id	sid	tid	token	lemma	pos
ejpam-6129	1	1	european	european	PROPN
ejpam-6129	1	2	journal	journal	PROPN
ejpam-6129	1	3	of	of	ADP
ejpam-6129	1	4	pure	pure	ADJ
ejpam-6129	1	5	and	and	CCONJ
ejpam-6129	1	6	applied	applied	ADJ
ejpam-6129	1	7	mathematics	mathematic	NOUN
ejpam-6129	1	8	2025	2025	NUM
ejpam-6129	1	9	,	,	PUNCT
ejpam-6129	1	10	vol	vol	NOUN
ejpam-6129	1	11	.	.	PROPN
ejpam-6129	1	12	18	18	NUM
ejpam-6129	1	13	,	,	PUNCT
ejpam-6129	1	14	issue	issue	NOUN
ejpam-6129	1	15	3	3	NUM
ejpam-6129	1	16	,	,	PUNCT
ejpam-6129	1	17	article	article	NOUN
ejpam-6129	1	18	number	number	NOUN
ejpam-6129	1	19	6129	6129	NUM
ejpam-6129	1	20	issn	issn	PROPN
ejpam-6129	1	21	1307	1307	NUM
ejpam-6129	1	22	-	-	SYM
ejpam-6129	1	23	5543	5543	NUM
ejpam-6129	1	24	–	–	PUNCT
ejpam-6129	1	25	ejpam.com	ejpam.com	X
ejpam-6129	1	26	published	publish	VERB
ejpam-6129	1	27	by	by	ADP
ejpam-6129	1	28	new	new	PROPN
ejpam-6129	1	29	york	york	PROPN
ejpam-6129	1	30	business	business	PROPN
ejpam-6129	1	31	global	global	ADJ
ejpam-6129	1	32	optimal	optimal	ADJ
ejpam-6129	1	33	control	control	NOUN
ejpam-6129	1	34	strategies	strategy	NOUN
ejpam-6129	1	35	applied	apply	VERB
ejpam-6129	1	36	to	to	ADP
ejpam-6129	1	37	a	a	DET
ejpam-6129	1	38	mathematical	mathematical	ADJ
ejpam-6129	1	39	model	model	NOUN
ejpam-6129	1	40	of	of	ADP
ejpam-6129	1	41	meningitis	meningitis	PROPN
ejpam-6129	1	42	sahar	sahar	PROPN
ejpam-6129	1	43	a.	a.	PROPN
ejpam-6129	1	44	mohamed1	mohamed1	PROPN
ejpam-6129	1	45	,	,	PUNCT
ejpam-6129	1	46	hasim	hasim	ADJ
ejpam-6129	1	47	a.	a.	NOUN
ejpam-6129	1	48	obaid2,3,∗	obaid2,3,∗	PROPN
ejpam-6129	1	49	,	,	PUNCT
ejpam-6129	1	50	eihab	eihab	PROPN
ejpam-6129	1	51	b.	b.	PROPN
ejpam-6129	1	52	m.	m.	PROPN
ejpam-6129	1	53	bashier4	bashier4	PROPN
ejpam-6129	1	54	,	,	PUNCT
ejpam-6129	1	55	kailash	kailash	PROPN
ejpam-6129	1	56	c.	c.	PROPN
ejpam-6129	1	57	patidar	patidar	PROPN
ejpam-6129	1	58	5	5	NUM
ejpam-6129	1	59	1	1	NUM
ejpam-6129	1	60	department	department	NOUN
ejpam-6129	1	61	of	of	ADP
ejpam-6129	1	62	physics	physics	PROPN
ejpam-6129	1	63	,	,	PUNCT
ejpam-6129	1	64	faculty	faculty	NOUN
ejpam-6129	1	65	of	of	ADP
ejpam-6129	1	66	science	science	NOUN
ejpam-6129	1	67	and	and	CCONJ
ejpam-6129	1	68	technology	technology	NOUN
ejpam-6129	1	69	,	,	PUNCT
ejpam-6129	1	70	al	al	PROPN
ejpam-6129	1	71	neelain	neelain	NOUN
ejpam-6129	1	72	uiversity	uiversity	NOUN
ejpam-6129	1	73	,	,	PUNCT
ejpam-6129	1	74	khartoum	khartoum	PROPN
ejpam-6129	1	75	,	,	PUNCT
ejpam-6129	1	76	sudan	sudan	PROPN
ejpam-6129	1	77	2	2	NUM
ejpam-6129	1	78	department	department	NOUN
ejpam-6129	1	79	of	of	ADP
ejpam-6129	1	80	applied	apply	VERB
ejpam-6129	1	81	mathematics	mathematic	NOUN
ejpam-6129	1	82	,	,	PUNCT
ejpam-6129	1	83	faculty	faculty	NOUN
ejpam-6129	1	84	of	of	ADP
ejpam-6129	1	85	mathematical	mathematical	ADJ
ejpam-6129	1	86	sciences	sciences	PROPN
ejpam-6129	1	87	and	and	CCONJ
ejpam-6129	1	88	informatics	informatic	NOUN
ejpam-6129	1	89	,	,	PUNCT
ejpam-6129	1	90	university	university	PROPN
ejpam-6129	1	91	of	of	ADP
ejpam-6129	1	92	khartoum	khartoum	PROPN
ejpam-6129	1	93	,	,	PUNCT
ejpam-6129	1	94	khartoum	khartoum	PROPN
ejpam-6129	1	95	,	,	PUNCT
ejpam-6129	1	96	sudan	sudan	PROPN
ejpam-6129	1	97	3	3	NUM
ejpam-6129	1	98	ahmed	ahmed	PROPN
ejpam-6129	1	99	bin	bin	PROPN
ejpam-6129	1	100	mohammed	mohammed	PROPN
ejpam-6129	1	101	military	military	PROPN
ejpam-6129	1	102	college	college	PROPN
ejpam-6129	1	103	,	,	PUNCT
ejpam-6129	1	104	doha	doha	PROPN
ejpam-6129	1	105	,	,	PUNCT
ejpam-6129	1	106	qatar	qatar	PROPN
ejpam-6129	1	107	4department	4department	NUM
ejpam-6129	1	108	of	of	ADP
ejpam-6129	1	109	mathematics	mathematic	NOUN
ejpam-6129	1	110	,	,	PUNCT
ejpam-6129	1	111	faculty	faculty	NOUN
ejpam-6129	1	112	of	of	ADP
ejpam-6129	1	113	education	education	NOUN
ejpam-6129	1	114	and	and	CCONJ
ejpam-6129	1	115	arts	art	NOUN
ejpam-6129	1	116	,	,	PUNCT
ejpam-6129	1	117	university	university	PROPN
ejpam-6129	1	118	of	of	ADP
ejpam-6129	1	119	sohar	sohar	PROPN
ejpam-6129	1	120	,	,	PUNCT
ejpam-6129	1	121	sohar	sohar	PROPN
ejpam-6129	1	122	,	,	PUNCT
ejpam-6129	1	123	oman	oman	PROPN
ejpam-6129	1	124	5department	5department	NUM
ejpam-6129	1	125	of	of	ADP
ejpam-6129	1	126	mathematics	mathematic	NOUN
ejpam-6129	1	127	and	and	CCONJ
ejpam-6129	1	128	applied	applied	ADJ
ejpam-6129	1	129	mathematics	mathematic	NOUN
ejpam-6129	1	130	,	,	PUNCT
ejpam-6129	1	131	faculty	faculty	NOUN
ejpam-6129	1	132	of	of	ADP
ejpam-6129	1	133	natural	natural	ADJ
ejpam-6129	1	134	sciences	science	NOUN
ejpam-6129	1	135	,	,	PUNCT
ejpam-6129	1	136	university	university	NOUN
ejpam-6129	1	137	of	of	ADP
ejpam-6129	1	138	the	the	DET
ejpam-6129	1	139	western	western	ADJ
ejpam-6129	1	140	cape	cape	NOUN
ejpam-6129	1	141	,	,	PUNCT
ejpam-6129	1	142	bellville	bellville	PROPN
ejpam-6129	1	143	,	,	PUNCT
ejpam-6129	1	144	south	south	PROPN
ejpam-6129	1	145	africa	africa	PROPN
ejpam-6129	1	146	abstract	abstract	PROPN
ejpam-6129	1	147	.	.	PUNCT
ejpam-6129	2	1	in	in	ADP
ejpam-6129	2	2	this	this	DET
ejpam-6129	2	3	paper	paper	NOUN
ejpam-6129	2	4	,	,	PUNCT
ejpam-6129	2	5	we	we	PRON
ejpam-6129	2	6	deal	deal	VERB
ejpam-6129	2	7	with	with	ADP
ejpam-6129	2	8	the	the	DET
ejpam-6129	2	9	problem	problem	NOUN
ejpam-6129	2	10	of	of	ADP
ejpam-6129	2	11	optimal	optimal	ADJ
ejpam-6129	2	12	control	control	NOUN
ejpam-6129	2	13	for	for	ADP
ejpam-6129	2	14	the	the	DET
ejpam-6129	2	15	transmission	transmission	NOUN
ejpam-6129	2	16	dynamics	dynamic	NOUN
ejpam-6129	2	17	of	of	ADP
ejpam-6129	2	18	the	the	DET
ejpam-6129	2	19	meningococcal	meningococcal	ADJ
ejpam-6129	2	20	meningitis	meningitis	NOUN
ejpam-6129	2	21	.	.	PUNCT
ejpam-6129	3	1	the	the	DET
ejpam-6129	3	2	problem	problem	NOUN
ejpam-6129	3	3	is	be	AUX
ejpam-6129	3	4	a	a	DET
ejpam-6129	3	5	mathematical	mathematical	ADJ
ejpam-6129	3	6	model	model	NOUN
ejpam-6129	3	7	described	describe	VERB
ejpam-6129	3	8	by	by	ADP
ejpam-6129	3	9	a	a	DET
ejpam-6129	3	10	system	system	NOUN
ejpam-6129	3	11	of	of	ADP
ejpam-6129	3	12	nonlinear	nonlinear	ADJ
ejpam-6129	3	13	differential	differential	ADJ
ejpam-6129	3	14	equations	equation	NOUN
ejpam-6129	3	15	.	.	PUNCT
ejpam-6129	4	1	based	base	VERB
ejpam-6129	4	2	on	on	ADP
ejpam-6129	4	3	this	this	PRON
ejpam-6129	4	4	,	,	PUNCT
ejpam-6129	4	5	two	two	NUM
ejpam-6129	4	6	controls	control	NOUN
ejpam-6129	4	7	are	be	AUX
ejpam-6129	4	8	formulated	formulate	VERB
ejpam-6129	4	9	and	and	CCONJ
ejpam-6129	4	10	the	the	DET
ejpam-6129	4	11	resulting	result	VERB
ejpam-6129	4	12	system	system	NOUN
ejpam-6129	4	13	is	be	AUX
ejpam-6129	4	14	solved	solve	VERB
ejpam-6129	4	15	as	as	ADP
ejpam-6129	4	16	an	an	DET
ejpam-6129	4	17	optimal	optimal	ADJ
ejpam-6129	4	18	control	control	NOUN
ejpam-6129	4	19	problem	problem	NOUN
ejpam-6129	4	20	.	.	PUNCT
ejpam-6129	5	1	aiming	aim	VERB
ejpam-6129	5	2	to	to	PART
ejpam-6129	5	3	minimize	minimize	VERB
ejpam-6129	5	4	the	the	DET
ejpam-6129	5	5	number	number	NOUN
ejpam-6129	5	6	of	of	ADP
ejpam-6129	5	7	illnesses	illness	NOUN
ejpam-6129	5	8	or	or	CCONJ
ejpam-6129	5	9	deaths	death	NOUN
ejpam-6129	5	10	in	in	ADP
ejpam-6129	5	11	the	the	DET
ejpam-6129	5	12	population	population	NOUN
ejpam-6129	5	13	,	,	PUNCT
ejpam-6129	5	14	we	we	PRON
ejpam-6129	5	15	use	use	VERB
ejpam-6129	5	16	a	a	DET
ejpam-6129	5	17	control	control	NOUN
ejpam-6129	5	18	representing	represent	VERB
ejpam-6129	5	19	a	a	DET
ejpam-6129	5	20	vaccination	vaccination	NOUN
ejpam-6129	5	21	and	and	CCONJ
ejpam-6129	5	22	another	another	DET
ejpam-6129	5	23	one	one	NUM
ejpam-6129	5	24	representing	represent	VERB
ejpam-6129	5	25	a	a	DET
ejpam-6129	5	26	treatment	treatment	NOUN
ejpam-6129	5	27	strategy	strategy	NOUN
ejpam-6129	5	28	.	.	PUNCT
ejpam-6129	6	1	we	we	PRON
ejpam-6129	6	2	prove	prove	VERB
ejpam-6129	6	3	that	that	SCONJ
ejpam-6129	6	4	these	these	DET
ejpam-6129	6	5	controls	control	NOUN
ejpam-6129	6	6	are	be	AUX
ejpam-6129	6	7	capable	capable	ADJ
ejpam-6129	6	8	of	of	ADP
ejpam-6129	6	9	reducing	reduce	VERB
ejpam-6129	6	10	the	the	DET
ejpam-6129	6	11	number	number	NOUN
ejpam-6129	6	12	of	of	ADP
ejpam-6129	6	13	carriers	carrier	NOUN
ejpam-6129	6	14	and	and	CCONJ
ejpam-6129	6	15	infectious	infectious	ADJ
ejpam-6129	6	16	individuals	individual	NOUN
ejpam-6129	6	17	.	.	PUNCT
ejpam-6129	7	1	numerical	numerical	ADJ
ejpam-6129	7	2	simulations	simulation	NOUN
ejpam-6129	7	3	are	be	AUX
ejpam-6129	7	4	carried	carry	VERB
ejpam-6129	7	5	out	out	ADP
ejpam-6129	7	6	to	to	PART
ejpam-6129	7	7	show	show	VERB
ejpam-6129	7	8	how	how	SCONJ
ejpam-6129	7	9	to	to	PART
ejpam-6129	7	10	perform	perform	VERB
ejpam-6129	7	11	the	the	DET
ejpam-6129	7	12	two	two	NUM
ejpam-6129	7	13	strategies	strategy	NOUN
ejpam-6129	7	14	.	.	PUNCT
ejpam-6129	8	1	2020	2020	NUM
ejpam-6129	8	2	mathematics	mathematic	NOUN
ejpam-6129	8	3	subject	subject	NOUN
ejpam-6129	8	4	classifications	classification	NOUN
ejpam-6129	8	5	:	:	PUNCT
ejpam-6129	8	6	49j15	49j15	NUM
ejpam-6129	8	7	,	,	PUNCT
ejpam-6129	8	8	49k15	49k15	NUM
ejpam-6129	8	9	,	,	PUNCT
ejpam-6129	8	10	34a12	34a12	NUM
ejpam-6129	8	11	,	,	PUNCT
ejpam-6129	8	12	34a45	34a45	NUM
ejpam-6129	8	13	key	key	ADJ
ejpam-6129	8	14	words	word	NOUN
ejpam-6129	8	15	and	and	CCONJ
ejpam-6129	8	16	phrases	phrase	NOUN
ejpam-6129	8	17	:	:	PUNCT
ejpam-6129	8	18	mathematical	mathematical	ADJ
ejpam-6129	8	19	biology	biology	NOUN
ejpam-6129	8	20	,	,	PUNCT
ejpam-6129	8	21	meningitis	meningitis	NOUN
ejpam-6129	8	22	,	,	PUNCT
ejpam-6129	8	23	optimal	optimal	ADJ
ejpam-6129	8	24	control	control	NOUN
ejpam-6129	8	25	,	,	PUNCT
ejpam-6129	8	26	vaccination	vaccination	NOUN
ejpam-6129	8	27	,	,	PUNCT
ejpam-6129	8	28	treatment	treatment	NOUN
ejpam-6129	8	29	1	1	NUM
ejpam-6129	8	30	.	.	PUNCT
ejpam-6129	9	1	introduction	introduction	NOUN
ejpam-6129	9	2	meningitis	meningitis	NOUN
ejpam-6129	9	3	is	be	AUX
ejpam-6129	9	4	an	an	DET
ejpam-6129	9	5	inflammation	inflammation	NOUN
ejpam-6129	9	6	of	of	ADP
ejpam-6129	9	7	a	a	DET
ejpam-6129	9	8	membrane	membrane	NOUN
ejpam-6129	9	9	,	,	PUNCT
ejpam-6129	9	10	called	call	VERB
ejpam-6129	9	11	the	the	DET
ejpam-6129	9	12	meninges	meninge	NOUN
ejpam-6129	9	13	,	,	PUNCT
ejpam-6129	9	14	that	that	PRON
ejpam-6129	9	15	covers	cover	VERB
ejpam-6129	9	16	the	the	DET
ejpam-6129	9	17	brain	brain	NOUN
ejpam-6129	9	18	and	and	CCONJ
ejpam-6129	9	19	spinal	spinal	ADJ
ejpam-6129	9	20	cord	cord	NOUN
ejpam-6129	9	21	.	.	PUNCT
ejpam-6129	10	1	meningitis	meningitis	NOUN
ejpam-6129	10	2	is	be	AUX
ejpam-6129	10	3	a	a	DET
ejpam-6129	10	4	severe	severe	ADJ
ejpam-6129	10	5	acute	acute	ADJ
ejpam-6129	10	6	infectious	infectious	ADJ
ejpam-6129	10	7	disease	disease	NOUN
ejpam-6129	10	8	caused	cause	VERB
ejpam-6129	10	9	by	by	ADP
ejpam-6129	10	10	several	several	ADJ
ejpam-6129	10	11	microorganisms	microorganism	NOUN
ejpam-6129	10	12	,	,	PUNCT
ejpam-6129	10	13	including	include	VERB
ejpam-6129	10	14	viruses	virus	NOUN
ejpam-6129	10	15	,	,	PUNCT
ejpam-6129	10	16	bacteria	bacteria	NOUN
ejpam-6129	10	17	,	,	PUNCT
ejpam-6129	10	18	parasites	parasite	NOUN
ejpam-6129	10	19	,	,	PUNCT
ejpam-6129	10	20	and	and	CCONJ
ejpam-6129	10	21	fungi	fungi	PROPN
ejpam-6129	10	22	.	.	PUNCT
ejpam-6129	11	1	fatality	fatality	NOUN
ejpam-6129	11	2	rates	rate	NOUN
ejpam-6129	11	3	associated	associate	VERB
ejpam-6129	11	4	with	with	ADP
ejpam-6129	11	5	this	this	DET
ejpam-6129	11	6	disease	disease	NOUN
ejpam-6129	11	7	can	can	AUX
ejpam-6129	11	8	be	be	AUX
ejpam-6129	11	9	as	as	ADV
ejpam-6129	11	10	low	low	ADJ
ejpam-6129	11	11	as	as	ADP
ejpam-6129	11	12	2	2	NUM
ejpam-6129	11	13	%	%	NOUN
ejpam-6129	11	14	in	in	ADP
ejpam-6129	11	15	infants	infant	NOUN
ejpam-6129	11	16	and	and	CCONJ
ejpam-6129	11	17	children	child	NOUN
ejpam-6129	11	18	,	,	PUNCT
ejpam-6129	11	19	and	and	CCONJ
ejpam-6129	11	20	as	as	ADV
ejpam-6129	11	21	high	high	ADJ
ejpam-6129	11	22	as	as	ADP
ejpam-6129	11	23	20–30	20–30	NUM
ejpam-6129	11	24	%	%	NOUN
ejpam-6129	11	25	in	in	ADP
ejpam-6129	11	26	∗corresponding	∗corresponde	VERB
ejpam-6129	11	27	author	author	NOUN
ejpam-6129	11	28	.	.	PUNCT
ejpam-6129	12	1	doi	doi	NOUN
ejpam-6129	12	2	:	:	PUNCT
ejpam-6129	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6129	https://doi.org/10.29020/nybg.ejpam.v18i3.6129	ADJ
ejpam-6129	12	4	email	email	NOUN
ejpam-6129	12	5	addresses	address	NOUN
ejpam-6129	12	6	:	:	PUNCT
ejpam-6129	12	7	abdeensahar@yahoo.com	abdeensahar@yahoo.com	X
ejpam-6129	12	8	(	(	PUNCT
ejpam-6129	12	9	s.	s.	PROPN
ejpam-6129	12	10	a.	a.	PROPN
ejpam-6129	12	11	mohamed	mohamed	PROPN
ejpam-6129	12	12	)	)	PUNCT
ejpam-6129	12	13	,	,	PUNCT
ejpam-6129	12	14	hassem.ab@abmmc.edu.qa	hassem.ab@abmmc.edu.qa	PRON
ejpam-6129	12	15	(	(	PUNCT
ejpam-6129	12	16	h.	h.	PROPN
ejpam-6129	12	17	a.	a.	PROPN
ejpam-6129	12	18	obaid	obaid	PROPN
ejpam-6129	12	19	)	)	PUNCT
ejpam-6129	12	20	,	,	PUNCT
ejpam-6129	12	21	ebashier@su.edu.om	ebashier@su.edu.om	PROPN
ejpam-6129	12	22	(	(	PUNCT
ejpam-6129	12	23	e.	e.	PROPN
ejpam-6129	12	24	b.	b.	PROPN
ejpam-6129	12	25	m.	m.	PROPN
ejpam-6129	12	26	bashier	bashier	PROPN
ejpam-6129	12	27	)	)	PUNCT
ejpam-6129	12	28	,	,	PUNCT
ejpam-6129	12	29	kpatidar@uwc.ac.za	kpatidar@uwc.ac.za	NOUN
ejpam-6129	12	30	(	(	PUNCT
ejpam-6129	12	31	k.	k.	PROPN
ejpam-6129	12	32	c.	c.	PROPN
ejpam-6129	12	33	patidar	patidar	PROPN
ejpam-6129	12	34	)	)	PUNCT
ejpam-6129	12	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6129	13	1	1	1	NUM
ejpam-6129	13	2	copyright	copyright	NOUN
ejpam-6129	13	3	:	:	PUNCT
ejpam-6129	13	4	©	©	PROPN
ejpam-6129	13	5	2025	2025	NUM
ejpam-6129	13	6	the	the	DET
ejpam-6129	13	7	author(s	author(s	NOUN
ejpam-6129	13	8	)	)	PUNCT
ejpam-6129	13	9	.	.	PUNCT
ejpam-6129	14	1	(	(	PUNCT
ejpam-6129	14	2	cc	cc	NOUN
ejpam-6129	14	3	by	by	ADP
ejpam-6129	14	4	-	-	PUNCT
ejpam-6129	14	5	nc	nc	PROPN
ejpam-6129	14	6	4.0	4.0	NUM
ejpam-6129	14	7	)	)	PUNCT
ejpam-6129	14	8	s.	s.	PROPN
ejpam-6129	14	9	a.	a.	PROPN
ejpam-6129	14	10	mohamed	mohamed	PROPN
ejpam-6129	14	11	et	et	PROPN
ejpam-6129	14	12	al	al	PROPN
ejpam-6129	14	13	.	.	PUNCT
ejpam-6129	14	14	/	/	SYM
ejpam-6129	14	15	eur	eur	PROPN
ejpam-6129	14	16	.	.	PUNCT
ejpam-6129	15	1	j.	j.	PROPN
ejpam-6129	15	2	pure	pure	PROPN
ejpam-6129	15	3	appl	appl	PROPN
ejpam-6129	15	4	.	.	PROPN
ejpam-6129	15	5	math	math	PROPN
ejpam-6129	15	6	,	,	PUNCT
ejpam-6129	15	7	18	18	NUM
ejpam-6129	15	8	(	(	PUNCT
ejpam-6129	15	9	3	3	NUM
ejpam-6129	15	10	)	)	PUNCT
ejpam-6129	15	11	(	(	PUNCT
ejpam-6129	15	12	2025	2025	NUM
ejpam-6129	15	13	)	)	PUNCT
ejpam-6129	15	14	,	,	PUNCT
ejpam-6129	15	15	6129	6129	NUM
ejpam-6129	15	16	2	2	NUM
ejpam-6129	15	17	of	of	ADP
ejpam-6129	15	18	17	17	NUM
ejpam-6129	15	19	neonates	neonate	NOUN
ejpam-6129	15	20	and	and	CCONJ
ejpam-6129	15	21	adults	adult	NOUN
ejpam-6129	16	1	[	[	X
ejpam-6129	16	2	1	1	NUM
ejpam-6129	16	3	]	]	PUNCT
ejpam-6129	16	4	.	.	PUNCT
ejpam-6129	17	1	damage	damage	NOUN
ejpam-6129	17	2	to	to	ADP
ejpam-6129	17	3	the	the	DET
ejpam-6129	17	4	meninges	meninge	NOUN
ejpam-6129	17	5	produces	produce	VERB
ejpam-6129	17	6	a	a	DET
ejpam-6129	17	7	variety	variety	NOUN
ejpam-6129	17	8	of	of	ADP
ejpam-6129	17	9	problems	problem	NOUN
ejpam-6129	17	10	,	,	PUNCT
ejpam-6129	17	11	ranging	range	VERB
ejpam-6129	17	12	from	from	ADP
ejpam-6129	17	13	a	a	DET
ejpam-6129	17	14	high	high	ADJ
ejpam-6129	17	15	fever	fever	NOUN
ejpam-6129	17	16	with	with	ADP
ejpam-6129	17	17	headaches	headache	NOUN
ejpam-6129	17	18	to	to	ADP
ejpam-6129	17	19	unconsciousness	unconsciousness	NOUN
ejpam-6129	17	20	and	and	CCONJ
ejpam-6129	17	21	death	death	NOUN
ejpam-6129	18	1	[	[	X
ejpam-6129	18	2	2	2	NUM
ejpam-6129	18	3	]	]	PUNCT
ejpam-6129	18	4	.	.	PUNCT
ejpam-6129	19	1	as	as	SCONJ
ejpam-6129	19	2	mentioned	mention	VERB
ejpam-6129	19	3	in	in	ADP
ejpam-6129	19	4	[	[	X
ejpam-6129	19	5	3	3	NUM
ejpam-6129	19	6	]	]	PUNCT
ejpam-6129	19	7	,	,	PUNCT
ejpam-6129	19	8	meningococcal	meningococcal	ADJ
ejpam-6129	19	9	meningitis	meningitis	NOUN
ejpam-6129	19	10	affects	affect	VERB
ejpam-6129	19	11	sub	sub	ADJ
ejpam-6129	19	12	-	-	ADJ
ejpam-6129	19	13	saharan	saharan	ADJ
ejpam-6129	19	14	africa	africa	PROPN
ejpam-6129	19	15	in	in	ADP
ejpam-6129	19	16	a	a	DET
ejpam-6129	19	17	unique	unique	ADJ
ejpam-6129	19	18	and	and	CCONJ
ejpam-6129	19	19	distinctive	distinctive	ADJ
ejpam-6129	19	20	way	way	NOUN
ejpam-6129	19	21	.	.	PUNCT
ejpam-6129	20	1	in	in	ADP
ejpam-6129	20	2	a	a	DET
ejpam-6129	20	3	region	region	NOUN
ejpam-6129	20	4	known	know	VERB
ejpam-6129	20	5	as	as	ADP
ejpam-6129	20	6	the	the	DET
ejpam-6129	20	7	meningitis	meningitis	NOUN
ejpam-6129	20	8	belt	belt	NOUN
ejpam-6129	20	9	,	,	PUNCT
ejpam-6129	20	10	which	which	PRON
ejpam-6129	20	11	spans	span	VERB
ejpam-6129	20	12	the	the	DET
ejpam-6129	20	13	continent	continent	NOUN
ejpam-6129	20	14	from	from	ADP
ejpam-6129	20	15	senegal	senegal	NOUN
ejpam-6129	20	16	to	to	ADP
ejpam-6129	20	17	ethiopia	ethiopia	PROPN
ejpam-6129	20	18	there	there	PRON
ejpam-6129	20	19	is	be	VERB
ejpam-6129	20	20	an	an	DET
ejpam-6129	20	21	increase	increase	NOUN
ejpam-6129	20	22	in	in	ADP
ejpam-6129	20	23	incidence	incidence	NOUN
ejpam-6129	20	24	of	of	ADP
ejpam-6129	20	25	meningococcal	meningococcal	ADJ
ejpam-6129	20	26	meningitis	meningitis	NOUN
ejpam-6129	20	27	every	every	DET
ejpam-6129	20	28	dry	dry	ADJ
ejpam-6129	20	29	season	season	NOUN
ejpam-6129	20	30	,	,	PUNCT
ejpam-6129	20	31	which	which	PRON
ejpam-6129	20	32	dies	die	VERB
ejpam-6129	20	33	out	out	ADP
ejpam-6129	20	34	when	when	SCONJ
ejpam-6129	20	35	the	the	DET
ejpam-6129	20	36	first	first	ADJ
ejpam-6129	20	37	rains	rain	NOUN
ejpam-6129	20	38	arrive	arrive	VERB
ejpam-6129	20	39	.	.	PUNCT
ejpam-6129	21	1	at	at	ADP
ejpam-6129	21	2	intervals	interval	NOUN
ejpam-6129	21	3	ranging	range	VERB
ejpam-6129	21	4	from	from	ADP
ejpam-6129	21	5	6	6	NUM
ejpam-6129	21	6	to	to	PART
ejpam-6129	21	7	14	14	NUM
ejpam-6129	21	8	years	year	NOUN
ejpam-6129	21	9	,	,	PUNCT
ejpam-6129	21	10	major	major	ADJ
ejpam-6129	21	11	epidemics	epidemic	NOUN
ejpam-6129	21	12	occur	occur	VERB
ejpam-6129	21	13	,	,	PUNCT
ejpam-6129	21	14	the	the	DET
ejpam-6129	21	15	largest	large	ADJ
ejpam-6129	21	16	of	of	ADP
ejpam-6129	21	17	which	which	PRON
ejpam-6129	21	18	killed	kill	VERB
ejpam-6129	21	19	more	more	ADJ
ejpam-6129	21	20	than	than	ADP
ejpam-6129	21	21	25	25	NUM
ejpam-6129	21	22	000	000	NUM
ejpam-6129	21	23	people	people	NOUN
ejpam-6129	21	24	in	in	ADP
ejpam-6129	21	25	10	10	NUM
ejpam-6129	21	26	countries	country	NOUN
ejpam-6129	21	27	in	in	ADP
ejpam-6129	21	28	1996	1996	NUM
ejpam-6129	21	29	–	–	PUNCT
ejpam-6129	21	30	1997	1997	NUM
ejpam-6129	21	31	.	.	PUNCT
ejpam-6129	22	1	in	in	ADP
ejpam-6129	22	2	some	some	DET
ejpam-6129	22	3	areas	area	NOUN
ejpam-6129	22	4	,	,	PUNCT
ejpam-6129	22	5	this	this	DET
ejpam-6129	22	6	epidemic	epidemic	NOUN
ejpam-6129	22	7	lasts	last	VERB
ejpam-6129	22	8	for	for	ADP
ejpam-6129	22	9	more	more	ADJ
ejpam-6129	22	10	than	than	ADP
ejpam-6129	22	11	1	1	NUM
ejpam-6129	22	12	year	year	NOUN
ejpam-6129	22	13	,	,	PUNCT
ejpam-6129	22	14	dying	die	VERB
ejpam-6129	22	15	out	out	ADP
ejpam-6129	22	16	in	in	ADP
ejpam-6129	22	17	the	the	DET
ejpam-6129	22	18	rainy	rainy	ADJ
ejpam-6129	22	19	season	season	NOUN
ejpam-6129	22	20	,	,	PUNCT
ejpam-6129	22	21	only	only	ADV
ejpam-6129	22	22	to	to	PART
ejpam-6129	22	23	return	return	VERB
ejpam-6129	22	24	afterwards	afterwards	ADV
ejpam-6129	22	25	.	.	PUNCT
ejpam-6129	23	1	in	in	ADP
ejpam-6129	23	2	a	a	DET
ejpam-6129	23	3	single	single	ADJ
ejpam-6129	23	4	community	community	NOUN
ejpam-6129	23	5	,	,	PUNCT
ejpam-6129	23	6	however	however	ADV
ejpam-6129	23	7	,	,	PUNCT
ejpam-6129	23	8	an	an	DET
ejpam-6129	23	9	epidemic	epidemic	NOUN
ejpam-6129	23	10	may	may	AUX
ejpam-6129	23	11	last	last	VERB
ejpam-6129	23	12	only	only	ADV
ejpam-6129	23	13	a	a	DET
ejpam-6129	23	14	few	few	ADJ
ejpam-6129	23	15	weeks	week	NOUN
ejpam-6129	23	16	.	.	PUNCT
ejpam-6129	24	1	it	it	PRON
ejpam-6129	24	2	is	be	AUX
ejpam-6129	24	3	well	well	ADV
ejpam-6129	24	4	known	know	VERB
ejpam-6129	24	5	that	that	SCONJ
ejpam-6129	24	6	mathematical	mathematical	ADJ
ejpam-6129	24	7	models	model	NOUN
ejpam-6129	24	8	play	play	VERB
ejpam-6129	24	9	a	a	DET
ejpam-6129	24	10	significant	significant	ADJ
ejpam-6129	24	11	role	role	NOUN
ejpam-6129	24	12	in	in	ADP
ejpam-6129	24	13	understanding	understand	VERB
ejpam-6129	24	14	the	the	DET
ejpam-6129	24	15	dynamics	dynamic	NOUN
ejpam-6129	24	16	of	of	ADP
ejpam-6129	24	17	biological	biological	ADJ
ejpam-6129	24	18	systems	system	NOUN
ejpam-6129	24	19	.	.	PUNCT
ejpam-6129	25	1	in	in	ADP
ejpam-6129	25	2	most	most	ADJ
ejpam-6129	25	3	cases	case	NOUN
ejpam-6129	25	4	,	,	PUNCT
ejpam-6129	25	5	these	these	DET
ejpam-6129	25	6	models	model	NOUN
ejpam-6129	25	7	are	be	AUX
ejpam-6129	25	8	described	describe	VERB
ejpam-6129	25	9	by	by	ADP
ejpam-6129	25	10	autonomous	autonomous	ADJ
ejpam-6129	25	11	systems	system	NOUN
ejpam-6129	25	12	of	of	ADP
ejpam-6129	25	13	nonlinear	nonlinear	ADJ
ejpam-6129	25	14	ordinary	ordinary	ADJ
ejpam-6129	25	15	/	/	SYM
ejpam-6129	25	16	or	or	CCONJ
ejpam-6129	25	17	partial	partial	ADJ
ejpam-6129	25	18	differential	differential	ADJ
ejpam-6129	25	19	equations	equation	NOUN
ejpam-6129	25	20	.	.	PUNCT
ejpam-6129	26	1	mathematical	mathematical	ADJ
ejpam-6129	26	2	models	model	NOUN
ejpam-6129	26	3	for	for	ADP
ejpam-6129	26	4	meningitis	meningiti	NOUN
ejpam-6129	26	5	are	be	AUX
ejpam-6129	26	6	explored	explore	VERB
ejpam-6129	26	7	by	by	ADP
ejpam-6129	26	8	many	many	ADJ
ejpam-6129	26	9	researchers	researcher	NOUN
ejpam-6129	26	10	.	.	PUNCT
ejpam-6129	27	1	below	below	ADV
ejpam-6129	27	2	,	,	PUNCT
ejpam-6129	27	3	we	we	PRON
ejpam-6129	27	4	mention	mention	VERB
ejpam-6129	27	5	a	a	DET
ejpam-6129	27	6	few	few	ADJ
ejpam-6129	27	7	of	of	ADP
ejpam-6129	27	8	them	they	PRON
ejpam-6129	27	9	.	.	PUNCT
ejpam-6129	28	1	mart́ınez	mart́ınez	INTJ
ejpam-6129	28	2	et	et	NOUN
ejpam-6129	28	3	al	al	PROPN
ejpam-6129	28	4	.	.	PUNCT
ejpam-6129	29	1	[	[	X
ejpam-6129	29	2	4	4	X
ejpam-6129	29	3	]	]	PUNCT
ejpam-6129	29	4	introduced	introduce	VERB
ejpam-6129	29	5	a	a	DET
ejpam-6129	29	6	novel	novel	ADJ
ejpam-6129	29	7	mathematical	mathematical	ADJ
ejpam-6129	29	8	model	model	NOUN
ejpam-6129	29	9	to	to	PART
ejpam-6129	29	10	study	study	VERB
ejpam-6129	29	11	the	the	DET
ejpam-6129	29	12	spreading	spreading	NOUN
ejpam-6129	29	13	of	of	ADP
ejpam-6129	29	14	meningococcal	meningococcal	ADJ
ejpam-6129	29	15	meningitis	meningiti	NOUN
ejpam-6129	29	16	.	.	PUNCT
ejpam-6129	30	1	the	the	DET
ejpam-6129	30	2	model	model	NOUN
ejpam-6129	30	3	is	be	AUX
ejpam-6129	30	4	a	a	DET
ejpam-6129	30	5	discrete	discrete	ADJ
ejpam-6129	30	6	mathematical	mathematical	ADJ
ejpam-6129	30	7	model	model	NOUN
ejpam-6129	30	8	based	base	VERB
ejpam-6129	30	9	on	on	ADP
ejpam-6129	30	10	cellular	cellular	ADJ
ejpam-6129	30	11	automata	automata	NOUN
ejpam-6129	30	12	where	where	SCONJ
ejpam-6129	30	13	the	the	DET
ejpam-6129	30	14	population	population	NOUN
ejpam-6129	30	15	is	be	AUX
ejpam-6129	30	16	divided	divide	VERB
ejpam-6129	30	17	in	in	ADP
ejpam-6129	30	18	five	five	NUM
ejpam-6129	30	19	classes	class	NOUN
ejpam-6129	30	20	:	:	PUNCT
ejpam-6129	30	21	susceptible	susceptible	ADJ
ejpam-6129	30	22	,	,	PUNCT
ejpam-6129	30	23	asymptomatic	asymptomatic	ADJ
ejpam-6129	30	24	infected	infect	VERB
ejpam-6129	30	25	,	,	PUNCT
ejpam-6129	30	26	infected	infect	VERB
ejpam-6129	30	27	with	with	ADP
ejpam-6129	30	28	symptoms	symptom	NOUN
ejpam-6129	30	29	,	,	PUNCT
ejpam-6129	30	30	carriers	carrier	NOUN
ejpam-6129	30	31	,	,	PUNCT
ejpam-6129	30	32	recovered	recover	VERB
ejpam-6129	30	33	and	and	CCONJ
ejpam-6129	30	34	died	die	VERB
ejpam-6129	30	35	.	.	PUNCT
ejpam-6129	31	1	it	it	PRON
ejpam-6129	31	2	catches	catch	VERB
ejpam-6129	31	3	the	the	DET
ejpam-6129	31	4	individual	individual	ADJ
ejpam-6129	31	5	characteristics	characteristic	NOUN
ejpam-6129	31	6	of	of	ADP
ejpam-6129	31	7	people	people	NOUN
ejpam-6129	31	8	in	in	ADP
ejpam-6129	31	9	order	order	NOUN
ejpam-6129	31	10	to	to	PART
ejpam-6129	31	11	give	give	VERB
ejpam-6129	31	12	a	a	DET
ejpam-6129	31	13	prediction	prediction	NOUN
ejpam-6129	31	14	of	of	ADP
ejpam-6129	31	15	both	both	CCONJ
ejpam-6129	31	16	the	the	DET
ejpam-6129	31	17	individual	individual	ADJ
ejpam-6129	31	18	behavior	behavior	NOUN
ejpam-6129	31	19	,	,	PUNCT
ejpam-6129	31	20	and	and	CCONJ
ejpam-6129	31	21	whole	whole	ADJ
ejpam-6129	31	22	evolution	evolution	NOUN
ejpam-6129	31	23	of	of	ADP
ejpam-6129	31	24	population	population	NOUN
ejpam-6129	31	25	.	.	PUNCT
ejpam-6129	32	1	they	they	PRON
ejpam-6129	32	2	found	find	VERB
ejpam-6129	32	3	that	that	SCONJ
ejpam-6129	32	4	both	both	CCONJ
ejpam-6129	32	5	the	the	DET
ejpam-6129	32	6	global	global	ADJ
ejpam-6129	32	7	and	and	CCONJ
ejpam-6129	32	8	the	the	DET
ejpam-6129	32	9	individual	individual	ADJ
ejpam-6129	32	10	behavior	behavior	NOUN
ejpam-6129	32	11	of	of	ADP
ejpam-6129	32	12	the	the	DET
ejpam-6129	32	13	disease	disease	NOUN
ejpam-6129	32	14	can	can	AUX
ejpam-6129	32	15	be	be	AUX
ejpam-6129	32	16	predicted	predict	VERB
ejpam-6129	32	17	and	and	CCONJ
ejpam-6129	32	18	the	the	DET
ejpam-6129	32	19	simulations	simulation	NOUN
ejpam-6129	32	20	that	that	PRON
ejpam-6129	32	21	they	they	PRON
ejpam-6129	32	22	did	do	AUX
ejpam-6129	32	23	give	give	VERB
ejpam-6129	32	24	results	result	NOUN
ejpam-6129	32	25	that	that	PRON
ejpam-6129	32	26	agree	agree	VERB
ejpam-6129	32	27	with	with	ADP
ejpam-6129	32	28	empirical	empirical	ADJ
ejpam-6129	32	29	predictions	prediction	NOUN
ejpam-6129	32	30	regarding	regard	VERB
ejpam-6129	32	31	the	the	DET
ejpam-6129	32	32	basic	basic	ADJ
ejpam-6129	32	33	role	role	NOUN
ejpam-6129	32	34	played	play	VERB
ejpam-6129	32	35	by	by	ADP
ejpam-6129	32	36	the	the	DET
ejpam-6129	32	37	carriers	carrier	NOUN
ejpam-6129	32	38	.	.	PUNCT
ejpam-6129	33	1	lawi	lawi	PROPN
ejpam-6129	33	2	et	et	PROPN
ejpam-6129	33	3	al	al	PROPN
ejpam-6129	33	4	.	.	PUNCT
ejpam-6129	34	1	[	[	X
ejpam-6129	34	2	5	5	NUM
ejpam-6129	34	3	]	]	PUNCT
ejpam-6129	34	4	presented	present	VERB
ejpam-6129	34	5	and	and	CCONJ
ejpam-6129	34	6	analyzed	analyze	VERB
ejpam-6129	34	7	a	a	DET
ejpam-6129	34	8	deterministic	deterministic	ADJ
ejpam-6129	34	9	model	model	NOUN
ejpam-6129	34	10	for	for	ADP
ejpam-6129	34	11	the	the	DET
ejpam-6129	34	12	dynamics	dynamic	NOUN
ejpam-6129	34	13	of	of	ADP
ejpam-6129	34	14	malaria	malaria	NOUN
ejpam-6129	34	15	and	and	CCONJ
ejpam-6129	34	16	meningitis	meningitis	NOUN
ejpam-6129	34	17	co	co	NOUN
ejpam-6129	34	18	-	-	NOUN
ejpam-6129	34	19	infection	infection	NOUN
ejpam-6129	34	20	.	.	PUNCT
ejpam-6129	35	1	they	they	PRON
ejpam-6129	35	2	established	establish	VERB
ejpam-6129	35	3	the	the	DET
ejpam-6129	35	4	basic	basic	ADJ
ejpam-6129	35	5	reproduction	reproduction	NOUN
ejpam-6129	35	6	number	number	NOUN
ejpam-6129	35	7	rmm	rmm	NOUN
ejpam-6129	35	8	.	.	PUNCT
ejpam-6129	36	1	the	the	DET
ejpam-6129	36	2	analysis	analysis	NOUN
ejpam-6129	36	3	showed	show	VERB
ejpam-6129	36	4	that	that	SCONJ
ejpam-6129	36	5	the	the	DET
ejpam-6129	36	6	disease	disease	NOUN
ejpam-6129	36	7	free	free	ADJ
ejpam-6129	36	8	equilibrium	equilibrium	NOUN
ejpam-6129	36	9	of	of	ADP
ejpam-6129	36	10	the	the	DET
ejpam-6129	36	11	model	model	NOUN
ejpam-6129	36	12	may	may	AUX
ejpam-6129	36	13	not	not	PART
ejpam-6129	36	14	be	be	AUX
ejpam-6129	36	15	globally	globally	ADV
ejpam-6129	36	16	asymptotically	asymptotically	ADV
ejpam-6129	36	17	stable	stable	ADJ
ejpam-6129	36	18	whenever	whenever	SCONJ
ejpam-6129	36	19	rmm	rmm	PROPN
ejpam-6129	36	20	<	<	X
ejpam-6129	36	21	1	1	X
ejpam-6129	36	22	.	.	PUNCT
ejpam-6129	37	1	the	the	DET
ejpam-6129	37	2	centre	centre	NOUN
ejpam-6129	37	3	manifold	manifold	ADJ
ejpam-6129	37	4	theory	theory	NOUN
ejpam-6129	37	5	was	be	AUX
ejpam-6129	37	6	used	use	VERB
ejpam-6129	37	7	to	to	PART
ejpam-6129	37	8	show	show	VERB
ejpam-6129	37	9	that	that	SCONJ
ejpam-6129	37	10	the	the	DET
ejpam-6129	37	11	model	model	NOUN
ejpam-6129	37	12	has	have	VERB
ejpam-6129	37	13	a	a	DET
ejpam-6129	37	14	unique	unique	ADJ
ejpam-6129	37	15	endemic	endemic	ADJ
ejpam-6129	37	16	equilibrium	equilibrium	NOUN
ejpam-6129	37	17	which	which	PRON
ejpam-6129	37	18	is	be	AUX
ejpam-6129	37	19	locally	locally	ADV
ejpam-6129	37	20	asymptotically	asymptotically	ADV
ejpam-6129	37	21	stable	stable	ADJ
ejpam-6129	37	22	when	when	SCONJ
ejpam-6129	37	23	rmm	rmm	PROPN
ejpam-6129	37	24	<	<	X
ejpam-6129	37	25	1	1	NUM
ejpam-6129	37	26	and	and	CCONJ
ejpam-6129	37	27	unstable	unstable	ADJ
ejpam-6129	37	28	when	when	SCONJ
ejpam-6129	37	29	rmm	rmm	PROPN
ejpam-6129	37	30	>	>	X
ejpam-6129	37	31	1	1	X
ejpam-6129	37	32	.	.	PUNCT
ejpam-6129	38	1	it	it	PRON
ejpam-6129	38	2	was	be	AUX
ejpam-6129	38	3	deduced	deduce	VERB
ejpam-6129	38	4	further	far	ADV
ejpam-6129	38	5	that	that	SCONJ
ejpam-6129	38	6	a	a	DET
ejpam-6129	38	7	reduction	reduction	NOUN
ejpam-6129	38	8	in	in	ADP
ejpam-6129	38	9	malaria	malaria	NOUN
ejpam-6129	38	10	infection	infection	NOUN
ejpam-6129	38	11	cases	case	NOUN
ejpam-6129	38	12	either	either	CCONJ
ejpam-6129	38	13	through	through	ADP
ejpam-6129	38	14	protection	protection	NOUN
ejpam-6129	38	15	or	or	CCONJ
ejpam-6129	38	16	prompt	prompt	ADJ
ejpam-6129	38	17	effective	effective	ADJ
ejpam-6129	38	18	treatment	treatment	NOUN
ejpam-6129	38	19	,	,	PUNCT
ejpam-6129	38	20	which	which	PRON
ejpam-6129	38	21	is	be	AUX
ejpam-6129	38	22	dependent	dependent	ADJ
ejpam-6129	38	23	on	on	ADP
ejpam-6129	38	24	the	the	DET
ejpam-6129	38	25	socio	socio	NOUN
ejpam-6129	38	26	-	-	PUNCT
ejpam-6129	38	27	economic	economic	ADJ
ejpam-6129	38	28	status	status	NOUN
ejpam-6129	38	29	of	of	ADP
ejpam-6129	38	30	a	a	DET
ejpam-6129	38	31	community	community	NOUN
ejpam-6129	38	32	,	,	PUNCT
ejpam-6129	38	33	would	would	AUX
ejpam-6129	38	34	reduce	reduce	VERB
ejpam-6129	38	35	the	the	DET
ejpam-6129	38	36	number	number	NOUN
ejpam-6129	38	37	of	of	ADP
ejpam-6129	38	38	new	new	ADJ
ejpam-6129	38	39	co	co	ADJ
ejpam-6129	38	40	-	-	ADJ
ejpam-6129	38	41	infection	infection	NOUN
ejpam-6129	38	42	cases	case	NOUN
ejpam-6129	38	43	.	.	PUNCT
ejpam-6129	39	1	in	in	ADP
ejpam-6129	39	2	[	[	X
ejpam-6129	39	3	6	6	NUM
ejpam-6129	39	4	]	]	PUNCT
ejpam-6129	39	5	,	,	PUNCT
ejpam-6129	39	6	opoku	opoku	PROPN
ejpam-6129	39	7	et	et	PROPN
ejpam-6129	39	8	al	al	PROPN
ejpam-6129	39	9	.	.	PROPN
ejpam-6129	39	10	proposed	propose	VERB
ejpam-6129	39	11	an	an	DET
ejpam-6129	39	12	epidemiological	epidemiological	ADJ
ejpam-6129	39	13	model	model	NOUN
ejpam-6129	39	14	to	to	PART
ejpam-6129	39	15	accurately	accurately	ADV
ejpam-6129	39	16	estimate	estimate	VERB
ejpam-6129	39	17	meningitis	meningitis	NOUN
ejpam-6129	39	18	occurrence	occurrence	NOUN
ejpam-6129	39	19	and	and	CCONJ
ejpam-6129	39	20	transmission	transmission	NOUN
ejpam-6129	39	21	in	in	ADP
ejpam-6129	39	22	ghana	ghana	PROPN
ejpam-6129	39	23	.	.	PUNCT
ejpam-6129	40	1	they	they	PRON
ejpam-6129	40	2	used	use	VERB
ejpam-6129	40	3	optimal	optimal	ADJ
ejpam-6129	40	4	control	control	NOUN
ejpam-6129	40	5	theory	theory	NOUN
ejpam-6129	40	6	to	to	PART
ejpam-6129	40	7	identify	identify	VERB
ejpam-6129	40	8	the	the	DET
ejpam-6129	40	9	ideal	ideal	ADJ
ejpam-6129	40	10	strategies	strategy	NOUN
ejpam-6129	40	11	for	for	ADP
ejpam-6129	40	12	disease	disease	NOUN
ejpam-6129	40	13	eradication	eradication	NOUN
ejpam-6129	40	14	and	and	CCONJ
ejpam-6129	40	15	to	to	PART
ejpam-6129	40	16	study	study	VERB
ejpam-6129	40	17	the	the	DET
ejpam-6129	40	18	the	the	DET
ejpam-6129	40	19	impact	impact	NOUN
ejpam-6129	40	20	of	of	ADP
ejpam-6129	40	21	vaccination	vaccination	NOUN
ejpam-6129	40	22	and	and	CCONJ
ejpam-6129	40	23	treatment	treatment	NOUN
ejpam-6129	40	24	plans	plan	NOUN
ejpam-6129	40	25	.	.	PUNCT
ejpam-6129	41	1	it	it	PRON
ejpam-6129	41	2	was	be	AUX
ejpam-6129	41	3	deduced	deduce	VERB
ejpam-6129	41	4	from	from	ADP
ejpam-6129	41	5	the	the	DET
ejpam-6129	41	6	numerical	numerical	ADJ
ejpam-6129	41	7	simulations	simulation	NOUN
ejpam-6129	41	8	that	that	PRON
ejpam-6129	41	9	high	high	ADJ
ejpam-6129	41	10	coverage	coverage	NOUN
ejpam-6129	41	11	of	of	ADP
ejpam-6129	41	12	susceptible	susceptible	ADJ
ejpam-6129	41	13	individuals	individual	NOUN
ejpam-6129	41	14	receiving	receive	VERB
ejpam-6129	41	15	vaccinations	vaccination	NOUN
ejpam-6129	41	16	,	,	PUNCT
ejpam-6129	41	17	combined	combine	VERB
ejpam-6129	41	18	with	with	ADP
ejpam-6129	41	19	the	the	DET
ejpam-6129	41	20	development	development	NOUN
ejpam-6129	41	21	of	of	ADP
ejpam-6129	41	22	an	an	DET
ejpam-6129	41	23	efficient	efficient	ADJ
ejpam-6129	41	24	vaccine	vaccine	NOUN
ejpam-6129	41	25	,	,	PUNCT
ejpam-6129	41	26	is	be	AUX
ejpam-6129	41	27	the	the	DET
ejpam-6129	41	28	best	good	ADJ
ejpam-6129	41	29	strategy	strategy	NOUN
ejpam-6129	41	30	for	for	ADP
ejpam-6129	41	31	managing	manage	VERB
ejpam-6129	41	32	the	the	DET
ejpam-6129	41	33	bacteria	bacteria	NOUN
ejpam-6129	41	34	.	.	PUNCT
ejpam-6129	42	1	tilahun	tilahun	PROPN
ejpam-6129	43	1	[	[	X
ejpam-6129	43	2	7	7	X
ejpam-6129	43	3	]	]	PUNCT
ejpam-6129	43	4	proposed	propose	VERB
ejpam-6129	43	5	a	a	DET
ejpam-6129	43	6	deterministic	deterministic	ADJ
ejpam-6129	43	7	model	model	NOUN
ejpam-6129	43	8	of	of	ADP
ejpam-6129	43	9	pneumonia	pneumonia	NOUN
ejpam-6129	43	10	-	-	PUNCT
ejpam-6129	43	11	meningitis	meningitis	NOUN
ejpam-6129	43	12	coinfection	coinfection	NOUN
ejpam-6129	43	13	.	.	PUNCT
ejpam-6129	44	1	firstly	firstly	ADV
ejpam-6129	44	2	,	,	PUNCT
ejpam-6129	44	3	the	the	DET
ejpam-6129	44	4	qualitative	qualitative	ADJ
ejpam-6129	44	5	behaviours	behaviour	NOUN
ejpam-6129	44	6	of	of	ADP
ejpam-6129	44	7	the	the	DET
ejpam-6129	44	8	model	model	NOUN
ejpam-6129	44	9	were	be	AUX
ejpam-6129	44	10	studied	study	VERB
ejpam-6129	44	11	,	,	PUNCT
ejpam-6129	44	12	and	and	CCONJ
ejpam-6129	44	13	then	then	ADV
ejpam-6129	44	14	the	the	DET
ejpam-6129	44	15	basic	basic	ADJ
ejpam-6129	44	16	model	model	NOUN
ejpam-6129	44	17	was	be	AUX
ejpam-6129	44	18	extended	extend	VERB
ejpam-6129	44	19	to	to	ADP
ejpam-6129	44	20	optimal	optimal	ADJ
ejpam-6129	44	21	control	control	NOUN
ejpam-6129	44	22	by	by	ADP
ejpam-6129	44	23	incorporating	incorporate	VERB
ejpam-6129	44	24	four	four	NUM
ejpam-6129	44	25	control	control	NOUN
ejpam-6129	44	26	interventions	intervention	NOUN
ejpam-6129	44	27	,	,	PUNCT
ejpam-6129	44	28	such	such	ADJ
ejpam-6129	44	29	as	as	ADP
ejpam-6129	44	30	prevention	prevention	NOUN
ejpam-6129	44	31	of	of	ADP
ejpam-6129	44	32	pneumonia	pneumonia	NOUN
ejpam-6129	44	33	as	as	ADV
ejpam-6129	44	34	well	well	ADV
ejpam-6129	44	35	as	as	ADP
ejpam-6129	44	36	meningitis	meningitis	NOUN
ejpam-6129	44	37	and	and	CCONJ
ejpam-6129	44	38	also	also	ADV
ejpam-6129	44	39	treatment	treatment	NOUN
ejpam-6129	44	40	of	of	ADP
ejpam-6129	44	41	pneumonia	pneumonia	NOUN
ejpam-6129	44	42	and	and	CCONJ
ejpam-6129	44	43	meningitis	meningitis	NOUN
ejpam-6129	44	44	diseases	disease	NOUN
ejpam-6129	44	45	.	.	PUNCT
ejpam-6129	45	1	their	their	PRON
ejpam-6129	45	2	findings	finding	NOUN
ejpam-6129	45	3	showed	show	VERB
ejpam-6129	45	4	that	that	SCONJ
ejpam-6129	45	5	each	each	PRON
ejpam-6129	45	6	of	of	ADP
ejpam-6129	45	7	the	the	DET
ejpam-6129	45	8	listed	list	VERB
ejpam-6129	45	9	strategies	strategy	NOUN
ejpam-6129	45	10	is	be	AUX
ejpam-6129	45	11	effective	effective	ADJ
ejpam-6129	45	12	in	in	ADP
ejpam-6129	45	13	minimizing	minimize	VERB
ejpam-6129	45	14	the	the	DET
ejpam-6129	45	15	expansion	expansion	NOUN
ejpam-6129	45	16	of	of	ADP
ejpam-6129	45	17	pneumonia	pneumonia	NOUN
ejpam-6129	45	18	-	-	PUNCT
ejpam-6129	45	19	only	only	ADV
ejpam-6129	45	20	,	,	PUNCT
ejpam-6129	45	21	meningitis	meningiti	NOUN
ejpam-6129	45	22	-	-	PUNCT
ejpam-6129	45	23	only	only	ADV
ejpam-6129	45	24	,	,	PUNCT
ejpam-6129	45	25	and	and	CCONJ
ejpam-6129	45	26	coinfectious	coinfectious	ADJ
ejpam-6129	45	27	population	population	NOUN
ejpam-6129	45	28	in	in	ADP
ejpam-6129	45	29	the	the	DET
ejpam-6129	45	30	specified	specify	VERB
ejpam-6129	45	31	s.	s.	PROPN
ejpam-6129	45	32	a.	a.	PROPN
ejpam-6129	45	33	mohamed	mohamed	PROPN
ejpam-6129	45	34	et	et	PROPN
ejpam-6129	45	35	al	al	PROPN
ejpam-6129	45	36	.	.	PUNCT
ejpam-6129	45	37	/	/	SYM
ejpam-6129	45	38	eur	eur	PROPN
ejpam-6129	45	39	.	.	PUNCT
ejpam-6129	46	1	j.	j.	PROPN
ejpam-6129	46	2	pure	pure	PROPN
ejpam-6129	46	3	appl	appl	PROPN
ejpam-6129	46	4	.	.	PROPN
ejpam-6129	46	5	math	math	PROPN
ejpam-6129	46	6	,	,	PUNCT
ejpam-6129	46	7	18	18	NUM
ejpam-6129	46	8	(	(	PUNCT
ejpam-6129	46	9	3	3	NUM
ejpam-6129	46	10	)	)	PUNCT
ejpam-6129	46	11	(	(	PUNCT
ejpam-6129	46	12	2025	2025	NUM
ejpam-6129	46	13	)	)	PUNCT
ejpam-6129	46	14	,	,	PUNCT
ejpam-6129	46	15	6129	6129	NUM
ejpam-6129	46	16	3	3	NUM
ejpam-6129	46	17	of	of	ADP
ejpam-6129	46	18	17	17	NUM
ejpam-6129	46	19	period	period	NOUN
ejpam-6129	46	20	of	of	ADP
ejpam-6129	46	21	time	time	NOUN
ejpam-6129	46	22	.	.	PUNCT
ejpam-6129	47	1	a	a	DET
ejpam-6129	47	2	mathematical	mathematical	ADJ
ejpam-6129	47	3	model	model	NOUN
ejpam-6129	47	4	that	that	PRON
ejpam-6129	47	5	governs	govern	VERB
ejpam-6129	47	6	the	the	DET
ejpam-6129	47	7	epidemiology	epidemiology	NOUN
ejpam-6129	47	8	of	of	ADP
ejpam-6129	47	9	cerebrospinal	cerebrospinal	ADJ
ejpam-6129	47	10	meningitis	meningitis	NOUN
ejpam-6129	47	11	in	in	ADP
ejpam-6129	47	12	jirapa	jirapa	ADJ
ejpam-6129	47	13	,	,	PUNCT
ejpam-6129	47	14	ghana	ghana	PROPN
ejpam-6129	47	15	was	be	AUX
ejpam-6129	47	16	developed	develop	VERB
ejpam-6129	47	17	by	by	ADP
ejpam-6129	47	18	wiah	wiah	PROPN
ejpam-6129	47	19	and	and	CCONJ
ejpam-6129	47	20	adetunde	adetunde	VERB
ejpam-6129	48	1	[	[	X
ejpam-6129	48	2	8	8	NUM
ejpam-6129	48	3	]	]	PUNCT
ejpam-6129	48	4	.	.	PUNCT
ejpam-6129	49	1	they	they	PRON
ejpam-6129	49	2	studied	study	VERB
ejpam-6129	49	3	the	the	DET
ejpam-6129	49	4	dynamics	dynamic	NOUN
ejpam-6129	49	5	of	of	ADP
ejpam-6129	49	6	the	the	DET
ejpam-6129	49	7	model	model	NOUN
ejpam-6129	49	8	where	where	SCONJ
ejpam-6129	49	9	existence	existence	NOUN
ejpam-6129	49	10	of	of	ADP
ejpam-6129	49	11	a	a	DET
ejpam-6129	49	12	solution	solution	NOUN
ejpam-6129	49	13	,	,	PUNCT
ejpam-6129	49	14	the	the	DET
ejpam-6129	49	15	stability	stability	NOUN
ejpam-6129	49	16	of	of	ADP
ejpam-6129	49	17	equilibria	equilibrium	NOUN
ejpam-6129	49	18	,	,	PUNCT
ejpam-6129	49	19	and	and	CCONJ
ejpam-6129	49	20	bifurcations	bifurcation	NOUN
ejpam-6129	49	21	of	of	ADP
ejpam-6129	49	22	the	the	DET
ejpam-6129	49	23	system	system	NOUN
ejpam-6129	49	24	were	be	AUX
ejpam-6129	49	25	investigated	investigate	VERB
ejpam-6129	49	26	.	.	PUNCT
ejpam-6129	50	1	they	they	PRON
ejpam-6129	50	2	showed	show	VERB
ejpam-6129	50	3	that	that	SCONJ
ejpam-6129	50	4	the	the	DET
ejpam-6129	50	5	epidemic	epidemic	NOUN
ejpam-6129	50	6	of	of	ADP
ejpam-6129	50	7	meningococcal	meningococcal	ADJ
ejpam-6129	50	8	disease	disease	NOUN
ejpam-6129	50	9	was	be	AUX
ejpam-6129	50	10	already	already	ADV
ejpam-6129	50	11	on	on	ADP
ejpam-6129	50	12	the	the	DET
ejpam-6129	50	13	decline	decline	NOUN
ejpam-6129	50	14	when	when	SCONJ
ejpam-6129	50	15	nationwide	nationwide	ADJ
ejpam-6129	50	16	vaccination	vaccination	NOUN
ejpam-6129	50	17	campaign	campaign	NOUN
ejpam-6129	50	18	was	be	AUX
ejpam-6129	50	19	launched	launch	VERB
ejpam-6129	50	20	.	.	PUNCT
ejpam-6129	51	1	they	they	PRON
ejpam-6129	51	2	found	find	VERB
ejpam-6129	51	3	that	that	SCONJ
ejpam-6129	51	4	the	the	DET
ejpam-6129	51	5	introduction	introduction	NOUN
ejpam-6129	51	6	of	of	ADP
ejpam-6129	51	7	the	the	DET
ejpam-6129	51	8	vaccine	vaccine	NOUN
ejpam-6129	51	9	reduced	reduce	VERB
ejpam-6129	51	10	the	the	DET
ejpam-6129	51	11	incidence	incidence	NOUN
ejpam-6129	51	12	of	of	ADP
ejpam-6129	51	13	infection	infection	NOUN
ejpam-6129	51	14	to	to	ADP
ejpam-6129	51	15	a	a	DET
ejpam-6129	51	16	predicted	predict	VERB
ejpam-6129	51	17	low	low	NOUN
ejpam-6129	51	18	of	of	ADP
ejpam-6129	51	19	five	five	NUM
ejpam-6129	51	20	cases	case	NOUN
ejpam-6129	51	21	per	per	ADP
ejpam-6129	51	22	year	year	NOUN
ejpam-6129	51	23	,	,	PUNCT
ejpam-6129	51	24	compared	compare	VERB
ejpam-6129	51	25	with	with	ADP
ejpam-6129	51	26	40	40	NUM
ejpam-6129	51	27	per	per	ADP
ejpam-6129	51	28	year	year	NOUN
ejpam-6129	51	29	with	with	ADP
ejpam-6129	51	30	no	no	DET
ejpam-6129	51	31	vaccination	vaccination	NOUN
ejpam-6129	51	32	.	.	PUNCT
ejpam-6129	52	1	yano	yano	PROPN
ejpam-6129	52	2	et	et	PROPN
ejpam-6129	52	3	al	al	PROPN
ejpam-6129	52	4	.	.	PUNCT
ejpam-6129	53	1	[	[	X
ejpam-6129	53	2	9	9	NUM
ejpam-6129	53	3	]	]	PUNCT
ejpam-6129	53	4	formulated	formulated	ADJ
ejpam-6129	53	5	and	and	CCONJ
ejpam-6129	53	6	analyzed	analyze	VERB
ejpam-6129	53	7	a	a	DET
ejpam-6129	53	8	meningococcal	meningococcal	ADJ
ejpam-6129	53	9	meningitis	meningitis	NOUN
ejpam-6129	53	10	epidemic	epidemic	NOUN
ejpam-6129	53	11	model	model	NOUN
ejpam-6129	53	12	that	that	PRON
ejpam-6129	53	13	describes	describe	VERB
ejpam-6129	53	14	the	the	DET
ejpam-6129	53	15	spreading	spread	VERB
ejpam-6129	53	16	mechanisms	mechanism	NOUN
ejpam-6129	53	17	of	of	ADP
ejpam-6129	53	18	meningitis	meningitis	NOUN
ejpam-6129	53	19	in	in	ADP
ejpam-6129	53	20	a	a	DET
ejpam-6129	53	21	community	community	NOUN
ejpam-6129	53	22	with	with	ADP
ejpam-6129	53	23	varying	vary	VERB
ejpam-6129	53	24	population	population	NOUN
ejpam-6129	53	25	.	.	PUNCT
ejpam-6129	54	1	using	use	VERB
ejpam-6129	54	2	pontryagin	pontryagin	NOUN
ejpam-6129	54	3	’s	’s	PART
ejpam-6129	54	4	approach	approach	NOUN
ejpam-6129	54	5	to	to	ADP
ejpam-6129	54	6	an	an	DET
ejpam-6129	54	7	optimal	optimal	ADJ
ejpam-6129	54	8	problem	problem	NOUN
ejpam-6129	54	9	,	,	PUNCT
ejpam-6129	54	10	their	their	PRON
ejpam-6129	54	11	model	model	NOUN
ejpam-6129	54	12	was	be	AUX
ejpam-6129	54	13	extended	extend	VERB
ejpam-6129	54	14	to	to	PART
ejpam-6129	54	15	include	include	VERB
ejpam-6129	54	16	the	the	DET
ejpam-6129	54	17	four	four	NUM
ejpam-6129	54	18	control	control	NOUN
ejpam-6129	54	19	intervention	intervention	NOUN
ejpam-6129	54	20	measures	measure	NOUN
ejpam-6129	54	21	:	:	PUNCT
ejpam-6129	54	22	effort	effort	NOUN
ejpam-6129	54	23	to	to	PART
ejpam-6129	54	24	prevent	prevent	VERB
ejpam-6129	54	25	a	a	DET
ejpam-6129	54	26	disease	disease	NOUN
ejpam-6129	54	27	infection	infection	NOUN
ejpam-6129	54	28	,	,	PUNCT
ejpam-6129	54	29	efforts	effort	NOUN
ejpam-6129	54	30	to	to	PART
ejpam-6129	54	31	treat	treat	VERB
ejpam-6129	54	32	sensitive	sensitive	ADJ
ejpam-6129	54	33	and	and	CCONJ
ejpam-6129	54	34	resistant	resistant	ADJ
ejpam-6129	54	35	strains	strain	NOUN
ejpam-6129	54	36	and	and	CCONJ
ejpam-6129	54	37	immunity	immunity	NOUN
ejpam-6129	54	38	control	control	NOUN
ejpam-6129	54	39	effort	effort	NOUN
ejpam-6129	54	40	.	.	PUNCT
ejpam-6129	55	1	their	their	PRON
ejpam-6129	55	2	optimal	optimal	ADJ
ejpam-6129	55	3	control	control	NOUN
ejpam-6129	55	4	study	study	NOUN
ejpam-6129	55	5	revealed	reveal	VERB
ejpam-6129	55	6	that	that	SCONJ
ejpam-6129	55	7	the	the	DET
ejpam-6129	55	8	use	use	NOUN
ejpam-6129	55	9	of	of	ADP
ejpam-6129	55	10	these	these	DET
ejpam-6129	55	11	prevention	prevention	NOUN
ejpam-6129	55	12	techniques	technique	NOUN
ejpam-6129	55	13	and	and	CCONJ
ejpam-6129	55	14	treatment	treatment	NOUN
ejpam-6129	55	15	efforts	effort	NOUN
ejpam-6129	55	16	led	lead	VERB
ejpam-6129	55	17	to	to	ADP
ejpam-6129	55	18	a	a	DET
ejpam-6129	55	19	larger	large	ADJ
ejpam-6129	55	20	decrease	decrease	NOUN
ejpam-6129	55	21	of	of	ADP
ejpam-6129	55	22	infections	infection	NOUN
ejpam-6129	55	23	.	.	PUNCT
ejpam-6129	56	1	the	the	DET
ejpam-6129	56	2	above	above	ADJ
ejpam-6129	56	3	are	be	AUX
ejpam-6129	56	4	a	a	DET
ejpam-6129	56	5	few	few	ADJ
ejpam-6129	56	6	works	work	NOUN
ejpam-6129	56	7	regarding	regard	VERB
ejpam-6129	56	8	mathematically	mathematically	ADV
ejpam-6129	56	9	modeling	model	VERB
ejpam-6129	56	10	the	the	DET
ejpam-6129	56	11	meningitis	meningitis	NOUN
ejpam-6129	56	12	disease	disease	NOUN
ejpam-6129	56	13	.	.	PUNCT
ejpam-6129	57	1	one	one	PRON
ejpam-6129	57	2	can	can	AUX
ejpam-6129	57	3	find	find	VERB
ejpam-6129	57	4	more	more	ADJ
ejpam-6129	57	5	studies	study	NOUN
ejpam-6129	57	6	dealing	deal	VERB
ejpam-6129	57	7	with	with	ADP
ejpam-6129	57	8	different	different	ADJ
ejpam-6129	57	9	aspects	aspect	NOUN
ejpam-6129	57	10	of	of	ADP
ejpam-6129	57	11	meningitis	meningitis	NOUN
ejpam-6129	57	12	,	,	PUNCT
ejpam-6129	57	13	for	for	ADP
ejpam-6129	57	14	instance	instance	NOUN
ejpam-6129	57	15	[	[	X
ejpam-6129	57	16	10	10	NUM
ejpam-6129	57	17	–	–	PUNCT
ejpam-6129	57	18	12	12	NUM
ejpam-6129	57	19	]	]	PUNCT
ejpam-6129	57	20	.	.	PUNCT
ejpam-6129	58	1	it	it	PRON
ejpam-6129	58	2	worth	worth	ADJ
ejpam-6129	58	3	mentioning	mention	VERB
ejpam-6129	58	4	that	that	SCONJ
ejpam-6129	58	5	,	,	PUNCT
ejpam-6129	58	6	as	as	SCONJ
ejpam-6129	58	7	can	can	AUX
ejpam-6129	58	8	be	be	AUX
ejpam-6129	58	9	seen	see	VERB
ejpam-6129	58	10	in	in	ADP
ejpam-6129	58	11	the	the	DET
ejpam-6129	58	12	above	above	ADJ
ejpam-6129	58	13	studies	study	NOUN
ejpam-6129	58	14	,	,	PUNCT
ejpam-6129	58	15	optimal	optimal	ADJ
ejpam-6129	58	16	control	control	NOUN
ejpam-6129	58	17	strategies	strategy	NOUN
ejpam-6129	58	18	have	have	AUX
ejpam-6129	58	19	not	not	PART
ejpam-6129	58	20	been	be	AUX
ejpam-6129	58	21	applied	apply	VERB
ejpam-6129	58	22	widely	widely	ADV
ejpam-6129	58	23	in	in	ADP
ejpam-6129	58	24	the	the	DET
ejpam-6129	58	25	models	model	NOUN
ejpam-6129	58	26	describing	describe	VERB
ejpam-6129	58	27	meningitis	meningiti	NOUN
ejpam-6129	58	28	.	.	PUNCT
ejpam-6129	59	1	to	to	PART
ejpam-6129	59	2	control	control	VERB
ejpam-6129	59	3	the	the	DET
ejpam-6129	59	4	meningitis	meningitis	NOUN
ejpam-6129	59	5	disease	disease	NOUN
ejpam-6129	59	6	,	,	PUNCT
ejpam-6129	59	7	some	some	DET
ejpam-6129	59	8	models	model	NOUN
ejpam-6129	59	9	include	include	VERB
ejpam-6129	59	10	vaccination	vaccination	NOUN
ejpam-6129	59	11	as	as	ADP
ejpam-6129	59	12	strategies	strategy	NOUN
ejpam-6129	59	13	to	to	PART
ejpam-6129	59	14	tackle	tackle	VERB
ejpam-6129	59	15	the	the	DET
ejpam-6129	59	16	evolution	evolution	NOUN
ejpam-6129	59	17	of	of	ADP
ejpam-6129	59	18	the	the	DET
ejpam-6129	59	19	disease	disease	NOUN
ejpam-6129	59	20	[	[	X
ejpam-6129	59	21	4	4	NUM
ejpam-6129	59	22	,	,	PUNCT
ejpam-6129	59	23	8	8	NUM
ejpam-6129	59	24	,	,	PUNCT
ejpam-6129	59	25	13	13	NUM
ejpam-6129	59	26	]	]	PUNCT
ejpam-6129	59	27	.	.	PUNCT
ejpam-6129	60	1	however	however	ADV
ejpam-6129	60	2	,	,	PUNCT
ejpam-6129	60	3	such	such	ADJ
ejpam-6129	60	4	models	model	NOUN
ejpam-6129	60	5	did	do	AUX
ejpam-6129	60	6	not	not	PART
ejpam-6129	60	7	account	account	VERB
ejpam-6129	60	8	for	for	ADP
ejpam-6129	60	9	time	time	NOUN
ejpam-6129	60	10	dependent	dependent	ADJ
ejpam-6129	60	11	control	control	NOUN
ejpam-6129	60	12	strategies	strategy	NOUN
ejpam-6129	60	13	,	,	PUNCT
ejpam-6129	60	14	rather	rather	ADV
ejpam-6129	60	15	fixed	fix	VERB
ejpam-6129	60	16	parameters	parameter	NOUN
ejpam-6129	60	17	values	value	NOUN
ejpam-6129	60	18	were	be	AUX
ejpam-6129	60	19	used	use	VERB
ejpam-6129	60	20	.	.	PUNCT
ejpam-6129	61	1	optimal	optimal	ADJ
ejpam-6129	61	2	control	control	NOUN
ejpam-6129	61	3	strategies	strategy	NOUN
ejpam-6129	61	4	have	have	AUX
ejpam-6129	61	5	been	be	AUX
ejpam-6129	61	6	applied	apply	VERB
ejpam-6129	61	7	for	for	ADP
ejpam-6129	61	8	various	various	ADJ
ejpam-6129	61	9	mathematical	mathematical	ADJ
ejpam-6129	61	10	models	model	NOUN
ejpam-6129	61	11	of	of	ADP
ejpam-6129	61	12	epidemic	epidemic	NOUN
ejpam-6129	61	13	diseases	disease	NOUN
ejpam-6129	61	14	,	,	PUNCT
ejpam-6129	61	15	for	for	ADP
ejpam-6129	61	16	example	example	NOUN
ejpam-6129	61	17	one	one	PRON
ejpam-6129	61	18	can	can	AUX
ejpam-6129	61	19	refer	refer	VERB
ejpam-6129	61	20	to	to	ADP
ejpam-6129	61	21	[	[	X
ejpam-6129	61	22	14–22	14–22	NUM
ejpam-6129	61	23	]	]	PUNCT
ejpam-6129	61	24	.	.	PUNCT
ejpam-6129	62	1	results	result	NOUN
ejpam-6129	62	2	obtained	obtain	VERB
ejpam-6129	62	3	in	in	ADP
ejpam-6129	62	4	these	these	DET
ejpam-6129	62	5	works	work	NOUN
ejpam-6129	62	6	as	as	ADV
ejpam-6129	62	7	well	well	ADV
ejpam-6129	62	8	as	as	ADP
ejpam-6129	62	9	in	in	ADP
ejpam-6129	62	10	other	other	ADJ
ejpam-6129	62	11	works	work	NOUN
ejpam-6129	62	12	are	be	AUX
ejpam-6129	62	13	of	of	ADP
ejpam-6129	62	14	high	high	ADJ
ejpam-6129	62	15	interest	interest	NOUN
ejpam-6129	62	16	and	and	CCONJ
ejpam-6129	62	17	can	can	AUX
ejpam-6129	62	18	be	be	AUX
ejpam-6129	62	19	used	use	VERB
ejpam-6129	62	20	to	to	PART
ejpam-6129	62	21	propose	propose	VERB
ejpam-6129	62	22	and	and	CCONJ
ejpam-6129	62	23	design	design	VERB
ejpam-6129	62	24	programs	program	NOUN
ejpam-6129	62	25	for	for	ADP
ejpam-6129	62	26	controlling	control	VERB
ejpam-6129	62	27	epidemic	epidemic	NOUN
ejpam-6129	62	28	diseases	disease	NOUN
ejpam-6129	62	29	.	.	PUNCT
ejpam-6129	63	1	in	in	ADP
ejpam-6129	63	2	this	this	DET
ejpam-6129	63	3	paper	paper	NOUN
ejpam-6129	63	4	,	,	PUNCT
ejpam-6129	63	5	we	we	PRON
ejpam-6129	63	6	consider	consider	VERB
ejpam-6129	63	7	two	two	NUM
ejpam-6129	63	8	optimal	optimal	ADJ
ejpam-6129	63	9	control	control	NOUN
ejpam-6129	63	10	strategies	strategy	NOUN
ejpam-6129	63	11	applied	apply	VERB
ejpam-6129	63	12	to	to	ADP
ejpam-6129	63	13	a	a	DET
ejpam-6129	63	14	meningitis	meningitis	NOUN
ejpam-6129	63	15	transmission	transmission	NOUN
ejpam-6129	63	16	model	model	NOUN
ejpam-6129	63	17	developed	develop	VERB
ejpam-6129	63	18	in	in	ADP
ejpam-6129	63	19	[	[	X
ejpam-6129	63	20	3	3	NUM
ejpam-6129	63	21	]	]	PUNCT
ejpam-6129	63	22	.	.	PUNCT
ejpam-6129	64	1	aiming	aim	VERB
ejpam-6129	64	2	to	to	PART
ejpam-6129	64	3	reduce	reduce	VERB
ejpam-6129	64	4	the	the	DET
ejpam-6129	64	5	number	number	NOUN
ejpam-6129	64	6	of	of	ADP
ejpam-6129	64	7	individuals	individual	NOUN
ejpam-6129	64	8	developing	develop	VERB
ejpam-6129	64	9	meningitis	meningiti	NOUN
ejpam-6129	64	10	,	,	PUNCT
ejpam-6129	64	11	the	the	DET
ejpam-6129	64	12	first	first	ADJ
ejpam-6129	64	13	control	control	NOUN
ejpam-6129	64	14	is	be	AUX
ejpam-6129	64	15	associated	associate	VERB
ejpam-6129	64	16	with	with	ADP
ejpam-6129	64	17	vaccination	vaccination	NOUN
ejpam-6129	64	18	to	to	PART
ejpam-6129	64	19	represent	represent	VERB
ejpam-6129	64	20	the	the	DET
ejpam-6129	64	21	fraction	fraction	NOUN
ejpam-6129	64	22	of	of	ADP
ejpam-6129	64	23	individuals	individual	NOUN
ejpam-6129	64	24	who	who	PRON
ejpam-6129	64	25	are	be	AUX
ejpam-6129	64	26	vaccinated	vaccinate	VERB
ejpam-6129	64	27	and	and	CCONJ
ejpam-6129	64	28	considered	consider	VERB
ejpam-6129	64	29	as	as	ADP
ejpam-6129	64	30	immune	immune	ADJ
ejpam-6129	64	31	individuals	individual	NOUN
ejpam-6129	64	32	,	,	PUNCT
ejpam-6129	64	33	while	while	SCONJ
ejpam-6129	64	34	the	the	DET
ejpam-6129	64	35	second	second	ADJ
ejpam-6129	64	36	control	control	NOUN
ejpam-6129	64	37	is	be	AUX
ejpam-6129	64	38	associated	associate	VERB
ejpam-6129	64	39	with	with	ADP
ejpam-6129	64	40	the	the	DET
ejpam-6129	64	41	treatment	treatment	NOUN
ejpam-6129	64	42	strategy	strategy	NOUN
ejpam-6129	64	43	.	.	PUNCT
ejpam-6129	65	1	the	the	DET
ejpam-6129	65	2	rest	rest	NOUN
ejpam-6129	65	3	of	of	ADP
ejpam-6129	65	4	the	the	DET
ejpam-6129	65	5	paper	paper	NOUN
ejpam-6129	65	6	is	be	AUX
ejpam-6129	65	7	organized	organize	VERB
ejpam-6129	65	8	as	as	SCONJ
ejpam-6129	65	9	follows	follow	VERB
ejpam-6129	65	10	.	.	PUNCT
ejpam-6129	66	1	section	section	NOUN
ejpam-6129	66	2	2	2	NUM
ejpam-6129	66	3	is	be	AUX
ejpam-6129	66	4	devoted	devote	VERB
ejpam-6129	66	5	to	to	ADP
ejpam-6129	66	6	the	the	DET
ejpam-6129	66	7	problem	problem	NOUN
ejpam-6129	66	8	statement	statement	NOUN
ejpam-6129	66	9	where	where	SCONJ
ejpam-6129	66	10	the	the	DET
ejpam-6129	66	11	mathematical	mathematical	ADJ
ejpam-6129	66	12	model	model	NOUN
ejpam-6129	66	13	along	along	ADP
ejpam-6129	66	14	with	with	ADP
ejpam-6129	66	15	the	the	DET
ejpam-6129	66	16	set	set	NOUN
ejpam-6129	66	17	of	of	ADP
ejpam-6129	66	18	controls	control	NOUN
ejpam-6129	66	19	provided	provide	VERB
ejpam-6129	66	20	.	.	PUNCT
ejpam-6129	67	1	analysis	analysis	NOUN
ejpam-6129	67	2	of	of	ADP
ejpam-6129	67	3	the	the	DET
ejpam-6129	67	4	optimal	optimal	ADJ
ejpam-6129	67	5	control	control	NOUN
ejpam-6129	67	6	problem	problem	NOUN
ejpam-6129	67	7	is	be	AUX
ejpam-6129	67	8	presented	present	VERB
ejpam-6129	67	9	in	in	ADP
ejpam-6129	67	10	section	section	NOUN
ejpam-6129	67	11	3	3	NUM
ejpam-6129	67	12	.	.	PUNCT
ejpam-6129	68	1	we	we	PRON
ejpam-6129	68	2	solve	solve	VERB
ejpam-6129	68	3	the	the	DET
ejpam-6129	68	4	resulting	result	VERB
ejpam-6129	68	5	optimality	optimality	NOUN
ejpam-6129	68	6	system	system	NOUN
ejpam-6129	68	7	numerically	numerically	ADV
ejpam-6129	68	8	in	in	ADP
ejpam-6129	68	9	section	section	NOUN
ejpam-6129	68	10	4	4	NUM
ejpam-6129	68	11	.	.	PUNCT
ejpam-6129	69	1	a	a	DET
ejpam-6129	69	2	thorough	thorough	ADJ
ejpam-6129	69	3	discussion	discussion	NOUN
ejpam-6129	69	4	on	on	ADP
ejpam-6129	69	5	the	the	DET
ejpam-6129	69	6	results	result	NOUN
ejpam-6129	69	7	obtained	obtain	VERB
ejpam-6129	69	8	is	be	AUX
ejpam-6129	69	9	presented	present	VERB
ejpam-6129	69	10	in	in	ADP
ejpam-6129	69	11	section	section	NOUN
ejpam-6129	69	12	5	5	NUM
ejpam-6129	69	13	.	.	PUNCT
ejpam-6129	70	1	s.	s.	PROPN
ejpam-6129	70	2	a.	a.	PROPN
ejpam-6129	70	3	mohamed	mohamed	PROPN
ejpam-6129	70	4	et	et	PROPN
ejpam-6129	70	5	al	al	PROPN
ejpam-6129	70	6	.	.	PUNCT
ejpam-6129	70	7	/	/	SYM
ejpam-6129	70	8	eur	eur	PROPN
ejpam-6129	70	9	.	.	PUNCT
ejpam-6129	71	1	j.	j.	PROPN
ejpam-6129	71	2	pure	pure	PROPN
ejpam-6129	71	3	appl	appl	PROPN
ejpam-6129	71	4	.	.	PROPN
ejpam-6129	71	5	math	math	PROPN
ejpam-6129	71	6	,	,	PUNCT
ejpam-6129	71	7	18	18	NUM
ejpam-6129	71	8	(	(	PUNCT
ejpam-6129	71	9	3	3	NUM
ejpam-6129	71	10	)	)	PUNCT
ejpam-6129	71	11	(	(	PUNCT
ejpam-6129	71	12	2025	2025	NUM
ejpam-6129	71	13	)	)	PUNCT
ejpam-6129	71	14	,	,	PUNCT
ejpam-6129	71	15	6129	6129	NUM
ejpam-6129	71	16	4	4	NUM
ejpam-6129	71	17	of	of	ADP
ejpam-6129	71	18	17	17	NUM
ejpam-6129	71	19	2	2	NUM
ejpam-6129	71	20	.	.	PUNCT
ejpam-6129	72	1	a	a	DET
ejpam-6129	72	2	model	model	NOUN
ejpam-6129	72	3	for	for	ADP
ejpam-6129	72	4	optimal	optimal	ADJ
ejpam-6129	72	5	control	control	NOUN
ejpam-6129	72	6	of	of	ADP
ejpam-6129	72	7	meningitis	meningitis	NOUN
ejpam-6129	72	8	in	in	ADP
ejpam-6129	72	9	this	this	DET
ejpam-6129	72	10	section	section	NOUN
ejpam-6129	72	11	,	,	PUNCT
ejpam-6129	72	12	we	we	PRON
ejpam-6129	72	13	consider	consider	VERB
ejpam-6129	72	14	the	the	DET
ejpam-6129	72	15	deterministic	deterministic	ADJ
ejpam-6129	72	16	model	model	NOUN
ejpam-6129	72	17	presented	present	VERB
ejpam-6129	72	18	in	in	ADP
ejpam-6129	72	19	[	[	X
ejpam-6129	72	20	3	3	NUM
ejpam-6129	72	21	]	]	PUNCT
ejpam-6129	72	22	where	where	SCONJ
ejpam-6129	72	23	the	the	DET
ejpam-6129	72	24	state	state	NOUN
ejpam-6129	72	25	system	system	NOUN
ejpam-6129	72	26	is	be	AUX
ejpam-6129	72	27	described	describe	VERB
ejpam-6129	72	28	by	by	ADP
ejpam-6129	72	29	the	the	DET
ejpam-6129	72	30	following	following	ADJ
ejpam-6129	72	31	nonlinear	nonlinear	ADJ
ejpam-6129	72	32	system	system	NOUN
ejpam-6129	72	33	of	of	ADP
ejpam-6129	72	34	ordinary	ordinary	ADJ
ejpam-6129	72	35	differential	differential	ADJ
ejpam-6129	72	36	equations	equation	NOUN
ejpam-6129	72	37	ds	ds	ADJ
ejpam-6129	72	38	dt	dt	NOUN
ejpam-6129	72	39	=	=	SYM
ejpam-6129	72	40	µn	µn	PROPN
ejpam-6129	72	41	+	+	X
ejpam-6129	72	42	γi	γi	X
ejpam-6129	72	43	+	+	CCONJ
ejpam-6129	72	44	φr−	φr−	NUM
ejpam-6129	72	45	β(1−	β(1−	NOUN
ejpam-6129	72	46	u2)s(c	u2)s(c	ADJ
ejpam-6129	72	47	+	+	ADJ
ejpam-6129	72	48	i)−	i)−	ADJ
ejpam-6129	72	49	µs	µs	NOUN
ejpam-6129	72	50	−	−	NOUN
ejpam-6129	72	51	u1s	u1s	PROPN
ejpam-6129	72	52	,	,	PUNCT
ejpam-6129	72	53	dc	dc	PROPN
ejpam-6129	72	54	dt	dt	X
ejpam-6129	72	55	=	=	PUNCT
ejpam-6129	72	56	β(1−	β(1−	X
ejpam-6129	73	1	u2)s(c	u2)s(c	ADJ
ejpam-6129	73	2	+	+	CCONJ
ejpam-6129	73	3	i)−	i)−	PROPN
ejpam-6129	73	4	(	(	PUNCT
ejpam-6129	73	5	a+	a+	PRON
ejpam-6129	73	6	α+	α+	X
ejpam-6129	73	7	µ)c	µ)c	X
ejpam-6129	73	8	,	,	PUNCT
ejpam-6129	73	9	di	di	INTJ
ejpam-6129	73	10	dt	dt	NOUN
ejpam-6129	73	11	=	=	PUNCT
ejpam-6129	73	12	ac	ac	PROPN
ejpam-6129	73	13	−	−	PROPN
ejpam-6129	73	14	(	(	PUNCT
ejpam-6129	73	15	ρ+	ρ+	NUM
ejpam-6129	73	16	γ	γ	X
ejpam-6129	73	17	+	+	X
ejpam-6129	73	18	µ)i	µ)i	ADJ
ejpam-6129	73	19	,	,	PUNCT
ejpam-6129	73	20	dr	dr	PROPN
ejpam-6129	73	21	dt	dt	PROPN
ejpam-6129	73	22	=	=	PROPN
ejpam-6129	73	23	ρi	ρi	PROPN
ejpam-6129	73	24	+	+	CCONJ
ejpam-6129	73	25	αc	αc	PROPN
ejpam-6129	73	26	−	−	PROPN
ejpam-6129	73	27	(	(	PUNCT
ejpam-6129	73	28	φ+	φ+	X
ejpam-6129	73	29	µ)r+	µ)r+	X
ejpam-6129	73	30	u1s	u1s	ADJ
ejpam-6129	73	31	,	,	PUNCT
ejpam-6129	73	32	(	(	PUNCT
ejpam-6129	73	33	1	1	X
ejpam-6129	73	34	)	)	PUNCT
ejpam-6129	73	35	where	where	SCONJ
ejpam-6129	73	36	n	n	NOUN
ejpam-6129	73	37	=	=	SYM
ejpam-6129	73	38	s+c+i+r	s+c+i+r	NOUN
ejpam-6129	73	39	with	with	ADP
ejpam-6129	73	40	initial	initial	ADJ
ejpam-6129	73	41	conditions	condition	NOUN
ejpam-6129	73	42	s(0	s(0	PROPN
ejpam-6129	73	43	)	)	PUNCT
ejpam-6129	73	44	≥	≥	NOUN
ejpam-6129	73	45	0	0	NUM
ejpam-6129	73	46	,	,	PUNCT
ejpam-6129	73	47	c(0	c(0	NOUN
ejpam-6129	73	48	)	)	PUNCT
ejpam-6129	73	49	≥	≥	NOUN
ejpam-6129	73	50	0	0	NUM
ejpam-6129	73	51	,	,	PUNCT
ejpam-6129	73	52	i(0	i(0	PROPN
ejpam-6129	73	53	)	)	PUNCT
ejpam-6129	73	54	≥	≥	NOUN
ejpam-6129	73	55	0	0	NUM
ejpam-6129	73	56	and	and	CCONJ
ejpam-6129	73	57	r(0	r(0	PROPN
ejpam-6129	73	58	)	)	PUNCT
ejpam-6129	73	59	≥	≥	NOUN
ejpam-6129	73	60	0	0	NUM
ejpam-6129	73	61	.	.	PUNCT
ejpam-6129	74	1	the	the	DET
ejpam-6129	74	2	host	host	NOUN
ejpam-6129	74	3	population	population	NOUN
ejpam-6129	74	4	is	be	AUX
ejpam-6129	74	5	divided	divide	VERB
ejpam-6129	74	6	into	into	ADP
ejpam-6129	74	7	susceptible	susceptible	ADJ
ejpam-6129	74	8	s	s	NOUN
ejpam-6129	74	9	,	,	PUNCT
ejpam-6129	74	10	an	an	DET
ejpam-6129	74	11	asymptomatic	asymptomatic	ADJ
ejpam-6129	74	12	carrier	carrier	NOUN
ejpam-6129	74	13	c	c	PROPN
ejpam-6129	74	14	,	,	PUNCT
ejpam-6129	74	15	ill	ill	ADJ
ejpam-6129	74	16	i	i	NOUN
ejpam-6129	74	17	,	,	PUNCT
ejpam-6129	74	18	and	and	CCONJ
ejpam-6129	74	19	immune	immune	PROPN
ejpam-6129	74	20	r.	r.	NOUN
ejpam-6129	74	21	the	the	DET
ejpam-6129	74	22	parameters	parameter	NOUN
ejpam-6129	74	23	used	use	VERB
ejpam-6129	74	24	in	in	ADP
ejpam-6129	74	25	the	the	DET
ejpam-6129	74	26	model	model	NOUN
ejpam-6129	74	27	are	be	AUX
ejpam-6129	74	28	defined	define	VERB
ejpam-6129	74	29	in	in	ADP
ejpam-6129	74	30	[	[	X
ejpam-6129	74	31	3	3	NUM
ejpam-6129	74	32	]	]	PUNCT
ejpam-6129	74	33	as	as	SCONJ
ejpam-6129	74	34	follows	follow	VERB
ejpam-6129	74	35	.	.	PUNCT
ejpam-6129	75	1	µ	µ	X
ejpam-6129	75	2	:	:	PUNCT
ejpam-6129	75	3	the	the	DET
ejpam-6129	75	4	natural	natural	ADJ
ejpam-6129	75	5	death	death	NOUN
ejpam-6129	75	6	rate	rate	NOUN
ejpam-6129	75	7	;	;	PUNCT
ejpam-6129	75	8	ρ	ρ	NUM
ejpam-6129	75	9	:	:	PUNCT
ejpam-6129	75	10	the	the	DET
ejpam-6129	75	11	recovery	recovery	NOUN
ejpam-6129	75	12	rate	rate	NOUN
ejpam-6129	75	13	;	;	PUNCT
ejpam-6129	75	14	γ	γ	X
ejpam-6129	75	15	:	:	PUNCT
ejpam-6129	75	16	the	the	DET
ejpam-6129	75	17	rate	rate	NOUN
ejpam-6129	75	18	of	of	ADP
ejpam-6129	75	19	death	death	NOUN
ejpam-6129	75	20	from	from	ADP
ejpam-6129	75	21	disease	disease	NOUN
ejpam-6129	75	22	;	;	PUNCT
ejpam-6129	75	23	β	β	NOUN
ejpam-6129	75	24	:	:	PUNCT
ejpam-6129	75	25	the	the	DET
ejpam-6129	75	26	transmission	transmission	NOUN
ejpam-6129	75	27	rate	rate	NOUN
ejpam-6129	75	28	;	;	PUNCT
ejpam-6129	75	29	α	α	X
ejpam-6129	75	30	:	:	PUNCT
ejpam-6129	75	31	the	the	DET
ejpam-6129	75	32	rate	rate	NOUN
ejpam-6129	75	33	of	of	ADP
ejpam-6129	75	34	loss	loss	NOUN
ejpam-6129	75	35	of	of	ADP
ejpam-6129	75	36	carriage	carriage	NOUN
ejpam-6129	75	37	;	;	PUNCT
ejpam-6129	75	38	a	a	PRON
ejpam-6129	75	39	:	:	PUNCT
ejpam-6129	75	40	the	the	DET
ejpam-6129	75	41	rate	rate	NOUN
ejpam-6129	75	42	at	at	ADP
ejpam-6129	75	43	which	which	PRON
ejpam-6129	75	44	carriers	carrier	NOUN
ejpam-6129	75	45	become	become	VERB
ejpam-6129	75	46	ill	ill	ADJ
ejpam-6129	75	47	;	;	PUNCT
ejpam-6129	75	48	φ	φ	NUM
ejpam-6129	75	49	:	:	PUNCT
ejpam-6129	75	50	the	the	DET
ejpam-6129	75	51	rate	rate	NOUN
ejpam-6129	75	52	of	of	ADP
ejpam-6129	75	53	loss	loss	NOUN
ejpam-6129	75	54	of	of	ADP
ejpam-6129	75	55	immunity	immunity	NOUN
ejpam-6129	75	56	.	.	PUNCT
ejpam-6129	76	1	to	to	PART
ejpam-6129	76	2	minimize	minimize	VERB
ejpam-6129	76	3	the	the	DET
ejpam-6129	76	4	carrier	carrier	NOUN
ejpam-6129	76	5	individuals	individual	NOUN
ejpam-6129	76	6	and	and	CCONJ
ejpam-6129	76	7	,	,	PUNCT
ejpam-6129	76	8	therefore	therefore	ADV
ejpam-6129	76	9	,	,	PUNCT
ejpam-6129	76	10	to	to	PART
ejpam-6129	76	11	minimize	minimize	VERB
ejpam-6129	76	12	the	the	DET
ejpam-6129	76	13	total	total	ADJ
ejpam-6129	76	14	number	number	NOUN
ejpam-6129	76	15	of	of	ADP
ejpam-6129	76	16	ill	ill	ADJ
ejpam-6129	76	17	individuals	individual	NOUN
ejpam-6129	76	18	,	,	PUNCT
ejpam-6129	76	19	controls	control	VERB
ejpam-6129	76	20	on	on	ADP
ejpam-6129	76	21	vaccination	vaccination	NOUN
ejpam-6129	76	22	and	and	CCONJ
ejpam-6129	76	23	treatment	treatment	NOUN
ejpam-6129	76	24	are	be	AUX
ejpam-6129	76	25	used	use	VERB
ejpam-6129	76	26	.	.	PUNCT
ejpam-6129	77	1	these	these	DET
ejpam-6129	77	2	controls	control	NOUN
ejpam-6129	77	3	are	be	AUX
ejpam-6129	77	4	represented	represent	VERB
ejpam-6129	77	5	as	as	ADP
ejpam-6129	77	6	functions	function	NOUN
ejpam-6129	77	7	of	of	ADP
ejpam-6129	77	8	time	time	NOUN
ejpam-6129	77	9	and	and	CCONJ
ejpam-6129	77	10	assigned	assign	VERB
ejpam-6129	77	11	reasonable	reasonable	ADJ
ejpam-6129	77	12	upper	upper	ADJ
ejpam-6129	77	13	and	and	CCONJ
ejpam-6129	77	14	lower	low	ADJ
ejpam-6129	77	15	bounds	bound	NOUN
ejpam-6129	77	16	as	as	SCONJ
ejpam-6129	77	17	indicated	indicate	VERB
ejpam-6129	77	18	in	in	ADP
ejpam-6129	77	19	the	the	DET
ejpam-6129	77	20	subsequent	subsequent	ADJ
ejpam-6129	77	21	discussion	discussion	NOUN
ejpam-6129	77	22	in	in	ADP
ejpam-6129	77	23	this	this	DET
ejpam-6129	77	24	paper	paper	NOUN
ejpam-6129	77	25	.	.	PUNCT
ejpam-6129	78	1	the	the	DET
ejpam-6129	78	2	first	first	ADJ
ejpam-6129	78	3	control	control	NOUN
ejpam-6129	78	4	function	function	VERB
ejpam-6129	78	5	u1(t	u1(t	PRON
ejpam-6129	78	6	)	)	PUNCT
ejpam-6129	78	7	is	be	AUX
ejpam-6129	78	8	inserted	insert	VERB
ejpam-6129	78	9	into	into	ADP
ejpam-6129	78	10	the	the	DET
ejpam-6129	78	11	model	model	NOUN
ejpam-6129	78	12	to	to	PART
ejpam-6129	78	13	represent	represent	VERB
ejpam-6129	78	14	the	the	DET
ejpam-6129	78	15	fraction	fraction	NOUN
ejpam-6129	78	16	of	of	ADP
ejpam-6129	78	17	individuals	individual	NOUN
ejpam-6129	78	18	who	who	PRON
ejpam-6129	78	19	are	be	AUX
ejpam-6129	78	20	vaccinated	vaccinate	VERB
ejpam-6129	78	21	and	and	CCONJ
ejpam-6129	78	22	considered	consider	VERB
ejpam-6129	78	23	as	as	ADP
ejpam-6129	78	24	immune	immune	ADJ
ejpam-6129	78	25	individuals	individual	NOUN
ejpam-6129	78	26	,	,	PUNCT
ejpam-6129	78	27	and	and	CCONJ
ejpam-6129	78	28	the	the	DET
ejpam-6129	78	29	second	second	ADJ
ejpam-6129	78	30	control	control	NOUN
ejpam-6129	78	31	function	function	NOUN
ejpam-6129	78	32	u2(t	u2(t	NOUN
ejpam-6129	78	33	)	)	PUNCT
ejpam-6129	78	34	is	be	AUX
ejpam-6129	78	35	inserted	insert	VERB
ejpam-6129	78	36	to	to	PART
ejpam-6129	78	37	represent	represent	VERB
ejpam-6129	78	38	the	the	DET
ejpam-6129	78	39	effectiveness	effectiveness	NOUN
ejpam-6129	78	40	of	of	ADP
ejpam-6129	78	41	treatment	treatment	NOUN
ejpam-6129	78	42	.	.	PUNCT
ejpam-6129	79	1	therefore	therefore	ADV
ejpam-6129	79	2	,	,	PUNCT
ejpam-6129	79	3	(	(	PUNCT
ejpam-6129	79	4	1	1	NUM
ejpam-6129	79	5	−	−	NOUN
ejpam-6129	79	6	u2(t	u2(t	NOUN
ejpam-6129	79	7	)	)	PUNCT
ejpam-6129	79	8	)	)	PUNCT
ejpam-6129	79	9	represents	represent	VERB
ejpam-6129	79	10	the	the	DET
ejpam-6129	79	11	fraction	fraction	NOUN
ejpam-6129	79	12	of	of	ADP
ejpam-6129	79	13	individuals	individual	NOUN
ejpam-6129	79	14	developing	develop	VERB
ejpam-6129	79	15	the	the	DET
ejpam-6129	79	16	disease	disease	NOUN
ejpam-6129	79	17	and	and	CCONJ
ejpam-6129	79	18	hence	hence	ADV
ejpam-6129	79	19	increasing	increase	VERB
ejpam-6129	79	20	the	the	DET
ejpam-6129	79	21	value	value	NOUN
ejpam-6129	79	22	of	of	ADP
ejpam-6129	79	23	u2(t	u2(t	NOUN
ejpam-6129	79	24	)	)	PUNCT
ejpam-6129	79	25	causes	cause	VERB
ejpam-6129	79	26	reduction	reduction	NOUN
ejpam-6129	79	27	in	in	ADP
ejpam-6129	79	28	the	the	DET
ejpam-6129	79	29	number	number	NOUN
ejpam-6129	79	30	of	of	ADP
ejpam-6129	79	31	ill	ill	ADJ
ejpam-6129	79	32	individuals	individual	NOUN
ejpam-6129	79	33	.	.	PUNCT
ejpam-6129	80	1	the	the	DET
ejpam-6129	80	2	functions	function	NOUN
ejpam-6129	80	3	u1(t	u1(t	ADP
ejpam-6129	80	4	)	)	PUNCT
ejpam-6129	80	5	and	and	CCONJ
ejpam-6129	80	6	u2(t	u2(t	NOUN
ejpam-6129	80	7	)	)	PUNCT
ejpam-6129	80	8	are	be	AUX
ejpam-6129	80	9	bounded	bound	VERB
ejpam-6129	80	10	and	and	CCONJ
ejpam-6129	80	11	lebesgue	lebesgue	VERB
ejpam-6129	80	12	integrable	integrable	ADJ
ejpam-6129	80	13	functions	function	NOUN
ejpam-6129	80	14	.	.	PUNCT
ejpam-6129	81	1	we	we	PRON
ejpam-6129	81	2	define	define	VERB
ejpam-6129	81	3	the	the	DET
ejpam-6129	81	4	objective	objective	ADJ
ejpam-6129	81	5	functional	functional	NOUN
ejpam-6129	81	6	as	as	ADP
ejpam-6129	81	7	j(u1	j(u1	NOUN
ejpam-6129	81	8	,	,	PUNCT
ejpam-6129	81	9	u2	u2	NOUN
ejpam-6129	81	10	)	)	PUNCT
ejpam-6129	81	11	=	=	SYM
ejpam-6129	81	12	min	min	PROPN
ejpam-6129	82	1	u1,u2	u1,u2	PROPN
ejpam-6129	82	2	∫	∫	PROPN
ejpam-6129	82	3	tf	tf	INTJ
ejpam-6129	82	4	0	0	NUM
ejpam-6129	83	1	(	(	PUNCT
ejpam-6129	83	2	c	c	X
ejpam-6129	83	3	+	+	CCONJ
ejpam-6129	83	4	a	a	DET
ejpam-6129	83	5	2	2	NUM
ejpam-6129	83	6	u21	u21	NOUN
ejpam-6129	83	7	+	+	CCONJ
ejpam-6129	83	8	b	b	SYM
ejpam-6129	83	9	2	2	NUM
ejpam-6129	83	10	u22	u22	PROPN
ejpam-6129	83	11	)	)	PUNCT
ejpam-6129	84	1	dt	dt	PROPN
ejpam-6129	84	2	,	,	PUNCT
ejpam-6129	84	3	(	(	PUNCT
ejpam-6129	84	4	2	2	X
ejpam-6129	84	5	)	)	PUNCT
ejpam-6129	84	6	where	where	SCONJ
ejpam-6129	84	7	tf	tf	PROPN
ejpam-6129	84	8	is	be	AUX
ejpam-6129	84	9	the	the	DET
ejpam-6129	84	10	specified	specified	ADJ
ejpam-6129	84	11	and	and	CCONJ
ejpam-6129	84	12	finite	finite	ADJ
ejpam-6129	84	13	final	final	ADJ
ejpam-6129	84	14	time	time	NOUN
ejpam-6129	84	15	and	and	CCONJ
ejpam-6129	84	16	the	the	DET
ejpam-6129	84	17	constants	constant	NOUN
ejpam-6129	84	18	a	a	PRON
ejpam-6129	84	19	and	and	CCONJ
ejpam-6129	84	20	b	b	NOUN
ejpam-6129	84	21	are	be	AUX
ejpam-6129	84	22	the	the	DET
ejpam-6129	84	23	balancing	balance	VERB
ejpam-6129	84	24	cost	cost	NOUN
ejpam-6129	84	25	factors	factor	NOUN
ejpam-6129	84	26	.	.	PUNCT
ejpam-6129	85	1	our	our	PRON
ejpam-6129	85	2	goal	goal	NOUN
ejpam-6129	85	3	is	be	AUX
ejpam-6129	85	4	to	to	PART
ejpam-6129	85	5	find	find	VERB
ejpam-6129	85	6	two	two	NUM
ejpam-6129	85	7	optimal	optimal	ADJ
ejpam-6129	85	8	controls	control	NOUN
ejpam-6129	85	9	,	,	PUNCT
ejpam-6129	85	10	u∗1	u∗1	NOUN
ejpam-6129	85	11	and	and	CCONJ
ejpam-6129	85	12	u∗2	u∗2	NOUN
ejpam-6129	85	13	,	,	PUNCT
ejpam-6129	85	14	such	such	ADJ
ejpam-6129	85	15	that	that	DET
ejpam-6129	85	16	j(u∗1	j(u∗1	NOUN
ejpam-6129	85	17	,	,	PUNCT
ejpam-6129	85	18	u	u	NOUN
ejpam-6129	85	19	∗	∗	NOUN
ejpam-6129	85	20	2	2	NUM
ejpam-6129	85	21	)	)	PUNCT
ejpam-6129	85	22	=	=	SYM
ejpam-6129	85	23	min	min	PROPN
ejpam-6129	85	24	ψ	ψ	NOUN
ejpam-6129	85	25	j(u1	j(u1	NOUN
ejpam-6129	85	26	,	,	PUNCT
ejpam-6129	85	27	u2	u2	PROPN
ejpam-6129	85	28	)	)	PUNCT
ejpam-6129	85	29	,	,	PUNCT
ejpam-6129	85	30	(	(	PUNCT
ejpam-6129	85	31	3	3	X
ejpam-6129	85	32	)	)	PUNCT
ejpam-6129	85	33	where	where	SCONJ
ejpam-6129	85	34	ψ	ψ	NOUN
ejpam-6129	85	35	=	=	SYM
ejpam-6129	85	36	{	{	PUNCT
ejpam-6129	85	37	(	(	PUNCT
ejpam-6129	85	38	u1	u1	NOUN
ejpam-6129	85	39	,	,	PUNCT
ejpam-6129	85	40	u2	u2	PROPN
ejpam-6129	85	41	)	)	PUNCT
ejpam-6129	85	42	∈	∈	PROPN
ejpam-6129	85	43	l1(0	l1(0	PROPN
ejpam-6129	85	44	,	,	PUNCT
ejpam-6129	85	45	tf	tf	INTJ
ejpam-6129	85	46	)	)	PUNCT
ejpam-6129	85	47	|ai	|ai	NUM
ejpam-6129	85	48	≤	≤	NUM
ejpam-6129	85	49	ui	ui	NOUN
ejpam-6129	85	50	≤	≤	NUM
ejpam-6129	85	51	bi	bi	NOUN
ejpam-6129	85	52	,	,	PUNCT
ejpam-6129	85	53	i	i	PRON
ejpam-6129	85	54	=	=	NOUN
ejpam-6129	85	55	1	1	NUM
ejpam-6129	85	56	,	,	PUNCT
ejpam-6129	85	57	2	2	NUM
ejpam-6129	85	58	}	}	PUNCT
ejpam-6129	85	59	,	,	PUNCT
ejpam-6129	85	60	(	(	PUNCT
ejpam-6129	85	61	4	4	NUM
ejpam-6129	85	62	)	)	PUNCT
ejpam-6129	85	63	and	and	CCONJ
ejpam-6129	85	64	ai	ai	VERB
ejpam-6129	85	65	,	,	PUNCT
ejpam-6129	85	66	bi	bi	NOUN
ejpam-6129	85	67	;	;	PUNCT
ejpam-6129	85	68	i	i	NOUN
ejpam-6129	85	69	=	=	NOUN
ejpam-6129	85	70	1	1	NUM
ejpam-6129	85	71	,	,	PUNCT
ejpam-6129	85	72	2	2	NUM
ejpam-6129	85	73	,	,	PUNCT
ejpam-6129	85	74	are	be	AUX
ejpam-6129	85	75	positive	positive	ADJ
ejpam-6129	85	76	constants	constant	NOUN
ejpam-6129	85	77	representing	represent	VERB
ejpam-6129	85	78	the	the	DET
ejpam-6129	85	79	bounds	bound	NOUN
ejpam-6129	85	80	on	on	ADP
ejpam-6129	85	81	the	the	DET
ejpam-6129	85	82	two	two	NUM
ejpam-6129	85	83	controls	control	NOUN
ejpam-6129	85	84	.	.	PUNCT
ejpam-6129	86	1	s.	s.	PROPN
ejpam-6129	86	2	a.	a.	PROPN
ejpam-6129	86	3	mohamed	mohamed	PROPN
ejpam-6129	86	4	et	et	PROPN
ejpam-6129	86	5	al	al	PROPN
ejpam-6129	86	6	.	.	PUNCT
ejpam-6129	86	7	/	/	SYM
ejpam-6129	86	8	eur	eur	PROPN
ejpam-6129	86	9	.	.	PUNCT
ejpam-6129	87	1	j.	j.	PROPN
ejpam-6129	87	2	pure	pure	PROPN
ejpam-6129	87	3	appl	appl	PROPN
ejpam-6129	87	4	.	.	PROPN
ejpam-6129	87	5	math	math	PROPN
ejpam-6129	87	6	,	,	PUNCT
ejpam-6129	87	7	18	18	NUM
ejpam-6129	87	8	(	(	PUNCT
ejpam-6129	87	9	3	3	NUM
ejpam-6129	87	10	)	)	PUNCT
ejpam-6129	87	11	(	(	PUNCT
ejpam-6129	87	12	2025	2025	NUM
ejpam-6129	87	13	)	)	PUNCT
ejpam-6129	87	14	,	,	PUNCT
ejpam-6129	87	15	6129	6129	NUM
ejpam-6129	87	16	5	5	NUM
ejpam-6129	87	17	of	of	ADP
ejpam-6129	87	18	17	17	NUM
ejpam-6129	87	19	3	3	NUM
ejpam-6129	87	20	.	.	PUNCT
ejpam-6129	88	1	analysis	analysis	NOUN
ejpam-6129	88	2	of	of	ADP
ejpam-6129	88	3	the	the	DET
ejpam-6129	88	4	optimal	optimal	ADJ
ejpam-6129	88	5	control	control	NOUN
ejpam-6129	88	6	problem	problem	NOUN
ejpam-6129	88	7	in	in	ADP
ejpam-6129	88	8	this	this	DET
ejpam-6129	88	9	section	section	NOUN
ejpam-6129	88	10	,	,	PUNCT
ejpam-6129	88	11	we	we	PRON
ejpam-6129	88	12	use	use	VERB
ejpam-6129	88	13	the	the	DET
ejpam-6129	88	14	pontryagin	pontryagin	NOUN
ejpam-6129	88	15	’s	’s	PART
ejpam-6129	88	16	maximum	maximum	ADJ
ejpam-6129	88	17	principle	principle	NOUN
ejpam-6129	88	18	[	[	X
ejpam-6129	88	19	23	23	NUM
ejpam-6129	88	20	]	]	PUNCT
ejpam-6129	88	21	to	to	PART
ejpam-6129	88	22	derive	derive	VERB
ejpam-6129	88	23	the	the	DET
ejpam-6129	88	24	necessary	necessary	ADJ
ejpam-6129	88	25	conditions	condition	NOUN
ejpam-6129	88	26	that	that	SCONJ
ejpam-6129	88	27	an	an	DET
ejpam-6129	88	28	optimal	optimal	ADJ
ejpam-6129	88	29	problem	problem	NOUN
ejpam-6129	88	30	must	must	AUX
ejpam-6129	88	31	satisfy	satisfy	VERB
ejpam-6129	88	32	.	.	PUNCT
ejpam-6129	89	1	this	this	DET
ejpam-6129	89	2	principle	principle	NOUN
ejpam-6129	89	3	is	be	AUX
ejpam-6129	89	4	used	use	VERB
ejpam-6129	89	5	to	to	PART
ejpam-6129	89	6	convert	convert	VERB
ejpam-6129	89	7	(	(	PUNCT
ejpam-6129	89	8	1	1	NUM
ejpam-6129	89	9	)	)	PUNCT
ejpam-6129	89	10	,	,	PUNCT
ejpam-6129	89	11	(	(	PUNCT
ejpam-6129	89	12	2	2	NUM
ejpam-6129	89	13	)	)	PUNCT
ejpam-6129	89	14	,	,	PUNCT
ejpam-6129	89	15	and	and	CCONJ
ejpam-6129	89	16	(	(	PUNCT
ejpam-6129	89	17	3	3	X
ejpam-6129	89	18	)	)	PUNCT
ejpam-6129	89	19	into	into	ADP
ejpam-6129	89	20	a	a	DET
ejpam-6129	89	21	problem	problem	NOUN
ejpam-6129	89	22	of	of	ADP
ejpam-6129	89	23	minimizing	minimize	VERB
ejpam-6129	89	24	a	a	DET
ejpam-6129	89	25	pointwise	pointwise	ADJ
ejpam-6129	89	26	hamiltonian	hamiltonian	ADJ
ejpam-6129	89	27	,	,	PUNCT
ejpam-6129	89	28	h	h	NOUN
ejpam-6129	89	29	,	,	PUNCT
ejpam-6129	89	30	with	with	ADP
ejpam-6129	89	31	respect	respect	NOUN
ejpam-6129	89	32	to	to	ADP
ejpam-6129	89	33	u1	u1	VERB
ejpam-6129	89	34	and	and	CCONJ
ejpam-6129	89	35	u2	u2	NOUN
ejpam-6129	89	36	:	:	PUNCT
ejpam-6129	89	37	h	h	NOUN
ejpam-6129	89	38	=	=	PUNCT
ejpam-6129	89	39	c	c	PROPN
ejpam-6129	89	40	+	+	CCONJ
ejpam-6129	89	41	a	a	DET
ejpam-6129	89	42	2	2	NUM
ejpam-6129	89	43	u21	u21	NOUN
ejpam-6129	89	44	+	+	CCONJ
ejpam-6129	89	45	b	b	SYM
ejpam-6129	89	46	2	2	NUM
ejpam-6129	89	47	u22	u22	NOUN
ejpam-6129	89	48	+	+	CCONJ
ejpam-6129	89	49	4∑	4∑	NOUN
ejpam-6129	89	50	i=1	i=1	PROPN
ejpam-6129	89	51	λigi	λigi	NOUN
ejpam-6129	89	52	,	,	PUNCT
ejpam-6129	89	53	(	(	PUNCT
ejpam-6129	89	54	5	5	NUM
ejpam-6129	89	55	)	)	PUNCT
ejpam-6129	89	56	where	where	SCONJ
ejpam-6129	89	57	gi	gi	INTJ
ejpam-6129	89	58	and	and	CCONJ
ejpam-6129	89	59	λi	λi	CCONJ
ejpam-6129	89	60	,	,	PUNCT
ejpam-6129	89	61	i	i	NOUN
ejpam-6129	89	62	=	=	NOUN
ejpam-6129	89	63	1	1	NUM
ejpam-6129	89	64	,	,	PUNCT
ejpam-6129	89	65	...	...	PUNCT
ejpam-6129	89	66	,	,	PUNCT
ejpam-6129	89	67	4	4	NUM
ejpam-6129	89	68	,	,	PUNCT
ejpam-6129	89	69	are	be	AUX
ejpam-6129	89	70	the	the	DET
ejpam-6129	89	71	right	right	ADJ
ejpam-6129	89	72	hand	hand	NOUN
ejpam-6129	89	73	side	side	NOUN
ejpam-6129	89	74	of	of	ADP
ejpam-6129	89	75	the	the	DET
ejpam-6129	89	76	differential	differential	ADJ
ejpam-6129	89	77	equation	equation	NOUN
ejpam-6129	89	78	and	and	CCONJ
ejpam-6129	89	79	the	the	DET
ejpam-6129	89	80	associated	associated	ADJ
ejpam-6129	89	81	adjoint	adjoint	NOUN
ejpam-6129	89	82	for	for	ADP
ejpam-6129	89	83	the	the	DET
ejpam-6129	89	84	ith	ith	PROPN
ejpam-6129	89	85	state	state	NOUN
ejpam-6129	89	86	variable	variable	NOUN
ejpam-6129	89	87	of	of	ADP
ejpam-6129	89	88	system	system	NOUN
ejpam-6129	89	89	(	(	PUNCT
ejpam-6129	89	90	1	1	NUM
ejpam-6129	89	91	)	)	PUNCT
ejpam-6129	89	92	.	.	PUNCT
ejpam-6129	90	1	by	by	ADP
ejpam-6129	90	2	applying	apply	VERB
ejpam-6129	90	3	pontryagin	pontryagin	NOUN
ejpam-6129	90	4	’s	’s	PART
ejpam-6129	90	5	maximum	maximum	ADJ
ejpam-6129	90	6	principle	principle	NOUN
ejpam-6129	90	7	[	[	X
ejpam-6129	90	8	23	23	NUM
ejpam-6129	90	9	]	]	PUNCT
ejpam-6129	90	10	and	and	CCONJ
ejpam-6129	90	11	existence	existence	NOUN
ejpam-6129	90	12	result	result	VERB
ejpam-6129	90	13	for	for	ADP
ejpam-6129	90	14	the	the	DET
ejpam-6129	90	15	optimal	optimal	ADJ
ejpam-6129	90	16	control	control	NOUN
ejpam-6129	90	17	pair	pair	NOUN
ejpam-6129	90	18	from	from	ADP
ejpam-6129	90	19	[	[	X
ejpam-6129	90	20	24	24	NUM
ejpam-6129	90	21	]	]	PUNCT
ejpam-6129	90	22	,	,	PUNCT
ejpam-6129	90	23	we	we	PRON
ejpam-6129	90	24	obtain	obtain	VERB
ejpam-6129	90	25	the	the	DET
ejpam-6129	90	26	following	follow	VERB
ejpam-6129	90	27	theorem	theorem	VERB
ejpam-6129	90	28	.	.	PUNCT
ejpam-6129	90	29	theorem	theorem	NOUN
ejpam-6129	90	30	1	1	NUM
ejpam-6129	90	31	.	.	PUNCT
ejpam-6129	91	1	there	there	PRON
ejpam-6129	91	2	exists	exist	VERB
ejpam-6129	91	3	optimal	optimal	ADJ
ejpam-6129	91	4	control	control	NOUN
ejpam-6129	91	5	pair	pair	NOUN
ejpam-6129	91	6	(	(	PUNCT
ejpam-6129	91	7	u∗1	u∗1	NOUN
ejpam-6129	91	8	,	,	PUNCT
ejpam-6129	91	9	u	u	NOUN
ejpam-6129	91	10	∗	∗	NOUN
ejpam-6129	91	11	2	2	NUM
ejpam-6129	91	12	)	)	PUNCT
ejpam-6129	91	13	and	and	CCONJ
ejpam-6129	91	14	solution	solution	NOUN
ejpam-6129	91	15	(	(	PUNCT
ejpam-6129	91	16	s∗	s∗	PROPN
ejpam-6129	91	17	,	,	PUNCT
ejpam-6129	91	18	c∗	c∗	NOUN
ejpam-6129	91	19	,	,	PUNCT
ejpam-6129	91	20	i∗	i∗	NOUN
ejpam-6129	91	21	,	,	PUNCT
ejpam-6129	91	22	r∗	r∗	PROPN
ejpam-6129	91	23	)	)	PUNCT
ejpam-6129	91	24	for	for	ADP
ejpam-6129	91	25	the	the	DET
ejpam-6129	91	26	state	state	NOUN
ejpam-6129	91	27	system	system	NOUN
ejpam-6129	91	28	(	(	PUNCT
ejpam-6129	91	29	1	1	X
ejpam-6129	91	30	)	)	PUNCT
ejpam-6129	91	31	that	that	PRON
ejpam-6129	91	32	minimizes	minimize	VERB
ejpam-6129	91	33	j(u1	j(u1	NOUN
ejpam-6129	91	34	,	,	PUNCT
ejpam-6129	91	35	u2	u2	PROPN
ejpam-6129	91	36	)	)	PUNCT
ejpam-6129	91	37	,	,	PUNCT
ejpam-6129	91	38	given	give	VERB
ejpam-6129	91	39	by	by	ADP
ejpam-6129	91	40	(	(	PUNCT
ejpam-6129	91	41	2	2	NUM
ejpam-6129	91	42	)	)	PUNCT
ejpam-6129	91	43	,	,	PUNCT
ejpam-6129	91	44	over	over	ADP
ejpam-6129	91	45	ψ	ψ	X
ejpam-6129	91	46	.	.	PUNCT
ejpam-6129	92	1	furthermore	furthermore	ADV
ejpam-6129	92	2	,	,	PUNCT
ejpam-6129	92	3	there	there	PRON
ejpam-6129	92	4	exists	exist	VERB
ejpam-6129	92	5	a	a	DET
ejpam-6129	92	6	vector	vector	NOUN
ejpam-6129	92	7	of	of	ADP
ejpam-6129	92	8	adjoint	adjoint	NOUN
ejpam-6129	92	9	functions	function	NOUN
ejpam-6129	92	10	,	,	PUNCT
ejpam-6129	92	11	(	(	PUNCT
ejpam-6129	92	12	λ1(t	λ1(t	PROPN
ejpam-6129	92	13	)	)	PUNCT
ejpam-6129	92	14	,	,	PUNCT
ejpam-6129	92	15	...	...	PUNCT
ejpam-6129	92	16	,	,	PUNCT
ejpam-6129	92	17	λ4(t	λ4(t	PROPN
ejpam-6129	92	18	)	)	PUNCT
ejpam-6129	92	19	)	)	PUNCT
ejpam-6129	92	20	,	,	PUNCT
ejpam-6129	92	21	such	such	ADJ
ejpam-6129	92	22	that	that	SCONJ
ejpam-6129	92	23	dλ1	dλ1	NOUN
ejpam-6129	92	24	dt	dt	PUNCT
ejpam-6129	92	25	=	=	PUNCT
ejpam-6129	92	26	(	(	PUNCT
ejpam-6129	92	27	β(1−	β(1−	NOUN
ejpam-6129	92	28	u2)(c	u2)(c	NOUN
ejpam-6129	92	29	∗	∗	NOUN
ejpam-6129	92	30	+	+	X
ejpam-6129	92	31	i∗	i∗	NOUN
ejpam-6129	92	32	)	)	PUNCT
ejpam-6129	93	1	+	+	CCONJ
ejpam-6129	93	2	u1)λ1	u1)λ1	VERB
ejpam-6129	93	3	−	−	NOUN
ejpam-6129	93	4	β(1−	β(1−	NOUN
ejpam-6129	94	1	u2)(c	u2)(c	NOUN
ejpam-6129	94	2	∗	∗	NOUN
ejpam-6129	94	3	+	+	X
ejpam-6129	94	4	i∗)λ2	i∗)λ2	PROPN
ejpam-6129	94	5	−	−	PROPN
ejpam-6129	94	6	u1λ4	u1λ4	PROPN
ejpam-6129	94	7	,	,	PUNCT
ejpam-6129	94	8	dλ2	dλ2	NOUN
ejpam-6129	94	9	dt	dt	NOUN
ejpam-6129	94	10	=	=	SYM
ejpam-6129	94	11	−1−	−1−	PROPN
ejpam-6129	94	12	(	(	PUNCT
ejpam-6129	94	13	µ−	µ−	PROPN
ejpam-6129	94	14	β(1−	β(1−	NOUN
ejpam-6129	95	1	u2)s	u2)s	PROPN
ejpam-6129	95	2	∗)λ1	∗)λ1	PROPN
ejpam-6129	95	3	−	−	PROPN
ejpam-6129	95	4	(	(	PUNCT
ejpam-6129	95	5	β(1−	β(1−	NOUN
ejpam-6129	95	6	u2)s	u2)s	NOUN
ejpam-6129	95	7	∗	∗	NOUN
ejpam-6129	95	8	−	−	PROPN
ejpam-6129	95	9	(	(	PUNCT
ejpam-6129	95	10	a+	a+	X
ejpam-6129	95	11	α+	α+	NOUN
ejpam-6129	95	12	µ))λ2	µ))λ2	NUM
ejpam-6129	95	13	−	−	PROPN
ejpam-6129	95	14	aλ3	aλ3	NOUN
ejpam-6129	95	15	−	−	PROPN
ejpam-6129	95	16	αλ4	αλ4	NOUN
ejpam-6129	95	17	,	,	PUNCT
ejpam-6129	96	1	dλ3	dλ3	NOUN
ejpam-6129	96	2	dt	dt	NOUN
ejpam-6129	96	3	=	=	SYM
ejpam-6129	97	1	−(µ+	−(µ+	NUM
ejpam-6129	97	2	γ	γ	NOUN
ejpam-6129	97	3	−	−	NOUN
ejpam-6129	97	4	β(1−	β(1−	NOUN
ejpam-6129	97	5	u2)s	u2)s	NOUN
ejpam-6129	97	6	∗)λ1	∗)λ1	PROPN
ejpam-6129	97	7	−	−	PROPN
ejpam-6129	97	8	β(1−	β(1−	NOUN
ejpam-6129	98	1	u2)s	u2)s	ADJ
ejpam-6129	98	2	∗λ2	∗λ2	NOUN
ejpam-6129	98	3	+	+	CCONJ
ejpam-6129	98	4	(	(	PUNCT
ejpam-6129	98	5	ρ+	ρ+	X
ejpam-6129	98	6	γ	γ	X
ejpam-6129	98	7	+	+	CCONJ
ejpam-6129	98	8	µ)λ3	µ)λ3	PROPN
ejpam-6129	98	9	−	−	NOUN
ejpam-6129	98	10	ρλ4	ρλ4	NOUN
ejpam-6129	98	11	,	,	PUNCT
ejpam-6129	98	12	dλ4	dλ4	VERB
ejpam-6129	98	13	dt	dt	NOUN
ejpam-6129	99	1	=	=	PUNCT
ejpam-6129	100	1	(	(	PUNCT
ejpam-6129	100	2	ϕ+	ϕ+	ADP
ejpam-6129	100	3	µ)(λ4	µ)(λ4	ADJ
ejpam-6129	100	4	−	−	PROPN
ejpam-6129	100	5	λ1	λ1	NUM
ejpam-6129	100	6	)	)	PUNCT
ejpam-6129	100	7	,	,	PUNCT
ejpam-6129	100	8	(	(	PUNCT
ejpam-6129	100	9	6	6	NUM
ejpam-6129	100	10	)	)	PUNCT
ejpam-6129	100	11	with	with	ADP
ejpam-6129	100	12	transversality	transversality	NOUN
ejpam-6129	100	13	conditions	condition	NOUN
ejpam-6129	100	14	λi(tf	λi(tf	NOUN
ejpam-6129	100	15	)	)	PUNCT
ejpam-6129	101	1	=	=	SYM
ejpam-6129	101	2	0	0	NUM
ejpam-6129	101	3	,	,	PUNCT
ejpam-6129	101	4	i	i	PRON
ejpam-6129	101	5	=	=	NOUN
ejpam-6129	101	6	1	1	NUM
ejpam-6129	101	7	,	,	PUNCT
ejpam-6129	101	8	...	...	PUNCT
ejpam-6129	101	9	,	,	PUNCT
ejpam-6129	101	10	4	4	NUM
ejpam-6129	101	11	,	,	PUNCT
ejpam-6129	101	12	(	(	PUNCT
ejpam-6129	101	13	7	7	NUM
ejpam-6129	101	14	)	)	PUNCT
ejpam-6129	101	15	and	and	CCONJ
ejpam-6129	101	16	the	the	DET
ejpam-6129	101	17	following	follow	VERB
ejpam-6129	101	18	characterization	characterization	NOUN
ejpam-6129	101	19	u∗1	u∗1	NOUN
ejpam-6129	101	20	=	=	SYM
ejpam-6129	101	21	min	min	PROPN
ejpam-6129	101	22	(	(	PUNCT
ejpam-6129	101	23	max	max	PROPN
ejpam-6129	101	24	(	(	PUNCT
ejpam-6129	101	25	a1	a1	PROPN
ejpam-6129	101	26	,	,	PUNCT
ejpam-6129	101	27	s∗	s∗	PROPN
ejpam-6129	101	28	(	(	PUNCT
ejpam-6129	101	29	λ1	λ1	PROPN
ejpam-6129	101	30	−	−	PROPN
ejpam-6129	101	31	λ4	λ4	PROPN
ejpam-6129	101	32	)	)	PUNCT
ejpam-6129	101	33	a	a	PRON
ejpam-6129	101	34	)	)	PUNCT
ejpam-6129	101	35	,	,	PUNCT
ejpam-6129	101	36	b1	b1	NOUN
ejpam-6129	101	37	)	)	PUNCT
ejpam-6129	101	38	,	,	PUNCT
ejpam-6129	101	39	u∗2	u∗2	NOUN
ejpam-6129	101	40	=	=	SYM
ejpam-6129	101	41	min	min	PROPN
ejpam-6129	101	42	(	(	PUNCT
ejpam-6129	101	43	max	max	PROPN
ejpam-6129	101	44	(	(	PUNCT
ejpam-6129	101	45	a2	a2	PROPN
ejpam-6129	101	46	,	,	PUNCT
ejpam-6129	101	47	βs∗	βs∗	X
ejpam-6129	101	48	(	(	PUNCT
ejpam-6129	101	49	c∗	c∗	NOUN
ejpam-6129	101	50	+	+	CCONJ
ejpam-6129	101	51	i∗	i∗	NOUN
ejpam-6129	101	52	)	)	PUNCT
ejpam-6129	101	53	(	(	PUNCT
ejpam-6129	101	54	λ2	λ2	NOUN
ejpam-6129	101	55	−	−	PROPN
ejpam-6129	101	56	λ1	λ1	PROPN
ejpam-6129	101	57	)	)	PUNCT
ejpam-6129	101	58	b	b	NOUN
ejpam-6129	101	59	)	)	PUNCT
ejpam-6129	101	60	,	,	PUNCT
ejpam-6129	101	61	b2	b2	NOUN
ejpam-6129	101	62	)	)	PUNCT
ejpam-6129	101	63	.	.	PUNCT
ejpam-6129	102	1	(	(	PUNCT
ejpam-6129	102	2	8)	8)	NUM
ejpam-6129	102	3	proof	proof	NOUN
ejpam-6129	102	4	.	.	PUNCT
ejpam-6129	103	1	by	by	ADP
ejpam-6129	103	2	using	use	VERB
ejpam-6129	103	3	a	a	DET
ejpam-6129	103	4	results	result	NOUN
ejpam-6129	103	5	from	from	ADP
ejpam-6129	103	6	[	[	X
ejpam-6129	103	7	24	24	NUM
ejpam-6129	103	8	]	]	PUNCT
ejpam-6129	103	9	,	,	PUNCT
ejpam-6129	103	10	we	we	PRON
ejpam-6129	103	11	can	can	AUX
ejpam-6129	103	12	obtain	obtain	VERB
ejpam-6129	103	13	the	the	DET
ejpam-6129	103	14	existence	existence	NOUN
ejpam-6129	103	15	of	of	ADP
ejpam-6129	103	16	an	an	DET
ejpam-6129	103	17	optimal	optimal	ADJ
ejpam-6129	103	18	control	control	NOUN
ejpam-6129	103	19	pair	pair	NOUN
ejpam-6129	103	20	due	due	ADP
ejpam-6129	103	21	to	to	ADP
ejpam-6129	103	22	the	the	DET
ejpam-6129	103	23	convexity	convexity	NOUN
ejpam-6129	103	24	of	of	ADP
ejpam-6129	103	25	integrand	integrand	NOUN
ejpam-6129	103	26	of	of	ADP
ejpam-6129	103	27	j	j	PROPN
ejpam-6129	103	28	with	with	ADP
ejpam-6129	103	29	respect	respect	NOUN
ejpam-6129	103	30	to	to	ADP
ejpam-6129	103	31	(	(	PUNCT
ejpam-6129	103	32	u1	u1	NOUN
ejpam-6129	103	33	,	,	PUNCT
ejpam-6129	103	34	u2	u2	PROPN
ejpam-6129	103	35	)	)	PUNCT
ejpam-6129	103	36	,	,	PUNCT
ejpam-6129	103	37	a	a	DET
ejpam-6129	103	38	priori	priori	ADJ
ejpam-6129	103	39	boundedness	boundedness	NOUN
ejpam-6129	103	40	of	of	ADP
ejpam-6129	103	41	the	the	DET
ejpam-6129	103	42	state	state	NOUN
ejpam-6129	103	43	solutions	solution	NOUN
ejpam-6129	103	44	,	,	PUNCT
ejpam-6129	103	45	and	and	CCONJ
ejpam-6129	103	46	the	the	DET
ejpam-6129	103	47	lipschitz	lipschitz	ADJ
ejpam-6129	103	48	property	property	NOUN
ejpam-6129	103	49	of	of	ADP
ejpam-6129	103	50	the	the	DET
ejpam-6129	103	51	state	state	NOUN
ejpam-6129	103	52	system	system	NOUN
ejpam-6129	103	53	with	with	ADP
ejpam-6129	103	54	respect	respect	NOUN
ejpam-6129	103	55	to	to	ADP
ejpam-6129	103	56	the	the	DET
ejpam-6129	103	57	s.	s.	PROPN
ejpam-6129	103	58	a.	a.	PROPN
ejpam-6129	103	59	mohamed	mohamed	PROPN
ejpam-6129	103	60	et	et	PROPN
ejpam-6129	104	1	al	al	PROPN
ejpam-6129	104	2	.	.	PUNCT
ejpam-6129	104	3	/	/	SYM
ejpam-6129	104	4	eur	eur	PROPN
ejpam-6129	104	5	.	.	PUNCT
ejpam-6129	105	1	j.	j.	PROPN
ejpam-6129	105	2	pure	pure	PROPN
ejpam-6129	105	3	appl	appl	PROPN
ejpam-6129	105	4	.	.	PROPN
ejpam-6129	105	5	math	math	PROPN
ejpam-6129	105	6	,	,	PUNCT
ejpam-6129	105	7	18	18	NUM
ejpam-6129	105	8	(	(	PUNCT
ejpam-6129	105	9	3	3	NUM
ejpam-6129	105	10	)	)	PUNCT
ejpam-6129	105	11	(	(	PUNCT
ejpam-6129	105	12	2025	2025	NUM
ejpam-6129	105	13	)	)	PUNCT
ejpam-6129	105	14	,	,	PUNCT
ejpam-6129	105	15	6129	6129	NUM
ejpam-6129	105	16	6	6	NUM
ejpam-6129	105	17	of	of	ADP
ejpam-6129	105	18	17	17	NUM
ejpam-6129	105	19	state	state	NOUN
ejpam-6129	105	20	variables	variable	NOUN
ejpam-6129	105	21	.	.	PUNCT
ejpam-6129	106	1	by	by	ADP
ejpam-6129	106	2	applying	apply	VERB
ejpam-6129	106	3	the	the	DET
ejpam-6129	106	4	pontryagin	pontryagin	NOUN
ejpam-6129	106	5	’s	’s	PART
ejpam-6129	106	6	maximum	maximum	ADJ
ejpam-6129	106	7	principle	principle	NOUN
ejpam-6129	106	8	[	[	X
ejpam-6129	106	9	23	23	NUM
ejpam-6129	106	10	]	]	PUNCT
ejpam-6129	106	11	,	,	PUNCT
ejpam-6129	106	12	we	we	PRON
ejpam-6129	106	13	obtain	obtain	VERB
ejpam-6129	106	14	dλ1	dλ1	PROPN
ejpam-6129	106	15	dt	dt	PUNCT
ejpam-6129	106	16	=	=	SYM
ejpam-6129	107	1	−∂h	−∂h	PROPN
ejpam-6129	107	2	∂s	∂s	PROPN
ejpam-6129	107	3	,	,	PUNCT
ejpam-6129	107	4	λ1(tf	λ1(tf	X
ejpam-6129	107	5	)	)	PUNCT
ejpam-6129	107	6	=	=	SYM
ejpam-6129	107	7	0	0	NUM
ejpam-6129	107	8	,	,	PUNCT
ejpam-6129	107	9	dλ2	dλ2	NOUN
ejpam-6129	107	10	dt	dt	NOUN
ejpam-6129	107	11	=	=	SYM
ejpam-6129	107	12	−∂h	−∂h	PROPN
ejpam-6129	107	13	∂c	∂c	PROPN
ejpam-6129	107	14	,	,	PUNCT
ejpam-6129	107	15	λ2(tf	λ2(tf	X
ejpam-6129	107	16	)	)	PUNCT
ejpam-6129	107	17	=	=	SYM
ejpam-6129	107	18	0	0	NUM
ejpam-6129	107	19	,	,	PUNCT
ejpam-6129	107	20	dλ3	dλ3	NOUN
ejpam-6129	107	21	dt	dt	NOUN
ejpam-6129	107	22	=	=	SYM
ejpam-6129	107	23	−∂h	−∂h	PROPN
ejpam-6129	107	24	∂i	∂i	PROPN
ejpam-6129	107	25	,	,	PUNCT
ejpam-6129	107	26	λ3(tf	λ3(tf	PROPN
ejpam-6129	107	27	)	)	PUNCT
ejpam-6129	107	28	=	=	SYM
ejpam-6129	108	1	0	0	NUM
ejpam-6129	108	2	,	,	PUNCT
ejpam-6129	108	3	dλ4	dλ4	VERB
ejpam-6129	108	4	dt	dt	NOUN
ejpam-6129	108	5	=	=	SYM
ejpam-6129	108	6	−∂h	−∂h	PROPN
ejpam-6129	108	7	∂r	∂r	NUM
ejpam-6129	108	8	,	,	PUNCT
ejpam-6129	108	9	λ4(tf	λ4(tf	PROPN
ejpam-6129	108	10	)	)	PUNCT
ejpam-6129	108	11	=	=	SYM
ejpam-6129	108	12	0	0	NUM
ejpam-6129	108	13	,	,	PUNCT
ejpam-6129	108	14	(	(	PUNCT
ejpam-6129	108	15	9	9	X
ejpam-6129	108	16	)	)	PUNCT
ejpam-6129	108	17	evaluated	evaluate	VERB
ejpam-6129	108	18	at	at	ADP
ejpam-6129	108	19	the	the	DET
ejpam-6129	108	20	optimal	optimal	ADJ
ejpam-6129	108	21	control	control	NOUN
ejpam-6129	108	22	pair	pair	NOUN
ejpam-6129	108	23	(	(	PUNCT
ejpam-6129	108	24	u∗1	u∗1	NOUN
ejpam-6129	108	25	,	,	PUNCT
ejpam-6129	108	26	u	u	NOUN
ejpam-6129	108	27	∗	∗	NOUN
ejpam-6129	108	28	2	2	NUM
ejpam-6129	108	29	)	)	PUNCT
ejpam-6129	108	30	and	and	CCONJ
ejpam-6129	108	31	the	the	DET
ejpam-6129	108	32	corresponding	correspond	VERB
ejpam-6129	108	33	states	state	NOUN
ejpam-6129	108	34	s	s	PART
ejpam-6129	108	35	,	,	PUNCT
ejpam-6129	108	36	c	c	X
ejpam-6129	108	37	,	,	PUNCT
ejpam-6129	108	38	i	i	PRON
ejpam-6129	108	39	,	,	PUNCT
ejpam-6129	108	40	r	r	NOUN
ejpam-6129	108	41	,	,	PUNCT
ejpam-6129	108	42	which	which	PRON
ejpam-6129	108	43	results	result	VERB
ejpam-6129	108	44	in	in	ADP
ejpam-6129	108	45	the	the	DET
ejpam-6129	108	46	stated	state	VERB
ejpam-6129	108	47	adjoint	adjoint	NOUN
ejpam-6129	108	48	system	system	NOUN
ejpam-6129	108	49	(	(	PUNCT
ejpam-6129	108	50	6	6	NUM
ejpam-6129	108	51	)	)	PUNCT
ejpam-6129	108	52	.	.	PUNCT
ejpam-6129	109	1	the	the	DET
ejpam-6129	109	2	characterization	characterization	NOUN
ejpam-6129	109	3	(	(	PUNCT
ejpam-6129	109	4	8)	8)	NUM
ejpam-6129	109	5	can	can	AUX
ejpam-6129	109	6	be	be	AUX
ejpam-6129	109	7	derived	derive	VERB
ejpam-6129	109	8	by	by	ADP
ejpam-6129	109	9	considering	consider	VERB
ejpam-6129	109	10	the	the	DET
ejpam-6129	109	11	optimality	optimality	NOUN
ejpam-6129	109	12	conditions	condition	NOUN
ejpam-6129	109	13	∂h	∂h	X
ejpam-6129	109	14	∂u1	∂u1	ADJ
ejpam-6129	109	15	=	=	SYM
ejpam-6129	109	16	0	0	NUM
ejpam-6129	109	17	and	and	CCONJ
ejpam-6129	109	18	∂h	∂h	PROPN
ejpam-6129	109	19	∂u2	∂u2	NOUN
ejpam-6129	109	20	=	=	SYM
ejpam-6129	109	21	0	0	NUM
ejpam-6129	109	22	,	,	PUNCT
ejpam-6129	109	23	(	(	PUNCT
ejpam-6129	109	24	10	10	NUM
ejpam-6129	109	25	)	)	PUNCT
ejpam-6129	109	26	and	and	CCONJ
ejpam-6129	109	27	solving	solve	VERB
ejpam-6129	109	28	for	for	ADP
ejpam-6129	109	29	u∗1	u∗1	NOUN
ejpam-6129	109	30	and	and	CCONJ
ejpam-6129	109	31	u∗2	u∗2	NOUN
ejpam-6129	109	32	,	,	PUNCT
ejpam-6129	109	33	subject	subject	ADJ
ejpam-6129	109	34	to	to	ADP
ejpam-6129	109	35	the	the	DET
ejpam-6129	109	36	constraints	constraint	NOUN
ejpam-6129	109	37	(	(	PUNCT
ejpam-6129	109	38	4	4	NUM
ejpam-6129	109	39	)	)	PUNCT
ejpam-6129	109	40	.	.	PUNCT
ejpam-6129	110	1	the	the	DET
ejpam-6129	110	2	characterization	characterization	NOUN
ejpam-6129	110	3	for	for	ADP
ejpam-6129	110	4	u∗1	u∗1	NOUN
ejpam-6129	110	5	can	can	AUX
ejpam-6129	110	6	be	be	AUX
ejpam-6129	110	7	obtained	obtain	VERB
ejpam-6129	110	8	from	from	ADP
ejpam-6129	110	9	the	the	DET
ejpam-6129	110	10	first	first	ADJ
ejpam-6129	110	11	equation	equation	NOUN
ejpam-6129	110	12	of	of	ADP
ejpam-6129	110	13	(	(	PUNCT
ejpam-6129	110	14	10	10	NUM
ejpam-6129	110	15	)	)	PUNCT
ejpam-6129	110	16	∂h	∂h	PROPN
ejpam-6129	110	17	∂u1	∂u1	PROPN
ejpam-6129	111	1	=	=	PUNCT
ejpam-6129	112	1	au1	au1	PRON
ejpam-6129	112	2	−	−	NOUN
ejpam-6129	112	3	s∗λ1	s∗λ1	NOUN
ejpam-6129	112	4	+	+	CCONJ
ejpam-6129	112	5	s∗λ4	s∗λ4	NOUN
ejpam-6129	112	6	,	,	PUNCT
ejpam-6129	112	7	(	(	PUNCT
ejpam-6129	112	8	11	11	NUM
ejpam-6129	112	9	)	)	PUNCT
ejpam-6129	112	10	by	by	ADP
ejpam-6129	112	11	considering	consider	VERB
ejpam-6129	112	12	three	three	NUM
ejpam-6129	112	13	cases	case	NOUN
ejpam-6129	112	14	:	:	PUNCT
ejpam-6129	113	1	∂h	∂h	ADP
ejpam-6129	113	2	∂u1	∂u1	PRON
ejpam-6129	113	3	<	<	X
ejpam-6129	113	4	0	0	PUNCT
ejpam-6129	113	5	=	=	AUX
ejpam-6129	113	6	⇒	⇒	NOUN
ejpam-6129	113	7	u1(t	u1(t	PRON
ejpam-6129	113	8	)	)	PUNCT
ejpam-6129	113	9	=	=	SYM
ejpam-6129	114	1	a1	a1	NOUN
ejpam-6129	114	2	=	=	NOUN
ejpam-6129	114	3	⇒	⇒	NOUN
ejpam-6129	114	4	a1	a1	NOUN
ejpam-6129	114	5	<	<	X
ejpam-6129	114	6	s∗(λ1	s∗(λ1	PROPN
ejpam-6129	114	7	−	−	PROPN
ejpam-6129	114	8	λ4	λ4	PROPN
ejpam-6129	114	9	)	)	PUNCT
ejpam-6129	114	10	a	a	PRON
ejpam-6129	114	11	,	,	PUNCT
ejpam-6129	114	12	∂h	∂h	PROPN
ejpam-6129	114	13	∂u1	∂u1	PROPN
ejpam-6129	114	14	=	=	SYM
ejpam-6129	114	15	0	0	PUNCT
ejpam-6129	115	1	=	=	NOUN
ejpam-6129	115	2	⇒	⇒	NOUN
ejpam-6129	115	3	u1(t	u1(t	PRON
ejpam-6129	115	4	)	)	PUNCT
ejpam-6129	115	5	=	=	SYM
ejpam-6129	116	1	s∗(λ1	s∗(λ1	PROPN
ejpam-6129	116	2	−	−	NOUN
ejpam-6129	116	3	λ4	λ4	PROPN
ejpam-6129	116	4	)	)	PUNCT
ejpam-6129	116	5	a	a	DET
ejpam-6129	116	6	=	=	NOUN
ejpam-6129	116	7	⇒	⇒	NOUN
ejpam-6129	116	8	a1	a1	NOUN
ejpam-6129	116	9	≤	≤	ADJ
ejpam-6129	116	10	s∗(λ1	s∗(λ1	PROPN
ejpam-6129	116	11	−	−	NOUN
ejpam-6129	116	12	λ4	λ4	PROPN
ejpam-6129	116	13	)	)	PUNCT
ejpam-6129	116	14	a	a	DET
ejpam-6129	116	15	≤	≤	NUM
ejpam-6129	116	16	b1	b1	NOUN
ejpam-6129	116	17	,	,	PUNCT
ejpam-6129	116	18	∂h	∂h	PROPN
ejpam-6129	116	19	∂u1	∂u1	PROPN
ejpam-6129	116	20	>	>	X
ejpam-6129	116	21	0	0	PUNCT
ejpam-6129	117	1	=	=	NOUN
ejpam-6129	117	2	⇒	⇒	NOUN
ejpam-6129	117	3	u1(t	u1(t	PRON
ejpam-6129	117	4	)	)	PUNCT
ejpam-6129	117	5	=	=	SYM
ejpam-6129	117	6	b1	b1	NOUN
ejpam-6129	117	7	=	=	NOUN
ejpam-6129	117	8	⇒	⇒	PROPN
ejpam-6129	117	9	b1	b1	NOUN
ejpam-6129	117	10	>	>	X
ejpam-6129	117	11	s∗(λ1	s∗(λ1	PROPN
ejpam-6129	117	12	−	−	PROPN
ejpam-6129	117	13	λ4	λ4	PROPN
ejpam-6129	117	14	)	)	PUNCT
ejpam-6129	117	15	a	a	PRON
ejpam-6129	117	16	,	,	PUNCT
ejpam-6129	117	17	and	and	CCONJ
ejpam-6129	117	18	hence	hence	ADV
ejpam-6129	117	19	,	,	PUNCT
ejpam-6129	117	20	u∗1	u∗1	NOUN
ejpam-6129	117	21	=	=	SYM
ejpam-6129	117	22			NUM
ejpam-6129	117	23	a1	a1	NOUN
ejpam-6129	117	24	;	;	PUNCT
ejpam-6129	117	25	s∗(λ1−λ4	s∗(λ1−λ4	PROPN
ejpam-6129	117	26	)	)	PUNCT
ejpam-6129	117	27	a	a	DET
ejpam-6129	117	28	<	<	X
ejpam-6129	117	29	a1	a1	NOUN
ejpam-6129	117	30	,	,	PUNCT
ejpam-6129	117	31	s∗(λ1−λ4	s∗(λ1−λ4	PROPN
ejpam-6129	117	32	)	)	PUNCT
ejpam-6129	117	33	a	a	NOUN
ejpam-6129	117	34	;	;	PUNCT
ejpam-6129	117	35	a1	a1	NOUN
ejpam-6129	117	36	≤	≤	NUM
ejpam-6129	117	37	s∗(λ1−λ4	s∗(λ1−λ4	PROPN
ejpam-6129	117	38	)	)	PUNCT
ejpam-6129	117	39	a	a	DET
ejpam-6129	117	40	≤	≤	NUM
ejpam-6129	117	41	b1	b1	NOUN
ejpam-6129	117	42	,	,	PUNCT
ejpam-6129	117	43	b1	b1	NOUN
ejpam-6129	117	44	;	;	PUNCT
ejpam-6129	117	45	s∗(λ1−λ4	s∗(λ1−λ4	PROPN
ejpam-6129	117	46	)	)	PUNCT
ejpam-6129	117	47	a	a	DET
ejpam-6129	117	48	>	>	X
ejpam-6129	117	49	b1	b1	PROPN
ejpam-6129	117	50	.	.	PUNCT
ejpam-6129	118	1	(	(	PUNCT
ejpam-6129	118	2	12	12	NUM
ejpam-6129	118	3	)	)	PUNCT
ejpam-6129	118	4	therefore	therefore	ADV
ejpam-6129	118	5	,	,	PUNCT
ejpam-6129	118	6	the	the	DET
ejpam-6129	118	7	characterization	characterization	NOUN
ejpam-6129	118	8	of	of	ADP
ejpam-6129	118	9	u∗1	u∗1	NOUN
ejpam-6129	118	10	in	in	ADP
ejpam-6129	118	11	compact	compact	ADJ
ejpam-6129	118	12	form	form	NOUN
ejpam-6129	118	13	can	can	AUX
ejpam-6129	118	14	be	be	AUX
ejpam-6129	118	15	written	write	VERB
ejpam-6129	118	16	as	as	ADP
ejpam-6129	118	17	u∗1	u∗1	NOUN
ejpam-6129	118	18	=	=	SYM
ejpam-6129	118	19	min	min	PROPN
ejpam-6129	118	20	(	(	PUNCT
ejpam-6129	118	21	b1,max	b1,max	X
ejpam-6129	118	22	(	(	PUNCT
ejpam-6129	118	23	a1	a1	NOUN
ejpam-6129	118	24	,	,	PUNCT
ejpam-6129	118	25	s∗(λ1	s∗(λ1	PROPN
ejpam-6129	118	26	−	−	PROPN
ejpam-6129	118	27	λ4	λ4	PROPN
ejpam-6129	118	28	)	)	PUNCT
ejpam-6129	118	29	a	a	PRON
ejpam-6129	118	30	)	)	PUNCT
ejpam-6129	118	31	)	)	PUNCT
ejpam-6129	118	32	.	.	PUNCT
ejpam-6129	119	1	(	(	PUNCT
ejpam-6129	119	2	13	13	NUM
ejpam-6129	119	3	)	)	PUNCT
ejpam-6129	119	4	in	in	ADP
ejpam-6129	119	5	a	a	DET
ejpam-6129	119	6	similar	similar	ADJ
ejpam-6129	119	7	manner	manner	NOUN
ejpam-6129	119	8	,	,	PUNCT
ejpam-6129	119	9	we	we	PRON
ejpam-6129	119	10	can	can	AUX
ejpam-6129	119	11	derive	derive	VERB
ejpam-6129	119	12	the	the	DET
ejpam-6129	119	13	characterization	characterization	NOUN
ejpam-6129	119	14	of	of	ADP
ejpam-6129	119	15	u∗2	u∗2	ADJ
ejpam-6129	119	16	which	which	PRON
ejpam-6129	119	17	in	in	ADP
ejpam-6129	119	18	compact	compact	ADJ
ejpam-6129	119	19	form	form	NOUN
ejpam-6129	119	20	as	as	ADP
ejpam-6129	119	21	u∗2	u∗2	ADJ
ejpam-6129	119	22	=	=	SYM
ejpam-6129	119	23	min	min	NOUN
ejpam-6129	119	24	(	(	PUNCT
ejpam-6129	119	25	b2,max	b2,max	X
ejpam-6129	119	26	(	(	PUNCT
ejpam-6129	119	27	a2	a2	PROPN
ejpam-6129	119	28	,	,	PUNCT
ejpam-6129	119	29	βs∗(c∗	βs∗(c∗	PROPN
ejpam-6129	119	30	+	+	CCONJ
ejpam-6129	119	31	i∗)(λ2	i∗)(λ2	ADP
ejpam-6129	119	32	−	−	PROPN
ejpam-6129	119	33	λ1	λ1	PROPN
ejpam-6129	119	34	)	)	PUNCT
ejpam-6129	119	35	b	b	NOUN
ejpam-6129	119	36	)	)	PUNCT
ejpam-6129	119	37	)	)	PUNCT
ejpam-6129	119	38	.	.	PUNCT
ejpam-6129	120	1	(	(	PUNCT
ejpam-6129	120	2	14	14	NUM
ejpam-6129	120	3	)	)	PUNCT
ejpam-6129	120	4	s.	s.	PROPN
ejpam-6129	120	5	a.	a.	PROPN
ejpam-6129	120	6	mohamed	mohamed	PROPN
ejpam-6129	120	7	et	et	PROPN
ejpam-6129	120	8	al	al	PROPN
ejpam-6129	120	9	.	.	PUNCT
ejpam-6129	120	10	/	/	SYM
ejpam-6129	120	11	eur	eur	PROPN
ejpam-6129	120	12	.	.	PUNCT
ejpam-6129	121	1	j.	j.	PROPN
ejpam-6129	121	2	pure	pure	PROPN
ejpam-6129	121	3	appl	appl	PROPN
ejpam-6129	121	4	.	.	PROPN
ejpam-6129	121	5	math	math	PROPN
ejpam-6129	121	6	,	,	PUNCT
ejpam-6129	121	7	18	18	NUM
ejpam-6129	121	8	(	(	PUNCT
ejpam-6129	121	9	3	3	NUM
ejpam-6129	121	10	)	)	PUNCT
ejpam-6129	121	11	(	(	PUNCT
ejpam-6129	121	12	2025	2025	NUM
ejpam-6129	121	13	)	)	PUNCT
ejpam-6129	121	14	,	,	PUNCT
ejpam-6129	121	15	6129	6129	NUM
ejpam-6129	121	16	7	7	NUM
ejpam-6129	121	17	of	of	ADP
ejpam-6129	121	18	17	17	NUM
ejpam-6129	121	19	with	with	ADP
ejpam-6129	121	20	the	the	DET
ejpam-6129	121	21	existence	existence	NOUN
ejpam-6129	121	22	of	of	ADP
ejpam-6129	121	23	the	the	DET
ejpam-6129	121	24	optimal	optimal	ADJ
ejpam-6129	121	25	control	control	NOUN
ejpam-6129	121	26	pair	pair	NOUN
ejpam-6129	121	27	established	establish	VERB
ejpam-6129	121	28	,	,	PUNCT
ejpam-6129	121	29	we	we	PRON
ejpam-6129	121	30	point	point	VERB
ejpam-6129	121	31	out	out	ADP
ejpam-6129	121	32	that	that	SCONJ
ejpam-6129	121	33	the	the	DET
ejpam-6129	121	34	uniqueness	uniqueness	NOUN
ejpam-6129	121	35	of	of	ADP
ejpam-6129	121	36	the	the	DET
ejpam-6129	121	37	optimal	optimal	ADJ
ejpam-6129	121	38	control	control	NOUN
ejpam-6129	121	39	pair	pair	NOUN
ejpam-6129	121	40	follows	follow	VERB
ejpam-6129	121	41	from	from	ADP
ejpam-6129	121	42	the	the	DET
ejpam-6129	121	43	uniqueness	uniqueness	NOUN
ejpam-6129	121	44	of	of	ADP
ejpam-6129	121	45	the	the	DET
ejpam-6129	121	46	optimality	optimality	NOUN
ejpam-6129	121	47	system	system	NOUN
ejpam-6129	121	48	the	the	DET
ejpam-6129	121	49	pair	pair	NOUN
ejpam-6129	121	50	must	must	AUX
ejpam-6129	121	51	satisfy	satisfy	VERB
ejpam-6129	121	52	,	,	PUNCT
ejpam-6129	121	53	which	which	PRON
ejpam-6129	121	54	consists	consist	VERB
ejpam-6129	121	55	of	of	ADP
ejpam-6129	121	56	the	the	DET
ejpam-6129	121	57	state	state	NOUN
ejpam-6129	121	58	system	system	NOUN
ejpam-6129	121	59	(	(	PUNCT
ejpam-6129	121	60	1	1	NUM
ejpam-6129	121	61	)	)	PUNCT
ejpam-6129	121	62	with	with	ADP
ejpam-6129	121	63	the	the	DET
ejpam-6129	121	64	its	its	PRON
ejpam-6129	121	65	initial	initial	ADJ
ejpam-6129	121	66	conditions	condition	NOUN
ejpam-6129	121	67	,	,	PUNCT
ejpam-6129	121	68	the	the	DET
ejpam-6129	121	69	adjoint	adjoint	NOUN
ejpam-6129	121	70	system	system	NOUN
ejpam-6129	121	71	(	(	PUNCT
ejpam-6129	121	72	6	6	NUM
ejpam-6129	121	73	)	)	PUNCT
ejpam-6129	121	74	with	with	ADP
ejpam-6129	121	75	the	the	DET
ejpam-6129	121	76	transversality	transversality	NOUN
ejpam-6129	121	77	conditions	condition	NOUN
ejpam-6129	121	78	(	(	PUNCT
ejpam-6129	121	79	7	7	NUM
ejpam-6129	121	80	)	)	PUNCT
ejpam-6129	121	81	,	,	PUNCT
ejpam-6129	121	82	and	and	CCONJ
ejpam-6129	121	83	the	the	DET
ejpam-6129	121	84	optimality	optimality	NOUN
ejpam-6129	121	85	condition	condition	NOUN
ejpam-6129	121	86	(	(	PUNCT
ejpam-6129	121	87	8)	8)	NUM
ejpam-6129	121	88	.	.	PUNCT
ejpam-6129	122	1	as	as	SCONJ
ejpam-6129	122	2	mentioned	mention	VERB
ejpam-6129	122	3	in	in	ADP
ejpam-6129	122	4	[	[	X
ejpam-6129	122	5	17	17	NUM
ejpam-6129	122	6	]	]	PUNCT
ejpam-6129	122	7	,	,	PUNCT
ejpam-6129	122	8	one	one	PRON
ejpam-6129	122	9	can	can	AUX
ejpam-6129	122	10	obtain	obtain	VERB
ejpam-6129	122	11	the	the	DET
ejpam-6129	122	12	uniqueness	uniqueness	NOUN
ejpam-6129	122	13	of	of	ADP
ejpam-6129	122	14	the	the	DET
ejpam-6129	122	15	optimal	optimal	ADJ
ejpam-6129	122	16	control	control	NOUN
ejpam-6129	122	17	for	for	ADP
ejpam-6129	122	18	small	small	ADJ
ejpam-6129	122	19	tf	tf	X
ejpam-6129	122	20	due	due	ADP
ejpam-6129	122	21	to	to	ADP
ejpam-6129	122	22	a	a	DET
ejpam-6129	122	23	-	-	PUNCT
ejpam-6129	122	24	priori	priori	ADJ
ejpam-6129	122	25	boundedness	boundedness	NOUN
ejpam-6129	122	26	of	of	ADP
ejpam-6129	122	27	the	the	DET
ejpam-6129	122	28	state	state	NOUN
ejpam-6129	122	29	and	and	CCONJ
ejpam-6129	122	30	adjoint	adjoint	NOUN
ejpam-6129	122	31	functions	function	NOUN
ejpam-6129	122	32	and	and	CCONJ
ejpam-6129	122	33	the	the	DET
ejpam-6129	122	34	resulting	result	VERB
ejpam-6129	122	35	lipschitz	lipschitz	NOUN
ejpam-6129	122	36	structure	structure	NOUN
ejpam-6129	122	37	of	of	ADP
ejpam-6129	122	38	the	the	DET
ejpam-6129	122	39	odes	ode	NOUN
ejpam-6129	122	40	.	.	PUNCT
ejpam-6129	123	1	the	the	DET
ejpam-6129	123	2	finiteness	finiteness	NOUN
ejpam-6129	123	3	of	of	ADP
ejpam-6129	123	4	tf	tf	PROPN
ejpam-6129	123	5	guarantees	guarantee	VERB
ejpam-6129	123	6	the	the	DET
ejpam-6129	123	7	uniqueness	uniqueness	NOUN
ejpam-6129	123	8	of	of	ADP
ejpam-6129	123	9	the	the	DET
ejpam-6129	123	10	optimality	optimality	NOUN
ejpam-6129	123	11	system	system	NOUN
ejpam-6129	123	12	.	.	PUNCT
ejpam-6129	124	1	this	this	DET
ejpam-6129	124	2	finiteness	finiteness	ADJ
ejpam-6129	124	3	restriction	restriction	NOUN
ejpam-6129	124	4	on	on	ADP
ejpam-6129	124	5	the	the	DET
ejpam-6129	124	6	length	length	NOUN
ejpam-6129	124	7	on	on	ADP
ejpam-6129	124	8	the	the	DET
ejpam-6129	124	9	time	time	NOUN
ejpam-6129	124	10	interval	interval	NOUN
ejpam-6129	124	11	is	be	AUX
ejpam-6129	124	12	due	due	ADJ
ejpam-6129	124	13	to	to	ADP
ejpam-6129	124	14	the	the	DET
ejpam-6129	124	15	opposite	opposite	ADJ
ejpam-6129	124	16	time	time	NOUN
ejpam-6129	124	17	orientations	orientation	NOUN
ejpam-6129	124	18	of	of	ADP
ejpam-6129	124	19	(	(	PUNCT
ejpam-6129	124	20	1	1	NUM
ejpam-6129	124	21	)	)	PUNCT
ejpam-6129	124	22	,	,	PUNCT
ejpam-6129	124	23	(	(	PUNCT
ejpam-6129	124	24	6	6	NUM
ejpam-6129	124	25	)	)	PUNCT
ejpam-6129	124	26	,	,	PUNCT
ejpam-6129	124	27	and	and	CCONJ
ejpam-6129	124	28	(	(	PUNCT
ejpam-6129	124	29	7	7	X
ejpam-6129	124	30	)	)	PUNCT
ejpam-6129	124	31	where	where	SCONJ
ejpam-6129	124	32	the	the	DET
ejpam-6129	124	33	state	state	NOUN
ejpam-6129	124	34	problem	problem	NOUN
ejpam-6129	124	35	has	have	VERB
ejpam-6129	124	36	initial	initial	ADJ
ejpam-6129	124	37	values	value	NOUN
ejpam-6129	124	38	and	and	CCONJ
ejpam-6129	124	39	the	the	DET
ejpam-6129	124	40	adjoint	adjoint	NOUN
ejpam-6129	124	41	problem	problem	NOUN
ejpam-6129	124	42	has	have	VERB
ejpam-6129	124	43	final	final	ADJ
ejpam-6129	124	44	values	value	NOUN
ejpam-6129	124	45	.	.	PUNCT
ejpam-6129	125	1	next	next	ADV
ejpam-6129	125	2	,	,	PUNCT
ejpam-6129	125	3	we	we	PRON
ejpam-6129	125	4	discuss	discuss	VERB
ejpam-6129	125	5	the	the	DET
ejpam-6129	125	6	numerical	numerical	ADJ
ejpam-6129	125	7	solutions	solution	NOUN
ejpam-6129	125	8	of	of	ADP
ejpam-6129	125	9	the	the	DET
ejpam-6129	125	10	optimality	optimality	NOUN
ejpam-6129	125	11	system	system	NOUN
ejpam-6129	125	12	and	and	CCONJ
ejpam-6129	125	13	the	the	DET
ejpam-6129	125	14	corresponding	corresponding	ADJ
ejpam-6129	125	15	results	result	NOUN
ejpam-6129	125	16	of	of	ADP
ejpam-6129	125	17	varying	vary	VERB
ejpam-6129	125	18	the	the	DET
ejpam-6129	125	19	optimal	optimal	ADJ
ejpam-6129	125	20	controls	control	NOUN
ejpam-6129	125	21	u1	u1	NOUN
ejpam-6129	125	22	and	and	CCONJ
ejpam-6129	125	23	u2	u2	NOUN
ejpam-6129	125	24	along	along	ADP
ejpam-6129	125	25	with	with	ADP
ejpam-6129	125	26	the	the	DET
ejpam-6129	125	27	interpretations	interpretation	NOUN
ejpam-6129	125	28	for	for	ADP
ejpam-6129	125	29	different	different	ADJ
ejpam-6129	125	30	scenarios	scenario	NOUN
ejpam-6129	125	31	.	.	PUNCT
ejpam-6129	126	1	4	4	X
ejpam-6129	126	2	.	.	X
ejpam-6129	126	3	numerical	numerical	ADJ
ejpam-6129	126	4	results	result	NOUN
ejpam-6129	126	5	in	in	ADP
ejpam-6129	126	6	this	this	DET
ejpam-6129	126	7	section	section	NOUN
ejpam-6129	126	8	,	,	PUNCT
ejpam-6129	126	9	the	the	DET
ejpam-6129	126	10	optimality	optimality	NOUN
ejpam-6129	126	11	system	system	NOUN
ejpam-6129	126	12	consisting	consist	VERB
ejpam-6129	126	13	of	of	ADP
ejpam-6129	126	14	the	the	DET
ejpam-6129	126	15	equations	equation	NOUN
ejpam-6129	126	16	of	of	ADP
ejpam-6129	126	17	(	(	PUNCT
ejpam-6129	126	18	1	1	NUM
ejpam-6129	126	19	)	)	PUNCT
ejpam-6129	126	20	and	and	CCONJ
ejpam-6129	126	21	(	(	PUNCT
ejpam-6129	126	22	6	6	NUM
ejpam-6129	126	23	)	)	PUNCT
ejpam-6129	126	24	,	,	PUNCT
ejpam-6129	126	25	is	be	AUX
ejpam-6129	126	26	solved	solve	VERB
ejpam-6129	126	27	iteratively	iteratively	ADV
ejpam-6129	126	28	using	use	VERB
ejpam-6129	126	29	a	a	DET
ejpam-6129	126	30	fourth	fourth	ADJ
ejpam-6129	126	31	order	order	NOUN
ejpam-6129	126	32	runge	runge	NOUN
ejpam-6129	126	33	-	-	PUNCT
ejpam-6129	126	34	kutta	kutta	NOUN
ejpam-6129	126	35	method	method	NOUN
ejpam-6129	126	36	to	to	PART
ejpam-6129	126	37	obtain	obtain	VERB
ejpam-6129	126	38	the	the	DET
ejpam-6129	126	39	optimal	optimal	ADJ
ejpam-6129	126	40	strategies	strategy	NOUN
ejpam-6129	126	41	regarding	regard	VERB
ejpam-6129	126	42	the	the	DET
ejpam-6129	126	43	vaccination	vaccination	NOUN
ejpam-6129	126	44	and	and	CCONJ
ejpam-6129	126	45	treatment	treatment	NOUN
ejpam-6129	126	46	.	.	PUNCT
ejpam-6129	127	1	the	the	DET
ejpam-6129	127	2	state	state	NOUN
ejpam-6129	127	3	system	system	NOUN
ejpam-6129	127	4	is	be	AUX
ejpam-6129	127	5	solved	solve	VERB
ejpam-6129	127	6	forward	forward	ADV
ejpam-6129	127	7	in	in	ADP
ejpam-6129	127	8	time	time	NOUN
ejpam-6129	127	9	while	while	SCONJ
ejpam-6129	127	10	the	the	DET
ejpam-6129	127	11	adjoint	adjoint	NOUN
ejpam-6129	127	12	system	system	NOUN
ejpam-6129	127	13	is	be	AUX
ejpam-6129	127	14	solved	solve	VERB
ejpam-6129	127	15	backward	backward	ADV
ejpam-6129	127	16	in	in	ADP
ejpam-6129	127	17	time	time	NOUN
ejpam-6129	127	18	.	.	PUNCT
ejpam-6129	128	1	the	the	DET
ejpam-6129	128	2	two	two	NUM
ejpam-6129	128	3	controls	control	NOUN
ejpam-6129	128	4	are	be	AUX
ejpam-6129	128	5	updated	update	VERB
ejpam-6129	128	6	at	at	ADP
ejpam-6129	128	7	the	the	DET
ejpam-6129	128	8	end	end	NOUN
ejpam-6129	128	9	of	of	ADP
ejpam-6129	128	10	each	each	DET
ejpam-6129	128	11	iteration	iteration	NOUN
ejpam-6129	128	12	using	use	VERB
ejpam-6129	128	13	(	(	PUNCT
ejpam-6129	128	14	8)	8)	NUM
ejpam-6129	128	15	.	.	PUNCT
ejpam-6129	129	1	the	the	DET
ejpam-6129	129	2	iterations	iteration	NOUN
ejpam-6129	129	3	continue	continue	VERB
ejpam-6129	129	4	until	until	SCONJ
ejpam-6129	129	5	a	a	DET
ejpam-6129	129	6	required	require	VERB
ejpam-6129	129	7	convergence	convergence	NOUN
ejpam-6129	129	8	is	be	AUX
ejpam-6129	129	9	achieved	achieve	VERB
ejpam-6129	129	10	.	.	PUNCT
ejpam-6129	130	1	the	the	DET
ejpam-6129	130	2	readers	reader	NOUN
ejpam-6129	130	3	may	may	AUX
ejpam-6129	130	4	note	note	VERB
ejpam-6129	130	5	that	that	SCONJ
ejpam-6129	130	6	the	the	DET
ejpam-6129	130	7	main	main	ADJ
ejpam-6129	130	8	goal	goal	NOUN
ejpam-6129	130	9	of	of	ADP
ejpam-6129	130	10	this	this	DET
ejpam-6129	130	11	paper	paper	NOUN
ejpam-6129	130	12	is	be	AUX
ejpam-6129	130	13	to	to	PART
ejpam-6129	130	14	design	design	VERB
ejpam-6129	130	15	the	the	DET
ejpam-6129	130	16	optimal	optimal	ADJ
ejpam-6129	130	17	control	control	NOUN
ejpam-6129	130	18	strategy	strategy	NOUN
ejpam-6129	130	19	and	and	CCONJ
ejpam-6129	130	20	not	not	PART
ejpam-6129	130	21	to	to	PART
ejpam-6129	130	22	find	find	VERB
ejpam-6129	130	23	a	a	DET
ejpam-6129	130	24	robust	robust	ADJ
ejpam-6129	130	25	numerical	numerical	ADJ
ejpam-6129	130	26	solver	solver	NOUN
ejpam-6129	130	27	.	.	PUNCT
ejpam-6129	131	1	the	the	DET
ejpam-6129	131	2	results	result	NOUN
ejpam-6129	131	3	obtained	obtain	VERB
ejpam-6129	131	4	by	by	ADP
ejpam-6129	131	5	using	use	VERB
ejpam-6129	131	6	rk-4	rk-4	PUNCT
ejpam-6129	131	7	are	be	AUX
ejpam-6129	131	8	already	already	ADV
ejpam-6129	131	9	convincing	convincing	ADJ
ejpam-6129	131	10	and	and	CCONJ
ejpam-6129	131	11	therefore	therefore	ADV
ejpam-6129	131	12	we	we	PRON
ejpam-6129	131	13	did	do	AUX
ejpam-6129	131	14	not	not	PART
ejpam-6129	131	15	attempt	attempt	VERB
ejpam-6129	131	16	to	to	PART
ejpam-6129	131	17	use	use	VERB
ejpam-6129	131	18	variants	variant	NOUN
ejpam-6129	131	19	of	of	ADP
ejpam-6129	131	20	rk	rk	PRON
ejpam-6129	131	21	,	,	PUNCT
ejpam-6129	131	22	e.g	e.g	PROPN
ejpam-6129	131	23	,	,	PUNCT
ejpam-6129	131	24	etdrk	etdrk	PROPN
ejpam-6129	131	25	or	or	CCONJ
ejpam-6129	131	26	any	any	DET
ejpam-6129	131	27	other	other	ADJ
ejpam-6129	131	28	methods	method	NOUN
ejpam-6129	131	29	that	that	PRON
ejpam-6129	131	30	we	we	PRON
ejpam-6129	131	31	are	be	AUX
ejpam-6129	131	32	already	already	ADV
ejpam-6129	131	33	familiar	familiar	ADJ
ejpam-6129	131	34	with	with	ADP
ejpam-6129	131	35	.	.	PUNCT
ejpam-6129	132	1	by	by	ADP
ejpam-6129	132	2	using	use	VERB
ejpam-6129	132	3	different	different	ADJ
ejpam-6129	132	4	combinations	combination	NOUN
ejpam-6129	132	5	of	of	ADP
ejpam-6129	132	6	the	the	DET
ejpam-6129	132	7	balancing	balancing	NOUN
ejpam-6129	132	8	factors	factor	NOUN
ejpam-6129	132	9	a	a	PRON
ejpam-6129	132	10	and	and	CCONJ
ejpam-6129	132	11	b	b	NOUN
ejpam-6129	132	12	,	,	PUNCT
ejpam-6129	132	13	several	several	ADJ
ejpam-6129	132	14	vaccination	vaccination	NOUN
ejpam-6129	132	15	and	and	CCONJ
ejpam-6129	132	16	treatment	treatment	NOUN
ejpam-6129	132	17	schedules	schedule	NOUN
ejpam-6129	132	18	can	can	AUX
ejpam-6129	132	19	be	be	AUX
ejpam-6129	132	20	derived	derive	VERB
ejpam-6129	132	21	.	.	PUNCT
ejpam-6129	133	1	keeping	keep	VERB
ejpam-6129	133	2	the	the	DET
ejpam-6129	133	3	bounds	bound	NOUN
ejpam-6129	133	4	for	for	ADP
ejpam-6129	133	5	the	the	DET
ejpam-6129	133	6	controls	control	NOUN
ejpam-6129	133	7	fixed	fix	VERB
ejpam-6129	133	8	,	,	PUNCT
ejpam-6129	133	9	time	time	NOUN
ejpam-6129	133	10	period	period	NOUN
ejpam-6129	133	11	is	be	AUX
ejpam-6129	133	12	90	90	NUM
ejpam-6129	133	13	days	day	NOUN
ejpam-6129	133	14	,	,	PUNCT
ejpam-6129	133	15	β	β	X
ejpam-6129	133	16	=	=	SYM
ejpam-6129	133	17	0.24658	0.24658	NUM
ejpam-6129	133	18	,	,	PUNCT
ejpam-6129	133	19	α	α	NOUN
ejpam-6129	133	20	=	=	NOUN
ejpam-6129	133	21	0.071233	0.071233	NUM
ejpam-6129	133	22	,	,	PUNCT
ejpam-6129	133	23	a	a	DET
ejpam-6129	133	24	=	=	SYM
ejpam-6129	133	25	0.00054795	0.00054795	NUM
ejpam-6129	133	26	,	,	PUNCT
ejpam-6129	133	27	ϕ	ϕ	X
ejpam-6129	133	28	=	=	SYM
ejpam-6129	133	29	0.00068493	0.00068493	PROPN
ejpam-6129	133	30	and	and	CCONJ
ejpam-6129	133	31	rest	rest	NOUN
ejpam-6129	133	32	of	of	ADP
ejpam-6129	133	33	the	the	DET
ejpam-6129	133	34	parameters	parameter	NOUN
ejpam-6129	133	35	unchanged	unchanged	ADJ
ejpam-6129	133	36	,	,	PUNCT
ejpam-6129	133	37	we	we	PRON
ejpam-6129	133	38	illustrate	illustrate	VERB
ejpam-6129	133	39	different	different	ADJ
ejpam-6129	133	40	scenarios	scenario	NOUN
ejpam-6129	133	41	by	by	ADP
ejpam-6129	133	42	varying	vary	VERB
ejpam-6129	133	43	the	the	DET
ejpam-6129	133	44	values	value	NOUN
ejpam-6129	133	45	of	of	ADP
ejpam-6129	133	46	the	the	DET
ejpam-6129	133	47	balancing	balancing	NOUN
ejpam-6129	133	48	factors	factor	NOUN
ejpam-6129	133	49	.	.	PUNCT
ejpam-6129	134	1	in	in	ADP
ejpam-6129	134	2	the	the	DET
ejpam-6129	134	3	simulations	simulation	NOUN
ejpam-6129	134	4	below	below	ADV
ejpam-6129	134	5	,	,	PUNCT
ejpam-6129	134	6	we	we	PRON
ejpam-6129	134	7	use	use	VERB
ejpam-6129	134	8	the	the	DET
ejpam-6129	134	9	following	following	ADJ
ejpam-6129	134	10	initial	initial	ADJ
ejpam-6129	134	11	conditions	condition	NOUN
ejpam-6129	134	12	,	,	PUNCT
ejpam-6129	134	13	as	as	SCONJ
ejpam-6129	134	14	given	give	VERB
ejpam-6129	134	15	in	in	ADP
ejpam-6129	134	16	[	[	X
ejpam-6129	134	17	3	3	NUM
ejpam-6129	134	18	]	]	PUNCT
ejpam-6129	134	19	,	,	PUNCT
ejpam-6129	134	20	s(t0	s(t0	NOUN
ejpam-6129	134	21	)	)	PUNCT
ejpam-6129	134	22	=	=	SYM
ejpam-6129	134	23	9000	9000	NUM
ejpam-6129	134	24	,	,	PUNCT
ejpam-6129	134	25	c(t0	c(t0	NOUN
ejpam-6129	134	26	)	)	PUNCT
ejpam-6129	134	27	=	=	SYM
ejpam-6129	134	28	996	996	NUM
ejpam-6129	134	29	,	,	PUNCT
ejpam-6129	134	30	i(t0	i(t0	NOUN
ejpam-6129	134	31	)	)	PUNCT
ejpam-6129	134	32	=	=	SYM
ejpam-6129	134	33	2	2	NUM
ejpam-6129	134	34	,	,	PUNCT
ejpam-6129	134	35	and	and	CCONJ
ejpam-6129	134	36	r(t0	r(t0	NOUN
ejpam-6129	134	37	)	)	PUNCT
ejpam-6129	134	38	=	=	SYM
ejpam-6129	135	1	2	2	X
ejpam-6129	135	2	.	.	PUNCT
ejpam-6129	135	3	when	when	SCONJ
ejpam-6129	135	4	a	a	DET
ejpam-6129	135	5	=	=	SYM
ejpam-6129	135	6	10	10	NUM
ejpam-6129	135	7	and	and	CCONJ
ejpam-6129	135	8	b	b	NOUN
ejpam-6129	135	9	=	=	SYM
ejpam-6129	135	10	10	10	NUM
ejpam-6129	135	11	,	,	PUNCT
ejpam-6129	135	12	the	the	DET
ejpam-6129	135	13	two	two	NUM
ejpam-6129	135	14	controls	control	NOUN
ejpam-6129	135	15	are	be	AUX
ejpam-6129	135	16	plotted	plot	VERB
ejpam-6129	135	17	as	as	ADP
ejpam-6129	135	18	functions	function	NOUN
ejpam-6129	135	19	of	of	ADP
ejpam-6129	135	20	time	time	NOUN
ejpam-6129	135	21	in	in	ADP
ejpam-6129	135	22	figure	figure	NOUN
ejpam-6129	135	23	1	1	NUM
ejpam-6129	135	24	.	.	PUNCT
ejpam-6129	136	1	in	in	ADP
ejpam-6129	136	2	figure	figure	NOUN
ejpam-6129	136	3	2	2	NUM
ejpam-6129	136	4	,	,	PUNCT
ejpam-6129	136	5	we	we	PRON
ejpam-6129	136	6	can	can	AUX
ejpam-6129	136	7	see	see	VERB
ejpam-6129	136	8	the	the	DET
ejpam-6129	136	9	effect	effect	NOUN
ejpam-6129	136	10	of	of	ADP
ejpam-6129	136	11	this	this	DET
ejpam-6129	136	12	scenario	scenario	NOUN
ejpam-6129	136	13	,	,	PUNCT
ejpam-6129	136	14	the	the	DET
ejpam-6129	136	15	number	number	NOUN
ejpam-6129	136	16	of	of	ADP
ejpam-6129	136	17	the	the	DET
ejpam-6129	136	18	susceptible	susceptible	ADJ
ejpam-6129	136	19	individuals	individual	NOUN
ejpam-6129	136	20	s(t	s(t	PROPN
ejpam-6129	136	21	)	)	PUNCT
ejpam-6129	136	22	is	be	AUX
ejpam-6129	136	23	dropped	drop	VERB
ejpam-6129	136	24	very	very	ADV
ejpam-6129	136	25	quickly	quickly	ADV
ejpam-6129	136	26	in	in	ADP
ejpam-6129	136	27	the	the	DET
ejpam-6129	136	28	first	first	ADJ
ejpam-6129	136	29	10	10	NUM
ejpam-6129	136	30	days	day	NOUN
ejpam-6129	136	31	when	when	SCONJ
ejpam-6129	136	32	using	use	VERB
ejpam-6129	136	33	the	the	DET
ejpam-6129	136	34	two	two	NUM
ejpam-6129	136	35	controls	control	NOUN
ejpam-6129	136	36	as	as	SCONJ
ejpam-6129	136	37	the	the	DET
ejpam-6129	136	38	treated	treat	VERB
ejpam-6129	136	39	individuals	individual	NOUN
ejpam-6129	136	40	return	return	VERB
ejpam-6129	136	41	back	back	ADV
ejpam-6129	136	42	to	to	ADP
ejpam-6129	136	43	the	the	DET
ejpam-6129	136	44	susceptible	susceptible	ADJ
ejpam-6129	136	45	class	class	NOUN
ejpam-6129	136	46	and	and	CCONJ
ejpam-6129	136	47	these	these	DET
ejpam-6129	136	48	individuals	individual	NOUN
ejpam-6129	136	49	will	will	AUX
ejpam-6129	136	50	be	be	AUX
ejpam-6129	136	51	vaccinated	vaccinate	VERB
ejpam-6129	136	52	and	and	CCONJ
ejpam-6129	136	53	then	then	ADV
ejpam-6129	136	54	removed	remove	VERB
ejpam-6129	136	55	to	to	ADP
ejpam-6129	136	56	the	the	DET
ejpam-6129	136	57	recovered	recovered	ADJ
ejpam-6129	136	58	class	class	NOUN
ejpam-6129	136	59	r(t	r(t	NOUN
ejpam-6129	136	60	)	)	PUNCT
ejpam-6129	136	61	.	.	PUNCT
ejpam-6129	137	1	this	this	PRON
ejpam-6129	137	2	explains	explain	VERB
ejpam-6129	137	3	the	the	DET
ejpam-6129	137	4	increment	increment	NOUN
ejpam-6129	137	5	in	in	ADP
ejpam-6129	137	6	the	the	DET
ejpam-6129	137	7	number	number	NOUN
ejpam-6129	137	8	of	of	ADP
ejpam-6129	137	9	the	the	DET
ejpam-6129	137	10	recovered	recover	VERB
ejpam-6129	137	11	individuals	individual	NOUN
ejpam-6129	137	12	as	as	SCONJ
ejpam-6129	137	13	indicated	indicate	VERB
ejpam-6129	137	14	in	in	ADP
ejpam-6129	137	15	the	the	DET
ejpam-6129	137	16	last	last	ADJ
ejpam-6129	137	17	simulation	simulation	NOUN
ejpam-6129	137	18	in	in	ADP
ejpam-6129	137	19	the	the	DET
ejpam-6129	137	20	same	same	ADJ
ejpam-6129	137	21	figure	figure	NOUN
ejpam-6129	137	22	.	.	PUNCT
ejpam-6129	138	1	similarly	similarly	ADV
ejpam-6129	138	2	,	,	PUNCT
ejpam-6129	138	3	one	one	PRON
ejpam-6129	138	4	can	can	AUX
ejpam-6129	138	5	see	see	VERB
ejpam-6129	138	6	the	the	DET
ejpam-6129	138	7	sharp	sharp	ADJ
ejpam-6129	138	8	decrease	decrease	NOUN
ejpam-6129	138	9	in	in	ADP
ejpam-6129	138	10	the	the	DET
ejpam-6129	138	11	carrier	carrier	NOUN
ejpam-6129	138	12	population	population	NOUN
ejpam-6129	138	13	c(t	c(t	PROPN
ejpam-6129	138	14	)	)	PUNCT
ejpam-6129	138	15	.	.	PUNCT
ejpam-6129	139	1	without	without	ADP
ejpam-6129	139	2	using	use	VERB
ejpam-6129	139	3	any	any	DET
ejpam-6129	139	4	control	control	NOUN
ejpam-6129	139	5	strategies	strategy	NOUN
ejpam-6129	139	6	,	,	PUNCT
ejpam-6129	139	7	we	we	PRON
ejpam-6129	139	8	find	find	VERB
ejpam-6129	139	9	that	that	SCONJ
ejpam-6129	139	10	the	the	DET
ejpam-6129	139	11	number	number	NOUN
ejpam-6129	139	12	of	of	ADP
ejpam-6129	139	13	carriers	carrier	NOUN
ejpam-6129	139	14	c(t	c(t	NOUN
ejpam-6129	139	15	)	)	PUNCT
ejpam-6129	139	16	increases	increase	VERB
ejpam-6129	139	17	for	for	ADP
ejpam-6129	139	18	the	the	DET
ejpam-6129	139	19	first	first	ADJ
ejpam-6129	139	20	17	17	NUM
ejpam-6129	139	21	days	day	NOUN
ejpam-6129	139	22	until	until	SCONJ
ejpam-6129	139	23	it	it	PRON
ejpam-6129	139	24	reaches	reach	VERB
ejpam-6129	139	25	its	its	PRON
ejpam-6129	139	26	maximum	maximum	NOUN
ejpam-6129	139	27	at	at	ADP
ejpam-6129	139	28	3811	3811	NUM
ejpam-6129	139	29	individuals	individual	NOUN
ejpam-6129	139	30	and	and	CCONJ
ejpam-6129	139	31	then	then	ADV
ejpam-6129	139	32	it	it	PRON
ejpam-6129	139	33	declines	decline	VERB
ejpam-6129	139	34	until	until	ADP
ejpam-6129	139	35	≈	≈	PROPN
ejpam-6129	139	36	84	84	NUM
ejpam-6129	139	37	at	at	ADP
ejpam-6129	139	38	the	the	DET
ejpam-6129	139	39	end	end	NOUN
ejpam-6129	139	40	of	of	ADP
ejpam-6129	139	41	the	the	DET
ejpam-6129	139	42	interval	interval	NOUN
ejpam-6129	139	43	.	.	PUNCT
ejpam-6129	140	1	however	however	ADV
ejpam-6129	140	2	,	,	PUNCT
ejpam-6129	140	3	when	when	SCONJ
ejpam-6129	140	4	we	we	PRON
ejpam-6129	140	5	use	use	VERB
ejpam-6129	140	6	the	the	DET
ejpam-6129	140	7	control	control	NOUN
ejpam-6129	140	8	strategies	strategy	NOUN
ejpam-6129	140	9	described	describe	VERB
ejpam-6129	140	10	above	above	ADV
ejpam-6129	140	11	,	,	PUNCT
ejpam-6129	140	12	we	we	PRON
ejpam-6129	140	13	can	can	AUX
ejpam-6129	140	14	see	see	VERB
ejpam-6129	140	15	that	that	PRON
ejpam-6129	140	16	starting	start	VERB
ejpam-6129	140	17	c(t	c(t	PROPN
ejpam-6129	140	18	)	)	PUNCT
ejpam-6129	140	19	with	with	ADP
ejpam-6129	140	20	996	996	NUM
ejpam-6129	140	21	individuals	individual	NOUN
ejpam-6129	140	22	,	,	PUNCT
ejpam-6129	140	23	it	it	PRON
ejpam-6129	140	24	drops	drop	VERB
ejpam-6129	140	25	immediately	immediately	ADV
ejpam-6129	140	26	and	and	CCONJ
ejpam-6129	140	27	continue	continue	VERB
ejpam-6129	140	28	decreasing	decrease	VERB
ejpam-6129	140	29	without	without	ADP
ejpam-6129	140	30	fluctuations	fluctuation	NOUN
ejpam-6129	140	31	until	until	SCONJ
ejpam-6129	140	32	it	it	PRON
ejpam-6129	140	33	reaches	reach	VERB
ejpam-6129	140	34	≈	≈	PROPN
ejpam-6129	140	35	2	2	NUM
ejpam-6129	140	36	individuals	individual	NOUN
ejpam-6129	140	37	indicating	indicate	VERB
ejpam-6129	140	38	the	the	DET
ejpam-6129	140	39	effectiveness	effectiveness	NOUN
ejpam-6129	140	40	of	of	ADP
ejpam-6129	140	41	the	the	DET
ejpam-6129	140	42	strategy	strategy	NOUN
ejpam-6129	140	43	s.	s.	PROPN
ejpam-6129	140	44	a.	a.	PROPN
ejpam-6129	140	45	mohamed	mohamed	PROPN
ejpam-6129	140	46	et	et	PROPN
ejpam-6129	140	47	al	al	PROPN
ejpam-6129	140	48	.	.	PUNCT
ejpam-6129	140	49	/	/	SYM
ejpam-6129	140	50	eur	eur	PROPN
ejpam-6129	140	51	.	.	PUNCT
ejpam-6129	141	1	j.	j.	PROPN
ejpam-6129	141	2	pure	pure	PROPN
ejpam-6129	141	3	appl	appl	PROPN
ejpam-6129	141	4	.	.	PROPN
ejpam-6129	141	5	math	math	PROPN
ejpam-6129	141	6	,	,	PUNCT
ejpam-6129	141	7	18	18	NUM
ejpam-6129	141	8	(	(	PUNCT
ejpam-6129	141	9	3	3	NUM
ejpam-6129	141	10	)	)	PUNCT
ejpam-6129	141	11	(	(	PUNCT
ejpam-6129	141	12	2025	2025	NUM
ejpam-6129	141	13	)	)	PUNCT
ejpam-6129	141	14	,	,	PUNCT
ejpam-6129	141	15	6129	6129	NUM
ejpam-6129	141	16	8	8	NUM
ejpam-6129	141	17	of	of	ADP
ejpam-6129	141	18	17	17	NUM
ejpam-6129	141	19	used	use	VERB
ejpam-6129	141	20	.	.	PUNCT
ejpam-6129	142	1	in	in	ADP
ejpam-6129	142	2	the	the	DET
ejpam-6129	142	3	third	third	ADJ
ejpam-6129	142	4	plot	plot	NOUN
ejpam-6129	142	5	of	of	ADP
ejpam-6129	142	6	figure	figure	NOUN
ejpam-6129	142	7	2	2	NUM
ejpam-6129	142	8	we	we	PRON
ejpam-6129	142	9	notice	notice	VERB
ejpam-6129	142	10	that	that	SCONJ
ejpam-6129	142	11	starting	start	VERB
ejpam-6129	142	12	with	with	ADP
ejpam-6129	142	13	i(t	i(t	NOUN
ejpam-6129	142	14	)	)	PUNCT
ejpam-6129	142	15	=	=	SYM
ejpam-6129	142	16	2	2	NUM
ejpam-6129	142	17	individuals	individual	NOUN
ejpam-6129	142	18	,	,	PUNCT
ejpam-6129	142	19	the	the	DET
ejpam-6129	142	20	number	number	NOUN
ejpam-6129	142	21	of	of	ADP
ejpam-6129	142	22	population	population	NOUN
ejpam-6129	142	23	in	in	ADP
ejpam-6129	142	24	this	this	DET
ejpam-6129	142	25	class	class	NOUN
ejpam-6129	142	26	increases	increase	NOUN
ejpam-6129	142	27	until	until	SCONJ
ejpam-6129	142	28	it	it	PRON
ejpam-6129	142	29	reaches	reach	VERB
ejpam-6129	142	30	its	its	PRON
ejpam-6129	142	31	maximum	maximum	ADJ
ejpam-6129	142	32	≈	≈	PROPN
ejpam-6129	142	33	12	12	NUM
ejpam-6129	142	34	by	by	ADP
ejpam-6129	142	35	the	the	DET
ejpam-6129	142	36	23rd	23rd	ADJ
ejpam-6129	142	37	day	day	NOUN
ejpam-6129	142	38	without	without	ADP
ejpam-6129	142	39	incorporating	incorporate	VERB
ejpam-6129	142	40	the	the	DET
ejpam-6129	142	41	controls	control	NOUN
ejpam-6129	142	42	.	.	PUNCT
ejpam-6129	143	1	when	when	SCONJ
ejpam-6129	143	2	end	end	NOUN
ejpam-6129	143	3	of	of	ADP
ejpam-6129	143	4	interval	interval	NOUN
ejpam-6129	143	5	reached	reach	VERB
ejpam-6129	143	6	,	,	PUNCT
ejpam-6129	143	7	the	the	DET
ejpam-6129	143	8	value	value	NOUN
ejpam-6129	143	9	of	of	ADP
ejpam-6129	143	10	i(t	i(t	NOUN
ejpam-6129	143	11	)	)	PUNCT
ejpam-6129	143	12	is	be	AUX
ejpam-6129	143	13	≈	≈	PROPN
ejpam-6129	143	14	zero	zero	NUM
ejpam-6129	143	15	.	.	PUNCT
ejpam-6129	144	1	however	however	ADV
ejpam-6129	144	2	,	,	PUNCT
ejpam-6129	144	3	when	when	SCONJ
ejpam-6129	144	4	controls	control	NOUN
ejpam-6129	144	5	are	be	AUX
ejpam-6129	144	6	used	use	VERB
ejpam-6129	144	7	,	,	PUNCT
ejpam-6129	144	8	it	it	PRON
ejpam-6129	144	9	is	be	AUX
ejpam-6129	144	10	shown	show	VERB
ejpam-6129	144	11	that	that	SCONJ
ejpam-6129	144	12	the	the	DET
ejpam-6129	144	13	number	number	NOUN
ejpam-6129	144	14	of	of	ADP
ejpam-6129	144	15	infectious	infectious	ADJ
ejpam-6129	144	16	individuals	individual	NOUN
ejpam-6129	144	17	increases	increase	VERB
ejpam-6129	144	18	in	in	ADP
ejpam-6129	144	19	the	the	DET
ejpam-6129	144	20	first	first	ADJ
ejpam-6129	144	21	7	7	NUM
ejpam-6129	144	22	days	day	NOUN
ejpam-6129	144	23	,	,	PUNCT
ejpam-6129	144	24	but	but	CCONJ
ejpam-6129	144	25	remains	remain	VERB
ejpam-6129	144	26	below	below	ADP
ejpam-6129	144	27	the	the	DET
ejpam-6129	144	28	curve	curve	NOUN
ejpam-6129	144	29	for	for	ADP
ejpam-6129	144	30	the	the	DET
ejpam-6129	144	31	infectious	infectious	ADJ
ejpam-6129	144	32	without	without	ADP
ejpam-6129	144	33	controls	control	NOUN
ejpam-6129	144	34	,	,	PUNCT
ejpam-6129	144	35	and	and	CCONJ
ejpam-6129	144	36	then	then	ADV
ejpam-6129	144	37	it	it	PRON
ejpam-6129	144	38	declines	decline	VERB
ejpam-6129	144	39	until	until	SCONJ
ejpam-6129	144	40	it	it	PRON
ejpam-6129	144	41	reaches	reach	VERB
ejpam-6129	144	42	i(t	i(t	PROPN
ejpam-6129	144	43	)	)	PUNCT
ejpam-6129	145	1	≈	≈	PROPN
ejpam-6129	145	2	0	0	NUM
ejpam-6129	145	3	by	by	ADP
ejpam-6129	145	4	the	the	DET
ejpam-6129	145	5	end	end	NOUN
ejpam-6129	145	6	of	of	ADP
ejpam-6129	145	7	the	the	DET
ejpam-6129	145	8	time	time	NOUN
ejpam-6129	145	9	interval	interval	NOUN
ejpam-6129	145	10	.	.	PUNCT
ejpam-6129	146	1	0	0	NUM
ejpam-6129	147	1	10	10	NUM
ejpam-6129	147	2	20	20	NUM
ejpam-6129	147	3	30	30	NUM
ejpam-6129	147	4	40	40	NUM
ejpam-6129	147	5	50	50	NUM
ejpam-6129	147	6	60	60	NUM
ejpam-6129	147	7	70	70	NUM
ejpam-6129	147	8	80	80	NUM
ejpam-6129	147	9	90	90	NUM
ejpam-6129	147	10	0	0	NUM
ejpam-6129	147	11	0.1	0.1	NUM
ejpam-6129	147	12	0.2	0.2	NUM
ejpam-6129	147	13	0.3	0.3	NUM
ejpam-6129	147	14	0.4	0.4	NUM
ejpam-6129	147	15	0.5	0.5	NUM
ejpam-6129	147	16	0.6	0.6	NUM
ejpam-6129	147	17	0.7	0.7	NUM
ejpam-6129	147	18	time	time	NOUN
ejpam-6129	147	19	(	(	PUNCT
ejpam-6129	147	20	days	day	NOUN
ejpam-6129	147	21	)	)	PUNCT
ejpam-6129	147	22	t	t	NOUN
ejpam-6129	147	23	h	h	NOUN
ejpam-6129	148	1	e	e	NOUN
ejpam-6129	148	2	c	c	NOUN
ejpam-6129	148	3	o	o	X
ejpam-6129	148	4	n	n	PRON
ejpam-6129	148	5	tr	tr	NOUN
ejpam-6129	148	6	o	o	NOUN
ejpam-6129	148	7	l	l	NOUN
ejpam-6129	148	8	u	u	NOUN
ejpam-6129	148	9	1	1	NUM
ejpam-6129	148	10	(	(	PUNCT
ejpam-6129	148	11	t	t	NOUN
ejpam-6129	148	12	)	)	PUNCT
ejpam-6129	148	13	−	−	PROPN
ejpam-6129	148	14	v	v	ADP
ejpam-6129	148	15	a	a	DET
ejpam-6129	148	16	c	c	NOUN
ejpam-6129	148	17	c	c	NOUN
ejpam-6129	148	18	in	in	ADP
ejpam-6129	148	19	a	a	DET
ejpam-6129	148	20	ti	ti	NOUN
ejpam-6129	148	21	o	o	NOUN
ejpam-6129	148	22	n	n	CCONJ
ejpam-6129	148	23	0	0	NUM
ejpam-6129	148	24	10	10	NUM
ejpam-6129	148	25	20	20	NUM
ejpam-6129	148	26	30	30	NUM
ejpam-6129	148	27	40	40	NUM
ejpam-6129	148	28	50	50	NUM
ejpam-6129	148	29	60	60	NUM
ejpam-6129	148	30	70	70	NUM
ejpam-6129	148	31	80	80	NUM
ejpam-6129	148	32	90	90	NUM
ejpam-6129	148	33	0	0	NUM
ejpam-6129	148	34	0.1	0.1	NUM
ejpam-6129	148	35	0.2	0.2	NUM
ejpam-6129	148	36	0.3	0.3	NUM
ejpam-6129	148	37	0.4	0.4	NUM
ejpam-6129	148	38	0.5	0.5	NUM
ejpam-6129	148	39	0.6	0.6	NUM
ejpam-6129	148	40	0.7	0.7	NUM
ejpam-6129	148	41	time	time	NOUN
ejpam-6129	148	42	(	(	PUNCT
ejpam-6129	148	43	days	day	NOUN
ejpam-6129	148	44	)	)	PUNCT
ejpam-6129	148	45	t	t	NOUN
ejpam-6129	148	46	h	h	NOUN
ejpam-6129	149	1	e	e	NOUN
ejpam-6129	149	2	c	c	NOUN
ejpam-6129	149	3	o	o	X
ejpam-6129	149	4	n	n	PRON
ejpam-6129	149	5	tr	tr	NOUN
ejpam-6129	149	6	o	o	NOUN
ejpam-6129	149	7	l	l	NOUN
ejpam-6129	149	8	u	u	NOUN
ejpam-6129	149	9	2	2	NUM
ejpam-6129	149	10	−	−	NOUN
ejpam-6129	149	11	c	c	NOUN
ejpam-6129	149	12	h	h	NOUN
ejpam-6129	150	1	e	e	NOUN
ejpam-6129	150	2	m	m	VERB
ejpam-6129	150	3	o	o	X
ejpam-6129	150	4	p	p	X
ejpam-6129	150	5	ro	ro	INTJ
ejpam-6129	150	6	h	h	NOUN
ejpam-6129	150	7	y	y	PROPN
ejpam-6129	150	8	la	la	PROPN
ejpam-6129	150	9	x	x	VERB
ejpam-6129	150	10	is	be	AUX
ejpam-6129	150	11	t	t	PROPN
ejpam-6129	150	12	re	re	PROPN
ejpam-6129	150	13	a	a	DET
ejpam-6129	150	14	tm	tm	NOUN
ejpam-6129	150	15	e	e	PROPN
ejpam-6129	150	16	n	n	PROPN
ejpam-6129	150	17	t	t	PROPN
ejpam-6129	150	18	figure	figure	NOUN
ejpam-6129	150	19	1	1	NUM
ejpam-6129	150	20	:	:	PUNCT
ejpam-6129	150	21	values	value	NOUN
ejpam-6129	150	22	of	of	ADP
ejpam-6129	150	23	the	the	DET
ejpam-6129	150	24	optimal	optimal	ADJ
ejpam-6129	150	25	controls	control	NOUN
ejpam-6129	150	26	when	when	SCONJ
ejpam-6129	150	27	a	a	PRON
ejpam-6129	150	28	=	=	SYM
ejpam-6129	150	29	10	10	NUM
ejpam-6129	150	30	and	and	CCONJ
ejpam-6129	150	31	b	b	NOUN
ejpam-6129	150	32	=	=	SYM
ejpam-6129	150	33	10	10	NUM
ejpam-6129	150	34	.	.	NOUN
ejpam-6129	150	35	0	0	NUM
ejpam-6129	151	1	10	10	NUM
ejpam-6129	151	2	20	20	NUM
ejpam-6129	151	3	30	30	NUM
ejpam-6129	151	4	40	40	NUM
ejpam-6129	151	5	50	50	NUM
ejpam-6129	151	6	60	60	NUM
ejpam-6129	151	7	70	70	NUM
ejpam-6129	151	8	80	80	NUM
ejpam-6129	151	9	90	90	NUM
ejpam-6129	151	10	0	0	NUM
ejpam-6129	151	11	1000	1000	NUM
ejpam-6129	151	12	2000	2000	NUM
ejpam-6129	151	13	3000	3000	NUM
ejpam-6129	151	14	4000	4000	NUM
ejpam-6129	151	15	5000	5000	NUM
ejpam-6129	151	16	6000	6000	NUM
ejpam-6129	151	17	7000	7000	NUM
ejpam-6129	151	18	8000	8000	NUM
ejpam-6129	151	19	9000	9000	NUM
ejpam-6129	151	20	time	time	NOUN
ejpam-6129	151	21	(	(	PUNCT
ejpam-6129	151	22	days	day	NOUN
ejpam-6129	151	23	)	)	PUNCT
ejpam-6129	151	24	s	s	PART
ejpam-6129	151	25	u	u	NOUN
ejpam-6129	151	26	s	s	PRON
ejpam-6129	151	27	c	c	NOUN
ejpam-6129	151	28	e	e	NOUN
ejpam-6129	151	29	p	p	X
ejpam-6129	151	30	ti	ti	PROPN
ejpam-6129	151	31	b	b	X
ejpam-6129	151	32	le	le	X
ejpam-6129	151	33	i	i	PRON
ejpam-6129	152	1	n	n	VERB
ejpam-6129	152	2	d	d	NOUN
ejpam-6129	152	3	iv	iv	X
ejpam-6129	153	1	i	i	PROPN
ejpam-6129	153	2	d	d	PROPN
ejpam-6129	153	3	u	u	PROPN
ejpam-6129	153	4	a	a	DET
ejpam-6129	153	5	ls	ls	X
ejpam-6129	153	6	(	(	PUNCT
ejpam-6129	153	7	s	s	X
ejpam-6129	153	8	(	(	PUNCT
ejpam-6129	153	9	t	t	NOUN
ejpam-6129	153	10	)	)	PUNCT
ejpam-6129	153	11	)	)	PUNCT
ejpam-6129	153	12	with	with	ADP
ejpam-6129	153	13	controls	control	NOUN
ejpam-6129	153	14	without	without	ADP
ejpam-6129	153	15	controls	control	NOUN
ejpam-6129	153	16	0	0	NUM
ejpam-6129	154	1	10	10	NUM
ejpam-6129	154	2	20	20	NUM
ejpam-6129	154	3	30	30	NUM
ejpam-6129	154	4	40	40	NUM
ejpam-6129	154	5	50	50	NUM
ejpam-6129	154	6	60	60	NUM
ejpam-6129	154	7	70	70	NUM
ejpam-6129	154	8	80	80	NUM
ejpam-6129	154	9	90	90	NUM
ejpam-6129	154	10	0	0	NUM
ejpam-6129	154	11	500	500	NUM
ejpam-6129	154	12	1000	1000	NUM
ejpam-6129	154	13	1500	1500	NUM
ejpam-6129	154	14	2000	2000	NUM
ejpam-6129	154	15	2500	2500	NUM
ejpam-6129	154	16	3000	3000	NUM
ejpam-6129	154	17	3500	3500	NUM
ejpam-6129	154	18	4000	4000	NUM
ejpam-6129	154	19	time	time	NOUN
ejpam-6129	154	20	(	(	PUNCT
ejpam-6129	154	21	days	day	NOUN
ejpam-6129	154	22	)	)	PUNCT
ejpam-6129	154	23	c	c	PROPN
ejpam-6129	154	24	a	a	DET
ejpam-6129	154	25	rr	rr	X
ejpam-6129	154	26	ie	ie	ADP
ejpam-6129	154	27	r	r	NOUN
ejpam-6129	154	28	in	in	ADP
ejpam-6129	154	29	d	d	NOUN
ejpam-6129	154	30	iv	iv	INTJ
ejpam-6129	154	31	i	i	PROPN
ejpam-6129	154	32	d	d	PROPN
ejpam-6129	154	33	u	u	PROPN
ejpam-6129	154	34	a	a	DET
ejpam-6129	154	35	ls	ls	X
ejpam-6129	154	36	(	(	PUNCT
ejpam-6129	154	37	c	c	PROPN
ejpam-6129	154	38	(	(	PUNCT
ejpam-6129	154	39	t	t	PROPN
ejpam-6129	154	40	)	)	PUNCT
ejpam-6129	154	41	)	)	PUNCT
ejpam-6129	154	42	with	with	ADP
ejpam-6129	154	43	controls	control	NOUN
ejpam-6129	154	44	without	without	ADP
ejpam-6129	154	45	controls	control	NOUN
ejpam-6129	154	46	0	0	NUM
ejpam-6129	154	47	10	10	NUM
ejpam-6129	154	48	20	20	NUM
ejpam-6129	154	49	30	30	NUM
ejpam-6129	154	50	40	40	NUM
ejpam-6129	154	51	50	50	NUM
ejpam-6129	154	52	60	60	NUM
ejpam-6129	154	53	70	70	NUM
ejpam-6129	154	54	80	80	NUM
ejpam-6129	154	55	90	90	NUM
ejpam-6129	154	56	0	0	NUM
ejpam-6129	154	57	2	2	NUM
ejpam-6129	154	58	4	4	NUM
ejpam-6129	154	59	6	6	NUM
ejpam-6129	154	60	8	8	NUM
ejpam-6129	154	61	10	10	NUM
ejpam-6129	154	62	12	12	NUM
ejpam-6129	154	63	time	time	NOUN
ejpam-6129	154	64	(	(	PUNCT
ejpam-6129	154	65	days	day	NOUN
ejpam-6129	154	66	)	)	PUNCT
ejpam-6129	154	67	in	in	ADP
ejpam-6129	154	68	fe	fe	X
ejpam-6129	154	69	c	c	NOUN
ejpam-6129	154	70	ti	ti	NOUN
ejpam-6129	154	71	o	o	X
ejpam-6129	154	72	u	u	NOUN
ejpam-6129	154	73	s	s	PROPN
ejpam-6129	154	74	i	i	PRON
ejpam-6129	154	75	n	n	NOUN
ejpam-6129	154	76	d	d	NOUN
ejpam-6129	154	77	iv	iv	X
ejpam-6129	154	78	i	i	PROPN
ejpam-6129	154	79	d	d	PROPN
ejpam-6129	154	80	u	u	PROPN
ejpam-6129	154	81	a	a	DET
ejpam-6129	154	82	ls	ls	X
ejpam-6129	154	83	(	(	PUNCT
ejpam-6129	154	84	i	i	PROPN
ejpam-6129	154	85	(	(	PUNCT
ejpam-6129	154	86	t	t	PROPN
ejpam-6129	154	87	)	)	PUNCT
ejpam-6129	154	88	)	)	PUNCT
ejpam-6129	154	89	with	with	ADP
ejpam-6129	154	90	controls	control	NOUN
ejpam-6129	154	91	without	without	ADP
ejpam-6129	154	92	controls	control	NOUN
ejpam-6129	154	93	0	0	NUM
ejpam-6129	154	94	10	10	NUM
ejpam-6129	154	95	20	20	NUM
ejpam-6129	154	96	30	30	NUM
ejpam-6129	154	97	40	40	NUM
ejpam-6129	154	98	50	50	NUM
ejpam-6129	154	99	60	60	NUM
ejpam-6129	154	100	70	70	NUM
ejpam-6129	154	101	80	80	NUM
ejpam-6129	154	102	90	90	NUM
ejpam-6129	154	103	0	0	NUM
ejpam-6129	154	104	1000	1000	NUM
ejpam-6129	154	105	2000	2000	NUM
ejpam-6129	154	106	3000	3000	NUM
ejpam-6129	154	107	4000	4000	NUM
ejpam-6129	154	108	5000	5000	NUM
ejpam-6129	154	109	6000	6000	NUM
ejpam-6129	154	110	7000	7000	NUM
ejpam-6129	154	111	8000	8000	NUM
ejpam-6129	154	112	9000	9000	NUM
ejpam-6129	154	113	10000	10000	NUM
ejpam-6129	154	114	time	time	NOUN
ejpam-6129	154	115	(	(	PUNCT
ejpam-6129	154	116	days	day	NOUN
ejpam-6129	154	117	)	)	PUNCT
ejpam-6129	154	118	r	r	NOUN
ejpam-6129	154	119	e	e	NOUN
ejpam-6129	154	120	c	c	NOUN
ejpam-6129	154	121	o	o	X
ejpam-6129	154	122	v	v	X
ejpam-6129	154	123	e	e	X
ejpam-6129	154	124	re	re	NOUN
ejpam-6129	154	125	d	d	PROPN
ejpam-6129	154	126	i	i	PRON
ejpam-6129	154	127	n	n	PROPN
ejpam-6129	154	128	d	d	NOUN
ejpam-6129	154	129	iv	iv	X
ejpam-6129	154	130	i	i	PROPN
ejpam-6129	154	131	d	d	PROPN
ejpam-6129	154	132	u	u	PROPN
ejpam-6129	154	133	a	a	DET
ejpam-6129	154	134	ls	ls	X
ejpam-6129	154	135	(	(	PUNCT
ejpam-6129	154	136	r	r	NOUN
ejpam-6129	154	137	(	(	PUNCT
ejpam-6129	154	138	t	t	NOUN
ejpam-6129	154	139	)	)	PUNCT
ejpam-6129	154	140	)	)	PUNCT
ejpam-6129	154	141	with	with	ADP
ejpam-6129	154	142	controls	control	NOUN
ejpam-6129	154	143	without	without	ADP
ejpam-6129	154	144	controls	control	NOUN
ejpam-6129	154	145	figure	figure	NOUN
ejpam-6129	154	146	2	2	NUM
ejpam-6129	154	147	:	:	PUNCT
ejpam-6129	154	148	effect	effect	NOUN
ejpam-6129	154	149	of	of	ADP
ejpam-6129	154	150	optimal	optimal	ADJ
ejpam-6129	154	151	vaccination	vaccination	NOUN
ejpam-6129	154	152	and	and	CCONJ
ejpam-6129	154	153	treatment	treatment	NOUN
ejpam-6129	154	154	strategies	strategy	NOUN
ejpam-6129	154	155	when	when	SCONJ
ejpam-6129	154	156	a	a	DET
ejpam-6129	154	157	=	=	SYM
ejpam-6129	154	158	10	10	NUM
ejpam-6129	154	159	and	and	CCONJ
ejpam-6129	154	160	b	b	NOUN
ejpam-6129	154	161	=	=	SYM
ejpam-6129	154	162	10	10	NUM
ejpam-6129	154	163	.	.	PUNCT
ejpam-6129	155	1	s.	s.	PROPN
ejpam-6129	155	2	a.	a.	PROPN
ejpam-6129	155	3	mohamed	mohamed	PROPN
ejpam-6129	155	4	et	et	PROPN
ejpam-6129	155	5	al	al	PROPN
ejpam-6129	155	6	.	.	PUNCT
ejpam-6129	155	7	/	/	SYM
ejpam-6129	155	8	eur	eur	PROPN
ejpam-6129	155	9	.	.	PUNCT
ejpam-6129	156	1	j.	j.	PROPN
ejpam-6129	156	2	pure	pure	PROPN
ejpam-6129	156	3	appl	appl	PROPN
ejpam-6129	156	4	.	.	PROPN
ejpam-6129	156	5	math	math	PROPN
ejpam-6129	156	6	,	,	PUNCT
ejpam-6129	156	7	18	18	NUM
ejpam-6129	156	8	(	(	PUNCT
ejpam-6129	156	9	3	3	NUM
ejpam-6129	156	10	)	)	PUNCT
ejpam-6129	156	11	(	(	PUNCT
ejpam-6129	156	12	2025	2025	NUM
ejpam-6129	156	13	)	)	PUNCT
ejpam-6129	156	14	,	,	PUNCT
ejpam-6129	156	15	6129	6129	NUM
ejpam-6129	156	16	9	9	NUM
ejpam-6129	156	17	of	of	ADP
ejpam-6129	156	18	17	17	NUM
ejpam-6129	156	19	figure	figure	NOUN
ejpam-6129	156	20	3	3	NUM
ejpam-6129	156	21	shows	show	VERB
ejpam-6129	156	22	the	the	DET
ejpam-6129	156	23	different	different	ADJ
ejpam-6129	156	24	profiles	profile	NOUN
ejpam-6129	156	25	of	of	ADP
ejpam-6129	156	26	the	the	DET
ejpam-6129	156	27	two	two	NUM
ejpam-6129	156	28	controls	control	NOUN
ejpam-6129	156	29	u1	u1	NOUN
ejpam-6129	156	30	and	and	CCONJ
ejpam-6129	156	31	u2	u2	NOUN
ejpam-6129	156	32	for	for	ADP
ejpam-6129	156	33	different	different	ADJ
ejpam-6129	156	34	values	value	NOUN
ejpam-6129	156	35	of	of	ADP
ejpam-6129	156	36	the	the	DET
ejpam-6129	156	37	balancing	balancing	NOUN
ejpam-6129	156	38	factors	factor	NOUN
ejpam-6129	156	39	a	a	PRON
ejpam-6129	156	40	and	and	CCONJ
ejpam-6129	156	41	b.	b.	PROPN
ejpam-6129	156	42	as	as	SCONJ
ejpam-6129	156	43	expected	expect	VERB
ejpam-6129	156	44	,	,	PUNCT
ejpam-6129	156	45	increasing	increase	VERB
ejpam-6129	156	46	the	the	DET
ejpam-6129	156	47	values	value	NOUN
ejpam-6129	156	48	of	of	ADP
ejpam-6129	156	49	these	these	DET
ejpam-6129	156	50	constants	constant	NOUN
ejpam-6129	156	51	reduces	reduce	VERB
ejpam-6129	156	52	the	the	DET
ejpam-6129	156	53	values	value	NOUN
ejpam-6129	156	54	of	of	ADP
ejpam-6129	156	55	the	the	DET
ejpam-6129	156	56	controls	control	NOUN
ejpam-6129	156	57	and	and	CCONJ
ejpam-6129	156	58	hence	hence	ADV
ejpam-6129	156	59	their	their	PRON
ejpam-6129	156	60	effect	effect	NOUN
ejpam-6129	156	61	is	be	AUX
ejpam-6129	156	62	also	also	ADV
ejpam-6129	156	63	reduced	reduce	VERB
ejpam-6129	156	64	,	,	PUNCT
ejpam-6129	156	65	whereas	whereas	SCONJ
ejpam-6129	156	66	decreasing	decrease	VERB
ejpam-6129	156	67	their	their	PRON
ejpam-6129	156	68	values	value	NOUN
ejpam-6129	156	69	causes	cause	VERB
ejpam-6129	156	70	the	the	DET
ejpam-6129	156	71	controls	control	NOUN
ejpam-6129	156	72	last	last	VERB
ejpam-6129	156	73	longer	long	ADV
ejpam-6129	156	74	at	at	ADP
ejpam-6129	156	75	their	their	PRON
ejpam-6129	156	76	upper	upper	ADJ
ejpam-6129	156	77	bounds	bound	NOUN
ejpam-6129	156	78	before	before	SCONJ
ejpam-6129	156	79	they	they	PRON
ejpam-6129	156	80	decrease	decrease	VERB
ejpam-6129	156	81	again	again	ADV
ejpam-6129	156	82	but	but	CCONJ
ejpam-6129	156	83	still	still	ADV
ejpam-6129	156	84	at	at	ADP
ejpam-6129	156	85	larger	large	ADJ
ejpam-6129	156	86	scales	scale	NOUN
ejpam-6129	156	87	than	than	ADP
ejpam-6129	156	88	before	before	ADV
ejpam-6129	156	89	.	.	PUNCT
ejpam-6129	157	1	0	0	NUM
ejpam-6129	158	1	10	10	NUM
ejpam-6129	158	2	20	20	NUM
ejpam-6129	158	3	30	30	NUM
ejpam-6129	158	4	40	40	NUM
ejpam-6129	158	5	50	50	NUM
ejpam-6129	158	6	60	60	NUM
ejpam-6129	158	7	70	70	NUM
ejpam-6129	158	8	80	80	NUM
ejpam-6129	158	9	90	90	NUM
ejpam-6129	158	10	0	0	NUM
ejpam-6129	158	11	0.1	0.1	NUM
ejpam-6129	158	12	0.2	0.2	NUM
ejpam-6129	158	13	0.3	0.3	NUM
ejpam-6129	158	14	0.4	0.4	NUM
ejpam-6129	158	15	0.5	0.5	NUM
ejpam-6129	158	16	0.6	0.6	NUM
ejpam-6129	158	17	0.7	0.7	NUM
ejpam-6129	158	18	time	time	NOUN
ejpam-6129	158	19	(	(	PUNCT
ejpam-6129	158	20	days	day	NOUN
ejpam-6129	158	21	)	)	PUNCT
ejpam-6129	158	22	t	t	NOUN
ejpam-6129	158	23	h	h	NOUN
ejpam-6129	159	1	e	e	NOUN
ejpam-6129	159	2	c	c	NOUN
ejpam-6129	159	3	o	o	X
ejpam-6129	159	4	n	n	PRON
ejpam-6129	159	5	tr	tr	NOUN
ejpam-6129	159	6	o	o	NOUN
ejpam-6129	159	7	l	l	NOUN
ejpam-6129	159	8	u	u	NOUN
ejpam-6129	159	9	1	1	NUM
ejpam-6129	159	10	(	(	PUNCT
ejpam-6129	159	11	t	t	NOUN
ejpam-6129	159	12	)	)	PUNCT
ejpam-6129	159	13	−	−	PROPN
ejpam-6129	159	14	v	v	ADP
ejpam-6129	159	15	a	a	DET
ejpam-6129	159	16	c	c	NOUN
ejpam-6129	159	17	c	c	NOUN
ejpam-6129	159	18	in	in	ADP
ejpam-6129	159	19	a	a	DET
ejpam-6129	159	20	ti	ti	NOUN
ejpam-6129	159	21	o	o	NOUN
ejpam-6129	159	22	n	n	PRON
ejpam-6129	159	23	a=1	a=1	X
ejpam-6129	159	24	,	,	PUNCT
ejpam-6129	159	25	b=1	b=1	X
ejpam-6129	159	26	a=50	a=50	PROPN
ejpam-6129	159	27	,	,	PUNCT
ejpam-6129	159	28	b=50	b=50	PROPN
ejpam-6129	159	29	a=1000	a=1000	PROPN
ejpam-6129	159	30	,	,	PUNCT
ejpam-6129	159	31	b=5000	b=5000	PROPN
ejpam-6129	159	32	a=10000	a=10000	PROPN
ejpam-6129	159	33	,	,	PUNCT
ejpam-6129	159	34	b=20000	b=20000	PROPN
ejpam-6129	159	35	a=50000	a=50000	PROPN
ejpam-6129	159	36	,	,	PUNCT
ejpam-6129	159	37	b=30000	b=30000	PROPN
ejpam-6129	159	38	0	0	NUM
ejpam-6129	159	39	10	10	NUM
ejpam-6129	159	40	20	20	NUM
ejpam-6129	159	41	30	30	NUM
ejpam-6129	159	42	40	40	NUM
ejpam-6129	159	43	50	50	NUM
ejpam-6129	159	44	60	60	NUM
ejpam-6129	159	45	70	70	NUM
ejpam-6129	159	46	80	80	NUM
ejpam-6129	159	47	90	90	NUM
ejpam-6129	159	48	0	0	NUM
ejpam-6129	159	49	0.1	0.1	NUM
ejpam-6129	159	50	0.2	0.2	NUM
ejpam-6129	159	51	0.3	0.3	NUM
ejpam-6129	159	52	0.4	0.4	NUM
ejpam-6129	159	53	0.5	0.5	NUM
ejpam-6129	159	54	0.6	0.6	NUM
ejpam-6129	159	55	0.7	0.7	NUM
ejpam-6129	159	56	time	time	NOUN
ejpam-6129	159	57	(	(	PUNCT
ejpam-6129	159	58	days	day	NOUN
ejpam-6129	159	59	)	)	PUNCT
ejpam-6129	159	60	t	t	NOUN
ejpam-6129	159	61	h	h	NOUN
ejpam-6129	160	1	e	e	NOUN
ejpam-6129	160	2	c	c	NOUN
ejpam-6129	160	3	o	o	X
ejpam-6129	160	4	n	n	PRON
ejpam-6129	160	5	tr	tr	NOUN
ejpam-6129	160	6	o	o	NOUN
ejpam-6129	160	7	l	l	NOUN
ejpam-6129	160	8	u	u	NOUN
ejpam-6129	160	9	2	2	NUM
ejpam-6129	160	10	(	(	PUNCT
ejpam-6129	160	11	t	t	NOUN
ejpam-6129	160	12	)	)	PUNCT
ejpam-6129	160	13	−	−	PROPN
ejpam-6129	160	14	t	t	PROPN
ejpam-6129	160	15	re	re	VERB
ejpam-6129	160	16	a	a	DET
ejpam-6129	160	17	tm	tm	NOUN
ejpam-6129	160	18	e	e	PROPN
ejpam-6129	160	19	n	n	PROPN
ejpam-6129	160	20	t	t	PROPN
ejpam-6129	160	21	a=1	a=1	PROPN
ejpam-6129	160	22	,	,	PUNCT
ejpam-6129	160	23	b=1	b=1	X
ejpam-6129	160	24	a=50	a=50	PROPN
ejpam-6129	160	25	,	,	PUNCT
ejpam-6129	160	26	b=50	b=50	PROPN
ejpam-6129	160	27	a=1000	a=1000	PROPN
ejpam-6129	160	28	,	,	PUNCT
ejpam-6129	160	29	b=5000	b=5000	PROPN
ejpam-6129	160	30	a=10000,b=20000	a=10000,b=20000	PROPN
ejpam-6129	160	31	a=50000	a=50000	PROPN
ejpam-6129	160	32	,	,	PUNCT
ejpam-6129	160	33	b=30000	b=30000	PROPN
ejpam-6129	160	34	figure	figure	VERB
ejpam-6129	160	35	3	3	NUM
ejpam-6129	160	36	:	:	PUNCT
ejpam-6129	160	37	plots	plot	NOUN
ejpam-6129	160	38	for	for	ADP
ejpam-6129	160	39	controls	control	NOUN
ejpam-6129	160	40	u1	u1	NOUN
ejpam-6129	160	41	and	and	CCONJ
ejpam-6129	160	42	u2	u2	NOUN
ejpam-6129	160	43	for	for	ADP
ejpam-6129	160	44	various	various	ADJ
ejpam-6129	160	45	values	value	NOUN
ejpam-6129	160	46	of	of	ADP
ejpam-6129	160	47	the	the	DET
ejpam-6129	160	48	balancing	balancing	NOUN
ejpam-6129	160	49	factors	factor	NOUN
ejpam-6129	160	50	a	a	PRON
ejpam-6129	160	51	and	and	CCONJ
ejpam-6129	160	52	b.	b.	X
ejpam-6129	160	53	the	the	DET
ejpam-6129	160	54	effects	effect	NOUN
ejpam-6129	160	55	of	of	ADP
ejpam-6129	160	56	these	these	DET
ejpam-6129	160	57	controls	control	NOUN
ejpam-6129	160	58	on	on	ADP
ejpam-6129	160	59	other	other	ADJ
ejpam-6129	160	60	state	state	NOUN
ejpam-6129	160	61	variables	variable	NOUN
ejpam-6129	160	62	are	be	AUX
ejpam-6129	160	63	shown	show	VERB
ejpam-6129	160	64	in	in	ADP
ejpam-6129	160	65	figure	figure	NOUN
ejpam-6129	160	66	4	4	NUM
ejpam-6129	160	67	,	,	PUNCT
ejpam-6129	160	68	where	where	SCONJ
ejpam-6129	160	69	we	we	PRON
ejpam-6129	160	70	use	use	VERB
ejpam-6129	160	71	the	the	DET
ejpam-6129	160	72	same	same	ADJ
ejpam-6129	160	73	values	value	NOUN
ejpam-6129	160	74	of	of	ADP
ejpam-6129	160	75	a	a	PRON
ejpam-6129	160	76	and	and	CCONJ
ejpam-6129	160	77	b	b	NOUN
ejpam-6129	160	78	used	use	VERB
ejpam-6129	160	79	in	in	ADP
ejpam-6129	160	80	figure	figure	NOUN
ejpam-6129	160	81	3	3	NUM
ejpam-6129	160	82	.	.	PUNCT
ejpam-6129	161	1	as	as	SCONJ
ejpam-6129	161	2	can	can	AUX
ejpam-6129	161	3	be	be	AUX
ejpam-6129	161	4	seen	see	VERB
ejpam-6129	161	5	,	,	PUNCT
ejpam-6129	161	6	the	the	DET
ejpam-6129	161	7	simulations	simulation	NOUN
ejpam-6129	161	8	verify	verify	VERB
ejpam-6129	161	9	the	the	DET
ejpam-6129	161	10	fact	fact	NOUN
ejpam-6129	161	11	that	that	SCONJ
ejpam-6129	161	12	increasing	increase	VERB
ejpam-6129	161	13	the	the	DET
ejpam-6129	161	14	values	value	NOUN
ejpam-6129	161	15	of	of	ADP
ejpam-6129	161	16	the	the	DET
ejpam-6129	161	17	two	two	NUM
ejpam-6129	161	18	controls	control	NOUN
ejpam-6129	161	19	reduces	reduce	VERB
ejpam-6129	161	20	c(t	c(t	PROPN
ejpam-6129	161	21	)	)	PUNCT
ejpam-6129	161	22	and	and	CCONJ
ejpam-6129	161	23	i(t	i(t	NOUN
ejpam-6129	161	24	)	)	PUNCT
ejpam-6129	161	25	and	and	CCONJ
ejpam-6129	161	26	causes	cause	VERB
ejpam-6129	161	27	s(t	s(t	PROPN
ejpam-6129	161	28	)	)	PUNCT
ejpam-6129	161	29	to	to	PART
ejpam-6129	161	30	decrease	decrease	VERB
ejpam-6129	161	31	and	and	CCONJ
ejpam-6129	161	32	r(t	r(t	NOUN
ejpam-6129	161	33	)	)	PUNCT
ejpam-6129	161	34	to	to	PART
ejpam-6129	161	35	increase	increase	VERB
ejpam-6129	161	36	because	because	SCONJ
ejpam-6129	161	37	in	in	ADP
ejpam-6129	161	38	this	this	DET
ejpam-6129	161	39	case	case	NOUN
ejpam-6129	161	40	more	more	ADJ
ejpam-6129	161	41	susceptibles	susceptible	NOUN
ejpam-6129	161	42	are	be	AUX
ejpam-6129	161	43	vaccinated	vaccinate	VERB
ejpam-6129	161	44	and	and	CCONJ
ejpam-6129	161	45	more	more	ADV
ejpam-6129	161	46	infectious	infectious	ADJ
ejpam-6129	161	47	are	be	AUX
ejpam-6129	161	48	successfully	successfully	ADV
ejpam-6129	161	49	treated	treat	VERB
ejpam-6129	161	50	.	.	PUNCT
ejpam-6129	162	1	s.	s.	PROPN
ejpam-6129	162	2	a.	a.	PROPN
ejpam-6129	162	3	mohamed	mohamed	PROPN
ejpam-6129	162	4	et	et	PROPN
ejpam-6129	162	5	al	al	PROPN
ejpam-6129	162	6	.	.	PUNCT
ejpam-6129	162	7	/	/	SYM
ejpam-6129	162	8	eur	eur	PROPN
ejpam-6129	162	9	.	.	PUNCT
ejpam-6129	163	1	j.	j.	PROPN
ejpam-6129	163	2	pure	pure	PROPN
ejpam-6129	163	3	appl	appl	PROPN
ejpam-6129	163	4	.	.	PROPN
ejpam-6129	163	5	math	math	PROPN
ejpam-6129	163	6	,	,	PUNCT
ejpam-6129	163	7	18	18	NUM
ejpam-6129	163	8	(	(	PUNCT
ejpam-6129	163	9	3	3	NUM
ejpam-6129	163	10	)	)	PUNCT
ejpam-6129	163	11	(	(	PUNCT
ejpam-6129	163	12	2025	2025	NUM
ejpam-6129	163	13	)	)	PUNCT
ejpam-6129	163	14	,	,	PUNCT
ejpam-6129	163	15	6129	6129	NUM
ejpam-6129	163	16	10	10	NUM
ejpam-6129	163	17	of	of	ADP
ejpam-6129	163	18	17	17	NUM
ejpam-6129	163	19	0	0	NUM
ejpam-6129	163	20	10	10	NUM
ejpam-6129	163	21	20	20	NUM
ejpam-6129	163	22	30	30	NUM
ejpam-6129	163	23	40	40	NUM
ejpam-6129	163	24	50	50	NUM
ejpam-6129	163	25	60	60	NUM
ejpam-6129	163	26	70	70	NUM
ejpam-6129	163	27	80	80	NUM
ejpam-6129	163	28	90	90	NUM
ejpam-6129	163	29	0	0	NUM
ejpam-6129	163	30	1000	1000	NUM
ejpam-6129	163	31	2000	2000	NUM
ejpam-6129	163	32	3000	3000	NUM
ejpam-6129	163	33	4000	4000	NUM
ejpam-6129	163	34	5000	5000	NUM
ejpam-6129	163	35	6000	6000	NUM
ejpam-6129	163	36	7000	7000	NUM
ejpam-6129	163	37	8000	8000	NUM
ejpam-6129	163	38	9000	9000	NUM
ejpam-6129	163	39	time	time	NOUN
ejpam-6129	163	40	(	(	PUNCT
ejpam-6129	163	41	days	day	NOUN
ejpam-6129	163	42	)	)	PUNCT
ejpam-6129	163	43	s	s	PART
ejpam-6129	163	44	u	u	NOUN
ejpam-6129	163	45	s	s	PRON
ejpam-6129	163	46	c	c	NOUN
ejpam-6129	163	47	e	e	NOUN
ejpam-6129	163	48	p	p	X
ejpam-6129	163	49	ti	ti	PROPN
ejpam-6129	163	50	b	b	X
ejpam-6129	163	51	le	le	X
ejpam-6129	163	52	i	i	PRON
ejpam-6129	164	1	n	n	VERB
ejpam-6129	164	2	d	d	NOUN
ejpam-6129	164	3	iv	iv	X
ejpam-6129	165	1	i	i	PROPN
ejpam-6129	165	2	d	d	PROPN
ejpam-6129	165	3	u	u	PROPN
ejpam-6129	165	4	a	a	PRON
ejpam-6129	165	5	ls	ls	X
ejpam-6129	165	6	(	(	PUNCT
ejpam-6129	165	7	s	s	X
ejpam-6129	165	8	(	(	PUNCT
ejpam-6129	165	9	t	t	NOUN
ejpam-6129	165	10	)	)	PUNCT
ejpam-6129	165	11	)	)	PUNCT
ejpam-6129	166	1	a=1	a=1	X
ejpam-6129	166	2	,	,	PUNCT
ejpam-6129	166	3	b=1	b=1	X
ejpam-6129	166	4	a=50	a=50	PROPN
ejpam-6129	166	5	,	,	PUNCT
ejpam-6129	166	6	b=50	b=50	PROPN
ejpam-6129	166	7	a=1000	a=1000	PROPN
ejpam-6129	166	8	,	,	PUNCT
ejpam-6129	166	9	b=5000	b=5000	PROPN
ejpam-6129	166	10	a=10000,b=20000	a=10000,b=20000	PROPN
ejpam-6129	166	11	a=50000	a=50000	PROPN
ejpam-6129	166	12	,	,	PUNCT
ejpam-6129	166	13	b=30000	b=30000	PROPN
ejpam-6129	166	14	0	0	NUM
ejpam-6129	167	1	10	10	NUM
ejpam-6129	167	2	20	20	NUM
ejpam-6129	167	3	30	30	NUM
ejpam-6129	167	4	40	40	NUM
ejpam-6129	167	5	50	50	NUM
ejpam-6129	167	6	60	60	NUM
ejpam-6129	167	7	70	70	NUM
ejpam-6129	167	8	80	80	NUM
ejpam-6129	167	9	90	90	NUM
ejpam-6129	167	10	0	0	NUM
ejpam-6129	167	11	200	200	NUM
ejpam-6129	167	12	400	400	NUM
ejpam-6129	167	13	600	600	NUM
ejpam-6129	167	14	800	800	NUM
ejpam-6129	167	15	1000	1000	NUM
ejpam-6129	167	16	1200	1200	NUM
ejpam-6129	167	17	time	time	NOUN
ejpam-6129	167	18	(	(	PUNCT
ejpam-6129	167	19	days	day	NOUN
ejpam-6129	167	20	)	)	PUNCT
ejpam-6129	167	21	c	c	PROPN
ejpam-6129	167	22	a	a	DET
ejpam-6129	167	23	rr	rr	X
ejpam-6129	167	24	ie	ie	ADP
ejpam-6129	167	25	r	r	NOUN
ejpam-6129	167	26	in	in	ADP
ejpam-6129	167	27	d	d	NOUN
ejpam-6129	167	28	iv	iv	INTJ
ejpam-6129	167	29	i	i	PROPN
ejpam-6129	167	30	d	d	PROPN
ejpam-6129	167	31	u	u	PROPN
ejpam-6129	167	32	a	a	DET
ejpam-6129	167	33	ls	ls	X
ejpam-6129	167	34	(	(	PUNCT
ejpam-6129	167	35	c	c	PROPN
ejpam-6129	167	36	(	(	PUNCT
ejpam-6129	167	37	t	t	NOUN
ejpam-6129	167	38	)	)	PUNCT
ejpam-6129	167	39	)	)	PUNCT
ejpam-6129	168	1	a=1	a=1	X
ejpam-6129	168	2	,	,	PUNCT
ejpam-6129	168	3	b=1	b=1	X
ejpam-6129	168	4	a=50	a=50	PROPN
ejpam-6129	168	5	,	,	PUNCT
ejpam-6129	168	6	b=50	b=50	PROPN
ejpam-6129	168	7	a=1000	a=1000	PROPN
ejpam-6129	168	8	,	,	PUNCT
ejpam-6129	168	9	b=5000	b=5000	PROPN
ejpam-6129	168	10	a=10000,b=20000	a=10000,b=20000	PROPN
ejpam-6129	168	11	a=50000	a=50000	PROPN
ejpam-6129	168	12	,	,	PUNCT
ejpam-6129	168	13	b=30000	b=30000	PROPN
ejpam-6129	168	14	0	0	NUM
ejpam-6129	169	1	10	10	NUM
ejpam-6129	169	2	20	20	NUM
ejpam-6129	169	3	30	30	NUM
ejpam-6129	169	4	40	40	NUM
ejpam-6129	169	5	50	50	NUM
ejpam-6129	169	6	60	60	NUM
ejpam-6129	169	7	70	70	NUM
ejpam-6129	169	8	80	80	NUM
ejpam-6129	169	9	90	90	NUM
ejpam-6129	169	10	0	0	NUM
ejpam-6129	169	11	0.5	0.5	NUM
ejpam-6129	169	12	1	1	NUM
ejpam-6129	169	13	1.5	1.5	NUM
ejpam-6129	169	14	2	2	NUM
ejpam-6129	169	15	2.5	2.5	NUM
ejpam-6129	169	16	3	3	NUM
ejpam-6129	169	17	3.5	3.5	NUM
ejpam-6129	169	18	time	time	NOUN
ejpam-6129	169	19	(	(	PUNCT
ejpam-6129	169	20	days	day	NOUN
ejpam-6129	169	21	)	)	PUNCT
ejpam-6129	169	22	in	in	ADP
ejpam-6129	169	23	fe	fe	X
ejpam-6129	169	24	c	c	NOUN
ejpam-6129	169	25	ti	ti	NOUN
ejpam-6129	169	26	o	o	X
ejpam-6129	169	27	u	u	NOUN
ejpam-6129	169	28	s	s	PROPN
ejpam-6129	169	29	i	i	PRON
ejpam-6129	169	30	n	n	NOUN
ejpam-6129	169	31	d	d	NOUN
ejpam-6129	169	32	iv	iv	X
ejpam-6129	169	33	i	i	PROPN
ejpam-6129	169	34	d	d	PROPN
ejpam-6129	169	35	u	u	PROPN
ejpam-6129	169	36	a	a	DET
ejpam-6129	169	37	ls	ls	X
ejpam-6129	169	38	(	(	PUNCT
ejpam-6129	169	39	i	i	PROPN
ejpam-6129	169	40	(	(	PUNCT
ejpam-6129	169	41	t	t	PROPN
ejpam-6129	169	42	)	)	PUNCT
ejpam-6129	169	43	)	)	PUNCT
ejpam-6129	170	1	a=1	a=1	ADP
ejpam-6129	170	2	,	,	PUNCT
ejpam-6129	170	3	b=1	b=1	X
ejpam-6129	170	4	a=50	a=50	PROPN
ejpam-6129	170	5	,	,	PUNCT
ejpam-6129	170	6	b=50	b=50	PROPN
ejpam-6129	170	7	a=1000	a=1000	PROPN
ejpam-6129	170	8	,	,	PUNCT
ejpam-6129	170	9	b=5000	b=5000	PROPN
ejpam-6129	170	10	a=10000,b=20000	a=10000,b=20000	PROPN
ejpam-6129	170	11	a=50000	a=50000	PROPN
ejpam-6129	170	12	,	,	PUNCT
ejpam-6129	170	13	b=30000	b=30000	PROPN
ejpam-6129	170	14	0	0	NUM
ejpam-6129	171	1	10	10	NUM
ejpam-6129	171	2	20	20	NUM
ejpam-6129	171	3	30	30	NUM
ejpam-6129	171	4	40	40	NUM
ejpam-6129	171	5	50	50	NUM
ejpam-6129	171	6	60	60	NUM
ejpam-6129	171	7	70	70	NUM
ejpam-6129	171	8	80	80	NUM
ejpam-6129	171	9	90	90	NUM
ejpam-6129	171	10	0	0	NUM
ejpam-6129	171	11	1000	1000	NUM
ejpam-6129	171	12	2000	2000	NUM
ejpam-6129	171	13	3000	3000	NUM
ejpam-6129	171	14	4000	4000	NUM
ejpam-6129	171	15	5000	5000	NUM
ejpam-6129	171	16	6000	6000	NUM
ejpam-6129	171	17	7000	7000	NUM
ejpam-6129	171	18	8000	8000	NUM
ejpam-6129	171	19	9000	9000	NUM
ejpam-6129	171	20	10000	10000	NUM
ejpam-6129	171	21	time	time	NOUN
ejpam-6129	171	22	(	(	PUNCT
ejpam-6129	171	23	days	day	NOUN
ejpam-6129	171	24	)	)	PUNCT
ejpam-6129	171	25	r	r	NOUN
ejpam-6129	171	26	e	e	NOUN
ejpam-6129	171	27	c	c	NOUN
ejpam-6129	171	28	o	o	X
ejpam-6129	171	29	v	v	X
ejpam-6129	171	30	e	e	X
ejpam-6129	171	31	re	re	NOUN
ejpam-6129	171	32	d	d	PROPN
ejpam-6129	171	33	i	i	PRON
ejpam-6129	171	34	n	n	PROPN
ejpam-6129	171	35	d	d	NOUN
ejpam-6129	171	36	iv	iv	X
ejpam-6129	172	1	i	i	PROPN
ejpam-6129	172	2	d	d	PROPN
ejpam-6129	172	3	u	u	PROPN
ejpam-6129	172	4	a	a	DET
ejpam-6129	172	5	ls	ls	X
ejpam-6129	172	6	(	(	PUNCT
ejpam-6129	172	7	r	r	NOUN
ejpam-6129	172	8	(	(	PUNCT
ejpam-6129	172	9	t	t	NOUN
ejpam-6129	172	10	)	)	PUNCT
ejpam-6129	172	11	)	)	PUNCT
ejpam-6129	173	1	a=1	a=1	X
ejpam-6129	173	2	,	,	PUNCT
ejpam-6129	173	3	b=1	b=1	X
ejpam-6129	173	4	a=50	a=50	PROPN
ejpam-6129	173	5	,	,	PUNCT
ejpam-6129	173	6	b=50	b=50	PROPN
ejpam-6129	173	7	a=1000	a=1000	PROPN
ejpam-6129	173	8	,	,	PUNCT
ejpam-6129	173	9	b=5000	b=5000	PROPN
ejpam-6129	173	10	a=10000,b=20000	a=10000,b=20000	PROPN
ejpam-6129	173	11	a=50000	a=50000	PROPN
ejpam-6129	173	12	,	,	PUNCT
ejpam-6129	173	13	b=30000	b=30000	PROPN
ejpam-6129	173	14	figure	figure	VERB
ejpam-6129	173	15	4	4	NUM
ejpam-6129	173	16	:	:	PUNCT
ejpam-6129	173	17	effect	effect	NOUN
ejpam-6129	173	18	of	of	ADP
ejpam-6129	173	19	optimal	optimal	ADJ
ejpam-6129	173	20	vaccination	vaccination	NOUN
ejpam-6129	173	21	and	and	CCONJ
ejpam-6129	173	22	treatment	treatment	NOUN
ejpam-6129	173	23	strategies	strategy	NOUN
ejpam-6129	173	24	for	for	ADP
ejpam-6129	173	25	various	various	ADJ
ejpam-6129	173	26	values	value	NOUN
ejpam-6129	173	27	of	of	ADP
ejpam-6129	173	28	the	the	DET
ejpam-6129	173	29	balancing	balancing	NOUN
ejpam-6129	173	30	factors	factor	NOUN
ejpam-6129	173	31	a	a	PRON
ejpam-6129	173	32	and	and	CCONJ
ejpam-6129	173	33	b.	b.	PROPN
ejpam-6129	174	1	another	another	DET
ejpam-6129	174	2	scenario	scenario	NOUN
ejpam-6129	174	3	is	be	AUX
ejpam-6129	174	4	considered	consider	VERB
ejpam-6129	174	5	to	to	PART
ejpam-6129	174	6	compare	compare	VERB
ejpam-6129	174	7	the	the	DET
ejpam-6129	174	8	effect	effect	NOUN
ejpam-6129	174	9	of	of	ADP
ejpam-6129	174	10	applying	apply	VERB
ejpam-6129	174	11	the	the	DET
ejpam-6129	174	12	vaccination	vaccination	NOUN
ejpam-6129	174	13	and	and	CCONJ
ejpam-6129	174	14	treatment	treatment	NOUN
ejpam-6129	174	15	together	together	ADV
ejpam-6129	174	16	,	,	PUNCT
ejpam-6129	174	17	or	or	CCONJ
ejpam-6129	174	18	applying	apply	VERB
ejpam-6129	174	19	the	the	DET
ejpam-6129	174	20	vaccination	vaccination	NOUN
ejpam-6129	174	21	only	only	ADV
ejpam-6129	174	22	,	,	PUNCT
ejpam-6129	174	23	or	or	CCONJ
ejpam-6129	174	24	applying	apply	VERB
ejpam-6129	174	25	the	the	DET
ejpam-6129	174	26	treatment	treatment	NOUN
ejpam-6129	174	27	only	only	ADV
ejpam-6129	174	28	,	,	PUNCT
ejpam-6129	174	29	on	on	ADP
ejpam-6129	174	30	the	the	DET
ejpam-6129	174	31	solutions	solution	NOUN
ejpam-6129	174	32	of	of	ADP
ejpam-6129	174	33	the	the	DET
ejpam-6129	174	34	state	state	NOUN
ejpam-6129	174	35	system	system	NOUN
ejpam-6129	174	36	(	(	PUNCT
ejpam-6129	174	37	1	1	X
ejpam-6129	174	38	)	)	PUNCT
ejpam-6129	174	39	when	when	SCONJ
ejpam-6129	174	40	the	the	DET
ejpam-6129	174	41	values	value	NOUN
ejpam-6129	174	42	for	for	ADP
ejpam-6129	174	43	the	the	DET
ejpam-6129	174	44	balancing	balancing	NOUN
ejpam-6129	174	45	factors	factor	NOUN
ejpam-6129	174	46	a	a	PRON
ejpam-6129	174	47	and	and	CCONJ
ejpam-6129	174	48	b	b	NOUN
ejpam-6129	174	49	are	be	AUX
ejpam-6129	174	50	chosen	choose	VERB
ejpam-6129	174	51	to	to	PART
ejpam-6129	174	52	be	be	AUX
ejpam-6129	174	53	5000	5000	NUM
ejpam-6129	174	54	.	.	PUNCT
ejpam-6129	175	1	as	as	SCONJ
ejpam-6129	175	2	can	can	AUX
ejpam-6129	175	3	be	be	AUX
ejpam-6129	175	4	seen	see	VERB
ejpam-6129	175	5	in	in	ADP
ejpam-6129	175	6	figure	figure	NOUN
ejpam-6129	175	7	5	5	NUM
ejpam-6129	175	8	,	,	PUNCT
ejpam-6129	175	9	when	when	SCONJ
ejpam-6129	175	10	β	β	X
ejpam-6129	175	11	=	=	VERB
ejpam-6129	175	12	0.13699	0.13699	NUM
ejpam-6129	175	13	using	use	VERB
ejpam-6129	175	14	both	both	PRON
ejpam-6129	175	15	controls	control	NOUN
ejpam-6129	175	16	u1	u1	NOUN
ejpam-6129	175	17	and	and	CCONJ
ejpam-6129	175	18	u2	u2	PROPN
ejpam-6129	175	19	together	together	ADV
ejpam-6129	175	20	having	have	VERB
ejpam-6129	175	21	the	the	DET
ejpam-6129	175	22	same	same	ADJ
ejpam-6129	175	23	effect	effect	NOUN
ejpam-6129	175	24	as	as	ADP
ejpam-6129	175	25	using	use	VERB
ejpam-6129	175	26	the	the	DET
ejpam-6129	175	27	first	first	ADJ
ejpam-6129	175	28	control	control	NOUN
ejpam-6129	175	29	u1	u1	NOUN
ejpam-6129	175	30	only	only	ADV
ejpam-6129	175	31	.	.	PUNCT
ejpam-6129	176	1	we	we	PRON
ejpam-6129	176	2	further	far	ADV
ejpam-6129	176	3	notice	notice	VERB
ejpam-6129	176	4	that	that	SCONJ
ejpam-6129	176	5	inserting	insert	VERB
ejpam-6129	176	6	both	both	PRON
ejpam-6129	176	7	controls	control	NOUN
ejpam-6129	176	8	u1	u1	NOUN
ejpam-6129	176	9	and	and	CCONJ
ejpam-6129	176	10	u2	u2	PROPN
ejpam-6129	176	11	together	together	ADV
ejpam-6129	176	12	is	be	AUX
ejpam-6129	176	13	better	well	ADJ
ejpam-6129	176	14	than	than	ADP
ejpam-6129	176	15	using	use	VERB
ejpam-6129	176	16	the	the	DET
ejpam-6129	176	17	control	control	NOUN
ejpam-6129	176	18	u2	u2	NOUN
ejpam-6129	176	19	only	only	ADV
ejpam-6129	176	20	.	.	PUNCT
ejpam-6129	177	1	this	this	PRON
ejpam-6129	177	2	suggests	suggest	VERB
ejpam-6129	177	3	that	that	SCONJ
ejpam-6129	177	4	the	the	DET
ejpam-6129	177	5	effect	effect	NOUN
ejpam-6129	177	6	of	of	ADP
ejpam-6129	177	7	vaccination	vaccination	NOUN
ejpam-6129	177	8	and	and	CCONJ
ejpam-6129	177	9	treatment	treatment	NOUN
ejpam-6129	177	10	applied	apply	VERB
ejpam-6129	177	11	together	together	ADV
ejpam-6129	177	12	on	on	ADP
ejpam-6129	177	13	the	the	DET
ejpam-6129	177	14	model	model	NOUN
ejpam-6129	177	15	is	be	AUX
ejpam-6129	177	16	the	the	DET
ejpam-6129	177	17	same	same	ADJ
ejpam-6129	177	18	as	as	ADP
ejpam-6129	177	19	applying	apply	VERB
ejpam-6129	177	20	the	the	DET
ejpam-6129	177	21	vaccination	vaccination	NOUN
ejpam-6129	177	22	control	control	NOUN
ejpam-6129	177	23	only	only	ADV
ejpam-6129	177	24	.	.	PUNCT
ejpam-6129	178	1	finally	finally	ADV
ejpam-6129	178	2	,	,	PUNCT
ejpam-6129	178	3	the	the	DET
ejpam-6129	178	4	use	use	NOUN
ejpam-6129	178	5	these	these	DET
ejpam-6129	178	6	controls	control	NOUN
ejpam-6129	178	7	together	together	ADV
ejpam-6129	178	8	is	be	AUX
ejpam-6129	178	9	better	well	ADJ
ejpam-6129	178	10	as	as	SCONJ
ejpam-6129	178	11	compared	compare	VERB
ejpam-6129	178	12	to	to	ADP
ejpam-6129	178	13	the	the	DET
ejpam-6129	178	14	use	use	NOUN
ejpam-6129	178	15	of	of	ADP
ejpam-6129	178	16	treatment	treatment	NOUN
ejpam-6129	178	17	only	only	ADV
ejpam-6129	178	18	control	control	NOUN
ejpam-6129	178	19	.	.	PUNCT
ejpam-6129	179	1	therefore	therefore	ADV
ejpam-6129	179	2	,	,	PUNCT
ejpam-6129	179	3	under	under	ADP
ejpam-6129	179	4	the	the	DET
ejpam-6129	179	5	conditions	condition	NOUN
ejpam-6129	179	6	given	give	VERB
ejpam-6129	179	7	in	in	ADP
ejpam-6129	179	8	these	these	DET
ejpam-6129	179	9	simulations	simulation	NOUN
ejpam-6129	179	10	,	,	PUNCT
ejpam-6129	179	11	it	it	PRON
ejpam-6129	179	12	is	be	AUX
ejpam-6129	179	13	better	well	ADJ
ejpam-6129	179	14	to	to	PART
ejpam-6129	179	15	consider	consider	VERB
ejpam-6129	179	16	a	a	DET
ejpam-6129	179	17	strategy	strategy	NOUN
ejpam-6129	179	18	that	that	PRON
ejpam-6129	179	19	depends	depend	VERB
ejpam-6129	179	20	on	on	ADP
ejpam-6129	179	21	the	the	DET
ejpam-6129	179	22	vaccination	vaccination	NOUN
ejpam-6129	179	23	only	only	ADV
ejpam-6129	179	24	.	.	PUNCT
ejpam-6129	180	1	s.	s.	PROPN
ejpam-6129	180	2	a.	a.	PROPN
ejpam-6129	180	3	mohamed	mohamed	PROPN
ejpam-6129	180	4	et	et	PROPN
ejpam-6129	180	5	al	al	PROPN
ejpam-6129	180	6	.	.	PUNCT
ejpam-6129	180	7	/	/	SYM
ejpam-6129	180	8	eur	eur	PROPN
ejpam-6129	180	9	.	.	PUNCT
ejpam-6129	181	1	j.	j.	PROPN
ejpam-6129	181	2	pure	pure	PROPN
ejpam-6129	181	3	appl	appl	PROPN
ejpam-6129	181	4	.	.	PROPN
ejpam-6129	181	5	math	math	PROPN
ejpam-6129	181	6	,	,	PUNCT
ejpam-6129	181	7	18	18	NUM
ejpam-6129	181	8	(	(	PUNCT
ejpam-6129	181	9	3	3	NUM
ejpam-6129	181	10	)	)	PUNCT
ejpam-6129	181	11	(	(	PUNCT
ejpam-6129	181	12	2025	2025	NUM
ejpam-6129	181	13	)	)	PUNCT
ejpam-6129	181	14	,	,	PUNCT
ejpam-6129	181	15	6129	6129	NUM
ejpam-6129	181	16	11	11	NUM
ejpam-6129	181	17	of	of	ADP
ejpam-6129	181	18	17	17	NUM
ejpam-6129	181	19	0	0	NUM
ejpam-6129	181	20	10	10	NUM
ejpam-6129	181	21	20	20	NUM
ejpam-6129	181	22	30	30	NUM
ejpam-6129	181	23	40	40	NUM
ejpam-6129	181	24	50	50	NUM
ejpam-6129	181	25	60	60	NUM
ejpam-6129	181	26	70	70	NUM
ejpam-6129	181	27	80	80	NUM
ejpam-6129	181	28	90	90	NUM
ejpam-6129	181	29	0	0	NUM
ejpam-6129	181	30	1000	1000	NUM
ejpam-6129	181	31	2000	2000	NUM
ejpam-6129	181	32	3000	3000	NUM
ejpam-6129	181	33	4000	4000	NUM
ejpam-6129	181	34	5000	5000	NUM
ejpam-6129	181	35	6000	6000	NUM
ejpam-6129	181	36	7000	7000	NUM
ejpam-6129	181	37	8000	8000	NUM
ejpam-6129	181	38	9000	9000	NUM
ejpam-6129	181	39	time	time	NOUN
ejpam-6129	181	40	(	(	PUNCT
ejpam-6129	181	41	days	day	NOUN
ejpam-6129	181	42	)	)	PUNCT
ejpam-6129	181	43	s	s	PART
ejpam-6129	181	44	u	u	NOUN
ejpam-6129	181	45	s	s	PRON
ejpam-6129	181	46	c	c	NOUN
ejpam-6129	181	47	e	e	NOUN
ejpam-6129	181	48	p	p	X
ejpam-6129	181	49	ti	ti	PROPN
ejpam-6129	181	50	b	b	X
ejpam-6129	181	51	le	le	X
ejpam-6129	181	52	i	i	PRON
ejpam-6129	182	1	n	n	VERB
ejpam-6129	182	2	d	d	NOUN
ejpam-6129	182	3	iv	iv	X
ejpam-6129	183	1	i	i	PROPN
ejpam-6129	183	2	d	d	PROPN
ejpam-6129	183	3	u	u	PROPN
ejpam-6129	183	4	a	a	DET
ejpam-6129	183	5	ls	ls	X
ejpam-6129	183	6	(	(	PUNCT
ejpam-6129	183	7	s	s	X
ejpam-6129	183	8	(	(	PUNCT
ejpam-6129	183	9	t	t	NOUN
ejpam-6129	183	10	)	)	PUNCT
ejpam-6129	183	11	)	)	PUNCT
ejpam-6129	184	1	u	u	NOUN
ejpam-6129	184	2	1	1	NUM
ejpam-6129	184	3	>	>	SYM
ejpam-6129	184	4	0	0	NUM
ejpam-6129	184	5	,	,	PUNCT
ejpam-6129	184	6	u	u	NOUN
ejpam-6129	184	7	2	2	NUM
ejpam-6129	184	8	>	>	SYM
ejpam-6129	184	9	0	0	NUM
ejpam-6129	184	10	u	u	NOUN
ejpam-6129	184	11	1	1	NUM
ejpam-6129	184	12	>	>	SYM
ejpam-6129	184	13	0	0	NUM
ejpam-6129	184	14	,	,	PUNCT
ejpam-6129	184	15	u	u	NOUN
ejpam-6129	184	16	2	2	NUM
ejpam-6129	184	17	=	=	SYM
ejpam-6129	184	18	0	0	NUM
ejpam-6129	184	19	u	u	NOUN
ejpam-6129	184	20	1	1	NUM
ejpam-6129	184	21	=	=	SYM
ejpam-6129	184	22	0	0	NUM
ejpam-6129	184	23	,	,	PUNCT
ejpam-6129	184	24	u	u	NOUN
ejpam-6129	184	25	2	2	NUM
ejpam-6129	184	26	>	>	SYM
ejpam-6129	184	27	0	0	NUM
ejpam-6129	184	28	0	0	NUM
ejpam-6129	184	29	10	10	NUM
ejpam-6129	184	30	20	20	NUM
ejpam-6129	184	31	30	30	NUM
ejpam-6129	184	32	40	40	NUM
ejpam-6129	184	33	50	50	NUM
ejpam-6129	184	34	60	60	NUM
ejpam-6129	184	35	70	70	NUM
ejpam-6129	184	36	80	80	NUM
ejpam-6129	184	37	90	90	NUM
ejpam-6129	184	38	0	0	NUM
ejpam-6129	184	39	200	200	NUM
ejpam-6129	184	40	400	400	NUM
ejpam-6129	184	41	600	600	NUM
ejpam-6129	184	42	800	800	NUM
ejpam-6129	184	43	1000	1000	NUM
ejpam-6129	184	44	1200	1200	NUM
ejpam-6129	184	45	1400	1400	NUM
ejpam-6129	184	46	1600	1600	NUM
ejpam-6129	184	47	1800	1800	NUM
ejpam-6129	184	48	2000	2000	NUM
ejpam-6129	184	49	time	time	NOUN
ejpam-6129	184	50	(	(	PUNCT
ejpam-6129	184	51	days	day	NOUN
ejpam-6129	184	52	)	)	PUNCT
ejpam-6129	184	53	c	c	PROPN
ejpam-6129	184	54	a	a	DET
ejpam-6129	184	55	rr	rr	X
ejpam-6129	184	56	ie	ie	ADP
ejpam-6129	184	57	r	r	NOUN
ejpam-6129	184	58	in	in	ADP
ejpam-6129	184	59	d	d	NOUN
ejpam-6129	184	60	iv	iv	INTJ
ejpam-6129	184	61	i	i	PROPN
ejpam-6129	184	62	d	d	PROPN
ejpam-6129	184	63	u	u	PROPN
ejpam-6129	184	64	a	a	DET
ejpam-6129	184	65	ls	ls	X
ejpam-6129	184	66	(	(	PUNCT
ejpam-6129	184	67	c	c	PROPN
ejpam-6129	184	68	(	(	PUNCT
ejpam-6129	184	69	t	t	PROPN
ejpam-6129	184	70	)	)	PUNCT
ejpam-6129	184	71	)	)	PUNCT
ejpam-6129	185	1	u	u	NOUN
ejpam-6129	185	2	1	1	NUM
ejpam-6129	185	3	>	>	SYM
ejpam-6129	185	4	0	0	NUM
ejpam-6129	185	5	,	,	PUNCT
ejpam-6129	185	6	u	u	NOUN
ejpam-6129	185	7	2	2	NUM
ejpam-6129	185	8	>	>	SYM
ejpam-6129	185	9	0	0	NUM
ejpam-6129	185	10	u	u	NOUN
ejpam-6129	185	11	1	1	NUM
ejpam-6129	185	12	>	>	SYM
ejpam-6129	185	13	0	0	NUM
ejpam-6129	185	14	,	,	PUNCT
ejpam-6129	185	15	u	u	NOUN
ejpam-6129	185	16	2	2	NUM
ejpam-6129	185	17	=	=	SYM
ejpam-6129	185	18	0	0	NUM
ejpam-6129	185	19	u	u	NOUN
ejpam-6129	185	20	1	1	NUM
ejpam-6129	185	21	=	=	SYM
ejpam-6129	185	22	0	0	NUM
ejpam-6129	185	23	,	,	PUNCT
ejpam-6129	185	24	u	u	NOUN
ejpam-6129	185	25	2	2	NUM
ejpam-6129	185	26	>	>	SYM
ejpam-6129	185	27	0	0	NUM
ejpam-6129	185	28	0	0	NUM
ejpam-6129	185	29	10	10	NUM
ejpam-6129	185	30	20	20	NUM
ejpam-6129	185	31	30	30	NUM
ejpam-6129	185	32	40	40	NUM
ejpam-6129	185	33	50	50	NUM
ejpam-6129	185	34	60	60	NUM
ejpam-6129	185	35	70	70	NUM
ejpam-6129	185	36	80	80	NUM
ejpam-6129	185	37	90	90	NUM
ejpam-6129	185	38	0	0	NUM
ejpam-6129	185	39	1	1	NUM
ejpam-6129	185	40	2	2	NUM
ejpam-6129	185	41	3	3	NUM
ejpam-6129	185	42	4	4	NUM
ejpam-6129	185	43	5	5	NUM
ejpam-6129	185	44	6	6	NUM
ejpam-6129	185	45	7	7	NUM
ejpam-6129	185	46	time	time	NOUN
ejpam-6129	185	47	(	(	PUNCT
ejpam-6129	185	48	days	day	NOUN
ejpam-6129	185	49	)	)	PUNCT
ejpam-6129	185	50	in	in	ADP
ejpam-6129	185	51	fe	fe	X
ejpam-6129	185	52	c	c	NOUN
ejpam-6129	185	53	ti	ti	NOUN
ejpam-6129	185	54	o	o	X
ejpam-6129	185	55	u	u	NOUN
ejpam-6129	185	56	s	s	PROPN
ejpam-6129	185	57	i	i	PRON
ejpam-6129	185	58	n	n	NOUN
ejpam-6129	185	59	d	d	NOUN
ejpam-6129	185	60	iv	iv	X
ejpam-6129	186	1	i	i	PROPN
ejpam-6129	186	2	d	d	PROPN
ejpam-6129	186	3	u	u	PROPN
ejpam-6129	186	4	a	a	DET
ejpam-6129	186	5	ls	ls	X
ejpam-6129	186	6	(	(	PUNCT
ejpam-6129	186	7	i	i	PROPN
ejpam-6129	186	8	(	(	PUNCT
ejpam-6129	186	9	t	t	PROPN
ejpam-6129	186	10	)	)	PUNCT
ejpam-6129	186	11	)	)	PUNCT
ejpam-6129	187	1	u	u	NOUN
ejpam-6129	187	2	1	1	NUM
ejpam-6129	187	3	>	>	SYM
ejpam-6129	187	4	0	0	NUM
ejpam-6129	187	5	,	,	PUNCT
ejpam-6129	187	6	u	u	NOUN
ejpam-6129	187	7	2	2	NUM
ejpam-6129	187	8	>	>	SYM
ejpam-6129	187	9	0	0	NUM
ejpam-6129	187	10	u	u	NOUN
ejpam-6129	187	11	1	1	NUM
ejpam-6129	187	12	>	>	SYM
ejpam-6129	187	13	0	0	NUM
ejpam-6129	187	14	,	,	PUNCT
ejpam-6129	187	15	u	u	NOUN
ejpam-6129	187	16	2	2	NUM
ejpam-6129	187	17	=	=	SYM
ejpam-6129	187	18	0	0	NUM
ejpam-6129	187	19	u	u	NOUN
ejpam-6129	187	20	1	1	NUM
ejpam-6129	187	21	=	=	SYM
ejpam-6129	187	22	0	0	NUM
ejpam-6129	187	23	,	,	PUNCT
ejpam-6129	187	24	u	u	NOUN
ejpam-6129	187	25	2	2	NUM
ejpam-6129	187	26	>	>	SYM
ejpam-6129	187	27	0	0	NUM
ejpam-6129	187	28	0	0	NUM
ejpam-6129	187	29	10	10	NUM
ejpam-6129	187	30	20	20	NUM
ejpam-6129	187	31	30	30	NUM
ejpam-6129	187	32	40	40	NUM
ejpam-6129	187	33	50	50	NUM
ejpam-6129	187	34	60	60	NUM
ejpam-6129	187	35	70	70	NUM
ejpam-6129	187	36	80	80	NUM
ejpam-6129	187	37	90	90	NUM
ejpam-6129	187	38	0	0	NUM
ejpam-6129	187	39	1000	1000	NUM
ejpam-6129	187	40	2000	2000	NUM
ejpam-6129	187	41	3000	3000	NUM
ejpam-6129	187	42	4000	4000	NUM
ejpam-6129	187	43	5000	5000	NUM
ejpam-6129	187	44	6000	6000	NUM
ejpam-6129	187	45	7000	7000	NUM
ejpam-6129	187	46	8000	8000	NUM
ejpam-6129	187	47	9000	9000	NUM
ejpam-6129	187	48	10000	10000	NUM
ejpam-6129	187	49	time	time	NOUN
ejpam-6129	187	50	(	(	PUNCT
ejpam-6129	187	51	days	day	NOUN
ejpam-6129	187	52	)	)	PUNCT
ejpam-6129	188	1	r	r	NOUN
ejpam-6129	188	2	e	e	NOUN
ejpam-6129	188	3	c	c	NOUN
ejpam-6129	188	4	o	o	X
ejpam-6129	188	5	v	v	X
ejpam-6129	188	6	e	e	X
ejpam-6129	188	7	re	re	NOUN
ejpam-6129	188	8	d	d	PROPN
ejpam-6129	188	9	i	i	PRON
ejpam-6129	188	10	n	n	PROPN
ejpam-6129	188	11	d	d	NOUN
ejpam-6129	188	12	iv	iv	X
ejpam-6129	188	13	i	i	PROPN
ejpam-6129	188	14	d	d	PROPN
ejpam-6129	188	15	u	u	PROPN
ejpam-6129	188	16	a	a	DET
ejpam-6129	188	17	ls	ls	X
ejpam-6129	188	18	(	(	PUNCT
ejpam-6129	188	19	r	r	NOUN
ejpam-6129	188	20	(	(	PUNCT
ejpam-6129	188	21	t	t	NOUN
ejpam-6129	188	22	)	)	PUNCT
ejpam-6129	188	23	)	)	PUNCT
ejpam-6129	189	1	u	u	NOUN
ejpam-6129	189	2	1	1	NUM
ejpam-6129	189	3	>	>	SYM
ejpam-6129	189	4	0	0	NUM
ejpam-6129	189	5	,	,	PUNCT
ejpam-6129	189	6	u	u	NOUN
ejpam-6129	189	7	2	2	NUM
ejpam-6129	189	8	>	>	SYM
ejpam-6129	189	9	0	0	NUM
ejpam-6129	189	10	u	u	NOUN
ejpam-6129	189	11	1	1	NUM
ejpam-6129	189	12	>	>	SYM
ejpam-6129	189	13	0	0	NUM
ejpam-6129	189	14	,	,	PUNCT
ejpam-6129	189	15	u	u	NOUN
ejpam-6129	189	16	2	2	NUM
ejpam-6129	189	17	=	=	SYM
ejpam-6129	189	18	0	0	NUM
ejpam-6129	189	19	u	u	NOUN
ejpam-6129	189	20	1	1	NUM
ejpam-6129	189	21	=	=	SYM
ejpam-6129	189	22	0	0	NUM
ejpam-6129	189	23	,	,	PUNCT
ejpam-6129	189	24	u	u	NOUN
ejpam-6129	189	25	2	2	NUM
ejpam-6129	189	26	>	>	SYM
ejpam-6129	189	27	0	0	NUM
ejpam-6129	189	28	figure	figure	NOUN
ejpam-6129	189	29	5	5	NUM
ejpam-6129	189	30	:	:	PUNCT
ejpam-6129	189	31	effect	effect	NOUN
ejpam-6129	189	32	of	of	ADP
ejpam-6129	189	33	optimal	optimal	ADJ
ejpam-6129	189	34	vaccination	vaccination	NOUN
ejpam-6129	189	35	and	and	CCONJ
ejpam-6129	189	36	treatment	treatment	NOUN
ejpam-6129	189	37	strategies	strategy	NOUN
ejpam-6129	189	38	used	use	VERB
ejpam-6129	189	39	together	together	ADV
ejpam-6129	189	40	as	as	SCONJ
ejpam-6129	189	41	compared	compare	VERB
ejpam-6129	189	42	to	to	ADP
ejpam-6129	189	43	using	use	VERB
ejpam-6129	189	44	only	only	ADJ
ejpam-6129	189	45	vaccination	vaccination	NOUN
ejpam-6129	189	46	or	or	CCONJ
ejpam-6129	189	47	treatment	treatment	NOUN
ejpam-6129	189	48	strategies	strategy	NOUN
ejpam-6129	189	49	.	.	PUNCT
ejpam-6129	190	1	other	other	ADJ
ejpam-6129	190	2	parameters	parameter	NOUN
ejpam-6129	190	3	are	be	AUX
ejpam-6129	190	4	taken	take	VERB
ejpam-6129	190	5	as	as	ADP
ejpam-6129	190	6	a	a	DET
ejpam-6129	190	7	=	=	SYM
ejpam-6129	190	8	5000	5000	NUM
ejpam-6129	190	9	,	,	PUNCT
ejpam-6129	190	10	b	b	X
ejpam-6129	190	11	=	=	SYM
ejpam-6129	190	12	5000	5000	NUM
ejpam-6129	190	13	and	and	CCONJ
ejpam-6129	190	14	β	β	X
ejpam-6129	190	15	=	=	SYM
ejpam-6129	190	16	0.13699	0.13699	NUM
ejpam-6129	190	17	.	.	PUNCT
ejpam-6129	191	1	to	to	PART
ejpam-6129	191	2	further	far	ADV
ejpam-6129	191	3	corroborate	corroborate	VERB
ejpam-6129	191	4	this	this	DET
ejpam-6129	191	5	assertion	assertion	NOUN
ejpam-6129	191	6	,	,	PUNCT
ejpam-6129	191	7	we	we	PRON
ejpam-6129	191	8	consider	consider	VERB
ejpam-6129	191	9	three	three	NUM
ejpam-6129	191	10	other	other	ADJ
ejpam-6129	191	11	values	value	NOUN
ejpam-6129	191	12	of	of	ADP
ejpam-6129	191	13	β	β	PRON
ejpam-6129	191	14	and	and	CCONJ
ejpam-6129	191	15	repeat	repeat	VERB
ejpam-6129	191	16	the	the	DET
ejpam-6129	191	17	simulations	simulation	NOUN
ejpam-6129	191	18	,	,	PUNCT
ejpam-6129	191	19	results	result	NOUN
ejpam-6129	191	20	of	of	ADP
ejpam-6129	191	21	which	which	PRON
ejpam-6129	191	22	are	be	AUX
ejpam-6129	191	23	indicated	indicate	VERB
ejpam-6129	191	24	in	in	ADP
ejpam-6129	191	25	figure	figure	NOUN
ejpam-6129	191	26	6	6	NUM
ejpam-6129	191	27	(	(	PUNCT
ejpam-6129	191	28	for	for	ADP
ejpam-6129	191	29	β	β	X
ejpam-6129	191	30	=	=	SYM
ejpam-6129	191	31	0.24658	0.24658	NUM
ejpam-6129	191	32	)	)	PUNCT
ejpam-6129	191	33	,	,	PUNCT
ejpam-6129	191	34	figure	figure	VERB
ejpam-6129	191	35	7	7	NUM
ejpam-6129	191	36	(	(	PUNCT
ejpam-6129	191	37	for	for	ADP
ejpam-6129	191	38	β	β	X
ejpam-6129	191	39	=	=	SYM
ejpam-6129	191	40	0.35616	0.35616	NUM
ejpam-6129	191	41	)	)	PUNCT
ejpam-6129	191	42	and	and	CCONJ
ejpam-6129	191	43	figure	figure	VERB
ejpam-6129	191	44	8	8	NUM
ejpam-6129	191	45	(	(	PUNCT
ejpam-6129	191	46	for	for	ADP
ejpam-6129	191	47	β	β	X
ejpam-6129	191	48	=	=	SYM
ejpam-6129	191	49	0.54795	0.54795	NUM
ejpam-6129	191	50	)	)	PUNCT
ejpam-6129	191	51	.	.	PUNCT
ejpam-6129	192	1	it	it	PRON
ejpam-6129	192	2	is	be	AUX
ejpam-6129	192	3	clear	clear	ADJ
ejpam-6129	192	4	that	that	SCONJ
ejpam-6129	192	5	using	use	VERB
ejpam-6129	192	6	only	only	ADV
ejpam-6129	192	7	the	the	DET
ejpam-6129	192	8	second	second	ADJ
ejpam-6129	192	9	control	control	NOUN
ejpam-6129	192	10	u2	u2	NOUN
ejpam-6129	192	11	does	do	AUX
ejpam-6129	192	12	not	not	PART
ejpam-6129	192	13	give	give	VERB
ejpam-6129	192	14	better	well	ADJ
ejpam-6129	192	15	results	result	NOUN
ejpam-6129	192	16	as	as	ADP
ejpam-6129	192	17	compared	compare	VERB
ejpam-6129	192	18	to	to	ADP
ejpam-6129	192	19	using	use	VERB
ejpam-6129	192	20	u1	u1	NOUN
ejpam-6129	192	21	only	only	ADV
ejpam-6129	192	22	or	or	CCONJ
ejpam-6129	192	23	using	use	VERB
ejpam-6129	192	24	both	both	PRON
ejpam-6129	192	25	of	of	ADP
ejpam-6129	192	26	u1	u1	NOUN
ejpam-6129	192	27	and	and	CCONJ
ejpam-6129	192	28	u2	u2	PROPN
ejpam-6129	192	29	.	.	PUNCT
ejpam-6129	193	1	s.	s.	PROPN
ejpam-6129	193	2	a.	a.	PROPN
ejpam-6129	193	3	mohamed	mohamed	PROPN
ejpam-6129	193	4	et	et	PROPN
ejpam-6129	193	5	al	al	PROPN
ejpam-6129	193	6	.	.	PUNCT
ejpam-6129	193	7	/	/	SYM
ejpam-6129	193	8	eur	eur	PROPN
ejpam-6129	193	9	.	.	PUNCT
ejpam-6129	194	1	j.	j.	PROPN
ejpam-6129	194	2	pure	pure	PROPN
ejpam-6129	194	3	appl	appl	PROPN
ejpam-6129	194	4	.	.	PROPN
ejpam-6129	194	5	math	math	PROPN
ejpam-6129	194	6	,	,	PUNCT
ejpam-6129	194	7	18	18	NUM
ejpam-6129	194	8	(	(	PUNCT
ejpam-6129	194	9	3	3	NUM
ejpam-6129	194	10	)	)	PUNCT
ejpam-6129	194	11	(	(	PUNCT
ejpam-6129	194	12	2025	2025	NUM
ejpam-6129	194	13	)	)	PUNCT
ejpam-6129	194	14	,	,	PUNCT
ejpam-6129	194	15	6129	6129	NUM
ejpam-6129	194	16	12	12	NUM
ejpam-6129	194	17	of	of	ADP
ejpam-6129	194	18	17	17	NUM
ejpam-6129	194	19	0	0	NUM
ejpam-6129	194	20	10	10	NUM
ejpam-6129	194	21	20	20	NUM
ejpam-6129	194	22	30	30	NUM
ejpam-6129	194	23	40	40	NUM
ejpam-6129	194	24	50	50	NUM
ejpam-6129	194	25	60	60	NUM
ejpam-6129	194	26	70	70	NUM
ejpam-6129	194	27	80	80	NUM
ejpam-6129	194	28	90	90	NUM
ejpam-6129	194	29	0	0	NUM
ejpam-6129	194	30	1000	1000	NUM
ejpam-6129	194	31	2000	2000	NUM
ejpam-6129	194	32	3000	3000	NUM
ejpam-6129	194	33	4000	4000	NUM
ejpam-6129	194	34	5000	5000	NUM
ejpam-6129	194	35	6000	6000	NUM
ejpam-6129	194	36	7000	7000	NUM
ejpam-6129	194	37	8000	8000	NUM
ejpam-6129	194	38	9000	9000	NUM
ejpam-6129	194	39	time	time	NOUN
ejpam-6129	194	40	(	(	PUNCT
ejpam-6129	194	41	days	day	NOUN
ejpam-6129	194	42	)	)	PUNCT
ejpam-6129	194	43	s	s	PART
ejpam-6129	194	44	u	u	NOUN
ejpam-6129	194	45	s	s	PRON
ejpam-6129	194	46	c	c	NOUN
ejpam-6129	194	47	e	e	NOUN
ejpam-6129	194	48	p	p	X
ejpam-6129	194	49	ti	ti	PROPN
ejpam-6129	194	50	b	b	X
ejpam-6129	194	51	le	le	X
ejpam-6129	194	52	i	i	PRON
ejpam-6129	195	1	n	n	VERB
ejpam-6129	195	2	d	d	NOUN
ejpam-6129	195	3	iv	iv	X
ejpam-6129	196	1	i	i	PROPN
ejpam-6129	196	2	d	d	PROPN
ejpam-6129	196	3	u	u	PROPN
ejpam-6129	196	4	a	a	DET
ejpam-6129	196	5	ls	ls	X
ejpam-6129	196	6	(	(	PUNCT
ejpam-6129	196	7	s	s	X
ejpam-6129	196	8	(	(	PUNCT
ejpam-6129	196	9	t	t	NOUN
ejpam-6129	196	10	)	)	PUNCT
ejpam-6129	196	11	)	)	PUNCT
ejpam-6129	197	1	u	u	NOUN
ejpam-6129	197	2	1	1	NUM
ejpam-6129	197	3	>	>	SYM
ejpam-6129	197	4	0	0	NUM
ejpam-6129	197	5	and	and	CCONJ
ejpam-6129	197	6	u	u	NOUN
ejpam-6129	197	7	2	2	NUM
ejpam-6129	197	8	>	>	SYM
ejpam-6129	197	9	0	0	NUM
ejpam-6129	197	10	u	u	NOUN
ejpam-6129	197	11	1	1	NUM
ejpam-6129	197	12	>	>	SYM
ejpam-6129	197	13	0	0	NUM
ejpam-6129	197	14	and	and	CCONJ
ejpam-6129	197	15	u	u	NOUN
ejpam-6129	197	16	2	2	NUM
ejpam-6129	197	17	=	=	SYM
ejpam-6129	197	18	0	0	NUM
ejpam-6129	197	19	u	u	NOUN
ejpam-6129	197	20	1	1	NUM
ejpam-6129	197	21	=	=	SYM
ejpam-6129	197	22	0	0	NUM
ejpam-6129	197	23	and	and	CCONJ
ejpam-6129	197	24	u	u	NOUN
ejpam-6129	197	25	2	2	NUM
ejpam-6129	197	26	>	>	SYM
ejpam-6129	197	27	0	0	NUM
ejpam-6129	197	28	0	0	NUM
ejpam-6129	197	29	10	10	NUM
ejpam-6129	197	30	20	20	NUM
ejpam-6129	197	31	30	30	NUM
ejpam-6129	197	32	40	40	NUM
ejpam-6129	197	33	50	50	NUM
ejpam-6129	197	34	60	60	NUM
ejpam-6129	197	35	70	70	NUM
ejpam-6129	197	36	80	80	NUM
ejpam-6129	197	37	90	90	NUM
ejpam-6129	197	38	0	0	NUM
ejpam-6129	197	39	500	500	NUM
ejpam-6129	197	40	1000	1000	NUM
ejpam-6129	197	41	1500	1500	NUM
ejpam-6129	197	42	2000	2000	NUM
ejpam-6129	197	43	2500	2500	NUM
ejpam-6129	197	44	3000	3000	NUM
ejpam-6129	197	45	3500	3500	NUM
ejpam-6129	197	46	4000	4000	NUM
ejpam-6129	197	47	time	time	NOUN
ejpam-6129	197	48	(	(	PUNCT
ejpam-6129	197	49	days	day	NOUN
ejpam-6129	197	50	)	)	PUNCT
ejpam-6129	197	51	c	c	PROPN
ejpam-6129	197	52	a	a	DET
ejpam-6129	197	53	rr	rr	X
ejpam-6129	197	54	ie	ie	ADP
ejpam-6129	197	55	r	r	NOUN
ejpam-6129	197	56	in	in	ADP
ejpam-6129	197	57	d	d	NOUN
ejpam-6129	197	58	iv	iv	INTJ
ejpam-6129	197	59	i	i	PROPN
ejpam-6129	197	60	d	d	PROPN
ejpam-6129	197	61	u	u	PROPN
ejpam-6129	197	62	a	a	DET
ejpam-6129	197	63	ls	ls	X
ejpam-6129	197	64	(	(	PUNCT
ejpam-6129	197	65	c	c	PROPN
ejpam-6129	197	66	(	(	PUNCT
ejpam-6129	197	67	t	t	PROPN
ejpam-6129	197	68	)	)	PUNCT
ejpam-6129	197	69	)	)	PUNCT
ejpam-6129	198	1	u	u	NOUN
ejpam-6129	198	2	1	1	NUM
ejpam-6129	198	3	>	>	SYM
ejpam-6129	198	4	0	0	NUM
ejpam-6129	198	5	and	and	CCONJ
ejpam-6129	198	6	u	u	NOUN
ejpam-6129	198	7	2	2	NUM
ejpam-6129	198	8	>	>	SYM
ejpam-6129	198	9	0	0	NUM
ejpam-6129	198	10	u	u	NOUN
ejpam-6129	198	11	1	1	NUM
ejpam-6129	198	12	>	>	SYM
ejpam-6129	198	13	0	0	NUM
ejpam-6129	198	14	and	and	CCONJ
ejpam-6129	198	15	u	u	NOUN
ejpam-6129	198	16	2	2	NUM
ejpam-6129	198	17	=	=	SYM
ejpam-6129	198	18	0	0	NUM
ejpam-6129	198	19	u	u	NOUN
ejpam-6129	198	20	1	1	NUM
ejpam-6129	198	21	=	=	SYM
ejpam-6129	198	22	0	0	NUM
ejpam-6129	198	23	and	and	CCONJ
ejpam-6129	198	24	u	u	NOUN
ejpam-6129	198	25	2	2	NUM
ejpam-6129	198	26	>	>	SYM
ejpam-6129	198	27	0	0	NUM
ejpam-6129	198	28	0	0	NUM
ejpam-6129	198	29	10	10	NUM
ejpam-6129	198	30	20	20	NUM
ejpam-6129	198	31	30	30	NUM
ejpam-6129	198	32	40	40	NUM
ejpam-6129	198	33	50	50	NUM
ejpam-6129	198	34	60	60	NUM
ejpam-6129	198	35	70	70	NUM
ejpam-6129	198	36	80	80	NUM
ejpam-6129	198	37	90	90	NUM
ejpam-6129	198	38	0	0	NUM
ejpam-6129	198	39	2	2	NUM
ejpam-6129	198	40	4	4	NUM
ejpam-6129	198	41	6	6	NUM
ejpam-6129	198	42	8	8	NUM
ejpam-6129	198	43	10	10	NUM
ejpam-6129	198	44	12	12	NUM
ejpam-6129	198	45	time	time	NOUN
ejpam-6129	198	46	(	(	PUNCT
ejpam-6129	198	47	days	day	NOUN
ejpam-6129	198	48	)	)	PUNCT
ejpam-6129	198	49	in	in	ADP
ejpam-6129	198	50	fe	fe	X
ejpam-6129	198	51	c	c	NOUN
ejpam-6129	198	52	ti	ti	NOUN
ejpam-6129	198	53	o	o	X
ejpam-6129	198	54	u	u	NOUN
ejpam-6129	198	55	s	s	PROPN
ejpam-6129	198	56	i	i	PRON
ejpam-6129	198	57	n	n	NOUN
ejpam-6129	198	58	d	d	NOUN
ejpam-6129	198	59	iv	iv	X
ejpam-6129	199	1	i	i	PROPN
ejpam-6129	199	2	d	d	PROPN
ejpam-6129	199	3	u	u	PROPN
ejpam-6129	199	4	a	a	DET
ejpam-6129	199	5	ls	ls	X
ejpam-6129	199	6	(	(	PUNCT
ejpam-6129	199	7	i	i	PROPN
ejpam-6129	199	8	(	(	PUNCT
ejpam-6129	199	9	t	t	PROPN
ejpam-6129	199	10	)	)	PUNCT
ejpam-6129	199	11	)	)	PUNCT
ejpam-6129	200	1	u	u	NOUN
ejpam-6129	200	2	1	1	NUM
ejpam-6129	200	3	>	>	SYM
ejpam-6129	200	4	0	0	NUM
ejpam-6129	200	5	and	and	CCONJ
ejpam-6129	200	6	u	u	NOUN
ejpam-6129	200	7	2	2	NUM
ejpam-6129	200	8	>	>	SYM
ejpam-6129	200	9	0	0	NUM
ejpam-6129	200	10	u	u	NOUN
ejpam-6129	200	11	1	1	NUM
ejpam-6129	200	12	>	>	SYM
ejpam-6129	200	13	0	0	NUM
ejpam-6129	200	14	and	and	CCONJ
ejpam-6129	200	15	u	u	NOUN
ejpam-6129	200	16	2	2	NUM
ejpam-6129	200	17	=	=	SYM
ejpam-6129	200	18	0	0	NUM
ejpam-6129	200	19	u	u	NOUN
ejpam-6129	200	20	1	1	NUM
ejpam-6129	200	21	=	=	SYM
ejpam-6129	200	22	0	0	NUM
ejpam-6129	200	23	and	and	CCONJ
ejpam-6129	200	24	u	u	NOUN
ejpam-6129	200	25	2	2	NUM
ejpam-6129	200	26	>	>	SYM
ejpam-6129	200	27	0	0	NUM
ejpam-6129	200	28	0	0	NUM
ejpam-6129	200	29	10	10	NUM
ejpam-6129	200	30	20	20	NUM
ejpam-6129	200	31	30	30	NUM
ejpam-6129	200	32	40	40	NUM
ejpam-6129	200	33	50	50	NUM
ejpam-6129	200	34	60	60	NUM
ejpam-6129	200	35	70	70	NUM
ejpam-6129	200	36	80	80	NUM
ejpam-6129	200	37	90	90	NUM
ejpam-6129	200	38	0	0	NUM
ejpam-6129	200	39	1000	1000	NUM
ejpam-6129	200	40	2000	2000	NUM
ejpam-6129	200	41	3000	3000	NUM
ejpam-6129	200	42	4000	4000	NUM
ejpam-6129	200	43	5000	5000	NUM
ejpam-6129	200	44	6000	6000	NUM
ejpam-6129	200	45	7000	7000	NUM
ejpam-6129	200	46	8000	8000	NUM
ejpam-6129	200	47	9000	9000	NUM
ejpam-6129	200	48	10000	10000	NUM
ejpam-6129	200	49	time	time	NOUN
ejpam-6129	200	50	(	(	PUNCT
ejpam-6129	200	51	days	day	NOUN
ejpam-6129	200	52	)	)	PUNCT
ejpam-6129	201	1	r	r	NOUN
ejpam-6129	201	2	e	e	NOUN
ejpam-6129	201	3	c	c	NOUN
ejpam-6129	201	4	o	o	X
ejpam-6129	201	5	v	v	X
ejpam-6129	201	6	e	e	X
ejpam-6129	201	7	re	re	NOUN
ejpam-6129	201	8	d	d	PROPN
ejpam-6129	201	9	i	i	PRON
ejpam-6129	201	10	n	n	PROPN
ejpam-6129	201	11	d	d	NOUN
ejpam-6129	201	12	iv	iv	X
ejpam-6129	201	13	i	i	PROPN
ejpam-6129	201	14	d	d	PROPN
ejpam-6129	201	15	u	u	PROPN
ejpam-6129	201	16	a	a	DET
ejpam-6129	201	17	ls	ls	X
ejpam-6129	201	18	(	(	PUNCT
ejpam-6129	201	19	r	r	NOUN
ejpam-6129	201	20	(	(	PUNCT
ejpam-6129	201	21	t	t	NOUN
ejpam-6129	201	22	)	)	PUNCT
ejpam-6129	201	23	)	)	PUNCT
ejpam-6129	202	1	u	u	NOUN
ejpam-6129	202	2	1	1	NUM
ejpam-6129	202	3	>	>	SYM
ejpam-6129	202	4	0	0	NUM
ejpam-6129	202	5	and	and	CCONJ
ejpam-6129	202	6	u	u	NOUN
ejpam-6129	202	7	2	2	NUM
ejpam-6129	202	8	>	>	SYM
ejpam-6129	202	9	0	0	NUM
ejpam-6129	202	10	u	u	NOUN
ejpam-6129	202	11	1	1	NUM
ejpam-6129	202	12	>	>	SYM
ejpam-6129	202	13	0	0	NUM
ejpam-6129	202	14	and	and	CCONJ
ejpam-6129	202	15	u	u	NOUN
ejpam-6129	202	16	2	2	NUM
ejpam-6129	202	17	=	=	SYM
ejpam-6129	202	18	0	0	NUM
ejpam-6129	202	19	u	u	NOUN
ejpam-6129	202	20	1	1	NUM
ejpam-6129	202	21	=	=	SYM
ejpam-6129	202	22	0	0	NUM
ejpam-6129	202	23	and	and	CCONJ
ejpam-6129	202	24	u	u	NOUN
ejpam-6129	202	25	2	2	NUM
ejpam-6129	202	26	>	>	SYM
ejpam-6129	202	27	0	0	NUM
ejpam-6129	202	28	figure	figure	NOUN
ejpam-6129	202	29	6	6	NUM
ejpam-6129	202	30	:	:	PUNCT
ejpam-6129	202	31	effect	effect	NOUN
ejpam-6129	202	32	of	of	ADP
ejpam-6129	202	33	optimal	optimal	ADJ
ejpam-6129	202	34	vaccination	vaccination	NOUN
ejpam-6129	202	35	and	and	CCONJ
ejpam-6129	202	36	treatment	treatment	NOUN
ejpam-6129	202	37	strategies	strategy	NOUN
ejpam-6129	202	38	used	use	VERB
ejpam-6129	202	39	together	together	ADV
ejpam-6129	202	40	as	as	SCONJ
ejpam-6129	202	41	compared	compare	VERB
ejpam-6129	202	42	to	to	ADP
ejpam-6129	202	43	using	use	VERB
ejpam-6129	202	44	only	only	ADJ
ejpam-6129	202	45	vaccination	vaccination	NOUN
ejpam-6129	202	46	or	or	CCONJ
ejpam-6129	202	47	treatment	treatment	NOUN
ejpam-6129	202	48	strategies	strategy	NOUN
ejpam-6129	202	49	.	.	PUNCT
ejpam-6129	203	1	other	other	ADJ
ejpam-6129	203	2	parameters	parameter	NOUN
ejpam-6129	203	3	are	be	AUX
ejpam-6129	203	4	taken	take	VERB
ejpam-6129	203	5	as	as	ADP
ejpam-6129	203	6	a	a	DET
ejpam-6129	203	7	=	=	SYM
ejpam-6129	203	8	5000	5000	NUM
ejpam-6129	203	9	,	,	PUNCT
ejpam-6129	203	10	b	b	X
ejpam-6129	203	11	=	=	SYM
ejpam-6129	203	12	5000	5000	NUM
ejpam-6129	203	13	and	and	CCONJ
ejpam-6129	203	14	β	β	X
ejpam-6129	203	15	=	=	SYM
ejpam-6129	203	16	0.24658	0.24658	NUM
ejpam-6129	203	17	.	.	PUNCT
ejpam-6129	204	1	s.	s.	PROPN
ejpam-6129	204	2	a.	a.	PROPN
ejpam-6129	204	3	mohamed	mohamed	PROPN
ejpam-6129	204	4	et	et	PROPN
ejpam-6129	204	5	al	al	PROPN
ejpam-6129	204	6	.	.	PUNCT
ejpam-6129	204	7	/	/	SYM
ejpam-6129	204	8	eur	eur	PROPN
ejpam-6129	204	9	.	.	PUNCT
ejpam-6129	205	1	j.	j.	PROPN
ejpam-6129	205	2	pure	pure	PROPN
ejpam-6129	205	3	appl	appl	PROPN
ejpam-6129	205	4	.	.	PROPN
ejpam-6129	205	5	math	math	PROPN
ejpam-6129	205	6	,	,	PUNCT
ejpam-6129	205	7	18	18	NUM
ejpam-6129	205	8	(	(	PUNCT
ejpam-6129	205	9	3	3	NUM
ejpam-6129	205	10	)	)	PUNCT
ejpam-6129	205	11	(	(	PUNCT
ejpam-6129	205	12	2025	2025	NUM
ejpam-6129	205	13	)	)	PUNCT
ejpam-6129	205	14	,	,	PUNCT
ejpam-6129	205	15	6129	6129	NUM
ejpam-6129	205	16	13	13	NUM
ejpam-6129	205	17	of	of	ADP
ejpam-6129	205	18	17	17	NUM
ejpam-6129	205	19	0	0	NUM
ejpam-6129	205	20	10	10	NUM
ejpam-6129	205	21	20	20	NUM
ejpam-6129	205	22	30	30	NUM
ejpam-6129	205	23	40	40	NUM
ejpam-6129	205	24	50	50	NUM
ejpam-6129	205	25	60	60	NUM
ejpam-6129	205	26	70	70	NUM
ejpam-6129	205	27	80	80	NUM
ejpam-6129	205	28	90	90	NUM
ejpam-6129	205	29	0	0	NUM
ejpam-6129	205	30	1000	1000	NUM
ejpam-6129	205	31	2000	2000	NUM
ejpam-6129	205	32	3000	3000	NUM
ejpam-6129	205	33	4000	4000	NUM
ejpam-6129	205	34	5000	5000	NUM
ejpam-6129	205	35	6000	6000	NUM
ejpam-6129	205	36	7000	7000	NUM
ejpam-6129	205	37	8000	8000	NUM
ejpam-6129	205	38	9000	9000	NUM
ejpam-6129	205	39	time	time	NOUN
ejpam-6129	205	40	(	(	PUNCT
ejpam-6129	205	41	days	day	NOUN
ejpam-6129	205	42	)	)	PUNCT
ejpam-6129	205	43	s	s	PART
ejpam-6129	205	44	u	u	NOUN
ejpam-6129	205	45	s	s	PRON
ejpam-6129	205	46	c	c	NOUN
ejpam-6129	205	47	e	e	NOUN
ejpam-6129	205	48	p	p	X
ejpam-6129	205	49	ti	ti	PROPN
ejpam-6129	205	50	b	b	X
ejpam-6129	205	51	le	le	X
ejpam-6129	205	52	i	i	PRON
ejpam-6129	206	1	n	n	VERB
ejpam-6129	206	2	d	d	NOUN
ejpam-6129	206	3	iv	iv	X
ejpam-6129	207	1	i	i	PROPN
ejpam-6129	207	2	d	d	PROPN
ejpam-6129	207	3	u	u	PROPN
ejpam-6129	207	4	a	a	DET
ejpam-6129	207	5	ls	ls	X
ejpam-6129	207	6	(	(	PUNCT
ejpam-6129	207	7	s	s	X
ejpam-6129	207	8	(	(	PUNCT
ejpam-6129	207	9	t	t	NOUN
ejpam-6129	207	10	)	)	PUNCT
ejpam-6129	207	11	)	)	PUNCT
ejpam-6129	208	1	u	u	NOUN
ejpam-6129	208	2	1	1	NUM
ejpam-6129	208	3	>	>	SYM
ejpam-6129	208	4	0	0	NUM
ejpam-6129	208	5	,	,	PUNCT
ejpam-6129	208	6	u	u	NOUN
ejpam-6129	208	7	2	2	NUM
ejpam-6129	208	8	>	>	SYM
ejpam-6129	208	9	0	0	NUM
ejpam-6129	208	10	u	u	NOUN
ejpam-6129	208	11	1	1	NUM
ejpam-6129	208	12	>	>	SYM
ejpam-6129	208	13	0	0	NUM
ejpam-6129	208	14	,	,	PUNCT
ejpam-6129	208	15	u	u	NOUN
ejpam-6129	208	16	2	2	NUM
ejpam-6129	208	17	=	=	SYM
ejpam-6129	208	18	0	0	NUM
ejpam-6129	208	19	u	u	NOUN
ejpam-6129	208	20	1	1	NUM
ejpam-6129	208	21	=	=	SYM
ejpam-6129	208	22	0	0	NUM
ejpam-6129	208	23	,	,	PUNCT
ejpam-6129	208	24	u	u	NOUN
ejpam-6129	208	25	2	2	NUM
ejpam-6129	208	26	>	>	SYM
ejpam-6129	208	27	0	0	NUM
ejpam-6129	208	28	0	0	NUM
ejpam-6129	208	29	10	10	NUM
ejpam-6129	208	30	20	20	NUM
ejpam-6129	208	31	30	30	NUM
ejpam-6129	208	32	40	40	NUM
ejpam-6129	208	33	50	50	NUM
ejpam-6129	208	34	60	60	NUM
ejpam-6129	208	35	70	70	NUM
ejpam-6129	208	36	80	80	NUM
ejpam-6129	208	37	90	90	NUM
ejpam-6129	208	38	0	0	NUM
ejpam-6129	208	39	500	500	NUM
ejpam-6129	208	40	1000	1000	NUM
ejpam-6129	208	41	1500	1500	NUM
ejpam-6129	208	42	2000	2000	NUM
ejpam-6129	208	43	2500	2500	NUM
ejpam-6129	208	44	3000	3000	NUM
ejpam-6129	208	45	3500	3500	NUM
ejpam-6129	208	46	4000	4000	NUM
ejpam-6129	208	47	4500	4500	NUM
ejpam-6129	208	48	5000	5000	NUM
ejpam-6129	208	49	time	time	NOUN
ejpam-6129	208	50	(	(	PUNCT
ejpam-6129	208	51	days	day	NOUN
ejpam-6129	208	52	)	)	PUNCT
ejpam-6129	208	53	c	c	PROPN
ejpam-6129	208	54	a	a	DET
ejpam-6129	208	55	rr	rr	X
ejpam-6129	208	56	ie	ie	ADP
ejpam-6129	208	57	r	r	NOUN
ejpam-6129	208	58	in	in	ADP
ejpam-6129	208	59	d	d	NOUN
ejpam-6129	208	60	iv	iv	INTJ
ejpam-6129	208	61	i	i	PROPN
ejpam-6129	208	62	d	d	PROPN
ejpam-6129	208	63	u	u	PROPN
ejpam-6129	208	64	a	a	DET
ejpam-6129	208	65	ls	ls	X
ejpam-6129	208	66	(	(	PUNCT
ejpam-6129	208	67	c	c	PROPN
ejpam-6129	208	68	(	(	PUNCT
ejpam-6129	208	69	t	t	PROPN
ejpam-6129	208	70	)	)	PUNCT
ejpam-6129	208	71	)	)	PUNCT
ejpam-6129	209	1	u	u	NOUN
ejpam-6129	209	2	1	1	NUM
ejpam-6129	209	3	>	>	SYM
ejpam-6129	209	4	0	0	NUM
ejpam-6129	209	5	,	,	PUNCT
ejpam-6129	209	6	u	u	NOUN
ejpam-6129	209	7	2	2	NUM
ejpam-6129	209	8	>	>	SYM
ejpam-6129	209	9	0	0	NUM
ejpam-6129	209	10	u	u	NOUN
ejpam-6129	209	11	1	1	NUM
ejpam-6129	209	12	>	>	SYM
ejpam-6129	209	13	0	0	NUM
ejpam-6129	209	14	,	,	PUNCT
ejpam-6129	209	15	u	u	NOUN
ejpam-6129	209	16	2	2	NUM
ejpam-6129	209	17	=	=	SYM
ejpam-6129	209	18	0	0	NUM
ejpam-6129	209	19	u	u	NOUN
ejpam-6129	209	20	1	1	NUM
ejpam-6129	209	21	=	=	SYM
ejpam-6129	209	22	0	0	NUM
ejpam-6129	209	23	,	,	PUNCT
ejpam-6129	209	24	u	u	NOUN
ejpam-6129	209	25	2	2	NUM
ejpam-6129	209	26	>	>	SYM
ejpam-6129	209	27	0	0	NUM
ejpam-6129	209	28	0	0	NUM
ejpam-6129	209	29	10	10	NUM
ejpam-6129	209	30	20	20	NUM
ejpam-6129	209	31	30	30	NUM
ejpam-6129	209	32	40	40	NUM
ejpam-6129	209	33	50	50	NUM
ejpam-6129	209	34	60	60	NUM
ejpam-6129	209	35	70	70	NUM
ejpam-6129	209	36	80	80	NUM
ejpam-6129	209	37	90	90	NUM
ejpam-6129	209	38	0	0	NUM
ejpam-6129	209	39	5	5	NUM
ejpam-6129	209	40	10	10	NUM
ejpam-6129	209	41	15	15	NUM
ejpam-6129	209	42	time	time	NOUN
ejpam-6129	209	43	(	(	PUNCT
ejpam-6129	209	44	days	day	NOUN
ejpam-6129	209	45	)	)	PUNCT
ejpam-6129	209	46	in	in	ADP
ejpam-6129	209	47	fe	fe	X
ejpam-6129	209	48	c	c	NOUN
ejpam-6129	209	49	ti	ti	NOUN
ejpam-6129	209	50	o	o	X
ejpam-6129	209	51	u	u	NOUN
ejpam-6129	209	52	s	s	PROPN
ejpam-6129	209	53	i	i	PRON
ejpam-6129	209	54	n	n	NOUN
ejpam-6129	209	55	d	d	NOUN
ejpam-6129	209	56	iv	iv	X
ejpam-6129	210	1	i	i	PROPN
ejpam-6129	210	2	d	d	PROPN
ejpam-6129	210	3	u	u	PROPN
ejpam-6129	210	4	a	a	DET
ejpam-6129	210	5	ls	ls	X
ejpam-6129	210	6	(	(	PUNCT
ejpam-6129	210	7	i	i	PROPN
ejpam-6129	210	8	(	(	PUNCT
ejpam-6129	210	9	t	t	PROPN
ejpam-6129	210	10	)	)	PUNCT
ejpam-6129	210	11	)	)	PUNCT
ejpam-6129	211	1	u	u	NOUN
ejpam-6129	211	2	1	1	NUM
ejpam-6129	211	3	>	>	SYM
ejpam-6129	211	4	0	0	NUM
ejpam-6129	211	5	,	,	PUNCT
ejpam-6129	211	6	u	u	NOUN
ejpam-6129	211	7	2	2	NUM
ejpam-6129	211	8	>	>	SYM
ejpam-6129	211	9	0	0	NUM
ejpam-6129	211	10	u	u	NOUN
ejpam-6129	211	11	1	1	NUM
ejpam-6129	211	12	>	>	SYM
ejpam-6129	211	13	0	0	NUM
ejpam-6129	211	14	,	,	PUNCT
ejpam-6129	211	15	u	u	NOUN
ejpam-6129	211	16	2	2	NUM
ejpam-6129	211	17	=	=	SYM
ejpam-6129	211	18	0	0	NUM
ejpam-6129	211	19	u	u	NOUN
ejpam-6129	211	20	1	1	NUM
ejpam-6129	211	21	=	=	SYM
ejpam-6129	211	22	0	0	NUM
ejpam-6129	211	23	,	,	PUNCT
ejpam-6129	211	24	u	u	NOUN
ejpam-6129	211	25	2	2	NUM
ejpam-6129	211	26	>	>	SYM
ejpam-6129	211	27	0	0	NUM
ejpam-6129	211	28	0	0	NUM
ejpam-6129	211	29	10	10	NUM
ejpam-6129	211	30	20	20	NUM
ejpam-6129	211	31	30	30	NUM
ejpam-6129	211	32	40	40	NUM
ejpam-6129	211	33	50	50	NUM
ejpam-6129	211	34	60	60	NUM
ejpam-6129	211	35	70	70	NUM
ejpam-6129	211	36	80	80	NUM
ejpam-6129	211	37	90	90	NUM
ejpam-6129	211	38	0	0	NUM
ejpam-6129	211	39	1000	1000	NUM
ejpam-6129	211	40	2000	2000	NUM
ejpam-6129	211	41	3000	3000	NUM
ejpam-6129	211	42	4000	4000	NUM
ejpam-6129	211	43	5000	5000	NUM
ejpam-6129	211	44	6000	6000	NUM
ejpam-6129	211	45	7000	7000	NUM
ejpam-6129	211	46	8000	8000	NUM
ejpam-6129	211	47	9000	9000	NUM
ejpam-6129	211	48	10000	10000	NUM
ejpam-6129	211	49	time	time	NOUN
ejpam-6129	211	50	(	(	PUNCT
ejpam-6129	211	51	days	day	NOUN
ejpam-6129	211	52	)	)	PUNCT
ejpam-6129	212	1	r	r	NOUN
ejpam-6129	212	2	e	e	NOUN
ejpam-6129	212	3	c	c	NOUN
ejpam-6129	212	4	o	o	X
ejpam-6129	212	5	v	v	X
ejpam-6129	212	6	e	e	X
ejpam-6129	212	7	re	re	NOUN
ejpam-6129	212	8	d	d	PROPN
ejpam-6129	212	9	i	i	PRON
ejpam-6129	212	10	n	n	PROPN
ejpam-6129	212	11	d	d	NOUN
ejpam-6129	212	12	iv	iv	X
ejpam-6129	212	13	i	i	PROPN
ejpam-6129	212	14	d	d	PROPN
ejpam-6129	212	15	u	u	PROPN
ejpam-6129	212	16	a	a	DET
ejpam-6129	212	17	ls	ls	X
ejpam-6129	212	18	(	(	PUNCT
ejpam-6129	212	19	r	r	NOUN
ejpam-6129	212	20	(	(	PUNCT
ejpam-6129	212	21	t	t	NOUN
ejpam-6129	212	22	)	)	PUNCT
ejpam-6129	212	23	)	)	PUNCT
ejpam-6129	213	1	u	u	NOUN
ejpam-6129	213	2	1	1	NUM
ejpam-6129	213	3	>	>	SYM
ejpam-6129	213	4	0	0	NUM
ejpam-6129	213	5	,	,	PUNCT
ejpam-6129	213	6	u	u	NOUN
ejpam-6129	213	7	2	2	NUM
ejpam-6129	213	8	>	>	SYM
ejpam-6129	213	9	0	0	NUM
ejpam-6129	213	10	u	u	NOUN
ejpam-6129	213	11	1	1	NUM
ejpam-6129	213	12	>	>	SYM
ejpam-6129	213	13	0	0	NUM
ejpam-6129	213	14	,	,	PUNCT
ejpam-6129	213	15	u	u	NOUN
ejpam-6129	213	16	2	2	NUM
ejpam-6129	213	17	=	=	SYM
ejpam-6129	213	18	0	0	NUM
ejpam-6129	213	19	u	u	NOUN
ejpam-6129	213	20	1	1	NUM
ejpam-6129	213	21	=	=	SYM
ejpam-6129	213	22	0	0	NUM
ejpam-6129	213	23	,	,	PUNCT
ejpam-6129	213	24	u	u	NOUN
ejpam-6129	213	25	2	2	NUM
ejpam-6129	213	26	>	>	SYM
ejpam-6129	213	27	0	0	NUM
ejpam-6129	213	28	figure	figure	NOUN
ejpam-6129	213	29	7	7	NUM
ejpam-6129	213	30	:	:	PUNCT
ejpam-6129	213	31	effect	effect	NOUN
ejpam-6129	213	32	of	of	ADP
ejpam-6129	213	33	optimal	optimal	ADJ
ejpam-6129	213	34	vaccination	vaccination	NOUN
ejpam-6129	213	35	and	and	CCONJ
ejpam-6129	213	36	treatment	treatment	NOUN
ejpam-6129	213	37	strategies	strategy	NOUN
ejpam-6129	213	38	used	use	VERB
ejpam-6129	213	39	together	together	ADV
ejpam-6129	213	40	as	as	SCONJ
ejpam-6129	213	41	compared	compare	VERB
ejpam-6129	213	42	to	to	ADP
ejpam-6129	213	43	using	use	VERB
ejpam-6129	213	44	only	only	ADJ
ejpam-6129	213	45	vaccination	vaccination	NOUN
ejpam-6129	213	46	or	or	CCONJ
ejpam-6129	213	47	treatment	treatment	NOUN
ejpam-6129	213	48	strategies	strategy	NOUN
ejpam-6129	213	49	.	.	PUNCT
ejpam-6129	214	1	other	other	ADJ
ejpam-6129	214	2	parameters	parameter	NOUN
ejpam-6129	214	3	are	be	AUX
ejpam-6129	214	4	taken	take	VERB
ejpam-6129	214	5	as	as	ADP
ejpam-6129	214	6	a	a	DET
ejpam-6129	214	7	=	=	SYM
ejpam-6129	214	8	5000	5000	NUM
ejpam-6129	214	9	,	,	PUNCT
ejpam-6129	214	10	b	b	X
ejpam-6129	214	11	=	=	SYM
ejpam-6129	214	12	5000	5000	NUM
ejpam-6129	214	13	and	and	CCONJ
ejpam-6129	214	14	β	β	X
ejpam-6129	214	15	=	=	SYM
ejpam-6129	214	16	0.35616	0.35616	NUM
ejpam-6129	214	17	.	.	PUNCT
ejpam-6129	215	1	s.	s.	PROPN
ejpam-6129	215	2	a.	a.	PROPN
ejpam-6129	215	3	mohamed	mohamed	PROPN
ejpam-6129	215	4	et	et	PROPN
ejpam-6129	215	5	al	al	PROPN
ejpam-6129	215	6	.	.	PUNCT
ejpam-6129	215	7	/	/	SYM
ejpam-6129	215	8	eur	eur	PROPN
ejpam-6129	215	9	.	.	PUNCT
ejpam-6129	216	1	j.	j.	PROPN
ejpam-6129	216	2	pure	pure	PROPN
ejpam-6129	216	3	appl	appl	PROPN
ejpam-6129	216	4	.	.	PROPN
ejpam-6129	216	5	math	math	PROPN
ejpam-6129	216	6	,	,	PUNCT
ejpam-6129	216	7	18	18	NUM
ejpam-6129	216	8	(	(	PUNCT
ejpam-6129	216	9	3	3	NUM
ejpam-6129	216	10	)	)	PUNCT
ejpam-6129	216	11	(	(	PUNCT
ejpam-6129	216	12	2025	2025	NUM
ejpam-6129	216	13	)	)	PUNCT
ejpam-6129	216	14	,	,	PUNCT
ejpam-6129	216	15	6129	6129	NUM
ejpam-6129	216	16	14	14	NUM
ejpam-6129	216	17	of	of	ADP
ejpam-6129	216	18	17	17	NUM
ejpam-6129	216	19	0	0	NUM
ejpam-6129	216	20	10	10	NUM
ejpam-6129	216	21	20	20	NUM
ejpam-6129	216	22	30	30	NUM
ejpam-6129	216	23	40	40	NUM
ejpam-6129	216	24	50	50	NUM
ejpam-6129	216	25	60	60	NUM
ejpam-6129	216	26	70	70	NUM
ejpam-6129	216	27	80	80	NUM
ejpam-6129	216	28	90	90	NUM
ejpam-6129	216	29	0	0	NUM
ejpam-6129	216	30	1000	1000	NUM
ejpam-6129	216	31	2000	2000	NUM
ejpam-6129	216	32	3000	3000	NUM
ejpam-6129	216	33	4000	4000	NUM
ejpam-6129	216	34	5000	5000	NUM
ejpam-6129	216	35	6000	6000	NUM
ejpam-6129	216	36	7000	7000	NUM
ejpam-6129	216	37	8000	8000	NUM
ejpam-6129	216	38	9000	9000	NUM
ejpam-6129	216	39	time	time	NOUN
ejpam-6129	216	40	(	(	PUNCT
ejpam-6129	216	41	days	day	NOUN
ejpam-6129	216	42	)	)	PUNCT
ejpam-6129	216	43	s	s	PART
ejpam-6129	216	44	u	u	NOUN
ejpam-6129	216	45	s	s	PRON
ejpam-6129	216	46	c	c	NOUN
ejpam-6129	216	47	e	e	NOUN
ejpam-6129	216	48	p	p	X
ejpam-6129	216	49	ti	ti	PROPN
ejpam-6129	216	50	b	b	X
ejpam-6129	216	51	le	le	X
ejpam-6129	216	52	i	i	PRON
ejpam-6129	217	1	n	n	VERB
ejpam-6129	217	2	d	d	NOUN
ejpam-6129	217	3	iv	iv	X
ejpam-6129	218	1	i	i	PROPN
ejpam-6129	218	2	d	d	PROPN
ejpam-6129	218	3	u	u	PROPN
ejpam-6129	218	4	a	a	DET
ejpam-6129	218	5	ls	ls	X
ejpam-6129	218	6	(	(	PUNCT
ejpam-6129	218	7	s	s	X
ejpam-6129	218	8	(	(	PUNCT
ejpam-6129	218	9	t	t	NOUN
ejpam-6129	218	10	)	)	PUNCT
ejpam-6129	218	11	)	)	PUNCT
ejpam-6129	219	1	u	u	NOUN
ejpam-6129	219	2	1	1	NUM
ejpam-6129	219	3	>	>	SYM
ejpam-6129	219	4	0	0	NUM
ejpam-6129	219	5	,	,	PUNCT
ejpam-6129	219	6	u	u	NOUN
ejpam-6129	219	7	2	2	NUM
ejpam-6129	219	8	>	>	SYM
ejpam-6129	219	9	0	0	NUM
ejpam-6129	219	10	u	u	NOUN
ejpam-6129	219	11	1	1	NUM
ejpam-6129	219	12	>	>	SYM
ejpam-6129	219	13	0	0	NUM
ejpam-6129	219	14	,	,	PUNCT
ejpam-6129	219	15	u	u	NOUN
ejpam-6129	219	16	2	2	NUM
ejpam-6129	219	17	=	=	SYM
ejpam-6129	219	18	0	0	NUM
ejpam-6129	219	19	u	u	NOUN
ejpam-6129	219	20	1	1	NUM
ejpam-6129	219	21	=	=	SYM
ejpam-6129	219	22	0	0	NUM
ejpam-6129	219	23	,	,	PUNCT
ejpam-6129	219	24	u	u	NOUN
ejpam-6129	219	25	2	2	NUM
ejpam-6129	219	26	>	>	SYM
ejpam-6129	219	27	0	0	NUM
ejpam-6129	219	28	0	0	NUM
ejpam-6129	219	29	10	10	NUM
ejpam-6129	219	30	20	20	NUM
ejpam-6129	219	31	30	30	NUM
ejpam-6129	219	32	40	40	NUM
ejpam-6129	219	33	50	50	NUM
ejpam-6129	219	34	60	60	NUM
ejpam-6129	219	35	70	70	NUM
ejpam-6129	219	36	80	80	NUM
ejpam-6129	219	37	90	90	NUM
ejpam-6129	219	38	0	0	NUM
ejpam-6129	219	39	1000	1000	NUM
ejpam-6129	219	40	2000	2000	NUM
ejpam-6129	219	41	3000	3000	NUM
ejpam-6129	219	42	4000	4000	NUM
ejpam-6129	219	43	5000	5000	NUM
ejpam-6129	219	44	6000	6000	NUM
ejpam-6129	219	45	7000	7000	NUM
ejpam-6129	219	46	time	time	NOUN
ejpam-6129	219	47	(	(	PUNCT
ejpam-6129	219	48	days	day	NOUN
ejpam-6129	219	49	)	)	PUNCT
ejpam-6129	219	50	c	c	PROPN
ejpam-6129	219	51	a	a	DET
ejpam-6129	219	52	rr	rr	X
ejpam-6129	219	53	ie	ie	ADP
ejpam-6129	219	54	r	r	NOUN
ejpam-6129	219	55	in	in	ADP
ejpam-6129	219	56	d	d	NOUN
ejpam-6129	219	57	iv	iv	INTJ
ejpam-6129	219	58	i	i	PROPN
ejpam-6129	219	59	d	d	PROPN
ejpam-6129	219	60	u	u	PROPN
ejpam-6129	219	61	a	a	DET
ejpam-6129	219	62	ls	ls	X
ejpam-6129	219	63	(	(	PUNCT
ejpam-6129	219	64	c	c	PROPN
ejpam-6129	219	65	(	(	PUNCT
ejpam-6129	219	66	t	t	PROPN
ejpam-6129	219	67	)	)	PUNCT
ejpam-6129	219	68	)	)	PUNCT
ejpam-6129	220	1	u	u	NOUN
ejpam-6129	220	2	1	1	NUM
ejpam-6129	220	3	>	>	SYM
ejpam-6129	220	4	0	0	NUM
ejpam-6129	220	5	,	,	PUNCT
ejpam-6129	220	6	u	u	NOUN
ejpam-6129	220	7	2	2	NUM
ejpam-6129	220	8	>	>	SYM
ejpam-6129	220	9	0	0	NUM
ejpam-6129	220	10	u	u	NOUN
ejpam-6129	220	11	1	1	NUM
ejpam-6129	220	12	>	>	SYM
ejpam-6129	220	13	0	0	NUM
ejpam-6129	220	14	,	,	PUNCT
ejpam-6129	220	15	u	u	NOUN
ejpam-6129	220	16	2	2	NUM
ejpam-6129	220	17	=	=	SYM
ejpam-6129	220	18	0	0	NUM
ejpam-6129	220	19	u	u	NOUN
ejpam-6129	220	20	1	1	NUM
ejpam-6129	220	21	=	=	SYM
ejpam-6129	220	22	0	0	NUM
ejpam-6129	220	23	,	,	PUNCT
ejpam-6129	220	24	u	u	NOUN
ejpam-6129	220	25	2	2	NUM
ejpam-6129	220	26	>	>	SYM
ejpam-6129	220	27	0	0	NUM
ejpam-6129	220	28	0	0	NUM
ejpam-6129	220	29	10	10	NUM
ejpam-6129	220	30	20	20	NUM
ejpam-6129	220	31	30	30	NUM
ejpam-6129	220	32	40	40	NUM
ejpam-6129	220	33	50	50	NUM
ejpam-6129	220	34	60	60	NUM
ejpam-6129	220	35	70	70	NUM
ejpam-6129	220	36	80	80	NUM
ejpam-6129	220	37	90	90	NUM
ejpam-6129	220	38	0	0	NUM
ejpam-6129	220	39	2	2	NUM
ejpam-6129	220	40	4	4	NUM
ejpam-6129	220	41	6	6	NUM
ejpam-6129	220	42	8	8	NUM
ejpam-6129	220	43	10	10	NUM
ejpam-6129	220	44	12	12	NUM
ejpam-6129	220	45	14	14	NUM
ejpam-6129	220	46	16	16	NUM
ejpam-6129	220	47	18	18	NUM
ejpam-6129	220	48	time	time	NOUN
ejpam-6129	220	49	(	(	PUNCT
ejpam-6129	220	50	days	day	NOUN
ejpam-6129	220	51	)	)	PUNCT
ejpam-6129	220	52	in	in	ADP
ejpam-6129	220	53	fe	fe	X
ejpam-6129	220	54	c	c	NOUN
ejpam-6129	220	55	ti	ti	NOUN
ejpam-6129	220	56	o	o	X
ejpam-6129	220	57	u	u	NOUN
ejpam-6129	220	58	s	s	PROPN
ejpam-6129	220	59	i	i	PRON
ejpam-6129	220	60	n	n	NOUN
ejpam-6129	220	61	d	d	NOUN
ejpam-6129	220	62	iv	iv	X
ejpam-6129	221	1	i	i	PROPN
ejpam-6129	221	2	d	d	PROPN
ejpam-6129	221	3	u	u	PROPN
ejpam-6129	221	4	a	a	DET
ejpam-6129	221	5	ls	ls	X
ejpam-6129	221	6	(	(	PUNCT
ejpam-6129	221	7	i	i	PROPN
ejpam-6129	221	8	(	(	PUNCT
ejpam-6129	221	9	t	t	PROPN
ejpam-6129	221	10	)	)	PUNCT
ejpam-6129	221	11	)	)	PUNCT
ejpam-6129	222	1	u	u	NOUN
ejpam-6129	222	2	1	1	NUM
ejpam-6129	222	3	>	>	SYM
ejpam-6129	222	4	0	0	NUM
ejpam-6129	222	5	,	,	PUNCT
ejpam-6129	222	6	u	u	NOUN
ejpam-6129	222	7	2	2	NUM
ejpam-6129	222	8	>	>	SYM
ejpam-6129	222	9	0	0	NUM
ejpam-6129	222	10	u	u	NOUN
ejpam-6129	222	11	1	1	NUM
ejpam-6129	222	12	>	>	SYM
ejpam-6129	222	13	0	0	NUM
ejpam-6129	222	14	,	,	PUNCT
ejpam-6129	222	15	u	u	NOUN
ejpam-6129	222	16	2	2	NUM
ejpam-6129	222	17	=	=	SYM
ejpam-6129	222	18	0	0	NUM
ejpam-6129	222	19	u	u	NOUN
ejpam-6129	222	20	1	1	NUM
ejpam-6129	222	21	=	=	SYM
ejpam-6129	222	22	0	0	NUM
ejpam-6129	222	23	,	,	PUNCT
ejpam-6129	222	24	u	u	NOUN
ejpam-6129	222	25	2	2	NUM
ejpam-6129	222	26	>	>	SYM
ejpam-6129	222	27	0	0	NUM
ejpam-6129	222	28	0	0	NUM
ejpam-6129	222	29	10	10	NUM
ejpam-6129	222	30	20	20	NUM
ejpam-6129	222	31	30	30	NUM
ejpam-6129	222	32	40	40	NUM
ejpam-6129	222	33	50	50	NUM
ejpam-6129	222	34	60	60	NUM
ejpam-6129	222	35	70	70	NUM
ejpam-6129	222	36	80	80	NUM
ejpam-6129	222	37	90	90	NUM
ejpam-6129	222	38	0	0	NUM
ejpam-6129	222	39	1000	1000	NUM
ejpam-6129	222	40	2000	2000	NUM
ejpam-6129	222	41	3000	3000	NUM
ejpam-6129	222	42	4000	4000	NUM
ejpam-6129	222	43	5000	5000	NUM
ejpam-6129	222	44	6000	6000	NUM
ejpam-6129	222	45	7000	7000	NUM
ejpam-6129	222	46	8000	8000	NUM
ejpam-6129	222	47	9000	9000	NUM
ejpam-6129	222	48	10000	10000	NUM
ejpam-6129	222	49	time	time	NOUN
ejpam-6129	222	50	(	(	PUNCT
ejpam-6129	222	51	days	day	NOUN
ejpam-6129	222	52	)	)	PUNCT
ejpam-6129	223	1	r	r	NOUN
ejpam-6129	223	2	e	e	NOUN
ejpam-6129	223	3	c	c	NOUN
ejpam-6129	223	4	o	o	X
ejpam-6129	223	5	v	v	X
ejpam-6129	223	6	e	e	X
ejpam-6129	223	7	re	re	NOUN
ejpam-6129	223	8	d	d	PROPN
ejpam-6129	223	9	i	i	PRON
ejpam-6129	223	10	n	n	PROPN
ejpam-6129	223	11	d	d	NOUN
ejpam-6129	223	12	iv	iv	X
ejpam-6129	223	13	i	i	PROPN
ejpam-6129	223	14	d	d	PROPN
ejpam-6129	223	15	u	u	PROPN
ejpam-6129	223	16	a	a	DET
ejpam-6129	223	17	ls	ls	X
ejpam-6129	223	18	(	(	PUNCT
ejpam-6129	223	19	r	r	NOUN
ejpam-6129	223	20	(	(	PUNCT
ejpam-6129	223	21	t	t	NOUN
ejpam-6129	223	22	)	)	PUNCT
ejpam-6129	223	23	)	)	PUNCT
ejpam-6129	224	1	u	u	NOUN
ejpam-6129	224	2	1	1	NUM
ejpam-6129	224	3	>	>	SYM
ejpam-6129	224	4	0	0	NUM
ejpam-6129	224	5	,	,	PUNCT
ejpam-6129	224	6	u	u	NOUN
ejpam-6129	224	7	2	2	NUM
ejpam-6129	224	8	>	>	SYM
ejpam-6129	224	9	0	0	NUM
ejpam-6129	224	10	u	u	NOUN
ejpam-6129	224	11	1	1	NUM
ejpam-6129	224	12	>	>	SYM
ejpam-6129	224	13	0	0	NUM
ejpam-6129	224	14	,	,	PUNCT
ejpam-6129	224	15	u	u	NOUN
ejpam-6129	224	16	2	2	NUM
ejpam-6129	224	17	=	=	SYM
ejpam-6129	224	18	0	0	NUM
ejpam-6129	224	19	u	u	NOUN
ejpam-6129	224	20	1	1	NUM
ejpam-6129	224	21	=	=	SYM
ejpam-6129	224	22	0	0	NUM
ejpam-6129	224	23	,	,	PUNCT
ejpam-6129	224	24	u	u	NOUN
ejpam-6129	224	25	2	2	NUM
ejpam-6129	224	26	>	>	SYM
ejpam-6129	224	27	0	0	NUM
ejpam-6129	224	28	figure	figure	NOUN
ejpam-6129	224	29	8	8	NUM
ejpam-6129	224	30	:	:	PUNCT
ejpam-6129	224	31	effect	effect	NOUN
ejpam-6129	224	32	of	of	ADP
ejpam-6129	224	33	optimal	optimal	ADJ
ejpam-6129	224	34	vaccination	vaccination	NOUN
ejpam-6129	224	35	and	and	CCONJ
ejpam-6129	224	36	treatment	treatment	NOUN
ejpam-6129	224	37	strategies	strategy	NOUN
ejpam-6129	224	38	used	use	VERB
ejpam-6129	224	39	together	together	ADV
ejpam-6129	224	40	as	as	SCONJ
ejpam-6129	224	41	compared	compare	VERB
ejpam-6129	224	42	to	to	ADP
ejpam-6129	224	43	using	use	VERB
ejpam-6129	224	44	only	only	ADJ
ejpam-6129	224	45	vaccination	vaccination	NOUN
ejpam-6129	224	46	or	or	CCONJ
ejpam-6129	224	47	treatment	treatment	NOUN
ejpam-6129	224	48	strategies	strategy	NOUN
ejpam-6129	224	49	.	.	PUNCT
ejpam-6129	225	1	other	other	ADJ
ejpam-6129	225	2	parameters	parameter	NOUN
ejpam-6129	225	3	are	be	AUX
ejpam-6129	225	4	taken	take	VERB
ejpam-6129	225	5	as	as	ADP
ejpam-6129	225	6	a	a	DET
ejpam-6129	225	7	=	=	SYM
ejpam-6129	225	8	5000	5000	NUM
ejpam-6129	225	9	,	,	PUNCT
ejpam-6129	225	10	b	b	X
ejpam-6129	225	11	=	=	SYM
ejpam-6129	225	12	5000	5000	NUM
ejpam-6129	225	13	and	and	CCONJ
ejpam-6129	225	14	β	β	X
ejpam-6129	225	15	=	=	SYM
ejpam-6129	225	16	0.54795	0.54795	NUM
ejpam-6129	225	17	.	.	PUNCT
ejpam-6129	226	1	5	5	NUM
ejpam-6129	226	2	.	.	X
ejpam-6129	226	3	conclusion	conclusion	NOUN
ejpam-6129	226	4	in	in	ADP
ejpam-6129	226	5	this	this	DET
ejpam-6129	226	6	paper	paper	NOUN
ejpam-6129	226	7	,	,	PUNCT
ejpam-6129	226	8	we	we	PRON
ejpam-6129	226	9	considered	consider	VERB
ejpam-6129	226	10	two	two	NUM
ejpam-6129	226	11	optimal	optimal	ADJ
ejpam-6129	226	12	strategies	strategy	NOUN
ejpam-6129	226	13	associated	associate	VERB
ejpam-6129	226	14	with	with	ADP
ejpam-6129	226	15	the	the	DET
ejpam-6129	226	16	vaccination	vaccination	NOUN
ejpam-6129	226	17	and	and	CCONJ
ejpam-6129	226	18	treatment	treatment	NOUN
ejpam-6129	226	19	on	on	ADP
ejpam-6129	226	20	a	a	DET
ejpam-6129	226	21	mathematical	mathematical	ADJ
ejpam-6129	226	22	model	model	NOUN
ejpam-6129	226	23	of	of	ADP
ejpam-6129	226	24	meningitis	meningitis	NOUN
ejpam-6129	226	25	in	in	ADP
ejpam-6129	226	26	order	order	NOUN
ejpam-6129	226	27	to	to	PART
ejpam-6129	226	28	reduce	reduce	VERB
ejpam-6129	226	29	the	the	DET
ejpam-6129	226	30	numbers	number	NOUN
ejpam-6129	226	31	of	of	ADP
ejpam-6129	226	32	carrier	carrier	NOUN
ejpam-6129	226	33	and	and	CCONJ
ejpam-6129	226	34	infectious	infectious	ADJ
ejpam-6129	226	35	populations	population	NOUN
ejpam-6129	226	36	.	.	PUNCT
ejpam-6129	227	1	several	several	ADJ
ejpam-6129	227	2	scenarios	scenario	NOUN
ejpam-6129	227	3	are	be	AUX
ejpam-6129	227	4	dealt	deal	VERB
ejpam-6129	227	5	with	with	ADP
ejpam-6129	227	6	.	.	PUNCT
ejpam-6129	228	1	in	in	ADP
ejpam-6129	228	2	the	the	DET
ejpam-6129	228	3	first	first	ADJ
ejpam-6129	228	4	one	one	NUM
ejpam-6129	228	5	,	,	PUNCT
ejpam-6129	228	6	we	we	PRON
ejpam-6129	228	7	incorporated	incorporate	VERB
ejpam-6129	228	8	the	the	DET
ejpam-6129	228	9	two	two	NUM
ejpam-6129	228	10	strategies	strategy	NOUN
ejpam-6129	228	11	:	:	PUNCT
ejpam-6129	228	12	vaccination	vaccination	NOUN
ejpam-6129	228	13	and	and	CCONJ
ejpam-6129	228	14	treatment	treatment	NOUN
ejpam-6129	228	15	.	.	PUNCT
ejpam-6129	229	1	we	we	PRON
ejpam-6129	229	2	have	have	AUX
ejpam-6129	229	3	shown	show	VERB
ejpam-6129	229	4	that	that	SCONJ
ejpam-6129	229	5	both	both	DET
ejpam-6129	229	6	controls	control	NOUN
ejpam-6129	229	7	have	have	VERB
ejpam-6129	229	8	great	great	ADJ
ejpam-6129	229	9	impact	impact	NOUN
ejpam-6129	229	10	on	on	ADP
ejpam-6129	229	11	reducing	reduce	VERB
ejpam-6129	229	12	the	the	DET
ejpam-6129	229	13	carriers	carrier	NOUN
ejpam-6129	229	14	and	and	CCONJ
ejpam-6129	229	15	infectious	infectious	ADJ
ejpam-6129	229	16	individuals	individual	NOUN
ejpam-6129	229	17	and	and	CCONJ
ejpam-6129	229	18	hence	hence	ADV
ejpam-6129	229	19	on	on	ADP
ejpam-6129	229	20	increasing	increase	VERB
ejpam-6129	229	21	the	the	DET
ejpam-6129	229	22	recovered	recovered	ADJ
ejpam-6129	229	23	individuals	individual	NOUN
ejpam-6129	229	24	.	.	PUNCT
ejpam-6129	230	1	in	in	ADP
ejpam-6129	230	2	the	the	DET
ejpam-6129	230	3	second	second	ADJ
ejpam-6129	230	4	scenario	scenario	NOUN
ejpam-6129	230	5	it	it	PRON
ejpam-6129	230	6	is	be	AUX
ejpam-6129	230	7	shown	show	VERB
ejpam-6129	230	8	that	that	SCONJ
ejpam-6129	230	9	we	we	PRON
ejpam-6129	230	10	can	can	AUX
ejpam-6129	230	11	use	use	VERB
ejpam-6129	230	12	different	different	ADJ
ejpam-6129	230	13	combinations	combination	NOUN
ejpam-6129	230	14	of	of	ADP
ejpam-6129	230	15	the	the	DET
ejpam-6129	230	16	balancing	balance	VERB
ejpam-6129	230	17	factors	factor	NOUN
ejpam-6129	230	18	to	to	PART
ejpam-6129	230	19	achieve	achieve	VERB
ejpam-6129	230	20	the	the	DET
ejpam-6129	230	21	results	result	NOUN
ejpam-6129	230	22	required	require	VERB
ejpam-6129	230	23	,	,	PUNCT
ejpam-6129	230	24	and	and	CCONJ
ejpam-6129	230	25	all	all	DET
ejpam-6129	230	26	results	result	NOUN
ejpam-6129	230	27	obtained	obtain	VERB
ejpam-6129	230	28	numerically	numerically	ADV
ejpam-6129	230	29	were	be	AUX
ejpam-6129	230	30	satisfactory	satisfactory	ADJ
ejpam-6129	230	31	.	.	PUNCT
ejpam-6129	231	1	scenario	scenario	PROPN
ejpam-6129	231	2	three	three	NUM
ejpam-6129	231	3	involved	involve	VERB
ejpam-6129	231	4	a	a	DET
ejpam-6129	231	5	comparison	comparison	NOUN
ejpam-6129	231	6	of	of	ADP
ejpam-6129	231	7	application	application	NOUN
ejpam-6129	231	8	of	of	ADP
ejpam-6129	231	9	a	a	DET
ejpam-6129	231	10	single	single	ADJ
ejpam-6129	231	11	control	control	NOUN
ejpam-6129	231	12	vs	vs	ADP
ejpam-6129	231	13	application	application	NOUN
ejpam-6129	231	14	of	of	ADP
ejpam-6129	231	15	both	both	DET
ejpam-6129	231	16	controls	control	NOUN
ejpam-6129	231	17	.	.	PUNCT
ejpam-6129	232	1	we	we	PRON
ejpam-6129	232	2	found	find	VERB
ejpam-6129	232	3	that	that	SCONJ
ejpam-6129	232	4	it	it	PRON
ejpam-6129	232	5	is	be	AUX
ejpam-6129	232	6	better	well	ADJ
ejpam-6129	232	7	to	to	PART
ejpam-6129	232	8	apply	apply	VERB
ejpam-6129	232	9	both	both	DET
ejpam-6129	232	10	vaccination	vaccination	NOUN
ejpam-6129	232	11	and	and	CCONJ
ejpam-6129	232	12	treatment	treatment	NOUN
ejpam-6129	232	13	strategies	strategy	NOUN
ejpam-6129	232	14	together	together	ADV
ejpam-6129	232	15	than	than	ADP
ejpam-6129	232	16	applying	apply	VERB
ejpam-6129	232	17	only	only	ADV
ejpam-6129	232	18	the	the	DET
ejpam-6129	232	19	treatment	treatment	NOUN
ejpam-6129	232	20	.	.	PUNCT
ejpam-6129	233	1	on	on	ADP
ejpam-6129	233	2	the	the	DET
ejpam-6129	233	3	other	other	ADJ
ejpam-6129	233	4	hand	hand	NOUN
ejpam-6129	233	5	,	,	PUNCT
ejpam-6129	233	6	for	for	ADP
ejpam-6129	233	7	the	the	DET
ejpam-6129	233	8	set	set	NOUN
ejpam-6129	233	9	of	of	ADP
ejpam-6129	233	10	parameters	parameter	NOUN
ejpam-6129	233	11	and	and	CCONJ
ejpam-6129	233	12	initial	initial	ADJ
ejpam-6129	233	13	values	value	NOUN
ejpam-6129	233	14	given	give	VERB
ejpam-6129	233	15	for	for	ADP
ejpam-6129	233	16	the	the	DET
ejpam-6129	233	17	basic	basic	ADJ
ejpam-6129	233	18	model	model	NOUN
ejpam-6129	233	19	,	,	PUNCT
ejpam-6129	233	20	we	we	PRON
ejpam-6129	233	21	have	have	AUX
ejpam-6129	233	22	found	find	VERB
ejpam-6129	233	23	that	that	SCONJ
ejpam-6129	233	24	using	use	VERB
ejpam-6129	233	25	vaccination	vaccination	NOUN
ejpam-6129	233	26	and	and	CCONJ
ejpam-6129	233	27	treatment	treatment	NOUN
ejpam-6129	233	28	have	have	VERB
ejpam-6129	233	29	the	the	DET
ejpam-6129	233	30	same	same	ADJ
ejpam-6129	233	31	effect	effect	NOUN
ejpam-6129	233	32	as	as	ADP
ejpam-6129	233	33	using	use	VERB
ejpam-6129	233	34	the	the	DET
ejpam-6129	233	35	vaccination	vaccination	NOUN
ejpam-6129	233	36	only	only	ADV
ejpam-6129	233	37	.	.	PUNCT
ejpam-6129	234	1	from	from	ADP
ejpam-6129	234	2	the	the	DET
ejpam-6129	234	3	cost	cost	NOUN
ejpam-6129	234	4	effectiveness	effectiveness	NOUN
ejpam-6129	234	5	aspect	aspect	NOUN
ejpam-6129	234	6	,	,	PUNCT
ejpam-6129	234	7	this	this	PRON
ejpam-6129	234	8	suggests	suggest	VERB
ejpam-6129	234	9	that	that	SCONJ
ejpam-6129	234	10	one	one	PRON
ejpam-6129	234	11	can	can	AUX
ejpam-6129	234	12	adopt	adopt	VERB
ejpam-6129	234	13	a	a	DET
ejpam-6129	234	14	single	single	ADJ
ejpam-6129	234	15	strategy	strategy	NOUN
ejpam-6129	234	16	,	,	PUNCT
ejpam-6129	234	17	the	the	DET
ejpam-6129	234	18	vaccination	vaccination	NOUN
ejpam-6129	234	19	,	,	PUNCT
ejpam-6129	234	20	to	to	PART
ejpam-6129	234	21	effectively	effectively	ADV
ejpam-6129	234	22	reduce	reduce	VERB
ejpam-6129	234	23	the	the	DET
ejpam-6129	234	24	populations	population	NOUN
ejpam-6129	234	25	of	of	ADP
ejpam-6129	234	26	carriers	carrier	NOUN
ejpam-6129	234	27	and	and	CCONJ
ejpam-6129	234	28	infectious	infectious	ADJ
ejpam-6129	234	29	individuals	individual	NOUN
ejpam-6129	234	30	.	.	PUNCT
ejpam-6129	235	1	currently	currently	ADV
ejpam-6129	235	2	,	,	PUNCT
ejpam-6129	235	3	we	we	PRON
ejpam-6129	235	4	are	be	AUX
ejpam-6129	235	5	busy	busy	ADJ
ejpam-6129	235	6	investigating	investigate	VERB
ejpam-6129	235	7	the	the	DET
ejpam-6129	235	8	applicability	applicability	NOUN
ejpam-6129	235	9	of	of	ADP
ejpam-6129	235	10	numerical	numerical	ADJ
ejpam-6129	235	11	methods	method	NOUN
ejpam-6129	235	12	such	such	ADJ
ejpam-6129	235	13	as	as	ADP
ejpam-6129	235	14	s.	s.	PROPN
ejpam-6129	235	15	a.	a.	PROPN
ejpam-6129	235	16	mohamed	mohamed	PROPN
ejpam-6129	235	17	et	et	PROPN
ejpam-6129	235	18	al	al	PROPN
ejpam-6129	235	19	.	.	PUNCT
ejpam-6129	235	20	/	/	SYM
ejpam-6129	235	21	eur	eur	PROPN
ejpam-6129	235	22	.	.	PUNCT
ejpam-6129	236	1	j.	j.	PROPN
ejpam-6129	236	2	pure	pure	PROPN
ejpam-6129	236	3	appl	appl	PROPN
ejpam-6129	236	4	.	.	PROPN
ejpam-6129	236	5	math	math	PROPN
ejpam-6129	236	6	,	,	PUNCT
ejpam-6129	236	7	18	18	NUM
ejpam-6129	236	8	(	(	PUNCT
ejpam-6129	236	9	3	3	NUM
ejpam-6129	236	10	)	)	PUNCT
ejpam-6129	236	11	(	(	PUNCT
ejpam-6129	236	12	2025	2025	NUM
ejpam-6129	236	13	)	)	PUNCT
ejpam-6129	236	14	,	,	PUNCT
ejpam-6129	236	15	6129	6129	NUM
ejpam-6129	236	16	15	15	NUM
ejpam-6129	236	17	of	of	ADP
ejpam-6129	236	18	17	17	NUM
ejpam-6129	236	19	nonstandard	nonstandard	ADJ
ejpam-6129	236	20	finite	finite	ADJ
ejpam-6129	236	21	difference	difference	NOUN
ejpam-6129	236	22	methods	method	NOUN
ejpam-6129	236	23	to	to	PART
ejpam-6129	236	24	solve	solve	VERB
ejpam-6129	236	25	the	the	DET
ejpam-6129	236	26	state	state	NOUN
ejpam-6129	236	27	and	and	CCONJ
ejpam-6129	236	28	adjoint	adjoint	NOUN
ejpam-6129	236	29	systems	system	NOUN
ejpam-6129	236	30	as	as	SCONJ
ejpam-6129	236	31	these	these	DET
ejpam-6129	236	32	methods	method	NOUN
ejpam-6129	236	33	are	be	AUX
ejpam-6129	236	34	convenient	convenient	ADJ
ejpam-6129	236	35	when	when	SCONJ
ejpam-6129	236	36	dealing	deal	VERB
ejpam-6129	236	37	with	with	ADP
ejpam-6129	236	38	models	model	NOUN
ejpam-6129	236	39	describing	describe	VERB
ejpam-6129	236	40	populations	population	NOUN
ejpam-6129	236	41	because	because	SCONJ
ejpam-6129	236	42	they	they	PRON
ejpam-6129	236	43	preserves	preserve	VERB
ejpam-6129	236	44	the	the	DET
ejpam-6129	236	45	positivity	positivity	NOUN
ejpam-6129	236	46	of	of	ADP
ejpam-6129	236	47	the	the	DET
ejpam-6129	236	48	solution	solution	NOUN
ejpam-6129	236	49	.	.	PUNCT
ejpam-6129	237	1	this	this	PRON
ejpam-6129	237	2	is	be	AUX
ejpam-6129	237	3	an	an	DET
ejpam-6129	237	4	essential	essential	ADJ
ejpam-6129	237	5	requirement	requirement	NOUN
ejpam-6129	237	6	when	when	SCONJ
ejpam-6129	237	7	modeling	model	VERB
ejpam-6129	237	8	epidemic	epidemic	NOUN
ejpam-6129	237	9	diseases	disease	NOUN
ejpam-6129	237	10	.	.	PUNCT
ejpam-6129	238	1	acknowledgements	acknowledgement	NOUN
ejpam-6129	238	2	the	the	DET
ejpam-6129	238	3	authors	author	NOUN
ejpam-6129	238	4	acknowledge	acknowledge	VERB
ejpam-6129	238	5	the	the	DET
ejpam-6129	238	6	anonymous	anonymous	ADJ
ejpam-6129	238	7	referees	referee	NOUN
ejpam-6129	238	8	for	for	ADP
ejpam-6129	238	9	their	their	PRON
ejpam-6129	238	10	valuable	valuable	ADJ
ejpam-6129	238	11	comments	comment	NOUN
ejpam-6129	238	12	and	and	CCONJ
ejpam-6129	238	13	suggestions	suggestion	NOUN
ejpam-6129	238	14	.	.	PUNCT
ejpam-6129	239	1	funding	fund	VERB
ejpam-6129	239	2	h.	h.	PROPN
ejpam-6129	239	3	a.	a.	PROPN
ejpam-6129	239	4	obaid	obaid	PROPN
ejpam-6129	239	5	acknowledges	acknowledge	VERB
ejpam-6129	239	6	the	the	DET
ejpam-6129	239	7	faculty	faculty	NOUN
ejpam-6129	239	8	of	of	ADP
ejpam-6129	239	9	mathematical	mathematical	ADJ
ejpam-6129	239	10	sciences	sciences	PROPN
ejpam-6129	239	11	,	,	PUNCT
ejpam-6129	239	12	university	university	NOUN
ejpam-6129	239	13	of	of	ADP
ejpam-6129	239	14	khartoum	khartoum	PROPN
ejpam-6129	239	15	,	,	PUNCT
ejpam-6129	239	16	sudan	sudan	PROPN
ejpam-6129	239	17	,	,	PUNCT
ejpam-6129	239	18	for	for	ADP
ejpam-6129	239	19	the	the	DET
ejpam-6129	239	20	financial	financial	ADJ
ejpam-6129	239	21	support	support	NOUN
ejpam-6129	239	22	.	.	PUNCT
ejpam-6129	240	1	research	research	NOUN
ejpam-6129	240	2	of	of	ADP
ejpam-6129	240	3	kcp	kcp	PROPN
ejpam-6129	240	4	was	be	AUX
ejpam-6129	240	5	also	also	ADV
ejpam-6129	240	6	supported	support	VERB
ejpam-6129	240	7	by	by	ADP
ejpam-6129	240	8	the	the	DET
ejpam-6129	240	9	south	south	ADJ
ejpam-6129	240	10	african	african	ADJ
ejpam-6129	240	11	national	national	PROPN
ejpam-6129	240	12	research	research	PROPN
ejpam-6129	240	13	foundation	foundation	PROPN
ejpam-6129	240	14	.	.	PUNCT
ejpam-6129	241	1	conflict	conflict	NOUN
ejpam-6129	241	2	of	of	ADP
ejpam-6129	241	3	interest	interest	NOUN
ejpam-6129	241	4	.	.	PUNCT
ejpam-6129	242	1	the	the	DET
ejpam-6129	242	2	authors	author	NOUN
ejpam-6129	242	3	declare	declare	VERB
ejpam-6129	242	4	no	no	DET
ejpam-6129	242	5	conflict	conflict	NOUN
ejpam-6129	242	6	of	of	ADP
ejpam-6129	242	7	interest	interest	NOUN
ejpam-6129	242	8	.	.	PUNCT
ejpam-6129	243	1	references	reference	NOUN
ejpam-6129	243	2	[	[	X
ejpam-6129	243	3	1	1	NUM
ejpam-6129	243	4	]	]	PUNCT
ejpam-6129	243	5	x.	x.	NOUN
ejpam-6129	243	6	sáez	sáez	PROPN
ejpam-6129	243	7	-	-	NUM
ejpam-6129	243	8	liorens	liorens	PROPN
ejpam-6129	243	9	and	and	CCONJ
ejpam-6129	243	10	g.	g.	PROPN
ejpam-6129	243	11	h.	h.	PROPN
ejpam-6129	243	12	mccracken	mccracken	PROPN
ejpam-6129	243	13	.	.	PUNCT
ejpam-6129	244	1	bacterial	bacterial	ADJ
ejpam-6129	244	2	meningitis	meningitis	NOUN
ejpam-6129	244	3	in	in	ADP
ejpam-6129	244	4	children	child	NOUN
ejpam-6129	244	5	.	.	PUNCT
ejpam-6129	245	1	the	the	DET
ejpam-6129	245	2	lancet	lancet	NOUN
ejpam-6129	245	3	,	,	PUNCT
ejpam-6129	245	4	361:2139–48	361:2139–48	NUM
ejpam-6129	245	5	,	,	PUNCT
ejpam-6129	245	6	2003	2003	NUM
ejpam-6129	245	7	.	.	PUNCT
ejpam-6129	246	1	[	[	X
ejpam-6129	246	2	2	2	NUM
ejpam-6129	246	3	]	]	X
ejpam-6129	246	4	b.	b.	PROPN
ejpam-6129	246	5	r.	r.	PROPN
ejpam-6129	246	6	shmaefsky	shmaefsky	PROPN
ejpam-6129	246	7	.	.	PUNCT
ejpam-6129	247	1	deadly	deadly	ADJ
ejpam-6129	247	2	diseases	disease	NOUN
ejpam-6129	247	3	and	and	CCONJ
ejpam-6129	247	4	epidemics	epidemic	NOUN
ejpam-6129	247	5	:	:	PUNCT
ejpam-6129	247	6	meningitis	meningitis	PROPN
ejpam-6129	247	7	.	.	PUNCT
ejpam-6129	248	1	chelsea	chelsea	PROPN
ejpam-6129	248	2	house	house	PROPN
ejpam-6129	248	3	,	,	PUNCT
ejpam-6129	248	4	new	new	PROPN
ejpam-6129	248	5	york	york	PROPN
ejpam-6129	248	6	,	,	PUNCT
ejpam-6129	248	7	2010	2010	NUM
ejpam-6129	248	8	.	.	PUNCT
ejpam-6129	249	1	[	[	X
ejpam-6129	249	2	3	3	X
ejpam-6129	249	3	]	]	PUNCT
ejpam-6129	249	4	t.	t.	PROPN
ejpam-6129	249	5	j.	j.	PROPN
ejpam-6129	249	6	irving	irving	PROPN
ejpam-6129	249	7	,	,	PUNCT
ejpam-6129	249	8	k.	k.	PROPN
ejpam-6129	249	9	b.	b.	PROPN
ejpam-6129	249	10	blyuss	blyuss	PROPN
ejpam-6129	249	11	,	,	PUNCT
ejpam-6129	249	12	c.	c.	PROPN
ejpam-6129	249	13	colijn	colijn	PROPN
ejpam-6129	249	14	,	,	PUNCT
ejpam-6129	249	15	and	and	CCONJ
ejpam-6129	249	16	c.	c.	PROPN
ejpam-6129	249	17	l.	l.	PROPN
ejpam-6129	249	18	trotter	trotter	PROPN
ejpam-6129	249	19	.	.	PUNCT
ejpam-6129	250	1	modelling	model	VERB
ejpam-6129	250	2	meningococcal	meningococcal	ADJ
ejpam-6129	250	3	meningitis	meningitis	NOUN
ejpam-6129	250	4	in	in	ADP
ejpam-6129	250	5	the	the	DET
ejpam-6129	250	6	african	african	ADJ
ejpam-6129	250	7	meningitis	meningitis	NOUN
ejpam-6129	250	8	belt	belt	NOUN
ejpam-6129	250	9	.	.	PUNCT
ejpam-6129	251	1	epidemiology	epidemiology	NOUN
ejpam-6129	251	2	and	and	CCONJ
ejpam-6129	251	3	infection	infection	NOUN
ejpam-6129	251	4	,	,	PUNCT
ejpam-6129	251	5	140:897–905	140:897–905	NUM
ejpam-6129	251	6	,	,	PUNCT
ejpam-6129	251	7	2012	2012	NUM
ejpam-6129	251	8	.	.	PUNCT
ejpam-6129	252	1	[	[	X
ejpam-6129	252	2	4	4	NUM
ejpam-6129	252	3	]	]	X
ejpam-6129	252	4	m.j.f	m.j.f	NOUN
ejpam-6129	252	5	.	.	PUNCT
ejpam-6129	253	1	mart́ınez	mart́ınez	PROPN
ejpam-6129	253	2	,	,	PUNCT
ejpam-6129	253	3	e.g.	e.g.	ADV
ejpam-6129	253	4	merino	merino	NOUN
ejpam-6129	253	5	,	,	PUNCT
ejpam-6129	253	6	e.g.	e.g.	ADV
ejpam-6129	253	7	sánchez	sánchez	PROPN
ejpam-6129	253	8	,	,	PUNCT
ejpam-6129	253	9	j.e.g	j.e.g	PROPN
ejpam-6129	253	10	.	.	PUNCT
ejpam-6129	254	1	sánchez	sánchez	PROPN
ejpam-6129	254	2	,	,	PUNCT
ejpam-6129	254	3	a.m.	a.m.	PROPN
ejpam-6129	254	4	del	del	PROPN
ejpam-6129	254	5	rey	rey	PROPN
ejpam-6129	254	6	,	,	PUNCT
ejpam-6129	254	7	and	and	CCONJ
ejpam-6129	254	8	g.r	g.r	PROPN
ejpam-6129	254	9	.	.	PUNCT
ejpam-6129	255	1	sánchez	sánchez	PROPN
ejpam-6129	255	2	.	.	PUNCT
ejpam-6129	256	1	a	a	DET
ejpam-6129	256	2	mathematical	mathematical	ADJ
ejpam-6129	256	3	model	model	NOUN
ejpam-6129	256	4	to	to	PART
ejpam-6129	256	5	study	study	VERB
ejpam-6129	256	6	the	the	DET
ejpam-6129	256	7	meningococcal	meningococcal	ADJ
ejpam-6129	256	8	meningitis	meningitis	NOUN
ejpam-6129	256	9	.	.	PUNCT
ejpam-6129	257	1	procedia	procedia	PROPN
ejpam-6129	257	2	computer	computer	NOUN
ejpam-6129	257	3	science	science	NOUN
ejpam-6129	257	4	,	,	PUNCT
ejpam-6129	257	5	18:2492–2495	18:2492–2495	NUM
ejpam-6129	257	6	,	,	PUNCT
ejpam-6129	257	7	2013	2013	NUM
ejpam-6129	257	8	.	.	PUNCT
ejpam-6129	258	1	[	[	X
ejpam-6129	258	2	5	5	X
ejpam-6129	258	3	]	]	X
ejpam-6129	258	4	g.	g.	PROPN
ejpam-6129	258	5	o.	o.	PROPN
ejpam-6129	258	6	lawi	lawi	PROPN
ejpam-6129	258	7	,	,	PUNCT
ejpam-6129	258	8	j.	j.	PROPN
ejpam-6129	258	9	y.	y.	PROPN
ejpam-6129	258	10	t.	t.	PROPN
ejpam-6129	258	11	mugisha	mugisha	PROPN
ejpam-6129	258	12	,	,	PUNCT
ejpam-6129	258	13	and	and	CCONJ
ejpam-6129	258	14	n.	n.	PROPN
ejpam-6129	258	15	omolo	omolo	NOUN
ejpam-6129	258	16	-	-	PUNCT
ejpam-6129	258	17	ongati	ongati	NOUN
ejpam-6129	258	18	.	.	PUNCT
ejpam-6129	259	1	mathematical	mathematical	ADJ
ejpam-6129	259	2	model	model	NOUN
ejpam-6129	259	3	for	for	ADP
ejpam-6129	259	4	malaria	malaria	NOUN
ejpam-6129	259	5	and	and	CCONJ
ejpam-6129	259	6	meningitis	meningitis	NOUN
ejpam-6129	259	7	co	co	NOUN
ejpam-6129	259	8	-	-	NOUN
ejpam-6129	259	9	infection	infection	NOUN
ejpam-6129	259	10	among	among	ADP
ejpam-6129	259	11	children	child	NOUN
ejpam-6129	259	12	.	.	PUNCT
ejpam-6129	260	1	applied	apply	VERB
ejpam-6129	260	2	mathematical	mathematical	ADJ
ejpam-6129	260	3	sciences	science	NOUN
ejpam-6129	260	4	,	,	PUNCT
ejpam-6129	260	5	5(47):2337–2359	5(47):2337–2359	NUM
ejpam-6129	260	6	,	,	PUNCT
ejpam-6129	260	7	2011	2011	NUM
ejpam-6129	260	8	.	.	PUNCT
ejpam-6129	261	1	[	[	X
ejpam-6129	261	2	6	6	NUM
ejpam-6129	261	3	]	]	PUNCT
ejpam-6129	261	4	b.	b.	PROPN
ejpam-6129	261	5	opoku	opoku	PROPN
ejpam-6129	261	6	,	,	PUNCT
ejpam-6129	261	7	a.	a.	NOUN
ejpam-6129	261	8	sakyi	sakyi	NOUN
ejpam-6129	261	9	,	,	PUNCT
ejpam-6129	261	10	and	and	CCONJ
ejpam-6129	261	11	r.	r.	PROPN
ejpam-6129	261	12	n.	n.	PROPN
ejpam-6129	261	13	borkor	borkor	PROPN
ejpam-6129	261	14	.	.	PUNCT
ejpam-6129	262	1	mathematical	mathematical	ADJ
ejpam-6129	262	2	modelling	modelling	NOUN
ejpam-6129	262	3	of	of	ADP
ejpam-6129	262	4	meningitis	meningitis	NOUN
ejpam-6129	262	5	serogroups	serogroup	NOUN
ejpam-6129	262	6	a	a	PRON
ejpam-6129	262	7	and	and	CCONJ
ejpam-6129	262	8	c	c	NOUN
ejpam-6129	262	9	transmission	transmission	NOUN
ejpam-6129	262	10	in	in	ADP
ejpam-6129	262	11	sub	sub	ADJ
ejpam-6129	262	12	-	-	ADJ
ejpam-6129	262	13	saharan	saharan	ADJ
ejpam-6129	262	14	africa	africa	PROPN
ejpam-6129	262	15	:	:	PUNCT
ejpam-6129	262	16	a	a	DET
ejpam-6129	262	17	case	case	NOUN
ejpam-6129	262	18	study	study	NOUN
ejpam-6129	262	19	in	in	ADP
ejpam-6129	262	20	ghana	ghana	PROPN
ejpam-6129	262	21	.	.	PUNCT
ejpam-6129	263	1	scientific	scientific	ADJ
ejpam-6129	263	2	african	african	ADJ
ejpam-6129	263	3	,	,	PUNCT
ejpam-6129	263	4	29	29	NUM
ejpam-6129	263	5	:	:	PUNCT
ejpam-6129	263	6	e02758	e02758	NUM
ejpam-6129	263	7	,	,	PUNCT
ejpam-6129	263	8	2025	2025	NUM
ejpam-6129	263	9	.	.	PUNCT
ejpam-6129	264	1	[	[	X
ejpam-6129	264	2	7	7	X
ejpam-6129	264	3	]	]	X
ejpam-6129	264	4	g.	g.	PROPN
ejpam-6129	264	5	t.	t.	PROPN
ejpam-6129	264	6	tilahun	tilahun	PROPN
ejpam-6129	264	7	.	.	PUNCT
ejpam-6129	265	1	optimal	optimal	ADJ
ejpam-6129	265	2	control	control	NOUN
ejpam-6129	265	3	analysis	analysis	NOUN
ejpam-6129	265	4	of	of	ADP
ejpam-6129	265	5	pneumonia	pneumonia	NOUN
ejpam-6129	265	6	and	and	CCONJ
ejpam-6129	265	7	meningitis	meningitis	NOUN
ejpam-6129	265	8	coinfection	coinfection	NOUN
ejpam-6129	265	9	.	.	PUNCT
ejpam-6129	266	1	computational	computational	ADJ
ejpam-6129	266	2	and	and	CCONJ
ejpam-6129	266	3	mathematical	mathematical	ADJ
ejpam-6129	266	4	methods	method	NOUN
ejpam-6129	266	5	in	in	ADP
ejpam-6129	266	6	medicine	medicine	NOUN
ejpam-6129	266	7	,	,	PUNCT
ejpam-6129	266	8	2019	2019	NUM
ejpam-6129	266	9	:	:	PUNCT
ejpam-6129	266	10	article	article	NOUN
ejpam-6129	266	11	i	i	PROPN
ejpam-6129	266	12	d	d	PROPN
ejpam-6129	266	13	2658971	2658971	NUM
ejpam-6129	266	14	,	,	PUNCT
ejpam-6129	266	15	15	15	NUM
ejpam-6129	266	16	pages	page	NOUN
ejpam-6129	266	17	,	,	PUNCT
ejpam-6129	266	18	2019	2019	NUM
ejpam-6129	266	19	.	.	PUNCT
ejpam-6129	267	1	s.	s.	PROPN
ejpam-6129	267	2	a.	a.	PROPN
ejpam-6129	267	3	mohamed	mohamed	PROPN
ejpam-6129	267	4	et	et	PROPN
ejpam-6129	267	5	al	al	PROPN
ejpam-6129	267	6	.	.	PUNCT
ejpam-6129	267	7	/	/	SYM
ejpam-6129	267	8	eur	eur	PROPN
ejpam-6129	267	9	.	.	PUNCT
ejpam-6129	268	1	j.	j.	PROPN
ejpam-6129	268	2	pure	pure	PROPN
ejpam-6129	268	3	appl	appl	PROPN
ejpam-6129	268	4	.	.	PROPN
ejpam-6129	268	5	math	math	PROPN
ejpam-6129	268	6	,	,	PUNCT
ejpam-6129	268	7	18	18	NUM
ejpam-6129	268	8	(	(	PUNCT
ejpam-6129	268	9	3	3	NUM
ejpam-6129	268	10	)	)	PUNCT
ejpam-6129	268	11	(	(	PUNCT
ejpam-6129	268	12	2025	2025	NUM
ejpam-6129	268	13	)	)	PUNCT
ejpam-6129	268	14	,	,	PUNCT
ejpam-6129	268	15	6129	6129	NUM
ejpam-6129	268	16	16	16	NUM
ejpam-6129	268	17	of	of	ADP
ejpam-6129	268	18	17	17	NUM
ejpam-6129	268	19	[	[	SYM
ejpam-6129	268	20	8	8	NUM
ejpam-6129	268	21	]	]	PUNCT
ejpam-6129	268	22	e.	e.	PROPN
ejpam-6129	268	23	n.	n.	PROPN
ejpam-6129	268	24	wiah	wiah	PROPN
ejpam-6129	268	25	and	and	CCONJ
ejpam-6129	268	26	i.	i.	PROPN
ejpam-6129	268	27	a.	a.	PROPN
ejpam-6129	268	28	adetunde	adetunde	PROPN
ejpam-6129	268	29	.	.	PUNCT
ejpam-6129	269	1	a	a	DET
ejpam-6129	269	2	mathematical	mathematical	ADJ
ejpam-6129	269	3	model	model	NOUN
ejpam-6129	269	4	of	of	ADP
ejpam-6129	269	5	cerebrospinal	cerebrospinal	ADJ
ejpam-6129	269	6	meningitis	meningitis	NOUN
ejpam-6129	269	7	epidemic	epidemic	NOUN
ejpam-6129	269	8	:	:	PUNCT
ejpam-6129	269	9	a	a	DET
ejpam-6129	269	10	case	case	NOUN
ejpam-6129	269	11	study	study	NOUN
ejpam-6129	269	12	for	for	ADP
ejpam-6129	269	13	jirapa	jirapa	ADJ
ejpam-6129	269	14	district	district	PROPN
ejpam-6129	269	15	,	,	PUNCT
ejpam-6129	269	16	ghana	ghana	PROPN
ejpam-6129	269	17	.	.	PUNCT
ejpam-6129	270	1	kmitl	kmitl	PROPN
ejpam-6129	270	2	science	science	PROPN
ejpam-6129	270	3	and	and	CCONJ
ejpam-6129	270	4	technology	technology	NOUN
ejpam-6129	270	5	journal	journal	NOUN
ejpam-6129	270	6	,	,	PUNCT
ejpam-6129	270	7	10(2):63–73	10(2):63–73	NUM
ejpam-6129	270	8	,	,	PUNCT
ejpam-6129	270	9	2010	2010	NUM
ejpam-6129	270	10	.	.	PUNCT
ejpam-6129	271	1	[	[	X
ejpam-6129	271	2	9	9	NUM
ejpam-6129	271	3	]	]	PUNCT
ejpam-6129	271	4	t.	t.	PROPN
ejpam-6129	271	5	k.	k.	PROPN
ejpam-6129	271	6	yano	yano	PROPN
ejpam-6129	271	7	,	,	PUNCT
ejpam-6129	271	8	j.	j.	PROPN
ejpam-6129	271	9	bitok	bitok	PROPN
ejpam-6129	271	10	,	,	PUNCT
ejpam-6129	271	11	and	and	CCONJ
ejpam-6129	271	12	r.	r.	PROPN
ejpam-6129	271	13	jerop	jerop	PROPN
ejpam-6129	271	14	.	.	PUNCT
ejpam-6129	272	1	optimal	optimal	ADJ
ejpam-6129	272	2	control	control	NOUN
ejpam-6129	272	3	analysis	analysis	NOUN
ejpam-6129	272	4	of	of	ADP
ejpam-6129	272	5	meningococcal	meningococcal	ADJ
ejpam-6129	272	6	meningitis	meningitis	NOUN
ejpam-6129	272	7	disease	disease	NOUN
ejpam-6129	272	8	with	with	ADP
ejpam-6129	272	9	varying	vary	VERB
ejpam-6129	272	10	population	population	NOUN
ejpam-6129	272	11	size	size	NOUN
ejpam-6129	272	12	.	.	PUNCT
ejpam-6129	273	1	applied	apply	VERB
ejpam-6129	273	2	and	and	CCONJ
ejpam-6129	273	3	computational	computational	ADJ
ejpam-6129	273	4	mathematics	mathematic	NOUN
ejpam-6129	273	5	,	,	PUNCT
ejpam-6129	273	6	11(5):140–149	11(5):140–149	PRON
ejpam-6129	273	7	,	,	PUNCT
ejpam-6129	273	8	2022	2022	NUM
ejpam-6129	273	9	.	.	PUNCT
ejpam-6129	274	1	[	[	X
ejpam-6129	274	2	10	10	NUM
ejpam-6129	274	3	]	]	X
ejpam-6129	274	4	i.	i.	PROPN
ejpam-6129	274	5	p.	p.	PROPN
ejpam-6129	274	6	du	du	PROPN
ejpam-6129	274	7	châtelet	châtelet	PROPN
ejpam-6129	274	8	,	,	PUNCT
ejpam-6129	274	9	b.	b.	PROPN
ejpam-6129	274	10	d.	d.	PROPN
ejpam-6129	274	11	gessner	gessner	PROPN
ejpam-6129	274	12	,	,	PUNCT
ejpam-6129	274	13	and	and	CCONJ
ejpam-6129	274	14	a.	a.	PROPN
ejpam-6129	274	15	da	da	PROPN
ejpam-6129	274	16	silva	silva	PROPN
ejpam-6129	274	17	.	.	PUNCT
ejpam-6129	275	1	comparison	comparison	NOUN
ejpam-6129	275	2	of	of	ADP
ejpam-6129	275	3	cost	cost	NOUN
ejpam-6129	275	4	-	-	PUNCT
ejpam-6129	275	5	effectiveness	effectiveness	NOUN
ejpam-6129	275	6	of	of	ADP
ejpam-6129	275	7	preventive	preventive	ADJ
ejpam-6129	275	8	and	and	CCONJ
ejpam-6129	275	9	reactive	reactive	ADJ
ejpam-6129	275	10	mass	mass	NOUN
ejpam-6129	275	11	immunization	immunization	NOUN
ejpam-6129	275	12	campaigns	campaign	NOUN
ejpam-6129	275	13	against	against	ADP
ejpam-6129	275	14	meningococcal	meningococcal	ADJ
ejpam-6129	275	15	meningitis	meningitis	NOUN
ejpam-6129	275	16	in	in	ADP
ejpam-6129	275	17	west	west	PROPN
ejpam-6129	275	18	africa	africa	PROPN
ejpam-6129	275	19	:	:	PUNCT
ejpam-6129	275	20	a	a	DET
ejpam-6129	275	21	theoretical	theoretical	ADJ
ejpam-6129	275	22	modeling	modeling	NOUN
ejpam-6129	275	23	analysis	analysis	NOUN
ejpam-6129	275	24	.	.	PUNCT
ejpam-6129	276	1	vaccine	vaccine	NOUN
ejpam-6129	276	2	,	,	PUNCT
ejpam-6129	276	3	19:3420–3431	19:3420–3431	NUM
ejpam-6129	276	4	,	,	PUNCT
ejpam-6129	276	5	2001	2001	NUM
ejpam-6129	276	6	.	.	PUNCT
ejpam-6129	277	1	[	[	X
ejpam-6129	277	2	11	11	NUM
ejpam-6129	277	3	]	]	PUNCT
ejpam-6129	277	4	j.	j.	PROPN
ejpam-6129	277	5	e.	e.	PROPN
ejpam-6129	277	6	mueller	mueller	PROPN
ejpam-6129	277	7	and	and	CCONJ
ejpam-6129	277	8	b.	b.	PROPN
ejpam-6129	277	9	d.	d.	PROPN
ejpam-6129	277	10	gessner	gessner	PROPN
ejpam-6129	277	11	.	.	PUNCT
ejpam-6129	278	1	a	a	DET
ejpam-6129	278	2	hypothetical	hypothetical	ADJ
ejpam-6129	278	3	explanatory	explanatory	ADJ
ejpam-6129	278	4	model	model	NOUN
ejpam-6129	278	5	for	for	ADP
ejpam-6129	278	6	meningococcal	meningococcal	ADJ
ejpam-6129	278	7	meningitis	meningitis	NOUN
ejpam-6129	278	8	in	in	ADP
ejpam-6129	278	9	the	the	DET
ejpam-6129	278	10	african	african	ADJ
ejpam-6129	278	11	meningitis	meningitis	NOUN
ejpam-6129	278	12	belt	belt	NOUN
ejpam-6129	278	13	.	.	PUNCT
ejpam-6129	279	1	international	international	ADJ
ejpam-6129	279	2	journal	journal	NOUN
ejpam-6129	279	3	of	of	ADP
ejpam-6129	279	4	infectious	infectious	ADJ
ejpam-6129	279	5	diseases	disease	NOUN
ejpam-6129	279	6	,	,	PUNCT
ejpam-6129	279	7	14(7):553–559	14(7):553–559	NUM
ejpam-6129	279	8	,	,	PUNCT
ejpam-6129	279	9	2010	2010	NUM
ejpam-6129	279	10	.	.	PUNCT
ejpam-6129	280	1	[	[	X
ejpam-6129	280	2	12	12	NUM
ejpam-6129	280	3	]	]	PUNCT
ejpam-6129	280	4	b.	b.	PROPN
ejpam-6129	280	5	standaert	standaert	PROPN
ejpam-6129	280	6	,	,	PUNCT
ejpam-6129	280	7	n.	n.	PROPN
ejpam-6129	280	8	demarteau	demarteau	PROPN
ejpam-6129	280	9	,	,	PUNCT
ejpam-6129	280	10	s.	s.	PROPN
ejpam-6129	280	11	talbird	talbird	PROPN
ejpam-6129	280	12	,	,	PUNCT
ejpam-6129	280	13	and	and	CCONJ
ejpam-6129	280	14	j.	j.	PROPN
ejpam-6129	280	15	mauskop	mauskop	PROPN
ejpam-6129	280	16	.	.	PUNCT
ejpam-6129	281	1	modelling	model	VERB
ejpam-6129	281	2	the	the	DET
ejpam-6129	281	3	effect	effect	NOUN
ejpam-6129	281	4	of	of	ADP
ejpam-6129	281	5	conjugate	conjugate	ADJ
ejpam-6129	281	6	vaccines	vaccine	NOUN
ejpam-6129	281	7	in	in	ADP
ejpam-6129	281	8	pneumococcal	pneumococcal	ADJ
ejpam-6129	281	9	disease	disease	NOUN
ejpam-6129	281	10	:	:	PUNCT
ejpam-6129	281	11	cohort	cohort	NOUN
ejpam-6129	281	12	or	or	CCONJ
ejpam-6129	281	13	population	population	NOUN
ejpam-6129	281	14	models	model	NOUN
ejpam-6129	281	15	?	?	PUNCT
ejpam-6129	282	1	vaccine	vaccine	NOUN
ejpam-6129	282	2	,	,	PUNCT
ejpam-6129	282	3	28s	28s	NUM
ejpam-6129	282	4	:	:	PUNCT
ejpam-6129	282	5	g30	g30	NUM
ejpam-6129	282	6	–	–	PUNCT
ejpam-6129	282	7	g38	g38	NOUN
ejpam-6129	282	8	,	,	PUNCT
ejpam-6129	282	9	2010	2010	NUM
ejpam-6129	282	10	.	.	PUNCT
ejpam-6129	283	1	[	[	X
ejpam-6129	283	2	13	13	NUM
ejpam-6129	283	3	]	]	PUNCT
ejpam-6129	283	4	m.	m.	NOUN
ejpam-6129	283	5	i.	i.	PROPN
ejpam-6129	283	6	amar	amar	PROPN
ejpam-6129	283	7	,	,	PUNCT
ejpam-6129	283	8	m.	m.	PROPN
ejpam-6129	283	9	r.	r.	PROPN
ejpam-6129	283	10	nisardi	nisardi	PROPN
ejpam-6129	283	11	,	,	PUNCT
ejpam-6129	283	12	and	and	CCONJ
ejpam-6129	283	13	m.	m.	PROPN
ejpam-6129	283	14	f.	f.	PROPN
ejpam-6129	283	15	nurahmad	nurahmad	PROPN
ejpam-6129	283	16	.	.	PUNCT
ejpam-6129	284	1	a	a	DET
ejpam-6129	284	2	deterministic	deterministic	ADJ
ejpam-6129	284	3	mathematical	mathematical	ADJ
ejpam-6129	284	4	model	model	NOUN
ejpam-6129	284	5	of	of	ADP
ejpam-6129	284	6	meningitis	meningitis	NOUN
ejpam-6129	284	7	transmission	transmission	NOUN
ejpam-6129	284	8	dynamics	dynamic	NOUN
ejpam-6129	284	9	with	with	ADP
ejpam-6129	284	10	vaccination	vaccination	NOUN
ejpam-6129	284	11	and	and	CCONJ
ejpam-6129	284	12	screening	screening	NOUN
ejpam-6129	284	13	.	.	PUNCT
ejpam-6129	285	1	jurnal	jurnal	ADJ
ejpam-6129	285	2	matematika	matematika	PROPN
ejpam-6129	285	3	unand	unand	PROPN
ejpam-6129	285	4	,	,	PUNCT
ejpam-6129	285	5	14(1):14–30	14(1):14–30	NUM
ejpam-6129	285	6	,	,	PUNCT
ejpam-6129	285	7	2025	2025	NUM
ejpam-6129	285	8	.	.	PUNCT
ejpam-6129	286	1	[	[	X
ejpam-6129	286	2	14	14	NUM
ejpam-6129	286	3	]	]	PUNCT
ejpam-6129	286	4	a.	a.	NOUN
ejpam-6129	286	5	j.	j.	PROPN
ejpam-6129	286	6	coldman	coldman	PROPN
ejpam-6129	286	7	and	and	CCONJ
ejpam-6129	286	8	j.	j.	PROPN
ejpam-6129	286	9	m.	m.	PROPN
ejpam-6129	286	10	murray	murray	PROPN
ejpam-6129	286	11	.	.	PUNCT
ejpam-6129	287	1	optimal	optimal	ADJ
ejpam-6129	287	2	control	control	NOUN
ejpam-6129	287	3	for	for	ADP
ejpam-6129	287	4	a	a	DET
ejpam-6129	287	5	stochastic	stochastic	ADJ
ejpam-6129	287	6	model	model	NOUN
ejpam-6129	287	7	of	of	ADP
ejpam-6129	287	8	cancer	cancer	NOUN
ejpam-6129	287	9	chemotherapy	chemotherapy	NOUN
ejpam-6129	287	10	.	.	PUNCT
ejpam-6129	288	1	mathematical	mathematical	ADJ
ejpam-6129	288	2	biosciences	bioscience	NOUN
ejpam-6129	288	3	,	,	PUNCT
ejpam-6129	288	4	168:187–200	168:187–200	NUM
ejpam-6129	288	5	,	,	PUNCT
ejpam-6129	288	6	2000	2000	NUM
ejpam-6129	288	7	.	.	PUNCT
ejpam-6129	289	1	[	[	X
ejpam-6129	289	2	15	15	NUM
ejpam-6129	289	3	]	]	X
ejpam-6129	289	4	r.	r.	PROPN
ejpam-6129	289	5	v.	v.	PROPN
ejpam-6129	289	6	culshaw	culshaw	PROPN
ejpam-6129	289	7	,	,	PUNCT
ejpam-6129	289	8	s.	s.	PROPN
ejpam-6129	289	9	ruan	ruan	PROPN
ejpam-6129	289	10	,	,	PUNCT
ejpam-6129	289	11	and	and	CCONJ
ejpam-6129	289	12	r.	r.	PROPN
ejpam-6129	289	13	j.	j.	PROPN
ejpam-6129	289	14	spiteri	spiteri	PROPN
ejpam-6129	289	15	.	.	PUNCT
ejpam-6129	290	1	optimal	optimal	ADJ
ejpam-6129	290	2	hiv	hiv	PROPN
ejpam-6129	290	3	treatment	treatment	NOUN
ejpam-6129	290	4	by	by	ADP
ejpam-6129	290	5	maximising	maximise	VERB
ejpam-6129	290	6	immune	immune	ADJ
ejpam-6129	290	7	response	response	NOUN
ejpam-6129	290	8	.	.	PUNCT
ejpam-6129	291	1	journal	journal	PROPN
ejpam-6129	291	2	of	of	ADP
ejpam-6129	291	3	mathematical	mathematical	ADJ
ejpam-6129	291	4	biology	biology	NOUN
ejpam-6129	291	5	,	,	PUNCT
ejpam-6129	291	6	48:545–562	48:545–562	NUM
ejpam-6129	291	7	,	,	PUNCT
ejpam-6129	291	8	2004	2004	NUM
ejpam-6129	291	9	.	.	PUNCT
ejpam-6129	292	1	[	[	X
ejpam-6129	292	2	16	16	NUM
ejpam-6129	292	3	]	]	PUNCT
ejpam-6129	292	4	k.	k.	PROPN
ejpam-6129	292	5	r.	r.	PROPN
ejpam-6129	292	6	fister	fister	PROPN
ejpam-6129	292	7	,	,	PUNCT
ejpam-6129	292	8	s.	s.	PROPN
ejpam-6129	292	9	lenhart	lenhart	PROPN
ejpam-6129	292	10	,	,	PUNCT
ejpam-6129	292	11	and	and	CCONJ
ejpam-6129	292	12	j.	j.	PROPN
ejpam-6129	292	13	s.	s.	PROPN
ejpam-6129	292	14	mcnally	mcnally	PROPN
ejpam-6129	292	15	.	.	PUNCT
ejpam-6129	293	1	optimizing	optimize	VERB
ejpam-6129	293	2	chemotherapy	chemotherapy	NOUN
ejpam-6129	293	3	in	in	ADP
ejpam-6129	293	4	an	an	DET
ejpam-6129	293	5	hiv	hiv	PROPN
ejpam-6129	293	6	model	model	NOUN
ejpam-6129	293	7	.	.	PUNCT
ejpam-6129	294	1	electronic	electronic	ADJ
ejpam-6129	294	2	journal	journal	NOUN
ejpam-6129	294	3	of	of	ADP
ejpam-6129	294	4	differential	differential	ADJ
ejpam-6129	294	5	equations	equation	NOUN
ejpam-6129	294	6	,	,	PUNCT
ejpam-6129	294	7	1998(32):1–12	1998(32):1–12	NUM
ejpam-6129	294	8	,	,	PUNCT
ejpam-6129	294	9	1998	1998	NUM
ejpam-6129	294	10	.	.	PUNCT
ejpam-6129	295	1	[	[	X
ejpam-6129	295	2	17	17	NUM
ejpam-6129	295	3	]	]	X
ejpam-6129	295	4	e.	e.	PROPN
ejpam-6129	295	5	jung	jung	PROPN
ejpam-6129	295	6	,	,	PUNCT
ejpam-6129	295	7	s.	s.	PROPN
ejpam-6129	295	8	lenhart	lenhart	PROPN
ejpam-6129	295	9	,	,	PUNCT
ejpam-6129	295	10	and	and	CCONJ
ejpam-6129	295	11	z.	z.	PROPN
ejpam-6129	295	12	feng	feng	PROPN
ejpam-6129	295	13	.	.	PUNCT
ejpam-6129	296	1	optimal	optimal	ADJ
ejpam-6129	296	2	control	control	NOUN
ejpam-6129	296	3	of	of	ADP
ejpam-6129	296	4	treatments	treatment	NOUN
ejpam-6129	296	5	in	in	ADP
ejpam-6129	296	6	a	a	DET
ejpam-6129	296	7	two	two	NUM
ejpam-6129	296	8	-	-	PUNCT
ejpam-6129	296	9	strain	strain	NOUN
ejpam-6129	296	10	tuberculosis	tuberculosis	NOUN
ejpam-6129	296	11	model	model	NOUN
ejpam-6129	296	12	.	.	PUNCT
ejpam-6129	297	1	discrete	discrete	ADJ
ejpam-6129	297	2	and	and	CCONJ
ejpam-6129	297	3	continuous	continuous	ADJ
ejpam-6129	297	4	dynamical	dynamical	ADJ
ejpam-6129	297	5	systems	system	NOUN
ejpam-6129	297	6	-	-	PUNCT
ejpam-6129	297	7	series	series	NOUN
ejpam-6129	297	8	b	b	NOUN
ejpam-6129	297	9	,	,	PUNCT
ejpam-6129	297	10	2(4):473	2(4):473	NUM
ejpam-6129	297	11	–	–	PUNCT
ejpam-6129	297	12	482	482	NUM
ejpam-6129	297	13	,	,	PUNCT
ejpam-6129	297	14	2002	2002	NUM
ejpam-6129	297	15	.	.	PUNCT
ejpam-6129	298	1	[	[	X
ejpam-6129	298	2	18	18	NUM
ejpam-6129	298	3	]	]	X
ejpam-6129	298	4	d.	d.	PROPN
ejpam-6129	298	5	kirschner	kirschner	PROPN
ejpam-6129	298	6	,	,	PUNCT
ejpam-6129	298	7	s.	s.	PROPN
ejpam-6129	298	8	lenhart	lenhart	PROPN
ejpam-6129	298	9	,	,	PUNCT
ejpam-6129	298	10	and	and	CCONJ
ejpam-6129	298	11	s.	s.	PROPN
ejpam-6129	298	12	serbin	serbin	PROPN
ejpam-6129	298	13	.	.	PUNCT
ejpam-6129	299	1	optimal	optimal	ADJ
ejpam-6129	299	2	control	control	NOUN
ejpam-6129	299	3	of	of	ADP
ejpam-6129	299	4	the	the	DET
ejpam-6129	299	5	chemotherapy	chemotherapy	NOUN
ejpam-6129	299	6	of	of	ADP
ejpam-6129	299	7	hiv	hiv	PROPN
ejpam-6129	299	8	.	.	PUNCT
ejpam-6129	300	1	journal	journal	PROPN
ejpam-6129	300	2	of	of	ADP
ejpam-6129	300	3	mathematical	mathematical	ADJ
ejpam-6129	300	4	biology	biology	NOUN
ejpam-6129	300	5	,	,	PUNCT
ejpam-6129	300	6	35:775–792	35:775–792	NUM
ejpam-6129	300	7	,	,	PUNCT
ejpam-6129	300	8	1997	1997	NUM
ejpam-6129	300	9	.	.	PUNCT
ejpam-6129	301	1	[	[	X
ejpam-6129	301	2	19	19	NUM
ejpam-6129	301	3	]	]	X
ejpam-6129	301	4	s.	s.	PROPN
ejpam-6129	301	5	nanda	nanda	PROPN
ejpam-6129	301	6	,	,	PUNCT
ejpam-6129	301	7	h.	h.	PROPN
ejpam-6129	301	8	moore	moore	PROPN
ejpam-6129	301	9	,	,	PUNCT
ejpam-6129	301	10	and	and	CCONJ
ejpam-6129	301	11	s.	s.	PROPN
ejpam-6129	301	12	lenhart	lenhart	PROPN
ejpam-6129	301	13	.	.	PUNCT
ejpam-6129	302	1	optimal	optimal	ADJ
ejpam-6129	302	2	control	control	NOUN
ejpam-6129	302	3	of	of	ADP
ejpam-6129	302	4	treatment	treatment	NOUN
ejpam-6129	302	5	in	in	ADP
ejpam-6129	302	6	a	a	DET
ejpam-6129	302	7	mathematical	mathematical	ADJ
ejpam-6129	302	8	model	model	NOUN
ejpam-6129	302	9	of	of	ADP
ejpam-6129	302	10	chronic	chronic	ADJ
ejpam-6129	302	11	myelogenous	myelogenous	ADJ
ejpam-6129	302	12	leukemia	leukemia	NOUN
ejpam-6129	302	13	.	.	PUNCT
ejpam-6129	303	1	mathematical	mathematical	ADJ
ejpam-6129	303	2	biosciences	bioscience	NOUN
ejpam-6129	303	3	,	,	PUNCT
ejpam-6129	303	4	210:143–156	210:143–156	NUM
ejpam-6129	303	5	,	,	PUNCT
ejpam-6129	303	6	2007	2007	NUM
ejpam-6129	303	7	.	.	PUNCT
ejpam-6129	304	1	[	[	X
ejpam-6129	304	2	20	20	NUM
ejpam-6129	304	3	]	]	X
ejpam-6129	304	4	r.l.m	r.l.m	ADJ
ejpam-6129	304	5	.	.	PUNCT
ejpam-6129	304	6	neilan	neilan	PROPN
ejpam-6129	304	7	,	,	PUNCT
ejpam-6129	304	8	e.	e.	PROPN
ejpam-6129	304	9	schaefer	schaefer	PROPN
ejpam-6129	304	10	,	,	PUNCT
ejpam-6129	304	11	h.	h.	PROPN
ejpam-6129	304	12	gaff	gaff	PROPN
ejpam-6129	304	13	,	,	PUNCT
ejpam-6129	304	14	k.r	k.r	PROPN
ejpam-6129	304	15	.	.	PROPN
ejpam-6129	304	16	fisterd	fisterd	PROPN
ejpam-6129	304	17	,	,	PUNCT
ejpam-6129	304	18	and	and	CCONJ
ejpam-6129	304	19	s.	s.	PROPN
ejpam-6129	304	20	lenhart	lenhart	PROPN
ejpam-6129	304	21	.	.	PUNCT
ejpam-6129	305	1	modeling	model	VERB
ejpam-6129	305	2	optimal	optimal	ADJ
ejpam-6129	305	3	intervention	intervention	NOUN
ejpam-6129	305	4	strategies	strategy	NOUN
ejpam-6129	305	5	for	for	ADP
ejpam-6129	305	6	cholera	cholera	NOUN
ejpam-6129	305	7	.	.	PUNCT
ejpam-6129	306	1	bulletin	bulletin	NOUN
ejpam-6129	306	2	of	of	ADP
ejpam-6129	306	3	mathematical	mathematical	ADJ
ejpam-6129	306	4	biology	biology	NOUN
ejpam-6129	306	5	,	,	PUNCT
ejpam-6129	306	6	72:2004–2018	72:2004–2018	PROPN
ejpam-6129	306	7	,	,	PUNCT
ejpam-6129	306	8	2010	2010	NUM
ejpam-6129	306	9	.	.	PUNCT
ejpam-6129	307	1	[	[	X
ejpam-6129	307	2	21	21	NUM
ejpam-6129	307	3	]	]	X
ejpam-6129	307	4	r.	r.	PROPN
ejpam-6129	307	5	f.	f.	PROPN
ejpam-6129	307	6	stengel	stengel	PROPN
ejpam-6129	307	7	.	.	PUNCT
ejpam-6129	308	1	mutation	mutation	NOUN
ejpam-6129	308	2	and	and	CCONJ
ejpam-6129	308	3	control	control	NOUN
ejpam-6129	308	4	of	of	ADP
ejpam-6129	308	5	the	the	DET
ejpam-6129	308	6	human	human	ADJ
ejpam-6129	308	7	immunodeficiency	immunodeficiency	NOUN
ejpam-6129	308	8	virus	virus	NOUN
ejpam-6129	308	9	.	.	PUNCT
ejpam-6129	309	1	mathematical	mathematical	ADJ
ejpam-6129	309	2	biosciences	bioscience	NOUN
ejpam-6129	309	3	,	,	PUNCT
ejpam-6129	309	4	213:93–102	213:93–102	NUM
ejpam-6129	309	5	,	,	PUNCT
ejpam-6129	309	6	2008	2008	NUM
ejpam-6129	309	7	.	.	PUNCT
ejpam-6129	310	1	[	[	X
ejpam-6129	310	2	22	22	NUM
ejpam-6129	310	3	]	]	PUNCT
ejpam-6129	310	4	x.	x.	PROPN
ejpam-6129	310	5	yan	yan	PROPN
ejpam-6129	310	6	,	,	PUNCT
ejpam-6129	310	7	y.	y.	PROPN
ejpam-6129	310	8	zou	zou	PROPN
ejpam-6129	310	9	,	,	PUNCT
ejpam-6129	310	10	and	and	CCONJ
ejpam-6129	310	11	j.	j.	PROPN
ejpam-6129	310	12	li	li	PROPN
ejpam-6129	310	13	.	.	PROPN
ejpam-6129	311	1	optimal	optimal	ADJ
ejpam-6129	311	2	quarantine	quarantine	NOUN
ejpam-6129	311	3	and	and	CCONJ
ejpam-6129	311	4	isolation	isolation	NOUN
ejpam-6129	311	5	strategies	strategy	NOUN
ejpam-6129	311	6	in	in	ADP
ejpam-6129	311	7	epidemics	epidemic	NOUN
ejpam-6129	311	8	control	control	NOUN
ejpam-6129	311	9	.	.	PUNCT
ejpam-6129	312	1	world	world	PROPN
ejpam-6129	312	2	journal	journal	PROPN
ejpam-6129	312	3	of	of	ADP
ejpam-6129	312	4	modelling	modelling	NOUN
ejpam-6129	312	5	and	and	CCONJ
ejpam-6129	312	6	simulation	simulation	NOUN
ejpam-6129	312	7	,	,	PUNCT
ejpam-6129	312	8	3(3):202–211	3(3):202–211	NUM
ejpam-6129	312	9	,	,	PUNCT
ejpam-6129	312	10	2007	2007	NUM
ejpam-6129	312	11	.	.	PUNCT
ejpam-6129	313	1	[	[	X
ejpam-6129	313	2	23	23	NUM
ejpam-6129	313	3	]	]	PUNCT
ejpam-6129	313	4	l.	l.	PROPN
ejpam-6129	313	5	s.	s.	PROPN
ejpam-6129	313	6	pontryagin	pontryagin	PROPN
ejpam-6129	313	7	,	,	PUNCT
ejpam-6129	313	8	v.	v.	PROPN
ejpam-6129	313	9	g.	g.	PROPN
ejpam-6129	313	10	boltyanskii	boltyanskii	PROPN
ejpam-6129	313	11	,	,	PUNCT
ejpam-6129	313	12	r.	r.	PROPN
ejpam-6129	313	13	v.	v.	PROPN
ejpam-6129	313	14	gamkrelidze	gamkrelidze	PROPN
ejpam-6129	313	15	,	,	PUNCT
ejpam-6129	313	16	and	and	CCONJ
ejpam-6129	313	17	e.	e.	PROPN
ejpam-6129	313	18	f.	f.	PROPN
ejpam-6129	313	19	mishchenko	mishchenko	PROPN
ejpam-6129	313	20	.	.	PUNCT
ejpam-6129	314	1	the	the	DET
ejpam-6129	314	2	mathematical	mathematical	ADJ
ejpam-6129	314	3	theory	theory	NOUN
ejpam-6129	314	4	of	of	ADP
ejpam-6129	314	5	optimal	optimal	ADJ
ejpam-6129	314	6	processes	process	NOUN
ejpam-6129	314	7	.	.	PUNCT
ejpam-6129	315	1	university	university	NOUN
ejpam-6129	315	2	of	of	ADP
ejpam-6129	315	3	michigan	michigan	PROPN
ejpam-6129	315	4	press	press	PROPN
ejpam-6129	315	5	,	,	PUNCT
ejpam-6129	315	6	wileyinterscience	wileyinterscience	NOUN
ejpam-6129	315	7	,	,	PUNCT
ejpam-6129	315	8	los	los	PROPN
ejpam-6129	315	9	angeles	angeles	PROPN
ejpam-6129	315	10	,	,	PUNCT
ejpam-6129	315	11	1962	1962	NUM
ejpam-6129	315	12	.	.	PUNCT
ejpam-6129	316	1	[	[	X
ejpam-6129	316	2	24	24	NUM
ejpam-6129	316	3	]	]	X
ejpam-6129	316	4	w.	w.	PROPN
ejpam-6129	316	5	h.	h.	PROPN
ejpam-6129	316	6	fleming	fleming	PROPN
ejpam-6129	316	7	and	and	CCONJ
ejpam-6129	316	8	r.	r.	PROPN
ejpam-6129	316	9	w.	w.	PROPN
ejpam-6129	316	10	rishel	rishel	PROPN
ejpam-6129	316	11	.	.	PUNCT
ejpam-6129	317	1	adaptation	adaptation	NOUN
ejpam-6129	317	2	in	in	ADP
ejpam-6129	317	3	natural	natural	ADJ
ejpam-6129	317	4	and	and	CCONJ
ejpam-6129	317	5	artificial	artificial	ADJ
ejpam-6129	317	6	systems	system	NOUN
ejpam-6129	317	7	.	.	PUNCT
ejpam-6129	318	1	s.	s.	PROPN
ejpam-6129	318	2	a.	a.	PROPN
ejpam-6129	318	3	mohamed	mohamed	PROPN
ejpam-6129	318	4	et	et	PROPN
ejpam-6129	318	5	al	al	PROPN
ejpam-6129	318	6	.	.	PUNCT
ejpam-6129	318	7	/	/	SYM
ejpam-6129	318	8	eur	eur	PROPN
ejpam-6129	318	9	.	.	PUNCT
ejpam-6129	319	1	j.	j.	PROPN
ejpam-6129	319	2	pure	pure	PROPN
ejpam-6129	319	3	appl	appl	PROPN
ejpam-6129	319	4	.	.	PROPN
ejpam-6129	319	5	math	math	PROPN
ejpam-6129	319	6	,	,	PUNCT
ejpam-6129	319	7	18	18	NUM
ejpam-6129	319	8	(	(	PUNCT
ejpam-6129	319	9	3	3	NUM
ejpam-6129	319	10	)	)	PUNCT
ejpam-6129	319	11	(	(	PUNCT
ejpam-6129	319	12	2025	2025	NUM
ejpam-6129	319	13	)	)	PUNCT
ejpam-6129	319	14	,	,	PUNCT
ejpam-6129	319	15	6129	6129	NUM
ejpam-6129	319	16	17	17	NUM
ejpam-6129	319	17	of	of	ADP
ejpam-6129	319	18	17	17	NUM
ejpam-6129	319	19	university	university	PROPN
ejpam-6129	319	20	of	of	ADP
ejpam-6129	319	21	michigan	michigan	PROPN
ejpam-6129	319	22	press	press	PROPN
ejpam-6129	319	23	,	,	PUNCT
ejpam-6129	319	24	springer	springer	NOUN
ejpam-6129	319	25	verlag	verlag	PROPN
ejpam-6129	319	26	,	,	PUNCT
ejpam-6129	319	27	new	new	PROPN
ejpam-6129	319	28	york	york	PROPN
ejpam-6129	319	29	,	,	PUNCT
ejpam-6129	319	30	1975	1975	NUM
ejpam-6129	319	31	.	.	PUNCT