id	sid	tid	token	lemma	pos
ma-219	1	1	2024	2024	NUM
ma-219	1	2	ada	ada	PROPN
ma-219	1	3	academica	academica	PROPN
ma-219	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-219	1	5	.	.	PUNCT
ma-219	2	1	j.	j.	PROPN
ma-219	2	2	math	math	PROPN
ma-219	2	3	.	.	PUNCT
ma-219	3	1	anal	anal	ADJ
ma-219	3	2	.	.	PUNCT
ma-219	4	1	4	4	NUM
ma-219	4	2	(	(	PUNCT
ma-219	4	3	2024	2024	NUM
ma-219	4	4	)	)	PUNCT
ma-219	4	5	9doi	9doi	NOUN
ma-219	4	6	:	:	PUNCT
ma-219	4	7	10.28924	10.28924	NUM
ma-219	4	8	/	/	SYM
ma-219	4	9	ada	ada	PROPN
ma-219	4	10	/	/	SYM
ma-219	4	11	ma.4.9	ma.4.9	PROPN
ma-219	4	12	global	global	ADJ
ma-219	4	13	stability	stability	NOUN
ma-219	4	14	analysis	analysis	NOUN
ma-219	4	15	of	of	ADP
ma-219	4	16	onchocerciasis	onchocerciasis	NOUN
ma-219	4	17	transmission	transmission	NOUN
ma-219	4	18	dynamics	dynamic	NOUN
ma-219	4	19	with	with	ADP
ma-219	4	20	vigilant	vigilant	ADJ
ma-219	4	21	compartment	compartment	NOUN
ma-219	4	22	in	in	ADP
ma-219	4	23	two	two	NUM
ma-219	4	24	interacting	interact	VERB
ma-219	4	25	populations	population	NOUN
ma-219	4	26	k.	k.	PROPN
ma-219	4	27	m.	m.	PROPN
ma-219	4	28	adeyemo	adeyemo	PROPN
ma-219	4	29	department	department	PROPN
ma-219	4	30	of	of	ADP
ma-219	4	31	mathematics	mathematics	PROPN
ma-219	4	32	,	,	PUNCT
ma-219	4	33	hallmark	hallmark	ADJ
ma-219	4	34	university	university	NOUN
ma-219	4	35	ijebu	ijebu	NOUN
ma-219	4	36	-	-	PUNCT
ma-219	4	37	itele	itele	PROPN
ma-219	4	38	,	,	PUNCT
ma-219	4	39	ogun	ogun	PROPN
ma-219	4	40	state	state	PROPN
ma-219	4	41	,	,	PUNCT
ma-219	4	42	nigeria	nigeria	PROPN
ma-219	4	43	mikyade2019@gmail.com	mikyade2019@gmail.com	PROPN
ma-219	5	1	abstract	abstract	PROPN
ma-219	5	2	.	.	PUNCT
ma-219	6	1	a	a	DET
ma-219	6	2	deterministic	deterministic	ADJ
ma-219	6	3	compartmental	compartmental	NOUN
ma-219	6	4	model	model	NOUN
ma-219	6	5	for	for	ADP
ma-219	6	6	the	the	DET
ma-219	6	7	transmission	transmission	NOUN
ma-219	6	8	dynamics	dynamic	NOUN
ma-219	6	9	of	of	ADP
ma-219	6	10	onchocerciasis	onchocerciasis	NOUN
ma-219	6	11	withvigilant	withvigilant	NOUN
ma-219	6	12	compartment	compartment	NOUN
ma-219	6	13	in	in	ADP
ma-219	6	14	two	two	NUM
ma-219	6	15	interacting	interact	VERB
ma-219	6	16	populations	population	NOUN
ma-219	6	17	is	be	AUX
ma-219	6	18	studied	study	VERB
ma-219	6	19	.	.	PUNCT
ma-219	7	1	the	the	DET
ma-219	7	2	model	model	NOUN
ma-219	7	3	is	be	AUX
ma-219	7	4	qualitatively	qualitatively	ADV
ma-219	7	5	analyzedto	analyzedto	ADJ
ma-219	7	6	investigate	investigate	VERB
ma-219	7	7	its	its	PRON
ma-219	7	8	global	global	ADJ
ma-219	7	9	asymptotic	asymptotic	ADJ
ma-219	7	10	behavior	behavior	NOUN
ma-219	7	11	with	with	ADP
ma-219	7	12	respect	respect	NOUN
ma-219	7	13	to	to	ADP
ma-219	7	14	disease	disease	NOUN
ma-219	7	15	-	-	PUNCT
ma-219	7	16	free	free	ADJ
ma-219	7	17	and	and	CCONJ
ma-219	7	18	endemic	endemic	ADJ
ma-219	7	19	equilibria	equilibrium	NOUN
ma-219	7	20	.	.	PUNCT
ma-219	8	1	itis	itis	NOUN
ma-219	8	2	shown	show	VERB
ma-219	8	3	,	,	PUNCT
ma-219	8	4	using	use	VERB
ma-219	8	5	a	a	DET
ma-219	8	6	linear	linear	ADJ
ma-219	8	7	lyapunov	lyapunov	ADJ
ma-219	8	8	function	function	NOUN
ma-219	8	9	,	,	PUNCT
ma-219	8	10	that	that	SCONJ
ma-219	8	11	the	the	DET
ma-219	8	12	disease	disease	NOUN
ma-219	8	13	-	-	PUNCT
ma-219	8	14	free	free	ADJ
ma-219	8	15	equilibrium	equilibrium	NOUN
ma-219	8	16	is	be	AUX
ma-219	8	17	globally	globally	ADV
ma-219	8	18	asymptoti	asymptoti	NOUN
ma-219	8	19	-	-	PUNCT
ma-219	8	20	cally	cally	ADV
ma-219	8	21	stable	stable	ADJ
ma-219	8	22	when	when	SCONJ
ma-219	8	23	the	the	DET
ma-219	8	24	associated	associated	ADJ
ma-219	8	25	basic	basic	ADJ
ma-219	8	26	reproduction	reproduction	NOUN
ma-219	8	27	number	number	NOUN
ma-219	8	28	,	,	PUNCT
ma-219	8	29	r0	r0	NOUN
ma-219	8	30	<	<	X
ma-219	8	31	1	1	NUM
ma-219	8	32	.	.	PUNCT
ma-219	9	1	when	when	SCONJ
ma-219	9	2	the	the	DET
ma-219	9	3	basic	basic	ADJ
ma-219	9	4	reproductionnumber	reproductionnumber	NOUN
ma-219	9	5	r0	r0	NOUN
ma-219	9	6	>	>	X
ma-219	9	7	1	1	NUM
ma-219	9	8	,	,	PUNCT
ma-219	9	9	under	under	ADP
ma-219	9	10	some	some	DET
ma-219	9	11	certain	certain	ADJ
ma-219	9	12	conditions	condition	NOUN
ma-219	9	13	on	on	ADP
ma-219	9	14	the	the	DET
ma-219	9	15	model	model	NOUN
ma-219	9	16	parameters	parameter	NOUN
ma-219	9	17	,	,	PUNCT
ma-219	9	18	we	we	PRON
ma-219	9	19	prove	prove	VERB
ma-219	9	20	that	that	SCONJ
ma-219	9	21	the	the	DET
ma-219	9	22	endemicequilibrium	endemicequilibrium	NOUN
ma-219	9	23	is	be	AUX
ma-219	9	24	globally	globally	ADV
ma-219	9	25	asymptotically	asymptotically	ADV
ma-219	9	26	stable	stable	ADJ
ma-219	9	27	with	with	ADP
ma-219	9	28	the	the	DET
ma-219	9	29	aid	aid	NOUN
ma-219	9	30	of	of	ADP
ma-219	9	31	a	a	DET
ma-219	9	32	suitable	suitable	ADJ
ma-219	9	33	nonlinear	nonlinear	ADJ
ma-219	9	34	lyapunov	lyapunov	ADJ
ma-219	9	35	function	function	NOUN
ma-219	9	36	.	.	PUNCT
ma-219	10	1	1	1	X
ma-219	10	2	.	.	X
ma-219	10	3	introduction	introduction	NOUN
ma-219	10	4	onchocerciasis	onchocerciasis	NOUN
ma-219	10	5	is	be	AUX
ma-219	10	6	one	one	NUM
ma-219	10	7	of	of	ADP
ma-219	10	8	the	the	DET
ma-219	10	9	neglected	neglect	VERB
ma-219	10	10	tropical	tropical	ADJ
ma-219	10	11	diseases	disease	NOUN
ma-219	10	12	caused	cause	VERB
ma-219	10	13	by	by	ADP
ma-219	10	14	the	the	DET
ma-219	10	15	parasite	parasite	NOUN
ma-219	10	16	onchocercavolvulus	onchocercavolvulus	ADJ
ma-219	10	17	,	,	PUNCT
ma-219	10	18	a	a	DET
ma-219	10	19	filarial	filarial	ADJ
ma-219	10	20	nematode	nematode	NOUN
ma-219	10	21	[	[	X
ma-219	10	22	3	3	NUM
ma-219	10	23	]	]	PUNCT
ma-219	10	24	.	.	PUNCT
ma-219	11	1	the	the	DET
ma-219	11	2	disease	disease	NOUN
ma-219	11	3	is	be	AUX
ma-219	11	4	transmitted	transmit	VERB
ma-219	11	5	from	from	ADP
ma-219	11	6	one	one	NUM
ma-219	11	7	person	person	NOUN
ma-219	11	8	to	to	ADP
ma-219	11	9	another	another	PRON
ma-219	11	10	by	by	ADP
ma-219	11	11	re	re	VERB
ma-219	11	12	-	-	VERB
ma-219	11	13	peated	peated	ADJ
ma-219	11	14	bites	bite	NOUN
ma-219	11	15	of	of	ADP
ma-219	11	16	black	black	ADJ
ma-219	11	17	flies	fly	NOUN
ma-219	11	18	.	.	PUNCT
ma-219	12	1	the	the	DET
ma-219	12	2	disease	disease	NOUN
ma-219	12	3	is	be	AUX
ma-219	12	4	endemic	endemic	ADJ
ma-219	12	5	in	in	ADP
ma-219	12	6	sub	sub	ADJ
ma-219	12	7	-	-	ADJ
ma-219	12	8	saharan	saharan	ADJ
ma-219	12	9	africa	africa	PROPN
ma-219	12	10	.	.	PUNCT
ma-219	13	1	many	many	ADJ
ma-219	13	2	researchers	researcher	NOUN
ma-219	13	3	haveworked	haveworke	VERB
ma-219	13	4	on	on	ADP
ma-219	13	5	many	many	ADJ
ma-219	13	6	ways	way	NOUN
ma-219	13	7	to	to	PART
ma-219	13	8	reduce	reduce	VERB
ma-219	13	9	the	the	DET
ma-219	13	10	spread	spread	NOUN
ma-219	13	11	of	of	ADP
ma-219	13	12	the	the	DET
ma-219	13	13	disease	disease	NOUN
ma-219	13	14	.	.	PUNCT
ma-219	14	1	for	for	ADP
ma-219	14	2	instance	instance	NOUN
ma-219	14	3	,	,	PUNCT
ma-219	14	4	remme	remme	VERB
ma-219	14	5	et	et	PROPN
ma-219	14	6	al	al	PROPN
ma-219	14	7	.	.	PUNCT
ma-219	15	1	[	[	X
ma-219	15	2	14	14	NUM
ma-219	15	3	]	]	X
ma-219	15	4	usedskin	usedskin	NOUN
ma-219	15	5	snip	snip	NOUN
ma-219	15	6	survey	survey	NOUN
ma-219	15	7	in	in	ADP
ma-219	15	8	west	west	PROPN
ma-219	15	9	africa	africa	PROPN
ma-219	15	10	to	to	PART
ma-219	15	11	investigate	investigate	VERB
ma-219	15	12	the	the	DET
ma-219	15	13	impact	impact	NOUN
ma-219	15	14	of	of	ADP
ma-219	15	15	controlling	control	VERB
ma-219	15	16	black	black	ADJ
ma-219	15	17	flies	fly	NOUN
ma-219	15	18	by	by	ADP
ma-219	15	19	larviciding.plaisier	larviciding.plaisi	ADJ
ma-219	15	20	et	et	PROPN
ma-219	15	21	al	al	PROPN
ma-219	15	22	.	.	PUNCT
ma-219	16	1	[	[	X
ma-219	16	2	13	13	NUM
ma-219	16	3	]	]	PUNCT
ma-219	16	4	used	use	VERB
ma-219	16	5	micro	micro	PROPN
ma-219	16	6	simulation	simulation	PROPN
ma-219	16	7	model	model	PROPN
ma-219	16	8	to	to	PART
ma-219	16	9	determine	determine	VERB
ma-219	16	10	the	the	DET
ma-219	16	11	period	period	NOUN
ma-219	16	12	required	require	VERB
ma-219	16	13	for	for	ADP
ma-219	16	14	combiningannual	combiningannual	ADJ
ma-219	16	15	ivermectin	ivermectin	NOUN
ma-219	16	16	treatment	treatment	NOUN
ma-219	16	17	and	and	CCONJ
ma-219	16	18	vector	vector	NOUN
ma-219	16	19	control	control	NOUN
ma-219	16	20	in	in	ADP
ma-219	16	21	the	the	DET
ma-219	16	22	onchocerciasis	onchocerciasis	NOUN
ma-219	16	23	control	control	NOUN
ma-219	16	24	programme	programme	NOUN
ma-219	16	25	in	in	ADP
ma-219	16	26	westafrica	westafrica	PROPN
ma-219	16	27	.	.	PUNCT
ma-219	17	1	alley	alley	PROPN
ma-219	17	2	et	et	PROPN
ma-219	17	3	al	al	PROPN
ma-219	17	4	.	.	PUNCT
ma-219	18	1	[	[	X
ma-219	18	2	3	3	X
ma-219	18	3	]	]	PUNCT
ma-219	18	4	used	use	VERB
ma-219	18	5	a	a	DET
ma-219	18	6	computer	computer	NOUN
ma-219	18	7	simulation	simulation	NOUN
ma-219	18	8	model	model	NOUN
ma-219	18	9	to	to	PART
ma-219	18	10	study	study	VERB
ma-219	18	11	prevention	prevention	NOUN
ma-219	18	12	of	of	ADP
ma-219	18	13	onchocerciasis	onchocerciasis	NOUN
ma-219	18	14	byusing	byusing	NOUN
ma-219	18	15	macrofilaricide	macrofilaricide	NOUN
ma-219	18	16	which	which	PRON
ma-219	18	17	kills	kill	VERB
ma-219	18	18	the	the	DET
ma-219	18	19	adult	adult	NOUN
ma-219	18	20	worms	worm	NOUN
ma-219	18	21	.	.	PUNCT
ma-219	19	1	asha	asha	PROPN
ma-219	19	2	hassan	hassan	PROPN
ma-219	19	3	&	&	CCONJ
ma-219	19	4	nyimvua	nyimvua	PROPN
ma-219	19	5	shaban	shaban	PROPN
ma-219	20	1	[	[	X
ma-219	20	2	5	5	NUM
ma-219	20	3	]	]	X
ma-219	20	4	investigatedthe	investigatedthe	ADJ
ma-219	20	5	effects	effect	NOUN
ma-219	20	6	of	of	ADP
ma-219	20	7	four	four	NUM
ma-219	20	8	control	control	NOUN
ma-219	20	9	strategies	strategy	NOUN
ma-219	20	10	on	on	ADP
ma-219	20	11	the	the	DET
ma-219	20	12	spread	spread	NOUN
ma-219	20	13	of	of	ADP
ma-219	20	14	the	the	DET
ma-219	20	15	disease.in	disease.in	PRON
ma-219	20	16	this	this	DET
ma-219	20	17	paper	paper	NOUN
ma-219	20	18	,	,	PUNCT
ma-219	20	19	we	we	PRON
ma-219	20	20	consider	consider	VERB
ma-219	20	21	global	global	ADJ
ma-219	20	22	stability	stability	NOUN
ma-219	20	23	analysis	analysis	NOUN
ma-219	20	24	of	of	ADP
ma-219	20	25	onchocerciasis	onchocerciasis	NOUN
ma-219	20	26	transmission	transmission	NOUN
ma-219	20	27	dynamics	dynamic	NOUN
ma-219	20	28	withvigilant	withvigilant	ADJ
ma-219	20	29	compartment	compartment	NOUN
ma-219	20	30	.	.	PUNCT
ma-219	21	1	the	the	DET
ma-219	21	2	human	human	ADJ
ma-219	21	3	population	population	NOUN
ma-219	21	4	is	be	AUX
ma-219	21	5	sub	sub	ADJ
ma-219	21	6	-	-	ADJ
ma-219	21	7	divided	divide	VERB
ma-219	21	8	into	into	ADP
ma-219	21	9	four	four	NUM
ma-219	21	10	compartments	compartment	NOUN
ma-219	21	11	and	and	CCONJ
ma-219	21	12	the	the	DET
ma-219	21	13	vec	vec	NOUN
ma-219	21	14	-	-	PUNCT
ma-219	21	15	tor	tor	NOUN
ma-219	21	16	population	population	NOUN
ma-219	21	17	is	be	AUX
ma-219	21	18	sub	sub	ADJ
ma-219	21	19	-	-	ADJ
ma-219	21	20	divided	divide	VERB
ma-219	21	21	into	into	ADP
ma-219	21	22	three	three	NUM
ma-219	21	23	compartments	compartment	NOUN
ma-219	21	24	.	.	PUNCT
ma-219	22	1	we	we	PRON
ma-219	22	2	show	show	VERB
ma-219	22	3	global	global	ADJ
ma-219	22	4	asymptotic	asymptotic	ADJ
ma-219	22	5	behaviour	behaviour	NOUN
ma-219	22	6	indisease	indisease	NOUN
ma-219	22	7	-	-	PUNCT
ma-219	22	8	free	free	ADJ
ma-219	22	9	and	and	CCONJ
ma-219	22	10	endemic	endemic	ADJ
ma-219	22	11	equilibria	equilibrium	NOUN
ma-219	22	12	.	.	PUNCT
ma-219	23	1	this	this	PRON
ma-219	23	2	is	be	AUX
ma-219	23	3	an	an	DET
ma-219	23	4	extension	extension	NOUN
ma-219	23	5	of	of	ADP
ma-219	23	6	the	the	DET
ma-219	23	7	work	work	NOUN
ma-219	23	8	done	do	VERB
ma-219	23	9	in	in	ADP
ma-219	23	10	[	[	X
ma-219	23	11	1	1	X
ma-219	23	12	]	]	PUNCT
ma-219	23	13	where	where	SCONJ
ma-219	23	14	the	the	DET
ma-219	23	15	authorworked	authorworke	VERB
ma-219	23	16	on	on	ADP
ma-219	23	17	the	the	DET
ma-219	23	18	local	local	ADJ
ma-219	23	19	stability	stability	NOUN
ma-219	23	20	of	of	ADP
ma-219	23	21	the	the	DET
ma-219	23	22	model	model	NOUN
ma-219	23	23	without	without	ADP
ma-219	23	24	the	the	DET
ma-219	23	25	vigilant	vigilant	ADJ
ma-219	23	26	compartment	compartment	NOUN
ma-219	23	27	.	.	PUNCT
ma-219	24	1	received	receive	VERB
ma-219	24	2	:	:	PUNCT
ma-219	24	3	18	18	NUM
ma-219	24	4	jan	jan	PROPN
ma-219	24	5	2024	2024	NUM
ma-219	24	6	.	.	PUNCT
ma-219	25	1	key	key	ADJ
ma-219	25	2	words	word	NOUN
ma-219	25	3	and	and	CCONJ
ma-219	25	4	phrases	phrase	NOUN
ma-219	25	5	.	.	PUNCT
ma-219	26	1	onchocerciasis	onchocerciasis	NOUN
ma-219	26	2	epidemic	epidemic	NOUN
ma-219	26	3	model	model	NOUN
ma-219	26	4	;	;	PUNCT
ma-219	26	5	vigilant	vigilant	ADJ
ma-219	26	6	compartment	compartment	NOUN
ma-219	26	7	;	;	PUNCT
ma-219	26	8	global	global	ADJ
ma-219	26	9	dynamics	dynamic	NOUN
ma-219	26	10	;	;	PUNCT
ma-219	26	11	lyapunov	lyapunov	PROPN
ma-219	26	12	function.1	function.1	PROPN
ma-219	26	13	https://adac.ee	https://adac.ee	PROPN
ma-219	26	14	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	26	15	eur	eur	PROPN
ma-219	26	16	.	.	PUNCT
ma-219	27	1	j.	j.	PROPN
ma-219	27	2	math	math	PROPN
ma-219	27	3	.	.	PUNCT
ma-219	28	1	anal	anal	PROPN
ma-219	28	2	.	.	PUNCT
ma-219	29	1	10.28924	10.28924	NUM
ma-219	29	2	/	/	SYM
ma-219	29	3	ada	ada	PROPN
ma-219	29	4	/	/	SYM
ma-219	29	5	ma.4.9	ma.4.9	PROPN
ma-219	29	6	2the	2the	PRON
ma-219	29	7	case	case	NOUN
ma-219	29	8	of	of	ADP
ma-219	29	9	onchocerciasis	onchocerciasis	NOUN
ma-219	29	10	model	model	NOUN
ma-219	29	11	presented	present	VERB
ma-219	29	12	in	in	ADP
ma-219	29	13	this	this	DET
ma-219	29	14	paper	paper	NOUN
ma-219	29	15	incorporates	incorporate	VERB
ma-219	29	16	a	a	DET
ma-219	29	17	new	new	ADJ
ma-219	29	18	class	class	NOUN
ma-219	29	19	of	of	ADP
ma-219	29	20	humancompartment	humancompartment	NOUN
ma-219	29	21	called	call	VERB
ma-219	29	22	vigilant	vigilant	ADJ
ma-219	29	23	individuals	individual	NOUN
ma-219	29	24	denoted	denote	VERB
ma-219	29	25	by	by	ADP
ma-219	29	26	vh(t	vh(t	NUM
ma-219	29	27	,	,	PUNCT
ma-219	29	28	xi	xi	PROPN
ma-219	29	29	)	)	PUNCT
ma-219	29	30	.	.	PUNCT
ma-219	30	1	the	the	DET
ma-219	30	2	individuals	individual	NOUN
ma-219	30	3	in	in	ADP
ma-219	30	4	the	the	DET
ma-219	30	5	compartmentare	compartmentare	NOUN
ma-219	30	6	assumed	assume	VERB
ma-219	30	7	to	to	PART
ma-219	30	8	be	be	AUX
ma-219	30	9	tired	tired	ADJ
ma-219	30	10	of	of	ADP
ma-219	30	11	onchocerciasis	onchocerciasis	NOUN
ma-219	30	12	and	and	CCONJ
ma-219	30	13	guide	guide	VERB
ma-219	30	14	against	against	ADP
ma-219	30	15	it	it	PRON
ma-219	30	16	by	by	ADP
ma-219	30	17	strictly	strictly	ADV
ma-219	30	18	adhering	adhere	VERB
ma-219	30	19	to	to	ADP
ma-219	30	20	the	the	DET
ma-219	30	21	vectorcontrol	vectorcontrol	NOUN
ma-219	30	22	measures	measure	NOUN
ma-219	30	23	such	such	ADJ
ma-219	30	24	as	as	ADP
ma-219	30	25	:	:	PUNCT
ma-219	30	26	regular	regular	ADJ
ma-219	30	27	indoor	indoor	ADJ
ma-219	30	28	residual	residual	ADJ
ma-219	30	29	spraying	spraying	NOUN
ma-219	30	30	(	(	PUNCT
ma-219	30	31	irs	irs	PROPN
ma-219	30	32	)	)	PUNCT
ma-219	30	33	,	,	PUNCT
ma-219	30	34	insecticide	insecticide	NOUN
ma-219	30	35	-	-	PUNCT
ma-219	30	36	treated	treat	VERB
ma-219	30	37	bed	bed	NOUN
ma-219	30	38	-	-	PUNCT
ma-219	30	39	nets(itns	nets(itns	PROPN
ma-219	30	40	)	)	PUNCT
ma-219	30	41	,	,	PUNCT
ma-219	30	42	clearing	clearing	NOUN
ma-219	30	43	of	of	ADP
ma-219	30	44	stagnant	stagnant	ADJ
ma-219	30	45	water	water	NOUN
ma-219	30	46	bodies	body	NOUN
ma-219	30	47	and	and	CCONJ
ma-219	30	48	drainages	drainage	NOUN
ma-219	30	49	and	and	CCONJ
ma-219	30	50	the	the	DET
ma-219	30	51	use	use	NOUN
ma-219	30	52	of	of	ADP
ma-219	30	53	head	head	NOUN
ma-219	30	54	-	-	PUNCT
ma-219	30	55	nets	net	NOUN
ma-219	30	56	in	in	ADP
ma-219	30	57	the	the	DET
ma-219	30	58	outdoor.the	outdoor.the	DET
ma-219	30	59	rest	rest	NOUN
ma-219	30	60	of	of	ADP
ma-219	30	61	the	the	DET
ma-219	30	62	paper	paper	NOUN
ma-219	30	63	is	be	AUX
ma-219	30	64	organized	organize	VERB
ma-219	30	65	as	as	SCONJ
ma-219	30	66	follows	follow	VERB
ma-219	30	67	:	:	PUNCT
ma-219	30	68	the	the	DET
ma-219	30	69	description	description	NOUN
ma-219	30	70	of	of	ADP
ma-219	30	71	the	the	DET
ma-219	30	72	model	model	NOUN
ma-219	30	73	and	and	CCONJ
ma-219	30	74	theorems	theorem	NOUN
ma-219	30	75	on	on	ADP
ma-219	30	76	positivityof	positivityof	PROPN
ma-219	30	77	solutions	solution	NOUN
ma-219	30	78	and	and	CCONJ
ma-219	30	79	reproduction	reproduction	NOUN
ma-219	30	80	number	number	NOUN
ma-219	30	81	are	be	AUX
ma-219	30	82	given	give	VERB
ma-219	30	83	in	in	ADP
ma-219	30	84	section	section	NOUN
ma-219	30	85	2	2	NUM
ma-219	30	86	while	while	SCONJ
ma-219	30	87	section	section	NOUN
ma-219	30	88	3	3	NUM
ma-219	30	89	,	,	PUNCT
ma-219	30	90	we	we	PRON
ma-219	30	91	explored	explore	VERB
ma-219	30	92	the	the	DET
ma-219	30	93	globalasymptotic	globalasymptotic	ADJ
ma-219	30	94	stability	stability	NOUN
ma-219	30	95	of	of	ADP
ma-219	30	96	the	the	DET
ma-219	30	97	disease	disease	NOUN
ma-219	30	98	-	-	PUNCT
ma-219	30	99	free	free	ADJ
ma-219	30	100	equilibrium	equilibrium	NOUN
ma-219	30	101	and	and	CCONJ
ma-219	30	102	endemic	endemic	ADJ
ma-219	30	103	equilibrium	equilibrium	NOUN
ma-219	30	104	with	with	ADP
ma-219	30	105	a	a	DET
ma-219	30	106	concludingremark	concludingremark	NOUN
ma-219	30	107	.	.	PUNCT
ma-219	31	1	2	2	X
ma-219	31	2	.	.	X
ma-219	31	3	model	model	NOUN
ma-219	31	4	description	description	NOUN
ma-219	31	5	two	two	NUM
ma-219	31	6	interacting	interact	VERB
ma-219	31	7	populations	population	NOUN
ma-219	31	8	are	be	AUX
ma-219	31	9	considered	consider	VERB
ma-219	31	10	;	;	PUNCT
ma-219	31	11	the	the	DET
ma-219	31	12	humans	human	NOUN
ma-219	31	13	and	and	CCONJ
ma-219	31	14	the	the	DET
ma-219	31	15	black	black	ADJ
ma-219	31	16	-	-	PUNCT
ma-219	31	17	flies	fly	NOUN
ma-219	31	18	populations	population	NOUN
ma-219	31	19	.	.	PUNCT
ma-219	32	1	thehuman	thehuman	NOUN
ma-219	32	2	population	population	NOUN
ma-219	32	3	is	be	AUX
ma-219	32	4	partitioned	partition	VERB
ma-219	32	5	into	into	ADP
ma-219	32	6	four	four	NUM
ma-219	32	7	compartments	compartment	NOUN
ma-219	32	8	:	:	PUNCT
ma-219	32	9	the	the	DET
ma-219	32	10	susceptible	susceptible	ADJ
ma-219	32	11	human	human	ADJ
ma-219	32	12	compartment	compartment	NOUN
ma-219	32	13	;	;	PUNCT
ma-219	33	1	sh	sh	PROPN
ma-219	33	2	,	,	PUNCT
ma-219	33	3	the	the	DET
ma-219	33	4	exposed	expose	VERB
ma-219	33	5	compartment	compartment	NOUN
ma-219	33	6	;	;	PUNCT
ma-219	33	7	eh	eh	INTJ
ma-219	33	8	,	,	PUNCT
ma-219	33	9	the	the	DET
ma-219	33	10	infectious	infectious	ADJ
ma-219	33	11	human	human	ADJ
ma-219	33	12	compartment	compartment	NOUN
ma-219	33	13	;	;	PUNCT
ma-219	33	14	ih	ih	NOUN
ma-219	33	15	and	and	CCONJ
ma-219	33	16	the	the	DET
ma-219	33	17	vigilant	vigilant	ADJ
ma-219	33	18	compartment	compartment	NOUN
ma-219	33	19	;	;	PUNCT
ma-219	33	20	vh	vh	PROPN
ma-219	33	21	.	.	PUNCT
ma-219	34	1	the	the	DET
ma-219	34	2	black	black	ADJ
ma-219	34	3	-	-	PUNCT
ma-219	34	4	fly	fly	NOUN
ma-219	34	5	population	population	NOUN
ma-219	34	6	is	be	AUX
ma-219	34	7	partitioned	partition	VERB
ma-219	34	8	into	into	ADP
ma-219	34	9	three	three	NUM
ma-219	34	10	compartments	compartment	NOUN
ma-219	34	11	:	:	PUNCT
ma-219	34	12	susceptible	susceptible	ADJ
ma-219	34	13	vector	vector	NOUN
ma-219	34	14	;	;	PUNCT
ma-219	34	15	sv	sv	INTJ
ma-219	34	16	,	,	PUNCT
ma-219	34	17	theexposed	theexpose	VERB
ma-219	34	18	vector	vector	NOUN
ma-219	34	19	compartment	compartment	NOUN
ma-219	34	20	;	;	PUNCT
ma-219	34	21	ev	ev	X
ma-219	34	22	and	and	CCONJ
ma-219	34	23	the	the	DET
ma-219	34	24	infective	infective	ADJ
ma-219	34	25	vector	vector	NOUN
ma-219	34	26	compartment	compartment	NOUN
ma-219	34	27	.	.	PUNCT
ma-219	35	1	the	the	DET
ma-219	35	2	total	total	ADJ
ma-219	35	3	human	human	NOUN
ma-219	35	4	and	and	CCONJ
ma-219	35	5	vectorpopulations	vectorpopulation	NOUN
ma-219	35	6	at	at	ADP
ma-219	35	7	any	any	DET
ma-219	35	8	given	give	VERB
ma-219	35	9	time	time	NOUN
ma-219	35	10	,	,	PUNCT
ma-219	35	11	t	t	PROPN
ma-219	35	12	,	,	PUNCT
ma-219	35	13	are	be	AUX
ma-219	35	14	respectively	respectively	ADV
ma-219	35	15	given	give	VERB
ma-219	35	16	by	by	ADP
ma-219	35	17	;	;	PUNCT
ma-219	35	18	n	n	NOUN
ma-219	35	19	=	=	PUNCT
ma-219	35	20	sh(t	sh(t	X
ma-219	35	21	)	)	PUNCT
ma-219	35	22	+	+	NOUN
ma-219	35	23	eh(t	eh(t	NUM
ma-219	35	24	)	)	PUNCT
ma-219	35	25	+	+	CCONJ
ma-219	35	26	ih(t	ih(t	PRON
ma-219	35	27	)	)	PUNCT
ma-219	35	28	+	+	NOUN
ma-219	35	29	vh(t	vh(t	NUM
ma-219	35	30	)	)	PUNCT
ma-219	35	31	and	and	CCONJ
ma-219	35	32	v	v	NOUN
ma-219	35	33	e	e	NOUN
ma-219	35	34	=	=	SYM
ma-219	35	35	sv	sv	PROPN
ma-219	35	36	(	(	PUNCT
ma-219	35	37	t)+ev	t)+ev	PROPN
ma-219	35	38	(	(	PUNCT
ma-219	35	39	t)+iv	t)+iv	X
ma-219	35	40	(	(	PUNCT
ma-219	35	41	t	t	PROPN
ma-219	35	42	)	)	PUNCT
ma-219	35	43	.	.	PUNCT
ma-219	36	1	we	we	PRON
ma-219	36	2	assume	assume	VERB
ma-219	36	3	that	that	SCONJ
ma-219	36	4	the	the	DET
ma-219	36	5	transmission	transmission	NOUN
ma-219	36	6	of	of	ADP
ma-219	36	7	onchocerciaisis	onchocerciaisis	NOUN
ma-219	36	8	in	in	ADP
ma-219	36	9	susceptible	susceptible	ADJ
ma-219	36	10	hostsis	hostsis	NOUN
ma-219	36	11	only	only	ADV
ma-219	36	12	through	through	ADP
ma-219	36	13	contact	contact	NOUN
ma-219	36	14	with	with	ADP
ma-219	36	15	infectious	infectious	ADJ
ma-219	36	16	vector	vector	NOUN
ma-219	36	17	.	.	PUNCT
ma-219	37	1	we	we	PRON
ma-219	37	2	also	also	ADV
ma-219	37	3	assume	assume	VERB
ma-219	37	4	that	that	SCONJ
ma-219	37	5	susceptible	susceptible	ADJ
ma-219	37	6	vector	vector	NOUN
ma-219	37	7	becomesinfectious	becomesinfectious	ADJ
ma-219	37	8	as	as	ADP
ma-219	37	9	a	a	DET
ma-219	37	10	result	result	NOUN
ma-219	37	11	of	of	ADP
ma-219	37	12	contact	contact	NOUN
ma-219	37	13	with	with	ADP
ma-219	37	14	infectious	infectious	ADJ
ma-219	37	15	hosts	host	NOUN
ma-219	37	16	during	during	ADP
ma-219	37	17	blood	blood	NOUN
ma-219	37	18	meal	meal	NOUN
ma-219	37	19	.	.	PUNCT
ma-219	38	1	the	the	DET
ma-219	38	2	population	population	NOUN
ma-219	38	3	understudy	understudy	NOUN
ma-219	38	4	is	be	AUX
ma-219	38	5	assumed	assume	VERB
ma-219	38	6	to	to	PART
ma-219	38	7	be	be	AUX
ma-219	38	8	large	large	ADJ
ma-219	38	9	enough	enough	ADV
ma-219	38	10	to	to	PART
ma-219	38	11	be	be	AUX
ma-219	38	12	modelled	model	VERB
ma-219	38	13	deterministically	deterministically	ADV
ma-219	38	14	.	.	PUNCT
ma-219	39	1	the	the	DET
ma-219	39	2	following	follow	VERB
ma-219	39	3	systemof	systemof	ADJ
ma-219	39	4	non	non	ADJ
ma-219	39	5	-	-	ADJ
ma-219	39	6	linear	linear	ADJ
ma-219	39	7	ordinary	ordinary	ADJ
ma-219	39	8	differential	differential	ADJ
ma-219	39	9	equations	equation	NOUN
ma-219	39	10	,	,	PUNCT
ma-219	39	11	with	with	ADP
ma-219	39	12	non	non	ADJ
ma-219	39	13	-	-	ADJ
ma-219	39	14	negative	negative	ADJ
ma-219	39	15	initial	initial	ADJ
ma-219	39	16	conditions	condition	NOUN
ma-219	39	17	,	,	PUNCT
ma-219	39	18	describes	describe	VERB
ma-219	39	19	thedynamics	thedynamic	NOUN
ma-219	39	20	of	of	ADP
ma-219	39	21	onchocerciaisis	onchocerciaisis	NOUN
ma-219	39	22	epidemics	epidemic	NOUN
ma-219	39	23	.	.	PUNCT
ma-219	40	1	dsh(t	dsh(t	PROPN
ma-219	40	2	,	,	PUNCT
ma-219	40	3	xi	xi	X
ma-219	40	4	)	)	PUNCT
ma-219	40	5	dt	dt	PROPN
ma-219	41	1	=	=	PUNCT
ma-219	41	2	∑l	∑l	PROPN
ma-219	41	3	i=0(1−	i=0(1−	PROPN
ma-219	41	4	τ)ψh(xi)−	τ)ψh(xi)−	NOUN
ma-219	41	5	δλh(xi	δλh(xi	X
ma-219	41	6	)	)	PUNCT
ma-219	41	7	σh(t	σh(t	NUM
ma-219	41	8	,	,	PUNCT
ma-219	41	9	xi	xi	X
ma-219	41	10	)	)	PUNCT
ma-219	41	11	iv	iv	PROPN
ma-219	41	12	(	(	PUNCT
ma-219	41	13	t	t	NOUN
ma-219	41	14	)	)	PUNCT
ma-219	41	15	nh(t	nh(t	PROPN
ma-219	41	16	,	,	PUNCT
ma-219	41	17	xi	xi	X
ma-219	41	18	)	)	PUNCT
ma-219	41	19	−	−	PROPN
ma-219	41	20	µh(xi)sh(t	µh(xi)sh(t	SYM
ma-219	41	21	,	,	PUNCT
ma-219	41	22	xi	xi	ADJ
ma-219	41	23	)	)	PUNCT
ma-219	41	24	deh(t	deh(t	PROPN
ma-219	41	25	,	,	PUNCT
ma-219	41	26	xi	xi	NUM
ma-219	41	27	)	)	PUNCT
ma-219	41	28	dt	dt	PROPN
ma-219	42	1	=	=	PUNCT
ma-219	42	2	∑l	∑l	PROPN
ma-219	42	3	i=0	i=0	PROPN
ma-219	42	4	δλh(xi	δλh(xi	X
ma-219	42	5	)	)	PUNCT
ma-219	42	6	σsh(t	σsh(t	PROPN
ma-219	42	7	,	,	PUNCT
ma-219	42	8	xi	xi	NOUN
ma-219	42	9	)	)	PUNCT
ma-219	42	10	iv	iv	PROPN
ma-219	42	11	(	(	PUNCT
ma-219	42	12	t	t	NOUN
ma-219	42	13	)	)	PUNCT
ma-219	42	14	nh(t	nh(t	PROPN
ma-219	42	15	,	,	PUNCT
ma-219	42	16	xi	xi	X
ma-219	42	17	)	)	PUNCT
ma-219	42	18	−	−	PROPN
ma-219	42	19	(	(	PUNCT
ma-219	42	20	αh(xi	αh(xi	PROPN
ma-219	42	21	)	)	PUNCT
ma-219	43	1	+	+	NUM
ma-219	43	2	µh(xi))eh(t	µh(xi))eh(t	PROPN
ma-219	43	3	,	,	PUNCT
ma-219	43	4	xi	xi	X
ma-219	43	5	)	)	PUNCT
ma-219	43	6	d	d	NOUN
ma-219	43	7	ih(t	ih(t	PROPN
ma-219	43	8	,	,	PUNCT
ma-219	43	9	xi	xi	NUM
ma-219	43	10	)	)	PUNCT
ma-219	43	11	dt	dt	X
ma-219	44	1	=	=	PUNCT
ma-219	44	2	∑l	∑l	PROPN
ma-219	44	3	i=0(1−	i=0(1−	PROPN
ma-219	44	4	θ)αh(xi)eh	θ)αh(xi)eh	NUM
ma-219	44	5	−	−	PROPN
ma-219	44	6	(	(	PUNCT
ma-219	44	7	γ(xi	γ(xi	PROPN
ma-219	44	8	)	)	PUNCT
ma-219	44	9	+	+	CCONJ
ma-219	44	10	µh(xi))ih(t	µh(xi))ih(t	ADJ
ma-219	44	11	,	,	PUNCT
ma-219	44	12	xi	xi	ADJ
ma-219	44	13	)	)	PUNCT
ma-219	44	14	dvh(t	dvh(t	PROPN
ma-219	44	15	,	,	PUNCT
ma-219	44	16	xi	xi	X
ma-219	44	17	)	)	PUNCT
ma-219	44	18	dt	dt	X
ma-219	45	1	=	=	SYM
ma-219	45	2	τψh(xi)n(t	τψh(xi)n(t	PROPN
ma-219	45	3	,	,	PUNCT
ma-219	45	4	xi	xi	ADJ
ma-219	45	5	)	)	PUNCT
ma-219	45	6	+	+	CCONJ
ma-219	45	7	θαh(xi)eh(t	θαh(xi)eh(t	NOUN
ma-219	45	8	,	,	PUNCT
ma-219	45	9	xi	xi	ADJ
ma-219	45	10	)	)	PUNCT
ma-219	45	11	+	+	CCONJ
ma-219	45	12	γ(xi)ih(t	γ(xi)ih(t	PROPN
ma-219	45	13	,	,	PUNCT
ma-219	45	14	xi)−	xi)−	PROPN
ma-219	45	15	µh(xi)vh(t	µh(xi)vh(t	PROPN
ma-219	45	16	,	,	PUNCT
ma-219	45	17	xi	xi	ADJ
ma-219	45	18	)	)	PUNCT
ma-219	45	19	dsv	dsv	PROPN
ma-219	45	20	dt	dt	NOUN
ma-219	46	1	=	=	SYM
ma-219	46	2	ψv	ψv	PROPN
ma-219	46	3	−	−	PROPN
ma-219	46	4	δλv	δλv	PROPN
ma-219	46	5	(	(	PUNCT
ma-219	46	6	xi	xi	PROPN
ma-219	46	7	)	)	PUNCT
ma-219	46	8	sv	sv	PROPN
ma-219	46	9	(	(	PUNCT
ma-219	46	10	t)ih(t	t)ih(t	NUM
ma-219	46	11	,	,	PUNCT
ma-219	46	12	xi	xi	NUM
ma-219	46	13	)	)	PUNCT
ma-219	46	14	nh(t	nh(t	PROPN
ma-219	46	15	,	,	PUNCT
ma-219	46	16	xi	xi	NUM
ma-219	46	17	)	)	PUNCT
ma-219	46	18	−	−	PROPN
ma-219	46	19	µvsv	µvsv	ADJ
ma-219	46	20	(	(	PUNCT
ma-219	46	21	t	t	NOUN
ma-219	46	22	)	)	PUNCT
ma-219	46	23	dev	dev	NOUN
ma-219	46	24	dt	dt	NOUN
ma-219	47	1	=	=	SYM
ma-219	47	2	δλv	δλv	PROPN
ma-219	47	3	(	(	PUNCT
ma-219	47	4	xi	xi	PROPN
ma-219	47	5	)	)	PUNCT
ma-219	47	6	sv	sv	PROPN
ma-219	47	7	(	(	PUNCT
ma-219	47	8	t)ih(t	t)ih(t	NUM
ma-219	47	9	,	,	PUNCT
ma-219	47	10	xi	xi	NUM
ma-219	47	11	)	)	PUNCT
ma-219	47	12	n(t	n(t	PROPN
ma-219	47	13	,	,	PUNCT
ma-219	47	14	xi	xi	NUM
ma-219	47	15	)	)	PUNCT
ma-219	47	16	−	−	PROPN
ma-219	47	17	(	(	PUNCT
ma-219	47	18	αv	αv	ADP
ma-219	47	19	+	+	CCONJ
ma-219	47	20	µv	µv	PROPN
ma-219	47	21	)	)	PUNCT
ma-219	47	22	ev	ev	PROPN
ma-219	47	23	(	(	PUNCT
ma-219	47	24	t	t	PROPN
ma-219	47	25	)	)	PUNCT
ma-219	47	26	d	d	NOUN
ma-219	47	27	iv	iv	NUM
ma-219	47	28	dt	dt	NOUN
ma-219	47	29	=	=	SYM
ma-219	47	30	αvev	αvev	PROPN
ma-219	47	31	(	(	PUNCT
ma-219	47	32	t)−	t)−	PROPN
ma-219	47	33	µv	µv	NOUN
ma-219	47	34	iv	iv	NUM
ma-219	47	35	(	(	PUNCT
ma-219	47	36	t	t	NOUN
ma-219	47	37	)	)	PUNCT
ma-219	47	38			NOUN
ma-219	47	39	(	(	PUNCT
ma-219	47	40	2.1	2.1	NUM
ma-219	47	41	)	)	PUNCT
ma-219	47	42	subject	subject	NOUN
ma-219	47	43	to	to	ADP
ma-219	47	44	the	the	DET
ma-219	47	45	following	follow	VERB
ma-219	47	46	initial	initial	ADJ
ma-219	47	47	conditions	condition	NOUN
ma-219	47	48	:	:	PUNCT
ma-219	47	49	sh(0	sh(0	NOUN
ma-219	47	50	,	,	PUNCT
ma-219	47	51	xi	xi	ADJ
ma-219	47	52	)	)	PUNCT
ma-219	47	53	=	=	SYM
ma-219	47	54	s0h(xi	s0h(xi	PROPN
ma-219	47	55	)	)	PUNCT
ma-219	47	56	,	,	PUNCT
ma-219	47	57	eh(0	eh(0	NOUN
ma-219	47	58	,	,	PUNCT
ma-219	47	59	xi	xi	X
ma-219	47	60	)	)	PUNCT
ma-219	47	61	=	=	SYM
ma-219	47	62	e0h(xi	e0h(xi	NOUN
ma-219	47	63	)	)	PUNCT
ma-219	47	64	,	,	PUNCT
ma-219	47	65	ih(0	ih(0	PROPN
ma-219	47	66	,	,	PUNCT
ma-219	47	67	xi	xi	PROPN
ma-219	47	68	)	)	PUNCT
ma-219	47	69	=	=	SYM
ma-219	47	70	i0h(xi	i0h(xi	PROPN
ma-219	47	71	)	)	PUNCT
ma-219	47	72	,	,	PUNCT
ma-219	47	73	vh(0	vh(0	PROPN
ma-219	47	74	,	,	PUNCT
ma-219	47	75	xi	xi	X
ma-219	47	76	)	)	PUNCT
ma-219	47	77	=	=	SYM
ma-219	47	78	v0h(xi	v0h(xi	PROPN
ma-219	47	79	)	)	PUNCT
ma-219	47	80	(	(	PUNCT
ma-219	47	81	2.2	2.2	NUM
ma-219	47	82	)	)	PUNCT
ma-219	47	83	sv	sv	NOUN
ma-219	47	84	(	(	PUNCT
ma-219	47	85	0	0	NUM
ma-219	47	86	)	)	PUNCT
ma-219	47	87	=	=	PRON
ma-219	47	88	s0v	s0v	PROPN
ma-219	47	89	,	,	PUNCT
ma-219	47	90	ev	ev	X
ma-219	47	91	(	(	PUNCT
ma-219	47	92	0	0	NUM
ma-219	47	93	)	)	PUNCT
ma-219	47	94	=	=	PRON
ma-219	47	95	e0v	e0v	X
ma-219	47	96	,	,	PUNCT
ma-219	47	97	iv	iv	X
ma-219	47	98	(	(	PUNCT
ma-219	47	99	0	0	NUM
ma-219	47	100	)	)	PUNCT
ma-219	47	101	=	=	PRON
ma-219	48	1	i0v	i0v	PROPN
ma-219	48	2	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	48	3	eur	eur	PROPN
ma-219	48	4	.	.	PUNCT
ma-219	49	1	j.	j.	PROPN
ma-219	49	2	math	math	PROPN
ma-219	49	3	.	.	PUNCT
ma-219	50	1	anal	anal	PROPN
ma-219	50	2	.	.	PUNCT
ma-219	51	1	10.28924	10.28924	NUM
ma-219	51	2	/	/	SYM
ma-219	51	3	ada	ada	PROPN
ma-219	51	4	/	/	SYM
ma-219	51	5	ma.4.9	ma.4.9	PROPN
ma-219	51	6	3	3	NUM
ma-219	51	7	symbols	symbol	NOUN
ma-219	51	8	definitionss	definitions	NOUN
ma-219	51	9	sh(t	sh(t	PART
ma-219	51	10	,	,	PUNCT
ma-219	51	11	xi	xi	ADJ
ma-219	51	12	)	)	PUNCT
ma-219	51	13	number	number	NOUN
ma-219	51	14	of	of	ADP
ma-219	51	15	susceptible	susceptible	ADJ
ma-219	51	16	humans	human	NOUN
ma-219	51	17	at	at	ADP
ma-219	51	18	time	time	NOUN
ma-219	51	19	t	t	PROPN
ma-219	51	20	and	and	CCONJ
ma-219	51	21	discrete	discrete	VERB
ma-219	51	22	age	age	NOUN
ma-219	51	23	xi	xi	X
ma-219	51	24	eh(t	eh(t	PROPN
ma-219	51	25	,	,	PUNCT
ma-219	51	26	xi	xi	X
ma-219	51	27	)	)	PUNCT
ma-219	51	28	number	number	NOUN
ma-219	51	29	of	of	ADP
ma-219	51	30	exposed	expose	VERB
ma-219	51	31	humans	human	NOUN
ma-219	51	32	at	at	ADP
ma-219	51	33	time	time	NOUN
ma-219	51	34	t	t	PROPN
ma-219	51	35	and	and	CCONJ
ma-219	51	36	discrete	discrete	ADJ
ma-219	51	37	age	age	NOUN
ma-219	51	38	xi	xi	X
ma-219	51	39	ih(t	ih(t	PROPN
ma-219	51	40	,	,	PUNCT
ma-219	51	41	xi	xi	ADJ
ma-219	51	42	)	)	PUNCT
ma-219	51	43	number	number	NOUN
ma-219	51	44	of	of	ADP
ma-219	51	45	infectious	infectious	ADJ
ma-219	51	46	humans	human	NOUN
ma-219	51	47	at	at	ADP
ma-219	51	48	time	time	NOUN
ma-219	51	49	t	t	PROPN
ma-219	51	50	and	and	CCONJ
ma-219	51	51	discrete	discrete	ADJ
ma-219	51	52	age	age	NOUN
ma-219	51	53	xi	xi	X
ma-219	51	54	vh(t	vh(t	PROPN
ma-219	51	55	,	,	PUNCT
ma-219	51	56	ai	ai	VERB
ma-219	51	57	)	)	PUNCT
ma-219	51	58	number	number	NOUN
ma-219	51	59	of	of	ADP
ma-219	51	60	vigilant	vigilant	ADJ
ma-219	51	61	host	host	NOUN
ma-219	51	62	humans	human	NOUN
ma-219	51	63	at	at	ADP
ma-219	51	64	time	time	NOUN
ma-219	51	65	t	t	PROPN
ma-219	51	66	and	and	CCONJ
ma-219	51	67	discrete	discrete	ADJ
ma-219	51	68	age	age	NOUN
ma-219	51	69	xi	xi	X
ma-219	51	70	sv	sv	PROPN
ma-219	51	71	(	(	PUNCT
ma-219	51	72	t	t	NOUN
ma-219	51	73	)	)	PUNCT
ma-219	51	74	number	number	NOUN
ma-219	51	75	of	of	ADP
ma-219	51	76	susceptible	susceptible	ADJ
ma-219	51	77	black	black	NOUN
ma-219	51	78	-	-	PUNCT
ma-219	51	79	flies	fly	NOUN
ma-219	51	80	at	at	ADP
ma-219	51	81	time	time	NOUN
ma-219	51	82	t	t	PROPN
ma-219	51	83	ev	ev	X
ma-219	51	84	(	(	PUNCT
ma-219	51	85	t	t	PROPN
ma-219	51	86	)	)	PUNCT
ma-219	51	87	number	number	NOUN
ma-219	51	88	of	of	ADP
ma-219	51	89	exposed	expose	VERB
ma-219	51	90	black	black	NOUN
ma-219	51	91	-	-	PUNCT
ma-219	51	92	flies	fly	NOUN
ma-219	51	93	at	at	ADP
ma-219	51	94	time	time	NOUN
ma-219	51	95	t	t	PROPN
ma-219	51	96	iv	iv	NUM
ma-219	51	97	(	(	PUNCT
ma-219	51	98	t	t	NOUN
ma-219	51	99	)	)	PUNCT
ma-219	51	100	number	number	NOUN
ma-219	51	101	of	of	ADP
ma-219	51	102	infectious	infectious	ADJ
ma-219	51	103	black	black	NOUN
ma-219	51	104	-	-	PUNCT
ma-219	51	105	flies	fly	NOUN
ma-219	51	106	at	at	ADP
ma-219	51	107	time	time	NOUN
ma-219	51	108	t	t	PROPN
ma-219	51	109	ψh(xi	ψh(xi	ADJ
ma-219	51	110	)	)	PUNCT
ma-219	51	111	recruitment	recruitment	NOUN
ma-219	51	112	term	term	NOUN
ma-219	51	113	of	of	ADP
ma-219	51	114	the	the	DET
ma-219	51	115	susceptible	susceptible	ADJ
ma-219	51	116	humans	human	NOUN
ma-219	51	117	at	at	ADP
ma-219	51	118	discrete	discrete	ADJ
ma-219	51	119	age	age	NOUN
ma-219	51	120	xi	xi	X
ma-219	51	121	ψv	ψv	PROPN
ma-219	51	122	recruitment	recruitment	NOUN
ma-219	51	123	term	term	NOUN
ma-219	51	124	of	of	ADP
ma-219	51	125	the	the	DET
ma-219	51	126	susceptible	susceptible	ADJ
ma-219	51	127	vectors	vector	NOUN
ma-219	51	128	δ	δ	NOUN
ma-219	51	129	biting	bite	VERB
ma-219	51	130	rate	rate	NOUN
ma-219	51	131	of	of	ADP
ma-219	51	132	the	the	DET
ma-219	51	133	vector	vector	NOUN
ma-219	51	134	λh(xi	λh(xi	PROPN
ma-219	51	135	)	)	PUNCT
ma-219	51	136	probability	probability	NOUN
ma-219	51	137	that	that	SCONJ
ma-219	51	138	a	a	DET
ma-219	51	139	bite	bite	NOUN
ma-219	51	140	by	by	ADP
ma-219	51	141	an	an	DET
ma-219	51	142	infectious	infectious	ADJ
ma-219	51	143	vector	vector	NOUN
ma-219	51	144	results	result	NOUN
ma-219	51	145	in	in	ADP
ma-219	51	146	transmissionof	transmissionof	NOUN
ma-219	51	147	disease	disease	NOUN
ma-219	51	148	to	to	PART
ma-219	51	149	humanat	humanat	VERB
ma-219	51	150	discrete	discrete	ADJ
ma-219	51	151	age	age	NOUN
ma-219	52	1	xi	xi	X
ma-219	52	2	λv	λv	INTJ
ma-219	52	3	probability	probability	NOUN
ma-219	53	1	that	that	SCONJ
ma-219	53	2	a	a	DET
ma-219	53	3	bite	bite	NOUN
ma-219	53	4	results	result	NOUN
ma-219	53	5	in	in	ADP
ma-219	53	6	transmission	transmission	NOUN
ma-219	53	7	of	of	ADP
ma-219	53	8	parasiteto	parasiteto	NOUN
ma-219	53	9	a	a	DET
ma-219	53	10	susceptible	susceptible	ADJ
ma-219	53	11	vector	vector	NOUN
ma-219	53	12	µh(xi	µh(xi	PROPN
ma-219	53	13	)	)	PUNCT
ma-219	53	14	per	per	ADP
ma-219	53	15	capita	capita	NOUN
ma-219	53	16	death	death	NOUN
ma-219	53	17	rate	rate	NOUN
ma-219	53	18	of	of	ADP
ma-219	53	19	humans	human	NOUN
ma-219	53	20	at	at	ADP
ma-219	53	21	discrete	discrete	ADJ
ma-219	53	22	age	age	NOUN
ma-219	53	23	xi	xi	ADP
ma-219	53	24	µv	µv	PROPN
ma-219	53	25	per	per	ADP
ma-219	53	26	capita	capita	NOUN
ma-219	53	27	death	death	NOUN
ma-219	53	28	rate	rate	NOUN
ma-219	53	29	of	of	ADP
ma-219	53	30	vector	vector	NOUN
ma-219	53	31	γh(xi	γh(xi	PROPN
ma-219	53	32	)	)	PUNCT
ma-219	53	33	disease	disease	NOUN
ma-219	53	34	-	-	PUNCT
ma-219	53	35	induced	induce	VERB
ma-219	53	36	death	death	NOUN
ma-219	53	37	rate	rate	NOUN
ma-219	53	38	of	of	ADP
ma-219	53	39	humans	human	NOUN
ma-219	53	40	at	at	ADP
ma-219	53	41	discrete	discrete	ADJ
ma-219	53	42	age	age	NOUN
ma-219	53	43	xi	xi	NOUN
ma-219	53	44	γv	γv	NOUN
ma-219	53	45	disease	disease	NOUN
ma-219	53	46	-	-	PUNCT
ma-219	53	47	induced	induce	VERB
ma-219	53	48	death	death	NOUN
ma-219	53	49	rate	rate	NOUN
ma-219	53	50	of	of	ADP
ma-219	53	51	vectors	vector	NOUN
ma-219	53	52	αh(xi	αh(xi	PROPN
ma-219	53	53	)	)	PUNCT
ma-219	53	54	per	per	ADP
ma-219	53	55	capita	capita	NOUN
ma-219	53	56	rate	rate	NOUN
ma-219	53	57	of	of	ADP
ma-219	53	58	progression	progression	NOUN
ma-219	53	59	of	of	ADP
ma-219	53	60	humans	human	NOUN
ma-219	53	61	from	from	ADP
ma-219	53	62	the	the	DET
ma-219	53	63	exposed	expose	VERB
ma-219	53	64	state	state	NOUN
ma-219	53	65	to	to	ADP
ma-219	53	66	theinfectious	theinfectious	ADJ
ma-219	53	67	stateat	stateat	NOUN
ma-219	53	68	discrete	discrete	ADJ
ma-219	53	69	age	age	NOUN
ma-219	53	70	xi	xi	ADP
ma-219	53	71	αv	αv	ADP
ma-219	53	72	per	per	ADP
ma-219	53	73	capita	capita	NOUN
ma-219	53	74	rate	rate	NOUN
ma-219	53	75	of	of	ADP
ma-219	53	76	progression	progression	NOUN
ma-219	53	77	of	of	ADP
ma-219	53	78	vectors	vector	NOUN
ma-219	53	79	from	from	ADP
ma-219	53	80	the	the	DET
ma-219	53	81	exposed	expose	VERB
ma-219	53	82	state	state	NOUN
ma-219	53	83	to	to	ADP
ma-219	53	84	theinfectious	theinfectious	ADJ
ma-219	53	85	state	state	NOUN
ma-219	53	86	νh(xi	νh(xi	PROPN
ma-219	53	87	)	)	PUNCT
ma-219	53	88	humans	human	NOUN
ma-219	53	89	disease	disease	NOUN
ma-219	53	90	-	-	PUNCT
ma-219	53	91	inhibiting	inhibit	VERB
ma-219	53	92	factor	factor	NOUN
ma-219	53	93	at	at	ADP
ma-219	53	94	discrete	discrete	ADJ
ma-219	53	95	age	age	NOUN
ma-219	53	96	xi	xi	X
ma-219	53	97	νv	νv	PROPN
ma-219	53	98	vectors	vector	VERB
ma-219	53	99	disease	disease	NOUN
ma-219	53	100	-	-	PUNCT
ma-219	53	101	inhibiting	inhibit	VERB
ma-219	53	102	factor	factor	NOUN
ma-219	53	103	τ(xi	τ(xi	NOUN
ma-219	53	104	)	)	PUNCT
ma-219	53	105	proportion	proportion	NOUN
ma-219	53	106	of	of	ADP
ma-219	53	107	human	human	ADJ
ma-219	53	108	population	population	NOUN
ma-219	53	109	that	that	PRON
ma-219	53	110	is	be	AUX
ma-219	53	111	born	bear	VERB
ma-219	53	112	vigilant	vigilant	ADJ
ma-219	53	113	at	at	ADP
ma-219	53	114	discrete	discrete	ADJ
ma-219	53	115	age	age	NOUN
ma-219	53	116	xi	xi	ADP
ma-219	53	117	θ(xi	θ(xi	PROPN
ma-219	53	118	)	)	PUNCT
ma-219	53	119	proportion	proportion	NOUN
ma-219	53	120	of	of	ADP
ma-219	53	121	exposed	expose	VERB
ma-219	53	122	humans	human	NOUN
ma-219	53	123	that	that	PRON
ma-219	53	124	becomes	become	VERB
ma-219	53	125	vigilant	vigilant	ADJ
ma-219	53	126	at	at	ADP
ma-219	53	127	discrete	discrete	ADJ
ma-219	53	128	age	age	NOUN
ma-219	53	129	xi	xi	ADP
ma-219	53	130	γ(xi	γ(xi	PROPN
ma-219	53	131	)	)	PUNCT
ma-219	53	132	per	per	ADP
ma-219	53	133	capita	capita	NOUN
ma-219	53	134	recovery	recovery	NOUN
ma-219	53	135	rate	rate	NOUN
ma-219	53	136	of	of	ADP
ma-219	53	137	infectious	infectious	ADJ
ma-219	53	138	humans	human	NOUN
ma-219	53	139	to	to	ADP
ma-219	53	140	the	the	DET
ma-219	53	141	vigilant	vigilant	ADJ
ma-219	53	142	state	state	NOUN
ma-219	53	143	at	at	ADP
ma-219	53	144	discrete	discrete	ADJ
ma-219	53	145	age	age	NOUN
ma-219	54	1	xi	xi	X
ma-219	54	2	model	model	VERB
ma-219	54	3	assumptionsthe	assumptionsthe	DET
ma-219	54	4	formulation	formulation	NOUN
ma-219	54	5	of	of	ADP
ma-219	54	6	the	the	DET
ma-219	54	7	compartmental	compartmental	ADJ
ma-219	54	8	model	model	NOUN
ma-219	54	9	is	be	AUX
ma-219	54	10	based	base	VERB
ma-219	54	11	on	on	ADP
ma-219	54	12	the	the	DET
ma-219	54	13	following	follow	VERB
ma-219	54	14	assumptions	assumption	NOUN
ma-219	54	15	:	:	PUNCT
ma-219	55	1	1	1	X
ma-219	55	2	.	.	X
ma-219	55	3	that	that	SCONJ
ma-219	55	4	only	only	ADJ
ma-219	55	5	humans	human	NOUN
ma-219	55	6	are	be	AUX
ma-219	55	7	vigilant.2	vigilant.2	NOUN
ma-219	55	8	.	.	PUNCT
ma-219	56	1	that	that	SCONJ
ma-219	56	2	humans	human	NOUN
ma-219	56	3	are	be	AUX
ma-219	56	4	born	bear	VERB
ma-219	56	5	either	either	CCONJ
ma-219	56	6	susceptible	susceptible	ADJ
ma-219	56	7	or	or	CCONJ
ma-219	56	8	vigilant.3	vigilant.3	NOUN
ma-219	56	9	.	.	PROPN
ma-219	56	10	that	that	SCONJ
ma-219	56	11	exposed	expose	VERB
ma-219	56	12	humans	human	NOUN
ma-219	56	13	progress	progress	VERB
ma-219	56	14	to	to	PART
ma-219	56	15	either	either	CCONJ
ma-219	56	16	become	become	VERB
ma-219	56	17	infectious	infectious	ADJ
ma-219	56	18	or	or	CCONJ
ma-219	56	19	vigilant	vigilant	ADJ
ma-219	56	20	.	.	PUNCT
ma-219	57	1	the	the	DET
ma-219	57	2	assumption	assumption	NOUN
ma-219	57	3	thatexposed	thatexpose	VERB
ma-219	57	4	humans	human	NOUN
ma-219	57	5	can	can	AUX
ma-219	57	6	become	become	VERB
ma-219	57	7	vigilant	vigilant	ADJ
ma-219	57	8	is	be	AUX
ma-219	57	9	motivated	motivate	VERB
ma-219	57	10	by	by	ADP
ma-219	57	11	the	the	DET
ma-219	57	12	possibility	possibility	NOUN
ma-219	57	13	of	of	ADP
ma-219	57	14	treating	treat	VERB
ma-219	57	15	plasmodiumvivax	plasmodiumvivax	PROPN
ma-219	57	16	infection	infection	NOUN
ma-219	57	17	which	which	PRON
ma-219	57	18	is	be	AUX
ma-219	57	19	at	at	ADP
ma-219	57	20	the	the	DET
ma-219	57	21	dormant	dormant	ADJ
ma-219	57	22	liver	liver	NOUN
ma-219	57	23	stage4	stage4	PROPN
ma-219	57	24	.	.	PUNCT
ma-219	58	1	that	that	SCONJ
ma-219	58	2	all	all	DET
ma-219	58	3	infectious	infectious	ADJ
ma-219	58	4	humans	human	NOUN
ma-219	58	5	become	become	VERB
ma-219	58	6	vigilant	vigilant	ADJ
ma-219	58	7	upon	upon	SCONJ
ma-219	58	8	recovery	recovery	NOUN
ma-219	58	9	due	due	ADP
ma-219	58	10	to	to	ADP
ma-219	58	11	treatment5	treatment5	NOUN
ma-219	58	12	.	.	PUNCT
ma-219	59	1	that	that	DET
ma-219	59	2	strict	strict	ADJ
ma-219	59	3	adherence	adherence	NOUN
ma-219	59	4	to	to	ADP
ma-219	59	5	vector	vector	NOUN
ma-219	59	6	control	control	NOUN
ma-219	59	7	measures	measure	NOUN
ma-219	59	8	by	by	ADP
ma-219	59	9	the	the	DET
ma-219	59	10	vigilant	vigilant	ADJ
ma-219	59	11	humans	human	NOUN
ma-219	59	12	does	do	AUX
ma-219	59	13	not	not	PART
ma-219	59	14	result	result	VERB
ma-219	59	15	intore	intore	ADJ
ma-219	59	16	-	-	PUNCT
ma-219	59	17	infection	infection	NOUN
ma-219	59	18	.	.	PUNCT
ma-219	60	1	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	60	2	eur	eur	PROPN
ma-219	60	3	.	.	PUNCT
ma-219	61	1	j.	j.	PROPN
ma-219	61	2	math	math	PROPN
ma-219	61	3	.	.	PUNCT
ma-219	62	1	anal	anal	PROPN
ma-219	62	2	.	.	PUNCT
ma-219	63	1	10.28924	10.28924	NUM
ma-219	63	2	/	/	SYM
ma-219	63	3	ada	ada	PROPN
ma-219	63	4	/	/	SYM
ma-219	63	5	ma.4.9	ma.4.9	PROPN
ma-219	63	6	46	46	NUM
ma-219	63	7	.	.	PUNCT
ma-219	64	1	all	all	DET
ma-219	64	2	black	black	NOUN
ma-219	64	3	-	-	PUNCT
ma-219	64	4	flies	fly	NOUN
ma-219	64	5	are	be	AUX
ma-219	64	6	born	bear	VERB
ma-219	64	7	susceptible.7	susceptible.7	NOUN
ma-219	64	8	.	.	PUNCT
ma-219	65	1	that	that	SCONJ
ma-219	65	2	the	the	DET
ma-219	65	3	susceptible	susceptible	ADJ
ma-219	65	4	black	black	NOUN
ma-219	65	5	-	-	PUNCT
ma-219	65	6	flies	fly	NOUN
ma-219	65	7	,	,	PUNCT
ma-219	65	8	when	when	SCONJ
ma-219	65	9	infected	infect	VERB
ma-219	65	10	,	,	PUNCT
ma-219	65	11	becomes	becomes	AUX
ma-219	65	12	exposed	expose	VERB
ma-219	65	13	black	black	ADJ
ma-219	65	14	-	-	PUNCT
ma-219	65	15	flies	fly	NOUN
ma-219	65	16	who	who	PRON
ma-219	65	17	are	be	AUX
ma-219	65	18	notyet	notyet	ADV
ma-219	65	19	infectious.8	infectious.8	PROPN
ma-219	65	20	.	.	PUNCT
ma-219	66	1	that	that	SCONJ
ma-219	66	2	the	the	DET
ma-219	66	3	exposed	expose	VERB
ma-219	66	4	black	black	ADJ
ma-219	66	5	-	-	PUNCT
ma-219	66	6	flies	fly	NOUN
ma-219	66	7	progress	progress	NOUN
ma-219	66	8	to	to	PART
ma-219	66	9	become	become	VERB
ma-219	66	10	infectious	infectious	ADJ
ma-219	66	11	only.9	only.9	NOUN
ma-219	66	12	.	.	PUNCT
ma-219	66	13	that	that	SCONJ
ma-219	66	14	the	the	DET
ma-219	66	15	infectious	infectious	ADJ
ma-219	66	16	black	black	NOUN
ma-219	66	17	-	-	PUNCT
ma-219	66	18	flies	fly	NOUN
ma-219	66	19	remain	remain	VERB
ma-219	66	20	infectious	infectious	ADJ
ma-219	66	21	for	for	ADP
ma-219	66	22	life	life	NOUN
ma-219	66	23	.	.	PUNCT
ma-219	67	1	that	that	PRON
ma-219	67	2	is	be	AUX
ma-219	67	3	,	,	PUNCT
ma-219	67	4	there	there	PRON
ma-219	67	5	is	be	VERB
ma-219	67	6	no	no	DET
ma-219	67	7	recovered	recover	VERB
ma-219	67	8	classfor	classfor	ADP
ma-219	67	9	black	black	ADJ
ma-219	67	10	-	-	PUNCT
ma-219	67	11	fly	fly	NOUN
ma-219	67	12	population.10	population.10	NOUN
ma-219	67	13	.	.	PUNCT
ma-219	68	1	that	that	SCONJ
ma-219	68	2	a	a	DET
ma-219	68	3	proportion	proportion	NOUN
ma-219	68	4	of	of	ADP
ma-219	68	5	susceptible	susceptible	ADJ
ma-219	68	6	humans	human	NOUN
ma-219	68	7	is	be	AUX
ma-219	68	8	infected	infect	VERB
ma-219	68	9	by	by	ADP
ma-219	68	10	infectious	infectious	ADJ
ma-219	68	11	mosquitoes	mosquito	NOUN
ma-219	68	12	and	and	CCONJ
ma-219	68	13	thatsusceptible	thatsusceptible	ADJ
ma-219	68	14	mosquitoes	mosquito	NOUN
ma-219	68	15	become	become	AUX
ma-219	68	16	infected	infected	ADJ
ma-219	68	17	when	when	SCONJ
ma-219	68	18	in	in	ADP
ma-219	68	19	contact	contact	NOUN
ma-219	68	20	with	with	ADP
ma-219	68	21	a	a	DET
ma-219	68	22	proportion	proportion	NOUN
ma-219	68	23	of	of	ADP
ma-219	68	24	infectioushumansto	infectioushumansto	NOUN
ma-219	68	25	carry	carry	VERB
ma-219	68	26	out	out	ADP
ma-219	68	27	the	the	DET
ma-219	68	28	analysis	analysis	NOUN
ma-219	68	29	of	of	ADP
ma-219	68	30	the	the	DET
ma-219	68	31	formulated	formulated	ADJ
ma-219	68	32	model	model	NOUN
ma-219	68	33	(	(	PUNCT
ma-219	68	34	2.1	2.1	NUM
ma-219	68	35	)	)	PUNCT
ma-219	68	36	,	,	PUNCT
ma-219	68	37	it	it	PRON
ma-219	68	38	is	be	AUX
ma-219	68	39	convenient	convenient	ADJ
ma-219	68	40	to	to	PART
ma-219	68	41	rescale	rescale	VERB
ma-219	68	42	the	the	DET
ma-219	68	43	variablesby	variablesby	ADJ
ma-219	68	44	dividing	divide	VERB
ma-219	68	45	the	the	DET
ma-219	68	46	number	number	NOUN
ma-219	68	47	of	of	ADP
ma-219	68	48	the	the	DET
ma-219	68	49	individuals	individual	NOUN
ma-219	68	50	in	in	ADP
ma-219	68	51	the	the	DET
ma-219	68	52	subpopulations	subpopulation	NOUN
ma-219	68	53	by	by	ADP
ma-219	68	54	their	their	PRON
ma-219	68	55	respective	respective	ADJ
ma-219	68	56	total	total	NOUN
ma-219	68	57	numberof	numberof	NOUN
ma-219	68	58	populations	population	NOUN
ma-219	68	59	nh(t	nh(t	NOUN
ma-219	68	60	,	,	PUNCT
ma-219	68	61	xi	xi	ADJ
ma-219	68	62	)	)	PUNCT
ma-219	68	63	and	and	CCONJ
ma-219	68	64	nv	nv	PROPN
ma-219	68	65	(	(	PUNCT
ma-219	68	66	t	t	PROPN
ma-219	68	67	)	)	PUNCT
ma-219	68	68	.	.	PUNCT
ma-219	69	1	this	this	DET
ma-219	69	2	process	process	NOUN
ma-219	69	3	is	be	AUX
ma-219	69	4	achieved	achieve	VERB
ma-219	69	5	by	by	ADP
ma-219	69	6	making	make	VERB
ma-219	69	7	the	the	DET
ma-219	69	8	following	follow	VERB
ma-219	69	9	change	change	VERB
ma-219	69	10	ofvariables	ofvariable	NOUN
ma-219	69	11	:	:	PUNCT
ma-219	69	12	s̄h(t	s̄h(t	NOUN
ma-219	69	13	,	,	PUNCT
ma-219	69	14	xi	xi	ADJ
ma-219	69	15	)	)	PUNCT
ma-219	69	16	=	=	SYM
ma-219	70	1	sh(t	sh(t	X
ma-219	70	2	,	,	PUNCT
ma-219	70	3	xi	xi	NUM
ma-219	70	4	)	)	PUNCT
ma-219	70	5	nh(t	nh(t	PROPN
ma-219	70	6	,	,	PUNCT
ma-219	70	7	xi	xi	X
ma-219	70	8	)	)	PUNCT
ma-219	70	9	,	,	PUNCT
ma-219	70	10	ēh(t	ēh(t	NOUN
ma-219	70	11	,	,	PUNCT
ma-219	70	12	xi	xi	ADJ
ma-219	70	13	)	)	PUNCT
ma-219	70	14	=	=	PUNCT
ma-219	71	1	eh(t	eh(t	X
ma-219	71	2	,	,	PUNCT
ma-219	71	3	xi	xi	NUM
ma-219	71	4	)	)	PUNCT
ma-219	71	5	nh(t	nh(t	PROPN
ma-219	71	6	,	,	PUNCT
ma-219	71	7	xi	xi	X
ma-219	71	8	)	)	PUNCT
ma-219	72	1	,	,	PUNCT
ma-219	72	2	īh(t	īh(t	PROPN
ma-219	72	3	,	,	PUNCT
ma-219	72	4	xi	xi	ADJ
ma-219	72	5	)	)	PUNCT
ma-219	73	1	=	=	PUNCT
ma-219	73	2	ih(t	ih(t	PROPN
ma-219	73	3	,	,	PUNCT
ma-219	73	4	xi	xi	NUM
ma-219	73	5	)	)	PUNCT
ma-219	73	6	nh(t	nh(t	PROPN
ma-219	73	7	,	,	PUNCT
ma-219	73	8	xi	xi	X
ma-219	73	9	)	)	PUNCT
ma-219	73	10	,	,	PUNCT
ma-219	73	11	v̄h(t	v̄h(t	PROPN
ma-219	73	12	,	,	PUNCT
ma-219	73	13	xi	xi	X
ma-219	73	14	)	)	PUNCT
ma-219	73	15	=	=	SYM
ma-219	73	16	vh(t	vh(t	PROPN
ma-219	73	17	,	,	PUNCT
ma-219	73	18	xi	xi	NUM
ma-219	73	19	)	)	PUNCT
ma-219	73	20	nh(t	nh(t	PROPN
ma-219	73	21	,	,	PUNCT
ma-219	73	22	xi	xi	NUM
ma-219	73	23	)	)	PUNCT
ma-219	73	24	,	,	PUNCT
ma-219	73	25	s̄v	s̄v	PROPN
ma-219	73	26	(	(	PUNCT
ma-219	73	27	t	t	PROPN
ma-219	73	28	,	,	PUNCT
ma-219	73	29	xi	xi	X
ma-219	73	30	)	)	PUNCT
ma-219	73	31	=	=	SYM
ma-219	73	32	sv	sv	X
ma-219	73	33	(	(	PUNCT
ma-219	73	34	t	t	PROPN
ma-219	73	35	,	,	PUNCT
ma-219	73	36	xi	xi	PROPN
ma-219	73	37	)	)	PUNCT
ma-219	73	38	nv	nv	PROPN
ma-219	73	39	(	(	PUNCT
ma-219	73	40	t	t	PROPN
ma-219	73	41	,	,	PUNCT
ma-219	73	42	xi	xi	PROPN
ma-219	73	43	)	)	PUNCT
ma-219	73	44	,	,	PUNCT
ma-219	73	45	ēv	ēv	PROPN
ma-219	73	46	(	(	PUNCT
ma-219	73	47	t	t	PROPN
ma-219	73	48	,	,	PUNCT
ma-219	73	49	xi	xi	X
ma-219	73	50	)	)	PUNCT
ma-219	74	1	=	=	SYM
ma-219	74	2	ev	ev	X
ma-219	74	3	(	(	PUNCT
ma-219	74	4	t	t	PROPN
ma-219	74	5	,	,	PUNCT
ma-219	74	6	xi	xi	PROPN
ma-219	74	7	)	)	PUNCT
ma-219	74	8	nv	nv	PROPN
ma-219	74	9	(	(	PUNCT
ma-219	74	10	t	t	PROPN
ma-219	74	11	,	,	PUNCT
ma-219	74	12	xi	xi	PROPN
ma-219	74	13	)	)	PUNCT
ma-219	74	14	,	,	PUNCT
ma-219	74	15	īv	īv	NOUN
ma-219	74	16	(	(	PUNCT
ma-219	74	17	t	t	PROPN
ma-219	74	18	,	,	PUNCT
ma-219	74	19	xi	xi	X
ma-219	74	20	)	)	PUNCT
ma-219	74	21	=	=	SYM
ma-219	74	22	iv	iv	X
ma-219	74	23	(	(	PUNCT
ma-219	74	24	t	t	PROPN
ma-219	74	25	,	,	PUNCT
ma-219	74	26	xi	xi	PROPN
ma-219	74	27	)	)	PUNCT
ma-219	74	28	nv	nv	PROPN
ma-219	74	29	(	(	PUNCT
ma-219	74	30	t	t	PROPN
ma-219	74	31	,	,	PUNCT
ma-219	74	32	xi	xi	PROPN
ma-219	74	33	)	)	PUNCT
ma-219	74	34	so	so	ADV
ma-219	74	35	that̄	that̄	ADV
ma-219	74	36	sh(t	sh(t	ADJ
ma-219	74	37	,	,	PUNCT
ma-219	74	38	xi	xi	ADJ
ma-219	74	39	)	)	PUNCT
ma-219	74	40	+	+	CCONJ
ma-219	74	41	ēh(t	ēh(t	NOUN
ma-219	74	42	,	,	PUNCT
ma-219	74	43	xi	xi	ADJ
ma-219	74	44	)	)	PUNCT
ma-219	74	45	+	+	CCONJ
ma-219	74	46	īh(t	īh(t	ADJ
ma-219	74	47	,	,	PUNCT
ma-219	74	48	xi	xi	ADJ
ma-219	74	49	)	)	PUNCT
ma-219	74	50	+	+	CCONJ
ma-219	75	1	v̄h(t	v̄h(t	ADJ
ma-219	75	2	,	,	PUNCT
ma-219	75	3	xi	xi	X
ma-219	75	4	)	)	PUNCT
ma-219	75	5	=	=	SYM
ma-219	75	6	1	1	NUM
ma-219	75	7	and	and	CCONJ
ma-219	75	8	s̄v	s̄v	NUM
ma-219	75	9	(	(	PUNCT
ma-219	75	10	t	t	PROPN
ma-219	75	11	,	,	PUNCT
ma-219	75	12	xi	xi	PROPN
ma-219	75	13	)	)	PUNCT
ma-219	76	1	+	+	CCONJ
ma-219	76	2	ēv	ēv	PROPN
ma-219	76	3	(	(	PUNCT
ma-219	76	4	t	t	PROPN
ma-219	76	5	,	,	PUNCT
ma-219	76	6	xi	xi	ADJ
ma-219	76	7	)	)	PUNCT
ma-219	77	1	+	+	CCONJ
ma-219	77	2	īv	īv	NOUN
ma-219	77	3	(	(	PUNCT
ma-219	77	4	t	t	PROPN
ma-219	77	5	,	,	PUNCT
ma-219	77	6	xi	xi	X
ma-219	77	7	)	)	PUNCT
ma-219	77	8	=	=	SYM
ma-219	77	9	1	1	NUM
ma-219	77	10	the	the	DET
ma-219	77	11	consequence	consequence	NOUN
ma-219	77	12	of	of	ADP
ma-219	77	13	this	this	PRON
ma-219	77	14	,	,	PUNCT
ma-219	77	15	we	we	PRON
ma-219	77	16	have	have	AUX
ma-219	77	17	ψh(xi	ψh(xi	VERB
ma-219	77	18	)	)	PUNCT
ma-219	78	1	=	=	SYM
ma-219	78	2	µh(xi	µh(xi	PROPN
ma-219	78	3	)	)	PUNCT
ma-219	78	4	,	,	PUNCT
ma-219	78	5	ψv	ψv	PROPN
ma-219	78	6	(	(	PUNCT
ma-219	78	7	xi	xi	PROPN
ma-219	78	8	)	)	PUNCT
ma-219	78	9	=	=	PRON
ma-219	79	1	µv	µv	NOUN
ma-219	79	2	and	and	CCONJ
ma-219	79	3	σ	σ	PROPN
ma-219	79	4	=	=	PROPN
ma-219	79	5	nv	nv	PROPN
ma-219	79	6	(	(	PUNCT
ma-219	79	7	t	t	PROPN
ma-219	79	8	)	)	PUNCT
ma-219	79	9	nh(t	nh(t	PROPN
ma-219	79	10	,	,	PUNCT
ma-219	79	11	xi	xi	X
ma-219	79	12	)	)	PUNCT
ma-219	79	13	.	.	PUNCT
ma-219	80	1	after	after	ADP
ma-219	80	2	droppingof	droppingof	NOUN
ma-219	80	3	bars	bar	NOUN
ma-219	80	4	(	(	PUNCT
ma-219	80	5	̄	̄	NOUN
ma-219	80	6	)	)	PUNCT
ma-219	80	7	,	,	PUNCT
ma-219	80	8	model	model	NOUN
ma-219	80	9	(	(	PUNCT
ma-219	80	10	2.1	2.1	NUM
ma-219	80	11	)	)	PUNCT
ma-219	80	12	gives	give	VERB
ma-219	80	13	rise	rise	NOUN
ma-219	80	14	to	to	ADP
ma-219	80	15	the	the	DET
ma-219	80	16	following	follow	VERB
ma-219	80	17	system	system	NOUN
ma-219	80	18	of	of	ADP
ma-219	80	19	equations	equation	NOUN
ma-219	80	20	:	:	PUNCT
ma-219	80	21	dsh(t	dsh(t	PROPN
ma-219	80	22	,	,	PUNCT
ma-219	80	23	xi	xi	X
ma-219	80	24	)	)	PUNCT
ma-219	81	1	dt	dt	PROPN
ma-219	82	1	=	=	PUNCT
ma-219	83	1	(	(	PUNCT
ma-219	83	2	1−	1−	NUM
ma-219	83	3	τ)ψh(xi)−	τ)ψh(xi)−	NUM
ma-219	84	1	∑l	∑l	PRON
ma-219	84	2	i=0	i=0	PROPN
ma-219	84	3	δλh(xi)σh(t	δλh(xi)σh(t	NOUN
ma-219	84	4	,	,	PUNCT
ma-219	84	5	xi)iv	xi)iv	PUNCT
ma-219	85	1	(	(	PUNCT
ma-219	85	2	t)−	t)−	PROPN
ma-219	85	3	µh(xi)sh(t	µh(xi)sh(t	NUM
ma-219	85	4	,	,	PUNCT
ma-219	85	5	xi	xi	ADJ
ma-219	85	6	)	)	PUNCT
ma-219	85	7	deh(t	deh(t	PROPN
ma-219	85	8	,	,	PUNCT
ma-219	85	9	xi	xi	NUM
ma-219	85	10	)	)	PUNCT
ma-219	85	11	dt	dt	PROPN
ma-219	86	1	=	=	PUNCT
ma-219	86	2	∑l	∑l	PROPN
ma-219	86	3	i=0	i=0	PROPN
ma-219	86	4	δλh(xi)σsh(t	δλh(xi)σsh(t	X
ma-219	86	5	,	,	PUNCT
ma-219	86	6	xi)iv	xi)iv	PUNCT
ma-219	87	1	(	(	PUNCT
ma-219	87	2	t)−	t)−	PROPN
ma-219	87	3	(	(	PUNCT
ma-219	87	4	αh(xi	αh(xi	PROPN
ma-219	87	5	)	)	PUNCT
ma-219	87	6	+	+	NUM
ma-219	87	7	µh(xi))eh(t	µh(xi))eh(t	PROPN
ma-219	87	8	,	,	PUNCT
ma-219	87	9	xi	xi	X
ma-219	87	10	)	)	PUNCT
ma-219	87	11	d	d	NOUN
ma-219	87	12	ih(t	ih(t	PROPN
ma-219	87	13	,	,	PUNCT
ma-219	87	14	xi	xi	NUM
ma-219	87	15	)	)	PUNCT
ma-219	87	16	dt	dt	X
ma-219	88	1	=	=	PUNCT
ma-219	88	2	∑l	∑l	PROPN
ma-219	88	3	i=0(1−	i=0(1−	PROPN
ma-219	88	4	θ)αh(xi)eh	θ)αh(xi)eh	NUM
ma-219	88	5	−	−	PROPN
ma-219	88	6	(	(	PUNCT
ma-219	88	7	γ(xi	γ(xi	PROPN
ma-219	88	8	)	)	PUNCT
ma-219	88	9	+	+	CCONJ
ma-219	88	10	µh(xi))ih(t	µh(xi))ih(t	ADJ
ma-219	88	11	,	,	PUNCT
ma-219	88	12	xi	xi	ADJ
ma-219	88	13	)	)	PUNCT
ma-219	88	14	dvh(t	dvh(t	PROPN
ma-219	88	15	,	,	PUNCT
ma-219	88	16	xi	xi	X
ma-219	88	17	)	)	PUNCT
ma-219	88	18	dt	dt	PROPN
ma-219	88	19	=	=	SYM
ma-219	88	20	τψh(xi	τψh(xi	X
ma-219	88	21	)	)	PUNCT
ma-219	89	1	+	+	CCONJ
ma-219	89	2	θαh(xi)eh(t	θαh(xi)eh(t	NOUN
ma-219	89	3	,	,	PUNCT
ma-219	89	4	xi	xi	ADJ
ma-219	89	5	)	)	PUNCT
ma-219	89	6	+	+	CCONJ
ma-219	89	7	γ(xi)ih(t	γ(xi)ih(t	PROPN
ma-219	89	8	,	,	PUNCT
ma-219	89	9	xi)−	xi)−	PROPN
ma-219	89	10	µh(xi)vh(t	µh(xi)vh(t	PROPN
ma-219	89	11	,	,	PUNCT
ma-219	89	12	xi	xi	ADJ
ma-219	89	13	)	)	PUNCT
ma-219	89	14	dsv	dsv	PROPN
ma-219	89	15	dt	dt	NOUN
ma-219	90	1	=	=	SYM
ma-219	90	2	ψv	ψv	PROPN
ma-219	90	3	−	−	PROPN
ma-219	90	4	δλv	δλv	PROPN
ma-219	90	5	(	(	PUNCT
ma-219	90	6	xi)sv	xi)sv	X
ma-219	90	7	(	(	PUNCT
ma-219	90	8	t)ih(t	t)ih(t	NUM
ma-219	90	9	,	,	PUNCT
ma-219	90	10	xi)−	xi)−	ADV
ma-219	90	11	µvsv	µvsv	X
ma-219	90	12	(	(	PUNCT
ma-219	90	13	t	t	NOUN
ma-219	90	14	)	)	PUNCT
ma-219	90	15	dev	dev	NOUN
ma-219	90	16	dt	dt	NOUN
ma-219	91	1	=	=	SYM
ma-219	91	2	δλv	δλv	PROPN
ma-219	91	3	(	(	PUNCT
ma-219	91	4	xi)sv	xi)sv	X
ma-219	91	5	(	(	PUNCT
ma-219	91	6	t)ih(t	t)ih(t	NUM
ma-219	91	7	,	,	PUNCT
ma-219	91	8	xi)−	xi)−	PROPN
ma-219	91	9	(	(	PUNCT
ma-219	91	10	αv	αv	ADP
ma-219	91	11	+	+	CCONJ
ma-219	91	12	µv	µv	PROPN
ma-219	91	13	)	)	PUNCT
ma-219	91	14	ev	ev	PROPN
ma-219	91	15	(	(	PUNCT
ma-219	91	16	t	t	PROPN
ma-219	91	17	)	)	PUNCT
ma-219	91	18	d	d	NOUN
ma-219	91	19	iv	iv	NUM
ma-219	91	20	dt	dt	NOUN
ma-219	91	21	=	=	SYM
ma-219	91	22	αvev	αvev	PROPN
ma-219	91	23	(	(	PUNCT
ma-219	91	24	t)−	t)−	PROPN
ma-219	91	25	µv	µv	NOUN
ma-219	91	26	iv	iv	NUM
ma-219	91	27	(	(	PUNCT
ma-219	91	28	t	t	NOUN
ma-219	91	29	)	)	PUNCT
ma-219	91	30			NOUN
ma-219	91	31	(	(	PUNCT
ma-219	91	32	2.3	2.3	NUM
ma-219	91	33	)	)	PUNCT
ma-219	91	34	subject	subject	NOUN
ma-219	91	35	to	to	ADP
ma-219	91	36	the	the	DET
ma-219	91	37	following	follow	VERB
ma-219	91	38	initial	initial	ADJ
ma-219	91	39	conditions	condition	NOUN
ma-219	91	40	:	:	PUNCT
ma-219	91	41	sh(0	sh(0	NOUN
ma-219	91	42	,	,	PUNCT
ma-219	91	43	xi	xi	ADJ
ma-219	91	44	)	)	PUNCT
ma-219	91	45	=	=	SYM
ma-219	91	46	s0h(xi	s0h(xi	PROPN
ma-219	91	47	)	)	PUNCT
ma-219	91	48	,	,	PUNCT
ma-219	91	49	eh(0	eh(0	NOUN
ma-219	91	50	,	,	PUNCT
ma-219	91	51	xi	xi	X
ma-219	91	52	)	)	PUNCT
ma-219	91	53	=	=	SYM
ma-219	91	54	e0h(xi	e0h(xi	NOUN
ma-219	91	55	)	)	PUNCT
ma-219	91	56	,	,	PUNCT
ma-219	91	57	ih(0	ih(0	PROPN
ma-219	91	58	,	,	PUNCT
ma-219	91	59	xi	xi	PROPN
ma-219	91	60	)	)	PUNCT
ma-219	91	61	=	=	SYM
ma-219	91	62	i0h(xi	i0h(xi	PROPN
ma-219	91	63	)	)	PUNCT
ma-219	91	64	,	,	PUNCT
ma-219	91	65	vh(0	vh(0	PROPN
ma-219	91	66	,	,	PUNCT
ma-219	91	67	xi	xi	X
ma-219	91	68	)	)	PUNCT
ma-219	91	69	=	=	SYM
ma-219	91	70	v0h(xi	v0h(xi	PROPN
ma-219	91	71	)	)	PUNCT
ma-219	91	72	(	(	PUNCT
ma-219	91	73	2.4	2.4	NUM
ma-219	91	74	)	)	PUNCT
ma-219	91	75	sv	sv	NOUN
ma-219	91	76	(	(	PUNCT
ma-219	91	77	0	0	NUM
ma-219	91	78	)	)	PUNCT
ma-219	91	79	=	=	PRON
ma-219	91	80	s0v	s0v	PROPN
ma-219	91	81	,	,	PUNCT
ma-219	91	82	ev	ev	X
ma-219	91	83	(	(	PUNCT
ma-219	91	84	0	0	NUM
ma-219	91	85	)	)	PUNCT
ma-219	91	86	=	=	PRON
ma-219	91	87	e0v	e0v	X
ma-219	91	88	,	,	PUNCT
ma-219	91	89	iv	iv	X
ma-219	91	90	(	(	PUNCT
ma-219	91	91	0	0	NUM
ma-219	91	92	)	)	PUNCT
ma-219	91	93	=	=	VERB
ma-219	92	1	i0v	i0v	PROPN
ma-219	92	2	3	3	X
ma-219	92	3	.	.	PUNCT
ma-219	92	4	global	global	ADJ
ma-219	92	5	stability	stability	NOUN
ma-219	92	6	analysis	analysis	NOUN
ma-219	92	7	here	here	ADV
ma-219	92	8	,	,	PUNCT
ma-219	92	9	we	we	PRON
ma-219	92	10	explore	explore	VERB
ma-219	92	11	the	the	DET
ma-219	92	12	global	global	ADJ
ma-219	92	13	asymptotic	asymptotic	ADJ
ma-219	92	14	stability	stability	NOUN
ma-219	92	15	of	of	ADP
ma-219	92	16	the	the	DET
ma-219	92	17	dfe	dfe	PROPN
ma-219	92	18	and	and	CCONJ
ma-219	92	19	ee	ee	VERB
ma-219	92	20	for	for	ADP
ma-219	92	21	the	the	DET
ma-219	92	22	special	special	ADJ
ma-219	92	23	case	case	NOUN
ma-219	92	24	with	with	ADP
ma-219	92	25	noloss	noloss	NOUN
ma-219	92	26	of	of	ADP
ma-219	92	27	immunity	immunity	NOUN
ma-219	92	28	acquired	acquire	VERB
ma-219	92	29	by	by	ADP
ma-219	92	30	the	the	DET
ma-219	92	31	recovered	recovered	ADJ
ma-219	92	32	individuals	individual	NOUN
ma-219	92	33	.	.	PUNCT
ma-219	93	1	we	we	PRON
ma-219	93	2	use	use	VERB
ma-219	93	3	the	the	DET
ma-219	93	4	concept	concept	NOUN
ma-219	93	5	of	of	ADP
ma-219	93	6	lyapunov	lyapunov	PROPN
ma-219	93	7	functionsto	functionsto	NOUN
ma-219	93	8	analyze	analyze	VERB
ma-219	93	9	the	the	DET
ma-219	93	10	global	global	ADJ
ma-219	93	11	stability	stability	NOUN
ma-219	93	12	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	93	13	eur	eur	PROPN
ma-219	93	14	.	.	PUNCT
ma-219	94	1	j.	j.	PROPN
ma-219	94	2	math	math	PROPN
ma-219	94	3	.	.	PUNCT
ma-219	95	1	anal	anal	PROPN
ma-219	95	2	.	.	PUNCT
ma-219	96	1	10.28924	10.28924	NUM
ma-219	96	2	/	/	SYM
ma-219	96	3	ada	ada	PROPN
ma-219	96	4	/	/	SYM
ma-219	96	5	ma.4.9	ma.4.9	PROPN
ma-219	96	6	53.1	53.1	NUM
ma-219	96	7	.	.	PUNCT
ma-219	97	1	global	global	ADJ
ma-219	97	2	stability	stability	NOUN
ma-219	97	3	of	of	ADP
ma-219	97	4	disease	disease	NOUN
ma-219	97	5	-	-	PUNCT
ma-219	97	6	free	free	ADJ
ma-219	97	7	equilibrium	equilibrium	NOUN
ma-219	97	8	.	.	PUNCT
ma-219	98	1	the	the	DET
ma-219	98	2	following	following	ADJ
ma-219	98	3	result	result	NOUN
ma-219	98	4	establishes	establish	VERB
ma-219	98	5	the	the	DET
ma-219	98	6	globalasymptotic	globalasymptotic	ADJ
ma-219	98	7	behavior	behavior	NOUN
ma-219	98	8	of	of	ADP
ma-219	98	9	system	system	NOUN
ma-219	98	10	(	(	PUNCT
ma-219	98	11	2.1	2.1	NUM
ma-219	98	12	)	)	PUNCT
ma-219	98	13	around	around	ADP
ma-219	98	14	e0	e0	PROPN
ma-219	98	15	which	which	PRON
ma-219	98	16	is	be	AUX
ma-219	98	17	determined	determine	VERB
ma-219	98	18	by	by	ADP
ma-219	98	19	the	the	DET
ma-219	98	20	basic	basic	ADJ
ma-219	98	21	reproductionnumber	reproductionnumber	NOUN
ma-219	98	22	r0	r0	NOUN
ma-219	98	23	.	.	PUNCT
ma-219	99	1	theorem	theorem	VERB
ma-219	99	2	3	3	NUM
ma-219	99	3	:	:	PUNCT
ma-219	99	4	the	the	DET
ma-219	99	5	disease	disease	NOUN
ma-219	99	6	-	-	PUNCT
ma-219	99	7	free	free	ADJ
ma-219	99	8	equilibrium	equilibrium	NOUN
ma-219	99	9	(	(	PUNCT
ma-219	99	10	2.12	2.12	NUM
ma-219	99	11	)	)	PUNCT
ma-219	99	12	of	of	ADP
ma-219	99	13	model	model	NOUN
ma-219	99	14	(	(	PUNCT
ma-219	99	15	2.1	2.1	NUM
ma-219	99	16	)	)	PUNCT
ma-219	99	17	is	be	AUX
ma-219	99	18	globally	globally	ADV
ma-219	99	19	asymptotically	asymptotically	ADV
ma-219	99	20	stable	stable	ADJ
ma-219	99	21	in	in	ADP
ma-219	99	22	ω	ω	NUM
ma-219	99	23	whenever	whenever	SCONJ
ma-219	99	24	r0	r0	NOUN
ma-219	99	25	≤	≤	NOUN
ma-219	99	26	1	1	NUM
ma-219	99	27	proof	proof	NOUN
ma-219	99	28	:	:	PUNCT
ma-219	99	29	consider	consider	VERB
ma-219	99	30	the	the	DET
ma-219	99	31	linear	linear	ADJ
ma-219	99	32	lyapunov	lyapunov	ADJ
ma-219	99	33	function	function	NOUN
ma-219	99	34	of	of	ADP
ma-219	99	35	the	the	DET
ma-219	99	36	form	form	NOUN
ma-219	99	37	m	m	NOUN
ma-219	99	38	=	=	SYM
ma-219	99	39	d1eh(t	d1eh(t	PROPN
ma-219	99	40	,	,	PUNCT
ma-219	99	41	xi	xi	ADJ
ma-219	99	42	)	)	PUNCT
ma-219	99	43	+	+	CCONJ
ma-219	99	44	d2ih(t	d2ih(t	PROPN
ma-219	99	45	,	,	PUNCT
ma-219	99	46	xi	xi	ADJ
ma-219	99	47	)	)	PUNCT
ma-219	100	1	+	+	CCONJ
ma-219	100	2	d3ev	d3ev	X
ma-219	100	3	(	(	PUNCT
ma-219	100	4	t	t	NOUN
ma-219	100	5	)	)	PUNCT
ma-219	100	6	+	+	CCONJ
ma-219	100	7	d4iv	d4iv	NOUN
ma-219	100	8	(	(	PUNCT
ma-219	100	9	t	t	NOUN
ma-219	100	10	)	)	PUNCT
ma-219	100	11	(	(	PUNCT
ma-219	100	12	3.1	3.1	NUM
ma-219	100	13	)	)	PUNCT
ma-219	100	14	where	where	SCONJ
ma-219	100	15	d1	d1	PROPN
ma-219	100	16	=	=	PUNCT
ma-219	100	17	αh(xi)(1−	αh(xi)(1−	NUM
ma-219	100	18	θ	θ	PROPN
ma-219	100	19	)	)	PUNCT
ma-219	100	20	(	(	PUNCT
ma-219	100	21	αh(xi	αh(xi	PROPN
ma-219	100	22	)	)	PUNCT
ma-219	100	23	+	+	CCONJ
ma-219	100	24	µh(xi))(γ(xi	µh(xi))(γ(xi	ADJ
ma-219	100	25	)	)	PUNCT
ma-219	100	26	+	+	CCONJ
ma-219	100	27	µh(xi	µh(xi	X
ma-219	100	28	)	)	PUNCT
ma-219	100	29	)	)	PUNCT
ma-219	100	30	d2	d2	PROPN
ma-219	100	31	=	=	SYM
ma-219	100	32	1	1	NUM
ma-219	100	33	(	(	PUNCT
ma-219	100	34	γ(xi	γ(xi	PROPN
ma-219	100	35	)	)	PUNCT
ma-219	100	36	+	+	CCONJ
ma-219	100	37	µh(xi	µh(xi	X
ma-219	100	38	)	)	PUNCT
ma-219	100	39	)	)	PUNCT
ma-219	100	40	d3	d3	PROPN
ma-219	100	41	=	=	SYM
ma-219	100	42	1	1	NUM
ma-219	100	43	δλv	δλv	PROPN
ma-219	100	44	d4	d4	PROPN
ma-219	100	45	=	=	SYM
ma-219	100	46	αv	αv	PROPN
ma-219	100	47	+	+	CCONJ
ma-219	100	48	µv	µv	PROPN
ma-219	100	49	δλvαvin	δλvαvin	NOUN
ma-219	100	50	what	what	PRON
ma-219	100	51	follows	follow	VERB
ma-219	100	52	,	,	PUNCT
ma-219	100	53	the	the	DET
ma-219	100	54	time	time	NOUN
ma-219	100	55	derivative	derivative	NOUN
ma-219	100	56	of	of	ADP
ma-219	100	57	m	m	AUX
ma-219	100	58	given	give	VERB
ma-219	100	59	by	by	ADP
ma-219	100	60	(	(	PUNCT
ma-219	100	61	3.1	3.1	NUM
ma-219	100	62	)	)	PUNCT
ma-219	100	63	along	along	ADP
ma-219	100	64	the	the	DET
ma-219	100	65	solutions	solution	NOUN
ma-219	100	66	of	of	ADP
ma-219	100	67	the	the	DET
ma-219	100	68	model	model	NOUN
ma-219	100	69	(	(	PUNCT
ma-219	100	70	2.3)yields	2.3)yields	NUM
ma-219	100	71	ṁ	ṁ	NOUN
ma-219	100	72	=	=	SYM
ma-219	100	73	αh(xi)(1−	αh(xi)(1−	NUM
ma-219	100	74	θ)[δλh(xi)σh(t	θ)[δλh(xi)σh(t	PROPN
ma-219	100	75	,	,	PUNCT
ma-219	100	76	xi)iv	xi)iv	PUNCT
ma-219	101	1	−	−	PROPN
ma-219	101	2	(	(	PUNCT
ma-219	101	3	αh(xi)iv	αh(xi)iv	PROPN
ma-219	101	4	+	+	NUM
ma-219	101	5	µh(xi))eh(t	µh(xi))eh(t	NUM
ma-219	101	6	,	,	PUNCT
ma-219	101	7	xi	xi	X
ma-219	101	8	)	)	PUNCT
ma-219	101	9	]	]	PUNCT
ma-219	101	10	(	(	PUNCT
ma-219	101	11	αh(xi	αh(xi	PROPN
ma-219	101	12	)	)	PUNCT
ma-219	101	13	+	+	CCONJ
ma-219	101	14	µh(xi))(γ(xi	µh(xi))(γ(xi	ADJ
ma-219	101	15	)	)	PUNCT
ma-219	101	16	+	+	CCONJ
ma-219	101	17	µh(xi	µh(xi	X
ma-219	101	18	)	)	PUNCT
ma-219	101	19	)	)	PUNCT
ma-219	102	1	+	+	CCONJ
ma-219	102	2	l∑	l∑	X
ma-219	102	3	i=0	i=0	PROPN
ma-219	102	4	(	(	PUNCT
ma-219	102	5	γ(xi	γ(xi	PROPN
ma-219	102	6	)	)	PUNCT
ma-219	102	7	+	+	CCONJ
ma-219	103	1	µh(xi))[(1−	µh(xi))[(1−	PROPN
ma-219	103	2	θ)αh(xi)eh(t	θ)αh(xi)eh(t	NUM
ma-219	103	3	,	,	PUNCT
ma-219	103	4	xi)−	xi)−	NOUN
ma-219	103	5	(	(	PUNCT
ma-219	103	6	γ(xi	γ(xi	PROPN
ma-219	103	7	)	)	PUNCT
ma-219	103	8	+	+	CCONJ
ma-219	103	9	µh(xi))ih(t	µh(xi))ih(t	ADJ
ma-219	103	10	,	,	PUNCT
ma-219	103	11	xi	xi	ADJ
ma-219	103	12	)	)	PUNCT
ma-219	103	13	]	]	PUNCT
ma-219	104	1	+	+	CCONJ
ma-219	104	2	1	1	NUM
ma-219	104	3	δλv	δλv	PROPN
ma-219	104	4	[	[	X
ma-219	104	5	δλvsv	δλvsv	NOUN
ma-219	104	6	ih(t	ih(t	PRON
ma-219	104	7	,	,	PUNCT
ma-219	104	8	xi)−	xi)−	PROPN
ma-219	104	9	(	(	PUNCT
ma-219	104	10	αv	αv	ADP
ma-219	104	11	+	+	CCONJ
ma-219	104	12	µv	µv	NOUN
ma-219	104	13	)	)	PUNCT
ma-219	104	14	ev	ev	X
ma-219	104	15	]	]	X
ma-219	104	16	+	+	CCONJ
ma-219	104	17	αv	αv	X
ma-219	104	18	+	+	CCONJ
ma-219	104	19	µv	µv	PROPN
ma-219	104	20	δλvαv	δλvαv	NOUN
ma-219	105	1	[	[	X
ma-219	105	2	αvev	αvev	NOUN
ma-219	106	1	−	−	NOUN
ma-219	106	2	µv	µv	NOUN
ma-219	106	3	iv	iv	VERB
ma-219	106	4	]	]	PUNCT
ma-219	106	5	=	=	PUNCT
ma-219	106	6	l∑	l∑	X
ma-219	106	7	i=0	i=0	PROPN
ma-219	106	8	δλh(xi)σαh(xi)(1−	δλh(xi)σαh(xi)(1−	NOUN
ma-219	106	9	θ)sh(t	θ)sh(t	ADJ
ma-219	106	10	,	,	PUNCT
ma-219	106	11	xi)iv	xi)iv	PUNCT
ma-219	106	12	(	(	PUNCT
ma-219	106	13	αh(xi))(γ(xi	αh(xi))(γ(xi	PROPN
ma-219	106	14	)	)	PUNCT
ma-219	106	15	+	+	CCONJ
ma-219	106	16	µh(xi	µh(xi	ADJ
ma-219	106	17	)	)	PUNCT
ma-219	106	18	)	)	PUNCT
ma-219	107	1	−	−	PROPN
ma-219	107	2	αh(xi)(1−	αh(xi)(1−	NUM
ma-219	107	3	θ)eh(t	θ)eh(t	NUM
ma-219	107	4	,	,	PUNCT
ma-219	107	5	xi	xi	ADJ
ma-219	107	6	)	)	PUNCT
ma-219	107	7	γ(xi	γ(xi	PROPN
ma-219	107	8	)	)	PUNCT
ma-219	108	1	+	+	CCONJ
ma-219	108	2	µh(xi	µh(xi	X
ma-219	108	3	)	)	PUNCT
ma-219	109	1	+	+	CCONJ
ma-219	109	2	l∑	l∑	X
ma-219	110	1	i=0	i=0	PROPN
ma-219	110	2	(	(	PUNCT
ma-219	110	3	1−	1−	NUM
ma-219	110	4	θ)eh(t	θ)eh(t	NUM
ma-219	110	5	,	,	PUNCT
ma-219	110	6	xi	xi	NUM
ma-219	110	7	)	)	PUNCT
ma-219	110	8	(	(	PUNCT
ma-219	110	9	γ(xi	γ(xi	PROPN
ma-219	110	10	)	)	PUNCT
ma-219	110	11	+	+	CCONJ
ma-219	110	12	µh(xi	µh(xi	ADJ
ma-219	110	13	)	)	PUNCT
ma-219	110	14	)	)	PUNCT
ma-219	111	1	−	−	NOUN
ma-219	111	2	ih(t	ih(t	PUNCT
ma-219	111	3	,	,	PUNCT
ma-219	111	4	xi	xi	ADJ
ma-219	111	5	)	)	PUNCT
ma-219	112	1	+	+	CCONJ
ma-219	112	2	sv	sv	X
ma-219	112	3	ih(t	ih(t	PROPN
ma-219	112	4	,	,	PUNCT
ma-219	112	5	xi)−	xi)−	PROPN
ma-219	112	6	(	(	PUNCT
ma-219	112	7	αv	αv	ADP
ma-219	112	8	+	+	CCONJ
ma-219	112	9	µv	µv	NOUN
ma-219	112	10	)	)	PUNCT
ma-219	112	11	µv	µv	PROPN
ma-219	112	12	iv	iv	NUM
ma-219	112	13	δλvαv	δλvαv	NOUN
ma-219	112	14	≤	≤	NOUN
ma-219	112	15	l∑	l∑	PUNCT
ma-219	113	1	i=0	i=0	PROPN
ma-219	113	2	δλh(xi)σαh(xi)(1−	δλh(xi)σαh(xi)(1−	PROPN
ma-219	113	3	θ)(1−	θ)(1−	PROPN
ma-219	113	4	τ)iv	τ)iv	PROPN
ma-219	113	5	(	(	PUNCT
ma-219	113	6	αh(xi	αh(xi	PROPN
ma-219	113	7	)	)	PUNCT
ma-219	114	1	+	+	CCONJ
ma-219	114	2	µh(xi))(γ(xi	µh(xi))(γ(xi	ADJ
ma-219	114	3	)	)	PUNCT
ma-219	114	4	+	+	CCONJ
ma-219	114	5	µh(xi	µh(xi	X
ma-219	114	6	)	)	PUNCT
ma-219	114	7	)	)	PUNCT
ma-219	115	1	−	−	PROPN
ma-219	115	2	(	(	PUNCT
ma-219	115	3	αv	αv	ADP
ma-219	115	4	+	+	CCONJ
ma-219	115	5	µv	µv	NOUN
ma-219	115	6	)	)	PUNCT
ma-219	115	7	µv	µv	PROPN
ma-219	115	8	iv	iv	NUM
ma-219	115	9	δλvαv	δλvαv	NOUN
ma-219	115	10	=	=	PUNCT
ma-219	116	1	[	[	PUNCT
ma-219	116	2	l∑	l∑	X
ma-219	116	3	i=0	i=0	PROPN
ma-219	116	4	δλh(xi)σαh(xi)(1−	δλh(xi)σαh(xi)(1−	PROPN
ma-219	116	5	θ)(1−	θ)(1−	PROPN
ma-219	116	6	τ	τ	X
ma-219	116	7	)	)	PUNCT
ma-219	116	8	(	(	PUNCT
ma-219	116	9	αh(xi	αh(xi	PROPN
ma-219	116	10	)	)	PUNCT
ma-219	116	11	+	+	CCONJ
ma-219	116	12	µh(xi))(γ(xi	µh(xi))(γ(xi	ADJ
ma-219	116	13	)	)	PUNCT
ma-219	116	14	+	+	CCONJ
ma-219	116	15	µh(xi	µh(xi	X
ma-219	116	16	)	)	PUNCT
ma-219	116	17	)	)	PUNCT
ma-219	117	1	−	−	PROPN
ma-219	117	2	(	(	PUNCT
ma-219	117	3	αv	αv	ADP
ma-219	117	4	+	+	CCONJ
ma-219	117	5	µv	µv	NOUN
ma-219	117	6	)	)	PUNCT
ma-219	117	7	µv	µv	PROPN
ma-219	117	8	δλvαv	δλvαv	NOUN
ma-219	117	9	]	]	PUNCT
ma-219	117	10	iv	iv	X
ma-219	117	11	=	=	SYM
ma-219	117	12	(	(	PUNCT
ma-219	117	13	αv	αv	X
ma-219	117	14	+	+	CCONJ
ma-219	117	15	µv	µv	NOUN
ma-219	117	16	)	)	PUNCT
ma-219	117	17	µv	µv	PROPN
ma-219	117	18	δλvαv	δλvαv	NOUN
ma-219	118	1	[	[	X
ma-219	118	2	r20	r20	NOUN
ma-219	118	3	−	−	PROPN
ma-219	118	4	1]iv	1]iv	NUM
ma-219	118	5	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	118	6	eur	eur	PROPN
ma-219	118	7	.	.	PUNCT
ma-219	119	1	j.	j.	PROPN
ma-219	119	2	math	math	PROPN
ma-219	119	3	.	.	PUNCT
ma-219	120	1	anal	anal	PROPN
ma-219	120	2	.	.	PUNCT
ma-219	121	1	10.28924	10.28924	NUM
ma-219	121	2	/	/	SYM
ma-219	121	3	ada	ada	PROPN
ma-219	121	4	/	/	SYM
ma-219	121	5	ma.4.9	ma.4.9	PROPN
ma-219	121	6	6we	6we	NOUN
ma-219	121	7	have	have	VERB
ma-219	121	8	that	that	DET
ma-219	121	9	ṁ	ṁ	PROPN
ma-219	121	10	≤	≤	NOUN
ma-219	121	11	0	0	PUNCT
ma-219	122	1	whenever	whenever	SCONJ
ma-219	122	2	r0	r0	NOUN
ma-219	122	3	≤	≤	NOUN
ma-219	122	4	1	1	NUM
ma-219	122	5	with	with	ADP
ma-219	122	6	ṁ	ṁ	PROPN
ma-219	122	7	=	=	SYM
ma-219	122	8	0	0	PUNCT
ma-219	123	1	if	if	SCONJ
ma-219	123	2	and	and	CCONJ
ma-219	123	3	only	only	ADV
ma-219	123	4	if	if	SCONJ
ma-219	123	5	iv	iv	NUM
ma-219	123	6	=	=	SYM
ma-219	123	7	0	0	X
ma-219	123	8	.	.	PUNCT
ma-219	124	1	we	we	PRON
ma-219	124	2	also	also	ADV
ma-219	124	3	see	see	VERB
ma-219	124	4	that	that	PRON
ma-219	124	5	(	(	PUNCT
ma-219	124	6	sh(t	sh(t	X
ma-219	124	7	,	,	PUNCT
ma-219	124	8	xi	xi	ADJ
ma-219	124	9	)	)	PUNCT
ma-219	124	10	,	,	PUNCT
ma-219	124	11	eh(t	eh(t	PROPN
ma-219	124	12	,	,	PUNCT
ma-219	124	13	xi	xi	PROPN
ma-219	124	14	)	)	PUNCT
ma-219	124	15	,	,	PUNCT
ma-219	124	16	ih(t	ih(t	PROPN
ma-219	124	17	,	,	PUNCT
ma-219	124	18	xi	xi	ADJ
ma-219	124	19	)	)	PUNCT
ma-219	124	20	,	,	PUNCT
ma-219	124	21	vh(t	vh(t	PROPN
ma-219	124	22	,	,	PUNCT
ma-219	124	23	xi	xi	PROPN
ma-219	124	24	)	)	PUNCT
ma-219	124	25	,	,	PUNCT
ma-219	124	26	sv	sv	PROPN
ma-219	124	27	(	(	PUNCT
ma-219	124	28	t	t	PROPN
ma-219	124	29	)	)	PUNCT
ma-219	124	30	,	,	PUNCT
ma-219	124	31	ev	ev	X
ma-219	124	32	(	(	PUNCT
ma-219	124	33	t	t	PROPN
ma-219	124	34	)	)	PUNCT
ma-219	124	35	)	)	PUNCT
ma-219	124	36	tends	tend	VERB
ma-219	124	37	to	to	PART
ma-219	124	38	(	(	PUNCT
ma-219	124	39	(	(	PUNCT
ma-219	124	40	1−	1−	NUM
ma-219	124	41	τ	τ	NOUN
ma-219	124	42	)	)	PUNCT
ma-219	124	43	,	,	PUNCT
ma-219	124	44	0	0	NUM
ma-219	124	45	,	,	PUNCT
ma-219	124	46	0	0	NUM
ma-219	124	47	,	,	PUNCT
ma-219	124	48	0	0	NUM
ma-219	124	49	,	,	PUNCT
ma-219	124	50	1	1	NUM
ma-219	124	51	,	,	PUNCT
ma-219	124	52	0	0	NUM
ma-219	124	53	)	)	PUNCT
ma-219	124	54	as	as	ADP
ma-219	124	55	t	t	PROPN
ma-219	124	56	→∞	→∞	NUM
ma-219	124	57	since	since	SCONJ
ma-219	124	58	iv	iv	PROPN
ma-219	124	59	(	(	PUNCT
ma-219	124	60	t	t	NOUN
ma-219	124	61	)	)	PUNCT
ma-219	124	62	→	→	SYM
ma-219	124	63	0	0	NUM
ma-219	124	64	as	as	ADP
ma-219	124	65	t	t	PROPN
ma-219	124	66	→	→	SYM
ma-219	124	67	∞.	∞.	PROPN
ma-219	124	68	by	by	ADP
ma-219	124	69	lasalle	lasalle	PROPN
ma-219	124	70	’s	’s	PART
ma-219	124	71	principle	principle	NOUN
ma-219	124	72	[	[	X
ma-219	124	73	7	7	NUM
ma-219	124	74	]	]	PUNCT
ma-219	124	75	,	,	PUNCT
ma-219	124	76	one	one	PRON
ma-219	124	77	concludes	conclude	VERB
ma-219	124	78	that	that	SCONJ
ma-219	124	79	every	every	DET
ma-219	124	80	solution	solution	NOUN
ma-219	124	81	of	of	ADP
ma-219	124	82	the	the	DET
ma-219	124	83	model(2.3	model(2.3	NOUN
ma-219	124	84	)	)	PUNCT
ma-219	124	85	in	in	ADP
ma-219	124	86	ω	ω	PROPN
ma-219	124	87	approaches	approach	VERB
ma-219	124	88	the	the	DET
ma-219	124	89	disease	disease	NOUN
ma-219	124	90	-	-	PUNCT
ma-219	124	91	free	free	ADJ
ma-219	124	92	equilibrium	equilibrium	NOUN
ma-219	124	93	,	,	PUNCT
ma-219	124	94	e0	e0	PROPN
ma-219	124	95	,	,	PUNCT
ma-219	124	96	as	as	SCONJ
ma-219	124	97	t	t	PROPN
ma-219	124	98	→∞.we	→∞.we	NOUN
ma-219	124	99	have	have	VERB
ma-219	124	100	that	that	DET
ma-219	124	101	ṁ	ṁ	PROPN
ma-219	124	102	≤	≤	NOUN
ma-219	124	103	0	0	PUNCT
ma-219	125	1	whenever	whenever	SCONJ
ma-219	125	2	r0	r0	NOUN
ma-219	125	3	≤	≤	NOUN
ma-219	125	4	1	1	NUM
ma-219	125	5	with	with	ADP
ma-219	125	6	ṁ	ṁ	PROPN
ma-219	125	7	=	=	SYM
ma-219	125	8	0	0	PUNCT
ma-219	126	1	if	if	SCONJ
ma-219	126	2	and	and	CCONJ
ma-219	126	3	only	only	ADV
ma-219	126	4	if	if	SCONJ
ma-219	126	5	iv	iv	NUM
ma-219	126	6	=	=	SYM
ma-219	126	7	0	0	X
ma-219	126	8	.	.	PUNCT
ma-219	127	1	we	we	PRON
ma-219	127	2	also	also	ADV
ma-219	127	3	see	see	VERB
ma-219	127	4	that	that	PRON
ma-219	127	5	(	(	PUNCT
ma-219	127	6	sh(t	sh(t	X
ma-219	127	7	,	,	PUNCT
ma-219	127	8	xi	xi	ADJ
ma-219	127	9	)	)	PUNCT
ma-219	127	10	)	)	PUNCT
ma-219	127	11	,	,	PUNCT
ma-219	127	12	eh(t	eh(t	PROPN
ma-219	127	13	,	,	PUNCT
ma-219	127	14	xi	xi	PROPN
ma-219	127	15	)	)	PUNCT
ma-219	127	16	,	,	PUNCT
ma-219	127	17	ih(t	ih(t	PROPN
ma-219	127	18	,	,	PUNCT
ma-219	127	19	xi	xi	ADJ
ma-219	127	20	)	)	PUNCT
ma-219	127	21	,	,	PUNCT
ma-219	127	22	vh(t	vh(t	PROPN
ma-219	127	23	,	,	PUNCT
ma-219	127	24	xi	xi	PROPN
ma-219	127	25	)	)	PUNCT
ma-219	127	26	,	,	PUNCT
ma-219	127	27	sv	sv	PROPN
ma-219	127	28	(	(	PUNCT
ma-219	127	29	t	t	PROPN
ma-219	127	30	)	)	PUNCT
ma-219	127	31	,	,	PUNCT
ma-219	127	32	ev	ev	X
ma-219	127	33	(	(	PUNCT
ma-219	127	34	)	)	PUNCT
ma-219	127	35	)	)	PUNCT
ma-219	127	36	hence	hence	ADV
ma-219	127	37	e0	e0	PROPN
ma-219	127	38	is	be	AUX
ma-219	127	39	globally	globally	ADV
ma-219	127	40	asymptotically	asymptotically	ADV
ma-219	127	41	stable	stable	ADJ
ma-219	127	42	in	in	ADP
ma-219	127	43	ω	ω	NUM
ma-219	127	44	if	if	SCONJ
ma-219	127	45	r0	r0	NOUN
ma-219	127	46	≤	≤	NOUN
ma-219	127	47	1	1	NUM
ma-219	127	48	2the	2the	NUM
ma-219	127	49	global	global	ADJ
ma-219	127	50	asymptotic	asymptotic	ADJ
ma-219	127	51	stability	stability	NOUN
ma-219	127	52	analysis	analysis	NOUN
ma-219	127	53	of	of	ADP
ma-219	127	54	the	the	DET
ma-219	127	55	endemic	endemic	ADJ
ma-219	127	56	equilibrium	equilibrium	NOUN
ma-219	127	57	is	be	AUX
ma-219	127	58	considered	consider	VERB
ma-219	127	59	next	next	ADJ
ma-219	127	60	forthe	forthe	DET
ma-219	127	61	special	special	ADJ
ma-219	127	62	case	case	NOUN
ma-219	127	63	with	with	ADP
ma-219	127	64	τ	τ	PROPN
ma-219	127	65	=	=	SYM
ma-219	127	66	θ	θ	PROPN
ma-219	127	67	=	=	SYM
ma-219	127	68	0	0	X
ma-219	127	69	.	.	PUNCT
ma-219	128	1	the	the	DET
ma-219	128	2	disease	disease	NOUN
ma-219	128	3	-	-	PUNCT
ma-219	128	4	present	present	ADJ
ma-219	128	5	(	(	PUNCT
ma-219	128	6	endemic	endemic	ADJ
ma-219	128	7	)	)	PUNCT
ma-219	128	8	equilibrium	equilibrium	NOUN
ma-219	128	9	of	of	ADP
ma-219	128	10	the	the	DET
ma-219	128	11	model(2.3	model(2.3	NOUN
ma-219	128	12	)	)	PUNCT
ma-219	128	13	is	be	AUX
ma-219	128	14	referred	refer	VERB
ma-219	128	15	to	to	ADP
ma-219	128	16	the	the	DET
ma-219	128	17	steady	steady	ADJ
ma-219	128	18	-	-	PUNCT
ma-219	128	19	state	state	NOUN
ma-219	128	20	solution	solution	NOUN
ma-219	128	21	where	where	SCONJ
ma-219	128	22	at	at	ADV
ma-219	128	23	least	least	ADV
ma-219	128	24	one	one	NUM
ma-219	128	25	of	of	ADP
ma-219	128	26	the	the	DET
ma-219	128	27	infected	infect	VERB
ma-219	128	28	compartmentsis	compartmentsis	NOUN
ma-219	128	29	nonzero	nonzero	NOUN
ma-219	128	30	.	.	PUNCT
ma-219	129	1	let	let	VERB
ma-219	129	2	the	the	DET
ma-219	129	3	arbitrary	arbitrary	ADJ
ma-219	129	4	endemic	endemic	ADJ
ma-219	129	5	equilibrium	equilibrium	NOUN
ma-219	129	6	of	of	ADP
ma-219	129	7	the	the	DET
ma-219	129	8	model	model	NOUN
ma-219	129	9	(	(	PUNCT
ma-219	129	10	2.1	2.1	NUM
ma-219	129	11	)	)	PUNCT
ma-219	129	12	be	be	AUX
ma-219	129	13	represented	represent	VERB
ma-219	129	14	by	by	ADP
ma-219	129	15	ee	ee	PROPN
ma-219	129	16	=	=	SYM
ma-219	129	17	(	(	PUNCT
ma-219	129	18	s∗∗h	s∗∗h	PROPN
ma-219	129	19	(	(	PUNCT
ma-219	129	20	xi	xi	PROPN
ma-219	129	21	)	)	PUNCT
ma-219	129	22	,	,	PUNCT
ma-219	130	1	e	e	X
ma-219	130	2	∗∗	∗∗	PROPN
ma-219	130	3	h	h	X
ma-219	130	4	(	(	PUNCT
ma-219	130	5	xi	xi	PROPN
ma-219	130	6	)	)	PUNCT
ma-219	130	7	,	,	PUNCT
ma-219	130	8	i	i	PRON
ma-219	130	9	∗∗	∗∗	INTJ
ma-219	131	1	h	h	INTJ
ma-219	131	2	(	(	PUNCT
ma-219	131	3	xi	xi	PROPN
ma-219	131	4	)	)	PUNCT
ma-219	131	5	,	,	PUNCT
ma-219	131	6	v	v	ADP
ma-219	131	7	∗∗	∗∗	PROPN
ma-219	131	8	h	h	NOUN
ma-219	131	9	(	(	PUNCT
ma-219	131	10	xi	xi	PROPN
ma-219	131	11	)	)	PUNCT
ma-219	131	12	,	,	PUNCT
ma-219	131	13	s	s	VERB
ma-219	131	14	∗∗	∗∗	PROPN
ma-219	131	15	m	m	VERB
ma-219	131	16	,	,	PUNCT
ma-219	131	17	e	e	X
ma-219	131	18	∗∗	∗∗	PROPN
ma-219	131	19	m	m	VERB
ma-219	131	20	,	,	PUNCT
ma-219	131	21	i	i	PRON
ma-219	131	22	∗∗	∗∗	X
ma-219	131	23	m	m	VERB
ma-219	131	24	)	)	PUNCT
ma-219	131	25	in	in	ADP
ma-219	131	26	order	order	NOUN
ma-219	131	27	to	to	PART
ma-219	131	28	do	do	AUX
ma-219	131	29	this	this	PRON
ma-219	131	30	,	,	PUNCT
ma-219	131	31	nonlinear	nonlinear	ADJ
ma-219	131	32	lyapunov	lyapunov	ADJ
ma-219	131	33	function	function	NOUN
ma-219	131	34	isused	isuse	VERB
ma-219	131	35	of	of	ADP
ma-219	131	36	goh	goh	PROPN
ma-219	131	37	-	-	PUNCT
ma-219	131	38	volterra	volterra	PROPN
ma-219	131	39	type	type	NOUN
ma-219	132	1	[	[	X
ma-219	132	2	6	6	NUM
ma-219	132	3	,	,	PUNCT
ma-219	132	4	15	15	NUM
ma-219	132	5	]	]	PUNCT
ma-219	132	6	.	.	PUNCT
ma-219	133	1	theorem	theorem	ADJ
ma-219	133	2	4	4	NUM
ma-219	133	3	:	:	PUNCT
ma-219	133	4	the	the	DET
ma-219	133	5	unique	unique	ADJ
ma-219	133	6	endemic	endemic	ADJ
ma-219	133	7	equilibrium	equilibrium	NOUN
ma-219	133	8	,	,	PUNCT
ma-219	133	9	ee	ee	INTJ
ma-219	133	10	,	,	PUNCT
ma-219	133	11	of	of	ADP
ma-219	133	12	the	the	DET
ma-219	133	13	model	model	NOUN
ma-219	133	14	(	(	PUNCT
ma-219	133	15	2.3	2.3	NUM
ma-219	133	16	)	)	PUNCT
ma-219	133	17	is	be	AUX
ma-219	133	18	globally	globally	ADV
ma-219	133	19	asymptoticallystable	asymptoticallystable	ADJ
ma-219	133	20	if	if	SCONJ
ma-219	133	21	r0	r0	NOUN
ma-219	133	22	>	>	X
ma-219	133	23	1	1	X
ma-219	133	24	.	.	X
ma-219	134	1	proof	proof	NOUN
ma-219	134	2	:	:	PUNCT
ma-219	134	3	let	let	VERB
ma-219	134	4	r0	r0	VERB
ma-219	134	5	>	>	X
ma-219	134	6	1	1	NUM
ma-219	134	7	so	so	SCONJ
ma-219	134	8	that	that	SCONJ
ma-219	134	9	there	there	PRON
ma-219	134	10	exists	exist	VERB
ma-219	134	11	a	a	DET
ma-219	134	12	unique	unique	ADJ
ma-219	134	13	endemic	endemic	ADJ
ma-219	134	14	equilibrium	equilibrium	NOUN
ma-219	134	15	and	and	CCONJ
ma-219	134	16	consider	consider	VERB
ma-219	134	17	the	the	DET
ma-219	134	18	nonlinearlyapunov	nonlinearlyapunov	ADJ
ma-219	134	19	function	function	NOUN
ma-219	134	20	defined	define	VERB
ma-219	134	21	by	by	ADP
ma-219	134	22	m	m	PROPN
ma-219	134	23	=	=	PUNCT
ma-219	134	24	(	(	PUNCT
ma-219	134	25	sh(t	sh(t	X
ma-219	134	26	,	,	PUNCT
ma-219	134	27	xi)−	xi)−	PROPN
ma-219	134	28	s∗∗h	s∗∗h	PROPN
ma-219	134	29	(	(	PUNCT
ma-219	134	30	xi)−	xi)−	PROPN
ma-219	134	31	s∗∗h	s∗∗h	PROPN
ma-219	134	32	(	(	PUNCT
ma-219	134	33	xi	xi	PROPN
ma-219	134	34	)	)	PUNCT
ma-219	134	35	ln	ln	NOUN
ma-219	134	36	sh(t	sh(t	ADJ
ma-219	134	37	,	,	PUNCT
ma-219	134	38	xi	xi	ADJ
ma-219	134	39	)	)	PUNCT
ma-219	134	40	s∗∗h	s∗∗h	PROPN
ma-219	134	41	(	(	PUNCT
ma-219	134	42	xi	xi	PROPN
ma-219	134	43	)	)	PUNCT
ma-219	134	44	)	)	PUNCT
ma-219	135	1	+	+	CCONJ
ma-219	135	2	(	(	PUNCT
ma-219	135	3	eh(t	eh(t	X
ma-219	135	4	,	,	PUNCT
ma-219	135	5	xi)−	xi)−	PROPN
ma-219	135	6	e∗∗h	e∗∗h	PROPN
ma-219	135	7	(	(	PUNCT
ma-219	135	8	xi)−	xi)−	PROPN
ma-219	135	9	e∗∗h	e∗∗h	PROPN
ma-219	135	10	(	(	PUNCT
ma-219	135	11	xi	xi	PROPN
ma-219	135	12	)	)	PUNCT
ma-219	135	13	ln	ln	ADJ
ma-219	135	14	eh(t	eh(t	NOUN
ma-219	135	15	,	,	PUNCT
ma-219	135	16	xi	xi	X
ma-219	135	17	)	)	PUNCT
ma-219	135	18	e∗∗h	e∗∗h	NOUN
ma-219	135	19	(	(	PUNCT
ma-219	135	20	xi	xi	PROPN
ma-219	135	21	)	)	PUNCT
ma-219	135	22	)	)	PUNCT
ma-219	136	1	+	+	CCONJ
ma-219	136	2	l∑	l∑	X
ma-219	136	3	i=0	i=0	PROPN
ma-219	136	4	αh(xi	αh(xi	PROPN
ma-219	136	5	)	)	PUNCT
ma-219	137	1	+	+	CCONJ
ma-219	137	2	µh(xi	µh(xi	X
ma-219	137	3	)	)	PUNCT
ma-219	137	4	αh(xi	αh(xi	PROPN
ma-219	137	5	)	)	PUNCT
ma-219	137	6	[	[	PUNCT
ma-219	137	7	ih(t	ih(t	X
ma-219	137	8	,	,	PUNCT
ma-219	137	9	xi)−	xi)−	ADJ
ma-219	137	10	i∗∗h	i∗∗h	PROPN
ma-219	137	11	(	(	PUNCT
ma-219	137	12	xi)−	xi)−	ADJ
ma-219	137	13	i∗∗h	i∗∗h	PROPN
ma-219	137	14	(	(	PUNCT
ma-219	137	15	xi	xi	NOUN
ma-219	137	16	)	)	PUNCT
ma-219	137	17	ln	ln	NOUN
ma-219	137	18	ih(t	ih(t	PUNCT
ma-219	137	19	,	,	PUNCT
ma-219	137	20	xi	xi	PROPN
ma-219	137	21	)	)	PUNCT
ma-219	137	22	i∗∗h	i∗∗h	PROPN
ma-219	137	23	(	(	PUNCT
ma-219	137	24	xi	xi	PROPN
ma-219	137	25	)	)	PUNCT
ma-219	137	26	]	]	PUNCT
ma-219	138	1	+	+	CCONJ
ma-219	138	2	(	(	PUNCT
ma-219	138	3	sv	sv	INTJ
ma-219	138	4	−	−	PROPN
ma-219	138	5	s∗∗v	s∗∗v	PROPN
ma-219	138	6	−	−	PROPN
ma-219	138	7	s∗∗v	s∗∗v	PROPN
ma-219	138	8	ln	ln	PROPN
ma-219	138	9	sv	sv	INTJ
ma-219	138	10	s∗∗v	s∗∗v	PROPN
ma-219	138	11	)	)	PUNCT
ma-219	139	1	+	+	CCONJ
ma-219	139	2	(	(	PUNCT
ma-219	139	3	ev	ev	INTJ
ma-219	139	4	−	−	PROPN
ma-219	139	5	e∗∗v	e∗∗v	NOUN
ma-219	139	6	−	−	PROPN
ma-219	139	7	e∗∗v	e∗∗v	PROPN
ma-219	139	8	ln	ln	PROPN
ma-219	139	9	ev	ev	X
ma-219	139	10	e∗∗v	e∗∗v	PROPN
ma-219	139	11	)	)	PUNCT
ma-219	140	1	+	+	CCONJ
ma-219	140	2	αv	αv	X
ma-219	140	3	+	+	CCONJ
ma-219	140	4	µv	µv	PROPN
ma-219	140	5	αv	αv	PART
ma-219	140	6	[	[	PUNCT
ma-219	140	7	iv	iv	NUM
ma-219	140	8	−	−	PROPN
ma-219	140	9	i∗∗v	i∗∗v	NOUN
ma-219	140	10	−	−	PROPN
ma-219	140	11	i∗∗v	i∗∗v	NOUN
ma-219	140	12	ln	ln	NOUN
ma-219	140	13	iv	iv	X
ma-219	140	14	i∗∗v	i∗∗v	NOUN
ma-219	140	15	]	]	PUNCT
ma-219	140	16	with	with	ADP
ma-219	140	17	lyapunov	lyapunov	ADJ
ma-219	140	18	time	time	NOUN
ma-219	140	19	-	-	PUNCT
ma-219	140	20	derivative	derivative	NOUN
ma-219	140	21	given	give	VERB
ma-219	140	22	as	as	ADP
ma-219	140	23	ṁ	ṁ	PROPN
ma-219	140	24	=	=	SYM
ma-219	140	25	ṡh(t	ṡh(t	PROPN
ma-219	140	26	,	,	PUNCT
ma-219	140	27	xi)−	xi)−	PROPN
ma-219	140	28	s∗∗h	s∗∗h	PROPN
ma-219	140	29	(	(	PUNCT
ma-219	140	30	xi	xi	NOUN
ma-219	140	31	)	)	PUNCT
ma-219	140	32	sh(xi	sh(xi	NOUN
ma-219	140	33	)	)	PUNCT
ma-219	140	34	ṡh(t	ṡh(t	X
ma-219	140	35	,	,	PUNCT
ma-219	140	36	xi	xi	X
ma-219	140	37	)	)	PUNCT
ma-219	140	38	+	+	NUM
ma-219	140	39	ėh(t	ėh(t	NOUN
ma-219	140	40	,	,	PUNCT
ma-219	140	41	xi)−	xi)−	PROPN
ma-219	140	42	e∗∗h	e∗∗h	PROPN
ma-219	140	43	(	(	PUNCT
ma-219	140	44	xi	xi	NOUN
ma-219	140	45	)	)	PUNCT
ma-219	140	46	eh(xi	eh(xi	PROPN
ma-219	140	47	)	)	PUNCT
ma-219	140	48	ėh(t	ėh(t	PROPN
ma-219	140	49	,	,	PUNCT
ma-219	140	50	xi	xi	X
ma-219	140	51	)	)	PUNCT
ma-219	141	1	+	+	CCONJ
ma-219	141	2	l∑	l∑	X
ma-219	141	3	i=0	i=0	PROPN
ma-219	141	4	αh(xi	αh(xi	PROPN
ma-219	141	5	)	)	PUNCT
ma-219	142	1	+	+	CCONJ
ma-219	142	2	µh(xi	µh(xi	X
ma-219	142	3	)	)	PUNCT
ma-219	142	4	αh(xi	αh(xi	PROPN
ma-219	142	5	)	)	PUNCT
ma-219	142	6	(	(	PUNCT
ma-219	142	7	i̇h(t	i̇h(t	X
ma-219	142	8	,	,	PUNCT
ma-219	142	9	xi)−	xi)−	ADJ
ma-219	142	10	i∗∗h	i∗∗h	PROPN
ma-219	142	11	(	(	PUNCT
ma-219	142	12	xi	xi	NOUN
ma-219	142	13	)	)	PUNCT
ma-219	142	14	ih(xi	ih(xi	PROPN
ma-219	142	15	)	)	PUNCT
ma-219	142	16	i̇h(t	i̇h(t	PROPN
ma-219	142	17	,	,	PUNCT
ma-219	142	18	xi	xi	ADJ
ma-219	142	19	)	)	PUNCT
ma-219	142	20	)	)	PUNCT
ma-219	143	1	+	+	CCONJ
ma-219	143	2	ṡv	ṡv	PROPN
ma-219	143	3	−	−	PROPN
ma-219	143	4	s∗∗v	s∗∗v	PROPN
ma-219	143	5	sv	sv	PROPN
ma-219	143	6	ṡv	ṡv	PROPN
ma-219	143	7	+	+	CCONJ
ma-219	143	8	ėv	ėv	PROPN
ma-219	143	9	−	−	PROPN
ma-219	143	10	e∗∗v	e∗∗v	PROPN
ma-219	143	11	ev	ev	PROPN
ma-219	143	12	ėv	ėv	PROPN
ma-219	143	13	+	+	CCONJ
ma-219	143	14	αv	αv	X
ma-219	143	15	+	+	CCONJ
ma-219	143	16	µv	µv	PROPN
ma-219	143	17	αm	αm	INTJ
ma-219	143	18	(	(	PUNCT
ma-219	143	19	i̇v	i̇v	PROPN
ma-219	143	20	−	−	PROPN
ma-219	143	21	i∗∗v	i∗∗v	NOUN
ma-219	143	22	iv	iv	NUM
ma-219	143	23	i̇v	i̇v	PROPN
ma-219	143	24	)	)	PUNCT
ma-219	143	25	(	(	PUNCT
ma-219	143	26	3.2	3.2	NUM
ma-219	143	27	)	)	PUNCT
ma-219	143	28	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	143	29	eur	eur	PROPN
ma-219	143	30	.	.	PUNCT
ma-219	144	1	j.	j.	PROPN
ma-219	144	2	math	math	PROPN
ma-219	144	3	.	.	PUNCT
ma-219	145	1	anal	anal	PROPN
ma-219	145	2	.	.	PUNCT
ma-219	146	1	10.28924	10.28924	NUM
ma-219	146	2	/	/	SYM
ma-219	146	3	ada	ada	PROPN
ma-219	146	4	/	/	SYM
ma-219	146	5	ma.4.9	ma.4.9	PROPN
ma-219	146	6	7using	7using	PROPN
ma-219	146	7	equations	equation	NOUN
ma-219	146	8	of	of	ADP
ma-219	146	9	the	the	DET
ma-219	146	10	model	model	NOUN
ma-219	146	11	(	(	PUNCT
ma-219	146	12	2.3	2.3	NUM
ma-219	146	13	)	)	PUNCT
ma-219	146	14	in	in	ADP
ma-219	146	15	(	(	PUNCT
ma-219	146	16	3.3	3.3	NUM
ma-219	146	17	)	)	PUNCT
ma-219	146	18	we	we	PRON
ma-219	146	19	obtain	obtain	VERB
ma-219	146	20	ṁ	ṁ	NOUN
ma-219	146	21	=	=	SYM
ma-219	146	22	(	(	PUNCT
ma-219	146	23	1−	1−	NUM
ma-219	146	24	τ)ψh(xi)−	τ)ψh(xi)−	ADJ
ma-219	146	25	l∑	l∑	X
ma-219	146	26	i=0	i=0	ADJ
ma-219	146	27	δλh(xi)σsh(t	δλh(xi)σsh(t	X
ma-219	146	28	,	,	PUNCT
ma-219	146	29	xi)iv	xi)iv	PUNCT
ma-219	147	1	−	−	PROPN
ma-219	147	2	µh(xi)sh(t	µh(xi)sh(t	SYM
ma-219	147	3	,	,	PUNCT
ma-219	147	4	xi	xi	ADJ
ma-219	147	5	)	)	PUNCT
ma-219	147	6	(	(	PUNCT
ma-219	147	7	3.3	3.3	NUM
ma-219	147	8	)	)	PUNCT
ma-219	147	9	−	−	NOUN
ma-219	147	10	l∑	l∑	PUNCT
ma-219	148	1	i=0	i=0	PROPN
ma-219	148	2	s∗∗h	s∗∗h	PROPN
ma-219	148	3	(	(	PUNCT
ma-219	148	4	xi	xi	NOUN
ma-219	148	5	)	)	PUNCT
ma-219	148	6	sh(t	sh(t	X
ma-219	148	7	,	,	PUNCT
ma-219	148	8	xi	xi	ADJ
ma-219	148	9	)	)	PUNCT
ma-219	148	10	(	(	PUNCT
ma-219	148	11	ψh(xi)−	ψh(xi)−	PRON
ma-219	148	12	δλh(xi)σsh(t	δλh(xi)σsh(t	NOUN
ma-219	148	13	,	,	PUNCT
ma-219	148	14	xi)iv	xi)iv	PUNCT
ma-219	149	1	−	−	PROPN
ma-219	149	2	µh(xi)sh(t	µh(xi)sh(t	SYM
ma-219	149	3	,	,	PUNCT
ma-219	149	4	xi	xi	ADJ
ma-219	149	5	)	)	PUNCT
ma-219	149	6	)	)	PUNCT
ma-219	150	1	+	+	CCONJ
ma-219	150	2	l∑	l∑	X
ma-219	150	3	i=0	i=0	ADJ
ma-219	150	4	δλh(xi)sh(t	δλh(xi)sh(t	NUM
ma-219	150	5	,	,	PUNCT
ma-219	150	6	xi)iv	xi)iv	PUNCT
ma-219	151	1	+	+	PUNCT
ma-219	152	1	[	[	X
ma-219	152	2	αh	αh	NOUN
ma-219	152	3	+	+	CCONJ
ma-219	152	4	µh]eh(t	µh]eh(t	ADJ
ma-219	152	5	,	,	PUNCT
ma-219	152	6	xi)−	xi)−	PROPN
ma-219	152	7	l∑	l∑	PROPN
ma-219	153	1	i=0	i=0	PROPN
ma-219	153	2	e∗∗h	e∗∗h	X
ma-219	153	3	(	(	PUNCT
ma-219	153	4	xi	xi	PROPN
ma-219	153	5	)	)	PUNCT
ma-219	153	6	eh(t	eh(t	PUNCT
ma-219	153	7	,	,	PUNCT
ma-219	153	8	xi	xi	X
ma-219	153	9	)	)	PUNCT
ma-219	153	10	(	(	PUNCT
ma-219	153	11	δλh(xi)σsh(t	δλh(xi)σsh(t	NOUN
ma-219	153	12	,	,	PUNCT
ma-219	153	13	xi)iv	xi)iv	PUNCT
ma-219	154	1	+	+	PUNCT
ma-219	155	1	[	[	X
ma-219	155	2	αh	αh	NOUN
ma-219	155	3	+	+	CCONJ
ma-219	155	4	µh]eh(t	µh]eh(t	ADJ
ma-219	155	5	,	,	PUNCT
ma-219	155	6	xi	xi	ADJ
ma-219	155	7	)	)	PUNCT
ma-219	155	8	)	)	PUNCT
ma-219	156	1	+	+	CCONJ
ma-219	156	2	l∑	l∑	X
ma-219	156	3	i=0	i=0	PROPN
ma-219	156	4	αh(xi	αh(xi	PROPN
ma-219	156	5	)	)	PUNCT
ma-219	157	1	+	+	CCONJ
ma-219	157	2	µh(xi	µh(xi	X
ma-219	157	3	)	)	PUNCT
ma-219	157	4	αh(xi	αh(xi	PROPN
ma-219	157	5	)	)	PUNCT
ma-219	157	6	×	×	NOUN
ma-219	157	7	(	(	PUNCT
ma-219	157	8	(	(	PUNCT
ma-219	157	9	1−	1−	NUM
ma-219	157	10	θ)αh(xi)eh(t	θ)αh(xi)eh(t	NUM
ma-219	157	11	,	,	PUNCT
ma-219	157	12	xi)−	xi)−	PUNCT
ma-219	158	1	[	[	X
ma-219	158	2	r(xi	r(xi	X
ma-219	158	3	)	)	PUNCT
ma-219	158	4	+	+	CCONJ
ma-219	158	5	µh(xi	µh(xi	X
ma-219	158	6	)	)	PUNCT
ma-219	159	1	+	+	CCONJ
ma-219	159	2	γh(xi)])ih(t	γh(xi)])ih(t	X
ma-219	159	3	,	,	PUNCT
ma-219	159	4	xi	xi	PROPN
ma-219	159	5	)	)	PUNCT
ma-219	159	6	−	−	PROPN
ma-219	159	7	l∑	l∑	PUNCT
ma-219	160	1	i=0	i=0	PROPN
ma-219	160	2	i∗∗h	i∗∗h	X
ma-219	160	3	(	(	PUNCT
ma-219	160	4	xi)(αh(xi	xi)(αh(xi	PROPN
ma-219	160	5	)	)	PUNCT
ma-219	160	6	+	+	CCONJ
ma-219	160	7	µh(xi	µh(xi	X
ma-219	160	8	)	)	PUNCT
ma-219	160	9	)	)	PUNCT
ma-219	160	10	ih(t	ih(t	PUNCT
ma-219	160	11	,	,	PUNCT
ma-219	160	12	xi)αh(xi	xi)αh(xi	NUM
ma-219	160	13	)	)	PUNCT
ma-219	160	14	×	×	NOUN
ma-219	160	15	(	(	PUNCT
ma-219	160	16	(	(	PUNCT
ma-219	160	17	1−	1−	NUM
ma-219	160	18	θ)αh(xi)eh(t	θ)αh(xi)eh(t	NUM
ma-219	160	19	,	,	PUNCT
ma-219	160	20	xi)−	xi)−	PUNCT
ma-219	161	1	[	[	X
ma-219	161	2	r(xi	r(xi	X
ma-219	161	3	)	)	PUNCT
ma-219	161	4	+	+	CCONJ
ma-219	161	5	µh(xi	µh(xi	X
ma-219	161	6	)	)	PUNCT
ma-219	162	1	+	+	CCONJ
ma-219	162	2	γh(xi)])ih(t	γh(xi)])ih(t	X
ma-219	162	3	,	,	PUNCT
ma-219	162	4	xi	xi	ADJ
ma-219	162	5	)	)	PUNCT
ma-219	163	1	+	+	CCONJ
ma-219	163	2	ψv	ψv	ADP
ma-219	163	3	−	−	PROPN
ma-219	163	4	δλvsv	δλvsv	NOUN
ma-219	163	5	ih(t	ih(t	PRON
ma-219	163	6	,	,	PUNCT
ma-219	163	7	xi)−	xi)−	PROPN
ma-219	163	8	µvsv	µvsv	ADJ
ma-219	163	9	−	−	PROPN
ma-219	163	10	s∗∗v	s∗∗v	PROPN
ma-219	163	11	sv	sv	PROPN
ma-219	163	12	(	(	PUNCT
ma-219	163	13	ψv	ψv	ADP
ma-219	163	14	−	−	PROPN
ma-219	163	15	δλvsv	δλvsv	NOUN
ma-219	163	16	ih(t	ih(t	PRON
ma-219	163	17	,	,	PUNCT
ma-219	163	18	xi)−	xi)−	NOUN
ma-219	163	19	µvsv	µvsv	X
ma-219	163	20	)	)	PUNCT
ma-219	164	1	+	+	CCONJ
ma-219	164	2	δλvsv	δλvsv	NOUN
ma-219	164	3	ih(t	ih(t	PRON
ma-219	164	4	,	,	PUNCT
ma-219	164	5	xi	xi	ADJ
ma-219	164	6	)	)	PUNCT
ma-219	164	7	+	+	CCONJ
ma-219	165	1	[	[	X
ma-219	165	2	αv	αv	X
ma-219	165	3	+	+	CCONJ
ma-219	165	4	µv	µv	NOUN
ma-219	165	5	]	]	X
ma-219	165	6	ev	ev	X
ma-219	165	7	−	−	PROPN
ma-219	165	8	e∗∗v	e∗∗v	X
ma-219	165	9	eh(t	eh(t	PUNCT
ma-219	165	10	,	,	PUNCT
ma-219	165	11	xi	xi	PROPN
ma-219	165	12	)	)	PUNCT
ma-219	165	13	(	(	PUNCT
ma-219	165	14	δλh(xi)sh(t	δλh(xi)sh(t	X
ma-219	165	15	,	,	PUNCT
ma-219	165	16	xi)iv	xi)iv	PUNCT
ma-219	166	1	+	+	PUNCT
ma-219	167	1	[	[	X
ma-219	167	2	αh	αh	NOUN
ma-219	167	3	+	+	NUM
ma-219	167	4	µh]ev	µh]ev	NOUN
ma-219	167	5	)	)	PUNCT
ma-219	168	1	+	+	CCONJ
ma-219	168	2	αv	αv	X
ma-219	169	1	+	+	CCONJ
ma-219	169	2	µv	µv	PROPN
ma-219	169	3	αv	αv	ADP
ma-219	169	4	[	[	PUNCT
ma-219	169	5	αvev	αvev	NOUN
ma-219	169	6	−	−	PROPN
ma-219	170	1	[	[	X
ma-219	170	2	µv	µv	X
ma-219	170	3	+	+	NUM
ma-219	170	4	γv	γv	X
ma-219	170	5	]	]	X
ma-219	170	6	iv	iv	NUM
ma-219	170	7	−	−	PROPN
ma-219	170	8	i∗∗v	i∗∗v	NOUN
ma-219	170	9	iv	iv	X
ma-219	170	10	(	(	PUNCT
ma-219	170	11	αvev	αvev	NOUN
ma-219	170	12	−	−	PROPN
ma-219	171	1	[	[	X
ma-219	171	2	µv	µv	X
ma-219	171	3	+	+	X
ma-219	171	4	αv	αv	NOUN
ma-219	171	5	]	]	PUNCT
ma-219	171	6	iv	iv	X
ma-219	171	7	)	)	PUNCT
ma-219	171	8	]	]	PUNCT
ma-219	171	9	simplifying	simplify	VERB
ma-219	171	10	ṁ	ṁ	PROPN
ma-219	171	11	gives	give	VERB
ma-219	171	12	ṁ	ṁ	PROPN
ma-219	171	13	=	=	SYM
ma-219	171	14	l∑	l∑	NUM
ma-219	171	15	i=0	i=0	PROPN
ma-219	171	16	ψh(xi	ψh(xi	X
ma-219	171	17	)	)	PUNCT
ma-219	172	1	(	(	PUNCT
ma-219	172	2	1−	1−	NUM
ma-219	172	3	s∗∗h	s∗∗h	NOUN
ma-219	172	4	(	(	PUNCT
ma-219	172	5	xi	xi	NOUN
ma-219	172	6	)	)	PUNCT
ma-219	172	7	sh(t	sh(t	X
ma-219	172	8	,	,	PUNCT
ma-219	172	9	xi	xi	ADJ
ma-219	172	10	)	)	PUNCT
ma-219	172	11	)	)	PUNCT
ma-219	173	1	−	−	PROPN
ma-219	173	2	l∑	l∑	X
ma-219	174	1	i=0	i=0	PROPN
ma-219	174	2	µh(xi)sh(t	µh(xi)sh(t	X
ma-219	174	3	,	,	PUNCT
ma-219	174	4	xi	xi	ADJ
ma-219	174	5	)	)	PUNCT
ma-219	174	6	(	(	PUNCT
ma-219	174	7	1−	1−	NUM
ma-219	174	8	s∗∗h	s∗∗h	NOUN
ma-219	174	9	(	(	PUNCT
ma-219	174	10	xi	xi	NOUN
ma-219	174	11	)	)	PUNCT
ma-219	174	12	sh(t	sh(t	X
ma-219	174	13	,	,	PUNCT
ma-219	174	14	xi	xi	ADJ
ma-219	174	15	)	)	PUNCT
ma-219	174	16	)	)	PUNCT
ma-219	175	1	+	+	CCONJ
ma-219	175	2	l∑	l∑	X
ma-219	175	3	i=0	i=0	PROPN
ma-219	175	4	δλh(xi)s	δλh(xi)s	PROPN
ma-219	176	1	∗∗	∗∗	PROPN
ma-219	176	2	h	h	INTJ
ma-219	176	3	(	(	PUNCT
ma-219	176	4	xi)iv	xi)iv	PUNCT
ma-219	176	5	(	(	PUNCT
ma-219	176	6	3.4	3.4	NUM
ma-219	176	7	)	)	PUNCT
ma-219	176	8	−	−	NOUN
ma-219	176	9	l∑	l∑	PUNCT
ma-219	177	1	i=0	i=0	PROPN
ma-219	177	2	e∗∗h	e∗∗h	X
ma-219	177	3	(	(	PUNCT
ma-219	177	4	xi)δλh(xi)sh(t	xi)δλh(xi)sh(t	PROPN
ma-219	177	5	,	,	PUNCT
ma-219	177	6	xi)iv	xi)iv	PUNCT
ma-219	177	7	eh(t	eh(t	X
ma-219	177	8	,	,	PUNCT
ma-219	177	9	xi	xi	X
ma-219	177	10	)	)	PUNCT
ma-219	178	1	+	+	CCONJ
ma-219	178	2	l∑	l∑	X
ma-219	178	3	i=0	i=0	PROPN
ma-219	178	4	(	(	PUNCT
ma-219	178	5	αh(xi	αh(xi	PROPN
ma-219	178	6	)	)	PUNCT
ma-219	179	1	+	+	X
ma-219	179	2	µh(xi))e∗∗h	µh(xi))e∗∗h	X
ma-219	179	3	(	(	PUNCT
ma-219	179	4	xi	xi	PROPN
ma-219	179	5	)	)	PUNCT
ma-219	179	6	(	(	PUNCT
ma-219	179	7	3.5	3.5	NUM
ma-219	179	8	)	)	PUNCT
ma-219	179	9	−	−	NOUN
ma-219	179	10	l∑	l∑	PROPN
ma-219	180	1	i=0	i=0	PROPN
ma-219	180	2	(	(	PUNCT
ma-219	180	3	αh(xi	αh(xi	PROPN
ma-219	180	4	)	)	PUNCT
ma-219	180	5	+	+	CCONJ
ma-219	180	6	µh(xi	µh(xi	X
ma-219	180	7	)	)	PUNCT
ma-219	180	8	)	)	PUNCT
ma-219	180	9	αh(xi	αh(xi	PROPN
ma-219	180	10	)	)	PUNCT
ma-219	180	11	(	(	PUNCT
ma-219	180	12	r(xi	r(xi	PROPN
ma-219	180	13	)	)	PUNCT
ma-219	180	14	+	+	CCONJ
ma-219	180	15	µh(xi)γh(xi))ih(t	µh(xi)γh(xi))ih(t	PROPN
ma-219	180	16	,	,	PUNCT
ma-219	180	17	xi	xi	X
ma-219	180	18	)	)	PUNCT
ma-219	180	19	(	(	PUNCT
ma-219	180	20	3.6	3.6	NUM
ma-219	180	21	)	)	PUNCT
ma-219	180	22	−	−	NOUN
ma-219	180	23	l∑	l∑	PROPN
ma-219	181	1	i=0	i=0	PROPN
ma-219	181	2	(	(	PUNCT
ma-219	181	3	αh(xi	αh(xi	PROPN
ma-219	181	4	)	)	PUNCT
ma-219	182	1	+	+	CCONJ
ma-219	182	2	µh(xi))i∗∗h	µh(xi))i∗∗h	X
ma-219	182	3	(	(	PUNCT
ma-219	182	4	xi)eh(t	xi)eh(t	PROPN
ma-219	182	5	,	,	PUNCT
ma-219	182	6	xi	xi	NUM
ma-219	182	7	)	)	PUNCT
ma-219	182	8	ih(t	ih(t	PUNCT
ma-219	182	9	,	,	PUNCT
ma-219	182	10	xi	xi	ADJ
ma-219	182	11	)	)	PUNCT
ma-219	182	12	+	+	CCONJ
ma-219	182	13	l∑	l∑	X
ma-219	182	14	i=0	i=0	PROPN
ma-219	182	15	αh(xi	αh(xi	PROPN
ma-219	182	16	)	)	PUNCT
ma-219	182	17	+	+	CCONJ
ma-219	182	18	µh(xi	µh(xi	X
ma-219	182	19	)	)	PUNCT
ma-219	182	20	αh(xi	αh(xi	PROPN
ma-219	182	21	)	)	PUNCT
ma-219	182	22	(	(	PUNCT
ma-219	182	23	r(xi	r(xi	X
ma-219	182	24	)	)	PUNCT
ma-219	182	25	+	+	CCONJ
ma-219	182	26	µh(xi	µh(xi	X
ma-219	182	27	)	)	PUNCT
ma-219	183	1	+	+	CCONJ
ma-219	183	2	γh(xi))i∗∗h	γh(xi))i∗∗h	ADJ
ma-219	183	3	(	(	PUNCT
ma-219	183	4	xi	xi	PROPN
ma-219	183	5	)	)	PUNCT
ma-219	183	6	(	(	PUNCT
ma-219	183	7	3.7	3.7	NUM
ma-219	183	8	)	)	PUNCT
ma-219	184	1	+	+	CCONJ
ma-219	184	2	µv	µv	PRON
ma-219	184	3	(	(	PUNCT
ma-219	184	4	1−	1−	NUM
ma-219	184	5	s∗∗v	s∗∗v	PROPN
ma-219	184	6	sv	sv	PROPN
ma-219	184	7	)	)	PUNCT
ma-219	185	1	−	−	PROPN
ma-219	185	2	µvsv	µvsv	ADJ
ma-219	185	3	(	(	PUNCT
ma-219	185	4	1−	1−	NUM
ma-219	185	5	s∗∗v	s∗∗v	X
ma-219	185	6	sv	sv	PROPN
ma-219	185	7	)	)	PUNCT
ma-219	186	1	+	+	CCONJ
ma-219	186	2	δλvs	δλvs	NOUN
ma-219	186	3	∗∗	∗∗	NOUN
ma-219	186	4	v	v	X
ma-219	186	5	(	(	PUNCT
ma-219	186	6	xi)ih	xi)ih	PROPN
ma-219	186	7	−	−	PROPN
ma-219	186	8	e∗∗v	e∗∗v	ADV
ma-219	186	9	δλvsv	δλvsv	PROPN
ma-219	186	10	ih	ih	PROPN
ma-219	186	11	ev	ev	PROPN
ma-219	187	1	+	+	CCONJ
ma-219	187	2	(	(	PUNCT
ma-219	187	3	αv	αv	ADP
ma-219	187	4	+	+	CCONJ
ma-219	187	5	µv	µv	NOUN
ma-219	187	6	)	)	PUNCT
ma-219	187	7	e∗∗v	e∗∗v	X
ma-219	187	8	(	(	PUNCT
ma-219	187	9	3.8	3.8	NUM
ma-219	187	10	)	)	PUNCT
ma-219	187	11	−	−	PROPN
ma-219	187	12	(	(	PUNCT
ma-219	187	13	αv	αv	ADP
ma-219	187	14	+	+	CCONJ
ma-219	187	15	µv	µv	NOUN
ma-219	187	16	)	)	PUNCT
ma-219	187	17	(	(	PUNCT
ma-219	188	1	µv	µv	PROPN
ma-219	188	2	+	+	NUM
ma-219	188	3	γv	γv	X
ma-219	188	4	)	)	PUNCT
ma-219	188	5	iv	iv	X
ma-219	188	6	αv	αv	ADP
ma-219	188	7	−	−	PROPN
ma-219	188	8	(	(	PUNCT
ma-219	188	9	αv	αv	ADP
ma-219	188	10	+	+	CCONJ
ma-219	188	11	µv	µv	PROPN
ma-219	188	12	)	)	PUNCT
ma-219	188	13	i∗∗v	i∗∗v	NOUN
ma-219	188	14	ev	ev	INTJ
ma-219	188	15	iv	iv	X
ma-219	188	16	+	+	CCONJ
ma-219	188	17	(	(	PUNCT
ma-219	188	18	αv	αv	ADP
ma-219	188	19	+	+	CCONJ
ma-219	188	20	µv	µv	NOUN
ma-219	188	21	)	)	PUNCT
ma-219	188	22	(	(	PUNCT
ma-219	188	23	µv	µv	PROPN
ma-219	188	24	+	+	NUM
ma-219	188	25	γv	γv	X
ma-219	188	26	)	)	PUNCT
ma-219	188	27	iv	iv	X
ma-219	188	28	αv	αv	NOUN
ma-219	188	29	(	(	PUNCT
ma-219	188	30	3.9	3.9	NUM
ma-219	188	31	)	)	PUNCT
ma-219	188	32	at	at	ADP
ma-219	188	33	the	the	DET
ma-219	188	34	endemic	endemic	ADJ
ma-219	188	35	equilibrium	equilibrium	NOUN
ma-219	188	36	ee	ee	NOUN
ma-219	188	37	,	,	PUNCT
ma-219	188	38	we	we	PRON
ma-219	188	39	get	get	VERB
ma-219	188	40	from	from	ADP
ma-219	188	41	model	model	NOUN
ma-219	188	42	(	(	PUNCT
ma-219	188	43	2.4	2.4	NUM
ma-219	188	44	)	)	PUNCT
ma-219	188	45	that	that	PRON
ma-219	188	46	ψh(xi	ψh(xi	X
ma-219	188	47	)	)	PUNCT
ma-219	189	1	=	=	PUNCT
ma-219	189	2	∑l	∑l	PROPN
ma-219	189	3	i=0	i=0	PROPN
ma-219	189	4	δλh(xi)σ	δλh(xi)σ	NOUN
ma-219	189	5	∗	∗	NOUN
ma-219	189	6	h(xi)i	h(xi)i	PROPN
ma-219	189	7	∗	∗	NOUN
ma-219	189	8	v	v	NOUN
ma-219	189	9	+	+	CCONJ
ma-219	189	10	∑l	∑l	PROPN
ma-219	189	11	i=0	i=0	PROPN
ma-219	189	12	µh(xi)s	µh(xi)	NOUN
ma-219	189	13	∗	∗	NOUN
ma-219	189	14	h(xi	h(xi	PROPN
ma-219	189	15	)	)	PUNCT
ma-219	189	16	αh(xi	αh(xi	PROPN
ma-219	189	17	)	)	PUNCT
ma-219	190	1	+	+	CCONJ
ma-219	190	2	µh(xi	µh(xi	X
ma-219	190	3	)	)	PUNCT
ma-219	191	1	=	=	PUNCT
ma-219	191	2	∑l	∑l	PROPN
ma-219	191	3	i=0	i=0	ADJ
ma-219	191	4	δλh(xi	δλh(xi	X
ma-219	191	5	)	)	PUNCT
ma-219	191	6	σ	σ	PROPN
ma-219	191	7	∗	∗	NOUN
ma-219	191	8	hi	hi	INTJ
ma-219	191	9	∗	∗	NOUN
ma-219	191	10	v	v	NOUN
ma-219	191	11	e∗h(xi	e∗h(xi	PROPN
ma-219	191	12	)	)	PUNCT
ma-219	191	13	µh(xi	µh(xi	PROPN
ma-219	191	14	)	)	PUNCT
ma-219	192	1	+	+	CCONJ
ma-219	192	2	γh(xi	γh(xi	NOUN
ma-219	192	3	)	)	PUNCT
ma-219	193	1	=	=	PUNCT
ma-219	193	2	∑l	∑l	PRON
ma-219	193	3	i=0	i=0	PROPN
ma-219	193	4	αh(xi	αh(xi	PROPN
ma-219	193	5	)	)	PUNCT
ma-219	194	1	e	e	NOUN
ma-219	194	2	∗	∗	VERB
ma-219	194	3	h(xi	h(xi	NOUN
ma-219	194	4	)	)	PUNCT
ma-219	195	1	i∗h(xi	i∗h(xi	PROPN
ma-219	195	2	)	)	PUNCT
ma-219	196	1	ψv	ψv	PROPN
ma-219	196	2	=	=	SYM
ma-219	196	3	δλvs	δλvs	PROPN
ma-219	196	4	∗	∗	NOUN
ma-219	196	5	v	v	NOUN
ma-219	197	1	i	i	PRON
ma-219	197	2	∗	∗	NOUN
ma-219	197	3	h	h	NOUN
ma-219	198	1	+	+	CCONJ
ma-219	198	2	µvs	µvs	AUX
ma-219	198	3	∗	∗	NOUN
ma-219	198	4	v	v	NOUN
ma-219	198	5	αv	αv	NOUN
ma-219	199	1	+	+	CCONJ
ma-219	199	2	µv	µv	NOUN
ma-219	199	3	=	=	PRON
ma-219	199	4	δλvs∗v	δλvs∗v	VERB
ma-219	199	5	i	i	PRON
ma-219	199	6	∗	∗	NOUN
ma-219	199	7	h	h	PROPN
ma-219	199	8	e∗v	e∗v	NOUN
ma-219	200	1	µv	µv	PROPN
ma-219	200	2	+	+	SYM
ma-219	200	3	γv	γv	X
ma-219	200	4	=	=	SYM
ma-219	200	5	αve∗v	αve∗v	NUM
ma-219	200	6	i∗v	i∗v	PROPN
ma-219	200	7			NOUN
ma-219	200	8	(	(	PUNCT
ma-219	200	9	3.10	3.10	NUM
ma-219	200	10	)	)	PUNCT
ma-219	200	11	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	200	12	eur	eur	PROPN
ma-219	200	13	.	.	PUNCT
ma-219	201	1	j.	j.	PROPN
ma-219	201	2	math	math	PROPN
ma-219	201	3	.	.	PUNCT
ma-219	202	1	anal	anal	PROPN
ma-219	202	2	.	.	PUNCT
ma-219	203	1	10.28924	10.28924	NUM
ma-219	203	2	/	/	SYM
ma-219	203	3	ada	ada	PROPN
ma-219	203	4	/	/	SYM
ma-219	203	5	ma.4.9	ma.4.9	PROPN
ma-219	203	6	8using	8using	NUM
ma-219	203	7	(	(	PUNCT
ma-219	203	8	3.6	3.6	NUM
ma-219	203	9	)	)	PUNCT
ma-219	203	10	in	in	ADP
ma-219	203	11	(	(	PUNCT
ma-219	203	12	3.5	3.5	NUM
ma-219	203	13	)	)	PUNCT
ma-219	203	14	,	,	PUNCT
ma-219	203	15	we	we	PRON
ma-219	203	16	have	have	VERB
ma-219	203	17	ṁ	ṁ	NOUN
ma-219	203	18	=	=	SYM
ma-219	203	19	l∑	l∑	NUM
ma-219	203	20	i=0	i=0	PROPN
ma-219	203	21	µh(xi)σ	µh(xi)σ	X
ma-219	203	22	∗	∗	NOUN
ma-219	203	23	h	h	NOUN
ma-219	203	24	(	(	PUNCT
ma-219	203	25	2−	2−	NUM
ma-219	203	26	s∗h(xi	s∗h(xi	NOUN
ma-219	203	27	)	)	PUNCT
ma-219	203	28	sh(t	sh(t	X
ma-219	203	29	,	,	PUNCT
ma-219	203	30	xi	xi	ADJ
ma-219	203	31	)	)	PUNCT
ma-219	203	32	−	−	NOUN
ma-219	203	33	sh(t	sh(t	ADJ
ma-219	203	34	,	,	PUNCT
ma-219	203	35	xi	xi	ADJ
ma-219	203	36	)	)	PUNCT
ma-219	203	37	s∗h(xi	s∗h(xi	PROPN
ma-219	203	38	)	)	PUNCT
ma-219	203	39	)	)	PUNCT
ma-219	204	1	+	+	CCONJ
ma-219	204	2	l∑	l∑	X
ma-219	204	3	i=0	i=0	PROPN
ma-219	204	4	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	204	5	∗	∗	NOUN
ma-219	204	6	h(xi)i	h(xi)i	PROPN
ma-219	204	7	∗	∗	NOUN
ma-219	204	8	v	v	PROPN
ma-219	204	9	(	(	PUNCT
ma-219	204	10	3.11	3.11	NUM
ma-219	204	11	)	)	PUNCT
ma-219	204	12	−	−	PROPN
ma-219	204	13	l∑	l∑	ADP
ma-219	204	14	i=0	i=0	ADJ
ma-219	204	15	δλh(xi)(s∗h)2i∗v	δλh(xi)(s∗h)2i∗v	NOUN
ma-219	204	16	sh(xi	sh(xi	PROPN
ma-219	204	17	)	)	PUNCT
ma-219	205	1	+	+	NUM
ma-219	205	2	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	205	3	∗	∗	NOUN
ma-219	205	4	h(xi)iv	h(xi)iv	NOUN
ma-219	205	5	−	−	PROPN
ma-219	206	1	l∑	l∑	PUNCT
ma-219	207	1	i=0	i=0	PROPN
ma-219	207	2	e∗h(xi)δλh(xi)σsh(t	e∗h(xi)δλh(xi)σsh(t	PROPN
ma-219	207	3	,	,	PUNCT
ma-219	207	4	xi)iv	xi)iv	PUNCT
ma-219	207	5	eh(t	eh(t	X
ma-219	207	6	,	,	PUNCT
ma-219	207	7	xi	xi	X
ma-219	207	8	)	)	PUNCT
ma-219	208	1	+	+	NUM
ma-219	208	2	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	208	3	∗	∗	NOUN
ma-219	208	4	h(xi)iv	h(xi)iv	NOUN
ma-219	209	1	−	−	PROPN
ma-219	209	2	l∑	l∑	PUNCT
ma-219	209	3	i=0	i=0	PROPN
ma-219	209	4	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	209	5	∗	∗	NOUN
ma-219	209	6	h(xi)ih(t	h(xi)ih(t	PROPN
ma-219	209	7	,	,	PUNCT
ma-219	209	8	xi)i	xi)i	PROPN
ma-219	209	9	∗	∗	NOUN
ma-219	209	10	v	v	ADP
ma-219	209	11	i∗h(xi	i∗h(xi	PROPN
ma-219	209	12	)	)	PUNCT
ma-219	210	1	−	−	X
ma-219	210	2	l∑	l∑	PUNCT
ma-219	211	1	i=0	i=0	PROPN
ma-219	211	2	δλh(xi)i	δλh(xi)i	PROPN
ma-219	211	3	∗	∗	PROPN
ma-219	211	4	h(xi)eh(t	h(xi)eh(t	PROPN
ma-219	211	5	,	,	PUNCT
ma-219	211	6	xi)i	xi)i	PROPN
ma-219	211	7	∗	∗	NOUN
ma-219	211	8	v	v	ADP
ma-219	211	9	e∗h(xi)ih(t	e∗h(xi)ih(t	NOUN
ma-219	211	10	,	,	PUNCT
ma-219	211	11	xi	xi	ADJ
ma-219	211	12	)	)	PUNCT
ma-219	212	1	+	+	CCONJ
ma-219	212	2	l∑	l∑	X
ma-219	212	3	i=0	i=0	PROPN
ma-219	212	4	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	212	5	∗	∗	VERB
ma-219	212	6	hi	hi	INTJ
ma-219	212	7	∗	∗	NOUN
ma-219	212	8	v	v	NOUN
ma-219	212	9	+	+	CCONJ
ma-219	212	10	µvs	µvs	PROPN
ma-219	212	11	∗	∗	NOUN
ma-219	212	12	v	v	NOUN
ma-219	212	13	(	(	PUNCT
ma-219	212	14	2−	2−	NUM
ma-219	212	15	s∗∗v	s∗∗v	PROPN
ma-219	212	16	sv	sv	PROPN
ma-219	212	17	−	−	PROPN
ma-219	212	18	sv	sv	INTJ
ma-219	212	19	s∗v	s∗v	PROPN
ma-219	212	20	)	)	PUNCT
ma-219	212	21	−	−	PRON
ma-219	212	22	δλvs∗v	δλvs∗v	VERB
ma-219	212	23	i∗h	i∗h	NUM
ma-219	212	24	−	−	PROPN
ma-219	212	25	δλv	δλv	PROPN
ma-219	212	26	(	(	PUNCT
ma-219	212	27	s∗v	s∗v	NUM
ma-219	212	28	)	)	PUNCT
ma-219	212	29	2i∗h	2i∗h	NUM
ma-219	212	30	sv	sv	NOUN
ma-219	213	1	+	+	NUM
ma-219	213	2	δλvs	δλvs	PROPN
ma-219	213	3	∗	∗	NOUN
ma-219	213	4	v	v	NOUN
ma-219	213	5	ih	ih	PROPN
ma-219	213	6	−	−	PROPN
ma-219	213	7	e∗v	e∗v	NOUN
ma-219	213	8	δλvsv	δλvsv	NOUN
ma-219	213	9	ih	ih	PROPN
ma-219	213	10	ev	ev	PROPN
ma-219	213	11	+	+	CCONJ
ma-219	213	12	δλvs	δλvs	PROPN
ma-219	213	13	∗	∗	NOUN
ma-219	213	14	v	v	NOUN
ma-219	213	15	ih	ih	PROPN
ma-219	213	16	−	−	PROPN
ma-219	214	1	δλvs	δλvs	PROPN
ma-219	214	2	∗	∗	NOUN
ma-219	214	3	v	v	NOUN
ma-219	214	4	iv	iv	NUM
ma-219	215	1	i	i	PRON
ma-219	215	2	∗	∗	NOUN
ma-219	215	3	h	h	PROPN
ma-219	215	4	i∗v	i∗v	PROPN
ma-219	215	5	−	−	PROPN
ma-219	215	6	δλv	δλv	PROPN
ma-219	215	7	i	i	PRON
ma-219	215	8	∗	∗	VERB
ma-219	215	9	vev	vev	NOUN
ma-219	216	1	i	i	PRON
ma-219	216	2	∗	∗	VERB
ma-219	216	3	h	h	PROPN
ma-219	216	4	e∗v	e∗v	SYM
ma-219	216	5	iv	iv	NUM
ma-219	217	1	+	+	NUM
ma-219	217	2	δλvs	δλvs	PROPN
ma-219	217	3	∗	∗	NOUN
ma-219	217	4	v	v	NOUN
ma-219	218	1	i	i	PRON
ma-219	218	2	∗	∗	NOUN
ma-219	218	3	h	h	NOUN
ma-219	218	4	simplifying	simplify	VERB
ma-219	218	5	further	far	ADV
ma-219	218	6	,	,	PUNCT
ma-219	218	7	we	we	PRON
ma-219	218	8	have	have	VERB
ma-219	218	9	ṁ	ṁ	NOUN
ma-219	218	10	=	=	SYM
ma-219	218	11	l∑	l∑	NUM
ma-219	218	12	i=0	i=0	PROPN
ma-219	218	13	µh(xi)s	µh(xi)	NOUN
ma-219	218	14	∗	∗	NOUN
ma-219	218	15	h	h	NOUN
ma-219	218	16	(	(	PUNCT
ma-219	218	17	2−	2−	NUM
ma-219	218	18	s∗h(xi	s∗h(xi	NOUN
ma-219	218	19	)	)	PUNCT
ma-219	218	20	sh(t	sh(t	X
ma-219	218	21	,	,	PUNCT
ma-219	218	22	xi	xi	ADJ
ma-219	218	23	)	)	PUNCT
ma-219	218	24	−	−	NOUN
ma-219	218	25	sh(t	sh(t	ADJ
ma-219	218	26	,	,	PUNCT
ma-219	218	27	xi	xi	ADJ
ma-219	218	28	)	)	PUNCT
ma-219	218	29	s∗h(xi	s∗h(xi	PROPN
ma-219	218	30	)	)	PUNCT
ma-219	218	31	)	)	PUNCT
ma-219	219	1	+	+	CCONJ
ma-219	219	2	l∑	l∑	X
ma-219	219	3	i=0	i=0	PROPN
ma-219	219	4	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	220	1	∗∗	∗∗	NOUN
ma-219	220	2	h	h	NOUN
ma-219	221	1	i	i	PRON
ma-219	221	2	∗	∗	VERB
ma-219	221	3	v	v	NOUN
ma-219	221	4	(	(	PUNCT
ma-219	221	5	3.12	3.12	NUM
ma-219	221	6	)	)	PUNCT
ma-219	221	7	×	×	NOUN
ma-219	221	8	[	[	PUNCT
ma-219	221	9	4−	4−	NOUN
ma-219	221	10	s∗h(xi	s∗h(xi	NOUN
ma-219	221	11	)	)	PUNCT
ma-219	221	12	sh(t	sh(t	X
ma-219	221	13	,	,	PUNCT
ma-219	221	14	xi	xi	ADJ
ma-219	221	15	)	)	PUNCT
ma-219	221	16	−	−	PRON
ma-219	221	17	e∗h(xi)σsh(t	e∗h(xi)σsh(t	PROPN
ma-219	221	18	,	,	PUNCT
ma-219	221	19	xi)iv	xi)iv	PUNCT
ma-219	221	20	eh(t	eh(t	X
ma-219	221	21	,	,	PUNCT
ma-219	221	22	xi)σs	xi)σs	PUNCT
ma-219	222	1	∗	∗	NOUN
ma-219	222	2	hi	hi	INTJ
ma-219	222	3	∗	∗	NOUN
ma-219	222	4	v	v	NOUN
ma-219	222	5	−	−	PROPN
ma-219	222	6	i∗h(xi)eh(t	i∗h(xi)eh(t	NUM
ma-219	222	7	,	,	PUNCT
ma-219	222	8	xi	xi	ADJ
ma-219	222	9	)	)	PUNCT
ma-219	222	10	ih(t	ih(t	PROPN
ma-219	222	11	,	,	PUNCT
ma-219	222	12	xi)e	xi)e	PROPN
ma-219	222	13	∗	∗	NOUN
ma-219	222	14	h(xi	h(xi	NOUN
ma-219	222	15	)	)	PUNCT
ma-219	222	16	−	−	NOUN
ma-219	222	17	ih(t	ih(t	SYM
ma-219	222	18	,	,	PUNCT
ma-219	222	19	xi)i	xi)i	NUM
ma-219	222	20	∗	∗	NOUN
ma-219	222	21	v	v	NOUN
ma-219	222	22	i∗h(xi)iv	i∗h(xi)iv	NOUN
ma-219	222	23	]	]	PUNCT
ma-219	223	1	+	+	CCONJ
ma-219	223	2	l∑	l∑	X
ma-219	223	3	i=0	i=0	PROPN
ma-219	223	4	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	223	5	∗	∗	VERB
ma-219	223	6	hi	hi	INTJ
ma-219	223	7	∗	∗	NOUN
ma-219	223	8	v	v	NOUN
ma-219	223	9	−	−	NOUN
ma-219	223	10	δλ(xi)σs	δλ(xi)σs	NOUN
ma-219	223	11	∗	∗	NOUN
ma-219	223	12	h(xi)ih(t	h(xi)ih(t	PROPN
ma-219	223	13	,	,	PUNCT
ma-219	223	14	xi)i	xi)i	PROPN
ma-219	223	15	∗	∗	NOUN
ma-219	223	16	v	v	NOUN
ma-219	223	17	i∗h(xi	i∗h(xi	PROPN
ma-219	224	1	+	+	CCONJ
ma-219	224	2	l∑	l∑	ADP
ma-219	224	3	i=0	i=0	PROPN
ma-219	224	4	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	224	5	∗	∗	NOUN
ma-219	224	6	h(xi)ih(t	h(xi)ih(t	PROPN
ma-219	224	7	,	,	PUNCT
ma-219	224	8	xi)(i∗v	xi)(i∗v	X
ma-219	225	1	i∗h(xi)iv	i∗h(xi)iv	ADV
ma-219	225	2	−	−	PRON
ma-219	225	3	δλh(xi)σs	δλh(xi)σs	NOUN
ma-219	225	4	∗	∗	NOUN
ma-219	225	5	hi	hi	INTJ
ma-219	226	1	∗∗	∗∗	NOUN
ma-219	226	2	v	v	SYM
ma-219	226	3	+	+	CCONJ
ma-219	226	4	µvs	µvs	VERB
ma-219	226	5	∗∗	∗∗	PROPN
ma-219	226	6	v	v	NOUN
ma-219	226	7	(	(	PUNCT
ma-219	226	8	2−	2−	NUM
ma-219	226	9	s∗∗v	s∗∗v	PROPN
ma-219	226	10	sv	sv	PROPN
ma-219	226	11	−	−	PROPN
ma-219	226	12	sv	sv	INTJ
ma-219	226	13	s∗∗v	s∗∗v	PROPN
ma-219	226	14	)	)	PUNCT
ma-219	227	1	+	+	CCONJ
ma-219	227	2	δλvs	δλvs	PROPN
ma-219	227	3	∗	∗	NOUN
ma-219	227	4	v	v	NOUN
ma-219	228	1	i	i	PRON
ma-219	228	2	∗	∗	NOUN
ma-219	228	3	h	h	NOUN
ma-219	228	4	×	×	NOUN
ma-219	228	5	[	[	PUNCT
ma-219	228	6	4−	4−	NUM
ma-219	228	7	s∗v	s∗v	NUM
ma-219	228	8	sv	sv	NOUN
ma-219	228	9	−	−	PROPN
ma-219	228	10	e∗vsh(t	e∗vsh(t	PROPN
ma-219	228	11	,	,	PUNCT
ma-219	228	12	xi)g(ih	xi)g(ih	PROPN
ma-219	228	13	)	)	PUNCT
ma-219	228	14	evs∗∗v	evs∗∗v	ADV
ma-219	228	15	g(i∗∗h	g(i∗∗h	NUM
ma-219	228	16	)	)	PUNCT
ma-219	229	1	−	−	PROPN
ma-219	229	2	i∗∗v	i∗∗v	PROPN
ma-219	229	3	ev	ev	X
ma-219	229	4	ive∗∗v	ive∗∗v	PROPN
ma-219	229	5	−	−	PROPN
ma-219	229	6	ivg(i∗∗h	ivg(i∗∗h	PROPN
ma-219	229	7	)	)	PUNCT
ma-219	229	8	i∗∗v	i∗∗v	NOUN
ma-219	229	9	g(ih	g(ih	ADJ
ma-219	229	10	)	)	PUNCT
ma-219	229	11	]	]	PUNCT
ma-219	230	1	+	+	CCONJ
ma-219	230	2	δλvs	δλvs	PROPN
ma-219	230	3	∗	∗	NOUN
ma-219	230	4	v	v	NOUN
ma-219	231	1	i	i	PRON
ma-219	231	2	∗	∗	VERB
ma-219	231	3	h)−	h)−	PROPN
ma-219	231	4	δλvs	δλvs	PROPN
ma-219	231	5	∗	∗	NOUN
ma-219	231	6	v	v	NOUN
ma-219	232	1	iv	iv	NUM
ma-219	233	1	i	i	PRON
ma-219	233	2	∗	∗	NOUN
ma-219	233	3	h	h	NOUN
ma-219	233	4	)	)	PUNCT
ma-219	233	5	i∗v	i∗v	VERB
ma-219	234	1	+	+	NUM
ma-219	234	2	δλvs	δλvs	PROPN
ma-219	234	3	∗	∗	NOUN
ma-219	234	4	v	v	NOUN
ma-219	234	5	iv	iv	X
ma-219	234	6	(	(	PUNCT
ma-219	234	7	i∗h(xi	i∗h(xi	PROPN
ma-219	234	8	)	)	PUNCT
ma-219	234	9	)	)	PUNCT
ma-219	234	10	2	2	NUM
ma-219	234	11	i∗v	i∗v	NOUN
ma-219	234	12	ih	ih	NOUN
ma-219	234	13	−	−	PROPN
ma-219	234	14	δλvs∗v	δλvs∗v	VERB
ma-219	234	15	i∗h	i∗h	PUNCT
ma-219	234	16	further	further	ADJ
ma-219	234	17	simplification	simplification	NOUN
ma-219	234	18	yields	yield	NOUN
ma-219	234	19	ṁ	ṁ	NOUN
ma-219	234	20	=	=	SYM
ma-219	234	21	−ṁ1	−ṁ1	NUM
ma-219	234	22	−	−	PROPN
ma-219	234	23	ṁ2	ṁ2	PROPN
ma-219	234	24	−	−	NOUN
ma-219	234	25	l∑	l∑	PUNCT
ma-219	235	1	i=0	i=0	PROPN
ma-219	235	2	δλh(xi)s	δλh(xi)s	PROPN
ma-219	235	3	∗	∗	PROPN
ma-219	235	4	h(xi)i	h(xi)i	PROPN
ma-219	235	5	∗	∗	NOUN
ma-219	235	6	v	v	NOUN
ma-219	235	7	[	[	PUNCT
ma-219	235	8	1−	1−	NUM
ma-219	235	9	iv	iv	NUM
ma-219	235	10	i∗v	i∗v	NOUN
ma-219	235	11	+	+	CCONJ
ma-219	235	12	ih(t	ih(t	PRON
ma-219	235	13	,	,	PUNCT
ma-219	235	14	xi	xi	ADJ
ma-219	235	15	)	)	PUNCT
ma-219	235	16	i∗h(xi	i∗h(xi	PROPN
ma-219	235	17	)	)	PUNCT
ma-219	236	1	+	+	CCONJ
ma-219	236	2	ih(t	ih(t	PROPN
ma-219	236	3	,	,	PUNCT
ma-219	236	4	xi)i	xi)i	NUM
ma-219	236	5	∗	∗	NOUN
ma-219	236	6	v	v	NOUN
ma-219	236	7	i∗h(xi)iv	i∗h(xi)iv	NOUN
ma-219	236	8	]	]	PUNCT
ma-219	236	9	−	−	PROPN
ma-219	237	1	ṁ3	ṁ3	PROPN
ma-219	237	2	−	−	PROPN
ma-219	237	3	ṁ4	ṁ4	PROPN
ma-219	237	4	−	−	PROPN
ma-219	237	5	l∑	l∑	PUNCT
ma-219	238	1	i=0	i=0	PROPN
ma-219	238	2	δλvs	δλvs	PROPN
ma-219	239	1	∗∗	∗∗	NOUN
ma-219	239	2	v	v	X
ma-219	239	3	i	i	PRON
ma-219	239	4	∗	∗	NOUN
ma-219	239	5	h	h	NOUN
ma-219	240	1	[	[	PUNCT
ma-219	240	2	1−	1−	NUM
ma-219	240	3	ih	ih	NOUN
ma-219	240	4	i∗∗h	i∗∗h	NOUN
ma-219	240	5	+	+	CCONJ
ma-219	240	6	iv	iv	NUM
ma-219	240	7	i∗v	i∗v	NOUN
ma-219	240	8	+	+	CCONJ
ma-219	241	1	iv	iv	X
ma-219	242	1	i	i	PRON
ma-219	242	2	∗	∗	NOUN
ma-219	242	3	h	h	PROPN
ma-219	242	4	i∗v	i∗v	VERB
ma-219	242	5	ih	ih	X
ma-219	242	6	]	]	PUNCT
ma-219	242	7	(	(	PUNCT
ma-219	242	8	3.13	3.13	NUM
ma-219	242	9	)	)	PUNCT
ma-219	242	10	where	where	SCONJ
ma-219	242	11	m1	m1	PROPN
ma-219	242	12	=	=	PUNCT
ma-219	242	13	l∑	l∑	PROPN
ma-219	242	14	i=0	i=0	PROPN
ma-219	242	15	µh(xi)s	µh(xi)	NOUN
ma-219	242	16	∗	∗	NOUN
ma-219	242	17	h(xi	h(xi	NUM
ma-219	242	18	)	)	PUNCT
ma-219	242	19	(	(	PUNCT
ma-219	242	20	s∗h(xi	s∗h(xi	PROPN
ma-219	242	21	)	)	PUNCT
ma-219	242	22	sh(t	sh(t	X
ma-219	242	23	,	,	PUNCT
ma-219	242	24	xi	xi	ADJ
ma-219	242	25	)	)	PUNCT
ma-219	243	1	+	+	CCONJ
ma-219	243	2	sh(t	sh(t	X
ma-219	243	3	,	,	PUNCT
ma-219	243	4	xi	xi	ADJ
ma-219	243	5	)	)	PUNCT
ma-219	243	6	s∗h(xi	s∗h(xi	PROPN
ma-219	243	7	)	)	PUNCT
ma-219	243	8	−	−	PROPN
ma-219	243	9	2	2	NUM
ma-219	243	10	)	)	PUNCT
ma-219	243	11	,	,	PUNCT
ma-219	244	1	m2	m2	PROPN
ma-219	244	2	=	=	PUNCT
ma-219	244	3	l∑	l∑	PROPN
ma-219	244	4	i=0	i=0	PROPN
ma-219	244	5	δλh(xi)s	δλh(xi)s	PROPN
ma-219	244	6	∗	∗	PROPN
ma-219	244	7	h(xi)iv	h(xi)iv	PROPN
ma-219	244	8	×	×	NOUN
ma-219	244	9	[	[	PUNCT
ma-219	244	10	s∗h(xi	s∗h(xi	PROPN
ma-219	244	11	)	)	PUNCT
ma-219	244	12	sh(t	sh(t	X
ma-219	244	13	,	,	PUNCT
ma-219	244	14	xi	xi	ADJ
ma-219	244	15	)	)	PUNCT
ma-219	244	16	+	+	X
ma-219	244	17	e∗h(xi)sh(t	e∗h(xi)sh(t	X
ma-219	244	18	,	,	PUNCT
ma-219	244	19	xi)iv	xi)iv	PUNCT
ma-219	245	1	eh(t	eh(t	PROPN
ma-219	245	2	,	,	PUNCT
ma-219	245	3	xi)s	xi)s	PROPN
ma-219	245	4	∗	∗	VERB
ma-219	245	5	hi	hi	INTJ
ma-219	245	6	∗	∗	NOUN
ma-219	245	7	v	v	NOUN
ma-219	245	8	+	+	CCONJ
ma-219	245	9	i∗h(xi)eh(t	i∗h(xi)eh(t	NUM
ma-219	245	10	,	,	PUNCT
ma-219	245	11	xi	xi	ADJ
ma-219	245	12	)	)	PUNCT
ma-219	245	13	ih(t	ih(t	PROPN
ma-219	245	14	,	,	PUNCT
ma-219	245	15	xi)e	xi)e	PROPN
ma-219	245	16	∗	∗	NOUN
ma-219	245	17	h(xi	h(xi	NUM
ma-219	245	18	)	)	PUNCT
ma-219	246	1	+	+	CCONJ
ma-219	246	2	ih(t	ih(t	X
ma-219	246	3	,	,	PUNCT
ma-219	246	4	xi)i	xi)i	NUM
ma-219	246	5	∗	∗	NOUN
ma-219	246	6	v	v	NOUN
ma-219	246	7	i∗h(xi)iv	i∗h(xi)iv	NOUN
ma-219	246	8	−	−	NUM
ma-219	246	9	4	4	NUM
ma-219	246	10	]	]	PUNCT
ma-219	246	11	,	,	PUNCT
ma-219	246	12	m3	m3	PROPN
ma-219	246	13	=	=	PUNCT
ma-219	246	14	µvs	µvs	PROPN
ma-219	246	15	∗	∗	NOUN
ma-219	246	16	v	v	PROPN
ma-219	246	17	(	(	PUNCT
ma-219	246	18	s∗v	s∗v	NUM
ma-219	246	19	sv	sv	NOUN
ma-219	246	20	+	+	NOUN
ma-219	246	21	sv	sv	X
ma-219	246	22	s∗v	s∗v	NUM
ma-219	246	23	−	−	PROPN
ma-219	246	24	2	2	X
ma-219	246	25	)	)	PUNCT
ma-219	246	26	m4	m4	PROPN
ma-219	246	27	=	=	SYM
ma-219	246	28	δλvs	δλvs	PROPN
ma-219	246	29	∗	∗	NOUN
ma-219	246	30	[	[	PUNCT
ma-219	246	31	s∗v	s∗v	NUM
ma-219	246	32	sv	sv	NOUN
ma-219	246	33	+	+	NUM
ma-219	246	34	e∗vsv	e∗vsv	PROPN
ma-219	246	35	(	(	PUNCT
ma-219	246	36	t	t	PROPN
ma-219	246	37	,	,	PUNCT
ma-219	246	38	xi)g(ih	xi)g(ih	PROPN
ma-219	246	39	)	)	PUNCT
ma-219	246	40	evs∗v	evs∗v	PROPN
ma-219	247	1	i	i	PRON
ma-219	247	2	∗	∗	VERB
ma-219	247	3	h	h	NOUN
ma-219	248	1	+	+	CCONJ
ma-219	248	2	i∗vev	i∗vev	ADP
ma-219	248	3	ive∗v	ive∗v	NOUN
ma-219	249	1	+	+	CCONJ
ma-219	249	2	iv	iv	INTJ
ma-219	250	1	i	i	PRON
ma-219	250	2	∗	∗	NOUN
ma-219	250	3	h	h	PROPN
ma-219	250	4	i∗v	i∗v	VERB
ma-219	250	5	ih	ih	NOUN
ma-219	250	6	−	−	PROPN
ma-219	250	7	4	4	NUM
ma-219	250	8	]	]	PUNCT
ma-219	250	9	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	250	10	eur	eur	PROPN
ma-219	250	11	.	.	PUNCT
ma-219	251	1	j.	j.	PROPN
ma-219	251	2	math	math	PROPN
ma-219	251	3	.	.	PUNCT
ma-219	252	1	anal	anal	PROPN
ma-219	252	2	.	.	PUNCT
ma-219	253	1	10.28924	10.28924	NUM
ma-219	253	2	/	/	SYM
ma-219	253	3	ada	ada	PROPN
ma-219	253	4	/	/	SYM
ma-219	253	5	ma.4.9	ma.4.9	PROPN
ma-219	253	6	9	9	NUM
ma-219	253	7	conclusion	conclusion	NOUN
ma-219	253	8	:	:	PUNCT
ma-219	253	9	in	in	ADP
ma-219	253	10	this	this	DET
ma-219	253	11	article	article	NOUN
ma-219	253	12	,	,	PUNCT
ma-219	253	13	a	a	DET
ma-219	253	14	onchocerciasis	onchocerciasis	NOUN
ma-219	253	15	transmission	transmission	NOUN
ma-219	253	16	dynamics	dynamic	NOUN
ma-219	253	17	with	with	ADP
ma-219	253	18	vigilant	vigilant	ADJ
ma-219	253	19	compartmentgoverned	compartmentgoverne	VERB
ma-219	253	20	by	by	ADP
ma-219	253	21	system	system	NOUN
ma-219	253	22	of	of	ADP
ma-219	253	23	differential	differential	ADJ
ma-219	253	24	equations	equation	NOUN
ma-219	253	25	has	have	AUX
ma-219	253	26	been	be	AUX
ma-219	253	27	theoretically	theoretically	ADV
ma-219	253	28	analyzed	analyze	VERB
ma-219	253	29	.	.	PUNCT
ma-219	254	1	the	the	DET
ma-219	254	2	analysis	analysis	NOUN
ma-219	254	3	iscentered	iscentere	VERB
ma-219	254	4	on	on	ADP
ma-219	254	5	the	the	DET
ma-219	254	6	global	global	ADJ
ma-219	254	7	asymptotic	asymptotic	ADJ
ma-219	254	8	behavior	behavior	NOUN
ma-219	254	9	of	of	ADP
ma-219	254	10	solutions	solution	NOUN
ma-219	254	11	of	of	ADP
ma-219	254	12	the	the	DET
ma-219	254	13	system	system	NOUN
ma-219	254	14	(	(	PUNCT
ma-219	254	15	2.3	2.3	NUM
ma-219	254	16	)	)	PUNCT
ma-219	254	17	around	around	ADP
ma-219	254	18	the	the	DET
ma-219	254	19	disease	disease	NOUN
ma-219	254	20	-	-	PUNCT
ma-219	254	21	free	free	ADJ
ma-219	254	22	and	and	CCONJ
ma-219	254	23	endemic	endemic	ADJ
ma-219	254	24	equilibria	equilibrium	NOUN
ma-219	254	25	using	use	VERB
ma-219	254	26	lyapunov	lyapunov	ADJ
ma-219	254	27	functions	function	NOUN
ma-219	254	28	.	.	PUNCT
ma-219	255	1	the	the	DET
ma-219	255	2	system	system	NOUN
ma-219	255	3	has	have	VERB
ma-219	255	4	a	a	DET
ma-219	255	5	globally	globally	ADV
ma-219	255	6	asymptoticallystable	asymptoticallystable	ADJ
ma-219	255	7	disease	disease	NOUN
ma-219	255	8	-	-	PUNCT
ma-219	255	9	free	free	ADJ
ma-219	255	10	equilibrium	equilibrium	NOUN
ma-219	255	11	whenever	whenever	SCONJ
ma-219	255	12	the	the	DET
ma-219	255	13	basic	basic	ADJ
ma-219	255	14	reproduction	reproduction	NOUN
ma-219	255	15	r0	r0	NOUN
ma-219	255	16	<	<	X
ma-219	255	17	1	1	NUM
ma-219	255	18	.	.	PUNCT
ma-219	256	1	moreover	moreover	ADV
ma-219	256	2	,	,	PUNCT
ma-219	256	3	the	the	DET
ma-219	256	4	endemicequilibrium	endemicequilibrium	NOUN
ma-219	256	5	of	of	ADP
ma-219	256	6	the	the	DET
ma-219	256	7	system	system	NOUN
ma-219	256	8	,	,	PUNCT
ma-219	256	9	when	when	SCONJ
ma-219	256	10	it	it	PRON
ma-219	256	11	exists	exist	VERB
ma-219	256	12	,	,	PUNCT
ma-219	256	13	is	be	AUX
ma-219	256	14	shown	show	VERB
ma-219	256	15	to	to	PART
ma-219	256	16	be	be	AUX
ma-219	256	17	globally	globally	ADV
ma-219	256	18	asymptotically	asymptotically	ADV
ma-219	256	19	stable	stable	ADJ
ma-219	256	20	wheneverthe	wheneverthe	PROPN
ma-219	256	21	associated	associate	VERB
ma-219	256	22	basic	basic	ADJ
ma-219	256	23	reproduction	reproduction	NOUN
ma-219	256	24	number	number	NOUN
ma-219	256	25	r0	r0	NOUN
ma-219	256	26	>	>	X
ma-219	256	27	1	1	NUM
ma-219	256	28	.	.	PUNCT
ma-219	256	29	references	reference	NOUN
ma-219	256	30	[	[	X
ma-219	256	31	1	1	NUM
ma-219	256	32	]	]	X
ma-219	256	33	k.m	k.m	PROPN
ma-219	256	34	.	.	PROPN
ma-219	256	35	adeyemo	adeyemo	PROPN
ma-219	256	36	,	,	PUNCT
ma-219	256	37	local	local	ADJ
ma-219	256	38	stability	stability	NOUN
ma-219	256	39	of	of	ADP
ma-219	256	40	onchocerciasis	onchocerciasis	NOUN
ma-219	256	41	transmission	transmission	NOUN
ma-219	256	42	dynamics	dynamic	NOUN
ma-219	256	43	with	with	ADP
ma-219	256	44	nonlinear	nonlinear	ADJ
ma-219	256	45	incidence	incidence	NOUN
ma-219	256	46	functions	function	NOUN
ma-219	256	47	in	in	ADP
ma-219	256	48	twointeracting	twointeracting	NOUN
ma-219	256	49	populations	population	NOUN
ma-219	256	50	,	,	PUNCT
ma-219	256	51	eur	eur	PROPN
ma-219	256	52	.	.	PUNCT
ma-219	257	1	j.	j.	PROPN
ma-219	257	2	math	math	PROPN
ma-219	257	3	.	.	PUNCT
ma-219	258	1	anal	anal	ADJ
ma-219	258	2	.	.	PUNCT
ma-219	259	1	3	3	NUM
ma-219	259	2	(	(	PUNCT
ma-219	259	3	2023	2023	NUM
ma-219	259	4	)	)	PUNCT
ma-219	259	5	22.[2	22.[2	NUM
ma-219	259	6	]	]	X
ma-219	259	7	w.s	w.s	PROPN
ma-219	259	8	.	.	PROPN
ma-219	259	9	alley	alley	PROPN
ma-219	259	10	,	,	PUNCT
ma-219	259	11	b.a.b	b.a.b	PROPN
ma-219	259	12	.	.	PUNCT
ma-219	259	13	boatin	boatin	NOUN
ma-219	259	14	,	,	PUNCT
ma-219	259	15	n.j.d.n	n.j.d.n	PROPN
ma-219	259	16	.	.	PROPN
ma-219	259	17	nagelkerke	nagelkerke	PROPN
ma-219	259	18	,	,	PUNCT
ma-219	259	19	macrofilaricides	macrofilaricide	NOUN
ma-219	259	20	and	and	CCONJ
ma-219	259	21	onchocerciasis	onchocerciasis	NOUN
ma-219	259	22	control	control	NOUN
ma-219	259	23	,	,	PUNCT
ma-219	259	24	mathematical	mathematical	ADJ
ma-219	259	25	modellingof	modellingof	NOUN
ma-219	259	26	the	the	DET
ma-219	259	27	prospects	prospect	NOUN
ma-219	259	28	for	for	ADP
ma-219	259	29	elimination	elimination	NOUN
ma-219	259	30	,	,	PUNCT
ma-219	259	31	bmc	bmc	ADJ
ma-219	259	32	public	public	ADJ
ma-219	259	33	health	health	NOUN
ma-219	259	34	1	1	NUM
ma-219	259	35	(	(	PUNCT
ma-219	259	36	2001	2001	NUM
ma-219	259	37	)	)	PUNCT
ma-219	260	1	12.[3	12.[3	PROPN
ma-219	260	2	]	]	X
ma-219	260	3	u.	u.	PROPN
ma-219	260	4	amazigo	amazigo	PROPN
ma-219	260	5	,	,	PUNCT
ma-219	260	6	m.	m.	NOUN
ma-219	260	7	noma	noma	PROPN
ma-219	260	8	,	,	PUNCT
ma-219	260	9	j.	j.	PROPN
ma-219	260	10	bump	bump	PROPN
ma-219	260	11	,	,	PUNCT
ma-219	260	12	b.	b.	PROPN
ma-219	260	13	bentin	bentin	PROPN
ma-219	260	14	,	,	PUNCT
ma-219	260	15	b.	b.	PROPN
ma-219	260	16	liese	liese	PROPN
ma-219	260	17	,	,	PUNCT
ma-219	260	18	l.	l.	PROPN
ma-219	260	19	yameogo	yameogo	PROPN
ma-219	260	20	,	,	PUNCT
ma-219	260	21	h.	h.	PROPN
ma-219	260	22	zouré	zouré	PROPN
ma-219	260	23	,	,	PUNCT
ma-219	260	24	and	and	CCONJ
ma-219	260	25	a.	a.	NOUN
ma-219	260	26	seketeli	seketeli	NOUN
ma-219	260	27	,	,	PUNCT
ma-219	260	28	onchocerciasis	onchocerciasis	NOUN
ma-219	260	29	diseaseand	diseaseand	NOUN
ma-219	260	30	mortality	mortality	NOUN
ma-219	260	31	in	in	ADP
ma-219	260	32	sub	sub	PROPN
ma-219	260	33	saharan	saharan	PROPN
ma-219	260	34	africa	africa	PROPN
ma-219	260	35	,	,	PUNCT
ma-219	260	36	chapter	chapter	NOUN
ma-219	260	37	15	15	NUM
ma-219	260	38	,	,	PUNCT
ma-219	260	39	world	world	PROPN
ma-219	260	40	bank	bank	PROPN
ma-219	260	41	,	,	PUNCT
ma-219	260	42	washington	washington	PROPN
ma-219	260	43	,	,	PUNCT
ma-219	260	44	dc	dc	PROPN
ma-219	260	45	,	,	PUNCT
ma-219	260	46	2006.[4	2006.[4	NUM
ma-219	260	47	]	]	PUNCT
ma-219	260	48	a.	a.	NOUN
ma-219	260	49	hassan	hassan	PROPN
ma-219	260	50	,	,	PUNCT
ma-219	260	51	n.	n.	PROPN
ma-219	260	52	shaban	shaban	PROPN
ma-219	260	53	,	,	PUNCT
ma-219	260	54	onchocerciasis	onchocerciasis	NOUN
ma-219	260	55	dynamics	dynamic	NOUN
ma-219	260	56	:	:	PUNCT
ma-219	260	57	modelling	model	VERB
ma-219	260	58	the	the	DET
ma-219	260	59	effects	effect	NOUN
ma-219	260	60	of	of	ADP
ma-219	260	61	treatment	treatment	NOUN
ma-219	260	62	,	,	PUNCT
ma-219	260	63	education	education	NOUN
ma-219	260	64	and	and	CCONJ
ma-219	260	65	vector	vector	NOUN
ma-219	260	66	control	control	NOUN
ma-219	260	67	,	,	PUNCT
ma-219	260	68	j.	j.	PROPN
ma-219	260	69	biol	biol	PROPN
ma-219	260	70	.	.	PUNCT
ma-219	261	1	dyn	dyn	PROPN
ma-219	261	2	.	.	PUNCT
ma-219	262	1	14	14	NUM
ma-219	262	2	(	(	PUNCT
ma-219	262	3	2020	2020	NUM
ma-219	262	4	)	)	PUNCT
ma-219	262	5	245	245	NUM
ma-219	262	6	-	-	SYM
ma-219	262	7	268.[5	268.[5	NUM
ma-219	262	8	]	]	PUNCT
ma-219	262	9	c.	c.	PROPN
ma-219	262	10	castillo	castillo	PROPN
ma-219	262	11	-	-	PUNCT
ma-219	262	12	chavez	chavez	PROPN
ma-219	262	13	,	,	PUNCT
ma-219	262	14	b.	b.	PROPN
ma-219	262	15	song	song	PROPN
ma-219	262	16	,	,	PUNCT
ma-219	262	17	dynamical	dynamical	ADJ
ma-219	262	18	models	model	NOUN
ma-219	262	19	of	of	ADP
ma-219	262	20	tuberculosis	tuberculosis	NOUN
ma-219	262	21	and	and	CCONJ
ma-219	262	22	their	their	PRON
ma-219	262	23	applications	application	NOUN
ma-219	262	24	,	,	PUNCT
ma-219	262	25	math	math	NOUN
ma-219	262	26	.	.	PUNCT
ma-219	263	1	biosci	biosci	PROPN
ma-219	263	2	.	.	PUNCT
ma-219	264	1	eng	eng	PROPN
ma-219	264	2	.	.	PROPN
ma-219	264	3	1	1	NUM
ma-219	264	4	(	(	PUNCT
ma-219	264	5	2004)361	2004)361	NOUN
ma-219	264	6	-	-	SYM
ma-219	264	7	404.[6	404.[6	NUM
ma-219	264	8	]	]	X
ma-219	264	9	p.	p.	NOUN
ma-219	264	10	georgescu	georgescu	PROPN
ma-219	264	11	,	,	PUNCT
ma-219	264	12	h.	h.	PROPN
ma-219	264	13	zhang	zhang	PROPN
ma-219	264	14	,	,	PUNCT
ma-219	264	15	a	a	DET
ma-219	264	16	lyapunov	lyapunov	ADJ
ma-219	264	17	functional	functional	NOUN
ma-219	264	18	for	for	ADP
ma-219	264	19	a	a	DET
ma-219	264	20	siri	siri	NOUN
ma-219	264	21	model	model	NOUN
ma-219	264	22	with	with	ADP
ma-219	264	23	nonlinear	nonlinear	ADJ
ma-219	264	24	incidence	incidence	NOUN
ma-219	264	25	of	of	ADP
ma-219	264	26	infection	infection	NOUN
ma-219	264	27	and	and	CCONJ
ma-219	264	28	relapse	relapse	NOUN
ma-219	264	29	,	,	PUNCT
ma-219	264	30	appl	appl	PROPN
ma-219	264	31	.	.	PROPN
ma-219	264	32	math	math	PROPN
ma-219	264	33	.	.	PUNCT
ma-219	265	1	comp	comp	NOUN
ma-219	265	2	.	.	PUNCT
ma-219	266	1	219	219	NUM
ma-219	266	2	(	(	PUNCT
ma-219	266	3	2013	2013	NUM
ma-219	266	4	)	)	PUNCT
ma-219	266	5	8496	8496	NUM
ma-219	266	6	-	-	SYM
ma-219	266	7	8507.[7	8507.[7	NUM
ma-219	266	8	]	]	X
ma-219	266	9	j.p	j.p	PROPN
ma-219	266	10	.	.	PROPN
ma-219	266	11	lasalle	lasalle	PROPN
ma-219	266	12	,	,	PUNCT
ma-219	266	13	the	the	DET
ma-219	266	14	stability	stability	NOUN
ma-219	266	15	of	of	ADP
ma-219	266	16	dynamical	dynamical	ADJ
ma-219	266	17	systems	system	NOUN
ma-219	266	18	,	,	PUNCT
ma-219	266	19	siam	siam	PROPN
ma-219	266	20	,	,	PUNCT
ma-219	266	21	philadelphia	philadelphia	PROPN
ma-219	266	22	,	,	PUNCT
ma-219	266	23	1976.[8	1976.[8	NUM
ma-219	266	24	]	]	X
ma-219	267	1	e.m	e.m	PROPN
ma-219	267	2	.	.	PROPN
ma-219	267	3	poolman	poolman	PROPN
ma-219	267	4	,	,	PUNCT
ma-219	267	5	a.p	a.p	PROPN
ma-219	267	6	.	.	PROPN
ma-219	267	7	galvani	galvani	PROPN
ma-219	267	8	,	,	PUNCT
ma-219	267	9	modeling	model	VERB
ma-219	267	10	targeted	target	VERB
ma-219	267	11	ivermectin	ivermectin	NOUN
ma-219	267	12	treatment	treatment	NOUN
ma-219	267	13	for	for	ADP
ma-219	267	14	controlling	control	VERB
ma-219	267	15	river	river	NOUN
ma-219	267	16	blindness	blindness	NOUN
ma-219	267	17	,	,	PUNCT
ma-219	267	18	amer	amer	PROPN
ma-219	267	19	.	.	PUNCT
ma-219	268	1	j.	j.	PROPN
ma-219	268	2	trop.med	trop.med	PROPN
ma-219	268	3	.	.	PUNCT
ma-219	269	1	hyg	hyg	PROPN
ma-219	269	2	.	.	PROPN
ma-219	269	3	75	75	NUM
ma-219	269	4	(	(	PUNCT
ma-219	269	5	2006	2006	NUM
ma-219	269	6	)	)	PUNCT
ma-219	269	7	921–927.[9	921–927.[9	NUM
ma-219	269	8	]	]	X
ma-219	269	9	j.p	j.p	PROPN
ma-219	269	10	.	.	PROPN
ma-219	269	11	mopecha	mopecha	PROPN
ma-219	269	12	,	,	PUNCT
ma-219	269	13	h.r	h.r	PROPN
ma-219	269	14	.	.	PROPN
ma-219	269	15	thieme	thieme	NOUN
ma-219	269	16	,	,	PUNCT
ma-219	269	17	competitive	competitive	ADJ
ma-219	269	18	dynamics	dynamic	NOUN
ma-219	269	19	in	in	ADP
ma-219	269	20	a	a	DET
ma-219	269	21	model	model	NOUN
ma-219	269	22	for	for	ADP
ma-219	269	23	onchocerciasis	onchocerciasis	NOUN
ma-219	269	24	with	with	ADP
ma-219	269	25	cross	cross	NOUN
ma-219	269	26	-	-	NOUN
ma-219	269	27	immunity	immunity	NOUN
ma-219	269	28	,	,	PUNCT
ma-219	269	29	canad	canad	PROPN
ma-219	269	30	.	.	PUNCT
ma-219	270	1	appl.math	appl.math	NOUN
ma-219	270	2	.	.	PUNCT
ma-219	270	3	q.	q.	PROPN
ma-219	270	4	11	11	NUM
ma-219	270	5	(	(	PUNCT
ma-219	270	6	2003	2003	NUM
ma-219	270	7	)	)	PUNCT
ma-219	270	8	339–376.[10	339–376.[10	NUM
ma-219	270	9	]	]	X
ma-219	270	10	m.g	m.g	PROPN
ma-219	270	11	.	.	PROPN
ma-219	270	12	basáñez	basáñez	PROPN
ma-219	270	13	,	,	PUNCT
ma-219	270	14	m.	m.	NOUN
ma-219	270	15	boussinesq	boussinesq	PROPN
ma-219	270	16	,	,	PUNCT
ma-219	270	17	population	population	NOUN
ma-219	270	18	biology	biology	NOUN
ma-219	270	19	of	of	ADP
ma-219	270	20	human	human	ADJ
ma-219	270	21	onchocerciasis	onchocerciasis	NOUN
ma-219	270	22	,	,	PUNCT
ma-219	270	23	phil	phil	PROPN
ma-219	270	24	.	.	PUNCT
ma-219	271	1	trans	trans	PROPN
ma-219	271	2	.	.	PUNCT
ma-219	271	3	r.	r.	PROPN
ma-219	271	4	soc	soc	PROPN
ma-219	271	5	.	.	PUNCT
ma-219	272	1	lond	lond	PROPN
ma-219	272	2	.	.	PUNCT
ma-219	273	1	b	b	X
ma-219	273	2	:	:	PUNCT
ma-219	273	3	biol	biol	PROPN
ma-219	273	4	.	.	PUNCT
ma-219	274	1	sci.354	sci.354	PROPN
ma-219	274	2	(	(	PUNCT
ma-219	274	3	1999	1999	NUM
ma-219	274	4	)	)	PUNCT
ma-219	274	5	809–826.[11	809–826.[11	PROPN
ma-219	274	6	]	]	X
ma-219	274	7	m.g	m.g	PROPN
ma-219	274	8	.	.	PROPN
ma-219	274	9	basáñez	basáñez	PROPN
ma-219	274	10	,	,	PUNCT
ma-219	274	11	j.	j.	PROPN
ma-219	274	12	ricárdez	ricárdez	PROPN
ma-219	274	13	-	-	PUNCT
ma-219	274	14	esquinca	esquinca	NOUN
ma-219	274	15	,	,	PUNCT
ma-219	274	16	models	model	NOUN
ma-219	274	17	for	for	ADP
ma-219	274	18	the	the	DET
ma-219	274	19	population	population	NOUN
ma-219	274	20	biology	biology	NOUN
ma-219	274	21	and	and	CCONJ
ma-219	274	22	control	control	NOUN
ma-219	274	23	of	of	ADP
ma-219	274	24	human	human	ADJ
ma-219	274	25	onchocerciasis	onchocerciasis	NOUN
ma-219	274	26	,	,	PUNCT
ma-219	274	27	trendsparasitol	trendsparasitol	ADJ
ma-219	274	28	.	.	PUNCT
ma-219	275	1	17	17	NUM
ma-219	275	2	(	(	PUNCT
ma-219	275	3	2001	2001	NUM
ma-219	275	4	)	)	PUNCT
ma-219	275	5	430–438.[12	430–438.[12	PROPN
ma-219	275	6	]	]	X
ma-219	275	7	j.d	j.d	PROPN
ma-219	275	8	.	.	PROPN
ma-219	275	9	murray	murray	PROPN
ma-219	275	10	,	,	PUNCT
ma-219	275	11	mathematical	mathematical	ADJ
ma-219	275	12	biology	biology	NOUN
ma-219	275	13	i.	i.	NOUN
ma-219	275	14	,	,	PUNCT
ma-219	275	15	an	an	DET
ma-219	275	16	introduction	introduction	NOUN
ma-219	275	17	.	.	PUNCT
ma-219	276	1	3rd	3rd	ADJ
ma-219	276	2	ed	ed	NOUN
ma-219	276	3	.	.	PUNCT
ma-219	276	4	springer	springer	NOUN
ma-219	276	5	-	-	PUNCT
ma-219	276	6	verlag	verlag	PROPN
ma-219	276	7	,	,	PUNCT
ma-219	276	8	berlin	berlin	PROPN
ma-219	276	9	,	,	PUNCT
ma-219	276	10	2002.[13	2002.[13	PROPN
ma-219	276	11	]	]	X
ma-219	276	12	a.p	a.p	PROPN
ma-219	276	13	.	.	PROPN
ma-219	276	14	plaisier	plaisier	PROPN
ma-219	276	15	,	,	PUNCT
ma-219	276	16	e.s	e.s	PROPN
ma-219	276	17	.	.	PROPN
ma-219	276	18	alley	alley	PROPN
ma-219	276	19	,	,	PUNCT
ma-219	276	20	g.j	g.j	PROPN
ma-219	276	21	.	.	PROPN
ma-219	276	22	van	van	PROPN
ma-219	276	23	oortmarssen	oortmarssen	PROPN
ma-219	276	24	,	,	PUNCT
ma-219	276	25	b.a	b.a	PROPN
ma-219	276	26	.	.	PROPN
ma-219	276	27	boatin	boatin	PROPN
ma-219	276	28	,	,	PUNCT
ma-219	276	29	j.d.f	j.d.f	ADJ
ma-219	276	30	habbema	habbema	NOUN
ma-219	276	31	,	,	PUNCT
ma-219	276	32	required	require	VERB
ma-219	276	33	duration	duration	NOUN
ma-219	276	34	of	of	ADP
ma-219	276	35	combined	combine	VERB
ma-219	276	36	annualivermectin	annualivermectin	NOUN
ma-219	276	37	treatment	treatment	NOUN
ma-219	276	38	and	and	CCONJ
ma-219	276	39	vector	vector	NOUN
ma-219	276	40	control	control	NOUN
ma-219	276	41	program	program	NOUN
ma-219	276	42	in	in	ADP
ma-219	276	43	west	west	PROPN
ma-219	276	44	africa	africa	PROPN
ma-219	276	45	,	,	PUNCT
ma-219	276	46	bull	bull	PROPN
ma-219	276	47	.	.	PUNCT
ma-219	277	1	world	world	PROPN
ma-219	277	2	health	health	NOUN
ma-219	277	3	organ	organ	NOUN
ma-219	277	4	.	.	PUNCT
ma-219	278	1	75	75	NUM
ma-219	278	2	(	(	PUNCT
ma-219	278	3	1997	1997	NUM
ma-219	278	4	)	)	PUNCT
ma-219	279	1	237.[14	237.[14	NUM
ma-219	279	2	]	]	X
ma-219	279	3	j.	j.	PROPN
ma-219	279	4	remme	remme	PROPN
ma-219	279	5	,	,	PUNCT
ma-219	279	6	g.	g.	PROPN
ma-219	279	7	de	de	X
ma-219	279	8	sole	sole	PROPN
ma-219	279	9	,	,	PUNCT
ma-219	279	10	g.j	g.j	PROPN
ma-219	279	11	.	.	PROPN
ma-219	279	12	van	van	PROPN
ma-219	279	13	oortmarssen	oortmarssen	PROPN
ma-219	279	14	,	,	PUNCT
ma-219	279	15	the	the	DET
ma-219	279	16	predicted	predict	VERB
ma-219	279	17	and	and	CCONJ
ma-219	279	18	observed	observed	ADJ
ma-219	279	19	decline	decline	NOUN
ma-219	279	20	in	in	ADP
ma-219	279	21	onchocerciasis	onchocerciasis	NOUN
ma-219	279	22	infection	infection	NOUN
ma-219	279	23	during14	during14	NOUN
ma-219	279	24	years	year	NOUN
ma-219	279	25	of	of	ADP
ma-219	279	26	successful	successful	ADJ
ma-219	279	27	control	control	NOUN
ma-219	279	28	of	of	ADP
ma-219	279	29	black	black	ADJ
ma-219	279	30	flies	fly	NOUN
ma-219	279	31	in	in	ADP
ma-219	279	32	west	west	PROPN
ma-219	279	33	africa	africa	PROPN
ma-219	279	34	,	,	PUNCT
ma-219	279	35	bull	bull	PROPN
ma-219	279	36	.	.	PUNCT
ma-219	280	1	world	world	PROPN
ma-219	280	2	health	health	NOUN
ma-219	280	3	organ	organ	NOUN
ma-219	280	4	.	.	PUNCT
ma-219	281	1	68	68	NUM
ma-219	281	2	(	(	PUNCT
ma-219	281	3	1990	1990	NUM
ma-219	281	4	)	)	PUNCT
ma-219	281	5	331–339.[15	331–339.[15	PROPN
ma-219	281	6	]	]	X
ma-219	281	7	m.a	m.a	PROPN
ma-219	281	8	.	.	PROPN
ma-219	281	9	safi	safi	PROPN
ma-219	281	10	,	,	PUNCT
ma-219	281	11	s.m	s.m	PROPN
ma-219	281	12	.	.	PROPN
ma-219	281	13	garba	garba	PROPN
ma-219	281	14	,	,	PUNCT
ma-219	281	15	global	global	ADJ
ma-219	281	16	stability	stability	NOUN
ma-219	281	17	analysis	analysis	NOUN
ma-219	281	18	of	of	ADP
ma-219	281	19	seir	seir	ADJ
ma-219	281	20	model	model	NOUN
ma-219	281	21	with	with	ADP
ma-219	281	22	holling	holle	VERB
ma-219	281	23	type	type	NOUN
ma-219	281	24	ii	ii	NOUN
ma-219	281	25	incidence	incidence	NOUN
ma-219	281	26	function	function	NOUN
ma-219	281	27	,	,	PUNCT
ma-219	281	28	comp	comp	NOUN
ma-219	281	29	.	.	PUNCT
ma-219	282	1	math.meth	math.meth	PROPN
ma-219	282	2	.	.	PROPN
ma-219	282	3	med	med	PROPN
ma-219	282	4	.	.	PUNCT
ma-219	282	5	2012	2012	NUM
ma-219	282	6	(	(	PUNCT
ma-219	282	7	2012	2012	NUM
ma-219	282	8	)	)	PUNCT
ma-219	283	1	826052.[16	826052.[16	PROPN
ma-219	283	2	]	]	X
ma-219	283	3	s.i	s.i	PROPN
ma-219	283	4	.	.	PROPN
ma-219	283	5	omade	omade	PROPN
ma-219	283	6	,	,	PUNCT
ma-219	283	7	a.t	a.t	PROPN
ma-219	283	8	.	.	PROPN
ma-219	283	9	omotunde	omotunde	PROPN
ma-219	283	10	,	,	PUNCT
ma-219	283	11	a.s	a.s	PROPN
ma-219	283	12	.	.	PROPN
ma-219	283	13	gbenga	gbenga	PROPN
ma-219	283	14	,	,	PUNCT
ma-219	283	15	mathematical	mathematical	ADJ
ma-219	283	16	modeling	modeling	NOUN
ma-219	283	17	of	of	ADP
ma-219	283	18	river	river	NOUN
ma-219	283	19	blindness	blindness	NOUN
ma-219	283	20	disease	disease	NOUN
ma-219	283	21	with	with	ADP
ma-219	283	22	demography	demography	NOUN
ma-219	283	23	usingeuler	usingeuler	PROPN
ma-219	283	24	method	method	PROPN
ma-219	283	25	,	,	PUNCT
ma-219	283	26	math	math	NOUN
ma-219	283	27	.	.	PUNCT
ma-219	284	1	theory	theory	NOUN
ma-219	284	2	model	model	NOUN
ma-219	284	3	.	.	PROPN
ma-219	285	1	5	5	NUM
ma-219	285	2	(	(	PUNCT
ma-219	285	3	2015	2015	NUM
ma-219	285	4	)	)	PUNCT
ma-219	286	1	75–85.[17	75–85.[17	NUM
ma-219	286	2	]	]	PUNCT
ma-219	286	3	world	world	PROPN
ma-219	286	4	health	health	NOUN
ma-219	286	5	organization	organization	NOUN
ma-219	286	6	,	,	PUNCT
ma-219	286	7	african	african	ADJ
ma-219	286	8	programme	programme	NOUN
ma-219	286	9	for	for	ADP
ma-219	286	10	onchocerciasis	onchocerciasis	NOUN
ma-219	286	11	control	control	NOUN
ma-219	286	12	:	:	PUNCT
ma-219	286	13	meeting	meeting	NOUN
ma-219	286	14	of	of	ADP
ma-219	286	15	national	national	ADJ
ma-219	286	16	onchocerciasis	onchocerciasis	NOUN
ma-219	286	17	taskforces	taskforce	NOUN
ma-219	286	18	,	,	PUNCT
ma-219	286	19	september	september	PROPN
ma-219	286	20	2012	2012	NUM
ma-219	286	21	,	,	PUNCT
ma-219	286	22	weekly	weekly	ADJ
ma-219	286	23	epidemiol	epidemiol	NOUN
ma-219	286	24	.	.	PUNCT
ma-219	287	1	record	record	NOUN
ma-219	287	2	87	87	NUM
ma-219	287	3	(	(	PUNCT
ma-219	287	4	2012	2012	NUM
ma-219	287	5	)	)	PUNCT
ma-219	287	6	494–502	494–502	NUM
ma-219	287	7	.	.	PUNCT
ma-219	288	1	https://doi.org/10.28924/ada/ma.4.9	https://doi.org/10.28924/ada/ma.4.9	PROPN
ma-219	288	2	1	1	NUM
ma-219	288	3	.	.	PUNCT
ma-219	289	1	introduction	introduction	NOUN
ma-219	289	2	2	2	NUM
ma-219	289	3	.	.	PUNCT
ma-219	289	4	model	model	NOUN
ma-219	289	5	description	description	NOUN
ma-219	289	6	3	3	X
ma-219	289	7	.	.	PUNCT
ma-219	289	8	global	global	ADJ
ma-219	289	9	stability	stability	NOUN
ma-219	289	10	analysis	analysis	NOUN
ma-219	289	11	3.1	3.1	NUM
ma-219	289	12	.	.	PUNCT
ma-219	290	1	global	global	ADJ
ma-219	290	2	stability	stability	NOUN
ma-219	290	3	of	of	ADP
ma-219	290	4	disease	disease	NOUN
ma-219	290	5	-	-	PUNCT
ma-219	290	6	free	free	ADJ
ma-219	290	7	equilibrium	equilibrium	NOUN
ma-219	290	8	references	reference	NOUN