id	sid	tid	token	lemma	pos
ma-248	1	1	2024	2024	NUM
ma-248	1	2	ada	ada	PROPN
ma-248	1	3	academica	academica	PROPN
ma-248	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-248	1	5	.	.	PUNCT
ma-248	2	1	j.	j.	PROPN
ma-248	2	2	math	math	PROPN
ma-248	2	3	.	.	PUNCT
ma-248	3	1	anal	anal	ADJ
ma-248	3	2	.	.	PUNCT
ma-248	4	1	4	4	NUM
ma-248	4	2	(	(	PUNCT
ma-248	4	3	2024	2024	NUM
ma-248	4	4	)	)	PUNCT
ma-248	4	5	21doi	21doi	NOUN
ma-248	4	6	:	:	PUNCT
ma-248	4	7	10.28924	10.28924	NUM
ma-248	4	8	/	/	SYM
ma-248	4	9	ada	ada	PROPN
ma-248	4	10	/	/	SYM
ma-248	4	11	ma.4.21	ma.4.21	PROPN
ma-248	4	12	global	global	ADJ
ma-248	4	13	analysis	analysis	NOUN
ma-248	4	14	of	of	ADP
ma-248	4	15	meningitis	meningitis	NOUN
ma-248	4	16	disease	disease	NOUN
ma-248	4	17	with	with	ADP
ma-248	4	18	optimal	optimal	ADJ
ma-248	4	19	control	control	NOUN
ma-248	4	20	kwame	kwame	PROPN
ma-248	4	21	kyei	kyei	PROPN
ma-248	4	22	danquah1	danquah1	PROPN
ma-248	4	23	,	,	PUNCT
ma-248	4	24	sampson	sampson	PROPN
ma-248	4	25	takyi	takyi	PROPN
ma-248	4	26	appiah1	appiah1	PROPN
ma-248	4	27	,	,	PUNCT
ma-248	4	28	baaba	baaba	PROPN
ma-248	4	29	a.	a.	PROPN
ma-248	4	30	danquah1,bernard	danquah1,bernard	PROPN
ma-248	5	1	asamoah	asamoah	PROPN
ma-248	5	2	afful2,∗	afful2,∗	PROPN
ma-248	5	3	,	,	PUNCT
ma-248	5	4	godfred	godfred	PROPN
ma-248	5	5	agyemang	agyemang	PROPN
ma-248	5	6	safo3	safo3	PROPN
ma-248	6	1	1department	1department	NUM
ma-248	6	2	of	of	ADP
ma-248	6	3	mathematics	mathematic	NOUN
ma-248	6	4	and	and	CCONJ
ma-248	6	5	statistics	statistic	NOUN
ma-248	6	6	,	,	PUNCT
ma-248	6	7	university	university	NOUN
ma-248	6	8	of	of	ADP
ma-248	6	9	energy	energy	NOUN
ma-248	6	10	and	and	CCONJ
ma-248	6	11	natural	natural	ADJ
ma-248	6	12	resources	resource	NOUN
ma-248	6	13	,	,	PUNCT
ma-248	6	14	ghana	ghana	PROPN
ma-248	6	15	afriyiedanquah1@gmail.com	afriyiedanquah1@gmail.com	PROPN
ma-248	6	16	,	,	PUNCT
ma-248	6	17	sampson.appiah@uenr.edu.gh	sampson.appiah@uenr.edu.gh	PROPN
ma-248	6	18	,	,	PUNCT
ma-248	6	19	baaba.ghansah@uenr.edu.gh	baaba.ghansah@uenr.edu.gh	NOUN
ma-248	7	1	2department	2department	NUM
ma-248	7	2	of	of	ADP
ma-248	7	3	mathematics	mathematic	NOUN
ma-248	7	4	and	and	CCONJ
ma-248	7	5	statistics	statistic	NOUN
ma-248	7	6	,	,	PUNCT
ma-248	7	7	utah	utah	PROPN
ma-248	7	8	state	state	PROPN
ma-248	7	9	university	university	PROPN
ma-248	7	10	,	,	PUNCT
ma-248	7	11	logan	logan	PROPN
ma-248	7	12	,	,	PUNCT
ma-248	7	13	ut	ut	PROPN
ma-248	7	14	,	,	PUNCT
ma-248	7	15	usa	usa	PROPN
ma-248	7	16	bernard.afful@usu.edu	bernard.afful@usu.edu	PROPN
ma-248	7	17	3english	3english	NUM
ma-248	7	18	international	international	ADJ
ma-248	7	19	school	school	NOUN
ma-248	7	20	of	of	ADP
ma-248	7	21	bratislava	bratislava	PROPN
ma-248	7	22	,	,	PUNCT
ma-248	7	23	radničné	radničné	VERB
ma-248	7	24	námestie	námestie	PROPN
ma-248	7	25	4	4	NUM
ma-248	7	26	,	,	PUNCT
ma-248	7	27	bratislava	bratislava	PROPN
ma-248	7	28	,	,	PUNCT
ma-248	7	29	slovakia	slovakia	PROPN
ma-248	7	30	wisegas98@gmail.com	wisegas98@gmail.com	X
ma-248	8	1	∗correspondence	∗correspondence	NOUN
ma-248	8	2	:	:	PUNCT
ma-248	8	3	bernard.afful@usu.edu	bernard.afful@usu.edu	NOUN
ma-248	8	4	abstract	abstract	NOUN
ma-248	8	5	.	.	PUNCT
ma-248	9	1	the	the	DET
ma-248	9	2	meningitis	meningitis	NOUN
ma-248	9	3	epidemic	epidemic	NOUN
ma-248	9	4	has	have	AUX
ma-248	9	5	impacted	impact	VERB
ma-248	9	6	lives	life	NOUN
ma-248	9	7	negatively	negatively	ADV
ma-248	9	8	,	,	PUNCT
ma-248	9	9	especially	especially	ADV
ma-248	9	10	in	in	ADP
ma-248	9	11	sub	sub	ADJ
ma-248	9	12	-	-	ADJ
ma-248	9	13	sahara	sahara	ADJ
ma-248	9	14	africa	africa	PROPN
ma-248	9	15	,	,	PUNCT
ma-248	9	16	dubbed	dub	VERB
ma-248	9	17	the	the	DET
ma-248	9	18	‘	'	PUNCT
ma-248	9	19	meningitis	meningitis	NOUN
ma-248	9	20	belt	belt	NOUN
ma-248	9	21	’	'	PUNCT
ma-248	9	22	.	.	PUNCT
ma-248	10	1	the	the	DET
ma-248	10	2	epidemic	epidemic	NOUN
ma-248	10	3	has	have	AUX
ma-248	10	4	been	be	AUX
ma-248	10	5	a	a	DET
ma-248	10	6	public	public	ADJ
ma-248	10	7	health	health	NOUN
ma-248	10	8	concern	concern	NOUN
ma-248	10	9	due	due	ADP
ma-248	10	10	to	to	ADP
ma-248	10	11	an	an	DET
ma-248	10	12	improperunderstanding	improperunderstanding	NOUN
ma-248	10	13	of	of	ADP
ma-248	10	14	the	the	DET
ma-248	10	15	disease	disease	NOUN
ma-248	10	16	’s	’s	PART
ma-248	10	17	dynamics	dynamic	NOUN
ma-248	10	18	.	.	PUNCT
ma-248	11	1	to	to	PART
ma-248	11	2	implement	implement	VERB
ma-248	11	3	a	a	DET
ma-248	11	4	control	control	NOUN
ma-248	11	5	measure	measure	NOUN
ma-248	11	6	that	that	PRON
ma-248	11	7	will	will	AUX
ma-248	11	8	help	help	VERB
ma-248	11	9	minimize	minimize	VERB
ma-248	11	10	theepidemic	theepidemic	ADJ
ma-248	11	11	,	,	PUNCT
ma-248	11	12	we	we	PRON
ma-248	11	13	introduce	introduce	VERB
ma-248	11	14	a	a	DET
ma-248	11	15	non	non	ADJ
ma-248	11	16	-	-	ADJ
ma-248	11	17	linear	linear	ADJ
ma-248	11	18	meningitis	meningitis	NOUN
ma-248	11	19	model	model	NOUN
ma-248	11	20	that	that	PRON
ma-248	11	21	describes	describe	VERB
ma-248	11	22	the	the	DET
ma-248	11	23	dynamic	dynamic	ADJ
ma-248	11	24	behaviour	behaviour	NOUN
ma-248	11	25	of	of	ADP
ma-248	11	26	thedisease	thedisease	PROPN
ma-248	11	27	and	and	CCONJ
ma-248	11	28	explains	explain	VERB
ma-248	11	29	the	the	DET
ma-248	11	30	transmission	transmission	NOUN
ma-248	11	31	trend	trend	NOUN
ma-248	11	32	.	.	PUNCT
ma-248	12	1	the	the	DET
ma-248	12	2	model	model	NOUN
ma-248	12	3	explores	explore	VERB
ma-248	12	4	the	the	DET
ma-248	12	5	condition	condition	NOUN
ma-248	12	6	that	that	PRON
ma-248	12	7	leads	lead	VERB
ma-248	12	8	to	to	ADP
ma-248	12	9	local	local	ADJ
ma-248	12	10	orglobal	orglobal	ADJ
ma-248	12	11	asymptomatic	asymptomatic	ADJ
ma-248	12	12	stability	stability	NOUN
ma-248	12	13	of	of	ADP
ma-248	12	14	the	the	DET
ma-248	12	15	equilibria	equilibrium	NOUN
ma-248	12	16	.	.	PUNCT
ma-248	13	1	the	the	DET
ma-248	13	2	model	model	NOUN
ma-248	13	3	is	be	AUX
ma-248	13	4	subjected	subject	VERB
ma-248	13	5	to	to	ADP
ma-248	13	6	a	a	DET
ma-248	13	7	sensitivity	sensitivity	NOUN
ma-248	13	8	analysis	analysis	NOUN
ma-248	13	9	to	to	ADP
ma-248	13	10	findthe	findthe	DET
ma-248	13	11	parameters	parameter	NOUN
ma-248	13	12	that	that	PRON
ma-248	13	13	influence	influence	VERB
ma-248	13	14	the	the	DET
ma-248	13	15	r0	r0	NOUN
ma-248	13	16	.	.	PUNCT
ma-248	14	1	the	the	DET
ma-248	14	2	model	model	NOUN
ma-248	14	3	is	be	AUX
ma-248	14	4	modified	modify	VERB
ma-248	14	5	into	into	ADP
ma-248	14	6	an	an	DET
ma-248	14	7	optimal	optimal	ADJ
ma-248	14	8	control	control	NOUN
ma-248	14	9	by	by	ADP
ma-248	14	10	adding	add	VERB
ma-248	14	11	time	time	NOUN
ma-248	14	12	-	-	PUNCT
ma-248	14	13	dependent	dependent	ADJ
ma-248	14	14	controls	control	NOUN
ma-248	14	15	.	.	PUNCT
ma-248	15	1	the	the	DET
ma-248	15	2	control	control	NOUN
ma-248	15	3	model	model	NOUN
ma-248	15	4	is	be	AUX
ma-248	15	5	solved	solve	VERB
ma-248	15	6	qualitatively	qualitatively	ADV
ma-248	15	7	using	use	VERB
ma-248	15	8	pontryagin	pontryagin	NOUN
ma-248	15	9	’s	’s	PART
ma-248	15	10	maximum	maximum	ADJ
ma-248	15	11	principleand	principleand	NOUN
ma-248	15	12	numerically	numerically	ADV
ma-248	15	13	using	use	VERB
ma-248	15	14	matlab	matlab	PROPN
ma-248	15	15	and	and	CCONJ
ma-248	15	16	the	the	DET
ma-248	15	17	fourth	fourth	ADJ
ma-248	15	18	-	-	PUNCT
ma-248	15	19	order	order	NOUN
ma-248	15	20	runge	runge	NOUN
ma-248	15	21	-	-	PUNCT
ma-248	15	22	kutta	kutta	NOUN
ma-248	15	23	method	method	NOUN
ma-248	15	24	.	.	PUNCT
ma-248	16	1	we	we	PRON
ma-248	16	2	provide	provide	VERB
ma-248	16	3	a	a	DET
ma-248	16	4	controlstrategy	controlstrategy	NOUN
ma-248	16	5	that	that	PRON
ma-248	16	6	can	can	AUX
ma-248	16	7	be	be	AUX
ma-248	16	8	relied	rely	VERB
ma-248	16	9	on	on	ADP
ma-248	16	10	for	for	ADP
ma-248	16	11	management	management	NOUN
ma-248	16	12	decision	decision	NOUN
ma-248	16	13	-	-	PUNCT
ma-248	16	14	making	making	NOUN
ma-248	16	15	based	base	VERB
ma-248	16	16	on	on	ADP
ma-248	16	17	the	the	DET
ma-248	16	18	results	result	NOUN
ma-248	16	19	.	.	PUNCT
ma-248	17	1	1	1	X
ma-248	17	2	.	.	X
ma-248	17	3	introduction	introduction	NOUN
ma-248	17	4	meningitis	meningitis	PROPN
ma-248	17	5	,	,	PUNCT
ma-248	17	6	a	a	DET
ma-248	17	7	deadly	deadly	ADJ
ma-248	17	8	bacterial	bacterial	ADJ
ma-248	17	9	infection	infection	NOUN
ma-248	17	10	,	,	PUNCT
ma-248	17	11	is	be	AUX
ma-248	17	12	primarily	primarily	ADV
ma-248	17	13	attributed	attribute	VERB
ma-248	17	14	to	to	ADP
ma-248	17	15	meningococcal	meningococcal	ADJ
ma-248	17	16	meningitis.meningitis	meningitis.meningitis	PROPN
ma-248	17	17	kills	kill	NOUN
ma-248	17	18	over	over	ADP
ma-248	17	19	100,000	100,000	NUM
ma-248	17	20	individuals	individual	NOUN
ma-248	17	21	each	each	DET
ma-248	17	22	year	year	NOUN
ma-248	17	23	and	and	CCONJ
ma-248	17	24	affects	affect	VERB
ma-248	17	25	1.2	1.2	NUM
ma-248	17	26	million	million	NUM
ma-248	17	27	people	people	NOUN
ma-248	17	28	from	from	ADP
ma-248	17	29	all	all	ADV
ma-248	17	30	over	over	ADP
ma-248	17	31	theworld	theworld	NOUN
ma-248	17	32	.	.	PUNCT
ma-248	18	1	in	in	ADP
ma-248	18	2	africa	africa	PROPN
ma-248	18	3	,	,	PUNCT
ma-248	18	4	especially	especially	ADV
ma-248	18	5	the	the	DET
ma-248	18	6	sub	sub	ADJ
ma-248	18	7	-	-	ADJ
ma-248	18	8	saharan	saharan	ADJ
ma-248	18	9	africa	africa	PROPN
ma-248	18	10	meningitis	meningitis	PROPN
ma-248	18	11	belt	belt	NOUN
ma-248	18	12	,	,	PUNCT
ma-248	18	13	which	which	PRON
ma-248	18	14	extends	extend	VERB
ma-248	18	15	from	from	ADP
ma-248	18	16	senegal	senegal	ADJ
ma-248	18	17	toethiopia	toethiopia	NOUN
ma-248	18	18	,	,	PUNCT
ma-248	18	19	10,000	10,000	NUM
ma-248	18	20	people	people	NOUN
ma-248	18	21	are	be	AUX
ma-248	18	22	expected	expect	VERB
ma-248	18	23	to	to	PART
ma-248	18	24	die	die	VERB
ma-248	18	25	each	each	DET
ma-248	18	26	year	year	NOUN
ma-248	19	1	[	[	X
ma-248	19	2	2	2	NUM
ma-248	19	3	]	]	PUNCT
ma-248	19	4	.	.	PUNCT
ma-248	20	1	this	this	DET
ma-248	20	2	disease	disease	NOUN
ma-248	20	3	is	be	AUX
ma-248	20	4	widespread	widespread	ADJ
ma-248	20	5	across	across	ADP
ma-248	20	6	sub	sub	ADJ
ma-248	20	7	-	-	ADJ
ma-248	20	8	saharan	saharan	ADJ
ma-248	20	9	africa	africa	PROPN
ma-248	20	10	,	,	PUNCT
ma-248	20	11	stretching	stretch	VERB
ma-248	20	12	from	from	ADP
ma-248	20	13	the	the	DET
ma-248	20	14	meningitis	meningitis	NOUN
ma-248	20	15	belt	belt	NOUN
ma-248	20	16	in	in	ADP
ma-248	20	17	senegal	senegal	NOUN
ma-248	20	18	to	to	ADP
ma-248	20	19	ethiopia	ethiopia	PROPN
ma-248	20	20	.	.	PUNCT
ma-248	21	1	the	the	DET
ma-248	21	2	illness	illness	NOUN
ma-248	21	3	reappears	reappear	VERB
ma-248	21	4	atthe	atthe	ADJ
ma-248	21	5	start	start	NOUN
ma-248	21	6	of	of	ADP
ma-248	21	7	each	each	DET
ma-248	21	8	dry	dry	ADJ
ma-248	21	9	season	season	NOUN
ma-248	21	10	and	and	CCONJ
ma-248	21	11	disappears	disappear	VERB
ma-248	21	12	at	at	ADP
ma-248	21	13	the	the	DET
ma-248	21	14	start	start	NOUN
ma-248	21	15	of	of	ADP
ma-248	21	16	the	the	DET
ma-248	21	17	rainy	rainy	ADJ
ma-248	21	18	season	season	NOUN
ma-248	21	19	in	in	ADP
ma-248	21	20	africa	africa	PROPN
ma-248	21	21	,	,	PUNCT
ma-248	21	22	a	a	DET
ma-248	21	23	fascinatingpattern	fascinatingpattern	NOUN
ma-248	21	24	that	that	SCONJ
ma-248	21	25	warrants	warrant	NOUN
ma-248	21	26	further	further	ADJ
ma-248	21	27	study	study	NOUN
ma-248	21	28	.	.	PUNCT
ma-248	22	1	moreover	moreover	ADV
ma-248	22	2	,	,	PUNCT
ma-248	22	3	from	from	ADP
ma-248	22	4	the	the	DET
ma-248	22	5	year	year	NOUN
ma-248	22	6	2003	2003	NUM
ma-248	22	7	to	to	ADP
ma-248	22	8	2007	2007	NUM
ma-248	22	9	,	,	PUNCT
ma-248	22	10	about	about	ADV
ma-248	22	11	4100	4100	NUM
ma-248	22	12	casesof	casesof	VERB
ma-248	22	13	cerebrospinal	cerebrospinal	ADJ
ma-248	22	14	spinal	spinal	NOUN
ma-248	22	15	meningitis(csm	meningitis(csm	NOUN
ma-248	22	16	)	)	PUNCT
ma-248	22	17	were	be	AUX
ma-248	22	18	confirmed	confirm	VERB
ma-248	22	19	in	in	ADP
ma-248	22	20	the	the	DET
ma-248	22	21	united	united	PROPN
ma-248	22	22	states	states	PROPN
ma-248	22	23	(	(	PUNCT
ma-248	22	24	cdc	cdc	PROPN
ma-248	22	25	,	,	PUNCT
ma-248	22	26	2017	2017	NUM
ma-248	22	27	)	)	PUNCT
ma-248	23	1	[	[	X
ma-248	23	2	3].it	3].it	NUM
ma-248	23	3	is	be	AUX
ma-248	23	4	approximated	approximate	VERB
ma-248	23	5	that	that	SCONJ
ma-248	23	6	during	during	ADP
ma-248	23	7	most	most	ADJ
ma-248	23	8	significant	significant	ADJ
ma-248	23	9	epidemics	epidemic	NOUN
ma-248	23	10	,	,	PUNCT
ma-248	23	11	over	over	ADP
ma-248	23	12	1000	1000	NUM
ma-248	23	13	cases	case	NOUN
ma-248	23	14	of	of	ADP
ma-248	23	15	the	the	DET
ma-248	23	16	disease	disease	NOUN
ma-248	23	17	are	be	AUX
ma-248	23	18	received	receive	VERB
ma-248	23	19	:	:	PUNCT
ma-248	23	20	10	10	NUM
ma-248	23	21	jun	jun	PROPN
ma-248	23	22	2024	2024	NUM
ma-248	23	23	.	.	PUNCT
ma-248	24	1	key	key	ADJ
ma-248	24	2	words	word	NOUN
ma-248	24	3	and	and	CCONJ
ma-248	24	4	phrases	phrase	NOUN
ma-248	24	5	.	.	PUNCT
ma-248	25	1	meningitis	meningiti	NOUN
ma-248	25	2	disease	disease	NOUN
ma-248	25	3	;	;	PUNCT
ma-248	25	4	optimal	optimal	ADJ
ma-248	25	5	control	control	NOUN
ma-248	25	6	;	;	PUNCT
ma-248	25	7	global	global	ADJ
ma-248	25	8	stability	stability	NOUN
ma-248	25	9	;	;	PUNCT
ma-248	25	10	local	local	ADJ
ma-248	25	11	stability	stability	NOUN
ma-248	25	12	;	;	PUNCT
ma-248	25	13	sensitivity	sensitivity	NOUN
ma-248	25	14	analysis.1	analysis.1	PROPN
ma-248	25	15	https://adac.ee	https://adac.ee	PROPN
ma-248	25	16	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	25	17	https://orcid.org/0000-0001-8123-5757	https://orcid.org/0000-0001-8123-5757	PROPN
ma-248	25	18	eur	eur	PROPN
ma-248	25	19	.	.	PUNCT
ma-248	26	1	j.	j.	PROPN
ma-248	26	2	math	math	PROPN
ma-248	26	3	.	.	PUNCT
ma-248	27	1	anal	anal	PROPN
ma-248	27	2	.	.	PUNCT
ma-248	28	1	10.28924	10.28924	NUM
ma-248	28	2	/	/	SYM
ma-248	28	3	ada	ada	PROPN
ma-248	28	4	/	/	SYM
ma-248	28	5	ma.4.21	ma.4.21	NOUN
ma-248	28	6	2reported	2reported	NUM
ma-248	28	7	,	,	PUNCT
ma-248	28	8	typically	typically	ADV
ma-248	28	9	happening	happen	VERB
ma-248	28	10	every	every	DET
ma-248	28	11	5	5	NUM
ma-248	28	12	to	to	PART
ma-248	28	13	12	12	NUM
ma-248	28	14	years	year	NOUN
ma-248	29	1	[	[	X
ma-248	29	2	4	4	NUM
ma-248	29	3	]	]	PUNCT
ma-248	29	4	.	.	PUNCT
ma-248	30	1	the	the	DET
ma-248	30	2	bacteria	bacteria	NOUN
ma-248	30	3	is	be	AUX
ma-248	30	4	transmitted	transmit	VERB
ma-248	30	5	from	from	ADP
ma-248	30	6	infectedindividuals	infectedindividual	NOUN
ma-248	30	7	to	to	ADP
ma-248	30	8	susceptible	susceptible	ADJ
ma-248	30	9	ones	one	NOUN
ma-248	30	10	through	through	ADP
ma-248	30	11	contact	contact	NOUN
ma-248	30	12	with	with	ADP
ma-248	30	13	respiratory	respiratory	ADJ
ma-248	30	14	and	and	CCONJ
ma-248	30	15	throat	throat	NOUN
ma-248	30	16	secretions	secretion	NOUN
ma-248	30	17	like	like	ADP
ma-248	30	18	salivaand	salivaand	NOUN
ma-248	30	19	mucus	mucus	NOUN
ma-248	30	20	.	.	PUNCT
ma-248	31	1	however	however	ADV
ma-248	31	2	,	,	PUNCT
ma-248	31	3	unlike	unlike	ADP
ma-248	31	4	flu	flu	NOUN
ma-248	31	5	and	and	CCONJ
ma-248	31	6	common	common	ADJ
ma-248	31	7	cold	cold	ADJ
ma-248	31	8	viruses	virus	NOUN
ma-248	31	9	,	,	PUNCT
ma-248	31	10	the	the	DET
ma-248	31	11	bacteria	bacteria	NOUN
ma-248	31	12	are	be	AUX
ma-248	31	13	not	not	PART
ma-248	31	14	highly	highly	ADV
ma-248	31	15	contagious	contagious	ADJ
ma-248	31	16	,	,	PUNCT
ma-248	31	17	and	and	CCONJ
ma-248	31	18	it	it	PRON
ma-248	31	19	takes	take	VERB
ma-248	31	20	time	time	NOUN
ma-248	31	21	before	before	SCONJ
ma-248	31	22	transmission	transmission	NOUN
ma-248	31	23	occurs	occur	VERB
ma-248	31	24	.	.	PUNCT
ma-248	32	1	those	those	PRON
ma-248	32	2	at	at	ADP
ma-248	32	3	risk	risk	NOUN
ma-248	32	4	of	of	ADP
ma-248	32	5	contracting	contract	VERB
ma-248	32	6	the	the	DET
ma-248	32	7	disease	disease	NOUN
ma-248	32	8	are	be	AUX
ma-248	32	9	typicallyindividuals	typicallyindividual	NOUN
ma-248	32	10	near	near	ADP
ma-248	32	11	the	the	DET
ma-248	32	12	infected	infected	ADJ
ma-248	32	13	person	person	NOUN
ma-248	32	14	,	,	PUNCT
ma-248	32	15	such	such	ADJ
ma-248	32	16	as	as	ADP
ma-248	32	17	household	household	NOUN
ma-248	32	18	members	member	NOUN
ma-248	32	19	and	and	CCONJ
ma-248	32	20	roommates	roommate	NOUN
ma-248	32	21	[	[	X
ma-248	32	22	5	5	NUM
ma-248	32	23	]	]	PUNCT
ma-248	32	24	.	.	PUNCT
ma-248	33	1	the	the	DET
ma-248	33	2	mostcommon	mostcommon	NOUN
ma-248	33	3	signs	sign	NOUN
ma-248	33	4	of	of	ADP
ma-248	33	5	the	the	DET
ma-248	33	6	disease	disease	NOUN
ma-248	33	7	include	include	VERB
ma-248	33	8	fever	fever	NOUN
ma-248	33	9	,	,	PUNCT
ma-248	33	10	headache	headache	NOUN
ma-248	33	11	and	and	CCONJ
ma-248	33	12	stiffness	stiffness	NOUN
ma-248	33	13	of	of	ADP
ma-248	33	14	the	the	DET
ma-248	33	15	neck	neck	NOUN
ma-248	33	16	.	.	PUNCT
ma-248	34	1	diagnosing	diagnose	VERB
ma-248	34	2	thedisease	thedisease	NOUN
ma-248	34	3	is	be	AUX
ma-248	34	4	sometimes	sometimes	ADV
ma-248	34	5	difficult	difficult	ADJ
ma-248	34	6	since	since	SCONJ
ma-248	34	7	the	the	DET
ma-248	34	8	symptoms	symptom	NOUN
ma-248	34	9	are	be	AUX
ma-248	34	10	often	often	ADV
ma-248	34	11	similar	similar	ADJ
ma-248	34	12	to	to	ADP
ma-248	34	13	other	other	ADJ
ma-248	34	14	diseases	disease	NOUN
ma-248	34	15	[	[	X
ma-248	34	16	6	6	NUM
ma-248	34	17	]	]	PUNCT
ma-248	34	18	.	.	PUNCT
ma-248	35	1	currently	currently	ADV
ma-248	35	2	,	,	PUNCT
ma-248	35	3	a	a	DET
ma-248	35	4	vaccine	vaccine	NOUN
ma-248	35	5	for	for	ADP
ma-248	35	6	meningitis	meningitis	NOUN
ma-248	35	7	exists	exist	VERB
ma-248	35	8	,	,	PUNCT
ma-248	35	9	with	with	SCONJ
ma-248	35	10	the	the	DET
ma-248	35	11	available	available	ADJ
ma-248	35	12	vaccine	vaccine	NOUN
ma-248	35	13	primarily	primarily	ADV
ma-248	35	14	for	for	ADP
ma-248	35	15	bacteria	bacteria	NOUN
ma-248	35	16	such	such	ADJ
ma-248	35	17	as	as	ADP
ma-248	35	18	meningitis.bacterial	meningitis.bacterial	PROPN
ma-248	35	19	meningitis	meningitis	NOUN
ma-248	35	20	is	be	AUX
ma-248	35	21	fatal	fatal	ADJ
ma-248	35	22	when	when	SCONJ
ma-248	35	23	not	not	PART
ma-248	35	24	diagnosed	diagnose	VERB
ma-248	35	25	early	early	ADV
ma-248	35	26	[	[	X
ma-248	35	27	17	17	NUM
ma-248	35	28	]	]	X
ma-248	35	29	.	.	PUNCT
ma-248	36	1	generally	generally	ADV
ma-248	36	2	,	,	PUNCT
ma-248	36	3	infected	infect	VERB
ma-248	36	4	individuals	individual	NOUN
ma-248	36	5	recoverwith	recoverwith	ADP
ma-248	36	6	permanent	permanent	ADJ
ma-248	36	7	disabilities	disability	NOUN
ma-248	36	8	such	such	ADJ
ma-248	36	9	as	as	ADP
ma-248	36	10	hearing	hear	VERB
ma-248	36	11	loss	loss	NOUN
ma-248	36	12	and	and	CCONJ
ma-248	36	13	brain	brain	NOUN
ma-248	36	14	damage	damage	NOUN
ma-248	36	15	.	.	PUNCT
ma-248	37	1	these	these	DET
ma-248	37	2	disabilities	disability	NOUN
ma-248	37	3	and	and	CCONJ
ma-248	37	4	thedisease	thedisease	PROPN
ma-248	37	5	itself	itself	PRON
ma-248	37	6	are	be	AUX
ma-248	37	7	worsened	worsen	VERB
ma-248	37	8	when	when	SCONJ
ma-248	37	9	symptoms	symptom	NOUN
ma-248	37	10	are	be	AUX
ma-248	37	11	not	not	PART
ma-248	37	12	detected	detect	VERB
ma-248	37	13	on	on	ADP
ma-248	37	14	time.meningitis	time.meningitis	PROPN
ma-248	37	15	,	,	PUNCT
ma-248	37	16	a	a	DET
ma-248	37	17	bacterial	bacterial	ADJ
ma-248	37	18	illness	illness	NOUN
ma-248	37	19	,	,	PUNCT
ma-248	37	20	has	have	AUX
ma-248	37	21	been	be	AUX
ma-248	37	22	a	a	DET
ma-248	37	23	global	global	ADJ
ma-248	37	24	concern	concern	NOUN
ma-248	37	25	,	,	PUNCT
ma-248	37	26	affecting	affect	VERB
ma-248	37	27	numerous	numerous	ADJ
ma-248	37	28	parts	part	NOUN
ma-248	37	29	of	of	ADP
ma-248	37	30	the	the	DET
ma-248	37	31	world.the	world.the	DET
ma-248	37	32	disease	disease	NOUN
ma-248	37	33	has	have	AUX
ma-248	37	34	been	be	AUX
ma-248	37	35	endemic	endemic	ADJ
ma-248	37	36	in	in	ADP
ma-248	37	37	several	several	ADJ
ma-248	37	38	areas	area	NOUN
ma-248	37	39	,	,	PUNCT
ma-248	37	40	with	with	ADP
ma-248	37	41	sub	sub	ADJ
ma-248	37	42	-	-	ADJ
ma-248	37	43	saharan	saharan	ADJ
ma-248	37	44	africa	africa	PROPN
ma-248	37	45	being	be	AUX
ma-248	37	46	the	the	DET
ma-248	37	47	hardest	hard	ADJ
ma-248	37	48	hit.since	hit.since	NOUN
ma-248	37	49	its	its	PRON
ma-248	37	50	emergence	emergence	NOUN
ma-248	37	51	,	,	PUNCT
ma-248	37	52	numerous	numerous	ADJ
ma-248	37	53	models	model	NOUN
ma-248	37	54	have	have	AUX
ma-248	37	55	been	be	AUX
ma-248	37	56	developed	develop	VERB
ma-248	37	57	to	to	PART
ma-248	37	58	describe	describe	VERB
ma-248	37	59	the	the	DET
ma-248	37	60	disease	disease	NOUN
ma-248	37	61	’s	’s	PART
ma-248	37	62	transmissionpatterns	transmissionpattern	NOUN
ma-248	37	63	,	,	PUNCT
ma-248	37	64	yet	yet	CCONJ
ma-248	37	65	there	there	PRON
ma-248	37	66	remains	remain	VERB
ma-248	37	67	a	a	DET
ma-248	37	68	need	need	NOUN
ma-248	37	69	for	for	ADP
ma-248	37	70	further	further	ADJ
ma-248	37	71	understanding	understanding	NOUN
ma-248	37	72	of	of	ADP
ma-248	37	73	intervention	intervention	NOUN
ma-248	37	74	strategies	strategy	NOUN
ma-248	37	75	to	to	PART
ma-248	37	76	curb	curb	VERB
ma-248	37	77	thedisease	thedisease	NOUN
ma-248	37	78	in	in	ADP
ma-248	37	79	the	the	DET
ma-248	37	80	meningitis	meningitis	NOUN
ma-248	37	81	belt	belt	NOUN
ma-248	37	82	.	.	PUNCT
ma-248	38	1	in	in	ADP
ma-248	38	2	[	[	X
ma-248	38	3	15	15	NUM
ma-248	38	4	]	]	PUNCT
ma-248	38	5	,	,	PUNCT
ma-248	38	6	and	and	CCONJ
ma-248	38	7	[	[	X
ma-248	38	8	16	16	NUM
ma-248	38	9	]	]	PUNCT
ma-248	38	10	,	,	PUNCT
ma-248	38	11	the	the	DET
ma-248	38	12	dynamical	dynamical	ADJ
ma-248	38	13	behaviour	behaviour	NOUN
ma-248	38	14	of	of	ADP
ma-248	38	15	the	the	DET
ma-248	38	16	meningitis	meningitis	NOUN
ma-248	38	17	diseasewas	diseasewa	VERB
ma-248	38	18	studied	study	VERB
ma-248	38	19	;	;	PUNCT
ma-248	38	20	however	however	ADV
ma-248	38	21	,	,	PUNCT
ma-248	38	22	the	the	DET
ma-248	38	23	study	study	NOUN
ma-248	38	24	failed	fail	VERB
ma-248	38	25	to	to	PART
ma-248	38	26	provide	provide	VERB
ma-248	38	27	enough	enough	ADJ
ma-248	38	28	intervention	intervention	NOUN
ma-248	38	29	and	and	CCONJ
ma-248	38	30	treatment	treatment	NOUN
ma-248	38	31	strategies	strategy	NOUN
ma-248	38	32	tominimize	tominimize	VERB
ma-248	38	33	the	the	DET
ma-248	38	34	disease	disease	NOUN
ma-248	38	35	.	.	PUNCT
ma-248	39	1	against	against	ADP
ma-248	39	2	this	this	DET
ma-248	39	3	background	background	NOUN
ma-248	39	4	,	,	PUNCT
ma-248	39	5	we	we	PRON
ma-248	39	6	propose	propose	VERB
ma-248	39	7	a	a	DET
ma-248	39	8	non	non	ADJ
ma-248	39	9	-	-	ADJ
ma-248	39	10	linear	linear	ADJ
ma-248	39	11	mathematical	mathematical	ADJ
ma-248	39	12	meningitismodel	meningitismodel	NOUN
ma-248	39	13	that	that	PRON
ma-248	39	14	would	would	AUX
ma-248	39	15	analyse	analyse	VERB
ma-248	39	16	the	the	DET
ma-248	39	17	model	model	NOUN
ma-248	39	18	’s	’s	PART
ma-248	39	19	stability	stability	NOUN
ma-248	39	20	and	and	CCONJ
ma-248	39	21	characterize	characterize	VERB
ma-248	39	22	a	a	DET
ma-248	39	23	range	range	NOUN
ma-248	39	24	of	of	ADP
ma-248	39	25	feasible	feasible	ADJ
ma-248	39	26	control	control	NOUN
ma-248	39	27	strategiesthat	strategiesthat	PRON
ma-248	39	28	would	would	AUX
ma-248	39	29	aid	aid	VERB
ma-248	39	30	management	management	NOUN
ma-248	39	31	decision	decision	NOUN
ma-248	39	32	-	-	PUNCT
ma-248	39	33	making	making	NOUN
ma-248	39	34	to	to	PART
ma-248	39	35	curb	curb	VERB
ma-248	39	36	the	the	DET
ma-248	39	37	disease	disease	NOUN
ma-248	39	38	.	.	PUNCT
ma-248	40	1	in	in	ADP
ma-248	40	2	[	[	X
ma-248	40	3	31	31	NUM
ma-248	40	4	]	]	PUNCT
ma-248	40	5	,	,	PUNCT
ma-248	40	6	the	the	DET
ma-248	40	7	transmission	transmission	NOUN
ma-248	40	8	behaviourof	behaviourof	NOUN
ma-248	40	9	a	a	DET
ma-248	40	10	meningitis	meningitis	NOUN
ma-248	40	11	disease	disease	NOUN
ma-248	40	12	is	be	AUX
ma-248	40	13	disclosed	disclose	VERB
ma-248	40	14	using	use	VERB
ma-248	40	15	an	an	DET
ma-248	40	16	age	age	NOUN
ma-248	40	17	-	-	PUNCT
ma-248	40	18	structured	structure	VERB
ma-248	40	19	model	model	NOUN
ma-248	40	20	that	that	PRON
ma-248	40	21	impacts	impact	VERB
ma-248	40	22	the	the	DET
ma-248	40	23	carriers	carrier	NOUN
ma-248	40	24	’	'	PUNCT
ma-248	40	25	input	input	NOUN
ma-248	40	26	tothe	tothe	NOUN
ma-248	40	27	model	model	NOUN
ma-248	40	28	dynamics	dynamic	NOUN
ma-248	40	29	.	.	PUNCT
ma-248	41	1	the	the	DET
ma-248	41	2	transmission	transmission	NOUN
ma-248	41	3	behaviour	behaviour	NOUN
ma-248	41	4	of	of	ADP
ma-248	41	5	a	a	DET
ma-248	41	6	meningitis	meningitis	NOUN
ma-248	41	7	disease	disease	NOUN
ma-248	41	8	is	be	AUX
ma-248	41	9	revealed	reveal	VERB
ma-248	41	10	by	by	ADP
ma-248	41	11	building	build	VERB
ma-248	41	12	anage	anage	NOUN
ma-248	41	13	-	-	PUNCT
ma-248	41	14	structured	structure	VERB
ma-248	41	15	model	model	NOUN
ma-248	41	16	that	that	PRON
ma-248	41	17	affects	affect	VERB
ma-248	41	18	the	the	DET
ma-248	41	19	carriers	carrier	NOUN
ma-248	41	20	’	'	PUNCT
ma-248	41	21	contribution	contribution	NOUN
ma-248	41	22	to	to	ADP
ma-248	41	23	the	the	DET
ma-248	41	24	model	model	NOUN
ma-248	41	25	dynamics	dynamic	NOUN
ma-248	41	26	.	.	PUNCT
ma-248	42	1	[	[	X
ma-248	42	2	32	32	NUM
ma-248	42	3	]	]	PUNCT
ma-248	42	4	formulateda	formulateda	NOUN
ma-248	42	5	compartmental	compartmental	NOUN
ma-248	42	6	meningitis	meningitis	NOUN
ma-248	42	7	model	model	NOUN
ma-248	42	8	that	that	PRON
ma-248	42	9	predicted	predict	VERB
ma-248	42	10	the	the	DET
ma-248	42	11	behavioural	behavioural	ADJ
ma-248	42	12	pattern	pattern	NOUN
ma-248	42	13	of	of	ADP
ma-248	42	14	individuals	individual	NOUN
ma-248	42	15	and	and	CCONJ
ma-248	42	16	thepopulation	thepopulation	NOUN
ma-248	42	17	evolution	evolution	NOUN
ma-248	42	18	by	by	ADP
ma-248	42	19	studying	study	VERB
ma-248	42	20	the	the	DET
ma-248	42	21	dynamic	dynamic	ADJ
ma-248	42	22	trend	trend	NOUN
ma-248	42	23	of	of	ADP
ma-248	42	24	disease	disease	NOUN
ma-248	42	25	transmission	transmission	NOUN
ma-248	42	26	.	.	PUNCT
ma-248	43	1	in	in	ADP
ma-248	43	2	their	their	PRON
ma-248	43	3	study	study	NOUN
ma-248	43	4	,	,	PUNCT
ma-248	43	5	[	[	X
ma-248	43	6	33]studied	33]studie	VERB
ma-248	43	7	the	the	DET
ma-248	43	8	risk	risk	NOUN
ma-248	43	9	factor	factor	NOUN
ma-248	43	10	of	of	ADP
ma-248	43	11	meningitis	meningitis	NOUN
ma-248	43	12	in	in	ADP
ma-248	43	13	adults	adult	NOUN
ma-248	43	14	by	by	ADP
ma-248	43	15	employing	employ	VERB
ma-248	43	16	fuzzy	fuzzy	ADJ
ma-248	43	17	cognitive	cognitive	ADJ
ma-248	43	18	maps	map	NOUN
ma-248	43	19	and	and	CCONJ
ma-248	43	20	multi	multi	NOUN
ma-248	43	21	-	-	ADJ
ma-248	43	22	criteriatechniques	criteriatechnique	NOUN
ma-248	43	23	to	to	PART
ma-248	43	24	determine	determine	VERB
ma-248	43	25	the	the	DET
ma-248	43	26	ranks	rank	NOUN
ma-248	43	27	of	of	ADP
ma-248	43	28	the	the	DET
ma-248	43	29	various	various	ADJ
ma-248	43	30	scenarios	scenario	NOUN
ma-248	43	31	.	.	PUNCT
ma-248	44	1	[	[	X
ma-248	44	2	34	34	NUM
ma-248	44	3	]	]	PUNCT
ma-248	44	4	,	,	PUNCT
ma-248	44	5	determined	determine	VERB
ma-248	44	6	the	the	DET
ma-248	44	7	numerical	numerical	ADJ
ma-248	44	8	solutionof	solutionof	NOUN
ma-248	44	9	the	the	DET
ma-248	44	10	meningitis	meningitis	NOUN
ma-248	44	11	disease	disease	NOUN
ma-248	44	12	by	by	ADP
ma-248	44	13	considering	consider	VERB
ma-248	44	14	the	the	DET
ma-248	44	15	methods	method	NOUN
ma-248	44	16	of	of	ADP
ma-248	44	17	euler	euler	NOUN
ma-248	44	18	,	,	PUNCT
ma-248	44	19	heun	heun	NOUN
ma-248	44	20	,	,	PUNCT
ma-248	44	21	and	and	CCONJ
ma-248	44	22	the	the	DET
ma-248	44	23	fourth	fourth	ADJ
ma-248	44	24	-	-	PUNCT
ma-248	44	25	order	order	NOUN
ma-248	44	26	runge	runge	NOUN
ma-248	44	27	-	-	PUNCT
ma-248	44	28	kutta	kutta	NOUN
ma-248	44	29	.	.	PUNCT
ma-248	45	1	in	in	ADP
ma-248	45	2	[	[	X
ma-248	45	3	35	35	NUM
ma-248	45	4	]	]	PUNCT
ma-248	45	5	,	,	PUNCT
ma-248	45	6	the	the	DET
ma-248	45	7	authors	author	NOUN
ma-248	45	8	created	create	VERB
ma-248	45	9	a	a	DET
ma-248	45	10	mathematical	mathematical	ADJ
ma-248	45	11	model	model	NOUN
ma-248	45	12	to	to	PART
ma-248	45	13	investigate	investigate	VERB
ma-248	45	14	the	the	DET
ma-248	45	15	impact	impact	NOUN
ma-248	45	16	of	of	ADP
ma-248	45	17	sharedinformation	sharedinformation	NOUN
ma-248	45	18	on	on	ADP
ma-248	45	19	the	the	DET
ma-248	45	20	dynamics	dynamic	NOUN
ma-248	45	21	of	of	ADP
ma-248	45	22	meningitis	meningitis	NOUN
ma-248	45	23	disease	disease	NOUN
ma-248	45	24	.	.	PUNCT
ma-248	46	1	the	the	DET
ma-248	46	2	authors	author	NOUN
ma-248	46	3	in	in	ADP
ma-248	46	4	[	[	X
ma-248	46	5	36	36	NUM
ma-248	46	6	]	]	PUNCT
ma-248	46	7	modelled	model	VERB
ma-248	46	8	a	a	DET
ma-248	46	9	co	co	ADJ
ma-248	46	10	-	-	ADJ
ma-248	46	11	infectionmathematical	infectionmathematical	ADJ
ma-248	46	12	model	model	NOUN
ma-248	46	13	of	of	ADP
ma-248	46	14	listeriosis	listeriosis	NOUN
ma-248	46	15	and	and	CCONJ
ma-248	46	16	meningitis	meningitis	NOUN
ma-248	46	17	to	to	PART
ma-248	46	18	unveil	unveil	VERB
ma-248	46	19	the	the	DET
ma-248	46	20	parameters	parameter	NOUN
ma-248	46	21	that	that	PRON
ma-248	46	22	impact	impact	VERB
ma-248	46	23	the	the	DET
ma-248	46	24	dynamicsof	dynamicsof	NOUN
ma-248	46	25	the	the	DET
ma-248	46	26	co	co	NOUN
ma-248	46	27	-	-	NOUN
ma-248	46	28	infection	infection	NOUN
ma-248	46	29	model	model	NOUN
ma-248	46	30	.	.	PUNCT
ma-248	47	1	in	in	ADP
ma-248	47	2	[	[	X
ma-248	47	3	37	37	NUM
ma-248	47	4	]	]	PUNCT
ma-248	47	5	,	,	PUNCT
ma-248	47	6	the	the	DET
ma-248	47	7	authors	author	NOUN
ma-248	47	8	formulated	formulate	VERB
ma-248	47	9	a	a	DET
ma-248	47	10	mathematical	mathematical	ADJ
ma-248	47	11	model	model	NOUN
ma-248	47	12	of	of	ADP
ma-248	47	13	influenza	influenza	NOUN
ma-248	47	14	-	-	PUNCT
ma-248	47	15	meningitis	meningitis	NOUN
ma-248	47	16	co	co	NOUN
ma-248	47	17	-	-	NOUN
ma-248	47	18	infection	infection	NOUN
ma-248	47	19	that	that	PRON
ma-248	47	20	analysed	analyse	VERB
ma-248	47	21	the	the	DET
ma-248	47	22	infected	infect	VERB
ma-248	47	23	’s	’s	PART
ma-248	47	24	outcome	outcome	NOUN
ma-248	47	25	on	on	ADP
ma-248	47	26	the	the	DET
ma-248	47	27	model	model	NOUN
ma-248	47	28	’s	’s	PART
ma-248	47	29	dynamics	dynamic	NOUN
ma-248	47	30	.	.	PUNCT
ma-248	48	1	in	in	ADP
ma-248	48	2	the	the	DET
ma-248	48	3	paperby	paperby	NOUN
ma-248	48	4	[	[	X
ma-248	48	5	39	39	NUM
ma-248	48	6	]	]	PUNCT
ma-248	48	7	,	,	PUNCT
ma-248	48	8	the	the	DET
ma-248	48	9	authors	author	NOUN
ma-248	48	10	looked	look	VERB
ma-248	48	11	at	at	ADP
ma-248	48	12	a	a	DET
ma-248	48	13	mathematical	mathematical	ADJ
ma-248	48	14	model	model	NOUN
ma-248	48	15	of	of	ADP
ma-248	48	16	meningitis	meningitis	PRON
ma-248	48	17	that	that	PRON
ma-248	48	18	attempted	attempt	VERB
ma-248	48	19	to	to	PART
ma-248	48	20	explain	explain	VERB
ma-248	48	21	theinfection	theinfection	NOUN
ma-248	48	22	dynamics	dynamic	NOUN
ma-248	48	23	of	of	ADP
ma-248	48	24	the	the	DET
ma-248	48	25	disease	disease	NOUN
ma-248	48	26	in	in	ADP
ma-248	48	27	jirapa	jirapa	PROPN
ma-248	48	28	district	district	PROPN
ma-248	48	29	,	,	PUNCT
ma-248	48	30	ghana	ghana	PROPN
ma-248	48	31	.	.	PUNCT
ma-248	49	1	to	to	PART
ma-248	49	2	better	well	ADV
ma-248	49	3	understand	understand	VERB
ma-248	49	4	the	the	DET
ma-248	49	5	disease’stransmission	disease’stransmission	NOUN
ma-248	49	6	mechanisms	mechanism	NOUN
ma-248	49	7	,	,	PUNCT
ma-248	49	8	the	the	DET
ma-248	49	9	researchers	researcher	NOUN
ma-248	49	10	in	in	ADP
ma-248	49	11	[	[	X
ma-248	49	12	38	38	NUM
ma-248	49	13	]	]	PUNCT
ma-248	49	14	developed	develop	VERB
ma-248	49	15	a	a	DET
ma-248	49	16	mathematical	mathematical	ADJ
ma-248	49	17	meningitis	meningitis	NOUN
ma-248	49	18	model	model	NOUN
ma-248	49	19	.	.	PUNCT
ma-248	50	1	the	the	DET
ma-248	50	2	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	50	3	eur	eur	PROPN
ma-248	50	4	.	.	PUNCT
ma-248	51	1	j.	j.	PROPN
ma-248	51	2	math	math	PROPN
ma-248	51	3	.	.	PUNCT
ma-248	52	1	anal	anal	PROPN
ma-248	52	2	.	.	PUNCT
ma-248	53	1	10.28924	10.28924	NUM
ma-248	53	2	/	/	SYM
ma-248	53	3	ada	ada	PROPN
ma-248	53	4	/	/	SYM
ma-248	53	5	ma.4.21	ma.4.21	PROPN
ma-248	53	6	3model	3model	NUM
ma-248	53	7	was	be	AUX
ma-248	53	8	subjected	subject	VERB
ma-248	53	9	to	to	ADP
ma-248	53	10	a	a	DET
ma-248	53	11	thorough	thorough	ADJ
ma-248	53	12	stability	stability	NOUN
ma-248	53	13	study	study	NOUN
ma-248	53	14	,	,	PUNCT
ma-248	53	15	with	with	ADP
ma-248	53	16	disease	disease	NOUN
ma-248	53	17	-	-	PUNCT
ma-248	53	18	free	free	ADJ
ma-248	53	19	equilibrium	equilibrium	NOUN
ma-248	53	20	indicating	indicate	VERB
ma-248	53	21	stabilitywhen	stabilitywhen	NOUN
ma-248	53	22	r0	r0	VERB
ma-248	53	23	≤	≤	NUM
ma-248	53	24	1	1	NUM
ma-248	53	25	and	and	CCONJ
ma-248	53	26	endemic	endemic	ADJ
ma-248	53	27	stability	stability	NOUN
ma-248	53	28	when	when	SCONJ
ma-248	53	29	r0	r0	NOUN
ma-248	53	30	≥	≥	NOUN
ma-248	53	31	1.optimal	1.optimal	NUM
ma-248	53	32	controls	control	NOUN
ma-248	53	33	are	be	AUX
ma-248	53	34	extensively	extensively	ADV
ma-248	53	35	used	use	VERB
ma-248	53	36	in	in	ADP
ma-248	53	37	dynamical	dynamical	ADJ
ma-248	53	38	systems	system	NOUN
ma-248	53	39	,	,	PUNCT
ma-248	53	40	specifically	specifically	ADV
ma-248	53	41	those	those	PRON
ma-248	53	42	related	relate	VERB
ma-248	53	43	to	to	ADP
ma-248	53	44	non	non	ADJ
ma-248	53	45	-	-	ADJ
ma-248	53	46	linear	linear	ADJ
ma-248	53	47	ordinary	ordinary	ADJ
ma-248	53	48	differential	differential	ADJ
ma-248	53	49	equations	equation	NOUN
ma-248	53	50	,	,	PUNCT
ma-248	53	51	and	and	CCONJ
ma-248	53	52	perceived	perceive	VERB
ma-248	53	53	as	as	ADP
ma-248	53	54	an	an	DET
ma-248	53	55	intervention	intervention	NOUN
ma-248	53	56	technique	technique	NOUN
ma-248	53	57	within	within	ADP
ma-248	53	58	controltheory	controltheory	NOUN
ma-248	53	59	[	[	X
ma-248	53	60	40–43	40–43	NUM
ma-248	53	61	]	]	PUNCT
ma-248	53	62	.	.	PUNCT
ma-248	54	1	mathematical	mathematical	ADJ
ma-248	54	2	models	model	NOUN
ma-248	54	3	that	that	PRON
ma-248	54	4	involve	involve	VERB
ma-248	54	5	optimal	optimal	ADJ
ma-248	54	6	control	control	NOUN
ma-248	54	7	analysis	analysis	NOUN
ma-248	54	8	are	be	AUX
ma-248	54	9	essential	essential	ADJ
ma-248	54	10	for	for	ADP
ma-248	54	11	un	un	ADJ
ma-248	54	12	-	-	ADJ
ma-248	54	13	derstanding	derstande	VERB
ma-248	54	14	disease	disease	NOUN
ma-248	54	15	spread	spread	VERB
ma-248	54	16	and	and	CCONJ
ma-248	54	17	play	play	VERB
ma-248	54	18	a	a	DET
ma-248	54	19	vital	vital	ADJ
ma-248	54	20	role	role	NOUN
ma-248	54	21	in	in	ADP
ma-248	54	22	the	the	DET
ma-248	54	23	policy	policy	NOUN
ma-248	54	24	-	-	PUNCT
ma-248	54	25	making	make	VERB
ma-248	54	26	process	process	NOUN
ma-248	54	27	concerning	concern	VERB
ma-248	54	28	diseasecontrol	diseasecontrol	NOUN
ma-248	54	29	.	.	PUNCT
ma-248	55	1	the	the	DET
ma-248	55	2	authors	author	NOUN
ma-248	55	3	in	in	ADP
ma-248	55	4	[	[	X
ma-248	55	5	44	44	NUM
ma-248	55	6	]	]	PUNCT
ma-248	55	7	suggested	suggest	VERB
ma-248	55	8	a	a	DET
ma-248	55	9	nonlinear	nonlinear	ADJ
ma-248	55	10	mathematical	mathematical	ADJ
ma-248	55	11	model	model	NOUN
ma-248	55	12	to	to	PART
ma-248	55	13	see	see	VERB
ma-248	55	14	if	if	SCONJ
ma-248	55	15	public	public	ADJ
ma-248	55	16	awarenesscampaigns	awarenesscampaign	NOUN
ma-248	55	17	affect	affect	VERB
ma-248	55	18	the	the	DET
ma-248	55	19	spread	spread	NOUN
ma-248	55	20	of	of	ADP
ma-248	55	21	infectious	infectious	ADJ
ma-248	55	22	diseases	disease	NOUN
ma-248	55	23	.	.	PUNCT
ma-248	56	1	the	the	DET
ma-248	56	2	model	model	NOUN
ma-248	56	3	evaluated	evaluate	VERB
ma-248	56	4	the	the	DET
ma-248	56	5	population	population	NOUN
ma-248	56	6	’s	’s	PART
ma-248	56	7	responseto	responseto	ADJ
ma-248	56	8	media	medium	NOUN
ma-248	56	9	awareness	awareness	NOUN
ma-248	56	10	because	because	SCONJ
ma-248	56	11	diseases	disease	NOUN
ma-248	56	12	spread	spread	VERB
ma-248	56	13	through	through	ADP
ma-248	56	14	interaction	interaction	NOUN
ma-248	56	15	between	between	ADP
ma-248	56	16	infected	infected	ADJ
ma-248	56	17	and	and	CCONJ
ma-248	56	18	suscepti	suscepti	NOUN
ma-248	56	19	-	-	PUNCT
ma-248	56	20	ble	ble	ADJ
ma-248	56	21	people	people	NOUN
ma-248	56	22	.	.	PUNCT
ma-248	57	1	thus	thus	ADV
ma-248	57	2	,	,	PUNCT
ma-248	57	3	the	the	DET
ma-248	57	4	ability	ability	NOUN
ma-248	57	5	of	of	ADP
ma-248	57	6	the	the	DET
ma-248	57	7	susceptible	susceptible	ADJ
ma-248	57	8	individuals	individual	NOUN
ma-248	57	9	to	to	PART
ma-248	57	10	avoid	avoid	VERB
ma-248	57	11	contact	contact	NOUN
ma-248	57	12	with	with	ADP
ma-248	57	13	the	the	DET
ma-248	57	14	infectives.their	infectives.their	PROPN
ma-248	57	15	analysis	analysis	NOUN
ma-248	57	16	showed	show	VERB
ma-248	57	17	that	that	SCONJ
ma-248	57	18	infectious	infectious	ADJ
ma-248	57	19	disease	disease	NOUN
ma-248	57	20	spread	spread	NOUN
ma-248	57	21	can	can	AUX
ma-248	57	22	be	be	AUX
ma-248	57	23	controlled	control	VERB
ma-248	57	24	by	by	ADP
ma-248	57	25	employing	employ	VERB
ma-248	57	26	an	an	DET
ma-248	57	27	aware	aware	ADJ
ma-248	57	28	-	-	PUNCT
ma-248	57	29	ness	ness	ADJ
ma-248	57	30	program	program	NOUN
ma-248	57	31	.	.	PUNCT
ma-248	58	1	however	however	ADV
ma-248	58	2	,	,	PUNCT
ma-248	58	3	due	due	ADP
ma-248	58	4	to	to	ADP
ma-248	58	5	human	human	ADJ
ma-248	58	6	immigration	immigration	NOUN
ma-248	58	7	,	,	PUNCT
ma-248	58	8	diseases	disease	NOUN
ma-248	58	9	will	will	AUX
ma-248	58	10	always	always	ADV
ma-248	58	11	remain	remain	VERB
ma-248	58	12	endemic	endemic	ADJ
ma-248	58	13	.	.	PUNCT
ma-248	59	1	in	in	ADP
ma-248	59	2	[	[	PUNCT
ma-248	59	3	44],the	44],the	PRON
ma-248	59	4	authors	author	NOUN
ma-248	59	5	explored	explore	VERB
ma-248	59	6	the	the	DET
ma-248	59	7	impact	impact	NOUN
ma-248	59	8	of	of	ADP
ma-248	59	9	media	medium	NOUN
ma-248	59	10	coverage	coverage	NOUN
ma-248	59	11	on	on	ADP
ma-248	59	12	controlling	control	VERB
ma-248	59	13	disease	disease	NOUN
ma-248	59	14	spread	spread	VERB
ma-248	59	15	by	by	ADP
ma-248	59	16	formulating	formulate	VERB
ma-248	59	17	amathematical	amathematical	ADJ
ma-248	59	18	model	model	NOUN
ma-248	59	19	incorporating	incorporate	VERB
ma-248	59	20	media	medium	NOUN
ma-248	59	21	coverage	coverage	NOUN
ma-248	59	22	.	.	PUNCT
ma-248	60	1	the	the	DET
ma-248	60	2	analysis	analysis	NOUN
ma-248	60	3	indicates	indicate	VERB
ma-248	60	4	that	that	SCONJ
ma-248	60	5	,	,	PUNCT
ma-248	60	6	even	even	ADV
ma-248	60	7	though	though	SCONJ
ma-248	60	8	theexistence	theexistence	NOUN
ma-248	60	9	of	of	ADP
ma-248	60	10	media	medium	NOUN
ma-248	60	11	was	be	AUX
ma-248	60	12	not	not	PART
ma-248	60	13	the	the	DET
ma-248	60	14	sole	sole	ADJ
ma-248	60	15	factor	factor	NOUN
ma-248	60	16	in	in	ADP
ma-248	60	17	the	the	DET
ma-248	60	18	attempt	attempt	NOUN
ma-248	60	19	to	to	PART
ma-248	60	20	eradicate	eradicate	VERB
ma-248	60	21	the	the	DET
ma-248	60	22	disease	disease	NOUN
ma-248	60	23	,	,	PUNCT
ma-248	60	24	its	its	PRON
ma-248	60	25	presence	presence	NOUN
ma-248	60	26	,	,	PUNCT
ma-248	60	27	to	to	ADP
ma-248	60	28	some	some	DET
ma-248	60	29	extent	extent	NOUN
ma-248	60	30	,	,	PUNCT
ma-248	60	31	can	can	AUX
ma-248	60	32	minimize	minimize	VERB
ma-248	60	33	the	the	DET
ma-248	60	34	number	number	NOUN
ma-248	60	35	of	of	ADP
ma-248	60	36	infections	infection	NOUN
ma-248	60	37	.	.	PUNCT
ma-248	61	1	in	in	ADP
ma-248	61	2	[	[	X
ma-248	61	3	45	45	NUM
ma-248	61	4	]	]	PUNCT
ma-248	61	5	,	,	PUNCT
ma-248	61	6	the	the	DET
ma-248	61	7	authors	author	NOUN
ma-248	61	8	attempted	attempt	VERB
ma-248	61	9	to	to	PART
ma-248	61	10	reduceebola	reduceebola	VERB
ma-248	61	11	infection	infection	NOUN
ma-248	61	12	in	in	ADP
ma-248	61	13	the	the	DET
ma-248	61	14	susceptible	susceptible	ADJ
ma-248	61	15	by	by	ADP
ma-248	61	16	constructing	construct	VERB
ma-248	61	17	an	an	DET
ma-248	61	18	optimal	optimal	ADJ
ma-248	61	19	control	control	NOUN
ma-248	61	20	theory	theory	NOUN
ma-248	61	21	from	from	ADP
ma-248	61	22	ordinary	ordinary	ADJ
ma-248	61	23	differ	differ	NOUN
ma-248	61	24	-	-	PUNCT
ma-248	61	25	ential	ential	ADJ
ma-248	61	26	equation	equation	NOUN
ma-248	61	27	modelling	modelling	NOUN
ma-248	61	28	of	of	ADP
ma-248	61	29	the	the	DET
ma-248	61	30	ebola	ebola	PROPN
ma-248	61	31	virus	virus	NOUN
ma-248	61	32	.	.	PUNCT
ma-248	62	1	two	two	NUM
ma-248	62	2	control	control	NOUN
ma-248	62	3	functions	function	NOUN
ma-248	62	4	,	,	PUNCT
ma-248	62	5	education	education	NOUN
ma-248	62	6	and	and	CCONJ
ma-248	62	7	treatments	treatment	NOUN
ma-248	62	8	,	,	PUNCT
ma-248	62	9	were	be	AUX
ma-248	62	10	considered	consider	VERB
ma-248	62	11	in	in	ADP
ma-248	62	12	modelling	model	VERB
ma-248	62	13	the	the	DET
ma-248	62	14	control	control	NOUN
ma-248	62	15	problem	problem	NOUN
ma-248	62	16	.	.	PUNCT
ma-248	63	1	the	the	DET
ma-248	63	2	control	control	NOUN
ma-248	63	3	system	system	NOUN
ma-248	63	4	is	be	AUX
ma-248	63	5	solved	solve	VERB
ma-248	63	6	by	by	ADP
ma-248	63	7	applying	apply	VERB
ma-248	63	8	thetool	thetool	NOUN
ma-248	63	9	of	of	ADP
ma-248	63	10	pontryagin	pontryagin	NOUN
ma-248	63	11	’s	’s	PART
ma-248	63	12	maximum	maximum	ADJ
ma-248	63	13	principle	principle	NOUN
ma-248	63	14	.	.	PUNCT
ma-248	64	1	the	the	DET
ma-248	64	2	analysis	analysis	NOUN
ma-248	64	3	of	of	ADP
ma-248	64	4	the	the	DET
ma-248	64	5	numerical	numerical	ADJ
ma-248	64	6	results	result	NOUN
ma-248	64	7	showed	show	VERB
ma-248	64	8	the	the	DET
ma-248	64	9	controls’overall	controls’overall	ADJ
ma-248	64	10	effect	effect	NOUN
ma-248	64	11	in	in	ADP
ma-248	64	12	reducing	reduce	VERB
ma-248	64	13	the	the	DET
ma-248	64	14	disease	disease	NOUN
ma-248	64	15	.	.	PUNCT
ma-248	65	1	also	also	ADV
ma-248	65	2	,	,	PUNCT
ma-248	65	3	the	the	DET
ma-248	65	4	authors	author	NOUN
ma-248	65	5	in	in	ADP
ma-248	65	6	[	[	X
ma-248	65	7	16	16	NUM
ma-248	65	8	]	]	PUNCT
ma-248	65	9	constructed	construct	VERB
ma-248	65	10	a	a	DET
ma-248	65	11	mathematical	mathematical	ADJ
ma-248	65	12	modelof	modelof	NOUN
ma-248	65	13	syphilis	syphilis	NOUN
ma-248	65	14	transmission	transmission	NOUN
ma-248	65	15	dynamics	dynamic	NOUN
ma-248	65	16	to	to	PART
ma-248	65	17	aid	aid	VERB
ma-248	65	18	in	in	ADP
ma-248	65	19	selecting	select	VERB
ma-248	65	20	the	the	DET
ma-248	65	21	most	most	ADV
ma-248	65	22	effective	effective	ADJ
ma-248	65	23	syphilis	syphili	NOUN
ma-248	65	24	screening	screen	VERB
ma-248	65	25	choicesthe	choicesthe	NOUN
ma-248	65	26	model	model	NOUN
ma-248	65	27	created	create	VERB
ma-248	65	28	was	be	AUX
ma-248	65	29	an	an	DET
ma-248	65	30	agent	agent	NOUN
ma-248	65	31	-	-	PUNCT
ma-248	65	32	based	base	VERB
ma-248	65	33	dynamic	dynamic	ADJ
ma-248	65	34	model	model	NOUN
ma-248	65	35	that	that	PRON
ma-248	65	36	simulated	simulate	VERB
ma-248	65	37	a	a	DET
ma-248	65	38	critical	critical	ADJ
ma-248	65	39	population	population	NOUN
ma-248	65	40	of	of	ADP
ma-248	65	41	2,000people	2,000people	NUM
ma-248	65	42	.	.	PUNCT
ma-248	66	1	according	accord	VERB
ma-248	66	2	to	to	ADP
ma-248	66	3	the	the	DET
ma-248	66	4	model	model	NOUN
ma-248	66	5	’s	’s	PART
ma-248	66	6	results	result	NOUN
ma-248	66	7	,	,	PUNCT
ma-248	66	8	increasing	increase	VERB
ma-248	66	9	the	the	DET
ma-248	66	10	frequency	frequency	NOUN
ma-248	66	11	of	of	ADP
ma-248	66	12	syphilis	syphili	NOUN
ma-248	66	13	screening	screen	VERB
ma-248	66	14	to	to	ADP
ma-248	66	15	everythree	everythree	ADJ
ma-248	66	16	months	month	NOUN
ma-248	66	17	was	be	AUX
ma-248	66	18	very	very	ADV
ma-248	66	19	effective	effective	ADJ
ma-248	66	20	in	in	ADP
ma-248	66	21	reducing	reduce	VERB
ma-248	66	22	syphilis	syphili	NOUN
ma-248	66	23	infection	infection	NOUN
ma-248	66	24	cases	case	NOUN
ma-248	66	25	.	.	PUNCT
ma-248	67	1	in	in	ADP
ma-248	67	2	[	[	X
ma-248	67	3	46	46	NUM
ma-248	67	4	]	]	PUNCT
ma-248	67	5	,	,	PUNCT
ma-248	67	6	the	the	DET
ma-248	67	7	authors	author	NOUN
ma-248	67	8	devel	devel	NOUN
ma-248	67	9	-	-	PUNCT
ma-248	67	10	oped	ope	VERB
ma-248	67	11	a	a	DET
ma-248	67	12	mathematical	mathematical	ADJ
ma-248	67	13	model	model	NOUN
ma-248	67	14	of	of	ADP
ma-248	67	15	covid-19	covid-19	PROPN
ma-248	67	16	.	.	PUNCT
ma-248	68	1	to	to	PART
ma-248	68	2	characterize	characterize	VERB
ma-248	68	3	a	a	DET
ma-248	68	4	range	range	NOUN
ma-248	68	5	of	of	ADP
ma-248	68	6	feasible	feasible	ADJ
ma-248	68	7	controls	control	NOUN
ma-248	68	8	that	that	PRON
ma-248	68	9	mightbe	mightbe	VERB
ma-248	68	10	effective	effective	ADJ
ma-248	68	11	in	in	ADP
ma-248	68	12	minimizing	minimize	VERB
ma-248	68	13	the	the	DET
ma-248	68	14	disease	disease	NOUN
ma-248	68	15	,	,	PUNCT
ma-248	68	16	the	the	DET
ma-248	68	17	model	model	NOUN
ma-248	68	18	was	be	AUX
ma-248	68	19	changed	change	VERB
ma-248	68	20	to	to	ADP
ma-248	68	21	an	an	DET
ma-248	68	22	optimal	optimal	ADJ
ma-248	68	23	control	control	NOUN
ma-248	68	24	problem	problem	NOUN
ma-248	68	25	.	.	PUNCT
ma-248	69	1	anumerical	anumerical	ADJ
ma-248	69	2	simulation	simulation	NOUN
ma-248	69	3	of	of	ADP
ma-248	69	4	the	the	DET
ma-248	69	5	problem	problem	NOUN
ma-248	69	6	was	be	AUX
ma-248	69	7	performed	perform	VERB
ma-248	69	8	using	use	VERB
ma-248	69	9	a	a	DET
ma-248	69	10	forward	forward	ADV
ma-248	69	11	-	-	PUNCT
ma-248	69	12	backwards	backwards	ADV
ma-248	69	13	sweep	sweep	NOUN
ma-248	69	14	and	and	CCONJ
ma-248	69	15	fourth	fourth	ADJ
ma-248	69	16	-	-	PUNCT
ma-248	69	17	order	order	NOUN
ma-248	69	18	range	range	NOUN
ma-248	69	19	-	-	PUNCT
ma-248	69	20	kutta	kutta	NOUN
ma-248	69	21	method	method	NOUN
ma-248	69	22	.	.	PUNCT
ma-248	70	1	in	in	ADP
ma-248	70	2	[	[	X
ma-248	70	3	47	47	NUM
ma-248	70	4	]	]	PUNCT
ma-248	70	5	,	,	PUNCT
ma-248	70	6	the	the	DET
ma-248	70	7	authors	author	NOUN
ma-248	70	8	created	create	VERB
ma-248	70	9	a	a	DET
ma-248	70	10	mathematical	mathematical	ADJ
ma-248	70	11	model	model	NOUN
ma-248	70	12	for	for	ADP
ma-248	70	13	the	the	DET
ma-248	70	14	ongoingcoronavirus	ongoingcoronavirus	NOUN
ma-248	70	15	outbreak	outbreak	NOUN
ma-248	70	16	to	to	PART
ma-248	70	17	determine	determine	VERB
ma-248	70	18	intervention	intervention	NOUN
ma-248	70	19	approaches	approach	NOUN
ma-248	70	20	to	to	PART
ma-248	70	21	battle	battle	VERB
ma-248	70	22	it	it	PRON
ma-248	70	23	.	.	PUNCT
ma-248	71	1	the	the	DET
ma-248	71	2	model	model	NOUN
ma-248	71	3	was	be	AUX
ma-248	71	4	turned	turn	VERB
ma-248	71	5	intoan	intoan	ADJ
ma-248	71	6	optimal	optimal	ADJ
ma-248	71	7	control	control	NOUN
ma-248	71	8	problem	problem	NOUN
ma-248	71	9	to	to	PART
ma-248	71	10	provide	provide	VERB
ma-248	71	11	a	a	DET
ma-248	71	12	theoretical	theoretical	ADJ
ma-248	71	13	explanation	explanation	NOUN
ma-248	71	14	for	for	ADP
ma-248	71	15	the	the	DET
ma-248	71	16	disease	disease	NOUN
ma-248	71	17	,	,	PUNCT
ma-248	71	18	which	which	PRON
ma-248	71	19	was	be	AUX
ma-248	71	20	solvedqualitatively	solvedqualitatively	ADV
ma-248	71	21	by	by	ADP
ma-248	71	22	utilizing	utilize	VERB
ma-248	71	23	pontryagin	pontryagin	NOUN
ma-248	71	24	’s	’s	PART
ma-248	71	25	maximal	maximal	ADJ
ma-248	71	26	principle	principle	NOUN
ma-248	71	27	.	.	PUNCT
ma-248	72	1	matlab	matlab	PROPN
ma-248	72	2	and	and	CCONJ
ma-248	72	3	an	an	DET
ma-248	72	4	iterative	iterative	NOUN
ma-248	72	5	technique	technique	NOUN
ma-248	72	6	wereused	wereuse	VERB
ma-248	72	7	to	to	PART
ma-248	72	8	solve	solve	VERB
ma-248	72	9	the	the	DET
ma-248	72	10	models	model	NOUN
ma-248	72	11	numerically.the	numerically.the	DET
ma-248	72	12	objective	objective	NOUN
ma-248	72	13	of	of	ADP
ma-248	72	14	this	this	DET
ma-248	72	15	work	work	NOUN
ma-248	72	16	is	be	AUX
ma-248	72	17	to	to	PART
ma-248	72	18	design	design	VERB
ma-248	72	19	a	a	DET
ma-248	72	20	mathematical	mathematical	ADJ
ma-248	72	21	model	model	NOUN
ma-248	72	22	to	to	PART
ma-248	72	23	investigate	investigate	VERB
ma-248	72	24	meningitis	meningitis	PROPN
ma-248	72	25	transmis	transmis	PROPN
ma-248	72	26	-	-	PUNCT
ma-248	72	27	sion	sion	PROPN
ma-248	72	28	,	,	PUNCT
ma-248	72	29	to	to	PART
ma-248	72	30	examine	examine	VERB
ma-248	72	31	the	the	DET
ma-248	72	32	equilibrium	equilibrium	NOUN
ma-248	72	33	’s	’s	PART
ma-248	72	34	local	local	ADJ
ma-248	72	35	and	and	CCONJ
ma-248	72	36	global	global	ADJ
ma-248	72	37	stability	stability	NOUN
ma-248	72	38	,	,	PUNCT
ma-248	72	39	to	to	PART
ma-248	72	40	conduct	conduct	VERB
ma-248	72	41	a	a	DET
ma-248	72	42	sensitivity	sensitivity	NOUN
ma-248	72	43	analysis	analysis	NOUN
ma-248	72	44	of	of	ADP
ma-248	72	45	the	the	DET
ma-248	72	46	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	72	47	eur	eur	PROPN
ma-248	72	48	.	.	PUNCT
ma-248	73	1	j.	j.	PROPN
ma-248	73	2	math	math	PROPN
ma-248	73	3	.	.	PUNCT
ma-248	74	1	anal	anal	PROPN
ma-248	74	2	.	.	PUNCT
ma-248	75	1	10.28924	10.28924	NUM
ma-248	75	2	/	/	SYM
ma-248	75	3	ada	ada	PROPN
ma-248	75	4	/	/	SYM
ma-248	75	5	ma.4.21	ma.4.21	PROPN
ma-248	75	6	4model	4model	NUM
ma-248	75	7	parameters	parameter	NOUN
ma-248	75	8	to	to	PART
ma-248	75	9	identify	identify	VERB
ma-248	75	10	the	the	DET
ma-248	75	11	parameters	parameter	NOUN
ma-248	75	12	that	that	PRON
ma-248	75	13	significantly	significantly	ADV
ma-248	75	14	affect	affect	VERB
ma-248	75	15	the	the	DET
ma-248	75	16	r0	r0	NOUN
ma-248	75	17	,	,	PUNCT
ma-248	75	18	to	to	PART
ma-248	75	19	formulate	formulate	VERB
ma-248	75	20	a	a	DET
ma-248	75	21	controlmodel	controlmodel	NOUN
ma-248	75	22	for	for	ADP
ma-248	75	23	the	the	DET
ma-248	75	24	meningitis	meningitis	NOUN
ma-248	75	25	disease	disease	NOUN
ma-248	75	26	,	,	PUNCT
ma-248	75	27	and	and	CCONJ
ma-248	75	28	to	to	PART
ma-248	75	29	perform	perform	VERB
ma-248	75	30	a	a	DET
ma-248	75	31	numerical	numerical	ADJ
ma-248	75	32	simulation	simulation	NOUN
ma-248	75	33	for	for	ADP
ma-248	75	34	the	the	DET
ma-248	75	35	model.the	model.the	DET
ma-248	75	36	rest	rest	NOUN
ma-248	75	37	of	of	ADP
ma-248	75	38	the	the	DET
ma-248	75	39	research	research	NOUN
ma-248	75	40	is	be	AUX
ma-248	75	41	divided	divide	VERB
ma-248	75	42	into	into	ADP
ma-248	75	43	the	the	DET
ma-248	75	44	following	follow	VERB
ma-248	75	45	sections	section	NOUN
ma-248	75	46	:	:	PUNCT
ma-248	75	47	section	section	NOUN
ma-248	75	48	2	2	NUM
ma-248	75	49	focuses	focus	VERB
ma-248	75	50	on	on	ADP
ma-248	75	51	formulating	formulate	VERB
ma-248	75	52	anonlinear	anonlinear	ADJ
ma-248	75	53	model	model	NOUN
ma-248	75	54	for	for	ADP
ma-248	75	55	meningitis	meningitis	NOUN
ma-248	75	56	disease	disease	NOUN
ma-248	75	57	.	.	PUNCT
ma-248	76	1	section	section	NOUN
ma-248	76	2	3	3	NUM
ma-248	76	3	explores	explore	VERB
ma-248	76	4	the	the	DET
ma-248	76	5	qualitative	qualitative	ADJ
ma-248	76	6	properties	property	NOUN
ma-248	76	7	of	of	ADP
ma-248	76	8	the	the	DET
ma-248	76	9	model	model	NOUN
ma-248	76	10	,	,	PUNCT
ma-248	76	11	like	like	ADP
ma-248	76	12	positivity	positivity	NOUN
ma-248	76	13	,	,	PUNCT
ma-248	76	14	solutions	solution	NOUN
ma-248	76	15	’	'	PUNCT
ma-248	76	16	boundedness	boundedness	NOUN
ma-248	76	17	,	,	PUNCT
ma-248	76	18	basic	basic	ADJ
ma-248	76	19	reproduction	reproduction	NOUN
ma-248	76	20	numbers	number	NOUN
ma-248	76	21	,	,	PUNCT
ma-248	76	22	and	and	CCONJ
ma-248	76	23	the	the	DET
ma-248	76	24	existence	existence	NOUN
ma-248	76	25	of	of	ADP
ma-248	76	26	equilibriumalong	equilibriumalong	NOUN
ma-248	76	27	with	with	ADP
ma-248	76	28	the	the	DET
ma-248	76	29	local	local	ADJ
ma-248	76	30	and	and	CCONJ
ma-248	76	31	global	global	ADJ
ma-248	76	32	stability	stability	NOUN
ma-248	76	33	of	of	ADP
ma-248	76	34	disease	disease	NOUN
ma-248	76	35	-	-	PUNCT
ma-248	76	36	free	free	ADJ
ma-248	76	37	and	and	CCONJ
ma-248	76	38	endemic	endemic	ADJ
ma-248	76	39	equilibria	equilibrium	NOUN
ma-248	76	40	.	.	PUNCT
ma-248	77	1	section	section	NOUN
ma-248	77	2	4	4	NUM
ma-248	77	3	centres	centre	NOUN
ma-248	77	4	onexamining	onexamine	VERB
ma-248	77	5	the	the	DET
ma-248	77	6	sensitivity	sensitivity	NOUN
ma-248	77	7	of	of	ADP
ma-248	77	8	the	the	DET
ma-248	77	9	model	model	NOUN
ma-248	77	10	’s	’s	PART
ma-248	77	11	parameters	parameter	NOUN
ma-248	77	12	on	on	ADP
ma-248	77	13	r0	r0	NOUN
ma-248	77	14	using	use	VERB
ma-248	77	15	the	the	DET
ma-248	77	16	normalized	normalize	VERB
ma-248	77	17	forward	forward	ADJ
ma-248	77	18	sensitivityindex	sensitivityindex	NOUN
ma-248	77	19	.	.	PUNCT
ma-248	78	1	in	in	ADP
ma-248	78	2	section	section	NOUN
ma-248	78	3	5	5	NUM
ma-248	78	4	,	,	PUNCT
ma-248	78	5	the	the	DET
ma-248	78	6	model	model	NOUN
ma-248	78	7	is	be	AUX
ma-248	78	8	modified	modify	VERB
ma-248	78	9	by	by	ADP
ma-248	78	10	adding	add	VERB
ma-248	78	11	time	time	NOUN
ma-248	78	12	-	-	PUNCT
ma-248	78	13	dependent	dependent	ADJ
ma-248	78	14	and	and	CCONJ
ma-248	78	15	solved	solve	VERB
ma-248	78	16	with	with	ADP
ma-248	78	17	pontryagin’smaximum	pontryagin’smaximum	ADJ
ma-248	78	18	principle	principle	NOUN
ma-248	78	19	.	.	PUNCT
ma-248	79	1	section	section	NOUN
ma-248	79	2	6	6	NUM
ma-248	79	3	tackles	tackle	NOUN
ma-248	79	4	computational	computational	ADJ
ma-248	79	5	investigations	investigation	NOUN
ma-248	79	6	of	of	ADP
ma-248	79	7	the	the	DET
ma-248	79	8	optimal	optimal	ADJ
ma-248	79	9	control	control	NOUN
ma-248	79	10	modelbased	modelbase	VERB
ma-248	79	11	on	on	ADP
ma-248	79	12	the	the	DET
ma-248	79	13	three	three	NUM
ma-248	79	14	control	control	NOUN
ma-248	79	15	strategies	strategy	NOUN
ma-248	79	16	,	,	PUNCT
ma-248	79	17	and	and	CCONJ
ma-248	79	18	the	the	DET
ma-248	79	19	results	result	NOUN
ma-248	79	20	are	be	AUX
ma-248	79	21	illustrated	illustrate	VERB
ma-248	79	22	.	.	PUNCT
ma-248	80	1	then	then	ADV
ma-248	80	2	,	,	PUNCT
ma-248	80	3	finally	finally	ADV
ma-248	80	4	,	,	PUNCT
ma-248	80	5	we	we	PRON
ma-248	80	6	provideconclusions	provideconclusion	NOUN
ma-248	80	7	and	and	CCONJ
ma-248	80	8	discussions	discussion	NOUN
ma-248	80	9	of	of	ADP
ma-248	80	10	the	the	DET
ma-248	80	11	work	work	NOUN
ma-248	80	12	in	in	ADP
ma-248	80	13	section	section	NOUN
ma-248	80	14	7	7	NUM
ma-248	80	15	.	.	NOUN
ma-248	80	16	2	2	NUM
ma-248	80	17	.	.	NOUN
ma-248	80	18	mathematical	mathematical	ADJ
ma-248	80	19	model	model	NOUN
ma-248	80	20	in	in	ADP
ma-248	80	21	the	the	DET
ma-248	80	22	current	current	ADJ
ma-248	80	23	section	section	NOUN
ma-248	80	24	,	,	PUNCT
ma-248	80	25	a	a	DET
ma-248	80	26	deterministic	deterministic	ADJ
ma-248	80	27	model	model	NOUN
ma-248	80	28	for	for	ADP
ma-248	80	29	meningitis	meningitis	ADJ
ma-248	80	30	disease	disease	NOUN
ma-248	80	31	that	that	PRON
ma-248	80	32	partitions	partition	VERB
ma-248	80	33	the	the	DET
ma-248	80	34	totalpopulation	totalpopulation	NOUN
ma-248	80	35	into	into	ADP
ma-248	80	36	shh	shh	PROPN
ma-248	80	37	,	,	PUNCT
ma-248	80	38	susceptible	susceptible	ADJ
ma-248	80	39	,	,	PUNCT
ma-248	80	40	ehh	ehh	NOUN
ma-248	80	41	,	,	PUNCT
ma-248	80	42	exposed	expose	VERB
ma-248	80	43	,	,	PUNCT
ma-248	80	44	ahh	ahh	INTJ
ma-248	80	45	,	,	PUNCT
ma-248	80	46	asymptomatic	asymptomatic	NOUN
ma-248	80	47	,	,	PUNCT
ma-248	80	48	ihh	ihh	PROPN
ma-248	80	49	,	,	PUNCT
ma-248	80	50	symptomatic	symptomatic	ADJ
ma-248	80	51	,	,	PUNCT
ma-248	80	52	and	and	CCONJ
ma-248	80	53	rhh	rhh	PROPN
ma-248	80	54	,	,	PUNCT
ma-248	80	55	recovered	recover	VERB
ma-248	80	56	is	be	AUX
ma-248	80	57	formulated	formulate	VERB
ma-248	80	58	.	.	PUNCT
ma-248	81	1	the	the	DET
ma-248	81	2	population	population	NOUN
ma-248	81	3	n	n	AUX
ma-248	81	4	is	be	AUX
ma-248	81	5	given	give	VERB
ma-248	81	6	as	as	ADP
ma-248	81	7	n	n	PROPN
ma-248	81	8	=	=	SYM
ma-248	81	9	shh	shh	PROPN
ma-248	81	10	+	+	NOUN
ma-248	81	11	ehh	ehh	NOUN
ma-248	82	1	+	+	CCONJ
ma-248	82	2	ahh	ahh	PROPN
ma-248	83	1	+	+	CCONJ
ma-248	83	2	ihh	ihh	PROPN
ma-248	83	3	+	+	CCONJ
ma-248	83	4	rhh	rhh	X
ma-248	83	5	.	.	PUNCT
ma-248	84	1	themodel	themodel	NOUN
ma-248	84	2	assumes	assume	VERB
ma-248	84	3	that	that	SCONJ
ma-248	84	4	people	people	NOUN
ma-248	84	5	are	be	AUX
ma-248	84	6	recruited	recruit	VERB
ma-248	84	7	into	into	ADP
ma-248	84	8	the	the	DET
ma-248	84	9	population	population	NOUN
ma-248	84	10	by	by	ADP
ma-248	84	11	birth	birth	NOUN
ma-248	84	12	at	at	ADP
ma-248	84	13	the	the	DET
ma-248	84	14	rate	rate	NOUN
ma-248	84	15	λ	λ	PROPN
ma-248	84	16	.	.	PUNCT
ma-248	85	1	the	the	DET
ma-248	85	2	susceptiblebecome	susceptiblebecome	NOUN
ma-248	85	3	exposed	expose	VERB
ma-248	85	4	through	through	ADP
ma-248	85	5	contact	contact	NOUN
ma-248	85	6	with	with	ADP
ma-248	85	7	the	the	DET
ma-248	85	8	symptomatic	symptomatic	ADJ
ma-248	85	9	at	at	ADP
ma-248	85	10	rate	rate	NOUN
ma-248	85	11	η1	η1	NOUN
ma-248	85	12	.	.	PUNCT
ma-248	86	1	the	the	DET
ma-248	86	2	exposed	expose	VERB
ma-248	86	3	leaves	leave	NOUN
ma-248	86	4	at	at	ADP
ma-248	86	5	a	a	DET
ma-248	86	6	rate	rate	NOUN
ma-248	86	7	τ1and	τ1and	NOUN
ma-248	86	8	enters	enter	VERB
ma-248	86	9	the	the	DET
ma-248	86	10	symptomatic	symptomatic	ADJ
ma-248	86	11	while	while	SCONJ
ma-248	86	12	a	a	DET
ma-248	86	13	fraction	fraction	NOUN
ma-248	86	14	k1	k1	NOUN
ma-248	86	15	enters	enter	VERB
ma-248	86	16	the	the	DET
ma-248	86	17	asymptomatic	asymptomatic	NOUN
ma-248	86	18	.	.	PUNCT
ma-248	87	1	the	the	DET
ma-248	87	2	asymptomatic	asymptomatic	ADJ
ma-248	87	3	andsymptomatic	andsymptomatic	NOUN
ma-248	87	4	die	die	NOUN
ma-248	87	5	at	at	ADP
ma-248	87	6	rates	rate	NOUN
ma-248	87	7	τ3	τ3	NOUN
ma-248	87	8	and	and	CCONJ
ma-248	87	9	ψ2	ψ2	NOUN
ma-248	87	10	,	,	PUNCT
ma-248	87	11	respectively	respectively	ADV
ma-248	87	12	.	.	PUNCT
ma-248	88	1	the	the	DET
ma-248	88	2	asymptomatic	asymptomatic	NOUN
ma-248	88	3	can	can	AUX
ma-248	88	4	leave	leave	VERB
ma-248	88	5	to	to	ADP
ma-248	88	6	recovery	recovery	NOUN
ma-248	88	7	classdue	classdue	NOUN
ma-248	88	8	to	to	ADP
ma-248	88	9	natural	natural	ADJ
ma-248	88	10	immunity	immunity	NOUN
ma-248	88	11	at	at	ADP
ma-248	88	12	rate	rate	NOUN
ma-248	88	13	τ2	τ2	PROPN
ma-248	88	14	.	.	PUNCT
ma-248	89	1	the	the	DET
ma-248	89	2	symptomatic	symptomatic	ADJ
ma-248	89	3	enters	enter	VERB
ma-248	89	4	the	the	DET
ma-248	89	5	recovered	recovered	ADJ
ma-248	89	6	compartments	compartment	NOUN
ma-248	89	7	at	at	ADP
ma-248	89	8	a	a	DET
ma-248	89	9	rate	rate	NOUN
ma-248	89	10	ψ1	ψ1	NOUN
ma-248	89	11	.	.	PUNCT
ma-248	90	1	the	the	DET
ma-248	90	2	recovered	recover	VERB
ma-248	90	3	individuals	individual	NOUN
ma-248	90	4	could	could	AUX
ma-248	90	5	return	return	VERB
ma-248	90	6	to	to	ADP
ma-248	90	7	the	the	DET
ma-248	90	8	susceptible	susceptible	ADJ
ma-248	90	9	class	class	NOUN
ma-248	90	10	due	due	ADP
ma-248	90	11	to	to	ADP
ma-248	90	12	loss	loss	NOUN
ma-248	90	13	of	of	ADP
ma-248	90	14	immunity	immunity	NOUN
ma-248	90	15	at	at	ADP
ma-248	90	16	rate	rate	NOUN
ma-248	90	17	ω	ω	PROPN
ma-248	90	18	.	.	PUNCT
ma-248	91	1	with	with	ADP
ma-248	91	2	all	all	DET
ma-248	91	3	the	the	DET
ma-248	91	4	compartments	compartment	NOUN
ma-248	91	5	,	,	PUNCT
ma-248	91	6	natural	natural	ADJ
ma-248	91	7	death	death	NOUN
ma-248	91	8	occurs	occur	VERB
ma-248	91	9	at	at	ADP
ma-248	91	10	a	a	DET
ma-248	91	11	rate	rate	NOUN
ma-248	91	12	µ.	µ.	NOUN
ma-248	91	13	figure	figure	NOUN
ma-248	91	14	1	1	NUM
ma-248	91	15	.	.	PUNCT
ma-248	91	16	schematic	schematic	ADJ
ma-248	91	17	of	of	ADP
ma-248	91	18	the	the	DET
ma-248	91	19	meningitis	meningitis	NOUN
ma-248	91	20	model	model	NOUN
ma-248	91	21	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	91	22	eur	eur	PROPN
ma-248	91	23	.	.	PUNCT
ma-248	92	1	j.	j.	PROPN
ma-248	92	2	math	math	PROPN
ma-248	92	3	.	.	PUNCT
ma-248	93	1	anal	anal	PROPN
ma-248	93	2	.	.	PUNCT
ma-248	94	1	10.28924	10.28924	NUM
ma-248	94	2	/	/	SYM
ma-248	94	3	ada	ada	PROPN
ma-248	94	4	/	/	SYM
ma-248	94	5	ma.4.21	ma.4.21	NOUN
ma-248	94	6	5	5	NUM
ma-248	95	1	d	d	NOUN
ma-248	95	2	dt	dt	X
ma-248	96	1	shh	shh	NOUN
ma-248	96	2	=	=	PROPN
ma-248	96	3	λ−	λ−	PROPN
ma-248	96	4	µshh	µshh	PROPN
ma-248	96	5	−	−	PROPN
ma-248	96	6	η1ihhshh	η1ihhshh	PROPN
ma-248	96	7	+	+	CCONJ
ma-248	96	8	ωrhh	ωrhh	NOUN
ma-248	96	9	,	,	PUNCT
ma-248	96	10	d	d	X
ma-248	96	11	dt	dt	X
ma-248	96	12	ehh	ehh	NOUN
ma-248	96	13	=	=	PUNCT
ma-248	96	14	η1ihhshh	η1ihhshh	NOUN
ma-248	96	15	−	−	NOUN
ma-248	96	16	k1τ1ehh	k1τ1ehh	X
ma-248	96	17	−	−	PROPN
ma-248	96	18	(	(	PUNCT
ma-248	96	19	1−	1−	NUM
ma-248	96	20	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	96	21	−	−	NOUN
ma-248	96	22	µehh	µehh	NOUN
ma-248	96	23	,	,	PUNCT
ma-248	96	24	d	d	NOUN
ma-248	96	25	dt	dt	X
ma-248	96	26	ahh	ahh	INTJ
ma-248	96	27	=	=	PUNCT
ma-248	96	28	(	(	PUNCT
ma-248	96	29	1−	1−	NUM
ma-248	96	30	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	96	31	−	−	PROPN
ma-248	96	32	(	(	PUNCT
ma-248	96	33	τ2	τ2	NOUN
ma-248	96	34	+	+	NUM
ma-248	96	35	τ3	τ3	NOUN
ma-248	96	36	+	+	X
ma-248	96	37	µ)ahh	µ)ahh	NOUN
ma-248	96	38	,	,	PUNCT
ma-248	96	39	(	(	PUNCT
ma-248	96	40	1	1	X
ma-248	96	41	)	)	PUNCT
ma-248	96	42	d	d	NOUN
ma-248	96	43	dt	dt	X
ma-248	96	44	ihh	ihh	PROPN
ma-248	96	45	=	=	PUNCT
ma-248	96	46	k1τ1ehh	k1τ1ehh	X
ma-248	96	47	−	−	PROPN
ma-248	96	48	(	(	PUNCT
ma-248	96	49	ψ1	ψ1	NOUN
ma-248	96	50	+	+	CCONJ
ma-248	96	51	ψ2	ψ2	NOUN
ma-248	96	52	+	+	CCONJ
ma-248	96	53	µ)ihh	µ)ihh	NUM
ma-248	96	54	,	,	PUNCT
ma-248	96	55	d	d	PROPN
ma-248	96	56	dt	dt	X
ma-248	96	57	rhh	rhh	X
ma-248	96	58	=	=	PUNCT
ma-248	96	59	τ2ahh	τ2ahh	PROPN
ma-248	96	60	+	+	NUM
ma-248	96	61	ψ1ehh	ψ1ehh	NUM
ma-248	96	62	−	−	PROPN
ma-248	97	1	(	(	PUNCT
ma-248	97	2	ω	ω	PROPN
ma-248	97	3	+	+	X
ma-248	98	1	µ)rhh	µ)rhh	VERB
ma-248	98	2	,	,	PUNCT
ma-248	98	3	with	with	ADP
ma-248	98	4	:	:	PUNCT
ma-248	98	5	shh0	shh0	PROPN
ma-248	98	6	≥	≥	PROPN
ma-248	98	7	0	0	NUM
ma-248	98	8	,	,	PUNCT
ma-248	98	9	ehh0	ehh0	PROPN
ma-248	98	10	≥	≥	PROPN
ma-248	98	11	0	0	NUM
ma-248	98	12	,	,	PUNCT
ma-248	98	13	ahh0	ahh0	PROPN
ma-248	98	14	≥	≥	PROPN
ma-248	98	15	0	0	NUM
ma-248	98	16	,	,	PUNCT
ma-248	98	17	ihh0	ihh0	NOUN
ma-248	98	18	≥	≥	NUM
ma-248	98	19	0	0	NUM
ma-248	98	20	and	and	CCONJ
ma-248	98	21	rhh0	rhh0	PROPN
ma-248	98	22	≥	≥	NUM
ma-248	98	23	0	0	NUM
ma-248	98	24	.	.	PUNCT
ma-248	99	1	(	(	PUNCT
ma-248	99	2	2	2	NUM
ma-248	99	3	)	)	PUNCT
ma-248	99	4	3	3	NUM
ma-248	99	5	.	.	PUNCT
ma-248	99	6	qualitative	qualitative	ADJ
ma-248	99	7	properties	property	NOUN
ma-248	99	8	3.1	3.1	NUM
ma-248	99	9	.	.	PUNCT
ma-248	99	10	positivity	positivity	NOUN
ma-248	99	11	and	and	CCONJ
ma-248	99	12	boundedness	boundedness	PROPN
ma-248	99	13	.	.	PUNCT
ma-248	99	14	theorem	theorem	VERB
ma-248	99	15	3.1	3.1	NUM
ma-248	99	16	.	.	PUNCT
ma-248	100	1	the	the	DET
ma-248	100	2	set	set	NOUN
ma-248	100	3	{	{	PUNCT
ma-248	100	4	shh	shh	PROPN
ma-248	100	5	,	,	PUNCT
ma-248	100	6	ehh	ehh	PROPN
ma-248	100	7	,	,	PUNCT
ma-248	100	8	ahh	ahh	PROPN
ma-248	100	9	,	,	PUNCT
ma-248	100	10	ihh	ihh	PROPN
ma-248	100	11	,	,	PUNCT
ma-248	100	12	rhh	rhh	PROPN
ma-248	100	13	}	}	PUNCT
ma-248	100	14	being	be	AUX
ma-248	100	15	the	the	DET
ma-248	100	16	solution	solution	NOUN
ma-248	100	17	of	of	ADP
ma-248	100	18	the	the	DET
ma-248	100	19	state	state	NOUN
ma-248	100	20	system	system	NOUN
ma-248	100	21	(	(	PUNCT
ma-248	100	22	1	1	NUM
ma-248	100	23	)	)	PUNCT
ma-248	100	24	with	with	ADP
ma-248	100	25	parameters	parameter	NOUN
ma-248	100	26	which	which	PRON
ma-248	100	27	are	be	AUX
ma-248	100	28	non	non	NOUN
ma-248	100	29	-	-	NOUN
ma-248	100	30	negatives	negative	NOUN
ma-248	100	31	is	be	AUX
ma-248	100	32	positive	positive	ADJ
ma-248	100	33	with	with	ADP
ma-248	100	34	the	the	DET
ma-248	100	35	initial	initial	ADJ
ma-248	100	36	condition	condition	NOUN
ma-248	100	37	given	give	VERB
ma-248	100	38	by	by	ADP
ma-248	100	39	;	;	PUNCT
ma-248	100	40	{	{	PUNCT
ma-248	100	41	shh0	shh0	PROPN
ma-248	100	42	≥	≥	PROPN
ma-248	100	43	0	0	NUM
ma-248	100	44	,	,	PUNCT
ma-248	100	45	ehh0	ehh0	PROPN
ma-248	100	46	≥	≥	PROPN
ma-248	100	47	0	0	NUM
ma-248	100	48	,	,	PUNCT
ma-248	100	49	ahh0	ahh0	PROPN
ma-248	100	50	≥	≥	PROPN
ma-248	100	51	0	0	NUM
ma-248	100	52	,	,	PUNCT
ma-248	100	53	ihh0	ihh0	NOUN
ma-248	100	54	≥	≥	NUM
ma-248	100	55	0	0	NUM
ma-248	100	56	,	,	PUNCT
ma-248	100	57	rhh0	rhh0	NOUN
ma-248	100	58	≥	≥	NUM
ma-248	100	59	0	0	NUM
ma-248	100	60	}	}	PUNCT
ma-248	100	61	.	.	PUNCT
ma-248	101	1	proof	proof	NOUN
ma-248	101	2	.	.	PUNCT
ma-248	102	1	by	by	ADP
ma-248	102	2	inspection	inspection	NOUN
ma-248	102	3	,	,	PUNCT
ma-248	102	4	the	the	DET
ma-248	102	5	third	third	ADJ
ma-248	102	6	equation	equation	NOUN
ma-248	102	7	of	of	ADP
ma-248	102	8	model	model	NOUN
ma-248	102	9	(	(	PUNCT
ma-248	102	10	1	1	X
ma-248	102	11	)	)	PUNCT
ma-248	102	12	can	can	AUX
ma-248	102	13	be	be	AUX
ma-248	102	14	structured	structure	VERB
ma-248	102	15	into	into	ADP
ma-248	102	16	a	a	DET
ma-248	102	17	first	first	ADJ
ma-248	102	18	-	-	PUNCT
ma-248	102	19	order	order	NOUN
ma-248	102	20	differentialequation	differentialequation	NOUN
ma-248	102	21	standard	standard	ADJ
ma-248	102	22	form	form	NOUN
ma-248	102	23	as	as	ADP
ma-248	102	24	:	:	PUNCT
ma-248	102	25	d	d	X
ma-248	102	26	dt	dt	X
ma-248	102	27	ahh	ahh	INTJ
ma-248	103	1	+	+	CCONJ
ma-248	103	2	(	(	PUNCT
ma-248	103	3	τ2	τ2	NOUN
ma-248	103	4	+	+	NUM
ma-248	103	5	τ3	τ3	NOUN
ma-248	103	6	+	+	X
ma-248	103	7	µ)ahh	µ)ahh	PROPN
ma-248	103	8	=	=	SYM
ma-248	103	9	(	(	PUNCT
ma-248	103	10	1−	1−	NUM
ma-248	103	11	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	103	12	.	.	PUNCT
ma-248	104	1	(	(	PUNCT
ma-248	104	2	3	3	X
ma-248	104	3	)	)	PUNCT
ma-248	104	4	when	when	SCONJ
ma-248	104	5	equation	equation	NOUN
ma-248	104	6	(	(	PUNCT
ma-248	104	7	3	3	X
ma-248	104	8	)	)	PUNCT
ma-248	104	9	is	be	AUX
ma-248	104	10	solved	solve	VERB
ma-248	104	11	with	with	ADP
ma-248	104	12	the	the	DET
ma-248	104	13	integrating	integrate	VERB
ma-248	104	14	factor	factor	NOUN
ma-248	104	15	method	method	NOUN
ma-248	104	16	,	,	PUNCT
ma-248	104	17	we	we	PRON
ma-248	104	18	get	get	VERB
ma-248	104	19	ahh(t	ahh(t	PRON
ma-248	104	20	)	)	PUNCT
ma-248	104	21	=	=	SYM
ma-248	104	22	e−(τ2+τ3+µ)t	e−(τ2+τ3+µ)t	PROPN
ma-248	104	23	[	[	PUNCT
ma-248	104	24	ahh(0	ahh(0	NOUN
ma-248	104	25	)	)	PUNCT
ma-248	105	1	+	+	CCONJ
ma-248	105	2	(	(	PUNCT
ma-248	105	3	1−	1−	NUM
ma-248	105	4	k1)τ1	k1)τ1	X
ma-248	105	5	∫	∫	PROPN
ma-248	105	6	t	t	PROPN
ma-248	105	7	0	0	NUM
ma-248	106	1	e(s)e−(τ2+τ3+µ)sds	e(s)e−(τ2+τ3+µ)sds	NOUN
ma-248	106	2	]	]	PUNCT
ma-248	106	3	.	.	PUNCT
ma-248	107	1	the	the	DET
ma-248	107	2	same	same	ADJ
ma-248	107	3	method	method	NOUN
ma-248	107	4	,	,	PUNCT
ma-248	107	5	when	when	SCONJ
ma-248	107	6	applied	apply	VERB
ma-248	107	7	to	to	ADP
ma-248	107	8	the	the	DET
ma-248	107	9	fourth	fourth	ADJ
ma-248	107	10	equation	equation	NOUN
ma-248	107	11	,	,	PUNCT
ma-248	107	12	gives	give	VERB
ma-248	107	13	ihh(t	ihh(t	PRON
ma-248	107	14	)	)	PUNCT
ma-248	107	15	=	=	SYM
ma-248	107	16	e−(ψ1+ψ2+µ)t	e−(ψ1+ψ2+µ)t	PROPN
ma-248	107	17	[	[	PUNCT
ma-248	107	18	ihh(0	ihh(0	NOUN
ma-248	107	19	)	)	PUNCT
ma-248	108	1	+	+	CCONJ
ma-248	108	2	k1τ1	k1τ1	PROPN
ma-248	108	3	∫	∫	PROPN
ma-248	108	4	t	t	PROPN
ma-248	108	5	0	0	NUM
ma-248	108	6	e(s)e−(ψ1+ψ2+µ)sds	e(s)e−(ψ1+ψ2+µ)sds	ADP
ma-248	108	7	]	]	PUNCT
ma-248	108	8	.	.	PUNCT
ma-248	109	1	hence	hence	ADV
ma-248	109	2	,	,	PUNCT
ma-248	109	3	we	we	PRON
ma-248	109	4	observe	observe	VERB
ma-248	109	5	that	that	SCONJ
ma-248	109	6	d	d	NOUN
ma-248	109	7	dt	dt	X
ma-248	109	8	ahh	ahh	INTJ
ma-248	109	9	≥	≥	NOUN
ma-248	109	10	0	0	NUM
ma-248	109	11	at	at	ADP
ma-248	109	12	t0	t0	PRON
ma-248	109	13	,	,	PUNCT
ma-248	109	14	d	d	PROPN
ma-248	109	15	dt	dt	X
ma-248	109	16	ihh	ihh	PROPN
ma-248	109	17	≥	≥	NOUN
ma-248	109	18	0	0	NUM
ma-248	109	19	at	at	ADP
ma-248	109	20	t0	t0	PROPN
ma-248	109	21	.	.	PUNCT
ma-248	110	1	thus	thus	ADV
ma-248	110	2	,	,	PUNCT
ma-248	110	3	we	we	PRON
ma-248	110	4	can	can	AUX
ma-248	110	5	generalise	generalise	VERB
ma-248	110	6	that	that	SCONJ
ma-248	110	7	the	the	DET
ma-248	110	8	otherstate	otherstate	ADJ
ma-248	110	9	variables	variable	NOUN
ma-248	110	10	remain	remain	VERB
ma-248	110	11	positive	positive	ADJ
ma-248	110	12	at	at	ADP
ma-248	110	13	t	t	NOUN
ma-248	110	14	=	=	SYM
ma-248	110	15	0	0	NUM
ma-248	110	16	.	.	PUNCT
ma-248	111	1	hence	hence	ADV
ma-248	111	2	,	,	PUNCT
ma-248	111	3	the	the	DET
ma-248	111	4	state	state	NOUN
ma-248	111	5	model	model	NOUN
ma-248	111	6	system	system	NOUN
ma-248	111	7	1	1	NUM
ma-248	111	8	is	be	AUX
ma-248	111	9	positively	positively	ADV
ma-248	111	10	invariant	invariant	ADJ
ma-248	111	11	in	in	ADP
ma-248	111	12	r5	r5	PROPN
ma-248	111	13	+	+	PROPN
ma-248	111	14	.	.	PROPN
ma-248	111	15	�	�	PROPN
ma-248	111	16	theorem	theorem	VERB
ma-248	111	17	3.2	3.2	NUM
ma-248	111	18	.	.	PUNCT
ma-248	112	1	the	the	DET
ma-248	112	2	model	model	NOUN
ma-248	112	3	equation	equation	NOUN
ma-248	112	4	(	(	PUNCT
ma-248	112	5	1	1	X
ma-248	112	6	)	)	PUNCT
ma-248	112	7	is	be	AUX
ma-248	112	8	bounded	bound	VERB
ma-248	112	9	within	within	ADP
ma-248	112	10	the	the	DET
ma-248	112	11	invariant	invariant	ADJ
ma-248	112	12	region	region	NOUN
ma-248	112	13	,	,	PUNCT
ma-248	112	14	ϑ	ϑ	PROPN
ma-248	112	15	∈	∈	PROPN
ma-248	112	16	r5	r5	NOUN
ma-248	112	17	+	+	CCONJ
ma-248	112	18	given	give	VERB
ma-248	112	19	as	as	ADP
ma-248	112	20	;	;	PUNCT
ma-248	112	21	ϑ	ϑ	X
ma-248	112	22	=	=	X
ma-248	112	23	{	{	PUNCT
ma-248	112	24	(	(	PUNCT
ma-248	112	25	shh	shh	INTJ
ma-248	112	26	,	,	PUNCT
ma-248	112	27	ehh	ehh	PROPN
ma-248	112	28	,	,	PUNCT
ma-248	112	29	ahh	ahh	PROPN
ma-248	112	30	,	,	PUNCT
ma-248	112	31	ihh	ihh	PROPN
ma-248	112	32	,	,	PUNCT
ma-248	112	33	rhh	rhh	X
ma-248	112	34	)	)	PUNCT
ma-248	112	35	∈	∈	PROPN
ma-248	112	36	r5	r5	PROPN
ma-248	112	37	+	+	PROPN
ma-248	112	38	,	,	PUNCT
ma-248	112	39	shh	shh	INTJ
ma-248	113	1	+	+	NOUN
ma-248	113	2	ehh	ehh	NOUN
ma-248	114	1	+	+	CCONJ
ma-248	114	2	ahh	ahh	PROPN
ma-248	115	1	+	+	CCONJ
ma-248	115	2	ihh	ihh	PROPN
ma-248	115	3	+	+	CCONJ
ma-248	115	4	rhh	rhh	X
ma-248	115	5	≤	≤	ADV
ma-248	115	6	λ−	λ−	PROPN
ma-248	115	7	µn	µn	PROPN
ma-248	115	8	}	}	PUNCT
ma-248	115	9	.	.	PUNCT
ma-248	116	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	116	2	eur	eur	PROPN
ma-248	116	3	.	.	PUNCT
ma-248	117	1	j.	j.	PROPN
ma-248	117	2	math	math	PROPN
ma-248	117	3	.	.	PUNCT
ma-248	118	1	anal	anal	PROPN
ma-248	118	2	.	.	PUNCT
ma-248	119	1	10.28924	10.28924	NUM
ma-248	119	2	/	/	SYM
ma-248	119	3	ada	ada	PROPN
ma-248	119	4	/	/	SYM
ma-248	119	5	ma.4.21	ma.4.21	NOUN
ma-248	119	6	6	6	NUM
ma-248	119	7	proof	proof	NOUN
ma-248	119	8	.	.	PUNCT
ma-248	120	1	we	we	PRON
ma-248	120	2	add	add	VERB
ma-248	120	3	the	the	DET
ma-248	120	4	respective	respective	ADJ
ma-248	120	5	compartments	compartment	NOUN
ma-248	120	6	to	to	PART
ma-248	120	7	prove	prove	VERB
ma-248	120	8	the	the	DET
ma-248	120	9	boundedness	boundedness	NOUN
ma-248	120	10	of	of	ADP
ma-248	120	11	model	model	NOUN
ma-248	120	12	system	system	NOUN
ma-248	120	13	(	(	PUNCT
ma-248	120	14	1	1	NUM
ma-248	120	15	)	)	PUNCT
ma-248	120	16	.	.	PUNCT
ma-248	121	1	thus	thus	ADV
ma-248	121	2	,	,	PUNCT
ma-248	121	3	we	we	PRON
ma-248	121	4	get	get	VERB
ma-248	121	5	n(t	n(t	PRON
ma-248	121	6	)	)	PUNCT
ma-248	121	7	=	=	SYM
ma-248	122	1	λ−	λ−	PROPN
ma-248	122	2	µshh	µshh	PROPN
ma-248	122	3	−	−	PROPN
ma-248	122	4	τ3ahh	τ3ahh	PROPN
ma-248	123	1	−	−	PROPN
ma-248	123	2	µahh	µahh	PROPN
ma-248	123	3	−	−	PROPN
ma-248	123	4	µehh	µehh	NOUN
ma-248	123	5	−	−	NOUN
ma-248	123	6	ψ2ihh	ψ2ihh	NOUN
ma-248	123	7	−	−	NOUN
ma-248	123	8	µihh	µihh	NOUN
ma-248	123	9	−	−	PROPN
ma-248	123	10	µrhh	µrhh	X
ma-248	123	11	,	,	PUNCT
ma-248	123	12	dn(t	dn(t	ADJ
ma-248	123	13	)	)	PUNCT
ma-248	123	14	dt	dt	PART
ma-248	124	1	=	=	PUNCT
ma-248	124	2	λ−	λ−	PROPN
ma-248	124	3	τ3ahh	τ3ahh	NOUN
ma-248	125	1	−	−	ADP
ma-248	125	2	ψ2ihh	ψ2ihh	NOUN
ma-248	125	3	−	−	NOUN
ma-248	125	4	µn	µn	PROPN
ma-248	125	5	.	.	PUNCT
ma-248	125	6	(	(	PUNCT
ma-248	125	7	4	4	X
ma-248	125	8	)	)	PUNCT
ma-248	125	9	it	it	PRON
ma-248	125	10	follows	follow	VERB
ma-248	125	11	that	that	SCONJ
ma-248	125	12	from	from	ADP
ma-248	125	13	equation	equation	NOUN
ma-248	125	14	(	(	PUNCT
ma-248	125	15	4	4	NUM
ma-248	125	16	)	)	PUNCT
ma-248	125	17	,	,	PUNCT
ma-248	125	18	setting	set	VERB
ma-248	125	19	h	h	NOUN
ma-248	125	20	to	to	PART
ma-248	125	21	be	be	AUX
ma-248	125	22	a	a	DET
ma-248	125	23	solution	solution	NOUN
ma-248	125	24	of	of	ADP
ma-248	125	25	(	(	PUNCT
ma-248	125	26	4	4	NUM
ma-248	125	27	)	)	PUNCT
ma-248	125	28	,	,	PUNCT
ma-248	125	29	we	we	PRON
ma-248	125	30	have	have	VERB
ma-248	125	31	a	a	DET
ma-248	125	32	unique	unique	ADJ
ma-248	125	33	initial	initial	ADJ
ma-248	125	34	valueproblem	valueproblem	NOUN
ma-248	125	35	,	,	PUNCT
ma-248	125	36			PROPN
ma-248	125	37	d	d	NOUN
ma-248	125	38	dt	dt	X
ma-248	126	1	h1(t	h1(t	X
ma-248	126	2	)	)	PUNCT
ma-248	127	1	=	=	SYM
ma-248	127	2	λ−	λ−	PROPN
ma-248	127	3	µh1(t	µh1(t	PROPN
ma-248	127	4	)	)	PUNCT
ma-248	127	5	t	t	PROPN
ma-248	127	6	≥	≥	NOUN
ma-248	127	7	0	0	NUM
ma-248	127	8	h1(0	h1(0	PROPN
ma-248	127	9	)	)	PUNCT
ma-248	127	10	=	=	SYM
ma-248	127	11	n(0	n(0	PROPN
ma-248	127	12	)	)	PUNCT
ma-248	127	13	.	.	PUNCT
ma-248	128	1	(	(	PUNCT
ma-248	128	2	5	5	X
ma-248	128	3	)	)	PUNCT
ma-248	128	4	the	the	DET
ma-248	128	5	solution	solution	NOUN
ma-248	128	6	of	of	ADP
ma-248	128	7	(	(	PUNCT
ma-248	128	8	5	5	NUM
ma-248	128	9	)	)	PUNCT
ma-248	128	10	gives	give	VERB
ma-248	128	11	;	;	PUNCT
ma-248	128	12	h1(t	h1(t	X
ma-248	128	13	)	)	PUNCT
ma-248	128	14	=	=	SYM
ma-248	128	15	n(0)e−µt	n(0)e−µt	NOUN
ma-248	129	1	+	+	CCONJ
ma-248	129	2	λ	λ	X
ma-248	129	3	µ	µ	X
ma-248	129	4	(	(	PUNCT
ma-248	129	5	1−	1−	NUM
ma-248	129	6	e(−µt	e(−µt	PROPN
ma-248	129	7	)	)	PUNCT
ma-248	129	8	)	)	PUNCT
ma-248	129	9	.	.	PUNCT
ma-248	130	1	(	(	PUNCT
ma-248	130	2	6	6	X
ma-248	130	3	)	)	PUNCT
ma-248	130	4	what	what	PRON
ma-248	130	5	happens	happen	VERB
ma-248	130	6	next	next	ADV
ma-248	130	7	is	be	AUX
ma-248	130	8	that	that	SCONJ
ma-248	130	9	,	,	PUNCT
ma-248	130	10	from	from	ADP
ma-248	130	11	the	the	DET
ma-248	130	12	comparison	comparison	NOUN
ma-248	130	13	theorem	theorem	VERB
ma-248	130	14	in	in	ADP
ma-248	130	15	[	[	X
ma-248	130	16	1	1	NUM
ma-248	130	17	]	]	PUNCT
ma-248	130	18	,	,	PUNCT
ma-248	130	19	we	we	PRON
ma-248	130	20	notice	notice	VERB
ma-248	130	21	that	that	SCONJ
ma-248	130	22	,	,	PUNCT
ma-248	130	23	n(t	n(t	PROPN
ma-248	130	24	)	)	PUNCT
ma-248	131	1	=	=	SYM
ma-248	131	2	n(0)e−µt	n(0)e−µt	NOUN
ma-248	132	1	+	+	CCONJ
ma-248	132	2	λ	λ	X
ma-248	132	3	µ	µ	X
ma-248	132	4	(	(	PUNCT
ma-248	132	5	1−	1−	NUM
ma-248	132	6	e(−µt	e(−µt	PROPN
ma-248	132	7	)	)	PUNCT
ma-248	132	8	)	)	PUNCT
ma-248	132	9	.	.	PUNCT
ma-248	133	1	(	(	PUNCT
ma-248	133	2	7	7	NUM
ma-248	133	3	)	)	PUNCT
ma-248	133	4	therefore	therefore	ADV
ma-248	133	5	,	,	PUNCT
ma-248	133	6	from	from	ADP
ma-248	133	7	equation	equation	NOUN
ma-248	133	8	(	(	PUNCT
ma-248	133	9	7	7	X
ma-248	133	10	)	)	PUNCT
ma-248	133	11	the	the	DET
ma-248	133	12	state	state	NOUN
ma-248	133	13	variables	variable	NOUN
ma-248	133	14	(	(	PUNCT
ma-248	133	15	shh	shh	INTJ
ma-248	133	16	,	,	PUNCT
ma-248	133	17	ehh	ehh	PROPN
ma-248	133	18	,	,	PUNCT
ma-248	133	19	ahh	ahh	PROPN
ma-248	133	20	,	,	PUNCT
ma-248	133	21	ihh	ihh	PROPN
ma-248	133	22	,	,	PUNCT
ma-248	133	23	rhh	rhh	PROPN
ma-248	133	24	)	)	PUNCT
ma-248	133	25	has	have	VERB
ma-248	133	26	the	the	DET
ma-248	133	27	possible	possible	ADJ
ma-248	133	28	solutionset	solutionset	NOUN
ma-248	133	29	which	which	PRON
ma-248	133	30	bounded	bound	VERB
ma-248	133	31	and	and	CCONJ
ma-248	133	32	the	the	DET
ma-248	133	33	model	model	NOUN
ma-248	133	34	equation	equation	NOUN
ma-248	133	35	(	(	PUNCT
ma-248	133	36	1	1	X
ma-248	133	37	)	)	PUNCT
ma-248	133	38	is	be	AUX
ma-248	133	39	invariant	invariant	ADJ
ma-248	133	40	ϑ	ϑ	X
ma-248	133	41	∈	∈	PROPN
ma-248	133	42	r5	r5	PROPN
ma-248	133	43	+	+	NOUN
ma-248	133	44	.	.	PUNCT
ma-248	134	1	as	as	ADP
ma-248	134	2	a	a	DET
ma-248	134	3	result	result	NOUN
ma-248	134	4	,	,	PUNCT
ma-248	134	5	model	model	NOUN
ma-248	134	6	(	(	PUNCT
ma-248	134	7	1	1	NUM
ma-248	134	8	)	)	PUNCT
ma-248	134	9	ismathematically	ismathematically	ADV
ma-248	134	10	well	well	ADV
ma-248	134	11	-	-	PUNCT
ma-248	134	12	posed	pose	VERB
ma-248	134	13	and	and	CCONJ
ma-248	134	14	epidemiologically	epidemiologically	ADV
ma-248	134	15	feasible	feasible	ADJ
ma-248	134	16	.	.	PUNCT
ma-248	135	1	�	�	PROPN
ma-248	135	2	3.2	3.2	NUM
ma-248	135	3	.	.	PUNCT
ma-248	136	1	existence	existence	NOUN
ma-248	136	2	of	of	ADP
ma-248	136	3	disease	disease	NOUN
ma-248	136	4	-	-	PUNCT
ma-248	136	5	free	free	ADJ
ma-248	136	6	equilibrium	equilibrium	NOUN
ma-248	136	7	(	(	PUNCT
ma-248	136	8	dfe	dfe	PROPN
ma-248	136	9	)	)	PUNCT
ma-248	136	10	point	point	NOUN
ma-248	136	11	.	.	PUNCT
ma-248	137	1	model	model	NOUN
ma-248	137	2	system	system	NOUN
ma-248	137	3	(	(	PUNCT
ma-248	137	4	1	1	X
ma-248	137	5	)	)	PUNCT
ma-248	137	6	has	have	VERB
ma-248	137	7	a	a	DET
ma-248	137	8	trivial	trivial	ADJ
ma-248	137	9	point	point	NOUN
ma-248	137	10	(	(	PUNCT
ma-248	137	11	0	0	NUM
ma-248	137	12	,	,	PUNCT
ma-248	137	13	0	0	NUM
ma-248	137	14	,	,	PUNCT
ma-248	137	15	0	0	NUM
ma-248	137	16	,	,	PUNCT
ma-248	137	17	0	0	NUM
ma-248	137	18	,	,	PUNCT
ma-248	137	19	0	0	NUM
ma-248	137	20	)	)	PUNCT
ma-248	137	21	,	,	PUNCT
ma-248	137	22	which	which	PRON
ma-248	137	23	is	be	AUX
ma-248	137	24	usually	usually	ADV
ma-248	137	25	ignored	ignore	VERB
ma-248	137	26	in	in	ADP
ma-248	137	27	the	the	DET
ma-248	137	28	model	model	NOUN
ma-248	137	29	’s	’s	PART
ma-248	137	30	analysis	analysis	NOUN
ma-248	137	31	.	.	PUNCT
ma-248	138	1	the	the	DET
ma-248	138	2	right	right	ADJ
ma-248	138	3	-	-	PUNCT
ma-248	138	4	hand	hand	NOUN
ma-248	138	5	side	side	NOUN
ma-248	138	6	of	of	ADP
ma-248	138	7	(	(	PUNCT
ma-248	138	8	1	1	NUM
ma-248	138	9	)	)	PUNCT
ma-248	138	10	is	be	AUX
ma-248	138	11	set	set	VERB
ma-248	138	12	tozero	tozero	NOUN
ma-248	138	13	and	and	CCONJ
ma-248	138	14	solved	solve	VERB
ma-248	138	15	,	,	PUNCT
ma-248	138	16	the	the	DET
ma-248	138	17	disease	disease	NOUN
ma-248	138	18	-	-	PUNCT
ma-248	138	19	free	free	ADJ
ma-248	138	20	equilibrium	equilibrium	NOUN
ma-248	138	21	becomes	become	VERB
ma-248	138	22	e0	e0	PROPN
ma-248	138	23	=	=	PUNCT
ma-248	138	24	(	(	PUNCT
ma-248	138	25	λ	λ	X
ma-248	138	26	µ	µ	X
ma-248	138	27	,	,	PUNCT
ma-248	138	28	0	0	NUM
ma-248	138	29	,	,	PUNCT
ma-248	138	30	0	0	NUM
ma-248	138	31	,	,	PUNCT
ma-248	138	32	0	0	NUM
ma-248	138	33	,	,	PUNCT
ma-248	138	34	0	0	NUM
ma-248	138	35	)	)	PUNCT
ma-248	138	36	.	.	PUNCT
ma-248	139	1	(	(	PUNCT
ma-248	139	2	8)	8)	NUM
ma-248	139	3	3.3	3.3	NUM
ma-248	139	4	.	.	PUNCT
ma-248	139	5	basic	basic	ADJ
ma-248	139	6	reproduction	reproduction	NOUN
ma-248	139	7	number	number	NOUN
ma-248	139	8	.	.	PUNCT
ma-248	140	1	the	the	DET
ma-248	140	2	basic	basic	ADJ
ma-248	140	3	reproduction	reproduction	NOUN
ma-248	140	4	number	number	NOUN
ma-248	140	5	,	,	PUNCT
ma-248	140	6	r0	r0	NOUN
ma-248	140	7	,	,	PUNCT
ma-248	140	8	is	be	AUX
ma-248	140	9	one	one	NUM
ma-248	140	10	of	of	ADP
ma-248	140	11	the	the	DET
ma-248	140	12	things	thing	NOUN
ma-248	140	13	thatmodellers	thatmodeller	NOUN
ma-248	140	14	look	look	VERB
ma-248	140	15	for	for	ADP
ma-248	140	16	when	when	SCONJ
ma-248	140	17	it	it	PRON
ma-248	140	18	comes	come	VERB
ma-248	140	19	to	to	ADP
ma-248	140	20	infectious	infectious	ADJ
ma-248	140	21	disease	disease	NOUN
ma-248	140	22	modelling	modelling	NOUN
ma-248	140	23	.	.	PUNCT
ma-248	141	1	the	the	DET
ma-248	141	2	basic	basic	ADJ
ma-248	141	3	reproduction	reproduction	NOUN
ma-248	141	4	numberis	numberis	NOUN
ma-248	141	5	sufficient	sufficient	ADJ
ma-248	141	6	for	for	ADP
ma-248	141	7	determining	determine	VERB
ma-248	141	8	the	the	DET
ma-248	141	9	condition	condition	NOUN
ma-248	141	10	of	of	ADP
ma-248	141	11	the	the	DET
ma-248	141	12	disease	disease	NOUN
ma-248	141	13	.	.	PUNCT
ma-248	142	1	in	in	ADP
ma-248	142	2	a	a	DET
ma-248	142	3	completely	completely	ADV
ma-248	142	4	naive	naive	ADJ
ma-248	142	5	population	population	NOUN
ma-248	142	6	,	,	PUNCT
ma-248	142	7	thebasic	thebasic	ADJ
ma-248	142	8	reproduction	reproduction	NOUN
ma-248	142	9	number	number	NOUN
ma-248	142	10	is	be	AUX
ma-248	142	11	defined	define	VERB
ma-248	142	12	as	as	ADP
ma-248	142	13	the	the	DET
ma-248	142	14	number	number	NOUN
ma-248	142	15	of	of	ADP
ma-248	142	16	persons	person	NOUN
ma-248	142	17	one	one	NUM
ma-248	142	18	infected	infect	VERB
ma-248	142	19	person	person	NOUN
ma-248	142	20	may	may	AUX
ma-248	142	21	infect	infect	VERB
ma-248	142	22	.	.	PUNCT
ma-248	143	1	itis	itis	NOUN
ma-248	143	2	denoted	denote	VERB
ma-248	143	3	by	by	ADP
ma-248	143	4	r0	r0	NOUN
ma-248	143	5	,	,	PUNCT
ma-248	143	6	and	and	CCONJ
ma-248	143	7	when	when	SCONJ
ma-248	143	8	r0	r0	NOUN
ma-248	143	9	>	>	X
ma-248	143	10	1	1	NUM
ma-248	143	11	,	,	PUNCT
ma-248	143	12	it	it	PRON
ma-248	143	13	means	mean	VERB
ma-248	143	14	the	the	DET
ma-248	143	15	disease	disease	NOUN
ma-248	143	16	will	will	AUX
ma-248	143	17	spread	spread	VERB
ma-248	143	18	unless	unless	SCONJ
ma-248	143	19	preventive	preventive	ADJ
ma-248	143	20	strategiesare	strategiesare	NOUN
ma-248	143	21	cautiously	cautiously	ADV
ma-248	143	22	enacted	enact	VERB
ma-248	143	23	.	.	PUNCT
ma-248	144	1	however	however	ADV
ma-248	144	2	,	,	PUNCT
ma-248	144	3	when	when	SCONJ
ma-248	144	4	r0	r0	NOUN
ma-248	144	5	<	<	X
ma-248	144	6	1	1	NUM
ma-248	144	7	,	,	PUNCT
ma-248	144	8	the	the	DET
ma-248	144	9	infection	infection	NOUN
ma-248	144	10	dies	die	VERB
ma-248	144	11	without	without	ADP
ma-248	144	12	strenuous	strenuous	ADJ
ma-248	144	13	effort	effort	NOUN
ma-248	144	14	.	.	PUNCT
ma-248	145	1	thederivation	thederivation	NOUN
ma-248	145	2	of	of	ADP
ma-248	145	3	r0	r0	NOUN
ma-248	145	4	is	be	AUX
ma-248	145	5	important	important	ADJ
ma-248	145	6	in	in	ADP
ma-248	145	7	modelling	modelling	NOUN
ma-248	145	8	and	and	CCONJ
ma-248	145	9	can	can	AUX
ma-248	145	10	be	be	AUX
ma-248	145	11	derived	derive	VERB
ma-248	145	12	by	by	ADP
ma-248	145	13	the	the	DET
ma-248	145	14	method	method	NOUN
ma-248	145	15	of	of	ADP
ma-248	145	16	[	[	X
ma-248	145	17	19	19	NUM
ma-248	145	18	]	]	PUNCT
ma-248	145	19	.	.	PUNCT
ma-248	146	1	the	the	DET
ma-248	146	2	(	(	PUNCT
ma-248	146	3	9	9	NUM
ma-248	146	4	)	)	PUNCT
ma-248	146	5	is	be	AUX
ma-248	146	6	theformulae	theformulae	NOUN
ma-248	146	7	guaranteeing	guarantee	VERB
ma-248	146	8	r0	r0	NOUN
ma-248	146	9	derivation	derivation	NOUN
ma-248	146	10	.	.	PUNCT
ma-248	147	1	r0	r0	NOUN
ma-248	147	2	=	=	SYM
ma-248	147	3	ρ(fv−1	ρ(fv−1	PROPN
ma-248	147	4	)	)	PUNCT
ma-248	147	5	.	.	PUNCT
ma-248	148	1	(	(	PUNCT
ma-248	148	2	9	9	X
ma-248	148	3	)	)	PUNCT
ma-248	148	4	the	the	DET
ma-248	148	5	ρ	ρ	NOUN
ma-248	148	6	is	be	AUX
ma-248	148	7	considered	consider	VERB
ma-248	148	8	as	as	ADP
ma-248	148	9	the	the	DET
ma-248	148	10	largest	large	ADJ
ma-248	148	11	entry	entry	NOUN
ma-248	148	12	in	in	ADP
ma-248	148	13	the	the	DET
ma-248	148	14	derivation	derivation	NOUN
ma-248	148	15	of	of	ADP
ma-248	148	16	the	the	DET
ma-248	148	17	next	next	ADJ
ma-248	148	18	generation	generation	NOUN
ma-248	148	19	matrix	matrix	NOUN
ma-248	148	20	of	of	ADP
ma-248	148	21	r0	r0	NOUN
ma-248	148	22	=	=	SYM
ma-248	148	23	ρ(fv−1	ρ(fv−1	PROPN
ma-248	148	24	)	)	PUNCT
ma-248	148	25	,	,	PUNCT
ma-248	148	26	where	where	SCONJ
ma-248	148	27	f	f	PROPN
ma-248	148	28	is	be	AUX
ma-248	148	29	the	the	DET
ma-248	148	30	coming	come	VERB
ma-248	148	31	infection	infection	NOUN
ma-248	148	32	into	into	ADP
ma-248	148	33	compartment	compartment	NOUN
ma-248	148	34	i	i	PRON
ma-248	148	35	and	and	CCONJ
ma-248	148	36	v	v	NOUN
ma-248	148	37	.	.	PUNCT
ma-248	149	1	thus	thus	ADV
ma-248	149	2	,	,	PUNCT
ma-248	149	3	the	the	DET
ma-248	149	4	transfer	transfer	NOUN
ma-248	149	5	of	of	ADP
ma-248	149	6	indi	indi	NOUN
ma-248	149	7	-	-	PUNCT
ma-248	149	8	viduals	vidual	NOUN
ma-248	149	9	out	out	ADP
ma-248	149	10	of	of	ADP
ma-248	149	11	compartment	compartment	NOUN
ma-248	149	12	i	i	PRON
ma-248	149	13	by	by	ADP
ma-248	149	14	death	death	NOUN
ma-248	149	15	.	.	PUNCT
ma-248	150	1	technically	technically	ADV
ma-248	150	2	,	,	PUNCT
ma-248	150	3	the	the	DET
ma-248	150	4	r0	r0	NOUN
ma-248	150	5	becomes	become	VERB
ma-248	150	6	the	the	DET
ma-248	150	7	largest	large	ADJ
ma-248	150	8	eigenvalue	eigenvalue	NOUN
ma-248	150	9	of	of	ADP
ma-248	150	10	the	the	DET
ma-248	150	11	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	150	12	eur	eur	PROPN
ma-248	150	13	.	.	PUNCT
ma-248	151	1	j.	j.	PROPN
ma-248	151	2	math	math	PROPN
ma-248	151	3	.	.	PUNCT
ma-248	152	1	anal	anal	PROPN
ma-248	152	2	.	.	PUNCT
ma-248	153	1	10.28924	10.28924	NUM
ma-248	153	2	/	/	SYM
ma-248	153	3	ada	ada	PROPN
ma-248	153	4	/	/	SYM
ma-248	153	5	ma.4.21	ma.4.21	NOUN
ma-248	153	6	7matrix	7matrix	NUM
ma-248	153	7	resulting	result	VERB
ma-248	153	8	from	from	ADP
ma-248	153	9	the	the	DET
ma-248	153	10	partial	partial	ADJ
ma-248	153	11	derivative	derivative	NOUN
ma-248	153	12	of	of	ADP
ma-248	153	13	(	(	PUNCT
ma-248	153	14	9	9	NUM
ma-248	153	15	)	)	PUNCT
ma-248	153	16	.	.	PUNCT
ma-248	154	1	what	what	PRON
ma-248	154	2	happens	happen	VERB
ma-248	154	3	next	next	ADV
ma-248	154	4	is	be	AUX
ma-248	154	5	the	the	DET
ma-248	154	6	infected	infect	VERB
ma-248	154	7	compartmentsof	compartmentsof	NOUN
ma-248	154	8	model	model	NOUN
ma-248	154	9	(	(	PUNCT
ma-248	154	10	1	1	X
ma-248	154	11	)	)	PUNCT
ma-248	154	12	are	be	AUX
ma-248	154	13	given	give	VERB
ma-248	154	14	by	by	ADP
ma-248	154	15	d	d	PROPN
ma-248	154	16	dt	dt	NOUN
ma-248	154	17	ehh	ehh	NOUN
ma-248	154	18	=	=	PUNCT
ma-248	154	19	η1ihhshh	η1ihhshh	NOUN
ma-248	154	20	−	−	NOUN
ma-248	154	21	k1τ1ehh	k1τ1ehh	X
ma-248	154	22	−	−	PROPN
ma-248	155	1	(	(	PUNCT
ma-248	155	2	1−	1−	NUM
ma-248	155	3	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	155	4	−	−	NOUN
ma-248	155	5	µehh	µehh	NOUN
ma-248	155	6	,	,	PUNCT
ma-248	155	7	d	d	NOUN
ma-248	155	8	dt	dt	X
ma-248	155	9	ahh	ahh	INTJ
ma-248	155	10	=	=	PUNCT
ma-248	155	11	(	(	PUNCT
ma-248	155	12	1−	1−	NUM
ma-248	155	13	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	155	14	−	−	PROPN
ma-248	155	15	(	(	PUNCT
ma-248	155	16	τ2	τ2	NOUN
ma-248	155	17	+	+	NUM
ma-248	155	18	τ3	τ3	NOUN
ma-248	155	19	+	+	X
ma-248	155	20	µ)ahh	µ)ahh	PROPN
ma-248	155	21	,	,	PUNCT
ma-248	155	22	d	d	NOUN
ma-248	155	23	dt	dt	X
ma-248	155	24	ihh	ihh	PROPN
ma-248	155	25	=	=	PUNCT
ma-248	155	26	k1τ1ehh	k1τ1ehh	X
ma-248	155	27	−	−	PROPN
ma-248	155	28	(	(	PUNCT
ma-248	155	29	ψ1	ψ1	NOUN
ma-248	155	30	+	+	CCONJ
ma-248	155	31	ψ2	ψ2	NOUN
ma-248	155	32	+	+	CCONJ
ma-248	155	33	µ)ihh	µ)ihh	NOUN
ma-248	155	34	.	.	PUNCT
ma-248	156	1	we	we	PRON
ma-248	156	2	notice	notice	VERB
ma-248	156	3	from	from	ADP
ma-248	156	4	the	the	DET
ma-248	156	5	diseased	diseased	ADJ
ma-248	156	6	compartment	compartment	NOUN
ma-248	156	7	that	that	PRON
ma-248	156	8	,	,	PUNCT
ma-248	156	9	f	f	PROPN
ma-248	156	10	=	=	SYM
ma-248	156	11	η1ihhshh0	η1ihhshh0	PROPN
ma-248	156	12	0	0	NUM
ma-248	156	13			NOUN
ma-248	156	14	,	,	PUNCT
ma-248	156	15	and	and	CCONJ
ma-248	156	16	v	v	NOUN
ma-248	156	17	=	=	NOUN
ma-248	156	18			NOUN
ma-248	156	19	k1τ1ehh	k1τ1ehh	NOUN
ma-248	156	20	+	+	CCONJ
ma-248	156	21	(	(	PUNCT
ma-248	156	22	1−	1−	NUM
ma-248	156	23	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	156	24	+	+	CCONJ
ma-248	156	25	µehh	µehh	NOUN
ma-248	156	26	−(1−	−(1−	NOUN
ma-248	156	27	k1)τ1ehh	k1)τ1ehh	PROPN
ma-248	156	28	+	+	CCONJ
ma-248	156	29	(	(	PUNCT
ma-248	156	30	τ2	τ2	NOUN
ma-248	156	31	+	+	NUM
ma-248	156	32	τ3	τ3	NOUN
ma-248	156	33	+	+	X
ma-248	156	34	µ)ahh	µ)ahh	NOUN
ma-248	156	35	−k1τ1ehh	−k1τ1ehh	NOUN
ma-248	157	1	+	+	CCONJ
ma-248	157	2	(	(	PUNCT
ma-248	157	3	ψ1	ψ1	NOUN
ma-248	157	4	+	+	NUM
ma-248	157	5	ψ2	ψ2	NOUN
ma-248	157	6	+	+	CCONJ
ma-248	157	7	µ)ihh	µ)ihh	NOUN
ma-248	157	8			NOUN
ma-248	157	9	.	.	PUNCT
ma-248	158	1	(	(	PUNCT
ma-248	158	2	10	10	NUM
ma-248	158	3	)	)	PUNCT
ma-248	158	4	when	when	SCONJ
ma-248	158	5	f	f	PROPN
ma-248	158	6	is	be	AUX
ma-248	158	7	evaluated	evaluate	VERB
ma-248	158	8	at	at	ADP
ma-248	158	9	e0	e0	PROPN
ma-248	158	10	,	,	PUNCT
ma-248	158	11	then	then	ADV
ma-248	158	12	fe0	fe0	VERB
ma-248	158	13	becomes	become	VERB
ma-248	158	14	;	;	PUNCT
ma-248	158	15	fe0	fe0	NOUN
ma-248	158	16	=	=	SYM
ma-248	158	17			NOUN
ma-248	158	18	0	0	NUM
ma-248	158	19	0	0	NUM
ma-248	158	20	η1λ	η1λ	PROPN
ma-248	158	21	µ	µ	X
ma-248	158	22	0	0	NUM
ma-248	158	23	0	0	NUM
ma-248	158	24	0	0	NUM
ma-248	158	25	0	0	NUM
ma-248	158	26	0	0	SYM
ma-248	158	27	0	0	NUM
ma-248	158	28			ADJ
ma-248	158	29	.	.	PUNCT
ma-248	159	1	(	(	PUNCT
ma-248	159	2	11	11	X
ma-248	159	3	)	)	PUNCT
ma-248	159	4	evaluate	evaluate	VERB
ma-248	159	5	v	v	NOUN
ma-248	159	6	at	at	ADP
ma-248	159	7	e0	e0	PROPN
ma-248	159	8	,	,	PUNCT
ma-248	159	9	which	which	PRON
ma-248	159	10	gives	give	VERB
ma-248	159	11	;	;	PUNCT
ma-248	159	12	ve0	ve0	NOUN
ma-248	159	13	=	=	SYM
ma-248	159	14			NOUN
ma-248	159	15	(	(	PUNCT
ma-248	159	16	k1τ1	k1τ1	PROPN
ma-248	159	17	+	+	CCONJ
ma-248	159	18	µ+	µ+	X
ma-248	159	19	(	(	PUNCT
ma-248	159	20	1−	1−	NUM
ma-248	159	21	k1)τ1	k1)τ1	X
ma-248	159	22	)	)	PUNCT
ma-248	159	23	0	0	NUM
ma-248	159	24	0	0	NUM
ma-248	160	1	−(1−	−(1−	NOUN
ma-248	160	2	k1)τ1	k1)τ1	X
ma-248	160	3	(	(	PUNCT
ma-248	160	4	τ2	τ2	NOUN
ma-248	160	5	+	+	NUM
ma-248	160	6	τ3	τ3	NOUN
ma-248	160	7	+	+	CCONJ
ma-248	160	8	µ	µ	NOUN
ma-248	160	9	)	)	PUNCT
ma-248	160	10	0	0	NUM
ma-248	161	1	−k1τ1	−k1τ1	NOUN
ma-248	161	2	0	0	NUM
ma-248	161	3	(	(	PUNCT
ma-248	161	4	ψ1	ψ1	NOUN
ma-248	161	5	+	+	CCONJ
ma-248	161	6	ψ2	ψ2	NOUN
ma-248	161	7	+	+	CCONJ
ma-248	161	8	µ	µ	X
ma-248	161	9	)	)	PUNCT
ma-248	161	10			NOUN
ma-248	161	11	.	.	PUNCT
ma-248	162	1	(	(	PUNCT
ma-248	162	2	12	12	NUM
ma-248	162	3	)	)	PUNCT
ma-248	162	4	the	the	DET
ma-248	162	5	basic	basic	ADJ
ma-248	162	6	reproduction	reproduction	NOUN
ma-248	162	7	number	number	NOUN
ma-248	162	8	of	of	ADP
ma-248	162	9	model	model	NOUN
ma-248	162	10	system	system	NOUN
ma-248	162	11	(	(	PUNCT
ma-248	162	12	1	1	X
ma-248	162	13	)	)	PUNCT
ma-248	162	14	is	be	AUX
ma-248	162	15	determined	determine	VERB
ma-248	162	16	by	by	ADP
ma-248	162	17	using	use	VERB
ma-248	162	18	the	the	DET
ma-248	162	19	method	method	NOUN
ma-248	162	20	of	of	ADP
ma-248	162	21	[	[	X
ma-248	162	22	19],which	19],which	NUM
ma-248	162	23	gives	give	VERB
ma-248	162	24	;	;	PUNCT
ma-248	162	25	r0	r0	NOUN
ma-248	162	26	=	=	SYM
ma-248	162	27	η1λk1τ1	η1λk1τ1	PROPN
ma-248	162	28	µ(k1τ1	µ(k1τ1	NOUN
ma-248	162	29	+	+	CCONJ
ma-248	162	30	µ+	µ+	PUNCT
ma-248	162	31	(	(	PUNCT
ma-248	162	32	1−	1−	NUM
ma-248	162	33	k1)τ1)(ψ1	k1)τ1)(ψ1	NOUN
ma-248	162	34	+	+	CCONJ
ma-248	162	35	ψ2	ψ2	NOUN
ma-248	162	36	+	+	CCONJ
ma-248	162	37	µ	µ	NOUN
ma-248	162	38	)	)	PUNCT
ma-248	162	39	.	.	PUNCT
ma-248	163	1	(	(	PUNCT
ma-248	163	2	13	13	NUM
ma-248	163	3	)	)	PUNCT
ma-248	163	4	3.4	3.4	NUM
ma-248	163	5	.	.	PUNCT
ma-248	164	1	existence	existence	NOUN
ma-248	164	2	of	of	ADP
ma-248	164	3	an	an	DET
ma-248	164	4	endemic	endemic	ADJ
ma-248	164	5	equilibrium	equilibrium	NOUN
ma-248	164	6	point	point	NOUN
ma-248	164	7	(	(	PUNCT
ma-248	164	8	eep	eep	NOUN
ma-248	164	9	)	)	PUNCT
ma-248	164	10	.	.	PUNCT
ma-248	165	1	endemic	endemic	ADJ
ma-248	165	2	equilibrium	equilibrium	NOUN
ma-248	165	3	exists	exist	VERB
ma-248	165	4	when	when	SCONJ
ma-248	165	5	there	there	PRON
ma-248	165	6	isa	isa	VERB
ma-248	165	7	presence	presence	NOUN
ma-248	165	8	of	of	ADP
ma-248	165	9	infection	infection	NOUN
ma-248	165	10	.	.	PUNCT
ma-248	166	1	the	the	DET
ma-248	166	2	model	model	NOUN
ma-248	166	3	(	(	PUNCT
ma-248	166	4	1	1	X
ma-248	166	5	)	)	PUNCT
ma-248	166	6	has	have	VERB
ma-248	166	7	a	a	DET
ma-248	166	8	unique	unique	ADJ
ma-248	166	9	endemic	endemic	ADJ
ma-248	166	10	equilibrium	equilibrium	NOUN
ma-248	166	11	given	give	VERB
ma-248	166	12	by	by	ADP
ma-248	166	13	;	;	PUNCT
ma-248	166	14	e∗	e∗	PROPN
ma-248	166	15	=	=	SYM
ma-248	166	16	(	(	PUNCT
ma-248	166	17	s∗hh	s∗hh	PROPN
ma-248	166	18	,	,	PUNCT
ma-248	166	19	e	e	X
ma-248	166	20	∗	∗	NOUN
ma-248	166	21	hh	hh	PROPN
ma-248	166	22	,	,	PUNCT
ma-248	166	23	a	a	DET
ma-248	166	24	∗	∗	NOUN
ma-248	166	25	hh	hh	PROPN
ma-248	166	26	,	,	PUNCT
ma-248	166	27	i	i	PRON
ma-248	166	28	∗	∗	VERB
ma-248	166	29	hh	hh	PROPN
ma-248	166	30	,	,	PUNCT
ma-248	166	31	r	r	NOUN
ma-248	166	32	∗	∗	NOUN
ma-248	166	33	hh	hh	PROPN
ma-248	166	34	)	)	PUNCT
ma-248	166	35	,	,	PUNCT
ma-248	166	36	(	(	PUNCT
ma-248	166	37	14	14	NUM
ma-248	166	38	)	)	PUNCT
ma-248	166	39	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	166	40	eur	eur	PROPN
ma-248	166	41	.	.	PUNCT
ma-248	167	1	j.	j.	PROPN
ma-248	167	2	math	math	PROPN
ma-248	167	3	.	.	PUNCT
ma-248	168	1	anal	anal	PROPN
ma-248	168	2	.	.	PUNCT
ma-248	169	1	10.28924	10.28924	NUM
ma-248	169	2	/	/	SYM
ma-248	169	3	ada	ada	PROPN
ma-248	169	4	/	/	SYM
ma-248	169	5	ma.4.21	ma.4.21	NOUN
ma-248	169	6	8where	8where	NUM
ma-248	170	1	s∗hh	s∗hh	ADJ
ma-248	170	2	=	=	SYM
ma-248	170	3	λ	λ	NOUN
ma-248	170	4	+	+	NOUN
ma-248	170	5	ωr∗hh	ωr∗hh	PROPN
ma-248	170	6	µ+	µ+	PRON
ma-248	170	7	η1i	η1i	PROPN
ma-248	170	8	∗	∗	NOUN
ma-248	170	9	hh	hh	PROPN
ma-248	170	10	,	,	PUNCT
ma-248	170	11	e∗hh	e∗hh	PROPN
ma-248	170	12	=	=	SYM
ma-248	170	13	η1i	η1i	PROPN
ma-248	170	14	∗	∗	NOUN
ma-248	170	15	hhs	hhs	PROPN
ma-248	170	16	∗	∗	PROPN
ma-248	170	17	hh	hh	PROPN
ma-248	170	18	(	(	PUNCT
ma-248	170	19	µ+	µ+	NOUN
ma-248	170	20	τ1	τ1	NOUN
ma-248	170	21	)	)	PUNCT
ma-248	170	22	,	,	PUNCT
ma-248	170	23	a∗hh	a∗hh	PROPN
ma-248	170	24	=	=	SYM
ma-248	170	25	(	(	PUNCT
ma-248	170	26	1−	1−	NUM
ma-248	170	27	k1)τ1e∗hh	k1)τ1e∗hh	PROPN
ma-248	170	28	(	(	PUNCT
ma-248	170	29	τ2	τ2	NOUN
ma-248	170	30	+	+	NUM
ma-248	170	31	τ3	τ3	NOUN
ma-248	170	32	+	+	CCONJ
ma-248	170	33	µ	µ	NOUN
ma-248	170	34	)	)	PUNCT
ma-248	170	35	,	,	PUNCT
ma-248	170	36	i∗hh	i∗hh	PROPN
ma-248	170	37	=	=	SYM
ma-248	170	38	k1τ1e	k1τ1e	NUM
ma-248	170	39	∗	∗	NOUN
ma-248	170	40	hh	hh	PROPN
ma-248	170	41	(	(	PUNCT
ma-248	170	42	ψ1	ψ1	NOUN
ma-248	170	43	+	+	CCONJ
ma-248	170	44	ψ2	ψ2	NOUN
ma-248	170	45	+	+	CCONJ
ma-248	170	46	µ	µ	X
ma-248	170	47	)	)	PUNCT
ma-248	170	48	,	,	PUNCT
ma-248	170	49	r∗hh	r∗hh	PROPN
ma-248	170	50	=	=	PUNCT
ma-248	170	51	τ2a	τ2a	NOUN
ma-248	170	52	∗	∗	NOUN
ma-248	170	53	hh	hh	NOUN
ma-248	171	1	+	+	X
ma-248	171	2	ψ1e	ψ1e	NOUN
ma-248	171	3	∗	∗	NOUN
ma-248	171	4	hh	hh	PROPN
ma-248	171	5	(	(	PUNCT
ma-248	171	6	ω	ω	PROPN
ma-248	171	7	+	+	X
ma-248	171	8	µ	µ	NUM
ma-248	171	9	)	)	PUNCT
ma-248	171	10	.	.	PUNCT
ma-248	172	1	3.5	3.5	NUM
ma-248	172	2	.	.	PUNCT
ma-248	172	3	stability	stability	NOUN
ma-248	172	4	of	of	ADP
ma-248	172	5	the	the	DET
ma-248	172	6	disease	disease	NOUN
ma-248	172	7	-	-	PUNCT
ma-248	172	8	free	free	ADJ
ma-248	172	9	equilibrium	equilibrium	NOUN
ma-248	172	10	point	point	NOUN
ma-248	172	11	.	.	PUNCT
ma-248	173	1	here	here	ADV
ma-248	173	2	,	,	PUNCT
ma-248	173	3	the	the	DET
ma-248	173	4	global	global	ADJ
ma-248	173	5	and	and	CCONJ
ma-248	173	6	local	local	ADJ
ma-248	173	7	stability	stability	NOUN
ma-248	173	8	analysesof	analysesof	VERB
ma-248	173	9	the	the	DET
ma-248	173	10	meningitis	meningitis	NOUN
ma-248	173	11	model	model	NOUN
ma-248	173	12	(	(	PUNCT
ma-248	173	13	1	1	NUM
ma-248	173	14	)	)	PUNCT
ma-248	173	15	at	at	ADP
ma-248	173	16	the	the	DET
ma-248	173	17	disease	disease	NOUN
ma-248	173	18	-	-	PUNCT
ma-248	173	19	free	free	ADJ
ma-248	173	20	equilibrium	equilibrium	NOUN
ma-248	173	21	are	be	AUX
ma-248	173	22	studied	study	VERB
ma-248	173	23	.	.	PUNCT
ma-248	174	1	the	the	DET
ma-248	174	2	geometrical	geometrical	ADJ
ma-248	174	3	approachof	approachof	ADV
ma-248	174	4	lyapunov	lyapunov	ADJ
ma-248	174	5	function	function	NOUN
ma-248	174	6	theory	theory	NOUN
ma-248	174	7	by	by	ADP
ma-248	174	8	[	[	X
ma-248	174	9	20	20	NUM
ma-248	174	10	]	]	PUNCT
ma-248	174	11	would	would	AUX
ma-248	174	12	be	be	AUX
ma-248	174	13	used	use	VERB
ma-248	174	14	to	to	PART
ma-248	174	15	prove	prove	VERB
ma-248	174	16	that	that	DET
ma-248	174	17	model	model	NOUN
ma-248	174	18	(	(	PUNCT
ma-248	174	19	1	1	X
ma-248	174	20	)	)	PUNCT
ma-248	174	21	is	be	AUX
ma-248	174	22	globally	globally	ADV
ma-248	174	23	asymptoticallystable	asymptoticallystable	ADJ
ma-248	174	24	at	at	ADP
ma-248	174	25	the	the	DET
ma-248	174	26	disease	disease	NOUN
ma-248	174	27	-	-	PUNCT
ma-248	174	28	free	free	ADJ
ma-248	174	29	equilibrium	equilibrium	NOUN
ma-248	174	30	.	.	PUNCT
ma-248	175	1	the	the	DET
ma-248	175	2	results	result	NOUN
ma-248	175	3	are	be	AUX
ma-248	175	4	provided	provide	VERB
ma-248	175	5	as	as	SCONJ
ma-248	175	6	follows	follow	VERB
ma-248	175	7	;	;	PUNCT
ma-248	175	8	j	j	PROPN
ma-248	175	9	=	=	SYM
ma-248	175	10			ADJ
ma-248	175	11	−µ−	−µ−	NOUN
ma-248	175	12	η1ihh	η1ihh	VERB
ma-248	175	13	0	0	SYM
ma-248	175	14	0	0	NUM
ma-248	176	1	−η1shh	−η1shh	PROPN
ma-248	176	2	ω	ω	NUM
ma-248	176	3	η1ihh	η1ihh	VERB
ma-248	176	4	−	−	PROPN
ma-248	176	5	(	(	PUNCT
ma-248	176	6	k1τ1	k1τ1	PROPN
ma-248	176	7	+	+	CCONJ
ma-248	176	8	µ+	µ+	X
ma-248	176	9	(	(	PUNCT
ma-248	176	10	1−	1−	NUM
ma-248	176	11	k1)τ1	k1)τ1	X
ma-248	176	12	)	)	PUNCT
ma-248	176	13	0	0	PUNCT
ma-248	177	1	η1shh	η1shh	NOUN
ma-248	177	2	0	0	NUM
ma-248	177	3	0	0	NUM
ma-248	177	4	(	(	PUNCT
ma-248	177	5	1−	1−	NUM
ma-248	177	6	k1)τ1	k1)τ1	X
ma-248	177	7	−(τ2	−(τ2	NUM
ma-248	177	8	+	+	CCONJ
ma-248	177	9	τ3	τ3	NOUN
ma-248	177	10	+	+	CCONJ
ma-248	177	11	µ	µ	X
ma-248	177	12	)	)	PUNCT
ma-248	177	13	0	0	NUM
ma-248	177	14	0	0	NUM
ma-248	177	15	0	0	NUM
ma-248	177	16	k1τ1	k1τ1	NOUN
ma-248	177	17	0	0	NUM
ma-248	177	18	−(ψ1	−(ψ1	NOUN
ma-248	177	19	+	+	CCONJ
ma-248	177	20	ψ2	ψ2	NOUN
ma-248	177	21	+	+	CCONJ
ma-248	177	22	µ	µ	X
ma-248	177	23	)	)	PUNCT
ma-248	177	24	0	0	NUM
ma-248	177	25	0	0	NUM
ma-248	177	26	0	0	NUM
ma-248	177	27	τ2	τ2	ADJ
ma-248	177	28	ψ1	ψ1	ADJ
ma-248	177	29	−(ω	−(ω	NOUN
ma-248	177	30	+	+	CCONJ
ma-248	177	31	µ	µ	X
ma-248	177	32	)	)	PUNCT
ma-248	177	33			NOUN
ma-248	177	34	.	.	PUNCT
ma-248	178	1	(	(	PUNCT
ma-248	178	2	15)evaluating	15)evaluating	NUM
ma-248	178	3	the	the	DET
ma-248	178	4	jacobian	jacobian	PROPN
ma-248	178	5	in	in	ADP
ma-248	178	6	(	(	PUNCT
ma-248	178	7	15	15	NUM
ma-248	178	8	)	)	PUNCT
ma-248	178	9	at	at	ADP
ma-248	178	10	the	the	DET
ma-248	178	11	e0	e0	PROPN
ma-248	178	12	gives	give	VERB
ma-248	178	13	;	;	PUNCT
ma-248	178	14	j	j	PROPN
ma-248	178	15	=	=	SYM
ma-248	178	16			PROPN
ma-248	179	1	−µ	−µ	NOUN
ma-248	179	2	0	0	NUM
ma-248	179	3	0	0	NUM
ma-248	180	1	−η1	−η1	PROPN
ma-248	180	2	λ	λ	PROPN
ma-248	180	3	µ	µ	X
ma-248	180	4	ω	ω	X
ma-248	180	5	0	0	NUM
ma-248	181	1	−	−	PROPN
ma-248	182	1	(	(	PUNCT
ma-248	182	2	k1τ1	k1τ1	PROPN
ma-248	182	3	+	+	CCONJ
ma-248	182	4	µ+	µ+	X
ma-248	182	5	(	(	PUNCT
ma-248	182	6	1−	1−	NUM
ma-248	182	7	k1)τ1	k1)τ1	X
ma-248	182	8	)	)	PUNCT
ma-248	182	9	0	0	NUM
ma-248	182	10	η1	η1	NOUN
ma-248	182	11	λ	λ	X
ma-248	182	12	µ	µ	X
ma-248	182	13	0	0	NUM
ma-248	182	14	0	0	NUM
ma-248	183	1	(	(	PUNCT
ma-248	183	2	1−	1−	NUM
ma-248	183	3	k1)τ1	k1)τ1	X
ma-248	183	4	−(τ2	−(τ2	NUM
ma-248	183	5	+	+	CCONJ
ma-248	183	6	τ3	τ3	NOUN
ma-248	183	7	+	+	CCONJ
ma-248	183	8	µ	µ	X
ma-248	183	9	)	)	PUNCT
ma-248	183	10	0	0	NUM
ma-248	183	11	0	0	NUM
ma-248	183	12	0	0	NUM
ma-248	184	1	k1τ1	k1τ1	NOUN
ma-248	184	2	0	0	NUM
ma-248	184	3	−(ψ1	−(ψ1	NOUN
ma-248	184	4	+	+	CCONJ
ma-248	184	5	ψ2	ψ2	NOUN
ma-248	184	6	+	+	CCONJ
ma-248	184	7	µ	µ	X
ma-248	184	8	)	)	PUNCT
ma-248	184	9	0	0	NUM
ma-248	185	1	0	0	NUM
ma-248	185	2	0	0	NUM
ma-248	185	3	τ2	τ2	ADJ
ma-248	185	4	ψ1	ψ1	ADJ
ma-248	185	5	−(ω	−(ω	NOUN
ma-248	185	6	+	+	X
ma-248	185	7	µ	µ	X
ma-248	185	8	)	)	PUNCT
ma-248	185	9			NOUN
ma-248	185	10	.	.	PUNCT
ma-248	186	1	clearly	clearly	ADV
ma-248	186	2	,	,	PUNCT
ma-248	186	3	λ1	λ1	PROPN
ma-248	186	4	=	=	SYM
ma-248	186	5	−µ	−µ	NOUN
ma-248	186	6	,	,	PUNCT
ma-248	186	7	λ2	λ2	NOUN
ma-248	186	8	=	=	SYM
ma-248	186	9	−(ω	−(ω	NOUN
ma-248	186	10	+	+	X
ma-248	186	11	µ	µ	NOUN
ma-248	186	12	)	)	PUNCT
ma-248	186	13	,	,	PUNCT
ma-248	186	14	λ3	λ3	PROPN
ma-248	186	15	=	=	SYM
ma-248	186	16	−(τ2	−(τ2	X
ma-248	186	17	+	+	NUM
ma-248	186	18	τ3	τ3	NOUN
ma-248	186	19	+	+	CCONJ
ma-248	186	20	µ	µ	NOUN
ma-248	186	21	)	)	PUNCT
ma-248	186	22	.	.	PUNCT
ma-248	187	1	the	the	DET
ma-248	187	2	remaining	remain	VERB
ma-248	187	3	matrix	matrix	NOUN
ma-248	187	4	becomes	become	VERB
ma-248	187	5	;	;	PUNCT
ma-248	187	6	ĵ	ĵ	X
ma-248	187	7	=	=	PUNCT
ma-248	187	8	−(k1τ1	−(k1τ1	PROPN
ma-248	187	9	+	+	CCONJ
ma-248	187	10	µ+	µ+	X
ma-248	187	11	(	(	PUNCT
ma-248	187	12	1−	1−	NUM
ma-248	187	13	k1)τ1	k1)τ1	X
ma-248	187	14	)	)	PUNCT
ma-248	187	15	η1	η1	NOUN
ma-248	187	16	λ	λ	PROPN
ma-248	187	17	µ	µ	X
ma-248	187	18	k1τ1	k1τ1	PROPN
ma-248	187	19	−(ψ1	−(ψ1	NOUN
ma-248	187	20	+	+	CCONJ
ma-248	187	21	ψ2	ψ2	NOUN
ma-248	187	22	+	+	CCONJ
ma-248	187	23	µ	µ	X
ma-248	187	24	)	)	PUNCT
ma-248	187	25			NOUN
ma-248	187	26	.	.	PUNCT
ma-248	188	1	the	the	DET
ma-248	188	2	characteristic	characteristic	ADJ
ma-248	188	3	equation	equation	NOUN
ma-248	188	4	is	be	AUX
ma-248	188	5	given	give	VERB
ma-248	188	6	by	by	ADP
ma-248	188	7	λ2	λ2	NOUN
ma-248	188	8	+	+	CCONJ
ma-248	188	9	b1λ+	b1λ+	NOUN
ma-248	188	10	b2	b2	NOUN
ma-248	188	11	=	=	SYM
ma-248	188	12	0	0	NUM
ma-248	188	13	(	(	PUNCT
ma-248	188	14	16	16	NUM
ma-248	188	15	)	)	PUNCT
ma-248	188	16	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	188	17	eur	eur	PROPN
ma-248	188	18	.	.	PUNCT
ma-248	189	1	j.	j.	PROPN
ma-248	189	2	math	math	PROPN
ma-248	189	3	.	.	PUNCT
ma-248	190	1	anal	anal	PROPN
ma-248	190	2	.	.	PUNCT
ma-248	191	1	10.28924	10.28924	NUM
ma-248	191	2	/	/	SYM
ma-248	191	3	ada	ada	PROPN
ma-248	191	4	/	/	SYM
ma-248	191	5	ma.4.21	ma.4.21	NOUN
ma-248	191	6	9where	9where	NUM
ma-248	191	7	b1	b1	NOUN
ma-248	191	8	=	=	SYM
ma-248	191	9	(	(	PUNCT
ma-248	191	10	k1τ1	k1τ1	PROPN
ma-248	191	11	+	+	CCONJ
ma-248	191	12	µ+	µ+	X
ma-248	191	13	(	(	PUNCT
ma-248	191	14	1−	1−	NUM
ma-248	191	15	k1)τ1	k1)τ1	X
ma-248	191	16	+	+	CCONJ
ma-248	191	17	(	(	PUNCT
ma-248	191	18	ψ1	ψ1	NOUN
ma-248	191	19	+	+	CCONJ
ma-248	191	20	ψ2	ψ2	NOUN
ma-248	191	21	+	+	CCONJ
ma-248	191	22	µ	µ	NOUN
ma-248	191	23	)	)	PUNCT
ma-248	191	24	,	,	PUNCT
ma-248	191	25	b2	b2	NOUN
ma-248	191	26	=	=	SYM
ma-248	191	27	(	(	PUNCT
ma-248	191	28	k1τ1	k1τ1	PROPN
ma-248	191	29	+	+	CCONJ
ma-248	191	30	µ+	µ+	X
ma-248	191	31	(	(	PUNCT
ma-248	191	32	1−	1−	NUM
ma-248	191	33	k1)τ1(ψ1	k1)τ1(ψ1	NOUN
ma-248	191	34	+	+	CCONJ
ma-248	191	35	ψ2	ψ2	NOUN
ma-248	191	36	+	+	PUNCT
ma-248	191	37	µ)−	µ)−	NOUN
ma-248	191	38	λ	λ	PROPN
ma-248	191	39	µ	µ	PRON
ma-248	191	40	η1k1τ1	η1k1τ1	NOUN
ma-248	191	41	,	,	PUNCT
ma-248	191	42	then	then	ADV
ma-248	191	43	λ3,4	λ3,4	NOUN
ma-248	191	44	=	=	SYM
ma-248	191	45	−(b1)±	−(b1)±	NOUN
ma-248	192	1	√	√	NUM
ma-248	192	2	t1	t1	NOUN
ma-248	192	3	2	2	NUM
ma-248	192	4	,	,	PUNCT
ma-248	192	5	where	where	SCONJ
ma-248	192	6	t1	t1	NOUN
ma-248	192	7	=	=	SYM
ma-248	192	8	b21−4b2	b21−4b2	NOUN
ma-248	192	9	.	.	PUNCT
ma-248	193	1	if	if	SCONJ
ma-248	193	2	λ3	λ3	PROPN
ma-248	193	3	≤	≤	NOUN
ma-248	193	4	0	0	PUNCT
ma-248	194	1	and	and	CCONJ
ma-248	194	2	λ4	λ4	VERB
ma-248	194	3	≤	≤	PROPN
ma-248	194	4	0	0	NUM
ma-248	194	5	,	,	PUNCT
ma-248	194	6	then	then	ADV
ma-248	194	7	the	the	DET
ma-248	194	8	disease	disease	NOUN
ma-248	194	9	free	free	ADJ
ma-248	194	10	equilibrium	equilibrium	NOUN
ma-248	194	11	is	be	AUX
ma-248	194	12	stable	stable	ADJ
ma-248	194	13	.	.	PUNCT
ma-248	195	1	otherwise	otherwise	ADV
ma-248	195	2	,	,	PUNCT
ma-248	195	3	it	it	PRON
ma-248	195	4	is	be	AUX
ma-248	195	5	unstable	unstable	ADJ
ma-248	195	6	.	.	PUNCT
ma-248	196	1	theorem	theorem	VERB
ma-248	196	2	3.3	3.3	NUM
ma-248	196	3	.	.	PUNCT
ma-248	197	1	when	when	SCONJ
ma-248	197	2	r0	r0	VERB
ma-248	197	3	<	<	X
ma-248	197	4	1	1	NUM
ma-248	197	5	,	,	PUNCT
ma-248	197	6	the	the	DET
ma-248	197	7	disease	disease	NOUN
ma-248	197	8	-	-	PUNCT
ma-248	197	9	free	free	ADJ
ma-248	197	10	equilibrium	equilibrium	NOUN
ma-248	197	11	e0	e0	PROPN
ma-248	197	12	for	for	ADP
ma-248	197	13	the	the	DET
ma-248	197	14	meningitis	meningitis	NOUN
ma-248	197	15	model	model	NOUN
ma-248	197	16	(	(	PUNCT
ma-248	197	17	1	1	X
ma-248	197	18	)	)	PUNCT
ma-248	197	19	is	be	AUX
ma-248	197	20	globally	globally	ADV
ma-248	197	21	asymptotically	asymptotically	ADV
ma-248	197	22	stable	stable	ADJ
ma-248	197	23	in	in	ADP
ma-248	197	24	r5	r5	PROPN
ma-248	197	25	+	+	PROPN
ma-248	197	26	.	.	PUNCT
ma-248	198	1	proof	proof	NOUN
ma-248	198	2	.	.	PUNCT
ma-248	199	1	we	we	PRON
ma-248	199	2	construct	construct	VERB
ma-248	199	3	a	a	DET
ma-248	199	4	lyapunov	lyapunov	ADJ
ma-248	199	5	function	function	NOUN
ma-248	199	6	l	l	NOUN
ma-248	199	7	=	=	SYM
ma-248	199	8	k1	k1	PROPN
ma-248	199	9	(	(	PUNCT
ma-248	199	10	τ1	τ1	NOUN
ma-248	199	11	d1d2	d1d2	NOUN
ma-248	199	12	)	)	PUNCT
ma-248	199	13	ehh	ehh	NOUN
ma-248	200	1	+	+	CCONJ
ma-248	200	2	1	1	NUM
ma-248	200	3	d2	d2	PROPN
ma-248	200	4	ihh	ihh	PROPN
ma-248	200	5	,	,	PUNCT
ma-248	200	6	where	where	SCONJ
ma-248	200	7	d1	d1	PROPN
ma-248	200	8	=	=	SYM
ma-248	200	9	(	(	PUNCT
ma-248	200	10	k1τ1	k1τ1	PROPN
ma-248	200	11	+	+	CCONJ
ma-248	200	12	µ	µ	X
ma-248	200	13	+	+	CCONJ
ma-248	200	14	(	(	PUNCT
ma-248	200	15	1	1	NUM
ma-248	200	16	−	−	NOUN
ma-248	200	17	k1)τ1	k1)τ1	NOUN
ma-248	200	18	)	)	PUNCT
ma-248	200	19	and	and	CCONJ
ma-248	200	20	d2	d2	PROPN
ma-248	200	21	=	=	SYM
ma-248	200	22	(	(	PUNCT
ma-248	200	23	ψ1	ψ1	NOUN
ma-248	200	24	+	+	NUM
ma-248	200	25	ψ2	ψ2	NOUN
ma-248	200	26	+	+	CCONJ
ma-248	200	27	µ	µ	NOUN
ma-248	200	28	)	)	PUNCT
ma-248	200	29	.	.	PUNCT
ma-248	201	1	taking	take	VERB
ma-248	201	2	the	the	DET
ma-248	201	3	derivative	derivative	NOUN
ma-248	201	4	of	of	ADP
ma-248	201	5	l	l	NOUN
ma-248	201	6	withrespect	withrespect	ADJ
ma-248	201	7	to	to	ADP
ma-248	201	8	ehh	ehh	VERB
ma-248	201	9	and	and	CCONJ
ma-248	201	10	ihh	ihh	PROPN
ma-248	201	11	gives	give	VERB
ma-248	201	12	;	;	PUNCT
ma-248	201	13	dl	dl	PROPN
ma-248	201	14	dt	dt	NOUN
ma-248	202	1	=	=	PROPN
ma-248	202	2	k1	k1	PROPN
ma-248	202	3	(	(	PUNCT
ma-248	202	4	τ1	τ1	NOUN
ma-248	202	5	d1d2	d1d2	X
ma-248	202	6	)	)	PUNCT
ma-248	203	1	d	d	NOUN
ma-248	203	2	dt	dt	NOUN
ma-248	203	3	ehh	ehh	INTJ
ma-248	204	1	+	+	CCONJ
ma-248	204	2	1	1	NUM
ma-248	204	3	d2	d2	PROPN
ma-248	204	4	d	d	PROPN
ma-248	204	5	dt	dt	X
ma-248	204	6	ihh	ihh	PROPN
ma-248	204	7	,	,	PUNCT
ma-248	204	8	dl	dl	PROPN
ma-248	204	9	dt	dt	NOUN
ma-248	204	10	=	=	PROPN
ma-248	204	11	k1	k1	PROPN
ma-248	204	12	(	(	PUNCT
ma-248	204	13	τ1	τ1	NOUN
ma-248	204	14	d1d2	d1d2	X
ma-248	204	15	)	)	PUNCT
ma-248	204	16	(	(	PUNCT
ma-248	204	17	η1ihhshh	η1ihhshh	NOUN
ma-248	204	18	−	−	NOUN
ma-248	204	19	k1τ1ehh	k1τ1ehh	X
ma-248	204	20	−	−	PROPN
ma-248	204	21	(	(	PUNCT
ma-248	204	22	1−	1−	NUM
ma-248	204	23	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	204	24	−	−	NOUN
ma-248	204	25	µehh	µehh	NOUN
ma-248	204	26	)	)	PUNCT
ma-248	204	27	+	+	CCONJ
ma-248	204	28	1	1	NUM
ma-248	204	29	d2	d2	PROPN
ma-248	204	30	(	(	PUNCT
ma-248	204	31	k1τ1ehh	k1τ1ehh	NOUN
ma-248	204	32	−	−	PROPN
ma-248	204	33	(	(	PUNCT
ma-248	204	34	ψ1	ψ1	NOUN
ma-248	204	35	+	+	CCONJ
ma-248	204	36	ψ2	ψ2	NOUN
ma-248	204	37	+	+	CCONJ
ma-248	204	38	µ)ihh	µ)ihh	NOUN
ma-248	204	39	)	)	PUNCT
ma-248	204	40	,	,	PUNCT
ma-248	204	41	dl	dl	PROPN
ma-248	204	42	dt	dt	NOUN
ma-248	204	43	=	=	PROPN
ma-248	204	44	k1	k1	PROPN
ma-248	204	45	(	(	PUNCT
ma-248	204	46	τ1	τ1	NOUN
ma-248	204	47	d1d2	d1d2	X
ma-248	204	48	)	)	PUNCT
ma-248	204	49	(	(	PUNCT
ma-248	204	50	η1ihhshh	η1ihhshh	NOUN
ma-248	204	51	−	−	NOUN
ma-248	204	52	d1ehh	d1ehh	NOUN
ma-248	204	53	)	)	PUNCT
ma-248	205	1	+	+	CCONJ
ma-248	205	2	1	1	NUM
ma-248	205	3	d2	d2	PROPN
ma-248	205	4	(	(	PUNCT
ma-248	205	5	kτ1ehh	kτ1ehh	PROPN
ma-248	205	6	−	−	PROPN
ma-248	205	7	d2ihh	d2ihh	NOUN
ma-248	205	8	)	)	PUNCT
ma-248	205	9	.	.	PUNCT
ma-248	206	1	it	it	PRON
ma-248	206	2	follows	follow	VERB
ma-248	206	3	that	that	SCONJ
ma-248	206	4	shh	shh	PROPN
ma-248	207	1	=	=	SYM
ma-248	207	2	λ	λ	X
ma-248	207	3	µ	µ	NOUN
ma-248	207	4	at	at	ADP
ma-248	207	5	t0	t0	NOUN
ma-248	207	6	.	.	PUNCT
ma-248	208	1	hence	hence	ADV
ma-248	208	2	dl	dl	PROPN
ma-248	208	3	dt	dt	PROPN
ma-248	208	4	=	=	PROPN
ma-248	208	5	k1	k1	PROPN
ma-248	208	6	(	(	PUNCT
ma-248	208	7	τ1λ	τ1λ	PUNCT
ma-248	208	8	d1d2µ	d1d2µ	NUM
ma-248	208	9	)	)	PUNCT
ma-248	208	10	η1ihh	η1ihh	VERB
ma-248	209	1	−	−	PROPN
ma-248	209	2	k1τ1	k1τ1	PROPN
ma-248	209	3	d2	d2	PROPN
ma-248	209	4	ehh	ehh	PROPN
ma-248	210	1	+	+	CCONJ
ma-248	210	2	k1τ1	k1τ1	PROPN
ma-248	210	3	d2	d2	PROPN
ma-248	210	4	ehh	ehh	PROPN
ma-248	210	5	−	−	PROPN
ma-248	210	6	ihh	ihh	PROPN
ma-248	210	7	,	,	PUNCT
ma-248	210	8	=	=	PRON
ma-248	210	9	(	(	PUNCT
ma-248	210	10	r0	r0	NOUN
ma-248	210	11	−	−	PROPN
ma-248	210	12	1)ihh	1)ihh	NUM
ma-248	210	13	.	.	PUNCT
ma-248	210	14	from	from	ADP
ma-248	210	15	the	the	DET
ma-248	210	16	model	model	NOUN
ma-248	210	17	equation	equation	NOUN
ma-248	210	18	(	(	PUNCT
ma-248	210	19	1	1	NUM
ma-248	210	20	)	)	PUNCT
ma-248	211	1	,	,	PUNCT
ma-248	211	2	the	the	DET
ma-248	211	3	system	system	NOUN
ma-248	211	4	variables	variable	NOUN
ma-248	211	5	and	and	CCONJ
ma-248	211	6	parameters	parameter	NOUN
ma-248	211	7	are	be	AUX
ma-248	211	8	all	all	PRON
ma-248	211	9	non	non	ADJ
ma-248	211	10	-	-	ADJ
ma-248	211	11	negative	negative	ADJ
ma-248	211	12	,	,	PUNCT
ma-248	211	13	implyingthat	implyingthat	NOUN
ma-248	211	14	dl	dl	INTJ
ma-248	211	15	dt	dt	X
ma-248	211	16	<	<	X
ma-248	211	17	0	0	PUNCT
ma-248	211	18	when	when	SCONJ
ma-248	211	19	r0	r0	NOUN
ma-248	211	20	<	<	X
ma-248	211	21	1	1	NUM
ma-248	211	22	,	,	PUNCT
ma-248	211	23	with	with	ADP
ma-248	211	24	dl	dl	PROPN
ma-248	211	25	dt	dt	PROPN
ma-248	211	26	=	=	PUNCT
ma-248	211	27	0	0	NUM
ma-248	211	28	in	in	ADP
ma-248	211	29	the	the	DET
ma-248	211	30	disease	disease	NOUN
ma-248	211	31	-	-	PUNCT
ma-248	211	32	free	free	ADJ
ma-248	211	33	equilibrium	equilibrium	NOUN
ma-248	211	34	.	.	PUNCT
ma-248	212	1	hence	hence	ADV
ma-248	212	2	,	,	PUNCT
ma-248	212	3	l	l	NOUN
ma-248	212	4	is	be	AUX
ma-248	212	5	a	a	DET
ma-248	212	6	lyapunovfunction	lyapunovfunction	NOUN
ma-248	212	7	in	in	ADP
ma-248	212	8	ψ	ψ	NOUN
ma-248	212	9	.	.	PUNCT
ma-248	213	1	hence	hence	ADV
ma-248	213	2	,	,	PUNCT
ma-248	213	3	from	from	ADP
ma-248	213	4	[	[	X
ma-248	213	5	20	20	NUM
ma-248	213	6	]	]	X
ma-248	213	7	principle	principle	NOUN
ma-248	213	8	,	,	PUNCT
ma-248	213	9	(	(	PUNCT
ma-248	213	10	ehh(t	ehh(t	PROPN
ma-248	213	11	)	)	PUNCT
ma-248	213	12	,	,	PUNCT
ma-248	213	13	ihh(t))→	ihh(t))→	NOUN
ma-248	213	14	(	(	PUNCT
ma-248	213	15	0	0	NUM
ma-248	213	16	,	,	PUNCT
ma-248	213	17	0	0	NUM
ma-248	213	18	)	)	PUNCT
ma-248	213	19	as	as	ADP
ma-248	213	20	t	t	PROPN
ma-248	213	21	→∞.	→∞.	PUNCT
ma-248	213	22	�	�	PROPN
ma-248	213	23	3.6	3.6	NUM
ma-248	213	24	.	.	PUNCT
ma-248	214	1	stability	stability	NOUN
ma-248	214	2	of	of	ADP
ma-248	214	3	the	the	DET
ma-248	214	4	endemic	endemic	ADJ
ma-248	214	5	equilibrium	equilibrium	NOUN
ma-248	214	6	point	point	NOUN
ma-248	214	7	.	.	PUNCT
ma-248	215	1	here	here	ADV
ma-248	215	2	,	,	PUNCT
ma-248	215	3	we	we	PRON
ma-248	215	4	study	study	VERB
ma-248	215	5	the	the	DET
ma-248	215	6	global	global	ADJ
ma-248	215	7	and	and	CCONJ
ma-248	215	8	local	local	ADJ
ma-248	215	9	stabilityof	stabilityof	NOUN
ma-248	215	10	the	the	DET
ma-248	215	11	meningitis	meningitis	NOUN
ma-248	215	12	model	model	NOUN
ma-248	215	13	(	(	PUNCT
ma-248	215	14	1	1	NUM
ma-248	215	15	)	)	PUNCT
ma-248	215	16	at	at	ADP
ma-248	215	17	the	the	DET
ma-248	215	18	endemic	endemic	ADJ
ma-248	215	19	equilibrium	equilibrium	NOUN
ma-248	215	20	.	.	PUNCT
ma-248	216	1	the	the	DET
ma-248	216	2	lyapunov	lyapunov	ADJ
ma-248	216	3	function	function	NOUN
ma-248	216	4	method	method	NOUN
ma-248	216	5	by	by	ADP
ma-248	216	6	[	[	X
ma-248	216	7	21]is	21]is	PROPN
ma-248	216	8	employed	employ	VERB
ma-248	216	9	to	to	PART
ma-248	216	10	prove	prove	VERB
ma-248	216	11	the	the	DET
ma-248	216	12	globally	globally	ADV
ma-248	216	13	asymptotic	asymptotic	ADJ
ma-248	216	14	stability	stability	NOUN
ma-248	216	15	of	of	ADP
ma-248	216	16	model	model	NOUN
ma-248	216	17	(	(	PUNCT
ma-248	216	18	1	1	NUM
ma-248	216	19	)	)	PUNCT
ma-248	216	20	at	at	ADP
ma-248	216	21	endemic	endemic	ADJ
ma-248	216	22	equilibrium	equilibrium	NOUN
ma-248	216	23	.	.	PUNCT
ma-248	217	1	the	the	DET
ma-248	217	2	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	217	3	eur	eur	PROPN
ma-248	217	4	.	.	PUNCT
ma-248	218	1	j.	j.	PROPN
ma-248	218	2	math	math	PROPN
ma-248	218	3	.	.	PUNCT
ma-248	219	1	anal	anal	PROPN
ma-248	219	2	.	.	PUNCT
ma-248	220	1	10.28924	10.28924	NUM
ma-248	220	2	/	/	SYM
ma-248	220	3	ada	ada	PROPN
ma-248	220	4	/	/	SYM
ma-248	220	5	ma.4.21	ma.4.21	PROPN
ma-248	220	6	10underlying	10underlying	NUM
ma-248	220	7	steps	step	NOUN
ma-248	220	8	are	be	AUX
ma-248	220	9	,	,	PUNCT
ma-248	220	10	therefore	therefore	ADV
ma-248	220	11	,	,	PUNCT
ma-248	220	12	followed	follow	VERB
ma-248	220	13	.	.	PUNCT
ma-248	221	1	the	the	DET
ma-248	221	2	jacobian	jacobian	PROPN
ma-248	221	3	evaluated	evaluate	VERB
ma-248	221	4	at	at	ADP
ma-248	221	5	e∗	e∗	NOUN
ma-248	221	6	gives	give	VERB
ma-248	221	7	;	;	PUNCT
ma-248	221	8	j	j	PROPN
ma-248	221	9	=	=	SYM
ma-248	221	10			PROPN
ma-248	221	11	−µ−	−µ−	VERB
ma-248	221	12	η1i∗hh	η1i∗hh	PROPN
ma-248	221	13	0	0	NUM
ma-248	221	14	0	0	NUM
ma-248	221	15	−η1s∗hh	−η1s∗hh	PUNCT
ma-248	221	16	ω	ω	NUM
ma-248	221	17	η1i	η1i	PROPN
ma-248	221	18	∗	∗	NOUN
ma-248	221	19	hh	hh	PROPN
ma-248	222	1	−	−	PROPN
ma-248	223	1	(	(	PUNCT
ma-248	223	2	k1τ1	k1τ1	PROPN
ma-248	223	3	+	+	CCONJ
ma-248	223	4	µ+	µ+	X
ma-248	223	5	(	(	PUNCT
ma-248	223	6	1−	1−	NUM
ma-248	223	7	k1)τ1	k1)τ1	X
ma-248	223	8	)	)	PUNCT
ma-248	223	9	0	0	PUNCT
ma-248	224	1	η1s	η1s	PROPN
ma-248	224	2	∗	∗	VERB
ma-248	224	3	hh	hh	PROPN
ma-248	224	4	0	0	NUM
ma-248	224	5	0	0	NUM
ma-248	225	1	(	(	PUNCT
ma-248	225	2	1−	1−	NUM
ma-248	225	3	k1)τ1	k1)τ1	X
ma-248	225	4	−(τ2	−(τ2	NUM
ma-248	225	5	+	+	CCONJ
ma-248	225	6	τ3	τ3	NOUN
ma-248	225	7	+	+	CCONJ
ma-248	225	8	µ	µ	X
ma-248	225	9	)	)	PUNCT
ma-248	225	10	0	0	NUM
ma-248	225	11	0	0	NUM
ma-248	225	12	0	0	NUM
ma-248	226	1	k1τ1	k1τ1	NOUN
ma-248	226	2	0	0	NUM
ma-248	226	3	−(ψ1	−(ψ1	NOUN
ma-248	226	4	+	+	CCONJ
ma-248	226	5	ψ2	ψ2	NOUN
ma-248	226	6	+	+	CCONJ
ma-248	226	7	µ	µ	X
ma-248	226	8	)	)	PUNCT
ma-248	226	9	0	0	NUM
ma-248	227	1	0	0	NUM
ma-248	227	2	0	0	NUM
ma-248	227	3	τ2	τ2	ADJ
ma-248	227	4	ψ1	ψ1	ADJ
ma-248	227	5	−(ω	−(ω	NOUN
ma-248	227	6	+	+	CCONJ
ma-248	227	7	µ	µ	X
ma-248	227	8	)	)	PUNCT
ma-248	227	9			NOUN
ma-248	227	10	(	(	PUNCT
ma-248	227	11	17)we	17)we	NUM
ma-248	227	12	denote	denote	VERB
ma-248	227	13	a	a	DET
ma-248	227	14	=	=	X
ma-248	227	15	−µ	−µ	ADJ
ma-248	227	16	−	−	PROPN
ma-248	227	17	η1i∗hh	η1i∗hh	ADJ
ma-248	227	18	,	,	PUNCT
ma-248	227	19	b	b	X
ma-248	227	20	=	=	SYM
ma-248	227	21	−η1s∗hh	−η1s∗hh	PROPN
ma-248	227	22	,	,	PUNCT
ma-248	227	23	c	c	PROPN
ma-248	227	24	=	=	SYM
ma-248	227	25	ω	ω	PROPN
ma-248	227	26	,	,	PUNCT
ma-248	227	27	d	d	PROPN
ma-248	227	28	=	=	SYM
ma-248	227	29	η1i	η1i	PROPN
ma-248	227	30	∗	∗	VERB
ma-248	227	31	hh	hh	PROPN
ma-248	227	32	,	,	PUNCT
ma-248	227	33	e	e	PROPN
ma-248	227	34	=	=	PUNCT
ma-248	227	35	−	−	PROPN
ma-248	227	36	(	(	PUNCT
ma-248	227	37	k1τ1	k1τ1	PROPN
ma-248	227	38	+	+	CCONJ
ma-248	227	39	µ	µ	X
ma-248	227	40	+	+	CCONJ
ma-248	227	41	(	(	PUNCT
ma-248	227	42	1	1	NUM
ma-248	227	43	−	−	NOUN
ma-248	227	44	k1)τ1	k1)τ1	X
ma-248	227	45	)	)	PUNCT
ma-248	227	46	,	,	PUNCT
ma-248	227	47	f	f	X
ma-248	227	48	=	=	PUNCT
ma-248	227	49	η1s	η1s	PROPN
ma-248	227	50	∗	∗	VERB
ma-248	227	51	hh	hh	PROPN
ma-248	227	52	,	,	PUNCT
ma-248	227	53	g	g	NOUN
ma-248	227	54	=	=	PUNCT
ma-248	227	55	(	(	PUNCT
ma-248	227	56	1	1	NUM
ma-248	227	57	−	−	NOUN
ma-248	227	58	k1)τ1	k1)τ1	PROPN
ma-248	227	59	,	,	PUNCT
ma-248	227	60	h	h	NOUN
ma-248	227	61	=	=	PUNCT
ma-248	227	62	−(τ2	−(τ2	X
ma-248	227	63	+	+	NUM
ma-248	227	64	τ3	τ3	NOUN
ma-248	227	65	+	+	CCONJ
ma-248	227	66	µ	µ	NOUN
ma-248	227	67	)	)	PUNCT
ma-248	227	68	,	,	PUNCT
ma-248	227	69	i	i	PRON
ma-248	227	70	=	=	PUNCT
ma-248	227	71	k1τ1	k1τ1	PROPN
ma-248	227	72	,	,	PUNCT
ma-248	227	73	j	j	NOUN
ma-248	227	74	=	=	PUNCT
ma-248	227	75	−(ψ1	−(ψ1	X
ma-248	227	76	+	+	CCONJ
ma-248	227	77	ψ2	ψ2	NOUN
ma-248	227	78	+	+	CCONJ
ma-248	227	79	µ	µ	X
ma-248	227	80	)	)	PUNCT
ma-248	227	81	,	,	PUNCT
ma-248	227	82	k	k	PROPN
ma-248	227	83	=	=	SYM
ma-248	227	84	τ2	τ2	PROPN
ma-248	227	85	,	,	PUNCT
ma-248	227	86	l	l	NOUN
ma-248	227	87	=	=	PUNCT
ma-248	227	88	ψ1,and	ψ1,and	NOUN
ma-248	227	89	m	m	VERB
ma-248	227	90	=	=	NOUN
ma-248	227	91	−(ω	−(ω	NOUN
ma-248	227	92	+	+	X
ma-248	227	93	µ	µ	NOUN
ma-248	227	94	)	)	PUNCT
ma-248	227	95	.	.	PUNCT
ma-248	228	1	then	then	ADV
ma-248	228	2	,	,	PUNCT
ma-248	228	3	the	the	DET
ma-248	228	4	characteristics	characteristic	NOUN
ma-248	228	5	equation	equation	NOUN
ma-248	228	6	of	of	ADP
ma-248	228	7	model	model	NOUN
ma-248	228	8	(	(	PUNCT
ma-248	228	9	1	1	NUM
ma-248	228	10	)	)	PUNCT
ma-248	228	11	is	be	AUX
ma-248	228	12	given	give	VERB
ma-248	228	13	by	by	ADP
ma-248	228	14	y	y	PROPN
ma-248	228	15	5	5	NUM
ma-248	228	16	+	+	CCONJ
ma-248	228	17	a0y	a0y	PROPN
ma-248	228	18	4	4	NUM
ma-248	228	19	+	+	NOUN
ma-248	228	20	a1y	a1y	PROPN
ma-248	228	21	3	3	NUM
ma-248	228	22	+	+	CCONJ
ma-248	228	23	a2y	a2y	PROPN
ma-248	228	24	2	2	NUM
ma-248	228	25	+	+	CCONJ
ma-248	228	26	a3y	a3y	X
ma-248	228	27	+	+	PUNCT
ma-248	228	28	a4	a4	NOUN
ma-248	228	29	=	=	SYM
ma-248	228	30	0	0	NUM
ma-248	228	31	(	(	PUNCT
ma-248	228	32	18	18	NUM
ma-248	228	33	)	)	PUNCT
ma-248	228	34	with	with	ADP
ma-248	228	35	a0	a0	PROPN
ma-248	228	36	=	=	SYM
ma-248	228	37	(	(	PUNCT
ma-248	228	38	a	a	DET
ma-248	228	39	+	+	NOUN
ma-248	228	40	e	e	NOUN
ma-248	228	41	+	+	NOUN
ma-248	228	42	h	h	PROPN
ma-248	229	1	+	+	CCONJ
ma-248	229	2	j	j	PROPN
ma-248	229	3	+	+	PROPN
ma-248	229	4	m	m	NOUN
ma-248	229	5	)	)	PUNCT
ma-248	229	6	,	,	PUNCT
ma-248	229	7	a1	a1	NOUN
ma-248	229	8	=	=	SYM
ma-248	229	9	ae	ae	PROPN
ma-248	229	10	+	+	CCONJ
ma-248	229	11	ah	ah	INTJ
ma-248	229	12	+	+	NUM
ma-248	229	13	aj	aj	PROPN
ma-248	230	1	+	+	CCONJ
ma-248	230	2	eh	eh	INTJ
ma-248	230	3	+	+	NUM
ma-248	230	4	am	be	AUX
ma-248	230	5	+	+	X
ma-248	230	6	ej	ej	X
ma-248	231	1	+	+	NOUN
ma-248	231	2	−f	−f	PROPN
ma-248	231	3	i	i	PRON
ma-248	232	1	+	+	CCONJ
ma-248	232	2	em	em	PRON
ma-248	233	1	+	+	CCONJ
ma-248	233	2	hj	hj	X
ma-248	234	1	+	+	CCONJ
ma-248	234	2	hm	hm	INTJ
ma-248	235	1	+	+	CCONJ
ma-248	235	2	jm	jm	PROPN
ma-248	235	3	,	,	PUNCT
ma-248	235	4	a2	a2	PROPN
ma-248	235	5	=	=	SYM
ma-248	235	6	aeh	aeh	PROPN
ma-248	235	7	+	+	PROPN
ma-248	235	8	bdi	bdi	PROPN
ma-248	235	9	+	+	CCONJ
ma-248	235	10	aej	aej	PROPN
ma-248	236	1	−	−	NOUN
ma-248	236	2	af	af	VERB
ma-248	237	1	i	i	PRON
ma-248	237	2	+	+	CCONJ
ma-248	237	3	aem	aem	PROPN
ma-248	237	4	+	+	NUM
ma-248	237	5	ahj	ahj	PROPN
ma-248	237	6	+	+	CCONJ
ma-248	237	7	ahm	ahm	PROPN
ma-248	237	8	+	+	SYM
ma-248	237	9	ehj	ehj	NOUN
ma-248	237	10	−	−	PROPN
ma-248	237	11	f	f	PROPN
ma-248	237	12	hi	hi	INTJ
ma-248	238	1	+	+	CCONJ
ma-248	238	2	ajm	ajm	ADJ
ma-248	238	3	+	+	CCONJ
ma-248	238	4	ehm	ehm	PROPN
ma-248	239	1	+	+	PROPN
ma-248	239	2	ejm	ejm	PROPN
ma-248	240	1	−	−	PROPN
ma-248	240	2	f	f	PROPN
ma-248	241	1	i	i	PRON
ma-248	241	2	m	m	VERB
ma-248	241	3	+	+	CCONJ
ma-248	241	4	hjm	hjm	ADJ
ma-248	241	5	,	,	PUNCT
ma-248	241	6	a3	a3	NOUN
ma-248	241	7	=	=	SYM
ma-248	242	1	ehjm	ehjm	ADJ
ma-248	242	2	−	−	PROPN
ma-248	242	3	f	f	PROPN
ma-248	243	1	him	he	PRON
ma-248	243	2	+	+	CCONJ
ma-248	243	3	bdhi	bdhi	NOUN
ma-248	243	4	+	+	CCONJ
ma-248	243	5	aehj	aehj	NOUN
ma-248	243	6	−	−	NOUN
ma-248	243	7	af	af	INTJ
ma-248	243	8	hi	hi	INTJ
ma-248	243	9	−	−	PROPN
ma-248	243	10	cdgk	cdgk	NOUN
ma-248	243	11	+	+	CCONJ
ma-248	243	12	aehm	aehm	NOUN
ma-248	243	13	+	+	CCONJ
ma-248	243	14	bdim	bdim	PROPN
ma-248	243	15	−	−	PROPN
ma-248	243	16	cdi	cdi	PROPN
ma-248	243	17	l	l	PROPN
ma-248	243	18	+	+	PROPN
ma-248	243	19	aejm	aejm	PROPN
ma-248	243	20	−	−	PROPN
ma-248	243	21	af	af	VERB
ma-248	243	22	i	i	PRON
ma-248	243	23	m	m	VERB
ma-248	243	24	+	+	ADV
ma-248	243	25	ahjm	ahjm	ADJ
ma-248	243	26	,	,	PUNCT
ma-248	243	27	a4	a4	NOUN
ma-248	243	28	=	=	SYM
ma-248	243	29	−cdgjk	−cdgjk	NOUN
ma-248	243	30	+	+	CCONJ
ma-248	243	31	bdhim	bdhim	PROPN
ma-248	243	32	−	−	PROPN
ma-248	243	33	cdhi	cdhi	ADJ
ma-248	243	34	l	l	NOUN
ma-248	244	1	+	+	CCONJ
ma-248	244	2	aehjm	aehjm	VERB
ma-248	244	3	−	−	PROPN
ma-248	244	4	af	af	VERB
ma-248	244	5	him	he	PRON
ma-248	244	6	.	.	PUNCT
ma-248	245	1	based	base	VERB
ma-248	245	2	on	on	ADP
ma-248	245	3	the	the	DET
ma-248	245	4	routh	routh	PROPN
ma-248	245	5	-	-	PUNCT
ma-248	245	6	hurwitz	hurwitz	PROPN
ma-248	245	7	stability	stability	NOUN
ma-248	245	8	by	by	ADP
ma-248	245	9	[	[	X
ma-248	245	10	22	22	NUM
ma-248	245	11	]	]	PUNCT
ma-248	245	12	,	,	PUNCT
ma-248	245	13	the	the	DET
ma-248	245	14	condition	condition	NOUN
ma-248	245	15	for	for	ADP
ma-248	245	16	the	the	DET
ma-248	245	17	characteristics	characteristic	NOUN
ma-248	245	18	equation	equation	NOUN
ma-248	245	19	(	(	PUNCT
ma-248	245	20	18	18	NUM
ma-248	245	21	)	)	PUNCT
ma-248	245	22	isgiven	isgiven	VERB
ma-248	245	23	by	by	ADP
ma-248	245	24	yi	yi	PROPN
ma-248	245	25	=	=	PUNCT
ma-248	245	26			NOUN
ma-248	245	27	y1	y1	NOUN
ma-248	245	28	y3	y3	NOUN
ma-248	245	29	y5	y5	NOUN
ma-248	245	30	y0	y0	NOUN
ma-248	245	31	y2	y2	NOUN
ma-248	245	32	y4	y4	NOUN
ma-248	245	33	0	0	NUM
ma-248	246	1	y1	y1	NOUN
ma-248	246	2	y3	y3	NOUN
ma-248	246	3	0	0	NUM
ma-248	246	4	y0	y0	NUM
ma-248	246	5	y2	y2	NOUN
ma-248	246	6	0	0	NUM
ma-248	246	7	0	0	NUM
ma-248	246	8	y1	y1	NOUN
ma-248	246	9	0	0	NUM
ma-248	246	10	0	0	NUM
ma-248	247	1	y0	y0	NOUN
ma-248	247	2	0	0	NUM
ma-248	247	3	0	0	NUM
ma-248	247	4	0	0	NUM
ma-248	247	5			NUM
ma-248	247	6	>	>	X
ma-248	247	7	0	0	X
ma-248	247	8	.	.	PUNCT
ma-248	248	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	248	2	eur	eur	PROPN
ma-248	248	3	.	.	PUNCT
ma-248	249	1	j.	j.	PROPN
ma-248	249	2	math	math	PROPN
ma-248	249	3	.	.	PUNCT
ma-248	250	1	anal	anal	PROPN
ma-248	250	2	.	.	PUNCT
ma-248	251	1	10.28924	10.28924	NUM
ma-248	251	2	/	/	SYM
ma-248	251	3	ada	ada	PROPN
ma-248	251	4	/	/	SYM
ma-248	251	5	ma.4.21	ma.4.21	PROPN
ma-248	251	6	11the	11the	NOUN
ma-248	251	7	condition	condition	NOUN
ma-248	251	8	requires	require	VERB
ma-248	251	9	all	all	DET
ma-248	251	10	the	the	DET
ma-248	251	11	coefficients	coefficient	NOUN
ma-248	251	12	of	of	ADP
ma-248	251	13	the	the	DET
ma-248	251	14	characteristics	characteristic	NOUN
ma-248	251	15	equation	equation	NOUN
ma-248	251	16	(	(	PUNCT
ma-248	251	17	18	18	NUM
ma-248	251	18	)	)	PUNCT
ma-248	251	19	to	to	PART
ma-248	251	20	be	be	AUX
ma-248	251	21	positive	positive	ADJ
ma-248	251	22	,	,	PUNCT
ma-248	251	23	implyingthat	implyingthat	NOUN
ma-248	251	24	all	all	PRON
ma-248	251	25	eigenvalues	eigenvalue	VERB
ma-248	251	26	have	have	VERB
ma-248	251	27	negative	negative	ADJ
ma-248	251	28	real	real	ADJ
ma-248	251	29	parts	part	NOUN
ma-248	251	30	.	.	PUNCT
ma-248	252	1	if	if	SCONJ
ma-248	252	2	the	the	DET
ma-248	252	3	condition	condition	NOUN
ma-248	252	4	yi	yi	NOUN
ma-248	252	5	is	be	AUX
ma-248	252	6	satisfied	satisfied	ADJ
ma-248	252	7	,	,	PUNCT
ma-248	252	8	we	we	PRON
ma-248	252	9	conclude	conclude	VERB
ma-248	252	10	that	that	SCONJ
ma-248	252	11	themeningitis	themeningitis	PROPN
ma-248	252	12	model	model	NOUN
ma-248	252	13	at	at	ADP
ma-248	252	14	the	the	DET
ma-248	252	15	endemic	endemic	ADJ
ma-248	252	16	equilibrium	equilibrium	NOUN
ma-248	252	17	is	be	AUX
ma-248	252	18	stable	stable	ADJ
ma-248	252	19	and	and	CCONJ
ma-248	252	20	otherwise	otherwise	ADV
ma-248	252	21	unstable	unstable	ADJ
ma-248	252	22	.	.	PUNCT
ma-248	253	1	theorem	theorem	VERB
ma-248	253	2	3.4	3.4	NUM
ma-248	253	3	.	.	PUNCT
ma-248	254	1	when	when	SCONJ
ma-248	254	2	r0	r0	VERB
ma-248	254	3	≥	≥	NOUN
ma-248	254	4	1	1	NUM
ma-248	254	5	,	,	PUNCT
ma-248	254	6	the	the	DET
ma-248	254	7	endemic	endemic	ADJ
ma-248	254	8	equilibrium	equilibrium	NOUN
ma-248	254	9	e∗	e∗	PROPN
ma-248	254	10	of	of	ADP
ma-248	254	11	model	model	NOUN
ma-248	254	12	1	1	NUM
ma-248	254	13	is	be	AUX
ma-248	254	14	stable	stable	ADJ
ma-248	254	15	when	when	SCONJ
ma-248	254	16	shh	shh	PROPN
ma-248	254	17	=	=	NOUN
ma-248	254	18	s∗hh	s∗hh	PROPN
ma-248	254	19	,	,	PUNCT
ma-248	254	20	ehh	ehh	NOUN
ma-248	254	21	=	=	SYM
ma-248	254	22	e∗hh	e∗hh	PROPN
ma-248	254	23	,	,	PUNCT
ma-248	254	24	ahh	ahh	PROPN
ma-248	254	25	=	=	SYM
ma-248	254	26	a∗hh	a∗hh	PROPN
ma-248	254	27	,	,	PUNCT
ma-248	254	28	ihh	ihh	PROPN
ma-248	254	29	=	=	PUNCT
ma-248	254	30	i∗hh	i∗hh	PROPN
ma-248	254	31	,	,	PUNCT
ma-248	254	32	and	and	CCONJ
ma-248	254	33	rhh	rhh	X
ma-248	254	34	=	=	SYM
ma-248	254	35	r∗hh	r∗hh	PROPN
ma-248	254	36	,	,	PUNCT
ma-248	254	37	otherwise	otherwise	ADV
ma-248	254	38	unstable	unstable	ADJ
ma-248	254	39	.	.	PUNCT
ma-248	255	1	proof	proof	NOUN
ma-248	255	2	.	.	PUNCT
ma-248	256	1	we	we	PRON
ma-248	256	2	construct	construct	VERB
ma-248	256	3	a	a	DET
ma-248	256	4	lyapunov	lyapunov	NOUN
ma-248	256	5	function	function	NOUN
ma-248	256	6	lp	lp	NOUN
ma-248	256	7	=	=	PUNCT
ma-248	256	8	(	(	PUNCT
ma-248	256	9	shh	shh	INTJ
ma-248	256	10	−	−	PROPN
ma-248	256	11	s∗hh	s∗hh	ADJ
ma-248	256	12	−	−	PROPN
ma-248	256	13	s∗hh	s∗hh	PROPN
ma-248	256	14	ln	ln	NOUN
ma-248	257	1	(	(	PUNCT
ma-248	257	2	shh	shh	INTJ
ma-248	257	3	s∗hh	s∗hh	PROPN
ma-248	257	4	)	)	PUNCT
ma-248	257	5	)	)	PUNCT
ma-248	258	1	+	+	CCONJ
ma-248	258	2	(	(	PUNCT
ma-248	258	3	ehh	ehh	INTJ
ma-248	258	4	−	−	PROPN
ma-248	258	5	e∗hh	e∗hh	PROPN
ma-248	258	6	−	−	PROPN
ma-248	258	7	e∗hh	e∗hh	PROPN
ma-248	258	8	ln	ln	NOUN
ma-248	258	9	(	(	PUNCT
ma-248	258	10	ehh	ehh	INTJ
ma-248	258	11	e∗hh	e∗hh	PROPN
ma-248	258	12	)	)	PUNCT
ma-248	258	13	)	)	PUNCT
ma-248	259	1	+	+	CCONJ
ma-248	259	2	(	(	PUNCT
ma-248	259	3	ahh	ahh	INTJ
ma-248	259	4	−	−	PROPN
ma-248	259	5	a∗hh	a∗hh	PROPN
ma-248	259	6	−	−	PROPN
ma-248	259	7	a∗hh	a∗hh	PROPN
ma-248	259	8	ln	ln	INTJ
ma-248	260	1	(	(	PUNCT
ma-248	260	2	ahh	ahh	INTJ
ma-248	260	3	a∗hh	a∗hh	PROPN
ma-248	260	4	)	)	PUNCT
ma-248	260	5	)	)	PUNCT
ma-248	261	1	+	+	CCONJ
ma-248	261	2	(	(	PUNCT
ma-248	261	3	ihh	ihh	PROPN
ma-248	261	4	−	−	PROPN
ma-248	261	5	i∗hh	i∗hh	PROPN
ma-248	261	6	−	−	PROPN
ma-248	261	7	i∗hh	i∗hh	PROPN
ma-248	261	8	ln	ln	PROPN
ma-248	262	1	(	(	PUNCT
ma-248	262	2	ihh	ihh	PROPN
ma-248	262	3	i∗hh	i∗hh	PROPN
ma-248	262	4	)	)	PUNCT
ma-248	262	5	)	)	PUNCT
ma-248	263	1	+	+	CCONJ
ma-248	263	2	(	(	PUNCT
ma-248	263	3	rhh	rhh	X
ma-248	263	4	−	−	PROPN
ma-248	263	5	r∗hh	r∗hh	PROPN
ma-248	263	6	−	−	PROPN
ma-248	263	7	r∗hh	r∗hh	PROPN
ma-248	263	8	ln	ln	ADJ
ma-248	263	9	(	(	PUNCT
ma-248	263	10	rhh	rhh	X
ma-248	263	11	r∗hh	r∗hh	PROPN
ma-248	263	12	)	)	PUNCT
ma-248	263	13	)	)	PUNCT
ma-248	263	14	.	.	PUNCT
ma-248	264	1	the	the	DET
ma-248	264	2	derivative	derivative	NOUN
ma-248	264	3	of	of	ADP
ma-248	264	4	lp	lp	NOUN
ma-248	264	5	with	with	ADP
ma-248	264	6	respect	respect	NOUN
ma-248	264	7	to	to	ADP
ma-248	264	8	t	t	PROPN
ma-248	264	9	gives	give	VERB
ma-248	264	10	;	;	PUNCT
ma-248	264	11	dlp	dlp	NOUN
ma-248	264	12	dt	dt	NOUN
ma-248	264	13	=	=	PUNCT
ma-248	264	14	(	(	PUNCT
ma-248	264	15	shh	shh	INTJ
ma-248	264	16	−	−	PROPN
ma-248	264	17	s∗hh	s∗hh	PROPN
ma-248	264	18	shh	shh	NOUN
ma-248	264	19	)	)	PUNCT
ma-248	264	20	dshh	dshh	PROPN
ma-248	264	21	dt	dt	PROPN
ma-248	265	1	+	+	CCONJ
ma-248	265	2	(	(	PUNCT
ma-248	265	3	ehh	ehh	INTJ
ma-248	265	4	−	−	PROPN
ma-248	265	5	e∗hh	e∗hh	PROPN
ma-248	265	6	ehh	ehh	PROPN
ma-248	265	7	)	)	PUNCT
ma-248	266	1	dehh	dehh	NOUN
ma-248	266	2	dt	dt	PROPN
ma-248	267	1	+	+	CCONJ
ma-248	267	2	(	(	PUNCT
ma-248	267	3	ahh	ahh	INTJ
ma-248	267	4	−	−	PROPN
ma-248	267	5	a∗hh	a∗hh	PROPN
ma-248	267	6	ahh	ahh	PROPN
ma-248	267	7	)	)	PUNCT
ma-248	268	1	dahh	dahh	PROPN
ma-248	268	2	dt	dt	PROPN
ma-248	269	1	+	+	CCONJ
ma-248	269	2	(	(	PUNCT
ma-248	269	3	ihh	ihh	PROPN
ma-248	269	4	−	−	PROPN
ma-248	269	5	i∗hh	i∗hh	PROPN
ma-248	269	6	ihh	ihh	PROPN
ma-248	269	7	)	)	PUNCT
ma-248	269	8	dihh	dihh	PROPN
ma-248	269	9	dt	dt	PROPN
ma-248	269	10	+	+	CCONJ
ma-248	269	11	(	(	PUNCT
ma-248	269	12	rhh	rhh	X
ma-248	269	13	−	−	PROPN
ma-248	269	14	r∗hh	r∗hh	PROPN
ma-248	269	15	rhh	rhh	PROPN
ma-248	269	16	)	)	PUNCT
ma-248	269	17	drhh	drhh	PROPN
ma-248	269	18	dt	dt	NOUN
ma-248	269	19	.	.	PUNCT
ma-248	270	1	(	(	PUNCT
ma-248	270	2	19	19	NUM
ma-248	270	3	)	)	PUNCT
ma-248	270	4	hence	hence	ADV
ma-248	270	5	,	,	PUNCT
ma-248	270	6	substituting	substitute	VERB
ma-248	270	7	dshh	dshh	PROPN
ma-248	270	8	dt	dt	PROPN
ma-248	270	9	,	,	PUNCT
ma-248	270	10	dehhdt	dehhdt	PROPN
ma-248	270	11	,	,	PUNCT
ma-248	270	12	dahhdt	dahhdt	NOUN
ma-248	270	13	,	,	PUNCT
ma-248	270	14	dihhdt	dihhdt	PROPN
ma-248	270	15	and	and	CCONJ
ma-248	270	16	drhh	drhh	ADJ
ma-248	270	17	dt	dt	NOUN
ma-248	270	18	into	into	ADP
ma-248	270	19	equation	equation	NOUN
ma-248	270	20	(	(	PUNCT
ma-248	270	21	19	19	NUM
ma-248	270	22	)	)	PUNCT
ma-248	270	23	gives	give	VERB
ma-248	270	24	;	;	PUNCT
ma-248	270	25	dlp	dlp	NOUN
ma-248	270	26	dt	dt	NOUN
ma-248	270	27	=	=	PUNCT
ma-248	270	28	(	(	PUNCT
ma-248	270	29	shh	shh	INTJ
ma-248	270	30	−	−	PROPN
ma-248	270	31	s∗hh	s∗hh	PROPN
ma-248	270	32	shh	shh	NOUN
ma-248	270	33	)	)	PUNCT
ma-248	270	34	(	(	PUNCT
ma-248	270	35	λ−	λ−	PROPN
ma-248	270	36	µshh	µshh	PROPN
ma-248	270	37	−	−	PROPN
ma-248	270	38	η1ihhshh	η1ihhshh	PROPN
ma-248	270	39	+	+	CCONJ
ma-248	270	40	ωrhh	ωrhh	NOUN
ma-248	270	41	)	)	PUNCT
ma-248	271	1	+	+	CCONJ
ma-248	271	2	(	(	PUNCT
ma-248	271	3	ehh	ehh	INTJ
ma-248	271	4	−	−	PROPN
ma-248	271	5	e∗hh	e∗hh	PROPN
ma-248	271	6	ehh	ehh	NOUN
ma-248	271	7	)	)	PUNCT
ma-248	272	1	(	(	PUNCT
ma-248	272	2	η1ihhshh	η1ihhshh	NOUN
ma-248	272	3	−	−	PROPN
ma-248	272	4	kτ1ehh	kτ1ehh	NOUN
ma-248	272	5	−	−	PROPN
ma-248	272	6	(	(	PUNCT
ma-248	272	7	1−	1−	NUM
ma-248	272	8	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	272	9	−	−	NOUN
ma-248	272	10	µehh	µehh	NOUN
ma-248	272	11	)	)	PUNCT
ma-248	272	12	+	+	CCONJ
ma-248	273	1	(	(	PUNCT
ma-248	273	2	ahh	ahh	INTJ
ma-248	273	3	−	−	PROPN
ma-248	273	4	a∗hh	a∗hh	PROPN
ma-248	273	5	ahh	ahh	INTJ
ma-248	273	6	)	)	PUNCT
ma-248	273	7	(	(	PUNCT
ma-248	273	8	(	(	PUNCT
ma-248	273	9	1−	1−	NUM
ma-248	273	10	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	273	11	−	−	PROPN
ma-248	273	12	(	(	PUNCT
ma-248	273	13	τ2	τ2	NOUN
ma-248	273	14	+	+	NUM
ma-248	273	15	τ3	τ3	NOUN
ma-248	273	16	+	+	X
ma-248	273	17	µ)ahh	µ)ahh	NOUN
ma-248	273	18	)	)	PUNCT
ma-248	274	1	+	+	CCONJ
ma-248	274	2	(	(	PUNCT
ma-248	274	3	ihh	ihh	PROPN
ma-248	274	4	−	−	PROPN
ma-248	274	5	i∗hh	i∗hh	PROPN
ma-248	274	6	ihh	ihh	PROPN
ma-248	274	7	)	)	PUNCT
ma-248	274	8	(	(	PUNCT
ma-248	274	9	kτ1ehh	kτ1ehh	PROPN
ma-248	274	10	−	−	PROPN
ma-248	274	11	(	(	PUNCT
ma-248	274	12	ψ1	ψ1	NOUN
ma-248	274	13	+	+	CCONJ
ma-248	274	14	ψ2	ψ2	NOUN
ma-248	274	15	+	+	CCONJ
ma-248	274	16	µ)ihh	µ)ihh	NOUN
ma-248	274	17	)	)	PUNCT
ma-248	274	18	+	+	CCONJ
ma-248	274	19	(	(	PUNCT
ma-248	274	20	rhh	rhh	X
ma-248	274	21	−	−	PROPN
ma-248	274	22	r∗hh	r∗hh	PROPN
ma-248	274	23	rhh	rhh	PROPN
ma-248	274	24	)	)	PUNCT
ma-248	274	25	(	(	PUNCT
ma-248	274	26	τ2ahh	τ2ahh	PROPN
ma-248	274	27	+	+	NUM
ma-248	274	28	ψ1ehh	ψ1ehh	NUM
ma-248	274	29	−	−	PROPN
ma-248	274	30	(	(	PUNCT
ma-248	274	31	ω	ω	PROPN
ma-248	274	32	+	+	X
ma-248	274	33	µ)rhh	µ)rhh	NOUN
ma-248	274	34	)	)	PUNCT
ma-248	274	35	.	.	PUNCT
ma-248	275	1	hence	hence	ADV
ma-248	275	2	,	,	PUNCT
ma-248	275	3	for	for	ADP
ma-248	275	4	shh	shh	NOUN
ma-248	275	5	=	=	NOUN
ma-248	275	6	s∗hh	s∗hh	PROPN
ma-248	275	7	,	,	PUNCT
ma-248	275	8	ehh	ehh	NOUN
ma-248	275	9	=	=	SYM
ma-248	275	10	e∗hh	e∗hh	PROPN
ma-248	275	11	,	,	PUNCT
ma-248	275	12	ahh	ahh	PROPN
ma-248	275	13	=	=	SYM
ma-248	275	14	a∗hh	a∗hh	PROPN
ma-248	275	15	,	,	PUNCT
ma-248	275	16	ihh	ihh	PROPN
ma-248	275	17	=	=	PUNCT
ma-248	275	18	i∗hh	i∗hh	PROPN
ma-248	275	19	,	,	PUNCT
ma-248	275	20	and	and	CCONJ
ma-248	275	21	rhh	rhh	X
ma-248	275	22	=	=	NOUN
ma-248	275	23	r∗hh	r∗hh	PROPN
ma-248	275	24	.	.	PUNCT
ma-248	276	1	we	we	PRON
ma-248	276	2	have	have	VERB
ma-248	276	3	that	that	PRON
ma-248	276	4	,	,	PUNCT
ma-248	276	5	dlp	dlp	NOUN
ma-248	276	6	dt	dt	NOUN
ma-248	276	7	=	=	SYM
ma-248	276	8	λ−	λ−	PROPN
ma-248	276	9	λ	λ	PROPN
ma-248	276	10	(	(	PUNCT
ma-248	276	11	s∗hh	s∗hh	PROPN
ma-248	276	12	shh	shh	NOUN
ma-248	276	13	)	)	PUNCT
ma-248	276	14	−	−	PROPN
ma-248	276	15	µ	µ	X
ma-248	276	16	(	(	PUNCT
ma-248	276	17	(	(	PUNCT
ma-248	276	18	shh	shh	INTJ
ma-248	276	19	−	−	PROPN
ma-248	276	20	s∗hh)2	s∗hh)2	PROPN
ma-248	276	21	shh	shh	INTJ
ma-248	276	22	)	)	PUNCT
ma-248	276	23	−	−	PROPN
ma-248	277	1	η1(ihh	η1(ihh	NOUN
ma-248	277	2	−	−	PROPN
ma-248	277	3	i∗hh	i∗hh	PROPN
ma-248	277	4	)	)	PUNCT
ma-248	277	5	(	(	PUNCT
ma-248	277	6	(	(	PUNCT
ma-248	277	7	shh	shh	INTJ
ma-248	277	8	−	−	PROPN
ma-248	277	9	s∗hh)2	s∗hh)2	PROPN
ma-248	277	10	shh	shh	PROPN
ma-248	277	11	)	)	PUNCT
ma-248	278	1	+	+	CCONJ
ma-248	278	2	ω(rhh	ω(rhh	PRON
ma-248	278	3	−	−	PROPN
ma-248	278	4	r∗hh	r∗hh	NOUN
ma-248	278	5	)	)	PUNCT
ma-248	278	6	(	(	PUNCT
ma-248	278	7	shh	shh	INTJ
ma-248	278	8	−	−	PROPN
ma-248	278	9	s∗hh	s∗hh	PROPN
ma-248	278	10	shh	shh	NOUN
ma-248	278	11	)	)	PUNCT
ma-248	279	1	+	+	NUM
ma-248	279	2	η1	η1	NOUN
ma-248	279	3	(	(	PUNCT
ma-248	279	4	ehh	ehh	NOUN
ma-248	279	5	−	−	PROPN
ma-248	279	6	e∗hh	e∗hh	PROPN
ma-248	279	7	ehh	ehh	NOUN
ma-248	279	8	)	)	PUNCT
ma-248	280	1	(	(	PUNCT
ma-248	280	2	ihh	ihh	PROPN
ma-248	280	3	−	−	PROPN
ma-248	281	1	i∗hh)(shh	i∗hh)(shh	PROPN
ma-248	281	2	−	−	PROPN
ma-248	281	3	s∗hh	s∗hh	PROPN
ma-248	281	4	)	)	PUNCT
ma-248	281	5	−	−	PROPN
ma-248	281	6	kτ1	kτ1	NOUN
ma-248	281	7	(	(	PUNCT
ma-248	281	8	(	(	PUNCT
ma-248	281	9	ehh	ehh	INTJ
ma-248	281	10	−	−	NOUN
ma-248	282	1	e∗hh)2	e∗hh)2	INTJ
ma-248	282	2	ehh	ehh	NOUN
ma-248	282	3	)	)	PUNCT
ma-248	283	1	−	−	PROPN
ma-248	283	2	(	(	PUNCT
ma-248	283	3	1−	1−	NUM
ma-248	283	4	k1)τ1	k1)τ1	X
ma-248	283	5	(	(	PUNCT
ma-248	283	6	(	(	PUNCT
ma-248	283	7	ehh	ehh	INTJ
ma-248	283	8	−	−	NOUN
ma-248	283	9	e∗hh)2	e∗hh)2	INTJ
ma-248	283	10	ehh	ehh	NOUN
ma-248	283	11	)	)	PUNCT
ma-248	284	1	−	−	PROPN
ma-248	284	2	µ	µ	X
ma-248	284	3	(	(	PUNCT
ma-248	284	4	(	(	PUNCT
ma-248	284	5	ehh	ehh	INTJ
ma-248	284	6	−	−	NOUN
ma-248	284	7	e∗hh)2	e∗hh)2	INTJ
ma-248	284	8	ehh	ehh	NOUN
ma-248	284	9	)	)	PUNCT
ma-248	284	10	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	284	11	eur	eur	PROPN
ma-248	284	12	.	.	PUNCT
ma-248	285	1	j.	j.	PROPN
ma-248	285	2	math	math	PROPN
ma-248	285	3	.	.	PUNCT
ma-248	286	1	anal	anal	PROPN
ma-248	286	2	.	.	PUNCT
ma-248	287	1	10.28924	10.28924	NUM
ma-248	287	2	/	/	SYM
ma-248	287	3	ada	ada	PROPN
ma-248	287	4	/	/	SYM
ma-248	287	5	ma.4.21	ma.4.21	NOUN
ma-248	287	6	12	12	NUM
ma-248	288	1	+	+	CCONJ
ma-248	288	2	(	(	PUNCT
ma-248	288	3	1−	1−	NUM
ma-248	288	4	k1)τ1(ehh	k1)τ1(ehh	NOUN
ma-248	288	5	−	−	PROPN
ma-248	288	6	e∗hh	e∗hh	NOUN
ma-248	288	7	)	)	PUNCT
ma-248	288	8	(	(	PUNCT
ma-248	288	9	ahh	ahh	INTJ
ma-248	288	10	−	−	PROPN
ma-248	288	11	a∗hh	a∗hh	PROPN
ma-248	288	12	ahh	ahh	INTJ
ma-248	288	13	)	)	PUNCT
ma-248	289	1	−	−	PROPN
ma-248	289	2	(	(	PUNCT
ma-248	289	3	τ2	τ2	NOUN
ma-248	289	4	+	+	NUM
ma-248	289	5	τ3	τ3	NOUN
ma-248	289	6	+	+	CCONJ
ma-248	289	7	µ	µ	X
ma-248	289	8	)	)	PUNCT
ma-248	289	9	(	(	PUNCT
ma-248	289	10	(	(	PUNCT
ma-248	289	11	ahh	ahh	INTJ
ma-248	289	12	−	−	NOUN
ma-248	289	13	a∗hh)2	a∗hh)2	NOUN
ma-248	289	14	ahh	ahh	INTJ
ma-248	289	15	)	)	PUNCT
ma-248	290	1	+	+	CCONJ
ma-248	290	2	kτ1(ehh	kτ1(ehh	X
ma-248	290	3	−	−	PROPN
ma-248	290	4	e∗hh	e∗hh	NOUN
ma-248	290	5	)	)	PUNCT
ma-248	290	6	(	(	PUNCT
ma-248	290	7	ihh	ihh	PROPN
ma-248	290	8	−	−	PROPN
ma-248	290	9	i∗hh	i∗hh	PROPN
ma-248	290	10	ihh	ihh	PROPN
ma-248	290	11	)	)	PUNCT
ma-248	291	1	−	−	PROPN
ma-248	291	2	(	(	PUNCT
ma-248	291	3	ψ1	ψ1	NOUN
ma-248	291	4	+	+	CCONJ
ma-248	291	5	ψ2	ψ2	NOUN
ma-248	291	6	+	+	CCONJ
ma-248	291	7	µ	µ	X
ma-248	291	8	)	)	PUNCT
ma-248	291	9	(	(	PUNCT
ma-248	291	10	(	(	PUNCT
ma-248	291	11	ihh	ihh	PROPN
ma-248	291	12	−	−	PROPN
ma-248	291	13	i∗hh)2	i∗hh)2	INTJ
ma-248	291	14	ihh	ihh	PROPN
ma-248	291	15	)	)	PUNCT
ma-248	292	1	+	+	CCONJ
ma-248	292	2	τ2(ahh	τ2(ahh	PROPN
ma-248	292	3	−	−	PROPN
ma-248	292	4	a∗hh	a∗hh	PROPN
ma-248	292	5	)	)	PUNCT
ma-248	292	6	(	(	PUNCT
ma-248	292	7	rhh	rhh	X
ma-248	292	8	−	−	PROPN
ma-248	292	9	r∗hh	r∗hh	PROPN
ma-248	292	10	rhh	rhh	PROPN
ma-248	292	11	)	)	PUNCT
ma-248	293	1	+	+	CCONJ
ma-248	293	2	ψ1(ehh	ψ1(ehh	NOUN
ma-248	293	3	−	−	PROPN
ma-248	293	4	e∗hh	e∗hh	PROPN
ma-248	293	5	)	)	PUNCT
ma-248	293	6	(	(	PUNCT
ma-248	293	7	rhh	rhh	X
ma-248	293	8	−	−	PROPN
ma-248	293	9	r∗hh	r∗hh	PROPN
ma-248	293	10	rhh	rhh	PROPN
ma-248	293	11	)	)	PUNCT
ma-248	293	12	−	−	PROPN
ma-248	294	1	(	(	PUNCT
ma-248	294	2	ω	ω	PROPN
ma-248	294	3	+	+	X
ma-248	294	4	µ	µ	X
ma-248	294	5	)	)	PUNCT
ma-248	294	6	(	(	PUNCT
ma-248	294	7	(	(	PUNCT
ma-248	294	8	rhh	rhh	X
ma-248	294	9	−	−	NOUN
ma-248	294	10	r∗hh)2	r∗hh)2	VERB
ma-248	294	11	rhh	rhh	PROPN
ma-248	294	12	)	)	PUNCT
ma-248	294	13	.	.	PUNCT
ma-248	295	1	we	we	PRON
ma-248	295	2	generate	generate	VERB
ma-248	295	3	the	the	DET
ma-248	295	4	below	below	ADJ
ma-248	295	5	equation	equation	NOUN
ma-248	295	6	after	after	ADP
ma-248	295	7	thorough	thorough	ADJ
ma-248	295	8	algebraic	algebraic	ADJ
ma-248	295	9	manipulations	manipulation	NOUN
ma-248	295	10	;	;	PUNCT
ma-248	295	11	dlp	dlp	NOUN
ma-248	295	12	dt	dt	NOUN
ma-248	295	13	=	=	PUNCT
ma-248	295	14	g1	g1	PROPN
ma-248	295	15	−	−	PROPN
ma-248	295	16	g2	g2	PROPN
ma-248	295	17	,	,	PUNCT
ma-248	295	18	(	(	PUNCT
ma-248	295	19	20	20	NUM
ma-248	295	20	)	)	PUNCT
ma-248	295	21	where	where	SCONJ
ma-248	295	22	g1	g1	NOUN
ma-248	295	23	=	=	PUNCT
ma-248	295	24	λ	λ	PROPN
ma-248	295	25	+	+	CCONJ
ma-248	295	26	ω(rhh	ω(rhh	PRON
ma-248	295	27	−	−	PROPN
ma-248	295	28	r∗hh	r∗hh	PROPN
ma-248	295	29	)	)	PUNCT
ma-248	295	30	(	(	PUNCT
ma-248	295	31	shh	shh	INTJ
ma-248	295	32	−	−	PROPN
ma-248	295	33	s∗hh	s∗hh	PROPN
ma-248	295	34	shh	shh	NOUN
ma-248	295	35	)	)	PUNCT
ma-248	296	1	+	+	NUM
ma-248	296	2	η1	η1	NOUN
ma-248	296	3	(	(	PUNCT
ma-248	296	4	ehh	ehh	NOUN
ma-248	296	5	−	−	PROPN
ma-248	296	6	e∗hh	e∗hh	PROPN
ma-248	296	7	ehh	ehh	NOUN
ma-248	296	8	)	)	PUNCT
ma-248	297	1	(	(	PUNCT
ma-248	297	2	ihh	ihh	PROPN
ma-248	297	3	−	−	PROPN
ma-248	298	1	i∗hh)(shh	i∗hh)(shh	PROPN
ma-248	298	2	−	−	PROPN
ma-248	298	3	s∗hh	s∗hh	PROPN
ma-248	298	4	)	)	PUNCT
ma-248	299	1	+	+	CCONJ
ma-248	299	2	(	(	PUNCT
ma-248	299	3	1−	1−	NUM
ma-248	299	4	k1)τ1(ehh	k1)τ1(ehh	NOUN
ma-248	299	5	−	−	PROPN
ma-248	299	6	e∗hh	e∗hh	NOUN
ma-248	299	7	)	)	PUNCT
ma-248	299	8	(	(	PUNCT
ma-248	299	9	ahh	ahh	INTJ
ma-248	299	10	−	−	PROPN
ma-248	299	11	a∗hh	a∗hh	PROPN
ma-248	299	12	ahh	ahh	INTJ
ma-248	299	13	)	)	PUNCT
ma-248	300	1	+	+	CCONJ
ma-248	300	2	kτ1(ehh	kτ1(ehh	X
ma-248	300	3	−	−	PROPN
ma-248	300	4	e∗hh	e∗hh	NOUN
ma-248	300	5	)	)	PUNCT
ma-248	300	6	(	(	PUNCT
ma-248	300	7	ihh	ihh	PROPN
ma-248	300	8	−	−	PROPN
ma-248	300	9	i∗hh	i∗hh	PROPN
ma-248	300	10	ihh	ihh	PROPN
ma-248	300	11	)	)	PUNCT
ma-248	301	1	+	+	CCONJ
ma-248	301	2	τ2(ahh	τ2(ahh	PROPN
ma-248	301	3	−	−	PROPN
ma-248	301	4	a∗hh	a∗hh	PROPN
ma-248	301	5	)	)	PUNCT
ma-248	301	6	(	(	PUNCT
ma-248	301	7	rhh	rhh	X
ma-248	301	8	−	−	PROPN
ma-248	301	9	r∗hh	r∗hh	PROPN
ma-248	301	10	rhh	rhh	PROPN
ma-248	301	11	)	)	PUNCT
ma-248	301	12	,	,	PUNCT
ma-248	301	13	and	and	CCONJ
ma-248	302	1	g2	g2	PROPN
ma-248	302	2	=	=	SYM
ma-248	302	3	λ	λ	PROPN
ma-248	302	4	(	(	PUNCT
ma-248	302	5	s∗hh	s∗hh	PROPN
ma-248	302	6	shh	shh	NOUN
ma-248	302	7	)	)	PUNCT
ma-248	303	1	+	+	CCONJ
ma-248	303	2	µ	µ	X
ma-248	303	3	(	(	PUNCT
ma-248	303	4	(	(	PUNCT
ma-248	303	5	shh	shh	INTJ
ma-248	303	6	−	−	PROPN
ma-248	303	7	s∗hh)2	s∗hh)2	PROPN
ma-248	303	8	shh	shh	PROPN
ma-248	303	9	)	)	PUNCT
ma-248	304	1	+	+	CCONJ
ma-248	304	2	η1(ihh	η1(ihh	PROPN
ma-248	304	3	−	−	PROPN
ma-248	304	4	i∗hh	i∗hh	PROPN
ma-248	304	5	)	)	PUNCT
ma-248	304	6	(	(	PUNCT
ma-248	304	7	(	(	PUNCT
ma-248	304	8	shh	shh	INTJ
ma-248	304	9	−	−	PROPN
ma-248	304	10	s∗hh)2	s∗hh)2	PROPN
ma-248	304	11	shh	shh	NOUN
ma-248	304	12	)	)	PUNCT
ma-248	305	1	+	+	CCONJ
ma-248	305	2	kτ1	kτ1	NOUN
ma-248	305	3	(	(	PUNCT
ma-248	305	4	(	(	PUNCT
ma-248	305	5	ehh	ehh	INTJ
ma-248	305	6	−	−	NOUN
ma-248	305	7	e∗hh)2	e∗hh)2	INTJ
ma-248	305	8	ehh	ehh	NOUN
ma-248	305	9	)	)	PUNCT
ma-248	305	10	µ	µ	X
ma-248	305	11	(	(	PUNCT
ma-248	305	12	(	(	PUNCT
ma-248	305	13	ehh	ehh	INTJ
ma-248	305	14	−	−	NOUN
ma-248	305	15	e∗hh)2	e∗hh)2	INTJ
ma-248	305	16	ehh	ehh	NOUN
ma-248	305	17	)	)	PUNCT
ma-248	306	1	+	+	CCONJ
ma-248	306	2	(	(	PUNCT
ma-248	306	3	τ2	τ2	NOUN
ma-248	306	4	+	+	NUM
ma-248	306	5	τ3	τ3	NOUN
ma-248	306	6	+	+	CCONJ
ma-248	306	7	µ	µ	X
ma-248	306	8	)	)	PUNCT
ma-248	306	9	(	(	PUNCT
ma-248	306	10	(	(	PUNCT
ma-248	306	11	ahh	ahh	INTJ
ma-248	306	12	−	−	NOUN
ma-248	306	13	a∗hh)2	a∗hh)2	NOUN
ma-248	306	14	ahh	ahh	INTJ
ma-248	306	15	)	)	PUNCT
ma-248	307	1	+	+	CCONJ
ma-248	307	2	(	(	PUNCT
ma-248	307	3	ψ1	ψ1	NOUN
ma-248	307	4	+	+	CCONJ
ma-248	307	5	ψ2	ψ2	NOUN
ma-248	307	6	+	+	CCONJ
ma-248	307	7	µ	µ	X
ma-248	307	8	)	)	PUNCT
ma-248	307	9	(	(	PUNCT
ma-248	307	10	(	(	PUNCT
ma-248	307	11	ihh	ihh	PROPN
ma-248	307	12	−	−	PROPN
ma-248	307	13	i∗hh)2	i∗hh)2	INTJ
ma-248	307	14	ihh	ihh	PROPN
ma-248	307	15	)	)	PUNCT
ma-248	308	1	+	+	CCONJ
ma-248	308	2	(	(	PUNCT
ma-248	308	3	ω	ω	PROPN
ma-248	308	4	+	+	X
ma-248	308	5	µ	µ	X
ma-248	308	6	)	)	PUNCT
ma-248	308	7	(	(	PUNCT
ma-248	308	8	(	(	PUNCT
ma-248	308	9	rhh	rhh	X
ma-248	308	10	−	−	NOUN
ma-248	308	11	r∗hh)2	r∗hh)2	VERB
ma-248	308	12	rhh	rhh	PROPN
ma-248	308	13	)	)	PUNCT
ma-248	308	14	.	.	PUNCT
ma-248	309	1	hence	hence	ADV
ma-248	309	2	,	,	PUNCT
ma-248	309	3	dlpdt	dlpdt	NOUN
ma-248	309	4	=	=	NOUN
ma-248	309	5	0	0	NUM
ma-248	309	6	when	when	SCONJ
ma-248	309	7	shh	shh	PROPN
ma-248	309	8	=	=	NOUN
ma-248	309	9	s∗hh	s∗hh	PROPN
ma-248	309	10	,	,	PUNCT
ma-248	309	11	ehh	ehh	NOUN
ma-248	309	12	=	=	SYM
ma-248	309	13	e∗hh	e∗hh	PROPN
ma-248	309	14	,	,	PUNCT
ma-248	309	15	ahh	ahh	PROPN
ma-248	309	16	=	=	SYM
ma-248	309	17	a∗hh	a∗hh	PROPN
ma-248	309	18	,	,	PUNCT
ma-248	309	19	ihh	ihh	PROPN
ma-248	309	20	=	=	PUNCT
ma-248	309	21	i∗hh	i∗hh	PROPN
ma-248	309	22	,	,	PUNCT
ma-248	309	23	and	and	CCONJ
ma-248	309	24	rhh	rhh	X
ma-248	309	25	=	=	NOUN
ma-248	309	26	r∗hh	r∗hh	PROPN
ma-248	309	27	.	.	PUNCT
ma-248	310	1	it	it	PRON
ma-248	310	2	canbe	canbe	VERB
ma-248	310	3	shown	show	VERB
ma-248	310	4	that	that	SCONJ
ma-248	310	5	the	the	DET
ma-248	310	6	inequality	inequality	NOUN
ma-248	310	7	g1	g1	VERB
ma-248	310	8	≤	≤	PUNCT
ma-248	310	9	g2	g2	PROPN
ma-248	310	10	.	.	PUNCT
ma-248	311	1	evidently	evidently	ADV
ma-248	311	2	,	,	PUNCT
ma-248	311	3	it	it	PRON
ma-248	311	4	can	can	AUX
ma-248	311	5	be	be	AUX
ma-248	311	6	verified	verify	VERB
ma-248	311	7	that	that	SCONJ
ma-248	311	8	dlp	dlp	NOUN
ma-248	311	9	dt	dt	NOUN
ma-248	311	10	≤	≤	NUM
ma-248	311	11	0	0	NUM
ma-248	311	12	when	when	SCONJ
ma-248	311	13	g1	g1	NOUN
ma-248	311	14	≤	≤	PUNCT
ma-248	311	15	g2.hence	g2.hence	NOUN
ma-248	311	16	dlp	dlp	NOUN
ma-248	311	17	dt	dt	NOUN
ma-248	312	1	=	=	SYM
ma-248	312	2	0	0	PROPN
ma-248	312	3	,	,	PUNCT
ma-248	312	4	when	when	SCONJ
ma-248	312	5	shh	shh	PROPN
ma-248	312	6	=	=	NOUN
ma-248	312	7	s∗hh	s∗hh	PROPN
ma-248	312	8	,	,	PUNCT
ma-248	312	9	ehh	ehh	NOUN
ma-248	312	10	=	=	SYM
ma-248	312	11	e∗hh	e∗hh	PROPN
ma-248	312	12	,	,	PUNCT
ma-248	312	13	ahh	ahh	PROPN
ma-248	312	14	=	=	SYM
ma-248	312	15	a∗hh	a∗hh	PROPN
ma-248	312	16	,	,	PUNCT
ma-248	312	17	ihh	ihh	PROPN
ma-248	312	18	=	=	PUNCT
ma-248	312	19	i∗hh	i∗hh	PROPN
ma-248	312	20	and	and	CCONJ
ma-248	312	21	rhh	rhh	X
ma-248	312	22	=	=	NOUN
ma-248	312	23	r∗hh	r∗hh	PROPN
ma-248	312	24	.	.	PUNCT
ma-248	312	25	thisindicates	thisindicate	VERB
ma-248	312	26	that	that	SCONJ
ma-248	312	27	the	the	DET
ma-248	312	28	largest	large	ADJ
ma-248	312	29	compact	compact	ADJ
ma-248	312	30	invariant	invariant	ADJ
ma-248	312	31	set	set	NOUN
ma-248	312	32	is	be	AUX
ma-248	312	33	a	a	DET
ma-248	312	34	singleton	singleton	NOUN
ma-248	312	35	.	.	PUNCT
ma-248	313	1	hence	hence	ADV
ma-248	313	2	,	,	PUNCT
ma-248	313	3	from	from	ADP
ma-248	313	4	[	[	X
ma-248	313	5	20	20	NUM
ma-248	313	6	]	]	PUNCT
ma-248	313	7	,	,	PUNCT
ma-248	313	8	e∗	e∗	PROPN
ma-248	313	9	is	be	AUX
ma-248	313	10	globallystable	globallystable	ADJ
ma-248	313	11	.	.	PUNCT
ma-248	314	1	�	�	PROPN
ma-248	314	2	4	4	NUM
ma-248	314	3	.	.	PUNCT
ma-248	315	1	sensitivity	sensitivity	NOUN
ma-248	315	2	analysis	analysis	NOUN
ma-248	315	3	of	of	ADP
ma-248	315	4	r0	r0	NOUN
ma-248	315	5	getting	get	VERB
ma-248	315	6	the	the	DET
ma-248	315	7	correct	correct	ADJ
ma-248	315	8	estimation	estimation	NOUN
ma-248	315	9	of	of	ADP
ma-248	315	10	the	the	DET
ma-248	315	11	r0	r0	NOUN
ma-248	315	12	in	in	ADP
ma-248	315	13	infection	infection	NOUN
ma-248	315	14	disease	disease	NOUN
ma-248	315	15	modelling	modelling	NOUN
ma-248	315	16	is	be	AUX
ma-248	315	17	crucial	crucial	ADJ
ma-248	315	18	because	because	SCONJ
ma-248	315	19	ithelps	ithelp	VERB
ma-248	315	20	us	we	PRON
ma-248	315	21	in	in	ADP
ma-248	315	22	the	the	DET
ma-248	315	23	decisions	decision	NOUN
ma-248	315	24	concerning	concern	VERB
ma-248	315	25	the	the	DET
ma-248	315	26	management	management	NOUN
ma-248	315	27	of	of	ADP
ma-248	315	28	the	the	DET
ma-248	315	29	infection	infection	NOUN
ma-248	315	30	.	.	PUNCT
ma-248	316	1	however	however	ADV
ma-248	316	2	,	,	PUNCT
ma-248	316	3	the	the	DET
ma-248	316	4	possibilityof	possibilityof	ADJ
ma-248	316	5	the	the	DET
ma-248	316	6	parameters	parameter	NOUN
ma-248	316	7	linked	link	VERB
ma-248	316	8	to	to	ADP
ma-248	316	9	the	the	DET
ma-248	316	10	r0	r0	NOUN
ma-248	316	11	to	to	PART
ma-248	316	12	change	change	VERB
ma-248	316	13	makes	make	VERB
ma-248	316	14	sensitivity	sensitivity	NOUN
ma-248	316	15	analysis	analysis	NOUN
ma-248	316	16	an	an	DET
ma-248	316	17	important	important	ADJ
ma-248	316	18	subject	subject	NOUN
ma-248	316	19	inepidemiology	inepidemiology	NOUN
ma-248	316	20	.	.	PUNCT
ma-248	317	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	317	2	eur	eur	PROPN
ma-248	317	3	.	.	PUNCT
ma-248	318	1	j.	j.	PROPN
ma-248	318	2	math	math	PROPN
ma-248	318	3	.	.	PUNCT
ma-248	319	1	anal	anal	PROPN
ma-248	319	2	.	.	PUNCT
ma-248	320	1	10.28924	10.28924	NUM
ma-248	320	2	/	/	SYM
ma-248	320	3	ada	ada	PROPN
ma-248	320	4	/	/	SYM
ma-248	320	5	ma.4.21	ma.4.21	NOUN
ma-248	320	6	13	13	NUM
ma-248	320	7	definition	definition	NOUN
ma-248	320	8	4.1	4.1	NUM
ma-248	320	9	.	.	PUNCT
ma-248	321	1	the	the	PRON
ma-248	321	2	normalized	normalize	VERB
ma-248	321	3	forward	forward	ADJ
ma-248	321	4	sensitivity	sensitivity	NOUN
ma-248	321	5	index	index	NOUN
ma-248	321	6	of	of	ADP
ma-248	321	7	r0	r0	NOUN
ma-248	321	8	computed	compute	VERB
ma-248	321	9	using	use	VERB
ma-248	321	10	the	the	DET
ma-248	321	11	formula	formula	NOUN
ma-248	321	12	used	use	VERB
ma-248	321	13	by	by	ADP
ma-248	321	14	[	[	X
ma-248	321	15	23	23	NUM
ma-248	321	16	]	]	PUNCT
ma-248	321	17	for	for	ADP
ma-248	321	18	a	a	DET
ma-248	321	19	given	give	VERB
ma-248	321	20	parameter	parameter	NOUN
ma-248	321	21	α1	α1	PROPN
ma-248	321	22	is	be	AUX
ma-248	321	23	ϑr0α1	ϑr0α1	PROPN
ma-248	321	24	=	=	PUNCT
ma-248	322	1	∂r0	∂r0	ADP
ma-248	322	2	∂α1	∂α1	PROPN
ma-248	322	3	α1	α1	PROPN
ma-248	322	4	r0	r0	NOUN
ma-248	322	5	.	.	PUNCT
ma-248	323	1	(	(	PUNCT
ma-248	323	2	21	21	NUM
ma-248	323	3	)	)	PUNCT
ma-248	323	4	the	the	DET
ma-248	323	5	parameters	parameter	NOUN
ma-248	323	6	with	with	ADP
ma-248	323	7	positive	positive	ADJ
ma-248	323	8	indices	index	NOUN
ma-248	323	9	contribute	contribute	VERB
ma-248	323	10	to	to	ADP
ma-248	323	11	the	the	DET
ma-248	323	12	epidemic	epidemic	NOUN
ma-248	323	13	spreading	spread	VERB
ma-248	323	14	since	since	SCONJ
ma-248	323	15	they	they	PRON
ma-248	323	16	enhancethe	enhancethe	VERB
ma-248	323	17	r0	r0	NOUN
ma-248	323	18	.	.	PUNCT
ma-248	324	1	the	the	DET
ma-248	324	2	parameters	parameter	NOUN
ma-248	324	3	with	with	ADP
ma-248	324	4	a	a	DET
ma-248	324	5	negative	negative	ADJ
ma-248	324	6	index	index	NOUN
ma-248	324	7	,	,	PUNCT
ma-248	324	8	on	on	ADP
ma-248	324	9	the	the	DET
ma-248	324	10	other	other	ADJ
ma-248	324	11	hand	hand	NOUN
ma-248	324	12	,	,	PUNCT
ma-248	324	13	aid	aid	NOUN
ma-248	324	14	in	in	ADP
ma-248	324	15	disease	disease	NOUN
ma-248	324	16	control	control	NOUN
ma-248	324	17	by	by	ADP
ma-248	324	18	lowering	lower	VERB
ma-248	324	19	r0	r0	NOUN
ma-248	324	20	.	.	PUNCT
ma-248	325	1	from	from	ADP
ma-248	325	2	table	table	NOUN
ma-248	325	3	1	1	NUM
ma-248	325	4	,	,	PUNCT
ma-248	325	5	λ	λ	PROPN
ma-248	325	6	,	,	PUNCT
ma-248	325	7	τ1	τ1	NOUN
ma-248	325	8	,	,	PUNCT
ma-248	325	9	ψ1	ψ1	NOUN
ma-248	325	10	,	,	PUNCT
ma-248	325	11	η1	η1	NOUN
ma-248	325	12	,	,	PUNCT
ma-248	325	13	k1	k1	NOUN
ma-248	325	14	,	,	PUNCT
ma-248	325	15	µ	µ	NOUN
ma-248	325	16	,	,	PUNCT
ma-248	325	17	and	and	CCONJ
ma-248	325	18	ψ2	ψ2	NOUN
ma-248	325	19	are	be	AUX
ma-248	325	20	the	the	DET
ma-248	325	21	parameters	parameter	NOUN
ma-248	325	22	which	which	PRON
ma-248	325	23	are	be	AUX
ma-248	325	24	most	most	ADV
ma-248	325	25	sensitive	sensitive	ADJ
ma-248	325	26	on	on	ADP
ma-248	325	27	r0	r0	NOUN
ma-248	325	28	.	.	PUNCT
ma-248	326	1	table	table	NOUN
ma-248	326	2	1	1	NUM
ma-248	326	3	.	.	PUNCT
ma-248	326	4	model	model	NOUN
ma-248	326	5	parameter	parameter	PROPN
ma-248	326	6	sensitivity	sensitivity	NOUN
ma-248	326	7	indices	indice	VERB
ma-248	326	8	for	for	ADP
ma-248	326	9	the	the	DET
ma-248	326	10	reproduction	reproduction	NOUN
ma-248	326	11	number	number	NOUN
ma-248	326	12	parameter	parameter	NOUN
ma-248	326	13	sensitivity	sensitivity	NOUN
ma-248	326	14	index	index	NOUN
ma-248	326	15	λ	λ	PROPN
ma-248	326	16	1.000	1.000	NUM
ma-248	326	17	τ1	τ1	ADP
ma-248	326	18	−2.333	−2.333	NOUN
ma-248	326	19	ψ1	ψ1	ADJ
ma-248	326	20	−0.526	−0.526	NOUN
ma-248	326	21	ψ2	ψ2	NOUN
ma-248	326	22	−0.473	−0.473	X
ma-248	326	23	η1	η1	NOUN
ma-248	326	24	1.000	1.000	NUM
ma-248	326	25	µ	µ	NUM
ma-248	326	26	−1.000	−1.000	PROPN
ma-248	326	27	k1	k1	PROPN
ma-248	326	28	1.000	1.000	NUM
ma-248	326	29	this	this	PRON
ma-248	326	30	is	be	AUX
ma-248	326	31	because	because	SCONJ
ma-248	326	32	,	,	PUNCT
ma-248	326	33	any	any	DET
ma-248	326	34	increment	increment	NOUN
ma-248	326	35	in	in	ADP
ma-248	326	36	the	the	DET
ma-248	326	37	parameter	parameter	NOUN
ma-248	326	38	values	value	NOUN
ma-248	326	39	of	of	ADP
ma-248	326	40	λ	λ	PROPN
ma-248	326	41	,	,	PUNCT
ma-248	326	42	η1	η1	NOUN
ma-248	326	43	,	,	PUNCT
ma-248	326	44	and	and	CCONJ
ma-248	326	45	k1	k1	NOUN
ma-248	326	46	will	will	AUX
ma-248	326	47	lead	lead	VERB
ma-248	326	48	to	to	ADP
ma-248	326	49	a	a	DET
ma-248	326	50	100	100	NUM
ma-248	326	51	%	%	NOUN
ma-248	326	52	increasein	increasein	NOUN
ma-248	326	53	r0	r0	NOUN
ma-248	326	54	.	.	PUNCT
ma-248	327	1	also	also	ADV
ma-248	327	2	,	,	PUNCT
ma-248	327	3	an	an	DET
ma-248	327	4	increase	increase	NOUN
ma-248	327	5	in	in	ADP
ma-248	327	6	µ	µ	NUM
ma-248	327	7	,	,	PUNCT
ma-248	327	8	τ1	τ1	NOUN
ma-248	327	9	,	,	PUNCT
ma-248	327	10	ψ1	ψ1	NOUN
ma-248	327	11	,	,	PUNCT
ma-248	327	12	and	and	CCONJ
ma-248	327	13	ψ2	ψ2	NOUN
ma-248	327	14	,	,	PUNCT
ma-248	327	15	will	will	AUX
ma-248	327	16	decrease	decrease	VERB
ma-248	327	17	r0	r0	NOUN
ma-248	327	18	by	by	ADP
ma-248	327	19	100	100	NUM
ma-248	327	20	%	%	NOUN
ma-248	327	21	,	,	PUNCT
ma-248	327	22	233.3	233.3	NUM
ma-248	327	23	%	%	NOUN
ma-248	327	24	,	,	PUNCT
ma-248	327	25	52.6	52.6	NUM
ma-248	327	26	%	%	NOUN
ma-248	327	27	and	and	CCONJ
ma-248	327	28	47.3%respectively	47.3%respectively	NOUN
ma-248	327	29	.	.	PUNCT
ma-248	328	1	therefore	therefore	ADV
ma-248	328	2	,	,	PUNCT
ma-248	328	3	effective	effective	ADJ
ma-248	328	4	measures	measure	NOUN
ma-248	328	5	must	must	AUX
ma-248	328	6	be	be	AUX
ma-248	328	7	put	put	VERB
ma-248	328	8	in	in	ADP
ma-248	328	9	place	place	NOUN
ma-248	328	10	to	to	PART
ma-248	328	11	decrease	decrease	VERB
ma-248	328	12	λ	λ	PROPN
ma-248	328	13	,	,	PUNCT
ma-248	328	14	η1	η1	NOUN
ma-248	328	15	,	,	PUNCT
ma-248	328	16	and	and	CCONJ
ma-248	328	17	k1	k1	NOUN
ma-248	328	18	and	and	CCONJ
ma-248	328	19	toincrease	toincrease	NOUN
ma-248	328	20	µ	µ	NUM
ma-248	328	21	,	,	PUNCT
ma-248	328	22	τ1ψ1	τ1ψ1	ADP
ma-248	328	23	,	,	PUNCT
ma-248	328	24	and	and	CCONJ
ma-248	328	25	ψ2	ψ2	NOUN
ma-248	328	26	.	.	PUNCT
ma-248	329	1	although	although	SCONJ
ma-248	329	2	intervention	intervention	NOUN
ma-248	329	3	measures	measure	NOUN
ma-248	329	4	are	be	AUX
ma-248	329	5	geared	gear	VERB
ma-248	329	6	towards	towards	ADP
ma-248	329	7	increasing	increase	VERB
ma-248	329	8	and	and	CCONJ
ma-248	329	9	/	/	SYM
ma-248	329	10	orincreasing	orincrease	VERB
ma-248	329	11	the	the	DET
ma-248	329	12	most	most	ADV
ma-248	329	13	significant	significant	ADJ
ma-248	329	14	parameters	parameter	NOUN
ma-248	329	15	,	,	PUNCT
ma-248	329	16	it	it	PRON
ma-248	329	17	is	be	AUX
ma-248	329	18	paramount	paramount	ADJ
ma-248	329	19	that	that	SCONJ
ma-248	329	20	the	the	DET
ma-248	329	21	control	control	NOUN
ma-248	329	22	of	of	ADP
ma-248	329	23	the	the	DET
ma-248	329	24	other	other	ADJ
ma-248	329	25	parametersnot	parametersnot	NOUN
ma-248	329	26	be	be	AUX
ma-248	329	27	completely	completely	ADV
ma-248	329	28	ignored	ignore	VERB
ma-248	329	29	.	.	PUNCT
ma-248	330	1	5	5	X
ma-248	330	2	.	.	X
ma-248	330	3	optimal	optimal	ADJ
ma-248	330	4	control	control	NOUN
ma-248	330	5	analysis	analysis	NOUN
ma-248	330	6	in	in	ADP
ma-248	330	7	this	this	DET
ma-248	330	8	section	section	NOUN
ma-248	330	9	,	,	PUNCT
ma-248	330	10	model	model	NOUN
ma-248	330	11	system	system	NOUN
ma-248	330	12	(	(	PUNCT
ma-248	330	13	1	1	X
ma-248	330	14	)	)	PUNCT
ma-248	330	15	is	be	AUX
ma-248	330	16	modified	modify	VERB
ma-248	330	17	by	by	ADP
ma-248	330	18	putting	put	VERB
ma-248	330	19	in	in	ADP
ma-248	330	20	three	three	NUM
ma-248	330	21	time	time	NOUN
ma-248	330	22	-	-	PUNCT
ma-248	330	23	dependent	dependent	ADJ
ma-248	330	24	controls	control	NOUN
ma-248	330	25	,	,	PUNCT
ma-248	330	26	viz	viz	PROPN
ma-248	330	27	.	.	PROPN
ma-248	331	1	per	per	ADP
ma-248	331	2	-	-	PUNCT
ma-248	331	3	sonal	sonal	ADJ
ma-248	331	4	protection	protection	NOUN
ma-248	331	5	,	,	PUNCT
ma-248	331	6	vaccination	vaccination	NOUN
ma-248	331	7	and	and	CCONJ
ma-248	331	8	treatment	treatment	NOUN
ma-248	331	9	controls	control	NOUN
ma-248	331	10	,	,	PUNCT
ma-248	331	11	to	to	PART
ma-248	331	12	examine	examine	VERB
ma-248	331	13	the	the	DET
ma-248	331	14	impact	impact	NOUN
ma-248	331	15	of	of	ADP
ma-248	331	16	the	the	DET
ma-248	331	17	control	control	NOUN
ma-248	331	18	schemeson	schemeson	NOUN
ma-248	331	19	the	the	DET
ma-248	331	20	meningitis	meningitis	NOUN
ma-248	331	21	disease	disease	NOUN
ma-248	331	22	.	.	PUNCT
ma-248	332	1	in	in	ADP
ma-248	332	2	model	model	NOUN
ma-248	332	3	system	system	NOUN
ma-248	332	4	(	(	PUNCT
ma-248	332	5	1	1	NUM
ma-248	332	6	)	)	PUNCT
ma-248	332	7	,	,	PUNCT
ma-248	332	8	the	the	DET
ma-248	332	9	associated	associated	ADJ
ma-248	332	10	infection	infection	NOUN
ma-248	332	11	force	force	NOUN
ma-248	332	12	is	be	AUX
ma-248	332	13	lowered	lower	VERB
ma-248	332	14	by	by	ADP
ma-248	332	15	afactor	afactor	NOUN
ma-248	332	16	of	of	ADP
ma-248	332	17	(	(	PUNCT
ma-248	332	18	1	1	NUM
ma-248	332	19	−	−	NOUN
ma-248	332	20	u1	u1	NOUN
ma-248	332	21	)	)	PUNCT
ma-248	332	22	,	,	PUNCT
ma-248	332	23	where	where	SCONJ
ma-248	332	24	u1	u1	NOUN
ma-248	332	25	is	be	AUX
ma-248	332	26	the	the	DET
ma-248	332	27	personal	personal	ADJ
ma-248	332	28	protection	protection	NOUN
ma-248	332	29	control	control	NOUN
ma-248	332	30	that	that	PRON
ma-248	332	31	ensures	ensure	VERB
ma-248	332	32	the	the	DET
ma-248	332	33	attempt	attempt	NOUN
ma-248	332	34	to	to	PART
ma-248	332	35	reduceroom	reduceroom	VERB
ma-248	332	36	heat	heat	NOUN
ma-248	332	37	and	and	CCONJ
ma-248	332	38	avoid	avoid	VERB
ma-248	332	39	close	close	ADJ
ma-248	332	40	contact	contact	NOUN
ma-248	332	41	with	with	ADP
ma-248	332	42	the	the	DET
ma-248	332	43	infected	infect	VERB
ma-248	332	44	.	.	PUNCT
ma-248	333	1	the	the	DET
ma-248	333	2	rate	rate	NOUN
ma-248	333	3	of	of	ADP
ma-248	333	4	vaccinating	vaccinating	NOUN
ma-248	333	5	susceptible	susceptible	ADJ
ma-248	333	6	individualsagainst	individualsagainst	ADJ
ma-248	333	7	meningitis	meningitis	NOUN
ma-248	333	8	is	be	AUX
ma-248	333	9	represented	represent	VERB
ma-248	333	10	by	by	ADP
ma-248	333	11	the	the	DET
ma-248	333	12	control	control	NOUN
ma-248	333	13	function	function	PROPN
ma-248	333	14	u2	u2	PROPN
ma-248	333	15	.	.	PUNCT
ma-248	334	1	as	as	ADP
ma-248	334	2	a	a	DET
ma-248	334	3	result	result	NOUN
ma-248	334	4	,	,	PUNCT
ma-248	334	5	the	the	DET
ma-248	334	6	model	model	NOUN
ma-248	334	7	assumes	assume	VERB
ma-248	334	8	thatvaccinated	thatvaccinate	VERB
ma-248	334	9	individuals	individual	NOUN
ma-248	334	10	shift	shift	VERB
ma-248	334	11	from	from	ADP
ma-248	334	12	the	the	DET
ma-248	334	13	susceptible	susceptible	ADJ
ma-248	334	14	compartment	compartment	NOUN
ma-248	334	15	to	to	ADP
ma-248	334	16	the	the	DET
ma-248	334	17	removed	remove	VERB
ma-248	334	18	compartment	compartment	NOUN
ma-248	334	19	at	at	ADP
ma-248	334	20	anytime	anytime	NOUN
ma-248	334	21	.	.	PUNCT
ma-248	335	1	furthermore	furthermore	ADV
ma-248	335	2	,	,	PUNCT
ma-248	335	3	we	we	PRON
ma-248	335	4	assume	assume	VERB
ma-248	335	5	that	that	SCONJ
ma-248	335	6	the	the	DET
ma-248	335	7	control	control	NOUN
ma-248	335	8	function	function	NOUN
ma-248	335	9	u3	u3	PROPN
ma-248	335	10	reflects	reflect	VERB
ma-248	335	11	the	the	DET
ma-248	335	12	rate	rate	NOUN
ma-248	335	13	at	at	ADP
ma-248	335	14	which	which	PRON
ma-248	335	15	sick	sick	ADJ
ma-248	335	16	patients	patient	NOUN
ma-248	335	17	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	335	18	eur	eur	PROPN
ma-248	335	19	.	.	PUNCT
ma-248	336	1	j.	j.	PROPN
ma-248	336	2	math	math	PROPN
ma-248	336	3	.	.	PUNCT
ma-248	337	1	anal	anal	PROPN
ma-248	337	2	.	.	PUNCT
ma-248	338	1	10.28924	10.28924	NUM
ma-248	338	2	/	/	SYM
ma-248	338	3	ada	ada	PROPN
ma-248	338	4	/	/	SYM
ma-248	338	5	ma.4.21	ma.4.21	PROPN
ma-248	338	6	14are	14are	PROPN
ma-248	338	7	treated	treat	VERB
ma-248	338	8	.	.	PUNCT
ma-248	339	1	hence	hence	ADV
ma-248	339	2	,	,	PUNCT
ma-248	339	3	the	the	DET
ma-248	339	4	modified	modify	VERB
ma-248	339	5	nonlinear	nonlinear	ADJ
ma-248	339	6	control	control	NOUN
ma-248	339	7	system	system	NOUN
ma-248	339	8	becomes	become	VERB
ma-248	339	9	;	;	PUNCT
ma-248	339	10	dshh	dshh	PROPN
ma-248	339	11	dt	dt	PROPN
ma-248	339	12	=	=	SYM
ma-248	339	13	λ−	λ−	PROPN
ma-248	339	14	µshh	µshh	PROPN
ma-248	339	15	−	−	PROPN
ma-248	339	16	(	(	PUNCT
ma-248	339	17	1−	1−	NUM
ma-248	339	18	u1)η1ihhshh	u1)η1ihhshh	NOUN
ma-248	339	19	+	+	NUM
ma-248	339	20	ωrhh	ωrhh	PROPN
ma-248	339	21	−	−	PROPN
ma-248	339	22	u2shh	u2shh	PROPN
ma-248	339	23	,	,	PUNCT
ma-248	339	24	dehh	dehh	NOUN
ma-248	339	25	dt	dt	NOUN
ma-248	340	1	=	=	PUNCT
ma-248	340	2	(	(	PUNCT
ma-248	340	3	1−	1−	NUM
ma-248	340	4	u1)η1ihhshh	u1)η1ihhshh	NOUN
ma-248	340	5	−	−	PROPN
ma-248	340	6	kτ1ehh	kτ1ehh	NOUN
ma-248	340	7	−	−	PROPN
ma-248	340	8	(	(	PUNCT
ma-248	340	9	1−	1−	NUM
ma-248	340	10	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	340	11	−	−	NOUN
ma-248	340	12	µehh	µehh	NOUN
ma-248	340	13	,	,	PUNCT
ma-248	340	14	dahh	dahh	NOUN
ma-248	340	15	dt	dt	NOUN
ma-248	340	16	=	=	PUNCT
ma-248	340	17	(	(	PUNCT
ma-248	340	18	1−	1−	NUM
ma-248	340	19	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	340	20	−	−	PROPN
ma-248	340	21	(	(	PUNCT
ma-248	340	22	τ2	τ2	NOUN
ma-248	340	23	+	+	NUM
ma-248	340	24	τ3	τ3	NOUN
ma-248	340	25	+	+	X
ma-248	340	26	µ)ahh	µ)ahh	PROPN
ma-248	340	27	,	,	PUNCT
ma-248	340	28	(	(	PUNCT
ma-248	340	29	22	22	NUM
ma-248	340	30	)	)	PUNCT
ma-248	340	31	dihh	dihh	NOUN
ma-248	340	32	dt	dt	NOUN
ma-248	340	33	=	=	PUNCT
ma-248	340	34	kτ1ehh	kτ1ehh	PROPN
ma-248	340	35	−	−	PROPN
ma-248	340	36	(	(	PUNCT
ma-248	340	37	ψ1	ψ1	NOUN
ma-248	340	38	+	+	CCONJ
ma-248	340	39	ψ2	ψ2	NOUN
ma-248	340	40	+	+	CCONJ
ma-248	340	41	u3	u3	NOUN
ma-248	340	42	+	+	CCONJ
ma-248	340	43	µ)ihh	µ)ihh	PROPN
ma-248	340	44	,	,	PUNCT
ma-248	340	45	drhh	drhh	X
ma-248	340	46	dt	dt	NOUN
ma-248	340	47	=	=	PUNCT
ma-248	340	48	τ2ahh	τ2ahh	PROPN
ma-248	340	49	+	+	PUNCT
ma-248	340	50	ψ1ehh	ψ1ehh	NUM
ma-248	340	51	+	+	CCONJ
ma-248	340	52	u2shh	u2shh	PROPN
ma-248	340	53	+	+	CCONJ
ma-248	340	54	u3ihh	u3ihh	PROPN
ma-248	340	55	−	−	PROPN
ma-248	340	56	(	(	PUNCT
ma-248	340	57	ω	ω	PROPN
ma-248	340	58	+	+	X
ma-248	340	59	µ)rhh	µ)rhh	PROPN
ma-248	340	60	.	.	NOUN
ma-248	340	61	to	to	PART
ma-248	340	62	examine	examine	VERB
ma-248	340	63	the	the	DET
ma-248	340	64	efforts	effort	NOUN
ma-248	340	65	needed	need	VERB
ma-248	340	66	to	to	PART
ma-248	340	67	control	control	VERB
ma-248	340	68	the	the	DET
ma-248	340	69	disease	disease	NOUN
ma-248	340	70	,	,	PUNCT
ma-248	340	71	we	we	PRON
ma-248	340	72	define	define	VERB
ma-248	340	73	an	an	DET
ma-248	340	74	optimal	optimal	ADJ
ma-248	340	75	functional	functional	ADJ
ma-248	340	76	j	j	NOUN
ma-248	340	77	thatminimizes	thatminimize	VERB
ma-248	340	78	the	the	DET
ma-248	340	79	exposed	expose	VERB
ma-248	340	80	,	,	PUNCT
ma-248	340	81	asymptomatic	asymptomatic	ADJ
ma-248	340	82	and	and	CCONJ
ma-248	340	83	symptomatic	symptomatic	ADJ
ma-248	340	84	individuals	individual	NOUN
ma-248	340	85	and	and	CCONJ
ma-248	340	86	maximizes	maximize	VERB
ma-248	340	87	the	the	DET
ma-248	340	88	recoverythrough	recoverythrough	NOUN
ma-248	340	89	personal	personal	PROPN
ma-248	340	90	protection	protection	NOUN
ma-248	340	91	,	,	PUNCT
ma-248	340	92	vaccination	vaccination	NOUN
ma-248	340	93	and	and	CCONJ
ma-248	340	94	treatment	treatment	NOUN
ma-248	340	95	controls	control	NOUN
ma-248	340	96	of	of	ADP
ma-248	340	97	u1	u1	NOUN
ma-248	340	98	,	,	PUNCT
ma-248	340	99	u2	u2	NOUN
ma-248	340	100	and	and	CCONJ
ma-248	340	101	u3	u3	NOUN
ma-248	340	102	.	.	PUNCT
ma-248	341	1	hence	hence	ADV
ma-248	341	2	,	,	PUNCT
ma-248	341	3	theobjective	theobjective	VERB
ma-248	341	4	functional	functional	ADJ
ma-248	341	5	j	j	PROPN
ma-248	341	6	is	be	AUX
ma-248	341	7	given	give	VERB
ma-248	341	8	by	by	ADP
ma-248	341	9	;	;	PUNCT
ma-248	341	10	j	j	PROPN
ma-248	341	11	(	(	PUNCT
ma-248	341	12	u1	u1	PROPN
ma-248	341	13	,	,	PUNCT
ma-248	341	14	u2	u2	NOUN
ma-248	341	15	,	,	PUNCT
ma-248	341	16	u3	u3	NOUN
ma-248	341	17	)	)	PUNCT
ma-248	341	18	=	=	SYM
ma-248	342	1	∫	∫	PROPN
ma-248	342	2	tf	tf	INTJ
ma-248	342	3	0	0	NUM
ma-248	343	1	[	[	PUNCT
ma-248	343	2	b1ehh	b1ehh	NOUN
ma-248	343	3	+	+	CCONJ
ma-248	343	4	b2ahh	b2ahh	PROPN
ma-248	343	5	+	+	NUM
ma-248	343	6	b3ihh	b3ihh	NOUN
ma-248	344	1	+	+	CCONJ
ma-248	344	2	1	1	NUM
ma-248	344	3	2	2	NUM
ma-248	344	4	(	(	PUNCT
ma-248	344	5	u21d1	u21d1	NOUN
ma-248	344	6	+	+	CCONJ
ma-248	345	1	u22d2	u22d2	PROPN
ma-248	346	1	+	+	CCONJ
ma-248	347	1	u23d3	u23d3	X
ma-248	347	2	)	)	PUNCT
ma-248	347	3	]	]	PUNCT
ma-248	348	1	dt	dt	X
ma-248	348	2	.	.	PUNCT
ma-248	349	1	(	(	PUNCT
ma-248	349	2	23	23	NUM
ma-248	349	3	)	)	PUNCT
ma-248	349	4	referring	refer	VERB
ma-248	349	5	to	to	ADP
ma-248	349	6	(	(	PUNCT
ma-248	349	7	23	23	NUM
ma-248	349	8	)	)	PUNCT
ma-248	349	9	,	,	PUNCT
ma-248	349	10	the	the	DET
ma-248	349	11	quantities	quantity	NOUN
ma-248	349	12	b1	b1	NOUN
ma-248	349	13	,	,	PUNCT
ma-248	349	14	b2	b2	NOUN
ma-248	349	15	,	,	PUNCT
ma-248	349	16	and	and	CCONJ
ma-248	349	17	b3	b3	PROPN
ma-248	349	18	are	be	AUX
ma-248	349	19	the	the	DET
ma-248	349	20	weight	weight	NOUN
ma-248	349	21	coefficients	coefficient	NOUN
ma-248	349	22	of	of	ADP
ma-248	349	23	the	the	DET
ma-248	349	24	exposed	expose	VERB
ma-248	349	25	,	,	PUNCT
ma-248	349	26	asymp	asymp	NOUN
ma-248	349	27	-	-	PUNCT
ma-248	349	28	tomatic	tomatic	ADJ
ma-248	349	29	and	and	CCONJ
ma-248	349	30	symptomatic	symptomatic	ADJ
ma-248	349	31	individuals	individual	NOUN
ma-248	349	32	.	.	PUNCT
ma-248	350	1	in	in	ADP
ma-248	350	2	addition	addition	NOUN
ma-248	350	3	,	,	PUNCT
ma-248	350	4	the	the	DET
ma-248	350	5	terms	term	NOUN
ma-248	350	6	u21d1	u21d1	NOUN
ma-248	350	7	2	2	NUM
ma-248	350	8	,	,	PUNCT
ma-248	350	9	u22d22	u22d22	NOUN
ma-248	350	10	and	and	CCONJ
ma-248	350	11	u23d3	u23d3	NOUN
ma-248	350	12	2	2	NUM
ma-248	350	13	represents	represent	VERB
ma-248	350	14	the	the	DET
ma-248	350	15	costrelated	costrelate	VERB
ma-248	350	16	to	to	ADP
ma-248	350	17	minimizing	minimize	VERB
ma-248	350	18	the	the	DET
ma-248	350	19	exposed	expose	VERB
ma-248	350	20	,	,	PUNCT
ma-248	350	21	asymptomatic	asymptomatic	ADJ
ma-248	350	22	and	and	CCONJ
ma-248	350	23	symptomatic	symptomatic	ADJ
ma-248	350	24	individual	individual	NOUN
ma-248	350	25	.	.	PUNCT
ma-248	351	1	the	the	DET
ma-248	351	2	control	control	NOUN
ma-248	351	3	modelconsiders	modelconsider	VERB
ma-248	351	4	a	a	DET
ma-248	351	5	quadratic	quadratic	ADJ
ma-248	351	6	cost	cost	NOUN
ma-248	351	7	on	on	ADP
ma-248	351	8	the	the	DET
ma-248	351	9	controls	control	NOUN
ma-248	351	10	as	as	ADP
ma-248	351	11	in	in	ADP
ma-248	351	12	other	other	ADJ
ma-248	351	13	works	work	NOUN
ma-248	351	14	.	.	PUNCT
ma-248	352	1	we	we	PRON
ma-248	352	2	target	target	VERB
ma-248	352	3	optimal	optimal	ADJ
ma-248	352	4	control	control	NOUN
ma-248	352	5	u∗1	u∗1	NOUN
ma-248	352	6	,	,	PUNCT
ma-248	352	7	u∗2	u∗2	NOUN
ma-248	352	8	,	,	PUNCT
ma-248	352	9	u∗3such	u∗3such	ADP
ma-248	352	10	that	that	SCONJ
ma-248	352	11	j	j	PROPN
ma-248	352	12	(	(	PUNCT
ma-248	352	13	u∗1	u∗1	PROPN
ma-248	352	14	,	,	PUNCT
ma-248	352	15	u	u	NOUN
ma-248	352	16	∗	∗	NOUN
ma-248	352	17	2	2	NUM
ma-248	352	18	,	,	PUNCT
ma-248	352	19	u	u	NOUN
ma-248	352	20	∗	∗	NOUN
ma-248	352	21	3	3	NUM
ma-248	352	22	)	)	PUNCT
ma-248	352	23	=	=	SYM
ma-248	352	24	min{j	min{j	NOUN
ma-248	352	25	(	(	PUNCT
ma-248	352	26	u1	u1	NOUN
ma-248	352	27	,	,	PUNCT
ma-248	352	28	u2	u2	NOUN
ma-248	352	29	,	,	PUNCT
ma-248	352	30	u3	u3	NOUN
ma-248	352	31	)	)	PUNCT
ma-248	352	32	:	:	PUNCT
ma-248	352	33	(	(	PUNCT
ma-248	352	34	u1	u1	NOUN
ma-248	352	35	,	,	PUNCT
ma-248	352	36	u2	u2	NOUN
ma-248	352	37	,	,	PUNCT
ma-248	352	38	u3	u3	NOUN
ma-248	352	39	)	)	PUNCT
ma-248	352	40	∈	∈	PROPN
ma-248	352	41	u	u	NOUN
ma-248	352	42	}	}	PUNCT
ma-248	352	43	,	,	PUNCT
ma-248	352	44	(	(	PUNCT
ma-248	352	45	24	24	NUM
ma-248	352	46	)	)	PUNCT
ma-248	352	47	where	where	SCONJ
ma-248	352	48	u	u	NOUN
ma-248	352	49	=	=	PRON
ma-248	352	50	{	{	PUNCT
ma-248	352	51	(	(	PUNCT
ma-248	352	52	u1	u1	PROPN
ma-248	352	53	,	,	PUNCT
ma-248	352	54	u2	u2	NOUN
ma-248	352	55	,	,	PUNCT
ma-248	352	56	u3)|0	u3)|0	PROPN
ma-248	352	57	≤	≤	NUM
ma-248	352	58	ui	ui	NOUN
ma-248	352	59	≤	≤	NUM
ma-248	352	60	1	1	NUM
ma-248	352	61	,	,	PUNCT
ma-248	352	62	i	i	PRON
ma-248	352	63	=	=	NOUN
ma-248	352	64	1	1	NUM
ma-248	352	65	,	,	PUNCT
ma-248	352	66	2	2	NUM
ma-248	352	67	,	,	PUNCT
ma-248	352	68	3	3	NUM
ma-248	352	69	lebesgue	lebesgue	NOUN
ma-248	352	70	measurable	measurable	NOUN
ma-248	352	71	}	}	PUNCT
ma-248	352	72	(	(	PUNCT
ma-248	352	73	25	25	NUM
ma-248	352	74	)	)	PUNCT
ma-248	352	75	with	with	ADP
ma-248	352	76	the	the	DET
ma-248	352	77	method	method	NOUN
ma-248	352	78	of	of	ADP
ma-248	352	79	pontryagin	pontryagin	NOUN
ma-248	352	80	’s	’s	PART
ma-248	352	81	maximum	maximum	ADJ
ma-248	352	82	principle	principle	NOUN
ma-248	352	83	[	[	X
ma-248	352	84	24	24	NUM
ma-248	352	85	]	]	PUNCT
ma-248	352	86	,	,	PUNCT
ma-248	352	87	system	system	NOUN
ma-248	352	88	(	(	PUNCT
ma-248	352	89	22	22	NUM
ma-248	352	90	)	)	PUNCT
ma-248	352	91	and	and	CCONJ
ma-248	352	92	(	(	PUNCT
ma-248	352	93	23	23	NUM
ma-248	352	94	)	)	PUNCT
ma-248	352	95	are	be	AUX
ma-248	352	96	transformed	transform	VERB
ma-248	352	97	intoa	intoa	PROPN
ma-248	352	98	problem	problem	NOUN
ma-248	352	99	of	of	ADP
ma-248	352	100	hamiltonian	hamiltonian	ADJ
ma-248	352	101	minimization	minimization	NOUN
ma-248	352	102	h	h	NOUN
ma-248	352	103	with	with	ADP
ma-248	352	104	respect	respect	NOUN
ma-248	352	105	to	to	ADP
ma-248	352	106	the	the	DET
ma-248	352	107	controls	control	NOUN
ma-248	352	108	u1	u1	NOUN
ma-248	352	109	,	,	PUNCT
ma-248	352	110	u2	u2	NOUN
ma-248	352	111	and	and	CCONJ
ma-248	352	112	u3	u3	NOUN
ma-248	352	113	where	where	SCONJ
ma-248	352	114	;	;	PUNCT
ma-248	353	1	h	h	NOUN
ma-248	353	2	=	=	PUNCT
ma-248	354	1	[	[	PUNCT
ma-248	354	2	b1ehh	b1ehh	NOUN
ma-248	354	3	+	+	CCONJ
ma-248	354	4	b2ahh	b2ahh	PROPN
ma-248	354	5	+	+	NUM
ma-248	354	6	b3ihh	b3ihh	NOUN
ma-248	355	1	+	+	CCONJ
ma-248	355	2	1	1	NUM
ma-248	355	3	2	2	NUM
ma-248	355	4	(	(	PUNCT
ma-248	355	5	u21d1	u21d1	NOUN
ma-248	355	6	+	+	CCONJ
ma-248	356	1	u22d2	u22d2	PROPN
ma-248	357	1	+	+	CCONJ
ma-248	358	1	u23d3	u23d3	X
ma-248	358	2	)	)	PUNCT
ma-248	358	3	]	]	PUNCT
ma-248	359	1	,	,	PUNCT
ma-248	359	2	+	+	SYM
ma-248	359	3	λ1	λ1	PROPN
ma-248	359	4	{	{	PUNCT
ma-248	359	5	λ−	λ−	PROPN
ma-248	359	6	µshh	µshh	PROPN
ma-248	359	7	−	−	PROPN
ma-248	359	8	(	(	PUNCT
ma-248	359	9	1−	1−	NUM
ma-248	359	10	u1)η1ihhshh	u1)η1ihhshh	NOUN
ma-248	359	11	+	+	NUM
ma-248	359	12	ωrhh	ωrhh	PROPN
ma-248	359	13	−	−	PROPN
ma-248	359	14	u2shh	u2shh	PROPN
ma-248	359	15	}	}	PUNCT
ma-248	359	16	,	,	PUNCT
ma-248	359	17	+	+	NUM
ma-248	359	18	λ2	λ2	NOUN
ma-248	359	19	{	{	PUNCT
ma-248	359	20	(	(	PUNCT
ma-248	359	21	1−	1−	NUM
ma-248	359	22	u1)η1ihhshh	u1)η1ihhshh	NOUN
ma-248	359	23	−	−	PROPN
ma-248	359	24	kτ1ehh	kτ1ehh	NOUN
ma-248	359	25	−	−	PROPN
ma-248	359	26	(	(	PUNCT
ma-248	359	27	1−	1−	NUM
ma-248	359	28	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	360	1	−	−	PROPN
ma-248	360	2	µehh	µehh	NOUN
ma-248	360	3	}	}	PUNCT
ma-248	360	4	,	,	PUNCT
ma-248	360	5	(	(	PUNCT
ma-248	360	6	26	26	NUM
ma-248	360	7	)	)	PUNCT
ma-248	360	8	+	+	CCONJ
ma-248	360	9	λ3	λ3	PROPN
ma-248	360	10	{	{	PUNCT
ma-248	360	11	(	(	PUNCT
ma-248	360	12	1−	1−	NUM
ma-248	360	13	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	360	14	−	−	PROPN
ma-248	360	15	(	(	PUNCT
ma-248	360	16	τ2	τ2	NOUN
ma-248	360	17	+	+	NUM
ma-248	360	18	τ3	τ3	NOUN
ma-248	360	19	+	+	CCONJ
ma-248	360	20	µ)ahh	µ)ahh	NOUN
ma-248	360	21	}	}	PUNCT
ma-248	360	22	,	,	PUNCT
ma-248	360	23	+	+	CCONJ
ma-248	360	24	λ4	λ4	ADJ
ma-248	360	25	{	{	PUNCT
ma-248	360	26	kτ1ehh	kτ1ehh	PROPN
ma-248	360	27	−	−	PROPN
ma-248	360	28	(	(	PUNCT
ma-248	360	29	ψ1	ψ1	NOUN
ma-248	360	30	+	+	CCONJ
ma-248	360	31	ψ2	ψ2	NOUN
ma-248	360	32	+	+	CCONJ
ma-248	360	33	u3	u3	NOUN
ma-248	360	34	+	+	CCONJ
ma-248	360	35	µ)ihh	µ)ihh	PROPN
ma-248	360	36	}	}	PUNCT
ma-248	360	37	,	,	PUNCT
ma-248	360	38	+	+	CCONJ
ma-248	360	39	λ5	λ5	NOUN
ma-248	360	40	{	{	PUNCT
ma-248	360	41	τ2ahh	τ2ahh	PROPN
ma-248	360	42	+	+	NUM
ma-248	360	43	ψ1ehh	ψ1ehh	NUM
ma-248	361	1	+	+	CCONJ
ma-248	361	2	u2shh	u2shh	PROPN
ma-248	361	3	+	+	CCONJ
ma-248	361	4	u3ihh	u3ihh	PROPN
ma-248	361	5	−	−	PROPN
ma-248	361	6	(	(	PUNCT
ma-248	361	7	ω	ω	PROPN
ma-248	361	8	+	+	X
ma-248	361	9	µ)rhh	µ)rhh	NOUN
ma-248	361	10	}	}	PUNCT
ma-248	361	11	.	.	PUNCT
ma-248	362	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	362	2	eur	eur	PROPN
ma-248	362	3	.	.	PUNCT
ma-248	363	1	j.	j.	PROPN
ma-248	363	2	math	math	PROPN
ma-248	363	3	.	.	PUNCT
ma-248	364	1	anal	anal	PROPN
ma-248	364	2	.	.	PUNCT
ma-248	365	1	10.28924	10.28924	NUM
ma-248	365	2	/	/	SYM
ma-248	365	3	ada	ada	PROPN
ma-248	365	4	/	/	SYM
ma-248	365	5	ma.4.21	ma.4.21	PROPN
ma-248	365	6	15	15	NUM
ma-248	365	7	theorem	theorem	VERB
ma-248	365	8	5.1	5.1	NUM
ma-248	365	9	.	.	PUNCT
ma-248	366	1	there	there	PRON
ma-248	366	2	exists	exist	VERB
ma-248	366	3	an	an	DET
ma-248	366	4	optimal	optimal	ADJ
ma-248	366	5	control	control	NOUN
ma-248	366	6	u∗	u∗	NOUN
ma-248	366	7	=	=	PUNCT
ma-248	366	8	(	(	PUNCT
ma-248	366	9	u∗1	u∗1	PROPN
ma-248	366	10	,	,	PUNCT
ma-248	366	11	u	u	NOUN
ma-248	366	12	∗	∗	NOUN
ma-248	366	13	2	2	NUM
ma-248	366	14	,	,	PUNCT
ma-248	366	15	u	u	NOUN
ma-248	366	16	∗	∗	NOUN
ma-248	366	17	3	3	NUM
ma-248	366	18	)	)	PUNCT
ma-248	366	19	∈	∈	NOUN
ma-248	366	20	u	u	NOUN
ma-248	366	21	such	such	ADJ
ma-248	366	22	that	that	SCONJ
ma-248	366	23	j	j	PROPN
ma-248	366	24	(	(	PUNCT
ma-248	366	25	u∗1	u∗1	PROPN
ma-248	366	26	,	,	PUNCT
ma-248	366	27	u	u	NOUN
ma-248	366	28	∗	∗	NOUN
ma-248	366	29	2	2	NUM
ma-248	366	30	,	,	PUNCT
ma-248	366	31	u	u	NOUN
ma-248	366	32	∗	∗	NOUN
ma-248	366	33	3	3	NUM
ma-248	366	34	)	)	PUNCT
ma-248	366	35	=	=	SYM
ma-248	366	36	min	min	PROPN
ma-248	366	37	u∈u	u∈u	PROPN
ma-248	366	38	j	j	PROPN
ma-248	366	39	(	(	PUNCT
ma-248	366	40	u1	u1	PROPN
ma-248	366	41	,	,	PUNCT
ma-248	366	42	u2	u2	NOUN
ma-248	366	43	,	,	PUNCT
ma-248	366	44	u3	u3	NOUN
ma-248	366	45	)	)	PUNCT
ma-248	366	46	,	,	PUNCT
ma-248	366	47	(	(	PUNCT
ma-248	366	48	27	27	NUM
ma-248	366	49	)	)	PUNCT
ma-248	366	50	subject	subject	NOUN
ma-248	366	51	to	to	ADP
ma-248	366	52	the	the	DET
ma-248	366	53	control	control	NOUN
ma-248	366	54	system	system	NOUN
ma-248	366	55	22	22	NUM
ma-248	366	56	with	with	ADP
ma-248	366	57	the	the	DET
ma-248	366	58	initial	initial	ADJ
ma-248	366	59	conditions	condition	NOUN
ma-248	366	60	.	.	PUNCT
ma-248	367	1	proof	proof	NOUN
ma-248	367	2	.	.	PUNCT
ma-248	368	1	the	the	DET
ma-248	368	2	work	work	NOUN
ma-248	368	3	of	of	ADP
ma-248	368	4	[	[	X
ma-248	368	5	25	25	NUM
ma-248	368	6	]	]	PUNCT
ma-248	368	7	would	would	AUX
ma-248	368	8	be	be	AUX
ma-248	368	9	considered	consider	VERB
ma-248	368	10	the	the	DET
ma-248	368	11	grounds	ground	NOUN
ma-248	368	12	for	for	ADP
ma-248	368	13	proving	prove	VERB
ma-248	368	14	the	the	DET
ma-248	368	15	existence	existence	NOUN
ma-248	368	16	of	of	ADP
ma-248	368	17	optimal	optimal	ADJ
ma-248	368	18	control.in	control.in	NUM
ma-248	368	19	minimizing	minimize	VERB
ma-248	368	20	the	the	DET
ma-248	368	21	control	control	NOUN
ma-248	368	22	problem	problem	NOUN
ma-248	368	23	,	,	PUNCT
ma-248	368	24	the	the	DET
ma-248	368	25	necessary	necessary	ADJ
ma-248	368	26	and	and	CCONJ
ma-248	368	27	convexity	convexity	NOUN
ma-248	368	28	of	of	ADP
ma-248	368	29	the	the	DET
ma-248	368	30	objective	objective	ADJ
ma-248	368	31	functional	functional	NOUN
ma-248	368	32	in	in	ADP
ma-248	368	33	u1	u1	NOUN
ma-248	368	34	,	,	PUNCT
ma-248	368	35	u2and	u2and	NUM
ma-248	368	36	u3	u3	NOUN
ma-248	368	37	are	be	AUX
ma-248	368	38	satisfied	satisfied	ADJ
ma-248	368	39	.	.	PUNCT
ma-248	369	1	the	the	DET
ma-248	369	2	control	control	PROPN
ma-248	369	3	space	space	NOUN
ma-248	369	4	u	u	NOUN
ma-248	369	5	is	be	AUX
ma-248	369	6	also	also	ADV
ma-248	369	7	convex	convex	ADJ
ma-248	369	8	and	and	CCONJ
ma-248	369	9	closed	close	VERB
ma-248	369	10	by	by	ADP
ma-248	369	11	definition.the	definition.the	DET
ma-248	369	12	optimal	optimal	ADJ
ma-248	369	13	control	control	NOUN
ma-248	369	14	system	system	NOUN
ma-248	369	15	is	be	AUX
ma-248	369	16	bounded	bound	VERB
ma-248	369	17	,	,	PUNCT
ma-248	369	18	which	which	PRON
ma-248	369	19	verifies	verify	VERB
ma-248	369	20	the	the	DET
ma-248	369	21	compactness	compactness	NOUN
ma-248	369	22	necessary	necessary	ADJ
ma-248	369	23	for	for	ADP
ma-248	369	24	the	the	DET
ma-248	369	25	optimalcontrol	optimalcontrol	NOUN
ma-248	369	26	.	.	PUNCT
ma-248	370	1	also	also	ADV
ma-248	370	2	,	,	PUNCT
ma-248	370	3	the	the	DET
ma-248	370	4	integrand	integrand	NOUN
ma-248	370	5	in	in	ADP
ma-248	370	6	the	the	DET
ma-248	370	7	functional	functional	ADJ
ma-248	370	8	(	(	PUNCT
ma-248	370	9	23	23	NUM
ma-248	370	10	)	)	PUNCT
ma-248	370	11	is	be	AUX
ma-248	370	12	convex	convex	ADJ
ma-248	370	13	on	on	ADP
ma-248	370	14	u	u	PROPN
ma-248	370	15	.	.	PUNCT
ma-248	371	1	therefore	therefore	ADV
ma-248	371	2	,	,	PUNCT
ma-248	371	3	we	we	PRON
ma-248	371	4	notice	notice	VERB
ma-248	371	5	that	that	SCONJ
ma-248	371	6	thereexist	thereexist	VERB
ma-248	371	7	a	a	DET
ma-248	371	8	constant	constant	ADJ
ma-248	371	9	q	q	NOUN
ma-248	371	10	>	>	X
ma-248	371	11	1	1	NUM
ma-248	371	12	,	,	PUNCT
ma-248	371	13	positive	positive	ADJ
ma-248	371	14	numbers	number	NOUN
ma-248	371	15	u1	u1	VERB
ma-248	371	16	,	,	PUNCT
ma-248	371	17	u2	u2	NOUN
ma-248	371	18	and	and	CCONJ
ma-248	371	19	u3	u3	NOUN
ma-248	371	20	such	such	ADJ
ma-248	371	21	that	that	SCONJ
ma-248	371	22	,	,	PUNCT
ma-248	371	23	j(u1	j(u1	NOUN
ma-248	371	24	,	,	PUNCT
ma-248	371	25	u2	u2	NOUN
ma-248	371	26	,	,	PUNCT
ma-248	371	27	u3	u3	PROPN
ma-248	371	28	)	)	PUNCT
ma-248	371	29	≥	≥	NOUN
ma-248	371	30	u1	u1	NOUN
ma-248	371	31	(	(	PUNCT
ma-248	371	32	|u1|2	|u1|2	X
ma-248	371	33	+	+	CCONJ
ma-248	371	34	|u2|2	|u2|2	PUNCT
ma-248	371	35	+	+	CCONJ
ma-248	371	36	|u3|2	|u3|2	NOUN
ma-248	371	37	)	)	PUNCT
ma-248	371	38	q	q	NOUN
ma-248	371	39	2	2	NUM
ma-248	371	40	−	−	PROPN
ma-248	371	41	u2	u2	NOUN
ma-248	371	42	.	.	PUNCT
ma-248	372	1	�	�	PROPN
ma-248	372	2	hence	hence	ADV
ma-248	372	3	,	,	PUNCT
ma-248	372	4	there	there	PRON
ma-248	372	5	exists	exist	VERB
ma-248	372	6	an	an	DET
ma-248	372	7	optimal	optimal	ADJ
ma-248	372	8	control	control	NOUN
ma-248	372	9	.	.	PUNCT
ma-248	373	1	it	it	PRON
ma-248	373	2	follows	follow	VERB
ma-248	373	3	that	that	SCONJ
ma-248	373	4	determining	determine	VERB
ma-248	373	5	the	the	DET
ma-248	373	6	optimal	optimal	ADJ
ma-248	373	7	solution	solution	NOUN
ma-248	373	8	,	,	PUNCT
ma-248	373	9	thepontryagins	thepontryagin	NOUN
ma-248	373	10	’s	’s	PART
ma-248	373	11	maximum	maximum	ADJ
ma-248	373	12	principle	principle	NOUN
ma-248	373	13	by	by	ADP
ma-248	373	14	[	[	X
ma-248	373	15	26	26	NUM
ma-248	373	16	]	]	PUNCT
ma-248	373	17	is	be	AUX
ma-248	373	18	applied	apply	VERB
ma-248	373	19	to	to	ADP
ma-248	373	20	the	the	DET
ma-248	373	21	hamiltonian	hamiltonian	NOUN
ma-248	373	22	(	(	PUNCT
ma-248	373	23	26	26	NUM
ma-248	373	24	)	)	PUNCT
ma-248	373	25	such	such	ADJ
ma-248	373	26	that	that	SCONJ
ma-248	373	27	given	give	VERB
ma-248	373	28	(	(	PUNCT
ma-248	373	29	y	y	NOUN
ma-248	373	30	,	,	PUNCT
ma-248	373	31	u)is	u)is	PROPN
ma-248	373	32	an	an	DET
ma-248	373	33	optimal	optimal	ADJ
ma-248	373	34	solution	solution	NOUN
ma-248	373	35	of	of	ADP
ma-248	373	36	the	the	DET
ma-248	373	37	optimal	optimal	ADJ
ma-248	373	38	control	control	NOUN
ma-248	373	39	problem	problem	NOUN
ma-248	373	40	,	,	PUNCT
ma-248	373	41	then	then	ADV
ma-248	373	42	there	there	PRON
ma-248	373	43	exist	exist	VERB
ma-248	373	44	a	a	DET
ma-248	373	45	non	non	ADJ
ma-248	373	46	-	-	ADJ
ma-248	373	47	trivial	trivial	ADJ
ma-248	373	48	vector	vector	NOUN
ma-248	373	49	function	function	NOUN
ma-248	373	50	λ	λ	X
ma-248	373	51	=	=	SYM
ma-248	373	52	(	(	PUNCT
ma-248	373	53	λ1	λ1	PROPN
ma-248	373	54	,	,	PUNCT
ma-248	373	55	·	·	PUNCT
ma-248	373	56	·	·	PUNCT
ma-248	373	57	·	·	PUNCT
ma-248	373	58	,	,	PUNCT
ma-248	373	59	λ5	λ5	NOUN
ma-248	373	60	)	)	PUNCT
ma-248	373	61	satisfying	satisfy	VERB
ma-248	373	62	the	the	DET
ma-248	373	63	below	below	ADJ
ma-248	373	64	equation	equation	NOUN
ma-248	373	65	;	;	PUNCT
ma-248	374	1	dy	dy	NOUN
ma-248	374	2	dt	dt	NOUN
ma-248	374	3	=	=	PUNCT
ma-248	374	4	−	−	PROPN
ma-248	374	5	∂h(t	∂h(t	PROPN
ma-248	374	6	,	,	PUNCT
ma-248	374	7	y	y	PROPN
ma-248	374	8	,	,	PUNCT
ma-248	374	9	u	u	PROPN
ma-248	374	10	,	,	PUNCT
ma-248	374	11	λ	λ	NOUN
ma-248	374	12	)	)	PUNCT
ma-248	374	13	∂λ	∂λ	PROPN
ma-248	374	14	,	,	PUNCT
ma-248	374	15	0	0	NUM
ma-248	374	16	=	=	SYM
ma-248	374	17	∂h(t	∂h(t	PROPN
ma-248	374	18	,	,	PUNCT
ma-248	374	19	y	y	PROPN
ma-248	374	20	,	,	PUNCT
ma-248	374	21	u	u	PROPN
ma-248	374	22	,	,	PUNCT
ma-248	374	23	λ	λ	PROPN
ma-248	374	24	)	)	PUNCT
ma-248	374	25	∂u	∂u	PROPN
ma-248	374	26	,	,	PUNCT
ma-248	374	27	(	(	PUNCT
ma-248	374	28	28	28	NUM
ma-248	374	29	)	)	PUNCT
ma-248	374	30	dλ	dλ	NOUN
ma-248	374	31	dt	dt	NOUN
ma-248	374	32	=	=	SYM
ma-248	374	33	∂h(t	∂h(t	PROPN
ma-248	374	34	,	,	PUNCT
ma-248	374	35	y	y	PROPN
ma-248	374	36	,	,	PUNCT
ma-248	374	37	u	u	PROPN
ma-248	374	38	,	,	PUNCT
ma-248	374	39	λ	λ	PROPN
ma-248	374	40	)	)	PUNCT
ma-248	374	41	∂y	∂y	NOUN
ma-248	374	42	.	.	PUNCT
ma-248	375	1	hence	hence	ADV
ma-248	375	2	,	,	PUNCT
ma-248	375	3	the	the	DET
ma-248	375	4	necessary	necessary	ADJ
ma-248	375	5	condition	condition	NOUN
ma-248	375	6	related	relate	VERB
ma-248	375	7	to	to	ADP
ma-248	375	8	the	the	DET
ma-248	375	9	hamiltonian	hamiltonian	NOUN
ma-248	375	10	(	(	PUNCT
ma-248	375	11	26	26	NUM
ma-248	375	12	)	)	PUNCT
ma-248	375	13	is	be	AUX
ma-248	375	14	applied	apply	VERB
ma-248	375	15	.	.	PUNCT
ma-248	376	1	theorem	theorem	VERB
ma-248	376	2	5.2	5.2	NUM
ma-248	376	3	.	.	PUNCT
ma-248	377	1	given	give	VERB
ma-248	377	2	that	that	PRON
ma-248	377	3	s∗hh	s∗hh	PROPN
ma-248	377	4	,	,	PUNCT
ma-248	377	5	e∗hh	e∗hh	PROPN
ma-248	377	6	,	,	PUNCT
ma-248	377	7	ahh	ahh	PROPN
ma-248	377	8	,	,	PUNCT
ma-248	377	9	i∗hh	i∗hh	PROPN
ma-248	377	10	and	and	CCONJ
ma-248	377	11	r∗hh	r∗hh	PROPN
ma-248	377	12	are	be	AUX
ma-248	377	13	optimal	optimal	ADJ
ma-248	377	14	state	state	NOUN
ma-248	377	15	solutions	solution	NOUN
ma-248	377	16	with	with	ADP
ma-248	377	17	associated	associated	ADJ
ma-248	377	18	optimal	optimal	ADJ
ma-248	377	19	control	control	NOUN
ma-248	377	20	variables	variable	NOUN
ma-248	377	21	(	(	PUNCT
ma-248	377	22	u∗1	u∗1	NOUN
ma-248	377	23	,	,	PUNCT
ma-248	377	24	u	u	NOUN
ma-248	377	25	∗	∗	NOUN
ma-248	377	26	2	2	NUM
ma-248	377	27	,	,	PUNCT
ma-248	377	28	u	u	NOUN
ma-248	377	29	∗	∗	NOUN
ma-248	377	30	3	3	NUM
ma-248	377	31	)	)	PUNCT
ma-248	377	32	for	for	ADP
ma-248	377	33	the	the	DET
ma-248	377	34	optimal	optimal	ADJ
ma-248	377	35	control	control	NOUN
ma-248	377	36	problem	problem	NOUN
ma-248	377	37	(	(	PUNCT
ma-248	377	38	22	22	NUM
ma-248	377	39	)	)	PUNCT
ma-248	377	40	and	and	CCONJ
ma-248	377	41	(	(	PUNCT
ma-248	377	42	23	23	NUM
ma-248	377	43	)	)	PUNCT
ma-248	377	44	,	,	PUNCT
ma-248	377	45	then	then	ADV
ma-248	377	46	there	there	PRON
ma-248	377	47	exist	exist	VERB
ma-248	377	48	adjoint	adjoint	NOUN
ma-248	377	49	variables	variable	NOUN
ma-248	377	50	λi	λi	VERB
ma-248	377	51	for	for	ADP
ma-248	377	52	i	i	PRON
ma-248	377	53	=	=	NOUN
ma-248	377	54	1	1	NUM
ma-248	377	55	,	,	PUNCT
ma-248	377	56	.	.	PUNCT
ma-248	377	57	.	.	PUNCT
ma-248	378	1	.	.	PUNCT
ma-248	379	1	,	,	PUNCT
ma-248	379	2	5	5	NUM
ma-248	379	3	,	,	PUNCT
ma-248	379	4	satisfying	satisfying	ADJ
ma-248	379	5	;	;	PUNCT
ma-248	379	6	dλ1	dλ1	PROPN
ma-248	380	1	dt	dt	NOUN
ma-248	380	2	=	=	PUNCT
ma-248	380	3	(	(	PUNCT
ma-248	380	4	λ1	λ1	INTJ
ma-248	380	5	−	−	X
ma-248	380	6	λ2)(1−	λ2)(1−	NOUN
ma-248	380	7	u1)η1ihh	u1)η1ihh	NUM
ma-248	380	8	+	+	CCONJ
ma-248	380	9	(	(	PUNCT
ma-248	380	10	λ2	λ2	NOUN
ma-248	380	11	−	−	PROPN
ma-248	380	12	λ5)u2	λ5)u2	PROPN
ma-248	380	13	+	+	PROPN
ma-248	380	14	µλ1	µλ1	ADJ
ma-248	380	15	,	,	PUNCT
ma-248	380	16	dλ2	dλ2	NOUN
ma-248	380	17	dt	dt	NOUN
ma-248	380	18	=	=	SYM
ma-248	380	19	−b1	−b1	PROPN
ma-248	380	20	+	+	CCONJ
ma-248	380	21	(	(	PUNCT
ma-248	380	22	λ2	λ2	NOUN
ma-248	380	23	−	−	PROPN
ma-248	381	1	λ3)(1−	λ3)(1−	ADJ
ma-248	381	2	k1)τ1	k1)τ1	X
ma-248	381	3	+	+	SYM
ma-248	381	4	(	(	PUNCT
ma-248	381	5	λ2	λ2	NOUN
ma-248	381	6	−	−	NOUN
ma-248	381	7	λ4)kτ1	λ4)kτ1	NOUN
ma-248	381	8	+	+	X
ma-248	381	9	µλ2	µλ2	NUM
ma-248	381	10	,	,	PUNCT
ma-248	381	11	dλ3	dλ3	NOUN
ma-248	381	12	dt	dt	NOUN
ma-248	382	1	=	=	SYM
ma-248	382	2	−b2	−b2	PROPN
ma-248	382	3	+	+	CCONJ
ma-248	382	4	(	(	PUNCT
ma-248	382	5	τ3	τ3	NOUN
ma-248	382	6	+	+	X
ma-248	382	7	µ)λ3	µ)λ3	PROPN
ma-248	382	8	+	+	CCONJ
ma-248	382	9	(	(	PUNCT
ma-248	382	10	λ3	λ3	PROPN
ma-248	382	11	−	−	PROPN
ma-248	382	12	λ5)τ2	λ5)τ2	PROPN
ma-248	382	13	,	,	PUNCT
ma-248	382	14	(	(	PUNCT
ma-248	382	15	29	29	NUM
ma-248	382	16	)	)	PUNCT
ma-248	382	17	dλ4	dλ4	VERB
ma-248	382	18	dt	dt	NOUN
ma-248	382	19	=	=	SYM
ma-248	382	20	−b3	−b3	PROPN
ma-248	382	21	+	+	CCONJ
ma-248	382	22	(	(	PUNCT
ma-248	382	23	λ1	λ1	ADJ
ma-248	382	24	−	−	PROPN
ma-248	382	25	λ2)(1−	λ2)(1−	PROPN
ma-248	382	26	u1)η1shh	u1)η1shh	PROPN
ma-248	383	1	+	+	CCONJ
ma-248	383	2	(	(	PUNCT
ma-248	383	3	λ4	λ4	VERB
ma-248	383	4	−	−	PROPN
ma-248	383	5	λ5)ψ1	λ5)ψ1	X
ma-248	384	1	+	+	CCONJ
ma-248	384	2	(	(	PUNCT
ma-248	384	3	ψ2	ψ2	NOUN
ma-248	384	4	+	+	CCONJ
ma-248	384	5	µ)λ4	µ)λ4	PROPN
ma-248	384	6	+	+	CCONJ
ma-248	384	7	(	(	PUNCT
ma-248	384	8	λ4	λ4	ADJ
ma-248	384	9	−	−	PROPN
ma-248	384	10	λ5)u3	λ5)u3	PROPN
ma-248	384	11	,	,	PUNCT
ma-248	384	12	dλ5	dλ5	VERB
ma-248	384	13	dt	dt	NOUN
ma-248	384	14	=	=	PUNCT
ma-248	384	15	(	(	PUNCT
ma-248	384	16	λ5	λ5	VERB
ma-248	384	17	−	−	PROPN
ma-248	384	18	λ1)ω	λ1)ω	NOUN
ma-248	384	19	+	+	CCONJ
ma-248	384	20	µλ5	µλ5	PROPN
ma-248	384	21	,	,	PUNCT
ma-248	384	22	with	with	ADP
ma-248	384	23	boundary	boundary	ADJ
ma-248	384	24	condition	condition	NOUN
ma-248	384	25	;	;	PUNCT
ma-248	384	26	λi(tf	λi(tf	X
ma-248	384	27	)	)	PUNCT
ma-248	385	1	=	=	SYM
ma-248	385	2	0	0	NUM
ma-248	385	3	,	,	PUNCT
ma-248	385	4	i	i	PRON
ma-248	385	5	=	=	NOUN
ma-248	385	6	1	1	NUM
ma-248	385	7	,	,	PUNCT
ma-248	385	8	2	2	NUM
ma-248	385	9	,	,	PUNCT
ma-248	385	10	.	.	PUNCT
ma-248	385	11	.	.	PUNCT
ma-248	385	12	.	.	PUNCT
ma-248	386	1	,	,	PUNCT
ma-248	386	2	5	5	NUM
ma-248	386	3	,	,	PUNCT
ma-248	386	4	(	(	PUNCT
ma-248	386	5	30	30	NUM
ma-248	386	6	)	)	PUNCT
ma-248	386	7	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	386	8	eur	eur	PROPN
ma-248	386	9	.	.	PUNCT
ma-248	387	1	j.	j.	PROPN
ma-248	387	2	math	math	PROPN
ma-248	387	3	.	.	PUNCT
ma-248	388	1	anal	anal	PROPN
ma-248	388	2	.	.	PUNCT
ma-248	389	1	10.28924	10.28924	NUM
ma-248	389	2	/	/	SYM
ma-248	389	3	ada	ada	PROPN
ma-248	389	4	/	/	SYM
ma-248	389	5	ma.4.21	ma.4.21	NOUN
ma-248	389	6	16	16	NUM
ma-248	389	7	and	and	CCONJ
ma-248	389	8	the	the	DET
ma-248	389	9	optimal	optimal	ADJ
ma-248	389	10	control	control	NOUN
ma-248	389	11	u∗1	u∗1	NOUN
ma-248	389	12	,	,	PUNCT
ma-248	389	13	u∗2	u∗2	NOUN
ma-248	389	14	and	and	CCONJ
ma-248	389	15	u∗3	u∗3	NOUN
ma-248	389	16	are	be	AUX
ma-248	389	17	given	give	VERB
ma-248	389	18	by	by	NUM
ma-248	389	19	u∗1	u∗1	NOUN
ma-248	389	20	=	=	SYM
ma-248	389	21	min	min	PROPN
ma-248	389	22	{	{	PUNCT
ma-248	389	23	1,max	1,max	NUM
ma-248	389	24	{	{	PUNCT
ma-248	389	25	0	0	NUM
ma-248	389	26	,	,	PUNCT
ma-248	389	27	(	(	PUNCT
ma-248	389	28	(	(	PUNCT
ma-248	389	29	λ2	λ2	NOUN
ma-248	389	30	−	−	PROPN
ma-248	389	31	λ1	λ1	PROPN
ma-248	389	32	)	)	PUNCT
ma-248	389	33	η1ihhshh	η1ihhshh	NOUN
ma-248	389	34	d1	d1	PROPN
ma-248	389	35	)	)	PUNCT
ma-248	389	36	}	}	PUNCT
ma-248	389	37	}	}	PUNCT
ma-248	389	38	u∗2	u∗2	NOUN
ma-248	389	39	=	=	SYM
ma-248	389	40	min	min	NOUN
ma-248	389	41	{	{	PUNCT
ma-248	389	42	1,max	1,max	NUM
ma-248	389	43	{	{	PUNCT
ma-248	389	44	0	0	NUM
ma-248	389	45	,	,	PUNCT
ma-248	389	46	(	(	PUNCT
ma-248	389	47	λ1	λ1	ADJ
ma-248	389	48	−	−	NOUN
ma-248	389	49	λ5	λ5	NOUN
ma-248	389	50	)	)	PUNCT
ma-248	389	51	shh	shh	NOUN
ma-248	389	52	d2	d2	PROPN
ma-248	389	53	}	}	PUNCT
ma-248	389	54	}	}	PUNCT
ma-248	389	55	u∗3	u∗3	NOUN
ma-248	389	56	=	=	SYM
ma-248	389	57	min	min	NOUN
ma-248	389	58	{	{	PUNCT
ma-248	389	59	1,max	1,max	NUM
ma-248	389	60	{	{	PUNCT
ma-248	389	61	0	0	NUM
ma-248	389	62	,	,	PUNCT
ma-248	389	63	(	(	PUNCT
ma-248	389	64	λ4	λ4	ADJ
ma-248	389	65	−	−	PROPN
ma-248	389	66	λ5	λ5	NOUN
ma-248	389	67	)	)	PUNCT
ma-248	389	68	ihh	ihh	PROPN
ma-248	389	69	d3	d3	PROPN
ma-248	389	70	}	}	PUNCT
ma-248	389	71	}	}	PUNCT
ma-248	389	72	(	(	PUNCT
ma-248	389	73	31	31	NUM
ma-248	389	74	)	)	PUNCT
ma-248	389	75	proof	proof	NOUN
ma-248	389	76	.	.	PUNCT
ma-248	390	1	the	the	DET
ma-248	390	2	adjoint	adjoint	NOUN
ma-248	390	3	and	and	CCONJ
ma-248	390	4	transversality	transversality	NOUN
ma-248	390	5	conditions	condition	NOUN
ma-248	390	6	are	be	AUX
ma-248	390	7	derived	derive	VERB
ma-248	390	8	using	use	VERB
ma-248	390	9	the	the	DET
ma-248	390	10	hamiltonian	hamiltonian	NOUN
ma-248	390	11	(	(	PUNCT
ma-248	390	12	26	26	NUM
ma-248	390	13	)	)	PUNCT
ma-248	390	14	.	.	PUNCT
ma-248	391	1	thus	thus	ADV
ma-248	391	2	weequate	weequate	VERB
ma-248	391	3	shh	shh	PROPN
ma-248	391	4	=	=	PROPN
ma-248	391	5	s∗hh	s∗hh	PROPN
ma-248	391	6	,	,	PUNCT
ma-248	391	7	ehh	ehh	NOUN
ma-248	391	8	=	=	SYM
ma-248	391	9	e∗hh	e∗hh	PROPN
ma-248	391	10	,	,	PUNCT
ma-248	391	11	ahh	ahh	PROPN
ma-248	391	12	=	=	SYM
ma-248	391	13	a∗hh	a∗hh	PROPN
ma-248	391	14	,	,	PUNCT
ma-248	391	15	ihh	ihh	PROPN
ma-248	391	16	=	=	PUNCT
ma-248	391	17	i∗hh	i∗hh	PROPN
ma-248	391	18	and	and	CCONJ
ma-248	391	19	rhh	rhh	X
ma-248	391	20	=	=	SYM
ma-248	391	21	r∗hh	r∗hh	PROPN
ma-248	391	22	and	and	CCONJ
ma-248	391	23	differentiating	differentiate	VERB
ma-248	391	24	thehamiltonian	thehamiltonian	NOUN
ma-248	391	25	with	with	ADP
ma-248	391	26	respect	respect	NOUN
ma-248	391	27	to	to	ADP
ma-248	391	28	shh	shh	PROPN
ma-248	391	29	,	,	PUNCT
ma-248	391	30	ehh	ehh	PROPN
ma-248	391	31	,	,	PUNCT
ma-248	391	32	ahh	ahh	PROPN
ma-248	391	33	,	,	PUNCT
ma-248	391	34	ihh	ihh	PROPN
ma-248	391	35	and	and	CCONJ
ma-248	391	36	rhh	rhh	NOUN
ma-248	391	37	to	to	PART
ma-248	391	38	obtain	obtain	VERB
ma-248	391	39	(	(	PUNCT
ma-248	391	40	29	29	NUM
ma-248	391	41	)	)	PUNCT
ma-248	391	42	.	.	PUNCT
ma-248	392	1	further	far	ADV
ma-248	392	2	,	,	PUNCT
ma-248	392	3	the	the	DET
ma-248	392	4	equations	equation	NOUN
ma-248	392	5	∂h	∂h	X
ma-248	392	6	∂u1	∂u1	PROPN
ma-248	392	7	=	=	SYM
ma-248	392	8	0	0	NUM
ma-248	392	9	,	,	PUNCT
ma-248	392	10	∂h	∂h	PROPN
ma-248	392	11	∂u2	∂u2	NOUN
ma-248	392	12	=	=	SYM
ma-248	392	13	0	0	NUM
ma-248	392	14	,	,	PUNCT
ma-248	392	15	∂h	∂h	X
ma-248	392	16	∂u3	∂u3	NOUN
ma-248	392	17	=	=	NOUN
ma-248	392	18	0	0	X
ma-248	392	19	.	.	PUNCT
ma-248	393	1	(	(	PUNCT
ma-248	393	2	32	32	NUM
ma-248	393	3	)	)	PUNCT
ma-248	393	4	are	be	AUX
ma-248	393	5	determined	determine	VERB
ma-248	393	6	on	on	ADP
ma-248	393	7	the	the	DET
ma-248	393	8	interior	interior	NOUN
ma-248	393	9	of	of	ADP
ma-248	393	10	the	the	DET
ma-248	393	11	control	control	NOUN
ma-248	393	12	set	set	NOUN
ma-248	393	13	,	,	PUNCT
ma-248	393	14	and	and	CCONJ
ma-248	393	15	using	use	VERB
ma-248	393	16	the	the	DET
ma-248	393	17	optimality	optimality	NOUN
ma-248	393	18	conditions	condition	NOUN
ma-248	393	19	and	and	CCONJ
ma-248	393	20	theproperty	theproperty	NOUN
ma-248	393	21	of	of	ADP
ma-248	393	22	the	the	DET
ma-248	393	23	control	control	NOUN
ma-248	393	24	space	space	NOUN
ma-248	393	25	u1	u1	NOUN
ma-248	393	26	and	and	CCONJ
ma-248	393	27	u2	u2	NOUN
ma-248	393	28	,	,	PUNCT
ma-248	393	29	we	we	PRON
ma-248	393	30	can	can	AUX
ma-248	393	31	determine	determine	VERB
ma-248	393	32	(	(	PUNCT
ma-248	393	33	22	22	NUM
ma-248	393	34	)	)	PUNCT
ma-248	393	35	.	.	PUNCT
ma-248	394	1	from	from	ADP
ma-248	394	2	(	(	PUNCT
ma-248	394	3	22	22	NUM
ma-248	394	4	)	)	PUNCT
ma-248	394	5	,	,	PUNCT
ma-248	394	6	we	we	PRON
ma-248	394	7	can	can	AUX
ma-248	394	8	characterize	characterize	VERB
ma-248	394	9	thecontrol	thecontrol	NOUN
ma-248	394	10	found	find	VERB
ma-248	394	11	by	by	ADP
ma-248	394	12	solving	solve	VERB
ma-248	394	13	the	the	DET
ma-248	394	14	optimality	optimality	NOUN
ma-248	394	15	system	system	NOUN
ma-248	394	16	.	.	PUNCT
ma-248	395	1	in	in	ADP
ma-248	395	2	solving	solve	VERB
ma-248	395	3	the	the	DET
ma-248	395	4	optimality	optimality	NOUN
ma-248	395	5	system	system	NOUN
ma-248	395	6	,	,	PUNCT
ma-248	395	7	the	the	DET
ma-248	395	8	transversalityand	transversalityand	ADJ
ma-248	395	9	the	the	DET
ma-248	395	10	characterization	characterization	NOUN
ma-248	395	11	of	of	ADP
ma-248	395	12	the	the	DET
ma-248	395	13	optimal	optimal	ADJ
ma-248	395	14	control	control	NOUN
ma-248	395	15	(	(	PUNCT
ma-248	395	16	u1	u1	NOUN
ma-248	395	17	,	,	PUNCT
ma-248	395	18	u2	u2	NOUN
ma-248	395	19	,	,	PUNCT
ma-248	395	20	u3	u3	PROPN
ma-248	395	21	)	)	PUNCT
ma-248	395	22	are	be	AUX
ma-248	395	23	used	use	VERB
ma-248	395	24	.	.	PUNCT
ma-248	396	1	the	the	DET
ma-248	396	2	controls	control	NOUN
ma-248	396	3	u∗1	u∗1	NOUN
ma-248	396	4	,	,	PUNCT
ma-248	396	5	u∗2	u∗2	NOUN
ma-248	396	6	and	and	CCONJ
ma-248	396	7	u∗3when	u∗3when	ADV
ma-248	396	8	substituted	substitute	VERB
ma-248	396	9	into	into	ADP
ma-248	396	10	the	the	DET
ma-248	396	11	control	control	NOUN
ma-248	396	12	system	system	NOUN
ma-248	396	13	(	(	PUNCT
ma-248	396	14	22	22	NUM
ma-248	396	15	)	)	PUNCT
ma-248	396	16	gives;	gives;	NOUN
ma-248	396	17	dshh	dshh	PROPN
ma-248	396	18	dt	dt	PROPN
ma-248	396	19	=	=	SYM
ma-248	396	20	λ−	λ−	PROPN
ma-248	396	21	µshh	µshh	PROPN
ma-248	396	22	−	−	PROPN
ma-248	396	23	(	(	PUNCT
ma-248	396	24	1−min	1−min	PROPN
ma-248	396	25	{	{	PUNCT
ma-248	396	26	1,max	1,max	NUM
ma-248	396	27	{	{	PUNCT
ma-248	396	28	0	0	NUM
ma-248	396	29	,	,	PUNCT
ma-248	396	30	(	(	PUNCT
ma-248	396	31	(	(	PUNCT
ma-248	396	32	λ2	λ2	NOUN
ma-248	396	33	−	−	PROPN
ma-248	396	34	λ1	λ1	PROPN
ma-248	396	35	)	)	PUNCT
ma-248	396	36	η1ihhshh	η1ihhshh	NOUN
ma-248	396	37	d1	d1	PROPN
ma-248	396	38	)	)	PUNCT
ma-248	396	39	}	}	PUNCT
ma-248	396	40	}	}	PUNCT
ma-248	396	41	)	)	PUNCT
ma-248	396	42	η1ihhshh	η1ihhshh	PROPN
ma-248	396	43	+	+	PROPN
ma-248	396	44	ωrhh	ωrhh	PROPN
ma-248	396	45	−	−	PROPN
ma-248	396	46	(	(	PUNCT
ma-248	396	47	λ1	λ1	ADJ
ma-248	396	48	−	−	NOUN
ma-248	396	49	λ5	λ5	NOUN
ma-248	396	50	)	)	PUNCT
ma-248	396	51	shh	shh	PROPN
ma-248	396	52	d2	d2	PROPN
ma-248	396	53	shh	shh	PROPN
ma-248	396	54	,	,	PUNCT
ma-248	396	55	dehh	dehh	PROPN
ma-248	396	56	dt	dt	PROPN
ma-248	397	1	=	=	PUNCT
ma-248	398	1	(	(	PUNCT
ma-248	398	2	1−min	1−min	PROPN
ma-248	398	3	{	{	PUNCT
ma-248	398	4	1,max	1,max	NUM
ma-248	398	5	{	{	PUNCT
ma-248	398	6	0	0	NUM
ma-248	398	7	,	,	PUNCT
ma-248	398	8	(	(	PUNCT
ma-248	398	9	(	(	PUNCT
ma-248	398	10	λ2	λ2	NOUN
ma-248	398	11	−	−	PROPN
ma-248	398	12	λ1	λ1	PROPN
ma-248	398	13	)	)	PUNCT
ma-248	398	14	η1ihhshh	η1ihhshh	NOUN
ma-248	398	15	d1	d1	PROPN
ma-248	398	16	)	)	PUNCT
ma-248	398	17	}	}	PUNCT
ma-248	398	18	}	}	PUNCT
ma-248	398	19	)	)	PUNCT
ma-248	398	20	η1ihhshh	η1ihhshh	NOUN
ma-248	398	21	−kτ1ehh	−kτ1ehh	NOUN
ma-248	398	22	−	−	PROPN
ma-248	399	1	(	(	PUNCT
ma-248	399	2	1−	1−	NUM
ma-248	399	3	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	399	4	−	−	NOUN
ma-248	399	5	µehh	µehh	NOUN
ma-248	399	6	,	,	PUNCT
ma-248	399	7	dahh	dahh	NOUN
ma-248	399	8	dt	dt	NOUN
ma-248	400	1	=	=	PUNCT
ma-248	401	1	(	(	PUNCT
ma-248	401	2	1−	1−	NUM
ma-248	401	3	k1)τ1ehh	k1)τ1ehh	NOUN
ma-248	401	4	−	−	PROPN
ma-248	401	5	(	(	PUNCT
ma-248	401	6	τ2	τ2	NOUN
ma-248	401	7	+	+	NUM
ma-248	401	8	τ3	τ3	NOUN
ma-248	401	9	+	+	X
ma-248	401	10	µ)ahh	µ)ahh	PROPN
ma-248	401	11	,	,	PUNCT
ma-248	401	12	d	d	NOUN
ma-248	401	13	dt	dt	X
ma-248	401	14	ihh	ihh	PROPN
ma-248	401	15	=	=	PROPN
ma-248	401	16	kτ1ehh	kτ1ehh	PROPN
ma-248	401	17	−	−	PROPN
ma-248	401	18	(	(	PUNCT
ma-248	401	19	ψ1	ψ1	NOUN
ma-248	401	20	+	+	CCONJ
ma-248	401	21	ψ2	ψ2	NOUN
ma-248	401	22	+	+	CCONJ
ma-248	401	23	min	min	NOUN
ma-248	401	24	{	{	PUNCT
ma-248	401	25	1,max	1,max	NUM
ma-248	401	26	{	{	PUNCT
ma-248	401	27	0	0	NUM
ma-248	401	28	,	,	PUNCT
ma-248	401	29	(	(	PUNCT
ma-248	401	30	λ1	λ1	ADJ
ma-248	401	31	−	−	NOUN
ma-248	401	32	λ5	λ5	NOUN
ma-248	401	33	)	)	PUNCT
ma-248	401	34	shh	shh	NOUN
ma-248	401	35	d2	d2	PROPN
ma-248	401	36	}	}	PUNCT
ma-248	401	37	}	}	PUNCT
ma-248	402	1	+	+	CCONJ
ma-248	402	2	µ)ihh	µ)ihh	NUM
ma-248	402	3	,	,	PUNCT
ma-248	402	4	d	d	PROPN
ma-248	402	5	dt	dt	X
ma-248	402	6	rhh	rhh	X
ma-248	403	1	=	=	PUNCT
ma-248	403	2	τ2ahh	τ2ahh	PROPN
ma-248	403	3	+	+	NUM
ma-248	403	4	ψ1ehh	ψ1ehh	NUM
ma-248	403	5	+	+	NUM
ma-248	403	6	min	min	NOUN
ma-248	403	7	{	{	PUNCT
ma-248	403	8	1,max	1,max	NUM
ma-248	403	9	{	{	PUNCT
ma-248	403	10	0	0	NUM
ma-248	403	11	,	,	PUNCT
ma-248	403	12	(	(	PUNCT
ma-248	403	13	λ1	λ1	ADJ
ma-248	403	14	−	−	NOUN
ma-248	403	15	λ5	λ5	NOUN
ma-248	403	16	)	)	PUNCT
ma-248	403	17	shh	shh	NOUN
ma-248	403	18	d2	d2	PROPN
ma-248	403	19	}	}	PUNCT
ma-248	403	20	}	}	PUNCT
ma-248	403	21	shh	shh	PROPN
ma-248	404	1	+	+	CCONJ
ma-248	404	2	min	min	PROPN
ma-248	404	3	{	{	PUNCT
ma-248	404	4	1,max	1,max	NUM
ma-248	404	5	{	{	PUNCT
ma-248	404	6	0	0	NUM
ma-248	404	7	,	,	PUNCT
ma-248	404	8	(	(	PUNCT
ma-248	404	9	λ4	λ4	ADJ
ma-248	404	10	−	−	PROPN
ma-248	404	11	λ5	λ5	NOUN
ma-248	404	12	)	)	PUNCT
ma-248	404	13	ihh	ihh	PROPN
ma-248	404	14	d3	d3	PROPN
ma-248	404	15	}	}	PUNCT
ma-248	404	16	}	}	PUNCT
ma-248	404	17	ihh	ihh	NOUN
ma-248	404	18	−	−	PROPN
ma-248	404	19	(	(	PUNCT
ma-248	404	20	ω	ω	PROPN
ma-248	404	21	+	+	X
ma-248	405	1	µ)rhh	µ)rhh	PROPN
ma-248	405	2	.	.	PUNCT
ma-248	406	1	(	(	PUNCT
ma-248	406	2	33	33	NUM
ma-248	406	3	)	)	PUNCT
ma-248	406	4	�	�	PROPN
ma-248	406	5	6	6	NUM
ma-248	406	6	.	.	PUNCT
ma-248	406	7	numerical	numerical	PROPN
ma-248	406	8	simulation	simulation	PROPN
ma-248	406	9	and	and	CCONJ
ma-248	406	10	discussion	discussion	NOUN
ma-248	406	11	the	the	DET
ma-248	406	12	present	present	ADJ
ma-248	406	13	section	section	NOUN
ma-248	406	14	focuses	focus	VERB
ma-248	406	15	on	on	ADP
ma-248	406	16	obtaining	obtain	VERB
ma-248	406	17	a	a	DET
ma-248	406	18	numerical	numerical	ADJ
ma-248	406	19	solution	solution	NOUN
ma-248	406	20	for	for	ADP
ma-248	406	21	the	the	DET
ma-248	406	22	model	model	NOUN
ma-248	406	23	.	.	PUNCT
ma-248	407	1	besides	besides	SCONJ
ma-248	407	2	the	the	DET
ma-248	407	3	qual	qual	ADJ
ma-248	407	4	-	-	ADJ
ma-248	407	5	itative	itative	ADJ
ma-248	407	6	analysis	analysis	NOUN
ma-248	407	7	that	that	PRON
ma-248	407	8	has	have	AUX
ma-248	407	9	been	be	AUX
ma-248	407	10	carried	carry	VERB
ma-248	407	11	out	out	ADP
ma-248	407	12	,	,	PUNCT
ma-248	407	13	it	it	PRON
ma-248	407	14	becomes	become	VERB
ma-248	407	15	imperative	imperative	ADJ
ma-248	407	16	to	to	PART
ma-248	407	17	find	find	VERB
ma-248	407	18	a	a	DET
ma-248	407	19	numerical	numerical	ADJ
ma-248	407	20	solution	solution	NOUN
ma-248	407	21	forthe	forthe	PRON
ma-248	407	22	model	model	NOUN
ma-248	407	23	.	.	PUNCT
ma-248	408	1	hence	hence	ADV
ma-248	408	2	,	,	PUNCT
ma-248	408	3	our	our	PRON
ma-248	408	4	task	task	NOUN
ma-248	408	5	here	here	ADV
ma-248	408	6	is	be	AUX
ma-248	408	7	to	to	PART
ma-248	408	8	derive	derive	VERB
ma-248	408	9	a	a	DET
ma-248	408	10	numerical	numerical	ADJ
ma-248	408	11	solution	solution	NOUN
ma-248	408	12	that	that	PRON
ma-248	408	13	solves	solve	VERB
ma-248	408	14	the	the	DET
ma-248	408	15	without	without	ADP
ma-248	408	16	and	and	CCONJ
ma-248	408	17	withcontrol	withcontrol	NOUN
ma-248	408	18	models	model	NOUN
ma-248	408	19	and	and	CCONJ
ma-248	408	20	evaluates	evaluate	VERB
ma-248	408	21	the	the	DET
ma-248	408	22	effectiveness	effectiveness	NOUN
ma-248	408	23	of	of	ADP
ma-248	408	24	the	the	DET
ma-248	408	25	considered	consider	VERB
ma-248	408	26	control	control	NOUN
ma-248	408	27	strategies	strategy	NOUN
ma-248	408	28	.	.	PUNCT
ma-248	409	1	a	a	DET
ma-248	409	2	numericalalgorithm	numericalalgorithm	PROPN
ma-248	409	3	uses	use	VERB
ma-248	409	4	a	a	DET
ma-248	409	5	4th	4th	ADJ
ma-248	409	6	-	-	PUNCT
ma-248	409	7	order	order	NOUN
ma-248	409	8	runge	runge	NOUN
ma-248	409	9	-	-	PUNCT
ma-248	409	10	kutta	kutta	NOUN
ma-248	409	11	method	method	NOUN
ma-248	409	12	and	and	CCONJ
ma-248	409	13	matlab	matlab	NOUN
ma-248	409	14	to	to	PART
ma-248	409	15	solve	solve	VERB
ma-248	409	16	the	the	DET
ma-248	409	17	optimality	optimality	NOUN
ma-248	409	18	system	system	NOUN
ma-248	409	19	.	.	PUNCT
ma-248	410	1	thus	thus	ADV
ma-248	410	2	,	,	PUNCT
ma-248	410	3	a	a	DET
ma-248	410	4	numerical	numerical	ADJ
ma-248	410	5	solution	solution	NOUN
ma-248	410	6	of	of	ADP
ma-248	410	7	the	the	DET
ma-248	410	8	control	control	NOUN
ma-248	410	9	optimality	optimality	NOUN
ma-248	410	10	system	system	NOUN
ma-248	410	11	involves	involve	VERB
ma-248	410	12	running	run	VERB
ma-248	410	13	the	the	DET
ma-248	410	14	adjoint	adjoint	NOUN
ma-248	410	15	system	system	NOUN
ma-248	410	16	backwards	backwards	ADV
ma-248	410	17	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	410	18	eur	eur	PROPN
ma-248	410	19	.	.	PUNCT
ma-248	411	1	j.	j.	PROPN
ma-248	411	2	math	math	PROPN
ma-248	411	3	.	.	PUNCT
ma-248	412	1	anal	anal	PROPN
ma-248	412	2	.	.	PUNCT
ma-248	413	1	10.28924	10.28924	NUM
ma-248	413	2	/	/	SYM
ma-248	413	3	ada	ada	PROPN
ma-248	413	4	/	/	SYM
ma-248	413	5	ma.4.21	ma.4.21	PROPN
ma-248	413	6	17and	17and	PROPN
ma-248	413	7	the	the	DET
ma-248	413	8	state	state	NOUN
ma-248	413	9	forward	forward	ADV
ma-248	413	10	in	in	ADP
ma-248	413	11	time	time	NOUN
ma-248	413	12	,	,	PUNCT
ma-248	413	13	with	with	ADP
ma-248	413	14	the	the	DET
ma-248	413	15	associated	associated	ADJ
ma-248	413	16	boundary	boundary	ADJ
ma-248	413	17	conditions	condition	NOUN
ma-248	413	18	and	and	CCONJ
ma-248	413	19	the	the	DET
ma-248	413	20	controls	control	NOUN
ma-248	413	21	.	.	PUNCT
ma-248	414	1	the	the	DET
ma-248	414	2	pro	pro	ADJ
ma-248	414	3	-	-	ADJ
ma-248	414	4	cess	cess	ADJ
ma-248	414	5	involves	involve	NOUN
ma-248	414	6	continuously	continuously	ADV
ma-248	414	7	upgrading	upgrade	VERB
ma-248	414	8	the	the	DET
ma-248	414	9	controls	control	NOUN
ma-248	414	10	and	and	CCONJ
ma-248	414	11	the	the	DET
ma-248	414	12	characterization	characterization	NOUN
ma-248	414	13	value	value	NOUN
ma-248	414	14	until	until	SCONJ
ma-248	414	15	the	the	DET
ma-248	414	16	earlierresults	earlierresult	NOUN
ma-248	414	17	become	become	VERB
ma-248	414	18	close	close	ADJ
ma-248	414	19	to	to	ADP
ma-248	414	20	the	the	DET
ma-248	414	21	currently	currently	ADV
ma-248	414	22	obtained	obtain	VERB
ma-248	414	23	value	value	NOUN
ma-248	414	24	;	;	PUNCT
ma-248	414	25	then	then	ADV
ma-248	414	26	,	,	PUNCT
ma-248	414	27	the	the	DET
ma-248	414	28	algorithm	algorithm	NOUN
ma-248	414	29	stops	stop	VERB
ma-248	414	30	,	,	PUNCT
ma-248	414	31	and	and	CCONJ
ma-248	414	32	a	a	DET
ma-248	414	33	solution	solution	NOUN
ma-248	414	34	isobtained	isobtaine	VERB
ma-248	414	35	.	.	PUNCT
ma-248	415	1	the	the	DET
ma-248	415	2	matlab	matlab	PROPN
ma-248	415	3	simulation	simulation	NOUN
ma-248	415	4	was	be	AUX
ma-248	415	5	done	do	VERB
ma-248	415	6	with	with	ADP
ma-248	415	7	values	value	NOUN
ma-248	415	8	taken	take	VERB
ma-248	415	9	from	from	ADP
ma-248	415	10	the	the	DET
ma-248	415	11	published	publish	VERB
ma-248	415	12	work	work	NOUN
ma-248	415	13	.	.	PUNCT
ma-248	416	1	beloware	beloware	VERB
ma-248	416	2	the	the	DET
ma-248	416	3	parameters	parameter	NOUN
ma-248	416	4	considered	consider	VERB
ma-248	416	5	for	for	ADP
ma-248	416	6	the	the	DET
ma-248	416	7	simulation	simulation	NOUN
ma-248	416	8	.	.	PUNCT
ma-248	417	1	table	table	NOUN
ma-248	417	2	2	2	NUM
ma-248	417	3	.	.	PUNCT
ma-248	417	4	meningitis	meningitis	PROPN
ma-248	417	5	model	model	NOUN
ma-248	417	6	parameters	parameter	NOUN
ma-248	417	7	parameter	parameter	PROPN
ma-248	417	8	description	description	NOUN
ma-248	417	9	range	range	NOUN
ma-248	417	10	estimated	estimate	VERB
ma-248	417	11	value	value	NOUN
ma-248	417	12	reference	reference	NOUN
ma-248	417	13	λ	λ	PROPN
ma-248	417	14	recruitment	recruitment	NOUN
ma-248	417	15	rate	rate	NOUN
ma-248	417	16	(	(	PUNCT
ma-248	417	17	100−	100−	NOUN
ma-248	417	18	100000	100000	NUM
ma-248	417	19	)	)	PUNCT
ma-248	417	20	1000	1000	NUM
ma-248	418	1	[	[	X
ma-248	418	2	3	3	NUM
ma-248	418	3	]	]	PUNCT
ma-248	418	4	τ1	τ1	ADP
ma-248	418	5	modification	modification	NOUN
ma-248	418	6	parameter	parameter	NOUN
ma-248	418	7	(	(	PUNCT
ma-248	418	8	0.001−	0.001−	NUM
ma-248	418	9	0.8	0.8	NUM
ma-248	418	10	)	)	PUNCT
ma-248	418	11	0.3	0.3	NUM
ma-248	419	1	[	[	X
ma-248	419	2	3	3	NUM
ma-248	419	3	]	]	X
ma-248	419	4	τ2	τ2	ADJ
ma-248	419	5	rate	rate	NOUN
ma-248	419	6	at	at	ADP
ma-248	419	7	individuals	individual	NOUN
ma-248	419	8	leaves	leave	VERB
ma-248	419	9	theasymptomatic	theasymptomatic	ADJ
ma-248	419	10	class	class	NOUN
ma-248	419	11	(	(	PUNCT
ma-248	419	12	0.002−	0.002−	NUM
ma-248	419	13	0.3	0.3	NUM
ma-248	419	14	)	)	PUNCT
ma-248	419	15	0.03	0.03	NUM
ma-248	420	1	[	[	X
ma-248	420	2	3	3	NUM
ma-248	420	3	]	]	PUNCT
ma-248	420	4	τ3	τ3	NOUN
ma-248	420	5	disease	disease	NOUN
ma-248	420	6	induced	induce	VERB
ma-248	420	7	death	death	NOUN
ma-248	420	8	rate	rate	NOUN
ma-248	420	9	(	(	PUNCT
ma-248	420	10	0.002−	0.002−	NUM
ma-248	420	11	0.2	0.2	NUM
ma-248	420	12	)	)	PUNCT
ma-248	420	13	0.2	0.2	NUM
ma-248	421	1	[	[	SYM
ma-248	421	2	3	3	NUM
ma-248	421	3	]	]	X
ma-248	421	4	ψ1	ψ1	ADJ
ma-248	421	5	rate	rate	NOUN
ma-248	421	6	at	at	ADP
ma-248	421	7	which	which	PRON
ma-248	421	8	individuals	individual	NOUN
ma-248	421	9	leavethe	leavethe	ADP
ma-248	421	10	infected	infected	ADJ
ma-248	421	11	class	class	NOUN
ma-248	421	12	to	to	ADP
ma-248	421	13	the	the	DET
ma-248	421	14	recov	recov	NOUN
ma-248	421	15	-	-	PUNCT
ma-248	421	16	ered	ere	VERB
ma-248	421	17	class	class	NOUN
ma-248	421	18	(	(	PUNCT
ma-248	421	19	0.001−	0.001−	NUM
ma-248	421	20	0.1	0.1	NUM
ma-248	421	21	)	)	PUNCT
ma-248	421	22	0.02	0.02	NUM
ma-248	422	1	[	[	X
ma-248	422	2	27	27	NUM
ma-248	422	3	]	]	PUNCT
ma-248	422	4	ψ2	ψ2	NOUN
ma-248	422	5	disease	disease	NOUN
ma-248	422	6	induced	induce	VERB
ma-248	422	7	death	death	NOUN
ma-248	422	8	rate	rate	NOUN
ma-248	422	9	(	(	PUNCT
ma-248	422	10	0.002−	0.002−	NUM
ma-248	422	11	0.1	0.1	NUM
ma-248	422	12	)	)	PUNCT
ma-248	422	13	0.018	0.018	NUM
ma-248	423	1	[	[	X
ma-248	423	2	3	3	X
ma-248	423	3	]	]	PUNCT
ma-248	423	4	ω	ω	NUM
ma-248	423	5	loss	loss	NOUN
ma-248	423	6	of	of	ADP
ma-248	423	7	immunity	immunity	NOUN
ma-248	423	8	(	(	PUNCT
ma-248	423	9	0.01−	0.01−	NOUN
ma-248	423	10	0.1	0.1	NUM
ma-248	423	11	)	)	PUNCT
ma-248	423	12	0.084	0.084	NUM
ma-248	424	1	[	[	X
ma-248	424	2	48	48	NUM
ma-248	424	3	]	]	PUNCT
ma-248	424	4	η1	η1	NOUN
ma-248	424	5	contact	contact	NOUN
ma-248	424	6	rate	rate	NOUN
ma-248	424	7	(	(	PUNCT
ma-248	424	8	0.1−	0.1−	NOUN
ma-248	424	9	0.9	0.9	NUM
ma-248	424	10	)	)	PUNCT
ma-248	424	11	0.5	0.5	NUM
ma-248	425	1	[	[	X
ma-248	425	2	28	28	NUM
ma-248	425	3	]	]	PUNCT
ma-248	425	4	µ	µ	PRON
ma-248	425	5	rate	rate	NOUN
ma-248	425	6	at	at	ADP
ma-248	425	7	which	which	PRON
ma-248	425	8	individuals	individual	NOUN
ma-248	425	9	nat	nat	NOUN
ma-248	425	10	-	-	PUNCT
ma-248	425	11	urally	urally	ADV
ma-248	425	12	leaves	leave	VERB
ma-248	425	13	the	the	DET
ma-248	425	14	compartment	compartment	NOUN
ma-248	425	15	(	(	PUNCT
ma-248	425	16	0.00001−	0.00001−	NUM
ma-248	425	17	0.2	0.2	NUM
ma-248	425	18	)	)	PUNCT
ma-248	425	19	0.0000391	0.0000391	NUM
ma-248	426	1	[	[	X
ma-248	426	2	29	29	NUM
ma-248	426	3	]	]	X
ma-248	426	4	k1	k1	NOUN
ma-248	426	5	rate	rate	NOUN
ma-248	426	6	at	at	ADP
ma-248	426	7	which	which	PRON
ma-248	426	8	individualsleaves	individualsleave	VERB
ma-248	426	9	the	the	DET
ma-248	426	10	exposed	expose	VERB
ma-248	426	11	class	class	NOUN
ma-248	426	12	(	(	PUNCT
ma-248	426	13	0.01−	0.01−	NUM
ma-248	426	14	0.5	0.5	NUM
ma-248	426	15	)	)	PUNCT
ma-248	426	16	0.3	0.3	NUM
ma-248	427	1	[	[	X
ma-248	427	2	30	30	NUM
ma-248	427	3	]	]	PUNCT
ma-248	427	4	6.1	6.1	NUM
ma-248	427	5	.	.	PUNCT
ma-248	428	1	strategy	strategy	NOUN
ma-248	428	2	a	a	DET
ma-248	428	3	:	:	PUNCT
ma-248	428	4	u3	u3	NOUN
ma-248	428	5	=	=	SYM
ma-248	428	6	0	0	PROPN
ma-248	428	7	.	.	PUNCT
ma-248	428	8	strategy	strategy	NOUN
ma-248	428	9	a	a	PRON
ma-248	428	10	uses	use	VERB
ma-248	428	11	the	the	DET
ma-248	428	12	controls	control	NOUN
ma-248	428	13	u1	u1	NOUN
ma-248	428	14	and	and	CCONJ
ma-248	428	15	u2	u2	NOUN
ma-248	428	16	,	,	PUNCT
ma-248	428	17	with	with	ADP
ma-248	428	18	u3	u3	NOUN
ma-248	428	19	set	set	VERB
ma-248	428	20	to	to	ADP
ma-248	428	21	zero	zero	NUM
ma-248	428	22	.	.	PUNCT
ma-248	429	1	the	the	DET
ma-248	429	2	graphsof	graphsof	NOUN
ma-248	429	3	2a	2a	NUM
ma-248	429	4	,	,	PUNCT
ma-248	429	5	2b	2b	NOUN
ma-248	429	6	,	,	PUNCT
ma-248	429	7	2c	2c	NOUN
ma-248	429	8	and	and	CCONJ
ma-248	429	9	2d	2d	NOUN
ma-248	429	10	indicate	indicate	VERB
ma-248	429	11	the	the	DET
ma-248	429	12	exposed	expose	VERB
ma-248	429	13	,	,	PUNCT
ma-248	429	14	asymptomatic	asymptomatic	ADJ
ma-248	429	15	,	,	PUNCT
ma-248	429	16	and	and	CCONJ
ma-248	429	17	symptomatic	symptomatic	ADJ
ma-248	429	18	people	people	NOUN
ma-248	429	19	,	,	PUNCT
ma-248	429	20	as	as	ADV
ma-248	429	21	well	well	ADV
ma-248	429	22	as	as	ADP
ma-248	429	23	thecontrols	thecontrol	NOUN
ma-248	429	24	.	.	PUNCT
ma-248	430	1	the	the	DET
ma-248	430	2	without	without	ADP
ma-248	430	3	-	-	PUNCT
ma-248	430	4	control	control	NOUN
ma-248	430	5	graph	graph	NOUN
ma-248	430	6	of	of	ADP
ma-248	430	7	2a	2a	NUM
ma-248	430	8	showed	show	VERB
ma-248	430	9	a	a	DET
ma-248	430	10	swift	swift	ADJ
ma-248	430	11	increase	increase	NOUN
ma-248	430	12	of	of	ADP
ma-248	430	13	an	an	DET
ma-248	430	14	estimated	estimate	VERB
ma-248	430	15	5000	5000	NUM
ma-248	430	16	in	in	ADP
ma-248	430	17	the	the	DET
ma-248	430	18	first	first	ADJ
ma-248	430	19	20	20	NUM
ma-248	430	20	days	day	NOUN
ma-248	430	21	.	.	PUNCT
ma-248	431	1	moreover	moreover	ADV
ma-248	431	2	,	,	PUNCT
ma-248	431	3	it	it	PRON
ma-248	431	4	remained	remain	VERB
ma-248	431	5	at	at	ADP
ma-248	431	6	this	this	DET
ma-248	431	7	level	level	NOUN
ma-248	431	8	throughout	throughout	ADP
ma-248	431	9	the	the	DET
ma-248	431	10	remaining	remain	VERB
ma-248	431	11	simulated	simulate	VERB
ma-248	431	12	time	time	NOUN
ma-248	431	13	.	.	PUNCT
ma-248	432	1	with	with	ADP
ma-248	432	2	theasymptomatic	theasymptomatic	ADJ
ma-248	432	3	non	non	ADJ
ma-248	432	4	-	-	ADJ
ma-248	432	5	control	control	ADJ
ma-248	432	6	graph	graph	NOUN
ma-248	432	7	of	of	ADP
ma-248	432	8	2b	2b	NUM
ma-248	432	9	,	,	PUNCT
ma-248	432	10	we	we	PRON
ma-248	432	11	notice	notice	VERB
ma-248	432	12	a	a	DET
ma-248	432	13	gentle	gentle	ADJ
ma-248	432	14	rise	rise	NOUN
ma-248	432	15	of	of	ADP
ma-248	432	16	the	the	DET
ma-248	432	17	graph	graph	NOUN
ma-248	432	18	in	in	ADP
ma-248	432	19	the	the	DET
ma-248	432	20	first	first	ADJ
ma-248	432	21	20	20	NUM
ma-248	432	22	days	day	NOUN
ma-248	432	23	to	to	ADP
ma-248	432	24	4300	4300	NUM
ma-248	432	25	of	of	ADP
ma-248	432	26	the	the	DET
ma-248	432	27	asymptomatic	asymptomatic	ADJ
ma-248	432	28	population	population	NOUN
ma-248	432	29	.	.	PUNCT
ma-248	433	1	the	the	DET
ma-248	433	2	asymptomatic	asymptomatic	ADJ
ma-248	433	3	control	control	NOUN
ma-248	433	4	graph	graph	NOUN
ma-248	433	5	progressed	progress	VERB
ma-248	433	6	steadily	steadily	ADV
ma-248	433	7	to	to	ADP
ma-248	433	8	a	a	DET
ma-248	433	9	new	new	ADJ
ma-248	433	10	5000	5000	NUM
ma-248	433	11	in	in	ADP
ma-248	433	12	140	140	NUM
ma-248	433	13	days	day	NOUN
ma-248	433	14	and	and	CCONJ
ma-248	433	15	retained	retain	VERB
ma-248	433	16	it	it	PRON
ma-248	433	17	till	till	SCONJ
ma-248	433	18	the	the	DET
ma-248	433	19	end	end	NOUN
ma-248	433	20	of	of	ADP
ma-248	433	21	the	the	DET
ma-248	433	22	simulation	simulation	NOUN
ma-248	433	23	.	.	PUNCT
ma-248	434	1	the	the	DET
ma-248	434	2	symptomatic	symptomatic	ADJ
ma-248	434	3	non	non	ADJ
ma-248	434	4	-	-	ADJ
ma-248	434	5	control	control	ADJ
ma-248	434	6	graphof	graphof	ADJ
ma-248	434	7	2c	2c	NOUN
ma-248	434	8	increased	increase	VERB
ma-248	434	9	smoothly	smoothly	ADV
ma-248	434	10	and	and	CCONJ
ma-248	434	11	moved	move	VERB
ma-248	434	12	to	to	ADP
ma-248	434	13	the	the	DET
ma-248	434	14	maximum	maximum	ADJ
ma-248	434	15	height	height	NOUN
ma-248	434	16	of	of	ADP
ma-248	434	17	430	430	NUM
ma-248	434	18	of	of	ADP
ma-248	434	19	the	the	DET
ma-248	434	20	symptomatic	symptomatic	ADJ
ma-248	434	21	populationin	populationin	ADJ
ma-248	434	22	130	130	NUM
ma-248	434	23	days	day	NOUN
ma-248	434	24	,	,	PUNCT
ma-248	434	25	which	which	PRON
ma-248	434	26	remained	remain	VERB
ma-248	434	27	until	until	ADP
ma-248	434	28	the	the	DET
ma-248	434	29	end	end	NOUN
ma-248	434	30	of	of	ADP
ma-248	434	31	the	the	DET
ma-248	434	32	simulation	simulation	NOUN
ma-248	434	33	.	.	PUNCT
ma-248	435	1	control	control	NOUN
ma-248	435	2	figures	figure	NOUN
ma-248	435	3	of	of	ADP
ma-248	435	4	the	the	DET
ma-248	435	5	exposed	expose	VERB
ma-248	435	6	,	,	PUNCT
ma-248	435	7	asymptomatic	asymptomatic	ADJ
ma-248	435	8	and	and	CCONJ
ma-248	435	9	symptomatic	symptomatic	ADJ
ma-248	435	10	produced	produce	VERB
ma-248	435	11	results	result	NOUN
ma-248	435	12	with	with	ADP
ma-248	435	13	substantially	substantially	ADV
ma-248	435	14	minimized	minimized	ADJ
ma-248	435	15	graphs	graph	NOUN
ma-248	435	16	.	.	PUNCT
ma-248	436	1	from	from	ADP
ma-248	436	2	theexposed	theexpose	VERB
ma-248	436	3	graph	graph	NOUN
ma-248	436	4	of	of	ADP
ma-248	436	5	2a	2a	NUM
ma-248	436	6	,	,	PUNCT
ma-248	436	7	the	the	DET
ma-248	436	8	graph	graph	NOUN
ma-248	436	9	increases	increase	VERB
ma-248	436	10	similarly	similarly	ADV
ma-248	436	11	but	but	CCONJ
ma-248	436	12	could	could	AUX
ma-248	436	13	not	not	PART
ma-248	436	14	rise	rise	VERB
ma-248	436	15	to	to	ADP
ma-248	436	16	the	the	DET
ma-248	436	17	level	level	NOUN
ma-248	436	18	of	of	ADP
ma-248	436	19	the	the	PRON
ma-248	436	20	without	without	ADP
ma-248	436	21	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	436	22	eur	eur	PROPN
ma-248	436	23	.	.	PUNCT
ma-248	437	1	j.	j.	PROPN
ma-248	437	2	math	math	PROPN
ma-248	437	3	.	.	PUNCT
ma-248	438	1	anal	anal	PROPN
ma-248	438	2	.	.	PUNCT
ma-248	439	1	10.28924	10.28924	NUM
ma-248	439	2	/	/	SYM
ma-248	439	3	ada	ada	PROPN
ma-248	439	4	/	/	SYM
ma-248	439	5	ma.4.21	ma.4.21	PROPN
ma-248	439	6	18control	18control	NUM
ma-248	439	7	plot	plot	NOUN
ma-248	439	8	.	.	PUNCT
ma-248	440	1	we	we	PRON
ma-248	440	2	see	see	VERB
ma-248	440	3	that	that	SCONJ
ma-248	440	4	the	the	DET
ma-248	440	5	control	control	NOUN
ma-248	440	6	graph	graph	NOUN
ma-248	440	7	has	have	AUX
ma-248	440	8	been	be	AUX
ma-248	440	9	dramatically	dramatically	ADV
ma-248	440	10	minimized	minimize	VERB
ma-248	440	11	.	.	PUNCT
ma-248	441	1	the	the	DET
ma-248	441	2	control	control	PROPN
ma-248	441	3	figures2b	figures2b	PROPN
ma-248	441	4	of	of	ADP
ma-248	441	5	the	the	DET
ma-248	441	6	asymptomatic	asymptomatic	ADJ
ma-248	441	7	lie	lie	NOUN
ma-248	441	8	far	far	ADV
ma-248	441	9	below	below	ADP
ma-248	441	10	the	the	DET
ma-248	441	11	non	non	ADJ
ma-248	441	12	-	-	ADJ
ma-248	441	13	control	control	ADJ
ma-248	441	14	figure	figure	NOUN
ma-248	441	15	.	.	PUNCT
ma-248	442	1	the	the	DET
ma-248	442	2	symptomatic	symptomatic	ADJ
ma-248	442	3	control	control	NOUN
ma-248	442	4	figure	figure	NOUN
ma-248	442	5	of2c	of2c	PROPN
ma-248	442	6	lay	lie	VERB
ma-248	442	7	slightly	slightly	ADV
ma-248	442	8	above	above	ADP
ma-248	442	9	zero	zero	NUM
ma-248	442	10	and	and	CCONJ
ma-248	442	11	maintained	maintain	VERB
ma-248	442	12	the	the	DET
ma-248	442	13	level	level	NOUN
ma-248	442	14	throughout	throughout	ADP
ma-248	442	15	the	the	DET
ma-248	442	16	simulated	simulated	ADJ
ma-248	442	17	time	time	NOUN
ma-248	442	18	.	.	PUNCT
ma-248	443	1	figure	figure	VERB
ma-248	443	2	2d	2d	NUM
ma-248	443	3	isthe	isthe	PROPN
ma-248	443	4	control	control	PROPN
ma-248	443	5	profile	profile	PROPN
ma-248	443	6	plot	plot	NOUN
ma-248	443	7	of	of	ADP
ma-248	443	8	strategy	strategy	NOUN
ma-248	443	9	a.	a.	NOUN
ma-248	443	10	the	the	DET
ma-248	443	11	plot	plot	NOUN
ma-248	443	12	shows	show	VERB
ma-248	443	13	that	that	SCONJ
ma-248	443	14	the	the	DET
ma-248	443	15	personal	personal	ADJ
ma-248	443	16	protection	protection	NOUN
ma-248	443	17	procedure	procedure	NOUN
ma-248	443	18	u1remained	u1remaine	VERB
ma-248	443	19	at	at	ADP
ma-248	443	20	the	the	DET
ma-248	443	21	upper	upper	ADJ
ma-248	443	22	bound	bind	VERB
ma-248	443	23	throughout	throughout	ADP
ma-248	443	24	the	the	DET
ma-248	443	25	simulation	simulation	NOUN
ma-248	443	26	,	,	PUNCT
ma-248	443	27	while	while	SCONJ
ma-248	443	28	the	the	DET
ma-248	443	29	vaccine	vaccine	NOUN
ma-248	443	30	control	control	NOUN
ma-248	443	31	u2	u2	PROPN
ma-248	443	32	remained	remain	VERB
ma-248	443	33	atthe	atthe	ADJ
ma-248	443	34	upper	upper	ADJ
ma-248	443	35	bound	bind	VERB
ma-248	443	36	until	until	ADP
ma-248	443	37	178	178	NUM
ma-248	443	38	days	day	NOUN
ma-248	443	39	before	before	ADP
ma-248	443	40	dropping	drop	VERB
ma-248	443	41	to	to	ADP
ma-248	443	42	the	the	DET
ma-248	443	43	lower	lower	ADV
ma-248	443	44	bound	bind	VERB
ma-248	443	45	.	.	PUNCT
ma-248	444	1	6.2	6.2	NUM
ma-248	444	2	.	.	PUNCT
ma-248	445	1	strategy	strategy	NOUN
ma-248	445	2	b	b	PROPN
ma-248	445	3	:	:	PUNCT
ma-248	445	4	u2	u2	NOUN
ma-248	445	5	=	=	SYM
ma-248	445	6	0	0	PROPN
ma-248	445	7	.	.	PUNCT
ma-248	445	8	strategy	strategy	NOUN
ma-248	445	9	b	b	PROPN
ma-248	445	10	sets	set	VERB
ma-248	445	11	u2	u2	NOUN
ma-248	445	12	=	=	SYM
ma-248	445	13	0	0	PUNCT
ma-248	445	14	and	and	CCONJ
ma-248	445	15	generates	generate	VERB
ma-248	445	16	the	the	DET
ma-248	445	17	exposed	expose	VERB
ma-248	445	18	,	,	PUNCT
ma-248	445	19	asymptomatic	asymptomatic	ADJ
ma-248	445	20	,	,	PUNCT
ma-248	445	21	andsymptomatic	andsymptomatic	ADJ
ma-248	445	22	graphs	graph	NOUN
ma-248	445	23	.	.	PUNCT
ma-248	446	1	from	from	ADP
ma-248	446	2	the	the	DET
ma-248	446	3	exposed	expose	VERB
ma-248	446	4	graph	graph	NOUN
ma-248	446	5	of	of	ADP
ma-248	446	6	a	a	PRON
ma-248	446	7	,	,	PUNCT
ma-248	446	8	we	we	PRON
ma-248	446	9	observed	observe	VERB
ma-248	446	10	that	that	SCONJ
ma-248	446	11	the	the	DET
ma-248	446	12	without	without	ADP
ma-248	446	13	control	control	NOUN
ma-248	446	14	curve	curve	NOUN
ma-248	446	15	swiftlyraised	swiftlyraise	VERB
ma-248	446	16	to	to	ADP
ma-248	446	17	5000	5000	NUM
ma-248	446	18	when	when	SCONJ
ma-248	446	19	t	t	NOUN
ma-248	446	20	=	=	SYM
ma-248	446	21	20	20	NUM
ma-248	446	22	.	.	PUNCT
ma-248	447	1	it	it	PRON
ma-248	447	2	moved	move	VERB
ma-248	447	3	gently	gently	ADV
ma-248	447	4	to	to	ADP
ma-248	447	5	about	about	ADP
ma-248	447	6	5100	5100	NUM
ma-248	447	7	for	for	ADP
ma-248	447	8	the	the	DET
ma-248	447	9	next	next	ADJ
ma-248	447	10	20	20	NUM
ma-248	447	11	days	day	NOUN
ma-248	447	12	and	and	CCONJ
ma-248	447	13	remainedat	remainedat	VERB
ma-248	447	14	that	that	DET
ma-248	447	15	level	level	NOUN
ma-248	447	16	for	for	ADP
ma-248	447	17	the	the	DET
ma-248	447	18	remaining	remain	VERB
ma-248	447	19	time	time	NOUN
ma-248	447	20	.	.	PUNCT
ma-248	448	1	the	the	DET
ma-248	448	2	asymptomatic	asymptomatic	NOUN
ma-248	448	3	without	without	ADP
ma-248	448	4	control	control	NOUN
ma-248	448	5	curve	curve	NOUN
ma-248	448	6	steadily	steadily	ADV
ma-248	448	7	increasedin	increasedin	VERB
ma-248	448	8	the	the	DET
ma-248	448	9	early	early	ADJ
ma-248	448	10	days	day	NOUN
ma-248	448	11	of	of	ADP
ma-248	448	12	20	20	NUM
ma-248	448	13	to	to	ADP
ma-248	448	14	4500	4500	NUM
ma-248	448	15	,	,	PUNCT
ma-248	448	16	increased	increase	VERB
ma-248	448	17	gently	gently	ADV
ma-248	448	18	for	for	ADP
ma-248	448	19	the	the	DET
ma-248	448	20	next	next	ADJ
ma-248	448	21	120	120	NUM
ma-248	448	22	days	day	NOUN
ma-248	448	23	to	to	ADP
ma-248	448	24	5000	5000	NUM
ma-248	448	25	,	,	PUNCT
ma-248	448	26	and	and	CCONJ
ma-248	448	27	maintainedthe	maintainedthe	DET
ma-248	448	28	level	level	NOUN
ma-248	448	29	for	for	ADP
ma-248	448	30	the	the	DET
ma-248	448	31	remaining	remain	VERB
ma-248	448	32	time	time	NOUN
ma-248	448	33	.	.	PUNCT
ma-248	449	1	the	the	DET
ma-248	449	2	symptomatic	symptomatic	ADJ
ma-248	449	3	without	without	ADP
ma-248	449	4	control	control	NOUN
ma-248	449	5	graph	graph	NOUN
ma-248	449	6	increased	increase	VERB
ma-248	449	7	smoothly	smoothly	ADV
ma-248	449	8	andprogressed	andprogresse	VERB
ma-248	449	9	to	to	ADP
ma-248	449	10	a	a	DET
ma-248	449	11	height	height	NOUN
ma-248	449	12	of	of	ADP
ma-248	449	13	430	430	NUM
ma-248	449	14	at	at	ADP
ma-248	449	15	the	the	DET
ma-248	449	16	final	final	ADJ
ma-248	449	17	time	time	NOUN
ma-248	449	18	.	.	PUNCT
ma-248	450	1	the	the	DET
ma-248	450	2	exposed	expose	VERB
ma-248	450	3	,	,	PUNCT
ma-248	450	4	asymptomatic	asymptomatic	ADJ
ma-248	450	5	and	and	CCONJ
ma-248	450	6	symptomatic	symptomatic	ADJ
ma-248	450	7	controlgraphs	controlgraph	NOUN
ma-248	450	8	produced	produce	VERB
ma-248	450	9	graphs	graph	NOUN
ma-248	450	10	with	with	ADP
ma-248	450	11	desired	desire	VERB
ma-248	450	12	results	result	NOUN
ma-248	450	13	.	.	PUNCT
ma-248	451	1	thus	thus	ADV
ma-248	451	2	,	,	PUNCT
ma-248	451	3	we	we	PRON
ma-248	451	4	noticed	notice	VERB
ma-248	451	5	a	a	DET
ma-248	451	6	completely	completely	ADV
ma-248	451	7	minimized	minimized	ADJ
ma-248	451	8	exposure	exposure	NOUN
ma-248	451	9	,	,	PUNCT
ma-248	451	10	asymptomatic	asymptomatic	ADJ
ma-248	451	11	and	and	CCONJ
ma-248	451	12	symptomatic	symptomatic	ADJ
ma-248	451	13	,	,	PUNCT
ma-248	451	14	with	with	ADP
ma-248	451	15	the	the	DET
ma-248	451	16	control	control	NOUN
ma-248	451	17	simulations	simulation	NOUN
ma-248	451	18	.	.	PUNCT
ma-248	452	1	figure	figure	NOUN
ma-248	452	2	3d	3d	PROPN
ma-248	452	3	is	be	AUX
ma-248	452	4	the	the	DET
ma-248	452	5	control	control	NOUN
ma-248	452	6	profile	profile	VERB
ma-248	452	7	graph.the	graph.the	DET
ma-248	452	8	graph	graph	NOUN
ma-248	452	9	shows	show	VERB
ma-248	452	10	that	that	SCONJ
ma-248	452	11	the	the	DET
ma-248	452	12	personal	personal	ADJ
ma-248	452	13	protection	protection	NOUN
ma-248	452	14	and	and	CCONJ
ma-248	452	15	treatment	treatment	NOUN
ma-248	452	16	controls	control	NOUN
ma-248	452	17	remained	remain	VERB
ma-248	452	18	at	at	ADP
ma-248	452	19	the	the	DET
ma-248	452	20	upper	upper	ADJ
ma-248	452	21	bounduntil	bounduntil	NOUN
ma-248	452	22	100	100	NUM
ma-248	452	23	and	and	CCONJ
ma-248	452	24	98	98	NUM
ma-248	452	25	when	when	SCONJ
ma-248	452	26	they	they	PRON
ma-248	452	27	dropped	drop	VERB
ma-248	452	28	to	to	ADP
ma-248	452	29	the	the	DET
ma-248	452	30	lower	lower	ADV
ma-248	452	31	bound	bind	VERB
ma-248	452	32	.	.	PUNCT
ma-248	453	1	the	the	DET
ma-248	453	2	simulated	simulate	VERB
ma-248	453	3	plots	plot	NOUN
ma-248	453	4	of	of	ADP
ma-248	453	5	the	the	DET
ma-248	453	6	exposed	expose	VERB
ma-248	453	7	,	,	PUNCT
ma-248	453	8	asymptomatic	asymptomatic	ADJ
ma-248	453	9	and	and	CCONJ
ma-248	453	10	symptomatic	symptomatic	ADJ
ma-248	453	11	confirmed	confirm	VERB
ma-248	453	12	that	that	SCONJ
ma-248	453	13	strategy	strategy	NOUN
ma-248	453	14	b	b	NOUN
ma-248	453	15	is	be	AUX
ma-248	453	16	effective	effective	ADJ
ma-248	453	17	.	.	PUNCT
ma-248	454	1	6.3	6.3	NUM
ma-248	454	2	.	.	PUNCT
ma-248	455	1	strategy	strategy	NOUN
ma-248	455	2	c	c	NOUN
ma-248	455	3	:	:	PUNCT
ma-248	455	4	u1	u1	PROPN
ma-248	455	5	=	=	SYM
ma-248	455	6	0	0	PROPN
ma-248	455	7	.	.	PUNCT
ma-248	456	1	strategy	strategy	PROPN
ma-248	456	2	c	c	PROPN
ma-248	456	3	uses	use	VERB
ma-248	456	4	the	the	DET
ma-248	456	5	control	control	NOUN
ma-248	456	6	u1	u1	NOUN
ma-248	456	7	=	=	SYM
ma-248	456	8	0	0	NUM
ma-248	456	9	and	and	CCONJ
ma-248	456	10	the	the	DET
ma-248	456	11	remaining	remain	VERB
ma-248	456	12	controls	control	NOUN
ma-248	456	13	forthe	forthe	PRON
ma-248	456	14	simulated	simulate	VERB
ma-248	456	15	.	.	PUNCT
ma-248	457	1	the	the	DET
ma-248	457	2	graphs	graph	NOUN
ma-248	457	3	of	of	ADP
ma-248	457	4	4a	4a	NUM
ma-248	457	5	,	,	PUNCT
ma-248	457	6	4b	4b	NOUN
ma-248	457	7	,	,	PUNCT
ma-248	457	8	4c	4c	NOUN
ma-248	457	9	,	,	PUNCT
ma-248	457	10	and	and	CCONJ
ma-248	457	11	4d	4d	NUM
ma-248	457	12	are	be	AUX
ma-248	457	13	the	the	DET
ma-248	457	14	exposed	expose	VERB
ma-248	457	15	,	,	PUNCT
ma-248	457	16	asymptomatic	asymptomatic	ADJ
ma-248	457	17	,	,	PUNCT
ma-248	457	18	symptomatic	symptomatic	ADJ
ma-248	457	19	andcontrol	andcontrol	NOUN
ma-248	457	20	profile	profile	NOUN
ma-248	457	21	plots	plot	NOUN
ma-248	457	22	of	of	ADP
ma-248	457	23	strategy	strategy	NOUN
ma-248	457	24	c.	c.	PROPN
ma-248	457	25	in	in	ADP
ma-248	457	26	the	the	DET
ma-248	457	27	early	early	ADJ
ma-248	457	28	days	day	NOUN
ma-248	457	29	,	,	PUNCT
ma-248	457	30	the	the	DET
ma-248	457	31	exposure	exposure	NOUN
ma-248	457	32	surged	surge	VERB
ma-248	457	33	swiftly	swiftly	ADV
ma-248	457	34	for	for	ADP
ma-248	457	35	the	the	DET
ma-248	457	36	withoutcontrol	withoutcontrol	NOUN
ma-248	457	37	graphs	graph	NOUN
ma-248	457	38	but	but	CCONJ
ma-248	457	39	maintained	maintain	VERB
ma-248	457	40	a	a	DET
ma-248	457	41	stable	stable	ADJ
ma-248	457	42	level	level	NOUN
ma-248	457	43	after	after	ADP
ma-248	457	44	40	40	NUM
ma-248	457	45	days	day	NOUN
ma-248	457	46	.	.	PUNCT
ma-248	458	1	the	the	DET
ma-248	458	2	asymptomatic	asymptomatic	ADJ
ma-248	458	3	graph	graph	NOUN
ma-248	458	4	moved	move	VERB
ma-248	458	5	steeplyin	steeplyin	NOUN
ma-248	458	6	the	the	DET
ma-248	458	7	early	early	ADJ
ma-248	458	8	days	day	NOUN
ma-248	458	9	of	of	ADP
ma-248	458	10	20	20	NUM
ma-248	458	11	to	to	ADP
ma-248	458	12	4500	4500	NUM
ma-248	458	13	,	,	PUNCT
ma-248	458	14	increased	increase	VERB
ma-248	458	15	further	far	ADV
ma-248	458	16	to	to	ADP
ma-248	458	17	5000	5000	NUM
ma-248	458	18	for	for	ADP
ma-248	458	19	the	the	DET
ma-248	458	20	next	next	ADJ
ma-248	458	21	120	120	NUM
ma-248	458	22	,	,	PUNCT
ma-248	458	23	and	and	CCONJ
ma-248	458	24	retained	retain	VERB
ma-248	458	25	the	the	DET
ma-248	458	26	levelfor	levelfor	NOUN
ma-248	458	27	the	the	DET
ma-248	458	28	remaining	remain	VERB
ma-248	458	29	days	day	NOUN
ma-248	458	30	.	.	PUNCT
ma-248	459	1	the	the	DET
ma-248	459	2	symptomatic	symptomatic	ADJ
ma-248	459	3	graph	graph	NOUN
ma-248	459	4	gently	gently	ADV
ma-248	459	5	increased	increase	VERB
ma-248	459	6	throughout	throughout	ADP
ma-248	459	7	the	the	DET
ma-248	459	8	simulation	simulation	NOUN
ma-248	459	9	andmaintained	andmaintaine	VERB
ma-248	459	10	a	a	DET
ma-248	459	11	steady	steady	ADJ
ma-248	459	12	progression	progression	NOUN
ma-248	459	13	.	.	PUNCT
ma-248	460	1	the	the	DET
ma-248	460	2	exposed	expose	VERB
ma-248	460	3	control	control	NOUN
ma-248	460	4	plot	plot	NOUN
ma-248	460	5	showed	show	VERB
ma-248	460	6	a	a	DET
ma-248	460	7	swift	swift	ADJ
ma-248	460	8	increase	increase	NOUN
ma-248	460	9	in	in	ADP
ma-248	460	10	the	the	DET
ma-248	460	11	graphin	graphin	NOUN
ma-248	460	12	the	the	DET
ma-248	460	13	early	early	ADJ
ma-248	460	14	days	day	NOUN
ma-248	460	15	and	and	CCONJ
ma-248	460	16	progressed	progress	VERB
ma-248	460	17	gently	gently	ADV
ma-248	460	18	for	for	ADP
ma-248	460	19	the	the	DET
ma-248	460	20	entire	entire	ADJ
ma-248	460	21	simulated	simulate	VERB
ma-248	460	22	time	time	NOUN
ma-248	460	23	.	.	PUNCT
ma-248	461	1	the	the	DET
ma-248	461	2	asymptomatic	asymptomatic	ADJ
ma-248	461	3	controlgraph	controlgraph	NOUN
ma-248	461	4	smoothly	smoothly	ADV
ma-248	461	5	increased	increase	VERB
ma-248	461	6	in	in	ADP
ma-248	461	7	the	the	DET
ma-248	461	8	early	early	ADJ
ma-248	461	9	days	day	NOUN
ma-248	461	10	and	and	CCONJ
ma-248	461	11	progressed	progress	VERB
ma-248	461	12	with	with	ADP
ma-248	461	13	the	the	DET
ma-248	461	14	same	same	ADJ
ma-248	461	15	momentum	momentum	NOUN
ma-248	461	16	for	for	ADP
ma-248	461	17	the	the	DET
ma-248	461	18	rest	rest	NOUN
ma-248	461	19	ofthe	ofthe	NOUN
ma-248	461	20	simulation	simulation	NOUN
ma-248	461	21	.	.	PUNCT
ma-248	462	1	the	the	DET
ma-248	462	2	symptomatic	symptomatic	ADJ
ma-248	462	3	control	control	NOUN
ma-248	462	4	curve	curve	NOUN
ma-248	462	5	was	be	AUX
ma-248	462	6	noticed	notice	VERB
ma-248	462	7	to	to	PART
ma-248	462	8	be	be	AUX
ma-248	462	9	minimized	minimize	VERB
ma-248	462	10	throughout	throughout	ADP
ma-248	462	11	the	the	DET
ma-248	462	12	entiresimulation	entiresimulation	NOUN
ma-248	462	13	.	.	PUNCT
ma-248	463	1	the	the	DET
ma-248	463	2	plot	plot	NOUN
ma-248	463	3	of	of	ADP
ma-248	463	4	figure	figure	NOUN
ma-248	463	5	4d	4d	NOUN
ma-248	463	6	is	be	AUX
ma-248	463	7	the	the	DET
ma-248	463	8	optimal	optimal	ADJ
ma-248	463	9	control	control	NOUN
ma-248	463	10	profile	profile	NOUN
ma-248	463	11	of	of	ADP
ma-248	463	12	strategy	strategy	NOUN
ma-248	463	13	c.	c.	PROPN
ma-248	463	14	the	the	DET
ma-248	463	15	vaccine	vaccine	NOUN
ma-248	463	16	(	(	PUNCT
ma-248	463	17	u2	u2	NOUN
ma-248	463	18	)	)	PUNCT
ma-248	463	19	andtreatment	andtreatment	NOUN
ma-248	463	20	(	(	PUNCT
ma-248	463	21	u3	u3	NOUN
ma-248	463	22	)	)	PUNCT
ma-248	463	23	controls	control	NOUN
ma-248	463	24	remained	remain	VERB
ma-248	463	25	at	at	ADP
ma-248	463	26	the	the	DET
ma-248	463	27	upper	upper	ADJ
ma-248	463	28	bound	bind	VERB
ma-248	463	29	throughout	throughout	ADP
ma-248	463	30	the	the	DET
ma-248	463	31	simulation	simulation	NOUN
ma-248	463	32	until	until	ADP
ma-248	463	33	180	180	NUM
ma-248	463	34	days	day	NOUN
ma-248	463	35	,	,	PUNCT
ma-248	463	36	when	when	SCONJ
ma-248	463	37	they	they	PRON
ma-248	463	38	decreased	decrease	VERB
ma-248	463	39	to	to	ADP
ma-248	463	40	the	the	DET
ma-248	463	41	lower	lower	ADV
ma-248	463	42	bound	bind	VERB
ma-248	463	43	.	.	PUNCT
ma-248	464	1	6.4	6.4	NUM
ma-248	464	2	.	.	PUNCT
ma-248	465	1	strategy	strategy	NOUN
ma-248	465	2	d	d	NOUN
ma-248	465	3	:	:	PUNCT
ma-248	465	4	u1	u1	PROPN
ma-248	465	5	6=	6=	ADP
ma-248	465	6	0	0	NUM
ma-248	465	7	,	,	PUNCT
ma-248	465	8	u2	u2	PROPN
ma-248	465	9	6=	6=	ADP
ma-248	465	10	0	0	NUM
ma-248	465	11	and	and	CCONJ
ma-248	465	12	u3	u3	PROPN
ma-248	465	13	6=	6=	ADP
ma-248	465	14	0	0	NUM
ma-248	465	15	.	.	PUNCT
ma-248	466	1	strategy	strategy	NOUN
ma-248	467	1	d	d	PROPN
ma-248	467	2	considered	consider	VERB
ma-248	467	3	the	the	DET
ma-248	467	4	three	three	NUM
ma-248	467	5	controls	control	NOUN
ma-248	467	6	in	in	ADP
ma-248	467	7	itssimulation	itssimulation	NOUN
ma-248	467	8	and	and	CCONJ
ma-248	467	9	generated	generate	VERB
ma-248	467	10	the	the	DET
ma-248	467	11	exposed	expose	VERB
ma-248	467	12	,	,	PUNCT
ma-248	467	13	asymptomatic	asymptomatic	ADJ
ma-248	467	14	and	and	CCONJ
ma-248	467	15	symptomatic	symptomatic	ADJ
ma-248	467	16	plots	plot	NOUN
ma-248	467	17	.	.	PUNCT
ma-248	468	1	without	without	ADP
ma-248	468	2	control	control	NOUN
ma-248	468	3	,	,	PUNCT
ma-248	468	4	theexposed	theexpose	VERB
ma-248	468	5	graph	graph	NOUN
ma-248	468	6	sparked	spark	VERB
ma-248	468	7	to	to	ADP
ma-248	468	8	2000	2000	NUM
ma-248	468	9	at	at	ADP
ma-248	468	10	t	t	PROPN
ma-248	468	11	=	=	SYM
ma-248	468	12	0	0	X
ma-248	468	13	.	.	PUNCT
ma-248	469	1	the	the	DET
ma-248	469	2	graphs	graph	NOUN
ma-248	469	3	increased	increase	VERB
ma-248	469	4	steadily	steadily	ADV
ma-248	469	5	to	to	ADP
ma-248	469	6	5000	5000	NUM
ma-248	469	7	in	in	ADP
ma-248	469	8	20	20	NUM
ma-248	469	9	days	day	NOUN
ma-248	469	10	andthen	andthen	ADV
ma-248	469	11	retained	retain	VERB
ma-248	469	12	it	it	PRON
ma-248	469	13	for	for	ADP
ma-248	469	14	the	the	DET
ma-248	469	15	rest	rest	NOUN
ma-248	469	16	of	of	ADP
ma-248	469	17	the	the	DET
ma-248	469	18	time	time	NOUN
ma-248	469	19	.	.	PUNCT
ma-248	470	1	the	the	DET
ma-248	470	2	asymptomatic	asymptomatic	ADJ
ma-248	470	3	graph	graph	NOUN
ma-248	470	4	also	also	ADV
ma-248	470	5	increased	increase	VERB
ma-248	470	6	early	early	ADV
ma-248	470	7	in	in	ADP
ma-248	470	8	the	the	DET
ma-248	470	9	first	first	ADJ
ma-248	470	10	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	470	11	eur	eur	PROPN
ma-248	470	12	.	.	PUNCT
ma-248	471	1	j.	j.	PROPN
ma-248	471	2	math	math	PROPN
ma-248	471	3	.	.	PUNCT
ma-248	472	1	anal	anal	PROPN
ma-248	472	2	.	.	PUNCT
ma-248	473	1	10.28924	10.28924	NUM
ma-248	473	2	/	/	SYM
ma-248	473	3	ada	ada	PROPN
ma-248	473	4	/	/	SYM
ma-248	473	5	ma.4.21	ma.4.21	PROPN
ma-248	473	6	19	19	NUM
ma-248	473	7	0	0	NUM
ma-248	473	8	20	20	NUM
ma-248	473	9	40	40	NUM
ma-248	473	10	60	60	NUM
ma-248	473	11	80	80	NUM
ma-248	473	12	100	100	NUM
ma-248	473	13	120	120	NUM
ma-248	473	14	140	140	NUM
ma-248	473	15	160	160	NUM
ma-248	473	16	180	180	NUM
ma-248	473	17	time	time	NOUN
ma-248	473	18	(	(	PUNCT
ma-248	473	19	days	day	NOUN
ma-248	473	20	)	)	PUNCT
ma-248	473	21	0	0	NUM
ma-248	474	1	1000	1000	NUM
ma-248	474	2	2000	2000	NUM
ma-248	474	3	3000	3000	NUM
ma-248	474	4	4000	4000	NUM
ma-248	474	5	5000	5000	NUM
ma-248	474	6	6000	6000	NUM
ma-248	474	7	e	e	NOUN
ma-248	474	8	xp	xp	ADV
ma-248	474	9	os	os	INTJ
ma-248	474	10	ed	ed	PROPN
ma-248	474	11	u	u	NOUN
ma-248	474	12	1	1	NUM
ma-248	474	13	=	=	SYM
ma-248	474	14	0	0	NUM
ma-248	474	15	,	,	PUNCT
ma-248	474	16	u	u	NOUN
ma-248	474	17	2	2	NUM
ma-248	474	18	=	=	SYM
ma-248	474	19	0	0	NUM
ma-248	474	20	,	,	PUNCT
ma-248	474	21	u	u	NOUN
ma-248	474	22	3	3	NUM
ma-248	474	23	=	=	SYM
ma-248	474	24	0	0	NUM
ma-248	474	25	u	u	NOUN
ma-248	474	26	1	1	NUM
ma-248	474	27	0	0	NUM
ma-248	474	28	,	,	PUNCT
ma-248	474	29	u	u	NOUN
ma-248	474	30	2	2	NUM
ma-248	474	31	0	0	NUM
ma-248	474	32	,	,	PUNCT
ma-248	474	33	u	u	NOUN
ma-248	474	34	3	3	NUM
ma-248	474	35	=	=	SYM
ma-248	474	36	0	0	NUM
ma-248	474	37	(	(	PUNCT
ma-248	474	38	a	a	NOUN
ma-248	474	39	)	)	PUNCT
ma-248	474	40	0	0	NUM
ma-248	474	41	20	20	NUM
ma-248	474	42	40	40	NUM
ma-248	474	43	60	60	NUM
ma-248	474	44	80	80	NUM
ma-248	474	45	100	100	NUM
ma-248	474	46	120	120	NUM
ma-248	474	47	140	140	NUM
ma-248	474	48	160	160	NUM
ma-248	474	49	180	180	NUM
ma-248	474	50	time	time	NOUN
ma-248	474	51	(	(	PUNCT
ma-248	474	52	days	day	NOUN
ma-248	474	53	)	)	PUNCT
ma-248	474	54	0	0	NUM
ma-248	474	55	500	500	NUM
ma-248	474	56	1000	1000	NUM
ma-248	474	57	1500	1500	NUM
ma-248	474	58	2000	2000	NUM
ma-248	474	59	2500	2500	NUM
ma-248	474	60	3000	3000	NUM
ma-248	474	61	3500	3500	NUM
ma-248	474	62	4000	4000	NUM
ma-248	474	63	4500	4500	NUM
ma-248	474	64	5000	5000	NUM
ma-248	474	65	a	a	DET
ma-248	474	66	sy	sy	NOUN
ma-248	474	67	m	m	ADJ
ma-248	474	68	pt	pt	NOUN
ma-248	474	69	om	om	NOUN
ma-248	474	70	at	at	ADP
ma-248	474	71	ic	ic	PROPN
ma-248	474	72	u	u	NOUN
ma-248	474	73	1	1	NUM
ma-248	474	74	=	=	SYM
ma-248	474	75	0	0	NUM
ma-248	474	76	,	,	PUNCT
ma-248	474	77	u	u	NOUN
ma-248	474	78	2	2	NUM
ma-248	474	79	=	=	SYM
ma-248	474	80	0	0	NUM
ma-248	474	81	,	,	PUNCT
ma-248	474	82	u	u	NOUN
ma-248	474	83	3	3	NUM
ma-248	474	84	=	=	SYM
ma-248	474	85	0	0	NUM
ma-248	474	86	u	u	NOUN
ma-248	474	87	1	1	NUM
ma-248	474	88	0	0	NUM
ma-248	474	89	,	,	PUNCT
ma-248	474	90	u	u	NOUN
ma-248	474	91	2	2	NUM
ma-248	474	92	0	0	NUM
ma-248	474	93	,	,	PUNCT
ma-248	474	94	u	u	NOUN
ma-248	474	95	3	3	NUM
ma-248	474	96	=	=	SYM
ma-248	474	97	0	0	NUM
ma-248	474	98	(	(	PUNCT
ma-248	474	99	b	b	NOUN
ma-248	474	100	)	)	PUNCT
ma-248	474	101	0	0	NUM
ma-248	474	102	20	20	NUM
ma-248	474	103	40	40	NUM
ma-248	474	104	60	60	NUM
ma-248	474	105	80	80	NUM
ma-248	474	106	100	100	NUM
ma-248	474	107	120	120	NUM
ma-248	474	108	140	140	NUM
ma-248	474	109	160	160	NUM
ma-248	474	110	180	180	NUM
ma-248	474	111	time	time	NOUN
ma-248	474	112	(	(	PUNCT
ma-248	474	113	days	day	NOUN
ma-248	474	114	)	)	PUNCT
ma-248	474	115	0	0	NUM
ma-248	474	116	50	50	NUM
ma-248	474	117	100	100	NUM
ma-248	474	118	150	150	NUM
ma-248	474	119	200	200	NUM
ma-248	474	120	250	250	NUM
ma-248	474	121	300	300	NUM
ma-248	474	122	350	350	NUM
ma-248	474	123	400	400	NUM
ma-248	474	124	450	450	NUM
ma-248	474	125	s	s	NOUN
ma-248	474	126	ym	ym	INTJ
ma-248	474	127	pt	pt	NOUN
ma-248	474	128	om	om	PROPN
ma-248	474	129	at	at	ADP
ma-248	474	130	ic	ic	PROPN
ma-248	474	131	u	u	NOUN
ma-248	474	132	1	1	NUM
ma-248	474	133	=	=	SYM
ma-248	474	134	0	0	NUM
ma-248	474	135	,	,	PUNCT
ma-248	474	136	u	u	NOUN
ma-248	474	137	2	2	NUM
ma-248	474	138	=	=	SYM
ma-248	474	139	0	0	NUM
ma-248	474	140	,	,	PUNCT
ma-248	474	141	u	u	NOUN
ma-248	474	142	3	3	NUM
ma-248	474	143	=	=	SYM
ma-248	474	144	0	0	NUM
ma-248	474	145	u	u	NOUN
ma-248	474	146	1	1	NUM
ma-248	474	147	0	0	NUM
ma-248	474	148	,	,	PUNCT
ma-248	474	149	u	u	NOUN
ma-248	474	150	2	2	NUM
ma-248	474	151	0	0	NUM
ma-248	474	152	,	,	PUNCT
ma-248	474	153	u	u	NOUN
ma-248	474	154	3	3	NUM
ma-248	474	155	=	=	SYM
ma-248	474	156	0	0	NUM
ma-248	474	157	(	(	PUNCT
ma-248	474	158	c	c	NOUN
ma-248	474	159	)	)	PUNCT
ma-248	474	160	0	0	NUM
ma-248	474	161	20	20	NUM
ma-248	474	162	40	40	NUM
ma-248	474	163	60	60	NUM
ma-248	474	164	80	80	NUM
ma-248	474	165	100	100	NUM
ma-248	474	166	120	120	NUM
ma-248	474	167	140	140	NUM
ma-248	474	168	160	160	NUM
ma-248	474	169	180	180	NUM
ma-248	474	170	time	time	NOUN
ma-248	474	171	(	(	PUNCT
ma-248	474	172	days	day	NOUN
ma-248	474	173	)	)	PUNCT
ma-248	474	174	0.25	0.25	NUM
ma-248	474	175	0.3	0.3	NUM
ma-248	474	176	0.35	0.35	NUM
ma-248	474	177	0.4	0.4	NUM
ma-248	474	178	0.45	0.45	NUM
ma-248	474	179	0.5	0.5	NUM
ma-248	474	180	0.55	0.55	NUM
ma-248	474	181	0.6	0.6	NUM
ma-248	474	182	0.65	0.65	NUM
ma-248	474	183	0.7	0.7	NUM
ma-248	474	184	0.75	0.75	NUM
ma-248	474	185	c	c	NOUN
ma-248	474	186	on	on	ADP
ma-248	474	187	tr	tr	VERB
ma-248	474	188	ol	ol	PROPN
ma-248	474	189	p	p	PROPN
ma-248	474	190	ro	ro	X
ma-248	474	191	fil	fil	X
ma-248	474	192	e	e	PART
ma-248	474	193	u	u	PROPN
ma-248	474	194	1	1	NUM
ma-248	474	195	u	u	NOUN
ma-248	474	196	2	2	NUM
ma-248	474	197	(	(	PUNCT
ma-248	474	198	d	d	NOUN
ma-248	474	199	)	)	PUNCT
ma-248	474	200	figure	figure	NOUN
ma-248	474	201	2	2	NUM
ma-248	474	202	.	.	PUNCT
ma-248	474	203	plot	plot	NOUN
ma-248	474	204	of	of	ADP
ma-248	474	205	phase	phase	NOUN
ma-248	474	206	portraits	portrait	NOUN
ma-248	474	207	with	with	ADP
ma-248	474	208	u3	u3	NOUN
ma-248	474	209	=	=	SYM
ma-248	474	210	0	0	NUM
ma-248	474	211	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	474	212	eur	eur	PROPN
ma-248	474	213	.	.	PUNCT
ma-248	475	1	j.	j.	PROPN
ma-248	475	2	math	math	PROPN
ma-248	475	3	.	.	PUNCT
ma-248	476	1	anal	anal	PROPN
ma-248	476	2	.	.	PUNCT
ma-248	477	1	10.28924	10.28924	NUM
ma-248	477	2	/	/	SYM
ma-248	477	3	ada	ada	PROPN
ma-248	477	4	/	/	SYM
ma-248	477	5	ma.4.21	ma.4.21	NOUN
ma-248	478	1	20	20	NUM
ma-248	478	2	0	0	NUM
ma-248	478	3	20	20	NUM
ma-248	478	4	40	40	NUM
ma-248	478	5	60	60	NUM
ma-248	478	6	80	80	NUM
ma-248	478	7	100	100	NUM
ma-248	478	8	120	120	NUM
ma-248	478	9	140	140	NUM
ma-248	478	10	160	160	NUM
ma-248	478	11	180	180	NUM
ma-248	478	12	time	time	NOUN
ma-248	478	13	(	(	PUNCT
ma-248	478	14	days	day	NOUN
ma-248	478	15	)	)	PUNCT
ma-248	478	16	0	0	NUM
ma-248	479	1	1000	1000	NUM
ma-248	479	2	2000	2000	NUM
ma-248	479	3	3000	3000	NUM
ma-248	479	4	4000	4000	NUM
ma-248	479	5	5000	5000	NUM
ma-248	479	6	6000	6000	NUM
ma-248	479	7	e	e	NOUN
ma-248	479	8	xp	xp	ADV
ma-248	479	9	os	os	INTJ
ma-248	479	10	ed	ed	PROPN
ma-248	479	11	u	u	NOUN
ma-248	479	12	1	1	NUM
ma-248	479	13	=	=	SYM
ma-248	479	14	0	0	NUM
ma-248	479	15	,	,	PUNCT
ma-248	479	16	u	u	NOUN
ma-248	479	17	2	2	NUM
ma-248	479	18	=	=	SYM
ma-248	479	19	0	0	NUM
ma-248	479	20	,	,	PUNCT
ma-248	479	21	u	u	NOUN
ma-248	479	22	3	3	NUM
ma-248	479	23	=	=	SYM
ma-248	479	24	0	0	NUM
ma-248	479	25	u	u	NOUN
ma-248	479	26	1	1	NUM
ma-248	479	27	0	0	NUM
ma-248	479	28	,	,	PUNCT
ma-248	479	29	u	u	NOUN
ma-248	479	30	2	2	NUM
ma-248	479	31	=	=	SYM
ma-248	479	32	0	0	NUM
ma-248	479	33	,	,	PUNCT
ma-248	479	34	u	u	NOUN
ma-248	479	35	3	3	NUM
ma-248	479	36	0	0	NUM
ma-248	479	37	(	(	PUNCT
ma-248	479	38	a	a	NOUN
ma-248	479	39	)	)	PUNCT
ma-248	479	40	0	0	NUM
ma-248	479	41	20	20	NUM
ma-248	479	42	40	40	NUM
ma-248	479	43	60	60	NUM
ma-248	479	44	80	80	NUM
ma-248	479	45	100	100	NUM
ma-248	479	46	120	120	NUM
ma-248	479	47	140	140	NUM
ma-248	479	48	160	160	NUM
ma-248	479	49	180	180	NUM
ma-248	479	50	time	time	NOUN
ma-248	479	51	(	(	PUNCT
ma-248	479	52	days	day	NOUN
ma-248	479	53	)	)	PUNCT
ma-248	479	54	0	0	NUM
ma-248	479	55	500	500	NUM
ma-248	479	56	1000	1000	NUM
ma-248	479	57	1500	1500	NUM
ma-248	479	58	2000	2000	NUM
ma-248	479	59	2500	2500	NUM
ma-248	479	60	3000	3000	NUM
ma-248	479	61	3500	3500	NUM
ma-248	479	62	4000	4000	NUM
ma-248	479	63	4500	4500	NUM
ma-248	479	64	5000	5000	NUM
ma-248	479	65	a	a	DET
ma-248	479	66	sy	sy	NOUN
ma-248	479	67	m	m	ADJ
ma-248	479	68	pt	pt	NOUN
ma-248	479	69	om	om	NOUN
ma-248	479	70	at	at	ADP
ma-248	479	71	ic	ic	PROPN
ma-248	479	72	u	u	NOUN
ma-248	479	73	1	1	NUM
ma-248	479	74	=	=	SYM
ma-248	479	75	0	0	NUM
ma-248	479	76	,	,	PUNCT
ma-248	479	77	u	u	NOUN
ma-248	479	78	2	2	NUM
ma-248	479	79	=	=	SYM
ma-248	479	80	0	0	NUM
ma-248	479	81	,	,	PUNCT
ma-248	479	82	u	u	NOUN
ma-248	479	83	3	3	NUM
ma-248	479	84	=	=	SYM
ma-248	479	85	0	0	NUM
ma-248	479	86	u	u	NOUN
ma-248	479	87	1	1	NUM
ma-248	479	88	0	0	NUM
ma-248	479	89	,	,	PUNCT
ma-248	479	90	u	u	NOUN
ma-248	479	91	2	2	NUM
ma-248	479	92	=	=	SYM
ma-248	479	93	0	0	NUM
ma-248	479	94	,	,	PUNCT
ma-248	479	95	u	u	NOUN
ma-248	479	96	3	3	NUM
ma-248	479	97	0	0	NUM
ma-248	479	98	(	(	PUNCT
ma-248	479	99	b	b	NOUN
ma-248	479	100	)	)	PUNCT
ma-248	479	101	0	0	NUM
ma-248	479	102	20	20	NUM
ma-248	479	103	40	40	NUM
ma-248	479	104	60	60	NUM
ma-248	479	105	80	80	NUM
ma-248	479	106	100	100	NUM
ma-248	479	107	120	120	NUM
ma-248	479	108	140	140	NUM
ma-248	479	109	160	160	NUM
ma-248	479	110	180	180	NUM
ma-248	479	111	time	time	NOUN
ma-248	479	112	(	(	PUNCT
ma-248	479	113	days	day	NOUN
ma-248	479	114	)	)	PUNCT
ma-248	479	115	0	0	NUM
ma-248	479	116	50	50	NUM
ma-248	479	117	100	100	NUM
ma-248	479	118	150	150	NUM
ma-248	479	119	200	200	NUM
ma-248	479	120	250	250	NUM
ma-248	479	121	300	300	NUM
ma-248	479	122	350	350	NUM
ma-248	479	123	400	400	NUM
ma-248	479	124	450	450	NUM
ma-248	479	125	s	s	NOUN
ma-248	479	126	ym	ym	INTJ
ma-248	479	127	pt	pt	NOUN
ma-248	479	128	om	om	PROPN
ma-248	479	129	at	at	ADP
ma-248	479	130	ic	ic	PROPN
ma-248	479	131	u	u	NOUN
ma-248	479	132	1	1	NUM
ma-248	479	133	=	=	SYM
ma-248	479	134	0	0	NUM
ma-248	479	135	,	,	PUNCT
ma-248	479	136	u	u	NOUN
ma-248	479	137	2	2	NUM
ma-248	479	138	=	=	SYM
ma-248	479	139	0	0	NUM
ma-248	479	140	,	,	PUNCT
ma-248	479	141	u	u	NOUN
ma-248	479	142	3	3	NUM
ma-248	479	143	=	=	SYM
ma-248	479	144	0	0	NUM
ma-248	479	145	u	u	NOUN
ma-248	479	146	1	1	NUM
ma-248	479	147	0	0	NUM
ma-248	479	148	,	,	PUNCT
ma-248	479	149	u	u	NOUN
ma-248	479	150	2	2	NUM
ma-248	479	151	=	=	SYM
ma-248	479	152	0	0	NUM
ma-248	479	153	,	,	PUNCT
ma-248	479	154	u	u	NOUN
ma-248	479	155	3	3	NUM
ma-248	479	156	0	0	NUM
ma-248	479	157	(	(	PUNCT
ma-248	479	158	c	c	NOUN
ma-248	479	159	)	)	PUNCT
ma-248	479	160	0	0	NUM
ma-248	479	161	20	20	NUM
ma-248	479	162	40	40	NUM
ma-248	479	163	60	60	NUM
ma-248	479	164	80	80	NUM
ma-248	479	165	100	100	NUM
ma-248	479	166	120	120	NUM
ma-248	479	167	140	140	NUM
ma-248	479	168	160	160	NUM
ma-248	479	169	180	180	NUM
ma-248	479	170	time	time	NOUN
ma-248	479	171	(	(	PUNCT
ma-248	479	172	days	day	NOUN
ma-248	479	173	)	)	PUNCT
ma-248	479	174	0.25	0.25	NUM
ma-248	479	175	0.3	0.3	NUM
ma-248	479	176	0.35	0.35	NUM
ma-248	479	177	0.4	0.4	NUM
ma-248	479	178	0.45	0.45	NUM
ma-248	479	179	0.5	0.5	NUM
ma-248	479	180	0.55	0.55	NUM
ma-248	479	181	0.6	0.6	NUM
ma-248	479	182	0.65	0.65	NUM
ma-248	479	183	0.7	0.7	NUM
ma-248	479	184	0.75	0.75	NUM
ma-248	479	185	c	c	NOUN
ma-248	479	186	on	on	ADP
ma-248	479	187	tr	tr	VERB
ma-248	479	188	ol	ol	PROPN
ma-248	479	189	p	p	PROPN
ma-248	479	190	ro	ro	X
ma-248	479	191	fil	fil	X
ma-248	479	192	e	e	PART
ma-248	479	193	u	u	PROPN
ma-248	479	194	1	1	NUM
ma-248	479	195	u	u	NOUN
ma-248	479	196	3	3	NUM
ma-248	479	197	(	(	PUNCT
ma-248	479	198	d	d	NOUN
ma-248	479	199	)	)	PUNCT
ma-248	479	200	figure	figure	NOUN
ma-248	479	201	3	3	NUM
ma-248	479	202	.	.	PUNCT
ma-248	479	203	plot	plot	NOUN
ma-248	479	204	of	of	ADP
ma-248	479	205	phase	phase	NOUN
ma-248	479	206	portraits	portrait	NOUN
ma-248	479	207	with	with	ADP
ma-248	479	208	u2	u2	PROPN
ma-248	479	209	=	=	SYM
ma-248	479	210	0	0	NUM
ma-248	479	211	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	479	212	eur	eur	PROPN
ma-248	479	213	.	.	PUNCT
ma-248	480	1	j.	j.	PROPN
ma-248	480	2	math	math	PROPN
ma-248	480	3	.	.	PUNCT
ma-248	481	1	anal	anal	PROPN
ma-248	481	2	.	.	PUNCT
ma-248	482	1	10.28924	10.28924	NUM
ma-248	482	2	/	/	SYM
ma-248	482	3	ada	ada	PROPN
ma-248	482	4	/	/	SYM
ma-248	482	5	ma.4.21	ma.4.21	NOUN
ma-248	482	6	21	21	NUM
ma-248	482	7	0	0	NUM
ma-248	482	8	20	20	NUM
ma-248	482	9	40	40	NUM
ma-248	482	10	60	60	NUM
ma-248	482	11	80	80	NUM
ma-248	482	12	100	100	NUM
ma-248	482	13	120	120	NUM
ma-248	482	14	140	140	NUM
ma-248	482	15	160	160	NUM
ma-248	482	16	180	180	NUM
ma-248	482	17	time	time	NOUN
ma-248	482	18	(	(	PUNCT
ma-248	482	19	days	day	NOUN
ma-248	482	20	)	)	PUNCT
ma-248	482	21	0	0	NUM
ma-248	482	22	1000	1000	NUM
ma-248	482	23	2000	2000	NUM
ma-248	482	24	3000	3000	NUM
ma-248	482	25	4000	4000	NUM
ma-248	482	26	5000	5000	NUM
ma-248	482	27	6000	6000	NUM
ma-248	482	28	e	e	NOUN
ma-248	482	29	xp	xp	ADV
ma-248	482	30	os	os	INTJ
ma-248	482	31	ed	ed	PROPN
ma-248	482	32	u	u	NOUN
ma-248	482	33	1	1	NUM
ma-248	482	34	=	=	SYM
ma-248	482	35	0	0	NUM
ma-248	482	36	,	,	PUNCT
ma-248	482	37	u	u	NOUN
ma-248	482	38	2	2	NUM
ma-248	482	39	=	=	SYM
ma-248	482	40	0	0	NUM
ma-248	482	41	,	,	PUNCT
ma-248	482	42	u	u	NOUN
ma-248	482	43	3	3	NUM
ma-248	482	44	=	=	SYM
ma-248	482	45	0	0	NUM
ma-248	482	46	u	u	NOUN
ma-248	482	47	1	1	NUM
ma-248	482	48	=	=	SYM
ma-248	482	49	0	0	NUM
ma-248	482	50	,	,	PUNCT
ma-248	482	51	u	u	NOUN
ma-248	482	52	2	2	NUM
ma-248	482	53	0	0	NUM
ma-248	482	54	,	,	PUNCT
ma-248	482	55	u	u	NOUN
ma-248	482	56	3	3	NUM
ma-248	482	57	0	0	NUM
ma-248	482	58	(	(	PUNCT
ma-248	482	59	a	a	NOUN
ma-248	482	60	)	)	PUNCT
ma-248	482	61	0	0	NUM
ma-248	482	62	20	20	NUM
ma-248	482	63	40	40	NUM
ma-248	482	64	60	60	NUM
ma-248	482	65	80	80	NUM
ma-248	482	66	100	100	NUM
ma-248	482	67	120	120	NUM
ma-248	482	68	140	140	NUM
ma-248	482	69	160	160	NUM
ma-248	482	70	180	180	NUM
ma-248	482	71	time	time	NOUN
ma-248	482	72	(	(	PUNCT
ma-248	482	73	days	day	NOUN
ma-248	482	74	)	)	PUNCT
ma-248	482	75	0	0	NUM
ma-248	482	76	500	500	NUM
ma-248	482	77	1000	1000	NUM
ma-248	482	78	1500	1500	NUM
ma-248	482	79	2000	2000	NUM
ma-248	482	80	2500	2500	NUM
ma-248	482	81	3000	3000	NUM
ma-248	482	82	3500	3500	NUM
ma-248	482	83	4000	4000	NUM
ma-248	482	84	4500	4500	NUM
ma-248	482	85	5000	5000	NUM
ma-248	482	86	a	a	DET
ma-248	482	87	sy	sy	NOUN
ma-248	482	88	m	m	ADJ
ma-248	482	89	pt	pt	NOUN
ma-248	482	90	om	om	NOUN
ma-248	482	91	at	at	ADP
ma-248	482	92	ic	ic	PROPN
ma-248	482	93	u	u	NOUN
ma-248	482	94	1	1	NUM
ma-248	482	95	=	=	SYM
ma-248	482	96	0	0	NUM
ma-248	482	97	,	,	PUNCT
ma-248	482	98	u	u	NOUN
ma-248	482	99	2	2	NUM
ma-248	482	100	=	=	SYM
ma-248	482	101	0	0	NUM
ma-248	482	102	,	,	PUNCT
ma-248	482	103	u	u	NOUN
ma-248	482	104	3	3	NUM
ma-248	482	105	=	=	SYM
ma-248	482	106	0	0	NUM
ma-248	482	107	u	u	NOUN
ma-248	482	108	1	1	NUM
ma-248	482	109	=	=	SYM
ma-248	482	110	0	0	NUM
ma-248	482	111	,	,	PUNCT
ma-248	482	112	u	u	NOUN
ma-248	482	113	2	2	NUM
ma-248	482	114	0	0	NUM
ma-248	482	115	,	,	PUNCT
ma-248	482	116	u	u	NOUN
ma-248	482	117	3	3	NUM
ma-248	482	118	0	0	NUM
ma-248	482	119	(	(	PUNCT
ma-248	482	120	b	b	NOUN
ma-248	482	121	)	)	PUNCT
ma-248	482	122	0	0	NUM
ma-248	482	123	20	20	NUM
ma-248	482	124	40	40	NUM
ma-248	482	125	60	60	NUM
ma-248	482	126	80	80	NUM
ma-248	482	127	100	100	NUM
ma-248	482	128	120	120	NUM
ma-248	482	129	140	140	NUM
ma-248	482	130	160	160	NUM
ma-248	482	131	180	180	NUM
ma-248	482	132	time	time	NOUN
ma-248	482	133	(	(	PUNCT
ma-248	482	134	days	day	NOUN
ma-248	482	135	)	)	PUNCT
ma-248	482	136	0	0	NUM
ma-248	482	137	50	50	NUM
ma-248	482	138	100	100	NUM
ma-248	482	139	150	150	NUM
ma-248	482	140	200	200	NUM
ma-248	482	141	250	250	NUM
ma-248	482	142	300	300	NUM
ma-248	482	143	350	350	NUM
ma-248	482	144	400	400	NUM
ma-248	482	145	450	450	NUM
ma-248	482	146	s	s	NOUN
ma-248	482	147	ym	ym	INTJ
ma-248	482	148	pt	pt	NOUN
ma-248	482	149	om	om	PROPN
ma-248	482	150	at	at	ADP
ma-248	482	151	ic	ic	PROPN
ma-248	482	152	u	u	NOUN
ma-248	482	153	1	1	NUM
ma-248	482	154	=	=	SYM
ma-248	482	155	0	0	NUM
ma-248	482	156	,	,	PUNCT
ma-248	482	157	u	u	NOUN
ma-248	482	158	2	2	NUM
ma-248	482	159	=	=	SYM
ma-248	482	160	0	0	NUM
ma-248	482	161	,	,	PUNCT
ma-248	482	162	u	u	NOUN
ma-248	482	163	3	3	NUM
ma-248	482	164	=	=	SYM
ma-248	482	165	0	0	NUM
ma-248	482	166	u	u	NOUN
ma-248	482	167	1	1	NUM
ma-248	482	168	=	=	SYM
ma-248	482	169	0	0	NUM
ma-248	482	170	,	,	PUNCT
ma-248	482	171	u	u	NOUN
ma-248	482	172	2	2	NUM
ma-248	482	173	0	0	NUM
ma-248	482	174	,	,	PUNCT
ma-248	482	175	u	u	NOUN
ma-248	482	176	3	3	NUM
ma-248	482	177	0	0	NUM
ma-248	482	178	(	(	PUNCT
ma-248	482	179	c	c	NOUN
ma-248	482	180	)	)	PUNCT
ma-248	482	181	0	0	NUM
ma-248	482	182	20	20	NUM
ma-248	482	183	40	40	NUM
ma-248	482	184	60	60	NUM
ma-248	482	185	80	80	NUM
ma-248	482	186	100	100	NUM
ma-248	482	187	120	120	NUM
ma-248	482	188	140	140	NUM
ma-248	482	189	160	160	NUM
ma-248	482	190	180	180	NUM
ma-248	482	191	time	time	NOUN
ma-248	482	192	(	(	PUNCT
ma-248	482	193	days	day	NOUN
ma-248	482	194	)	)	PUNCT
ma-248	482	195	0.25	0.25	NUM
ma-248	482	196	0.3	0.3	NUM
ma-248	482	197	0.35	0.35	NUM
ma-248	482	198	0.4	0.4	NUM
ma-248	482	199	0.45	0.45	NUM
ma-248	482	200	0.5	0.5	NUM
ma-248	482	201	0.55	0.55	NUM
ma-248	482	202	0.6	0.6	NUM
ma-248	482	203	0.65	0.65	NUM
ma-248	482	204	0.7	0.7	NUM
ma-248	482	205	0.75	0.75	NUM
ma-248	482	206	c	c	NOUN
ma-248	482	207	on	on	ADP
ma-248	482	208	tr	tr	VERB
ma-248	482	209	ol	ol	PROPN
ma-248	482	210	p	p	PROPN
ma-248	482	211	ro	ro	X
ma-248	482	212	fil	fil	X
ma-248	482	213	e	e	NOUN
ma-248	482	214	u	u	PROPN
ma-248	482	215	2	2	NUM
ma-248	482	216	u	u	NOUN
ma-248	482	217	3	3	NUM
ma-248	482	218	(	(	PUNCT
ma-248	482	219	d	d	NOUN
ma-248	482	220	)	)	PUNCT
ma-248	482	221	figure	figure	NOUN
ma-248	482	222	4	4	NUM
ma-248	482	223	.	.	PUNCT
ma-248	482	224	plot	plot	NOUN
ma-248	482	225	of	of	ADP
ma-248	482	226	phase	phase	NOUN
ma-248	482	227	portraits	portrait	NOUN
ma-248	482	228	with	with	ADP
ma-248	482	229	u1	u1	NOUN
ma-248	482	230	=	=	SYM
ma-248	482	231	0	0	NUM
ma-248	482	232	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	482	233	eur	eur	PROPN
ma-248	482	234	.	.	PUNCT
ma-248	483	1	j.	j.	PROPN
ma-248	483	2	math	math	PROPN
ma-248	483	3	.	.	PUNCT
ma-248	484	1	anal	anal	PROPN
ma-248	484	2	.	.	PUNCT
ma-248	485	1	10.28924	10.28924	NUM
ma-248	485	2	/	/	SYM
ma-248	485	3	ada	ada	PROPN
ma-248	485	4	/	/	SYM
ma-248	485	5	ma.4.21	ma.4.21	NOUN
ma-248	485	6	22	22	NUM
ma-248	485	7	20	20	NUM
ma-248	485	8	days	day	NOUN
ma-248	485	9	to	to	ADP
ma-248	485	10	4500	4500	NUM
ma-248	485	11	and	and	CCONJ
ma-248	485	12	then	then	ADV
ma-248	485	13	smoothly	smoothly	ADV
ma-248	485	14	progressed	progress	VERB
ma-248	485	15	to	to	ADP
ma-248	485	16	5000	5000	NUM
ma-248	485	17	for	for	ADP
ma-248	485	18	the	the	DET
ma-248	485	19	next	next	ADJ
ma-248	485	20	100	100	NUM
ma-248	485	21	days	day	NOUN
ma-248	485	22	and	and	CCONJ
ma-248	485	23	maintained	maintain	VERB
ma-248	485	24	thelevel	thelevel	NOUN
ma-248	485	25	.	.	PUNCT
ma-248	486	1	the	the	DET
ma-248	486	2	symptomatic	symptomatic	ADJ
ma-248	486	3	level	level	NOUN
ma-248	486	4	gradually	gradually	ADV
ma-248	486	5	rose	rise	VERB
ma-248	486	6	from	from	ADP
ma-248	486	7	10	10	NUM
ma-248	486	8	in	in	ADP
ma-248	486	9	a	a	DET
ma-248	486	10	day	day	NOUN
ma-248	486	11	(	(	PUNCT
ma-248	486	12	1	1	NUM
ma-248	486	13	)	)	PUNCT
ma-248	486	14	to	to	ADP
ma-248	486	15	430	430	NUM
ma-248	486	16	in	in	ADP
ma-248	486	17	180	180	NUM
ma-248	486	18	days	day	NOUN
ma-248	486	19	.	.	PUNCT
ma-248	487	1	with	with	ADP
ma-248	487	2	thecontrol	thecontrol	NOUN
ma-248	487	3	application	application	NOUN
ma-248	487	4	,	,	PUNCT
ma-248	487	5	witnessed	witness	VERB
ma-248	487	6	the	the	DET
ma-248	487	7	exposure	exposure	NOUN
ma-248	487	8	raised	raise	VERB
ma-248	487	9	1000	1000	NUM
ma-248	487	10	to	to	ADP
ma-248	487	11	1900	1900	NUM
ma-248	487	12	in	in	ADP
ma-248	487	13	180	180	NUM
ma-248	487	14	days	day	NOUN
ma-248	487	15	.	.	PUNCT
ma-248	488	1	the	the	PRON
ma-248	488	2	asymptomaticslightly	asymptomaticslightly	ADV
ma-248	488	3	raised	raise	VERB
ma-248	488	4	slightly	slightly	ADV
ma-248	488	5	below	below	ADP
ma-248	488	6	500	500	NUM
ma-248	488	7	for	for	ADP
ma-248	488	8	the	the	DET
ma-248	488	9	1180	1180	NUM
ma-248	488	10	days	day	NOUN
ma-248	488	11	.	.	PUNCT
ma-248	489	1	the	the	DET
ma-248	489	2	symptoms	symptom	NOUN
ma-248	489	3	could	could	AUX
ma-248	489	4	barely	barely	ADV
ma-248	489	5	move	move	VERB
ma-248	489	6	above	above	ADP
ma-248	489	7	10.plot	10.plot	NUM
ma-248	489	8	4d	4d	NUM
ma-248	489	9	is	be	AUX
ma-248	489	10	the	the	DET
ma-248	489	11	control	control	NOUN
ma-248	489	12	profile	profile	NOUN
ma-248	489	13	plot	plot	NOUN
ma-248	489	14	of	of	ADP
ma-248	489	15	strategy	strategy	NOUN
ma-248	489	16	d	d	NOUN
ma-248	489	17	,	,	PUNCT
ma-248	489	18	we	we	PRON
ma-248	489	19	notice	notice	VERB
ma-248	489	20	from	from	ADP
ma-248	489	21	the	the	DET
ma-248	489	22	control	control	NOUN
ma-248	489	23	plot	plot	NOUN
ma-248	489	24	that	that	SCONJ
ma-248	489	25	the	the	DET
ma-248	489	26	personalprotection	personalprotection	NOUN
ma-248	489	27	,	,	PUNCT
ma-248	489	28	vaccination	vaccination	NOUN
ma-248	489	29	and	and	CCONJ
ma-248	489	30	treatment	treatment	NOUN
ma-248	489	31	controls	control	NOUN
ma-248	489	32	remained	remain	VERB
ma-248	489	33	at	at	ADP
ma-248	489	34	the	the	DET
ma-248	489	35	upper	upper	ADJ
ma-248	489	36	bound	bind	VERB
ma-248	489	37	until	until	ADP
ma-248	489	38	180	180	NUM
ma-248	489	39	,	,	PUNCT
ma-248	489	40	178	178	NUM
ma-248	489	41	,	,	PUNCT
ma-248	489	42	and177	and177	PROPN
ma-248	489	43	respectively	respectively	ADV
ma-248	489	44	when	when	SCONJ
ma-248	489	45	they	they	PRON
ma-248	489	46	dropped	drop	VERB
ma-248	489	47	to	to	ADP
ma-248	489	48	the	the	DET
ma-248	489	49	lower	lower	ADV
ma-248	489	50	bound	bind	VERB
ma-248	489	51	.	.	PUNCT
ma-248	490	1	7	7	X
ma-248	490	2	.	.	X
ma-248	490	3	discussion	discussion	NOUN
ma-248	490	4	and	and	CCONJ
ma-248	490	5	conclusion	conclusion	NOUN
ma-248	490	6	the	the	DET
ma-248	490	7	study	study	NOUN
ma-248	490	8	considered	consider	VERB
ma-248	490	9	a	a	DET
ma-248	490	10	non	non	ADJ
ma-248	490	11	-	-	ADJ
ma-248	490	12	linear	linear	ADJ
ma-248	490	13	compartmental	compartmental	ADJ
ma-248	490	14	model	model	NOUN
ma-248	490	15	of	of	ADP
ma-248	490	16	meningitis	meningitis	NOUN
ma-248	490	17	disease	disease	NOUN
ma-248	490	18	to	to	PART
ma-248	490	19	explain	explain	VERB
ma-248	490	20	thetransmission	thetransmission	NOUN
ma-248	490	21	dynamics	dynamic	NOUN
ma-248	490	22	.	.	PUNCT
ma-248	491	1	the	the	DET
ma-248	491	2	compartmental	compartmental	ADJ
ma-248	491	3	meningitis	meningitis	NOUN
ma-248	491	4	model	model	NOUN
ma-248	491	5	was	be	AUX
ma-248	491	6	presented	present	VERB
ma-248	491	7	,	,	PUNCT
ma-248	491	8	with	with	ADP
ma-248	491	9	compartmentsfor	compartmentsfor	PROPN
ma-248	491	10	susceptible(s	susceptible(s	PROPN
ma-248	491	11	)	)	PUNCT
ma-248	491	12	,	,	PUNCT
ma-248	491	13	exposed(e	exposed(e	PROPN
ma-248	491	14	)	)	PUNCT
ma-248	491	15	,	,	PUNCT
ma-248	491	16	asymptomatic(a	asymptomatic(a	NOUN
ma-248	491	17	)	)	PUNCT
ma-248	491	18	,	,	PUNCT
ma-248	491	19	symptomatic(i	symptomatic(i	PROPN
ma-248	491	20	)	)	PUNCT
ma-248	491	21	,	,	PUNCT
ma-248	491	22	and	and	CCONJ
ma-248	491	23	recovered(r	recovered(r	X
ma-248	491	24	)	)	PUNCT
ma-248	491	25	.	.	PUNCT
ma-248	492	1	the	the	DET
ma-248	492	2	model’sequilibria	model’sequilibria	PROPN
ma-248	492	3	and	and	CCONJ
ma-248	492	4	the	the	DET
ma-248	492	5	basic	basic	ADJ
ma-248	492	6	reproduction	reproduction	NOUN
ma-248	492	7	number	number	NOUN
ma-248	492	8	were	be	AUX
ma-248	492	9	determined	determine	VERB
ma-248	492	10	.	.	PUNCT
ma-248	493	1	the	the	DET
ma-248	493	2	model	model	NOUN
ma-248	493	3	’s	’s	PART
ma-248	493	4	local	local	ADJ
ma-248	493	5	stability	stability	NOUN
ma-248	493	6	at	at	ADP
ma-248	493	7	thetwo	thetwo	NUM
ma-248	493	8	equilibrium	equilibrium	NOUN
ma-248	493	9	points	point	NOUN
ma-248	493	10	,	,	PUNCT
ma-248	493	11	the	the	PRON
ma-248	493	12	disease	disease	NOUN
ma-248	493	13	-	-	PUNCT
ma-248	493	14	free	free	ADJ
ma-248	493	15	and	and	CCONJ
ma-248	493	16	endemic	endemic	ADJ
ma-248	493	17	,	,	PUNCT
ma-248	493	18	was	be	AUX
ma-248	493	19	determined	determine	VERB
ma-248	493	20	by	by	ADP
ma-248	493	21	using	use	VERB
ma-248	493	22	the	the	DET
ma-248	493	23	linearisationapproach	linearisationapproach	NOUN
ma-248	493	24	.	.	PUNCT
ma-248	494	1	the	the	DET
ma-248	494	2	global	global	ADJ
ma-248	494	3	stabilities	stability	NOUN
ma-248	494	4	of	of	ADP
ma-248	494	5	the	the	DET
ma-248	494	6	equilibria	equilibrium	NOUN
ma-248	494	7	were	be	AUX
ma-248	494	8	investigated	investigate	VERB
ma-248	494	9	by	by	ADP
ma-248	494	10	employing	employ	VERB
ma-248	494	11	the	the	DET
ma-248	494	12	geometricmethod	geometricmethod	NOUN
ma-248	494	13	of	of	ADP
ma-248	494	14	the	the	DET
ma-248	494	15	lyapunov	lyapunov	ADJ
ma-248	494	16	function	function	NOUN
ma-248	494	17	.	.	PUNCT
ma-248	495	1	in	in	ADP
ma-248	495	2	addition	addition	NOUN
ma-248	495	3	,	,	PUNCT
ma-248	495	4	a	a	DET
ma-248	495	5	sensitivity	sensitivity	NOUN
ma-248	495	6	analysis	analysis	NOUN
ma-248	495	7	was	be	AUX
ma-248	495	8	carried	carry	VERB
ma-248	495	9	out	out	ADP
ma-248	495	10	on	on	ADP
ma-248	495	11	the	the	DET
ma-248	495	12	r0to	r0to	PUNCT
ma-248	495	13	determine	determine	VERB
ma-248	495	14	the	the	DET
ma-248	495	15	parameters	parameter	NOUN
ma-248	495	16	that	that	PRON
ma-248	495	17	significantly	significantly	ADV
ma-248	495	18	affect	affect	VERB
ma-248	495	19	the	the	DET
ma-248	495	20	r0	r0	NOUN
ma-248	495	21	.	.	PUNCT
ma-248	496	1	it	it	PRON
ma-248	496	2	was	be	AUX
ma-248	496	3	seen	see	VERB
ma-248	496	4	that	that	SCONJ
ma-248	496	5	the	the	DET
ma-248	496	6	most	most	ADJ
ma-248	496	7	sensitiveparameters	sensitiveparameter	NOUN
ma-248	496	8	on	on	ADP
ma-248	496	9	r0	r0	NOUN
ma-248	496	10	are	be	AUX
ma-248	496	11	λ	λ	NOUN
ma-248	496	12	,	,	PUNCT
ma-248	496	13	τ1	τ1	NOUN
ma-248	496	14	,	,	PUNCT
ma-248	496	15	ψ1	ψ1	NOUN
ma-248	496	16	,	,	PUNCT
ma-248	496	17	η1	η1	NOUN
ma-248	496	18	,	,	PUNCT
ma-248	496	19	k1	k1	NOUN
ma-248	496	20	,	,	PUNCT
ma-248	496	21	µ	µ	NOUN
ma-248	496	22	,	,	PUNCT
ma-248	496	23	and	and	CCONJ
ma-248	496	24	ψ2.an	ψ2.an	NOUN
ma-248	496	25	optimal	optimal	ADJ
ma-248	496	26	control	control	NOUN
ma-248	496	27	model	model	NOUN
ma-248	496	28	was	be	AUX
ma-248	496	29	formulated	formulate	VERB
ma-248	496	30	by	by	ADP
ma-248	496	31	adding	add	VERB
ma-248	496	32	time	time	NOUN
ma-248	496	33	-	-	PUNCT
ma-248	496	34	dependent	dependent	ADJ
ma-248	496	35	optimal	optimal	ADJ
ma-248	496	36	controls	control	NOUN
ma-248	496	37	.	.	PUNCT
ma-248	497	1	by	by	ADP
ma-248	497	2	defin	defin	NOUN
ma-248	497	3	-	-	PUNCT
ma-248	497	4	ing	ing	ADJ
ma-248	497	5	time	time	NOUN
ma-248	497	6	-	-	PUNCT
ma-248	497	7	dependent	dependent	ADJ
ma-248	497	8	policies	policy	NOUN
ma-248	497	9	that	that	PRON
ma-248	497	10	might	might	AUX
ma-248	497	11	help	help	VERB
ma-248	497	12	decrease	decrease	VERB
ma-248	497	13	or	or	CCONJ
ma-248	497	14	eradicate	eradicate	VERB
ma-248	497	15	the	the	DET
ma-248	497	16	disease	disease	NOUN
ma-248	497	17	,	,	PUNCT
ma-248	497	18	the	the	DET
ma-248	497	19	model	model	NOUN
ma-248	497	20	waschanged	waschange	VERB
ma-248	497	21	into	into	ADP
ma-248	497	22	an	an	DET
ma-248	497	23	optimal	optimal	ADJ
ma-248	497	24	control	control	NOUN
ma-248	497	25	problem	problem	NOUN
ma-248	497	26	.	.	PUNCT
ma-248	498	1	to	to	PART
ma-248	498	2	discover	discover	VERB
ma-248	498	3	the	the	DET
ma-248	498	4	optimality	optimality	NOUN
ma-248	498	5	conditions	condition	NOUN
ma-248	498	6	of	of	ADP
ma-248	498	7	the	the	DET
ma-248	498	8	systems	system	NOUN
ma-248	498	9	,	,	PUNCT
ma-248	498	10	thecontrol	thecontrol	NOUN
ma-248	498	11	model	model	NOUN
ma-248	498	12	was	be	AUX
ma-248	498	13	solved	solve	VERB
ma-248	498	14	using	use	VERB
ma-248	498	15	pontryagin	pontryagin	NOUN
ma-248	498	16	’s	’s	PART
ma-248	498	17	maximum	maximum	ADJ
ma-248	498	18	principle	principle	NOUN
ma-248	498	19	.	.	PUNCT
ma-248	499	1	several	several	ADJ
ma-248	499	2	works	work	NOUN
ma-248	499	3	have	have	AUX
ma-248	499	4	been	be	AUX
ma-248	499	5	done	do	VERB
ma-248	499	6	onmeningitis	onmeningitis	NOUN
ma-248	499	7	transmission	transmission	NOUN
ma-248	499	8	,	,	PUNCT
ma-248	499	9	but	but	CCONJ
ma-248	499	10	few	few	ADJ
ma-248	499	11	have	have	AUX
ma-248	499	12	considered	consider	VERB
ma-248	499	13	optimal	optimal	ADJ
ma-248	499	14	control	control	NOUN
ma-248	499	15	.	.	PUNCT
ma-248	500	1	as	as	ADP
ma-248	500	2	a	a	DET
ma-248	500	3	result	result	NOUN
ma-248	500	4	,	,	PUNCT
ma-248	500	5	we	we	PRON
ma-248	500	6	formulated	formulate	VERB
ma-248	500	7	themeningitis	themeningitis	PROPN
ma-248	500	8	model	model	NOUN
ma-248	500	9	that	that	PRON
ma-248	500	10	was	be	AUX
ma-248	500	11	modified	modify	VERB
ma-248	500	12	to	to	ADP
ma-248	500	13	optimal	optimal	ADJ
ma-248	500	14	control	control	NOUN
ma-248	500	15	problems	problem	NOUN
ma-248	500	16	to	to	PART
ma-248	500	17	characterise	characterise	VERB
ma-248	500	18	a	a	DET
ma-248	500	19	range	range	NOUN
ma-248	500	20	of	of	ADP
ma-248	500	21	possiblestrategies	possiblestrategie	NOUN
ma-248	500	22	to	to	PART
ma-248	500	23	help	help	VERB
ma-248	500	24	control	control	VERB
ma-248	500	25	the	the	DET
ma-248	500	26	disease	disease	NOUN
ma-248	500	27	.	.	PUNCT
ma-248	501	1	therefore	therefore	ADV
ma-248	501	2	,	,	PUNCT
ma-248	501	3	we	we	PRON
ma-248	501	4	considered	consider	VERB
ma-248	501	5	possible	possible	ADJ
ma-248	501	6	pairing	pairing	NOUN
ma-248	501	7	of	of	ADP
ma-248	501	8	the	the	DET
ma-248	501	9	controls	control	NOUN
ma-248	501	10	toexamine	toexamine	VERB
ma-248	501	11	their	their	PRON
ma-248	501	12	combined	combine	VERB
ma-248	501	13	effect	effect	NOUN
ma-248	501	14	on	on	ADP
ma-248	501	15	the	the	DET
ma-248	501	16	disease.with	disease.with	PROPN
ma-248	501	17	strategy	strategy	NOUN
ma-248	501	18	a	a	PRON
ma-248	501	19	,	,	PUNCT
ma-248	501	20	the	the	DET
ma-248	501	21	controls	control	NOUN
ma-248	501	22	of	of	ADP
ma-248	501	23	personal	personal	ADJ
ma-248	501	24	protection	protection	NOUN
ma-248	501	25	and	and	CCONJ
ma-248	501	26	vaccination	vaccination	NOUN
ma-248	501	27	were	be	AUX
ma-248	501	28	considered	consider	VERB
ma-248	501	29	.	.	PUNCT
ma-248	502	1	thegraphs	thegraph	NOUN
ma-248	502	2	of	of	ADP
ma-248	502	3	2a	2a	NUM
ma-248	502	4	,	,	PUNCT
ma-248	502	5	2b	2b	NOUN
ma-248	502	6	,	,	PUNCT
ma-248	502	7	2c	2c	NUM
ma-248	502	8	,	,	PUNCT
ma-248	502	9	and	and	CCONJ
ma-248	502	10	2d	2d	NOUN
ma-248	502	11	denote	denote	VERB
ma-248	502	12	the	the	DET
ma-248	502	13	exposed	expose	VERB
ma-248	502	14	,	,	PUNCT
ma-248	502	15	asymptomatic	asymptomatic	ADJ
ma-248	502	16	and	and	CCONJ
ma-248	502	17	symptomatic	symptomatic	ADJ
ma-248	502	18	individuals	individual	NOUN
ma-248	502	19	andthe	andthe	PROPN
ma-248	502	20	control	control	NOUN
ma-248	502	21	profile	profile	NOUN
ma-248	502	22	.	.	PUNCT
ma-248	503	1	without	without	ADP
ma-248	503	2	control	control	NOUN
ma-248	503	3	,	,	PUNCT
ma-248	503	4	the	the	DET
ma-248	503	5	graph	graph	NOUN
ma-248	503	6	of	of	ADP
ma-248	503	7	2a	2a	NUM
ma-248	503	8	showed	show	VERB
ma-248	503	9	a	a	DET
ma-248	503	10	swift	swift	ADJ
ma-248	503	11	increase	increase	NOUN
ma-248	503	12	of	of	ADP
ma-248	503	13	an	an	DET
ma-248	503	14	estimated	estimate	VERB
ma-248	503	15	5000	5000	NUM
ma-248	503	16	in	in	ADP
ma-248	503	17	the	the	DET
ma-248	503	18	first	first	ADJ
ma-248	503	19	20	20	NUM
ma-248	503	20	days	day	NOUN
ma-248	503	21	.	.	PUNCT
ma-248	504	1	moreover	moreover	ADV
ma-248	504	2	,	,	PUNCT
ma-248	504	3	it	it	PRON
ma-248	504	4	remained	remain	VERB
ma-248	504	5	at	at	ADP
ma-248	504	6	this	this	DET
ma-248	504	7	level	level	NOUN
ma-248	504	8	throughout	throughout	ADP
ma-248	504	9	the	the	DET
ma-248	504	10	remaining	remain	VERB
ma-248	504	11	simulated	simulate	VERB
ma-248	504	12	time.with	time.with	ADP
ma-248	504	13	the	the	DET
ma-248	504	14	asymptomatic	asymptomatic	ADJ
ma-248	504	15	non	non	ADJ
ma-248	504	16	-	-	ADJ
ma-248	504	17	control	control	ADJ
ma-248	504	18	graph	graph	NOUN
ma-248	504	19	of	of	ADP
ma-248	504	20	2b	2b	NUM
ma-248	504	21	,	,	PUNCT
ma-248	504	22	we	we	PRON
ma-248	504	23	notice	notice	VERB
ma-248	504	24	a	a	DET
ma-248	504	25	gentle	gentle	ADJ
ma-248	504	26	rise	rise	NOUN
ma-248	504	27	of	of	ADP
ma-248	504	28	the	the	DET
ma-248	504	29	graph	graph	NOUN
ma-248	504	30	in	in	ADP
ma-248	504	31	the	the	DET
ma-248	504	32	first	first	ADJ
ma-248	504	33	20	20	NUM
ma-248	504	34	days	day	NOUN
ma-248	504	35	to	to	ADP
ma-248	504	36	4300	4300	NUM
ma-248	504	37	of	of	ADP
ma-248	504	38	the	the	DET
ma-248	504	39	asymptomatic	asymptomatic	ADJ
ma-248	504	40	population	population	NOUN
ma-248	504	41	.	.	PUNCT
ma-248	505	1	the	the	DET
ma-248	505	2	asymptomatic	asymptomatic	ADJ
ma-248	505	3	control	control	NOUN
ma-248	505	4	graph	graph	NOUN
ma-248	505	5	progressedsteadily	progressedsteadily	ADV
ma-248	505	6	to	to	ADP
ma-248	505	7	a	a	DET
ma-248	505	8	new	new	ADJ
ma-248	505	9	level	level	NOUN
ma-248	505	10	of	of	ADP
ma-248	505	11	5000	5000	NUM
ma-248	505	12	in	in	ADP
ma-248	505	13	140	140	NUM
ma-248	505	14	days	day	NOUN
ma-248	505	15	and	and	CCONJ
ma-248	505	16	retained	retain	VERB
ma-248	505	17	at	at	ADP
ma-248	505	18	that	that	DET
ma-248	505	19	level	level	NOUN
ma-248	505	20	till	till	SCONJ
ma-248	505	21	the	the	DET
ma-248	505	22	end	end	NOUN
ma-248	505	23	of	of	ADP
ma-248	505	24	the	the	DET
ma-248	505	25	simulation.the	simulation.the	DET
ma-248	505	26	symptomatic	symptomatic	ADJ
ma-248	505	27	non	non	ADJ
ma-248	505	28	-	-	ADJ
ma-248	505	29	control	control	ADJ
ma-248	505	30	graph	graph	NOUN
ma-248	505	31	of2c	of2c	PROPN
ma-248	505	32	increased	increase	VERB
ma-248	505	33	smoothly	smoothly	ADV
ma-248	505	34	and	and	CCONJ
ma-248	505	35	moved	move	VERB
ma-248	505	36	to	to	ADP
ma-248	505	37	the	the	DET
ma-248	505	38	maximum	maximum	ADJ
ma-248	505	39	height	height	NOUN
ma-248	505	40	of	of	ADP
ma-248	505	41	430	430	NUM
ma-248	505	42	of	of	ADP
ma-248	505	43	the	the	DET
ma-248	505	44	symptomatic	symptomatic	ADJ
ma-248	505	45	population	population	NOUN
ma-248	505	46	in	in	ADP
ma-248	505	47	130	130	NUM
ma-248	505	48	days	day	NOUN
ma-248	505	49	,	,	PUNCT
ma-248	505	50	which	which	PRON
ma-248	505	51	remained	remain	VERB
ma-248	505	52	until	until	ADP
ma-248	505	53	the	the	DET
ma-248	505	54	end	end	NOUN
ma-248	505	55	of	of	ADP
ma-248	505	56	the	the	DET
ma-248	505	57	simulation.control	simulation.control	NOUN
ma-248	505	58	figures	figure	NOUN
ma-248	505	59	of	of	ADP
ma-248	505	60	the	the	DET
ma-248	505	61	exposed	expose	VERB
ma-248	505	62	,	,	PUNCT
ma-248	505	63	asymptomatic	asymptomatic	ADJ
ma-248	505	64	and	and	CCONJ
ma-248	505	65	symptomatic	symptomatic	ADJ
ma-248	505	66	produced	produce	VERB
ma-248	505	67	results	result	NOUN
ma-248	505	68	with	with	ADP
ma-248	505	69	substantiallyminimized	substantiallyminimized	ADJ
ma-248	505	70	graphs	graph	NOUN
ma-248	505	71	.	.	PUNCT
ma-248	506	1	from	from	ADP
ma-248	506	2	the	the	DET
ma-248	506	3	exposed	expose	VERB
ma-248	506	4	graph	graph	NOUN
ma-248	506	5	of	of	ADP
ma-248	506	6	2c	2c	NUM
ma-248	506	7	,	,	PUNCT
ma-248	506	8	the	the	DET
ma-248	506	9	graph	graph	NOUN
ma-248	506	10	increases	increase	VERB
ma-248	506	11	similarly	similarly	ADV
ma-248	506	12	but	but	CCONJ
ma-248	506	13	could	could	AUX
ma-248	506	14	not	not	PART
ma-248	506	15	rise	rise	VERB
ma-248	506	16	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	506	17	eur	eur	PROPN
ma-248	506	18	.	.	PUNCT
ma-248	507	1	j.	j.	PROPN
ma-248	507	2	math	math	PROPN
ma-248	507	3	.	.	PUNCT
ma-248	508	1	anal	anal	PROPN
ma-248	508	2	.	.	PUNCT
ma-248	509	1	10.28924	10.28924	NUM
ma-248	509	2	/	/	SYM
ma-248	509	3	ada	ada	PROPN
ma-248	509	4	/	/	SYM
ma-248	509	5	ma.4.21	ma.4.21	NOUN
ma-248	510	1	23	23	NUM
ma-248	510	2	0	0	NUM
ma-248	510	3	20	20	NUM
ma-248	510	4	40	40	NUM
ma-248	510	5	60	60	NUM
ma-248	510	6	80	80	NUM
ma-248	510	7	100	100	NUM
ma-248	510	8	120	120	NUM
ma-248	510	9	140	140	NUM
ma-248	510	10	160	160	NUM
ma-248	510	11	180	180	NUM
ma-248	510	12	time	time	NOUN
ma-248	510	13	(	(	PUNCT
ma-248	510	14	days	day	NOUN
ma-248	510	15	)	)	PUNCT
ma-248	510	16	0	0	NUM
ma-248	510	17	1000	1000	NUM
ma-248	510	18	2000	2000	NUM
ma-248	510	19	3000	3000	NUM
ma-248	510	20	4000	4000	NUM
ma-248	510	21	5000	5000	NUM
ma-248	510	22	6000	6000	NUM
ma-248	510	23	e	e	NOUN
ma-248	510	24	xp	xp	ADV
ma-248	510	25	os	os	INTJ
ma-248	510	26	ed	ed	PROPN
ma-248	510	27	u	u	NOUN
ma-248	510	28	1	1	NUM
ma-248	510	29	=	=	SYM
ma-248	510	30	0	0	NUM
ma-248	510	31	,	,	PUNCT
ma-248	510	32	u	u	NOUN
ma-248	510	33	2	2	NUM
ma-248	510	34	=	=	SYM
ma-248	510	35	0	0	NUM
ma-248	510	36	,	,	PUNCT
ma-248	510	37	u	u	NOUN
ma-248	510	38	3	3	NUM
ma-248	510	39	=	=	SYM
ma-248	510	40	0	0	NUM
ma-248	510	41	u	u	NOUN
ma-248	510	42	1	1	NUM
ma-248	510	43	0	0	NUM
ma-248	510	44	,	,	PUNCT
ma-248	510	45	u	u	NOUN
ma-248	510	46	2	2	NUM
ma-248	510	47	0	0	NUM
ma-248	510	48	,	,	PUNCT
ma-248	510	49	u	u	NOUN
ma-248	510	50	3	3	NUM
ma-248	510	51	0	0	NUM
ma-248	510	52	(	(	PUNCT
ma-248	510	53	a	a	NOUN
ma-248	510	54	)	)	PUNCT
ma-248	510	55	0	0	NUM
ma-248	510	56	20	20	NUM
ma-248	510	57	40	40	NUM
ma-248	510	58	60	60	NUM
ma-248	510	59	80	80	NUM
ma-248	510	60	100	100	NUM
ma-248	510	61	120	120	NUM
ma-248	510	62	140	140	NUM
ma-248	510	63	160	160	NUM
ma-248	510	64	180	180	NUM
ma-248	510	65	time	time	NOUN
ma-248	510	66	(	(	PUNCT
ma-248	510	67	days	day	NOUN
ma-248	510	68	)	)	PUNCT
ma-248	510	69	0	0	NUM
ma-248	511	1	500	500	NUM
ma-248	511	2	1000	1000	NUM
ma-248	511	3	1500	1500	NUM
ma-248	511	4	2000	2000	NUM
ma-248	511	5	2500	2500	NUM
ma-248	511	6	3000	3000	NUM
ma-248	511	7	3500	3500	NUM
ma-248	511	8	4000	4000	NUM
ma-248	511	9	4500	4500	NUM
ma-248	511	10	5000	5000	NUM
ma-248	511	11	a	a	DET
ma-248	511	12	sy	sy	NOUN
ma-248	511	13	m	m	ADJ
ma-248	511	14	pt	pt	NOUN
ma-248	511	15	om	om	NOUN
ma-248	511	16	at	at	ADP
ma-248	511	17	ic	ic	PROPN
ma-248	511	18	u	u	NOUN
ma-248	511	19	1	1	NUM
ma-248	511	20	=	=	SYM
ma-248	511	21	0	0	NUM
ma-248	511	22	,	,	PUNCT
ma-248	511	23	u	u	NOUN
ma-248	511	24	2	2	NUM
ma-248	511	25	=	=	SYM
ma-248	511	26	0	0	NUM
ma-248	511	27	,	,	PUNCT
ma-248	511	28	u	u	NOUN
ma-248	511	29	3	3	NUM
ma-248	511	30	=	=	SYM
ma-248	511	31	0	0	NUM
ma-248	511	32	u	u	NOUN
ma-248	511	33	1	1	NUM
ma-248	511	34	0	0	NUM
ma-248	511	35	,	,	PUNCT
ma-248	511	36	u	u	NOUN
ma-248	511	37	2	2	NUM
ma-248	511	38	0	0	NUM
ma-248	511	39	,	,	PUNCT
ma-248	511	40	u	u	NOUN
ma-248	511	41	3	3	NUM
ma-248	511	42	0	0	NUM
ma-248	511	43	(	(	PUNCT
ma-248	511	44	b	b	NOUN
ma-248	511	45	)	)	PUNCT
ma-248	511	46	0	0	NUM
ma-248	511	47	20	20	NUM
ma-248	511	48	40	40	NUM
ma-248	511	49	60	60	NUM
ma-248	511	50	80	80	NUM
ma-248	511	51	100	100	NUM
ma-248	511	52	120	120	NUM
ma-248	511	53	140	140	NUM
ma-248	511	54	160	160	NUM
ma-248	511	55	180	180	NUM
ma-248	511	56	time	time	NOUN
ma-248	511	57	(	(	PUNCT
ma-248	511	58	days	day	NOUN
ma-248	511	59	)	)	PUNCT
ma-248	511	60	0	0	NUM
ma-248	511	61	50	50	NUM
ma-248	511	62	100	100	NUM
ma-248	511	63	150	150	NUM
ma-248	511	64	200	200	NUM
ma-248	511	65	250	250	NUM
ma-248	511	66	300	300	NUM
ma-248	511	67	350	350	NUM
ma-248	511	68	400	400	NUM
ma-248	511	69	450	450	NUM
ma-248	511	70	s	s	NOUN
ma-248	511	71	ym	ym	INTJ
ma-248	511	72	pt	pt	NOUN
ma-248	511	73	om	om	PROPN
ma-248	511	74	at	at	ADP
ma-248	511	75	ic	ic	PROPN
ma-248	511	76	u	u	NOUN
ma-248	511	77	1	1	NUM
ma-248	511	78	=	=	SYM
ma-248	511	79	0	0	NUM
ma-248	511	80	,	,	PUNCT
ma-248	511	81	u	u	NOUN
ma-248	511	82	2	2	NUM
ma-248	511	83	=	=	SYM
ma-248	511	84	0	0	NUM
ma-248	511	85	,	,	PUNCT
ma-248	511	86	u	u	NOUN
ma-248	511	87	3	3	NUM
ma-248	511	88	=	=	SYM
ma-248	511	89	0	0	NUM
ma-248	511	90	u	u	NOUN
ma-248	511	91	1	1	NUM
ma-248	511	92	0	0	NUM
ma-248	511	93	,	,	PUNCT
ma-248	511	94	u	u	NOUN
ma-248	511	95	2	2	NUM
ma-248	511	96	0	0	NUM
ma-248	511	97	,	,	PUNCT
ma-248	511	98	u	u	NOUN
ma-248	511	99	3	3	NUM
ma-248	511	100	0	0	NUM
ma-248	511	101	(	(	PUNCT
ma-248	511	102	c	c	NOUN
ma-248	511	103	)	)	PUNCT
ma-248	511	104	0	0	NUM
ma-248	511	105	20	20	NUM
ma-248	511	106	40	40	NUM
ma-248	511	107	60	60	NUM
ma-248	511	108	80	80	NUM
ma-248	511	109	100	100	NUM
ma-248	511	110	120	120	NUM
ma-248	511	111	140	140	NUM
ma-248	511	112	160	160	NUM
ma-248	511	113	180	180	NUM
ma-248	511	114	time	time	NOUN
ma-248	511	115	(	(	PUNCT
ma-248	511	116	days	day	NOUN
ma-248	511	117	)	)	PUNCT
ma-248	511	118	0.25	0.25	NUM
ma-248	511	119	0.3	0.3	NUM
ma-248	511	120	0.35	0.35	NUM
ma-248	511	121	0.4	0.4	NUM
ma-248	511	122	0.45	0.45	NUM
ma-248	511	123	0.5	0.5	NUM
ma-248	511	124	0.55	0.55	NUM
ma-248	511	125	0.6	0.6	NUM
ma-248	511	126	0.65	0.65	NUM
ma-248	511	127	0.7	0.7	NUM
ma-248	511	128	0.75	0.75	NUM
ma-248	511	129	c	c	NOUN
ma-248	511	130	on	on	ADP
ma-248	511	131	tr	tr	VERB
ma-248	511	132	ol	ol	PROPN
ma-248	511	133	p	p	PROPN
ma-248	511	134	ro	ro	X
ma-248	511	135	fil	fil	X
ma-248	511	136	e	e	PART
ma-248	511	137	u	u	PROPN
ma-248	511	138	1	1	NUM
ma-248	511	139	u	u	NOUN
ma-248	511	140	2	2	NUM
ma-248	511	141	u	u	NOUN
ma-248	511	142	3	3	NUM
ma-248	511	143	(	(	PUNCT
ma-248	511	144	d	d	NOUN
ma-248	511	145	)	)	PUNCT
ma-248	511	146	figure	figure	NOUN
ma-248	511	147	5	5	NUM
ma-248	511	148	.	.	PUNCT
ma-248	511	149	plot	plot	NOUN
ma-248	511	150	of	of	ADP
ma-248	511	151	phase	phase	NOUN
ma-248	511	152	portraits	portrait	NOUN
ma-248	511	153	with	with	ADP
ma-248	511	154	u1	u1	NOUN
ma-248	511	155	6=	6=	ADP
ma-248	511	156	0,u2	0,u2	PRON
ma-248	511	157	6=	6=	SYM
ma-248	511	158	0	0	NUM
ma-248	511	159	and	and	CCONJ
ma-248	511	160	u3	u3	PROPN
ma-248	511	161	6=	6=	ADP
ma-248	511	162	0	0	NUM
ma-248	511	163	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	511	164	eur	eur	PROPN
ma-248	511	165	.	.	PUNCT
ma-248	512	1	j.	j.	PROPN
ma-248	512	2	math	math	PROPN
ma-248	512	3	.	.	PUNCT
ma-248	513	1	anal	anal	PROPN
ma-248	513	2	.	.	PUNCT
ma-248	514	1	10.28924	10.28924	NUM
ma-248	514	2	/	/	SYM
ma-248	514	3	ada	ada	PROPN
ma-248	514	4	/	/	SYM
ma-248	514	5	ma.4.21	ma.4.21	PROPN
ma-248	514	6	24to	24to	NOUN
ma-248	514	7	the	the	DET
ma-248	514	8	level	level	NOUN
ma-248	514	9	of	of	ADP
ma-248	514	10	the	the	PRON
ma-248	514	11	without	without	ADP
ma-248	514	12	control	control	NOUN
ma-248	514	13	plot	plot	NOUN
ma-248	514	14	.	.	PUNCT
ma-248	515	1	we	we	PRON
ma-248	515	2	see	see	VERB
ma-248	515	3	that	that	SCONJ
ma-248	515	4	the	the	DET
ma-248	515	5	control	control	NOUN
ma-248	515	6	graph	graph	NOUN
ma-248	515	7	has	have	AUX
ma-248	515	8	been	be	AUX
ma-248	515	9	dramaticallyminimized	dramaticallyminimize	VERB
ma-248	515	10	.	.	PUNCT
ma-248	516	1	the	the	DET
ma-248	516	2	control	control	NOUN
ma-248	516	3	figures	figure	VERB
ma-248	516	4	2b	2b	NOUN
ma-248	516	5	of	of	ADP
ma-248	516	6	the	the	DET
ma-248	516	7	asymptomatic	asymptomatic	NOUN
ma-248	516	8	lies	lie	VERB
ma-248	516	9	far	far	ADV
ma-248	516	10	below	below	ADP
ma-248	516	11	the	the	DET
ma-248	516	12	non	non	ADJ
ma-248	516	13	-	-	ADJ
ma-248	516	14	control	control	ADJ
ma-248	516	15	figure	figure	NOUN
ma-248	516	16	.	.	PUNCT
ma-248	517	1	thesymptomatic	thesymptomatic	ADJ
ma-248	517	2	control	control	NOUN
ma-248	517	3	figure	figure	NOUN
ma-248	517	4	of	of	ADP
ma-248	517	5	2d	2d	NUM
ma-248	517	6	lay	lie	VERB
ma-248	517	7	slightly	slightly	ADV
ma-248	517	8	above	above	ADP
ma-248	517	9	zero	zero	NUM
ma-248	517	10	and	and	CCONJ
ma-248	517	11	maintained	maintain	VERB
ma-248	517	12	the	the	DET
ma-248	517	13	level	level	NOUN
ma-248	517	14	throughout	throughout	ADP
ma-248	517	15	thesimulated	thesimulate	VERB
ma-248	517	16	time.strategy	time.strategy	PROPN
ma-248	517	17	b	b	NOUN
ma-248	517	18	considered	consider	VERB
ma-248	517	19	personal	personal	ADJ
ma-248	517	20	protection	protection	NOUN
ma-248	517	21	and	and	CCONJ
ma-248	517	22	treatment	treatment	NOUN
ma-248	517	23	control	control	NOUN
ma-248	517	24	.	.	PUNCT
ma-248	518	1	from	from	ADP
ma-248	518	2	the	the	DET
ma-248	518	3	exposed	expose	VERB
ma-248	518	4	graph	graph	NOUN
ma-248	518	5	of2a	of2a	PRON
ma-248	518	6	,	,	PUNCT
ma-248	518	7	we	we	PRON
ma-248	518	8	observed	observe	VERB
ma-248	518	9	that	that	SCONJ
ma-248	518	10	the	the	DET
ma-248	518	11	without	without	SCONJ
ma-248	518	12	control	control	NOUN
ma-248	518	13	curve	curve	NOUN
ma-248	518	14	swiftly	swiftly	ADV
ma-248	518	15	raised	raise	VERB
ma-248	518	16	to	to	ADP
ma-248	518	17	5000	5000	NUM
ma-248	518	18	when	when	SCONJ
ma-248	518	19	t	t	NOUN
ma-248	518	20	=	=	SYM
ma-248	518	21	20	20	NUM
ma-248	518	22	.	.	PUNCT
ma-248	519	1	it	it	PRON
ma-248	519	2	movedgently	movedgently	ADV
ma-248	519	3	to	to	ADP
ma-248	519	4	about	about	ADP
ma-248	519	5	5100	5100	NUM
ma-248	519	6	for	for	ADP
ma-248	519	7	the	the	DET
ma-248	519	8	next	next	ADJ
ma-248	519	9	20	20	NUM
ma-248	519	10	days	day	NOUN
ma-248	519	11	and	and	CCONJ
ma-248	519	12	remained	remain	VERB
ma-248	519	13	at	at	ADP
ma-248	519	14	that	that	DET
ma-248	519	15	level	level	NOUN
ma-248	519	16	for	for	ADP
ma-248	519	17	the	the	DET
ma-248	519	18	remaining	remain	VERB
ma-248	519	19	time	time	NOUN
ma-248	519	20	.	.	PUNCT
ma-248	520	1	theasymptomatic	theasymptomatic	ADJ
ma-248	520	2	without	without	ADP
ma-248	520	3	control	control	NOUN
ma-248	520	4	curve	curve	NOUN
ma-248	520	5	steadily	steadily	ADV
ma-248	520	6	increased	increase	VERB
ma-248	520	7	in	in	ADP
ma-248	520	8	the	the	DET
ma-248	520	9	early	early	ADJ
ma-248	520	10	days	day	NOUN
ma-248	520	11	of	of	ADP
ma-248	520	12	20	20	NUM
ma-248	520	13	to	to	ADP
ma-248	520	14	4500	4500	NUM
ma-248	520	15	,	,	PUNCT
ma-248	520	16	increasedgently	increasedgently	ADV
ma-248	520	17	for	for	ADP
ma-248	520	18	the	the	DET
ma-248	520	19	next	next	ADJ
ma-248	520	20	120	120	NUM
ma-248	520	21	days	day	NOUN
ma-248	520	22	to	to	ADP
ma-248	520	23	5000	5000	NUM
ma-248	520	24	,	,	PUNCT
ma-248	520	25	and	and	CCONJ
ma-248	520	26	maintained	maintain	VERB
ma-248	520	27	the	the	DET
ma-248	520	28	level	level	NOUN
ma-248	520	29	for	for	ADP
ma-248	520	30	the	the	DET
ma-248	520	31	remaining	remain	VERB
ma-248	520	32	time	time	NOUN
ma-248	520	33	.	.	PUNCT
ma-248	521	1	thesymptomatic	thesymptomatic	NOUN
ma-248	521	2	without	without	ADP
ma-248	521	3	control	control	NOUN
ma-248	521	4	graph	graph	NOUN
ma-248	521	5	increased	increase	VERB
ma-248	521	6	smoothly	smoothly	ADV
ma-248	521	7	and	and	CCONJ
ma-248	521	8	progressed	progress	VERB
ma-248	521	9	to	to	ADP
ma-248	521	10	a	a	DET
ma-248	521	11	height	height	NOUN
ma-248	521	12	of	of	ADP
ma-248	521	13	430	430	NUM
ma-248	521	14	at	at	ADP
ma-248	521	15	the	the	DET
ma-248	521	16	finaltime	finaltime	NOUN
ma-248	521	17	.	.	PUNCT
ma-248	522	1	the	the	DET
ma-248	522	2	exposed	expose	VERB
ma-248	522	3	,	,	PUNCT
ma-248	522	4	asymptomatic	asymptomatic	ADJ
ma-248	522	5	and	and	CCONJ
ma-248	522	6	symptomatic	symptomatic	ADJ
ma-248	522	7	control	control	NOUN
ma-248	522	8	graphs	graph	NOUN
ma-248	522	9	produced	produce	VERB
ma-248	522	10	graphs	graph	NOUN
ma-248	522	11	with	with	ADP
ma-248	522	12	desiredresults	desiredresult	NOUN
ma-248	522	13	.	.	PUNCT
ma-248	523	1	thus	thus	ADV
ma-248	523	2	,	,	PUNCT
ma-248	523	3	we	we	PRON
ma-248	523	4	noticed	notice	VERB
ma-248	523	5	a	a	DET
ma-248	523	6	completely	completely	ADV
ma-248	523	7	minimized	minimized	ADJ
ma-248	523	8	exposure	exposure	NOUN
ma-248	523	9	,	,	PUNCT
ma-248	523	10	asymptomatic	asymptomatic	ADJ
ma-248	523	11	and	and	CCONJ
ma-248	523	12	symptomatic	symptomatic	ADJ
ma-248	523	13	,	,	PUNCT
ma-248	523	14	withthe	withthe	ADJ
ma-248	523	15	control	control	NOUN
ma-248	523	16	simulations.strategy	simulations.strategy	PROPN
ma-248	523	17	c	c	NOUN
ma-248	523	18	paired	pair	VERB
ma-248	523	19	the	the	DET
ma-248	523	20	vaccination	vaccination	NOUN
ma-248	523	21	and	and	CCONJ
ma-248	523	22	treatment	treatment	NOUN
ma-248	523	23	controls	control	NOUN
ma-248	523	24	.	.	PUNCT
ma-248	524	1	we	we	PRON
ma-248	524	2	noticed	notice	VERB
ma-248	524	3	that	that	SCONJ
ma-248	524	4	the	the	DET
ma-248	524	5	exposure	exposure	NOUN
ma-248	524	6	surgedswiftly	surgedswiftly	ADV
ma-248	524	7	for	for	ADP
ma-248	524	8	the	the	DET
ma-248	524	9	graphs	graph	NOUN
ma-248	524	10	without	without	ADP
ma-248	524	11	control	control	NOUN
ma-248	524	12	in	in	ADP
ma-248	524	13	the	the	DET
ma-248	524	14	early	early	ADJ
ma-248	524	15	days	day	NOUN
ma-248	524	16	but	but	CCONJ
ma-248	524	17	maintained	maintain	VERB
ma-248	524	18	a	a	DET
ma-248	524	19	stable	stable	ADJ
ma-248	524	20	level	level	NOUN
ma-248	524	21	after	after	SCONJ
ma-248	524	22	40	40	NUM
ma-248	524	23	days.the	days.the	DET
ma-248	524	24	asymptomatic	asymptomatic	ADJ
ma-248	524	25	graph	graph	NOUN
ma-248	524	26	moved	move	VERB
ma-248	524	27	steeply	steeply	ADV
ma-248	524	28	in	in	ADP
ma-248	524	29	the	the	DET
ma-248	524	30	early	early	ADJ
ma-248	524	31	days	day	NOUN
ma-248	524	32	of	of	ADP
ma-248	524	33	20	20	NUM
ma-248	524	34	to	to	ADP
ma-248	524	35	4500	4500	NUM
ma-248	524	36	,	,	PUNCT
ma-248	524	37	increased	increase	VERB
ma-248	524	38	further	far	ADV
ma-248	524	39	to	to	ADP
ma-248	524	40	5000for	5000for	ADP
ma-248	524	41	the	the	DET
ma-248	524	42	next	next	ADJ
ma-248	524	43	120	120	NUM
ma-248	524	44	,	,	PUNCT
ma-248	524	45	and	and	CCONJ
ma-248	524	46	retained	retain	VERB
ma-248	524	47	it	it	PRON
ma-248	524	48	for	for	ADP
ma-248	524	49	the	the	DET
ma-248	524	50	remaining	remain	VERB
ma-248	524	51	days	day	NOUN
ma-248	524	52	.	.	PUNCT
ma-248	525	1	the	the	DET
ma-248	525	2	symptomatic	symptomatic	ADJ
ma-248	525	3	graph	graph	NOUN
ma-248	525	4	gently	gently	ADV
ma-248	525	5	increasedthroughout	increasedthroughout	VERB
ma-248	525	6	the	the	DET
ma-248	525	7	simulation	simulation	NOUN
ma-248	525	8	and	and	CCONJ
ma-248	525	9	maintained	maintain	VERB
ma-248	525	10	a	a	DET
ma-248	525	11	steady	steady	ADJ
ma-248	525	12	progression	progression	NOUN
ma-248	525	13	.	.	PUNCT
ma-248	526	1	the	the	DET
ma-248	526	2	exposed	expose	VERB
ma-248	526	3	control	control	NOUN
ma-248	526	4	plot	plot	NOUN
ma-248	526	5	showeda	showeda	ADJ
ma-248	526	6	swift	swift	ADJ
ma-248	526	7	increase	increase	NOUN
ma-248	526	8	in	in	ADP
ma-248	526	9	the	the	DET
ma-248	526	10	graph	graph	NOUN
ma-248	526	11	in	in	ADP
ma-248	526	12	the	the	DET
ma-248	526	13	early	early	ADJ
ma-248	526	14	days	day	NOUN
ma-248	526	15	and	and	CCONJ
ma-248	526	16	progressed	progress	VERB
ma-248	526	17	gently	gently	ADV
ma-248	526	18	for	for	SCONJ
ma-248	526	19	the	the	DET
ma-248	526	20	entire	entire	ADJ
ma-248	526	21	simulated	simulate	VERB
ma-248	526	22	time.the	time.the	DET
ma-248	526	23	asymptomatic	asymptomatic	ADJ
ma-248	526	24	control	control	NOUN
ma-248	526	25	graph	graph	NOUN
ma-248	526	26	climbed	climb	VERB
ma-248	526	27	gradually	gradually	ADV
ma-248	526	28	in	in	ADP
ma-248	526	29	the	the	DET
ma-248	526	30	early	early	ADJ
ma-248	526	31	days	day	NOUN
ma-248	526	32	and	and	CCONJ
ma-248	526	33	continued	continue	VERB
ma-248	526	34	throughout	throughout	ADP
ma-248	526	35	thesimulation	thesimulation	NOUN
ma-248	526	36	.	.	PUNCT
ma-248	527	1	throughout	throughout	ADP
ma-248	527	2	the	the	DET
ma-248	527	3	simulation	simulation	NOUN
ma-248	527	4	,	,	PUNCT
ma-248	527	5	the	the	DET
ma-248	527	6	symptomatic	symptomatic	ADJ
ma-248	527	7	control	control	NOUN
ma-248	527	8	curve	curve	NOUN
ma-248	527	9	was	be	AUX
ma-248	527	10	found	find	VERB
ma-248	527	11	to	to	PART
ma-248	527	12	be	be	AUX
ma-248	527	13	minimized.strategy	minimized.strategy	NUM
ma-248	527	14	d	d	NOUN
ma-248	527	15	paired	pair	VERB
ma-248	527	16	all	all	DET
ma-248	527	17	three	three	NUM
ma-248	527	18	controls	control	NOUN
ma-248	527	19	.	.	PUNCT
ma-248	528	1	without	without	ADP
ma-248	528	2	control	control	NOUN
ma-248	528	3	,	,	PUNCT
ma-248	528	4	the	the	DET
ma-248	528	5	exposed	expose	VERB
ma-248	528	6	graph	graph	NOUN
ma-248	528	7	rose	rise	VERB
ma-248	528	8	to	to	ADP
ma-248	528	9	2000	2000	NUM
ma-248	528	10	at	at	ADP
ma-248	528	11	t	t	NOUN
ma-248	528	12	=	=	PUNCT
ma-248	528	13	0.the	0.the	DET
ma-248	528	14	graphs	graph	NOUN
ma-248	528	15	increased	increase	VERB
ma-248	528	16	steadily	steadily	ADV
ma-248	528	17	to	to	ADP
ma-248	528	18	5000	5000	NUM
ma-248	528	19	in	in	ADP
ma-248	528	20	day	day	NOUN
ma-248	528	21	20	20	NUM
ma-248	528	22	and	and	CCONJ
ma-248	528	23	then	then	ADV
ma-248	528	24	maintained	maintain	VERB
ma-248	528	25	that	that	DET
ma-248	528	26	level	level	NOUN
ma-248	528	27	for	for	ADP
ma-248	528	28	the	the	DET
ma-248	528	29	rest	rest	NOUN
ma-248	528	30	of	of	ADP
ma-248	528	31	thetime	thetime	NOUN
ma-248	528	32	.	.	PUNCT
ma-248	529	1	the	the	DET
ma-248	529	2	asymptomatic	asymptomatic	ADJ
ma-248	529	3	graph	graph	NOUN
ma-248	529	4	also	also	ADV
ma-248	529	5	increased	increase	VERB
ma-248	529	6	early	early	ADV
ma-248	529	7	in	in	ADP
ma-248	529	8	the	the	DET
ma-248	529	9	first	first	ADJ
ma-248	529	10	20	20	NUM
ma-248	529	11	days	day	NOUN
ma-248	529	12	to	to	ADP
ma-248	529	13	4500	4500	NUM
ma-248	529	14	and	and	CCONJ
ma-248	529	15	then	then	ADV
ma-248	529	16	smoothlyprogressed	smoothlyprogresse	VERB
ma-248	529	17	to	to	ADP
ma-248	529	18	5000	5000	NUM
ma-248	529	19	for	for	ADP
ma-248	529	20	the	the	DET
ma-248	529	21	next	next	ADJ
ma-248	529	22	100	100	NUM
ma-248	529	23	days	day	NOUN
ma-248	529	24	and	and	CCONJ
ma-248	529	25	retained	retain	VERB
ma-248	529	26	the	the	DET
ma-248	529	27	level	level	NOUN
ma-248	529	28	.	.	PUNCT
ma-248	530	1	the	the	DET
ma-248	530	2	symptomatic	symptomatic	ADJ
ma-248	530	3	level	level	NOUN
ma-248	530	4	graduallyrose	graduallyrose	NOUN
ma-248	530	5	from	from	ADP
ma-248	530	6	10	10	NUM
ma-248	530	7	in	in	ADP
ma-248	530	8	a	a	DET
ma-248	530	9	day	day	NOUN
ma-248	530	10	(	(	PUNCT
ma-248	530	11	1	1	NUM
ma-248	530	12	)	)	PUNCT
ma-248	530	13	to	to	ADP
ma-248	530	14	430	430	NUM
ma-248	530	15	in	in	ADP
ma-248	530	16	180	180	NUM
ma-248	530	17	days	day	NOUN
ma-248	530	18	.	.	PUNCT
ma-248	531	1	with	with	ADP
ma-248	531	2	the	the	DET
ma-248	531	3	control	control	NOUN
ma-248	531	4	application	application	NOUN
ma-248	531	5	,	,	PUNCT
ma-248	531	6	we	we	PRON
ma-248	531	7	witnessed	witness	VERB
ma-248	531	8	theexposed	theexposed	PROPN
ma-248	531	9	raised	raise	VERB
ma-248	531	10	1000	1000	NUM
ma-248	531	11	to	to	ADP
ma-248	531	12	1900	1900	NUM
ma-248	531	13	in	in	ADP
ma-248	531	14	180	180	NUM
ma-248	531	15	days	day	NOUN
ma-248	531	16	.	.	PUNCT
ma-248	532	1	the	the	DET
ma-248	532	2	asymptomatic	asymptomatic	NOUN
ma-248	532	3	slightly	slightly	ADV
ma-248	532	4	raised	raise	VERB
ma-248	532	5	slightly	slightly	ADV
ma-248	532	6	below	below	ADP
ma-248	532	7	500for	500for	ADP
ma-248	532	8	the	the	DET
ma-248	532	9	1180	1180	NUM
ma-248	532	10	days	day	NOUN
ma-248	532	11	.	.	PUNCT
ma-248	533	1	the	the	DET
ma-248	533	2	symptomatic	symptomatic	ADJ
ma-248	533	3	could	could	AUX
ma-248	533	4	not	not	PART
ma-248	533	5	move	move	VERB
ma-248	533	6	above	above	ADP
ma-248	533	7	10	10	NUM
ma-248	533	8	.	.	PUNCT
ma-248	534	1	the	the	DET
ma-248	534	2	simulated	simulate	VERB
ma-248	534	3	results	result	NOUN
ma-248	534	4	showed	show	VERB
ma-248	534	5	thatthe	thatthe	NOUN
ma-248	534	6	strategies	strategy	NOUN
ma-248	534	7	significantly	significantly	ADV
ma-248	534	8	minimise	minimise	VERB
ma-248	534	9	the	the	DET
ma-248	534	10	disease	disease	NOUN
ma-248	534	11	.	.	PUNCT
ma-248	535	1	it	it	PRON
ma-248	535	2	can	can	AUX
ma-248	535	3	be	be	AUX
ma-248	535	4	concluded	conclude	VERB
ma-248	535	5	that	that	SCONJ
ma-248	535	6	the	the	DET
ma-248	535	7	combination	combination	NOUN
ma-248	535	8	of	of	ADP
ma-248	535	9	thethree	thethree	NOUN
ma-248	535	10	controls	control	NOUN
ma-248	535	11	or	or	CCONJ
ma-248	535	12	two	two	NUM
ma-248	535	13	controls	control	NOUN
ma-248	535	14	can	can	AUX
ma-248	535	15	be	be	AUX
ma-248	535	16	employed	employ	VERB
ma-248	535	17	when	when	SCONJ
ma-248	535	18	it	it	PRON
ma-248	535	19	comes	come	VERB
ma-248	535	20	to	to	ADP
ma-248	535	21	meningitis	meningitis	PROPN
ma-248	535	22	control	control	NOUN
ma-248	535	23	.	.	PUNCT
ma-248	536	1	a	a	DET
ma-248	536	2	cost	cost	NOUN
ma-248	536	3	-	-	PUNCT
ma-248	536	4	benefitanalysis	benefitanalysis	NOUN
ma-248	536	5	of	of	ADP
ma-248	536	6	the	the	DET
ma-248	536	7	combinations	combination	NOUN
ma-248	536	8	shown	show	VERB
ma-248	536	9	needs	need	NOUN
ma-248	536	10	to	to	PART
ma-248	536	11	be	be	AUX
ma-248	536	12	performed	perform	VERB
ma-248	536	13	.	.	PUNCT
ma-248	537	1	references	reference	NOUN
ma-248	537	2	[	[	X
ma-248	537	3	1	1	X
ma-248	537	4	]	]	PUNCT
ma-248	537	5	j.	j.	PROPN
ma-248	537	6	k.	k.	PROPN
ma-248	537	7	k.	k.	PROPN
ma-248	538	1	asamoah	asamoah	PROPN
ma-248	538	2	,	,	PUNCT
ma-248	538	3	m.a	m.a	PROPN
ma-248	538	4	.	.	PROPN
ma-248	538	5	owusu	owusu	PROPN
ma-248	538	6	,	,	PUNCT
ma-248	538	7	z.	z.	PROPN
ma-248	538	8	jin	jin	PROPN
ma-248	538	9	,	,	PUNCT
ma-248	538	10	f.t	f.t	PROPN
ma-248	538	11	.	.	PROPN
ma-248	538	12	oduro	oduro	PROPN
ma-248	538	13	,	,	PUNCT
ma-248	538	14	a.	a.	NOUN
ma-248	538	15	abidemi	abidemi	PROPN
ma-248	538	16	,	,	PUNCT
ma-248	538	17	e.o	e.o	PROPN
ma-248	538	18	.	.	PROPN
ma-248	538	19	gyasi	gyasi	PROPN
ma-248	538	20	,	,	PUNCT
ma-248	538	21	global	global	ADJ
ma-248	538	22	stability	stability	NOUN
ma-248	538	23	and	and	CCONJ
ma-248	538	24	cost	cost	NOUN
ma-248	538	25	-	-	PUNCT
ma-248	538	26	effectivenessanalysis	effectivenessanalysis	NOUN
ma-248	538	27	of	of	ADP
ma-248	538	28	covid-19	covid-19	PROPN
ma-248	538	29	considering	consider	VERB
ma-248	538	30	the	the	DET
ma-248	538	31	impact	impact	NOUN
ma-248	538	32	of	of	ADP
ma-248	538	33	the	the	DET
ma-248	538	34	environment	environment	NOUN
ma-248	538	35	:	:	PUNCT
ma-248	538	36	using	use	VERB
ma-248	538	37	data	datum	NOUN
ma-248	538	38	from	from	ADP
ma-248	538	39	ghana	ghana	PROPN
ma-248	538	40	,	,	PUNCT
ma-248	538	41	chaos	chaos	NOUN
ma-248	538	42	solitons	soliton	NOUN
ma-248	538	43	fractals140	fractals140	PROPN
ma-248	538	44	(	(	PUNCT
ma-248	538	45	2020	2020	NUM
ma-248	538	46	)	)	PUNCT
ma-248	538	47	,	,	PUNCT
ma-248	538	48	110103	110103	NUM
ma-248	538	49	.	.	PUNCT
ma-248	539	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	539	2	eur	eur	PROPN
ma-248	539	3	.	.	PUNCT
ma-248	540	1	j.	j.	PROPN
ma-248	540	2	math	math	PROPN
ma-248	540	3	.	.	PUNCT
ma-248	541	1	anal	anal	PROPN
ma-248	541	2	.	.	PUNCT
ma-248	542	1	10.28924	10.28924	NUM
ma-248	542	2	/	/	SYM
ma-248	542	3	ada	ada	PROPN
ma-248	542	4	/	/	SYM
ma-248	542	5	ma.4.21	ma.4.21	NOUN
ma-248	542	6	25	25	NUM
ma-248	543	1	[	[	X
ma-248	543	2	2	2	X
ma-248	543	3	]	]	PUNCT
ma-248	543	4	d.	d.	PROPN
ma-248	543	5	a.	a.	NOUN
ma-248	543	6	caugant	caugant	PROPN
ma-248	543	7	,	,	PUNCT
ma-248	543	8	population	population	NOUN
ma-248	543	9	genetics	genetic	NOUN
ma-248	543	10	and	and	CCONJ
ma-248	543	11	molecular	molecular	ADJ
ma-248	543	12	epidemiology	epidemiology	NOUN
ma-248	543	13	of	of	ADP
ma-248	543	14	neisseria	neisseria	PROPN
ma-248	543	15	meningitidis	meningitidis	PROPN
ma-248	543	16	,	,	PUNCT
ma-248	543	17	apmis	apmis	PROPN
ma-248	543	18	.	.	PUNCT
ma-248	544	1	106	106	NUM
ma-248	544	2	(	(	PUNCT
ma-248	544	3	1998),505	1998),505	NUM
ma-248	544	4	-	-	SYM
ma-248	544	5	525.[3	525.[3	NUM
ma-248	544	6	]	]	PUNCT
ma-248	544	7	j.	j.	PROPN
ma-248	544	8	k.	k.	PROPN
ma-248	544	9	k.	k.	PROPN
ma-248	545	1	asamoah	asamoah	PROPN
ma-248	545	2	,	,	PUNCT
ma-248	545	3	f.	f.	PROPN
ma-248	545	4	nyabadza	nyabadza	PROPN
ma-248	545	5	,	,	PUNCT
ma-248	545	6	b.	b.	PROPN
ma-248	545	7	seidu	seidu	PROPN
ma-248	545	8	,	,	PUNCT
ma-248	545	9	m.	m.	PROPN
ma-248	545	10	chand	chand	PROPN
ma-248	545	11	,	,	PUNCT
ma-248	545	12	h.	h.	PROPN
ma-248	545	13	dutta	dutta	PROPN
ma-248	545	14	,	,	PUNCT
ma-248	545	15	mathematical	mathematical	ADJ
ma-248	545	16	modelling	modelling	NOUN
ma-248	545	17	of	of	ADP
ma-248	545	18	bacterial	bacterial	ADJ
ma-248	545	19	meningitistransmission	meningitistransmission	NOUN
ma-248	545	20	dynamics	dynamic	NOUN
ma-248	545	21	with	with	ADP
ma-248	545	22	control	control	NOUN
ma-248	545	23	measures	measure	NOUN
ma-248	545	24	,	,	PUNCT
ma-248	545	25	comp	comp	NOUN
ma-248	545	26	.	.	PUNCT
ma-248	545	27	math	math	NOUN
ma-248	545	28	.	.	PUNCT
ma-248	546	1	meth	meth	NOUN
ma-248	546	2	.	.	PUNCT
ma-248	547	1	med	med	PROPN
ma-248	547	2	.	.	PUNCT
ma-248	548	1	2018	2018	NUM
ma-248	548	2	(	(	PUNCT
ma-248	548	3	2018	2018	NUM
ma-248	548	4	)	)	PUNCT
ma-248	548	5	,	,	PUNCT
ma-248	548	6	2657461.[4	2657461.[4	NUM
ma-248	548	7	]	]	X
ma-248	548	8	f.	f.	PROPN
ma-248	548	9	m.	m.	PROPN
ma-248	548	10	laforce	laforce	PROPN
ma-248	548	11	,	,	PUNCT
ma-248	548	12	j.	j.	PROPN
ma-248	548	13	m.	m.	PROPN
ma-248	548	14	okwo	okwo	PROPN
ma-248	548	15	-	-	PUNCT
ma-248	548	16	bele	bele	PROPN
ma-248	548	17	,	,	PUNCT
ma-248	548	18	eliminating	eliminate	VERB
ma-248	548	19	epidemic	epidemic	NOUN
ma-248	548	20	group	group	NOUN
ma-248	548	21	a	a	DET
ma-248	548	22	meningococcal	meningococcal	ADJ
ma-248	548	23	meningitis	meningitis	NOUN
ma-248	548	24	in	in	ADP
ma-248	548	25	africa	africa	PROPN
ma-248	548	26	through	through	ADP
ma-248	548	27	a	a	DET
ma-248	548	28	newvaccine	newvaccine	NOUN
ma-248	548	29	.	.	PUNCT
ma-248	549	1	health	health	NOUN
ma-248	549	2	affairs	affair	NOUN
ma-248	549	3	(	(	PUNCT
ma-248	549	4	project	project	PROPN
ma-248	549	5	hope	hope	PROPN
ma-248	549	6	)	)	PUNCT
ma-248	549	7	,	,	PUNCT
ma-248	549	8	30	30	NUM
ma-248	549	9	(	(	PUNCT
ma-248	549	10	2011	2011	NUM
ma-248	549	11	)	)	PUNCT
ma-248	549	12	,	,	PUNCT
ma-248	549	13	1049–1057.[5	1049–1057.[5	NUM
ma-248	549	14	]	]	PUNCT
ma-248	549	15	b.	b.	PROPN
ma-248	549	16	sultan	sultan	PROPN
ma-248	549	17	,	,	PUNCT
ma-248	549	18	k.	k.	PROPN
ma-248	549	19	labadi	labadi	PROPN
ma-248	549	20	,	,	PUNCT
ma-248	549	21	j.	j.	PROPN
ma-248	549	22	f.	f.	PROPN
ma-248	549	23	guégan	guégan	PROPN
ma-248	549	24	,	,	PUNCT
ma-248	549	25	s.	s.	PROPN
ma-248	549	26	janicot	janicot	PROPN
ma-248	549	27	,	,	PUNCT
ma-248	549	28	climate	climate	NOUN
ma-248	549	29	drives	drive	VERB
ma-248	549	30	the	the	DET
ma-248	549	31	meningitis	meningitis	NOUN
ma-248	549	32	epidemics	epidemic	NOUN
ma-248	549	33	onset	onset	VERB
ma-248	549	34	in	in	ADP
ma-248	549	35	west	west	PROPN
ma-248	549	36	africa	africa	PROPN
ma-248	549	37	,	,	PUNCT
ma-248	549	38	plosmed	plosmed	ADJ
ma-248	549	39	.	.	X
ma-248	549	40	2	2	NUM
ma-248	549	41	(	(	PUNCT
ma-248	549	42	2005	2005	NUM
ma-248	549	43	)	)	PUNCT
ma-248	549	44	,	,	PUNCT
ma-248	549	45	e6.[6	e6.[6	PROPN
ma-248	549	46	]	]	X
ma-248	549	47	f.	f.	PROPN
ma-248	549	48	y.	y.	PROPN
ma-248	549	49	aku	aku	PROPN
ma-248	549	50	,	,	PUNCT
ma-248	549	51	f.	f.	PROPN
ma-248	549	52	c.	c.	PROPN
ma-248	549	53	lessa	lessa	PROPN
ma-248	549	54	,	,	PUNCT
ma-248	549	55	f.	f.	PROPN
ma-248	549	56	asiedu	asiedu	PROPN
ma-248	549	57	-	-	PUNCT
ma-248	549	58	bekoe	bekoe	PROPN
ma-248	549	59	,	,	PUNCT
ma-248	549	60	p.	p.	PROPN
ma-248	549	61	balagumyetime	balagumyetime	NOUN
ma-248	549	62	,	,	PUNCT
ma-248	549	63	w.	w.	PROPN
ma-248	549	64	ofosu	ofosu	PROPN
ma-248	549	65	,	,	PUNCT
ma-248	549	66	j.	j.	PROPN
ma-248	549	67	farrar	farrar	PROPN
ma-248	549	68	,	,	PUNCT
ma-248	549	69	et	et	PROPN
ma-248	549	70	al	al	PROPN
ma-248	549	71	.	.	PUNCT
ma-248	550	1	meningitis	meningitis	PROPN
ma-248	550	2	outbreak	outbreak	NOUN
ma-248	550	3	caused	cause	VERB
ma-248	550	4	byvaccine	byvaccine	ADJ
ma-248	550	5	-	-	PUNCT
ma-248	550	6	preventable	preventable	ADJ
ma-248	550	7	bacterial	bacterial	ADJ
ma-248	550	8	pathogens	pathogen	NOUN
ma-248	550	9	northern	northern	ADJ
ma-248	550	10	ghana	ghana	PROPN
ma-248	550	11	,	,	PUNCT
ma-248	550	12	2016	2016	NUM
ma-248	550	13	.	.	PUNCT
ma-248	551	1	mmwr	mmwr	NOUN
ma-248	551	2	.	.	PUNCT
ma-248	552	1	morb	morb	NOUN
ma-248	552	2	.	.	PUNCT
ma-248	553	1	mort	mort	PROPN
ma-248	553	2	.	.	PROPN
ma-248	553	3	weekly	weekly	PROPN
ma-248	553	4	rep	rep	PROPN
ma-248	553	5	.	.	PROPN
ma-248	553	6	66	66	NUM
ma-248	553	7	(	(	PUNCT
ma-248	553	8	2017),806–810.[7	2017),806–810.[7	NUM
ma-248	553	9	]	]	X
ma-248	553	10	e.	e.	PROPN
ma-248	553	11	j.	j.	PROPN
ma-248	553	12	c.	c.	PROPN
ma-248	553	13	goldstein	goldstein	PROPN
ma-248	553	14	,	,	PUNCT
ma-248	553	15	r.	r.	PROPN
ma-248	553	16	h.	h.	PROPN
ma-248	553	17	johnson	johnson	PROPN
ma-248	553	18	,	,	PUNCT
ma-248	553	19	h.	h.	PROPN
ma-248	553	20	e.	e.	PROPN
ma-248	553	21	einstein	einstein	PROPN
ma-248	553	22	,	,	PUNCT
ma-248	553	23	coccidioidal	coccidioidal	VERB
ma-248	553	24	meningitis	meningitis	NOUN
ma-248	553	25	.	.	PUNCT
ma-248	554	1	clinical	clinical	ADJ
ma-248	554	2	infectious	infectious	ADJ
ma-248	554	3	diseases	disease	NOUN
ma-248	554	4	,	,	PUNCT
ma-248	554	5	42	42	NUM
ma-248	554	6	(	(	PUNCT
ma-248	554	7	2006),103–107.[8	2006),103–107.[8	NUM
ma-248	554	8	]	]	X
ma-248	554	9	r.	r.	PROPN
ma-248	554	10	d.	d.	PROPN
ma-248	554	11	feigin	feigin	PROPN
ma-248	554	12	,	,	PUNCT
ma-248	555	1	g.	g.	PROPN
ma-248	555	2	h.	h.	PROPN
ma-248	555	3	mccracken	mccracken	PROPN
ma-248	555	4	,	,	PUNCT
ma-248	555	5	jr	jr	PROPN
ma-248	555	6	,	,	PUNCT
ma-248	555	7	j.	j.	PROPN
ma-248	555	8	o.	o.	PROPN
ma-248	555	9	klein	klein	PROPN
ma-248	555	10	,	,	PUNCT
ma-248	555	11	diagnosis	diagnosis	NOUN
ma-248	555	12	and	and	CCONJ
ma-248	555	13	management	management	NOUN
ma-248	555	14	of	of	ADP
ma-248	555	15	meningitis	meningitis	NOUN
ma-248	555	16	,	,	PUNCT
ma-248	555	17	pediatric	pediatric	ADJ
ma-248	555	18	infect	infect	NOUN
ma-248	555	19	.	.	PUNCT
ma-248	556	1	dis	dis	PROPN
ma-248	556	2	.	.	PUNCT
ma-248	557	1	j.	j.	PROPN
ma-248	557	2	11(1992	11(1992	NUM
ma-248	557	3	)	)	PUNCT
ma-248	557	4	,	,	PUNCT
ma-248	557	5	785–814.[9	785–814.[9	NUM
ma-248	557	6	]	]	PUNCT
ma-248	557	7	d.	d.	PROPN
ma-248	557	8	swanson	swanson	PROPN
ma-248	557	9	,	,	PUNCT
ma-248	557	10	meningitis	meningitis	NOUN
ma-248	557	11	,	,	PUNCT
ma-248	557	12	pediatr	pediatr	PROPN
ma-248	557	13	.	.	PUNCT
ma-248	557	14	rev	rev	PROPN
ma-248	557	15	.	.	PROPN
ma-248	557	16	36	36	NUM
ma-248	557	17	(	(	PUNCT
ma-248	557	18	2015	2015	NUM
ma-248	557	19	)	)	PUNCT
ma-248	557	20	,	,	PUNCT
ma-248	557	21	514–526.[10	514–526.[10	NUM
ma-248	557	22	]	]	PUNCT
ma-248	557	23	a.	a.	NOUN
ma-248	557	24	schuchat	schuchat	PROPN
ma-248	557	25	,	,	PUNCT
ma-248	557	26	k.	k.	PROPN
ma-248	557	27	robinson	robinson	PROPN
ma-248	557	28	,	,	PUNCT
ma-248	557	29	j.	j.	PROPN
ma-248	557	30	d.	d.	PROPN
ma-248	557	31	wenger	wenger	PROPN
ma-248	557	32	,	,	PUNCT
ma-248	557	33	l.h	l.h	PROPN
ma-248	557	34	.	.	PROPN
ma-248	557	35	harrison	harrison	PROPN
ma-248	557	36	,	,	PUNCT
ma-248	557	37	m.	m.	NOUN
ma-248	557	38	farley	farley	PROPN
ma-248	557	39	,	,	PUNCT
ma-248	557	40	a.	a.	PROPN
ma-248	557	41	l.	l.	PROPN
ma-248	557	42	reingold	reingold	PROPN
ma-248	557	43	,	,	PUNCT
ma-248	557	44	l.	l.	PROPN
ma-248	557	45	lefkowitz	lefkowitz	PROPN
ma-248	557	46	,	,	PUNCT
ma-248	557	47	b.	b.	PROPN
ma-248	557	48	a.	a.	PROPN
ma-248	557	49	perkins	perkins	PROPN
ma-248	557	50	,	,	PUNCT
ma-248	557	51	bacterial	bacterial	ADJ
ma-248	557	52	meningitis	meningitis	NOUN
ma-248	557	53	in	in	ADP
ma-248	557	54	the	the	DET
ma-248	557	55	united	united	PROPN
ma-248	557	56	states	states	PROPN
ma-248	557	57	in	in	ADP
ma-248	557	58	1995	1995	NUM
ma-248	557	59	,	,	PUNCT
ma-248	557	60	n.	n.	PROPN
ma-248	557	61	engl	engl	PROPN
ma-248	557	62	.	.	PUNCT
ma-248	558	1	j.	j.	PROPN
ma-248	558	2	med	med	PROPN
ma-248	558	3	.	.	PUNCT
ma-248	559	1	337	337	NUM
ma-248	559	2	(	(	PUNCT
ma-248	559	3	1997	1997	NUM
ma-248	559	4	)	)	PUNCT
ma-248	559	5	,	,	PUNCT
ma-248	559	6	970–976	970–976	NUM
ma-248	559	7	.	.	PUNCT
ma-248	560	1	https://doi.org/10	https://doi.org/10	PROPN
ma-248	560	2	.	.	PUNCT
ma-248	561	1	1056	1056	NUM
ma-248	561	2	/	/	SYM
ma-248	561	3	nejm199710023371404.[11	nejm199710023371404.[11	PROPN
ma-248	561	4	]	]	PUNCT
ma-248	561	5	m.	m.	PROPN
ma-248	561	6	c.	c.	PROPN
ma-248	561	7	thigpen	thigpen	PROPN
ma-248	561	8	,	,	PUNCT
ma-248	561	9	c.	c.	PROPN
ma-248	561	10	g.	g.	PROPN
ma-248	561	11	whitney	whitney	PROPN
ma-248	561	12	,	,	PUNCT
ma-248	561	13	n.	n.	PROPN
ma-248	561	14	e.	e.	PROPN
ma-248	561	15	messonnier	messonnier	PROPN
ma-248	561	16	,	,	PUNCT
ma-248	561	17	e.	e.	PROPN
ma-248	561	18	r.	r.	PROPN
ma-248	561	19	zell	zell	PROPN
ma-248	561	20	,	,	PUNCT
ma-248	561	21	et	et	PROPN
ma-248	561	22	al	al	PROPN
ma-248	561	23	.	.	PUNCT
ma-248	562	1	bacterial	bacterial	ADJ
ma-248	562	2	meningitis	meningitis	NOUN
ma-248	562	3	in	in	ADP
ma-248	562	4	the	the	DET
ma-248	562	5	united	united	PROPN
ma-248	562	6	states,1998–2007	states,1998–2007	PROPN
ma-248	562	7	,	,	PUNCT
ma-248	562	8	n.	n.	PROPN
ma-248	562	9	engl	engl	PROPN
ma-248	562	10	.	.	PUNCT
ma-248	563	1	j.	j.	PROPN
ma-248	563	2	med	med	PROPN
ma-248	563	3	.	.	PUNCT
ma-248	564	1	364	364	NUM
ma-248	564	2	(	(	PUNCT
ma-248	564	3	2011	2011	NUM
ma-248	564	4	)	)	PUNCT
ma-248	564	5	,	,	PUNCT
ma-248	564	6	2016–2025	2016–2025	NUM
ma-248	564	7	.	.	PUNCT
ma-248	565	1	https://doi.org/10.1056/nejmoa1005384.[12	https://doi.org/10.1056/nejmoa1005384.[12	PROPN
ma-248	565	2	]	]	X
ma-248	565	3	b.	b.	PROPN
ma-248	565	4	gleissner	gleissner	PROPN
ma-248	565	5	,	,	PUNCT
ma-248	565	6	m.	m.	NOUN
ma-248	565	7	c.	c.	PROPN
ma-248	565	8	chamberlain	chamberlain	PROPN
ma-248	565	9	,	,	PUNCT
ma-248	565	10	neoplastic	neoplastic	ADJ
ma-248	565	11	meningitis	meningitis	NOUN
ma-248	565	12	,	,	PUNCT
ma-248	565	13	lancet	lancet	PROPN
ma-248	565	14	neurol	neurol	NOUN
ma-248	565	15	.	.	PUNCT
ma-248	566	1	5	5	NUM
ma-248	566	2	(	(	PUNCT
ma-248	566	3	2006	2006	NUM
ma-248	566	4	)	)	PUNCT
ma-248	567	1	,	,	PUNCT
ma-248	567	2	443–452.[13	443–452.[13	PROPN
ma-248	567	3	]	]	PUNCT
ma-248	567	4	k.	k.	PROPN
ma-248	567	5	mann	mann	PROPN
ma-248	567	6	,	,	PUNCT
ma-248	567	7	m.	m.	PROPN
ma-248	567	8	a.	a.	PROPN
ma-248	567	9	jackson	jackson	PROPN
ma-248	567	10	,	,	PUNCT
ma-248	567	11	meningitis	meningitis	PROPN
ma-248	567	12	,	,	PUNCT
ma-248	567	13	pediatr	pediatr	PROPN
ma-248	567	14	.	.	PUNCT
ma-248	567	15	rev	rev	PROPN
ma-248	567	16	.	.	PROPN
ma-248	567	17	29	29	NUM
ma-248	567	18	(	(	PUNCT
ma-248	567	19	2008	2008	NUM
ma-248	567	20	)	)	PUNCT
ma-248	567	21	,	,	PUNCT
ma-248	567	22	417–430.[14	417–430.[14	PROPN
ma-248	567	23	]	]	PUNCT
ma-248	567	24	v.	v.	PROPN
ma-248	567	25	j.	j.	PROPN
ma-248	567	26	quagliarello	quagliarello	PROPN
ma-248	567	27	,	,	PUNCT
ma-248	567	28	w.	w.	PROPN
ma-248	567	29	m.	m.	PROPN
ma-248	567	30	scheld	scheld	PROPN
ma-248	567	31	,	,	PUNCT
ma-248	567	32	treatment	treatment	NOUN
ma-248	567	33	of	of	ADP
ma-248	567	34	bacterial	bacterial	ADJ
ma-248	567	35	meningitis	meningitis	NOUN
ma-248	567	36	,	,	PUNCT
ma-248	567	37	n.	n.	PROPN
ma-248	567	38	engl	engl	PROPN
ma-248	567	39	.	.	PUNCT
ma-248	568	1	j.	j.	PROPN
ma-248	568	2	med	med	PROPN
ma-248	568	3	.	.	PUNCT
ma-248	569	1	336	336	NUM
ma-248	569	2	(	(	PUNCT
ma-248	569	3	1997	1997	NUM
ma-248	569	4	)	)	PUNCT
ma-248	569	5	,	,	PUNCT
ma-248	569	6	708–716.[15	708–716.[15	NOUN
ma-248	569	7	]	]	PUNCT
ma-248	569	8	s.	s.	PROPN
ma-248	569	9	tartof	tartof	PROPN
ma-248	569	10	,	,	PUNCT
ma-248	569	11	a.	a.	PROPN
ma-248	569	12	cohn	cohn	PROPN
ma-248	569	13	,	,	PUNCT
ma-248	569	14	f.	f.	PROPN
ma-248	569	15	tarbangdo	tarbangdo	PROPN
ma-248	569	16	,	,	PUNCT
ma-248	569	17	m.h	m.h	PROPN
ma-248	569	18	.	.	PROPN
ma-248	569	19	djingarey	djingarey	PROPN
ma-248	569	20	,	,	PUNCT
ma-248	569	21	et	et	PROPN
ma-248	569	22	al	al	PROPN
ma-248	569	23	.	.	PUNCT
ma-248	570	1	identifying	identify	VERB
ma-248	570	2	optimal	optimal	ADJ
ma-248	570	3	vaccination	vaccination	NOUN
ma-248	570	4	strategies	strategy	NOUN
ma-248	570	5	for	for	ADP
ma-248	570	6	serogroup	serogroup	ADJ
ma-248	570	7	aneisseria	aneisseria	PROPN
ma-248	570	8	meningitidis	meningitidis	PROPN
ma-248	570	9	conjugate	conjugate	ADJ
ma-248	570	10	vaccine	vaccine	NOUN
ma-248	570	11	in	in	ADP
ma-248	570	12	the	the	DET
ma-248	570	13	african	african	ADJ
ma-248	570	14	meningitis	meningitis	NOUN
ma-248	570	15	belt	belt	NOUN
ma-248	570	16	,	,	PUNCT
ma-248	570	17	plos	plos	PROPN
ma-248	570	18	one	one	NUM
ma-248	570	19	8	8	NUM
ma-248	570	20	(	(	PUNCT
ma-248	570	21	2013	2013	NUM
ma-248	570	22	)	)	PUNCT
ma-248	570	23	,	,	PUNCT
ma-248	570	24	e63605.[16	e63605.[16	PROPN
ma-248	570	25	]	]	X
ma-248	570	26	a.	a.	PROPN
ma-248	570	27	r.	r.	PROPN
ma-248	570	28	tuite	tuite	PROPN
ma-248	570	29	,	,	PUNCT
ma-248	570	30	d.	d.	PROPN
ma-248	570	31	n.	n.	PROPN
ma-248	570	32	fisman	fisman	PROPN
ma-248	570	33	,	,	PUNCT
ma-248	570	34	s.	s.	PROPN
ma-248	570	35	mishra	mishra	PROPN
ma-248	570	36	,	,	PUNCT
ma-248	570	37	screen	screen	VERB
ma-248	570	38	more	more	ADJ
ma-248	570	39	or	or	CCONJ
ma-248	570	40	screen	screen	NOUN
ma-248	570	41	more	more	ADV
ma-248	570	42	often	often	ADV
ma-248	570	43	?	?	PUNCT
ma-248	571	1	using	use	VERB
ma-248	571	2	mathematical	mathematical	ADJ
ma-248	571	3	models	model	NOUN
ma-248	571	4	to	to	PART
ma-248	571	5	informsyphilis	informsyphilis	VERB
ma-248	571	6	control	control	NOUN
ma-248	571	7	strategies	strategy	NOUN
ma-248	571	8	,	,	PUNCT
ma-248	571	9	bmc	bmc	ADJ
ma-248	571	10	public	public	ADJ
ma-248	571	11	health	health	NOUN
ma-248	571	12	13	13	NUM
ma-248	571	13	(	(	PUNCT
ma-248	571	14	2013	2013	NUM
ma-248	571	15	)	)	PUNCT
ma-248	571	16	,	,	PUNCT
ma-248	571	17	606.[17	606.[17	PROPN
ma-248	571	18	]	]	X
ma-248	571	19	j.-p	j.-p	PROPN
ma-248	571	20	.	.	PUNCT
ma-248	572	1	chippaux	chippaux	PROPN
ma-248	572	2	,	,	PUNCT
ma-248	572	3	control	control	NOUN
ma-248	572	4	of	of	ADP
ma-248	572	5	meningococcal	meningococcal	ADJ
ma-248	572	6	meningitis	meningitis	NOUN
ma-248	572	7	outbreaks	outbreak	NOUN
ma-248	572	8	in	in	ADP
ma-248	572	9	sub	sub	ADJ
ma-248	572	10	-	-	ADJ
ma-248	572	11	saharan	saharan	ADJ
ma-248	572	12	africa	africa	PROPN
ma-248	572	13	,	,	PUNCT
ma-248	572	14	j.	j.	PROPN
ma-248	572	15	infect	infect	PROPN
ma-248	572	16	.	.	PUNCT
ma-248	573	1	develop	develop	VERB
ma-248	573	2	.	.	PUNCT
ma-248	574	1	countries	country	NOUN
ma-248	574	2	2(2008	2(2008	PROPN
ma-248	574	3	)	)	PUNCT
ma-248	574	4	,	,	PUNCT
ma-248	574	5	335–345.[18	335–345.[18	NUM
ma-248	574	6	]	]	X
ma-248	574	7	h.	h.	PROPN
ma-248	574	8	ritchie	ritchie	PROPN
ma-248	574	9	,	,	PUNCT
ma-248	574	10	l.	l.	PROPN
ma-248	574	11	rodés	rodés	PROPN
ma-248	574	12	-	-	PUNCT
ma-248	574	13	guirao	guirao	PROPN
ma-248	574	14	,	,	PUNCT
ma-248	574	15	e.	e.	PROPN
ma-248	574	16	mathieu	mathieu	PROPN
ma-248	574	17	,	,	PUNCT
ma-248	574	18	m.	m.	NOUN
ma-248	574	19	gerber	gerber	PROPN
ma-248	574	20	,	,	PUNCT
ma-248	574	21	e.	e.	PROPN
ma-248	574	22	ortiz	ortiz	PROPN
ma-248	574	23	-	-	PUNCT
ma-248	574	24	ospina	ospina	PROPN
ma-248	574	25	,	,	PUNCT
ma-248	574	26	et	et	PROPN
ma-248	574	27	al	al	PROPN
ma-248	574	28	.	.	PUNCT
ma-248	575	1	population	population	NOUN
ma-248	575	2	growth	growth	NOUN
ma-248	575	3	.	.	PUNCT
ma-248	576	1	https://	https://	NOUN
ma-248	576	2	ourworldindata.org/population-growth.[19	ourworldindata.org/population-growth.[19	PROPN
ma-248	576	3	]	]	PUNCT
ma-248	576	4	p.	p.	NOUN
ma-248	576	5	van	van	PROPN
ma-248	576	6	den	den	PROPN
ma-248	576	7	driessche	driessche	PROPN
ma-248	576	8	,	,	PUNCT
ma-248	576	9	j.	j.	PROPN
ma-248	576	10	watmough	watmough	PROPN
ma-248	576	11	,	,	PUNCT
ma-248	576	12	further	further	ADJ
ma-248	576	13	notes	note	NOUN
ma-248	576	14	on	on	ADP
ma-248	576	15	the	the	DET
ma-248	576	16	basic	basic	ADJ
ma-248	576	17	reproduction	reproduction	NOUN
ma-248	576	18	number	number	NOUN
ma-248	576	19	,	,	PUNCT
ma-248	576	20	in	in	ADP
ma-248	576	21	:	:	PUNCT
ma-248	576	22	f.	f.	PROPN
ma-248	576	23	brauer	brauer	PROPN
ma-248	576	24	,	,	PUNCT
ma-248	576	25	p.	p.	PROPN
ma-248	576	26	van	van	PROPN
ma-248	576	27	dendriessche	dendriessche	PROPN
ma-248	576	28	,	,	PUNCT
ma-248	576	29	j.	j.	PROPN
ma-248	576	30	wu	wu	PROPN
ma-248	576	31	(	(	PUNCT
ma-248	576	32	eds	eds	PROPN
ma-248	576	33	.	.	PUNCT
ma-248	576	34	)	)	PUNCT
ma-248	576	35	,	,	PUNCT
ma-248	576	36	mathematical	mathematical	ADJ
ma-248	576	37	epidemiology	epidemiology	NOUN
ma-248	576	38	,	,	PUNCT
ma-248	576	39	springer	springer	NOUN
ma-248	576	40	berlin	berlin	PROPN
ma-248	576	41	heidelberg	heidelberg	PROPN
ma-248	576	42	,	,	PUNCT
ma-248	576	43	berlin	berlin	PROPN
ma-248	576	44	,	,	PUNCT
ma-248	576	45	heidelberg	heidelberg	PROPN
ma-248	576	46	,	,	PUNCT
ma-248	576	47	2008	2008	NUM
ma-248	576	48	:	:	PUNCT
ma-248	576	49	pp.159–178.[20	pp.159–178.[20	PROPN
ma-248	576	50	]	]	PUNCT
ma-248	576	51	j.	j.	PROPN
ma-248	576	52	p.	p.	PROPN
ma-248	576	53	lasalle	lasalle	PROPN
ma-248	576	54	,	,	PUNCT
ma-248	576	55	the	the	DET
ma-248	576	56	stability	stability	NOUN
ma-248	576	57	of	of	ADP
ma-248	576	58	dynamical	dynamical	ADJ
ma-248	576	59	systems	system	NOUN
ma-248	576	60	,	,	PUNCT
ma-248	576	61	siam	siam	PROPN
ma-248	576	62	,	,	PUNCT
ma-248	576	63	(	(	PUNCT
ma-248	576	64	1976).[21	1976).[21	X
ma-248	576	65	]	]	X
ma-248	576	66	y.	y.	PROPN
ma-248	576	67	zhou	zhou	PROPN
ma-248	576	68	,	,	PUNCT
ma-248	576	69	b.	b.	PROPN
ma-248	576	70	song	song	PROPN
ma-248	576	71	,	,	PUNCT
ma-248	576	72	z.	z.	PROPN
ma-248	576	73	ma	ma	PROPN
ma-248	576	74	,	,	PUNCT
ma-248	576	75	the	the	DET
ma-248	576	76	global	global	ADJ
ma-248	576	77	stability	stability	NOUN
ma-248	576	78	analysis	analysis	NOUN
ma-248	576	79	for	for	ADP
ma-248	576	80	an	an	DET
ma-248	576	81	sis	sis	NOUN
ma-248	576	82	model	model	NOUN
ma-248	576	83	with	with	ADP
ma-248	576	84	age	age	NOUN
ma-248	576	85	and	and	CCONJ
ma-248	576	86	infection	infection	NOUN
ma-248	576	87	age	age	NOUN
ma-248	576	88	structures	structure	NOUN
ma-248	576	89	,	,	PUNCT
ma-248	576	90	in	in	ADP
ma-248	576	91	:	:	PUNCT
ma-248	576	92	c.castillo	c.castillo	ADJ
ma-248	576	93	-	-	PUNCT
ma-248	576	94	chavez	chavez	PROPN
ma-248	576	95	,	,	PUNCT
ma-248	576	96	s.	s.	PROPN
ma-248	576	97	blower	blower	PROPN
ma-248	576	98	,	,	PUNCT
ma-248	576	99	p.	p.	PROPN
ma-248	576	100	van	van	PROPN
ma-248	576	101	den	den	PROPN
ma-248	576	102	driessche	driessche	PROPN
ma-248	576	103	,	,	PUNCT
ma-248	576	104	d.	d.	PROPN
ma-248	576	105	kirschner	kirschner	PROPN
ma-248	576	106	,	,	PUNCT
ma-248	576	107	a.-a	a.-a	PROPN
ma-248	576	108	.	.	PUNCT
ma-248	577	1	yakubu	yakubu	PROPN
ma-248	577	2	(	(	PUNCT
ma-248	577	3	eds	eds	PROPN
ma-248	577	4	.	.	PUNCT
ma-248	577	5	)	)	PUNCT
ma-248	577	6	,	,	PUNCT
ma-248	577	7	mathematical	mathematical	ADJ
ma-248	577	8	approaches	approach	NOUN
ma-248	577	9	foremerging	foremerge	VERB
ma-248	577	10	and	and	CCONJ
ma-248	577	11	reemerging	reemerge	VERB
ma-248	577	12	infectious	infectious	ADJ
ma-248	577	13	diseases	disease	NOUN
ma-248	577	14	:	:	PUNCT
ma-248	577	15	models	model	NOUN
ma-248	577	16	,	,	PUNCT
ma-248	577	17	methods	method	NOUN
ma-248	577	18	,	,	PUNCT
ma-248	577	19	and	and	CCONJ
ma-248	577	20	theory	theory	NOUN
ma-248	577	21	,	,	PUNCT
ma-248	577	22	springer	springer	PROPN
ma-248	577	23	new	new	PROPN
ma-248	577	24	york	york	PROPN
ma-248	577	25	,	,	PUNCT
ma-248	577	26	new	new	PROPN
ma-248	577	27	york	york	PROPN
ma-248	577	28	,	,	PUNCT
ma-248	577	29	ny,2002	ny,2002	NOUN
ma-248	577	30	:	:	PUNCT
ma-248	577	31	pp	pp	X
ma-248	577	32	.	.	PUNCT
ma-248	578	1	313–335.[22	313–335.[22	NOUN
ma-248	578	2	]	]	X
ma-248	578	3	e.x	e.x	PROPN
ma-248	578	4	.	.	PROPN
ma-248	578	5	dejesus	dejesus	PROPN
ma-248	578	6	,	,	PUNCT
ma-248	578	7	c.	c.	PROPN
ma-248	578	8	kaufman	kaufman	PROPN
ma-248	578	9	,	,	PUNCT
ma-248	578	10	routh	routh	PROPN
ma-248	578	11	-	-	PUNCT
ma-248	578	12	hurwitz	hurwitz	PROPN
ma-248	578	13	criterion	criterion	NOUN
ma-248	578	14	in	in	ADP
ma-248	578	15	the	the	DET
ma-248	578	16	examination	examination	NOUN
ma-248	578	17	of	of	ADP
ma-248	578	18	eigenvalues	eigenvalue	NOUN
ma-248	578	19	of	of	ADP
ma-248	578	20	a	a	DET
ma-248	578	21	system	system	NOUN
ma-248	578	22	of	of	ADP
ma-248	578	23	nonlinearordinary	nonlinearordinary	ADJ
ma-248	578	24	differential	differential	ADJ
ma-248	578	25	equations	equation	NOUN
ma-248	578	26	,	,	PUNCT
ma-248	578	27	phys	phy	NOUN
ma-248	578	28	.	.	PUNCT
ma-248	578	29	rev	rev	PROPN
ma-248	578	30	.	.	PUNCT
ma-248	579	1	a	a	DET
ma-248	579	2	35	35	NUM
ma-248	579	3	(	(	PUNCT
ma-248	579	4	1987	1987	NUM
ma-248	579	5	)	)	PUNCT
ma-248	579	6	,	,	PUNCT
ma-248	579	7	5288–5290.[23	5288–5290.[23	NUM
ma-248	579	8	]	]	X
ma-248	579	9	e.	e.	PROPN
ma-248	579	10	bouza	bouza	PROPN
ma-248	579	11	,	,	PUNCT
ma-248	579	12	m.	m.	NOUN
ma-248	579	13	g.	g.	PROPN
ma-248	579	14	de	de	PROPN
ma-248	579	15	la	la	PROPN
ma-248	579	16	torre	torre	PROPN
ma-248	579	17	,	,	PUNCT
ma-248	579	18	f.	f.	PROPN
ma-248	579	19	parras	parras	PROPN
ma-248	579	20	,	,	PUNCT
ma-248	579	21	a.	a.	NOUN
ma-248	579	22	guerrero	guerrero	PROPN
ma-248	579	23	,	,	PUNCT
ma-248	579	24	m.	m.	NOUN
ma-248	579	25	rodriguez	rodriguez	NOUN
ma-248	579	26	-	-	PUNCT
ma-248	579	27	creixems	creixems	PROPN
ma-248	579	28	,	,	PUNCT
ma-248	579	29	j.	j.	PROPN
ma-248	579	30	gobernado	gobernado	PROPN
ma-248	579	31	,	,	PUNCT
ma-248	579	32	brucellar	brucellar	ADV
ma-248	579	33	meningitis	meningitis	NOUN
ma-248	579	34	,	,	PUNCT
ma-248	579	35	clin	clin	PROPN
ma-248	579	36	.	.	PUNCT
ma-248	580	1	infect	infect	VERB
ma-248	580	2	.	.	PUNCT
ma-248	581	1	dis	dis	PROPN
ma-248	581	2	.	.	PUNCT
ma-248	582	1	9	9	NUM
ma-248	582	2	(	(	PUNCT
ma-248	582	3	1987	1987	NUM
ma-248	582	4	)	)	PUNCT
ma-248	582	5	,	,	PUNCT
ma-248	582	6	810–822	810–822	NUM
ma-248	582	7	.	.	PUNCT
ma-248	583	1	https://doi.org/10.1093/clinids/9.4.810	https://doi.org/10.1093/clinids/9.4.810	NOUN
ma-248	583	2	.	.	PUNCT
ma-248	584	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	584	2	https://doi.org/10.1056/nejm199710023371404	https://doi.org/10.1056/nejm199710023371404	PROPN
ma-248	584	3	https://doi.org/10.1056/nejm199710023371404	https://doi.org/10.1056/nejm199710023371404	NOUN
ma-248	584	4	https://doi.org/10.1056/nejmoa1005384	https://doi.org/10.1056/nejmoa1005384	NOUN
ma-248	584	5	https://ourworldindata.org/population-growth	https://ourworldindata.org/population-growth	NOUN
ma-248	584	6	https://ourworldindata.org/population-growth	https://ourworldindata.org/population-growth	NOUN
ma-248	584	7	https://doi.org/10.1093/clinids/9.4.810	https://doi.org/10.1093/clinids/9.4.810	X
ma-248	584	8	eur	eur	PROPN
ma-248	584	9	.	.	PUNCT
ma-248	585	1	j.	j.	PROPN
ma-248	585	2	math	math	PROPN
ma-248	585	3	.	.	PUNCT
ma-248	586	1	anal	anal	PROPN
ma-248	586	2	.	.	PUNCT
ma-248	587	1	10.28924	10.28924	NUM
ma-248	587	2	/	/	SYM
ma-248	587	3	ada	ada	PROPN
ma-248	587	4	/	/	SYM
ma-248	587	5	ma.4.21	ma.4.21	NOUN
ma-248	587	6	26	26	NUM
ma-248	588	1	[	[	X
ma-248	588	2	24	24	NUM
ma-248	588	3	]	]	X
ma-248	588	4	h.	h.	PROPN
ma-248	588	5	j.	j.	PROPN
ma-248	588	6	kelley	kelley	PROPN
ma-248	588	7	,	,	PUNCT
ma-248	588	8	r.	r.	PROPN
ma-248	588	9	e.	e.	PROPN
ma-248	588	10	kopp	kopp	PROPN
ma-248	588	11	,	,	PUNCT
ma-248	588	12	h.	h.	PROPN
ma-248	588	13	g.	g.	PROPN
ma-248	588	14	moyer	moyer	PROPN
ma-248	588	15	,	,	PUNCT
ma-248	588	16	3	3	NUM
ma-248	588	17	singular	singular	ADJ
ma-248	588	18	extremals	extremal	NOUN
ma-248	588	19	,	,	PUNCT
ma-248	588	20	in	in	ADP
ma-248	588	21	:	:	PUNCT
ma-248	588	22	mathematics	mathematic	NOUN
ma-248	588	23	in	in	ADP
ma-248	588	24	science	science	NOUN
ma-248	588	25	and	and	CCONJ
ma-248	588	26	engineering	engineering	NOUN
ma-248	588	27	,	,	PUNCT
ma-248	588	28	elsevier,1967	elsevier,1967	ADJ
ma-248	588	29	:	:	PUNCT
ma-248	588	30	pp	pp	ADJ
ma-248	588	31	.	.	PUNCT
ma-248	589	1	63–101.[25	63–101.[25	X
ma-248	589	2	]	]	X
ma-248	589	3	w.	w.	PROPN
ma-248	589	4	h.	h.	PROPN
ma-248	589	5	fleming	fleming	PROPN
ma-248	589	6	,	,	PUNCT
ma-248	589	7	r.	r.	PROPN
ma-248	589	8	w.	w.	PROPN
ma-248	589	9	rishel	rishel	PROPN
ma-248	589	10	,	,	PUNCT
ma-248	589	11	g.	g.	PROPN
ma-248	589	12	i.	i.	PROPN
ma-248	589	13	marchuk	marchuk	PROPN
ma-248	589	14	,	,	PUNCT
ma-248	589	15	et	et	PROPN
ma-248	589	16	al	al	PROPN
ma-248	589	17	.	.	PROPN
ma-248	589	18	deterministic	deterministic	ADJ
ma-248	589	19	and	and	CCONJ
ma-248	589	20	stochastic	stochastic	ADJ
ma-248	589	21	optimal	optimal	ADJ
ma-248	589	22	control	control	NOUN
ma-248	589	23	,	,	PUNCT
ma-248	589	24	springer	springer	NOUN
ma-248	589	25	,	,	PUNCT
ma-248	589	26	(	(	PUNCT
ma-248	589	27	1975).[26	1975).[26	PROPN
ma-248	589	28	]	]	X
ma-248	589	29	r.e	r.e	PROPN
ma-248	589	30	.	.	PROPN
ma-248	589	31	kopp	kopp	PROPN
ma-248	589	32	,	,	PUNCT
ma-248	589	33	pontryagin	pontryagin	VERB
ma-248	589	34	maximum	maximum	ADJ
ma-248	589	35	principle	principle	NOUN
ma-248	589	36	,	,	PUNCT
ma-248	589	37	in	in	ADP
ma-248	589	38	:	:	PUNCT
ma-248	589	39	mathematics	mathematic	NOUN
ma-248	589	40	in	in	ADP
ma-248	589	41	science	science	NOUN
ma-248	589	42	and	and	CCONJ
ma-248	589	43	engineering	engineering	NOUN
ma-248	589	44	,	,	PUNCT
ma-248	589	45	elsevier	elsevier	NOUN
ma-248	589	46	,	,	PUNCT
ma-248	589	47	1962	1962	NUM
ma-248	589	48	:	:	PUNCT
ma-248	589	49	pp.255–279.[27	pp.255–279.[27	PROPN
ma-248	589	50	]	]	PUNCT
ma-248	589	51	g.	g.	PROPN
ma-248	589	52	t.	t.	PROPN
ma-248	589	53	tilahun	tilahun	PROPN
ma-248	589	54	,	,	PUNCT
ma-248	589	55	modeling	model	VERB
ma-248	589	56	co	co	NOUN
ma-248	589	57	-	-	NOUN
ma-248	589	58	dynamics	dynamic	NOUN
ma-248	589	59	of	of	ADP
ma-248	589	60	pneumonia	pneumonia	NOUN
ma-248	589	61	and	and	CCONJ
ma-248	589	62	meningitis	meningitis	NOUN
ma-248	589	63	diseases	disease	NOUN
ma-248	589	64	,	,	PUNCT
ma-248	589	65	advances	advance	NOUN
ma-248	589	66	in	in	ADP
ma-248	589	67	difference	difference	NOUN
ma-248	589	68	equations	equation	NOUN
ma-248	589	69	2019(2019	2019(2019	NUM
ma-248	589	70	)	)	PUNCT
ma-248	589	71	,	,	PUNCT
ma-248	589	72	149.[28	149.[28	X
ma-248	589	73	]	]	X
ma-248	589	74	t.	t.	PROPN
ma-248	589	75	koutangni	koutangni	PROPN
ma-248	589	76	,	,	PUNCT
ma-248	589	77	p.	p.	NOUN
ma-248	589	78	crépey	crépey	PROPN
ma-248	589	79	,	,	PUNCT
ma-248	589	80	m.	m.	NOUN
ma-248	589	81	woringer	woringer	NOUN
ma-248	589	82	,	,	PUNCT
ma-248	589	83	s.	s.	PROPN
ma-248	589	84	porgho	porgho	PROPN
ma-248	589	85	,	,	PUNCT
ma-248	589	86	b.w	b.w	PROPN
ma-248	589	87	.	.	PROPN
ma-248	589	88	bicaba	bicaba	PROPN
ma-248	589	89	,	,	PUNCT
ma-248	590	1	h.	h.	PROPN
ma-248	590	2	tall	tall	ADJ
ma-248	590	3	,	,	PUNCT
ma-248	590	4	j.e	j.e	PROPN
ma-248	590	5	.	.	PROPN
ma-248	590	6	mueller	mueller	PROPN
ma-248	590	7	,	,	PUNCT
ma-248	590	8	compartmental	compartmental	ADJ
ma-248	590	9	models	model	NOUN
ma-248	590	10	forseasonal	forseasonal	PROPN
ma-248	590	11	hyperendemic	hyperendemic	ADJ
ma-248	590	12	bacterial	bacterial	ADJ
ma-248	590	13	meningitis	meningitis	NOUN
ma-248	590	14	in	in	ADP
ma-248	590	15	the	the	DET
ma-248	590	16	african	african	ADJ
ma-248	590	17	meningitis	meningitis	NOUN
ma-248	590	18	belt	belt	NOUN
ma-248	590	19	,	,	PUNCT
ma-248	590	20	epidemiol	epidemiol	PROPN
ma-248	590	21	.	.	PUNCT
ma-248	591	1	infect	infect	VERB
ma-248	591	2	.	.	PUNCT
ma-248	592	1	147	147	NUM
ma-248	592	2	(	(	PUNCT
ma-248	592	3	2019	2019	NUM
ma-248	592	4	)	)	PUNCT
ma-248	592	5	,	,	PUNCT
ma-248	592	6	e14	e14	PROPN
ma-248	592	7	.	.	PUNCT
ma-248	593	1	https://doi.org/10.1017/s0950268818002625.[29	https://doi.org/10.1017/s0950268818002625.[29	PROPN
ma-248	593	2	]	]	X
ma-248	593	3	s.	s.	PROPN
ma-248	593	4	nana	nana	PROPN
ma-248	593	5	-	-	PUNCT
ma-248	593	6	kyere	kyere	PROPN
ma-248	593	7	,	,	PUNCT
ma-248	593	8	e.	e.	PROPN
ma-248	593	9	okyere	okyere	PROPN
ma-248	593	10	,	,	PUNCT
ma-248	593	11	j.	j.	PROPN
ma-248	593	12	de	de	PROPN
ma-248	593	13	-	-	NOUN
ma-248	593	14	graft	graft	ADJ
ma-248	593	15	ankamah	ankamah	NOUN
ma-248	593	16	,	,	PUNCT
ma-248	593	17	compartmental	compartmental	ADJ
ma-248	593	18	seirw	seirw	NOUN
ma-248	593	19	covid-19	covid-19	PROPN
ma-248	593	20	optimal	optimal	ADJ
ma-248	593	21	control	control	NOUN
ma-248	593	22	model	model	NOUN
ma-248	593	23	,	,	PUNCT
ma-248	593	24	comm.math	comm.math	PROPN
ma-248	593	25	.	.	PUNCT
ma-248	594	1	biol	biol	PROPN
ma-248	594	2	.	.	PUNCT
ma-248	595	1	neurosci	neurosci	PROPN
ma-248	595	2	.	.	PUNCT
ma-248	596	1	2020	2020	NUM
ma-248	596	2	(	(	PUNCT
ma-248	596	3	2020	2020	NUM
ma-248	596	4	)	)	PUNCT
ma-248	596	5	,	,	PUNCT
ma-248	596	6	87.[30	87.[30	PROPN
ma-248	596	7	]	]	X
ma-248	596	8	m.	m.	PROPN
ma-248	596	9	i.	i.	PROPN
ma-248	596	10	ossaiugbo	ossaiugbo	PROPN
ma-248	596	11	,	,	PUNCT
ma-248	596	12	n.	n.	PROPN
ma-248	596	13	i.	i.	PROPN
ma-248	596	14	okposo	okposo	PROPN
ma-248	596	15	,	,	PUNCT
ma-248	596	16	mathematical	mathematical	ADJ
ma-248	596	17	modeling	modeling	NOUN
ma-248	596	18	and	and	CCONJ
ma-248	596	19	analysis	analysis	NOUN
ma-248	596	20	of	of	ADP
ma-248	596	21	pneumonia	pneumonia	NOUN
ma-248	596	22	infection	infection	NOUN
ma-248	596	23	dynamics	dynamic	NOUN
ma-248	596	24	,	,	PUNCT
ma-248	596	25	sci	sci	PROPN
ma-248	596	26	.	.	PROPN
ma-248	596	27	world	world	PROPN
ma-248	597	1	j.16	j.16	PROPN
ma-248	597	2	(	(	PUNCT
ma-248	597	3	2021	2021	NUM
ma-248	597	4	)	)	PUNCT
ma-248	597	5	,	,	PUNCT
ma-248	597	6	73	73	NUM
ma-248	597	7	-	-	SYM
ma-248	597	8	80.[31	80.[31	PROPN
ma-248	597	9	]	]	X
ma-248	597	10	m.	m.	NOUN
ma-248	597	11	martcheva	martcheva	PROPN
ma-248	597	12	,	,	PUNCT
ma-248	597	13	g.	g.	PROPN
ma-248	597	14	crispino	crispino	PROPN
ma-248	597	15	-	-	PUNCT
ma-248	597	16	o’connell	o’connell	PROPN
ma-248	597	17	,	,	PUNCT
ma-248	597	18	the	the	DET
ma-248	597	19	transmission	transmission	NOUN
ma-248	597	20	of	of	ADP
ma-248	597	21	meningococcal	meningococcal	ADJ
ma-248	597	22	infection	infection	NOUN
ma-248	597	23	:	:	PUNCT
ma-248	597	24	a	a	DET
ma-248	597	25	mathematical	mathematical	ADJ
ma-248	597	26	study	study	NOUN
ma-248	597	27	,	,	PUNCT
ma-248	597	28	j.	j.	PROPN
ma-248	597	29	math.anal	math.anal	PROPN
ma-248	597	30	.	.	PUNCT
ma-248	597	31	appl	appl	PROPN
ma-248	597	32	.	.	PROPN
ma-248	598	1	283	283	NUM
ma-248	598	2	(	(	PUNCT
ma-248	598	3	2003	2003	NUM
ma-248	598	4	)	)	PUNCT
ma-248	598	5	,	,	PUNCT
ma-248	598	6	251–275.[32	251–275.[32	PROPN
ma-248	598	7	]	]	PUNCT
ma-248	598	8	m.	m.	PROPN
ma-248	598	9	j.	j.	PROPN
ma-248	598	10	f.	f.	PROPN
ma-248	598	11	martínez	martínez	PROPN
ma-248	598	12	,	,	PUNCT
ma-248	598	13	e.	e.	PROPN
ma-248	598	14	g.	g.	PROPN
ma-248	598	15	merino	merino	PROPN
ma-248	598	16	,	,	PUNCT
ma-248	598	17	e.	e.	PROPN
ma-248	598	18	g.	g.	PROPN
ma-248	598	19	sánchez	sánchez	PROPN
ma-248	598	20	,	,	PUNCT
ma-248	598	21	j.	j.	PROPN
ma-248	598	22	e.	e.	PROPN
ma-248	598	23	g.	g.	PROPN
ma-248	598	24	sánchez	sánchez	PROPN
ma-248	598	25	,	,	PUNCT
ma-248	598	26	a.	a.	PROPN
ma-248	598	27	m.	m.	PROPN
ma-248	598	28	d.	d.	PROPN
ma-248	598	29	rey	rey	PROPN
ma-248	598	30	,	,	PUNCT
ma-248	598	31	g.	g.	PROPN
ma-248	598	32	r.	r.	PROPN
ma-248	598	33	sánchez	sánchez	PROPN
ma-248	598	34	,	,	PUNCT
ma-248	598	35	a	a	DET
ma-248	598	36	mathematicalmodel	mathematicalmodel	NOUN
ma-248	598	37	to	to	PART
ma-248	598	38	study	study	VERB
ma-248	598	39	the	the	DET
ma-248	598	40	meningococcal	meningococcal	ADJ
ma-248	598	41	meningitis	meningitis	NOUN
ma-248	598	42	,	,	PUNCT
ma-248	598	43	proc	proc	NOUN
ma-248	598	44	.	.	PUNCT
ma-248	599	1	comp	comp	PROPN
ma-248	599	2	.	.	PUNCT
ma-248	600	1	sci	sci	PROPN
ma-248	600	2	.	.	PROPN
ma-248	601	1	18	18	NUM
ma-248	601	2	(	(	PUNCT
ma-248	601	3	2013	2013	NUM
ma-248	601	4	)	)	PUNCT
ma-248	601	5	,	,	PUNCT
ma-248	602	1	2492–2495.[33	2492–2495.[33	X
ma-248	602	2	]	]	X
ma-248	602	3	w.	w.	PROPN
ma-248	602	4	m.	m.	PROPN
ma-248	602	5	ritha	ritha	PROPN
ma-248	602	6	,	,	PUNCT
ma-248	602	7	w.	w.	PROPN
ma-248	602	8	lily	lily	PROPN
ma-248	602	9	,	,	PUNCT
ma-248	602	10	risk	risk	NOUN
ma-248	602	11	factors	factor	NOUN
ma-248	602	12	of	of	ADP
ma-248	602	13	meningitis	meningitis	NOUN
ma-248	602	14	in	in	ADP
ma-248	602	15	adults	adult	NOUN
ma-248	602	16	-	-	PUNCT
ma-248	602	17	an	an	DET
ma-248	602	18	analysis	analysis	NOUN
ma-248	602	19	using	use	VERB
ma-248	602	20	fuzzy	fuzzy	ADJ
ma-248	602	21	cognitive	cognitive	ADJ
ma-248	602	22	map	map	NOUN
ma-248	602	23	with	with	ADP
ma-248	602	24	topsis	topsis	NOUN
ma-248	602	25	,	,	PUNCT
ma-248	602	26	int.j	int.j	PROPN
ma-248	602	27	.	.	PUNCT
ma-248	603	1	sci	sci	PROPN
ma-248	603	2	.	.	PUNCT
ma-248	603	3	innov	innov	PROPN
ma-248	603	4	.	.	PUNCT
ma-248	604	1	math	math	NOUN
ma-248	604	2	.	.	PUNCT
ma-248	605	1	res	re	NOUN
ma-248	605	2	.	.	PROPN
ma-248	605	3	2	2	NUM
ma-248	605	4	(	(	PUNCT
ma-248	605	5	2014	2014	NUM
ma-248	605	6	)	)	PUNCT
ma-248	605	7	,	,	PUNCT
ma-248	605	8	418	418	NUM
ma-248	605	9	-	-	SYM
ma-248	605	10	425.[34	425.[34	NUM
ma-248	605	11	]	]	PUNCT
ma-248	605	12	r.	r.	PROPN
ma-248	605	13	u.	u.	PROPN
ma-248	605	14	hurit	hurit	PROPN
ma-248	605	15	,	,	PUNCT
ma-248	605	16	s.	s.	PROPN
ma-248	605	17	mungkasi	mungkasi	PROPN
ma-248	605	18	,	,	PUNCT
ma-248	605	19	the	the	DET
ma-248	605	20	euler	euler	NOUN
ma-248	605	21	,	,	PUNCT
ma-248	605	22	heun	heun	NOUN
ma-248	605	23	,	,	PUNCT
ma-248	605	24	and	and	CCONJ
ma-248	605	25	fourth	fourth	ADJ
ma-248	605	26	order	order	NOUN
ma-248	605	27	runge	runge	NOUN
ma-248	605	28	-	-	PUNCT
ma-248	605	29	kutta	kutta	NOUN
ma-248	605	30	solutions	solution	NOUN
ma-248	605	31	to	to	ADP
ma-248	605	32	seir	seir	ADJ
ma-248	605	33	model	model	NOUN
ma-248	605	34	for	for	ADP
ma-248	605	35	the	the	DET
ma-248	605	36	spreadof	spreadof	NOUN
ma-248	605	37	meningitis	meningiti	NOUN
ma-248	605	38	disease	disease	NOUN
ma-248	605	39	.	.	PUNCT
ma-248	606	1	mathline	mathline	NOUN
ma-248	606	2	6	6	NUM
ma-248	606	3	(	(	PUNCT
ma-248	606	4	2021	2021	NUM
ma-248	606	5	)	)	PUNCT
ma-248	606	6	,	,	PUNCT
ma-248	606	7	140	140	NUM
ma-248	606	8	-	-	SYM
ma-248	606	9	153.[35	153.[35	NUM
ma-248	606	10	]	]	PUNCT
ma-248	606	11	b.	b.	PROPN
ma-248	606	12	buonomo	buonomo	PROPN
ma-248	606	13	,	,	PUNCT
ma-248	606	14	a.	a.	NOUN
ma-248	606	15	d’onofrio	d’onofrio	PROPN
ma-248	606	16	,	,	PUNCT
ma-248	606	17	s.m	s.m	PROPN
ma-248	606	18	.	.	PROPN
ma-248	606	19	kassa	kassa	PROPN
ma-248	606	20	,	,	PUNCT
ma-248	606	21	y.h	y.h	PROPN
ma-248	606	22	.	.	PROPN
ma-248	606	23	workineh	workineh	PROPN
ma-248	606	24	,	,	PUNCT
ma-248	606	25	modeling	model	VERB
ma-248	606	26	the	the	DET
ma-248	606	27	effects	effect	NOUN
ma-248	606	28	of	of	ADP
ma-248	606	29	information	information	NOUN
ma-248	606	30	-	-	PUNCT
ma-248	606	31	dependent	dependent	ADJ
ma-248	606	32	vaccinationbehavior	vaccinationbehavior	NOUN
ma-248	606	33	on	on	ADP
ma-248	606	34	meningitis	meningitis	NOUN
ma-248	606	35	transmission	transmission	NOUN
ma-248	606	36	,	,	PUNCT
ma-248	606	37	math	math	NOUN
ma-248	606	38	.	.	PUNCT
ma-248	606	39	meth	meth	NOUN
ma-248	606	40	.	.	PUNCT
ma-248	607	1	appl	appl	PROPN
ma-248	607	2	.	.	PUNCT
ma-248	608	1	sci	sci	PROPN
ma-248	608	2	.	.	PROPN
ma-248	609	1	45	45	NUM
ma-248	609	2	(	(	PUNCT
ma-248	609	3	2022	2022	NUM
ma-248	609	4	)	)	PUNCT
ma-248	609	5	,	,	PUNCT
ma-248	609	6	732–748.[36	732–748.[36	NOUN
ma-248	609	7	]	]	PUNCT
ma-248	609	8	c.	c.	PROPN
ma-248	609	9	w.	w.	PROPN
ma-248	609	10	chukwu	chukwu	PROPN
ma-248	609	11	,	,	PUNCT
ma-248	609	12	j.	j.	PROPN
ma-248	609	13	mushanyu	mushanyu	PROPN
ma-248	609	14	,	,	PUNCT
ma-248	609	15	m.	m.	PROPN
ma-248	609	16	l.	l.	PROPN
ma-248	609	17	juga	juga	PROPN
ma-248	609	18	,	,	PUNCT
ma-248	609	19	fatmawati	fatmawati	PROPN
ma-248	609	20	,	,	PUNCT
ma-248	609	21	a	a	DET
ma-248	609	22	mathematical	mathematical	ADJ
ma-248	609	23	model	model	NOUN
ma-248	609	24	for	for	ADP
ma-248	609	25	co	co	NOUN
ma-248	609	26	-	-	NOUN
ma-248	609	27	dynamics	dynamic	NOUN
ma-248	609	28	of	of	ADP
ma-248	609	29	listeriosis	listeriosis	NOUN
ma-248	609	30	and	and	CCONJ
ma-248	609	31	bacterialmeningitis	bacterialmeningitis	NOUN
ma-248	609	32	diseases	disease	NOUN
ma-248	609	33	,	,	PUNCT
ma-248	609	34	comm	comm	NOUN
ma-248	609	35	.	.	PUNCT
ma-248	610	1	math	math	NOUN
ma-248	610	2	.	.	PUNCT
ma-248	611	1	biol	biol	PROPN
ma-248	611	2	.	.	PUNCT
ma-248	612	1	neurosci	neurosci	PROPN
ma-248	612	2	.	.	PUNCT
ma-248	613	1	2020	2020	NUM
ma-248	613	2	(	(	PUNCT
ma-248	613	3	2020	2020	NUM
ma-248	613	4	)	)	PUNCT
ma-248	613	5	,	,	PUNCT
ma-248	613	6	83.[37	83.[37	NUM
ma-248	613	7	]	]	PUNCT
ma-248	613	8	k.	k.	PROPN
ma-248	613	9	g.	g.	PROPN
ma-248	613	10	varshney	varshney	NOUN
ma-248	613	11	,	,	PUNCT
ma-248	613	12	y.	y.	PROPN
ma-248	613	13	k.	k.	PROPN
ma-248	613	14	dwivedi	dwivedi	PROPN
ma-248	613	15	,	,	PUNCT
ma-248	613	16	mathematical	mathematical	ADJ
ma-248	613	17	modelling	modelling	NOUN
ma-248	613	18	of	of	ADP
ma-248	613	19	influenza	influenza	NOUN
ma-248	613	20	-	-	PUNCT
ma-248	613	21	meningitis	meningitis	NOUN
ma-248	613	22	under	under	ADP
ma-248	613	23	the	the	DET
ma-248	613	24	quarantine	quarantine	NOUN
ma-248	613	25	effect	effect	NOUN
ma-248	613	26	ofinfluenza	ofinfluenza	PROPN
ma-248	613	27	.	.	PUNCT
ma-248	613	28	turk	turk	PROPN
ma-248	613	29	.	.	PUNCT
ma-248	614	1	j.	j.	PROPN
ma-248	614	2	comp	comp	PROPN
ma-248	614	3	.	.	PUNCT
ma-248	615	1	math	math	PROPN
ma-248	615	2	.	.	PUNCT
ma-248	616	1	educ	educ	PROPN
ma-248	616	2	.	.	PUNCT
ma-248	617	1	12	12	NUM
ma-248	617	2	(	(	PUNCT
ma-248	617	3	2021	2021	NUM
ma-248	617	4	)	)	PUNCT
ma-248	617	5	,	,	PUNCT
ma-248	617	6	7214	7214	NUM
ma-248	617	7	-	-	SYM
ma-248	617	8	7225.[38	7225.[38	NUM
ma-248	617	9	]	]	PUNCT
ma-248	617	10	m.	m.	NOUN
ma-248	617	11	a.	a.	NOUN
ma-248	617	12	afolabi	afolabi	PROPN
ma-248	617	13	,	,	PUNCT
ma-248	617	14	k.	k.	PROPN
ma-248	617	15	s.	s.	PROPN
ma-248	617	16	adewoye	adewoye	PROPN
ma-248	617	17	,	,	PUNCT
ma-248	617	18	a.	a.	PROPN
ma-248	617	19	i.	i.	PROPN
ma-248	617	20	folorunso	folorunso	PROPN
ma-248	617	21	,	,	PUNCT
ma-248	617	22	m.	m.	NOUN
ma-248	617	23	a.	a.	NOUN
ma-248	617	24	omoloye	omoloye	PROPN
ma-248	617	25	,	,	PUNCT
ma-248	617	26	a	a	DET
ma-248	617	27	mathematical	mathematical	ADJ
ma-248	617	28	model	model	NOUN
ma-248	617	29	on	on	ADP
ma-248	617	30	transmission	transmission	NOUN
ma-248	617	31	dynamics	dynamic	NOUN
ma-248	617	32	ofmeningococcal	ofmeningococcal	ADJ
ma-248	617	33	meningitis	meningitis	NOUN
ma-248	617	34	,	,	PUNCT
ma-248	617	35	iconic	iconic	ADJ
ma-248	617	36	res	re	NOUN
ma-248	617	37	.	.	PUNCT
ma-248	618	1	eng	eng	PROPN
ma-248	618	2	.	.	PUNCT
ma-248	619	1	j.	j.	PROPN
ma-248	619	2	4	4	NUM
ma-248	619	3	(	(	PUNCT
ma-248	619	4	2021	2021	NUM
ma-248	619	5	)	)	PUNCT
ma-248	619	6	,	,	PUNCT
ma-248	619	7	59	59	NUM
ma-248	619	8	-	-	SYM
ma-248	619	9	66.[39	66.[39	NUM
ma-248	619	10	]	]	X
ma-248	619	11	e.	e.	PROPN
ma-248	619	12	n.	n.	PROPN
ma-248	619	13	wiah	wiah	PROPN
ma-248	619	14	,	,	PUNCT
ma-248	619	15	i.	i.	PROPN
ma-248	619	16	a.	a.	PROPN
ma-248	619	17	adetunde	adetunde	PROPN
ma-248	619	18	,	,	PUNCT
ma-248	619	19	a	a	DET
ma-248	619	20	mathematical	mathematical	ADJ
ma-248	619	21	model	model	NOUN
ma-248	619	22	of	of	ADP
ma-248	619	23	cerebrospinal	cerebrospinal	ADJ
ma-248	619	24	meningitis	meningitis	NOUN
ma-248	619	25	epidemic	epidemic	NOUN
ma-248	619	26	:	:	PUNCT
ma-248	619	27	a	a	DET
ma-248	619	28	case	case	NOUN
ma-248	619	29	study	study	NOUN
ma-248	619	30	for	for	ADP
ma-248	619	31	jirapadistrict	jirapadistrict	PROPN
ma-248	619	32	,	,	PUNCT
ma-248	619	33	ghana	ghana	PROPN
ma-248	619	34	,	,	PUNCT
ma-248	619	35	curr	curr	PROPN
ma-248	619	36	.	.	PUNCT
ma-248	619	37	appl	appl	PROPN
ma-248	619	38	.	.	PUNCT
ma-248	620	1	sci	sci	PROPN
ma-248	620	2	.	.	PROPN
ma-248	620	3	technol	technol	PROPN
ma-248	620	4	.	.	PROPN
ma-248	621	1	10	10	NUM
ma-248	621	2	(	(	PUNCT
ma-248	621	3	2014	2014	NUM
ma-248	621	4	)	)	PUNCT
ma-248	621	5	,	,	PUNCT
ma-248	621	6	63	63	NUM
ma-248	621	7	-	-	SYM
ma-248	621	8	73.[40	73.[40	NUM
ma-248	621	9	]	]	X
ma-248	621	10	r.	r.	PROPN
ma-248	621	11	m.	m.	PROPN
ma-248	621	12	neilan	neilan	PROPN
ma-248	621	13	,	,	PUNCT
ma-248	621	14	s.	s.	PROPN
ma-248	621	15	m.	m.	PROPN
ma-248	621	16	lenhart	lenhart	PROPN
ma-248	621	17	,	,	PUNCT
ma-248	621	18	an	an	DET
ma-248	621	19	introduction	introduction	NOUN
ma-248	621	20	to	to	ADP
ma-248	621	21	optimal	optimal	ADJ
ma-248	621	22	control	control	NOUN
ma-248	621	23	with	with	ADP
ma-248	621	24	an	an	DET
ma-248	621	25	application	application	NOUN
ma-248	621	26	in	in	ADP
ma-248	621	27	disease	disease	NOUN
ma-248	621	28	modeling	modeling	NOUN
ma-248	621	29	,	,	PUNCT
ma-248	621	30	model.parad	model.parad	PROPN
ma-248	621	31	.	.	PROPN
ma-248	621	32	anal	anal	PROPN
ma-248	621	33	.	.	PUNCT
ma-248	622	1	dis	dis	PROPN
ma-248	622	2	.	.	PUNCT
ma-248	622	3	trasmiss	trasmiss	PROPN
ma-248	622	4	.	.	PUNCT
ma-248	623	1	models	model	NOUN
ma-248	623	2	,	,	PUNCT
ma-248	623	3	49	49	NUM
ma-248	623	4	(	(	PUNCT
ma-248	623	5	2010	2010	NUM
ma-248	623	6	)	)	PUNCT
ma-248	623	7	,	,	PUNCT
ma-248	623	8	67	67	NUM
ma-248	623	9	-	-	SYM
ma-248	623	10	82.[41	82.[41	NUM
ma-248	623	11	]	]	X
ma-248	623	12	i.	i.	PROPN
ma-248	623	13	m.	m.	PROPN
ma-248	623	14	ross	ross	PROPN
ma-248	623	15	,	,	PUNCT
ma-248	623	16	a	a	DET
ma-248	623	17	primer	primer	NOUN
ma-248	623	18	on	on	ADP
ma-248	623	19	pontryagin	pontryagin	NOUN
ma-248	623	20	’s	’s	PART
ma-248	623	21	principle	principle	NOUN
ma-248	623	22	in	in	ADP
ma-248	623	23	optimal	optimal	ADJ
ma-248	623	24	control	control	NOUN
ma-248	623	25	,	,	PUNCT
ma-248	623	26	collegiate	collegiate	ADJ
ma-248	623	27	publishers	publisher	NOUN
ma-248	623	28	,	,	PUNCT
ma-248	623	29	(	(	PUNCT
ma-248	623	30	2009).[42	2009).[42	X
ma-248	623	31	]	]	PUNCT
ma-248	623	32	s.	s.	PROPN
ma-248	623	33	lenhart	lenhart	PROPN
ma-248	623	34	,	,	PUNCT
ma-248	623	35	j.	j.	PROPN
ma-248	623	36	t.	t.	PROPN
ma-248	623	37	workman	workman	PROPN
ma-248	623	38	,	,	PUNCT
ma-248	623	39	optimal	optimal	ADJ
ma-248	623	40	control	control	NOUN
ma-248	623	41	applied	apply	VERB
ma-248	623	42	to	to	ADP
ma-248	623	43	biological	biological	ADJ
ma-248	623	44	models	model	NOUN
ma-248	623	45	,	,	PUNCT
ma-248	623	46	taylor	taylor	PROPN
ma-248	623	47	&	&	CCONJ
ma-248	623	48	francis	francis	PROPN
ma-248	623	49	,	,	PUNCT
ma-248	623	50	(	(	PUNCT
ma-248	623	51	2007).[43	2007).[43	X
ma-248	623	52	]	]	X
ma-248	623	53	o.	o.	NOUN
ma-248	623	54	sharomi	sharomi	PROPN
ma-248	623	55	,	,	PUNCT
ma-248	623	56	t.	t.	PROPN
ma-248	623	57	malik	malik	PROPN
ma-248	623	58	,	,	PUNCT
ma-248	623	59	optimal	optimal	ADJ
ma-248	623	60	control	control	NOUN
ma-248	623	61	in	in	ADP
ma-248	623	62	epidemiology	epidemiology	NOUN
ma-248	623	63	.	.	PUNCT
ma-248	624	1	ann	ann	PROPN
ma-248	624	2	.	.	PUNCT
ma-248	624	3	oper	oper	PROPN
ma-248	624	4	.	.	PUNCT
ma-248	625	1	res	re	NOUN
ma-248	625	2	.	.	PUNCT
ma-248	626	1	251	251	NUM
ma-248	626	2	(	(	PUNCT
ma-248	626	3	2017	2017	NUM
ma-248	626	4	)	)	PUNCT
ma-248	626	5	,	,	PUNCT
ma-248	626	6	55–71.[44	55–71.[44	NUM
ma-248	626	7	]	]	X
ma-248	626	8	a.k	a.k	PROPN
ma-248	626	9	.	.	PROPN
ma-248	626	10	misra	misra	PROPN
ma-248	626	11	,	,	PUNCT
ma-248	626	12	a.	a.	NOUN
ma-248	626	13	sharma	sharma	PROPN
ma-248	626	14	,	,	PUNCT
ma-248	626	15	j.b	j.b	PROPN
ma-248	626	16	.	.	PROPN
ma-248	626	17	shukla	shukla	NOUN
ma-248	626	18	,	,	PUNCT
ma-248	626	19	modeling	modeling	NOUN
ma-248	626	20	and	and	CCONJ
ma-248	626	21	analysis	analysis	NOUN
ma-248	626	22	of	of	ADP
ma-248	626	23	effects	effect	NOUN
ma-248	626	24	of	of	ADP
ma-248	626	25	awareness	awareness	NOUN
ma-248	626	26	programs	program	NOUN
ma-248	626	27	by	by	ADP
ma-248	626	28	media	medium	NOUN
ma-248	626	29	on	on	ADP
ma-248	626	30	the	the	DET
ma-248	626	31	spreadof	spreadof	ADJ
ma-248	626	32	infectious	infectious	ADJ
ma-248	626	33	diseases	disease	NOUN
ma-248	626	34	,	,	PUNCT
ma-248	626	35	math	math	NOUN
ma-248	626	36	.	.	PUNCT
ma-248	627	1	comp	comp	PROPN
ma-248	627	2	.	.	PUNCT
ma-248	627	3	model	model	PROPN
ma-248	627	4	.	.	PUNCT
ma-248	628	1	53	53	NUM
ma-248	628	2	(	(	PUNCT
ma-248	628	3	2011	2011	NUM
ma-248	628	4	)	)	PUNCT
ma-248	628	5	,	,	PUNCT
ma-248	628	6	1221–1228.[45	1221–1228.[45	NUM
ma-248	628	7	]	]	X
ma-248	628	8	e.	e.	PROPN
ma-248	628	9	bonyah	bonyah	PROPN
ma-248	628	10	,	,	PUNCT
ma-248	628	11	k.	k.	PROPN
ma-248	628	12	badu	badu	PROPN
ma-248	628	13	,	,	PUNCT
ma-248	628	14	s.k	s.k	PROPN
ma-248	628	15	.	.	PROPN
ma-248	628	16	asiedu	asiedu	PROPN
ma-248	628	17	-	-	PUNCT
ma-248	628	18	addo	addo	PROPN
ma-248	628	19	,	,	PUNCT
ma-248	628	20	optimal	optimal	ADJ
ma-248	628	21	control	control	NOUN
ma-248	628	22	application	application	NOUN
ma-248	628	23	to	to	ADP
ma-248	628	24	an	an	DET
ma-248	628	25	ebola	ebola	NOUN
ma-248	628	26	model	model	NOUN
ma-248	628	27	,	,	PUNCT
ma-248	628	28	asian	asian	PROPN
ma-248	628	29	pac	pac	PROPN
ma-248	628	30	.	.	PUNCT
ma-248	629	1	j.	j.	PROPN
ma-248	629	2	trop	trop	PROPN
ma-248	629	3	.	.	PUNCT
ma-248	630	1	biomed.6	biomed.6	PROPN
ma-248	630	2	(	(	PUNCT
ma-248	630	3	2016	2016	NUM
ma-248	630	4	)	)	PUNCT
ma-248	630	5	,	,	PUNCT
ma-248	630	6	283–289.[46	283–289.[46	PROPN
ma-248	630	7	]	]	PUNCT
ma-248	631	1	s.	s.	PROPN
ma-248	631	2	i̇ğret	i̇ğret	PROPN
ma-248	631	3	araz	araz	PROPN
ma-248	631	4	,	,	PUNCT
ma-248	631	5	analysis	analysis	NOUN
ma-248	631	6	of	of	ADP
ma-248	631	7	a	a	DET
ma-248	631	8	covid-19	covid-19	PROPN
ma-248	631	9	model	model	NOUN
ma-248	631	10	:	:	PUNCT
ma-248	631	11	optimal	optimal	ADJ
ma-248	631	12	control	control	NOUN
ma-248	631	13	,	,	PUNCT
ma-248	631	14	stability	stability	NOUN
ma-248	631	15	and	and	CCONJ
ma-248	631	16	simulations	simulation	NOUN
ma-248	631	17	,	,	PUNCT
ma-248	631	18	alex	alex	PROPN
ma-248	631	19	.	.	PUNCT
ma-248	632	1	eng	eng	PROPN
ma-248	632	2	.	.	PUNCT
ma-248	633	1	j.	j.	PROPN
ma-248	633	2	60	60	NUM
ma-248	633	3	(	(	PUNCT
ma-248	633	4	2021),647–658	2021),647–658	NUM
ma-248	633	5	.	.	PUNCT
ma-248	634	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	634	2	https://doi.org/10.1017/s0950268818002625	https://doi.org/10.1017/s0950268818002625	NUM
ma-248	634	3	eur	eur	NOUN
ma-248	634	4	.	.	PUNCT
ma-248	635	1	j.	j.	PROPN
ma-248	635	2	math	math	PROPN
ma-248	635	3	.	.	PUNCT
ma-248	636	1	anal	anal	PROPN
ma-248	636	2	.	.	PUNCT
ma-248	637	1	10.28924	10.28924	NUM
ma-248	637	2	/	/	SYM
ma-248	637	3	ada	ada	PROPN
ma-248	637	4	/	/	SYM
ma-248	637	5	ma.4.21	ma.4.21	NOUN
ma-248	637	6	27	27	NUM
ma-248	638	1	[	[	X
ma-248	638	2	47	47	NUM
ma-248	638	3	]	]	PUNCT
ma-248	638	4	x.	x.	PROPN
ma-248	638	5	yan	yan	PROPN
ma-248	638	6	,	,	PUNCT
ma-248	638	7	y.	y.	PROPN
ma-248	638	8	zou	zou	PROPN
ma-248	638	9	,	,	PUNCT
ma-248	638	10	optimal	optimal	ADJ
ma-248	638	11	and	and	CCONJ
ma-248	638	12	sub	sub	ADJ
ma-248	638	13	-	-	ADJ
ma-248	638	14	optimal	optimal	ADJ
ma-248	638	15	quarantine	quarantine	NOUN
ma-248	638	16	and	and	CCONJ
ma-248	638	17	isolation	isolation	NOUN
ma-248	638	18	control	control	NOUN
ma-248	638	19	in	in	ADP
ma-248	638	20	sars	sars	PROPN
ma-248	638	21	epidemics	epidemic	NOUN
ma-248	638	22	,	,	PUNCT
ma-248	638	23	math	math	NOUN
ma-248	638	24	.	.	PUNCT
ma-248	639	1	comp	comp	PROPN
ma-248	639	2	.	.	PUNCT
ma-248	640	1	model.47	model.47	PROPN
ma-248	640	2	(	(	PUNCT
ma-248	640	3	2008	2008	NUM
ma-248	640	4	)	)	PUNCT
ma-248	640	5	,	,	PUNCT
ma-248	640	6	235–245.[48	235–245.[48	NUM
ma-248	640	7	]	]	X
ma-248	640	8	a.	a.	NOUN
ma-248	640	9	karachaliou	karachaliou	NOUN
ma-248	640	10	,	,	PUNCT
ma-248	640	11	a.	a.	PROPN
ma-248	640	12	j.	j.	PROPN
ma-248	640	13	k.	k.	PROPN
ma-248	640	14	conlan	conlan	PROPN
ma-248	640	15	,	,	PUNCT
ma-248	640	16	m.	m.	NOUN
ma-248	640	17	p.	p.	NOUN
ma-248	640	18	preziosi	preziosi	NOUN
ma-248	640	19	,	,	PUNCT
ma-248	640	20	c.	c.	PROPN
ma-248	640	21	l.	l.	PROPN
ma-248	640	22	trotter	trotter	PROPN
ma-248	640	23	,	,	PUNCT
ma-248	640	24	modeling	model	VERB
ma-248	640	25	long	long	ADJ
ma-248	640	26	-	-	PUNCT
ma-248	640	27	term	term	NOUN
ma-248	640	28	vaccination	vaccination	NOUN
ma-248	640	29	strategies	strategy	NOUN
ma-248	640	30	withmenafrivac	withmenafrivac	NOUN
ma-248	640	31	in	in	ADP
ma-248	640	32	the	the	DET
ma-248	640	33	african	african	ADJ
ma-248	640	34	meningitis	meningitis	NOUN
ma-248	640	35	belt	belt	NOUN
ma-248	640	36	,	,	PUNCT
ma-248	640	37	clin	clin	PROPN
ma-248	640	38	.	.	PUNCT
ma-248	641	1	infect	infect	VERB
ma-248	641	2	.	.	PUNCT
ma-248	642	1	dis	dis	PROPN
ma-248	642	2	.	.	PUNCT
ma-248	643	1	61	61	NUM
ma-248	643	2	(	(	PUNCT
ma-248	643	3	2015	2015	NUM
ma-248	643	4	)	)	PUNCT
ma-248	643	5	,	,	PUNCT
ma-248	643	6	s594	s594	PROPN
ma-248	643	7	–	–	PUNCT
ma-248	643	8	s600	s600	NUM
ma-248	643	9	.	.	PUNCT
ma-248	644	1	https://doi.org/10.28924/ada/ma.4.21	https://doi.org/10.28924/ada/ma.4.21	PROPN
ma-248	644	2	1	1	NUM
ma-248	644	3	.	.	PUNCT
ma-248	644	4	introduction	introduction	NOUN
ma-248	644	5	2	2	NUM
ma-248	644	6	.	.	PUNCT
ma-248	644	7	mathematical	mathematical	ADJ
ma-248	644	8	model	model	NOUN
ma-248	644	9	3	3	NUM
ma-248	644	10	.	.	PUNCT
ma-248	644	11	qualitative	qualitative	ADJ
ma-248	644	12	properties	property	NOUN
ma-248	644	13	3.1	3.1	NUM
ma-248	644	14	.	.	PUNCT
ma-248	644	15	positivity	positivity	NOUN
ma-248	644	16	and	and	CCONJ
ma-248	644	17	boundedness	boundedness	NOUN
ma-248	644	18	3.2	3.2	NUM
ma-248	644	19	.	.	PUNCT
ma-248	645	1	existence	existence	NOUN
ma-248	645	2	of	of	ADP
ma-248	645	3	disease	disease	NOUN
ma-248	645	4	-	-	PUNCT
ma-248	645	5	free	free	ADJ
ma-248	645	6	equilibrium	equilibrium	NOUN
ma-248	645	7	(	(	PUNCT
ma-248	645	8	dfe	dfe	PROPN
ma-248	645	9	)	)	PUNCT
ma-248	645	10	point	point	NOUN
ma-248	645	11	3.3	3.3	NUM
ma-248	645	12	.	.	PUNCT
ma-248	646	1	basic	basic	ADJ
ma-248	646	2	reproduction	reproduction	NOUN
ma-248	646	3	number	number	NOUN
ma-248	646	4	3.4	3.4	NUM
ma-248	646	5	.	.	PUNCT
ma-248	646	6	existence	existence	NOUN
ma-248	646	7	of	of	ADP
ma-248	646	8	an	an	DET
ma-248	646	9	endemic	endemic	ADJ
ma-248	646	10	equilibrium	equilibrium	NOUN
ma-248	646	11	point	point	NOUN
ma-248	646	12	(	(	PUNCT
ma-248	646	13	eep	eep	NOUN
ma-248	646	14	)	)	PUNCT
ma-248	646	15	3.5	3.5	NUM
ma-248	646	16	.	.	PUNCT
ma-248	646	17	stability	stability	NOUN
ma-248	646	18	of	of	ADP
ma-248	646	19	the	the	DET
ma-248	646	20	disease	disease	NOUN
ma-248	646	21	-	-	PUNCT
ma-248	646	22	free	free	ADJ
ma-248	646	23	equilibrium	equilibrium	NOUN
ma-248	646	24	point	point	NOUN
ma-248	646	25	3.6	3.6	NUM
ma-248	646	26	.	.	PUNCT
ma-248	647	1	stability	stability	NOUN
ma-248	647	2	of	of	ADP
ma-248	647	3	the	the	DET
ma-248	647	4	endemic	endemic	ADJ
ma-248	647	5	equilibrium	equilibrium	NOUN
ma-248	647	6	point	point	NOUN
ma-248	647	7	4	4	NUM
ma-248	647	8	.	.	NOUN
ma-248	648	1	sensitivity	sensitivity	NOUN
ma-248	648	2	analysis	analysis	NOUN
ma-248	648	3	of	of	ADP
ma-248	648	4	5	5	NUM
ma-248	648	5	.	.	PUNCT
ma-248	649	1	optimal	optimal	ADJ
ma-248	649	2	control	control	NOUN
ma-248	649	3	analysis	analysis	NOUN
ma-248	649	4	6	6	NUM
ma-248	649	5	.	.	PUNCT
ma-248	649	6	numerical	numerical	PROPN
ma-248	649	7	simulation	simulation	NOUN
ma-248	649	8	and	and	CCONJ
ma-248	649	9	discussion	discussion	NOUN
ma-248	649	10	6.1	6.1	NUM
ma-248	649	11	.	.	PUNCT
ma-248	650	1	strategy	strategy	NOUN
ma-248	650	2	a	a	DET
ma-248	650	3	:	:	SYM
ma-248	650	4	6.2	6.2	NUM
ma-248	650	5	.	.	PUNCT
ma-248	651	1	strategy	strategy	PROPN
ma-248	651	2	b	b	PROPN
ma-248	651	3	:	:	PUNCT
ma-248	651	4	6.3	6.3	NUM
ma-248	651	5	.	.	PUNCT
ma-248	652	1	strategy	strategy	NOUN
ma-248	652	2	c	c	PROPN
ma-248	652	3	:	:	PUNCT
ma-248	652	4	6.4	6.4	NUM
ma-248	652	5	.	.	PUNCT
ma-248	653	1	strategy	strategy	NOUN
ma-248	653	2	d	d	NOUN
ma-248	653	3	:	:	PUNCT
ma-248	653	4	7	7	X
ma-248	653	5	.	.	NOUN
ma-248	653	6	discussion	discussion	NOUN
ma-248	653	7	and	and	CCONJ
ma-248	653	8	conclusion	conclusion	NOUN
ma-248	653	9	references	reference	NOUN