id	sid	tid	token	lemma	pos
ma-171	1	1	2023	2023	NUM
ma-171	1	2	ada	ada	PROPN
ma-171	1	3	academica	academica	PROPN
ma-171	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-171	1	5	.	.	PUNCT
ma-171	2	1	j.	j.	PROPN
ma-171	2	2	math	math	PROPN
ma-171	2	3	.	.	PUNCT
ma-171	3	1	anal	anal	ADJ
ma-171	3	2	.	.	PUNCT
ma-171	4	1	3	3	NUM
ma-171	4	2	(	(	PUNCT
ma-171	4	3	2023	2023	NUM
ma-171	4	4	)	)	PUNCT
ma-171	4	5	21doi	21doi	NOUN
ma-171	4	6	:	:	PUNCT
ma-171	4	7	10.28924	10.28924	NUM
ma-171	4	8	/	/	SYM
ma-171	4	9	ada	ada	PROPN
ma-171	4	10	/	/	SYM
ma-171	4	11	ma.3.21	ma.3.21	PROPN
ma-171	4	12	analysis	analysis	NOUN
ma-171	4	13	of	of	ADP
ma-171	4	14	a	a	DET
ma-171	4	15	mathematical	mathematical	ADJ
ma-171	4	16	model	model	NOUN
ma-171	4	17	incorporating	incorporate	VERB
ma-171	4	18	dual	dual	ADJ
ma-171	4	19	protection	protection	NOUN
ma-171	4	20	and	and	CCONJ
ma-171	4	21	art	art	NOUN
ma-171	4	22	adherence	adherence	NOUN
ma-171	4	23	for	for	ADP
ma-171	4	24	a	a	DET
ma-171	4	25	high	high	ADJ
ma-171	4	26	risk	risk	NOUN
ma-171	4	27	hiv	hiv	PROPN
ma-171	4	28	population	population	PROPN
ma-171	4	29	i.	i.	PROPN
ma-171	4	30	s.	s.	PROPN
ma-171	4	31	oriedo1	oriedo1	PROPN
ma-171	4	32	,	,	PUNCT
ma-171	4	33	g.	g.	PROPN
ma-171	4	34	o.	o.	PROPN
ma-171	4	35	lawi2	lawi2	PROPN
ma-171	4	36	,	,	PUNCT
ma-171	4	37	j.	j.	PROPN
ma-171	4	38	o.	o.	PROPN
ma-171	4	39	bonyo3,∗	bonyo3,∗	PROPN
ma-171	4	40	1department	1department	NUM
ma-171	4	41	of	of	ADP
ma-171	4	42	pure	pure	ADJ
ma-171	4	43	and	and	CCONJ
ma-171	4	44	applied	applied	ADJ
ma-171	4	45	mathematics	mathematic	NOUN
ma-171	4	46	,	,	PUNCT
ma-171	4	47	maseno	maseno	NOUN
ma-171	4	48	university	university	NOUN
ma-171	4	49	,	,	PUNCT
ma-171	4	50	p.o	p.o	PROPN
ma-171	4	51	.	.	PROPN
ma-171	4	52	box	box	PROPN
ma-171	4	53	333	333	NUM
ma-171	4	54	-	-	SYM
ma-171	4	55	40105	40105	NUM
ma-171	4	56	,	,	PUNCT
ma-171	4	57	maseno	maseno	NOUN
ma-171	4	58	,	,	PUNCT
ma-171	4	59	kenya	kenya	PROPN
ma-171	4	60	samsonoriedo@gmail.com	samsonoriedo@gmail.com	X
ma-171	5	1	2department	2department	NUM
ma-171	5	2	of	of	ADP
ma-171	5	3	mathematics	mathematic	NOUN
ma-171	5	4	,	,	PUNCT
ma-171	5	5	masinde	masinde	VERB
ma-171	5	6	muliro	muliro	PROPN
ma-171	5	7	university	university	PROPN
ma-171	5	8	of	of	ADP
ma-171	5	9	science	science	NOUN
ma-171	5	10	and	and	CCONJ
ma-171	5	11	technology	technology	NOUN
ma-171	5	12	,	,	PUNCT
ma-171	5	13	p.o	p.o	PROPN
ma-171	5	14	.	.	PROPN
ma-171	5	15	box	box	PROPN
ma-171	5	16	190	190	NUM
ma-171	5	17	-	-	SYM
ma-171	5	18	50100	50100	NUM
ma-171	5	19	,	,	PUNCT
ma-171	5	20	kakamega	kakamega	PROPN
ma-171	5	21	,	,	PUNCT
ma-171	5	22	kenya	kenya	PROPN
ma-171	5	23	glawi@mmust.ac.ke	glawi@mmust.ac.ke	PROPN
ma-171	5	24	3department	3department	NUM
ma-171	5	25	of	of	ADP
ma-171	5	26	mathematics	mathematic	NOUN
ma-171	5	27	,	,	PUNCT
ma-171	5	28	multimedia	multimedia	NOUN
ma-171	5	29	university	university	PROPN
ma-171	5	30	of	of	ADP
ma-171	5	31	kenya	kenya	PROPN
ma-171	5	32	,	,	PUNCT
ma-171	5	33	p.o	p.o	PROPN
ma-171	5	34	.	.	PROPN
ma-171	5	35	box	box	PROPN
ma-171	5	36	15653	15653	NUM
ma-171	5	37	-	-	SYM
ma-171	5	38	00503	00503	NUM
ma-171	5	39	,	,	PUNCT
ma-171	5	40	nairobi	nairobi	PROPN
ma-171	5	41	,	,	PUNCT
ma-171	5	42	kenya	kenya	PROPN
ma-171	5	43	jbonyo@mmu.ac.ke	jbonyo@mmu.ac.ke	PROPN
ma-171	5	44	∗correspondence	∗correspondence	NOUN
ma-171	5	45	:	:	PUNCT
ma-171	5	46	jobbonyo@maseno.ac.ke	jobbonyo@maseno.ac.ke	NOUN
ma-171	5	47	abstract	abstract	ADJ
ma-171	5	48	.	.	PUNCT
ma-171	6	1	in	in	ADP
ma-171	6	2	this	this	DET
ma-171	6	3	paper	paper	NOUN
ma-171	6	4	,	,	PUNCT
ma-171	6	5	a	a	DET
ma-171	6	6	mathematical	mathematical	ADJ
ma-171	6	7	model	model	NOUN
ma-171	6	8	for	for	ADP
ma-171	6	9	dual	dual	ADJ
ma-171	6	10	protection	protection	NOUN
ma-171	6	11	,	,	PUNCT
ma-171	6	12	incorporating	incorporate	VERB
ma-171	6	13	prep	prep	NOUN
ma-171	6	14	and	and	CCONJ
ma-171	6	15	condomuse	condomuse	NOUN
ma-171	6	16	,	,	PUNCT
ma-171	6	17	and	and	CCONJ
ma-171	6	18	art	art	NOUN
ma-171	6	19	adherence	adherence	NOUN
ma-171	6	20	is	be	AUX
ma-171	6	21	formulated	formulate	VERB
ma-171	6	22	,	,	PUNCT
ma-171	6	23	based	base	VERB
ma-171	6	24	on	on	ADP
ma-171	6	25	a	a	DET
ma-171	6	26	system	system	NOUN
ma-171	6	27	of	of	ADP
ma-171	6	28	ordinary	ordinary	ADJ
ma-171	6	29	differential	differential	ADJ
ma-171	6	30	equations	equation	NOUN
ma-171	6	31	andanalyzed	andanalyze	VERB
ma-171	6	32	.	.	PUNCT
ma-171	7	1	the	the	DET
ma-171	7	2	results	result	NOUN
ma-171	7	3	obtained	obtain	VERB
ma-171	7	4	from	from	ADP
ma-171	7	5	stability	stability	NOUN
ma-171	7	6	analysis	analysis	NOUN
ma-171	7	7	indicate	indicate	VERB
ma-171	7	8	that	that	SCONJ
ma-171	7	9	provided	provide	VERB
ma-171	7	10	the	the	DET
ma-171	7	11	basic	basic	ADJ
ma-171	7	12	reproductivenumber	reproductivenumber	NOUN
ma-171	7	13	is	be	AUX
ma-171	7	14	less	less	ADJ
ma-171	7	15	than	than	ADP
ma-171	7	16	unity	unity	NOUN
ma-171	7	17	,	,	PUNCT
ma-171	7	18	the	the	DET
ma-171	7	19	disease	disease	NOUN
ma-171	7	20	free	free	ADJ
ma-171	7	21	equilibrium	equilibrium	NOUN
ma-171	7	22	point	point	NOUN
ma-171	7	23	is	be	AUX
ma-171	7	24	both	both	PRON
ma-171	7	25	locally	locally	ADV
ma-171	7	26	and	and	CCONJ
ma-171	7	27	globally	globally	ADV
ma-171	7	28	asymptoticallystable	asymptoticallystable	ADJ
ma-171	7	29	,	,	PUNCT
ma-171	7	30	while	while	SCONJ
ma-171	7	31	provided	provide	VERB
ma-171	7	32	the	the	DET
ma-171	7	33	basic	basic	ADJ
ma-171	7	34	reproductive	reproductive	ADJ
ma-171	7	35	number	number	NOUN
ma-171	7	36	is	be	AUX
ma-171	7	37	greater	great	ADJ
ma-171	7	38	than	than	ADP
ma-171	7	39	unity	unity	NOUN
ma-171	7	40	,	,	PUNCT
ma-171	7	41	the	the	DET
ma-171	7	42	endemic	endemic	ADJ
ma-171	7	43	equilibriumpoint	equilibriumpoint	NOUN
ma-171	7	44	exists	exist	VERB
ma-171	7	45	and	and	CCONJ
ma-171	7	46	is	be	AUX
ma-171	7	47	locally	locally	ADV
ma-171	7	48	asymptotically	asymptotically	ADV
ma-171	7	49	stable	stable	ADJ
ma-171	7	50	.	.	PUNCT
ma-171	8	1	sensitivity	sensitivity	NOUN
ma-171	8	2	analysis	analysis	NOUN
ma-171	8	3	is	be	AUX
ma-171	8	4	undertaken	undertake	VERB
ma-171	8	5	to	to	PART
ma-171	8	6	establish	establish	VERB
ma-171	8	7	themost	themost	ADJ
ma-171	8	8	sensitive	sensitive	ADJ
ma-171	8	9	model	model	NOUN
ma-171	8	10	parameter	parameter	NOUN
ma-171	8	11	.	.	PUNCT
ma-171	9	1	the	the	DET
ma-171	9	2	most	most	ADV
ma-171	9	3	sensitive	sensitive	ADJ
ma-171	9	4	parameter	parameter	NOUN
ma-171	9	5	to	to	ADP
ma-171	9	6	the	the	DET
ma-171	9	7	value	value	NOUN
ma-171	9	8	of	of	ADP
ma-171	9	9	r0	r0	NOUN
ma-171	9	10	is	be	AUX
ma-171	9	11	β1	β1	PROPN
ma-171	9	12	,	,	PUNCT
ma-171	9	13	the	the	DET
ma-171	9	14	meancontact	meancontact	ADJ
ma-171	9	15	rate	rate	NOUN
ma-171	9	16	with	with	ADP
ma-171	9	17	undiagnosed	undiagnosed	ADJ
ma-171	9	18	infectives	infective	NOUN
ma-171	9	19	.	.	PUNCT
ma-171	10	1	this	this	PRON
ma-171	10	2	implies	imply	VERB
ma-171	10	3	that	that	SCONJ
ma-171	10	4	in	in	ADP
ma-171	10	5	order	order	NOUN
ma-171	10	6	to	to	PART
ma-171	10	7	control	control	VERB
ma-171	10	8	the	the	DET
ma-171	10	9	spread	spread	NOUN
ma-171	10	10	of	of	ADP
ma-171	10	11	hivin	hivin	PROPN
ma-171	10	12	a	a	DET
ma-171	10	13	high	high	ADJ
ma-171	10	14	risk	risk	NOUN
ma-171	10	15	population	population	NOUN
ma-171	10	16	,	,	PUNCT
ma-171	10	17	efforts	effort	NOUN
ma-171	10	18	should	should	AUX
ma-171	10	19	be	be	AUX
ma-171	10	20	geared	gear	VERB
ma-171	10	21	towards	towards	ADP
ma-171	10	22	reducing	reduce	VERB
ma-171	10	23	the	the	DET
ma-171	10	24	undiagnosed	undiagnosed	ADJ
ma-171	10	25	by	by	ADP
ma-171	10	26	testingand	testingand	NOUN
ma-171	10	27	enrolling	enrol	VERB
ma-171	10	28	them	they	PRON
ma-171	10	29	on	on	ADP
ma-171	10	30	art	art	NOUN
ma-171	10	31	treatment	treatment	NOUN
ma-171	10	32	.	.	PUNCT
ma-171	11	1	this	this	PRON
ma-171	11	2	in	in	ADP
ma-171	11	3	turn	turn	NOUN
ma-171	11	4	lowers	lower	VERB
ma-171	11	5	their	their	PRON
ma-171	11	6	infectivity	infectivity	NOUN
ma-171	11	7	as	as	ADV
ma-171	11	8	well	well	ADV
ma-171	11	9	as	as	ADP
ma-171	11	10	chances	chance	VERB
ma-171	11	11	ofprogressing	ofprogresse	VERB
ma-171	11	12	to	to	ADP
ma-171	11	13	the	the	DET
ma-171	11	14	aids	aids	PROPN
ma-171	11	15	class	class	NOUN
ma-171	11	16	.	.	PUNCT
ma-171	12	1	1	1	X
ma-171	12	2	.	.	X
ma-171	12	3	introduction	introduction	NOUN
ma-171	12	4	numerous	numerous	ADJ
ma-171	12	5	efforts	effort	NOUN
ma-171	12	6	have	have	AUX
ma-171	12	7	been	be	AUX
ma-171	12	8	made	make	VERB
ma-171	12	9	in	in	ADP
ma-171	12	10	an	an	DET
ma-171	12	11	attempt	attempt	NOUN
ma-171	12	12	to	to	PART
ma-171	12	13	control	control	VERB
ma-171	12	14	the	the	DET
ma-171	12	15	spread	spread	NOUN
ma-171	12	16	of	of	ADP
ma-171	12	17	hiv	hiv	PROPN
ma-171	12	18	,	,	PUNCT
ma-171	12	19	with	with	ADP
ma-171	12	20	the	the	DET
ma-171	12	21	aim	aim	NOUN
ma-171	12	22	ofreducing	ofreduce	VERB
ma-171	12	23	its	its	PRON
ma-171	12	24	effects	effect	NOUN
ma-171	12	25	.	.	PUNCT
ma-171	13	1	according	accord	VERB
ma-171	13	2	to	to	ADP
ma-171	13	3	the	the	DET
ma-171	13	4	unaids	unaid	NOUN
ma-171	13	5	fact	fact	NOUN
ma-171	13	6	sheet	sheet	NOUN
ma-171	13	7	2019	2019	NUM
ma-171	13	8	,	,	PUNCT
ma-171	13	9	at	at	ADP
ma-171	13	10	least	least	ADJ
ma-171	13	11	1.7	1.7	NUM
ma-171	13	12	million	million	NUM
ma-171	13	13	new	new	ADJ
ma-171	13	14	hivinfections	hivinfection	NOUN
ma-171	13	15	were	be	AUX
ma-171	13	16	reported	report	VERB
ma-171	13	17	by	by	ADP
ma-171	13	18	the	the	DET
ma-171	13	19	end	end	NOUN
ma-171	13	20	of	of	ADP
ma-171	13	21	the	the	DET
ma-171	13	22	year	year	NOUN
ma-171	13	23	2018	2018	NUM
ma-171	13	24	[	[	X
ma-171	13	25	13].scientific	13].scientific	PROPN
ma-171	13	26	as	as	ADV
ma-171	13	27	well	well	ADV
ma-171	13	28	as	as	ADP
ma-171	13	29	public	public	ADJ
ma-171	13	30	health	health	NOUN
ma-171	13	31	interventions	intervention	NOUN
ma-171	13	32	such	such	ADJ
ma-171	13	33	as	as	ADP
ma-171	13	34	testing	testing	NOUN
ma-171	13	35	and	and	CCONJ
ma-171	13	36	counseling	counseling	NOUN
ma-171	13	37	,	,	PUNCT
ma-171	13	38	circumcision	circumcision	NOUN
ma-171	13	39	,	,	PUNCT
ma-171	13	40	use	use	NOUN
ma-171	13	41	of	of	ADP
ma-171	13	42	prep	prep	NOUN
ma-171	13	43	(	(	PUNCT
ma-171	13	44	pre	pre	ADJ
ma-171	13	45	-	-	ADJ
ma-171	13	46	exposure	exposure	ADJ
ma-171	13	47	prophylaxis	prophylaxis	NOUN
ma-171	13	48	)	)	PUNCT
ma-171	13	49	,	,	PUNCT
ma-171	13	50	pep	pep	INTJ
ma-171	13	51	(	(	PUNCT
ma-171	13	52	post	post	ADJ
ma-171	13	53	-	-	ADJ
ma-171	13	54	exposure	exposure	ADJ
ma-171	13	55	prophylaxis	prophylaxis	NOUN
ma-171	13	56	)	)	PUNCT
ma-171	13	57	,	,	PUNCT
ma-171	13	58	condom	condom	NOUN
ma-171	13	59	use	use	NOUN
ma-171	13	60	,	,	PUNCT
ma-171	13	61	and	and	CCONJ
ma-171	13	62	an	an	DET
ma-171	13	63	-	-	PUNCT
ma-171	13	64	tiretroviral	tiretroviral	ADJ
ma-171	13	65	therapy	therapy	NOUN
ma-171	13	66	have	have	AUX
ma-171	13	67	been	be	AUX
ma-171	13	68	proposed	propose	VERB
ma-171	13	69	and	and	CCONJ
ma-171	13	70	utilized	utilize	VERB
ma-171	13	71	.	.	PUNCT
ma-171	14	1	consistent	consistent	ADJ
ma-171	14	2	use	use	NOUN
ma-171	14	3	of	of	ADP
ma-171	14	4	condoms	condom	NOUN
ma-171	14	5	can	can	AUX
ma-171	14	6	result	result	VERB
ma-171	14	7	to	to	ADP
ma-171	14	8	80%reduction	80%reduction	NOUN
ma-171	14	9	in	in	ADP
ma-171	14	10	hiv	hiv	PROPN
ma-171	14	11	incidence	incidence	NOUN
ma-171	14	12	among	among	ADP
ma-171	14	13	the	the	DET
ma-171	14	14	heterosexual	heterosexual	ADJ
ma-171	14	15	population	population	NOUN
ma-171	14	16	[	[	X
ma-171	14	17	2	2	NUM
ma-171	14	18	]	]	PUNCT
ma-171	14	19	,	,	PUNCT
ma-171	14	20	while	while	SCONJ
ma-171	14	21	the	the	DET
ma-171	14	22	effectiveness	effectiveness	NOUN
ma-171	14	23	of	of	ADP
ma-171	14	24	condom	condom	NOUN
ma-171	14	25	received	receive	VERB
ma-171	14	26	:	:	PUNCT
ma-171	14	27	1	1	NUM
ma-171	14	28	may	may	PROPN
ma-171	14	29	2023	2023	NUM
ma-171	14	30	.	.	PUNCT
ma-171	15	1	key	key	ADJ
ma-171	15	2	words	word	NOUN
ma-171	15	3	and	and	CCONJ
ma-171	15	4	phrases	phrase	NOUN
ma-171	15	5	.	.	PUNCT
ma-171	16	1	mathematical	mathematical	ADJ
ma-171	16	2	modeling	modeling	NOUN
ma-171	16	3	;	;	PUNCT
ma-171	16	4	prep	prep	NOUN
ma-171	16	5	;	;	PUNCT
ma-171	16	6	dual	dual	ADJ
ma-171	16	7	protection	protection	NOUN
ma-171	16	8	;	;	PUNCT
ma-171	16	9	hiv	hiv	PROPN
ma-171	16	10	/	/	SYM
ma-171	16	11	aids	aids	PROPN
ma-171	16	12	;	;	PUNCT
ma-171	16	13	stability	stability	NOUN
ma-171	16	14	analysis.1	analysis.1	PROPN
ma-171	16	15	https://adac.ee	https://adac.ee	PROPN
ma-171	16	16	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	16	17	https://orcid.org/0000-0002-6442-4211	https://orcid.org/0000-0002-6442-4211	PROPN
ma-171	16	18	eur	eur	PROPN
ma-171	16	19	.	.	PUNCT
ma-171	17	1	j.	j.	PROPN
ma-171	17	2	math	math	PROPN
ma-171	17	3	.	.	PUNCT
ma-171	18	1	anal	anal	PROPN
ma-171	18	2	.	.	PUNCT
ma-171	19	1	10.28924	10.28924	NUM
ma-171	19	2	/	/	SYM
ma-171	19	3	ada	ada	PROPN
ma-171	19	4	/	/	SYM
ma-171	19	5	ma.3.21	ma.3.21	PROPN
ma-171	19	6	2use	2use	PROPN
ma-171	19	7	for	for	ADP
ma-171	19	8	men	man	NOUN
ma-171	19	9	who	who	PRON
ma-171	19	10	have	have	VERB
ma-171	19	11	sex	sex	NOUN
ma-171	19	12	with	with	ADP
ma-171	19	13	men	man	NOUN
ma-171	19	14	is	be	AUX
ma-171	19	15	70	70	NUM
ma-171	19	16	%	%	NOUN
ma-171	19	17	[	[	X
ma-171	19	18	3	3	NUM
ma-171	19	19	]	]	PUNCT
ma-171	19	20	.	.	PUNCT
ma-171	20	1	proper	proper	ADJ
ma-171	20	2	use	use	NOUN
ma-171	20	3	(	(	PUNCT
ma-171	20	4	correctly	correctly	ADV
ma-171	20	5	and	and	CCONJ
ma-171	20	6	consistently	consistently	ADV
ma-171	20	7	)	)	PUNCT
ma-171	20	8	as	as	ADV
ma-171	20	9	well	well	ADV
ma-171	20	10	asquality	asquality	NOUN
ma-171	20	11	concerns	concern	NOUN
ma-171	20	12	have	have	AUX
ma-171	20	13	been	be	AUX
ma-171	20	14	directly	directly	ADV
ma-171	20	15	attributed	attribute	VERB
ma-171	20	16	to	to	ADP
ma-171	20	17	the	the	DET
ma-171	20	18	success	success	NOUN
ma-171	20	19	of	of	ADP
ma-171	20	20	this	this	DET
ma-171	20	21	approach.in	approach.in	NOUN
ma-171	20	22	2012	2012	NUM
ma-171	20	23	,	,	PUNCT
ma-171	20	24	the	the	DET
ma-171	20	25	u.s	u.s	PROPN
ma-171	20	26	food	food	PROPN
ma-171	20	27	and	and	CCONJ
ma-171	20	28	drug	drug	PROPN
ma-171	20	29	administration	administration	PROPN
ma-171	20	30	(	(	PUNCT
ma-171	20	31	fda	fda	PROPN
ma-171	20	32	)	)	PUNCT
ma-171	20	33	approved	approve	VERB
ma-171	20	34	the	the	DET
ma-171	20	35	use	use	NOUN
ma-171	20	36	of	of	ADP
ma-171	20	37	truvada	truvada	NOUN
ma-171	20	38	for	for	ADP
ma-171	20	39	prep	prep	NOUN
ma-171	20	40	asan	asan	ADJ
ma-171	20	41	oral	oral	ADJ
ma-171	20	42	pill	pill	NOUN
ma-171	20	43	taken	take	VERB
ma-171	20	44	once	once	ADV
ma-171	20	45	a	a	DET
ma-171	20	46	day	day	NOUN
ma-171	20	47	[	[	X
ma-171	20	48	14	14	NUM
ma-171	20	49	]	]	PUNCT
ma-171	20	50	.	.	PUNCT
ma-171	21	1	numerous	numerous	ADJ
ma-171	21	2	efficacy	efficacy	NOUN
ma-171	21	3	trials	trial	NOUN
ma-171	21	4	(	(	PUNCT
ma-171	21	5	by	by	ADP
ma-171	21	6	iprex	iprex	ADJ
ma-171	21	7	,	,	PUNCT
ma-171	21	8	partners	partner	NOUN
ma-171	21	9	prep	prep	NOUN
ma-171	21	10	,	,	PUNCT
ma-171	21	11	tdf2,e.t.c	tdf2,e.t.c	PROPN
ma-171	21	12	)	)	PUNCT
ma-171	21	13	have	have	AUX
ma-171	21	14	since	since	SCONJ
ma-171	21	15	been	be	AUX
ma-171	21	16	conducted	conduct	VERB
ma-171	21	17	to	to	PART
ma-171	21	18	ascertain	ascertain	VERB
ma-171	21	19	the	the	DET
ma-171	21	20	potential	potential	NOUN
ma-171	21	21	of	of	ADP
ma-171	21	22	prep	prep	NOUN
ma-171	21	23	to	to	PART
ma-171	21	24	prevent	prevent	VERB
ma-171	21	25	hiv	hiv	PROPN
ma-171	21	26	infection	infection	NOUN
ma-171	21	27	.	.	PUNCT
ma-171	22	1	theiprex	theiprex	PROPN
ma-171	22	2	trial	trial	NOUN
ma-171	22	3	demonstrated	demonstrate	VERB
ma-171	22	4	that	that	SCONJ
ma-171	22	5	prep	prep	NOUN
ma-171	22	6	has	have	VERB
ma-171	22	7	the	the	DET
ma-171	22	8	potential	potential	NOUN
ma-171	22	9	of	of	ADP
ma-171	22	10	reducing	reduce	VERB
ma-171	22	11	the	the	DET
ma-171	22	12	risk	risk	NOUN
ma-171	22	13	of	of	ADP
ma-171	22	14	hiv	hiv	PROPN
ma-171	22	15	infection	infection	NOUN
ma-171	22	16	amongtransgender	amongtransgender	PROPN
ma-171	22	17	women	woman	NOUN
ma-171	22	18	,	,	PUNCT
ma-171	22	19	bisexual	bisexual	ADJ
ma-171	22	20	men	man	NOUN
ma-171	22	21	,	,	PUNCT
ma-171	22	22	as	as	ADV
ma-171	22	23	well	well	ADV
ma-171	22	24	as	as	ADP
ma-171	22	25	men	man	NOUN
ma-171	22	26	who	who	PRON
ma-171	22	27	have	have	VERB
ma-171	22	28	sex	sex	NOUN
ma-171	22	29	with	with	ADP
ma-171	22	30	men	man	NOUN
ma-171	22	31	[	[	X
ma-171	22	32	8	8	NUM
ma-171	22	33	]	]	PUNCT
ma-171	22	34	.	.	PUNCT
ma-171	23	1	two	two	NUM
ma-171	23	2	major	major	ADJ
ma-171	23	3	studies;partners	studies;partner	NOUN
ma-171	23	4	prep	prep	NOUN
ma-171	23	5	,	,	PUNCT
ma-171	23	6	and	and	CCONJ
ma-171	23	7	tdf2	tdf2	PROPN
ma-171	23	8	demonstrated	demonstrate	VERB
ma-171	23	9	the	the	DET
ma-171	23	10	effectiveness	effectiveness	NOUN
ma-171	23	11	of	of	ADP
ma-171	23	12	prep	prep	NOUN
ma-171	23	13	among	among	ADP
ma-171	23	14	heterosexual	heterosexual	ADJ
ma-171	23	15	men	man	NOUN
ma-171	23	16	andwomen	andwomen	PROPN
ma-171	23	17	.	.	PUNCT
ma-171	24	1	out	out	ADP
ma-171	24	2	of	of	ADP
ma-171	24	3	all	all	DET
ma-171	24	4	these	these	DET
ma-171	24	5	studies	study	NOUN
ma-171	24	6	,	,	PUNCT
ma-171	24	7	none	none	NOUN
ma-171	24	8	displayed	display	VERB
ma-171	24	9	a	a	DET
ma-171	24	10	100	100	NUM
ma-171	24	11	%	%	NOUN
ma-171	24	12	effectiveness	effectiveness	NOUN
ma-171	24	13	[	[	X
ma-171	24	14	11	11	NUM
ma-171	24	15	]	]	PUNCT
ma-171	24	16	.	.	PUNCT
ma-171	25	1	adherence	adherence	NOUN
ma-171	25	2	has	have	VERB
ma-171	25	3	beenfound	beenfound	NOUN
ma-171	25	4	to	to	PART
ma-171	25	5	be	be	AUX
ma-171	25	6	directly	directly	ADV
ma-171	25	7	correlated	correlate	VERB
ma-171	25	8	with	with	ADP
ma-171	25	9	the	the	DET
ma-171	25	10	effectiveness	effectiveness	NOUN
ma-171	25	11	of	of	ADP
ma-171	25	12	prep	prep	NOUN
ma-171	25	13	[	[	X
ma-171	25	14	11	11	NUM
ma-171	25	15	]	]	PUNCT
ma-171	25	16	.	.	PUNCT
ma-171	26	1	in	in	ADP
ma-171	26	2	the	the	DET
ma-171	26	3	absence	absence	NOUN
ma-171	26	4	of	of	ADP
ma-171	26	5	adherence	adherence	NOUN
ma-171	26	6	,	,	PUNCT
ma-171	26	7	which	which	PRON
ma-171	26	8	guarantees	guarantee	VERB
ma-171	26	9	efficacy	efficacy	NOUN
ma-171	26	10	,	,	PUNCT
ma-171	26	11	prep	prep	NOUN
ma-171	26	12	failures	failure	NOUN
ma-171	26	13	have	have	AUX
ma-171	26	14	been	be	AUX
ma-171	26	15	characterized	characterize	VERB
ma-171	26	16	by	by	ADP
ma-171	26	17	;	;	PUNCT
ma-171	26	18	system	system	NOUN
ma-171	26	19	failures	failure	NOUN
ma-171	26	20	,	,	PUNCT
ma-171	26	21	people	people	NOUN
ma-171	26	22	fail	fail	ADJ
ma-171	26	23	-	-	PUNCT
ma-171	26	24	ures	ure	NOUN
ma-171	26	25	,	,	PUNCT
ma-171	26	26	doctor	doctor	NOUN
ma-171	26	27	failures	failure	NOUN
ma-171	26	28	,	,	PUNCT
ma-171	26	29	drug	drug	NOUN
ma-171	26	30	failures	failure	NOUN
ma-171	26	31	,	,	PUNCT
ma-171	26	32	as	as	ADV
ma-171	26	33	well	well	ADV
ma-171	26	34	as	as	ADP
ma-171	26	35	assay	assay	ADJ
ma-171	26	36	failures	failure	NOUN
ma-171	26	37	[	[	X
ma-171	26	38	9	9	NUM
ma-171	26	39	]	]	PUNCT
ma-171	26	40	.	.	PUNCT
ma-171	27	1	these	these	DET
ma-171	27	2	failures	failure	NOUN
ma-171	27	3	expose	expose	VERB
ma-171	27	4	prep	prep	NOUN
ma-171	27	5	usersto	usersto	NOUN
ma-171	27	6	the	the	DET
ma-171	27	7	risk	risk	NOUN
ma-171	27	8	of	of	ADP
ma-171	27	9	hiv	hiv	PROPN
ma-171	27	10	infection	infection	NOUN
ma-171	27	11	hence	hence	ADV
ma-171	27	12	the	the	DET
ma-171	27	13	need	need	NOUN
ma-171	27	14	for	for	ADP
ma-171	27	15	additional	additional	ADJ
ma-171	27	16	protection	protection	NOUN
ma-171	27	17	whenever	whenever	SCONJ
ma-171	27	18	prep	prep	NOUN
ma-171	27	19	has	have	VERB
ma-171	27	20	beenutilized.the	beenutilized.the	DET
ma-171	27	21	nature	nature	NOUN
ma-171	27	22	of	of	ADP
ma-171	27	23	storage	storage	NOUN
ma-171	27	24	,	,	PUNCT
ma-171	27	25	date	date	NOUN
ma-171	27	26	of	of	ADP
ma-171	27	27	manufacture	manufacture	NOUN
ma-171	27	28	,	,	PUNCT
ma-171	27	29	religious	religious	ADJ
ma-171	27	30	as	as	ADV
ma-171	27	31	well	well	ADV
ma-171	27	32	as	as	ADP
ma-171	27	33	socio	socio	NOUN
ma-171	27	34	-	-	PUNCT
ma-171	27	35	cultural	cultural	ADJ
ma-171	27	36	beliefs	belief	NOUN
ma-171	27	37	also	also	ADV
ma-171	27	38	influencehow	influencehow	SCONJ
ma-171	27	39	each	each	DET
ma-171	27	40	hiv	hiv	PROPN
ma-171	27	41	prevention	prevention	NOUN
ma-171	27	42	venture	venture	NOUN
ma-171	27	43	is	be	AUX
ma-171	27	44	utilized	utilize	VERB
ma-171	27	45	.	.	PUNCT
ma-171	28	1	the	the	DET
ma-171	28	2	challenges	challenge	NOUN
ma-171	28	3	experienced	experience	VERB
ma-171	28	4	when	when	SCONJ
ma-171	28	5	various	various	ADJ
ma-171	28	6	approachesare	approachesare	NOUN
ma-171	28	7	employed	employ	VERB
ma-171	28	8	in	in	ADP
ma-171	28	9	an	an	DET
ma-171	28	10	attempt	attempt	NOUN
ma-171	28	11	to	to	PART
ma-171	28	12	control	control	VERB
ma-171	28	13	the	the	DET
ma-171	28	14	spread	spread	NOUN
ma-171	28	15	of	of	ADP
ma-171	28	16	hiv	hiv	PROPN
ma-171	28	17	infection	infection	NOUN
ma-171	28	18	in	in	ADP
ma-171	28	19	a	a	DET
ma-171	28	20	high	high	ADJ
ma-171	28	21	risk	risk	NOUN
ma-171	28	22	population	population	NOUN
ma-171	28	23	form	form	NOUN
ma-171	28	24	thebasis	thebasis	NOUN
ma-171	28	25	for	for	ADP
ma-171	28	26	the	the	DET
ma-171	28	27	need	need	NOUN
ma-171	28	28	to	to	PART
ma-171	28	29	use	use	VERB
ma-171	28	30	dual	dual	ADJ
ma-171	28	31	protection	protection	NOUN
ma-171	28	32	in	in	ADP
ma-171	28	33	order	order	NOUN
ma-171	28	34	to	to	PART
ma-171	28	35	achieve	achieve	VERB
ma-171	28	36	maximum	maximum	ADJ
ma-171	28	37	protection	protection	NOUN
ma-171	28	38	.	.	PUNCT
ma-171	29	1	a	a	DET
ma-171	29	2	combinationprevention	combinationprevention	NOUN
ma-171	29	3	approach	approach	NOUN
ma-171	29	4	as	as	SCONJ
ma-171	29	5	proposed	propose	VERB
ma-171	29	6	by	by	ADP
ma-171	29	7	[	[	X
ma-171	29	8	6	6	NUM
ma-171	29	9	]	]	PUNCT
ma-171	29	10	,	,	PUNCT
ma-171	29	11	based	base	VERB
ma-171	29	12	on	on	ADP
ma-171	29	13	proven	prove	VERB
ma-171	29	14	efficacy	efficacy	NOUN
ma-171	29	15	interventions	intervention	NOUN
ma-171	29	16	,	,	PUNCT
ma-171	29	17	provides	provide	VERB
ma-171	29	18	one	one	NUM
ma-171	29	19	withthe	withthe	ADJ
ma-171	29	20	best	good	ADJ
ma-171	29	21	opportunity	opportunity	NOUN
ma-171	29	22	to	to	PART
ma-171	29	23	curb	curb	VERB
ma-171	29	24	the	the	DET
ma-171	29	25	spread	spread	NOUN
ma-171	29	26	of	of	ADP
ma-171	29	27	hiv	hiv	PROPN
ma-171	29	28	among	among	ADP
ma-171	29	29	the	the	DET
ma-171	29	30	high	high	ADJ
ma-171	29	31	risk	risk	NOUN
ma-171	29	32	population.in	population.in	NOUN
ma-171	29	33	this	this	DET
ma-171	29	34	study	study	NOUN
ma-171	29	35	,	,	PUNCT
ma-171	29	36	we	we	PRON
ma-171	29	37	propose	propose	VERB
ma-171	29	38	a	a	DET
ma-171	29	39	mathematical	mathematical	ADJ
ma-171	29	40	model	model	NOUN
ma-171	29	41	of	of	ADP
ma-171	29	42	dual	dual	ADJ
ma-171	29	43	protection	protection	NOUN
ma-171	29	44	against	against	ADP
ma-171	29	45	hiv	hiv	PROPN
ma-171	29	46	infection	infection	NOUN
ma-171	29	47	by	by	ADP
ma-171	29	48	the	the	DET
ma-171	29	49	useof	useof	ADJ
ma-171	29	50	condom	condom	NOUN
ma-171	29	51	and	and	CCONJ
ma-171	29	52	prep	prep	NOUN
ma-171	29	53	,	,	PUNCT
ma-171	29	54	and	and	CCONJ
ma-171	29	55	adherence	adherence	NOUN
ma-171	29	56	to	to	ADP
ma-171	29	57	art	art	NOUN
ma-171	29	58	treatment	treatment	NOUN
ma-171	29	59	,	,	PUNCT
ma-171	29	60	while	while	SCONJ
ma-171	29	61	focusing	focus	VERB
ma-171	29	62	on	on	ADP
ma-171	29	63	the	the	DET
ma-171	29	64	high	high	ADJ
ma-171	29	65	risk	risk	NOUN
ma-171	29	66	populationcollectively	populationcollectively	ADV
ma-171	29	67	.	.	PUNCT
ma-171	30	1	earlier	early	ADJ
ma-171	30	2	studies	study	NOUN
ma-171	30	3	have	have	AUX
ma-171	30	4	either	either	CCONJ
ma-171	30	5	narrowed	narrow	VERB
ma-171	30	6	down	down	ADP
ma-171	30	7	to	to	ADP
ma-171	30	8	a	a	DET
ma-171	30	9	particular	particular	ADJ
ma-171	30	10	category	category	NOUN
ma-171	30	11	of	of	ADP
ma-171	30	12	persons	person	NOUN
ma-171	30	13	at	at	ADP
ma-171	30	14	highrisk	highrisk	NOUN
ma-171	30	15	of	of	ADP
ma-171	30	16	infection	infection	NOUN
ma-171	30	17	[	[	X
ma-171	30	18	3	3	NUM
ma-171	30	19	]	]	PUNCT
ma-171	30	20	,	,	PUNCT
ma-171	30	21	or	or	CCONJ
ma-171	30	22	have	have	AUX
ma-171	30	23	used	use	VERB
ma-171	30	24	a	a	DET
ma-171	30	25	combination	combination	NOUN
ma-171	30	26	of	of	ADP
ma-171	30	27	prevention	prevention	NOUN
ma-171	30	28	techniques	technique	NOUN
ma-171	30	29	where	where	SCONJ
ma-171	30	30	one	one	NUM
ma-171	30	31	techniqueacts	techniqueact	VERB
ma-171	30	32	as	as	ADP
ma-171	30	33	a	a	DET
ma-171	30	34	supplement	supplement	NOUN
ma-171	30	35	to	to	ADP
ma-171	30	36	the	the	DET
ma-171	30	37	other	other	ADJ
ma-171	30	38	[	[	X
ma-171	30	39	4	4	NUM
ma-171	30	40	]	]	PUNCT
ma-171	30	41	,	,	PUNCT
ma-171	30	42	[	[	X
ma-171	30	43	5	5	NUM
ma-171	30	44	]	]	PUNCT
ma-171	30	45	.	.	PUNCT
ma-171	31	1	the	the	DET
ma-171	31	2	study	study	NOUN
ma-171	31	3	will	will	AUX
ma-171	31	4	focus	focus	VERB
ma-171	31	5	on	on	ADP
ma-171	31	6	the	the	DET
ma-171	31	7	impact	impact	NOUN
ma-171	31	8	of	of	ADP
ma-171	31	9	dual	dual	ADJ
ma-171	31	10	protectionon	protectionon	NOUN
ma-171	31	11	reducing	reduce	VERB
ma-171	31	12	the	the	DET
ma-171	31	13	number	number	NOUN
ma-171	31	14	of	of	ADP
ma-171	31	15	new	new	ADJ
ma-171	31	16	infections	infection	NOUN
ma-171	31	17	,	,	PUNCT
ma-171	31	18	and	and	CCONJ
ma-171	31	19	that	that	PRON
ma-171	31	20	of	of	ADP
ma-171	31	21	art	art	NOUN
ma-171	31	22	adherence	adherence	NOUN
ma-171	31	23	in	in	ADP
ma-171	31	24	ensuring	ensure	VERB
ma-171	31	25	those	those	PRON
ma-171	31	26	who	who	PRON
ma-171	31	27	areinfected	areinfecte	VERB
ma-171	31	28	remain	remain	VERB
ma-171	31	29	less	less	ADV
ma-171	31	30	infectious	infectious	ADJ
ma-171	31	31	.	.	PUNCT
ma-171	32	1	2	2	X
ma-171	32	2	.	.	NOUN
ma-171	32	3	model	model	NOUN
ma-171	32	4	formulation	formulation	NOUN
ma-171	32	5	and	and	CCONJ
ma-171	32	6	description	description	NOUN
ma-171	32	7	the	the	DET
ma-171	32	8	population	population	NOUN
ma-171	32	9	is	be	AUX
ma-171	32	10	subdivided	subdivide	VERB
ma-171	32	11	into	into	ADP
ma-171	32	12	the	the	DET
ma-171	32	13	classes	class	NOUN
ma-171	32	14	;	;	PUNCT
ma-171	32	15	susceptible	susceptible	ADJ
ma-171	32	16	,	,	PUNCT
ma-171	32	17	infected	infected	ADJ
ma-171	32	18	,	,	PUNCT
ma-171	32	19	and	and	CCONJ
ma-171	32	20	aids	aid	VERB
ma-171	32	21	individuals	individual	NOUN
ma-171	32	22	.	.	PUNCT
ma-171	33	1	thesusceptible	thesusceptible	ADJ
ma-171	33	2	class	class	NOUN
ma-171	33	3	has	have	AUX
ma-171	33	4	been	be	AUX
ma-171	33	5	further	far	ADV
ma-171	33	6	subdivided	subdivide	VERB
ma-171	33	7	into	into	ADP
ma-171	33	8	two	two	NUM
ma-171	33	9	compartments	compartment	NOUN
ma-171	33	10	on	on	ADP
ma-171	33	11	the	the	DET
ma-171	33	12	basis	basis	NOUN
ma-171	33	13	of	of	ADP
ma-171	33	14	degree	degree	NOUN
ma-171	33	15	ofrisk	ofrisk	NOUN
ma-171	33	16	of	of	ADP
ma-171	33	17	infection	infection	NOUN
ma-171	33	18	.	.	PUNCT
ma-171	34	1	these	these	PRON
ma-171	34	2	include	include	VERB
ma-171	34	3	susceptible	susceptible	ADJ
ma-171	34	4	individuals	individual	NOUN
ma-171	34	5	at	at	ADP
ma-171	34	6	high	high	ADJ
ma-171	34	7	risk	risk	NOUN
ma-171	34	8	of	of	ADP
ma-171	34	9	infection	infection	NOUN
ma-171	34	10	,	,	PUNCT
ma-171	34	11	denoted	denote	VERB
ma-171	34	12	by	by	ADP
ma-171	34	13	(	(	PUNCT
ma-171	34	14	sh),and	sh),and	X
ma-171	34	15	those	those	PRON
ma-171	34	16	at	at	ADP
ma-171	34	17	low	low	ADJ
ma-171	34	18	risk	risk	NOUN
ma-171	34	19	,	,	PUNCT
ma-171	34	20	denoted	denote	VERB
ma-171	34	21	by	by	ADP
ma-171	34	22	(	(	PUNCT
ma-171	34	23	sl	sl	NOUN
ma-171	34	24	)	)	PUNCT
ma-171	34	25	.	.	PUNCT
ma-171	35	1	the	the	DET
ma-171	35	2	high	high	ADJ
ma-171	35	3	risk	risk	NOUN
ma-171	35	4	population	population	NOUN
ma-171	35	5	incorporates	incorporate	VERB
ma-171	35	6	mainly	mainly	ADV
ma-171	35	7	commercialsex	commercialsex	PROPN
ma-171	35	8	workers	worker	NOUN
ma-171	35	9	,	,	PUNCT
ma-171	35	10	men	man	NOUN
ma-171	35	11	who	who	PRON
ma-171	35	12	have	have	VERB
ma-171	35	13	sex	sex	NOUN
ma-171	35	14	with	with	ADP
ma-171	35	15	men	man	NOUN
ma-171	35	16	(	(	PUNCT
ma-171	35	17	msm	msm	NOUN
ma-171	35	18	)	)	PUNCT
ma-171	35	19	,	,	PUNCT
ma-171	35	20	and	and	CCONJ
ma-171	35	21	hiv	hiv	NOUN
ma-171	35	22	-	-	PUNCT
ma-171	35	23	discordant	discordant	ADJ
ma-171	35	24	couples	couple	NOUN
ma-171	35	25	[	[	X
ma-171	35	26	8	8	NUM
ma-171	35	27	]	]	PUNCT
ma-171	35	28	.	.	PUNCT
ma-171	36	1	the	the	DET
ma-171	36	2	infectedclass	infectedclass	NOUN
ma-171	36	3	is	be	AUX
ma-171	36	4	subdivided	subdivide	VERB
ma-171	36	5	into	into	ADP
ma-171	36	6	two	two	NUM
ma-171	36	7	compartments	compartment	NOUN
ma-171	36	8	;	;	PUNCT
ma-171	36	9	those	those	PRON
ma-171	36	10	who	who	PRON
ma-171	36	11	are	be	AUX
ma-171	36	12	unaware	unaware	ADJ
ma-171	36	13	of	of	ADP
ma-171	36	14	their	their	PRON
ma-171	36	15	hiv	hiv	PROPN
ma-171	36	16	status	status	NOUN
ma-171	36	17	(	(	PUNCT
ma-171	36	18	i	i	NOUN
ma-171	36	19	)	)	PUNCT
ma-171	36	20	,	,	PUNCT
ma-171	36	21	andthose	andthose	X
ma-171	36	22	who	who	PRON
ma-171	36	23	have	have	AUX
ma-171	36	24	been	be	AUX
ma-171	36	25	diagnosed	diagnose	VERB
ma-171	36	26	and	and	CCONJ
ma-171	36	27	consequently	consequently	ADV
ma-171	36	28	enrolled	enrol	VERB
ma-171	36	29	for	for	ADP
ma-171	36	30	treatment	treatment	NOUN
ma-171	36	31	(	(	PUNCT
ma-171	36	32	td	td	NOUN
ma-171	36	33	)	)	PUNCT
ma-171	36	34	.	.	PUNCT
ma-171	37	1	the	the	DET
ma-171	37	2	individualswho	individualswho	PROPN
ma-171	37	3	are	be	AUX
ma-171	37	4	unaware	unaware	ADJ
ma-171	37	5	of	of	ADP
ma-171	37	6	their	their	PRON
ma-171	37	7	hiv	hiv	PROPN
ma-171	37	8	status	status	NOUN
ma-171	37	9	may	may	AUX
ma-171	37	10	progress	progress	VERB
ma-171	37	11	to	to	ADP
ma-171	37	12	the	the	DET
ma-171	37	13	td	td	NOUN
ma-171	37	14	compartment	compartment	NOUN
ma-171	37	15	after	after	ADP
ma-171	37	16	successful	successful	ADJ
ma-171	37	17	hiv	hiv	PROPN
ma-171	37	18	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	37	19	eur	eur	PROPN
ma-171	37	20	.	.	PUNCT
ma-171	38	1	j.	j.	PROPN
ma-171	38	2	math	math	PROPN
ma-171	38	3	.	.	PUNCT
ma-171	39	1	anal	anal	PROPN
ma-171	39	2	.	.	PUNCT
ma-171	40	1	10.28924	10.28924	NUM
ma-171	40	2	/	/	SYM
ma-171	40	3	ada	ada	PROPN
ma-171	40	4	/	/	SYM
ma-171	40	5	ma.3.21	ma.3.21	PROPN
ma-171	40	6	3awareness	3awareness	NUM
ma-171	40	7	campaigns	campaign	NOUN
ma-171	40	8	that	that	PRON
ma-171	40	9	will	will	AUX
ma-171	40	10	persuade	persuade	VERB
ma-171	40	11	them	they	PRON
ma-171	40	12	to	to	PART
ma-171	40	13	get	get	AUX
ma-171	40	14	tested	test	VERB
ma-171	40	15	,	,	PUNCT
ma-171	40	16	or	or	CCONJ
ma-171	40	17	when	when	SCONJ
ma-171	40	18	they	they	PRON
ma-171	40	19	develop	develop	VERB
ma-171	40	20	hiv	hiv	PROPN
ma-171	40	21	symptomsand	symptomsand	NOUN
ma-171	40	22	consequently	consequently	ADV
ma-171	40	23	enroll	enroll	VERB
ma-171	40	24	for	for	ADP
ma-171	40	25	art	art	NOUN
ma-171	40	26	treatment	treatment	NOUN
ma-171	40	27	.	.	PUNCT
ma-171	41	1	if	if	SCONJ
ma-171	41	2	art	art	NOUN
ma-171	41	3	treatment	treatment	NOUN
ma-171	41	4	fails	fail	VERB
ma-171	41	5	,	,	PUNCT
ma-171	41	6	the	the	DET
ma-171	41	7	individual	individual	ADJ
ma-171	41	8	progresses	progress	VERB
ma-171	41	9	to	to	ADP
ma-171	41	10	theaids	theaid	NOUN
ma-171	41	11	compartment	compartment	NOUN
ma-171	41	12	.	.	PUNCT
ma-171	42	1	this	this	PRON
ma-171	42	2	happens	happen	VERB
ma-171	42	3	when	when	SCONJ
ma-171	42	4	there	there	PRON
ma-171	42	5	is	be	VERB
ma-171	42	6	lack	lack	NOUN
ma-171	42	7	of	of	ADP
ma-171	42	8	adherence	adherence	NOUN
ma-171	42	9	to	to	ADP
ma-171	42	10	art	art	NOUN
ma-171	42	11	,	,	PUNCT
ma-171	42	12	which	which	PRON
ma-171	42	13	allows	allow	VERB
ma-171	42	14	the	the	DET
ma-171	42	15	virusto	virusto	NOUN
ma-171	42	16	multiply	multiply	ADV
ma-171	42	17	,	,	PUNCT
ma-171	42	18	thus	thus	ADV
ma-171	42	19	increasing	increase	VERB
ma-171	42	20	the	the	DET
ma-171	42	21	plasma	plasma	NOUN
ma-171	42	22	viral	viral	ADJ
ma-171	42	23	load	load	NOUN
ma-171	42	24	.	.	PUNCT
ma-171	43	1	this	this	DET
ma-171	43	2	results	result	VERB
ma-171	43	3	in	in	ADP
ma-171	43	4	weakening	weakening	NOUN
ma-171	43	5	of	of	ADP
ma-171	43	6	the	the	DET
ma-171	43	7	immune	immune	ADJ
ma-171	43	8	systemand	systemand	NOUN
ma-171	43	9	hence	hence	ADV
ma-171	43	10	the	the	DET
ma-171	43	11	aids	aid	NOUN
ma-171	43	12	symptoms	symptom	NOUN
ma-171	43	13	begin	begin	VERB
ma-171	43	14	to	to	PART
ma-171	43	15	manifest	manifest	VERB
ma-171	43	16	.	.	PUNCT
ma-171	44	1	the	the	DET
ma-171	44	2	aids	aids	PROPN
ma-171	44	3	compartment	compartment	NOUN
ma-171	44	4	comprises	comprise	NOUN
ma-171	44	5	of	of	ADP
ma-171	44	6	those	those	DET
ma-171	44	7	whoposses	whoposse	NOUN
ma-171	44	8	full	full	ADJ
ma-171	44	9	blown	blown	ADJ
ma-171	44	10	symptoms	symptom	NOUN
ma-171	44	11	,	,	PUNCT
ma-171	44	12	and	and	CCONJ
ma-171	44	13	are	be	AUX
ma-171	44	14	mostly	mostly	ADV
ma-171	44	15	bedridden	bedridden	ADJ
ma-171	44	16	,	,	PUNCT
ma-171	44	17	they	they	PRON
ma-171	44	18	thus	thus	ADV
ma-171	44	19	do	do	AUX
ma-171	44	20	not	not	PART
ma-171	44	21	significantly	significantly	ADV
ma-171	44	22	contribute	contribute	VERB
ma-171	44	23	tothe	tothe	DET
ma-171	44	24	spread	spread	NOUN
ma-171	44	25	of	of	ADP
ma-171	44	26	the	the	DET
ma-171	44	27	disease	disease	NOUN
ma-171	44	28	.	.	PUNCT
ma-171	45	1	exit	exit	NOUN
ma-171	45	2	from	from	ADP
ma-171	45	3	the	the	DET
ma-171	45	4	aids	aids	PROPN
ma-171	45	5	class	class	NOUN
ma-171	45	6	is	be	AUX
ma-171	45	7	through	through	ADP
ma-171	45	8	natural	natural	ADJ
ma-171	45	9	death.thus	death.thu	NOUN
ma-171	45	10	,	,	PUNCT
ma-171	45	11	considering	consider	VERB
ma-171	45	12	apopulation	apopulation	NOUN
ma-171	45	13	of	of	ADP
ma-171	45	14	size	size	NOUN
ma-171	45	15	n(t	n(t	PROPN
ma-171	45	16	)	)	PUNCT
ma-171	45	17	,	,	PUNCT
ma-171	45	18	at	at	ADP
ma-171	45	19	a	a	DET
ma-171	45	20	time	time	NOUN
ma-171	45	21	t	t	NOUN
ma-171	45	22	,	,	PUNCT
ma-171	45	23	n(t	n(t	PROPN
ma-171	45	24	)	)	PUNCT
ma-171	45	25	=	=	SYM
ma-171	45	26	sh(t	sh(t	X
ma-171	45	27	)	)	PUNCT
ma-171	45	28	+	+	NUM
ma-171	45	29	sl(t	sl(t	NOUN
ma-171	45	30	)	)	PUNCT
ma-171	46	1	+	+	CCONJ
ma-171	46	2	i(t	i(t	NOUN
ma-171	46	3	)	)	PUNCT
ma-171	46	4	+	+	NUM
ma-171	46	5	td(t	td(t	X
ma-171	46	6	)	)	PUNCT
ma-171	46	7	+	+	CCONJ
ma-171	46	8	a(t	a(t	NOUN
ma-171	46	9	)	)	PUNCT
ma-171	46	10	.	.	PUNCT
ma-171	47	1	(	(	PUNCT
ma-171	47	2	1	1	X
ma-171	47	3	)	)	PUNCT
ma-171	47	4	the	the	DET
ma-171	47	5	following	follow	VERB
ma-171	47	6	interventions	intervention	NOUN
ma-171	47	7	have	have	AUX
ma-171	47	8	been	be	AUX
ma-171	47	9	incorporated	incorporate	VERB
ma-171	47	10	in	in	ADP
ma-171	47	11	the	the	DET
ma-171	47	12	model;(a	model;(a	PROPN
ma-171	47	13	)	)	PUNCT
ma-171	47	14	0	0	NUM
ma-171	48	1	≤	≤	NUM
ma-171	48	2	φ1	φ1	NOUN
ma-171	48	3	≤	≤	ADJ
ma-171	48	4	1	1	NUM
ma-171	48	5	measures	measure	NOUN
ma-171	48	6	prep	prep	NOUN
ma-171	48	7	effectiveness	effectiveness	NOUN
ma-171	48	8	,	,	PUNCT
ma-171	48	9	including	include	VERB
ma-171	48	10	its	its	PRON
ma-171	48	11	awareness	awareness	NOUN
ma-171	48	12	and	and	CCONJ
ma-171	48	13	proper	proper	ADJ
ma-171	48	14	use	use	NOUN
ma-171	48	15	as	as	ADP
ma-171	48	16	a	a	DET
ma-171	48	17	meansto	meansto	NOUN
ma-171	48	18	prevent	prevent	NOUN
ma-171	48	19	susceptible	susceptible	ADJ
ma-171	48	20	individuals	individual	NOUN
ma-171	48	21	from	from	ADP
ma-171	48	22	being	be	AUX
ma-171	48	23	infected	infect	VERB
ma-171	48	24	.	.	PUNCT
ma-171	49	1	thus	thus	ADV
ma-171	49	2	,	,	PUNCT
ma-171	49	3	(	(	PUNCT
ma-171	49	4	1−	1−	NUM
ma-171	49	5	φ1	φ1	PROPN
ma-171	49	6	)	)	PUNCT
ma-171	49	7	measures	measure	NOUN
ma-171	49	8	prep	prep	NOUN
ma-171	49	9	failure.(b	failure.(b	ADV
ma-171	49	10	)	)	PUNCT
ma-171	49	11	0	0	NUM
ma-171	49	12	≤	≤	NUM
ma-171	49	13	φ2	φ2	NOUN
ma-171	49	14	≤	≤	NOUN
ma-171	49	15	1measures	1measures	NUM
ma-171	49	16	condom	condom	NOUN
ma-171	49	17	effectiveness	effectiveness	NOUN
ma-171	49	18	as	as	ADP
ma-171	49	19	a	a	DET
ma-171	49	20	result	result	NOUN
ma-171	49	21	of	of	ADP
ma-171	49	22	proper	proper	ADJ
ma-171	49	23	use	use	NOUN
ma-171	49	24	,	,	PUNCT
ma-171	49	25	following	follow	VERB
ma-171	49	26	adequateawareness	adequateawareness	NOUN
ma-171	49	27	campaigns	campaign	NOUN
ma-171	49	28	and	and	CCONJ
ma-171	49	29	availability	availability	NOUN
ma-171	49	30	.	.	PUNCT
ma-171	50	1	thus	thus	ADV
ma-171	50	2	,	,	PUNCT
ma-171	50	3	(	(	PUNCT
ma-171	50	4	1−	1−	NUM
ma-171	50	5	φ2	φ2	NOUN
ma-171	50	6	)	)	PUNCT
ma-171	50	7	measures	measure	NOUN
ma-171	50	8	condom	condom	NOUN
ma-171	50	9	failure.(c	failure.(c	NOUN
ma-171	50	10	)	)	PUNCT
ma-171	50	11	0	0	NUM
ma-171	50	12	≤	≤	NUM
ma-171	50	13	φ3	φ3	NOUN
ma-171	50	14	≤	≤	NUM
ma-171	50	15	1	1	NUM
ma-171	50	16	measures	measure	NOUN
ma-171	50	17	the	the	DET
ma-171	50	18	efficacy	efficacy	NOUN
ma-171	50	19	of	of	ADP
ma-171	50	20	art	art	NOUN
ma-171	50	21	treatment	treatment	NOUN
ma-171	50	22	,	,	PUNCT
ma-171	50	23	including	include	VERB
ma-171	50	24	uptake	uptake	NOUN
ma-171	50	25	with	with	ADP
ma-171	50	26	proper	proper	ADJ
ma-171	50	27	adherence	adherence	NOUN
ma-171	50	28	,	,	PUNCT
ma-171	50	29	with	with	ADP
ma-171	50	30	the	the	DET
ma-171	50	31	aim	aim	NOUN
ma-171	50	32	of	of	ADP
ma-171	50	33	reducing	reduce	VERB
ma-171	50	34	the	the	DET
ma-171	50	35	plasma	plasma	NOUN
ma-171	50	36	viral	viral	ADJ
ma-171	50	37	load	load	NOUN
ma-171	50	38	and	and	CCONJ
ma-171	50	39	reconstructing	reconstruct	VERB
ma-171	50	40	the	the	DET
ma-171	50	41	individual	individual	NOUN
ma-171	50	42	’s	’s	PART
ma-171	50	43	immune	immune	ADJ
ma-171	50	44	systemhence	systemhence	NOUN
ma-171	50	45	making	make	VERB
ma-171	50	46	them	they	PRON
ma-171	50	47	less	less	ADJ
ma-171	50	48	infectious.movement	infectious.movement	NOUN
ma-171	50	49	of	of	ADP
ma-171	50	50	individuals	individual	NOUN
ma-171	50	51	from	from	ADP
ma-171	50	52	the	the	DET
ma-171	50	53	susceptible	susceptible	ADJ
ma-171	50	54	to	to	ADP
ma-171	50	55	infected	infected	ADJ
ma-171	50	56	and	and	CCONJ
ma-171	50	57	then	then	ADV
ma-171	50	58	to	to	ADP
ma-171	50	59	the	the	DET
ma-171	50	60	aids	aids	PROPN
ma-171	50	61	classes	class	NOUN
ma-171	50	62	is	be	AUX
ma-171	50	63	illustratedby	illustratedby	VERB
ma-171	50	64	the	the	DET
ma-171	50	65	compartmental	compartmental	ADJ
ma-171	50	66	model	model	NOUN
ma-171	50	67	shown	show	VERB
ma-171	50	68	in	in	ADP
ma-171	50	69	figure	figure	NOUN
ma-171	50	70	1	1	NUM
ma-171	50	71	.	.	PUNCT
ma-171	51	1	sh	sh	INTJ
ma-171	51	2	sl	sl	VERB
ma-171	51	3	a	a	DET
ma-171	51	4	td	td	NOUN
ma-171	51	5	i	i	PRON
ma-171	51	6	�	�	PROPN
ma-171	51	7	�	�	PROPN
ma-171	51	8	(	(	PUNCT
ma-171	51	9	�	�	PROPN
ma-171	51	10	−	−	PROPN
ma-171	51	11	�	�	PROPN
ma-171	51	12	)	)	PUNCT
ma-171	51	13	�	�	PROPN
ma-171	51	14	(	(	PUNCT
ma-171	51	15	�	�	PROPN
ma-171	51	16	−	−	PROPN
ma-171	51	17	�	�	PROPN
ma-171	51	18	�	�	PROPN
ma-171	51	19	)	)	PUNCT
ma-171	51	20	(	(	PUNCT
ma-171	51	21	�	�	PROPN
ma-171	51	22	−	−	PROPN
ma-171	51	23	�	�	PROPN
ma-171	51	24	�	�	PROPN
ma-171	51	25	)	)	PUNCT
ma-171	51	26	�	�	PROPN
ma-171	51	27	�	�	PROPN
ma-171	51	28	�	�	PROPN
ma-171	51	29	(	(	PUNCT
ma-171	51	30	�	�	PROPN
ma-171	51	31	−	−	PROPN
ma-171	51	32	�	�	PROPN
ma-171	51	33	�	�	PROPN
ma-171	51	34	)	)	PUNCT
ma-171	51	35	�	�	PROPN
ma-171	51	36	�	�	PROPN
ma-171	51	37	�	�	PROPN
ma-171	51	38	�	�	PROPN
ma-171	51	39	sh	sh	PROPN
ma-171	51	40	�	�	PROPN
ma-171	51	41	sl	sl	PROPN
ma-171	51	42	�	�	PROPN
ma-171	51	43	�	�	PROPN
ma-171	51	44	�	�	PROPN
ma-171	51	45	(	(	PUNCT
ma-171	51	46	�	�	PROPN
ma-171	51	47	+	+	CCONJ
ma-171	51	48	�	�	PROPN
ma-171	51	49	)	)	PUNCT
ma-171	51	50	�	�	PROPN
ma-171	51	51	�	�	PROPN
ma-171	51	52	i	i	PROPN
ma-171	51	53	�	�	PROPN
ma-171	51	54	�	�	PROPN
ma-171	51	55	�	�	PROPN
ma-171	51	56	�	�	PROPN
ma-171	51	57	�	�	PROPN
ma-171	51	58	(	(	PUNCT
ma-171	51	59	�	�	PROPN
ma-171	51	60	−	−	PROPN
ma-171	51	61	�	�	PROPN
ma-171	51	62	�	�	PROPN
ma-171	51	63	)	)	PUNCT
ma-171	51	64	�	�	PROPN
ma-171	51	65	�	�	PROPN
ma-171	51	66	figure	figure	NOUN
ma-171	51	67	1	1	NUM
ma-171	51	68	.	.	PUNCT
ma-171	51	69	compartmental	compartmental	ADJ
ma-171	51	70	model	model	NOUN
ma-171	51	71	.	.	PUNCT
ma-171	52	1	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	52	2	eur	eur	PROPN
ma-171	52	3	.	.	PUNCT
ma-171	53	1	j.	j.	PROPN
ma-171	53	2	math	math	PROPN
ma-171	53	3	.	.	PUNCT
ma-171	54	1	anal	anal	PROPN
ma-171	54	2	.	.	PUNCT
ma-171	55	1	10.28924	10.28924	NUM
ma-171	55	2	/	/	SYM
ma-171	55	3	ada	ada	PROPN
ma-171	55	4	/	/	SYM
ma-171	55	5	ma.3.21	ma.3.21	PROPN
ma-171	55	6	4the	4the	PROPN
ma-171	55	7	following	follow	VERB
ma-171	55	8	symbols	symbol	NOUN
ma-171	55	9	will	will	AUX
ma-171	55	10	be	be	AUX
ma-171	55	11	used	use	VERB
ma-171	55	12	to	to	PART
ma-171	55	13	represent	represent	VERB
ma-171	55	14	various	various	ADJ
ma-171	55	15	phenomena	phenomenon	NOUN
ma-171	55	16	as	as	SCONJ
ma-171	55	17	described	describe	VERB
ma-171	55	18	in	in	ADP
ma-171	55	19	table	table	NOUN
ma-171	55	20	1	1	NUM
ma-171	55	21	.	.	PUNCT
ma-171	56	1	symbol	symbol	NOUN
ma-171	56	2	description	description	NOUN
ma-171	56	3	λ	λ	PROPN
ma-171	56	4	constant	constant	ADJ
ma-171	56	5	rate	rate	NOUN
ma-171	56	6	of	of	ADP
ma-171	56	7	recruitment	recruitment	NOUN
ma-171	56	8	of	of	ADP
ma-171	56	9	susceptible	susceptible	ADJ
ma-171	56	10	upon	upon	SCONJ
ma-171	56	11	becoming	become	VERB
ma-171	56	12	sexually	sexually	ADV
ma-171	56	13	active	active	ADJ
ma-171	56	14	.	.	PUNCT
ma-171	57	1	δ	δ	NOUN
ma-171	57	2	proportion	proportion	NOUN
ma-171	57	3	of	of	ADP
ma-171	57	4	susceptible	susceptible	ADJ
ma-171	57	5	individuals	individual	NOUN
ma-171	57	6	at	at	ADP
ma-171	57	7	high	high	ADJ
ma-171	57	8	risk	risk	NOUN
ma-171	57	9	of	of	ADP
ma-171	57	10	infection	infection	NOUN
ma-171	57	11	.	.	PUNCT
ma-171	58	1	(	(	PUNCT
ma-171	58	2	1−	1−	NUM
ma-171	58	3	δ	δ	NOUN
ma-171	58	4	)	)	PUNCT
ma-171	58	5	proportion	proportion	NOUN
ma-171	58	6	of	of	ADP
ma-171	58	7	susceptible	susceptible	ADJ
ma-171	58	8	population	population	NOUN
ma-171	58	9	at	at	ADP
ma-171	58	10	low	low	ADJ
ma-171	58	11	risk	risk	NOUN
ma-171	58	12	of	of	ADP
ma-171	58	13	hiv	hiv	PROPN
ma-171	58	14	infection	infection	NOUN
ma-171	58	15	.	.	PUNCT
ma-171	59	1	λ	λ	NOUN
ma-171	59	2	rate	rate	NOUN
ma-171	59	3	of	of	ADP
ma-171	59	4	acquisition	acquisition	NOUN
ma-171	59	5	of	of	ADP
ma-171	59	6	an	an	DET
ma-171	59	7	infection	infection	NOUN
ma-171	59	8	by	by	ADP
ma-171	59	9	susceptibles.it	susceptibles.it	PROPN
ma-171	59	10	is	be	AUX
ma-171	59	11	given	give	VERB
ma-171	59	12	by	by	ADP
ma-171	59	13	;	;	PUNCT
ma-171	59	14	λ	λ	X
ma-171	59	15	=	=	SYM
ma-171	59	16	(	(	PUNCT
ma-171	59	17	β1i+β2td	β1i+β2td	NOUN
ma-171	59	18	n	n	PROPN
ma-171	59	19	)	)	PUNCT
ma-171	59	20	,	,	PUNCT
ma-171	59	21	where	where	SCONJ
ma-171	59	22	β1	β1	PROPN
ma-171	59	23	,	,	PUNCT
ma-171	59	24	and	and	CCONJ
ma-171	59	25	β2	β2	NOUN
ma-171	59	26	are	be	AUX
ma-171	59	27	the	the	DET
ma-171	59	28	mean	mean	ADJ
ma-171	59	29	contact	contact	NOUN
ma-171	59	30	rates	rate	NOUN
ma-171	59	31	for	for	ADP
ma-171	59	32	thesusceptible	thesusceptible	ADJ
ma-171	59	33	individuals	individual	NOUN
ma-171	59	34	with	with	ADP
ma-171	59	35	i	i	PRON
ma-171	59	36	and	and	CCONJ
ma-171	59	37	td	td	VERB
ma-171	59	38	respectively	respectively	ADV
ma-171	59	39	.	.	PUNCT
ma-171	60	1	µ	µ	PRON
ma-171	60	2	natural	natural	ADJ
ma-171	60	3	removal	removal	NOUN
ma-171	60	4	rate	rate	NOUN
ma-171	60	5	by	by	ADP
ma-171	60	6	death	death	NOUN
ma-171	60	7	.	.	PUNCT
ma-171	61	1	σ	σ	PROPN
ma-171	61	2	aids	aids	PROPN
ma-171	61	3	induced	induce	VERB
ma-171	61	4	mortality	mortality	NOUN
ma-171	61	5	.	.	PUNCT
ma-171	62	1	α	α	PROPN
ma-171	62	2	represents	represent	VERB
ma-171	62	3	the	the	DET
ma-171	62	4	proportion	proportion	NOUN
ma-171	62	5	of	of	ADP
ma-171	62	6	infected	infect	VERB
ma-171	62	7	individuals	individual	NOUN
ma-171	62	8	who	who	PRON
ma-171	62	9	upon	upon	AUX
ma-171	62	10	beingtested	beingteste	VERB
ma-171	62	11	and	and	CCONJ
ma-171	62	12	found	find	VERB
ma-171	62	13	to	to	PART
ma-171	62	14	be	be	AUX
ma-171	62	15	hiv	hiv	PROPN
ma-171	62	16	positive	positive	ADJ
ma-171	62	17	,	,	PUNCT
ma-171	62	18	they	they	PRON
ma-171	62	19	enroll	enroll	VERB
ma-171	62	20	for	for	ADP
ma-171	62	21	art	art	NOUN
ma-171	62	22	treatment	treatment	NOUN
ma-171	62	23	.	.	PUNCT
ma-171	63	1	γ2	γ2	PROPN
ma-171	63	2	represents	represent	VERB
ma-171	63	3	the	the	DET
ma-171	63	4	proportion	proportion	NOUN
ma-171	63	5	of	of	ADP
ma-171	63	6	infected	infect	VERB
ma-171	63	7	individuals	individual	NOUN
ma-171	63	8	who	who	PRON
ma-171	63	9	do	do	AUX
ma-171	63	10	not	not	PART
ma-171	63	11	get	get	VERB
ma-171	63	12	testedhence	testedhence	NOUN
ma-171	63	13	remain	remain	VERB
ma-171	63	14	undiagnosed	undiagnosed	ADJ
ma-171	63	15	until	until	SCONJ
ma-171	63	16	they	they	PRON
ma-171	63	17	begin	begin	VERB
ma-171	63	18	to	to	PART
ma-171	63	19	exhibit	exhibit	VERB
ma-171	63	20	aids	aid	NOUN
ma-171	63	21	symptoms.table	symptoms.table	ADJ
ma-171	63	22	1	1	NUM
ma-171	63	23	.	.	PUNCT
ma-171	63	24	table	table	NOUN
ma-171	63	25	showing	show	VERB
ma-171	63	26	symbols	symbol	NOUN
ma-171	63	27	and	and	CCONJ
ma-171	63	28	their	their	PRON
ma-171	63	29	description	description	NOUN
ma-171	63	30	from	from	ADP
ma-171	63	31	the	the	DET
ma-171	63	32	dynamics	dynamic	NOUN
ma-171	63	33	described	describe	VERB
ma-171	63	34	above	above	ADV
ma-171	63	35	,	,	PUNCT
ma-171	63	36	the	the	DET
ma-171	63	37	following	follow	VERB
ma-171	63	38	system	system	NOUN
ma-171	63	39	of	of	ADP
ma-171	63	40	ordinary	ordinary	ADJ
ma-171	63	41	differential	differential	ADJ
ma-171	63	42	equations	equation	NOUN
ma-171	63	43	isformulated	isformulate	VERB
ma-171	63	44	.	.	PUNCT
ma-171	64	1	dsh	dsh	ADJ
ma-171	64	2	dt	dt	NOUN
ma-171	64	3	=	=	SYM
ma-171	64	4	δλ−	δλ−	PROPN
ma-171	64	5	(	(	PUNCT
ma-171	64	6	1−	1−	NUM
ma-171	64	7	φ1)(1−	φ1)(1−	NOUN
ma-171	64	8	φ2)λsh	φ2)λsh	VERB
ma-171	64	9	−	−	NOUN
ma-171	64	10	µsh	µsh	VERB
ma-171	64	11	dsl	dsl	ADJ
ma-171	64	12	dt	dt	NOUN
ma-171	64	13	=	=	SYM
ma-171	64	14	(	(	PUNCT
ma-171	64	15	1−	1−	NUM
ma-171	64	16	δ)λ−	δ)λ−	NOUN
ma-171	64	17	(	(	PUNCT
ma-171	64	18	1−	1−	NUM
ma-171	64	19	φ2)λsl	φ2)λsl	ADP
ma-171	64	20	−	−	PROPN
ma-171	64	21	µsl	µsl	VERB
ma-171	64	22	di	di	INTJ
ma-171	64	23	dt	dt	NOUN
ma-171	64	24	=	=	PUNCT
ma-171	64	25	(	(	PUNCT
ma-171	64	26	1−	1−	NUM
ma-171	64	27	φ1)(1−	φ1)(1−	NOUN
ma-171	64	28	φ2)λsh	φ2)λsh	VERB
ma-171	64	29	+	+	SYM
ma-171	64	30	(	(	PUNCT
ma-171	64	31	1−	1−	NUM
ma-171	64	32	φ2)λsl	φ2)λsl	ADP
ma-171	64	33	−	−	PROPN
ma-171	64	34	αi	αi	ADV
ma-171	64	35	−	−	PROPN
ma-171	65	1	γ2i	γ2i	PROPN
ma-171	65	2	−	−	PROPN
ma-171	66	1	µi	µi	PROPN
ma-171	66	2	dtd	dtd	NOUN
ma-171	66	3	dt	dt	X
ma-171	67	1	=	=	SYM
ma-171	67	2	αi	αi	PROPN
ma-171	67	3	−	−	PROPN
ma-171	68	1	(	(	PUNCT
ma-171	68	2	γ3	γ3	NOUN
ma-171	68	3	+	+	CCONJ
ma-171	68	4	µ)td	µ)td	PROPN
ma-171	68	5	da	da	NOUN
ma-171	68	6	dt	dt	NOUN
ma-171	69	1	=	=	PUNCT
ma-171	70	1	γ2i	γ2i	PROPN
ma-171	71	1	+	+	CCONJ
ma-171	71	2	γ3td	γ3td	PUNCT
ma-171	71	3	−	−	PROPN
ma-171	71	4	(	(	PUNCT
ma-171	71	5	µ+	µ+	X
ma-171	71	6	σ)a	σ)a	NOUN
ma-171	71	7	.	.	PUNCT
ma-171	72	1	(	(	PUNCT
ma-171	72	2	2	2	NUM
ma-171	72	3	)	)	PUNCT
ma-171	72	4	3	3	NUM
ma-171	72	5	.	.	PUNCT
ma-171	72	6	model	model	NOUN
ma-171	72	7	analysis	analysis	NOUN
ma-171	72	8	it	it	PRON
ma-171	72	9	can	can	AUX
ma-171	72	10	be	be	AUX
ma-171	72	11	shown	show	VERB
ma-171	72	12	that	that	SCONJ
ma-171	72	13	the	the	DET
ma-171	72	14	solutions	solution	NOUN
ma-171	72	15	for	for	ADP
ma-171	72	16	the	the	DET
ma-171	72	17	system	system	NOUN
ma-171	72	18	of	of	ADP
ma-171	72	19	ordinary	ordinary	ADJ
ma-171	72	20	differential	differential	ADJ
ma-171	72	21	equations	equation	NOUN
ma-171	72	22	(	(	PUNCT
ma-171	72	23	2	2	X
ma-171	72	24	)	)	PUNCT
ma-171	72	25	areall	areall	VERB
ma-171	72	26	positive	positive	ADJ
ma-171	72	27	and	and	CCONJ
ma-171	72	28	bounded	bound	VERB
ma-171	72	29	for	for	ADP
ma-171	72	30	all	all	DET
ma-171	72	31	t	t	PROPN
ma-171	72	32	>	>	X
ma-171	72	33	0	0	NUM
ma-171	72	34	,	,	PUNCT
ma-171	72	35	with	with	ADP
ma-171	72	36	positive	positive	ADJ
ma-171	72	37	initial	initial	ADJ
ma-171	72	38	conditions	condition	NOUN
ma-171	72	39	in	in	ADP
ma-171	72	40	the	the	DET
ma-171	72	41	feasible	feasible	ADJ
ma-171	72	42	region	region	NOUN
ma-171	72	43	γ	γ	X
ma-171	72	44	=	=	PRON
ma-171	72	45	{	{	PUNCT
ma-171	72	46	(	(	PUNCT
ma-171	72	47	sh(t	sh(t	X
ma-171	72	48	)	)	PUNCT
ma-171	72	49	,	,	PUNCT
ma-171	72	50	sl(t	sl(t	NOUN
ma-171	72	51	)	)	PUNCT
ma-171	72	52	,	,	PUNCT
ma-171	72	53	i(t	i(t	PROPN
ma-171	72	54	)	)	PUNCT
ma-171	72	55	,	,	PUNCT
ma-171	72	56	(	(	PUNCT
ma-171	72	57	td(t	td(t	NOUN
ma-171	72	58	)	)	PUNCT
ma-171	72	59	,	,	PUNCT
ma-171	72	60	a(t	a(t	NOUN
ma-171	72	61	)	)	PUNCT
ma-171	72	62	)	)	PUNCT
ma-171	73	1	∈	∈	PROPN
ma-171	73	2	r5	r5	PROPN
ma-171	73	3	+	+	CCONJ
ma-171	73	4	:	:	PUNCT
ma-171	73	5	n(t	n(t	NUM
ma-171	73	6	)	)	PUNCT
ma-171	73	7	≤	≤	PUNCT
ma-171	74	1	λ	λ	X
ma-171	74	2	µ	µ	X
ma-171	74	3	}	}	PUNCT
ma-171	74	4	.	.	PUNCT
ma-171	75	1	it	it	PRON
ma-171	75	2	therefore	therefore	ADV
ma-171	75	3	suffices	suffice	VERB
ma-171	75	4	to	to	PART
ma-171	75	5	study	study	VERB
ma-171	75	6	the	the	DET
ma-171	75	7	dynamicsof	dynamicsof	NOUN
ma-171	75	8	the	the	DET
ma-171	75	9	system	system	NOUN
ma-171	75	10	(	(	PUNCT
ma-171	75	11	2	2	NUM
ma-171	75	12	)	)	PUNCT
ma-171	75	13	in	in	ADP
ma-171	75	14	this	this	DET
ma-171	75	15	region.the	region.the	DET
ma-171	75	16	mathematical	mathematical	ADJ
ma-171	75	17	model	model	NOUN
ma-171	75	18	developed	develop	VERB
ma-171	75	19	in	in	ADP
ma-171	75	20	(	(	PUNCT
ma-171	75	21	2	2	NUM
ma-171	75	22	)	)	PUNCT
ma-171	75	23	has	have	VERB
ma-171	75	24	two	two	NUM
ma-171	75	25	unique	unique	ADJ
ma-171	75	26	equilibrium	equilibrium	NOUN
ma-171	75	27	points	point	NOUN
ma-171	75	28	,	,	PUNCT
ma-171	75	29	that	that	ADV
ma-171	75	30	is	is	ADV
ma-171	75	31	,	,	PUNCT
ma-171	75	32	the	the	DET
ma-171	75	33	diseasefree	diseasefree	PROPN
ma-171	75	34	equilibrium	equilibrium	NOUN
ma-171	75	35	(	(	PUNCT
ma-171	75	36	d.f.e	d.f.e	ADJ
ma-171	75	37	)	)	PUNCT
ma-171	75	38	,	,	PUNCT
ma-171	75	39	and	and	CCONJ
ma-171	75	40	the	the	DET
ma-171	75	41	endemic	endemic	ADJ
ma-171	75	42	equilibrium	equilibrium	NOUN
ma-171	75	43	(	(	PUNCT
ma-171	75	44	e.e	e.e	PROPN
ma-171	75	45	)	)	PUNCT
ma-171	75	46	.	.	PUNCT
ma-171	76	1	the	the	DET
ma-171	76	2	d.f.e	d.f.e	NOUN
ma-171	76	3	is	be	AUX
ma-171	76	4	obtained	obtain	VERB
ma-171	76	5	by	by	ADP
ma-171	76	6	setting	set	VERB
ma-171	76	7	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	76	8	eur	eur	NOUN
ma-171	76	9	.	.	PUNCT
ma-171	77	1	j.	j.	PROPN
ma-171	77	2	math	math	PROPN
ma-171	77	3	.	.	PUNCT
ma-171	78	1	anal	anal	PROPN
ma-171	78	2	.	.	PUNCT
ma-171	79	1	10.28924	10.28924	NUM
ma-171	79	2	/	/	SYM
ma-171	79	3	ada	ada	PROPN
ma-171	79	4	/	/	SYM
ma-171	79	5	ma.3.21	ma.3.21	PROPN
ma-171	79	6	5	5	NUM
ma-171	80	1	i	i	NOUN
ma-171	80	2	=	=	PUNCT
ma-171	80	3	td	td	NOUN
ma-171	80	4	=	=	PUNCT
ma-171	80	5	a	a	X
ma-171	80	6	=	=	SYM
ma-171	80	7	0	0	NUM
ma-171	80	8	in	in	ADP
ma-171	80	9	(	(	PUNCT
ma-171	80	10	2	2	NUM
ma-171	80	11	)	)	PUNCT
ma-171	80	12	to	to	PART
ma-171	80	13	yield	yield	VERB
ma-171	80	14	e0	e0	PROPN
ma-171	80	15	=	=	PUNCT
ma-171	80	16	(	(	PUNCT
ma-171	80	17	δλ	δλ	PROPN
ma-171	80	18	µ	µ	X
ma-171	80	19	,	,	PUNCT
ma-171	80	20	(	(	PUNCT
ma-171	80	21	1−	1−	NUM
ma-171	80	22	δ)λ	δ)λ	NOUN
ma-171	80	23	µ	µ	X
ma-171	80	24	,	,	PUNCT
ma-171	80	25	0	0	NUM
ma-171	80	26	,	,	PUNCT
ma-171	80	27	0	0	NUM
ma-171	80	28	,	,	PUNCT
ma-171	80	29	0	0	NUM
ma-171	80	30	)	)	PUNCT
ma-171	80	31	.	.	PUNCT
ma-171	81	1	(	(	PUNCT
ma-171	81	2	3	3	X
ma-171	81	3	)	)	PUNCT
ma-171	81	4	the	the	DET
ma-171	81	5	basic	basic	ADJ
ma-171	81	6	reproduction	reproduction	NOUN
ma-171	81	7	number	number	NOUN
ma-171	81	8	(	(	PUNCT
ma-171	81	9	r0	r0	NOUN
ma-171	81	10	)	)	PUNCT
ma-171	81	11	of	of	ADP
ma-171	81	12	the	the	DET
ma-171	81	13	system	system	NOUN
ma-171	81	14	(	(	PUNCT
ma-171	81	15	2	2	NUM
ma-171	81	16	)	)	PUNCT
ma-171	81	17	,	,	PUNCT
ma-171	81	18	computed	compute	VERB
ma-171	81	19	using	use	VERB
ma-171	81	20	the	the	DET
ma-171	81	21	next	next	ADJ
ma-171	81	22	generation	generation	NOUN
ma-171	81	23	matrixapproach	matrixapproach	NOUN
ma-171	82	1	[	[	X
ma-171	82	2	10	10	NUM
ma-171	82	3	]	]	PUNCT
ma-171	82	4	is	be	AUX
ma-171	82	5	given	give	VERB
ma-171	82	6	by	by	ADP
ma-171	82	7	r0	r0	NOUN
ma-171	82	8	=	=	SYM
ma-171	82	9	β3	β3	PROPN
ma-171	82	10	q1	q1	PROPN
ma-171	82	11	+	+	CCONJ
ma-171	82	12	αβ4	αβ4	NUM
ma-171	82	13	q1q2	q1q2	NOUN
ma-171	82	14	.	.	PUNCT
ma-171	83	1	(	(	PUNCT
ma-171	83	2	4)by	4)by	NUM
ma-171	84	1	[	[	X
ma-171	84	2	10	10	NUM
ma-171	84	3	,	,	PUNCT
ma-171	84	4	theorem	theorem	VERB
ma-171	84	5	2	2	NUM
ma-171	84	6	]	]	PUNCT
ma-171	84	7	,	,	PUNCT
ma-171	84	8	the	the	DET
ma-171	84	9	following	following	ADJ
ma-171	84	10	result	result	NOUN
ma-171	84	11	is	be	AUX
ma-171	84	12	thus	thus	ADV
ma-171	84	13	established	establish	VERB
ma-171	84	14	.	.	PUNCT
ma-171	85	1	theorem	theorem	VERB
ma-171	85	2	3.1	3.1	NUM
ma-171	85	3	.	.	PUNCT
ma-171	86	1	the	the	DET
ma-171	86	2	disease	disease	NOUN
ma-171	86	3	free	free	VERB
ma-171	86	4	equilibrium	equilibrium	NOUN
ma-171	86	5	of	of	ADP
ma-171	86	6	the	the	DET
ma-171	86	7	model	model	NOUN
ma-171	86	8	(	(	PUNCT
ma-171	86	9	2	2	NUM
ma-171	86	10	)	)	PUNCT
ma-171	86	11	,	,	PUNCT
ma-171	86	12	e0	e0	PROPN
ma-171	86	13	=	=	PUNCT
ma-171	86	14	(	(	PUNCT
ma-171	86	15	δλ	δλ	PROPN
ma-171	86	16	µ	µ	X
ma-171	86	17	,	,	PUNCT
ma-171	86	18	(	(	PUNCT
ma-171	86	19	1−δ)λ	1−δ)λ	NOUN
ma-171	86	20	µ	µ	X
ma-171	86	21	,	,	PUNCT
ma-171	86	22	0	0	NUM
ma-171	86	23	,	,	PUNCT
ma-171	86	24	0	0	NUM
ma-171	86	25	,	,	PUNCT
ma-171	86	26	0	0	NUM
ma-171	86	27	)	)	PUNCT
ma-171	86	28	,	,	PUNCT
ma-171	86	29	is	be	AUX
ma-171	86	30	locally	locally	ADV
ma-171	86	31	asymptotically	asymptotically	ADV
ma-171	86	32	stable	stable	ADJ
ma-171	86	33	whenever	whenever	SCONJ
ma-171	86	34	r0	r0	NOUN
ma-171	86	35	<	<	X
ma-171	86	36	1	1	NUM
ma-171	86	37	and	and	CCONJ
ma-171	86	38	unstable	unstable	ADJ
ma-171	86	39	otherwise	otherwise	ADV
ma-171	86	40	.	.	PUNCT
ma-171	87	1	proof	proof	NOUN
ma-171	87	2	.	.	PUNCT
ma-171	88	1	the	the	DET
ma-171	88	2	proof	proof	NOUN
ma-171	88	3	follows	follow	VERB
ma-171	88	4	immediately	immediately	ADV
ma-171	88	5	from	from	ADP
ma-171	88	6	the	the	DET
ma-171	88	7	computation	computation	NOUN
ma-171	88	8	of	of	ADP
ma-171	88	9	r0	r0	NOUN
ma-171	88	10	above	above	ADV
ma-171	88	11	and	and	CCONJ
ma-171	88	12	theorem	theorem	VERB
ma-171	88	13	2	2	NUM
ma-171	88	14	of	of	ADP
ma-171	88	15	van	van	PROPN
ma-171	88	16	dendriessche	dendriessche	PROPN
ma-171	88	17	and	and	CCONJ
ma-171	88	18	watmough	watmough	NOUN
ma-171	88	19	[	[	X
ma-171	88	20	10	10	NUM
ma-171	88	21	]	]	PUNCT
ma-171	88	22	.	.	PUNCT
ma-171	89	1	�	�	PROPN
ma-171	89	2	mathematically	mathematically	ADV
ma-171	89	3	,	,	PUNCT
ma-171	89	4	theorem	theorem	ADJ
ma-171	89	5	(	(	PUNCT
ma-171	89	6	3.1	3.1	NUM
ma-171	89	7	)	)	PUNCT
ma-171	89	8	implies	imply	VERB
ma-171	89	9	that	that	SCONJ
ma-171	89	10	whenever	whenever	SCONJ
ma-171	89	11	there	there	PRON
ma-171	89	12	is	be	VERB
ma-171	89	13	a	a	DET
ma-171	89	14	small	small	ADJ
ma-171	89	15	perturbation	perturbation	NOUN
ma-171	89	16	on	on	ADP
ma-171	89	17	the	the	DET
ma-171	89	18	system	system	NOUN
ma-171	89	19	,	,	PUNCT
ma-171	89	20	the	the	DET
ma-171	89	21	system	system	NOUN
ma-171	89	22	returns	return	VERB
ma-171	89	23	to	to	ADP
ma-171	89	24	the	the	DET
ma-171	89	25	disease	disease	NOUN
ma-171	89	26	free	free	ADJ
ma-171	89	27	equilibrium	equilibrium	NOUN
ma-171	89	28	.	.	PUNCT
ma-171	90	1	epidemiologically	epidemiologically	PROPN
ma-171	90	2	,	,	PUNCT
ma-171	90	3	this	this	PRON
ma-171	90	4	implies	imply	VERB
ma-171	90	5	that	that	SCONJ
ma-171	90	6	when	when	SCONJ
ma-171	90	7	a	a	DET
ma-171	90	8	fewhiv	fewhiv	PROPN
ma-171	90	9	infectious	infectious	ADJ
ma-171	90	10	individuals	individual	NOUN
ma-171	90	11	are	be	AUX
ma-171	90	12	introduced	introduce	VERB
ma-171	90	13	in	in	ADP
ma-171	90	14	a	a	DET
ma-171	90	15	population	population	NOUN
ma-171	90	16	that	that	PRON
ma-171	90	17	is	be	AUX
ma-171	90	18	fully	fully	ADV
ma-171	90	19	susceptible	susceptible	ADJ
ma-171	90	20	to	to	ADP
ma-171	90	21	hiv	hiv	PROPN
ma-171	90	22	infection	infection	NOUN
ma-171	90	23	,	,	PUNCT
ma-171	90	24	the	the	DET
ma-171	90	25	disease	disease	NOUN
ma-171	90	26	dies	die	VERB
ma-171	90	27	out	out	ADP
ma-171	90	28	whenever	whenever	SCONJ
ma-171	90	29	r0	r0	VERB
ma-171	90	30	<	<	X
ma-171	90	31	1	1	NUM
ma-171	90	32	,	,	PUNCT
ma-171	90	33	otherwise	otherwise	ADV
ma-171	90	34	,	,	PUNCT
ma-171	90	35	the	the	DET
ma-171	90	36	disease	disease	NOUN
ma-171	90	37	will	will	AUX
ma-171	90	38	spread	spread	VERB
ma-171	90	39	.	.	PUNCT
ma-171	91	1	it	it	PRON
ma-171	91	2	is	be	AUX
ma-171	91	3	therefore	therefore	ADV
ma-171	91	4	necessaryto	necessaryto	ADV
ma-171	91	5	show	show	VERB
ma-171	91	6	that	that	SCONJ
ma-171	91	7	eliminating	eliminate	VERB
ma-171	91	8	hiv	hiv	PROPN
ma-171	91	9	in	in	ADP
ma-171	91	10	a	a	DET
ma-171	91	11	population	population	NOUN
ma-171	91	12	is	be	AUX
ma-171	91	13	independent	independent	ADJ
ma-171	91	14	of	of	ADP
ma-171	91	15	the	the	DET
ma-171	91	16	size	size	NOUN
ma-171	91	17	of	of	ADP
ma-171	91	18	the	the	DET
ma-171	91	19	initial	initial	ADJ
ma-171	91	20	sub	sub	ADJ
ma-171	91	21	-	-	ADJ
ma-171	91	22	populationby	populationby	ADJ
ma-171	91	23	proving	prove	VERB
ma-171	91	24	the	the	DET
ma-171	91	25	global	global	ADJ
ma-171	91	26	asymptotic	asymptotic	ADJ
ma-171	91	27	stability	stability	NOUN
ma-171	91	28	of	of	ADP
ma-171	91	29	the	the	DET
ma-171	91	30	disease	disease	NOUN
ma-171	91	31	free	free	ADJ
ma-171	91	32	equilibrium	equilibrium	NOUN
ma-171	91	33	.	.	PUNCT
ma-171	92	1	theorem	theorem	VERB
ma-171	92	2	3.2	3.2	NUM
ma-171	92	3	.	.	PUNCT
ma-171	93	1	the	the	DET
ma-171	93	2	disease	disease	NOUN
ma-171	93	3	free	free	ADJ
ma-171	93	4	equilibrium	equilibrium	NOUN
ma-171	93	5	e0	e0	PROPN
ma-171	93	6	=	=	PUNCT
ma-171	93	7	(	(	PUNCT
ma-171	93	8	δλ	δλ	PROPN
ma-171	93	9	µ	µ	X
ma-171	93	10	,	,	PUNCT
ma-171	93	11	(	(	PUNCT
ma-171	93	12	1−δ)λ	1−δ)λ	NOUN
ma-171	93	13	µ	µ	X
ma-171	93	14	,	,	PUNCT
ma-171	93	15	0	0	NUM
ma-171	93	16	,	,	PUNCT
ma-171	93	17	0	0	NUM
ma-171	93	18	,	,	PUNCT
ma-171	93	19	0	0	NUM
ma-171	93	20	)	)	PUNCT
ma-171	93	21	of	of	ADP
ma-171	93	22	the	the	DET
ma-171	93	23	system	system	NOUN
ma-171	93	24	(	(	PUNCT
ma-171	93	25	2	2	X
ma-171	93	26	)	)	PUNCT
ma-171	93	27	is	be	AUX
ma-171	93	28	globally	globally	ADV
ma-171	93	29	asymptotically	asymptotically	ADV
ma-171	93	30	stable	stable	ADJ
ma-171	93	31	whenever	whenever	SCONJ
ma-171	93	32	r0	r0	NOUN
ma-171	93	33	<	<	X
ma-171	93	34	1	1	NUM
ma-171	93	35	.	.	PUNCT
ma-171	93	36	proof	proof	NOUN
ma-171	93	37	.	.	PUNCT
ma-171	94	1	castillo	castillo	PROPN
ma-171	94	2	chavez	chavez	PROPN
ma-171	94	3	’s	’s	PROPN
ma-171	94	4	theorem	theorem	PROPN
ma-171	94	5	[	[	X
ma-171	94	6	1	1	NUM
ma-171	94	7	]	]	PUNCT
ma-171	94	8	is	be	AUX
ma-171	94	9	used	use	VERB
ma-171	94	10	to	to	PART
ma-171	94	11	analyze	analyze	VERB
ma-171	94	12	the	the	DET
ma-171	94	13	global	global	ADJ
ma-171	94	14	asymptotic	asymptotic	ADJ
ma-171	94	15	stability	stability	NOUN
ma-171	94	16	of	of	ADP
ma-171	94	17	the	the	DET
ma-171	94	18	math	math	NOUN
ma-171	94	19	-	-	PUNCT
ma-171	94	20	ematical	ematical	ADJ
ma-171	94	21	model	model	NOUN
ma-171	94	22	(	(	PUNCT
ma-171	94	23	2	2	NUM
ma-171	94	24	)	)	PUNCT
ma-171	94	25	such	such	ADJ
ma-171	94	26	that	that	DET
ma-171	94	27	e0	e0	PROPN
ma-171	94	28	=	=	PUNCT
ma-171	94	29	(	(	PUNCT
ma-171	94	30	x∗,0	x∗,0	PROPN
ma-171	94	31	)	)	PUNCT
ma-171	94	32	,	,	PUNCT
ma-171	94	33	x	x	X
ma-171	94	34	=	=	PRON
ma-171	94	35	(	(	PUNCT
ma-171	94	36	sh	sh	PROPN
ma-171	94	37	,	,	PUNCT
ma-171	94	38	sl	sl	PROPN
ma-171	94	39	)	)	PUNCT
ma-171	94	40	and	and	CCONJ
ma-171	94	41	z	z	NOUN
ma-171	94	42	=	=	SYM
ma-171	94	43	(	(	PUNCT
ma-171	94	44	i	i	NOUN
ma-171	94	45	,	,	PUNCT
ma-171	94	46	td	td	NOUN
ma-171	94	47	,	,	PUNCT
ma-171	94	48	a).now	a).now	NOUN
ma-171	94	49	;	;	PUNCT
ma-171	94	50	f	f	PROPN
ma-171	94	51	(	(	PUNCT
ma-171	94	52	x,0	x,0	PROPN
ma-171	94	53	)	)	PUNCT
ma-171	95	1	=	=	PRON
ma-171	95	2	(	(	PUNCT
ma-171	95	3	δλ−	δλ−	NUM
ma-171	95	4	µsh	µsh	PROPN
ma-171	95	5	(	(	PUNCT
ma-171	95	6	1−	1−	NUM
ma-171	95	7	δ)λ−	δ)λ−	NOUN
ma-171	95	8	µsl	µsl	VERB
ma-171	95	9	)	)	PUNCT
ma-171	95	10	and	and	CCONJ
ma-171	95	11	g(x	g(x	NOUN
ma-171	95	12	,	,	PUNCT
ma-171	95	13	z	z	NOUN
ma-171	95	14	)	)	PUNCT
ma-171	95	15	=	=	SYM
ma-171	96	1	pz−	pz−	NUM
ma-171	96	2	g̃(x	g̃(x	PROPN
ma-171	96	3	,	,	PUNCT
ma-171	96	4	z	z	NOUN
ma-171	96	5	)	)	PUNCT
ma-171	96	6	.	.	PUNCT
ma-171	97	1	matrix	matrix	NOUN
ma-171	97	2	p	p	NOUN
ma-171	97	3	is	be	AUX
ma-171	97	4	given	give	VERB
ma-171	97	5	by	by	NOUN
ma-171	97	6	h1β1sh	h1β1sh	X
ma-171	97	7	n	n	NOUN
ma-171	98	1	+	+	CCONJ
ma-171	98	2	(	(	PUNCT
ma-171	98	3	1−	1−	NUM
ma-171	98	4	φ2)β1sl	φ2)β1sl	NOUN
ma-171	98	5	n	n	NUM
ma-171	98	6	−	−	PROPN
ma-171	98	7	(	(	PUNCT
ma-171	98	8	α+	α+	X
ma-171	98	9	γ2	γ2	PROPN
ma-171	98	10	+	+	CCONJ
ma-171	98	11	µ	µ	X
ma-171	98	12	)	)	PUNCT
ma-171	98	13	h1β2sh	h1β2sh	VERB
ma-171	98	14	n	n	NOUN
ma-171	98	15	+	+	CCONJ
ma-171	98	16	(	(	PUNCT
ma-171	98	17	1−	1−	NUM
ma-171	98	18	φ2)β2sl	φ2)β2sl	PROPN
ma-171	98	19	n	n	ADV
ma-171	98	20	0	0	NUM
ma-171	98	21	α	α	NOUN
ma-171	98	22	−(γ3	−(γ3	X
ma-171	98	23	+	+	ADJ
ma-171	98	24	µ	µ	X
ma-171	98	25	)	)	PUNCT
ma-171	98	26	0	0	NUM
ma-171	99	1	γ2	γ2	PROPN
ma-171	99	2	γ3	γ3	NOUN
ma-171	99	3	−(σ	−(σ	NOUN
ma-171	99	4	+	+	CCONJ
ma-171	99	5	µ	µ	X
ma-171	99	6	)	)	PUNCT
ma-171	99	7			NOUN
ma-171	99	8	,	,	PUNCT
ma-171	99	9	where	where	SCONJ
ma-171	99	10	h1	h1	NOUN
ma-171	99	11	=	=	SYM
ma-171	99	12	(	(	PUNCT
ma-171	99	13	1−	1−	NUM
ma-171	99	14	φ1)(1−	φ1)(1−	ADJ
ma-171	99	15	φ2	φ2	NOUN
ma-171	99	16	)	)	PUNCT
ma-171	99	17	,	,	PUNCT
ma-171	99	18	and	and	CCONJ
ma-171	99	19	pz	pz	NOUN
ma-171	99	20	is	be	AUX
ma-171	99	21	given	give	VERB
ma-171	99	22	by	by	NOUN
ma-171	99	23	h1β1ish	h1β1ish	PUNCT
ma-171	99	24	n	n	NOUN
ma-171	99	25	+	+	CCONJ
ma-171	99	26	(	(	PUNCT
ma-171	99	27	1−	1−	NUM
ma-171	99	28	φ2)β1isl	φ2)β1isl	PROPN
ma-171	99	29	n	n	PRON
ma-171	99	30	−	−	PROPN
ma-171	99	31	(	(	PUNCT
ma-171	99	32	α+	α+	X
ma-171	99	33	γ2	γ2	PROPN
ma-171	99	34	+	+	CCONJ
ma-171	99	35	µ	µ	X
ma-171	99	36	)	)	PUNCT
ma-171	99	37	+	+	CCONJ
ma-171	99	38	h1β2tdsh	h1β2tdsh	PROPN
ma-171	99	39	n	n	NOUN
ma-171	99	40	+	+	CCONJ
ma-171	99	41	(	(	PUNCT
ma-171	99	42	1−	1−	NUM
ma-171	99	43	φ2)β2tdsl	φ2)β2tdsl	NOUN
ma-171	99	44	n	n	PROPN
ma-171	99	45	αi	αi	VERB
ma-171	99	46	−	−	PROPN
ma-171	100	1	(	(	PUNCT
ma-171	100	2	γ3	γ3	NOUN
ma-171	100	3	+	+	CCONJ
ma-171	100	4	µ)td	µ)td	PROPN
ma-171	100	5	γ2i	γ2i	PROPN
ma-171	100	6	+	+	CCONJ
ma-171	100	7	γ3td	γ3td	PUNCT
ma-171	101	1	−	−	PROPN
ma-171	101	2	(	(	PUNCT
ma-171	101	3	σ	σ	NOUN
ma-171	101	4	+	+	CCONJ
ma-171	101	5	µ)a	µ)a	VERB
ma-171	101	6			X
ma-171	101	7	.	.	PUNCT
ma-171	102	1	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	102	2	eur	eur	PROPN
ma-171	102	3	.	.	PUNCT
ma-171	103	1	j.	j.	PROPN
ma-171	103	2	math	math	PROPN
ma-171	103	3	.	.	PUNCT
ma-171	104	1	anal	anal	PROPN
ma-171	104	2	.	.	PUNCT
ma-171	105	1	10.28924	10.28924	NUM
ma-171	105	2	/	/	SYM
ma-171	105	3	ada	ada	PROPN
ma-171	105	4	/	/	SYM
ma-171	105	5	ma.3.21	ma.3.21	PROPN
ma-171	105	6	6moreover	6moreover	NUM
ma-171	105	7	,	,	PUNCT
ma-171	105	8	g(x	g(x	NOUN
ma-171	105	9	,	,	PUNCT
ma-171	105	10	z	z	NOUN
ma-171	105	11	)	)	PUNCT
ma-171	105	12	is	be	AUX
ma-171	105	13	given	give	VERB
ma-171	105	14	by	by	NOUN
ma-171	105	15	(	(	PUNCT
ma-171	105	16	1−	1−	NUM
ma-171	105	17	φ1)(1−	φ1)(1−	ADJ
ma-171	105	18	φ2	φ2	NOUN
ma-171	105	19	)	)	PUNCT
ma-171	105	20	(	(	PUNCT
ma-171	105	21	β1i	β1i	PUNCT
ma-171	105	22	+	+	CCONJ
ma-171	105	23	β2td	β2td	SYM
ma-171	105	24	n	n	X
ma-171	105	25	)	)	PUNCT
ma-171	106	1	sh	sh	INTJ
ma-171	107	1	+	+	PUNCT
ma-171	107	2	(	(	PUNCT
ma-171	107	3	1−	1−	NUM
ma-171	107	4	φ2	φ2	PROPN
ma-171	107	5	)	)	PUNCT
ma-171	107	6	(	(	PUNCT
ma-171	107	7	β1i	β1i	PUNCT
ma-171	107	8	+	+	CCONJ
ma-171	107	9	β2td	β2td	SYM
ma-171	107	10	n	n	X
ma-171	107	11	)	)	PUNCT
ma-171	108	1	sl	sl	INTJ
ma-171	108	2	−	−	PROPN
ma-171	108	3	(	(	PUNCT
ma-171	108	4	α+	α+	X
ma-171	108	5	γ2	γ2	NOUN
ma-171	108	6	+	+	CCONJ
ma-171	108	7	µ)i	µ)i	X
ma-171	108	8	αi	αi	PRON
ma-171	108	9	−	−	PROPN
ma-171	109	1	(	(	PUNCT
ma-171	109	2	γ3	γ3	NOUN
ma-171	109	3	+	+	CCONJ
ma-171	109	4	µ)td	µ)td	PROPN
ma-171	109	5	γ2i	γ2i	PROPN
ma-171	109	6	+	+	CCONJ
ma-171	109	7	γ3td	γ3td	PUNCT
ma-171	110	1	−	−	PROPN
ma-171	110	2	(	(	PUNCT
ma-171	110	3	σ	σ	NOUN
ma-171	110	4	+	+	CCONJ
ma-171	110	5	µ)a	µ)a	VERB
ma-171	110	6			X
ma-171	110	7	,	,	PUNCT
ma-171	110	8	and	and	CCONJ
ma-171	110	9	therefore	therefore	ADV
ma-171	110	10	g̃(x	g̃(x	PROPN
ma-171	110	11	,	,	PUNCT
ma-171	110	12	z	z	NOUN
ma-171	110	13	)	)	PUNCT
ma-171	110	14	=	=	SYM
ma-171	110	15	pz	pz	NOUN
ma-171	110	16	−	−	PROPN
ma-171	111	1	g(x	g(x	PROPN
ma-171	111	2	,	,	PUNCT
ma-171	111	3	z)=	z)=	PROPN
ma-171	111	4	g̃1(x	g̃1(x	NOUN
ma-171	111	5	,	,	PUNCT
ma-171	111	6	z	z	NOUN
ma-171	111	7	)	)	PUNCT
ma-171	111	8	g̃2(x	g̃2(x	PROPN
ma-171	111	9	,	,	PUNCT
ma-171	111	10	z	z	NOUN
ma-171	111	11	)	)	PUNCT
ma-171	111	12	g̃3(x	g̃3(x	PROPN
ma-171	111	13	,	,	PUNCT
ma-171	111	14	z	z	NOUN
ma-171	111	15	)	)	PUNCT
ma-171	111	16	=	=	ADJ
ma-171	111	17	0	0	NOUN
ma-171	111	18	0	0	NUM
ma-171	111	19	0	0	NUM
ma-171	111	20			NOUN
ma-171	111	21	.	.	PUNCT
ma-171	112	1	hence	hence	ADV
ma-171	112	2	conditions	condition	VERB
ma-171	112	3	h1	h1	PROPN
ma-171	112	4	and	and	CCONJ
ma-171	112	5	h2	h2	NOUN
ma-171	112	6	are	be	AUX
ma-171	112	7	satisfied	satisfied	ADJ
ma-171	112	8	.	.	PUNCT
ma-171	113	1	also	also	ADV
ma-171	113	2	from	from	ADP
ma-171	113	3	theorem	theorem	ADJ
ma-171	113	4	(	(	PUNCT
ma-171	113	5	3.1	3.1	NUM
ma-171	113	6	)	)	PUNCT
ma-171	113	7	,	,	PUNCT
ma-171	113	8	e0	e0	PROPN
ma-171	113	9	is	be	AUX
ma-171	113	10	locally	locally	ADV
ma-171	113	11	asymptotically	asymptotically	ADV
ma-171	113	12	stable	stable	ADJ
ma-171	113	13	whenever	whenever	SCONJ
ma-171	113	14	r0	r0	NOUN
ma-171	113	15	<	<	X
ma-171	113	16	1	1	NUM
ma-171	113	17	.	.	PUNCT
ma-171	114	1	thereforefollowing	thereforefollowe	VERB
ma-171	114	2	castillo	castillo	PROPN
ma-171	114	3	chavez	chavez	PROPN
ma-171	114	4	’s	’s	PART
ma-171	114	5	theorem	theorem	PROPN
ma-171	114	6	,	,	PUNCT
ma-171	114	7	e0	e0	PROPN
ma-171	114	8	is	be	AUX
ma-171	114	9	globally	globally	ADV
ma-171	114	10	asymptotically	asymptotically	ADV
ma-171	114	11	stable	stable	ADJ
ma-171	114	12	whenever	whenever	SCONJ
ma-171	114	13	r0	r0	NOUN
ma-171	114	14	<	<	X
ma-171	114	15	1	1	NUM
ma-171	114	16	,	,	PUNCT
ma-171	114	17	asdesired	asdesire	VERB
ma-171	114	18	.	.	PUNCT
ma-171	115	1	�	�	PROPN
ma-171	115	2	this	this	PRON
ma-171	115	3	implies	imply	VERB
ma-171	115	4	that	that	SCONJ
ma-171	115	5	with	with	ADP
ma-171	115	6	a	a	DET
ma-171	115	7	large	large	ADJ
ma-171	115	8	perturbation	perturbation	NOUN
ma-171	115	9	of	of	ADP
ma-171	115	10	the	the	DET
ma-171	115	11	disease	disease	NOUN
ma-171	115	12	free	free	ADJ
ma-171	115	13	equilibrium	equilibrium	NOUN
ma-171	115	14	,	,	PUNCT
ma-171	115	15	solutions	solution	NOUN
ma-171	115	16	of	of	ADP
ma-171	115	17	the	the	DET
ma-171	115	18	modelrepresented	modelrepresente	VERB
ma-171	115	19	by	by	ADP
ma-171	115	20	the	the	DET
ma-171	115	21	system	system	NOUN
ma-171	115	22	(	(	PUNCT
ma-171	115	23	3.2	3.2	NUM
ma-171	115	24	)	)	PUNCT
ma-171	115	25	converge	converge	VERB
ma-171	115	26	to	to	PART
ma-171	115	27	d.f.e	d.f.e	VERB
ma-171	115	28	whenever	whenever	SCONJ
ma-171	115	29	r0	r0	VERB
ma-171	115	30	<	<	X
ma-171	115	31	1	1	NUM
ma-171	115	32	.	.	PUNCT
ma-171	115	33	epidemiologically	epidemiologically	NOUN
ma-171	115	34	,	,	PUNCT
ma-171	115	35	this	this	PRON
ma-171	115	36	impliesthat	impliesthat	VERB
ma-171	115	37	if	if	SCONJ
ma-171	115	38	a	a	DET
ma-171	115	39	sufficiently	sufficiently	ADV
ma-171	115	40	large	large	ADJ
ma-171	115	41	number	number	NOUN
ma-171	115	42	of	of	ADP
ma-171	115	43	hiv	hiv	PROPN
ma-171	115	44	infected	infect	VERB
ma-171	115	45	individuals	individual	NOUN
ma-171	115	46	are	be	AUX
ma-171	115	47	introduced	introduce	VERB
ma-171	115	48	in	in	ADP
ma-171	115	49	a	a	DET
ma-171	115	50	population	population	NOUN
ma-171	115	51	thatis	thatis	NOUN
ma-171	115	52	fully	fully	ADV
ma-171	115	53	susceptible	susceptible	ADJ
ma-171	115	54	to	to	ADP
ma-171	115	55	hiv	hiv	PROPN
ma-171	115	56	infection	infection	NOUN
ma-171	115	57	,	,	PUNCT
ma-171	115	58	the	the	DET
ma-171	115	59	disease	disease	NOUN
ma-171	115	60	will	will	AUX
ma-171	115	61	die	die	VERB
ma-171	115	62	out	out	ADP
ma-171	115	63	whenever	whenever	SCONJ
ma-171	115	64	r0	r0	VERB
ma-171	115	65	<	<	X
ma-171	115	66	1	1	NUM
ma-171	115	67	.	.	NOUN
ma-171	115	68	3.1	3.1	NUM
ma-171	115	69	.	.	PUNCT
ma-171	116	1	existence	existence	NOUN
ma-171	116	2	of	of	ADP
ma-171	116	3	the	the	DET
ma-171	116	4	endemic	endemic	ADJ
ma-171	116	5	steady	steady	ADJ
ma-171	116	6	state	state	NOUN
ma-171	116	7	.	.	PUNCT
ma-171	117	1	theorem	theorem	VERB
ma-171	117	2	3.3	3.3	NUM
ma-171	117	3	.	.	PUNCT
ma-171	118	1	an	an	DET
ma-171	118	2	endemic	endemic	ADJ
ma-171	118	3	equilibrium	equilibrium	NOUN
ma-171	118	4	point	point	NOUN
ma-171	118	5	e1	e1	NOUN
ma-171	118	6	=	=	SYM
ma-171	118	7	(	(	PUNCT
ma-171	118	8	s∗∗h	s∗∗h	PROPN
ma-171	118	9	,	,	PUNCT
ma-171	118	10	s	s	PART
ma-171	118	11	∗∗	∗∗	PROPN
ma-171	118	12	l	l	NOUN
ma-171	118	13	,	,	PUNCT
ma-171	118	14	i	i	PRON
ma-171	118	15	∗∗	∗∗	PROPN
ma-171	118	16	,	,	PUNCT
ma-171	118	17	t	t	PROPN
ma-171	119	1	∗∗d	∗∗d	AUX
ma-171	119	2	,	,	PUNCT
ma-171	119	3	a	a	DET
ma-171	119	4	∗∗	∗∗	NOUN
ma-171	119	5	)	)	PUNCT
ma-171	119	6	,	,	PUNCT
ma-171	119	7	of	of	ADP
ma-171	119	8	the	the	DET
ma-171	119	9	system	system	NOUN
ma-171	119	10	(	(	PUNCT
ma-171	119	11	2	2	X
ma-171	119	12	)	)	PUNCT
ma-171	119	13	exists	exist	VERB
ma-171	119	14	whenever	whenever	SCONJ
ma-171	119	15	r0	r0	NOUN
ma-171	119	16	>	>	X
ma-171	119	17	1	1	X
ma-171	119	18	.	.	PUNCT
ma-171	120	1	proof	proof	NOUN
ma-171	120	2	.	.	PUNCT
ma-171	121	1	equating	equate	VERB
ma-171	121	2	the	the	DET
ma-171	121	3	right	right	ADJ
ma-171	121	4	hand	hand	NOUN
ma-171	121	5	side	side	NOUN
ma-171	121	6	of	of	ADP
ma-171	121	7	each	each	DET
ma-171	121	8	equation	equation	NOUN
ma-171	121	9	in	in	ADP
ma-171	121	10	the	the	DET
ma-171	121	11	system	system	NOUN
ma-171	121	12	(	(	PUNCT
ma-171	121	13	2	2	NUM
ma-171	121	14	)	)	PUNCT
ma-171	121	15	to	to	ADP
ma-171	121	16	zero	zero	NUM
ma-171	121	17	and	and	CCONJ
ma-171	121	18	simplifyingyields	simplifyingyield	NOUN
ma-171	121	19	;	;	PUNCT
ma-171	121	20	δλ−	δλ−	NUM
ma-171	121	21	(	(	PUNCT
ma-171	121	22	1−	1−	NUM
ma-171	121	23	φ1)(1−	φ1)(1−	ADJ
ma-171	121	24	φ2	φ2	NOUN
ma-171	121	25	)	)	PUNCT
ma-171	121	26	(	(	PUNCT
ma-171	121	27	β1i	β1i	PUNCT
ma-171	121	28	∗∗	∗∗	X
ma-171	121	29	+	+	SYM
ma-171	121	30	β2	β2	PROPN
ma-171	121	31	t	t	NOUN
ma-171	121	32	∗∗	∗∗	PROPN
ma-171	121	33	d	d	SYM
ma-171	121	34	n	n	CCONJ
ma-171	121	35	)	)	PUNCT
ma-171	121	36	s∗∗h	s∗∗h	PROPN
ma-171	121	37	−	−	PROPN
ma-171	121	38	µs∗∗h	µs∗∗h	PROPN
ma-171	121	39	=	=	SYM
ma-171	121	40	0	0	NUM
ma-171	121	41	,	,	PUNCT
ma-171	121	42	(	(	PUNCT
ma-171	121	43	5	5	NUM
ma-171	121	44	)	)	PUNCT
ma-171	121	45	(	(	PUNCT
ma-171	121	46	1−	1−	NUM
ma-171	121	47	δ)λ−	δ)λ−	NOUN
ma-171	121	48	(	(	PUNCT
ma-171	121	49	1−	1−	NUM
ma-171	121	50	φ2	φ2	PROPN
ma-171	121	51	)	)	PUNCT
ma-171	121	52	(	(	PUNCT
ma-171	121	53	β1i	β1i	PUNCT
ma-171	121	54	∗∗	∗∗	X
ma-171	121	55	+	+	SYM
ma-171	121	56	β2	β2	PROPN
ma-171	121	57	t	t	NOUN
ma-171	121	58	∗∗	∗∗	PROPN
ma-171	121	59	d	d	SYM
ma-171	121	60	n	n	CCONJ
ma-171	121	61	)	)	PUNCT
ma-171	121	62	s∗∗l	s∗∗l	NOUN
ma-171	121	63	−	−	NOUN
ma-171	121	64	µs∗∗l	µs∗∗l	NOUN
ma-171	121	65	=	=	SYM
ma-171	121	66	0	0	NUM
ma-171	121	67	,	,	PUNCT
ma-171	121	68	(	(	PUNCT
ma-171	121	69	6	6	NUM
ma-171	121	70	)	)	PUNCT
ma-171	121	71	(	(	PUNCT
ma-171	121	72	1−	1−	NUM
ma-171	121	73	φ1)(1−	φ1)(1−	ADJ
ma-171	121	74	φ2	φ2	NOUN
ma-171	121	75	)	)	PUNCT
ma-171	121	76	(	(	PUNCT
ma-171	121	77	β1i	β1i	PUNCT
ma-171	121	78	∗∗	∗∗	X
ma-171	121	79	+	+	SYM
ma-171	121	80	β2	β2	PROPN
ma-171	121	81	t	t	NOUN
ma-171	121	82	∗∗	∗∗	PROPN
ma-171	121	83	d	d	SYM
ma-171	121	84	n	n	CCONJ
ma-171	121	85	)	)	PUNCT
ma-171	121	86	s∗∗h	s∗∗h	PROPN
ma-171	121	87	+	+	CCONJ
ma-171	121	88	(	(	PUNCT
ma-171	121	89	1−	1−	NUM
ma-171	121	90	φ2	φ2	PROPN
ma-171	121	91	)	)	PUNCT
ma-171	121	92	(	(	PUNCT
ma-171	121	93	β1i	β1i	PUNCT
ma-171	121	94	∗∗	∗∗	X
ma-171	121	95	+	+	SYM
ma-171	121	96	β2	β2	PROPN
ma-171	121	97	t	t	NOUN
ma-171	121	98	∗∗	∗∗	PROPN
ma-171	121	99	d	d	SYM
ma-171	121	100	n	n	CCONJ
ma-171	121	101	)	)	PUNCT
ma-171	121	102	s∗∗l	s∗∗l	NOUN
ma-171	121	103	−	−	PROPN
ma-171	121	104	(	(	PUNCT
ma-171	121	105	α+	α+	PUNCT
ma-171	121	106	γ2	γ2	NOUN
ma-171	121	107	+	+	CCONJ
ma-171	121	108	µ)i∗∗	µ)i∗∗	X
ma-171	121	109	=	=	SYM
ma-171	121	110	0	0	PROPN
ma-171	121	111	,	,	PUNCT
ma-171	121	112	(	(	PUNCT
ma-171	121	113	7	7	X
ma-171	121	114	)	)	PUNCT
ma-171	121	115	αi∗∗	αi∗∗	NOUN
ma-171	121	116	−	−	NOUN
ma-171	122	1	(	(	PUNCT
ma-171	122	2	γ3	γ3	NOUN
ma-171	122	3	+	+	CCONJ
ma-171	122	4	µ)t	µ)t	NOUN
ma-171	123	1	∗∗d	∗∗d	X
ma-171	123	2	=	=	SYM
ma-171	123	3	0	0	NUM
ma-171	123	4	,	,	PUNCT
ma-171	123	5	(	(	PUNCT
ma-171	123	6	8)	8)	NUM
ma-171	123	7	γ2i	γ2i	NOUN
ma-171	123	8	∗∗	∗∗	PROPN
ma-171	124	1	+	+	CCONJ
ma-171	124	2	γ3	γ3	NOUN
ma-171	124	3	t	t	NOUN
ma-171	124	4	∗∗	∗∗	PROPN
ma-171	125	1	d	d	X
ma-171	125	2	−	−	PROPN
ma-171	125	3	(	(	PUNCT
ma-171	125	4	µ+	µ+	X
ma-171	125	5	σ)a∗∗	σ)a∗∗	PROPN
ma-171	125	6	=	=	NOUN
ma-171	125	7	0	0	PROPN
ma-171	125	8	.	.	PUNCT
ma-171	125	9	(	(	PUNCT
ma-171	125	10	9	9	NUM
ma-171	125	11	)	)	PUNCT
ma-171	125	12	from	from	ADP
ma-171	125	13	equation	equation	NOUN
ma-171	125	14	(	(	PUNCT
ma-171	125	15	8)	8)	NUM
ma-171	125	16	,	,	PUNCT
ma-171	125	17	t	t	NOUN
ma-171	125	18	∗∗d	∗∗d	NOUN
ma-171	125	19	=	=	SYM
ma-171	125	20	α	α	PROPN
ma-171	125	21	q2	q2	NOUN
ma-171	125	22	i∗∗.substituting	i∗∗.substitute	VERB
ma-171	125	23	for	for	ADP
ma-171	125	24	t	t	PROPN
ma-171	125	25	∗∗td	∗∗td	PROPN
ma-171	125	26	in	in	ADP
ma-171	125	27	equation	equation	NOUN
ma-171	125	28	(	(	PUNCT
ma-171	125	29	9	9	NUM
ma-171	125	30	)	)	PUNCT
ma-171	125	31	and	and	CCONJ
ma-171	125	32	simplifying	simplifying	NOUN
ma-171	125	33	gives	give	VERB
ma-171	125	34	a∗∗	a∗∗	NOUN
ma-171	126	1	=	=	PRON
ma-171	126	2	(	(	PUNCT
ma-171	126	3	γ2	γ2	PROPN
ma-171	126	4	q3	q3	PROPN
ma-171	126	5	+	+	CCONJ
ma-171	126	6	αγ3	αγ3	PROPN
ma-171	126	7	q2q3	q2q3	NOUN
ma-171	126	8	)	)	PUNCT
ma-171	126	9	i∗∗.	i∗∗.	PROPN
ma-171	126	10	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	126	11	eur	eur	PROPN
ma-171	126	12	.	.	PUNCT
ma-171	127	1	j.	j.	PROPN
ma-171	127	2	math	math	PROPN
ma-171	127	3	.	.	PUNCT
ma-171	128	1	anal	anal	PROPN
ma-171	128	2	.	.	PUNCT
ma-171	129	1	10.28924	10.28924	NUM
ma-171	129	2	/	/	SYM
ma-171	129	3	ada	ada	PROPN
ma-171	129	4	/	/	SYM
ma-171	129	5	ma.3.21	ma.3.21	PROPN
ma-171	129	6	7using	7using	NUM
ma-171	129	7	equation	equation	NOUN
ma-171	129	8	(	(	PUNCT
ma-171	129	9	5	5	NUM
ma-171	129	10	)	)	PUNCT
ma-171	129	11	and	and	CCONJ
ma-171	129	12	substituting	substitute	VERB
ma-171	129	13	t	t	NOUN
ma-171	129	14	∗∗d	∗∗d	NUM
ma-171	129	15	gives	give	VERB
ma-171	129	16	δλn	δλn	NOUN
ma-171	129	17	−	−	PROPN
ma-171	129	18	(	(	PUNCT
ma-171	129	19	1−	1−	NUM
ma-171	129	20	φ1)(1−	φ1)(1−	ADJ
ma-171	129	21	φ2	φ2	NOUN
ma-171	129	22	)	)	PUNCT
ma-171	129	23	(	(	PUNCT
ma-171	129	24	β1	β1	X
ma-171	129	25	+	+	CCONJ
ma-171	129	26	β2α	β2α	X
ma-171	129	27	q2	q2	NOUN
ma-171	129	28	)	)	PUNCT
ma-171	129	29	i∗∗s∗∗h	i∗∗s∗∗h	ADJ
ma-171	129	30	−	−	NOUN
ma-171	129	31	µns∗∗h	µns∗∗h	NOUN
ma-171	129	32	=	=	SYM
ma-171	129	33	0	0	NUM
ma-171	129	34	⇒	⇒	PROPN
ma-171	129	35	s∗∗h	s∗∗h	PROPN
ma-171	129	36	=	=	X
ma-171	129	37	δλn	δλn	PROPN
ma-171	129	38	a1i∗∗	a1i∗∗	PROPN
ma-171	129	39	+	+	CCONJ
ma-171	129	40	µn	µn	PROPN
ma-171	129	41	,	,	PUNCT
ma-171	129	42	where	where	SCONJ
ma-171	129	43	a1	a1	NOUN
ma-171	129	44	=	=	SYM
ma-171	129	45	(	(	PUNCT
ma-171	129	46	1	1	NUM
ma-171	129	47	−	−	NOUN
ma-171	129	48	φ1)(1	φ1)(1	PROPN
ma-171	129	49	−	−	PROPN
ma-171	129	50	φ2	φ2	PROPN
ma-171	129	51	)	)	PUNCT
ma-171	129	52	(	(	PUNCT
ma-171	129	53	β1	β1	X
ma-171	129	54	+	+	CCONJ
ma-171	129	55	β2α	β2α	X
ma-171	129	56	q2	q2	NOUN
ma-171	129	57	)	)	PUNCT
ma-171	129	58	.	.	PUNCT
ma-171	130	1	in	in	ADP
ma-171	130	2	a	a	DET
ma-171	130	3	similar	similar	ADJ
ma-171	130	4	manner	manner	NOUN
ma-171	130	5	,	,	PUNCT
ma-171	130	6	s∗∗l	s∗∗l	PROPN
ma-171	130	7	is	be	AUX
ma-171	130	8	expressed	express	VERB
ma-171	130	9	as	as	ADP
ma-171	130	10	s∗∗l	s∗∗l	PROPN
ma-171	130	11	=	=	PUNCT
ma-171	130	12	(	(	PUNCT
ma-171	130	13	1−	1−	NUM
ma-171	130	14	δ)λn	δ)λn	PROPN
ma-171	130	15	a2i∗	a2i∗	PROPN
ma-171	130	16	+	+	CCONJ
ma-171	130	17	µn	µn	PROPN
ma-171	130	18	,	,	PUNCT
ma-171	130	19	where	where	SCONJ
ma-171	130	20	a2	a2	PROPN
ma-171	130	21	=	=	SYM
ma-171	130	22	(	(	PUNCT
ma-171	130	23	1−	1−	NUM
ma-171	130	24	φ2	φ2	PROPN
ma-171	130	25	)	)	PUNCT
ma-171	130	26	(	(	PUNCT
ma-171	130	27	β1	β1	X
ma-171	130	28	+	+	CCONJ
ma-171	130	29	β2α	β2α	X
ma-171	130	30	q2	q2	NOUN
ma-171	130	31	)	)	PUNCT
ma-171	130	32	.using	.use	VERB
ma-171	130	33	equation	equation	NOUN
ma-171	130	34	(	(	PUNCT
ma-171	130	35	7	7	NUM
ma-171	130	36	)	)	PUNCT
ma-171	130	37	and	and	CCONJ
ma-171	130	38	substituting	substitute	VERB
ma-171	130	39	for	for	ADP
ma-171	130	40	s∗∗h	s∗∗h	NOUN
ma-171	130	41	and	and	CCONJ
ma-171	130	42	s∗∗l	s∗∗l	NOUN
ma-171	130	43	,	,	PUNCT
ma-171	130	44	we	we	PRON
ma-171	130	45	obtain	obtain	VERB
ma-171	130	46	a1i	a1i	PROPN
ma-171	130	47	∗∗δλ	∗∗δλ	X
ma-171	130	48	a1i∗∗	a1i∗∗	NOUN
ma-171	130	49	+	+	CCONJ
ma-171	130	50	µn∗∗	µn∗∗	NOUN
ma-171	130	51	+	+	CCONJ
ma-171	130	52	a2i	a2i	NOUN
ma-171	130	53	∗∗(1−	∗∗(1−	NOUN
ma-171	130	54	δ)λ	δ)λ	NOUN
ma-171	130	55	a2i∗∗	a2i∗∗	NOUN
ma-171	130	56	+	+	CCONJ
ma-171	130	57	µn∗∗	µn∗∗	NUM
ma-171	130	58	−q1i	−q1i	X
ma-171	130	59	∗∗	∗∗	X
ma-171	130	60	=	=	SYM
ma-171	130	61	0	0	PUNCT
ma-171	130	62	(	(	PUNCT
ma-171	130	63	10	10	NUM
ma-171	130	64	)	)	PUNCT
ma-171	130	65	thus	thus	ADV
ma-171	130	66	from	from	ADP
ma-171	130	67	equation	equation	NOUN
ma-171	130	68	(	(	PUNCT
ma-171	130	69	10	10	NUM
ma-171	130	70	)	)	PUNCT
ma-171	130	71	,	,	PUNCT
ma-171	130	72	(	(	PUNCT
ma-171	130	73	a1δλ	a1δλ	X
ma-171	130	74	a1i∗∗	a1i∗∗	PROPN
ma-171	131	1	+	+	CCONJ
ma-171	131	2	µn∗∗	µn∗∗	NOUN
ma-171	131	3	+	+	CCONJ
ma-171	131	4	a2(1−	a2(1−	NOUN
ma-171	131	5	δ)λ	δ)λ	NOUN
ma-171	131	6	a2i∗∗	a2i∗∗	NOUN
ma-171	131	7	+	+	CCONJ
ma-171	131	8	µn∗∗	µn∗∗	NUM
ma-171	131	9	−q1	−q1	NOUN
ma-171	131	10	)	)	PUNCT
ma-171	131	11	i∗∗	i∗∗	PROPN
ma-171	131	12	=	=	NOUN
ma-171	131	13	0	0	X
ma-171	131	14	.	.	PUNCT
ma-171	132	1	(	(	PUNCT
ma-171	132	2	11	11	NUM
ma-171	132	3	)	)	PUNCT
ma-171	132	4	from	from	ADP
ma-171	132	5	equation	equation	NOUN
ma-171	132	6	(	(	PUNCT
ma-171	132	7	11	11	NUM
ma-171	132	8	)	)	PUNCT
ma-171	132	9	,	,	PUNCT
ma-171	132	10	i∗∗	i∗∗	PROPN
ma-171	132	11	=	=	SYM
ma-171	132	12	0	0	NUM
ma-171	132	13	corresponds	correspond	NOUN
ma-171	132	14	to	to	ADP
ma-171	132	15	the	the	DET
ma-171	132	16	disease	disease	NOUN
ma-171	132	17	free	free	ADJ
ma-171	132	18	equilibrium	equilibrium	NOUN
ma-171	132	19	point	point	NOUN
ma-171	132	20	of	of	ADP
ma-171	132	21	the	the	DET
ma-171	132	22	system	system	NOUN
ma-171	132	23	(	(	PUNCT
ma-171	132	24	2),denoted	2),denote	VERB
ma-171	132	25	by	by	ADP
ma-171	132	26	(	(	PUNCT
ma-171	132	27	e0	e0	PROPN
ma-171	132	28	)	)	PUNCT
ma-171	132	29	.	.	PUNCT
ma-171	133	1	the	the	DET
ma-171	133	2	other	other	ADJ
ma-171	133	3	solution	solution	NOUN
ma-171	133	4	of	of	ADP
ma-171	133	5	(	(	PUNCT
ma-171	133	6	11	11	NUM
ma-171	133	7	)	)	PUNCT
ma-171	133	8	when	when	SCONJ
ma-171	133	9	i∗∗	i∗∗	PROPN
ma-171	133	10	6=	6=	ADP
ma-171	133	11	0	0	NUM
ma-171	133	12	corresponds	correspond	NOUN
ma-171	133	13	to	to	ADP
ma-171	133	14	the	the	DET
ma-171	133	15	endemic	endemic	ADJ
ma-171	133	16	equilibriumpoint	equilibriumpoint	NOUN
ma-171	133	17	of	of	ADP
ma-171	133	18	the	the	DET
ma-171	133	19	system	system	NOUN
ma-171	133	20	such	such	ADJ
ma-171	133	21	that	that	PRON
ma-171	133	22	,	,	PUNCT
ma-171	133	23	a1δλ	a1δλ	X
ma-171	133	24	a1i∗∗	a1i∗∗	PROPN
ma-171	134	1	+	+	CCONJ
ma-171	134	2	µn∗∗	µn∗∗	NOUN
ma-171	134	3	+	+	CCONJ
ma-171	134	4	a2(1−	a2(1−	NOUN
ma-171	134	5	δ)λ	δ)λ	NOUN
ma-171	134	6	a2i∗∗	a2i∗∗	NOUN
ma-171	134	7	+	+	CCONJ
ma-171	134	8	µn∗∗	µn∗∗	NUM
ma-171	134	9	−q1	−q1	NOUN
ma-171	134	10	=	=	SYM
ma-171	134	11	0	0	PROPN
ma-171	134	12	.	.	PUNCT
ma-171	135	1	(	(	PUNCT
ma-171	135	2	12	12	NUM
ma-171	135	3	)	)	PUNCT
ma-171	135	4	multiplying	multiply	VERB
ma-171	135	5	through	through	ADP
ma-171	135	6	by	by	ADP
ma-171	135	7	(	(	PUNCT
ma-171	135	8	a1i	a1i	VERB
ma-171	135	9	∗∗	∗∗	X
ma-171	136	1	+	+	CCONJ
ma-171	136	2	µn∗∗)(a2i	µn∗∗)(a2i	X
ma-171	136	3	∗∗	∗∗	PROPN
ma-171	136	4	+	+	CCONJ
ma-171	136	5	µn∗∗	µn∗∗	NUM
ma-171	136	6	)	)	PUNCT
ma-171	136	7	yields	yield	NOUN
ma-171	136	8	ci∗∗2	ci∗∗2	NOUN
ma-171	137	1	+	+	NOUN
ma-171	138	1	di∗∗	di∗∗	NOUN
ma-171	138	2	+	+	SYM
ma-171	138	3	e	e	X
ma-171	138	4	=	=	SYM
ma-171	138	5	0	0	PROPN
ma-171	138	6	.	.	PUNCT
ma-171	139	1	(	(	PUNCT
ma-171	139	2	13	13	NUM
ma-171	139	3	)	)	PUNCT
ma-171	140	1	where	where	SCONJ
ma-171	140	2	:	:	PUNCT
ma-171	140	3	c	c	X
ma-171	140	4	=	=	SYM
ma-171	140	5	−q1a1a2	−q1a1a2	X
ma-171	140	6	,	,	PUNCT
ma-171	140	7	d	d	X
ma-171	140	8	=	=	PUNCT
ma-171	140	9	(	(	PUNCT
ma-171	140	10	a1a2δλ	a1a2δλ	ADP
ma-171	140	11	+	+	CCONJ
ma-171	140	12	a1a2(1−	a1a2(1−	PROPN
ma-171	140	13	δ)λ)−	δ)λ)−	PUNCT
ma-171	140	14	(	(	PUNCT
ma-171	140	15	q1a1µn	q1a1µn	PROPN
ma-171	140	16	+	+	NOUN
ma-171	140	17	q1a2µn	q1a2µn	PROPN
ma-171	140	18	)	)	PUNCT
ma-171	140	19	,	,	PUNCT
ma-171	140	20	and	and	CCONJ
ma-171	140	21	e	e	X
ma-171	140	22	=	=	PROPN
ma-171	140	23	a1δλµn	a1δλµn	PROPN
ma-171	140	24	+	+	CCONJ
ma-171	140	25	a2(1−	a2(1−	VERB
ma-171	140	26	δ)λµn	δ)λµn	PROPN
ma-171	140	27	−q1µnµn	−q1µnµn	PROPN
ma-171	140	28	.the	.the	PRON
ma-171	140	29	endemic	endemic	ADJ
ma-171	140	30	equilibrium	equilibrium	NOUN
ma-171	140	31	of	of	ADP
ma-171	140	32	the	the	DET
ma-171	140	33	system	system	NOUN
ma-171	140	34	exists	exist	VERB
ma-171	140	35	if	if	SCONJ
ma-171	140	36	the	the	DET
ma-171	140	37	roots	root	NOUN
ma-171	140	38	of	of	ADP
ma-171	140	39	equation	equation	NOUN
ma-171	140	40	(	(	PUNCT
ma-171	140	41	13	13	NUM
ma-171	140	42	)	)	PUNCT
ma-171	140	43	are	be	AUX
ma-171	140	44	real	real	ADJ
ma-171	140	45	and	and	CCONJ
ma-171	140	46	positive.descarte	positive.descarte	PROPN
ma-171	140	47	’s	’s	PART
ma-171	140	48	rule	rule	NOUN
ma-171	140	49	of	of	ADP
ma-171	140	50	signs	sign	NOUN
ma-171	140	51	is	be	AUX
ma-171	140	52	used	use	VERB
ma-171	140	53	to	to	PART
ma-171	140	54	check	check	VERB
ma-171	140	55	the	the	DET
ma-171	140	56	possible	possible	ADJ
ma-171	140	57	number	number	NOUN
ma-171	140	58	of	of	ADP
ma-171	140	59	real	real	ADJ
ma-171	140	60	roots	root	NOUN
ma-171	140	61	of	of	ADP
ma-171	140	62	the	the	DET
ma-171	140	63	polynomial	polynomial	NOUN
ma-171	140	64	.	.	PUNCT
ma-171	141	1	thenumber	thenumber	NOUN
ma-171	141	2	of	of	ADP
ma-171	141	3	positive	positive	ADJ
ma-171	141	4	real	real	ADJ
ma-171	141	5	roots	root	NOUN
ma-171	141	6	is	be	AUX
ma-171	141	7	equal	equal	ADJ
ma-171	141	8	to	to	ADP
ma-171	141	9	the	the	DET
ma-171	141	10	number	number	NOUN
ma-171	141	11	of	of	ADP
ma-171	141	12	sign	sign	NOUN
ma-171	141	13	changes	change	NOUN
ma-171	141	14	in	in	ADP
ma-171	141	15	the	the	DET
ma-171	141	16	coefficients	coefficient	NOUN
ma-171	141	17	of	of	ADP
ma-171	141	18	theterms	theterm	NOUN
ma-171	141	19	of	of	ADP
ma-171	141	20	a	a	DET
ma-171	141	21	polynomial	polynomial	ADJ
ma-171	142	1	[	[	X
ma-171	142	2	15	15	NUM
ma-171	142	3	]	]	PUNCT
ma-171	142	4	.	.	PUNCT
ma-171	143	1	considering	consider	VERB
ma-171	143	2	that	that	SCONJ
ma-171	143	3	all	all	DET
ma-171	143	4	the	the	DET
ma-171	143	5	parameters	parameter	NOUN
ma-171	143	6	used	use	VERB
ma-171	143	7	are	be	AUX
ma-171	143	8	positive	positive	ADJ
ma-171	143	9	,	,	PUNCT
ma-171	143	10	the	the	DET
ma-171	143	11	sign	sign	NOUN
ma-171	143	12	of	of	ADP
ma-171	143	13	c	c	PROPN
ma-171	143	14	isnegative	isnegative	ADJ
ma-171	143	15	.	.	PUNCT
ma-171	144	1	the	the	DET
ma-171	144	2	sign	sign	NOUN
ma-171	144	3	of	of	ADP
ma-171	144	4	e	e	PROPN
ma-171	144	5	is	be	AUX
ma-171	144	6	then	then	ADV
ma-171	144	7	checked	check	VERB
ma-171	144	8	as	as	SCONJ
ma-171	144	9	follows	follow	VERB
ma-171	144	10	;	;	PUNCT
ma-171	144	11	e	e	X
ma-171	144	12	=	=	PROPN
ma-171	144	13	a1δλµn	a1δλµn	PROPN
ma-171	144	14	+	+	CCONJ
ma-171	144	15	a2(1−	a2(1−	VERB
ma-171	144	16	δ)λµn	δ)λµn	PROPN
ma-171	144	17	−q1µnµn	−q1µnµn	PROPN
ma-171	144	18	=	=	PUNCT
ma-171	144	19	(	(	PUNCT
ma-171	144	20	1−	1−	NUM
ma-171	144	21	φ1)(1−	φ1)(1−	ADJ
ma-171	144	22	φ2	φ2	NOUN
ma-171	144	23	)	)	PUNCT
ma-171	144	24	(	(	PUNCT
ma-171	144	25	β1	β1	X
ma-171	144	26	+	+	CCONJ
ma-171	144	27	β2α	β2α	X
ma-171	144	28	q2	q2	NOUN
ma-171	144	29	)	)	PUNCT
ma-171	145	1	δλµn	δλµn	PROPN
ma-171	145	2	+	+	CCONJ
ma-171	145	3	(	(	PUNCT
ma-171	145	4	1−	1−	NUM
ma-171	145	5	φ2	φ2	PROPN
ma-171	145	6	)	)	PUNCT
ma-171	145	7	(	(	PUNCT
ma-171	145	8	β1	β1	X
ma-171	145	9	+	+	CCONJ
ma-171	145	10	β2α	β2α	X
ma-171	145	11	q2	q2	NOUN
ma-171	145	12	)	)	PUNCT
ma-171	145	13	(	(	PUNCT
ma-171	145	14	1−	1−	NUM
ma-171	145	15	δ)λµn	δ)λµn	PROPN
ma-171	145	16	−q1µnµn	−q1µnµn	PROPN
ma-171	145	17	=	=	PUNCT
ma-171	145	18	(	(	PUNCT
ma-171	145	19	1−	1−	NUM
ma-171	145	20	φ1)(1−	φ1)(1−	ADJ
ma-171	145	21	φ2)(β1	φ2)(β1	NOUN
ma-171	145	22	+	+	X
ma-171	145	23	β2α)δλµn	β2α)δλµn	PUNCT
ma-171	146	1	+	+	CCONJ
ma-171	146	2	(	(	PUNCT
ma-171	146	3	1−	1−	NUM
ma-171	146	4	φ2)(β1	φ2)(β1	NOUN
ma-171	146	5	+	+	CCONJ
ma-171	146	6	β2α)(1−	β2α)(1−	NOUN
ma-171	146	7	δ)λµn	δ)λµn	PROPN
ma-171	146	8	−q1q2µnµn	−q1q2µnµn	PROPN
ma-171	146	9	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	146	10	eur	eur	PROPN
ma-171	146	11	.	.	PUNCT
ma-171	147	1	j.	j.	PROPN
ma-171	147	2	math	math	PROPN
ma-171	147	3	.	.	PUNCT
ma-171	148	1	anal	anal	PROPN
ma-171	148	2	.	.	PUNCT
ma-171	149	1	10.28924	10.28924	NUM
ma-171	149	2	/	/	SYM
ma-171	149	3	ada	ada	PROPN
ma-171	149	4	/	/	SYM
ma-171	149	5	ma.3.21	ma.3.21	NOUN
ma-171	149	6	8	8	NUM
ma-171	149	7	using	use	VERB
ma-171	149	8	r0	r0	NOUN
ma-171	149	9	=	=	SYM
ma-171	149	10	β3	β3	PROPN
ma-171	149	11	q1	q1	PROPN
ma-171	149	12	+	+	CCONJ
ma-171	149	13	αβ4	αβ4	PROPN
ma-171	149	14	q1q2	q1q2	NOUN
ma-171	149	15	and	and	CCONJ
ma-171	149	16	the	the	DET
ma-171	149	17	limiting	limit	VERB
ma-171	149	18	value	value	NOUN
ma-171	149	19	of	of	ADP
ma-171	149	20	n	n	NOUN
ma-171	149	21	=	=	SYM
ma-171	149	22	λ	λ	X
ma-171	149	23	µ	µ	X
ma-171	149	24	,	,	PUNCT
ma-171	149	25	we	we	PRON
ma-171	149	26	obtain	obtain	VERB
ma-171	149	27	e	e	X
ma-171	149	28	=	=	PUNCT
ma-171	149	29	(	(	PUNCT
ma-171	149	30	r0	r0	NOUN
ma-171	149	31	−	−	PROPN
ma-171	149	32	1)λ2	1)λ2	NUM
ma-171	149	33	.	.	PUNCT
ma-171	150	1	thus	thus	ADV
ma-171	150	2	e	e	X
ma-171	150	3	>	>	X
ma-171	150	4	0iff	0iff	PROPN
ma-171	150	5	r0	r0	NOUN
ma-171	150	6	>	>	X
ma-171	150	7	1	1	NUM
ma-171	150	8	.	.	PUNCT
ma-171	151	1	since	since	SCONJ
ma-171	151	2	c	c	PROPN
ma-171	151	3	is	be	AUX
ma-171	151	4	negative	negative	ADJ
ma-171	151	5	,	,	PUNCT
ma-171	151	6	and	and	CCONJ
ma-171	151	7	e	e	NOUN
ma-171	151	8	is	be	AUX
ma-171	151	9	positive	positive	ADJ
ma-171	151	10	,	,	PUNCT
ma-171	151	11	we	we	PRON
ma-171	151	12	see	see	VERB
ma-171	151	13	that	that	SCONJ
ma-171	151	14	there	there	PRON
ma-171	151	15	is	be	VERB
ma-171	151	16	at	at	ADV
ma-171	151	17	least	least	ADJ
ma-171	151	18	one	one	NUM
ma-171	151	19	sign	sign	NOUN
ma-171	151	20	changeregardless	changeregardless	NOUN
ma-171	151	21	of	of	ADP
ma-171	151	22	the	the	DET
ma-171	151	23	sign	sign	NOUN
ma-171	151	24	of	of	ADP
ma-171	151	25	d.	d.	PROPN
ma-171	151	26	this	this	PRON
ma-171	151	27	implies	imply	VERB
ma-171	151	28	that	that	SCONJ
ma-171	151	29	equation	equation	NOUN
ma-171	151	30	(	(	PUNCT
ma-171	151	31	13	13	NUM
ma-171	151	32	)	)	PUNCT
ma-171	151	33	has	have	VERB
ma-171	151	34	at	at	ADV
ma-171	151	35	least	least	ADV
ma-171	151	36	one	one	NUM
ma-171	151	37	positive	positive	ADJ
ma-171	151	38	real	real	ADJ
ma-171	151	39	root.hence	root.hence	NOUN
ma-171	151	40	an	an	DET
ma-171	151	41	endemic	endemic	ADJ
ma-171	151	42	equilibrium	equilibrium	NOUN
ma-171	151	43	point	point	NOUN
ma-171	151	44	of	of	ADP
ma-171	151	45	the	the	DET
ma-171	151	46	system	system	NOUN
ma-171	151	47	(	(	PUNCT
ma-171	151	48	2	2	X
ma-171	151	49	)	)	PUNCT
ma-171	151	50	exists	exist	VERB
ma-171	151	51	whenever	whenever	SCONJ
ma-171	151	52	r0	r0	NOUN
ma-171	151	53	>	>	X
ma-171	151	54	1	1	X
ma-171	151	55	.	.	PUNCT
ma-171	151	56	�	�	PROPN
ma-171	151	57	3.2	3.2	NUM
ma-171	151	58	.	.	PUNCT
ma-171	152	1	local	local	ADJ
ma-171	152	2	stability	stability	NOUN
ma-171	152	3	of	of	ADP
ma-171	152	4	the	the	DET
ma-171	152	5	endemic	endemic	ADJ
ma-171	152	6	equilibrium	equilibrium	NOUN
ma-171	152	7	.	.	PUNCT
ma-171	153	1	at	at	ADP
ma-171	153	2	the	the	DET
ma-171	153	3	endemic	endemic	ADJ
ma-171	153	4	equilibrium	equilibrium	NOUN
ma-171	153	5	,	,	PUNCT
ma-171	153	6	there	there	PRON
ma-171	153	7	is	be	VERB
ma-171	153	8	persistenceof	persistenceof	ADJ
ma-171	153	9	hiv	hiv	NOUN
ma-171	153	10	infection	infection	NOUN
ma-171	153	11	in	in	ADP
ma-171	153	12	the	the	DET
ma-171	153	13	population	population	NOUN
ma-171	153	14	.	.	PUNCT
ma-171	154	1	theorem	theorem	VERB
ma-171	154	2	3.4	3.4	NUM
ma-171	154	3	.	.	PUNCT
ma-171	155	1	the	the	DET
ma-171	155	2	endemic	endemic	ADJ
ma-171	155	3	equilibrium	equilibrium	NOUN
ma-171	155	4	point	point	NOUN
ma-171	155	5	e1	e1	NOUN
ma-171	155	6	=	=	SYM
ma-171	155	7	(	(	PUNCT
ma-171	155	8	s∗∗h	s∗∗h	PROPN
ma-171	155	9	,	,	PUNCT
ma-171	155	10	s	s	PART
ma-171	155	11	∗∗	∗∗	PROPN
ma-171	155	12	l	l	NOUN
ma-171	155	13	,	,	PUNCT
ma-171	155	14	i	i	PRON
ma-171	155	15	∗∗	∗∗	PROPN
ma-171	155	16	,	,	PUNCT
ma-171	155	17	t	t	PROPN
ma-171	156	1	∗∗d	∗∗d	AUX
ma-171	156	2	,	,	PUNCT
ma-171	156	3	a	a	DET
ma-171	156	4	∗∗	∗∗	NOUN
ma-171	156	5	)	)	PUNCT
ma-171	156	6	of	of	ADP
ma-171	156	7	system	system	NOUN
ma-171	156	8	(	(	PUNCT
ma-171	156	9	2	2	X
ma-171	156	10	)	)	PUNCT
ma-171	156	11	is	be	AUX
ma-171	156	12	locally	locally	ADV
ma-171	156	13	asymptotically	asymptotically	ADV
ma-171	156	14	stable	stable	ADJ
ma-171	156	15	if	if	SCONJ
ma-171	156	16	r0	r0	NOUN
ma-171	156	17	>	>	X
ma-171	156	18	1	1	X
ma-171	156	19	.	.	PUNCT
ma-171	156	20	proof	proof	NOUN
ma-171	156	21	.	.	PUNCT
ma-171	157	1	the	the	DET
ma-171	157	2	jacobian	jacobian	ADJ
ma-171	157	3	matrix	matrix	NOUN
ma-171	157	4	of	of	ADP
ma-171	157	5	the	the	DET
ma-171	157	6	system	system	NOUN
ma-171	157	7	(	(	PUNCT
ma-171	157	8	2	2	X
ma-171	157	9	)	)	PUNCT
ma-171	157	10	evaluated	evaluate	VERB
ma-171	157	11	at	at	ADP
ma-171	157	12	endemic	endemic	ADJ
ma-171	157	13	equilibrium	equilibrium	NOUN
ma-171	157	14	is	be	AUX
ma-171	157	15	j(e1	j(e1	NOUN
ma-171	157	16	)	)	PUNCT
ma-171	158	1	=	=	SYM
ma-171	158	2			NOUN
ma-171	158	3	−b1	−b1	NOUN
ma-171	158	4	0	0	NUM
ma-171	159	1	−b2	−b2	ADJ
ma-171	159	2	−b3	−b3	NOUN
ma-171	159	3	0	0	NUM
ma-171	159	4	0	0	NUM
ma-171	159	5	−b4	−b4	PROPN
ma-171	159	6	−b5	−b5	PROPN
ma-171	159	7	−b6	−b6	PROPN
ma-171	159	8	0	0	NUM
ma-171	159	9	b7	b7	PROPN
ma-171	159	10	b8	b8	PROPN
ma-171	159	11	b9	b9	PROPN
ma-171	159	12	−q1	−q1	PROPN
ma-171	159	13	b10	b10	PROPN
ma-171	159	14	0	0	NUM
ma-171	159	15	0	0	NUM
ma-171	159	16	0	0	NUM
ma-171	160	1	α	α	PRON
ma-171	160	2	−q2	−q2	NOUN
ma-171	160	3	0	0	NUM
ma-171	160	4	0	0	NUM
ma-171	160	5	0	0	NUM
ma-171	161	1	γ2	γ2	PROPN
ma-171	161	2	γ3	γ3	NOUN
ma-171	161	3	−q3	−q3	PROPN
ma-171	161	4			PROPN
ma-171	161	5	where	where	SCONJ
ma-171	161	6	b1	b1	NOUN
ma-171	161	7	=	=	SYM
ma-171	161	8	(	(	PUNCT
ma-171	161	9	1−φ1)(1−φ2)(β1q2+β2α)µi∗∗+q2µλ	1−φ1)(1−φ2)(β1q2+β2α)µi∗∗+q2µλ	PROPN
ma-171	161	10	q2λ	q2λ	PROPN
ma-171	161	11	,	,	PUNCT
ma-171	161	12	b2	b2	NOUN
ma-171	161	13	=	=	SYM
ma-171	161	14	(	(	PUNCT
ma-171	161	15	1−φ1)(1−φ2)β1a1δλi∗∗	1−φ1)(1−φ2)β1a1δλi∗∗	NUM
ma-171	161	16	a1i∗∗+λ	a1i∗∗+λ	PROPN
ma-171	161	17	,	,	PUNCT
ma-171	161	18	b3	b3	PROPN
ma-171	161	19	=	=	SYM
ma-171	161	20	(	(	PUNCT
ma-171	161	21	1−φ1)(1−φ2)β2a1δλi∗∗	1−φ1)(1−φ2)β2a1δλi∗∗	NUM
ma-171	161	22	a1i∗∗+λ	a1i∗∗+λ	PROPN
ma-171	161	23	b4	b4	NOUN
ma-171	161	24	=	=	SYM
ma-171	161	25	(	(	PUNCT
ma-171	161	26	1−φ2)(β1q2+β2α)µi∗∗+q2µλ	1−φ2)(β1q2+β2α)µi∗∗+q2µλ	NUM
ma-171	161	27	q2λ	q2λ	PROPN
ma-171	161	28	,	,	PUNCT
ma-171	161	29	b5	b5	PROPN
ma-171	161	30	=	=	PUNCT
ma-171	161	31	(	(	PUNCT
ma-171	161	32	1−φ2)(1−δ)λβ1a2i	1−φ2)(1−δ)λβ1a2i	NUM
ma-171	161	33	∗∗	∗∗	X
ma-171	161	34	a2i∗∗+λ	a2i∗∗+λ	PROPN
ma-171	161	35	,	,	PUNCT
ma-171	161	36	b6	b6	NOUN
ma-171	161	37	=	=	SYM
ma-171	161	38	(	(	PUNCT
ma-171	161	39	1−φ2)(1−δ)λβ2a2i	1−φ2)(1−δ)λβ2a2i	NUM
ma-171	161	40	∗∗	∗∗	PROPN
ma-171	162	1	a2i∗∗+λ	a2i∗∗+λ	PROPN
ma-171	162	2	b7	b7	PROPN
ma-171	162	3	=	=	PROPN
ma-171	162	4	(	(	PUNCT
ma-171	162	5	1−φ1)(1−φ2)(β1q2+β2α)µi∗∗+q2µλ	1−φ1)(1−φ2)(β1q2+β2α)µi∗∗+q2µλ	PROPN
ma-171	162	6	q2λ	q2λ	PROPN
ma-171	162	7	,	,	PUNCT
ma-171	162	8	b8	b8	PROPN
ma-171	162	9	=	=	SYM
ma-171	162	10	(	(	PUNCT
ma-171	162	11	1−φ2)(β1q2+β2α)µi∗∗+q2µλ	1−φ2)(β1q2+β2α)µi∗∗+q2µλ	NUM
ma-171	162	12	q2λ	q2λ	PROPN
ma-171	162	13	b9	b9	PROPN
ma-171	162	14	=	=	PUNCT
ma-171	162	15	(	(	PUNCT
ma-171	162	16	1−φ1)(1−φ2)β1a1δλi∗∗	1−φ1)(1−φ2)β1a1δλi∗∗	NUM
ma-171	162	17	a1i∗∗+λ	a1i∗∗+λ	PROPN
ma-171	162	18	+	+	CCONJ
ma-171	162	19	(	(	PUNCT
ma-171	162	20	1−φ2)(1−δ)λβ1a2i	1−φ2)(1−δ)λβ1a2i	NUM
ma-171	162	21	∗∗	∗∗	X
ma-171	163	1	a2i∗∗+λ	a2i∗∗+λ	PROPN
ma-171	163	2	,	,	PUNCT
ma-171	163	3	b10	b10	PROPN
ma-171	163	4	=	=	SYM
ma-171	163	5	(	(	PUNCT
ma-171	163	6	1−φ1)(1−φ2)β2a1δλi∗∗	1−φ1)(1−φ2)β2a1δλi∗∗	NUM
ma-171	163	7	a1i∗∗+λ	a1i∗∗+λ	PROPN
ma-171	163	8	+	+	CCONJ
ma-171	163	9	(	(	PUNCT
ma-171	163	10	1−φ2)(1−δ)λβ2a2i	1−φ2)(1−δ)λβ2a2i	NUM
ma-171	163	11	∗∗	∗∗	X
ma-171	163	12	a2i∗∗+λclearly	a2i∗∗+λclearly	ADV
ma-171	163	13	,	,	PUNCT
ma-171	163	14	−q3	−q3	PROPN
ma-171	163	15	is	be	AUX
ma-171	163	16	an	an	DET
ma-171	163	17	eigenvalue	eigenvalue	NOUN
ma-171	163	18	of	of	ADP
ma-171	163	19	the	the	DET
ma-171	163	20	jacobian	jacobian	ADJ
ma-171	163	21	matrix	matrix	NOUN
ma-171	163	22	j(e1	j(e1	NOUN
ma-171	163	23	)	)	PUNCT
ma-171	163	24	.	.	PUNCT
ma-171	164	1	the	the	DET
ma-171	164	2	other	other	ADJ
ma-171	164	3	eigenvalues	eigenvalue	NOUN
ma-171	164	4	can	can	AUX
ma-171	164	5	be	be	AUX
ma-171	164	6	computedby	computedby	NOUN
ma-171	164	7	finding	find	VERB
ma-171	164	8	the	the	DET
ma-171	164	9	solution	solution	NOUN
ma-171	164	10	to	to	ADP
ma-171	164	11	the	the	DET
ma-171	164	12	equation	equation	NOUN
ma-171	164	13	p	p	X
ma-171	164	14	(	(	PUNCT
ma-171	164	15	λ	λ	NOUN
ma-171	164	16	)	)	PUNCT
ma-171	164	17	=	=	SYM
ma-171	164	18	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ma-171	164	19	λ+	λ+	NUM
ma-171	164	20	b1	b1	NOUN
ma-171	164	21	0	0	NUM
ma-171	165	1	−b2	−b2	ADJ
ma-171	165	2	−b3	−b3	PROPN
ma-171	165	3	0	0	NUM
ma-171	165	4	λ+	λ+	PUNCT
ma-171	165	5	b4	b4	NOUN
ma-171	165	6	−b5	−b5	PROPN
ma-171	165	7	−b6	−b6	PROPN
ma-171	165	8	b7	b7	PROPN
ma-171	165	9	b8	b8	PROPN
ma-171	165	10	λ−	λ−	PROPN
ma-171	165	11	(	(	PUNCT
ma-171	165	12	b9	b9	PROPN
ma-171	165	13	+	+	PROPN
ma-171	165	14	q1	q1	PROPN
ma-171	165	15	)	)	PUNCT
ma-171	165	16	b10	b10	PROPN
ma-171	165	17	0	0	NUM
ma-171	165	18	0	0	NUM
ma-171	166	1	α	α	PRON
ma-171	166	2	λ+q2	λ+q2	NOUN
ma-171	166	3	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ma-171	167	1	=	=	SYM
ma-171	167	2	0	0	PROPN
ma-171	167	3	the	the	DET
ma-171	167	4	characteristic	characteristic	ADJ
ma-171	167	5	equation	equation	NOUN
ma-171	167	6	of	of	ADP
ma-171	167	7	j(e1)is	j(e1)is	NOUN
ma-171	167	8	then	then	ADV
ma-171	167	9	given	give	VERB
ma-171	167	10	by	by	ADP
ma-171	167	11	;	;	PUNCT
ma-171	167	12	p	p	X
ma-171	167	13	(	(	PUNCT
ma-171	167	14	λ	λ	NOUN
ma-171	167	15	)	)	PUNCT
ma-171	167	16	=	=	VERB
ma-171	167	17	λ4	λ4	PROPN
ma-171	167	18	+	+	CCONJ
ma-171	167	19	c0λ	c0λ	ADJ
ma-171	167	20	3	3	X
ma-171	167	21	+	+	CCONJ
ma-171	167	22	c1λ	c1λ	PROPN
ma-171	167	23	2	2	NUM
ma-171	167	24	+	+	CCONJ
ma-171	167	25	c2λ+	c2λ+	ADJ
ma-171	167	26	c3	c3	X
ma-171	167	27	=	=	SYM
ma-171	167	28	0	0	NUM
ma-171	167	29	(	(	PUNCT
ma-171	167	30	14	14	NUM
ma-171	167	31	)	)	PUNCT
ma-171	167	32	where	where	SCONJ
ma-171	167	33	;	;	PUNCT
ma-171	167	34	c0	c0	PROPN
ma-171	167	35	=	=	SYM
ma-171	167	36	b1	b1	PROPN
ma-171	167	37	+	+	CCONJ
ma-171	167	38	b4	b4	PROPN
ma-171	167	39	−	−	PROPN
ma-171	167	40	b9	b9	PROPN
ma-171	167	41	−q1	−q1	PROPN
ma-171	167	42	+	+	PROPN
ma-171	167	43	q2	q2	PROPN
ma-171	167	44	c1	c1	NOUN
ma-171	167	45	=	=	PUNCT
ma-171	168	1	b1b4	b1b4	X
ma-171	169	1	+	+	CCONJ
ma-171	169	2	b2b7	b2b7	X
ma-171	169	3	+	+	NUM
ma-171	169	4	b5b8	b5b8	NOUN
ma-171	169	5	−	−	NOUN
ma-171	169	6	b1b9	b1b9	NOUN
ma-171	170	1	−	−	NOUN
ma-171	170	2	b4b9	b4b9	ADP
ma-171	171	1	−	−	PROPN
ma-171	171	2	αb10	αb10	PROPN
ma-171	171	3	−	−	NOUN
ma-171	171	4	b1q1	b1q1	NOUN
ma-171	171	5	−	−	PROPN
ma-171	172	1	b4q1	b4q1	PROPN
ma-171	172	2	+	+	CCONJ
ma-171	172	3	b1q2	b1q2	PROPN
ma-171	172	4	+	+	ADP
ma-171	172	5	b4q2	b4q2	ADP
ma-171	172	6	−	−	NOUN
ma-171	172	7	b9q2	b9q2	PUNCT
ma-171	172	8	−q1q2	−q1q2	NOUN
ma-171	172	9	c2	c2	PROPN
ma-171	172	10	=	=	PUNCT
ma-171	172	11	−αb3b7	−αb3b7	PROPN
ma-171	172	12	+	+	X
ma-171	172	13	b2b4b7	b2b4b7	ADJ
ma-171	172	14	+	+	VERB
ma-171	172	15	b1b5b8−αb6b8−b1b4b9−alphab1b10−alphab4b10−b1b4q1	b1b5b8−αb6b8−b1b4b9−alphab1b10−alphab4b10−b1b4q1	PUNCT
ma-171	172	16	+	+	NOUN
ma-171	172	17	b1b4q2	b1b4q2	NOUN
ma-171	172	18	+	+	CCONJ
ma-171	172	19	b2b7q2	b2b7q2	PRON
ma-171	172	20	+	+	CCONJ
ma-171	172	21	b5b8q2	b5b8q2	ADJ
ma-171	172	22	−	−	PROPN
ma-171	172	23	b1b9q2	b1b9q2	NOUN
ma-171	172	24	−	−	NOUN
ma-171	172	25	b4b9q2	b4b9q2	ADJ
ma-171	172	26	−	−	PROPN
ma-171	172	27	b1q1q2	b1q1q2	NOUN
ma-171	172	28	−	−	PROPN
ma-171	172	29	b4q1q2	b4q1q2	PROPN
ma-171	172	30	c3	c3	NOUN
ma-171	172	31	=	=	PROPN
ma-171	173	1	−αb3b4b7	−αb3b4b7	NUM
ma-171	173	2	−	−	PROPN
ma-171	174	1	αb1b6b8	αb1b6b8	NUM
ma-171	174	2	−	−	PROPN
ma-171	174	3	αb1b4b10	αb1b4b10	PROPN
ma-171	174	4	+	+	NUM
ma-171	174	5	b2b4b7q2	b2b4b7q2	PROPN
ma-171	174	6	+	+	CCONJ
ma-171	174	7	b1b5b8q2	b1b5b8q2	PROPN
ma-171	174	8	−	−	PROPN
ma-171	174	9	b1b4b9q2	b1b4b9q2	VERB
ma-171	174	10	−	−	NOUN
ma-171	174	11	b1b4q1q2the	b1b4q1q2the	DET
ma-171	174	12	number	number	NOUN
ma-171	174	13	of	of	ADP
ma-171	174	14	negative	negative	ADJ
ma-171	174	15	zeros	zero	NOUN
ma-171	174	16	of	of	ADP
ma-171	174	17	equation	equation	NOUN
ma-171	174	18	(	(	PUNCT
ma-171	174	19	14	14	NUM
ma-171	174	20	)	)	PUNCT
ma-171	174	21	depends	depend	VERB
ma-171	174	22	on	on	ADP
ma-171	174	23	the	the	DET
ma-171	174	24	signs	sign	NOUN
ma-171	174	25	of	of	ADP
ma-171	174	26	c0	c0	NOUN
ma-171	174	27	,	,	PUNCT
ma-171	174	28	c1	c1	PROPN
ma-171	174	29	,	,	PUNCT
ma-171	174	30	c2	c2	PROPN
ma-171	174	31	and	and	CCONJ
ma-171	174	32	c3	c3	PROPN
ma-171	174	33	.	.	PUNCT
ma-171	175	1	descarte	descarte	PROPN
ma-171	175	2	’s	’s	PART
ma-171	175	3	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	175	4	eur	eur	PROPN
ma-171	175	5	.	.	PUNCT
ma-171	176	1	j.	j.	PROPN
ma-171	176	2	math	math	PROPN
ma-171	176	3	.	.	PUNCT
ma-171	177	1	anal	anal	PROPN
ma-171	177	2	.	.	PUNCT
ma-171	178	1	10.28924	10.28924	NUM
ma-171	178	2	/	/	SYM
ma-171	178	3	ada	ada	PROPN
ma-171	178	4	/	/	SYM
ma-171	178	5	ma.3.21	ma.3.21	PROPN
ma-171	178	6	9rule	9rule	PROPN
ma-171	178	7	of	of	ADP
ma-171	178	8	signs	sign	NOUN
ma-171	178	9	is	be	AUX
ma-171	178	10	applied	apply	VERB
ma-171	178	11	to	to	PART
ma-171	178	12	study	study	VERB
ma-171	178	13	the	the	DET
ma-171	178	14	number	number	NOUN
ma-171	178	15	of	of	ADP
ma-171	178	16	negative	negative	ADJ
ma-171	178	17	real	real	ADJ
ma-171	178	18	roots	root	NOUN
ma-171	178	19	of	of	ADP
ma-171	178	20	the	the	DET
ma-171	178	21	polynomialp	polynomialp	NOUN
ma-171	178	22	(	(	PUNCT
ma-171	178	23	λ1	λ1	PROPN
ma-171	178	24	)	)	PUNCT
ma-171	178	25	com	com	NOUN
ma-171	178	26	-	-	PUNCT
ma-171	178	27	prising	prising	NOUN
ma-171	178	28	of	of	ADP
ma-171	178	29	the	the	DET
ma-171	178	30	coefficients	coefficient	NOUN
ma-171	178	31	c0	c0	PROPN
ma-171	178	32	,	,	PUNCT
ma-171	178	33	c1	c1	PROPN
ma-171	178	34	,	,	PUNCT
ma-171	178	35	c2	c2	PROPN
ma-171	178	36	and	and	CCONJ
ma-171	178	37	c3	c3	PROPN
ma-171	178	38	given	give	VERB
ma-171	178	39	by	by	ADP
ma-171	178	40	;	;	PUNCT
ma-171	178	41	p	p	X
ma-171	178	42	(	(	PUNCT
ma-171	178	43	λ1	λ1	PROPN
ma-171	178	44	)	)	PUNCT
ma-171	178	45	=	=	SYM
ma-171	178	46	c0λ	c0λ	X
ma-171	178	47	3	3	NUM
ma-171	178	48	+	+	CCONJ
ma-171	178	49	c1λ	c1λ	PROPN
ma-171	178	50	2	2	NUM
ma-171	178	51	+	+	CCONJ
ma-171	178	52	c2λ+	c2λ+	ADJ
ma-171	178	53	c3	c3	X
ma-171	178	54	=	=	SYM
ma-171	178	55	0	0	NUM
ma-171	178	56	(	(	PUNCT
ma-171	178	57	15	15	NUM
ma-171	178	58	)	)	PUNCT
ma-171	178	59	descarte	descarte	NOUN
ma-171	178	60	’s	’s	PART
ma-171	178	61	rule	rule	NOUN
ma-171	178	62	of	of	ADP
ma-171	178	63	signs	sign	NOUN
ma-171	178	64	states	state	VERB
ma-171	178	65	that	that	SCONJ
ma-171	178	66	the	the	DET
ma-171	178	67	number	number	NOUN
ma-171	178	68	of	of	ADP
ma-171	178	69	negative	negative	ADJ
ma-171	178	70	real	real	ADJ
ma-171	178	71	zeros	zero	NOUN
ma-171	178	72	of	of	ADP
ma-171	178	73	p	p	PROPN
ma-171	178	74	(	(	PUNCT
ma-171	178	75	λ	λ	NOUN
ma-171	178	76	)	)	PUNCT
ma-171	178	77	is	be	AUX
ma-171	178	78	either	either	CCONJ
ma-171	178	79	equal	equal	ADJ
ma-171	178	80	tothe	tothe	ADJ
ma-171	178	81	variations	variation	NOUN
ma-171	178	82	in	in	ADP
ma-171	178	83	sign	sign	NOUN
ma-171	178	84	of	of	ADP
ma-171	178	85	p	p	X
ma-171	178	86	(	(	PUNCT
ma-171	178	87	−λ	−λ	NOUN
ma-171	178	88	)	)	PUNCT
ma-171	178	89	or	or	CCONJ
ma-171	178	90	less	less	ADJ
ma-171	178	91	than	than	ADP
ma-171	178	92	this	this	PRON
ma-171	178	93	by	by	ADP
ma-171	178	94	an	an	DET
ma-171	178	95	even	even	ADJ
ma-171	178	96	number	number	NOUN
ma-171	178	97	[	[	X
ma-171	178	98	15	15	NUM
ma-171	178	99	]	]	PUNCT
ma-171	178	100	.	.	PUNCT
ma-171	179	1	the	the	DET
ma-171	179	2	possibilities	possibility	NOUN
ma-171	179	3	ofnegative	ofnegative	VERB
ma-171	179	4	real	real	ADJ
ma-171	179	5	zeros	zero	NOUN
ma-171	179	6	of	of	ADP
ma-171	179	7	p	p	PROPN
ma-171	179	8	(	(	PUNCT
ma-171	179	9	λ	λ	NOUN
ma-171	179	10	)	)	PUNCT
ma-171	179	11	,	,	PUNCT
ma-171	179	12	is	be	AUX
ma-171	179	13	as	as	SCONJ
ma-171	179	14	summarized	summarize	VERB
ma-171	179	15	in	in	ADP
ma-171	179	16	table	table	NOUN
ma-171	179	17	2	2	NUM
ma-171	179	18	.	.	PUNCT
ma-171	180	1	the	the	DET
ma-171	180	2	maximum	maximum	ADJ
ma-171	180	3	number	number	NOUN
ma-171	180	4	of	of	ADP
ma-171	180	5	variationsof	variationsof	NOUN
ma-171	180	6	signs	sign	NOUN
ma-171	180	7	in	in	ADP
ma-171	180	8	p	p	PROPN
ma-171	180	9	(	(	PUNCT
ma-171	180	10	−λ	−λ	NOUN
ma-171	180	11	)	)	PUNCT
ma-171	180	12	is	be	AUX
ma-171	180	13	3	3	NUM
ma-171	180	14	,	,	PUNCT
ma-171	180	15	hence	hence	ADV
ma-171	180	16	the	the	DET
ma-171	180	17	characteristic	characteristic	ADJ
ma-171	180	18	polynomial	polynomial	NOUN
ma-171	180	19	(	(	PUNCT
ma-171	180	20	15	15	NUM
ma-171	180	21	)	)	PUNCT
ma-171	180	22	has	have	VERB
ma-171	180	23	three	three	NUM
ma-171	180	24	negative	negative	ADJ
ma-171	180	25	roots	root	NOUN
ma-171	180	26	.	.	PUNCT
ma-171	181	1	thus	thus	ADV
ma-171	181	2	p	p	X
ma-171	181	3	(	(	PUNCT
ma-171	181	4	−λ	−λ	NOUN
ma-171	181	5	)	)	PUNCT
ma-171	181	6	=	=	VERB
ma-171	182	1	λ4	λ4	ADJ
ma-171	182	2	−	−	PROPN
ma-171	182	3	c0λ	c0λ	ADJ
ma-171	182	4	3	3	NUM
ma-171	182	5	+	+	CCONJ
ma-171	182	6	c1λ	c1λ	PROPN
ma-171	182	7	2	2	NUM
ma-171	182	8	−	−	PROPN
ma-171	182	9	c2λ	c2λ	NOUN
ma-171	182	10	+	+	CCONJ
ma-171	182	11	c3	c3	X
ma-171	182	12	=	=	SYM
ma-171	182	13	0	0	PROPN
ma-171	182	14	has	have	VERB
ma-171	182	15	negative	negative	ADJ
ma-171	182	16	roots.therefore	roots.therefore	NOUN
ma-171	182	17	,	,	PUNCT
ma-171	182	18	given	give	VERB
ma-171	182	19	that	that	SCONJ
ma-171	182	20	cases	case	NOUN
ma-171	182	21	1	1	NUM
ma-171	182	22	-	-	SYM
ma-171	182	23	8	8	NUM
ma-171	182	24	intable	intable	ADJ
ma-171	182	25	1	1	NUM
ma-171	182	26	are	be	AUX
ma-171	182	27	satisfied	satisfied	ADJ
ma-171	182	28	,	,	PUNCT
ma-171	182	29	model	model	NOUN
ma-171	182	30	(	(	PUNCT
ma-171	182	31	2	2	NUM
ma-171	182	32	)	)	PUNCT
ma-171	182	33	is	be	AUX
ma-171	182	34	locally	locally	ADV
ma-171	182	35	asymptotically	asymptotically	ADV
ma-171	182	36	stable	stable	ADJ
ma-171	182	37	if	if	SCONJ
ma-171	182	38	r0	r0	NOUN
ma-171	182	39	>	>	X
ma-171	182	40	1	1	X
ma-171	182	41	.	.	X
ma-171	182	42	�	�	PROPN
ma-171	182	43	table	table	NOUN
ma-171	182	44	2	2	NUM
ma-171	182	45	.	.	PUNCT
ma-171	183	1	the	the	DET
ma-171	183	2	zeros	zero	NOUN
ma-171	183	3	of	of	ADP
ma-171	183	4	the	the	DET
ma-171	183	5	characteristic	characteristic	ADJ
ma-171	183	6	equation	equation	NOUN
ma-171	183	7	(	(	PUNCT
ma-171	183	8	14	14	NUM
ma-171	183	9	)	)	PUNCT
ma-171	183	10	cases	case	NOUN
ma-171	183	11	c0	c0	PROPN
ma-171	183	12	c1	c1	PROPN
ma-171	183	13	c2	c2	PROPN
ma-171	183	14	c3	c3	PROPN
ma-171	183	15	r0	r0	PROPN
ma-171	183	16	>	>	X
ma-171	183	17	1	1	NUM
ma-171	183	18	sign	sign	NOUN
ma-171	183	19	change	change	NOUN
ma-171	183	20	no	no	INTJ
ma-171	183	21	.	.	PUNCT
ma-171	183	22	of	of	ADP
ma-171	183	23	roots1	roots1	NOUN
ma-171	183	24	+	+	CCONJ
ma-171	183	25	−	−	PROPN
ma-171	183	26	−	−	NOUN
ma-171	184	1	+	+	CCONJ
ma-171	184	2	r0	r0	NOUN
ma-171	184	3	>	>	X
ma-171	184	4	1	1	NUM
ma-171	184	5	2	2	NUM
ma-171	184	6	2,02	2,02	NUM
ma-171	184	7	+	+	CCONJ
ma-171	184	8	−	−	PROPN
ma-171	185	1	+	+	CCONJ
ma-171	185	2	+	+	NUM
ma-171	185	3	r0	r0	NOUN
ma-171	185	4	>	>	X
ma-171	185	5	1	1	NUM
ma-171	185	6	2	2	NUM
ma-171	185	7	2,03	2,03	NUM
ma-171	185	8	−	−	NOUN
ma-171	185	9	−	−	PROPN
ma-171	186	1	+	+	CCONJ
ma-171	186	2	−	−	PROPN
ma-171	186	3	r0	r0	NOUN
ma-171	186	4	>	>	X
ma-171	186	5	1	1	NUM
ma-171	186	6	2	2	NUM
ma-171	186	7	2,04	2,04	NUM
ma-171	186	8	+	+	CCONJ
ma-171	186	9	+	+	CCONJ
ma-171	186	10	−	−	ADP
ma-171	186	11	−	−	NOUN
ma-171	186	12	r0	r0	NOUN
ma-171	186	13	>	>	X
ma-171	186	14	1	1	NUM
ma-171	186	15	1	1	NUM
ma-171	186	16	05	05	NUM
ma-171	186	17	−	−	NOUN
ma-171	186	18	−	−	PROPN
ma-171	187	1	+	+	CCONJ
ma-171	187	2	+	+	NUM
ma-171	187	3	r0	r0	NOUN
ma-171	187	4	>	>	X
ma-171	187	5	1	1	NUM
ma-171	187	6	1	1	NUM
ma-171	187	7	06	06	NUM
ma-171	188	1	+	+	CCONJ
ma-171	188	2	+	+	PUNCT
ma-171	188	3	+	+	CCONJ
ma-171	188	4	−	−	PROPN
ma-171	188	5	r0	r0	NOUN
ma-171	188	6	>	>	X
ma-171	188	7	1	1	NUM
ma-171	188	8	1	1	NUM
ma-171	188	9	07	07	NUM
ma-171	188	10	−	−	NOUN
ma-171	188	11	+	+	CCONJ
ma-171	188	12	−	−	PROPN
ma-171	189	1	+	+	CCONJ
ma-171	189	2	r0	r0	NOUN
ma-171	189	3	>	>	X
ma-171	189	4	1	1	NUM
ma-171	189	5	3	3	NUM
ma-171	189	6	3,18	3,18	NUM
ma-171	189	7	−	−	ADP
ma-171	189	8	−	−	NOUN
ma-171	189	9	−	−	PROPN
ma-171	189	10	−	−	PROPN
ma-171	189	11	r0	r0	NOUN
ma-171	189	12	>	>	X
ma-171	189	13	1	1	NUM
ma-171	189	14	0	0	NUM
ma-171	189	15	0	0	NUM
ma-171	189	16	this	this	PRON
ma-171	189	17	implies	imply	VERB
ma-171	189	18	that	that	SCONJ
ma-171	189	19	for	for	ADP
ma-171	189	20	a	a	DET
ma-171	189	21	small	small	ADJ
ma-171	189	22	pertubation	pertubation	NOUN
ma-171	189	23	of	of	ADP
ma-171	189	24	the	the	DET
ma-171	189	25	e1	e1	NOUN
ma-171	189	26	,	,	PUNCT
ma-171	189	27	solutions	solution	NOUN
ma-171	189	28	of	of	ADP
ma-171	189	29	the	the	DET
ma-171	189	30	mathematical	mathematical	ADJ
ma-171	189	31	model	model	NOUN
ma-171	189	32	representedby	representedby	VERB
ma-171	189	33	the	the	DET
ma-171	189	34	system	system	NOUN
ma-171	189	35	(	(	PUNCT
ma-171	189	36	2	2	X
ma-171	189	37	)	)	PUNCT
ma-171	189	38	always	always	ADV
ma-171	189	39	converge	converge	VERB
ma-171	189	40	to	to	ADP
ma-171	189	41	e1	e1	NOUN
ma-171	189	42	,	,	PUNCT
ma-171	189	43	whenever	whenever	SCONJ
ma-171	189	44	r0	r0	NOUN
ma-171	189	45	>	>	X
ma-171	189	46	1	1	X
ma-171	189	47	.	.	PUNCT
ma-171	189	48	epidemiologically	epidemiologically	NOUN
ma-171	189	49	,	,	PUNCT
ma-171	189	50	it	it	PRON
ma-171	189	51	implies	imply	VERB
ma-171	189	52	that	that	SCONJ
ma-171	189	53	ifa	ifa	PROPN
ma-171	189	54	few	few	ADJ
ma-171	189	55	hiv	hiv	PROPN
ma-171	189	56	infected	infect	VERB
ma-171	189	57	individuals	individual	NOUN
ma-171	189	58	are	be	AUX
ma-171	189	59	introduces	introduce	NOUN
ma-171	189	60	in	in	ADP
ma-171	189	61	a	a	DET
ma-171	189	62	fully	fully	ADV
ma-171	189	63	susceptible	susceptible	ADJ
ma-171	189	64	population	population	NOUN
ma-171	189	65	,	,	PUNCT
ma-171	189	66	the	the	DET
ma-171	189	67	disease	disease	NOUN
ma-171	189	68	willpersist	willpersist	NOUN
ma-171	189	69	provided	provide	VERB
ma-171	189	70	r0	r0	PROPN
ma-171	189	71	>	>	X
ma-171	190	1	1	1	NUM
ma-171	190	2	.	.	NOUN
ma-171	191	1	4	4	NUM
ma-171	191	2	.	.	NOUN
ma-171	191	3	sensitivity	sensitivity	NOUN
ma-171	191	4	analysis	analysis	NOUN
ma-171	191	5	in	in	ADP
ma-171	191	6	mathematical	mathematical	ADJ
ma-171	191	7	modeling	modeling	NOUN
ma-171	191	8	,	,	PUNCT
ma-171	191	9	sensitivity	sensitivity	NOUN
ma-171	191	10	refers	refer	VERB
ma-171	191	11	to	to	ADP
ma-171	191	12	the	the	DET
ma-171	191	13	degree	degree	NOUN
ma-171	191	14	to	to	PART
ma-171	191	15	which	which	PRON
ma-171	191	16	a	a	DET
ma-171	191	17	given	give	VERB
ma-171	191	18	input	input	NOUN
ma-171	191	19	parameterin	parameterin	PROPN
ma-171	191	20	a	a	DET
ma-171	191	21	mathematical	mathematical	ADJ
ma-171	191	22	model	model	NOUN
ma-171	191	23	influences	influence	VERB
ma-171	191	24	its	its	PRON
ma-171	191	25	output	output	NOUN
ma-171	191	26	.	.	PUNCT
ma-171	192	1	sensitive	sensitive	ADJ
ma-171	192	2	parameters	parameter	NOUN
ma-171	192	3	are	be	AUX
ma-171	192	4	thus	thus	ADV
ma-171	192	5	those	those	PRON
ma-171	192	6	that	that	PRON
ma-171	192	7	cause	cause	VERB
ma-171	192	8	asignificant	asignificant	ADJ
ma-171	192	9	impact	impact	NOUN
ma-171	192	10	on	on	ADP
ma-171	192	11	the	the	DET
ma-171	192	12	disease	disease	NOUN
ma-171	192	13	transmission	transmission	NOUN
ma-171	192	14	dynamics	dynamic	NOUN
ma-171	192	15	.	.	PUNCT
ma-171	193	1	sensitivity	sensitivity	NOUN
ma-171	193	2	analysis	analysis	NOUN
ma-171	193	3	will	will	AUX
ma-171	193	4	aid	aid	VERB
ma-171	193	5	in	in	ADP
ma-171	193	6	identify	identify	VERB
ma-171	193	7	-	-	PUNCT
ma-171	193	8	ing	e	VERB
ma-171	193	9	the	the	DET
ma-171	193	10	parameters	parameter	NOUN
ma-171	193	11	which	which	PRON
ma-171	193	12	greatly	greatly	ADV
ma-171	193	13	impact	impact	VERB
ma-171	193	14	on	on	ADP
ma-171	193	15	the	the	DET
ma-171	193	16	value	value	NOUN
ma-171	193	17	of	of	ADP
ma-171	193	18	the	the	DET
ma-171	193	19	basic	basic	ADJ
ma-171	193	20	reproductive	reproductive	ADJ
ma-171	193	21	number	number	NOUN
ma-171	193	22	r0	r0	NOUN
ma-171	193	23	,	,	PUNCT
ma-171	193	24	andhence	andhence	NOUN
ma-171	193	25	ought	ought	AUX
ma-171	193	26	to	to	PART
ma-171	193	27	be	be	AUX
ma-171	193	28	targeted	target	VERB
ma-171	193	29	when	when	SCONJ
ma-171	193	30	coming	come	VERB
ma-171	193	31	up	up	ADP
ma-171	193	32	with	with	ADP
ma-171	193	33	intervention	intervention	NOUN
ma-171	193	34	strategies	strategy	NOUN
ma-171	193	35	.	.	PUNCT
ma-171	194	1	the	the	DET
ma-171	194	2	sensitivity	sensitivity	NOUN
ma-171	194	3	of	of	ADP
ma-171	194	4	modelparameters	modelparameter	NOUN
ma-171	194	5	is	be	AUX
ma-171	194	6	calculated	calculate	VERB
ma-171	194	7	using	use	VERB
ma-171	194	8	the	the	DET
ma-171	194	9	normalized	normalize	VERB
ma-171	194	10	forward	forward	ADJ
ma-171	194	11	sensitivity	sensitivity	NOUN
ma-171	194	12	index	index	NOUN
ma-171	194	13	.	.	PUNCT
ma-171	195	1	the	the	DET
ma-171	195	2	normalized	normalize	VERB
ma-171	195	3	forwardsensitivity	forwardsensitivity	NOUN
ma-171	195	4	index	index	NOUN
ma-171	195	5	of	of	ADP
ma-171	195	6	the	the	DET
ma-171	195	7	basic	basic	ADJ
ma-171	195	8	reproductive	reproductive	ADJ
ma-171	195	9	number	number	NOUN
ma-171	195	10	is	be	AUX
ma-171	195	11	given	give	VERB
ma-171	195	12	by	by	ADP
ma-171	195	13	sr0	sr0	NOUN
ma-171	195	14	w	w	NOUN
ma-171	195	15	=	=	PUNCT
ma-171	196	1	∂r0	∂r0	PROPN
ma-171	196	2	∂w	∂w	PROPN
ma-171	196	3	×	×	NOUN
ma-171	196	4	w	w	NOUN
ma-171	196	5	r0	r0	NOUN
ma-171	196	6	,	,	PUNCT
ma-171	196	7	where	where	SCONJ
ma-171	196	8	w	w	NOUN
ma-171	196	9	is	be	AUX
ma-171	196	10	the	the	DET
ma-171	196	11	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	196	12	eur	eur	NOUN
ma-171	196	13	.	.	PUNCT
ma-171	197	1	j.	j.	PROPN
ma-171	197	2	math	math	PROPN
ma-171	197	3	.	.	PUNCT
ma-171	198	1	anal	anal	PROPN
ma-171	198	2	.	.	PUNCT
ma-171	199	1	10.28924	10.28924	NUM
ma-171	199	2	/	/	SYM
ma-171	199	3	ada	ada	PROPN
ma-171	199	4	/	/	SYM
ma-171	199	5	ma.3.21	ma.3.21	PROPN
ma-171	199	6	10parameter	10parameter	NUM
ma-171	199	7	whose	whose	DET
ma-171	199	8	sensitivity	sensitivity	NOUN
ma-171	199	9	is	be	AUX
ma-171	199	10	to	to	PART
ma-171	199	11	be	be	AUX
ma-171	199	12	determined	determine	VERB
ma-171	199	13	[	[	PUNCT
ma-171	199	14	7	7	NUM
ma-171	199	15	]	]	PUNCT
ma-171	199	16	.	.	PUNCT
ma-171	200	1	r0	r0	NOUN
ma-171	200	2	is	be	AUX
ma-171	200	3	given	give	VERB
ma-171	200	4	by	by	ADP
ma-171	200	5	r0	r0	NOUN
ma-171	200	6	=	=	SYM
ma-171	200	7	(	(	PUNCT
ma-171	200	8	1−	1−	NUM
ma-171	200	9	φ1)(1−	φ1)(1−	NOUN
ma-171	200	10	φ2)β1δ	φ2)β1δ	X
ma-171	200	11	+	+	CCONJ
ma-171	200	12	(	(	PUNCT
ma-171	200	13	1−	1−	NUM
ma-171	200	14	φ2)(1−	φ2)(1−	PROPN
ma-171	200	15	δ)β1	δ)β1	X
ma-171	200	16	α+	α+	X
ma-171	200	17	γ2	γ2	NOUN
ma-171	200	18	+	+	CCONJ
ma-171	200	19	µ	µ	X
ma-171	200	20	+	+	NUM
ma-171	200	21	α(1−	α(1−	ADJ
ma-171	200	22	φ1)(1−	φ1)(1−	NOUN
ma-171	200	23	φ2)β2δ	φ2)β2δ	NOUN
ma-171	200	24	+	+	CCONJ
ma-171	200	25	(	(	PUNCT
ma-171	200	26	1−	1−	NUM
ma-171	200	27	φ2)(1−	φ2)(1−	PROPN
ma-171	200	28	δ)β2	δ)β2	PROPN
ma-171	200	29	(	(	PUNCT
ma-171	200	30	α+	α+	X
ma-171	200	31	γ2	γ2	NOUN
ma-171	200	32	+	+	CCONJ
ma-171	200	33	µ)(γ3	µ)(γ3	NOUN
ma-171	200	34	+	+	CCONJ
ma-171	200	35	µ	µ	NOUN
ma-171	200	36	)	)	PUNCT
ma-171	200	37	.	.	PUNCT
ma-171	201	1	(	(	PUNCT
ma-171	201	2	16	16	NUM
ma-171	201	3	)	)	PUNCT
ma-171	201	4	forβ1	forβ1	NOUN
ma-171	201	5	,	,	PUNCT
ma-171	201	6	s	s	AUX
ma-171	201	7	r0	r0	NOUN
ma-171	201	8	β1	β1	NOUN
ma-171	201	9	=	=	PUNCT
ma-171	202	1	β1(γ3	β1(γ3	NOUN
ma-171	202	2	+	+	NOUN
ma-171	202	3	µ	µ	X
ma-171	202	4	)	)	PUNCT
ma-171	202	5	β1(γ3	β1(γ3	NOUN
ma-171	202	6	+	+	NOUN
ma-171	202	7	µ	µ	X
ma-171	202	8	)	)	PUNCT
ma-171	202	9	+	+	CCONJ
ma-171	202	10	αβ2	αβ2	ADJ
ma-171	202	11	.	.	PUNCT
ma-171	203	1	forβ2	forβ2	PROPN
ma-171	203	2	,	,	PUNCT
ma-171	203	3	s	s	PART
ma-171	203	4	r0	r0	NOUN
ma-171	203	5	β2	β2	NOUN
ma-171	203	6	=	=	SYM
ma-171	203	7	αβ2	αβ2	VERB
ma-171	203	8	β1(γ3	β1(γ3	NOUN
ma-171	203	9	+	+	NOUN
ma-171	203	10	µ	µ	X
ma-171	203	11	)	)	PUNCT
ma-171	204	1	+	+	CCONJ
ma-171	204	2	αβ2	αβ2	ADJ
ma-171	204	3	.	.	PUNCT
ma-171	205	1	for	for	ADP
ma-171	205	2	α	α	NOUN
ma-171	205	3	,	,	PUNCT
ma-171	205	4	sr0	sr0	NOUN
ma-171	205	5	α	α	NOUN
ma-171	205	6	=	=	PUNCT
ma-171	206	1	[	[	X
ma-171	206	2	β2(α+	β2(α+	PUNCT
ma-171	206	3	γ2	γ2	NOUN
ma-171	206	4	+	+	CCONJ
ma-171	206	5	µ)−	µ)−	NOUN
ma-171	206	6	(	(	PUNCT
ma-171	206	7	β1(γ3	β1(γ3	NOUN
ma-171	206	8	+	+	NOUN
ma-171	206	9	µ	µ	X
ma-171	206	10	)	)	PUNCT
ma-171	206	11	+	+	NUM
ma-171	206	12	αβ2)]α	αβ2)]α	NOUN
ma-171	206	13	(	(	PUNCT
ma-171	206	14	α+	α+	X
ma-171	206	15	γ2	γ2	NOUN
ma-171	206	16	+	+	CCONJ
ma-171	206	17	µ)(β1(γ3	µ)(β1(γ3	NOUN
ma-171	206	18	+	+	X
ma-171	206	19	µ	µ	X
ma-171	206	20	)	)	PUNCT
ma-171	206	21	+	+	CCONJ
ma-171	206	22	αβ2	αβ2	ADJ
ma-171	206	23	)	)	PUNCT
ma-171	206	24	.	.	PUNCT
ma-171	207	1	forγ2	forγ2	NOUN
ma-171	207	2	,	,	PUNCT
ma-171	207	3	s	s	VERB
ma-171	207	4	r0	r0	NOUN
ma-171	207	5	γ2	γ2	NOUN
ma-171	207	6	=	=	SYM
ma-171	207	7	(	(	PUNCT
ma-171	207	8	αγ2	αγ2	NOUN
ma-171	207	9	+	+	CCONJ
ma-171	207	10	γ2	γ2	PROPN
ma-171	207	11	2	2	NUM
ma-171	207	12	+	+	CCONJ
ma-171	207	13	µγ2	µγ2	NOUN
ma-171	207	14	)	)	PUNCT
ma-171	207	15	ln	ln	NOUN
ma-171	207	16	|α+	|α+	X
ma-171	207	17	γ2	γ2	PROPN
ma-171	207	18	+	+	CCONJ
ma-171	207	19	µ|	µ|	PROPN
ma-171	207	20	.	.	PUNCT
ma-171	208	1	forγ3	forγ3	PROPN
ma-171	208	2	,	,	PUNCT
ma-171	208	3	s	s	NOUN
ma-171	208	4	r0	r0	NOUN
ma-171	208	5	γ3	γ3	NOUN
ma-171	208	6	=	=	PUNCT
ma-171	208	7	−αβ2γ3	−αβ2γ3	NOUN
ma-171	208	8	(	(	PUNCT
ma-171	208	9	β1(γ3	β1(γ3	NOUN
ma-171	208	10	+	+	CCONJ
ma-171	208	11	µ)2	µ)2	NOUN
ma-171	208	12	+	+	CCONJ
ma-171	208	13	αβ2(γ3	αβ2(γ3	NUM
ma-171	208	14	+	+	SYM
ma-171	208	15	µ	µ	X
ma-171	208	16	)	)	PUNCT
ma-171	208	17	.	.	PUNCT
ma-171	209	1	for	for	ADP
ma-171	209	2	δ	δ	PROPN
ma-171	209	3	,	,	PUNCT
ma-171	209	4	sr0	sr0	NOUN
ma-171	209	5	δ	δ	NOUN
ma-171	209	6	=	=	SYM
ma-171	209	7	−φ1δ	−φ1δ	NUM
ma-171	209	8	1−	1−	NUM
ma-171	209	9	δφ1for	δφ1for	ADP
ma-171	209	10	µ	µ	NUM
ma-171	209	11	,	,	PUNCT
ma-171	209	12	sr0	sr0	NOUN
ma-171	209	13	µ	µ	NOUN
ma-171	209	14	=	=	SYM
ma-171	210	1	[	[	X
ma-171	210	2	(	(	PUNCT
ma-171	210	3	α+	α+	PUNCT
ma-171	210	4	γ2	γ2	NOUN
ma-171	210	5	+	+	CCONJ
ma-171	210	6	µ)(γ3	µ)(γ3	NOUN
ma-171	210	7	+	+	CCONJ
ma-171	210	8	µ)β1	µ)β1	NOUN
ma-171	210	9	+	+	PUNCT
ma-171	210	10	(	(	PUNCT
ma-171	210	11	(	(	PUNCT
ma-171	210	12	γ3	γ3	NOUN
ma-171	210	13	+	+	CCONJ
ma-171	210	14	µ)β1	µ)β1	PROPN
ma-171	210	15	+	+	NUM
ma-171	210	16	αβ2)(α+	αβ2)(α+	NOUN
ma-171	210	17	γ2	γ2	NOUN
ma-171	210	18	+	+	CCONJ
ma-171	210	19	γ3	γ3	NOUN
ma-171	210	20	+	+	CCONJ
ma-171	210	21	2µ)]µ	2µ)]µ	PROPN
ma-171	210	22	(	(	PUNCT
ma-171	210	23	α+	α+	X
ma-171	210	24	γ2	γ2	NOUN
ma-171	210	25	+	+	CCONJ
ma-171	210	26	µ)(γ3	µ)(γ3	NOUN
ma-171	210	27	+	+	SYM
ma-171	210	28	µ)((β1(γ3	µ)((β1(γ3	PUNCT
ma-171	210	29	+	+	NUM
ma-171	210	30	µ	µ	X
ma-171	210	31	)	)	PUNCT
ma-171	210	32	+	+	CCONJ
ma-171	210	33	αβ2	αβ2	NOUN
ma-171	210	34	)	)	PUNCT
ma-171	210	35	)	)	PUNCT
ma-171	210	36	.	.	PUNCT
ma-171	211	1	based	base	VERB
ma-171	211	2	on	on	ADP
ma-171	211	3	the	the	DET
ma-171	211	4	sensitivity	sensitivity	NOUN
ma-171	211	5	indices	index	NOUN
ma-171	211	6	in	in	ADP
ma-171	211	7	table	table	NOUN
ma-171	211	8	3	3	NUM
ma-171	211	9	,	,	PUNCT
ma-171	211	10	the	the	DET
ma-171	211	11	most	most	ADV
ma-171	211	12	sensitive	sensitive	ADJ
ma-171	211	13	parameter	parameter	NOUN
ma-171	211	14	to	to	ADP
ma-171	211	15	the	the	DET
ma-171	211	16	value	value	NOUN
ma-171	211	17	of	of	ADP
ma-171	211	18	r0	r0	NOUN
ma-171	211	19	is	be	AUX
ma-171	211	20	β1	β1	NOUN
ma-171	211	21	,	,	PUNCT
ma-171	211	22	table	table	NOUN
ma-171	211	23	3	3	NUM
ma-171	211	24	.	.	PUNCT
ma-171	212	1	sensitivity	sensitivity	NOUN
ma-171	212	2	indices	indice	VERB
ma-171	212	3	for	for	ADP
ma-171	212	4	the	the	DET
ma-171	212	5	model	model	NOUN
ma-171	212	6	parameters	parameter	NOUN
ma-171	212	7	parameter	parameter	NOUN
ma-171	212	8	description	description	NOUN
ma-171	212	9	sensitivity	sensitivity	NOUN
ma-171	212	10	index	index	NOUN
ma-171	212	11	δ	δ	PROPN
ma-171	212	12	proportion	proportion	NOUN
ma-171	212	13	of	of	ADP
ma-171	212	14	high	high	ADJ
ma-171	212	15	risk	risk	NOUN
ma-171	212	16	sussceptibles	sussceptible	NOUN
ma-171	212	17	−0.36986	−0.36986	ADJ
ma-171	212	18	φ1	φ1	PROPN
ma-171	212	19	prep	prep	NOUN
ma-171	212	20	effectiveness	effectiveness	NOUN
ma-171	212	21	−0.041095	−0.041095	NOUN
ma-171	212	22	φ2	φ2	PROPN
ma-171	212	23	condom	condom	NOUN
ma-171	212	24	effectiveness	effectiveness	NOUN
ma-171	212	25	−0.11111	−0.11111	X
ma-171	212	26	γ3	γ3	NOUN
ma-171	212	27	art	art	NOUN
ma-171	212	28	failure	failure	NOUN
ma-171	212	29	−0.27182	−0.27182	NOUN
ma-171	212	30	β1	β1	NOUN
ma-171	212	31	mean	mean	VERB
ma-171	212	32	contact	contact	NOUN
ma-171	212	33	rate	rate	NOUN
ma-171	212	34	with	with	ADP
ma-171	212	35	i	i	PRON
ma-171	212	36	0.72345	0.72345	NUM
ma-171	212	37	β2	β2	NOUN
ma-171	212	38	mean	mean	VERB
ma-171	212	39	contact	contact	NOUN
ma-171	212	40	rate	rate	NOUN
ma-171	212	41	with	with	ADP
ma-171	212	42	td	td	NOUN
ma-171	212	43	0.27654	0.27654	NUM
ma-171	212	44	α	α	NOUN
ma-171	212	45	progression	progression	NOUN
ma-171	212	46	from	from	ADP
ma-171	212	47	i	i	PRON
ma-171	212	48	to	to	ADP
ma-171	212	49	td	td	VERB
ma-171	212	50	−0.40225	−0.40225	PUNCT
ma-171	212	51	γ2	γ2	ADJ
ma-171	212	52	progression	progression	NOUN
ma-171	212	53	from	from	ADP
ma-171	212	54	i	i	PRON
ma-171	212	55	to	to	ADP
ma-171	212	56	a	a	DET
ma-171	212	57	−0.05123	−0.05123	NOUN
ma-171	212	58	µ	µ	DET
ma-171	212	59	natural	natural	ADJ
ma-171	212	60	mortality	mortality	NOUN
ma-171	212	61	rate	rate	NOUN
ma-171	212	62	−0.02969	−0.02969	ADP
ma-171	212	63	the	the	DET
ma-171	212	64	mean	mean	ADJ
ma-171	212	65	contact	contact	NOUN
ma-171	212	66	rate	rate	NOUN
ma-171	212	67	with	with	ADP
ma-171	212	68	undiagnosed	undiagnosed	ADJ
ma-171	212	69	infectives	infective	NOUN
ma-171	212	70	.	.	PUNCT
ma-171	213	1	this	this	PRON
ma-171	213	2	implies	imply	VERB
ma-171	213	3	that	that	SCONJ
ma-171	213	4	in	in	ADP
ma-171	213	5	order	order	NOUN
ma-171	213	6	to	to	PART
ma-171	213	7	control	control	VERB
ma-171	213	8	the	the	DET
ma-171	213	9	spreadof	spreadof	NOUN
ma-171	213	10	hiv	hiv	PROPN
ma-171	213	11	in	in	ADP
ma-171	213	12	a	a	DET
ma-171	213	13	high	high	ADJ
ma-171	213	14	risk	risk	NOUN
ma-171	213	15	population	population	NOUN
ma-171	213	16	,	,	PUNCT
ma-171	213	17	efforts	effort	NOUN
ma-171	213	18	should	should	AUX
ma-171	213	19	be	be	AUX
ma-171	213	20	geared	gear	VERB
ma-171	213	21	towards	towards	ADP
ma-171	213	22	reducing	reduce	VERB
ma-171	213	23	the	the	DET
ma-171	213	24	number	number	NOUN
ma-171	213	25	of	of	ADP
ma-171	213	26	thosewho	thosewho	NOUN
ma-171	213	27	are	be	AUX
ma-171	213	28	undiagnosed	undiagnosed	ADJ
ma-171	213	29	by	by	ADP
ma-171	213	30	testing	test	VERB
ma-171	213	31	them	they	PRON
ma-171	213	32	and	and	CCONJ
ma-171	213	33	enrolling	enrol	VERB
ma-171	213	34	them	they	PRON
ma-171	213	35	on	on	ADP
ma-171	213	36	art	art	NOUN
ma-171	213	37	treatment	treatment	NOUN
ma-171	213	38	.	.	PUNCT
ma-171	214	1	this	this	DET
ma-171	214	2	in	in	ADP
ma-171	214	3	turn	turn	NOUN
ma-171	214	4	lowerstheir	lowerstheir	NOUN
ma-171	214	5	infectivity	infectivity	NOUN
ma-171	214	6	as	as	ADV
ma-171	214	7	well	well	ADV
ma-171	214	8	as	as	ADP
ma-171	214	9	chances	chance	NOUN
ma-171	214	10	of	of	ADP
ma-171	214	11	progressing	progress	VERB
ma-171	214	12	to	to	ADP
ma-171	214	13	the	the	DET
ma-171	214	14	aids	aids	PROPN
ma-171	214	15	class	class	NOUN
ma-171	214	16	.	.	PUNCT
ma-171	215	1	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	215	2	eur	eur	PROPN
ma-171	215	3	.	.	PUNCT
ma-171	216	1	j.	j.	PROPN
ma-171	216	2	math	math	PROPN
ma-171	216	3	.	.	PUNCT
ma-171	217	1	anal	anal	PROPN
ma-171	217	2	.	.	PUNCT
ma-171	218	1	10.28924	10.28924	NUM
ma-171	218	2	/	/	SYM
ma-171	218	3	ada	ada	PROPN
ma-171	218	4	/	/	SYM
ma-171	218	5	ma.3.21	ma.3.21	PROPN
ma-171	218	6	115	115	NUM
ma-171	218	7	.	.	PUNCT
ma-171	219	1	conclusion	conclusion	NOUN
ma-171	219	2	in	in	ADP
ma-171	219	3	this	this	DET
ma-171	219	4	study	study	NOUN
ma-171	219	5	,	,	PUNCT
ma-171	219	6	a	a	DET
ma-171	219	7	mathematical	mathematical	ADJ
ma-171	219	8	model	model	NOUN
ma-171	219	9	is	be	AUX
ma-171	219	10	formulated	formulate	VERB
ma-171	219	11	,	,	PUNCT
ma-171	219	12	based	base	VERB
ma-171	219	13	on	on	ADP
ma-171	219	14	a	a	DET
ma-171	219	15	system	system	NOUN
ma-171	219	16	of	of	ADP
ma-171	219	17	ordinary	ordinary	ADJ
ma-171	219	18	differentialequations	differentialequation	NOUN
ma-171	219	19	,	,	PUNCT
ma-171	219	20	incorporating	incorporate	VERB
ma-171	219	21	the	the	DET
ma-171	219	22	impact	impact	NOUN
ma-171	219	23	of	of	ADP
ma-171	219	24	dual	dual	ADJ
ma-171	219	25	protection	protection	NOUN
ma-171	219	26	and	and	CCONJ
ma-171	219	27	art	art	NOUN
ma-171	219	28	adherence	adherence	NOUN
ma-171	219	29	in	in	ADP
ma-171	219	30	preventing	prevent	VERB
ma-171	219	31	the	the	DET
ma-171	219	32	spreadof	spreadof	NOUN
ma-171	219	33	hiv	hiv	PROPN
ma-171	219	34	among	among	ADP
ma-171	219	35	persons	person	NOUN
ma-171	219	36	at	at	ADP
ma-171	219	37	high	high	ADJ
ma-171	219	38	risk	risk	NOUN
ma-171	219	39	of	of	ADP
ma-171	219	40	infection.stability	infection.stability	NOUN
ma-171	219	41	analysis	analysis	NOUN
ma-171	219	42	of	of	ADP
ma-171	219	43	the	the	DET
ma-171	219	44	model	model	NOUN
ma-171	219	45	was	be	AUX
ma-171	219	46	done	do	VERB
ma-171	219	47	and	and	CCONJ
ma-171	219	48	depicted	depict	VERB
ma-171	219	49	that	that	SCONJ
ma-171	219	50	when	when	SCONJ
ma-171	219	51	r0	r0	NOUN
ma-171	219	52	<	<	X
ma-171	219	53	1	1	NUM
ma-171	219	54	,	,	PUNCT
ma-171	219	55	the	the	DET
ma-171	219	56	disease	disease	NOUN
ma-171	219	57	freeequilibrium	freeequilibrium	NOUN
ma-171	219	58	is	be	AUX
ma-171	219	59	both	both	CCONJ
ma-171	219	60	locally	locally	ADV
ma-171	219	61	and	and	CCONJ
ma-171	219	62	globally	globally	ADV
ma-171	219	63	asymptotically	asymptotically	ADV
ma-171	219	64	stable	stable	ADJ
ma-171	219	65	.	.	PUNCT
ma-171	220	1	the	the	DET
ma-171	220	2	endemic	endemic	ADJ
ma-171	220	3	equilibrium	equilibrium	NOUN
ma-171	220	4	of	of	ADP
ma-171	220	5	themathematical	themathematical	ADJ
ma-171	220	6	model	model	NOUN
ma-171	220	7	exists	exist	VERB
ma-171	220	8	and	and	CCONJ
ma-171	220	9	was	be	AUX
ma-171	220	10	shown	show	VERB
ma-171	220	11	to	to	PART
ma-171	220	12	be	be	AUX
ma-171	220	13	locally	locally	ADV
ma-171	220	14	asymptotically	asymptotically	ADV
ma-171	220	15	stable	stable	ADJ
ma-171	220	16	whenever	whenever	SCONJ
ma-171	220	17	r0	r0	NOUN
ma-171	220	18	>	>	X
ma-171	220	19	1,implying	1,implye	VERB
ma-171	220	20	that	that	SCONJ
ma-171	220	21	there	there	PRON
ma-171	220	22	is	be	VERB
ma-171	220	23	persistence	persistence	NOUN
ma-171	220	24	of	of	ADP
ma-171	220	25	hiv	hiv	PROPN
ma-171	220	26	infection	infection	NOUN
ma-171	220	27	in	in	ADP
ma-171	220	28	the	the	DET
ma-171	220	29	population	population	NOUN
ma-171	220	30	provided	provide	VERB
ma-171	220	31	that	that	SCONJ
ma-171	220	32	r0	r0	NOUN
ma-171	220	33	is	be	AUX
ma-171	220	34	greaterthan	greaterthan	ADP
ma-171	220	35	unity	unity	NOUN
ma-171	220	36	.	.	PUNCT
ma-171	221	1	sensitivity	sensitivity	NOUN
ma-171	221	2	analysis	analysis	NOUN
ma-171	221	3	was	be	AUX
ma-171	221	4	conducted	conduct	VERB
ma-171	221	5	,	,	PUNCT
ma-171	221	6	depicting	depict	VERB
ma-171	221	7	that	that	SCONJ
ma-171	221	8	the	the	DET
ma-171	221	9	most	most	ADV
ma-171	221	10	sensitive	sensitive	ADJ
ma-171	221	11	parameter	parameter	NOUN
ma-171	221	12	is	be	AUX
ma-171	221	13	β1,the	β1,the	DET
ma-171	221	14	mean	mean	ADJ
ma-171	221	15	contact	contact	NOUN
ma-171	221	16	rate	rate	NOUN
ma-171	221	17	with	with	ADP
ma-171	221	18	the	the	DET
ma-171	221	19	un	un	ADJ
ma-171	221	20	-	-	ADJ
ma-171	221	21	diagnosed	diagnose	VERB
ma-171	221	22	infectives	infective	NOUN
ma-171	221	23	.	.	PUNCT
ma-171	222	1	therefore	therefore	ADV
ma-171	222	2	,	,	PUNCT
ma-171	222	3	in	in	ADP
ma-171	222	4	order	order	NOUN
ma-171	222	5	to	to	PART
ma-171	222	6	control	control	VERB
ma-171	222	7	the	the	DET
ma-171	222	8	spreadof	spreadof	NOUN
ma-171	222	9	hiv	hiv	PROPN
ma-171	222	10	among	among	ADP
ma-171	222	11	the	the	DET
ma-171	222	12	high	high	ADJ
ma-171	222	13	risk	risk	NOUN
ma-171	222	14	population	population	NOUN
ma-171	222	15	,	,	PUNCT
ma-171	222	16	efforts	effort	NOUN
ma-171	222	17	ought	ought	AUX
ma-171	222	18	to	to	PART
ma-171	222	19	be	be	AUX
ma-171	222	20	channeled	channel	VERB
ma-171	222	21	towards	towards	ADP
ma-171	222	22	the	the	DET
ma-171	222	23	undiagnosedpopulation	undiagnosedpopulation	NOUN
ma-171	222	24	by	by	ADP
ma-171	222	25	frequently	frequently	ADV
ma-171	222	26	testing	test	VERB
ma-171	222	27	and	and	CCONJ
ma-171	222	28	enrolling	enrol	VERB
ma-171	222	29	them	they	PRON
ma-171	222	30	on	on	ADP
ma-171	222	31	art	art	NOUN
ma-171	222	32	treatmentwhich	treatmentwhich	PROPN
ma-171	222	33	guarantees	guarantee	VERB
ma-171	222	34	low	low	ADJ
ma-171	222	35	viral	viral	ADJ
ma-171	222	36	load	load	NOUN
ma-171	222	37	within	within	ADP
ma-171	222	38	the	the	DET
ma-171	222	39	infected	infected	ADJ
ma-171	222	40	individual	individual	NOUN
ma-171	222	41	,	,	PUNCT
ma-171	222	42	making	make	VERB
ma-171	222	43	them	they	PRON
ma-171	222	44	less	less	ADV
ma-171	222	45	infective	infective	ADJ
ma-171	222	46	.	.	PUNCT
ma-171	223	1	thusdual	thusdual	ADJ
ma-171	223	2	protection	protection	NOUN
ma-171	223	3	and	and	CCONJ
ma-171	223	4	art	art	NOUN
ma-171	223	5	adherence	adherence	NOUN
ma-171	223	6	are	be	AUX
ma-171	223	7	essential	essential	ADJ
ma-171	223	8	in	in	ADP
ma-171	223	9	the	the	DET
ma-171	223	10	fight	fight	NOUN
ma-171	223	11	against	against	ADP
ma-171	223	12	the	the	DET
ma-171	223	13	spread	spread	NOUN
ma-171	223	14	of	of	ADP
ma-171	223	15	hiv	hiv	PROPN
ma-171	223	16	among	among	ADP
ma-171	223	17	thehigh	thehigh	ADJ
ma-171	223	18	risk	risk	NOUN
ma-171	223	19	population	population	NOUN
ma-171	223	20	.	.	PUNCT
ma-171	224	1	references	reference	NOUN
ma-171	224	2	[	[	X
ma-171	224	3	1	1	NUM
ma-171	224	4	]	]	PUNCT
ma-171	224	5	c.	c.	PROPN
ma-171	224	6	castillo	castillo	PROPN
ma-171	224	7	-	-	PUNCT
ma-171	224	8	chavez	chavez	PROPN
ma-171	224	9	,	,	PUNCT
ma-171	224	10	z.	z.	PROPN
ma-171	224	11	feng	feng	PROPN
ma-171	224	12	,	,	PUNCT
ma-171	224	13	w.	w.	PROPN
ma-171	224	14	huang	huang	PROPN
ma-171	224	15	,	,	PUNCT
ma-171	224	16	on	on	ADP
ma-171	224	17	the	the	DET
ma-171	224	18	computation	computation	NOUN
ma-171	224	19	of	of	ADP
ma-171	224	20	r0	r0	NOUN
ma-171	224	21	and	and	CCONJ
ma-171	224	22	its	its	PRON
ma-171	224	23	role	role	NOUN
ma-171	224	24	on	on	ADP
ma-171	224	25	global	global	ADJ
ma-171	224	26	stability	stability	NOUN
ma-171	224	27	,	,	PUNCT
ma-171	224	28	in	in	ADP
ma-171	224	29	:	:	PUNCT
ma-171	224	30	c.	c.	PROPN
ma-171	224	31	castillo	castillo	PROPN
ma-171	224	32	-	-	PUNCT
ma-171	224	33	chavez	chavez	PROPN
ma-171	224	34	,	,	PUNCT
ma-171	224	35	s.	s.	PROPN
ma-171	224	36	blower	blower	PROPN
ma-171	224	37	,	,	PUNCT
ma-171	224	38	p.	p.	PROPN
ma-171	224	39	van	van	PROPN
ma-171	224	40	den	den	PROPN
ma-171	224	41	driessche	driessche	PROPN
ma-171	224	42	,	,	PUNCT
ma-171	224	43	d.	d.	PROPN
ma-171	224	44	kirschner	kirschner	PROPN
ma-171	224	45	,	,	PUNCT
ma-171	224	46	a.-a	a.-a	PROPN
ma-171	224	47	.	.	PUNCT
ma-171	225	1	yakubu	yakubu	PROPN
ma-171	225	2	(	(	PUNCT
ma-171	225	3	eds	eds	PROPN
ma-171	225	4	.	.	PUNCT
ma-171	225	5	)	)	PUNCT
ma-171	225	6	,	,	PUNCT
ma-171	225	7	mathematical	mathematical	ADJ
ma-171	225	8	approaches	approach	NOUN
ma-171	225	9	for	for	ADP
ma-171	225	10	emergingand	emergingand	NOUN
ma-171	225	11	reemerging	reemerge	VERB
ma-171	225	12	infectious	infectious	ADJ
ma-171	225	13	diseases	disease	NOUN
ma-171	225	14	:	:	PUNCT
ma-171	225	15	an	an	DET
ma-171	225	16	introduction	introduction	NOUN
ma-171	225	17	,	,	PUNCT
ma-171	225	18	springer	springer	NOUN
ma-171	225	19	new	new	PROPN
ma-171	225	20	york	york	PROPN
ma-171	225	21	,	,	PUNCT
ma-171	225	22	new	new	PROPN
ma-171	225	23	york	york	PROPN
ma-171	225	24	,	,	PUNCT
ma-171	225	25	ny	ny	PROPN
ma-171	225	26	,	,	PUNCT
ma-171	225	27	2002	2002	NUM
ma-171	225	28	:	:	PUNCT
ma-171	226	1	pp	pp	ADJ
ma-171	226	2	.	.	PUNCT
ma-171	227	1	229	229	NUM
ma-171	227	2	-	-	SYM
ma-171	227	3	250	250	NUM
ma-171	227	4	.	.	PUNCT
ma-171	228	1	https://doi.org/10.1007/978-1-4757-3667-0_13.[2	https://doi.org/10.1007/978-1-4757-3667-0_13.[2	X
ma-171	228	2	]	]	X
ma-171	228	3	s.c	s.c	PROPN
ma-171	228	4	.	.	PROPN
ma-171	228	5	weller	weller	PROPN
ma-171	228	6	,	,	PUNCT
ma-171	228	7	k.	k.	PROPN
ma-171	228	8	davis	davis	PROPN
ma-171	228	9	-	-	PUNCT
ma-171	228	10	beaty	beaty	PROPN
ma-171	228	11	,	,	PUNCT
ma-171	228	12	condom	condom	NOUN
ma-171	228	13	effectiveness	effectiveness	NOUN
ma-171	228	14	in	in	ADP
ma-171	228	15	reducing	reduce	VERB
ma-171	228	16	heterosexual	heterosexual	ADJ
ma-171	228	17	hiv	hiv	PROPN
ma-171	228	18	transmission	transmission	NOUN
ma-171	228	19	,	,	PUNCT
ma-171	228	20	cochrane	cochrane	PROPN
ma-171	228	21	databasesyst	databasesyst	PROPN
ma-171	228	22	.	.	PUNCT
ma-171	229	1	rev	rev	PROPN
ma-171	229	2	.	.	PROPN
ma-171	229	3	2012	2012	NUM
ma-171	229	4	(	(	PUNCT
ma-171	229	5	2002	2002	NUM
ma-171	229	6	)	)	PUNCT
ma-171	229	7	.	.	PUNCT
ma-171	230	1	https://doi.org/10.1002/14651858.cd003255.[3	https://doi.org/10.1002/14651858.cd003255.[3	PROPN
ma-171	230	2	]	]	X
ma-171	230	3	d.k	d.k	PROPN
ma-171	230	4	.	.	PROPN
ma-171	230	5	smith	smith	PROPN
ma-171	230	6	,	,	PUNCT
ma-171	230	7	j.h	j.h	PROPN
ma-171	230	8	.	.	PROPN
ma-171	230	9	herbst	herbst	PROPN
ma-171	230	10	,	,	PUNCT
ma-171	230	11	x.	x.	PROPN
ma-171	230	12	zhang	zhang	PROPN
ma-171	230	13	,	,	PUNCT
ma-171	230	14	c.e	c.e	PROPN
ma-171	230	15	.	.	PROPN
ma-171	230	16	rose	rise	VERB
ma-171	230	17	,	,	PUNCT
ma-171	230	18	condom	condom	NOUN
ma-171	230	19	effectiveness	effectiveness	NOUN
ma-171	230	20	for	for	ADP
ma-171	230	21	hiv	hiv	PROPN
ma-171	230	22	prevention	prevention	NOUN
ma-171	230	23	by	by	ADP
ma-171	230	24	consistency	consistency	NOUN
ma-171	230	25	of	of	ADP
ma-171	230	26	use	use	NOUN
ma-171	230	27	amongmen	amongman	NOUN
ma-171	230	28	who	who	PRON
ma-171	230	29	have	have	VERB
ma-171	230	30	sex	sex	NOUN
ma-171	230	31	with	with	ADP
ma-171	230	32	men	man	NOUN
ma-171	230	33	in	in	ADP
ma-171	230	34	the	the	DET
ma-171	230	35	united	united	PROPN
ma-171	230	36	states	states	PROPN
ma-171	230	37	,	,	PUNCT
ma-171	230	38	jaids	jaids	PROPN
ma-171	230	39	j.	j.	PROPN
ma-171	230	40	acq	acq	PROPN
ma-171	230	41	.	.	PROPN
ma-171	230	42	immune	immune	PROPN
ma-171	230	43	defic	defic	PROPN
ma-171	230	44	.	.	PUNCT
ma-171	231	1	syndr	syndr	PROPN
ma-171	231	2	.	.	PUNCT
ma-171	232	1	68	68	NUM
ma-171	232	2	(	(	PUNCT
ma-171	232	3	2015	2015	NUM
ma-171	232	4	)	)	PUNCT
ma-171	232	5	337	337	NUM
ma-171	232	6	-	-	SYM
ma-171	232	7	344	344	NUM
ma-171	232	8	.	.	PUNCT
ma-171	232	9	https	https	NOUN
ma-171	232	10	:	:	PUNCT
ma-171	232	11	//doi.org/10.1097	//doi.org/10.1097	X
ma-171	232	12	/	/	SYM
ma-171	232	13	qai.0000000000000461.[4	qai.0000000000000461.[4	PROPN
ma-171	232	14	]	]	X
ma-171	232	15	e.o	e.o	PROPN
ma-171	232	16	.	.	PROPN
ma-171	232	17	omondi	omondi	PROPN
ma-171	232	18	,	,	PUNCT
ma-171	232	19	r.w	r.w	PROPN
ma-171	232	20	.	.	PROPN
ma-171	232	21	mbogo	mbogo	PROPN
ma-171	232	22	,	,	PUNCT
ma-171	232	23	l.s	l.s	PROPN
ma-171	232	24	.	.	PROPN
ma-171	232	25	luboobi	luboobi	PROPN
ma-171	232	26	,	,	PUNCT
ma-171	232	27	mathematical	mathematical	ADJ
ma-171	232	28	modelling	modelling	NOUN
ma-171	232	29	of	of	ADP
ma-171	232	30	the	the	DET
ma-171	232	31	impact	impact	NOUN
ma-171	232	32	of	of	ADP
ma-171	232	33	testing	testing	NOUN
ma-171	232	34	,	,	PUNCT
ma-171	232	35	treatment	treatment	NOUN
ma-171	232	36	and	and	CCONJ
ma-171	232	37	control	control	NOUN
ma-171	232	38	ofhiv	ofhiv	ADJ
ma-171	232	39	transmission	transmission	NOUN
ma-171	232	40	in	in	ADP
ma-171	232	41	kenya	kenya	PROPN
ma-171	232	42	,	,	PUNCT
ma-171	232	43	cogent	cogent	ADJ
ma-171	232	44	math	math	NOUN
ma-171	232	45	.	.	PUNCT
ma-171	233	1	stat	stat	PROPN
ma-171	233	2	.	.	PUNCT
ma-171	234	1	5	5	NUM
ma-171	234	2	(	(	PUNCT
ma-171	234	3	2018	2018	NUM
ma-171	234	4	)	)	PUNCT
ma-171	234	5	1475590	1475590	NUM
ma-171	234	6	.	.	PUNCT
ma-171	235	1	https://doi.org/10.1080/25742558.2018	https://doi.org/10.1080/25742558.2018	X
ma-171	235	2	.	.	PUNCT
ma-171	236	1	1475590.[5	1475590.[5	NUM
ma-171	236	2	]	]	X
ma-171	236	3	f.k	f.k	PROPN
ma-171	236	4	.	.	PROPN
ma-171	236	5	tireito	tireito	PROPN
ma-171	236	6	,	,	PUNCT
ma-171	236	7	g.o	g.o	PROPN
ma-171	236	8	.	.	PROPN
ma-171	236	9	lawi	lawi	PROPN
ma-171	236	10	,	,	PUNCT
ma-171	236	11	o.a	o.a	PROPN
ma-171	236	12	.	.	PROPN
ma-171	236	13	colleta	colleta	PROPN
ma-171	236	14	,	,	PUNCT
ma-171	236	15	mathematical	mathematical	ADJ
ma-171	236	16	analysis	analysis	NOUN
ma-171	236	17	of	of	ADP
ma-171	236	18	hiv	hiv	PROPN
ma-171	236	19	/	/	SYM
ma-171	236	20	aids	aids	PROPN
ma-171	236	21	anti	anti	ADJ
ma-171	236	22	-	-	ADJ
ma-171	236	23	retroviral	retroviral	ADJ
ma-171	236	24	treatment	treatment	NOUN
ma-171	236	25	incorporatingadherence	incorporatingadherence	NOUN
ma-171	236	26	,	,	PUNCT
ma-171	236	27	asian	asian	ADJ
ma-171	236	28	res	re	NOUN
ma-171	236	29	.	.	PUNCT
ma-171	237	1	j.	j.	PROPN
ma-171	237	2	math	math	PROPN
ma-171	237	3	.	.	PUNCT
ma-171	238	1	10	10	NUM
ma-171	238	2	(	(	PUNCT
ma-171	238	3	2018	2018	NUM
ma-171	238	4	)	)	PUNCT
ma-171	238	5	1	1	NUM
ma-171	238	6	-	-	SYM
ma-171	238	7	13	13	NUM
ma-171	238	8	.	.	PUNCT
ma-171	239	1	https://doi.org/10.9734/arjom/2018/42830.[6	https://doi.org/10.9734/arjom/2018/42830.[6	X
ma-171	239	2	]	]	X
ma-171	239	3	i.	i.	NOUN
ma-171	239	4	cremin	cremin	PROPN
ma-171	239	5	,	,	PUNCT
ma-171	239	6	r.	r.	PROPN
ma-171	239	7	alsallaq	alsallaq	PROPN
ma-171	239	8	,	,	PUNCT
ma-171	239	9	m.	m.	NOUN
ma-171	239	10	dybul	dybul	PROPN
ma-171	239	11	,	,	PUNCT
ma-171	239	12	p.	p.	PROPN
ma-171	239	13	piot	piot	PROPN
ma-171	239	14	,	,	PUNCT
ma-171	239	15	g.	g.	PROPN
ma-171	239	16	garnett	garnett	PROPN
ma-171	239	17	,	,	PUNCT
ma-171	239	18	t.b	t.b	PROPN
ma-171	239	19	.	.	PROPN
ma-171	239	20	hallett	hallett	PROPN
ma-171	239	21	,	,	PUNCT
ma-171	239	22	the	the	DET
ma-171	239	23	new	new	ADJ
ma-171	239	24	role	role	NOUN
ma-171	239	25	of	of	ADP
ma-171	239	26	antiretrovirals	antiretroviral	NOUN
ma-171	239	27	in	in	ADP
ma-171	239	28	combinationhiv	combinationhiv	PROPN
ma-171	239	29	prevention	prevention	NOUN
ma-171	239	30	:	:	PUNCT
ma-171	239	31	a	a	DET
ma-171	239	32	mathematical	mathematical	ADJ
ma-171	239	33	modelling	modelling	NOUN
ma-171	239	34	analysis	analysis	NOUN
ma-171	239	35	,	,	PUNCT
ma-171	239	36	aids	aids	PROPN
ma-171	239	37	.	.	PUNCT
ma-171	239	38	27	27	NUM
ma-171	239	39	(	(	PUNCT
ma-171	239	40	2013	2013	NUM
ma-171	239	41	)	)	PUNCT
ma-171	239	42	447	447	NUM
ma-171	239	43	-	-	SYM
ma-171	239	44	458	458	NUM
ma-171	239	45	.	.	PUNCT
ma-171	240	1	https://doi.org/10.1097/qad	https://doi.org/10.1097/qad	INTJ
ma-171	240	2	.	.	PUNCT
ma-171	241	1	0b013e32835ca2dd.[7	0b013e32835ca2dd.[7	PROPN
ma-171	241	2	]	]	X
ma-171	241	3	j.c	j.c	PROPN
ma-171	241	4	.	.	PROPN
ma-171	241	5	helton	helton	PROPN
ma-171	241	6	,	,	PUNCT
ma-171	241	7	r.l	r.l	PROPN
ma-171	241	8	.	.	PROPN
ma-171	241	9	iman	iman	PROPN
ma-171	241	10	,	,	PUNCT
ma-171	241	11	j.b	j.b	PROPN
ma-171	241	12	.	.	PROPN
ma-171	241	13	brown	brown	PROPN
ma-171	241	14	,	,	PUNCT
ma-171	241	15	sensitivity	sensitivity	NOUN
ma-171	241	16	analysis	analysis	NOUN
ma-171	241	17	of	of	ADP
ma-171	241	18	the	the	DET
ma-171	241	19	asymptotic	asymptotic	ADJ
ma-171	241	20	behavior	behavior	NOUN
ma-171	241	21	of	of	ADP
ma-171	241	22	a	a	DET
ma-171	241	23	model	model	NOUN
ma-171	241	24	for	for	ADP
ma-171	241	25	the	the	DET
ma-171	241	26	environmentalmovement	environmentalmovement	NOUN
ma-171	241	27	of	of	ADP
ma-171	241	28	radionuclides	radionuclide	NOUN
ma-171	241	29	,	,	PUNCT
ma-171	241	30	ecol	ecol	NOUN
ma-171	241	31	.	.	PUNCT
ma-171	242	1	model	model	NOUN
ma-171	242	2	.	.	PUNCT
ma-171	243	1	28	28	NUM
ma-171	243	2	(	(	PUNCT
ma-171	243	3	1985	1985	NUM
ma-171	243	4	)	)	PUNCT
ma-171	243	5	243	243	NUM
ma-171	243	6	-	-	SYM
ma-171	243	7	278	278	NUM
ma-171	243	8	.	.	PUNCT
ma-171	244	1	https://doi.org/10.1016/0304-3800(85)90077-8.[8	https://doi.org/10.1016/0304-3800(85)90077-8.[8	X
ma-171	244	2	]	]	X
ma-171	244	3	j.m	j.m	PROPN
ma-171	244	4	.	.	PROPN
ma-171	244	5	baeten	baeten	PROPN
ma-171	244	6	,	,	PUNCT
ma-171	244	7	j.e	j.e	PROPN
ma-171	244	8	.	.	PROPN
ma-171	244	9	haberer	haberer	PROPN
ma-171	244	10	,	,	PUNCT
ma-171	244	11	a.y	a.y	PROPN
ma-171	244	12	.	.	PROPN
ma-171	244	13	liu	liu	PROPN
ma-171	244	14	,	,	PUNCT
ma-171	244	15	n.	n.	PROPN
ma-171	244	16	sista	sista	NOUN
ma-171	244	17	.	.	PUNCT
ma-171	245	1	pre	pre	ADJ
ma-171	245	2	-	-	ADJ
ma-171	245	3	exposure	exposure	ADJ
ma-171	245	4	prophylaxis	prophylaxis	NOUN
ma-171	245	5	for	for	ADP
ma-171	245	6	hiv	hiv	PROPN
ma-171	245	7	prevention	prevention	NOUN
ma-171	245	8	:	:	PUNCT
ma-171	246	1	where	where	SCONJ
ma-171	246	2	have	have	AUX
ma-171	246	3	we	we	PRON
ma-171	246	4	beenand	beenand	VERB
ma-171	246	5	where	where	SCONJ
ma-171	246	6	are	be	AUX
ma-171	246	7	we	we	PRON
ma-171	246	8	going	go	VERB
ma-171	246	9	?	?	PUNCT
ma-171	247	1	j.	j.	PROPN
ma-171	247	2	acq	acq	PROPN
ma-171	247	3	.	.	PROPN
ma-171	247	4	immune	immune	PROPN
ma-171	247	5	defic	defic	PROPN
ma-171	247	6	.	.	PUNCT
ma-171	248	1	syndr	syndr	PROPN
ma-171	248	2	.	.	PUNCT
ma-171	249	1	63	63	NUM
ma-171	249	2	(	(	PUNCT
ma-171	249	3	2013	2013	NUM
ma-171	249	4	)	)	PUNCT
ma-171	249	5	122	122	NUM
ma-171	249	6	-	-	SYM
ma-171	249	7	129	129	NUM
ma-171	249	8	.	.	PUNCT
ma-171	250	1	https://doi.org/10.1097/qai	https://doi.org/10.1097/qai	NOUN
ma-171	250	2	.	.	PUNCT
ma-171	251	1	0b013e3182986f69.[9	0b013e3182986f69.[9	NUM
ma-171	251	2	]	]	X
ma-171	251	3	j.m	j.m	PROPN
ma-171	251	4	.	.	PROPN
ma-171	251	5	molina	molina	PROPN
ma-171	251	6	.	.	PUNCT
ma-171	252	1	prep	prep	NOUN
ma-171	252	2	failures	failure	NOUN
ma-171	252	3	:	:	PUNCT
ma-171	252	4	diagnosis	diagnosis	NOUN
ma-171	252	5	,	,	PUNCT
ma-171	252	6	resistance	resistance	NOUN
ma-171	252	7	,	,	PUNCT
ma-171	252	8	and	and	CCONJ
ma-171	252	9	treatment	treatment	NOUN
ma-171	252	10	.	.	PUNCT
ma-171	253	1	conference	conference	NOUN
ma-171	253	2	on	on	ADP
ma-171	253	3	retroviruses	retrovirus	NOUN
ma-171	253	4	and	and	CCONJ
ma-171	253	5	opportunisticinfections	opportunisticinfection	NOUN
ma-171	253	6	.	.	PUNCT
ma-171	254	1	4	4	NUM
ma-171	254	2	-	-	SYM
ma-171	254	3	7	7	NUM
ma-171	254	4	march	march	NOUN
ma-171	254	5	2019	2019	NUM
ma-171	254	6	.	.	PUNCT
ma-171	255	1	https://www.croiwebcasts.org/p/2019croi/160	https://www.croiwebcasts.org/p/2019croi/160	PROPN
ma-171	255	2	.	.	PUNCT
ma-171	256	1	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	256	2	https://doi.org/10.1007/978-1-4757-3667-0_13	https://doi.org/10.1007/978-1-4757-3667-0_13	PROPN
ma-171	256	3	https://doi.org/10.1002/14651858.cd003255	https://doi.org/10.1002/14651858.cd003255	NOUN
ma-171	256	4	https://doi.org/10.1097/qai.0000000000000461	https://doi.org/10.1097/qai.0000000000000461	ADJ
ma-171	256	5	https://doi.org/10.1097/qai.0000000000000461	https://doi.org/10.1097/qai.0000000000000461	NOUN
ma-171	256	6	https://doi.org/10.1080/25742558.2018.1475590	https://doi.org/10.1080/25742558.2018.1475590	PROPN
ma-171	256	7	https://doi.org/10.1080/25742558.2018.1475590	https://doi.org/10.1080/25742558.2018.1475590	PROPN
ma-171	256	8	https://doi.org/10.9734/arjom/2018/42830	https://doi.org/10.9734/arjom/2018/42830	NOUN
ma-171	256	9	https://doi.org/10.1097/qad.0b013e32835ca2dd	https://doi.org/10.1097/qad.0b013e32835ca2dd	PROPN
ma-171	256	10	https://doi.org/10.1097/qad.0b013e32835ca2dd	https://doi.org/10.1097/qad.0b013e32835ca2dd	PROPN
ma-171	256	11	https://doi.org/10.1016/0304-3800(85)90077-8	https://doi.org/10.1016/0304-3800(85)90077-8	PROPN
ma-171	256	12	https://doi.org/10.1097/qai.0b013e3182986f69	https://doi.org/10.1097/qai.0b013e3182986f69	PROPN
ma-171	256	13	https://doi.org/10.1097/qai.0b013e3182986f69	https://doi.org/10.1097/qai.0b013e3182986f69	PROPN
ma-171	256	14	https://www.croiwebcasts.org/p/2019croi/160	https://www.croiwebcasts.org/p/2019croi/160	NOUN
ma-171	256	15	eur	eur	NOUN
ma-171	256	16	.	.	PUNCT
ma-171	257	1	j.	j.	PROPN
ma-171	257	2	math	math	PROPN
ma-171	257	3	.	.	PUNCT
ma-171	258	1	anal	anal	PROPN
ma-171	258	2	.	.	PUNCT
ma-171	259	1	10.28924	10.28924	NUM
ma-171	259	2	/	/	SYM
ma-171	259	3	ada	ada	PROPN
ma-171	259	4	/	/	SYM
ma-171	259	5	ma.3.21	ma.3.21	PROPN
ma-171	259	6	12	12	NUM
ma-171	260	1	[	[	SYM
ma-171	260	2	10	10	NUM
ma-171	260	3	]	]	PUNCT
ma-171	260	4	p.	p.	NOUN
ma-171	260	5	van	van	PROPN
ma-171	260	6	den	den	PROPN
ma-171	260	7	driessche	driessche	PROPN
ma-171	260	8	,	,	PUNCT
ma-171	260	9	j.	j.	PROPN
ma-171	260	10	watmough	watmough	PROPN
ma-171	260	11	,	,	PUNCT
ma-171	260	12	reproduction	reproduction	NOUN
ma-171	260	13	numbers	number	NOUN
ma-171	260	14	and	and	CCONJ
ma-171	260	15	sub	sub	ADJ
ma-171	260	16	-	-	ADJ
ma-171	260	17	threshold	threshold	ADJ
ma-171	260	18	endemic	endemic	ADJ
ma-171	260	19	equilibria	equilibrium	NOUN
ma-171	260	20	for	for	ADP
ma-171	260	21	compartmentalmodels	compartmentalmodel	NOUN
ma-171	260	22	of	of	ADP
ma-171	260	23	disease	disease	NOUN
ma-171	260	24	transmission	transmission	NOUN
ma-171	260	25	,	,	PUNCT
ma-171	260	26	math	math	NOUN
ma-171	260	27	.	.	PUNCT
ma-171	261	1	biosci	biosci	PROPN
ma-171	261	2	.	.	PUNCT
ma-171	262	1	180	180	NUM
ma-171	262	2	(	(	PUNCT
ma-171	262	3	2002	2002	NUM
ma-171	262	4	)	)	PUNCT
ma-171	262	5	29	29	NUM
ma-171	262	6	-	-	SYM
ma-171	262	7	48	48	NUM
ma-171	262	8	.	.	PUNCT
ma-171	263	1	https://doi.org/10.1016/s0025-5564(02	https://doi.org/10.1016/s0025-5564(02	NOUN
ma-171	263	2	)	)	PUNCT
ma-171	263	3	00108	00108	NUM
ma-171	263	4	-	-	SYM
ma-171	263	5	6.[11	6.[11	NUM
ma-171	263	6	]	]	X
ma-171	263	7	k.r	k.r	PROPN
ma-171	263	8	.	.	PROPN
ma-171	263	9	amico	amico	PROPN
ma-171	263	10	,	,	PUNCT
ma-171	263	11	m.j	m.j	PROPN
ma-171	263	12	.	.	PROPN
ma-171	263	13	stirratt	stirratt	PROPN
ma-171	263	14	,	,	PUNCT
ma-171	263	15	adherence	adherence	NOUN
ma-171	263	16	to	to	ADP
ma-171	263	17	preexposure	preexposure	NOUN
ma-171	263	18	prophylaxis	prophylaxis	NOUN
ma-171	263	19	:	:	PUNCT
ma-171	263	20	current	current	ADJ
ma-171	263	21	,	,	PUNCT
ma-171	263	22	emerging	emerge	VERB
ma-171	263	23	,	,	PUNCT
ma-171	263	24	and	and	CCONJ
ma-171	263	25	anticipated	anticipate	VERB
ma-171	263	26	bases	basis	NOUN
ma-171	263	27	of	of	ADP
ma-171	263	28	evi	evi	NOUN
ma-171	263	29	-	-	PUNCT
ma-171	263	30	dence	dence	NOUN
ma-171	263	31	,	,	PUNCT
ma-171	263	32	clin	clin	PROPN
ma-171	263	33	.	.	PUNCT
ma-171	264	1	infect	infect	VERB
ma-171	264	2	.	.	PUNCT
ma-171	265	1	dis	dis	PROPN
ma-171	265	2	.	.	PUNCT
ma-171	266	1	59	59	NUM
ma-171	266	2	(	(	PUNCT
ma-171	266	3	2014	2014	NUM
ma-171	266	4	)	)	PUNCT
ma-171	266	5	s55	s55	PROPN
ma-171	266	6	-	-	PUNCT
ma-171	266	7	s60	s60	NOUN
ma-171	266	8	.	.	PUNCT
ma-171	267	1	https://doi.org/10.1093/cid/ciu266.[12	https://doi.org/10.1093/cid/ciu266.[12	PROPN
ma-171	267	2	]	]	X
ma-171	267	3	t.t	t.t	PROPN
ma-171	267	4	.	.	PROPN
ma-171	267	5	yusuf	yusuf	PROPN
ma-171	267	6	,	,	PUNCT
ma-171	267	7	f.	f.	PROPN
ma-171	267	8	benyah	benyah	PROPN
ma-171	267	9	,	,	PUNCT
ma-171	267	10	optimal	optimal	ADJ
ma-171	267	11	strategy	strategy	NOUN
ma-171	267	12	for	for	ADP
ma-171	267	13	controlling	control	VERB
ma-171	267	14	the	the	DET
ma-171	267	15	spread	spread	NOUN
ma-171	267	16	of	of	ADP
ma-171	267	17	hiv	hiv	PROPN
ma-171	267	18	/	/	SYM
ma-171	267	19	aids	aids	PROPN
ma-171	267	20	disease	disease	NOUN
ma-171	267	21	:	:	PUNCT
ma-171	267	22	a	a	DET
ma-171	267	23	case	case	NOUN
ma-171	267	24	study	study	NOUN
ma-171	267	25	of	of	ADP
ma-171	267	26	southafrica	southafrica	PROPN
ma-171	267	27	,	,	PUNCT
ma-171	267	28	j.	j.	PROPN
ma-171	267	29	biol	biol	PROPN
ma-171	267	30	.	.	PUNCT
ma-171	268	1	dyn	dyn	PROPN
ma-171	268	2	.	.	PUNCT
ma-171	269	1	6	6	NUM
ma-171	269	2	(	(	PUNCT
ma-171	269	3	2012	2012	NUM
ma-171	269	4	)	)	PUNCT
ma-171	269	5	475	475	NUM
ma-171	269	6	-	-	SYM
ma-171	269	7	494	494	NUM
ma-171	269	8	.	.	PUNCT
ma-171	270	1	https://doi.org/10.1080/17513758.2011.628700.[13	https://doi.org/10.1080/17513758.2011.628700.[13	NOUN
ma-171	270	2	]	]	PUNCT
ma-171	270	3	unaids	unaid	NOUN
ma-171	270	4	.	.	PUNCT
ma-171	271	1	global	global	PROPN
ma-171	271	2	hiv	hiv	PROPN
ma-171	271	3	and	and	CCONJ
ma-171	271	4	aids	aids	PROPN
ma-171	271	5	statistics	statistic	NOUN
ma-171	271	6	:	:	PUNCT
ma-171	271	7	2019	2019	NUM
ma-171	271	8	fact	fact	NOUN
ma-171	271	9	sheet	sheet	NOUN
ma-171	271	10	:	:	PUNCT
ma-171	271	11	https://www.unaids.org/en/resources/	https://www.unaids.org/en/resources/	ADJ
ma-171	271	12	fact	fact	NOUN
ma-171	271	13	-	-	PUNCT
ma-171	271	14	sheet[14	sheet[14	PROPN
ma-171	271	15	]	]	X
ma-171	271	16	u.s	u.s	PROPN
ma-171	271	17	food	food	NOUN
ma-171	271	18	and	and	CCONJ
ma-171	271	19	drug	drug	PROPN
ma-171	271	20	administration	administration	NOUN
ma-171	271	21	(	(	PUNCT
ma-171	272	1	f.d.a).u.s	f.d.a).u.s	PROPN
ma-171	272	2	f.d.a	f.d.a	NOUN
ma-171	272	3	approves	approve	VERB
ma-171	272	4	first	first	ADJ
ma-171	272	5	drug	drug	NOUN
ma-171	272	6	for	for	ADP
ma-171	272	7	reducing	reduce	VERB
ma-171	272	8	the	the	DET
ma-171	272	9	riskof	riskof	NOUN
ma-171	272	10	sexually	sexually	ADV
ma-171	272	11	acquired	acquire	VERB
ma-171	272	12	h.i.v	h.i.v	ADV
ma-171	272	13	infectionjuly	infectionjuly	ADV
ma-171	272	14	.	.	PUNCT
ma-171	273	1	2011	2011	NUM
ma-171	273	2	.	.	PUNCT
ma-171	274	1	https://aidsinfo.nih.gov/news/1254/fda-approves-{\@	https://aidsinfo.nih.gov/news/1254/fda-approves-{\@	PRON
ma-171	274	2	@par}rst	@par}rst	ADJ
ma-171	274	3	-	-	PUNCT
ma-171	274	4	drug	drug	NOUN
ma-171	274	5	-	-	PUNCT
ma-171	274	6	for	for	ADP
ma-171	274	7	-	-	PUNCT
ma-171	274	8	reducing	reduce	VERB
ma-171	274	9	-	-	PUNCT
ma-171	274	10	the	the	DET
ma-171	274	11	-	-	PUNCT
ma-171	274	12	risk	risk	NOUN
ma-171	274	13	-	-	PUNCT
ma-171	274	14	of	of	ADP
ma-171	274	15	-	-	PUNCT
ma-171	274	16	sexually	sexually	ADV
ma-171	274	17	-	-	PUNCT
ma-171	274	18	acquired	acquire	VERB
ma-171	274	19	-	-	PUNCT
ma-171	274	20	hiv	hiv	NOUN
ma-171	274	21	-	-	PUNCT
ma-171	274	22	infection[15	infection[15	X
ma-171	274	23	]	]	PUNCT
ma-171	274	24	x.	x.	PROPN
ma-171	274	25	wang	wang	PROPN
ma-171	274	26	,	,	PUNCT
ma-171	274	27	a	a	DET
ma-171	274	28	simple	simple	ADJ
ma-171	274	29	proof	proof	NOUN
ma-171	274	30	of	of	ADP
ma-171	274	31	descartes	descartes	PROPN
ma-171	274	32	’s	’s	PART
ma-171	274	33	rule	rule	NOUN
ma-171	274	34	of	of	ADP
ma-171	274	35	signs	sign	NOUN
ma-171	274	36	,	,	PUNCT
ma-171	274	37	amer	amer	PROPN
ma-171	274	38	.	.	PROPN
ma-171	274	39	math	math	PROPN
ma-171	274	40	.	.	PUNCT
ma-171	275	1	mon	mon	PROPN
ma-171	275	2	.	.	PROPN
ma-171	276	1	111	111	NUM
ma-171	276	2	(	(	PUNCT
ma-171	276	3	2004	2004	NUM
ma-171	276	4	)	)	PUNCT
ma-171	276	5	525	525	NUM
ma-171	276	6	-	-	SYM
ma-171	276	7	526	526	NUM
ma-171	276	8	.	.	PUNCT
ma-171	277	1	https://doi.org/	https://doi.org/	PROPN
ma-171	277	2	10.2307/4145072	10.2307/4145072	NUM
ma-171	277	3	.	.	PUNCT
ma-171	278	1	https://doi.org/10.28924/ada/ma.3.21	https://doi.org/10.28924/ada/ma.3.21	PROPN
ma-171	278	2	https://doi.org/10.1016/s0025-5564(02)00108-6	https://doi.org/10.1016/s0025-5564(02)00108-6	PROPN
ma-171	278	3	https://doi.org/10.1016/s0025-5564(02)00108-6	https://doi.org/10.1016/s0025-5564(02)00108-6	PROPN
ma-171	278	4	https://doi.org/10.1093/cid/ciu266	https://doi.org/10.1093/cid/ciu266	PROPN
ma-171	278	5	https://doi.org/10.1080/17513758.2011.628700	https://doi.org/10.1080/17513758.2011.628700	PROPN
ma-171	278	6	https://www.unaids.org/en/resources/fact-sheet	https://www.unaids.org/en/resources/fact-sheet	PROPN
ma-171	278	7	https://www.unaids.org/en/resources/fact-sheet	https://www.unaids.org/en/resources/fact-sheet	PROPN
ma-171	278	8	https://aidsinfo.nih.gov/news/1254/fda-approves-{\@@par	https://aidsinfo.nih.gov/news/1254/fda-approves-{\@@par	ADJ
ma-171	278	9	}	}	PUNCT
ma-171	278	10	rst	rst	ADJ
ma-171	278	11	-	-	PUNCT
ma-171	278	12	drug	drug	NOUN
ma-171	278	13	-	-	PUNCT
ma-171	278	14	for	for	ADP
ma-171	278	15	-	-	PUNCT
ma-171	278	16	reducing	reduce	VERB
ma-171	278	17	-	-	PUNCT
ma-171	278	18	the	the	DET
ma-171	278	19	-	-	PUNCT
ma-171	278	20	risk	risk	NOUN
ma-171	278	21	-	-	PUNCT
ma-171	278	22	of	of	ADP
ma-171	278	23	-	-	PUNCT
ma-171	278	24	sexually	sexually	ADV
ma-171	278	25	-	-	PUNCT
ma-171	278	26	acquired	acquire	VERB
ma-171	278	27	-	-	PUNCT
ma-171	278	28	hiv	hiv	NOUN
ma-171	278	29	-	-	PUNCT
ma-171	278	30	infection	infection	NOUN
ma-171	278	31	https://aidsinfo.nih.gov/news/1254/fda-approves-{\@@par	https://aidsinfo.nih.gov/news/1254/fda-approves-{\@@par	NOUN
ma-171	278	32	}	}	PUNCT
ma-171	278	33	rst	rst	VERB
ma-171	278	34	-	-	PUNCT
ma-171	278	35	drug	drug	NOUN
ma-171	278	36	-	-	PUNCT
ma-171	278	37	for	for	ADP
ma-171	278	38	-	-	PUNCT
ma-171	278	39	reducing	reduce	VERB
ma-171	278	40	-	-	PUNCT
ma-171	278	41	the	the	DET
ma-171	278	42	-	-	PUNCT
ma-171	278	43	risk	risk	NOUN
ma-171	278	44	-	-	PUNCT
ma-171	278	45	of	of	ADP
ma-171	278	46	-	-	PUNCT
ma-171	278	47	sexually	sexually	ADV
ma-171	278	48	-	-	PUNCT
ma-171	278	49	acquired	acquire	VERB
ma-171	278	50	-	-	PUNCT
ma-171	278	51	hiv	hiv	NOUN
ma-171	278	52	-	-	PUNCT
ma-171	278	53	infection	infection	NOUN
ma-171	278	54	https://doi.org/10.2307/4145072	https://doi.org/10.2307/4145072	NOUN
ma-171	278	55	https://doi.org/10.2307/4145072	https://doi.org/10.2307/4145072	NOUN
ma-171	278	56	1	1	NUM
ma-171	278	57	.	.	PUNCT
ma-171	278	58	introduction	introduction	NOUN
ma-171	278	59	2	2	NUM
ma-171	278	60	.	.	PUNCT
ma-171	278	61	model	model	NOUN
ma-171	278	62	formulation	formulation	NOUN
ma-171	278	63	and	and	CCONJ
ma-171	278	64	description	description	NOUN
ma-171	278	65	3	3	NUM
ma-171	278	66	.	.	PUNCT
ma-171	278	67	model	model	NOUN
ma-171	278	68	analysis	analysis	NOUN
ma-171	278	69	3.1	3.1	NUM
ma-171	278	70	.	.	PUNCT
ma-171	279	1	existence	existence	NOUN
ma-171	279	2	of	of	ADP
ma-171	279	3	the	the	DET
ma-171	279	4	endemic	endemic	ADJ
ma-171	279	5	steady	steady	ADJ
ma-171	279	6	state	state	NOUN
ma-171	279	7	3.2	3.2	NUM
ma-171	279	8	.	.	PUNCT
ma-171	280	1	local	local	ADJ
ma-171	280	2	stability	stability	NOUN
ma-171	280	3	of	of	ADP
ma-171	280	4	the	the	DET
ma-171	280	5	endemic	endemic	ADJ
ma-171	280	6	equilibrium	equilibrium	NOUN
ma-171	280	7	4	4	NUM
ma-171	280	8	.	.	PUNCT
ma-171	281	1	sensitivity	sensitivity	NOUN
ma-171	281	2	analysis	analysis	NOUN
ma-171	281	3	5	5	NUM
ma-171	281	4	.	.	PUNCT
ma-171	282	1	conclusion	conclusion	NOUN
ma-171	282	2	references	reference	NOUN