-1064	507	4	reinfection	reinfection	NOUN
ijassa-1064	507	5	and	and	CCONJ
ijassa-1064	507	6	relapse	relapse	NOUN
ijassa-1064	507	7	in	in	ADP
ijassa-1064	507	8	malaria	malaria	NOUN
ijassa-1064	507	9	dynamics	dynamic	NOUN
ijassa-1064	507	10	,	,	PUNCT
ijassa-1064	507	11	appl	appl	PROPN
ijassa-1064	507	12	.	.	PROPN
ijassa-1064	507	13	math	math	PROPN
ijassa-1064	507	14	.	.	PUNCT
ijassa-1064	508	1	comput	comput	NOUN
ijassa-1064	508	2	.	.	PUNCT
ijassa-1064	508	3	,	,	PUNCT
ijassa-1064	508	4	373	373	NUM
ijassa-1064	508	5	,	,	PUNCT
ijassa-1064	508	6	125044	125044	NUM
ijassa-1064	508	7	.	.	PUNCT
ijassa-1064	509	1	https://doi.org/10.1016/j.amc.2020.125044	https://doi.org/10.1016/j.amc.2020.125044	PROPN
ijassa-1064	509	2	15	15	NUM
ijassa-1064	509	3	.	.	PUNCT
ijassa-1064	510	1	goswami	goswami	PROPN
ijassa-1064	510	2	,	,	PUNCT
ijassa-1064	510	3	n.k	n.k	PROPN
ijassa-1064	510	4	.	.	PROPN
ijassa-1064	510	5	and	and	CCONJ
ijassa-1064	510	6	shanmukha	shanmukha	PROPN
ijassa-1064	510	7	,	,	PUNCT
ijassa-1064	510	8	b.	b.	PROPN
ijassa-1064	510	9	(	(	PUNCT
ijassa-1064	510	10	2021	2021	NUM
ijassa-1064	510	11	)	)	PUNCT
ijassa-1064	510	12	.	.	PUNCT
ijassa-1064	511	1	a	a	DET
ijassa-1064	511	2	mathematical	mathematical	ADJ
ijassa-1064	511	3	analysis	analysis	NOUN
ijassa-1064	511	4	of	of	ADP
ijassa-1064	511	5	zika	zika	X
ijassa-1064	511	6	virus	virus	NOUN
ijassa-1064	511	7	transmission	transmission	NOUN
ijassa-1064	511	8	with	with	ADP
ijassa-1064	511	9	optimal	optimal	ADJ
ijassa-1064	511	10	control	control	NOUN
ijassa-1064	511	11	strategies	strategy	NOUN
ijassa-1064	511	12	,	,	PUNCT
ijassa-1064	511	13	comput	comput	NOUN
ijassa-1064	511	14	.	.	PUNCT
ijassa-1064	512	1	meth	meth	NOUN
ijassa-1064	512	2	.	.	PUNCT
ijassa-1064	513	1	diff	diff	PROPN
ijassa-1064	513	2	.	.	PUNCT
ijassa-1064	514	1	equ	equ	PROPN
ijassa-1064	514	2	.	.	PROPN
ijassa-1064	514	3	,	,	PUNCT
ijassa-1064	514	4	9(1	9(1	NUM
ijassa-1064	514	5	)	)	PUNCT
ijassa-1064	514	6	,	,	PUNCT
ijassa-1064	514	7	117–145	117–145	NUM
ijassa-1064	514	8	.	.	PUNCT
ijassa-1064	515	1	16	16	NUM
ijassa-1064	515	2	.	.	PUNCT
ijassa-1064	516	1	hugo	hugo	PROPN
ijassa-1064	516	2	,	,	PUNCT
ijassa-1064	516	3	a.	a.	PROPN
ijassa-1064	516	4	,	,	PUNCT
ijassa-1064	516	5	makinde	makinde	PROPN
ijassa-1064	516	6	,	,	PUNCT
ijassa-1064	516	7	o.d	o.d	PROPN
ijassa-1064	516	8	.	.	PROPN
ijassa-1064	516	9	,	,	PUNCT
ijassa-1064	516	10	kumar	kumar	PROPN
ijassa-1064	516	11	,	,	PUNCT
ijassa-1064	516	12	s.	s.	PROPN
ijassa-1064	516	13	and	and	CCONJ
ijassa-1064	516	14	chibwana	chibwana	PROPN
ijassa-1064	516	15	,	,	PUNCT
ijassa-1064	516	16	f.f	f.f	PROPN
ijassa-1064	516	17	.	.	PROPN
ijassa-1064	516	18	(	(	PUNCT
ijassa-1064	516	19	2017	2017	NUM
ijassa-1064	516	20	)	)	PUNCT
ijassa-1064	516	21	.	.	PUNCT
ijassa-1064	517	1	optimal	optimal	ADJ
ijassa-1064	517	2	control	control	NOUN
ijassa-1064	517	3	and	and	CCONJ
ijassa-1064	517	4	cost	cost	NOUN
ijassa-1064	517	5	effectiveness	effectiveness	NOUN
ijassa-1064	517	6	analysis	analysis	NOUN
ijassa-1064	517	7	for	for	ADP
ijassa-1064	517	8	newcastle	newcastle	PROPN
ijassa-1064	517	9	disease	disease	PROPN
ijassa-1064	517	10	eco	eco	PROPN
ijassa-1064	517	11	-	-	PUNCT
ijassa-1064	517	12	epidemiological	epidemiological	ADJ
ijassa-1064	517	13	model	model	NOUN
ijassa-1064	517	14	in	in	ADP
ijassa-1064	517	15	tanzania	tanzania	PROPN
ijassa-1064	517	16	,	,	PUNCT
ijassa-1064	517	17	j.	j.	PROPN
ijassa-1064	517	18	biol	biol	PROPN
ijassa-1064	517	19	.	.	PUNCT
ijassa-1064	518	1	dyn	dyn	PROPN
ijassa-1064	518	2	.	.	PUNCT
ijassa-1064	518	3	,	,	PUNCT
ijassa-1064	518	4	11	11	NUM
ijassa-1064	518	5	,	,	PUNCT
ijassa-1064	518	6	190–209	190–209	NUM
ijassa-1064	518	7	.	.	PUNCT
ijassa-1064	519	1	17	17	NUM
ijassa-1064	519	2	.	.	PUNCT
ijassa-1064	520	1	kumar	kumar	PROPN
ijassa-1064	520	2	,	,	PUNCT
ijassa-1064	520	3	v.	v.	PROPN
ijassa-1064	520	4	and	and	CCONJ
ijassa-1064	520	5	kumari	kumari	PROPN
ijassa-1064	520	6	,	,	PUNCT
ijassa-1064	520	7	n.	n.	NOUN
ijassa-1064	520	8	(	(	PUNCT
ijassa-1064	520	9	2019	2019	NUM
ijassa-1064	520	10	)	)	PUNCT
ijassa-1064	520	11	.	.	PUNCT
ijassa-1064	521	1	controlling	control	VERB
ijassa-1064	521	2	chaos	chaos	NOUN
ijassa-1064	521	3	in	in	ADP
ijassa-1064	521	4	three	three	NUM
ijassa-1064	521	5	species	specie	NOUN
ijassa-1064	521	6	food	food	NOUN
ijassa-1064	521	7	chain	chain	NOUN
ijassa-1064	521	8	model	model	NOUN
ijassa-1064	521	9	with	with	ADP
ijassa-1064	521	10	fear	fear	NOUN
ijassa-1064	521	11	effect	effect	NOUN
ijassa-1064	521	12	,	,	PUNCT
ijassa-1064	521	13	aims	aim	VERB
ijassa-1064	521	14	math	math	NOUN
ijassa-1064	521	15	.	.	PUNCT
ijassa-1064	521	16	,	,	PUNCT
ijassa-1064	521	17	5(2	5(2	NUM
ijassa-1064	521	18	)	)	PUNCT
ijassa-1064	521	19	,	,	PUNCT
ijassa-1064	521	20	828–842	828–842	NUM
ijassa-1064	521	21	.	.	PROPN
ijassa-1064	521	22	18	18	NUM
ijassa-1064	521	23	.	.	PUNCT
ijassa-1064	522	1	lenhart	lenhart	PROPN
ijassa-1064	522	2	,	,	PUNCT
ijassa-1064	522	3	s.	s.	PROPN
ijassa-1064	522	4	and	and	CCONJ
ijassa-1064	522	5	workman	workman	PROPN
ijassa-1064	522	6	,	,	PUNCT
ijassa-1064	522	7	j.t	j.t	PROPN
ijassa-1064	522	8	.	.	PROPN
ijassa-1064	522	9	(	(	PUNCT
ijassa-1064	522	10	2007	2007	NUM
ijassa-1064	522	11	)	)	PUNCT
ijassa-1064	522	12	.	.	PUNCT
ijassa-1064	523	1	optimal	optimal	ADJ
ijassa-1064	523	2	control	control	NOUN
ijassa-1064	523	3	applied	apply	VERB
ijassa-1064	523	4	to	to	ADP
ijassa-1064	523	5	biological	biological	ADJ
ijassa-1064	523	6	models	model	NOUN
ijassa-1064	523	7	.	.	PUNCT
ijassa-1064	524	1	london	london	PROPN
ijassa-1064	524	2	:	:	PUNCT
ijassa-1064	524	3	chapman	chapman	PROPN
ijassa-1064	524	4	&	&	CCONJ
ijassa-1064	524	5	hall	hall	PROPN
ijassa-1064	524	6	.	.	PUNCT
ijassa-1064	525	1	19	19	NUM
ijassa-1064	525	2	.	.	X
ijassa-1064	525	3	lasalle	lasalle	PROPN
ijassa-1064	525	4	,	,	PUNCT
ijassa-1064	525	5	j.p	j.p	PROPN
ijassa-1064	525	6	.	.	PROPN
ijassa-1064	525	7	(	(	PUNCT
ijassa-1064	525	8	1976	1976	NUM
ijassa-1064	525	9	)	)	PUNCT
ijassa-1064	525	10	.	.	PUNCT
ijassa-1064	526	1	the	the	DET
ijassa-1064	526	2	stability	stability	NOUN
ijassa-1064	526	3	of	of	ADP
ijassa-1064	526	4	dynamical	dynamical	ADJ
ijassa-1064	526	5	dystems	dystem	NOUN
ijassa-1064	526	6	,	,	PUNCT
ijassa-1064	526	7	regional	regional	ADJ
ijassa-1064	526	8	conference	conference	NOUN
ijassa-1064	526	9	series	series	NOUN
ijassa-1064	526	10	in	in	ADP
ijassa-1064	526	11	applied	applied	ADJ
ijassa-1064	526	12	mathematics	mathematic	NOUN
ijassa-1064	526	13	.	.	PUNCT
ijassa-1064	527	1	philadelphia	philadelphia	PROPN
ijassa-1064	527	2	pa	pa	PROPN
ijassa-1064	527	3	:	:	PUNCT
ijassa-1064	527	4	siam	siam	PROPN
ijassa-1064	527	5	.	.	PROPN
ijassa-1064	528	1	20	20	NUM
ijassa-1064	528	2	.	.	X
ijassa-1064	529	1	lotka	lotka	PROPN
ijassa-1064	529	2	,	,	PUNCT
ijassa-1064	529	3	a.j	a.j	PROPN
ijassa-1064	529	4	.	.	PROPN
ijassa-1064	529	5	(	(	PUNCT
ijassa-1064	529	6	1925	1925	NUM
ijassa-1064	529	7	)	)	PUNCT
ijassa-1064	529	8	.	.	PUNCT
ijassa-1064	530	1	elements	element	NOUN
ijassa-1064	530	2	of	of	ADP
ijassa-1064	530	3	physical	physical	ADJ
ijassa-1064	530	4	biology	biology	NOUN
ijassa-1064	530	5	.	.	PUNCT
ijassa-1064	531	1	baltimore	baltimore	PROPN
ijassa-1064	531	2	:	:	PUNCT
ijassa-1064	531	3	williams	williams	PROPN
ijassa-1064	531	4	and	and	CCONJ
ijassa-1064	531	5	wilkins	wilkins	PROPN
ijassa-1064	531	6	.	.	PUNCT
ijassa-1064	532	1	21	21	NUM
ijassa-1064	532	2	.	.	PUNCT
ijassa-1064	533	1	nandi	nandi	NOUN
ijassa-1064	533	2	,	,	PUNCT
ijassa-1064	533	3	s.k	s.k	PROPN
ijassa-1064	533	4	.	.	PROPN
ijassa-1064	533	5	,	,	PUNCT
ijassa-1064	533	6	mondal	mondal	PROPN
ijassa-1064	533	7	,	,	PUNCT
ijassa-1064	533	8	p.k	p.k	PROPN
ijassa-1064	533	9	.	.	PROPN
ijassa-1064	533	10	,	,	PUNCT
ijassa-1064	533	11	jana	jana	PROPN
ijassa-1064	533	12	,	,	PUNCT
ijassa-1064	533	13	s.	s.	PROPN
ijassa-1064	533	14	,	,	PUNCT
ijassa-1064	533	15	haldar	haldar	NOUN
ijassa-1064	533	16	,	,	PUNCT
ijassa-1064	533	17	p.	p.	NOUN
ijassa-1064	533	18	and	and	CCONJ
ijassa-1064	533	19	kar	kar	PROPN
ijassa-1064	533	20	,	,	PUNCT
ijassa-1064	533	21	t.k	t.k	PROPN
ijassa-1064	533	22	.	.	PROPN
ijassa-1064	533	23	(	(	PUNCT
ijassa-1064	533	24	2015	2015	NUM
ijassa-1064	533	25	)	)	PUNCT
ijassa-1064	533	26	.	.	PUNCT
ijassa-1064	534	1	prey	prey	NOUN
ijassa-1064	534	2	-	-	PUNCT
ijassa-1064	534	3	predator	predator	NOUN
ijassa-1064	534	4	model	model	NOUN
ijassa-1064	534	5	with	with	ADP
ijassa-1064	534	6	two	two	NUM
ijassa-1064	534	7	-	-	PUNCT
ijassa-1064	534	8	stage	stage	NOUN
ijassa-1064	534	9	infection	infection	NOUN
ijassa-1064	534	10	in	in	ADP
ijassa-1064	534	11	prey	prey	NOUN
ijassa-1064	534	12	:	:	PUNCT
ijassa-1064	534	13	concerning	concern	VERB
ijassa-1064	534	14	pest	pest	NOUN
ijassa-1064	534	15	control	control	NOUN
ijassa-1064	534	16	,	,	PUNCT
ijassa-1064	534	17	j.	j.	PROPN
ijassa-1064	534	18	nonlinear	nonlinear	PROPN
ijassa-1064	534	19	dynam	dynam	PROPN
ijassa-1064	534	20	.	.	PUNCT
ijassa-1064	534	21	,	,	PUNCT
ijassa-1064	534	22	article	article	NOUN
ijassa-1064	534	23	i	i	PROPN
ijassa-1064	534	24	d	d	PROPN
ijassa-1064	534	25	948728	948728	NUM
ijassa-1064	534	26	(	(	PUNCT
ijassa-1064	534	27	2015	2015	NUM
ijassa-1064	534	28	)	)	PUNCT
ijassa-1064	534	29	,	,	PUNCT
ijassa-1064	534	30	1–13	1–13	NOUN
ijassa-1064	534	31	.	.	PUNCT
ijassa-1064	535	1	22	22	NUM
ijassa-1064	535	2	.	.	PUNCT
ijassa-1064	536	1	obabiyi	obabiyi	PROPN
ijassa-1064	536	2	,	,	PUNCT
ijassa-1064	536	3	o.s	o.s	PROPN
ijassa-1064	536	4	.	.	PROPN
ijassa-1064	536	5	and	and	CCONJ
ijassa-1064	536	6	olaniyi	olaniyi	PROPN
ijassa-1064	536	7	,	,	PUNCT
ijassa-1064	536	8	s.	s.	PROPN
ijassa-1064	536	9	(	(	PUNCT
ijassa-1064	536	10	2019	2019	NUM
ijassa-1064	536	11	)	)	PUNCT
ijassa-1064	536	12	.	.	PUNCT
ijassa-1064	537	1	global	global	ADJ
ijassa-1064	537	2	stability	stability	NOUN
ijassa-1064	537	3	analysis	analysis	NOUN
ijassa-1064	537	4	of	of	ADP
ijassa-1064	537	5	malaria	malaria	NOUN
ijassa-1064	537	6	transmission	transmission	NOUN
ijassa-1064	537	7	dynamics	dynamic	NOUN
ijassa-1064	537	8	with	with	ADP
ijassa-1064	537	9	vigilant	vigilant	ADJ
ijassa-1064	537	10	compartment	compartment	NOUN
ijassa-1064	537	11	,	,	PUNCT
ijassa-1064	537	12	electron	electron	NOUN
ijassa-1064	537	13	.	.	PUNCT
ijassa-1064	538	1	j.	j.	PROPN
ijassa-1064	538	2	differential	differential	PROPN
ijassa-1064	538	3	equations	equations	PROPN
ijassa-1064	538	4	.	.	PUNCT
ijassa-1064	538	5	,	,	PUNCT
ijassa-1064	538	6	2019(09	2019(09	NUM
ijassa-1064	538	7	)	)	PUNCT
ijassa-1064	538	8	,	,	PUNCT
ijassa-1064	538	9	1	1	NUM
ijassa-1064	538	10	–	–	PUNCT
ijassa-1064	538	11	10	10	NUM
ijassa-1064	538	12	.	.	X
ijassa-1064	538	13	23	23	NUM
ijassa-1064	538	14	.	.	PUNCT
ijassa-1064	539	1	okyere	okyere	INTJ
ijassa-1064	539	2	,	,	PUNCT
ijassa-1064	539	3	e.	e.	PROPN
ijassa-1064	539	4	,	,	PUNCT
ijassa-1064	539	5	olaniyi	olaniyi	PROPN
ijassa-1064	539	6	,	,	PUNCT
ijassa-1064	539	7	s.	s.	PROPN
ijassa-1064	539	8	and	and	CCONJ
ijassa-1064	539	9	bonyah	bonyah	PROPN
ijassa-1064	539	10	,	,	PUNCT
ijassa-1064	539	11	e.	e.	PROPN
ijassa-1064	539	12	(	(	PUNCT
ijassa-1064	539	13	2020	2020	NUM
ijassa-1064	539	14	)	)	PUNCT
ijassa-1064	539	15	.	.	PUNCT
ijassa-1064	540	1	analysis	analysis	NOUN
ijassa-1064	540	2	of	of	ADP
ijassa-1064	540	3	zika	zika	X
ijassa-1064	540	4	virus	virus	NOUN
ijassa-1064	540	5	dynamics	dynamic	NOUN
ijassa-1064	540	6	with	with	ADP
ijassa-1064	540	7	sexual	sexual	ADJ
ijassa-1064	540	8	transmission	transmission	NOUN
ijassa-1064	540	9	route	route	NOUN
ijassa-1064	540	10	using	use	VERB
ijassa-1064	540	11	multiple	multiple	ADJ
ijassa-1064	540	12	optimal	optimal	ADJ
ijassa-1064	540	13	controls	control	NOUN
ijassa-1064	540	14	.	.	PUNCT
ijassa-1064	541	1	scientific	scientific	ADJ
ijassa-1064	541	2	african	african	ADJ
ijassa-1064	541	3	,	,	PUNCT
ijassa-1064	541	4	9	9	NUM
ijassa-1064	541	5	,	,	PUNCT
ijassa-1064	541	6	e00532	e00532	NOUN
ijassa-1064	541	7	.	.	PUNCT
ijassa-1064	541	8	https://doi.org/10.1016/j.sciaf.2020.e00532	https://doi.org/10.1016/j.sciaf.2020.e00532	NOUN
ijassa-1064	542	1	24	24	NUM
ijassa-1064	542	2	.	.	PUNCT
ijassa-1064	542	3	olaniyi	olaniyi	PROPN
ijassa-1064	542	4	,	,	PUNCT
ijassa-1064	542	5	s.	s.	PROPN
ijassa-1064	542	6	,	,	PUNCT
ijassa-1064	542	7	okosun	okosun	PROPN
ijassa-1064	542	8	,	,	PUNCT
ijassa-1064	542	9	k.o	k.o	PROPN
ijassa-1064	542	10	.	.	PROPN
ijassa-1064	542	11	,	,	PUNCT
ijassa-1064	542	12	adesanya	adesanya	PROPN
ijassa-1064	542	13	,	,	PUNCT
ijassa-1064	542	14	s.o	s.o	PROPN
ijassa-1064	542	15	.	.	PROPN
ijassa-1064	542	16	and	and	CCONJ
ijassa-1064	542	17	lebelo	lebelo	PROPN
ijassa-1064	542	18	,	,	PUNCT
ijassa-1064	542	19	r.s	r.s	PROPN
ijassa-1064	542	20	.	.	PROPN
ijassa-1064	542	21	(	(	PUNCT
ijassa-1064	542	22	2020	2020	NUM
ijassa-1064	542	23	)	)	PUNCT
ijassa-1064	542	24	.	.	PUNCT
ijassa-1064	543	1	modelling	model	VERB
ijassa-1064	543	2	malaria	malaria	NOUN
ijassa-1064	543	3	dynamics	dynamic	NOUN
ijassa-1064	543	4	with	with	ADP
ijassa-1064	543	5	partial	partial	ADJ
ijassa-1064	543	6	immunity	immunity	NOUN
ijassa-1064	543	7	and	and	CCONJ
ijassa-1064	543	8	protected	protect	VERB
ijassa-1064	543	9	travelers	traveler	NOUN
ijassa-1064	543	10	:	:	PUNCT
ijassa-1064	543	11	optimal	optimal	ADJ
ijassa-1064	543	12	control	control	NOUN
ijassa-1064	543	13	and	and	CCONJ
ijassa-1064	543	14	costeffectiveness	costeffectiveness	NOUN
ijassa-1064	543	15	analysis	analysis	NOUN
ijassa-1064	543	16	.	.	PUNCT
ijassa-1064	544	1	j.	j.	PROPN
ijassa-1064	544	2	biol	biol	PROPN
ijassa-1064	544	3	.	.	PUNCT
ijassa-1064	545	1	dyn	dyn	PROPN
ijassa-1064	545	2	.	.	PUNCT
ijassa-1064	545	3	,	,	PUNCT
ijassa-1064	545	4	14	14	NUM
ijassa-1064	545	5	,	,	PUNCT
ijassa-1064	545	6	90–115	90–115	PROPN
ijassa-1064	545	7	.	.	PUNCT
ijassa-1064	546	1	copyright	copyright	NOUN
ijassa-1064	546	2	©	©	PROPN
ijassa-1064	546	3	2021	2021	NUM
ijassa-1064	546	4	assa	assa	NOUN
ijassa-1064	546	5	.	.	PUNCT
ijassa-1064	547	1	adv	adv	PROPN
ijassa-1064	547	2	syst	syst	PROPN
ijassa-1064	547	3	sci	sci	PROPN
ijassa-1064	547	4	appl	appl	PROPN
ijassa-1064	547	5	(	(	PUNCT
ijassa-1064	547	6	2021	2021	NUM
ijassa-1064	547	7	)	)	PUNCT
ijassa-1064	547	8	stability	stability	NOUN
ijassa-1064	547	9	analysis	analysis	NOUN
ijassa-1064	547	10	and	and	CCONJ
ijassa-1064	547	11	optimal	optimal	ADJ
ijassa-1064	547	12	measure	measure	NOUN
ijassa-1064	547	13	103	103	NUM
ijassa-1064	547	14	25	25	NUM
ijassa-1064	547	15	.	.	PUNCT
ijassa-1064	548	1	olaniyi	olaniyi	PROPN
ijassa-1064	548	2	,	,	PUNCT
ijassa-1064	548	3	s.	s.	PROPN
ijassa-1064	548	4	,	,	PUNCT
ijassa-1064	548	5	obabiyi	obabiyi	PROPN
ijassa-1064	548	6	,	,	PUNCT
ijassa-1064	548	7	o.s	o.s	PROPN
ijassa-1064	548	8	.	.	PROPN
ijassa-1064	548	9	,	,	PUNCT
ijassa-1064	548	10	okosun	okosun	PROPN
ijassa-1064	548	11	,	,	PUNCT
ijassa-1064	548	12	k.o	k.o	PROPN
ijassa-1064	548	13	.	.	PROPN
ijassa-1064	548	14	,	,	PUNCT
ijassa-1064	548	15	oladipo	oladipo	PROPN
ijassa-1064	548	16	,	,	PUNCT
ijassa-1064	548	17	a.t	a.t	PROPN
ijassa-1064	548	18	.	.	PROPN
ijassa-1064	548	19	and	and	CCONJ
ijassa-1064	548	20	adewale	adewale	PROPN
ijassa-1064	548	21	,	,	PUNCT
ijassa-1064	548	22	s.o	s.o	PROPN
ijassa-1064	548	23	.	.	PROPN
ijassa-1064	548	24	(	(	PUNCT
ijassa-1064	548	25	2020	2020	NUM
ijassa-1064	548	26	)	)	PUNCT
ijassa-1064	548	27	.	.	PUNCT
ijassa-1064	549	1	mathematical	mathematical	ADJ
ijassa-1064	549	2	modelling	modelling	NOUN
ijassa-1064	549	3	and	and	CCONJ
ijassa-1064	549	4	optimal	optimal	ADJ
ijassa-1064	549	5	cost	cost	NOUN
ijassa-1064	549	6	-	-	PUNCT
ijassa-1064	549	7	effective	effective	ADJ
ijassa-1064	549	8	control	control	NOUN
ijassa-1064	549	9	of	of	ADP
ijassa-1064	549	10	covid-19	covid-19	PROPN
ijassa-1064	549	11	transmission	transmission	NOUN
ijassa-1064	549	12	dynamics	dynamic	NOUN
ijassa-1064	549	13	,	,	PUNCT
ijassa-1064	549	14	eur	eur	NOUN
ijassa-1064	549	15	.	.	PUNCT
ijassa-1064	549	16	phys	phy	NOUN
ijassa-1064	549	17	.	.	PUNCT
ijassa-1064	550	1	j.	j.	PROPN
ijassa-1064	550	2	plus	plus	PROPN
ijassa-1064	550	3	,	,	PUNCT
ijassa-1064	550	4	135	135	NUM
ijassa-1064	550	5	,	,	PUNCT
ijassa-1064	550	6	938	938	NUM
ijassa-1064	550	7	.	.	PUNCT
ijassa-1064	551	1	https://doi.org/10.1140/epjp/s13360-020-00954z	https://doi.org/10.1140/epjp/s13360-020-00954z	PROPN
ijassa-1064	551	2	26	26	NUM
ijassa-1064	551	3	.	.	PUNCT
ijassa-1064	552	1	pontryagin	pontryagin	NOUN
ijassa-1064	552	2	,	,	PUNCT
ijassa-1064	552	3	l.s	l.s	PROPN
ijassa-1064	552	4	.	.	PROPN
ijassa-1064	552	5	,	,	PUNCT
ijassa-1064	552	6	boltyanskii	boltyanskii	PROPN
ijassa-1064	552	7	,	,	PUNCT
ijassa-1064	552	8	v.g	v.g	PROPN
ijassa-1064	552	9	.	.	PROPN
ijassa-1064	552	10	,	,	PUNCT
ijassa-1064	552	11	gamkrelidze	gamkrelidze	PROPN
ijassa-1064	552	12	,	,	PUNCT
ijassa-1064	552	13	r.v	r.v	PROPN
ijassa-1064	552	14	.	.	PROPN
ijassa-1064	552	15	and	and	CCONJ
ijassa-1064	552	16	mishchenko	mishchenko	PROPN
ijassa-1064	552	17	,	,	PUNCT
ijassa-1064	552	18	e.f	e.f	PROPN
ijassa-1064	552	19	.	.	PROPN
ijassa-1064	552	20	(	(	PUNCT
ijassa-1064	552	21	1962	1962	NUM
ijassa-1064	552	22	)	)	PUNCT
ijassa-1064	552	23	.	.	PUNCT
ijassa-1064	553	1	the	the	DET
ijassa-1064	553	2	mathematical	mathematical	ADJ
ijassa-1064	553	3	theory	theory	NOUN
ijassa-1064	553	4	of	of	ADP
ijassa-1064	553	5	optimal	optimal	ADJ
ijassa-1064	553	6	processes	process	NOUN
ijassa-1064	553	7	,	,	PUNCT
ijassa-1064	553	8	new	new	PROPN
ijassa-1064	553	9	york	york	PROPN
ijassa-1064	553	10	:	:	PUNCT
ijassa-1064	553	11	wiley	wiley	PROPN
ijassa-1064	553	12	.	.	PUNCT
ijassa-1064	554	1	27	27	NUM
ijassa-1064	554	2	.	.	PUNCT
ijassa-1064	555	1	prasad	prasad	PROPN
ijassa-1064	555	2	,	,	PUNCT
ijassa-1064	555	3	b.s.r.v	b.s.r.v	PROPN
ijassa-1064	555	4	.	.	PROPN
ijassa-1064	555	5	,	,	PUNCT
ijassa-1064	555	6	banerjee	banerjee	PROPN
ijassa-1064	555	7	,	,	PUNCT
ijassa-1064	555	8	m.	m.	NOUN
ijassa-1064	555	9	and	and	CCONJ
ijassa-1064	555	10	srinivasu	srinivasu	NOUN
ijassa-1064	555	11	,	,	PUNCT
ijassa-1064	555	12	p.d.n	p.d.n	PROPN
ijassa-1064	555	13	.	.	PUNCT
ijassa-1064	556	1	(	(	PUNCT
ijassa-1064	556	2	2013	2013	NUM
ijassa-1064	556	3	)	)	PUNCT
ijassa-1064	556	4	.	.	PUNCT
ijassa-1064	557	1	dynamics	dynamic	NOUN
ijassa-1064	557	2	of	of	ADP
ijassa-1064	557	3	additional	additional	ADJ
ijassa-1064	557	4	food	food	NOUN
ijassa-1064	557	5	provided	provide	VERB
ijassa-1064	557	6	predator	predator	NOUN
ijassa-1064	557	7	-	-	PUNCT
ijassa-1064	557	8	prey	prey	NOUN
ijassa-1064	557	9	system	system	NOUN
ijassa-1064	557	10	with	with	ADP
ijassa-1064	557	11	mutually	mutually	ADV
ijassa-1064	557	12	interfering	interfere	VERB
ijassa-1064	557	13	predators	predator	NOUN
ijassa-1064	557	14	.	.	PUNCT
ijassa-1064	558	1	math	math	NOUN
ijassa-1064	558	2	.	.	PUNCT
ijassa-1064	559	1	biosci	biosci	PROPN
ijassa-1064	559	2	.	.	PUNCT
ijassa-1064	559	3	,	,	PUNCT
ijassa-1064	559	4	246	246	NUM
ijassa-1064	559	5	,	,	PUNCT
ijassa-1064	559	6	176–190	176–190	NUM
ijassa-1064	559	7	.	.	NOUN
ijassa-1064	559	8	28	28	NUM
ijassa-1064	559	9	.	.	X
ijassa-1064	560	1	safi	safi	PROPN
ijassa-1064	560	2	,	,	PUNCT
ijassa-1064	560	3	m.a	m.a	PROPN
ijassa-1064	560	4	.	.	PROPN
ijassa-1064	560	5	and	and	CCONJ
ijassa-1064	560	6	darassi	darassi	PROPN
ijassa-1064	560	7	,	,	PUNCT
ijassa-1064	560	8	m.h	m.h	PROPN
ijassa-1064	560	9	.	.	PROPN
ijassa-1064	560	10	(	(	PUNCT
ijassa-1064	560	11	2018	2018	NUM
ijassa-1064	560	12	)	)	PUNCT
ijassa-1064	560	13	.	.	PUNCT
ijassa-1064	561	1	mathematical	mathematical	ADJ
ijassa-1064	561	2	analysis	analysis	NOUN
ijassa-1064	561	3	of	of	ADP
ijassa-1064	561	4	a	a	DET
ijassa-1064	561	5	model	model	NOUN
ijassa-1064	561	6	for	for	ADP
ijassa-1064	561	7	ectoparasite	ectoparasite	ADJ
ijassa-1064	561	8	-	-	PUNCT
ijassa-1064	561	9	borne	bear	VERB
ijassa-1064	561	10	diseases	disease	NOUN
ijassa-1064	561	11	,	,	PUNCT
ijassa-1064	561	12	math	math	NOUN
ijassa-1064	561	13	.	.	PUNCT
ijassa-1064	562	1	meth	meth	NOUN
ijassa-1064	562	2	.	.	PUNCT
ijassa-1064	563	1	appl	appl	PROPN
ijassa-1064	563	2	.	.	PUNCT
ijassa-1064	564	1	sci	sci	PROPN
ijassa-1064	564	2	.	.	PROPN
ijassa-1064	564	3	,	,	PUNCT
ijassa-1064	564	4	41(17	41(17	PROPN
ijassa-1064	564	5	)	)	PUNCT
ijassa-1064	564	6	,	,	PUNCT
ijassa-1064	564	7	8248–8257	8248–8257	NUM
ijassa-1064	564	8	.	.	PUNCT
ijassa-1064	565	1	29	29	NUM
ijassa-1064	565	2	.	.	X
ijassa-1064	566	1	sani	sani	PROPN
ijassa-1064	566	2	,	,	PUNCT
ijassa-1064	566	3	a.	a.	PROPN
ijassa-1064	566	4	,	,	PUNCT
ijassa-1064	566	5	cahyono	cahyono	PROPN
ijassa-1064	566	6	,	,	PUNCT
ijassa-1064	566	7	e.	e.	PROPN
ijassa-1064	566	8	,	,	PUNCT
ijassa-1064	566	9	mukhsar	mukhsar	PROPN
ijassa-1064	566	10	and	and	CCONJ
ijassa-1064	566	11	rahman	rahman	PROPN
ijassa-1064	566	12	,	,	PUNCT
ijassa-1064	566	13	g.a	g.a	PROPN
ijassa-1064	566	14	.	.	PROPN
ijassa-1064	566	15	(	(	PUNCT
ijassa-1064	566	16	2014	2014	NUM
ijassa-1064	566	17	)	)	PUNCT
ijassa-1064	566	18	.	.	PUNCT
ijassa-1064	567	1	dynamics	dynamic	NOUN
ijassa-1064	567	2	of	of	ADP
ijassa-1064	567	3	disease	disease	NOUN
ijassa-1064	567	4	spread	spread	VERB
ijassa-1064	567	5	in	in	ADP
ijassa-1064	567	6	a	a	DET
ijassa-1064	567	7	predator	predator	NOUN
ijassa-1064	567	8	-	-	PUNCT
ijassa-1064	567	9	prey	prey	NOUN
ijassa-1064	567	10	system	system	NOUN
ijassa-1064	567	11	,	,	PUNCT
ijassa-1064	567	12	adv	adv	PROPN
ijassa-1064	567	13	.	.	PUNCT
ijassa-1064	567	14	stud	stud	PROPN
ijassa-1064	567	15	.	.	PUNCT
ijassa-1064	568	1	biol	biol	PROPN
ijassa-1064	568	2	.	.	PUNCT
ijassa-1064	569	1	6	6	NUM
ijassa-1064	569	2	,	,	PUNCT
ijassa-1064	569	3	169–179	169–179	NUM
ijassa-1064	569	4	.	.	PUNCT
ijassa-1064	569	5	30	30	NUM
ijassa-1064	569	6	.	.	PUNCT
ijassa-1064	570	1	van	van	PROPN
ijassa-1064	570	2	den	den	PROPN
ijassa-1064	570	3	driessche	driessche	PROPN
ijassa-1064	570	4	,	,	PUNCT
ijassa-1064	570	5	p.	p.	NOUN
ijassa-1064	570	6	and	and	CCONJ
ijassa-1064	570	7	watmough	watmough	PROPN
ijassa-1064	570	8	,	,	PUNCT
ijassa-1064	570	9	j.	j.	PROPN
ijassa-1064	570	10	(	(	PUNCT
ijassa-1064	570	11	2002	2002	NUM
ijassa-1064	570	12	)	)	PUNCT
ijassa-1064	570	13	.	.	PUNCT
ijassa-1064	571	1	reproduction	reproduction	NOUN
ijassa-1064	571	2	numbers	number	NOUN
ijassa-1064	571	3	and	and	CCONJ
ijassa-1064	571	4	subthreshold	subthreshold	ADJ
ijassa-1064	571	5	endemic	endemic	ADJ
ijassa-1064	571	6	equilibria	equilibrium	NOUN
ijassa-1064	571	7	for	for	ADP
ijassa-1064	571	8	compartmental	compartmental	ADJ
ijassa-1064	571	9	models	model	NOUN
ijassa-1064	571	10	of	of	ADP
ijassa-1064	571	11	disease	disease	NOUN
ijassa-1064	571	12	transmission	transmission	NOUN
ijassa-1064	571	13	,	,	PUNCT
ijassa-1064	571	14	math	math	NOUN
ijassa-1064	571	15	.	.	PUNCT
ijassa-1064	572	1	biosci	biosci	PROPN
ijassa-1064	572	2	.	.	PUNCT
ijassa-1064	573	1	180	180	NUM
ijassa-1064	573	2	,	,	PUNCT
ijassa-1064	573	3	29–48	29–48	NUM
ijassa-1064	573	4	.	.	PUNCT
ijassa-1064	574	1	31	31	NUM
ijassa-1064	574	2	.	.	X
ijassa-1064	575	1	volterra	volterra	PROPN
ijassa-1064	575	2	,	,	PUNCT
ijassa-1064	575	3	v.	v.	PROPN
ijassa-1064	575	4	(	(	PUNCT
ijassa-1064	575	5	1926	1926	NUM
ijassa-1064	575	6	)	)	PUNCT
ijassa-1064	575	7	.	.	PUNCT
ijassa-1064	576	1	variazioni	variazioni	NOUN
ijassa-1064	576	2	e	e	X
ijassa-1064	576	3	fluttaazioni	fluttaazioni	NOUN
ijassa-1064	576	4	of	of	ADP
ijassa-1064	576	5	numero	numero	PROPN
ijassa-1064	576	6	di	di	PROPN
ijassa-1064	576	7	individul	individul	PROPN
ijassa-1064	576	8	in	in	ADP
ijassa-1064	576	9	specie	specie	PROPN
ijassa-1064	576	10	animali	animali	PROPN
ijassa-1064	576	11	conviventi	conviventi	PROPN
ijassa-1064	576	12	,	,	PUNCT
ijassa-1064	576	13	mem	mem	PROPN
ijassa-1064	576	14	.	.	PUNCT
ijassa-1064	576	15	accd	accd	PROPN
ijassa-1064	576	16	.	.	PUNCT
ijassa-1064	577	1	linc	linc	PROPN
ijassa-1064	577	2	.	.	PROPN
ijassa-1064	577	3	,	,	PUNCT
ijassa-1064	577	4	2	2	NUM
ijassa-1064	577	5	,	,	PUNCT
ijassa-1064	577	6	31–113	31–113	PROPN
ijassa-1064	577	7	.	.	PUNCT
ijassa-1064	578	1	copyright	copyright	NOUN
ijassa-1064	578	2	©	©	PROPN
ijassa-1064	578	3	2021	2021	NUM
ijassa-1064	578	4	assa	assa	NOUN
ijassa-1064	578	5	.	.	PUNCT
ijassa-1064	579	1	adv	adv	PROPN
ijassa-1064	579	2	syst	syst	PROPN
ijassa-1064	579	3	sci	sci	PROPN
ijassa-1064	579	4	appl	appl	PROPN
ijassa-1064	579	5	(	(	PUNCT
ijassa-1064	579	6	2021	2021	NUM
ijassa-1064	579	7	)	)	PUNCT
ijassa-1064	579	8	introduction	introduction	NOUN
ijassa-1064	579	9	model	model	NOUN
ijassa-1064	579	10	formulation	formulation	NOUN
ijassa-1064	579	11	well	well	ADJ
ijassa-1064	579	12	-	-	PUNCT
ijassa-1064	579	13	posedness	posedness	NOUN
ijassa-1064	579	14	of	of	ADP
ijassa-1064	579	15	the	the	DET
ijassa-1064	579	16	model	model	NOUN
ijassa-1064	579	17	boundedness	boundedness	NOUN
ijassa-1064	579	18	of	of	ADP
ijassa-1064	579	19	solutions	solution	NOUN
ijassa-1064	579	20	positivity	positivity	NOUN
ijassa-1064	579	21	of	of	ADP
ijassa-1064	579	22	solutions	solution	NOUN
ijassa-1064	579	23	analysis	analysis	NOUN
ijassa-1064	579	24	of	of	ADP
ijassa-1064	579	25	the	the	DET
ijassa-1064	579	26	model	model	NOUN
ijassa-1064	579	27	existence	existence	NOUN
ijassa-1064	579	28	of	of	ADP
ijassa-1064	579	29	equilibrium	equilibrium	NOUN
ijassa-1064	579	30	points	point	NOUN
ijassa-1064	579	31	trivial	trivial	ADJ
ijassa-1064	579	32	equilibrium	equilibrium	NOUN
ijassa-1064	579	33	point	point	NOUN
ijassa-1064	579	34	(	(	PUNCT
ijassa-1064	579	35	e0	e0	PROPN
ijassa-1064	579	36	)	)	PUNCT
ijassa-1064	579	37	axial	axial	ADJ
ijassa-1064	579	38	equilibrium	equilibrium	NOUN
ijassa-1064	579	39	point	point	NOUN
ijassa-1064	579	40	(	(	PUNCT
ijassa-1064	579	41	e1	e1	NOUN
ijassa-1064	579	42	)	)	PUNCT
ijassa-1064	579	43	disease	disease	NOUN
ijassa-1064	579	44	-	-	PUNCT
ijassa-1064	579	45	free	free	ADJ
ijassa-1064	579	46	equilibrium	equilibrium	NOUN
ijassa-1064	579	47	point	point	NOUN
ijassa-1064	579	48	(	(	PUNCT
ijassa-1064	579	49	e2	e2	NOUN
ijassa-1064	579	50	)	)	PUNCT
ijassa-1064	579	51	predator	predator	NOUN
ijassa-1064	579	52	-	-	PUNCT
ijassa-1064	579	53	free	free	ADJ
ijassa-1064	579	54	equilibrium	equilibrium	NOUN
ijassa-1064	579	55	point	point	NOUN
ijassa-1064	579	56	(	(	PUNCT
ijassa-1064	579	57	e3	e3	NOUN
ijassa-1064	579	58	)	)	PUNCT
ijassa-1064	579	59	infected	infect	VERB
ijassa-1064	579	60	prey	prey	NOUN
ijassa-1064	579	61	-	-	PUNCT
ijassa-1064	579	62	free	free	ADJ
ijassa-1064	579	63	equilibrium	equilibrium	NOUN
ijassa-1064	579	64	(	(	PUNCT
ijassa-1064	579	65	e4	e4	PROPN
ijassa-1064	579	66	)	)	PUNCT
ijassa-1064	579	67	infected	infect	VERB
ijassa-1064	579	68	predator	predator	NOUN
ijassa-1064	579	69	-	-	PUNCT
ijassa-1064	579	70	free	free	ADJ
ijassa-1064	579	71	equilibrium	equilibrium	NOUN
ijassa-1064	579	72	(	(	PUNCT
ijassa-1064	579	73	e5	e5	NOUN
ijassa-1064	579	74	)	)	PUNCT
ijassa-1064	579	75	interior	interior	ADJ
ijassa-1064	579	76	equilibrium	equilibrium	NOUN
ijassa-1064	579	77	point	point	NOUN
ijassa-1064	579	78	(	(	PUNCT
ijassa-1064	579	79	e6	e6	PROPN
ijassa-1064	579	80	)	)	PUNCT
ijassa-1064	579	81	stability	stability	NOUN
ijassa-1064	579	82	analysis	analysis	NOUN
ijassa-1064	579	83	stability	stability	NOUN
ijassa-1064	579	84	of	of	ADP
ijassa-1064	579	85	e0	e0	PROPN
ijassa-1064	579	86	stability	stability	NOUN
ijassa-1064	579	87	of	of	ADP
ijassa-1064	579	88	e1	e1	ADJ
ijassa-1064	579	89	stability	stability	NOUN
ijassa-1064	579	90	of	of	ADP
ijassa-1064	579	91	e2	e2	PROPN
ijassa-1064	579	92	stability	stability	NOUN
ijassa-1064	579	93	of	of	ADP
ijassa-1064	579	94	e3	e3	NOUN
ijassa-1064	579	95	stability	stability	NOUN
ijassa-1064	579	96	of	of	ADP
ijassa-1064	579	97	e4	e4	PROPN
ijassa-1064	579	98	stability	stability	NOUN
ijassa-1064	579	99	of	of	ADP
ijassa-1064	579	100	e5	e5	PROPN
ijassa-1064	579	101	stability	stability	NOUN
ijassa-1064	579	102	of	of	ADP
ijassa-1064	579	103	e6	e6	PROPN
ijassa-1064	579	104	optimal	optimal	ADJ
ijassa-1064	579	105	control	control	NOUN
ijassa-1064	579	106	model	model	NOUN
ijassa-1064	579	107	analysis	analysis	NOUN
ijassa-1064	579	108	of	of	ADP
ijassa-1064	579	109	the	the	DET
ijassa-1064	579	110	control	control	NOUN
ijassa-1064	579	111	model	model	NOUN
ijassa-1064	579	112	simulations	simulation	NOUN
ijassa-1064	579	113	of	of	ADP
ijassa-1064	579	114	the	the	DET
ijassa-1064	579	115	control	control	NOUN
ijassa-1064	579	116	model	model	NOUN
ijassa-1064	579	117	conclusion	conclusion	NOUN