id	sid	tid	token	lemma	pos
ma-168	1	1	2023	2023	NUM
ma-168	1	2	ada	ada	PROPN
ma-168	1	3	academica	academica	PROPN
ma-168	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-168	1	5	.	.	PUNCT
ma-168	2	1	j.	j.	PROPN
ma-168	2	2	math	math	PROPN
ma-168	2	3	.	.	PUNCT
ma-168	3	1	anal	anal	ADJ
ma-168	3	2	.	.	PUNCT
ma-168	4	1	3	3	NUM
ma-168	4	2	(	(	PUNCT
ma-168	4	3	2023	2023	NUM
ma-168	4	4	)	)	PUNCT
ma-168	4	5	22doi	22doi	NOUN
ma-168	4	6	:	:	PUNCT
ma-168	4	7	10.28924	10.28924	NUM
ma-168	4	8	/	/	SYM
ma-168	4	9	ada	ada	PROPN
ma-168	4	10	/	/	SYM
ma-168	4	11	ma.3.22	ma.3.22	PROPN
ma-168	4	12	local	local	ADJ
ma-168	4	13	stability	stability	NOUN
ma-168	4	14	analysis	analysis	NOUN
ma-168	4	15	of	of	ADP
ma-168	4	16	onchocerciasis	onchocerciasis	NOUN
ma-168	4	17	transmission	transmission	NOUN
ma-168	4	18	dynamics	dynamic	NOUN
ma-168	4	19	with	with	ADP
ma-168	4	20	nonlinear	nonlinear	ADJ
ma-168	4	21	incidence	incidence	NOUN
ma-168	4	22	functions	function	NOUN
ma-168	4	23	in	in	ADP
ma-168	4	24	two	two	NUM
ma-168	4	25	interacting	interact	VERB
ma-168	4	26	populations	population	NOUN
ma-168	4	27	k.	k.	PROPN
ma-168	4	28	m.	m.	PROPN
ma-168	4	29	adeyemo	adeyemo	PROPN
ma-168	4	30	department	department	PROPN
ma-168	4	31	of	of	ADP
ma-168	4	32	mathematics	mathematics	PROPN
ma-168	4	33	,	,	PUNCT
ma-168	4	34	hallmark	hallmark	ADJ
ma-168	4	35	university	university	NOUN
ma-168	4	36	ijebu	ijebu	NOUN
ma-168	4	37	-	-	PUNCT
ma-168	4	38	itele	itele	PROPN
ma-168	4	39	,	,	PUNCT
ma-168	4	40	ogun	ogun	PROPN
ma-168	4	41	state	state	PROPN
ma-168	4	42	,	,	PUNCT
ma-168	4	43	nigeria	nigeria	PROPN
ma-168	4	44	∗correspondence	∗correspondence	NOUN
ma-168	4	45	:	:	PUNCT
ma-168	4	46	mikyade2019@gmail.com	mikyade2019@gmail.com	X
ma-168	4	47	abstract	abstract	PROPN
ma-168	4	48	.	.	PUNCT
ma-168	5	1	a	a	DET
ma-168	5	2	deterministic	deterministic	ADJ
ma-168	5	3	compartmental	compartmental	NOUN
ma-168	5	4	model	model	NOUN
ma-168	5	5	for	for	ADP
ma-168	5	6	the	the	DET
ma-168	5	7	transmission	transmission	NOUN
ma-168	5	8	dynamics	dynamic	NOUN
ma-168	5	9	of	of	ADP
ma-168	5	10	onchocerciasis	onchocerciasis	NOUN
ma-168	5	11	withnonlinear	withnonlinear	NOUN
ma-168	5	12	incidence	incidence	NOUN
ma-168	5	13	functions	function	NOUN
ma-168	5	14	in	in	ADP
ma-168	5	15	two	two	NUM
ma-168	5	16	interacting	interact	VERB
ma-168	5	17	populations	population	NOUN
ma-168	5	18	is	be	AUX
ma-168	5	19	studied	study	VERB
ma-168	5	20	.	.	PUNCT
ma-168	6	1	the	the	DET
ma-168	6	2	model	model	NOUN
ma-168	6	3	is	be	AUX
ma-168	6	4	qualitatively	qualitatively	ADV
ma-168	6	5	an	an	PRON
ma-168	6	6	-	-	PUNCT
ma-168	6	7	alyzed	alyze	VERB
ma-168	6	8	to	to	PART
ma-168	6	9	investigate	investigate	VERB
ma-168	6	10	its	its	PRON
ma-168	6	11	local	local	ADJ
ma-168	6	12	asymptotic	asymptotic	ADJ
ma-168	6	13	behavior	behavior	NOUN
ma-168	6	14	with	with	ADP
ma-168	6	15	respect	respect	NOUN
ma-168	6	16	to	to	ADP
ma-168	6	17	disease	disease	NOUN
ma-168	6	18	-	-	PUNCT
ma-168	6	19	free	free	ADJ
ma-168	6	20	and	and	CCONJ
ma-168	6	21	endemic	endemic	ADJ
ma-168	6	22	equilibria.it	equilibria.it	PRON
ma-168	6	23	is	be	AUX
ma-168	6	24	shown	show	VERB
ma-168	6	25	,	,	PUNCT
ma-168	6	26	using	use	VERB
ma-168	6	27	routh	routh	PROPN
ma-168	6	28	-	-	PUNCT
ma-168	6	29	hurwitz	hurwitz	PROPN
ma-168	6	30	criteria	criterion	NOUN
ma-168	6	31	,	,	PUNCT
ma-168	6	32	that	that	SCONJ
ma-168	6	33	the	the	DET
ma-168	6	34	disease	disease	NOUN
ma-168	6	35	-	-	PUNCT
ma-168	6	36	free	free	ADJ
ma-168	6	37	equilibrium	equilibrium	NOUN
ma-168	6	38	is	be	AUX
ma-168	6	39	locally	locally	ADV
ma-168	6	40	asymptoticallystable	asymptoticallystable	ADJ
ma-168	6	41	when	when	SCONJ
ma-168	6	42	the	the	DET
ma-168	6	43	associated	associated	ADJ
ma-168	6	44	basic	basic	ADJ
ma-168	6	45	reproduction	reproduction	NOUN
ma-168	6	46	number	number	NOUN
ma-168	6	47	is	be	AUX
ma-168	6	48	less	less	ADJ
ma-168	6	49	than	than	ADP
ma-168	6	50	the	the	DET
ma-168	6	51	unity	unity	NOUN
ma-168	6	52	.	.	PUNCT
ma-168	7	1	when	when	SCONJ
ma-168	7	2	the	the	DET
ma-168	7	3	basic	basic	ADJ
ma-168	7	4	repro	repro	NOUN
ma-168	7	5	-	-	PUNCT
ma-168	7	6	duction	duction	NOUN
ma-168	7	7	number	number	NOUN
ma-168	7	8	is	be	AUX
ma-168	7	9	greater	great	ADJ
ma-168	7	10	than	than	ADP
ma-168	7	11	the	the	DET
ma-168	7	12	unity	unity	NOUN
ma-168	7	13	,	,	PUNCT
ma-168	7	14	we	we	PRON
ma-168	7	15	prove	prove	VERB
ma-168	7	16	the	the	DET
ma-168	7	17	existence	existence	NOUN
ma-168	7	18	of	of	ADP
ma-168	7	19	a	a	DET
ma-168	7	20	locally	locally	ADV
ma-168	7	21	asymptotically	asymptotically	ADV
ma-168	7	22	stableendemic	stableendemic	ADJ
ma-168	7	23	equilibrium	equilibrium	NOUN
ma-168	7	24	.	.	PUNCT
ma-168	8	1	1	1	X
ma-168	8	2	.	.	X
ma-168	8	3	introduction	introduction	NOUN
ma-168	8	4	onchocerciasis	onchocerciasis	NOUN
ma-168	8	5	is	be	AUX
ma-168	8	6	one	one	NUM
ma-168	8	7	of	of	ADP
ma-168	8	8	the	the	DET
ma-168	8	9	neglected	neglect	VERB
ma-168	8	10	tropical	tropical	ADJ
ma-168	8	11	diseases	disease	NOUN
ma-168	8	12	caused	cause	VERB
ma-168	8	13	by	by	ADP
ma-168	8	14	the	the	DET
ma-168	8	15	parasite	parasite	NOUN
ma-168	8	16	onchocercavolvulus	onchocercavolvulus	ADJ
ma-168	8	17	,	,	PUNCT
ma-168	8	18	a	a	DET
ma-168	8	19	filarial	filarial	ADJ
ma-168	8	20	nematode	nematode	NOUN
ma-168	8	21	[	[	X
ma-168	8	22	2	2	NUM
ma-168	8	23	]	]	PUNCT
ma-168	8	24	.	.	PUNCT
ma-168	9	1	the	the	DET
ma-168	9	2	disease	disease	NOUN
ma-168	9	3	is	be	AUX
ma-168	9	4	transmitted	transmit	VERB
ma-168	9	5	from	from	ADP
ma-168	9	6	one	one	NUM
ma-168	9	7	person	person	NOUN
ma-168	9	8	to	to	ADP
ma-168	9	9	another	another	PRON
ma-168	9	10	by	by	ADP
ma-168	9	11	repeatedbites	repeatedbite	NOUN
ma-168	9	12	of	of	ADP
ma-168	9	13	black	black	ADJ
ma-168	9	14	flies	fly	NOUN
ma-168	9	15	.	.	PUNCT
ma-168	10	1	the	the	DET
ma-168	10	2	disease	disease	NOUN
ma-168	10	3	is	be	AUX
ma-168	10	4	endemic	endemic	ADJ
ma-168	10	5	in	in	ADP
ma-168	10	6	sub	sub	ADJ
ma-168	10	7	-	-	ADJ
ma-168	10	8	saharan	saharan	ADJ
ma-168	10	9	africa	africa	PROPN
ma-168	10	10	.	.	PUNCT
ma-168	11	1	many	many	ADJ
ma-168	11	2	researchers	researcher	NOUN
ma-168	11	3	have	have	AUX
ma-168	11	4	workedon	workedon	ADJ
ma-168	11	5	many	many	ADJ
ma-168	11	6	ways	way	NOUN
ma-168	11	7	to	to	PART
ma-168	11	8	reduce	reduce	VERB
ma-168	11	9	the	the	DET
ma-168	11	10	spread	spread	NOUN
ma-168	11	11	of	of	ADP
ma-168	11	12	the	the	DET
ma-168	11	13	disease	disease	NOUN
ma-168	11	14	.	.	PUNCT
ma-168	12	1	for	for	ADP
ma-168	12	2	instance	instance	NOUN
ma-168	12	3	,	,	PUNCT
ma-168	12	4	remme	remme	VERB
ma-168	12	5	et	et	PROPN
ma-168	12	6	al	al	PROPN
ma-168	12	7	.	.	PUNCT
ma-168	13	1	[	[	X
ma-168	13	2	10	10	NUM
ma-168	13	3	]	]	PUNCT
ma-168	13	4	used	use	VERB
ma-168	13	5	skin	skin	NOUN
ma-168	13	6	snipsurvey	snipsurvey	NOUN
ma-168	13	7	in	in	ADP
ma-168	13	8	west	west	PROPN
ma-168	13	9	africa	africa	PROPN
ma-168	13	10	to	to	PART
ma-168	13	11	investigate	investigate	VERB
ma-168	13	12	the	the	DET
ma-168	13	13	impact	impact	NOUN
ma-168	13	14	of	of	ADP
ma-168	13	15	controlling	control	VERB
ma-168	13	16	black	black	ADJ
ma-168	13	17	flies	fly	NOUN
ma-168	13	18	by	by	ADP
ma-168	13	19	larviciding	larvicide	VERB
ma-168	13	20	.	.	PUNCT
ma-168	14	1	plaisieret	plaisieret	PROPN
ma-168	14	2	al	al	PROPN
ma-168	14	3	.	.	PUNCT
ma-168	15	1	[	[	X
ma-168	15	2	9	9	NUM
ma-168	15	3	]	]	PUNCT
ma-168	15	4	used	use	VERB
ma-168	15	5	micro	micro	PROPN
ma-168	15	6	simulation	simulation	PROPN
ma-168	15	7	model	model	PROPN
ma-168	15	8	to	to	PART
ma-168	15	9	determine	determine	VERB
ma-168	15	10	the	the	DET
ma-168	15	11	period	period	NOUN
ma-168	15	12	required	require	VERB
ma-168	15	13	for	for	ADP
ma-168	15	14	combining	combine	VERB
ma-168	15	15	annualivermectin	annualivermectin	NOUN
ma-168	15	16	treatment	treatment	NOUN
ma-168	15	17	and	and	CCONJ
ma-168	15	18	vector	vector	NOUN
ma-168	15	19	control	control	NOUN
ma-168	15	20	in	in	ADP
ma-168	15	21	the	the	DET
ma-168	15	22	onchocerciasis	onchocerciasis	NOUN
ma-168	15	23	control	control	NOUN
ma-168	15	24	programme	programme	NOUN
ma-168	15	25	in	in	ADP
ma-168	15	26	west	west	PROPN
ma-168	15	27	africa.alley	africa.alley	PROPN
ma-168	15	28	et	et	PROPN
ma-168	15	29	al	al	PROPN
ma-168	15	30	.	.	PUNCT
ma-168	16	1	[	[	X
ma-168	16	2	1	1	X
ma-168	16	3	]	]	PUNCT
ma-168	16	4	used	use	VERB
ma-168	16	5	a	a	DET
ma-168	16	6	computer	computer	NOUN
ma-168	16	7	simulation	simulation	NOUN
ma-168	16	8	model	model	NOUN
ma-168	16	9	to	to	PART
ma-168	16	10	study	study	VERB
ma-168	16	11	prevention	prevention	NOUN
ma-168	16	12	of	of	ADP
ma-168	16	13	onchocerciasis	onchocerciasis	NOUN
ma-168	16	14	by	by	ADP
ma-168	16	15	usingmacrofilaricide	usingmacrofilaricide	ADV
ma-168	16	16	which	which	PRON
ma-168	16	17	kills	kill	VERB
ma-168	16	18	the	the	DET
ma-168	16	19	adult	adult	NOUN
ma-168	16	20	worms	worm	NOUN
ma-168	16	21	.	.	PUNCT
ma-168	17	1	asha	asha	PROPN
ma-168	17	2	hassan	hassan	PROPN
ma-168	17	3	&	&	CCONJ
ma-168	17	4	nyimvua	nyimvua	PROPN
ma-168	17	5	shaban	shaban	PROPN
ma-168	18	1	[	[	X
ma-168	18	2	3	3	NUM
ma-168	18	3	]	]	PUNCT
ma-168	18	4	investigated	investigate	VERB
ma-168	18	5	theeffects	theeffect	NOUN
ma-168	18	6	of	of	ADP
ma-168	18	7	four	four	NUM
ma-168	18	8	control	control	NOUN
ma-168	18	9	strategies	strategy	NOUN
ma-168	18	10	on	on	ADP
ma-168	18	11	the	the	DET
ma-168	18	12	spread	spread	NOUN
ma-168	18	13	of	of	ADP
ma-168	18	14	the	the	DET
ma-168	18	15	disease.in	disease.in	PRON
ma-168	18	16	this	this	DET
ma-168	18	17	paper	paper	NOUN
ma-168	18	18	,	,	PUNCT
ma-168	18	19	we	we	PRON
ma-168	18	20	consider	consider	VERB
ma-168	18	21	onchocerciasis	onchocerciasis	NOUN
ma-168	18	22	transmission	transmission	NOUN
ma-168	18	23	dynamics	dynamic	NOUN
ma-168	18	24	with	with	ADP
ma-168	18	25	nonlinear	nonlinear	ADJ
ma-168	18	26	incidence	incidence	NOUN
ma-168	18	27	functions.the	functions.the	PRON
ma-168	18	28	human	human	ADJ
ma-168	18	29	population	population	NOUN
ma-168	18	30	is	be	AUX
ma-168	18	31	sub	sub	ADJ
ma-168	18	32	-	-	ADJ
ma-168	18	33	divided	divide	VERB
ma-168	18	34	into	into	ADP
ma-168	18	35	four	four	NUM
ma-168	18	36	compartments	compartment	NOUN
ma-168	18	37	and	and	CCONJ
ma-168	18	38	the	the	DET
ma-168	18	39	vector	vector	NOUN
ma-168	18	40	population	population	NOUN
ma-168	18	41	is	be	AUX
ma-168	18	42	sub	sub	ADJ
ma-168	18	43	-	-	ADJ
ma-168	18	44	divided	divide	VERB
ma-168	18	45	into	into	ADP
ma-168	18	46	three	three	NUM
ma-168	18	47	compartments	compartment	NOUN
ma-168	18	48	.	.	PUNCT
ma-168	19	1	we	we	PRON
ma-168	19	2	show	show	VERB
ma-168	19	3	local	local	ADJ
ma-168	19	4	asymptotic	asymptotic	ADJ
ma-168	19	5	behaviour	behaviour	NOUN
ma-168	19	6	in	in	ADP
ma-168	19	7	disease	disease	NOUN
ma-168	19	8	-	-	PUNCT
ma-168	19	9	free	free	ADJ
ma-168	19	10	and	and	CCONJ
ma-168	19	11	endemicequilibria	endemicequilibria	ADJ
ma-168	19	12	.	.	PUNCT
ma-168	20	1	the	the	DET
ma-168	20	2	rest	rest	NOUN
ma-168	20	3	of	of	ADP
ma-168	20	4	the	the	DET
ma-168	20	5	paper	paper	NOUN
ma-168	20	6	is	be	AUX
ma-168	20	7	organized	organize	VERB
ma-168	20	8	as	as	SCONJ
ma-168	20	9	follows	follow	VERB
ma-168	20	10	:	:	PUNCT
ma-168	20	11	the	the	DET
ma-168	20	12	description	description	NOUN
ma-168	20	13	of	of	ADP
ma-168	20	14	the	the	DET
ma-168	20	15	model	model	NOUN
ma-168	20	16	and	and	CCONJ
ma-168	20	17	theorems	theorem	NOUN
ma-168	20	18	received	receive	VERB
ma-168	20	19	:	:	PUNCT
ma-168	20	20	27	27	NUM
ma-168	20	21	apr	apr	NOUN
ma-168	20	22	2023	2023	NUM
ma-168	20	23	.	.	PUNCT
ma-168	21	1	key	key	ADJ
ma-168	21	2	words	word	NOUN
ma-168	21	3	and	and	CCONJ
ma-168	21	4	phrases	phrase	NOUN
ma-168	21	5	.	.	PUNCT
ma-168	22	1	basic	basic	ADJ
ma-168	22	2	reproduction	reproduction	NOUN
ma-168	22	3	number	number	NOUN
ma-168	22	4	;	;	PUNCT
ma-168	22	5	diseases	disease	NOUN
ma-168	22	6	free	free	ADJ
ma-168	22	7	equilibrium	equilibrium	NOUN
ma-168	22	8	;	;	PUNCT
ma-168	22	9	onchocerciasis	onchocerciasis	NOUN
ma-168	22	10	epidemic	epidemic	NOUN
ma-168	22	11	model	model	NOUN
ma-168	22	12	;	;	PUNCT
ma-168	22	13	non	non	ADJ
ma-168	22	14	-	-	ADJ
ma-168	22	15	linear	linear	ADJ
ma-168	22	16	incidence	incidence	NOUN
ma-168	22	17	function	function	NOUN
ma-168	22	18	.	.	PUNCT
ma-168	23	1	1	1	NUM
ma-168	24	1	https://adac.ee	https://adac.ee	PROPN
ma-168	24	2	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	24	3	eur	eur	PROPN
ma-168	24	4	.	.	PUNCT
ma-168	25	1	j.	j.	PROPN
ma-168	25	2	math	math	PROPN
ma-168	25	3	.	.	PUNCT
ma-168	26	1	anal	anal	PROPN
ma-168	26	2	.	.	PUNCT
ma-168	27	1	10.28924	10.28924	NUM
ma-168	27	2	/	/	SYM
ma-168	27	3	ada	ada	PROPN
ma-168	27	4	/	/	SYM
ma-168	27	5	ma.3.22	ma.3.22	NOUN
ma-168	27	6	2on	2on	NOUN
ma-168	27	7	positivity	positivity	NOUN
ma-168	27	8	of	of	ADP
ma-168	27	9	solutions	solution	NOUN
ma-168	27	10	are	be	AUX
ma-168	27	11	given	give	VERB
ma-168	27	12	in	in	ADP
ma-168	27	13	section	section	NOUN
ma-168	27	14	2	2	NUM
ma-168	27	15	while	while	SCONJ
ma-168	27	16	section	section	NOUN
ma-168	27	17	3	3	NUM
ma-168	27	18	is	be	AUX
ma-168	27	19	devoted	devote	VERB
ma-168	27	20	to	to	ADP
ma-168	27	21	the	the	DET
ma-168	27	22	proof	proof	ADJ
ma-168	27	23	local	local	ADJ
ma-168	27	24	stabilitytheorems	stabilitytheorem	NOUN
ma-168	27	25	.	.	PUNCT
ma-168	28	1	2	2	X
ma-168	28	2	.	.	X
ma-168	28	3	model	model	NOUN
ma-168	28	4	description	description	NOUN
ma-168	28	5	two	two	NUM
ma-168	28	6	interacting	interact	VERB
ma-168	28	7	populations	population	NOUN
ma-168	28	8	are	be	AUX
ma-168	28	9	considered	consider	VERB
ma-168	28	10	;	;	PUNCT
ma-168	28	11	the	the	DET
ma-168	28	12	humans	human	NOUN
ma-168	28	13	and	and	CCONJ
ma-168	28	14	the	the	DET
ma-168	28	15	black	black	ADJ
ma-168	28	16	-	-	PUNCT
ma-168	28	17	flies	fly	NOUN
ma-168	28	18	populations	population	NOUN
ma-168	28	19	.	.	PUNCT
ma-168	29	1	thehuman	thehuman	NOUN
ma-168	29	2	population	population	NOUN
ma-168	29	3	is	be	AUX
ma-168	29	4	partitioned	partition	VERB
ma-168	29	5	into	into	ADP
ma-168	29	6	four	four	NUM
ma-168	29	7	compartments	compartment	NOUN
ma-168	29	8	:	:	PUNCT
ma-168	29	9	the	the	DET
ma-168	29	10	susceptible	susceptible	ADJ
ma-168	29	11	human	human	ADJ
ma-168	29	12	compartment	compartment	NOUN
ma-168	29	13	;	;	PUNCT
ma-168	30	1	sh	sh	PROPN
ma-168	30	2	„	„	PUNCT
ma-168	30	3	the	the	DET
ma-168	30	4	exposed	expose	VERB
ma-168	30	5	compartment	compartment	NOUN
ma-168	30	6	;	;	PUNCT
ma-168	30	7	eh	eh	INTJ
ma-168	30	8	,	,	PUNCT
ma-168	30	9	the	the	DET
ma-168	30	10	infectious	infectious	ADJ
ma-168	30	11	human	human	ADJ
ma-168	30	12	compartment	compartment	NOUN
ma-168	30	13	;	;	PUNCT
ma-168	30	14	ih	ih	NOUN
ma-168	30	15	and	and	CCONJ
ma-168	30	16	the	the	DET
ma-168	30	17	recoveredhuman	recoveredhuman	NOUN
ma-168	30	18	compartment	compartment	NOUN
ma-168	30	19	;	;	PUNCT
ma-168	30	20	rh	rh	PROPN
ma-168	30	21	.	.	PUNCT
ma-168	31	1	the	the	DET
ma-168	31	2	black	black	ADJ
ma-168	31	3	-	-	PUNCT
ma-168	31	4	fly	fly	NOUN
ma-168	31	5	population	population	NOUN
ma-168	31	6	is	be	AUX
ma-168	31	7	partitioned	partition	VERB
ma-168	31	8	into	into	ADP
ma-168	31	9	three	three	NUM
ma-168	31	10	compartments	compartment	NOUN
ma-168	31	11	:	:	PUNCT
ma-168	31	12	susceptible	susceptible	ADJ
ma-168	31	13	vector	vector	NOUN
ma-168	31	14	;	;	PUNCT
ma-168	31	15	sv	sv	INTJ
ma-168	31	16	,	,	PUNCT
ma-168	31	17	the	the	DET
ma-168	31	18	exposed	expose	VERB
ma-168	31	19	vector	vector	NOUN
ma-168	31	20	compartment	compartment	NOUN
ma-168	31	21	;	;	PUNCT
ma-168	31	22	ev	ev	X
ma-168	31	23	and	and	CCONJ
ma-168	31	24	the	the	DET
ma-168	31	25	infective	infective	ADJ
ma-168	31	26	vector	vector	NOUN
ma-168	31	27	compart	compart	NOUN
ma-168	31	28	-	-	PUNCT
ma-168	31	29	ment	ment	NOUN
ma-168	31	30	.	.	PUNCT
ma-168	32	1	the	the	DET
ma-168	32	2	total	total	ADJ
ma-168	32	3	human	human	ADJ
ma-168	32	4	and	and	CCONJ
ma-168	32	5	vector	vector	NOUN
ma-168	32	6	populations	population	NOUN
ma-168	32	7	at	at	ADP
ma-168	32	8	any	any	DET
ma-168	32	9	given	give	VERB
ma-168	32	10	time	time	NOUN
ma-168	32	11	,	,	PUNCT
ma-168	32	12	t	t	PROPN
ma-168	32	13	,	,	PUNCT
ma-168	32	14	are	be	AUX
ma-168	32	15	respectively	respectively	ADV
ma-168	32	16	given	give	VERB
ma-168	32	17	by	by	ADP
ma-168	32	18	;	;	PUNCT
ma-168	32	19	n	n	NOUN
ma-168	32	20	=	=	PUNCT
ma-168	32	21	sh(t	sh(t	X
ma-168	32	22	)	)	PUNCT
ma-168	32	23	+	+	NUM
ma-168	32	24	eh(t	eh(t	PUNCT
ma-168	32	25	)	)	PUNCT
ma-168	32	26	+	+	CCONJ
ma-168	32	27	ih(t	ih(t	PRON
ma-168	32	28	)	)	PUNCT
ma-168	32	29	+	+	CCONJ
ma-168	32	30	rh(t	rh(t	X
ma-168	32	31	)	)	PUNCT
ma-168	32	32	and	and	CCONJ
ma-168	32	33	v	v	X
ma-168	32	34	=	=	SYM
ma-168	32	35	sv	sv	PROPN
ma-168	32	36	(	(	PUNCT
ma-168	32	37	t	t	PROPN
ma-168	32	38	)	)	PUNCT
ma-168	32	39	+	+	CCONJ
ma-168	32	40	ev	ev	X
ma-168	32	41	(	(	PUNCT
ma-168	32	42	t	t	PROPN
ma-168	32	43	)	)	PUNCT
ma-168	32	44	+	+	NUM
ma-168	32	45	iv	iv	NUM
ma-168	32	46	(	(	PUNCT
ma-168	32	47	t	t	NOUN
ma-168	32	48	)	)	PUNCT
ma-168	32	49	.	.	PUNCT
ma-168	33	1	we	we	PRON
ma-168	33	2	assume	assume	VERB
ma-168	33	3	that	that	DET
ma-168	33	4	thetransmission	thetransmission	NOUN
ma-168	33	5	of	of	ADP
ma-168	33	6	onchocerciaisis	onchocerciaisis	NOUN
ma-168	33	7	in	in	ADP
ma-168	33	8	susceptible	susceptible	ADJ
ma-168	33	9	hosts	host	NOUN
ma-168	33	10	is	be	AUX
ma-168	33	11	only	only	ADV
ma-168	33	12	through	through	ADP
ma-168	33	13	contact	contact	NOUN
ma-168	33	14	with	with	ADP
ma-168	33	15	infectious	infectious	ADJ
ma-168	33	16	vector.we	vector.we	NOUN
ma-168	33	17	also	also	ADV
ma-168	33	18	assume	assume	VERB
ma-168	33	19	that	that	SCONJ
ma-168	33	20	susceptible	susceptible	ADJ
ma-168	33	21	vector	vector	NOUN
ma-168	33	22	becomes	become	VERB
ma-168	33	23	infectious	infectious	ADJ
ma-168	33	24	as	as	ADP
ma-168	33	25	a	a	DET
ma-168	33	26	result	result	NOUN
ma-168	33	27	of	of	ADP
ma-168	33	28	contact	contact	NOUN
ma-168	33	29	with	with	ADP
ma-168	33	30	infectioushosts	infectioushost	NOUN
ma-168	33	31	during	during	ADP
ma-168	33	32	blood	blood	NOUN
ma-168	33	33	meal	meal	NOUN
ma-168	33	34	.	.	PUNCT
ma-168	34	1	the	the	DET
ma-168	34	2	population	population	NOUN
ma-168	34	3	under	under	ADP
ma-168	34	4	study	study	NOUN
ma-168	34	5	is	be	AUX
ma-168	34	6	assumed	assume	VERB
ma-168	34	7	to	to	PART
ma-168	34	8	be	be	AUX
ma-168	34	9	large	large	ADJ
ma-168	34	10	enough	enough	ADV
ma-168	34	11	to	to	PART
ma-168	34	12	bemodelled	bemodelle	VERB
ma-168	34	13	deterministically	deterministically	ADV
ma-168	34	14	.	.	PUNCT
ma-168	35	1	the	the	DET
ma-168	35	2	following	follow	VERB
ma-168	35	3	system	system	NOUN
ma-168	35	4	of	of	ADP
ma-168	35	5	non	non	ADJ
ma-168	35	6	-	-	ADJ
ma-168	35	7	linear	linear	ADJ
ma-168	35	8	ordinary	ordinary	ADJ
ma-168	35	9	differential	differential	ADJ
ma-168	35	10	equations	equation	NOUN
ma-168	35	11	,	,	PUNCT
ma-168	35	12	with	with	ADP
ma-168	35	13	non	non	ADJ
ma-168	35	14	-	-	ADJ
ma-168	35	15	negative	negative	ADJ
ma-168	35	16	initial	initial	ADJ
ma-168	35	17	conditions	condition	NOUN
ma-168	35	18	,	,	PUNCT
ma-168	35	19	describes	describe	VERB
ma-168	35	20	the	the	DET
ma-168	35	21	dynamics	dynamic	NOUN
ma-168	35	22	of	of	ADP
ma-168	35	23	onchocerciaisis	onchocerciaisis	NOUN
ma-168	35	24	epidemics	epidemic	NOUN
ma-168	35	25	.	.	PUNCT
ma-168	36	1	dsh(t	dsh(t	PROPN
ma-168	36	2	,	,	PUNCT
ma-168	36	3	xi	xi	X
ma-168	36	4	)	)	PUNCT
ma-168	36	5	dt	dt	PROPN
ma-168	37	1	=	=	SYM
ma-168	37	2	ψh(xi)−	ψh(xi)−	PRON
ma-168	37	3	∑l	∑l	PROPN
ma-168	37	4	i=0	i=0	ADJ
ma-168	37	5	δλh(xi	δλh(xi	X
ma-168	37	6	)	)	PUNCT
ma-168	37	7	sh(t	sh(t	X
ma-168	37	8	,	,	PUNCT
ma-168	37	9	xi	xi	X
ma-168	37	10	)	)	PUNCT
ma-168	37	11	iv	iv	PROPN
ma-168	37	12	(	(	PUNCT
ma-168	37	13	t	t	PROPN
ma-168	37	14	)	)	PUNCT
ma-168	37	15	1+νh(xi	1+νh(xi	NUM
ma-168	37	16	)	)	PUNCT
ma-168	37	17	iv	iv	X
ma-168	37	18	(	(	PUNCT
ma-168	37	19	t	t	NOUN
ma-168	37	20	)	)	PUNCT
ma-168	37	21	−	−	PROPN
ma-168	38	1	µh(xi)sh	µh(xi)sh	PROPN
ma-168	38	2	+	+	CCONJ
ma-168	38	3	w(xi)rh(t	w(xi)rh(t	PROPN
ma-168	38	4	,	,	PUNCT
ma-168	38	5	xi	xi	NOUN
ma-168	38	6	)	)	PUNCT
ma-168	38	7	)	)	PUNCT
ma-168	39	1	deh(t	deh(t	PROPN
ma-168	39	2	,	,	PUNCT
ma-168	39	3	xi	xi	NUM
ma-168	39	4	)	)	PUNCT
ma-168	39	5	dt	dt	PROPN
ma-168	40	1	=	=	PUNCT
ma-168	40	2	∑l	∑l	PROPN
ma-168	40	3	i=0	i=0	PROPN
ma-168	40	4	δλh(xi	δλh(xi	X
ma-168	40	5	)	)	PUNCT
ma-168	40	6	sh(t	sh(t	X
ma-168	40	7	,	,	PUNCT
ma-168	40	8	xi	xi	X
ma-168	40	9	)	)	PUNCT
ma-168	40	10	iv	iv	PROPN
ma-168	40	11	(	(	PUNCT
ma-168	40	12	t	t	PROPN
ma-168	40	13	)	)	PUNCT
ma-168	40	14	1+νh(xi	1+νh(xi	NUM
ma-168	40	15	)	)	PUNCT
ma-168	41	1	iv	iv	X
ma-168	41	2	(	(	PUNCT
ma-168	41	3	t	t	NOUN
ma-168	41	4	)	)	PUNCT
ma-168	41	5	−	−	PROPN
ma-168	41	6	(	(	PUNCT
ma-168	41	7	αh(xi	αh(xi	PROPN
ma-168	41	8	)	)	PUNCT
ma-168	41	9	+	+	NUM
ma-168	41	10	µh(xi))eh(t	µh(xi))eh(t	PROPN
ma-168	41	11	,	,	PUNCT
ma-168	41	12	xi	xi	X
ma-168	41	13	)	)	PUNCT
ma-168	41	14	d	d	NOUN
ma-168	41	15	ih(t	ih(t	PROPN
ma-168	41	16	,	,	PUNCT
ma-168	41	17	xi	xi	NUM
ma-168	41	18	)	)	PUNCT
ma-168	41	19	dt	dt	PROPN
ma-168	42	1	=	=	PUNCT
ma-168	42	2	∑l	∑l	INTJ
ma-168	42	3	i=0	i=0	PROPN
ma-168	42	4	αh(xi)eh	αh(xi)eh	PRON
ma-168	42	5	−	−	PROPN
ma-168	42	6	(	(	PUNCT
ma-168	42	7	r(xi	r(xi	PROPN
ma-168	42	8	)	)	PUNCT
ma-168	42	9	+	+	NUM
ma-168	42	10	γh(xi	γh(xi	NOUN
ma-168	42	11	)	)	PUNCT
ma-168	43	1	+	+	CCONJ
ma-168	43	2	µh(xi))ih(t	µh(xi))ih(t	ADJ
ma-168	43	3	,	,	PUNCT
ma-168	43	4	xi	xi	ADJ
ma-168	43	5	)	)	PUNCT
ma-168	43	6	drh(t	drh(t	PROPN
ma-168	43	7	,	,	PUNCT
ma-168	43	8	xi	xi	X
ma-168	43	9	)	)	PUNCT
ma-168	43	10	dt	dt	PROPN
ma-168	44	1	=	=	PUNCT
ma-168	44	2	∑l	∑l	PROPN
ma-168	44	3	i=0	i=0	ADJ
ma-168	44	4	r(xi)ih	r(xi)ih	X
ma-168	44	5	−	−	PROPN
ma-168	44	6	(	(	PUNCT
ma-168	44	7	µh(xi	µh(xi	X
ma-168	44	8	)	)	PUNCT
ma-168	45	1	+	+	CCONJ
ma-168	46	1	w(xi))rh(t	w(xi))rh(t	ADJ
ma-168	46	2	,	,	PUNCT
ma-168	46	3	xi	xi	ADJ
ma-168	46	4	)	)	PUNCT
ma-168	46	5	dsv	dsv	PROPN
ma-168	46	6	dt	dt	NOUN
ma-168	47	1	=	=	SYM
ma-168	47	2	ψv	ψv	PROPN
ma-168	47	3	−	−	PROPN
ma-168	47	4	δλv	δλv	PROPN
ma-168	47	5	(	(	PUNCT
ma-168	47	6	xi	xi	PROPN
ma-168	47	7	)	)	PUNCT
ma-168	47	8	sv	sv	PROPN
ma-168	47	9	(	(	PUNCT
ma-168	47	10	t)ih(xi	t)ih(xi	INTJ
ma-168	47	11	,	,	PUNCT
ma-168	47	12	t	t	PROPN
ma-168	47	13	)	)	PUNCT
ma-168	47	14	1+νv	1+νv	PROPN
ma-168	47	15	ih(xi	ih(xi	PROPN
ma-168	47	16	,	,	PUNCT
ma-168	47	17	t	t	PROPN
ma-168	47	18	)	)	PUNCT
ma-168	47	19	−	−	PROPN
ma-168	47	20	µvsv	µvsv	ADJ
ma-168	47	21	(	(	PUNCT
ma-168	47	22	t	t	NOUN
ma-168	47	23	)	)	PUNCT
ma-168	47	24	dev	dev	NOUN
ma-168	47	25	dt	dt	NOUN
ma-168	48	1	=	=	SYM
ma-168	48	2	δλv	δλv	PROPN
ma-168	48	3	(	(	PUNCT
ma-168	48	4	xi	xi	PROPN
ma-168	48	5	)	)	PUNCT
ma-168	48	6	sv	sv	PROPN
ma-168	48	7	(	(	PUNCT
ma-168	48	8	t)ih(xi	t)ih(xi	INTJ
ma-168	48	9	,	,	PUNCT
ma-168	48	10	t	t	PROPN
ma-168	48	11	)	)	PUNCT
ma-168	48	12	1+νv	1+νv	PROPN
ma-168	48	13	ih(xi	ih(xi	PROPN
ma-168	48	14	,	,	PUNCT
ma-168	48	15	t	t	PROPN
ma-168	48	16	)	)	PUNCT
ma-168	48	17	−	−	PROPN
ma-168	48	18	(	(	PUNCT
ma-168	48	19	αv	αv	ADP
ma-168	48	20	+	+	CCONJ
ma-168	48	21	µv	µv	PROPN
ma-168	48	22	)	)	PUNCT
ma-168	48	23	ev	ev	PROPN
ma-168	48	24	(	(	PUNCT
ma-168	48	25	t	t	PROPN
ma-168	48	26	)	)	PUNCT
ma-168	48	27	d	d	NOUN
ma-168	48	28	iv	iv	NUM
ma-168	48	29	dt	dt	NOUN
ma-168	48	30	=	=	PUNCT
ma-168	48	31	αvev	αvev	PROPN
ma-168	48	32	(	(	PUNCT
ma-168	48	33	t)−	t)−	PROPN
ma-168	48	34	(	(	PUNCT
ma-168	48	35	µv	µv	PROPN
ma-168	48	36	+	+	NUM
ma-168	48	37	γv	γv	X
ma-168	48	38	)	)	PUNCT
ma-168	48	39	iv	iv	X
ma-168	48	40	(	(	PUNCT
ma-168	48	41	t	t	NOUN
ma-168	48	42	)	)	PUNCT
ma-168	48	43			NOUN
ma-168	48	44	(	(	PUNCT
ma-168	48	45	2.1	2.1	NUM
ma-168	48	46	)	)	PUNCT
ma-168	48	47	subject	subject	NOUN
ma-168	48	48	to	to	ADP
ma-168	48	49	the	the	DET
ma-168	48	50	following	follow	VERB
ma-168	48	51	initial	initial	ADJ
ma-168	48	52	conditions	condition	NOUN
ma-168	48	53	:	:	PUNCT
ma-168	48	54	sh(0	sh(0	NOUN
ma-168	48	55	,	,	PUNCT
ma-168	48	56	xi	xi	ADJ
ma-168	48	57	)	)	PUNCT
ma-168	48	58	=	=	SYM
ma-168	48	59	s0h(xi	s0h(xi	PROPN
ma-168	48	60	)	)	PUNCT
ma-168	48	61	,	,	PUNCT
ma-168	48	62	eh(0	eh(0	NOUN
ma-168	48	63	,	,	PUNCT
ma-168	48	64	xi	xi	X
ma-168	48	65	)	)	PUNCT
ma-168	48	66	=	=	SYM
ma-168	48	67	e0h(xi	e0h(xi	NOUN
ma-168	48	68	)	)	PUNCT
ma-168	48	69	,	,	PUNCT
ma-168	48	70	ih(0	ih(0	PROPN
ma-168	48	71	,	,	PUNCT
ma-168	48	72	xi	xi	PROPN
ma-168	48	73	)	)	PUNCT
ma-168	48	74	=	=	SYM
ma-168	48	75	i0h(xi	i0h(xi	PROPN
ma-168	48	76	)	)	PUNCT
ma-168	48	77	,	,	PUNCT
ma-168	48	78	rh(0	rh(0	NOUN
ma-168	48	79	,	,	PUNCT
ma-168	48	80	xi	xi	X
ma-168	48	81	)	)	PUNCT
ma-168	48	82	=	=	SYM
ma-168	48	83	r0h(xi	r0h(xi	PROPN
ma-168	48	84	)	)	PUNCT
ma-168	48	85	sm(0	sm(0	NOUN
ma-168	48	86	)	)	PUNCT
ma-168	48	87	=	=	PROPN
ma-168	48	88	s0	s0	PROPN
ma-168	48	89	m	m	PROPN
ma-168	48	90	,	,	PUNCT
ma-168	48	91	em(0	em(0	X
ma-168	48	92	)	)	PUNCT
ma-168	48	93	=	=	SYM
ma-168	48	94	e0	e0	PROPN
ma-168	48	95	m	m	PROPN
ma-168	48	96	,	,	PUNCT
ma-168	48	97	im(0	im(0	NOUN
ma-168	48	98	)	)	PUNCT
ma-168	48	99	=	=	SYM
ma-168	48	100	i0	i0	PROPN
ma-168	48	101	m	m	X
ma-168	48	102	(	(	PUNCT
ma-168	48	103	2.2	2.2	NUM
ma-168	48	104	)	)	PUNCT
ma-168	48	105	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	48	106	eur	eur	PROPN
ma-168	48	107	.	.	PUNCT
ma-168	49	1	j.	j.	PROPN
ma-168	49	2	math	math	PROPN
ma-168	49	3	.	.	PUNCT
ma-168	50	1	anal	anal	PROPN
ma-168	50	2	.	.	PUNCT
ma-168	51	1	10.28924	10.28924	NUM
ma-168	51	2	/	/	SYM
ma-168	51	3	ada	ada	PROPN
ma-168	51	4	/	/	SYM
ma-168	51	5	ma.3.22	ma.3.22	NOUN
ma-168	51	6	3	3	NUM
ma-168	51	7	symbols	symbol	NOUN
ma-168	51	8	definitionss	definitions	NOUN
ma-168	51	9	sh(t	sh(t	PART
ma-168	51	10	,	,	PUNCT
ma-168	51	11	xi	xi	NOUN
ma-168	51	12	)	)	PUNCT
ma-168	51	13	number	number	NOUN
ma-168	51	14	of	of	ADP
ma-168	51	15	susceptible	susceptible	ADJ
ma-168	51	16	humans	human	NOUN
ma-168	51	17	at	at	ADP
ma-168	51	18	time	time	NOUN
ma-168	51	19	t	t	PROPN
ma-168	51	20	and	and	CCONJ
ma-168	51	21	discrete	discrete	VERB
ma-168	51	22	age	age	NOUN
ma-168	51	23	xi	xi	X
ma-168	51	24	eh(t	eh(t	PROPN
ma-168	51	25	,	,	PUNCT
ma-168	51	26	xi	xi	X
ma-168	51	27	)	)	PUNCT
ma-168	51	28	number	number	NOUN
ma-168	51	29	of	of	ADP
ma-168	51	30	exposed	expose	VERB
ma-168	51	31	humans	human	NOUN
ma-168	51	32	at	at	ADP
ma-168	51	33	time	time	NOUN
ma-168	51	34	t	t	PROPN
ma-168	51	35	and	and	CCONJ
ma-168	51	36	discrete	discrete	ADJ
ma-168	51	37	age	age	NOUN
ma-168	51	38	xi	xi	X
ma-168	51	39	ih(t	ih(t	PROPN
ma-168	51	40	,	,	PUNCT
ma-168	51	41	xi	xi	NOUN
ma-168	51	42	)	)	PUNCT
ma-168	51	43	number	number	NOUN
ma-168	51	44	of	of	ADP
ma-168	51	45	infectious	infectious	ADJ
ma-168	51	46	humans	human	NOUN
ma-168	51	47	at	at	ADP
ma-168	51	48	time	time	NOUN
ma-168	51	49	t	t	PROPN
ma-168	51	50	and	and	CCONJ
ma-168	51	51	discrete	discrete	ADJ
ma-168	51	52	age	age	NOUN
ma-168	51	53	xi	xi	X
ma-168	51	54	rh(t	rh(t	ADV
ma-168	51	55	,	,	PUNCT
ma-168	51	56	ai	ai	VERB
ma-168	51	57	)	)	PUNCT
ma-168	51	58	number	number	NOUN
ma-168	51	59	of	of	ADP
ma-168	51	60	recovered	recovered	ADJ
ma-168	51	61	humans	human	NOUN
ma-168	51	62	at	at	ADP
ma-168	51	63	time	time	NOUN
ma-168	51	64	t	t	PROPN
ma-168	51	65	and	and	CCONJ
ma-168	51	66	discrete	discrete	ADJ
ma-168	51	67	age	age	NOUN
ma-168	51	68	xi	xi	X
ma-168	51	69	sv	sv	PROPN
ma-168	51	70	(	(	PUNCT
ma-168	51	71	t	t	NOUN
ma-168	51	72	)	)	PUNCT
ma-168	51	73	number	number	NOUN
ma-168	51	74	of	of	ADP
ma-168	51	75	susceptible	susceptible	ADJ
ma-168	51	76	black	black	NOUN
ma-168	51	77	-	-	PUNCT
ma-168	51	78	flies	fly	NOUN
ma-168	51	79	at	at	ADP
ma-168	51	80	time	time	NOUN
ma-168	51	81	t	t	PROPN
ma-168	51	82	ev	ev	X
ma-168	51	83	(	(	PUNCT
ma-168	51	84	t	t	PROPN
ma-168	51	85	)	)	PUNCT
ma-168	51	86	number	number	NOUN
ma-168	51	87	of	of	ADP
ma-168	51	88	exposed	expose	VERB
ma-168	51	89	black	black	NOUN
ma-168	51	90	-	-	PUNCT
ma-168	51	91	flies	fly	NOUN
ma-168	51	92	at	at	ADP
ma-168	51	93	time	time	NOUN
ma-168	51	94	t	t	PROPN
ma-168	51	95	iv	iv	NUM
ma-168	51	96	(	(	PUNCT
ma-168	51	97	t	t	NOUN
ma-168	51	98	)	)	PUNCT
ma-168	51	99	number	number	NOUN
ma-168	51	100	of	of	ADP
ma-168	51	101	infectious	infectious	ADJ
ma-168	51	102	black	black	NOUN
ma-168	51	103	-	-	PUNCT
ma-168	51	104	flies	fly	NOUN
ma-168	51	105	at	at	ADP
ma-168	51	106	time	time	NOUN
ma-168	51	107	t	t	PROPN
ma-168	51	108	ψh(xi	ψh(xi	PUNCT
ma-168	51	109	)	)	PUNCT
ma-168	52	1	recruitment	recruitment	NOUN
ma-168	52	2	term	term	NOUN
ma-168	52	3	of	of	ADP
ma-168	52	4	the	the	DET
ma-168	52	5	susceptible	susceptible	ADJ
ma-168	52	6	humans	human	NOUN
ma-168	52	7	at	at	ADP
ma-168	52	8	discrete	discrete	ADJ
ma-168	52	9	age	age	NOUN
ma-168	52	10	xi	xi	X
ma-168	52	11	ψv	ψv	PROPN
ma-168	52	12	recruitment	recruitment	NOUN
ma-168	52	13	term	term	NOUN
ma-168	52	14	of	of	ADP
ma-168	52	15	the	the	DET
ma-168	52	16	susceptible	susceptible	ADJ
ma-168	52	17	vectors	vector	NOUN
ma-168	52	18	δ	δ	NOUN
ma-168	52	19	biting	bite	VERB
ma-168	52	20	rate	rate	NOUN
ma-168	52	21	of	of	ADP
ma-168	52	22	the	the	DET
ma-168	52	23	vector	vector	NOUN
ma-168	52	24	λh(xi	λh(xi	PROPN
ma-168	52	25	)	)	PUNCT
ma-168	52	26	probability	probability	NOUN
ma-168	52	27	that	that	SCONJ
ma-168	52	28	a	a	DET
ma-168	52	29	bite	bite	NOUN
ma-168	52	30	by	by	ADP
ma-168	52	31	an	an	DET
ma-168	52	32	infectious	infectious	ADJ
ma-168	52	33	vector	vector	NOUN
ma-168	52	34	results	result	NOUN
ma-168	52	35	in	in	ADP
ma-168	52	36	transmission	transmission	NOUN
ma-168	52	37	of	of	ADP
ma-168	52	38	disease	disease	NOUN
ma-168	52	39	to	to	ADP
ma-168	52	40	human	human	NOUN
ma-168	52	41	at	at	ADP
ma-168	52	42	discrete	discrete	ADJ
ma-168	52	43	age	age	NOUN
ma-168	53	1	xi	xi	X
ma-168	53	2	λv	λv	INTJ
ma-168	53	3	probability	probability	NOUN
ma-168	53	4	that	that	SCONJ
ma-168	53	5	a	a	DET
ma-168	53	6	bite	bite	NOUN
ma-168	53	7	results	result	NOUN
ma-168	53	8	in	in	ADP
ma-168	53	9	transmission	transmission	NOUN
ma-168	53	10	of	of	ADP
ma-168	53	11	parasite	parasite	NOUN
ma-168	53	12	to	to	ADP
ma-168	53	13	a	a	DET
ma-168	53	14	susceptible	susceptible	ADJ
ma-168	53	15	vector	vector	NOUN
ma-168	53	16	µh(xi	µh(xi	PROPN
ma-168	53	17	)	)	PUNCT
ma-168	53	18	per	per	ADP
ma-168	53	19	capita	capita	NOUN
ma-168	53	20	death	death	NOUN
ma-168	53	21	rate	rate	NOUN
ma-168	53	22	of	of	ADP
ma-168	53	23	humans	human	NOUN
ma-168	53	24	at	at	ADP
ma-168	53	25	discrete	discrete	ADJ
ma-168	53	26	age	age	NOUN
ma-168	53	27	xi	xi	ADP
ma-168	53	28	µv	µv	PROPN
ma-168	53	29	per	per	ADP
ma-168	53	30	capita	capita	NOUN
ma-168	53	31	death	death	NOUN
ma-168	53	32	rate	rate	NOUN
ma-168	53	33	of	of	ADP
ma-168	53	34	vector	vector	NOUN
ma-168	53	35	γh(xi	γh(xi	NOUN
ma-168	53	36	)	)	PUNCT
ma-168	53	37	disease	disease	NOUN
ma-168	53	38	-	-	PUNCT
ma-168	53	39	induced	induce	VERB
ma-168	53	40	death	death	NOUN
ma-168	53	41	rate	rate	NOUN
ma-168	53	42	of	of	ADP
ma-168	53	43	humans	human	NOUN
ma-168	53	44	at	at	ADP
ma-168	53	45	discrete	discrete	ADJ
ma-168	53	46	age	age	NOUN
ma-168	53	47	xi	xi	NOUN
ma-168	53	48	γv	γv	NOUN
ma-168	53	49	disease	disease	NOUN
ma-168	53	50	-	-	PUNCT
ma-168	53	51	induced	induce	VERB
ma-168	53	52	death	death	NOUN
ma-168	53	53	rate	rate	NOUN
ma-168	53	54	of	of	ADP
ma-168	53	55	vectors	vector	NOUN
ma-168	53	56	αh(xi	αh(xi	PROPN
ma-168	53	57	)	)	PUNCT
ma-168	53	58	per	per	ADP
ma-168	53	59	capita	capita	NOUN
ma-168	53	60	rate	rate	NOUN
ma-168	53	61	of	of	ADP
ma-168	53	62	progression	progression	NOUN
ma-168	53	63	of	of	ADP
ma-168	53	64	humans	human	NOUN
ma-168	53	65	from	from	ADP
ma-168	53	66	the	the	DET
ma-168	53	67	exposed	expose	VERB
ma-168	53	68	state	state	NOUN
ma-168	53	69	to	to	ADP
ma-168	53	70	the	the	DET
ma-168	53	71	infectious	infectious	ADJ
ma-168	53	72	state	state	NOUN
ma-168	53	73	at	at	ADP
ma-168	53	74	discrete	discrete	ADJ
ma-168	53	75	age	age	NOUN
ma-168	53	76	xi	xi	ADP
ma-168	53	77	αv	αv	ADP
ma-168	53	78	per	per	ADP
ma-168	53	79	capita	capita	NOUN
ma-168	53	80	rate	rate	NOUN
ma-168	53	81	of	of	ADP
ma-168	53	82	progression	progression	NOUN
ma-168	53	83	of	of	ADP
ma-168	53	84	vectors	vector	NOUN
ma-168	53	85	from	from	ADP
ma-168	53	86	the	the	DET
ma-168	53	87	exposed	expose	VERB
ma-168	53	88	state	state	NOUN
ma-168	53	89	to	to	ADP
ma-168	53	90	the	the	DET
ma-168	53	91	infectious	infectious	ADJ
ma-168	53	92	state	state	NOUN
ma-168	53	93	r(xi	r(xi	PROPN
ma-168	53	94	)	)	PUNCT
ma-168	53	95	per	per	ADP
ma-168	53	96	capita	capita	NOUN
ma-168	53	97	recovery	recovery	NOUN
ma-168	53	98	rate	rate	NOUN
ma-168	53	99	for	for	ADP
ma-168	53	100	humans	human	NOUN
ma-168	53	101	from	from	ADP
ma-168	53	102	the	the	DET
ma-168	53	103	infectious	infectious	ADJ
ma-168	53	104	state	state	NOUN
ma-168	53	105	to	to	ADP
ma-168	53	106	the	the	DET
ma-168	53	107	recovered	recovered	ADJ
ma-168	53	108	state	state	NOUN
ma-168	53	109	due	due	ADP
ma-168	53	110	to	to	ADP
ma-168	53	111	treatment	treatment	NOUN
ma-168	53	112	at	at	ADP
ma-168	53	113	discrete	discrete	ADJ
ma-168	53	114	age	age	NOUN
ma-168	53	115	xi	xi	ADP
ma-168	53	116	ω(xi	ω(xi	PROPN
ma-168	53	117	)	)	PUNCT
ma-168	53	118	per	per	ADP
ma-168	53	119	capita	capita	NOUN
ma-168	53	120	transition	transition	NOUN
ma-168	53	121	rate	rate	NOUN
ma-168	53	122	of	of	ADP
ma-168	53	123	recovered	recover	VERB
ma-168	53	124	humans	human	NOUN
ma-168	53	125	to	to	ADP
ma-168	53	126	the	the	DET
ma-168	53	127	susceptible	susceptible	ADJ
ma-168	53	128	state	state	NOUN
ma-168	53	129	at	at	ADP
ma-168	53	130	discrete	discrete	ADJ
ma-168	53	131	age	age	NOUN
ma-168	53	132	xi	xi	ADP
ma-168	53	133	νh(xi	νh(xi	PROPN
ma-168	53	134	)	)	PUNCT
ma-168	54	1	humans	human	NOUN
ma-168	54	2	disease	disease	NOUN
ma-168	54	3	-	-	PUNCT
ma-168	54	4	inhibiting	inhibit	VERB
ma-168	54	5	factor	factor	NOUN
ma-168	54	6	at	at	ADP
ma-168	54	7	discrete	discrete	ADJ
ma-168	54	8	age	age	NOUN
ma-168	54	9	xi	xi	X
ma-168	54	10	νv	νv	PROPN
ma-168	54	11	vectors	vector	VERB
ma-168	54	12	disease	disease	NOUN
ma-168	54	13	-	-	PUNCT
ma-168	54	14	inhibiting	inhibit	VERB
ma-168	54	15	factor	factor	NOUN
ma-168	54	16	model	model	NOUN
ma-168	54	17	assumptionsthe	assumptionsthe	DET
ma-168	54	18	formulation	formulation	NOUN
ma-168	54	19	of	of	ADP
ma-168	54	20	the	the	DET
ma-168	54	21	compartmental	compartmental	ADJ
ma-168	54	22	model	model	NOUN
ma-168	54	23	is	be	AUX
ma-168	54	24	based	base	VERB
ma-168	54	25	on	on	ADP
ma-168	54	26	the	the	DET
ma-168	54	27	following	follow	VERB
ma-168	54	28	assumptions	assumption	NOUN
ma-168	54	29	:	:	PUNCT
ma-168	54	30	1	1	X
ma-168	54	31	.	.	X
ma-168	54	32	that	that	SCONJ
ma-168	54	33	all	all	DET
ma-168	54	34	humans	human	NOUN
ma-168	54	35	are	be	AUX
ma-168	54	36	born	bear	VERB
ma-168	54	37	susceptible	susceptible	ADJ
ma-168	54	38	.	.	PUNCT
ma-168	55	1	that	that	PRON
ma-168	55	2	is	be	AUX
ma-168	55	3	,	,	PUNCT
ma-168	55	4	humans	human	NOUN
ma-168	55	5	are	be	AUX
ma-168	55	6	liable	liable	ADJ
ma-168	55	7	to	to	PART
ma-168	55	8	contract	contract	VERB
ma-168	55	9	the	the	DET
ma-168	55	10	disease.2	disease.2	PROPN
ma-168	55	11	.	.	PROPN
ma-168	55	12	that	that	SCONJ
ma-168	55	13	the	the	DET
ma-168	55	14	susceptible	susceptible	ADJ
ma-168	55	15	humans	human	NOUN
ma-168	55	16	,	,	PUNCT
ma-168	55	17	when	when	SCONJ
ma-168	55	18	infected	infect	VERB
ma-168	55	19	,	,	PUNCT
ma-168	55	20	becomes	becomes	AUX
ma-168	55	21	exposed	expose	VERB
ma-168	55	22	humans	human	NOUN
ma-168	55	23	who	who	PRON
ma-168	55	24	are	be	AUX
ma-168	55	25	not	not	PART
ma-168	55	26	yetinfectious.3	yetinfectious.3	PROPN
ma-168	55	27	.	.	PUNCT
ma-168	56	1	that	that	SCONJ
ma-168	56	2	the	the	DET
ma-168	56	3	exposed	expose	VERB
ma-168	56	4	humans	human	NOUN
ma-168	56	5	progress	progress	VERB
ma-168	56	6	to	to	PART
ma-168	56	7	become	become	VERB
ma-168	56	8	infectious	infectious	ADJ
ma-168	56	9	only.4	only.4	NOUN
ma-168	56	10	.	.	PUNCT
ma-168	57	1	that	that	SCONJ
ma-168	57	2	the	the	DET
ma-168	57	3	infectious	infectious	ADJ
ma-168	57	4	humans	human	NOUN
ma-168	57	5	may	may	AUX
ma-168	57	6	either	either	CCONJ
ma-168	57	7	die	die	VERB
ma-168	57	8	naturally	naturally	ADV
ma-168	57	9	or	or	CCONJ
ma-168	57	10	as	as	ADP
ma-168	57	11	a	a	DET
ma-168	57	12	result	result	NOUN
ma-168	57	13	of	of	ADP
ma-168	57	14	the	the	DET
ma-168	57	15	disease	disease	NOUN
ma-168	57	16	,	,	PUNCT
ma-168	57	17	and	and	CCONJ
ma-168	57	18	ifnot	ifnot	ADV
ma-168	57	19	,	,	PUNCT
ma-168	57	20	they	they	PRON
ma-168	57	21	become	become	VERB
ma-168	57	22	recovered	recover	VERB
ma-168	57	23	humans	human	NOUN
ma-168	57	24	due	due	ADJ
ma-168	57	25	to	to	ADP
ma-168	57	26	treatment.5	treatment.5	PROPN
ma-168	57	27	.	.	PUNCT
ma-168	58	1	that	that	SCONJ
ma-168	58	2	the	the	DET
ma-168	58	3	recovered	recovered	ADJ
ma-168	58	4	humans	human	NOUN
ma-168	58	5	become	become	VERB
ma-168	58	6	susceptible	susceptible	ADJ
ma-168	58	7	again.6	again.6	PROPN
ma-168	58	8	.	.	PUNCT
ma-168	59	1	all	all	DET
ma-168	59	2	black	black	NOUN
ma-168	59	3	-	-	PUNCT
ma-168	59	4	flies	fly	NOUN
ma-168	59	5	are	be	AUX
ma-168	59	6	born	bear	VERB
ma-168	59	7	susceptible.7	susceptible.7	NOUN
ma-168	59	8	.	.	PUNCT
ma-168	60	1	that	that	SCONJ
ma-168	60	2	the	the	DET
ma-168	60	3	susceptible	susceptible	ADJ
ma-168	60	4	black	black	NOUN
ma-168	60	5	-	-	PUNCT
ma-168	60	6	flies	fly	NOUN
ma-168	60	7	,	,	PUNCT
ma-168	60	8	when	when	SCONJ
ma-168	60	9	infected	infect	VERB
ma-168	60	10	,	,	PUNCT
ma-168	60	11	becomes	becomes	AUX
ma-168	60	12	exposed	expose	VERB
ma-168	60	13	black	black	ADJ
ma-168	60	14	-	-	PUNCT
ma-168	60	15	flies	fly	NOUN
ma-168	60	16	who	who	PRON
ma-168	60	17	are	be	AUX
ma-168	60	18	notyet	notyet	ADV
ma-168	60	19	infectious.8	infectious.8	PROPN
ma-168	60	20	.	.	PUNCT
ma-168	61	1	that	that	SCONJ
ma-168	61	2	the	the	DET
ma-168	61	3	exposed	expose	VERB
ma-168	61	4	black	black	ADJ
ma-168	61	5	-	-	PUNCT
ma-168	61	6	flies	fly	NOUN
ma-168	61	7	progress	progress	NOUN
ma-168	61	8	to	to	PART
ma-168	61	9	become	become	VERB
ma-168	61	10	infectious	infectious	ADJ
ma-168	61	11	only.9	only.9	NOUN
ma-168	61	12	.	.	PUNCT
ma-168	61	13	that	that	SCONJ
ma-168	61	14	the	the	DET
ma-168	61	15	infectious	infectious	ADJ
ma-168	61	16	black	black	NOUN
ma-168	61	17	-	-	PUNCT
ma-168	61	18	flies	fly	NOUN
ma-168	61	19	remain	remain	VERB
ma-168	61	20	infectious	infectious	ADJ
ma-168	61	21	for	for	ADP
ma-168	61	22	life	life	NOUN
ma-168	61	23	.	.	PUNCT
ma-168	62	1	that	that	PRON
ma-168	62	2	is	be	AUX
ma-168	62	3	,	,	PUNCT
ma-168	62	4	there	there	PRON
ma-168	62	5	is	be	VERB
ma-168	62	6	no	no	DET
ma-168	62	7	recovered	recover	VERB
ma-168	62	8	classfor	classfor	ADP
ma-168	62	9	black	black	NOUN
ma-168	62	10	-	-	PUNCT
ma-168	62	11	fly	fly	NOUN
ma-168	62	12	population	population	NOUN
ma-168	62	13	.	.	PUNCT
ma-168	63	1	2.1	2.1	NUM
ma-168	63	2	.	.	PUNCT
ma-168	63	3	existence	existence	NOUN
ma-168	63	4	and	and	CCONJ
ma-168	63	5	positivity	positivity	NOUN
ma-168	63	6	of	of	ADP
ma-168	63	7	solutions	solution	NOUN
ma-168	63	8	.	.	PUNCT
ma-168	64	1	in	in	ADP
ma-168	64	2	this	this	DET
ma-168	64	3	section	section	NOUN
ma-168	64	4	,	,	PUNCT
ma-168	64	5	we	we	PRON
ma-168	64	6	analyse	analyse	VERB
ma-168	64	7	the	the	DET
ma-168	64	8	general	general	ADJ
ma-168	64	9	properties	property	NOUN
ma-168	64	10	ofthe	ofthe	ADJ
ma-168	64	11	system	system	NOUN
ma-168	64	12	(	(	PUNCT
ma-168	64	13	2.1	2.1	NUM
ma-168	64	14	)	)	PUNCT
ma-168	64	15	with	with	ADP
ma-168	64	16	positive	positive	ADJ
ma-168	64	17	initial	initial	ADJ
ma-168	64	18	conditions	condition	NOUN
ma-168	64	19	.	.	PUNCT
ma-168	65	1	it	it	PRON
ma-168	65	2	describes	describe	VERB
ma-168	65	3	the	the	DET
ma-168	65	4	population	population	NOUN
ma-168	65	5	dynamics	dynamic	NOUN
ma-168	65	6	both	both	CCONJ
ma-168	65	7	in	in	ADP
ma-168	65	8	humanand	humanand	ADJ
ma-168	65	9	black	black	ADJ
ma-168	65	10	-	-	PUNCT
ma-168	65	11	fly	fly	NOUN
ma-168	65	12	populations	population	NOUN
ma-168	65	13	.	.	PUNCT
ma-168	66	1	the	the	DET
ma-168	66	2	system	system	NOUN
ma-168	66	3	is	be	AUX
ma-168	66	4	biologically	biologically	ADV
ma-168	66	5	relevant	relevant	ADJ
ma-168	66	6	in	in	ADP
ma-168	66	7	the	the	DET
ma-168	66	8	set	set	NOUN
ma-168	66	9	given	give	VERB
ma-168	66	10	by	by	ADP
ma-168	66	11	ω	ω	PROPN
ma-168	66	12	=	=	SYM
ma-168	66	13	(	(	PUNCT
ma-168	66	14	sh(t	sh(t	X
ma-168	66	15	,	,	PUNCT
ma-168	66	16	xi	xi	ADJ
ma-168	66	17	)	)	PUNCT
ma-168	66	18	,	,	PUNCT
ma-168	66	19	eh(t	eh(t	PROPN
ma-168	66	20	,	,	PUNCT
ma-168	66	21	xi	xi	PROPN
ma-168	66	22	)	)	PUNCT
ma-168	66	23	,	,	PUNCT
ma-168	66	24	ih(t	ih(t	PROPN
ma-168	66	25	,	,	PUNCT
ma-168	66	26	xi	xi	ADJ
ma-168	66	27	)	)	PUNCT
ma-168	66	28	,	,	PUNCT
ma-168	66	29	rh(t	rh(t	X
ma-168	66	30	,	,	PUNCT
ma-168	66	31	xi	xi	ADJ
ma-168	66	32	)	)	PUNCT
ma-168	66	33	)	)	PUNCT
ma-168	67	1	∈	∈	PROPN
ma-168	67	2	r4	r4	NOUN
ma-168	67	3	+	+	CCONJ
ma-168	67	4	:	:	PUNCT
ma-168	67	5	nh	nh	ADJ
ma-168	67	6	≤	≤	NOUN
ma-168	67	7	l∑	l∑	PUNCT
ma-168	67	8	i=0	i=0	PROPN
ma-168	67	9	ψh(xi	ψh(xi	X
ma-168	67	10	)	)	PUNCT
ma-168	67	11	µh(xi	µh(xi	PROPN
ma-168	67	12	)	)	PUNCT
ma-168	67	13	,	,	PUNCT
ma-168	67	14	(	(	PUNCT
ma-168	67	15	sv	sv	X
ma-168	67	16	(	(	PUNCT
ma-168	67	17	t	t	PROPN
ma-168	67	18	)	)	PUNCT
ma-168	67	19	,	,	PUNCT
ma-168	67	20	ev	ev	X
ma-168	67	21	(	(	PUNCT
ma-168	67	22	t	t	PROPN
ma-168	67	23	)	)	PUNCT
ma-168	67	24	,	,	PUNCT
ma-168	67	25	iv	iv	X
ma-168	67	26	(	(	PUNCT
ma-168	67	27	t	t	NOUN
ma-168	67	28	)	)	PUNCT
ma-168	67	29	)	)	PUNCT
ma-168	68	1	∈	∈	PROPN
ma-168	68	2	r3	r3	PROPN
ma-168	68	3	+	+	CCONJ
ma-168	68	4	:	:	PUNCT
ma-168	68	5	nv	nv	PROPN
ma-168	68	6	≤	≤	PROPN
ma-168	68	7	ψv	ψv	ADP
ma-168	68	8	µv	µv	PROPN
ma-168	68	9	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	68	10	eur	eur	PROPN
ma-168	68	11	.	.	PUNCT
ma-168	69	1	j.	j.	PROPN
ma-168	69	2	math	math	PROPN
ma-168	69	3	.	.	PUNCT
ma-168	70	1	anal	anal	PROPN
ma-168	70	2	.	.	PUNCT
ma-168	71	1	10.28924	10.28924	NUM
ma-168	71	2	/	/	SYM
ma-168	71	3	ada	ada	PROPN
ma-168	71	4	/	/	SYM
ma-168	71	5	ma.3.22	ma.3.22	NOUN
ma-168	71	6	4here	4here	NUM
ma-168	71	7	,	,	PUNCT
ma-168	71	8	the	the	DET
ma-168	71	9	following	follow	VERB
ma-168	71	10	results	result	NOUN
ma-168	71	11	are	be	AUX
ma-168	71	12	provided	provide	VERB
ma-168	71	13	which	which	PRON
ma-168	71	14	guarantee	guarantee	VERB
ma-168	71	15	that	that	SCONJ
ma-168	71	16	the	the	DET
ma-168	71	17	model	model	NOUN
ma-168	71	18	governed	govern	VERB
ma-168	71	19	by	by	ADP
ma-168	71	20	system	system	NOUN
ma-168	71	21	(	(	PUNCT
ma-168	71	22	2.1)is	2.1)is	NUM
ma-168	71	23	mathematically	mathematically	ADV
ma-168	71	24	well	well	ADV
ma-168	71	25	-	-	PUNCT
ma-168	71	26	posed	pose	VERB
ma-168	71	27	in	in	ADP
ma-168	71	28	a	a	DET
ma-168	71	29	feasible	feasible	ADJ
ma-168	71	30	region	region	NOUN
ma-168	71	31	ω	ω	NUM
ma-168	71	32	defined	define	VERB
ma-168	71	33	by	by	ADP
ma-168	71	34	:	:	PUNCT
ma-168	71	35	ω	ω	PROPN
ma-168	71	36	=	=	SYM
ma-168	71	37	ωh	ωh	PROPN
ma-168	71	38	×ωv	×ωv	PROPN
ma-168	71	39	⊂	⊂	PRON
ma-168	71	40	r4	r4	PROPN
ma-168	71	41	×	×	PROPN
ma-168	71	42	r3	r3	PROPN
ma-168	71	43	theorem	theorem	VERB
ma-168	71	44	1	1	NUM
ma-168	71	45	:	:	PUNCT
ma-168	71	46	there	there	PRON
ma-168	71	47	exists	exist	VERB
ma-168	71	48	a	a	DET
ma-168	71	49	domain	domain	NOUN
ma-168	71	50	ω	ω	NOUN
ma-168	71	51	in	in	ADP
ma-168	71	52	which	which	PRON
ma-168	71	53	the	the	DET
ma-168	71	54	solution	solution	NOUN
ma-168	71	55	set	set	VERB
ma-168	71	56	sh(t	sh(t	ADP
ma-168	71	57	,	,	PUNCT
ma-168	71	58	xi	xi	ADJ
ma-168	71	59	)	)	PUNCT
ma-168	71	60	,	,	PUNCT
ma-168	71	61	eh(t	eh(t	PROPN
ma-168	71	62	,	,	PUNCT
ma-168	71	63	xi	xi	PROPN
ma-168	71	64	)	)	PUNCT
ma-168	71	65	,	,	PUNCT
ma-168	71	66	ih(t	ih(t	PROPN
ma-168	71	67	,	,	PUNCT
ma-168	71	68	xi	xi	ADJ
ma-168	71	69	)	)	PUNCT
ma-168	71	70	,	,	PUNCT
ma-168	71	71	rh(t	rh(t	X
ma-168	71	72	,	,	PUNCT
ma-168	71	73	xi	xi	PROPN
ma-168	71	74	)	)	PUNCT
ma-168	71	75	,	,	PUNCT
ma-168	71	76	sv	sv	PROPN
ma-168	71	77	(	(	PUNCT
ma-168	71	78	t	t	PROPN
ma-168	71	79	)	)	PUNCT
ma-168	71	80	,	,	PUNCT
ma-168	71	81	ev	ev	X
ma-168	71	82	(	(	PUNCT
ma-168	71	83	t	t	PROPN
ma-168	71	84	)	)	PUNCT
ma-168	71	85	,	,	PUNCT
ma-168	71	86	iv	iv	X
ma-168	71	87	(	(	PUNCT
ma-168	71	88	t)is	t)is	PROPN
ma-168	71	89	contained	contain	VERB
ma-168	71	90	and	and	CCONJ
ma-168	71	91	bounded	bound	VERB
ma-168	71	92	.	.	PUNCT
ma-168	72	1	proofif	proofif	VERB
ma-168	72	2	the	the	DET
ma-168	72	3	total	total	ADJ
ma-168	72	4	human	human	ADJ
ma-168	72	5	population	population	NOUN
ma-168	72	6	size	size	NOUN
ma-168	72	7	is	be	AUX
ma-168	72	8	given	give	VERB
ma-168	72	9	by	by	ADP
ma-168	72	10	nh	nh	PROPN
ma-168	72	11	=	=	NOUN
ma-168	72	12	sh(t	sh(t	X
ma-168	72	13	,	,	PUNCT
ma-168	72	14	xi	xi	ADJ
ma-168	72	15	)	)	PUNCT
ma-168	73	1	+	+	NOUN
ma-168	73	2	eh(t	eh(t	NOUN
ma-168	73	3	,	,	PUNCT
ma-168	73	4	xi	xi	X
ma-168	73	5	)	)	PUNCT
ma-168	74	1	+	+	CCONJ
ma-168	74	2	ih(t	ih(t	PRON
ma-168	74	3	,	,	PUNCT
ma-168	74	4	xi	xi	ADJ
ma-168	74	5	)	)	PUNCT
ma-168	75	1	+	+	ADV
ma-168	75	2	rh(t	rh(t	ADJ
ma-168	75	3	,	,	PUNCT
ma-168	75	4	xi	xi	PROPN
ma-168	75	5	)	)	PUNCT
ma-168	75	6	,	,	PUNCT
ma-168	75	7	andthe	andthe	ADJ
ma-168	75	8	total	total	ADJ
ma-168	75	9	size	size	NOUN
ma-168	75	10	of	of	ADP
ma-168	75	11	black	black	ADJ
ma-168	75	12	-	-	PUNCT
ma-168	75	13	fly	fly	NOUN
ma-168	75	14	population	population	NOUN
ma-168	75	15	is	be	AUX
ma-168	75	16	nv	nv	PROPN
ma-168	75	17	=	=	PUNCT
ma-168	75	18	sv	sv	PROPN
ma-168	75	19	(	(	PUNCT
ma-168	75	20	t	t	PROPN
ma-168	75	21	)	)	PUNCT
ma-168	76	1	+	+	CCONJ
ma-168	76	2	ev	ev	X
ma-168	76	3	(	(	PUNCT
ma-168	76	4	t	t	PROPN
ma-168	76	5	)	)	PUNCT
ma-168	76	6	+	+	NUM
ma-168	76	7	iv	iv	NUM
ma-168	76	8	(	(	PUNCT
ma-168	76	9	t	t	NOUN
ma-168	76	10	)	)	PUNCT
ma-168	76	11	.	.	PUNCT
ma-168	77	1	from	from	ADP
ma-168	77	2	model	model	NOUN
ma-168	77	3	(	(	PUNCT
ma-168	77	4	2.1	2.1	NUM
ma-168	77	5	)	)	PUNCT
ma-168	77	6	,	,	PUNCT
ma-168	77	7	we	we	PRON
ma-168	77	8	havethat	havethat	VERB
ma-168	77	9	dnh(t	dnh(t	PROPN
ma-168	77	10	,	,	PUNCT
ma-168	77	11	xi	xi	PROPN
ma-168	77	12	)	)	PUNCT
ma-168	78	1	dt	dt	NOUN
ma-168	78	2	≤	≤	NOUN
ma-168	79	1	ψh(xi)−	ψh(xi)−	ADP
ma-168	79	2	l∑	l∑	PUNCT
ma-168	80	1	i=0	i=0	PROPN
ma-168	80	2	µh(xi)nh(t	µh(xi)nh(t	NUM
ma-168	80	3	,	,	PUNCT
ma-168	80	4	xi	xi	ADJ
ma-168	80	5	)	)	PUNCT
ma-168	80	6	(	(	PUNCT
ma-168	80	7	2.3	2.3	NUM
ma-168	80	8	)	)	PUNCT
ma-168	80	9	and	and	CCONJ
ma-168	81	1	dnv	dnv	PROPN
ma-168	81	2	dt	dt	PROPN
ma-168	81	3	≤	≤	PROPN
ma-168	81	4	ψv	ψv	ADP
ma-168	81	5	−	−	PROPN
ma-168	81	6	µvnv	µvnv	NOUN
ma-168	81	7	(	(	PUNCT
ma-168	81	8	2.4)it	2.4)it	PROPN
ma-168	81	9	follows	follow	VERB
ma-168	81	10	from	from	ADP
ma-168	81	11	(	(	PUNCT
ma-168	81	12	2.3	2.3	NUM
ma-168	81	13	)	)	PUNCT
ma-168	81	14	and	and	CCONJ
ma-168	81	15	(	(	PUNCT
ma-168	81	16	2.4	2.4	NUM
ma-168	81	17	)	)	PUNCT
ma-168	81	18	that	that	PRON
ma-168	81	19	nh(t	nh(t	ADJ
ma-168	81	20	,	,	PUNCT
ma-168	81	21	xi	xi	X
ma-168	81	22	)	)	PUNCT
ma-168	81	23	≤	≤	NUM
ma-168	82	1	ψh(xi	ψh(xi	ADJ
ma-168	82	2	)	)	PUNCT
ma-168	82	3	µh(xi	µh(xi	PROPN
ma-168	82	4	)	)	PUNCT
ma-168	83	1	[	[	X
ma-168	83	2	1−	1−	NUM
ma-168	83	3	e1−µh(xi	e1−µh(xi	ADJ
ma-168	83	4	)	)	PUNCT
ma-168	83	5	t]+nh(0,xi	t]+nh(0,xi	PUNCT
ma-168	83	6	)	)	PUNCT
ma-168	83	7	e	e	X
ma-168	83	8	−µh(xi	−µh(xi	NOUN
ma-168	83	9	)	)	PUNCT
ma-168	83	10	t	t	X
ma-168	83	11	]	]	PUNCT
ma-168	83	12	and	and	CCONJ
ma-168	83	13	nv	nv	PROPN
ma-168	83	14	≤	≤	PROPN
ma-168	83	15	ψv	ψv	ADP
ma-168	83	16	µv	µv	PROPN
ma-168	84	1	[	[	X
ma-168	84	2	1−	1−	NUM
ma-168	84	3	e−µv	e−µv	NOUN
ma-168	84	4	t	t	X
ma-168	84	5	]	]	PUNCT
ma-168	85	1	+	+	CCONJ
ma-168	85	2	nv	nv	PROPN
ma-168	85	3	(	(	PUNCT
ma-168	85	4	0)e−µv	0)e−µv	NUM
ma-168	85	5	t	t	PROPN
ma-168	85	6	taking	take	VERB
ma-168	85	7	the	the	DET
ma-168	85	8	lim	lim	PROPN
ma-168	85	9	sup	sup	PROPN
ma-168	85	10	as	as	ADP
ma-168	85	11	t	t	PROPN
ma-168	85	12	→	→	SYM
ma-168	85	13	∞	∞	PROPN
ma-168	85	14	gives	give	VERB
ma-168	85	15	nh	nh	PROPN
ma-168	85	16	≤	≤	NUM
ma-168	85	17	ψh(xi	ψh(xi	PUNCT
ma-168	85	18	)	)	PUNCT
ma-168	86	1	µh(xi	µh(xi	PROPN
ma-168	86	2	)	)	PUNCT
ma-168	86	3	and	and	CCONJ
ma-168	86	4	nv	nv	PROPN
ma-168	86	5	≤	≤	PROPN
ma-168	86	6	ψv	ψv	ADP
ma-168	86	7	µv	µv	PROPN
ma-168	86	8	.	.	PUNCT
ma-168	87	1	this	this	PRON
ma-168	87	2	shows	show	VERB
ma-168	87	3	that	that	SCONJ
ma-168	87	4	all	all	DET
ma-168	87	5	solu	solu	NOUN
ma-168	87	6	-	-	PUNCT
ma-168	87	7	tions	tion	NOUN
ma-168	87	8	of	of	ADP
ma-168	87	9	the	the	DET
ma-168	87	10	humans	human	NOUN
ma-168	87	11	population	population	NOUN
ma-168	87	12	only	only	ADV
ma-168	87	13	are	be	AUX
ma-168	87	14	confined	confine	VERB
ma-168	87	15	in	in	ADP
ma-168	87	16	the	the	DET
ma-168	87	17	solution	solution	NOUN
ma-168	87	18	set	set	VERB
ma-168	87	19	ωh	ωh	ADP
ma-168	87	20	and	and	CCONJ
ma-168	87	21	all	all	DET
ma-168	87	22	solutions	solution	NOUN
ma-168	87	23	of	of	ADP
ma-168	87	24	theblack	theblack	NOUN
ma-168	87	25	-	-	PUNCT
ma-168	87	26	fly	fly	NOUN
ma-168	87	27	population	population	NOUN
ma-168	87	28	are	be	AUX
ma-168	87	29	confined	confine	VERB
ma-168	87	30	in	in	ADP
ma-168	87	31	ωv	ωv	PRON
ma-168	87	32	.	.	PUNCT
ma-168	88	1	it	it	PRON
ma-168	88	2	also	also	ADV
ma-168	88	3	suffices	suffice	VERB
ma-168	88	4	to	to	PART
ma-168	88	5	say	say	VERB
ma-168	88	6	that	that	SCONJ
ma-168	88	7	ω	ω	PROPN
ma-168	88	8	is	be	AUX
ma-168	88	9	positively	positively	ADV
ma-168	88	10	invariant	invariant	ADJ
ma-168	88	11	as	as	ADP
ma-168	88	12	nh(t	nh(t	NOUN
ma-168	88	13	,	,	PUNCT
ma-168	88	14	xi	xi	X
ma-168	88	15	)	)	PUNCT
ma-168	88	16	≤	≤	NOUN
ma-168	89	1	∑l	∑l	VERB
ma-168	89	2	i=0	i=0	PROPN
ma-168	89	3	ψh(xi	ψh(xi	X
ma-168	89	4	)	)	PUNCT
ma-168	90	1	µh(xi	µh(xi	PROPN
ma-168	90	2	)	)	PUNCT
ma-168	91	1	whenever	whenever	SCONJ
ma-168	91	2	nh(0	nh(0	NOUN
ma-168	91	3	,	,	PUNCT
ma-168	91	4	xi	xi	NOUN
ma-168	91	5	)	)	PUNCT
ma-168	91	6	≤	≤	NOUN
ma-168	92	1	ψh(xi	ψh(xi	PUNCT
ma-168	92	2	)	)	PUNCT
ma-168	93	1	µh(xi	µh(xi	PROPN
ma-168	93	2	)	)	PUNCT
ma-168	93	3	and	and	CCONJ
ma-168	93	4	nv	nv	PROPN
ma-168	93	5	(	(	PUNCT
ma-168	93	6	t	t	PROPN
ma-168	93	7	)	)	PUNCT
ma-168	93	8	≤	≤	NOUN
ma-168	93	9	ψv	ψv	ADP
ma-168	93	10	µv	µv	PRON
ma-168	93	11	if	if	SCONJ
ma-168	93	12	nv	nv	PROPN
ma-168	93	13	(	(	PUNCT
ma-168	93	14	0	0	NUM
ma-168	93	15	)	)	PUNCT
ma-168	93	16	≤	≤	NOUN
ma-168	93	17	ψv	ψv	ADP
ma-168	93	18	µv	µv	PRON
ma-168	93	19	,	,	PUNCT
ma-168	93	20	therefore	therefore	ADV
ma-168	93	21	thesolution	thesolution	NOUN
ma-168	93	22	set	set	VERB
ma-168	93	23	for	for	ADP
ma-168	93	24	the	the	DET
ma-168	93	25	model	model	NOUN
ma-168	93	26	(	(	PUNCT
ma-168	93	27	2.1	2.1	NUM
ma-168	93	28	)	)	PUNCT
ma-168	93	29	exists	exist	VERB
ma-168	93	30	and	and	CCONJ
ma-168	93	31	is	be	AUX
ma-168	93	32	given	give	VERB
ma-168	93	33	by	by	ADP
ma-168	93	34	ω	ω	PROPN
ma-168	93	35	=	=	SYM
ma-168	93	36	ωh	ωh	PROPN
ma-168	93	37	×ωv	×ωv	PROPN
ma-168	93	38	⊂	⊂	PRON
ma-168	93	39	r4	r4	PROPN
ma-168	93	40	+	+	CCONJ
ma-168	93	41	×	×	PROPN
ma-168	93	42	r3	r3	PROPN
ma-168	93	43	+	+	CCONJ
ma-168	93	44	2it	2it	NOUN
ma-168	93	45	remains	remain	VERB
ma-168	93	46	to	to	PART
ma-168	93	47	show	show	VERB
ma-168	93	48	that	that	SCONJ
ma-168	93	49	the	the	DET
ma-168	93	50	solutions	solution	NOUN
ma-168	93	51	of	of	ADP
ma-168	93	52	system	system	NOUN
ma-168	93	53	(	(	PUNCT
ma-168	93	54	2.1	2.1	NUM
ma-168	93	55	)	)	PUNCT
ma-168	93	56	are	be	AUX
ma-168	93	57	nonnegative	nonnegative	ADJ
ma-168	93	58	in	in	ADP
ma-168	93	59	ω	ω	PROPN
ma-168	93	60	for	for	ADP
ma-168	93	61	any	any	DET
ma-168	93	62	time	time	NOUN
ma-168	93	63	t	t	X
ma-168	93	64	>	>	X
ma-168	93	65	0	0	NUM
ma-168	94	1	sincethe	sincethe	PRON
ma-168	94	2	variables	variable	NOUN
ma-168	94	3	represent	represent	VERB
ma-168	94	4	human	human	ADJ
ma-168	94	5	and	and	CCONJ
ma-168	94	6	black	black	ADJ
ma-168	94	7	-	-	PUNCT
ma-168	94	8	fly	fly	NOUN
ma-168	94	9	populations	population	NOUN
ma-168	94	10	.	.	PUNCT
ma-168	95	1	theorem	theorem	VERB
ma-168	95	2	2	2	NUM
ma-168	95	3	:	:	PUNCT
ma-168	95	4	the	the	DET
ma-168	95	5	solutions	solution	NOUN
ma-168	95	6	,	,	PUNCT
ma-168	95	7	sh(t	sh(t	X
ma-168	95	8	,	,	PUNCT
ma-168	95	9	xi	xi	ADJ
ma-168	95	10	)	)	PUNCT
ma-168	95	11	,	,	PUNCT
ma-168	95	12	eh(t	eh(t	PROPN
ma-168	95	13	,	,	PUNCT
ma-168	95	14	xi	xi	PROPN
ma-168	95	15	)	)	PUNCT
ma-168	95	16	,	,	PUNCT
ma-168	95	17	ih(t	ih(t	PROPN
ma-168	95	18	,	,	PUNCT
ma-168	95	19	xi	xi	ADJ
ma-168	95	20	)	)	PUNCT
ma-168	95	21	,	,	PUNCT
ma-168	95	22	rh(t	rh(t	X
ma-168	95	23	,	,	PUNCT
ma-168	95	24	xi	xi	PROPN
ma-168	95	25	)	)	PUNCT
ma-168	95	26	,	,	PUNCT
ma-168	95	27	sv	sv	PROPN
ma-168	95	28	(	(	PUNCT
ma-168	95	29	t	t	PROPN
ma-168	95	30	)	)	PUNCT
ma-168	95	31	,	,	PUNCT
ma-168	95	32	ev	ev	X
ma-168	95	33	(	(	PUNCT
ma-168	95	34	t	t	PROPN
ma-168	95	35	)	)	PUNCT
ma-168	95	36	,	,	PUNCT
ma-168	95	37	iv	iv	X
ma-168	95	38	(	(	PUNCT
ma-168	95	39	t	t	PROPN
ma-168	95	40	)	)	PUNCT
ma-168	95	41	,	,	PUNCT
ma-168	95	42	of	of	ADP
ma-168	95	43	model	model	NOUN
ma-168	95	44	(	(	PUNCT
ma-168	95	45	2.1	2.1	NUM
ma-168	95	46	)	)	PUNCT
ma-168	95	47	with	with	ADP
ma-168	95	48	non	non	ADJ
ma-168	95	49	-	-	ADJ
ma-168	95	50	negative	negative	ADJ
ma-168	95	51	initial	initial	ADJ
ma-168	95	52	conditions	condition	NOUN
ma-168	95	53	in	in	ADP
ma-168	95	54	ω	ω	PROPN
ma-168	95	55	,	,	PUNCT
ma-168	95	56	remain	remain	VERB
ma-168	95	57	nonnegative	nonnegative	ADJ
ma-168	95	58	in	in	ADP
ma-168	95	59	ω	ω	PROPN
ma-168	95	60	for	for	ADP
ma-168	95	61	all	all	DET
ma-168	95	62	t	t	PROPN
ma-168	95	63	>	>	X
ma-168	95	64	0	0	X
ma-168	95	65	.	.	PUNCT
ma-168	96	1	proof	proof	NOUN
ma-168	96	2	:	:	PUNCT
ma-168	96	3	given	give	VERB
ma-168	96	4	that	that	SCONJ
ma-168	96	5	the	the	DET
ma-168	96	6	initial	initial	ADJ
ma-168	96	7	conditions	condition	NOUN
ma-168	96	8	,	,	PUNCT
ma-168	96	9	s0h(xi	s0h(xi	PROPN
ma-168	96	10	)	)	PUNCT
ma-168	96	11	,	,	PUNCT
ma-168	96	12	e0h(xi	e0h(xi	NOUN
ma-168	96	13	)	)	PUNCT
ma-168	96	14	,	,	PUNCT
ma-168	96	15	i0h(xi	i0h(xi	PROPN
ma-168	96	16	)	)	PUNCT
ma-168	96	17	,	,	PUNCT
ma-168	96	18	r0h(xi	r0h(xi	PROPN
ma-168	96	19	)	)	PUNCT
ma-168	96	20	,	,	PUNCT
ma-168	96	21	s0v	s0v	PROPN
ma-168	96	22	,	,	PUNCT
ma-168	96	23	e0v	e0v	X
ma-168	96	24	,	,	PUNCT
ma-168	96	25	i0v	i0v	PROPN
ma-168	96	26	,	,	PUNCT
ma-168	96	27	are	be	AUX
ma-168	96	28	non	non	ADJ
ma-168	96	29	-	-	ADJ
ma-168	96	30	negative	negative	ADJ
ma-168	96	31	and	and	CCONJ
ma-168	96	32	from	from	ADP
ma-168	96	33	(	(	PUNCT
ma-168	96	34	2.1	2.1	NUM
ma-168	96	35	)	)	PUNCT
ma-168	96	36	,	,	PUNCT
ma-168	96	37	dsh(t	dsh(t	PROPN
ma-168	96	38	,	,	PUNCT
ma-168	96	39	xi	xi	NUM
ma-168	96	40	)	)	PUNCT
ma-168	96	41	dt	dt	NOUN
ma-168	97	1	+	+	CCONJ
ma-168	97	2	l∑	l∑	X
ma-168	98	1	i=0	i=0	PROPN
ma-168	98	2	[	[	PUNCT
ma-168	98	3	bλh(xi)iv	bλh(xi)iv	X
ma-168	98	4	(	(	PUNCT
ma-168	98	5	t	t	NOUN
ma-168	98	6	)	)	PUNCT
ma-168	98	7	1	1	NUM
ma-168	99	1	+	+	NUM
ma-168	99	2	νh(xi)iv	νh(xi)iv	ADP
ma-168	99	3	(	(	PUNCT
ma-168	99	4	t	t	PROPN
ma-168	99	5	)	)	PUNCT
ma-168	100	1	+	+	CCONJ
ma-168	100	2	µh(xi	µh(xi	X
ma-168	100	3	)	)	PUNCT
ma-168	100	4	]	]	PUNCT
ma-168	101	1	sh(t	sh(t	X
ma-168	101	2	,	,	PUNCT
ma-168	101	3	xi	xi	PROPN
ma-168	101	4	)	)	PUNCT
ma-168	101	5	≥	≥	NOUN
ma-168	101	6	0	0	NUM
ma-168	102	1	so	so	SCONJ
ma-168	102	2	that	that	SCONJ
ma-168	102	3	d	d	NOUN
ma-168	102	4	dt	dt	X
ma-168	102	5	[	[	PUNCT
ma-168	102	6	l∑	l∑	X
ma-168	102	7	i=0	i=0	X
ma-168	102	8	sh(t	sh(t	X
ma-168	102	9	,	,	PUNCT
ma-168	102	10	xi)exp	xi)exp	PROPN
ma-168	102	11	(	(	PUNCT
ma-168	102	12	∫	∫	PROPN
ma-168	102	13	t	t	PROPN
ma-168	102	14	0	0	NUM
ma-168	103	1	bλh(xi)iv	bλh(xi)iv	PRON
ma-168	103	2	(	(	PUNCT
ma-168	103	3	η	η	NOUN
ma-168	103	4	)	)	PUNCT
ma-168	103	5	1	1	NUM
ma-168	104	1	+	+	NUM
ma-168	104	2	νh(xi)iv	νh(xi)iv	ADP
ma-168	104	3	(	(	PUNCT
ma-168	104	4	η	η	NOUN
ma-168	104	5	)	)	PUNCT
ma-168	104	6	dη	dη	NOUN
ma-168	104	7	+	+	NOUN
ma-168	104	8	µh(xi)t	µh(xi)t	NOUN
ma-168	104	9	)	)	PUNCT
ma-168	104	10	]	]	PUNCT
ma-168	104	11	≥	≥	NOUN
ma-168	104	12	0	0	NUM
ma-168	104	13	,	,	PUNCT
ma-168	104	14	(	(	PUNCT
ma-168	104	15	2.5	2.5	NUM
ma-168	104	16	)	)	PUNCT
ma-168	104	17	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	104	18	eur	eur	PROPN
ma-168	104	19	.	.	PUNCT
ma-168	105	1	j.	j.	PROPN
ma-168	105	2	math	math	PROPN
ma-168	105	3	.	.	PUNCT
ma-168	106	1	anal	anal	PROPN
ma-168	106	2	.	.	PUNCT
ma-168	107	1	10.28924	10.28924	NUM
ma-168	107	2	/	/	SYM
ma-168	107	3	ada	ada	PROPN
ma-168	107	4	/	/	SYM
ma-168	107	5	ma.3.22	ma.3.22	NOUN
ma-168	107	6	5integrating	5integrating	PROPN
ma-168	107	7	(	(	PUNCT
ma-168	107	8	2.5	2.5	NUM
ma-168	107	9	)	)	PUNCT
ma-168	107	10	,	,	PUNCT
ma-168	107	11	we	we	PRON
ma-168	107	12	have	have	VERB
ma-168	107	13	l∑	l∑	ADV
ma-168	108	1	i=0	i=0	X
ma-168	108	2	sh(t	sh(t	X
ma-168	108	3	,	,	PUNCT
ma-168	108	4	xi	xi	ADJ
ma-168	108	5	)	)	PUNCT
ma-168	108	6	≥	≥	NOUN
ma-168	108	7	l∑	l∑	PUNCT
ma-168	109	1	i=0	i=0	PROPN
ma-168	109	2	s0h(xi)exp	s0h(xi)exp	PROPN
ma-168	109	3	[	[	PUNCT
ma-168	109	4	−	−	PROPN
ma-168	109	5	(	(	PUNCT
ma-168	109	6	∫	∫	PROPN
ma-168	109	7	t	t	PROPN
ma-168	109	8	0	0	NUM
ma-168	109	9	bλh(xi)iv	bλh(xi)iv	DET
ma-168	109	10	(	(	PUNCT
ma-168	109	11	η	η	NOUN
ma-168	109	12	)	)	PUNCT
ma-168	109	13	1	1	NUM
ma-168	109	14	+	+	NUM
ma-168	109	15	νh(xi)iv	νh(xi)iv	ADP
ma-168	109	16	(	(	PUNCT
ma-168	109	17	η	η	NOUN
ma-168	109	18	)	)	PUNCT
ma-168	109	19	dη	dη	NOUN
ma-168	109	20	+	+	NOUN
ma-168	109	21	µh(xi)t	µh(xi)t	NOUN
ma-168	109	22	)	)	PUNCT
ma-168	109	23	]	]	PUNCT
ma-168	109	24	≥	≥	NOUN
ma-168	109	25	0	0	NUM
ma-168	109	26	,	,	PUNCT
ma-168	109	27	which	which	PRON
ma-168	109	28	implies	imply	VERB
ma-168	109	29	that	that	SCONJ
ma-168	109	30	for	for	ADP
ma-168	109	31	all	all	DET
ma-168	109	32	t	t	NOUN
ma-168	109	33	>	>	X
ma-168	109	34	0	0	PUNCT
ma-168	109	35	and	and	CCONJ
ma-168	109	36	for	for	ADP
ma-168	109	37	all	all	DET
ma-168	109	38	a	a	DET
ma-168	109	39	∈	∈	NOUN
ma-168	109	40	r+	r+	NOUN
ma-168	109	41	,	,	PUNCT
ma-168	109	42	we	we	PRON
ma-168	109	43	have	have	VERB
ma-168	109	44	sh(t	sh(t	ADJ
ma-168	109	45	,	,	PUNCT
ma-168	109	46	xi	xi	ADJ
ma-168	109	47	)	)	PUNCT
ma-168	109	48	≥	≥	NOUN
ma-168	109	49	l∑	l∑	PUNCT
ma-168	110	1	i=0	i=0	PROPN
ma-168	110	2	s0h(xi)exp	s0h(xi)exp	PROPN
ma-168	110	3	[	[	PUNCT
ma-168	110	4	−	−	PROPN
ma-168	110	5	(	(	PUNCT
ma-168	110	6	∫	∫	PROPN
ma-168	110	7	t	t	PROPN
ma-168	110	8	0	0	NUM
ma-168	110	9	bλh(xi)iv	bλh(xi)iv	DET
ma-168	110	10	(	(	PUNCT
ma-168	110	11	η	η	NOUN
ma-168	110	12	)	)	PUNCT
ma-168	110	13	1	1	NUM
ma-168	110	14	+	+	NUM
ma-168	110	15	νh(xi)iv	νh(xi)iv	ADP
ma-168	110	16	(	(	PUNCT
ma-168	110	17	η	η	NOUN
ma-168	110	18	)	)	PUNCT
ma-168	110	19	dη	dη	NOUN
ma-168	110	20	+	+	NOUN
ma-168	110	21	µh(xi)t	µh(xi)t	NOUN
ma-168	110	22	)	)	PUNCT
ma-168	110	23	]	]	PUNCT
ma-168	110	24	≥	≥	NOUN
ma-168	110	25	0	0	NUM
ma-168	110	26	.	.	PUNCT
ma-168	111	1	hence	hence	ADV
ma-168	111	2	,	,	PUNCT
ma-168	111	3	sh(t	sh(t	X
ma-168	111	4	,	,	PUNCT
ma-168	111	5	xi	xi	ADJ
ma-168	111	6	)	)	PUNCT
ma-168	111	7	>	>	X
ma-168	111	8	0	0	PUNCT
ma-168	112	1	for	for	ADP
ma-168	112	2	any	any	DET
ma-168	112	3	arbitrary	arbitrary	ADJ
ma-168	112	4	xi	xi	X
ma-168	112	5	.	.	PUNCT
ma-168	113	1	also	also	ADV
ma-168	113	2	,	,	PUNCT
ma-168	113	3	we	we	PRON
ma-168	113	4	have	have	VERB
ma-168	113	5	deh(t	deh(t	PROPN
ma-168	113	6	,	,	PUNCT
ma-168	113	7	xi	xi	ADJ
ma-168	113	8	)	)	PUNCT
ma-168	113	9	dt	dt	PROPN
ma-168	114	1	+	+	CCONJ
ma-168	114	2	l∑	l∑	PROPN
ma-168	114	3	i=0	i=0	PROPN
ma-168	114	4	(	(	PUNCT
ma-168	114	5	(	(	PUNCT
ma-168	114	6	αh(xi	αh(xi	PROPN
ma-168	114	7	)	)	PUNCT
ma-168	115	1	+	+	CCONJ
ma-168	115	2	µh(xi)))eh(t	µh(xi)))eh(t	PROPN
ma-168	115	3	,	,	PUNCT
ma-168	115	4	xi	xi	PROPN
ma-168	115	5	)	)	PUNCT
ma-168	115	6	≥	≥	NOUN
ma-168	115	7	0	0	NUM
ma-168	116	1	so	so	SCONJ
ma-168	116	2	that	that	SCONJ
ma-168	116	3	d	d	NOUN
ma-168	116	4	dt	dt	X
ma-168	116	5	[	[	PUNCT
ma-168	116	6	l∑	l∑	X
ma-168	116	7	i=0	i=0	X
ma-168	116	8	eh(t	eh(t	X
ma-168	116	9	,	,	PUNCT
ma-168	116	10	(	(	PUNCT
ma-168	116	11	xi))exp(αh(xi	xi))exp(αh(xi	PROPN
ma-168	116	12	)	)	PUNCT
ma-168	117	1	+	+	CCONJ
ma-168	117	2	µh(xi)t	µh(xi)t	NOUN
ma-168	117	3	)	)	PUNCT
ma-168	117	4	]	]	PUNCT
ma-168	117	5	≥	≥	X
ma-168	117	6	0	0	NUM
ma-168	117	7	(	(	PUNCT
ma-168	117	8	2.6	2.6	NUM
ma-168	117	9	)	)	PUNCT
ma-168	117	10	integrating	integrating	NOUN
ma-168	117	11	(	(	PUNCT
ma-168	117	12	2.6	2.6	NUM
ma-168	117	13	)	)	PUNCT
ma-168	117	14	,	,	PUNCT
ma-168	117	15	we	we	PRON
ma-168	117	16	have	have	VERB
ma-168	117	17	for	for	ADP
ma-168	117	18	all	all	DET
ma-168	117	19	t	t	NOUN
ma-168	117	20	>	>	X
ma-168	117	21	0	0	PUNCT
ma-168	117	22	and	and	CCONJ
ma-168	117	23	for	for	ADP
ma-168	117	24	all	all	DET
ma-168	117	25	a	a	DET
ma-168	117	26	∈	∈	NOUN
ma-168	117	27	mathbbr+	mathbbr+	NOUN
ma-168	117	28	,	,	PUNCT
ma-168	117	29	that	that	PRON
ma-168	117	30	eh(t	eh(t	ADJ
ma-168	117	31	,	,	PUNCT
ma-168	117	32	a	a	PRON
ma-168	117	33	)	)	PUNCT
ma-168	117	34	≥	≥	NOUN
ma-168	117	35	l∑	l∑	PUNCT
ma-168	118	1	i=0	i=0	PROPN
ma-168	118	2	e0h(xi)exp	e0h(xi)exp	PROPN
ma-168	118	3	[	[	X
ma-168	118	4	−(αh(xi	−(αh(xi	NOUN
ma-168	118	5	)	)	PUNCT
ma-168	119	1	+	+	CCONJ
ma-168	119	2	µh(xi))t	µh(xi))t	NOUN
ma-168	119	3	]	]	PUNCT
ma-168	119	4	hence	hence	ADV
ma-168	119	5	,	,	PUNCT
ma-168	119	6	eh(t	eh(t	ADJ
ma-168	119	7	,	,	PUNCT
ma-168	119	8	xi	xi	PROPN
ma-168	119	9	)	)	PUNCT
ma-168	119	10	>	>	X
ma-168	119	11	0	0	PUNCT
ma-168	119	12	for	for	ADP
ma-168	119	13	any	any	DET
ma-168	119	14	arbitrary	arbitrary	ADJ
ma-168	119	15	xi	xi	ADP
ma-168	119	16	also	also	ADV
ma-168	119	17	we	we	PRON
ma-168	119	18	have	have	VERB
ma-168	119	19	d	d	PROPN
ma-168	119	20	ih(t	ih(t	X
ma-168	119	21	,	,	PUNCT
ma-168	119	22	xi	xi	PROPN
ma-168	119	23	)	)	PUNCT
ma-168	119	24	dt	dt	X
ma-168	119	25	≥	≥	NOUN
ma-168	119	26	−	−	X
ma-168	119	27	l∑	l∑	X
ma-168	120	1	i=0	i=0	PROPN
ma-168	120	2	(	(	PUNCT
ma-168	120	3	r(xi	r(xi	PROPN
ma-168	120	4	)	)	PUNCT
ma-168	120	5	+	+	NUM
ma-168	120	6	γh(xi	γh(xi	NOUN
ma-168	120	7	)	)	PUNCT
ma-168	121	1	+	+	CCONJ
ma-168	121	2	µh(xi))ih(t	µh(xi))ih(t	X
ma-168	121	3	)	)	PUNCT
ma-168	122	1	so	so	SCONJ
ma-168	122	2	that	that	SCONJ
ma-168	122	3	d	d	NOUN
ma-168	122	4	dt	dt	X
ma-168	123	1	[	[	X
ma-168	123	2	ih(t)exp(r(xi	ih(t)exp(r(xi	X
ma-168	123	3	)	)	PUNCT
ma-168	124	1	+	+	NUM
ma-168	124	2	γh(xi	γh(xi	NOUN
ma-168	124	3	)	)	PUNCT
ma-168	125	1	+	+	CCONJ
ma-168	125	2	µh(xi))t	µh(xi))t	NOUN
ma-168	125	3	]	]	X
ma-168	125	4	≥	≥	X
ma-168	125	5	0	0	NUM
ma-168	125	6	(	(	PUNCT
ma-168	125	7	2.7	2.7	NUM
ma-168	125	8	)	)	PUNCT
ma-168	125	9	similarly	similarly	ADV
ma-168	125	10	,	,	PUNCT
ma-168	125	11	(	(	PUNCT
ma-168	125	12	2.7	2.7	NUM
ma-168	125	13	)	)	PUNCT
ma-168	125	14	becomes	become	VERB
ma-168	125	15	ih(t	ih(t	PUNCT
ma-168	125	16	,	,	PUNCT
ma-168	125	17	a	a	PRON
ma-168	125	18	)	)	PUNCT
ma-168	125	19	≥	≥	NOUN
ma-168	125	20	l∑	l∑	PUNCT
ma-168	126	1	i=0	i=0	PROPN
ma-168	126	2	i0hexp	i0hexp	PROPN
ma-168	127	1	[	[	X
ma-168	127	2	−(r(xi	−(r(xi	PROPN
ma-168	127	3	)	)	PUNCT
ma-168	127	4	+	+	NUM
ma-168	127	5	γh(xi	γh(xi	NOUN
ma-168	127	6	)	)	PUNCT
ma-168	128	1	+	+	CCONJ
ma-168	128	2	µh(xi))t	µh(xi))t	NOUN
ma-168	128	3	]	]	PUNCT
ma-168	128	4	>	>	X
ma-168	128	5	0for	0for	ADP
ma-168	128	6	all	all	DET
ma-168	128	7	t	t	PROPN
ma-168	128	8	>	>	X
ma-168	128	9	0	0	PUNCT
ma-168	129	1	for	for	ADP
ma-168	129	2	all	all	DET
ma-168	129	3	a	a	DET
ma-168	129	4	∈	∈	NOUN
ma-168	129	5	r+	r+	NOUN
ma-168	129	6	hence	hence	ADV
ma-168	129	7	,	,	PUNCT
ma-168	129	8	ih(t	ih(t	PROPN
ma-168	129	9	,	,	PUNCT
ma-168	129	10	xi	xi	PROPN
ma-168	129	11	)	)	PUNCT
ma-168	129	12	>	>	X
ma-168	129	13	0	0	PUNCT
ma-168	130	1	for	for	ADP
ma-168	130	2	any	any	DET
ma-168	130	3	arbitrary	arbitrary	ADJ
ma-168	130	4	xi	xi	X
ma-168	130	5	.	.	PUNCT
ma-168	131	1	also	also	ADV
ma-168	131	2	from	from	ADP
ma-168	131	3	(	(	PUNCT
ma-168	131	4	2.1	2.1	NUM
ma-168	131	5	)	)	PUNCT
ma-168	131	6	,	,	PUNCT
ma-168	131	7	we	we	PRON
ma-168	131	8	have	have	VERB
ma-168	131	9	drh(t	drh(t	PROPN
ma-168	131	10	,	,	PUNCT
ma-168	131	11	xi	xi	ADJ
ma-168	131	12	)	)	PUNCT
ma-168	131	13	dt	dt	PROPN
ma-168	132	1	+	+	CCONJ
ma-168	132	2	l∑	l∑	PROPN
ma-168	132	3	i=0	i=0	PROPN
ma-168	132	4	(	(	PUNCT
ma-168	132	5	µh(xi	µh(xi	X
ma-168	132	6	)	)	PUNCT
ma-168	133	1	+	+	CCONJ
ma-168	134	1	w(xi))rh(t	w(xi))rh(t	ADJ
ma-168	134	2	,	,	PUNCT
ma-168	134	3	xi	xi	ADJ
ma-168	134	4	)	)	PUNCT
ma-168	134	5	≥	≥	NOUN
ma-168	134	6	0	0	NUM
ma-168	135	1	and	and	CCONJ
ma-168	135	2	we	we	PRON
ma-168	135	3	have	have	VERB
ma-168	135	4	d	d	NOUN
ma-168	135	5	dt	dt	X
ma-168	135	6	[	[	PUNCT
ma-168	135	7	l∑	l∑	X
ma-168	135	8	i=0	i=0	PROPN
ma-168	135	9	rh(t	rh(t	X
ma-168	135	10	,	,	PUNCT
ma-168	135	11	xi)exp((µh(xi	xi)exp((µh(xi	PROPN
ma-168	135	12	)	)	PUNCT
ma-168	136	1	+	+	NUM
ma-168	136	2	w(xi))t	w(xi))t	NOUN
ma-168	136	3	]	]	PUNCT
ma-168	136	4	≥	≥	X
ma-168	136	5	0	0	NUM
ma-168	136	6	(	(	PUNCT
ma-168	136	7	2.8	2.8	NUM
ma-168	136	8	)	)	PUNCT
ma-168	136	9	integrating	integrating	NOUN
ma-168	136	10	(	(	PUNCT
ma-168	136	11	2.8	2.8	NUM
ma-168	136	12	)	)	PUNCT
ma-168	136	13	,	,	PUNCT
ma-168	136	14	we	we	PRON
ma-168	136	15	have	have	VERB
ma-168	136	16	,	,	PUNCT
ma-168	136	17	for	for	ADP
ma-168	136	18	all	all	DET
ma-168	136	19	t	t	NOUN
ma-168	136	20	>	>	X
ma-168	136	21	0	0	PUNCT
ma-168	137	1	and	and	CCONJ
ma-168	137	2	a	a	DET
ma-168	137	3	∈	∈	PROPN
ma-168	137	4	r	r	NOUN
ma-168	137	5	,	,	PUNCT
ma-168	137	6	that	that	PRON
ma-168	137	7	rh(t	rh(t	ADV
ma-168	137	8	,	,	PUNCT
ma-168	137	9	a	a	DET
ma-168	137	10	)	)	PUNCT
ma-168	137	11	≥	≥	NOUN
ma-168	137	12	l∑	l∑	X
ma-168	137	13	i=0	i=0	PROPN
ma-168	137	14	r0h(xi)exp(−(µh(xi	r0h(xi)exp(−(µh(xi	X
ma-168	137	15	)	)	PUNCT
ma-168	137	16	+	+	NUM
ma-168	137	17	w(xi))t	w(xi))t	NOUN
ma-168	137	18	)	)	PUNCT
ma-168	137	19	>	>	X
ma-168	137	20	0	0	NUM
ma-168	138	1	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	138	2	eur	eur	PROPN
ma-168	138	3	.	.	PUNCT
ma-168	139	1	j.	j.	PROPN
ma-168	139	2	math	math	PROPN
ma-168	139	3	.	.	PUNCT
ma-168	140	1	anal	anal	PROPN
ma-168	140	2	.	.	PUNCT
ma-168	141	1	10.28924	10.28924	NUM
ma-168	141	2	/	/	SYM
ma-168	141	3	ada	ada	PROPN
ma-168	141	4	/	/	SYM
ma-168	141	5	ma.3.22	ma.3.22	PROPN
ma-168	141	6	6hence	6hence	NUM
ma-168	141	7	,	,	PUNCT
ma-168	141	8	rh(t	rh(t	ADV
ma-168	141	9	,	,	PUNCT
ma-168	141	10	xi	xi	PROPN
ma-168	141	11	)	)	PUNCT
ma-168	141	12	>	>	X
ma-168	141	13	0	0	PUNCT
ma-168	142	1	for	for	ADP
ma-168	142	2	any	any	DET
ma-168	142	3	arbitrary	arbitrary	ADJ
ma-168	142	4	xi	xi	X
ma-168	142	5	.	.	PUNCT
ma-168	143	1	in	in	ADP
ma-168	143	2	a	a	DET
ma-168	143	3	similar	similar	ADJ
ma-168	143	4	manner	manner	NOUN
ma-168	143	5	,	,	PUNCT
ma-168	143	6	we	we	PRON
ma-168	143	7	have	have	VERB
ma-168	143	8	dsv	dsv	PROPN
ma-168	143	9	dt	dt	PROPN
ma-168	144	1	+	+	CCONJ
ma-168	144	2	[	[	PUNCT
ma-168	144	3	l∑	l∑	X
ma-168	144	4	i=0	i=0	PROPN
ma-168	144	5	bλv	bλv	PROPN
ma-168	144	6	ih(t	ih(t	PUNCT
ma-168	144	7	)	)	PUNCT
ma-168	144	8	)	)	PUNCT
ma-168	145	1	1	1	NUM
ma-168	146	1	+	+	CCONJ
ma-168	146	2	νv	νv	PRON
ma-168	146	3	ih(t	ih(t	PUNCT
ma-168	146	4	)	)	PUNCT
ma-168	147	1	+	+	CCONJ
ma-168	147	2	µv	µv	X
ma-168	147	3	]	]	X
ma-168	147	4	sv	sv	PROPN
ma-168	147	5	(	(	PUNCT
ma-168	147	6	t	t	PROPN
ma-168	147	7	)	)	PUNCT
ma-168	147	8	≥	≥	NOUN
ma-168	147	9	0	0	NUM
ma-168	148	1	so	so	SCONJ
ma-168	148	2	that	that	SCONJ
ma-168	148	3	d	d	NOUN
ma-168	148	4	dt	dt	X
ma-168	148	5	[	[	PUNCT
ma-168	148	6	sv	sv	X
ma-168	148	7	(	(	PUNCT
ma-168	148	8	t)exp	t)exp	PROPN
ma-168	148	9	(	(	PUNCT
ma-168	148	10	∫	∫	PROPN
ma-168	148	11	t	t	PROPN
ma-168	148	12	0	0	NUM
ma-168	148	13	bλv	bλv	PROPN
ma-168	148	14	ih(η	ih(η	NOUN
ma-168	148	15	)	)	PUNCT
ma-168	148	16	)	)	PUNCT
ma-168	148	17	1	1	NUM
ma-168	148	18	+	+	CCONJ
ma-168	148	19	νv	νv	PRON
ma-168	148	20	ih(η	ih(η	NOUN
ma-168	148	21	)	)	PUNCT
ma-168	148	22	d(η	d(η	NOUN
ma-168	148	23	)	)	PUNCT
ma-168	148	24	+	+	CCONJ
ma-168	148	25	µv	µv	PROPN
ma-168	148	26	t	t	PROPN
ma-168	148	27	)	)	PUNCT
ma-168	148	28	]	]	PUNCT
ma-168	148	29	≥	≥	X
ma-168	148	30	0	0	NUM
ma-168	148	31	(	(	PUNCT
ma-168	148	32	2.9	2.9	NUM
ma-168	148	33	)	)	PUNCT
ma-168	148	34	integrating	integrating	NOUN
ma-168	148	35	(	(	PUNCT
ma-168	148	36	2.9	2.9	NUM
ma-168	148	37	)	)	PUNCT
ma-168	148	38	,	,	PUNCT
ma-168	148	39	we	we	PRON
ma-168	148	40	have	have	VERB
ma-168	148	41	sv	sv	INTJ
ma-168	148	42	(	(	PUNCT
ma-168	148	43	t	t	PROPN
ma-168	148	44	)	)	PUNCT
ma-168	148	45	≥	≥	NOUN
ma-168	148	46	s0vexp	s0vexp	PROPN
ma-168	148	47	[	[	PUNCT
ma-168	148	48	−	−	PROPN
ma-168	148	49	(	(	PUNCT
ma-168	148	50	∫	∫	PROPN
ma-168	148	51	t	t	PROPN
ma-168	148	52	0	0	NUM
ma-168	148	53	bλv	bλv	PROPN
ma-168	148	54	ih(η	ih(η	NOUN
ma-168	148	55	)	)	PUNCT
ma-168	148	56	)	)	PUNCT
ma-168	148	57	1	1	NUM
ma-168	149	1	+	+	CCONJ
ma-168	149	2	νv	νv	PRON
ma-168	149	3	ih(η	ih(η	NOUN
ma-168	149	4	)	)	PUNCT
ma-168	149	5	d(η	d(η	NOUN
ma-168	149	6	)	)	PUNCT
ma-168	150	1	+	+	CCONJ
ma-168	150	2	µv	µv	PROPN
ma-168	150	3	t	t	PROPN
ma-168	150	4	)	)	PUNCT
ma-168	150	5	]	]	PUNCT
ma-168	150	6	>	>	X
ma-168	150	7	0	0	NUM
ma-168	150	8	∀	∀	X
ma-168	150	9	t	t	X
ma-168	150	10	>	>	X
ma-168	150	11	0	0	PUNCT
ma-168	151	1	also	also	ADV
ma-168	151	2	we	we	PRON
ma-168	151	3	have	have	VERB
ma-168	151	4	dev	dev	PROPN
ma-168	151	5	dt	dt	NOUN
ma-168	151	6	≥	≥	PROPN
ma-168	152	1	−(αv	−(αv	PROPN
ma-168	152	2	+	+	CCONJ
ma-168	152	3	µv	µv	PROPN
ma-168	152	4	)	)	PUNCT
ma-168	152	5	ev	ev	PROPN
ma-168	152	6	(	(	PUNCT
ma-168	152	7	t	t	PROPN
ma-168	152	8	)	)	PUNCT
ma-168	152	9	which	which	PRON
ma-168	152	10	on	on	ADP
ma-168	152	11	integration	integration	NOUN
ma-168	152	12	gives	give	VERB
ma-168	152	13	ev	ev	PROPN
ma-168	152	14	(	(	PUNCT
ma-168	152	15	t	t	PROPN
ma-168	152	16	)	)	PUNCT
ma-168	152	17	≥	≥	NOUN
ma-168	152	18	ev	ev	X
ma-168	152	19	(	(	PUNCT
ma-168	152	20	0)exp	0)exp	NUM
ma-168	152	21	[	[	X
ma-168	152	22	−(αv	−(αv	X
ma-168	152	23	+	+	PROPN
ma-168	152	24	µv	µv	PROPN
ma-168	152	25	)	)	PUNCT
ma-168	152	26	t	t	X
ma-168	152	27	]	]	PUNCT
ma-168	152	28	>	>	X
ma-168	152	29	0	0	NUM
ma-168	152	30	∀	∀	PUNCT
ma-168	152	31	t	t	X
ma-168	152	32	>	>	X
ma-168	152	33	0	0	PUNCT
ma-168	153	1	(	(	PUNCT
ma-168	153	2	2.10	2.10	NUM
ma-168	153	3	)	)	PUNCT
ma-168	153	4	and	and	CCONJ
ma-168	153	5	finally	finally	ADV
ma-168	153	6	,	,	PUNCT
ma-168	153	7	we	we	PRON
ma-168	153	8	have	have	VERB
ma-168	153	9	d	d	PROPN
ma-168	153	10	iv	iv	ADP
ma-168	153	11	dt	dt	NOUN
ma-168	154	1	+	+	CCONJ
ma-168	154	2	(	(	PUNCT
ma-168	154	3	µv	µv	PROPN
ma-168	154	4	+	+	NUM
ma-168	154	5	γv	γv	X
ma-168	154	6	)	)	PUNCT
ma-168	154	7	iv	iv	X
ma-168	154	8	(	(	PUNCT
ma-168	154	9	t	t	NOUN
ma-168	154	10	)	)	PUNCT
ma-168	155	1	so	so	SCONJ
ma-168	155	2	that	that	SCONJ
ma-168	156	1	d	d	NOUN
ma-168	156	2	dt	dt	X
ma-168	157	1	[	[	X
ma-168	157	2	iv	iv	X
ma-168	157	3	(	(	PUNCT
ma-168	157	4	t)exp(µv	t)exp(µv	NOUN
ma-168	157	5	+	+	SYM
ma-168	157	6	γv	γv	X
ma-168	157	7	)	)	PUNCT
ma-168	157	8	t	t	X
ma-168	157	9	]	]	PUNCT
ma-168	157	10	≥	≥	X
ma-168	157	11	0	0	NUM
ma-168	157	12	(	(	PUNCT
ma-168	157	13	2.11	2.11	NUM
ma-168	157	14	)	)	PUNCT
ma-168	157	15	and	and	CCONJ
ma-168	157	16	we	we	PRON
ma-168	157	17	have	have	VERB
ma-168	157	18	iv	iv	NUM
ma-168	157	19	(	(	PUNCT
ma-168	157	20	t	t	PROPN
ma-168	157	21	)	)	PUNCT
ma-168	157	22	≥	≥	NOUN
ma-168	157	23	iv	iv	NUM
ma-168	157	24	(	(	PUNCT
ma-168	157	25	0)exp	0)exp	NUM
ma-168	157	26	[	[	X
ma-168	157	27	−(µv	−(µv	X
ma-168	157	28	+	+	NOUN
ma-168	157	29	γv	γv	X
ma-168	157	30	)	)	PUNCT
ma-168	157	31	t	t	X
ma-168	157	32	]	]	PUNCT
ma-168	157	33	>	>	X
ma-168	157	34	0	0	NUM
ma-168	157	35	,	,	PUNCT
ma-168	157	36	∀	∀	X
ma-168	157	37	t	t	NOUN
ma-168	157	38	>	>	X
ma-168	157	39	0	0	PUNCT
ma-168	158	1	this	this	PRON
ma-168	158	2	completes	complete	VERB
ma-168	158	3	the	the	DET
ma-168	158	4	proof	proof	NOUN
ma-168	158	5	2	2	NUM
ma-168	158	6	3	3	NUM
ma-168	158	7	.	.	PUNCT
ma-168	159	1	existence	existence	NOUN
ma-168	159	2	and	and	CCONJ
ma-168	159	3	stability	stability	NOUN
ma-168	159	4	of	of	ADP
ma-168	159	5	the	the	DET
ma-168	159	6	equilibrium	equilibrium	NOUN
ma-168	159	7	points	point	NOUN
ma-168	159	8	3.1	3.1	NUM
ma-168	159	9	.	.	PUNCT
ma-168	159	10	disease	disease	NOUN
ma-168	159	11	-	-	PUNCT
ma-168	159	12	free	free	ADJ
ma-168	159	13	equilibrium	equilibrium	NOUN
ma-168	159	14	.	.	PUNCT
ma-168	160	1	the	the	DET
ma-168	160	2	disease	disease	NOUN
ma-168	160	3	-	-	PUNCT
ma-168	160	4	free	free	ADJ
ma-168	160	5	equilibrium	equilibrium	NOUN
ma-168	160	6	(	(	PUNCT
ma-168	160	7	dfe	dfe	PROPN
ma-168	160	8	)	)	PUNCT
ma-168	160	9	points	point	NOUN
ma-168	160	10	are	be	AUX
ma-168	160	11	steady	steady	ADJ
ma-168	160	12	state	state	NOUN
ma-168	160	13	solu	solu	NOUN
ma-168	160	14	-	-	PUNCT
ma-168	160	15	tions	tion	NOUN
ma-168	160	16	that	that	PRON
ma-168	160	17	depict	depict	VERB
ma-168	160	18	the	the	DET
ma-168	160	19	absence	absence	NOUN
ma-168	160	20	of	of	ADP
ma-168	160	21	infection	infection	NOUN
ma-168	160	22	in	in	ADP
ma-168	160	23	both	both	CCONJ
ma-168	160	24	the	the	DET
ma-168	160	25	human	human	ADJ
ma-168	160	26	host	host	NOUN
ma-168	160	27	and	and	CCONJ
ma-168	160	28	black	black	ADJ
ma-168	160	29	-	-	PUNCT
ma-168	160	30	fly	fly	NOUN
ma-168	160	31	vector	vector	NOUN
ma-168	160	32	populations	population	NOUN
ma-168	160	33	,	,	PUNCT
ma-168	160	34	i.e	i.e	PRON
ma-168	160	35	,	,	PUNCT
ma-168	160	36	onchocerciasis	onchocerciasis	NOUN
ma-168	160	37	does	do	AUX
ma-168	160	38	not	not	PART
ma-168	160	39	exist	exist	VERB
ma-168	160	40	in	in	ADP
ma-168	160	41	the	the	DET
ma-168	160	42	population	population	NOUN
ma-168	160	43	.	.	PUNCT
ma-168	161	1	thus	thus	ADV
ma-168	161	2	,	,	PUNCT
ma-168	161	3	the	the	DET
ma-168	161	4	disease	disease	NOUN
ma-168	161	5	-	-	PUNCT
ma-168	161	6	free	free	ADJ
ma-168	161	7	equilibrium	equilibrium	NOUN
ma-168	161	8	point	point	NOUN
ma-168	161	9	,	,	PUNCT
ma-168	161	10	e0	e0	PROPN
ma-168	161	11	,	,	PUNCT
ma-168	161	12	forthe	forthe	PROPN
ma-168	161	13	model	model	NOUN
ma-168	161	14	(	(	PUNCT
ma-168	161	15	2.1	2.1	NUM
ma-168	161	16	)	)	PUNCT
ma-168	161	17	implies	imply	VERB
ma-168	161	18	that	that	DET
ma-168	161	19	s∗(xi)h	s∗(xi)h	NOUN
ma-168	161	20	6=	6=	ADP
ma-168	161	21	0	0	NUM
ma-168	161	22	,	,	PUNCT
ma-168	161	23	e∗h(xi	e∗h(xi	PROPN
ma-168	161	24	)	)	PUNCT
ma-168	161	25	=	=	PUNCT
ma-168	162	1	i∗h	i∗h	PUNCT
ma-168	162	2	=	=	SYM
ma-168	162	3	0(xi	0(xi	NUM
ma-168	162	4	)	)	PUNCT
ma-168	163	1	=	=	PUNCT
ma-168	163	2	r∗h(xi	r∗h(xi	ADJ
ma-168	163	3	)	)	PUNCT
ma-168	163	4	=	=	SYM
ma-168	163	5	0	0	NUM
ma-168	163	6	,	,	PUNCT
ma-168	163	7	s∗v	s∗v	NUM
ma-168	163	8	6=	6=	NUM
ma-168	163	9	0	0	NUM
ma-168	163	10	,	,	PUNCT
ma-168	163	11	ev	ev	X
ma-168	163	12	=	=	SYM
ma-168	163	13	iv	iv	PROPN
ma-168	163	14	=	=	SYM
ma-168	163	15	0and	0and	NOUN
ma-168	163	16	putting	put	VERB
ma-168	163	17	these	these	PRON
ma-168	163	18	into	into	ADP
ma-168	163	19	(	(	PUNCT
ma-168	163	20	2.1	2.1	NUM
ma-168	163	21	)	)	PUNCT
ma-168	163	22	,	,	PUNCT
ma-168	163	23	we	we	PRON
ma-168	163	24	have	have	VERB
ma-168	163	25	s∗(xi)h	s∗(xi)h	X
ma-168	163	26	=	=	SYM
ma-168	163	27	ψh(xi	ψh(xi	X
ma-168	163	28	)	)	PUNCT
ma-168	164	1	µh(xi	µh(xi	PROPN
ma-168	164	2	)	)	PUNCT
ma-168	164	3	and	and	CCONJ
ma-168	164	4	s∗v	s∗v	NUM
ma-168	164	5	=	=	SYM
ma-168	164	6	ψv	ψv	ADP
ma-168	164	7	µv	µv	NOUN
ma-168	164	8	.	.	PUNCT
ma-168	165	1	consequently	consequently	ADV
ma-168	165	2	we	we	PRON
ma-168	165	3	obtain	obtain	VERB
ma-168	165	4	e0as	e0as	X
ma-168	165	5	e0	e0	PROPN
ma-168	166	1	=	=	PUNCT
ma-168	167	1	(	(	PUNCT
ma-168	167	2	ψh(xi	ψh(xi	ADJ
ma-168	167	3	)	)	PUNCT
ma-168	167	4	µh(xi	µh(xi	PROPN
ma-168	167	5	)	)	PUNCT
ma-168	167	6	,	,	PUNCT
ma-168	167	7	0	0	NUM
ma-168	167	8	,	,	PUNCT
ma-168	167	9	0	0	NUM
ma-168	167	10	,	,	PUNCT
ma-168	167	11	0	0	NUM
ma-168	167	12	,	,	PUNCT
ma-168	167	13	ψv	ψv	PROPN
ma-168	167	14	µv	µv	PROPN
ma-168	167	15	,	,	PUNCT
ma-168	167	16	0	0	NUM
ma-168	167	17	,	,	PUNCT
ma-168	167	18	0	0	NUM
ma-168	167	19	)	)	PUNCT
ma-168	167	20	(	(	PUNCT
ma-168	167	21	3.1	3.1	NUM
ma-168	167	22	)	)	PUNCT
ma-168	167	23	a	a	DET
ma-168	167	24	key	key	ADJ
ma-168	167	25	notion	notion	NOUN
ma-168	167	26	in	in	ADP
ma-168	167	27	the	the	DET
ma-168	167	28	analysis	analysis	NOUN
ma-168	167	29	of	of	ADP
ma-168	167	30	infectious	infectious	ADJ
ma-168	167	31	disease	disease	NOUN
ma-168	167	32	models	model	NOUN
ma-168	167	33	is	be	AUX
ma-168	167	34	the	the	DET
ma-168	167	35	basic	basic	ADJ
ma-168	167	36	reproduction	reproduction	NOUN
ma-168	167	37	number	number	NOUN
ma-168	167	38	r0	r0	NOUN
ma-168	167	39	,	,	PUNCT
ma-168	167	40	anepidemiological	anepidemiological	ADJ
ma-168	167	41	threshold	threshold	NOUN
ma-168	167	42	that	that	PRON
ma-168	167	43	determines	determine	VERB
ma-168	167	44	whether	whether	SCONJ
ma-168	167	45	disease	disease	NOUN
ma-168	167	46	dies	die	VERB
ma-168	167	47	out	out	ADV
ma-168	167	48	or	or	CCONJ
ma-168	167	49	persists	persist	VERB
ma-168	167	50	in	in	ADP
ma-168	167	51	the	the	DET
ma-168	167	52	population.thebasic	population.thebasic	ADJ
ma-168	167	53	reproduction	reproduction	NOUN
ma-168	167	54	number	number	NOUN
ma-168	167	55	r0	r0	NOUN
ma-168	167	56	of	of	ADP
ma-168	167	57	the	the	DET
ma-168	167	58	system	system	NOUN
ma-168	167	59	(	(	PUNCT
ma-168	167	60	2.1	2.1	NUM
ma-168	167	61	)	)	PUNCT
ma-168	167	62	is	be	AUX
ma-168	167	63	computed	compute	VERB
ma-168	167	64	using	use	VERB
ma-168	167	65	the	the	DET
ma-168	167	66	next	next	ADJ
ma-168	167	67	generation	generation	NOUN
ma-168	167	68	matrixmethod	matrixmethod	NOUN
ma-168	167	69	and	and	CCONJ
ma-168	167	70	is	be	AUX
ma-168	167	71	given	give	VERB
ma-168	167	72	by	by	ADP
ma-168	167	73	r0	r0	NOUN
ma-168	167	74	=	=	SYM
ma-168	167	75	√	√	PROPN
ma-168	167	76	rhrv	rhrv	NOUN
ma-168	167	77	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	167	78	eur	eur	PROPN
ma-168	167	79	.	.	PUNCT
ma-168	168	1	j.	j.	PROPN
ma-168	168	2	math	math	PROPN
ma-168	168	3	.	.	PUNCT
ma-168	169	1	anal	anal	PROPN
ma-168	169	2	.	.	PUNCT
ma-168	170	1	10.28924	10.28924	NUM
ma-168	170	2	/	/	SYM
ma-168	170	3	ada	ada	PROPN
ma-168	170	4	/	/	SYM
ma-168	170	5	ma.3.22	ma.3.22	NOUN
ma-168	170	6	7	7	NUM
ma-168	170	7	where	where	SCONJ
ma-168	170	8	rh	rh	PROPN
ma-168	170	9	=	=	PUNCT
ma-168	170	10	∑l	∑l	PROPN
ma-168	170	11	i=0	i=0	PROPN
ma-168	170	12	δαhλh(xi	δαhλh(xi	PROPN
ma-168	170	13	)	)	PUNCT
ma-168	170	14	ψh(xi	ψh(xi	PROPN
ma-168	170	15	)	)	PUNCT
ma-168	171	1	µh(xi	µh(xi	X
ma-168	171	2	)	)	PUNCT
ma-168	171	3	(	(	PUNCT
ma-168	171	4	αh(xi	αh(xi	PROPN
ma-168	171	5	)	)	PUNCT
ma-168	172	1	+	+	PROPN
ma-168	172	2	µh(xi	µh(xi	PROPN
ma-168	172	3	)	)	PUNCT
ma-168	172	4	)	)	PUNCT
ma-168	172	5	(	(	PUNCT
ma-168	172	6	r(xi	r(xi	PROPN
ma-168	172	7	)	)	PUNCT
ma-168	173	1	+	+	NUM
ma-168	173	2	γh(xi	γh(xi	PROPN
ma-168	173	3	)	)	PUNCT
ma-168	174	1	+	+	ADJ
ma-168	174	2	µh(xi	µh(xi	PROPN
ma-168	174	3	)	)	PUNCT
ma-168	174	4	)	)	PUNCT
ma-168	174	5	and	and	CCONJ
ma-168	174	6	rv	rv	NOUN
ma-168	174	7	=	=	NOUN
ma-168	174	8	δαvλvψv	δαvλvψv	PROPN
ma-168	174	9	µv	µv	PROPN
ma-168	174	10	(	(	PUNCT
ma-168	174	11	αv+µv	αv+µv	X
ma-168	174	12	)	)	PUNCT
ma-168	174	13	(	(	PUNCT
ma-168	174	14	γv+µv	γv+µv	PROPN
ma-168	174	15	)	)	PUNCT
ma-168	174	16	.	.	PUNCT
ma-168	175	1	the	the	DET
ma-168	175	2	basicreproduction	basicreproduction	NOUN
ma-168	175	3	number	number	NOUN
ma-168	175	4	r0	r0	NOUN
ma-168	175	5	,	,	PUNCT
ma-168	175	6	determines	determine	VERB
ma-168	175	7	whether	whether	SCONJ
ma-168	175	8	onchocerciasis	onchocerciasis	NOUN
ma-168	175	9	dies	die	VERB
ma-168	175	10	out	out	ADV
ma-168	175	11	or	or	CCONJ
ma-168	175	12	persists	persist	VERB
ma-168	175	13	in	in	ADP
ma-168	175	14	the	the	DET
ma-168	175	15	population.therefore	population.therefore	NOUN
ma-168	175	16	,	,	PUNCT
ma-168	175	17	rh	rh	PROPN
ma-168	175	18	describes	describe	VERB
ma-168	175	19	the	the	DET
ma-168	175	20	number	number	NOUN
ma-168	175	21	of	of	ADP
ma-168	175	22	humans	human	NOUN
ma-168	175	23	that	that	SCONJ
ma-168	175	24	one	one	NUM
ma-168	175	25	infectious	infectious	ADJ
ma-168	175	26	black	black	NOUN
ma-168	175	27	-	-	PUNCT
ma-168	175	28	fly	fly	NOUN
ma-168	175	29	infects	infect	NOUN
ma-168	175	30	over	over	ADP
ma-168	175	31	its	its	PRON
ma-168	175	32	expectedinfectious	expectedinfectious	ADJ
ma-168	175	33	period	period	NOUN
ma-168	175	34	in	in	ADP
ma-168	175	35	a	a	DET
ma-168	175	36	completely	completely	ADV
ma-168	175	37	susceptible	susceptible	ADJ
ma-168	175	38	humans	human	NOUN
ma-168	175	39	population	population	NOUN
ma-168	175	40	,	,	PUNCT
ma-168	175	41	while	while	SCONJ
ma-168	175	42	rv	rv	PROPN
ma-168	175	43	is	be	AUX
ma-168	175	44	the	the	DET
ma-168	175	45	number	number	NOUN
ma-168	175	46	of	of	ADP
ma-168	175	47	blac	blac	NOUN
ma-168	175	48	-	-	PUNCT
ma-168	175	49	flies	fly	NOUN
ma-168	175	50	infected	infect	VERB
ma-168	175	51	by	by	ADP
ma-168	175	52	one	one	NUM
ma-168	175	53	infectious	infectious	ADJ
ma-168	175	54	human	human	NOUN
ma-168	175	55	during	during	ADP
ma-168	175	56	the	the	DET
ma-168	175	57	period	period	NOUN
ma-168	175	58	of	of	ADP
ma-168	175	59	infectiousness	infectiousness	NOUN
ma-168	175	60	in	in	ADP
ma-168	175	61	a	a	DET
ma-168	175	62	completely	completely	ADV
ma-168	175	63	susceptibleblack	susceptibleblack	NOUN
ma-168	175	64	-	-	PUNCT
ma-168	175	65	fly	fly	NOUN
ma-168	175	66	population	population	NOUN
ma-168	175	67	.	.	PUNCT
ma-168	176	1	3.2	3.2	NUM
ma-168	176	2	.	.	PUNCT
ma-168	177	1	local	local	ADJ
ma-168	177	2	stability	stability	NOUN
ma-168	177	3	of	of	ADP
ma-168	177	4	the	the	DET
ma-168	177	5	disease	disease	NOUN
ma-168	177	6	-	-	PUNCT
ma-168	177	7	free	free	ADJ
ma-168	177	8	equilibrium	equilibrium	NOUN
ma-168	177	9	point	point	NOUN
ma-168	177	10	e0	e0	PROPN
ma-168	177	11	.	.	PUNCT
ma-168	178	1	using	use	VERB
ma-168	178	2	the	the	DET
ma-168	178	3	basic	basic	ADJ
ma-168	178	4	reproduction	reproduction	NOUN
ma-168	178	5	num	num	ADJ
ma-168	178	6	-	-	PUNCT
ma-168	178	7	ber	ber	NOUN
ma-168	178	8	obtained	obtain	VERB
ma-168	178	9	for	for	ADP
ma-168	178	10	the	the	DET
ma-168	178	11	model	model	NOUN
ma-168	178	12	(	(	PUNCT
ma-168	178	13	2.1	2.1	NUM
ma-168	178	14	)	)	PUNCT
ma-168	178	15	,	,	PUNCT
ma-168	178	16	we	we	PRON
ma-168	178	17	analyse	analyse	VERB
ma-168	178	18	the	the	DET
ma-168	178	19	stability	stability	NOUN
ma-168	178	20	of	of	ADP
ma-168	178	21	the	the	DET
ma-168	178	22	equilibrium	equilibrium	NOUN
ma-168	178	23	point	point	NOUN
ma-168	178	24	in	in	ADP
ma-168	178	25	the	the	DET
ma-168	178	26	followingresult	followingresult	NOUN
ma-168	178	27	.	.	PUNCT
ma-168	179	1	theorem	theorem	VERB
ma-168	179	2	3	3	NUM
ma-168	179	3	:	:	PUNCT
ma-168	179	4	the	the	DET
ma-168	179	5	disease	disease	NOUN
ma-168	179	6	-	-	PUNCT
ma-168	179	7	free	free	ADJ
ma-168	179	8	equilibrium	equilibrium	NOUN
ma-168	179	9	point	point	NOUN
ma-168	179	10	,	,	PUNCT
ma-168	179	11	e0	e0	PROPN
ma-168	179	12	,	,	PUNCT
ma-168	179	13	is	be	AUX
ma-168	179	14	locally	locally	ADV
ma-168	179	15	asymptotically	asymptotically	ADV
ma-168	179	16	stable	stable	ADJ
ma-168	179	17	if	if	SCONJ
ma-168	179	18	r0	r0	NOUN
ma-168	179	19	<	<	X
ma-168	179	20	1	1	NUM
ma-168	179	21	,	,	PUNCT
ma-168	179	22	and	and	CCONJ
ma-168	179	23	unstable	unstable	ADJ
ma-168	179	24	if	if	SCONJ
ma-168	179	25	r0	r0	NOUN
ma-168	179	26	>	>	X
ma-168	179	27	1	1	X
ma-168	179	28	.	.	X
ma-168	180	1	proof	proof	NOUN
ma-168	180	2	:	:	PUNCT
ma-168	180	3	the	the	DET
ma-168	180	4	jacobian	jacobian	ADJ
ma-168	180	5	matrix	matrix	NOUN
ma-168	180	6	of	of	ADP
ma-168	180	7	the	the	DET
ma-168	180	8	system	system	NOUN
ma-168	180	9	(	(	PUNCT
ma-168	180	10	2.1	2.1	NUM
ma-168	180	11	)	)	PUNCT
ma-168	180	12	evaluated	evaluate	VERB
ma-168	180	13	at	at	ADP
ma-168	180	14	the	the	DET
ma-168	180	15	disease	disease	NOUN
ma-168	180	16	-	-	PUNCT
ma-168	180	17	free	free	ADJ
ma-168	180	18	equilibrium	equilibrium	NOUN
ma-168	180	19	point	point	NOUN
ma-168	180	20	e0,is	e0,is	PROPN
ma-168	180	21	obtained	obtain	VERB
ma-168	180	22	as	as	ADP
ma-168	180	23	m(e0	m(e0	NOUN
ma-168	180	24	)	)	PUNCT
ma-168	181	1	=	=	SYM
ma-168	181	2			NOUN
ma-168	181	3	m11	m11	NOUN
ma-168	181	4	0	0	NUM
ma-168	181	5	0	0	NUM
ma-168	182	1	m14	m14	NOUN
ma-168	182	2	0	0	NUM
ma-168	182	3	0	0	NUM
ma-168	183	1	m17	m17	NOUN
ma-168	183	2	0	0	PUNCT
ma-168	184	1	m22	m22	PROPN
ma-168	184	2	0	0	NUM
ma-168	184	3	0	0	NUM
ma-168	184	4	0	0	SYM
ma-168	184	5	0	0	NUM
ma-168	184	6	m27	m27	PROPN
ma-168	184	7	0	0	PROPN
ma-168	184	8	m32	m32	PROPN
ma-168	184	9	m33	m33	PROPN
ma-168	184	10	0	0	NUM
ma-168	184	11	0	0	NUM
ma-168	184	12	0	0	NUM
ma-168	184	13	0	0	NUM
ma-168	184	14	0	0	NUM
ma-168	184	15	0	0	NUM
ma-168	184	16	m43	m43	ADJ
ma-168	184	17	m44	m44	NOUN
ma-168	184	18	0	0	NUM
ma-168	184	19	0	0	NUM
ma-168	184	20	0	0	NUM
ma-168	184	21	0	0	NUM
ma-168	184	22	0	0	NUM
ma-168	185	1	m53	m53	NOUN
ma-168	185	2	0	0	NUM
ma-168	185	3	m55	m55	X
ma-168	185	4	0	0	NUM
ma-168	185	5	0	0	NUM
ma-168	185	6	0	0	NUM
ma-168	185	7	0	0	NUM
ma-168	185	8	m63	m63	NOUN
ma-168	185	9	0	0	NUM
ma-168	185	10	0	0	NUM
ma-168	185	11	m66	m66	NOUN
ma-168	185	12	0	0	NUM
ma-168	185	13	0	0	NUM
ma-168	185	14	0	0	NUM
ma-168	185	15	0	0	NUM
ma-168	185	16	0	0	NUM
ma-168	185	17	0	0	NUM
ma-168	185	18	m76	m76	PROPN
ma-168	185	19	m77	m77	PROPN
ma-168	185	20			PROPN
ma-168	185	21	where	where	SCONJ
ma-168	185	22	m11	m11	NOUN
ma-168	185	23	=	=	SYM
ma-168	185	24	−µh(xi	−µh(xi	PROPN
ma-168	185	25	)	)	PUNCT
ma-168	185	26	,	,	PUNCT
ma-168	185	27	m14	m14	NOUN
ma-168	185	28	=	=	PUNCT
ma-168	185	29	w(a1	w(a1	NOUN
ma-168	185	30	)	)	PUNCT
ma-168	185	31	,	,	PUNCT
ma-168	185	32	m17	m17	NOUN
ma-168	185	33	=	=	SYM
ma-168	185	34	−	−	PROPN
ma-168	185	35	∑l	∑l	INTJ
ma-168	185	36	i=0	i=0	ADJ
ma-168	185	37	δλh(xi	δλh(xi	X
ma-168	185	38	)	)	PUNCT
ma-168	185	39	ψh(xi	ψh(xi	PUNCT
ma-168	185	40	)	)	PUNCT
ma-168	186	1	µh(xi	µh(xi	PROPN
ma-168	186	2	)	)	PUNCT
ma-168	186	3	,	,	PUNCT
ma-168	186	4	m22	m22	PROPN
ma-168	186	5	=	=	SYM
ma-168	186	6	−(αh(xi	−(αh(xi	PROPN
ma-168	186	7	)	)	PUNCT
ma-168	186	8	+	+	CCONJ
ma-168	186	9	µh(xi	µh(xi	PROPN
ma-168	186	10	)	)	PUNCT
ma-168	186	11	)	)	PUNCT
ma-168	186	12	,	,	PUNCT
ma-168	186	13	m27	m27	PROPN
ma-168	186	14	=	=	PUNCT
ma-168	186	15	∑l	∑l	PROPN
ma-168	186	16	i=0	i=0	PROPN
ma-168	186	17	δλh(xi	δλh(xi	X
ma-168	186	18	)	)	PUNCT
ma-168	187	1	ψh(xi	ψh(xi	PUNCT
ma-168	187	2	)	)	PUNCT
ma-168	188	1	µh(xi	µh(xi	PROPN
ma-168	188	2	)	)	PUNCT
ma-168	188	3	,	,	PUNCT
ma-168	188	4	m32	m32	PROPN
ma-168	188	5	=	=	SYM
ma-168	188	6	αh(xi	αh(xi	PROPN
ma-168	188	7	)	)	PUNCT
ma-168	188	8	,	,	PUNCT
ma-168	188	9	m33	m33	PROPN
ma-168	188	10	=	=	SYM
ma-168	188	11	−(r(xi	−(r(xi	PROPN
ma-168	188	12	)	)	PUNCT
ma-168	188	13	+	+	NUM
ma-168	188	14	γh(xi	γh(xi	NOUN
ma-168	188	15	)	)	PUNCT
ma-168	189	1	+	+	CCONJ
ma-168	189	2	µh(xi	µh(xi	ADJ
ma-168	189	3	)	)	PUNCT
ma-168	189	4	)	)	PUNCT
ma-168	189	5	,	,	PUNCT
ma-168	189	6	m43	m43	PROPN
ma-168	189	7	=	=	SYM
ma-168	189	8	r(xi	r(xi	PROPN
ma-168	189	9	)	)	PUNCT
ma-168	189	10	,	,	PUNCT
ma-168	189	11	m44	m44	PROPN
ma-168	189	12	=	=	SYM
ma-168	189	13	−(µh(xi	−(µh(xi	X
ma-168	189	14	)	)	PUNCT
ma-168	190	1	+	+	CCONJ
ma-168	190	2	w(xi	w(xi	NUM
ma-168	190	3	)	)	PUNCT
ma-168	190	4	)	)	PUNCT
ma-168	191	1	,	,	PUNCT
ma-168	191	2	m53	m53	NOUN
ma-168	191	3	=	=	SYM
ma-168	191	4	−	−	PROPN
ma-168	191	5	δλvψv	δλvψv	NOUN
ma-168	191	6	µv	µv	NOUN
ma-168	191	7	,	,	PUNCT
ma-168	191	8	m55	m55	PROPN
ma-168	191	9	=	=	SYM
ma-168	191	10	−µv	−µv	PROPN
ma-168	191	11	,	,	PUNCT
ma-168	191	12	m63	m63	NOUN
ma-168	191	13	=	=	SYM
ma-168	191	14	δλvψv	δλvψv	NOUN
ma-168	191	15	µv	µv	NOUN
ma-168	191	16	,	,	PUNCT
ma-168	191	17	m66	m66	PROPN
ma-168	191	18	=	=	SYM
ma-168	191	19	−(αv	−(αv	PROPN
ma-168	191	20	+	+	PROPN
ma-168	191	21	µv	µv	PROPN
ma-168	191	22	)	)	PUNCT
ma-168	191	23	,	,	PUNCT
ma-168	191	24	m76	m76	X
ma-168	191	25	=	=	SYM
ma-168	191	26	αv	αv	NOUN
ma-168	191	27	,	,	PUNCT
ma-168	191	28	m77	m77	PROPN
ma-168	191	29	=	=	SYM
ma-168	191	30	−(µv	−(µv	PROPN
ma-168	191	31	+	+	X
ma-168	191	32	γv	γv	NOUN
ma-168	191	33	)	)	PUNCT
ma-168	191	34	we	we	PRON
ma-168	191	35	need	need	VERB
ma-168	191	36	to	to	PART
ma-168	191	37	show	show	VERB
ma-168	191	38	that	that	SCONJ
ma-168	191	39	all	all	DET
ma-168	191	40	the	the	DET
ma-168	191	41	eigenvalues	eigenvalue	NOUN
ma-168	191	42	of	of	ADP
ma-168	191	43	m(e0	m(e0	NOUN
ma-168	191	44	)	)	PUNCT
ma-168	191	45	are	be	AUX
ma-168	191	46	negative	negative	ADJ
ma-168	191	47	.	.	PUNCT
ma-168	192	1	as	as	SCONJ
ma-168	192	2	the	the	DET
ma-168	192	3	firstand	firstand	NOUN
ma-168	192	4	fifth	fifth	ADJ
ma-168	192	5	columns	column	NOUN
ma-168	192	6	form	form	VERB
ma-168	192	7	the	the	DET
ma-168	192	8	two	two	NUM
ma-168	192	9	negative	negative	ADJ
ma-168	192	10	eigenvalues	eigenvalue	NOUN
ma-168	192	11	,	,	PUNCT
ma-168	192	12	h(xi	h(xi	NUM
ma-168	192	13	)	)	PUNCT
ma-168	192	14	and	and	CCONJ
ma-168	192	15	−v	−v	NOUN
ma-168	192	16	,	,	PUNCT
ma-168	192	17	the	the	DET
ma-168	192	18	other	other	ADJ
ma-168	192	19	five	five	NUM
ma-168	192	20	eigenvalues	eigenvalue	NOUN
ma-168	192	21	canbe	canbe	NOUN
ma-168	192	22	obtained	obtain	VERB
ma-168	192	23	from	from	ADP
ma-168	192	24	the	the	DET
ma-168	192	25	sub	sub	NOUN
ma-168	192	26	-	-	NOUN
ma-168	192	27	matrix	matrix	ADJ
ma-168	192	28	,	,	PUNCT
ma-168	192	29	m1(e0	m1(e0	NOUN
ma-168	192	30	)	)	PUNCT
ma-168	192	31	,	,	PUNCT
ma-168	192	32	formed	form	VERB
ma-168	192	33	by	by	ADP
ma-168	192	34	excluding	exclude	VERB
ma-168	192	35	the	the	DET
ma-168	192	36	first	first	ADJ
ma-168	192	37	and	and	CCONJ
ma-168	192	38	fifth	fifth	ADJ
ma-168	192	39	rows	row	NOUN
ma-168	192	40	and	and	CCONJ
ma-168	192	41	columnsof	columnsof	ADJ
ma-168	192	42	m(e0	m(e0	NOUN
ma-168	192	43	)	)	PUNCT
ma-168	192	44	.	.	PUNCT
ma-168	193	1	hence	hence	ADV
ma-168	193	2	m1(e0	m1(e0	NOUN
ma-168	193	3	)	)	PUNCT
ma-168	193	4	=	=	PUNCT
ma-168	194	1			NOUN
ma-168	194	2	m	m	VERB
ma-168	194	3	′11	′11	VERB
ma-168	194	4	0	0	NUM
ma-168	194	5	0	0	NUM
ma-168	194	6	0	0	NUM
ma-168	194	7	m	m	VERB
ma-168	194	8	′15	′15	NOUN
ma-168	194	9	αh(xi	αh(xi	PROPN
ma-168	194	10	)	)	PUNCT
ma-168	195	1	m	m	PROPN
ma-168	195	2	′22	′22	PROPN
ma-168	195	3	0	0	NUM
ma-168	195	4	0	0	NUM
ma-168	195	5	0	0	NUM
ma-168	195	6	0	0	NUM
ma-168	195	7	r(xi	r(xi	PROPN
ma-168	195	8	)	)	PUNCT
ma-168	195	9	m	m	VERB
ma-168	195	10	′33	′33	ADV
ma-168	195	11	0	0	NUM
ma-168	195	12	0	0	NUM
ma-168	195	13	0	0	NUM
ma-168	195	14	0	0	NUM
ma-168	195	15	δλvψv	δλvψv	NOUN
ma-168	195	16	µv	µv	NOUN
ma-168	195	17	0	0	PUNCT
ma-168	196	1	−(αv	−(αv	PROPN
ma-168	196	2	+	+	PROPN
ma-168	196	3	µv	µv	PROPN
ma-168	196	4	)	)	PUNCT
ma-168	196	5	0	0	NUM
ma-168	196	6	0	0	NUM
ma-168	196	7	0	0	NUM
ma-168	196	8	0	0	NUM
ma-168	196	9	αv	αv	NOUN
ma-168	196	10	−(µv	−(µv	PROPN
ma-168	196	11	+	+	NUM
ma-168	196	12	λv	λv	X
ma-168	196	13	)	)	PUNCT
ma-168	196	14			PROPN
ma-168	196	15	in	in	ADP
ma-168	196	16	the	the	DET
ma-168	196	17	same	same	ADJ
ma-168	196	18	way	way	NOUN
ma-168	196	19	,	,	PUNCT
ma-168	196	20	the	the	DET
ma-168	196	21	third	third	ADJ
ma-168	196	22	column	column	NOUN
ma-168	196	23	of	of	ADP
ma-168	196	24	m1(e0	m1(e0	NOUN
ma-168	196	25	)	)	PUNCT
ma-168	196	26	contains	contain	VERB
ma-168	196	27	only	only	ADV
ma-168	196	28	the	the	DET
ma-168	196	29	diagonal	diagonal	ADJ
ma-168	196	30	term	term	NOUN
ma-168	196	31	which	which	PRON
ma-168	196	32	forms	form	VERB
ma-168	196	33	anegative	anegative	ADJ
ma-168	196	34	eigenvalue	eigenvalue	NOUN
ma-168	196	35	,	,	PUNCT
ma-168	196	36	(	(	PUNCT
ma-168	196	37	µh(xi	µh(xi	X
ma-168	196	38	)	)	PUNCT
ma-168	197	1	+	+	NUM
ma-168	197	2	w(xi	w(xi	NUM
ma-168	197	3	)	)	PUNCT
ma-168	197	4	)	)	PUNCT
ma-168	197	5	.	.	PUNCT
ma-168	198	1	the	the	DET
ma-168	198	2	remaining	remain	VERB
ma-168	198	3	four	four	NUM
ma-168	198	4	eigenvalues	eigenvalue	NOUN
ma-168	198	5	are	be	AUX
ma-168	198	6	obtained	obtain	VERB
ma-168	198	7	from	from	ADP
ma-168	198	8	the	the	DET
ma-168	198	9	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	198	10	eur	eur	PROPN
ma-168	198	11	.	.	PUNCT
ma-168	199	1	j.	j.	PROPN
ma-168	199	2	math	math	PROPN
ma-168	199	3	.	.	PUNCT
ma-168	200	1	anal	anal	PROPN
ma-168	200	2	.	.	PUNCT
ma-168	201	1	10.28924	10.28924	NUM
ma-168	201	2	/	/	SYM
ma-168	201	3	ada	ada	PROPN
ma-168	201	4	/	/	SYM
ma-168	201	5	ma.3.22	ma.3.22	NOUN
ma-168	201	6	8sub	8sub	ADJ
ma-168	201	7	-	-	NOUN
ma-168	201	8	matrix	matrix	NOUN
ma-168	201	9	m2(e0	m2(e0	NOUN
ma-168	201	10	)	)	PUNCT
ma-168	201	11	given	give	VERB
ma-168	201	12	by	by	ADP
ma-168	201	13	m2(e0	m2(e0	PRON
ma-168	201	14	)	)	PUNCT
ma-168	201	15	=	=	SYM
ma-168	202	1			ADJ
ma-168	202	2	m	m	VERB
ma-168	202	3	′′11	′′11	PROPN
ma-168	202	4	0	0	NUM
ma-168	202	5	0	0	NUM
ma-168	202	6	m	m	PROPN
ma-168	202	7	′′14	′′14	PROPN
ma-168	202	8	αh(xi	αh(xi	PROPN
ma-168	202	9	)	)	PUNCT
ma-168	203	1	m	m	PROPN
ma-168	203	2	′22	′22	PROPN
ma-168	203	3	0	0	NUM
ma-168	203	4	0	0	NUM
ma-168	203	5	0	0	NUM
ma-168	203	6	δλvψv	δλvψv	NOUN
ma-168	203	7	µv	µv	NOUN
ma-168	204	1	−(αv	−(αv	PROPN
ma-168	204	2	+	+	CCONJ
ma-168	204	3	µv	µv	PROPN
ma-168	204	4	)	)	PUNCT
ma-168	204	5	0	0	NUM
ma-168	205	1	0	0	NUM
ma-168	205	2	0	0	NUM
ma-168	205	3	αv	αv	NOUN
ma-168	205	4	−(µv	−(µv	PROPN
ma-168	206	1	+	+	PROPN
ma-168	206	2	λv	λv	X
ma-168	206	3	)	)	PUNCT
ma-168	206	4			PROPN
ma-168	207	1	thus	thus	ADV
ma-168	207	2	,	,	PUNCT
ma-168	207	3	the	the	DET
ma-168	207	4	eigenvalues	eigenvalue	NOUN
ma-168	207	5	of	of	ADP
ma-168	207	6	the	the	DET
ma-168	207	7	matrix	matrix	NOUN
ma-168	207	8	m2(e0	m2(e0	NOUN
ma-168	207	9	)	)	PUNCT
ma-168	207	10	are	be	AUX
ma-168	207	11	the	the	DET
ma-168	207	12	roots	root	NOUN
ma-168	207	13	of	of	ADP
ma-168	207	14	the	the	DET
ma-168	207	15	characteristic	characteristic	ADJ
ma-168	207	16	equation	equation	NOUN
ma-168	207	17	of	of	ADP
ma-168	207	18	the	the	DET
ma-168	207	19	form	form	NOUN
ma-168	207	20	(	(	PUNCT
ma-168	207	21	ξ+αh(xi))(ξ+	ξ+αh(xi))(ξ+	ADJ
ma-168	207	22	r(xi	r(xi	X
ma-168	207	23	)	)	PUNCT
ma-168	207	24	+	+	NUM
ma-168	207	25	γh(xi	γh(xi	PROPN
ma-168	207	26	)	)	PUNCT
ma-168	208	1	+	+	ADP
ma-168	208	2	µh(xi))(ξ+µv	µh(xi))(ξ+µv	NOUN
ma-168	208	3	+	+	ADJ
ma-168	208	4	γ)−	γ)−	PROPN
ma-168	208	5	l∑	l∑	X
ma-168	208	6	i=0	i=0	ADJ
ma-168	208	7	δ2αh(xi)λh(xi)ψh(xi)vλvψv	δ2αh(xi)λh(xi)ψh(xi)vλvψv	ADJ
ma-168	208	8	µh(xi)µv	µh(xi)µv	NOUN
ma-168	208	9	=	=	SYM
ma-168	208	10	0	0	NUM
ma-168	208	11	(	(	PUNCT
ma-168	208	12	3.2	3.2	NUM
ma-168	208	13	)	)	PUNCT
ma-168	208	14	if	if	SCONJ
ma-168	208	15	we	we	PRON
ma-168	208	16	let	let	VERB
ma-168	208	17	y1	y1	NOUN
ma-168	208	18	=	=	SYM
ma-168	208	19	αh(xi	αh(xi	PROPN
ma-168	208	20	)	)	PUNCT
ma-168	208	21	+	+	CCONJ
ma-168	208	22	µh(xi	µh(xi	X
ma-168	208	23	)	)	PUNCT
ma-168	208	24	,	,	PUNCT
ma-168	208	25	y2	y2	PROPN
ma-168	208	26	=	=	SYM
ma-168	208	27	r(xi	r(xi	PROPN
ma-168	208	28	)	)	PUNCT
ma-168	208	29	+	+	NUM
ma-168	208	30	γh(xi	γh(xi	NOUN
ma-168	208	31	)	)	PUNCT
ma-168	209	1	+	+	CCONJ
ma-168	209	2	µh(xi	µh(xi	X
ma-168	209	3	)	)	PUNCT
ma-168	209	4	,	,	PUNCT
ma-168	209	5	y3	y3	NOUN
ma-168	209	6	=	=	SYM
ma-168	209	7	αv	αv	NOUN
ma-168	209	8	+	+	CCONJ
ma-168	209	9	µv	µv	NOUN
ma-168	209	10	,	,	PUNCT
ma-168	209	11	and	and	CCONJ
ma-168	209	12	y4	y4	NOUN
ma-168	209	13	=	=	PUNCT
ma-168	210	1	µv	µv	PROPN
ma-168	210	2	+	+	NUM
ma-168	210	3	γv	γv	NOUN
ma-168	210	4	,	,	PUNCT
ma-168	210	5	then(3.2	then(3.2	X
ma-168	210	6	)	)	PUNCT
ma-168	210	7	becomes	become	VERB
ma-168	210	8	x4ξ	x4ξ	PROPN
ma-168	210	9	4	4	NUM
ma-168	210	10	+	+	NOUN
ma-168	210	11	x3ξ	x3ξ	PROPN
ma-168	210	12	3	3	NUM
ma-168	211	1	+	+	NOUN
ma-168	211	2	x2ξ	x2ξ	PROPN
ma-168	211	3	2	2	NUM
ma-168	211	4	+	+	NOUN
ma-168	211	5	x1ξ	x1ξ	PROPN
ma-168	212	1	+	+	ADJ
ma-168	212	2	x0	x0	PROPN
ma-168	212	3	=	=	SYM
ma-168	212	4	0	0	NUM
ma-168	212	5	,	,	PUNCT
ma-168	212	6	(	(	PUNCT
ma-168	212	7	3.3	3.3	NUM
ma-168	212	8	)	)	PUNCT
ma-168	213	1	where	where	SCONJ
ma-168	213	2	x4	x4	PROPN
ma-168	213	3	=	=	SYM
ma-168	213	4	1	1	NUM
ma-168	213	5	x3	x3	NOUN
ma-168	213	6	=	=	SYM
ma-168	213	7	y1	y1	NOUN
ma-168	213	8	+	+	CCONJ
ma-168	213	9	y2	y2	NOUN
ma-168	213	10	+	+	CCONJ
ma-168	213	11	y3	y3	NOUN
ma-168	213	12	+	+	CCONJ
ma-168	213	13	y4	y4	ADJ
ma-168	213	14	x2	x2	PROPN
ma-168	214	1	=	=	PRON
ma-168	214	2	(	(	PUNCT
ma-168	214	3	y1	y1	INTJ
ma-168	214	4	+	+	CCONJ
ma-168	214	5	y2)(y2	y2)(y2	NOUN
ma-168	214	6	+	+	CCONJ
ma-168	214	7	y4	y4	NUM
ma-168	214	8	)	)	PUNCT
ma-168	215	1	+	+	NUM
ma-168	215	2	y1y2	y1y2	PUNCT
ma-168	216	1	+	+	NUM
ma-168	216	2	y3y4	y3y4	PROPN
ma-168	216	3	x1	x1	NOUN
ma-168	216	4	=	=	SYM
ma-168	216	5	(	(	PUNCT
ma-168	216	6	y1	y1	INTJ
ma-168	216	7	+	+	NUM
ma-168	216	8	y2)y3y4	y2)y3y4	NOUN
ma-168	216	9	+	+	CCONJ
ma-168	216	10	(	(	PUNCT
ma-168	216	11	y3	y3	NOUN
ma-168	216	12	+	+	CCONJ
ma-168	216	13	y4)y1y2	y4)y1y2	ADJ
ma-168	216	14	x0	x0	NOUN
ma-168	216	15	=	=	PUNCT
ma-168	217	1	y1y2y3y4	y1y2y3y4	NOUN
ma-168	217	2	−	−	PROPN
ma-168	217	3	∑l	∑l	INTJ
ma-168	217	4	i=0	i=0	PROPN
ma-168	217	5	δ2αh(xi	δ2αh(xi	PROPN
ma-168	217	6	)	)	PUNCT
ma-168	218	1	λh(xi	λh(xi	PROPN
ma-168	218	2	)	)	PUNCT
ma-168	219	1	ψh(xi	ψh(xi	PUNCT
ma-168	219	2	)	)	PUNCT
ma-168	220	1	vλvψv	vλvψv	PROPN
ma-168	220	2	µh(xi	µh(xi	PROPN
ma-168	220	3	)	)	PUNCT
ma-168	220	4	µv	µv	AUX
ma-168	220	5			ADJ
ma-168	220	6	(	(	PUNCT
ma-168	220	7	3.4	3.4	NUM
ma-168	220	8	)	)	PUNCT
ma-168	220	9	expressing	express	VERB
ma-168	220	10	x0	x0	PROPN
ma-168	220	11	in	in	ADP
ma-168	220	12	terms	term	NOUN
ma-168	220	13	of	of	ADP
ma-168	220	14	reproduction	reproduction	NOUN
ma-168	220	15	number	number	NOUN
ma-168	220	16	r0	r0	NOUN
ma-168	220	17	,	,	PUNCT
ma-168	220	18	we	we	PRON
ma-168	220	19	have	have	VERB
ma-168	220	20	x0	x0	PROPN
ma-168	220	21	=	=	SYM
ma-168	220	22	y1y2y3y4(1−r2	y1y2y3y4(1−r2	NOUN
ma-168	220	23	0	0	NUM
ma-168	220	24	)	)	PUNCT
ma-168	220	25	(	(	PUNCT
ma-168	220	26	3.5	3.5	NUM
ma-168	220	27	)	)	PUNCT
ma-168	220	28	we	we	PRON
ma-168	220	29	can	can	AUX
ma-168	220	30	see	see	VERB
ma-168	220	31	from	from	ADP
ma-168	220	32	(	(	PUNCT
ma-168	220	33	3.4	3.4	NUM
ma-168	220	34	)	)	PUNCT
ma-168	221	1	that	that	PRON
ma-168	222	1	x1	x1	PROPN
ma-168	222	2	>	>	X
ma-168	222	3	0	0	PROPN
ma-168	222	4	,	,	PUNCT
ma-168	222	5	x2	x2	PROPN
ma-168	222	6	>	>	X
ma-168	222	7	0	0	NUM
ma-168	222	8	,	,	PUNCT
ma-168	222	9	x3	x3	VERB
ma-168	222	10	>	>	X
ma-168	222	11	0	0	NUM
ma-168	222	12	,	,	PUNCT
ma-168	222	13	x4	x4	X
ma-168	222	14	>	>	X
ma-168	222	15	0	0	NUM
ma-168	222	16	,	,	PUNCT
ma-168	222	17	since	since	SCONJ
ma-168	222	18	all	all	DET
ma-168	222	19	yis	yis	NOUN
ma-168	222	20	are	be	AUX
ma-168	222	21	positive	positive	ADJ
ma-168	222	22	.	.	PUNCT
ma-168	223	1	moreover	moreover	ADV
ma-168	223	2	,	,	PUNCT
ma-168	223	3	if	if	SCONJ
ma-168	223	4	r0	r0	NOUN
ma-168	223	5	<	<	X
ma-168	223	6	1	1	NUM
ma-168	223	7	,	,	PUNCT
ma-168	223	8	it	it	PRON
ma-168	223	9	follows	follow	VERB
ma-168	223	10	from	from	ADP
ma-168	223	11	(	(	PUNCT
ma-168	223	12	3.5	3.5	NUM
ma-168	223	13	)	)	PUNCT
ma-168	223	14	that	that	PRON
ma-168	223	15	x0	x0	PROPN
ma-168	223	16	>	>	X
ma-168	223	17	0	0	X
ma-168	223	18	.	.	PUNCT
ma-168	224	1	thus	thus	ADV
ma-168	224	2	,	,	PUNCT
ma-168	224	3	using	use	VERB
ma-168	224	4	the	the	DET
ma-168	224	5	routh	routh	PROPN
ma-168	224	6	-	-	PUNCT
ma-168	224	7	hurwitz	hurwitz	PROPN
ma-168	224	8	criterion	criterion	NOUN
ma-168	224	9	,	,	PUNCT
ma-168	224	10	we	we	PRON
ma-168	224	11	have	have	VERB
ma-168	224	12	h1	h1	NOUN
ma-168	224	13	=	=	SYM
ma-168	224	14	x3	x3	VERB
ma-168	224	15	>	>	X
ma-168	224	16	0	0	NUM
ma-168	224	17	h2	h2	PROPN
ma-168	224	18	=	=	SYM
ma-168	225	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-168	225	2	x3	x3	PROPN
ma-168	226	1	x4	x4	PROPN
ma-168	226	2	x1	x1	PROPN
ma-168	227	1	x2	x2	X
ma-168	227	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-168	228	1	=	=	SYM
ma-168	228	2	y1(y2	y1(y2	PROPN
ma-168	228	3	+	+	NUM
ma-168	228	4	y3	y3	NOUN
ma-168	228	5	+	+	CCONJ
ma-168	228	6	y4)(y1	y4)(y1	ADJ
ma-168	228	7	+	+	CCONJ
ma-168	228	8	y2	y2	NOUN
ma-168	228	9	+	+	CCONJ
ma-168	228	10	y3	y3	NOUN
ma-168	228	11	+	+	CCONJ
ma-168	228	12	y4	y4	NUM
ma-168	228	13	)	)	PUNCT
ma-168	229	1	+	+	CCONJ
ma-168	229	2	(	(	PUNCT
ma-168	229	3	y2	y2	VERB
ma-168	229	4	+	+	CCONJ
ma-168	229	5	y3)(y2	y3)(y2	PROPN
ma-168	230	1	+	+	NUM
ma-168	230	2	y4)(y3	y4)(y3	NOUN
ma-168	230	3	+	+	CCONJ
ma-168	230	4	y4	y4	NUM
ma-168	230	5	)	)	PUNCT
ma-168	231	1	>	>	X
ma-168	232	1	0similarly	0similarly	ADV
ma-168	232	2	we	we	PRON
ma-168	232	3	have	have	VERB
ma-168	232	4	h3	h3	NOUN
ma-168	232	5	>	>	X
ma-168	232	6	0	0	PUNCT
ma-168	232	7	and	and	CCONJ
ma-168	232	8	h4	h4	PROPN
ma-168	232	9	>	>	X
ma-168	232	10	0	0	NUM
ma-168	232	11	where	where	SCONJ
ma-168	232	12	h3	h3	NOUN
ma-168	232	13	=	=	SYM
ma-168	232	14	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ma-168	232	15	x3	x3	PROPN
ma-168	232	16	x4	x4	PROPN
ma-168	232	17	0	0	PUNCT
ma-168	233	1	x1	x1	PRON
ma-168	234	1	x2	x2	NOUN
ma-168	234	2	x3	x3	ADJ
ma-168	234	3	0	0	NUM
ma-168	235	1	x0	x0	PROPN
ma-168	235	2	x1	x1	PROPN
ma-168	235	3	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ma-168	235	4	and	and	CCONJ
ma-168	235	5	h4	h4	PROPN
ma-168	235	6	=	=	SYM
ma-168	235	7	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ma-168	235	8	x3	x3	PROPN
ma-168	235	9	x4	x4	PROPN
ma-168	235	10	0	0	NUM
ma-168	235	11	0	0	NUM
ma-168	236	1	x1	x1	NUM
ma-168	237	1	x2	x2	NOUN
ma-168	237	2	x3	x3	PROPN
ma-168	237	3	x4	x4	PROPN
ma-168	237	4	0	0	NUM
ma-168	238	1	x0	x0	PROPN
ma-168	238	2	x1	x1	PROPN
ma-168	239	1	x2	x2	NOUN
ma-168	239	2	0	0	NUM
ma-168	239	3	0	0	NUM
ma-168	239	4	0	0	NUM
ma-168	239	5	x0	x0	PROPN
ma-168	239	6	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ma-168	239	7	theref	theref	PROPN
ma-168	239	8	ore	ore	NOUN
ma-168	239	9	,	,	PUNCT
ma-168	239	10	al	al	PROPN
ma-168	239	11	ltheeigenvaluesof	ltheeigenvaluesof	VERB
ma-168	239	12	thejacobianmatr	thejacobianmatr	ADV
ma-168	239	13	ixm(e0	ixm(e0	NOUN
ma-168	239	14	)	)	PUNCT
ma-168	239	15	have	have	VERB
ma-168	239	16	negative	negative	ADJ
ma-168	239	17	real	real	ADJ
ma-168	239	18	parts	part	NOUN
ma-168	239	19	when	when	SCONJ
ma-168	239	20	r0	r0	VERB
ma-168	239	21	<	<	X
ma-168	239	22	1	1	NUM
ma-168	239	23	and	and	CCONJ
ma-168	239	24	the	the	DET
ma-168	239	25	disease	disease	NOUN
ma-168	239	26	-	-	PUNCT
ma-168	239	27	free	free	ADJ
ma-168	239	28	equilibrium	equilibrium	NOUN
ma-168	239	29	point	point	NOUN
ma-168	239	30	is	be	AUX
ma-168	239	31	locally	locally	ADV
ma-168	239	32	asymptotically	asymptotically	ADV
ma-168	239	33	stable	stable	ADJ
ma-168	239	34	.	.	PUNCT
ma-168	240	1	however	however	ADV
ma-168	240	2	,	,	PUNCT
ma-168	240	3	when	when	SCONJ
ma-168	240	4	r0	r0	NOUN
ma-168	240	5	>	>	X
ma-168	240	6	1,we	1,we	NUM
ma-168	240	7	see	see	VERB
ma-168	240	8	that	that	SCONJ
ma-168	240	9	x0	x0	PROPN
ma-168	240	10	<	<	X
ma-168	240	11	0	0	PUNCT
ma-168	240	12	and	and	CCONJ
ma-168	240	13	there	there	PRON
ma-168	240	14	is	be	VERB
ma-168	240	15	one	one	NUM
ma-168	240	16	eigenvalue	eigenvalue	NOUN
ma-168	240	17	with	with	ADP
ma-168	240	18	positive	positive	ADJ
ma-168	240	19	real	real	ADJ
ma-168	240	20	part	part	NOUN
ma-168	240	21	and	and	CCONJ
ma-168	240	22	therefore	therefore	ADV
ma-168	240	23	the	the	DET
ma-168	240	24	disease	disease	NOUN
ma-168	240	25	-	-	PUNCT
ma-168	240	26	free	free	ADJ
ma-168	240	27	equilibrium	equilibrium	NOUN
ma-168	240	28	point	point	NOUN
ma-168	240	29	is	be	AUX
ma-168	240	30	unstable	unstable	ADJ
ma-168	240	31	2	2	NUM
ma-168	240	32	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	240	33	eur	eur	PROPN
ma-168	240	34	.	.	PUNCT
ma-168	241	1	j.	j.	PROPN
ma-168	241	2	math	math	PROPN
ma-168	241	3	.	.	PUNCT
ma-168	242	1	anal	anal	PROPN
ma-168	242	2	.	.	PUNCT
ma-168	243	1	10.28924	10.28924	NUM
ma-168	243	2	/	/	SYM
ma-168	243	3	ada	ada	PROPN
ma-168	243	4	/	/	SYM
ma-168	243	5	ma.3.22	ma.3.22	NOUN
ma-168	243	6	93.3	93.3	NUM
ma-168	243	7	.	.	PUNCT
ma-168	244	1	endemic	endemic	ADJ
ma-168	244	2	equilibrium	equilibrium	NOUN
ma-168	244	3	point	point	NOUN
ma-168	244	4	ee	ee	INTJ
ma-168	244	5	.	.	PUNCT
ma-168	245	1	we	we	PRON
ma-168	245	2	shall	shall	AUX
ma-168	245	3	show	show	VERB
ma-168	245	4	that	that	SCONJ
ma-168	245	5	the	the	DET
ma-168	245	6	formulated	formulated	ADJ
ma-168	245	7	model	model	NOUN
ma-168	245	8	(	(	PUNCT
ma-168	245	9	2.1	2.1	NUM
ma-168	245	10	)	)	PUNCT
ma-168	245	11	has	have	VERB
ma-168	245	12	an	an	DET
ma-168	245	13	endemicequilibrium	endemicequilibrium	NOUN
ma-168	245	14	point	point	NOUN
ma-168	245	15	,	,	PUNCT
ma-168	245	16	ee	ee	INTJ
ma-168	245	17	.	.	PUNCT
ma-168	246	1	the	the	DET
ma-168	246	2	endemic	endemic	ADJ
ma-168	246	3	equilibrium	equilibrium	NOUN
ma-168	246	4	point	point	NOUN
ma-168	246	5	is	be	AUX
ma-168	246	6	a	a	DET
ma-168	246	7	positive	positive	ADJ
ma-168	246	8	steady	steady	ADJ
ma-168	246	9	state	state	NOUN
ma-168	246	10	solution	solution	NOUN
ma-168	246	11	where	where	SCONJ
ma-168	246	12	thedisease	thedisease	PROPN
ma-168	246	13	persists	persist	VERB
ma-168	246	14	in	in	ADP
ma-168	246	15	the	the	DET
ma-168	246	16	population	population	NOUN
ma-168	246	17	.	.	PUNCT
ma-168	247	1	theorem	theorem	VERB
ma-168	247	2	4	4	NUM
ma-168	247	3	:	:	PUNCT
ma-168	247	4	the	the	DET
ma-168	247	5	model	model	NOUN
ma-168	247	6	(	(	PUNCT
ma-168	247	7	2.1	2.1	NUM
ma-168	247	8	)	)	PUNCT
ma-168	247	9	has	have	VERB
ma-168	247	10	a	a	DET
ma-168	247	11	unique	unique	ADJ
ma-168	247	12	endemic	endemic	ADJ
ma-168	247	13	equilibrium	equilibrium	NOUN
ma-168	247	14	ee	ee	INTJ
ma-168	247	15	whenever	whenever	SCONJ
ma-168	247	16	r0	r0	VERB
ma-168	247	17	>	>	X
ma-168	247	18	1	1	X
ma-168	247	19	.	.	X
ma-168	248	1	proof	proof	NOUN
ma-168	248	2	:	:	PUNCT
ma-168	248	3	let	let	VERB
ma-168	248	4	ee	ee	VERB
ma-168	248	5	=	=	SYM
ma-168	248	6	(	(	PUNCT
ma-168	248	7	s′′h(xi	s′′h(xi	PROPN
ma-168	248	8	)	)	PUNCT
ma-168	248	9	,	,	PUNCT
ma-168	248	10	e	e	X
ma-168	248	11	′′	′′	PROPN
ma-168	248	12	h	h	NOUN
ma-168	248	13	(	(	PUNCT
ma-168	248	14	xi	xi	PROPN
ma-168	248	15	)	)	PUNCT
ma-168	248	16	,	,	PUNCT
ma-168	248	17	i	i	PRON
ma-168	248	18	′′	′′	PROPN
ma-168	248	19	h	h	NOUN
ma-168	248	20	(	(	PUNCT
ma-168	248	21	xi	xi	PROPN
ma-168	248	22	)	)	PUNCT
ma-168	248	23	,	,	PUNCT
ma-168	248	24	r	r	NOUN
ma-168	248	25	′′	′′	PROPN
ma-168	248	26	h(xi	h(xi	PROPN
ma-168	248	27	)	)	PUNCT
ma-168	248	28	,	,	PUNCT
ma-168	248	29	s	s	VERB
ma-168	248	30	′′	′′	PROPN
ma-168	248	31	v	v	NOUN
ma-168	248	32	,	,	PUNCT
ma-168	248	33	e	e	X
ma-168	248	34	′′	′′	PROPN
ma-168	248	35	v	v	NOUN
ma-168	248	36	,	,	PUNCT
ma-168	248	37	i	i	PRON
ma-168	249	1	′′	′′	PROPN
ma-168	249	2	v	v	X
ma-168	249	3	)	)	PUNCT
ma-168	249	4	be	be	AUX
ma-168	249	5	a	a	DET
ma-168	249	6	nontrivial	nontrivial	ADJ
ma-168	249	7	equilibrium	equilibrium	NOUN
ma-168	249	8	of	of	ADP
ma-168	249	9	the	the	DET
ma-168	249	10	model(2.1	model(2.1	NOUN
ma-168	249	11	)	)	PUNCT
ma-168	249	12	.	.	PUNCT
ma-168	250	1	that	that	PRON
ma-168	250	2	is	be	AUX
ma-168	250	3	,	,	PUNCT
ma-168	250	4	all	all	DET
ma-168	250	5	components	component	NOUN
ma-168	250	6	of	of	ADP
ma-168	250	7	ee	ee	PROPN
ma-168	250	8	are	be	AUX
ma-168	250	9	positive	positive	ADJ
ma-168	250	10	.	.	PUNCT
ma-168	251	1	then	then	ADV
ma-168	251	2	the	the	DET
ma-168	251	3	onchocerciasis	onchocerciasis	NOUN
ma-168	251	4	model	model	NOUN
ma-168	251	5	(	(	PUNCT
ma-168	251	6	2.1	2.1	NUM
ma-168	251	7	)	)	PUNCT
ma-168	251	8	at	at	ADP
ma-168	251	9	steady	steady	ADJ
ma-168	251	10	-	-	PUNCT
ma-168	251	11	statebecomes	statebecome	NOUN
ma-168	251	12	ψh(xi)−	ψh(xi)−	NOUN
ma-168	251	13	l∑	l∑	PUNCT
ma-168	252	1	i=0	i=0	PROPN
ma-168	252	2	(	(	PUNCT
ma-168	252	3	δλh(xi)s	δλh(xi)s	PROPN
ma-168	252	4	′′	′′	PROPN
ma-168	252	5	h(xi)iv	h(xi)iv	VERB
ma-168	252	6	1	1	NUM
ma-168	252	7	+	+	CCONJ
ma-168	252	8	νh(xi)i	νh(xi)i	NOUN
ma-168	252	9	′′v	′′v	NOUN
ma-168	252	10	−	−	PROPN
ma-168	252	11	µh(xi)s	µh(xi)s	PUNCT
ma-168	252	12	′	′	NUM
ma-168	252	13	h(xi	h(xi	NOUN
ma-168	252	14	)	)	PUNCT
ma-168	253	1	+	+	CCONJ
ma-168	253	2	ω(xi)r	ω(xi)r	NUM
ma-168	253	3	′′	′′	PROPN
ma-168	253	4	h(xi	h(xi	X
ma-168	253	5	)	)	PUNCT
ma-168	253	6	)	)	PUNCT
ma-168	254	1	=	=	SYM
ma-168	254	2	0	0	PUNCT
ma-168	254	3	(	(	PUNCT
ma-168	254	4	3.6	3.6	NUM
ma-168	254	5	)	)	PUNCT
ma-168	254	6	l∑	l∑	PUNCT
ma-168	255	1	i=0	i=0	PROPN
ma-168	255	2	(	(	PUNCT
ma-168	255	3	δλh(xi)s	δλh(xi)s	PROPN
ma-168	255	4	′′	′′	PROPN
ma-168	255	5	h(xi)iv	h(xi)iv	VERB
ma-168	255	6	1	1	NUM
ma-168	255	7	+	+	CCONJ
ma-168	255	8	νh(xi)i	νh(xi)i	NOUN
ma-168	255	9	′′v	′′v	NOUN
ma-168	255	10	−	−	PROPN
ma-168	255	11	(	(	PUNCT
ma-168	255	12	αh(xi	αh(xi	PROPN
ma-168	255	13	)	)	PUNCT
ma-168	256	1	+	+	CCONJ
ma-168	256	2	µh(xi))e′′h	µh(xi))e′′h	X
ma-168	256	3	(	(	PUNCT
ma-168	256	4	xi	xi	NOUN
ma-168	256	5	)	)	PUNCT
ma-168	256	6	)	)	PUNCT
ma-168	257	1	=	=	SYM
ma-168	257	2	0	0	PUNCT
ma-168	257	3	(	(	PUNCT
ma-168	257	4	3.7	3.7	NUM
ma-168	257	5	)	)	PUNCT
ma-168	257	6	l∑	l∑	AUX
ma-168	258	1	i=0	i=0	PROPN
ma-168	258	2	(	(	PUNCT
ma-168	258	3	αh(xi)e	αh(xi)e	NUM
ma-168	258	4	′′	′′	PROPN
ma-168	258	5	h	h	PROPN
ma-168	258	6	(	(	PUNCT
ma-168	258	7	xi)−	xi)−	PROPN
ma-168	258	8	(	(	PUNCT
ma-168	258	9	r(xi	r(xi	PROPN
ma-168	258	10	)	)	PUNCT
ma-168	258	11	+	+	CCONJ
ma-168	258	12	µh(xi	µh(xi	X
ma-168	258	13	)	)	PUNCT
ma-168	259	1	+	+	CCONJ
ma-168	259	2	γh(xi))i	γh(xi))i	ADJ
ma-168	259	3	′′h	′′h	NOUN
ma-168	259	4	(	(	PUNCT
ma-168	259	5	xi	xi	NOUN
ma-168	259	6	)	)	PUNCT
ma-168	259	7	)	)	PUNCT
ma-168	260	1	=	=	SYM
ma-168	260	2	0	0	PUNCT
ma-168	260	3	(	(	PUNCT
ma-168	260	4	3.8	3.8	NUM
ma-168	260	5	)	)	PUNCT
ma-168	260	6	l∑	l∑	PUNCT
ma-168	261	1	i=0	i=0	PROPN
ma-168	261	2	r(xi)i	r(xi)i	PROPN
ma-168	261	3	′′	′′	PROPN
ma-168	261	4	h	h	PROPN
ma-168	261	5	(	(	PUNCT
ma-168	261	6	xi)−	xi)−	PROPN
ma-168	261	7	(	(	PUNCT
ma-168	261	8	µh(xi	µh(xi	X
ma-168	261	9	)	)	PUNCT
ma-168	261	10	+	+	SYM
ma-168	261	11	ω(xi))r′′h(xi	ω(xi))r′′h(xi	NOUN
ma-168	261	12	)	)	PUNCT
ma-168	261	13	=	=	SYM
ma-168	261	14	0	0	NUM
ma-168	261	15	(	(	PUNCT
ma-168	261	16	3.9	3.9	NUM
ma-168	261	17	)	)	PUNCT
ma-168	261	18	ψv	ψv	ADP
ma-168	261	19	−	−	PROPN
ma-168	261	20	δλvs	δλvs	PROPN
ma-168	262	1	′′	′′	PROPN
ma-168	262	2	v	v	PROPN
ma-168	262	3	ih(xi	ih(xi	PROPN
ma-168	262	4	)	)	PUNCT
ma-168	262	5	1	1	NUM
ma-168	263	1	+	+	CCONJ
ma-168	263	2	νv	νv	PRON
ma-168	263	3	(	(	PUNCT
ma-168	263	4	xi)i	xi)i	NUM
ma-168	264	1	′′	′′	PROPN
ma-168	264	2	h	h	NOUN
ma-168	264	3	(	(	PUNCT
ma-168	264	4	xi	xi	PROPN
ma-168	264	5	)	)	PUNCT
ma-168	264	6	−	−	PROPN
ma-168	265	1	µvs′′v	µvs′′v	PROPN
ma-168	265	2	=	=	SYM
ma-168	265	3	0	0	NUM
ma-168	265	4	(	(	PUNCT
ma-168	265	5	3.10	3.10	NUM
ma-168	265	6	)	)	PUNCT
ma-168	265	7	δλvs	δλvs	NOUN
ma-168	265	8	′′	′′	PROPN
ma-168	265	9	v	v	PROPN
ma-168	265	10	ih(xi	ih(xi	PROPN
ma-168	265	11	)	)	PUNCT
ma-168	265	12	1	1	NUM
ma-168	266	1	+	+	CCONJ
ma-168	266	2	νv	νv	PRON
ma-168	266	3	(	(	PUNCT
ma-168	266	4	xi)i	xi)i	NUM
ma-168	267	1	′′	′′	PROPN
ma-168	267	2	h	h	NOUN
ma-168	267	3	(	(	PUNCT
ma-168	267	4	xi	xi	PROPN
ma-168	267	5	)	)	PUNCT
ma-168	267	6	−	−	PROPN
ma-168	267	7	(	(	PUNCT
ma-168	267	8	αv	αv	ADP
ma-168	267	9	+	+	CCONJ
ma-168	267	10	µv	µv	NOUN
ma-168	267	11	)	)	PUNCT
ma-168	268	1	e′′v	e′′v	PROPN
ma-168	268	2	=	=	PUNCT
ma-168	268	3	0	0	PUNCT
ma-168	268	4	(	(	PUNCT
ma-168	268	5	3.11	3.11	NUM
ma-168	268	6	)	)	PUNCT
ma-168	268	7	αve	αve	NOUN
ma-168	269	1	′′	′′	PROPN
ma-168	269	2	v	v	ADP
ma-168	269	3	−	−	PROPN
ma-168	269	4	(	(	PUNCT
ma-168	269	5	µv	µv	PROPN
ma-168	269	6	+	+	NUM
ma-168	269	7	γv	γv	X
ma-168	269	8	)	)	PUNCT
ma-168	270	1	i	i	PRON
ma-168	270	2	′′v	′′v	NOUN
ma-168	271	1	=	=	SYM
ma-168	271	2	0	0	PUNCT
ma-168	271	3	(	(	PUNCT
ma-168	271	4	3.12)from	3.12)from	NUM
ma-168	271	5	the	the	DET
ma-168	271	6	last	last	ADJ
ma-168	271	7	three	three	NUM
ma-168	271	8	equations	equation	NOUN
ma-168	271	9	,	,	PUNCT
ma-168	271	10	we	we	PRON
ma-168	271	11	have	have	VERB
ma-168	271	12	i	i	PRON
ma-168	271	13	′′v	′′v	NOUN
ma-168	272	1	=	=	SYM
ma-168	272	2	αve	αve	NOUN
ma-168	272	3	′′	′′	PROPN
ma-168	272	4	v	v	ADP
ma-168	272	5	µv	µv	NOUN
ma-168	272	6	+	+	NUM
ma-168	272	7	γv	γv	X
ma-168	272	8	(	(	PUNCT
ma-168	272	9	3.13	3.13	NUM
ma-168	272	10	)	)	PUNCT
ma-168	272	11	e′′v	e′′v	PROPN
ma-168	272	12	=	=	SYM
ma-168	272	13	δλvs	δλvs	PROPN
ma-168	273	1	′′	′′	PROPN
ma-168	273	2	v	v	PROPN
ma-168	273	3	ih(xi	ih(xi	PROPN
ma-168	273	4	)	)	PUNCT
ma-168	273	5	1	1	NUM
ma-168	274	1	+	+	CCONJ
ma-168	274	2	νv	νv	PRON
ma-168	274	3	(	(	PUNCT
ma-168	274	4	xi)i	xi)i	NUM
ma-168	274	5	′′	′′	PROPN
ma-168	274	6	h	h	NOUN
ma-168	274	7	(	(	PUNCT
ma-168	274	8	xi)(αv	xi)(αv	PROPN
ma-168	274	9	+	+	CCONJ
ma-168	274	10	µv	µv	NOUN
ma-168	274	11	)	)	PUNCT
ma-168	274	12	(	(	PUNCT
ma-168	274	13	3.14	3.14	NUM
ma-168	274	14	)	)	PUNCT
ma-168	274	15	and	and	CCONJ
ma-168	274	16	s′′v	s′′v	PROPN
ma-168	274	17	=	=	PUNCT
ma-168	274	18	ψv	ψv	PROPN
ma-168	274	19	δλvs′′v	δλvs′′v	PROPN
ma-168	274	20	ih(xi	ih(xi	PROPN
ma-168	274	21	)	)	PUNCT
ma-168	274	22	1+νv	1+νv	PROPN
ma-168	274	23	(	(	PUNCT
ma-168	274	24	xi	xi	NOUN
ma-168	274	25	)	)	PUNCT
ma-168	274	26	i	i	PRON
ma-168	275	1	′′	′′	PROPN
ma-168	275	2	h	h	NOUN
ma-168	275	3	(	(	PUNCT
ma-168	275	4	xi	xi	PROPN
ma-168	275	5	)	)	PUNCT
ma-168	276	1	+	+	CCONJ
ma-168	276	2	µv	µv	PROPN
ma-168	276	3	(	(	PUNCT
ma-168	276	4	3.15	3.15	NUM
ma-168	276	5	)	)	PUNCT
ma-168	276	6	substituting	substituting	NOUN
ma-168	276	7	(	(	PUNCT
ma-168	276	8	3.14	3.14	NUM
ma-168	276	9	)	)	PUNCT
ma-168	276	10	and	and	CCONJ
ma-168	276	11	(	(	PUNCT
ma-168	276	12	3.15	3.15	NUM
ma-168	276	13	)	)	PUNCT
ma-168	276	14	into	into	ADP
ma-168	276	15	(	(	PUNCT
ma-168	276	16	3.13	3.13	NUM
ma-168	276	17	)	)	PUNCT
ma-168	276	18	yields	yield	NOUN
ma-168	276	19	i	i	PRON
ma-168	276	20	′′v	′′v	PUNCT
ma-168	276	21	=	=	VERB
ma-168	276	22	rvµv	rvµv	NOUN
ma-168	276	23	i	i	PRON
ma-168	276	24	′′h	′′h	VERB
ma-168	276	25	(	(	PUNCT
ma-168	276	26	xi	xi	X
ma-168	276	27	)	)	PUNCT
ma-168	276	28	µv	µv	PROPN
ma-168	277	1	+	+	CCONJ
ma-168	277	2	(	(	PUNCT
ma-168	277	3	δλv	δλv	PROPN
ma-168	277	4	+	+	CCONJ
ma-168	277	5	µvνv	µvνv	NOUN
ma-168	277	6	)	)	PUNCT
ma-168	278	1	i	i	PRON
ma-168	278	2	′′h	′′h	VERB
ma-168	278	3	(	(	PUNCT
ma-168	278	4	xi	xi	PROPN
ma-168	278	5	)	)	PUNCT
ma-168	278	6	(	(	PUNCT
ma-168	278	7	3.16	3.16	NUM
ma-168	278	8	)	)	PUNCT
ma-168	278	9	from	from	ADP
ma-168	278	10	(	(	PUNCT
ma-168	278	11	3.8	3.8	NUM
ma-168	278	12	)	)	PUNCT
ma-168	278	13	and	and	CCONJ
ma-168	278	14	(	(	PUNCT
ma-168	278	15	3.9	3.9	NUM
ma-168	278	16	)	)	PUNCT
ma-168	278	17	,	,	PUNCT
ma-168	278	18	we	we	PRON
ma-168	278	19	have	have	VERB
ma-168	278	20	e′′h	e′′h	PROPN
ma-168	278	21	(	(	PUNCT
ma-168	278	22	xi	xi	PROPN
ma-168	278	23	)	)	PUNCT
ma-168	278	24	=	=	VERB
ma-168	278	25	l∑	l∑	PROPN
ma-168	278	26	i=0	i=0	PROPN
ma-168	278	27	(	(	PUNCT
ma-168	278	28	r(xi	r(xi	PROPN
ma-168	278	29	)	)	PUNCT
ma-168	278	30	+	+	CCONJ
ma-168	278	31	µh(xi	µh(xi	X
ma-168	278	32	)	)	PUNCT
ma-168	279	1	+	+	CCONJ
ma-168	279	2	γh(xi))ih(xi	γh(xi))ih(xi	X
ma-168	279	3	)	)	PUNCT
ma-168	279	4	αh(xi	αh(xi	PROPN
ma-168	279	5	)	)	PUNCT
ma-168	279	6	(	(	PUNCT
ma-168	279	7	3.17	3.17	NUM
ma-168	279	8	)	)	PUNCT
ma-168	279	9	and	and	CCONJ
ma-168	279	10	r′′h(xi	r′′h(xi	PROPN
ma-168	279	11	)	)	PUNCT
ma-168	280	1	=	=	PUNCT
ma-168	280	2	l∑	l∑	PROPN
ma-168	281	1	i=0	i=0	PROPN
ma-168	281	2	r(xi)i	r(xi)i	PROPN
ma-168	281	3	′′(xi	′′(xi	PROPN
ma-168	281	4	)	)	PUNCT
ma-168	281	5	µh(xi	µh(xi	PROPN
ma-168	281	6	)	)	PUNCT
ma-168	281	7	+	+	CCONJ
ma-168	281	8	ω(xi	ω(xi	NUM
ma-168	281	9	)	)	PUNCT
ma-168	281	10	(	(	PUNCT
ma-168	281	11	3.18	3.18	NUM
ma-168	281	12	)	)	PUNCT
ma-168	281	13	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	281	14	eur	eur	PROPN
ma-168	281	15	.	.	PUNCT
ma-168	282	1	j.	j.	PROPN
ma-168	282	2	math	math	PROPN
ma-168	282	3	.	.	PUNCT
ma-168	283	1	anal	anal	PROPN
ma-168	283	2	.	.	PUNCT
ma-168	284	1	10.28924	10.28924	NUM
ma-168	284	2	/	/	SYM
ma-168	284	3	ada	ada	PROPN
ma-168	284	4	/	/	SYM
ma-168	284	5	ma.3.22	ma.3.22	NOUN
ma-168	284	6	10if	10if	NOUN
ma-168	284	7	we	we	PRON
ma-168	284	8	put	put	VERB
ma-168	284	9	(	(	PUNCT
ma-168	284	10	3.16	3.16	NUM
ma-168	284	11	)	)	PUNCT
ma-168	284	12	and	and	CCONJ
ma-168	284	13	(	(	PUNCT
ma-168	284	14	3,17	3,17	NUM
ma-168	284	15	)	)	PUNCT
ma-168	284	16	in	in	ADP
ma-168	284	17	(	(	PUNCT
ma-168	284	18	3.7	3.7	NUM
ma-168	284	19	)	)	PUNCT
ma-168	284	20	in	in	ADP
ma-168	284	21	terms	term	NOUN
ma-168	284	22	of	of	ADP
ma-168	284	23	r0	r0	NOUN
ma-168	284	24	,	,	PUNCT
ma-168	284	25	we	we	PRON
ma-168	284	26	have	have	AUX
ma-168	284	27	s′′h(xi	s′′h(xi	VERB
ma-168	284	28	)	)	PUNCT
ma-168	285	1	=	=	PUNCT
ma-168	285	2	∑l	∑l	PROPN
ma-168	285	3	i=0	i=0	PROPN
ma-168	285	4	ψh(xi)[µv	ψh(xi)[µv	PROPN
ma-168	285	5	+	+	CCONJ
ma-168	285	6	(	(	PUNCT
ma-168	285	7	δλv	δλv	PROPN
ma-168	285	8	+	+	CCONJ
ma-168	285	9	µvνv	µvνv	NOUN
ma-168	285	10	+	+	CCONJ
ma-168	285	11	νh(xi)µvrv	νh(xi)µvrv	NOUN
ma-168	285	12	)	)	PUNCT
ma-168	285	13	i	i	PRON
ma-168	285	14	′′h	′′h	VERB
ma-168	285	15	(	(	PUNCT
ma-168	285	16	xi	xi	PROPN
ma-168	285	17	)	)	PUNCT
ma-168	285	18	]	]	PUNCT
ma-168	286	1	µh(xi)µvr2	µh(xi)µvr2	PROPN
ma-168	286	2	0	0	PUNCT
ma-168	286	3	(	(	PUNCT
ma-168	286	4	3.19	3.19	NUM
ma-168	286	5	)	)	PUNCT
ma-168	286	6	finally	finally	ADV
ma-168	286	7	,	,	PUNCT
ma-168	286	8	using	use	VERB
ma-168	286	9	(	(	PUNCT
ma-168	286	10	3.16	3.16	NUM
ma-168	286	11	)	)	PUNCT
ma-168	286	12	,	,	PUNCT
ma-168	286	13	(	(	PUNCT
ma-168	286	14	3.18	3.18	NUM
ma-168	286	15	)	)	PUNCT
ma-168	286	16	and	and	CCONJ
ma-168	286	17	(	(	PUNCT
ma-168	286	18	3.19	3.19	NUM
ma-168	286	19	)	)	PUNCT
ma-168	286	20	in	in	ADP
ma-168	286	21	(	(	PUNCT
ma-168	286	22	3.7	3.7	NUM
ma-168	286	23	)	)	PUNCT
ma-168	286	24	,	,	PUNCT
ma-168	286	25	we	we	PRON
ma-168	286	26	have	have	VERB
ma-168	286	27	i	i	PRON
ma-168	286	28	′′h	′′h	VERB
ma-168	286	29	(	(	PUNCT
ma-168	286	30	xi	xi	X
ma-168	286	31	)	)	PUNCT
ma-168	286	32	=	=	SYM
ma-168	286	33	l∑	l∑	PROPN
ma-168	286	34	i=0	i=0	ADJ
ma-168	286	35	µh(xi)µvψh(xi)(µh(xi	µh(xi)µvψh(xi)(µh(xi	NOUN
ma-168	286	36	)	)	PUNCT
ma-168	286	37	+	+	NUM
ma-168	286	38	ω(xi	ω(xi	NUM
ma-168	286	39	)	)	PUNCT
ma-168	286	40	)	)	PUNCT
ma-168	287	1	(	(	PUNCT
ma-168	287	2	r2	r2	PROPN
ma-168	287	3	0	0	NUM
ma-168	287	4	−	−	NOUN
ma-168	287	5	1	1	X
ma-168	287	6	)	)	PUNCT
ma-168	287	7	ρ	ρ	NOUN
ma-168	287	8	(	(	PUNCT
ma-168	287	9	3.20	3.20	NUM
ma-168	287	10	)	)	PUNCT
ma-168	288	1	where	where	SCONJ
ma-168	288	2	ρ	ρ	NOUN
ma-168	288	3	=	=	PUNCT
ma-168	288	4	l∑	l∑	PROPN
ma-168	288	5	i=0	i=0	PROPN
ma-168	288	6	(	(	PUNCT
ma-168	288	7	µh(xi)+ω(xi))[δλh(xi)µvrv+ψh(xiµh(xi)(δλv+µvνv+νh(xi)µv	µh(xi)+ω(xi))[δλh(xi)µvrv+ψh(xiµh(xi)(δλv+µvνv+νh(xi)µv	PROPN
ma-168	288	8	)	)	PUNCT
ma-168	288	9	rm)]−	rm)]−	NOUN
ma-168	288	10	l∑	l∑	PUNCT
ma-168	288	11	i=0	i=0	PROPN
ma-168	288	12	µh(xi)µvω(xi)r(xi)r2	µh(xi)µvω(xi)r(xi)r2	NOUN
ma-168	288	13	0.(3.21)if	0.(3.21)if	NOUN
ma-168	288	14	in	in	ADP
ma-168	288	15	(	(	PUNCT
ma-168	288	16	3.20	3.20	NUM
ma-168	288	17	)	)	PUNCT
ma-168	288	18	,	,	PUNCT
ma-168	288	19	ω(xi	ω(xi	NUM
ma-168	288	20	)	)	PUNCT
ma-168	289	1	=	=	SYM
ma-168	289	2	0	0	PUNCT
ma-168	290	1	then	then	ADV
ma-168	290	2	ρ	ρ	X
ma-168	290	3	>	>	X
ma-168	290	4	0	0	PROPN
ma-168	290	5	.	.	PUNCT
ma-168	291	1	from	from	ADP
ma-168	291	2	this	this	PRON
ma-168	291	3	,	,	PUNCT
ma-168	291	4	one	one	PRON
ma-168	291	5	sees	see	VERB
ma-168	291	6	that	that	DET
ma-168	291	7	model	model	NOUN
ma-168	291	8	(	(	PUNCT
ma-168	291	9	2.1	2.1	NUM
ma-168	291	10	)	)	PUNCT
ma-168	291	11	has	have	AUX
ma-168	291	12	no	no	DET
ma-168	291	13	positive	positive	ADJ
ma-168	291	14	solutionwhen	solutionwhen	NOUN
ma-168	291	15	r0	r0	VERB
ma-168	291	16	<	<	X
ma-168	291	17	1	1	NUM
ma-168	291	18	.	.	PUNCT
ma-168	292	1	however	however	ADV
ma-168	292	2	,	,	PUNCT
ma-168	292	3	with	with	ADP
ma-168	292	4	ω(xi	ω(xi	NUM
ma-168	292	5	)	)	PUNCT
ma-168	292	6	=	=	SYM
ma-168	292	7	0	0	NUM
ma-168	292	8	,	,	PUNCT
ma-168	292	9	a	a	DET
ma-168	292	10	unique	unique	ADJ
ma-168	292	11	endemic	endemic	ADJ
ma-168	292	12	equilibrium	equilibrium	NOUN
ma-168	292	13	exists	exist	VERB
ma-168	292	14	when	when	SCONJ
ma-168	292	15	r0	r0	NOUN
ma-168	292	16	>	>	X
ma-168	292	17	1	1	X
ma-168	292	18	.	.	PUNCT
ma-168	292	19	thiscompletes	thiscomplete	VERB
ma-168	292	20	the	the	DET
ma-168	292	21	proof	proof	NOUN
ma-168	292	22	.	.	PUNCT
ma-168	293	1	2	2	NUM
ma-168	293	2	remark	remark	NOUN
ma-168	293	3	1	1	NUM
ma-168	293	4	:	:	PUNCT
ma-168	293	5	it	it	PRON
ma-168	293	6	is	be	AUX
ma-168	293	7	important	important	ADJ
ma-168	293	8	to	to	PART
ma-168	293	9	have	have	VERB
ma-168	293	10	a	a	DET
ma-168	293	11	remark	remark	NOUN
ma-168	293	12	that	that	SCONJ
ma-168	293	13	positive	positive	ADJ
ma-168	293	14	solution	solution	NOUN
ma-168	293	15	exists	exist	VERB
ma-168	293	16	for	for	ADP
ma-168	293	17	the	the	DET
ma-168	293	18	model	model	NOUN
ma-168	293	19	(	(	PUNCT
ma-168	293	20	2.1	2.1	NUM
ma-168	293	21	)	)	PUNCT
ma-168	293	22	in	in	ADP
ma-168	293	23	acase	acase	NOUN
ma-168	293	24	where	where	SCONJ
ma-168	293	25	ρ	ρ	PROPN
ma-168	293	26	<	<	X
ma-168	293	27	0	0	PUNCT
ma-168	293	28	and	and	CCONJ
ma-168	293	29	r0	r0	VERB
ma-168	293	30	<	<	X
ma-168	293	31	1	1	NUM
ma-168	293	32	.	.	PUNCT
ma-168	294	1	this	this	PRON
ma-168	294	2	implies	imply	VERB
ma-168	294	3	that	that	SCONJ
ma-168	294	4	the	the	DET
ma-168	294	5	disease	disease	NOUN
ma-168	294	6	-	-	PUNCT
ma-168	294	7	free	free	ADJ
ma-168	294	8	equilibrium	equilibrium	NOUN
ma-168	294	9	co	co	NOUN
ma-168	294	10	-	-	NOUN
ma-168	294	11	exists	exist	VERB
ma-168	294	12	with	with	ADP
ma-168	294	13	theendemic	theendemic	ADJ
ma-168	294	14	equilibrium	equilibrium	NOUN
ma-168	294	15	state	state	NOUN
ma-168	294	16	when	when	SCONJ
ma-168	294	17	r0	r0	NOUN
ma-168	294	18	is	be	AUX
ma-168	294	19	slightly	slightly	ADV
ma-168	294	20	less	less	ADJ
ma-168	294	21	than	than	ADP
ma-168	294	22	unity	unity	NOUN
ma-168	294	23	resulting	result	VERB
ma-168	294	24	into	into	ADP
ma-168	294	25	a	a	DET
ma-168	294	26	phenomenon	phenomenon	NOUN
ma-168	294	27	ofsubcritical	ofsubcritical	ADJ
ma-168	294	28	(	(	PUNCT
ma-168	294	29	backward	backward	ADJ
ma-168	294	30	)	)	PUNCT
ma-168	294	31	bifurcation	bifurcation	NOUN
ma-168	294	32	.	.	PUNCT
ma-168	295	1	references	reference	NOUN
ma-168	295	2	[	[	X
ma-168	295	3	1	1	NUM
ma-168	295	4	]	]	X
ma-168	295	5	w.s	w.s	PROPN
ma-168	295	6	.	.	PROPN
ma-168	295	7	alley	alley	PROPN
ma-168	295	8	,	,	PUNCT
ma-168	295	9	b.a.b	b.a.b	PROPN
ma-168	295	10	.	.	PUNCT
ma-168	295	11	boatin	boatin	NOUN
ma-168	295	12	,	,	PUNCT
ma-168	295	13	n.j.d.n	n.j.d.n	PROPN
ma-168	295	14	.	.	PROPN
ma-168	295	15	nagelkerke	nagelkerke	PROPN
ma-168	295	16	,	,	PUNCT
ma-168	295	17	macrofilaricides	macrofilaricide	NOUN
ma-168	295	18	and	and	CCONJ
ma-168	295	19	onchocerciasis	onchocerciasis	NOUN
ma-168	295	20	control	control	NOUN
ma-168	295	21	,	,	PUNCT
ma-168	295	22	mathematical	mathematical	ADJ
ma-168	295	23	modellingof	modellingof	NOUN
ma-168	295	24	the	the	DET
ma-168	295	25	prospects	prospect	NOUN
ma-168	295	26	for	for	ADP
ma-168	295	27	elimination	elimination	NOUN
ma-168	295	28	.	.	PUNCT
ma-168	296	1	bmc	bmc	ADJ
ma-168	296	2	public	public	ADJ
ma-168	296	3	health	health	NOUN
ma-168	296	4	.	.	PUNCT
ma-168	297	1	1	1	NUM
ma-168	297	2	(	(	PUNCT
ma-168	297	3	2001	2001	NUM
ma-168	297	4	)	)	PUNCT
ma-168	297	5	12.[2	12.[2	PROPN
ma-168	297	6	]	]	X
ma-168	297	7	u.	u.	PROPN
ma-168	297	8	amazigo	amazigo	PROPN
ma-168	297	9	,	,	PUNCT
ma-168	297	10	m.	m.	NOUN
ma-168	297	11	noma	noma	PROPN
ma-168	297	12	,	,	PUNCT
ma-168	297	13	j.	j.	PROPN
ma-168	297	14	bump	bump	PROPN
ma-168	297	15	,	,	PUNCT
ma-168	297	16	b.	b.	PROPN
ma-168	297	17	bentin	bentin	PROPN
ma-168	297	18	,	,	PUNCT
ma-168	297	19	b.	b.	PROPN
ma-168	297	20	liese	liese	PROPN
ma-168	297	21	,	,	PUNCT
ma-168	297	22	l.	l.	PROPN
ma-168	297	23	yameogo	yameogo	PROPN
ma-168	297	24	,	,	PUNCT
ma-168	297	25	h.	h.	PROPN
ma-168	297	26	zouré	zouré	PROPN
ma-168	297	27	,	,	PUNCT
ma-168	297	28	and	and	CCONJ
ma-168	297	29	a.	a.	NOUN
ma-168	297	30	seketeli	seketeli	NOUN
ma-168	297	31	,	,	PUNCT
ma-168	297	32	onchocerciasis	onchocerciasis	NOUN
ma-168	297	33	diseaseand	diseaseand	NOUN
ma-168	297	34	mortality	mortality	NOUN
ma-168	297	35	in	in	ADP
ma-168	297	36	sub	sub	PROPN
ma-168	297	37	saharan	saharan	PROPN
ma-168	297	38	africa	africa	PROPN
ma-168	297	39	,	,	PUNCT
ma-168	297	40	chapter	chapter	NOUN
ma-168	297	41	15	15	NUM
ma-168	297	42	,	,	PUNCT
ma-168	297	43	world	world	PROPN
ma-168	297	44	bank	bank	PROPN
ma-168	297	45	,	,	PUNCT
ma-168	297	46	washington	washington	PROPN
ma-168	297	47	,	,	PUNCT
ma-168	297	48	dc	dc	PROPN
ma-168	297	49	,	,	PUNCT
ma-168	297	50	2006.[3	2006.[3	NUM
ma-168	297	51	]	]	X
ma-168	297	52	a.	a.	PROPN
ma-168	297	53	hassan	hassan	PROPN
ma-168	297	54	,	,	PUNCT
ma-168	297	55	n.	n.	PROPN
ma-168	297	56	shaban	shaban	PROPN
ma-168	297	57	,	,	PUNCT
ma-168	297	58	onchocerciasis	onchocerciasis	NOUN
ma-168	297	59	dynamics	dynamic	NOUN
ma-168	297	60	:	:	PUNCT
ma-168	297	61	modelling	model	VERB
ma-168	297	62	the	the	DET
ma-168	297	63	effects	effect	NOUN
ma-168	297	64	of	of	ADP
ma-168	297	65	treatment	treatment	NOUN
ma-168	297	66	,	,	PUNCT
ma-168	297	67	education	education	NOUN
ma-168	297	68	and	and	CCONJ
ma-168	297	69	vector	vector	NOUN
ma-168	297	70	control	control	NOUN
ma-168	297	71	,	,	PUNCT
ma-168	297	72	j.	j.	PROPN
ma-168	297	73	biol	biol	PROPN
ma-168	297	74	.	.	PUNCT
ma-168	298	1	dyn	dyn	PROPN
ma-168	298	2	.	.	PUNCT
ma-168	299	1	14	14	NUM
ma-168	299	2	(	(	PUNCT
ma-168	299	3	2020	2020	NUM
ma-168	299	4	)	)	PUNCT
ma-168	299	5	245	245	NUM
ma-168	300	1	-	-	SYM
ma-168	300	2	268.[4	268.[4	NUM
ma-168	300	3	]	]	X
ma-168	300	4	e.m	e.m	PROPN
ma-168	300	5	.	.	PROPN
ma-168	300	6	poolman	poolman	PROPN
ma-168	300	7	,	,	PUNCT
ma-168	300	8	a.p	a.p	PROPN
ma-168	300	9	.	.	PROPN
ma-168	300	10	galvani	galvani	PROPN
ma-168	300	11	,	,	PUNCT
ma-168	300	12	modeling	model	VERB
ma-168	300	13	targeted	target	VERB
ma-168	300	14	ivermectin	ivermectin	NOUN
ma-168	300	15	treatment	treatment	NOUN
ma-168	300	16	for	for	ADP
ma-168	300	17	controlling	control	VERB
ma-168	300	18	river	river	NOUN
ma-168	300	19	blindness	blindness	NOUN
ma-168	300	20	,	,	PUNCT
ma-168	300	21	amer	amer	PROPN
ma-168	300	22	.	.	PUNCT
ma-168	301	1	j.	j.	PROPN
ma-168	301	2	trop.med	trop.med	PROPN
ma-168	301	3	.	.	PUNCT
ma-168	302	1	hygiene	hygiene	NOUN
ma-168	302	2	,	,	PUNCT
ma-168	302	3	75	75	NUM
ma-168	302	4	(	(	PUNCT
ma-168	302	5	2006	2006	NUM
ma-168	302	6	)	)	PUNCT
ma-168	302	7	921–927.[5	921–927.[5	NUM
ma-168	302	8	]	]	X
ma-168	302	9	j.p	j.p	PROPN
ma-168	302	10	.	.	PROPN
ma-168	302	11	mopecha	mopecha	PROPN
ma-168	302	12	,	,	PUNCT
ma-168	302	13	h.r	h.r	PROPN
ma-168	302	14	.	.	PROPN
ma-168	302	15	thieme	thieme	NOUN
ma-168	302	16	,	,	PUNCT
ma-168	302	17	competitive	competitive	ADJ
ma-168	302	18	dynamics	dynamic	NOUN
ma-168	302	19	in	in	ADP
ma-168	302	20	a	a	DET
ma-168	302	21	model	model	NOUN
ma-168	302	22	for	for	ADP
ma-168	302	23	onchocerciasis	onchocerciasis	NOUN
ma-168	302	24	with	with	ADP
ma-168	302	25	cross	cross	NOUN
ma-168	302	26	-	-	NOUN
ma-168	302	27	immunity	immunity	NOUN
ma-168	302	28	,	,	PUNCT
ma-168	302	29	can	can	AUX
ma-168	302	30	.	.	PUNCT
ma-168	303	1	appl.math	appl.math	NOUN
ma-168	303	2	.	.	PUNCT
ma-168	303	3	quart	quart	NOUN
ma-168	303	4	.	.	PUNCT
ma-168	304	1	11	11	NUM
ma-168	304	2	(	(	PUNCT
ma-168	304	3	2003	2003	NUM
ma-168	304	4	)	)	PUNCT
ma-168	305	1	339–376.[6	339–376.[6	NUM
ma-168	305	2	]	]	X
ma-168	305	3	m.g	m.g	PROPN
ma-168	305	4	.	.	PROPN
ma-168	305	5	basanez	basanez	PROPN
ma-168	305	6	,	,	PUNCT
ma-168	305	7	m.	m.	NOUN
ma-168	305	8	boussinesq	boussinesq	PROPN
ma-168	305	9	,	,	PUNCT
ma-168	305	10	population	population	NOUN
ma-168	305	11	biology	biology	NOUN
ma-168	305	12	of	of	ADP
ma-168	305	13	human	human	ADJ
ma-168	305	14	onchocerciasis	onchocerciasis	NOUN
ma-168	305	15	,	,	PUNCT
ma-168	305	16	phil	phil	PROPN
ma-168	305	17	.	.	PUNCT
ma-168	306	1	trans	trans	PROPN
ma-168	306	2	.	.	PUNCT
ma-168	306	3	r.	r.	PROPN
ma-168	306	4	soc	soc	PROPN
ma-168	306	5	.	.	PUNCT
ma-168	307	1	lond	lond	PROPN
ma-168	307	2	.	.	PUNCT
ma-168	308	1	b	b	X
ma-168	308	2	:	:	PUNCT
ma-168	308	3	biol	biol	PROPN
ma-168	308	4	.	.	PUNCT
ma-168	309	1	sci.354	sci.354	PROPN
ma-168	309	2	(	(	PUNCT
ma-168	309	3	1999	1999	NUM
ma-168	309	4	)	)	PUNCT
ma-168	309	5	809–826.[7	809–826.[7	NUM
ma-168	309	6	]	]	X
ma-168	309	7	m.g	m.g	PROPN
ma-168	309	8	.	.	PROPN
ma-168	309	9	basanez	basanez	PROPN
ma-168	309	10	,	,	PUNCT
ma-168	309	11	j.	j.	PROPN
ma-168	309	12	ricardez	ricardez	PROPN
ma-168	309	13	-	-	PUNCT
ma-168	309	14	esquinca	esquinca	PROPN
ma-168	309	15	,	,	PUNCT
ma-168	309	16	models	model	NOUN
ma-168	309	17	for	for	ADP
ma-168	309	18	the	the	DET
ma-168	309	19	population	population	NOUN
ma-168	309	20	biology	biology	NOUN
ma-168	309	21	and	and	CCONJ
ma-168	309	22	control	control	NOUN
ma-168	309	23	of	of	ADP
ma-168	309	24	human	human	ADJ
ma-168	309	25	onchocerciasis	onchocerciasis	NOUN
ma-168	309	26	,	,	PUNCT
ma-168	309	27	trendsparasitol	trendsparasitol	ADJ
ma-168	309	28	.	.	PUNCT
ma-168	310	1	17	17	NUM
ma-168	310	2	(	(	PUNCT
ma-168	310	3	2001	2001	NUM
ma-168	310	4	)	)	PUNCT
ma-168	310	5	430–438.[8	430–438.[8	NUM
ma-168	310	6	]	]	SYM
ma-168	310	7	j.d	j.d	PROPN
ma-168	310	8	.	.	PROPN
ma-168	310	9	murray	murray	PROPN
ma-168	310	10	,	,	PUNCT
ma-168	310	11	mathematical	mathematical	ADJ
ma-168	310	12	biology	biology	NOUN
ma-168	310	13	i.	i.	NOUN
ma-168	310	14	,	,	PUNCT
ma-168	310	15	an	an	DET
ma-168	310	16	introduction	introduction	NOUN
ma-168	310	17	.	.	PUNCT
ma-168	311	1	3rd	3rd	ADJ
ma-168	311	2	ed	ed	NOUN
ma-168	311	3	.	.	PUNCT
ma-168	312	1	heidelberg	heidelberg	PROPN
ma-168	312	2	:	:	PUNCT
ma-168	312	3	springer	springer	NOUN
ma-168	312	4	-	-	PUNCT
ma-168	312	5	verlag	verlag	PROPN
ma-168	312	6	berlin	berlin	PROPN
ma-168	312	7	,	,	PUNCT
ma-168	312	8	2002.[9	2002.[9	NUM
ma-168	312	9	]	]	X
ma-168	312	10	a.p	a.p	PROPN
ma-168	312	11	.	.	PROPN
ma-168	312	12	plaisier	plaisier	PROPN
ma-168	312	13	,	,	PUNCT
ma-168	312	14	e.s	e.s	PROPN
ma-168	312	15	.	.	PROPN
ma-168	312	16	alley	alley	PROPN
ma-168	312	17	,	,	PUNCT
ma-168	312	18	g.j	g.j	PROPN
ma-168	312	19	.	.	PROPN
ma-168	312	20	van	van	PROPN
ma-168	312	21	oortmarssen	oortmarssen	PROPN
ma-168	312	22	,	,	PUNCT
ma-168	312	23	b.a	b.a	PROPN
ma-168	312	24	.	.	PROPN
ma-168	312	25	boatin	boatin	PROPN
ma-168	312	26	,	,	PUNCT
ma-168	312	27	j.d.f	j.d.f	ADJ
ma-168	312	28	habbema	habbema	NOUN
ma-168	312	29	,	,	PUNCT
ma-168	312	30	required	require	VERB
ma-168	312	31	duration	duration	NOUN
ma-168	312	32	of	of	ADP
ma-168	312	33	combined	combine	VERB
ma-168	312	34	annualivermectin	annualivermectin	NOUN
ma-168	312	35	treatment	treatment	NOUN
ma-168	312	36	and	and	CCONJ
ma-168	312	37	vector	vector	NOUN
ma-168	312	38	control	control	NOUN
ma-168	312	39	program	program	NOUN
ma-168	312	40	in	in	ADP
ma-168	312	41	west	west	PROPN
ma-168	312	42	africa	africa	PROPN
ma-168	312	43	,	,	PUNCT
ma-168	312	44	bull	bull	PROPN
ma-168	312	45	.	.	PUNCT
ma-168	313	1	world	world	PROPN
ma-168	313	2	health	health	NOUN
ma-168	313	3	organ	organ	NOUN
ma-168	313	4	.	.	PUNCT
ma-168	314	1	75	75	NUM
ma-168	314	2	(	(	PUNCT
ma-168	314	3	1997	1997	NUM
ma-168	314	4	)	)	PUNCT
ma-168	314	5	237	237	NUM
ma-168	314	6	-	-	SYM
ma-168	314	7	245.[10	245.[10	NUM
ma-168	314	8	]	]	PUNCT
ma-168	314	9	j.	j.	PROPN
ma-168	314	10	remme	remme	PROPN
ma-168	314	11	,	,	PUNCT
ma-168	314	12	g.	g.	PROPN
ma-168	314	13	de	de	X
ma-168	314	14	sole	sole	PROPN
ma-168	314	15	,	,	PUNCT
ma-168	314	16	g.j	g.j	PROPN
ma-168	314	17	.	.	PROPN
ma-168	314	18	van	van	PROPN
ma-168	314	19	oortmarssen	oortmarssen	PROPN
ma-168	314	20	,	,	PUNCT
ma-168	314	21	the	the	DET
ma-168	314	22	predicted	predict	VERB
ma-168	314	23	and	and	CCONJ
ma-168	314	24	observed	observed	ADJ
ma-168	314	25	decline	decline	NOUN
ma-168	314	26	in	in	ADP
ma-168	314	27	onchocerciasis	onchocerciasis	NOUN
ma-168	314	28	infection	infection	NOUN
ma-168	314	29	during14	during14	NOUN
ma-168	314	30	years	year	NOUN
ma-168	314	31	of	of	ADP
ma-168	314	32	successful	successful	ADJ
ma-168	314	33	control	control	NOUN
ma-168	314	34	of	of	ADP
ma-168	314	35	black	black	ADJ
ma-168	314	36	flies	fly	NOUN
ma-168	314	37	in	in	ADP
ma-168	314	38	west	west	PROPN
ma-168	314	39	africa	africa	PROPN
ma-168	314	40	,	,	PUNCT
ma-168	314	41	bull	bull	PROPN
ma-168	314	42	.	.	PUNCT
ma-168	315	1	world	world	PROPN
ma-168	315	2	health	health	NOUN
ma-168	315	3	organ	organ	NOUN
ma-168	315	4	.	.	PUNCT
ma-168	316	1	68	68	NUM
ma-168	316	2	(	(	PUNCT
ma-168	316	3	1990	1990	NUM
ma-168	316	4	)	)	PUNCT
ma-168	317	1	331–339	331–339	NUM
ma-168	317	2	.	.	PUNCT
ma-168	318	1	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	PROPN
ma-168	318	2	eur	eur	PROPN
ma-168	318	3	.	.	PUNCT
ma-168	319	1	j.	j.	PROPN
ma-168	319	2	math	math	PROPN
ma-168	319	3	.	.	PUNCT
ma-168	320	1	anal	anal	PROPN
ma-168	320	2	.	.	PUNCT
ma-168	321	1	10.28924	10.28924	NUM
ma-168	321	2	/	/	SYM
ma-168	321	3	ada	ada	PROPN
ma-168	321	4	/	/	SYM
ma-168	321	5	ma.3.22	ma.3.22	NOUN
ma-168	321	6	11	11	NUM
ma-168	322	1	[	[	X
ma-168	322	2	11	11	NUM
ma-168	322	3	]	]	X
ma-168	322	4	s.i	s.i	PROPN
ma-168	322	5	.	.	PROPN
ma-168	322	6	omade	omade	PROPN
ma-168	322	7	,	,	PUNCT
ma-168	322	8	a.t	a.t	PROPN
ma-168	322	9	.	.	PROPN
ma-168	322	10	omotunde	omotunde	PROPN
ma-168	322	11	,	,	PUNCT
ma-168	322	12	a.s	a.s	PROPN
ma-168	322	13	.	.	PROPN
ma-168	322	14	gbenga	gbenga	PROPN
ma-168	322	15	,	,	PUNCT
ma-168	322	16	mathematical	mathematical	ADJ
ma-168	322	17	modeling	modeling	NOUN
ma-168	322	18	of	of	ADP
ma-168	322	19	river	river	NOUN
ma-168	322	20	blindness	blindness	NOUN
ma-168	322	21	disease	disease	NOUN
ma-168	322	22	with	with	ADP
ma-168	322	23	demography	demography	NOUN
ma-168	322	24	usingeuler	usingeuler	PROPN
ma-168	322	25	method	method	PROPN
ma-168	322	26	,	,	PUNCT
ma-168	322	27	math	math	NOUN
ma-168	322	28	.	.	PUNCT
ma-168	323	1	theory	theory	NOUN
ma-168	323	2	model	model	NOUN
ma-168	323	3	.	.	PROPN
ma-168	324	1	5	5	NUM
ma-168	324	2	(	(	PUNCT
ma-168	324	3	2015	2015	NUM
ma-168	324	4	)	)	PUNCT
ma-168	324	5	,	,	PUNCT
ma-168	324	6	75–85.[12	75–85.[12	PROPN
ma-168	324	7	]	]	X
ma-168	324	8	world	world	PROPN
ma-168	324	9	health	health	PROPN
ma-168	324	10	organization	organization	NOUN
ma-168	324	11	,	,	PUNCT
ma-168	324	12	african	african	ADJ
ma-168	324	13	programme	programme	NOUN
ma-168	324	14	for	for	ADP
ma-168	324	15	onchocerciasis	onchocerciasis	NOUN
ma-168	324	16	control	control	NOUN
ma-168	324	17	:	:	PUNCT
ma-168	324	18	meeting	meeting	NOUN
ma-168	324	19	of	of	ADP
ma-168	324	20	national	national	ADJ
ma-168	324	21	onchocerciasis	onchocerciasis	NOUN
ma-168	324	22	taskforces	taskforce	NOUN
ma-168	324	23	,	,	PUNCT
ma-168	324	24	september	september	PROPN
ma-168	324	25	2012	2012	NUM
ma-168	324	26	,	,	PUNCT
ma-168	324	27	weekly	weekly	ADJ
ma-168	324	28	epidemiol	epidemiol	NOUN
ma-168	324	29	.	.	PUNCT
ma-168	325	1	record	record	NOUN
ma-168	325	2	87(49–50	87(49–50	NUM
ma-168	325	3	)	)	PUNCT
ma-168	325	4	(	(	PUNCT
ma-168	325	5	2012	2012	NUM
ma-168	325	6	)	)	PUNCT
ma-168	325	7	,	,	PUNCT
ma-168	325	8	pp	pp	ADP
ma-168	325	9	.	.	PUNCT
ma-168	326	1	494–502	494–502	NUM
ma-168	326	2	.	.	PUNCT
ma-168	327	1	https://doi.org/10.28924/ada/ma.3.22	https://doi.org/10.28924/ada/ma.3.22	NOUN
ma-168	327	2	1	1	NUM
ma-168	327	3	.	.	PUNCT
ma-168	327	4	introduction	introduction	NOUN
ma-168	327	5	2	2	NUM
ma-168	327	6	.	.	PUNCT
ma-168	327	7	model	model	NOUN
ma-168	327	8	description	description	NOUN
ma-168	327	9	2.1	2.1	NUM
ma-168	327	10	.	.	PUNCT
ma-168	327	11	existence	existence	NOUN
ma-168	327	12	and	and	CCONJ
ma-168	327	13	positivity	positivity	NOUN
ma-168	327	14	of	of	ADP
ma-168	327	15	solutions	solution	NOUN
ma-168	327	16	3	3	NUM
ma-168	327	17	.	.	NOUN
ma-168	327	18	existence	existence	NOUN
ma-168	327	19	and	and	CCONJ
ma-168	327	20	stability	stability	NOUN
ma-168	327	21	of	of	ADP
ma-168	327	22	the	the	DET
ma-168	327	23	equilibrium	equilibrium	NOUN
ma-168	327	24	points	point	NOUN
ma-168	327	25	3.1	3.1	NUM
ma-168	327	26	.	.	PUNCT
ma-168	328	1	disease	disease	NOUN
ma-168	328	2	-	-	PUNCT
ma-168	328	3	free	free	ADJ
ma-168	328	4	equilibrium	equilibrium	NOUN
ma-168	328	5	3.2	3.2	NUM
ma-168	328	6	.	.	PUNCT
ma-168	329	1	local	local	ADJ
ma-168	329	2	stability	stability	NOUN
ma-168	329	3	of	of	ADP
ma-168	329	4	the	the	DET
ma-168	329	5	disease	disease	NOUN
ma-168	329	6	-	-	PUNCT
ma-168	329	7	free	free	ADJ
ma-168	329	8	equilibrium	equilibrium	NOUN
ma-168	329	9	point	point	NOUN
ma-168	329	10	e0	e0	PROPN
ma-168	329	11	3.3	3.3	NUM
ma-168	329	12	.	.	PUNCT
ma-168	330	1	endemic	endemic	ADJ
ma-168	330	2	equilibrium	equilibrium	NOUN
ma-168	330	3	point	point	NOUN
ma-168	330	4	ee	ee	ADP
ma-168	330	5	references	reference	NOUN