id	sid	tid	token	lemma	pos
ejpam-6142	1	1	european	european	PROPN
ejpam-6142	1	2	journal	journal	PROPN
ejpam-6142	1	3	of	of	ADP
ejpam-6142	1	4	pure	pure	ADJ
ejpam-6142	1	5	and	and	CCONJ
ejpam-6142	1	6	applied	applied	ADJ
ejpam-6142	1	7	mathematics	mathematic	NOUN
ejpam-6142	1	8	2025	2025	NUM
ejpam-6142	1	9	,	,	PUNCT
ejpam-6142	1	10	vol	vol	NOUN
ejpam-6142	1	11	.	.	PROPN
ejpam-6142	1	12	18	18	NUM
ejpam-6142	1	13	,	,	PUNCT
ejpam-6142	1	14	issue	issue	NOUN
ejpam-6142	1	15	2	2	NUM
ejpam-6142	1	16	,	,	PUNCT
ejpam-6142	1	17	article	article	NOUN
ejpam-6142	1	18	number	number	NOUN
ejpam-6142	1	19	6142	6142	NUM
ejpam-6142	1	20	issn	issn	VERB
ejpam-6142	1	21	1307	1307	NUM
ejpam-6142	1	22	-	-	SYM
ejpam-6142	1	23	5543	5543	NUM
ejpam-6142	1	24	–	–	PUNCT
ejpam-6142	1	25	ejpam.com	ejpam.com	X
ejpam-6142	1	26	published	publish	VERB
ejpam-6142	1	27	by	by	ADP
ejpam-6142	1	28	new	new	PROPN
ejpam-6142	1	29	york	york	PROPN
ejpam-6142	1	30	business	business	PROPN
ejpam-6142	1	31	global	global	ADJ
ejpam-6142	1	32	understanding	understanding	NOUN
ejpam-6142	1	33	transmission	transmission	NOUN
ejpam-6142	1	34	dynamics	dynamic	NOUN
ejpam-6142	1	35	of	of	ADP
ejpam-6142	1	36	hiv	hiv	PROPN
ejpam-6142	1	37	/	/	SYM
ejpam-6142	1	38	aids	aids	PROPN
ejpam-6142	1	39	with	with	ADP
ejpam-6142	1	40	sensitivity	sensitivity	NOUN
ejpam-6142	1	41	analysis	analysis	NOUN
ejpam-6142	1	42	and	and	CCONJ
ejpam-6142	1	43	optimal	optimal	ADJ
ejpam-6142	1	44	control	control	NOUN
ejpam-6142	1	45	strategies	strategy	NOUN
ejpam-6142	1	46	saiwan	saiwan	PROPN
ejpam-6142	1	47	m.	m.	NOUN
ejpam-6142	1	48	fatah1	fatah1	PROPN
ejpam-6142	1	49	,	,	PUNCT
ejpam-6142	1	50	sarbaz	sarbaz	PROPN
ejpam-6142	1	51	h.	h.	PROPN
ejpam-6142	1	52	a.	a.	PROPN
ejpam-6142	1	53	khoshnaw2,∗	khoshnaw2,∗	PROPN
ejpam-6142	1	54	,	,	PUNCT
ejpam-6142	1	55	arkan	arkan	ADJ
ejpam-6142	1	56	n.	n.	NOUN
ejpam-6142	1	57	mustafa1	mustafa1	PROPN
ejpam-6142	1	58	1	1	NUM
ejpam-6142	1	59	department	department	NOUN
ejpam-6142	1	60	of	of	ADP
ejpam-6142	1	61	mathematics	mathematic	NOUN
ejpam-6142	1	62	,	,	PUNCT
ejpam-6142	1	63	college	college	NOUN
ejpam-6142	1	64	of	of	ADP
ejpam-6142	1	65	education	education	NOUN
ejpam-6142	1	66	,	,	PUNCT
ejpam-6142	1	67	university	university	NOUN
ejpam-6142	1	68	of	of	ADP
ejpam-6142	1	69	sulaimani	sulaimani	PROPN
ejpam-6142	1	70	,	,	PUNCT
ejpam-6142	1	71	sulaymaniah	sulaymaniah	PROPN
ejpam-6142	1	72	46001	46001	NUM
ejpam-6142	1	73	,	,	PUNCT
ejpam-6142	1	74	iraq	iraq	PROPN
ejpam-6142	1	75	2	2	NUM
ejpam-6142	1	76	department	department	NOUN
ejpam-6142	1	77	of	of	ADP
ejpam-6142	1	78	mathematics	mathematic	NOUN
ejpam-6142	1	79	,	,	PUNCT
ejpam-6142	1	80	college	college	NOUN
ejpam-6142	1	81	of	of	ADP
ejpam-6142	1	82	basic	basic	ADJ
ejpam-6142	1	83	education	education	NOUN
ejpam-6142	1	84	,	,	PUNCT
ejpam-6142	1	85	university	university	NOUN
ejpam-6142	1	86	of	of	ADP
ejpam-6142	1	87	raparin	raparin	PROPN
ejpam-6142	1	88	,	,	PUNCT
ejpam-6142	1	89	kurdistan	kurdistan	ADJ
ejpam-6142	1	90	region	region	NOUN
ejpam-6142	1	91	of	of	ADP
ejpam-6142	1	92	iraq	iraq	PROPN
ejpam-6142	1	93	abstract	abstract	NOUN
ejpam-6142	1	94	.	.	PUNCT
ejpam-6142	2	1	in	in	ADP
ejpam-6142	2	2	this	this	DET
ejpam-6142	2	3	article	article	NOUN
ejpam-6142	2	4	,	,	PUNCT
ejpam-6142	2	5	we	we	PRON
ejpam-6142	2	6	propose	propose	VERB
ejpam-6142	2	7	a	a	DET
ejpam-6142	2	8	comprehensive	comprehensive	ADJ
ejpam-6142	2	9	mathematical	mathematical	ADJ
ejpam-6142	2	10	model	model	NOUN
ejpam-6142	2	11	that	that	PRON
ejpam-6142	2	12	investigates	investigate	VERB
ejpam-6142	2	13	the	the	DET
ejpam-6142	2	14	dynamics	dynamic	NOUN
ejpam-6142	2	15	of	of	ADP
ejpam-6142	2	16	hiv	hiv	PROPN
ejpam-6142	2	17	/	/	SYM
ejpam-6142	2	18	aids	aids	PROPN
ejpam-6142	2	19	transmission	transmission	NOUN
ejpam-6142	2	20	,	,	PUNCT
ejpam-6142	2	21	concentrating	concentrate	VERB
ejpam-6142	2	22	on	on	ADP
ejpam-6142	2	23	two	two	NUM
ejpam-6142	2	24	distinct	distinct	ADJ
ejpam-6142	2	25	groups	group	NOUN
ejpam-6142	2	26	:	:	PUNCT
ejpam-6142	2	27	males	male	NOUN
ejpam-6142	2	28	and	and	CCONJ
ejpam-6142	2	29	females	female	NOUN
ejpam-6142	2	30	.	.	PUNCT
ejpam-6142	3	1	within	within	ADP
ejpam-6142	3	2	this	this	DET
ejpam-6142	3	3	theoretical	theoretical	ADJ
ejpam-6142	3	4	framework	framework	NOUN
ejpam-6142	3	5	,	,	PUNCT
ejpam-6142	3	6	seven	seven	NUM
ejpam-6142	3	7	classes	class	NOUN
ejpam-6142	3	8	of	of	ADP
ejpam-6142	3	9	individuals	individual	NOUN
ejpam-6142	3	10	are	be	AUX
ejpam-6142	3	11	considered	consider	VERB
ejpam-6142	3	12	for	for	ADP
ejpam-6142	3	13	each	each	DET
ejpam-6142	3	14	gender	gender	NOUN
ejpam-6142	3	15	.	.	PUNCT
ejpam-6142	4	1	we	we	PRON
ejpam-6142	4	2	compute	compute	VERB
ejpam-6142	4	3	the	the	DET
ejpam-6142	4	4	basic	basic	ADJ
ejpam-6142	4	5	reproduction	reproduction	NOUN
ejpam-6142	4	6	number	number	NOUN
ejpam-6142	4	7	r0	r0	NOUN
ejpam-6142	4	8	,	,	PUNCT
ejpam-6142	4	9	which	which	PRON
ejpam-6142	4	10	is	be	AUX
ejpam-6142	4	11	crucial	crucial	ADJ
ejpam-6142	4	12	to	to	PART
ejpam-6142	4	13	determine	determine	VERB
ejpam-6142	4	14	the	the	DET
ejpam-6142	4	15	risk	risk	NOUN
ejpam-6142	4	16	of	of	ADP
ejpam-6142	4	17	disease	disease	NOUN
ejpam-6142	4	18	transmission	transmission	NOUN
ejpam-6142	4	19	among	among	ADP
ejpam-6142	4	20	these	these	DET
ejpam-6142	4	21	populations	population	NOUN
ejpam-6142	4	22	.	.	PUNCT
ejpam-6142	5	1	furthermore	furthermore	ADV
ejpam-6142	5	2	,	,	PUNCT
ejpam-6142	5	3	routh	routh	PROPN
ejpam-6142	5	4	-	-	PUNCT
ejpam-6142	5	5	hurwitz	hurwitz	PROPN
ejpam-6142	5	6	criterion	criterion	NOUN
ejpam-6142	5	7	is	be	AUX
ejpam-6142	5	8	used	use	VERB
ejpam-6142	5	9	in	in	ADP
ejpam-6142	5	10	stability	stability	NOUN
ejpam-6142	5	11	analysis	analysis	NOUN
ejpam-6142	5	12	of	of	ADP
ejpam-6142	5	13	disease	disease	NOUN
ejpam-6142	5	14	-	-	PUNCT
ejpam-6142	5	15	free	free	ADJ
ejpam-6142	5	16	and	and	CCONJ
ejpam-6142	5	17	endemic	endemic	ADJ
ejpam-6142	5	18	equilibrium	equilibrium	NOUN
ejpam-6142	5	19	points	point	NOUN
ejpam-6142	5	20	.	.	PUNCT
ejpam-6142	6	1	the	the	DET
ejpam-6142	6	2	stability	stability	NOUN
ejpam-6142	6	3	analysis	analysis	NOUN
ejpam-6142	6	4	of	of	ADP
ejpam-6142	6	5	the	the	DET
ejpam-6142	6	6	model	model	NOUN
ejpam-6142	6	7	provides	provide	VERB
ejpam-6142	6	8	that	that	SCONJ
ejpam-6142	6	9	at	at	ADP
ejpam-6142	6	10	the	the	DET
ejpam-6142	6	11	disease	disease	NOUN
ejpam-6142	6	12	-	-	PUNCT
ejpam-6142	6	13	free	free	ADJ
ejpam-6142	6	14	equilibrium	equilibrium	NOUN
ejpam-6142	6	15	point	point	NOUN
ejpam-6142	6	16	the	the	DET
ejpam-6142	6	17	system	system	NOUN
ejpam-6142	6	18	is	be	AUX
ejpam-6142	6	19	locally	locally	ADV
ejpam-6142	6	20	asymptotically	asymptotically	ADV
ejpam-6142	6	21	stable	stable	ADJ
ejpam-6142	6	22	when	when	SCONJ
ejpam-6142	6	23	r0	r0	NOUN
ejpam-6142	6	24	<	<	X
ejpam-6142	6	25	1	1	NUM
ejpam-6142	6	26	,	,	PUNCT
ejpam-6142	6	27	and	and	CCONJ
ejpam-6142	6	28	if	if	SCONJ
ejpam-6142	6	29	r0	r0	NOUN
ejpam-6142	6	30	>	>	X
ejpam-6142	6	31	1	1	NUM
ejpam-6142	6	32	the	the	DET
ejpam-6142	6	33	system	system	NOUN
ejpam-6142	6	34	is	be	AUX
ejpam-6142	6	35	locally	locally	ADV
ejpam-6142	6	36	asymptotically	asymptotically	ADV
ejpam-6142	6	37	unstable	unstable	ADJ
ejpam-6142	6	38	at	at	ADP
ejpam-6142	6	39	the	the	DET
ejpam-6142	6	40	endemic	endemic	ADJ
ejpam-6142	6	41	equilibrium	equilibrium	NOUN
ejpam-6142	6	42	point	point	NOUN
ejpam-6142	6	43	.	.	PUNCT
ejpam-6142	7	1	additionally	additionally	ADV
ejpam-6142	7	2	,	,	PUNCT
ejpam-6142	7	3	the	the	DET
ejpam-6142	7	4	sensitivity	sensitivity	NOUN
ejpam-6142	7	5	of	of	ADP
ejpam-6142	7	6	both	both	DET
ejpam-6142	7	7	reproduction	reproduction	NOUN
ejpam-6142	7	8	number	number	NOUN
ejpam-6142	7	9	and	and	CCONJ
ejpam-6142	7	10	the	the	DET
ejpam-6142	7	11	state	state	NOUN
ejpam-6142	7	12	variables	variable	VERB
ejpam-6142	7	13	with	with	ADP
ejpam-6142	7	14	the	the	DET
ejpam-6142	7	15	key	key	ADJ
ejpam-6142	7	16	parameters	parameter	NOUN
ejpam-6142	7	17	are	be	AUX
ejpam-6142	7	18	explored	explore	VERB
ejpam-6142	7	19	in	in	ADP
ejpam-6142	7	20	order	order	NOUN
ejpam-6142	7	21	to	to	ADP
ejpam-6142	7	22	revealing	reveal	VERB
ejpam-6142	7	23	the	the	DET
ejpam-6142	7	24	most	most	ADV
ejpam-6142	7	25	influential	influential	ADJ
ejpam-6142	7	26	parameters	parameter	NOUN
ejpam-6142	7	27	that	that	PRON
ejpam-6142	7	28	affect	affect	VERB
ejpam-6142	7	29	the	the	DET
ejpam-6142	7	30	disease	disease	NOUN
ejpam-6142	7	31	transmission	transmission	NOUN
ejpam-6142	7	32	.	.	PUNCT
ejpam-6142	8	1	this	this	DET
ejpam-6142	8	2	study	study	NOUN
ejpam-6142	8	3	develops	develop	VERB
ejpam-6142	8	4	an	an	DET
ejpam-6142	8	5	optimal	optimal	ADJ
ejpam-6142	8	6	control	control	NOUN
ejpam-6142	8	7	framework	framework	NOUN
ejpam-6142	8	8	incorporating	incorporate	VERB
ejpam-6142	8	9	prevention	prevention	NOUN
ejpam-6142	8	10	,	,	PUNCT
ejpam-6142	8	11	screening	screening	NOUN
ejpam-6142	8	12	,	,	PUNCT
ejpam-6142	8	13	and	and	CCONJ
ejpam-6142	8	14	treatment	treatment	NOUN
ejpam-6142	8	15	interventions	intervention	NOUN
ejpam-6142	8	16	to	to	PART
ejpam-6142	8	17	combat	combat	VERB
ejpam-6142	8	18	hiv	hiv	PROPN
ejpam-6142	8	19	/	/	SYM
ejpam-6142	8	20	aids	aids	PROPN
ejpam-6142	8	21	transmission	transmission	NOUN
ejpam-6142	8	22	in	in	ADP
ejpam-6142	8	23	genderstratified	genderstratifie	VERB
ejpam-6142	8	24	populations	population	NOUN
ejpam-6142	8	25	.	.	PUNCT
ejpam-6142	9	1	using	use	VERB
ejpam-6142	9	2	fourth	fourth	ADJ
ejpam-6142	9	3	-	-	PUNCT
ejpam-6142	9	4	order	order	NOUN
ejpam-6142	9	5	runge	runge	NOUN
ejpam-6142	9	6	-	-	PUNCT
ejpam-6142	9	7	kutta	kutta	NOUN
ejpam-6142	9	8	methods	method	NOUN
ejpam-6142	9	9	implemented	implement	VERB
ejpam-6142	9	10	in	in	ADP
ejpam-6142	9	11	matlab	matlab	PROPN
ejpam-6142	9	12	,	,	PUNCT
ejpam-6142	9	13	we	we	PRON
ejpam-6142	9	14	numerically	numerically	ADV
ejpam-6142	9	15	solve	solve	VERB
ejpam-6142	9	16	the	the	DET
ejpam-6142	9	17	control	control	NOUN
ejpam-6142	9	18	system	system	NOUN
ejpam-6142	9	19	and	and	CCONJ
ejpam-6142	9	20	simulate	simulate	VERB
ejpam-6142	9	21	population	population	NOUN
ejpam-6142	9	22	dynamics	dynamic	NOUN
ejpam-6142	9	23	under	under	ADP
ejpam-6142	9	24	various	various	ADJ
ejpam-6142	9	25	intervention	intervention	NOUN
ejpam-6142	9	26	scenarios	scenario	NOUN
ejpam-6142	9	27	.	.	PUNCT
ejpam-6142	10	1	our	our	PRON
ejpam-6142	10	2	results	result	NOUN
ejpam-6142	10	3	demonstrate	demonstrate	VERB
ejpam-6142	10	4	that	that	SCONJ
ejpam-6142	10	5	the	the	DET
ejpam-6142	10	6	combined	combined	ADJ
ejpam-6142	10	7	implementation	implementation	NOUN
ejpam-6142	10	8	of	of	ADP
ejpam-6142	10	9	all	all	DET
ejpam-6142	10	10	three	three	NUM
ejpam-6142	10	11	interventions	intervention	NOUN
ejpam-6142	10	12	yields	yield	VERB
ejpam-6142	10	13	superior	superior	ADJ
ejpam-6142	10	14	infection	infection	NOUN
ejpam-6142	10	15	reduction	reduction	NOUN
ejpam-6142	10	16	compared	compare	VERB
ejpam-6142	10	17	to	to	ADP
ejpam-6142	10	18	isolated	isolated	ADJ
ejpam-6142	10	19	measures	measure	NOUN
ejpam-6142	10	20	,	,	PUNCT
ejpam-6142	10	21	with	with	ADP
ejpam-6142	10	22	significant	significant	ADJ
ejpam-6142	10	23	decreases	decrease	NOUN
ejpam-6142	10	24	in	in	ADP
ejpam-6142	10	25	prevalence	prevalence	NOUN
ejpam-6142	10	26	rates	rate	NOUN
ejpam-6142	10	27	observed	observe	VERB
ejpam-6142	10	28	for	for	ADP
ejpam-6142	10	29	both	both	DET
ejpam-6142	10	30	genders	gender	NOUN
ejpam-6142	10	31	.	.	PUNCT
ejpam-6142	11	1	these	these	DET
ejpam-6142	11	2	findings	finding	NOUN
ejpam-6142	11	3	provide	provide	VERB
ejpam-6142	11	4	quantitative	quantitative	ADJ
ejpam-6142	11	5	evidence	evidence	NOUN
ejpam-6142	11	6	for	for	ADP
ejpam-6142	11	7	public	public	ADJ
ejpam-6142	11	8	health	health	NOUN
ejpam-6142	11	9	decision	decision	NOUN
ejpam-6142	11	10	-	-	PUNCT
ejpam-6142	11	11	making	making	NOUN
ejpam-6142	11	12	,	,	PUNCT
ejpam-6142	11	13	offering	offer	VERB
ejpam-6142	11	14	both	both	DET
ejpam-6142	11	15	a	a	DET
ejpam-6142	11	16	validated	validate	VERB
ejpam-6142	11	17	mathematical	mathematical	ADJ
ejpam-6142	11	18	tool	tool	NOUN
ejpam-6142	11	19	for	for	ADP
ejpam-6142	11	20	epidemic	epidemic	NOUN
ejpam-6142	11	21	modeling	modeling	NOUN
ejpam-6142	11	22	and	and	CCONJ
ejpam-6142	11	23	practical	practical	ADJ
ejpam-6142	11	24	insights	insight	NOUN
ejpam-6142	11	25	for	for	ADP
ejpam-6142	11	26	optimizing	optimize	VERB
ejpam-6142	11	27	resource	resource	NOUN
ejpam-6142	11	28	allocation	allocation	NOUN
ejpam-6142	11	29	in	in	ADP
ejpam-6142	11	30	hiv	hiv	PROPN
ejpam-6142	11	31	/	/	SYM
ejpam-6142	11	32	aids	aids	PROPN
ejpam-6142	11	33	control	control	NOUN
ejpam-6142	11	34	programs	program	NOUN
ejpam-6142	11	35	.	.	PUNCT
ejpam-6142	12	1	the	the	DET
ejpam-6142	12	2	framework	framework	NOUN
ejpam-6142	12	3	advances	advance	VERB
ejpam-6142	12	4	current	current	ADJ
ejpam-6142	12	5	methodologies	methodology	NOUN
ejpam-6142	12	6	by	by	ADP
ejpam-6142	12	7	systematically	systematically	ADV
ejpam-6142	12	8	evaluating	evaluate	VERB
ejpam-6142	12	9	intervention	intervention	NOUN
ejpam-6142	12	10	effectiveness	effectiveness	NOUN
ejpam-6142	12	11	while	while	SCONJ
ejpam-6142	12	12	accounting	account	VERB
ejpam-6142	12	13	for	for	ADP
ejpam-6142	12	14	gender	gender	NOUN
ejpam-6142	12	15	-	-	PUNCT
ejpam-6142	12	16	specific	specific	ADJ
ejpam-6142	12	17	transmission	transmission	NOUN
ejpam-6142	12	18	dynamics	dynamic	NOUN
ejpam-6142	12	19	.	.	PUNCT
ejpam-6142	13	1	2020	2020	NUM
ejpam-6142	13	2	mathematics	mathematic	NOUN
ejpam-6142	13	3	subject	subject	NOUN
ejpam-6142	13	4	classifications	classification	NOUN
ejpam-6142	13	5	:	:	PUNCT
ejpam-6142	13	6	92c42	92c42	NUM
ejpam-6142	13	7	,	,	PUNCT
ejpam-6142	13	8	34c60	34c60	NUM
ejpam-6142	13	9	,	,	PUNCT
ejpam-6142	13	10	92d25	92d25	NUM
ejpam-6142	13	11	,	,	PUNCT
ejpam-6142	13	12	92d30	92d30	NUM
ejpam-6142	13	13	,	,	PUNCT
ejpam-6142	13	14	37n25	37n25	NUM
ejpam-6142	13	15	key	key	ADJ
ejpam-6142	13	16	words	word	NOUN
ejpam-6142	13	17	and	and	CCONJ
ejpam-6142	13	18	phrases	phrase	NOUN
ejpam-6142	13	19	:	:	PUNCT
ejpam-6142	13	20	hiv	hiv	PROPN
ejpam-6142	13	21	/	/	SYM
ejpam-6142	13	22	aids	aids	PROPN
ejpam-6142	13	23	model	model	NOUN
ejpam-6142	13	24	,	,	PUNCT
ejpam-6142	13	25	stability	stability	NOUN
ejpam-6142	13	26	,	,	PUNCT
ejpam-6142	13	27	sensitivity	sensitivity	NOUN
ejpam-6142	13	28	,	,	PUNCT
ejpam-6142	13	29	optimal	optimal	ADJ
ejpam-6142	13	30	control	control	NOUN
ejpam-6142	13	31	,	,	PUNCT
ejpam-6142	13	32	numerical	numerical	PROPN
ejpam-6142	13	33	simulation	simulation	PROPN
ejpam-6142	13	34	∗corresponding	∗corresponde	VERB
ejpam-6142	13	35	author	author	NOUN
ejpam-6142	13	36	.	.	PUNCT
ejpam-6142	14	1	doi	doi	NOUN
ejpam-6142	14	2	:	:	PUNCT
ejpam-6142	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6142	https://doi.org/10.29020/nybg.ejpam.v18i2.6142	PRON
ejpam-6142	14	4	email	email	NOUN
ejpam-6142	14	5	addresses	address	NOUN
ejpam-6142	14	6	:	:	PUNCT
ejpam-6142	14	7	saiwan.fatah@univsul.edu.iq	saiwan.fatah@univsul.edu.iq	NOUN
ejpam-6142	14	8	(	(	PUNCT
ejpam-6142	14	9	saiwan	saiwan	PROPN
ejpam-6142	14	10	m.	m.	PROPN
ejpam-6142	14	11	fatah	fatah	PROPN
ejpam-6142	14	12	)	)	PUNCT
ejpam-6142	14	13	,	,	PUNCT
ejpam-6142	14	14	sarbaz.hamza@uor.edu.krd	sarbaz.hamza@uor.edu.krd	NOUN
ejpam-6142	14	15	(	(	PUNCT
ejpam-6142	14	16	sarbaz	sarbaz	PROPN
ejpam-6142	14	17	h.	h.	PROPN
ejpam-6142	14	18	a.	a.	PROPN
ejpam-6142	14	19	khoshnaw),arkan.mustafa@univsul.edu.iq	khoshnaw),arkan.mustafa@univsul.edu.iq	PROPN
ejpam-6142	14	20	(	(	PUNCT
ejpam-6142	14	21	arkan	arkan	PROPN
ejpam-6142	14	22	n.	n.	PROPN
ejpam-6142	14	23	mustafa	mustafa	PROPN
ejpam-6142	14	24	)	)	PUNCT
ejpam-6142	14	25	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6142	14	26	1	1	NUM
ejpam-6142	14	27	copyright	copyright	NOUN
ejpam-6142	14	28	:	:	PUNCT
ejpam-6142	15	1	©	©	PROPN
ejpam-6142	15	2	2025	2025	NUM
ejpam-6142	15	3	the	the	DET
ejpam-6142	15	4	author(s	author(s	NOUN
ejpam-6142	15	5	)	)	PUNCT
ejpam-6142	15	6	.	.	PUNCT
ejpam-6142	16	1	(	(	PUNCT
ejpam-6142	16	2	cc	cc	NOUN
ejpam-6142	16	3	by	by	ADP
ejpam-6142	16	4	-	-	PUNCT
ejpam-6142	16	5	nc	nc	PROPN
ejpam-6142	16	6	4.0	4.0	NUM
ejpam-6142	16	7	)	)	PUNCT
ejpam-6142	16	8	s.	s.	PROPN
ejpam-6142	16	9	m.	m.	PROPN
ejpam-6142	16	10	fatah	fatah	PROPN
ejpam-6142	16	11	,	,	PUNCT
ejpam-6142	16	12	s.	s.	PROPN
ejpam-6142	16	13	h.	h.	PROPN
ejpam-6142	16	14	a.	a.	PROPN
ejpam-6142	16	15	khoshnaw	khoshnaw	PROPN
ejpam-6142	16	16	,	,	PUNCT
ejpam-6142	16	17	a.	a.	PROPN
ejpam-6142	16	18	n.	n.	PROPN
ejpam-6142	16	19	mustafa	mustafa	PROPN
ejpam-6142	16	20	/	/	SYM
ejpam-6142	16	21	eur	eur	PROPN
ejpam-6142	16	22	.	.	PUNCT
ejpam-6142	17	1	j.	j.	PROPN
ejpam-6142	17	2	pure	pure	PROPN
ejpam-6142	17	3	appl	appl	PROPN
ejpam-6142	17	4	.	.	PROPN
ejpam-6142	17	5	math	math	PROPN
ejpam-6142	17	6	,	,	PUNCT
ejpam-6142	17	7	18	18	NUM
ejpam-6142	17	8	(	(	PUNCT
ejpam-6142	17	9	2	2	NUM
ejpam-6142	17	10	)	)	PUNCT
ejpam-6142	17	11	(	(	PUNCT
ejpam-6142	17	12	2025	2025	NUM
ejpam-6142	17	13	)	)	PUNCT
ejpam-6142	17	14	,	,	PUNCT
ejpam-6142	17	15	6142	6142	NUM
ejpam-6142	17	16	2	2	NUM
ejpam-6142	17	17	of	of	ADP
ejpam-6142	17	18	33	33	NUM
ejpam-6142	17	19	1	1	NUM
ejpam-6142	17	20	.	.	PUNCT
ejpam-6142	17	21	introduction	introduction	NOUN
ejpam-6142	17	22	in	in	ADP
ejpam-6142	17	23	1981	1981	NUM
ejpam-6142	17	24	,	,	PUNCT
ejpam-6142	17	25	for	for	ADP
ejpam-6142	17	26	the	the	DET
ejpam-6142	17	27	first	first	ADJ
ejpam-6142	17	28	time	time	NOUN
ejpam-6142	17	29	acquired	acquire	VERB
ejpam-6142	17	30	immunodeficiency	immunodeficiency	NOUN
ejpam-6142	17	31	syndrome	syndrome	NOUN
ejpam-6142	17	32	(	(	PUNCT
ejpam-6142	17	33	aids	aids	PROPN
ejpam-6142	17	34	)	)	PUNCT
ejpam-6142	17	35	was	be	AUX
ejpam-6142	17	36	initially	initially	ADV
ejpam-6142	17	37	recognized	recognize	VERB
ejpam-6142	17	38	as	as	ADP
ejpam-6142	17	39	a	a	DET
ejpam-6142	17	40	new	new	ADJ
ejpam-6142	17	41	infectious	infectious	ADJ
ejpam-6142	17	42	disease	disease	NOUN
ejpam-6142	17	43	within	within	ADP
ejpam-6142	17	44	the	the	DET
ejpam-6142	17	45	community	community	NOUN
ejpam-6142	17	46	of	of	ADP
ejpam-6142	17	47	homosexual	homosexual	NOUN
ejpam-6142	17	48	in	in	ADP
ejpam-6142	17	49	los	los	PROPN
ejpam-6142	17	50	angeles	angeles	PROPN
ejpam-6142	17	51	and	and	CCONJ
ejpam-6142	17	52	san	san	PROPN
ejpam-6142	17	53	francisco	francisco	PROPN
ejpam-6142	18	1	[	[	X
ejpam-6142	18	2	1	1	NUM
ejpam-6142	18	3	,	,	PUNCT
ejpam-6142	18	4	2	2	NUM
ejpam-6142	18	5	]	]	PUNCT
ejpam-6142	18	6	.	.	PUNCT
ejpam-6142	19	1	over	over	ADP
ejpam-6142	19	2	the	the	DET
ejpam-6142	19	3	past	past	ADJ
ejpam-6142	19	4	forty	forty	NUM
ejpam-6142	19	5	years	year	NOUN
ejpam-6142	19	6	,	,	PUNCT
ejpam-6142	19	7	the	the	DET
ejpam-6142	19	8	human	human	ADJ
ejpam-6142	19	9	immunodeficiency	immunodeficiency	NOUN
ejpam-6142	19	10	virus	virus	NOUN
ejpam-6142	19	11	(	(	PUNCT
ejpam-6142	19	12	hiv	hiv	PROPN
ejpam-6142	19	13	)	)	PUNCT
ejpam-6142	19	14	has	have	AUX
ejpam-6142	19	15	caused	cause	VERB
ejpam-6142	19	16	the	the	DET
ejpam-6142	19	17	deaths	death	NOUN
ejpam-6142	19	18	of	of	ADP
ejpam-6142	19	19	numerous	numerous	ADJ
ejpam-6142	19	20	individuals	individual	NOUN
ejpam-6142	19	21	,	,	PUNCT
ejpam-6142	19	22	including	include	VERB
ejpam-6142	19	23	men	man	NOUN
ejpam-6142	19	24	,	,	PUNCT
ejpam-6142	19	25	women	woman	NOUN
ejpam-6142	19	26	,	,	PUNCT
ejpam-6142	19	27	and	and	CCONJ
ejpam-6142	19	28	children	child	NOUN
ejpam-6142	19	29	worldwide	worldwide	ADV
ejpam-6142	19	30	,	,	PUNCT
ejpam-6142	19	31	for	for	ADP
ejpam-6142	19	32	instance	instance	NOUN
ejpam-6142	19	33	in	in	ADP
ejpam-6142	19	34	2003	2003	NUM
ejpam-6142	19	35	each	each	DET
ejpam-6142	19	36	day	day	NOUN
ejpam-6142	19	37	there	there	PRON
ejpam-6142	19	38	were	be	VERB
ejpam-6142	19	39	15000	15000	NUM
ejpam-6142	19	40	new	new	ADJ
ejpam-6142	19	41	infected	infect	VERB
ejpam-6142	19	42	individuals	individual	NOUN
ejpam-6142	19	43	and	and	CCONJ
ejpam-6142	19	44	8000	8000	NUM
ejpam-6142	19	45	died	die	VERB
ejpam-6142	19	46	with	with	ADP
ejpam-6142	19	47	hiv	hiv	PROPN
ejpam-6142	19	48	in	in	ADP
ejpam-6142	19	49	the	the	DET
ejpam-6142	19	50	world	world	NOUN
ejpam-6142	20	1	[	[	X
ejpam-6142	20	2	1	1	NUM
ejpam-6142	20	3	]	]	PUNCT
ejpam-6142	20	4	.	.	PUNCT
ejpam-6142	21	1	the	the	DET
ejpam-6142	21	2	world	world	PROPN
ejpam-6142	21	3	health	health	PROPN
ejpam-6142	21	4	organization	organization	NOUN
ejpam-6142	21	5	(	(	PUNCT
ejpam-6142	21	6	who	who	PRON
ejpam-6142	21	7	)	)	PUNCT
ejpam-6142	21	8	reports	report	VERB
ejpam-6142	21	9	that	that	SCONJ
ejpam-6142	21	10	71.3	71.3	NUM
ejpam-6142	21	11	-	-	SYM
ejpam-6142	21	12	112.8	112.8	NUM
ejpam-6142	21	13	million	million	NUM
ejpam-6142	21	14	people	people	NOUN
ejpam-6142	21	15	have	have	AUX
ejpam-6142	21	16	contracted	contract	VERB
ejpam-6142	21	17	hiv	hiv	PROPN
ejpam-6142	21	18	,	,	PUNCT
ejpam-6142	21	19	and	and	CCONJ
ejpam-6142	21	20	that	that	SCONJ
ejpam-6142	21	21	35.7	35.7	NUM
ejpam-6142	21	22	-	-	SYM
ejpam-6142	21	23	51.1	51.1	NUM
ejpam-6142	21	24	million	million	NUM
ejpam-6142	21	25	people	people	NOUN
ejpam-6142	21	26	have	have	AUX
ejpam-6142	21	27	lost	lose	VERB
ejpam-6142	21	28	their	their	PRON
ejpam-6142	21	29	lives	life	NOUN
ejpam-6142	21	30	to	to	ADP
ejpam-6142	21	31	the	the	DET
ejpam-6142	21	32	disease	disease	NOUN
ejpam-6142	21	33	since	since	SCONJ
ejpam-6142	21	34	the	the	DET
ejpam-6142	21	35	virus	virus	NOUN
ejpam-6142	21	36	’s	’s	PART
ejpam-6142	21	37	inception	inception	NOUN
ejpam-6142	21	38	.	.	PUNCT
ejpam-6142	22	1	there	there	PRON
ejpam-6142	22	2	were	be	VERB
ejpam-6142	22	3	39.9	39.9	NUM
ejpam-6142	22	4	million	million	NUM
ejpam-6142	22	5	hiv	hiv	NOUN
ejpam-6142	22	6	-	-	PUNCT
ejpam-6142	22	7	positive	positive	ADJ
ejpam-6142	22	8	individuals	individual	NOUN
ejpam-6142	22	9	worldwide	worldwide	ADV
ejpam-6142	22	10	by	by	ADP
ejpam-6142	22	11	the	the	DET
ejpam-6142	22	12	end	end	NOUN
ejpam-6142	22	13	of	of	ADP
ejpam-6142	22	14	2023	2023	NUM
ejpam-6142	22	15	and	and	CCONJ
ejpam-6142	22	16	in	in	ADP
ejpam-6142	22	17	the	the	DET
ejpam-6142	22	18	year	year	NOUN
ejpam-6142	22	19	2023	2023	NUM
ejpam-6142	22	20	the	the	DET
ejpam-6142	22	21	number	number	NOUN
ejpam-6142	22	22	of	of	ADP
ejpam-6142	22	23	people	people	NOUN
ejpam-6142	22	24	who	who	PRON
ejpam-6142	22	25	died	die	VERB
ejpam-6142	22	26	of	of	ADP
ejpam-6142	22	27	hiv	hiv	PROPN
ejpam-6142	22	28	related	relate	VERB
ejpam-6142	22	29	illness	illness	NOUN
ejpam-6142	22	30	is	be	AUX
ejpam-6142	22	31	630000	630000	NUM
ejpam-6142	22	32	globally	globally	ADV
ejpam-6142	23	1	[	[	X
ejpam-6142	23	2	3	3	NUM
ejpam-6142	23	3	]	]	PUNCT
ejpam-6142	23	4	.	.	PUNCT
ejpam-6142	24	1	worldwide	worldwide	ADV
ejpam-6142	24	2	,	,	PUNCT
ejpam-6142	24	3	it	it	PRON
ejpam-6142	24	4	is	be	AUX
ejpam-6142	24	5	estimated	estimate	VERB
ejpam-6142	24	6	that	that	SCONJ
ejpam-6142	24	7	0.6−0.7	0.6−0.7	NOUN
ejpam-6142	24	8	%	%	NOUN
ejpam-6142	24	9	of	of	ADP
ejpam-6142	24	10	individuals	individual	NOUN
ejpam-6142	24	11	aged	age	VERB
ejpam-6142	24	12	15	15	NUM
ejpam-6142	24	13	to	to	PART
ejpam-6142	24	14	49	49	NUM
ejpam-6142	24	15	are	be	AUX
ejpam-6142	24	16	infected	infect	VERB
ejpam-6142	24	17	with	with	ADP
ejpam-6142	24	18	hiv	hiv	PROPN
ejpam-6142	24	19	,	,	PUNCT
ejpam-6142	24	20	however	however	ADV
ejpam-6142	24	21	the	the	DET
ejpam-6142	24	22	impact	impact	NOUN
ejpam-6142	24	23	of	of	ADP
ejpam-6142	24	24	the	the	DET
ejpam-6142	24	25	pandemic	pandemic	NOUN
ejpam-6142	24	26	significantly	significantly	ADV
ejpam-6142	24	27	differs	differ	VERB
ejpam-6142	24	28	among	among	ADP
ejpam-6142	24	29	countries	country	NOUN
ejpam-6142	24	30	and	and	CCONJ
ejpam-6142	24	31	regions	region	NOUN
ejpam-6142	24	32	.	.	PUNCT
ejpam-6142	25	1	the	the	DET
ejpam-6142	25	2	world	world	PROPN
ejpam-6142	25	3	health	health	PROPN
ejpam-6142	25	4	organization	organization	PROPN
ejpam-6142	25	5	reports	report	VERB
ejpam-6142	25	6	that	that	SCONJ
ejpam-6142	25	7	the	the	DET
ejpam-6142	25	8	most	most	ADV
ejpam-6142	25	9	severely	severely	ADV
ejpam-6142	25	10	affected	affect	VERB
ejpam-6142	25	11	is	be	AUX
ejpam-6142	25	12	the	the	DET
ejpam-6142	25	13	african	african	ADJ
ejpam-6142	25	14	region	region	NOUN
ejpam-6142	25	15	continues	continue	VERB
ejpam-6142	25	16	with	with	ADP
ejpam-6142	25	17	3.4	3.4	NUM
ejpam-6142	25	18	%	%	NOUN
ejpam-6142	25	19	of	of	ADP
ejpam-6142	25	20	adults	adult	NOUN
ejpam-6142	25	21	living	live	VERB
ejpam-6142	25	22	with	with	ADP
ejpam-6142	25	23	hiv	hiv	PROPN
ejpam-6142	25	24	which	which	PRON
ejpam-6142	25	25	is	be	AUX
ejpam-6142	25	26	almost	almost	ADV
ejpam-6142	25	27	two	two	NUM
ejpam-6142	25	28	-	-	PUNCT
ejpam-6142	25	29	thirds	third	NOUN
ejpam-6142	25	30	of	of	ADP
ejpam-6142	25	31	all	all	DET
ejpam-6142	25	32	hiv	hiv	NOUN
ejpam-6142	25	33	-	-	PUNCT
ejpam-6142	25	34	positive	positive	ADJ
ejpam-6142	25	35	people	people	NOUN
ejpam-6142	25	36	globally	globally	ADV
ejpam-6142	25	37	.	.	PUNCT
ejpam-6142	26	1	there	there	PRON
ejpam-6142	26	2	are	be	VERB
ejpam-6142	26	3	several	several	ADJ
ejpam-6142	26	4	ways	way	NOUN
ejpam-6142	26	5	in	in	ADP
ejpam-6142	26	6	which	which	PRON
ejpam-6142	26	7	hiv	hiv	PROPN
ejpam-6142	26	8	transmitted	transmit	VERB
ejpam-6142	26	9	from	from	ADP
ejpam-6142	26	10	an	an	DET
ejpam-6142	26	11	infected	infect	VERB
ejpam-6142	26	12	to	to	ADP
ejpam-6142	26	13	a	a	DET
ejpam-6142	26	14	victim	victim	NOUN
ejpam-6142	26	15	and	and	CCONJ
ejpam-6142	26	16	the	the	DET
ejpam-6142	26	17	most	most	ADV
ejpam-6142	26	18	common	common	ADJ
ejpam-6142	26	19	ones	one	NOUN
ejpam-6142	26	20	are	be	AUX
ejpam-6142	26	21	vertical	vertical	ADJ
ejpam-6142	26	22	transmission	transmission	NOUN
ejpam-6142	26	23	from	from	ADP
ejpam-6142	26	24	mother	mother	NOUN
ejpam-6142	26	25	to	to	ADP
ejpam-6142	26	26	child	child	NOUN
ejpam-6142	26	27	,	,	PUNCT
ejpam-6142	26	28	homosexual	homosexual	ADJ
ejpam-6142	26	29	contact	contact	NOUN
ejpam-6142	26	30	,	,	PUNCT
ejpam-6142	26	31	blood	blood	NOUN
ejpam-6142	26	32	transfusions	transfusion	NOUN
ejpam-6142	26	33	,	,	PUNCT
ejpam-6142	26	34	and	and	CCONJ
ejpam-6142	26	35	shared	share	VERB
ejpam-6142	26	36	drug	drug	NOUN
ejpam-6142	26	37	injection	injection	NOUN
ejpam-6142	26	38	needles	needle	NOUN
ejpam-6142	26	39	[	[	X
ejpam-6142	26	40	4–6	4–6	X
ejpam-6142	26	41	]	]	X
ejpam-6142	26	42	.	.	PUNCT
ejpam-6142	27	1	understanding	understand	VERB
ejpam-6142	27	2	hiv	hiv	PROPN
ejpam-6142	27	3	infection	infection	NOUN
ejpam-6142	27	4	illness	illness	NOUN
ejpam-6142	27	5	and	and	CCONJ
ejpam-6142	27	6	researching	research	VERB
ejpam-6142	27	7	the	the	DET
ejpam-6142	27	8	epidemiological	epidemiological	ADJ
ejpam-6142	27	9	dynamics	dynamic	NOUN
ejpam-6142	27	10	of	of	ADP
ejpam-6142	27	11	hiv	hiv	PROPN
ejpam-6142	27	12	are	be	AUX
ejpam-6142	27	13	made	make	VERB
ejpam-6142	27	14	possible	possible	ADJ
ejpam-6142	27	15	in	in	ADP
ejpam-6142	27	16	large	large	ADJ
ejpam-6142	27	17	part	part	NOUN
ejpam-6142	27	18	by	by	ADP
ejpam-6142	27	19	mathematical	mathematical	ADJ
ejpam-6142	27	20	modeling	modeling	NOUN
ejpam-6142	27	21	.	.	PUNCT
ejpam-6142	28	1	during	during	ADP
ejpam-6142	28	2	the	the	DET
ejpam-6142	28	3	years	year	NOUN
ejpam-6142	28	4	1986	1986	NUM
ejpam-6142	28	5	-	-	SYM
ejpam-6142	28	6	1988	1988	NUM
ejpam-6142	28	7	a	a	DET
ejpam-6142	28	8	series	series	NOUN
ejpam-6142	28	9	of	of	ADP
ejpam-6142	28	10	researches	research	NOUN
ejpam-6142	28	11	on	on	ADP
ejpam-6142	28	12	the	the	DET
ejpam-6142	28	13	role	role	NOUN
ejpam-6142	28	14	of	of	ADP
ejpam-6142	28	15	mathematical	mathematical	ADJ
ejpam-6142	28	16	modelling	modelling	NOUN
ejpam-6142	28	17	on	on	ADP
ejpam-6142	28	18	hiv	hiv	PROPN
ejpam-6142	28	19	transmission	transmission	NOUN
ejpam-6142	28	20	and	and	CCONJ
ejpam-6142	28	21	the	the	DET
ejpam-6142	28	22	transmission	transmission	NOUN
ejpam-6142	28	23	dynamics	dynamic	NOUN
ejpam-6142	28	24	of	of	ADP
ejpam-6142	28	25	aids	aid	NOUN
ejpam-6142	28	26	were	be	AUX
ejpam-6142	28	27	published	publish	VERB
ejpam-6142	28	28	(	(	PUNCT
ejpam-6142	28	29	see	see	VERB
ejpam-6142	28	30	for	for	ADP
ejpam-6142	28	31	example	example	NOUN
ejpam-6142	28	32	[	[	X
ejpam-6142	28	33	7–10	7–10	X
ejpam-6142	28	34	]	]	X
ejpam-6142	28	35	)	)	PUNCT
ejpam-6142	28	36	.	.	PUNCT
ejpam-6142	29	1	researchers	researcher	NOUN
ejpam-6142	29	2	interested	interested	ADJ
ejpam-6142	29	3	in	in	ADP
ejpam-6142	29	4	hiv	hiv	PROPN
ejpam-6142	29	5	dynamics	dynamic	NOUN
ejpam-6142	29	6	and	and	CCONJ
ejpam-6142	29	7	transmission	transmission	NOUN
ejpam-6142	29	8	including	include	VERB
ejpam-6142	29	9	both	both	CCONJ
ejpam-6142	29	10	applied	apply	VERB
ejpam-6142	29	11	mathematicians	mathematician	NOUN
ejpam-6142	29	12	and	and	CCONJ
ejpam-6142	29	13	biologists	biologist	NOUN
ejpam-6142	29	14	.	.	PUNCT
ejpam-6142	30	1	through	through	ADP
ejpam-6142	30	2	the	the	DET
ejpam-6142	30	3	last	last	ADJ
ejpam-6142	30	4	four	four	NUM
ejpam-6142	30	5	decades	decade	NOUN
ejpam-6142	30	6	a	a	DET
ejpam-6142	30	7	huge	huge	ADJ
ejpam-6142	30	8	number	number	NOUN
ejpam-6142	30	9	of	of	ADP
ejpam-6142	30	10	researches	research	NOUN
ejpam-6142	30	11	on	on	ADP
ejpam-6142	30	12	the	the	DET
ejpam-6142	30	13	development	development	NOUN
ejpam-6142	30	14	of	of	ADP
ejpam-6142	30	15	the	the	DET
ejpam-6142	30	16	mathematical	mathematical	ADJ
ejpam-6142	30	17	models	model	NOUN
ejpam-6142	30	18	of	of	ADP
ejpam-6142	30	19	the	the	DET
ejpam-6142	30	20	disease	disease	NOUN
ejpam-6142	30	21	and	and	CCONJ
ejpam-6142	30	22	dynamics	dynamic	NOUN
ejpam-6142	30	23	behavior	behavior	NOUN
ejpam-6142	30	24	,	,	PUNCT
ejpam-6142	30	25	stability	stability	NOUN
ejpam-6142	30	26	and	and	CCONJ
ejpam-6142	30	27	sensitivity	sensitivity	NOUN
ejpam-6142	30	28	analysis	analysis	NOUN
ejpam-6142	30	29	of	of	ADP
ejpam-6142	30	30	the	the	DET
ejpam-6142	30	31	model	model	NOUN
ejpam-6142	30	32	,	,	PUNCT
ejpam-6142	30	33	and	and	CCONJ
ejpam-6142	30	34	the	the	DET
ejpam-6142	30	35	role	role	NOUN
ejpam-6142	30	36	of	of	ADP
ejpam-6142	30	37	basic	basic	ADJ
ejpam-6142	30	38	reproduction	reproduction	NOUN
ejpam-6142	30	39	number	number	NOUN
ejpam-6142	30	40	r0	r0	NOUN
ejpam-6142	30	41	in	in	ADP
ejpam-6142	30	42	controlling	control	VERB
ejpam-6142	30	43	the	the	DET
ejpam-6142	30	44	spread	spread	NOUN
ejpam-6142	30	45	of	of	ADP
ejpam-6142	30	46	aids	aid	NOUN
ejpam-6142	30	47	have	have	AUX
ejpam-6142	30	48	been	be	AUX
ejpam-6142	30	49	published	publish	VERB
ejpam-6142	30	50	.	.	PUNCT
ejpam-6142	31	1	some	some	DET
ejpam-6142	31	2	researchers	researcher	NOUN
ejpam-6142	31	3	have	have	AUX
ejpam-6142	31	4	developed	develop	VERB
ejpam-6142	31	5	and	and	CCONJ
ejpam-6142	31	6	examined	examine	VERB
ejpam-6142	31	7	the	the	DET
ejpam-6142	31	8	stability	stability	NOUN
ejpam-6142	31	9	of	of	ADP
ejpam-6142	31	10	equilibrium	equilibrium	NOUN
ejpam-6142	31	11	points	point	NOUN
ejpam-6142	31	12	within	within	ADP
ejpam-6142	31	13	hiv	hiv	PROPN
ejpam-6142	31	14	/	/	SYM
ejpam-6142	31	15	aids	aids	PROPN
ejpam-6142	31	16	models	model	NOUN
ejpam-6142	31	17	.	.	PUNCT
ejpam-6142	32	1	contingent	contingent	NOUN
ejpam-6142	32	2	upon	upon	SCONJ
ejpam-6142	32	3	whether	whether	SCONJ
ejpam-6142	32	4	the	the	DET
ejpam-6142	32	5	reproduction	reproduction	NOUN
ejpam-6142	32	6	number	number	NOUN
ejpam-6142	32	7	r0	r0	NOUN
ejpam-6142	32	8	exceeds	exceed	NOUN
ejpam-6142	32	9	or	or	CCONJ
ejpam-6142	32	10	falls	fall	VERB
ejpam-6142	32	11	below	below	ADP
ejpam-6142	32	12	unity	unity	NOUN
ejpam-6142	32	13	,	,	PUNCT
ejpam-6142	32	14	they	they	PRON
ejpam-6142	32	15	conducted	conduct	VERB
ejpam-6142	32	16	an	an	DET
ejpam-6142	32	17	analysis	analysis	NOUN
ejpam-6142	32	18	on	on	ADP
ejpam-6142	32	19	the	the	DET
ejpam-6142	32	20	stability	stability	NOUN
ejpam-6142	32	21	and	and	CCONJ
ejpam-6142	32	22	examined	examine	VERB
ejpam-6142	32	23	at	at	ADP
ejpam-6142	32	24	both	both	CCONJ
ejpam-6142	32	25	endemic	endemic	ADJ
ejpam-6142	32	26	and	and	CCONJ
ejpam-6142	32	27	disease	disease	NOUN
ejpam-6142	32	28	-	-	PUNCT
ejpam-6142	32	29	free	free	ADJ
ejpam-6142	32	30	equilibrium	equilibrium	NOUN
ejpam-6142	32	31	points	point	NOUN
ejpam-6142	33	1	[	[	X
ejpam-6142	33	2	6	6	NUM
ejpam-6142	33	3	,	,	PUNCT
ejpam-6142	33	4	11	11	NUM
ejpam-6142	33	5	,	,	PUNCT
ejpam-6142	33	6	12	12	NUM
ejpam-6142	33	7	]	]	PUNCT
ejpam-6142	33	8	.	.	PUNCT
ejpam-6142	34	1	a	a	DET
ejpam-6142	34	2	mathematical	mathematical	ADJ
ejpam-6142	34	3	model	model	NOUN
ejpam-6142	34	4	of	of	ADP
ejpam-6142	34	5	hiv	hiv	PROPN
ejpam-6142	34	6	was	be	AUX
ejpam-6142	34	7	created	create	VERB
ejpam-6142	34	8	by	by	ADP
ejpam-6142	34	9	doyle	doyle	PROPN
ejpam-6142	34	10	et	et	PROPN
ejpam-6142	34	11	al	al	PROPN
ejpam-6142	34	12	.	.	PUNCT
ejpam-6142	35	1	[	[	X
ejpam-6142	35	2	13	13	NUM
ejpam-6142	35	3	]	]	PUNCT
ejpam-6142	35	4	to	to	PART
ejpam-6142	35	5	simulate	simulate	VERB
ejpam-6142	35	6	how	how	SCONJ
ejpam-6142	35	7	the	the	DET
ejpam-6142	35	8	virus	virus	NOUN
ejpam-6142	35	9	spreads	spread	VERB
ejpam-6142	35	10	through	through	ADP
ejpam-6142	35	11	sexual	sexual	ADJ
ejpam-6142	35	12	contact	contact	NOUN
ejpam-6142	35	13	in	in	ADP
ejpam-6142	35	14	a	a	DET
ejpam-6142	35	15	heterosexual	heterosexual	ADJ
ejpam-6142	35	16	population	population	NOUN
ejpam-6142	35	17	and	and	CCONJ
ejpam-6142	35	18	the	the	DET
ejpam-6142	35	19	stability	stability	NOUN
ejpam-6142	35	20	at	at	ADP
ejpam-6142	35	21	the	the	DET
ejpam-6142	35	22	equilibrium	equilibrium	NOUN
ejpam-6142	35	23	points	point	NOUN
ejpam-6142	35	24	are	be	AUX
ejpam-6142	35	25	carried	carry	VERB
ejpam-6142	35	26	out	out	ADP
ejpam-6142	35	27	.	.	PUNCT
ejpam-6142	36	1	they	they	PRON
ejpam-6142	36	2	designed	design	VERB
ejpam-6142	36	3	their	their	PRON
ejpam-6142	36	4	model	model	NOUN
ejpam-6142	36	5	to	to	PART
ejpam-6142	36	6	explore	explore	VERB
ejpam-6142	36	7	the	the	DET
ejpam-6142	36	8	implications	implication	NOUN
ejpam-6142	36	9	of	of	ADP
ejpam-6142	36	10	a	a	DET
ejpam-6142	36	11	basic	basic	ADJ
ejpam-6142	36	12	constraint	constraint	NOUN
ejpam-6142	36	13	in	in	ADP
ejpam-6142	36	14	any	any	DET
ejpam-6142	36	15	sexual	sexual	ADJ
ejpam-6142	36	16	mixing	mixing	NOUN
ejpam-6142	36	17	process	process	NOUN
ejpam-6142	36	18	heterosexual	heterosexual	ADJ
ejpam-6142	36	19	population	population	NOUN
ejpam-6142	36	20	.	.	PUNCT
ejpam-6142	37	1	kaur	kaur	PROPN
ejpam-6142	37	2	et	et	PROPN
ejpam-6142	37	3	al	al	PROPN
ejpam-6142	37	4	.	.	PUNCT
ejpam-6142	38	1	[	[	X
ejpam-6142	38	2	14	14	NUM
ejpam-6142	38	3	]	]	PUNCT
ejpam-6142	38	4	investigated	investigate	VERB
ejpam-6142	38	5	the	the	DET
ejpam-6142	38	6	impact	impact	NOUN
ejpam-6142	38	7	of	of	ADP
ejpam-6142	38	8	screening	screen	VERB
ejpam-6142	38	9	awareness	awareness	NOUN
ejpam-6142	38	10	and	and	CCONJ
ejpam-6142	38	11	counseling	counseling	NOUN
ejpam-6142	38	12	on	on	ADP
ejpam-6142	38	13	hiv	hiv	PROPN
ejpam-6142	38	14	transmission	transmission	NOUN
ejpam-6142	38	15	in	in	ADP
ejpam-6142	38	16	the	the	DET
ejpam-6142	38	17	endemic	endemic	ADJ
ejpam-6142	38	18	region	region	NOUN
ejpam-6142	38	19	using	use	VERB
ejpam-6142	38	20	a	a	DET
ejpam-6142	38	21	mathematical	mathematical	ADJ
ejpam-6142	38	22	model	model	NOUN
ejpam-6142	38	23	in	in	ADP
ejpam-6142	38	24	nonlinear	nonlinear	ADJ
ejpam-6142	38	25	form	form	NOUN
ejpam-6142	38	26	.	.	PUNCT
ejpam-6142	39	1	they	they	PRON
ejpam-6142	39	2	studied	study	VERB
ejpam-6142	39	3	the	the	DET
ejpam-6142	39	4	impact	impact	NOUN
ejpam-6142	39	5	of	of	ADP
ejpam-6142	39	6	suitable	suitable	ADJ
ejpam-6142	39	7	choice	choice	NOUN
ejpam-6142	39	8	of	of	ADP
ejpam-6142	39	9	parameters	parameter	NOUN
ejpam-6142	39	10	to	to	PART
ejpam-6142	39	11	be	be	AUX
ejpam-6142	39	12	consistent	consistent	ADJ
ejpam-6142	39	13	with	with	ADP
ejpam-6142	39	14	screening	screen	VERB
ejpam-6142	39	15	awareness	awareness	NOUN
ejpam-6142	39	16	and	and	CCONJ
ejpam-6142	39	17	counselling	counsel	VERB
ejpam-6142	39	18	the	the	DET
ejpam-6142	39	19	disease	disease	NOUN
ejpam-6142	39	20	can	can	AUX
ejpam-6142	39	21	be	be	AUX
ejpam-6142	39	22	removed	remove	VERB
ejpam-6142	39	23	in	in	ADP
ejpam-6142	39	24	the	the	DET
ejpam-6142	39	25	population	population	NOUN
ejpam-6142	39	26	in	in	ADP
ejpam-6142	39	27	a	a	DET
ejpam-6142	39	28	reasonable	reasonable	ADJ
ejpam-6142	39	29	period	period	NOUN
ejpam-6142	39	30	of	of	ADP
ejpam-6142	39	31	time	time	NOUN
ejpam-6142	39	32	.	.	PUNCT
ejpam-6142	40	1	naresh	naresh	INTJ
ejpam-6142	40	2	et	et	NOUN
ejpam-6142	40	3	ai	ai	VERB
ejpam-6142	40	4	.	.	PUNCT
ejpam-6142	41	1	in	in	ADP
ejpam-6142	41	2	[	[	X
ejpam-6142	41	3	15	15	NUM
ejpam-6142	41	4	]	]	PUNCT
ejpam-6142	41	5	and	and	CCONJ
ejpam-6142	41	6	waziri	waziri	PROPN
ejpam-6142	41	7	et	et	PROPN
ejpam-6142	41	8	al	al	PROPN
ejpam-6142	41	9	.	.	PUNCT
ejpam-6142	42	1	in	in	ADP
ejpam-6142	42	2	[	[	X
ejpam-6142	42	3	16	16	NUM
ejpam-6142	42	4	]	]	PUNCT
ejpam-6142	42	5	proposed	propose	VERB
ejpam-6142	42	6	nonlinear	nonlinear	PROPN
ejpam-6142	42	7	mathematical	mathematical	ADJ
ejpam-6142	42	8	models	model	NOUN
ejpam-6142	42	9	to	to	ADP
ejpam-6142	42	10	for	for	ADP
ejpam-6142	42	11	examine	examine	VERB
ejpam-6142	42	12	the	the	DET
ejpam-6142	42	13	vertical	vertical	ADJ
ejpam-6142	42	14	transmission	transmission	NOUN
ejpam-6142	42	15	of	of	ADP
ejpam-6142	42	16	hiv	hiv	PROPN
ejpam-6142	42	17	dynamics	dynamic	NOUN
ejpam-6142	42	18	.	.	PUNCT
ejpam-6142	43	1	in	in	ADP
ejpam-6142	43	2	order	order	NOUN
ejpam-6142	43	3	to	to	PART
ejpam-6142	43	4	minimize	minimize	VERB
ejpam-6142	43	5	the	the	DET
ejpam-6142	43	6	risk	risk	NOUN
ejpam-6142	43	7	of	of	ADP
ejpam-6142	43	8	transmitting	transmit	VERB
ejpam-6142	43	9	the	the	DET
ejpam-6142	43	10	infection	infection	NOUN
ejpam-6142	43	11	to	to	ADP
ejpam-6142	43	12	future	future	ADJ
ejpam-6142	43	13	generations	generation	NOUN
ejpam-6142	43	14	,	,	PUNCT
ejpam-6142	43	15	providing	provide	VERB
ejpam-6142	43	16	treatment	treatment	NOUN
ejpam-6142	43	17	to	to	ADP
ejpam-6142	43	18	individuals	individual	NOUN
ejpam-6142	43	19	with	with	ADP
ejpam-6142	43	20	hiv	hiv	PROPN
ejpam-6142	43	21	before	before	SCONJ
ejpam-6142	43	22	they	they	PRON
ejpam-6142	43	23	develop	develop	VERB
ejpam-6142	43	24	aids	aid	NOUN
ejpam-6142	43	25	can	can	AUX
ejpam-6142	43	26	significantly	significantly	ADV
ejpam-6142	43	27	decrease	decrease	VERB
ejpam-6142	43	28	the	the	DET
ejpam-6142	43	29	probability	probability	NOUN
ejpam-6142	43	30	of	of	ADP
ejpam-6142	43	31	transmission	transmission	NOUN
ejpam-6142	43	32	.	.	PUNCT
ejpam-6142	44	1	s.	s.	PROPN
ejpam-6142	44	2	m.	m.	PROPN
ejpam-6142	44	3	fatah	fatah	PROPN
ejpam-6142	44	4	,	,	PUNCT
ejpam-6142	44	5	s.	s.	PROPN
ejpam-6142	44	6	h.	h.	PROPN
ejpam-6142	44	7	a.	a.	PROPN
ejpam-6142	44	8	khoshnaw	khoshnaw	PROPN
ejpam-6142	44	9	,	,	PUNCT
ejpam-6142	44	10	a.	a.	PROPN
ejpam-6142	44	11	n.	n.	PROPN
ejpam-6142	44	12	mustafa	mustafa	PROPN
ejpam-6142	44	13	/	/	SYM
ejpam-6142	44	14	eur	eur	PROPN
ejpam-6142	44	15	.	.	PUNCT
ejpam-6142	45	1	j.	j.	PROPN
ejpam-6142	45	2	pure	pure	PROPN
ejpam-6142	45	3	appl	appl	PROPN
ejpam-6142	45	4	.	.	PROPN
ejpam-6142	45	5	math	math	PROPN
ejpam-6142	45	6	,	,	PUNCT
ejpam-6142	45	7	18	18	NUM
ejpam-6142	45	8	(	(	PUNCT
ejpam-6142	45	9	2	2	NUM
ejpam-6142	45	10	)	)	PUNCT
ejpam-6142	45	11	(	(	PUNCT
ejpam-6142	45	12	2025	2025	NUM
ejpam-6142	45	13	)	)	PUNCT
ejpam-6142	45	14	,	,	PUNCT
ejpam-6142	45	15	6142	6142	NUM
ejpam-6142	45	16	3	3	NUM
ejpam-6142	45	17	of	of	ADP
ejpam-6142	45	18	33	33	NUM
ejpam-6142	45	19	the	the	DET
ejpam-6142	45	20	obtained	obtain	VERB
ejpam-6142	45	21	results	result	NOUN
ejpam-6142	45	22	in	in	ADP
ejpam-6142	45	23	their	their	PRON
ejpam-6142	45	24	study	study	NOUN
ejpam-6142	45	25	showed	show	VERB
ejpam-6142	45	26	that	that	SCONJ
ejpam-6142	45	27	in	in	ADP
ejpam-6142	45	28	1997	1997	NUM
ejpam-6142	45	29	in	in	ADP
ejpam-6142	45	30	the	the	DET
ejpam-6142	45	31	u.s	u.s	PROPN
ejpam-6142	45	32	fewer	few	ADJ
ejpam-6142	45	33	than	than	ADP
ejpam-6142	45	34	300	300	NUM
ejpam-6142	45	35	infants	infant	NOUN
ejpam-6142	45	36	acquired	acquire	VERB
ejpam-6142	45	37	hiv	hiv	PROPN
ejpam-6142	45	38	through	through	ADP
ejpam-6142	45	39	vertical	vertical	ADJ
ejpam-6142	45	40	transmission	transmission	NOUN
ejpam-6142	45	41	.	.	PUNCT
ejpam-6142	46	1	during	during	ADP
ejpam-6142	46	2	the	the	DET
ejpam-6142	46	3	last	last	ADJ
ejpam-6142	46	4	few	few	ADJ
ejpam-6142	46	5	years	year	NOUN
ejpam-6142	46	6	,	,	PUNCT
ejpam-6142	46	7	in	in	ADP
ejpam-6142	46	8	studying	study	VERB
ejpam-6142	46	9	the	the	DET
ejpam-6142	46	10	transmission	transmission	NOUN
ejpam-6142	46	11	and	and	CCONJ
ejpam-6142	46	12	development	development	NOUN
ejpam-6142	46	13	of	of	ADP
ejpam-6142	46	14	hiv	hiv	PROPN
ejpam-6142	46	15	models	model	NOUN
ejpam-6142	46	16	within	within	ADP
ejpam-6142	46	17	the	the	DET
ejpam-6142	46	18	population	population	NOUN
ejpam-6142	46	19	and	and	CCONJ
ejpam-6142	46	20	to	to	ADP
ejpam-6142	46	21	the	the	DET
ejpam-6142	46	22	reflection	reflection	NOUN
ejpam-6142	46	23	of	of	ADP
ejpam-6142	46	24	dynamics	dynamic	NOUN
ejpam-6142	46	25	hiv	hiv	PROPN
ejpam-6142	46	26	epidemic	epidemic	NOUN
ejpam-6142	46	27	,	,	PUNCT
ejpam-6142	46	28	many	many	ADJ
ejpam-6142	46	29	scholars	scholar	NOUN
ejpam-6142	46	30	adopted	adopt	VERB
ejpam-6142	46	31	the	the	DET
ejpam-6142	46	32	idea	idea	NOUN
ejpam-6142	46	33	of	of	ADP
ejpam-6142	46	34	compartment	compartment	NOUN
ejpam-6142	46	35	modelling	modelling	NOUN
ejpam-6142	46	36	,	,	PUNCT
ejpam-6142	46	37	which	which	PRON
ejpam-6142	46	38	is	be	AUX
ejpam-6142	46	39	the	the	DET
ejpam-6142	46	40	division	division	NOUN
ejpam-6142	46	41	of	of	ADP
ejpam-6142	46	42	the	the	DET
ejpam-6142	46	43	total	total	ADJ
ejpam-6142	46	44	population	population	NOUN
ejpam-6142	46	45	and	and	CCONJ
ejpam-6142	46	46	corresponding	correspond	VERB
ejpam-6142	46	47	categories	category	NOUN
ejpam-6142	46	48	.	.	PUNCT
ejpam-6142	47	1	these	these	DET
ejpam-6142	47	2	models	model	NOUN
ejpam-6142	47	3	can	can	AUX
ejpam-6142	47	4	be	be	AUX
ejpam-6142	47	5	used	use	VERB
ejpam-6142	47	6	in	in	ADP
ejpam-6142	47	7	prediction	prediction	NOUN
ejpam-6142	47	8	of	of	ADP
ejpam-6142	47	9	hiv	hiv	PROPN
ejpam-6142	47	10	incidence	incidence	NOUN
ejpam-6142	47	11	in	in	ADP
ejpam-6142	47	12	a	a	DET
ejpam-6142	47	13	shorter	short	ADJ
ejpam-6142	47	14	long	long	ADJ
ejpam-6142	47	15	-	-	PUNCT
ejpam-6142	47	16	term	term	NOUN
ejpam-6142	47	17	,	,	PUNCT
ejpam-6142	47	18	they	they	PRON
ejpam-6142	47	19	also	also	ADV
ejpam-6142	47	20	become	become	VERB
ejpam-6142	47	21	an	an	DET
ejpam-6142	47	22	important	important	ADJ
ejpam-6142	47	23	tool	tool	NOUN
ejpam-6142	47	24	in	in	ADP
ejpam-6142	47	25	analyzing	analyze	VERB
ejpam-6142	47	26	the	the	DET
ejpam-6142	47	27	transmission	transmission	NOUN
ejpam-6142	47	28	and	and	CCONJ
ejpam-6142	47	29	control	control	NOUN
ejpam-6142	47	30	of	of	ADP
ejpam-6142	47	31	hiv	hiv	PROPN
ejpam-6142	48	1	[	[	X
ejpam-6142	48	2	17	17	NUM
ejpam-6142	48	3	]	]	PUNCT
ejpam-6142	48	4	.	.	PUNCT
ejpam-6142	49	1	sensitivity	sensitivity	NOUN
ejpam-6142	49	2	analysis	analysis	NOUN
ejpam-6142	49	3	and	and	CCONJ
ejpam-6142	49	4	optimal	optimal	ADJ
ejpam-6142	49	5	control	control	NOUN
ejpam-6142	49	6	of	of	ADP
ejpam-6142	49	7	human	human	ADJ
ejpam-6142	49	8	immunodeficiency	immunodeficiency	NOUN
ejpam-6142	49	9	virus	virus	NOUN
ejpam-6142	49	10	have	have	AUX
ejpam-6142	49	11	studied	study	VERB
ejpam-6142	49	12	by	by	ADP
ejpam-6142	49	13	many	many	ADJ
ejpam-6142	49	14	researchers	researcher	NOUN
ejpam-6142	49	15	to	to	PART
ejpam-6142	49	16	show	show	VERB
ejpam-6142	49	17	the	the	DET
ejpam-6142	49	18	effect	effect	NOUN
ejpam-6142	49	19	of	of	ADP
ejpam-6142	49	20	parameters	parameter	NOUN
ejpam-6142	49	21	on	on	ADP
ejpam-6142	49	22	the	the	DET
ejpam-6142	49	23	dynamics	dynamic	NOUN
ejpam-6142	49	24	of	of	ADP
ejpam-6142	49	25	the	the	DET
ejpam-6142	49	26	transmission	transmission	NOUN
ejpam-6142	49	27	of	of	ADP
ejpam-6142	49	28	hiv	hiv	PROPN
ejpam-6142	49	29	in	in	ADP
ejpam-6142	49	30	a	a	DET
ejpam-6142	49	31	population	population	NOUN
ejpam-6142	49	32	.	.	PUNCT
ejpam-6142	50	1	various	various	ADJ
ejpam-6142	50	2	strategies	strategy	NOUN
ejpam-6142	50	3	such	such	ADJ
ejpam-6142	50	4	as	as	ADP
ejpam-6142	50	5	treatment	treatment	NOUN
ejpam-6142	50	6	,	,	PUNCT
ejpam-6142	50	7	prevention	prevention	NOUN
ejpam-6142	50	8	,	,	PUNCT
ejpam-6142	50	9	and	and	CCONJ
ejpam-6142	50	10	screening	screening	NOUN
ejpam-6142	50	11	are	be	AUX
ejpam-6142	50	12	used	use	VERB
ejpam-6142	50	13	to	to	PART
ejpam-6142	50	14	control	control	VERB
ejpam-6142	50	15	the	the	DET
ejpam-6142	50	16	disease	disease	NOUN
ejpam-6142	51	1	[	[	X
ejpam-6142	51	2	18–23	18–23	NUM
ejpam-6142	51	3	]	]	PUNCT
ejpam-6142	51	4	.	.	PUNCT
ejpam-6142	52	1	mathematical	mathematical	ADJ
ejpam-6142	52	2	model	model	NOUN
ejpam-6142	52	3	is	be	AUX
ejpam-6142	52	4	a	a	DET
ejpam-6142	52	5	very	very	ADV
ejpam-6142	52	6	important	important	ADJ
ejpam-6142	52	7	scientific	scientific	ADJ
ejpam-6142	52	8	tool	tool	NOUN
ejpam-6142	52	9	in	in	ADP
ejpam-6142	52	10	representing	represent	VERB
ejpam-6142	52	11	the	the	DET
ejpam-6142	52	12	biological	biological	ADJ
ejpam-6142	52	13	problems	problem	NOUN
ejpam-6142	52	14	to	to	ADP
ejpam-6142	52	15	the	the	DET
ejpam-6142	52	16	form	form	NOUN
ejpam-6142	52	17	of	of	ADP
ejpam-6142	52	18	mathematical	mathematical	ADJ
ejpam-6142	52	19	equations	equation	NOUN
ejpam-6142	52	20	.	.	PUNCT
ejpam-6142	53	1	in	in	ADP
ejpam-6142	53	2	this	this	DET
ejpam-6142	53	3	instance	instance	NOUN
ejpam-6142	53	4	,	,	PUNCT
ejpam-6142	53	5	we	we	PRON
ejpam-6142	53	6	examine	examine	VERB
ejpam-6142	53	7	and	and	CCONJ
ejpam-6142	53	8	evaluate	evaluate	VERB
ejpam-6142	53	9	an	an	DET
ejpam-6142	53	10	hiv	hiv	PROPN
ejpam-6142	53	11	model	model	NOUN
ejpam-6142	53	12	where	where	SCONJ
ejpam-6142	53	13	people	people	NOUN
ejpam-6142	53	14	are	be	AUX
ejpam-6142	53	15	categorized	categorize	VERB
ejpam-6142	53	16	as	as	ADP
ejpam-6142	53	17	male	male	ADJ
ejpam-6142	53	18	or	or	CCONJ
ejpam-6142	53	19	female	female	NOUN
ejpam-6142	53	20	.	.	PUNCT
ejpam-6142	54	1	we	we	PRON
ejpam-6142	54	2	discuss	discuss	VERB
ejpam-6142	54	3	the	the	DET
ejpam-6142	54	4	role	role	NOUN
ejpam-6142	54	5	of	of	ADP
ejpam-6142	54	6	the	the	DET
ejpam-6142	54	7	basic	basic	ADJ
ejpam-6142	54	8	reproduction	reproduction	NOUN
ejpam-6142	54	9	number	number	NOUN
ejpam-6142	54	10	in	in	ADP
ejpam-6142	54	11	the	the	DET
ejpam-6142	54	12	study	study	NOUN
ejpam-6142	54	13	of	of	ADP
ejpam-6142	54	14	stability	stability	NOUN
ejpam-6142	54	15	analysis	analysis	NOUN
ejpam-6142	54	16	.	.	PUNCT
ejpam-6142	55	1	moreover	moreover	ADV
ejpam-6142	55	2	,	,	PUNCT
ejpam-6142	55	3	the	the	DET
ejpam-6142	55	4	elasticity	elasticity	NOUN
ejpam-6142	55	5	of	of	ADP
ejpam-6142	55	6	the	the	DET
ejpam-6142	55	7	parameters	parameter	NOUN
ejpam-6142	55	8	in	in	ADP
ejpam-6142	55	9	which	which	DET
ejpam-6142	55	10	increase	increase	NOUN
ejpam-6142	55	11	or	or	CCONJ
ejpam-6142	55	12	decrease	decrease	VERB
ejpam-6142	55	13	the	the	DET
ejpam-6142	55	14	value	value	NOUN
ejpam-6142	55	15	of	of	ADP
ejpam-6142	55	16	the	the	DET
ejpam-6142	55	17	reproduction	reproduction	NOUN
ejpam-6142	55	18	number	number	NOUN
ejpam-6142	55	19	is	be	AUX
ejpam-6142	55	20	analyzed	analyze	VERB
ejpam-6142	55	21	.	.	PUNCT
ejpam-6142	56	1	additionally	additionally	ADV
ejpam-6142	56	2	,	,	PUNCT
ejpam-6142	56	3	different	different	ADJ
ejpam-6142	56	4	control	control	NOUN
ejpam-6142	56	5	strategies	strategy	NOUN
ejpam-6142	56	6	are	be	AUX
ejpam-6142	56	7	used	use	VERB
ejpam-6142	56	8	in	in	ADP
ejpam-6142	56	9	order	order	NOUN
ejpam-6142	56	10	to	to	PART
ejpam-6142	56	11	reduce	reduce	VERB
ejpam-6142	56	12	or	or	CCONJ
ejpam-6142	56	13	stop	stop	VERB
ejpam-6142	56	14	of	of	ADP
ejpam-6142	56	15	hiv	hiv	PROPN
ejpam-6142	56	16	transmission	transmission	NOUN
ejpam-6142	56	17	in	in	ADP
ejpam-6142	56	18	human	human	ADJ
ejpam-6142	56	19	population	population	NOUN
ejpam-6142	56	20	.	.	PUNCT
ejpam-6142	57	1	the	the	DET
ejpam-6142	57	2	article	article	NOUN
ejpam-6142	57	3	is	be	AUX
ejpam-6142	57	4	arranged	arrange	VERB
ejpam-6142	57	5	as	as	SCONJ
ejpam-6142	57	6	follows	follow	VERB
ejpam-6142	57	7	:	:	PUNCT
ejpam-6142	57	8	in	in	ADP
ejpam-6142	57	9	section	section	NOUN
ejpam-6142	57	10	1	1	NUM
ejpam-6142	57	11	,	,	PUNCT
ejpam-6142	57	12	the	the	DET
ejpam-6142	57	13	parameters	parameter	NOUN
ejpam-6142	57	14	and	and	CCONJ
ejpam-6142	57	15	variables	variable	NOUN
ejpam-6142	57	16	are	be	AUX
ejpam-6142	57	17	introduced	introduce	VERB
ejpam-6142	57	18	and	and	CCONJ
ejpam-6142	57	19	the	the	DET
ejpam-6142	57	20	mathematical	mathematical	ADJ
ejpam-6142	57	21	model	model	NOUN
ejpam-6142	57	22	is	be	AUX
ejpam-6142	57	23	formulated	formulate	VERB
ejpam-6142	57	24	.	.	PUNCT
ejpam-6142	58	1	in	in	ADP
ejpam-6142	58	2	section	section	NOUN
ejpam-6142	58	3	2	2	NUM
ejpam-6142	58	4	,	,	PUNCT
ejpam-6142	58	5	the	the	DET
ejpam-6142	58	6	formulated	formulated	ADJ
ejpam-6142	58	7	model	model	NOUN
ejpam-6142	58	8	is	be	AUX
ejpam-6142	58	9	analyzed	analyze	VERB
ejpam-6142	58	10	mathematically	mathematically	ADV
ejpam-6142	58	11	to	to	PART
ejpam-6142	58	12	find	find	VERB
ejpam-6142	58	13	the	the	DET
ejpam-6142	58	14	invariant	invariant	ADJ
ejpam-6142	58	15	region	region	NOUN
ejpam-6142	58	16	and	and	CCONJ
ejpam-6142	58	17	provided	provide	VERB
ejpam-6142	58	18	that	that	SCONJ
ejpam-6142	58	19	the	the	DET
ejpam-6142	58	20	solutions	solution	NOUN
ejpam-6142	58	21	of	of	ADP
ejpam-6142	58	22	the	the	DET
ejpam-6142	58	23	model	model	NOUN
ejpam-6142	58	24	are	be	AUX
ejpam-6142	58	25	positive	positive	ADJ
ejpam-6142	58	26	.	.	PUNCT
ejpam-6142	59	1	in	in	ADP
ejpam-6142	59	2	section	section	NOUN
ejpam-6142	59	3	3	3	NUM
ejpam-6142	59	4	,	,	PUNCT
ejpam-6142	59	5	the	the	DET
ejpam-6142	59	6	equilibrium	equilibrium	NOUN
ejpam-6142	59	7	points	point	NOUN
ejpam-6142	59	8	and	and	CCONJ
ejpam-6142	59	9	the	the	DET
ejpam-6142	59	10	basic	basic	ADJ
ejpam-6142	59	11	reproduction	reproduction	NOUN
ejpam-6142	59	12	number	number	NOUN
ejpam-6142	59	13	r0	r0	NOUN
ejpam-6142	59	14	are	be	AUX
ejpam-6142	59	15	computed	compute	VERB
ejpam-6142	59	16	.	.	PUNCT
ejpam-6142	60	1	in	in	ADP
ejpam-6142	60	2	section	section	NOUN
ejpam-6142	60	3	4	4	NUM
ejpam-6142	60	4	,	,	PUNCT
ejpam-6142	60	5	the	the	DET
ejpam-6142	60	6	local	local	ADJ
ejpam-6142	60	7	stability	stability	NOUN
ejpam-6142	60	8	of	of	ADP
ejpam-6142	60	9	the	the	DET
ejpam-6142	60	10	system	system	NOUN
ejpam-6142	60	11	of	of	ADP
ejpam-6142	60	12	equations	equation	NOUN
ejpam-6142	60	13	at	at	ADP
ejpam-6142	60	14	the	the	DET
ejpam-6142	60	15	equilibrium	equilibrium	NOUN
ejpam-6142	60	16	points	point	NOUN
ejpam-6142	60	17	are	be	AUX
ejpam-6142	60	18	studied	study	VERB
ejpam-6142	60	19	.	.	PUNCT
ejpam-6142	61	1	in	in	ADP
ejpam-6142	61	2	section	section	NOUN
ejpam-6142	61	3	5	5	NUM
ejpam-6142	61	4	,	,	PUNCT
ejpam-6142	61	5	local	local	ADJ
ejpam-6142	61	6	sensitivity	sensitivity	NOUN
ejpam-6142	61	7	analysis	analysis	NOUN
ejpam-6142	61	8	is	be	AUX
ejpam-6142	61	9	discussed	discuss	VERB
ejpam-6142	61	10	by	by	ADP
ejpam-6142	61	11	using	use	VERB
ejpam-6142	61	12	three	three	NUM
ejpam-6142	61	13	different	different	ADJ
ejpam-6142	61	14	techniques	technique	NOUN
ejpam-6142	61	15	.	.	PUNCT
ejpam-6142	62	1	section	section	NOUN
ejpam-6142	62	2	6	6	NUM
ejpam-6142	62	3	describes	describe	VERB
ejpam-6142	62	4	the	the	DET
ejpam-6142	62	5	expansion	expansion	NOUN
ejpam-6142	62	6	of	of	ADP
ejpam-6142	62	7	the	the	DET
ejpam-6142	62	8	model	model	NOUN
ejpam-6142	62	9	with	with	ADP
ejpam-6142	62	10	the	the	DET
ejpam-6142	62	11	incorporation	incorporation	NOUN
ejpam-6142	62	12	of	of	ADP
ejpam-6142	62	13	optimal	optimal	ADJ
ejpam-6142	62	14	control	control	NOUN
ejpam-6142	62	15	and	and	CCONJ
ejpam-6142	62	16	analyzed	analyze	VERB
ejpam-6142	62	17	.	.	PUNCT
ejpam-6142	63	1	in	in	ADP
ejpam-6142	63	2	section	section	NOUN
ejpam-6142	63	3	7	7	NUM
ejpam-6142	63	4	,	,	PUNCT
ejpam-6142	63	5	the	the	DET
ejpam-6142	63	6	numerical	numerical	ADJ
ejpam-6142	63	7	simulation	simulation	NOUN
ejpam-6142	63	8	for	for	ADP
ejpam-6142	63	9	different	different	ADJ
ejpam-6142	63	10	combinations	combination	NOUN
ejpam-6142	63	11	of	of	ADP
ejpam-6142	63	12	strategies	strategy	NOUN
ejpam-6142	63	13	is	be	AUX
ejpam-6142	63	14	illustrated	illustrate	VERB
ejpam-6142	63	15	.	.	PUNCT
ejpam-6142	64	1	in	in	ADP
ejpam-6142	64	2	section	section	NOUN
ejpam-6142	64	3	8	8	NUM
ejpam-6142	64	4	,	,	PUNCT
ejpam-6142	64	5	conclusion	conclusion	NOUN
ejpam-6142	64	6	is	be	AUX
ejpam-6142	64	7	provided	provide	VERB
ejpam-6142	64	8	.	.	PUNCT
ejpam-6142	65	1	2	2	X
ejpam-6142	65	2	.	.	PUNCT
ejpam-6142	65	3	model	model	NOUN
ejpam-6142	65	4	equation	equation	NOUN
ejpam-6142	65	5	in	in	ADP
ejpam-6142	65	6	this	this	DET
ejpam-6142	65	7	section	section	NOUN
ejpam-6142	65	8	,	,	PUNCT
ejpam-6142	65	9	the	the	DET
ejpam-6142	65	10	proposed	propose	VERB
ejpam-6142	65	11	model	model	NOUN
ejpam-6142	65	12	equation	equation	NOUN
ejpam-6142	65	13	is	be	AUX
ejpam-6142	65	14	formulated	formulate	VERB
ejpam-6142	65	15	.	.	PUNCT
ejpam-6142	66	1	the	the	DET
ejpam-6142	66	2	total	total	ADJ
ejpam-6142	66	3	number	number	NOUN
ejpam-6142	66	4	of	of	ADP
ejpam-6142	66	5	individuals	individual	NOUN
ejpam-6142	66	6	n(t	n(t	PROPN
ejpam-6142	66	7	)	)	PUNCT
ejpam-6142	66	8	at	at	ADP
ejpam-6142	66	9	time	time	NOUN
ejpam-6142	66	10	t	t	PROPN
ejpam-6142	66	11	is	be	AUX
ejpam-6142	66	12	split	split	VERB
ejpam-6142	66	13	into	into	ADP
ejpam-6142	66	14	seven	seven	NUM
ejpam-6142	66	15	sub	sub	NOUN
ejpam-6142	66	16	-	-	NOUN
ejpam-6142	66	17	populations	population	NOUN
ejpam-6142	66	18	for	for	ADP
ejpam-6142	66	19	females	female	NOUN
ejpam-6142	66	20	and	and	CCONJ
ejpam-6142	66	21	seven	seven	NUM
ejpam-6142	66	22	subpopulations	subpopulation	NOUN
ejpam-6142	66	23	for	for	ADP
ejpam-6142	66	24	males	male	NOUN
ejpam-6142	66	25	which	which	PRON
ejpam-6142	66	26	are	be	AUX
ejpam-6142	66	27	fourteen	fourteen	NUM
ejpam-6142	66	28	sub	sub	NOUN
ejpam-6142	66	29	-	-	NOUN
ejpam-6142	66	30	populations	population	NOUN
ejpam-6142	66	31	in	in	ADP
ejpam-6142	66	32	total	total	ADJ
ejpam-6142	66	33	:	:	PUNCT
ejpam-6142	66	34	susceptible	susceptible	ADJ
ejpam-6142	66	35	populations	population	NOUN
ejpam-6142	66	36	sf	sf	X
ejpam-6142	66	37	(	(	PUNCT
ejpam-6142	66	38	t	t	PROPN
ejpam-6142	66	39	)	)	PUNCT
ejpam-6142	66	40	and	and	CCONJ
ejpam-6142	66	41	sm(t	sm(t	NUM
ejpam-6142	66	42	)	)	PUNCT
ejpam-6142	66	43	,	,	PUNCT
ejpam-6142	66	44	exposed	expose	VERB
ejpam-6142	66	45	populations	population	NOUN
ejpam-6142	66	46	ef	ef	X
ejpam-6142	66	47	(	(	PUNCT
ejpam-6142	66	48	t	t	PROPN
ejpam-6142	66	49	)	)	PUNCT
ejpam-6142	66	50	and	and	CCONJ
ejpam-6142	66	51	em(t	em(t	NUM
ejpam-6142	66	52	)	)	PUNCT
ejpam-6142	66	53	which	which	PRON
ejpam-6142	66	54	have	have	AUX
ejpam-6142	66	55	got	get	VERB
ejpam-6142	66	56	the	the	DET
ejpam-6142	66	57	sickness	sickness	NOUN
ejpam-6142	66	58	,	,	PUNCT
ejpam-6142	66	59	but	but	CCONJ
ejpam-6142	66	60	are	be	AUX
ejpam-6142	66	61	not	not	PART
ejpam-6142	66	62	yet	yet	ADV
ejpam-6142	66	63	infectious	infectious	ADJ
ejpam-6142	66	64	,	,	PUNCT
ejpam-6142	66	65	infected	infected	ADJ
ejpam-6142	66	66	populations	population	NOUN
ejpam-6142	66	67	if	if	SCONJ
ejpam-6142	66	68	(	(	PUNCT
ejpam-6142	66	69	t	t	NOUN
ejpam-6142	66	70	)	)	PUNCT
ejpam-6142	66	71	and	and	CCONJ
ejpam-6142	66	72	im(t	im(t	NOUN
ejpam-6142	66	73	)	)	PUNCT
ejpam-6142	66	74	,	,	PUNCT
ejpam-6142	66	75	undetected	undetecte	VERB
ejpam-6142	66	76	populations	population	NOUN
ejpam-6142	66	77	uf	uf	X
ejpam-6142	66	78	(	(	PUNCT
ejpam-6142	66	79	t	t	PROPN
ejpam-6142	66	80	)	)	PUNCT
ejpam-6142	66	81	and	and	CCONJ
ejpam-6142	66	82	um(t	um(t	NUM
ejpam-6142	66	83	)	)	PUNCT
ejpam-6142	66	84	,	,	PUNCT
ejpam-6142	66	85	detected	detect	VERB
ejpam-6142	66	86	populations	population	NOUN
ejpam-6142	66	87	df	df	NOUN
ejpam-6142	66	88	(	(	PUNCT
ejpam-6142	66	89	t	t	PROPN
ejpam-6142	66	90	)	)	PUNCT
ejpam-6142	66	91	and	and	CCONJ
ejpam-6142	66	92	dm(t	dm(t	NOUN
ejpam-6142	66	93	)	)	PUNCT
ejpam-6142	66	94	,	,	PUNCT
ejpam-6142	66	95	treating	treat	VERB
ejpam-6142	66	96	populations	population	NOUN
ejpam-6142	66	97	tf	tf	X
ejpam-6142	66	98	(	(	PUNCT
ejpam-6142	66	99	t	t	PROPN
ejpam-6142	66	100	)	)	PUNCT
ejpam-6142	66	101	and	and	CCONJ
ejpam-6142	66	102	tm(t	tm(t	NOUN
ejpam-6142	66	103	)	)	PUNCT
ejpam-6142	66	104	,	,	PUNCT
ejpam-6142	66	105	and	and	CCONJ
ejpam-6142	66	106	aids	aids	PROPN
ejpam-6142	66	107	populations	population	NOUN
ejpam-6142	66	108	af	af	X
ejpam-6142	66	109	(	(	PUNCT
ejpam-6142	66	110	t	t	PROPN
ejpam-6142	66	111	)	)	PUNCT
ejpam-6142	66	112	and	and	CCONJ
ejpam-6142	66	113	am(t	am(t	NOUN
ejpam-6142	66	114	)	)	PUNCT
ejpam-6142	66	115	.	.	PUNCT
ejpam-6142	67	1	therefore	therefore	ADV
ejpam-6142	67	2	,	,	PUNCT
ejpam-6142	67	3	n(t	n(t	PROPN
ejpam-6142	67	4	)	)	PUNCT
ejpam-6142	67	5	=	=	SYM
ejpam-6142	67	6	sf	sf	PROPN
ejpam-6142	67	7	(	(	PUNCT
ejpam-6142	67	8	t)+sm(t	t)+sm(t	PROPN
ejpam-6142	67	9	)	)	PUNCT
ejpam-6142	68	1	+	+	CCONJ
ejpam-6142	68	2	ef	ef	PROPN
ejpam-6142	68	3	(	(	PUNCT
ejpam-6142	68	4	t	t	PROPN
ejpam-6142	68	5	)	)	PUNCT
ejpam-6142	68	6	+	+	NUM
ejpam-6142	68	7	em(t	em(t	NUM
ejpam-6142	68	8	)	)	PUNCT
ejpam-6142	69	1	+	+	CCONJ
ejpam-6142	69	2	if	if	SCONJ
ejpam-6142	69	3	(	(	PUNCT
ejpam-6142	69	4	t	t	NOUN
ejpam-6142	69	5	)	)	PUNCT
ejpam-6142	69	6	+	+	NUM
ejpam-6142	69	7	im(t	im(t	NUM
ejpam-6142	69	8	)	)	PUNCT
ejpam-6142	70	1	+	+	CCONJ
ejpam-6142	70	2	uf	uf	PROPN
ejpam-6142	70	3	(	(	PUNCT
ejpam-6142	70	4	t	t	PROPN
ejpam-6142	70	5	)	)	PUNCT
ejpam-6142	70	6	+	+	NUM
ejpam-6142	70	7	um(t	um(t	NUM
ejpam-6142	70	8	)	)	PUNCT
ejpam-6142	71	1	+	+	NOUN
ejpam-6142	71	2	df	df	PROPN
ejpam-6142	71	3	(	(	PUNCT
ejpam-6142	71	4	t	t	PROPN
ejpam-6142	71	5	)	)	PUNCT
ejpam-6142	71	6	+	+	NOUN
ejpam-6142	71	7	dm(t	dm(t	NUM
ejpam-6142	71	8	)	)	PUNCT
ejpam-6142	72	1	+	+	CCONJ
ejpam-6142	72	2	tf	tf	X
ejpam-6142	72	3	(	(	PUNCT
ejpam-6142	72	4	t	t	PROPN
ejpam-6142	72	5	)	)	PUNCT
ejpam-6142	72	6	+	+	NUM
ejpam-6142	72	7	tm(t	tm(t	NOUN
ejpam-6142	72	8	)	)	PUNCT
ejpam-6142	73	1	+	+	X
ejpam-6142	73	2	af	af	PROPN
ejpam-6142	73	3	(	(	PUNCT
ejpam-6142	73	4	t	t	PROPN
ejpam-6142	73	5	)	)	PUNCT
ejpam-6142	73	6	+	+	NOUN
ejpam-6142	73	7	am(t	am(t	NOUN
ejpam-6142	73	8	)	)	PUNCT
ejpam-6142	73	9	at	at	ADP
ejpam-6142	73	10	a	a	DET
ejpam-6142	73	11	constant	constant	ADJ
ejpam-6142	73	12	rate	rate	NOUN
ejpam-6142	73	13	λ	λ	PROPN
ejpam-6142	73	14	,	,	PUNCT
ejpam-6142	73	15	the	the	DET
ejpam-6142	73	16	population	population	NOUN
ejpam-6142	73	17	enters	enter	VERB
ejpam-6142	73	18	the	the	DET
ejpam-6142	73	19	susceptible	susceptible	ADJ
ejpam-6142	73	20	compartment	compartment	NOUN
ejpam-6142	73	21	.	.	PUNCT
ejpam-6142	74	1	infection	infection	NOUN
ejpam-6142	74	2	occurs	occur	VERB
ejpam-6142	74	3	only	only	ADV
ejpam-6142	74	4	through	through	ADP
ejpam-6142	74	5	successful	successful	ADJ
ejpam-6142	74	6	contact	contact	NOUN
ejpam-6142	74	7	between	between	ADP
ejpam-6142	74	8	susceptible	susceptible	ADJ
ejpam-6142	74	9	females	female	NOUN
ejpam-6142	74	10	sf	sf	PROPN
ejpam-6142	74	11	and	and	CCONJ
ejpam-6142	74	12	infected	infected	ADJ
ejpam-6142	74	13	males	male	NOUN
ejpam-6142	75	1	i	i	PRON
ejpam-6142	75	2	m	m	VERB
ejpam-6142	75	3	and	and	CCONJ
ejpam-6142	75	4	s.	s.	PROPN
ejpam-6142	75	5	m.	m.	PROPN
ejpam-6142	75	6	fatah	fatah	PROPN
ejpam-6142	75	7	,	,	PUNCT
ejpam-6142	75	8	s.	s.	PROPN
ejpam-6142	75	9	h.	h.	PROPN
ejpam-6142	75	10	a.	a.	PROPN
ejpam-6142	75	11	khoshnaw	khoshnaw	PROPN
ejpam-6142	75	12	,	,	PUNCT
ejpam-6142	75	13	a.	a.	PROPN
ejpam-6142	75	14	n.	n.	PROPN
ejpam-6142	75	15	mustafa	mustafa	PROPN
ejpam-6142	75	16	/	/	SYM
ejpam-6142	75	17	eur	eur	PROPN
ejpam-6142	75	18	.	.	PUNCT
ejpam-6142	76	1	j.	j.	PROPN
ejpam-6142	76	2	pure	pure	PROPN
ejpam-6142	76	3	appl	appl	PROPN
ejpam-6142	76	4	.	.	PROPN
ejpam-6142	76	5	math	math	PROPN
ejpam-6142	76	6	,	,	PUNCT
ejpam-6142	76	7	18	18	NUM
ejpam-6142	76	8	(	(	PUNCT
ejpam-6142	76	9	2	2	NUM
ejpam-6142	76	10	)	)	PUNCT
ejpam-6142	76	11	(	(	PUNCT
ejpam-6142	76	12	2025	2025	NUM
ejpam-6142	76	13	)	)	PUNCT
ejpam-6142	76	14	,	,	PUNCT
ejpam-6142	76	15	6142	6142	NUM
ejpam-6142	76	16	4	4	NUM
ejpam-6142	76	17	of	of	ADP
ejpam-6142	76	18	33	33	NUM
ejpam-6142	76	19	susceptible	susceptible	ADJ
ejpam-6142	76	20	males	male	NOUN
ejpam-6142	76	21	sm	sm	ADV
ejpam-6142	76	22	and	and	CCONJ
ejpam-6142	76	23	infected	infect	VERB
ejpam-6142	76	24	females	female	NOUN
ejpam-6142	76	25	if	if	SCONJ
ejpam-6142	76	26	,	,	PUNCT
ejpam-6142	76	27	with	with	ADP
ejpam-6142	76	28	probabilities	probability	NOUN
ejpam-6142	76	29	βf	βf	ADV
ejpam-6142	76	30	or	or	CCONJ
ejpam-6142	76	31	βm	βm	VERB
ejpam-6142	76	32	respectively	respectively	ADV
ejpam-6142	76	33	.	.	PUNCT
ejpam-6142	77	1	abstinence	abstinence	NOUN
ejpam-6142	77	2	avoiding	avoid	VERB
ejpam-6142	77	3	all	all	DET
ejpam-6142	77	4	forms	form	NOUN
ejpam-6142	77	5	of	of	ADP
ejpam-6142	77	6	vaginal	vaginal	ADJ
ejpam-6142	77	7	,	,	PUNCT
ejpam-6142	77	8	anal	anal	ADJ
ejpam-6142	77	9	,	,	PUNCT
ejpam-6142	77	10	and	and	CCONJ
ejpam-6142	77	11	oral	oral	ADJ
ejpam-6142	77	12	sex	sex	NOUN
ejpam-6142	77	13	are	be	AUX
ejpam-6142	77	14	the	the	DET
ejpam-6142	77	15	most	most	ADV
ejpam-6142	77	16	efficient	efficient	ADJ
ejpam-6142	77	17	methods	method	NOUN
ejpam-6142	77	18	of	of	ADP
ejpam-6142	77	19	preventing	prevent	VERB
ejpam-6142	77	20	the	the	DET
ejpam-6142	77	21	sexual	sexual	ADJ
ejpam-6142	77	22	transmission	transmission	NOUN
ejpam-6142	77	23	of	of	ADP
ejpam-6142	77	24	hiv	hiv	PROPN
ejpam-6142	77	25	.	.	PUNCT
ejpam-6142	78	1	for	for	ADP
ejpam-6142	78	2	the	the	DET
ejpam-6142	78	3	suggested	suggest	VERB
ejpam-6142	78	4	model	model	NOUN
ejpam-6142	78	5	,	,	PUNCT
ejpam-6142	78	6	we	we	PRON
ejpam-6142	78	7	account	account	VERB
ejpam-6142	78	8	for	for	ADP
ejpam-6142	78	9	the	the	DET
ejpam-6142	78	10	use	use	NOUN
ejpam-6142	78	11	of	of	ADP
ejpam-6142	78	12	male	male	ADJ
ejpam-6142	78	13	or	or	CCONJ
ejpam-6142	78	14	female	female	ADJ
ejpam-6142	78	15	condoms	condom	NOUN
ejpam-6142	78	16	,	,	PUNCT
ejpam-6142	78	17	which	which	PRON
ejpam-6142	78	18	can	can	AUX
ejpam-6142	78	19	prevent	prevent	VERB
ejpam-6142	78	20	hiv	hiv	PROPN
ejpam-6142	78	21	transmission	transmission	NOUN
ejpam-6142	78	22	.	.	PUNCT
ejpam-6142	79	1	the	the	DET
ejpam-6142	79	2	parameters	parameter	NOUN
ejpam-6142	79	3	ϵ	ϵ	X
ejpam-6142	79	4	and	and	CCONJ
ejpam-6142	79	5	κ	κ	PROPN
ejpam-6142	79	6	represent	represent	VERB
ejpam-6142	79	7	the	the	DET
ejpam-6142	79	8	effectiveness	effectiveness	NOUN
ejpam-6142	79	9	of	of	ADP
ejpam-6142	79	10	condoms	condom	NOUN
ejpam-6142	79	11	and	and	CCONJ
ejpam-6142	79	12	the	the	DET
ejpam-6142	79	13	percentage	percentage	NOUN
ejpam-6142	79	14	of	of	ADP
ejpam-6142	79	15	people	people	NOUN
ejpam-6142	79	16	who	who	PRON
ejpam-6142	79	17	use	use	VERB
ejpam-6142	79	18	condoms	condom	NOUN
ejpam-6142	79	19	respectively	respectively	ADV
ejpam-6142	79	20	.	.	PUNCT
ejpam-6142	80	1	this	this	PRON
ejpam-6142	80	2	leads	lead	VERB
ejpam-6142	80	3	to	to	ADP
ejpam-6142	80	4	a	a	DET
ejpam-6142	80	5	reduction	reduction	NOUN
ejpam-6142	80	6	in	in	ADP
ejpam-6142	80	7	transmission	transmission	NOUN
ejpam-6142	80	8	rates	rate	NOUN
ejpam-6142	80	9	βf	βf	CCONJ
ejpam-6142	80	10	and	and	CCONJ
ejpam-6142	80	11	βm	βm	VERB
ejpam-6142	80	12	by	by	ADP
ejpam-6142	80	13	a	a	DET
ejpam-6142	80	14	factor	factor	NOUN
ejpam-6142	80	15	of	of	ADP
ejpam-6142	80	16	1−κ	1−κ	NUM
ejpam-6142	80	17	∈	∈	PROPN
ejpam-6142	80	18	where	where	SCONJ
ejpam-6142	80	19	0	0	NUM
ejpam-6142	80	20	<	<	X
ejpam-6142	80	21	ϵ	ϵ	X
ejpam-6142	80	22	<	<	X
ejpam-6142	80	23	1	1	NUM
ejpam-6142	80	24	and	and	CCONJ
ejpam-6142	80	25	0	0	NUM
ejpam-6142	80	26	<	<	X
ejpam-6142	80	27	κ	κ	X
ejpam-6142	80	28	<	<	X
ejpam-6142	80	29	1	1	NUM
ejpam-6142	80	30	.	.	PUNCT
ejpam-6142	80	31	higher	high	ADJ
ejpam-6142	80	32	values	value	NOUN
ejpam-6142	80	33	of	of	ADP
ejpam-6142	80	34	κ	κ	NOUN
ejpam-6142	80	35	and	and	CCONJ
ejpam-6142	80	36	ϵ	ϵ	X
ejpam-6142	80	37	indicate	indicate	VERB
ejpam-6142	80	38	a	a	DET
ejpam-6142	80	39	better	well	ADJ
ejpam-6142	80	40	condom	condom	NOUN
ejpam-6142	80	41	a	a	DET
ejpam-6142	80	42	situation	situation	NOUN
ejpam-6142	80	43	in	in	ADP
ejpam-6142	80	44	which	which	PRON
ejpam-6142	80	45	more	more	ADJ
ejpam-6142	80	46	individuals	individual	NOUN
ejpam-6142	80	47	use	use	VERB
ejpam-6142	80	48	condoms	condom	NOUN
ejpam-6142	80	49	when	when	SCONJ
ejpam-6142	80	50	having	have	VERB
ejpam-6142	80	51	sex	sex	NOUN
ejpam-6142	80	52	respectively	respectively	ADV
ejpam-6142	80	53	.	.	PUNCT
ejpam-6142	81	1	in	in	ADP
ejpam-6142	81	2	this	this	DET
ejpam-6142	81	3	model	model	NOUN
ejpam-6142	81	4	,	,	PUNCT
ejpam-6142	81	5	the	the	DET
ejpam-6142	81	6	transition	transition	NOUN
ejpam-6142	81	7	rates	rate	NOUN
ejpam-6142	81	8	from	from	ADP
ejpam-6142	81	9	sf	sf	PROPN
ejpam-6142	81	10	to	to	ADP
ejpam-6142	81	11	ef	ef	PROPN
ejpam-6142	81	12	and	and	CCONJ
ejpam-6142	81	13	sm	sm	VERB
ejpam-6142	81	14	to	to	ADP
ejpam-6142	81	15	em	em	PRON
ejpam-6142	81	16	are	be	AUX
ejpam-6142	81	17	(	(	PUNCT
ejpam-6142	81	18	1	1	NUM
ejpam-6142	81	19	−	−	NOUN
ejpam-6142	81	20	κϵ)βf	κϵ)βf	PUNCT
ejpam-6142	82	1	and	and	CCONJ
ejpam-6142	82	2	(	(	PUNCT
ejpam-6142	82	3	1	1	NUM
ejpam-6142	82	4	−	−	NOUN
ejpam-6142	82	5	κϵ)βm	κϵ)βm	NOUN
ejpam-6142	82	6	respectively	respectively	ADV
ejpam-6142	82	7	.	.	PUNCT
ejpam-6142	83	1	besides	besides	SCONJ
ejpam-6142	83	2	,	,	PUNCT
ejpam-6142	83	3	the	the	DET
ejpam-6142	83	4	transitions	transition	NOUN
ejpam-6142	83	5	from	from	ADP
ejpam-6142	83	6	ef	ef	PROPN
ejpam-6142	83	7	and	and	CCONJ
ejpam-6142	83	8	em	em	PRON
ejpam-6142	83	9	to	to	PART
ejpam-6142	83	10	if	if	SCONJ
ejpam-6142	84	1	and	and	CCONJ
ejpam-6142	84	2	i	i	PRON
ejpam-6142	84	3	m	m	VERB
ejpam-6142	84	4	are	be	AUX
ejpam-6142	84	5	denoted	denote	VERB
ejpam-6142	84	6	by	by	ADP
ejpam-6142	84	7	αf	αf	PRON
ejpam-6142	84	8	and	and	CCONJ
ejpam-6142	84	9	αm	αm	VERB
ejpam-6142	84	10	respectively	respectively	ADV
ejpam-6142	84	11	.	.	PUNCT
ejpam-6142	85	1	additionally	additionally	ADV
ejpam-6142	85	2	,	,	PUNCT
ejpam-6142	85	3	we	we	PRON
ejpam-6142	85	4	have	have	VERB
ejpam-6142	85	5	transitions	transition	NOUN
ejpam-6142	85	6	from	from	ADP
ejpam-6142	85	7	if	if	SCONJ
ejpam-6142	85	8	to	to	ADP
ejpam-6142	85	9	both	both	CCONJ
ejpam-6142	85	10	df	df	NOUN
ejpam-6142	85	11	and	and	CCONJ
ejpam-6142	85	12	uf	uf	PROPN
ejpam-6142	85	13	which	which	PRON
ejpam-6142	85	14	are	be	AUX
ejpam-6142	85	15	symbolized	symbolize	VERB
ejpam-6142	85	16	by	by	ADP
ejpam-6142	85	17	γf	γf	PROPN
ejpam-6142	85	18	and	and	CCONJ
ejpam-6142	85	19	θf	θf	VERB
ejpam-6142	85	20	respectively	respectively	ADV
ejpam-6142	85	21	,	,	PUNCT
ejpam-6142	85	22	also	also	ADV
ejpam-6142	85	23	from	from	ADP
ejpam-6142	85	24	i	i	PRON
ejpam-6142	85	25	m	m	VERB
ejpam-6142	85	26	to	to	ADP
ejpam-6142	85	27	both	both	DET
ejpam-6142	85	28	dm	dm	PROPN
ejpam-6142	85	29	and	and	CCONJ
ejpam-6142	85	30	um	um	INTJ
ejpam-6142	85	31	which	which	PRON
ejpam-6142	85	32	are	be	AUX
ejpam-6142	85	33	symbolized	symbolize	VERB
ejpam-6142	85	34	by	by	ADP
ejpam-6142	85	35	γm	γm	ADJ
ejpam-6142	85	36	and	and	CCONJ
ejpam-6142	85	37	θm	θm	ADV
ejpam-6142	85	38	respectively	respectively	ADV
ejpam-6142	85	39	.	.	PUNCT
ejpam-6142	86	1	furthermore	furthermore	ADV
ejpam-6142	86	2	,	,	PUNCT
ejpam-6142	86	3	there	there	PRON
ejpam-6142	86	4	are	be	VERB
ejpam-6142	86	5	a	a	DET
ejpam-6142	86	6	transition	transition	NOUN
ejpam-6142	86	7	from	from	ADP
ejpam-6142	86	8	df	df	PROPN
ejpam-6142	86	9	and	and	CCONJ
ejpam-6142	86	10	dm	dm	X
ejpam-6142	86	11	to	to	ADP
ejpam-6142	86	12	tf	tf	INTJ
ejpam-6142	86	13	and	and	CCONJ
ejpam-6142	86	14	tm	tm	NOUN
ejpam-6142	86	15	as	as	ADP
ejpam-6142	86	16	a	a	DET
ejpam-6142	86	17	result	result	NOUN
ejpam-6142	86	18	of	of	ADP
ejpam-6142	86	19	an	an	DET
ejpam-6142	86	20	identification	identification	NOUN
ejpam-6142	86	21	of	of	ADP
ejpam-6142	86	22	hiv	hiv	PROPN
ejpam-6142	86	23	through	through	ADP
ejpam-6142	86	24	medical	medical	ADJ
ejpam-6142	86	25	test	test	NOUN
ejpam-6142	86	26	and	and	CCONJ
ejpam-6142	86	27	denoted	denote	VERB
ejpam-6142	86	28	by	by	ADP
ejpam-6142	86	29	ρf	ρf	PRON
ejpam-6142	86	30	and	and	CCONJ
ejpam-6142	86	31	ρm	ρm	PRON
ejpam-6142	86	32	respectively	respectively	ADV
ejpam-6142	86	33	.	.	PUNCT
ejpam-6142	87	1	moreover	moreover	ADV
ejpam-6142	87	2	,	,	PUNCT
ejpam-6142	87	3	the	the	DET
ejpam-6142	87	4	transitions	transition	NOUN
ejpam-6142	87	5	from	from	ADP
ejpam-6142	87	6	both	both	DET
ejpam-6142	87	7	uf	uf	PROPN
ejpam-6142	87	8	and	and	CCONJ
ejpam-6142	87	9	tf	tf	INTJ
ejpam-6142	87	10	to	to	PART
ejpam-6142	87	11	af	af	PROPN
ejpam-6142	87	12	are	be	AUX
ejpam-6142	87	13	given	give	VERB
ejpam-6142	87	14	by	by	ADP
ejpam-6142	87	15	λf	λf	ADP
ejpam-6142	87	16	and	and	CCONJ
ejpam-6142	87	17	ωf	ωf	ADV
ejpam-6142	87	18	respectively	respectively	ADV
ejpam-6142	87	19	and	and	CCONJ
ejpam-6142	87	20	from	from	ADP
ejpam-6142	87	21	both	both	DET
ejpam-6142	87	22	um	um	INTJ
ejpam-6142	87	23	and	and	CCONJ
ejpam-6142	87	24	tm	tm	NOUN
ejpam-6142	87	25	to	to	PART
ejpam-6142	87	26	am	am	VERB
ejpam-6142	87	27	are	be	AUX
ejpam-6142	87	28	denoted	denote	VERB
ejpam-6142	87	29	by	by	ADP
ejpam-6142	87	30	λm	λm	X
ejpam-6142	87	31	and	and	CCONJ
ejpam-6142	87	32	ωm	ωm	PUNCT
ejpam-6142	87	33	respectively	respectively	ADV
ejpam-6142	87	34	.	.	PUNCT
ejpam-6142	88	1	the	the	DET
ejpam-6142	88	2	natural	natural	ADJ
ejpam-6142	88	3	death	death	NOUN
ejpam-6142	88	4	rate	rate	NOUN
ejpam-6142	88	5	of	of	ADP
ejpam-6142	88	6	each	each	DET
ejpam-6142	88	7	compartment	compartment	NOUN
ejpam-6142	88	8	is	be	AUX
ejpam-6142	88	9	symbolized	symbolize	VERB
ejpam-6142	88	10	by	by	ADP
ejpam-6142	88	11	η	η	PROPN
ejpam-6142	88	12	and	and	CCONJ
ejpam-6142	88	13	there	there	PRON
ejpam-6142	88	14	is	be	VERB
ejpam-6142	88	15	an	an	DET
ejpam-6142	88	16	additional	additional	ADJ
ejpam-6142	88	17	death	death	NOUN
ejpam-6142	88	18	rate	rate	NOUN
ejpam-6142	88	19	denoted	denote	VERB
ejpam-6142	88	20	by	by	ADP
ejpam-6142	88	21	µ	µ	PRON
ejpam-6142	88	22	due	due	ADP
ejpam-6142	88	23	to	to	ADP
ejpam-6142	88	24	the	the	DET
ejpam-6142	88	25	disease	disease	NOUN
ejpam-6142	88	26	for	for	ADP
ejpam-6142	88	27	all	all	DET
ejpam-6142	88	28	compartments	compartment	NOUN
ejpam-6142	88	29	except	except	SCONJ
ejpam-6142	88	30	sf	sf	PROPN
ejpam-6142	88	31	,	,	PUNCT
ejpam-6142	88	32	ef	ef	PROPN
ejpam-6142	88	33	,	,	PUNCT
ejpam-6142	88	34	sm	sm	PROPN
ejpam-6142	88	35	,	,	PUNCT
ejpam-6142	88	36	and	and	CCONJ
ejpam-6142	88	37	em	em	PRON
ejpam-6142	88	38	.	.	PUNCT
ejpam-6142	89	1	the	the	DET
ejpam-6142	89	2	transmission	transmission	NOUN
ejpam-6142	89	3	of	of	ADP
ejpam-6142	89	4	the	the	DET
ejpam-6142	89	5	disease	disease	NOUN
ejpam-6142	89	6	from	from	ADP
ejpam-6142	89	7	an	an	DET
ejpam-6142	89	8	infected	infected	ADJ
ejpam-6142	89	9	female	female	NOUN
ejpam-6142	89	10	to	to	ADP
ejpam-6142	89	11	a	a	DET
ejpam-6142	89	12	healthy	healthy	ADJ
ejpam-6142	89	13	male	male	NOUN
ejpam-6142	89	14	or	or	CCONJ
ejpam-6142	89	15	from	from	ADP
ejpam-6142	89	16	an	an	DET
ejpam-6142	89	17	infected	infected	ADJ
ejpam-6142	89	18	male	male	NOUN
ejpam-6142	89	19	to	to	ADP
ejpam-6142	89	20	a	a	DET
ejpam-6142	89	21	healthy	healthy	ADJ
ejpam-6142	89	22	female	female	NOUN
ejpam-6142	89	23	is	be	AUX
ejpam-6142	89	24	only	only	ADV
ejpam-6142	89	25	through	through	ADP
ejpam-6142	89	26	sexual	sexual	ADJ
ejpam-6142	89	27	contact	contact	NOUN
ejpam-6142	89	28	.	.	PUNCT
ejpam-6142	90	1	in	in	ADP
ejpam-6142	90	2	figure	figure	NOUN
ejpam-6142	90	3	1	1	NUM
ejpam-6142	90	4	,	,	PUNCT
ejpam-6142	90	5	the	the	DET
ejpam-6142	90	6	male	male	ADJ
ejpam-6142	90	7	and	and	CCONJ
ejpam-6142	90	8	female	female	ADJ
ejpam-6142	90	9	subpopulations	subpopulation	NOUN
ejpam-6142	90	10	are	be	AUX
ejpam-6142	90	11	shown	show	VERB
ejpam-6142	90	12	where	where	SCONJ
ejpam-6142	90	13	coupling	coupling	NOUN
ejpam-6142	90	14	represented	represent	VERB
ejpam-6142	90	15	by	by	ADP
ejpam-6142	90	16	the	the	DET
ejpam-6142	90	17	dashed	dash	VERB
ejpam-6142	90	18	arrows	arrow	NOUN
ejpam-6142	90	19	.	.	PUNCT
ejpam-6142	91	1	figure	figure	NOUN
ejpam-6142	91	2	1	1	NUM
ejpam-6142	91	3	:	:	PUNCT
ejpam-6142	91	4	flow	flow	NOUN
ejpam-6142	91	5	diagram	diagram	NOUN
ejpam-6142	91	6	of	of	ADP
ejpam-6142	91	7	the	the	DET
ejpam-6142	91	8	model	model	NOUN
ejpam-6142	91	9	s.	s.	PROPN
ejpam-6142	91	10	m.	m.	PROPN
ejpam-6142	91	11	fatah	fatah	PROPN
ejpam-6142	91	12	,	,	PUNCT
ejpam-6142	91	13	s.	s.	PROPN
ejpam-6142	91	14	h.	h.	PROPN
ejpam-6142	91	15	a.	a.	PROPN
ejpam-6142	91	16	khoshnaw	khoshnaw	PROPN
ejpam-6142	91	17	,	,	PUNCT
ejpam-6142	91	18	a.	a.	PROPN
ejpam-6142	91	19	n.	n.	PROPN
ejpam-6142	91	20	mustafa	mustafa	PROPN
ejpam-6142	91	21	/	/	SYM
ejpam-6142	91	22	eur	eur	PROPN
ejpam-6142	91	23	.	.	PUNCT
ejpam-6142	92	1	j.	j.	PROPN
ejpam-6142	92	2	pure	pure	PROPN
ejpam-6142	92	3	appl	appl	PROPN
ejpam-6142	92	4	.	.	PROPN
ejpam-6142	92	5	math	math	PROPN
ejpam-6142	92	6	,	,	PUNCT
ejpam-6142	92	7	18	18	NUM
ejpam-6142	92	8	(	(	PUNCT
ejpam-6142	92	9	2	2	NUM
ejpam-6142	92	10	)	)	PUNCT
ejpam-6142	92	11	(	(	PUNCT
ejpam-6142	92	12	2025	2025	NUM
ejpam-6142	92	13	)	)	PUNCT
ejpam-6142	92	14	,	,	PUNCT
ejpam-6142	92	15	6142	6142	NUM
ejpam-6142	92	16	5	5	NUM
ejpam-6142	92	17	of	of	ADP
ejpam-6142	92	18	33	33	NUM
ejpam-6142	92	19	based	base	VERB
ejpam-6142	92	20	on	on	ADP
ejpam-6142	92	21	the	the	DET
ejpam-6142	92	22	above	above	ADJ
ejpam-6142	92	23	diagram	diagram	NOUN
ejpam-6142	92	24	(	(	PUNCT
ejpam-6142	92	25	figure	figure	NOUN
ejpam-6142	92	26	1	1	NUM
ejpam-6142	92	27	)	)	PUNCT
ejpam-6142	92	28	and	and	CCONJ
ejpam-6142	92	29	the	the	DET
ejpam-6142	92	30	considered	consider	VERB
ejpam-6142	92	31	assumptions	assumption	NOUN
ejpam-6142	92	32	,	,	PUNCT
ejpam-6142	92	33	the	the	DET
ejpam-6142	92	34	following	follow	VERB
ejpam-6142	92	35	system	system	NOUN
ejpam-6142	92	36	of	of	ADP
ejpam-6142	92	37	differential	differential	ADJ
ejpam-6142	92	38	equations	equation	NOUN
ejpam-6142	92	39	represents	represent	VERB
ejpam-6142	92	40	the	the	DET
ejpam-6142	92	41	mathematical	mathematical	ADJ
ejpam-6142	92	42	model	model	NOUN
ejpam-6142	92	43	dsf	dsf	NOUN
ejpam-6142	92	44	dt	dt	PROPN
ejpam-6142	92	45	=	=	SYM
ejpam-6142	92	46	λ−	λ−	PROPN
ejpam-6142	92	47	(	(	PUNCT
ejpam-6142	92	48	1−	1−	NUM
ejpam-6142	92	49	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	92	50	−	−	PROPN
ejpam-6142	92	51	ηsf	ηsf	INTJ
ejpam-6142	92	52	dsm	dsm	PROPN
ejpam-6142	92	53	dt	dt	PROPN
ejpam-6142	93	1	=	=	SYM
ejpam-6142	93	2	λ−	λ−	PROPN
ejpam-6142	93	3	(	(	PUNCT
ejpam-6142	93	4	1−	1−	NUM
ejpam-6142	93	5	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	93	6	−	−	PROPN
ejpam-6142	93	7	ηsm	ηsm	NOUN
ejpam-6142	93	8	def	def	NOUN
ejpam-6142	93	9	dt	dt	X
ejpam-6142	93	10	=	=	SYM
ejpam-6142	93	11	(	(	PUNCT
ejpam-6142	93	12	1−	1−	NUM
ejpam-6142	93	13	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	93	14	−	−	PROPN
ejpam-6142	93	15	(	(	PUNCT
ejpam-6142	93	16	αf	αf	ADP
ejpam-6142	93	17	+	+	CCONJ
ejpam-6142	94	1	η)ef	η)ef	PROPN
ejpam-6142	94	2	dem	dem	ADJ
ejpam-6142	94	3	dt	dt	X
ejpam-6142	94	4	=	=	SYM
ejpam-6142	94	5	(	(	PUNCT
ejpam-6142	94	6	1−	1−	NUM
ejpam-6142	94	7	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	94	8	−	−	PROPN
ejpam-6142	94	9	(	(	PUNCT
ejpam-6142	94	10	αm	αm	NOUN
ejpam-6142	94	11	+	+	CCONJ
ejpam-6142	95	1	η)em	η)em	PROPN
ejpam-6142	95	2	dif	dif	ADV
ejpam-6142	95	3	dt	dt	X
ejpam-6142	95	4	=	=	SYM
ejpam-6142	95	5	αfef	αfef	NOUN
ejpam-6142	95	6	−	−	PROPN
ejpam-6142	95	7	(	(	PUNCT
ejpam-6142	95	8	µ+	µ+	X
ejpam-6142	95	9	η	η	PROPN
ejpam-6142	95	10	+	+	PROPN
ejpam-6142	95	11	γf	γf	PRON
ejpam-6142	95	12	+	+	CCONJ
ejpam-6142	95	13	θf	θf	NOUN
ejpam-6142	95	14	)	)	PUNCT
ejpam-6142	95	15	if	if	SCONJ
ejpam-6142	95	16	dim	dim	ADJ
ejpam-6142	95	17	dt	dt	NOUN
ejpam-6142	95	18	=	=	PUNCT
ejpam-6142	95	19	αmem	αmem	ADJ
ejpam-6142	95	20	−	−	PROPN
ejpam-6142	95	21	(	(	PUNCT
ejpam-6142	95	22	µ+	µ+	X
ejpam-6142	95	23	η	η	PROPN
ejpam-6142	95	24	+	+	X
ejpam-6142	95	25	γm	γm	PROPN
ejpam-6142	95	26	+	+	NUM
ejpam-6142	95	27	θm	θm	NOUN
ejpam-6142	95	28	)	)	PUNCT
ejpam-6142	95	29	i	i	PROPN
ejpam-6142	95	30	m	m	VERB
ejpam-6142	95	31	ddf	ddf	NOUN
ejpam-6142	95	32	dt	dt	PROPN
ejpam-6142	95	33	=	=	PUNCT
ejpam-6142	95	34	γfif	γfif	PROPN
ejpam-6142	95	35	−	−	PROPN
ejpam-6142	95	36	(	(	PUNCT
ejpam-6142	95	37	µ+	µ+	X
ejpam-6142	95	38	η	η	PROPN
ejpam-6142	95	39	+	+	PROPN
ejpam-6142	95	40	ρf	ρf	X
ejpam-6142	95	41	)	)	PUNCT
ejpam-6142	95	42	df	df	PROPN
ejpam-6142	95	43	ddm	ddm	PROPN
ejpam-6142	95	44	dt	dt	NOUN
ejpam-6142	96	1	=	=	PUNCT
ejpam-6142	96	2	γmim	γmim	NOUN
ejpam-6142	96	3	−	−	PROPN
ejpam-6142	96	4	(	(	PUNCT
ejpam-6142	96	5	µ+	µ+	X
ejpam-6142	96	6	η	η	PROPN
ejpam-6142	96	7	+	+	PROPN
ejpam-6142	96	8	ρm)dm	ρm)dm	PROPN
ejpam-6142	96	9	dtf	dtf	PROPN
ejpam-6142	96	10	dt	dt	NOUN
ejpam-6142	96	11	=	=	PUNCT
ejpam-6142	96	12	ρfdf	ρfdf	PROPN
ejpam-6142	96	13	−	−	PROPN
ejpam-6142	96	14	(	(	PUNCT
ejpam-6142	96	15	µ+	µ+	X
ejpam-6142	96	16	η	η	PROPN
ejpam-6142	96	17	+	+	PROPN
ejpam-6142	96	18	ωf	ωf	PROPN
ejpam-6142	96	19	)	)	PUNCT
ejpam-6142	97	1	tf	tf	PROPN
ejpam-6142	97	2	dtm	dtm	PROPN
ejpam-6142	97	3	dt	dt	PROPN
ejpam-6142	98	1	=	=	PUNCT
ejpam-6142	98	2	ρmdm	ρmdm	PROPN
ejpam-6142	98	3	−	−	PROPN
ejpam-6142	98	4	(	(	PUNCT
ejpam-6142	98	5	µ+	µ+	X
ejpam-6142	98	6	η	η	PROPN
ejpam-6142	98	7	+	+	PROPN
ejpam-6142	98	8	ωm)tm	ωm)tm	ADJ
ejpam-6142	98	9	duf	duf	NOUN
ejpam-6142	98	10	dt	dt	NOUN
ejpam-6142	98	11	=	=	PROPN
ejpam-6142	98	12	θfif	θfif	PROPN
ejpam-6142	98	13	−	−	PROPN
ejpam-6142	98	14	(	(	PUNCT
ejpam-6142	98	15	µ+	µ+	X
ejpam-6142	98	16	η	η	PROPN
ejpam-6142	98	17	+	+	PROPN
ejpam-6142	98	18	λf	λf	PROPN
ejpam-6142	98	19	)	)	PUNCT
ejpam-6142	98	20	uf	uf	PROPN
ejpam-6142	98	21	dum	dum	NOUN
ejpam-6142	98	22	dt	dt	X
ejpam-6142	99	1	=	=	SYM
ejpam-6142	99	2	θmim	θmim	PROPN
ejpam-6142	99	3	−	−	PROPN
ejpam-6142	99	4	(	(	PUNCT
ejpam-6142	99	5	µ+	µ+	X
ejpam-6142	99	6	η	η	PROPN
ejpam-6142	99	7	+	+	PROPN
ejpam-6142	99	8	λm)um	λm)um	X
ejpam-6142	99	9	daf	daf	NOUN
ejpam-6142	99	10	dt	dt	NOUN
ejpam-6142	100	1	=	=	PUNCT
ejpam-6142	100	2	λfuf	λfuf	PROPN
ejpam-6142	101	1	+	+	NUM
ejpam-6142	101	2	ωftf	ωftf	NOUN
ejpam-6142	101	3	−	−	PROPN
ejpam-6142	101	4	(	(	PUNCT
ejpam-6142	101	5	µ+	µ+	X
ejpam-6142	101	6	η)af	η)af	PROPN
ejpam-6142	101	7	dam	dam	NOUN
ejpam-6142	101	8	dt	dt	NOUN
ejpam-6142	101	9	=	=	PUNCT
ejpam-6142	101	10	λmum	λmum	ADJ
ejpam-6142	101	11	+	+	CCONJ
ejpam-6142	101	12	ωmtm	ωmtm	ADJ
ejpam-6142	101	13	−	−	PROPN
ejpam-6142	101	14	(	(	PUNCT
ejpam-6142	101	15	µ+	µ+	PROPN
ejpam-6142	101	16	η)am	η)am	PROPN
ejpam-6142	101	17	(	(	PUNCT
ejpam-6142	101	18	1	1	NUM
ejpam-6142	101	19	)	)	PUNCT
ejpam-6142	101	20	with	with	ADP
ejpam-6142	101	21	the	the	DET
ejpam-6142	101	22	initial	initial	ADJ
ejpam-6142	101	23	conditions	condition	NOUN
ejpam-6142	101	24	sf	sf	X
ejpam-6142	101	25	(	(	PUNCT
ejpam-6142	101	26	0	0	NUM
ejpam-6142	101	27	)	)	PUNCT
ejpam-6142	101	28	,	,	PUNCT
ejpam-6142	101	29	sm(0	sm(0	NOUN
ejpam-6142	101	30	)	)	PUNCT
ejpam-6142	101	31	>	>	X
ejpam-6142	101	32	0	0	NUM
ejpam-6142	101	33	,	,	PUNCT
ejpam-6142	101	34	and	and	CCONJ
ejpam-6142	101	35	ef	ef	PROPN
ejpam-6142	101	36	(	(	PUNCT
ejpam-6142	101	37	0	0	NUM
ejpam-6142	101	38	)	)	PUNCT
ejpam-6142	101	39	,	,	PUNCT
ejpam-6142	101	40	em(0	em(0	NOUN
ejpam-6142	101	41	)	)	PUNCT
ejpam-6142	101	42	,	,	PUNCT
ejpam-6142	101	43	if	if	SCONJ
ejpam-6142	101	44	(	(	PUNCT
ejpam-6142	101	45	0	0	NUM
ejpam-6142	101	46	)	)	PUNCT
ejpam-6142	101	47	,	,	PUNCT
ejpam-6142	101	48	im(0	im(0	NOUN
ejpam-6142	101	49	)	)	PUNCT
ejpam-6142	101	50	,	,	PUNCT
ejpam-6142	101	51	df	df	PROPN
ejpam-6142	101	52	(	(	PUNCT
ejpam-6142	101	53	0	0	NUM
ejpam-6142	101	54	)	)	PUNCT
ejpam-6142	101	55	,	,	PUNCT
ejpam-6142	101	56	dm(0	dm(0	NOUN
ejpam-6142	101	57	)	)	PUNCT
ejpam-6142	101	58	,	,	PUNCT
ejpam-6142	101	59	tf	tf	X
ejpam-6142	101	60	(	(	PUNCT
ejpam-6142	101	61	0	0	NUM
ejpam-6142	101	62	)	)	PUNCT
ejpam-6142	101	63	,	,	PUNCT
ejpam-6142	101	64	tm(0	tm(0	NOUN
ejpam-6142	101	65	)	)	PUNCT
ejpam-6142	101	66	,	,	PUNCT
ejpam-6142	101	67	uf	uf	PROPN
ejpam-6142	101	68	(	(	PUNCT
ejpam-6142	101	69	0	0	NUM
ejpam-6142	101	70	)	)	PUNCT
ejpam-6142	101	71	,	,	PUNCT
ejpam-6142	101	72	um(0	um(0	NOUN
ejpam-6142	101	73	)	)	PUNCT
ejpam-6142	101	74	,	,	PUNCT
ejpam-6142	101	75	af	af	PROPN
ejpam-6142	101	76	(	(	PUNCT
ejpam-6142	101	77	0	0	NUM
ejpam-6142	101	78	)	)	PUNCT
ejpam-6142	101	79	,	,	PUNCT
ejpam-6142	101	80	am(0	am(0	NOUN
ejpam-6142	101	81	)	)	PUNCT
ejpam-6142	101	82	≥	≥	NOUN
ejpam-6142	101	83	0	0	NUM
ejpam-6142	101	84	in	in	ADP
ejpam-6142	101	85	table	table	NOUN
ejpam-6142	101	86	1	1	NUM
ejpam-6142	101	87	,	,	PUNCT
ejpam-6142	101	88	the	the	DET
ejpam-6142	101	89	parameter	parameter	NOUN
ejpam-6142	101	90	values	value	NOUN
ejpam-6142	101	91	and	and	CCONJ
ejpam-6142	101	92	initial	initial	ADJ
ejpam-6142	101	93	variables	variable	NOUN
ejpam-6142	101	94	of	of	ADP
ejpam-6142	101	95	the	the	DET
ejpam-6142	101	96	model	model	NOUN
ejpam-6142	101	97	1	1	NUM
ejpam-6142	101	98	are	be	AUX
ejpam-6142	101	99	provided	provide	VERB
ejpam-6142	101	100	.	.	PUNCT
ejpam-6142	101	101	table	table	NOUN
ejpam-6142	101	102	1	1	NUM
ejpam-6142	101	103	:	:	PUNCT
ejpam-6142	101	104	initial	initial	ADJ
ejpam-6142	101	105	estimated	estimate	VERB
ejpam-6142	101	106	values	value	NOUN
ejpam-6142	101	107	of	of	ADP
ejpam-6142	101	108	model	model	NOUN
ejpam-6142	101	109	states	state	NOUN
ejpam-6142	101	110	and	and	CCONJ
ejpam-6142	101	111	parameters	parameter	NOUN
ejpam-6142	101	112	symbols	symbol	NOUN
ejpam-6142	101	113	biological	biological	ADJ
ejpam-6142	101	114	meaning	mean	VERB
ejpam-6142	101	115	estimated	estimate	VERB
ejpam-6142	101	116	values	value	NOUN
ejpam-6142	101	117	sm(0	sm(0	NOUN
ejpam-6142	101	118	)	)	PUNCT
ejpam-6142	101	119	initial	initial	ADJ
ejpam-6142	101	120	susceptible	susceptible	ADJ
ejpam-6142	101	121	males	male	NOUN
ejpam-6142	101	122	19000000	19000000	NUM
ejpam-6142	101	123	assumed	assume	VERB
ejpam-6142	101	124	sf	sf	PROPN
ejpam-6142	101	125	(	(	PUNCT
ejpam-6142	101	126	0	0	NUM
ejpam-6142	101	127	)	)	PUNCT
ejpam-6142	101	128	initial	initial	ADJ
ejpam-6142	101	129	susceptible	susceptible	ADJ
ejpam-6142	101	130	females	female	NOUN
ejpam-6142	101	131	20000000	20000000	NUM
ejpam-6142	101	132	assumed	assume	VERB
ejpam-6142	101	133	em(0	em(0	NOUN
ejpam-6142	101	134	)	)	PUNCT
ejpam-6142	101	135	initial	initial	ADJ
ejpam-6142	101	136	exposed	expose	VERB
ejpam-6142	101	137	males	male	NOUN
ejpam-6142	101	138	100000	100000	NUM
ejpam-6142	101	139	assumed	assume	VERB
ejpam-6142	101	140	ef	ef	PROPN
ejpam-6142	101	141	(	(	PUNCT
ejpam-6142	101	142	0	0	NUM
ejpam-6142	101	143	)	)	PUNCT
ejpam-6142	101	144	initial	initial	ADJ
ejpam-6142	101	145	exposed	expose	VERB
ejpam-6142	101	146	females	female	NOUN
ejpam-6142	101	147	120000	120000	NUM
ejpam-6142	101	148	assumed	assume	VERB
ejpam-6142	101	149	im(0	im(0	NOUN
ejpam-6142	101	150	)	)	PUNCT
ejpam-6142	101	151	initial	initial	ADJ
ejpam-6142	101	152	infectious	infectious	ADJ
ejpam-6142	101	153	males	male	NOUN
ejpam-6142	101	154	60000	60000	NUM
ejpam-6142	101	155	assumed	assume	VERB
ejpam-6142	101	156	if	if	SCONJ
ejpam-6142	101	157	(	(	PUNCT
ejpam-6142	101	158	0	0	X
ejpam-6142	101	159	)	)	PUNCT
ejpam-6142	101	160	initial	initial	ADJ
ejpam-6142	101	161	infectious	infectious	ADJ
ejpam-6142	101	162	females	female	NOUN
ejpam-6142	101	163	65000	65000	NUM
ejpam-6142	101	164	assumed	assume	VERB
ejpam-6142	101	165	dm(0	dm(0	NOUN
ejpam-6142	101	166	)	)	PUNCT
ejpam-6142	101	167	initial	initial	ADJ
ejpam-6142	101	168	detected	detect	VERB
ejpam-6142	101	169	males	male	NOUN
ejpam-6142	101	170	25000	25000	NUM
ejpam-6142	101	171	assumed	assume	VERB
ejpam-6142	101	172	df	df	PROPN
ejpam-6142	101	173	(	(	PUNCT
ejpam-6142	101	174	0	0	NUM
ejpam-6142	101	175	)	)	PUNCT
ejpam-6142	101	176	initial	initial	ADJ
ejpam-6142	101	177	detected	detect	VERB
ejpam-6142	101	178	females	female	NOUN
ejpam-6142	101	179	28000	28000	NUM
ejpam-6142	101	180	assumed	assume	VERB
ejpam-6142	101	181	um(0	um(0	NOUN
ejpam-6142	101	182	)	)	PUNCT
ejpam-6142	101	183	initial	initial	ADJ
ejpam-6142	101	184	undetected	undetecte	VERB
ejpam-6142	101	185	males	male	NOUN
ejpam-6142	101	186	52000	52000	NUM
ejpam-6142	101	187	assumed	assume	VERB
ejpam-6142	101	188	uf	uf	PROPN
ejpam-6142	101	189	(	(	PUNCT
ejpam-6142	101	190	0	0	NUM
ejpam-6142	101	191	)	)	PUNCT
ejpam-6142	101	192	initial	initial	ADJ
ejpam-6142	101	193	undetected	undetecte	VERB
ejpam-6142	101	194	males	male	NOUN
ejpam-6142	101	195	60000	60000	NUM
ejpam-6142	101	196	assumed	assume	VERB
ejpam-6142	101	197	tm(0	tm(0	NOUN
ejpam-6142	101	198	)	)	PUNCT
ejpam-6142	101	199	initial	initial	ADJ
ejpam-6142	101	200	treated	treat	VERB
ejpam-6142	101	201	males	male	NOUN
ejpam-6142	101	202	9500	9500	NUM
ejpam-6142	101	203	assumed	assume	VERB
ejpam-6142	101	204	tf	tf	PROPN
ejpam-6142	101	205	(	(	PUNCT
ejpam-6142	101	206	0	0	NUM
ejpam-6142	101	207	)	)	PUNCT
ejpam-6142	101	208	initial	initial	ADJ
ejpam-6142	101	209	treated	treat	VERB
ejpam-6142	101	210	females	female	NOUN
ejpam-6142	101	211	11000	11000	NUM
ejpam-6142	101	212	assumed	assume	VERB
ejpam-6142	101	213	am(0	am(0	NOUN
ejpam-6142	101	214	)	)	PUNCT
ejpam-6142	101	215	initial	initial	ADJ
ejpam-6142	101	216	symptomatic	symptomatic	ADJ
ejpam-6142	101	217	aids	aid	NOUN
ejpam-6142	101	218	males	male	NOUN
ejpam-6142	101	219	2500	2500	NUM
ejpam-6142	101	220	assumed	assume	VERB
ejpam-6142	101	221	af	af	PROPN
ejpam-6142	101	222	(	(	PUNCT
ejpam-6142	101	223	0	0	NUM
ejpam-6142	101	224	)	)	PUNCT
ejpam-6142	101	225	initial	initial	ADJ
ejpam-6142	101	226	symptomatic	symptomatic	ADJ
ejpam-6142	101	227	aids	aid	NOUN
ejpam-6142	101	228	females	female	NOUN
ejpam-6142	101	229	2600	2600	NUM
ejpam-6142	101	230	assumed	assume	VERB
ejpam-6142	101	231	λ	λ	PROPN
ejpam-6142	101	232	net	net	ADJ
ejpam-6142	101	233	flow	flow	NOUN
ejpam-6142	101	234	rate	rate	NOUN
ejpam-6142	101	235	into	into	ADP
ejpam-6142	101	236	the	the	DET
ejpam-6142	101	237	susceptible	susceptible	ADJ
ejpam-6142	101	238	100,000	100,000	NUM
ejpam-6142	101	239	[	[	SYM
ejpam-6142	101	240	22	22	NUM
ejpam-6142	101	241	]	]	PUNCT
ejpam-6142	101	242	s.	s.	PROPN
ejpam-6142	101	243	m.	m.	PROPN
ejpam-6142	101	244	fatah	fatah	PROPN
ejpam-6142	101	245	,	,	PUNCT
ejpam-6142	101	246	s.	s.	PROPN
ejpam-6142	101	247	h.	h.	PROPN
ejpam-6142	101	248	a.	a.	PROPN
ejpam-6142	101	249	khoshnaw	khoshnaw	PROPN
ejpam-6142	101	250	,	,	PUNCT
ejpam-6142	101	251	a.	a.	PROPN
ejpam-6142	101	252	n.	n.	PROPN
ejpam-6142	101	253	mustafa	mustafa	PROPN
ejpam-6142	101	254	/	/	SYM
ejpam-6142	101	255	eur	eur	PROPN
ejpam-6142	101	256	.	.	PUNCT
ejpam-6142	102	1	j.	j.	PROPN
ejpam-6142	102	2	pure	pure	PROPN
ejpam-6142	102	3	appl	appl	PROPN
ejpam-6142	102	4	.	.	PROPN
ejpam-6142	102	5	math	math	PROPN
ejpam-6142	102	6	,	,	PUNCT
ejpam-6142	102	7	18	18	NUM
ejpam-6142	102	8	(	(	PUNCT
ejpam-6142	102	9	2	2	NUM
ejpam-6142	102	10	)	)	PUNCT
ejpam-6142	102	11	(	(	PUNCT
ejpam-6142	102	12	2025	2025	NUM
ejpam-6142	102	13	)	)	PUNCT
ejpam-6142	102	14	,	,	PUNCT
ejpam-6142	102	15	6142	6142	NUM
ejpam-6142	102	16	6	6	NUM
ejpam-6142	102	17	of	of	ADP
ejpam-6142	102	18	33	33	NUM
ejpam-6142	102	19	symbols	symbol	NOUN
ejpam-6142	102	20	biological	biological	ADJ
ejpam-6142	102	21	meaning	meaning	NOUN
ejpam-6142	102	22	estimated	estimate	VERB
ejpam-6142	102	23	values	value	NOUN
ejpam-6142	102	24	η	η	PROPN
ejpam-6142	102	25	natural	natural	ADJ
ejpam-6142	102	26	mortality	mortality	NOUN
ejpam-6142	102	27	rate	rate	NOUN
ejpam-6142	102	28	0.0222	0.0222	NUM
ejpam-6142	102	29	[	[	X
ejpam-6142	102	30	24	24	NUM
ejpam-6142	102	31	]	]	SYM
ejpam-6142	102	32	µ	µ	DET
ejpam-6142	102	33	disease	disease	NOUN
ejpam-6142	102	34	-	-	PUNCT
ejpam-6142	102	35	induced	induce	VERB
ejpam-6142	102	36	death	death	NOUN
ejpam-6142	102	37	rate	rate	NOUN
ejpam-6142	102	38	0.333	0.333	NUM
ejpam-6142	102	39	[	[	X
ejpam-6142	102	40	25	25	NUM
ejpam-6142	102	41	]	]	PUNCT
ejpam-6142	102	42	ϵ	ϵ	PRON
ejpam-6142	102	43	efficiency	efficiency	NOUN
ejpam-6142	102	44	rate	rate	NOUN
ejpam-6142	102	45	of	of	ADP
ejpam-6142	102	46	condom	condom	NOUN
ejpam-6142	102	47	[	[	X
ejpam-6142	102	48	0,1	0,1	X
ejpam-6142	102	49	]	]	X
ejpam-6142	103	1	[	[	X
ejpam-6142	103	2	23	23	NUM
ejpam-6142	103	3	]	]	PUNCT
ejpam-6142	103	4	κ	κ	NOUN
ejpam-6142	103	5	rate	rate	NOUN
ejpam-6142	103	6	of	of	ADP
ejpam-6142	103	7	people	people	NOUN
ejpam-6142	103	8	who	who	PRON
ejpam-6142	103	9	use	use	VERB
ejpam-6142	103	10	condoms	condom	NOUN
ejpam-6142	103	11	[	[	X
ejpam-6142	103	12	0,1	0,1	NUM
ejpam-6142	103	13	]	]	X
ejpam-6142	104	1	[	[	X
ejpam-6142	104	2	23	23	NUM
ejpam-6142	104	3	]	]	PUNCT
ejpam-6142	104	4	βm	βm	VERB
ejpam-6142	104	5	male	male	ADJ
ejpam-6142	104	6	effective	effective	ADJ
ejpam-6142	104	7	contact	contact	NOUN
ejpam-6142	104	8	rate	rate	NOUN
ejpam-6142	104	9	0.025	0.025	NUM
ejpam-6142	105	1	[	[	X
ejpam-6142	105	2	22	22	NUM
ejpam-6142	105	3	]	]	PUNCT
ejpam-6142	105	4	βf	βf	X
ejpam-6142	105	5	female	female	ADJ
ejpam-6142	105	6	effective	effective	ADJ
ejpam-6142	105	7	contact	contact	NOUN
ejpam-6142	105	8	rate	rate	NOUN
ejpam-6142	105	9	0.015	0.015	NUM
ejpam-6142	106	1	[	[	X
ejpam-6142	106	2	22	22	NUM
ejpam-6142	106	3	]	]	X
ejpam-6142	106	4	αm	αm	NOUN
ejpam-6142	106	5	rate	rate	NOUN
ejpam-6142	106	6	at	at	ADP
ejpam-6142	106	7	which	which	PRON
ejpam-6142	106	8	expose	expose	VERB
ejpam-6142	106	9	males	male	NOUN
ejpam-6142	106	10	are	be	AUX
ejpam-6142	106	11	infected	infect	VERB
ejpam-6142	106	12	0.75	0.75	NUM
ejpam-6142	106	13	assumed	assume	VERB
ejpam-6142	106	14	αf	αf	ADP
ejpam-6142	106	15	rate	rate	NOUN
ejpam-6142	106	16	at	at	ADP
ejpam-6142	106	17	which	which	PRON
ejpam-6142	106	18	exposed	expose	VERB
ejpam-6142	106	19	females	female	NOUN
ejpam-6142	106	20	are	be	AUX
ejpam-6142	106	21	infected	infect	VERB
ejpam-6142	106	22	0.8	0.8	NUM
ejpam-6142	106	23	assumed	assume	VERB
ejpam-6142	106	24	γm	γm	ADJ
ejpam-6142	106	25	rate	rate	NOUN
ejpam-6142	106	26	at	at	ADP
ejpam-6142	106	27	which	which	PRON
ejpam-6142	106	28	infected	infect	VERB
ejpam-6142	106	29	males	male	NOUN
ejpam-6142	106	30	are	be	AUX
ejpam-6142	106	31	detected	detect	VERB
ejpam-6142	106	32	0.512	0.512	NUM
ejpam-6142	106	33	[	[	X
ejpam-6142	106	34	22	22	NUM
ejpam-6142	106	35	]	]	PUNCT
ejpam-6142	106	36	γf	γf	ADJ
ejpam-6142	106	37	rate	rate	NOUN
ejpam-6142	106	38	at	at	ADP
ejpam-6142	106	39	which	which	PRON
ejpam-6142	106	40	infected	infected	ADJ
ejpam-6142	106	41	female	female	NOUN
ejpam-6142	106	42	are	be	AUX
ejpam-6142	106	43	detected	detect	VERB
ejpam-6142	106	44	0.675	0.675	NUM
ejpam-6142	106	45	[	[	X
ejpam-6142	106	46	22	22	NUM
ejpam-6142	106	47	]	]	PUNCT
ejpam-6142	106	48	ρm	ρm	PRON
ejpam-6142	106	49	treatment	treatment	NOUN
ejpam-6142	106	50	rate	rate	NOUN
ejpam-6142	106	51	of	of	ADP
ejpam-6142	106	52	detected	detect	VERB
ejpam-6142	106	53	male	male	NOUN
ejpam-6142	106	54	[	[	X
ejpam-6142	106	55	0,1	0,1	NUM
ejpam-6142	106	56	]	]	PUNCT
ejpam-6142	106	57	assumed	assume	VERB
ejpam-6142	106	58	ρf	ρf	ADP
ejpam-6142	106	59	treatment	treatment	NOUN
ejpam-6142	106	60	rate	rate	NOUN
ejpam-6142	106	61	of	of	ADP
ejpam-6142	106	62	detected	detect	VERB
ejpam-6142	106	63	female	female	ADJ
ejpam-6142	106	64	[	[	X
ejpam-6142	106	65	0,1	0,1	NUM
ejpam-6142	106	66	]	]	PUNCT
ejpam-6142	106	67	assumed	assume	VERB
ejpam-6142	106	68	ωm	ωm	PUNCT
ejpam-6142	106	69	progression	progression	NOUN
ejpam-6142	106	70	rate	rate	NOUN
ejpam-6142	106	71	of	of	ADP
ejpam-6142	106	72	males	male	NOUN
ejpam-6142	106	73	under	under	ADP
ejpam-6142	106	74	treatment	treatment	NOUN
ejpam-6142	106	75	to	to	ADP
ejpam-6142	106	76	aids	aids	NOUN
ejpam-6142	106	77	0.004	0.004	NUM
ejpam-6142	107	1	[	[	X
ejpam-6142	107	2	22	22	NUM
ejpam-6142	107	3	]	]	PUNCT
ejpam-6142	107	4	ωf	ωf	PROPN
ejpam-6142	107	5	progression	progression	NOUN
ejpam-6142	107	6	rate	rate	NOUN
ejpam-6142	107	7	of	of	ADP
ejpam-6142	107	8	females	female	NOUN
ejpam-6142	107	9	under	under	ADP
ejpam-6142	107	10	treatment	treatment	NOUN
ejpam-6142	107	11	to	to	ADP
ejpam-6142	107	12	aids	aids	NOUN
ejpam-6142	107	13	0.004	0.004	NUM
ejpam-6142	108	1	[	[	X
ejpam-6142	108	2	22	22	NUM
ejpam-6142	108	3	]	]	PUNCT
ejpam-6142	108	4	θm	θm	PROPN
ejpam-6142	108	5	transmission	transmission	NOUN
ejpam-6142	108	6	rate	rate	NOUN
ejpam-6142	108	7	of	of	ADP
ejpam-6142	108	8	infected	infect	VERB
ejpam-6142	108	9	males	male	NOUN
ejpam-6142	108	10	to	to	PART
ejpam-6142	108	11	undetected	undetected	VERB
ejpam-6142	108	12	0.12	0.12	NUM
ejpam-6142	108	13	assumed	assume	VERB
ejpam-6142	108	14	θf	θf	ADP
ejpam-6142	108	15	transmission	transmission	NOUN
ejpam-6142	108	16	rate	rate	NOUN
ejpam-6142	108	17	of	of	ADP
ejpam-6142	108	18	infected	infected	ADJ
ejpam-6142	108	19	females	female	NOUN
ejpam-6142	108	20	to	to	PART
ejpam-6142	108	21	undetected	undetected	VERB
ejpam-6142	108	22	0.12	0.12	NUM
ejpam-6142	108	23	assumed	assume	VERB
ejpam-6142	108	24	λm	λm	ADP
ejpam-6142	108	25	progression	progression	NOUN
ejpam-6142	108	26	rate	rate	NOUN
ejpam-6142	108	27	of	of	ADP
ejpam-6142	108	28	undetected	undetected	ADJ
ejpam-6142	108	29	males	male	NOUN
ejpam-6142	108	30	to	to	PART
ejpam-6142	108	31	aids	aids	PROPN
ejpam-6142	108	32	0.34	0.34	NUM
ejpam-6142	108	33	assumed	assume	VERB
ejpam-6142	108	34	λf	λf	ADP
ejpam-6142	108	35	progression	progression	NOUN
ejpam-6142	108	36	rate	rate	NOUN
ejpam-6142	108	37	of	of	ADP
ejpam-6142	108	38	undetected	undetected	ADJ
ejpam-6142	108	39	females	female	NOUN
ejpam-6142	108	40	to	to	PART
ejpam-6142	108	41	aids	aids	PROPN
ejpam-6142	108	42	0.34	0.34	NUM
ejpam-6142	108	43	assumed	assume	VERB
ejpam-6142	108	44	3	3	NUM
ejpam-6142	108	45	.	.	PUNCT
ejpam-6142	108	46	model	model	NOUN
ejpam-6142	108	47	analysis	analysis	NOUN
ejpam-6142	108	48	this	this	DET
ejpam-6142	108	49	section	section	NOUN
ejpam-6142	108	50	looks	look	VERB
ejpam-6142	108	51	at	at	ADP
ejpam-6142	108	52	the	the	DET
ejpam-6142	108	53	model	model	NOUN
ejpam-6142	108	54	solution	solution	NOUN
ejpam-6142	108	55	’s	’s	PART
ejpam-6142	108	56	positivity	positivity	NOUN
ejpam-6142	108	57	and	and	CCONJ
ejpam-6142	108	58	locates	locate	VERB
ejpam-6142	108	59	the	the	DET
ejpam-6142	108	60	invariant	invariant	ADJ
ejpam-6142	108	61	area	area	NOUN
ejpam-6142	108	62	.	.	PUNCT
ejpam-6142	109	1	first	first	ADV
ejpam-6142	109	2	,	,	PUNCT
ejpam-6142	109	3	we	we	PRON
ejpam-6142	109	4	discuss	discuss	VERB
ejpam-6142	109	5	the	the	DET
ejpam-6142	109	6	invariant	invariant	ADJ
ejpam-6142	109	7	region	region	NOUN
ejpam-6142	109	8	in	in	ADP
ejpam-6142	109	9	the	the	DET
ejpam-6142	109	10	following	follow	VERB
ejpam-6142	109	11	theorem	theorem	PROPN
ejpam-6142	109	12	.	.	PUNCT
ejpam-6142	109	13	theorem	theorem	NOUN
ejpam-6142	109	14	1	1	NUM
ejpam-6142	109	15	.	.	PUNCT
ejpam-6142	109	16	with	with	ADP
ejpam-6142	109	17	a	a	DET
ejpam-6142	109	18	non	non	ADJ
ejpam-6142	109	19	-	-	ADJ
ejpam-6142	109	20	negative	negative	ADJ
ejpam-6142	109	21	initial	initial	ADJ
ejpam-6142	109	22	condition	condition	NOUN
ejpam-6142	109	23	in	in	ADP
ejpam-6142	109	24	r14	r14	NOUN
ejpam-6142	109	25	+	+	CCONJ
ejpam-6142	109	26	,	,	PUNCT
ejpam-6142	109	27	all	all	DET
ejpam-6142	109	28	solutions	solution	NOUN
ejpam-6142	109	29	of	of	ADP
ejpam-6142	109	30	the	the	DET
ejpam-6142	109	31	hiv	hiv	PROPN
ejpam-6142	109	32	/	/	SYM
ejpam-6142	109	33	aids	aids	PROPN
ejpam-6142	109	34	model	model	NOUN
ejpam-6142	109	35	in	in	ADP
ejpam-6142	109	36	system	system	NOUN
ejpam-6142	109	37	(	(	PUNCT
ejpam-6142	109	38	1	1	X
ejpam-6142	109	39	)	)	PUNCT
ejpam-6142	109	40	stays	stay	VERB
ejpam-6142	109	41	positive	positive	ADJ
ejpam-6142	109	42	for	for	ADP
ejpam-6142	109	43	all	all	DET
ejpam-6142	109	44	time	time	NOUN
ejpam-6142	109	45	t	t	X
ejpam-6142	109	46	>	>	X
ejpam-6142	109	47	0	0	X
ejpam-6142	109	48	.	.	PUNCT
ejpam-6142	110	1	proof	proof	NOUN
ejpam-6142	110	2	.	.	PUNCT
ejpam-6142	111	1	from	from	ADP
ejpam-6142	111	2	the	the	DET
ejpam-6142	111	3	first	first	ADJ
ejpam-6142	111	4	equation	equation	NOUN
ejpam-6142	111	5	of	of	ADP
ejpam-6142	111	6	model	model	NOUN
ejpam-6142	111	7	(	(	PUNCT
ejpam-6142	111	8	1	1	X
ejpam-6142	111	9	)	)	PUNCT
ejpam-6142	111	10	we	we	PRON
ejpam-6142	111	11	have	have	VERB
ejpam-6142	111	12	that	that	DET
ejpam-6142	111	13	dsf	dsf	NOUN
ejpam-6142	111	14	dt	dt	NOUN
ejpam-6142	111	15	=	=	SYM
ejpam-6142	111	16	λ−	λ−	PROPN
ejpam-6142	111	17	(	(	PUNCT
ejpam-6142	111	18	1−	1−	NUM
ejpam-6142	111	19	κϵ)βfimsf	κϵ)βfimsf	PROPN
ejpam-6142	111	20	−	−	PROPN
ejpam-6142	111	21	ηsf	ηsf	PROPN
ejpam-6142	111	22	>	>	X
ejpam-6142	111	23	−	−	PROPN
ejpam-6142	112	1	[	[	X
ejpam-6142	112	2	(	(	PUNCT
ejpam-6142	112	3	1−	1−	NUM
ejpam-6142	112	4	κϵ)βfim	κϵ)βfim	NOUN
ejpam-6142	112	5	−	−	PROPN
ejpam-6142	112	6	η]sf	η]sf	PROPN
ejpam-6142	112	7	,	,	PUNCT
ejpam-6142	112	8	so	so	SCONJ
ejpam-6142	112	9	that	that	SCONJ
ejpam-6142	112	10	,	,	PUNCT
ejpam-6142	112	11	dsf	dsf	NOUN
ejpam-6142	112	12	dt	dt	PROPN
ejpam-6142	112	13	>	>	PUNCT
ejpam-6142	112	14	−	−	PROPN
ejpam-6142	113	1	[	[	X
ejpam-6142	113	2	(	(	PUNCT
ejpam-6142	113	3	1−	1−	NUM
ejpam-6142	113	4	κϵ)βfim	κϵ)βfim	NOUN
ejpam-6142	113	5	+	+	CCONJ
ejpam-6142	113	6	η]sf	η]sf	PROPN
ejpam-6142	113	7	solving	solve	VERB
ejpam-6142	113	8	the	the	DET
ejpam-6142	113	9	above	above	ADJ
ejpam-6142	113	10	inequality	inequality	NOUN
ejpam-6142	113	11	,	,	PUNCT
ejpam-6142	113	12	we	we	PRON
ejpam-6142	113	13	obtain	obtain	VERB
ejpam-6142	113	14	sf	sf	PROPN
ejpam-6142	113	15	(	(	PUNCT
ejpam-6142	113	16	t	t	PROPN
ejpam-6142	113	17	)	)	PUNCT
ejpam-6142	113	18	>	>	X
ejpam-6142	114	1	sf	sf	INTJ
ejpam-6142	114	2	(	(	PUNCT
ejpam-6142	114	3	0)e	0)e	ADJ
ejpam-6142	114	4	−	−	PROPN
ejpam-6142	114	5	∫	∫	PROPN
ejpam-6142	114	6	t	t	NOUN
ejpam-6142	114	7	0	0	NUM
ejpam-6142	115	1	[	[	X
ejpam-6142	115	2	(	(	PUNCT
ejpam-6142	115	3	1−κϵ)βf	1−κϵ)βf	NUM
ejpam-6142	115	4	im(x)+η]dx	im(x)+η]dx	NOUN
ejpam-6142	115	5	.	.	PUNCT
ejpam-6142	116	1	it	it	PRON
ejpam-6142	116	2	is	be	AUX
ejpam-6142	116	3	given	give	VERB
ejpam-6142	116	4	that	that	SCONJ
ejpam-6142	116	5	sf	sf	PROPN
ejpam-6142	116	6	(	(	PUNCT
ejpam-6142	116	7	0	0	NUM
ejpam-6142	116	8	)	)	PUNCT
ejpam-6142	116	9	>	>	X
ejpam-6142	116	10	0	0	PUNCT
ejpam-6142	116	11	and	and	CCONJ
ejpam-6142	116	12	clearly	clearly	ADV
ejpam-6142	116	13	e−	e−	ADJ
ejpam-6142	116	14	∫	∫	PROPN
ejpam-6142	117	1	t	t	NOUN
ejpam-6142	117	2	0	0	NUM
ejpam-6142	118	1	[	[	X
ejpam-6142	118	2	(	(	PUNCT
ejpam-6142	118	3	1−κϵ)βf	1−κϵ)βf	NUM
ejpam-6142	118	4	im(x)+η]dx	im(x)+η]dx	NOUN
ejpam-6142	118	5	is	be	AUX
ejpam-6142	118	6	nonnegative	nonnegative	ADJ
ejpam-6142	118	7	.	.	PUNCT
ejpam-6142	119	1	therefore	therefore	ADV
ejpam-6142	119	2	,	,	PUNCT
ejpam-6142	119	3	sf	sf	PROPN
ejpam-6142	119	4	(	(	PUNCT
ejpam-6142	119	5	t	t	PROPN
ejpam-6142	119	6	)	)	PUNCT
ejpam-6142	119	7	is	be	AUX
ejpam-6142	119	8	nonnegative	nonnegative	ADJ
ejpam-6142	119	9	for	for	ADP
ejpam-6142	119	10	all	all	DET
ejpam-6142	119	11	time	time	NOUN
ejpam-6142	119	12	t	t	X
ejpam-6142	119	13	>	>	X
ejpam-6142	119	14	0	0	X
ejpam-6142	119	15	.	.	PUNCT
ejpam-6142	120	1	by	by	ADP
ejpam-6142	120	2	the	the	DET
ejpam-6142	120	3	same	same	ADJ
ejpam-6142	120	4	manner	manner	NOUN
ejpam-6142	120	5	,	,	PUNCT
ejpam-6142	120	6	we	we	PRON
ejpam-6142	120	7	can	can	AUX
ejpam-6142	120	8	show	show	VERB
ejpam-6142	120	9	that	that	SCONJ
ejpam-6142	120	10	the	the	DET
ejpam-6142	120	11	solutions	solution	NOUN
ejpam-6142	120	12	for	for	ADP
ejpam-6142	120	13	the	the	DET
ejpam-6142	120	14	rest	rest	NOUN
ejpam-6142	120	15	of	of	ADP
ejpam-6142	120	16	variables	variable	NOUN
ejpam-6142	120	17	of	of	ADP
ejpam-6142	120	18	system	system	NOUN
ejpam-6142	120	19	(	(	PUNCT
ejpam-6142	120	20	1	1	X
ejpam-6142	120	21	)	)	PUNCT
ejpam-6142	120	22	are	be	AUX
ejpam-6142	120	23	nonnegative	nonnegative	ADJ
ejpam-6142	120	24	.	.	PUNCT
ejpam-6142	121	1	hence	hence	ADV
ejpam-6142	121	2	,	,	PUNCT
ejpam-6142	121	3	we	we	PRON
ejpam-6142	121	4	obtained	obtain	VERB
ejpam-6142	121	5	nonnegative	nonnegative	ADJ
ejpam-6142	121	6	solutions	solution	NOUN
ejpam-6142	121	7	for	for	ADP
ejpam-6142	121	8	the	the	DET
ejpam-6142	121	9	model	model	NOUN
ejpam-6142	121	10	.	.	PUNCT
ejpam-6142	122	1	s.	s.	PROPN
ejpam-6142	122	2	m.	m.	PROPN
ejpam-6142	122	3	fatah	fatah	PROPN
ejpam-6142	122	4	,	,	PUNCT
ejpam-6142	122	5	s.	s.	PROPN
ejpam-6142	122	6	h.	h.	PROPN
ejpam-6142	122	7	a.	a.	PROPN
ejpam-6142	122	8	khoshnaw	khoshnaw	PROPN
ejpam-6142	122	9	,	,	PUNCT
ejpam-6142	122	10	a.	a.	PROPN
ejpam-6142	122	11	n.	n.	PROPN
ejpam-6142	122	12	mustafa	mustafa	PROPN
ejpam-6142	122	13	/	/	SYM
ejpam-6142	122	14	eur	eur	PROPN
ejpam-6142	122	15	.	.	PUNCT
ejpam-6142	123	1	j.	j.	PROPN
ejpam-6142	123	2	pure	pure	PROPN
ejpam-6142	123	3	appl	appl	PROPN
ejpam-6142	123	4	.	.	PROPN
ejpam-6142	123	5	math	math	PROPN
ejpam-6142	123	6	,	,	PUNCT
ejpam-6142	123	7	18	18	NUM
ejpam-6142	123	8	(	(	PUNCT
ejpam-6142	123	9	2	2	NUM
ejpam-6142	123	10	)	)	PUNCT
ejpam-6142	123	11	(	(	PUNCT
ejpam-6142	123	12	2025	2025	NUM
ejpam-6142	123	13	)	)	PUNCT
ejpam-6142	123	14	,	,	PUNCT
ejpam-6142	123	15	6142	6142	NUM
ejpam-6142	123	16	7	7	NUM
ejpam-6142	123	17	of	of	ADP
ejpam-6142	123	18	33	33	NUM
ejpam-6142	123	19	now	now	ADV
ejpam-6142	123	20	,	,	PUNCT
ejpam-6142	123	21	in	in	ADP
ejpam-6142	123	22	the	the	DET
ejpam-6142	123	23	following	following	NOUN
ejpam-6142	123	24	theorem	theorem	NOUN
ejpam-6142	123	25	we	we	PRON
ejpam-6142	123	26	find	find	VERB
ejpam-6142	123	27	the	the	DET
ejpam-6142	123	28	positive	positive	ADJ
ejpam-6142	123	29	invariant	invariant	ADJ
ejpam-6142	123	30	area	area	NOUN
ejpam-6142	123	31	for	for	ADP
ejpam-6142	123	32	the	the	DET
ejpam-6142	123	33	model	model	NOUN
ejpam-6142	123	34	(	(	PUNCT
ejpam-6142	123	35	1	1	NUM
ejpam-6142	123	36	)	)	PUNCT
ejpam-6142	123	37	.	.	PUNCT
ejpam-6142	124	1	theorem	theorem	NOUN
ejpam-6142	124	2	2	2	NUM
ejpam-6142	124	3	.	.	PUNCT
ejpam-6142	125	1	the	the	DET
ejpam-6142	125	2	initial	initial	ADJ
ejpam-6142	125	3	conditions	condition	NOUN
ejpam-6142	125	4	are	be	AUX
ejpam-6142	125	5	bounded	bound	VERB
ejpam-6142	125	6	within	within	ADP
ejpam-6142	125	7	a	a	DET
ejpam-6142	125	8	bounded	bounded	ADJ
ejpam-6142	125	9	region	region	NOUN
ejpam-6142	125	10	σ	σ	PROPN
ejpam-6142	125	11	⊂	⊂	PROPN
ejpam-6142	125	12	r5	r5	PROPN
ejpam-6142	125	13	+	+	PROPN
ejpam-6142	125	14	,	,	PUNCT
ejpam-6142	125	15	ensuring	ensure	VERB
ejpam-6142	125	16	that	that	SCONJ
ejpam-6142	125	17	all	all	DET
ejpam-6142	125	18	solutions	solution	NOUN
ejpam-6142	125	19	of	of	ADP
ejpam-6142	125	20	the	the	DET
ejpam-6142	125	21	model	model	NOUN
ejpam-6142	125	22	remain	remain	VERB
ejpam-6142	125	23	bounded	bounded	ADJ
ejpam-6142	125	24	within	within	ADP
ejpam-6142	125	25	this	this	DET
ejpam-6142	125	26	specified	specified	ADJ
ejpam-6142	125	27	region	region	NOUN
ejpam-6142	125	28	.	.	PUNCT
ejpam-6142	126	1	so	so	ADV
ejpam-6142	126	2	that	that	SCONJ
ejpam-6142	126	3	,	,	PUNCT
ejpam-6142	126	4	σ	σ	PROPN
ejpam-6142	126	5	=	=	SYM
ejpam-6142	126	6	{	{	PUNCT
ejpam-6142	126	7	sf	sf	PROPN
ejpam-6142	126	8	(	(	PUNCT
ejpam-6142	126	9	t	t	PROPN
ejpam-6142	126	10	)	)	PUNCT
ejpam-6142	126	11	,	,	PUNCT
ejpam-6142	126	12	sm(t	sm(t	PROPN
ejpam-6142	126	13	)	)	PUNCT
ejpam-6142	126	14	,	,	PUNCT
ejpam-6142	126	15	ef	ef	PROPN
ejpam-6142	126	16	(	(	PUNCT
ejpam-6142	126	17	t	t	PROPN
ejpam-6142	126	18	)	)	PUNCT
ejpam-6142	126	19	,	,	PUNCT
ejpam-6142	126	20	em(t	em(t	NOUN
ejpam-6142	126	21	)	)	PUNCT
ejpam-6142	126	22	,	,	PUNCT
ejpam-6142	126	23	if	if	SCONJ
ejpam-6142	126	24	(	(	PUNCT
ejpam-6142	126	25	t	t	NOUN
ejpam-6142	126	26	)	)	PUNCT
ejpam-6142	126	27	,	,	PUNCT
ejpam-6142	126	28	im(t	im(t	NOUN
ejpam-6142	126	29	)	)	PUNCT
ejpam-6142	126	30	,	,	PUNCT
ejpam-6142	126	31	uf	uf	PROPN
ejpam-6142	126	32	(	(	PUNCT
ejpam-6142	126	33	t	t	PROPN
ejpam-6142	126	34	)	)	PUNCT
ejpam-6142	126	35	,	,	PUNCT
ejpam-6142	126	36	um(t	um(t	NUM
ejpam-6142	126	37	)	)	PUNCT
ejpam-6142	126	38	,	,	PUNCT
ejpam-6142	126	39	df	df	PROPN
ejpam-6142	126	40	(	(	PUNCT
ejpam-6142	126	41	t	t	PROPN
ejpam-6142	126	42	)	)	PUNCT
ejpam-6142	126	43	,	,	PUNCT
ejpam-6142	126	44	dm(t	dm(t	NOUN
ejpam-6142	126	45	)	)	PUNCT
ejpam-6142	126	46	,	,	PUNCT
ejpam-6142	126	47	tf	tf	PROPN
ejpam-6142	126	48	(	(	PUNCT
ejpam-6142	126	49	t	t	PROPN
ejpam-6142	126	50	)	)	PUNCT
ejpam-6142	126	51	,	,	PUNCT
ejpam-6142	126	52	tm(t	tm(t	NOUN
ejpam-6142	126	53	)	)	PUNCT
ejpam-6142	126	54	,	,	PUNCT
ejpam-6142	126	55	af	af	PROPN
ejpam-6142	126	56	(	(	PUNCT
ejpam-6142	126	57	t	t	PROPN
ejpam-6142	126	58	)	)	PUNCT
ejpam-6142	126	59	,	,	PUNCT
ejpam-6142	126	60	am(t	am(t	NOUN
ejpam-6142	126	61	)	)	PUNCT
ejpam-6142	126	62	∈	∈	PROPN
ejpam-6142	126	63	r14	r14	NOUN
ejpam-6142	126	64	+	+	CCONJ
ejpam-6142	126	65	:	:	PUNCT
ejpam-6142	126	66	n(t	n(t	NUM
ejpam-6142	126	67	)	)	PUNCT
ejpam-6142	126	68	≤	≤	NOUN
ejpam-6142	126	69	2λ	2λ	PROPN
ejpam-6142	126	70	η	η	PROPN
ejpam-6142	126	71	}	}	PUNCT
ejpam-6142	126	72	.	.	PUNCT
ejpam-6142	127	1	proof	proof	NOUN
ejpam-6142	127	2	.	.	PUNCT
ejpam-6142	128	1	n(t	n(t	NOUN
ejpam-6142	128	2	)	)	PUNCT
ejpam-6142	128	3	denotes	denote	VERB
ejpam-6142	128	4	the	the	DET
ejpam-6142	128	5	total	total	ADJ
ejpam-6142	128	6	population	population	NOUN
ejpam-6142	128	7	number	number	NOUN
ejpam-6142	128	8	at	at	ADP
ejpam-6142	128	9	time	time	NOUN
ejpam-6142	128	10	t	t	PROPN
ejpam-6142	128	11	which	which	PRON
ejpam-6142	128	12	is	be	AUX
ejpam-6142	128	13	the	the	DET
ejpam-6142	128	14	sum	sum	NOUN
ejpam-6142	128	15	of	of	ADP
ejpam-6142	128	16	all	all	DET
ejpam-6142	128	17	populations	population	NOUN
ejpam-6142	128	18	and	and	CCONJ
ejpam-6142	128	19	given	give	VERB
ejpam-6142	128	20	by	by	ADP
ejpam-6142	128	21	n(t	n(t	PRON
ejpam-6142	128	22	)	)	PUNCT
ejpam-6142	129	1	=	=	SYM
ejpam-6142	129	2	sf	sf	PROPN
ejpam-6142	129	3	(	(	PUNCT
ejpam-6142	129	4	t)+sm(t	t)+sm(t	PROPN
ejpam-6142	129	5	)	)	PUNCT
ejpam-6142	130	1	+	+	CCONJ
ejpam-6142	130	2	ef	ef	PROPN
ejpam-6142	130	3	(	(	PUNCT
ejpam-6142	130	4	t	t	PROPN
ejpam-6142	130	5	)	)	PUNCT
ejpam-6142	130	6	+	+	NUM
ejpam-6142	130	7	em(t	em(t	NUM
ejpam-6142	130	8	)	)	PUNCT
ejpam-6142	131	1	+	+	CCONJ
ejpam-6142	131	2	if	if	SCONJ
ejpam-6142	131	3	(	(	PUNCT
ejpam-6142	131	4	t	t	NOUN
ejpam-6142	131	5	)	)	PUNCT
ejpam-6142	131	6	+	+	NUM
ejpam-6142	131	7	im(t	im(t	NUM
ejpam-6142	131	8	)	)	PUNCT
ejpam-6142	132	1	+	+	CCONJ
ejpam-6142	132	2	uf	uf	PROPN
ejpam-6142	132	3	(	(	PUNCT
ejpam-6142	132	4	t	t	PROPN
ejpam-6142	132	5	)	)	PUNCT
ejpam-6142	132	6	+	+	NUM
ejpam-6142	132	7	um(t	um(t	NUM
ejpam-6142	132	8	)	)	PUNCT
ejpam-6142	133	1	+	+	NOUN
ejpam-6142	133	2	df	df	PROPN
ejpam-6142	133	3	(	(	PUNCT
ejpam-6142	133	4	t	t	PROPN
ejpam-6142	133	5	)	)	PUNCT
ejpam-6142	133	6	+	+	NOUN
ejpam-6142	133	7	dm(t	dm(t	NUM
ejpam-6142	133	8	)	)	PUNCT
ejpam-6142	134	1	+	+	CCONJ
ejpam-6142	134	2	tf	tf	X
ejpam-6142	134	3	(	(	PUNCT
ejpam-6142	134	4	t	t	PROPN
ejpam-6142	134	5	)	)	PUNCT
ejpam-6142	134	6	+	+	NUM
ejpam-6142	134	7	tm(t	tm(t	NOUN
ejpam-6142	134	8	)	)	PUNCT
ejpam-6142	135	1	+	+	X
ejpam-6142	135	2	af	af	PROPN
ejpam-6142	135	3	(	(	PUNCT
ejpam-6142	135	4	t	t	PROPN
ejpam-6142	135	5	)	)	PUNCT
ejpam-6142	135	6	+	+	NOUN
ejpam-6142	135	7	am(t	am(t	NOUN
ejpam-6142	135	8	)	)	PUNCT
ejpam-6142	135	9	differentiating	differentiate	VERB
ejpam-6142	135	10	both	both	DET
ejpam-6142	135	11	sides	side	NOUN
ejpam-6142	135	12	of	of	ADP
ejpam-6142	135	13	the	the	DET
ejpam-6142	135	14	above	above	ADJ
ejpam-6142	135	15	equation	equation	NOUN
ejpam-6142	135	16	and	and	CCONJ
ejpam-6142	135	17	simplifying	simplifying	NOUN
ejpam-6142	135	18	,	,	PUNCT
ejpam-6142	135	19	we	we	PRON
ejpam-6142	135	20	acquire	acquire	VERB
ejpam-6142	135	21	the	the	DET
ejpam-6142	135	22	following	follow	VERB
ejpam-6142	135	23	result	result	NOUN
ejpam-6142	135	24	dn	dn	ADP
ejpam-6142	135	25	dt	dt	NOUN
ejpam-6142	136	1	=	=	SYM
ejpam-6142	137	1	2λ−	2λ−	NUM
ejpam-6142	137	2	ηn	ηn	ADJ
ejpam-6142	137	3	−	−	PROPN
ejpam-6142	137	4	µn	µn	PROPN
ejpam-6142	137	5	+	+	X
ejpam-6142	137	6	µ	µ	X
ejpam-6142	137	7	(	(	PUNCT
ejpam-6142	137	8	sf	sf	PROPN
ejpam-6142	137	9	+	+	CCONJ
ejpam-6142	137	10	sm	sm	NOUN
ejpam-6142	137	11	)	)	PUNCT
ejpam-6142	137	12	dn	dn	NOUN
ejpam-6142	137	13	dt	dt	NOUN
ejpam-6142	137	14	≤	≤	PROPN
ejpam-6142	138	1	2λ−	2λ−	NUM
ejpam-6142	138	2	ηn	ηn	ADJ
ejpam-6142	138	3	applying	apply	VERB
ejpam-6142	138	4	the	the	DET
ejpam-6142	138	5	comparison	comparison	NOUN
ejpam-6142	138	6	theorem	theorem	VERB
ejpam-6142	138	7	to	to	ADP
ejpam-6142	138	8	the	the	DET
ejpam-6142	138	9	above	above	ADJ
ejpam-6142	138	10	inequality	inequality	NOUN
ejpam-6142	138	11	we	we	PRON
ejpam-6142	138	12	get	get	VERB
ejpam-6142	138	13	that	that	PRON
ejpam-6142	138	14	,	,	PUNCT
ejpam-6142	138	15	n(t	n(t	PROPN
ejpam-6142	138	16	)	)	PUNCT
ejpam-6142	138	17	≤	≤	NOUN
ejpam-6142	139	1	n(0)e−ηt	n(0)e−ηt	NOUN
ejpam-6142	139	2	+	+	CCONJ
ejpam-6142	139	3	2λ	2λ	PROPN
ejpam-6142	139	4	η	η	PROPN
ejpam-6142	139	5	(	(	PUNCT
ejpam-6142	139	6	1−	1−	NUM
ejpam-6142	139	7	e−ηt	e−ηt	ADJ
ejpam-6142	139	8	)	)	PUNCT
ejpam-6142	139	9	n(t	n(t	PROPN
ejpam-6142	139	10	)	)	PUNCT
ejpam-6142	139	11	≤	≤	NOUN
ejpam-6142	140	1	2λ	2λ	PROPN
ejpam-6142	140	2	η	η	PROPN
ejpam-6142	140	3	+	+	PROPN
ejpam-6142	140	4	(	(	PUNCT
ejpam-6142	140	5	n(0)−	n(0)−	PROPN
ejpam-6142	140	6	2λ	2λ	PROPN
ejpam-6142	140	7	η	η	PROPN
ejpam-6142	140	8	)	)	PUNCT
ejpam-6142	140	9	e−ηt	e−ηt	PROPN
ejpam-6142	140	10	it	it	PRON
ejpam-6142	140	11	follows	follow	VERB
ejpam-6142	140	12	that	that	SCONJ
ejpam-6142	140	13	n(t	n(t	PRON
ejpam-6142	140	14	)	)	PUNCT
ejpam-6142	140	15	→	→	SYM
ejpam-6142	140	16	2λ	2λ	PROPN
ejpam-6142	140	17	η	η	PROPN
ejpam-6142	140	18	as	as	ADP
ejpam-6142	140	19	t	t	PROPN
ejpam-6142	140	20	→	→	SYM
ejpam-6142	140	21	∞.	∞.	PROPN
ejpam-6142	140	22	hence	hence	ADV
ejpam-6142	140	23	,	,	PUNCT
ejpam-6142	140	24	n(t	n(t	PROPN
ejpam-6142	140	25	)	)	PUNCT
ejpam-6142	140	26	≤	≤	NOUN
ejpam-6142	140	27	2λ	2λ	PROPN
ejpam-6142	140	28	η	η	PROPN
ejpam-6142	140	29	.	.	PUNCT
ejpam-6142	141	1	we	we	PRON
ejpam-6142	141	2	conclude	conclude	VERB
ejpam-6142	141	3	that	that	SCONJ
ejpam-6142	141	4	the	the	DET
ejpam-6142	141	5	invariant	invariant	ADJ
ejpam-6142	141	6	region	region	NOUN
ejpam-6142	141	7	σ	σ	PROPN
ejpam-6142	141	8	represents	represent	VERB
ejpam-6142	141	9	the	the	DET
ejpam-6142	141	10	feasible	feasible	ADJ
ejpam-6142	141	11	solution	solution	NOUN
ejpam-6142	141	12	region	region	NOUN
ejpam-6142	141	13	of	of	ADP
ejpam-6142	141	14	the	the	DET
ejpam-6142	141	15	model	model	NOUN
ejpam-6142	141	16	.	.	PUNCT
ejpam-6142	142	1	from	from	ADP
ejpam-6142	142	2	theorem	theorem	ADJ
ejpam-6142	142	3	1	1	NUM
ejpam-6142	142	4	and	and	CCONJ
ejpam-6142	142	5	theorem	theorem	VERB
ejpam-6142	142	6	2	2	NUM
ejpam-6142	142	7	,	,	PUNCT
ejpam-6142	142	8	it	it	PRON
ejpam-6142	142	9	is	be	AUX
ejpam-6142	142	10	sufficient	sufficient	ADJ
ejpam-6142	142	11	to	to	PART
ejpam-6142	142	12	take	take	VERB
ejpam-6142	142	13	into	into	ADP
ejpam-6142	142	14	account	account	NOUN
ejpam-6142	142	15	the	the	DET
ejpam-6142	142	16	dynamics	dynamic	NOUN
ejpam-6142	142	17	of	of	ADP
ejpam-6142	142	18	the	the	DET
ejpam-6142	142	19	system	system	NOUN
ejpam-6142	142	20	1	1	NUM
ejpam-6142	142	21	in	in	ADP
ejpam-6142	142	22	the	the	DET
ejpam-6142	142	23	region	region	NOUN
ejpam-6142	142	24	σ	σ	NUM
ejpam-6142	142	25	where	where	SCONJ
ejpam-6142	142	26	the	the	DET
ejpam-6142	142	27	positiveness	positiveness	NOUN
ejpam-6142	142	28	,	,	PUNCT
ejpam-6142	142	29	existence	existence	NOUN
ejpam-6142	142	30	,	,	PUNCT
ejpam-6142	142	31	and	and	CCONJ
ejpam-6142	142	32	uniqueness	uniqueness	NOUN
ejpam-6142	142	33	of	of	ADP
ejpam-6142	142	34	the	the	DET
ejpam-6142	142	35	solution	solution	NOUN
ejpam-6142	142	36	hold	hold	NOUN
ejpam-6142	142	37	.	.	PUNCT
ejpam-6142	143	1	4	4	X
ejpam-6142	143	2	.	.	X
ejpam-6142	143	3	equilibrium	equilibrium	NOUN
ejpam-6142	143	4	points	point	NOUN
ejpam-6142	143	5	and	and	CCONJ
ejpam-6142	143	6	basic	basic	ADJ
ejpam-6142	143	7	reproduction	reproduction	NOUN
ejpam-6142	143	8	number	number	NOUN
ejpam-6142	143	9	r0	r0	NOUN
ejpam-6142	143	10	in	in	ADP
ejpam-6142	143	11	this	this	DET
ejpam-6142	143	12	section	section	NOUN
ejpam-6142	143	13	,	,	PUNCT
ejpam-6142	143	14	we	we	PRON
ejpam-6142	143	15	compute	compute	VERB
ejpam-6142	143	16	two	two	NUM
ejpam-6142	143	17	key	key	ADJ
ejpam-6142	143	18	points	point	NOUN
ejpam-6142	143	19	for	for	ADP
ejpam-6142	143	20	system	system	NOUN
ejpam-6142	143	21	1	1	NUM
ejpam-6142	143	22	:	:	PUNCT
ejpam-6142	143	23	the	the	DET
ejpam-6142	143	24	disease	disease	NOUN
ejpam-6142	143	25	-	-	PUNCT
ejpam-6142	143	26	free	free	ADJ
ejpam-6142	143	27	equilibrium	equilibrium	NOUN
ejpam-6142	143	28	(	(	PUNCT
ejpam-6142	143	29	dfe	dfe	PROPN
ejpam-6142	143	30	)	)	PUNCT
ejpam-6142	143	31	in	in	ADP
ejpam-6142	143	32	the	the	DET
ejpam-6142	143	33	absence	absence	NOUN
ejpam-6142	143	34	of	of	ADP
ejpam-6142	143	35	the	the	DET
ejpam-6142	143	36	disease	disease	NOUN
ejpam-6142	143	37	,	,	PUNCT
ejpam-6142	143	38	and	and	CCONJ
ejpam-6142	143	39	the	the	DET
ejpam-6142	143	40	endemic	endemic	ADJ
ejpam-6142	143	41	equilibrium	equilibrium	NOUN
ejpam-6142	143	42	(	(	PUNCT
ejpam-6142	143	43	ee	ee	PROPN
ejpam-6142	143	44	)	)	PUNCT
ejpam-6142	143	45	during	during	ADP
ejpam-6142	143	46	an	an	DET
ejpam-6142	143	47	outbreak	outbreak	NOUN
ejpam-6142	143	48	.	.	PUNCT
ejpam-6142	144	1	in	in	ADP
ejpam-6142	144	2	addition	addition	NOUN
ejpam-6142	144	3	,	,	PUNCT
ejpam-6142	144	4	we	we	PRON
ejpam-6142	144	5	utilize	utilize	VERB
ejpam-6142	144	6	the	the	DET
ejpam-6142	144	7	next	next	ADJ
ejpam-6142	144	8	-	-	PUNCT
ejpam-6142	144	9	generation	generation	NOUN
ejpam-6142	144	10	matrix	matrix	NOUN
ejpam-6142	144	11	in	in	ADP
ejpam-6142	144	12	calculating	calculate	VERB
ejpam-6142	144	13	the	the	DET
ejpam-6142	144	14	basic	basic	ADJ
ejpam-6142	144	15	reproduction	reproduction	NOUN
ejpam-6142	144	16	number	number	NOUN
ejpam-6142	144	17	,	,	PUNCT
ejpam-6142	144	18	r0	r0	NOUN
ejpam-6142	144	19	.	.	PUNCT
ejpam-6142	145	1	in	in	ADP
ejpam-6142	145	2	the	the	DET
ejpam-6142	145	3	model	model	NOUN
ejpam-6142	145	4	1	1	NUM
ejpam-6142	145	5	,	,	PUNCT
ejpam-6142	145	6	we	we	PRON
ejpam-6142	145	7	set	set	VERB
ejpam-6142	145	8	s.	s.	PROPN
ejpam-6142	145	9	m.	m.	PROPN
ejpam-6142	145	10	fatah	fatah	PROPN
ejpam-6142	145	11	,	,	PUNCT
ejpam-6142	145	12	s.	s.	PROPN
ejpam-6142	145	13	h.	h.	PROPN
ejpam-6142	145	14	a.	a.	PROPN
ejpam-6142	145	15	khoshnaw	khoshnaw	PROPN
ejpam-6142	145	16	,	,	PUNCT
ejpam-6142	145	17	a.	a.	PROPN
ejpam-6142	145	18	n.	n.	PROPN
ejpam-6142	145	19	mustafa	mustafa	PROPN
ejpam-6142	145	20	/	/	SYM
ejpam-6142	145	21	eur	eur	PROPN
ejpam-6142	145	22	.	.	PUNCT
ejpam-6142	146	1	j.	j.	PROPN
ejpam-6142	146	2	pure	pure	PROPN
ejpam-6142	146	3	appl	appl	PROPN
ejpam-6142	146	4	.	.	PROPN
ejpam-6142	146	5	math	math	PROPN
ejpam-6142	146	6	,	,	PUNCT
ejpam-6142	146	7	18	18	NUM
ejpam-6142	146	8	(	(	PUNCT
ejpam-6142	146	9	2	2	NUM
ejpam-6142	146	10	)	)	PUNCT
ejpam-6142	146	11	(	(	PUNCT
ejpam-6142	146	12	2025	2025	NUM
ejpam-6142	146	13	)	)	PUNCT
ejpam-6142	146	14	,	,	PUNCT
ejpam-6142	146	15	6142	6142	NUM
ejpam-6142	146	16	8	8	NUM
ejpam-6142	146	17	of	of	ADP
ejpam-6142	146	18	33	33	NUM
ejpam-6142	146	19	γf	γf	NOUN
ejpam-6142	146	20	=	=	SYM
ejpam-6142	146	21	αf	αf	PROPN
ejpam-6142	146	22	+	+	X
ejpam-6142	146	23	η	η	PROPN
ejpam-6142	146	24	,	,	PUNCT
ejpam-6142	146	25	γm	γm	ADJ
ejpam-6142	146	26	=	=	PUNCT
ejpam-6142	146	27	αm	αm	NOUN
ejpam-6142	146	28	+	+	CCONJ
ejpam-6142	146	29	η	η	PROPN
ejpam-6142	146	30	,	,	PUNCT
ejpam-6142	146	31	∆f	∆f	PROPN
ejpam-6142	146	32	=	=	SYM
ejpam-6142	146	33	µ+	µ+	X
ejpam-6142	146	34	η	η	PROPN
ejpam-6142	146	35	+	+	PROPN
ejpam-6142	146	36	γf	γf	PROPN
ejpam-6142	147	1	+	+	CCONJ
ejpam-6142	147	2	θf	θf	INTJ
ejpam-6142	147	3	,	,	PUNCT
ejpam-6142	147	4	∆m	∆m	PROPN
ejpam-6142	147	5	=	=	SYM
ejpam-6142	147	6	µ+	µ+	PROPN
ejpam-6142	147	7	η	η	PROPN
ejpam-6142	147	8	+	+	X
ejpam-6142	147	9	γm	γm	PROPN
ejpam-6142	147	10	+	+	NUM
ejpam-6142	147	11	θm	θm	PROPN
ejpam-6142	147	12	ωf	ωf	ADP
ejpam-6142	147	13	=	=	PUNCT
ejpam-6142	147	14	µ+	µ+	X
ejpam-6142	147	15	η	η	PROPN
ejpam-6142	147	16	+	+	PROPN
ejpam-6142	147	17	ρf	ρf	PROPN
ejpam-6142	147	18	,	,	PUNCT
ejpam-6142	147	19	ωm	ωm	PROPN
ejpam-6142	147	20	=	=	SYM
ejpam-6142	147	21	µ+	µ+	PROPN
ejpam-6142	147	22	η	η	PROPN
ejpam-6142	147	23	+	+	PROPN
ejpam-6142	147	24	ρm	ρm	PROPN
ejpam-6142	147	25	,	,	PUNCT
ejpam-6142	147	26	ψf	ψf	X
ejpam-6142	147	27	=	=	PUNCT
ejpam-6142	147	28	µ+	µ+	PUNCT
ejpam-6142	147	29	η	η	PROPN
ejpam-6142	147	30	+	+	PROPN
ejpam-6142	147	31	ωf	ωf	PROPN
ejpam-6142	147	32	,	,	PUNCT
ejpam-6142	147	33	ψm	ψm	PROPN
ejpam-6142	147	34	=	=	SYM
ejpam-6142	147	35	µ+	µ+	PUNCT
ejpam-6142	147	36	η	η	PROPN
ejpam-6142	147	37	+	+	CCONJ
ejpam-6142	147	38	ωm	ωm	X
ejpam-6142	147	39	φf	φf	X
ejpam-6142	147	40	=	=	PUNCT
ejpam-6142	147	41	µ+	µ+	X
ejpam-6142	147	42	η	η	PROPN
ejpam-6142	147	43	+	+	PROPN
ejpam-6142	147	44	λf	λf	PROPN
ejpam-6142	147	45	,	,	PUNCT
ejpam-6142	147	46	φm	φm	ADP
ejpam-6142	147	47	=	=	PUNCT
ejpam-6142	147	48	µ+	µ+	PUNCT
ejpam-6142	147	49	η	η	PROPN
ejpam-6142	147	50	+	+	PROPN
ejpam-6142	147	51	λm	λm	PROPN
ejpam-6142	147	52	,	,	PUNCT
ejpam-6142	147	53	ζ	ζ	NOUN
ejpam-6142	147	54	=	=	SYM
ejpam-6142	147	55	µ+	µ+	PUNCT
ejpam-6142	147	56	η	η	PROPN
ejpam-6142	147	57	the	the	DET
ejpam-6142	147	58	system	system	NOUN
ejpam-6142	147	59	1	1	NUM
ejpam-6142	147	60	becomes	become	VERB
ejpam-6142	147	61	,	,	PUNCT
ejpam-6142	147	62	dsf	dsf	NOUN
ejpam-6142	148	1	dt	dt	NOUN
ejpam-6142	148	2	=	=	SYM
ejpam-6142	148	3	λ−	λ−	PROPN
ejpam-6142	148	4	(	(	PUNCT
ejpam-6142	148	5	1−	1−	NUM
ejpam-6142	148	6	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	148	7	−	−	PROPN
ejpam-6142	148	8	ηsf	ηsf	INTJ
ejpam-6142	148	9	dsm	dsm	PROPN
ejpam-6142	148	10	dt	dt	PROPN
ejpam-6142	149	1	=	=	SYM
ejpam-6142	149	2	λ−	λ−	PROPN
ejpam-6142	149	3	(	(	PUNCT
ejpam-6142	149	4	1−	1−	NUM
ejpam-6142	149	5	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	149	6	−	−	PROPN
ejpam-6142	149	7	ηsm	ηsm	NOUN
ejpam-6142	149	8	def	def	NOUN
ejpam-6142	149	9	dt	dt	X
ejpam-6142	149	10	=	=	SYM
ejpam-6142	149	11	(	(	PUNCT
ejpam-6142	149	12	1−	1−	NUM
ejpam-6142	149	13	κϵ)βfimsf	κϵ)βfimsf	PROPN
ejpam-6142	149	14	−	−	PROPN
ejpam-6142	149	15	γfef	γfef	NOUN
ejpam-6142	149	16	dem	dem	NOUN
ejpam-6142	149	17	dt	dt	X
ejpam-6142	150	1	=	=	SYM
ejpam-6142	150	2	(	(	PUNCT
ejpam-6142	150	3	1−	1−	NUM
ejpam-6142	150	4	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	150	5	−	−	PROPN
ejpam-6142	150	6	γmem	γmem	NOUN
ejpam-6142	150	7	dif	dif	ADV
ejpam-6142	150	8	dt	dt	X
ejpam-6142	151	1	=	=	SYM
ejpam-6142	151	2	αfef	αfef	NOUN
ejpam-6142	151	3	−∆fif	−∆fif	NOUN
ejpam-6142	151	4	dim	dim	NOUN
ejpam-6142	151	5	dt	dt	NOUN
ejpam-6142	151	6	=	=	SYM
ejpam-6142	151	7	αmem	αmem	ADJ
ejpam-6142	151	8	−∆mim	−∆mim	PROPN
ejpam-6142	151	9	ddf	ddf	NOUN
ejpam-6142	151	10	dt	dt	NOUN
ejpam-6142	151	11	=	=	PUNCT
ejpam-6142	151	12	γfif	γfif	PROPN
ejpam-6142	151	13	−	−	PROPN
ejpam-6142	151	14	ωfdf	ωfdf	VERB
ejpam-6142	151	15	ddm	ddm	NOUN
ejpam-6142	151	16	dt	dt	NOUN
ejpam-6142	151	17	=	=	PUNCT
ejpam-6142	151	18	γmim	γmim	NOUN
ejpam-6142	151	19	−	−	PROPN
ejpam-6142	151	20	ωmdm	ωmdm	ADJ
ejpam-6142	151	21	dtf	dtf	NOUN
ejpam-6142	151	22	dt	dt	NOUN
ejpam-6142	152	1	=	=	PUNCT
ejpam-6142	152	2	ρfdf	ρfdf	NOUN
ejpam-6142	152	3	−ψftf	−ψftf	NOUN
ejpam-6142	153	1	dtm	dtm	PROPN
ejpam-6142	153	2	dt	dt	NOUN
ejpam-6142	154	1	=	=	PUNCT
ejpam-6142	154	2	ρmdm	ρmdm	PROPN
ejpam-6142	154	3	−ψmtm	−ψmtm	PUNCT
ejpam-6142	154	4	duf	duf	NOUN
ejpam-6142	154	5	dt	dt	NOUN
ejpam-6142	154	6	=	=	SYM
ejpam-6142	154	7	θfif	θfif	PROPN
ejpam-6142	154	8	−	−	PROPN
ejpam-6142	154	9	φfuf	φfuf	NOUN
ejpam-6142	154	10	dum	dum	NOUN
ejpam-6142	154	11	dt	dt	X
ejpam-6142	154	12	=	=	SYM
ejpam-6142	154	13	θmim	θmim	PROPN
ejpam-6142	154	14	−	−	PROPN
ejpam-6142	154	15	φmum	φmum	ADJ
ejpam-6142	154	16	daf	daf	NOUN
ejpam-6142	154	17	dt	dt	X
ejpam-6142	155	1	=	=	PUNCT
ejpam-6142	155	2	λfuf	λfuf	NOUN
ejpam-6142	156	1	+	+	NUM
ejpam-6142	156	2	ωftf	ωftf	NOUN
ejpam-6142	156	3	−	−	PROPN
ejpam-6142	156	4	ζaf	ζaf	NOUN
ejpam-6142	156	5	dam	dam	NOUN
ejpam-6142	156	6	dt	dt	NOUN
ejpam-6142	156	7	=	=	PUNCT
ejpam-6142	156	8	λmum	λmum	ADJ
ejpam-6142	156	9	+	+	CCONJ
ejpam-6142	156	10	ωmtm	ωmtm	ADJ
ejpam-6142	156	11	−	−	NOUN
ejpam-6142	156	12	ζam	ζam	ADJ
ejpam-6142	156	13	(	(	PUNCT
ejpam-6142	156	14	2	2	NUM
ejpam-6142	156	15	)	)	PUNCT
ejpam-6142	156	16	4.1	4.1	NUM
ejpam-6142	156	17	.	.	PUNCT
ejpam-6142	157	1	disease	disease	NOUN
ejpam-6142	157	2	-	-	PUNCT
ejpam-6142	157	3	free	free	ADJ
ejpam-6142	157	4	equilibrium	equilibrium	NOUN
ejpam-6142	157	5	point	point	NOUN
ejpam-6142	157	6	(	(	PUNCT
ejpam-6142	157	7	e0	e0	PROPN
ejpam-6142	157	8	)	)	PUNCT
ejpam-6142	157	9	the	the	DET
ejpam-6142	157	10	equilibrium	equilibrium	NOUN
ejpam-6142	157	11	point	point	NOUN
ejpam-6142	157	12	without	without	ADP
ejpam-6142	157	13	the	the	DET
ejpam-6142	157	14	disease	disease	NOUN
ejpam-6142	157	15	for	for	ADP
ejpam-6142	157	16	the	the	DET
ejpam-6142	157	17	system	system	NOUN
ejpam-6142	157	18	2	2	NUM
ejpam-6142	157	19	represents	represent	VERB
ejpam-6142	157	20	a	a	DET
ejpam-6142	157	21	stable	stable	ADJ
ejpam-6142	157	22	state	state	NOUN
ejpam-6142	157	23	in	in	ADP
ejpam-6142	157	24	which	which	PRON
ejpam-6142	157	25	the	the	DET
ejpam-6142	157	26	population	population	NOUN
ejpam-6142	157	27	is	be	AUX
ejpam-6142	157	28	uninfected	uninfected	ADJ
ejpam-6142	157	29	by	by	ADP
ejpam-6142	157	30	hiv	hiv	PROPN
ejpam-6142	157	31	/	/	SYM
ejpam-6142	157	32	aids	aids	PROPN
ejpam-6142	157	33	.	.	PUNCT
ejpam-6142	158	1	we	we	PRON
ejpam-6142	158	2	set	set	VERB
ejpam-6142	158	3	all	all	DET
ejpam-6142	158	4	the	the	DET
ejpam-6142	158	5	variables	variable	NOUN
ejpam-6142	158	6	to	to	PART
ejpam-6142	158	7	be	be	AUX
ejpam-6142	158	8	zero	zero	NUM
ejpam-6142	158	9	except	except	SCONJ
ejpam-6142	158	10	sf	sf	PROPN
ejpam-6142	158	11	and	and	CCONJ
ejpam-6142	158	12	sm	sm	PROPN
ejpam-6142	158	13	.	.	PUNCT
ejpam-6142	159	1	hence	hence	ADV
ejpam-6142	159	2	,	,	PUNCT
ejpam-6142	159	3	ef	ef	PROPN
ejpam-6142	159	4	=	=	PUNCT
ejpam-6142	159	5	em	em	PRON
ejpam-6142	159	6	=	=	PUNCT
ejpam-6142	159	7	if	if	SCONJ
ejpam-6142	159	8	=	=	PUNCT
ejpam-6142	159	9	i	i	PRON
ejpam-6142	159	10	m	m	VERB
ejpam-6142	159	11	=	=	ADJ
ejpam-6142	159	12	uf	uf	PROPN
ejpam-6142	159	13	=	=	PUNCT
ejpam-6142	159	14	um	um	INTJ
ejpam-6142	159	15	=	=	SYM
ejpam-6142	159	16	df	df	PROPN
ejpam-6142	159	17	=	=	SYM
ejpam-6142	159	18	dm	dm	PROPN
ejpam-6142	159	19	=	=	PUNCT
ejpam-6142	159	20	tf	tf	NOUN
ejpam-6142	159	21	=	=	PUNCT
ejpam-6142	159	22	tm	tm	NOUN
ejpam-6142	159	23	=	=	NOUN
ejpam-6142	159	24	af	af	PROPN
ejpam-6142	159	25	=	=	SYM
ejpam-6142	159	26	am	be	AUX
ejpam-6142	159	27	=	=	NOUN
ejpam-6142	159	28	0	0	NUM
ejpam-6142	159	29	then	then	ADV
ejpam-6142	159	30	we	we	PRON
ejpam-6142	159	31	equal	equal	VERB
ejpam-6142	159	32	the	the	DET
ejpam-6142	159	33	right	right	ADJ
ejpam-6142	159	34	-	-	PUNCT
ejpam-6142	159	35	hand	hand	NOUN
ejpam-6142	159	36	side	side	NOUN
ejpam-6142	159	37	of	of	ADP
ejpam-6142	159	38	all	all	DET
ejpam-6142	159	39	equations	equation	NOUN
ejpam-6142	159	40	in	in	ADP
ejpam-6142	159	41	system	system	NOUN
ejpam-6142	159	42	(	(	PUNCT
ejpam-6142	159	43	2	2	NUM
ejpam-6142	159	44	)	)	PUNCT
ejpam-6142	159	45	to	to	ADP
ejpam-6142	159	46	zero	zero	NUM
ejpam-6142	159	47	,	,	PUNCT
ejpam-6142	159	48	we	we	PRON
ejpam-6142	159	49	obtain	obtain	VERB
ejpam-6142	159	50	that	that	DET
ejpam-6142	159	51	sf	sf	NOUN
ejpam-6142	159	52	=	=	PUNCT
ejpam-6142	159	53	sm	sm	PROPN
ejpam-6142	159	54	=	=	SYM
ejpam-6142	159	55	λ	λ	X
ejpam-6142	159	56	η	η	PROPN
ejpam-6142	159	57	,	,	PUNCT
ejpam-6142	159	58	and	and	CCONJ
ejpam-6142	159	59	ef	ef	X
ejpam-6142	159	60	=	=	PUNCT
ejpam-6142	159	61	em	em	PRON
ejpam-6142	160	1	=	=	PUNCT
ejpam-6142	160	2	if	if	SCONJ
ejpam-6142	160	3	=	=	PUNCT
ejpam-6142	160	4	i	i	PRON
ejpam-6142	160	5	m	m	VERB
ejpam-6142	160	6	=	=	ADJ
ejpam-6142	160	7	uf	uf	PROPN
ejpam-6142	160	8	=	=	PUNCT
ejpam-6142	160	9	um	um	INTJ
ejpam-6142	160	10	=	=	SYM
ejpam-6142	160	11	df	df	PROPN
ejpam-6142	160	12	=	=	SYM
ejpam-6142	160	13	dm	dm	PROPN
ejpam-6142	160	14	=	=	PUNCT
ejpam-6142	160	15	tf	tf	NOUN
ejpam-6142	160	16	=	=	PUNCT
ejpam-6142	160	17	tm	tm	NOUN
ejpam-6142	160	18	=	=	NOUN
ejpam-6142	160	19	af	af	PROPN
ejpam-6142	160	20	=	=	SYM
ejpam-6142	160	21	am	be	AUX
ejpam-6142	160	22	=	=	ADJ
ejpam-6142	160	23	0	0	NUM
ejpam-6142	160	24	.	.	PUNCT
ejpam-6142	161	1	thus	thus	ADV
ejpam-6142	161	2	,	,	PUNCT
ejpam-6142	161	3	the	the	DET
ejpam-6142	161	4	disease	disease	NOUN
ejpam-6142	161	5	-	-	PUNCT
ejpam-6142	161	6	free	free	ADJ
ejpam-6142	161	7	equilibrium	equilibrium	NOUN
ejpam-6142	161	8	is	be	AUX
ejpam-6142	161	9	e0	e0	PROPN
ejpam-6142	161	10	=	=	PUNCT
ejpam-6142	161	11	(	(	PUNCT
ejpam-6142	161	12	sf	sf	INTJ
ejpam-6142	161	13	,	,	PUNCT
ejpam-6142	161	14	ef	ef	PROPN
ejpam-6142	161	15	,	,	PUNCT
ejpam-6142	161	16	if	if	SCONJ
ejpam-6142	161	17	,	,	PUNCT
ejpam-6142	161	18	df	df	PROPN
ejpam-6142	161	19	,	,	PUNCT
ejpam-6142	161	20	tf	tf	INTJ
ejpam-6142	161	21	,	,	PUNCT
ejpam-6142	161	22	uf	uf	PROPN
ejpam-6142	161	23	,	,	PUNCT
ejpam-6142	161	24	af	af	PROPN
ejpam-6142	161	25	,	,	PUNCT
ejpam-6142	161	26	sm	sm	PROPN
ejpam-6142	161	27	,	,	PUNCT
ejpam-6142	161	28	em	em	PRON
ejpam-6142	161	29	,	,	PUNCT
ejpam-6142	161	30	i	i	PRON
ejpam-6142	161	31	m	m	PROPN
ejpam-6142	161	32	,	,	PUNCT
ejpam-6142	161	33	dm	dm	PROPN
ejpam-6142	161	34	,	,	PUNCT
ejpam-6142	161	35	tm	tm	NOUN
ejpam-6142	161	36	,	,	PUNCT
ejpam-6142	161	37	um	um	INTJ
ejpam-6142	161	38	,	,	PUNCT
ejpam-6142	161	39	am	be	AUX
ejpam-6142	161	40	)	)	PUNCT
ejpam-6142	161	41	=	=	SYM
ejpam-6142	161	42	(	(	PUNCT
ejpam-6142	161	43	λ	λ	X
ejpam-6142	161	44	η	η	PROPN
ejpam-6142	161	45	,	,	PUNCT
ejpam-6142	161	46	0	0	NUM
ejpam-6142	161	47	,	,	PUNCT
ejpam-6142	161	48	0	0	NUM
ejpam-6142	161	49	,	,	PUNCT
ejpam-6142	161	50	0	0	NUM
ejpam-6142	161	51	,	,	PUNCT
ejpam-6142	161	52	0	0	NUM
ejpam-6142	161	53	,	,	PUNCT
ejpam-6142	161	54	0	0	NUM
ejpam-6142	161	55	,	,	PUNCT
ejpam-6142	161	56	0	0	NUM
ejpam-6142	161	57	,	,	PUNCT
ejpam-6142	161	58	λ	λ	PROPN
ejpam-6142	161	59	η	η	PROPN
ejpam-6142	161	60	,	,	PUNCT
ejpam-6142	161	61	0	0	NUM
ejpam-6142	161	62	,	,	PUNCT
ejpam-6142	161	63	0	0	NUM
ejpam-6142	161	64	,	,	PUNCT
ejpam-6142	161	65	0	0	NUM
ejpam-6142	161	66	,	,	PUNCT
ejpam-6142	161	67	0	0	NUM
ejpam-6142	161	68	,	,	PUNCT
ejpam-6142	161	69	0	0	NUM
ejpam-6142	161	70	,	,	PUNCT
ejpam-6142	161	71	0	0	NUM
ejpam-6142	161	72	)	)	PUNCT
ejpam-6142	161	73	.	.	PUNCT
ejpam-6142	162	1	4.2	4.2	NUM
ejpam-6142	162	2	.	.	PUNCT
ejpam-6142	162	3	basic	basic	ADJ
ejpam-6142	162	4	reproduction	reproduction	NOUN
ejpam-6142	162	5	number	number	NOUN
ejpam-6142	162	6	(	(	PUNCT
ejpam-6142	162	7	r0	r0	NOUN
ejpam-6142	162	8	)	)	PUNCT
ejpam-6142	162	9	we	we	PRON
ejpam-6142	162	10	compute	compute	VERB
ejpam-6142	162	11	r0	r0	NOUN
ejpam-6142	162	12	by	by	ADP
ejpam-6142	162	13	utilizing	utilize	VERB
ejpam-6142	162	14	the	the	DET
ejpam-6142	162	15	next	next	ADJ
ejpam-6142	162	16	generation	generation	NOUN
ejpam-6142	162	17	matrix	matrix	NOUN
ejpam-6142	162	18	.	.	PUNCT
ejpam-6142	163	1	the	the	DET
ejpam-6142	163	2	matrix	matrix	NOUN
ejpam-6142	163	3	serves	serve	VERB
ejpam-6142	163	4	the	the	DET
ejpam-6142	163	5	purpose	purpose	NOUN
ejpam-6142	163	6	of	of	ADP
ejpam-6142	163	7	calculating	calculate	VERB
ejpam-6142	163	8	the	the	DET
ejpam-6142	163	9	reproductive	reproductive	ADJ
ejpam-6142	163	10	number	number	NOUN
ejpam-6142	163	11	,	,	PUNCT
ejpam-6142	163	12	denoted	denote	VERB
ejpam-6142	163	13	as	as	ADP
ejpam-6142	163	14	r0	r0	NOUN
ejpam-6142	163	15	.	.	PUNCT
ejpam-6142	164	1	this	this	DET
ejpam-6142	164	2	technique	technique	NOUN
ejpam-6142	164	3	defines	define	VERB
ejpam-6142	164	4	r0	r0	NOUN
ejpam-6142	164	5	as	as	ADP
ejpam-6142	164	6	the	the	DET
ejpam-6142	164	7	greatest	great	ADJ
ejpam-6142	164	8	absolute	absolute	ADJ
ejpam-6142	164	9	eigenvalue	eigenvalue	NOUN
ejpam-6142	164	10	within	within	ADP
ejpam-6142	164	11	the	the	DET
ejpam-6142	164	12	next	next	ADJ
ejpam-6142	164	13	-	-	PUNCT
ejpam-6142	164	14	generation	generation	NOUN
ejpam-6142	164	15	matrix	matrix	NOUN
ejpam-6142	164	16	.	.	PUNCT
ejpam-6142	165	1	in	in	ADP
ejpam-6142	165	2	creating	create	VERB
ejpam-6142	165	3	this	this	DET
ejpam-6142	165	4	matrix	matrix	NOUN
ejpam-6142	165	5	,	,	PUNCT
ejpam-6142	165	6	we	we	PRON
ejpam-6142	165	7	categorize	categorize	VERB
ejpam-6142	165	8	all	all	DET
ejpam-6142	165	9	terms	term	NOUN
ejpam-6142	165	10	of	of	ADP
ejpam-6142	165	11	the	the	DET
ejpam-6142	165	12	disease	disease	NOUN
ejpam-6142	165	13	classes	class	NOUN
ejpam-6142	165	14	of	of	ADP
ejpam-6142	165	15	the	the	DET
ejpam-6142	165	16	model	model	NOUN
ejpam-6142	165	17	into	into	ADP
ejpam-6142	165	18	two	two	NUM
ejpam-6142	165	19	groups	group	NOUN
ejpam-6142	165	20	,	,	PUNCT
ejpam-6142	165	21	v	v	NOUN
ejpam-6142	165	22	represents	represent	VERB
ejpam-6142	165	23	the	the	DET
ejpam-6142	165	24	matrix	matrix	NOUN
ejpam-6142	165	25	for	for	ADP
ejpam-6142	165	26	transition	transition	NOUN
ejpam-6142	165	27	cases	case	NOUN
ejpam-6142	165	28	,	,	PUNCT
ejpam-6142	165	29	while	while	SCONJ
ejpam-6142	165	30	f	f	PROPN
ejpam-6142	165	31	represents	represent	VERB
ejpam-6142	165	32	the	the	DET
ejpam-6142	165	33	matrix	matrix	NOUN
ejpam-6142	165	34	for	for	ADP
ejpam-6142	165	35	newly	newly	ADV
ejpam-6142	165	36	infected	infect	VERB
ejpam-6142	165	37	cases	case	NOUN
ejpam-6142	165	38	.	.	PUNCT
ejpam-6142	166	1	s.	s.	PROPN
ejpam-6142	166	2	m.	m.	PROPN
ejpam-6142	166	3	fatah	fatah	PROPN
ejpam-6142	166	4	,	,	PUNCT
ejpam-6142	166	5	s.	s.	PROPN
ejpam-6142	166	6	h.	h.	PROPN
ejpam-6142	166	7	a.	a.	PROPN
ejpam-6142	166	8	khoshnaw	khoshnaw	PROPN
ejpam-6142	166	9	,	,	PUNCT
ejpam-6142	166	10	a.	a.	PROPN
ejpam-6142	166	11	n.	n.	PROPN
ejpam-6142	166	12	mustafa	mustafa	PROPN
ejpam-6142	166	13	/	/	SYM
ejpam-6142	166	14	eur	eur	PROPN
ejpam-6142	166	15	.	.	PUNCT
ejpam-6142	167	1	j.	j.	PROPN
ejpam-6142	167	2	pure	pure	PROPN
ejpam-6142	167	3	appl	appl	PROPN
ejpam-6142	167	4	.	.	PROPN
ejpam-6142	167	5	math	math	PROPN
ejpam-6142	167	6	,	,	PUNCT
ejpam-6142	167	7	18	18	NUM
ejpam-6142	167	8	(	(	PUNCT
ejpam-6142	167	9	2	2	NUM
ejpam-6142	167	10	)	)	PUNCT
ejpam-6142	167	11	(	(	PUNCT
ejpam-6142	167	12	2025	2025	NUM
ejpam-6142	167	13	)	)	PUNCT
ejpam-6142	167	14	,	,	PUNCT
ejpam-6142	167	15	6142	6142	NUM
ejpam-6142	167	16	9	9	NUM
ejpam-6142	167	17	of	of	ADP
ejpam-6142	167	18	33	33	NUM
ejpam-6142	167	19	the	the	DET
ejpam-6142	167	20	disease	disease	NOUN
ejpam-6142	167	21	classes	class	NOUN
ejpam-6142	167	22	are	be	AUX
ejpam-6142	167	23	def	def	ADJ
ejpam-6142	167	24	dt	dt	X
ejpam-6142	167	25	=	=	SYM
ejpam-6142	167	26	(	(	PUNCT
ejpam-6142	167	27	1−	1−	NUM
ejpam-6142	167	28	κϵ)βfimsf	κϵ)βfimsf	PROPN
ejpam-6142	167	29	−	−	PROPN
ejpam-6142	167	30	γfef	γfef	NOUN
ejpam-6142	168	1	dem	dem	NOUN
ejpam-6142	168	2	dt	dt	X
ejpam-6142	169	1	=	=	SYM
ejpam-6142	169	2	(	(	PUNCT
ejpam-6142	169	3	1−	1−	NUM
ejpam-6142	169	4	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	169	5	−	−	PROPN
ejpam-6142	169	6	γmem	γmem	NOUN
ejpam-6142	169	7	dif	dif	ADV
ejpam-6142	169	8	dt	dt	X
ejpam-6142	170	1	=	=	SYM
ejpam-6142	170	2	αfef	αfef	NOUN
ejpam-6142	170	3	−∆fif	−∆fif	NOUN
ejpam-6142	170	4	dim	dim	NOUN
ejpam-6142	170	5	dt	dt	NOUN
ejpam-6142	170	6	=	=	SYM
ejpam-6142	170	7	αmem	αmem	ADJ
ejpam-6142	170	8	−∆mim	−∆mim	PROPN
ejpam-6142	170	9	ddf	ddf	NOUN
ejpam-6142	170	10	dt	dt	NOUN
ejpam-6142	170	11	=	=	PUNCT
ejpam-6142	170	12	γfif	γfif	PROPN
ejpam-6142	170	13	−	−	PROPN
ejpam-6142	170	14	ωfdf	ωfdf	VERB
ejpam-6142	170	15	ddm	ddm	NOUN
ejpam-6142	170	16	dt	dt	NOUN
ejpam-6142	170	17	=	=	PUNCT
ejpam-6142	170	18	γmim	γmim	NOUN
ejpam-6142	170	19	−	−	PROPN
ejpam-6142	170	20	ωmdm	ωmdm	ADJ
ejpam-6142	170	21	dtf	dtf	NOUN
ejpam-6142	170	22	dt	dt	NOUN
ejpam-6142	171	1	=	=	PUNCT
ejpam-6142	171	2	ρfdf	ρfdf	NOUN
ejpam-6142	171	3	−ψftf	−ψftf	NOUN
ejpam-6142	172	1	dtm	dtm	PROPN
ejpam-6142	172	2	dt	dt	NOUN
ejpam-6142	173	1	=	=	PUNCT
ejpam-6142	173	2	ρmdm	ρmdm	PROPN
ejpam-6142	173	3	−ψmtm	−ψmtm	PUNCT
ejpam-6142	173	4	duf	duf	NOUN
ejpam-6142	173	5	dt	dt	NOUN
ejpam-6142	173	6	=	=	SYM
ejpam-6142	173	7	θfif	θfif	PROPN
ejpam-6142	173	8	−	−	PROPN
ejpam-6142	173	9	φfuf	φfuf	NOUN
ejpam-6142	173	10	dum	dum	NOUN
ejpam-6142	173	11	dt	dt	X
ejpam-6142	173	12	=	=	SYM
ejpam-6142	173	13	θmim	θmim	PROPN
ejpam-6142	173	14	−	−	PROPN
ejpam-6142	173	15	φmum	φmum	ADJ
ejpam-6142	173	16	daf	daf	NOUN
ejpam-6142	173	17	dt	dt	X
ejpam-6142	174	1	=	=	PUNCT
ejpam-6142	174	2	λfuf	λfuf	NOUN
ejpam-6142	175	1	+	+	NUM
ejpam-6142	175	2	ωftf	ωftf	NOUN
ejpam-6142	175	3	−	−	PROPN
ejpam-6142	175	4	ζaf	ζaf	NOUN
ejpam-6142	175	5	dam	dam	NOUN
ejpam-6142	175	6	dt	dt	NOUN
ejpam-6142	175	7	=	=	PUNCT
ejpam-6142	175	8	λmum	λmum	ADJ
ejpam-6142	175	9	+	+	CCONJ
ejpam-6142	175	10	ωmtm	ωmtm	ADJ
ejpam-6142	175	11	−	−	NOUN
ejpam-6142	175	12	ζam	ζam	ADJ
ejpam-6142	175	13	(	(	PUNCT
ejpam-6142	175	14	3	3	NUM
ejpam-6142	175	15	)	)	PUNCT
ejpam-6142	175	16	in	in	ADP
ejpam-6142	175	17	the	the	DET
ejpam-6142	175	18	system	system	NOUN
ejpam-6142	175	19	3	3	NUM
ejpam-6142	175	20	,	,	PUNCT
ejpam-6142	175	21	the	the	DET
ejpam-6142	175	22	newly	newly	ADV
ejpam-6142	175	23	infected	infect	VERB
ejpam-6142	175	24	cases	case	NOUN
ejpam-6142	175	25	appear	appear	VERB
ejpam-6142	175	26	in	in	ADP
ejpam-6142	175	27	the	the	DET
ejpam-6142	175	28	equations	equation	NOUN
ejpam-6142	175	29	def	def	VERB
ejpam-6142	175	30	dt	dt	NOUN
ejpam-6142	175	31	and	and	CCONJ
ejpam-6142	175	32	dem	dem	PROPN
ejpam-6142	175	33	dt	dt	X
ejpam-6142	175	34	which	which	PRON
ejpam-6142	175	35	are	be	AUX
ejpam-6142	175	36	f1	f1	NOUN
ejpam-6142	175	37	=	=	SYM
ejpam-6142	175	38	(	(	PUNCT
ejpam-6142	175	39	1	1	NUM
ejpam-6142	175	40	−	−	PROPN
ejpam-6142	175	41	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	175	42	and	and	CCONJ
ejpam-6142	175	43	f7	f7	PROPN
ejpam-6142	175	44	=	=	PUNCT
ejpam-6142	175	45	(	(	PUNCT
ejpam-6142	175	46	1	1	NUM
ejpam-6142	175	47	−	−	PROPN
ejpam-6142	175	48	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	175	49	respectively	respectively	ADV
ejpam-6142	175	50	and	and	CCONJ
ejpam-6142	175	51	the	the	DET
ejpam-6142	175	52	last	last	ADJ
ejpam-6142	175	53	twelve	twelve	NUM
ejpam-6142	175	54	equations	equation	NOUN
ejpam-6142	175	55	are	be	AUX
ejpam-6142	175	56	zero	zero	NUM
ejpam-6142	175	57	f2	f2	ADJ
ejpam-6142	175	58	=	=	SYM
ejpam-6142	175	59	f3	f3	NOUN
ejpam-6142	175	60	=	=	SYM
ejpam-6142	175	61	f4	f4	PROPN
ejpam-6142	175	62	=	=	SYM
ejpam-6142	175	63	f5	f5	NOUN
ejpam-6142	175	64	=	=	SYM
ejpam-6142	175	65	f6	f6	NOUN
ejpam-6142	175	66	=	=	SYM
ejpam-6142	175	67	f8	f8	PROPN
ejpam-6142	175	68	=	=	SYM
ejpam-6142	175	69	f9	f9	PROPN
ejpam-6142	175	70	=	=	PUNCT
ejpam-6142	175	71	f10	f10	PROPN
ejpam-6142	175	72	=	=	SYM
ejpam-6142	175	73	f11	f11	NOUN
ejpam-6142	175	74	=	=	SYM
ejpam-6142	175	75	f12	f12	NOUN
ejpam-6142	175	76	=	=	NOUN
ejpam-6142	175	77	0	0	NUM
ejpam-6142	175	78	.	.	PUNCT
ejpam-6142	176	1	the	the	DET
ejpam-6142	176	2	rest	rest	NOUN
ejpam-6142	176	3	of	of	ADP
ejpam-6142	176	4	terms	term	NOUN
ejpam-6142	176	5	in	in	ADP
ejpam-6142	176	6	each	each	DET
ejpam-6142	176	7	equation	equation	NOUN
ejpam-6142	176	8	are	be	AUX
ejpam-6142	176	9	v1	v1	NOUN
ejpam-6142	176	10	,	,	PUNCT
ejpam-6142	176	11	v2	v2	NOUN
ejpam-6142	176	12	,	,	PUNCT
ejpam-6142	176	13	.	.	PUNCT
ejpam-6142	176	14	.	.	PUNCT
ejpam-6142	177	1	.	.	PUNCT
ejpam-6142	178	1	,	,	PUNCT
ejpam-6142	178	2	v12	v12	VERB
ejpam-6142	178	3	.	.	PUNCT
ejpam-6142	179	1	hence	hence	ADV
ejpam-6142	179	2	f	f	PROPN
ejpam-6142	179	3	and	and	CCONJ
ejpam-6142	179	4	v	v	NOUN
ejpam-6142	179	5	are	be	AUX
ejpam-6142	179	6	as	as	SCONJ
ejpam-6142	179	7	follows	follow	VERB
ejpam-6142	179	8	f	f	PROPN
ejpam-6142	179	9	=	=	SYM
ejpam-6142	179	10			NOUN
ejpam-6142	179	11	f1	f1	NOUN
ejpam-6142	179	12	f2	f2	PROPN
ejpam-6142	179	13	f3	f3	VERB
ejpam-6142	179	14	f4	f4	NUM
ejpam-6142	179	15	f5	f5	PROPN
ejpam-6142	179	16	f6	f6	PROPN
ejpam-6142	179	17	f7	f7	PROPN
ejpam-6142	179	18	f8	f8	PROPN
ejpam-6142	179	19	f9	f9	PROPN
ejpam-6142	179	20	f10	f10	PROPN
ejpam-6142	179	21	f11	f11	PROPN
ejpam-6142	179	22	f12	f12	NOUN
ejpam-6142	179	23			NOUN
ejpam-6142	179	24	=	=	SYM
ejpam-6142	179	25			NOUN
ejpam-6142	179	26	(	(	PUNCT
ejpam-6142	179	27	1−	1−	NUM
ejpam-6142	179	28	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	179	29	0	0	NUM
ejpam-6142	179	30	0	0	NUM
ejpam-6142	179	31	0	0	NUM
ejpam-6142	179	32	0	0	NUM
ejpam-6142	179	33	0	0	NUM
ejpam-6142	180	1	(	(	PUNCT
ejpam-6142	180	2	1−	1−	NUM
ejpam-6142	180	3	κϵ)βmifsm	κϵ)βmifsm	PROPN
ejpam-6142	180	4	0	0	NUM
ejpam-6142	180	5	0	0	NUM
ejpam-6142	180	6	0	0	NUM
ejpam-6142	180	7	0	0	NUM
ejpam-6142	180	8	0	0	NUM
ejpam-6142	180	9			NUM
ejpam-6142	180	10	and	and	CCONJ
ejpam-6142	180	11	v	v	NOUN
ejpam-6142	180	12	=	=	SYM
ejpam-6142	180	13			NOUN
ejpam-6142	180	14	v1	v1	PROPN
ejpam-6142	180	15	v2	v2	PROPN
ejpam-6142	180	16	v3	v3	PROPN
ejpam-6142	180	17	v4	v4	PROPN
ejpam-6142	180	18	v5	v5	PROPN
ejpam-6142	180	19	v6	v6	NOUN
ejpam-6142	180	20	v7	v7	VERB
ejpam-6142	180	21	v8	v8	PROPN
ejpam-6142	180	22	v9	v9	PROPN
ejpam-6142	180	23	v10	v10	PROPN
ejpam-6142	180	24	v11	v11	NOUN
ejpam-6142	180	25	v12	v12	VERB
ejpam-6142	180	26			NOUN
ejpam-6142	180	27	=	=	SYM
ejpam-6142	180	28			NOUN
ejpam-6142	180	29	ef	ef	NOUN
ejpam-6142	180	30	−αfef	−αfef	VERB
ejpam-6142	180	31	+	+	NOUN
ejpam-6142	180	32	∆fif	∆fif	PROPN
ejpam-6142	180	33	−γfif	−γfif	PROPN
ejpam-6142	180	34	+	+	PROPN
ejpam-6142	180	35	ωfdf	ωfdf	NOUN
ejpam-6142	180	36	−ρfdf	−ρfdf	VERB
ejpam-6142	181	1	+	+	ADJ
ejpam-6142	181	2	ψftf	ψftf	ADJ
ejpam-6142	181	3	−θfif	−θfif	PROPN
ejpam-6142	181	4	+	+	SYM
ejpam-6142	181	5	φfuf	φfuf	NOUN
ejpam-6142	181	6	−λfuf	−λfuf	NOUN
ejpam-6142	181	7	−	−	PROPN
ejpam-6142	181	8	ωftf	ωftf	NOUN
ejpam-6142	181	9	+	+	CCONJ
ejpam-6142	181	10	ζaf	ζaf	PROPN
ejpam-6142	181	11	γmem	γmem	NOUN
ejpam-6142	181	12	−αmem	−αmem	PUNCT
ejpam-6142	182	1	+	+	NOUN
ejpam-6142	182	2	∆mim	∆mim	NOUN
ejpam-6142	182	3	−γmim	−γmim	PROPN
ejpam-6142	183	1	+	+	NOUN
ejpam-6142	183	2	ωmdm	ωmdm	ADJ
ejpam-6142	183	3	−ρmdm	−ρmdm	PUNCT
ejpam-6142	183	4	+	+	NOUN
ejpam-6142	183	5	ψmtm	ψmtm	ADJ
ejpam-6142	183	6	−θmim	−θmim	X
ejpam-6142	184	1	+	+	ADJ
ejpam-6142	184	2	φmum	φmum	NOUN
ejpam-6142	184	3	−λmum	−λmum	DET
ejpam-6142	184	4	−	−	NOUN
ejpam-6142	184	5	ωmtm	ωmtm	ADJ
ejpam-6142	184	6	+	+	CCONJ
ejpam-6142	184	7	ζam	ζam	VERB
ejpam-6142	184	8			NOUN
ejpam-6142	184	9	the	the	DET
ejpam-6142	184	10	jacobian	jacobian	NOUN
ejpam-6142	184	11	of	of	ADP
ejpam-6142	184	12	f	f	PROPN
ejpam-6142	184	13	and	and	CCONJ
ejpam-6142	184	14	v	v	NOUN
ejpam-6142	184	15	at	at	ADP
ejpam-6142	184	16	e0	e0	PROPN
ejpam-6142	184	17	are	be	AUX
ejpam-6142	184	18	symbolized	symbolize	VERB
ejpam-6142	184	19	by	by	ADP
ejpam-6142	184	20	f	f	PROPN
ejpam-6142	184	21	and	and	CCONJ
ejpam-6142	184	22	v	v	ADP
ejpam-6142	184	23	respectively	respectively	ADV
ejpam-6142	184	24	.	.	PUNCT
ejpam-6142	185	1	the	the	DET
ejpam-6142	185	2	nextgeneration	nextgeneration	NOUN
ejpam-6142	185	3	matrix	matrix	NOUN
ejpam-6142	185	4	could	could	AUX
ejpam-6142	185	5	be	be	AUX
ejpam-6142	185	6	computed	compute	VERB
ejpam-6142	185	7	from	from	ADP
ejpam-6142	185	8	fv	fv	PROPN
ejpam-6142	185	9	−1	−1	NOUN
ejpam-6142	185	10	which	which	PRON
ejpam-6142	185	11	is	be	AUX
ejpam-6142	185	12	a	a	DET
ejpam-6142	185	13	12	12	NUM
ejpam-6142	185	14	×	×	NOUN
ejpam-6142	185	15	12	12	NUM
ejpam-6142	185	16	matrix	matrix	NOUN
ejpam-6142	185	17	and	and	CCONJ
ejpam-6142	185	18	its	its	PRON
ejpam-6142	185	19	absolute	absolute	ADJ
ejpam-6142	185	20	eigenvalues	eigenvalue	NOUN
ejpam-6142	185	21	are	be	AUX
ejpam-6142	185	22	provided	provide	VERB
ejpam-6142	185	23	below	below	ADP
ejpam-6142	185	24	λ∗	λ∗	PROPN
ejpam-6142	185	25	1	1	NUM
ejpam-6142	185	26	=	=	SYM
ejpam-6142	185	27	0	0	NUM
ejpam-6142	185	28	,	,	PUNCT
ejpam-6142	185	29	λ∗	λ∗	NOUN
ejpam-6142	185	30	2	2	NUM
ejpam-6142	185	31	=	=	SYM
ejpam-6142	185	32	0	0	NUM
ejpam-6142	185	33	,	,	PUNCT
ejpam-6142	185	34	λ∗	λ∗	NOUN
ejpam-6142	185	35	3	3	NUM
ejpam-6142	185	36	=	=	SYM
ejpam-6142	185	37	0	0	NUM
ejpam-6142	185	38	,	,	PUNCT
ejpam-6142	185	39	λ∗	λ∗	NOUN
ejpam-6142	185	40	4	4	NUM
ejpam-6142	185	41	=	=	SYM
ejpam-6142	185	42	0	0	NUM
ejpam-6142	185	43	,	,	PUNCT
ejpam-6142	185	44	λ∗	λ∗	NOUN
ejpam-6142	185	45	5	5	NUM
ejpam-6142	185	46	=	=	SYM
ejpam-6142	185	47	0	0	NUM
ejpam-6142	185	48	,	,	PUNCT
ejpam-6142	185	49	λ∗	λ∗	NOUN
ejpam-6142	185	50	6	6	NUM
ejpam-6142	185	51	=	=	SYM
ejpam-6142	185	52	0	0	NUM
ejpam-6142	185	53	,	,	PUNCT
ejpam-6142	185	54	λ∗	λ∗	NOUN
ejpam-6142	185	55	7	7	NUM
ejpam-6142	185	56	=	=	SYM
ejpam-6142	185	57	0	0	NUM
ejpam-6142	185	58	,	,	PUNCT
ejpam-6142	185	59	λ∗	λ∗	NOUN
ejpam-6142	185	60	8	8	NUM
ejpam-6142	185	61	=	=	SYM
ejpam-6142	185	62	0	0	NUM
ejpam-6142	185	63	,	,	PUNCT
ejpam-6142	185	64	λ∗	λ∗	NOUN
ejpam-6142	185	65	9	9	NUM
ejpam-6142	185	66	=	=	SYM
ejpam-6142	185	67	0	0	NUM
ejpam-6142	185	68	,	,	PUNCT
ejpam-6142	185	69	λ∗	λ∗	NOUN
ejpam-6142	185	70	10	10	NUM
ejpam-6142	185	71	=	=	SYM
ejpam-6142	185	72	0	0	NUM
ejpam-6142	185	73	,	,	PUNCT
ejpam-6142	185	74	|λ∗	|λ∗	PROPN
ejpam-6142	185	75	11|	11|	NOUN
ejpam-6142	185	76	=	=	PUNCT
ejpam-6142	186	1	|λ∗	|λ∗	PROPN
ejpam-6142	186	2	12|	12|	NUM
ejpam-6142	186	3	=	=	SYM
ejpam-6142	186	4	λ(1−	λ(1−	PROPN
ejpam-6142	186	5	ϵκ	ϵκ	NOUN
ejpam-6142	186	6	)	)	PUNCT
ejpam-6142	187	1	√	√	ADP
ejpam-6142	187	2	∆f∆mγfγmαfαmβfβm	∆f∆mγfγmαfαmβfβm	PROPN
ejpam-6142	188	1	∆f∆mγfγmη	∆f∆mγfγmη	X
ejpam-6142	188	2	.	.	PUNCT
ejpam-6142	189	1	r0	r0	NOUN
ejpam-6142	189	2	is	be	AUX
ejpam-6142	189	3	the	the	DET
ejpam-6142	189	4	greatest	great	ADJ
ejpam-6142	189	5	absolute	absolute	ADJ
ejpam-6142	189	6	eigenvalue	eigenvalue	NOUN
ejpam-6142	189	7	of	of	ADP
ejpam-6142	189	8	the	the	DET
ejpam-6142	189	9	next	next	ADJ
ejpam-6142	189	10	-	-	PUNCT
ejpam-6142	189	11	generation	generation	NOUN
ejpam-6142	189	12	matrix	matrix	NOUN
ejpam-6142	189	13	which	which	PRON
ejpam-6142	189	14	is	be	AUX
ejpam-6142	189	15	|λ∗	|λ∗	PROPN
ejpam-6142	189	16	11|	11|	PROPN
ejpam-6142	189	17	or	or	CCONJ
ejpam-6142	189	18	|λ∗	|λ∗	PROPN
ejpam-6142	189	19	12|	12|	PROPN
ejpam-6142	189	20	.	.	PUNCT
ejpam-6142	190	1	therefore	therefore	ADV
ejpam-6142	190	2	,	,	PUNCT
ejpam-6142	190	3	r0	r0	NOUN
ejpam-6142	190	4	is	be	AUX
ejpam-6142	190	5	expressed	express	VERB
ejpam-6142	190	6	as	as	ADP
ejpam-6142	190	7	r0	r0	NOUN
ejpam-6142	190	8	=	=	SYM
ejpam-6142	190	9	λ(1−	λ(1−	PROPN
ejpam-6142	190	10	ϵκ	ϵκ	NOUN
ejpam-6142	190	11	)	)	PUNCT
ejpam-6142	190	12	η	η	PROPN
ejpam-6142	190	13	√	√	PROPN
ejpam-6142	190	14	αfαmβfβm	αfαmβfβm	NOUN
ejpam-6142	190	15	∆f∆mγfγm	∆f∆mγfγm	PROPN
ejpam-6142	190	16	.	.	PUNCT
ejpam-6142	191	1	or	or	CCONJ
ejpam-6142	191	2	s.	s.	PROPN
ejpam-6142	191	3	m.	m.	PROPN
ejpam-6142	191	4	fatah	fatah	PROPN
ejpam-6142	191	5	,	,	PUNCT
ejpam-6142	191	6	s.	s.	PROPN
ejpam-6142	191	7	h.	h.	PROPN
ejpam-6142	191	8	a.	a.	PROPN
ejpam-6142	191	9	khoshnaw	khoshnaw	PROPN
ejpam-6142	191	10	,	,	PUNCT
ejpam-6142	191	11	a.	a.	PROPN
ejpam-6142	191	12	n.	n.	PROPN
ejpam-6142	191	13	mustafa	mustafa	PROPN
ejpam-6142	191	14	/	/	SYM
ejpam-6142	191	15	eur	eur	PROPN
ejpam-6142	191	16	.	.	PUNCT
ejpam-6142	192	1	j.	j.	PROPN
ejpam-6142	192	2	pure	pure	PROPN
ejpam-6142	192	3	appl	appl	PROPN
ejpam-6142	192	4	.	.	PROPN
ejpam-6142	192	5	math	math	PROPN
ejpam-6142	192	6	,	,	PUNCT
ejpam-6142	192	7	18	18	NUM
ejpam-6142	192	8	(	(	PUNCT
ejpam-6142	192	9	2	2	NUM
ejpam-6142	192	10	)	)	PUNCT
ejpam-6142	192	11	(	(	PUNCT
ejpam-6142	192	12	2025	2025	NUM
ejpam-6142	192	13	)	)	PUNCT
ejpam-6142	192	14	,	,	PUNCT
ejpam-6142	192	15	6142	6142	NUM
ejpam-6142	192	16	10	10	NUM
ejpam-6142	192	17	of	of	ADP
ejpam-6142	192	18	33	33	NUM
ejpam-6142	192	19	r0	r0	NOUN
ejpam-6142	192	20	=	=	SYM
ejpam-6142	192	21	λ(1−	λ(1−	PROPN
ejpam-6142	192	22	ϵκ	ϵκ	NOUN
ejpam-6142	192	23	)	)	PUNCT
ejpam-6142	192	24	η	η	PROPN
ejpam-6142	192	25	√	√	PROPN
ejpam-6142	192	26	αfαmβfβm	αfαmβfβm	NOUN
ejpam-6142	192	27	(	(	PUNCT
ejpam-6142	192	28	µ+	µ+	X
ejpam-6142	192	29	η	η	PROPN
ejpam-6142	192	30	+	+	PROPN
ejpam-6142	192	31	γf	γf	PROPN
ejpam-6142	192	32	+	+	CCONJ
ejpam-6142	192	33	θf	θf	NOUN
ejpam-6142	192	34	)	)	PUNCT
ejpam-6142	192	35	(	(	PUNCT
ejpam-6142	192	36	µ+	µ+	X
ejpam-6142	192	37	η	η	PROPN
ejpam-6142	192	38	+	+	X
ejpam-6142	192	39	γm	γm	PROPN
ejpam-6142	192	40	+	+	X
ejpam-6142	192	41	θm	θm	NOUN
ejpam-6142	192	42	)	)	PUNCT
ejpam-6142	192	43	(	(	PUNCT
ejpam-6142	192	44	αf	αf	X
ejpam-6142	192	45	+	+	NUM
ejpam-6142	192	46	η	η	NOUN
ejpam-6142	192	47	)	)	PUNCT
ejpam-6142	192	48	(	(	PUNCT
ejpam-6142	192	49	αm	αm	NOUN
ejpam-6142	192	50	+	+	CCONJ
ejpam-6142	192	51	η	η	PROPN
ejpam-6142	192	52	)	)	PUNCT
ejpam-6142	192	53	the	the	DET
ejpam-6142	192	54	basic	basic	ADJ
ejpam-6142	192	55	reproduction	reproduction	NOUN
ejpam-6142	192	56	number	number	NOUN
ejpam-6142	192	57	,	,	PUNCT
ejpam-6142	192	58	r0	r0	NOUN
ejpam-6142	192	59	,	,	PUNCT
ejpam-6142	192	60	in	in	ADP
ejpam-6142	192	61	this	this	DET
ejpam-6142	192	62	hiv	hiv	PROPN
ejpam-6142	192	63	model	model	NOUN
ejpam-6142	192	64	is	be	AUX
ejpam-6142	192	65	strongly	strongly	ADV
ejpam-6142	192	66	influenced	influence	VERB
ejpam-6142	192	67	by	by	ADP
ejpam-6142	192	68	key	key	ADJ
ejpam-6142	192	69	epidemiological	epidemiological	ADJ
ejpam-6142	192	70	factors	factor	NOUN
ejpam-6142	192	71	.	.	PUNCT
ejpam-6142	193	1	it	it	PRON
ejpam-6142	193	2	increases	increase	VERB
ejpam-6142	193	3	with	with	ADP
ejpam-6142	193	4	higher	high	ADJ
ejpam-6142	193	5	transmission	transmission	NOUN
ejpam-6142	193	6	rates	rate	NOUN
ejpam-6142	193	7	between	between	ADP
ejpam-6142	193	8	partners	partner	NOUN
ejpam-6142	193	9	(	(	PUNCT
ejpam-6142	193	10	βf	βf	ADV
ejpam-6142	193	11	and	and	CCONJ
ejpam-6142	193	12	βm	βm	VERB
ejpam-6142	193	13	)	)	PUNCT
ejpam-6142	193	14	,	,	PUNCT
ejpam-6142	193	15	as	as	ADV
ejpam-6142	193	16	well	well	ADV
ejpam-6142	193	17	as	as	ADP
ejpam-6142	193	18	with	with	ADP
ejpam-6142	193	19	a	a	DET
ejpam-6142	193	20	greater	great	ADJ
ejpam-6142	193	21	rate	rate	NOUN
ejpam-6142	193	22	of	of	ADP
ejpam-6142	193	23	new	new	ADJ
ejpam-6142	193	24	individuals	individual	NOUN
ejpam-6142	193	25	entering	enter	VERB
ejpam-6142	193	26	the	the	DET
ejpam-6142	193	27	susceptible	susceptible	ADJ
ejpam-6142	193	28	population	population	NOUN
ejpam-6142	193	29	(	(	PUNCT
ejpam-6142	193	30	λ	λ	NOUN
ejpam-6142	193	31	)	)	PUNCT
ejpam-6142	193	32	.	.	PUNCT
ejpam-6142	194	1	on	on	ADP
ejpam-6142	194	2	the	the	DET
ejpam-6142	194	3	other	other	ADJ
ejpam-6142	194	4	hand	hand	NOUN
ejpam-6142	194	5	,	,	PUNCT
ejpam-6142	194	6	r0	r0	NOUN
ejpam-6142	194	7	decreases	decrease	NOUN
ejpam-6142	194	8	when	when	SCONJ
ejpam-6142	194	9	the	the	DET
ejpam-6142	194	10	natural	natural	ADJ
ejpam-6142	194	11	death	death	NOUN
ejpam-6142	194	12	rate	rate	NOUN
ejpam-6142	194	13	(	(	PUNCT
ejpam-6142	194	14	η	η	NOUN
ejpam-6142	194	15	)	)	PUNCT
ejpam-6142	194	16	,	,	PUNCT
ejpam-6142	194	17	diseaserelated	diseaserelate	VERB
ejpam-6142	194	18	death	death	NOUN
ejpam-6142	194	19	rate	rate	NOUN
ejpam-6142	194	20	(	(	PUNCT
ejpam-6142	194	21	µ	µ	NOUN
ejpam-6142	194	22	)	)	PUNCT
ejpam-6142	194	23	,	,	PUNCT
ejpam-6142	194	24	and	and	CCONJ
ejpam-6142	194	25	the	the	DET
ejpam-6142	194	26	rates	rate	NOUN
ejpam-6142	194	27	of	of	ADP
ejpam-6142	194	28	treatment	treatment	NOUN
ejpam-6142	194	29	and	and	CCONJ
ejpam-6142	194	30	behavior	behavior	NOUN
ejpam-6142	194	31	change	change	NOUN
ejpam-6142	194	32	due	due	ADP
ejpam-6142	194	33	to	to	ADP
ejpam-6142	194	34	interventions	intervention	NOUN
ejpam-6142	194	35	(	(	PUNCT
ejpam-6142	194	36	γf	γf	INTJ
ejpam-6142	194	37	,	,	PUNCT
ejpam-6142	194	38	γm	γm	ADJ
ejpam-6142	194	39	,	,	PUNCT
ejpam-6142	194	40	θf	θf	NOUN
ejpam-6142	194	41	and	and	CCONJ
ejpam-6142	194	42	θm	θm	PROPN
ejpam-6142	194	43	)	)	PUNCT
ejpam-6142	194	44	are	be	AUX
ejpam-6142	194	45	higher	high	ADJ
ejpam-6142	194	46	.	.	PUNCT
ejpam-6142	195	1	additionally	additionally	ADV
ejpam-6142	195	2	,	,	PUNCT
ejpam-6142	195	3	reducing	reduce	VERB
ejpam-6142	195	4	the	the	DET
ejpam-6142	195	5	effectiveness	effectiveness	NOUN
ejpam-6142	195	6	of	of	ADP
ejpam-6142	195	7	intervention	intervention	NOUN
ejpam-6142	195	8	parameters	parameter	NOUN
ejpam-6142	195	9	(	(	PUNCT
ejpam-6142	195	10	ϵκ	ϵκ	NOUN
ejpam-6142	195	11	)	)	PUNCT
ejpam-6142	195	12	leads	lead	VERB
ejpam-6142	195	13	to	to	ADP
ejpam-6142	195	14	a	a	DET
ejpam-6142	195	15	rise	rise	NOUN
ejpam-6142	195	16	in	in	ADP
ejpam-6142	195	17	r0	r0	NOUN
ejpam-6142	195	18	.	.	PUNCT
ejpam-6142	196	1	to	to	PART
ejpam-6142	196	2	bring	bring	VERB
ejpam-6142	196	3	r0	r0	NOUN
ejpam-6142	196	4	below	below	ADP
ejpam-6142	196	5	1	1	NUM
ejpam-6142	196	6	an	an	DET
ejpam-6142	196	7	important	important	ADJ
ejpam-6142	196	8	threshold	threshold	NOUN
ejpam-6142	196	9	for	for	ADP
ejpam-6142	196	10	controlling	control	VERB
ejpam-6142	196	11	the	the	DET
ejpam-6142	196	12	spread	spread	NOUN
ejpam-6142	196	13	of	of	ADP
ejpam-6142	196	14	hiv	hiv	PROPN
ejpam-6142	196	15	,	,	PUNCT
ejpam-6142	196	16	public	public	ADJ
ejpam-6142	196	17	health	health	NOUN
ejpam-6142	196	18	strategies	strategy	NOUN
ejpam-6142	196	19	should	should	AUX
ejpam-6142	196	20	focus	focus	VERB
ejpam-6142	196	21	on	on	ADP
ejpam-6142	196	22	three	three	NUM
ejpam-6142	196	23	main	main	ADJ
ejpam-6142	196	24	areas	area	NOUN
ejpam-6142	196	25	:	:	PUNCT
ejpam-6142	196	26	raising	raise	VERB
ejpam-6142	196	27	γf	γf	PROPN
ejpam-6142	196	28	and	and	CCONJ
ejpam-6142	196	29	γm	γm	ADJ
ejpam-6142	196	30	,	,	PUNCT
ejpam-6142	196	31	and	and	CCONJ
ejpam-6142	196	32	lowering	lower	VERB
ejpam-6142	196	33	βf	βf	INTJ
ejpam-6142	196	34	,	,	PUNCT
ejpam-6142	196	35	and	and	CCONJ
ejpam-6142	196	36	βm	βm	VERB
ejpam-6142	196	37	and	and	CCONJ
ejpam-6142	196	38	enhancing	enhance	VERB
ejpam-6142	196	39	prevention	prevention	NOUN
ejpam-6142	196	40	efforts	effort	NOUN
ejpam-6142	196	41	(	(	PUNCT
ejpam-6142	196	42	maximizing	maximize	VERB
ejpam-6142	196	43	the	the	DET
ejpam-6142	196	44	impact	impact	NOUN
ejpam-6142	196	45	of	of	ADP
ejpam-6142	196	46	ϵκ	ϵκ	NOUN
ejpam-6142	196	47	)	)	PUNCT
ejpam-6142	196	48	.	.	PUNCT
ejpam-6142	197	1	this	this	DET
ejpam-6142	197	2	approach	approach	NOUN
ejpam-6142	197	3	is	be	AUX
ejpam-6142	197	4	in	in	ADP
ejpam-6142	197	5	line	line	NOUN
ejpam-6142	197	6	with	with	ADP
ejpam-6142	197	7	established	establish	VERB
ejpam-6142	197	8	hiv	hiv	PROPN
ejpam-6142	197	9	control	control	NOUN
ejpam-6142	197	10	strategies	strategy	NOUN
ejpam-6142	197	11	,	,	PUNCT
ejpam-6142	197	12	which	which	PRON
ejpam-6142	197	13	emphasize	emphasize	VERB
ejpam-6142	197	14	that	that	SCONJ
ejpam-6142	197	15	combining	combine	VERB
ejpam-6142	197	16	early	early	ADJ
ejpam-6142	197	17	treatment	treatment	NOUN
ejpam-6142	197	18	with	with	ADP
ejpam-6142	197	19	strong	strong	ADJ
ejpam-6142	197	20	prevention	prevention	NOUN
ejpam-6142	197	21	measures	measure	NOUN
ejpam-6142	197	22	is	be	AUX
ejpam-6142	197	23	the	the	DET
ejpam-6142	197	24	most	most	ADV
ejpam-6142	197	25	effective	effective	ADJ
ejpam-6142	197	26	way	way	NOUN
ejpam-6142	197	27	to	to	PART
ejpam-6142	197	28	reduce	reduce	VERB
ejpam-6142	197	29	the	the	DET
ejpam-6142	197	30	spread	spread	NOUN
ejpam-6142	197	31	of	of	ADP
ejpam-6142	197	32	the	the	DET
ejpam-6142	197	33	virus	virus	NOUN
ejpam-6142	197	34	.	.	PUNCT
ejpam-6142	198	1	4.3	4.3	NUM
ejpam-6142	198	2	.	.	PUNCT
ejpam-6142	198	3	endemic	endemic	ADJ
ejpam-6142	198	4	equilibrium	equilibrium	NOUN
ejpam-6142	198	5	point	point	NOUN
ejpam-6142	198	6	(	(	PUNCT
ejpam-6142	198	7	e1	e1	PROPN
ejpam-6142	198	8	)	)	PUNCT
ejpam-6142	198	9	the	the	DET
ejpam-6142	198	10	endemic	endemic	ADJ
ejpam-6142	198	11	equilibrium	equilibrium	NOUN
ejpam-6142	198	12	refers	refer	VERB
ejpam-6142	198	13	to	to	ADP
ejpam-6142	198	14	a	a	DET
ejpam-6142	198	15	state	state	NOUN
ejpam-6142	198	16	of	of	ADP
ejpam-6142	198	17	stability	stability	NOUN
ejpam-6142	198	18	when	when	SCONJ
ejpam-6142	198	19	the	the	DET
ejpam-6142	198	20	illness	illness	NOUN
ejpam-6142	198	21	continues	continue	VERB
ejpam-6142	198	22	to	to	PART
ejpam-6142	198	23	exit	exit	VERB
ejpam-6142	198	24	among	among	ADP
ejpam-6142	198	25	the	the	DET
ejpam-6142	198	26	population	population	NOUN
ejpam-6142	198	27	.	.	PUNCT
ejpam-6142	199	1	to	to	PART
ejpam-6142	199	2	determine	determine	VERB
ejpam-6142	199	3	this	this	DET
ejpam-6142	199	4	equilibrium	equilibrium	NOUN
ejpam-6142	199	5	,	,	PUNCT
ejpam-6142	199	6	we	we	PRON
ejpam-6142	199	7	solve	solve	VERB
ejpam-6142	199	8	system	system	NOUN
ejpam-6142	199	9	2	2	NUM
ejpam-6142	199	10	for	for	ADP
ejpam-6142	199	11	variables	variable	NOUN
ejpam-6142	199	12	in	in	ADP
ejpam-6142	199	13	terms	term	NOUN
ejpam-6142	199	14	of	of	ADP
ejpam-6142	199	15	the	the	DET
ejpam-6142	199	16	parameters	parameter	NOUN
ejpam-6142	199	17	by	by	ADP
ejpam-6142	199	18	equating	equate	VERB
ejpam-6142	199	19	the	the	DET
ejpam-6142	199	20	expressions	expression	NOUN
ejpam-6142	199	21	on	on	ADP
ejpam-6142	199	22	the	the	DET
ejpam-6142	199	23	right	right	ADJ
ejpam-6142	199	24	side	side	NOUN
ejpam-6142	199	25	of	of	ADP
ejpam-6142	199	26	the	the	DET
ejpam-6142	199	27	system	system	NOUN
ejpam-6142	199	28	.	.	PUNCT
ejpam-6142	200	1	therefore	therefore	ADV
ejpam-6142	200	2	,	,	PUNCT
ejpam-6142	200	3	the	the	DET
ejpam-6142	200	4	obtained	obtain	VERB
ejpam-6142	200	5	endemic	endemic	ADJ
ejpam-6142	200	6	equilibrium	equilibrium	NOUN
ejpam-6142	200	7	point	point	NOUN
ejpam-6142	200	8	is	be	AUX
ejpam-6142	200	9	e1	e1	NOUN
ejpam-6142	200	10	=	=	SYM
ejpam-6142	200	11	(	(	PUNCT
ejpam-6142	200	12	s∗	s∗	PROPN
ejpam-6142	200	13	f	f	PROPN
ejpam-6142	200	14	,	,	PUNCT
ejpam-6142	200	15	e	e	X
ejpam-6142	200	16	∗	∗	NOUN
ejpam-6142	200	17	f	f	PROPN
ejpam-6142	200	18	,	,	PUNCT
ejpam-6142	201	1	i	i	PRON
ejpam-6142	201	2	∗	∗	VERB
ejpam-6142	201	3	f	f	PROPN
ejpam-6142	201	4	,	,	PUNCT
ejpam-6142	202	1	d	d	AUX
ejpam-6142	202	2	∗	∗	X
ejpam-6142	202	3	f	f	PROPN
ejpam-6142	202	4	,	,	PUNCT
ejpam-6142	202	5	t	t	PROPN
ejpam-6142	202	6	∗	∗	NOUN
ejpam-6142	202	7	f	f	PROPN
ejpam-6142	202	8	,	,	PUNCT
ejpam-6142	202	9	u	u	NOUN
ejpam-6142	202	10	∗	∗	NOUN
ejpam-6142	202	11	f	f	PROPN
ejpam-6142	202	12	,	,	PUNCT
ejpam-6142	202	13	a	a	DET
ejpam-6142	202	14	∗	∗	X
ejpam-6142	202	15	f	f	NOUN
ejpam-6142	202	16	,	,	PUNCT
ejpam-6142	202	17	s	s	PART
ejpam-6142	202	18	∗	∗	NOUN
ejpam-6142	202	19	m	m	PROPN
ejpam-6142	202	20	,	,	PUNCT
ejpam-6142	202	21	e∗	e∗	PROPN
ejpam-6142	202	22	m	m	PROPN
ejpam-6142	202	23	,	,	PUNCT
ejpam-6142	202	24	i∗m	i∗m	X
ejpam-6142	202	25	,	,	PUNCT
ejpam-6142	202	26	d∗	d∗	PROPN
ejpam-6142	202	27	m	m	PROPN
ejpam-6142	202	28	,	,	PUNCT
ejpam-6142	202	29	t	t	PROPN
ejpam-6142	202	30	∗	∗	NOUN
ejpam-6142	202	31	m	m	PROPN
ejpam-6142	202	32	,	,	PUNCT
ejpam-6142	202	33	u∗	u∗	PROPN
ejpam-6142	202	34	m	m	PROPN
ejpam-6142	202	35	,	,	PUNCT
ejpam-6142	202	36	a∗	a∗	PROPN
ejpam-6142	202	37	m	m	PROPN
ejpam-6142	202	38	)	)	PUNCT
ejpam-6142	203	1	where	where	SCONJ
ejpam-6142	203	2	,	,	PUNCT
ejpam-6142	203	3	s∗	s∗	PROPN
ejpam-6142	203	4	f	f	PROPN
ejpam-6142	203	5	=	=	PUNCT
ejpam-6142	203	6	∆mγm	∆mγm	PUNCT
ejpam-6142	203	7	(	(	PUNCT
ejpam-6142	203	8	λαfβm(ϵκ−	λαfβm(ϵκ−	PROPN
ejpam-6142	203	9	1)−∆fγfη	1)−∆fγfη	NUM
ejpam-6142	203	10	)	)	PUNCT
ejpam-6142	203	11	αfβm(ϵκ−	αfβm(ϵκ−	NUM
ejpam-6142	203	12	1	1	NUM
ejpam-6142	203	13	)	)	PUNCT
ejpam-6142	203	14	(	(	PUNCT
ejpam-6142	203	15	∆mγmη	∆mγmη	X
ejpam-6142	203	16	+	+	CCONJ
ejpam-6142	203	17	λαmβf	λαmβf	ADJ
ejpam-6142	203	18	(	(	PUNCT
ejpam-6142	203	19	1−	1−	NUM
ejpam-6142	203	20	ϵκ	ϵκ	NOUN
ejpam-6142	203	21	)	)	PUNCT
ejpam-6142	203	22	)	)	PUNCT
ejpam-6142	203	23	,	,	PUNCT
ejpam-6142	203	24	i∗f	i∗f	X
ejpam-6142	203	25	=	=	SYM
ejpam-6142	203	26	λ2αfαmβfβm(ϵκ−	λ2αfαmβfβm(ϵκ−	PROPN
ejpam-6142	203	27	1)2	1)2	NUM
ejpam-6142	203	28	−∆f∆mγfγmη2	−∆f∆mγfγmη2	NUM
ejpam-6142	203	29	∆fγfβm(ϵκ−	∆fγfβm(ϵκ−	PROPN
ejpam-6142	203	30	1	1	NUM
ejpam-6142	203	31	)	)	PUNCT
ejpam-6142	203	32	(	(	PUNCT
ejpam-6142	203	33	λαmβf	λαmβf	VERB
ejpam-6142	203	34	(	(	PUNCT
ejpam-6142	203	35	ϵκ−	ϵκ−	NUM
ejpam-6142	203	36	1)−∆mγmη	1)−∆mγmη	NOUN
ejpam-6142	203	37	)	)	PUNCT
ejpam-6142	203	38	,	,	PUNCT
ejpam-6142	203	39	e∗	e∗	PROPN
ejpam-6142	203	40	f	f	PROPN
ejpam-6142	203	41	=	=	SYM
ejpam-6142	203	42	∆f	∆f	PROPN
ejpam-6142	203	43	αf	αf	NOUN
ejpam-6142	203	44	i∗f	i∗f	NUM
ejpam-6142	203	45	,	,	PUNCT
ejpam-6142	203	46	d∗	d∗	PROPN
ejpam-6142	203	47	f	f	PROPN
ejpam-6142	203	48	=	=	PRON
ejpam-6142	203	49	γf	γf	ADJ
ejpam-6142	203	50	ωf	ωf	PROPN
ejpam-6142	203	51	i∗f	i∗f	PROPN
ejpam-6142	203	52	,	,	PUNCT
ejpam-6142	203	53	t	t	PROPN
ejpam-6142	203	54	∗	∗	NOUN
ejpam-6142	203	55	f	f	X
ejpam-6142	203	56	=	=	PUNCT
ejpam-6142	203	57	γfρf	γfρf	PROPN
ejpam-6142	203	58	ωfψf	ωfψf	NOUN
ejpam-6142	203	59	i∗f	i∗f	PUNCT
ejpam-6142	203	60	,	,	PUNCT
ejpam-6142	203	61	u∗	u∗	INTJ
ejpam-6142	203	62	f	f	PROPN
ejpam-6142	204	1	=	=	PRON
ejpam-6142	204	2	θf	θf	NOUN
ejpam-6142	204	3	φf	φf	ADP
ejpam-6142	204	4	i∗f	i∗f	NUM
ejpam-6142	204	5	,	,	PUNCT
ejpam-6142	204	6	a∗	a∗	PROPN
ejpam-6142	204	7	f	f	NOUN
ejpam-6142	204	8	=	=	PROPN
ejpam-6142	204	9	ωfψfλfθf	ωfψfλfθf	PROPN
ejpam-6142	205	1	+	+	NOUN
ejpam-6142	205	2	φfγfωfρf	φfγfωfρf	ADJ
ejpam-6142	205	3	ωfφfψfζ	ωfφfψfζ	NOUN
ejpam-6142	205	4	,	,	PUNCT
ejpam-6142	205	5	s∗	s∗	PROPN
ejpam-6142	205	6	m	m	PROPN
ejpam-6142	205	7	=	=	SYM
ejpam-6142	205	8	∆fγf	∆fγf	NOUN
ejpam-6142	205	9	(	(	PUNCT
ejpam-6142	205	10	λαmβf	λαmβf	VERB
ejpam-6142	205	11	(	(	PUNCT
ejpam-6142	205	12	ϵκ−	ϵκ−	NUM
ejpam-6142	205	13	1)−∆mγmη	1)−∆mγmη	NOUN
ejpam-6142	205	14	)	)	PUNCT
ejpam-6142	205	15	αmβf	αmβf	PROPN
ejpam-6142	205	16	(	(	PUNCT
ejpam-6142	205	17	ϵκ−	ϵκ−	X
ejpam-6142	205	18	1	1	NUM
ejpam-6142	205	19	)	)	PUNCT
ejpam-6142	205	20	(	(	PUNCT
ejpam-6142	205	21	∆fγfη	∆fγfη	NUM
ejpam-6142	205	22	+	+	NUM
ejpam-6142	205	23	λαfβm(1−	λαfβm(1−	PROPN
ejpam-6142	205	24	ϵκ	ϵκ	NOUN
ejpam-6142	205	25	)	)	PUNCT
ejpam-6142	205	26	)	)	PUNCT
ejpam-6142	205	27	,	,	PUNCT
ejpam-6142	205	28	i∗m	i∗m	X
ejpam-6142	205	29	=	=	SYM
ejpam-6142	205	30	−∆f∆mγfγmη2	−∆f∆mγfγmη2	PROPN
ejpam-6142	205	31	+	+	CCONJ
ejpam-6142	205	32	λ2αfαmβfβm(ϵκ−	λ2αfαmβfβm(ϵκ−	PROPN
ejpam-6142	205	33	1)2	1)2	NUM
ejpam-6142	205	34	∆mγmβf	∆mγmβf	VERB
ejpam-6142	205	35	(	(	PUNCT
ejpam-6142	205	36	ϵκ−	ϵκ−	X
ejpam-6142	205	37	1	1	NUM
ejpam-6142	205	38	)	)	PUNCT
ejpam-6142	205	39	(	(	PUNCT
ejpam-6142	205	40	λαfβm(ϵκ−	λαfβm(ϵκ−	X
ejpam-6142	205	41	1)−∆fγfη	1)−∆fγfη	NUM
ejpam-6142	205	42	)	)	PUNCT
ejpam-6142	205	43	′	′	NUM
ejpam-6142	205	44	,	,	PUNCT
ejpam-6142	205	45	e∗	e∗	PROPN
ejpam-6142	205	46	m	m	PROPN
ejpam-6142	205	47	=	=	SYM
ejpam-6142	205	48	∆m	∆m	PROPN
ejpam-6142	205	49	αm	αm	NUM
ejpam-6142	205	50	i∗m	i∗m	NOUN
ejpam-6142	205	51	,	,	PUNCT
ejpam-6142	205	52	d∗	d∗	PROPN
ejpam-6142	205	53	m	m	NOUN
ejpam-6142	205	54	=	=	NOUN
ejpam-6142	205	55	γm	γm	ADJ
ejpam-6142	205	56	ωm	ωm	X
ejpam-6142	205	57	i∗m	i∗m	NOUN
ejpam-6142	205	58	,	,	PUNCT
ejpam-6142	205	59	t	t	PROPN
ejpam-6142	205	60	∗	∗	NOUN
ejpam-6142	205	61	m	m	NOUN
ejpam-6142	205	62	=	=	ADJ
ejpam-6142	205	63	γmρm	γmρm	NOUN
ejpam-6142	205	64	ωmψm	ωmψm	PROPN
ejpam-6142	205	65	i∗m	i∗m	PROPN
ejpam-6142	205	66	,	,	PUNCT
ejpam-6142	205	67	u∗	u∗	NOUN
ejpam-6142	205	68	m	m	NOUN
ejpam-6142	205	69	=	=	PUNCT
ejpam-6142	205	70	θm	θm	PROPN
ejpam-6142	205	71	φm	φm	X
ejpam-6142	205	72	i∗m	i∗m	NOUN
ejpam-6142	205	73	,	,	PUNCT
ejpam-6142	205	74	a∗	a∗	PROPN
ejpam-6142	205	75	m	m	NOUN
ejpam-6142	205	76	=	=	NOUN
ejpam-6142	205	77	ωmψmλmθm	ωmψmλmθm	ADJ
ejpam-6142	205	78	+	+	ADJ
ejpam-6142	205	79	φmγmωmρm	φmγmωmρm	NOUN
ejpam-6142	205	80	ωmφmψmζ	ωmφmψmζ	NOUN
ejpam-6142	205	81	i∗m	i∗m	PUNCT
ejpam-6142	205	82	.	.	PUNCT
ejpam-6142	205	83	s.	s.	PROPN
ejpam-6142	205	84	m.	m.	PROPN
ejpam-6142	205	85	fatah	fatah	PROPN
ejpam-6142	205	86	,	,	PUNCT
ejpam-6142	205	87	s.	s.	PROPN
ejpam-6142	205	88	h.	h.	PROPN
ejpam-6142	205	89	a.	a.	PROPN
ejpam-6142	205	90	khoshnaw	khoshnaw	PROPN
ejpam-6142	205	91	,	,	PUNCT
ejpam-6142	205	92	a.	a.	PROPN
ejpam-6142	205	93	n.	n.	PROPN
ejpam-6142	205	94	mustafa	mustafa	PROPN
ejpam-6142	205	95	/	/	SYM
ejpam-6142	205	96	eur	eur	PROPN
ejpam-6142	205	97	.	.	PUNCT
ejpam-6142	206	1	j.	j.	PROPN
ejpam-6142	206	2	pure	pure	PROPN
ejpam-6142	206	3	appl	appl	PROPN
ejpam-6142	206	4	.	.	PROPN
ejpam-6142	206	5	math	math	PROPN
ejpam-6142	206	6	,	,	PUNCT
ejpam-6142	206	7	18	18	NUM
ejpam-6142	206	8	(	(	PUNCT
ejpam-6142	206	9	2	2	NUM
ejpam-6142	206	10	)	)	PUNCT
ejpam-6142	206	11	(	(	PUNCT
ejpam-6142	206	12	2025	2025	NUM
ejpam-6142	206	13	)	)	PUNCT
ejpam-6142	206	14	,	,	PUNCT
ejpam-6142	206	15	6142	6142	NUM
ejpam-6142	206	16	11	11	NUM
ejpam-6142	206	17	of	of	ADP
ejpam-6142	206	18	33	33	NUM
ejpam-6142	206	19	since	since	SCONJ
ejpam-6142	206	20	ϵ	ϵ	NOUN
ejpam-6142	206	21	,	,	PUNCT
ejpam-6142	206	22	κ	κ	PROPN
ejpam-6142	206	23	∈	∈	PROPN
ejpam-6142	206	24	(	(	PUNCT
ejpam-6142	206	25	0	0	NUM
ejpam-6142	206	26	,	,	PUNCT
ejpam-6142	206	27	1	1	NUM
ejpam-6142	206	28	)	)	PUNCT
ejpam-6142	206	29	,	,	PUNCT
ejpam-6142	206	30	hence	hence	ADV
ejpam-6142	206	31	(	(	PUNCT
ejpam-6142	206	32	ϵκ	ϵκ	NOUN
ejpam-6142	206	33	−	−	NOUN
ejpam-6142	206	34	1	1	NUM
ejpam-6142	206	35	)	)	PUNCT
ejpam-6142	206	36	is	be	AUX
ejpam-6142	206	37	always	always	ADV
ejpam-6142	206	38	negative	negative	ADJ
ejpam-6142	206	39	and	and	CCONJ
ejpam-6142	206	40	clearly	clearly	ADV
ejpam-6142	206	41	s∗	s∗	PROPN
ejpam-6142	206	42	f	f	PROPN
ejpam-6142	206	43	,	,	PUNCT
ejpam-6142	206	44	s	s	PART
ejpam-6142	206	45	∗	∗	NOUN
ejpam-6142	206	46	m	m	VERB
ejpam-6142	206	47	>	>	X
ejpam-6142	206	48	0	0	X
ejpam-6142	206	49	.	.	PUNCT
ejpam-6142	207	1	furthermore	furthermore	ADV
ejpam-6142	207	2	,	,	PUNCT
ejpam-6142	207	3	i∗f	i∗f	NUM
ejpam-6142	207	4	,	,	PUNCT
ejpam-6142	207	5	i	i	PRON
ejpam-6142	207	6	∗	∗	VERB
ejpam-6142	207	7	m	m	VERB
ejpam-6142	207	8	>	>	X
ejpam-6142	207	9	0	0	PUNCT
ejpam-6142	208	1	if	if	SCONJ
ejpam-6142	208	2	and	and	CCONJ
ejpam-6142	208	3	only	only	ADV
ejpam-6142	208	4	if	if	SCONJ
ejpam-6142	208	5	r0	r0	NOUN
ejpam-6142	208	6	>	>	X
ejpam-6142	208	7	1	1	X
ejpam-6142	208	8	.	.	PUNCT
ejpam-6142	209	1	therefore	therefore	ADV
ejpam-6142	209	2	,	,	PUNCT
ejpam-6142	209	3	all	all	DET
ejpam-6142	209	4	components	component	NOUN
ejpam-6142	209	5	of	of	ADP
ejpam-6142	209	6	e1	e1	NOUN
ejpam-6142	209	7	are	be	AUX
ejpam-6142	209	8	positive	positive	ADJ
ejpam-6142	209	9	if	if	SCONJ
ejpam-6142	209	10	and	and	CCONJ
ejpam-6142	209	11	only	only	ADV
ejpam-6142	209	12	if	if	SCONJ
ejpam-6142	209	13	r0	r0	NOUN
ejpam-6142	209	14	>	>	X
ejpam-6142	209	15	1	1	NUM
ejpam-6142	209	16	.	.	X
ejpam-6142	209	17	5	5	NUM
ejpam-6142	209	18	.	.	X
ejpam-6142	209	19	stability	stability	NOUN
ejpam-6142	209	20	analysis	analysis	NOUN
ejpam-6142	209	21	of	of	ADP
ejpam-6142	209	22	the	the	DET
ejpam-6142	209	23	model	model	NOUN
ejpam-6142	209	24	at	at	ADP
ejpam-6142	209	25	equilibrium	equilibrium	NOUN
ejpam-6142	209	26	points	point	NOUN
ejpam-6142	209	27	when	when	SCONJ
ejpam-6142	209	28	there	there	PRON
ejpam-6142	209	29	is	be	VERB
ejpam-6142	209	30	no	no	DET
ejpam-6142	209	31	disease	disease	NOUN
ejpam-6142	209	32	,	,	PUNCT
ejpam-6142	209	33	the	the	DET
ejpam-6142	209	34	model	model	NOUN
ejpam-6142	209	35	possesses	possess	VERB
ejpam-6142	209	36	a	a	DET
ejpam-6142	209	37	unique	unique	ADJ
ejpam-6142	209	38	disease	disease	NOUN
ejpam-6142	209	39	-	-	PUNCT
ejpam-6142	209	40	free	free	ADJ
ejpam-6142	209	41	steady	steady	ADJ
ejpam-6142	209	42	-	-	PUNCT
ejpam-6142	209	43	state	state	NOUN
ejpam-6142	209	44	denoted	denote	VERB
ejpam-6142	209	45	as	as	ADP
ejpam-6142	209	46	e0	e0	PROPN
ejpam-6142	209	47	.	.	PUNCT
ejpam-6142	210	1	conversely	conversely	ADV
ejpam-6142	210	2	,	,	PUNCT
ejpam-6142	210	3	if	if	SCONJ
ejpam-6142	210	4	there	there	PRON
ejpam-6142	210	5	is	be	VERB
ejpam-6142	210	6	the	the	DET
ejpam-6142	210	7	disease	disease	NOUN
ejpam-6142	210	8	,	,	PUNCT
ejpam-6142	210	9	the	the	DET
ejpam-6142	210	10	model	model	NOUN
ejpam-6142	210	11	features	feature	VERB
ejpam-6142	210	12	an	an	DET
ejpam-6142	210	13	endemic	endemic	ADJ
ejpam-6142	210	14	equilibrium	equilibrium	NOUN
ejpam-6142	210	15	which	which	PRON
ejpam-6142	210	16	is	be	AUX
ejpam-6142	210	17	unique	unique	ADJ
ejpam-6142	210	18	and	and	CCONJ
ejpam-6142	210	19	denoted	denote	VERB
ejpam-6142	210	20	by	by	ADP
ejpam-6142	210	21	e1	e1	NOUN
ejpam-6142	210	22	.	.	PUNCT
ejpam-6142	211	1	in	in	ADP
ejpam-6142	211	2	the	the	DET
ejpam-6142	211	3	following	follow	VERB
ejpam-6142	211	4	theorems	theorem	NOUN
ejpam-6142	211	5	,	,	PUNCT
ejpam-6142	211	6	we	we	PRON
ejpam-6142	211	7	study	study	VERB
ejpam-6142	211	8	local	local	ADJ
ejpam-6142	211	9	stability	stability	NOUN
ejpam-6142	211	10	at	at	ADP
ejpam-6142	211	11	both	both	DET
ejpam-6142	211	12	disease	disease	NOUN
ejpam-6142	211	13	-	-	PUNCT
ejpam-6142	211	14	free	free	ADJ
ejpam-6142	211	15	and	and	CCONJ
ejpam-6142	211	16	endemic	endemic	ADJ
ejpam-6142	211	17	equilibrium	equilibrium	NOUN
ejpam-6142	211	18	points	point	NOUN
ejpam-6142	211	19	.	.	PUNCT
ejpam-6142	212	1	theorem	theorem	NOUN
ejpam-6142	212	2	3	3	NUM
ejpam-6142	212	3	.	.	PUNCT
ejpam-6142	213	1	the	the	DET
ejpam-6142	213	2	disease	disease	NOUN
ejpam-6142	213	3	-	-	PUNCT
ejpam-6142	213	4	free	free	ADJ
ejpam-6142	213	5	equilibrium	equilibrium	NOUN
ejpam-6142	213	6	point	point	NOUN
ejpam-6142	213	7	is	be	AUX
ejpam-6142	213	8	locally	locally	ADV
ejpam-6142	213	9	asymptotically	asymptotically	ADV
ejpam-6142	213	10	stable	stable	ADJ
ejpam-6142	213	11	if	if	SCONJ
ejpam-6142	213	12	and	and	CCONJ
ejpam-6142	213	13	only	only	ADV
ejpam-6142	213	14	if	if	SCONJ
ejpam-6142	213	15	r0	r0	NOUN
ejpam-6142	213	16	<	<	X
ejpam-6142	213	17	0	0	X
ejpam-6142	213	18	.	.	PUNCT
ejpam-6142	213	19	proof	proof	NOUN
ejpam-6142	213	20	.	.	PUNCT
ejpam-6142	214	1	the	the	DET
ejpam-6142	214	2	jacobian	jacobian	ADJ
ejpam-6142	214	3	matrix	matrix	NOUN
ejpam-6142	214	4	of	of	ADP
ejpam-6142	214	5	the	the	DET
ejpam-6142	214	6	system	system	NOUN
ejpam-6142	214	7	at	at	ADP
ejpam-6142	214	8	the	the	DET
ejpam-6142	214	9	disease	disease	NOUN
ejpam-6142	214	10	-	-	PUNCT
ejpam-6142	214	11	free	free	ADJ
ejpam-6142	214	12	equilibrium	equilibrium	NOUN
ejpam-6142	214	13	point	point	NOUN
ejpam-6142	214	14	e0	e0	PROPN
ejpam-6142	214	15	is	be	AUX
ejpam-6142	214	16	a	a	DET
ejpam-6142	214	17	14×	14×	NUM
ejpam-6142	214	18	14	14	NUM
ejpam-6142	214	19	which	which	PRON
ejpam-6142	214	20	is	be	AUX
ejpam-6142	214	21	j(e0	j(e0	ADJ
ejpam-6142	214	22	)	)	PUNCT
ejpam-6142	215	1	=	=	SYM
ejpam-6142	215	2			NOUN
ejpam-6142	215	3	−η	−η	NOUN
ejpam-6142	215	4	0	0	NUM
ejpam-6142	215	5	0	0	NUM
ejpam-6142	215	6	0	0	NUM
ejpam-6142	215	7	0	0	NUM
ejpam-6142	215	8	0	0	NUM
ejpam-6142	215	9	0	0	NUM
ejpam-6142	215	10	0	0	NUM
ejpam-6142	215	11	0	0	NUM
ejpam-6142	215	12	(	(	PUNCT
ejpam-6142	215	13	ϵκ−1)βfλ	ϵκ−1)βfλ	X
ejpam-6142	215	14	η	η	PROPN
ejpam-6142	215	15	0	0	PROPN
ejpam-6142	215	16	0	0	NUM
ejpam-6142	215	17	0	0	NUM
ejpam-6142	215	18	0	0	NUM
ejpam-6142	215	19	0	0	NUM
ejpam-6142	215	20	−γf	−γf	NUM
ejpam-6142	215	21	0	0	NUM
ejpam-6142	215	22	0	0	NUM
ejpam-6142	215	23	0	0	NUM
ejpam-6142	215	24	0	0	NUM
ejpam-6142	215	25	0	0	NUM
ejpam-6142	215	26	0	0	NUM
ejpam-6142	215	27	0	0	NUM
ejpam-6142	215	28	(	(	PUNCT
ejpam-6142	215	29	−ϵκ+1)βfλ	−ϵκ+1)βfλ	X
ejpam-6142	215	30	η	η	PROPN
ejpam-6142	215	31	0	0	NUM
ejpam-6142	215	32	0	0	NUM
ejpam-6142	215	33	0	0	NUM
ejpam-6142	215	34	0	0	NUM
ejpam-6142	215	35	0	0	NUM
ejpam-6142	215	36	αf	αf	ADP
ejpam-6142	215	37	−∆f	−∆f	NUM
ejpam-6142	215	38	0	0	NUM
ejpam-6142	215	39	0	0	NUM
ejpam-6142	215	40	0	0	NUM
ejpam-6142	215	41	0	0	NUM
ejpam-6142	215	42	0	0	NUM
ejpam-6142	215	43	0	0	NUM
ejpam-6142	215	44	0	0	NUM
ejpam-6142	215	45	0	0	NUM
ejpam-6142	215	46	0	0	NUM
ejpam-6142	215	47	0	0	NUM
ejpam-6142	215	48	0	0	NUM
ejpam-6142	215	49	0	0	NUM
ejpam-6142	215	50	0	0	NUM
ejpam-6142	216	1	γf	γf	PROPN
ejpam-6142	216	2	−ωf	−ωf	ADJ
ejpam-6142	216	3	0	0	NUM
ejpam-6142	216	4	0	0	NUM
ejpam-6142	216	5	0	0	NUM
ejpam-6142	216	6	0	0	NUM
ejpam-6142	216	7	0	0	NUM
ejpam-6142	216	8	0	0	NUM
ejpam-6142	216	9	0	0	NUM
ejpam-6142	216	10	0	0	NUM
ejpam-6142	216	11	0	0	NUM
ejpam-6142	216	12	0	0	NUM
ejpam-6142	216	13	0	0	NUM
ejpam-6142	216	14	0	0	NUM
ejpam-6142	216	15	0	0	NUM
ejpam-6142	217	1	ρf	ρf	DET
ejpam-6142	217	2	−ψf	−ψf	NOUN
ejpam-6142	217	3	0	0	NUM
ejpam-6142	217	4	0	0	NUM
ejpam-6142	217	5	0	0	NUM
ejpam-6142	217	6	0	0	NUM
ejpam-6142	217	7	0	0	NUM
ejpam-6142	217	8	0	0	NUM
ejpam-6142	217	9	0	0	NUM
ejpam-6142	217	10	0	0	NUM
ejpam-6142	217	11	0	0	NUM
ejpam-6142	217	12	0	0	NUM
ejpam-6142	217	13	0	0	NUM
ejpam-6142	217	14	θf	θf	NOUN
ejpam-6142	217	15	0	0	NUM
ejpam-6142	217	16	0	0	NUM
ejpam-6142	217	17	−φf	−φf	NOUN
ejpam-6142	217	18	0	0	NUM
ejpam-6142	217	19	0	0	NUM
ejpam-6142	217	20	0	0	NUM
ejpam-6142	217	21	0	0	NUM
ejpam-6142	217	22	0	0	NUM
ejpam-6142	217	23	0	0	NUM
ejpam-6142	217	24	0	0	NUM
ejpam-6142	217	25	0	0	NUM
ejpam-6142	217	26	0	0	NUM
ejpam-6142	217	27	0	0	NUM
ejpam-6142	217	28	0	0	NUM
ejpam-6142	217	29	0	0	NUM
ejpam-6142	217	30	ωf	ωf	PROPN
ejpam-6142	217	31	λf	λf	PROPN
ejpam-6142	217	32	−ζ	−ζ	NOUN
ejpam-6142	217	33	0	0	NUM
ejpam-6142	217	34	0	0	NUM
ejpam-6142	217	35	0	0	NUM
ejpam-6142	217	36	0	0	NUM
ejpam-6142	217	37	0	0	NUM
ejpam-6142	217	38	0	0	NUM
ejpam-6142	217	39	0	0	NUM
ejpam-6142	217	40	0	0	NUM
ejpam-6142	217	41	0	0	NUM
ejpam-6142	218	1	(	(	PUNCT
ejpam-6142	218	2	ϵκ−1)βmλ	ϵκ−1)βmλ	PROPN
ejpam-6142	218	3	η	η	PROPN
ejpam-6142	218	4	0	0	PROPN
ejpam-6142	218	5	0	0	NUM
ejpam-6142	218	6	0	0	NUM
ejpam-6142	218	7	0	0	NUM
ejpam-6142	218	8	−η	−η	NOUN
ejpam-6142	218	9	0	0	NUM
ejpam-6142	218	10	0	0	NUM
ejpam-6142	218	11	0	0	NUM
ejpam-6142	218	12	0	0	NUM
ejpam-6142	218	13	0	0	NUM
ejpam-6142	218	14	0	0	NUM
ejpam-6142	218	15	0	0	NUM
ejpam-6142	218	16	0	0	NUM
ejpam-6142	218	17	(	(	PUNCT
ejpam-6142	218	18	−ϵκ+1)βmλ	−ϵκ+1)βmλ	PROPN
ejpam-6142	218	19	η	η	PROPN
ejpam-6142	218	20	0	0	NUM
ejpam-6142	218	21	0	0	NUM
ejpam-6142	218	22	0	0	NUM
ejpam-6142	218	23	0	0	NUM
ejpam-6142	218	24	0	0	NUM
ejpam-6142	218	25	−γm	−γm	NOUN
ejpam-6142	218	26	0	0	NUM
ejpam-6142	218	27	0	0	NUM
ejpam-6142	218	28	0	0	NUM
ejpam-6142	218	29	0	0	NUM
ejpam-6142	218	30	0	0	NUM
ejpam-6142	218	31	0	0	NUM
ejpam-6142	218	32	0	0	NUM
ejpam-6142	218	33	0	0	NUM
ejpam-6142	218	34	0	0	NUM
ejpam-6142	218	35	0	0	NUM
ejpam-6142	218	36	0	0	NUM
ejpam-6142	218	37	0	0	NUM
ejpam-6142	218	38	0	0	NUM
ejpam-6142	218	39	αm	αm	NOUN
ejpam-6142	218	40	−∆m	−∆m	PROPN
ejpam-6142	218	41	0	0	NUM
ejpam-6142	218	42	0	0	NUM
ejpam-6142	218	43	0	0	NUM
ejpam-6142	218	44	0	0	NUM
ejpam-6142	218	45	0	0	NUM
ejpam-6142	218	46	0	0	NUM
ejpam-6142	218	47	0	0	NUM
ejpam-6142	218	48	0	0	NUM
ejpam-6142	218	49	0	0	NUM
ejpam-6142	218	50	0	0	NUM
ejpam-6142	218	51	0	0	NUM
ejpam-6142	218	52	0	0	NUM
ejpam-6142	218	53	0	0	NUM
ejpam-6142	219	1	γm	γm	ADJ
ejpam-6142	219	2	−ωm	−ωm	PROPN
ejpam-6142	219	3	0	0	NUM
ejpam-6142	219	4	0	0	NUM
ejpam-6142	219	5	0	0	NUM
ejpam-6142	219	6	0	0	NUM
ejpam-6142	219	7	0	0	NUM
ejpam-6142	219	8	0	0	NUM
ejpam-6142	219	9	0	0	NUM
ejpam-6142	219	10	0	0	NUM
ejpam-6142	219	11	0	0	NUM
ejpam-6142	219	12	0	0	NUM
ejpam-6142	219	13	0	0	NUM
ejpam-6142	219	14	0	0	NUM
ejpam-6142	219	15	0	0	NUM
ejpam-6142	220	1	ρm	ρm	PRON
ejpam-6142	220	2	−ψm	−ψm	NOUN
ejpam-6142	220	3	0	0	NUM
ejpam-6142	220	4	0	0	NUM
ejpam-6142	220	5	0	0	NUM
ejpam-6142	220	6	0	0	NUM
ejpam-6142	220	7	0	0	NUM
ejpam-6142	220	8	0	0	NUM
ejpam-6142	220	9	0	0	NUM
ejpam-6142	220	10	0	0	NUM
ejpam-6142	220	11	0	0	NUM
ejpam-6142	220	12	0	0	NUM
ejpam-6142	220	13	0	0	NUM
ejpam-6142	221	1	θm	θm	ADV
ejpam-6142	221	2	0	0	NUM
ejpam-6142	221	3	0	0	NUM
ejpam-6142	221	4	−φm	−φm	PROPN
ejpam-6142	221	5	0	0	NUM
ejpam-6142	221	6	0	0	NUM
ejpam-6142	221	7	0	0	NUM
ejpam-6142	221	8	0	0	NUM
ejpam-6142	221	9	0	0	NUM
ejpam-6142	221	10	0	0	NUM
ejpam-6142	221	11	0	0	NUM
ejpam-6142	221	12	0	0	NUM
ejpam-6142	221	13	0	0	NUM
ejpam-6142	221	14	0	0	NUM
ejpam-6142	221	15	0	0	NUM
ejpam-6142	221	16	0	0	NUM
ejpam-6142	221	17	ωm	ωm	PUNCT
ejpam-6142	221	18	λm	λm	ADP
ejpam-6142	221	19	−ζ	−ζ	NOUN
ejpam-6142	221	20			PROPN
ejpam-6142	221	21	the	the	DET
ejpam-6142	221	22	eigenvalues	eigenvalue	NOUN
ejpam-6142	221	23	of	of	ADP
ejpam-6142	221	24	the	the	DET
ejpam-6142	221	25	jacobian	jacobian	ADJ
ejpam-6142	221	26	matrix	matrix	NOUN
ejpam-6142	221	27	are	be	AUX
ejpam-6142	221	28	provided	provide	VERB
ejpam-6142	221	29	below	below	ADP
ejpam-6142	221	30	γ1,2	γ1,2	ADJ
ejpam-6142	221	31	=	=	SYM
ejpam-6142	221	32	−η	−η	NOUN
ejpam-6142	221	33	,	,	PUNCT
ejpam-6142	221	34	γ3,4	γ3,4	ADJ
ejpam-6142	221	35	=	=	SYM
ejpam-6142	221	36	−ζ	−ζ	NOUN
ejpam-6142	221	37	,	,	PUNCT
ejpam-6142	221	38	γ5	γ5	NOUN
ejpam-6142	221	39	=	=	SYM
ejpam-6142	221	40	−ωf	−ωf	ADJ
ejpam-6142	221	41	,	,	PUNCT
ejpam-6142	221	42	γ6	γ6	PROPN
ejpam-6142	221	43	=	=	SYM
ejpam-6142	221	44	−ωm	−ωm	PROPN
ejpam-6142	221	45	,	,	PUNCT
ejpam-6142	221	46	γ7	γ7	NOUN
ejpam-6142	221	47	=	=	NOUN
ejpam-6142	221	48	−ψf	−ψf	NOUN
ejpam-6142	221	49	,	,	PUNCT
ejpam-6142	221	50	γ8	γ8	NOUN
ejpam-6142	221	51	=	=	SYM
ejpam-6142	221	52	−ψm	−ψm	PROPN
ejpam-6142	221	53	,	,	PUNCT
ejpam-6142	221	54	γ9	γ9	NOUN
ejpam-6142	221	55	=	=	SYM
ejpam-6142	221	56	−φf	−φf	NOUN
ejpam-6142	221	57	,	,	PUNCT
ejpam-6142	221	58	γ10	γ10	PROPN
ejpam-6142	221	59	=	=	SYM
ejpam-6142	221	60	−φm	−φm	PROPN
ejpam-6142	221	61	s.	s.	PROPN
ejpam-6142	221	62	m.	m.	PROPN
ejpam-6142	221	63	fatah	fatah	PROPN
ejpam-6142	221	64	,	,	PUNCT
ejpam-6142	221	65	s.	s.	PROPN
ejpam-6142	221	66	h.	h.	PROPN
ejpam-6142	221	67	a.	a.	PROPN
ejpam-6142	221	68	khoshnaw	khoshnaw	PROPN
ejpam-6142	221	69	,	,	PUNCT
ejpam-6142	221	70	a.	a.	PROPN
ejpam-6142	221	71	n.	n.	PROPN
ejpam-6142	221	72	mustafa	mustafa	PROPN
ejpam-6142	221	73	/	/	SYM
ejpam-6142	221	74	eur	eur	PROPN
ejpam-6142	221	75	.	.	PUNCT
ejpam-6142	222	1	j.	j.	PROPN
ejpam-6142	222	2	pure	pure	PROPN
ejpam-6142	222	3	appl	appl	PROPN
ejpam-6142	222	4	.	.	PROPN
ejpam-6142	222	5	math	math	PROPN
ejpam-6142	222	6	,	,	PUNCT
ejpam-6142	222	7	18	18	NUM
ejpam-6142	222	8	(	(	PUNCT
ejpam-6142	222	9	2	2	NUM
ejpam-6142	222	10	)	)	PUNCT
ejpam-6142	222	11	(	(	PUNCT
ejpam-6142	222	12	2025	2025	NUM
ejpam-6142	222	13	)	)	PUNCT
ejpam-6142	222	14	,	,	PUNCT
ejpam-6142	222	15	6142	6142	NUM
ejpam-6142	222	16	12	12	NUM
ejpam-6142	222	17	of	of	ADP
ejpam-6142	222	18	33	33	NUM
ejpam-6142	222	19	and	and	CCONJ
ejpam-6142	222	20	the	the	DET
ejpam-6142	222	21	last	last	ADJ
ejpam-6142	222	22	four	four	NUM
ejpam-6142	222	23	eigenvalues	eigenvalue	NOUN
ejpam-6142	222	24	γ11	γ11	NOUN
ejpam-6142	222	25	,	,	PUNCT
ejpam-6142	222	26	γ12	γ12	NOUN
ejpam-6142	222	27	,	,	PUNCT
ejpam-6142	222	28	γ13	γ13	NOUN
ejpam-6142	222	29	,	,	PUNCT
ejpam-6142	222	30	γ14	γ14	PROPN
ejpam-6142	222	31	are	be	AUX
ejpam-6142	222	32	the	the	DET
ejpam-6142	222	33	roots	root	NOUN
ejpam-6142	222	34	of	of	ADP
ejpam-6142	222	35	the	the	DET
ejpam-6142	222	36	following	follow	VERB
ejpam-6142	222	37	degree	degree	NOUN
ejpam-6142	222	38	four	four	NUM
ejpam-6142	222	39	polynomial	polynomial	ADJ
ejpam-6142	222	40	f(γ	f(γ	NOUN
ejpam-6142	222	41	)	)	PUNCT
ejpam-6142	222	42	=	=	SYM
ejpam-6142	222	43	γ4	γ4	NOUN
ejpam-6142	222	44	+	+	CCONJ
ejpam-6142	222	45	d̃1γ	d̃1γ	ADJ
ejpam-6142	222	46	3	3	NUM
ejpam-6142	222	47	+	+	NOUN
ejpam-6142	222	48	d̃2γ	d̃2γ	NOUN
ejpam-6142	222	49	2	2	NUM
ejpam-6142	222	50	+	+	CCONJ
ejpam-6142	222	51	d̃3γ	d̃3γ	PROPN
ejpam-6142	222	52	+	+	CCONJ
ejpam-6142	222	53	d̃4	d̃4	PROPN
ejpam-6142	222	54	,	,	PUNCT
ejpam-6142	222	55	where	where	SCONJ
ejpam-6142	222	56	d̃1	d̃1	PROPN
ejpam-6142	222	57	=	=	SYM
ejpam-6142	222	58	γf	γf	PROPN
ejpam-6142	222	59	+	+	PUNCT
ejpam-6142	222	60	γm	γm	ADJ
ejpam-6142	223	1	+	+	ADJ
ejpam-6142	223	2	∆f	∆f	ADJ
ejpam-6142	223	3	+	+	ADJ
ejpam-6142	223	4	∆m	∆m	PROPN
ejpam-6142	223	5	d̃2	d̃2	PROPN
ejpam-6142	223	6	=	=	PRON
ejpam-6142	223	7	γfγm	γfγm	VERB
ejpam-6142	224	1	+	+	NOUN
ejpam-6142	225	1	∆f∆m	∆f∆m	NOUN
ejpam-6142	226	1	+	+	ADP
ejpam-6142	226	2	∆mγm	∆mγm	ADJ
ejpam-6142	227	1	+	+	NOUN
ejpam-6142	227	2	∆mγf	∆mγf	VERB
ejpam-6142	227	3	+	+	NOUN
ejpam-6142	227	4	∆fγm	∆fγm	NUM
ejpam-6142	227	5	+	+	NOUN
ejpam-6142	227	6	∆fγf	∆fγf	X
ejpam-6142	227	7	d̃3	d̃3	NOUN
ejpam-6142	227	8	=	=	PRON
ejpam-6142	227	9	∆mγfγm	∆mγfγm	VERB
ejpam-6142	227	10	+	+	NOUN
ejpam-6142	227	11	∆fγfγm	∆fγfγm	VERB
ejpam-6142	227	12	+	+	ADJ
ejpam-6142	227	13	∆f∆mγm	∆f∆mγm	PROPN
ejpam-6142	227	14	+	+	ADJ
ejpam-6142	227	15	∆f∆mγf	∆f∆mγf	ADJ
ejpam-6142	227	16	d̃4	d̃4	NOUN
ejpam-6142	227	17	=	=	PUNCT
ejpam-6142	227	18	∆f∆mγfγm	∆f∆mγfγm	NOUN
ejpam-6142	227	19	−	−	NOUN
ejpam-6142	227	20	αfαmβfβmλ2	αfαmβfβmλ2	NOUN
ejpam-6142	227	21	η2	η2	NOUN
ejpam-6142	227	22	(	(	PUNCT
ejpam-6142	227	23	1−	1−	NUM
ejpam-6142	227	24	ϵκ)2	ϵκ)2	PROPN
ejpam-6142	227	25	clearly	clearly	ADV
ejpam-6142	227	26	d̃1	d̃1	PROPN
ejpam-6142	227	27	>	>	X
ejpam-6142	227	28	0	0	NUM
ejpam-6142	227	29	,	,	PUNCT
ejpam-6142	227	30	d̃2	d̃2	PROPN
ejpam-6142	227	31	>	>	X
ejpam-6142	227	32	0	0	NUM
ejpam-6142	227	33	,	,	PUNCT
ejpam-6142	227	34	and	and	CCONJ
ejpam-6142	227	35	d̃3	d̃3	VERB
ejpam-6142	227	36	>	>	X
ejpam-6142	227	37	0	0	NUM
ejpam-6142	227	38	,	,	PUNCT
ejpam-6142	227	39	and	and	CCONJ
ejpam-6142	227	40	also	also	ADV
ejpam-6142	227	41	d̃4	d̃4	PRON
ejpam-6142	227	42	>	>	X
ejpam-6142	227	43	0	0	PUNCT
ejpam-6142	228	1	if	if	SCONJ
ejpam-6142	228	2	and	and	CCONJ
ejpam-6142	228	3	only	only	ADV
ejpam-6142	228	4	if	if	SCONJ
ejpam-6142	228	5	r0	r0	NOUN
ejpam-6142	228	6	<	<	X
ejpam-6142	228	7	1	1	NUM
ejpam-6142	228	8	(	(	PUNCT
ejpam-6142	228	9	d̃1d̃2	d̃1d̃2	PROPN
ejpam-6142	228	10	−	−	PROPN
ejpam-6142	228	11	d̃3	d̃3	PROPN
ejpam-6142	228	12	)	)	PUNCT
ejpam-6142	228	13	d̃3	d̃3	PROPN
ejpam-6142	228	14	−	−	NOUN
ejpam-6142	228	15	d̃1d̃4	d̃1d̃4	NOUN
ejpam-6142	228	16	=	=	PUNCT
ejpam-6142	228	17	(	(	PUNCT
ejpam-6142	228	18	(	(	PUNCT
ejpam-6142	228	19	γf	γf	PART
ejpam-6142	228	20	+	+	X
ejpam-6142	228	21	γm	γm	ADJ
ejpam-6142	229	1	+	+	ADJ
ejpam-6142	229	2	∆f	∆f	ADJ
ejpam-6142	229	3	+	+	ADJ
ejpam-6142	229	4	∆m)(γfγm	∆m)(γfγm	NOUN
ejpam-6142	229	5	+	+	ADJ
ejpam-6142	229	6	∆f∆m	∆f∆m	NOUN
ejpam-6142	229	7	+	+	ADP
ejpam-6142	229	8	∆mγm	∆mγm	ADJ
ejpam-6142	229	9	+	+	NOUN
ejpam-6142	229	10	∆mγf	∆mγf	ADJ
ejpam-6142	229	11	∆fγm	∆fγm	NUM
ejpam-6142	229	12	+	+	SYM
ejpam-6142	229	13	∆fγf	∆fγf	NOUN
ejpam-6142	229	14	)	)	PUNCT
ejpam-6142	229	15	−	−	PROPN
ejpam-6142	229	16	(	(	PUNCT
ejpam-6142	229	17	∆mγfγm	∆mγfγm	VERB
ejpam-6142	229	18	+	+	ADV
ejpam-6142	229	19	∆fγfγm	∆fγfγm	VERB
ejpam-6142	229	20	+	+	ADJ
ejpam-6142	229	21	∆f∆mγm	∆f∆mγm	PROPN
ejpam-6142	229	22	+	+	ADJ
ejpam-6142	229	23	∆f∆mγf	∆f∆mγf	NOUN
ejpam-6142	229	24	)	)	PUNCT
ejpam-6142	229	25	)	)	PUNCT
ejpam-6142	230	1	(	(	PUNCT
ejpam-6142	230	2	∆mγfγm	∆mγfγm	VERB
ejpam-6142	230	3	+	+	ADV
ejpam-6142	230	4	∆fγfγm	∆fγfγm	VERB
ejpam-6142	230	5	+	+	ADJ
ejpam-6142	230	6	∆f∆mγm	∆f∆mγm	PROPN
ejpam-6142	230	7	+	+	ADJ
ejpam-6142	230	8	∆f∆mγf	∆f∆mγf	NOUN
ejpam-6142	230	9	)	)	PUNCT
ejpam-6142	230	10	−	−	PROPN
ejpam-6142	230	11	(	(	PUNCT
ejpam-6142	230	12	γf	γf	PROPN
ejpam-6142	230	13	+	+	PUNCT
ejpam-6142	230	14	γm	γm	ADJ
ejpam-6142	230	15	+	+	ADJ
ejpam-6142	230	16	∆f	∆f	ADJ
ejpam-6142	230	17	+	+	ADJ
ejpam-6142	230	18	∆m)2(∆f∆mγfγm	∆m)2(∆f∆mγfγm	PROPN
ejpam-6142	230	19	−	−	PROPN
ejpam-6142	230	20	αfαmβfβmλ2	αfαmβfβmλ2	NOUN
ejpam-6142	230	21	η2	η2	PROPN
ejpam-6142	230	22	(	(	PUNCT
ejpam-6142	230	23	ϵκ−	ϵκ−	X
ejpam-6142	230	24	1)2	1)2	NUM
ejpam-6142	230	25	)	)	PUNCT
ejpam-6142	230	26	by	by	ADP
ejpam-6142	230	27	expanding	expand	VERB
ejpam-6142	230	28	the	the	DET
ejpam-6142	230	29	above	above	ADJ
ejpam-6142	230	30	expression	expression	NOUN
ejpam-6142	230	31	,	,	PUNCT
ejpam-6142	230	32	we	we	PRON
ejpam-6142	230	33	obtain	obtain	VERB
ejpam-6142	230	34	that	that	SCONJ
ejpam-6142	230	35	(	(	PUNCT
ejpam-6142	230	36	d̃1d̃2	d̃1d̃2	PROPN
ejpam-6142	230	37	−	−	PROPN
ejpam-6142	230	38	d̃3	d̃3	PROPN
ejpam-6142	230	39	)	)	PUNCT
ejpam-6142	230	40	d̃3	d̃3	PROPN
ejpam-6142	230	41	−	−	PROPN
ejpam-6142	230	42	d̃1	d̃1	PROPN
ejpam-6142	230	43	2d̃4	2d̃4	PROPN
ejpam-6142	230	44	>	>	X
ejpam-6142	230	45	0	0	NUM
ejpam-6142	230	46	.	.	PUNCT
ejpam-6142	231	1	thus	thus	ADV
ejpam-6142	231	2	,	,	PUNCT
ejpam-6142	231	3	routh	routh	PROPN
ejpam-6142	231	4	-	-	PUNCT
ejpam-6142	231	5	hurwitz	hurwitz	PROPN
ejpam-6142	231	6	criterion	criterion	NOUN
ejpam-6142	231	7	yields	yield	NOUN
ejpam-6142	231	8	that	that	PRON
ejpam-6142	231	9	all	all	DET
ejpam-6142	231	10	roots	root	NOUN
ejpam-6142	231	11	of	of	ADP
ejpam-6142	231	12	the	the	DET
ejpam-6142	231	13	polynomial	polynomial	ADJ
ejpam-6142	231	14	f(γ	f(γ	NOUN
ejpam-6142	231	15	)	)	PUNCT
ejpam-6142	231	16	have	have	VERB
ejpam-6142	231	17	negative	negative	ADJ
ejpam-6142	231	18	real	real	ADJ
ejpam-6142	231	19	parts	part	NOUN
ejpam-6142	231	20	.	.	PUNCT
ejpam-6142	232	1	this	this	PRON
ejpam-6142	232	2	follows	follow	VERB
ejpam-6142	232	3	that	that	SCONJ
ejpam-6142	232	4	all	all	PRON
ejpam-6142	232	5	eigenvalues	eigenvalue	VERB
ejpam-6142	232	6	γ11	γ11	NOUN
ejpam-6142	232	7	,	,	PUNCT
ejpam-6142	232	8	γ12	γ12	NOUN
ejpam-6142	232	9	,	,	PUNCT
ejpam-6142	232	10	γ13	γ13	NOUN
ejpam-6142	232	11	,	,	PUNCT
ejpam-6142	232	12	γ14	γ14	NOUN
ejpam-6142	232	13	have	have	VERB
ejpam-6142	232	14	negative	negative	ADJ
ejpam-6142	232	15	real	real	ADJ
ejpam-6142	232	16	parts	part	NOUN
ejpam-6142	232	17	.	.	PUNCT
ejpam-6142	233	1	hence	hence	ADV
ejpam-6142	233	2	,	,	PUNCT
ejpam-6142	233	3	all	all	DET
ejpam-6142	233	4	eigenvalues	eigenvalue	NOUN
ejpam-6142	233	5	of	of	ADP
ejpam-6142	233	6	the	the	DET
ejpam-6142	233	7	jacobian	jacobian	ADJ
ejpam-6142	233	8	matrix	matrix	NOUN
ejpam-6142	233	9	j	j	PROPN
ejpam-6142	233	10	(	(	PUNCT
ejpam-6142	233	11	e0	e0	PROPN
ejpam-6142	233	12	)	)	PUNCT
ejpam-6142	233	13	have	have	VERB
ejpam-6142	233	14	negative	negative	ADJ
ejpam-6142	233	15	real	real	ADJ
ejpam-6142	233	16	parts	part	NOUN
ejpam-6142	233	17	.	.	PUNCT
ejpam-6142	234	1	it	it	PRON
ejpam-6142	234	2	is	be	AUX
ejpam-6142	234	3	concluded	conclude	VERB
ejpam-6142	234	4	that	that	SCONJ
ejpam-6142	234	5	,	,	PUNCT
ejpam-6142	234	6	the	the	DET
ejpam-6142	234	7	disease	disease	NOUN
ejpam-6142	234	8	-	-	PUNCT
ejpam-6142	234	9	free	free	ADJ
ejpam-6142	234	10	equilibrium	equilibrium	NOUN
ejpam-6142	234	11	point	point	NOUN
ejpam-6142	234	12	e0	e0	PROPN
ejpam-6142	234	13	is	be	AUX
ejpam-6142	234	14	locally	locally	ADV
ejpam-6142	234	15	asymptotically	asymptotically	ADV
ejpam-6142	234	16	stable	stable	ADJ
ejpam-6142	234	17	if	if	SCONJ
ejpam-6142	234	18	and	and	CCONJ
ejpam-6142	234	19	only	only	ADV
ejpam-6142	234	20	if	if	SCONJ
ejpam-6142	234	21	r0	r0	NOUN
ejpam-6142	234	22	<	<	X
ejpam-6142	234	23	1	1	NUM
ejpam-6142	234	24	.	.	PUNCT
ejpam-6142	234	25	theorem	theorem	NOUN
ejpam-6142	234	26	4	4	NUM
ejpam-6142	234	27	.	.	PUNCT
ejpam-6142	235	1	the	the	DET
ejpam-6142	235	2	endemic	endemic	ADJ
ejpam-6142	235	3	equilibrium	equilibrium	NOUN
ejpam-6142	235	4	point	point	NOUN
ejpam-6142	235	5	e1	e1	NOUN
ejpam-6142	235	6	is	be	AUX
ejpam-6142	235	7	locally	locally	ADV
ejpam-6142	235	8	asymptotically	asymptotically	ADV
ejpam-6142	235	9	stable	stable	ADJ
ejpam-6142	235	10	if	if	SCONJ
ejpam-6142	235	11	and	and	CCONJ
ejpam-6142	235	12	only	only	ADV
ejpam-6142	235	13	if	if	SCONJ
ejpam-6142	235	14	r0	r0	NOUN
ejpam-6142	235	15	>	>	X
ejpam-6142	235	16	1	1	X
ejpam-6142	235	17	.	.	PUNCT
ejpam-6142	235	18	proof	proof	NOUN
ejpam-6142	235	19	.	.	PUNCT
ejpam-6142	236	1	at	at	ADP
ejpam-6142	236	2	the	the	DET
ejpam-6142	236	3	endemic	endemic	ADJ
ejpam-6142	236	4	equilibrium	equilibrium	NOUN
ejpam-6142	236	5	point	point	NOUN
ejpam-6142	236	6	e1	e1	NOUN
ejpam-6142	236	7	,	,	PUNCT
ejpam-6142	236	8	the	the	DET
ejpam-6142	236	9	jacobian	jacobian	ADJ
ejpam-6142	236	10	matrix	matrix	NOUN
ejpam-6142	236	11	j	j	PROPN
ejpam-6142	236	12	(	(	PUNCT
ejpam-6142	236	13	e1	e1	PROPN
ejpam-6142	236	14	)	)	PUNCT
ejpam-6142	236	15	has	have	AUX
ejpam-6142	236	16	14	14	NUM
ejpam-6142	236	17	eigenvalues	eigenvalue	NOUN
ejpam-6142	236	18	which	which	PRON
ejpam-6142	236	19	are	be	AUX
ejpam-6142	236	20	given	give	VERB
ejpam-6142	236	21	below	below	ADP
ejpam-6142	236	22	γ∗1	γ∗1	NOUN
ejpam-6142	236	23	=	=	PUNCT
ejpam-6142	236	24	−ωf	−ωf	ADJ
ejpam-6142	236	25	,	,	PUNCT
ejpam-6142	236	26	γ∗2	γ∗2	NOUN
ejpam-6142	236	27	=	=	NOUN
ejpam-6142	236	28	−ψf	−ψf	NOUN
ejpam-6142	236	29	,	,	PUNCT
ejpam-6142	236	30	γ∗3	γ∗3	NOUN
ejpam-6142	236	31	=	=	SYM
ejpam-6142	236	32	−φf	−φf	NOUN
ejpam-6142	236	33	,	,	PUNCT
ejpam-6142	236	34	γ∗4	γ∗4	NOUN
ejpam-6142	236	35	=	=	SYM
ejpam-6142	236	36	−ωm	−ωm	PROPN
ejpam-6142	236	37	,	,	PUNCT
ejpam-6142	236	38	γ∗5	γ∗5	NOUN
ejpam-6142	236	39	=	=	SYM
ejpam-6142	236	40	−ψm	−ψm	PROPN
ejpam-6142	236	41	,	,	PUNCT
ejpam-6142	236	42	γ∗6	γ∗6	NOUN
ejpam-6142	236	43	=	=	SYM
ejpam-6142	236	44	−φm	−φm	PROPN
ejpam-6142	236	45	,	,	PUNCT
ejpam-6142	236	46	γ∗7,8	γ∗7,8	PROPN
ejpam-6142	236	47	=	=	SYM
ejpam-6142	236	48	ζ	ζ	NOUN
ejpam-6142	236	49	and	and	CCONJ
ejpam-6142	236	50	the	the	DET
ejpam-6142	236	51	roots	root	NOUN
ejpam-6142	236	52	of	of	ADP
ejpam-6142	236	53	the	the	DET
ejpam-6142	236	54	following	follow	VERB
ejpam-6142	236	55	degree	degree	NOUN
ejpam-6142	236	56	six	six	NUM
ejpam-6142	236	57	polynomial	polynomial	NOUN
ejpam-6142	236	58	are	be	AUX
ejpam-6142	236	59	the	the	DET
ejpam-6142	236	60	last	last	ADJ
ejpam-6142	236	61	six	six	NUM
ejpam-6142	236	62	eigenvalues	eigenvalue	NOUN
ejpam-6142	236	63	f	f	X
ejpam-6142	236	64	(	(	PUNCT
ejpam-6142	236	65	γ∗	γ∗	PROPN
ejpam-6142	236	66	)	)	PUNCT
ejpam-6142	237	1	=	=	VERB
ejpam-6142	237	2	γ∗6	γ∗6	NOUN
ejpam-6142	237	3	+	+	CCONJ
ejpam-6142	237	4	c̃1γ	c̃1γ	ADJ
ejpam-6142	237	5	∗5	∗5	NOUN
ejpam-6142	237	6	+	+	NUM
ejpam-6142	237	7	c̃2γ	c̃2γ	NOUN
ejpam-6142	237	8	∗4	∗4	ADP
ejpam-6142	238	1	+	+	CCONJ
ejpam-6142	238	2	c̃3γ	c̃3γ	PROPN
ejpam-6142	238	3	∗3	∗3	PROPN
ejpam-6142	238	4	+	+	CCONJ
ejpam-6142	238	5	c̃4γ	c̃4γ	PROPN
ejpam-6142	238	6	∗2	∗2	PROPN
ejpam-6142	238	7	+	+	CCONJ
ejpam-6142	238	8	c̃5γ	c̃5γ	X
ejpam-6142	238	9	∗	∗	NOUN
ejpam-6142	238	10	+	+	X
ejpam-6142	239	1	c̃6	c̃6	NOUN
ejpam-6142	239	2	,	,	PUNCT
ejpam-6142	239	3	where	where	SCONJ
ejpam-6142	239	4	c̃1	c̃1	PROPN
ejpam-6142	239	5	=	=	NOUN
ejpam-6142	239	6	w̃1i	w̃1i	NOUN
ejpam-6142	239	7	∗	∗	NOUN
ejpam-6142	239	8	m	m	VERB
ejpam-6142	239	9	+	+	NOUN
ejpam-6142	239	10	w̃2i	w̃2i	PROPN
ejpam-6142	239	11	∗	∗	NOUN
ejpam-6142	239	12	f	f	PROPN
ejpam-6142	240	1	+	+	NOUN
ejpam-6142	240	2	∆f	∆f	PROPN
ejpam-6142	240	3	+	+	PROPN
ejpam-6142	240	4	∆m	∆m	PROPN
ejpam-6142	240	5	+	+	CCONJ
ejpam-6142	240	6	γf	γf	PROPN
ejpam-6142	240	7	+	+	CCONJ
ejpam-6142	240	8	γm	γm	ADJ
ejpam-6142	240	9	+	+	NUM
ejpam-6142	240	10	2η	2η	X
ejpam-6142	240	11	c̃2	c̃2	NOUN
ejpam-6142	240	12	=	=	NOUN
ejpam-6142	240	13	w̃1w̃2i	w̃1w̃2i	X
ejpam-6142	240	14	∗	∗	NOUN
ejpam-6142	240	15	f	f	PROPN
ejpam-6142	241	1	i	i	PRON
ejpam-6142	241	2	∗	∗	VERB
ejpam-6142	241	3	m	m	VERB
ejpam-6142	241	4	+	+	NOUN
ejpam-6142	241	5	∆fw̃1i	∆fw̃1i	NOUN
ejpam-6142	241	6	∗	∗	NOUN
ejpam-6142	241	7	m	m	VERB
ejpam-6142	241	8	+	+	NOUN
ejpam-6142	241	9	∆fw̃2i	∆fw̃2i	NOUN
ejpam-6142	241	10	∗	∗	NOUN
ejpam-6142	241	11	f	f	NOUN
ejpam-6142	242	1	+	+	NUM
ejpam-6142	242	2	∆mw̃1i	∆mw̃1i	PROPN
ejpam-6142	242	3	∗	∗	NOUN
ejpam-6142	242	4	m	m	VERB
ejpam-6142	243	1	+	+	NOUN
ejpam-6142	243	2	∆mw̃2i	∆mw̃2i	X
ejpam-6142	243	3	∗	∗	NOUN
ejpam-6142	243	4	f	f	NOUN
ejpam-6142	243	5	+	+	CCONJ
ejpam-6142	243	6	γfw̃1i	γfw̃1i	NOUN
ejpam-6142	243	7	∗	∗	NOUN
ejpam-6142	243	8	m	m	VERB
ejpam-6142	243	9	+	+	CCONJ
ejpam-6142	243	10	γfw̃2i	γfw̃2i	NOUN
ejpam-6142	243	11	∗	∗	NOUN
ejpam-6142	243	12	f	f	NOUN
ejpam-6142	244	1	+	+	CCONJ
ejpam-6142	244	2	γmw̃1i	γmw̃1i	PROPN
ejpam-6142	244	3	∗	∗	NOUN
ejpam-6142	244	4	m	m	VERB
ejpam-6142	245	1	+	+	X
ejpam-6142	245	2	γmw̃2i	γmw̃2i	ADP
ejpam-6142	245	3	∗	∗	NOUN
ejpam-6142	245	4	f	f	NOUN
ejpam-6142	246	1	+	+	NUM
ejpam-6142	246	2	w̃1ηi	w̃1ηi	NOUN
ejpam-6142	246	3	∗	∗	NOUN
ejpam-6142	246	4	m	m	VERB
ejpam-6142	247	1	+	+	NUM
ejpam-6142	247	2	w̃2ηi	w̃2ηi	NOUN
ejpam-6142	247	3	∗	∗	NOUN
ejpam-6142	247	4	f	f	PROPN
ejpam-6142	248	1	+	+	ADJ
ejpam-6142	248	2	∆f∆m	∆f∆m	PROPN
ejpam-6142	248	3	+	+	SYM
ejpam-6142	248	4	∆fγf	∆fγf	X
ejpam-6142	248	5	+	+	NOUN
ejpam-6142	248	6	∆fγm	∆fγm	NUM
ejpam-6142	248	7	+	+	NUM
ejpam-6142	248	8	2η∆f	2η∆f	NUM
ejpam-6142	249	1	+	+	NOUN
ejpam-6142	249	2	∆mγf	∆mγf	VERB
ejpam-6142	249	3	+	+	NOUN
ejpam-6142	249	4	∆mγm	∆mγm	ADJ
ejpam-6142	249	5	+	+	NUM
ejpam-6142	249	6	2η∆m	2η∆m	NUM
ejpam-6142	249	7	+	+	CCONJ
ejpam-6142	249	8	γfγm	γfγm	NOUN
ejpam-6142	249	9	+	+	CCONJ
ejpam-6142	249	10	2ηγf	2ηγf	NUM
ejpam-6142	249	11	+	+	CCONJ
ejpam-6142	249	12	2ηγm	2ηγm	NUM
ejpam-6142	249	13	+	+	CCONJ
ejpam-6142	249	14	η2	η2	PROPN
ejpam-6142	249	15	,	,	PUNCT
ejpam-6142	249	16	s.	s.	PROPN
ejpam-6142	249	17	m.	m.	PROPN
ejpam-6142	249	18	fatah	fatah	PROPN
ejpam-6142	249	19	,	,	PUNCT
ejpam-6142	249	20	s.	s.	PROPN
ejpam-6142	249	21	h.	h.	PROPN
ejpam-6142	249	22	a.	a.	PROPN
ejpam-6142	249	23	khoshnaw	khoshnaw	PROPN
ejpam-6142	249	24	,	,	PUNCT
ejpam-6142	249	25	a.	a.	PROPN
ejpam-6142	249	26	n.	n.	PROPN
ejpam-6142	249	27	mustafa	mustafa	PROPN
ejpam-6142	249	28	/	/	SYM
ejpam-6142	249	29	eur	eur	PROPN
ejpam-6142	249	30	.	.	PUNCT
ejpam-6142	250	1	j.	j.	PROPN
ejpam-6142	250	2	pure	pure	PROPN
ejpam-6142	250	3	appl	appl	PROPN
ejpam-6142	250	4	.	.	PROPN
ejpam-6142	250	5	math	math	PROPN
ejpam-6142	250	6	,	,	PUNCT
ejpam-6142	250	7	18	18	NUM
ejpam-6142	250	8	(	(	PUNCT
ejpam-6142	250	9	2	2	NUM
ejpam-6142	250	10	)	)	PUNCT
ejpam-6142	250	11	(	(	PUNCT
ejpam-6142	250	12	2025	2025	NUM
ejpam-6142	250	13	)	)	PUNCT
ejpam-6142	250	14	,	,	PUNCT
ejpam-6142	250	15	6142	6142	NUM
ejpam-6142	250	16	13	13	NUM
ejpam-6142	250	17	of	of	ADP
ejpam-6142	250	18	33	33	NUM
ejpam-6142	250	19	c̃3	c̃3	PROPN
ejpam-6142	250	20	=	=	PUNCT
ejpam-6142	250	21	w̃1w̃2∆fi	w̃1w̃2∆fi	NOUN
ejpam-6142	250	22	∗	∗	NOUN
ejpam-6142	250	23	f	f	PROPN
ejpam-6142	251	1	i	i	PRON
ejpam-6142	251	2	∗	∗	VERB
ejpam-6142	251	3	m	m	VERB
ejpam-6142	252	1	+	+	NUM
ejpam-6142	252	2	w̃1w̃2∆mi∗f	w̃1w̃2∆mi∗f	AUX
ejpam-6142	252	3	i	i	PRON
ejpam-6142	252	4	∗	∗	VERB
ejpam-6142	252	5	m	m	VERB
ejpam-6142	252	6	+	+	X
ejpam-6142	252	7	w̃1w̃2γfi	w̃1w̃2γfi	NOUN
ejpam-6142	252	8	∗	∗	NOUN
ejpam-6142	252	9	f	f	NOUN
ejpam-6142	253	1	i	i	PRON
ejpam-6142	253	2	∗	∗	VERB
ejpam-6142	253	3	m	m	VERB
ejpam-6142	254	1	+	+	X
ejpam-6142	254	2	w̃1w̃2γmi∗f	w̃1w̃2γmi∗f	PUNCT
ejpam-6142	254	3	i	i	PRON
ejpam-6142	254	4	∗	∗	VERB
ejpam-6142	254	5	m	m	VERB
ejpam-6142	254	6	+	+	NUM
ejpam-6142	254	7	w̃1∆f∆mi∗m	w̃1∆f∆mi∗m	NOUN
ejpam-6142	254	8	+	+	CCONJ
ejpam-6142	254	9	w̃2∆f∆mi∗f	w̃2∆f∆mi∗f	ADJ
ejpam-6142	254	10	+	+	CCONJ
ejpam-6142	254	11	w̃1∆fγfi	w̃1∆fγfi	NOUN
ejpam-6142	254	12	∗	∗	NOUN
ejpam-6142	254	13	m	m	VERB
ejpam-6142	255	1	+	+	CCONJ
ejpam-6142	255	2	w̃2∆fγfi	w̃2∆fγfi	PRON
ejpam-6142	255	3	∗	∗	NOUN
ejpam-6142	255	4	f	f	PROPN
ejpam-6142	255	5	+	+	CCONJ
ejpam-6142	255	6	w̃1∆fγmi∗m	w̃1∆fγmi∗m	NOUN
ejpam-6142	255	7	+	+	CCONJ
ejpam-6142	255	8	w̃2∆fγmi∗f	w̃2∆fγmi∗f	VERB
ejpam-6142	255	9	+	+	CCONJ
ejpam-6142	255	10	w̃1∆fηi	w̃1∆fηi	NOUN
ejpam-6142	255	11	∗	∗	NOUN
ejpam-6142	255	12	m	m	VERB
ejpam-6142	255	13	+	+	CCONJ
ejpam-6142	255	14	w̃2∆fηi	w̃2∆fηi	NOUN
ejpam-6142	255	15	∗	∗	NOUN
ejpam-6142	255	16	f	f	NOUN
ejpam-6142	256	1	+	+	CCONJ
ejpam-6142	256	2	w̃1∆mγfi	w̃1∆mγfi	NOUN
ejpam-6142	256	3	∗	∗	NOUN
ejpam-6142	256	4	m	m	VERB
ejpam-6142	256	5	+	+	X
ejpam-6142	256	6	w̃2∆mγfi	w̃2∆mγfi	NOUN
ejpam-6142	256	7	∗	∗	NOUN
ejpam-6142	256	8	f	f	NOUN
ejpam-6142	257	1	+	+	NUM
ejpam-6142	257	2	w̃1∆mγmi∗m	w̃1∆mγmi∗m	NOUN
ejpam-6142	257	3	+	+	CCONJ
ejpam-6142	257	4	w̃2∆mγmi∗f	w̃2∆mγmi∗f	NOUN
ejpam-6142	257	5	+	+	CCONJ
ejpam-6142	257	6	w̃1∆mηi∗m	w̃1∆mηi∗m	PROPN
ejpam-6142	257	7	+	+	CCONJ
ejpam-6142	257	8	w̃2∆mηi∗f	w̃2∆mηi∗f	PROPN
ejpam-6142	258	1	+	+	NUM
ejpam-6142	258	2	w̃1γfγmi∗m	w̃1γfγmi∗m	NOUN
ejpam-6142	258	3	+	+	CCONJ
ejpam-6142	258	4	w̃2γfγmi∗f	w̃2γfγmi∗f	X
ejpam-6142	258	5	+	+	X
ejpam-6142	258	6	w̃1γfηi	w̃1γfηi	NOUN
ejpam-6142	258	7	∗	∗	NOUN
ejpam-6142	258	8	m	m	VERB
ejpam-6142	259	1	+	+	X
ejpam-6142	259	2	w̃2γfηi	w̃2γfηi	ADJ
ejpam-6142	259	3	∗	∗	NOUN
ejpam-6142	259	4	f	f	NOUN
ejpam-6142	259	5	+	+	CCONJ
ejpam-6142	259	6	w̃1γmηi∗m	w̃1γmηi∗m	X
ejpam-6142	260	1	+	+	CCONJ
ejpam-6142	260	2	w̃2γmηi∗f	w̃2γmηi∗f	ADJ
ejpam-6142	260	3	+	+	ADJ
ejpam-6142	260	4	∆f∆mγf	∆f∆mγf	ADJ
ejpam-6142	260	5	+	+	ADJ
ejpam-6142	260	6	∆f∆mγm	∆f∆mγm	NOUN
ejpam-6142	260	7	+	+	ADJ
ejpam-6142	260	8	2∆f∆mη	2∆f∆mη	NUM
ejpam-6142	261	1	+	+	PUNCT
ejpam-6142	261	2	∆fγfγm	∆fγfγm	NOUN
ejpam-6142	261	3	+	+	NOUN
ejpam-6142	261	4	2∆fγfη	2∆fγfη	NUM
ejpam-6142	261	5	+	+	CCONJ
ejpam-6142	261	6	2∆fγmη	2∆fγmη	NUM
ejpam-6142	261	7	+	+	ADJ
ejpam-6142	261	8	∆fη	∆fη	PROPN
ejpam-6142	261	9	2	2	NUM
ejpam-6142	261	10	+	+	NOUN
ejpam-6142	261	11	∆mγfγm	∆mγfγm	VERB
ejpam-6142	261	12	+	+	NOUN
ejpam-6142	261	13	2∆mγfη	2∆mγfη	NUM
ejpam-6142	261	14	+	+	NUM
ejpam-6142	261	15	2∆mγmη	2∆mγmη	NUM
ejpam-6142	262	1	+	+	ADP
ejpam-6142	262	2	∆mη2	∆mη2	PROPN
ejpam-6142	262	3	+	+	PROPN
ejpam-6142	262	4	2γfγmη	2γfγmη	NUM
ejpam-6142	262	5	+	+	CCONJ
ejpam-6142	262	6	γfη	γfη	DET
ejpam-6142	262	7	2	2	NUM
ejpam-6142	262	8	+	+	CCONJ
ejpam-6142	262	9	γmη2	γmη2	PROPN
ejpam-6142	262	10	,	,	PUNCT
ejpam-6142	262	11	c̃4	c̃4	PROPN
ejpam-6142	262	12	=	=	PUNCT
ejpam-6142	262	13	∆f∆mw̃1w̃2i	∆f∆mw̃1w̃2i	NOUN
ejpam-6142	262	14	∗	∗	NOUN
ejpam-6142	262	15	f	f	PROPN
ejpam-6142	263	1	i	i	PRON
ejpam-6142	263	2	∗	∗	VERB
ejpam-6142	263	3	m	m	VERB
ejpam-6142	263	4	+	+	NOUN
ejpam-6142	263	5	∆fγfw̃1w̃2i	∆fγfw̃1w̃2i	X
ejpam-6142	263	6	∗	∗	NOUN
ejpam-6142	263	7	f	f	NOUN
ejpam-6142	264	1	i	i	PRON
ejpam-6142	264	2	∗	∗	VERB
ejpam-6142	264	3	m	m	VERB
ejpam-6142	264	4	+	+	NOUN
ejpam-6142	264	5	∆fγmw̃1w̃2i	∆fγmw̃1w̃2i	X
ejpam-6142	264	6	∗	∗	X
ejpam-6142	264	7	f	f	NOUN
ejpam-6142	265	1	i	i	PRON
ejpam-6142	265	2	∗	∗	VERB
ejpam-6142	265	3	m	m	VERB
ejpam-6142	265	4	+	+	NOUN
ejpam-6142	265	5	∆mγfw̃1w̃2i	∆mγfw̃1w̃2i	X
ejpam-6142	265	6	∗	∗	NOUN
ejpam-6142	265	7	f	f	NOUN
ejpam-6142	266	1	i	i	PRON
ejpam-6142	266	2	∗	∗	VERB
ejpam-6142	266	3	m	m	VERB
ejpam-6142	266	4	+	+	ADJ
ejpam-6142	266	5	∆mγmw̃1w̃2i	∆mγmw̃1w̃2i	ADJ
ejpam-6142	266	6	∗	∗	NOUN
ejpam-6142	266	7	f	f	NOUN
ejpam-6142	267	1	i	i	PRON
ejpam-6142	267	2	∗	∗	VERB
ejpam-6142	267	3	m	m	VERB
ejpam-6142	267	4	+	+	NOUN
ejpam-6142	267	5	γfγmw̃1w̃2i	γfγmw̃1w̃2i	NOUN
ejpam-6142	267	6	∗	∗	NOUN
ejpam-6142	267	7	f	f	NOUN
ejpam-6142	268	1	i	i	PRON
ejpam-6142	268	2	∗	∗	VERB
ejpam-6142	268	3	m	m	VERB
ejpam-6142	268	4	−	−	PROPN
ejpam-6142	268	5	w̃1w̃2αfαms∗	w̃1w̃2αfαms∗	NOUN
ejpam-6142	268	6	fs	fs	ADP
ejpam-6142	268	7	∗	∗	NOUN
ejpam-6142	268	8	m	m	NOUN
ejpam-6142	268	9	+	+	PROPN
ejpam-6142	268	10	∆f∆mγfw̃1i	∆f∆mγfw̃1i	PROPN
ejpam-6142	268	11	∗	∗	NOUN
ejpam-6142	268	12	m	m	VERB
ejpam-6142	269	1	+	+	ADJ
ejpam-6142	269	2	∆f∆mγfw̃2i	∆f∆mγfw̃2i	PROPN
ejpam-6142	269	3	∗	∗	NOUN
ejpam-6142	269	4	f	f	NOUN
ejpam-6142	270	1	+	+	PUNCT
ejpam-6142	270	2	∆f∆mγmw̃1i	∆f∆mγmw̃1i	ADP
ejpam-6142	270	3	∗	∗	NOUN
ejpam-6142	270	4	m	m	VERB
ejpam-6142	270	5	+	+	ADJ
ejpam-6142	270	6	∆f∆mγmw̃2i	∆f∆mγmw̃2i	PROPN
ejpam-6142	270	7	∗	∗	NOUN
ejpam-6142	270	8	f	f	NOUN
ejpam-6142	271	1	+	+	NOUN
ejpam-6142	271	2	∆f∆mw̃1ηi	∆f∆mw̃1ηi	PROPN
ejpam-6142	271	3	∗	∗	NOUN
ejpam-6142	271	4	m	m	VERB
ejpam-6142	271	5	+	+	ADJ
ejpam-6142	271	6	∆f∆mw̃2ηi	∆f∆mw̃2ηi	X
ejpam-6142	271	7	∗	∗	NOUN
ejpam-6142	271	8	f	f	PROPN
ejpam-6142	272	1	+	+	ADP
ejpam-6142	272	2	∆fγfγmw̃1i	∆fγfγmw̃1i	PROPN
ejpam-6142	272	3	∗	∗	NOUN
ejpam-6142	272	4	m	m	VERB
ejpam-6142	273	1	+	+	NOUN
ejpam-6142	273	2	∆fγfγmw̃2i	∆fγfγmw̃2i	NOUN
ejpam-6142	273	3	∗	∗	NOUN
ejpam-6142	273	4	f	f	NOUN
ejpam-6142	274	1	+	+	ADJ
ejpam-6142	274	2	∆fγfw̃1ηi	∆fγfw̃1ηi	PROPN
ejpam-6142	274	3	∗	∗	NOUN
ejpam-6142	274	4	m	m	VERB
ejpam-6142	275	1	+	+	ADJ
ejpam-6142	276	1	∆fγfw̃2ηi	∆fγfw̃2ηi	NOUN
ejpam-6142	276	2	∗	∗	NOUN
ejpam-6142	276	3	f	f	NOUN
ejpam-6142	277	1	+	+	NOUN
ejpam-6142	277	2	∆fγmw̃1ηi	∆fγmw̃1ηi	PROPN
ejpam-6142	277	3	∗	∗	NOUN
ejpam-6142	277	4	m	m	VERB
ejpam-6142	277	5	+	+	NOUN
ejpam-6142	277	6	∆fγmw̃2ηi	∆fγmw̃2ηi	NOUN
ejpam-6142	277	7	∗	∗	NOUN
ejpam-6142	277	8	f	f	NOUN
ejpam-6142	278	1	+	+	NOUN
ejpam-6142	278	2	∆mγfγmw̃1i	∆mγfγmw̃1i	NOUN
ejpam-6142	278	3	∗	∗	NOUN
ejpam-6142	278	4	m	m	VERB
ejpam-6142	279	1	+	+	NOUN
ejpam-6142	279	2	∆mγfγmw̃2i	∆mγfγmw̃2i	NOUN
ejpam-6142	279	3	∗	∗	NOUN
ejpam-6142	279	4	f	f	PROPN
ejpam-6142	280	1	+	+	NOUN
ejpam-6142	280	2	∆mγfw̃1ηi	∆mγfw̃1ηi	PROPN
ejpam-6142	280	3	∗	∗	NOUN
ejpam-6142	280	4	m	m	VERB
ejpam-6142	280	5	+	+	NOUN
ejpam-6142	280	6	∆mγfw̃2ηi	∆mγfw̃2ηi	NOUN
ejpam-6142	280	7	∗	∗	NOUN
ejpam-6142	280	8	f	f	PROPN
ejpam-6142	281	1	+	+	NOUN
ejpam-6142	281	2	∆mγmw̃1ηi	∆mγmw̃1ηi	PROPN
ejpam-6142	281	3	∗	∗	NOUN
ejpam-6142	281	4	m	m	VERB
ejpam-6142	281	5	+	+	ADJ
ejpam-6142	281	6	∆mγmw̃2ηi	∆mγmw̃2ηi	NOUN
ejpam-6142	281	7	∗	∗	NOUN
ejpam-6142	281	8	f	f	NOUN
ejpam-6142	281	9	+	+	CCONJ
ejpam-6142	281	10	γfγmw̃1ηi	γfγmw̃1ηi	NOUN
ejpam-6142	281	11	∗	∗	NOUN
ejpam-6142	281	12	m	m	VERB
ejpam-6142	281	13	+	+	NUM
ejpam-6142	281	14	γfγmw̃2ηi	γfγmw̃2ηi	PROPN
ejpam-6142	281	15	∗	∗	NOUN
ejpam-6142	281	16	f	f	NOUN
ejpam-6142	282	1	+	+	NOUN
ejpam-6142	282	2	∆f∆mγfγm	∆f∆mγfγm	PROPN
ejpam-6142	282	3	+	+	SYM
ejpam-6142	282	4	2∆f∆mγfη	2∆f∆mγfη	NOUN
ejpam-6142	282	5	+	+	CCONJ
ejpam-6142	282	6	2∆f∆mγmη	2∆f∆mγmη	NUM
ejpam-6142	283	1	+	+	ADJ
ejpam-6142	283	2	∆f∆mη2	∆f∆mη2	ADJ
ejpam-6142	283	3	+	+	CCONJ
ejpam-6142	283	4	2∆fγfγmη	2∆fγfγmη	NUM
ejpam-6142	284	1	+	+	NOUN
ejpam-6142	284	2	∆fγfη	∆fγfη	NUM
ejpam-6142	284	3	2	2	NUM
ejpam-6142	284	4	+	+	NOUN
ejpam-6142	284	5	∆fγmη2	∆fγmη2	NOUN
ejpam-6142	284	6	+	+	CCONJ
ejpam-6142	284	7	2∆mγfγmη	2∆mγfγmη	NUM
ejpam-6142	285	1	+	+	PRON
ejpam-6142	285	2	∆mγfη	∆mγfη	NOUN
ejpam-6142	285	3	2	2	NUM
ejpam-6142	285	4	+	+	VERB
ejpam-6142	285	5	∆mγmη2	∆mγmη2	ADJ
ejpam-6142	285	6	+	+	CCONJ
ejpam-6142	285	7	γfγmη2	γfγmη2	ADJ
ejpam-6142	285	8	,	,	PUNCT
ejpam-6142	285	9	c̃5	c̃5	PROPN
ejpam-6142	285	10	=	=	PROPN
ejpam-6142	285	11	∆f∆mγfw̃1w̃2i	∆f∆mγfw̃1w̃2i	PROPN
ejpam-6142	285	12	∗	∗	NOUN
ejpam-6142	285	13	f	f	NOUN
ejpam-6142	286	1	i	i	PRON
ejpam-6142	286	2	∗	∗	VERB
ejpam-6142	286	3	m	m	VERB
ejpam-6142	286	4	+	+	NOUN
ejpam-6142	286	5	∆f∆mγmw̃1w̃2i	∆f∆mγmw̃1w̃2i	PROPN
ejpam-6142	286	6	∗	∗	NOUN
ejpam-6142	287	1	f	f	NOUN
ejpam-6142	288	1	i	i	PRON
ejpam-6142	288	2	∗	∗	VERB
ejpam-6142	288	3	m	m	VERB
ejpam-6142	288	4	+	+	ADV
ejpam-6142	288	5	∆fγfγmw̃1w̃2i	∆fγfγmw̃1w̃2i	NOUN
ejpam-6142	288	6	∗	∗	NOUN
ejpam-6142	289	1	f	f	NOUN
ejpam-6142	290	1	i	i	PRON
ejpam-6142	290	2	∗	∗	VERB
ejpam-6142	290	3	m	m	VERB
ejpam-6142	290	4	+	+	NOUN
ejpam-6142	290	5	∆mγfγmw̃1w̃2i	∆mγfγmw̃1w̃2i	PROPN
ejpam-6142	290	6	∗	∗	NOUN
ejpam-6142	291	1	f	f	NOUN
ejpam-6142	292	1	i	i	PRON
ejpam-6142	292	2	∗	∗	VERB
ejpam-6142	292	3	m	m	VERB
ejpam-6142	292	4	−	−	PROPN
ejpam-6142	292	5	2w̃1w̃2αfαmηs∗	2w̃1w̃2αfαmηs∗	NUM
ejpam-6142	292	6	fs	fs	ADP
ejpam-6142	292	7	∗	∗	NOUN
ejpam-6142	292	8	m	m	VERB
ejpam-6142	293	1	+	+	PROPN
ejpam-6142	293	2	∆f∆mγfγmw̃1i	∆f∆mγfγmw̃1i	PROPN
ejpam-6142	293	3	∗	∗	NOUN
ejpam-6142	293	4	m	m	VERB
ejpam-6142	293	5	+	+	ADJ
ejpam-6142	293	6	∆f∆mγfγmw̃2i	∆f∆mγfγmw̃2i	PROPN
ejpam-6142	293	7	∗	∗	NOUN
ejpam-6142	293	8	f	f	NOUN
ejpam-6142	294	1	+	+	NOUN
ejpam-6142	294	2	∆f∆mγfw̃1ηi	∆f∆mγfw̃1ηi	NOUN
ejpam-6142	294	3	∗	∗	NOUN
ejpam-6142	294	4	m	m	VERB
ejpam-6142	294	5	+	+	PRON
ejpam-6142	294	6	∆f∆mγfw̃2ηi	∆f∆mγfw̃2ηi	NOUN
ejpam-6142	294	7	∗	∗	NOUN
ejpam-6142	294	8	f	f	NOUN
ejpam-6142	295	1	+	+	NOUN
ejpam-6142	295	2	∆f∆mγmw̃1ηi	∆f∆mγmw̃1ηi	NOUN
ejpam-6142	295	3	∗	∗	NOUN
ejpam-6142	295	4	m	m	VERB
ejpam-6142	296	1	+	+	NOUN
ejpam-6142	296	2	∆f∆mγmw̃2ηi	∆f∆mγmw̃2ηi	NOUN
ejpam-6142	296	3	∗	∗	NOUN
ejpam-6142	296	4	f	f	NOUN
ejpam-6142	297	1	+	+	ADP
ejpam-6142	297	2	∆fγfγmw̃1ηi	∆fγfγmw̃1ηi	NOUN
ejpam-6142	297	3	∗	∗	NOUN
ejpam-6142	297	4	m	m	VERB
ejpam-6142	297	5	+	+	ADJ
ejpam-6142	297	6	∆fγfγmw̃2ηi	∆fγfγmw̃2ηi	NOUN
ejpam-6142	297	7	∗	∗	NOUN
ejpam-6142	297	8	f	f	NOUN
ejpam-6142	298	1	+	+	NOUN
ejpam-6142	298	2	∆mγfγmw̃1ηi	∆mγfγmw̃1ηi	PROPN
ejpam-6142	298	3	∗	∗	NOUN
ejpam-6142	298	4	m	m	VERB
ejpam-6142	298	5	+	+	NOUN
ejpam-6142	298	6	∆mγfγmw̃2ηi	∆mγfγmw̃2ηi	NOUN
ejpam-6142	298	7	∗	∗	NOUN
ejpam-6142	298	8	f	f	NOUN
ejpam-6142	299	1	+	+	NUM
ejpam-6142	299	2	2∆f∆mγfγmη	2∆f∆mγfγmη	NOUN
ejpam-6142	300	1	+	+	ADP
ejpam-6142	300	2	∆f∆mγfη	∆f∆mγfη	PROPN
ejpam-6142	300	3	2	2	NUM
ejpam-6142	300	4	+	+	NOUN
ejpam-6142	300	5	∆f∆mγmη2	∆f∆mγmη2	PROPN
ejpam-6142	300	6	+	+	PROPN
ejpam-6142	300	7	∆fγfγmη2	∆fγfγmη2	PROPN
ejpam-6142	300	8	+	+	ADJ
ejpam-6142	300	9	∆mγfγmη2	∆mγfγmη2	PROPN
ejpam-6142	300	10	,	,	PUNCT
ejpam-6142	300	11	c̃6	c̃6	NOUN
ejpam-6142	300	12	=	=	PUNCT
ejpam-6142	300	13	∆f∆mγfγmw̃1w̃2i	∆f∆mγfγmw̃1w̃2i	NOUN
ejpam-6142	300	14	∗	∗	NOUN
ejpam-6142	300	15	f	f	NOUN
ejpam-6142	301	1	i	i	PRON
ejpam-6142	301	2	∗	∗	VERB
ejpam-6142	301	3	m	m	VERB
ejpam-6142	301	4	−	−	PROPN
ejpam-6142	301	5	w̃1w̃2αfαmη2s∗	w̃1w̃2αfαmη2s∗	PROPN
ejpam-6142	301	6	fs	fs	ADP
ejpam-6142	301	7	∗	∗	NOUN
ejpam-6142	301	8	m	m	VERB
ejpam-6142	302	1	+	+	NOUN
ejpam-6142	302	2	∆f∆mγfγmw̃1ηi	∆f∆mγfγmw̃1ηi	NOUN
ejpam-6142	302	3	∗	∗	NOUN
ejpam-6142	302	4	m	m	VERB
ejpam-6142	302	5	+	+	ADJ
ejpam-6142	302	6	∆f∆mγfγmw̃2ηi	∆f∆mγfγmw̃2ηi	NOUN
ejpam-6142	302	7	∗	∗	NOUN
ejpam-6142	302	8	f	f	NOUN
ejpam-6142	303	1	+	+	ADV
ejpam-6142	303	2	∆f∆mγfγmη2	∆f∆mγfγmη2	PROPN
ejpam-6142	303	3	,	,	PUNCT
ejpam-6142	303	4	here	here	ADV
ejpam-6142	303	5	,	,	PUNCT
ejpam-6142	303	6	w̃1	w̃1	PROPN
ejpam-6142	303	7	=	=	PUNCT
ejpam-6142	303	8	(	(	PUNCT
ejpam-6142	303	9	1−	1−	NUM
ejpam-6142	303	10	ϵκ)βf	ϵκ)βf	SYM
ejpam-6142	303	11	>	>	X
ejpam-6142	303	12	0	0	PROPN
ejpam-6142	303	13	,	,	PUNCT
ejpam-6142	303	14	w̃2	w̃2	PROPN
ejpam-6142	303	15	=	=	SYM
ejpam-6142	303	16	(	(	PUNCT
ejpam-6142	303	17	1−	1−	NUM
ejpam-6142	303	18	ϵκ)βm	ϵκ)βm	PUNCT
ejpam-6142	303	19	>	>	X
ejpam-6142	303	20	0	0	PUNCT
ejpam-6142	304	1	if	if	SCONJ
ejpam-6142	304	2	r0	r0	NOUN
ejpam-6142	304	3	>	>	X
ejpam-6142	304	4	1	1	NUM
ejpam-6142	304	5	,	,	PUNCT
ejpam-6142	304	6	it	it	PRON
ejpam-6142	304	7	is	be	AUX
ejpam-6142	304	8	easy	easy	ADJ
ejpam-6142	304	9	to	to	PART
ejpam-6142	304	10	show	show	VERB
ejpam-6142	304	11	that	that	SCONJ
ejpam-6142	304	12	c̃1	c̃1	PROPN
ejpam-6142	304	13	,	,	PUNCT
ejpam-6142	304	14	c̃2	c̃2	PROPN
ejpam-6142	304	15	,	,	PUNCT
ejpam-6142	304	16	c̃3	c̃3	PROPN
ejpam-6142	304	17	,	,	PUNCT
ejpam-6142	304	18	c̃4	c̃4	PROPN
ejpam-6142	304	19	,	,	PUNCT
ejpam-6142	304	20	c̃5	c̃5	NOUN
ejpam-6142	304	21	,	,	PUNCT
ejpam-6142	304	22	c̃6	c̃6	PROPN
ejpam-6142	304	23	are	be	AUX
ejpam-6142	304	24	all	all	ADV
ejpam-6142	304	25	positive	positive	ADJ
ejpam-6142	304	26	as	as	SCONJ
ejpam-6142	304	27	follows	follow	VERB
ejpam-6142	304	28	:	:	PUNCT
ejpam-6142	304	29	clearly	clearly	ADV
ejpam-6142	304	30	c̃1	c̃1	PROPN
ejpam-6142	304	31	>	>	X
ejpam-6142	304	32	0	0	NUM
ejpam-6142	304	33	,	,	PUNCT
ejpam-6142	304	34	c̃2	c̃2	ADP
ejpam-6142	304	35	>	>	NOUN
ejpam-6142	304	36	0	0	NUM
ejpam-6142	304	37	,	,	PUNCT
ejpam-6142	304	38	and	and	CCONJ
ejpam-6142	304	39	c̃3	c̃3	PROPN
ejpam-6142	304	40	>	>	X
ejpam-6142	305	1	0	0	X
ejpam-6142	305	2	.	.	PUNCT
ejpam-6142	306	1	the	the	DET
ejpam-6142	306	2	only	only	ADJ
ejpam-6142	306	3	negative	negative	ADJ
ejpam-6142	306	4	term	term	NOUN
ejpam-6142	306	5	in	in	ADP
ejpam-6142	306	6	c̃4	c̃4	PROPN
ejpam-6142	306	7	is	be	AUX
ejpam-6142	306	8	w̃1w̃2αfαms∗	w̃1w̃2αfαms∗	VERB
ejpam-6142	306	9	fs	fs	ADP
ejpam-6142	306	10	∗	∗	NOUN
ejpam-6142	306	11	m	m	PROPN
ejpam-6142	306	12	,	,	PUNCT
ejpam-6142	306	13	and	and	CCONJ
ejpam-6142	306	14	∆f∆mγfγm−w̃1w̃2αfαms∗	∆f∆mγfγm−w̃1w̃2αfαms∗	NUM
ejpam-6142	306	15	fs	fs	ADP
ejpam-6142	306	16	∗	∗	NOUN
ejpam-6142	306	17	m	m	NOUN
ejpam-6142	307	1	=	=	NOUN
ejpam-6142	308	1	0	0	X
ejpam-6142	308	2	.	.	PUNCT
ejpam-6142	309	1	hence	hence	ADV
ejpam-6142	309	2	c̃4	c̃4	VERB
ejpam-6142	309	3	>	>	X
ejpam-6142	309	4	0	0	PUNCT
ejpam-6142	309	5	.	.	PUNCT
ejpam-6142	310	1	in	in	ADP
ejpam-6142	310	2	c̃5	c̃5	PROPN
ejpam-6142	310	3	there	there	PRON
ejpam-6142	310	4	is	be	VERB
ejpam-6142	310	5	only	only	ADV
ejpam-6142	310	6	one	one	NUM
ejpam-6142	310	7	negative	negative	ADJ
ejpam-6142	310	8	term	term	NOUN
ejpam-6142	310	9	which	which	PRON
ejpam-6142	310	10	are	be	AUX
ejpam-6142	310	11	2w̃1w̃2αfαmηs∗	2w̃1w̃2αfαmηs∗	NUM
ejpam-6142	310	12	fs	fs	ADP
ejpam-6142	310	13	∗	∗	NOUN
ejpam-6142	310	14	m	m	PROPN
ejpam-6142	310	15	,	,	PUNCT
ejpam-6142	310	16	and	and	CCONJ
ejpam-6142	310	17	2∆f∆mγfγmη−2w̃1w̃2αfαmηs∗	2∆f∆mγfγmη−2w̃1w̃2αfαmηs∗	NUM
ejpam-6142	310	18	fs	fs	ADP
ejpam-6142	310	19	∗	∗	NOUN
ejpam-6142	310	20	m	m	NOUN
ejpam-6142	310	21	=	=	NOUN
ejpam-6142	310	22	0	0	NUM
ejpam-6142	310	23	.	.	PUNCT
ejpam-6142	311	1	thus	thus	ADV
ejpam-6142	311	2	,	,	PUNCT
ejpam-6142	311	3	s.	s.	PROPN
ejpam-6142	311	4	m.	m.	PROPN
ejpam-6142	311	5	fatah	fatah	PROPN
ejpam-6142	311	6	,	,	PUNCT
ejpam-6142	311	7	s.	s.	PROPN
ejpam-6142	311	8	h.	h.	PROPN
ejpam-6142	311	9	a.	a.	PROPN
ejpam-6142	311	10	khoshnaw	khoshnaw	PROPN
ejpam-6142	311	11	,	,	PUNCT
ejpam-6142	311	12	a.	a.	PROPN
ejpam-6142	311	13	n.	n.	PROPN
ejpam-6142	311	14	mustafa	mustafa	PROPN
ejpam-6142	311	15	/	/	SYM
ejpam-6142	311	16	eur	eur	PROPN
ejpam-6142	311	17	.	.	PUNCT
ejpam-6142	312	1	j.	j.	PROPN
ejpam-6142	312	2	pure	pure	PROPN
ejpam-6142	312	3	appl	appl	PROPN
ejpam-6142	312	4	.	.	PROPN
ejpam-6142	312	5	math	math	PROPN
ejpam-6142	312	6	,	,	PUNCT
ejpam-6142	312	7	18	18	NUM
ejpam-6142	312	8	(	(	PUNCT
ejpam-6142	312	9	2	2	NUM
ejpam-6142	312	10	)	)	PUNCT
ejpam-6142	312	11	(	(	PUNCT
ejpam-6142	312	12	2025	2025	NUM
ejpam-6142	312	13	)	)	PUNCT
ejpam-6142	312	14	,	,	PUNCT
ejpam-6142	312	15	6142	6142	NUM
ejpam-6142	312	16	14	14	NUM
ejpam-6142	312	17	of	of	ADP
ejpam-6142	312	18	33	33	NUM
ejpam-6142	312	19	c̃5	c̃5	PROPN
ejpam-6142	312	20	>	>	X
ejpam-6142	312	21	0	0	NUM
ejpam-6142	312	22	.	.	PUNCT
ejpam-6142	313	1	for	for	ADP
ejpam-6142	313	2	c̃6	c̃6	PROPN
ejpam-6142	313	3	,	,	PUNCT
ejpam-6142	313	4	since	since	SCONJ
ejpam-6142	313	5	∆f∆mγfγmη2	∆f∆mγfγmη2	PROPN
ejpam-6142	313	6	−	−	PROPN
ejpam-6142	313	7	w̃1w̃2αfαmη2s∗	w̃1w̃2αfαmη2s∗	NOUN
ejpam-6142	313	8	fs	fs	ADP
ejpam-6142	313	9	∗	∗	NOUN
ejpam-6142	313	10	m	m	VERB
ejpam-6142	314	1	=	=	SYM
ejpam-6142	314	2	0	0	NUM
ejpam-6142	314	3	,	,	PUNCT
ejpam-6142	314	4	it	it	PRON
ejpam-6142	314	5	follows	follow	VERB
ejpam-6142	314	6	that	that	SCONJ
ejpam-6142	315	1	c̃6	c̃6	PROPN
ejpam-6142	315	2	>	>	X
ejpam-6142	315	3	0	0	X
ejpam-6142	315	4	.	.	PUNCT
ejpam-6142	316	1	the	the	DET
ejpam-6142	316	2	necessary	necessary	ADJ
ejpam-6142	316	3	condition	condition	NOUN
ejpam-6142	316	4	for	for	ADP
ejpam-6142	316	5	stability	stability	NOUN
ejpam-6142	316	6	of	of	ADP
ejpam-6142	316	7	routh	routh	PROPN
ejpam-6142	316	8	-	-	PUNCT
ejpam-6142	316	9	hurwitz	hurwitz	PROPN
ejpam-6142	316	10	criterion	criterion	NOUN
ejpam-6142	316	11	holds	hold	VERB
ejpam-6142	316	12	as	as	ADP
ejpam-6142	316	13	c̃l	c̃l	NOUN
ejpam-6142	316	14	>	>	X
ejpam-6142	316	15	0	0	NUM
ejpam-6142	316	16	,	,	PUNCT
ejpam-6142	316	17	for	for	ADP
ejpam-6142	316	18	i	i	PROPN
ejpam-6142	316	19	=	=	SYM
ejpam-6142	316	20	1	1	NUM
ejpam-6142	316	21	,	,	PUNCT
ejpam-6142	316	22	2	2	NUM
ejpam-6142	316	23	,	,	PUNCT
ejpam-6142	316	24	3	3	NUM
ejpam-6142	316	25	,	,	PUNCT
ejpam-6142	316	26	4	4	NUM
ejpam-6142	316	27	,	,	PUNCT
ejpam-6142	316	28	5	5	NUM
ejpam-6142	316	29	,	,	PUNCT
ejpam-6142	316	30	6	6	NUM
ejpam-6142	316	31	if	if	SCONJ
ejpam-6142	316	32	and	and	CCONJ
ejpam-6142	316	33	only	only	ADV
ejpam-6142	316	34	if	if	SCONJ
ejpam-6142	316	35	r0	r0	NOUN
ejpam-6142	316	36	>	>	X
ejpam-6142	316	37	1	1	X
ejpam-6142	316	38	.	.	PUNCT
ejpam-6142	317	1	the	the	DET
ejpam-6142	317	2	routh	routh	PROPN
ejpam-6142	317	3	-	-	PUNCT
ejpam-6142	317	4	hurwitz	hurwitz	PROPN
ejpam-6142	317	5	criterion	criterion	NOUN
ejpam-6142	317	6	array	array	NOUN
ejpam-6142	317	7	for	for	ADP
ejpam-6142	317	8	f	f	PROPN
ejpam-6142	317	9	(	(	PUNCT
ejpam-6142	317	10	γ∗	γ∗	PROPN
ejpam-6142	317	11	)	)	PUNCT
ejpam-6142	317	12	is	be	AUX
ejpam-6142	317	13	given	give	VERB
ejpam-6142	317	14	by	by	ADP
ejpam-6142	317	15	λ∗6	λ∗6	NOUN
ejpam-6142	317	16	:	:	PUNCT
ejpam-6142	317	17	a0	a0	PROPN
ejpam-6142	317	18	a2	a2	PROPN
ejpam-6142	317	19	a4	a4	PROPN
ejpam-6142	317	20	a6	a6	NOUN
ejpam-6142	317	21	0	0	PUNCT
ejpam-6142	318	1	λ∗5	λ∗5	NOUN
ejpam-6142	318	2	:	:	PUNCT
ejpam-6142	318	3	a1	a1	NOUN
ejpam-6142	318	4	a3	a3	NOUN
ejpam-6142	318	5	a5	a5	PROPN
ejpam-6142	318	6	0	0	NUM
ejpam-6142	318	7	0	0	NUM
ejpam-6142	319	1	λ∗4	λ∗4	NOUN
ejpam-6142	319	2	:	:	PUNCT
ejpam-6142	319	3	b1	b1	NOUN
ejpam-6142	319	4	b2	b2	NOUN
ejpam-6142	319	5	b3	b3	PROPN
ejpam-6142	319	6	b4	b4	PROPN
ejpam-6142	319	7	0	0	NUM
ejpam-6142	319	8	λ∗3	λ∗3	NOUN
ejpam-6142	319	9	:	:	PUNCT
ejpam-6142	319	10	c1	c1	PROPN
ejpam-6142	319	11	c2	c2	PROPN
ejpam-6142	319	12	c3	c3	PROPN
ejpam-6142	319	13	c4	c4	PROPN
ejpam-6142	319	14	0	0	PROPN
ejpam-6142	320	1	λ∗2	λ∗2	ADJ
ejpam-6142	320	2	:	:	PUNCT
ejpam-6142	320	3	d1	d1	PROPN
ejpam-6142	320	4	d2	d2	PROPN
ejpam-6142	320	5	d3	d3	PROPN
ejpam-6142	320	6	d4	d4	PROPN
ejpam-6142	320	7	0	0	NUM
ejpam-6142	321	1	λ∗1	λ∗1	ADJ
ejpam-6142	321	2	:	:	PUNCT
ejpam-6142	321	3	e1	e1	PROPN
ejpam-6142	321	4	e2	e2	PROPN
ejpam-6142	321	5	e3	e3	NOUN
ejpam-6142	321	6	e4	e4	PROPN
ejpam-6142	321	7	0	0	NUM
ejpam-6142	321	8	λ∗0	λ∗0	NOUN
ejpam-6142	321	9	:	:	PUNCT
ejpam-6142	321	10	f1	f1	PROPN
ejpam-6142	321	11	f2	f2	PROPN
ejpam-6142	321	12	f3	f3	VERB
ejpam-6142	321	13	f4	f4	NOUN
ejpam-6142	321	14	0	0	NUM
ejpam-6142	321	15	where	where	SCONJ
ejpam-6142	321	16	a0	a0	NOUN
ejpam-6142	321	17	=	=	SYM
ejpam-6142	321	18	1	1	NUM
ejpam-6142	321	19	,	,	PUNCT
ejpam-6142	321	20	a1	a1	NOUN
ejpam-6142	321	21	=	=	SYM
ejpam-6142	321	22	c̃1	c̃1	PROPN
ejpam-6142	321	23	,	,	PUNCT
ejpam-6142	321	24	a2	a2	PROPN
ejpam-6142	321	25	=	=	SYM
ejpam-6142	321	26	c̃2	c̃2	PROPN
ejpam-6142	321	27	,	,	PUNCT
ejpam-6142	321	28	a3	a3	NOUN
ejpam-6142	321	29	=	=	SYM
ejpam-6142	321	30	c̃3	c̃3	PROPN
ejpam-6142	321	31	,	,	PUNCT
ejpam-6142	321	32	a4	a4	NOUN
ejpam-6142	321	33	=	=	SYM
ejpam-6142	321	34	c̃4	c̃4	PROPN
ejpam-6142	321	35	,	,	PUNCT
ejpam-6142	321	36	a5	a5	PROPN
ejpam-6142	321	37	=	=	SYM
ejpam-6142	321	38	c̃5	c̃5	PROPN
ejpam-6142	321	39	,	,	PUNCT
ejpam-6142	321	40	a6	a6	NOUN
ejpam-6142	321	41	=	=	SYM
ejpam-6142	321	42	c̃6	c̃6	PROPN
ejpam-6142	321	43	,	,	PUNCT
ejpam-6142	321	44	a7	a7	PROPN
ejpam-6142	321	45	=	=	SYM
ejpam-6142	321	46	0	0	NUM
ejpam-6142	321	47	,	,	PUNCT
ejpam-6142	321	48	b1	b1	NOUN
ejpam-6142	321	49	=	=	SYM
ejpam-6142	321	50	a1a2	a1a2	ADP
ejpam-6142	321	51	−	−	NOUN
ejpam-6142	321	52	a0a3	a0a3	PUNCT
ejpam-6142	321	53	a1	a1	NOUN
ejpam-6142	321	54	,	,	PUNCT
ejpam-6142	321	55	b2	b2	NOUN
ejpam-6142	321	56	=	=	SYM
ejpam-6142	321	57	a1a4	a1a4	PROPN
ejpam-6142	321	58	−	−	NOUN
ejpam-6142	321	59	a0a5	a0a5	NOUN
ejpam-6142	321	60	a1	a1	NOUN
ejpam-6142	321	61	,	,	PUNCT
ejpam-6142	321	62	b3	b3	NOUN
ejpam-6142	321	63	=	=	SYM
ejpam-6142	322	1	a1a6	a1a6	PROPN
ejpam-6142	322	2	−	−	NOUN
ejpam-6142	322	3	a0a7	a0a7	INTJ
ejpam-6142	322	4	a1	a1	NOUN
ejpam-6142	322	5	,	,	PUNCT
ejpam-6142	322	6	b4	b4	NOUN
ejpam-6142	322	7	=	=	SYM
ejpam-6142	322	8	0	0	PROPN
ejpam-6142	322	9	,	,	PUNCT
ejpam-6142	322	10	c1	c1	NOUN
ejpam-6142	322	11	=	=	PUNCT
ejpam-6142	322	12	b1a3	b1a3	PUNCT
ejpam-6142	322	13	−	−	PROPN
ejpam-6142	322	14	a1b2	a1b2	PROPN
ejpam-6142	322	15	b1	b1	PROPN
ejpam-6142	322	16	,	,	PUNCT
ejpam-6142	322	17	c2	c2	PROPN
ejpam-6142	322	18	=	=	PUNCT
ejpam-6142	322	19	b1a5	b1a5	PROPN
ejpam-6142	322	20	−	−	NOUN
ejpam-6142	322	21	a1b3	a1b3	NOUN
ejpam-6142	322	22	b1	b1	NOUN
ejpam-6142	322	23	,	,	PUNCT
ejpam-6142	322	24	c3	c3	X
ejpam-6142	322	25	=	=	PUNCT
ejpam-6142	322	26	b1a7	b1a7	SYM
ejpam-6142	322	27	−	−	NOUN
ejpam-6142	322	28	a1b4	a1b4	SYM
ejpam-6142	322	29	b1	b1	NOUN
ejpam-6142	322	30	,	,	PUNCT
ejpam-6142	322	31	c4	c4	NOUN
ejpam-6142	322	32	=	=	SYM
ejpam-6142	322	33	0	0	NUM
ejpam-6142	322	34	,	,	PUNCT
ejpam-6142	322	35	d1	d1	NOUN
ejpam-6142	322	36	=	=	SYM
ejpam-6142	322	37	c1b2	c1b2	NOUN
ejpam-6142	322	38	−	−	PROPN
ejpam-6142	322	39	b1c2	b1c2	PROPN
ejpam-6142	322	40	c1	c1	PROPN
ejpam-6142	322	41	,	,	PUNCT
ejpam-6142	322	42	d2	d2	PROPN
ejpam-6142	322	43	=	=	SYM
ejpam-6142	323	1	c1b3	c1b3	PROPN
ejpam-6142	323	2	−	−	NOUN
ejpam-6142	323	3	b1c3	b1c3	PROPN
ejpam-6142	323	4	c1	c1	PROPN
ejpam-6142	323	5	,	,	PUNCT
ejpam-6142	323	6	d3	d3	PROPN
ejpam-6142	323	7	=	=	PUNCT
ejpam-6142	324	1	c1b4	c1b4	NOUN
ejpam-6142	324	2	−	−	NOUN
ejpam-6142	324	3	b1c4	b1c4	NOUN
ejpam-6142	324	4	c1	c1	NOUN
ejpam-6142	324	5	,	,	PUNCT
ejpam-6142	324	6	d4	d4	PROPN
ejpam-6142	324	7	=	=	SYM
ejpam-6142	324	8	0	0	NUM
ejpam-6142	324	9	,	,	PUNCT
ejpam-6142	324	10	e1	e1	NOUN
ejpam-6142	324	11	=	=	SYM
ejpam-6142	324	12	d1c2	d1c2	NOUN
ejpam-6142	324	13	−	−	NOUN
ejpam-6142	325	1	c1d2	c1d2	PUNCT
ejpam-6142	325	2	d1	d1	PROPN
ejpam-6142	325	3	,	,	PUNCT
ejpam-6142	325	4	e2	e2	PROPN
ejpam-6142	325	5	=	=	PUNCT
ejpam-6142	326	1	d1c3	d1c3	NOUN
ejpam-6142	327	1	−	−	NOUN
ejpam-6142	327	2	c1d3	c1d3	AUX
ejpam-6142	327	3	d1	d1	PROPN
ejpam-6142	327	4	,	,	PUNCT
ejpam-6142	327	5	e3	e3	NOUN
ejpam-6142	327	6	=	=	SYM
ejpam-6142	328	1	d1c4	d1c4	NOUN
ejpam-6142	328	2	−	−	NOUN
ejpam-6142	328	3	c1d4	c1d4	NOUN
ejpam-6142	328	4	d1	d1	PROPN
ejpam-6142	328	5	,	,	PUNCT
ejpam-6142	328	6	e4	e4	PROPN
ejpam-6142	328	7	=	=	SYM
ejpam-6142	328	8	0	0	NUM
ejpam-6142	328	9	,	,	PUNCT
ejpam-6142	328	10	f1	f1	NOUN
ejpam-6142	328	11	=	=	PUNCT
ejpam-6142	328	12	e1d2	e1d2	PROPN
ejpam-6142	328	13	−	−	PROPN
ejpam-6142	328	14	d1e2	d1e2	X
ejpam-6142	328	15	e1	e1	PROPN
ejpam-6142	328	16	,	,	PUNCT
ejpam-6142	328	17	f2	f2	PROPN
ejpam-6142	328	18	=	=	SYM
ejpam-6142	328	19	e1d3	e1d3	NUM
ejpam-6142	328	20	−	−	NOUN
ejpam-6142	328	21	d1e3	d1e3	PROPN
ejpam-6142	328	22	e1	e1	PROPN
ejpam-6142	328	23	,	,	PUNCT
ejpam-6142	328	24	f3	f3	NOUN
ejpam-6142	328	25	=	=	SYM
ejpam-6142	328	26	e1d4	e1d4	SYM
ejpam-6142	328	27	−	−	PROPN
ejpam-6142	328	28	d1e4	d1e4	PROPN
ejpam-6142	328	29	e1	e1	PROPN
ejpam-6142	328	30	,	,	PUNCT
ejpam-6142	328	31	f4	f4	PROPN
ejpam-6142	328	32	=	=	SYM
ejpam-6142	328	33	0	0	NUM
ejpam-6142	328	34	.	.	PUNCT
ejpam-6142	329	1	for	for	ADP
ejpam-6142	329	2	r0	r0	NOUN
ejpam-6142	329	3	>	>	X
ejpam-6142	329	4	1	1	NUM
ejpam-6142	329	5	all	all	DET
ejpam-6142	329	6	entries	entry	NOUN
ejpam-6142	329	7	of	of	ADP
ejpam-6142	329	8	the	the	DET
ejpam-6142	329	9	first	first	ADJ
ejpam-6142	329	10	column	column	NOUN
ejpam-6142	329	11	of	of	ADP
ejpam-6142	329	12	routh	routh	PROPN
ejpam-6142	329	13	-	-	PUNCT
ejpam-6142	329	14	hurwitz	hurwitz	PROPN
ejpam-6142	329	15	criterion	criterion	NOUN
ejpam-6142	329	16	array	array	NOUN
ejpam-6142	329	17	are	be	AUX
ejpam-6142	329	18	positive	positive	ADJ
ejpam-6142	329	19	.	.	PUNCT
ejpam-6142	330	1	therefore	therefore	ADV
ejpam-6142	330	2	,	,	PUNCT
ejpam-6142	330	3	all	all	DET
ejpam-6142	330	4	roots	root	NOUN
ejpam-6142	330	5	of	of	ADP
ejpam-6142	330	6	f	f	PROPN
ejpam-6142	330	7	(	(	PUNCT
ejpam-6142	330	8	γ∗	γ∗	PROPN
ejpam-6142	330	9	)	)	PUNCT
ejpam-6142	330	10	have	have	VERB
ejpam-6142	330	11	negative	negative	ADJ
ejpam-6142	330	12	real	real	ADJ
ejpam-6142	330	13	parts	part	NOUN
ejpam-6142	330	14	.	.	PUNCT
ejpam-6142	331	1	thus	thus	ADV
ejpam-6142	331	2	,	,	PUNCT
ejpam-6142	331	3	it	it	PRON
ejpam-6142	331	4	is	be	AUX
ejpam-6142	331	5	concluded	conclude	VERB
ejpam-6142	331	6	that	that	SCONJ
ejpam-6142	331	7	all	all	PRON
ejpam-6142	331	8	eigenvalues	eigenvalue	VERB
ejpam-6142	331	9	γ∗i	γ∗i	NUM
ejpam-6142	331	10	for	for	ADP
ejpam-6142	331	11	i	i	PRON
ejpam-6142	331	12	=	=	NOUN
ejpam-6142	331	13	1	1	NUM
ejpam-6142	331	14	,	,	PUNCT
ejpam-6142	331	15	2	2	NUM
ejpam-6142	331	16	,	,	PUNCT
ejpam-6142	331	17	.	.	PUNCT
ejpam-6142	331	18	.	.	PUNCT
ejpam-6142	331	19	.	.	PUNCT
ejpam-6142	332	1	14	14	NUM
ejpam-6142	332	2	have	have	VERB
ejpam-6142	332	3	negative	negative	ADJ
ejpam-6142	332	4	real	real	ADJ
ejpam-6142	332	5	parts	part	NOUN
ejpam-6142	332	6	.	.	PUNCT
ejpam-6142	333	1	therefore	therefore	ADV
ejpam-6142	333	2	,	,	PUNCT
ejpam-6142	333	3	the	the	DET
ejpam-6142	333	4	endemic	endemic	ADJ
ejpam-6142	333	5	equilibrium	equilibrium	NOUN
ejpam-6142	333	6	point	point	NOUN
ejpam-6142	333	7	e1	e1	NOUN
ejpam-6142	333	8	is	be	AUX
ejpam-6142	333	9	locally	locally	ADV
ejpam-6142	333	10	asymptotically	asymptotically	ADV
ejpam-6142	333	11	stable	stable	ADJ
ejpam-6142	333	12	if	if	SCONJ
ejpam-6142	333	13	and	and	CCONJ
ejpam-6142	333	14	only	only	ADV
ejpam-6142	333	15	if	if	SCONJ
ejpam-6142	333	16	r0	r0	NOUN
ejpam-6142	333	17	>	>	X
ejpam-6142	333	18	1	1	NUM
ejpam-6142	333	19	.	.	NOUN
ejpam-6142	333	20	6	6	NUM
ejpam-6142	333	21	.	.	X
ejpam-6142	334	1	sensitivity	sensitivity	NOUN
ejpam-6142	334	2	analysis	analysis	NOUN
ejpam-6142	334	3	of	of	ADP
ejpam-6142	334	4	the	the	DET
ejpam-6142	334	5	model	model	NOUN
ejpam-6142	334	6	and	and	CCONJ
ejpam-6142	334	7	basic	basic	ADJ
ejpam-6142	334	8	reproduction	reproduction	NOUN
ejpam-6142	334	9	number	number	NOUN
ejpam-6142	334	10	r0	r0	NOUN
ejpam-6142	334	11	sensitivity	sensitivity	NOUN
ejpam-6142	334	12	analysis	analysis	NOUN
ejpam-6142	334	13	is	be	AUX
ejpam-6142	334	14	used	use	VERB
ejpam-6142	334	15	to	to	PART
ejpam-6142	334	16	determine	determine	VERB
ejpam-6142	334	17	how	how	SCONJ
ejpam-6142	334	18	variables	variable	NOUN
ejpam-6142	334	19	react	react	VERB
ejpam-6142	334	20	to	to	PART
ejpam-6142	334	21	change	change	VERB
ejpam-6142	334	22	in	in	ADP
ejpam-6142	334	23	the	the	DET
ejpam-6142	334	24	parameters	parameter	NOUN
ejpam-6142	334	25	.	.	PUNCT
ejpam-6142	335	1	the	the	DET
ejpam-6142	335	2	normalized	normalize	VERB
ejpam-6142	335	3	forward	forward	ADJ
ejpam-6142	335	4	sensitivity	sensitivity	NOUN
ejpam-6142	335	5	index	index	NOUN
ejpam-6142	335	6	of	of	ADP
ejpam-6142	335	7	r0	r0	NOUN
ejpam-6142	335	8	with	with	ADP
ejpam-6142	335	9	respect	respect	NOUN
ejpam-6142	335	10	to	to	ADP
ejpam-6142	335	11	a	a	DET
ejpam-6142	335	12	parameter	parameter	NOUN
ejpam-6142	335	13	p	p	NOUN
ejpam-6142	335	14	is	be	AUX
ejpam-6142	335	15	as	as	SCONJ
ejpam-6142	335	16	follows	follow	VERB
ejpam-6142	335	17	:	:	PUNCT
ejpam-6142	335	18	εr0	εr0	NOUN
ejpam-6142	335	19	p	p	NOUN
ejpam-6142	336	1	=	=	PUNCT
ejpam-6142	336	2	∂r0	∂r0	ADP
ejpam-6142	336	3	∂p	∂p	PROPN
ejpam-6142	336	4	×	×	NOUN
ejpam-6142	336	5	p	p	NOUN
ejpam-6142	336	6	r0	r0	NOUN
ejpam-6142	336	7	we	we	PRON
ejpam-6142	336	8	already	already	ADV
ejpam-6142	336	9	shown	show	VERB
ejpam-6142	336	10	that	that	SCONJ
ejpam-6142	336	11	the	the	DET
ejpam-6142	336	12	expression	expression	NOUN
ejpam-6142	336	13	of	of	ADP
ejpam-6142	336	14	r0	r0	NOUN
ejpam-6142	336	15	is	be	AUX
ejpam-6142	336	16	given	give	VERB
ejpam-6142	336	17	by	by	ADP
ejpam-6142	336	18	r0	r0	NOUN
ejpam-6142	336	19	=	=	SYM
ejpam-6142	336	20	λ(1−	λ(1−	PROPN
ejpam-6142	336	21	ϵκ	ϵκ	NOUN
ejpam-6142	336	22	)	)	PUNCT
ejpam-6142	336	23	η	η	PROPN
ejpam-6142	336	24	√	√	PROPN
ejpam-6142	336	25	αfαmβfβm	αfαmβfβm	NOUN
ejpam-6142	336	26	(	(	PUNCT
ejpam-6142	336	27	µ+	µ+	X
ejpam-6142	336	28	η	η	PROPN
ejpam-6142	336	29	+	+	PROPN
ejpam-6142	336	30	γf	γf	PROPN
ejpam-6142	336	31	+	+	CCONJ
ejpam-6142	336	32	θf	θf	NOUN
ejpam-6142	336	33	)	)	PUNCT
ejpam-6142	336	34	(	(	PUNCT
ejpam-6142	336	35	µ+	µ+	X
ejpam-6142	336	36	η	η	PROPN
ejpam-6142	336	37	+	+	X
ejpam-6142	336	38	γm	γm	PROPN
ejpam-6142	336	39	+	+	X
ejpam-6142	336	40	θm	θm	NOUN
ejpam-6142	336	41	)	)	PUNCT
ejpam-6142	336	42	(	(	PUNCT
ejpam-6142	336	43	αf	αf	X
ejpam-6142	336	44	+	+	NUM
ejpam-6142	336	45	η	η	NOUN
ejpam-6142	336	46	)	)	PUNCT
ejpam-6142	336	47	(	(	PUNCT
ejpam-6142	336	48	αm	αm	NOUN
ejpam-6142	336	49	+	+	CCONJ
ejpam-6142	336	50	η	η	NOUN
ejpam-6142	336	51	)	)	PUNCT
ejpam-6142	336	52	.	.	PUNCT
ejpam-6142	337	1	s.	s.	PROPN
ejpam-6142	337	2	m.	m.	PROPN
ejpam-6142	337	3	fatah	fatah	PROPN
ejpam-6142	337	4	,	,	PUNCT
ejpam-6142	337	5	s.	s.	PROPN
ejpam-6142	337	6	h.	h.	PROPN
ejpam-6142	337	7	a.	a.	PROPN
ejpam-6142	337	8	khoshnaw	khoshnaw	PROPN
ejpam-6142	337	9	,	,	PUNCT
ejpam-6142	337	10	a.	a.	PROPN
ejpam-6142	337	11	n.	n.	PROPN
ejpam-6142	337	12	mustafa	mustafa	PROPN
ejpam-6142	337	13	/	/	SYM
ejpam-6142	337	14	eur	eur	PROPN
ejpam-6142	337	15	.	.	PUNCT
ejpam-6142	338	1	j.	j.	PROPN
ejpam-6142	338	2	pure	pure	PROPN
ejpam-6142	338	3	appl	appl	PROPN
ejpam-6142	338	4	.	.	PROPN
ejpam-6142	338	5	math	math	PROPN
ejpam-6142	338	6	,	,	PUNCT
ejpam-6142	338	7	18	18	NUM
ejpam-6142	338	8	(	(	PUNCT
ejpam-6142	338	9	2	2	NUM
ejpam-6142	338	10	)	)	PUNCT
ejpam-6142	338	11	(	(	PUNCT
ejpam-6142	338	12	2025	2025	NUM
ejpam-6142	338	13	)	)	PUNCT
ejpam-6142	338	14	,	,	PUNCT
ejpam-6142	338	15	6142	6142	NUM
ejpam-6142	338	16	15	15	NUM
ejpam-6142	338	17	of	of	ADP
ejpam-6142	338	18	33	33	NUM
ejpam-6142	338	19	r0	r0	NOUN
ejpam-6142	338	20	’s	’	VERB
ejpam-6142	338	21	normalized	normalize	VERB
ejpam-6142	338	22	forward	forward	ADJ
ejpam-6142	338	23	sensitivity	sensitivity	NOUN
ejpam-6142	338	24	indices	index	NOUN
ejpam-6142	338	25	for	for	ADP
ejpam-6142	338	26	its	its	PRON
ejpam-6142	338	27	parameters	parameter	NOUN
ejpam-6142	338	28	are	be	AUX
ejpam-6142	338	29	as	as	SCONJ
ejpam-6142	338	30	follows	follow	VERB
ejpam-6142	338	31	:	:	PUNCT
ejpam-6142	338	32	εr0	εr0	NOUN
ejpam-6142	338	33	λ	λ	NOUN
ejpam-6142	339	1	=	=	PUNCT
ejpam-6142	340	1	∂r0	∂r0	ADP
ejpam-6142	340	2	∂λ	∂λ	PROPN
ejpam-6142	340	3	×	×	PROPN
ejpam-6142	340	4	λ	λ	X
ejpam-6142	340	5	r0	r0	NOUN
ejpam-6142	340	6	=	=	SYM
ejpam-6142	340	7	1	1	NUM
ejpam-6142	340	8	,	,	PUNCT
ejpam-6142	340	9	εr0	εr0	X
ejpam-6142	340	10	αf	αf	NOUN
ejpam-6142	340	11	=	=	PUNCT
ejpam-6142	341	1	∂r0	∂r0	ADP
ejpam-6142	341	2	∂αf	∂αf	PROPN
ejpam-6142	341	3	×	×	NOUN
ejpam-6142	341	4	αf	αf	NOUN
ejpam-6142	341	5	r0	r0	NOUN
ejpam-6142	341	6	=	=	PUNCT
ejpam-6142	341	7	η	η	X
ejpam-6142	341	8	2	2	NUM
ejpam-6142	341	9	(	(	PUNCT
ejpam-6142	341	10	αf	αf	PROPN
ejpam-6142	341	11	+	+	NUM
ejpam-6142	341	12	η	η	NOUN
ejpam-6142	341	13	)	)	PUNCT
ejpam-6142	341	14	,	,	PUNCT
ejpam-6142	341	15	εr0	εr0	X
ejpam-6142	341	16	αm	αm	NOUN
ejpam-6142	342	1	=	=	PUNCT
ejpam-6142	343	1	∂r0	∂r0	PROPN
ejpam-6142	343	2	∂αm	∂αm	PROPN
ejpam-6142	343	3	×	×	PROPN
ejpam-6142	343	4	αm	αm	NOUN
ejpam-6142	343	5	r0	r0	NOUN
ejpam-6142	343	6	=	=	SYM
ejpam-6142	343	7	η	η	PROPN
ejpam-6142	343	8	2	2	NUM
ejpam-6142	343	9	(	(	PUNCT
ejpam-6142	343	10	αf	αf	PROPN
ejpam-6142	343	11	+	+	NUM
ejpam-6142	343	12	η	η	NOUN
ejpam-6142	343	13	)	)	PUNCT
ejpam-6142	343	14	,	,	PUNCT
ejpam-6142	343	15	εr0	εr0	X
ejpam-6142	343	16	βf	βf	NOUN
ejpam-6142	344	1	=	=	PUNCT
ejpam-6142	345	1	∂r0	∂r0	ADP
ejpam-6142	345	2	∂βf	∂βf	PROPN
ejpam-6142	345	3	×	×	NOUN
ejpam-6142	345	4	βf	βf	CCONJ
ejpam-6142	345	5	r0	r0	NOUN
ejpam-6142	345	6	=	=	NOUN
ejpam-6142	345	7	1	1	NUM
ejpam-6142	345	8	2	2	NUM
ejpam-6142	345	9	,	,	PUNCT
ejpam-6142	345	10	εr0	εr0	X
ejpam-6142	345	11	βm	βm	VERB
ejpam-6142	345	12	=	=	PUNCT
ejpam-6142	345	13	∂r0	∂r0	ADP
ejpam-6142	345	14	∂βm	∂βm	PROPN
ejpam-6142	345	15	×	×	NOUN
ejpam-6142	345	16	βm	βm	NOUN
ejpam-6142	345	17	r0	r0	NOUN
ejpam-6142	345	18	=	=	NOUN
ejpam-6142	345	19	1	1	NUM
ejpam-6142	345	20	2	2	NUM
ejpam-6142	345	21	,	,	PUNCT
ejpam-6142	345	22	εr0	εr0	NOUN
ejpam-6142	345	23	κ	κ	NOUN
ejpam-6142	345	24	=	=	PUNCT
ejpam-6142	346	1	∂r0	∂r0	PROPN
ejpam-6142	346	2	∂κ	∂κ	PROPN
ejpam-6142	346	3	×	×	NOUN
ejpam-6142	346	4	κ	κ	NOUN
ejpam-6142	346	5	r0	r0	NOUN
ejpam-6142	346	6	=	=	PUNCT
ejpam-6142	346	7	ϵκ	ϵκ	PROPN
ejpam-6142	346	8	ϵκ−	ϵκ−	NUM
ejpam-6142	346	9	1	1	NUM
ejpam-6142	346	10	,	,	PUNCT
ejpam-6142	346	11	εr0	εr0	X
ejpam-6142	346	12	ϵ	ϵ	X
ejpam-6142	347	1	=	=	PUNCT
ejpam-6142	348	1	∂r0	∂r0	ADP
ejpam-6142	348	2	∂ϵ	∂ϵ	NUM
ejpam-6142	348	3	×	×	NOUN
ejpam-6142	348	4	ϵ	ϵ	X
ejpam-6142	348	5	r0	r0	NOUN
ejpam-6142	348	6	=	=	SYM
ejpam-6142	348	7	ϵκ	ϵκ	NOUN
ejpam-6142	348	8	ϵκ−	ϵκ−	NUM
ejpam-6142	348	9	1	1	NUM
ejpam-6142	348	10	,	,	PUNCT
ejpam-6142	348	11	εr0	εr0	X
ejpam-6142	348	12	µ	µ	X
ejpam-6142	348	13	=	=	PUNCT
ejpam-6142	348	14	∂r0	∂r0	ADP
ejpam-6142	348	15	∂µ	∂µ	PROPN
ejpam-6142	348	16	×	×	NOUN
ejpam-6142	348	17	µ	µ	DET
ejpam-6142	348	18	r0	r0	NOUN
ejpam-6142	348	19	=	=	SYM
ejpam-6142	348	20	−	−	PROPN
ejpam-6142	349	1	(	(	PUNCT
ejpam-6142	349	2	2µ+	2µ+	NUM
ejpam-6142	349	3	2η	2η	NUM
ejpam-6142	350	1	+	+	CCONJ
ejpam-6142	350	2	γf	γf	PRON
ejpam-6142	351	1	+	+	CCONJ
ejpam-6142	351	2	θf	θf	NOUN
ejpam-6142	351	3	+	+	CCONJ
ejpam-6142	351	4	γm	γm	ADJ
ejpam-6142	351	5	+	+	CCONJ
ejpam-6142	351	6	θm)µ	θm)µ	PROPN
ejpam-6142	351	7	2	2	NUM
ejpam-6142	351	8	(	(	PUNCT
ejpam-6142	351	9	µ+	µ+	X
ejpam-6142	351	10	η	η	PROPN
ejpam-6142	351	11	+	+	PROPN
ejpam-6142	351	12	γf	γf	PROPN
ejpam-6142	352	1	+	+	CCONJ
ejpam-6142	353	1	θf	θf	NOUN
ejpam-6142	353	2	)	)	PUNCT
ejpam-6142	353	3	(	(	PUNCT
ejpam-6142	353	4	µ+	µ+	X
ejpam-6142	353	5	η	η	PROPN
ejpam-6142	353	6	+	+	X
ejpam-6142	353	7	γm	γm	PROPN
ejpam-6142	353	8	+	+	NUM
ejpam-6142	353	9	θm	θm	NOUN
ejpam-6142	353	10	)	)	PUNCT
ejpam-6142	353	11	,	,	PUNCT
ejpam-6142	353	12	εr0	εr0	VERB
ejpam-6142	353	13	γf	γf	NOUN
ejpam-6142	353	14	=	=	PUNCT
ejpam-6142	354	1	∂r0	∂r0	ADP
ejpam-6142	354	2	∂γf	∂γf	PROPN
ejpam-6142	354	3	×	×	NOUN
ejpam-6142	354	4	γf	γf	PROPN
ejpam-6142	354	5	r0	r0	NOUN
ejpam-6142	354	6	=	=	PUNCT
ejpam-6142	355	1	−	−	PROPN
ejpam-6142	355	2	γf	γf	ADJ
ejpam-6142	355	3	2	2	NUM
ejpam-6142	355	4	(	(	PUNCT
ejpam-6142	355	5	µ+	µ+	X
ejpam-6142	355	6	η	η	PROPN
ejpam-6142	355	7	+	+	PROPN
ejpam-6142	355	8	γf	γf	PROPN
ejpam-6142	355	9	+	+	CCONJ
ejpam-6142	355	10	θf	θf	NOUN
ejpam-6142	355	11	)	)	PUNCT
ejpam-6142	355	12	,	,	PUNCT
ejpam-6142	355	13	εr0	εr0	VERB
ejpam-6142	355	14	γm	γm	ADJ
ejpam-6142	355	15	=	=	X
ejpam-6142	355	16	∂r0	∂r0	ADP
ejpam-6142	355	17	∂γm	∂γm	NOUN
ejpam-6142	355	18	×	×	NOUN
ejpam-6142	355	19	γm	γm	ADJ
ejpam-6142	355	20	r0	r0	NOUN
ejpam-6142	355	21	=	=	PUNCT
ejpam-6142	356	1	−	−	PROPN
ejpam-6142	356	2	γm	γm	ADJ
ejpam-6142	356	3	2	2	NUM
ejpam-6142	356	4	(	(	PUNCT
ejpam-6142	356	5	µ+	µ+	X
ejpam-6142	356	6	η	η	PROPN
ejpam-6142	356	7	+	+	X
ejpam-6142	356	8	γm	γm	PROPN
ejpam-6142	356	9	+	+	NUM
ejpam-6142	356	10	θm	θm	NOUN
ejpam-6142	356	11	)	)	PUNCT
ejpam-6142	356	12	,	,	PUNCT
ejpam-6142	356	13	εr0	εr0	X
ejpam-6142	356	14	θf	θf	NOUN
ejpam-6142	356	15	=	=	SYM
ejpam-6142	356	16	∂r0	∂r0	ADP
ejpam-6142	356	17	∂θf	∂θf	PROPN
ejpam-6142	356	18	×	×	NOUN
ejpam-6142	356	19	θf	θf	NOUN
ejpam-6142	356	20	r0	r0	NOUN
ejpam-6142	356	21	=	=	PUNCT
ejpam-6142	357	1	−	−	PROPN
ejpam-6142	357	2	θf	θf	INTJ
ejpam-6142	357	3	2	2	NUM
ejpam-6142	357	4	(	(	PUNCT
ejpam-6142	357	5	µ+	µ+	X
ejpam-6142	357	6	η	η	PROPN
ejpam-6142	357	7	+	+	PROPN
ejpam-6142	357	8	γf	γf	PROPN
ejpam-6142	357	9	+	+	CCONJ
ejpam-6142	357	10	θf	θf	NOUN
ejpam-6142	357	11	)	)	PUNCT
ejpam-6142	357	12	,	,	PUNCT
ejpam-6142	357	13	∂r0	∂r0	ADP
ejpam-6142	357	14	∂θm	∂θm	PROPN
ejpam-6142	357	15	×	×	NOUN
ejpam-6142	357	16	θm	θm	PROPN
ejpam-6142	357	17	r0	r0	NOUN
ejpam-6142	357	18	=	=	PUNCT
ejpam-6142	358	1	−	−	PROPN
ejpam-6142	358	2	θm	θm	PROPN
ejpam-6142	358	3	2	2	NUM
ejpam-6142	358	4	(	(	PUNCT
ejpam-6142	358	5	µ+	µ+	X
ejpam-6142	358	6	η	η	PROPN
ejpam-6142	358	7	+	+	X
ejpam-6142	358	8	γm	γm	PROPN
ejpam-6142	358	9	+	+	NUM
ejpam-6142	358	10	θm	θm	NOUN
ejpam-6142	358	11	)	)	PUNCT
ejpam-6142	358	12	,	,	PUNCT
ejpam-6142	359	1	εr0	εr0	X
ejpam-6142	359	2	η	η	NOUN
ejpam-6142	359	3	=	=	PROPN
ejpam-6142	359	4	∂r0	∂r0	PROPN
ejpam-6142	359	5	∂η	∂η	PROPN
ejpam-6142	359	6	×	×	PROPN
ejpam-6142	359	7	η	η	PROPN
ejpam-6142	359	8	r0	r0	NOUN
ejpam-6142	359	9	=	=	PUNCT
ejpam-6142	359	10	−	−	PROPN
ejpam-6142	359	11	6η4	6η4	NUM
ejpam-6142	360	1	+	+	CCONJ
ejpam-6142	360	2	5η3h1	5η3h1	NUM
ejpam-6142	360	3	+	+	SYM
ejpam-6142	360	4	4η2µh2	4η2µh2	NUM
ejpam-6142	361	1	+	+	CCONJ
ejpam-6142	361	2	4η2h3	4η2h3	NUM
ejpam-6142	362	1	+	+	CCONJ
ejpam-6142	362	2	3ηµh4	3ηµh4	NUM
ejpam-6142	362	3	+	+	NOUN
ejpam-6142	362	4	3ηαfαmh5	3ηαfαmh5	NUM
ejpam-6142	362	5	+	+	CCONJ
ejpam-6142	362	6	3ηh6	3ηh6	NUM
ejpam-6142	363	1	+	+	CCONJ
ejpam-6142	363	2	2αfαmh7	2αfαmh7	NUM
ejpam-6142	363	3	2	2	NUM
ejpam-6142	363	4	(	(	PUNCT
ejpam-6142	363	5	αf	αf	NOUN
ejpam-6142	363	6	+	+	NUM
ejpam-6142	363	7	η	η	NOUN
ejpam-6142	363	8	)	)	PUNCT
ejpam-6142	363	9	(	(	PUNCT
ejpam-6142	363	10	αm	αm	NOUN
ejpam-6142	363	11	+	+	CCONJ
ejpam-6142	363	12	η	η	PROPN
ejpam-6142	363	13	)	)	PUNCT
ejpam-6142	363	14	(	(	PUNCT
ejpam-6142	363	15	µ+	µ+	X
ejpam-6142	363	16	η	η	PROPN
ejpam-6142	363	17	+	+	PROPN
ejpam-6142	363	18	γf	γf	PROPN
ejpam-6142	363	19	+	+	CCONJ
ejpam-6142	363	20	θf	θf	NOUN
ejpam-6142	363	21	)	)	PUNCT
ejpam-6142	363	22	(	(	PUNCT
ejpam-6142	363	23	µ+	µ+	X
ejpam-6142	363	24	η	η	PROPN
ejpam-6142	363	25	+	+	X
ejpam-6142	363	26	γm	γm	PROPN
ejpam-6142	363	27	+	+	NUM
ejpam-6142	363	28	θm	θm	NOUN
ejpam-6142	363	29	)	)	PUNCT
ejpam-6142	363	30	where	where	SCONJ
ejpam-6142	363	31	,	,	PUNCT
ejpam-6142	363	32	h1	h1	NOUN
ejpam-6142	363	33	=	=	NOUN
ejpam-6142	363	34	2µ+	2µ+	NUM
ejpam-6142	363	35	αfαm	αfαm	NOUN
ejpam-6142	363	36	+	+	CCONJ
ejpam-6142	363	37	γf	γf	PRON
ejpam-6142	363	38	+	+	CCONJ
ejpam-6142	363	39	γm	γm	ADJ
ejpam-6142	364	1	+	+	CCONJ
ejpam-6142	364	2	θf	θf	NOUN
ejpam-6142	364	3	+	+	NOUN
ejpam-6142	364	4	θm	θm	PROPN
ejpam-6142	364	5	h2	h2	NOUN
ejpam-6142	364	6	=	=	PUNCT
ejpam-6142	364	7	µ+	µ+	PUNCT
ejpam-6142	364	8	2αf	2αf	ADJ
ejpam-6142	364	9	+	+	CCONJ
ejpam-6142	364	10	2αm	2αm	ADJ
ejpam-6142	365	1	+	+	CCONJ
ejpam-6142	365	2	γf	γf	PRON
ejpam-6142	365	3	+	+	CCONJ
ejpam-6142	365	4	γm	γm	ADJ
ejpam-6142	366	1	+	+	CCONJ
ejpam-6142	366	2	θf	θf	NOUN
ejpam-6142	366	3	+	+	CCONJ
ejpam-6142	366	4	θm	θm	NOUN
ejpam-6142	366	5	h3	h3	NOUN
ejpam-6142	366	6	=	=	NOUN
ejpam-6142	366	7	αfαm	αfαm	NOUN
ejpam-6142	366	8	+	+	CCONJ
ejpam-6142	366	9	(	(	PUNCT
ejpam-6142	366	10	αf	αf	ADP
ejpam-6142	366	11	+	+	NOUN
ejpam-6142	366	12	αm	αm	X
ejpam-6142	366	13	)	)	PUNCT
ejpam-6142	366	14	(	(	PUNCT
ejpam-6142	366	15	γf	γf	PROPN
ejpam-6142	366	16	+	+	CCONJ
ejpam-6142	366	17	γm	γm	ADJ
ejpam-6142	367	1	+	+	CCONJ
ejpam-6142	367	2	θf	θf	NOUN
ejpam-6142	367	3	+	+	SYM
ejpam-6142	367	4	θm	θm	PROPN
ejpam-6142	367	5	)	)	PUNCT
ejpam-6142	367	6	+	+	CCONJ
ejpam-6142	367	7	γfγm	γfγm	NOUN
ejpam-6142	367	8	+	+	CCONJ
ejpam-6142	367	9	γfθm	γfθm	ADJ
ejpam-6142	367	10	+	+	CCONJ
ejpam-6142	367	11	γmθf	γmθf	ADJ
ejpam-6142	367	12	+	+	NUM
ejpam-6142	367	13	θfθm	θfθm	NOUN
ejpam-6142	367	14	h4	h4	NOUN
ejpam-6142	367	15	=	=	SYM
ejpam-6142	367	16	(	(	PUNCT
ejpam-6142	367	17	αf	αf	NUM
ejpam-6142	367	18	+	+	CCONJ
ejpam-6142	367	19	αm	αm	X
ejpam-6142	367	20	)	)	PUNCT
ejpam-6142	367	21	(	(	PUNCT
ejpam-6142	367	22	µ+	µ+	X
ejpam-6142	367	23	γf	γf	X
ejpam-6142	367	24	+	+	CCONJ
ejpam-6142	367	25	γm	γm	ADJ
ejpam-6142	367	26	+	+	CCONJ
ejpam-6142	367	27	θf	θf	NOUN
ejpam-6142	367	28	+	+	SYM
ejpam-6142	367	29	θm	θm	NOUN
ejpam-6142	367	30	)	)	PUNCT
ejpam-6142	367	31	+	+	CCONJ
ejpam-6142	367	32	2αfαm	2αfαm	NUM
ejpam-6142	367	33	h5	h5	NOUN
ejpam-6142	367	34	=	=	SYM
ejpam-6142	367	35	γf	γf	PROPN
ejpam-6142	367	36	+	+	CCONJ
ejpam-6142	367	37	γm	γm	ADJ
ejpam-6142	367	38	+	+	CCONJ
ejpam-6142	367	39	θf	θf	NOUN
ejpam-6142	367	40	+	+	ADJ
ejpam-6142	367	41	θm	θm	PROPN
ejpam-6142	367	42	h6	h6	PROPN
ejpam-6142	367	43	=	=	PUNCT
ejpam-6142	367	44	(	(	PUNCT
ejpam-6142	367	45	αf	αf	NUM
ejpam-6142	367	46	+	+	CCONJ
ejpam-6142	367	47	αm	αm	X
ejpam-6142	367	48	)	)	PUNCT
ejpam-6142	367	49	(	(	PUNCT
ejpam-6142	367	50	γfγm	γfγm	X
ejpam-6142	367	51	+	+	NUM
ejpam-6142	367	52	γfθm	γfθm	ADJ
ejpam-6142	367	53	+	+	CCONJ
ejpam-6142	367	54	γmθf	γmθf	ADJ
ejpam-6142	367	55	+	+	CCONJ
ejpam-6142	367	56	θfθm	θfθm	ADJ
ejpam-6142	367	57	)	)	PUNCT
ejpam-6142	367	58	h7	h7	PROPN
ejpam-6142	368	1	=	=	PUNCT
ejpam-6142	368	2	µ2	µ2	PROPN
ejpam-6142	368	3	+	+	CCONJ
ejpam-6142	368	4	µγf	µγf	PRON
ejpam-6142	368	5	+	+	ADJ
ejpam-6142	368	6	µγm	µγm	NOUN
ejpam-6142	368	7	+	+	CCONJ
ejpam-6142	368	8	µθf	µθf	VERB
ejpam-6142	368	9	+	+	CCONJ
ejpam-6142	368	10	µθm	µθm	ADJ
ejpam-6142	368	11	+	+	CCONJ
ejpam-6142	368	12	γfγm	γfγm	ADJ
ejpam-6142	368	13	+	+	CCONJ
ejpam-6142	368	14	γfθm	γfθm	ADJ
ejpam-6142	368	15	+	+	CCONJ
ejpam-6142	368	16	γmθf	γmθf	ADJ
ejpam-6142	368	17	+	+	CCONJ
ejpam-6142	368	18	θfθm	θfθm	NOUN
ejpam-6142	368	19	in	in	ADP
ejpam-6142	368	20	the	the	DET
ejpam-6142	368	21	below	below	ADJ
ejpam-6142	368	22	table	table	NOUN
ejpam-6142	368	23	,	,	PUNCT
ejpam-6142	368	24	the	the	DET
ejpam-6142	368	25	sensitivity	sensitivity	NOUN
ejpam-6142	368	26	index	index	NOUN
ejpam-6142	368	27	for	for	ADP
ejpam-6142	368	28	the	the	DET
ejpam-6142	368	29	estimated	estimate	VERB
ejpam-6142	368	30	values	value	NOUN
ejpam-6142	368	31	of	of	ADP
ejpam-6142	368	32	parameters	parameter	NOUN
ejpam-6142	368	33	are	be	AUX
ejpam-6142	368	34	given	give	VERB
ejpam-6142	368	35	from	from	ADP
ejpam-6142	368	36	the	the	DET
ejpam-6142	368	37	information	information	NOUN
ejpam-6142	368	38	in	in	ADP
ejpam-6142	368	39	table	table	NOUN
ejpam-6142	368	40	2	2	NUM
ejpam-6142	368	41	,	,	PUNCT
ejpam-6142	368	42	we	we	PRON
ejpam-6142	368	43	can	can	AUX
ejpam-6142	368	44	observe	observe	VERB
ejpam-6142	368	45	positive	positive	ADJ
ejpam-6142	368	46	sensitivity	sensitivity	NOUN
ejpam-6142	368	47	indices	index	NOUN
ejpam-6142	368	48	for	for	ADP
ejpam-6142	368	49	the	the	DET
ejpam-6142	368	50	parameters	parameter	NOUN
ejpam-6142	368	51	λ	λ	PROPN
ejpam-6142	368	52	,	,	PUNCT
ejpam-6142	368	53	αf	αf	PRON
ejpam-6142	368	54	,	,	PUNCT
ejpam-6142	368	55	αm	αm	INTJ
ejpam-6142	368	56	,	,	PUNCT
ejpam-6142	368	57	βf	βf	INTJ
ejpam-6142	368	58	,	,	PUNCT
ejpam-6142	368	59	and	and	CCONJ
ejpam-6142	368	60	βm	βm	VERB
ejpam-6142	368	61	while	while	SCONJ
ejpam-6142	368	62	the	the	DET
ejpam-6142	368	63	other	other	ADJ
ejpam-6142	368	64	parameters	parameter	NOUN
ejpam-6142	368	65	κ	κ	VERB
ejpam-6142	368	66	,	,	PUNCT
ejpam-6142	368	67	ϵ	ϵ	X
ejpam-6142	368	68	,	,	PUNCT
ejpam-6142	368	69	µ	µ	PRON
ejpam-6142	368	70	,	,	PUNCT
ejpam-6142	368	71	η	η	NOUN
ejpam-6142	368	72	,	,	PUNCT
ejpam-6142	368	73	γf	γf	ADJ
ejpam-6142	368	74	,	,	PUNCT
ejpam-6142	368	75	γm	γm	ADJ
ejpam-6142	368	76	,	,	PUNCT
ejpam-6142	368	77	θf	θf	INTJ
ejpam-6142	368	78	,	,	PUNCT
ejpam-6142	368	79	and	and	CCONJ
ejpam-6142	368	80	θm	θm	PROPN
ejpam-6142	368	81	exhibit	exhibit	VERB
ejpam-6142	368	82	negative	negative	ADJ
ejpam-6142	368	83	sensitivity	sensitivity	NOUN
ejpam-6142	368	84	indices	index	NOUN
ejpam-6142	368	85	.	.	PUNCT
ejpam-6142	369	1	additionally	additionally	ADV
ejpam-6142	369	2	,	,	PUNCT
ejpam-6142	369	3	these	these	DET
ejpam-6142	369	4	parameters	parameter	NOUN
ejpam-6142	369	5	play	play	VERB
ejpam-6142	369	6	a	a	DET
ejpam-6142	369	7	crucial	crucial	ADJ
ejpam-6142	369	8	role	role	NOUN
ejpam-6142	369	9	in	in	ADP
ejpam-6142	369	10	determining	determine	VERB
ejpam-6142	369	11	the	the	DET
ejpam-6142	369	12	value	value	NOUN
ejpam-6142	369	13	of	of	ADP
ejpam-6142	369	14	the	the	DET
ejpam-6142	369	15	reproduction	reproduction	NOUN
ejpam-6142	369	16	number	number	NOUN
ejpam-6142	369	17	r0	r0	NOUN
ejpam-6142	369	18	,	,	PUNCT
ejpam-6142	369	19	which	which	PRON
ejpam-6142	369	20	aids	aid	VERB
ejpam-6142	369	21	in	in	ADP
ejpam-6142	369	22	analyzing	analyze	VERB
ejpam-6142	369	23	the	the	DET
ejpam-6142	369	24	persistence	persistence	NOUN
ejpam-6142	369	25	or	or	CCONJ
ejpam-6142	369	26	extinction	extinction	NOUN
ejpam-6142	369	27	of	of	ADP
ejpam-6142	369	28	the	the	DET
ejpam-6142	369	29	disease	disease	NOUN
ejpam-6142	369	30	within	within	ADP
ejpam-6142	369	31	the	the	DET
ejpam-6142	369	32	population	population	NOUN
ejpam-6142	369	33	.	.	PUNCT
ejpam-6142	370	1	it	it	PRON
ejpam-6142	370	2	’s	’	VERB
ejpam-6142	370	3	noteworthy	noteworthy	ADJ
ejpam-6142	370	4	that	that	SCONJ
ejpam-6142	370	5	an	an	DET
ejpam-6142	370	6	s.	s.	PROPN
ejpam-6142	370	7	m.	m.	PROPN
ejpam-6142	370	8	fatah	fatah	PROPN
ejpam-6142	370	9	,	,	PUNCT
ejpam-6142	370	10	s.	s.	PROPN
ejpam-6142	370	11	h.	h.	PROPN
ejpam-6142	370	12	a.	a.	PROPN
ejpam-6142	370	13	khoshnaw	khoshnaw	PROPN
ejpam-6142	370	14	,	,	PUNCT
ejpam-6142	370	15	a.	a.	PROPN
ejpam-6142	370	16	n.	n.	PROPN
ejpam-6142	370	17	mustafa	mustafa	PROPN
ejpam-6142	370	18	/	/	SYM
ejpam-6142	370	19	eur	eur	PROPN
ejpam-6142	370	20	.	.	PUNCT
ejpam-6142	371	1	j.	j.	PROPN
ejpam-6142	371	2	pure	pure	PROPN
ejpam-6142	371	3	appl	appl	PROPN
ejpam-6142	371	4	.	.	PROPN
ejpam-6142	371	5	math	math	PROPN
ejpam-6142	371	6	,	,	PUNCT
ejpam-6142	371	7	18	18	NUM
ejpam-6142	371	8	(	(	PUNCT
ejpam-6142	371	9	2	2	NUM
ejpam-6142	371	10	)	)	PUNCT
ejpam-6142	371	11	(	(	PUNCT
ejpam-6142	371	12	2025	2025	NUM
ejpam-6142	371	13	)	)	PUNCT
ejpam-6142	371	14	,	,	PUNCT
ejpam-6142	371	15	6142	6142	NUM
ejpam-6142	371	16	16	16	NUM
ejpam-6142	371	17	of	of	ADP
ejpam-6142	371	18	33	33	NUM
ejpam-6142	371	19	table	table	NOUN
ejpam-6142	371	20	2	2	NUM
ejpam-6142	371	21	:	:	PUNCT
ejpam-6142	371	22	sensitivity	sensitivity	NOUN
ejpam-6142	371	23	index	index	NOUN
ejpam-6142	371	24	of	of	ADP
ejpam-6142	371	25	r0	r0	NOUN
ejpam-6142	371	26	parameters	parameter	NOUN
ejpam-6142	371	27	estimated	estimate	VERB
ejpam-6142	371	28	values	value	NOUN
ejpam-6142	371	29	sensitivity	sensitivity	NOUN
ejpam-6142	371	30	index	index	NOUN
ejpam-6142	371	31	sign	sign	NOUN
ejpam-6142	371	32	sources	source	NOUN
ejpam-6142	371	33	λ	λ	VERB
ejpam-6142	371	34	100000	100000	NUM
ejpam-6142	371	35	1	1	NUM
ejpam-6142	371	36	positive	positive	ADJ
ejpam-6142	371	37	[	[	X
ejpam-6142	371	38	22	22	NUM
ejpam-6142	371	39	]	]	PUNCT
ejpam-6142	371	40	αf	αf	VERB
ejpam-6142	371	41	0.8	0.8	NUM
ejpam-6142	371	42	0.01350036488	0.01350036488	NUM
ejpam-6142	371	43	positive	positive	ADJ
ejpam-6142	371	44	assumed	assume	VERB
ejpam-6142	371	45	αm	αm	NOUN
ejpam-6142	371	46	0.75	0.75	NUM
ejpam-6142	371	47	0.01437451438	0.01437451438	NUM
ejpam-6142	371	48	positive	positive	ADJ
ejpam-6142	371	49	assumed	assume	VERB
ejpam-6142	371	50	βf	βf	ADV
ejpam-6142	371	51	0.015	0.015	NUM
ejpam-6142	371	52	0.5	0.5	NUM
ejpam-6142	371	53	positive	positive	ADJ
ejpam-6142	372	1	[	[	X
ejpam-6142	372	2	22	22	NUM
ejpam-6142	372	3	]	]	PUNCT
ejpam-6142	372	4	βm	βm	VERB
ejpam-6142	372	5	0.025	0.025	NUM
ejpam-6142	372	6	0.5	0.5	NUM
ejpam-6142	372	7	positive	positive	ADJ
ejpam-6142	372	8	[	[	X
ejpam-6142	372	9	22	22	NUM
ejpam-6142	372	10	]	]	SYM
ejpam-6142	372	11	κ	κ	X
ejpam-6142	373	1	[	[	X
ejpam-6142	373	2	0	0	NUM
ejpam-6142	373	3	,	,	PUNCT
ejpam-6142	373	4	1	1	NUM
ejpam-6142	373	5	]	]	PUNCT
ejpam-6142	373	6	-0.2500000000	-0.2500000000	NOUN
ejpam-6142	373	7	negative	negative	ADJ
ejpam-6142	374	1	[	[	X
ejpam-6142	374	2	23	23	NUM
ejpam-6142	374	3	]	]	SYM
ejpam-6142	374	4	ϵ	ϵ	X
ejpam-6142	375	1	[	[	X
ejpam-6142	375	2	0	0	NUM
ejpam-6142	375	3	,	,	PUNCT
ejpam-6142	375	4	1	1	NUM
ejpam-6142	375	5	]	]	PUNCT
ejpam-6142	375	6	-0.25000000000	-0.25000000000	X
ejpam-6142	376	1	negative	negative	ADJ
ejpam-6142	376	2	[	[	X
ejpam-6142	376	3	23	23	NUM
ejpam-6142	376	4	]	]	SYM
ejpam-6142	376	5	µ	µ	PROPN
ejpam-6142	376	6	0.333	0.333	NUM
ejpam-6142	376	7	-0.3134162666	-0.3134162666	NOUN
ejpam-6142	376	8	negative	negative	ADJ
ejpam-6142	376	9	[	[	X
ejpam-6142	376	10	25	25	NUM
ejpam-6142	376	11	]	]	PUNCT
ejpam-6142	376	12	η	η	X
ejpam-6142	376	13	0.0222	0.0222	NUM
ejpam-6142	376	14	-1.048769296	-1.048769296	NOUN
ejpam-6142	376	15	negative	negative	ADJ
ejpam-6142	376	16	[	[	X
ejpam-6142	376	17	24	24	NUM
ejpam-6142	376	18	]	]	X
ejpam-6142	376	19	γf	γf	NOUN
ejpam-6142	376	20	0.675	0.675	NUM
ejpam-6142	376	21	-0.2934272300	-0.2934272300	VERB
ejpam-6142	376	22	negative	negative	ADJ
ejpam-6142	376	23	[	[	X
ejpam-6142	376	24	22	22	NUM
ejpam-6142	376	25	]	]	SYM
ejpam-6142	376	26	γm	γm	NOUN
ejpam-6142	376	27	0.512	0.512	NUM
ejpam-6142	376	28	-0.2593192868	-0.2593192868	NOUN
ejpam-6142	376	29	negative	negative	ADJ
ejpam-6142	377	1	[	[	X
ejpam-6142	377	2	22	22	NUM
ejpam-6142	377	3	]	]	PUNCT
ejpam-6142	377	4	θf	θf	NOUN
ejpam-6142	377	5	0.12	0.12	NUM
ejpam-6142	377	6	-0.05216484090	-0.05216484090	X
ejpam-6142	377	7	negative	negative	ADJ
ejpam-6142	377	8	assumed	assume	VERB
ejpam-6142	377	9	θm	θm	PROPN
ejpam-6142	377	10	0.12	0.12	NUM
ejpam-6142	377	11	-0.06077795785	-0.06077795785	PUNCT
ejpam-6142	377	12	negative	negative	ADJ
ejpam-6142	377	13	assumed	assumed	ADJ
ejpam-6142	377	14	increase	increase	NOUN
ejpam-6142	377	15	in	in	ADP
ejpam-6142	377	16	positive	positive	ADJ
ejpam-6142	377	17	parameter	parameter	NOUN
ejpam-6142	377	18	values	value	NOUN
ejpam-6142	377	19	leads	lead	VERB
ejpam-6142	377	20	to	to	ADP
ejpam-6142	377	21	an	an	DET
ejpam-6142	377	22	elevation	elevation	NOUN
ejpam-6142	377	23	in	in	ADP
ejpam-6142	377	24	the	the	DET
ejpam-6142	377	25	value	value	NOUN
ejpam-6142	377	26	of	of	ADP
ejpam-6142	377	27	r0	r0	NOUN
ejpam-6142	377	28	,	,	PUNCT
ejpam-6142	377	29	indicating	indicate	VERB
ejpam-6142	377	30	a	a	DET
ejpam-6142	377	31	substantial	substantial	ADJ
ejpam-6142	377	32	rise	rise	NOUN
ejpam-6142	377	33	in	in	ADP
ejpam-6142	377	34	disease	disease	NOUN
ejpam-6142	377	35	transmission	transmission	NOUN
ejpam-6142	377	36	.	.	PUNCT
ejpam-6142	378	1	in	in	ADP
ejpam-6142	378	2	contrast	contrast	NOUN
ejpam-6142	378	3	,	,	PUNCT
ejpam-6142	378	4	increasing	increase	VERB
ejpam-6142	378	5	negative	negative	ADJ
ejpam-6142	378	6	parameter	parameter	NOUN
ejpam-6142	378	7	values	value	NOUN
ejpam-6142	378	8	reduces	reduce	VERB
ejpam-6142	378	9	the	the	DET
ejpam-6142	378	10	reproduction	reproduction	NOUN
ejpam-6142	378	11	number	number	NOUN
ejpam-6142	378	12	to	to	ADP
ejpam-6142	378	13	some	some	DET
ejpam-6142	378	14	amount	amount	NOUN
ejpam-6142	378	15	.	.	PUNCT
ejpam-6142	379	1	we	we	PRON
ejpam-6142	379	2	now	now	ADV
ejpam-6142	379	3	analyze	analyze	VERB
ejpam-6142	379	4	the	the	DET
ejpam-6142	379	5	local	local	ADJ
ejpam-6142	379	6	sensitivities	sensitivity	NOUN
ejpam-6142	379	7	.	.	PUNCT
ejpam-6142	380	1	in	in	ADP
ejpam-6142	380	2	the	the	DET
ejpam-6142	380	3	model	model	NOUN
ejpam-6142	380	4	1	1	NUM
ejpam-6142	380	5	,	,	PUNCT
ejpam-6142	380	6	there	there	PRON
ejpam-6142	380	7	are	be	VERB
ejpam-6142	380	8	fourteen	fourteen	NUM
ejpam-6142	380	9	compartments	compartment	NOUN
ejpam-6142	380	10	and	and	CCONJ
ejpam-6142	380	11	nineteen	nineteen	NUM
ejpam-6142	380	12	parameters	parameter	NOUN
ejpam-6142	380	13	,	,	PUNCT
ejpam-6142	380	14	we	we	PRON
ejpam-6142	380	15	can	can	AUX
ejpam-6142	380	16	use	use	VERB
ejpam-6142	380	17	three	three	NUM
ejpam-6142	380	18	different	different	ADJ
ejpam-6142	380	19	methods	method	NOUN
ejpam-6142	380	20	to	to	PART
ejpam-6142	380	21	calculate	calculate	VERB
ejpam-6142	380	22	the	the	DET
ejpam-6142	380	23	local	local	ADJ
ejpam-6142	380	24	sensitivities	sensitivity	NOUN
ejpam-6142	380	25	which	which	PRON
ejpam-6142	380	26	are	be	AUX
ejpam-6142	380	27	fullnormalization	fullnormalization	NOUN
ejpam-6142	380	28	,	,	PUNCT
ejpam-6142	380	29	half	half	ADJ
ejpam-6142	380	30	-	-	PUNCT
ejpam-6142	380	31	normalization	normalization	NOUN
ejpam-6142	380	32	,	,	PUNCT
ejpam-6142	380	33	and	and	CCONJ
ejpam-6142	380	34	non	non	NOUN
ejpam-6142	380	35	-	-	NOUN
ejpam-6142	380	36	normalization	normalization	NOUN
ejpam-6142	380	37	.	.	PUNCT
ejpam-6142	381	1	first	first	ADV
ejpam-6142	381	2	,	,	PUNCT
ejpam-6142	381	3	the	the	DET
ejpam-6142	381	4	non	non	NOUN
ejpam-6142	381	5	-	-	NOUN
ejpam-6142	381	6	normalization	normalization	NOUN
ejpam-6142	381	7	’s	’s	PART
ejpam-6142	381	8	equation	equation	NOUN
ejpam-6142	381	9	is	be	AUX
ejpam-6142	381	10	given	give	VERB
ejpam-6142	381	11	by	by	ADP
ejpam-6142	381	12	εaiπj	εaiπj	NOUN
ejpam-6142	381	13	=	=	SYM
ejpam-6142	382	1	∂ai	∂ai	PROPN
ejpam-6142	382	2	∂πj	∂πj	PROPN
ejpam-6142	382	3	,	,	PUNCT
ejpam-6142	382	4	where	where	SCONJ
ejpam-6142	382	5	εaiπj	εaiπj	NOUN
ejpam-6142	382	6	denotes	denote	VERB
ejpam-6142	382	7	the	the	DET
ejpam-6142	382	8	sensitivity	sensitivity	NOUN
ejpam-6142	382	9	coefficient	coefficient	NOUN
ejpam-6142	382	10	of	of	ADP
ejpam-6142	382	11	each	each	DET
ejpam-6142	382	12	variable	variable	NOUN
ejpam-6142	382	13	ai	ai	VERB
ejpam-6142	382	14	with	with	ADP
ejpam-6142	382	15	respect	respect	NOUN
ejpam-6142	382	16	to	to	ADP
ejpam-6142	382	17	each	each	DET
ejpam-6142	382	18	parameter	parameter	NOUN
ejpam-6142	382	19	πj	πj	VERB
ejpam-6142	382	20	.	.	PUNCT
ejpam-6142	383	1	the	the	DET
ejpam-6142	383	2	half	half	ADJ
ejpam-6142	383	3	-	-	PUNCT
ejpam-6142	383	4	normalization	normalization	NOUN
ejpam-6142	383	5	sensitivities	sensitivity	NOUN
ejpam-6142	383	6	formula	formula	NOUN
ejpam-6142	383	7	is	be	AUX
ejpam-6142	383	8	therefore	therefore	ADV
ejpam-6142	383	9	defined	define	VERB
ejpam-6142	383	10	as	as	SCONJ
ejpam-6142	383	11	follows	follow	VERB
ejpam-6142	383	12	:	:	PUNCT
ejpam-6142	384	1	εaiπj	εaiπj	NOUN
ejpam-6142	384	2	=	=	SYM
ejpam-6142	385	1	∂ai	∂ai	PROPN
ejpam-6142	385	2	∂πj	∂πj	PROPN
ejpam-6142	385	3	×	×	NOUN
ejpam-6142	385	4	1	1	NUM
ejpam-6142	385	5	ai	ai	VERB
ejpam-6142	385	6	lastly	lastly	ADV
ejpam-6142	385	7	,	,	PUNCT
ejpam-6142	385	8	full	full	ADJ
ejpam-6142	385	9	-	-	PUNCT
ejpam-6142	385	10	normalization	normalization	NOUN
ejpam-6142	385	11	sensitivities	sensitivity	NOUN
ejpam-6142	385	12	equation	equation	NOUN
ejpam-6142	385	13	is	be	AUX
ejpam-6142	385	14	defined	define	VERB
ejpam-6142	385	15	by	by	ADP
ejpam-6142	385	16	εaiπj	εaiπj	NOUN
ejpam-6142	385	17	=	=	SYM
ejpam-6142	386	1	∂ai	∂ai	PROPN
ejpam-6142	386	2	∂πj	∂πj	PROPN
ejpam-6142	386	3	×	×	NOUN
ejpam-6142	387	1	πj	πj	INTJ
ejpam-6142	387	2	ai	ai	VERB
ejpam-6142	387	3	we	we	PRON
ejpam-6142	387	4	have	have	AUX
ejpam-6142	387	5	employed	employ	VERB
ejpam-6142	387	6	matlab	matlab	NOUN
ejpam-6142	387	7	for	for	ADP
ejpam-6142	387	8	computational	computational	ADJ
ejpam-6142	387	9	simulations	simulation	NOUN
ejpam-6142	387	10	using	use	VERB
ejpam-6142	387	11	the	the	DET
ejpam-6142	387	12	estimated	estimate	VERB
ejpam-6142	387	13	parameters	parameter	NOUN
ejpam-6142	387	14	and	and	CCONJ
ejpam-6142	387	15	initial	initial	ADJ
ejpam-6142	387	16	variables	variable	NOUN
ejpam-6142	387	17	provided	provide	VERB
ejpam-6142	387	18	in	in	ADP
ejpam-6142	387	19	table	table	NOUN
ejpam-6142	387	20	1	1	NUM
ejpam-6142	387	21	.	.	PUNCT
ejpam-6142	388	1	the	the	DET
ejpam-6142	388	2	work	work	NOUN
ejpam-6142	388	3	’s	’s	PART
ejpam-6142	388	4	findings	finding	NOUN
ejpam-6142	388	5	offer	offer	VERB
ejpam-6142	388	6	a	a	DET
ejpam-6142	388	7	significant	significant	ADJ
ejpam-6142	388	8	advancement	advancement	NOUN
ejpam-6142	388	9	in	in	ADP
ejpam-6142	388	10	our	our	PRON
ejpam-6142	388	11	understanding	understanding	NOUN
ejpam-6142	388	12	of	of	ADP
ejpam-6142	388	13	the	the	DET
ejpam-6142	388	14	dynamics	dynamic	NOUN
ejpam-6142	388	15	of	of	ADP
ejpam-6142	388	16	the	the	DET
ejpam-6142	388	17	model	model	NOUN
ejpam-6142	388	18	.	.	PUNCT
ejpam-6142	389	1	this	this	DET
ejpam-6142	389	2	aids	aid	NOUN
ejpam-6142	389	3	in	in	ADP
ejpam-6142	389	4	the	the	DET
ejpam-6142	389	5	identification	identification	NOUN
ejpam-6142	389	6	of	of	ADP
ejpam-6142	389	7	crucial	crucial	ADJ
ejpam-6142	389	8	model	model	NOUN
ejpam-6142	389	9	parameters	parameter	NOUN
ejpam-6142	389	10	as	as	ADV
ejpam-6142	389	11	well	well	ADV
ejpam-6142	389	12	as	as	ADP
ejpam-6142	389	13	the	the	DET
ejpam-6142	389	14	ways	way	NOUN
ejpam-6142	389	15	in	in	ADP
ejpam-6142	389	16	which	which	PRON
ejpam-6142	389	17	the	the	DET
ejpam-6142	389	18	parameters	parameter	NOUN
ejpam-6142	389	19	impact	impact	VERB
ejpam-6142	389	20	each	each	DET
ejpam-6142	389	21	model	model	NOUN
ejpam-6142	389	22	state	state	NOUN
ejpam-6142	389	23	.	.	PUNCT
ejpam-6142	390	1	s.	s.	PROPN
ejpam-6142	390	2	m.	m.	PROPN
ejpam-6142	390	3	fatah	fatah	PROPN
ejpam-6142	390	4	,	,	PUNCT
ejpam-6142	390	5	s.	s.	PROPN
ejpam-6142	390	6	h.	h.	PROPN
ejpam-6142	390	7	a.	a.	PROPN
ejpam-6142	390	8	khoshnaw	khoshnaw	PROPN
ejpam-6142	390	9	,	,	PUNCT
ejpam-6142	390	10	a.	a.	PROPN
ejpam-6142	390	11	n.	n.	PROPN
ejpam-6142	390	12	mustafa	mustafa	PROPN
ejpam-6142	390	13	/	/	SYM
ejpam-6142	390	14	eur	eur	PROPN
ejpam-6142	390	15	.	.	PUNCT
ejpam-6142	391	1	j.	j.	PROPN
ejpam-6142	391	2	pure	pure	PROPN
ejpam-6142	391	3	appl	appl	PROPN
ejpam-6142	391	4	.	.	PROPN
ejpam-6142	391	5	math	math	PROPN
ejpam-6142	391	6	,	,	PUNCT
ejpam-6142	391	7	18	18	NUM
ejpam-6142	391	8	(	(	PUNCT
ejpam-6142	391	9	2	2	NUM
ejpam-6142	391	10	)	)	PUNCT
ejpam-6142	391	11	(	(	PUNCT
ejpam-6142	391	12	2025	2025	NUM
ejpam-6142	391	13	)	)	PUNCT
ejpam-6142	391	14	,	,	PUNCT
ejpam-6142	391	15	6142	6142	NUM
ejpam-6142	391	16	17	17	NUM
ejpam-6142	391	17	of	of	ADP
ejpam-6142	391	18	33	33	NUM
ejpam-6142	391	19	figure	figure	NOUN
ejpam-6142	391	20	2	2	NUM
ejpam-6142	391	21	:	:	PUNCT
ejpam-6142	391	22	local	local	ADJ
ejpam-6142	391	23	sensitivity	sensitivity	NOUN
ejpam-6142	391	24	analysis	analysis	NOUN
ejpam-6142	391	25	using	use	VERB
ejpam-6142	391	26	techniques	technique	NOUN
ejpam-6142	391	27	non	non	NOUN
ejpam-6142	391	28	-	-	NOUN
ejpam-6142	391	29	normalization	normalization	NOUN
ejpam-6142	391	30	(	(	PUNCT
ejpam-6142	391	31	a	a	X
ejpam-6142	391	32	)	)	PUNCT
ejpam-6142	391	33	,	,	PUNCT
ejpam-6142	391	34	half	half	ADJ
ejpam-6142	391	35	-	-	PUNCT
ejpam-6142	391	36	normalization	normalization	NOUN
ejpam-6142	391	37	(	(	PUNCT
ejpam-6142	391	38	b	b	NOUN
ejpam-6142	391	39	,	,	PUNCT
ejpam-6142	391	40	c	c	NOUN
ejpam-6142	391	41	)	)	PUNCT
ejpam-6142	391	42	,	,	PUNCT
ejpam-6142	391	43	and	and	CCONJ
ejpam-6142	391	44	fullnormalization	fullnormalization	NOUN
ejpam-6142	391	45	(	(	PUNCT
ejpam-6142	391	46	d	d	NOUN
ejpam-6142	391	47	)	)	PUNCT
ejpam-6142	391	48	figure	figure	NOUN
ejpam-6142	391	49	2	2	NUM
ejpam-6142	391	50	illustrates	illustrate	VERB
ejpam-6142	391	51	that	that	SCONJ
ejpam-6142	391	52	the	the	DET
ejpam-6142	391	53	non	non	ADJ
ejpam-6142	391	54	-	-	ADJ
ejpam-6142	391	55	normalization	normalization	ADJ
ejpam-6142	391	56	technique	technique	NOUN
ejpam-6142	391	57	significantly	significantly	ADV
ejpam-6142	391	58	affects	affect	VERB
ejpam-6142	391	59	the	the	DET
ejpam-6142	391	60	sensitivity	sensitivity	NOUN
ejpam-6142	391	61	of	of	ADP
ejpam-6142	391	62	almost	almost	ADV
ejpam-6142	391	63	all	all	PRON
ejpam-6142	391	64	of	of	ADP
ejpam-6142	391	65	the	the	DET
ejpam-6142	391	66	model	model	NOUN
ejpam-6142	391	67	’s	’s	PART
ejpam-6142	391	68	variables	variable	NOUN
ejpam-6142	391	69	to	to	ADP
ejpam-6142	391	70	the	the	DET
ejpam-6142	391	71	model	model	NOUN
ejpam-6142	391	72	parameters	parameters	PROPN
ejpam-6142	391	73	η	η	PROPN
ejpam-6142	391	74	,	,	PUNCT
ejpam-6142	391	75	µ	µ	PRON
ejpam-6142	391	76	,	,	PUNCT
ejpam-6142	391	77	αm	αm	INTJ
ejpam-6142	391	78	,	,	PUNCT
ejpam-6142	391	79	γf	γf	ADJ
ejpam-6142	391	80	,	,	PUNCT
ejpam-6142	391	81	γm	γm	ADJ
ejpam-6142	391	82	,	,	PUNCT
ejpam-6142	391	83	θf	θf	INTJ
ejpam-6142	391	84	,	,	PUNCT
ejpam-6142	391	85	and	and	CCONJ
ejpam-6142	391	86	θm	θm	PROPN
ejpam-6142	391	87	,	,	PUNCT
ejpam-6142	391	88	while	while	SCONJ
ejpam-6142	391	89	they	they	PRON
ejpam-6142	391	90	are	be	AUX
ejpam-6142	391	91	less	less	ADV
ejpam-6142	391	92	sensitive	sensitive	ADJ
ejpam-6142	391	93	with	with	ADP
ejpam-6142	391	94	the	the	DET
ejpam-6142	391	95	rest	rest	NOUN
ejpam-6142	391	96	parameters	parameter	NOUN
ejpam-6142	391	97	of	of	ADP
ejpam-6142	391	98	the	the	DET
ejpam-6142	391	99	model	model	NOUN
ejpam-6142	391	100	;	;	PUNCT
ejpam-6142	391	101	see	see	VERB
ejpam-6142	391	102	figure	figure	NOUN
ejpam-6142	391	103	2(a	2(a	NUM
ejpam-6142	391	104	)	)	PUNCT
ejpam-6142	391	105	.	.	PUNCT
ejpam-6142	392	1	in	in	ADP
ejpam-6142	392	2	addition	addition	NOUN
ejpam-6142	392	3	,	,	PUNCT
ejpam-6142	392	4	the	the	DET
ejpam-6142	392	5	half	half	ADJ
ejpam-6142	392	6	-	-	PUNCT
ejpam-6142	392	7	normalization	normalization	NOUN
ejpam-6142	392	8	method	method	NOUN
ejpam-6142	392	9	depicts	depict	VERB
ejpam-6142	392	10	that	that	SCONJ
ejpam-6142	392	11	the	the	DET
ejpam-6142	392	12	model	model	NOUN
ejpam-6142	392	13	states	state	VERB
ejpam-6142	392	14	sf	sf	PROPN
ejpam-6142	392	15	and	and	CCONJ
ejpam-6142	392	16	sm	sm	PROPN
ejpam-6142	392	17	are	be	AUX
ejpam-6142	392	18	highly	highly	ADV
ejpam-6142	392	19	sensitive	sensitive	ADJ
ejpam-6142	392	20	to	to	ADP
ejpam-6142	392	21	the	the	DET
ejpam-6142	392	22	parameters	parameter	NOUN
ejpam-6142	392	23	of	of	ADP
ejpam-6142	392	24	the	the	DET
ejpam-6142	392	25	model	model	NOUN
ejpam-6142	392	26	βf	βf	CCONJ
ejpam-6142	392	27	and	and	CCONJ
ejpam-6142	392	28	βm	βm	VERB
ejpam-6142	392	29	respectively	respectively	ADV
ejpam-6142	392	30	,	,	PUNCT
ejpam-6142	392	31	whereas	whereas	SCONJ
ejpam-6142	392	32	the	the	DET
ejpam-6142	392	33	other	other	ADJ
ejpam-6142	392	34	system	system	NOUN
ejpam-6142	392	35	variables	variable	NOUN
ejpam-6142	392	36	are	be	AUX
ejpam-6142	392	37	less	less	ADV
ejpam-6142	392	38	sensitive	sensitive	ADJ
ejpam-6142	392	39	to	to	ADP
ejpam-6142	392	40	the	the	DET
ejpam-6142	392	41	system	system	NOUN
ejpam-6142	392	42	parameters	parameter	NOUN
ejpam-6142	392	43	;	;	PUNCT
ejpam-6142	392	44	see	see	VERB
ejpam-6142	392	45	figures	figure	NOUN
ejpam-6142	392	46	2(b)and	2(b)and	PRON
ejpam-6142	392	47	2(c	2(c	NUM
ejpam-6142	392	48	)	)	PUNCT
ejpam-6142	392	49	.	.	PUNCT
ejpam-6142	393	1	finally	finally	ADV
ejpam-6142	393	2	,	,	PUNCT
ejpam-6142	393	3	by	by	ADP
ejpam-6142	393	4	utilizing	utilize	VERB
ejpam-6142	393	5	the	the	DET
ejpam-6142	393	6	full	full	ADJ
ejpam-6142	393	7	-	-	PUNCT
ejpam-6142	393	8	normalization	normalization	NOUN
ejpam-6142	393	9	technique	technique	NOUN
ejpam-6142	393	10	demonstrates	demonstrate	VERB
ejpam-6142	393	11	that	that	SCONJ
ejpam-6142	393	12	almost	almost	ADV
ejpam-6142	393	13	all	all	DET
ejpam-6142	393	14	model	model	NOUN
ejpam-6142	393	15	variables	variable	NOUN
ejpam-6142	393	16	are	be	AUX
ejpam-6142	393	17	extremely	extremely	ADV
ejpam-6142	393	18	sensitive	sensitive	ADJ
ejpam-6142	393	19	to	to	ADP
ejpam-6142	393	20	the	the	DET
ejpam-6142	393	21	parameters	parameter	NOUN
ejpam-6142	393	22	of	of	ADP
ejpam-6142	393	23	the	the	DET
ejpam-6142	393	24	model	model	PROPN
ejpam-6142	393	25	λ	λ	PROPN
ejpam-6142	393	26	,	,	PUNCT
ejpam-6142	393	27	η	η	PROPN
ejpam-6142	393	28	,	,	PUNCT
ejpam-6142	393	29	µ	µ	NOUN
ejpam-6142	393	30	,	,	PUNCT
ejpam-6142	393	31	αf	αf	X
ejpam-6142	393	32	,	,	PUNCT
ejpam-6142	393	33	αm	αm	INTJ
ejpam-6142	393	34	,	,	PUNCT
ejpam-6142	393	35	γf	γf	ADJ
ejpam-6142	393	36	,	,	PUNCT
ejpam-6142	393	37	γm	γm	ADJ
ejpam-6142	393	38	,	,	PUNCT
ejpam-6142	393	39	θf	θf	INTJ
ejpam-6142	393	40	,	,	PUNCT
ejpam-6142	393	41	θm	θm	PROPN
ejpam-6142	393	42	,	,	PUNCT
ejpam-6142	393	43	λf	λf	ADV
ejpam-6142	393	44	,	,	PUNCT
ejpam-6142	393	45	and	and	CCONJ
ejpam-6142	393	46	λm	λm	ADP
ejpam-6142	393	47	,	,	PUNCT
ejpam-6142	393	48	while	while	SCONJ
ejpam-6142	393	49	they	they	PRON
ejpam-6142	393	50	are	be	AUX
ejpam-6142	393	51	less	less	ADV
ejpam-6142	393	52	sensitive	sensitive	ADJ
ejpam-6142	393	53	to	to	ADP
ejpam-6142	393	54	the	the	DET
ejpam-6142	393	55	other	other	ADJ
ejpam-6142	393	56	model	model	NOUN
ejpam-6142	393	57	parameters	parameter	NOUN
ejpam-6142	393	58	,	,	PUNCT
ejpam-6142	393	59	as	as	SCONJ
ejpam-6142	393	60	shown	show	VERB
ejpam-6142	393	61	in	in	ADP
ejpam-6142	393	62	figure	figure	NOUN
ejpam-6142	393	63	2(d	2(d	NUM
ejpam-6142	393	64	)	)	PUNCT
ejpam-6142	393	65	.	.	PUNCT
ejpam-6142	394	1	7	7	X
ejpam-6142	394	2	.	.	X
ejpam-6142	394	3	optimal	optimal	ADJ
ejpam-6142	394	4	control	control	NOUN
ejpam-6142	394	5	in	in	ADP
ejpam-6142	394	6	this	this	DET
ejpam-6142	394	7	section	section	NOUN
ejpam-6142	394	8	,	,	PUNCT
ejpam-6142	394	9	we	we	PRON
ejpam-6142	394	10	incorporate	incorporate	VERB
ejpam-6142	394	11	three	three	NUM
ejpam-6142	394	12	time	time	NOUN
ejpam-6142	394	13	-	-	PUNCT
ejpam-6142	394	14	dependent	dependent	ADJ
ejpam-6142	394	15	control	control	NOUN
ejpam-6142	394	16	strategies	strategy	NOUN
ejpam-6142	394	17	to	to	ADP
ejpam-6142	394	18	our	our	PRON
ejpam-6142	394	19	model	model	NOUN
ejpam-6142	394	20	1	1	NUM
ejpam-6142	394	21	with	with	ADP
ejpam-6142	394	22	the	the	DET
ejpam-6142	394	23	goal	goal	NOUN
ejpam-6142	394	24	of	of	ADP
ejpam-6142	394	25	determining	determine	VERB
ejpam-6142	394	26	the	the	DET
ejpam-6142	394	27	best	good	ADJ
ejpam-6142	394	28	effective	effective	ADJ
ejpam-6142	394	29	method	method	NOUN
ejpam-6142	394	30	for	for	ADP
ejpam-6142	394	31	controlling	control	VERB
ejpam-6142	394	32	and	and	CCONJ
ejpam-6142	394	33	reducing	reduce	VERB
ejpam-6142	394	34	the	the	DET
ejpam-6142	394	35	number	number	NOUN
ejpam-6142	394	36	of	of	ADP
ejpam-6142	394	37	people	people	NOUN
ejpam-6142	394	38	with	with	ADP
ejpam-6142	394	39	aids	aid	NOUN
ejpam-6142	394	40	within	within	ADP
ejpam-6142	394	41	a	a	DET
ejpam-6142	394	42	specific	specific	ADJ
ejpam-6142	394	43	period	period	NOUN
ejpam-6142	394	44	of	of	ADP
ejpam-6142	394	45	time	time	NOUN
ejpam-6142	394	46	.	.	PUNCT
ejpam-6142	395	1	the	the	DET
ejpam-6142	395	2	optimum	optimum	ADJ
ejpam-6142	395	3	control	control	NOUN
ejpam-6142	395	4	problem	problem	NOUN
ejpam-6142	395	5	introduces	introduce	VERB
ejpam-6142	395	6	the	the	DET
ejpam-6142	395	7	use	use	NOUN
ejpam-6142	395	8	of	of	ADP
ejpam-6142	395	9	the	the	DET
ejpam-6142	395	10	following	follow	VERB
ejpam-6142	395	11	time	time	NOUN
ejpam-6142	395	12	-	-	PUNCT
ejpam-6142	395	13	dependent	dependent	ADJ
ejpam-6142	395	14	control	control	NOUN
ejpam-6142	395	15	measures	measure	NOUN
ejpam-6142	395	16	.	.	PUNCT
ejpam-6142	396	1	•	•	NUM
ejpam-6142	396	2	preventive	preventive	ADJ
ejpam-6142	396	3	control	control	NOUN
ejpam-6142	396	4	measure	measure	NOUN
ejpam-6142	396	5	:	:	PUNCT
ejpam-6142	396	6	symbolized	symbolize	VERB
ejpam-6142	396	7	by	by	ADP
ejpam-6142	396	8	u1	u1	NOUN
ejpam-6142	396	9	include	include	VERB
ejpam-6142	396	10	hiv	hiv	PROPN
ejpam-6142	396	11	/	/	SYM
ejpam-6142	396	12	aids	aids	PROPN
ejpam-6142	396	13	awareness	awareness	NOUN
ejpam-6142	396	14	and	and	CCONJ
ejpam-6142	396	15	s.	s.	PROPN
ejpam-6142	396	16	m.	m.	PROPN
ejpam-6142	396	17	fatah	fatah	PROPN
ejpam-6142	396	18	,	,	PUNCT
ejpam-6142	396	19	s.	s.	PROPN
ejpam-6142	396	20	h.	h.	PROPN
ejpam-6142	396	21	a.	a.	PROPN
ejpam-6142	396	22	khoshnaw	khoshnaw	PROPN
ejpam-6142	396	23	,	,	PUNCT
ejpam-6142	396	24	a.	a.	PROPN
ejpam-6142	396	25	n.	n.	PROPN
ejpam-6142	396	26	mustafa	mustafa	PROPN
ejpam-6142	396	27	/	/	SYM
ejpam-6142	396	28	eur	eur	PROPN
ejpam-6142	396	29	.	.	PUNCT
ejpam-6142	397	1	j.	j.	PROPN
ejpam-6142	397	2	pure	pure	PROPN
ejpam-6142	397	3	appl	appl	PROPN
ejpam-6142	397	4	.	.	PROPN
ejpam-6142	397	5	math	math	PROPN
ejpam-6142	397	6	,	,	PUNCT
ejpam-6142	397	7	18	18	NUM
ejpam-6142	397	8	(	(	PUNCT
ejpam-6142	397	9	2	2	NUM
ejpam-6142	397	10	)	)	PUNCT
ejpam-6142	397	11	(	(	PUNCT
ejpam-6142	397	12	2025	2025	NUM
ejpam-6142	397	13	)	)	PUNCT
ejpam-6142	397	14	,	,	PUNCT
ejpam-6142	397	15	6142	6142	NUM
ejpam-6142	397	16	18	18	NUM
ejpam-6142	397	17	of	of	ADP
ejpam-6142	397	18	33	33	NUM
ejpam-6142	397	19	education	education	NOUN
ejpam-6142	397	20	campaigns	campaign	NOUN
ejpam-6142	397	21	through	through	ADP
ejpam-6142	397	22	health	health	NOUN
ejpam-6142	397	23	centers	center	NOUN
ejpam-6142	397	24	and	and	CCONJ
ejpam-6142	397	25	social	social	ADJ
ejpam-6142	397	26	media	medium	NOUN
ejpam-6142	397	27	to	to	PART
ejpam-6142	397	28	safeguard	safeguard	VERB
ejpam-6142	397	29	the	the	DET
ejpam-6142	397	30	individuals	individual	NOUN
ejpam-6142	397	31	who	who	PRON
ejpam-6142	397	32	are	be	AUX
ejpam-6142	397	33	unaware	unaware	ADJ
ejpam-6142	397	34	of	of	ADP
ejpam-6142	397	35	their	their	PRON
ejpam-6142	397	36	susceptibility	susceptibility	NOUN
ejpam-6142	397	37	to	to	ADP
ejpam-6142	397	38	hiv	hiv	PROPN
ejpam-6142	397	39	.	.	PUNCT
ejpam-6142	398	1	•	•	PUNCT
ejpam-6142	398	2	screening	screen	VERB
ejpam-6142	398	3	control	control	NOUN
ejpam-6142	398	4	measure	measure	NOUN
ejpam-6142	398	5	:	:	PUNCT
ejpam-6142	398	6	denoted	denote	VERB
ejpam-6142	398	7	by	by	ADP
ejpam-6142	398	8	u2	u2	PROPN
ejpam-6142	398	9	to	to	PART
ejpam-6142	398	10	assist	assist	VERB
ejpam-6142	398	11	undiagnosed	undiagnosed	ADJ
ejpam-6142	398	12	infected	infect	VERB
ejpam-6142	398	13	persons	person	NOUN
ejpam-6142	398	14	in	in	ADP
ejpam-6142	398	15	screening	screen	VERB
ejpam-6142	398	16	themselves	themselves	PRON
ejpam-6142	398	17	.	.	PUNCT
ejpam-6142	399	1	•	•	NUM
ejpam-6142	399	2	treatment	treatment	NOUN
ejpam-6142	399	3	control	control	NOUN
ejpam-6142	399	4	measure	measure	NOUN
ejpam-6142	399	5	,	,	PUNCT
ejpam-6142	399	6	represented	represent	VERB
ejpam-6142	399	7	by	by	ADP
ejpam-6142	399	8	u3	u3	NOUN
ejpam-6142	399	9	,	,	PUNCT
ejpam-6142	399	10	is	be	AUX
ejpam-6142	399	11	utilized	utilize	VERB
ejpam-6142	399	12	by	by	ADP
ejpam-6142	399	13	patients	patient	NOUN
ejpam-6142	399	14	to	to	PART
ejpam-6142	399	15	reduce	reduce	VERB
ejpam-6142	399	16	viral	viral	ADJ
ejpam-6142	399	17	load	load	NOUN
ejpam-6142	399	18	in	in	ADP
ejpam-6142	399	19	the	the	DET
ejpam-6142	399	20	body	body	NOUN
ejpam-6142	399	21	and	and	CCONJ
ejpam-6142	399	22	prevent	prevent	VERB
ejpam-6142	399	23	virus	virus	NOUN
ejpam-6142	399	24	progression	progression	NOUN
ejpam-6142	399	25	.	.	PUNCT
ejpam-6142	400	1	integrating	integrate	VERB
ejpam-6142	400	2	the	the	DET
ejpam-6142	400	3	control	control	NOUN
ejpam-6142	400	4	measures	measure	NOUN
ejpam-6142	400	5	u1	u1	NOUN
ejpam-6142	400	6	,	,	PUNCT
ejpam-6142	400	7	u2	u2	NOUN
ejpam-6142	400	8	and	and	CCONJ
ejpam-6142	400	9	u3	u3	NOUN
ejpam-6142	400	10	into	into	ADP
ejpam-6142	400	11	model	model	NOUN
ejpam-6142	400	12	1	1	NUM
ejpam-6142	400	13	yields	yield	NOUN
ejpam-6142	400	14	the	the	DET
ejpam-6142	400	15	optimal	optimal	ADJ
ejpam-6142	400	16	control	control	NOUN
ejpam-6142	400	17	model	model	NOUN
ejpam-6142	400	18	that	that	PRON
ejpam-6142	400	19	results	result	VERB
ejpam-6142	400	20	as	as	SCONJ
ejpam-6142	400	21	follows	follow	VERB
ejpam-6142	400	22	:	:	PUNCT
ejpam-6142	401	1	dsf	dsf	NOUN
ejpam-6142	401	2	dt	dt	NOUN
ejpam-6142	401	3	=	=	SYM
ejpam-6142	401	4	λ−	λ−	PROPN
ejpam-6142	401	5	(	(	PUNCT
ejpam-6142	401	6	1−	1−	NUM
ejpam-6142	401	7	u1	u1	NOUN
ejpam-6142	401	8	)	)	PUNCT
ejpam-6142	401	9	(	(	PUNCT
ejpam-6142	401	10	1−	1−	NUM
ejpam-6142	401	11	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	401	12	−	−	PROPN
ejpam-6142	401	13	ηsf	ηsf	INTJ
ejpam-6142	401	14	dsm	dsm	PROPN
ejpam-6142	401	15	dt	dt	PROPN
ejpam-6142	402	1	=	=	SYM
ejpam-6142	402	2	λ−	λ−	PROPN
ejpam-6142	402	3	(	(	PUNCT
ejpam-6142	402	4	1−	1−	NUM
ejpam-6142	402	5	u1	u1	NOUN
ejpam-6142	402	6	)	)	PUNCT
ejpam-6142	402	7	(	(	PUNCT
ejpam-6142	402	8	1−	1−	NUM
ejpam-6142	402	9	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	402	10	−	−	PROPN
ejpam-6142	402	11	ηsm	ηsm	NOUN
ejpam-6142	402	12	def	def	NOUN
ejpam-6142	402	13	dt	dt	X
ejpam-6142	402	14	=	=	SYM
ejpam-6142	402	15	(	(	PUNCT
ejpam-6142	402	16	1−	1−	NUM
ejpam-6142	402	17	u1	u1	NOUN
ejpam-6142	402	18	)	)	PUNCT
ejpam-6142	402	19	(	(	PUNCT
ejpam-6142	402	20	1−	1−	NUM
ejpam-6142	402	21	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	402	22	−	−	PROPN
ejpam-6142	402	23	(	(	PUNCT
ejpam-6142	402	24	αf	αf	ADP
ejpam-6142	402	25	+	+	CCONJ
ejpam-6142	403	1	η)ef	η)ef	PROPN
ejpam-6142	403	2	dem	dem	ADJ
ejpam-6142	403	3	dt	dt	X
ejpam-6142	403	4	=	=	SYM
ejpam-6142	403	5	(	(	PUNCT
ejpam-6142	403	6	1−	1−	NUM
ejpam-6142	403	7	u1	u1	NOUN
ejpam-6142	403	8	)	)	PUNCT
ejpam-6142	403	9	(	(	PUNCT
ejpam-6142	403	10	1−	1−	NUM
ejpam-6142	403	11	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	403	12	−	−	PROPN
ejpam-6142	404	1	(	(	PUNCT
ejpam-6142	404	2	αm	αm	NOUN
ejpam-6142	404	3	+	+	CCONJ
ejpam-6142	405	1	η)em	η)em	PROPN
ejpam-6142	405	2	dif	dif	ADV
ejpam-6142	405	3	dt	dt	X
ejpam-6142	405	4	=	=	SYM
ejpam-6142	405	5	αfef	αfef	NOUN
ejpam-6142	405	6	−	−	PROPN
ejpam-6142	406	1	(	(	PUNCT
ejpam-6142	406	2	u2	u2	PROPN
ejpam-6142	406	3	+	+	CCONJ
ejpam-6142	406	4	µ+	µ+	PROPN
ejpam-6142	406	5	η	η	PROPN
ejpam-6142	406	6	+	+	PROPN
ejpam-6142	406	7	γf	γf	PROPN
ejpam-6142	407	1	+	+	CCONJ
ejpam-6142	407	2	θf	θf	NOUN
ejpam-6142	407	3	)	)	PUNCT
ejpam-6142	407	4	if	if	SCONJ
ejpam-6142	407	5	dlm	dlm	PROPN
ejpam-6142	407	6	dt	dt	X
ejpam-6142	407	7	=	=	PUNCT
ejpam-6142	407	8	αmem	αmem	ADJ
ejpam-6142	407	9	−	−	PROPN
ejpam-6142	408	1	(	(	PUNCT
ejpam-6142	408	2	u2	u2	PROPN
ejpam-6142	408	3	+	+	CCONJ
ejpam-6142	408	4	µ+	µ+	PROPN
ejpam-6142	408	5	η	η	PROPN
ejpam-6142	408	6	+	+	X
ejpam-6142	408	7	γm	γm	PROPN
ejpam-6142	408	8	+	+	NUM
ejpam-6142	408	9	θm	θm	NOUN
ejpam-6142	408	10	)	)	PUNCT
ejpam-6142	408	11	i	i	PROPN
ejpam-6142	408	12	m	m	VERB
ejpam-6142	408	13	ddf	ddf	NOUN
ejpam-6142	408	14	dt	dt	PROPN
ejpam-6142	409	1	=	=	PUNCT
ejpam-6142	409	2	(	(	PUNCT
ejpam-6142	409	3	u2	u2	PROPN
ejpam-6142	409	4	+	+	CCONJ
ejpam-6142	409	5	γf	γf	PROPN
ejpam-6142	409	6	)	)	PUNCT
ejpam-6142	409	7	if	if	SCONJ
ejpam-6142	409	8	−	−	PROPN
ejpam-6142	409	9	(	(	PUNCT
ejpam-6142	409	10	u3	u3	NOUN
ejpam-6142	409	11	+	+	CCONJ
ejpam-6142	409	12	µ+	µ+	PROPN
ejpam-6142	409	13	η	η	PROPN
ejpam-6142	409	14	+	+	PROPN
ejpam-6142	409	15	ρf	ρf	X
ejpam-6142	409	16	)	)	PUNCT
ejpam-6142	409	17	df	df	PROPN
ejpam-6142	409	18	ddm	ddm	PROPN
ejpam-6142	409	19	dt	dt	PROPN
ejpam-6142	409	20	=	=	PUNCT
ejpam-6142	409	21	(	(	PUNCT
ejpam-6142	409	22	u2	u2	PROPN
ejpam-6142	409	23	+	+	CCONJ
ejpam-6142	409	24	γm	γm	NOUN
ejpam-6142	409	25	)	)	PUNCT
ejpam-6142	410	1	i	i	PRON
ejpam-6142	410	2	m	m	VERB
ejpam-6142	410	3	−	−	NOUN
ejpam-6142	410	4	(	(	PUNCT
ejpam-6142	410	5	u3	u3	NOUN
ejpam-6142	410	6	+	+	CCONJ
ejpam-6142	410	7	µ+	µ+	PROPN
ejpam-6142	410	8	η	η	PROPN
ejpam-6142	410	9	+	+	PROPN
ejpam-6142	410	10	ρm)dm	ρm)dm	PROPN
ejpam-6142	410	11	dtf	dtf	PROPN
ejpam-6142	410	12	dt	dt	NOUN
ejpam-6142	410	13	=	=	PUNCT
ejpam-6142	410	14	u3af	u3af	X
ejpam-6142	410	15	+	+	CCONJ
ejpam-6142	410	16	(	(	PUNCT
ejpam-6142	410	17	u3	u3	NOUN
ejpam-6142	410	18	+	+	CCONJ
ejpam-6142	410	19	ρf	ρf	NOUN
ejpam-6142	410	20	)	)	PUNCT
ejpam-6142	410	21	df	df	PROPN
ejpam-6142	410	22	−	−	PROPN
ejpam-6142	410	23	(	(	PUNCT
ejpam-6142	410	24	µ+	µ+	PROPN
ejpam-6142	410	25	η	η	PROPN
ejpam-6142	410	26	+	+	PROPN
ejpam-6142	410	27	(	(	PUNCT
ejpam-6142	410	28	1−	1−	NUM
ejpam-6142	410	29	u3)ωf	u3)ωf	ADJ
ejpam-6142	410	30	)	)	PUNCT
ejpam-6142	411	1	tf	tf	PROPN
ejpam-6142	411	2	dtm	dtm	PROPN
ejpam-6142	411	3	dt	dt	PROPN
ejpam-6142	411	4	=	=	PUNCT
ejpam-6142	411	5	u3am	u3am	PUNCT
ejpam-6142	412	1	+	+	CCONJ
ejpam-6142	412	2	(	(	PUNCT
ejpam-6142	412	3	u3	u3	NOUN
ejpam-6142	412	4	+	+	CCONJ
ejpam-6142	412	5	ρm)dm	ρm)dm	NUM
ejpam-6142	412	6	−	−	PROPN
ejpam-6142	412	7	(	(	PUNCT
ejpam-6142	412	8	µ+	µ+	X
ejpam-6142	412	9	η	η	PROPN
ejpam-6142	412	10	+	+	PROPN
ejpam-6142	412	11	(	(	PUNCT
ejpam-6142	412	12	1−	1−	NUM
ejpam-6142	412	13	u3)ωm)tm	u3)ωm)tm	NOUN
ejpam-6142	412	14	duf	duf	NOUN
ejpam-6142	412	15	dt	dt	NOUN
ejpam-6142	412	16	=	=	PROPN
ejpam-6142	412	17	θfif	θfif	PROPN
ejpam-6142	412	18	−	−	PROPN
ejpam-6142	412	19	(	(	PUNCT
ejpam-6142	412	20	µ+	µ+	X
ejpam-6142	412	21	η	η	PROPN
ejpam-6142	412	22	+	+	PROPN
ejpam-6142	412	23	λf	λf	PROPN
ejpam-6142	412	24	)	)	PUNCT
ejpam-6142	412	25	uf	uf	PROPN
ejpam-6142	412	26	dum	dum	NOUN
ejpam-6142	412	27	dt	dt	X
ejpam-6142	412	28	=	=	SYM
ejpam-6142	412	29	θmim	θmim	PROPN
ejpam-6142	412	30	−	−	PROPN
ejpam-6142	412	31	(	(	PUNCT
ejpam-6142	412	32	µ+	µ+	X
ejpam-6142	412	33	η	η	PROPN
ejpam-6142	412	34	+	+	PROPN
ejpam-6142	412	35	λm)um	λm)um	X
ejpam-6142	413	1	dtf	dtf	NOUN
ejpam-6142	413	2	dt	dt	NOUN
ejpam-6142	414	1	=	=	PUNCT
ejpam-6142	415	1	λfuf	λfuf	PROPN
ejpam-6142	416	1	+	+	CCONJ
ejpam-6142	417	1	(	(	PUNCT
ejpam-6142	417	2	1−	1−	NUM
ejpam-6142	417	3	u3)ωftf	u3)ωftf	NOUN
ejpam-6142	417	4	−	−	PROPN
ejpam-6142	417	5	(	(	PUNCT
ejpam-6142	417	6	u3	u3	NOUN
ejpam-6142	417	7	+	+	CCONJ
ejpam-6142	417	8	µ+	µ+	PROPN
ejpam-6142	417	9	η)af	η)af	PROPN
ejpam-6142	417	10	dam	dam	NOUN
ejpam-6142	417	11	dt	dt	NOUN
ejpam-6142	417	12	=	=	PUNCT
ejpam-6142	417	13	λmum	λmum	ADJ
ejpam-6142	417	14	+	+	CCONJ
ejpam-6142	417	15	(	(	PUNCT
ejpam-6142	417	16	1−	1−	NUM
ejpam-6142	417	17	u3)ωmtm	u3)ωmtm	PROPN
ejpam-6142	417	18	−	−	PROPN
ejpam-6142	417	19	(	(	PUNCT
ejpam-6142	417	20	u3	u3	NOUN
ejpam-6142	417	21	+	+	CCONJ
ejpam-6142	417	22	µ+	µ+	PROPN
ejpam-6142	417	23	η)am	η)am	PROPN
ejpam-6142	417	24	(	(	PUNCT
ejpam-6142	417	25	4	4	NUM
ejpam-6142	417	26	)	)	PUNCT
ejpam-6142	417	27	where	where	SCONJ
ejpam-6142	417	28	ef	ef	PROPN
ejpam-6142	417	29	(	(	PUNCT
ejpam-6142	417	30	0	0	NUM
ejpam-6142	417	31	)	)	PUNCT
ejpam-6142	417	32	,	,	PUNCT
ejpam-6142	417	33	em(0	em(0	NOUN
ejpam-6142	417	34	)	)	PUNCT
ejpam-6142	417	35	,	,	PUNCT
ejpam-6142	417	36	if	if	SCONJ
ejpam-6142	417	37	(	(	PUNCT
ejpam-6142	417	38	0	0	NUM
ejpam-6142	417	39	)	)	PUNCT
ejpam-6142	417	40	,	,	PUNCT
ejpam-6142	417	41	im(0	im(0	NOUN
ejpam-6142	417	42	)	)	PUNCT
ejpam-6142	417	43	,	,	PUNCT
ejpam-6142	417	44	df	df	PROPN
ejpam-6142	417	45	(	(	PUNCT
ejpam-6142	417	46	0	0	NUM
ejpam-6142	417	47	)	)	PUNCT
ejpam-6142	417	48	,	,	PUNCT
ejpam-6142	417	49	dm(0	dm(0	NOUN
ejpam-6142	417	50	)	)	PUNCT
ejpam-6142	417	51	,	,	PUNCT
ejpam-6142	417	52	tf	tf	X
ejpam-6142	417	53	(	(	PUNCT
ejpam-6142	417	54	0	0	NUM
ejpam-6142	417	55	)	)	PUNCT
ejpam-6142	417	56	,	,	PUNCT
ejpam-6142	417	57	tm(0	tm(0	NOUN
ejpam-6142	417	58	)	)	PUNCT
ejpam-6142	417	59	,	,	PUNCT
ejpam-6142	417	60	uf	uf	PROPN
ejpam-6142	417	61	(	(	PUNCT
ejpam-6142	417	62	0	0	NUM
ejpam-6142	417	63	)	)	PUNCT
ejpam-6142	417	64	,	,	PUNCT
ejpam-6142	417	65	um(0	um(0	NOUN
ejpam-6142	417	66	)	)	PUNCT
ejpam-6142	417	67	,	,	PUNCT
ejpam-6142	417	68	af	af	PROPN
ejpam-6142	417	69	(	(	PUNCT
ejpam-6142	417	70	0	0	NUM
ejpam-6142	417	71	)	)	PUNCT
ejpam-6142	417	72	,	,	PUNCT
ejpam-6142	417	73	am(0	am(0	NOUN
ejpam-6142	417	74	)	)	PUNCT
ejpam-6142	417	75	≥	≥	NOUN
ejpam-6142	417	76	0	0	NUM
ejpam-6142	417	77	.	.	PUNCT
ejpam-6142	418	1	s.	s.	PROPN
ejpam-6142	418	2	m.	m.	PROPN
ejpam-6142	418	3	fatah	fatah	PROPN
ejpam-6142	418	4	,	,	PUNCT
ejpam-6142	418	5	s.	s.	PROPN
ejpam-6142	418	6	h.	h.	PROPN
ejpam-6142	418	7	a.	a.	PROPN
ejpam-6142	418	8	khoshnaw	khoshnaw	PROPN
ejpam-6142	418	9	,	,	PUNCT
ejpam-6142	418	10	a.	a.	PROPN
ejpam-6142	418	11	n.	n.	PROPN
ejpam-6142	418	12	mustafa	mustafa	PROPN
ejpam-6142	418	13	/	/	SYM
ejpam-6142	418	14	eur	eur	PROPN
ejpam-6142	418	15	.	.	PUNCT
ejpam-6142	419	1	j.	j.	PROPN
ejpam-6142	419	2	pure	pure	PROPN
ejpam-6142	419	3	appl	appl	PROPN
ejpam-6142	419	4	.	.	PROPN
ejpam-6142	419	5	math	math	PROPN
ejpam-6142	419	6	,	,	PUNCT
ejpam-6142	419	7	18	18	NUM
ejpam-6142	419	8	(	(	PUNCT
ejpam-6142	419	9	2	2	NUM
ejpam-6142	419	10	)	)	PUNCT
ejpam-6142	419	11	(	(	PUNCT
ejpam-6142	419	12	2025	2025	NUM
ejpam-6142	419	13	)	)	PUNCT
ejpam-6142	419	14	,	,	PUNCT
ejpam-6142	419	15	6142	6142	NUM
ejpam-6142	419	16	19	19	NUM
ejpam-6142	419	17	of	of	ADP
ejpam-6142	419	18	33	33	NUM
ejpam-6142	419	19	to	to	PART
ejpam-6142	419	20	analyze	analyze	VERB
ejpam-6142	419	21	the	the	DET
ejpam-6142	419	22	levels	level	NOUN
ejpam-6142	419	23	of	of	ADP
ejpam-6142	419	24	optimal	optimal	ADJ
ejpam-6142	419	25	controls	control	NOUN
ejpam-6142	419	26	,	,	PUNCT
ejpam-6142	419	27	it	it	PRON
ejpam-6142	419	28	is	be	AUX
ejpam-6142	419	29	necessary	necessary	ADJ
ejpam-6142	419	30	to	to	PART
ejpam-6142	419	31	establish	establish	VERB
ejpam-6142	419	32	the	the	DET
ejpam-6142	419	33	set	set	ADJ
ejpam-6142	419	34	u	u	NOUN
ejpam-6142	419	35	of	of	ADP
ejpam-6142	419	36	lebesgue	lebesgue	PROPN
ejpam-6142	419	37	measurable	measurable	ADJ
ejpam-6142	419	38	controls	control	VERB
ejpam-6142	419	39	u	u	NOUN
ejpam-6142	419	40	=	=	PRON
ejpam-6142	419	41	{	{	PUNCT
ejpam-6142	419	42	(	(	PUNCT
ejpam-6142	419	43	u1(t	u1(t	PROPN
ejpam-6142	419	44	)	)	PUNCT
ejpam-6142	419	45	,	,	PUNCT
ejpam-6142	419	46	u2(t	u2(t	PROPN
ejpam-6142	419	47	)	)	PUNCT
ejpam-6142	419	48	,	,	PUNCT
ejpam-6142	419	49	u3(t	u3(t	PROPN
ejpam-6142	419	50	)	)	PUNCT
ejpam-6142	419	51	)	)	PUNCT
ejpam-6142	419	52	:	:	PUNCT
ejpam-6142	419	53	0	0	NUM
ejpam-6142	419	54	≤	≤	NUM
ejpam-6142	419	55	u1	u1	NOUN
ejpam-6142	419	56	≤	≤	ADV
ejpam-6142	419	57	1	1	NUM
ejpam-6142	419	58	,	,	PUNCT
ejpam-6142	419	59	0	0	NUM
ejpam-6142	419	60	≤	≤	NUM
ejpam-6142	419	61	u2	u2	PROPN
ejpam-6142	419	62	≤	≤	NUM
ejpam-6142	419	63	1	1	NUM
ejpam-6142	419	64	,	,	PUNCT
ejpam-6142	419	65	0	0	NUM
ejpam-6142	419	66	≤	≤	NUM
ejpam-6142	419	67	u3	u3	NOUN
ejpam-6142	419	68	≤	≤	NUM
ejpam-6142	419	69	1	1	NUM
ejpam-6142	419	70	,	,	PUNCT
ejpam-6142	419	71	0	0	NUM
ejpam-6142	419	72	≤	≤	NUM
ejpam-6142	419	73	t	t	NOUN
ejpam-6142	419	74	≤	≤	NUM
ejpam-6142	419	75	tf	tf	NUM
ejpam-6142	419	76	}	}	PUNCT
ejpam-6142	419	77	.	.	PUNCT
ejpam-6142	420	1	the	the	DET
ejpam-6142	420	2	objective	objective	ADJ
ejpam-6142	420	3	functional	functional	NOUN
ejpam-6142	420	4	used	use	VERB
ejpam-6142	420	5	in	in	ADP
ejpam-6142	420	6	this	this	DET
ejpam-6142	420	7	paper	paper	NOUN
ejpam-6142	420	8	extends	extend	VERB
ejpam-6142	420	9	the	the	DET
ejpam-6142	420	10	hiv	hiv	PROPN
ejpam-6142	420	11	control	control	PROPN
ejpam-6142	420	12	framework	framework	NOUN
ejpam-6142	420	13	[	[	X
ejpam-6142	420	14	1	1	NUM
ejpam-6142	420	15	,	,	PUNCT
ejpam-6142	420	16	18	18	NUM
ejpam-6142	420	17	]	]	PUNCT
ejpam-6142	420	18	.	.	PUNCT
ejpam-6142	421	1	by	by	ADP
ejpam-6142	421	2	incorporating	incorporate	VERB
ejpam-6142	421	3	gender	gender	NOUN
ejpam-6142	421	4	-	-	PUNCT
ejpam-6142	421	5	stratified	stratify	VERB
ejpam-6142	421	6	compartments	compartment	NOUN
ejpam-6142	421	7	(	(	PUNCT
ejpam-6142	421	8	sf	sf	INTJ
ejpam-6142	421	9	,	,	PUNCT
ejpam-6142	421	10	ef	ef	PROPN
ejpam-6142	421	11	,	,	PUNCT
ejpam-6142	421	12	if	if	SCONJ
ejpam-6142	421	13	,	,	PUNCT
ejpam-6142	421	14	df	df	PROPN
ejpam-6142	421	15	,	,	PUNCT
ejpam-6142	421	16	tf	tf	INTJ
ejpam-6142	421	17	,	,	PUNCT
ejpam-6142	421	18	uf	uf	PROPN
ejpam-6142	421	19	,	,	PUNCT
ejpam-6142	421	20	af	af	PROPN
ejpam-6142	421	21	,	,	PUNCT
ejpam-6142	421	22	sm	sm	PROPN
ejpam-6142	421	23	,	,	PUNCT
ejpam-6142	421	24	em	em	PRON
ejpam-6142	421	25	,	,	PUNCT
ejpam-6142	421	26	i	i	PRON
ejpam-6142	421	27	m	m	PROPN
ejpam-6142	421	28	,	,	PUNCT
ejpam-6142	421	29	dm	dm	PROPN
ejpam-6142	421	30	,	,	PUNCT
ejpam-6142	421	31	tm	tm	NOUN
ejpam-6142	421	32	,	,	PUNCT
ejpam-6142	421	33	um	um	INTJ
ejpam-6142	421	34	,	,	PUNCT
ejpam-6142	421	35	am	be	AUX
ejpam-6142	421	36	)	)	PUNCT
ejpam-6142	421	37	and	and	CCONJ
ejpam-6142	421	38	three	three	NUM
ejpam-6142	421	39	intervention	intervention	NOUN
ejpam-6142	421	40	controls	control	NOUN
ejpam-6142	421	41	.	.	PUNCT
ejpam-6142	422	1	this	this	DET
ejpam-6142	422	2	work	work	NOUN
ejpam-6142	422	3	adopts	adopt	VERB
ejpam-6142	422	4	the	the	DET
ejpam-6142	422	5	pontryagin	pontryagin	NOUN
ejpam-6142	422	6	maximum	maximum	ADJ
ejpam-6142	422	7	principle	principle	NOUN
ejpam-6142	422	8	discussed	discuss	VERB
ejpam-6142	422	9	in	in	ADP
ejpam-6142	422	10	[	[	X
ejpam-6142	422	11	26	26	NUM
ejpam-6142	422	12	]	]	PUNCT
ejpam-6142	422	13	to	to	PART
ejpam-6142	422	14	derive	derive	VERB
ejpam-6142	422	15	necessary	necessary	ADJ
ejpam-6142	422	16	conditions	condition	NOUN
ejpam-6142	422	17	for	for	ADP
ejpam-6142	422	18	optimality	optimality	NOUN
ejpam-6142	422	19	.	.	PUNCT
ejpam-6142	423	1	the	the	DET
ejpam-6142	423	2	proposed	propose	VERB
ejpam-6142	423	3	control	control	NOUN
ejpam-6142	423	4	method	method	NOUN
ejpam-6142	423	5	applies	apply	VERB
ejpam-6142	423	6	the	the	DET
ejpam-6142	423	7	pontryagin	pontryagin	NOUN
ejpam-6142	423	8	maximum	maximum	ADJ
ejpam-6142	423	9	principle	principle	NOUN
ejpam-6142	423	10	to	to	ADP
ejpam-6142	423	11	a	a	DET
ejpam-6142	423	12	genderstratified	genderstratifie	VERB
ejpam-6142	423	13	hiv	hiv	PROPN
ejpam-6142	423	14	model	model	NOUN
ejpam-6142	423	15	,	,	PUNCT
ejpam-6142	423	16	enabling	enable	VERB
ejpam-6142	423	17	the	the	DET
ejpam-6142	423	18	derivation	derivation	NOUN
ejpam-6142	423	19	of	of	ADP
ejpam-6142	423	20	optimal	optimal	ADJ
ejpam-6142	423	21	intervention	intervention	NOUN
ejpam-6142	423	22	strategies	strategy	NOUN
ejpam-6142	423	23	across	across	ADP
ejpam-6142	423	24	three	three	NUM
ejpam-6142	423	25	control	control	NOUN
ejpam-6142	423	26	measures	measure	NOUN
ejpam-6142	423	27	:	:	PUNCT
ejpam-6142	423	28	prevention	prevention	NOUN
ejpam-6142	423	29	,	,	PUNCT
ejpam-6142	423	30	screening	screening	NOUN
ejpam-6142	423	31	,	,	PUNCT
ejpam-6142	423	32	and	and	CCONJ
ejpam-6142	423	33	treatment	treatment	NOUN
ejpam-6142	423	34	.	.	PUNCT
ejpam-6142	424	1	unlike	unlike	ADP
ejpam-6142	424	2	traditional	traditional	ADJ
ejpam-6142	424	3	control	control	NOUN
ejpam-6142	424	4	approaches	approach	NOUN
ejpam-6142	424	5	that	that	PRON
ejpam-6142	424	6	often	often	ADV
ejpam-6142	424	7	assume	assume	VERB
ejpam-6142	424	8	uniform	uniform	ADJ
ejpam-6142	424	9	populations	population	NOUN
ejpam-6142	424	10	or	or	CCONJ
ejpam-6142	424	11	apply	apply	VERB
ejpam-6142	424	12	single	single	ADJ
ejpam-6142	424	13	interventions	intervention	NOUN
ejpam-6142	424	14	in	in	ADP
ejpam-6142	424	15	isolation	isolation	NOUN
ejpam-6142	424	16	,	,	PUNCT
ejpam-6142	424	17	this	this	DET
ejpam-6142	424	18	method	method	NOUN
ejpam-6142	424	19	accounts	account	VERB
ejpam-6142	424	20	for	for	ADP
ejpam-6142	424	21	gender	gender	NOUN
ejpam-6142	424	22	-	-	PUNCT
ejpam-6142	424	23	specific	specific	ADJ
ejpam-6142	424	24	disease	disease	NOUN
ejpam-6142	424	25	dynamics	dynamic	NOUN
ejpam-6142	424	26	and	and	CCONJ
ejpam-6142	424	27	interaction	interaction	NOUN
ejpam-6142	424	28	patterns	pattern	NOUN
ejpam-6142	424	29	.	.	PUNCT
ejpam-6142	425	1	this	this	DET
ejpam-6142	425	2	stratification	stratification	NOUN
ejpam-6142	425	3	allows	allow	VERB
ejpam-6142	425	4	for	for	ADP
ejpam-6142	425	5	more	more	ADV
ejpam-6142	425	6	precise	precise	ADJ
ejpam-6142	425	7	targeting	targeting	NOUN
ejpam-6142	425	8	of	of	ADP
ejpam-6142	425	9	interventions	intervention	NOUN
ejpam-6142	425	10	,	,	PUNCT
ejpam-6142	425	11	improving	improve	VERB
ejpam-6142	425	12	the	the	DET
ejpam-6142	425	13	effectiveness	effectiveness	NOUN
ejpam-6142	425	14	of	of	ADP
ejpam-6142	425	15	resource	resource	NOUN
ejpam-6142	425	16	allocation	allocation	NOUN
ejpam-6142	425	17	.	.	PUNCT
ejpam-6142	426	1	additionally	additionally	ADV
ejpam-6142	426	2	,	,	PUNCT
ejpam-6142	426	3	by	by	ADP
ejpam-6142	426	4	formulating	formulate	VERB
ejpam-6142	426	5	the	the	DET
ejpam-6142	426	6	control	control	NOUN
ejpam-6142	426	7	problem	problem	NOUN
ejpam-6142	426	8	as	as	ADP
ejpam-6142	426	9	an	an	DET
ejpam-6142	426	10	optimal	optimal	ADJ
ejpam-6142	426	11	control	control	NOUN
ejpam-6142	426	12	system	system	NOUN
ejpam-6142	426	13	,	,	PUNCT
ejpam-6142	426	14	the	the	DET
ejpam-6142	426	15	method	method	NOUN
ejpam-6142	426	16	provides	provide	VERB
ejpam-6142	426	17	a	a	DET
ejpam-6142	426	18	rigorous	rigorous	ADJ
ejpam-6142	426	19	mathematical	mathematical	ADJ
ejpam-6142	426	20	framework	framework	NOUN
ejpam-6142	426	21	for	for	ADP
ejpam-6142	426	22	identifying	identify	VERB
ejpam-6142	426	23	time	time	NOUN
ejpam-6142	426	24	-	-	PUNCT
ejpam-6142	426	25	dependent	dependent	ADJ
ejpam-6142	426	26	strategies	strategy	NOUN
ejpam-6142	426	27	that	that	PRON
ejpam-6142	426	28	minimize	minimize	VERB
ejpam-6142	426	29	infection	infection	NOUN
ejpam-6142	426	30	levels	level	NOUN
ejpam-6142	426	31	.	.	PUNCT
ejpam-6142	427	1	our	our	PRON
ejpam-6142	427	2	objective	objective	NOUN
ejpam-6142	427	3	is	be	AUX
ejpam-6142	427	4	to	to	PART
ejpam-6142	427	5	determine	determine	VERB
ejpam-6142	427	6	the	the	DET
ejpam-6142	427	7	optimal	optimal	ADJ
ejpam-6142	427	8	controls	control	NOUN
ejpam-6142	427	9	u∗1	u∗1	NOUN
ejpam-6142	427	10	,	,	PUNCT
ejpam-6142	427	11	u	u	NOUN
ejpam-6142	427	12	∗	∗	NOUN
ejpam-6142	427	13	2	2	NUM
ejpam-6142	427	14	and	and	CCONJ
ejpam-6142	427	15	u∗3	u∗3	NOUN
ejpam-6142	427	16	along	along	ADP
ejpam-6142	427	17	with	with	ADP
ejpam-6142	427	18	the	the	DET
ejpam-6142	427	19	optimal	optimal	ADJ
ejpam-6142	427	20	solutions	solution	NOUN
ejpam-6142	427	21	s∗	s∗	PROPN
ejpam-6142	427	22	f	f	X
ejpam-6142	427	23	,	,	PUNCT
ejpam-6142	427	24	e	e	X
ejpam-6142	427	25	∗	∗	NOUN
ejpam-6142	427	26	f	f	PROPN
ejpam-6142	427	27	,	,	PUNCT
ejpam-6142	427	28	i	i	PRON
ejpam-6142	427	29	∗	∗	VERB
ejpam-6142	427	30	f	f	PROPN
ejpam-6142	427	31	,	,	PUNCT
ejpam-6142	428	1	d	d	AUX
ejpam-6142	428	2	∗	∗	X
ejpam-6142	428	3	f	f	PROPN
ejpam-6142	428	4	,	,	PUNCT
ejpam-6142	428	5	t	t	PROPN
ejpam-6142	428	6	∗	∗	NOUN
ejpam-6142	428	7	f	f	PROPN
ejpam-6142	428	8	,	,	PUNCT
ejpam-6142	428	9	u	u	NOUN
ejpam-6142	428	10	∗	∗	NOUN
ejpam-6142	428	11	f	f	PROPN
ejpam-6142	428	12	,	,	PUNCT
ejpam-6142	428	13	a	a	DET
ejpam-6142	428	14	∗	∗	X
ejpam-6142	428	15	f	f	NOUN
ejpam-6142	428	16	,	,	PUNCT
ejpam-6142	428	17	s	s	PART
ejpam-6142	428	18	∗	∗	NOUN
ejpam-6142	428	19	m	m	PROPN
ejpam-6142	428	20	,	,	PUNCT
ejpam-6142	428	21	e∗	e∗	PROPN
ejpam-6142	428	22	m	m	PROPN
ejpam-6142	428	23	,	,	PUNCT
ejpam-6142	428	24	i∗m	i∗m	X
ejpam-6142	428	25	,	,	PUNCT
ejpam-6142	428	26	d∗	d∗	PROPN
ejpam-6142	428	27	m	m	PROPN
ejpam-6142	428	28	,	,	PUNCT
ejpam-6142	428	29	t	t	PROPN
ejpam-6142	428	30	∗	∗	NOUN
ejpam-6142	428	31	m	m	PROPN
ejpam-6142	428	32	,	,	PUNCT
ejpam-6142	428	33	u∗	u∗	PROPN
ejpam-6142	428	34	m	m	NOUN
ejpam-6142	428	35	and	and	CCONJ
ejpam-6142	428	36	a∗	a∗	PROPN
ejpam-6142	428	37	m	m	VERB
ejpam-6142	428	38	by	by	ADP
ejpam-6142	428	39	setting	set	VERB
ejpam-6142	428	40	the	the	DET
ejpam-6142	428	41	terminal	terminal	ADJ
ejpam-6142	428	42	time	time	NOUN
ejpam-6142	428	43	tf	tf	INTJ
ejpam-6142	428	44	in	in	ADP
ejpam-6142	428	45	order	order	NOUN
ejpam-6142	428	46	to	to	PART
ejpam-6142	428	47	minimize	minimize	VERB
ejpam-6142	428	48	the	the	DET
ejpam-6142	428	49	objective	objective	ADJ
ejpam-6142	428	50	functional	functional	ADJ
ejpam-6142	428	51	j	j	PROPN
ejpam-6142	428	52	defined	define	VERB
ejpam-6142	428	53	by	by	ADP
ejpam-6142	428	54	:	:	PUNCT
ejpam-6142	428	55	j	j	PROPN
ejpam-6142	428	56	(	(	PUNCT
ejpam-6142	428	57	u1	u1	PROPN
ejpam-6142	428	58	,	,	PUNCT
ejpam-6142	428	59	u2	u2	NOUN
ejpam-6142	428	60	,	,	PUNCT
ejpam-6142	428	61	u3	u3	NOUN
ejpam-6142	428	62	)	)	PUNCT
ejpam-6142	429	1	=	=	SYM
ejpam-6142	429	2	min	min	PROPN
ejpam-6142	429	3	u1,u2,u3	u1,u2,u3	PROPN
ejpam-6142	429	4	∫	∫	PROPN
ejpam-6142	429	5	tf	tf	INTJ
ejpam-6142	429	6	0	0	NUM
ejpam-6142	429	7	(	(	PUNCT
ejpam-6142	429	8	b1ef	b1ef	X
ejpam-6142	429	9	+	+	CCONJ
ejpam-6142	429	10	b2if	b2if	NOUN
ejpam-6142	429	11	+	+	CCONJ
ejpam-6142	429	12	b3df	b3df	PUNCT
ejpam-6142	429	13	+	+	NUM
ejpam-6142	429	14	b4tf	b4tf	X
ejpam-6142	429	15	+	+	X
ejpam-6142	429	16	b5uf	b5uf	X
ejpam-6142	429	17	+	+	SYM
ejpam-6142	429	18	b6af	b6af	X
ejpam-6142	429	19	+	+	CCONJ
ejpam-6142	429	20	b7em	b7em	PUNCT
ejpam-6142	429	21	+	+	CCONJ
ejpam-6142	429	22	b8im+	b8im+	PROPN
ejpam-6142	429	23	b9	b9	PROPN
ejpam-6142	429	24	dm	dm	PROPN
ejpam-6142	429	25	+	+	NUM
ejpam-6142	429	26	b10tm	b10tm	PUNCT
ejpam-6142	429	27	+	+	CCONJ
ejpam-6142	429	28	b11um	b11um	PROPN
ejpam-6142	429	29	+	+	CCONJ
ejpam-6142	429	30	b12am	b12am	PROPN
ejpam-6142	429	31	+	+	CCONJ
ejpam-6142	429	32	1	1	NUM
ejpam-6142	429	33	2	2	NUM
ejpam-6142	429	34	(	(	PUNCT
ejpam-6142	429	35	w1u21	w1u21	PROPN
ejpam-6142	429	36	+	+	CCONJ
ejpam-6142	429	37	w2u22	w2u22	PROPN
ejpam-6142	429	38	+	+	CCONJ
ejpam-6142	429	39	w3u23	w3u23	NOUN
ejpam-6142	429	40	)	)	PUNCT
ejpam-6142	429	41	)	)	PUNCT
ejpam-6142	429	42	dt	dt	X
ejpam-6142	430	1	(	(	PUNCT
ejpam-6142	430	2	5	5	NUM
ejpam-6142	430	3	)	)	PUNCT
ejpam-6142	430	4	here	here	ADV
ejpam-6142	430	5	,	,	PUNCT
ejpam-6142	430	6	bi	bi	NOUN
ejpam-6142	430	7	,	,	PUNCT
ejpam-6142	430	8	i	i	NOUN
ejpam-6142	430	9	=	=	NOUN
ejpam-6142	430	10	1	1	NUM
ejpam-6142	430	11	,	,	PUNCT
ejpam-6142	430	12	.	.	PUNCT
ejpam-6142	430	13	.	.	PUNCT
ejpam-6142	431	1	.	.	PUNCT
ejpam-6142	432	1	,	,	PUNCT
ejpam-6142	432	2	12	12	NUM
ejpam-6142	432	3	and	and	CCONJ
ejpam-6142	432	4	w1	w1	NOUN
ejpam-6142	432	5	,	,	PUNCT
ejpam-6142	432	6	w2	w2	NOUN
ejpam-6142	432	7	,	,	PUNCT
ejpam-6142	432	8	and	and	CCONJ
ejpam-6142	432	9	w3	w3	PROPN
ejpam-6142	432	10	are	be	AUX
ejpam-6142	432	11	positive	positive	ADJ
ejpam-6142	432	12	constants	constant	NOUN
ejpam-6142	432	13	.	.	PUNCT
ejpam-6142	433	1	the	the	DET
ejpam-6142	433	2	terms	term	NOUN
ejpam-6142	433	3	0.5w1u	0.5w1u	NUM
ejpam-6142	433	4	2	2	NUM
ejpam-6142	433	5	1	1	NUM
ejpam-6142	433	6	,	,	PUNCT
ejpam-6142	433	7	0.5w2u	0.5w2u	NUM
ejpam-6142	433	8	2	2	NUM
ejpam-6142	433	9	2	2	NUM
ejpam-6142	433	10	and	and	CCONJ
ejpam-6142	433	11	0.5w3u	0.5w3u	NUM
ejpam-6142	433	12	2	2	NUM
ejpam-6142	433	13	3	3	NUM
ejpam-6142	433	14	represent	represent	VERB
ejpam-6142	433	15	costs	cost	NOUN
ejpam-6142	433	16	associated	associate	VERB
ejpam-6142	433	17	with	with	ADP
ejpam-6142	433	18	the	the	DET
ejpam-6142	433	19	controls	control	NOUN
ejpam-6142	433	20	.	.	PUNCT
ejpam-6142	434	1	our	our	PRON
ejpam-6142	434	2	goal	goal	NOUN
ejpam-6142	434	3	is	be	AUX
ejpam-6142	434	4	to	to	PART
ejpam-6142	434	5	reduce	reduce	VERB
ejpam-6142	434	6	the	the	DET
ejpam-6142	434	7	population	population	NOUN
ejpam-6142	434	8	sizes	size	NOUN
ejpam-6142	434	9	of	of	ADP
ejpam-6142	434	10	infected	infected	ADJ
ejpam-6142	434	11	compartments	compartment	NOUN
ejpam-6142	434	12	by	by	ADP
ejpam-6142	434	13	intervening	intervene	VERB
ejpam-6142	434	14	with	with	ADP
ejpam-6142	434	15	control	control	NOUN
ejpam-6142	434	16	measures	measure	NOUN
ejpam-6142	434	17	u1(t	u1(t	PRON
ejpam-6142	434	18	)	)	PUNCT
ejpam-6142	434	19	,	,	PUNCT
ejpam-6142	434	20	u2(t	u2(t	PROPN
ejpam-6142	434	21	)	)	PUNCT
ejpam-6142	434	22	and	and	CCONJ
ejpam-6142	434	23	u3(t	u3(t	NUM
ejpam-6142	434	24	)	)	PUNCT
ejpam-6142	434	25	as	as	ADV
ejpam-6142	434	26	well	well	ADV
ejpam-6142	434	27	as	as	ADP
ejpam-6142	434	28	the	the	DET
ejpam-6142	434	29	related	related	ADJ
ejpam-6142	434	30	costs	cost	NOUN
ejpam-6142	434	31	.	.	PUNCT
ejpam-6142	435	1	we	we	PRON
ejpam-6142	435	2	have	have	VERB
ejpam-6142	435	3	the	the	DET
ejpam-6142	435	4	following	following	NOUN
ejpam-6142	435	5	for	for	ADP
ejpam-6142	435	6	the	the	DET
ejpam-6142	435	7	three	three	NUM
ejpam-6142	435	8	optimal	optimal	ADJ
ejpam-6142	435	9	controllers	controller	NOUN
ejpam-6142	435	10	u∗1	u∗1	NOUN
ejpam-6142	435	11	,	,	PUNCT
ejpam-6142	435	12	u	u	NOUN
ejpam-6142	435	13	∗	∗	NOUN
ejpam-6142	435	14	2	2	NUM
ejpam-6142	435	15	and	and	CCONJ
ejpam-6142	435	16	u∗3	u∗3	NOUN
ejpam-6142	435	17	:	:	PUNCT
ejpam-6142	435	18	j	j	PROPN
ejpam-6142	435	19	(	(	PUNCT
ejpam-6142	435	20	u∗1	u∗1	PROPN
ejpam-6142	435	21	,	,	PUNCT
ejpam-6142	435	22	u	u	NOUN
ejpam-6142	435	23	∗	∗	NOUN
ejpam-6142	435	24	2	2	NUM
ejpam-6142	435	25	,	,	PUNCT
ejpam-6142	435	26	u	u	NOUN
ejpam-6142	435	27	∗	∗	NOUN
ejpam-6142	435	28	3	3	NUM
ejpam-6142	435	29	)	)	PUNCT
ejpam-6142	435	30	=	=	SYM
ejpam-6142	435	31	min	min	PROPN
ejpam-6142	435	32	{	{	PUNCT
ejpam-6142	435	33	j	j	PROPN
ejpam-6142	435	34	(	(	PUNCT
ejpam-6142	435	35	u1	u1	PROPN
ejpam-6142	435	36	,	,	PUNCT
ejpam-6142	435	37	u2	u2	NOUN
ejpam-6142	435	38	,	,	PUNCT
ejpam-6142	435	39	u3	u3	NOUN
ejpam-6142	435	40	)	)	PUNCT
ejpam-6142	435	41	,	,	PUNCT
ejpam-6142	435	42	u1	u1	NOUN
ejpam-6142	435	43	,	,	PUNCT
ejpam-6142	435	44	u2	u2	NOUN
ejpam-6142	435	45	,	,	PUNCT
ejpam-6142	435	46	u3	u3	NOUN
ejpam-6142	435	47	∈	∈	PROPN
ejpam-6142	435	48	u	u	NOUN
ejpam-6142	435	49	}	}	PUNCT
ejpam-6142	435	50	theorem	theorem	VERB
ejpam-6142	435	51	5	5	NUM
ejpam-6142	435	52	.	.	PUNCT
ejpam-6142	435	53	(	(	PUNCT
ejpam-6142	435	54	existence	existence	NOUN
ejpam-6142	435	55	of	of	ADP
ejpam-6142	435	56	optimal	optimal	ADJ
ejpam-6142	435	57	control	control	NOUN
ejpam-6142	435	58	solution	solution	NOUN
ejpam-6142	435	59	)	)	PUNCT
ejpam-6142	435	60	there	there	PRON
ejpam-6142	435	61	is	be	VERB
ejpam-6142	435	62	the	the	DET
ejpam-6142	435	63	optimal	optimal	ADJ
ejpam-6142	435	64	control	control	NOUN
ejpam-6142	435	65	(	(	PUNCT
ejpam-6142	435	66	u∗1	u∗1	NOUN
ejpam-6142	435	67	,	,	PUNCT
ejpam-6142	435	68	u	u	NOUN
ejpam-6142	435	69	∗	∗	NOUN
ejpam-6142	435	70	2	2	NUM
ejpam-6142	435	71	,	,	PUNCT
ejpam-6142	435	72	u	u	NOUN
ejpam-6142	435	73	∗	∗	NOUN
ejpam-6142	435	74	3	3	NUM
ejpam-6142	435	75	)	)	PUNCT
ejpam-6142	435	76	along	along	ADP
ejpam-6142	435	77	with	with	ADP
ejpam-6142	435	78	their	their	PRON
ejpam-6142	435	79	associated	associated	ADJ
ejpam-6142	435	80	state	state	NOUN
ejpam-6142	435	81	variable	variable	ADJ
ejpam-6142	435	82	solutions	solution	NOUN
ejpam-6142	435	83	s∗	s∗	PROPN
ejpam-6142	435	84	f	f	PROPN
ejpam-6142	435	85	,	,	PUNCT
ejpam-6142	435	86	e	e	X
ejpam-6142	435	87	∗	∗	NOUN
ejpam-6142	435	88	f	f	PROPN
ejpam-6142	435	89	,	,	PUNCT
ejpam-6142	436	1	i	i	PRON
ejpam-6142	436	2	∗	∗	VERB
ejpam-6142	436	3	f	f	PROPN
ejpam-6142	436	4	,	,	PUNCT
ejpam-6142	437	1	d	d	AUX
ejpam-6142	437	2	∗	∗	X
ejpam-6142	437	3	f	f	PROPN
ejpam-6142	437	4	,	,	PUNCT
ejpam-6142	437	5	t	t	PROPN
ejpam-6142	437	6	∗	∗	NOUN
ejpam-6142	437	7	f	f	PROPN
ejpam-6142	437	8	,	,	PUNCT
ejpam-6142	437	9	u	u	NOUN
ejpam-6142	437	10	∗	∗	NOUN
ejpam-6142	437	11	f	f	PROPN
ejpam-6142	437	12	,	,	PUNCT
ejpam-6142	437	13	a	a	DET
ejpam-6142	437	14	∗	∗	X
ejpam-6142	437	15	f	f	NOUN
ejpam-6142	437	16	,	,	PUNCT
ejpam-6142	437	17	s	s	PART
ejpam-6142	437	18	∗	∗	NOUN
ejpam-6142	437	19	m	m	PROPN
ejpam-6142	437	20	,	,	PUNCT
ejpam-6142	437	21	e∗	e∗	PROPN
ejpam-6142	437	22	m	m	PROPN
ejpam-6142	437	23	,	,	PUNCT
ejpam-6142	437	24	i∗m	i∗m	X
ejpam-6142	437	25	,	,	PUNCT
ejpam-6142	437	26	d∗	d∗	PROPN
ejpam-6142	437	27	m	m	PROPN
ejpam-6142	437	28	,	,	PUNCT
ejpam-6142	437	29	t	t	PROPN
ejpam-6142	437	30	∗	∗	NOUN
ejpam-6142	437	31	m	m	PROPN
ejpam-6142	437	32	,	,	PUNCT
ejpam-6142	437	33	u∗	u∗	PROPN
ejpam-6142	437	34	m	m	NOUN
ejpam-6142	437	35	and	and	CCONJ
ejpam-6142	437	36	a∗	a∗	PROPN
ejpam-6142	437	37	m	m	PROPN
ejpam-6142	437	38	for	for	ADP
ejpam-6142	437	39	the	the	DET
ejpam-6142	437	40	state	state	NOUN
ejpam-6142	437	41	initial	initial	ADJ
ejpam-6142	437	42	value	value	NOUN
ejpam-6142	437	43	problem	problem	NOUN
ejpam-6142	437	44	defined	define	VERB
ejpam-6142	437	45	in	in	ADP
ejpam-6142	437	46	(	(	PUNCT
ejpam-6142	437	47	4	4	NUM
ejpam-6142	437	48	)	)	PUNCT
ejpam-6142	437	49	and	and	CCONJ
ejpam-6142	437	50	(	(	PUNCT
ejpam-6142	437	51	5	5	X
ejpam-6142	437	52	)	)	PUNCT
ejpam-6142	437	53	that	that	PRON
ejpam-6142	437	54	minimizes	minimize	VERB
ejpam-6142	437	55	j	j	PROPN
ejpam-6142	437	56	(	(	PUNCT
ejpam-6142	437	57	u1	u1	PROPN
ejpam-6142	437	58	,	,	PUNCT
ejpam-6142	437	59	u2	u2	NOUN
ejpam-6142	437	60	,	,	PUNCT
ejpam-6142	437	61	u3	u3	NOUN
ejpam-6142	437	62	)	)	PUNCT
ejpam-6142	437	63	over	over	ADP
ejpam-6142	437	64	the	the	DET
ejpam-6142	437	65	set	set	ADJ
ejpam-6142	437	66	u	u	NOUN
ejpam-6142	437	67	.	.	PUNCT
ejpam-6142	438	1	proof	proof	NOUN
ejpam-6142	438	2	.	.	PUNCT
ejpam-6142	439	1	we	we	PRON
ejpam-6142	439	2	apply	apply	VERB
ejpam-6142	439	3	the	the	DET
ejpam-6142	439	4	method	method	NOUN
ejpam-6142	439	5	used	use	VERB
ejpam-6142	439	6	in	in	ADP
ejpam-6142	439	7	[	[	X
ejpam-6142	439	8	27	27	NUM
ejpam-6142	439	9	]	]	PUNCT
ejpam-6142	439	10	theorem	theorem	VERB
ejpam-6142	439	11	4	4	NUM
ejpam-6142	439	12	to	to	PART
ejpam-6142	439	13	proof	proof	VERB
ejpam-6142	439	14	the	the	DET
ejpam-6142	439	15	existence	existence	NOUN
ejpam-6142	439	16	of	of	ADP
ejpam-6142	439	17	optimal	optimal	ADJ
ejpam-6142	439	18	control	control	NOUN
ejpam-6142	439	19	solution	solution	NOUN
ejpam-6142	439	20	.	.	PUNCT
ejpam-6142	440	1	by	by	ADP
ejpam-6142	440	2	applying	apply	VERB
ejpam-6142	440	3	the	the	DET
ejpam-6142	440	4	pontryagin	pontryagin	NOUN
ejpam-6142	440	5	maximum	maximum	ADJ
ejpam-6142	440	6	principle	principle	NOUN
ejpam-6142	440	7	(	(	PUNCT
ejpam-6142	440	8	pmp	pmp	INTJ
ejpam-6142	440	9	)	)	PUNCT
ejpam-6142	440	10	as	as	SCONJ
ejpam-6142	440	11	outlined	outline	VERB
ejpam-6142	440	12	in	in	ADP
ejpam-6142	440	13	[	[	X
ejpam-6142	440	14	26	26	NUM
ejpam-6142	440	15	]	]	PUNCT
ejpam-6142	440	16	,	,	PUNCT
ejpam-6142	440	17	we	we	PRON
ejpam-6142	440	18	derive	derive	VERB
ejpam-6142	440	19	the	the	DET
ejpam-6142	440	20	essential	essential	ADJ
ejpam-6142	440	21	conditions	condition	NOUN
ejpam-6142	440	22	that	that	PRON
ejpam-6142	440	23	are	be	AUX
ejpam-6142	440	24	met	meet	VERB
ejpam-6142	440	25	by	by	ADP
ejpam-6142	440	26	the	the	DET
ejpam-6142	440	27	optimal	optimal	ADJ
ejpam-6142	440	28	pair	pair	NOUN
ejpam-6142	440	29	.	.	PUNCT
ejpam-6142	441	1	hence	hence	ADV
ejpam-6142	441	2	,	,	PUNCT
ejpam-6142	441	3	the	the	DET
ejpam-6142	441	4	hamiltonian	hamiltonian	ADJ
ejpam-6142	441	5	function	function	PROPN
ejpam-6142	441	6	s.	s.	PROPN
ejpam-6142	441	7	m.	m.	PROPN
ejpam-6142	441	8	fatah	fatah	PROPN
ejpam-6142	441	9	,	,	PUNCT
ejpam-6142	441	10	s.	s.	PROPN
ejpam-6142	441	11	h.	h.	PROPN
ejpam-6142	441	12	a.	a.	PROPN
ejpam-6142	441	13	khoshnaw	khoshnaw	PROPN
ejpam-6142	441	14	,	,	PUNCT
ejpam-6142	441	15	a.	a.	PROPN
ejpam-6142	441	16	n.	n.	PROPN
ejpam-6142	441	17	mustafa	mustafa	PROPN
ejpam-6142	441	18	/	/	SYM
ejpam-6142	441	19	eur	eur	PROPN
ejpam-6142	441	20	.	.	PUNCT
ejpam-6142	442	1	j.	j.	PROPN
ejpam-6142	442	2	pure	pure	PROPN
ejpam-6142	442	3	appl	appl	PROPN
ejpam-6142	442	4	.	.	PROPN
ejpam-6142	442	5	math	math	PROPN
ejpam-6142	442	6	,	,	PUNCT
ejpam-6142	442	7	18	18	NUM
ejpam-6142	442	8	(	(	PUNCT
ejpam-6142	442	9	2	2	NUM
ejpam-6142	442	10	)	)	PUNCT
ejpam-6142	442	11	(	(	PUNCT
ejpam-6142	442	12	2025	2025	NUM
ejpam-6142	442	13	)	)	PUNCT
ejpam-6142	442	14	,	,	PUNCT
ejpam-6142	442	15	6142	6142	NUM
ejpam-6142	442	16	20	20	NUM
ejpam-6142	442	17	of	of	ADP
ejpam-6142	442	18	33	33	NUM
ejpam-6142	442	19	(	(	PUNCT
ejpam-6142	442	20	h	h	NOUN
ejpam-6142	442	21	)	)	PUNCT
ejpam-6142	442	22	can	can	AUX
ejpam-6142	442	23	be	be	AUX
ejpam-6142	442	24	obtained	obtain	VERB
ejpam-6142	442	25	by	by	ADP
ejpam-6142	442	26	this	this	DET
ejpam-6142	442	27	principle	principle	NOUN
ejpam-6142	442	28	which	which	PRON
ejpam-6142	442	29	is	be	AUX
ejpam-6142	442	30	defined	define	VERB
ejpam-6142	442	31	as	as	ADP
ejpam-6142	442	32	h	h	NOUN
ejpam-6142	442	33	(	(	PUNCT
ejpam-6142	442	34	sf	sf	PROPN
ejpam-6142	442	35	,	,	PUNCT
ejpam-6142	442	36	ef	ef	PROPN
ejpam-6142	442	37	,	,	PUNCT
ejpam-6142	442	38	if	if	SCONJ
ejpam-6142	442	39	,	,	PUNCT
ejpam-6142	442	40	df	df	PROPN
ejpam-6142	442	41	,	,	PUNCT
ejpam-6142	442	42	tf	tf	INTJ
ejpam-6142	442	43	,	,	PUNCT
ejpam-6142	442	44	uf	uf	PROPN
ejpam-6142	442	45	,	,	PUNCT
ejpam-6142	442	46	af	af	PROPN
ejpam-6142	442	47	,	,	PUNCT
ejpam-6142	442	48	sm	sm	PROPN
ejpam-6142	442	49	,	,	PUNCT
ejpam-6142	442	50	em	em	PRON
ejpam-6142	442	51	,	,	PUNCT
ejpam-6142	442	52	i	i	PRON
ejpam-6142	442	53	m	m	PROPN
ejpam-6142	442	54	,	,	PUNCT
ejpam-6142	442	55	dm	dm	PROPN
ejpam-6142	442	56	,	,	PUNCT
ejpam-6142	442	57	tm	tm	NOUN
ejpam-6142	442	58	,	,	PUNCT
ejpam-6142	442	59	um	um	INTJ
ejpam-6142	442	60	,	,	PUNCT
ejpam-6142	442	61	am	be	AUX
ejpam-6142	442	62	,	,	PUNCT
ejpam-6142	442	63	u1	u1	NOUN
ejpam-6142	442	64	,	,	PUNCT
ejpam-6142	442	65	u2	u2	NOUN
ejpam-6142	442	66	,	,	PUNCT
ejpam-6142	442	67	u3	u3	NOUN
ejpam-6142	442	68	)	)	PUNCT
ejpam-6142	442	69	=	=	NOUN
ejpam-6142	442	70	b1ef	b1ef	NOUN
ejpam-6142	443	1	+	+	CCONJ
ejpam-6142	443	2	b2if	b2if	NOUN
ejpam-6142	443	3	+	+	CCONJ
ejpam-6142	443	4	b3df	b3df	PUNCT
ejpam-6142	443	5	+	+	NUM
ejpam-6142	443	6	b4tf	b4tf	X
ejpam-6142	443	7	+	+	X
ejpam-6142	443	8	b5uf	b5uf	X
ejpam-6142	443	9	+	+	SYM
ejpam-6142	443	10	b6af	b6af	X
ejpam-6142	443	11	+	+	CCONJ
ejpam-6142	443	12	b7em	b7em	PUNCT
ejpam-6142	443	13	+	+	CCONJ
ejpam-6142	443	14	b8im	b8im	SYM
ejpam-6142	443	15	+	+	CCONJ
ejpam-6142	443	16	b9	b9	NOUN
ejpam-6142	443	17	dm	dm	NOUN
ejpam-6142	443	18	+	+	NUM
ejpam-6142	443	19	b10tm	b10tm	PUNCT
ejpam-6142	444	1	+	+	CCONJ
ejpam-6142	444	2	b11um	b11um	PROPN
ejpam-6142	444	3	+	+	CCONJ
ejpam-6142	444	4	b12am	b12am	PROPN
ejpam-6142	444	5	+	+	CCONJ
ejpam-6142	444	6	1	1	NUM
ejpam-6142	444	7	2	2	NUM
ejpam-6142	444	8	(	(	PUNCT
ejpam-6142	444	9	w1u	w1u	NOUN
ejpam-6142	444	10	2	2	NUM
ejpam-6142	444	11	1	1	NUM
ejpam-6142	444	12	+	+	CCONJ
ejpam-6142	444	13	w2u	w2u	ADJ
ejpam-6142	444	14	2	2	NUM
ejpam-6142	444	15	2	2	NUM
ejpam-6142	444	16	+	+	CCONJ
ejpam-6142	444	17	w3u	w3u	PROPN
ejpam-6142	444	18	2	2	NUM
ejpam-6142	444	19	3	3	NUM
ejpam-6142	444	20	)	)	PUNCT
ejpam-6142	444	21	+	+	CCONJ
ejpam-6142	445	1	λ1	λ1	ADJ
ejpam-6142	445	2	dsf	dsf	NOUN
ejpam-6142	445	3	dt	dt	NOUN
ejpam-6142	446	1	+	+	CCONJ
ejpam-6142	446	2	λ2	λ2	NOUN
ejpam-6142	446	3	def	def	ADJ
ejpam-6142	446	4	dt	dt	NOUN
ejpam-6142	447	1	+	+	CCONJ
ejpam-6142	447	2	λ3	λ3	PROPN
ejpam-6142	447	3	dif	dif	ADV
ejpam-6142	447	4	dt	dt	PUNCT
ejpam-6142	448	1	+	+	CCONJ
ejpam-6142	448	2	λ4	λ4	ADJ
ejpam-6142	448	3	ddf	ddf	NOUN
ejpam-6142	448	4	dt	dt	PROPN
ejpam-6142	448	5	+	+	CCONJ
ejpam-6142	448	6	λ5	λ5	PROPN
ejpam-6142	448	7	dtf	dtf	PROPN
ejpam-6142	448	8	dt	dt	PROPN
ejpam-6142	448	9	+	+	CCONJ
ejpam-6142	448	10	λ6	λ6	PROPN
ejpam-6142	448	11	duf	duf	NOUN
ejpam-6142	448	12	dt	dt	NOUN
ejpam-6142	449	1	+	+	CCONJ
ejpam-6142	449	2	λ7	λ7	ADJ
ejpam-6142	449	3	daf	daf	NOUN
ejpam-6142	449	4	dt	dt	X
ejpam-6142	450	1	+	+	CCONJ
ejpam-6142	450	2	λ8	λ8	VERB
ejpam-6142	450	3	dsm	dsm	ADJ
ejpam-6142	450	4	dt	dt	NOUN
ejpam-6142	450	5	+	+	CCONJ
ejpam-6142	450	6	λ9	λ9	ADJ
ejpam-6142	450	7	dem	dem	ADJ
ejpam-6142	450	8	dt	dt	NOUN
ejpam-6142	450	9	+	+	CCONJ
ejpam-6142	450	10	λ10	λ10	NOUN
ejpam-6142	450	11	dim	dim	NOUN
ejpam-6142	450	12	dt	dt	NOUN
ejpam-6142	450	13	+	+	CCONJ
ejpam-6142	450	14	λ11	λ11	PROPN
ejpam-6142	450	15	ddm	ddm	PROPN
ejpam-6142	450	16	dt	dt	PROPN
ejpam-6142	451	1	+	+	PROPN
ejpam-6142	451	2	λ12	λ12	PROPN
ejpam-6142	451	3	dtm	dtm	PROPN
ejpam-6142	451	4	dt	dt	NOUN
ejpam-6142	451	5	+	+	CCONJ
ejpam-6142	451	6	λ13	λ13	PROPN
ejpam-6142	451	7	dum	dum	NOUN
ejpam-6142	451	8	dt	dt	NOUN
ejpam-6142	451	9	+	+	CCONJ
ejpam-6142	451	10	λ14	λ14	PROPN
ejpam-6142	451	11	dam	dam	NOUN
ejpam-6142	451	12	dt	dt	X
ejpam-6142	451	13	(	(	PUNCT
ejpam-6142	451	14	6	6	NUM
ejpam-6142	451	15	)	)	PUNCT
ejpam-6142	451	16	here	here	ADV
ejpam-6142	451	17	,	,	PUNCT
ejpam-6142	451	18	λi	λi	ADP
ejpam-6142	451	19	,	,	PUNCT
ejpam-6142	451	20	where	where	SCONJ
ejpam-6142	451	21	i	i	PRON
ejpam-6142	451	22	=	=	NOUN
ejpam-6142	451	23	1	1	NUM
ejpam-6142	451	24	,	,	PUNCT
ejpam-6142	451	25	2	2	NUM
ejpam-6142	451	26	,	,	PUNCT
ejpam-6142	451	27	.	.	PUNCT
ejpam-6142	451	28	.	.	PUNCT
ejpam-6142	451	29	.	.	PUNCT
ejpam-6142	452	1	,	,	PUNCT
ejpam-6142	452	2	14	14	NUM
ejpam-6142	452	3	,	,	PUNCT
ejpam-6142	452	4	denotes	denote	VERB
ejpam-6142	452	5	the	the	DET
ejpam-6142	452	6	adjoint	adjoint	PROPN
ejpam-6142	452	7	variables	variable	NOUN
ejpam-6142	452	8	associated	associate	VERB
ejpam-6142	452	9	with	with	ADP
ejpam-6142	452	10	the	the	DET
ejpam-6142	452	11	state	state	NOUN
ejpam-6142	452	12	variables	variable	NOUN
ejpam-6142	452	13	sf	sf	PROPN
ejpam-6142	452	14	,	,	PUNCT
ejpam-6142	452	15	ef	ef	PROPN
ejpam-6142	452	16	,	,	PUNCT
ejpam-6142	452	17	if	if	SCONJ
ejpam-6142	452	18	,	,	PUNCT
ejpam-6142	452	19	df	df	PROPN
ejpam-6142	452	20	,	,	PUNCT
ejpam-6142	452	21	tf	tf	INTJ
ejpam-6142	452	22	,	,	PUNCT
ejpam-6142	452	23	uf	uf	PROPN
ejpam-6142	452	24	,	,	PUNCT
ejpam-6142	452	25	af	af	PROPN
ejpam-6142	452	26	,	,	PUNCT
ejpam-6142	452	27	sm	sm	PROPN
ejpam-6142	452	28	,	,	PUNCT
ejpam-6142	452	29	em	em	PRON
ejpam-6142	452	30	,	,	PUNCT
ejpam-6142	452	31	i	i	PRON
ejpam-6142	452	32	m	m	PROPN
ejpam-6142	452	33	,	,	PUNCT
ejpam-6142	452	34	dm	dm	PROPN
ejpam-6142	452	35	,	,	PUNCT
ejpam-6142	452	36	tm	tm	NOUN
ejpam-6142	452	37	,	,	PUNCT
ejpam-6142	452	38	um	um	INTJ
ejpam-6142	452	39	and	and	CCONJ
ejpam-6142	452	40	am	be	AUX
ejpam-6142	452	41	,	,	PUNCT
ejpam-6142	452	42	respectively	respectively	ADV
ejpam-6142	452	43	,	,	PUNCT
ejpam-6142	452	44	which	which	PRON
ejpam-6142	452	45	must	must	AUX
ejpam-6142	452	46	be	be	AUX
ejpam-6142	452	47	ascertained	ascertain	VERB
ejpam-6142	452	48	utilising	utilise	VERB
ejpam-6142	452	49	pontryagin	pontryagin	NOUN
ejpam-6142	452	50	’s	’s	PART
ejpam-6142	452	51	maximum	maximum	ADJ
ejpam-6142	452	52	principle	principle	NOUN
ejpam-6142	452	53	to	to	PART
ejpam-6142	452	54	establish	establish	VERB
ejpam-6142	452	55	the	the	DET
ejpam-6142	452	56	existence	existence	NOUN
ejpam-6142	452	57	of	of	ADP
ejpam-6142	452	58	optimal	optimal	ADJ
ejpam-6142	452	59	pairs	pair	NOUN
ejpam-6142	452	60	.	.	PUNCT
ejpam-6142	453	1	theorem	theorem	NOUN
ejpam-6142	453	2	6	6	NUM
ejpam-6142	453	3	.	.	PUNCT
ejpam-6142	454	1	let	let	VERB
ejpam-6142	454	2	sf	sf	PROPN
ejpam-6142	454	3	,	,	PUNCT
ejpam-6142	454	4	ef	ef	INTJ
ejpam-6142	454	5	,	,	PUNCT
ejpam-6142	454	6	if	if	SCONJ
ejpam-6142	454	7	,	,	PUNCT
ejpam-6142	454	8	df	df	PROPN
ejpam-6142	454	9	,	,	PUNCT
ejpam-6142	454	10	tf	tf	INTJ
ejpam-6142	454	11	,	,	PUNCT
ejpam-6142	454	12	uf	uf	PROPN
ejpam-6142	454	13	,	,	PUNCT
ejpam-6142	454	14	af	af	PROPN
ejpam-6142	454	15	,	,	PUNCT
ejpam-6142	454	16	sm	sm	PROPN
ejpam-6142	454	17	,	,	PUNCT
ejpam-6142	454	18	em	em	PRON
ejpam-6142	454	19	,	,	PUNCT
ejpam-6142	454	20	i	i	PRON
ejpam-6142	454	21	m	m	PROPN
ejpam-6142	454	22	,	,	PUNCT
ejpam-6142	454	23	dm	dm	PROPN
ejpam-6142	454	24	,	,	PUNCT
ejpam-6142	454	25	tm	tm	NOUN
ejpam-6142	454	26	,	,	PUNCT
ejpam-6142	454	27	um	um	INTJ
ejpam-6142	454	28	and	and	CCONJ
ejpam-6142	454	29	am	be	AUX
ejpam-6142	454	30	denote	denote	VERB
ejpam-6142	454	31	optimum	optimum	ADJ
ejpam-6142	454	32	state	state	NOUN
ejpam-6142	454	33	solutions	solution	NOUN
ejpam-6142	454	34	associated	associate	VERB
ejpam-6142	454	35	with	with	ADP
ejpam-6142	454	36	the	the	DET
ejpam-6142	454	37	optimal	optimal	ADJ
ejpam-6142	454	38	control	control	NOUN
ejpam-6142	454	39	variables	variable	NOUN
ejpam-6142	454	40	u1	u1	NOUN
ejpam-6142	454	41	,	,	PUNCT
ejpam-6142	454	42	u2	u2	NOUN
ejpam-6142	454	43	and	and	CCONJ
ejpam-6142	454	44	u3	u3	NOUN
ejpam-6142	454	45	within	within	ADP
ejpam-6142	454	46	the	the	DET
ejpam-6142	454	47	optimal	optimal	ADJ
ejpam-6142	454	48	control	control	NOUN
ejpam-6142	454	49	model	model	NOUN
ejpam-6142	454	50	.	.	PUNCT
ejpam-6142	455	1	correspondingly	correspondingly	ADV
ejpam-6142	455	2	,	,	PUNCT
ejpam-6142	455	3	there	there	PRON
ejpam-6142	455	4	exist	exist	VERB
ejpam-6142	455	5	co	co	NOUN
ejpam-6142	455	6	-	-	NOUN
ejpam-6142	455	7	state	state	ADJ
ejpam-6142	455	8	variables	variable	NOUN
ejpam-6142	455	9	λi	λi	ADP
ejpam-6142	455	10	,	,	PUNCT
ejpam-6142	455	11	where	where	SCONJ
ejpam-6142	455	12	i	i	PRON
ejpam-6142	455	13	=	=	NOUN
ejpam-6142	455	14	1	1	NUM
ejpam-6142	455	15	,	,	PUNCT
ejpam-6142	455	16	2	2	NUM
ejpam-6142	455	17	,	,	PUNCT
ejpam-6142	455	18	.	.	PUNCT
ejpam-6142	455	19	.	.	PUNCT
ejpam-6142	456	1	.	.	PUNCT
ejpam-6142	457	1	,	,	PUNCT
ejpam-6142	457	2	14	14	NUM
ejpam-6142	457	3	such	such	ADJ
ejpam-6142	457	4	that	that	PRON
ejpam-6142	457	5	:	:	PUNCT
ejpam-6142	457	6	dλi	dλi	PROPN
ejpam-6142	457	7	dt	dt	NOUN
ejpam-6142	457	8	=	=	SYM
ejpam-6142	457	9	−∂h	−∂h	PROPN
ejpam-6142	457	10	∂j	∂j	NOUN
ejpam-6142	457	11	considering	consider	VERB
ejpam-6142	457	12	transversality	transversality	NOUN
ejpam-6142	457	13	or	or	CCONJ
ejpam-6142	457	14	final	final	ADJ
ejpam-6142	457	15	time	time	NOUN
ejpam-6142	457	16	conditions	condition	NOUN
ejpam-6142	457	17	,	,	PUNCT
ejpam-6142	457	18	where	where	SCONJ
ejpam-6142	457	19	λi	λi	INTJ
ejpam-6142	457	20	(	(	PUNCT
ejpam-6142	457	21	tf	tf	INTJ
ejpam-6142	457	22	)	)	PUNCT
ejpam-6142	457	23	=	=	SYM
ejpam-6142	457	24	0	0	PUNCT
ejpam-6142	457	25	for	for	ADP
ejpam-6142	457	26	i	i	PRON
ejpam-6142	457	27	=	=	NOUN
ejpam-6142	457	28	1	1	NUM
ejpam-6142	457	29	,	,	PUNCT
ejpam-6142	457	30	2	2	NUM
ejpam-6142	457	31	,	,	PUNCT
ejpam-6142	457	32	.	.	PUNCT
ejpam-6142	457	33	.	.	PUNCT
ejpam-6142	457	34	.	.	PUNCT
ejpam-6142	458	1	,	,	PUNCT
ejpam-6142	458	2	14	14	NUM
ejpam-6142	458	3	,	,	PUNCT
ejpam-6142	458	4	j	j	X
ejpam-6142	459	1	=	=	PUNCT
ejpam-6142	459	2	sf	sf	PROPN
ejpam-6142	459	3	,	,	PUNCT
ejpam-6142	459	4	ef	ef	PROPN
ejpam-6142	459	5	,	,	PUNCT
ejpam-6142	459	6	if	if	SCONJ
ejpam-6142	459	7	,	,	PUNCT
ejpam-6142	459	8	df	df	PROPN
ejpam-6142	459	9	,	,	PUNCT
ejpam-6142	459	10	tf	tf	INTJ
ejpam-6142	459	11	,	,	PUNCT
ejpam-6142	459	12	uf	uf	PROPN
ejpam-6142	459	13	,	,	PUNCT
ejpam-6142	459	14	af	af	PROPN
ejpam-6142	459	15	,	,	PUNCT
ejpam-6142	459	16	sm	sm	PROPN
ejpam-6142	459	17	,	,	PUNCT
ejpam-6142	459	18	em	em	PRON
ejpam-6142	459	19	,	,	PUNCT
ejpam-6142	459	20	i	i	PRON
ejpam-6142	459	21	m	m	PROPN
ejpam-6142	459	22	,	,	PUNCT
ejpam-6142	459	23	dm	dm	PROPN
ejpam-6142	459	24	,	,	PUNCT
ejpam-6142	459	25	tm	tm	NOUN
ejpam-6142	459	26	,	,	PUNCT
ejpam-6142	459	27	um	um	INTJ
ejpam-6142	459	28	,	,	PUNCT
ejpam-6142	459	29	am	be	AUX
ejpam-6142	459	30	,	,	PUNCT
ejpam-6142	459	31	and	and	CCONJ
ejpam-6142	459	32	h	h	NOUN
ejpam-6142	459	33	is	be	AUX
ejpam-6142	459	34	the	the	DET
ejpam-6142	459	35	hamiltonian	hamiltonian	ADJ
ejpam-6142	459	36	function	function	NOUN
ejpam-6142	459	37	as	as	SCONJ
ejpam-6142	459	38	defined	define	VERB
ejpam-6142	459	39	in	in	ADP
ejpam-6142	459	40	equation	equation	NOUN
ejpam-6142	459	41	6	6	NUM
ejpam-6142	459	42	.	.	PUNCT
ejpam-6142	460	1	additionally	additionally	ADV
ejpam-6142	460	2	,	,	PUNCT
ejpam-6142	460	3	the	the	DET
ejpam-6142	460	4	optimal	optimal	ADJ
ejpam-6142	460	5	controls	control	NOUN
ejpam-6142	460	6	u∗1	u∗1	NOUN
ejpam-6142	460	7	,	,	PUNCT
ejpam-6142	460	8	u	u	NOUN
ejpam-6142	460	9	∗	∗	NOUN
ejpam-6142	460	10	2	2	NUM
ejpam-6142	460	11	and	and	CCONJ
ejpam-6142	460	12	u∗3	u∗3	NOUN
ejpam-6142	460	13	are	be	AUX
ejpam-6142	460	14	u∗1	u∗1	NOUN
ejpam-6142	460	15	=	=	SYM
ejpam-6142	460	16	max	max	PROPN
ejpam-6142	460	17	{	{	PUNCT
ejpam-6142	460	18	min	min	NOUN
ejpam-6142	460	19	{	{	PUNCT
ejpam-6142	460	20	1	1	NUM
ejpam-6142	460	21	,	,	PUNCT
ejpam-6142	460	22	(	(	PUNCT
ejpam-6142	460	23	1−kϵ)[βf	1−kϵ)[βf	NUM
ejpam-6142	460	24	imsf	imsf	NOUN
ejpam-6142	460	25	(	(	PUNCT
ejpam-6142	460	26	λ2−λ1)+βmifsm(λ9−λ8	λ2−λ1)+βmifsm(λ9−λ8	ADJ
ejpam-6142	460	27	)	)	PUNCT
ejpam-6142	460	28	]	]	PUNCT
ejpam-6142	460	29	w1	w1	NOUN
ejpam-6142	460	30	}	}	PUNCT
ejpam-6142	460	31	,	,	PUNCT
ejpam-6142	460	32	0	0	NUM
ejpam-6142	460	33	}	}	PUNCT
ejpam-6142	460	34	,	,	PUNCT
ejpam-6142	460	35	u∗2	u∗2	NOUN
ejpam-6142	460	36	=	=	SYM
ejpam-6142	460	37	max	max	PROPN
ejpam-6142	460	38	{	{	PUNCT
ejpam-6142	460	39	min	min	NOUN
ejpam-6142	460	40	{	{	PUNCT
ejpam-6142	460	41	1	1	NUM
ejpam-6142	460	42	,	,	PUNCT
ejpam-6142	460	43	if	if	SCONJ
ejpam-6142	460	44	(	(	PUNCT
ejpam-6142	460	45	λ3−λ4)+im(λ10−λ11	λ3−λ4)+im(λ10−λ11	NOUN
ejpam-6142	460	46	)	)	PUNCT
ejpam-6142	460	47	w2	w2	NOUN
ejpam-6142	460	48	}	}	PUNCT
ejpam-6142	460	49	,	,	PUNCT
ejpam-6142	460	50	0	0	NUM
ejpam-6142	460	51	}	}	PUNCT
ejpam-6142	460	52	,	,	PUNCT
ejpam-6142	460	53	u∗3	u∗3	NOUN
ejpam-6142	460	54	=	=	SYM
ejpam-6142	460	55	max	max	PROPN
ejpam-6142	460	56	{	{	PUNCT
ejpam-6142	460	57	min	min	NOUN
ejpam-6142	460	58	{	{	PUNCT
ejpam-6142	460	59	1	1	NUM
ejpam-6142	460	60	,	,	PUNCT
ejpam-6142	460	61	(	(	PUNCT
ejpam-6142	460	62	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	SYM
ejpam-6142	460	63	)	)	PUNCT
ejpam-6142	460	64	w3	w3	NOUN
ejpam-6142	460	65	}	}	PUNCT
ejpam-6142	460	66	,	,	PUNCT
ejpam-6142	460	67	0	0	NUM
ejpam-6142	460	68	}	}	PUNCT
ejpam-6142	460	69	.	.	PUNCT
ejpam-6142	461	1	proof	proof	NOUN
ejpam-6142	461	2	.	.	PUNCT
ejpam-6142	462	1	the	the	DET
ejpam-6142	462	2	hamiltonian	hamiltonian	ADJ
ejpam-6142	462	3	h	h	PROPN
ejpam-6142	462	4	corresponding	correspond	VERB
ejpam-6142	462	5	to	to	ADP
ejpam-6142	462	6	the	the	DET
ejpam-6142	462	7	optimum	optimum	ADJ
ejpam-6142	462	8	model	model	NOUN
ejpam-6142	462	9	is	be	AUX
ejpam-6142	462	10	expressed	express	VERB
ejpam-6142	462	11	as	as	ADP
ejpam-6142	462	12	h	h	NOUN
ejpam-6142	462	13	=	=	NOUN
ejpam-6142	462	14	b1ef	b1ef	NOUN
ejpam-6142	463	1	+	+	CCONJ
ejpam-6142	463	2	b2if	b2if	NOUN
ejpam-6142	463	3	+	+	CCONJ
ejpam-6142	463	4	b3df	b3df	PUNCT
ejpam-6142	463	5	+	+	NUM
ejpam-6142	463	6	b4tf	b4tf	X
ejpam-6142	463	7	+	+	X
ejpam-6142	463	8	b5uf	b5uf	X
ejpam-6142	463	9	+	+	SYM
ejpam-6142	463	10	b6af	b6af	X
ejpam-6142	463	11	+	+	CCONJ
ejpam-6142	463	12	b7em	b7em	PUNCT
ejpam-6142	463	13	+	+	CCONJ
ejpam-6142	463	14	b8im	b8im	SYM
ejpam-6142	463	15	+	+	CCONJ
ejpam-6142	463	16	b9	b9	NOUN
ejpam-6142	463	17	dm	dm	NOUN
ejpam-6142	463	18	+	+	NUM
ejpam-6142	463	19	b10tm	b10tm	PUNCT
ejpam-6142	464	1	+	+	CCONJ
ejpam-6142	464	2	b11um	b11um	PROPN
ejpam-6142	464	3	+	+	CCONJ
ejpam-6142	464	4	b12am	b12am	PROPN
ejpam-6142	464	5	+	+	CCONJ
ejpam-6142	464	6	1	1	NUM
ejpam-6142	464	7	2	2	NUM
ejpam-6142	464	8	(	(	PUNCT
ejpam-6142	464	9	w1u	w1u	NOUN
ejpam-6142	464	10	2	2	NUM
ejpam-6142	464	11	1	1	NUM
ejpam-6142	464	12	+	+	CCONJ
ejpam-6142	464	13	w2u	w2u	ADJ
ejpam-6142	464	14	2	2	NUM
ejpam-6142	464	15	2	2	NUM
ejpam-6142	464	16	+	+	CCONJ
ejpam-6142	464	17	w3u	w3u	PROPN
ejpam-6142	464	18	2	2	NUM
ejpam-6142	464	19	3	3	NUM
ejpam-6142	464	20	)	)	PUNCT
ejpam-6142	464	21	+	+	CCONJ
ejpam-6142	465	1	λ1	λ1	ADJ
ejpam-6142	465	2	dsf	dsf	NOUN
ejpam-6142	465	3	dt	dt	NOUN
ejpam-6142	466	1	+	+	CCONJ
ejpam-6142	466	2	λ2	λ2	NOUN
ejpam-6142	466	3	def	def	ADJ
ejpam-6142	466	4	dt	dt	NOUN
ejpam-6142	467	1	+	+	CCONJ
ejpam-6142	467	2	λ3	λ3	PROPN
ejpam-6142	467	3	dif	dif	ADV
ejpam-6142	467	4	dt	dt	PUNCT
ejpam-6142	468	1	+	+	CCONJ
ejpam-6142	468	2	λ4	λ4	ADJ
ejpam-6142	468	3	ddf	ddf	NOUN
ejpam-6142	468	4	dt	dt	PROPN
ejpam-6142	468	5	+	+	CCONJ
ejpam-6142	468	6	λ5	λ5	PROPN
ejpam-6142	468	7	dtf	dtf	PROPN
ejpam-6142	468	8	dt	dt	PROPN
ejpam-6142	468	9	+	+	CCONJ
ejpam-6142	468	10	λ6	λ6	PROPN
ejpam-6142	468	11	duf	duf	NOUN
ejpam-6142	468	12	dt	dt	NOUN
ejpam-6142	469	1	+	+	CCONJ
ejpam-6142	469	2	λ7	λ7	ADJ
ejpam-6142	469	3	daf	daf	NOUN
ejpam-6142	469	4	dt	dt	X
ejpam-6142	470	1	+	+	CCONJ
ejpam-6142	470	2	λ8	λ8	VERB
ejpam-6142	470	3	dsm	dsm	ADJ
ejpam-6142	470	4	dt	dt	NOUN
ejpam-6142	470	5	+	+	CCONJ
ejpam-6142	470	6	λ9	λ9	ADJ
ejpam-6142	470	7	dem	dem	ADJ
ejpam-6142	470	8	dt	dt	NOUN
ejpam-6142	470	9	+	+	CCONJ
ejpam-6142	470	10	λ10	λ10	NOUN
ejpam-6142	470	11	dim	dim	NOUN
ejpam-6142	470	12	dt	dt	NOUN
ejpam-6142	470	13	+	+	CCONJ
ejpam-6142	470	14	λ11	λ11	PROPN
ejpam-6142	470	15	ddm	ddm	PROPN
ejpam-6142	470	16	dt	dt	PROPN
ejpam-6142	471	1	+	+	PROPN
ejpam-6142	471	2	λ12	λ12	PROPN
ejpam-6142	471	3	dtm	dtm	PROPN
ejpam-6142	471	4	dt	dt	NOUN
ejpam-6142	471	5	+	+	CCONJ
ejpam-6142	471	6	λ13	λ13	PROPN
ejpam-6142	471	7	dum	dum	NOUN
ejpam-6142	471	8	dt	dt	NOUN
ejpam-6142	471	9	+	+	CCONJ
ejpam-6142	471	10	λ14	λ14	PROPN
ejpam-6142	471	11	dam	dam	NOUN
ejpam-6142	471	12	dt	dt	NOUN
ejpam-6142	472	1	so	so	ADV
ejpam-6142	472	2	,	,	PUNCT
ejpam-6142	472	3	it	it	PRON
ejpam-6142	472	4	can	can	AUX
ejpam-6142	472	5	be	be	AUX
ejpam-6142	472	6	written	write	VERB
ejpam-6142	472	7	as	as	ADP
ejpam-6142	472	8	s.	s.	PROPN
ejpam-6142	472	9	m.	m.	PROPN
ejpam-6142	472	10	fatah	fatah	PROPN
ejpam-6142	472	11	,	,	PUNCT
ejpam-6142	472	12	s.	s.	PROPN
ejpam-6142	472	13	h.	h.	PROPN
ejpam-6142	472	14	a.	a.	PROPN
ejpam-6142	472	15	khoshnaw	khoshnaw	PROPN
ejpam-6142	472	16	,	,	PUNCT
ejpam-6142	472	17	a.	a.	PROPN
ejpam-6142	472	18	n.	n.	PROPN
ejpam-6142	472	19	mustafa	mustafa	PROPN
ejpam-6142	472	20	/	/	SYM
ejpam-6142	472	21	eur	eur	PROPN
ejpam-6142	472	22	.	.	PUNCT
ejpam-6142	473	1	j.	j.	PROPN
ejpam-6142	473	2	pure	pure	PROPN
ejpam-6142	473	3	appl	appl	PROPN
ejpam-6142	473	4	.	.	PROPN
ejpam-6142	473	5	math	math	PROPN
ejpam-6142	473	6	,	,	PUNCT
ejpam-6142	473	7	18	18	NUM
ejpam-6142	473	8	(	(	PUNCT
ejpam-6142	473	9	2	2	NUM
ejpam-6142	473	10	)	)	PUNCT
ejpam-6142	473	11	(	(	PUNCT
ejpam-6142	473	12	2025	2025	NUM
ejpam-6142	473	13	)	)	PUNCT
ejpam-6142	473	14	,	,	PUNCT
ejpam-6142	473	15	6142	6142	NUM
ejpam-6142	473	16	21	21	NUM
ejpam-6142	473	17	of	of	ADP
ejpam-6142	473	18	33	33	NUM
ejpam-6142	473	19	h	h	NOUN
ejpam-6142	473	20	=	=	PUNCT
ejpam-6142	473	21	b1ef	b1ef	NOUN
ejpam-6142	474	1	+	+	CCONJ
ejpam-6142	474	2	b2if	b2if	NOUN
ejpam-6142	474	3	+	+	CCONJ
ejpam-6142	474	4	b3df	b3df	PUNCT
ejpam-6142	474	5	+	+	NUM
ejpam-6142	474	6	b4tf	b4tf	X
ejpam-6142	474	7	+	+	X
ejpam-6142	474	8	b5uf	b5uf	X
ejpam-6142	474	9	+	+	SYM
ejpam-6142	474	10	b6af	b6af	X
ejpam-6142	474	11	+	+	CCONJ
ejpam-6142	474	12	b7em	b7em	PUNCT
ejpam-6142	474	13	+	+	CCONJ
ejpam-6142	474	14	b8im	b8im	SYM
ejpam-6142	474	15	+	+	CCONJ
ejpam-6142	474	16	b9	b9	NOUN
ejpam-6142	474	17	dm	dm	NOUN
ejpam-6142	474	18	+	+	NUM
ejpam-6142	474	19	b10tm	b10tm	PUNCT
ejpam-6142	475	1	+	+	CCONJ
ejpam-6142	475	2	b11um	b11um	PROPN
ejpam-6142	475	3	+	+	CCONJ
ejpam-6142	475	4	b12am	b12am	PROPN
ejpam-6142	475	5	+	+	CCONJ
ejpam-6142	475	6	1	1	NUM
ejpam-6142	475	7	2	2	NUM
ejpam-6142	475	8	(	(	PUNCT
ejpam-6142	475	9	w1u	w1u	NOUN
ejpam-6142	475	10	2	2	NUM
ejpam-6142	475	11	1	1	NUM
ejpam-6142	475	12	+	+	CCONJ
ejpam-6142	475	13	w2u	w2u	ADJ
ejpam-6142	475	14	2	2	NUM
ejpam-6142	475	15	2	2	NUM
ejpam-6142	475	16	+	+	CCONJ
ejpam-6142	475	17	w3u	w3u	PROPN
ejpam-6142	475	18	2	2	NUM
ejpam-6142	475	19	3	3	NUM
ejpam-6142	475	20	)	)	PUNCT
ejpam-6142	476	1	+	+	CCONJ
ejpam-6142	476	2	λ1	λ1	ADJ
ejpam-6142	476	3	(	(	PUNCT
ejpam-6142	476	4	λ−	λ−	PROPN
ejpam-6142	476	5	(	(	PUNCT
ejpam-6142	476	6	1−	1−	NUM
ejpam-6142	476	7	u1	u1	NOUN
ejpam-6142	476	8	)	)	PUNCT
ejpam-6142	476	9	(	(	PUNCT
ejpam-6142	476	10	1−	1−	NUM
ejpam-6142	476	11	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	476	12	−	−	PROPN
ejpam-6142	476	13	ηsf	ηsf	PROPN
ejpam-6142	476	14	)	)	PUNCT
ejpam-6142	477	1	+	+	NUM
ejpam-6142	477	2	λ2	λ2	NOUN
ejpam-6142	477	3	(	(	PUNCT
ejpam-6142	477	4	(	(	PUNCT
ejpam-6142	477	5	1−	1−	NUM
ejpam-6142	477	6	u1	u1	NOUN
ejpam-6142	477	7	)	)	PUNCT
ejpam-6142	477	8	(	(	PUNCT
ejpam-6142	477	9	1−	1−	NUM
ejpam-6142	477	10	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	477	11	−	−	PROPN
ejpam-6142	477	12	(	(	PUNCT
ejpam-6142	477	13	αf	αf	ADP
ejpam-6142	477	14	+	+	X
ejpam-6142	477	15	η)ef	η)ef	PROPN
ejpam-6142	477	16	)	)	PUNCT
ejpam-6142	478	1	+	+	CCONJ
ejpam-6142	478	2	λ3	λ3	PROPN
ejpam-6142	478	3	(	(	PUNCT
ejpam-6142	478	4	αfef	αfef	NOUN
ejpam-6142	478	5	−	−	PROPN
ejpam-6142	478	6	(	(	PUNCT
ejpam-6142	478	7	u2	u2	PROPN
ejpam-6142	478	8	+	+	CCONJ
ejpam-6142	478	9	µ+	µ+	PROPN
ejpam-6142	478	10	η	η	PROPN
ejpam-6142	478	11	+	+	PROPN
ejpam-6142	478	12	γf	γf	PROPN
ejpam-6142	478	13	+	+	CCONJ
ejpam-6142	478	14	θf	θf	NOUN
ejpam-6142	478	15	)	)	PUNCT
ejpam-6142	478	16	if	if	SCONJ
ejpam-6142	478	17	)	)	PUNCT
ejpam-6142	479	1	+	+	CCONJ
ejpam-6142	479	2	λ4	λ4	ADJ
ejpam-6142	479	3	(	(	PUNCT
ejpam-6142	479	4	(	(	PUNCT
ejpam-6142	479	5	u2	u2	NOUN
ejpam-6142	479	6	+	+	CCONJ
ejpam-6142	479	7	γf	γf	PROPN
ejpam-6142	479	8	)	)	PUNCT
ejpam-6142	479	9	if	if	SCONJ
ejpam-6142	479	10	−	−	PROPN
ejpam-6142	479	11	(	(	PUNCT
ejpam-6142	479	12	u3	u3	NOUN
ejpam-6142	479	13	+	+	CCONJ
ejpam-6142	479	14	µ+	µ+	PROPN
ejpam-6142	479	15	η	η	PROPN
ejpam-6142	479	16	+	+	PROPN
ejpam-6142	479	17	ρf	ρf	ADJ
ejpam-6142	479	18	)	)	PUNCT
ejpam-6142	479	19	df	df	PROPN
ejpam-6142	479	20	)	)	PUNCT
ejpam-6142	480	1	+	+	CCONJ
ejpam-6142	480	2	λ5	λ5	NOUN
ejpam-6142	480	3	(	(	PUNCT
ejpam-6142	480	4	u3af	u3af	X
ejpam-6142	480	5	+	+	CCONJ
ejpam-6142	480	6	(	(	PUNCT
ejpam-6142	480	7	u3	u3	NOUN
ejpam-6142	480	8	+	+	CCONJ
ejpam-6142	480	9	ρf	ρf	NOUN
ejpam-6142	480	10	)	)	PUNCT
ejpam-6142	480	11	df	df	PROPN
ejpam-6142	480	12	−	−	PROPN
ejpam-6142	480	13	(	(	PUNCT
ejpam-6142	480	14	µ+	µ+	PROPN
ejpam-6142	480	15	η	η	PROPN
ejpam-6142	480	16	+	+	PROPN
ejpam-6142	480	17	(	(	PUNCT
ejpam-6142	480	18	1−	1−	NUM
ejpam-6142	480	19	u3)ωf	u3)ωf	NOUN
ejpam-6142	480	20	)	)	PUNCT
ejpam-6142	480	21	tf	tf	X
ejpam-6142	480	22	)	)	PUNCT
ejpam-6142	481	1	+	+	CCONJ
ejpam-6142	481	2	λ6	λ6	PROPN
ejpam-6142	481	3	(	(	PUNCT
ejpam-6142	481	4	θfif	θfif	PROPN
ejpam-6142	481	5	−	−	PROPN
ejpam-6142	481	6	(	(	PUNCT
ejpam-6142	481	7	µ+	µ+	X
ejpam-6142	481	8	η	η	PROPN
ejpam-6142	481	9	+	+	PROPN
ejpam-6142	481	10	λf	λf	PROPN
ejpam-6142	481	11	)	)	PUNCT
ejpam-6142	481	12	uf	uf	NOUN
ejpam-6142	481	13	)	)	PUNCT
ejpam-6142	482	1	+	+	CCONJ
ejpam-6142	482	2	λ7	λ7	ADJ
ejpam-6142	482	3	(	(	PUNCT
ejpam-6142	482	4	λfuf	λfuf	PROPN
ejpam-6142	482	5	+	+	CCONJ
ejpam-6142	482	6	(	(	PUNCT
ejpam-6142	482	7	1−	1−	NUM
ejpam-6142	482	8	u3)ωftf	u3)ωftf	NOUN
ejpam-6142	482	9	−	−	PROPN
ejpam-6142	482	10	(	(	PUNCT
ejpam-6142	482	11	u3	u3	NOUN
ejpam-6142	482	12	+	+	CCONJ
ejpam-6142	482	13	µ+	µ+	PROPN
ejpam-6142	482	14	η)af	η)af	PROPN
ejpam-6142	482	15	)	)	PUNCT
ejpam-6142	483	1	+	+	CCONJ
ejpam-6142	483	2	λ8	λ8	ADJ
ejpam-6142	483	3	(	(	PUNCT
ejpam-6142	483	4	λ−	λ−	PROPN
ejpam-6142	483	5	(	(	PUNCT
ejpam-6142	483	6	1−	1−	NUM
ejpam-6142	483	7	u1	u1	NOUN
ejpam-6142	483	8	)	)	PUNCT
ejpam-6142	483	9	(	(	PUNCT
ejpam-6142	483	10	1−	1−	NUM
ejpam-6142	483	11	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	483	12	−	−	PROPN
ejpam-6142	483	13	ηsm	ηsm	NOUN
ejpam-6142	483	14	)	)	PUNCT
ejpam-6142	483	15	+	+	CCONJ
ejpam-6142	483	16	λ9	λ9	ADJ
ejpam-6142	483	17	(	(	PUNCT
ejpam-6142	483	18	(	(	PUNCT
ejpam-6142	483	19	1−	1−	NUM
ejpam-6142	483	20	u1	u1	NOUN
ejpam-6142	483	21	)	)	PUNCT
ejpam-6142	483	22	(	(	PUNCT
ejpam-6142	483	23	1−	1−	NUM
ejpam-6142	483	24	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	483	25	−	−	PROPN
ejpam-6142	484	1	(	(	PUNCT
ejpam-6142	484	2	αm	αm	NOUN
ejpam-6142	484	3	+	+	PROPN
ejpam-6142	484	4	η)em	η)em	PROPN
ejpam-6142	484	5	)	)	PUNCT
ejpam-6142	485	1	+	+	NUM
ejpam-6142	485	2	λ10	λ10	NOUN
ejpam-6142	485	3	(	(	PUNCT
ejpam-6142	485	4	αmem	αmem	ADJ
ejpam-6142	485	5	−	−	PROPN
ejpam-6142	486	1	(	(	PUNCT
ejpam-6142	487	1	u2	u2	PROPN
ejpam-6142	487	2	+	+	CCONJ
ejpam-6142	487	3	µ+	µ+	PROPN
ejpam-6142	487	4	η	η	PROPN
ejpam-6142	487	5	+	+	X
ejpam-6142	487	6	γm	γm	PROPN
ejpam-6142	487	7	+	+	NUM
ejpam-6142	487	8	θm	θm	NOUN
ejpam-6142	487	9	)	)	PUNCT
ejpam-6142	487	10	i	i	PRON
ejpam-6142	487	11	m	m	VERB
ejpam-6142	487	12	)	)	PUNCT
ejpam-6142	488	1	+	+	CCONJ
ejpam-6142	488	2	λ11	λ11	INTJ
ejpam-6142	488	3	(	(	PUNCT
ejpam-6142	488	4	(	(	PUNCT
ejpam-6142	488	5	u2	u2	NOUN
ejpam-6142	488	6	+	+	CCONJ
ejpam-6142	488	7	γm	γm	NOUN
ejpam-6142	488	8	)	)	PUNCT
ejpam-6142	488	9	i	i	PRON
ejpam-6142	488	10	m	m	VERB
ejpam-6142	488	11	−	−	NOUN
ejpam-6142	488	12	(	(	PUNCT
ejpam-6142	488	13	u3	u3	NOUN
ejpam-6142	488	14	+	+	CCONJ
ejpam-6142	488	15	µ+	µ+	PROPN
ejpam-6142	488	16	η	η	PROPN
ejpam-6142	488	17	+	+	PROPN
ejpam-6142	488	18	ρm)dm	ρm)dm	PROPN
ejpam-6142	488	19	)	)	PUNCT
ejpam-6142	488	20	+	+	CCONJ
ejpam-6142	488	21	λ12	λ12	ADP
ejpam-6142	488	22	(	(	PUNCT
ejpam-6142	488	23	u3am	u3am	PUNCT
ejpam-6142	488	24	+	+	CCONJ
ejpam-6142	488	25	(	(	PUNCT
ejpam-6142	488	26	u3	u3	NOUN
ejpam-6142	488	27	+	+	CCONJ
ejpam-6142	488	28	ρm)dm	ρm)dm	NUM
ejpam-6142	488	29	−	−	PROPN
ejpam-6142	488	30	(	(	PUNCT
ejpam-6142	488	31	µ+	µ+	X
ejpam-6142	488	32	η	η	PROPN
ejpam-6142	488	33	+	+	PROPN
ejpam-6142	488	34	(	(	PUNCT
ejpam-6142	488	35	1−	1−	NUM
ejpam-6142	488	36	u3)ωm)tm	u3)ωm)tm	NUM
ejpam-6142	488	37	)	)	PUNCT
ejpam-6142	489	1	+	+	CCONJ
ejpam-6142	489	2	λ13	λ13	X
ejpam-6142	489	3	(	(	PUNCT
ejpam-6142	489	4	θmim	θmim	NOUN
ejpam-6142	489	5	−	−	PROPN
ejpam-6142	489	6	(	(	PUNCT
ejpam-6142	489	7	µ+	µ+	X
ejpam-6142	489	8	η	η	PROPN
ejpam-6142	489	9	+	+	NOUN
ejpam-6142	489	10	λm)um	λm)um	PRON
ejpam-6142	489	11	)	)	PUNCT
ejpam-6142	490	1	+	+	CCONJ
ejpam-6142	490	2	λ14	λ14	NOUN
ejpam-6142	490	3	(	(	PUNCT
ejpam-6142	490	4	λmum	λmum	ADJ
ejpam-6142	490	5	+	+	CCONJ
ejpam-6142	490	6	(	(	PUNCT
ejpam-6142	490	7	1−	1−	NUM
ejpam-6142	490	8	u3)ωmtm	u3)ωmtm	PROPN
ejpam-6142	490	9	−	−	PROPN
ejpam-6142	490	10	(	(	PUNCT
ejpam-6142	490	11	u3	u3	NOUN
ejpam-6142	490	12	+	+	CCONJ
ejpam-6142	490	13	µ+	µ+	PROPN
ejpam-6142	490	14	η)am	η)am	PROPN
ejpam-6142	490	15	)	)	PUNCT
ejpam-6142	490	16	based	base	VERB
ejpam-6142	490	17	on	on	ADP
ejpam-6142	490	18	the	the	DET
ejpam-6142	490	19	pmp	pmp	PROPN
ejpam-6142	490	20	’s	’s	PART
ejpam-6142	490	21	second	second	ADJ
ejpam-6142	490	22	condition	condition	NOUN
ejpam-6142	490	23	,	,	PUNCT
ejpam-6142	490	24	adjoint	adjoint	NOUN
ejpam-6142	490	25	variables	variable	NOUN
ejpam-6142	490	26	λi	λi	ADP
ejpam-6142	490	27	,	,	PUNCT
ejpam-6142	490	28	where	where	SCONJ
ejpam-6142	490	29	i	i	PRON
ejpam-6142	490	30	=	=	NOUN
ejpam-6142	490	31	1	1	NUM
ejpam-6142	490	32	,	,	PUNCT
ejpam-6142	490	33	2	2	NUM
ejpam-6142	490	34	,	,	PUNCT
ejpam-6142	490	35	.	.	PUNCT
ejpam-6142	490	36	.	.	PUNCT
ejpam-6142	490	37	.	.	PUNCT
ejpam-6142	491	1	,	,	PUNCT
ejpam-6142	491	2	14	14	NUM
ejpam-6142	491	3	exist	exist	VERB
ejpam-6142	491	4	such	such	ADJ
ejpam-6142	491	5	that	that	SCONJ
ejpam-6142	491	6	dλi	dλi	VERB
ejpam-6142	491	7	dt	dt	NOUN
ejpam-6142	491	8	=	=	SYM
ejpam-6142	491	9	−∂h	−∂h	PROPN
ejpam-6142	491	10	∂j	∂j	NOUN
ejpam-6142	491	11	,	,	PUNCT
ejpam-6142	491	12	where	where	SCONJ
ejpam-6142	491	13	i	i	PRON
ejpam-6142	491	14	=	=	NOUN
ejpam-6142	491	15	1	1	NUM
ejpam-6142	491	16	,	,	PUNCT
ejpam-6142	491	17	2	2	NUM
ejpam-6142	491	18	..	..	SYM
ejpam-6142	491	19	14	14	NUM
ejpam-6142	491	20	,	,	PUNCT
ejpam-6142	491	21	and	and	CCONJ
ejpam-6142	491	22	j	j	X
ejpam-6142	491	23	=	=	SYM
ejpam-6142	491	24	sf	sf	PROPN
ejpam-6142	491	25	,	,	PUNCT
ejpam-6142	491	26	ef	ef	PROPN
ejpam-6142	491	27	,	,	PUNCT
ejpam-6142	491	28	if	if	SCONJ
ejpam-6142	491	29	,	,	PUNCT
ejpam-6142	491	30	df	df	PROPN
ejpam-6142	491	31	,	,	PUNCT
ejpam-6142	491	32	tf	tf	INTJ
ejpam-6142	491	33	,	,	PUNCT
ejpam-6142	491	34	uf	uf	PROPN
ejpam-6142	491	35	,	,	PUNCT
ejpam-6142	491	36	af	af	PROPN
ejpam-6142	491	37	,	,	PUNCT
ejpam-6142	491	38	sm	sm	PROPN
ejpam-6142	491	39	,	,	PUNCT
ejpam-6142	491	40	em	em	PRON
ejpam-6142	491	41	,	,	PUNCT
ejpam-6142	491	42	i	i	PRON
ejpam-6142	491	43	m	m	PROPN
ejpam-6142	491	44	,	,	PUNCT
ejpam-6142	491	45	dm	dm	PROPN
ejpam-6142	491	46	,	,	PUNCT
ejpam-6142	491	47	tm	tm	NOUN
ejpam-6142	491	48	,	,	PUNCT
ejpam-6142	491	49	um	um	INTJ
ejpam-6142	491	50	,	,	PUNCT
ejpam-6142	491	51	am	be	AUX
ejpam-6142	491	52	hence	hence	ADV
ejpam-6142	491	53	,	,	PUNCT
ejpam-6142	491	54	the	the	DET
ejpam-6142	491	55	expressions	expression	NOUN
ejpam-6142	491	56	for	for	ADP
ejpam-6142	491	57	the	the	DET
ejpam-6142	491	58	adjoint	adjoint	PROPN
ejpam-6142	491	59	equations	equation	NOUN
ejpam-6142	491	60	can	can	AUX
ejpam-6142	491	61	be	be	AUX
ejpam-6142	491	62	formulated	formulate	VERB
ejpam-6142	491	63	as	as	ADP
ejpam-6142	491	64	:	:	PUNCT
ejpam-6142	491	65	dλ1	dλ1	NOUN
ejpam-6142	491	66	dt	dt	PUNCT
ejpam-6142	492	1	=	=	PUNCT
ejpam-6142	492	2	−	−	PROPN
ejpam-6142	492	3	∂h	∂h	PROPN
ejpam-6142	493	1	∂sf	∂sf	PROPN
ejpam-6142	493	2	=	=	SYM
ejpam-6142	493	3	(	(	PUNCT
ejpam-6142	493	4	1−	1−	NUM
ejpam-6142	493	5	u1	u1	NOUN
ejpam-6142	493	6	)	)	PUNCT
ejpam-6142	493	7	(	(	PUNCT
ejpam-6142	493	8	1−	1−	NUM
ejpam-6142	493	9	κϵ)βfim	κϵ)βfim	NOUN
ejpam-6142	493	10	(	(	PUNCT
ejpam-6142	493	11	λ1	λ1	PROPN
ejpam-6142	493	12	−	−	PROPN
ejpam-6142	493	13	λ2	λ2	PROPN
ejpam-6142	493	14	)	)	PUNCT
ejpam-6142	493	15	+	+	CCONJ
ejpam-6142	493	16	ηλ1	ηλ1	ADJ
ejpam-6142	493	17	,	,	PUNCT
ejpam-6142	493	18	dλ2	dλ2	NOUN
ejpam-6142	493	19	dt	dt	NOUN
ejpam-6142	493	20	=	=	PUNCT
ejpam-6142	493	21	−	−	PROPN
ejpam-6142	494	1	∂h	∂h	PROPN
ejpam-6142	494	2	∂ef	∂ef	PROPN
ejpam-6142	494	3	=	=	PROPN
ejpam-6142	494	4	−b1	−b1	PROPN
ejpam-6142	494	5	+	+	NUM
ejpam-6142	494	6	ηλ2	ηλ2	NOUN
ejpam-6142	494	7	+	+	CCONJ
ejpam-6142	494	8	αf	αf	PROPN
ejpam-6142	494	9	(	(	PUNCT
ejpam-6142	494	10	λ2	λ2	PROPN
ejpam-6142	494	11	−	−	PROPN
ejpam-6142	494	12	λ3	λ3	PROPN
ejpam-6142	494	13	)	)	PUNCT
ejpam-6142	494	14	,	,	PUNCT
ejpam-6142	494	15	dλ3	dλ3	NOUN
ejpam-6142	495	1	dt	dt	AUX
ejpam-6142	495	2	=	=	PUNCT
ejpam-6142	495	3	−∂h	−∂h	NOUN
ejpam-6142	495	4	∂if	∂if	NOUN
ejpam-6142	495	5	=	=	PUNCT
ejpam-6142	495	6	−b2	−b2	PROPN
ejpam-6142	495	7	+	+	CCONJ
ejpam-6142	495	8	(	(	PUNCT
ejpam-6142	495	9	µ+	µ+	X
ejpam-6142	495	10	η)λ3	η)λ3	NOUN
ejpam-6142	495	11	+	+	CCONJ
ejpam-6142	495	12	(	(	PUNCT
ejpam-6142	495	13	u2	u2	PROPN
ejpam-6142	495	14	+	+	CCONJ
ejpam-6142	495	15	γf	γf	PROPN
ejpam-6142	495	16	)	)	PUNCT
ejpam-6142	495	17	(	(	PUNCT
ejpam-6142	495	18	λ3	λ3	PROPN
ejpam-6142	495	19	−	−	PROPN
ejpam-6142	495	20	λ4	λ4	PROPN
ejpam-6142	495	21	)	)	PUNCT
ejpam-6142	496	1	+	+	CCONJ
ejpam-6142	496	2	θf	θf	PROPN
ejpam-6142	496	3	(	(	PUNCT
ejpam-6142	496	4	λ3	λ3	PROPN
ejpam-6142	496	5	−	−	PROPN
ejpam-6142	496	6	λ6	λ6	PROPN
ejpam-6142	496	7	)	)	PUNCT
ejpam-6142	496	8	+	+	CCONJ
ejpam-6142	496	9	(	(	PUNCT
ejpam-6142	496	10	1−	1−	NUM
ejpam-6142	496	11	u1	u1	NOUN
ejpam-6142	496	12	)	)	PUNCT
ejpam-6142	496	13	(	(	PUNCT
ejpam-6142	496	14	1−	1−	NUM
ejpam-6142	496	15	κϵ)βmsm	κϵ)βmsm	NOUN
ejpam-6142	496	16	(	(	PUNCT
ejpam-6142	496	17	λ8	λ8	VERB
ejpam-6142	496	18	−	−	NOUN
ejpam-6142	496	19	λ9	λ9	NOUN
ejpam-6142	496	20	)	)	PUNCT
ejpam-6142	496	21	,	,	PUNCT
ejpam-6142	496	22	dλ4	dλ4	VERB
ejpam-6142	496	23	dt	dt	NOUN
ejpam-6142	496	24	=	=	PUNCT
ejpam-6142	496	25	−	−	PROPN
ejpam-6142	497	1	∂h	∂h	PROPN
ejpam-6142	497	2	∂df	∂df	ADJ
ejpam-6142	497	3	=	=	PUNCT
ejpam-6142	497	4	−b3	−b3	PROPN
ejpam-6142	497	5	+	+	CCONJ
ejpam-6142	497	6	(	(	PUNCT
ejpam-6142	497	7	µ+	µ+	X
ejpam-6142	497	8	η)λ4	η)λ4	PROPN
ejpam-6142	497	9	+	+	CCONJ
ejpam-6142	497	10	(	(	PUNCT
ejpam-6142	497	11	u3	u3	NOUN
ejpam-6142	497	12	+	+	CCONJ
ejpam-6142	497	13	ρf	ρf	NOUN
ejpam-6142	497	14	)	)	PUNCT
ejpam-6142	497	15	(	(	PUNCT
ejpam-6142	497	16	λ4	λ4	NOUN
ejpam-6142	497	17	−	−	PROPN
ejpam-6142	497	18	λ5	λ5	NOUN
ejpam-6142	497	19	)	)	PUNCT
ejpam-6142	497	20	,	,	PUNCT
ejpam-6142	497	21	dλ5	dλ5	INTJ
ejpam-6142	497	22	dt	dt	NOUN
ejpam-6142	497	23	=	=	PUNCT
ejpam-6142	497	24	−	−	PROPN
ejpam-6142	498	1	∂h	∂h	PROPN
ejpam-6142	498	2	∂tf	∂tf	NOUN
ejpam-6142	498	3	=	=	PROPN
ejpam-6142	498	4	−b4	−b4	PROPN
ejpam-6142	498	5	+	+	CCONJ
ejpam-6142	498	6	(	(	PUNCT
ejpam-6142	498	7	µ+	µ+	DET
ejpam-6142	498	8	η)λ5	η)λ5	PROPN
ejpam-6142	498	9	+	+	CCONJ
ejpam-6142	498	10	(	(	PUNCT
ejpam-6142	498	11	1−	1−	NUM
ejpam-6142	498	12	u3)ωf	u3)ωf	NOUN
ejpam-6142	498	13	(	(	PUNCT
ejpam-6142	498	14	λ5	λ5	VERB
ejpam-6142	498	15	−	−	PROPN
ejpam-6142	498	16	λ7	λ7	PROPN
ejpam-6142	498	17	)	)	PUNCT
ejpam-6142	498	18	,	,	PUNCT
ejpam-6142	498	19	dλ6	dλ6	VERB
ejpam-6142	498	20	dt	dt	NOUN
ejpam-6142	499	1	=	=	SYM
ejpam-6142	499	2	−	−	PROPN
ejpam-6142	499	3	∂h	∂h	NOUN
ejpam-6142	499	4	∂uf	∂uf	PROPN
ejpam-6142	499	5	=	=	PUNCT
ejpam-6142	499	6	−b5	−b5	NOUN
ejpam-6142	499	7	+	+	CCONJ
ejpam-6142	499	8	(	(	PUNCT
ejpam-6142	499	9	µ+	µ+	X
ejpam-6142	499	10	η)λ6	η)λ6	PROPN
ejpam-6142	499	11	+	+	CCONJ
ejpam-6142	499	12	λf	λf	PROPN
ejpam-6142	499	13	(	(	PUNCT
ejpam-6142	499	14	λ6	λ6	PROPN
ejpam-6142	499	15	−	−	PROPN
ejpam-6142	499	16	λ7	λ7	PROPN
ejpam-6142	499	17	)	)	PUNCT
ejpam-6142	499	18	dλ7	dλ7	PROPN
ejpam-6142	499	19	dt	dt	PUNCT
ejpam-6142	500	1	=	=	PUNCT
ejpam-6142	500	2	−	−	PROPN
ejpam-6142	500	3	∂h	∂h	PROPN
ejpam-6142	500	4	∂af	∂af	NOUN
ejpam-6142	500	5	=	=	SYM
ejpam-6142	500	6	−b6	−b6	PROPN
ejpam-6142	500	7	+	+	CCONJ
ejpam-6142	500	8	(	(	PUNCT
ejpam-6142	500	9	u3	u3	NOUN
ejpam-6142	500	10	+	+	CCONJ
ejpam-6142	500	11	µ+	µ+	X
ejpam-6142	500	12	η)λ7	η)λ7	PROPN
ejpam-6142	500	13	−	−	NOUN
ejpam-6142	500	14	u3λ5	u3λ5	NOUN
ejpam-6142	501	1	dλ8	dλ8	ADJ
ejpam-6142	501	2	dt	dt	X
ejpam-6142	501	3	=	=	SYM
ejpam-6142	501	4	−	−	PROPN
ejpam-6142	502	1	∂h	∂h	PROPN
ejpam-6142	502	2	∂sm	∂sm	NOUN
ejpam-6142	502	3	=	=	SYM
ejpam-6142	502	4	(	(	PUNCT
ejpam-6142	502	5	1−	1−	NUM
ejpam-6142	502	6	u1	u1	NOUN
ejpam-6142	502	7	)	)	PUNCT
ejpam-6142	502	8	(	(	PUNCT
ejpam-6142	502	9	1−	1−	NUM
ejpam-6142	502	10	κϵ)βmif	κϵ)βmif	X
ejpam-6142	502	11	(	(	PUNCT
ejpam-6142	502	12	λ8	λ8	VERB
ejpam-6142	502	13	−	−	NOUN
ejpam-6142	502	14	λ9	λ9	NOUN
ejpam-6142	502	15	)	)	PUNCT
ejpam-6142	502	16	+	+	CCONJ
ejpam-6142	502	17	ηλ8	ηλ8	PROPN
ejpam-6142	502	18	dλ9	dλ9	NOUN
ejpam-6142	502	19	dt	dt	NOUN
ejpam-6142	503	1	=	=	SYM
ejpam-6142	504	1	−	−	PROPN
ejpam-6142	505	1	∂h	∂h	PROPN
ejpam-6142	505	2	∂em	∂em	PROPN
ejpam-6142	505	3	=	=	SYM
ejpam-6142	505	4	−b7	−b7	PROPN
ejpam-6142	505	5	+	+	NUM
ejpam-6142	505	6	ηλ9	ηλ9	NOUN
ejpam-6142	505	7	+	+	X
ejpam-6142	505	8	αm	αm	NOUN
ejpam-6142	505	9	(	(	PUNCT
ejpam-6142	505	10	λ9	λ9	ADJ
ejpam-6142	505	11	−	−	NOUN
ejpam-6142	505	12	λ10	λ10	NOUN
ejpam-6142	505	13	)	)	PUNCT
ejpam-6142	505	14	s.	s.	PROPN
ejpam-6142	505	15	m.	m.	PROPN
ejpam-6142	505	16	fatah	fatah	PROPN
ejpam-6142	505	17	,	,	PUNCT
ejpam-6142	505	18	s.	s.	PROPN
ejpam-6142	505	19	h.	h.	PROPN
ejpam-6142	505	20	a.	a.	PROPN
ejpam-6142	505	21	khoshnaw	khoshnaw	PROPN
ejpam-6142	505	22	,	,	PUNCT
ejpam-6142	505	23	a.	a.	PROPN
ejpam-6142	505	24	n.	n.	PROPN
ejpam-6142	505	25	mustafa	mustafa	PROPN
ejpam-6142	505	26	/	/	SYM
ejpam-6142	505	27	eur	eur	PROPN
ejpam-6142	505	28	.	.	PUNCT
ejpam-6142	506	1	j.	j.	PROPN
ejpam-6142	506	2	pure	pure	PROPN
ejpam-6142	506	3	appl	appl	PROPN
ejpam-6142	506	4	.	.	PROPN
ejpam-6142	506	5	math	math	PROPN
ejpam-6142	506	6	,	,	PUNCT
ejpam-6142	506	7	18	18	NUM
ejpam-6142	506	8	(	(	PUNCT
ejpam-6142	506	9	2	2	NUM
ejpam-6142	506	10	)	)	PUNCT
ejpam-6142	506	11	(	(	PUNCT
ejpam-6142	506	12	2025	2025	NUM
ejpam-6142	506	13	)	)	PUNCT
ejpam-6142	506	14	,	,	PUNCT
ejpam-6142	506	15	6142	6142	NUM
ejpam-6142	506	16	22	22	NUM
ejpam-6142	506	17	of	of	ADP
ejpam-6142	506	18	33	33	NUM
ejpam-6142	506	19	dλ10	dλ10	PROPN
ejpam-6142	506	20	dt	dt	NOUN
ejpam-6142	507	1	=	=	PUNCT
ejpam-6142	507	2	−	−	PROPN
ejpam-6142	507	3	∂h	∂h	PROPN
ejpam-6142	507	4	∂im	∂im	PROPN
ejpam-6142	508	1	=	=	PUNCT
ejpam-6142	509	1	−b8	−b8	PROPN
ejpam-6142	509	2	+	+	CCONJ
ejpam-6142	509	3	(	(	PUNCT
ejpam-6142	509	4	µ+	µ+	X
ejpam-6142	509	5	η)λ10	η)λ10	PROPN
ejpam-6142	509	6	+	+	CCONJ
ejpam-6142	509	7	(	(	PUNCT
ejpam-6142	509	8	u2	u2	NOUN
ejpam-6142	509	9	+	+	CCONJ
ejpam-6142	509	10	γm	γm	NOUN
ejpam-6142	509	11	)	)	PUNCT
ejpam-6142	509	12	(	(	PUNCT
ejpam-6142	509	13	λ10	λ10	NOUN
ejpam-6142	509	14	−	−	PROPN
ejpam-6142	509	15	λ11	λ11	PROPN
ejpam-6142	509	16	)	)	PUNCT
ejpam-6142	510	1	+	+	NUM
ejpam-6142	510	2	θm	θm	PROPN
ejpam-6142	510	3	(	(	PUNCT
ejpam-6142	510	4	λ10	λ10	NOUN
ejpam-6142	510	5	−	−	PROPN
ejpam-6142	510	6	λ13	λ13	PROPN
ejpam-6142	510	7	)	)	PUNCT
ejpam-6142	511	1	+	+	CCONJ
ejpam-6142	511	2	(	(	PUNCT
ejpam-6142	511	3	1−	1−	NUM
ejpam-6142	511	4	u1	u1	NOUN
ejpam-6142	511	5	)	)	PUNCT
ejpam-6142	511	6	(	(	PUNCT
ejpam-6142	511	7	1−	1−	NUM
ejpam-6142	511	8	κϵ)βfsf	κϵ)βfsf	X
ejpam-6142	511	9	(	(	PUNCT
ejpam-6142	511	10	λ1	λ1	PROPN
ejpam-6142	511	11	−	−	PROPN
ejpam-6142	511	12	λ2	λ2	PROPN
ejpam-6142	511	13	)	)	PUNCT
ejpam-6142	511	14	,	,	PUNCT
ejpam-6142	512	1	dλ11	dλ11	PROPN
ejpam-6142	512	2	dt	dt	X
ejpam-6142	512	3	=	=	PUNCT
ejpam-6142	512	4	−	−	PROPN
ejpam-6142	512	5	∂h	∂h	PROPN
ejpam-6142	512	6	∂dm	∂dm	NOUN
ejpam-6142	512	7	=	=	PUNCT
ejpam-6142	512	8	−b9	−b9	PROPN
ejpam-6142	512	9	+	+	CCONJ
ejpam-6142	512	10	(	(	PUNCT
ejpam-6142	512	11	µ+	µ+	X
ejpam-6142	512	12	η)λ11	η)λ11	PROPN
ejpam-6142	512	13	+	+	CCONJ
ejpam-6142	512	14	(	(	PUNCT
ejpam-6142	512	15	u3	u3	PROPN
ejpam-6142	512	16	+	+	CCONJ
ejpam-6142	512	17	ρm	ρm	NOUN
ejpam-6142	512	18	)	)	PUNCT
ejpam-6142	512	19	(	(	PUNCT
ejpam-6142	512	20	λ11	λ11	NOUN
ejpam-6142	512	21	−	−	PROPN
ejpam-6142	512	22	λ12	λ12	PROPN
ejpam-6142	512	23	)	)	PUNCT
ejpam-6142	512	24	,	,	PUNCT
ejpam-6142	512	25	dλ12	dλ12	PROPN
ejpam-6142	512	26	dt	dt	NOUN
ejpam-6142	512	27	=	=	SYM
ejpam-6142	512	28	−	−	PROPN
ejpam-6142	512	29	∂h	∂h	PROPN
ejpam-6142	512	30	∂tm	∂tm	PROPN
ejpam-6142	512	31	=	=	PUNCT
ejpam-6142	512	32	−b10	−b10	PUNCT
ejpam-6142	512	33	+	+	CCONJ
ejpam-6142	512	34	(	(	PUNCT
ejpam-6142	512	35	µ+	µ+	X
ejpam-6142	512	36	η)λ12	η)λ12	ADJ
ejpam-6142	512	37	+	+	NUM
ejpam-6142	512	38	(	(	PUNCT
ejpam-6142	512	39	1−	1−	NUM
ejpam-6142	512	40	u3)ωm	u3)ωm	PROPN
ejpam-6142	512	41	(	(	PUNCT
ejpam-6142	512	42	λ12	λ12	ADJ
ejpam-6142	512	43	−	−	PROPN
ejpam-6142	512	44	λ14	λ14	PROPN
ejpam-6142	512	45	)	)	PUNCT
ejpam-6142	512	46	dλ13	dλ13	PROPN
ejpam-6142	512	47	dt	dt	NOUN
ejpam-6142	512	48	=	=	SYM
ejpam-6142	512	49	−	−	PROPN
ejpam-6142	513	1	∂h	∂h	PROPN
ejpam-6142	513	2	∂um	∂um	PROPN
ejpam-6142	513	3	=	=	PUNCT
ejpam-6142	514	1	−b11	−b11	PUNCT
ejpam-6142	514	2	+	+	CCONJ
ejpam-6142	514	3	(	(	PUNCT
ejpam-6142	514	4	µ+	µ+	X
ejpam-6142	514	5	η)λ13	η)λ13	PROPN
ejpam-6142	514	6	+	+	CCONJ
ejpam-6142	514	7	λm	λm	X
ejpam-6142	514	8	(	(	PUNCT
ejpam-6142	514	9	λ13	λ13	PROPN
ejpam-6142	514	10	−	−	PROPN
ejpam-6142	514	11	λ14	λ14	PROPN
ejpam-6142	514	12	)	)	PUNCT
ejpam-6142	515	1	dλ14	dλ14	PROPN
ejpam-6142	515	2	dt	dt	NOUN
ejpam-6142	515	3	=	=	PUNCT
ejpam-6142	516	1	−	−	PROPN
ejpam-6142	516	2	∂h	∂h	PROPN
ejpam-6142	516	3	∂am	∂am	PROPN
ejpam-6142	516	4	=	=	PUNCT
ejpam-6142	516	5	−b12	−b12	PUNCT
ejpam-6142	516	6	+	+	CCONJ
ejpam-6142	516	7	(	(	PUNCT
ejpam-6142	516	8	u3	u3	NOUN
ejpam-6142	516	9	+	+	CCONJ
ejpam-6142	516	10	µ+	µ+	VERB
ejpam-6142	516	11	η)λ14	η)λ14	NOUN
ejpam-6142	516	12	−	−	NOUN
ejpam-6142	516	13	u3λ12	u3λ12	ADJ
ejpam-6142	516	14	further	far	ADV
ejpam-6142	516	15	,	,	PUNCT
ejpam-6142	516	16	the	the	DET
ejpam-6142	516	17	optimality	optimality	NOUN
ejpam-6142	516	18	conditions	condition	NOUN
ejpam-6142	516	19	give	give	VERB
ejpam-6142	516	20	us	we	PRON
ejpam-6142	516	21	∂h	∂h	PROPN
ejpam-6142	516	22	∂ui	∂ui	PROPN
ejpam-6142	516	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6142	516	24	ui	ui	NOUN
ejpam-6142	517	1	=	=	NOUN
ejpam-6142	518	1	u∗	u∗	NOUN
ejpam-6142	519	1	i	i	NOUN
ejpam-6142	519	2	=	=	NOUN
ejpam-6142	519	3	0	0	PROPN
ejpam-6142	519	4	,	,	PUNCT
ejpam-6142	519	5	where	where	SCONJ
ejpam-6142	519	6	i	i	PRON
ejpam-6142	519	7	=	=	NOUN
ejpam-6142	519	8	1	1	NUM
ejpam-6142	519	9	,	,	PUNCT
ejpam-6142	519	10	2	2	NUM
ejpam-6142	519	11	,	,	PUNCT
ejpam-6142	519	12	3	3	NUM
ejpam-6142	519	13	then	then	ADV
ejpam-6142	519	14	solving	solve	VERB
ejpam-6142	519	15	for	for	ADP
ejpam-6142	519	16	u∗1	u∗1	NOUN
ejpam-6142	519	17	,	,	PUNCT
ejpam-6142	519	18	u	u	NOUN
ejpam-6142	519	19	∗	∗	NOUN
ejpam-6142	519	20	2	2	NUM
ejpam-6142	519	21	and	and	CCONJ
ejpam-6142	519	22	u∗3	u∗3	NOUN
ejpam-6142	519	23	,	,	PUNCT
ejpam-6142	519	24	we	we	PRON
ejpam-6142	519	25	obtain	obtain	VERB
ejpam-6142	519	26	u∗1	u∗1	NOUN
ejpam-6142	519	27	=	=	SYM
ejpam-6142	519	28	(	(	PUNCT
ejpam-6142	519	29	1−κϵ)[βf	1−κϵ)[βf	NUM
ejpam-6142	519	30	imsf	imsf	NOUN
ejpam-6142	519	31	(	(	PUNCT
ejpam-6142	519	32	λ2−λ1)+βmifsm(λ9−λ8	λ2−λ1)+βmifsm(λ9−λ8	ADJ
ejpam-6142	519	33	)	)	PUNCT
ejpam-6142	519	34	]	]	X
ejpam-6142	520	1	w1	w1	NOUN
ejpam-6142	520	2	,	,	PUNCT
ejpam-6142	520	3	u∗2	u∗2	NOUN
ejpam-6142	520	4	=	=	SYM
ejpam-6142	520	5	if	if	SCONJ
ejpam-6142	520	6	(	(	PUNCT
ejpam-6142	520	7	λ3−λ4)+im(λ10−λ11	λ3−λ4)+im(λ10−λ11	NOUN
ejpam-6142	520	8	)	)	PUNCT
ejpam-6142	520	9	w2	w2	NOUN
ejpam-6142	520	10	,	,	PUNCT
ejpam-6142	520	11	and	and	CCONJ
ejpam-6142	520	12	u∗3	u∗3	NOUN
ejpam-6142	520	13	=	=	SYM
ejpam-6142	520	14	(	(	PUNCT
ejpam-6142	520	15	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	NOUN
ejpam-6142	520	16	)	)	PUNCT
ejpam-6142	520	17	w3	w3	NOUN
ejpam-6142	520	18	.	.	PUNCT
ejpam-6142	521	1	hence	hence	ADV
ejpam-6142	521	2	,	,	PUNCT
ejpam-6142	521	3	taking	take	VERB
ejpam-6142	521	4	into	into	ADP
ejpam-6142	521	5	account	account	NOUN
ejpam-6142	521	6	the	the	DET
ejpam-6142	521	7	control	control	NOUN
ejpam-6142	521	8	constraints	constraint	VERB
ejpam-6142	521	9	0	0	NUM
ejpam-6142	521	10	≤	≤	NUM
ejpam-6142	521	11	ui	ui	NOUN
ejpam-6142	521	12	≤	≤	NUM
ejpam-6142	521	13	1	1	NUM
ejpam-6142	521	14	where	where	SCONJ
ejpam-6142	521	15	i	i	PRON
ejpam-6142	521	16	=	=	NOUN
ejpam-6142	521	17	1	1	NUM
ejpam-6142	521	18	,	,	PUNCT
ejpam-6142	521	19	2	2	NUM
ejpam-6142	521	20	,	,	PUNCT
ejpam-6142	521	21	3	3	NUM
ejpam-6142	521	22	,	,	PUNCT
ejpam-6142	521	23	the	the	DET
ejpam-6142	521	24	optimal	optimal	ADJ
ejpam-6142	521	25	control	control	NOUN
ejpam-6142	521	26	variables	variable	NOUN
ejpam-6142	521	27	are	be	AUX
ejpam-6142	521	28	expressed	express	VERB
ejpam-6142	521	29	as	as	ADP
ejpam-6142	521	30	:	:	PUNCT
ejpam-6142	521	31	u∗1	u∗1	NOUN
ejpam-6142	521	32	=	=	PUNCT
ejpam-6142	522	1			PROPN
ejpam-6142	522	2	0	0	PUNCT
ejpam-6142	523	1	if	if	SCONJ
ejpam-6142	523	2	(	(	PUNCT
ejpam-6142	523	3	1−κϵ)[βf	1−κϵ)[βf	NUM
ejpam-6142	523	4	imsf	imsf	NOUN
ejpam-6142	523	5	(	(	PUNCT
ejpam-6142	523	6	λ2−λ1)+βmifsm(λ9−λ8	λ2−λ1)+βmifsm(λ9−λ8	ADJ
ejpam-6142	523	7	)	)	PUNCT
ejpam-6142	523	8	]	]	PUNCT
ejpam-6142	523	9	w1	w1	NOUN
ejpam-6142	523	10	<	<	X
ejpam-6142	523	11	0	0	PUNCT
ejpam-6142	523	12	g1	g1	PROPN
ejpam-6142	523	13	w1	w1	NOUN
ejpam-6142	523	14	if	if	SCONJ
ejpam-6142	523	15	0	0	NUM
ejpam-6142	523	16	<	<	X
ejpam-6142	523	17	(	(	PUNCT
ejpam-6142	523	18	1−κϵ)[βf	1−κϵ)[βf	NUM
ejpam-6142	523	19	imsf	imsf	NOUN
ejpam-6142	523	20	(	(	PUNCT
ejpam-6142	523	21	λ2−λ1)+βmifsm(λ9−λ8	λ2−λ1)+βmifsm(λ9−λ8	ADJ
ejpam-6142	523	22	)	)	PUNCT
ejpam-6142	523	23	]	]	PUNCT
ejpam-6142	523	24	w1	w1	NOUN
ejpam-6142	523	25	<	<	X
ejpam-6142	523	26	1	1	NUM
ejpam-6142	523	27	1	1	NUM
ejpam-6142	523	28	if	if	SCONJ
ejpam-6142	523	29	1	1	NUM
ejpam-6142	523	30	<	<	X
ejpam-6142	523	31	(	(	PUNCT
ejpam-6142	523	32	1−κϵ)[βf	1−κϵ)[βf	NUM
ejpam-6142	523	33	imsf	imsf	NOUN
ejpam-6142	523	34	(	(	PUNCT
ejpam-6142	523	35	λ2−λ1)+βmifsm(λ9−λ8	λ2−λ1)+βmifsm(λ9−λ8	ADJ
ejpam-6142	523	36	)	)	PUNCT
ejpam-6142	523	37	]	]	PUNCT
ejpam-6142	523	38	w1	w1	NOUN
ejpam-6142	523	39	u∗2	u∗2	NOUN
ejpam-6142	523	40	=	=	PUNCT
ejpam-6142	523	41			NOUN
ejpam-6142	523	42	0	0	PUNCT
ejpam-6142	524	1	if	if	SCONJ
ejpam-6142	524	2	if	if	SCONJ
ejpam-6142	524	3	(	(	PUNCT
ejpam-6142	524	4	λ3−λ4)+im(λ10−λ11	λ3−λ4)+im(λ10−λ11	NOUN
ejpam-6142	524	5	)	)	PUNCT
ejpam-6142	524	6	w2	w2	NOUN
ejpam-6142	524	7	<	<	X
ejpam-6142	524	8	0	0	NUM
ejpam-6142	524	9	g2	g2	PROPN
ejpam-6142	524	10	w2	w2	NOUN
ejpam-6142	524	11	if	if	SCONJ
ejpam-6142	524	12	0	0	NUM
ejpam-6142	524	13	<	<	X
ejpam-6142	524	14	if	if	SCONJ
ejpam-6142	524	15	(	(	PUNCT
ejpam-6142	524	16	λ3−λ4)+im(λ10−λ11	λ3−λ4)+im(λ10−λ11	NOUN
ejpam-6142	524	17	)	)	PUNCT
ejpam-6142	524	18	w2	w2	NOUN
ejpam-6142	524	19	<	<	X
ejpam-6142	524	20	1	1	NUM
ejpam-6142	524	21	1	1	NUM
ejpam-6142	524	22	if	if	SCONJ
ejpam-6142	524	23	1	1	NUM
ejpam-6142	524	24	<	<	X
ejpam-6142	524	25	if	if	SCONJ
ejpam-6142	524	26	(	(	PUNCT
ejpam-6142	524	27	λ3−λ4)+im(λ10−λ11	λ3−λ4)+im(λ10−λ11	NOUN
ejpam-6142	524	28	)	)	PUNCT
ejpam-6142	524	29	w2	w2	NOUN
ejpam-6142	524	30	u∗3	u∗3	NOUN
ejpam-6142	525	1	=	=	PUNCT
ejpam-6142	525	2			PROPN
ejpam-6142	525	3	0	0	PUNCT
ejpam-6142	526	1	if	if	SCONJ
ejpam-6142	526	2	(	(	PUNCT
ejpam-6142	526	3	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	NOUN
ejpam-6142	526	4	)	)	PUNCT
ejpam-6142	526	5	w3	w3	NOUN
ejpam-6142	526	6	<	<	X
ejpam-6142	526	7	0	0	PROPN
ejpam-6142	526	8	g3	g3	PROPN
ejpam-6142	526	9	w3	w3	PROPN
ejpam-6142	526	10	if	if	SCONJ
ejpam-6142	526	11	0	0	NUM
ejpam-6142	526	12	<	<	X
ejpam-6142	526	13	(	(	PUNCT
ejpam-6142	526	14	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	SYM
ejpam-6142	526	15	)	)	PUNCT
ejpam-6142	526	16	w3	w3	NOUN
ejpam-6142	526	17	<	<	X
ejpam-6142	526	18	1	1	NUM
ejpam-6142	526	19	1	1	NUM
ejpam-6142	526	20	if	if	SCONJ
ejpam-6142	526	21	1	1	NUM
ejpam-6142	526	22	<	<	X
ejpam-6142	526	23	(	(	PUNCT
ejpam-6142	526	24	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	SYM
ejpam-6142	526	25	)	)	PUNCT
ejpam-6142	526	26	w3	w3	NOUN
ejpam-6142	526	27	where	where	SCONJ
ejpam-6142	526	28	s.	s.	PROPN
ejpam-6142	526	29	m.	m.	PROPN
ejpam-6142	526	30	fatah	fatah	PROPN
ejpam-6142	526	31	,	,	PUNCT
ejpam-6142	526	32	s.	s.	PROPN
ejpam-6142	526	33	h.	h.	PROPN
ejpam-6142	526	34	a.	a.	PROPN
ejpam-6142	526	35	khoshnaw	khoshnaw	PROPN
ejpam-6142	526	36	,	,	PUNCT
ejpam-6142	526	37	a.	a.	PROPN
ejpam-6142	526	38	n.	n.	PROPN
ejpam-6142	526	39	mustafa	mustafa	PROPN
ejpam-6142	526	40	/	/	SYM
ejpam-6142	526	41	eur	eur	PROPN
ejpam-6142	526	42	.	.	PUNCT
ejpam-6142	527	1	j.	j.	PROPN
ejpam-6142	527	2	pure	pure	PROPN
ejpam-6142	527	3	appl	appl	PROPN
ejpam-6142	527	4	.	.	PROPN
ejpam-6142	527	5	math	math	PROPN
ejpam-6142	527	6	,	,	PUNCT
ejpam-6142	527	7	18	18	NUM
ejpam-6142	527	8	(	(	PUNCT
ejpam-6142	527	9	2	2	NUM
ejpam-6142	527	10	)	)	PUNCT
ejpam-6142	527	11	(	(	PUNCT
ejpam-6142	527	12	2025	2025	NUM
ejpam-6142	527	13	)	)	PUNCT
ejpam-6142	527	14	,	,	PUNCT
ejpam-6142	527	15	6142	6142	NUM
ejpam-6142	527	16	23	23	NUM
ejpam-6142	527	17	of	of	ADP
ejpam-6142	527	18	33	33	NUM
ejpam-6142	527	19	g1	g1	NOUN
ejpam-6142	527	20	=	=	SYM
ejpam-6142	527	21	(	(	PUNCT
ejpam-6142	527	22	1−	1−	NUM
ejpam-6142	527	23	κϵ	κϵ	NOUN
ejpam-6142	527	24	)	)	PUNCT
ejpam-6142	528	1	[	[	X
ejpam-6142	528	2	βfimsf	βfimsf	NOUN
ejpam-6142	528	3	(	(	PUNCT
ejpam-6142	528	4	λ2	λ2	NOUN
ejpam-6142	528	5	−	−	PROPN
ejpam-6142	528	6	λ1	λ1	PROPN
ejpam-6142	528	7	)	)	PUNCT
ejpam-6142	528	8	+	+	NUM
ejpam-6142	528	9	βmifsm	βmifsm	NOUN
ejpam-6142	528	10	(	(	PUNCT
ejpam-6142	528	11	λ9	λ9	ADJ
ejpam-6142	528	12	−	−	NOUN
ejpam-6142	528	13	λ8	λ8	NOUN
ejpam-6142	528	14	)	)	PUNCT
ejpam-6142	528	15	]	]	PUNCT
ejpam-6142	528	16	,	,	PUNCT
ejpam-6142	528	17	g2	g2	PROPN
ejpam-6142	528	18	=	=	PUNCT
ejpam-6142	529	1	if	if	SCONJ
ejpam-6142	529	2	(	(	PUNCT
ejpam-6142	529	3	λ3	λ3	PROPN
ejpam-6142	529	4	−	−	PROPN
ejpam-6142	529	5	λ4	λ4	PROPN
ejpam-6142	529	6	)	)	PUNCT
ejpam-6142	530	1	+	+	CCONJ
ejpam-6142	530	2	i	i	PRON
ejpam-6142	530	3	m	m	VERB
ejpam-6142	530	4	(	(	PUNCT
ejpam-6142	530	5	λ10	λ10	NOUN
ejpam-6142	530	6	−	−	PROPN
ejpam-6142	530	7	λ11	λ11	PROPN
ejpam-6142	530	8	)	)	PUNCT
ejpam-6142	530	9	g3	g3	PROPN
ejpam-6142	530	10	=	=	SYM
ejpam-6142	530	11	(	(	PUNCT
ejpam-6142	530	12	λ4	λ4	ADJ
ejpam-6142	530	13	−	−	PROPN
ejpam-6142	530	14	λ5)df	λ5)df	NOUN
ejpam-6142	530	15	+	+	CCONJ
ejpam-6142	530	16	(	(	PUNCT
ejpam-6142	530	17	λ7	λ7	PRON
ejpam-6142	530	18	−	−	PROPN
ejpam-6142	530	19	λ5	λ5	NOUN
ejpam-6142	530	20	)	)	PUNCT
ejpam-6142	530	21	(	(	PUNCT
ejpam-6142	530	22	af	af	PROPN
ejpam-6142	530	23	+	+	X
ejpam-6142	530	24	ωftf	ωftf	NOUN
ejpam-6142	530	25	)	)	PUNCT
ejpam-6142	531	1	+	+	CCONJ
ejpam-6142	531	2	(	(	PUNCT
ejpam-6142	531	3	λ11	λ11	INTJ
ejpam-6142	531	4	−	−	PROPN
ejpam-6142	531	5	λ12)dm	λ12)dm	PROPN
ejpam-6142	531	6	+	+	CCONJ
ejpam-6142	531	7	(	(	PUNCT
ejpam-6142	531	8	λ14	λ14	PROPN
ejpam-6142	531	9	−	−	PROPN
ejpam-6142	531	10	λ12	λ12	PROPN
ejpam-6142	531	11	)	)	PUNCT
ejpam-6142	531	12	(	(	PUNCT
ejpam-6142	531	13	am	be	AUX
ejpam-6142	531	14	+	+	CCONJ
ejpam-6142	531	15	ωmtm	ωmtm	ADJ
ejpam-6142	531	16	)	)	PUNCT
ejpam-6142	531	17	concisely	concisely	ADV
ejpam-6142	531	18	,	,	PUNCT
ejpam-6142	531	19	the	the	DET
ejpam-6142	531	20	optimal	optimal	ADJ
ejpam-6142	531	21	controls	control	NOUN
ejpam-6142	531	22	can	can	AUX
ejpam-6142	531	23	be	be	AUX
ejpam-6142	531	24	expressed	express	VERB
ejpam-6142	531	25	in	in	ADP
ejpam-6142	531	26	a	a	DET
ejpam-6142	531	27	compact	compact	ADJ
ejpam-6142	531	28	form	form	NOUN
ejpam-6142	531	29	as	as	ADP
ejpam-6142	531	30	:	:	PUNCT
ejpam-6142	531	31	u∗1	u∗1	NOUN
ejpam-6142	531	32	=	=	SYM
ejpam-6142	531	33	max	max	PROPN
ejpam-6142	531	34	{	{	PUNCT
ejpam-6142	531	35	min	min	NOUN
ejpam-6142	531	36	{	{	PUNCT
ejpam-6142	531	37	1	1	NUM
ejpam-6142	531	38	,	,	PUNCT
ejpam-6142	531	39	k1	k1	NOUN
ejpam-6142	531	40	}	}	PUNCT
ejpam-6142	531	41	,	,	PUNCT
ejpam-6142	531	42	0	0	NUM
ejpam-6142	531	43	}	}	PUNCT
ejpam-6142	531	44	,	,	PUNCT
ejpam-6142	531	45	u∗2	u∗2	NOUN
ejpam-6142	531	46	=	=	SYM
ejpam-6142	531	47	max	max	PROPN
ejpam-6142	531	48	{	{	PUNCT
ejpam-6142	531	49	min	min	NOUN
ejpam-6142	531	50	{	{	PUNCT
ejpam-6142	531	51	1	1	NUM
ejpam-6142	531	52	,	,	PUNCT
ejpam-6142	531	53	k2	k2	ADJ
ejpam-6142	531	54	}	}	PUNCT
ejpam-6142	531	55	,	,	PUNCT
ejpam-6142	531	56	0	0	NUM
ejpam-6142	531	57	}	}	PUNCT
ejpam-6142	531	58	,	,	PUNCT
ejpam-6142	531	59	u∗3	u∗3	NOUN
ejpam-6142	531	60	=	=	SYM
ejpam-6142	531	61	max	max	PROPN
ejpam-6142	531	62	{	{	PUNCT
ejpam-6142	531	63	min	min	NOUN
ejpam-6142	531	64	{	{	PUNCT
ejpam-6142	531	65	1	1	NUM
ejpam-6142	531	66	,	,	PUNCT
ejpam-6142	531	67	k3	k3	VERB
ejpam-6142	531	68	}	}	PUNCT
ejpam-6142	531	69	,	,	PUNCT
ejpam-6142	531	70	0	0	NUM
ejpam-6142	531	71	}	}	PUNCT
ejpam-6142	531	72	,	,	PUNCT
ejpam-6142	531	73	where	where	SCONJ
ejpam-6142	531	74	.	.	PUNCT
ejpam-6142	532	1	k1	k1	PROPN
ejpam-6142	532	2	=	=	SYM
ejpam-6142	532	3	(	(	PUNCT
ejpam-6142	532	4	1−κϵ)[βf	1−κϵ)[βf	NUM
ejpam-6142	532	5	imsf	imsf	NOUN
ejpam-6142	532	6	(	(	PUNCT
ejpam-6142	532	7	λ2−λ1)+βmifsm(λ9−λ8	λ2−λ1)+βmifsm(λ9−λ8	ADJ
ejpam-6142	532	8	)	)	PUNCT
ejpam-6142	532	9	]	]	PUNCT
ejpam-6142	533	1	w1	w1	PROPN
ejpam-6142	533	2	k2	k2	PROPN
ejpam-6142	533	3	=	=	PROPN
ejpam-6142	533	4	if	if	SCONJ
ejpam-6142	533	5	(	(	PUNCT
ejpam-6142	533	6	λ3−λ4)+im(λ10−λ11	λ3−λ4)+im(λ10−λ11	NOUN
ejpam-6142	533	7	)	)	PUNCT
ejpam-6142	533	8	w2	w2	NOUN
ejpam-6142	533	9	k3	k3	NOUN
ejpam-6142	533	10	=	=	SYM
ejpam-6142	533	11	(	(	PUNCT
ejpam-6142	533	12	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	λ4−λ5)df+(λ7−λ5)(af+ωftf)+(λ11−λ12)dm+(λ14−λ12)(am+ωmtm	NOUN
ejpam-6142	533	13	)	)	PUNCT
ejpam-6142	533	14	w3	w3	NOUN
ejpam-6142	533	15	therefore	therefore	ADV
ejpam-6142	533	16	,	,	PUNCT
ejpam-6142	533	17	we	we	PRON
ejpam-6142	533	18	formulate	formulate	VERB
ejpam-6142	533	19	the	the	DET
ejpam-6142	533	20	optimality	optimality	NOUN
ejpam-6142	533	21	system	system	NOUN
ejpam-6142	533	22	by	by	ADP
ejpam-6142	533	23	combining	combine	VERB
ejpam-6142	533	24	the	the	DET
ejpam-6142	533	25	set	set	NOUN
ejpam-6142	533	26	of	of	ADP
ejpam-6142	533	27	equations	equation	NOUN
ejpam-6142	533	28	for	for	ADP
ejpam-6142	533	29	the	the	DET
ejpam-6142	533	30	state	state	NOUN
ejpam-6142	533	31	variables	variable	NOUN
ejpam-6142	533	32	and	and	CCONJ
ejpam-6142	533	33	the	the	DET
ejpam-6142	533	34	set	set	NOUN
ejpam-6142	533	35	of	of	ADP
ejpam-6142	533	36	equations	equation	NOUN
ejpam-6142	533	37	for	for	ADP
ejpam-6142	533	38	the	the	DET
ejpam-6142	533	39	adjoint	adjoint	NOUN
ejpam-6142	533	40	variables	variable	NOUN
ejpam-6142	533	41	with	with	ADP
ejpam-6142	533	42	the	the	DET
ejpam-6142	533	43	initial	initial	ADJ
ejpam-6142	533	44	conditions	condition	NOUN
ejpam-6142	533	45	and	and	CCONJ
ejpam-6142	533	46	final	final	ADJ
ejpam-6142	533	47	time	time	NOUN
ejpam-6142	533	48	conditions	condition	NOUN
ejpam-6142	533	49	respectively	respectively	ADV
ejpam-6142	533	50	dsf	dsf	VERB
ejpam-6142	533	51	dt	dt	PROPN
ejpam-6142	533	52	=	=	SYM
ejpam-6142	533	53	λ−	λ−	PROPN
ejpam-6142	533	54	(	(	PUNCT
ejpam-6142	533	55	1−	1−	NUM
ejpam-6142	533	56	u1	u1	NOUN
ejpam-6142	533	57	)	)	PUNCT
ejpam-6142	533	58	(	(	PUNCT
ejpam-6142	533	59	1−	1−	NUM
ejpam-6142	533	60	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	533	61	−	−	PROPN
ejpam-6142	533	62	ηsf	ηsf	PROPN
ejpam-6142	533	63	def	def	PROPN
ejpam-6142	533	64	dt	dt	PROPN
ejpam-6142	534	1	=	=	SYM
ejpam-6142	534	2	(	(	PUNCT
ejpam-6142	534	3	1−	1−	NUM
ejpam-6142	534	4	u1	u1	NOUN
ejpam-6142	534	5	)	)	PUNCT
ejpam-6142	534	6	(	(	PUNCT
ejpam-6142	534	7	1−	1−	NUM
ejpam-6142	534	8	κϵ)βfimsf	κϵ)βfimsf	NOUN
ejpam-6142	534	9	−	−	PROPN
ejpam-6142	534	10	(	(	PUNCT
ejpam-6142	534	11	αf	αf	ADP
ejpam-6142	534	12	+	+	CCONJ
ejpam-6142	534	13	η)ef	η)ef	PROPN
ejpam-6142	534	14	dif	dif	ADV
ejpam-6142	534	15	dt	dt	PUNCT
ejpam-6142	535	1	=	=	VERB
ejpam-6142	535	2	αfef	αfef	NOUN
ejpam-6142	535	3	−	−	PROPN
ejpam-6142	536	1	(	(	PUNCT
ejpam-6142	536	2	u2	u2	PROPN
ejpam-6142	536	3	+	+	CCONJ
ejpam-6142	536	4	µ+	µ+	PROPN
ejpam-6142	536	5	η	η	PROPN
ejpam-6142	536	6	+	+	PROPN
ejpam-6142	536	7	γf	γf	PROPN
ejpam-6142	537	1	+	+	CCONJ
ejpam-6142	537	2	θf	θf	NOUN
ejpam-6142	537	3	)	)	PUNCT
ejpam-6142	537	4	if	if	SCONJ
ejpam-6142	537	5	ddf	ddf	NOUN
ejpam-6142	538	1	dt	dt	PROPN
ejpam-6142	538	2	=	=	PUNCT
ejpam-6142	538	3	(	(	PUNCT
ejpam-6142	538	4	u2	u2	PROPN
ejpam-6142	538	5	+	+	CCONJ
ejpam-6142	538	6	γf	γf	PROPN
ejpam-6142	538	7	)	)	PUNCT
ejpam-6142	538	8	if	if	SCONJ
ejpam-6142	538	9	−	−	PROPN
ejpam-6142	538	10	(	(	PUNCT
ejpam-6142	538	11	u3	u3	NOUN
ejpam-6142	538	12	+	+	CCONJ
ejpam-6142	538	13	µ+	µ+	PROPN
ejpam-6142	538	14	η	η	PROPN
ejpam-6142	538	15	+	+	PROPN
ejpam-6142	538	16	ρf	ρf	NOUN
ejpam-6142	538	17	)	)	PUNCT
ejpam-6142	538	18	df	df	PROPN
ejpam-6142	538	19	dtf	dtf	PROPN
ejpam-6142	538	20	dt	dt	PROPN
ejpam-6142	539	1	=	=	PUNCT
ejpam-6142	540	1	u3af	u3af	X
ejpam-6142	541	1	+	+	CCONJ
ejpam-6142	541	2	(	(	PUNCT
ejpam-6142	541	3	u3	u3	NOUN
ejpam-6142	541	4	+	+	CCONJ
ejpam-6142	541	5	ρf	ρf	NOUN
ejpam-6142	541	6	)	)	PUNCT
ejpam-6142	541	7	df	df	PROPN
ejpam-6142	541	8	−	−	PROPN
ejpam-6142	541	9	(	(	PUNCT
ejpam-6142	541	10	µ+	µ+	PROPN
ejpam-6142	541	11	η	η	PROPN
ejpam-6142	541	12	+	+	PROPN
ejpam-6142	541	13	(	(	PUNCT
ejpam-6142	541	14	1−	1−	NUM
ejpam-6142	541	15	u3)ωf	u3)ωf	NOUN
ejpam-6142	541	16	)	)	PUNCT
ejpam-6142	541	17	tf	tf	PROPN
ejpam-6142	541	18	duf	duf	NOUN
ejpam-6142	541	19	dt	dt	PROPN
ejpam-6142	541	20	=	=	PROPN
ejpam-6142	541	21	θfif	θfif	PROPN
ejpam-6142	541	22	−	−	PROPN
ejpam-6142	541	23	(	(	PUNCT
ejpam-6142	541	24	µ+	µ+	X
ejpam-6142	541	25	η	η	PROPN
ejpam-6142	541	26	+	+	PROPN
ejpam-6142	541	27	λf	λf	PROPN
ejpam-6142	541	28	)	)	PUNCT
ejpam-6142	541	29	uf	uf	PROPN
ejpam-6142	541	30	daf	daf	NOUN
ejpam-6142	541	31	dt	dt	PROPN
ejpam-6142	542	1	=	=	PUNCT
ejpam-6142	542	2	λfuf	λfuf	PROPN
ejpam-6142	542	3	+	+	CCONJ
ejpam-6142	542	4	(	(	PUNCT
ejpam-6142	542	5	1−	1−	NUM
ejpam-6142	542	6	u3)ωftf	u3)ωftf	NOUN
ejpam-6142	542	7	−	−	PROPN
ejpam-6142	542	8	(	(	PUNCT
ejpam-6142	542	9	u3	u3	NOUN
ejpam-6142	542	10	+	+	CCONJ
ejpam-6142	542	11	µ+	µ+	DET
ejpam-6142	542	12	η)af	η)af	PROPN
ejpam-6142	542	13	dsm	dsm	NOUN
ejpam-6142	542	14	dt	dt	NOUN
ejpam-6142	542	15	=	=	SYM
ejpam-6142	542	16	λ−	λ−	PROPN
ejpam-6142	542	17	(	(	PUNCT
ejpam-6142	542	18	1−	1−	NUM
ejpam-6142	542	19	u1	u1	NOUN
ejpam-6142	542	20	)	)	PUNCT
ejpam-6142	542	21	(	(	PUNCT
ejpam-6142	542	22	1−	1−	NUM
ejpam-6142	542	23	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	542	24	−	−	PROPN
ejpam-6142	542	25	ηsm	ηsm	NOUN
ejpam-6142	542	26	dem	dem	NOUN
ejpam-6142	542	27	dt	dt	X
ejpam-6142	542	28	=	=	SYM
ejpam-6142	542	29	(	(	PUNCT
ejpam-6142	542	30	1−	1−	NUM
ejpam-6142	542	31	u1	u1	NOUN
ejpam-6142	542	32	)	)	PUNCT
ejpam-6142	542	33	(	(	PUNCT
ejpam-6142	542	34	1−	1−	NUM
ejpam-6142	542	35	κϵ)βmifsm	κϵ)βmifsm	ADJ
ejpam-6142	542	36	−	−	PROPN
ejpam-6142	542	37	(	(	PUNCT
ejpam-6142	542	38	αm	αm	NOUN
ejpam-6142	542	39	+	+	PROPN
ejpam-6142	542	40	η)em	η)em	PROPN
ejpam-6142	542	41	dim	dim	ADJ
ejpam-6142	542	42	dt	dt	NOUN
ejpam-6142	542	43	=	=	PUNCT
ejpam-6142	542	44	αmem	αmem	ADJ
ejpam-6142	542	45	−	−	PROPN
ejpam-6142	543	1	(	(	PUNCT
ejpam-6142	543	2	u2	u2	PROPN
ejpam-6142	543	3	+	+	CCONJ
ejpam-6142	543	4	µ+	µ+	PROPN
ejpam-6142	543	5	η	η	PROPN
ejpam-6142	543	6	+	+	X
ejpam-6142	543	7	γm	γm	PROPN
ejpam-6142	543	8	+	+	NUM
ejpam-6142	543	9	θm	θm	NOUN
ejpam-6142	543	10	)	)	PUNCT
ejpam-6142	543	11	i	i	PROPN
ejpam-6142	543	12	m	m	PROPN
ejpam-6142	543	13	ddm	ddm	NOUN
ejpam-6142	543	14	dt	dt	NOUN
ejpam-6142	544	1	=	=	PUNCT
ejpam-6142	544	2	(	(	PUNCT
ejpam-6142	544	3	u2	u2	PROPN
ejpam-6142	544	4	+	+	CCONJ
ejpam-6142	544	5	γm	γm	NOUN
ejpam-6142	544	6	)	)	PUNCT
ejpam-6142	544	7	i	i	PRON
ejpam-6142	544	8	m	m	VERB
ejpam-6142	544	9	−	−	NOUN
ejpam-6142	544	10	(	(	PUNCT
ejpam-6142	544	11	u3	u3	NOUN
ejpam-6142	544	12	+	+	CCONJ
ejpam-6142	544	13	µ+	µ+	PROPN
ejpam-6142	544	14	η	η	PROPN
ejpam-6142	544	15	+	+	PROPN
ejpam-6142	544	16	ρm)dm	ρm)dm	PROPN
ejpam-6142	544	17	s.	s.	PROPN
ejpam-6142	544	18	m.	m.	PROPN
ejpam-6142	544	19	fatah	fatah	PROPN
ejpam-6142	544	20	,	,	PUNCT
ejpam-6142	544	21	s.	s.	PROPN
ejpam-6142	544	22	h.	h.	PROPN
ejpam-6142	544	23	a.	a.	PROPN
ejpam-6142	544	24	khoshnaw	khoshnaw	PROPN
ejpam-6142	544	25	,	,	PUNCT
ejpam-6142	544	26	a.	a.	PROPN
ejpam-6142	544	27	n.	n.	PROPN
ejpam-6142	544	28	mustafa	mustafa	PROPN
ejpam-6142	544	29	/	/	SYM
ejpam-6142	544	30	eur	eur	PROPN
ejpam-6142	544	31	.	.	PUNCT
ejpam-6142	545	1	j.	j.	PROPN
ejpam-6142	545	2	pure	pure	PROPN
ejpam-6142	545	3	appl	appl	PROPN
ejpam-6142	545	4	.	.	PROPN
ejpam-6142	545	5	math	math	PROPN
ejpam-6142	545	6	,	,	PUNCT
ejpam-6142	545	7	18	18	NUM
ejpam-6142	545	8	(	(	PUNCT
ejpam-6142	545	9	2	2	NUM
ejpam-6142	545	10	)	)	PUNCT
ejpam-6142	545	11	(	(	PUNCT
ejpam-6142	545	12	2025	2025	NUM
ejpam-6142	545	13	)	)	PUNCT
ejpam-6142	545	14	,	,	PUNCT
ejpam-6142	545	15	6142	6142	NUM
ejpam-6142	545	16	24	24	NUM
ejpam-6142	545	17	of	of	ADP
ejpam-6142	545	18	33	33	NUM
ejpam-6142	545	19	dtm	dtm	NOUN
ejpam-6142	545	20	dt	dt	NOUN
ejpam-6142	545	21	=	=	PUNCT
ejpam-6142	545	22	u3am	u3am	PUNCT
ejpam-6142	546	1	+	+	CCONJ
ejpam-6142	546	2	(	(	PUNCT
ejpam-6142	546	3	u3	u3	NOUN
ejpam-6142	546	4	+	+	CCONJ
ejpam-6142	546	5	ρm)dm	ρm)dm	NUM
ejpam-6142	546	6	−	−	PROPN
ejpam-6142	546	7	(	(	PUNCT
ejpam-6142	546	8	µ+	µ+	X
ejpam-6142	546	9	η	η	PROPN
ejpam-6142	546	10	+	+	PROPN
ejpam-6142	546	11	(	(	PUNCT
ejpam-6142	546	12	1−	1−	NUM
ejpam-6142	546	13	u3)ωm)tm	u3)ωm)tm	NOUN
ejpam-6142	547	1	dum	dum	NOUN
ejpam-6142	547	2	dt	dt	X
ejpam-6142	547	3	=	=	SYM
ejpam-6142	547	4	θmim	θmim	PROPN
ejpam-6142	547	5	−	−	PROPN
ejpam-6142	547	6	(	(	PUNCT
ejpam-6142	547	7	µ+	µ+	X
ejpam-6142	547	8	η	η	PROPN
ejpam-6142	547	9	+	+	PROPN
ejpam-6142	547	10	λm)um	λm)um	X
ejpam-6142	547	11	dam	dam	NOUN
ejpam-6142	547	12	dt	dt	NOUN
ejpam-6142	547	13	=	=	PUNCT
ejpam-6142	547	14	λmum	λmum	ADJ
ejpam-6142	547	15	+	+	CCONJ
ejpam-6142	547	16	(	(	PUNCT
ejpam-6142	547	17	1−	1−	NUM
ejpam-6142	547	18	u3)ωmtm	u3)ωmtm	PROPN
ejpam-6142	547	19	−	−	PROPN
ejpam-6142	547	20	(	(	PUNCT
ejpam-6142	547	21	u3	u3	NOUN
ejpam-6142	547	22	+	+	CCONJ
ejpam-6142	547	23	µ+	µ+	PROPN
ejpam-6142	547	24	η)am	η)am	PROPN
ejpam-6142	547	25	dλ1	dλ1	NOUN
ejpam-6142	547	26	dt	dt	NOUN
ejpam-6142	547	27	=	=	SYM
ejpam-6142	547	28	(	(	PUNCT
ejpam-6142	547	29	1−	1−	NUM
ejpam-6142	547	30	u1	u1	NOUN
ejpam-6142	547	31	)	)	PUNCT
ejpam-6142	547	32	(	(	PUNCT
ejpam-6142	547	33	1−	1−	NUM
ejpam-6142	547	34	κϵ)βfim	κϵ)βfim	NOUN
ejpam-6142	547	35	(	(	PUNCT
ejpam-6142	547	36	λ1	λ1	PROPN
ejpam-6142	547	37	−	−	PROPN
ejpam-6142	547	38	λ2	λ2	PROPN
ejpam-6142	547	39	)	)	PUNCT
ejpam-6142	547	40	+	+	NUM
ejpam-6142	547	41	ηλ1	ηλ1	VERB
ejpam-6142	547	42	dλ2	dλ2	NOUN
ejpam-6142	547	43	dt	dt	NOUN
ejpam-6142	547	44	=	=	SYM
ejpam-6142	547	45	−b1	−b1	PROPN
ejpam-6142	547	46	+	+	NUM
ejpam-6142	547	47	ηλ2	ηλ2	NOUN
ejpam-6142	547	48	+	+	CCONJ
ejpam-6142	547	49	αf	αf	PROPN
ejpam-6142	547	50	(	(	PUNCT
ejpam-6142	547	51	λ2	λ2	PROPN
ejpam-6142	547	52	−	−	PROPN
ejpam-6142	547	53	λ3	λ3	PROPN
ejpam-6142	547	54	)	)	PUNCT
ejpam-6142	547	55	dλ3	dλ3	NOUN
ejpam-6142	548	1	dt	dt	NOUN
ejpam-6142	548	2	=	=	SYM
ejpam-6142	548	3	−b2	−b2	PROPN
ejpam-6142	548	4	+	+	CCONJ
ejpam-6142	548	5	(	(	PUNCT
ejpam-6142	548	6	µ+	µ+	X
ejpam-6142	548	7	η)λ3	η)λ3	NOUN
ejpam-6142	548	8	+	+	CCONJ
ejpam-6142	548	9	(	(	PUNCT
ejpam-6142	548	10	u2	u2	PROPN
ejpam-6142	548	11	+	+	CCONJ
ejpam-6142	548	12	γf	γf	PROPN
ejpam-6142	548	13	)	)	PUNCT
ejpam-6142	548	14	(	(	PUNCT
ejpam-6142	548	15	λ3	λ3	PROPN
ejpam-6142	548	16	−	−	PROPN
ejpam-6142	548	17	λ4	λ4	PROPN
ejpam-6142	548	18	)	)	PUNCT
ejpam-6142	549	1	+	+	CCONJ
ejpam-6142	549	2	θf	θf	PROPN
ejpam-6142	549	3	(	(	PUNCT
ejpam-6142	549	4	λ3	λ3	PROPN
ejpam-6142	549	5	−	−	PROPN
ejpam-6142	549	6	λ6	λ6	PROPN
ejpam-6142	549	7	)	)	PUNCT
ejpam-6142	549	8	+	+	CCONJ
ejpam-6142	549	9	(	(	PUNCT
ejpam-6142	549	10	1−	1−	NUM
ejpam-6142	549	11	u1	u1	NOUN
ejpam-6142	549	12	)	)	PUNCT
ejpam-6142	549	13	(	(	PUNCT
ejpam-6142	549	14	1−	1−	NUM
ejpam-6142	549	15	κϵ)βmsm	κϵ)βmsm	NOUN
ejpam-6142	549	16	(	(	PUNCT
ejpam-6142	549	17	λ8	λ8	VERB
ejpam-6142	549	18	−	−	NOUN
ejpam-6142	549	19	λ9	λ9	NOUN
ejpam-6142	549	20	)	)	PUNCT
ejpam-6142	549	21	dλ4	dλ4	VERB
ejpam-6142	549	22	dt	dt	NOUN
ejpam-6142	549	23	=	=	SYM
ejpam-6142	549	24	−b3	−b3	PROPN
ejpam-6142	549	25	+	+	CCONJ
ejpam-6142	549	26	(	(	PUNCT
ejpam-6142	549	27	µ+	µ+	X
ejpam-6142	549	28	η)λ4	η)λ4	PROPN
ejpam-6142	549	29	+	+	CCONJ
ejpam-6142	549	30	(	(	PUNCT
ejpam-6142	549	31	u3	u3	NOUN
ejpam-6142	549	32	+	+	CCONJ
ejpam-6142	549	33	ρf	ρf	NOUN
ejpam-6142	549	34	)	)	PUNCT
ejpam-6142	549	35	(	(	PUNCT
ejpam-6142	549	36	λ4	λ4	NOUN
ejpam-6142	549	37	−	−	NOUN
ejpam-6142	549	38	λ5	λ5	NOUN
ejpam-6142	549	39	)	)	PUNCT
ejpam-6142	549	40	dλ5	dλ5	NOUN
ejpam-6142	549	41	dt	dt	NOUN
ejpam-6142	549	42	=	=	PUNCT
ejpam-6142	549	43	−b4	−b4	PROPN
ejpam-6142	549	44	+	+	CCONJ
ejpam-6142	549	45	(	(	PUNCT
ejpam-6142	549	46	µ+	µ+	DET
ejpam-6142	549	47	η)λ5	η)λ5	PROPN
ejpam-6142	549	48	+	+	CCONJ
ejpam-6142	549	49	ωf	ωf	PROPN
ejpam-6142	549	50	(	(	PUNCT
ejpam-6142	549	51	λ5	λ5	NOUN
ejpam-6142	549	52	−	−	PROPN
ejpam-6142	549	53	λ7	λ7	PROPN
ejpam-6142	549	54	)	)	PUNCT
ejpam-6142	549	55	dλ6	dλ6	NOUN
ejpam-6142	549	56	dt	dt	NOUN
ejpam-6142	550	1	=	=	PUNCT
ejpam-6142	551	1	−b5	−b5	NOUN
ejpam-6142	552	1	+	+	CCONJ
ejpam-6142	553	1	(	(	PUNCT
ejpam-6142	553	2	µ+	µ+	X
ejpam-6142	553	3	η)λ6	η)λ6	PROPN
ejpam-6142	553	4	+	+	CCONJ
ejpam-6142	553	5	λf	λf	PROPN
ejpam-6142	553	6	(	(	PUNCT
ejpam-6142	553	7	λ6	λ6	PROPN
ejpam-6142	553	8	−	−	PROPN
ejpam-6142	553	9	λ7	λ7	PROPN
ejpam-6142	553	10	)	)	PUNCT
ejpam-6142	553	11	dλ7	dλ7	PROPN
ejpam-6142	554	1	dt	dt	PUNCT
ejpam-6142	555	1	=	=	PUNCT
ejpam-6142	555	2	−b6	−b6	PROPN
ejpam-6142	555	3	+	+	CCONJ
ejpam-6142	555	4	(	(	PUNCT
ejpam-6142	555	5	µ+	µ+	X
ejpam-6142	555	6	η)λ7	η)λ7	PROPN
ejpam-6142	555	7	dλ8	dλ8	NOUN
ejpam-6142	555	8	dt	dt	NOUN
ejpam-6142	555	9	=	=	SYM
ejpam-6142	555	10	(	(	PUNCT
ejpam-6142	555	11	1−	1−	NUM
ejpam-6142	555	12	u1	u1	NOUN
ejpam-6142	555	13	)	)	PUNCT
ejpam-6142	555	14	(	(	PUNCT
ejpam-6142	555	15	1−	1−	NUM
ejpam-6142	555	16	κϵ)βmif	κϵ)βmif	X
ejpam-6142	555	17	(	(	PUNCT
ejpam-6142	555	18	λ8	λ8	VERB
ejpam-6142	555	19	−	−	NOUN
ejpam-6142	555	20	λ9	λ9	NOUN
ejpam-6142	555	21	)	)	PUNCT
ejpam-6142	555	22	+	+	CCONJ
ejpam-6142	555	23	ηλ8	ηλ8	PROPN
ejpam-6142	555	24	dλ9	dλ9	NOUN
ejpam-6142	555	25	dt	dt	NOUN
ejpam-6142	556	1	=	=	PUNCT
ejpam-6142	556	2	−b7	−b7	PROPN
ejpam-6142	556	3	+	+	NUM
ejpam-6142	556	4	ηλ9	ηλ9	NOUN
ejpam-6142	556	5	+	+	X
ejpam-6142	556	6	αm	αm	NOUN
ejpam-6142	556	7	(	(	PUNCT
ejpam-6142	556	8	λ9	λ9	ADJ
ejpam-6142	556	9	−	−	NOUN
ejpam-6142	556	10	λ10	λ10	NOUN
ejpam-6142	556	11	)	)	PUNCT
ejpam-6142	557	1	dλ10	dλ10	PROPN
ejpam-6142	557	2	dt	dt	X
ejpam-6142	558	1	=	=	PUNCT
ejpam-6142	558	2	−b8	−b8	PROPN
ejpam-6142	558	3	+	+	CCONJ
ejpam-6142	558	4	(	(	PUNCT
ejpam-6142	558	5	µ+	µ+	X
ejpam-6142	558	6	η)λ10	η)λ10	PROPN
ejpam-6142	558	7	+	+	CCONJ
ejpam-6142	558	8	(	(	PUNCT
ejpam-6142	558	9	u2	u2	NOUN
ejpam-6142	558	10	+	+	CCONJ
ejpam-6142	558	11	γm	γm	NOUN
ejpam-6142	558	12	)	)	PUNCT
ejpam-6142	558	13	(	(	PUNCT
ejpam-6142	558	14	λ10	λ10	NOUN
ejpam-6142	558	15	−	−	PROPN
ejpam-6142	558	16	λ11	λ11	PROPN
ejpam-6142	558	17	)	)	PUNCT
ejpam-6142	559	1	+	+	NUM
ejpam-6142	559	2	θm	θm	PROPN
ejpam-6142	559	3	(	(	PUNCT
ejpam-6142	559	4	λ10	λ10	NOUN
ejpam-6142	559	5	−	−	PROPN
ejpam-6142	559	6	λ13	λ13	PROPN
ejpam-6142	559	7	)	)	PUNCT
ejpam-6142	560	1	+	+	CCONJ
ejpam-6142	560	2	(	(	PUNCT
ejpam-6142	560	3	1−	1−	NUM
ejpam-6142	560	4	u1	u1	NOUN
ejpam-6142	560	5	)	)	PUNCT
ejpam-6142	560	6	(	(	PUNCT
ejpam-6142	560	7	1−	1−	NUM
ejpam-6142	560	8	κϵ)βfsf	κϵ)βfsf	X
ejpam-6142	560	9	(	(	PUNCT
ejpam-6142	560	10	λ1	λ1	PROPN
ejpam-6142	560	11	−	−	PROPN
ejpam-6142	560	12	λ2	λ2	PROPN
ejpam-6142	560	13	)	)	PUNCT
ejpam-6142	561	1	dλ11	dλ11	PROPN
ejpam-6142	561	2	dt	dt	NOUN
ejpam-6142	561	3	=	=	PUNCT
ejpam-6142	561	4	−b9	−b9	PROPN
ejpam-6142	561	5	+	+	CCONJ
ejpam-6142	561	6	(	(	PUNCT
ejpam-6142	561	7	µ+	µ+	X
ejpam-6142	561	8	η)λ11	η)λ11	PROPN
ejpam-6142	561	9	+	+	CCONJ
ejpam-6142	561	10	(	(	PUNCT
ejpam-6142	561	11	u3	u3	PROPN
ejpam-6142	561	12	+	+	CCONJ
ejpam-6142	561	13	ρm	ρm	NOUN
ejpam-6142	561	14	)	)	PUNCT
ejpam-6142	561	15	(	(	PUNCT
ejpam-6142	561	16	λ11	λ11	NOUN
ejpam-6142	561	17	−	−	PROPN
ejpam-6142	561	18	λ12	λ12	ADJ
ejpam-6142	561	19	)	)	PUNCT
ejpam-6142	561	20	dλ12	dλ12	PROPN
ejpam-6142	561	21	dt	dt	NOUN
ejpam-6142	561	22	=	=	PUNCT
ejpam-6142	561	23	−b10	−b10	PUNCT
ejpam-6142	561	24	+	+	CCONJ
ejpam-6142	561	25	(	(	PUNCT
ejpam-6142	561	26	µ+	µ+	X
ejpam-6142	561	27	η)λ12	η)λ12	PROPN
ejpam-6142	561	28	+	+	CCONJ
ejpam-6142	561	29	ωm	ωm	PUNCT
ejpam-6142	561	30	(	(	PUNCT
ejpam-6142	561	31	λ12	λ12	PROPN
ejpam-6142	561	32	−	−	PROPN
ejpam-6142	561	33	λ14	λ14	PROPN
ejpam-6142	561	34	)	)	PUNCT
ejpam-6142	561	35	dλ13	dλ13	PROPN
ejpam-6142	561	36	dt	dt	X
ejpam-6142	561	37	=	=	PUNCT
ejpam-6142	562	1	−b11	−b11	PUNCT
ejpam-6142	562	2	+	+	CCONJ
ejpam-6142	562	3	(	(	PUNCT
ejpam-6142	562	4	µ+	µ+	X
ejpam-6142	562	5	η)λ13	η)λ13	PROPN
ejpam-6142	562	6	+	+	CCONJ
ejpam-6142	562	7	λm	λm	X
ejpam-6142	562	8	(	(	PUNCT
ejpam-6142	562	9	λ13	λ13	PROPN
ejpam-6142	562	10	−	−	PROPN
ejpam-6142	562	11	λ14	λ14	PROPN
ejpam-6142	562	12	)	)	PUNCT
ejpam-6142	563	1	dλ14	dλ14	PROPN
ejpam-6142	563	2	dt	dt	NOUN
ejpam-6142	563	3	=	=	PUNCT
ejpam-6142	564	1	−b12	−b12	PUNCT
ejpam-6142	565	1	+	+	CCONJ
ejpam-6142	565	2	(	(	PUNCT
ejpam-6142	565	3	µ+	µ+	X
ejpam-6142	565	4	η)λ14	η)λ14	NOUN
ejpam-6142	565	5	with	with	ADP
ejpam-6142	565	6	conditions	condition	NOUN
ejpam-6142	565	7	λi	λi	INTJ
ejpam-6142	565	8	(	(	PUNCT
ejpam-6142	565	9	tf	tf	INTJ
ejpam-6142	565	10	)	)	PUNCT
ejpam-6142	565	11	=	=	PUNCT
ejpam-6142	565	12	0	0	NUM
ejpam-6142	565	13	where	where	SCONJ
ejpam-6142	565	14	i	i	PRON
ejpam-6142	565	15	=	=	NOUN
ejpam-6142	565	16	1	1	NUM
ejpam-6142	565	17	,	,	PUNCT
ejpam-6142	565	18	2	2	NUM
ejpam-6142	565	19	,	,	PUNCT
ejpam-6142	565	20	.	.	PUNCT
ejpam-6142	565	21	.	.	PUNCT
ejpam-6142	565	22	.	.	PUNCT
ejpam-6142	566	1	,	,	PUNCT
ejpam-6142	566	2	14	14	NUM
ejpam-6142	566	3	,	,	PUNCT
ejpam-6142	566	4	sf	sf	X
ejpam-6142	566	5	(	(	PUNCT
ejpam-6142	566	6	0	0	NUM
ejpam-6142	566	7	)	)	PUNCT
ejpam-6142	566	8	,	,	PUNCT
ejpam-6142	566	9	sm(0	sm(0	NOUN
ejpam-6142	566	10	)	)	PUNCT
ejpam-6142	566	11	>	>	X
ejpam-6142	566	12	0	0	NUM
ejpam-6142	566	13	,	,	PUNCT
ejpam-6142	566	14	and	and	CCONJ
ejpam-6142	566	15	ef	ef	PROPN
ejpam-6142	566	16	(	(	PUNCT
ejpam-6142	566	17	0	0	NUM
ejpam-6142	566	18	)	)	PUNCT
ejpam-6142	566	19	,	,	PUNCT
ejpam-6142	566	20	em(0	em(0	NOUN
ejpam-6142	566	21	)	)	PUNCT
ejpam-6142	566	22	,	,	PUNCT
ejpam-6142	566	23	if	if	SCONJ
ejpam-6142	566	24	(	(	PUNCT
ejpam-6142	566	25	0	0	NUM
ejpam-6142	566	26	)	)	PUNCT
ejpam-6142	566	27	,	,	PUNCT
ejpam-6142	566	28	im(0	im(0	NOUN
ejpam-6142	566	29	)	)	PUNCT
ejpam-6142	566	30	,	,	PUNCT
ejpam-6142	566	31	df	df	PROPN
ejpam-6142	566	32	(	(	PUNCT
ejpam-6142	566	33	0	0	NUM
ejpam-6142	566	34	)	)	PUNCT
ejpam-6142	566	35	,	,	PUNCT
ejpam-6142	566	36	dm(0	dm(0	NOUN
ejpam-6142	566	37	)	)	PUNCT
ejpam-6142	566	38	,	,	PUNCT
ejpam-6142	566	39	tf	tf	X
ejpam-6142	566	40	(	(	PUNCT
ejpam-6142	566	41	0	0	NUM
ejpam-6142	566	42	)	)	PUNCT
ejpam-6142	566	43	,	,	PUNCT
ejpam-6142	566	44	tm(0	tm(0	NOUN
ejpam-6142	566	45	)	)	PUNCT
ejpam-6142	566	46	,	,	PUNCT
ejpam-6142	566	47	uf	uf	PROPN
ejpam-6142	566	48	(	(	PUNCT
ejpam-6142	566	49	0	0	NUM
ejpam-6142	566	50	)	)	PUNCT
ejpam-6142	566	51	,	,	PUNCT
ejpam-6142	566	52	um(0	um(0	NOUN
ejpam-6142	566	53	)	)	PUNCT
ejpam-6142	566	54	,	,	PUNCT
ejpam-6142	566	55	af	af	PROPN
ejpam-6142	566	56	(	(	PUNCT
ejpam-6142	566	57	0	0	NUM
ejpam-6142	566	58	)	)	PUNCT
ejpam-6142	566	59	,	,	PUNCT
ejpam-6142	566	60	am(0	am(0	NOUN
ejpam-6142	566	61	)	)	PUNCT
ejpam-6142	566	62	≥	≥	NOUN
ejpam-6142	566	63	0	0	NUM
ejpam-6142	566	64	s.	s.	PROPN
ejpam-6142	566	65	m.	m.	PROPN
ejpam-6142	566	66	fatah	fatah	PROPN
ejpam-6142	566	67	,	,	PUNCT
ejpam-6142	566	68	s.	s.	PROPN
ejpam-6142	566	69	h.	h.	PROPN
ejpam-6142	566	70	a.	a.	PROPN
ejpam-6142	566	71	khoshnaw	khoshnaw	PROPN
ejpam-6142	566	72	,	,	PUNCT
ejpam-6142	566	73	a.	a.	PROPN
ejpam-6142	566	74	n.	n.	PROPN
ejpam-6142	566	75	mustafa	mustafa	PROPN
ejpam-6142	566	76	/	/	SYM
ejpam-6142	566	77	eur	eur	PROPN
ejpam-6142	566	78	.	.	PUNCT
ejpam-6142	567	1	j.	j.	PROPN
ejpam-6142	567	2	pure	pure	PROPN
ejpam-6142	567	3	appl	appl	PROPN
ejpam-6142	567	4	.	.	PROPN
ejpam-6142	567	5	math	math	PROPN
ejpam-6142	567	6	,	,	PUNCT
ejpam-6142	567	7	18	18	NUM
ejpam-6142	567	8	(	(	PUNCT
ejpam-6142	567	9	2	2	NUM
ejpam-6142	567	10	)	)	PUNCT
ejpam-6142	567	11	(	(	PUNCT
ejpam-6142	567	12	2025	2025	NUM
ejpam-6142	567	13	)	)	PUNCT
ejpam-6142	567	14	,	,	PUNCT
ejpam-6142	567	15	6142	6142	NUM
ejpam-6142	567	16	25	25	NUM
ejpam-6142	567	17	of	of	ADP
ejpam-6142	567	18	33	33	NUM
ejpam-6142	567	19	8	8	NUM
ejpam-6142	567	20	.	.	PUNCT
ejpam-6142	568	1	numerical	numerical	ADJ
ejpam-6142	568	2	simulations	simulation	NOUN
ejpam-6142	568	3	this	this	DET
ejpam-6142	568	4	section	section	NOUN
ejpam-6142	568	5	qualitatively	qualitatively	ADV
ejpam-6142	568	6	examines	examine	VERB
ejpam-6142	568	7	the	the	DET
ejpam-6142	568	8	influence	influence	NOUN
ejpam-6142	568	9	of	of	ADP
ejpam-6142	568	10	optimum	optimum	ADJ
ejpam-6142	568	11	control	control	NOUN
ejpam-6142	568	12	measures	measure	NOUN
ejpam-6142	568	13	on	on	ADP
ejpam-6142	568	14	the	the	DET
ejpam-6142	568	15	transmission	transmission	NOUN
ejpam-6142	568	16	of	of	ADP
ejpam-6142	568	17	hiv	hiv	PROPN
ejpam-6142	568	18	/	/	SYM
ejpam-6142	568	19	aids	aids	PROPN
ejpam-6142	568	20	within	within	ADP
ejpam-6142	568	21	a	a	DET
ejpam-6142	568	22	community	community	NOUN
ejpam-6142	568	23	.	.	PUNCT
ejpam-6142	569	1	this	this	DET
ejpam-6142	569	2	work	work	NOUN
ejpam-6142	569	3	utilizes	utilize	VERB
ejpam-6142	569	4	the	the	DET
ejpam-6142	569	5	fourth	fourth	ADJ
ejpam-6142	569	6	-	-	PUNCT
ejpam-6142	569	7	order	order	NOUN
ejpam-6142	569	8	runge	runge	NOUN
ejpam-6142	569	9	-	-	PUNCT
ejpam-6142	569	10	kutta	kutta	NOUN
ejpam-6142	569	11	technique	technique	NOUN
ejpam-6142	569	12	which	which	PRON
ejpam-6142	569	13	enables	enable	VERB
ejpam-6142	569	14	precise	precise	ADJ
ejpam-6142	569	15	modelling	modelling	NOUN
ejpam-6142	569	16	of	of	ADP
ejpam-6142	569	17	hiv	hiv	PROPN
ejpam-6142	569	18	transmission	transmission	NOUN
ejpam-6142	569	19	dynamics	dynamic	NOUN
ejpam-6142	569	20	and	and	CCONJ
ejpam-6142	569	21	the	the	DET
ejpam-6142	569	22	effects	effect	NOUN
ejpam-6142	569	23	of	of	ADP
ejpam-6142	569	24	various	various	ADJ
ejpam-6142	569	25	interventions	intervention	NOUN
ejpam-6142	569	26	across	across	ADP
ejpam-6142	569	27	time	time	NOUN
ejpam-6142	569	28	.	.	PUNCT
ejpam-6142	570	1	this	this	DET
ejpam-6142	570	2	method	method	NOUN
ejpam-6142	570	3	allows	allow	VERB
ejpam-6142	570	4	the	the	DET
ejpam-6142	570	5	evaluation	evaluation	NOUN
ejpam-6142	570	6	of	of	ADP
ejpam-6142	570	7	how	how	SCONJ
ejpam-6142	570	8	various	various	ADJ
ejpam-6142	570	9	combinations	combination	NOUN
ejpam-6142	570	10	of	of	ADP
ejpam-6142	570	11	strategies	strategy	NOUN
ejpam-6142	570	12	preventative	preventative	ADJ
ejpam-6142	570	13	,	,	PUNCT
ejpam-6142	570	14	screening	screening	NOUN
ejpam-6142	570	15	,	,	PUNCT
ejpam-6142	570	16	and	and	CCONJ
ejpam-6142	570	17	treatment	treatment	NOUN
ejpam-6142	570	18	might	might	AUX
ejpam-6142	570	19	collectively	collectively	ADV
ejpam-6142	570	20	impact	impact	VERB
ejpam-6142	570	21	the	the	DET
ejpam-6142	570	22	different	different	ADJ
ejpam-6142	570	23	compartments	compartment	NOUN
ejpam-6142	570	24	including	include	VERB
ejpam-6142	570	25	infected	infect	VERB
ejpam-6142	570	26	and	and	CCONJ
ejpam-6142	570	27	aids	aid	NOUN
ejpam-6142	570	28	-	-	PUNCT
ejpam-6142	570	29	stage	stage	NOUN
ejpam-6142	570	30	individuals	individual	NOUN
ejpam-6142	570	31	.	.	PUNCT
ejpam-6142	571	1	numerical	numerical	ADJ
ejpam-6142	571	2	simulations	simulation	NOUN
ejpam-6142	571	3	are	be	AUX
ejpam-6142	571	4	performed	perform	VERB
ejpam-6142	571	5	to	to	PART
ejpam-6142	571	6	demonstrate	demonstrate	VERB
ejpam-6142	571	7	the	the	DET
ejpam-6142	571	8	analytical	analytical	ADJ
ejpam-6142	571	9	results	result	NOUN
ejpam-6142	571	10	from	from	ADP
ejpam-6142	571	11	the	the	DET
ejpam-6142	571	12	aforementioned	aforementioned	ADJ
ejpam-6142	571	13	study	study	NOUN
ejpam-6142	571	14	by	by	ADP
ejpam-6142	571	15	using	use	VERB
ejpam-6142	571	16	the	the	DET
ejpam-6142	571	17	initial	initial	ADJ
ejpam-6142	571	18	conditions	condition	NOUN
ejpam-6142	571	19	and	and	CCONJ
ejpam-6142	571	20	parameter	parameter	NOUN
ejpam-6142	571	21	values	value	NOUN
ejpam-6142	571	22	provided	provide	VERB
ejpam-6142	571	23	in	in	ADP
ejpam-6142	571	24	table	table	NOUN
ejpam-6142	571	25	1	1	NUM
ejpam-6142	571	26	and	and	CCONJ
ejpam-6142	571	27	setting	set	VERB
ejpam-6142	571	28	the	the	DET
ejpam-6142	571	29	terminal	terminal	ADJ
ejpam-6142	571	30	time	time	NOUN
ejpam-6142	572	1	tf	tf	X
ejpam-6142	572	2	=	=	SYM
ejpam-6142	572	3	20	20	NUM
ejpam-6142	572	4	.	.	PUNCT
ejpam-6142	573	1	additionally	additionally	ADV
ejpam-6142	573	2	,	,	PUNCT
ejpam-6142	573	3	the	the	DET
ejpam-6142	573	4	values	value	NOUN
ejpam-6142	573	5	of	of	ADP
ejpam-6142	573	6	parameters	parameter	NOUN
ejpam-6142	573	7	in	in	ADP
ejpam-6142	573	8	the	the	DET
ejpam-6142	573	9	objective	objective	ADJ
ejpam-6142	573	10	functional	functional	NOUN
ejpam-6142	573	11	are	be	AUX
ejpam-6142	573	12	assumed	assume	VERB
ejpam-6142	573	13	and	and	CCONJ
ejpam-6142	573	14	given	give	VERB
ejpam-6142	573	15	in	in	ADP
ejpam-6142	573	16	table	table	NOUN
ejpam-6142	573	17	3	3	NUM
ejpam-6142	573	18	.	.	PUNCT
ejpam-6142	573	19	table	table	NOUN
ejpam-6142	573	20	3	3	NUM
ejpam-6142	573	21	:	:	PUNCT
ejpam-6142	573	22	values	value	NOUN
ejpam-6142	573	23	of	of	ADP
ejpam-6142	573	24	parameters	parameter	NOUN
ejpam-6142	573	25	in	in	ADP
ejpam-6142	573	26	the	the	DET
ejpam-6142	573	27	objective	objective	ADJ
ejpam-6142	573	28	functional	functional	ADJ
ejpam-6142	573	29	cost	cost	NOUN
ejpam-6142	573	30	parameters	parameter	NOUN
ejpam-6142	573	31	values	value	NOUN
ejpam-6142	573	32	cost	cost	VERB
ejpam-6142	573	33	parameters	parameter	NOUN
ejpam-6142	573	34	values	value	NOUN
ejpam-6142	573	35	b1	b1	VERB
ejpam-6142	573	36	15	15	NUM
ejpam-6142	573	37	b2	b2	NOUN
ejpam-6142	573	38	20	20	NUM
ejpam-6142	573	39	b3	b3	PROPN
ejpam-6142	573	40	20	20	NUM
ejpam-6142	573	41	b4	b4	NOUN
ejpam-6142	573	42	25	25	NUM
ejpam-6142	573	43	b5	b5	PROPN
ejpam-6142	573	44	10	10	NUM
ejpam-6142	573	45	b6	b6	NOUN
ejpam-6142	573	46	18	18	NUM
ejpam-6142	573	47	b7	b7	PROPN
ejpam-6142	573	48	15	15	NUM
ejpam-6142	573	49	b8	b8	PROPN
ejpam-6142	573	50	20	20	NUM
ejpam-6142	573	51	b9	b9	PROPN
ejpam-6142	573	52	20	20	NUM
ejpam-6142	573	53	b10	b10	PROPN
ejpam-6142	573	54	25	25	NUM
ejpam-6142	573	55	b11	b11	PROPN
ejpam-6142	573	56	10	10	NUM
ejpam-6142	573	57	b12	b12	NOUN
ejpam-6142	573	58	18	18	NUM
ejpam-6142	573	59	w1	w1	NOUN
ejpam-6142	573	60	10	10	NUM
ejpam-6142	573	61	w2	w2	NOUN
ejpam-6142	573	62	15	15	NUM
ejpam-6142	573	63	w3	w3	PROPN
ejpam-6142	573	64	20	20	NUM
ejpam-6142	573	65	we	we	PRON
ejpam-6142	573	66	used	use	VERB
ejpam-6142	573	67	matlab	matlab	PROPN
ejpam-6142	573	68	software	software	NOUN
ejpam-6142	573	69	to	to	PART
ejpam-6142	573	70	provide	provide	VERB
ejpam-6142	573	71	graphical	graphical	ADJ
ejpam-6142	573	72	representations	representation	NOUN
ejpam-6142	573	73	of	of	ADP
ejpam-6142	573	74	the	the	DET
ejpam-6142	573	75	state	state	NOUN
ejpam-6142	573	76	system	system	NOUN
ejpam-6142	573	77	with	with	ADP
ejpam-6142	573	78	and	and	CCONJ
ejpam-6142	573	79	without	without	ADP
ejpam-6142	573	80	optimum	optimum	ADJ
ejpam-6142	573	81	control	control	NOUN
ejpam-6142	573	82	,	,	PUNCT
ejpam-6142	573	83	as	as	ADV
ejpam-6142	573	84	well	well	ADV
ejpam-6142	573	85	as	as	ADP
ejpam-6142	573	86	the	the	DET
ejpam-6142	573	87	adjoint	adjoint	NOUN
ejpam-6142	573	88	systems	system	NOUN
ejpam-6142	573	89	within	within	ADP
ejpam-6142	573	90	different	different	ADJ
ejpam-6142	573	91	scenarios	scenario	NOUN
ejpam-6142	573	92	.	.	PUNCT
ejpam-6142	574	1	the	the	DET
ejpam-6142	574	2	optimal	optimal	ADJ
ejpam-6142	574	3	control	control	NOUN
ejpam-6142	574	4	profiles	profile	NOUN
ejpam-6142	574	5	for	for	ADP
ejpam-6142	574	6	each	each	DET
ejpam-6142	574	7	strategy	strategy	NOUN
ejpam-6142	574	8	and	and	CCONJ
ejpam-6142	574	9	state	state	NOUN
ejpam-6142	574	10	system	system	NOUN
ejpam-6142	574	11	for	for	ADP
ejpam-6142	574	12	both	both	CCONJ
ejpam-6142	574	13	male	male	ADJ
ejpam-6142	574	14	and	and	CCONJ
ejpam-6142	574	15	female	female	ADJ
ejpam-6142	574	16	are	be	AUX
ejpam-6142	574	17	displayed	display	VERB
ejpam-6142	574	18	together	together	ADV
ejpam-6142	574	19	in	in	ADP
ejpam-6142	574	20	all	all	DET
ejpam-6142	574	21	the	the	DET
ejpam-6142	574	22	graphs	graph	NOUN
ejpam-6142	574	23	.	.	PUNCT
ejpam-6142	575	1	figure	figure	VERB
ejpam-6142	575	2	3	3	NUM
ejpam-6142	575	3	highlights	highlight	NOUN
ejpam-6142	575	4	the	the	DET
ejpam-6142	575	5	effect	effect	NOUN
ejpam-6142	575	6	of	of	ADP
ejpam-6142	575	7	preventative	preventative	ADJ
ejpam-6142	575	8	efforts	effort	NOUN
ejpam-6142	575	9	in	in	ADP
ejpam-6142	575	10	the	the	DET
ejpam-6142	575	11	absence	absence	NOUN
ejpam-6142	575	12	of	of	ADP
ejpam-6142	575	13	screening	screening	NOUN
ejpam-6142	575	14	and	and	CCONJ
ejpam-6142	575	15	treatment	treatment	NOUN
ejpam-6142	575	16	strategies	strategy	NOUN
ejpam-6142	575	17	in	in	ADP
ejpam-6142	575	18	controlling	control	VERB
ejpam-6142	575	19	hiv	hiv	PROPN
ejpam-6142	575	20	/	/	SYM
ejpam-6142	575	21	aids	aids	PROPN
ejpam-6142	575	22	epidemic	epidemic	NOUN
ejpam-6142	575	23	,	,	PUNCT
ejpam-6142	575	24	showing	show	VERB
ejpam-6142	575	25	significant	significant	ADJ
ejpam-6142	575	26	reductions	reduction	NOUN
ejpam-6142	575	27	in	in	ADP
ejpam-6142	575	28	both	both	DET
ejpam-6142	575	29	infections	infection	NOUN
ejpam-6142	575	30	and	and	CCONJ
ejpam-6142	575	31	aids	aid	NOUN
ejpam-6142	575	32	cases	case	NOUN
ejpam-6142	575	33	over	over	ADP
ejpam-6142	575	34	time	time	NOUN
ejpam-6142	575	35	for	for	ADP
ejpam-6142	575	36	both	both	DET
ejpam-6142	575	37	genders	gender	NOUN
ejpam-6142	575	38	.	.	PUNCT
ejpam-6142	576	1	it	it	PRON
ejpam-6142	576	2	is	be	AUX
ejpam-6142	576	3	shown	show	VERB
ejpam-6142	576	4	in	in	ADP
ejpam-6142	576	5	figure	figure	NOUN
ejpam-6142	576	6	3(a	3(a	NUM
ejpam-6142	576	7	)	)	PUNCT
ejpam-6142	576	8	that	that	SCONJ
ejpam-6142	576	9	the	the	DET
ejpam-6142	576	10	infections	infection	NOUN
ejpam-6142	576	11	peak	peak	VERB
ejpam-6142	576	12	sharply	sharply	ADV
ejpam-6142	576	13	around	around	ADP
ejpam-6142	576	14	year	year	NOUN
ejpam-6142	576	15	2	2	NUM
ejpam-6142	576	16	which	which	PRON
ejpam-6142	576	17	is	be	AUX
ejpam-6142	576	18	about	about	ADV
ejpam-6142	576	19	six	six	NUM
ejpam-6142	576	20	million	million	NUM
ejpam-6142	576	21	for	for	ADP
ejpam-6142	576	22	both	both	DET
ejpam-6142	576	23	males	male	NOUN
ejpam-6142	576	24	and	and	CCONJ
ejpam-6142	576	25	females	female	NOUN
ejpam-6142	576	26	.	.	PUNCT
ejpam-6142	577	1	contrastingly	contrastingly	ADV
ejpam-6142	577	2	,	,	PUNCT
ejpam-6142	577	3	the	the	DET
ejpam-6142	577	4	infected	infected	ADJ
ejpam-6142	577	5	populations	population	NOUN
ejpam-6142	577	6	reduced	reduce	VERB
ejpam-6142	577	7	dramatically	dramatically	ADV
ejpam-6142	577	8	with	with	ADP
ejpam-6142	577	9	prevention	prevention	NOUN
ejpam-6142	577	10	and	and	CCONJ
ejpam-6142	577	11	staying	stay	VERB
ejpam-6142	577	12	below	below	ADP
ejpam-6142	577	13	200,000	200,000	NUM
ejpam-6142	577	14	in	in	ADP
ejpam-6142	577	15	the	the	DET
ejpam-6142	577	16	period	period	NOUN
ejpam-6142	577	17	.	.	PUNCT
ejpam-6142	578	1	on	on	ADP
ejpam-6142	578	2	the	the	DET
ejpam-6142	578	3	other	other	ADJ
ejpam-6142	578	4	hand	hand	NOUN
ejpam-6142	578	5	,	,	PUNCT
ejpam-6142	578	6	as	as	SCONJ
ejpam-6142	578	7	demonstrated	demonstrate	VERB
ejpam-6142	578	8	in	in	ADP
ejpam-6142	578	9	figure	figure	NOUN
ejpam-6142	578	10	3(b	3(b	NUM
ejpam-6142	578	11	)	)	PUNCT
ejpam-6142	578	12	the	the	DET
ejpam-6142	578	13	aids	aids	PROPN
ejpam-6142	578	14	compartments	compartment	NOUN
ejpam-6142	578	15	peak	peak	VERB
ejpam-6142	578	16	around	around	ADP
ejpam-6142	578	17	year	year	NOUN
ejpam-6142	578	18	5	5	NUM
ejpam-6142	578	19	and	and	CCONJ
ejpam-6142	578	20	reach	reach	VERB
ejpam-6142	578	21	about	about	ADV
ejpam-6142	578	22	450	450	NUM
ejpam-6142	578	23	thousand	thousand	NUM
ejpam-6142	578	24	with	with	ADP
ejpam-6142	578	25	slightly	slightly	ADV
ejpam-6142	578	26	fewer	few	ADJ
ejpam-6142	578	27	female	female	ADJ
ejpam-6142	578	28	cases	case	NOUN
ejpam-6142	578	29	,	,	PUNCT
ejpam-6142	578	30	whereas	whereas	SCONJ
ejpam-6142	578	31	with	with	ADP
ejpam-6142	578	32	prevention	prevention	NOUN
ejpam-6142	578	33	strategy	strategy	NOUN
ejpam-6142	578	34	is	be	AUX
ejpam-6142	578	35	much	much	ADV
ejpam-6142	578	36	lower	low	ADJ
ejpam-6142	578	37	about	about	ADP
ejpam-6142	578	38	25,000	25,000	NUM
ejpam-6142	578	39	cases	case	NOUN
ejpam-6142	578	40	.	.	PUNCT
ejpam-6142	579	1	the	the	DET
ejpam-6142	579	2	aids	aids	PROPN
ejpam-6142	579	3	cases	case	NOUN
ejpam-6142	579	4	with	with	ADP
ejpam-6142	579	5	prevention	prevention	NOUN
ejpam-6142	579	6	approach	approach	NOUN
ejpam-6142	579	7	zero	zero	NUM
ejpam-6142	579	8	by	by	ADP
ejpam-6142	579	9	the	the	DET
ejpam-6142	579	10	year	year	NOUN
ejpam-6142	579	11	20	20	NUM
ejpam-6142	579	12	while	while	NOUN
ejpam-6142	579	13	without	without	ADP
ejpam-6142	579	14	prevention	prevention	NOUN
ejpam-6142	579	15	it	it	PRON
ejpam-6142	579	16	remains	remain	VERB
ejpam-6142	579	17	significant	significant	ADJ
ejpam-6142	579	18	.	.	PUNCT
ejpam-6142	580	1	prevention	prevention	NOUN
ejpam-6142	580	2	not	not	PART
ejpam-6142	580	3	only	only	ADV
ejpam-6142	580	4	reduces	reduce	VERB
ejpam-6142	580	5	case	case	NOUN
ejpam-6142	580	6	the	the	DET
ejpam-6142	580	7	number	number	NOUN
ejpam-6142	580	8	of	of	ADP
ejpam-6142	580	9	males	male	NOUN
ejpam-6142	580	10	and	and	CCONJ
ejpam-6142	580	11	females	female	NOUN
ejpam-6142	580	12	but	but	CCONJ
ejpam-6142	580	13	also	also	ADV
ejpam-6142	580	14	shortens	shorten	VERB
ejpam-6142	580	15	and	and	CCONJ
ejpam-6142	580	16	flattens	flatten	VERB
ejpam-6142	580	17	the	the	DET
ejpam-6142	580	18	epidemic	epidemic	NOUN
ejpam-6142	580	19	curves	curve	NOUN
ejpam-6142	580	20	for	for	ADP
ejpam-6142	580	21	both	both	DET
ejpam-6142	580	22	infections	infection	NOUN
ejpam-6142	580	23	and	and	CCONJ
ejpam-6142	580	24	aids	aid	NOUN
ejpam-6142	580	25	.	.	PUNCT
ejpam-6142	581	1	the	the	DET
ejpam-6142	581	2	graphs	graph	NOUN
ejpam-6142	581	3	indicate	indicate	VERB
ejpam-6142	581	4	that	that	SCONJ
ejpam-6142	581	5	females	female	NOUN
ejpam-6142	581	6	are	be	AUX
ejpam-6142	581	7	somewhat	somewhat	ADV
ejpam-6142	581	8	less	less	ADV
ejpam-6142	581	9	impacted	impact	VERB
ejpam-6142	581	10	in	in	ADP
ejpam-6142	581	11	both	both	CCONJ
ejpam-6142	581	12	the	the	DET
ejpam-6142	581	13	infected	infect	VERB
ejpam-6142	581	14	and	and	CCONJ
ejpam-6142	581	15	aids	aid	NOUN
ejpam-6142	581	16	stages	stage	NOUN
ejpam-6142	581	17	;	;	PUNCT
ejpam-6142	581	18	s.	s.	PROPN
ejpam-6142	581	19	m.	m.	PROPN
ejpam-6142	581	20	fatah	fatah	PROPN
ejpam-6142	581	21	,	,	PUNCT
ejpam-6142	581	22	s.	s.	PROPN
ejpam-6142	581	23	h.	h.	PROPN
ejpam-6142	581	24	a.	a.	PROPN
ejpam-6142	581	25	khoshnaw	khoshnaw	PROPN
ejpam-6142	581	26	,	,	PUNCT
ejpam-6142	581	27	a.	a.	PROPN
ejpam-6142	581	28	n.	n.	PROPN
ejpam-6142	581	29	mustafa	mustafa	PROPN
ejpam-6142	581	30	/	/	SYM
ejpam-6142	581	31	eur	eur	PROPN
ejpam-6142	581	32	.	.	PUNCT
ejpam-6142	582	1	j.	j.	PROPN
ejpam-6142	582	2	pure	pure	PROPN
ejpam-6142	582	3	appl	appl	PROPN
ejpam-6142	582	4	.	.	PROPN
ejpam-6142	582	5	math	math	PROPN
ejpam-6142	582	6	,	,	PUNCT
ejpam-6142	582	7	18	18	NUM
ejpam-6142	582	8	(	(	PUNCT
ejpam-6142	582	9	2	2	NUM
ejpam-6142	582	10	)	)	PUNCT
ejpam-6142	582	11	(	(	PUNCT
ejpam-6142	582	12	2025	2025	NUM
ejpam-6142	582	13	)	)	PUNCT
ejpam-6142	582	14	,	,	PUNCT
ejpam-6142	582	15	6142	6142	NUM
ejpam-6142	582	16	26	26	NUM
ejpam-6142	582	17	of	of	ADP
ejpam-6142	582	18	33	33	NUM
ejpam-6142	582	19	figure	figure	NOUN
ejpam-6142	582	20	3	3	NUM
ejpam-6142	582	21	:	:	PUNCT
ejpam-6142	582	22	simulation	simulation	NOUN
ejpam-6142	582	23	of	of	ADP
ejpam-6142	582	24	optimal	optimal	ADJ
ejpam-6142	582	25	control	control	NOUN
ejpam-6142	582	26	of	of	ADP
ejpam-6142	582	27	infected	infected	ADJ
ejpam-6142	582	28	and	and	CCONJ
ejpam-6142	582	29	aids	aid	NOUN
ejpam-6142	582	30	population	population	NOUN
ejpam-6142	582	31	for	for	ADP
ejpam-6142	582	32	both	both	CCONJ
ejpam-6142	582	33	male	male	ADJ
ejpam-6142	582	34	and	and	CCONJ
ejpam-6142	582	35	female	female	ADJ
ejpam-6142	582	36	with	with	ADP
ejpam-6142	582	37	prevention	prevention	NOUN
ejpam-6142	582	38	however	however	ADV
ejpam-6142	582	39	,	,	PUNCT
ejpam-6142	582	40	preventative	preventative	ADJ
ejpam-6142	582	41	measures	measure	NOUN
ejpam-6142	582	42	reduce	reduce	VERB
ejpam-6142	582	43	this	this	DET
ejpam-6142	582	44	gender	gender	NOUN
ejpam-6142	582	45	disparity	disparity	NOUN
ejpam-6142	582	46	.	.	PUNCT
ejpam-6142	583	1	figure	figure	VERB
ejpam-6142	583	2	4	4	NUM
ejpam-6142	583	3	:	:	PUNCT
ejpam-6142	583	4	simulation	simulation	NOUN
ejpam-6142	583	5	of	of	ADP
ejpam-6142	583	6	optimal	optimal	ADJ
ejpam-6142	583	7	control	control	NOUN
ejpam-6142	583	8	of	of	ADP
ejpam-6142	583	9	infected	infected	ADJ
ejpam-6142	583	10	and	and	CCONJ
ejpam-6142	583	11	aids	aid	NOUN
ejpam-6142	583	12	population	population	NOUN
ejpam-6142	583	13	for	for	ADP
ejpam-6142	583	14	both	both	CCONJ
ejpam-6142	583	15	male	male	ADJ
ejpam-6142	583	16	and	and	CCONJ
ejpam-6142	583	17	female	female	ADJ
ejpam-6142	583	18	with	with	ADP
ejpam-6142	583	19	screening	screen	VERB
ejpam-6142	583	20	in	in	ADP
ejpam-6142	583	21	figure	figure	NOUN
ejpam-6142	583	22	4	4	NUM
ejpam-6142	583	23	,	,	PUNCT
ejpam-6142	583	24	the	the	DET
ejpam-6142	583	25	simulation	simulation	NOUN
ejpam-6142	583	26	of	of	ADP
ejpam-6142	583	27	both	both	CCONJ
ejpam-6142	583	28	infected	infected	ADJ
ejpam-6142	583	29	and	and	CCONJ
ejpam-6142	583	30	aids	aid	NOUN
ejpam-6142	583	31	populations	population	NOUN
ejpam-6142	583	32	for	for	ADP
ejpam-6142	583	33	males	male	NOUN
ejpam-6142	583	34	and	and	CCONJ
ejpam-6142	583	35	females	female	NOUN
ejpam-6142	583	36	are	be	AUX
ejpam-6142	583	37	depicted	depict	VERB
ejpam-6142	583	38	with	with	ADP
ejpam-6142	583	39	and	and	CCONJ
ejpam-6142	583	40	without	without	ADP
ejpam-6142	583	41	screening	screen	VERB
ejpam-6142	583	42	control	control	NOUN
ejpam-6142	583	43	interventions	intervention	NOUN
ejpam-6142	583	44	and	and	CCONJ
ejpam-6142	583	45	excluding	exclude	VERB
ejpam-6142	583	46	prevention	prevention	NOUN
ejpam-6142	583	47	and	and	CCONJ
ejpam-6142	583	48	treatment	treatment	NOUN
ejpam-6142	583	49	.	.	PUNCT
ejpam-6142	584	1	the	the	DET
ejpam-6142	584	2	figures	figure	NOUN
ejpam-6142	584	3	4(a	4(a	NUM
ejpam-6142	584	4	)	)	PUNCT
ejpam-6142	584	5	and	and	CCONJ
ejpam-6142	584	6	4(b	4(b	NUM
ejpam-6142	584	7	)	)	PUNCT
ejpam-6142	584	8	demonstrate	demonstrate	VERB
ejpam-6142	584	9	the	the	DET
ejpam-6142	584	10	significant	significant	ADJ
ejpam-6142	584	11	role	role	NOUN
ejpam-6142	584	12	of	of	ADP
ejpam-6142	584	13	screening	screen	VERB
ejpam-6142	584	14	in	in	ADP
ejpam-6142	584	15	decreasing	decrease	VERB
ejpam-6142	584	16	the	the	DET
ejpam-6142	584	17	hiv	hiv	PROPN
ejpam-6142	584	18	/	/	SYM
ejpam-6142	584	19	aids	aids	PROPN
ejpam-6142	584	20	epidemic	epidemic	NOUN
ejpam-6142	584	21	.	.	PUNCT
ejpam-6142	585	1	while	while	SCONJ
ejpam-6142	585	2	not	not	PART
ejpam-6142	585	3	as	as	ADP
ejpam-6142	585	4	dramatically	dramatically	ADV
ejpam-6142	585	5	effective	effective	ADJ
ejpam-6142	585	6	as	as	ADP
ejpam-6142	585	7	prevention	prevention	NOUN
ejpam-6142	585	8	strategies	strategy	NOUN
ejpam-6142	585	9	,	,	PUNCT
ejpam-6142	585	10	screening	screen	VERB
ejpam-6142	585	11	shows	show	VERB
ejpam-6142	585	12	substantial	substantial	ADJ
ejpam-6142	585	13	benefits	benefit	NOUN
ejpam-6142	585	14	in	in	ADP
ejpam-6142	585	15	reducing	reduce	VERB
ejpam-6142	585	16	both	both	DET
ejpam-6142	585	17	infection	infection	NOUN
ejpam-6142	585	18	rates	rate	NOUN
ejpam-6142	585	19	and	and	CCONJ
ejpam-6142	585	20	aids	aid	NOUN
ejpam-6142	585	21	cases	case	NOUN
ejpam-6142	585	22	for	for	ADP
ejpam-6142	585	23	males	male	NOUN
ejpam-6142	585	24	and	and	CCONJ
ejpam-6142	585	25	females	female	NOUN
ejpam-6142	585	26	.	.	PUNCT
ejpam-6142	586	1	figure	figure	NOUN
ejpam-6142	586	2	5	5	NUM
ejpam-6142	586	3	illustrates	illustrate	VERB
ejpam-6142	586	4	the	the	DET
ejpam-6142	586	5	dynamics	dynamic	NOUN
ejpam-6142	586	6	of	of	ADP
ejpam-6142	586	7	infected	infected	ADJ
ejpam-6142	586	8	and	and	CCONJ
ejpam-6142	586	9	aids	aids	PROPN
ejpam-6142	586	10	population	population	NOUN
ejpam-6142	586	11	’s	’s	PART
ejpam-6142	586	12	progression	progression	NOUN
ejpam-6142	586	13	over	over	ADP
ejpam-6142	586	14	a	a	DET
ejpam-6142	586	15	20	20	NUM
ejpam-6142	586	16	-	-	PUNCT
ejpam-6142	586	17	year	year	NOUN
ejpam-6142	586	18	period	period	NOUN
ejpam-6142	586	19	,	,	PUNCT
ejpam-6142	586	20	comparing	compare	VERB
ejpam-6142	586	21	scenarios	scenario	NOUN
ejpam-6142	586	22	with	with	ADP
ejpam-6142	586	23	and	and	CCONJ
ejpam-6142	586	24	without	without	ADP
ejpam-6142	586	25	treatment	treatment	NOUN
ejpam-6142	586	26	interventions	intervention	NOUN
ejpam-6142	586	27	in	in	ADP
ejpam-6142	586	28	the	the	DET
ejpam-6142	586	29	absence	absence	NOUN
ejpam-6142	586	30	of	of	ADP
ejpam-6142	586	31	prevention	prevention	NOUN
ejpam-6142	586	32	and	and	CCONJ
ejpam-6142	586	33	screening	screening	NOUN
ejpam-6142	586	34	controls	control	NOUN
ejpam-6142	586	35	for	for	ADP
ejpam-6142	586	36	both	both	DET
ejpam-6142	586	37	males	male	NOUN
ejpam-6142	586	38	and	and	CCONJ
ejpam-6142	586	39	females	female	NOUN
ejpam-6142	586	40	.	.	PUNCT
ejpam-6142	587	1	with	with	ADP
ejpam-6142	587	2	treatment	treatment	NOUN
ejpam-6142	587	3	,	,	PUNCT
ejpam-6142	587	4	there	there	PRON
ejpam-6142	587	5	is	be	VERB
ejpam-6142	587	6	minimal	minimal	ADJ
ejpam-6142	587	7	visible	visible	ADJ
ejpam-6142	587	8	impact	impact	NOUN
ejpam-6142	587	9	on	on	ADP
ejpam-6142	587	10	the	the	DET
ejpam-6142	587	11	infection	infection	NOUN
ejpam-6142	587	12	rates	rate	NOUN
ejpam-6142	587	13	and	and	CCONJ
ejpam-6142	587	14	the	the	DET
ejpam-6142	587	15	curves	curve	NOUN
ejpam-6142	587	16	for	for	ADP
ejpam-6142	587	17	treated	treat	VERB
ejpam-6142	587	18	and	and	CCONJ
ejpam-6142	587	19	untreated	untreated	ADJ
ejpam-6142	587	20	scenarios	scenario	NOUN
ejpam-6142	587	21	are	be	AUX
ejpam-6142	587	22	almost	almost	ADV
ejpam-6142	587	23	identical	identical	ADJ
ejpam-6142	587	24	this	this	PRON
ejpam-6142	587	25	is	be	AUX
ejpam-6142	587	26	provided	provide	VERB
ejpam-6142	587	27	in	in	ADP
ejpam-6142	587	28	figure	figure	NOUN
ejpam-6142	587	29	5(a	5(a	NUM
ejpam-6142	587	30	)	)	PUNCT
ejpam-6142	587	31	.	.	PUNCT
ejpam-6142	588	1	it	it	PRON
ejpam-6142	588	2	clearly	clearly	ADV
ejpam-6142	588	3	can	can	AUX
ejpam-6142	588	4	be	be	AUX
ejpam-6142	588	5	s.	s.	PROPN
ejpam-6142	588	6	m.	m.	PROPN
ejpam-6142	588	7	fatah	fatah	PROPN
ejpam-6142	588	8	,	,	PUNCT
ejpam-6142	588	9	s.	s.	PROPN
ejpam-6142	588	10	h.	h.	PROPN
ejpam-6142	588	11	a.	a.	PROPN
ejpam-6142	588	12	khoshnaw	khoshnaw	PROPN
ejpam-6142	588	13	,	,	PUNCT
ejpam-6142	588	14	a.	a.	PROPN
ejpam-6142	588	15	n.	n.	PROPN
ejpam-6142	588	16	mustafa	mustafa	PROPN
ejpam-6142	588	17	/	/	SYM
ejpam-6142	588	18	eur	eur	PROPN
ejpam-6142	588	19	.	.	PUNCT
ejpam-6142	589	1	j.	j.	PROPN
ejpam-6142	589	2	pure	pure	PROPN
ejpam-6142	589	3	appl	appl	PROPN
ejpam-6142	589	4	.	.	PROPN
ejpam-6142	589	5	math	math	PROPN
ejpam-6142	589	6	,	,	PUNCT
ejpam-6142	589	7	18	18	NUM
ejpam-6142	589	8	(	(	PUNCT
ejpam-6142	589	9	2	2	NUM
ejpam-6142	589	10	)	)	PUNCT
ejpam-6142	589	11	(	(	PUNCT
ejpam-6142	589	12	2025	2025	NUM
ejpam-6142	589	13	)	)	PUNCT
ejpam-6142	589	14	,	,	PUNCT
ejpam-6142	589	15	6142	6142	NUM
ejpam-6142	589	16	27	27	NUM
ejpam-6142	589	17	of	of	ADP
ejpam-6142	589	18	33	33	NUM
ejpam-6142	589	19	figure	figure	NOUN
ejpam-6142	589	20	5	5	NUM
ejpam-6142	589	21	:	:	PUNCT
ejpam-6142	589	22	simulation	simulation	NOUN
ejpam-6142	589	23	of	of	ADP
ejpam-6142	589	24	optimal	optimal	ADJ
ejpam-6142	589	25	control	control	NOUN
ejpam-6142	589	26	of	of	ADP
ejpam-6142	589	27	infected	infected	ADJ
ejpam-6142	589	28	and	and	CCONJ
ejpam-6142	589	29	aids	aid	NOUN
ejpam-6142	589	30	population	population	NOUN
ejpam-6142	589	31	for	for	ADP
ejpam-6142	589	32	both	both	CCONJ
ejpam-6142	589	33	male	male	ADJ
ejpam-6142	589	34	and	and	CCONJ
ejpam-6142	589	35	female	female	ADJ
ejpam-6142	589	36	with	with	ADP
ejpam-6142	589	37	treatment	treatment	NOUN
ejpam-6142	589	38	seen	see	VERB
ejpam-6142	589	39	in	in	ADP
ejpam-6142	589	40	figure	figure	NOUN
ejpam-6142	589	41	5(b	5(b	NUM
ejpam-6142	589	42	)	)	PUNCT
ejpam-6142	589	43	that	that	SCONJ
ejpam-6142	589	44	the	the	DET
ejpam-6142	589	45	peak	peak	NOUN
ejpam-6142	589	46	of	of	ADP
ejpam-6142	589	47	aids	aids	PROPN
ejpam-6142	589	48	population	population	NOUN
ejpam-6142	589	49	of	of	ADP
ejpam-6142	589	50	both	both	DET
ejpam-6142	589	51	genders	gender	NOUN
ejpam-6142	589	52	with	with	ADP
ejpam-6142	589	53	treatment	treatment	NOUN
ejpam-6142	589	54	is	be	AUX
ejpam-6142	589	55	substantially	substantially	ADV
ejpam-6142	589	56	lowered	lower	VERB
ejpam-6142	589	57	to	to	ADP
ejpam-6142	589	58	about	about	ADV
ejpam-6142	589	59	170,000	170,000	NUM
ejpam-6142	589	60	cases	case	NOUN
ejpam-6142	589	61	for	for	ADP
ejpam-6142	589	62	males	male	NOUN
ejpam-6142	589	63	and	and	CCONJ
ejpam-6142	589	64	160,000	160,000	NUM
ejpam-6142	589	65	for	for	ADP
ejpam-6142	589	66	females	female	NOUN
ejpam-6142	589	67	and	and	CCONJ
ejpam-6142	589	68	approach	approach	NOUN
ejpam-6142	589	69	zero	zero	NUM
ejpam-6142	589	70	by	by	ADP
ejpam-6142	589	71	year	year	NOUN
ejpam-6142	589	72	20	20	NUM
ejpam-6142	589	73	.	.	PUNCT
ejpam-6142	590	1	this	this	PRON
ejpam-6142	590	2	underscores	underscore	VERB
ejpam-6142	590	3	the	the	DET
ejpam-6142	590	4	importance	importance	NOUN
ejpam-6142	590	5	of	of	ADP
ejpam-6142	590	6	treatment	treatment	NOUN
ejpam-6142	590	7	in	in	ADP
ejpam-6142	590	8	improving	improve	VERB
ejpam-6142	590	9	quality	quality	NOUN
ejpam-6142	590	10	of	of	ADP
ejpam-6142	590	11	life	life	NOUN
ejpam-6142	590	12	and	and	CCONJ
ejpam-6142	590	13	survival	survival	NOUN
ejpam-6142	590	14	for	for	ADP
ejpam-6142	590	15	those	those	PRON
ejpam-6142	590	16	who	who	PRON
ejpam-6142	590	17	infected	infect	VERB
ejpam-6142	590	18	with	with	ADP
ejpam-6142	590	19	hiv	hiv	PROPN
ejpam-6142	590	20	.	.	PUNCT
ejpam-6142	591	1	the	the	DET
ejpam-6142	591	2	model	model	NOUN
ejpam-6142	591	3	suggests	suggest	VERB
ejpam-6142	591	4	that	that	SCONJ
ejpam-6142	591	5	comprehensive	comprehensive	ADJ
ejpam-6142	591	6	hiv	hiv	PROPN
ejpam-6142	591	7	/	/	SYM
ejpam-6142	591	8	aids	aids	PROPN
ejpam-6142	591	9	management	management	NOUN
ejpam-6142	591	10	should	should	AUX
ejpam-6142	591	11	combine	combine	VERB
ejpam-6142	591	12	treatment	treatment	NOUN
ejpam-6142	591	13	with	with	ADP
ejpam-6142	591	14	other	other	ADJ
ejpam-6142	591	15	strategies	strategy	NOUN
ejpam-6142	591	16	like	like	ADP
ejpam-6142	591	17	prevention	prevention	NOUN
ejpam-6142	591	18	and	and	CCONJ
ejpam-6142	591	19	screening	screen	VERB
ejpam-6142	591	20	to	to	PART
ejpam-6142	591	21	address	address	VERB
ejpam-6142	591	22	both	both	DET
ejpam-6142	591	23	infection	infection	NOUN
ejpam-6142	591	24	rates	rate	NOUN
ejpam-6142	591	25	and	and	CCONJ
ejpam-6142	591	26	disease	disease	NOUN
ejpam-6142	591	27	progression	progression	NOUN
ejpam-6142	591	28	.	.	PUNCT
ejpam-6142	592	1	figure	figure	VERB
ejpam-6142	592	2	6	6	NUM
ejpam-6142	592	3	:	:	PUNCT
ejpam-6142	592	4	simulation	simulation	NOUN
ejpam-6142	592	5	of	of	ADP
ejpam-6142	592	6	optimal	optimal	ADJ
ejpam-6142	592	7	control	control	NOUN
ejpam-6142	592	8	of	of	ADP
ejpam-6142	592	9	infected	infected	ADJ
ejpam-6142	592	10	and	and	CCONJ
ejpam-6142	592	11	aids	aid	NOUN
ejpam-6142	592	12	population	population	NOUN
ejpam-6142	592	13	for	for	ADP
ejpam-6142	592	14	both	both	CCONJ
ejpam-6142	592	15	male	male	ADJ
ejpam-6142	592	16	and	and	CCONJ
ejpam-6142	592	17	female	female	ADJ
ejpam-6142	592	18	with	with	ADP
ejpam-6142	592	19	prevention	prevention	NOUN
ejpam-6142	592	20	and	and	CCONJ
ejpam-6142	592	21	screening	screening	NOUN
ejpam-6142	592	22	figure	figure	NOUN
ejpam-6142	592	23	6	6	NUM
ejpam-6142	592	24	shows	show	VERB
ejpam-6142	592	25	how	how	SCONJ
ejpam-6142	592	26	the	the	DET
ejpam-6142	592	27	combination	combination	NOUN
ejpam-6142	592	28	of	of	ADP
ejpam-6142	592	29	preventive	preventive	ADJ
ejpam-6142	592	30	and	and	CCONJ
ejpam-6142	592	31	screening	screen	VERB
ejpam-6142	592	32	strategies	strategy	NOUN
ejpam-6142	592	33	affects	affect	VERB
ejpam-6142	592	34	both	both	CCONJ
ejpam-6142	592	35	infected	infected	ADJ
ejpam-6142	592	36	and	and	CCONJ
ejpam-6142	592	37	aids	aids	PROPN
ejpam-6142	592	38	population	population	NOUN
ejpam-6142	592	39	’s	’s	PART
ejpam-6142	592	40	dynamics	dynamic	NOUN
ejpam-6142	592	41	over	over	ADP
ejpam-6142	592	42	the	the	DET
ejpam-6142	592	43	period	period	NOUN
ejpam-6142	592	44	.	.	PUNCT
ejpam-6142	593	1	there	there	PRON
ejpam-6142	593	2	is	be	VERB
ejpam-6142	593	3	a	a	DET
ejpam-6142	593	4	remarkable	remarkable	ADJ
ejpam-6142	593	5	drop	drop	NOUN
ejpam-6142	593	6	in	in	ADP
ejpam-6142	593	7	using	use	VERB
ejpam-6142	593	8	both	both	DET
ejpam-6142	593	9	prevention	prevention	NOUN
ejpam-6142	593	10	and	and	CCONJ
ejpam-6142	593	11	screening	screen	VERB
ejpam-6142	593	12	strategies	strategy	NOUN
ejpam-6142	593	13	together	together	ADV
ejpam-6142	593	14	in	in	ADP
ejpam-6142	593	15	infected	infected	ADJ
ejpam-6142	593	16	and	and	CCONJ
ejpam-6142	593	17	aids	aid	NOUN
ejpam-6142	593	18	compartments	compartment	NOUN
ejpam-6142	593	19	for	for	ADP
ejpam-6142	593	20	both	both	CCONJ
ejpam-6142	593	21	male	male	ADJ
ejpam-6142	593	22	and	and	CCONJ
ejpam-6142	593	23	female	female	ADJ
ejpam-6142	593	24	populations	population	NOUN
ejpam-6142	593	25	this	this	PRON
ejpam-6142	593	26	can	can	AUX
ejpam-6142	593	27	be	be	AUX
ejpam-6142	593	28	seen	see	VERB
ejpam-6142	593	29	in	in	ADP
ejpam-6142	593	30	figures	figure	NOUN
ejpam-6142	593	31	6(a	6(a	NUM
ejpam-6142	593	32	)	)	PUNCT
ejpam-6142	593	33	and	and	CCONJ
ejpam-6142	593	34	6(b	6(b	NUM
ejpam-6142	593	35	)	)	PUNCT
ejpam-6142	593	36	.	.	PUNCT
ejpam-6142	594	1	the	the	DET
ejpam-6142	594	2	intervention	intervention	PROPN
ejpam-6142	594	3	scenario	scenario	PROPN
ejpam-6142	594	4	considerably	considerably	ADV
ejpam-6142	594	5	flattens	flatten	VERB
ejpam-6142	594	6	the	the	DET
ejpam-6142	594	7	epidemic	epidemic	NOUN
ejpam-6142	594	8	curves	curve	NOUN
ejpam-6142	594	9	,	,	PUNCT
ejpam-6142	594	10	eliminating	eliminate	VERB
ejpam-6142	594	11	new	new	ADJ
ejpam-6142	594	12	infections	infection	NOUN
ejpam-6142	594	13	and	and	CCONJ
ejpam-6142	594	14	bringing	bring	VERB
ejpam-6142	594	15	aids	aid	NOUN
ejpam-6142	594	16	incidence	incidence	NOUN
ejpam-6142	594	17	to	to	ADP
ejpam-6142	594	18	a	a	DET
ejpam-6142	594	19	minimum	minimum	NOUN
ejpam-6142	594	20	by	by	ADP
ejpam-6142	594	21	year	year	NOUN
ejpam-6142	594	22	20	20	NUM
ejpam-6142	594	23	.	.	PUNCT
ejpam-6142	595	1	the	the	DET
ejpam-6142	595	2	significant	significant	ADJ
ejpam-6142	595	3	decrease	decrease	NOUN
ejpam-6142	595	4	in	in	ADP
ejpam-6142	595	5	both	both	DET
ejpam-6142	595	6	compartments	compartment	NOUN
ejpam-6142	595	7	signifies	signify	VERB
ejpam-6142	595	8	that	that	SCONJ
ejpam-6142	595	9	this	this	DET
ejpam-6142	595	10	integrated	integrate	VERB
ejpam-6142	595	11	strategy	strategy	NOUN
ejpam-6142	595	12	address	address	NOUN
ejpam-6142	595	13	both	both	DET
ejpam-6142	595	14	new	new	ADJ
ejpam-6142	595	15	infections	infection	NOUN
ejpam-6142	595	16	by	by	ADP
ejpam-6142	595	17	prevention	prevention	NOUN
ejpam-6142	595	18	and	and	CCONJ
ejpam-6142	595	19	the	the	DET
ejpam-6142	595	20	progression	progression	NOUN
ejpam-6142	595	21	to	to	PART
ejpam-6142	595	22	aids	aids	VERB
ejpam-6142	595	23	through	through	ADP
ejpam-6142	595	24	screening	screening	NOUN
ejpam-6142	595	25	and	and	CCONJ
ejpam-6142	595	26	probable	probable	ADJ
ejpam-6142	595	27	early	early	ADJ
ejpam-6142	595	28	treatment	treatment	NOUN
ejpam-6142	595	29	s.	s.	PROPN
ejpam-6142	595	30	m.	m.	PROPN
ejpam-6142	595	31	fatah	fatah	PROPN
ejpam-6142	595	32	,	,	PUNCT
ejpam-6142	595	33	s.	s.	PROPN
ejpam-6142	595	34	h.	h.	PROPN
ejpam-6142	595	35	a.	a.	PROPN
ejpam-6142	595	36	khoshnaw	khoshnaw	PROPN
ejpam-6142	595	37	,	,	PUNCT
ejpam-6142	595	38	a.	a.	PROPN
ejpam-6142	595	39	n.	n.	PROPN
ejpam-6142	595	40	mustafa	mustafa	PROPN
ejpam-6142	595	41	/	/	SYM
ejpam-6142	595	42	eur	eur	PROPN
ejpam-6142	595	43	.	.	PUNCT
ejpam-6142	596	1	j.	j.	PROPN
ejpam-6142	596	2	pure	pure	PROPN
ejpam-6142	596	3	appl	appl	PROPN
ejpam-6142	596	4	.	.	PROPN
ejpam-6142	596	5	math	math	PROPN
ejpam-6142	596	6	,	,	PUNCT
ejpam-6142	596	7	18	18	NUM
ejpam-6142	596	8	(	(	PUNCT
ejpam-6142	596	9	2	2	NUM
ejpam-6142	596	10	)	)	PUNCT
ejpam-6142	596	11	(	(	PUNCT
ejpam-6142	596	12	2025	2025	NUM
ejpam-6142	596	13	)	)	PUNCT
ejpam-6142	596	14	,	,	PUNCT
ejpam-6142	596	15	6142	6142	NUM
ejpam-6142	596	16	28	28	NUM
ejpam-6142	596	17	of	of	ADP
ejpam-6142	596	18	33	33	NUM
ejpam-6142	596	19	commencement	commencement	NOUN
ejpam-6142	596	20	.	.	PUNCT
ejpam-6142	597	1	figure	figure	VERB
ejpam-6142	597	2	7	7	NUM
ejpam-6142	597	3	:	:	PUNCT
ejpam-6142	597	4	simulation	simulation	NOUN
ejpam-6142	597	5	of	of	ADP
ejpam-6142	597	6	optimal	optimal	ADJ
ejpam-6142	597	7	control	control	NOUN
ejpam-6142	597	8	of	of	ADP
ejpam-6142	597	9	infected	infected	ADJ
ejpam-6142	597	10	and	and	CCONJ
ejpam-6142	597	11	aids	aid	NOUN
ejpam-6142	597	12	population	population	NOUN
ejpam-6142	597	13	for	for	ADP
ejpam-6142	597	14	both	both	CCONJ
ejpam-6142	597	15	male	male	ADJ
ejpam-6142	597	16	and	and	CCONJ
ejpam-6142	597	17	female	female	ADJ
ejpam-6142	597	18	with	with	ADP
ejpam-6142	597	19	prevention	prevention	NOUN
ejpam-6142	597	20	and	and	CCONJ
ejpam-6142	597	21	treatment	treatment	NOUN
ejpam-6142	597	22	figure	figure	NOUN
ejpam-6142	597	23	7	7	NUM
ejpam-6142	597	24	depicts	depict	VERB
ejpam-6142	597	25	the	the	DET
ejpam-6142	597	26	infection	infection	NOUN
ejpam-6142	597	27	and	and	CCONJ
ejpam-6142	597	28	aids	aid	NOUN
ejpam-6142	597	29	populations	population	NOUN
ejpam-6142	597	30	with	with	ADP
ejpam-6142	597	31	and	and	CCONJ
ejpam-6142	597	32	without	without	ADP
ejpam-6142	597	33	prevention	prevention	NOUN
ejpam-6142	597	34	and	and	CCONJ
ejpam-6142	597	35	treatment	treatment	NOUN
ejpam-6142	597	36	strategies	strategy	NOUN
ejpam-6142	597	37	and	and	CCONJ
ejpam-6142	597	38	how	how	SCONJ
ejpam-6142	597	39	the	the	DET
ejpam-6142	597	40	interventions	intervention	NOUN
ejpam-6142	597	41	affect	affect	VERB
ejpam-6142	597	42	the	the	DET
ejpam-6142	597	43	reduction	reduction	NOUN
ejpam-6142	597	44	of	of	ADP
ejpam-6142	597	45	both	both	DET
ejpam-6142	597	46	compartments	compartment	NOUN
ejpam-6142	597	47	for	for	ADP
ejpam-6142	597	48	males	male	NOUN
ejpam-6142	597	49	and	and	CCONJ
ejpam-6142	597	50	females	female	NOUN
ejpam-6142	597	51	.	.	PUNCT
ejpam-6142	598	1	combining	combine	VERB
ejpam-6142	598	2	prevention	prevention	NOUN
ejpam-6142	598	3	and	and	CCONJ
ejpam-6142	598	4	treatment	treatment	NOUN
ejpam-6142	598	5	controls	control	NOUN
ejpam-6142	598	6	significantly	significantly	ADV
ejpam-6142	598	7	decreases	decrease	VERB
ejpam-6142	598	8	infection	infection	NOUN
ejpam-6142	598	9	rates	rate	NOUN
ejpam-6142	598	10	and	and	CCONJ
ejpam-6142	598	11	aids	aid	NOUN
ejpam-6142	598	12	cases	case	NOUN
ejpam-6142	598	13	for	for	ADP
ejpam-6142	598	14	both	both	DET
ejpam-6142	598	15	sexes	sex	NOUN
ejpam-6142	598	16	,	,	PUNCT
ejpam-6142	598	17	maintaining	maintain	VERB
ejpam-6142	598	18	them	they	PRON
ejpam-6142	598	19	at	at	ADP
ejpam-6142	598	20	minimal	minimal	ADJ
ejpam-6142	598	21	levels	level	NOUN
ejpam-6142	598	22	over	over	ADP
ejpam-6142	598	23	the	the	DET
ejpam-6142	598	24	time	time	NOUN
ejpam-6142	598	25	period	period	NOUN
ejpam-6142	598	26	.	.	PUNCT
ejpam-6142	599	1	integrating	integrate	VERB
ejpam-6142	599	2	preventative	preventative	ADJ
ejpam-6142	599	3	and	and	CCONJ
ejpam-6142	599	4	treatment	treatment	NOUN
ejpam-6142	599	5	techniques	technique	NOUN
ejpam-6142	599	6	can	can	AUX
ejpam-6142	599	7	successfully	successfully	ADV
ejpam-6142	599	8	manage	manage	VERB
ejpam-6142	599	9	the	the	DET
ejpam-6142	599	10	transmission	transmission	NOUN
ejpam-6142	599	11	of	of	ADP
ejpam-6142	599	12	infection	infection	NOUN
ejpam-6142	599	13	and	and	CCONJ
ejpam-6142	599	14	progression	progression	NOUN
ejpam-6142	599	15	to	to	AUX
ejpam-6142	599	16	aids	aid	NOUN
ejpam-6142	599	17	over	over	ADP
ejpam-6142	599	18	the	the	DET
ejpam-6142	599	19	period	period	NOUN
ejpam-6142	599	20	.	.	PUNCT
ejpam-6142	600	1	figure	figure	VERB
ejpam-6142	600	2	8	8	NUM
ejpam-6142	600	3	:	:	PUNCT
ejpam-6142	600	4	simulation	simulation	NOUN
ejpam-6142	600	5	of	of	ADP
ejpam-6142	600	6	optimal	optimal	ADJ
ejpam-6142	600	7	control	control	NOUN
ejpam-6142	600	8	of	of	ADP
ejpam-6142	600	9	infected	infected	ADJ
ejpam-6142	600	10	and	and	CCONJ
ejpam-6142	600	11	aids	aid	NOUN
ejpam-6142	600	12	population	population	NOUN
ejpam-6142	600	13	for	for	ADP
ejpam-6142	600	14	both	both	CCONJ
ejpam-6142	600	15	male	male	ADJ
ejpam-6142	600	16	and	and	CCONJ
ejpam-6142	600	17	female	female	ADJ
ejpam-6142	600	18	with	with	ADP
ejpam-6142	600	19	screening	screening	NOUN
ejpam-6142	600	20	and	and	CCONJ
ejpam-6142	600	21	treatment	treatment	NOUN
ejpam-6142	600	22	figure	figure	NOUN
ejpam-6142	600	23	8	8	NUM
ejpam-6142	600	24	demonstrates	demonstrate	VERB
ejpam-6142	600	25	the	the	DET
ejpam-6142	600	26	substantial	substantial	ADJ
ejpam-6142	600	27	influence	influence	NOUN
ejpam-6142	600	28	of	of	ADP
ejpam-6142	600	29	screening	screening	NOUN
ejpam-6142	600	30	and	and	CCONJ
ejpam-6142	600	31	treatment	treatment	NOUN
ejpam-6142	600	32	strategies	strategy	NOUN
ejpam-6142	600	33	on	on	ADP
ejpam-6142	600	34	the	the	DET
ejpam-6142	600	35	management	management	NOUN
ejpam-6142	600	36	of	of	ADP
ejpam-6142	600	37	both	both	DET
ejpam-6142	600	38	infection	infection	NOUN
ejpam-6142	600	39	and	and	CCONJ
ejpam-6142	600	40	aids	aid	NOUN
ejpam-6142	600	41	populations	population	NOUN
ejpam-6142	600	42	for	for	ADP
ejpam-6142	600	43	men	man	NOUN
ejpam-6142	600	44	and	and	CCONJ
ejpam-6142	600	45	women	woman	NOUN
ejpam-6142	600	46	over	over	ADP
ejpam-6142	600	47	20	20	NUM
ejpam-6142	600	48	years	year	NOUN
ejpam-6142	600	49	,	,	PUNCT
ejpam-6142	600	50	even	even	ADV
ejpam-6142	600	51	without	without	ADP
ejpam-6142	600	52	preventive	preventive	ADJ
ejpam-6142	600	53	efforts	effort	NOUN
ejpam-6142	600	54	.	.	PUNCT
ejpam-6142	601	1	through	through	ADP
ejpam-6142	601	2	screening	screening	NOUN
ejpam-6142	601	3	and	and	CCONJ
ejpam-6142	601	4	treatment	treatment	NOUN
ejpam-6142	601	5	,	,	PUNCT
ejpam-6142	601	6	as	as	SCONJ
ejpam-6142	601	7	shown	show	VERB
ejpam-6142	601	8	in	in	ADP
ejpam-6142	601	9	figure	figure	NOUN
ejpam-6142	601	10	8(a	8(a	NUM
ejpam-6142	601	11	)	)	PUNCT
ejpam-6142	601	12	the	the	DET
ejpam-6142	601	13	number	number	NOUN
ejpam-6142	601	14	of	of	ADP
ejpam-6142	601	15	infections	infection	NOUN
ejpam-6142	601	16	for	for	ADP
ejpam-6142	601	17	both	both	DET
ejpam-6142	601	18	genders	gender	NOUN
ejpam-6142	601	19	reach	reach	VERB
ejpam-6142	601	20	a	a	DET
ejpam-6142	601	21	lower	low	ADJ
ejpam-6142	601	22	high	high	NOUN
ejpam-6142	601	23	of	of	ADP
ejpam-6142	601	24	around	around	ADV
ejpam-6142	601	25	4	4	NUM
ejpam-6142	601	26	million	million	NUM
ejpam-6142	601	27	whereas	whereas	SCONJ
ejpam-6142	601	28	aids	aid	NOUN
ejpam-6142	601	29	cases	case	NOUN
ejpam-6142	601	30	for	for	ADP
ejpam-6142	601	31	both	both	DET
ejpam-6142	601	32	sexes	sex	NOUN
ejpam-6142	601	33	peak	peak	VERB
ejpam-6142	601	34	significantly	significantly	ADV
ejpam-6142	601	35	lower	lower	ADV
ejpam-6142	601	36	,	,	PUNCT
ejpam-6142	601	37	at	at	ADP
ejpam-6142	601	38	around	around	ADP
ejpam-6142	601	39	100,000	100,000	NUM
ejpam-6142	601	40	which	which	PRON
ejpam-6142	601	41	s.	s.	PROPN
ejpam-6142	601	42	m.	m.	PROPN
ejpam-6142	601	43	fatah	fatah	PROPN
ejpam-6142	601	44	,	,	PUNCT
ejpam-6142	601	45	s.	s.	PROPN
ejpam-6142	601	46	h.	h.	PROPN
ejpam-6142	601	47	a.	a.	PROPN
ejpam-6142	601	48	khoshnaw	khoshnaw	PROPN
ejpam-6142	601	49	,	,	PUNCT
ejpam-6142	601	50	a.	a.	PROPN
ejpam-6142	601	51	n.	n.	PROPN
ejpam-6142	601	52	mustafa	mustafa	PROPN
ejpam-6142	601	53	/	/	SYM
ejpam-6142	601	54	eur	eur	PROPN
ejpam-6142	601	55	.	.	PUNCT
ejpam-6142	602	1	j.	j.	PROPN
ejpam-6142	602	2	pure	pure	PROPN
ejpam-6142	602	3	appl	appl	PROPN
ejpam-6142	602	4	.	.	PROPN
ejpam-6142	602	5	math	math	PROPN
ejpam-6142	602	6	,	,	PUNCT
ejpam-6142	602	7	18	18	NUM
ejpam-6142	602	8	(	(	PUNCT
ejpam-6142	602	9	2	2	NUM
ejpam-6142	602	10	)	)	PUNCT
ejpam-6142	602	11	(	(	PUNCT
ejpam-6142	602	12	2025	2025	NUM
ejpam-6142	602	13	)	)	PUNCT
ejpam-6142	602	14	,	,	PUNCT
ejpam-6142	602	15	6142	6142	NUM
ejpam-6142	602	16	29	29	NUM
ejpam-6142	602	17	of	of	ADP
ejpam-6142	602	18	33	33	NUM
ejpam-6142	602	19	can	can	AUX
ejpam-6142	602	20	be	be	AUX
ejpam-6142	602	21	seen	see	VERB
ejpam-6142	602	22	in	in	ADP
ejpam-6142	602	23	figure	figure	NOUN
ejpam-6142	602	24	8(b	8(b	NUM
ejpam-6142	602	25	)	)	PUNCT
ejpam-6142	602	26	.	.	PUNCT
ejpam-6142	603	1	screening	screening	NOUN
ejpam-6142	603	2	and	and	CCONJ
ejpam-6142	603	3	treatment	treatment	NOUN
ejpam-6142	603	4	interventions	intervention	NOUN
ejpam-6142	603	5	substantially	substantially	ADV
ejpam-6142	603	6	decrease	decrease	VERB
ejpam-6142	603	7	infective	infective	ADJ
ejpam-6142	603	8	and	and	CCONJ
ejpam-6142	603	9	aids	aid	NOUN
ejpam-6142	603	10	populations	population	NOUN
ejpam-6142	603	11	for	for	ADP
ejpam-6142	603	12	both	both	DET
ejpam-6142	603	13	sexes	sex	NOUN
ejpam-6142	603	14	,	,	PUNCT
ejpam-6142	603	15	but	but	CCONJ
ejpam-6142	603	16	not	not	PART
ejpam-6142	603	17	as	as	ADV
ejpam-6142	603	18	markedly	markedly	ADV
ejpam-6142	603	19	as	as	SCONJ
ejpam-6142	603	20	when	when	SCONJ
ejpam-6142	603	21	prevention	prevention	NOUN
ejpam-6142	603	22	was	be	AUX
ejpam-6142	603	23	incorporated	incorporate	VERB
ejpam-6142	603	24	in	in	ADP
ejpam-6142	603	25	the	the	DET
ejpam-6142	603	26	prior	prior	ADJ
ejpam-6142	603	27	scenarios	scenario	NOUN
ejpam-6142	603	28	.	.	PUNCT
ejpam-6142	604	1	figure	figure	VERB
ejpam-6142	604	2	9	9	NUM
ejpam-6142	604	3	:	:	PUNCT
ejpam-6142	604	4	simulation	simulation	NOUN
ejpam-6142	604	5	of	of	ADP
ejpam-6142	604	6	optimal	optimal	ADJ
ejpam-6142	604	7	control	control	NOUN
ejpam-6142	604	8	of	of	ADP
ejpam-6142	604	9	infected	infected	ADJ
ejpam-6142	604	10	and	and	CCONJ
ejpam-6142	604	11	aids	aid	NOUN
ejpam-6142	604	12	population	population	NOUN
ejpam-6142	604	13	for	for	ADP
ejpam-6142	604	14	both	both	CCONJ
ejpam-6142	604	15	male	male	ADJ
ejpam-6142	604	16	and	and	CCONJ
ejpam-6142	604	17	female	female	ADJ
ejpam-6142	604	18	with	with	ADP
ejpam-6142	604	19	prevention	prevention	NOUN
ejpam-6142	604	20	,	,	PUNCT
ejpam-6142	604	21	screening	screening	NOUN
ejpam-6142	604	22	and	and	CCONJ
ejpam-6142	604	23	treatment	treatment	NOUN
ejpam-6142	604	24	figure	figure	NOUN
ejpam-6142	604	25	9	9	NUM
ejpam-6142	604	26	presents	present	NOUN
ejpam-6142	604	27	how	how	SCONJ
ejpam-6142	604	28	the	the	DET
ejpam-6142	604	29	infected	infected	ADJ
ejpam-6142	604	30	and	and	CCONJ
ejpam-6142	604	31	aids	aids	NOUN
ejpam-6142	604	32	populations	population	NOUN
ejpam-6142	604	33	change	change	VERB
ejpam-6142	604	34	with	with	ADP
ejpam-6142	604	35	and	and	CCONJ
ejpam-6142	604	36	without	without	ADP
ejpam-6142	604	37	combining	combine	VERB
ejpam-6142	604	38	prevention	prevention	NOUN
ejpam-6142	604	39	,	,	PUNCT
ejpam-6142	604	40	screening	screening	NOUN
ejpam-6142	604	41	and	and	CCONJ
ejpam-6142	604	42	treatment	treatment	NOUN
ejpam-6142	604	43	strategies	strategy	NOUN
ejpam-6142	604	44	for	for	ADP
ejpam-6142	604	45	both	both	DET
ejpam-6142	604	46	genders	gender	NOUN
ejpam-6142	604	47	over	over	ADP
ejpam-6142	604	48	time	time	NOUN
ejpam-6142	604	49	.	.	PUNCT
ejpam-6142	605	1	in	in	ADP
ejpam-6142	605	2	figure	figure	NOUN
ejpam-6142	605	3	9(a	9(a	NUM
ejpam-6142	605	4	)	)	PUNCT
ejpam-6142	605	5	,	,	PUNCT
ejpam-6142	605	6	it	it	PRON
ejpam-6142	605	7	is	be	AUX
ejpam-6142	605	8	shown	show	VERB
ejpam-6142	605	9	that	that	SCONJ
ejpam-6142	605	10	the	the	DET
ejpam-6142	605	11	number	number	NOUN
ejpam-6142	605	12	of	of	ADP
ejpam-6142	605	13	infected	infected	ADJ
ejpam-6142	605	14	individuals	individual	NOUN
ejpam-6142	605	15	is	be	AUX
ejpam-6142	605	16	dramatically	dramatically	ADV
ejpam-6142	605	17	reduced	reduce	VERB
ejpam-6142	605	18	with	with	ADP
ejpam-6142	605	19	the	the	DET
ejpam-6142	605	20	interventions	intervention	NOUN
ejpam-6142	605	21	.	.	PUNCT
ejpam-6142	606	1	this	this	PRON
ejpam-6142	606	2	indicates	indicate	VERB
ejpam-6142	606	3	that	that	SCONJ
ejpam-6142	606	4	the	the	DET
ejpam-6142	606	5	combination	combination	NOUN
ejpam-6142	606	6	of	of	ADP
ejpam-6142	606	7	prevention	prevention	NOUN
ejpam-6142	606	8	,	,	PUNCT
ejpam-6142	606	9	screening	screening	NOUN
ejpam-6142	606	10	and	and	CCONJ
ejpam-6142	606	11	treatment	treatment	NOUN
ejpam-6142	606	12	is	be	AUX
ejpam-6142	606	13	highly	highly	ADV
ejpam-6142	606	14	effective	effective	ADJ
ejpam-6142	606	15	in	in	ADP
ejpam-6142	606	16	spreading	spread	VERB
ejpam-6142	606	17	the	the	DET
ejpam-6142	606	18	disease	disease	NOUN
ejpam-6142	606	19	.	.	PUNCT
ejpam-6142	607	1	on	on	ADP
ejpam-6142	607	2	the	the	DET
ejpam-6142	607	3	other	other	ADJ
ejpam-6142	607	4	hand	hand	NOUN
ejpam-6142	607	5	,	,	PUNCT
ejpam-6142	607	6	the	the	DET
ejpam-6142	607	7	interventions	intervention	NOUN
ejpam-6142	607	8	have	have	VERB
ejpam-6142	607	9	a	a	DET
ejpam-6142	607	10	considerable	considerable	ADJ
ejpam-6142	607	11	impact	impact	NOUN
ejpam-6142	607	12	on	on	ADP
ejpam-6142	607	13	minimizing	minimize	VERB
ejpam-6142	607	14	the	the	DET
ejpam-6142	607	15	number	number	NOUN
ejpam-6142	607	16	of	of	ADP
ejpam-6142	607	17	aids	aids	PROPN
ejpam-6142	607	18	cases	case	NOUN
ejpam-6142	607	19	,	,	PUNCT
ejpam-6142	607	20	similar	similar	ADJ
ejpam-6142	607	21	to	to	ADP
ejpam-6142	607	22	the	the	DET
ejpam-6142	607	23	infection	infection	NOUN
ejpam-6142	607	24	graph	graph	NOUN
ejpam-6142	607	25	which	which	PRON
ejpam-6142	607	26	is	be	AUX
ejpam-6142	607	27	provided	provide	VERB
ejpam-6142	607	28	in	in	ADP
ejpam-6142	607	29	figure	figure	NOUN
ejpam-6142	607	30	9(b	9(b	NUM
ejpam-6142	607	31	)	)	PUNCT
ejpam-6142	607	32	.	.	PUNCT
ejpam-6142	608	1	this	this	PRON
ejpam-6142	608	2	signifies	signify	VERB
ejpam-6142	608	3	that	that	SCONJ
ejpam-6142	608	4	the	the	DET
ejpam-6142	608	5	therapies	therapy	NOUN
ejpam-6142	608	6	are	be	AUX
ejpam-6142	608	7	also	also	ADV
ejpam-6142	608	8	effective	effective	ADJ
ejpam-6142	608	9	in	in	ADP
ejpam-6142	608	10	stopping	stop	VERB
ejpam-6142	608	11	the	the	DET
ejpam-6142	608	12	progression	progression	NOUN
ejpam-6142	608	13	to	to	ADP
ejpam-6142	608	14	aids	aids	PROPN
ejpam-6142	608	15	.	.	PUNCT
ejpam-6142	609	1	the	the	DET
ejpam-6142	609	2	treatments	treatment	NOUN
ejpam-6142	609	3	appear	appear	VERB
ejpam-6142	609	4	to	to	PART
ejpam-6142	609	5	exert	exert	VERB
ejpam-6142	609	6	an	an	DET
ejpam-6142	609	7	immediate	immediate	ADJ
ejpam-6142	609	8	and	and	CCONJ
ejpam-6142	609	9	sustained	sustained	ADJ
ejpam-6142	609	10	impact	impact	NOUN
ejpam-6142	609	11	,	,	PUNCT
ejpam-6142	609	12	preventing	prevent	VERB
ejpam-6142	609	13	the	the	DET
ejpam-6142	609	14	sharp	sharp	ADJ
ejpam-6142	609	15	increase	increase	NOUN
ejpam-6142	609	16	in	in	ADP
ejpam-6142	609	17	infections	infection	NOUN
ejpam-6142	609	18	and	and	CCONJ
ejpam-6142	609	19	progression	progression	NOUN
ejpam-6142	609	20	to	to	ADP
ejpam-6142	609	21	aids	aid	NOUN
ejpam-6142	609	22	cases	case	NOUN
ejpam-6142	609	23	,	,	PUNCT
ejpam-6142	609	24	even	even	ADV
ejpam-6142	609	25	two	two	NUM
ejpam-6142	609	26	decades	decade	NOUN
ejpam-6142	609	27	later	later	ADV
ejpam-6142	609	28	,	,	PUNCT
ejpam-6142	609	29	a	a	DET
ejpam-6142	609	30	significant	significant	ADJ
ejpam-6142	609	31	disparity	disparity	NOUN
ejpam-6142	609	32	persists	persist	VERB
ejpam-6142	609	33	between	between	ADP
ejpam-6142	609	34	intervention	intervention	NOUN
ejpam-6142	609	35	and	and	CCONJ
ejpam-6142	609	36	non	non	ADJ
ejpam-6142	609	37	-	-	ADJ
ejpam-6142	609	38	intervention	intervention	ADJ
ejpam-6142	609	39	situations	situation	NOUN
ejpam-6142	609	40	in	in	ADP
ejpam-6142	609	41	figure	figure	NOUN
ejpam-6142	609	42	10	10	NUM
ejpam-6142	609	43	,	,	PUNCT
ejpam-6142	609	44	the	the	DET
ejpam-6142	609	45	impact	impact	NOUN
ejpam-6142	609	46	of	of	ADP
ejpam-6142	609	47	different	different	ADJ
ejpam-6142	609	48	combinations	combination	NOUN
ejpam-6142	609	49	of	of	ADP
ejpam-6142	609	50	prevention	prevention	NOUN
ejpam-6142	609	51	,	,	PUNCT
ejpam-6142	609	52	screening	screening	NOUN
ejpam-6142	609	53	,	,	PUNCT
ejpam-6142	609	54	and	and	CCONJ
ejpam-6142	609	55	treatment	treatment	NOUN
ejpam-6142	609	56	interventions	intervention	NOUN
ejpam-6142	609	57	on	on	ADP
ejpam-6142	609	58	infected	infected	ADJ
ejpam-6142	609	59	and	and	CCONJ
ejpam-6142	609	60	aids	aid	NOUN
ejpam-6142	609	61	populations	population	NOUN
ejpam-6142	609	62	for	for	ADP
ejpam-6142	609	63	both	both	DET
ejpam-6142	609	64	genders	gender	NOUN
ejpam-6142	609	65	over	over	ADP
ejpam-6142	609	66	20	20	NUM
ejpam-6142	609	67	years	year	NOUN
ejpam-6142	609	68	period	period	NOUN
ejpam-6142	609	69	are	be	AUX
ejpam-6142	609	70	illustrated	illustrate	VERB
ejpam-6142	609	71	.	.	PUNCT
ejpam-6142	610	1	in	in	ADP
ejpam-6142	610	2	figure	figure	NOUN
ejpam-6142	610	3	10(a	10(a	NUM
ejpam-6142	610	4	)	)	PUNCT
ejpam-6142	610	5	,	,	PUNCT
ejpam-6142	610	6	the	the	DET
ejpam-6142	610	7	green	green	ADJ
ejpam-6142	610	8	line	line	NOUN
ejpam-6142	610	9	is	be	AUX
ejpam-6142	610	10	the	the	DET
ejpam-6142	610	11	female	female	ADJ
ejpam-6142	610	12	infected	infect	VERB
ejpam-6142	610	13	population	population	NOUN
ejpam-6142	610	14	which	which	PRON
ejpam-6142	610	15	peaks	peak	VERB
ejpam-6142	610	16	at	at	ADP
ejpam-6142	610	17	around	around	ADV
ejpam-6142	610	18	6	6	NUM
ejpam-6142	610	19	million	million	NUM
ejpam-6142	610	20	about	about	ADP
ejpam-6142	610	21	year	year	NOUN
ejpam-6142	610	22	2	2	NUM
ejpam-6142	610	23	.	.	PUNCT
ejpam-6142	611	1	in	in	ADP
ejpam-6142	611	2	addition	addition	NOUN
ejpam-6142	611	3	,	,	PUNCT
ejpam-6142	611	4	there	there	PRON
ejpam-6142	611	5	is	be	VERB
ejpam-6142	611	6	some	some	DET
ejpam-6142	611	7	reduction	reduction	NOUN
ejpam-6142	611	8	of	of	ADP
ejpam-6142	611	9	women	woman	NOUN
ejpam-6142	611	10	infected	infect	VERB
ejpam-6142	611	11	individuals	individual	NOUN
ejpam-6142	611	12	in	in	ADP
ejpam-6142	611	13	the	the	DET
ejpam-6142	611	14	use	use	NOUN
ejpam-6142	611	15	of	of	ADP
ejpam-6142	611	16	a	a	DET
ejpam-6142	611	17	single	single	ADJ
ejpam-6142	611	18	intervention	intervention	NOUN
ejpam-6142	611	19	,	,	PUNCT
ejpam-6142	611	20	while	while	SCONJ
ejpam-6142	611	21	the	the	DET
ejpam-6142	611	22	combination	combination	NOUN
ejpam-6142	611	23	of	of	ADP
ejpam-6142	611	24	two	two	NUM
ejpam-6142	611	25	interventions	intervention	NOUN
ejpam-6142	611	26	presents	present	VERB
ejpam-6142	611	27	a	a	DET
ejpam-6142	611	28	greater	great	ADJ
ejpam-6142	611	29	reduction	reduction	NOUN
ejpam-6142	611	30	and	and	CCONJ
ejpam-6142	611	31	all	all	DET
ejpam-6142	611	32	three	three	NUM
ejpam-6142	611	33	strategies	strategy	NOUN
ejpam-6142	611	34	together	together	ADV
ejpam-6142	611	35	is	be	AUX
ejpam-6142	611	36	the	the	DET
ejpam-6142	611	37	highly	highly	ADV
ejpam-6142	611	38	effective	effective	ADJ
ejpam-6142	611	39	in	in	ADP
ejpam-6142	611	40	minimizing	minimize	VERB
ejpam-6142	611	41	infections	infection	NOUN
ejpam-6142	611	42	which	which	PRON
ejpam-6142	611	43	is	be	AUX
ejpam-6142	611	44	drawn	draw	VERB
ejpam-6142	611	45	by	by	ADP
ejpam-6142	611	46	black	black	ADJ
ejpam-6142	611	47	color	color	NOUN
ejpam-6142	611	48	.	.	PUNCT
ejpam-6142	612	1	the	the	DET
ejpam-6142	612	2	graphs	graph	NOUN
ejpam-6142	612	3	of	of	ADP
ejpam-6142	612	4	female	female	ADJ
ejpam-6142	612	5	aids	aid	NOUN
ejpam-6142	612	6	cases	case	NOUN
ejpam-6142	612	7	with	with	ADP
ejpam-6142	612	8	various	various	ADJ
ejpam-6142	612	9	scenarios	scenario	NOUN
ejpam-6142	612	10	are	be	AUX
ejpam-6142	612	11	provided	provide	VERB
ejpam-6142	612	12	in	in	ADP
ejpam-6142	612	13	figure	figure	NOUN
ejpam-6142	612	14	10(b	10(b	NUM
ejpam-6142	612	15	)	)	PUNCT
ejpam-6142	612	16	.	.	PUNCT
ejpam-6142	613	1	women	woman	NOUN
ejpam-6142	613	2	aids	aid	VERB
ejpam-6142	613	3	population	population	NOUN
ejpam-6142	613	4	peaks	peak	NOUN
ejpam-6142	613	5	approximately	approximately	ADV
ejpam-6142	613	6	at	at	ADP
ejpam-6142	613	7	4.3	4.3	NUM
ejpam-6142	613	8	million	million	NUM
ejpam-6142	613	9	about	about	ADP
ejpam-6142	613	10	year	year	NOUN
ejpam-6142	613	11	5	5	NUM
ejpam-6142	613	12	.	.	PUNCT
ejpam-6142	614	1	moreover	moreover	ADV
ejpam-6142	614	2	,	,	PUNCT
ejpam-6142	614	3	in	in	ADP
ejpam-6142	614	4	the	the	DET
ejpam-6142	614	5	case	case	NOUN
ejpam-6142	614	6	of	of	ADP
ejpam-6142	614	7	including	include	VERB
ejpam-6142	614	8	a	a	DET
ejpam-6142	614	9	single	single	ADJ
ejpam-6142	614	10	and	and	CCONJ
ejpam-6142	614	11	double	double	ADJ
ejpam-6142	614	12	interventions	intervention	NOUN
ejpam-6142	614	13	exhibit	exhibit	VERB
ejpam-6142	614	14	different	different	ADJ
ejpam-6142	614	15	level	level	NOUN
ejpam-6142	614	16	of	of	ADP
ejpam-6142	614	17	reduction	reduction	NOUN
ejpam-6142	614	18	whereas	whereas	SCONJ
ejpam-6142	614	19	all	all	DET
ejpam-6142	614	20	three	three	NUM
ejpam-6142	614	21	strategies	strategy	NOUN
ejpam-6142	614	22	together	together	ADV
ejpam-6142	614	23	yield	yield	VERB
ejpam-6142	614	24	the	the	DET
ejpam-6142	614	25	fewest	few	ADJ
ejpam-6142	614	26	female	female	ADJ
ejpam-6142	614	27	aids	aid	NOUN
ejpam-6142	614	28	cases	case	NOUN
ejpam-6142	614	29	.	.	PUNCT
ejpam-6142	615	1	further	far	ADV
ejpam-6142	615	2	,	,	PUNCT
ejpam-6142	615	3	in	in	ADP
ejpam-6142	615	4	figure	figure	NOUN
ejpam-6142	615	5	10(c	10(c	NUM
ejpam-6142	615	6	)	)	PUNCT
ejpam-6142	616	1	it	it	PRON
ejpam-6142	616	2	is	be	AUX
ejpam-6142	616	3	shown	show	VERB
ejpam-6142	616	4	that	that	SCONJ
ejpam-6142	616	5	the	the	DET
ejpam-6142	616	6	male	male	ADJ
ejpam-6142	616	7	infected	infected	ADJ
ejpam-6142	616	8	population	population	NOUN
ejpam-6142	616	9	has	have	VERB
ejpam-6142	616	10	analogous	analogous	ADJ
ejpam-6142	616	11	patterns	pattern	NOUN
ejpam-6142	616	12	to	to	ADP
ejpam-6142	616	13	the	the	DET
ejpam-6142	616	14	infected	infected	ADJ
ejpam-6142	616	15	female	female	ADJ
ejpam-6142	616	16	population	population	NOUN
ejpam-6142	616	17	with	with	ADP
ejpam-6142	616	18	all	all	DET
ejpam-6142	616	19	different	different	ADJ
ejpam-6142	616	20	s.	s.	PROPN
ejpam-6142	616	21	m.	m.	PROPN
ejpam-6142	616	22	fatah	fatah	PROPN
ejpam-6142	616	23	,	,	PUNCT
ejpam-6142	616	24	s.	s.	PROPN
ejpam-6142	616	25	h.	h.	PROPN
ejpam-6142	616	26	a.	a.	PROPN
ejpam-6142	616	27	khoshnaw	khoshnaw	PROPN
ejpam-6142	616	28	,	,	PUNCT
ejpam-6142	616	29	a.	a.	PROPN
ejpam-6142	616	30	n.	n.	PROPN
ejpam-6142	616	31	mustafa	mustafa	PROPN
ejpam-6142	616	32	/	/	SYM
ejpam-6142	616	33	eur	eur	PROPN
ejpam-6142	616	34	.	.	PUNCT
ejpam-6142	617	1	j.	j.	PROPN
ejpam-6142	617	2	pure	pure	PROPN
ejpam-6142	617	3	appl	appl	PROPN
ejpam-6142	617	4	.	.	PROPN
ejpam-6142	617	5	math	math	PROPN
ejpam-6142	617	6	,	,	PUNCT
ejpam-6142	617	7	18	18	NUM
ejpam-6142	617	8	(	(	PUNCT
ejpam-6142	617	9	2	2	NUM
ejpam-6142	617	10	)	)	PUNCT
ejpam-6142	617	11	(	(	PUNCT
ejpam-6142	617	12	2025	2025	NUM
ejpam-6142	617	13	)	)	PUNCT
ejpam-6142	617	14	,	,	PUNCT
ejpam-6142	617	15	6142	6142	NUM
ejpam-6142	617	16	30	30	NUM
ejpam-6142	617	17	of	of	ADP
ejpam-6142	617	18	33	33	NUM
ejpam-6142	617	19	figure	figure	NOUN
ejpam-6142	617	20	10	10	NUM
ejpam-6142	617	21	:	:	PUNCT
ejpam-6142	617	22	simulation	simulation	NOUN
ejpam-6142	617	23	of	of	ADP
ejpam-6142	617	24	optimal	optimal	ADJ
ejpam-6142	617	25	control	control	NOUN
ejpam-6142	617	26	of	of	ADP
ejpam-6142	617	27	infected	infected	ADJ
ejpam-6142	617	28	and	and	CCONJ
ejpam-6142	617	29	aids	aid	NOUN
ejpam-6142	617	30	population	population	NOUN
ejpam-6142	617	31	for	for	ADP
ejpam-6142	617	32	both	both	DET
ejpam-6142	617	33	males	male	NOUN
ejpam-6142	617	34	and	and	CCONJ
ejpam-6142	617	35	females	female	NOUN
ejpam-6142	617	36	with	with	ADP
ejpam-6142	617	37	all	all	DET
ejpam-6142	617	38	scenarios	scenario	NOUN
ejpam-6142	617	39	combinations	combination	NOUN
ejpam-6142	617	40	of	of	ADP
ejpam-6142	617	41	the	the	DET
ejpam-6142	617	42	interventions	intervention	NOUN
ejpam-6142	617	43	,	,	PUNCT
ejpam-6142	617	44	although	although	SCONJ
ejpam-6142	617	45	male	male	ADJ
ejpam-6142	617	46	infections	infection	NOUN
ejpam-6142	617	47	appear	appear	VERB
ejpam-6142	617	48	to	to	PART
ejpam-6142	617	49	peak	peak	VERB
ejpam-6142	617	50	slightly	slightly	ADV
ejpam-6142	617	51	higher	high	ADJ
ejpam-6142	617	52	than	than	ADP
ejpam-6142	617	53	female	female	ADJ
ejpam-6142	617	54	infections	infection	NOUN
ejpam-6142	617	55	in	in	ADP
ejpam-6142	617	56	the	the	DET
ejpam-6142	617	57	absence	absence	NOUN
ejpam-6142	617	58	of	of	ADP
ejpam-6142	617	59	interventions	intervention	NOUN
ejpam-6142	617	60	.	.	PUNCT
ejpam-6142	618	1	additionally	additionally	ADV
ejpam-6142	618	2	,	,	PUNCT
ejpam-6142	618	3	the	the	DET
ejpam-6142	618	4	illustration	illustration	NOUN
ejpam-6142	618	5	of	of	ADP
ejpam-6142	618	6	male	male	ADJ
ejpam-6142	618	7	aids	aid	NOUN
ejpam-6142	618	8	cases	case	NOUN
ejpam-6142	618	9	with	with	ADP
ejpam-6142	618	10	different	different	ADJ
ejpam-6142	618	11	combinations	combination	NOUN
ejpam-6142	618	12	of	of	ADP
ejpam-6142	618	13	interventions	intervention	NOUN
ejpam-6142	618	14	are	be	AUX
ejpam-6142	618	15	given	give	VERB
ejpam-6142	618	16	in	in	ADP
ejpam-6142	618	17	figure	figure	NOUN
ejpam-6142	618	18	10(d	10(d	NUM
ejpam-6142	618	19	)	)	PUNCT
ejpam-6142	618	20	which	which	PRON
ejpam-6142	618	21	closely	closely	ADV
ejpam-6142	618	22	have	have	VERB
ejpam-6142	618	23	a	a	DET
ejpam-6142	618	24	similar	similar	ADJ
ejpam-6142	618	25	pattern	pattern	NOUN
ejpam-6142	618	26	as	as	ADP
ejpam-6142	618	27	female	female	ADJ
ejpam-6142	618	28	aids	aid	NOUN
ejpam-6142	618	29	cases	case	NOUN
ejpam-6142	618	30	.	.	PUNCT
ejpam-6142	619	1	however	however	ADV
ejpam-6142	619	2	,	,	PUNCT
ejpam-6142	619	3	male	male	ADJ
ejpam-6142	619	4	aids	aid	NOUN
ejpam-6142	619	5	individuals	individual	NOUN
ejpam-6142	619	6	peak	peak	VERB
ejpam-6142	619	7	at	at	ADP
ejpam-6142	619	8	around	around	ADP
ejpam-6142	619	9	4.5	4.5	NUM
ejpam-6142	619	10	million	million	NUM
ejpam-6142	619	11	at	at	ADP
ejpam-6142	619	12	year	year	NOUN
ejpam-6142	619	13	5	5	NUM
ejpam-6142	619	14	without	without	ADP
ejpam-6142	619	15	interventions	intervention	NOUN
ejpam-6142	619	16	which	which	PRON
ejpam-6142	619	17	is	be	AUX
ejpam-6142	619	18	higher	high	ADJ
ejpam-6142	619	19	than	than	ADP
ejpam-6142	619	20	the	the	DET
ejpam-6142	619	21	peak	peak	NOUN
ejpam-6142	619	22	of	of	ADP
ejpam-6142	619	23	female	female	ADJ
ejpam-6142	619	24	aids	aid	NOUN
ejpam-6142	619	25	cases	case	NOUN
ejpam-6142	619	26	.	.	PUNCT
ejpam-6142	620	1	the	the	DET
ejpam-6142	620	2	results	result	NOUN
ejpam-6142	620	3	show	show	VERB
ejpam-6142	620	4	that	that	SCONJ
ejpam-6142	620	5	the	the	DET
ejpam-6142	620	6	simultaneous	simultaneous	ADJ
ejpam-6142	620	7	use	use	NOUN
ejpam-6142	620	8	of	of	ADP
ejpam-6142	620	9	all	all	DET
ejpam-6142	620	10	three	three	NUM
ejpam-6142	620	11	interventions	intervention	NOUN
ejpam-6142	620	12	(	(	PUNCT
ejpam-6142	620	13	prevention	prevention	NOUN
ejpam-6142	620	14	,	,	PUNCT
ejpam-6142	620	15	screening	screening	NOUN
ejpam-6142	620	16	,	,	PUNCT
ejpam-6142	620	17	and	and	CCONJ
ejpam-6142	620	18	treatment	treatment	NOUN
ejpam-6142	620	19	)	)	PUNCT
ejpam-6142	620	20	is	be	AUX
ejpam-6142	620	21	the	the	DET
ejpam-6142	620	22	most	most	ADV
ejpam-6142	620	23	successful	successful	ADJ
ejpam-6142	620	24	method	method	NOUN
ejpam-6142	620	25	for	for	ADP
ejpam-6142	620	26	lowering	lower	VERB
ejpam-6142	620	27	infections	infection	NOUN
ejpam-6142	620	28	and	and	CCONJ
ejpam-6142	620	29	aids	aid	NOUN
ejpam-6142	620	30	cases	case	NOUN
ejpam-6142	620	31	in	in	ADP
ejpam-6142	620	32	both	both	DET
ejpam-6142	620	33	genders	gender	NOUN
ejpam-6142	620	34	.	.	PUNCT
ejpam-6142	621	1	furthermore	furthermore	ADV
ejpam-6142	621	2	,	,	PUNCT
ejpam-6142	621	3	the	the	DET
ejpam-6142	621	4	patterns	pattern	NOUN
ejpam-6142	621	5	for	for	ADP
ejpam-6142	621	6	males	male	NOUN
ejpam-6142	621	7	and	and	CCONJ
ejpam-6142	621	8	females	female	NOUN
ejpam-6142	621	9	are	be	AUX
ejpam-6142	621	10	quite	quite	ADV
ejpam-6142	621	11	comparable	comparable	ADJ
ejpam-6142	621	12	,	,	PUNCT
ejpam-6142	621	13	suggesting	suggest	VERB
ejpam-6142	621	14	that	that	SCONJ
ejpam-6142	621	15	interventions	intervention	NOUN
ejpam-6142	621	16	are	be	AUX
ejpam-6142	621	17	equally	equally	ADV
ejpam-6142	621	18	successful	successful	ADJ
ejpam-6142	621	19	for	for	ADP
ejpam-6142	621	20	both	both	DET
ejpam-6142	621	21	genders	gender	NOUN
ejpam-6142	621	22	.	.	PUNCT
ejpam-6142	622	1	although	although	SCONJ
ejpam-6142	622	2	all	all	DET
ejpam-6142	622	3	interventions	intervention	NOUN
ejpam-6142	622	4	are	be	AUX
ejpam-6142	622	5	beneficial	beneficial	ADJ
ejpam-6142	622	6	,	,	PUNCT
ejpam-6142	622	7	treatment	treatment	NOUN
ejpam-6142	622	8	alone	alone	ADV
ejpam-6142	622	9	appears	appear	VERB
ejpam-6142	622	10	to	to	PART
ejpam-6142	622	11	be	be	AUX
ejpam-6142	622	12	less	less	ADV
ejpam-6142	622	13	successful	successful	ADJ
ejpam-6142	622	14	than	than	ADP
ejpam-6142	622	15	preventive	preventive	ADJ
ejpam-6142	622	16	or	or	CCONJ
ejpam-6142	622	17	screening	screen	VERB
ejpam-6142	622	18	alone	alone	ADV
ejpam-6142	622	19	,	,	PUNCT
ejpam-6142	622	20	particularly	particularly	ADV
ejpam-6142	622	21	in	in	ADP
ejpam-6142	622	22	decreasing	decrease	VERB
ejpam-6142	622	23	initial	initial	ADJ
ejpam-6142	622	24	infection	infection	NOUN
ejpam-6142	622	25	rates	rate	NOUN
ejpam-6142	622	26	.	.	PUNCT
ejpam-6142	623	1	to	to	PART
ejpam-6142	623	2	sum	sum	VERB
ejpam-6142	623	3	up	up	ADP
ejpam-6142	623	4	,	,	PUNCT
ejpam-6142	623	5	the	the	DET
ejpam-6142	623	6	presented	present	VERB
ejpam-6142	623	7	model	model	NOUN
ejpam-6142	623	8	strongly	strongly	ADV
ejpam-6142	623	9	supports	support	VERB
ejpam-6142	623	10	the	the	DET
ejpam-6142	623	11	implementation	implementation	NOUN
ejpam-6142	623	12	of	of	ADP
ejpam-6142	623	13	comprehensive	comprehensive	ADJ
ejpam-6142	623	14	hiv	hiv	PROPN
ejpam-6142	623	15	/	/	SYM
ejpam-6142	623	16	aids	aids	PROPN
ejpam-6142	623	17	control	control	NOUN
ejpam-6142	623	18	measures	measure	NOUN
ejpam-6142	623	19	that	that	PRON
ejpam-6142	623	20	include	include	VERB
ejpam-6142	623	21	prevention	prevention	NOUN
ejpam-6142	623	22	,	,	PUNCT
ejpam-6142	623	23	screening	screening	NOUN
ejpam-6142	623	24	,	,	PUNCT
ejpam-6142	623	25	and	and	CCONJ
ejpam-6142	623	26	treatment	treatment	NOUN
ejpam-6142	623	27	.	.	PUNCT
ejpam-6142	624	1	it	it	PRON
ejpam-6142	624	2	illustrates	illustrate	VERB
ejpam-6142	624	3	that	that	SCONJ
ejpam-6142	624	4	although	although	SCONJ
ejpam-6142	624	5	s.	s.	PROPN
ejpam-6142	624	6	m.	m.	PROPN
ejpam-6142	624	7	fatah	fatah	PROPN
ejpam-6142	624	8	,	,	PUNCT
ejpam-6142	624	9	s.	s.	PROPN
ejpam-6142	624	10	h.	h.	PROPN
ejpam-6142	624	11	a.	a.	PROPN
ejpam-6142	624	12	khoshnaw	khoshnaw	PROPN
ejpam-6142	624	13	,	,	PUNCT
ejpam-6142	624	14	a.	a.	PROPN
ejpam-6142	624	15	n.	n.	PROPN
ejpam-6142	624	16	mustafa	mustafa	PROPN
ejpam-6142	624	17	/	/	SYM
ejpam-6142	624	18	eur	eur	PROPN
ejpam-6142	624	19	.	.	PUNCT
ejpam-6142	625	1	j.	j.	PROPN
ejpam-6142	625	2	pure	pure	PROPN
ejpam-6142	625	3	appl	appl	PROPN
ejpam-6142	625	4	.	.	PROPN
ejpam-6142	625	5	math	math	PROPN
ejpam-6142	625	6	,	,	PUNCT
ejpam-6142	625	7	18	18	NUM
ejpam-6142	625	8	(	(	PUNCT
ejpam-6142	625	9	2	2	NUM
ejpam-6142	625	10	)	)	PUNCT
ejpam-6142	625	11	(	(	PUNCT
ejpam-6142	625	12	2025	2025	NUM
ejpam-6142	625	13	)	)	PUNCT
ejpam-6142	625	14	,	,	PUNCT
ejpam-6142	625	15	6142	6142	NUM
ejpam-6142	625	16	31	31	NUM
ejpam-6142	625	17	of	of	ADP
ejpam-6142	625	18	33	33	NUM
ejpam-6142	625	19	single	single	ADJ
ejpam-6142	625	20	interventions	intervention	NOUN
ejpam-6142	625	21	are	be	AUX
ejpam-6142	625	22	advantageous	advantageous	ADJ
ejpam-6142	625	23	,	,	PUNCT
ejpam-6142	625	24	a	a	DET
ejpam-6142	625	25	comprehensive	comprehensive	ADJ
ejpam-6142	625	26	strategy	strategy	NOUN
ejpam-6142	625	27	is	be	AUX
ejpam-6142	625	28	significantly	significantly	ADV
ejpam-6142	625	29	more	more	ADV
ejpam-6142	625	30	successful	successful	ADJ
ejpam-6142	625	31	in	in	ADP
ejpam-6142	625	32	managing	manage	VERB
ejpam-6142	625	33	the	the	DET
ejpam-6142	625	34	pandemic	pandemic	NOUN
ejpam-6142	625	35	for	for	ADP
ejpam-6142	625	36	both	both	DET
ejpam-6142	625	37	genders	gender	NOUN
ejpam-6142	625	38	over	over	ADP
ejpam-6142	625	39	time	time	NOUN
ejpam-6142	625	40	.	.	PUNCT
ejpam-6142	626	1	9	9	X
ejpam-6142	626	2	.	.	NUM
ejpam-6142	626	3	limitations	limitation	NOUN
ejpam-6142	626	4	and	and	CCONJ
ejpam-6142	626	5	future	future	ADJ
ejpam-6142	626	6	directions	direction	NOUN
ejpam-6142	626	7	while	while	SCONJ
ejpam-6142	626	8	this	this	DET
ejpam-6142	626	9	study	study	NOUN
ejpam-6142	626	10	provides	provide	VERB
ejpam-6142	626	11	valuable	valuable	ADJ
ejpam-6142	626	12	insights	insight	NOUN
ejpam-6142	626	13	into	into	ADP
ejpam-6142	626	14	gender	gender	NOUN
ejpam-6142	626	15	-	-	PUNCT
ejpam-6142	626	16	specific	specific	ADJ
ejpam-6142	626	17	hiv	hiv	NOUN
ejpam-6142	626	18	transmission	transmission	NOUN
ejpam-6142	626	19	dynamics	dynamic	NOUN
ejpam-6142	626	20	,	,	PUNCT
ejpam-6142	626	21	several	several	ADJ
ejpam-6142	626	22	limitations	limitation	NOUN
ejpam-6142	626	23	should	should	AUX
ejpam-6142	626	24	be	be	AUX
ejpam-6142	626	25	considered	consider	VERB
ejpam-6142	626	26	.	.	PUNCT
ejpam-6142	627	1	the	the	DET
ejpam-6142	627	2	deterministic	deterministic	ADJ
ejpam-6142	627	3	modeling	modeling	NOUN
ejpam-6142	627	4	approach	approach	NOUN
ejpam-6142	627	5	can	can	AUX
ejpam-6142	627	6	not	not	PART
ejpam-6142	627	7	account	account	VERB
ejpam-6142	627	8	for	for	ADP
ejpam-6142	627	9	random	random	ADJ
ejpam-6142	627	10	transmission	transmission	NOUN
ejpam-6142	627	11	events	event	NOUN
ejpam-6142	627	12	that	that	PRON
ejpam-6142	627	13	occur	occur	VERB
ejpam-6142	627	14	in	in	ADP
ejpam-6142	627	15	real	real	ADJ
ejpam-6142	627	16	populations	population	NOUN
ejpam-6142	627	17	.	.	PUNCT
ejpam-6142	628	1	although	although	SCONJ
ejpam-6142	628	2	gender	gender	NOUN
ejpam-6142	628	3	stratification	stratification	NOUN
ejpam-6142	628	4	offers	offer	VERB
ejpam-6142	628	5	important	important	ADJ
ejpam-6142	628	6	granularity	granularity	NOUN
ejpam-6142	628	7	,	,	PUNCT
ejpam-6142	628	8	additional	additional	ADJ
ejpam-6142	628	9	factors	factor	NOUN
ejpam-6142	628	10	like	like	ADP
ejpam-6142	628	11	age	age	NOUN
ejpam-6142	628	12	differences	difference	NOUN
ejpam-6142	628	13	and	and	CCONJ
ejpam-6142	628	14	risk	risk	NOUN
ejpam-6142	628	15	-	-	PUNCT
ejpam-6142	628	16	group	group	NOUN
ejpam-6142	628	17	variations	variation	NOUN
ejpam-6142	628	18	would	would	AUX
ejpam-6142	628	19	further	far	ADV
ejpam-6142	628	20	improve	improve	VERB
ejpam-6142	628	21	the	the	DET
ejpam-6142	628	22	model	model	NOUN
ejpam-6142	628	23	’s	’s	PART
ejpam-6142	628	24	accuracy	accuracy	NOUN
ejpam-6142	628	25	.	.	PUNCT
ejpam-6142	629	1	our	our	PRON
ejpam-6142	629	2	analysis	analysis	NOUN
ejpam-6142	629	3	also	also	ADV
ejpam-6142	629	4	assumes	assume	VERB
ejpam-6142	629	5	perfect	perfect	ADJ
ejpam-6142	629	6	adherence	adherence	NOUN
ejpam-6142	629	7	to	to	ADP
ejpam-6142	629	8	control	control	NOUN
ejpam-6142	629	9	measures	measure	NOUN
ejpam-6142	629	10	,	,	PUNCT
ejpam-6142	629	11	while	while	SCONJ
ejpam-6142	629	12	actual	actual	ADJ
ejpam-6142	629	13	implementation	implementation	NOUN
ejpam-6142	629	14	faces	face	VERB
ejpam-6142	629	15	behavioral	behavioral	ADJ
ejpam-6142	629	16	challenges	challenge	NOUN
ejpam-6142	629	17	like	like	ADP
ejpam-6142	629	18	risk	risk	NOUN
ejpam-6142	629	19	compensation	compensation	NOUN
ejpam-6142	629	20	.	.	PUNCT
ejpam-6142	630	1	nevertheless	nevertheless	ADV
ejpam-6142	630	2	,	,	PUNCT
ejpam-6142	630	3	despite	despite	SCONJ
ejpam-6142	630	4	these	these	DET
ejpam-6142	630	5	simplifications	simplification	NOUN
ejpam-6142	630	6	,	,	PUNCT
ejpam-6142	630	7	the	the	DET
ejpam-6142	630	8	current	current	ADJ
ejpam-6142	630	9	model	model	NOUN
ejpam-6142	630	10	establishes	establish	VERB
ejpam-6142	630	11	a	a	DET
ejpam-6142	630	12	useful	useful	ADJ
ejpam-6142	630	13	foundation	foundation	NOUN
ejpam-6142	630	14	for	for	ADP
ejpam-6142	630	15	assessing	assess	VERB
ejpam-6142	630	16	gender	gender	NOUN
ejpam-6142	630	17	-	-	PUNCT
ejpam-6142	630	18	targeted	target	VERB
ejpam-6142	630	19	hiv	hiv	PROPN
ejpam-6142	630	20	interventions	intervention	NOUN
ejpam-6142	630	21	and	and	CCONJ
ejpam-6142	630	22	can	can	AUX
ejpam-6142	630	23	be	be	AUX
ejpam-6142	630	24	progressively	progressively	ADV
ejpam-6142	630	25	refined	refine	VERB
ejpam-6142	630	26	to	to	PART
ejpam-6142	630	27	better	well	ADV
ejpam-6142	630	28	reflect	reflect	VERB
ejpam-6142	630	29	real	real	ADJ
ejpam-6142	630	30	-	-	PUNCT
ejpam-6142	630	31	world	world	NOUN
ejpam-6142	630	32	complexity	complexity	NOUN
ejpam-6142	630	33	.	.	PUNCT
ejpam-6142	631	1	this	this	DET
ejpam-6142	631	2	framework	framework	NOUN
ejpam-6142	631	3	can	can	AUX
ejpam-6142	631	4	be	be	AUX
ejpam-6142	631	5	extended	extend	VERB
ejpam-6142	631	6	by	by	ADP
ejpam-6142	631	7	incorporating	incorporate	VERB
ejpam-6142	631	8	age	age	NOUN
ejpam-6142	631	9	-	-	PUNCT
ejpam-6142	631	10	structured	structure	VERB
ejpam-6142	631	11	transmission	transmission	NOUN
ejpam-6142	631	12	,	,	PUNCT
ejpam-6142	631	13	stochastic	stochastic	ADJ
ejpam-6142	631	14	dynamics	dynamic	NOUN
ejpam-6142	631	15	,	,	PUNCT
ejpam-6142	631	16	and	and	CCONJ
ejpam-6142	631	17	behavioral	behavioral	ADJ
ejpam-6142	631	18	feedback	feedback	NOUN
ejpam-6142	631	19	mechanisms	mechanism	NOUN
ejpam-6142	631	20	to	to	PART
ejpam-6142	631	21	more	more	ADV
ejpam-6142	631	22	accurately	accurately	ADV
ejpam-6142	631	23	represent	represent	VERB
ejpam-6142	631	24	real	real	ADJ
ejpam-6142	631	25	-	-	PUNCT
ejpam-6142	631	26	world	world	NOUN
ejpam-6142	631	27	hiv	hiv	PROPN
ejpam-6142	631	28	transmission	transmission	NOUN
ejpam-6142	631	29	.	.	PUNCT
ejpam-6142	632	1	future	future	ADJ
ejpam-6142	632	2	research	research	NOUN
ejpam-6142	632	3	should	should	AUX
ejpam-6142	632	4	include	include	VERB
ejpam-6142	632	5	cost	cost	NOUN
ejpam-6142	632	6	-	-	PUNCT
ejpam-6142	632	7	effectiveness	effectiveness	NOUN
ejpam-6142	632	8	analyses	analysis	NOUN
ejpam-6142	632	9	to	to	PART
ejpam-6142	632	10	inform	inform	VERB
ejpam-6142	632	11	optimal	optimal	ADJ
ejpam-6142	632	12	allocation	allocation	NOUN
ejpam-6142	632	13	of	of	ADP
ejpam-6142	632	14	intervention	intervention	NOUN
ejpam-6142	632	15	resources	resource	NOUN
ejpam-6142	632	16	and	and	CCONJ
ejpam-6142	632	17	validate	validate	VERB
ejpam-6142	632	18	the	the	DET
ejpam-6142	632	19	model	model	NOUN
ejpam-6142	632	20	using	use	VERB
ejpam-6142	632	21	country	country	NOUN
ejpam-6142	632	22	-	-	PUNCT
ejpam-6142	632	23	specific	specific	ADJ
ejpam-6142	632	24	data	datum	NOUN
ejpam-6142	632	25	.	.	PUNCT
ejpam-6142	633	1	incorporating	incorporate	VERB
ejpam-6142	633	2	machine	machine	NOUN
ejpam-6142	633	3	learning	learning	NOUN
ejpam-6142	633	4	techniques	technique	NOUN
ejpam-6142	633	5	may	may	AUX
ejpam-6142	633	6	enhance	enhance	VERB
ejpam-6142	633	7	predictive	predictive	ADJ
ejpam-6142	633	8	accuracy	accuracy	NOUN
ejpam-6142	633	9	,	,	PUNCT
ejpam-6142	633	10	while	while	SCONJ
ejpam-6142	633	11	network	network	NOUN
ejpam-6142	633	12	-	-	PUNCT
ejpam-6142	633	13	based	base	VERB
ejpam-6142	633	14	extensions	extension	NOUN
ejpam-6142	633	15	could	could	AUX
ejpam-6142	633	16	improve	improve	VERB
ejpam-6142	633	17	targeting	target	VERB
ejpam-6142	633	18	of	of	ADP
ejpam-6142	633	19	high	high	ADJ
ejpam-6142	633	20	-	-	PUNCT
ejpam-6142	633	21	risk	risk	NOUN
ejpam-6142	633	22	populations	population	NOUN
ejpam-6142	633	23	.	.	PUNCT
ejpam-6142	634	1	furthermore	furthermore	ADV
ejpam-6142	634	2	,	,	PUNCT
ejpam-6142	634	3	the	the	DET
ejpam-6142	634	4	model	model	NOUN
ejpam-6142	634	5	is	be	AUX
ejpam-6142	634	6	adaptable	adaptable	ADJ
ejpam-6142	634	7	to	to	ADP
ejpam-6142	634	8	other	other	ADJ
ejpam-6142	634	9	infectious	infectious	ADJ
ejpam-6142	634	10	diseases	disease	NOUN
ejpam-6142	634	11	,	,	PUNCT
ejpam-6142	634	12	providing	provide	VERB
ejpam-6142	634	13	policymakers	policymaker	NOUN
ejpam-6142	634	14	with	with	ADP
ejpam-6142	634	15	a	a	DET
ejpam-6142	634	16	flexible	flexible	ADJ
ejpam-6142	634	17	tool	tool	NOUN
ejpam-6142	634	18	for	for	ADP
ejpam-6142	634	19	evaluating	evaluate	VERB
ejpam-6142	634	20	integrated	integrate	VERB
ejpam-6142	634	21	prevention	prevention	NOUN
ejpam-6142	634	22	strategies	strategy	NOUN
ejpam-6142	634	23	under	under	ADP
ejpam-6142	634	24	resource	resource	NOUN
ejpam-6142	634	25	constraints	constraint	NOUN
ejpam-6142	634	26	10	10	NUM
ejpam-6142	634	27	.	.	PUNCT
ejpam-6142	635	1	conclusion	conclusion	NOUN
ejpam-6142	635	2	this	this	DET
ejpam-6142	635	3	paper	paper	NOUN
ejpam-6142	635	4	presents	present	VERB
ejpam-6142	635	5	a	a	DET
ejpam-6142	635	6	framework	framework	NOUN
ejpam-6142	635	7	for	for	ADP
ejpam-6142	635	8	understanding	understand	VERB
ejpam-6142	635	9	hiv	hiv	PROPN
ejpam-6142	635	10	/	/	SYM
ejpam-6142	635	11	aids	aids	PROPN
ejpam-6142	635	12	transmission	transmission	NOUN
ejpam-6142	635	13	dynamics	dynamic	NOUN
ejpam-6142	635	14	between	between	ADP
ejpam-6142	635	15	male	male	ADJ
ejpam-6142	635	16	and	and	CCONJ
ejpam-6142	635	17	female	female	ADJ
ejpam-6142	635	18	populations	population	NOUN
ejpam-6142	635	19	.	.	PUNCT
ejpam-6142	636	1	we	we	PRON
ejpam-6142	636	2	analyzed	analyze	VERB
ejpam-6142	636	3	the	the	DET
ejpam-6142	636	4	model	model	NOUN
ejpam-6142	636	5	’s	’s	PART
ejpam-6142	636	6	equilibrium	equilibrium	NOUN
ejpam-6142	636	7	points	point	NOUN
ejpam-6142	636	8	and	and	CCONJ
ejpam-6142	636	9	determined	determine	VERB
ejpam-6142	636	10	the	the	DET
ejpam-6142	636	11	basic	basic	ADJ
ejpam-6142	636	12	reproduction	reproduction	NOUN
ejpam-6142	636	13	number	number	NOUN
ejpam-6142	636	14	,	,	PUNCT
ejpam-6142	636	15	r0	r0	NOUN
ejpam-6142	636	16	.	.	PUNCT
ejpam-6142	637	1	the	the	DET
ejpam-6142	637	2	stability	stability	NOUN
ejpam-6142	637	3	analysis	analysis	NOUN
ejpam-6142	637	4	showed	show	VERB
ejpam-6142	637	5	that	that	SCONJ
ejpam-6142	637	6	the	the	DET
ejpam-6142	637	7	disease	disease	NOUN
ejpam-6142	637	8	-	-	PUNCT
ejpam-6142	637	9	free	free	ADJ
ejpam-6142	637	10	equilibrium	equilibrium	NOUN
ejpam-6142	637	11	is	be	AUX
ejpam-6142	637	12	stable	stable	ADJ
ejpam-6142	637	13	when	when	SCONJ
ejpam-6142	637	14	r0	r0	NOUN
ejpam-6142	637	15	<	<	X
ejpam-6142	637	16	1	1	NUM
ejpam-6142	637	17	,	,	PUNCT
ejpam-6142	637	18	while	while	SCONJ
ejpam-6142	637	19	the	the	DET
ejpam-6142	637	20	endemic	endemic	ADJ
ejpam-6142	637	21	equilibrium	equilibrium	NOUN
ejpam-6142	637	22	is	be	AUX
ejpam-6142	637	23	stable	stable	ADJ
ejpam-6142	637	24	when	when	SCONJ
ejpam-6142	637	25	r0	r0	NOUN
ejpam-6142	637	26	>	>	X
ejpam-6142	637	27	1	1	X
ejpam-6142	637	28	.	.	PUNCT
ejpam-6142	637	29	to	to	PART
ejpam-6142	637	30	identify	identify	VERB
ejpam-6142	637	31	the	the	DET
ejpam-6142	637	32	most	most	ADV
ejpam-6142	637	33	influential	influential	ADJ
ejpam-6142	637	34	factors	factor	NOUN
ejpam-6142	637	35	,	,	PUNCT
ejpam-6142	637	36	we	we	PRON
ejpam-6142	637	37	conducted	conduct	VERB
ejpam-6142	637	38	local	local	ADJ
ejpam-6142	637	39	sensitivity	sensitivity	NOUN
ejpam-6142	637	40	analysis	analysis	NOUN
ejpam-6142	637	41	using	use	VERB
ejpam-6142	637	42	fullnormalization	fullnormalization	NOUN
ejpam-6142	637	43	,	,	PUNCT
ejpam-6142	637	44	half	half	ADJ
ejpam-6142	637	45	-	-	PUNCT
ejpam-6142	637	46	normalization	normalization	NOUN
ejpam-6142	637	47	,	,	PUNCT
ejpam-6142	637	48	and	and	CCONJ
ejpam-6142	637	49	non	non	ADJ
ejpam-6142	637	50	-	-	ADJ
ejpam-6142	637	51	normalization	normalization	ADJ
ejpam-6142	637	52	methods	method	NOUN
ejpam-6142	637	53	.	.	PUNCT
ejpam-6142	638	1	we	we	PRON
ejpam-6142	638	2	also	also	ADV
ejpam-6142	638	3	examined	examine	VERB
ejpam-6142	638	4	how	how	SCONJ
ejpam-6142	638	5	key	key	ADJ
ejpam-6142	638	6	parameters	parameter	NOUN
ejpam-6142	638	7	affect	affect	VERB
ejpam-6142	638	8	r0	r0	NOUN
ejpam-6142	638	9	.	.	PUNCT
ejpam-6142	639	1	optimal	optimal	ADJ
ejpam-6142	639	2	control	control	NOUN
ejpam-6142	639	3	strategies	strategy	NOUN
ejpam-6142	639	4	prevention	prevention	NOUN
ejpam-6142	639	5	,	,	PUNCT
ejpam-6142	639	6	screening	screening	NOUN
ejpam-6142	639	7	,	,	PUNCT
ejpam-6142	639	8	and	and	CCONJ
ejpam-6142	639	9	treatment	treatment	NOUN
ejpam-6142	639	10	were	be	AUX
ejpam-6142	639	11	then	then	ADV
ejpam-6142	639	12	introduced	introduce	VERB
ejpam-6142	639	13	.	.	PUNCT
ejpam-6142	640	1	the	the	DET
ejpam-6142	640	2	control	control	NOUN
ejpam-6142	640	3	problem	problem	NOUN
ejpam-6142	640	4	was	be	AUX
ejpam-6142	640	5	formulated	formulate	VERB
ejpam-6142	640	6	and	and	CCONJ
ejpam-6142	640	7	solved	solve	VERB
ejpam-6142	640	8	numerically	numerically	ADV
ejpam-6142	640	9	,	,	PUNCT
ejpam-6142	640	10	revealing	reveal	VERB
ejpam-6142	640	11	the	the	DET
ejpam-6142	640	12	most	most	ADV
ejpam-6142	640	13	efficient	efficient	ADJ
ejpam-6142	640	14	use	use	NOUN
ejpam-6142	640	15	of	of	ADP
ejpam-6142	640	16	resources	resource	NOUN
ejpam-6142	640	17	and	and	CCONJ
ejpam-6142	640	18	timing	timing	NOUN
ejpam-6142	640	19	for	for	ADP
ejpam-6142	640	20	interventions	intervention	NOUN
ejpam-6142	640	21	.	.	PUNCT
ejpam-6142	641	1	results	result	NOUN
ejpam-6142	641	2	showed	show	VERB
ejpam-6142	641	3	that	that	SCONJ
ejpam-6142	641	4	combining	combine	VERB
ejpam-6142	641	5	all	all	DET
ejpam-6142	641	6	three	three	NUM
ejpam-6142	641	7	strategies	strategy	NOUN
ejpam-6142	641	8	significantly	significantly	ADV
ejpam-6142	641	9	reduces	reduce	VERB
ejpam-6142	641	10	the	the	DET
ejpam-6142	641	11	number	number	NOUN
ejpam-6142	641	12	of	of	ADP
ejpam-6142	641	13	infections	infection	NOUN
ejpam-6142	641	14	and	and	CCONJ
ejpam-6142	641	15	aids	aid	NOUN
ejpam-6142	641	16	cases	case	NOUN
ejpam-6142	641	17	in	in	ADP
ejpam-6142	641	18	both	both	DET
ejpam-6142	641	19	sexes	sex	NOUN
ejpam-6142	641	20	.	.	PUNCT
ejpam-6142	642	1	numerical	numerical	ADJ
ejpam-6142	642	2	simulations	simulation	NOUN
ejpam-6142	642	3	supported	support	VERB
ejpam-6142	642	4	the	the	DET
ejpam-6142	642	5	effectiveness	effectiveness	NOUN
ejpam-6142	642	6	of	of	ADP
ejpam-6142	642	7	these	these	DET
ejpam-6142	642	8	interventions	intervention	NOUN
ejpam-6142	642	9	in	in	ADP
ejpam-6142	642	10	reducing	reduce	VERB
ejpam-6142	642	11	hiv	hiv	PROPN
ejpam-6142	642	12	/	/	SYM
ejpam-6142	642	13	aids	aids	PROPN
ejpam-6142	642	14	prevalence	prevalence	NOUN
ejpam-6142	642	15	over	over	ADP
ejpam-6142	642	16	time	time	NOUN
ejpam-6142	642	17	.	.	PUNCT
ejpam-6142	643	1	these	these	DET
ejpam-6142	643	2	findings	finding	NOUN
ejpam-6142	643	3	highlight	highlight	VERB
ejpam-6142	643	4	the	the	DET
ejpam-6142	643	5	significance	significance	NOUN
ejpam-6142	643	6	of	of	ADP
ejpam-6142	643	7	focused	focused	ADJ
ejpam-6142	643	8	,	,	PUNCT
ejpam-6142	643	9	evidence	evidence	NOUN
ejpam-6142	643	10	-	-	PUNCT
ejpam-6142	643	11	driven	drive	VERB
ejpam-6142	643	12	strategies	strategy	NOUN
ejpam-6142	643	13	in	in	ADP
ejpam-6142	643	14	public	public	ADJ
ejpam-6142	643	15	health	health	NOUN
ejpam-6142	643	16	policy	policy	NOUN
ejpam-6142	643	17	.	.	PUNCT
ejpam-6142	644	1	this	this	DET
ejpam-6142	644	2	study	study	NOUN
ejpam-6142	644	3	not	not	PART
ejpam-6142	644	4	only	only	ADV
ejpam-6142	644	5	improves	improve	VERB
ejpam-6142	644	6	our	our	PRON
ejpam-6142	644	7	understanding	understanding	NOUN
ejpam-6142	644	8	of	of	ADP
ejpam-6142	644	9	hiv	hiv	PROPN
ejpam-6142	644	10	/	/	SYM
ejpam-6142	644	11	aids	aids	PROPN
ejpam-6142	644	12	dynamics	dynamic	NOUN
ejpam-6142	644	13	in	in	ADP
ejpam-6142	644	14	s.	s.	PROPN
ejpam-6142	644	15	m.	m.	PROPN
ejpam-6142	644	16	fatah	fatah	PROPN
ejpam-6142	644	17	,	,	PUNCT
ejpam-6142	644	18	s.	s.	PROPN
ejpam-6142	644	19	h.	h.	PROPN
ejpam-6142	644	20	a.	a.	PROPN
ejpam-6142	644	21	khoshnaw	khoshnaw	PROPN
ejpam-6142	644	22	,	,	PUNCT
ejpam-6142	644	23	a.	a.	PROPN
ejpam-6142	644	24	n.	n.	PROPN
ejpam-6142	644	25	mustafa	mustafa	PROPN
ejpam-6142	644	26	/	/	SYM
ejpam-6142	644	27	eur	eur	PROPN
ejpam-6142	644	28	.	.	PUNCT
ejpam-6142	645	1	j.	j.	PROPN
ejpam-6142	645	2	pure	pure	PROPN
ejpam-6142	645	3	appl	appl	PROPN
ejpam-6142	645	4	.	.	PROPN
ejpam-6142	645	5	math	math	PROPN
ejpam-6142	645	6	,	,	PUNCT
ejpam-6142	645	7	18	18	NUM
ejpam-6142	645	8	(	(	PUNCT
ejpam-6142	645	9	2	2	NUM
ejpam-6142	645	10	)	)	PUNCT
ejpam-6142	645	11	(	(	PUNCT
ejpam-6142	645	12	2025	2025	NUM
ejpam-6142	645	13	)	)	PUNCT
ejpam-6142	645	14	,	,	PUNCT
ejpam-6142	645	15	6142	6142	NUM
ejpam-6142	645	16	32	32	NUM
ejpam-6142	645	17	of	of	ADP
ejpam-6142	645	18	33	33	NUM
ejpam-6142	645	19	different	different	ADJ
ejpam-6142	645	20	populations	population	NOUN
ejpam-6142	645	21	but	but	CCONJ
ejpam-6142	645	22	also	also	ADV
ejpam-6142	645	23	provides	provide	VERB
ejpam-6142	645	24	the	the	DET
ejpam-6142	645	25	path	path	NOUN
ejpam-6142	645	26	for	for	ADP
ejpam-6142	645	27	effective	effective	ADJ
ejpam-6142	645	28	intervention	intervention	NOUN
ejpam-6142	645	29	strategies	strategy	NOUN
ejpam-6142	645	30	that	that	PRON
ejpam-6142	645	31	can	can	AUX
ejpam-6142	645	32	have	have	VERB
ejpam-6142	645	33	a	a	DET
ejpam-6142	645	34	dramatic	dramatic	ADJ
ejpam-6142	645	35	impact	impact	NOUN
ejpam-6142	645	36	on	on	ADP
ejpam-6142	645	37	public	public	ADJ
ejpam-6142	645	38	health	health	NOUN
ejpam-6142	645	39	outcomes	outcome	NOUN
ejpam-6142	645	40	.	.	PUNCT
ejpam-6142	646	1	references	reference	NOUN
ejpam-6142	646	2	[	[	X
ejpam-6142	646	3	1	1	NUM
ejpam-6142	646	4	]	]	PUNCT
ejpam-6142	646	5	priti	priti	NOUN
ejpam-6142	646	6	kumar	kumar	PROPN
ejpam-6142	646	7	roy	roy	PROPN
ejpam-6142	646	8	et	et	PROPN
ejpam-6142	646	9	al	al	PROPN
ejpam-6142	646	10	.	.	PROPN
ejpam-6142	646	11	mathematical	mathematical	ADJ
ejpam-6142	646	12	models	model	NOUN
ejpam-6142	646	13	for	for	ADP
ejpam-6142	646	14	therapeutic	therapeutic	ADJ
ejpam-6142	646	15	approaches	approach	NOUN
ejpam-6142	646	16	to	to	PART
ejpam-6142	646	17	control	control	VERB
ejpam-6142	646	18	hiv	hiv	PROPN
ejpam-6142	646	19	disease	disease	NOUN
ejpam-6142	646	20	transmission	transmission	NOUN
ejpam-6142	646	21	.	.	PUNCT
ejpam-6142	647	1	springer	springer	NOUN
ejpam-6142	647	2	,	,	PUNCT
ejpam-6142	647	3	2015	2015	NUM
ejpam-6142	647	4	.	.	PUNCT
ejpam-6142	648	1	[	[	X
ejpam-6142	648	2	2	2	NUM
ejpam-6142	648	3	]	]	PUNCT
ejpam-6142	648	4	xiaodan	xiaodan	PROPN
ejpam-6142	648	5	sun	sun	PROPN
ejpam-6142	648	6	,	,	PUNCT
ejpam-6142	648	7	hiroshi	hiroshi	PROPN
ejpam-6142	648	8	nishiura	nishiura	PROPN
ejpam-6142	648	9	,	,	PUNCT
ejpam-6142	648	10	and	and	CCONJ
ejpam-6142	648	11	yanni	yanni	PROPN
ejpam-6142	648	12	xiao	xiao	PROPN
ejpam-6142	648	13	.	.	PROPN
ejpam-6142	649	1	modeling	modeling	NOUN
ejpam-6142	649	2	methods	method	NOUN
ejpam-6142	649	3	for	for	ADP
ejpam-6142	649	4	estimating	estimate	VERB
ejpam-6142	649	5	hiv	hiv	PROPN
ejpam-6142	649	6	incidence	incidence	NOUN
ejpam-6142	649	7	:	:	PUNCT
ejpam-6142	649	8	a	a	DET
ejpam-6142	649	9	mathematical	mathematical	ADJ
ejpam-6142	649	10	review	review	NOUN
ejpam-6142	649	11	.	.	PUNCT
ejpam-6142	650	1	theoretical	theoretical	ADJ
ejpam-6142	650	2	biology	biology	NOUN
ejpam-6142	650	3	and	and	CCONJ
ejpam-6142	650	4	medical	medical	ADJ
ejpam-6142	650	5	modelling	modelling	NOUN
ejpam-6142	650	6	,	,	PUNCT
ejpam-6142	650	7	17(1	17(1	NUM
ejpam-6142	650	8	)	)	PUNCT
ejpam-6142	650	9	,	,	PUNCT
ejpam-6142	650	10	2020	2020	NUM
ejpam-6142	650	11	.	.	PUNCT
ejpam-6142	651	1	[	[	X
ejpam-6142	651	2	3	3	X
ejpam-6142	651	3	]	]	PUNCT
ejpam-6142	651	4	world	world	NOUN
ejpam-6142	651	5	health	health	NOUN
ejpam-6142	651	6	organization	organization	NOUN
ejpam-6142	651	7	.	.	PUNCT
ejpam-6142	652	1	hiv	hiv	PROPN
ejpam-6142	652	2	/	/	SYM
ejpam-6142	652	3	aids	aids	PROPN
ejpam-6142	652	4	,	,	PUNCT
ejpam-6142	652	5	2024	2024	NUM
ejpam-6142	652	6	.	.	PUNCT
ejpam-6142	653	1	[	[	X
ejpam-6142	653	2	4	4	NUM
ejpam-6142	653	3	]	]	X
ejpam-6142	653	4	ram	ram	PROPN
ejpam-6142	653	5	naresh	naresh	PROPN
ejpam-6142	653	6	,	,	PUNCT
ejpam-6142	653	7	agraj	agraj	PROPN
ejpam-6142	653	8	tripathi	tripathi	PROPN
ejpam-6142	653	9	,	,	PUNCT
ejpam-6142	653	10	and	and	CCONJ
ejpam-6142	653	11	dileep	dileep	PROPN
ejpam-6142	653	12	sharma	sharma	PROPN
ejpam-6142	653	13	.	.	PUNCT
ejpam-6142	653	14	modelling	modelling	NOUN
ejpam-6142	653	15	and	and	CCONJ
ejpam-6142	653	16	analysis	analysis	NOUN
ejpam-6142	653	17	of	of	ADP
ejpam-6142	653	18	the	the	DET
ejpam-6142	653	19	spread	spread	NOUN
ejpam-6142	653	20	of	of	ADP
ejpam-6142	653	21	aids	aid	NOUN
ejpam-6142	653	22	epidemic	epidemic	NOUN
ejpam-6142	653	23	with	with	ADP
ejpam-6142	653	24	immigration	immigration	NOUN
ejpam-6142	653	25	of	of	ADP
ejpam-6142	653	26	hiv	hiv	PROPN
ejpam-6142	653	27	infectives	infective	NOUN
ejpam-6142	653	28	.	.	PUNCT
ejpam-6142	654	1	mathematical	mathematical	ADJ
ejpam-6142	654	2	and	and	CCONJ
ejpam-6142	654	3	computer	computer	NOUN
ejpam-6142	654	4	modelling	modelling	NOUN
ejpam-6142	654	5	,	,	PUNCT
ejpam-6142	654	6	49(5	49(5	NUM
ejpam-6142	654	7	-	-	NOUN
ejpam-6142	654	8	6):880–892	6):880–892	NOUN
ejpam-6142	654	9	,	,	PUNCT
ejpam-6142	654	10	2009	2009	NUM
ejpam-6142	654	11	.	.	PUNCT
ejpam-6142	655	1	[	[	X
ejpam-6142	655	2	5	5	NUM
ejpam-6142	655	3	]	]	X
ejpam-6142	655	4	fred	fred	PROPN
ejpam-6142	655	5	brauer	brauer	PROPN
ejpam-6142	655	6	,	,	PUNCT
ejpam-6142	655	7	carlos	carlos	PROPN
ejpam-6142	655	8	castillo	castillo	PROPN
ejpam-6142	655	9	-	-	PUNCT
ejpam-6142	655	10	chavez	chavez	PROPN
ejpam-6142	655	11	,	,	PUNCT
ejpam-6142	655	12	zhilan	zhilan	PROPN
ejpam-6142	655	13	feng	feng	PROPN
ejpam-6142	655	14	,	,	PUNCT
ejpam-6142	655	15	et	et	PROPN
ejpam-6142	655	16	al	al	PROPN
ejpam-6142	655	17	.	.	PROPN
ejpam-6142	655	18	mathematical	mathematical	ADJ
ejpam-6142	655	19	models	model	NOUN
ejpam-6142	655	20	in	in	ADP
ejpam-6142	655	21	epidemiology	epidemiology	NOUN
ejpam-6142	655	22	,	,	PUNCT
ejpam-6142	655	23	volume	volume	NOUN
ejpam-6142	655	24	32	32	NUM
ejpam-6142	655	25	.	.	PUNCT
ejpam-6142	655	26	springer	springer	NOUN
ejpam-6142	655	27	,	,	PUNCT
ejpam-6142	655	28	2019	2019	NUM
ejpam-6142	655	29	.	.	PUNCT
ejpam-6142	656	1	[	[	X
ejpam-6142	656	2	6	6	NUM
ejpam-6142	656	3	]	]	SYM
ejpam-6142	656	4	da	da	NOUN
ejpam-6142	656	5	munawwaroh	munawwaroh	NOUN
ejpam-6142	656	6	,	,	PUNCT
ejpam-6142	656	7	r	r	NOUN
ejpam-6142	656	8	heri	heri	NOUN
ejpam-6142	656	9	,	,	PUNCT
ejpam-6142	656	10	sus	sus	PROPN
ejpam-6142	656	11	khabibah	khabibah	PROPN
ejpam-6142	656	12	,	,	PUNCT
ejpam-6142	656	13	hp	hp	PROPN
ejpam-6142	656	14	anindita	anindita	PROPN
ejpam-6142	656	15	,	,	PUNCT
ejpam-6142	656	16	et	et	PROPN
ejpam-6142	656	17	al	al	PROPN
ejpam-6142	656	18	.	.	PROPN
ejpam-6142	656	19	analysis	analysis	NOUN
ejpam-6142	656	20	stability	stability	NOUN
ejpam-6142	656	21	of	of	ADP
ejpam-6142	656	22	hiv	hiv	PROPN
ejpam-6142	656	23	/	/	SYM
ejpam-6142	656	24	aids	aids	PROPN
ejpam-6142	656	25	epidemic	epidemic	NOUN
ejpam-6142	656	26	model	model	NOUN
ejpam-6142	656	27	of	of	ADP
ejpam-6142	656	28	different	different	ADJ
ejpam-6142	656	29	infection	infection	NOUN
ejpam-6142	656	30	stage	stage	NOUN
ejpam-6142	656	31	in	in	ADP
ejpam-6142	656	32	closed	closed	ADJ
ejpam-6142	656	33	community	community	NOUN
ejpam-6142	656	34	.	.	PUNCT
ejpam-6142	657	1	in	in	ADP
ejpam-6142	657	2	journal	journal	PROPN
ejpam-6142	657	3	of	of	ADP
ejpam-6142	657	4	physics	physics	PROPN
ejpam-6142	657	5	:	:	PUNCT
ejpam-6142	657	6	conference	conference	NOUN
ejpam-6142	657	7	series	series	NOUN
ejpam-6142	657	8	,	,	PUNCT
ejpam-6142	657	9	volume	volume	NOUN
ejpam-6142	657	10	1524	1524	NUM
ejpam-6142	657	11	,	,	PUNCT
ejpam-6142	657	12	page	page	NOUN
ejpam-6142	657	13	012130	012130	NUM
ejpam-6142	657	14	.	.	PUNCT
ejpam-6142	658	1	iop	iop	PROPN
ejpam-6142	658	2	publishing	publishing	NOUN
ejpam-6142	658	3	,	,	PUNCT
ejpam-6142	658	4	2020	2020	NUM
ejpam-6142	658	5	.	.	PUNCT
ejpam-6142	659	1	[	[	X
ejpam-6142	659	2	7	7	X
ejpam-6142	659	3	]	]	X
ejpam-6142	659	4	roy	roy	PROPN
ejpam-6142	659	5	m	m	PROPN
ejpam-6142	659	6	anderson	anderson	PROPN
ejpam-6142	659	7	.	.	PUNCT
ejpam-6142	660	1	the	the	DET
ejpam-6142	660	2	epidemiology	epidemiology	NOUN
ejpam-6142	660	3	of	of	ADP
ejpam-6142	660	4	hiv	hiv	PROPN
ejpam-6142	660	5	infection	infection	NOUN
ejpam-6142	660	6	:	:	PUNCT
ejpam-6142	660	7	variable	variable	ADJ
ejpam-6142	660	8	incubation	incubation	NOUN
ejpam-6142	660	9	plus	plus	CCONJ
ejpam-6142	660	10	infectious	infectious	ADJ
ejpam-6142	660	11	periods	period	NOUN
ejpam-6142	660	12	and	and	CCONJ
ejpam-6142	660	13	heterogeneity	heterogeneity	NOUN
ejpam-6142	660	14	in	in	ADP
ejpam-6142	660	15	sexual	sexual	ADJ
ejpam-6142	660	16	activity	activity	NOUN
ejpam-6142	660	17	.	.	PUNCT
ejpam-6142	661	1	journal	journal	NOUN
ejpam-6142	661	2	of	of	ADP
ejpam-6142	661	3	the	the	DET
ejpam-6142	661	4	royal	royal	ADJ
ejpam-6142	661	5	statistical	statistical	ADJ
ejpam-6142	661	6	society	society	NOUN
ejpam-6142	661	7	:	:	PUNCT
ejpam-6142	661	8	series	series	PROPN
ejpam-6142	661	9	a	a	PROPN
ejpam-6142	661	10	(	(	PUNCT
ejpam-6142	661	11	statistics	statistic	NOUN
ejpam-6142	661	12	in	in	ADP
ejpam-6142	661	13	society	society	NOUN
ejpam-6142	661	14	)	)	PUNCT
ejpam-6142	661	15	,	,	PUNCT
ejpam-6142	661	16	151(1):66–93	151(1):66–93	NUM
ejpam-6142	661	17	,	,	PUNCT
ejpam-6142	661	18	1988	1988	NUM
ejpam-6142	661	19	.	.	PUNCT
ejpam-6142	662	1	[	[	X
ejpam-6142	662	2	8	8	NUM
ejpam-6142	662	3	]	]	X
ejpam-6142	662	4	roy	roy	PROPN
ejpam-6142	662	5	m	m	PROPN
ejpam-6142	662	6	anderson	anderson	PROPN
ejpam-6142	662	7	.	.	PUNCT
ejpam-6142	663	1	the	the	DET
ejpam-6142	663	2	role	role	NOUN
ejpam-6142	663	3	of	of	ADP
ejpam-6142	663	4	mathematical	mathematical	ADJ
ejpam-6142	663	5	models	model	NOUN
ejpam-6142	663	6	in	in	ADP
ejpam-6142	663	7	the	the	DET
ejpam-6142	663	8	study	study	NOUN
ejpam-6142	663	9	of	of	ADP
ejpam-6142	663	10	hiv	hiv	PROPN
ejpam-6142	663	11	transmission	transmission	NOUN
ejpam-6142	663	12	and	and	CCONJ
ejpam-6142	663	13	the	the	DET
ejpam-6142	663	14	epidemiology	epidemiology	NOUN
ejpam-6142	663	15	of	of	ADP
ejpam-6142	663	16	aids	aids	PROPN
ejpam-6142	663	17	.	.	PUNCT
ejpam-6142	664	1	journal	journal	PROPN
ejpam-6142	664	2	of	of	ADP
ejpam-6142	664	3	acquired	acquire	VERB
ejpam-6142	664	4	immune	immune	ADJ
ejpam-6142	664	5	deficiency	deficiency	NOUN
ejpam-6142	664	6	syndromes	syndrome	NOUN
ejpam-6142	664	7	,	,	PUNCT
ejpam-6142	664	8	1(3):241–256	1(3):241–256	NUM
ejpam-6142	664	9	,	,	PUNCT
ejpam-6142	664	10	1988	1988	NUM
ejpam-6142	664	11	.	.	PUNCT
ejpam-6142	665	1	[	[	X
ejpam-6142	665	2	9	9	NUM
ejpam-6142	665	3	]	]	X
ejpam-6142	665	4	robert	robert	PROPN
ejpam-6142	665	5	m	m	PROPN
ejpam-6142	665	6	may	may	AUX
ejpam-6142	665	7	and	and	CCONJ
ejpam-6142	665	8	roy	roy	PROPN
ejpam-6142	665	9	m	m	PROPN
ejpam-6142	665	10	anderson	anderson	PROPN
ejpam-6142	665	11	.	.	PUNCT
ejpam-6142	666	1	commentary	commentary	NOUN
ejpam-6142	666	2	transmission	transmission	NOUN
ejpam-6142	666	3	dynamics	dynamic	NOUN
ejpam-6142	666	4	of	of	ADP
ejpam-6142	666	5	hiv	hiv	PROPN
ejpam-6142	666	6	infection	infection	NOUN
ejpam-6142	666	7	.	.	PUNCT
ejpam-6142	667	1	nature	nature	NOUN
ejpam-6142	667	2	,	,	PUNCT
ejpam-6142	667	3	326(137):10–1038	326(137):10–1038	PROPN
ejpam-6142	667	4	,	,	PUNCT
ejpam-6142	667	5	1987	1987	NUM
ejpam-6142	667	6	.	.	PUNCT
ejpam-6142	668	1	[	[	X
ejpam-6142	668	2	10	10	NUM
ejpam-6142	668	3	]	]	X
ejpam-6142	668	4	rm	rm	PROPN
ejpam-6142	668	5	anderson	anderson	PROPN
ejpam-6142	668	6	,	,	PUNCT
ejpam-6142	668	7	gf	gf	PROPN
ejpam-6142	668	8	medley	medley	NOUN
ejpam-6142	668	9	,	,	PUNCT
ejpam-6142	668	10	rm	rm	PROPN
ejpam-6142	668	11	may	may	AUX
ejpam-6142	668	12	,	,	PUNCT
ejpam-6142	668	13	and	and	CCONJ
ejpam-6142	668	14	am	be	AUX
ejpam-6142	668	15	johnson	johnson	PROPN
ejpam-6142	668	16	.	.	PUNCT
ejpam-6142	669	1	a	a	DET
ejpam-6142	669	2	preliminary	preliminary	ADJ
ejpam-6142	669	3	study	study	NOUN
ejpam-6142	669	4	of	of	ADP
ejpam-6142	669	5	the	the	DET
ejpam-6142	669	6	transmission	transmission	NOUN
ejpam-6142	669	7	dynamics	dynamic	NOUN
ejpam-6142	669	8	of	of	ADP
ejpam-6142	669	9	the	the	DET
ejpam-6142	669	10	human	human	ADJ
ejpam-6142	669	11	immunodeficiency	immunodeficiency	NOUN
ejpam-6142	669	12	virus	virus	NOUN
ejpam-6142	669	13	(	(	PUNCT
ejpam-6142	669	14	hiv	hiv	PROPN
ejpam-6142	669	15	)	)	PUNCT
ejpam-6142	669	16	,	,	PUNCT
ejpam-6142	669	17	the	the	DET
ejpam-6142	669	18	causative	causative	ADJ
ejpam-6142	669	19	agent	agent	NOUN
ejpam-6142	669	20	of	of	ADP
ejpam-6142	669	21	aids	aids	PROPN
ejpam-6142	669	22	.	.	PUNCT
ejpam-6142	670	1	mathematical	mathematical	ADJ
ejpam-6142	670	2	medicine	medicine	NOUN
ejpam-6142	670	3	and	and	CCONJ
ejpam-6142	670	4	biology	biology	NOUN
ejpam-6142	670	5	:	:	PUNCT
ejpam-6142	670	6	a	a	DET
ejpam-6142	670	7	journal	journal	NOUN
ejpam-6142	670	8	of	of	ADP
ejpam-6142	670	9	the	the	DET
ejpam-6142	670	10	i	i	PROPN
ejpam-6142	670	11	m	m	PROPN
ejpam-6142	670	12	a	a	PROPN
ejpam-6142	670	13	,	,	PUNCT
ejpam-6142	670	14	3(4):229–263	3(4):229–263	NUM
ejpam-6142	670	15	,	,	PUNCT
ejpam-6142	670	16	1986	1986	NUM
ejpam-6142	670	17	.	.	PUNCT
ejpam-6142	671	1	[	[	X
ejpam-6142	671	2	11	11	NUM
ejpam-6142	671	3	]	]	X
ejpam-6142	671	4	hai	hai	PROPN
ejpam-6142	671	5	-	-	PUNCT
ejpam-6142	671	6	feng	feng	PROPN
ejpam-6142	671	7	huo	huo	PROPN
ejpam-6142	671	8	,	,	PUNCT
ejpam-6142	671	9	rui	rui	PROPN
ejpam-6142	671	10	chen	chen	PROPN
ejpam-6142	671	11	,	,	PUNCT
ejpam-6142	671	12	and	and	CCONJ
ejpam-6142	671	13	xun	xun	PROPN
ejpam-6142	671	14	-	-	PUNCT
ejpam-6142	671	15	yang	yang	PROPN
ejpam-6142	671	16	wang	wang	PROPN
ejpam-6142	671	17	.	.	PUNCT
ejpam-6142	672	1	modelling	modelling	NOUN
ejpam-6142	672	2	and	and	CCONJ
ejpam-6142	672	3	stability	stability	NOUN
ejpam-6142	672	4	of	of	ADP
ejpam-6142	672	5	hiv	hiv	PROPN
ejpam-6142	672	6	/	/	SYM
ejpam-6142	672	7	aids	aids	PROPN
ejpam-6142	672	8	epidemic	epidemic	NOUN
ejpam-6142	672	9	model	model	NOUN
ejpam-6142	672	10	with	with	ADP
ejpam-6142	672	11	treatment	treatment	NOUN
ejpam-6142	672	12	.	.	PUNCT
ejpam-6142	673	1	applied	apply	VERB
ejpam-6142	673	2	mathematical	mathematical	ADJ
ejpam-6142	673	3	modelling	modelling	NOUN
ejpam-6142	673	4	,	,	PUNCT
ejpam-6142	673	5	40(13	40(13	NOUN
ejpam-6142	673	6	-	-	SYM
ejpam-6142	673	7	14):6550	14):6550	NUM
ejpam-6142	673	8	–	–	PUNCT
ejpam-6142	673	9	6559	6559	NUM
ejpam-6142	673	10	,	,	PUNCT
ejpam-6142	673	11	2016	2016	NUM
ejpam-6142	673	12	.	.	PUNCT
ejpam-6142	674	1	[	[	X
ejpam-6142	674	2	12	12	NUM
ejpam-6142	674	3	]	]	PUNCT
ejpam-6142	674	4	h.	h.	PROPN
ejpam-6142	674	5	r	r	PROPN
ejpam-6142	674	6	joshi	joshi	PROPN
ejpam-6142	674	7	.	.	PUNCT
ejpam-6142	675	1	optimal	optimal	ADJ
ejpam-6142	675	2	control	control	NOUN
ejpam-6142	675	3	of	of	ADP
ejpam-6142	675	4	an	an	DET
ejpam-6142	675	5	hiv	hiv	PROPN
ejpam-6142	675	6	immunology	immunology	NOUN
ejpam-6142	675	7	model	model	NOUN
ejpam-6142	675	8	.	.	PUNCT
ejpam-6142	676	1	applied	apply	VERB
ejpam-6142	676	2	mathematics	mathematic	NOUN
ejpam-6142	676	3	and	and	CCONJ
ejpam-6142	676	4	computation	computation	NOUN
ejpam-6142	676	5	,	,	PUNCT
ejpam-6142	676	6	178(2):262–272	178(2):262–272	NUM
ejpam-6142	676	7	,	,	PUNCT
ejpam-6142	676	8	2006	2006	NUM
ejpam-6142	676	9	.	.	PUNCT
ejpam-6142	677	1	[	[	X
ejpam-6142	677	2	13	13	NUM
ejpam-6142	677	3	]	]	PUNCT
ejpam-6142	677	4	murray	murray	PROPN
ejpam-6142	677	5	doyle	doyle	PROPN
ejpam-6142	677	6	,	,	PUNCT
ejpam-6142	677	7	david	david	PROPN
ejpam-6142	677	8	greenhalgh	greenhalgh	PROPN
ejpam-6142	677	9	,	,	PUNCT
ejpam-6142	677	10	and	and	CCONJ
ejpam-6142	677	11	steve	steve	PROPN
ejpam-6142	677	12	blythe	blythe	PROPN
ejpam-6142	677	13	.	.	PUNCT
ejpam-6142	678	1	equilibrium	equilibrium	NOUN
ejpam-6142	678	2	analysis	analysis	NOUN
ejpam-6142	678	3	of	of	ADP
ejpam-6142	678	4	a	a	DET
ejpam-6142	678	5	mathematical	mathematical	ADJ
ejpam-6142	678	6	model	model	NOUN
ejpam-6142	678	7	for	for	ADP
ejpam-6142	678	8	the	the	DET
ejpam-6142	678	9	spread	spread	NOUN
ejpam-6142	678	10	of	of	ADP
ejpam-6142	678	11	aids	aid	NOUN
ejpam-6142	678	12	in	in	ADP
ejpam-6142	678	13	a	a	DET
ejpam-6142	678	14	two	two	NUM
ejpam-6142	678	15	sex	sex	NOUN
ejpam-6142	678	16	population	population	NOUN
ejpam-6142	678	17	with	with	ADP
ejpam-6142	678	18	mixing	mix	VERB
ejpam-6142	678	19	constraints	constraint	NOUN
ejpam-6142	678	20	.	.	PUNCT
ejpam-6142	679	1	journal	journal	NOUN
ejpam-6142	679	2	of	of	ADP
ejpam-6142	679	3	biological	biological	ADJ
ejpam-6142	679	4	systems	system	NOUN
ejpam-6142	679	5	,	,	PUNCT
ejpam-6142	679	6	6(02):159–185	6(02):159–185	NUM
ejpam-6142	679	7	,	,	PUNCT
ejpam-6142	679	8	1998	1998	NUM
ejpam-6142	679	9	.	.	PUNCT
ejpam-6142	680	1	[	[	X
ejpam-6142	680	2	14	14	NUM
ejpam-6142	680	3	]	]	X
ejpam-6142	680	4	navjot	navjot	PROPN
ejpam-6142	680	5	kaur	kaur	PROPN
ejpam-6142	680	6	,	,	PUNCT
ejpam-6142	680	7	mini	mini	PROPN
ejpam-6142	680	8	ghosh	ghosh	NOUN
ejpam-6142	680	9	,	,	PUNCT
ejpam-6142	680	10	and	and	CCONJ
ejpam-6142	680	11	s	s	PROPN
ejpam-6142	680	12	bhatia	bhatia	PROPN
ejpam-6142	680	13	.	.	PUNCT
ejpam-6142	681	1	modelling	model	VERB
ejpam-6142	681	2	the	the	DET
ejpam-6142	681	3	role	role	NOUN
ejpam-6142	681	4	of	of	ADP
ejpam-6142	681	5	awareness	awareness	NOUN
ejpam-6142	681	6	and	and	CCONJ
ejpam-6142	681	7	screening	screening	NOUN
ejpam-6142	681	8	of	of	ADP
ejpam-6142	681	9	infectives	infective	NOUN
ejpam-6142	681	10	in	in	ADP
ejpam-6142	681	11	the	the	DET
ejpam-6142	681	12	transmission	transmission	NOUN
ejpam-6142	681	13	dynamics	dynamic	NOUN
ejpam-6142	681	14	of	of	ADP
ejpam-6142	681	15	hiv	hiv	PROPN
ejpam-6142	681	16	.	.	PUNCT
ejpam-6142	682	1	world	world	PROPN
ejpam-6142	682	2	j	j	PROPN
ejpam-6142	682	3	modelling	modelling	NOUN
ejpam-6142	682	4	and	and	CCONJ
ejpam-6142	682	5	simul	simul	PROPN
ejpam-6142	682	6	,	,	PUNCT
ejpam-6142	682	7	12(2):97–111	12(2):97–111	NUM
ejpam-6142	682	8	,	,	PUNCT
ejpam-6142	682	9	2016	2016	NUM
ejpam-6142	682	10	.	.	PUNCT
ejpam-6142	683	1	[	[	X
ejpam-6142	683	2	15	15	NUM
ejpam-6142	683	3	]	]	X
ejpam-6142	683	4	ram	ram	PROPN
ejpam-6142	683	5	naresh	naresh	PROPN
ejpam-6142	683	6	,	,	PUNCT
ejpam-6142	683	7	agraj	agraj	PROPN
ejpam-6142	683	8	tripathi	tripathi	PROPN
ejpam-6142	683	9	,	,	PUNCT
ejpam-6142	683	10	and	and	CCONJ
ejpam-6142	683	11	sandip	sandip	PROPN
ejpam-6142	683	12	omar	omar	PROPN
ejpam-6142	683	13	.	.	PUNCT
ejpam-6142	684	1	modelling	model	VERB
ejpam-6142	684	2	the	the	DET
ejpam-6142	684	3	spread	spread	NOUN
ejpam-6142	684	4	of	of	ADP
ejpam-6142	684	5	aids	aids	PROPN
ejpam-6142	684	6	epidemic	epidemic	PROPN
ejpam-6142	684	7	s.	s.	PROPN
ejpam-6142	684	8	m.	m.	PROPN
ejpam-6142	684	9	fatah	fatah	PROPN
ejpam-6142	684	10	,	,	PUNCT
ejpam-6142	684	11	s.	s.	PROPN
ejpam-6142	684	12	h.	h.	PROPN
ejpam-6142	684	13	a.	a.	PROPN
ejpam-6142	684	14	khoshnaw	khoshnaw	PROPN
ejpam-6142	684	15	,	,	PUNCT
ejpam-6142	684	16	a.	a.	PROPN
ejpam-6142	684	17	n.	n.	PROPN
ejpam-6142	684	18	mustafa	mustafa	PROPN
ejpam-6142	684	19	/	/	SYM
ejpam-6142	684	20	eur	eur	PROPN
ejpam-6142	684	21	.	.	PUNCT
ejpam-6142	685	1	j.	j.	PROPN
ejpam-6142	685	2	pure	pure	PROPN
ejpam-6142	685	3	appl	appl	PROPN
ejpam-6142	685	4	.	.	PROPN
ejpam-6142	685	5	math	math	PROPN
ejpam-6142	685	6	,	,	PUNCT
ejpam-6142	685	7	18	18	NUM
ejpam-6142	685	8	(	(	PUNCT
ejpam-6142	685	9	2	2	NUM
ejpam-6142	685	10	)	)	PUNCT
ejpam-6142	685	11	(	(	PUNCT
ejpam-6142	685	12	2025	2025	NUM
ejpam-6142	685	13	)	)	PUNCT
ejpam-6142	685	14	,	,	PUNCT
ejpam-6142	685	15	6142	6142	NUM
ejpam-6142	685	16	33	33	NUM
ejpam-6142	685	17	of	of	ADP
ejpam-6142	685	18	33	33	NUM
ejpam-6142	685	19	with	with	ADP
ejpam-6142	685	20	vertical	vertical	ADJ
ejpam-6142	685	21	transmission	transmission	NOUN
ejpam-6142	685	22	.	.	PUNCT
ejpam-6142	686	1	applied	apply	VERB
ejpam-6142	686	2	mathematics	mathematic	NOUN
ejpam-6142	686	3	and	and	CCONJ
ejpam-6142	686	4	computation	computation	NOUN
ejpam-6142	686	5	,	,	PUNCT
ejpam-6142	686	6	178(2):262–272	178(2):262–272	NUM
ejpam-6142	686	7	,	,	PUNCT
ejpam-6142	686	8	2006	2006	NUM
ejpam-6142	686	9	.	.	PUNCT
ejpam-6142	687	1	[	[	X
ejpam-6142	687	2	16	16	NUM
ejpam-6142	687	3	]	]	X
ejpam-6142	687	4	abdallah	abdallah	PROPN
ejpam-6142	687	5	s	s	PROPN
ejpam-6142	687	6	waziri	waziri	PROPN
ejpam-6142	687	7	,	,	PUNCT
ejpam-6142	687	8	estomih	estomih	PROPN
ejpam-6142	687	9	s	s	PART
ejpam-6142	687	10	massawe	massawe	NOUN
ejpam-6142	687	11	,	,	PUNCT
ejpam-6142	687	12	and	and	CCONJ
ejpam-6142	687	13	oluwole	oluwole	PROPN
ejpam-6142	687	14	daniel	daniel	PROPN
ejpam-6142	687	15	makinde	makinde	PROPN
ejpam-6142	687	16	.	.	PUNCT
ejpam-6142	688	1	mathematical	mathematical	ADJ
ejpam-6142	688	2	modelling	modelling	NOUN
ejpam-6142	688	3	of	of	ADP
ejpam-6142	688	4	hiv	hiv	PROPN
ejpam-6142	688	5	/	/	SYM
ejpam-6142	688	6	aids	aids	PROPN
ejpam-6142	688	7	dynamics	dynamic	NOUN
ejpam-6142	688	8	with	with	ADP
ejpam-6142	688	9	treatment	treatment	NOUN
ejpam-6142	688	10	and	and	CCONJ
ejpam-6142	688	11	vertical	vertical	ADJ
ejpam-6142	688	12	transmission	transmission	NOUN
ejpam-6142	688	13	.	.	PUNCT
ejpam-6142	689	1	appl	appl	PROPN
ejpam-6142	689	2	.	.	PROPN
ejpam-6142	689	3	math	math	PROPN
ejpam-6142	689	4	,	,	PUNCT
ejpam-6142	689	5	2(3):77–89	2(3):77–89	NUM
ejpam-6142	689	6	,	,	PUNCT
ejpam-6142	689	7	2012	2012	NUM
ejpam-6142	689	8	.	.	PUNCT
ejpam-6142	690	1	[	[	X
ejpam-6142	690	2	17	17	NUM
ejpam-6142	690	3	]	]	X
ejpam-6142	690	4	nawei	nawei	PROPN
ejpam-6142	690	5	chen	chen	PROPN
ejpam-6142	690	6	,	,	PUNCT
ejpam-6142	690	7	shenglong	shenglong	PROPN
ejpam-6142	690	8	chen	chen	PROPN
ejpam-6142	690	9	,	,	PUNCT
ejpam-6142	690	10	xiaoyu	xiaoyu	PROPN
ejpam-6142	690	11	li	li	PROPN
ejpam-6142	690	12	,	,	PUNCT
ejpam-6142	690	13	and	and	CCONJ
ejpam-6142	690	14	zhiming	zhime	VERB
ejpam-6142	690	15	li	li	PROPN
ejpam-6142	690	16	.	.	PROPN
ejpam-6142	690	17	modelling	modelling	NOUN
ejpam-6142	690	18	and	and	CCONJ
ejpam-6142	690	19	analysis	analysis	NOUN
ejpam-6142	690	20	of	of	ADP
ejpam-6142	690	21	the	the	DET
ejpam-6142	690	22	hiv	hiv	PROPN
ejpam-6142	690	23	/	/	SYM
ejpam-6142	690	24	aids	aids	PROPN
ejpam-6142	690	25	epidemic	epidemic	NOUN
ejpam-6142	690	26	with	with	ADP
ejpam-6142	690	27	fast	fast	ADJ
ejpam-6142	690	28	and	and	CCONJ
ejpam-6142	690	29	slow	slow	ADJ
ejpam-6142	690	30	asymptomatic	asymptomatic	ADJ
ejpam-6142	690	31	infections	infection	NOUN
ejpam-6142	690	32	in	in	ADP
ejpam-6142	690	33	china	china	PROPN
ejpam-6142	690	34	from	from	ADP
ejpam-6142	690	35	2008	2008	NUM
ejpam-6142	690	36	to	to	ADP
ejpam-6142	690	37	2021	2021	NUM
ejpam-6142	690	38	.	.	PUNCT
ejpam-6142	691	1	math	math	PROPN
ejpam-6142	691	2	biosci	biosci	PROPN
ejpam-6142	691	3	eng	eng	PROPN
ejpam-6142	691	4	,	,	PUNCT
ejpam-6142	691	5	20(12):20770–20794	20(12):20770–20794	NUM
ejpam-6142	691	6	,	,	PUNCT
ejpam-6142	691	7	2023	2023	NUM
ejpam-6142	691	8	.	.	PUNCT
ejpam-6142	692	1	[	[	X
ejpam-6142	692	2	18	18	NUM
ejpam-6142	692	3	]	]	PUNCT
ejpam-6142	692	4	kumama	kumama	NOUN
ejpam-6142	692	5	regassa	regassa	NOUN
ejpam-6142	692	6	cheneke	cheneke	ADJ
ejpam-6142	692	7	,	,	PUNCT
ejpam-6142	692	8	koya	koya	PROPN
ejpam-6142	692	9	purnachandra	purnachandra	PROPN
ejpam-6142	692	10	rao	rao	PROPN
ejpam-6142	692	11	,	,	PUNCT
ejpam-6142	692	12	and	and	CCONJ
ejpam-6142	692	13	geremew	geremew	PROPN
ejpam-6142	692	14	kenassa	kenassa	VERB
ejpam-6142	692	15	edessa	edessa	NOUN
ejpam-6142	692	16	.	.	PUNCT
ejpam-6142	693	1	bifurcation	bifurcation	NOUN
ejpam-6142	693	2	and	and	CCONJ
ejpam-6142	693	3	stabillity	stabillity	NOUN
ejpam-6142	693	4	analysis	analysis	NOUN
ejpam-6142	693	5	of	of	ADP
ejpam-6142	693	6	hiv	hiv	PROPN
ejpam-6142	693	7	transmission	transmission	NOUN
ejpam-6142	693	8	model	model	NOUN
ejpam-6142	693	9	with	with	ADP
ejpam-6142	693	10	optimal	optimal	ADJ
ejpam-6142	693	11	control	control	NOUN
ejpam-6142	693	12	.	.	PUNCT
ejpam-6142	694	1	journal	journal	NOUN
ejpam-6142	694	2	of	of	ADP
ejpam-6142	694	3	mathematics	mathematic	NOUN
ejpam-6142	694	4	,	,	PUNCT
ejpam-6142	694	5	2021(1):7471290	2021(1):7471290	NUM
ejpam-6142	694	6	,	,	PUNCT
ejpam-6142	694	7	2021	2021	NUM
ejpam-6142	694	8	.	.	PUNCT
ejpam-6142	695	1	[	[	X
ejpam-6142	695	2	19	19	NUM
ejpam-6142	695	3	]	]	X
ejpam-6142	695	4	dm	dm	X
ejpam-6142	695	5	bortz	bortz	NOUN
ejpam-6142	695	6	and	and	CCONJ
ejpam-6142	695	7	pw	pw	PROPN
ejpam-6142	695	8	nelson	nelson	PROPN
ejpam-6142	695	9	.	.	PUNCT
ejpam-6142	696	1	sensitivity	sensitivity	NOUN
ejpam-6142	696	2	analysis	analysis	NOUN
ejpam-6142	696	3	of	of	ADP
ejpam-6142	696	4	a	a	DET
ejpam-6142	696	5	nonlinear	nonlinear	NOUN
ejpam-6142	696	6	lumped	lump	VERB
ejpam-6142	696	7	parameter	parameter	NOUN
ejpam-6142	696	8	model	model	NOUN
ejpam-6142	696	9	of	of	ADP
ejpam-6142	696	10	hiv	hiv	PROPN
ejpam-6142	696	11	infection	infection	NOUN
ejpam-6142	696	12	dynamics	dynamic	NOUN
ejpam-6142	696	13	.	.	PUNCT
ejpam-6142	697	1	bulletin	bulletin	NOUN
ejpam-6142	697	2	of	of	ADP
ejpam-6142	697	3	mathematical	mathematical	ADJ
ejpam-6142	697	4	biology	biology	NOUN
ejpam-6142	697	5	,	,	PUNCT
ejpam-6142	697	6	66:1009–1026	66:1009–1026	PROPN
ejpam-6142	697	7	,	,	PUNCT
ejpam-6142	697	8	2004	2004	NUM
ejpam-6142	697	9	.	.	PUNCT
ejpam-6142	698	1	[	[	X
ejpam-6142	698	2	20	20	NUM
ejpam-6142	698	3	]	]	X
ejpam-6142	698	4	marjono	marjono	PROPN
ejpam-6142	698	5	marsudi	marsudi	PROPN
ejpam-6142	698	6	and	and	CCONJ
ejpam-6142	698	7	ari	ari	PROPN
ejpam-6142	698	8	andari	andari	PROPN
ejpam-6142	698	9	.	.	PUNCT
ejpam-6142	699	1	sensitivity	sensitivity	NOUN
ejpam-6142	699	2	analysis	analysis	NOUN
ejpam-6142	699	3	of	of	ADP
ejpam-6142	699	4	effect	effect	NOUN
ejpam-6142	699	5	of	of	ADP
ejpam-6142	699	6	screening	screening	NOUN
ejpam-6142	699	7	and	and	CCONJ
ejpam-6142	699	8	hiv	hiv	PROPN
ejpam-6142	699	9	therapy	therapy	NOUN
ejpam-6142	699	10	on	on	ADP
ejpam-6142	699	11	the	the	DET
ejpam-6142	699	12	dynamics	dynamic	NOUN
ejpam-6142	699	13	of	of	ADP
ejpam-6142	699	14	spread	spread	NOUN
ejpam-6142	699	15	of	of	ADP
ejpam-6142	699	16	hiv	hiv	PROPN
ejpam-6142	699	17	.	.	PUNCT
ejpam-6142	700	1	applied	apply	VERB
ejpam-6142	700	2	mathematical	mathematical	ADJ
ejpam-6142	700	3	sciences	sciences	PROPN
ejpam-6142	700	4	,	,	PUNCT
ejpam-6142	700	5	8(155):7749–7763	8(155):7749–7763	NUM
ejpam-6142	700	6	,	,	PUNCT
ejpam-6142	700	7	2014	2014	NUM
ejpam-6142	700	8	.	.	PUNCT
ejpam-6142	701	1	[	[	X
ejpam-6142	701	2	21	21	NUM
ejpam-6142	701	3	]	]	X
ejpam-6142	701	4	honar	honar	PROPN
ejpam-6142	701	5	j	j	PROPN
ejpam-6142	701	6	hamad	hamad	PROPN
ejpam-6142	701	7	,	,	PUNCT
ejpam-6142	701	8	sarbaz	sarbaz	PROPN
ejpam-6142	701	9	ha	ha	INTJ
ejpam-6142	701	10	khoshnaw	khoshnaw	NOUN
ejpam-6142	701	11	,	,	PUNCT
ejpam-6142	701	12	and	and	CCONJ
ejpam-6142	701	13	muhammad	muhammad	PROPN
ejpam-6142	701	14	shahzad	shahzad	PROPN
ejpam-6142	701	15	.	.	PUNCT
ejpam-6142	702	1	model	model	NOUN
ejpam-6142	702	2	analysis	analysis	NOUN
ejpam-6142	702	3	for	for	ADP
ejpam-6142	702	4	an	an	DET
ejpam-6142	702	5	hiv	hiv	PROPN
ejpam-6142	702	6	infectious	infectious	ADJ
ejpam-6142	702	7	disease	disease	NOUN
ejpam-6142	702	8	using	use	VERB
ejpam-6142	702	9	elasticity	elasticity	NOUN
ejpam-6142	702	10	and	and	CCONJ
ejpam-6142	702	11	sensitivity	sensitivity	NOUN
ejpam-6142	702	12	techniques	technique	NOUN
ejpam-6142	702	13	.	.	PUNCT
ejpam-6142	703	1	aims	aim	VERB
ejpam-6142	703	2	bioengineering	bioengineering	NOUN
ejpam-6142	703	3	,	,	PUNCT
ejpam-6142	703	4	11(3):281–300	11(3):281–300	NUM
ejpam-6142	703	5	,	,	PUNCT
ejpam-6142	703	6	2024	2024	NUM
ejpam-6142	703	7	.	.	PUNCT
ejpam-6142	704	1	[	[	X
ejpam-6142	704	2	22	22	NUM
ejpam-6142	704	3	]	]	X
ejpam-6142	704	4	augustine	augustine	PROPN
ejpam-6142	704	5	s	s	PART
ejpam-6142	704	6	mbitila	mbitila	PROPN
ejpam-6142	704	7	and	and	CCONJ
ejpam-6142	704	8	jean	jean	PROPN
ejpam-6142	704	9	m	m	PROPN
ejpam-6142	704	10	tchuenche	tchuenche	PROPN
ejpam-6142	704	11	.	.	PUNCT
ejpam-6142	705	1	hiv	hiv	PROPN
ejpam-6142	705	2	/	/	SYM
ejpam-6142	705	3	aids	aids	PROPN
ejpam-6142	705	4	model	model	NOUN
ejpam-6142	705	5	with	with	ADP
ejpam-6142	705	6	early	early	ADJ
ejpam-6142	705	7	detection	detection	NOUN
ejpam-6142	705	8	and	and	CCONJ
ejpam-6142	705	9	treatment	treatment	NOUN
ejpam-6142	705	10	.	.	PUNCT
ejpam-6142	706	1	international	international	ADJ
ejpam-6142	706	2	scholarly	scholarly	ADJ
ejpam-6142	706	3	research	research	NOUN
ejpam-6142	706	4	notices	notice	NOUN
ejpam-6142	706	5	,	,	PUNCT
ejpam-6142	706	6	2012(1):185939	2012(1):185939	NUM
ejpam-6142	706	7	,	,	PUNCT
ejpam-6142	706	8	2012	2012	NUM
ejpam-6142	706	9	.	.	PUNCT
ejpam-6142	707	1	[	[	X
ejpam-6142	707	2	23	23	NUM
ejpam-6142	707	3	]	]	X
ejpam-6142	707	4	dipo	dipo	PROPN
ejpam-6142	707	5	aldila	aldila	PROPN
ejpam-6142	707	6	,	,	PUNCT
ejpam-6142	707	7	ranandha	ranandha	VERB
ejpam-6142	707	8	p	p	PROPN
ejpam-6142	707	9	dhanendra	dhanendra	NOUN
ejpam-6142	707	10	,	,	PUNCT
ejpam-6142	707	11	sarbaz	sarbaz	NOUN
ejpam-6142	707	12	ha	ha	INTJ
ejpam-6142	707	13	khoshnaw	khoshnaw	PROPN
ejpam-6142	707	14	,	,	PUNCT
ejpam-6142	707	15	juni	juni	PROPN
ejpam-6142	707	16	wijayanti	wijayanti	VERB
ejpam-6142	707	17	puspita	puspita	PROPN
ejpam-6142	707	18	,	,	PUNCT
ejpam-6142	707	19	putri	putri	PROPN
ejpam-6142	707	20	zahra	zahra	PROPN
ejpam-6142	707	21	kamalia	kamalia	PROPN
ejpam-6142	707	22	,	,	PUNCT
ejpam-6142	707	23	and	and	CCONJ
ejpam-6142	707	24	muhammad	muhammad	PROPN
ejpam-6142	707	25	shahzad	shahzad	PROPN
ejpam-6142	707	26	.	.	PUNCT
ejpam-6142	708	1	understanding	understand	VERB
ejpam-6142	708	2	hiv	hiv	PROPN
ejpam-6142	708	3	/	/	SYM
ejpam-6142	708	4	aids	aids	PROPN
ejpam-6142	708	5	dynamics	dynamic	NOUN
ejpam-6142	708	6	:	:	PUNCT
ejpam-6142	708	7	insights	insight	NOUN
ejpam-6142	708	8	from	from	ADP
ejpam-6142	708	9	cd4	cd4	PROPN
ejpam-6142	708	10	+	+	PROPN
ejpam-6142	708	11	t	t	NOUN
ejpam-6142	708	12	cells	cell	NOUN
ejpam-6142	708	13	,	,	PUNCT
ejpam-6142	708	14	antiretroviral	antiretroviral	ADJ
ejpam-6142	708	15	treatment	treatment	NOUN
ejpam-6142	708	16	,	,	PUNCT
ejpam-6142	708	17	and	and	CCONJ
ejpam-6142	708	18	country	country	NOUN
ejpam-6142	708	19	-	-	PUNCT
ejpam-6142	708	20	specific	specific	ADJ
ejpam-6142	708	21	analysis	analysis	NOUN
ejpam-6142	708	22	.	.	PUNCT
ejpam-6142	709	1	frontiers	frontier	NOUN
ejpam-6142	709	2	in	in	ADP
ejpam-6142	709	3	public	public	ADJ
ejpam-6142	709	4	health	health	NOUN
ejpam-6142	709	5	,	,	PUNCT
ejpam-6142	709	6	12:1324858	12:1324858	PRON
ejpam-6142	709	7	,	,	PUNCT
ejpam-6142	709	8	2024	2024	NUM
ejpam-6142	709	9	.	.	PUNCT
ejpam-6142	710	1	[	[	X
ejpam-6142	710	2	24	24	NUM
ejpam-6142	710	3	]	]	PUNCT
ejpam-6142	710	4	who	who	PRON
ejpam-6142	710	5	/	/	SYM
ejpam-6142	710	6	unaids	unaid	NOUN
ejpam-6142	710	7	.	.	PUNCT
ejpam-6142	710	8	unaids	unaid	NOUN
ejpam-6142	710	9	report	report	VERB
ejpam-6142	710	10	on	on	ADP
ejpam-6142	710	11	the	the	DET
ejpam-6142	710	12	global	global	ADJ
ejpam-6142	710	13	aids	aids	PROPN
ejpam-6142	710	14	epidemic	epidemic	PROPN
ejpam-6142	710	15	2010	2010	NUM
ejpam-6142	710	16	.	.	PUNCT
ejpam-6142	711	1	unaids/10.11e	unaids/10.11e	PROPN
ejpam-6142	711	2	jc1958e,2010	jc1958e,2010	PROPN
ejpam-6142	711	3	,	,	PUNCT
ejpam-6142	711	4	2010	2010	NUM
ejpam-6142	711	5	.	.	PUNCT
ejpam-6142	712	1	[	[	X
ejpam-6142	712	2	25	25	NUM
ejpam-6142	712	3	]	]	X
ejpam-6142	712	4	z	z	NOUN
ejpam-6142	712	5	mukandavire	mukandavire	NOUN
ejpam-6142	712	6	and	and	CCONJ
ejpam-6142	712	7	w	w	PROPN
ejpam-6142	712	8	garira	garira	PROPN
ejpam-6142	712	9	.	.	PUNCT
ejpam-6142	713	1	sex	sex	NOUN
ejpam-6142	713	2	-	-	PUNCT
ejpam-6142	713	3	structured	structure	VERB
ejpam-6142	713	4	hiv	hiv	PROPN
ejpam-6142	713	5	/	/	SYM
ejpam-6142	713	6	aids	aids	PROPN
ejpam-6142	713	7	model	model	NOUN
ejpam-6142	713	8	to	to	PART
ejpam-6142	713	9	analyse	analyse	VERB
ejpam-6142	713	10	the	the	DET
ejpam-6142	713	11	effects	effect	NOUN
ejpam-6142	713	12	of	of	ADP
ejpam-6142	713	13	condom	condom	NOUN
ejpam-6142	713	14	use	use	NOUN
ejpam-6142	713	15	with	with	ADP
ejpam-6142	713	16	application	application	NOUN
ejpam-6142	713	17	to	to	ADP
ejpam-6142	713	18	zimbabwe	zimbabwe	PROPN
ejpam-6142	713	19	.	.	PUNCT
ejpam-6142	714	1	journal	journal	PROPN
ejpam-6142	714	2	of	of	ADP
ejpam-6142	714	3	mathematical	mathematical	ADJ
ejpam-6142	714	4	biology	biology	NOUN
ejpam-6142	714	5	,	,	PUNCT
ejpam-6142	714	6	54(5):669–699	54(5):669–699	NOUN
ejpam-6142	714	7	,	,	PUNCT
ejpam-6142	714	8	2007	2007	NUM
ejpam-6142	714	9	.	.	PUNCT
ejpam-6142	715	1	[	[	X
ejpam-6142	715	2	26	26	NUM
ejpam-6142	715	3	]	]	X
ejpam-6142	715	4	lev	lev	NOUN
ejpam-6142	715	5	semenovich	semenovich	PROPN
ejpam-6142	715	6	pontryagin	pontryagin	NOUN
ejpam-6142	715	7	.	.	PUNCT
ejpam-6142	716	1	mathematical	mathematical	ADJ
ejpam-6142	716	2	theory	theory	NOUN
ejpam-6142	716	3	of	of	ADP
ejpam-6142	716	4	optimal	optimal	ADJ
ejpam-6142	716	5	processes	process	NOUN
ejpam-6142	716	6	.	.	PUNCT
ejpam-6142	717	1	routledge	routledge	PROPN
ejpam-6142	717	2	,	,	PUNCT
ejpam-6142	717	3	2018	2018	NUM
ejpam-6142	717	4	.	.	PUNCT
ejpam-6142	718	1	[	[	X
ejpam-6142	718	2	27	27	NUM
ejpam-6142	718	3	]	]	X
ejpam-6142	718	4	tigabu	tigabu	PROPN
ejpam-6142	718	5	kasia	kasia	PROPN
ejpam-6142	718	6	ayele	ayele	PROPN
ejpam-6142	718	7	,	,	PUNCT
ejpam-6142	718	8	emile	emile	PROPN
ejpam-6142	718	9	franc	franc	PROPN
ejpam-6142	718	10	doungmo	doungmo	PROPN
ejpam-6142	718	11	goufo	goufo	PROPN
ejpam-6142	718	12	,	,	PUNCT
ejpam-6142	718	13	and	and	CCONJ
ejpam-6142	718	14	stella	stella	PROPN
ejpam-6142	718	15	mugisha	mugisha	PROPN
ejpam-6142	718	16	.	.	PUNCT
ejpam-6142	719	1	mathematical	mathematical	ADJ
ejpam-6142	719	2	modeling	modeling	NOUN
ejpam-6142	719	3	of	of	ADP
ejpam-6142	719	4	hiv	hiv	PROPN
ejpam-6142	719	5	/	/	SYM
ejpam-6142	719	6	aids	aids	PROPN
ejpam-6142	719	7	with	with	ADP
ejpam-6142	719	8	optimal	optimal	ADJ
ejpam-6142	719	9	control	control	NOUN
ejpam-6142	719	10	:	:	PUNCT
ejpam-6142	719	11	a	a	DET
ejpam-6142	719	12	case	case	NOUN
ejpam-6142	719	13	study	study	NOUN
ejpam-6142	719	14	in	in	ADP
ejpam-6142	719	15	ethiopia	ethiopia	PROPN
ejpam-6142	719	16	.	.	PUNCT
ejpam-6142	720	1	results	result	NOUN
ejpam-6142	720	2	in	in	ADP
ejpam-6142	720	3	physics	physics	NOUN
ejpam-6142	720	4	,	,	PUNCT
ejpam-6142	720	5	26:104263	26:104263	NUM
ejpam-6142	720	6	,	,	PUNCT
ejpam-6142	720	7	2021	2021	NUM
ejpam-6142	720	8	.	.	PUNCT