id	sid	tid	token	lemma	pos
ejpam-6670	1	1	european	european	PROPN
ejpam-6670	1	2	journal	journal	PROPN
ejpam-6670	1	3	of	of	ADP
ejpam-6670	1	4	pure	pure	ADJ
ejpam-6670	1	5	and	and	CCONJ
ejpam-6670	1	6	applied	applied	ADJ
ejpam-6670	1	7	mathematics	mathematic	NOUN
ejpam-6670	1	8	2025	2025	NUM
ejpam-6670	1	9	,	,	PUNCT
ejpam-6670	1	10	vol	vol	NOUN
ejpam-6670	1	11	.	.	PROPN
ejpam-6670	1	12	18	18	NUM
ejpam-6670	1	13	,	,	PUNCT
ejpam-6670	1	14	issue	issue	NOUN
ejpam-6670	1	15	3	3	NUM
ejpam-6670	1	16	,	,	PUNCT
ejpam-6670	1	17	article	article	NOUN
ejpam-6670	1	18	number	number	NOUN
ejpam-6670	1	19	6670	6670	NUM
ejpam-6670	1	20	issn	issn	PROPN
ejpam-6670	1	21	1307	1307	NUM
ejpam-6670	1	22	-	-	SYM
ejpam-6670	1	23	5543	5543	NUM
ejpam-6670	1	24	–	–	PUNCT
ejpam-6670	1	25	ejpam.com	ejpam.com	X
ejpam-6670	1	26	published	publish	VERB
ejpam-6670	1	27	by	by	ADP
ejpam-6670	1	28	new	new	PROPN
ejpam-6670	1	29	york	york	PROPN
ejpam-6670	1	30	business	business	PROPN
ejpam-6670	1	31	global	global	PROPN
ejpam-6670	1	32	numerical	numerical	ADJ
ejpam-6670	1	33	assessment	assessment	NOUN
ejpam-6670	1	34	of	of	ADP
ejpam-6670	1	35	the	the	DET
ejpam-6670	1	36	hepatitis	hepatitis	PROPN
ejpam-6670	1	37	b	b	PROPN
ejpam-6670	1	38	virus	virus	NOUN
ejpam-6670	1	39	transmission	transmission	NOUN
ejpam-6670	1	40	model	model	NOUN
ejpam-6670	1	41	using	use	VERB
ejpam-6670	1	42	a	a	DET
ejpam-6670	1	43	non	non	ADJ
ejpam-6670	1	44	-	-	ADJ
ejpam-6670	1	45	standard	standard	ADJ
ejpam-6670	1	46	finite	finite	ADJ
ejpam-6670	1	47	difference	difference	NOUN
ejpam-6670	1	48	scheme	scheme	NOUN
ejpam-6670	1	49	and	and	CCONJ
ejpam-6670	1	50	a	a	DET
ejpam-6670	1	51	feedforward	feedforward	ADJ
ejpam-6670	1	52	neural	neural	ADJ
ejpam-6670	1	53	network	network	NOUN
ejpam-6670	1	54	tahir	tahir	PROPN
ejpam-6670	1	55	khan1	khan1	PROPN
ejpam-6670	1	56	,	,	PUNCT
ejpam-6670	1	57	ii	ii	PROPN
ejpam-6670	1	58	hyo	hyo	PROPN
ejpam-6670	1	59	jung1,∗	jung1,∗	PROPN
ejpam-6670	1	60	,	,	PUNCT
ejpam-6670	1	61	gul	gul	PROPN
ejpam-6670	1	62	zaman2	zaman2	PROPN
ejpam-6670	1	63	,	,	PUNCT
ejpam-6670	1	64	ilyas	ilyas	PROPN
ejpam-6670	1	65	khan3	khan3	PROPN
ejpam-6670	1	66	1	1	NUM
ejpam-6670	1	67	department	department	NOUN
ejpam-6670	1	68	of	of	ADP
ejpam-6670	1	69	mathematics	mathematics	PROPN
ejpam-6670	1	70	/	/	SYM
ejpam-6670	1	71	institute	institute	PROPN
ejpam-6670	1	72	of	of	ADP
ejpam-6670	1	73	mathematical	mathematical	ADJ
ejpam-6670	1	74	science	science	NOUN
ejpam-6670	1	75	,	,	PUNCT
ejpam-6670	1	76	pusan	pusan	PROPN
ejpam-6670	1	77	national	national	PROPN
ejpam-6670	1	78	university	university	PROPN
ejpam-6670	1	79	,	,	PUNCT
ejpam-6670	1	80	busan	busan	PROPN
ejpam-6670	1	81	,	,	PUNCT
ejpam-6670	1	82	republic	republic	NOUN
ejpam-6670	1	83	of	of	ADP
ejpam-6670	1	84	korea	korea	PROPN
ejpam-6670	1	85	2	2	PROPN
ejpam-6670	1	86	department	department	NOUN
ejpam-6670	1	87	of	of	ADP
ejpam-6670	1	88	mathematics	mathematics	PROPN
ejpam-6670	1	89	,	,	PUNCT
ejpam-6670	1	90	university	university	NOUN
ejpam-6670	1	91	of	of	ADP
ejpam-6670	1	92	malakand	malakand	PROPN
ejpam-6670	1	93	chakdara	chakdara	PROPN
ejpam-6670	1	94	,	,	PUNCT
ejpam-6670	1	95	dir	dir	NOUN
ejpam-6670	1	96	(	(	PUNCT
ejpam-6670	1	97	l	l	NOUN
ejpam-6670	1	98	)	)	PUNCT
ejpam-6670	1	99	,	,	PUNCT
ejpam-6670	1	100	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6670	1	101	,	,	PUNCT
ejpam-6670	1	102	pakistan	pakistan	PROPN
ejpam-6670	1	103	3	3	NUM
ejpam-6670	1	104	faculty	faculty	NOUN
ejpam-6670	1	105	of	of	ADP
ejpam-6670	1	106	mathematics	mathematic	NOUN
ejpam-6670	1	107	and	and	CCONJ
ejpam-6670	1	108	statistics	statistic	NOUN
ejpam-6670	1	109	,	,	PUNCT
ejpam-6670	1	110	ton	ton	PROPN
ejpam-6670	1	111	duc	duc	PROPN
ejpam-6670	1	112	thang	thang	PROPN
ejpam-6670	1	113	university	university	PROPN
ejpam-6670	1	114	,	,	PUNCT
ejpam-6670	1	115	ho	ho	PROPN
ejpam-6670	1	116	chi	chi	PROPN
ejpam-6670	1	117	minh	minh	PROPN
ejpam-6670	1	118	city	city	PROPN
ejpam-6670	1	119	,	,	PUNCT
ejpam-6670	1	120	vietnam	vietnam	PROPN
ejpam-6670	1	121	abstract	abstract	NOUN
ejpam-6670	1	122	.	.	PUNCT
ejpam-6670	2	1	hepatitis	hepatitis	PROPN
ejpam-6670	2	2	b	b	PROPN
ejpam-6670	2	3	virus	virus	NOUN
ejpam-6670	2	4	(	(	PUNCT
ejpam-6670	2	5	hbv	hbv	NOUN
ejpam-6670	2	6	)	)	PUNCT
ejpam-6670	2	7	infection	infection	NOUN
ejpam-6670	2	8	is	be	AUX
ejpam-6670	2	9	one	one	NUM
ejpam-6670	2	10	of	of	ADP
ejpam-6670	2	11	the	the	DET
ejpam-6670	2	12	leading	lead	VERB
ejpam-6670	2	13	causes	cause	NOUN
ejpam-6670	2	14	of	of	ADP
ejpam-6670	2	15	death	death	NOUN
ejpam-6670	2	16	and	and	CCONJ
ejpam-6670	2	17	is	be	AUX
ejpam-6670	2	18	a	a	DET
ejpam-6670	2	19	contagious	contagious	ADJ
ejpam-6670	2	20	disease	disease	NOUN
ejpam-6670	2	21	that	that	PRON
ejpam-6670	2	22	produces	produce	VERB
ejpam-6670	2	23	chronic	chronic	ADJ
ejpam-6670	2	24	liver	liver	NOUN
ejpam-6670	2	25	infection	infection	NOUN
ejpam-6670	2	26	.	.	PUNCT
ejpam-6670	3	1	the	the	DET
ejpam-6670	3	2	infection	infection	NOUN
ejpam-6670	3	3	of	of	ADP
ejpam-6670	3	4	hepatitis	hepatitis	PROPN
ejpam-6670	3	5	b	b	PROPN
ejpam-6670	3	6	has	have	VERB
ejpam-6670	3	7	a	a	DET
ejpam-6670	3	8	complex	complex	ADJ
ejpam-6670	3	9	nature	nature	NOUN
ejpam-6670	3	10	involving	involve	VERB
ejpam-6670	3	11	multiple	multiple	ADJ
ejpam-6670	3	12	and	and	CCONJ
ejpam-6670	3	13	long	long	ADJ
ejpam-6670	3	14	infectious	infectious	ADJ
ejpam-6670	3	15	periods	period	NOUN
ejpam-6670	3	16	,	,	PUNCT
ejpam-6670	3	17	behavioral	behavioral	ADJ
ejpam-6670	3	18	changes	change	NOUN
ejpam-6670	3	19	,	,	PUNCT
ejpam-6670	3	20	and	and	CCONJ
ejpam-6670	3	21	healthcare	healthcare	NOUN
ejpam-6670	3	22	limitations	limitation	NOUN
ejpam-6670	3	23	.	.	PUNCT
ejpam-6670	4	1	the	the	DET
ejpam-6670	4	2	multiple	multiple	ADJ
ejpam-6670	4	3	infection	infection	NOUN
ejpam-6670	4	4	phases	phase	NOUN
ejpam-6670	4	5	,	,	PUNCT
ejpam-6670	4	6	immune	immune	ADJ
ejpam-6670	4	7	system	system	NOUN
ejpam-6670	4	8	,	,	PUNCT
ejpam-6670	4	9	behavioral	behavioral	ADJ
ejpam-6670	4	10	changes	change	NOUN
ejpam-6670	4	11	,	,	PUNCT
ejpam-6670	4	12	and	and	CCONJ
ejpam-6670	4	13	healthcare	healthcare	NOUN
ejpam-6670	4	14	saturation	saturation	NOUN
ejpam-6670	4	15	have	have	VERB
ejpam-6670	4	16	a	a	DET
ejpam-6670	4	17	significant	significant	ADJ
ejpam-6670	4	18	impact	impact	NOUN
ejpam-6670	4	19	on	on	ADP
ejpam-6670	4	20	the	the	DET
ejpam-6670	4	21	dynamics	dynamic	NOUN
ejpam-6670	4	22	of	of	ADP
ejpam-6670	4	23	hepatitis	hepatitis	PROPN
ejpam-6670	4	24	b	b	PROPN
ejpam-6670	4	25	virus	virus	NOUN
ejpam-6670	4	26	transmission	transmission	NOUN
ejpam-6670	4	27	.	.	PUNCT
ejpam-6670	5	1	since	since	SCONJ
ejpam-6670	5	2	hbv	hbv	NOUN
ejpam-6670	5	3	can	can	AUX
ejpam-6670	5	4	persist	persist	VERB
ejpam-6670	5	5	in	in	ADP
ejpam-6670	5	6	the	the	DET
ejpam-6670	5	7	body	body	NOUN
ejpam-6670	5	8	for	for	ADP
ejpam-6670	5	9	years	year	NOUN
ejpam-6670	5	10	,	,	PUNCT
ejpam-6670	5	11	the	the	DET
ejpam-6670	5	12	number	number	NOUN
ejpam-6670	5	13	of	of	ADP
ejpam-6670	5	14	infectious	infectious	ADJ
ejpam-6670	5	15	individuals	individual	NOUN
ejpam-6670	5	16	accumulates	accumulate	VERB
ejpam-6670	5	17	,	,	PUNCT
ejpam-6670	5	18	and	and	CCONJ
ejpam-6670	5	19	people	people	NOUN
ejpam-6670	5	20	take	take	VERB
ejpam-6670	5	21	precautionary	precautionary	ADJ
ejpam-6670	5	22	measures	measure	NOUN
ejpam-6670	5	23	as	as	ADP
ejpam-6670	5	24	awareness	awareness	NOUN
ejpam-6670	5	25	increases	increase	NOUN
ejpam-6670	5	26	.	.	PUNCT
ejpam-6670	6	1	considering	consider	VERB
ejpam-6670	6	2	the	the	DET
ejpam-6670	6	3	multiple	multiple	ADJ
ejpam-6670	6	4	stages	stage	NOUN
ejpam-6670	6	5	of	of	ADP
ejpam-6670	6	6	the	the	DET
ejpam-6670	6	7	disease	disease	NOUN
ejpam-6670	6	8	and	and	CCONJ
ejpam-6670	6	9	the	the	DET
ejpam-6670	6	10	saturation	saturation	NOUN
ejpam-6670	6	11	level	level	NOUN
ejpam-6670	6	12	,	,	PUNCT
ejpam-6670	6	13	we	we	PRON
ejpam-6670	6	14	propose	propose	VERB
ejpam-6670	6	15	an	an	DET
ejpam-6670	6	16	innovative	innovative	ADJ
ejpam-6670	6	17	hybrid	hybrid	NOUN
ejpam-6670	6	18	approach	approach	NOUN
ejpam-6670	6	19	combining	combine	VERB
ejpam-6670	6	20	a	a	DET
ejpam-6670	6	21	mathematical	mathematical	ADJ
ejpam-6670	6	22	model	model	NOUN
ejpam-6670	6	23	with	with	ADP
ejpam-6670	6	24	a	a	DET
ejpam-6670	6	25	saturated	saturate	VERB
ejpam-6670	6	26	incidence	incidence	NOUN
ejpam-6670	6	27	rate	rate	NOUN
ejpam-6670	6	28	and	and	CCONJ
ejpam-6670	6	29	a	a	DET
ejpam-6670	6	30	forward	forward	ADJ
ejpam-6670	6	31	neural	neural	ADJ
ejpam-6670	6	32	network	network	NOUN
ejpam-6670	6	33	to	to	PART
ejpam-6670	6	34	represent	represent	VERB
ejpam-6670	6	35	the	the	DET
ejpam-6670	6	36	transmission	transmission	NOUN
ejpam-6670	6	37	dynamics	dynamic	NOUN
ejpam-6670	6	38	of	of	ADP
ejpam-6670	6	39	the	the	DET
ejpam-6670	6	40	hepatitis	hepatitis	PROPN
ejpam-6670	6	41	b	b	PROPN
ejpam-6670	6	42	virus	virus	NOUN
ejpam-6670	6	43	.	.	PUNCT
ejpam-6670	7	1	first	first	ADV
ejpam-6670	7	2	,	,	PUNCT
ejpam-6670	7	3	we	we	PRON
ejpam-6670	7	4	prove	prove	VERB
ejpam-6670	7	5	the	the	DET
ejpam-6670	7	6	biological	biological	ADJ
ejpam-6670	7	7	and	and	CCONJ
ejpam-6670	7	8	mathematical	mathematical	ADJ
ejpam-6670	7	9	feasibility	feasibility	NOUN
ejpam-6670	7	10	to	to	PART
ejpam-6670	7	11	show	show	VERB
ejpam-6670	7	12	that	that	SCONJ
ejpam-6670	7	13	the	the	DET
ejpam-6670	7	14	model	model	NOUN
ejpam-6670	7	15	under	under	ADP
ejpam-6670	7	16	consideration	consideration	NOUN
ejpam-6670	7	17	is	be	AUX
ejpam-6670	7	18	well	well	ADV
ejpam-6670	7	19	-	-	PUNCT
ejpam-6670	7	20	posed	pose	VERB
ejpam-6670	7	21	.	.	PUNCT
ejpam-6670	8	1	we	we	PRON
ejpam-6670	8	2	also	also	ADV
ejpam-6670	8	3	investigate	investigate	VERB
ejpam-6670	8	4	the	the	DET
ejpam-6670	8	5	dynamics	dynamic	NOUN
ejpam-6670	8	6	of	of	ADP
ejpam-6670	8	7	the	the	DET
ejpam-6670	8	8	model	model	NOUN
ejpam-6670	8	9	using	use	VERB
ejpam-6670	8	10	linear	linear	PROPN
ejpam-6670	8	11	stability	stability	NOUN
ejpam-6670	8	12	analysis	analysis	NOUN
ejpam-6670	8	13	to	to	PART
ejpam-6670	8	14	derive	derive	VERB
ejpam-6670	8	15	the	the	DET
ejpam-6670	8	16	stability	stability	NOUN
ejpam-6670	8	17	conditions	condition	NOUN
ejpam-6670	8	18	.	.	PUNCT
ejpam-6670	9	1	in	in	ADP
ejpam-6670	9	2	addition	addition	NOUN
ejpam-6670	9	3	,	,	PUNCT
ejpam-6670	9	4	we	we	PRON
ejpam-6670	9	5	perform	perform	VERB
ejpam-6670	9	6	the	the	DET
ejpam-6670	9	7	numerical	numerical	ADJ
ejpam-6670	9	8	assessment	assessment	NOUN
ejpam-6670	9	9	of	of	ADP
ejpam-6670	9	10	the	the	DET
ejpam-6670	9	11	model	model	NOUN
ejpam-6670	9	12	using	use	VERB
ejpam-6670	9	13	a	a	DET
ejpam-6670	9	14	novel	novel	ADJ
ejpam-6670	9	15	hybrid	hybrid	NOUN
ejpam-6670	9	16	approach	approach	NOUN
ejpam-6670	9	17	of	of	ADP
ejpam-6670	9	18	nsfd	nsfd	ADJ
ejpam-6670	9	19	–	–	PUNCT
ejpam-6670	9	20	ffnn	ffnn	NOUN
ejpam-6670	9	21	framework	framework	NOUN
ejpam-6670	9	22	to	to	PART
ejpam-6670	9	23	show	show	VERB
ejpam-6670	9	24	the	the	DET
ejpam-6670	9	25	accuracy	accuracy	NOUN
ejpam-6670	9	26	and	and	CCONJ
ejpam-6670	9	27	large	large	ADJ
ejpam-6670	9	28	-	-	PUNCT
ejpam-6670	9	29	scale	scale	NOUN
ejpam-6670	9	30	numerical	numerical	ADJ
ejpam-6670	9	31	simulations	simulation	NOUN
ejpam-6670	9	32	.	.	PUNCT
ejpam-6670	10	1	2020	2020	NUM
ejpam-6670	10	2	mathematics	mathematic	NOUN
ejpam-6670	10	3	subject	subject	NOUN
ejpam-6670	10	4	classifications	classification	NOUN
ejpam-6670	10	5	:	:	PUNCT
ejpam-6670	10	6	92d30	92d30	NUM
ejpam-6670	10	7	,	,	PUNCT
ejpam-6670	10	8	65l12	65l12	NUM
ejpam-6670	10	9	,	,	PUNCT
ejpam-6670	10	10	65m06	65m06	NUM
ejpam-6670	10	11	,	,	PUNCT
ejpam-6670	10	12	68t07	68t07	NUM
ejpam-6670	10	13	key	key	ADJ
ejpam-6670	10	14	words	word	NOUN
ejpam-6670	10	15	and	and	CCONJ
ejpam-6670	10	16	phrases	phrase	NOUN
ejpam-6670	10	17	:	:	PUNCT
ejpam-6670	10	18	stability	stability	NOUN
ejpam-6670	10	19	analysis	analysis	NOUN
ejpam-6670	10	20	,	,	PUNCT
ejpam-6670	10	21	non	non	ADJ
ejpam-6670	10	22	-	-	ADJ
ejpam-6670	10	23	standard	standard	ADJ
ejpam-6670	10	24	finite	finite	ADJ
ejpam-6670	10	25	difference	difference	NOUN
ejpam-6670	10	26	scheme	scheme	NOUN
ejpam-6670	10	27	,	,	PUNCT
ejpam-6670	10	28	feed	feed	NOUN
ejpam-6670	10	29	-	-	PUNCT
ejpam-6670	10	30	forward	forward	NOUN
ejpam-6670	10	31	neural	neural	ADJ
ejpam-6670	10	32	network	network	NOUN
ejpam-6670	10	33	,	,	PUNCT
ejpam-6670	10	34	numerical	numerical	ADJ
ejpam-6670	10	35	simulations	simulation	NOUN
ejpam-6670	10	36	1	1	NUM
ejpam-6670	10	37	.	.	PUNCT
ejpam-6670	11	1	introduction	introduction	NOUN
ejpam-6670	11	2	living	live	VERB
ejpam-6670	11	3	things	thing	NOUN
ejpam-6670	11	4	,	,	PUNCT
ejpam-6670	11	5	particularly	particularly	ADV
ejpam-6670	11	6	humans	human	NOUN
ejpam-6670	11	7	,	,	PUNCT
ejpam-6670	11	8	are	be	AUX
ejpam-6670	11	9	constantly	constantly	ADV
ejpam-6670	11	10	at	at	ADP
ejpam-6670	11	11	risk	risk	NOUN
ejpam-6670	11	12	from	from	ADP
ejpam-6670	11	13	infectious	infectious	ADJ
ejpam-6670	11	14	diseases	disease	NOUN
ejpam-6670	11	15	.	.	PUNCT
ejpam-6670	12	1	every	every	DET
ejpam-6670	12	2	person	person	NOUN
ejpam-6670	12	3	may	may	AUX
ejpam-6670	12	4	experience	experience	VERB
ejpam-6670	12	5	an	an	DET
ejpam-6670	12	6	infectious	infectious	ADJ
ejpam-6670	12	7	disease	disease	NOUN
ejpam-6670	12	8	once	once	ADV
ejpam-6670	12	9	or	or	CCONJ
ejpam-6670	12	10	multiple	multiple	ADJ
ejpam-6670	12	11	times	time	NOUN
ejpam-6670	12	12	during	during	ADP
ejpam-6670	12	13	their	their	PRON
ejpam-6670	12	14	∗corresponding	∗corresponde	VERB
ejpam-6670	12	15	author	author	NOUN
ejpam-6670	12	16	.	.	PUNCT
ejpam-6670	13	1	doi	doi	NOUN
ejpam-6670	13	2	:	:	PUNCT
ejpam-6670	13	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6670	https://doi.org/10.29020/nybg.ejpam.v18i3.6670	ADP
ejpam-6670	13	4	email	email	NOUN
ejpam-6670	13	5	addresses	address	NOUN
ejpam-6670	13	6	:	:	PUNCT
ejpam-6670	13	7	tahirmaths200014@gmail.com	tahirmaths200014@gmail.com	X
ejpam-6670	13	8	(	(	PUNCT
ejpam-6670	13	9	t.	t.	PROPN
ejpam-6670	13	10	khan	khan	PROPN
ejpam-6670	13	11	)	)	PUNCT
ejpam-6670	13	12	,	,	PUNCT
ejpam-6670	13	13	ilhjung@pusan.ac.kr	ilhjung@pusan.ac.kr	PROPN
ejpam-6670	13	14	(	(	PUNCT
ejpam-6670	13	15	i.	i.	PROPN
ejpam-6670	13	16	h.	h.	PROPN
ejpam-6670	13	17	jung	jung	PROPN
ejpam-6670	13	18	)	)	PUNCT
ejpam-6670	13	19	,	,	PUNCT
ejpam-6670	13	20	gzaman@uom.edu.pk	gzaman@uom.edu.pk	NOUN
ejpam-6670	13	21	(	(	PUNCT
ejpam-6670	13	22	g.	g.	PROPN
ejpam-6670	13	23	zaman	zaman	PROPN
ejpam-6670	13	24	)	)	PUNCT
ejpam-6670	13	25	,	,	PUNCT
ejpam-6670	13	26	ilyaskhanqau@yahoo.com	ilyaskhanqau@yahoo.com	PROPN
ejpam-6670	13	27	(	(	PUNCT
ejpam-6670	13	28	i.	i.	PROPN
ejpam-6670	13	29	khan	khan	PROPN
ejpam-6670	13	30	)	)	PUNCT
ejpam-6670	13	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6670	14	1	1	1	NUM
ejpam-6670	14	2	copyright	copyright	NOUN
ejpam-6670	14	3	:	:	PUNCT
ejpam-6670	14	4	©	©	PROPN
ejpam-6670	14	5	2025	2025	NUM
ejpam-6670	14	6	the	the	DET
ejpam-6670	14	7	author(s	author(s	NOUN
ejpam-6670	14	8	)	)	PUNCT
ejpam-6670	14	9	.	.	PUNCT
ejpam-6670	15	1	(	(	PUNCT
ejpam-6670	15	2	cc	cc	NOUN
ejpam-6670	15	3	by	by	ADP
ejpam-6670	15	4	-	-	PUNCT
ejpam-6670	15	5	nc	nc	PROPN
ejpam-6670	15	6	4.0	4.0	NUM
ejpam-6670	15	7	)	)	PUNCT
ejpam-6670	15	8	t.	t.	PROPN
ejpam-6670	15	9	khan	khan	PROPN
ejpam-6670	15	10	et	et	PROPN
ejpam-6670	15	11	al	al	PROPN
ejpam-6670	15	12	.	.	PUNCT
ejpam-6670	15	13	/	/	SYM
ejpam-6670	15	14	eur	eur	PROPN
ejpam-6670	15	15	.	.	PUNCT
ejpam-6670	16	1	j.	j.	PROPN
ejpam-6670	16	2	pure	pure	PROPN
ejpam-6670	16	3	appl	appl	PROPN
ejpam-6670	16	4	.	.	PROPN
ejpam-6670	16	5	math	math	PROPN
ejpam-6670	16	6	,	,	PUNCT
ejpam-6670	16	7	18	18	NUM
ejpam-6670	16	8	(	(	PUNCT
ejpam-6670	16	9	3	3	NUM
ejpam-6670	16	10	)	)	PUNCT
ejpam-6670	16	11	(	(	PUNCT
ejpam-6670	16	12	2025	2025	NUM
ejpam-6670	16	13	)	)	PUNCT
ejpam-6670	16	14	,	,	PUNCT
ejpam-6670	16	15	6670	6670	NUM
ejpam-6670	16	16	2	2	NUM
ejpam-6670	16	17	of	of	ADP
ejpam-6670	16	18	22	22	NUM
ejpam-6670	16	19	lifetime	lifetime	NOUN
ejpam-6670	16	20	.	.	PUNCT
ejpam-6670	17	1	the	the	DET
ejpam-6670	17	2	infection	infection	NOUN
ejpam-6670	17	3	could	could	AUX
ejpam-6670	17	4	be	be	AUX
ejpam-6670	17	5	acute	acute	ADJ
ejpam-6670	17	6	or	or	CCONJ
ejpam-6670	17	7	chronic	chronic	ADJ
ejpam-6670	17	8	,	,	PUNCT
ejpam-6670	17	9	i.e.	i.e.	X
ejpam-6670	17	10	,	,	PUNCT
ejpam-6670	17	11	short	short	ADJ
ejpam-6670	17	12	-	-	PUNCT
ejpam-6670	17	13	term	term	NOUN
ejpam-6670	17	14	or	or	CCONJ
ejpam-6670	17	15	long	long	ADJ
ejpam-6670	17	16	-	-	PUNCT
ejpam-6670	17	17	term	term	NOUN
ejpam-6670	17	18	,	,	PUNCT
ejpam-6670	17	19	but	but	CCONJ
ejpam-6670	17	20	cause	cause	VERB
ejpam-6670	17	21	mortality	mortality	NOUN
ejpam-6670	17	22	.	.	PUNCT
ejpam-6670	18	1	the	the	DET
ejpam-6670	18	2	second	second	ADJ
ejpam-6670	18	3	leading	leading	ADJ
ejpam-6670	18	4	cause	cause	NOUN
ejpam-6670	18	5	of	of	ADP
ejpam-6670	18	6	death	death	NOUN
ejpam-6670	18	7	and	and	CCONJ
ejpam-6670	18	8	disability	disability	NOUN
ejpam-6670	18	9	in	in	ADP
ejpam-6670	18	10	human	human	ADJ
ejpam-6670	18	11	beings	being	NOUN
ejpam-6670	18	12	and	and	CCONJ
ejpam-6670	18	13	other	other	ADJ
ejpam-6670	18	14	living	live	VERB
ejpam-6670	18	15	organisms	organism	NOUN
ejpam-6670	18	16	is	be	AUX
ejpam-6670	18	17	infectious	infectious	ADJ
ejpam-6670	18	18	diseases	disease	NOUN
ejpam-6670	18	19	around	around	ADP
ejpam-6670	18	20	the	the	DET
ejpam-6670	18	21	globe	globe	NOUN
ejpam-6670	18	22	,	,	PUNCT
ejpam-6670	18	23	according	accord	VERB
ejpam-6670	18	24	to	to	ADP
ejpam-6670	18	25	the	the	DET
ejpam-6670	18	26	who	who	PRON
ejpam-6670	18	27	.	.	PUNCT
ejpam-6670	19	1	in	in	ADP
ejpam-6670	19	2	the	the	DET
ejpam-6670	19	3	current	current	ADJ
ejpam-6670	19	4	century	century	NOUN
ejpam-6670	19	5	,	,	PUNCT
ejpam-6670	19	6	millions	million	NOUN
ejpam-6670	19	7	of	of	ADP
ejpam-6670	19	8	people	people	NOUN
ejpam-6670	19	9	suffer	suffer	VERB
ejpam-6670	19	10	due	due	ADP
ejpam-6670	19	11	to	to	ADP
ejpam-6670	19	12	the	the	DET
ejpam-6670	19	13	consequences	consequence	NOUN
ejpam-6670	19	14	of	of	ADP
ejpam-6670	19	15	infectious	infectious	ADJ
ejpam-6670	19	16	diseases	disease	NOUN
ejpam-6670	19	17	.	.	PUNCT
ejpam-6670	20	1	among	among	ADP
ejpam-6670	20	2	these	these	PRON
ejpam-6670	20	3	are	be	AUX
ejpam-6670	20	4	tuberculosis	tuberculosis	NOUN
ejpam-6670	20	5	,	,	PUNCT
ejpam-6670	20	6	diarrheal	diarrheal	ADJ
ejpam-6670	20	7	diseases	disease	NOUN
ejpam-6670	20	8	,	,	PUNCT
ejpam-6670	20	9	malaria	malaria	NOUN
ejpam-6670	20	10	,	,	PUNCT
ejpam-6670	20	11	hepatitis	hepatitis	PROPN
ejpam-6670	20	12	,	,	PUNCT
ejpam-6670	20	13	hiv	hiv	PROPN
ejpam-6670	20	14	/	/	SYM
ejpam-6670	20	15	aids	aids	PROPN
ejpam-6670	20	16	,	,	PUNCT
ejpam-6670	20	17	etc	etc	X
ejpam-6670	20	18	.	.	X
ejpam-6670	21	1	the	the	DET
ejpam-6670	21	2	liver	liver	NOUN
ejpam-6670	21	3	is	be	AUX
ejpam-6670	21	4	one	one	NUM
ejpam-6670	21	5	of	of	ADP
ejpam-6670	21	6	the	the	DET
ejpam-6670	21	7	important	important	ADJ
ejpam-6670	21	8	organs	organ	NOUN
ejpam-6670	21	9	in	in	ADP
ejpam-6670	21	10	the	the	DET
ejpam-6670	21	11	human	human	ADJ
ejpam-6670	21	12	body	body	NOUN
ejpam-6670	21	13	,	,	PUNCT
ejpam-6670	21	14	located	locate	VERB
ejpam-6670	21	15	in	in	ADP
ejpam-6670	21	16	the	the	DET
ejpam-6670	21	17	upper	upper	ADJ
ejpam-6670	21	18	right	right	ADJ
ejpam-6670	21	19	-	-	PUNCT
ejpam-6670	21	20	hand	hand	NOUN
ejpam-6670	21	21	part	part	NOUN
ejpam-6670	21	22	of	of	ADP
ejpam-6670	21	23	the	the	DET
ejpam-6670	21	24	abdomen	abdoman	NOUN
ejpam-6670	21	25	.	.	PUNCT
ejpam-6670	22	1	hepatitis	hepatitis	PROPN
ejpam-6670	22	2	b	b	PROPN
ejpam-6670	22	3	is	be	AUX
ejpam-6670	22	4	one	one	NUM
ejpam-6670	22	5	of	of	ADP
ejpam-6670	22	6	the	the	DET
ejpam-6670	22	7	severe	severe	ADJ
ejpam-6670	22	8	types	type	NOUN
ejpam-6670	22	9	of	of	ADP
ejpam-6670	22	10	hepatitis	hepatitis	NOUN
ejpam-6670	22	11	that	that	PRON
ejpam-6670	22	12	produces	produce	VERB
ejpam-6670	22	13	inflammation	inflammation	NOUN
ejpam-6670	22	14	of	of	ADP
ejpam-6670	22	15	the	the	DET
ejpam-6670	22	16	liver	liver	NOUN
ejpam-6670	22	17	and	and	CCONJ
ejpam-6670	22	18	leads	lead	VERB
ejpam-6670	22	19	to	to	ADP
ejpam-6670	22	20	cirrhosis	cirrhosis	NOUN
ejpam-6670	22	21	[	[	X
ejpam-6670	22	22	1	1	NUM
ejpam-6670	22	23	]	]	PUNCT
ejpam-6670	22	24	.	.	PUNCT
ejpam-6670	23	1	hepatitis	hepatitis	PROPN
ejpam-6670	23	2	b	b	PROPN
ejpam-6670	23	3	is	be	AUX
ejpam-6670	23	4	transmitted	transmit	VERB
ejpam-6670	23	5	from	from	ADP
ejpam-6670	23	6	one	one	NUM
ejpam-6670	23	7	individual	individual	NOUN
ejpam-6670	23	8	to	to	ADP
ejpam-6670	23	9	another	another	PRON
ejpam-6670	23	10	by	by	ADP
ejpam-6670	23	11	direct	direct	ADJ
ejpam-6670	23	12	contact	contact	NOUN
ejpam-6670	23	13	or	or	CCONJ
ejpam-6670	23	14	indirect	indirect	ADJ
ejpam-6670	23	15	contact	contact	NOUN
ejpam-6670	23	16	[	[	X
ejpam-6670	23	17	2	2	NUM
ejpam-6670	23	18	]	]	PUNCT
ejpam-6670	23	19	.	.	PUNCT
ejpam-6670	24	1	hepatitis	hepatitis	PROPN
ejpam-6670	24	2	b	b	PROPN
ejpam-6670	24	3	virus	virus	NOUN
ejpam-6670	24	4	(	(	PUNCT
ejpam-6670	24	5	hbv	hbv	NOUN
ejpam-6670	24	6	)	)	PUNCT
ejpam-6670	24	7	infection	infection	NOUN
ejpam-6670	24	8	progresses	progress	VERB
ejpam-6670	24	9	through	through	ADP
ejpam-6670	24	10	multiple	multiple	ADJ
ejpam-6670	24	11	phases	phase	NOUN
ejpam-6670	24	12	,	,	PUNCT
ejpam-6670	24	13	most	most	ADV
ejpam-6670	24	14	notably	notably	ADV
ejpam-6670	24	15	the	the	DET
ejpam-6670	24	16	acute	acute	ADJ
ejpam-6670	24	17	and	and	CCONJ
ejpam-6670	24	18	chronic	chronic	ADJ
ejpam-6670	24	19	stages	stage	NOUN
ejpam-6670	24	20	,	,	PUNCT
ejpam-6670	24	21	which	which	PRON
ejpam-6670	24	22	are	be	AUX
ejpam-6670	24	23	critical	critical	ADJ
ejpam-6670	24	24	in	in	ADP
ejpam-6670	24	25	understanding	understand	VERB
ejpam-6670	24	26	its	its	PRON
ejpam-6670	24	27	clinical	clinical	ADJ
ejpam-6670	24	28	and	and	CCONJ
ejpam-6670	24	29	epidemiological	epidemiological	ADJ
ejpam-6670	24	30	impact	impact	NOUN
ejpam-6670	24	31	.	.	PUNCT
ejpam-6670	25	1	during	during	ADP
ejpam-6670	25	2	the	the	DET
ejpam-6670	25	3	acute	acute	ADJ
ejpam-6670	25	4	phase	phase	NOUN
ejpam-6670	25	5	,	,	PUNCT
ejpam-6670	25	6	individuals	individual	NOUN
ejpam-6670	25	7	often	often	ADV
ejpam-6670	25	8	remain	remain	VERB
ejpam-6670	25	9	asymptomatic	asymptomatic	ADJ
ejpam-6670	25	10	and	and	CCONJ
ejpam-6670	25	11	may	may	AUX
ejpam-6670	25	12	recover	recover	VERB
ejpam-6670	25	13	spontaneously	spontaneously	ADV
ejpam-6670	25	14	without	without	ADP
ejpam-6670	25	15	the	the	DET
ejpam-6670	25	16	need	need	NOUN
ejpam-6670	25	17	for	for	ADP
ejpam-6670	25	18	antiviral	antiviral	ADJ
ejpam-6670	25	19	treatment	treatment	NOUN
ejpam-6670	25	20	.	.	PUNCT
ejpam-6670	26	1	however	however	ADV
ejpam-6670	26	2	,	,	PUNCT
ejpam-6670	26	3	a	a	DET
ejpam-6670	26	4	subset	subset	NOUN
ejpam-6670	26	5	of	of	ADP
ejpam-6670	26	6	infected	infected	ADJ
ejpam-6670	26	7	individuals	individual	NOUN
ejpam-6670	26	8	fail	fail	VERB
ejpam-6670	26	9	to	to	PART
ejpam-6670	26	10	clear	clear	VERB
ejpam-6670	26	11	the	the	DET
ejpam-6670	26	12	virus	virus	NOUN
ejpam-6670	26	13	,	,	PUNCT
ejpam-6670	26	14	leading	lead	VERB
ejpam-6670	26	15	to	to	ADP
ejpam-6670	26	16	the	the	DET
ejpam-6670	26	17	development	development	NOUN
ejpam-6670	26	18	of	of	ADP
ejpam-6670	26	19	a	a	DET
ejpam-6670	26	20	chronic	chronic	ADJ
ejpam-6670	26	21	infection	infection	NOUN
ejpam-6670	26	22	,	,	PUNCT
ejpam-6670	26	23	which	which	PRON
ejpam-6670	26	24	may	may	AUX
ejpam-6670	26	25	persist	persist	VERB
ejpam-6670	26	26	for	for	ADP
ejpam-6670	26	27	life	life	NOUN
ejpam-6670	26	28	[	[	X
ejpam-6670	26	29	3	3	NUM
ejpam-6670	26	30	]	]	PUNCT
ejpam-6670	26	31	.	.	PUNCT
ejpam-6670	27	1	globally	globally	ADV
ejpam-6670	27	2	,	,	PUNCT
ejpam-6670	27	3	an	an	DET
ejpam-6670	27	4	estimated	estimate	VERB
ejpam-6670	27	5	300	300	NUM
ejpam-6670	27	6	million	million	NUM
ejpam-6670	27	7	people	people	NOUN
ejpam-6670	27	8	are	be	AUX
ejpam-6670	27	9	chronic	chronic	ADJ
ejpam-6670	27	10	carriers	carrier	NOUN
ejpam-6670	27	11	of	of	ADP
ejpam-6670	27	12	hbv	hbv	NOUN
ejpam-6670	27	13	,	,	PUNCT
ejpam-6670	27	14	facing	face	VERB
ejpam-6670	27	15	significantly	significantly	ADV
ejpam-6670	27	16	increased	increase	VERB
ejpam-6670	27	17	risks	risk	NOUN
ejpam-6670	27	18	of	of	ADP
ejpam-6670	27	19	hbv	hbv	NOUN
ejpam-6670	27	20	-	-	PUNCT
ejpam-6670	27	21	related	relate	VERB
ejpam-6670	27	22	mortality	mortality	NOUN
ejpam-6670	27	23	.	.	PUNCT
ejpam-6670	28	1	known	know	VERB
ejpam-6670	28	2	as	as	ADP
ejpam-6670	28	3	a	a	DET
ejpam-6670	28	4	silent	silent	ADJ
ejpam-6670	28	5	killer	killer	NOUN
ejpam-6670	28	6	,	,	PUNCT
ejpam-6670	28	7	hbv	hbv	NOUN
ejpam-6670	28	8	frequently	frequently	ADV
ejpam-6670	28	9	progresses	progress	VERB
ejpam-6670	28	10	unnoticed	unnoticed	ADJ
ejpam-6670	28	11	,	,	PUNCT
ejpam-6670	28	12	particularly	particularly	ADV
ejpam-6670	28	13	in	in	ADP
ejpam-6670	28	14	its	its	PRON
ejpam-6670	28	15	chronic	chronic	ADJ
ejpam-6670	28	16	form	form	NOUN
ejpam-6670	28	17	.	.	PUNCT
ejpam-6670	29	1	the	the	DET
ejpam-6670	29	2	acute	acute	ADJ
ejpam-6670	29	3	phase	phase	NOUN
ejpam-6670	29	4	typically	typically	ADV
ejpam-6670	29	5	lasts	last	VERB
ejpam-6670	29	6	up	up	ADP
ejpam-6670	29	7	to	to	PART
ejpam-6670	29	8	six	six	NUM
ejpam-6670	29	9	months	month	NOUN
ejpam-6670	29	10	,	,	PUNCT
ejpam-6670	29	11	during	during	ADP
ejpam-6670	29	12	which	which	PRON
ejpam-6670	29	13	the	the	DET
ejpam-6670	29	14	immune	immune	ADJ
ejpam-6670	29	15	system	system	NOUN
ejpam-6670	29	16	may	may	AUX
ejpam-6670	29	17	successfully	successfully	ADV
ejpam-6670	29	18	eliminate	eliminate	VERB
ejpam-6670	29	19	the	the	DET
ejpam-6670	29	20	virus	virus	NOUN
ejpam-6670	29	21	from	from	ADP
ejpam-6670	29	22	the	the	DET
ejpam-6670	29	23	host	host	NOUN
ejpam-6670	29	24	.	.	PUNCT
ejpam-6670	30	1	in	in	ADP
ejpam-6670	30	2	contrast	contrast	NOUN
ejpam-6670	30	3	,	,	PUNCT
ejpam-6670	30	4	the	the	DET
ejpam-6670	30	5	chronic	chronic	ADJ
ejpam-6670	30	6	phase	phase	NOUN
ejpam-6670	30	7	is	be	AUX
ejpam-6670	30	8	more	more	ADV
ejpam-6670	30	9	severe	severe	ADJ
ejpam-6670	30	10	and	and	CCONJ
ejpam-6670	30	11	symptomatic	symptomatic	ADJ
ejpam-6670	30	12	,	,	PUNCT
ejpam-6670	30	13	with	with	ADP
ejpam-6670	30	14	the	the	DET
ejpam-6670	30	15	virus	virus	NOUN
ejpam-6670	30	16	persisting	persist	VERB
ejpam-6670	30	17	in	in	ADP
ejpam-6670	30	18	the	the	DET
ejpam-6670	30	19	body	body	NOUN
ejpam-6670	30	20	.	.	PUNCT
ejpam-6670	31	1	this	this	DET
ejpam-6670	31	2	long	long	ADJ
ejpam-6670	31	3	-	-	PUNCT
ejpam-6670	31	4	term	term	NOUN
ejpam-6670	31	5	infection	infection	NOUN
ejpam-6670	31	6	can	can	AUX
ejpam-6670	31	7	lead	lead	VERB
ejpam-6670	31	8	to	to	ADP
ejpam-6670	31	9	serious	serious	ADJ
ejpam-6670	31	10	complications	complication	NOUN
ejpam-6670	31	11	,	,	PUNCT
ejpam-6670	31	12	including	include	VERB
ejpam-6670	31	13	liver	liver	NOUN
ejpam-6670	31	14	cirrhosis	cirrhosis	NOUN
ejpam-6670	31	15	and	and	CCONJ
ejpam-6670	31	16	liver	liver	NOUN
ejpam-6670	31	17	failure	failure	NOUN
ejpam-6670	31	18	[	[	X
ejpam-6670	31	19	4	4	NUM
ejpam-6670	31	20	,	,	PUNCT
ejpam-6670	31	21	5	5	NUM
ejpam-6670	31	22	]	]	PUNCT
ejpam-6670	31	23	.	.	PUNCT
ejpam-6670	32	1	while	while	SCONJ
ejpam-6670	32	2	antiviral	antiviral	ADJ
ejpam-6670	32	3	treatment	treatment	NOUN
ejpam-6670	32	4	is	be	AUX
ejpam-6670	32	5	generally	generally	ADV
ejpam-6670	32	6	unnecessary	unnecessary	ADJ
ejpam-6670	32	7	during	during	ADP
ejpam-6670	32	8	the	the	DET
ejpam-6670	32	9	acute	acute	ADJ
ejpam-6670	32	10	phase	phase	NOUN
ejpam-6670	32	11	,	,	PUNCT
ejpam-6670	32	12	where	where	SCONJ
ejpam-6670	32	13	rest	rest	NOUN
ejpam-6670	32	14	,	,	PUNCT
ejpam-6670	32	15	hydration	hydration	NOUN
ejpam-6670	32	16	,	,	PUNCT
ejpam-6670	32	17	and	and	CCONJ
ejpam-6670	32	18	proper	proper	ADJ
ejpam-6670	32	19	nutrition	nutrition	NOUN
ejpam-6670	32	20	are	be	AUX
ejpam-6670	32	21	recommended	recommend	VERB
ejpam-6670	32	22	—	—	PUNCT
ejpam-6670	32	23	immediate	immediate	ADJ
ejpam-6670	32	24	medical	medical	ADJ
ejpam-6670	32	25	intervention	intervention	NOUN
ejpam-6670	32	26	becomes	become	VERB
ejpam-6670	32	27	essential	essential	ADJ
ejpam-6670	32	28	if	if	SCONJ
ejpam-6670	32	29	the	the	DET
ejpam-6670	32	30	infection	infection	NOUN
ejpam-6670	32	31	progresses	progress	VERB
ejpam-6670	32	32	to	to	ADP
ejpam-6670	32	33	the	the	DET
ejpam-6670	32	34	chronic	chronic	ADJ
ejpam-6670	32	35	stage	stage	NOUN
ejpam-6670	32	36	.	.	PUNCT
ejpam-6670	33	1	mathematical	mathematical	ADJ
ejpam-6670	33	2	modeling	modeling	NOUN
ejpam-6670	33	3	refers	refer	VERB
ejpam-6670	33	4	to	to	ADP
ejpam-6670	33	5	the	the	DET
ejpam-6670	33	6	process	process	NOUN
ejpam-6670	33	7	of	of	ADP
ejpam-6670	33	8	representing	represent	VERB
ejpam-6670	33	9	real	real	ADJ
ejpam-6670	33	10	-	-	PUNCT
ejpam-6670	33	11	world	world	NOUN
ejpam-6670	33	12	phenomena	phenomenon	NOUN
ejpam-6670	33	13	using	use	VERB
ejpam-6670	33	14	mathematical	mathematical	ADJ
ejpam-6670	33	15	expressions	expression	NOUN
ejpam-6670	33	16	,	,	PUNCT
ejpam-6670	33	17	and	and	CCONJ
ejpam-6670	33	18	it	it	PRON
ejpam-6670	33	19	is	be	AUX
ejpam-6670	33	20	widely	widely	ADV
ejpam-6670	33	21	applied	apply	VERB
ejpam-6670	33	22	across	across	ADP
ejpam-6670	33	23	various	various	ADJ
ejpam-6670	33	24	disciplines	discipline	NOUN
ejpam-6670	33	25	,	,	PUNCT
ejpam-6670	33	26	including	include	VERB
ejpam-6670	33	27	physics	physics	NOUN
ejpam-6670	33	28	,	,	PUNCT
ejpam-6670	33	29	computer	computer	NOUN
ejpam-6670	33	30	science	science	NOUN
ejpam-6670	33	31	,	,	PUNCT
ejpam-6670	33	32	and	and	CCONJ
ejpam-6670	33	33	biology	biology	NOUN
ejpam-6670	34	1	[	[	X
ejpam-6670	34	2	6–9	6–9	NOUN
ejpam-6670	34	3	]	]	PUNCT
ejpam-6670	34	4	.	.	PUNCT
ejpam-6670	35	1	in	in	ADP
ejpam-6670	35	2	the	the	DET
ejpam-6670	35	3	context	context	NOUN
ejpam-6670	35	4	of	of	ADP
ejpam-6670	35	5	epidemiology	epidemiology	NOUN
ejpam-6670	35	6	,	,	PUNCT
ejpam-6670	35	7	mathematical	mathematical	ADJ
ejpam-6670	35	8	models	model	NOUN
ejpam-6670	35	9	play	play	VERB
ejpam-6670	35	10	a	a	DET
ejpam-6670	35	11	crucial	crucial	ADJ
ejpam-6670	35	12	role	role	NOUN
ejpam-6670	35	13	in	in	ADP
ejpam-6670	35	14	understanding	understand	VERB
ejpam-6670	35	15	the	the	DET
ejpam-6670	35	16	transmission	transmission	NOUN
ejpam-6670	35	17	dynamics	dynamic	NOUN
ejpam-6670	35	18	of	of	ADP
ejpam-6670	35	19	infectious	infectious	ADJ
ejpam-6670	35	20	diseases	disease	NOUN
ejpam-6670	35	21	,	,	PUNCT
ejpam-6670	35	22	evaluating	evaluate	VERB
ejpam-6670	35	23	control	control	NOUN
ejpam-6670	35	24	strategies	strategy	NOUN
ejpam-6670	35	25	,	,	PUNCT
ejpam-6670	35	26	and	and	CCONJ
ejpam-6670	35	27	predicting	predict	VERB
ejpam-6670	35	28	both	both	CCONJ
ejpam-6670	35	29	short	short	ADJ
ejpam-6670	35	30	and	and	CCONJ
ejpam-6670	35	31	long	long	ADJ
ejpam-6670	35	32	-	-	PUNCT
ejpam-6670	35	33	term	term	NOUN
ejpam-6670	35	34	outcomes	outcome	NOUN
ejpam-6670	35	35	[	[	X
ejpam-6670	35	36	10	10	NUM
ejpam-6670	35	37	,	,	PUNCT
ejpam-6670	35	38	11	11	NUM
ejpam-6670	35	39	]	]	PUNCT
ejpam-6670	35	40	.	.	PUNCT
ejpam-6670	36	1	these	these	DET
ejpam-6670	36	2	models	model	NOUN
ejpam-6670	36	3	consist	consist	VERB
ejpam-6670	36	4	of	of	ADP
ejpam-6670	36	5	differential	differential	ADJ
ejpam-6670	36	6	equations	equation	NOUN
ejpam-6670	36	7	,	,	PUNCT
ejpam-6670	36	8	which	which	PRON
ejpam-6670	36	9	describe	describe	VERB
ejpam-6670	36	10	a	a	DET
ejpam-6670	36	11	framework	framework	NOUN
ejpam-6670	36	12	to	to	PART
ejpam-6670	36	13	show	show	VERB
ejpam-6670	36	14	the	the	DET
ejpam-6670	36	15	temporal	temporal	ADJ
ejpam-6670	36	16	evolution	evolution	NOUN
ejpam-6670	36	17	of	of	ADP
ejpam-6670	36	18	disease	disease	NOUN
ejpam-6670	36	19	spread	spread	NOUN
ejpam-6670	36	20	(	(	PUNCT
ejpam-6670	36	21	see	see	VERB
ejpam-6670	36	22	,	,	PUNCT
ejpam-6670	36	23	e.g.	e.g.	ADV
ejpam-6670	36	24	,	,	PUNCT
ejpam-6670	36	25	[	[	X
ejpam-6670	36	26	12	12	NUM
ejpam-6670	36	27	,	,	PUNCT
ejpam-6670	36	28	13	13	NUM
ejpam-6670	36	29	]	]	NUM
ejpam-6670	36	30	)	)	PUNCT
ejpam-6670	36	31	.	.	PUNCT
ejpam-6670	37	1	however	however	ADV
ejpam-6670	37	2	,	,	PUNCT
ejpam-6670	37	3	analyzing	analyze	VERB
ejpam-6670	37	4	the	the	DET
ejpam-6670	37	5	mathematical	mathematical	ADJ
ejpam-6670	37	6	properties	property	NOUN
ejpam-6670	37	7	of	of	ADP
ejpam-6670	37	8	such	such	ADJ
ejpam-6670	37	9	models	model	NOUN
ejpam-6670	37	10	and	and	CCONJ
ejpam-6670	37	11	finding	find	VERB
ejpam-6670	37	12	their	their	PRON
ejpam-6670	37	13	exact	exact	ADJ
ejpam-6670	37	14	or	or	CCONJ
ejpam-6670	37	15	approximate	approximate	ADJ
ejpam-6670	37	16	solutions	solution	NOUN
ejpam-6670	37	17	is	be	AUX
ejpam-6670	37	18	challenging	challenging	ADJ
ejpam-6670	37	19	,	,	PUNCT
ejpam-6670	37	20	but	but	CCONJ
ejpam-6670	37	21	one	one	PRON
ejpam-6670	37	22	must	must	AUX
ejpam-6670	37	23	also	also	ADV
ejpam-6670	37	24	look	look	VERB
ejpam-6670	37	25	for	for	ADP
ejpam-6670	37	26	alternative	alternative	ADJ
ejpam-6670	37	27	approaches	approach	NOUN
ejpam-6670	37	28	while	while	SCONJ
ejpam-6670	37	29	dealing	deal	VERB
ejpam-6670	37	30	with	with	ADP
ejpam-6670	37	31	their	their	PRON
ejpam-6670	37	32	solutions	solution	NOUN
ejpam-6670	37	33	.	.	PUNCT
ejpam-6670	38	1	to	to	PART
ejpam-6670	38	2	address	address	VERB
ejpam-6670	38	3	this	this	PRON
ejpam-6670	38	4	,	,	PUNCT
ejpam-6670	38	5	alternative	alternative	ADJ
ejpam-6670	38	6	computational	computational	ADJ
ejpam-6670	38	7	techniques	technique	NOUN
ejpam-6670	38	8	,	,	PUNCT
ejpam-6670	38	9	particularly	particularly	ADV
ejpam-6670	38	10	neural	neural	ADJ
ejpam-6670	38	11	network	network	NOUN
ejpam-6670	38	12	-	-	PUNCT
ejpam-6670	38	13	based	base	VERB
ejpam-6670	38	14	methods	method	NOUN
ejpam-6670	38	15	,	,	PUNCT
ejpam-6670	38	16	have	have	AUX
ejpam-6670	38	17	been	be	AUX
ejpam-6670	38	18	increasingly	increasingly	ADV
ejpam-6670	38	19	employed	employ	VERB
ejpam-6670	38	20	to	to	PART
ejpam-6670	38	21	obtain	obtain	VERB
ejpam-6670	38	22	accurate	accurate	ADJ
ejpam-6670	38	23	and	and	CCONJ
ejpam-6670	38	24	efficient	efficient	ADJ
ejpam-6670	38	25	solutions	solution	NOUN
ejpam-6670	38	26	.	.	PUNCT
ejpam-6670	39	1	given	give	VERB
ejpam-6670	39	2	that	that	SCONJ
ejpam-6670	39	3	many	many	ADJ
ejpam-6670	39	4	real	real	ADJ
ejpam-6670	39	5	-	-	PUNCT
ejpam-6670	39	6	world	world	NOUN
ejpam-6670	39	7	systems	system	NOUN
ejpam-6670	39	8	are	be	AUX
ejpam-6670	39	9	inherently	inherently	ADV
ejpam-6670	39	10	governed	govern	VERB
ejpam-6670	39	11	by	by	ADP
ejpam-6670	39	12	differential	differential	ADJ
ejpam-6670	39	13	equations	equation	NOUN
ejpam-6670	39	14	,	,	PUNCT
ejpam-6670	39	15	solving	solve	VERB
ejpam-6670	39	16	them	they	PRON
ejpam-6670	39	17	using	use	VERB
ejpam-6670	39	18	neural	neural	ADJ
ejpam-6670	39	19	networks	network	NOUN
ejpam-6670	39	20	is	be	AUX
ejpam-6670	39	21	an	an	DET
ejpam-6670	39	22	emerging	emerge	VERB
ejpam-6670	39	23	and	and	CCONJ
ejpam-6670	39	24	rapidly	rapidly	ADV
ejpam-6670	39	25	growing	grow	VERB
ejpam-6670	39	26	field	field	NOUN
ejpam-6670	39	27	of	of	ADP
ejpam-6670	39	28	research	research	NOUN
ejpam-6670	39	29	[	[	X
ejpam-6670	39	30	14	14	NUM
ejpam-6670	39	31	]	]	PUNCT
ejpam-6670	39	32	.	.	PUNCT
ejpam-6670	40	1	in	in	ADP
ejpam-6670	40	2	recent	recent	ADJ
ejpam-6670	40	3	years	year	NOUN
ejpam-6670	40	4	,	,	PUNCT
ejpam-6670	40	5	significant	significant	ADJ
ejpam-6670	40	6	progress	progress	NOUN
ejpam-6670	40	7	has	have	AUX
ejpam-6670	40	8	been	be	AUX
ejpam-6670	40	9	made	make	VERB
ejpam-6670	40	10	,	,	PUNCT
ejpam-6670	40	11	highlighting	highlight	VERB
ejpam-6670	40	12	the	the	DET
ejpam-6670	40	13	promising	promising	ADJ
ejpam-6670	40	14	interplay	interplay	NOUN
ejpam-6670	40	15	between	between	ADP
ejpam-6670	40	16	neural	neural	ADJ
ejpam-6670	40	17	networks	network	NOUN
ejpam-6670	40	18	and	and	CCONJ
ejpam-6670	40	19	differential	differential	ADJ
ejpam-6670	40	20	equation	equation	NOUN
ejpam-6670	40	21	solvers	solver	NOUN
ejpam-6670	40	22	[	[	X
ejpam-6670	40	23	15	15	NUM
ejpam-6670	40	24	]	]	PUNCT
ejpam-6670	40	25	.	.	PUNCT
ejpam-6670	41	1	neural	neural	ADJ
ejpam-6670	41	2	networks	network	NOUN
ejpam-6670	41	3	are	be	AUX
ejpam-6670	41	4	computational	computational	ADJ
ejpam-6670	41	5	models	model	NOUN
ejpam-6670	41	6	inspired	inspire	VERB
ejpam-6670	41	7	by	by	ADP
ejpam-6670	41	8	the	the	DET
ejpam-6670	41	9	architecture	architecture	NOUN
ejpam-6670	41	10	and	and	CCONJ
ejpam-6670	41	11	functioning	functioning	NOUN
ejpam-6670	41	12	of	of	ADP
ejpam-6670	41	13	the	the	DET
ejpam-6670	41	14	human	human	ADJ
ejpam-6670	41	15	brain	brain	NOUN
ejpam-6670	41	16	.	.	PUNCT
ejpam-6670	42	1	they	they	PRON
ejpam-6670	42	2	consist	consist	VERB
ejpam-6670	42	3	of	of	ADP
ejpam-6670	42	4	interconnected	interconnected	ADJ
ejpam-6670	42	5	artificial	artificial	ADJ
ejpam-6670	42	6	neurons	neuron	NOUN
ejpam-6670	42	7	organized	organize	VERB
ejpam-6670	42	8	into	into	ADP
ejpam-6670	42	9	multiple	multiple	ADJ
ejpam-6670	42	10	layers	layer	NOUN
ejpam-6670	42	11	,	,	PUNCT
ejpam-6670	42	12	typically	typically	ADV
ejpam-6670	42	13	including	include	VERB
ejpam-6670	42	14	an	an	DET
ejpam-6670	42	15	input	input	NOUN
ejpam-6670	42	16	layer	layer	NOUN
ejpam-6670	42	17	,	,	PUNCT
ejpam-6670	42	18	one	one	NUM
ejpam-6670	42	19	or	or	CCONJ
ejpam-6670	42	20	more	more	ADV
ejpam-6670	42	21	hidden	hidden	ADJ
ejpam-6670	42	22	layers	layer	NOUN
ejpam-6670	42	23	,	,	PUNCT
ejpam-6670	42	24	and	and	CCONJ
ejpam-6670	42	25	an	an	DET
ejpam-6670	42	26	output	output	NOUN
ejpam-6670	42	27	layer	layer	NOUN
ejpam-6670	43	1	[	[	X
ejpam-6670	43	2	16	16	NUM
ejpam-6670	43	3	]	]	PUNCT
ejpam-6670	43	4	.	.	PUNCT
ejpam-6670	44	1	input	input	PROPN
ejpam-6670	44	2	data	datum	NOUN
ejpam-6670	44	3	passes	pass	VERB
ejpam-6670	44	4	through	through	ADP
ejpam-6670	44	5	these	these	DET
ejpam-6670	44	6	layers	layer	NOUN
ejpam-6670	44	7	,	,	PUNCT
ejpam-6670	44	8	where	where	SCONJ
ejpam-6670	44	9	mathematical	mathematical	ADJ
ejpam-6670	44	10	operations	operation	NOUN
ejpam-6670	44	11	t.	t.	PROPN
ejpam-6670	44	12	khan	khan	PROPN
ejpam-6670	44	13	et	et	PROPN
ejpam-6670	44	14	al	al	PROPN
ejpam-6670	44	15	.	.	PUNCT
ejpam-6670	44	16	/	/	SYM
ejpam-6670	44	17	eur	eur	PROPN
ejpam-6670	44	18	.	.	PUNCT
ejpam-6670	45	1	j.	j.	PROPN
ejpam-6670	45	2	pure	pure	PROPN
ejpam-6670	45	3	appl	appl	PROPN
ejpam-6670	45	4	.	.	PROPN
ejpam-6670	45	5	math	math	PROPN
ejpam-6670	45	6	,	,	PUNCT
ejpam-6670	45	7	18	18	NUM
ejpam-6670	45	8	(	(	PUNCT
ejpam-6670	45	9	3	3	NUM
ejpam-6670	45	10	)	)	PUNCT
ejpam-6670	45	11	(	(	PUNCT
ejpam-6670	45	12	2025	2025	NUM
ejpam-6670	45	13	)	)	PUNCT
ejpam-6670	45	14	,	,	PUNCT
ejpam-6670	45	15	6670	6670	NUM
ejpam-6670	45	16	3	3	NUM
ejpam-6670	45	17	of	of	ADP
ejpam-6670	45	18	22	22	NUM
ejpam-6670	45	19	produce	produce	VERB
ejpam-6670	45	20	an	an	DET
ejpam-6670	45	21	output	output	NOUN
ejpam-6670	45	22	.	.	PUNCT
ejpam-6670	46	1	each	each	DET
ejpam-6670	46	2	artificial	artificial	ADJ
ejpam-6670	46	3	neuron	neuron	NOUN
ejpam-6670	46	4	processes	process	VERB
ejpam-6670	46	5	incoming	incoming	ADJ
ejpam-6670	46	6	signals	signal	NOUN
ejpam-6670	46	7	by	by	ADP
ejpam-6670	46	8	applying	apply	VERB
ejpam-6670	46	9	weighted	weight	VERB
ejpam-6670	46	10	sums	sum	NOUN
ejpam-6670	46	11	to	to	ADP
ejpam-6670	46	12	the	the	DET
ejpam-6670	46	13	inputs	input	NOUN
ejpam-6670	46	14	,	,	PUNCT
ejpam-6670	46	15	followed	follow	VERB
ejpam-6670	46	16	by	by	ADP
ejpam-6670	46	17	the	the	DET
ejpam-6670	46	18	application	application	NOUN
ejpam-6670	46	19	of	of	ADP
ejpam-6670	46	20	an	an	DET
ejpam-6670	46	21	activation	activation	NOUN
ejpam-6670	46	22	(	(	PUNCT
ejpam-6670	46	23	or	or	CCONJ
ejpam-6670	46	24	merit	merit	NOUN
ejpam-6670	46	25	)	)	PUNCT
ejpam-6670	46	26	function	function	NOUN
ejpam-6670	46	27	,	,	PUNCT
ejpam-6670	46	28	which	which	PRON
ejpam-6670	46	29	introduces	introduce	VERB
ejpam-6670	46	30	nonlinearity	nonlinearity	NOUN
ejpam-6670	46	31	and	and	CCONJ
ejpam-6670	46	32	determines	determine	VERB
ejpam-6670	46	33	whether	whether	SCONJ
ejpam-6670	46	34	the	the	DET
ejpam-6670	46	35	signal	signal	NOUN
ejpam-6670	46	36	passes	pass	VERB
ejpam-6670	46	37	to	to	ADP
ejpam-6670	46	38	the	the	DET
ejpam-6670	46	39	next	next	ADJ
ejpam-6670	46	40	layer	layer	NOUN
ejpam-6670	46	41	.	.	PUNCT
ejpam-6670	47	1	this	this	DET
ejpam-6670	47	2	layered	layered	ADJ
ejpam-6670	47	3	structure	structure	NOUN
ejpam-6670	47	4	enables	enable	VERB
ejpam-6670	47	5	the	the	DET
ejpam-6670	47	6	network	network	NOUN
ejpam-6670	47	7	to	to	PART
ejpam-6670	47	8	learn	learn	VERB
ejpam-6670	47	9	and	and	CCONJ
ejpam-6670	47	10	model	model	NOUN
ejpam-6670	47	11	complex	complex	NOUN
ejpam-6670	47	12	,	,	PUNCT
ejpam-6670	47	13	nonlinear	nonlinear	ADJ
ejpam-6670	47	14	relationships	relationship	NOUN
ejpam-6670	47	15	in	in	ADP
ejpam-6670	47	16	data	datum	NOUN
ejpam-6670	47	17	.	.	PUNCT
ejpam-6670	48	1	among	among	ADP
ejpam-6670	48	2	neural	neural	ADJ
ejpam-6670	48	3	network	network	NOUN
ejpam-6670	48	4	architectures	architecture	NOUN
ejpam-6670	48	5	,	,	PUNCT
ejpam-6670	48	6	the	the	DET
ejpam-6670	48	7	feed	feed	NOUN
ejpam-6670	48	8	-	-	PUNCT
ejpam-6670	48	9	forward	forward	ADV
ejpam-6670	48	10	neural	neural	ADJ
ejpam-6670	48	11	network	network	NOUN
ejpam-6670	48	12	(	(	PUNCT
ejpam-6670	48	13	ffnn	ffnn	NOUN
ejpam-6670	48	14	)	)	PUNCT
ejpam-6670	48	15	is	be	AUX
ejpam-6670	48	16	particularly	particularly	ADV
ejpam-6670	48	17	significant	significant	ADJ
ejpam-6670	48	18	.	.	PUNCT
ejpam-6670	49	1	in	in	ADP
ejpam-6670	49	2	ffnns	ffnns	NOUN
ejpam-6670	49	3	,	,	PUNCT
ejpam-6670	49	4	data	datum	NOUN
ejpam-6670	49	5	flows	flow	NOUN
ejpam-6670	49	6	in	in	ADP
ejpam-6670	49	7	one	one	NUM
ejpam-6670	49	8	direction	direction	NOUN
ejpam-6670	49	9	from	from	ADP
ejpam-6670	49	10	input	input	NOUN
ejpam-6670	49	11	to	to	ADP
ejpam-6670	49	12	output	output	NOUN
ejpam-6670	49	13	,	,	PUNCT
ejpam-6670	49	14	without	without	ADP
ejpam-6670	49	15	feedback	feedback	NOUN
ejpam-6670	49	16	loops	loop	NOUN
ejpam-6670	49	17	.	.	PUNCT
ejpam-6670	50	1	they	they	PRON
ejpam-6670	50	2	are	be	AUX
ejpam-6670	50	3	widely	widely	ADV
ejpam-6670	50	4	used	use	VERB
ejpam-6670	50	5	in	in	ADP
ejpam-6670	50	6	the	the	DET
ejpam-6670	50	7	analysis	analysis	NOUN
ejpam-6670	50	8	of	of	ADP
ejpam-6670	50	9	epidemiological	epidemiological	ADJ
ejpam-6670	50	10	models	model	NOUN
ejpam-6670	50	11	,	,	PUNCT
ejpam-6670	50	12	where	where	SCONJ
ejpam-6670	50	13	they	they	PRON
ejpam-6670	50	14	approximate	approximate	VERB
ejpam-6670	50	15	nonlinear	nonlinear	ADJ
ejpam-6670	50	16	dynamics	dynamic	NOUN
ejpam-6670	50	17	involved	involve	VERB
ejpam-6670	50	18	in	in	ADP
ejpam-6670	50	19	the	the	DET
ejpam-6670	50	20	transmission	transmission	NOUN
ejpam-6670	50	21	of	of	ADP
ejpam-6670	50	22	infectious	infectious	ADJ
ejpam-6670	50	23	diseases	disease	NOUN
ejpam-6670	50	24	.	.	PUNCT
ejpam-6670	51	1	by	by	ADP
ejpam-6670	51	2	learning	learn	VERB
ejpam-6670	51	3	from	from	ADP
ejpam-6670	51	4	data	datum	NOUN
ejpam-6670	51	5	,	,	PUNCT
ejpam-6670	51	6	ffnns	ffnns	NOUN
ejpam-6670	51	7	offer	offer	VERB
ejpam-6670	51	8	a	a	DET
ejpam-6670	51	9	powerful	powerful	ADJ
ejpam-6670	51	10	,	,	PUNCT
ejpam-6670	51	11	data	data	NOUN
ejpam-6670	51	12	-	-	PUNCT
ejpam-6670	51	13	driven	drive	VERB
ejpam-6670	51	14	approach	approach	NOUN
ejpam-6670	51	15	for	for	ADP
ejpam-6670	51	16	forecasting	forecasting	NOUN
ejpam-6670	51	17	disease	disease	NOUN
ejpam-6670	51	18	trends	trend	NOUN
ejpam-6670	51	19	and	and	CCONJ
ejpam-6670	51	20	enhancing	enhance	VERB
ejpam-6670	51	21	the	the	DET
ejpam-6670	51	22	understanding	understanding	NOUN
ejpam-6670	51	23	of	of	ADP
ejpam-6670	51	24	epidemic	epidemic	NOUN
ejpam-6670	51	25	processes	process	NOUN
ejpam-6670	51	26	with	with	ADP
ejpam-6670	51	27	high	high	ADJ
ejpam-6670	51	28	predictive	predictive	ADJ
ejpam-6670	51	29	accuracy	accuracy	NOUN
ejpam-6670	51	30	.	.	PUNCT
ejpam-6670	52	1	with	with	ADP
ejpam-6670	52	2	the	the	DET
ejpam-6670	52	3	aid	aid	NOUN
ejpam-6670	52	4	of	of	ADP
ejpam-6670	52	5	nonlinear	nonlinear	ADJ
ejpam-6670	52	6	activation	activation	NOUN
ejpam-6670	52	7	functions	function	NOUN
ejpam-6670	52	8	and	and	CCONJ
ejpam-6670	52	9	multiple	multiple	ADJ
ejpam-6670	52	10	layers	layer	NOUN
ejpam-6670	52	11	of	of	ADP
ejpam-6670	52	12	neurons	neuron	NOUN
ejpam-6670	52	13	,	,	PUNCT
ejpam-6670	52	14	ffnns	ffnns	NOUN
ejpam-6670	52	15	can	can	AUX
ejpam-6670	52	16	approximate	approximate	VERB
ejpam-6670	52	17	the	the	DET
ejpam-6670	52	18	disease	disease	NOUN
ejpam-6670	52	19	transmission	transmission	NOUN
ejpam-6670	52	20	mechanisms	mechanism	NOUN
ejpam-6670	52	21	to	to	PART
ejpam-6670	52	22	help	help	VERB
ejpam-6670	52	23	estimate	estimate	VERB
ejpam-6670	52	24	the	the	DET
ejpam-6670	52	25	key	key	ADJ
ejpam-6670	52	26	epidemic	epidemic	NOUN
ejpam-6670	52	27	parameters	parameter	NOUN
ejpam-6670	52	28	(	(	PUNCT
ejpam-6670	52	29	infection	infection	NOUN
ejpam-6670	52	30	rate	rate	NOUN
ejpam-6670	52	31	,	,	PUNCT
ejpam-6670	52	32	recovery	recovery	NOUN
ejpam-6670	52	33	rate	rate	NOUN
ejpam-6670	52	34	,	,	PUNCT
ejpam-6670	52	35	and	and	CCONJ
ejpam-6670	52	36	transmission	transmission	NOUN
ejpam-6670	52	37	probability	probability	NOUN
ejpam-6670	52	38	)	)	PUNCT
ejpam-6670	52	39	.	.	PUNCT
ejpam-6670	53	1	moreover	moreover	ADV
ejpam-6670	53	2	,	,	PUNCT
ejpam-6670	53	3	ffnns	ffnns	NOUN
ejpam-6670	53	4	are	be	AUX
ejpam-6670	53	5	highly	highly	ADV
ejpam-6670	53	6	adaptable	adaptable	ADJ
ejpam-6670	53	7	and	and	CCONJ
ejpam-6670	53	8	can	can	AUX
ejpam-6670	53	9	integrate	integrate	VERB
ejpam-6670	53	10	real	real	ADJ
ejpam-6670	53	11	-	-	PUNCT
ejpam-6670	53	12	world	world	NOUN
ejpam-6670	53	13	datasets	dataset	NOUN
ejpam-6670	53	14	,	,	PUNCT
ejpam-6670	53	15	including	include	VERB
ejpam-6670	53	16	time	time	NOUN
ejpam-6670	53	17	series	series	PROPN
ejpam-6670	53	18	infection	infection	NOUN
ejpam-6670	53	19	data	datum	NOUN
ejpam-6670	53	20	,	,	PUNCT
ejpam-6670	53	21	demographic	demographic	ADJ
ejpam-6670	53	22	information	information	NOUN
ejpam-6670	53	23	,	,	PUNCT
ejpam-6670	53	24	and	and	CCONJ
ejpam-6670	53	25	vaccination	vaccination	NOUN
ejpam-6670	53	26	,	,	PUNCT
ejpam-6670	53	27	making	make	VERB
ejpam-6670	53	28	them	they	PRON
ejpam-6670	53	29	more	more	ADV
ejpam-6670	53	30	effective	effective	ADJ
ejpam-6670	53	31	in	in	ADP
ejpam-6670	53	32	forecasting	forecast	VERB
ejpam-6670	53	33	outbreaks	outbreak	NOUN
ejpam-6670	53	34	in	in	ADP
ejpam-6670	53	35	uncertain	uncertain	ADJ
ejpam-6670	53	36	environments	environment	NOUN
ejpam-6670	53	37	.	.	PUNCT
ejpam-6670	54	1	when	when	SCONJ
ejpam-6670	54	2	applied	apply	VERB
ejpam-6670	54	3	to	to	ADP
ejpam-6670	54	4	epidemiological	epidemiological	ADJ
ejpam-6670	54	5	models	model	NOUN
ejpam-6670	54	6	,	,	PUNCT
ejpam-6670	54	7	ffnns	ffnns	NOUN
ejpam-6670	54	8	improve	improve	VERB
ejpam-6670	54	9	predictive	predictive	ADJ
ejpam-6670	54	10	accuracy	accuracy	NOUN
ejpam-6670	54	11	,	,	PUNCT
ejpam-6670	54	12	decision	decision	NOUN
ejpam-6670	54	13	-	-	PUNCT
ejpam-6670	54	14	making	making	NOUN
ejpam-6670	54	15	,	,	PUNCT
ejpam-6670	54	16	intervention	intervention	NOUN
ejpam-6670	54	17	strategies	strategy	NOUN
ejpam-6670	54	18	,	,	PUNCT
ejpam-6670	54	19	policy	policy	NOUN
ejpam-6670	54	20	implementation	implementation	NOUN
ejpam-6670	54	21	,	,	PUNCT
ejpam-6670	54	22	assisting	assist	VERB
ejpam-6670	54	23	public	public	ADJ
ejpam-6670	54	24	health	health	NOUN
ejpam-6670	54	25	authorities	authority	NOUN
ejpam-6670	54	26	in	in	ADP
ejpam-6670	54	27	resource	resource	NOUN
ejpam-6670	54	28	allocation	allocation	NOUN
ejpam-6670	54	29	,	,	PUNCT
ejpam-6670	54	30	and	and	CCONJ
ejpam-6670	54	31	early	early	ADJ
ejpam-6670	54	32	warning	warning	NOUN
ejpam-6670	54	33	for	for	ADP
ejpam-6670	54	34	outbreaks	outbreak	NOUN
ejpam-6670	54	35	.	.	PUNCT
ejpam-6670	55	1	various	various	ADJ
ejpam-6670	55	2	neural	neural	ADJ
ejpam-6670	55	3	network	network	NOUN
ejpam-6670	55	4	procedures	procedure	NOUN
ejpam-6670	55	5	are	be	AUX
ejpam-6670	55	6	utilized	utilize	VERB
ejpam-6670	55	7	to	to	PART
ejpam-6670	55	8	analyze	analyze	VERB
ejpam-6670	55	9	the	the	DET
ejpam-6670	55	10	models	model	NOUN
ejpam-6670	55	11	as	as	SCONJ
ejpam-6670	55	12	reported	report	VERB
ejpam-6670	55	13	in	in	ADP
ejpam-6670	55	14	[	[	X
ejpam-6670	55	15	17–19	17–19	NUM
ejpam-6670	55	16	]	]	PUNCT
ejpam-6670	55	17	.	.	PUNCT
ejpam-6670	56	1	however	however	ADV
ejpam-6670	56	2	,	,	PUNCT
ejpam-6670	56	3	the	the	DET
ejpam-6670	56	4	proposed	propose	VERB
ejpam-6670	56	5	epidemiological	epidemiological	ADJ
ejpam-6670	56	6	problem	problem	NOUN
ejpam-6670	56	7	has	have	AUX
ejpam-6670	56	8	never	never	ADV
ejpam-6670	56	9	been	be	AUX
ejpam-6670	56	10	considered	consider	VERB
ejpam-6670	56	11	or	or	CCONJ
ejpam-6670	56	12	solved	solve	VERB
ejpam-6670	56	13	with	with	ADP
ejpam-6670	56	14	the	the	DET
ejpam-6670	56	15	help	help	NOUN
ejpam-6670	56	16	of	of	ADP
ejpam-6670	56	17	the	the	DET
ejpam-6670	56	18	proposed	propose	VERB
ejpam-6670	56	19	approaches	approach	NOUN
ejpam-6670	56	20	.	.	PUNCT
ejpam-6670	57	1	the	the	DET
ejpam-6670	57	2	main	main	ADJ
ejpam-6670	57	3	objective	objective	NOUN
ejpam-6670	57	4	of	of	ADP
ejpam-6670	57	5	the	the	DET
ejpam-6670	57	6	proposed	propose	VERB
ejpam-6670	57	7	work	work	NOUN
ejpam-6670	57	8	is	be	AUX
ejpam-6670	57	9	to	to	PART
ejpam-6670	57	10	introduce	introduce	VERB
ejpam-6670	57	11	a	a	DET
ejpam-6670	57	12	model	model	NOUN
ejpam-6670	57	13	representing	represent	VERB
ejpam-6670	57	14	the	the	DET
ejpam-6670	57	15	dynamics	dynamic	NOUN
ejpam-6670	57	16	of	of	ADP
ejpam-6670	57	17	the	the	DET
ejpam-6670	57	18	hepatitis	hepatitis	PROPN
ejpam-6670	57	19	b	b	PROPN
ejpam-6670	57	20	virus	virus	NOUN
ejpam-6670	57	21	with	with	ADP
ejpam-6670	57	22	reasonable	reasonable	ADJ
ejpam-6670	57	23	assumptions	assumption	NOUN
ejpam-6670	57	24	and	and	CCONJ
ejpam-6670	57	25	to	to	PART
ejpam-6670	57	26	analyze	analyze	VERB
ejpam-6670	57	27	it	it	PRON
ejpam-6670	57	28	with	with	ADP
ejpam-6670	57	29	the	the	DET
ejpam-6670	57	30	aid	aid	NOUN
ejpam-6670	57	31	of	of	ADP
ejpam-6670	57	32	dynamical	dynamical	ADJ
ejpam-6670	57	33	system	system	NOUN
ejpam-6670	57	34	theory	theory	NOUN
ejpam-6670	57	35	,	,	PUNCT
ejpam-6670	57	36	non	non	ADJ
ejpam-6670	57	37	-	-	ADJ
ejpam-6670	57	38	standard	standard	ADJ
ejpam-6670	57	39	finite	finite	ADJ
ejpam-6670	57	40	difference	difference	NOUN
ejpam-6670	57	41	(	(	PUNCT
ejpam-6670	57	42	nsfd	nsfd	ADJ
ejpam-6670	57	43	)	)	PUNCT
ejpam-6670	57	44	scheme	scheme	NOUN
ejpam-6670	57	45	,	,	PUNCT
ejpam-6670	57	46	and	and	CCONJ
ejpam-6670	57	47	feedforward	feedforward	ADJ
ejpam-6670	57	48	neural	neural	ADJ
ejpam-6670	57	49	network	network	NOUN
ejpam-6670	57	50	(	(	PUNCT
ejpam-6670	57	51	ffnn	ffnn	NOUN
ejpam-6670	57	52	)	)	PUNCT
ejpam-6670	57	53	framework	framework	NOUN
ejpam-6670	57	54	.	.	PUNCT
ejpam-6670	58	1	precisely	precisely	ADV
ejpam-6670	58	2	,	,	PUNCT
ejpam-6670	58	3	we	we	PRON
ejpam-6670	58	4	have	have	VERB
ejpam-6670	58	5	the	the	DET
ejpam-6670	58	6	following	follow	VERB
ejpam-6670	58	7	contributions	contribution	NOUN
ejpam-6670	58	8	.	.	PUNCT
ejpam-6670	59	1	1	1	X
ejpam-6670	59	2	.	.	X
ejpam-6670	59	3	since	since	SCONJ
ejpam-6670	59	4	the	the	DET
ejpam-6670	59	5	multiple	multiple	ADJ
ejpam-6670	59	6	phases	phase	NOUN
ejpam-6670	59	7	of	of	ADP
ejpam-6670	59	8	hepatitis	hepatitis	PROPN
ejpam-6670	59	9	b	b	PROPN
ejpam-6670	59	10	have	have	VERB
ejpam-6670	59	11	a	a	DET
ejpam-6670	59	12	significant	significant	ADJ
ejpam-6670	59	13	impact	impact	NOUN
ejpam-6670	59	14	on	on	ADP
ejpam-6670	59	15	the	the	DET
ejpam-6670	59	16	transmission	transmission	NOUN
ejpam-6670	59	17	dynamics	dynamic	NOUN
ejpam-6670	59	18	of	of	ADP
ejpam-6670	59	19	the	the	DET
ejpam-6670	59	20	disease	disease	NOUN
ejpam-6670	59	21	,	,	PUNCT
ejpam-6670	59	22	we	we	PRON
ejpam-6670	59	23	will	will	AUX
ejpam-6670	59	24	consider	consider	VERB
ejpam-6670	59	25	the	the	DET
ejpam-6670	59	26	different	different	ADJ
ejpam-6670	59	27	infectious	infectious	ADJ
ejpam-6670	59	28	phases	phase	NOUN
ejpam-6670	59	29	(	(	PUNCT
ejpam-6670	59	30	latent	latent	NOUN
ejpam-6670	59	31	,	,	PUNCT
ejpam-6670	59	32	acute	acute	NOUN
ejpam-6670	59	33	,	,	PUNCT
ejpam-6670	59	34	and	and	CCONJ
ejpam-6670	59	35	chronic	chronic	ADJ
ejpam-6670	59	36	)	)	PUNCT
ejpam-6670	59	37	of	of	ADP
ejpam-6670	59	38	the	the	DET
ejpam-6670	59	39	disease	disease	NOUN
ejpam-6670	59	40	while	while	SCONJ
ejpam-6670	59	41	formulating	formulate	VERB
ejpam-6670	59	42	the	the	DET
ejpam-6670	59	43	proposed	propose	VERB
ejpam-6670	59	44	model	model	NOUN
ejpam-6670	59	45	.	.	PUNCT
ejpam-6670	60	1	2	2	X
ejpam-6670	60	2	.	.	X
ejpam-6670	60	3	incorporating	incorporate	VERB
ejpam-6670	60	4	the	the	DET
ejpam-6670	60	5	saturated	saturate	VERB
ejpam-6670	60	6	incidence	incidence	NOUN
ejpam-6670	60	7	rate	rate	NOUN
ejpam-6670	60	8	is	be	AUX
ejpam-6670	60	9	also	also	ADV
ejpam-6670	60	10	an	an	DET
ejpam-6670	60	11	important	important	ADJ
ejpam-6670	60	12	consideration	consideration	NOUN
ejpam-6670	60	13	of	of	ADP
ejpam-6670	60	14	the	the	DET
ejpam-6670	60	15	proposed	propose	VERB
ejpam-6670	60	16	work	work	NOUN
ejpam-6670	60	17	because	because	SCONJ
ejpam-6670	60	18	the	the	DET
ejpam-6670	60	19	bilinear	bilinear	NOUN
ejpam-6670	60	20	incidence	incidence	NOUN
ejpam-6670	60	21	only	only	ADV
ejpam-6670	60	22	assumes	assume	VERB
ejpam-6670	60	23	that	that	SCONJ
ejpam-6670	60	24	the	the	DET
ejpam-6670	60	25	incidence	incidence	NOUN
ejpam-6670	60	26	rate	rate	NOUN
ejpam-6670	60	27	is	be	AUX
ejpam-6670	60	28	proportional	proportional	ADJ
ejpam-6670	60	29	to	to	ADP
ejpam-6670	60	30	the	the	DET
ejpam-6670	60	31	amount	amount	NOUN
ejpam-6670	60	32	of	of	ADP
ejpam-6670	60	33	susceptible	susceptible	ADJ
ejpam-6670	60	34	and	and	CCONJ
ejpam-6670	60	35	infectious	infectious	ADJ
ejpam-6670	60	36	population	population	NOUN
ejpam-6670	60	37	;	;	PUNCT
ejpam-6670	60	38	however	however	ADV
ejpam-6670	60	39	,	,	PUNCT
ejpam-6670	60	40	this	this	PRON
ejpam-6670	60	41	is	be	AUX
ejpam-6670	60	42	not	not	PART
ejpam-6670	60	43	the	the	DET
ejpam-6670	60	44	case	case	NOUN
ejpam-6670	60	45	in	in	ADP
ejpam-6670	60	46	hepatitis	hepatitis	PROPN
ejpam-6670	60	47	b	b	PROPN
ejpam-6670	60	48	virus	virus	NOUN
ejpam-6670	60	49	transmission	transmission	NOUN
ejpam-6670	60	50	.	.	PUNCT
ejpam-6670	61	1	besides	besides	SCONJ
ejpam-6670	61	2	this	this	DET
ejpam-6670	61	3	one	one	NOUN
ejpam-6670	61	4	,	,	PUNCT
ejpam-6670	61	5	the	the	DET
ejpam-6670	61	6	saturated	saturate	VERB
ejpam-6670	61	7	incidence	incidence	NOUN
ejpam-6670	61	8	assumes	assume	VERB
ejpam-6670	61	9	the	the	DET
ejpam-6670	61	10	fact	fact	NOUN
ejpam-6670	61	11	that	that	SCONJ
ejpam-6670	61	12	transmission	transmission	NOUN
ejpam-6670	61	13	may	may	AUX
ejpam-6670	61	14	plateau	plateau	VERB
ejpam-6670	61	15	as	as	SCONJ
ejpam-6670	61	16	the	the	DET
ejpam-6670	61	17	ratio	ratio	NOUN
ejpam-6670	61	18	of	of	ADP
ejpam-6670	61	19	the	the	DET
ejpam-6670	61	20	infectious	infectious	ADJ
ejpam-6670	61	21	population	population	NOUN
ejpam-6670	61	22	reaches	reach	VERB
ejpam-6670	61	23	a	a	DET
ejpam-6670	61	24	certain	certain	ADJ
ejpam-6670	61	25	threshold	threshold	NOUN
ejpam-6670	61	26	.	.	PUNCT
ejpam-6670	62	1	because	because	SCONJ
ejpam-6670	62	2	the	the	DET
ejpam-6670	62	3	virus	virus	NOUN
ejpam-6670	62	4	persists	persist	VERB
ejpam-6670	62	5	in	in	ADP
ejpam-6670	62	6	individuals	individual	NOUN
ejpam-6670	62	7	for	for	ADP
ejpam-6670	62	8	a	a	DET
ejpam-6670	62	9	long	long	ADJ
ejpam-6670	62	10	time	time	NOUN
ejpam-6670	62	11	,	,	PUNCT
ejpam-6670	62	12	the	the	DET
ejpam-6670	62	13	ratio	ratio	NOUN
ejpam-6670	62	14	of	of	ADP
ejpam-6670	62	15	infected	infected	ADJ
ejpam-6670	62	16	individuals	individual	NOUN
ejpam-6670	62	17	may	may	AUX
ejpam-6670	62	18	not	not	PART
ejpam-6670	62	19	be	be	AUX
ejpam-6670	62	20	directly	directly	ADV
ejpam-6670	62	21	proportional	proportional	ADJ
ejpam-6670	62	22	to	to	ADP
ejpam-6670	62	23	the	the	DET
ejpam-6670	62	24	number	number	NOUN
ejpam-6670	62	25	of	of	ADP
ejpam-6670	62	26	susceptible	susceptible	ADJ
ejpam-6670	62	27	individuals	individual	NOUN
ejpam-6670	62	28	.	.	PUNCT
ejpam-6670	63	1	3	3	X
ejpam-6670	63	2	.	.	X
ejpam-6670	63	3	the	the	DET
ejpam-6670	63	4	framework	framework	NOUN
ejpam-6670	63	5	of	of	ADP
ejpam-6670	63	6	nsfd	nsfd	NOUN
ejpam-6670	63	7	and	and	CCONJ
ejpam-6670	63	8	ffnn	ffnn	NOUN
ejpam-6670	63	9	will	will	AUX
ejpam-6670	63	10	be	be	AUX
ejpam-6670	63	11	utilized	utilize	VERB
ejpam-6670	63	12	to	to	PART
ejpam-6670	63	13	present	present	VERB
ejpam-6670	63	14	the	the	DET
ejpam-6670	63	15	accurate	accurate	ADJ
ejpam-6670	63	16	dynamics	dynamic	NOUN
ejpam-6670	63	17	and	and	CCONJ
ejpam-6670	63	18	to	to	PART
ejpam-6670	63	19	show	show	VERB
ejpam-6670	63	20	the	the	DET
ejpam-6670	63	21	close	close	ADJ
ejpam-6670	63	22	match	match	NOUN
ejpam-6670	63	23	between	between	ADP
ejpam-6670	63	24	predicted	predict	VERB
ejpam-6670	63	25	and	and	CCONJ
ejpam-6670	63	26	true	true	ADJ
ejpam-6670	63	27	values	value	NOUN
ejpam-6670	63	28	,	,	PUNCT
ejpam-6670	63	29	as	as	ADV
ejpam-6670	63	30	well	well	ADV
ejpam-6670	63	31	as	as	ADP
ejpam-6670	63	32	to	to	PART
ejpam-6670	63	33	investigate	investigate	VERB
ejpam-6670	63	34	the	the	DET
ejpam-6670	63	35	robustness	robustness	NOUN
ejpam-6670	63	36	of	of	ADP
ejpam-6670	63	37	the	the	DET
ejpam-6670	63	38	proposed	propose	VERB
ejpam-6670	63	39	framework	framework	NOUN
ejpam-6670	63	40	while	while	SCONJ
ejpam-6670	63	41	modeling	model	VERB
ejpam-6670	63	42	the	the	DET
ejpam-6670	63	43	dynamics	dynamic	NOUN
ejpam-6670	63	44	of	of	ADP
ejpam-6670	63	45	hbv	hbv	NOUN
ejpam-6670	63	46	.	.	PUNCT
ejpam-6670	64	1	the	the	DET
ejpam-6670	64	2	paper	paper	NOUN
ejpam-6670	64	3	is	be	AUX
ejpam-6670	64	4	organized	organize	VERB
ejpam-6670	64	5	as	as	SCONJ
ejpam-6670	64	6	follows	follow	VERB
ejpam-6670	64	7	.	.	PUNCT
ejpam-6670	65	1	the	the	DET
ejpam-6670	65	2	detailed	detailed	ADJ
ejpam-6670	65	3	formulation	formulation	NOUN
ejpam-6670	65	4	of	of	ADP
ejpam-6670	65	5	the	the	DET
ejpam-6670	65	6	model	model	NOUN
ejpam-6670	65	7	is	be	AUX
ejpam-6670	65	8	provided	provide	VERB
ejpam-6670	65	9	t.	t.	PROPN
ejpam-6670	65	10	khan	khan	PROPN
ejpam-6670	65	11	et	et	PROPN
ejpam-6670	65	12	al	al	PROPN
ejpam-6670	65	13	.	.	PUNCT
ejpam-6670	65	14	/	/	SYM
ejpam-6670	65	15	eur	eur	PROPN
ejpam-6670	65	16	.	.	PUNCT
ejpam-6670	66	1	j.	j.	PROPN
ejpam-6670	66	2	pure	pure	PROPN
ejpam-6670	66	3	appl	appl	PROPN
ejpam-6670	66	4	.	.	PROPN
ejpam-6670	66	5	math	math	PROPN
ejpam-6670	66	6	,	,	PUNCT
ejpam-6670	66	7	18	18	NUM
ejpam-6670	66	8	(	(	PUNCT
ejpam-6670	66	9	3	3	NUM
ejpam-6670	66	10	)	)	PUNCT
ejpam-6670	66	11	(	(	PUNCT
ejpam-6670	66	12	2025	2025	NUM
ejpam-6670	66	13	)	)	PUNCT
ejpam-6670	66	14	,	,	PUNCT
ejpam-6670	66	15	6670	6670	NUM
ejpam-6670	66	16	4	4	NUM
ejpam-6670	66	17	of	of	ADP
ejpam-6670	66	18	22	22	NUM
ejpam-6670	66	19	in	in	ADP
ejpam-6670	66	20	section	section	NOUN
ejpam-6670	66	21	2	2	NUM
ejpam-6670	66	22	.	.	PUNCT
ejpam-6670	67	1	we	we	PRON
ejpam-6670	67	2	also	also	ADV
ejpam-6670	67	3	discuss	discuss	VERB
ejpam-6670	67	4	the	the	DET
ejpam-6670	67	5	biological	biological	ADJ
ejpam-6670	67	6	and	and	CCONJ
ejpam-6670	67	7	mathematical	mathematical	ADJ
ejpam-6670	67	8	feasibility	feasibility	NOUN
ejpam-6670	67	9	of	of	ADP
ejpam-6670	67	10	the	the	DET
ejpam-6670	67	11	model	model	NOUN
ejpam-6670	67	12	in	in	ADP
ejpam-6670	67	13	subsection	subsection	NOUN
ejpam-6670	67	14	2.1	2.1	NUM
ejpam-6670	67	15	.	.	PUNCT
ejpam-6670	68	1	we	we	PRON
ejpam-6670	68	2	linearize	linearize	VERB
ejpam-6670	68	3	the	the	DET
ejpam-6670	68	4	proposed	propose	VERB
ejpam-6670	68	5	model	model	NOUN
ejpam-6670	68	6	and	and	CCONJ
ejpam-6670	68	7	find	find	VERB
ejpam-6670	68	8	the	the	DET
ejpam-6670	68	9	reproductive	reproductive	ADJ
ejpam-6670	68	10	number	number	NOUN
ejpam-6670	68	11	in	in	ADP
ejpam-6670	68	12	subsections	subsection	NOUN
ejpam-6670	68	13	2.2	2.2	NUM
ejpam-6670	68	14	and	and	CCONJ
ejpam-6670	68	15	2.3	2.3	NUM
ejpam-6670	68	16	respectively	respectively	ADV
ejpam-6670	68	17	.	.	PUNCT
ejpam-6670	69	1	the	the	DET
ejpam-6670	69	2	dynamical	dynamical	ADJ
ejpam-6670	69	3	properties	property	NOUN
ejpam-6670	69	4	of	of	ADP
ejpam-6670	69	5	the	the	DET
ejpam-6670	69	6	model	model	NOUN
ejpam-6670	69	7	take	take	VERB
ejpam-6670	69	8	place	place	NOUN
ejpam-6670	69	9	in	in	ADP
ejpam-6670	69	10	subsections	subsection	NOUN
ejpam-6670	69	11	2.4	2.4	NUM
ejpam-6670	69	12	and	and	CCONJ
ejpam-6670	69	13	2.5	2.5	NUM
ejpam-6670	69	14	.	.	PUNCT
ejpam-6670	70	1	we	we	PRON
ejpam-6670	70	2	provide	provide	VERB
ejpam-6670	70	3	the	the	DET
ejpam-6670	70	4	framework	framework	NOUN
ejpam-6670	70	5	of	of	ADP
ejpam-6670	70	6	the	the	DET
ejpam-6670	70	7	nsfd	nsfd	NOUN
ejpam-6670	70	8	and	and	CCONJ
ejpam-6670	70	9	ffnn	ffnn	NOUN
ejpam-6670	70	10	in	in	ADP
ejpam-6670	70	11	section	section	NOUN
ejpam-6670	70	12	3	3	NUM
ejpam-6670	70	13	.	.	PUNCT
ejpam-6670	71	1	we	we	PRON
ejpam-6670	71	2	conclude	conclude	VERB
ejpam-6670	71	3	our	our	PRON
ejpam-6670	71	4	work	work	NOUN
ejpam-6670	71	5	in	in	ADP
ejpam-6670	71	6	section	section	NOUN
ejpam-6670	71	7	4	4	NUM
ejpam-6670	71	8	.	.	NOUN
ejpam-6670	71	9	2	2	NUM
ejpam-6670	71	10	.	.	NOUN
ejpam-6670	71	11	mathematical	mathematical	ADJ
ejpam-6670	71	12	model	model	NOUN
ejpam-6670	71	13	formulation	formulation	NOUN
ejpam-6670	71	14	in	in	ADP
ejpam-6670	71	15	this	this	DET
ejpam-6670	71	16	section	section	NOUN
ejpam-6670	71	17	,	,	PUNCT
ejpam-6670	71	18	we	we	PRON
ejpam-6670	71	19	will	will	AUX
ejpam-6670	71	20	present	present	VERB
ejpam-6670	71	21	an	an	DET
ejpam-6670	71	22	epidemic	epidemic	NOUN
ejpam-6670	71	23	model	model	NOUN
ejpam-6670	71	24	for	for	ADP
ejpam-6670	71	25	the	the	DET
ejpam-6670	71	26	transmission	transmission	NOUN
ejpam-6670	71	27	of	of	ADP
ejpam-6670	71	28	hbv	hbv	NOUN
ejpam-6670	71	29	.	.	PUNCT
ejpam-6670	72	1	keeping	keep	VERB
ejpam-6670	72	2	the	the	DET
ejpam-6670	72	3	complex	complex	ADJ
ejpam-6670	72	4	nature	nature	NOUN
ejpam-6670	72	5	and	and	CCONJ
ejpam-6670	72	6	multiple	multiple	ADJ
ejpam-6670	72	7	phases	phase	NOUN
ejpam-6670	72	8	of	of	ADP
ejpam-6670	72	9	hbv	hbv	NOUN
ejpam-6670	72	10	according	accord	VERB
ejpam-6670	72	11	to	to	ADP
ejpam-6670	72	12	the	the	DET
ejpam-6670	72	13	disease	disease	NOUN
ejpam-6670	72	14	characteristics	characteristic	NOUN
ejpam-6670	72	15	,	,	PUNCT
ejpam-6670	72	16	we	we	PRON
ejpam-6670	72	17	assume	assume	VERB
ejpam-6670	72	18	three	three	NUM
ejpam-6670	72	19	infected	infected	ADJ
ejpam-6670	72	20	population	population	NOUN
ejpam-6670	72	21	groups	group	NOUN
ejpam-6670	72	22	of	of	ADP
ejpam-6670	72	23	latently	latently	ADV
ejpam-6670	72	24	,	,	PUNCT
ejpam-6670	72	25	acutely	acutely	ADV
ejpam-6670	72	26	and	and	CCONJ
ejpam-6670	72	27	chronically	chronically	ADV
ejpam-6670	72	28	infected	infect	VERB
ejpam-6670	72	29	populations	population	NOUN
ejpam-6670	72	30	to	to	PART
ejpam-6670	72	31	acknowledge	acknowledge	VERB
ejpam-6670	72	32	the	the	DET
ejpam-6670	72	33	biological	biological	ADJ
ejpam-6670	72	34	importance	importance	NOUN
ejpam-6670	72	35	of	of	ADP
ejpam-6670	72	36	the	the	DET
ejpam-6670	72	37	latent	latent	NOUN
ejpam-6670	72	38	,	,	PUNCT
ejpam-6670	72	39	acute	acute	ADJ
ejpam-6670	72	40	and	and	CCONJ
ejpam-6670	72	41	chronic	chronic	ADJ
ejpam-6670	72	42	stage	stage	NOUN
ejpam-6670	72	43	in	in	ADP
ejpam-6670	72	44	hbv	hbv	NOUN
ejpam-6670	72	45	infection	infection	NOUN
ejpam-6670	72	46	.	.	PUNCT
ejpam-6670	73	1	moreover	moreover	ADV
ejpam-6670	73	2	,	,	PUNCT
ejpam-6670	73	3	the	the	DET
ejpam-6670	73	4	infection	infection	NOUN
ejpam-6670	73	5	has	have	VERB
ejpam-6670	73	6	long	long	ADJ
ejpam-6670	73	7	infectious	infectious	ADJ
ejpam-6670	73	8	periods	period	NOUN
ejpam-6670	73	9	and	and	CCONJ
ejpam-6670	73	10	can	can	AUX
ejpam-6670	73	11	persist	persist	VERB
ejpam-6670	73	12	in	in	ADP
ejpam-6670	73	13	the	the	DET
ejpam-6670	73	14	body	body	NOUN
ejpam-6670	73	15	for	for	ADP
ejpam-6670	73	16	years	year	NOUN
ejpam-6670	73	17	,	,	PUNCT
ejpam-6670	73	18	and	and	CCONJ
ejpam-6670	73	19	as	as	ADP
ejpam-6670	73	20	awareness	awareness	NOUN
ejpam-6670	73	21	increases	increase	NOUN
ejpam-6670	73	22	,	,	PUNCT
ejpam-6670	73	23	the	the	DET
ejpam-6670	73	24	people	people	NOUN
ejpam-6670	73	25	take	take	VERB
ejpam-6670	73	26	precautionary	precautionary	ADJ
ejpam-6670	73	27	measures	measure	NOUN
ejpam-6670	73	28	,	,	PUNCT
ejpam-6670	73	29	so	so	CCONJ
ejpam-6670	73	30	the	the	DET
ejpam-6670	73	31	number	number	NOUN
ejpam-6670	73	32	of	of	ADP
ejpam-6670	73	33	infectious	infectious	ADJ
ejpam-6670	73	34	individuals	individual	NOUN
ejpam-6670	73	35	accumulates	accumulate	VERB
ejpam-6670	73	36	,	,	PUNCT
ejpam-6670	73	37	therefore	therefore	ADV
ejpam-6670	73	38	,	,	PUNCT
ejpam-6670	73	39	we	we	PRON
ejpam-6670	73	40	use	use	VERB
ejpam-6670	73	41	saturated	saturated	ADJ
ejpam-6670	73	42	incidence	incidence	NOUN
ejpam-6670	73	43	rate	rate	NOUN
ejpam-6670	73	44	βsi/(1	βsi/(1	PUNCT
ejpam-6670	74	1	+	+	CCONJ
ejpam-6670	74	2	γi	γi	NOUN
ejpam-6670	74	3	)	)	PUNCT
ejpam-6670	74	4	,	,	PUNCT
ejpam-6670	74	5	to	to	PART
ejpam-6670	74	6	better	well	ADV
ejpam-6670	74	7	reflects	reflect	VERB
ejpam-6670	74	8	the	the	DET
ejpam-6670	74	9	transmission	transmission	NOUN
ejpam-6670	74	10	scenarios	scenario	NOUN
ejpam-6670	74	11	.	.	PUNCT
ejpam-6670	75	1	the	the	DET
ejpam-6670	75	2	susceptible	susceptible	ADJ
ejpam-6670	75	3	individuals	individual	NOUN
ejpam-6670	75	4	may	may	AUX
ejpam-6670	75	5	transition	transition	VERB
ejpam-6670	75	6	to	to	ADP
ejpam-6670	75	7	latent	latent	NOUN
ejpam-6670	75	8	,	,	PUNCT
ejpam-6670	75	9	acute	acute	NOUN
ejpam-6670	75	10	and	and	CCONJ
ejpam-6670	75	11	then	then	ADV
ejpam-6670	75	12	chronically	chronically	ADV
ejpam-6670	75	13	infected	infect	VERB
ejpam-6670	75	14	group	group	NOUN
ejpam-6670	75	15	of	of	ADP
ejpam-6670	75	16	population	population	NOUN
ejpam-6670	75	17	after	after	ADP
ejpam-6670	75	18	successful	successful	ADJ
ejpam-6670	75	19	interaction	interaction	NOUN
ejpam-6670	75	20	with	with	ADP
ejpam-6670	75	21	the	the	DET
ejpam-6670	75	22	infected	infected	ADJ
ejpam-6670	75	23	individual	individual	NOUN
ejpam-6670	75	24	.	.	PUNCT
ejpam-6670	76	1	since	since	SCONJ
ejpam-6670	76	2	,	,	PUNCT
ejpam-6670	76	3	there	there	PRON
ejpam-6670	76	4	is	be	VERB
ejpam-6670	76	5	no	no	DET
ejpam-6670	76	6	need	need	NOUN
ejpam-6670	76	7	of	of	ADP
ejpam-6670	76	8	proper	proper	ADJ
ejpam-6670	76	9	treatment	treatment	NOUN
ejpam-6670	76	10	in	in	ADP
ejpam-6670	76	11	acute	acute	ADJ
ejpam-6670	76	12	stage	stage	NOUN
ejpam-6670	76	13	and	and	CCONJ
ejpam-6670	76	14	those	those	PRON
ejpam-6670	76	15	who	who	PRON
ejpam-6670	76	16	recover	recover	VERB
ejpam-6670	76	17	naturally	naturally	ADV
ejpam-6670	76	18	will	will	AUX
ejpam-6670	76	19	transit	transit	VERB
ejpam-6670	76	20	to	to	PART
ejpam-6670	76	21	recover	recover	VERB
ejpam-6670	76	22	compartment	compartment	NOUN
ejpam-6670	76	23	,	,	PUNCT
ejpam-6670	76	24	however	however	ADV
ejpam-6670	76	25	,	,	PUNCT
ejpam-6670	76	26	those	those	PRON
ejpam-6670	76	27	who	who	PRON
ejpam-6670	76	28	produce	produce	VERB
ejpam-6670	76	29	complication	complication	NOUN
ejpam-6670	76	30	will	will	AUX
ejpam-6670	76	31	leads	lead	VERB
ejpam-6670	76	32	to	to	ADP
ejpam-6670	76	33	chronically	chronically	ADV
ejpam-6670	76	34	infected	infect	VERB
ejpam-6670	76	35	population	population	NOUN
ejpam-6670	76	36	group	group	NOUN
ejpam-6670	76	37	.	.	PUNCT
ejpam-6670	77	1	these	these	DET
ejpam-6670	77	2	infected	infect	VERB
ejpam-6670	77	3	individuals	individual	NOUN
ejpam-6670	77	4	leave	leave	VERB
ejpam-6670	77	5	their	their	PRON
ejpam-6670	77	6	compartments	compartment	NOUN
ejpam-6670	77	7	due	due	ADJ
ejpam-6670	77	8	death	death	NOUN
ejpam-6670	77	9	or	or	CCONJ
ejpam-6670	77	10	full	full	ADJ
ejpam-6670	77	11	recovery	recovery	NOUN
ejpam-6670	77	12	.	.	PUNCT
ejpam-6670	78	1	parentally	parentally	ADV
ejpam-6670	78	2	infected	infect	VERB
ejpam-6670	78	3	individuals	individual	NOUN
ejpam-6670	78	4	will	will	AUX
ejpam-6670	78	5	directly	directly	ADV
ejpam-6670	78	6	transit	transit	VERB
ejpam-6670	78	7	to	to	ADP
ejpam-6670	78	8	chronically	chronically	ADV
ejpam-6670	78	9	infected	infect	VERB
ejpam-6670	78	10	population	population	NOUN
ejpam-6670	78	11	.	.	PUNCT
ejpam-6670	79	1	vaccine	vaccine	NOUN
ejpam-6670	79	2	of	of	ADP
ejpam-6670	79	3	hepatitis	hepatitis	PROPN
ejpam-6670	79	4	b	b	PROPN
ejpam-6670	79	5	are	be	AUX
ejpam-6670	79	6	also	also	ADV
ejpam-6670	79	7	very	very	ADV
ejpam-6670	79	8	effective	effective	ADJ
ejpam-6670	79	9	and	and	CCONJ
ejpam-6670	79	10	provide	provide	VERB
ejpam-6670	79	11	immunity	immunity	NOUN
ejpam-6670	79	12	,	,	PUNCT
ejpam-6670	79	13	so	so	SCONJ
ejpam-6670	79	14	those	those	PRON
ejpam-6670	79	15	who	who	PRON
ejpam-6670	79	16	vaccinated	vaccinate	VERB
ejpam-6670	79	17	successfully	successfully	ADV
ejpam-6670	79	18	will	will	AUX
ejpam-6670	79	19	transit	transit	VERB
ejpam-6670	79	20	to	to	ADP
ejpam-6670	79	21	vaccinated	vaccinated	ADJ
ejpam-6670	79	22	compartment	compartment	NOUN
ejpam-6670	79	23	.	.	PUNCT
ejpam-6670	80	1	thus	thus	ADV
ejpam-6670	80	2	,	,	PUNCT
ejpam-6670	80	3	the	the	DET
ejpam-6670	80	4	total	total	ADJ
ejpam-6670	80	5	population	population	NOUN
ejpam-6670	80	6	groups	group	NOUN
ejpam-6670	80	7	are	be	AUX
ejpam-6670	80	8	distributed	distribute	VERB
ejpam-6670	80	9	in	in	ADP
ejpam-6670	80	10	six	six	NUM
ejpam-6670	80	11	epidemiological	epidemiological	ADJ
ejpam-6670	80	12	subclasses	subclass	NOUN
ejpam-6670	80	13	i.e.	i.e.	X
ejpam-6670	80	14	s	s	X
ejpam-6670	80	15	,	,	PUNCT
ejpam-6670	80	16	l	l	NOUN
ejpam-6670	80	17	,	,	PUNCT
ejpam-6670	80	18	a	a	PRON
ejpam-6670	80	19	,	,	PUNCT
ejpam-6670	80	20	c	c	NOUN
ejpam-6670	80	21	,	,	PUNCT
ejpam-6670	80	22	r	r	NOUN
ejpam-6670	80	23	and	and	CCONJ
ejpam-6670	80	24	v	v	ADP
ejpam-6670	80	25	respectively	respectively	ADV
ejpam-6670	80	26	,	,	PUNCT
ejpam-6670	80	27	represent	represent	VERB
ejpam-6670	80	28	the	the	DET
ejpam-6670	80	29	susceptible	susceptible	ADJ
ejpam-6670	80	30	,	,	PUNCT
ejpam-6670	80	31	latent	latent	NOUN
ejpam-6670	80	32	,	,	PUNCT
ejpam-6670	80	33	acute	acute	PROPN
ejpam-6670	80	34	infected	infect	VERB
ejpam-6670	80	35	,	,	PUNCT
ejpam-6670	80	36	chronic	chronic	ADJ
ejpam-6670	80	37	carrier	carrier	NOUN
ejpam-6670	80	38	infectious	infectious	ADJ
ejpam-6670	80	39	,	,	PUNCT
ejpam-6670	80	40	recovered	recovered	ADJ
ejpam-6670	80	41	and	and	CCONJ
ejpam-6670	80	42	vaccinated	vaccinated	ADJ
ejpam-6670	80	43	individuals	individual	NOUN
ejpam-6670	80	44	,	,	PUNCT
ejpam-6670	80	45	whose	whose	DET
ejpam-6670	80	46	the	the	DET
ejpam-6670	80	47	schematic	schematic	ADJ
ejpam-6670	80	48	process	process	NOUN
ejpam-6670	80	49	of	of	ADP
ejpam-6670	80	50	the	the	DET
ejpam-6670	80	51	disease	disease	NOUN
ejpam-6670	80	52	propagation	propagation	NOUN
ejpam-6670	80	53	among	among	ADP
ejpam-6670	80	54	different	different	ADJ
ejpam-6670	80	55	epidemiological	epidemiological	ADJ
ejpam-6670	80	56	groups	group	NOUN
ejpam-6670	80	57	of	of	ADP
ejpam-6670	80	58	population	population	NOUN
ejpam-6670	80	59	is	be	AUX
ejpam-6670	80	60	illustrated	illustrate	VERB
ejpam-6670	80	61	by	by	ADP
ejpam-6670	80	62	a	a	DET
ejpam-6670	80	63	flowchart	flowchart	NOUN
ejpam-6670	80	64	as	as	SCONJ
ejpam-6670	80	65	given	give	VERB
ejpam-6670	80	66	in	in	ADP
ejpam-6670	80	67	figure	figure	NOUN
ejpam-6670	80	68	1	1	NUM
ejpam-6670	80	69	.	.	PUNCT
ejpam-6670	81	1	eventually	eventually	ADV
ejpam-6670	81	2	,	,	PUNCT
ejpam-6670	81	3	the	the	DET
ejpam-6670	81	4	dynamics	dynamic	NOUN
ejpam-6670	81	5	of	of	ADP
ejpam-6670	81	6	these	these	DET
ejpam-6670	81	7	compartments	compartment	NOUN
ejpam-6670	81	8	are	be	AUX
ejpam-6670	81	9	governed	govern	VERB
ejpam-6670	81	10	by	by	ADP
ejpam-6670	81	11	the	the	DET
ejpam-6670	81	12	following	follow	VERB
ejpam-6670	81	13	system	system	NOUN
ejpam-6670	81	14	of	of	ADP
ejpam-6670	81	15	nonlinear	nonlinear	ADJ
ejpam-6670	81	16	differential	differential	NOUN
ejpam-6670	81	17	equations:	equations:	PROPN
ejpam-6670	81	18	ds(t	ds(t	NOUN
ejpam-6670	81	19	)	)	PUNCT
ejpam-6670	81	20	dt	dt	NOUN
ejpam-6670	82	1	=	=	SYM
ejpam-6670	82	2	gη(1−	gη(1−	PROPN
ejpam-6670	82	3	φc(t	φc(t	NOUN
ejpam-6670	82	4	)	)	PUNCT
ejpam-6670	82	5	)	)	PUNCT
ejpam-6670	83	1	+	+	CCONJ
ejpam-6670	83	2	πv(t)−	πv(t)−	PROPN
ejpam-6670	83	3	αs(t)a(t	αs(t)a(t	PROPN
ejpam-6670	83	4	)	)	PUNCT
ejpam-6670	83	5	1	1	NUM
ejpam-6670	84	1	+	+	SYM
ejpam-6670	84	2	βc(t	βc(t	NOUN
ejpam-6670	84	3	)	)	PUNCT
ejpam-6670	85	1	−	−	PUNCT
ejpam-6670	86	1	λαs(t)c(t	λαs(t)c(t	SYM
ejpam-6670	86	2	)	)	PUNCT
ejpam-6670	86	3	1	1	NUM
ejpam-6670	86	4	+	+	SYM
ejpam-6670	86	5	βc(t	βc(t	NOUN
ejpam-6670	86	6	)	)	PUNCT
ejpam-6670	86	7	−	−	PROPN
ejpam-6670	87	1	(	(	PUNCT
ejpam-6670	87	2	µ0	µ0	NOUN
ejpam-6670	87	3	+	+	X
ejpam-6670	87	4	λ3)s(t	λ3)s(t	NOUN
ejpam-6670	87	5	)	)	PUNCT
ejpam-6670	87	6	,	,	PUNCT
ejpam-6670	87	7	dl(t	dl(t	NOUN
ejpam-6670	87	8	)	)	PUNCT
ejpam-6670	87	9	dt	dt	X
ejpam-6670	88	1	=	=	SYM
ejpam-6670	88	2	αs(t)a(t	αs(t)a(t	PROPN
ejpam-6670	88	3	)	)	PUNCT
ejpam-6670	88	4	1	1	NUM
ejpam-6670	89	1	+	+	CCONJ
ejpam-6670	89	2	βc(t	βc(t	NUM
ejpam-6670	89	3	)	)	PUNCT
ejpam-6670	90	1	+	+	PUNCT
ejpam-6670	91	1	λαs(t)c(t	λαs(t)c(t	X
ejpam-6670	91	2	)	)	PUNCT
ejpam-6670	91	3	1	1	NUM
ejpam-6670	91	4	+	+	SYM
ejpam-6670	91	5	βc(t	βc(t	NOUN
ejpam-6670	91	6	)	)	PUNCT
ejpam-6670	91	7	−	−	PROPN
ejpam-6670	92	1	(	(	PUNCT
ejpam-6670	92	2	µ0	µ0	NOUN
ejpam-6670	92	3	+	+	X
ejpam-6670	92	4	θ)l(t	θ)l(t	NOUN
ejpam-6670	92	5	)	)	PUNCT
ejpam-6670	92	6	,	,	PUNCT
ejpam-6670	92	7	da(t	da(t	NOUN
ejpam-6670	92	8	)	)	PUNCT
ejpam-6670	92	9	dt	dt	NOUN
ejpam-6670	93	1	=	=	SYM
ejpam-6670	93	2	θl(t)−	θl(t)−	PROPN
ejpam-6670	93	3	(	(	PUNCT
ejpam-6670	93	4	µ0	µ0	NOUN
ejpam-6670	93	5	+	+	X
ejpam-6670	93	6	λ1)a(t	λ1)a(t	NOUN
ejpam-6670	93	7	)	)	PUNCT
ejpam-6670	93	8	,	,	PUNCT
ejpam-6670	93	9	dc(t	dc(t	NOUN
ejpam-6670	93	10	)	)	PUNCT
ejpam-6670	93	11	dt	dt	NOUN
ejpam-6670	93	12	=	=	SYM
ejpam-6670	93	13	gηφc(t	gηφc(t	PROPN
ejpam-6670	93	14	)	)	PUNCT
ejpam-6670	94	1	+	+	CCONJ
ejpam-6670	94	2	qλ1a(t)−	qλ1a(t)−	PROPN
ejpam-6670	94	3	(	(	PUNCT
ejpam-6670	94	4	µ0	µ0	NOUN
ejpam-6670	94	5	+	+	SYM
ejpam-6670	94	6	µ1	µ1	PROPN
ejpam-6670	94	7	+	+	SYM
ejpam-6670	94	8	λ2)c(t	λ2)c(t	PROPN
ejpam-6670	94	9	)	)	PUNCT
ejpam-6670	94	10	,	,	PUNCT
ejpam-6670	94	11	dr(t	dr(t	NUM
ejpam-6670	94	12	)	)	PUNCT
ejpam-6670	94	13	dt	dt	NOUN
ejpam-6670	95	1	=	=	SYM
ejpam-6670	95	2	λ2c(t	λ2c(t	PROPN
ejpam-6670	95	3	)	)	PUNCT
ejpam-6670	96	1	+	+	CCONJ
ejpam-6670	96	2	(	(	PUNCT
ejpam-6670	96	3	1−	1−	NUM
ejpam-6670	96	4	q)λ1a(t)−	q)λ1a(t)−	PROPN
ejpam-6670	96	5	µ0r(t	µ0r(t	PROPN
ejpam-6670	96	6	)	)	PUNCT
ejpam-6670	96	7	,	,	PUNCT
ejpam-6670	96	8	dv(t	dv(t	X
ejpam-6670	96	9	)	)	PUNCT
ejpam-6670	96	10	dt	dt	X
ejpam-6670	97	1	=	=	PUNCT
ejpam-6670	97	2	g(1−	g(1−	X
ejpam-6670	97	3	η	η	PROPN
ejpam-6670	97	4	)	)	PUNCT
ejpam-6670	97	5	+	+	CCONJ
ejpam-6670	97	6	λ3s(t)−	λ3s(t)−	PUNCT
ejpam-6670	97	7	(	(	PUNCT
ejpam-6670	97	8	µ0	µ0	NOUN
ejpam-6670	97	9	+	+	X
ejpam-6670	97	10	π)v(t	π)v(t	NOUN
ejpam-6670	97	11	)	)	PUNCT
ejpam-6670	97	12	,	,	PUNCT
ejpam-6670	97	13	(	(	PUNCT
ejpam-6670	97	14	1	1	X
ejpam-6670	97	15	)	)	PUNCT
ejpam-6670	97	16	t.	t.	NOUN
ejpam-6670	97	17	khan	khan	PROPN
ejpam-6670	97	18	et	et	PROPN
ejpam-6670	97	19	al	al	PROPN
ejpam-6670	97	20	.	.	PUNCT
ejpam-6670	97	21	/	/	SYM
ejpam-6670	97	22	eur	eur	PROPN
ejpam-6670	97	23	.	.	PUNCT
ejpam-6670	98	1	j.	j.	PROPN
ejpam-6670	98	2	pure	pure	PROPN
ejpam-6670	98	3	appl	appl	PROPN
ejpam-6670	98	4	.	.	PROPN
ejpam-6670	98	5	math	math	PROPN
ejpam-6670	98	6	,	,	PUNCT
ejpam-6670	98	7	18	18	NUM
ejpam-6670	98	8	(	(	PUNCT
ejpam-6670	98	9	3	3	NUM
ejpam-6670	98	10	)	)	PUNCT
ejpam-6670	98	11	(	(	PUNCT
ejpam-6670	98	12	2025	2025	NUM
ejpam-6670	98	13	)	)	PUNCT
ejpam-6670	98	14	,	,	PUNCT
ejpam-6670	98	15	6670	6670	NUM
ejpam-6670	98	16	5	5	NUM
ejpam-6670	98	17	of	of	ADP
ejpam-6670	98	18	22	22	NUM
ejpam-6670	98	19	figure	figure	NOUN
ejpam-6670	98	20	1	1	NUM
ejpam-6670	98	21	:	:	PUNCT
ejpam-6670	98	22	the	the	DET
ejpam-6670	98	23	plot	plot	NOUN
ejpam-6670	98	24	represent	represent	VERB
ejpam-6670	98	25	the	the	DET
ejpam-6670	98	26	schematic	schematic	ADJ
ejpam-6670	98	27	process	process	NOUN
ejpam-6670	98	28	of	of	ADP
ejpam-6670	98	29	the	the	DET
ejpam-6670	98	30	hbv	hbv	NOUN
ejpam-6670	98	31	propagation	propagation	NOUN
ejpam-6670	98	32	among	among	ADP
ejpam-6670	98	33	different	different	ADJ
ejpam-6670	98	34	epidemiological	epidemiological	ADJ
ejpam-6670	98	35	groups	group	NOUN
ejpam-6670	98	36	of	of	ADP
ejpam-6670	98	37	population	population	NOUN
ejpam-6670	98	38	.	.	PUNCT
ejpam-6670	99	1	along	along	ADP
ejpam-6670	99	2	with	with	ADP
ejpam-6670	99	3	non	non	ADJ
ejpam-6670	99	4	-	-	ADJ
ejpam-6670	99	5	negative	negative	ADJ
ejpam-6670	99	6	initial	initial	ADJ
ejpam-6670	99	7	population	population	NOUN
ejpam-6670	99	8	sizes	size	NOUN
ejpam-6670	99	9	s(0	s(0	PROPN
ejpam-6670	99	10	)	)	PUNCT
ejpam-6670	99	11	,	,	PUNCT
ejpam-6670	99	12	v(0	v(0	PROPN
ejpam-6670	99	13	)	)	PUNCT
ejpam-6670	99	14	>	>	X
ejpam-6670	99	15	0	0	NUM
ejpam-6670	99	16	,	,	PUNCT
ejpam-6670	99	17	l(0	l(0	PROPN
ejpam-6670	99	18	)	)	PUNCT
ejpam-6670	99	19	,	,	PUNCT
ejpam-6670	99	20	a(0	a(0	PROPN
ejpam-6670	99	21	)	)	PUNCT
ejpam-6670	99	22	,	,	PUNCT
ejpam-6670	99	23	c(0	c(0	PROPN
ejpam-6670	99	24	)	)	PUNCT
ejpam-6670	99	25	,	,	PUNCT
ejpam-6670	99	26	r(0	r(0	PROPN
ejpam-6670	99	27	)	)	PUNCT
ejpam-6670	99	28	≥	≥	NOUN
ejpam-6670	99	29	0	0	NUM
ejpam-6670	99	30	.	.	PUNCT
ejpam-6670	100	1	(	(	PUNCT
ejpam-6670	100	2	2	2	X
ejpam-6670	100	3	)	)	PUNCT
ejpam-6670	100	4	in	in	ADP
ejpam-6670	100	5	the	the	DET
ejpam-6670	100	6	model	model	NOUN
ejpam-6670	100	7	(	(	PUNCT
ejpam-6670	100	8	1	1	NUM
ejpam-6670	100	9	)	)	PUNCT
ejpam-6670	100	10	,	,	PUNCT
ejpam-6670	100	11	g	g	PROPN
ejpam-6670	100	12	represents	represent	VERB
ejpam-6670	100	13	the	the	DET
ejpam-6670	100	14	birth	birth	NOUN
ejpam-6670	100	15	rate	rate	NOUN
ejpam-6670	100	16	while	while	SCONJ
ejpam-6670	100	17	the	the	DET
ejpam-6670	100	18	rate	rate	NOUN
ejpam-6670	100	19	of	of	ADP
ejpam-6670	100	20	birth	birth	NOUN
ejpam-6670	100	21	without	without	ADP
ejpam-6670	100	22	successful	successful	ADJ
ejpam-6670	100	23	vaccination	vaccination	NOUN
ejpam-6670	100	24	is	be	AUX
ejpam-6670	100	25	represented	represent	VERB
ejpam-6670	100	26	by	by	ADP
ejpam-6670	100	27	η	η	PROPN
ejpam-6670	100	28	.	.	PROPN
ejpam-6670	100	29	the	the	DET
ejpam-6670	100	30	quantity	quantity	NOUN
ejpam-6670	100	31	of	of	ADP
ejpam-6670	100	32	maternally	maternally	ADV
ejpam-6670	100	33	distorted	distort	VERB
ejpam-6670	100	34	individuals	individual	NOUN
ejpam-6670	100	35	is	be	AUX
ejpam-6670	100	36	denoted	denote	VERB
ejpam-6670	100	37	by	by	ADP
ejpam-6670	100	38	φ	φ	PROPN
ejpam-6670	100	39	,	,	PUNCT
ejpam-6670	100	40	and	and	CCONJ
ejpam-6670	100	41	the	the	DET
ejpam-6670	100	42	rate	rate	NOUN
ejpam-6670	100	43	of	of	ADP
ejpam-6670	100	44	waning	wane	VERB
ejpam-6670	100	45	vaccine	vaccine	NOUN
ejpam-6670	100	46	-	-	PUNCT
ejpam-6670	100	47	induced	induce	VERB
ejpam-6670	100	48	immunity	immunity	NOUN
ejpam-6670	100	49	is	be	AUX
ejpam-6670	100	50	π	π	X
ejpam-6670	100	51	.	.	PUNCT
ejpam-6670	101	1	we	we	PRON
ejpam-6670	101	2	symbolize	symbolize	VERB
ejpam-6670	101	3	the	the	DET
ejpam-6670	101	4	transmission	transmission	NOUN
ejpam-6670	101	5	rate	rate	NOUN
ejpam-6670	101	6	from	from	ADP
ejpam-6670	101	7	susceptible	susceptible	ADJ
ejpam-6670	101	8	to	to	ADP
ejpam-6670	101	9	infected	infect	VERB
ejpam-6670	101	10	,	,	PUNCT
ejpam-6670	101	11	denoted	denote	VERB
ejpam-6670	101	12	by	by	ADP
ejpam-6670	101	13	the	the	DET
ejpam-6670	101	14	parameters	parameter	NOUN
ejpam-6670	101	15	α	α	NOUN
ejpam-6670	101	16	and	and	CCONJ
ejpam-6670	101	17	λ	λ	PROPN
ejpam-6670	101	18	,	,	PUNCT
ejpam-6670	101	19	as	as	ADP
ejpam-6670	101	20	the	the	DET
ejpam-6670	101	21	reduced	reduced	ADJ
ejpam-6670	101	22	transmission	transmission	NOUN
ejpam-6670	101	23	rate	rate	NOUN
ejpam-6670	101	24	.	.	PUNCT
ejpam-6670	102	1	µ0	µ0	NOUN
ejpam-6670	102	2	represents	represent	VERB
ejpam-6670	102	3	rate	rate	NOUN
ejpam-6670	102	4	of	of	ADP
ejpam-6670	102	5	natural	natural	ADJ
ejpam-6670	102	6	death	death	NOUN
ejpam-6670	102	7	.	.	PUNCT
ejpam-6670	103	1	the	the	DET
ejpam-6670	103	2	rate	rate	NOUN
ejpam-6670	103	3	of	of	ADP
ejpam-6670	103	4	vaccination	vaccination	NOUN
ejpam-6670	103	5	is	be	AUX
ejpam-6670	103	6	λ3	λ3	PROPN
ejpam-6670	103	7	,	,	PUNCT
ejpam-6670	103	8	and	and	CCONJ
ejpam-6670	103	9	the	the	DET
ejpam-6670	103	10	amount	amount	NOUN
ejpam-6670	103	11	at	at	ADP
ejpam-6670	103	12	which	which	PRON
ejpam-6670	103	13	the	the	DET
ejpam-6670	103	14	latent	latent	NOUN
ejpam-6670	103	15	individuals	individual	NOUN
ejpam-6670	103	16	lead	lead	VERB
ejpam-6670	103	17	to	to	ADP
ejpam-6670	103	18	acute	acute	ADJ
ejpam-6670	103	19	class	class	NOUN
ejpam-6670	103	20	is	be	AUX
ejpam-6670	103	21	represented	represent	VERB
ejpam-6670	103	22	by	by	ADP
ejpam-6670	103	23	θ	θ	PROPN
ejpam-6670	103	24	.	.	PUNCT
ejpam-6670	104	1	in	in	ADP
ejpam-6670	104	2	contrast	contrast	NOUN
ejpam-6670	104	3	,	,	PUNCT
ejpam-6670	104	4	the	the	DET
ejpam-6670	104	5	portion	portion	NOUN
ejpam-6670	104	6	of	of	ADP
ejpam-6670	104	7	individuals	individual	NOUN
ejpam-6670	104	8	who	who	PRON
ejpam-6670	104	9	transition	transition	VERB
ejpam-6670	104	10	from	from	ADP
ejpam-6670	104	11	the	the	DET
ejpam-6670	104	12	acute	acute	ADJ
ejpam-6670	104	13	population	population	NOUN
ejpam-6670	104	14	to	to	ADP
ejpam-6670	104	15	the	the	DET
ejpam-6670	104	16	chronic	chronic	ADJ
ejpam-6670	104	17	carrier	carrier	NOUN
ejpam-6670	104	18	is	be	AUX
ejpam-6670	104	19	represented	represent	VERB
ejpam-6670	104	20	by	by	ADP
ejpam-6670	104	21	λ1	λ1	PROPN
ejpam-6670	104	22	.	.	PUNCT
ejpam-6670	105	1	we	we	PRON
ejpam-6670	105	2	also	also	ADV
ejpam-6670	105	3	denote	denote	VERB
ejpam-6670	105	4	the	the	DET
ejpam-6670	105	5	rate	rate	NOUN
ejpam-6670	105	6	at	at	ADP
ejpam-6670	105	7	which	which	PRON
ejpam-6670	105	8	the	the	DET
ejpam-6670	105	9	individuals	individual	NOUN
ejpam-6670	105	10	move	move	VERB
ejpam-6670	105	11	from	from	ADP
ejpam-6670	105	12	chronic	chronic	ADJ
ejpam-6670	105	13	carrier	carrier	NOUN
ejpam-6670	105	14	to	to	ADP
ejpam-6670	105	15	the	the	DET
ejpam-6670	105	16	immune	immune	ADJ
ejpam-6670	105	17	class	class	NOUN
ejpam-6670	105	18	by	by	ADP
ejpam-6670	105	19	λ2	λ2	PROPN
ejpam-6670	105	20	,	,	PUNCT
ejpam-6670	105	21	and	and	CCONJ
ejpam-6670	105	22	the	the	DET
ejpam-6670	105	23	parameter	parameter	NOUN
ejpam-6670	105	24	µ1	µ1	PROPN
ejpam-6670	105	25	is	be	AUX
ejpam-6670	105	26	the	the	DET
ejpam-6670	105	27	death	death	NOUN
ejpam-6670	105	28	that	that	PRON
ejpam-6670	105	29	occurs	occur	VERB
ejpam-6670	105	30	from	from	ADP
ejpam-6670	105	31	hepatitis	hepatitis	PROPN
ejpam-6670	105	32	b.	b.	PROPN
ejpam-6670	106	1	moreover	moreover	ADV
ejpam-6670	106	2	,	,	PUNCT
ejpam-6670	106	3	we	we	PRON
ejpam-6670	106	4	assume	assume	VERB
ejpam-6670	106	5	that	that	SCONJ
ejpam-6670	106	6	q	q	NOUN
ejpam-6670	106	7	is	be	AUX
ejpam-6670	106	8	the	the	DET
ejpam-6670	106	9	average	average	ADJ
ejpam-6670	106	10	rate	rate	NOUN
ejpam-6670	106	11	of	of	ADP
ejpam-6670	106	12	those	those	DET
ejpam-6670	106	13	individuals	individual	NOUN
ejpam-6670	106	14	who	who	PRON
ejpam-6670	106	15	become	become	VERB
ejpam-6670	106	16	unsuccessful	unsuccessful	ADJ
ejpam-6670	106	17	in	in	ADP
ejpam-6670	106	18	recovering	recover	VERB
ejpam-6670	106	19	from	from	ADP
ejpam-6670	106	20	hepatitis	hepatitis	PROPN
ejpam-6670	106	21	b	b	PROPN
ejpam-6670	106	22	in	in	ADP
ejpam-6670	106	23	the	the	DET
ejpam-6670	106	24	primary	primary	ADJ
ejpam-6670	106	25	stage	stage	NOUN
ejpam-6670	106	26	of	of	ADP
ejpam-6670	106	27	hepatitis	hepatitis	PROPN
ejpam-6670	106	28	b	b	PROPN
ejpam-6670	106	29	(	(	PUNCT
ejpam-6670	106	30	acute	acute	NOUN
ejpam-6670	106	31	)	)	PUNCT
ejpam-6670	106	32	and	and	CCONJ
ejpam-6670	106	33	move	move	VERB
ejpam-6670	106	34	to	to	ADP
ejpam-6670	106	35	the	the	DET
ejpam-6670	106	36	chronic	chronic	ADJ
ejpam-6670	106	37	stage	stage	NOUN
ejpam-6670	106	38	.	.	PUNCT
ejpam-6670	107	1	having	having	AUX
ejpam-6670	107	2	presented	present	VERB
ejpam-6670	107	3	the	the	DET
ejpam-6670	107	4	detailed	detailed	ADJ
ejpam-6670	107	5	model	model	NOUN
ejpam-6670	107	6	formulation	formulation	NOUN
ejpam-6670	107	7	,	,	PUNCT
ejpam-6670	107	8	we	we	PRON
ejpam-6670	107	9	proceed	proceed	VERB
ejpam-6670	107	10	to	to	PART
ejpam-6670	107	11	analyze	analyze	VERB
ejpam-6670	107	12	the	the	DET
ejpam-6670	107	13	proposed	propose	VERB
ejpam-6670	107	14	epidemic	epidemic	NOUN
ejpam-6670	107	15	model	model	NOUN
ejpam-6670	107	16	by	by	ADP
ejpam-6670	107	17	establishing	establish	VERB
ejpam-6670	107	18	its	its	PRON
ejpam-6670	107	19	well	well	NOUN
ejpam-6670	107	20	-	-	PUNCT
ejpam-6670	107	21	posedness	posedness	NOUN
ejpam-6670	107	22	,	,	PUNCT
ejpam-6670	107	23	ensuring	ensure	VERB
ejpam-6670	107	24	that	that	SCONJ
ejpam-6670	107	25	it	it	PRON
ejpam-6670	107	26	is	be	AUX
ejpam-6670	107	27	both	both	PRON
ejpam-6670	107	28	biologically	biologically	ADV
ejpam-6670	107	29	and	and	CCONJ
ejpam-6670	107	30	mathematically	mathematically	ADV
ejpam-6670	107	31	meaningful	meaningful	ADJ
ejpam-6670	107	32	.	.	PUNCT
ejpam-6670	108	1	2.1	2.1	NUM
ejpam-6670	108	2	.	.	PUNCT
ejpam-6670	109	1	well	well	ADJ
ejpam-6670	109	2	-	-	PUNCT
ejpam-6670	109	3	posedness	posedness	NOUN
ejpam-6670	109	4	we	we	PRON
ejpam-6670	109	5	discuss	discuss	VERB
ejpam-6670	109	6	the	the	DET
ejpam-6670	109	7	well	well	NOUN
ejpam-6670	109	8	-	-	PUNCT
ejpam-6670	109	9	posedness	posedness	NOUN
ejpam-6670	109	10	of	of	ADP
ejpam-6670	109	11	the	the	DET
ejpam-6670	109	12	proposed	propose	VERB
ejpam-6670	109	13	system	system	NOUN
ejpam-6670	109	14	to	to	PART
ejpam-6670	109	15	show	show	VERB
ejpam-6670	109	16	that	that	SCONJ
ejpam-6670	109	17	the	the	DET
ejpam-6670	109	18	epidemic	epidemic	NOUN
ejpam-6670	109	19	model	model	NOUN
ejpam-6670	109	20	is	be	AUX
ejpam-6670	109	21	feasible	feasible	ADJ
ejpam-6670	109	22	in	in	ADP
ejpam-6670	109	23	both	both	DET
ejpam-6670	109	24	senses	sense	NOUN
ejpam-6670	109	25	,	,	PUNCT
ejpam-6670	109	26	biologically	biologically	ADV
ejpam-6670	109	27	and	and	CCONJ
ejpam-6670	109	28	mathematically	mathematically	ADV
ejpam-6670	109	29	.	.	PUNCT
ejpam-6670	110	1	for	for	ADP
ejpam-6670	110	2	this	this	PRON
ejpam-6670	110	3	,	,	PUNCT
ejpam-6670	110	4	we	we	PRON
ejpam-6670	110	5	assume	assume	VERB
ejpam-6670	110	6	that	that	SCONJ
ejpam-6670	110	7	the	the	DET
ejpam-6670	110	8	total	total	ADJ
ejpam-6670	110	9	population	population	NOUN
ejpam-6670	110	10	is	be	AUX
ejpam-6670	110	11	represented	represent	VERB
ejpam-6670	110	12	by	by	ADP
ejpam-6670	110	13	n(t	n(t	PROPN
ejpam-6670	110	14	)	)	PUNCT
ejpam-6670	110	15	with	with	ADP
ejpam-6670	110	16	n	n	NOUN
ejpam-6670	110	17	=	=	PUNCT
ejpam-6670	110	18	v+l+a+s+r+c	v+l+a+s+r+c	NOUN
ejpam-6670	110	19	.	.	PUNCT
ejpam-6670	111	1	the	the	DET
ejpam-6670	111	2	model	model	NOUN
ejpam-6670	111	3	(	(	PUNCT
ejpam-6670	111	4	1	1	NUM
ejpam-6670	111	5	)	)	PUNCT
ejpam-6670	111	6	,	,	PUNCT
ejpam-6670	111	7	together	together	ADV
ejpam-6670	111	8	t.	t.	PROPN
ejpam-6670	111	9	khan	khan	PROPN
ejpam-6670	111	10	et	et	PROPN
ejpam-6670	111	11	al	al	PROPN
ejpam-6670	111	12	.	.	PUNCT
ejpam-6670	111	13	/	/	SYM
ejpam-6670	111	14	eur	eur	PROPN
ejpam-6670	111	15	.	.	PUNCT
ejpam-6670	112	1	j.	j.	PROPN
ejpam-6670	112	2	pure	pure	PROPN
ejpam-6670	112	3	appl	appl	PROPN
ejpam-6670	112	4	.	.	PROPN
ejpam-6670	112	5	math	math	PROPN
ejpam-6670	112	6	,	,	PUNCT
ejpam-6670	112	7	18	18	NUM
ejpam-6670	112	8	(	(	PUNCT
ejpam-6670	112	9	3	3	NUM
ejpam-6670	112	10	)	)	PUNCT
ejpam-6670	112	11	(	(	PUNCT
ejpam-6670	112	12	2025	2025	NUM
ejpam-6670	112	13	)	)	PUNCT
ejpam-6670	112	14	,	,	PUNCT
ejpam-6670	112	15	6670	6670	NUM
ejpam-6670	112	16	6	6	NUM
ejpam-6670	112	17	of	of	ADP
ejpam-6670	112	18	22	22	NUM
ejpam-6670	112	19	with	with	ADP
ejpam-6670	112	20	initial	initial	ADJ
ejpam-6670	112	21	conditions	condition	NOUN
ejpam-6670	112	22	(	(	PUNCT
ejpam-6670	112	23	2	2	X
ejpam-6670	112	24	)	)	PUNCT
ejpam-6670	112	25	satisfies	satisfie	NOUN
ejpam-6670	112	26	that	that	SCONJ
ejpam-6670	112	27	n(t	n(t	PROPN
ejpam-6670	112	28	)	)	PUNCT
ejpam-6670	112	29	≥	≥	X
ejpam-6670	112	30	0	0	NUM
ejpam-6670	112	31	implies	imply	VERB
ejpam-6670	112	32	that	that	SCONJ
ejpam-6670	112	33	n(t	n(t	PROPN
ejpam-6670	112	34	)	)	PUNCT
ejpam-6670	112	35	(	(	PUNCT
ejpam-6670	112	36	total	total	ADJ
ejpam-6670	112	37	population	population	NOUN
ejpam-6670	112	38	)	)	PUNCT
ejpam-6670	112	39	is	be	AUX
ejpam-6670	112	40	bounded	bound	VERB
ejpam-6670	112	41	and	and	CCONJ
ejpam-6670	112	42	positive	positive	ADJ
ejpam-6670	112	43	for	for	ADP
ejpam-6670	112	44	t	t	PROPN
ejpam-6670	112	45	>	>	X
ejpam-6670	112	46	0	0	PROPN
ejpam-6670	112	47	,	,	PUNCT
ejpam-6670	112	48	thus	thus	ADV
ejpam-6670	112	49	the	the	DET
ejpam-6670	112	50	time	time	NOUN
ejpam-6670	112	51	derivative	derivative	NOUN
ejpam-6670	112	52	of	of	ADP
ejpam-6670	112	53	n(t	n(t	PROPN
ejpam-6670	112	54	)	)	PUNCT
ejpam-6670	112	55	gives	give	VERB
ejpam-6670	112	56	dn(t	dn(t	NOUN
ejpam-6670	112	57	)	)	PUNCT
ejpam-6670	112	58	dt	dt	NOUN
ejpam-6670	113	1	=	=	PUNCT
ejpam-6670	113	2	g	g	PROPN
ejpam-6670	113	3	−	−	PROPN
ejpam-6670	113	4	µ0n(t)−	µ0n(t)−	PROPN
ejpam-6670	113	5	µ1c(t	µ1c(t	PROPN
ejpam-6670	113	6	)	)	PUNCT
ejpam-6670	113	7	,	,	PUNCT
ejpam-6670	113	8	(	(	PUNCT
ejpam-6670	113	9	3	3	X
ejpam-6670	113	10	)	)	PUNCT
ejpam-6670	113	11	which	which	PRON
ejpam-6670	113	12	shows	show	VERB
ejpam-6670	113	13	that	that	SCONJ
ejpam-6670	113	14	as	as	ADP
ejpam-6670	113	15	t	t	PROPN
ejpam-6670	113	16	→	→	SYM
ejpam-6670	113	17	∞	∞	PROPN
ejpam-6670	113	18	,	,	PUNCT
ejpam-6670	113	19	n(t	n(t	NOUN
ejpam-6670	113	20	)	)	PUNCT
ejpam-6670	113	21	≤	≤	NOUN
ejpam-6670	113	22	g	g	NOUN
ejpam-6670	113	23	µ0	µ0	NOUN
ejpam-6670	113	24	,	,	PUNCT
ejpam-6670	113	25	hence	hence	ADV
ejpam-6670	113	26	ω	ω	NUM
ejpam-6670	113	27	=	=	SYM
ejpam-6670	113	28	{	{	PUNCT
ejpam-6670	113	29	(	(	PUNCT
ejpam-6670	113	30	s(t	s(t	PROPN
ejpam-6670	113	31	)	)	PUNCT
ejpam-6670	113	32	,	,	PUNCT
ejpam-6670	113	33	l(t	l(t	PROPN
ejpam-6670	113	34	)	)	PUNCT
ejpam-6670	113	35	,	,	PUNCT
ejpam-6670	113	36	a(t	a(t	NOUN
ejpam-6670	113	37	)	)	PUNCT
ejpam-6670	113	38	,	,	PUNCT
ejpam-6670	113	39	c(t	c(t	PROPN
ejpam-6670	113	40	)	)	PUNCT
ejpam-6670	113	41	,	,	PUNCT
ejpam-6670	113	42	r(t	r(t	NOUN
ejpam-6670	113	43	)	)	PUNCT
ejpam-6670	113	44	,	,	PUNCT
ejpam-6670	113	45	v(t	v(t	NOUN
ejpam-6670	113	46	)	)	PUNCT
ejpam-6670	113	47	)	)	PUNCT
ejpam-6670	114	1	∈	∈	PROPN
ejpam-6670	114	2	r6	r6	NOUN
ejpam-6670	114	3	+	+	PROPN
ejpam-6670	114	4	,	,	PUNCT
ejpam-6670	114	5	n(t	n(t	NOUN
ejpam-6670	114	6	)	)	PUNCT
ejpam-6670	114	7	≤	≤	NOUN
ejpam-6670	114	8	g	g	ADP
ejpam-6670	114	9	µ0	µ0	PROPN
ejpam-6670	114	10	}	}	PUNCT
ejpam-6670	114	11	.	.	PUNCT
ejpam-6670	115	1	(	(	PUNCT
ejpam-6670	115	2	4	4	X
ejpam-6670	115	3	)	)	PUNCT
ejpam-6670	115	4	is	be	AUX
ejpam-6670	115	5	the	the	DET
ejpam-6670	115	6	feasible	feasible	ADJ
ejpam-6670	115	7	region	region	NOUN
ejpam-6670	115	8	.	.	PUNCT
ejpam-6670	116	1	to	to	PART
ejpam-6670	116	2	show	show	VERB
ejpam-6670	116	3	the	the	DET
ejpam-6670	116	4	existence	existence	NOUN
ejpam-6670	116	5	analysis	analysis	NOUN
ejpam-6670	116	6	,	,	PUNCT
ejpam-6670	116	7	we	we	PRON
ejpam-6670	116	8	can	can	AUX
ejpam-6670	116	9	express	express	VERB
ejpam-6670	116	10	the	the	DET
ejpam-6670	116	11	proposed	propose	VERB
ejpam-6670	116	12	epidemic	epidemic	NOUN
ejpam-6670	116	13	problem	problem	NOUN
ejpam-6670	116	14	as	as	ADP
ejpam-6670	116	15	initial	initial	ADJ
ejpam-6670	116	16	value	value	NOUN
ejpam-6670	116	17	problem	problem	NOUN
ejpam-6670	116	18	as	as	SCONJ
ejpam-6670	116	19	follows	follow	VERB
ejpam-6670	116	20	:	:	PUNCT
ejpam-6670	116	21	h′	h′	PROPN
ejpam-6670	116	22	(	(	PUNCT
ejpam-6670	116	23	t	t	NOUN
ejpam-6670	116	24	)	)	PUNCT
ejpam-6670	116	25	=	=	SYM
ejpam-6670	116	26	f(y	f(y	NOUN
ejpam-6670	116	27	)	)	PUNCT
ejpam-6670	116	28	,	,	PUNCT
ejpam-6670	116	29	y(0	y(0	PROPN
ejpam-6670	116	30	)	)	PUNCT
ejpam-6670	116	31	=	=	SYM
ejpam-6670	116	32	y0	y0	NOUN
ejpam-6670	116	33	,	,	PUNCT
ejpam-6670	116	34	(	(	PUNCT
ejpam-6670	116	35	5	5	NUM
ejpam-6670	116	36	)	)	PUNCT
ejpam-6670	116	37	where	where	SCONJ
ejpam-6670	116	38	y	y	NOUN
ejpam-6670	116	39	=	=	SYM
ejpam-6670	116	40	(	(	PUNCT
ejpam-6670	116	41	s	s	PROPN
ejpam-6670	116	42	,	,	PUNCT
ejpam-6670	116	43	l	l	NOUN
ejpam-6670	116	44	,	,	PUNCT
ejpam-6670	116	45	a	a	PRON
ejpam-6670	116	46	,	,	PUNCT
ejpam-6670	116	47	c	c	NOUN
ejpam-6670	116	48	,	,	PUNCT
ejpam-6670	116	49	r	r	NOUN
ejpam-6670	116	50	,	,	PUNCT
ejpam-6670	116	51	v)t	v)t	NOUN
ejpam-6670	116	52	and	and	CCONJ
ejpam-6670	116	53	f	f	X
ejpam-6670	116	54	=	=	PUNCT
ejpam-6670	116	55	(	(	PUNCT
ejpam-6670	116	56	f1	f1	PROPN
ejpam-6670	116	57	,	,	PUNCT
ejpam-6670	116	58	f2	f2	PROPN
ejpam-6670	116	59	,	,	PUNCT
ejpam-6670	116	60	.	.	PUNCT
ejpam-6670	116	61	.	.	PUNCT
ejpam-6670	117	1	.	.	PUNCT
ejpam-6670	118	1	,	,	PUNCT
ejpam-6670	118	2	f6	f6	PROPN
ejpam-6670	118	3	)	)	PUNCT
ejpam-6670	118	4	t.	t.	NOUN
ejpam-6670	118	5	to	to	PART
ejpam-6670	118	6	proceed	proceed	VERB
ejpam-6670	118	7	further	far	ADV
ejpam-6670	118	8	,	,	PUNCT
ejpam-6670	118	9	we	we	PRON
ejpam-6670	118	10	recall	recall	VERB
ejpam-6670	118	11	the	the	DET
ejpam-6670	118	12	definition	definition	NOUN
ejpam-6670	118	13	of	of	ADP
ejpam-6670	118	14	lipschitz	lipschitz	ADJ
ejpam-6670	118	15	continuity	continuity	NOUN
ejpam-6670	118	16	as	as	SCONJ
ejpam-6670	118	17	follows	follow	VERB
ejpam-6670	118	18	.	.	PUNCT
ejpam-6670	119	1	definition	definition	NOUN
ejpam-6670	119	2	1	1	NUM
ejpam-6670	119	3	.	.	PUNCT
ejpam-6670	120	1	[	[	X
ejpam-6670	120	2	20	20	NUM
ejpam-6670	120	3	]	]	PUNCT
ejpam-6670	120	4	the	the	DET
ejpam-6670	120	5	function	function	NOUN
ejpam-6670	120	6	f(y	f(y	NOUN
ejpam-6670	120	7	)	)	PUNCT
ejpam-6670	120	8	is	be	AUX
ejpam-6670	120	9	said	say	VERB
ejpam-6670	120	10	to	to	PART
ejpam-6670	120	11	be	be	AUX
ejpam-6670	120	12	lipschitz	lipschitz	VERB
ejpam-6670	120	13	continuous	continuous	ADJ
ejpam-6670	120	14	if	if	SCONJ
ejpam-6670	120	15	there	there	PRON
ejpam-6670	120	16	exists	exist	VERB
ejpam-6670	120	17	a	a	DET
ejpam-6670	120	18	constant	constant	ADJ
ejpam-6670	120	19	m	m	NOUN
ejpam-6670	120	20	>	>	X
ejpam-6670	120	21	0	0	NUM
ejpam-6670	120	22	such	such	ADJ
ejpam-6670	120	23	that	that	SCONJ
ejpam-6670	120	24	∥f(y1)−f(y2)∥	∥f(y1)−f(y2)∥	PROPN
ejpam-6670	120	25	≤	≤	NOUN
ejpam-6670	120	26	m∥y1	m∥y1	PUNCT
ejpam-6670	120	27	−	−	PROPN
ejpam-6670	120	28	y2∥.	y2∥.	NOUN
ejpam-6670	120	29	thus	thus	ADV
ejpam-6670	120	30	,	,	PUNCT
ejpam-6670	120	31	regarding	regard	VERB
ejpam-6670	120	32	existence	existence	NOUN
ejpam-6670	120	33	of	of	ADP
ejpam-6670	120	34	solution	solution	NOUN
ejpam-6670	120	35	,	,	PUNCT
ejpam-6670	120	36	we	we	PRON
ejpam-6670	120	37	prove	prove	VERB
ejpam-6670	120	38	the	the	DET
ejpam-6670	120	39	following	follow	VERB
ejpam-6670	120	40	proposition	proposition	NOUN
ejpam-6670	120	41	.	.	PUNCT
ejpam-6670	121	1	proposition	proposition	NOUN
ejpam-6670	121	2	2.1	2.1	NUM
ejpam-6670	121	3	.	.	PUNCT
ejpam-6670	122	1	there	there	PRON
ejpam-6670	122	2	exists	exist	VERB
ejpam-6670	122	3	a	a	DET
ejpam-6670	122	4	unique	unique	ADJ
ejpam-6670	122	5	solution	solution	NOUN
ejpam-6670	122	6	of	of	ADP
ejpam-6670	122	7	the	the	DET
ejpam-6670	122	8	system	system	NOUN
ejpam-6670	122	9	(	(	PUNCT
ejpam-6670	122	10	5	5	X
ejpam-6670	122	11	)	)	PUNCT
ejpam-6670	122	12	analogous	analogous	ADJ
ejpam-6670	122	13	to	to	ADP
ejpam-6670	122	14	the	the	DET
ejpam-6670	122	15	proposed	propose	VERB
ejpam-6670	122	16	model	model	NOUN
ejpam-6670	122	17	(	(	PUNCT
ejpam-6670	122	18	1	1	NUM
ejpam-6670	122	19	)	)	PUNCT
ejpam-6670	122	20	and	and	CCONJ
ejpam-6670	122	21	(	(	PUNCT
ejpam-6670	122	22	2	2	NUM
ejpam-6670	122	23	)	)	PUNCT
ejpam-6670	122	24	.	.	PUNCT
ejpam-6670	123	1	proof	proof	NOUN
ejpam-6670	123	2	.	.	PUNCT
ejpam-6670	124	1	to	to	PART
ejpam-6670	124	2	show	show	VERB
ejpam-6670	124	3	that	that	SCONJ
ejpam-6670	124	4	the	the	DET
ejpam-6670	124	5	model	model	NOUN
ejpam-6670	124	6	posses	posse	VERB
ejpam-6670	124	7	a	a	DET
ejpam-6670	124	8	unique	unique	ADJ
ejpam-6670	124	9	solution	solution	NOUN
ejpam-6670	124	10	,	,	PUNCT
ejpam-6670	124	11	it	it	PRON
ejpam-6670	124	12	is	be	AUX
ejpam-6670	124	13	sufficient	sufficient	ADJ
ejpam-6670	124	14	to	to	PART
ejpam-6670	124	15	prove	prove	VERB
ejpam-6670	124	16	that	that	SCONJ
ejpam-6670	124	17	the	the	DET
ejpam-6670	124	18	function	function	NOUN
ejpam-6670	124	19	f(y	f(y	NOUN
ejpam-6670	124	20	)	)	PUNCT
ejpam-6670	124	21	satisfies	satisfy	VERB
ejpam-6670	124	22	the	the	DET
ejpam-6670	124	23	lipschitz	lipschitz	NOUN
ejpam-6670	124	24	condition	condition	NOUN
ejpam-6670	124	25	provided	provide	VERB
ejpam-6670	124	26	in	in	ADP
ejpam-6670	124	27	the	the	DET
ejpam-6670	124	28	above	above	ADJ
ejpam-6670	124	29	definition	definition	NOUN
ejpam-6670	124	30	.	.	PUNCT
ejpam-6670	125	1	keeping	keep	VERB
ejpam-6670	125	2	in	in	ADP
ejpam-6670	125	3	mind	mind	NOUN
ejpam-6670	125	4	the	the	DET
ejpam-6670	125	5	set	set	PROPN
ejpam-6670	125	6	ω	ω	PROPN
ejpam-6670	125	7	and	and	CCONJ
ejpam-6670	125	8	n(t	n(t	NUM
ejpam-6670	125	9	)	)	PUNCT
ejpam-6670	125	10	≤	≤	NUM
ejpam-6670	125	11	g/µ0	g/µ0	NOUN
ejpam-6670	125	12	,	,	PUNCT
ejpam-6670	125	13	which	which	PRON
ejpam-6670	125	14	implies	imply	VERB
ejpam-6670	125	15	that	that	SCONJ
ejpam-6670	125	16	all	all	DET
ejpam-6670	125	17	the	the	DET
ejpam-6670	125	18	state	state	NOUN
ejpam-6670	125	19	variables	variable	VERB
ejpam-6670	125	20	for	for	ADP
ejpam-6670	125	21	i	i	PRON
ejpam-6670	125	22	=	=	NOUN
ejpam-6670	125	23	1	1	NUM
ejpam-6670	125	24	,	,	PUNCT
ejpam-6670	125	25	2	2	NUM
ejpam-6670	125	26	,	,	PUNCT
ejpam-6670	125	27	si	si	X
ejpam-6670	125	28	,	,	PUNCT
ejpam-6670	125	29	li	li	PROPN
ejpam-6670	125	30	,	,	PUNCT
ejpam-6670	125	31	ai	ai	VERB
ejpam-6670	125	32	,	,	PUNCT
ejpam-6670	125	33	ci	ci	PROPN
ejpam-6670	125	34	,	,	PUNCT
ejpam-6670	125	35	ri	ri	PROPN
ejpam-6670	125	36	and	and	CCONJ
ejpam-6670	125	37	vi	vi	PROPN
ejpam-6670	125	38	are	be	AUX
ejpam-6670	125	39	bounded	bound	VERB
ejpam-6670	125	40	.	.	PUNCT
ejpam-6670	126	1	one	one	PRON
ejpam-6670	126	2	can	can	AUX
ejpam-6670	126	3	proceed	proceed	VERB
ejpam-6670	126	4	as	as	SCONJ
ejpam-6670	126	5	follows	follow	VERB
ejpam-6670	126	6	:	:	PUNCT
ejpam-6670	126	7	∥f1(y1)−	∥f1(y1)−	PROPN
ejpam-6670	126	8	f1(y2)∥	f1(y2)∥	PROPN
ejpam-6670	126	9	=	=	SYM
ejpam-6670	126	10	∥∥∥∥gηφ(c2	∥∥∥∥gηφ(c2	PROPN
ejpam-6670	126	11	−	−	PROPN
ejpam-6670	126	12	c1	c1	PROPN
ejpam-6670	126	13	)	)	PUNCT
ejpam-6670	127	1	+	+	PUNCT
ejpam-6670	127	2	π(v1	π(v1	ADJ
ejpam-6670	127	3	−	−	NOUN
ejpam-6670	127	4	v2)−	v2)−	NOUN
ejpam-6670	127	5	α	α	NOUN
ejpam-6670	127	6	(	(	PUNCT
ejpam-6670	127	7	s1a1	s1a1	PROPN
ejpam-6670	127	8	1	1	NUM
ejpam-6670	127	9	+	+	CCONJ
ejpam-6670	127	10	βc1	βc1	NOUN
ejpam-6670	127	11	−	−	NOUN
ejpam-6670	127	12	s2a2	s2a2	NOUN
ejpam-6670	127	13	1	1	NUM
ejpam-6670	127	14	+	+	CCONJ
ejpam-6670	127	15	βc2	βc2	NUM
ejpam-6670	127	16	)	)	PUNCT
ejpam-6670	127	17	−λα	−λα	NOUN
ejpam-6670	127	18	(	(	PUNCT
ejpam-6670	127	19	s1c1	s1c1	NOUN
ejpam-6670	127	20	1	1	NUM
ejpam-6670	127	21	+	+	NUM
ejpam-6670	127	22	βc1	βc1	NOUN
ejpam-6670	128	1	−	−	X
ejpam-6670	128	2	s2c2	s2c2	X
ejpam-6670	128	3	1	1	NUM
ejpam-6670	128	4	+	+	CCONJ
ejpam-6670	128	5	βc2	βc2	NUM
ejpam-6670	128	6	)	)	PUNCT
ejpam-6670	128	7	−	−	PROPN
ejpam-6670	129	1	(	(	PUNCT
ejpam-6670	129	2	µ0	µ0	NOUN
ejpam-6670	129	3	+	+	NOUN
ejpam-6670	129	4	λ3)(s1	λ3)(s1	X
ejpam-6670	129	5	−	−	X
ejpam-6670	129	6	s2	s2	PROPN
ejpam-6670	129	7	)	)	PUNCT
ejpam-6670	129	8	∥∥∥∥	∥∥∥∥	NUM
ejpam-6670	129	9	,	,	PUNCT
ejpam-6670	129	10	which	which	PRON
ejpam-6670	129	11	implies	imply	VERB
ejpam-6670	129	12	that	that	SCONJ
ejpam-6670	129	13	∥f1(y1)−	∥f1(y1)−	PROPN
ejpam-6670	129	14	f1(y2)∥	f1(y2)∥	PROPN
ejpam-6670	129	15	≤	≤	NOUN
ejpam-6670	129	16	gηφ∥c1	gηφ∥c1	PROPN
ejpam-6670	129	17	−	−	PROPN
ejpam-6670	129	18	c2∥+	c2∥+	NOUN
ejpam-6670	129	19	π∥v1	π∥v1	PUNCT
ejpam-6670	130	1	−	−	PROPN
ejpam-6670	130	2	v2∥+	v2∥+	NOUN
ejpam-6670	130	3	(	(	PUNCT
ejpam-6670	130	4	µ0	µ0	NOUN
ejpam-6670	130	5	+	+	X
ejpam-6670	130	6	λ3)∥s1	λ3)∥s1	ADJ
ejpam-6670	130	7	−	−	NOUN
ejpam-6670	130	8	s2∥	s2∥	NOUN
ejpam-6670	131	1	+	+	CCONJ
ejpam-6670	131	2	α	α	PROPN
ejpam-6670	131	3	∥∥∥∥	∥∥∥∥	ADJ
ejpam-6670	131	4	s1a1	s1a1	X
ejpam-6670	131	5	1	1	NUM
ejpam-6670	131	6	+	+	CCONJ
ejpam-6670	131	7	βc1	βc1	NOUN
ejpam-6670	131	8	−	−	NOUN
ejpam-6670	131	9	s2a2	s2a2	NOUN
ejpam-6670	131	10	1	1	NUM
ejpam-6670	131	11	+	+	CCONJ
ejpam-6670	131	12	βc2	βc2	PRON
ejpam-6670	131	13	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-6670	131	14	λα	λα	PRON
ejpam-6670	131	15	∥∥∥∥	∥∥∥∥	NUM
ejpam-6670	131	16	s1c1	s1c1	NOUN
ejpam-6670	131	17	1	1	NUM
ejpam-6670	131	18	+	+	NUM
ejpam-6670	131	19	βc1	βc1	NOUN
ejpam-6670	131	20	−	−	X
ejpam-6670	131	21	s2c2	s2c2	X
ejpam-6670	131	22	1	1	NUM
ejpam-6670	131	23	+	+	CCONJ
ejpam-6670	131	24	βc2	βc2	NUM
ejpam-6670	131	25	∥∥∥∥	∥∥∥∥	NUM
ejpam-6670	131	26	.	.	PUNCT
ejpam-6670	132	1	(	(	PUNCT
ejpam-6670	132	2	6	6	NUM
ejpam-6670	132	3	)	)	PUNCT
ejpam-6670	132	4	to	to	PART
ejpam-6670	132	5	simplify	simplify	VERB
ejpam-6670	132	6	the	the	DET
ejpam-6670	132	7	above	above	ADJ
ejpam-6670	132	8	inequality	inequality	NOUN
ejpam-6670	132	9	,	,	PUNCT
ejpam-6670	132	10	we	we	PRON
ejpam-6670	132	11	use	use	VERB
ejpam-6670	132	12	some	some	DET
ejpam-6670	132	13	algebraic	algebraic	ADJ
ejpam-6670	132	14	manipulation	manipulation	NOUN
ejpam-6670	132	15	as	as	SCONJ
ejpam-6670	132	16	follows	follow	VERB
ejpam-6670	132	17	s1a1	s1a1	ADJ
ejpam-6670	132	18	1	1	NUM
ejpam-6670	132	19	+	+	CCONJ
ejpam-6670	132	20	βc1	βc1	NOUN
ejpam-6670	132	21	−	−	NOUN
ejpam-6670	132	22	s2a2	s2a2	NOUN
ejpam-6670	132	23	1	1	NUM
ejpam-6670	132	24	+	+	CCONJ
ejpam-6670	132	25	βc2	βc2	NOUN
ejpam-6670	133	1	=	=	NOUN
ejpam-6670	133	2	s1a1	s1a1	PROPN
ejpam-6670	133	3	−	−	X
ejpam-6670	133	4	s2a2	s2a2	NOUN
ejpam-6670	133	5	1	1	NUM
ejpam-6670	133	6	+	+	CCONJ
ejpam-6670	133	7	βc1	βc1	NOUN
ejpam-6670	133	8	−	−	NOUN
ejpam-6670	133	9	s2a2	s2a2	NOUN
ejpam-6670	133	10	(	(	PUNCT
ejpam-6670	133	11	1	1	NUM
ejpam-6670	133	12	1	1	NUM
ejpam-6670	133	13	+	+	CCONJ
ejpam-6670	133	14	βc1	βc1	NOUN
ejpam-6670	133	15	−	−	NUM
ejpam-6670	133	16	1	1	NUM
ejpam-6670	133	17	1	1	NUM
ejpam-6670	133	18	+	+	CCONJ
ejpam-6670	133	19	βc2	βc2	NUM
ejpam-6670	133	20	)	)	PUNCT
ejpam-6670	133	21	,	,	PUNCT
ejpam-6670	133	22	s1c1	s1c1	NOUN
ejpam-6670	133	23	1	1	NUM
ejpam-6670	133	24	+	+	NUM
ejpam-6670	133	25	βc1	βc1	NOUN
ejpam-6670	133	26	−	−	X
ejpam-6670	133	27	s2c2	s2c2	X
ejpam-6670	133	28	1	1	NUM
ejpam-6670	133	29	+	+	CCONJ
ejpam-6670	133	30	βc2	βc2	NOUN
ejpam-6670	133	31	=	=	NOUN
ejpam-6670	133	32	s1c1	s1c1	NOUN
ejpam-6670	133	33	−	−	X
ejpam-6670	133	34	s2c2	s2c2	X
ejpam-6670	133	35	1	1	NUM
ejpam-6670	133	36	+	+	CCONJ
ejpam-6670	133	37	βc1	βc1	NOUN
ejpam-6670	134	1	−	−	X
ejpam-6670	135	1	s2c2	s2c2	PRON
ejpam-6670	136	1	(	(	PUNCT
ejpam-6670	136	2	1	1	NUM
ejpam-6670	136	3	1	1	NUM
ejpam-6670	136	4	+	+	CCONJ
ejpam-6670	136	5	βc1	βc1	NOUN
ejpam-6670	136	6	−	−	NUM
ejpam-6670	136	7	1	1	NUM
ejpam-6670	136	8	1	1	NUM
ejpam-6670	136	9	+	+	CCONJ
ejpam-6670	136	10	βc2	βc2	NUM
ejpam-6670	136	11	)	)	PUNCT
ejpam-6670	136	12	.	.	PUNCT
ejpam-6670	137	1	t.	t.	PROPN
ejpam-6670	137	2	khan	khan	PROPN
ejpam-6670	137	3	et	et	PROPN
ejpam-6670	137	4	al	al	PROPN
ejpam-6670	137	5	.	.	PUNCT
ejpam-6670	137	6	/	/	SYM
ejpam-6670	137	7	eur	eur	PROPN
ejpam-6670	137	8	.	.	PUNCT
ejpam-6670	138	1	j.	j.	PROPN
ejpam-6670	138	2	pure	pure	PROPN
ejpam-6670	138	3	appl	appl	PROPN
ejpam-6670	138	4	.	.	PROPN
ejpam-6670	138	5	math	math	PROPN
ejpam-6670	138	6	,	,	PUNCT
ejpam-6670	138	7	18	18	NUM
ejpam-6670	138	8	(	(	PUNCT
ejpam-6670	138	9	3	3	NUM
ejpam-6670	138	10	)	)	PUNCT
ejpam-6670	138	11	(	(	PUNCT
ejpam-6670	138	12	2025	2025	NUM
ejpam-6670	138	13	)	)	PUNCT
ejpam-6670	138	14	,	,	PUNCT
ejpam-6670	138	15	6670	6670	NUM
ejpam-6670	138	16	7	7	NUM
ejpam-6670	138	17	of	of	ADP
ejpam-6670	138	18	22	22	NUM
ejpam-6670	138	19	also	also	ADV
ejpam-6670	138	20	∥s1a1	∥s1a1	ADV
ejpam-6670	139	1	−	−	ADP
ejpam-6670	139	2	s2a2∥	s2a2∥	ADJ
ejpam-6670	139	3	≤	≤	NOUN
ejpam-6670	139	4	∥s1∥∥a1	∥s1∥∥a1	NUM
ejpam-6670	139	5	−	−	PROPN
ejpam-6670	139	6	a2∥+	a2∥+	ADJ
ejpam-6670	139	7	∥a2∥∥s1	∥a2∥∥s1	NUM
ejpam-6670	139	8	−	−	NOUN
ejpam-6670	139	9	s2∥	s2∥	NOUN
ejpam-6670	139	10	,	,	PUNCT
ejpam-6670	139	11	∥s1c1	∥s1c1	X
ejpam-6670	140	1	−	−	PROPN
ejpam-6670	140	2	s2c2∥	s2c2∥	NOUN
ejpam-6670	140	3	≤	≤	PUNCT
ejpam-6670	140	4	∥s1∥∥c1	∥s1∥∥c1	PUNCT
ejpam-6670	140	5	−	−	PROPN
ejpam-6670	140	6	c2∥+	c2∥+	NOUN
ejpam-6670	140	7	∥c2∥∥s1	∥c2∥∥s1	PUNCT
ejpam-6670	140	8	−	−	NOUN
ejpam-6670	140	9	s2∥	s2∥	NOUN
ejpam-6670	140	10	,	,	PUNCT
ejpam-6670	140	11	and	and	CCONJ
ejpam-6670	140	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-6670	140	13	1	1	NUM
ejpam-6670	140	14	1	1	NUM
ejpam-6670	140	15	+	+	CCONJ
ejpam-6670	140	16	βc1	βc1	NOUN
ejpam-6670	140	17	−	−	NUM
ejpam-6670	140	18	1	1	NUM
ejpam-6670	140	19	1	1	NUM
ejpam-6670	140	20	+	+	CCONJ
ejpam-6670	140	21	βc2	βc2	NUM
ejpam-6670	140	22	∥∥∥∥	∥∥∥∥	NUM
ejpam-6670	140	23	≤	≤	NUM
ejpam-6670	140	24	β∥c1	β∥c1	PUNCT
ejpam-6670	140	25	−	−	PROPN
ejpam-6670	140	26	c2∥	c2∥	PROPN
ejpam-6670	140	27	∥(1	∥(1	NOUN
ejpam-6670	140	28	+	+	CCONJ
ejpam-6670	140	29	βc1)(1	βc1)(1	NOUN
ejpam-6670	140	30	+	+	CCONJ
ejpam-6670	140	31	βc2)∥	βc2)∥	PROPN
ejpam-6670	140	32	≤	≤	NOUN
ejpam-6670	140	33	β∥c1	β∥c1	PUNCT
ejpam-6670	141	1	−	−	PROPN
ejpam-6670	141	2	c2∥.	c2∥.	NOUN
ejpam-6670	141	3	using	use	VERB
ejpam-6670	141	4	the	the	DET
ejpam-6670	141	5	above	above	ADJ
ejpam-6670	141	6	algebraic	algebraic	ADJ
ejpam-6670	141	7	manipulations	manipulation	NOUN
ejpam-6670	141	8	,	,	PUNCT
ejpam-6670	141	9	the	the	DET
ejpam-6670	141	10	equation	equation	NOUN
ejpam-6670	141	11	(	(	PUNCT
ejpam-6670	141	12	6	6	NUM
ejpam-6670	141	13	)	)	PUNCT
ejpam-6670	141	14	leads	lead	VERB
ejpam-6670	141	15	to	to	ADP
ejpam-6670	141	16	the	the	DET
ejpam-6670	141	17	following	follow	VERB
ejpam-6670	141	18	inequality	inequality	NOUN
ejpam-6670	141	19	∥f1(y1)−	∥f1(y1)−	PROPN
ejpam-6670	141	20	f1(y2)∥	f1(y2)∥	PROPN
ejpam-6670	141	21	≤	≤	PROPN
ejpam-6670	141	22	{	{	PUNCT
ejpam-6670	141	23	µ0	µ0	NOUN
ejpam-6670	141	24	+	+	NOUN
ejpam-6670	142	1	λ3	λ3	PROPN
ejpam-6670	142	2	+	+	NOUN
ejpam-6670	142	3	α∥a2∥+	α∥a2∥+	NUM
ejpam-6670	142	4	λα∥c2∥	λα∥c2∥	PUNCT
ejpam-6670	142	5	}	}	PUNCT
ejpam-6670	142	6	∥s1	∥s1	PART
ejpam-6670	142	7	−	−	PROPN
ejpam-6670	142	8	s2∥+	s2∥+	NOUN
ejpam-6670	142	9	α∥s1∥∥a1	α∥s1∥∥a1	NUM
ejpam-6670	142	10	−	−	NOUN
ejpam-6670	142	11	a2∥	a2∥	NOUN
ejpam-6670	142	12	+	+	CCONJ
ejpam-6670	142	13	{	{	PUNCT
ejpam-6670	142	14	gηφ+	gηφ+	NOUN
ejpam-6670	142	15	αβ∥s2∥∥a2∥+	αβ∥s2∥∥a2∥+	NOUN
ejpam-6670	142	16	αβλ∥s2∥∥c2∥+	αβλ∥s2∥∥c2∥+	VERB
ejpam-6670	142	17	αλ∥s1∥	αλ∥s1∥	NUM
ejpam-6670	142	18	}	}	PUNCT
ejpam-6670	142	19	∥c1	∥c1	NOUN
ejpam-6670	142	20	−	−	PROPN
ejpam-6670	142	21	c2∥+	c2∥+	NOUN
ejpam-6670	142	22	π∥v1	π∥v1	X
ejpam-6670	142	23	−	−	PROPN
ejpam-6670	143	1	v2∥.	v2∥.	NOUN
ejpam-6670	143	2	let	let	VERB
ejpam-6670	143	3	us	we	PRON
ejpam-6670	143	4	assume	assume	VERB
ejpam-6670	143	5	that	that	SCONJ
ejpam-6670	143	6	the	the	DET
ejpam-6670	143	7	m1	m1	NOUN
ejpam-6670	143	8	,	,	PUNCT
ejpam-6670	143	9	m2	m2	PROPN
ejpam-6670	143	10	and	and	CCONJ
ejpam-6670	143	11	m3	m3	PROPN
ejpam-6670	143	12	are	be	AUX
ejpam-6670	143	13	any	any	DET
ejpam-6670	143	14	positive	positive	ADJ
ejpam-6670	143	15	constants	constant	NOUN
ejpam-6670	143	16	,	,	PUNCT
ejpam-6670	143	17	then	then	ADV
ejpam-6670	143	18	the	the	DET
ejpam-6670	143	19	above	above	ADJ
ejpam-6670	143	20	equation	equation	NOUN
ejpam-6670	143	21	takes	take	VERB
ejpam-6670	143	22	the	the	DET
ejpam-6670	143	23	form	form	NOUN
ejpam-6670	143	24	∥f1(y1)−	∥f1(y1)−	PROPN
ejpam-6670	143	25	f1(y2)∥	f1(y2)∥	PROPN
ejpam-6670	143	26	≤	≤	PUNCT
ejpam-6670	143	27	m1∥s1	m1∥s1	VERB
ejpam-6670	143	28	−	−	PROPN
ejpam-6670	143	29	s2∥+m2∥a1	s2∥+m2∥a1	PROPN
ejpam-6670	143	30	−	−	PROPN
ejpam-6670	143	31	a2∥+m3∥c1	a2∥+m3∥c1	VERB
ejpam-6670	143	32	−	−	PROPN
ejpam-6670	143	33	c2∥+	c2∥+	NOUN
ejpam-6670	143	34	π∥v1	π∥v1	X
ejpam-6670	144	1	−	−	PROPN
ejpam-6670	144	2	v2∥.	v2∥.	NOUN
ejpam-6670	144	3	let	let	VERB
ejpam-6670	144	4	m	m	NOUN
ejpam-6670	144	5	=	=	NOUN
ejpam-6670	144	6	max{m1,m2,m3	max{m1,m2,m3	NOUN
ejpam-6670	144	7	,	,	PUNCT
ejpam-6670	144	8	π	π	NOUN
ejpam-6670	144	9	}	}	PUNCT
ejpam-6670	144	10	,	,	PUNCT
ejpam-6670	144	11	the	the	DET
ejpam-6670	144	12	last	last	ADJ
ejpam-6670	144	13	inequality	inequality	NOUN
ejpam-6670	144	14	can	can	AUX
ejpam-6670	144	15	be	be	AUX
ejpam-6670	144	16	re	re	VERB
ejpam-6670	144	17	-	-	VERB
ejpam-6670	144	18	written	write	VERB
ejpam-6670	144	19	as	as	ADP
ejpam-6670	144	20	∥f1(y1)−	∥f1(y1)−	PROPN
ejpam-6670	144	21	f1(y2)∥	f1(y2)∥	PROPN
ejpam-6670	144	22	≤	≤	NUM
ejpam-6670	144	23	m	m	VERB
ejpam-6670	145	1	(	(	PUNCT
ejpam-6670	145	2	∥s1−	∥s1−	PROPN
ejpam-6670	145	3	s2∥+	s2∥+	NOUN
ejpam-6670	145	4	∥a1−	∥a1−	ADP
ejpam-6670	145	5	a2∥+	a2∥+	PROPN
ejpam-6670	145	6	∥c1−	∥c1−	PROPN
ejpam-6670	145	7	c2∥+	c2∥+	PROPN
ejpam-6670	145	8	∥v1−	∥v1−	PROPN
ejpam-6670	145	9	v2∥	v2∥	PROPN
ejpam-6670	145	10	)	)	PUNCT
ejpam-6670	145	11	≤	≤	PROPN
ejpam-6670	145	12	m∥y1−	m∥y1−	ADJ
ejpam-6670	145	13	y2∥.	y2∥.	NOUN
ejpam-6670	145	14	(	(	PUNCT
ejpam-6670	145	15	7	7	NUM
ejpam-6670	145	16	)	)	PUNCT
ejpam-6670	145	17	the	the	DET
ejpam-6670	145	18	second	second	ADJ
ejpam-6670	145	19	equation	equation	NOUN
ejpam-6670	145	20	of	of	ADP
ejpam-6670	145	21	the	the	DET
ejpam-6670	145	22	model	model	NOUN
ejpam-6670	145	23	(	(	PUNCT
ejpam-6670	145	24	1	1	NUM
ejpam-6670	145	25	)	)	PUNCT
ejpam-6670	145	26	,	,	PUNCT
ejpam-6670	145	27	implies	imply	VERB
ejpam-6670	145	28	that	that	SCONJ
ejpam-6670	145	29	∥f2(y1)−	∥f2(y1)−	PUNCT
ejpam-6670	145	30	f2(y2)∥	f2(y2)∥	INTJ
ejpam-6670	145	31	≤	≤	NOUN
ejpam-6670	145	32	{	{	PUNCT
ejpam-6670	145	33	α∥a2∥+	α∥a2∥+	ADP
ejpam-6670	145	34	λα∥c2∥	λα∥c2∥	PUNCT
ejpam-6670	145	35	}	}	PUNCT
ejpam-6670	145	36	∥s1	∥s1	PART
ejpam-6670	145	37	−	−	PROPN
ejpam-6670	145	38	s2∥+	s2∥+	NOUN
ejpam-6670	145	39	(	(	PUNCT
ejpam-6670	145	40	µ0	µ0	NOUN
ejpam-6670	145	41	+	+	X
ejpam-6670	145	42	θ)∥l1	θ)∥l1	ADJ
ejpam-6670	145	43	−	−	PROPN
ejpam-6670	146	1	l2∥+	l2∥+	ADJ
ejpam-6670	146	2	α∥s1∥∥a1	α∥s1∥∥a1	PROPN
ejpam-6670	147	1	−	−	PROPN
ejpam-6670	147	2	a2∥	a2∥	NOUN
ejpam-6670	147	3	+	+	CCONJ
ejpam-6670	147	4	{	{	PUNCT
ejpam-6670	147	5	αβ∥s2∥∥a2∥+	αβ∥s2∥∥a2∥+	PRON
ejpam-6670	147	6	αβλ∥s2∥∥c2∥+	αβλ∥s2∥∥c2∥+	VERB
ejpam-6670	147	7	αλ∥s1∥	αλ∥s1∥	NUM
ejpam-6670	147	8	}	}	PUNCT
ejpam-6670	147	9	∥c1	∥c1	NOUN
ejpam-6670	147	10	−	−	PROPN
ejpam-6670	147	11	c2∥.	c2∥.	NOUN
ejpam-6670	147	12	if	if	SCONJ
ejpam-6670	147	13	n1	n1	NOUN
ejpam-6670	147	14	,	,	PUNCT
ejpam-6670	147	15	n2	n2	NOUN
ejpam-6670	147	16	,	,	PUNCT
ejpam-6670	147	17	n3	n3	NOUN
ejpam-6670	147	18	and	and	CCONJ
ejpam-6670	147	19	n4	n4	PROPN
ejpam-6670	147	20	are	be	AUX
ejpam-6670	147	21	positive	positive	ADJ
ejpam-6670	147	22	constants	constant	NOUN
ejpam-6670	147	23	,	,	PUNCT
ejpam-6670	147	24	and	and	CCONJ
ejpam-6670	147	25	n	n	CCONJ
ejpam-6670	147	26	=	=	SYM
ejpam-6670	147	27	max{n1,n2,n3,n4	max{n1,n2,n3,n4	PROPN
ejpam-6670	147	28	}	}	PUNCT
ejpam-6670	147	29	,	,	PUNCT
ejpam-6670	147	30	then	then	ADV
ejpam-6670	147	31	the	the	DET
ejpam-6670	147	32	above	above	ADJ
ejpam-6670	147	33	inequality	inequality	NOUN
ejpam-6670	147	34	gives	give	VERB
ejpam-6670	147	35	∥f2(y1)−	∥f2(y1)−	PROPN
ejpam-6670	147	36	f2(y2)∥	f2(y2)∥	PROPN
ejpam-6670	147	37	=	=	SYM
ejpam-6670	147	38	n	n	PROPN
ejpam-6670	147	39	{	{	PUNCT
ejpam-6670	147	40	∥s1	∥s1	NOUN
ejpam-6670	147	41	−	−	PROPN
ejpam-6670	147	42	s2∥+	s2∥+	NOUN
ejpam-6670	147	43	∥l1	∥l1	VERB
ejpam-6670	147	44	−	−	NOUN
ejpam-6670	147	45	l2∥+	l2∥+	ADJ
ejpam-6670	147	46	∥∥a1	∥∥a1	NOUN
ejpam-6670	147	47	−	−	NOUN
ejpam-6670	147	48	a2∥+	a2∥+	NOUN
ejpam-6670	147	49	∥c1	∥c1	NOUN
ejpam-6670	147	50	−	−	PROPN
ejpam-6670	147	51	c2∥	c2∥	VERB
ejpam-6670	147	52	≤	≤	NOUN
ejpam-6670	147	53	n∥y1	n∥y1	PUNCT
ejpam-6670	147	54	−	−	PROPN
ejpam-6670	147	55	y2∥	y2∥	PROPN
ejpam-6670	147	56	}	}	PUNCT
ejpam-6670	147	57	.	.	PUNCT
ejpam-6670	148	1	(	(	PUNCT
ejpam-6670	148	2	8)	8)	NUM
ejpam-6670	148	3	from	from	ADP
ejpam-6670	148	4	the	the	DET
ejpam-6670	148	5	third	third	ADJ
ejpam-6670	148	6	equation	equation	NOUN
ejpam-6670	148	7	of	of	ADP
ejpam-6670	148	8	the	the	DET
ejpam-6670	148	9	model	model	NOUN
ejpam-6670	148	10	(	(	PUNCT
ejpam-6670	148	11	1	1	NUM
ejpam-6670	148	12	)	)	PUNCT
ejpam-6670	148	13	,	,	PUNCT
ejpam-6670	148	14	we	we	PRON
ejpam-6670	148	15	obtain	obtain	VERB
ejpam-6670	148	16	∥f3(y1)−	∥f3(y1)−	PROPN
ejpam-6670	148	17	f3(y2)∥	f3(y2)∥	PROPN
ejpam-6670	148	18	≤	≤	PUNCT
ejpam-6670	148	19	θ∥l1	θ∥l1	VERB
ejpam-6670	148	20	−	−	PUNCT
ejpam-6670	149	1	l2∥+	l2∥+	ADV
ejpam-6670	149	2	(	(	PUNCT
ejpam-6670	149	3	µ0	µ0	NOUN
ejpam-6670	149	4	+	+	NUM
ejpam-6670	149	5	λ1)∥a1	λ1)∥a1	NOUN
ejpam-6670	149	6	−	−	PROPN
ejpam-6670	149	7	a2∥	a2∥	NOUN
ejpam-6670	149	8	≤	≤	NOUN
ejpam-6670	149	9	o∥y1	o∥y1	PUNCT
ejpam-6670	150	1	−	−	PROPN
ejpam-6670	150	2	y2∥	y2∥	PROPN
ejpam-6670	150	3	,	,	PUNCT
ejpam-6670	150	4	(	(	PUNCT
ejpam-6670	150	5	9	9	NUM
ejpam-6670	150	6	)	)	PUNCT
ejpam-6670	150	7	where	where	SCONJ
ejpam-6670	150	8	o	o	NOUN
ejpam-6670	150	9	=	=	PUNCT
ejpam-6670	150	10	{	{	PUNCT
ejpam-6670	150	11	θ	θ	PROPN
ejpam-6670	150	12	,	,	PUNCT
ejpam-6670	150	13	(	(	PUNCT
ejpam-6670	150	14	µ0	µ0	NOUN
ejpam-6670	150	15	+	+	X
ejpam-6670	150	16	λ1	λ1	ADJ
ejpam-6670	150	17	)	)	PUNCT
ejpam-6670	150	18	}	}	PUNCT
ejpam-6670	150	19	.	.	PUNCT
ejpam-6670	151	1	the	the	DET
ejpam-6670	151	2	fourth	fourth	ADJ
ejpam-6670	151	3	equation	equation	NOUN
ejpam-6670	151	4	of	of	ADP
ejpam-6670	151	5	the	the	DET
ejpam-6670	151	6	model	model	NOUN
ejpam-6670	151	7	(	(	PUNCT
ejpam-6670	151	8	1	1	NUM
ejpam-6670	151	9	)	)	PUNCT
ejpam-6670	151	10	implies	imply	VERB
ejpam-6670	151	11	that	that	SCONJ
ejpam-6670	151	12	∥f4(y1)−	∥f4(y1)−	PROPN
ejpam-6670	151	13	f4(y2)∥	f4(y2)∥	PROPN
ejpam-6670	151	14	≤	≤	NUM
ejpam-6670	151	15	qλ1∥a1	qλ1∥a1	NOUN
ejpam-6670	151	16	−	−	PROPN
ejpam-6670	151	17	a2∥+	a2∥+	NOUN
ejpam-6670	151	18	(	(	PUNCT
ejpam-6670	151	19	gηφ+	gηφ+	NOUN
ejpam-6670	151	20	µ0	µ0	NOUN
ejpam-6670	151	21	+	+	CCONJ
ejpam-6670	151	22	µ1	µ1	PROPN
ejpam-6670	151	23	+	+	SYM
ejpam-6670	151	24	λ2	λ2	NOUN
ejpam-6670	151	25	)	)	PUNCT
ejpam-6670	151	26	∥c1	∥c1	NOUN
ejpam-6670	151	27	−	−	PROPN
ejpam-6670	151	28	c2∥	c2∥	VERB
ejpam-6670	151	29	≤	≤	NUM
ejpam-6670	151	30	p∥y1	p∥y1	PUNCT
ejpam-6670	152	1	−	−	PROPN
ejpam-6670	152	2	y2∥	y2∥	PROPN
ejpam-6670	152	3	,	,	PUNCT
ejpam-6670	152	4	(	(	PUNCT
ejpam-6670	152	5	10	10	NUM
ejpam-6670	152	6	)	)	PUNCT
ejpam-6670	152	7	where	where	SCONJ
ejpam-6670	152	8	p	p	NOUN
ejpam-6670	152	9	=	=	X
ejpam-6670	152	10	{	{	PUNCT
ejpam-6670	152	11	qλ1	qλ1	NOUN
ejpam-6670	152	12	,	,	PUNCT
ejpam-6670	152	13	(	(	PUNCT
ejpam-6670	152	14	gηφ+	gηφ+	NOUN
ejpam-6670	152	15	µ0	µ0	NOUN
ejpam-6670	152	16	+	+	CCONJ
ejpam-6670	152	17	µ1	µ1	PROPN
ejpam-6670	152	18	+	+	SYM
ejpam-6670	152	19	λ2	λ2	NOUN
ejpam-6670	152	20	)	)	PUNCT
ejpam-6670	152	21	}	}	PUNCT
ejpam-6670	152	22	.	.	PUNCT
ejpam-6670	153	1	in	in	ADP
ejpam-6670	153	2	a	a	DET
ejpam-6670	153	3	similar	similar	ADJ
ejpam-6670	153	4	way	way	NOUN
ejpam-6670	153	5	,	,	PUNCT
ejpam-6670	153	6	the	the	DET
ejpam-6670	153	7	last	last	ADJ
ejpam-6670	153	8	two	two	NUM
ejpam-6670	153	9	equation	equation	NOUN
ejpam-6670	153	10	of	of	ADP
ejpam-6670	153	11	the	the	DET
ejpam-6670	153	12	proposed	propose	VERB
ejpam-6670	153	13	model	model	NOUN
ejpam-6670	153	14	gives	give	VERB
ejpam-6670	153	15	∥f5(y1)−	∥f5(y1)−	PROPN
ejpam-6670	153	16	f5(y2)∥	f5(y2)∥	PROPN
ejpam-6670	153	17	≤	≤	NUM
ejpam-6670	153	18	(	(	PUNCT
ejpam-6670	153	19	1−	1−	NUM
ejpam-6670	153	20	q)λ1∥a1	q)λ1∥a1	NUM
ejpam-6670	153	21	−	−	NOUN
ejpam-6670	153	22	a2∥+	a2∥+	NOUN
ejpam-6670	153	23	λ2∥c1	λ2∥c1	PUNCT
ejpam-6670	153	24	−	−	PROPN
ejpam-6670	153	25	c2∥+	c2∥+	NOUN
ejpam-6670	153	26	µ0∥r1	µ0∥r1	VERB
ejpam-6670	153	27	−	−	NOUN
ejpam-6670	154	1	r2∥	r2∥	VERB
ejpam-6670	154	2	≤	≤	NOUN
ejpam-6670	154	3	q∥y1	q∥y1	PUNCT
ejpam-6670	154	4	−	−	PROPN
ejpam-6670	154	5	y2∥	y2∥	PROPN
ejpam-6670	154	6	,	,	PUNCT
ejpam-6670	154	7	∥f6(y1)−	∥f6(y1)−	PROPN
ejpam-6670	154	8	f6(y2)∥	f6(y2)∥	PROPN
ejpam-6670	154	9	≤	≤	PUNCT
ejpam-6670	154	10	λ3∥s1	λ3∥s1	PUNCT
ejpam-6670	154	11	−	−	NOUN
ejpam-6670	154	12	s2∥+	s2∥+	NOUN
ejpam-6670	154	13	(	(	PUNCT
ejpam-6670	154	14	µ0	µ0	NOUN
ejpam-6670	154	15	+	+	X
ejpam-6670	154	16	π)∥v1	π)∥v1	PROPN
ejpam-6670	154	17	−	−	PROPN
ejpam-6670	154	18	v2∥	v2∥	PROPN
ejpam-6670	154	19	≤	≤	PROPN
ejpam-6670	154	20	s∥y1	s∥y1	PUNCT
ejpam-6670	155	1	−	−	PROPN
ejpam-6670	155	2	y2∥	y2∥	PROPN
ejpam-6670	155	3	,	,	PUNCT
ejpam-6670	155	4	(	(	PUNCT
ejpam-6670	155	5	11	11	NUM
ejpam-6670	155	6	)	)	PUNCT
ejpam-6670	155	7	t.	t.	NOUN
ejpam-6670	155	8	khan	khan	PROPN
ejpam-6670	155	9	et	et	PROPN
ejpam-6670	155	10	al	al	PROPN
ejpam-6670	155	11	.	.	PUNCT
ejpam-6670	155	12	/	/	SYM
ejpam-6670	155	13	eur	eur	PROPN
ejpam-6670	155	14	.	.	PUNCT
ejpam-6670	156	1	j.	j.	PROPN
ejpam-6670	156	2	pure	pure	PROPN
ejpam-6670	156	3	appl	appl	PROPN
ejpam-6670	156	4	.	.	PROPN
ejpam-6670	156	5	math	math	PROPN
ejpam-6670	156	6	,	,	PUNCT
ejpam-6670	156	7	18	18	NUM
ejpam-6670	156	8	(	(	PUNCT
ejpam-6670	156	9	3	3	NUM
ejpam-6670	156	10	)	)	PUNCT
ejpam-6670	156	11	(	(	PUNCT
ejpam-6670	156	12	2025	2025	NUM
ejpam-6670	156	13	)	)	PUNCT
ejpam-6670	156	14	,	,	PUNCT
ejpam-6670	156	15	6670	6670	NUM
ejpam-6670	156	16	8	8	NUM
ejpam-6670	156	17	of	of	ADP
ejpam-6670	156	18	22	22	NUM
ejpam-6670	157	1	where	where	SCONJ
ejpam-6670	157	2	q	q	NOUN
ejpam-6670	157	3	=	=	PRON
ejpam-6670	157	4	{	{	PUNCT
ejpam-6670	157	5	(	(	PUNCT
ejpam-6670	157	6	1−	1−	NUM
ejpam-6670	157	7	q)λ1	q)λ1	PROPN
ejpam-6670	157	8	,	,	PUNCT
ejpam-6670	157	9	λ2	λ2	PROPN
ejpam-6670	157	10	,	,	PUNCT
ejpam-6670	157	11	µ0	µ0	NOUN
ejpam-6670	157	12	}	}	PUNCT
ejpam-6670	157	13	and	and	CCONJ
ejpam-6670	157	14	s	s	NOUN
ejpam-6670	157	15	=	=	PUNCT
ejpam-6670	157	16	{	{	PUNCT
ejpam-6670	157	17	λ3	λ3	PROPN
ejpam-6670	157	18	,	,	PUNCT
ejpam-6670	157	19	(	(	PUNCT
ejpam-6670	157	20	µ0	µ0	NOUN
ejpam-6670	157	21	+	+	X
ejpam-6670	157	22	π	π	NOUN
ejpam-6670	157	23	)	)	PUNCT
ejpam-6670	157	24	}	}	PUNCT
ejpam-6670	157	25	.	.	PUNCT
ejpam-6670	158	1	combining	combine	VERB
ejpam-6670	158	2	equation	equation	NOUN
ejpam-6670	158	3	(	(	PUNCT
ejpam-6670	158	4	7	7	NUM
ejpam-6670	158	5	)	)	PUNCT
ejpam-6670	158	6	to	to	ADP
ejpam-6670	158	7	(	(	PUNCT
ejpam-6670	158	8	11	11	NUM
ejpam-6670	158	9	)	)	PUNCT
ejpam-6670	158	10	,	,	PUNCT
ejpam-6670	158	11	we	we	PRON
ejpam-6670	158	12	obtain	obtain	VERB
ejpam-6670	158	13	∥f(y1)−f(y2)∥	∥f(y1)−f(y2)∥	X
ejpam-6670	158	14	=	=	PUNCT
ejpam-6670	158	15	h∥y1	h∥y1	X
ejpam-6670	159	1	−	−	PROPN
ejpam-6670	159	2	y2∥	y2∥	PROPN
ejpam-6670	159	3	,	,	PUNCT
ejpam-6670	159	4	where	where	SCONJ
ejpam-6670	159	5	h	h	NOUN
ejpam-6670	159	6	=	=	SYM
ejpam-6670	159	7	max{m	max{m	PROPN
ejpam-6670	159	8	,	,	PUNCT
ejpam-6670	159	9	n	n	PRON
ejpam-6670	159	10	,	,	PUNCT
ejpam-6670	159	11	o	o	NOUN
ejpam-6670	159	12	,	,	PUNCT
ejpam-6670	159	13	p	p	X
ejpam-6670	159	14	,	,	PUNCT
ejpam-6670	159	15	q	q	ADJ
ejpam-6670	159	16	,	,	PUNCT
ejpam-6670	159	17	s	s	PART
ejpam-6670	159	18	}	}	PUNCT
ejpam-6670	159	19	,	,	PUNCT
ejpam-6670	159	20	ensure	ensure	VERB
ejpam-6670	159	21	that	that	SCONJ
ejpam-6670	159	22	the	the	DET
ejpam-6670	159	23	function	function	NOUN
ejpam-6670	159	24	f(y	f(y	NOUN
ejpam-6670	159	25	)	)	PUNCT
ejpam-6670	159	26	is	be	AUX
ejpam-6670	159	27	lipschitz	lipschitz	NOUN
ejpam-6670	159	28	continuous	continuous	ADJ
ejpam-6670	159	29	,	,	PUNCT
ejpam-6670	159	30	and	and	CCONJ
ejpam-6670	159	31	hence	hence	ADV
ejpam-6670	159	32	the	the	DET
ejpam-6670	159	33	model	model	NOUN
ejpam-6670	159	34	posses	posse	VERB
ejpam-6670	159	35	a	a	DET
ejpam-6670	159	36	unique	unique	ADJ
ejpam-6670	159	37	solution	solution	NOUN
ejpam-6670	159	38	.	.	PUNCT
ejpam-6670	160	1	proposition	proposition	NOUN
ejpam-6670	160	2	2.2	2.2	NUM
ejpam-6670	160	3	.	.	PUNCT
ejpam-6670	161	1	let	let	VERB
ejpam-6670	161	2	us	we	PRON
ejpam-6670	161	3	consider	consider	VERB
ejpam-6670	161	4	that	that	PRON
ejpam-6670	161	5	(	(	PUNCT
ejpam-6670	161	6	s(t	s(t	PROPN
ejpam-6670	161	7	)	)	PUNCT
ejpam-6670	161	8	,	,	PUNCT
ejpam-6670	161	9	l(t	l(t	PROPN
ejpam-6670	161	10	)	)	PUNCT
ejpam-6670	161	11	,	,	PUNCT
ejpam-6670	161	12	a(t	a(t	NOUN
ejpam-6670	161	13	)	)	PUNCT
ejpam-6670	161	14	,	,	PUNCT
ejpam-6670	161	15	c(t	c(t	PROPN
ejpam-6670	161	16	)	)	PUNCT
ejpam-6670	161	17	,	,	PUNCT
ejpam-6670	161	18	r(t	r(t	NOUN
ejpam-6670	161	19	)	)	PUNCT
ejpam-6670	161	20	,	,	PUNCT
ejpam-6670	161	21	v(t	v(t	NOUN
ejpam-6670	161	22	)	)	PUNCT
ejpam-6670	161	23	)	)	PUNCT
ejpam-6670	161	24	is	be	AUX
ejpam-6670	161	25	the	the	DET
ejpam-6670	161	26	solution	solution	NOUN
ejpam-6670	161	27	of	of	ADP
ejpam-6670	161	28	the	the	DET
ejpam-6670	161	29	model	model	NOUN
ejpam-6670	161	30	with	with	ADP
ejpam-6670	161	31	non	non	ADJ
ejpam-6670	161	32	-	-	ADJ
ejpam-6670	161	33	negative	negative	ADJ
ejpam-6670	161	34	initial	initial	ADJ
ejpam-6670	161	35	conditions	condition	NOUN
ejpam-6670	161	36	,	,	PUNCT
ejpam-6670	161	37	and	and	CCONJ
ejpam-6670	161	38	the	the	DET
ejpam-6670	161	39	closed	closed	ADJ
ejpam-6670	161	40	set	set	ADJ
ejpam-6670	161	41	ω	ω	PROPN
ejpam-6670	161	42	is	be	AUX
ejpam-6670	161	43	the	the	DET
ejpam-6670	161	44	attracting	attracting	NOUN
ejpam-6670	161	45	under	under	ADP
ejpam-6670	161	46	the	the	DET
ejpam-6670	161	47	flow	flow	NOUN
ejpam-6670	161	48	described	describe	VERB
ejpam-6670	161	49	by	by	ADP
ejpam-6670	161	50	equation	equation	NOUN
ejpam-6670	161	51	(	(	PUNCT
ejpam-6670	161	52	1	1	NUM
ejpam-6670	161	53	)	)	PUNCT
ejpam-6670	161	54	that	that	PRON
ejpam-6670	161	55	is	be	AUX
ejpam-6670	161	56	positive	positive	ADJ
ejpam-6670	161	57	invariant	invariant	ADJ
ejpam-6670	161	58	.	.	PUNCT
ejpam-6670	162	1	proof	proof	NOUN
ejpam-6670	162	2	.	.	PUNCT
ejpam-6670	163	1	let	let	VERB
ejpam-6670	163	2	us	we	PRON
ejpam-6670	163	3	assume	assume	VERB
ejpam-6670	163	4	a	a	DET
ejpam-6670	163	5	function	function	NOUN
ejpam-6670	163	6	l(t	l(t	NOUN
ejpam-6670	163	7	)	)	PUNCT
ejpam-6670	163	8	given	give	VERB
ejpam-6670	163	9	by	by	ADP
ejpam-6670	163	10	l(t	l(t	NOUN
ejpam-6670	163	11	)	)	PUNCT
ejpam-6670	163	12	=	=	SYM
ejpam-6670	163	13	s(t	s(t	PROPN
ejpam-6670	163	14	)	)	PUNCT
ejpam-6670	164	1	+	+	NUM
ejpam-6670	164	2	l(t	l(t	NOUN
ejpam-6670	164	3	)	)	PUNCT
ejpam-6670	165	1	+	+	CCONJ
ejpam-6670	165	2	a(t	a(t	NOUN
ejpam-6670	165	3	)	)	PUNCT
ejpam-6670	165	4	+	+	X
ejpam-6670	165	5	c(t	c(t	PROPN
ejpam-6670	165	6	)	)	PUNCT
ejpam-6670	165	7	+	+	NUM
ejpam-6670	165	8	r(t	r(t	NOUN
ejpam-6670	165	9	)	)	PUNCT
ejpam-6670	165	10	+	+	CCONJ
ejpam-6670	165	11	v(t	v(t	NOUN
ejpam-6670	165	12	)	)	PUNCT
ejpam-6670	165	13	,	,	PUNCT
ejpam-6670	165	14	(	(	PUNCT
ejpam-6670	165	15	12	12	NUM
ejpam-6670	165	16	)	)	PUNCT
ejpam-6670	165	17	then	then	ADV
ejpam-6670	165	18	the	the	DET
ejpam-6670	165	19	time	time	NOUN
ejpam-6670	165	20	differentiation	differentiation	NOUN
ejpam-6670	165	21	with	with	ADP
ejpam-6670	165	22	the	the	DET
ejpam-6670	165	23	implementation	implementation	NOUN
ejpam-6670	165	24	of	of	ADP
ejpam-6670	165	25	equation	equation	NOUN
ejpam-6670	165	26	(	(	PUNCT
ejpam-6670	165	27	1	1	X
ejpam-6670	165	28	)	)	PUNCT
ejpam-6670	165	29	leads	lead	VERB
ejpam-6670	165	30	to	to	ADP
ejpam-6670	165	31	dl(t	dl(t	NOUN
ejpam-6670	165	32	)	)	PUNCT
ejpam-6670	165	33	dt	dt	NOUN
ejpam-6670	166	1	=	=	PUNCT
ejpam-6670	166	2	g	g	PROPN
ejpam-6670	166	3	−	−	PROPN
ejpam-6670	166	4	µ0l(t)−	µ0l(t)−	PROPN
ejpam-6670	166	5	µ1c(t	µ1c(t	PROPN
ejpam-6670	166	6	)	)	PUNCT
ejpam-6670	166	7	,	,	PUNCT
ejpam-6670	166	8	(	(	PUNCT
ejpam-6670	166	9	13	13	NUM
ejpam-6670	166	10	)	)	PUNCT
ejpam-6670	166	11	which	which	PRON
ejpam-6670	166	12	implies	imply	VERB
ejpam-6670	166	13	that	that	PRON
ejpam-6670	166	14	dl(t	dl(t	NOUN
ejpam-6670	166	15	)	)	PUNCT
ejpam-6670	166	16	dt	dt	ADP
ejpam-6670	166	17	≤	≤	ADV
ejpam-6670	167	1	g	g	ADP
ejpam-6670	167	2	−	−	PROPN
ejpam-6670	167	3	µ0l(t	µ0l(t	PROPN
ejpam-6670	167	4	)	)	PUNCT
ejpam-6670	167	5	≤	≤	NOUN
ejpam-6670	167	6	0	0	NUM
ejpam-6670	167	7	.	.	PUNCT
ejpam-6670	168	1	(	(	PUNCT
ejpam-6670	168	2	14	14	NUM
ejpam-6670	168	3	)	)	PUNCT
ejpam-6670	168	4	it	it	PRON
ejpam-6670	168	5	is	be	AUX
ejpam-6670	168	6	clear	clear	ADJ
ejpam-6670	168	7	from	from	ADP
ejpam-6670	168	8	the	the	DET
ejpam-6670	168	9	equation	equation	NOUN
ejpam-6670	168	10	(	(	PUNCT
ejpam-6670	168	11	14	14	NUM
ejpam-6670	168	12	)	)	PUNCT
ejpam-6670	168	13	,	,	PUNCT
ejpam-6670	168	14	that	that	PRON
ejpam-6670	168	15	dl(t	dl(t	PUNCT
ejpam-6670	168	16	)	)	PUNCT
ejpam-6670	168	17	dt	dt	VERB
ejpam-6670	169	1	≤	≤	NUM
ejpam-6670	169	2	0	0	NUM
ejpam-6670	169	3	,	,	PUNCT
ejpam-6670	169	4	which	which	PRON
ejpam-6670	169	5	indicates	indicate	VERB
ejpam-6670	169	6	that	that	SCONJ
ejpam-6670	169	7	the	the	DET
ejpam-6670	169	8	set	set	NOUN
ejpam-6670	169	9	φ	φ	PROPN
ejpam-6670	169	10	is	be	AUX
ejpam-6670	169	11	positively	positively	ADV
ejpam-6670	169	12	invariant	invariant	ADJ
ejpam-6670	169	13	.	.	PUNCT
ejpam-6670	170	1	also	also	ADV
ejpam-6670	170	2	,	,	PUNCT
ejpam-6670	170	3	0	0	NUM
ejpam-6670	170	4	≤	≤	NUM
ejpam-6670	170	5	l(t	l(t	NOUN
ejpam-6670	170	6	)	)	PUNCT
ejpam-6670	170	7	≤	≤	NOUN
ejpam-6670	170	8	l(0)e−µ0	l(0)e−µ0	NOUN
ejpam-6670	171	1	t	t	NOUN
ejpam-6670	172	1	+	+	CCONJ
ejpam-6670	172	2	g	g	PROPN
ejpam-6670	172	3	µ0	µ0	NOUN
ejpam-6670	172	4	(	(	PUNCT
ejpam-6670	172	5	1−	1−	NUM
ejpam-6670	172	6	e−µ0	e−µ0	NUM
ejpam-6670	172	7	t	t	PROPN
ejpam-6670	172	8	)	)	PUNCT
ejpam-6670	172	9	.	.	PUNCT
ejpam-6670	173	1	thus	thus	ADV
ejpam-6670	173	2	,	,	PUNCT
ejpam-6670	173	3	as	as	ADP
ejpam-6670	173	4	t	t	PROPN
ejpam-6670	173	5	→	→	SYM
ejpam-6670	173	6	∞	∞	PROPN
ejpam-6670	173	7	,	,	PUNCT
ejpam-6670	173	8	0	0	NUM
ejpam-6670	173	9	≤	≤	NUM
ejpam-6670	173	10	l(t	l(t	NOUN
ejpam-6670	173	11	)	)	PUNCT
ejpam-6670	173	12	≤	≤	NOUN
ejpam-6670	173	13	g	g	NOUN
ejpam-6670	173	14	µ0	µ0	NOUN
ejpam-6670	173	15	,	,	PUNCT
ejpam-6670	173	16	which	which	PRON
ejpam-6670	173	17	is	be	AUX
ejpam-6670	173	18	sufficient	sufficient	ADJ
ejpam-6670	173	19	to	to	PART
ejpam-6670	173	20	prove	prove	VERB
ejpam-6670	173	21	that	that	SCONJ
ejpam-6670	173	22	ω	ω	PROPN
ejpam-6670	173	23	is	be	AUX
ejpam-6670	173	24	an	an	DET
ejpam-6670	173	25	attracting	attract	VERB
ejpam-6670	173	26	set	set	NOUN
ejpam-6670	173	27	.	.	PUNCT
ejpam-6670	174	1	the	the	DET
ejpam-6670	174	2	above	above	ADJ
ejpam-6670	174	3	proposition	proposition	NOUN
ejpam-6670	174	4	confirms	confirm	VERB
ejpam-6670	174	5	that	that	SCONJ
ejpam-6670	174	6	the	the	DET
ejpam-6670	174	7	proposed	propose	VERB
ejpam-6670	174	8	model	model	NOUN
ejpam-6670	174	9	is	be	AUX
ejpam-6670	174	10	well	well	ADV
ejpam-6670	174	11	-	-	PUNCT
ejpam-6670	174	12	posed	pose	VERB
ejpam-6670	174	13	.	.	PUNCT
ejpam-6670	175	1	we	we	PRON
ejpam-6670	175	2	now	now	ADV
ejpam-6670	175	3	proceed	proceed	VERB
ejpam-6670	175	4	with	with	ADP
ejpam-6670	175	5	the	the	DET
ejpam-6670	175	6	linearization	linearization	NOUN
ejpam-6670	175	7	of	of	ADP
ejpam-6670	175	8	the	the	DET
ejpam-6670	175	9	model	model	NOUN
ejpam-6670	175	10	,	,	PUNCT
ejpam-6670	175	11	computation	computation	NOUN
ejpam-6670	175	12	of	of	ADP
ejpam-6670	175	13	the	the	DET
ejpam-6670	175	14	threshold	threshold	NOUN
ejpam-6670	175	15	quantity	quantity	NOUN
ejpam-6670	175	16	,	,	PUNCT
ejpam-6670	175	17	identification	identification	NOUN
ejpam-6670	175	18	of	of	ADP
ejpam-6670	175	19	the	the	DET
ejpam-6670	175	20	model	model	NOUN
ejpam-6670	175	21	equilibria	equilibria	NOUN
ejpam-6670	175	22	,	,	PUNCT
ejpam-6670	175	23	and	and	CCONJ
ejpam-6670	175	24	its	its	PRON
ejpam-6670	175	25	stability	stability	NOUN
ejpam-6670	175	26	analysis	analysis	NOUN
ejpam-6670	175	27	,	,	PUNCT
ejpam-6670	175	28	as	as	SCONJ
ejpam-6670	175	29	outlined	outline	VERB
ejpam-6670	175	30	below	below	ADV
ejpam-6670	175	31	.	.	PUNCT
ejpam-6670	176	1	2.2	2.2	NUM
ejpam-6670	176	2	.	.	PUNCT
ejpam-6670	176	3	linearization	linearization	NOUN
ejpam-6670	176	4	of	of	ADP
ejpam-6670	176	5	the	the	DET
ejpam-6670	176	6	model	model	NOUN
ejpam-6670	176	7	using	use	VERB
ejpam-6670	176	8	the	the	DET
ejpam-6670	176	9	methods	method	NOUN
ejpam-6670	176	10	of	of	ADP
ejpam-6670	176	11	dynamical	dynamical	ADJ
ejpam-6670	176	12	systems	system	NOUN
ejpam-6670	176	13	to	to	PART
ejpam-6670	176	14	linearize	linearize	VERB
ejpam-6670	176	15	the	the	DET
ejpam-6670	176	16	model	model	NOUN
ejpam-6670	176	17	that	that	PRON
ejpam-6670	176	18	is	be	AUX
ejpam-6670	176	19	under	under	ADP
ejpam-6670	176	20	consideration	consideration	NOUN
ejpam-6670	176	21	.	.	PUNCT
ejpam-6670	177	1	to	to	PART
ejpam-6670	177	2	make	make	VERB
ejpam-6670	177	3	our	our	PRON
ejpam-6670	177	4	calculation	calculation	NOUN
ejpam-6670	177	5	simpler	simple	ADJ
ejpam-6670	177	6	,	,	PUNCT
ejpam-6670	177	7	we	we	PRON
ejpam-6670	177	8	take	take	VERB
ejpam-6670	177	9	the	the	DET
ejpam-6670	177	10	jacobian	jacobian	ADJ
ejpam-6670	177	11	matrix	matrix	NOUN
ejpam-6670	177	12	of	of	ADP
ejpam-6670	177	13	the	the	DET
ejpam-6670	177	14	reduced	reduce	VERB
ejpam-6670	177	15	system	system	NOUN
ejpam-6670	177	16	(	(	PUNCT
ejpam-6670	177	17	without	without	ADP
ejpam-6670	177	18	the	the	DET
ejpam-6670	177	19	5th	5th	ADJ
ejpam-6670	177	20	equation	equation	NOUN
ejpam-6670	177	21	)	)	PUNCT
ejpam-6670	177	22	,	,	PUNCT
ejpam-6670	177	23	which	which	PRON
ejpam-6670	177	24	looks	look	VERB
ejpam-6670	177	25	like	like	ADP
ejpam-6670	177	26	j	j	NOUN
ejpam-6670	177	27	=	=	PUNCT
ejpam-6670	177	28			NOUN
ejpam-6670	177	29	−x11	−x11	ADP
ejpam-6670	177	30	0	0	NUM
ejpam-6670	177	31	−x13	−x13	NUM
ejpam-6670	177	32	x14	x14	PROPN
ejpam-6670	177	33	π	π	PROPN
ejpam-6670	177	34	x21	x21	PROPN
ejpam-6670	178	1	−x22	−x22	NUM
ejpam-6670	178	2	x23	x23	PROPN
ejpam-6670	178	3	−x24	−x24	NUM
ejpam-6670	179	1	0	0	NUM
ejpam-6670	179	2	0	0	NUM
ejpam-6670	179	3	θ	θ	NOUN
ejpam-6670	179	4	−x33	−x33	X
ejpam-6670	179	5	0	0	NUM
ejpam-6670	179	6	0	0	NUM
ejpam-6670	179	7	0	0	NUM
ejpam-6670	179	8	0	0	NUM
ejpam-6670	179	9	qλ1	qλ1	NOUN
ejpam-6670	179	10	−x44	−x44	NOUN
ejpam-6670	179	11	0	0	NUM
ejpam-6670	180	1	λ3	λ3	PROPN
ejpam-6670	180	2	0	0	NUM
ejpam-6670	180	3	0	0	NUM
ejpam-6670	180	4	0	0	NUM
ejpam-6670	180	5	−x55	−x55	NOUN
ejpam-6670	180	6			NOUN
ejpam-6670	180	7	,	,	PUNCT
ejpam-6670	180	8	where	where	SCONJ
ejpam-6670	180	9	x11	x11	NOUN
ejpam-6670	180	10	=	=	SYM
ejpam-6670	180	11	αa(t	αa(t	X
ejpam-6670	180	12	)	)	PUNCT
ejpam-6670	180	13	1	1	NUM
ejpam-6670	180	14	+	+	CCONJ
ejpam-6670	180	15	βc(t	βc(t	NUM
ejpam-6670	180	16	)	)	PUNCT
ejpam-6670	180	17	+	+	CCONJ
ejpam-6670	180	18	λαc(t	λαc(t	X
ejpam-6670	180	19	)	)	PUNCT
ejpam-6670	180	20	1	1	NUM
ejpam-6670	180	21	+	+	CCONJ
ejpam-6670	180	22	βc(t	βc(t	NUM
ejpam-6670	180	23	)	)	PUNCT
ejpam-6670	181	1	+	+	CCONJ
ejpam-6670	181	2	µ0	µ0	NOUN
ejpam-6670	181	3	+	+	X
ejpam-6670	181	4	λ3	λ3	PROPN
ejpam-6670	181	5	,	,	PUNCT
ejpam-6670	181	6	x13	x13	PROPN
ejpam-6670	181	7	=	=	PUNCT
ejpam-6670	181	8	αs(t	αs(t	X
ejpam-6670	181	9	)	)	PUNCT
ejpam-6670	181	10	1	1	NUM
ejpam-6670	181	11	+	+	NUM
ejpam-6670	181	12	βc(t	βc(t	NOUN
ejpam-6670	181	13	)	)	PUNCT
ejpam-6670	181	14	=	=	SYM
ejpam-6670	181	15	x23	x23	PROPN
ejpam-6670	181	16	,	,	PUNCT
ejpam-6670	181	17	x14	x14	PROPN
ejpam-6670	181	18	=	=	SYM
ejpam-6670	181	19	βαs(t)a(t	βαs(t)a(t	PROPN
ejpam-6670	181	20	)	)	PUNCT
ejpam-6670	181	21	1	1	NUM
ejpam-6670	182	1	+	+	CCONJ
ejpam-6670	182	2	βc(t)2	βc(t)2	PROPN
ejpam-6670	182	3	−	−	PROPN
ejpam-6670	182	4	λαs(t	λαs(t	PROPN
ejpam-6670	182	5	)	)	PUNCT
ejpam-6670	182	6	1	1	NUM
ejpam-6670	182	7	+	+	NUM
ejpam-6670	182	8	βc(t)2	βc(t)2	PROPN
ejpam-6670	182	9	=	=	SYM
ejpam-6670	182	10	−x24	−x24	PROPN
ejpam-6670	182	11	,	,	PUNCT
ejpam-6670	182	12	x21	x21	PROPN
ejpam-6670	182	13	=	=	SYM
ejpam-6670	182	14	x11	x11	PROPN
ejpam-6670	182	15	−	−	PROPN
ejpam-6670	183	1	(	(	PUNCT
ejpam-6670	183	2	µ0	µ0	NOUN
ejpam-6670	183	3	+	+	X
ejpam-6670	183	4	λ3	λ3	PROPN
ejpam-6670	183	5	)	)	PUNCT
ejpam-6670	183	6	,	,	PUNCT
ejpam-6670	183	7	x22	x22	X
ejpam-6670	184	1	=	=	SYM
ejpam-6670	184	2	µ0	µ0	PROPN
ejpam-6670	184	3	+	+	CCONJ
ejpam-6670	184	4	θ	θ	PROPN
ejpam-6670	184	5	,	,	PUNCT
ejpam-6670	184	6	x33	x33	NOUN
ejpam-6670	184	7	=	=	SYM
ejpam-6670	184	8	µ0	µ0	PROPN
ejpam-6670	185	1	+	+	X
ejpam-6670	185	2	λ1	λ1	ADJ
ejpam-6670	185	3	,	,	PUNCT
ejpam-6670	185	4	x44	x44	NOUN
ejpam-6670	185	5	=	=	SYM
ejpam-6670	185	6	gηφ−	gηφ−	PROPN
ejpam-6670	185	7	µ0	µ0	NOUN
ejpam-6670	185	8	−	−	PROPN
ejpam-6670	185	9	µ1	µ1	PROPN
ejpam-6670	185	10	−	−	PROPN
ejpam-6670	185	11	λ2	λ2	PROPN
ejpam-6670	185	12	,	,	PUNCT
ejpam-6670	185	13	x55	x55	NOUN
ejpam-6670	185	14	=	=	SYM
ejpam-6670	185	15	µ0	µ0	PROPN
ejpam-6670	186	1	+	+	X
ejpam-6670	186	2	π	π	NOUN
ejpam-6670	186	3	.	.	PUNCT
ejpam-6670	187	1	t.	t.	PROPN
ejpam-6670	187	2	khan	khan	PROPN
ejpam-6670	187	3	et	et	PROPN
ejpam-6670	187	4	al	al	PROPN
ejpam-6670	187	5	.	.	PUNCT
ejpam-6670	187	6	/	/	SYM
ejpam-6670	187	7	eur	eur	PROPN
ejpam-6670	187	8	.	.	PUNCT
ejpam-6670	188	1	j.	j.	PROPN
ejpam-6670	188	2	pure	pure	PROPN
ejpam-6670	188	3	appl	appl	PROPN
ejpam-6670	188	4	.	.	PROPN
ejpam-6670	188	5	math	math	PROPN
ejpam-6670	188	6	,	,	PUNCT
ejpam-6670	188	7	18	18	NUM
ejpam-6670	188	8	(	(	PUNCT
ejpam-6670	188	9	3	3	NUM
ejpam-6670	188	10	)	)	PUNCT
ejpam-6670	188	11	(	(	PUNCT
ejpam-6670	188	12	2025	2025	NUM
ejpam-6670	188	13	)	)	PUNCT
ejpam-6670	188	14	,	,	PUNCT
ejpam-6670	188	15	6670	6670	NUM
ejpam-6670	188	16	9	9	NUM
ejpam-6670	188	17	of	of	ADP
ejpam-6670	188	18	22	22	NUM
ejpam-6670	188	19	2.3	2.3	NUM
ejpam-6670	188	20	.	.	PUNCT
ejpam-6670	189	1	basic	basic	ADJ
ejpam-6670	189	2	reproduction	reproduction	NOUN
ejpam-6670	189	3	number	number	NOUN
ejpam-6670	189	4	in	in	ADP
ejpam-6670	189	5	epidemiological	epidemiological	ADJ
ejpam-6670	189	6	models	model	NOUN
ejpam-6670	189	7	,	,	PUNCT
ejpam-6670	189	8	the	the	DET
ejpam-6670	189	9	threshold	threshold	NOUN
ejpam-6670	189	10	quantity	quantity	NOUN
ejpam-6670	189	11	,	,	PUNCT
ejpam-6670	189	12	called	call	VERB
ejpam-6670	189	13	the	the	DET
ejpam-6670	189	14	disease	disease	NOUN
ejpam-6670	189	15	’s	’s	PART
ejpam-6670	189	16	basic	basic	ADJ
ejpam-6670	189	17	reproduction	reproduction	NOUN
ejpam-6670	189	18	number	number	NOUN
ejpam-6670	189	19	,	,	PUNCT
ejpam-6670	189	20	is	be	AUX
ejpam-6670	189	21	an	an	DET
ejpam-6670	189	22	essential	essential	ADJ
ejpam-6670	189	23	quantity	quantity	NOUN
ejpam-6670	189	24	which	which	PRON
ejpam-6670	189	25	describes	describe	VERB
ejpam-6670	189	26	the	the	DET
ejpam-6670	189	27	predicted	predict	VERB
ejpam-6670	189	28	average	average	ADJ
ejpam-6670	189	29	rate	rate	NOUN
ejpam-6670	189	30	of	of	ADP
ejpam-6670	189	31	infections	infection	NOUN
ejpam-6670	189	32	induced	induce	VERB
ejpam-6670	189	33	by	by	ADP
ejpam-6670	189	34	a	a	DET
ejpam-6670	189	35	single	single	ADJ
ejpam-6670	189	36	infective	infective	NOUN
ejpam-6670	189	37	after	after	ADP
ejpam-6670	189	38	introducing	introduce	VERB
ejpam-6670	189	39	into	into	ADP
ejpam-6670	189	40	an	an	DET
ejpam-6670	189	41	entirely	entirely	ADV
ejpam-6670	189	42	susceptible	susceptible	ADJ
ejpam-6670	189	43	community	community	NOUN
ejpam-6670	189	44	.	.	PUNCT
ejpam-6670	190	1	to	to	PART
ejpam-6670	190	2	calculate	calculate	VERB
ejpam-6670	190	3	this	this	DET
ejpam-6670	190	4	quantity	quantity	NOUN
ejpam-6670	190	5	for	for	ADP
ejpam-6670	190	6	the	the	DET
ejpam-6670	190	7	proposed	propose	VERB
ejpam-6670	190	8	problem	problem	NOUN
ejpam-6670	190	9	,	,	PUNCT
ejpam-6670	190	10	we	we	PRON
ejpam-6670	190	11	follow	follow	VERB
ejpam-6670	190	12	the	the	DET
ejpam-6670	190	13	methodology	methodology	NOUN
ejpam-6670	190	14	introduced	introduce	VERB
ejpam-6670	190	15	by	by	ADP
ejpam-6670	190	16	watmough	watmough	NOUN
ejpam-6670	190	17	and	and	CCONJ
ejpam-6670	190	18	driessche	driessche	NOUN
ejpam-6670	190	19	[	[	X
ejpam-6670	190	20	21	21	NUM
ejpam-6670	190	21	]	]	PUNCT
ejpam-6670	190	22	,	,	PUNCT
ejpam-6670	190	23	therefore	therefore	ADV
ejpam-6670	190	24	assume	assume	VERB
ejpam-6670	190	25	that	that	SCONJ
ejpam-6670	190	26	y	y	PROPN
ejpam-6670	190	27	=	=	PRON
ejpam-6670	190	28	(	(	PUNCT
ejpam-6670	190	29	l(t	l(t	PROPN
ejpam-6670	190	30	)	)	PUNCT
ejpam-6670	190	31	,	,	PUNCT
ejpam-6670	190	32	a(t	a(t	NOUN
ejpam-6670	190	33	)	)	PUNCT
ejpam-6670	190	34	,	,	PUNCT
ejpam-6670	190	35	c(t	c(t	PROPN
ejpam-6670	190	36	)	)	PUNCT
ejpam-6670	190	37	)	)	PUNCT
ejpam-6670	190	38	,	,	PUNCT
ejpam-6670	190	39	then	then	ADV
ejpam-6670	190	40	the	the	DET
ejpam-6670	190	41	model	model	NOUN
ejpam-6670	190	42	(	(	PUNCT
ejpam-6670	190	43	1	1	X
ejpam-6670	190	44	)	)	PUNCT
ejpam-6670	190	45	yields	yield	NOUN
ejpam-6670	190	46	dy	dy	NOUN
ejpam-6670	190	47	dt	dt	NOUN
ejpam-6670	191	1	=	=	SYM
ejpam-6670	191	2	f	f	PROPN
ejpam-6670	192	1	−	−	PROPN
ejpam-6670	192	2	v.	v.	CCONJ
ejpam-6670	192	3	(	(	PUNCT
ejpam-6670	192	4	15	15	NUM
ejpam-6670	192	5	)	)	PUNCT
ejpam-6670	192	6	in	in	ADP
ejpam-6670	192	7	equation	equation	NOUN
ejpam-6670	192	8	(	(	PUNCT
ejpam-6670	192	9	15	15	NUM
ejpam-6670	192	10	)	)	PUNCT
ejpam-6670	192	11	,	,	PUNCT
ejpam-6670	192	12	the	the	DET
ejpam-6670	192	13	matrices	matrix	NOUN
ejpam-6670	192	14	are	be	AUX
ejpam-6670	192	15	define	define	ADJ
ejpam-6670	192	16	as	as	ADP
ejpam-6670	192	17	:	:	PUNCT
ejpam-6670	192	18	f	f	X
ejpam-6670	192	19	=	=	PUNCT
ejpam-6670	192	20			NOUN
ejpam-6670	192	21	βs(t)a(t	βs(t)a(t	NOUN
ejpam-6670	192	22	)	)	PUNCT
ejpam-6670	192	23	1+βc(t	1+βc(t	NUM
ejpam-6670	192	24	)	)	PUNCT
ejpam-6670	192	25	+	+	PUNCT
ejpam-6670	192	26	λαs(t)c(t	λαs(t)c(t	X
ejpam-6670	192	27	)	)	PUNCT
ejpam-6670	192	28	1+βc(t	1+βc(t	NUM
ejpam-6670	192	29	)	)	PUNCT
ejpam-6670	192	30	0	0	NUM
ejpam-6670	192	31	0	0	NUM
ejpam-6670	193	1			NUM
ejpam-6670	193	2	,	,	PUNCT
ejpam-6670	193	3	v	v	NOUN
ejpam-6670	193	4	=	=	SYM
ejpam-6670	193	5			PROPN
ejpam-6670	193	6	(	(	PUNCT
ejpam-6670	193	7	θ	θ	NOUN
ejpam-6670	193	8	+	+	SYM
ejpam-6670	193	9	µ0)l(t	µ0)l(t	NOUN
ejpam-6670	193	10	)	)	PUNCT
ejpam-6670	193	11	(	(	PUNCT
ejpam-6670	193	12	µ0	µ0	NOUN
ejpam-6670	193	13	+	+	X
ejpam-6670	193	14	λ1)a(t)−	λ1)a(t)−	PROPN
ejpam-6670	193	15	θl(t	θl(t	NOUN
ejpam-6670	193	16	)	)	PUNCT
ejpam-6670	193	17	(	(	PUNCT
ejpam-6670	193	18	µ0	µ0	NOUN
ejpam-6670	193	19	+	+	SYM
ejpam-6670	193	20	µ1	µ1	PROPN
ejpam-6670	194	1	+	+	CCONJ
ejpam-6670	195	1	λ2)c(t)−	λ2)c(t)−	PROPN
ejpam-6670	195	2	qλ1a(t)−	qλ1a(t)−	PROPN
ejpam-6670	195	3	gηφc(t	gηφc(t	PROPN
ejpam-6670	195	4	)	)	PUNCT
ejpam-6670	195	5			NOUN
ejpam-6670	195	6	.	.	PUNCT
ejpam-6670	196	1	let	let	VERB
ejpam-6670	196	2	f	f	PROPN
ejpam-6670	196	3	and	and	CCONJ
ejpam-6670	196	4	v	v	NOUN
ejpam-6670	196	5	are	be	AUX
ejpam-6670	196	6	the	the	DET
ejpam-6670	196	7	jacobian	jacobian	NOUN
ejpam-6670	196	8	of	of	ADP
ejpam-6670	196	9	f	f	PROPN
ejpam-6670	196	10	and	and	CCONJ
ejpam-6670	196	11	v	v	NOUN
ejpam-6670	196	12	at	at	ADP
ejpam-6670	196	13	f0	f0	PROPN
ejpam-6670	196	14	,	,	PUNCT
ejpam-6670	196	15	then	then	ADV
ejpam-6670	196	16	it	it	PRON
ejpam-6670	196	17	becomes	become	VERB
ejpam-6670	196	18	f	f	PROPN
ejpam-6670	196	19	=	=	SYM
ejpam-6670	196	20	jacobian	jacobian	PROPN
ejpam-6670	196	21	of	of	ADP
ejpam-6670	196	22	f	f	PROPN
ejpam-6670	196	23	=	=	SYM
ejpam-6670	196	24			PROPN
ejpam-6670	196	25	0	0	NUM
ejpam-6670	196	26	αs0	αs0	ADJ
ejpam-6670	196	27	λαs0	λαs0	PROPN
ejpam-6670	196	28	0	0	NUM
ejpam-6670	197	1	0	0	NUM
ejpam-6670	197	2	0	0	NUM
ejpam-6670	197	3	0	0	NUM
ejpam-6670	197	4	0	0	NUM
ejpam-6670	197	5	0	0	NUM
ejpam-6670	197	6			NOUN
ejpam-6670	197	7	,	,	PUNCT
ejpam-6670	197	8	v	v	NOUN
ejpam-6670	197	9	=	=	SYM
ejpam-6670	197	10	jacobian	jacobian	NOUN
ejpam-6670	197	11	of	of	ADP
ejpam-6670	197	12	v	v	NOUN
ejpam-6670	197	13	=	=	SYM
ejpam-6670	197	14			PROPN
ejpam-6670	197	15	x11	x11	NOUN
ejpam-6670	197	16	0	0	NUM
ejpam-6670	197	17	0	0	NUM
ejpam-6670	198	1	−θ	−θ	VERB
ejpam-6670	198	2	x22	x22	PROPN
ejpam-6670	198	3	0	0	SYM
ejpam-6670	198	4	0	0	NUM
ejpam-6670	198	5	−qλ1	−qλ1	PROPN
ejpam-6670	198	6	x33	x33	NUM
ejpam-6670	198	7			NOUN
ejpam-6670	198	8	,	,	PUNCT
ejpam-6670	198	9	where	where	SCONJ
ejpam-6670	198	10	x11	x11	NOUN
ejpam-6670	198	11	=	=	SYM
ejpam-6670	198	12	θ	θ	PROPN
ejpam-6670	198	13	+	+	NUM
ejpam-6670	198	14	µ0	µ0	NOUN
ejpam-6670	198	15	,	,	PUNCT
ejpam-6670	198	16	x22	x22	NOUN
ejpam-6670	198	17	=	=	SYM
ejpam-6670	198	18	µ0	µ0	PROPN
ejpam-6670	198	19	+	+	X
ejpam-6670	199	1	λ1	λ1	ADJ
ejpam-6670	199	2	and	and	CCONJ
ejpam-6670	199	3	x33	x33	NUM
ejpam-6670	199	4	=	=	SYM
ejpam-6670	199	5	µ0	µ0	PROPN
ejpam-6670	199	6	+	+	CCONJ
ejpam-6670	200	1	µ1	µ1	PROPN
ejpam-6670	201	1	+	+	CCONJ
ejpam-6670	201	2	λ2	λ2	NOUN
ejpam-6670	201	3	−	−	NOUN
ejpam-6670	201	4	gηφ	gηφ	NOUN
ejpam-6670	201	5	.	.	PUNCT
ejpam-6670	202	1	˜thus	˜thu	NOUN
ejpam-6670	202	2	,	,	PUNCT
ejpam-6670	202	3	the	the	DET
ejpam-6670	202	4	basic	basic	ADJ
ejpam-6670	202	5	reproductive	reproductive	ADJ
ejpam-6670	202	6	number	number	NOUN
ejpam-6670	202	7	r0	r0	NOUN
ejpam-6670	202	8	is	be	AUX
ejpam-6670	202	9	the	the	DET
ejpam-6670	202	10	spectral	spectral	ADJ
ejpam-6670	202	11	radius	radius	NOUN
ejpam-6670	202	12	of	of	ADP
ejpam-6670	202	13	k	k	PROPN
ejpam-6670	202	14	=	=	SYM
ejpam-6670	202	15	fv−1	fv−1	PROPN
ejpam-6670	202	16	(	(	PUNCT
ejpam-6670	202	17	r0	r0	NOUN
ejpam-6670	202	18	=	=	SYM
ejpam-6670	202	19	ρ(fv−1	ρ(fv−1	NOUN
ejpam-6670	202	20	)	)	PUNCT
ejpam-6670	202	21	)	)	PUNCT
ejpam-6670	202	22	.	.	PUNCT
ejpam-6670	203	1	so	so	ADV
ejpam-6670	203	2	the	the	DET
ejpam-6670	203	3	basic	basic	ADJ
ejpam-6670	203	4	reproductive	reproductive	ADJ
ejpam-6670	203	5	quantity	quantity	NOUN
ejpam-6670	203	6	r0	r0	NOUN
ejpam-6670	203	7	of	of	ADP
ejpam-6670	203	8	our	our	PRON
ejpam-6670	203	9	suggested	suggested	ADJ
ejpam-6670	203	10	model	model	NOUN
ejpam-6670	203	11	(	(	PUNCT
ejpam-6670	203	12	1	1	X
ejpam-6670	203	13	)	)	PUNCT
ejpam-6670	203	14	looks	look	VERB
ejpam-6670	203	15	like	like	ADP
ejpam-6670	203	16	r0	r0	NOUN
ejpam-6670	203	17	=	=	PROPN
ejpam-6670	203	18	r1	r1	PROPN
ejpam-6670	203	19	+	+	CCONJ
ejpam-6670	203	20	r2	r2	PROPN
ejpam-6670	203	21	,	,	PUNCT
ejpam-6670	203	22	(	(	PUNCT
ejpam-6670	203	23	16	16	NUM
ejpam-6670	203	24	)	)	PUNCT
ejpam-6670	203	25	where	where	SCONJ
ejpam-6670	203	26	r1	r1	PROPN
ejpam-6670	203	27	=	=	SYM
ejpam-6670	203	28	θαs0	θαs0	PROPN
ejpam-6670	203	29	(	(	PUNCT
ejpam-6670	203	30	µ0	µ0	NOUN
ejpam-6670	203	31	+	+	X
ejpam-6670	203	32	θ)(µ0	θ)(µ0	X
ejpam-6670	203	33	+	+	X
ejpam-6670	203	34	λ1	λ1	ADJ
ejpam-6670	203	35	)	)	PUNCT
ejpam-6670	203	36	,	,	PUNCT
ejpam-6670	203	37	r2	r2	PROPN
ejpam-6670	203	38	=	=	SYM
ejpam-6670	203	39	θαs0λλ1q	θαs0λλ1q	PROPN
ejpam-6670	203	40	(	(	PUNCT
ejpam-6670	203	41	µ0	µ0	NOUN
ejpam-6670	203	42	+	+	X
ejpam-6670	203	43	θ)(µ0	θ)(µ0	X
ejpam-6670	203	44	+	+	CCONJ
ejpam-6670	203	45	λ1)(µ0	λ1)(µ0	NOUN
ejpam-6670	203	46	+	+	CCONJ
ejpam-6670	203	47	µ1	µ1	NOUN
ejpam-6670	203	48	+	+	CCONJ
ejpam-6670	203	49	λ2	λ2	NOUN
ejpam-6670	203	50	−	−	PROPN
ejpam-6670	203	51	gηφ	gηφ	NOUN
ejpam-6670	203	52	)	)	PUNCT
ejpam-6670	203	53	.	.	PUNCT
ejpam-6670	204	1	2.4	2.4	NUM
ejpam-6670	204	2	.	.	PUNCT
ejpam-6670	205	1	equilibrium	equilibrium	NOUN
ejpam-6670	205	2	analysis	analysis	NOUN
ejpam-6670	205	3	to	to	PART
ejpam-6670	205	4	study	study	VERB
ejpam-6670	205	5	the	the	DET
ejpam-6670	205	6	dynamics	dynamic	NOUN
ejpam-6670	205	7	of	of	ADP
ejpam-6670	205	8	the	the	DET
ejpam-6670	205	9	model	model	NOUN
ejpam-6670	205	10	that	that	PRON
ejpam-6670	205	11	is	be	AUX
ejpam-6670	205	12	under	under	ADP
ejpam-6670	205	13	consideration	consideration	NOUN
ejpam-6670	205	14	(	(	PUNCT
ejpam-6670	205	15	1	1	NUM
ejpam-6670	205	16	)	)	PUNCT
ejpam-6670	205	17	,	,	PUNCT
ejpam-6670	205	18	we	we	PRON
ejpam-6670	205	19	first	first	ADV
ejpam-6670	205	20	find	find	VERB
ejpam-6670	205	21	the	the	DET
ejpam-6670	205	22	model	model	NOUN
ejpam-6670	205	23	equilibria	equilibria	NOUN
ejpam-6670	205	24	.	.	PUNCT
ejpam-6670	206	1	for	for	ADP
ejpam-6670	206	2	this	this	PRON
ejpam-6670	206	3	,	,	PUNCT
ejpam-6670	206	4	we	we	PRON
ejpam-6670	206	5	assume	assume	VERB
ejpam-6670	206	6	that	that	SCONJ
ejpam-6670	206	7	the	the	DET
ejpam-6670	206	8	infection	infection	NOUN
ejpam-6670	206	9	-	-	PUNCT
ejpam-6670	206	10	free	free	ADJ
ejpam-6670	206	11	state	state	NOUN
ejpam-6670	206	12	of	of	ADP
ejpam-6670	206	13	system	system	NOUN
ejpam-6670	206	14	(	(	PUNCT
ejpam-6670	206	15	1	1	X
ejpam-6670	206	16	)	)	PUNCT
ejpam-6670	206	17	is	be	AUX
ejpam-6670	206	18	t.	t.	PROPN
ejpam-6670	206	19	khan	khan	PROPN
ejpam-6670	206	20	et	et	PROPN
ejpam-6670	206	21	al	al	PROPN
ejpam-6670	206	22	.	.	PUNCT
ejpam-6670	206	23	/	/	SYM
ejpam-6670	206	24	eur	eur	PROPN
ejpam-6670	206	25	.	.	PUNCT
ejpam-6670	207	1	j.	j.	PROPN
ejpam-6670	207	2	pure	pure	PROPN
ejpam-6670	207	3	appl	appl	PROPN
ejpam-6670	207	4	.	.	PROPN
ejpam-6670	207	5	math	math	PROPN
ejpam-6670	207	6	,	,	PUNCT
ejpam-6670	207	7	18	18	NUM
ejpam-6670	207	8	(	(	PUNCT
ejpam-6670	207	9	3	3	NUM
ejpam-6670	207	10	)	)	PUNCT
ejpam-6670	207	11	(	(	PUNCT
ejpam-6670	207	12	2025	2025	NUM
ejpam-6670	207	13	)	)	PUNCT
ejpam-6670	207	14	,	,	PUNCT
ejpam-6670	207	15	6670	6670	NUM
ejpam-6670	207	16	10	10	NUM
ejpam-6670	207	17	of	of	ADP
ejpam-6670	207	18	22	22	NUM
ejpam-6670	207	19	symbolized	symbolize	VERB
ejpam-6670	207	20	by	by	ADP
ejpam-6670	207	21	f0	f0	PROPN
ejpam-6670	207	22	and	and	CCONJ
ejpam-6670	207	23	f0	f0	PROPN
ejpam-6670	207	24	=	=	SYM
ejpam-6670	207	25	(	(	PUNCT
ejpam-6670	207	26	s0	s0	PROPN
ejpam-6670	207	27	,	,	PUNCT
ejpam-6670	207	28	0	0	NUM
ejpam-6670	207	29	,	,	PUNCT
ejpam-6670	207	30	0	0	NUM
ejpam-6670	207	31	,	,	PUNCT
ejpam-6670	207	32	0	0	NUM
ejpam-6670	207	33	,	,	PUNCT
ejpam-6670	207	34	0	0	NUM
ejpam-6670	207	35	,	,	PUNCT
ejpam-6670	207	36	v0	v0	PROPN
ejpam-6670	207	37	)	)	PUNCT
ejpam-6670	207	38	,	,	PUNCT
ejpam-6670	207	39	where	where	SCONJ
ejpam-6670	207	40	s0	s0	PROPN
ejpam-6670	207	41	=	=	PUNCT
ejpam-6670	207	42	g{π	g{π	PROPN
ejpam-6670	207	43	+	+	CCONJ
ejpam-6670	207	44	ηµ0	ηµ0	NOUN
ejpam-6670	207	45	}	}	PUNCT
ejpam-6670	207	46	µ0{π	µ0{π	PRON
ejpam-6670	207	47	+	+	PUNCT
ejpam-6670	207	48	µ0	µ0	NOUN
ejpam-6670	207	49	+	+	X
ejpam-6670	207	50	λ3	λ3	PROPN
ejpam-6670	207	51	}	}	PUNCT
ejpam-6670	207	52	,	,	PUNCT
ejpam-6670	207	53	v0	v0	NOUN
ejpam-6670	207	54	=	=	SYM
ejpam-6670	207	55	g{µ0	g{µ0	X
ejpam-6670	207	56	−	−	NUM
ejpam-6670	207	57	µ0η	µ0η	PUNCT
ejpam-6670	207	58	+	+	CCONJ
ejpam-6670	207	59	λ3	λ3	PROPN
ejpam-6670	207	60	}	}	PUNCT
ejpam-6670	207	61	µ0{π	µ0{π	PRON
ejpam-6670	207	62	+	+	NUM
ejpam-6670	207	63	λ3	λ3	PROPN
ejpam-6670	207	64	+	+	NUM
ejpam-6670	207	65	µ0	µ0	NOUN
ejpam-6670	207	66	}	}	PUNCT
ejpam-6670	207	67	.	.	PUNCT
ejpam-6670	208	1	(	(	PUNCT
ejpam-6670	208	2	17	17	NUM
ejpam-6670	208	3	)	)	PUNCT
ejpam-6670	208	4	similarly	similarly	ADV
ejpam-6670	208	5	,	,	PUNCT
ejpam-6670	208	6	to	to	PART
ejpam-6670	208	7	find	find	VERB
ejpam-6670	208	8	the	the	DET
ejpam-6670	208	9	endemic	endemic	ADJ
ejpam-6670	208	10	states	state	NOUN
ejpam-6670	208	11	of	of	ADP
ejpam-6670	208	12	the	the	DET
ejpam-6670	208	13	model	model	NOUN
ejpam-6670	208	14	,	,	PUNCT
ejpam-6670	208	15	we	we	PRON
ejpam-6670	208	16	assume	assume	VERB
ejpam-6670	208	17	p1	p1	PROPN
ejpam-6670	208	18	=	=	SYM
ejpam-6670	208	19	(	(	PUNCT
ejpam-6670	208	20	µ0+λ3	µ0+λ3	PROPN
ejpam-6670	208	21	)	)	PUNCT
ejpam-6670	208	22	,	,	PUNCT
ejpam-6670	208	23	p2	p2	PROPN
ejpam-6670	208	24	=	=	SYM
ejpam-6670	208	25	(	(	PUNCT
ejpam-6670	208	26	µ0+θ	µ0+θ	ADJ
ejpam-6670	208	27	)	)	PUNCT
ejpam-6670	208	28	,	,	PUNCT
ejpam-6670	208	29	p3	p3	PROPN
ejpam-6670	208	30	=	=	SYM
ejpam-6670	208	31	(	(	PUNCT
ejpam-6670	208	32	µ0	µ0	NOUN
ejpam-6670	208	33	+	+	X
ejpam-6670	208	34	λ1	λ1	ADJ
ejpam-6670	208	35	)	)	PUNCT
ejpam-6670	208	36	,	,	PUNCT
ejpam-6670	208	37	p4	p4	NOUN
ejpam-6670	208	38	=	=	SYM
ejpam-6670	208	39	(	(	PUNCT
ejpam-6670	208	40	µ0	µ0	NOUN
ejpam-6670	208	41	+	+	SYM
ejpam-6670	208	42	µ1	µ1	PROPN
ejpam-6670	208	43	+	+	CCONJ
ejpam-6670	208	44	λ2	λ2	NOUN
ejpam-6670	208	45	−	−	PROPN
ejpam-6670	208	46	gηφ	gηφ	NOUN
ejpam-6670	208	47	)	)	PUNCT
ejpam-6670	208	48	and	and	CCONJ
ejpam-6670	208	49	p5	p5	NOUN
ejpam-6670	208	50	=	=	SYM
ejpam-6670	208	51	(	(	PUNCT
ejpam-6670	208	52	µ0	µ0	NOUN
ejpam-6670	208	53	+	+	X
ejpam-6670	208	54	π	π	NOUN
ejpam-6670	208	55	)	)	PUNCT
ejpam-6670	208	56	for	for	ADP
ejpam-6670	208	57	the	the	DET
ejpam-6670	208	58	shake	shake	NOUN
ejpam-6670	208	59	of	of	ADP
ejpam-6670	208	60	simplicity	simplicity	NOUN
ejpam-6670	208	61	,	,	PUNCT
ejpam-6670	208	62	then	then	ADV
ejpam-6670	208	63	the	the	DET
ejpam-6670	208	64	endemic	endemic	ADJ
ejpam-6670	208	65	state	state	NOUN
ejpam-6670	208	66	becomes	become	VERB
ejpam-6670	208	67	f1	f1	NOUN
ejpam-6670	208	68	=	=	PUNCT
ejpam-6670	208	69	(	(	PUNCT
ejpam-6670	208	70	s∗	s∗	PROPN
ejpam-6670	208	71	,	,	PUNCT
ejpam-6670	208	72	l∗	l∗	PROPN
ejpam-6670	208	73	,	,	PUNCT
ejpam-6670	208	74	a∗	a∗	PROPN
ejpam-6670	208	75	,	,	PUNCT
ejpam-6670	208	76	c∗	c∗	PROPN
ejpam-6670	208	77	,	,	PUNCT
ejpam-6670	208	78	r∗	r∗	PROPN
ejpam-6670	208	79	,	,	PUNCT
ejpam-6670	208	80	v∗	v∗	PROPN
ejpam-6670	208	81	)	)	PUNCT
ejpam-6670	208	82	,	,	PUNCT
ejpam-6670	208	83	where	where	SCONJ
ejpam-6670	208	84	s∗	s∗	PROPN
ejpam-6670	208	85	=	=	SYM
ejpam-6670	208	86	{	{	PUNCT
ejpam-6670	208	87	p5gη	p5gη	X
ejpam-6670	208	88	+	+	CCONJ
ejpam-6670	208	89	πg(1−	πg(1−	PROPN
ejpam-6670	208	90	η	η	NOUN
ejpam-6670	208	91	)	)	PUNCT
ejpam-6670	208	92	}	}	PUNCT
ejpam-6670	208	93	{	{	PUNCT
ejpam-6670	208	94	p1p5	p1p5	X
ejpam-6670	208	95	−	−	PROPN
ejpam-6670	208	96	πλ3	πλ3	NOUN
ejpam-6670	208	97	}	}	PUNCT
ejpam-6670	208	98	,	,	PUNCT
ejpam-6670	208	99	l∗	l∗	NOUN
ejpam-6670	208	100	=	=	PUNCT
ejpam-6670	208	101	p2p3p4µ0{µ0	p2p3p4µ0{µ0	NOUN
ejpam-6670	208	102	+	+	X
ejpam-6670	208	103	π	π	X
ejpam-6670	208	104	+	+	CCONJ
ejpam-6670	208	105	λ3}(r0	λ3}(r0	ADP
ejpam-6670	208	106	−	−	NUM
ejpam-6670	208	107	1	1	NUM
ejpam-6670	208	108	)	)	PUNCT
ejpam-6670	209	1	+	+	NUM
ejpam-6670	209	2	p2p3p4πλ3	p2p3p4πλ3	NOUN
ejpam-6670	209	3	p2θ{p4p5α+	p2θ{p4p5α+	NOUN
ejpam-6670	209	4	p5λαqλ1	p5λαqλ1	NOUN
ejpam-6670	209	5	+	+	CCONJ
ejpam-6670	209	6	p1p5βqλ1	p1p5βqλ1	ADJ
ejpam-6670	209	7	−	−	NOUN
ejpam-6670	209	8	βqλ1πλ3	βqλ1πλ3	INTJ
ejpam-6670	209	9	}	}	PUNCT
ejpam-6670	209	10	,	,	PUNCT
ejpam-6670	209	11	a∗	a∗	NOUN
ejpam-6670	209	12	=	=	SYM
ejpam-6670	209	13	p2p4µ0{µ0	p2p4µ0{µ0	NOUN
ejpam-6670	209	14	+	+	CCONJ
ejpam-6670	209	15	π	π	PROPN
ejpam-6670	209	16	+	+	CCONJ
ejpam-6670	209	17	λ3}(r0	λ3}(r0	ADP
ejpam-6670	209	18	−	−	NUM
ejpam-6670	209	19	1	1	NUM
ejpam-6670	209	20	)	)	PUNCT
ejpam-6670	209	21	+	+	NUM
ejpam-6670	209	22	p2p3p4πλ3	p2p3p4πλ3	VERB
ejpam-6670	210	1	p2{αp4p5	p2{αp4p5	NOUN
ejpam-6670	210	2	+	+	CCONJ
ejpam-6670	210	3	p5λαqλ1	p5λαqλ1	NOUN
ejpam-6670	210	4	+	+	CCONJ
ejpam-6670	210	5	p1p5βqλ1	p1p5βqλ1	ADJ
ejpam-6670	210	6	−	−	NOUN
ejpam-6670	210	7	βqλ1πλ3	βqλ1πλ3	INTJ
ejpam-6670	210	8	}	}	PUNCT
ejpam-6670	210	9	,	,	PUNCT
ejpam-6670	210	10	r∗	r∗	PROPN
ejpam-6670	210	11	=	=	SYM
ejpam-6670	210	12	1	1	NUM
ejpam-6670	210	13	µ0	µ0	NOUN
ejpam-6670	210	14	{	{	PUNCT
ejpam-6670	210	15	λ2c+	λ2c+	X
ejpam-6670	210	16	(	(	PUNCT
ejpam-6670	210	17	1−	1−	NUM
ejpam-6670	210	18	q)λ1a	q)λ1a	NOUN
ejpam-6670	210	19	}	}	PUNCT
ejpam-6670	210	20	,	,	PUNCT
ejpam-6670	211	1	c∗	c∗	NOUN
ejpam-6670	211	2	=	=	SYM
ejpam-6670	211	3	p2qλ1µ0{µ0	p2qλ1µ0{µ0	NOUN
ejpam-6670	211	4	+	+	NUM
ejpam-6670	211	5	π	π	X
ejpam-6670	212	1	+	+	CCONJ
ejpam-6670	212	2	λ3}(r0	λ3}(r0	ADP
ejpam-6670	212	3	−	−	NUM
ejpam-6670	212	4	1	1	NUM
ejpam-6670	212	5	)	)	PUNCT
ejpam-6670	212	6	+	+	CCONJ
ejpam-6670	212	7	p2p3p4πqλ1λ3	p2p3p4πqλ1λ3	NOUN
ejpam-6670	212	8	p2{αp4p5	p2{αp4p5	NOUN
ejpam-6670	212	9	+	+	CCONJ
ejpam-6670	212	10	p5	p5	ADJ
ejpam-6670	212	11	+	+	CCONJ
ejpam-6670	212	12	p5λαqλ1	p5λαqλ1	NOUN
ejpam-6670	212	13	+	+	CCONJ
ejpam-6670	212	14	p1p5βqλ1	p1p5βqλ1	ADJ
ejpam-6670	212	15	−	−	NOUN
ejpam-6670	212	16	βqλ1πλ3	βqλ1πλ3	INTJ
ejpam-6670	212	17	}	}	PUNCT
ejpam-6670	212	18	,	,	PUNCT
ejpam-6670	212	19	v∗	v∗	NOUN
ejpam-6670	212	20	=	=	SYM
ejpam-6670	212	21	1	1	NUM
ejpam-6670	212	22	p5	p5	ADJ
ejpam-6670	212	23	{	{	PUNCT
ejpam-6670	212	24	g(1−	g(1−	PROPN
ejpam-6670	212	25	η	η	PROPN
ejpam-6670	212	26	)	)	PUNCT
ejpam-6670	212	27	+	+	NUM
ejpam-6670	212	28	λ3s	λ3s	NOUN
ejpam-6670	212	29	}	}	PUNCT
ejpam-6670	212	30	.	.	PUNCT
ejpam-6670	213	1	(	(	PUNCT
ejpam-6670	213	2	18	18	NUM
ejpam-6670	213	3	)	)	PUNCT
ejpam-6670	213	4	now	now	ADV
ejpam-6670	213	5	we	we	PRON
ejpam-6670	213	6	describe	describe	VERB
ejpam-6670	213	7	the	the	DET
ejpam-6670	213	8	asymptotic	asymptotic	ADJ
ejpam-6670	213	9	stabilities	stability	NOUN
ejpam-6670	213	10	of	of	ADP
ejpam-6670	213	11	the	the	DET
ejpam-6670	213	12	model	model	NOUN
ejpam-6670	213	13	that	that	PRON
ejpam-6670	213	14	is	be	AUX
ejpam-6670	213	15	under	under	ADP
ejpam-6670	213	16	consideration	consideration	NOUN
ejpam-6670	213	17	in	in	ADP
ejpam-6670	213	18	the	the	DET
ejpam-6670	213	19	upcoming	upcoming	ADJ
ejpam-6670	213	20	sections	section	NOUN
ejpam-6670	213	21	.	.	PUNCT
ejpam-6670	214	1	2.5	2.5	NUM
ejpam-6670	214	2	.	.	PUNCT
ejpam-6670	215	1	dynamical	dynamical	ADJ
ejpam-6670	215	2	properties	property	NOUN
ejpam-6670	215	3	of	of	ADP
ejpam-6670	215	4	the	the	DET
ejpam-6670	215	5	model	model	NOUN
ejpam-6670	215	6	we	we	PRON
ejpam-6670	215	7	discuss	discuss	VERB
ejpam-6670	215	8	the	the	DET
ejpam-6670	215	9	local	local	ADJ
ejpam-6670	215	10	analysis	analysis	NOUN
ejpam-6670	215	11	of	of	ADP
ejpam-6670	215	12	the	the	DET
ejpam-6670	215	13	model	model	NOUN
ejpam-6670	215	14	to	to	PART
ejpam-6670	215	15	investigate	investigate	VERB
ejpam-6670	215	16	the	the	DET
ejpam-6670	215	17	local	local	ADJ
ejpam-6670	215	18	asymptotic	asymptotic	ADJ
ejpam-6670	215	19	stability	stability	NOUN
ejpam-6670	215	20	of	of	ADP
ejpam-6670	215	21	the	the	DET
ejpam-6670	215	22	proposed	propose	VERB
ejpam-6670	215	23	problem	problem	NOUN
ejpam-6670	215	24	at	at	ADP
ejpam-6670	215	25	f0	f0	PROPN
ejpam-6670	215	26	and	and	CCONJ
ejpam-6670	215	27	f1	f1	NOUN
ejpam-6670	215	28	.	.	PUNCT
ejpam-6670	216	1	to	to	PART
ejpam-6670	216	2	do	do	VERB
ejpam-6670	216	3	this	this	PRON
ejpam-6670	216	4	,	,	PUNCT
ejpam-6670	216	5	we	we	PRON
ejpam-6670	216	6	follow	follow	VERB
ejpam-6670	216	7	linearization	linearization	NOUN
ejpam-6670	216	8	and	and	CCONJ
ejpam-6670	216	9	routhhurwitz	routhhurwitz	ADJ
ejpam-6670	216	10	criteria	criterion	NOUN
ejpam-6670	216	11	.	.	PUNCT
ejpam-6670	217	1	thus	thus	ADV
ejpam-6670	217	2	,	,	PUNCT
ejpam-6670	217	3	we	we	PRON
ejpam-6670	217	4	state	state	VERB
ejpam-6670	217	5	the	the	DET
ejpam-6670	217	6	following	follow	VERB
ejpam-6670	217	7	results	result	NOUN
ejpam-6670	217	8	.	.	PUNCT
ejpam-6670	218	1	theorem	theorem	NOUN
ejpam-6670	218	2	1	1	NUM
ejpam-6670	218	3	.	.	PUNCT
ejpam-6670	219	1	the	the	DET
ejpam-6670	219	2	proposed	propose	VERB
ejpam-6670	219	3	model	model	NOUN
ejpam-6670	219	4	at	at	ADP
ejpam-6670	219	5	f0	f0	PROPN
ejpam-6670	219	6	is	be	AUX
ejpam-6670	219	7	locally	locally	ADV
ejpam-6670	219	8	asymptotic	asymptotic	ADJ
ejpam-6670	219	9	stable	stable	ADJ
ejpam-6670	219	10	whenever	whenever	SCONJ
ejpam-6670	219	11	r0	r0	NOUN
ejpam-6670	219	12	<	<	X
ejpam-6670	219	13	1	1	NUM
ejpam-6670	219	14	and	and	CCONJ
ejpam-6670	219	15	gηφ	gηφ	VERB
ejpam-6670	219	16	>	>	X
ejpam-6670	220	1	µ0	µ0	NOUN
ejpam-6670	220	2	+	+	CCONJ
ejpam-6670	220	3	µ1	µ1	PROPN
ejpam-6670	220	4	+	+	X
ejpam-6670	220	5	λ2	λ2	NOUN
ejpam-6670	220	6	.	.	PUNCT
ejpam-6670	221	1	proof	proof	NOUN
ejpam-6670	221	2	.	.	PUNCT
ejpam-6670	222	1	the	the	DET
ejpam-6670	222	2	characteristic	characteristic	ADJ
ejpam-6670	222	3	equation	equation	NOUN
ejpam-6670	222	4	of	of	ADP
ejpam-6670	222	5	the	the	DET
ejpam-6670	222	6	matrix	matrix	NOUN
ejpam-6670	222	7	j	j	PROPN
ejpam-6670	222	8	at	at	ADP
ejpam-6670	222	9	f0	f0	PROPN
ejpam-6670	222	10	takes	take	VERB
ejpam-6670	222	11	the	the	DET
ejpam-6670	222	12	following	follow	VERB
ejpam-6670	222	13	form	form	NOUN
ejpam-6670	222	14	:	:	PUNCT
ejpam-6670	222	15	(	(	PUNCT
ejpam-6670	222	16	λ+	λ+	PUNCT
ejpam-6670	222	17	x44)(λ	x44)(λ	PROPN
ejpam-6670	222	18	4	4	NUM
ejpam-6670	222	19	+	+	CCONJ
ejpam-6670	222	20	x1λ	x1λ	X
ejpam-6670	222	21	3	3	NUM
ejpam-6670	222	22	+	+	CCONJ
ejpam-6670	222	23	x2λ	x2λ	PROPN
ejpam-6670	222	24	2	2	NUM
ejpam-6670	222	25	+	+	CCONJ
ejpam-6670	222	26	x3λ+	x3λ+	X
ejpam-6670	222	27	x4	x4	PROPN
ejpam-6670	222	28	)	)	PUNCT
ejpam-6670	222	29	=	=	SYM
ejpam-6670	223	1	0	0	NUM
ejpam-6670	223	2	,	,	PUNCT
ejpam-6670	223	3	(	(	PUNCT
ejpam-6670	223	4	19	19	NUM
ejpam-6670	223	5	)	)	PUNCT
ejpam-6670	223	6	where	where	SCONJ
ejpam-6670	223	7	x1	x1	PROPN
ejpam-6670	223	8	=	=	PUNCT
ejpam-6670	223	9	x11	x11	PROPN
ejpam-6670	223	10	+	+	CCONJ
ejpam-6670	223	11	x22	x22	NUM
ejpam-6670	223	12	+	+	CCONJ
ejpam-6670	223	13	x33	x33	NOUN
ejpam-6670	223	14	+	+	CCONJ
ejpam-6670	223	15	x44	x44	PROPN
ejpam-6670	223	16	+	+	CCONJ
ejpam-6670	223	17	x55	x55	NUM
ejpam-6670	223	18	,	,	PUNCT
ejpam-6670	223	19	x2	x2	PROPN
ejpam-6670	223	20	=	=	SYM
ejpam-6670	223	21	x11x22	x11x22	PROPN
ejpam-6670	224	1	+	+	CCONJ
ejpam-6670	224	2	x11x33	x11x33	NOUN
ejpam-6670	224	3	+	+	CCONJ
ejpam-6670	224	4	x11x55	x11x55	PROPN
ejpam-6670	224	5	+	+	CCONJ
ejpam-6670	224	6	x22x55	x22x55	PROPN
ejpam-6670	224	7	+	+	CCONJ
ejpam-6670	224	8	x33x55	x33x55	PROPN
ejpam-6670	224	9	+	+	CCONJ
ejpam-6670	224	10	x22x33(1−	x22x33(1−	PROPN
ejpam-6670	224	11	r1	r1	PROPN
ejpam-6670	224	12	)	)	PUNCT
ejpam-6670	224	13	,	,	PUNCT
ejpam-6670	224	14	x3	x3	NOUN
ejpam-6670	224	15	=	=	PUNCT
ejpam-6670	225	1	µ0(µ0	µ0(µ0	NOUN
ejpam-6670	225	2	+	+	ADP
ejpam-6670	225	3	π	π	PROPN
ejpam-6670	225	4	+	+	PROPN
ejpam-6670	225	5	λ3)(x22	λ3)(x22	PROPN
ejpam-6670	225	6	+	+	CCONJ
ejpam-6670	225	7	x33	x33	ADJ
ejpam-6670	225	8	)	)	PUNCT
ejpam-6670	225	9	+	+	CCONJ
ejpam-6670	225	10	x22x33(x11	x22x33(x11	PROPN
ejpam-6670	225	11	+	+	CCONJ
ejpam-6670	225	12	x55)(1−	x55)(1−	PROPN
ejpam-6670	225	13	r1	r1	PROPN
ejpam-6670	225	14	)	)	PUNCT
ejpam-6670	225	15	,	,	PUNCT
ejpam-6670	225	16	x4	x4	PROPN
ejpam-6670	225	17	=	=	PUNCT
ejpam-6670	226	1	µ0(µ0	µ0(µ0	NOUN
ejpam-6670	226	2	+	+	ADP
ejpam-6670	226	3	π	π	X
ejpam-6670	226	4	+	+	CCONJ
ejpam-6670	226	5	λ3)x22x33(1−	λ3)x22x33(1−	PROPN
ejpam-6670	226	6	r1	r1	PROPN
ejpam-6670	226	7	)	)	PUNCT
ejpam-6670	226	8	.	.	PUNCT
ejpam-6670	227	1	clearly	clearly	ADV
ejpam-6670	227	2	,	,	PUNCT
ejpam-6670	227	3	one	one	NUM
ejpam-6670	227	4	eigenvalue	eigenvalue	NOUN
ejpam-6670	227	5	λ1	λ1	PROPN
ejpam-6670	227	6	has	have	VERB
ejpam-6670	227	7	negative	negative	ADJ
ejpam-6670	227	8	real	real	ADJ
ejpam-6670	227	9	part	part	NOUN
ejpam-6670	227	10	,	,	PUNCT
ejpam-6670	227	11	if	if	SCONJ
ejpam-6670	227	12	gηφ	gηφ	VERB
ejpam-6670	227	13	>	>	X
ejpam-6670	227	14	µ0+µ1+λ2	µ0+µ1+λ2	PROPN
ejpam-6670	227	15	.	.	PUNCT
ejpam-6670	228	1	for	for	ADP
ejpam-6670	228	2	the	the	DET
ejpam-6670	228	3	remaining	remain	VERB
ejpam-6670	228	4	,	,	PUNCT
ejpam-6670	228	5	if	if	SCONJ
ejpam-6670	228	6	r0	r0	NOUN
ejpam-6670	228	7	<	<	X
ejpam-6670	228	8	1	1	NUM
ejpam-6670	228	9	,	,	PUNCT
ejpam-6670	228	10	we	we	PRON
ejpam-6670	228	11	have	have	VERB
ejpam-6670	228	12	0	0	NUM
ejpam-6670	228	13	<	<	X
ejpam-6670	228	14	rj	rj	X
ejpam-6670	228	15	<	<	X
ejpam-6670	228	16	1	1	NUM
ejpam-6670	228	17	,	,	PUNCT
ejpam-6670	228	18	j	j	PROPN
ejpam-6670	229	1	=	=	SYM
ejpam-6670	229	2	1	1	NUM
ejpam-6670	229	3	,	,	PUNCT
ejpam-6670	229	4	2	2	NUM
ejpam-6670	229	5	.	.	PUNCT
ejpam-6670	230	1	so	so	ADV
ejpam-6670	230	2	xi	xi	INTJ
ejpam-6670	230	3	>	>	X
ejpam-6670	230	4	0	0	NUM
ejpam-6670	230	5	,	,	PUNCT
ejpam-6670	230	6	for	for	ADP
ejpam-6670	230	7	i	i	PROPN
ejpam-6670	230	8	=	=	SYM
ejpam-6670	230	9	1	1	NUM
ejpam-6670	230	10	,	,	PUNCT
ejpam-6670	230	11	2	2	NUM
ejpam-6670	230	12	,	,	PUNCT
ejpam-6670	230	13	3	3	NUM
ejpam-6670	230	14	,	,	PUNCT
ejpam-6670	230	15	4	4	NUM
ejpam-6670	230	16	,	,	PUNCT
ejpam-6670	230	17	and	and	CCONJ
ejpam-6670	230	18	x1x2x3	x1x2x3	PROPN
ejpam-6670	230	19	>	>	X
ejpam-6670	230	20	x23+x21x4	x23+x21x4	PROPN
ejpam-6670	231	1	holds	hold	VERB
ejpam-6670	231	2	,	,	PUNCT
ejpam-6670	231	3	which	which	PRON
ejpam-6670	231	4	implies	imply	VERB
ejpam-6670	231	5	that	that	SCONJ
ejpam-6670	231	6	the	the	DET
ejpam-6670	231	7	routh	routh	PROPN
ejpam-6670	231	8	-	-	PUNCT
ejpam-6670	231	9	hurwitz	hurwitz	PROPN
ejpam-6670	231	10	criterion	criterion	NOUN
ejpam-6670	231	11	for	for	ADP
ejpam-6670	231	12	stability	stability	NOUN
ejpam-6670	231	13	of	of	ADP
ejpam-6670	231	14	the	the	DET
ejpam-6670	231	15	model	model	NOUN
ejpam-6670	231	16	holds	hold	VERB
ejpam-6670	231	17	.	.	PUNCT
ejpam-6670	232	1	hence	hence	ADV
ejpam-6670	232	2	,	,	PUNCT
ejpam-6670	232	3	the	the	DET
ejpam-6670	232	4	proposed	propose	VERB
ejpam-6670	232	5	model	model	NOUN
ejpam-6670	232	6	is	be	AUX
ejpam-6670	232	7	locally	locally	ADV
ejpam-6670	232	8	asymptotically	asymptotically	ADV
ejpam-6670	232	9	stable	stable	ADJ
ejpam-6670	232	10	at	at	ADP
ejpam-6670	232	11	the	the	DET
ejpam-6670	232	12	f0	f0	PROPN
ejpam-6670	232	13	,	,	PUNCT
ejpam-6670	232	14	if	if	SCONJ
ejpam-6670	232	15	r0	r0	NOUN
ejpam-6670	232	16	<	<	X
ejpam-6670	232	17	1	1	NUM
ejpam-6670	232	18	.	.	PUNCT
ejpam-6670	233	1	following	follow	VERB
ejpam-6670	233	2	the	the	DET
ejpam-6670	233	3	same	same	ADJ
ejpam-6670	233	4	procedure	procedure	NOUN
ejpam-6670	233	5	,	,	PUNCT
ejpam-6670	233	6	we	we	PRON
ejpam-6670	233	7	can	can	AUX
ejpam-6670	233	8	discuss	discuss	VERB
ejpam-6670	233	9	the	the	DET
ejpam-6670	233	10	local	local	ADJ
ejpam-6670	233	11	dynamics	dynamic	NOUN
ejpam-6670	233	12	of	of	ADP
ejpam-6670	233	13	the	the	DET
ejpam-6670	233	14	model	model	NOUN
ejpam-6670	233	15	at	at	ADP
ejpam-6670	233	16	the	the	DET
ejpam-6670	233	17	endemic	endemic	ADJ
ejpam-6670	233	18	state	state	NOUN
ejpam-6670	233	19	by	by	ADP
ejpam-6670	233	20	the	the	DET
ejpam-6670	233	21	subsequent	subsequent	ADJ
ejpam-6670	233	22	theorem	theorem	NOUN
ejpam-6670	233	23	.	.	PUNCT
ejpam-6670	234	1	t.	t.	PROPN
ejpam-6670	234	2	khan	khan	PROPN
ejpam-6670	234	3	et	et	PROPN
ejpam-6670	234	4	al	al	PROPN
ejpam-6670	234	5	.	.	PUNCT
ejpam-6670	234	6	/	/	SYM
ejpam-6670	234	7	eur	eur	PROPN
ejpam-6670	234	8	.	.	PUNCT
ejpam-6670	235	1	j.	j.	PROPN
ejpam-6670	235	2	pure	pure	PROPN
ejpam-6670	235	3	appl	appl	PROPN
ejpam-6670	235	4	.	.	PROPN
ejpam-6670	235	5	math	math	PROPN
ejpam-6670	235	6	,	,	PUNCT
ejpam-6670	235	7	18	18	NUM
ejpam-6670	235	8	(	(	PUNCT
ejpam-6670	235	9	3	3	NUM
ejpam-6670	235	10	)	)	PUNCT
ejpam-6670	235	11	(	(	PUNCT
ejpam-6670	235	12	2025	2025	NUM
ejpam-6670	235	13	)	)	PUNCT
ejpam-6670	235	14	,	,	PUNCT
ejpam-6670	235	15	6670	6670	NUM
ejpam-6670	235	16	11	11	NUM
ejpam-6670	235	17	of	of	ADP
ejpam-6670	235	18	22	22	NUM
ejpam-6670	235	19	theorem	theorem	NOUN
ejpam-6670	235	20	2	2	NUM
ejpam-6670	235	21	.	.	X
ejpam-6670	236	1	for	for	ADP
ejpam-6670	236	2	r0	r0	PROPN
ejpam-6670	236	3	>	>	X
ejpam-6670	236	4	1	1	NUM
ejpam-6670	236	5	,	,	PUNCT
ejpam-6670	236	6	the	the	DET
ejpam-6670	236	7	model	model	NOUN
ejpam-6670	236	8	is	be	AUX
ejpam-6670	236	9	stable	stable	ADJ
ejpam-6670	236	10	locally	locally	ADV
ejpam-6670	236	11	asymptotically	asymptotically	ADV
ejpam-6670	236	12	if	if	SCONJ
ejpam-6670	236	13	the	the	DET
ejpam-6670	236	14	following	follow	VERB
ejpam-6670	236	15	conditions	condition	NOUN
ejpam-6670	236	16	hold	hold	VERB
ejpam-6670	236	17	:	:	PUNCT
ejpam-6670	236	18	1	1	X
ejpam-6670	236	19	.	.	X
ejpam-6670	236	20	βαs∗	βαs∗	NOUN
ejpam-6670	236	21	<	<	X
ejpam-6670	237	1	(	(	PUNCT
ejpam-6670	237	2	1	1	NUM
ejpam-6670	237	3	+	+	NUM
ejpam-6670	237	4	βc∗)(µ0	βc∗)(µ0	PUNCT
ejpam-6670	238	1	+	+	CCONJ
ejpam-6670	238	2	θ)(µ0	θ)(µ0	X
ejpam-6670	238	3	+	+	X
ejpam-6670	238	4	λ1	λ1	ADJ
ejpam-6670	238	5	)	)	PUNCT
ejpam-6670	238	6	.	.	PUNCT
ejpam-6670	239	1	2	2	X
ejpam-6670	239	2	.	.	X
ejpam-6670	239	3	βαs∗	βαs∗	NOUN
ejpam-6670	239	4	<	<	X
ejpam-6670	240	1	(	(	PUNCT
ejpam-6670	240	2	µ0	µ0	NOUN
ejpam-6670	240	3	+	+	X
ejpam-6670	240	4	θ){αa∗	θ){αa∗	NUM
ejpam-6670	241	1	+	+	CCONJ
ejpam-6670	241	2	λαc∗	λαc∗	ADP
ejpam-6670	241	3	+	+	CCONJ
ejpam-6670	241	4	(	(	PUNCT
ejpam-6670	241	5	1	1	NUM
ejpam-6670	241	6	+	+	NUM
ejpam-6670	241	7	βc∗)(µ0	βc∗)(µ0	PUNCT
ejpam-6670	242	1	+	+	CCONJ
ejpam-6670	242	2	λ3	λ3	PROPN
ejpam-6670	242	3	)	)	PUNCT
ejpam-6670	242	4	}	}	PUNCT
ejpam-6670	242	5	.	.	PUNCT
ejpam-6670	243	1	proof	proof	NOUN
ejpam-6670	243	2	.	.	PUNCT
ejpam-6670	244	1	the	the	DET
ejpam-6670	244	2	characteristic	characteristic	ADJ
ejpam-6670	244	3	equation	equation	NOUN
ejpam-6670	244	4	of	of	ADP
ejpam-6670	244	5	the	the	DET
ejpam-6670	244	6	matrix	matrix	NOUN
ejpam-6670	244	7	j	j	NOUN
ejpam-6670	244	8	at	at	ADP
ejpam-6670	244	9	endemic	endemic	ADJ
ejpam-6670	244	10	equilibrium	equilibrium	NOUN
ejpam-6670	244	11	f1	f1	NOUN
ejpam-6670	244	12	looks	look	VERB
ejpam-6670	244	13	like	like	ADP
ejpam-6670	244	14	λ5	λ5	NOUN
ejpam-6670	244	15	+	+	CCONJ
ejpam-6670	244	16	d1λ	d1λ	PROPN
ejpam-6670	244	17	4	4	NUM
ejpam-6670	244	18	+	+	CCONJ
ejpam-6670	244	19	d2λ	d2λ	PROPN
ejpam-6670	244	20	3	3	NUM
ejpam-6670	244	21	+	+	CCONJ
ejpam-6670	244	22	d3λ	d3λ	PROPN
ejpam-6670	244	23	2	2	NUM
ejpam-6670	244	24	+	+	NUM
ejpam-6670	244	25	d4λ+	d4λ+	NOUN
ejpam-6670	244	26	d5	d5	NOUN
ejpam-6670	244	27	=	=	SYM
ejpam-6670	244	28	0	0	NUM
ejpam-6670	244	29	,	,	PUNCT
ejpam-6670	244	30	(	(	PUNCT
ejpam-6670	244	31	20	20	NUM
ejpam-6670	244	32	)	)	PUNCT
ejpam-6670	244	33	where	where	SCONJ
ejpam-6670	244	34	d1	d1	PROPN
ejpam-6670	244	35	=	=	NOUN
ejpam-6670	244	36	x11	x11	PROPN
ejpam-6670	244	37	+	+	NOUN
ejpam-6670	244	38	x22	x22	NUM
ejpam-6670	244	39	+	+	CCONJ
ejpam-6670	244	40	x33	x33	NOUN
ejpam-6670	244	41	+	+	CCONJ
ejpam-6670	244	42	x44	x44	PROPN
ejpam-6670	244	43	+	+	PROPN
ejpam-6670	244	44	x55	x55	PROPN
ejpam-6670	244	45	,	,	PUNCT
ejpam-6670	244	46	d2	d2	PROPN
ejpam-6670	244	47	=	=	SYM
ejpam-6670	244	48	{	{	PUNCT
ejpam-6670	244	49	µ0	µ0	NOUN
ejpam-6670	244	50	+	+	NOUN
ejpam-6670	244	51	π}x21	π}x21	NOUN
ejpam-6670	245	1	+	+	CCONJ
ejpam-6670	245	2	µ0{µ0	µ0{µ0	NOUN
ejpam-6670	245	3	+	+	ADJ
ejpam-6670	245	4	λ3	λ3	PROPN
ejpam-6670	245	5	+	+	PROPN
ejpam-6670	245	6	π}+	π}+	PROPN
ejpam-6670	245	7	x11x22	x11x22	PROPN
ejpam-6670	246	1	+	+	CCONJ
ejpam-6670	246	2	x11x33	x11x33	VERB
ejpam-6670	246	3	+	+	CCONJ
ejpam-6670	246	4	x11x44	x11x44	NOUN
ejpam-6670	246	5	+	+	NUM
ejpam-6670	246	6	x22x33	x22x33	VERB
ejpam-6670	246	7	+	+	CCONJ
ejpam-6670	246	8	x22x44	x22x44	PROPN
ejpam-6670	247	1	+	+	CCONJ
ejpam-6670	247	2	x22x55	x22x55	PROPN
ejpam-6670	248	1	+	+	CCONJ
ejpam-6670	248	2	x33x44	x33x44	PROPN
ejpam-6670	249	1	+	+	CCONJ
ejpam-6670	249	2	x33x55	x33x55	X
ejpam-6670	249	3	+	+	CCONJ
ejpam-6670	249	4	x44x55	x44x55	PROPN
ejpam-6670	250	1	−	−	PROPN
ejpam-6670	250	2	θx22	θx22	PROPN
ejpam-6670	250	3	,	,	PUNCT
ejpam-6670	250	4	d3	d3	PROPN
ejpam-6670	250	5	=	=	SYM
ejpam-6670	250	6	θqλ1x24	θqλ1x24	NOUN
ejpam-6670	250	7	+	+	X
ejpam-6670	250	8	x11{x22x33	x11{x22x33	NUM
ejpam-6670	250	9	−	−	NOUN
ejpam-6670	250	10	θx23}+	θx23}+	ADP
ejpam-6670	250	11	x44{x11x22	x44{x11x22	PROPN
ejpam-6670	250	12	−	−	PROPN
ejpam-6670	250	13	θx23}+	θx23}+	ADV
ejpam-6670	250	14	x11x33x44	x11x33x44	PROPN
ejpam-6670	251	1	+	+	CCONJ
ejpam-6670	251	2	θx21x13	θx21x13	PROPN
ejpam-6670	251	3	+	+	CCONJ
ejpam-6670	251	4	{	{	PUNCT
ejpam-6670	251	5	x22	x22	PROPN
ejpam-6670	251	6	+	+	CCONJ
ejpam-6670	251	7	x33	x33	NUM
ejpam-6670	251	8	+	+	X
ejpam-6670	251	9	x44}{(µ0	x44}{(µ0	PUNCT
ejpam-6670	252	1	+	+	X
ejpam-6670	252	2	π	π	X
ejpam-6670	252	3	)	)	PUNCT
ejpam-6670	253	1	+	+	CCONJ
ejpam-6670	253	2	µ0(µ0	µ0(µ0	ADJ
ejpam-6670	253	3	+	+	NOUN
ejpam-6670	253	4	π	π	X
ejpam-6670	254	1	+	+	CCONJ
ejpam-6670	255	1	λ3)}+	λ3)}+	PROPN
ejpam-6670	255	2	x55{x22x33	x55{x22x33	NUM
ejpam-6670	255	3	−	−	PUNCT
ejpam-6670	255	4	θx23	θx23	PROPN
ejpam-6670	255	5	}	}	PUNCT
ejpam-6670	255	6	+	+	CCONJ
ejpam-6670	255	7	x22x44x55	x22x44x55	PROPN
ejpam-6670	256	1	+	+	CCONJ
ejpam-6670	256	2	x33x44x55	x33x44x55	PROPN
ejpam-6670	257	1	+	+	NUM
ejpam-6670	257	2	x22x33x44	x22x33x44	PROPN
ejpam-6670	258	1	+	+	NUM
ejpam-6670	258	2	x21	x21	PROPN
ejpam-6670	258	3	,	,	PUNCT
ejpam-6670	258	4	d4	d4	PROPN
ejpam-6670	258	5	=	=	PROPN
ejpam-6670	258	6	θx21x31x55	θx21x31x55	X
ejpam-6670	258	7	+	+	CCONJ
ejpam-6670	258	8	{	{	PUNCT
ejpam-6670	258	9	(	(	PUNCT
ejpam-6670	258	10	µ0	µ0	NOUN
ejpam-6670	258	11	+	+	X
ejpam-6670	258	12	π)x21	π)x21	PROPN
ejpam-6670	259	1	+	+	CCONJ
ejpam-6670	259	2	µ0(µ0	µ0(µ0	ADJ
ejpam-6670	259	3	+	+	NOUN
ejpam-6670	259	4	π	π	X
ejpam-6670	259	5	+	+	CCONJ
ejpam-6670	260	1	λ3)}{x22x33	λ3)}{x22x33	ADJ
ejpam-6670	260	2	+	+	NUM
ejpam-6670	260	3	x22x44	x22x44	PROPN
ejpam-6670	260	4	+	+	CCONJ
ejpam-6670	260	5	x33x44	x33x44	PROPN
ejpam-6670	260	6	}	}	PUNCT
ejpam-6670	261	1	+	+	CCONJ
ejpam-6670	261	2	θqλ1(x55	θqλ1(x55	NUM
ejpam-6670	261	3	−	−	PROPN
ejpam-6670	261	4	x14	x14	PROPN
ejpam-6670	261	5	)	)	PUNCT
ejpam-6670	262	1	+	+	PROPN
ejpam-6670	263	1	x44x55(x22x33	x44x55(x22x33	ADJ
ejpam-6670	263	2	−	−	X
ejpam-6670	264	1	θx23	θx23	PROPN
ejpam-6670	264	2	)	)	PUNCT
ejpam-6670	265	1	+	+	NUM
ejpam-6670	266	1	x11x44{x22x33	x11x44{x22x33	NUM
ejpam-6670	266	2	−	−	NOUN
ejpam-6670	266	3	θx23}+	θx23}+	ADP
ejpam-6670	266	4	θx21x13x44	θx21x13x44	PROPN
ejpam-6670	266	5	+	+	CCONJ
ejpam-6670	266	6	θπλ3x23	θπλ3x23	ADJ
ejpam-6670	266	7	+	+	CCONJ
ejpam-6670	266	8	θqλ1x11x24	θqλ1x11x24	NOUN
ejpam-6670	266	9	−	−	PROPN
ejpam-6670	266	10	θx11x23x55	θx11x23x55	PROPN
ejpam-6670	266	11	,	,	PUNCT
ejpam-6670	266	12	d5	d5	NOUN
ejpam-6670	266	13	=	=	NOUN
ejpam-6670	266	14	{	{	PUNCT
ejpam-6670	266	15	(	(	PUNCT
ejpam-6670	266	16	µ0	µ0	NOUN
ejpam-6670	266	17	+	+	X
ejpam-6670	266	18	π)x21	π)x21	PROPN
ejpam-6670	267	1	+	+	CCONJ
ejpam-6670	267	2	µ0(µ0	µ0(µ0	ADJ
ejpam-6670	267	3	+	+	NOUN
ejpam-6670	267	4	π	π	X
ejpam-6670	267	5	+	+	CCONJ
ejpam-6670	267	6	λ3)}x22x33x44	λ3)}x22x33x44	PROPN
ejpam-6670	267	7	+	+	PROPN
ejpam-6670	267	8	θλ3πx23x44θλ3πqλ1x24	θλ3πx23x44θλ3πqλ1x24	PROPN
ejpam-6670	267	9	+	+	CCONJ
ejpam-6670	267	10	θqλ1x55{x11x24	θqλ1x55{x11x24	PROPN
ejpam-6670	268	1	−	−	PROPN
ejpam-6670	268	2	x14}+	x14}+	PROPN
ejpam-6670	268	3	θx13x24x44x55	θx13x24x44x55	PROPN
ejpam-6670	268	4	−	−	PROPN
ejpam-6670	268	5	θx11x23x44x55	θx11x23x44x55	PROPN
ejpam-6670	268	6	.	.	PUNCT
ejpam-6670	269	1	all	all	PRON
ejpam-6670	269	2	di	di	X
ejpam-6670	269	3	>	>	X
ejpam-6670	269	4	0	0	NUM
ejpam-6670	269	5	,	,	PUNCT
ejpam-6670	269	6	for	for	ADP
ejpam-6670	269	7	i	i	PROPN
ejpam-6670	269	8	=	=	SYM
ejpam-6670	269	9	1	1	NUM
ejpam-6670	269	10	,	,	PUNCT
ejpam-6670	269	11	2	2	NUM
ejpam-6670	269	12	,	,	PUNCT
ejpam-6670	269	13	3	3	NUM
ejpam-6670	269	14	,	,	PUNCT
ejpam-6670	269	15	4	4	NUM
ejpam-6670	269	16	,	,	PUNCT
ejpam-6670	269	17	5	5	NUM
ejpam-6670	269	18	and	and	CCONJ
ejpam-6670	269	19	h0	h0	NOUN
ejpam-6670	269	20	:	:	PUNCT
ejpam-6670	269	21	{	{	PUNCT
ejpam-6670	269	22	r0	r0	NOUN
ejpam-6670	269	23	>	>	X
ejpam-6670	269	24	1	1	NUM
ejpam-6670	269	25	,	,	PUNCT
ejpam-6670	269	26	d1d2d3	d1d2d3	VERB
ejpam-6670	269	27	>	>	X
ejpam-6670	269	28	d23	d23	PROPN
ejpam-6670	269	29	+	+	CCONJ
ejpam-6670	269	30	d21d4	d21d4	PROPN
ejpam-6670	269	31	,	,	PUNCT
ejpam-6670	269	32	(	(	PUNCT
ejpam-6670	269	33	d1d4	d1d4	NOUN
ejpam-6670	269	34	−	−	PROPN
ejpam-6670	269	35	d5	d5	NOUN
ejpam-6670	269	36	)	)	PUNCT
ejpam-6670	269	37	(	(	PUNCT
ejpam-6670	269	38	d1d2d3	d1d2d3	NOUN
ejpam-6670	269	39	−	−	PROPN
ejpam-6670	269	40	d23	d23	NOUN
ejpam-6670	269	41	−	−	PROPN
ejpam-6670	269	42	d21d4	d21d4	PROPN
ejpam-6670	269	43	)	)	PUNCT
ejpam-6670	269	44	>	>	X
ejpam-6670	269	45	d5	d5	NOUN
ejpam-6670	269	46	(	(	PUNCT
ejpam-6670	269	47	d1d2	d1d2	X
ejpam-6670	269	48	−	−	PROPN
ejpam-6670	269	49	d23	d23	NOUN
ejpam-6670	269	50	)	)	PUNCT
ejpam-6670	269	51	2	2	PROPN
ejpam-6670	270	1	+	+	CCONJ
ejpam-6670	270	2	x1x	x1x	PROPN
ejpam-6670	270	3	2	2	NUM
ejpam-6670	270	4	5	5	NUM
ejpam-6670	270	5	}	}	PUNCT
ejpam-6670	270	6	,	,	PUNCT
ejpam-6670	270	7	holds	hold	VERB
ejpam-6670	270	8	implies	imply	VERB
ejpam-6670	270	9	that	that	SCONJ
ejpam-6670	270	10	h0	h0	NOUN
ejpam-6670	270	11	is	be	AUX
ejpam-6670	270	12	satisfied	satisfied	ADJ
ejpam-6670	270	13	if	if	SCONJ
ejpam-6670	270	14	conditions	condition	NOUN
ejpam-6670	270	15	1	1	NUM
ejpam-6670	270	16	and	and	CCONJ
ejpam-6670	270	17	2	2	NUM
ejpam-6670	270	18	hold	hold	NOUN
ejpam-6670	270	19	.	.	PUNCT
ejpam-6670	271	1	thus	thus	ADV
ejpam-6670	271	2	,	,	PUNCT
ejpam-6670	271	3	it	it	PRON
ejpam-6670	271	4	ensures	ensure	VERB
ejpam-6670	271	5	that	that	SCONJ
ejpam-6670	271	6	the	the	DET
ejpam-6670	271	7	routh	routh	PROPN
ejpam-6670	271	8	-	-	PUNCT
ejpam-6670	271	9	hurwitz	hurwitz	PROPN
ejpam-6670	271	10	stability	stability	NOUN
ejpam-6670	271	11	criteria	criterion	NOUN
ejpam-6670	271	12	are	be	AUX
ejpam-6670	271	13	satisfied	satisfied	ADJ
ejpam-6670	271	14	,	,	PUNCT
ejpam-6670	271	15	and	and	CCONJ
ejpam-6670	271	16	we	we	PRON
ejpam-6670	271	17	conclude	conclude	VERB
ejpam-6670	271	18	that	that	SCONJ
ejpam-6670	271	19	the	the	DET
ejpam-6670	271	20	endemic	endemic	ADJ
ejpam-6670	271	21	state	state	NOUN
ejpam-6670	271	22	f1	f1	NOUN
ejpam-6670	271	23	is	be	AUX
ejpam-6670	271	24	locally	locally	ADV
ejpam-6670	271	25	asymptotically	asymptotically	ADV
ejpam-6670	271	26	stable	stable	ADJ
ejpam-6670	271	27	.	.	PUNCT
ejpam-6670	272	1	upon	upon	SCONJ
ejpam-6670	272	2	establishing	establish	VERB
ejpam-6670	272	3	the	the	DET
ejpam-6670	272	4	analytical	analytical	ADJ
ejpam-6670	272	5	results	result	NOUN
ejpam-6670	272	6	,	,	PUNCT
ejpam-6670	272	7	we	we	PRON
ejpam-6670	272	8	now	now	ADV
ejpam-6670	272	9	proceed	proceed	VERB
ejpam-6670	272	10	to	to	PART
ejpam-6670	272	11	numerically	numerically	ADV
ejpam-6670	272	12	simulate	simulate	VERB
ejpam-6670	272	13	the	the	DET
ejpam-6670	272	14	model	model	NOUN
ejpam-6670	272	15	in	in	ADP
ejpam-6670	272	16	order	order	NOUN
ejpam-6670	272	17	to	to	PART
ejpam-6670	272	18	validate	validate	VERB
ejpam-6670	272	19	our	our	PRON
ejpam-6670	272	20	theoretical	theoretical	ADJ
ejpam-6670	272	21	findings	finding	NOUN
ejpam-6670	272	22	,	,	PUNCT
ejpam-6670	272	23	as	as	SCONJ
ejpam-6670	272	24	detailed	detailed	ADJ
ejpam-6670	272	25	in	in	ADP
ejpam-6670	272	26	the	the	DET
ejpam-6670	272	27	following	follow	VERB
ejpam-6670	272	28	section	section	NOUN
ejpam-6670	272	29	.	.	PUNCT
ejpam-6670	273	1	3	3	X
ejpam-6670	273	2	.	.	X
ejpam-6670	273	3	numerical	numerical	PROPN
ejpam-6670	273	4	simulation	simulation	PROPN
ejpam-6670	273	5	in	in	ADP
ejpam-6670	273	6	this	this	DET
ejpam-6670	273	7	section	section	NOUN
ejpam-6670	273	8	,	,	PUNCT
ejpam-6670	273	9	we	we	PRON
ejpam-6670	273	10	carry	carry	VERB
ejpam-6670	273	11	out	out	ADP
ejpam-6670	273	12	numerical	numerical	ADJ
ejpam-6670	273	13	experiments	experiment	NOUN
ejpam-6670	273	14	to	to	PART
ejpam-6670	273	15	validate	validate	VERB
ejpam-6670	273	16	the	the	DET
ejpam-6670	273	17	analytical	analytical	ADJ
ejpam-6670	273	18	results	result	NOUN
ejpam-6670	273	19	and	and	CCONJ
ejpam-6670	273	20	demonstrate	demonstrate	VERB
ejpam-6670	273	21	the	the	DET
ejpam-6670	273	22	robustness	robustness	NOUN
ejpam-6670	273	23	of	of	ADP
ejpam-6670	273	24	the	the	DET
ejpam-6670	273	25	proposed	propose	VERB
ejpam-6670	273	26	hybrid	hybrid	NOUN
ejpam-6670	273	27	approach	approach	NOUN
ejpam-6670	273	28	.	.	PUNCT
ejpam-6670	274	1	we	we	PRON
ejpam-6670	274	2	begin	begin	VERB
ejpam-6670	274	3	by	by	ADP
ejpam-6670	274	4	discretizing	discretize	VERB
ejpam-6670	274	5	the	the	DET
ejpam-6670	274	6	model	model	NOUN
ejpam-6670	274	7	using	use	VERB
ejpam-6670	274	8	the	the	DET
ejpam-6670	274	9	nonstandard	nonstandard	ADJ
ejpam-6670	274	10	finite	finite	ADJ
ejpam-6670	274	11	difference	difference	NOUN
ejpam-6670	274	12	(	(	PUNCT
ejpam-6670	274	13	nsfd	nsfd	ADJ
ejpam-6670	274	14	)	)	PUNCT
ejpam-6670	274	15	scheme	scheme	NOUN
ejpam-6670	274	16	,	,	PUNCT
ejpam-6670	274	17	followed	follow	VERB
ejpam-6670	274	18	by	by	ADP
ejpam-6670	274	19	a	a	DET
ejpam-6670	274	20	summary	summary	NOUN
ejpam-6670	274	21	of	of	ADP
ejpam-6670	274	22	the	the	DET
ejpam-6670	274	23	architecture	architecture	NOUN
ejpam-6670	274	24	of	of	ADP
ejpam-6670	274	25	the	the	DET
ejpam-6670	274	26	proposed	propose	VERB
ejpam-6670	274	27	feed	feed	NOUN
ejpam-6670	274	28	-	-	PUNCT
ejpam-6670	274	29	forward	forward	NOUN
ejpam-6670	274	30	neural	neural	ADJ
ejpam-6670	274	31	network	network	NOUN
ejpam-6670	274	32	(	(	PUNCT
ejpam-6670	274	33	ffnn	ffnn	NOUN
ejpam-6670	274	34	)	)	PUNCT
ejpam-6670	274	35	.	.	PUNCT
ejpam-6670	275	1	t.	t.	PROPN
ejpam-6670	275	2	khan	khan	PROPN
ejpam-6670	275	3	et	et	PROPN
ejpam-6670	275	4	al	al	PROPN
ejpam-6670	275	5	.	.	PUNCT
ejpam-6670	275	6	/	/	SYM
ejpam-6670	275	7	eur	eur	PROPN
ejpam-6670	275	8	.	.	PUNCT
ejpam-6670	276	1	j.	j.	PROPN
ejpam-6670	276	2	pure	pure	PROPN
ejpam-6670	276	3	appl	appl	PROPN
ejpam-6670	276	4	.	.	PROPN
ejpam-6670	276	5	math	math	PROPN
ejpam-6670	276	6	,	,	PUNCT
ejpam-6670	276	7	18	18	NUM
ejpam-6670	276	8	(	(	PUNCT
ejpam-6670	276	9	3	3	NUM
ejpam-6670	276	10	)	)	PUNCT
ejpam-6670	276	11	(	(	PUNCT
ejpam-6670	276	12	2025	2025	NUM
ejpam-6670	276	13	)	)	PUNCT
ejpam-6670	276	14	,	,	PUNCT
ejpam-6670	276	15	6670	6670	NUM
ejpam-6670	276	16	12	12	NUM
ejpam-6670	276	17	of	of	ADP
ejpam-6670	276	18	22	22	NUM
ejpam-6670	276	19	3.1	3.1	NUM
ejpam-6670	276	20	.	.	PUNCT
ejpam-6670	277	1	non	non	ADJ
ejpam-6670	277	2	-	-	ADJ
ejpam-6670	277	3	standard	standard	ADJ
ejpam-6670	277	4	finite	finite	ADJ
ejpam-6670	277	5	difference	difference	NOUN
ejpam-6670	277	6	scheme	scheme	NOUN
ejpam-6670	277	7	and	and	CCONJ
ejpam-6670	277	8	the	the	DET
ejpam-6670	277	9	architecture	architecture	NOUN
ejpam-6670	277	10	of	of	ADP
ejpam-6670	277	11	the	the	DET
ejpam-6670	277	12	neural	neural	ADJ
ejpam-6670	277	13	network	network	NOUN
ejpam-6670	277	14	in	in	ADP
ejpam-6670	277	15	this	this	DET
ejpam-6670	277	16	section	section	NOUN
ejpam-6670	277	17	,	,	PUNCT
ejpam-6670	277	18	we	we	PRON
ejpam-6670	277	19	present	present	VERB
ejpam-6670	277	20	the	the	DET
ejpam-6670	277	21	model	model	NOUN
ejpam-6670	277	22	discretization	discretization	NOUN
ejpam-6670	277	23	with	with	ADP
ejpam-6670	277	24	the	the	DET
ejpam-6670	277	25	aid	aid	NOUN
ejpam-6670	277	26	of	of	ADP
ejpam-6670	277	27	nsfd	nsfd	NOUN
ejpam-6670	277	28	and	and	CCONJ
ejpam-6670	277	29	provide	provide	VERB
ejpam-6670	277	30	the	the	DET
ejpam-6670	277	31	architecture	architecture	NOUN
ejpam-6670	277	32	of	of	ADP
ejpam-6670	277	33	the	the	DET
ejpam-6670	277	34	neural	neural	ADJ
ejpam-6670	277	35	network	network	NOUN
ejpam-6670	277	36	that	that	PRON
ejpam-6670	277	37	will	will	AUX
ejpam-6670	277	38	be	be	AUX
ejpam-6670	277	39	used	use	VERB
ejpam-6670	277	40	for	for	ADP
ejpam-6670	277	41	the	the	DET
ejpam-6670	277	42	learning	learning	NOUN
ejpam-6670	277	43	process	process	NOUN
ejpam-6670	277	44	.	.	PUNCT
ejpam-6670	278	1	it	it	PRON
ejpam-6670	278	2	is	be	AUX
ejpam-6670	278	3	obvious	obvious	ADJ
ejpam-6670	278	4	that	that	SCONJ
ejpam-6670	278	5	the	the	DET
ejpam-6670	278	6	proposed	propose	VERB
ejpam-6670	278	7	model	model	NOUN
ejpam-6670	278	8	has	have	VERB
ejpam-6670	278	9	six	six	NUM
ejpam-6670	278	10	state	state	NOUN
ejpam-6670	278	11	variables	variable	NOUN
ejpam-6670	278	12	i.e.	i.e.	X
ejpam-6670	278	13	s(t	s(t	PROPN
ejpam-6670	278	14	)	)	PUNCT
ejpam-6670	278	15	,	,	PUNCT
ejpam-6670	278	16	l(t	l(t	PROPN
ejpam-6670	278	17	)	)	PUNCT
ejpam-6670	278	18	,	,	PUNCT
ejpam-6670	278	19	a(t	a(t	NOUN
ejpam-6670	278	20	)	)	PUNCT
ejpam-6670	278	21	,	,	PUNCT
ejpam-6670	278	22	c(t	c(t	PROPN
ejpam-6670	278	23	)	)	PUNCT
ejpam-6670	278	24	,	,	PUNCT
ejpam-6670	278	25	r(t	r(t	NOUN
ejpam-6670	278	26	)	)	PUNCT
ejpam-6670	278	27	,	,	PUNCT
ejpam-6670	278	28	and	and	CCONJ
ejpam-6670	278	29	v(t	v(t	NOUN
ejpam-6670	278	30	)	)	PUNCT
ejpam-6670	278	31	,	,	PUNCT
ejpam-6670	278	32	and	and	CCONJ
ejpam-6670	278	33	g	g	PROPN
ejpam-6670	278	34	,	,	PUNCT
ejpam-6670	278	35	η	η	PROPN
ejpam-6670	278	36	,	,	PUNCT
ejpam-6670	278	37	π	π	PROPN
ejpam-6670	278	38	,	,	PUNCT
ejpam-6670	278	39	α	α	PROPN
ejpam-6670	278	40	,	,	PUNCT
ejpam-6670	278	41	β	β	X
ejpam-6670	278	42	,	,	PUNCT
ejpam-6670	278	43	λ	λ	PROPN
ejpam-6670	278	44	,	,	PUNCT
ejpam-6670	278	45	λ1	λ1	ADJ
ejpam-6670	278	46	,	,	PUNCT
ejpam-6670	278	47	λ2	λ2	PROPN
ejpam-6670	278	48	,	,	PUNCT
ejpam-6670	278	49	λ3	λ3	PROPN
ejpam-6670	278	50	,	,	PUNCT
ejpam-6670	278	51	µ0	µ0	PROPN
ejpam-6670	278	52	,	,	PUNCT
ejpam-6670	278	53	θ	θ	PROPN
ejpam-6670	278	54	,	,	PUNCT
ejpam-6670	278	55	q	q	PUNCT
ejpam-6670	278	56	and	and	CCONJ
ejpam-6670	278	57	µ1	µ1	PROPN
ejpam-6670	278	58	are	be	AUX
ejpam-6670	278	59	the	the	DET
ejpam-6670	278	60	parameters	parameter	NOUN
ejpam-6670	278	61	.	.	PUNCT
ejpam-6670	279	1	to	to	PART
ejpam-6670	279	2	approximate	approximate	VERB
ejpam-6670	279	3	the	the	DET
ejpam-6670	279	4	model	model	NOUN
ejpam-6670	279	5	,	,	PUNCT
ejpam-6670	279	6	we	we	PRON
ejpam-6670	279	7	use	use	VERB
ejpam-6670	279	8	a	a	DET
ejpam-6670	279	9	non	non	ADJ
ejpam-6670	279	10	-	-	ADJ
ejpam-6670	279	11	standard	standard	ADJ
ejpam-6670	279	12	finite	finite	ADJ
ejpam-6670	279	13	difference	difference	NOUN
ejpam-6670	279	14	scheme	scheme	NOUN
ejpam-6670	279	15	given	give	VERB
ejpam-6670	279	16	by	by	ADP
ejpam-6670	279	17	yn+1	yn+1	PROPN
ejpam-6670	279	18	=	=	SYM
ejpam-6670	279	19	yn	yn	PROPN
ejpam-6670	279	20	+	+	NOUN
ejpam-6670	279	21	∆t.h(yn	∆t.h(yn	NOUN
ejpam-6670	279	22	)	)	PUNCT
ejpam-6670	279	23	,	,	PUNCT
ejpam-6670	279	24	(	(	PUNCT
ejpam-6670	279	25	21	21	NUM
ejpam-6670	279	26	)	)	PUNCT
ejpam-6670	279	27	for	for	ADP
ejpam-6670	279	28	every	every	DET
ejpam-6670	279	29	y	y	PROPN
ejpam-6670	279	30	∈	∈	PROPN
ejpam-6670	279	31	{	{	PUNCT
ejpam-6670	279	32	s	s	PROPN
ejpam-6670	279	33	,	,	PUNCT
ejpam-6670	279	34	l	l	NOUN
ejpam-6670	279	35	,	,	PUNCT
ejpam-6670	279	36	a	a	PRON
ejpam-6670	279	37	,	,	PUNCT
ejpam-6670	279	38	c	c	NOUN
ejpam-6670	279	39	,	,	PUNCT
ejpam-6670	279	40	r	r	NOUN
ejpam-6670	279	41	,	,	PUNCT
ejpam-6670	279	42	v	v	NOUN
ejpam-6670	279	43	}	}	PUNCT
ejpam-6670	279	44	,	,	PUNCT
ejpam-6670	279	45	and	and	CCONJ
ejpam-6670	279	46	h(yn	h(yn	NOUN
ejpam-6670	279	47	)	)	PUNCT
ejpam-6670	279	48	represents	represent	VERB
ejpam-6670	279	49	the	the	DET
ejpam-6670	279	50	right	right	ADJ
ejpam-6670	279	51	side	side	NOUN
ejpam-6670	279	52	of	of	ADP
ejpam-6670	279	53	proposed	propose	VERB
ejpam-6670	279	54	model	model	NOUN
ejpam-6670	279	55	.	.	PUNCT
ejpam-6670	280	1	let	let	VERB
ejpam-6670	280	2	∆t	∆t	PROPN
ejpam-6670	280	3	is	be	AUX
ejpam-6670	280	4	the	the	DET
ejpam-6670	280	5	discrete	discrete	ADJ
ejpam-6670	280	6	time	time	NOUN
ejpam-6670	280	7	step	step	NOUN
ejpam-6670	280	8	represent	represent	VERB
ejpam-6670	280	9	the	the	DET
ejpam-6670	280	10	approximation	approximation	NOUN
ejpam-6670	280	11	at	at	ADP
ejpam-6670	280	12	t	t	PROPN
ejpam-6670	280	13	=	=	SYM
ejpam-6670	280	14	n∆t	n∆t	PROPN
ejpam-6670	280	15	,	,	PUNCT
ejpam-6670	280	16	then	then	ADV
ejpam-6670	280	17	sn	sn	PROPN
ejpam-6670	280	18	≈	≈	PROPN
ejpam-6670	280	19	s(n∆t	s(n∆t	PROPN
ejpam-6670	280	20	)	)	PUNCT
ejpam-6670	280	21	,	,	PUNCT
ejpam-6670	280	22	ln	ln	PROPN
ejpam-6670	280	23	≈	≈	PROPN
ejpam-6670	280	24	l(n∆t	l(n∆t	PROPN
ejpam-6670	280	25	)	)	PUNCT
ejpam-6670	280	26	,	,	PUNCT
ejpam-6670	280	27	an	an	DET
ejpam-6670	280	28	≈	≈	PROPN
ejpam-6670	280	29	a(n∆t	a(n∆t	PROPN
ejpam-6670	280	30	)	)	PUNCT
ejpam-6670	280	31	,	,	PUNCT
ejpam-6670	280	32	cn	cn	PROPN
ejpam-6670	280	33	≈	≈	PROPN
ejpam-6670	280	34	c(n∆t	c(n∆t	PROPN
ejpam-6670	280	35	)	)	PUNCT
ejpam-6670	280	36	,	,	PUNCT
ejpam-6670	280	37	rn	rn	PROPN
ejpam-6670	280	38	≈	≈	PROPN
ejpam-6670	280	39	r(n∆t	r(n∆t	PROPN
ejpam-6670	280	40	)	)	PUNCT
ejpam-6670	280	41	,	,	PUNCT
ejpam-6670	280	42	vn	vn	PROPN
ejpam-6670	280	43	≈	≈	PROPN
ejpam-6670	280	44	v(n∆t	v(n∆t	PROPN
ejpam-6670	280	45	)	)	PUNCT
ejpam-6670	280	46	.	.	PUNCT
ejpam-6670	281	1	using	use	VERB
ejpam-6670	281	2	nsfd	nsfd	ADJ
ejpam-6670	281	3	discretization	discretization	NOUN
ejpam-6670	281	4	,	,	PUNCT
ejpam-6670	281	5	the	the	DET
ejpam-6670	281	6	proposed	propose	VERB
ejpam-6670	281	7	model	model	NOUN
ejpam-6670	281	8	takes	take	VERB
ejpam-6670	281	9	the	the	DET
ejpam-6670	281	10	following	follow	VERB
ejpam-6670	281	11	form	form	NOUN
ejpam-6670	281	12	sn+1	sn+1	X
ejpam-6670	282	1	=	=	SYM
ejpam-6670	282	2	sn	sn	PROPN
ejpam-6670	282	3	+	+	PROPN
ejpam-6670	282	4	∆t	∆t	PROPN
ejpam-6670	282	5	{	{	PUNCT
ejpam-6670	282	6	gη(1−	gη(1−	NOUN
ejpam-6670	282	7	φcn	φcn	NOUN
ejpam-6670	282	8	+	+	CCONJ
ejpam-6670	282	9	πvn)−	πvn)−	NOUN
ejpam-6670	282	10	αsnan	αsnan	VERB
ejpam-6670	282	11	1	1	NUM
ejpam-6670	282	12	+	+	CCONJ
ejpam-6670	282	13	βcn	βcn	PRON
ejpam-6670	282	14	−	−	PROPN
ejpam-6670	282	15	λαsncn	λαsncn	NOUN
ejpam-6670	282	16	1	1	NUM
ejpam-6670	282	17	+	+	CCONJ
ejpam-6670	282	18	βcn	βcn	NOUN
ejpam-6670	282	19	−	−	PROPN
ejpam-6670	282	20	(	(	PUNCT
ejpam-6670	282	21	µ0	µ0	NOUN
ejpam-6670	282	22	+	+	X
ejpam-6670	282	23	λ3)sn	λ3)sn	NOUN
ejpam-6670	282	24	}	}	PUNCT
ejpam-6670	282	25	,	,	PUNCT
ejpam-6670	282	26	ln+1	ln+1	PROPN
ejpam-6670	282	27	=	=	PUNCT
ejpam-6670	282	28	ln	ln	PROPN
ejpam-6670	282	29	+	+	NOUN
ejpam-6670	282	30	∆t	∆t	ADJ
ejpam-6670	282	31	{	{	PUNCT
ejpam-6670	282	32	αsnan	αsnan	NOUN
ejpam-6670	282	33	1	1	NUM
ejpam-6670	282	34	+	+	CCONJ
ejpam-6670	282	35	βcn	βcn	NOUN
ejpam-6670	282	36	+	+	CCONJ
ejpam-6670	282	37	λαsncn	λαsncn	NOUN
ejpam-6670	282	38	1	1	NUM
ejpam-6670	283	1	+	+	CCONJ
ejpam-6670	283	2	βcn	βcn	NOUN
ejpam-6670	283	3	−	−	PROPN
ejpam-6670	283	4	(	(	PUNCT
ejpam-6670	283	5	µ0	µ0	NOUN
ejpam-6670	283	6	+	+	X
ejpam-6670	283	7	θ)ln	θ)ln	PROPN
ejpam-6670	283	8	}	}	PUNCT
ejpam-6670	283	9	,	,	PUNCT
ejpam-6670	283	10	an+1	an+1	NOUN
ejpam-6670	283	11	=	=	SYM
ejpam-6670	283	12	an	an	DET
ejpam-6670	283	13	+	+	NOUN
ejpam-6670	283	14	∆t	∆t	NOUN
ejpam-6670	283	15	{	{	PUNCT
ejpam-6670	283	16	θln	θln	NOUN
ejpam-6670	283	17	−	−	PROPN
ejpam-6670	283	18	(	(	PUNCT
ejpam-6670	283	19	µ0	µ0	NOUN
ejpam-6670	283	20	+	+	X
ejpam-6670	283	21	λ1)an	λ1)an	PROPN
ejpam-6670	283	22	}	}	PUNCT
ejpam-6670	283	23	,	,	PUNCT
ejpam-6670	283	24	cn+1	cn+1	X
ejpam-6670	283	25	=	=	SYM
ejpam-6670	283	26	cn	cn	PROPN
ejpam-6670	284	1	+	+	NOUN
ejpam-6670	284	2	∆t	∆t	PROPN
ejpam-6670	284	3	{	{	PUNCT
ejpam-6670	284	4	gηφcn	gηφcn	ADV
ejpam-6670	285	1	+	+	ADP
ejpam-6670	285	2	qλ1an	qλ1an	ADJ
ejpam-6670	285	3	−	−	PROPN
ejpam-6670	285	4	(	(	PUNCT
ejpam-6670	285	5	µ0	µ0	NOUN
ejpam-6670	285	6	+	+	CCONJ
ejpam-6670	285	7	µ1	µ1	PROPN
ejpam-6670	285	8	+	+	X
ejpam-6670	285	9	λ2)cn	λ2)cn	PROPN
ejpam-6670	285	10	}	}	PUNCT
ejpam-6670	285	11	,	,	PUNCT
ejpam-6670	285	12	rn+1	rn+1	PROPN
ejpam-6670	285	13	=	=	SYM
ejpam-6670	285	14	rn	rn	PROPN
ejpam-6670	285	15	+	+	PROPN
ejpam-6670	285	16	∆t	∆t	PROPN
ejpam-6670	285	17	{	{	PUNCT
ejpam-6670	285	18	λ2cn	λ2cn	X
ejpam-6670	285	19	+	+	PUNCT
ejpam-6670	285	20	(	(	PUNCT
ejpam-6670	285	21	1−	1−	NUM
ejpam-6670	285	22	q)λ1an	q)λ1an	NOUN
ejpam-6670	285	23	−	−	NOUN
ejpam-6670	285	24	µ0rn	µ0rn	NOUN
ejpam-6670	285	25	}	}	PUNCT
ejpam-6670	285	26	,	,	PUNCT
ejpam-6670	285	27	vn+1	vn+1	PROPN
ejpam-6670	285	28	=	=	SYM
ejpam-6670	285	29	vn	vn	PROPN
ejpam-6670	286	1	+	+	PROPN
ejpam-6670	286	2	∆t	∆t	PROPN
ejpam-6670	286	3	{	{	PUNCT
ejpam-6670	286	4	g(1−	g(1−	PROPN
ejpam-6670	286	5	η	η	PROPN
ejpam-6670	286	6	)	)	PUNCT
ejpam-6670	286	7	+	+	CCONJ
ejpam-6670	286	8	λ3sn	λ3sn	PUNCT
ejpam-6670	286	9	−	−	PROPN
ejpam-6670	286	10	(	(	PUNCT
ejpam-6670	286	11	µ0	µ0	NOUN
ejpam-6670	286	12	+	+	X
ejpam-6670	286	13	π)vn	π)vn	PROPN
ejpam-6670	286	14	}	}	PUNCT
ejpam-6670	286	15	.	.	PUNCT
ejpam-6670	287	1	(	(	PUNCT
ejpam-6670	287	2	22	22	X
ejpam-6670	287	3	)	)	PUNCT
ejpam-6670	287	4	using	use	VERB
ejpam-6670	287	5	the	the	DET
ejpam-6670	287	6	hypothetical	hypothetical	ADJ
ejpam-6670	287	7	values	value	NOUN
ejpam-6670	287	8	of	of	ADP
ejpam-6670	287	9	the	the	DET
ejpam-6670	287	10	model	model	NOUN
ejpam-6670	287	11	parameters	parameter	NOUN
ejpam-6670	287	12	as	as	ADP
ejpam-6670	287	13	:	:	PUNCT
ejpam-6670	287	14	g	g	NOUN
ejpam-6670	287	15	=	=	SYM
ejpam-6670	287	16	0.7	0.7	NUM
ejpam-6670	287	17	,	,	PUNCT
ejpam-6670	287	18	η	η	NOUN
ejpam-6670	287	19	=	=	SYM
ejpam-6670	287	20	0.85	0.85	NUM
ejpam-6670	287	21	,	,	PUNCT
ejpam-6670	287	22	φ	φ	NOUN
ejpam-6670	287	23	=	=	SYM
ejpam-6670	287	24	0.05	0.05	NUM
ejpam-6670	287	25	,	,	PUNCT
ejpam-6670	287	26	π	π	NOUN
ejpam-6670	287	27	=	=	SYM
ejpam-6670	287	28	0.08	0.08	NUM
ejpam-6670	287	29	,	,	PUNCT
ejpam-6670	287	30	α	α	NOUN
ejpam-6670	287	31	=	=	SYM
ejpam-6670	287	32	0.4	0.4	NUM
ejpam-6670	287	33	,	,	PUNCT
ejpam-6670	287	34	β	β	X
ejpam-6670	287	35	=	=	PUNCT
ejpam-6670	287	36	0.15	0.15	NUM
ejpam-6670	287	37	,	,	PUNCT
ejpam-6670	287	38	λ	λ	X
ejpam-6670	287	39	=	=	NOUN
ejpam-6670	287	40	0.35	0.35	NUM
ejpam-6670	287	41	,	,	PUNCT
ejpam-6670	287	42	λ1	λ1	PROPN
ejpam-6670	287	43	=	=	SYM
ejpam-6670	287	44	0.12	0.12	NUM
ejpam-6670	287	45	,	,	PUNCT
ejpam-6670	287	46	λ2	λ2	NOUN
ejpam-6670	287	47	=	=	SYM
ejpam-6670	287	48	0.06	0.06	NUM
ejpam-6670	287	49	,	,	PUNCT
ejpam-6670	287	50	λ3	λ3	PROPN
ejpam-6670	287	51	=	=	PROPN
ejpam-6670	287	52	0.03	0.03	NUM
ejpam-6670	287	53	,	,	PUNCT
ejpam-6670	287	54	µ0	µ0	NOUN
ejpam-6670	287	55	=	=	NOUN
ejpam-6670	287	56	0.02	0.02	NUM
ejpam-6670	287	57	,	,	PUNCT
ejpam-6670	287	58	θ	θ	X
ejpam-6670	287	59	=	=	PUNCT
ejpam-6670	287	60	0.15	0.15	NUM
ejpam-6670	287	61	,	,	PUNCT
ejpam-6670	287	62	q	q	X
ejpam-6670	287	63	=	=	NOUN
ejpam-6670	287	64	0.75	0.75	NUM
ejpam-6670	287	65	,	,	PUNCT
ejpam-6670	287	66	µ1	µ1	PROPN
ejpam-6670	287	67	=	=	SYM
ejpam-6670	287	68	0.025	0.025	NUM
ejpam-6670	287	69	.	.	PUNCT
ejpam-6670	287	70	to	to	PART
ejpam-6670	287	71	approximate	approximate	VERB
ejpam-6670	287	72	the	the	DET
ejpam-6670	287	73	proposed	propose	VERB
ejpam-6670	287	74	system	system	NOUN
ejpam-6670	287	75	numerically	numerically	ADV
ejpam-6670	287	76	,	,	PUNCT
ejpam-6670	287	77	we	we	PRON
ejpam-6670	287	78	then	then	ADV
ejpam-6670	287	79	use	use	VERB
ejpam-6670	287	80	a	a	DET
ejpam-6670	287	81	standard	standard	ADJ
ejpam-6670	287	82	feed	feed	NOUN
ejpam-6670	287	83	-	-	PUNCT
ejpam-6670	287	84	forward	forward	NOUN
ejpam-6670	287	85	neural	neural	ADJ
ejpam-6670	287	86	network	network	NOUN
ejpam-6670	287	87	(	(	PUNCT
ejpam-6670	287	88	ffnn	ffnn	NOUN
ejpam-6670	287	89	)	)	PUNCT
ejpam-6670	287	90	with	with	ADP
ejpam-6670	287	91	one	one	NUM
ejpam-6670	287	92	hidden	hide	VERB
ejpam-6670	287	93	layer	layer	NOUN
ejpam-6670	287	94	consisting	consist	VERB
ejpam-6670	287	95	of	of	ADP
ejpam-6670	287	96	input	input	NOUN
ejpam-6670	287	97	layer	layer	NOUN
ejpam-6670	287	98	t	t	X
ejpam-6670	287	99	∈	∈	PROPN
ejpam-6670	287	100	r	r	NOUN
ejpam-6670	287	101	,	,	PUNCT
ejpam-6670	287	102	number	number	NOUN
ejpam-6670	287	103	of	of	ADP
ejpam-6670	287	104	neurons	neuron	NOUN
ejpam-6670	287	105	nh	nh	PROPN
ejpam-6670	288	1	=	=	SYM
ejpam-6670	288	2	10	10	NUM
ejpam-6670	288	3	,	,	PUNCT
ejpam-6670	288	4	and	and	CCONJ
ejpam-6670	288	5	activation	activation	NOUN
ejpam-6670	288	6	function	function	NOUN
ejpam-6670	288	7	(	(	PUNCT
ejpam-6670	288	8	relu	relu	NOUN
ejpam-6670	288	9	)	)	PUNCT
ejpam-6670	288	10	σ	σ	PROPN
ejpam-6670	288	11	(	(	PUNCT
ejpam-6670	288	12	.	.	PUNCT
ejpam-6670	288	13	)	)	PUNCT
ejpam-6670	288	14	.	.	PUNCT
ejpam-6670	289	1	let	let	VERB
ejpam-6670	289	2	w	w	NOUN
ejpam-6670	289	3	(	(	PUNCT
ejpam-6670	289	4	1	1	X
ejpam-6670	289	5	)	)	PUNCT
ejpam-6670	289	6	∈	∈	PROPN
ejpam-6670	289	7	rnh×1	rnh×1	PROPN
ejpam-6670	289	8	represent	represent	VERB
ejpam-6670	289	9	the	the	DET
ejpam-6670	289	10	weights	weight	NOUN
ejpam-6670	289	11	from	from	ADP
ejpam-6670	289	12	input	input	NOUN
ejpam-6670	289	13	to	to	ADP
ejpam-6670	289	14	the	the	DET
ejpam-6670	289	15	hidden	hide	VERB
ejpam-6670	289	16	layer	layer	NOUN
ejpam-6670	289	17	and	and	CCONJ
ejpam-6670	289	18	b(1	b(1	PROPN
ejpam-6670	289	19	)	)	PUNCT
ejpam-6670	289	20	∈	∈	PROPN
ejpam-6670	289	21	rnh	rnh	NOUN
ejpam-6670	289	22	is	be	AUX
ejpam-6670	289	23	the	the	DET
ejpam-6670	289	24	biases	bias	NOUN
ejpam-6670	289	25	in	in	ADP
ejpam-6670	289	26	the	the	DET
ejpam-6670	289	27	hidden	hide	VERB
ejpam-6670	289	28	layer	layer	NOUN
ejpam-6670	289	29	,	,	PUNCT
ejpam-6670	289	30	then	then	ADV
ejpam-6670	289	31	the	the	DET
ejpam-6670	289	32	hidden	hidden	ADJ
ejpam-6670	289	33	layer	layer	NOUN
ejpam-6670	289	34	out	out	ADP
ejpam-6670	289	35	is	be	AUX
ejpam-6670	289	36	given	give	VERB
ejpam-6670	289	37	by	by	ADP
ejpam-6670	289	38	h	h	NOUN
ejpam-6670	289	39	=	=	SYM
ejpam-6670	289	40	σ	σ	PROPN
ejpam-6670	289	41	(	(	PUNCT
ejpam-6670	289	42	w	w	PROPN
ejpam-6670	289	43	1t+	1t+	NUM
ejpam-6670	289	44	b(1	b(1	PROPN
ejpam-6670	289	45	)	)	PUNCT
ejpam-6670	289	46	)	)	PUNCT
ejpam-6670	290	1	∈	∈	NOUN
ejpam-6670	290	2	rnh	rnh	NOUN
ejpam-6670	290	3	.	.	PUNCT
ejpam-6670	291	1	(	(	PUNCT
ejpam-6670	291	2	23	23	NUM
ejpam-6670	291	3	)	)	PUNCT
ejpam-6670	291	4	likewise	likewise	ADV
ejpam-6670	291	5	,	,	PUNCT
ejpam-6670	291	6	the	the	DET
ejpam-6670	291	7	output	output	NOUN
ejpam-6670	291	8	layer	layer	NOUN
ejpam-6670	291	9	is	be	AUX
ejpam-6670	291	10	a	a	DET
ejpam-6670	291	11	six	six	NUM
ejpam-6670	291	12	-	-	PUNCT
ejpam-6670	291	13	dimensional	dimensional	ADJ
ejpam-6670	291	14	vector	vector	NOUN
ejpam-6670	291	15	(	(	PUNCT
ejpam-6670	291	16	s	s	PROPN
ejpam-6670	291	17	,	,	PUNCT
ejpam-6670	291	18	l	l	NOUN
ejpam-6670	291	19	,	,	PUNCT
ejpam-6670	291	20	a	a	PRON
ejpam-6670	291	21	,	,	PUNCT
ejpam-6670	291	22	c	c	NOUN
ejpam-6670	291	23	,	,	PUNCT
ejpam-6670	291	24	r	r	NOUN
ejpam-6670	291	25	,	,	PUNCT
ejpam-6670	291	26	v	v	NOUN
ejpam-6670	291	27	)	)	PUNCT
ejpam-6670	291	28	.	.	PUNCT
ejpam-6670	292	1	let	let	VERB
ejpam-6670	292	2	w	w	NOUN
ejpam-6670	292	3	(	(	PUNCT
ejpam-6670	292	4	2	2	NUM
ejpam-6670	292	5	)	)	PUNCT
ejpam-6670	292	6	∈	∈	PROPN
ejpam-6670	292	7	r6×nh	r6×nh	NOUN
ejpam-6670	292	8	represent	represent	VERB
ejpam-6670	292	9	the	the	DET
ejpam-6670	292	10	weights	weight	NOUN
ejpam-6670	292	11	from	from	ADP
ejpam-6670	292	12	hidden	hide	VERB
ejpam-6670	292	13	to	to	ADP
ejpam-6670	292	14	output	output	NOUN
ejpam-6670	292	15	layer	layer	NOUN
ejpam-6670	292	16	,	,	PUNCT
ejpam-6670	292	17	and	and	CCONJ
ejpam-6670	292	18	b2	b2	NOUN
ejpam-6670	292	19	∈	∈	PROPN
ejpam-6670	292	20	r6	r6	NOUN
ejpam-6670	292	21	represent	represent	VERB
ejpam-6670	292	22	the	the	DET
ejpam-6670	292	23	biases	bias	NOUN
ejpam-6670	292	24	in	in	ADP
ejpam-6670	292	25	output	output	NOUN
ejpam-6670	292	26	layer	layer	NOUN
ejpam-6670	292	27	.	.	PUNCT
ejpam-6670	293	1	then	then	ADV
ejpam-6670	293	2	the	the	DET
ejpam-6670	293	3	predicted	predict	VERB
ejpam-6670	293	4	output	output	NOUN
ejpam-6670	293	5	becomes	become	VERB
ejpam-6670	293	6	ŷ(t	ŷ(t	PRON
ejpam-6670	293	7	)	)	PUNCT
ejpam-6670	294	1	=	=	SYM
ejpam-6670	294	2	w	w	PROPN
ejpam-6670	294	3	(	(	PUNCT
ejpam-6670	294	4	2)h+	2)h+	PROPN
ejpam-6670	294	5	b(2	b(2	PROPN
ejpam-6670	294	6	)	)	PUNCT
ejpam-6670	294	7	∈	∈	PROPN
ejpam-6670	294	8	r6	r6	NOUN
ejpam-6670	294	9	.	.	PUNCT
ejpam-6670	295	1	(	(	PUNCT
ejpam-6670	295	2	24	24	NUM
ejpam-6670	295	3	)	)	PUNCT
ejpam-6670	295	4	combining	combine	VERB
ejpam-6670	295	5	all	all	PRON
ejpam-6670	295	6	,	,	PUNCT
ejpam-6670	295	7	we	we	PRON
ejpam-6670	295	8	get	get	VERB
ejpam-6670	295	9	the	the	DET
ejpam-6670	295	10	following	follow	VERB
ejpam-6670	295	11	expression	expression	NOUN
ejpam-6670	295	12	ŷ(t	ŷ(t	NOUN
ejpam-6670	295	13	)	)	PUNCT
ejpam-6670	296	1	=	=	SYM
ejpam-6670	296	2	w	w	X
ejpam-6670	297	1	(	(	PUNCT
ejpam-6670	298	1	2)hσ	2)hσ	PROPN
ejpam-6670	298	2	(	(	PUNCT
ejpam-6670	298	3	w	w	PROPN
ejpam-6670	298	4	(	(	PUNCT
ejpam-6670	298	5	1)t	1)t	PROPN
ejpam-6670	298	6	+	+	NUM
ejpam-6670	298	7	b(1	b(1	PROPN
ejpam-6670	298	8	)	)	PUNCT
ejpam-6670	298	9	)	)	PUNCT
ejpam-6670	298	10	+	+	CCONJ
ejpam-6670	299	1	b(2	b(2	NOUN
ejpam-6670	299	2	)	)	PUNCT
ejpam-6670	299	3	,	,	PUNCT
ejpam-6670	299	4	(	(	PUNCT
ejpam-6670	299	5	25	25	NUM
ejpam-6670	299	6	)	)	PUNCT
ejpam-6670	299	7	t.	t.	NOUN
ejpam-6670	299	8	khan	khan	PROPN
ejpam-6670	299	9	et	et	PROPN
ejpam-6670	299	10	al	al	PROPN
ejpam-6670	299	11	.	.	PUNCT
ejpam-6670	299	12	/	/	SYM
ejpam-6670	299	13	eur	eur	PROPN
ejpam-6670	299	14	.	.	PUNCT
ejpam-6670	300	1	j.	j.	PROPN
ejpam-6670	300	2	pure	pure	PROPN
ejpam-6670	300	3	appl	appl	PROPN
ejpam-6670	300	4	.	.	PROPN
ejpam-6670	300	5	math	math	PROPN
ejpam-6670	300	6	,	,	PUNCT
ejpam-6670	300	7	18	18	NUM
ejpam-6670	300	8	(	(	PUNCT
ejpam-6670	300	9	3	3	NUM
ejpam-6670	300	10	)	)	PUNCT
ejpam-6670	300	11	(	(	PUNCT
ejpam-6670	300	12	2025	2025	NUM
ejpam-6670	300	13	)	)	PUNCT
ejpam-6670	300	14	,	,	PUNCT
ejpam-6670	300	15	6670	6670	NUM
ejpam-6670	300	16	13	13	NUM
ejpam-6670	300	17	of	of	ADP
ejpam-6670	300	18	22	22	NUM
ejpam-6670	300	19	where	where	SCONJ
ejpam-6670	300	20	ŷ(t	ŷ(t	NOUN
ejpam-6670	300	21	)	)	PUNCT
ejpam-6670	300	22	=	=	PUNCT
ejpam-6670	300	23	[	[	PUNCT
ejpam-6670	300	24	ŝ(t	ŝ(t	NOUN
ejpam-6670	300	25	)	)	PUNCT
ejpam-6670	300	26	,	,	PUNCT
ejpam-6670	300	27	l̂(t	l̂(t	NOUN
ejpam-6670	300	28	)	)	PUNCT
ejpam-6670	300	29	,	,	PUNCT
ejpam-6670	300	30	â(t	â(t	NOUN
ejpam-6670	300	31	)	)	PUNCT
ejpam-6670	300	32	,	,	PUNCT
ejpam-6670	300	33	ĉ(t	ĉ(t	NOUN
ejpam-6670	300	34	)	)	PUNCT
ejpam-6670	300	35	,	,	PUNCT
ejpam-6670	300	36	r̂(t	r̂(t	NOUN
ejpam-6670	300	37	)	)	PUNCT
ejpam-6670	300	38	,	,	PUNCT
ejpam-6670	300	39	v̂(t	v̂(t	ADJ
ejpam-6670	300	40	)	)	PUNCT
ejpam-6670	300	41	]	]	X
ejpam-6670	300	42	t	t	PROPN
ejpam-6670	300	43	and	and	CCONJ
ejpam-6670	300	44	σ	σ	PROPN
ejpam-6670	300	45	(	(	PUNCT
ejpam-6670	300	46	.	.	PUNCT
ejpam-6670	300	47	)	)	PUNCT
ejpam-6670	300	48	is	be	AUX
ejpam-6670	300	49	the	the	DET
ejpam-6670	300	50	activation	activation	NOUN
ejpam-6670	300	51	function	function	NOUN
ejpam-6670	300	52	.	.	PUNCT
ejpam-6670	301	1	further	far	ADV
ejpam-6670	301	2	,	,	PUNCT
ejpam-6670	301	3	to	to	PART
ejpam-6670	301	4	minimize	minimize	VERB
ejpam-6670	301	5	the	the	DET
ejpam-6670	301	6	mean	mean	ADJ
ejpam-6670	301	7	squared	square	VERB
ejpam-6670	301	8	error	error	NOUN
ejpam-6670	301	9	(	(	PUNCT
ejpam-6670	301	10	mse	mse	NOUN
ejpam-6670	301	11	)	)	PUNCT
ejpam-6670	301	12	,	,	PUNCT
ejpam-6670	301	13	we	we	PRON
ejpam-6670	301	14	train	train	VERB
ejpam-6670	301	15	the	the	DET
ejpam-6670	301	16	network	network	NOUN
ejpam-6670	301	17	to	to	PART
ejpam-6670	301	18	minimize	minimize	VERB
ejpam-6670	301	19	the	the	DET
ejpam-6670	301	20	error	error	NOUN
ejpam-6670	301	21	between	between	ADP
ejpam-6670	301	22	the	the	DET
ejpam-6670	301	23	true	true	ADJ
ejpam-6670	301	24	and	and	CCONJ
ejpam-6670	301	25	predicted	predict	VERB
ejpam-6670	301	26	values	value	NOUN
ejpam-6670	301	27	over	over	ADP
ejpam-6670	301	28	the	the	DET
ejpam-6670	301	29	training	training	NOUN
ejpam-6670	301	30	set	set	NOUN
ejpam-6670	301	31	{	{	PUNCT
ejpam-6670	301	32	(	(	PUNCT
ejpam-6670	301	33	ti	ti	NOUN
ejpam-6670	301	34	,	,	PUNCT
ejpam-6670	301	35	yi)}ni=1	yi)}ni=1	PROPN
ejpam-6670	301	36	,	,	PUNCT
ejpam-6670	301	37	which	which	PRON
ejpam-6670	301	38	is	be	AUX
ejpam-6670	301	39	given	give	VERB
ejpam-6670	301	40	by	by	ADP
ejpam-6670	301	41	mse	mse	NOUN
ejpam-6670	301	42	=	=	SYM
ejpam-6670	301	43	1	1	NUM
ejpam-6670	301	44	6n	6n	NUM
ejpam-6670	301	45	n∑	n∑	PROPN
ejpam-6670	302	1	i=1	i=1	PROPN
ejpam-6670	302	2	∥yi	∥yi	PROPN
ejpam-6670	302	3	−	−	PROPN
ejpam-6670	302	4	ŷ(ti)∥2	ŷ(ti)∥2	PROPN
ejpam-6670	302	5	,	,	PUNCT
ejpam-6670	302	6	(	(	PUNCT
ejpam-6670	302	7	26	26	NUM
ejpam-6670	302	8	)	)	PUNCT
ejpam-6670	302	9	where	where	SCONJ
ejpam-6670	302	10	yi	yi	NOUN
ejpam-6670	303	1	=	=	PUNCT
ejpam-6670	304	1	[	[	X
ejpam-6670	304	2	s(ti	s(ti	PROPN
ejpam-6670	304	3	)	)	PUNCT
ejpam-6670	304	4	,	,	PUNCT
ejpam-6670	304	5	l(ti	l(ti	PROPN
ejpam-6670	304	6	)	)	PUNCT
ejpam-6670	304	7	,	,	PUNCT
ejpam-6670	304	8	a(ti	a(ti	NOUN
ejpam-6670	304	9	)	)	PUNCT
ejpam-6670	304	10	,	,	PUNCT
ejpam-6670	304	11	c(ti	c(ti	NOUN
ejpam-6670	304	12	)	)	PUNCT
ejpam-6670	304	13	,	,	PUNCT
ejpam-6670	304	14	r(ti	r(ti	PROPN
ejpam-6670	304	15	)	)	PUNCT
ejpam-6670	304	16	,	,	PUNCT
ejpam-6670	304	17	v(ti	v(ti	NOUN
ejpam-6670	304	18	)	)	PUNCT
ejpam-6670	304	19	]	]	PUNCT
ejpam-6670	305	1	t	t	PROPN
ejpam-6670	305	2	and	and	CCONJ
ejpam-6670	305	3	ŷ(ti	ŷ(ti	PROPN
ejpam-6670	305	4	)	)	PUNCT
ejpam-6670	305	5	is	be	AUX
ejpam-6670	305	6	the	the	DET
ejpam-6670	305	7	network	network	NOUN
ejpam-6670	305	8	output	output	NOUN
ejpam-6670	305	9	.	.	PUNCT
ejpam-6670	306	1	3.2	3.2	NUM
ejpam-6670	306	2	.	.	PUNCT
ejpam-6670	307	1	numerical	numerical	ADJ
ejpam-6670	307	2	experiment	experiment	NOUN
ejpam-6670	307	3	to	to	PART
ejpam-6670	307	4	perform	perform	VERB
ejpam-6670	307	5	the	the	DET
ejpam-6670	307	6	numerical	numerical	ADJ
ejpam-6670	307	7	experiment	experiment	NOUN
ejpam-6670	307	8	,	,	PUNCT
ejpam-6670	307	9	we	we	PRON
ejpam-6670	307	10	use	use	VERB
ejpam-6670	307	11	the	the	DET
ejpam-6670	307	12	discretized	discretized	ADJ
ejpam-6670	307	13	system	system	NOUN
ejpam-6670	307	14	(	(	PUNCT
ejpam-6670	307	15	22	22	NUM
ejpam-6670	307	16	)	)	PUNCT
ejpam-6670	307	17	to	to	PART
ejpam-6670	307	18	generate	generate	VERB
ejpam-6670	307	19	the	the	DET
ejpam-6670	307	20	data	datum	NOUN
ejpam-6670	307	21	for	for	ADP
ejpam-6670	307	22	the	the	DET
ejpam-6670	307	23	learning	learning	NOUN
ejpam-6670	307	24	process	process	NOUN
ejpam-6670	307	25	,	,	PUNCT
ejpam-6670	307	26	and	and	CCONJ
ejpam-6670	307	27	then	then	ADV
ejpam-6670	307	28	use	use	VERB
ejpam-6670	307	29	a	a	DET
ejpam-6670	307	30	feed	feed	NOUN
ejpam-6670	307	31	-	-	PUNCT
ejpam-6670	307	32	forward	forward	ADV
ejpam-6670	307	33	neural	neural	ADJ
ejpam-6670	307	34	network	network	NOUN
ejpam-6670	307	35	(	(	PUNCT
ejpam-6670	307	36	ffnn	ffnn	NOUN
ejpam-6670	307	37	)	)	PUNCT
ejpam-6670	307	38	to	to	PART
ejpam-6670	307	39	forecast	forecast	VERB
ejpam-6670	307	40	the	the	DET
ejpam-6670	307	41	dynamics	dynamic	NOUN
ejpam-6670	307	42	of	of	ADP
ejpam-6670	307	43	the	the	DET
ejpam-6670	307	44	proposed	propose	VERB
ejpam-6670	307	45	model	model	NOUN
ejpam-6670	307	46	in	in	ADP
ejpam-6670	307	47	the	the	DET
ejpam-6670	307	48	long	long	ADJ
ejpam-6670	307	49	run	run	NOUN
ejpam-6670	307	50	.	.	PUNCT
ejpam-6670	308	1	for	for	ADP
ejpam-6670	308	2	each	each	DET
ejpam-6670	308	3	state	state	NOUN
ejpam-6670	308	4	(	(	PUNCT
ejpam-6670	308	5	s	s	PROPN
ejpam-6670	308	6	,	,	PUNCT
ejpam-6670	308	7	l	l	NOUN
ejpam-6670	308	8	,	,	PUNCT
ejpam-6670	308	9	a	a	PRON
ejpam-6670	308	10	,	,	PUNCT
ejpam-6670	308	11	c	c	NOUN
ejpam-6670	308	12	,	,	PUNCT
ejpam-6670	308	13	r	r	NOUN
ejpam-6670	308	14	,	,	PUNCT
ejpam-6670	308	15	v	v	NOUN
ejpam-6670	308	16	)	)	PUNCT
ejpam-6670	308	17	of	of	ADP
ejpam-6670	308	18	the	the	DET
ejpam-6670	308	19	model	model	NOUN
ejpam-6670	308	20	,	,	PUNCT
ejpam-6670	308	21	we	we	PRON
ejpam-6670	308	22	present	present	VERB
ejpam-6670	308	23	the	the	DET
ejpam-6670	308	24	dynamics	dynamic	NOUN
ejpam-6670	308	25	as	as	SCONJ
ejpam-6670	308	26	reported	report	VERB
ejpam-6670	308	27	in	in	ADP
ejpam-6670	308	28	figures	figure	NOUN
ejpam-6670	308	29	2	2	NUM
ejpam-6670	308	30	to	to	PART
ejpam-6670	308	31	7	7	NUM
ejpam-6670	308	32	.	.	PUNCT
ejpam-6670	309	1	each	each	DET
ejpam-6670	309	2	figure	figure	NOUN
ejpam-6670	309	3	represents	represent	VERB
ejpam-6670	309	4	the	the	DET
ejpam-6670	309	5	dynamics	dynamic	NOUN
ejpam-6670	309	6	of	of	ADP
ejpam-6670	309	7	the	the	DET
ejpam-6670	309	8	compartmental	compartmental	ADJ
ejpam-6670	309	9	population	population	NOUN
ejpam-6670	309	10	of	of	ADP
ejpam-6670	309	11	the	the	DET
ejpam-6670	309	12	proposed	propose	VERB
ejpam-6670	309	13	model	model	NOUN
ejpam-6670	309	14	with	with	ADP
ejpam-6670	309	15	absolute	absolute	ADJ
ejpam-6670	309	16	error	error	NOUN
ejpam-6670	309	17	.	.	PUNCT
ejpam-6670	310	1	the	the	DET
ejpam-6670	310	2	blue	blue	ADJ
ejpam-6670	310	3	line	line	NOUN
ejpam-6670	310	4	demonstrates	demonstrate	VERB
ejpam-6670	310	5	the	the	DET
ejpam-6670	310	6	true	true	ADJ
ejpam-6670	310	7	values	value	NOUN
ejpam-6670	310	8	of	of	ADP
ejpam-6670	310	9	the	the	DET
ejpam-6670	310	10	model	model	NOUN
ejpam-6670	310	11	states	state	NOUN
ejpam-6670	310	12	over	over	ADP
ejpam-6670	310	13	time	time	NOUN
ejpam-6670	310	14	using	use	VERB
ejpam-6670	310	15	nsfd	nsfd	NOUN
ejpam-6670	310	16	,	,	PUNCT
ejpam-6670	310	17	and	and	CCONJ
ejpam-6670	310	18	the	the	DET
ejpam-6670	310	19	red	red	ADJ
ejpam-6670	310	20	dashed	dash	VERB
ejpam-6670	310	21	line	line	NOUN
ejpam-6670	310	22	shows	show	VERB
ejpam-6670	310	23	the	the	DET
ejpam-6670	310	24	predicted	predict	VERB
ejpam-6670	310	25	values	value	NOUN
ejpam-6670	310	26	of	of	ADP
ejpam-6670	310	27	the	the	DET
ejpam-6670	310	28	model	model	NOUN
ejpam-6670	310	29	states	state	NOUN
ejpam-6670	310	30	over	over	ADP
ejpam-6670	310	31	time	time	NOUN
ejpam-6670	310	32	using	use	VERB
ejpam-6670	310	33	ffnn	ffnn	NOUN
ejpam-6670	310	34	.	.	PUNCT
ejpam-6670	311	1	clearly	clearly	ADV
ejpam-6670	311	2	,	,	PUNCT
ejpam-6670	311	3	the	the	DET
ejpam-6670	311	4	results	result	NOUN
ejpam-6670	311	5	show	show	VERB
ejpam-6670	311	6	how	how	SCONJ
ejpam-6670	311	7	the	the	DET
ejpam-6670	311	8	true	true	ADJ
ejpam-6670	311	9	and	and	CCONJ
ejpam-6670	311	10	approximated	approximated	ADJ
ejpam-6670	311	11	values	value	NOUN
ejpam-6670	311	12	are	be	AUX
ejpam-6670	311	13	closer	close	ADJ
ejpam-6670	311	14	because	because	SCONJ
ejpam-6670	311	15	the	the	DET
ejpam-6670	311	16	blue	blue	ADJ
ejpam-6670	311	17	line	line	NOUN
ejpam-6670	311	18	follows	follow	VERB
ejpam-6670	311	19	the	the	DET
ejpam-6670	311	20	red	red	NOUN
ejpam-6670	311	21	-	-	PUNCT
ejpam-6670	311	22	dashed	dash	VERB
ejpam-6670	311	23	line	line	NOUN
ejpam-6670	311	24	,	,	PUNCT
ejpam-6670	311	25	which	which	PRON
ejpam-6670	311	26	guarantees	guarantee	VERB
ejpam-6670	311	27	a	a	DET
ejpam-6670	311	28	better	well	ADJ
ejpam-6670	311	29	prediction	prediction	NOUN
ejpam-6670	311	30	.	.	PUNCT
ejpam-6670	312	1	we	we	PRON
ejpam-6670	312	2	also	also	ADV
ejpam-6670	312	3	provided	provide	VERB
ejpam-6670	312	4	the	the	DET
ejpam-6670	312	5	associated	associated	ADJ
ejpam-6670	312	6	absolute	absolute	ADJ
ejpam-6670	312	7	error	error	NOUN
ejpam-6670	312	8	graphs	graph	NOUN
ejpam-6670	312	9	as	as	SCONJ
ejpam-6670	312	10	shown	show	VERB
ejpam-6670	312	11	by	by	ADP
ejpam-6670	312	12	a	a	DET
ejpam-6670	312	13	magenta	magenta	NOUN
ejpam-6670	312	14	line	line	NOUN
ejpam-6670	312	15	for	for	ADP
ejpam-6670	312	16	each	each	DET
ejpam-6670	312	17	state	state	NOUN
ejpam-6670	312	18	of	of	ADP
ejpam-6670	312	19	the	the	DET
ejpam-6670	312	20	model	model	NOUN
ejpam-6670	312	21	,	,	PUNCT
ejpam-6670	312	22	which	which	PRON
ejpam-6670	312	23	shows	show	VERB
ejpam-6670	312	24	the	the	DET
ejpam-6670	312	25	magnitude	magnitude	NOUN
ejpam-6670	312	26	of	of	ADP
ejpam-6670	312	27	error	error	NOUN
ejpam-6670	312	28	,	,	PUNCT
ejpam-6670	312	29	describing	describe	VERB
ejpam-6670	312	30	how	how	SCONJ
ejpam-6670	312	31	far	far	ADV
ejpam-6670	312	32	off	off	ADP
ejpam-6670	312	33	the	the	DET
ejpam-6670	312	34	prediction	prediction	NOUN
ejpam-6670	312	35	is	be	AUX
ejpam-6670	312	36	(	(	PUNCT
ejpam-6670	312	37	see	see	VERB
ejpam-6670	312	38	figures	figure	NOUN
ejpam-6670	312	39	2	2	NUM
ejpam-6670	312	40	to	to	ADP
ejpam-6670	312	41	7	7	NUM
ejpam-6670	312	42	)	)	PUNCT
ejpam-6670	312	43	.	.	PUNCT
ejpam-6670	313	1	to	to	PART
ejpam-6670	313	2	quantify	quantify	VERB
ejpam-6670	313	3	the	the	DET
ejpam-6670	313	4	overall	overall	ADJ
ejpam-6670	313	5	error	error	NOUN
ejpam-6670	313	6	prediction	prediction	NOUN
ejpam-6670	313	7	for	for	ADP
ejpam-6670	313	8	each	each	DET
ejpam-6670	313	9	model	model	NOUN
ejpam-6670	313	10	state	state	NOUN
ejpam-6670	313	11	variable	variable	NOUN
ejpam-6670	313	12	(	(	PUNCT
ejpam-6670	313	13	s	s	PROPN
ejpam-6670	313	14	,	,	PUNCT
ejpam-6670	313	15	l	l	NOUN
ejpam-6670	313	16	,	,	PUNCT
ejpam-6670	313	17	a	a	PRON
ejpam-6670	313	18	,	,	PUNCT
ejpam-6670	313	19	c	c	NOUN
ejpam-6670	313	20	,	,	PUNCT
ejpam-6670	313	21	r	r	NOUN
ejpam-6670	313	22	,	,	PUNCT
ejpam-6670	313	23	and	and	CCONJ
ejpam-6670	313	24	v	v	NOUN
ejpam-6670	313	25	)	)	PUNCT
ejpam-6670	313	26	,	,	PUNCT
ejpam-6670	313	27	a	a	DET
ejpam-6670	313	28	mean	mean	ADJ
ejpam-6670	313	29	square	square	ADJ
ejpam-6670	313	30	error	error	NOUN
ejpam-6670	313	31	(	(	PUNCT
ejpam-6670	313	32	mse	mse	NOUN
ejpam-6670	313	33	)	)	PUNCT
ejpam-6670	313	34	bar	bar	NOUN
ejpam-6670	313	35	graph	graph	NOUN
ejpam-6670	313	36	is	be	AUX
ejpam-6670	313	37	presented	present	VERB
ejpam-6670	313	38	as	as	SCONJ
ejpam-6670	313	39	shown	show	VERB
ejpam-6670	313	40	by	by	ADP
ejpam-6670	313	41	figure	figure	NOUN
ejpam-6670	313	42	8	8	NUM
ejpam-6670	313	43	.	.	PUNCT
ejpam-6670	314	1	this	this	PRON
ejpam-6670	314	2	provides	provide	VERB
ejpam-6670	314	3	the	the	DET
ejpam-6670	314	4	overall	overall	ADJ
ejpam-6670	314	5	performance	performance	NOUN
ejpam-6670	314	6	of	of	ADP
ejpam-6670	314	7	the	the	DET
ejpam-6670	314	8	proposed	propose	VERB
ejpam-6670	314	9	ffnn	ffnn	NOUN
ejpam-6670	314	10	on	on	ADP
ejpam-6670	314	11	each	each	DET
ejpam-6670	314	12	state	state	NOUN
ejpam-6670	314	13	variable	variable	NOUN
ejpam-6670	314	14	.	.	PUNCT
ejpam-6670	315	1	on	on	ADP
ejpam-6670	315	2	the	the	DET
ejpam-6670	315	3	x	x	NOUN
ejpam-6670	315	4	-	-	NOUN
ejpam-6670	315	5	axis	axis	ADJ
ejpam-6670	315	6	,	,	PUNCT
ejpam-6670	315	7	the	the	DET
ejpam-6670	315	8	indices	index	NOUN
ejpam-6670	315	9	of	of	ADP
ejpam-6670	315	10	the	the	DET
ejpam-6670	315	11	variables	variable	NOUN
ejpam-6670	315	12	s	s	PROPN
ejpam-6670	315	13	,	,	PUNCT
ejpam-6670	315	14	l	l	NOUN
ejpam-6670	315	15	,	,	PUNCT
ejpam-6670	315	16	a	a	PRON
ejpam-6670	315	17	,	,	PUNCT
ejpam-6670	315	18	c	c	NOUN
ejpam-6670	315	19	,	,	PUNCT
ejpam-6670	315	20	r	r	NOUN
ejpam-6670	315	21	,	,	PUNCT
ejpam-6670	315	22	and	and	CCONJ
ejpam-6670	315	23	v	v	NOUN
ejpam-6670	315	24	are	be	AUX
ejpam-6670	315	25	taken	take	VERB
ejpam-6670	315	26	,	,	PUNCT
ejpam-6670	315	27	while	while	SCONJ
ejpam-6670	315	28	on	on	ADP
ejpam-6670	315	29	the	the	DET
ejpam-6670	315	30	y	y	NOUN
ejpam-6670	315	31	-	-	PUNCT
ejpam-6670	315	32	axis	axis	NOUN
ejpam-6670	315	33	,	,	PUNCT
ejpam-6670	315	34	the	the	DET
ejpam-6670	315	35	mean	mean	ADJ
ejpam-6670	315	36	square	square	ADJ
ejpam-6670	315	37	error	error	NOUN
ejpam-6670	315	38	(	(	PUNCT
ejpam-6670	315	39	mse	mse	NOUN
ejpam-6670	315	40	)	)	PUNCT
ejpam-6670	315	41	values	value	NOUN
ejpam-6670	315	42	are	be	AUX
ejpam-6670	315	43	plotted	plot	VERB
ejpam-6670	315	44	,	,	PUNCT
ejpam-6670	315	45	which	which	PRON
ejpam-6670	315	46	clearly	clearly	ADV
ejpam-6670	315	47	shows	show	VERB
ejpam-6670	315	48	that	that	SCONJ
ejpam-6670	315	49	the	the	DET
ejpam-6670	315	50	low	low	ADJ
ejpam-6670	315	51	mse	mse	PROPN
ejpam-6670	315	52	guarantees	guarantee	VERB
ejpam-6670	315	53	better	well	ADJ
ejpam-6670	315	54	ffnn	ffnn	NOUN
ejpam-6670	315	55	performance	performance	NOUN
ejpam-6670	315	56	.	.	PUNCT
ejpam-6670	316	1	in	in	ADP
ejpam-6670	316	2	addition	addition	NOUN
ejpam-6670	316	3	,	,	PUNCT
ejpam-6670	316	4	the	the	DET
ejpam-6670	316	5	validation	validation	NOUN
ejpam-6670	316	6	checks	check	NOUN
ejpam-6670	316	7	,	,	PUNCT
ejpam-6670	316	8	damping	damp	VERB
ejpam-6670	316	9	factor	factor	NOUN
ejpam-6670	316	10	(	(	PUNCT
ejpam-6670	316	11	µ	µ	NOUN
ejpam-6670	316	12	)	)	PUNCT
ejpam-6670	316	13	,	,	PUNCT
ejpam-6670	316	14	and	and	CCONJ
ejpam-6670	316	15	gradient	gradient	ADJ
ejpam-6670	316	16	interpretation	interpretation	NOUN
ejpam-6670	316	17	are	be	AUX
ejpam-6670	316	18	provided	provide	VERB
ejpam-6670	316	19	as	as	SCONJ
ejpam-6670	316	20	shown	show	VERB
ejpam-6670	316	21	in	in	ADP
ejpam-6670	316	22	figure	figure	NOUN
ejpam-6670	316	23	9	9	NUM
ejpam-6670	316	24	.	.	PUNCT
ejpam-6670	317	1	more	more	ADV
ejpam-6670	317	2	precisely	precisely	ADV
ejpam-6670	317	3	,	,	PUNCT
ejpam-6670	317	4	this	this	PRON
ejpam-6670	317	5	demonstrates	demonstrate	VERB
ejpam-6670	317	6	the	the	DET
ejpam-6670	317	7	performance	performance	NOUN
ejpam-6670	317	8	of	of	ADP
ejpam-6670	317	9	the	the	DET
ejpam-6670	317	10	validation	validation	NOUN
ejpam-6670	317	11	set	set	VERB
ejpam-6670	317	12	against	against	ADP
ejpam-6670	317	13	epochs	epoch	NOUN
ejpam-6670	317	14	.	.	PUNCT
ejpam-6670	318	1	every	every	DET
ejpam-6670	318	2	time	time	NOUN
ejpam-6670	318	3	the	the	DET
ejpam-6670	318	4	check	check	NOUN
ejpam-6670	318	5	occurs	occur	VERB
ejpam-6670	318	6	,	,	PUNCT
ejpam-6670	318	7	if	if	SCONJ
ejpam-6670	318	8	the	the	DET
ejpam-6670	318	9	performance	performance	NOUN
ejpam-6670	318	10	fails	fail	VERB
ejpam-6670	318	11	to	to	PART
ejpam-6670	318	12	improve	improve	VERB
ejpam-6670	318	13	for	for	ADP
ejpam-6670	318	14	a	a	DET
ejpam-6670	318	15	specific	specific	ADJ
ejpam-6670	318	16	number	number	NOUN
ejpam-6670	318	17	of	of	ADP
ejpam-6670	318	18	epochs	epoch	NOUN
ejpam-6670	318	19	,	,	PUNCT
ejpam-6670	318	20	however	however	ADV
ejpam-6670	318	21	,	,	PUNCT
ejpam-6670	318	22	the	the	DET
ejpam-6670	318	23	training	training	NOUN
ejpam-6670	318	24	stops	stop	VERB
ejpam-6670	318	25	,	,	PUNCT
ejpam-6670	318	26	if	if	SCONJ
ejpam-6670	318	27	the	the	DET
ejpam-6670	318	28	performance	performance	NOUN
ejpam-6670	318	29	on	on	ADP
ejpam-6670	318	30	these	these	DET
ejpam-6670	318	31	validations	validation	NOUN
ejpam-6670	318	32	set	set	VERB
ejpam-6670	318	33	does	do	AUX
ejpam-6670	318	34	not	not	PART
ejpam-6670	318	35	improve	improve	VERB
ejpam-6670	318	36	over	over	ADP
ejpam-6670	318	37	these	these	DET
ejpam-6670	318	38	checks	check	NOUN
ejpam-6670	318	39	.	.	PUNCT
ejpam-6670	319	1	also	also	ADV
ejpam-6670	319	2	,	,	PUNCT
ejpam-6670	319	3	to	to	PART
ejpam-6670	319	4	show	show	VERB
ejpam-6670	319	5	the	the	DET
ejpam-6670	319	6	training	training	NOUN
ejpam-6670	319	7	efficiency	efficiency	NOUN
ejpam-6670	319	8	,	,	PUNCT
ejpam-6670	319	9	the	the	DET
ejpam-6670	319	10	damping	damp	VERB
ejpam-6670	319	11	factor	factor	NOUN
ejpam-6670	319	12	µ	µ	NOUN
ejpam-6670	319	13	is	be	AUX
ejpam-6670	319	14	visualized	visualize	VERB
ejpam-6670	319	15	as	as	SCONJ
ejpam-6670	319	16	shown	show	VERB
ejpam-6670	319	17	in	in	ADP
ejpam-6670	319	18	figure	figure	NOUN
ejpam-6670	319	19	9	9	NUM
ejpam-6670	319	20	.	.	PUNCT
ejpam-6670	319	21	similarly	similarly	ADV
ejpam-6670	319	22	,	,	PUNCT
ejpam-6670	319	23	to	to	PART
ejpam-6670	319	24	show	show	VERB
ejpam-6670	319	25	the	the	DET
ejpam-6670	319	26	performance	performance	NOUN
ejpam-6670	319	27	of	of	ADP
ejpam-6670	319	28	the	the	DET
ejpam-6670	319	29	gradient	gradient	NOUN
ejpam-6670	319	30	with	with	ADP
ejpam-6670	319	31	respect	respect	NOUN
ejpam-6670	319	32	to	to	ADP
ejpam-6670	319	33	the	the	DET
ejpam-6670	319	34	biases	bias	NOUN
ejpam-6670	319	35	and	and	CCONJ
ejpam-6670	319	36	weights	weight	NOUN
ejpam-6670	319	37	,	,	PUNCT
ejpam-6670	319	38	that	that	ADV
ejpam-6670	319	39	is	is	ADV
ejpam-6670	319	40	,	,	PUNCT
ejpam-6670	319	41	how	how	SCONJ
ejpam-6670	319	42	steep	steep	ADJ
ejpam-6670	319	43	the	the	DET
ejpam-6670	319	44	slope	slope	NOUN
ejpam-6670	319	45	is	be	AUX
ejpam-6670	319	46	at	at	ADP
ejpam-6670	319	47	the	the	DET
ejpam-6670	319	48	current	current	ADJ
ejpam-6670	319	49	point	point	NOUN
ejpam-6670	319	50	in	in	ADP
ejpam-6670	319	51	the	the	DET
ejpam-6670	319	52	error	error	NOUN
ejpam-6670	319	53	surface	surface	NOUN
ejpam-6670	319	54	,	,	PUNCT
ejpam-6670	319	55	we	we	PRON
ejpam-6670	319	56	interpret	interpret	VERB
ejpam-6670	319	57	the	the	DET
ejpam-6670	319	58	gradient	gradient	NOUN
ejpam-6670	319	59	.	.	PUNCT
ejpam-6670	320	1	in	in	ADP
ejpam-6670	320	2	the	the	DET
ejpam-6670	320	3	end	end	NOUN
ejpam-6670	320	4	,	,	PUNCT
ejpam-6670	320	5	the	the	DET
ejpam-6670	320	6	regression	regression	NOUN
ejpam-6670	320	7	plots	plot	NOUN
ejpam-6670	320	8	are	be	AUX
ejpam-6670	320	9	provided	provide	VERB
ejpam-6670	320	10	for	for	ADP
ejpam-6670	320	11	the	the	DET
ejpam-6670	320	12	ffnn	ffnn	NOUN
ejpam-6670	320	13	training	training	NOUN
ejpam-6670	320	14	to	to	PART
ejpam-6670	320	15	present	present	VERB
ejpam-6670	320	16	the	the	DET
ejpam-6670	320	17	correlation	correlation	NOUN
ejpam-6670	320	18	between	between	ADP
ejpam-6670	320	19	the	the	DET
ejpam-6670	320	20	actual	actual	ADJ
ejpam-6670	320	21	and	and	CCONJ
ejpam-6670	320	22	predicted	predict	VERB
ejpam-6670	320	23	values	value	NOUN
ejpam-6670	320	24	for	for	ADP
ejpam-6670	320	25	the	the	DET
ejpam-6670	320	26	data	datum	NOUN
ejpam-6670	320	27	set	set	VERB
ejpam-6670	320	28	and	and	CCONJ
ejpam-6670	320	29	r	r	NOUN
ejpam-6670	320	30	-	-	PUNCT
ejpam-6670	320	31	value	value	NOUN
ejpam-6670	320	32	as	as	SCONJ
ejpam-6670	320	33	illustrated	illustrate	VERB
ejpam-6670	320	34	in	in	ADP
ejpam-6670	320	35	figure	figure	NOUN
ejpam-6670	320	36	9	9	NUM
ejpam-6670	320	37	,	,	PUNCT
ejpam-6670	320	38	which	which	PRON
ejpam-6670	320	39	shows	show	VERB
ejpam-6670	320	40	the	the	DET
ejpam-6670	320	41	performance	performance	NOUN
ejpam-6670	320	42	of	of	ADP
ejpam-6670	320	43	the	the	DET
ejpam-6670	320	44	trained	train	VERB
ejpam-6670	320	45	ffnn	ffnn	NOUN
ejpam-6670	320	46	.	.	PUNCT
ejpam-6670	321	1	in	in	ADP
ejpam-6670	321	2	every	every	DET
ejpam-6670	321	3	subplot	subplot	NOUN
ejpam-6670	321	4	of	of	ADP
ejpam-6670	321	5	figure	figure	NOUN
ejpam-6670	321	6	10	10	NUM
ejpam-6670	321	7	,	,	PUNCT
ejpam-6670	321	8	representing	represent	VERB
ejpam-6670	321	9	perfect	perfect	ADJ
ejpam-6670	321	10	agreement	agreement	NOUN
ejpam-6670	321	11	.	.	PUNCT
ejpam-6670	322	1	the	the	DET
ejpam-6670	322	2	regression	regression	NOUN
ejpam-6670	322	3	lines	line	NOUN
ejpam-6670	322	4	fitted	fit	VERB
ejpam-6670	322	5	to	to	ADP
ejpam-6670	322	6	the	the	DET
ejpam-6670	322	7	data	datum	NOUN
ejpam-6670	322	8	lie	lie	VERB
ejpam-6670	322	9	almost	almost	ADV
ejpam-6670	322	10	exactly	exactly	ADV
ejpam-6670	322	11	on	on	ADP
ejpam-6670	322	12	the	the	DET
ejpam-6670	322	13	identity	identity	NOUN
ejpam-6670	322	14	line	line	NOUN
ejpam-6670	322	15	,	,	PUNCT
ejpam-6670	322	16	with	with	ADP
ejpam-6670	322	17	negligible	negligible	ADJ
ejpam-6670	322	18	intercepts	intercept	NOUN
ejpam-6670	322	19	,	,	PUNCT
ejpam-6670	322	20	suggesting	suggest	VERB
ejpam-6670	322	21	minimal	minimal	ADJ
ejpam-6670	322	22	prediction	prediction	NOUN
ejpam-6670	322	23	bias	bias	NOUN
ejpam-6670	322	24	.	.	PUNCT
ejpam-6670	323	1	moreover	moreover	ADV
ejpam-6670	323	2	,	,	PUNCT
ejpam-6670	323	3	the	the	DET
ejpam-6670	323	4	close	close	ADJ
ejpam-6670	323	5	alignment	alignment	NOUN
ejpam-6670	323	6	verifies	verifie	NOUN
ejpam-6670	323	7	that	that	SCONJ
ejpam-6670	323	8	the	the	DET
ejpam-6670	323	9	network	network	NOUN
ejpam-6670	323	10	has	have	AUX
ejpam-6670	323	11	learned	learn	VERB
ejpam-6670	323	12	well	well	INTJ
ejpam-6670	323	13	the	the	DET
ejpam-6670	323	14	underlying	underlie	VERB
ejpam-6670	323	15	mapping	mapping	NOUN
ejpam-6670	323	16	with	with	ADP
ejpam-6670	323	17	high	high	ADJ
ejpam-6670	323	18	precision	precision	NOUN
ejpam-6670	323	19	.	.	PUNCT
ejpam-6670	324	1	the	the	DET
ejpam-6670	324	2	results	result	NOUN
ejpam-6670	324	3	highlight	highlight	VERB
ejpam-6670	324	4	the	the	DET
ejpam-6670	324	5	accuracy	accuracy	NOUN
ejpam-6670	324	6	and	and	CCONJ
ejpam-6670	324	7	robustness	robustness	NOUN
ejpam-6670	324	8	of	of	ADP
ejpam-6670	324	9	the	the	DET
ejpam-6670	324	10	t.	t.	PROPN
ejpam-6670	324	11	khan	khan	PROPN
ejpam-6670	324	12	et	et	PROPN
ejpam-6670	324	13	al	al	PROPN
ejpam-6670	324	14	.	.	PUNCT
ejpam-6670	324	15	/	/	SYM
ejpam-6670	324	16	eur	eur	PROPN
ejpam-6670	324	17	.	.	PUNCT
ejpam-6670	325	1	j.	j.	PROPN
ejpam-6670	325	2	pure	pure	PROPN
ejpam-6670	325	3	appl	appl	PROPN
ejpam-6670	325	4	.	.	PROPN
ejpam-6670	325	5	math	math	PROPN
ejpam-6670	325	6	,	,	PUNCT
ejpam-6670	325	7	18	18	NUM
ejpam-6670	325	8	(	(	PUNCT
ejpam-6670	325	9	3	3	NUM
ejpam-6670	325	10	)	)	PUNCT
ejpam-6670	325	11	(	(	PUNCT
ejpam-6670	325	12	2025	2025	NUM
ejpam-6670	325	13	)	)	PUNCT
ejpam-6670	325	14	,	,	PUNCT
ejpam-6670	325	15	6670	6670	NUM
ejpam-6670	325	16	14	14	NUM
ejpam-6670	325	17	of	of	ADP
ejpam-6670	325	18	22	22	NUM
ejpam-6670	325	19	hybrid	hybrid	ADJ
ejpam-6670	325	20	approach	approach	NOUN
ejpam-6670	325	21	of	of	ADP
ejpam-6670	325	22	nsfd	nsfd	ADJ
ejpam-6670	325	23	–	–	PUNCT
ejpam-6670	325	24	ffnn	ffnn	NOUN
ejpam-6670	325	25	,	,	PUNCT
ejpam-6670	325	26	demonstrating	demonstrate	VERB
ejpam-6670	325	27	its	its	PRON
ejpam-6670	325	28	effectiveness	effectiveness	NOUN
ejpam-6670	325	29	in	in	ADP
ejpam-6670	325	30	capturing	capture	VERB
ejpam-6670	325	31	the	the	DET
ejpam-6670	325	32	complex	complex	ADJ
ejpam-6670	325	33	nonlinear	nonlinear	ADJ
ejpam-6670	325	34	dynamics	dynamic	NOUN
ejpam-6670	325	35	of	of	ADP
ejpam-6670	325	36	the	the	DET
ejpam-6670	325	37	modeled	model	VERB
ejpam-6670	325	38	system	system	NOUN
ejpam-6670	325	39	.	.	PUNCT
ejpam-6670	326	1	0	0	NUM
ejpam-6670	327	1	20	20	NUM
ejpam-6670	327	2	40	40	NUM
ejpam-6670	327	3	60	60	NUM
ejpam-6670	327	4	80	80	NUM
ejpam-6670	327	5	100	100	NUM
ejpam-6670	327	6	0.4	0.4	NUM
ejpam-6670	327	7	0.6	0.6	NUM
ejpam-6670	327	8	0.8	0.8	NUM
ejpam-6670	327	9	1	1	NUM
ejpam-6670	327	10	1.2	1.2	NUM
ejpam-6670	327	11	1.4	1.4	NUM
ejpam-6670	327	12	1.6	1.6	NUM
ejpam-6670	327	13	1.8	1.8	NUM
ejpam-6670	327	14	2	2	NUM
ejpam-6670	327	15	2.2	2.2	NUM
ejpam-6670	327	16	2.4	2.4	NUM
ejpam-6670	327	17	t	t	NOUN
ejpam-6670	327	18	s	s	VERB
ejpam-6670	327	19	true	true	ADJ
ejpam-6670	327	20	predicted	predict	VERB
ejpam-6670	327	21	0	0	NUM
ejpam-6670	327	22	20	20	NUM
ejpam-6670	327	23	40	40	NUM
ejpam-6670	327	24	60	60	NUM
ejpam-6670	327	25	80	80	NUM
ejpam-6670	327	26	100	100	NUM
ejpam-6670	327	27	0	0	NUM
ejpam-6670	327	28	0.005	0.005	NUM
ejpam-6670	327	29	0.01	0.01	NUM
ejpam-6670	327	30	0.015	0.015	NUM
ejpam-6670	327	31	0.02	0.02	NUM
ejpam-6670	327	32	0.025	0.025	NUM
ejpam-6670	327	33	t	t	PROPN
ejpam-6670	327	34	a	a	DET
ejpam-6670	327	35	b	b	PROPN
ejpam-6670	327	36	s	s	X
ejpam-6670	327	37	o	o	X
ejpam-6670	327	38	lu	lu	NOUN
ejpam-6670	327	39	te	te	PROPN
ejpam-6670	328	1	e	e	NOUN
ejpam-6670	328	2	rr	rr	NOUN
ejpam-6670	328	3	o	o	NOUN
ejpam-6670	328	4	r	r	NOUN
ejpam-6670	328	5	figure	figure	NOUN
ejpam-6670	328	6	2	2	NUM
ejpam-6670	328	7	:	:	PUNCT
ejpam-6670	328	8	the	the	DET
ejpam-6670	328	9	graphs	graph	NOUN
ejpam-6670	328	10	represents	represent	VERB
ejpam-6670	328	11	the	the	DET
ejpam-6670	328	12	temporal	temporal	ADJ
ejpam-6670	328	13	dynamics	dynamic	NOUN
ejpam-6670	328	14	of	of	ADP
ejpam-6670	328	15	the	the	DET
ejpam-6670	328	16	state	state	NOUN
ejpam-6670	328	17	s	s	PROPN
ejpam-6670	328	18	and	and	CCONJ
ejpam-6670	328	19	its	its	PRON
ejpam-6670	328	20	associated	associated	ADJ
ejpam-6670	328	21	absolute	absolute	ADJ
ejpam-6670	328	22	error	error	NOUN
ejpam-6670	328	23	.	.	PUNCT
ejpam-6670	329	1	overall	overall	ADV
ejpam-6670	329	2	,	,	PUNCT
ejpam-6670	329	3	we	we	PRON
ejpam-6670	329	4	observe	observe	VERB
ejpam-6670	329	5	that	that	SCONJ
ejpam-6670	329	6	the	the	DET
ejpam-6670	329	7	feed	feed	NOUN
ejpam-6670	329	8	-	-	PUNCT
ejpam-6670	329	9	forward	forward	ADV
ejpam-6670	329	10	neural	neural	ADJ
ejpam-6670	329	11	network	network	NOUN
ejpam-6670	329	12	(	(	PUNCT
ejpam-6670	329	13	ffnn	ffnn	NOUN
ejpam-6670	329	14	)	)	PUNCT
ejpam-6670	329	15	learned	learn	VERB
ejpam-6670	329	16	from	from	ADP
ejpam-6670	329	17	the	the	DET
ejpam-6670	329	18	data	datum	NOUN
ejpam-6670	329	19	simulated	simulate	VERB
ejpam-6670	329	20	by	by	ADP
ejpam-6670	329	21	nsfd	nsfd	ADJ
ejpam-6670	329	22	exhibits	exhibit	VERB
ejpam-6670	329	23	an	an	DET
ejpam-6670	329	24	excellent	excellent	ADJ
ejpam-6670	329	25	learning	learning	NOUN
ejpam-6670	329	26	and	and	CCONJ
ejpam-6670	329	27	generalization	generalization	NOUN
ejpam-6670	329	28	capacity	capacity	NOUN
ejpam-6670	329	29	.	.	PUNCT
ejpam-6670	330	1	the	the	DET
ejpam-6670	330	2	validation	validation	NOUN
ejpam-6670	330	3	checks	check	NOUN
ejpam-6670	330	4	describe	describe	VERB
ejpam-6670	330	5	minimal	minimal	ADJ
ejpam-6670	330	6	overfitting	overfitting	NOUN
ejpam-6670	330	7	,	,	PUNCT
ejpam-6670	330	8	and	and	CCONJ
ejpam-6670	330	9	the	the	DET
ejpam-6670	330	10	trajectory	trajectory	NOUN
ejpam-6670	330	11	of	of	ADP
ejpam-6670	330	12	the	the	DET
ejpam-6670	330	13	damping	damp	VERB
ejpam-6670	330	14	factor	factor	NOUN
ejpam-6670	330	15	(	(	PUNCT
ejpam-6670	330	16	µ	µ	NOUN
ejpam-6670	330	17	)	)	PUNCT
ejpam-6670	330	18	shows	show	VERB
ejpam-6670	330	19	adaptive	adaptive	ADJ
ejpam-6670	330	20	learning	learning	NOUN
ejpam-6670	330	21	and	and	CCONJ
ejpam-6670	330	22	stable	stable	ADJ
ejpam-6670	330	23	behavior	behavior	NOUN
ejpam-6670	330	24	,	,	PUNCT
ejpam-6670	330	25	as	as	ADV
ejpam-6670	330	26	well	well	ADV
ejpam-6670	330	27	as	as	ADP
ejpam-6670	330	28	effective	effective	ADJ
ejpam-6670	330	29	convergence	convergence	NOUN
ejpam-6670	330	30	,	,	PUNCT
ejpam-6670	330	31	as	as	SCONJ
ejpam-6670	330	32	seen	see	VERB
ejpam-6670	330	33	by	by	ADP
ejpam-6670	330	34	the	the	DET
ejpam-6670	330	35	gradient	gradient	ADJ
ejpam-6670	330	36	descent	descent	NOUN
ejpam-6670	330	37	pattern	pattern	NOUN
ejpam-6670	330	38	.	.	PUNCT
ejpam-6670	331	1	the	the	DET
ejpam-6670	331	2	regression	regression	NOUN
ejpam-6670	331	3	analysis	analysis	NOUN
ejpam-6670	331	4	shows	show	VERB
ejpam-6670	331	5	that	that	SCONJ
ejpam-6670	331	6	the	the	DET
ejpam-6670	331	7	clustering	clustering	NOUN
ejpam-6670	331	8	of	of	ADP
ejpam-6670	331	9	points	point	NOUN
ejpam-6670	331	10	around	around	ADP
ejpam-6670	331	11	the	the	DET
ejpam-6670	331	12	diagonal	diagonal	ADJ
ejpam-6670	331	13	line	line	NOUN
ejpam-6670	331	14	indicates	indicate	VERB
ejpam-6670	331	15	that	that	SCONJ
ejpam-6670	331	16	the	the	DET
ejpam-6670	331	17	proposed	propose	VERB
ejpam-6670	331	18	network	network	NOUN
ejpam-6670	331	19	has	have	AUX
ejpam-6670	331	20	efficiently	efficiently	ADV
ejpam-6670	331	21	captured	capture	VERB
ejpam-6670	331	22	the	the	DET
ejpam-6670	331	23	nonlinear	nonlinear	ADJ
ejpam-6670	331	24	dynamics	dynamic	NOUN
ejpam-6670	331	25	of	of	ADP
ejpam-6670	331	26	the	the	DET
ejpam-6670	331	27	proposed	propose	VERB
ejpam-6670	331	28	epidemiological	epidemiological	ADJ
ejpam-6670	331	29	model	model	NOUN
ejpam-6670	331	30	simulated	simulate	VERB
ejpam-6670	331	31	by	by	ADP
ejpam-6670	331	32	nsfd	nsfd	NOUN
ejpam-6670	331	33	,	,	PUNCT
ejpam-6670	331	34	which	which	PRON
ejpam-6670	331	35	confirms	confirm	VERB
ejpam-6670	331	36	the	the	DET
ejpam-6670	331	37	robustness	robustness	NOUN
ejpam-6670	331	38	of	of	ADP
ejpam-6670	331	39	the	the	DET
ejpam-6670	331	40	underlying	underlie	VERB
ejpam-6670	331	41	hybrid	hybrid	ADJ
ejpam-6670	331	42	nsfd	nsfd	NOUN
ejpam-6670	331	43	–	–	PUNCT
ejpam-6670	331	44	ffnn	ffnn	NOUN
ejpam-6670	331	45	framework	framework	NOUN
ejpam-6670	331	46	.	.	PUNCT
ejpam-6670	332	1	0	0	NUM
ejpam-6670	333	1	20	20	NUM
ejpam-6670	333	2	40	40	NUM
ejpam-6670	333	3	60	60	NUM
ejpam-6670	333	4	80	80	NUM
ejpam-6670	333	5	100	100	NUM
ejpam-6670	333	6	0	0	NUM
ejpam-6670	333	7	0.5	0.5	NUM
ejpam-6670	333	8	1	1	NUM
ejpam-6670	333	9	1.5	1.5	NUM
ejpam-6670	333	10	2	2	NUM
ejpam-6670	333	11	2.5	2.5	NUM
ejpam-6670	333	12	3	3	NUM
ejpam-6670	333	13	3.5	3.5	NUM
ejpam-6670	333	14	4	4	NUM
ejpam-6670	333	15	t	t	NOUN
ejpam-6670	333	16	l	l	NOUN
ejpam-6670	333	17	true	true	ADJ
ejpam-6670	333	18	predicted	predict	VERB
ejpam-6670	333	19	0	0	NUM
ejpam-6670	333	20	20	20	NUM
ejpam-6670	333	21	40	40	NUM
ejpam-6670	333	22	60	60	NUM
ejpam-6670	333	23	80	80	NUM
ejpam-6670	333	24	100	100	NUM
ejpam-6670	333	25	0	0	NUM
ejpam-6670	333	26	0.002	0.002	NUM
ejpam-6670	333	27	0.004	0.004	NUM
ejpam-6670	333	28	0.006	0.006	NUM
ejpam-6670	333	29	0.008	0.008	NUM
ejpam-6670	333	30	0.01	0.01	NUM
ejpam-6670	333	31	0.012	0.012	NUM
ejpam-6670	333	32	0.014	0.014	NUM
ejpam-6670	333	33	t	t	PROPN
ejpam-6670	333	34	a	a	DET
ejpam-6670	333	35	b	b	PROPN
ejpam-6670	333	36	s	s	X
ejpam-6670	333	37	o	o	X
ejpam-6670	333	38	lu	lu	NOUN
ejpam-6670	333	39	te	te	PROPN
ejpam-6670	334	1	e	e	NOUN
ejpam-6670	334	2	rr	rr	NOUN
ejpam-6670	334	3	o	o	NOUN
ejpam-6670	334	4	r	r	NOUN
ejpam-6670	334	5	figure	figure	NOUN
ejpam-6670	334	6	3	3	NUM
ejpam-6670	334	7	:	:	PUNCT
ejpam-6670	334	8	the	the	DET
ejpam-6670	334	9	time	time	NOUN
ejpam-6670	334	10	dynamics	dynamic	NOUN
ejpam-6670	334	11	of	of	ADP
ejpam-6670	334	12	the	the	DET
ejpam-6670	334	13	state	state	NOUN
ejpam-6670	334	14	l	l	NOUN
ejpam-6670	334	15	with	with	ADP
ejpam-6670	334	16	its	its	PRON
ejpam-6670	334	17	absolute	absolute	ADJ
ejpam-6670	334	18	error	error	NOUN
ejpam-6670	334	19	.	.	PUNCT
ejpam-6670	335	1	t.	t.	PROPN
ejpam-6670	335	2	khan	khan	PROPN
ejpam-6670	335	3	et	et	PROPN
ejpam-6670	335	4	al	al	PROPN
ejpam-6670	335	5	.	.	PUNCT
ejpam-6670	335	6	/	/	SYM
ejpam-6670	335	7	eur	eur	PROPN
ejpam-6670	335	8	.	.	PUNCT
ejpam-6670	336	1	j.	j.	PROPN
ejpam-6670	336	2	pure	pure	PROPN
ejpam-6670	336	3	appl	appl	PROPN
ejpam-6670	336	4	.	.	PROPN
ejpam-6670	336	5	math	math	PROPN
ejpam-6670	336	6	,	,	PUNCT
ejpam-6670	336	7	18	18	NUM
ejpam-6670	336	8	(	(	PUNCT
ejpam-6670	336	9	3	3	NUM
ejpam-6670	336	10	)	)	PUNCT
ejpam-6670	336	11	(	(	PUNCT
ejpam-6670	336	12	2025	2025	NUM
ejpam-6670	336	13	)	)	PUNCT
ejpam-6670	336	14	,	,	PUNCT
ejpam-6670	336	15	6670	6670	NUM
ejpam-6670	336	16	15	15	NUM
ejpam-6670	336	17	of	of	ADP
ejpam-6670	336	18	22	22	NUM
ejpam-6670	336	19	0	0	NUM
ejpam-6670	336	20	20	20	NUM
ejpam-6670	336	21	40	40	NUM
ejpam-6670	336	22	60	60	NUM
ejpam-6670	336	23	80	80	NUM
ejpam-6670	336	24	100	100	NUM
ejpam-6670	336	25	0	0	NUM
ejpam-6670	336	26	0.5	0.5	NUM
ejpam-6670	336	27	1	1	NUM
ejpam-6670	336	28	1.5	1.5	NUM
ejpam-6670	336	29	2	2	NUM
ejpam-6670	336	30	2.5	2.5	NUM
ejpam-6670	336	31	3	3	NUM
ejpam-6670	336	32	3.5	3.5	NUM
ejpam-6670	336	33	4	4	NUM
ejpam-6670	336	34	t	t	NOUN
ejpam-6670	336	35	a	a	DET
ejpam-6670	336	36	true	true	ADJ
ejpam-6670	336	37	predicted	predict	VERB
ejpam-6670	336	38	0	0	NUM
ejpam-6670	336	39	20	20	NUM
ejpam-6670	336	40	40	40	NUM
ejpam-6670	336	41	60	60	NUM
ejpam-6670	336	42	80	80	NUM
ejpam-6670	336	43	100	100	NUM
ejpam-6670	336	44	0	0	NUM
ejpam-6670	336	45	0.002	0.002	NUM
ejpam-6670	336	46	0.004	0.004	NUM
ejpam-6670	336	47	0.006	0.006	NUM
ejpam-6670	336	48	0.008	0.008	NUM
ejpam-6670	336	49	0.01	0.01	NUM
ejpam-6670	336	50	0.012	0.012	NUM
ejpam-6670	336	51	0.014	0.014	NUM
ejpam-6670	336	52	0.016	0.016	NUM
ejpam-6670	336	53	t	t	PROPN
ejpam-6670	336	54	a	a	DET
ejpam-6670	336	55	b	b	PROPN
ejpam-6670	336	56	s	s	X
ejpam-6670	336	57	o	o	X
ejpam-6670	336	58	lu	lu	NOUN
ejpam-6670	336	59	te	te	PROPN
ejpam-6670	336	60	e	e	NOUN
ejpam-6670	336	61	rr	rr	NOUN
ejpam-6670	336	62	o	o	NOUN
ejpam-6670	336	63	r	r	NOUN
ejpam-6670	336	64	figure	figure	NOUN
ejpam-6670	336	65	4	4	NUM
ejpam-6670	336	66	:	:	PUNCT
ejpam-6670	336	67	this	this	PRON
ejpam-6670	336	68	demonstrate	demonstrate	VERB
ejpam-6670	336	69	the	the	DET
ejpam-6670	336	70	dynamics	dynamic	NOUN
ejpam-6670	336	71	of	of	ADP
ejpam-6670	336	72	state	state	NOUN
ejpam-6670	336	73	a	a	PRON
ejpam-6670	336	74	and	and	CCONJ
ejpam-6670	336	75	its	its	PRON
ejpam-6670	336	76	absolute	absolute	ADJ
ejpam-6670	336	77	error	error	NOUN
ejpam-6670	336	78	.	.	PUNCT
ejpam-6670	337	1	0	0	NUM
ejpam-6670	338	1	20	20	NUM
ejpam-6670	338	2	40	40	NUM
ejpam-6670	338	3	60	60	NUM
ejpam-6670	338	4	80	80	NUM
ejpam-6670	338	5	100	100	NUM
ejpam-6670	338	6	0	0	NUM
ejpam-6670	338	7	0.5	0.5	NUM
ejpam-6670	338	8	1	1	NUM
ejpam-6670	338	9	1.5	1.5	NUM
ejpam-6670	338	10	2	2	NUM
ejpam-6670	338	11	2.5	2.5	NUM
ejpam-6670	338	12	3	3	NUM
ejpam-6670	338	13	3.5	3.5	NUM
ejpam-6670	338	14	4	4	NUM
ejpam-6670	338	15	t	t	NOUN
ejpam-6670	338	16	c	c	NOUN
ejpam-6670	338	17	true	true	ADJ
ejpam-6670	338	18	predicted	predict	VERB
ejpam-6670	338	19	0	0	NUM
ejpam-6670	338	20	20	20	NUM
ejpam-6670	338	21	40	40	NUM
ejpam-6670	338	22	60	60	NUM
ejpam-6670	338	23	80	80	NUM
ejpam-6670	338	24	100	100	NUM
ejpam-6670	338	25	0	0	NUM
ejpam-6670	338	26	0.2	0.2	NUM
ejpam-6670	338	27	0.4	0.4	NUM
ejpam-6670	338	28	0.6	0.6	NUM
ejpam-6670	338	29	0.8	0.8	NUM
ejpam-6670	338	30	1	1	NUM
ejpam-6670	338	31	1.2	1.2	NUM
ejpam-6670	338	32	1.4	1.4	NUM
ejpam-6670	338	33	1.6	1.6	NUM
ejpam-6670	338	34	x	x	SYM
ejpam-6670	338	35	10	10	NUM
ejpam-6670	338	36	−3	−3	NOUN
ejpam-6670	338	37	t	t	PROPN
ejpam-6670	338	38	a	a	DET
ejpam-6670	338	39	b	b	PROPN
ejpam-6670	338	40	s	s	X
ejpam-6670	338	41	o	o	X
ejpam-6670	338	42	lu	lu	NOUN
ejpam-6670	338	43	te	te	PROPN
ejpam-6670	339	1	e	e	NOUN
ejpam-6670	339	2	rr	rr	NOUN
ejpam-6670	339	3	o	o	NOUN
ejpam-6670	339	4	r	r	NOUN
ejpam-6670	339	5	figure	figure	NOUN
ejpam-6670	339	6	5	5	NUM
ejpam-6670	339	7	:	:	PUNCT
ejpam-6670	339	8	the	the	DET
ejpam-6670	339	9	graphs	graph	NOUN
ejpam-6670	339	10	visualizes	visualize	VERB
ejpam-6670	339	11	the	the	DET
ejpam-6670	339	12	dynamics	dynamic	NOUN
ejpam-6670	339	13	of	of	ADP
ejpam-6670	339	14	the	the	DET
ejpam-6670	339	15	model	model	NOUN
ejpam-6670	339	16	state	state	PROPN
ejpam-6670	339	17	c	c	PROPN
ejpam-6670	339	18	with	with	ADP
ejpam-6670	339	19	its	its	PRON
ejpam-6670	339	20	associated	associated	ADJ
ejpam-6670	339	21	absolute	absolute	ADJ
ejpam-6670	339	22	error	error	NOUN
ejpam-6670	339	23	.	.	PUNCT
ejpam-6670	340	1	t.	t.	PROPN
ejpam-6670	340	2	khan	khan	PROPN
ejpam-6670	340	3	et	et	PROPN
ejpam-6670	340	4	al	al	PROPN
ejpam-6670	340	5	.	.	PUNCT
ejpam-6670	340	6	/	/	SYM
ejpam-6670	340	7	eur	eur	PROPN
ejpam-6670	340	8	.	.	PUNCT
ejpam-6670	341	1	j.	j.	PROPN
ejpam-6670	341	2	pure	pure	PROPN
ejpam-6670	341	3	appl	appl	PROPN
ejpam-6670	341	4	.	.	PROPN
ejpam-6670	341	5	math	math	PROPN
ejpam-6670	341	6	,	,	PUNCT
ejpam-6670	341	7	18	18	NUM
ejpam-6670	341	8	(	(	PUNCT
ejpam-6670	341	9	3	3	NUM
ejpam-6670	341	10	)	)	PUNCT
ejpam-6670	341	11	(	(	PUNCT
ejpam-6670	341	12	2025	2025	NUM
ejpam-6670	341	13	)	)	PUNCT
ejpam-6670	341	14	,	,	PUNCT
ejpam-6670	341	15	6670	6670	NUM
ejpam-6670	341	16	16	16	NUM
ejpam-6670	341	17	of	of	ADP
ejpam-6670	341	18	22	22	NUM
ejpam-6670	341	19	0	0	NUM
ejpam-6670	341	20	20	20	NUM
ejpam-6670	341	21	40	40	NUM
ejpam-6670	341	22	60	60	NUM
ejpam-6670	341	23	80	80	NUM
ejpam-6670	341	24	100	100	NUM
ejpam-6670	341	25	0	0	NUM
ejpam-6670	341	26	2	2	NUM
ejpam-6670	341	27	4	4	NUM
ejpam-6670	341	28	6	6	NUM
ejpam-6670	341	29	8	8	NUM
ejpam-6670	341	30	10	10	NUM
ejpam-6670	341	31	12	12	NUM
ejpam-6670	341	32	14	14	NUM
ejpam-6670	341	33	t	t	NOUN
ejpam-6670	341	34	r	r	NOUN
ejpam-6670	341	35	true	true	ADV
ejpam-6670	341	36	predicted	predict	VERB
ejpam-6670	341	37	0	0	NUM
ejpam-6670	341	38	20	20	NUM
ejpam-6670	341	39	40	40	NUM
ejpam-6670	341	40	60	60	NUM
ejpam-6670	341	41	80	80	NUM
ejpam-6670	341	42	100	100	NUM
ejpam-6670	341	43	0	0	NUM
ejpam-6670	341	44	0.5	0.5	NUM
ejpam-6670	341	45	1	1	NUM
ejpam-6670	341	46	1.5	1.5	NUM
ejpam-6670	341	47	2	2	NUM
ejpam-6670	341	48	2.5	2.5	NUM
ejpam-6670	341	49	x	x	SYM
ejpam-6670	341	50	10	10	NUM
ejpam-6670	341	51	−3	−3	NOUN
ejpam-6670	341	52	t	t	PROPN
ejpam-6670	341	53	a	a	DET
ejpam-6670	341	54	b	b	PROPN
ejpam-6670	341	55	s	s	X
ejpam-6670	341	56	o	o	X
ejpam-6670	341	57	lu	lu	NOUN
ejpam-6670	341	58	te	te	PROPN
ejpam-6670	342	1	e	e	NOUN
ejpam-6670	343	1	rr	rr	NOUN
ejpam-6670	343	2	o	o	NOUN
ejpam-6670	343	3	r	r	NOUN
ejpam-6670	343	4	figure	figure	NOUN
ejpam-6670	343	5	6	6	NUM
ejpam-6670	343	6	:	:	PUNCT
ejpam-6670	343	7	dynamics	dynamic	NOUN
ejpam-6670	343	8	of	of	ADP
ejpam-6670	343	9	the	the	DET
ejpam-6670	343	10	model	model	NOUN
ejpam-6670	343	11	state	state	NOUN
ejpam-6670	343	12	r	r	NOUN
ejpam-6670	343	13	with	with	ADP
ejpam-6670	343	14	absolute	absolute	ADJ
ejpam-6670	343	15	error	error	NOUN
ejpam-6670	343	16	.	.	PUNCT
ejpam-6670	343	17	0	0	NUM
ejpam-6670	344	1	20	20	NUM
ejpam-6670	344	2	40	40	NUM
ejpam-6670	344	3	60	60	NUM
ejpam-6670	344	4	80	80	NUM
ejpam-6670	344	5	100	100	NUM
ejpam-6670	344	6	0	0	NUM
ejpam-6670	344	7	0.2	0.2	NUM
ejpam-6670	344	8	0.4	0.4	NUM
ejpam-6670	344	9	0.6	0.6	NUM
ejpam-6670	344	10	0.8	0.8	NUM
ejpam-6670	344	11	1	1	NUM
ejpam-6670	344	12	1.2	1.2	NUM
ejpam-6670	344	13	1.4	1.4	NUM
ejpam-6670	344	14	t	t	NOUN
ejpam-6670	344	15	v	v	PRON
ejpam-6670	344	16	true	true	ADJ
ejpam-6670	344	17	predicted	predict	VERB
ejpam-6670	344	18	0	0	NUM
ejpam-6670	344	19	20	20	NUM
ejpam-6670	344	20	40	40	NUM
ejpam-6670	344	21	60	60	NUM
ejpam-6670	344	22	80	80	NUM
ejpam-6670	344	23	100	100	NUM
ejpam-6670	344	24	0	0	NUM
ejpam-6670	344	25	1	1	NUM
ejpam-6670	344	26	2	2	NUM
ejpam-6670	344	27	3	3	NUM
ejpam-6670	344	28	4	4	NUM
ejpam-6670	344	29	5	5	NUM
ejpam-6670	344	30	6	6	NUM
ejpam-6670	344	31	7	7	NUM
ejpam-6670	344	32	x	x	SYM
ejpam-6670	344	33	10	10	NUM
ejpam-6670	344	34	−3	−3	NOUN
ejpam-6670	344	35	t	t	PROPN
ejpam-6670	344	36	a	a	DET
ejpam-6670	344	37	b	b	PROPN
ejpam-6670	344	38	s	s	X
ejpam-6670	344	39	o	o	X
ejpam-6670	344	40	lu	lu	NOUN
ejpam-6670	344	41	te	te	PROPN
ejpam-6670	344	42	e	e	NOUN
ejpam-6670	344	43	rr	rr	NOUN
ejpam-6670	344	44	o	o	NOUN
ejpam-6670	344	45	r	r	NOUN
ejpam-6670	344	46	figure	figure	NOUN
ejpam-6670	344	47	7	7	NUM
ejpam-6670	344	48	:	:	PUNCT
ejpam-6670	344	49	the	the	DET
ejpam-6670	344	50	dynamics	dynamic	NOUN
ejpam-6670	344	51	of	of	ADP
ejpam-6670	344	52	the	the	DET
ejpam-6670	344	53	model	model	NOUN
ejpam-6670	344	54	state	state	PROPN
ejpam-6670	344	55	v	v	PROPN
ejpam-6670	344	56	with	with	ADP
ejpam-6670	344	57	its	its	PRON
ejpam-6670	344	58	associated	associated	ADJ
ejpam-6670	344	59	absolute	absolute	ADJ
ejpam-6670	344	60	error	error	NOUN
ejpam-6670	344	61	.	.	PUNCT
ejpam-6670	345	1	t.	t.	PROPN
ejpam-6670	345	2	khan	khan	PROPN
ejpam-6670	345	3	et	et	PROPN
ejpam-6670	345	4	al	al	PROPN
ejpam-6670	345	5	.	.	PUNCT
ejpam-6670	345	6	/	/	SYM
ejpam-6670	345	7	eur	eur	PROPN
ejpam-6670	345	8	.	.	PUNCT
ejpam-6670	346	1	j.	j.	PROPN
ejpam-6670	346	2	pure	pure	PROPN
ejpam-6670	346	3	appl	appl	PROPN
ejpam-6670	346	4	.	.	PROPN
ejpam-6670	346	5	math	math	PROPN
ejpam-6670	346	6	,	,	PUNCT
ejpam-6670	346	7	18	18	NUM
ejpam-6670	346	8	(	(	PUNCT
ejpam-6670	346	9	3	3	NUM
ejpam-6670	346	10	)	)	PUNCT
ejpam-6670	346	11	(	(	PUNCT
ejpam-6670	346	12	2025	2025	NUM
ejpam-6670	346	13	)	)	PUNCT
ejpam-6670	346	14	,	,	PUNCT
ejpam-6670	346	15	6670	6670	NUM
ejpam-6670	346	16	17	17	NUM
ejpam-6670	346	17	of	of	ADP
ejpam-6670	346	18	22	22	NUM
ejpam-6670	346	19	0	0	NUM
ejpam-6670	346	20	500	500	NUM
ejpam-6670	346	21	1000	1000	NUM
ejpam-6670	346	22	1500	1500	NUM
ejpam-6670	346	23	2000	2000	NUM
ejpam-6670	346	24	2500	2500	NUM
ejpam-6670	346	25	3000	3000	NUM
ejpam-6670	346	26	3500	3500	NUM
ejpam-6670	346	27	4000	4000	NUM
ejpam-6670	346	28	4500	4500	NUM
ejpam-6670	346	29	5000	5000	NUM
ejpam-6670	346	30	error	error	NOUN
ejpam-6670	346	31	histogram	histogram	NOUN
ejpam-6670	346	32	with	with	ADP
ejpam-6670	346	33	20	20	NUM
ejpam-6670	346	34	bins	bin	NOUN
ejpam-6670	346	35	in	in	ADP
ejpam-6670	346	36	st	st	PROPN
ejpam-6670	346	37	a	a	PROPN
ejpam-6670	346	38	n	n	NUM
ejpam-6670	346	39	ce	ce	PROPN
ejpam-6670	346	40	s	s	PART
ejpam-6670	346	41	errors	error	NOUN
ejpam-6670	346	42	=	=	SYM
ejpam-6670	346	43	targets	target	NOUN
ejpam-6670	346	44	−	−	PROPN
ejpam-6670	346	45	outputs	output	NOUN
ejpam-6670	346	46	−	−	PROPN
ejpam-6670	346	47	0	0	NUM
ejpam-6670	347	1	.0	.0	NUM
ejpam-6670	347	2	2	2	NUM
ejpam-6670	347	3	1	1	NUM
ejpam-6670	347	4	1	1	NUM
ejpam-6670	347	5	−	−	NOUN
ejpam-6670	347	6	0	0	NUM
ejpam-6670	347	7	.0	.0	NUM
ejpam-6670	347	8	1	1	NUM
ejpam-6670	347	9	9	9	NUM
ejpam-6670	347	10	3	3	NUM
ejpam-6670	347	11	2	2	NUM
ejpam-6670	347	12	−	−	NOUN
ejpam-6670	347	13	0	0	NUM
ejpam-6670	348	1	.0	.0	NUM
ejpam-6670	349	1	1	1	NUM
ejpam-6670	349	2	7	7	NUM
ejpam-6670	349	3	5	5	NUM
ejpam-6670	349	4	4	4	NUM
ejpam-6670	349	5	−	−	NOUN
ejpam-6670	349	6	0	0	NUM
ejpam-6670	350	1	.0	.0	NUM
ejpam-6670	350	2	1	1	NUM
ejpam-6670	350	3	5	5	NUM
ejpam-6670	350	4	7	7	NUM
ejpam-6670	350	5	6	6	NUM
ejpam-6670	350	6	−	−	NOUN
ejpam-6670	350	7	0	0	NUM
ejpam-6670	351	1	.0	.0	NUM
ejpam-6670	351	2	1	1	NUM
ejpam-6670	351	3	3	3	NUM
ejpam-6670	351	4	9	9	NUM
ejpam-6670	351	5	8	8	NUM
ejpam-6670	351	6	−	−	NOUN
ejpam-6670	351	7	0	0	NUM
ejpam-6670	352	1	.0	.0	NUM
ejpam-6670	352	2	1	1	NUM
ejpam-6670	352	3	2	2	NUM
ejpam-6670	352	4	2	2	NUM
ejpam-6670	352	5	−	−	NOUN
ejpam-6670	352	6	0	0	NUM
ejpam-6670	353	1	.0	.0	NUM
ejpam-6670	353	2	1	1	NUM
ejpam-6670	353	3	0	0	NUM
ejpam-6670	353	4	4	4	NUM
ejpam-6670	353	5	2	2	NUM
ejpam-6670	353	6	−	−	NOUN
ejpam-6670	353	7	0	0	NUM
ejpam-6670	354	1	.0	.0	NUM
ejpam-6670	354	2	0	0	NUM
ejpam-6670	354	3	8	8	NUM
ejpam-6670	354	4	6	6	NUM
ejpam-6670	354	5	4	4	NUM
ejpam-6670	354	6	−	−	NOUN
ejpam-6670	354	7	0	0	NUM
ejpam-6670	355	1	.0	.0	NUM
ejpam-6670	355	2	0	0	NUM
ejpam-6670	355	3	6	6	NUM
ejpam-6670	355	4	8	8	NUM
ejpam-6670	355	5	6	6	NUM
ejpam-6670	355	6	−	−	NOUN
ejpam-6670	355	7	0	0	NUM
ejpam-6670	356	1	.0	.0	NUM
ejpam-6670	356	2	0	0	NUM
ejpam-6670	356	3	5	5	NUM
ejpam-6670	356	4	0	0	NUM
ejpam-6670	356	5	8	8	NUM
ejpam-6670	356	6	−	−	NOUN
ejpam-6670	356	7	0	0	NUM
ejpam-6670	357	1	.0	.0	NUM
ejpam-6670	357	2	0	0	NUM
ejpam-6670	357	3	3	3	NUM
ejpam-6670	357	4	3	3	NUM
ejpam-6670	357	5	−	−	NOUN
ejpam-6670	357	6	0	0	NUM
ejpam-6670	358	1	.0	.0	NUM
ejpam-6670	358	2	0	0	NUM
ejpam-6670	358	3	1	1	NUM
ejpam-6670	358	4	5	5	NUM
ejpam-6670	358	5	2	2	NUM
ejpam-6670	358	6	0	0	NUM
ejpam-6670	358	7	.0	.0	NUM
ejpam-6670	358	8	0	0	NUM
ejpam-6670	358	9	0	0	NUM
ejpam-6670	358	10	2	2	NUM
ejpam-6670	358	11	5	5	NUM
ejpam-6670	358	12	8	8	NUM
ejpam-6670	358	13	0	0	NUM
ejpam-6670	358	14	.0	.0	NUM
ejpam-6670	358	15	0	0	NUM
ejpam-6670	358	16	2	2	NUM
ejpam-6670	358	17	0	0	NUM
ejpam-6670	358	18	3	3	NUM
ejpam-6670	358	19	8	8	NUM
ejpam-6670	358	20	0	0	NUM
ejpam-6670	358	21	.0	.0	NUM
ejpam-6670	358	22	0	0	NUM
ejpam-6670	358	23	3	3	NUM
ejpam-6670	358	24	8	8	NUM
ejpam-6670	358	25	1	1	NUM
ejpam-6670	358	26	8	8	NUM
ejpam-6670	358	27	0	0	NUM
ejpam-6670	358	28	.0	.0	NUM
ejpam-6670	358	29	0	0	NUM
ejpam-6670	358	30	5	5	NUM
ejpam-6670	358	31	5	5	NUM
ejpam-6670	358	32	9	9	NUM
ejpam-6670	358	33	8	8	NUM
ejpam-6670	358	34	0	0	NUM
ejpam-6670	358	35	.0	.0	NUM
ejpam-6670	358	36	0	0	NUM
ejpam-6670	358	37	7	7	NUM
ejpam-6670	358	38	3	3	NUM
ejpam-6670	358	39	7	7	NUM
ejpam-6670	358	40	8	8	NUM
ejpam-6670	358	41	0	0	NUM
ejpam-6670	358	42	.0	.0	NUM
ejpam-6670	358	43	0	0	NUM
ejpam-6670	358	44	9	9	NUM
ejpam-6670	358	45	1	1	NUM
ejpam-6670	358	46	5	5	NUM
ejpam-6670	358	47	9	9	NUM
ejpam-6670	358	48	0	0	NUM
ejpam-6670	358	49	.0	.0	NUM
ejpam-6670	358	50	1	1	NUM
ejpam-6670	358	51	0	0	NUM
ejpam-6670	358	52	9	9	NUM
ejpam-6670	358	53	4	4	NUM
ejpam-6670	358	54	0	0	NUM
ejpam-6670	358	55	.0	.0	NUM
ejpam-6670	358	56	1	1	NUM
ejpam-6670	358	57	2	2	NUM
ejpam-6670	358	58	7	7	NUM
ejpam-6670	358	59	2	2	NUM
ejpam-6670	358	60	training	training	NOUN
ejpam-6670	358	61	validation	validation	NOUN
ejpam-6670	358	62	test	test	NOUN
ejpam-6670	358	63	zero	zero	NUM
ejpam-6670	358	64	error	error	NOUN
ejpam-6670	358	65	figure	figure	NOUN
ejpam-6670	358	66	8	8	NUM
ejpam-6670	358	67	:	:	PUNCT
ejpam-6670	358	68	the	the	DET
ejpam-6670	358	69	graphs	graph	NOUN
ejpam-6670	358	70	show	show	VERB
ejpam-6670	358	71	time	time	NOUN
ejpam-6670	358	72	dynamics	dynamic	NOUN
ejpam-6670	358	73	of	of	ADP
ejpam-6670	358	74	the	the	DET
ejpam-6670	358	75	compartmental	compartmental	ADJ
ejpam-6670	358	76	population	population	NOUN
ejpam-6670	358	77	of	of	ADP
ejpam-6670	358	78	the	the	DET
ejpam-6670	358	79	model	model	NOUN
ejpam-6670	358	80	that	that	PRON
ejpam-6670	358	81	is	be	AUX
ejpam-6670	358	82	under	under	ADP
ejpam-6670	358	83	consideration	consideration	NOUN
ejpam-6670	358	84	at	at	ADP
ejpam-6670	358	85	the	the	DET
ejpam-6670	358	86	disease	disease	NOUN
ejpam-6670	358	87	free	free	ADJ
ejpam-6670	358	88	equilibrium	equilibrium	NOUN
ejpam-6670	358	89	state	state	NOUN
ejpam-6670	358	90	.	.	PUNCT
ejpam-6670	359	1	t.	t.	PROPN
ejpam-6670	359	2	khan	khan	PROPN
ejpam-6670	359	3	et	et	PROPN
ejpam-6670	359	4	al	al	PROPN
ejpam-6670	359	5	.	.	PUNCT
ejpam-6670	359	6	/	/	SYM
ejpam-6670	359	7	eur	eur	PROPN
ejpam-6670	359	8	.	.	PUNCT
ejpam-6670	360	1	j.	j.	PROPN
ejpam-6670	360	2	pure	pure	PROPN
ejpam-6670	360	3	appl	appl	PROPN
ejpam-6670	360	4	.	.	PROPN
ejpam-6670	360	5	math	math	PROPN
ejpam-6670	360	6	,	,	PUNCT
ejpam-6670	360	7	18	18	NUM
ejpam-6670	360	8	(	(	PUNCT
ejpam-6670	360	9	3	3	NUM
ejpam-6670	360	10	)	)	PUNCT
ejpam-6670	360	11	(	(	PUNCT
ejpam-6670	360	12	2025	2025	NUM
ejpam-6670	360	13	)	)	PUNCT
ejpam-6670	360	14	,	,	PUNCT
ejpam-6670	360	15	6670	6670	NUM
ejpam-6670	360	16	18	18	NUM
ejpam-6670	360	17	of	of	ADP
ejpam-6670	360	18	22	22	NUM
ejpam-6670	360	19	10	10	NUM
ejpam-6670	360	20	−10	−10	NUM
ejpam-6670	360	21	10	10	NUM
ejpam-6670	360	22	0	0	NUM
ejpam-6670	360	23	10	10	NUM
ejpam-6670	360	24	10	10	NUM
ejpam-6670	360	25	g	g	NOUN
ejpam-6670	360	26	ra	ra	PROPN
ejpam-6670	361	1	d	d	NOUN
ejpam-6670	361	2	ie	ie	X
ejpam-6670	361	3	n	n	PROPN
ejpam-6670	361	4	t	t	NOUN
ejpam-6670	361	5	gradient	gradient	NOUN
ejpam-6670	361	6	=	=	SYM
ejpam-6670	361	7	8.8342e−06	8.8342e−06	NUM
ejpam-6670	361	8	,	,	PUNCT
ejpam-6670	361	9	at	at	ADP
ejpam-6670	361	10	epoch	epoch	NOUN
ejpam-6670	361	11	1000	1000	NUM
ejpam-6670	361	12	10	10	NUM
ejpam-6670	361	13	−10	−10	NUM
ejpam-6670	361	14	10	10	NUM
ejpam-6670	361	15	−5	−5	ADV
ejpam-6670	361	16	10	10	NUM
ejpam-6670	361	17	0	0	NUM
ejpam-6670	361	18	m	m	VERB
ejpam-6670	361	19	u	u	NOUN
ejpam-6670	361	20	mu	mu	NOUN
ejpam-6670	361	21	=	=	SYM
ejpam-6670	361	22	1e−06	1e−06	NUM
ejpam-6670	361	23	,	,	PUNCT
ejpam-6670	361	24	at	at	ADP
ejpam-6670	361	25	epoch	epoch	NOUN
ejpam-6670	361	26	1000	1000	NUM
ejpam-6670	361	27	0	0	NUM
ejpam-6670	361	28	200	200	NUM
ejpam-6670	361	29	400	400	NUM
ejpam-6670	361	30	600	600	NUM
ejpam-6670	361	31	800	800	NUM
ejpam-6670	361	32	1000	1000	NUM
ejpam-6670	361	33	0	0	NUM
ejpam-6670	361	34	0.5	0.5	NUM
ejpam-6670	361	35	1	1	NUM
ejpam-6670	361	36	v	v	ADP
ejpam-6670	361	37	a	a	DET
ejpam-6670	361	38	l	l	NOUN
ejpam-6670	361	39	fa	fa	X
ejpam-6670	361	40	il	il	PROPN
ejpam-6670	361	41	1000	1000	NUM
ejpam-6670	361	42	epochs	epoch	NOUN
ejpam-6670	361	43	validation	validation	NOUN
ejpam-6670	361	44	checks	check	NOUN
ejpam-6670	361	45	=	=	SYM
ejpam-6670	361	46	0	0	NUM
ejpam-6670	361	47	,	,	PUNCT
ejpam-6670	361	48	at	at	ADP
ejpam-6670	361	49	epoch	epoch	NOUN
ejpam-6670	361	50	1000	1000	NUM
ejpam-6670	361	51	figure	figure	NOUN
ejpam-6670	361	52	9	9	NUM
ejpam-6670	361	53	:	:	PUNCT
ejpam-6670	361	54	the	the	DET
ejpam-6670	361	55	graphs	graph	NOUN
ejpam-6670	361	56	show	show	VERB
ejpam-6670	361	57	time	time	NOUN
ejpam-6670	361	58	dynamics	dynamic	NOUN
ejpam-6670	361	59	of	of	ADP
ejpam-6670	361	60	the	the	DET
ejpam-6670	361	61	compartmental	compartmental	ADJ
ejpam-6670	361	62	population	population	NOUN
ejpam-6670	361	63	of	of	ADP
ejpam-6670	361	64	the	the	DET
ejpam-6670	361	65	model	model	NOUN
ejpam-6670	361	66	that	that	PRON
ejpam-6670	361	67	is	be	AUX
ejpam-6670	361	68	under	under	ADP
ejpam-6670	361	69	consideration	consideration	NOUN
ejpam-6670	361	70	at	at	ADP
ejpam-6670	361	71	the	the	DET
ejpam-6670	361	72	disease	disease	NOUN
ejpam-6670	361	73	free	free	ADJ
ejpam-6670	361	74	equilibrium	equilibrium	NOUN
ejpam-6670	361	75	state	state	NOUN
ejpam-6670	361	76	.	.	PUNCT
ejpam-6670	362	1	t.	t.	PROPN
ejpam-6670	362	2	khan	khan	PROPN
ejpam-6670	362	3	et	et	PROPN
ejpam-6670	362	4	al	al	PROPN
ejpam-6670	362	5	.	.	PUNCT
ejpam-6670	362	6	/	/	SYM
ejpam-6670	362	7	eur	eur	PROPN
ejpam-6670	362	8	.	.	PUNCT
ejpam-6670	363	1	j.	j.	PROPN
ejpam-6670	363	2	pure	pure	PROPN
ejpam-6670	363	3	appl	appl	PROPN
ejpam-6670	363	4	.	.	PROPN
ejpam-6670	363	5	math	math	PROPN
ejpam-6670	363	6	,	,	PUNCT
ejpam-6670	363	7	18	18	NUM
ejpam-6670	363	8	(	(	PUNCT
ejpam-6670	363	9	3	3	NUM
ejpam-6670	363	10	)	)	PUNCT
ejpam-6670	363	11	(	(	PUNCT
ejpam-6670	363	12	2025	2025	NUM
ejpam-6670	363	13	)	)	PUNCT
ejpam-6670	363	14	,	,	PUNCT
ejpam-6670	363	15	6670	6670	NUM
ejpam-6670	363	16	19	19	NUM
ejpam-6670	363	17	of	of	ADP
ejpam-6670	363	18	22	22	NUM
ejpam-6670	363	19	2	2	NUM
ejpam-6670	363	20	4	4	NUM
ejpam-6670	363	21	6	6	NUM
ejpam-6670	363	22	8	8	NUM
ejpam-6670	363	23	10	10	NUM
ejpam-6670	363	24	12	12	NUM
ejpam-6670	363	25	2	2	NUM
ejpam-6670	363	26	4	4	NUM
ejpam-6670	363	27	6	6	NUM
ejpam-6670	363	28	8	8	NUM
ejpam-6670	363	29	10	10	NUM
ejpam-6670	363	30	12	12	NUM
ejpam-6670	363	31	target	target	NOUN
ejpam-6670	363	32	o	o	X
ejpam-6670	363	33	ut	ut	PROPN
ejpam-6670	363	34	pu	pu	PROPN
ejpam-6670	363	35	t	t	PROPN
ejpam-6670	363	36	~	~	PUNCT
ejpam-6670	363	37	=	=	SYM
ejpam-6670	364	1	1	1	X
ejpam-6670	364	2	*	*	PUNCT
ejpam-6670	364	3	ta	ta	PART
ejpam-6670	364	4	rg	rg	VERB
ejpam-6670	364	5	et	et	NOUN
ejpam-6670	364	6	+	+	CCONJ
ejpam-6670	364	7	5	5	NUM
ejpam-6670	364	8	.9	.9	NUM
ejpam-6670	364	9	e−	e−	PROPN
ejpam-6670	364	10	07	07	NUM
ejpam-6670	364	11	training	training	NOUN
ejpam-6670	364	12	:	:	PUNCT
ejpam-6670	364	13	r=1	r=1	NOUN
ejpam-6670	364	14	data	datum	NOUN
ejpam-6670	364	15	fit	fit	ADJ
ejpam-6670	364	16	y	y	PROPN
ejpam-6670	364	17	=	=	SYM
ejpam-6670	364	18	t	t	PROPN
ejpam-6670	364	19	2	2	NUM
ejpam-6670	364	20	4	4	NUM
ejpam-6670	364	21	6	6	NUM
ejpam-6670	364	22	8	8	NUM
ejpam-6670	364	23	10	10	NUM
ejpam-6670	364	24	12	12	NUM
ejpam-6670	364	25	2	2	NUM
ejpam-6670	364	26	4	4	NUM
ejpam-6670	364	27	6	6	NUM
ejpam-6670	364	28	8	8	NUM
ejpam-6670	364	29	10	10	NUM
ejpam-6670	364	30	12	12	NUM
ejpam-6670	364	31	target	target	NOUN
ejpam-6670	364	32	o	o	X
ejpam-6670	364	33	ut	ut	PROPN
ejpam-6670	364	34	pu	pu	PROPN
ejpam-6670	364	35	t	t	PROPN
ejpam-6670	364	36	~	~	PUNCT
ejpam-6670	364	37	=	=	SYM
ejpam-6670	365	1	1	1	X
ejpam-6670	365	2	*	*	PUNCT
ejpam-6670	365	3	ta	ta	PART
ejpam-6670	365	4	rg	rg	VERB
ejpam-6670	365	5	et	et	NOUN
ejpam-6670	365	6	+	+	CCONJ
ejpam-6670	365	7	9	9	NUM
ejpam-6670	365	8	.5	.5	NUM
ejpam-6670	365	9	e−	e−	X
ejpam-6670	365	10	05	05	NUM
ejpam-6670	365	11	validation	validation	NOUN
ejpam-6670	365	12	:	:	PUNCT
ejpam-6670	365	13	r=1	r=1	NOUN
ejpam-6670	365	14	data	datum	NOUN
ejpam-6670	365	15	fit	fit	ADJ
ejpam-6670	365	16	y	y	PROPN
ejpam-6670	365	17	=	=	SYM
ejpam-6670	365	18	t	t	PROPN
ejpam-6670	365	19	2	2	NUM
ejpam-6670	365	20	4	4	NUM
ejpam-6670	365	21	6	6	NUM
ejpam-6670	365	22	8	8	NUM
ejpam-6670	365	23	10	10	NUM
ejpam-6670	365	24	12	12	NUM
ejpam-6670	365	25	2	2	NUM
ejpam-6670	365	26	4	4	NUM
ejpam-6670	365	27	6	6	NUM
ejpam-6670	365	28	8	8	NUM
ejpam-6670	365	29	10	10	NUM
ejpam-6670	365	30	12	12	NUM
ejpam-6670	365	31	target	target	NOUN
ejpam-6670	365	32	o	o	X
ejpam-6670	365	33	ut	ut	PROPN
ejpam-6670	365	34	pu	pu	PROPN
ejpam-6670	365	35	t	t	PROPN
ejpam-6670	365	36	~	~	PUNCT
ejpam-6670	365	37	=	=	SYM
ejpam-6670	366	1	1	1	X
ejpam-6670	366	2	*	*	PUNCT
ejpam-6670	366	3	ta	ta	PART
ejpam-6670	366	4	rg	rg	VERB
ejpam-6670	366	5	et	et	PROPN
ejpam-6670	366	6	+	+	CCONJ
ejpam-6670	366	7	3	3	NUM
ejpam-6670	366	8	e−	e−	PROPN
ejpam-6670	366	9	06	06	NUM
ejpam-6670	366	10	test	test	NOUN
ejpam-6670	366	11	:	:	PUNCT
ejpam-6670	366	12	r=1	r=1	NOUN
ejpam-6670	366	13	data	datum	NOUN
ejpam-6670	366	14	fit	fit	ADJ
ejpam-6670	366	15	y	y	PROPN
ejpam-6670	366	16	=	=	SYM
ejpam-6670	366	17	t	t	PROPN
ejpam-6670	366	18	2	2	NUM
ejpam-6670	366	19	4	4	NUM
ejpam-6670	366	20	6	6	NUM
ejpam-6670	366	21	8	8	NUM
ejpam-6670	366	22	10	10	NUM
ejpam-6670	366	23	12	12	NUM
ejpam-6670	366	24	2	2	NUM
ejpam-6670	366	25	4	4	NUM
ejpam-6670	366	26	6	6	NUM
ejpam-6670	366	27	8	8	NUM
ejpam-6670	366	28	10	10	NUM
ejpam-6670	366	29	12	12	NUM
ejpam-6670	366	30	target	target	NOUN
ejpam-6670	366	31	o	o	X
ejpam-6670	366	32	ut	ut	PROPN
ejpam-6670	366	33	pu	pu	PROPN
ejpam-6670	366	34	t	t	PROPN
ejpam-6670	366	35	~	~	PUNCT
ejpam-6670	366	36	=	=	SYM
ejpam-6670	367	1	1	1	X
ejpam-6670	367	2	*	*	PUNCT
ejpam-6670	367	3	ta	ta	PART
ejpam-6670	367	4	rg	rg	VERB
ejpam-6670	367	5	et	et	NOUN
ejpam-6670	367	6	+	+	CCONJ
ejpam-6670	367	7	1	1	NUM
ejpam-6670	367	8	.5	.5	NUM
ejpam-6670	368	1	e−	e−	X
ejpam-6670	368	2	05	05	NUM
ejpam-6670	369	1	all	all	PRON
ejpam-6670	369	2	:	:	PUNCT
ejpam-6670	369	3	r=1	r=1	NOUN
ejpam-6670	369	4	data	datum	NOUN
ejpam-6670	369	5	fit	fit	ADJ
ejpam-6670	369	6	y	y	PROPN
ejpam-6670	369	7	=	=	SYM
ejpam-6670	369	8	t	t	PROPN
ejpam-6670	369	9	figure	figure	NOUN
ejpam-6670	369	10	10	10	NUM
ejpam-6670	369	11	:	:	PUNCT
ejpam-6670	369	12	the	the	DET
ejpam-6670	369	13	graphs	graph	NOUN
ejpam-6670	369	14	show	show	VERB
ejpam-6670	369	15	time	time	NOUN
ejpam-6670	369	16	dynamics	dynamic	NOUN
ejpam-6670	369	17	of	of	ADP
ejpam-6670	369	18	the	the	DET
ejpam-6670	369	19	compartmental	compartmental	ADJ
ejpam-6670	369	20	population	population	NOUN
ejpam-6670	369	21	of	of	ADP
ejpam-6670	369	22	the	the	DET
ejpam-6670	369	23	model	model	NOUN
ejpam-6670	369	24	that	that	PRON
ejpam-6670	369	25	is	be	AUX
ejpam-6670	369	26	under	under	ADP
ejpam-6670	369	27	consideration	consideration	NOUN
ejpam-6670	369	28	at	at	ADP
ejpam-6670	369	29	the	the	DET
ejpam-6670	369	30	disease	disease	NOUN
ejpam-6670	369	31	free	free	ADJ
ejpam-6670	369	32	equilibrium	equilibrium	NOUN
ejpam-6670	369	33	state	state	NOUN
ejpam-6670	369	34	.	.	PUNCT
ejpam-6670	370	1	4	4	X
ejpam-6670	370	2	.	.	X
ejpam-6670	370	3	conclusion	conclusion	NOUN
ejpam-6670	370	4	in	in	ADP
ejpam-6670	370	5	this	this	DET
ejpam-6670	370	6	paper	paper	NOUN
ejpam-6670	370	7	,	,	PUNCT
ejpam-6670	370	8	we	we	PRON
ejpam-6670	370	9	investigated	investigate	VERB
ejpam-6670	370	10	the	the	DET
ejpam-6670	370	11	transmission	transmission	NOUN
ejpam-6670	370	12	dynamics	dynamic	NOUN
ejpam-6670	370	13	of	of	ADP
ejpam-6670	370	14	hepatitis	hepatitis	PROPN
ejpam-6670	370	15	b	b	PROPN
ejpam-6670	370	16	virus	virus	NOUN
ejpam-6670	370	17	(	(	PUNCT
ejpam-6670	370	18	hbv	hbv	NOUN
ejpam-6670	370	19	)	)	PUNCT
ejpam-6670	370	20	using	use	VERB
ejpam-6670	370	21	the	the	DET
ejpam-6670	370	22	integration	integration	NOUN
ejpam-6670	370	23	of	of	ADP
ejpam-6670	370	24	an	an	DET
ejpam-6670	370	25	epidemic	epidemic	NOUN
ejpam-6670	370	26	model	model	NOUN
ejpam-6670	370	27	ffnn	ffnn	NOUN
ejpam-6670	370	28	.	.	PUNCT
ejpam-6670	371	1	the	the	DET
ejpam-6670	371	2	model	model	NOUN
ejpam-6670	371	3	has	have	AUX
ejpam-6670	371	4	been	be	AUX
ejpam-6670	371	5	carefully	carefully	ADV
ejpam-6670	371	6	constructed	construct	VERB
ejpam-6670	371	7	to	to	PART
ejpam-6670	371	8	reflect	reflect	VERB
ejpam-6670	371	9	the	the	DET
ejpam-6670	371	10	key	key	ADJ
ejpam-6670	371	11	biological	biological	ADJ
ejpam-6670	371	12	features	feature	NOUN
ejpam-6670	371	13	of	of	ADP
ejpam-6670	371	14	hbv	hbv	NOUN
ejpam-6670	371	15	,	,	PUNCT
ejpam-6670	371	16	including	include	VERB
ejpam-6670	371	17	its	its	PRON
ejpam-6670	371	18	various	various	ADJ
ejpam-6670	371	19	infection	infection	NOUN
ejpam-6670	371	20	stages	stage	NOUN
ejpam-6670	371	21	(	(	PUNCT
ejpam-6670	371	22	latent	latent	NOUN
ejpam-6670	371	23	,	,	PUNCT
ejpam-6670	371	24	acute	acute	NOUN
ejpam-6670	371	25	,	,	PUNCT
ejpam-6670	371	26	and	and	CCONJ
ejpam-6670	371	27	chronic	chronic	ADJ
ejpam-6670	371	28	)	)	PUNCT
ejpam-6670	371	29	,	,	PUNCT
ejpam-6670	371	30	as	as	ADV
ejpam-6670	371	31	well	well	ADV
ejpam-6670	371	32	as	as	ADP
ejpam-6670	371	33	a	a	DET
ejpam-6670	371	34	saturated	saturate	VERB
ejpam-6670	371	35	incidence	incidence	NOUN
ejpam-6670	371	36	rate	rate	NOUN
ejpam-6670	371	37	to	to	PART
ejpam-6670	371	38	capture	capture	VERB
ejpam-6670	371	39	the	the	DET
ejpam-6670	371	40	behavioral	behavioral	ADJ
ejpam-6670	371	41	and	and	CCONJ
ejpam-6670	371	42	healthcare	healthcare	NOUN
ejpam-6670	371	43	constraints	constraint	NOUN
ejpam-6670	371	44	associated	associate	VERB
ejpam-6670	371	45	with	with	ADP
ejpam-6670	371	46	hbv	hbv	NOUN
ejpam-6670	371	47	transmission	transmission	NOUN
ejpam-6670	371	48	.	.	PUNCT
ejpam-6670	372	1	we	we	PRON
ejpam-6670	372	2	established	establish	VERB
ejpam-6670	372	3	the	the	DET
ejpam-6670	372	4	wellposedness	wellposedness	NOUN
ejpam-6670	372	5	of	of	ADP
ejpam-6670	372	6	the	the	DET
ejpam-6670	372	7	model	model	NOUN
ejpam-6670	372	8	to	to	PART
ejpam-6670	372	9	ensure	ensure	VERB
ejpam-6670	372	10	biological	biological	ADJ
ejpam-6670	372	11	and	and	CCONJ
ejpam-6670	372	12	mathematical	mathematical	ADJ
ejpam-6670	372	13	feasibility	feasibility	NOUN
ejpam-6670	372	14	of	of	ADP
ejpam-6670	372	15	the	the	DET
ejpam-6670	372	16	problem	problem	NOUN
ejpam-6670	372	17	.	.	PUNCT
ejpam-6670	373	1	we	we	PRON
ejpam-6670	373	2	also	also	ADV
ejpam-6670	373	3	derived	derive	VERB
ejpam-6670	373	4	the	the	DET
ejpam-6670	373	5	basic	basic	ADJ
ejpam-6670	373	6	reproduction	reproduction	NOUN
ejpam-6670	373	7	number	number	NOUN
ejpam-6670	373	8	,	,	PUNCT
ejpam-6670	373	9	and	and	CCONJ
ejpam-6670	373	10	studied	study	VERB
ejpam-6670	373	11	a	a	DET
ejpam-6670	373	12	comprehensive	comprehensive	ADJ
ejpam-6670	373	13	stability	stability	NOUN
ejpam-6670	373	14	analysis	analysis	NOUN
ejpam-6670	373	15	to	to	PART
ejpam-6670	373	16	assess	assess	VERB
ejpam-6670	373	17	the	the	DET
ejpam-6670	373	18	conditions	condition	NOUN
ejpam-6670	373	19	under	under	ADP
ejpam-6670	373	20	which	which	PRON
ejpam-6670	373	21	the	the	DET
ejpam-6670	373	22	disease	disease	NOUN
ejpam-6670	373	23	-	-	PUNCT
ejpam-6670	373	24	free	free	ADJ
ejpam-6670	373	25	and	and	CCONJ
ejpam-6670	373	26	endemic	endemic	ADJ
ejpam-6670	373	27	states	state	NOUN
ejpam-6670	373	28	are	be	AUX
ejpam-6670	373	29	stable	stable	ADJ
ejpam-6670	373	30	.	.	PUNCT
ejpam-6670	374	1	to	to	PART
ejpam-6670	374	2	validate	validate	VERB
ejpam-6670	374	3	the	the	DET
ejpam-6670	374	4	analytical	analytical	ADJ
ejpam-6670	374	5	findings	finding	NOUN
ejpam-6670	374	6	and	and	CCONJ
ejpam-6670	374	7	explore	explore	VERB
ejpam-6670	374	8	the	the	DET
ejpam-6670	374	9	model	model	NOUN
ejpam-6670	374	10	’s	’s	PART
ejpam-6670	374	11	behavior	behavior	NOUN
ejpam-6670	374	12	,	,	PUNCT
ejpam-6670	374	13	we	we	PRON
ejpam-6670	374	14	employed	employ	VERB
ejpam-6670	374	15	a	a	DET
ejpam-6670	374	16	novel	novel	ADJ
ejpam-6670	374	17	hybrid	hybrid	ADJ
ejpam-6670	374	18	numerical	numerical	ADJ
ejpam-6670	374	19	framework	framework	NOUN
ejpam-6670	374	20	combining	combine	VERB
ejpam-6670	374	21	the	the	DET
ejpam-6670	374	22	nonstandard	nonstandard	ADJ
ejpam-6670	374	23	finite	finite	ADJ
ejpam-6670	374	24	difference	difference	NOUN
ejpam-6670	374	25	(	(	PUNCT
ejpam-6670	374	26	nsfd	nsfd	ADJ
ejpam-6670	374	27	)	)	PUNCT
ejpam-6670	374	28	scheme	scheme	NOUN
ejpam-6670	374	29	with	with	ADP
ejpam-6670	374	30	a	a	DET
ejpam-6670	374	31	feed	feed	NOUN
ejpam-6670	374	32	-	-	PUNCT
ejpam-6670	374	33	forward	forward	ADV
ejpam-6670	374	34	neural	neural	ADJ
ejpam-6670	374	35	network	network	NOUN
ejpam-6670	374	36	(	(	PUNCT
ejpam-6670	374	37	ffnn	ffnn	NOUN
ejpam-6670	374	38	)	)	PUNCT
ejpam-6670	374	39	.	.	PUNCT
ejpam-6670	375	1	the	the	DET
ejpam-6670	375	2	numerical	numerical	ADJ
ejpam-6670	375	3	results	result	NOUN
ejpam-6670	375	4	demonstrated	demonstrate	VERB
ejpam-6670	375	5	a	a	DET
ejpam-6670	375	6	high	high	ADJ
ejpam-6670	375	7	degree	degree	NOUN
ejpam-6670	375	8	of	of	ADP
ejpam-6670	375	9	accuracy	accuracy	NOUN
ejpam-6670	375	10	,	,	PUNCT
ejpam-6670	375	11	evidenced	evidence	VERB
ejpam-6670	375	12	by	by	ADP
ejpam-6670	375	13	low	low	ADJ
ejpam-6670	375	14	mean	mean	NOUN
ejpam-6670	375	15	squared	square	VERB
ejpam-6670	375	16	error	error	NOUN
ejpam-6670	375	17	and	and	CCONJ
ejpam-6670	375	18	a	a	DET
ejpam-6670	375	19	strong	strong	ADJ
ejpam-6670	375	20	agreement	agreement	NOUN
ejpam-6670	375	21	between	between	ADP
ejpam-6670	375	22	the	the	DET
ejpam-6670	375	23	true	true	ADJ
ejpam-6670	375	24	trajectories	trajectory	NOUN
ejpam-6670	375	25	produced	produce	VERB
ejpam-6670	375	26	by	by	ADP
ejpam-6670	375	27	nsfd	nsfd	NOUN
ejpam-6670	375	28	and	and	CCONJ
ejpam-6670	375	29	predicted	predict	VERB
ejpam-6670	375	30	trajectories	trajectory	NOUN
ejpam-6670	375	31	provided	provide	VERB
ejpam-6670	375	32	by	by	ADP
ejpam-6670	375	33	t.	t.	PROPN
ejpam-6670	375	34	khan	khan	PROPN
ejpam-6670	375	35	et	et	PROPN
ejpam-6670	375	36	al	al	PROPN
ejpam-6670	375	37	.	.	PUNCT
ejpam-6670	375	38	/	/	SYM
ejpam-6670	375	39	eur	eur	PROPN
ejpam-6670	375	40	.	.	PUNCT
ejpam-6670	376	1	j.	j.	PROPN
ejpam-6670	376	2	pure	pure	PROPN
ejpam-6670	376	3	appl	appl	PROPN
ejpam-6670	376	4	.	.	PROPN
ejpam-6670	376	5	math	math	PROPN
ejpam-6670	376	6	,	,	PUNCT
ejpam-6670	376	7	18	18	NUM
ejpam-6670	376	8	(	(	PUNCT
ejpam-6670	376	9	3	3	NUM
ejpam-6670	376	10	)	)	PUNCT
ejpam-6670	376	11	(	(	PUNCT
ejpam-6670	376	12	2025	2025	NUM
ejpam-6670	376	13	)	)	PUNCT
ejpam-6670	376	14	,	,	PUNCT
ejpam-6670	376	15	6670	6670	NUM
ejpam-6670	376	16	20	20	NUM
ejpam-6670	376	17	of	of	ADP
ejpam-6670	376	18	22	22	NUM
ejpam-6670	376	19	ffnn	ffnn	NOUN
ejpam-6670	376	20	.	.	PUNCT
ejpam-6670	377	1	this	this	PRON
ejpam-6670	377	2	confirms	confirm	VERB
ejpam-6670	377	3	the	the	DET
ejpam-6670	377	4	robustness	robustness	NOUN
ejpam-6670	377	5	and	and	CCONJ
ejpam-6670	377	6	reliability	reliability	NOUN
ejpam-6670	377	7	of	of	ADP
ejpam-6670	377	8	both	both	PRON
ejpam-6670	377	9	the	the	DET
ejpam-6670	377	10	proposed	propose	VERB
ejpam-6670	377	11	model	model	NOUN
ejpam-6670	377	12	and	and	CCONJ
ejpam-6670	377	13	the	the	DET
ejpam-6670	377	14	computational	computational	ADJ
ejpam-6670	377	15	approach	approach	NOUN
ejpam-6670	377	16	.	.	PUNCT
ejpam-6670	378	1	the	the	DET
ejpam-6670	378	2	study	study	NOUN
ejpam-6670	378	3	not	not	PART
ejpam-6670	378	4	only	only	ADV
ejpam-6670	378	5	provides	provide	VERB
ejpam-6670	378	6	valuable	valuable	ADJ
ejpam-6670	378	7	insights	insight	NOUN
ejpam-6670	378	8	into	into	ADP
ejpam-6670	378	9	the	the	DET
ejpam-6670	378	10	complex	complex	ADJ
ejpam-6670	378	11	dynamics	dynamic	NOUN
ejpam-6670	378	12	of	of	ADP
ejpam-6670	378	13	hbv	hbv	NOUN
ejpam-6670	378	14	transmission	transmission	NOUN
ejpam-6670	378	15	but	but	CCONJ
ejpam-6670	378	16	also	also	ADV
ejpam-6670	378	17	provides	provide	VERB
ejpam-6670	378	18	evidence	evidence	NOUN
ejpam-6670	378	19	of	of	ADP
ejpam-6670	378	20	the	the	DET
ejpam-6670	378	21	effectiveness	effectiveness	NOUN
ejpam-6670	378	22	of	of	ADP
ejpam-6670	378	23	a	a	DET
ejpam-6670	378	24	hybrid	hybrid	ADJ
ejpam-6670	378	25	approach	approach	NOUN
ejpam-6670	378	26	capturing	capture	VERB
ejpam-6670	378	27	the	the	DET
ejpam-6670	378	28	progression	progression	NOUN
ejpam-6670	378	29	of	of	ADP
ejpam-6670	378	30	infectious	infectious	ADJ
ejpam-6670	378	31	diseases	disease	NOUN
ejpam-6670	378	32	.	.	PUNCT
ejpam-6670	379	1	moreover	moreover	ADV
ejpam-6670	379	2	,	,	PUNCT
ejpam-6670	379	3	the	the	DET
ejpam-6670	379	4	proposed	propose	VERB
ejpam-6670	379	5	approach	approach	NOUN
ejpam-6670	379	6	is	be	AUX
ejpam-6670	379	7	computationally	computationally	ADV
ejpam-6670	379	8	stable	stable	ADJ
ejpam-6670	379	9	,	,	PUNCT
ejpam-6670	379	10	sound	sound	ADJ
ejpam-6670	379	11	,	,	PUNCT
ejpam-6670	379	12	and	and	CCONJ
ejpam-6670	379	13	adaptable	adaptable	ADJ
ejpam-6670	379	14	,	,	PUNCT
ejpam-6670	379	15	which	which	PRON
ejpam-6670	379	16	offers	offer	VERB
ejpam-6670	379	17	a	a	DET
ejpam-6670	379	18	promising	promising	ADJ
ejpam-6670	379	19	tool	tool	NOUN
ejpam-6670	379	20	for	for	ADP
ejpam-6670	379	21	other	other	ADJ
ejpam-6670	379	22	epidemiological	epidemiological	ADJ
ejpam-6670	379	23	models	model	NOUN
ejpam-6670	379	24	.	.	PUNCT
ejpam-6670	380	1	in	in	ADP
ejpam-6670	380	2	future	future	NOUN
ejpam-6670	380	3	,	,	PUNCT
ejpam-6670	380	4	we	we	PRON
ejpam-6670	380	5	will	will	AUX
ejpam-6670	380	6	extend	extend	VERB
ejpam-6670	380	7	the	the	DET
ejpam-6670	380	8	model	model	NOUN
ejpam-6670	380	9	to	to	PART
ejpam-6670	380	10	incorporate	incorporate	VERB
ejpam-6670	380	11	the	the	DET
ejpam-6670	380	12	stochastic	stochastic	ADJ
ejpam-6670	380	13	perturbation	perturbation	NOUN
ejpam-6670	380	14	to	to	ADP
ejpam-6670	380	15	capturing	capture	VERB
ejpam-6670	380	16	disease	disease	NOUN
ejpam-6670	380	17	uncertainty	uncertainty	NOUN
ejpam-6670	380	18	in	in	ADP
ejpam-6670	380	19	heterogeneous	heterogeneous	ADJ
ejpam-6670	380	20	environments	environment	NOUN
ejpam-6670	380	21	,	,	PUNCT
ejpam-6670	380	22	and	and	CCONJ
ejpam-6670	380	23	the	the	PRON
ejpam-6670	380	24	integrate	integrate	VERB
ejpam-6670	380	25	it	it	PRON
ejpam-6670	380	26	with	with	ADP
ejpam-6670	380	27	machine	machine	NOUN
ejpam-6670	380	28	learning	learn	VERB
ejpam-6670	380	29	with	with	ADP
ejpam-6670	380	30	the	the	DET
ejpam-6670	380	31	help	help	NOUN
ejpam-6670	380	32	of	of	ADP
ejpam-6670	380	33	feed	feed	NOUN
ejpam-6670	380	34	-	-	PUNCT
ejpam-6670	380	35	forward	forward	ADV
ejpam-6670	380	36	neural	neural	ADJ
ejpam-6670	380	37	network	network	NOUN
ejpam-6670	380	38	.	.	PUNCT
ejpam-6670	381	1	the	the	DET
ejpam-6670	381	2	ffnns	ffnns	NOUN
ejpam-6670	381	3	will	will	AUX
ejpam-6670	381	4	be	be	AUX
ejpam-6670	381	5	used	use	VERB
ejpam-6670	381	6	to	to	PART
ejpam-6670	381	7	learn	learn	VERB
ejpam-6670	381	8	the	the	DET
ejpam-6670	381	9	underlying	underlying	ADJ
ejpam-6670	381	10	nonlinear	nonlinear	ADJ
ejpam-6670	381	11	dynamics	dynamic	NOUN
ejpam-6670	381	12	governed	govern	VERB
ejpam-6670	381	13	by	by	ADP
ejpam-6670	381	14	the	the	DET
ejpam-6670	381	15	associated	associated	ADJ
ejpam-6670	381	16	stochastic	stochastic	ADJ
ejpam-6670	381	17	differential	differential	ADJ
ejpam-6670	381	18	equations	equation	NOUN
ejpam-6670	381	19	(	(	PUNCT
ejpam-6670	381	20	sdes	sde	NOUN
ejpam-6670	381	21	)	)	PUNCT
ejpam-6670	381	22	and	and	CCONJ
ejpam-6670	381	23	predict	predict	VERB
ejpam-6670	381	24	for	for	ADP
ejpam-6670	381	25	the	the	DET
ejpam-6670	381	26	long	long	ADJ
ejpam-6670	381	27	run	run	NOUN
ejpam-6670	381	28	.	.	PUNCT
ejpam-6670	382	1	acknowledgements	acknowledgement	NOUN
ejpam-6670	382	2	this	this	DET
ejpam-6670	382	3	work	work	NOUN
ejpam-6670	382	4	was	be	AUX
ejpam-6670	382	5	supported	support	VERB
ejpam-6670	382	6	by	by	ADP
ejpam-6670	382	7	the	the	DET
ejpam-6670	382	8	national	national	PROPN
ejpam-6670	382	9	research	research	PROPN
ejpam-6670	382	10	foundation	foundation	PROPN
ejpam-6670	382	11	of	of	ADP
ejpam-6670	382	12	korea	korea	PROPN
ejpam-6670	382	13	(	(	PUNCT
ejpam-6670	382	14	nrf	nrf	NOUN
ejpam-6670	382	15	)	)	PUNCT
ejpam-6670	382	16	grant	grant	NOUN
ejpam-6670	382	17	funded	fund	VERB
ejpam-6670	382	18	by	by	ADP
ejpam-6670	382	19	the	the	DET
ejpam-6670	382	20	korean	korean	ADJ
ejpam-6670	382	21	government	government	NOUN
ejpam-6670	382	22	(	(	PUNCT
ejpam-6670	382	23	msit	msit	PROPN
ejpam-6670	382	24	)	)	PUNCT
ejpam-6670	382	25	(	(	PUNCT
ejpam-6670	382	26	no	no	INTJ
ejpam-6670	382	27	.	.	PUNCT
ejpam-6670	383	1	rs-2024	rs-2024	NOUN
ejpam-6670	383	2	-	-	PUNCT
ejpam-6670	383	3	00342113	00342113	NUM
ejpam-6670	383	4	and	and	CCONJ
ejpam-6670	383	5	2022r1a5a1033624	2022r1a5a1033624	NUM
ejpam-6670	383	6	)	)	PUNCT
ejpam-6670	383	7	.	.	PUNCT
ejpam-6670	384	1	references	reference	NOUN
ejpam-6670	384	2	[	[	X
ejpam-6670	384	3	1	1	NUM
ejpam-6670	384	4	]	]	X
ejpam-6670	384	5	scott	scott	PROPN
ejpam-6670	384	6	d	d	PROPN
ejpam-6670	384	7	holmberg	holmberg	PROPN
ejpam-6670	384	8	,	,	PUNCT
ejpam-6670	384	9	anil	anil	PROPN
ejpam-6670	384	10	suryaprasad	suryaprasad	PROPN
ejpam-6670	384	11	,	,	PUNCT
ejpam-6670	384	12	and	and	CCONJ
ejpam-6670	384	13	john	john	PROPN
ejpam-6670	384	14	w	w	PROPN
ejpam-6670	384	15	ward	ward	PROPN
ejpam-6670	384	16	.	.	PUNCT
ejpam-6670	385	1	updated	update	VERB
ejpam-6670	385	2	cdc	cdc	NOUN
ejpam-6670	385	3	recommendations	recommendation	NOUN
ejpam-6670	385	4	for	for	ADP
ejpam-6670	385	5	the	the	DET
ejpam-6670	385	6	management	management	NOUN
ejpam-6670	385	7	of	of	ADP
ejpam-6670	385	8	hepatitis	hepatitis	PROPN
ejpam-6670	385	9	b	b	PROPN
ejpam-6670	385	10	virus	virus	NOUN
ejpam-6670	385	11	infected	infect	VERB
ejpam-6670	385	12	health	health	NOUN
ejpam-6670	385	13	care	care	NOUN
ejpam-6670	385	14	providers	provider	NOUN
ejpam-6670	385	15	and	and	CCONJ
ejpam-6670	385	16	students	student	NOUN
ejpam-6670	385	17	.	.	PUNCT
ejpam-6670	386	1	2012	2012	NUM
ejpam-6670	386	2	.	.	PUNCT
ejpam-6670	387	1	[	[	X
ejpam-6670	387	2	2	2	NUM
ejpam-6670	387	3	]	]	PUNCT
ejpam-6670	387	4	sonia	sonia	NOUN
ejpam-6670	387	5	altizer	altizer	NOUN
ejpam-6670	387	6	,	,	PUNCT
ejpam-6670	387	7	andrew	andrew	PROPN
ejpam-6670	387	8	dobson	dobson	PROPN
ejpam-6670	387	9	,	,	PUNCT
ejpam-6670	387	10	parviez	parviez	PROPN
ejpam-6670	387	11	hosseini	hosseini	PROPN
ejpam-6670	387	12	,	,	PUNCT
ejpam-6670	387	13	peter	peter	PROPN
ejpam-6670	387	14	hudson	hudson	PROPN
ejpam-6670	387	15	,	,	PUNCT
ejpam-6670	387	16	mercedes	mercedes	PROPN
ejpam-6670	387	17	pascual	pascual	PROPN
ejpam-6670	387	18	,	,	PUNCT
ejpam-6670	387	19	and	and	CCONJ
ejpam-6670	387	20	pejman	pejman	ADJ
ejpam-6670	387	21	rohani	rohani	PROPN
ejpam-6670	387	22	.	.	PUNCT
ejpam-6670	387	23	seasonality	seasonality	NOUN
ejpam-6670	387	24	and	and	CCONJ
ejpam-6670	387	25	the	the	DET
ejpam-6670	387	26	dynamics	dynamic	NOUN
ejpam-6670	387	27	of	of	ADP
ejpam-6670	387	28	infectious	infectious	ADJ
ejpam-6670	387	29	diseases	disease	NOUN
ejpam-6670	387	30	.	.	PUNCT
ejpam-6670	388	1	ecology	ecology	NOUN
ejpam-6670	388	2	letters	letter	NOUN
ejpam-6670	388	3	,	,	PUNCT
ejpam-6670	388	4	9(4):467–484	9(4):467–484	NUM
ejpam-6670	388	5	,	,	PUNCT
ejpam-6670	388	6	2006	2006	NUM
ejpam-6670	388	7	.	.	PUNCT
ejpam-6670	389	1	[	[	X
ejpam-6670	389	2	3	3	NUM
ejpam-6670	389	3	]	]	X
ejpam-6670	389	4	brian	brian	PROPN
ejpam-6670	389	5	j	j	PROPN
ejpam-6670	389	6	mcmahon	mcmahon	PROPN
ejpam-6670	389	7	.	.	PUNCT
ejpam-6670	390	1	epidemiology	epidemiology	NOUN
ejpam-6670	390	2	and	and	CCONJ
ejpam-6670	390	3	natural	natural	ADJ
ejpam-6670	390	4	history	history	NOUN
ejpam-6670	390	5	of	of	ADP
ejpam-6670	390	6	hepatitis	hepatitis	PROPN
ejpam-6670	390	7	b.	b.	PROPN
ejpam-6670	390	8	in	in	ADP
ejpam-6670	390	9	seminars	seminar	NOUN
ejpam-6670	390	10	in	in	ADP
ejpam-6670	390	11	liver	liver	NOUN
ejpam-6670	390	12	disease	disease	NOUN
ejpam-6670	390	13	,	,	PUNCT
ejpam-6670	390	14	volume	volume	NOUN
ejpam-6670	390	15	25	25	NUM
ejpam-6670	390	16	,	,	PUNCT
ejpam-6670	390	17	pages	page	NOUN
ejpam-6670	390	18	3–8	3–8	NUM
ejpam-6670	390	19	.	.	PUNCT
ejpam-6670	390	20	published	publish	VERB
ejpam-6670	390	21	in	in	ADP
ejpam-6670	390	22	2005	2005	NUM
ejpam-6670	390	23	by	by	ADP
ejpam-6670	390	24	thieme	thieme	NOUN
ejpam-6670	390	25	medical	medical	ADJ
ejpam-6670	390	26	publishers	publisher	NOUN
ejpam-6670	390	27	,	,	PUNCT
ejpam-6670	390	28	inc	inc	PROPN
ejpam-6670	390	29	.	.	PROPN
ejpam-6670	390	30	,	,	PUNCT
ejpam-6670	390	31	333	333	NUM
ejpam-6670	390	32	seventh	seventh	ADJ
ejpam-6670	390	33	avenue	avenue	NOUN
ejpam-6670	390	34	.	.	PUNCT
ejpam-6670	390	35	.	.	PUNCT
ejpam-6670	391	1	.	.	PUNCT
ejpam-6670	392	1	,	,	PUNCT
ejpam-6670	392	2	2005	2005	NUM
ejpam-6670	392	3	.	.	PUNCT
ejpam-6670	393	1	[	[	X
ejpam-6670	393	2	4	4	NUM
ejpam-6670	393	3	]	]	PUNCT
ejpam-6670	393	4	yukihiko	yukihiko	NOUN
ejpam-6670	393	5	nakata	nakata	NOUN
ejpam-6670	393	6	and	and	CCONJ
ejpam-6670	393	7	toshikazu	toshikazu	NOUN
ejpam-6670	393	8	kuniya	kuniya	PROPN
ejpam-6670	393	9	.	.	PUNCT
ejpam-6670	394	1	global	global	ADJ
ejpam-6670	394	2	dynamics	dynamic	NOUN
ejpam-6670	394	3	of	of	ADP
ejpam-6670	394	4	a	a	DET
ejpam-6670	394	5	class	class	NOUN
ejpam-6670	394	6	of	of	ADP
ejpam-6670	394	7	seirs	seir	NOUN
ejpam-6670	394	8	epidemic	epidemic	NOUN
ejpam-6670	394	9	models	model	NOUN
ejpam-6670	394	10	in	in	ADP
ejpam-6670	394	11	a	a	DET
ejpam-6670	394	12	periodic	periodic	ADJ
ejpam-6670	394	13	environment	environment	NOUN
ejpam-6670	394	14	.	.	PUNCT
ejpam-6670	395	1	journal	journal	PROPN
ejpam-6670	395	2	of	of	ADP
ejpam-6670	395	3	mathematical	mathematical	ADJ
ejpam-6670	395	4	analysis	analysis	NOUN
ejpam-6670	395	5	and	and	CCONJ
ejpam-6670	395	6	applications	application	NOUN
ejpam-6670	395	7	,	,	PUNCT
ejpam-6670	395	8	363(1):230–237	363(1):230–237	NUM
ejpam-6670	395	9	,	,	PUNCT
ejpam-6670	395	10	2010	2010	NUM
ejpam-6670	395	11	.	.	PUNCT
ejpam-6670	396	1	[	[	X
ejpam-6670	396	2	5	5	X
ejpam-6670	396	3	]	]	PUNCT
ejpam-6670	396	4	marc	marc	PROPN
ejpam-6670	396	5	ringehan	ringehan	PROPN
ejpam-6670	396	6	,	,	PUNCT
ejpam-6670	396	7	jane	jane	NOUN
ejpam-6670	396	8	a	a	DET
ejpam-6670	396	9	mckeating	mckeating	NOUN
ejpam-6670	396	10	,	,	PUNCT
ejpam-6670	396	11	and	and	CCONJ
ejpam-6670	396	12	ulrike	ulrike	PROPN
ejpam-6670	396	13	protzer	protzer	NOUN
ejpam-6670	396	14	.	.	PUNCT
ejpam-6670	397	1	viral	viral	ADJ
ejpam-6670	397	2	hepatitis	hepatitis	NOUN
ejpam-6670	397	3	and	and	CCONJ
ejpam-6670	397	4	liver	liver	NOUN
ejpam-6670	397	5	cancer	cancer	NOUN
ejpam-6670	397	6	.	.	PUNCT
ejpam-6670	398	1	philosophical	philosophical	ADJ
ejpam-6670	398	2	transactions	transaction	NOUN
ejpam-6670	398	3	of	of	ADP
ejpam-6670	398	4	the	the	DET
ejpam-6670	398	5	royal	royal	ADJ
ejpam-6670	398	6	society	society	NOUN
ejpam-6670	398	7	b	b	PROPN
ejpam-6670	398	8	:	:	PUNCT
ejpam-6670	398	9	biological	biological	ADJ
ejpam-6670	398	10	sciences	science	NOUN
ejpam-6670	398	11	,	,	PUNCT
ejpam-6670	398	12	372(1732):20160274	372(1732):20160274	NOUN
ejpam-6670	398	13	,	,	PUNCT
ejpam-6670	398	14	2017	2017	NUM
ejpam-6670	398	15	.	.	PUNCT
ejpam-6670	399	1	[	[	X
ejpam-6670	399	2	6	6	NUM
ejpam-6670	399	3	]	]	X
ejpam-6670	399	4	abubakar	abubakar	PROPN
ejpam-6670	399	5	mwasa	mwasa	PROPN
ejpam-6670	399	6	and	and	CCONJ
ejpam-6670	399	7	jean	jean	PROPN
ejpam-6670	399	8	m	m	PROPN
ejpam-6670	399	9	tchuenche	tchuenche	PROPN
ejpam-6670	399	10	.	.	PUNCT
ejpam-6670	400	1	mathematical	mathematical	ADJ
ejpam-6670	400	2	analysis	analysis	NOUN
ejpam-6670	400	3	of	of	ADP
ejpam-6670	400	4	a	a	DET
ejpam-6670	400	5	cholera	cholera	NOUN
ejpam-6670	400	6	model	model	NOUN
ejpam-6670	400	7	with	with	ADP
ejpam-6670	400	8	public	public	ADJ
ejpam-6670	400	9	health	health	NOUN
ejpam-6670	400	10	interventions	intervention	NOUN
ejpam-6670	400	11	.	.	PUNCT
ejpam-6670	401	1	biosystems	biosystem	NOUN
ejpam-6670	401	2	,	,	PUNCT
ejpam-6670	401	3	105(3):190–200	105(3):190–200	NUM
ejpam-6670	401	4	,	,	PUNCT
ejpam-6670	401	5	2011	2011	NUM
ejpam-6670	401	6	.	.	PUNCT
ejpam-6670	402	1	[	[	X
ejpam-6670	402	2	7	7	X
ejpam-6670	402	3	]	]	SYM
ejpam-6670	402	4	tailei	tailei	PROPN
ejpam-6670	402	5	zhang	zhang	PROPN
ejpam-6670	402	6	,	,	PUNCT
ejpam-6670	402	7	kai	kai	PROPN
ejpam-6670	402	8	wang	wang	PROPN
ejpam-6670	402	9	,	,	PUNCT
ejpam-6670	402	10	and	and	CCONJ
ejpam-6670	402	11	xueliang	xueliang	PROPN
ejpam-6670	402	12	zhang	zhang	PROPN
ejpam-6670	402	13	.	.	PUNCT
ejpam-6670	403	1	modeling	modeling	NOUN
ejpam-6670	403	2	and	and	CCONJ
ejpam-6670	403	3	analyzing	analyze	VERB
ejpam-6670	403	4	the	the	DET
ejpam-6670	403	5	transmission	transmission	NOUN
ejpam-6670	403	6	dynamics	dynamic	NOUN
ejpam-6670	403	7	of	of	ADP
ejpam-6670	403	8	hbv	hbv	NOUN
ejpam-6670	403	9	epidemic	epidemic	NOUN
ejpam-6670	403	10	in	in	ADP
ejpam-6670	403	11	xinjiang	xinjiang	PROPN
ejpam-6670	403	12	,	,	PUNCT
ejpam-6670	403	13	china	china	PROPN
ejpam-6670	403	14	.	.	PUNCT
ejpam-6670	404	1	plos	plos	PROPN
ejpam-6670	404	2	one	one	NUM
ejpam-6670	404	3	,	,	PUNCT
ejpam-6670	404	4	10(9):e0138765	10(9):e0138765	PROPN
ejpam-6670	404	5	,	,	PUNCT
ejpam-6670	404	6	2015	2015	NUM
ejpam-6670	404	7	.	.	PUNCT
ejpam-6670	405	1	[	[	X
ejpam-6670	405	2	8	8	NUM
ejpam-6670	405	3	]	]	X
ejpam-6670	405	4	kamil	kamil	PROPN
ejpam-6670	405	5	shah	shah	PROPN
ejpam-6670	405	6	,	,	PUNCT
ejpam-6670	405	7	jamal	jamal	PROPN
ejpam-6670	405	8	shah	shah	PROPN
ejpam-6670	405	9	,	,	PUNCT
ejpam-6670	405	10	ebenezer	ebenezer	PROPN
ejpam-6670	405	11	bonyah	bonyah	PROPN
ejpam-6670	405	12	,	,	PUNCT
ejpam-6670	405	13	tmader	tmader	NOUN
ejpam-6670	405	14	alballa	alballa	PROPN
ejpam-6670	405	15	,	,	PUNCT
ejpam-6670	405	16	hamiden	hamiden	PROPN
ejpam-6670	405	17	abd	abd	PROPN
ejpam-6670	405	18	elwahed	elwahe	VERB
ejpam-6670	405	19	khalifa	khalifa	PROPN
ejpam-6670	405	20	,	,	PUNCT
ejpam-6670	405	21	usman	usman	PROPN
ejpam-6670	405	22	khan	khan	PROPN
ejpam-6670	405	23	,	,	PUNCT
ejpam-6670	405	24	and	and	CCONJ
ejpam-6670	405	25	hameed	hameed	PROPN
ejpam-6670	405	26	khan	khan	PROPN
ejpam-6670	405	27	.	.	PUNCT
ejpam-6670	406	1	optimal	optimal	ADJ
ejpam-6670	406	2	control	control	NOUN
ejpam-6670	406	3	of	of	ADP
ejpam-6670	406	4	covid-19	covid-19	PROPN
ejpam-6670	406	5	through	through	ADP
ejpam-6670	406	6	strategic	strategic	ADJ
ejpam-6670	406	7	mathematical	mathematical	ADJ
ejpam-6670	406	8	modeling	modeling	NOUN
ejpam-6670	406	9	:	:	PUNCT
ejpam-6670	406	10	incorporating	incorporate	VERB
ejpam-6670	406	11	harmonic	harmonic	ADJ
ejpam-6670	406	12	mean	mean	NOUN
ejpam-6670	406	13	incident	incident	NOUN
ejpam-6670	406	14	rate	rate	NOUN
ejpam-6670	406	15	and	and	CCONJ
ejpam-6670	406	16	vaccination	vaccination	NOUN
ejpam-6670	406	17	.	.	PUNCT
ejpam-6670	407	1	aip	aip	PROPN
ejpam-6670	407	2	advances	advance	NOUN
ejpam-6670	407	3	,	,	PUNCT
ejpam-6670	407	4	14(9	14(9	NUM
ejpam-6670	407	5	)	)	PUNCT
ejpam-6670	407	6	,	,	PUNCT
ejpam-6670	407	7	2024	2024	NUM
ejpam-6670	407	8	.	.	PUNCT
ejpam-6670	408	1	t.	t.	PROPN
ejpam-6670	408	2	khan	khan	PROPN
ejpam-6670	408	3	et	et	PROPN
ejpam-6670	408	4	al	al	PROPN
ejpam-6670	408	5	.	.	PUNCT
ejpam-6670	408	6	/	/	SYM
ejpam-6670	408	7	eur	eur	PROPN
ejpam-6670	408	8	.	.	PUNCT
ejpam-6670	409	1	j.	j.	PROPN
ejpam-6670	409	2	pure	pure	PROPN
ejpam-6670	409	3	appl	appl	PROPN
ejpam-6670	409	4	.	.	PROPN
ejpam-6670	409	5	math	math	PROPN
ejpam-6670	409	6	,	,	PUNCT
ejpam-6670	409	7	18	18	NUM
ejpam-6670	409	8	(	(	PUNCT
ejpam-6670	409	9	3	3	NUM
ejpam-6670	409	10	)	)	PUNCT
ejpam-6670	409	11	(	(	PUNCT
ejpam-6670	409	12	2025	2025	NUM
ejpam-6670	409	13	)	)	PUNCT
ejpam-6670	409	14	,	,	PUNCT
ejpam-6670	409	15	6670	6670	NUM
ejpam-6670	409	16	21	21	NUM
ejpam-6670	409	17	of	of	ADP
ejpam-6670	409	18	22	22	NUM
ejpam-6670	410	1	[	[	X
ejpam-6670	410	2	9	9	NUM
ejpam-6670	410	3	]	]	X
ejpam-6670	410	4	muhammad	muhammad	PROPN
ejpam-6670	410	5	farhan	farhan	PROPN
ejpam-6670	410	6	,	,	PUNCT
ejpam-6670	410	7	fahad	fahad	PROPN
ejpam-6670	410	8	aljuaydi	aljuaydi	PROPN
ejpam-6670	410	9	,	,	PUNCT
ejpam-6670	410	10	zahir	zahir	ADJ
ejpam-6670	410	11	shah	shah	NOUN
ejpam-6670	410	12	,	,	PUNCT
ejpam-6670	410	13	ebraheem	ebraheem	NOUN
ejpam-6670	410	14	alzahrani	alzahrani	PROPN
ejpam-6670	410	15	,	,	PUNCT
ejpam-6670	410	16	ebenezer	ebenezer	PROPN
ejpam-6670	410	17	bonyah	bonyah	PROPN
ejpam-6670	410	18	,	,	PUNCT
ejpam-6670	410	19	and	and	CCONJ
ejpam-6670	410	20	saeed	saeed	PROPN
ejpam-6670	410	21	islam	islam	PROPN
ejpam-6670	410	22	.	.	PUNCT
ejpam-6670	411	1	a	a	DET
ejpam-6670	411	2	fractional	fractional	ADJ
ejpam-6670	411	3	modeling	modeling	NOUN
ejpam-6670	411	4	approach	approach	NOUN
ejpam-6670	411	5	to	to	ADP
ejpam-6670	411	6	a	a	DET
ejpam-6670	411	7	new	new	ADJ
ejpam-6670	411	8	hepatitis	hepatitis	NOUN
ejpam-6670	411	9	b	b	PROPN
ejpam-6670	411	10	model	model	NOUN
ejpam-6670	411	11	in	in	ADP
ejpam-6670	411	12	light	light	NOUN
ejpam-6670	411	13	of	of	ADP
ejpam-6670	411	14	asymptomatic	asymptomatic	ADJ
ejpam-6670	411	15	carriers	carrier	NOUN
ejpam-6670	411	16	,	,	PUNCT
ejpam-6670	411	17	vaccination	vaccination	NOUN
ejpam-6670	411	18	and	and	CCONJ
ejpam-6670	411	19	treatment	treatment	NOUN
ejpam-6670	411	20	.	.	PUNCT
ejpam-6670	412	1	scientific	scientific	ADJ
ejpam-6670	412	2	african	african	ADJ
ejpam-6670	412	3	,	,	PUNCT
ejpam-6670	412	4	24	24	NUM
ejpam-6670	412	5	:	:	PUNCT
ejpam-6670	412	6	e02127	e02127	PROPN
ejpam-6670	412	7	,	,	PUNCT
ejpam-6670	412	8	2024	2024	NUM
ejpam-6670	412	9	.	.	PUNCT
ejpam-6670	413	1	[	[	X
ejpam-6670	413	2	10	10	NUM
ejpam-6670	413	3	]	]	X
ejpam-6670	413	4	lan	lan	PROPN
ejpam-6670	413	5	zou	zou	PROPN
ejpam-6670	413	6	,	,	PUNCT
ejpam-6670	413	7	weinian	weinian	PROPN
ejpam-6670	413	8	zhang	zhang	PROPN
ejpam-6670	413	9	,	,	PUNCT
ejpam-6670	413	10	and	and	CCONJ
ejpam-6670	413	11	shigui	shigui	NOUN
ejpam-6670	413	12	ruan	ruan	PROPN
ejpam-6670	413	13	.	.	PUNCT
ejpam-6670	414	1	modeling	model	VERB
ejpam-6670	414	2	the	the	DET
ejpam-6670	414	3	transmission	transmission	NOUN
ejpam-6670	414	4	dynamics	dynamic	NOUN
ejpam-6670	414	5	and	and	CCONJ
ejpam-6670	414	6	control	control	NOUN
ejpam-6670	414	7	of	of	ADP
ejpam-6670	414	8	hepatitis	hepatitis	PROPN
ejpam-6670	414	9	b	b	PROPN
ejpam-6670	414	10	virus	virus	NOUN
ejpam-6670	414	11	in	in	ADP
ejpam-6670	414	12	china	china	PROPN
ejpam-6670	414	13	.	.	PUNCT
ejpam-6670	415	1	journal	journal	PROPN
ejpam-6670	415	2	of	of	ADP
ejpam-6670	415	3	theoretical	theoretical	ADJ
ejpam-6670	415	4	biology	biology	NOUN
ejpam-6670	415	5	,	,	PUNCT
ejpam-6670	415	6	262(2):330–338	262(2):330–338	NUM
ejpam-6670	415	7	,	,	PUNCT
ejpam-6670	415	8	2010	2010	NUM
ejpam-6670	415	9	.	.	PUNCT
ejpam-6670	416	1	[	[	X
ejpam-6670	416	2	11	11	NUM
ejpam-6670	416	3	]	]	PUNCT
ejpam-6670	416	4	junjie	junjie	PROPN
ejpam-6670	416	5	zhu	zhu	PROPN
ejpam-6670	416	6	,	,	PUNCT
ejpam-6670	416	7	misbah	misbah	PROPN
ejpam-6670	416	8	ullah	ullah	PROPN
ejpam-6670	416	9	,	,	PUNCT
ejpam-6670	416	10	saif	saif	PROPN
ejpam-6670	416	11	ullah	ullah	PROPN
ejpam-6670	416	12	,	,	PUNCT
ejpam-6670	416	13	muhammad	muhammad	PROPN
ejpam-6670	416	14	bilal	bilal	PROPN
ejpam-6670	416	15	riaz	riaz	PROPN
ejpam-6670	416	16	,	,	PUNCT
ejpam-6670	416	17	abdul	abdul	PROPN
ejpam-6670	416	18	baseer	baseer	PROPN
ejpam-6670	416	19	saqib	saqib	PROPN
ejpam-6670	416	20	,	,	PUNCT
ejpam-6670	416	21	atif	atif	PROPN
ejpam-6670	416	22	m	m	VERB
ejpam-6670	416	23	alamri	alamri	ADJ
ejpam-6670	416	24	,	,	PUNCT
ejpam-6670	416	25	and	and	CCONJ
ejpam-6670	416	26	salman	salman	PROPN
ejpam-6670	416	27	a	a	DET
ejpam-6670	416	28	alqahtani	alqahtani	PROPN
ejpam-6670	416	29	.	.	PUNCT
ejpam-6670	417	1	a	a	DET
ejpam-6670	417	2	novel	novel	ADJ
ejpam-6670	417	3	numerical	numerical	ADJ
ejpam-6670	417	4	solution	solution	NOUN
ejpam-6670	417	5	of	of	ADP
ejpam-6670	417	6	nonlinear	nonlinear	ADJ
ejpam-6670	417	7	stochastic	stochastic	ADJ
ejpam-6670	417	8	model	model	NOUN
ejpam-6670	417	9	for	for	ADP
ejpam-6670	417	10	the	the	DET
ejpam-6670	417	11	propagation	propagation	NOUN
ejpam-6670	417	12	of	of	ADP
ejpam-6670	417	13	malicious	malicious	ADJ
ejpam-6670	417	14	codes	code	NOUN
ejpam-6670	417	15	in	in	ADP
ejpam-6670	417	16	wireless	wireless	ADJ
ejpam-6670	417	17	sensor	sensor	NOUN
ejpam-6670	417	18	networks	network	NOUN
ejpam-6670	417	19	using	use	VERB
ejpam-6670	417	20	a	a	DET
ejpam-6670	417	21	high	high	ADJ
ejpam-6670	417	22	order	order	NOUN
ejpam-6670	417	23	spectral	spectral	ADJ
ejpam-6670	417	24	collocation	collocation	NOUN
ejpam-6670	417	25	technique	technique	NOUN
ejpam-6670	417	26	.	.	PUNCT
ejpam-6670	418	1	scientific	scientific	ADJ
ejpam-6670	418	2	reports	report	NOUN
ejpam-6670	418	3	,	,	PUNCT
ejpam-6670	418	4	15(1):228	15(1):228	NUM
ejpam-6670	418	5	,	,	PUNCT
ejpam-6670	418	6	2025	2025	NUM
ejpam-6670	418	7	.	.	PUNCT
ejpam-6670	419	1	[	[	X
ejpam-6670	419	2	12	12	NUM
ejpam-6670	419	3	]	]	PUNCT
ejpam-6670	419	4	anwarud	anwarud	PROPN
ejpam-6670	419	5	din	din	PROPN
ejpam-6670	419	6	and	and	CCONJ
ejpam-6670	419	7	yongjin	yongjin	PROPN
ejpam-6670	419	8	li	li	PROPN
ejpam-6670	419	9	.	.	PROPN
ejpam-6670	419	10	optimizing	optimize	VERB
ejpam-6670	419	11	hiv	hiv	PROPN
ejpam-6670	419	12	/	/	SYM
ejpam-6670	419	13	aids	aids	PROPN
ejpam-6670	419	14	dynamics	dynamic	NOUN
ejpam-6670	419	15	:	:	PUNCT
ejpam-6670	419	16	stochastic	stochastic	ADJ
ejpam-6670	419	17	control	control	NOUN
ejpam-6670	419	18	strategies	strategy	NOUN
ejpam-6670	419	19	with	with	ADP
ejpam-6670	419	20	education	education	NOUN
ejpam-6670	419	21	and	and	CCONJ
ejpam-6670	419	22	treatment	treatment	NOUN
ejpam-6670	419	23	.	.	PUNCT
ejpam-6670	420	1	the	the	DET
ejpam-6670	420	2	european	european	PROPN
ejpam-6670	420	3	physical	physical	PROPN
ejpam-6670	420	4	journal	journal	PROPN
ejpam-6670	420	5	plus	plus	CCONJ
ejpam-6670	420	6	,	,	PUNCT
ejpam-6670	420	7	139(9):812	139(9):812	NUM
ejpam-6670	420	8	,	,	PUNCT
ejpam-6670	420	9	2024	2024	NUM
ejpam-6670	420	10	.	.	PUNCT
ejpam-6670	421	1	[	[	X
ejpam-6670	421	2	13	13	NUM
ejpam-6670	421	3	]	]	X
ejpam-6670	421	4	wan	wan	PROPN
ejpam-6670	421	5	yang	yang	PROPN
ejpam-6670	421	6	,	,	PUNCT
ejpam-6670	421	7	alicia	alicia	PROPN
ejpam-6670	421	8	karspeck	karspeck	PROPN
ejpam-6670	421	9	,	,	PUNCT
ejpam-6670	421	10	and	and	CCONJ
ejpam-6670	421	11	jeffrey	jeffrey	PROPN
ejpam-6670	421	12	shaman	shaman	PROPN
ejpam-6670	421	13	.	.	PUNCT
ejpam-6670	422	1	comparison	comparison	NOUN
ejpam-6670	422	2	of	of	ADP
ejpam-6670	422	3	filtering	filter	VERB
ejpam-6670	422	4	methods	method	NOUN
ejpam-6670	422	5	for	for	ADP
ejpam-6670	422	6	the	the	DET
ejpam-6670	422	7	modeling	modeling	NOUN
ejpam-6670	422	8	and	and	CCONJ
ejpam-6670	422	9	retrospective	retrospective	ADJ
ejpam-6670	422	10	forecasting	forecasting	NOUN
ejpam-6670	422	11	of	of	ADP
ejpam-6670	422	12	influenza	influenza	NOUN
ejpam-6670	422	13	epidemics	epidemic	NOUN
ejpam-6670	422	14	.	.	PUNCT
ejpam-6670	423	1	plos	plos	PROPN
ejpam-6670	423	2	computational	computational	ADJ
ejpam-6670	423	3	biology	biology	NOUN
ejpam-6670	423	4	,	,	PUNCT
ejpam-6670	423	5	10(4):e1003583	10(4):e1003583	NOUN
ejpam-6670	423	6	,	,	PUNCT
ejpam-6670	423	7	2014	2014	NUM
ejpam-6670	423	8	.	.	PUNCT
ejpam-6670	424	1	[	[	X
ejpam-6670	424	2	14	14	NUM
ejpam-6670	424	3	]	]	X
ejpam-6670	424	4	suthep	suthep	NOUN
ejpam-6670	424	5	suantai	suantai	VERB
ejpam-6670	424	6	,	,	PUNCT
ejpam-6670	424	7	zulqurnain	zulqurnain	PROPN
ejpam-6670	424	8	sabir	sabir	PROPN
ejpam-6670	424	9	,	,	PUNCT
ejpam-6670	424	10	muhammad	muhammad	PROPN
ejpam-6670	424	11	asif	asif	PROPN
ejpam-6670	424	12	zahoor	zahoor	PROPN
ejpam-6670	424	13	raja	raja	PROPN
ejpam-6670	424	14	,	,	PUNCT
ejpam-6670	424	15	and	and	CCONJ
ejpam-6670	424	16	watcharaporn	watcharaporn	VERB
ejpam-6670	424	17	cholamjiak	cholamjiak	PROPN
ejpam-6670	424	18	.	.	PUNCT
ejpam-6670	425	1	a	a	DET
ejpam-6670	425	2	stochastic	stochastic	ADJ
ejpam-6670	425	3	bayesian	bayesian	NOUN
ejpam-6670	425	4	neural	neural	ADJ
ejpam-6670	425	5	network	network	NOUN
ejpam-6670	425	6	for	for	ADP
ejpam-6670	425	7	the	the	DET
ejpam-6670	425	8	mosquito	mosquito	NOUN
ejpam-6670	425	9	dispersal	dispersal	PROPN
ejpam-6670	425	10	mathematical	mathematical	ADJ
ejpam-6670	425	11	system	system	NOUN
ejpam-6670	425	12	.	.	PUNCT
ejpam-6670	426	1	fractal	fractal	ADJ
ejpam-6670	426	2	and	and	CCONJ
ejpam-6670	426	3	fractional	fractional	ADJ
ejpam-6670	426	4	,	,	PUNCT
ejpam-6670	426	5	6(10):604	6(10):604	NUM
ejpam-6670	426	6	,	,	PUNCT
ejpam-6670	426	7	2022	2022	NUM
ejpam-6670	426	8	.	.	PUNCT
ejpam-6670	427	1	[	[	X
ejpam-6670	427	2	15	15	NUM
ejpam-6670	427	3	]	]	X
ejpam-6670	427	4	atifa	atifa	PROPN
ejpam-6670	427	5	asghar	asghar	PROPN
ejpam-6670	427	6	,	,	PUNCT
ejpam-6670	427	7	mohsan	mohsan	PROPN
ejpam-6670	427	8	hassan	hassan	PROPN
ejpam-6670	427	9	,	,	PUNCT
ejpam-6670	427	10	zulqurnain	zulqurnain	PROPN
ejpam-6670	427	11	sabir	sabir	PROPN
ejpam-6670	427	12	,	,	PUNCT
ejpam-6670	427	13	shahid	shahid	PROPN
ejpam-6670	427	14	ahmad	ahmad	PROPN
ejpam-6670	427	15	bhat	bhat	PROPN
ejpam-6670	427	16	,	,	PUNCT
ejpam-6670	427	17	and	and	CCONJ
ejpam-6670	427	18	sharifah	sharifah	PROPN
ejpam-6670	427	19	e	e	PROPN
ejpam-6670	427	20	alhazmi	alhazmi	PROPN
ejpam-6670	427	21	.	.	PUNCT
ejpam-6670	428	1	a	a	DET
ejpam-6670	428	2	design	design	NOUN
ejpam-6670	428	3	of	of	ADP
ejpam-6670	428	4	computational	computational	ADJ
ejpam-6670	428	5	stochastic	stochastic	ADJ
ejpam-6670	428	6	framework	framework	NOUN
ejpam-6670	428	7	for	for	ADP
ejpam-6670	428	8	the	the	DET
ejpam-6670	428	9	mathematical	mathematical	ADJ
ejpam-6670	428	10	severe	severe	ADJ
ejpam-6670	428	11	acute	acute	ADJ
ejpam-6670	428	12	respiratory	respiratory	ADJ
ejpam-6670	428	13	syndrome	syndrome	NOUN
ejpam-6670	428	14	coronavirus	coronavirus	NOUN
ejpam-6670	428	15	model	model	NOUN
ejpam-6670	428	16	.	.	PUNCT
ejpam-6670	429	1	biomedical	biomedical	ADJ
ejpam-6670	429	2	signal	signal	NOUN
ejpam-6670	429	3	processing	processing	NOUN
ejpam-6670	429	4	and	and	CCONJ
ejpam-6670	429	5	control	control	NOUN
ejpam-6670	429	6	,	,	PUNCT
ejpam-6670	429	7	100:107049	100:107049	NUM
ejpam-6670	429	8	,	,	PUNCT
ejpam-6670	429	9	2025	2025	NUM
ejpam-6670	429	10	.	.	PUNCT
ejpam-6670	430	1	[	[	X
ejpam-6670	430	2	16	16	NUM
ejpam-6670	430	3	]	]	X
ejpam-6670	430	4	muhammad	muhammad	PROPN
ejpam-6670	430	5	farhan	farhan	PROPN
ejpam-6670	430	6	,	,	PUNCT
ejpam-6670	430	7	saif	saif	PROPN
ejpam-6670	430	8	ullah	ullah	PROPN
ejpam-6670	430	9	,	,	PUNCT
ejpam-6670	430	10	waseem	waseem	PROPN
ejpam-6670	430	11	,	,	PUNCT
ejpam-6670	430	12	muath	muath	NOUN
ejpam-6670	430	13	suliman	suliman	NOUN
ejpam-6670	430	14	,	,	PUNCT
ejpam-6670	430	15	abdul	abdul	PROPN
ejpam-6670	430	16	baseer	baseer	PROPN
ejpam-6670	430	17	saqib	saqib	PROPN
ejpam-6670	430	18	,	,	PUNCT
ejpam-6670	430	19	and	and	CCONJ
ejpam-6670	430	20	mohammed	mohammed	PROPN
ejpam-6670	430	21	qeshta	qeshta	PROPN
ejpam-6670	430	22	.	.	PUNCT
ejpam-6670	431	1	deep	deep	ADJ
ejpam-6670	431	2	learning	learning	NOUN
ejpam-6670	431	3	-	-	PUNCT
ejpam-6670	431	4	driven	drive	VERB
ejpam-6670	431	5	insights	insight	NOUN
ejpam-6670	431	6	into	into	ADP
ejpam-6670	431	7	the	the	DET
ejpam-6670	431	8	transmission	transmission	NOUN
ejpam-6670	431	9	dynamics	dynamic	NOUN
ejpam-6670	431	10	of	of	ADP
ejpam-6670	431	11	hepatitis	hepatitis	PROPN
ejpam-6670	431	12	b	b	PROPN
ejpam-6670	431	13	virus	virus	NOUN
ejpam-6670	431	14	with	with	ADP
ejpam-6670	431	15	treatment	treatment	NOUN
ejpam-6670	431	16	.	.	PUNCT
ejpam-6670	432	1	scientific	scientific	ADJ
ejpam-6670	432	2	reports	report	NOUN
ejpam-6670	432	3	,	,	PUNCT
ejpam-6670	432	4	15(1):23741	15(1):23741	NUM
ejpam-6670	432	5	,	,	PUNCT
ejpam-6670	432	6	2025	2025	NUM
ejpam-6670	432	7	.	.	PUNCT
ejpam-6670	433	1	[	[	X
ejpam-6670	433	2	17	17	NUM
ejpam-6670	433	3	]	]	X
ejpam-6670	433	4	zulqurnain	zulqurnain	PROPN
ejpam-6670	433	5	sabir	sabir	PROPN
ejpam-6670	433	6	,	,	PUNCT
ejpam-6670	433	7	thongchai	thongchai	PROPN
ejpam-6670	433	8	botmart	botmart	PROPN
ejpam-6670	433	9	,	,	PUNCT
ejpam-6670	433	10	muhammad	muhammad	PROPN
ejpam-6670	433	11	asif	asif	PROPN
ejpam-6670	433	12	zahoor	zahoor	PROPN
ejpam-6670	433	13	raja	raja	PROPN
ejpam-6670	433	14	,	,	PUNCT
ejpam-6670	433	15	r	r	NOUN
ejpam-6670	433	16	sadat	sadat	NOUN
ejpam-6670	433	17	,	,	PUNCT
ejpam-6670	433	18	mohamed	mohamed	PROPN
ejpam-6670	433	19	r	r	PROPN
ejpam-6670	433	20	ali	ali	PROPN
ejpam-6670	433	21	,	,	PUNCT
ejpam-6670	433	22	abdulaziz	abdulaziz	PROPN
ejpam-6670	433	23	a	a	DET
ejpam-6670	433	24	alsulami	alsulami	NOUN
ejpam-6670	433	25	,	,	PUNCT
ejpam-6670	433	26	abdullah	abdullah	PROPN
ejpam-6670	433	27	alghamdi	alghamdi	PROPN
ejpam-6670	433	28	,	,	PUNCT
ejpam-6670	433	29	et	et	PROPN
ejpam-6670	433	30	al	al	PROPN
ejpam-6670	433	31	.	.	PUNCT
ejpam-6670	433	32	artificial	artificial	ADJ
ejpam-6670	433	33	neural	neural	ADJ
ejpam-6670	433	34	network	network	NOUN
ejpam-6670	433	35	scheme	scheme	NOUN
ejpam-6670	433	36	to	to	PART
ejpam-6670	433	37	solve	solve	VERB
ejpam-6670	433	38	the	the	DET
ejpam-6670	433	39	nonlinear	nonlinear	ADJ
ejpam-6670	433	40	influenza	influenza	NOUN
ejpam-6670	433	41	disease	disease	NOUN
ejpam-6670	433	42	model	model	PROPN
ejpam-6670	433	43	.	.	PUNCT
ejpam-6670	434	1	biomedical	biomedical	ADJ
ejpam-6670	434	2	signal	signal	NOUN
ejpam-6670	434	3	processing	processing	NOUN
ejpam-6670	434	4	and	and	CCONJ
ejpam-6670	434	5	control	control	NOUN
ejpam-6670	434	6	,	,	PUNCT
ejpam-6670	434	7	75:103594	75:103594	NOUN
ejpam-6670	434	8	,	,	PUNCT
ejpam-6670	434	9	2022	2022	NUM
ejpam-6670	434	10	.	.	PUNCT
ejpam-6670	435	1	[	[	X
ejpam-6670	435	2	18	18	NUM
ejpam-6670	435	3	]	]	X
ejpam-6670	435	4	kanit	kanit	PROPN
ejpam-6670	435	5	mukdasai	mukdasai	PROPN
ejpam-6670	435	6	,	,	PUNCT
ejpam-6670	435	7	zulqurnain	zulqurnain	PROPN
ejpam-6670	435	8	sabir	sabir	PROPN
ejpam-6670	435	9	,	,	PUNCT
ejpam-6670	435	10	muhammad	muhammad	PROPN
ejpam-6670	435	11	asif	asif	PROPN
ejpam-6670	435	12	zahoor	zahoor	PROPN
ejpam-6670	435	13	raja	raja	PROPN
ejpam-6670	435	14	,	,	PUNCT
ejpam-6670	435	15	peerapongpat	peerapongpat	PROPN
ejpam-6670	435	16	singkibud	singkibud	NOUN
ejpam-6670	435	17	,	,	PUNCT
ejpam-6670	435	18	r	r	NOUN
ejpam-6670	435	19	sadat	sadat	NOUN
ejpam-6670	435	20	,	,	PUNCT
ejpam-6670	435	21	and	and	CCONJ
ejpam-6670	435	22	mohamed	mohamed	PROPN
ejpam-6670	435	23	r	r	PROPN
ejpam-6670	435	24	ali	ali	PROPN
ejpam-6670	435	25	.	.	PUNCT
ejpam-6670	436	1	a	a	DET
ejpam-6670	436	2	computational	computational	ADJ
ejpam-6670	436	3	supervised	supervised	ADJ
ejpam-6670	436	4	neural	neural	ADJ
ejpam-6670	436	5	network	network	NOUN
ejpam-6670	436	6	procedure	procedure	NOUN
ejpam-6670	436	7	for	for	ADP
ejpam-6670	436	8	the	the	DET
ejpam-6670	436	9	fractional	fractional	ADJ
ejpam-6670	436	10	siq	siq	PROPN
ejpam-6670	436	11	mathematical	mathematical	PROPN
ejpam-6670	436	12	model	model	NOUN
ejpam-6670	436	13	.	.	PUNCT
ejpam-6670	437	1	the	the	DET
ejpam-6670	437	2	european	european	PROPN
ejpam-6670	437	3	physical	physical	PROPN
ejpam-6670	437	4	journal	journal	PROPN
ejpam-6670	437	5	special	special	ADJ
ejpam-6670	437	6	topics	topic	NOUN
ejpam-6670	437	7	,	,	PUNCT
ejpam-6670	437	8	232(5):535–546	232(5):535–546	NUM
ejpam-6670	437	9	,	,	PUNCT
ejpam-6670	437	10	2023	2023	NUM
ejpam-6670	437	11	.	.	PUNCT
ejpam-6670	438	1	[	[	X
ejpam-6670	438	2	19	19	NUM
ejpam-6670	438	3	]	]	X
ejpam-6670	438	4	muhammad	muhammad	PROPN
ejpam-6670	438	5	farhan	farhan	PROPN
ejpam-6670	438	6	,	,	PUNCT
ejpam-6670	438	7	zhi	zhi	PROPN
ejpam-6670	438	8	ling	ling	PROPN
ejpam-6670	438	9	,	,	PUNCT
ejpam-6670	438	10	saif	saif	PROPN
ejpam-6670	438	11	ullah	ullah	PROPN
ejpam-6670	438	12	,	,	PUNCT
ejpam-6670	438	13	almetwally	almetwally	ADV
ejpam-6670	438	14	m	m	PROPN
ejpam-6670	438	15	mostafa	mostafa	PROPN
ejpam-6670	438	16	,	,	PUNCT
ejpam-6670	438	17	salman	salman	PROPN
ejpam-6670	438	18	a	a	DET
ejpam-6670	438	19	alqahtani	alqahtani	PROPN
ejpam-6670	438	20	,	,	PUNCT
ejpam-6670	438	21	et	et	PROPN
ejpam-6670	438	22	al	al	PROPN
ejpam-6670	438	23	.	.	PUNCT
ejpam-6670	439	1	a	a	DET
ejpam-6670	439	2	novel	novel	ADJ
ejpam-6670	439	3	intelligent	intelligent	ADJ
ejpam-6670	439	4	framework	framework	NOUN
ejpam-6670	439	5	for	for	ADP
ejpam-6670	439	6	assessing	assess	VERB
ejpam-6670	439	7	within	within	ADP
ejpam-6670	439	8	-	-	PUNCT
ejpam-6670	439	9	host	host	NOUN
ejpam-6670	439	10	transmission	transmission	NOUN
ejpam-6670	439	11	dynamics	dynamic	NOUN
ejpam-6670	439	12	of	of	ADP
ejpam-6670	439	13	chikungunya	chikungunya	NOUN
ejpam-6670	439	14	virus	virus	NOUN
ejpam-6670	439	15	using	use	VERB
ejpam-6670	439	16	an	an	DET
ejpam-6670	439	17	unsupervised	unsupervised	ADJ
ejpam-6670	439	18	stochastic	stochastic	ADJ
ejpam-6670	439	19	neural	neural	ADJ
ejpam-6670	439	20	network	network	NOUN
ejpam-6670	439	21	approach	approach	NOUN
ejpam-6670	439	22	.	.	PUNCT
ejpam-6670	440	1	computational	computational	ADJ
ejpam-6670	440	2	biology	biology	NOUN
ejpam-6670	440	3	and	and	CCONJ
ejpam-6670	440	4	chemistry	chemistry	NOUN
ejpam-6670	440	5	,	,	PUNCT
ejpam-6670	440	6	117:108380	117:108380	NUM
ejpam-6670	440	7	,	,	PUNCT
ejpam-6670	440	8	2025	2025	NUM
ejpam-6670	440	9	.	.	PUNCT
ejpam-6670	441	1	[	[	X
ejpam-6670	441	2	20	20	NUM
ejpam-6670	441	3	]	]	X
ejpam-6670	441	4	jamiu	jamiu	X
ejpam-6670	441	5	adeyemi	adeyemi	ADP
ejpam-6670	441	6	ademosu	ademosu	PROPN
ejpam-6670	441	7	,	,	PUNCT
ejpam-6670	441	8	samson	samson	PROPN
ejpam-6670	441	9	olaniyi	olaniyi	PROPN
ejpam-6670	441	10	,	,	PUNCT
ejpam-6670	441	11	sulaimon	sulaimon	PROPN
ejpam-6670	441	12	femi	femi	PROPN
ejpam-6670	441	13	abimbade	abimbade	PROPN
ejpam-6670	441	14	,	,	PUNCT
ejpam-6670	441	15	furaha	furaha	PROPN
ejpam-6670	441	16	michael	michael	PROPN
ejpam-6670	441	17	chuma	chuma	PROPN
ejpam-6670	441	18	,	,	PUNCT
ejpam-6670	441	19	richard	richard	PROPN
ejpam-6670	441	20	chinedu	chinedu	PROPN
ejpam-6670	441	21	ogbonna	ogbonna	PROPN
ejpam-6670	441	22	,	,	PUNCT
ejpam-6670	441	23	ramoshweu	ramoshweu	PROPN
ejpam-6670	441	24	solomon	solomon	PROPN
ejpam-6670	441	25	lebelo	lebelo	PROPN
ejpam-6670	441	26	,	,	PUNCT
ejpam-6670	441	27	and	and	CCONJ
ejpam-6670	441	28	kazeem	kazeem	PROPN
ejpam-6670	441	29	oare	oare	PROPN
ejpam-6670	441	30	okosun	okosun	PROPN
ejpam-6670	441	31	.	.	PUNCT
ejpam-6670	442	1	modelling	model	VERB
ejpam-6670	442	2	population	population	NOUN
ejpam-6670	442	3	dynamics	dynamic	NOUN
ejpam-6670	442	4	of	of	ADP
ejpam-6670	442	5	substance	substance	NOUN
ejpam-6670	442	6	abuse	abuse	NOUN
ejpam-6670	442	7	in	in	ADP
ejpam-6670	442	8	the	the	DET
ejpam-6670	442	9	presence	presence	NOUN
ejpam-6670	442	10	of	of	ADP
ejpam-6670	442	11	addicted	addicted	ADJ
ejpam-6670	442	12	immigrant	immigrant	NOUN
ejpam-6670	442	13	with	with	ADP
ejpam-6670	442	14	real	real	ADJ
ejpam-6670	442	15	data	datum	NOUN
ejpam-6670	442	16	of	of	ADP
ejpam-6670	442	17	rehabilitation	rehabilitation	NOUN
ejpam-6670	442	18	cases	case	NOUN
ejpam-6670	442	19	.	.	PUNCT
ejpam-6670	443	1	journal	journal	NOUN
ejpam-6670	443	2	of	of	ADP
ejpam-6670	443	3	applied	apply	VERB
ejpam-6670	443	4	t.	t.	PROPN
ejpam-6670	443	5	khan	khan	PROPN
ejpam-6670	443	6	et	et	PROPN
ejpam-6670	443	7	al	al	PROPN
ejpam-6670	443	8	.	.	PUNCT
ejpam-6670	443	9	/	/	SYM
ejpam-6670	443	10	eur	eur	PROPN
ejpam-6670	443	11	.	.	PUNCT
ejpam-6670	444	1	j.	j.	PROPN
ejpam-6670	444	2	pure	pure	PROPN
ejpam-6670	444	3	appl	appl	PROPN
ejpam-6670	444	4	.	.	PROPN
ejpam-6670	444	5	math	math	PROPN
ejpam-6670	444	6	,	,	PUNCT
ejpam-6670	444	7	18	18	NUM
ejpam-6670	444	8	(	(	PUNCT
ejpam-6670	444	9	3	3	NUM
ejpam-6670	444	10	)	)	PUNCT
ejpam-6670	444	11	(	(	PUNCT
ejpam-6670	444	12	2025	2025	NUM
ejpam-6670	444	13	)	)	PUNCT
ejpam-6670	444	14	,	,	PUNCT
ejpam-6670	444	15	6670	6670	NUM
ejpam-6670	444	16	22	22	NUM
ejpam-6670	444	17	of	of	ADP
ejpam-6670	444	18	22	22	NUM
ejpam-6670	444	19	mathematics	mathematic	NOUN
ejpam-6670	444	20	,	,	PUNCT
ejpam-6670	444	21	2025(1):2241780	2025(1):2241780	NUM
ejpam-6670	444	22	,	,	PUNCT
ejpam-6670	444	23	2025	2025	NUM
ejpam-6670	444	24	.	.	PUNCT
ejpam-6670	445	1	[	[	X
ejpam-6670	445	2	21	21	NUM
ejpam-6670	445	3	]	]	X
ejpam-6670	445	4	pauline	pauline	PROPN
ejpam-6670	445	5	van	van	PROPN
ejpam-6670	445	6	den	den	PROPN
ejpam-6670	445	7	driessche	driessche	NOUN
ejpam-6670	445	8	and	and	CCONJ
ejpam-6670	445	9	james	james	PROPN
ejpam-6670	445	10	watmough	watmough	PROPN
ejpam-6670	445	11	.	.	PUNCT
ejpam-6670	446	1	reproduction	reproduction	NOUN
ejpam-6670	446	2	numbers	number	NOUN
ejpam-6670	446	3	and	and	CCONJ
ejpam-6670	446	4	subthreshold	subthreshold	ADJ
ejpam-6670	446	5	endemic	endemic	ADJ
ejpam-6670	446	6	equilibria	equilibrium	NOUN
ejpam-6670	446	7	for	for	ADP
ejpam-6670	446	8	compartmental	compartmental	ADJ
ejpam-6670	446	9	models	model	NOUN
ejpam-6670	446	10	of	of	ADP
ejpam-6670	446	11	disease	disease	NOUN
ejpam-6670	446	12	transmission	transmission	NOUN
ejpam-6670	446	13	.	.	PUNCT
ejpam-6670	447	1	mathematical	mathematical	ADJ
ejpam-6670	447	2	biosciences	bioscience	NOUN
ejpam-6670	447	3	,	,	PUNCT
ejpam-6670	447	4	180(1	180(1	NUM
ejpam-6670	447	5	-	-	SYM
ejpam-6670	447	6	2):29–48	2):29–48	NUM
ejpam-6670	447	7	,	,	PUNCT
ejpam-6670	447	8	2002	2002	NUM
ejpam-6670	447	9	.	.	PUNCT